diff --git a/benchmarks/inference/mii/plot_effective_throughput.py b/benchmarks/inference/mii/plot_effective_throughput.py index 357fc7f9e..4f527c3d9 100644 --- a/benchmarks/inference/mii/plot_effective_throughput.py +++ b/benchmarks/inference/mii/plot_effective_throughput.py @@ -1,11 +1,11 @@ import argparse -from pathlib import Path import glob +from pathlib import Path + import matplotlib.pyplot as plt import numpy as np import pandas as pd - -from postprocess_results import read_json, get_tokenizer +from postprocess_results import get_tokenizer, read_json RAGGED_BATCH_SIZE = 768 SLA_PROMPT_TOKENS_PER_SEC = 512 diff --git a/benchmarks/inference/mii/plot_latency_percentile.py b/benchmarks/inference/mii/plot_latency_percentile.py index c91c78bf1..cea70d3e5 100644 --- a/benchmarks/inference/mii/plot_latency_percentile.py +++ b/benchmarks/inference/mii/plot_latency_percentile.py @@ -1,11 +1,11 @@ import argparse import glob +import itertools from pathlib import Path + import matplotlib.pyplot as plt import numpy as np -import itertools - -from postprocess_results import read_json, get_token_latency +from postprocess_results import get_token_latency, read_json bs = 768 SKIP_HEAD_TOKEN_NUM = 2 diff --git a/benchmarks/inference/mii/plot_repl_scale.py b/benchmarks/inference/mii/plot_repl_scale.py index 394c54588..940cdfaa7 100644 --- a/benchmarks/inference/mii/plot_repl_scale.py +++ b/benchmarks/inference/mii/plot_repl_scale.py @@ -1,10 +1,10 @@ -import glob -import matplotlib.pyplot as plt import argparse +import glob from pathlib import Path -import numpy as np -from postprocess_results import read_json, get_summary +import matplotlib.pyplot as plt +import numpy as np +from postprocess_results import get_summary, read_json bs = 768 diff --git a/benchmarks/inference/mii/plot_th_lat.py b/benchmarks/inference/mii/plot_th_lat.py index 8ede6e818..9cfca000c 100644 --- a/benchmarks/inference/mii/plot_th_lat.py +++ b/benchmarks/inference/mii/plot_th_lat.py @@ -1,10 +1,10 @@ -import glob -import matplotlib.pyplot as plt import argparse +import glob from pathlib import Path -import numpy as np -from postprocess_results import read_json, get_summary +import matplotlib.pyplot as plt +import numpy as np +from postprocess_results import get_summary, read_json bs = 768 diff --git a/benchmarks/inference/mii/plot_tp_sizes.py b/benchmarks/inference/mii/plot_tp_sizes.py index 546310258..f40c22aab 100644 --- a/benchmarks/inference/mii/plot_tp_sizes.py +++ b/benchmarks/inference/mii/plot_tp_sizes.py @@ -1,10 +1,10 @@ -import glob -import matplotlib.pyplot as plt import argparse +import glob from pathlib import Path -import numpy as np -from postprocess_results import read_json, get_summary +import matplotlib.pyplot as plt +import numpy as np +from postprocess_results import get_summary, read_json bs = 768 diff --git a/benchmarks/inference/mii/postprocess_results.py b/benchmarks/inference/mii/postprocess_results.py index cb2000d5f..b531a0a72 100644 --- a/benchmarks/inference/mii/postprocess_results.py +++ b/benchmarks/inference/mii/postprocess_results.py @@ -1,15 +1,14 @@ import argparse -from pathlib import Path import json -import numpy as np -from statistics import mean -from functools import reduce from dataclasses import dataclass +from functools import reduce +from pathlib import Path +from statistics import mean from typing import List +import numpy as np from transformers import AutoTokenizer - tokenizer = None @@ -43,7 +42,8 @@ def parse_args(): def get_tokenizer(): global tokenizer if tokenizer is None: - tokenizer = AutoTokenizer.from_pretrained("meta-llama/Llama-2-7b-hf") + #tokenizer = AutoTokenizer.from_pretrained("meta-llama/Llama-2-7b-hf") + tokenizer = AutoTokenizer.from_pretrained("/models/llama-2-70b-chat-hf") return tokenizer @@ -60,18 +60,35 @@ def read_json(file_path): return args, response_details +def calculate_stats(lt): + _max = max(lt) + _min = min(lt) + mean = sum(lt)//len(lt) + return f'min: {_min}, max: {_max}, mean: {mean}' + + def get_summary(args, response_details): client_num = args["client_num"] # Calculate latency and throughput using P95 latency - latency = mean([r.end_time - r.start_time for r in response_details]) + start_time = min([r.start_time for r in response_details]) + end_time = max([r.end_time for r in response_details]) + latency = max([r.end_time - r.start_time for r in response_details]) + generated_tokens = [len(r.generated_tokens) for r in response_details] + prompt_tokens = [len(r.prompt_tokens) for r in response_details] + print(f'prompt_tokens: {calculate_stats(prompt_tokens)}') + print(f'generated_tokens: {calculate_stats(generated_tokens)}') + # for i in range(len(response_details)): + # r = response_details[i] + # print(r.start_time, r.end_time, r.start_time-r.end_time) + print(f'real latency: {end_time-start_time}') throughput = client_num / latency tokens_per_sec = mean([(len(get_tokenizer().tokenize(r.prompt)) + len(r.generated_tokens)) / (r.end_time - r.start_time) for r in response_details]) - first_token_latency = mean([r.token_gen_time[0] for r in response_details]) + first_token_latency = 0 # mean([r.token_gen_time[0] for r in response_details]) - token_gen_latency_flat = reduce(list.__add__, [r.token_gen_time[1:-1] for r in response_details if len(r.token_gen_time) > 2]) - token_gen_latency = mean([t for t in token_gen_latency_flat]) + token_gen_latency_flat = 0 # reduce(list.__add__, [r.token_gen_time[1:-1] for r in response_details if len(r.token_gen_time) > 2]) + token_gen_latency = 0 # mean([t for t in token_gen_latency_flat]) return ProfilingSummary(throughput, latency, token_gen_latency, first_token_latency, tokens_per_sec) diff --git a/benchmarks/inference/mii/prompts/arxiv.csv b/benchmarks/inference/mii/prompts/arxiv.csv new file mode 100644 index 000000000..5af8a5d84 --- /dev/null +++ b/benchmarks/inference/mii/prompts/arxiv.csv @@ -0,0 +1,1024 @@ +"for about 20 years the problem of properties of short - term changes of solar activity has been considered extensively . many investigators studied the short - term periodicities of the various indices of solar activity . several periodicities were detected , but the periodicities about 155 days and from the interval of @xmath3 $ ] days ( @xmath4 $ ] years ) are mentioned most often . first of them was discovered by @xcite in the occurence rate of gamma - ray flares detected by the gamma - ray spectrometer aboard the _ solar maximum mission ( smm ) . this periodicity was confirmed for other solar flares data and for the same time period @xcite . it was also found in proton flares during solar cycles 19 and 20 @xcite , but it was not found in the solar flares data during solar cycles 22 @xcite . _ several autors confirmed above results for the daily sunspot area data . @xcite studied the sunspot data from 18741984 . she found the 155-day periodicity in data records from 31 years . this periodicity is always characteristic for one of the solar hemispheres ( the southern hemisphere for cycles 1215 and the northern hemisphere for cycles 1621 ) . moreover , it is only present during epochs of maximum activity ( in episodes of 13 years ) . similarinvestigationswerecarriedoutby + @xcite . they applied the same power spectrum method as lean , but the daily sunspot area data ( cycles 1221 ) were divided into 10 shorter time series . the periodicities were searched for the frequency interval 57115 nhz ( 100200 days ) and for each of 10 time series . the authors showed that the periodicity between 150160 days is statistically significant during all cycles from 16 to 21 . the considered peaks were remained unaltered after removing the 11-year cycle and applying the power spectrum analysis . @xcite used the wavelet technique for the daily sunspot areas between 1874 and 1993 . they determined the epochs of appearance of this periodicity and concluded that it presents around the maximum activity period in cycles 16 to 21 . moreover , the power of this periodicity started growing at cycle 19 , decreased in cycles 20 and 21 and disappered after cycle 21 . similaranalyseswerepresentedby + @xcite , but for sunspot number , solar wind plasma , interplanetary magnetic field and geomagnetic activity index @xmath5 . during 1964 - 2000 the sunspot number wavelet power of periods less than one year shows a cyclic evolution with the phase of the solar cycle.the 154-day period is prominent and its strenth is stronger around the 1982 - 1984 interval in almost all solar wind parameters . the existence of the 156-day periodicity in sunspot data were confirmed by @xcite . they considered the possible relation between the 475-day ( 1.3-year ) and 156-day periodicities . the 475-day ( 1.3-year ) periodicity was also detected in variations of the interplanetary magnetic field , geomagnetic activity helioseismic data and in the solar wind speed @xcite . @xcite concluded that the region of larger wavelet power shifts from 475-day ( 1.3-year ) period to 620-day ( 1.7-year ) period and then back to 475-day ( 1.3-year ) . the periodicities from the interval @xmath6 $ ] days ( @xmath4 $ ] years ) have been considered from 1968 . @xcite mentioned a 16.3-month ( 490-day ) periodicity in the sunspot numbers and in the geomagnetic data . @xcite analysed the occurrence rate of major flares during solar cycles 19 . they found a 18-month ( 540-day ) periodicity in flare rate of the norhern hemisphere . @xcite confirmed this result for the @xmath7 flare data for solar cycles 20 and 21 and found a peak in the power spectra near 510540 days . @xcite found a 17-month ( 510-day ) periodicity of sunspot groups and their areas from 1969 to 1986 . these authors concluded that the length of this period is variable and the reason of this periodicity is still not understood . @xcite and + @xcite obtained statistically significant peaks of power at around 158 days for daily sunspot data from 1923 - 1933 ( cycle 16 ) . in this paper the problem of the existence of this periodicity for sunspot data from cycle 16 is considered . the daily sunspot areas , the mean sunspot areas per carrington rotation , the monthly sunspot numbers and their fluctuations , which are obtained after removing the 11-year cycle are analysed . in section 2 the properties of the power spectrum methods are described . in section 3 a new approach to the problem of aliases in the power spectrum analysis is presented . in section 4 numerical results of the new method of the diagnosis of an echo - effect for sunspot area data are discussed . in section 5 the problem of the existence of the periodicity of about 155 days during the maximum activity period for sunspot data from the whole solar disk and from each solar hemisphere separately is considered . to find periodicities in a given time series the power spectrum analysis is applied . in this paper two methods are used : the fast fourier transformation algorithm with the hamming window function ( fft ) and the blackman - tukey ( bt ) power spectrum method @xcite . the bt method is used for the diagnosis of the reasons of the existence of peaks , which are obtained by the fft method . the bt method consists in the smoothing of a cosine transform of an autocorrelation function using a 3-point weighting average . such an estimator is consistent and unbiased . moreover , the peaks are uncorrelated and their sum is a variance of a considered time series . the main disadvantage of this method is a weak resolution of the periodogram points , particularly for low frequences . for example , if the autocorrelation function is evaluated for @xmath8 , then the distribution points in the time domain are : @xmath9 thus , it is obvious that this method should not be used for detecting low frequency periodicities with a fairly good resolution . however , because of an application of the autocorrelation function , the bt method can be used to verify a reality of peaks which are computed using a method giving the better resolution ( for example the fft method ) . it is valuable to remember that the power spectrum methods should be applied very carefully . the difficulties in the interpretation of significant peaks could be caused by at least four effects : a sampling of a continuos function , an echo - effect , a contribution of long - term periodicities and a random noise . first effect exists because periodicities , which are shorter than the sampling interval , may mix with longer periodicities . in result , this effect can be reduced by an decrease of the sampling interval between observations . the echo - effect occurs when there is a latent harmonic of frequency @xmath10 in the time series , giving a spectral peak at @xmath10 , and also periodic terms of frequency @xmath11 etc . this may be detected by the autocorrelation function for time series with a large variance . time series often contain long - term periodicities , that influence short - term peaks . they could rise periodogram s peaks at lower frequencies . however , it is also easy to notice the influence of the long - term periodicities on short - term peaks in the graphs of the autocorrelation functions . this effect is observed for the time series of solar activity indexes which are limited by the 11-year cycle . to find statistically significant periodicities it is reasonable to use the autocorrelation function and the power spectrum method with a high resolution . in the case of a stationary time series they give similar results . moreover , for a stationary time series with the mean zero the fourier transform is equivalent to the cosine transform of an autocorrelation function @xcite . thus , after a comparison of a periodogram with an appropriate autocorrelation function one can detect peaks which are in the graph of the first function and do not exist in the graph of the second function . the reasons of their existence could be explained by the long - term periodicities and the echo - effect . below method enables one to detect these effects . ( solid line ) and the 95% confidence level basing on thered noise ( dotted line ) . the periodogram values are presented on the left axis . the lower curve illustrates the autocorrelation function of the same time series ( solid line ) . the dotted lines represent two standard errors of the autocorrelation function . the dashed horizontal line shows the zero level . the autocorrelation values are shown in the right axis . ] because the statistical tests indicate that the time series is a white noise the confidence level is not marked . ] . ] the method of the diagnosis of an echo - effect in the power spectrum ( de ) consists in an analysis of a periodogram of a given time series computed using the bt method . the bt method bases on the cosine transform of the autocorrelation function which creates peaks which are in the periodogram , but not in the autocorrelation function . the de method is used for peaks which are computed by the fft method ( with high resolution ) and are statistically significant . the time series of sunspot activity indexes with the spacing interval one rotation or one month contain a markov - type persistence , which means a tendency for the successive values of the time series to remember their antecendent values . thus , i use a confidence level basing on the red noise of markov @xcite for the choice of the significant peaks of the periodogram computed by the fft method . when a time series does not contain the markov - type persistence i apply the fisher test and the kolmogorov - smirnov test at the significance level @xmath12 @xcite to verify a statistically significance of periodograms peaks . the fisher test checks the null hypothesis that the time series is white noise agains the alternative hypothesis that the time series contains an added deterministic periodic component of unspecified frequency . because the fisher test tends to be severe in rejecting peaks as insignificant the kolmogorov - smirnov test is also used . the de method analyses raw estimators of the power spectrum . they are given as follows @xmath13 for @xmath14 + where @xmath15 for @xmath16 + @xmath17 is the length of the time series @xmath18 and @xmath19 is the mean value . the first term of the estimator @xmath20 is constant . the second term takes two values ( depending on odd or even @xmath21 ) which are not significant because @xmath22 for large m. thus , the third term of ( 1 ) should be analysed . looking for intervals of @xmath23 for which @xmath24 has the same sign and different signs one can find such parts of the function @xmath25 which create the value @xmath20 . let the set of values of the independent variable of the autocorrelation function be called @xmath26 and it can be divided into the sums of disjoint sets : @xmath27 where + @xmath28 + @xmath29 @xmath30 @xmath31 + @xmath32 + @xmath33 @xmath34 @xmath35 @xmath36 @xmath37 @xmath38 @xmath39 @xmath40 well , the set @xmath41 contains all integer values of @xmath23 from the interval of @xmath42 for which the autocorrelation function and the cosinus function with the period @xmath43 $ ] are positive . the index @xmath44 indicates successive parts of the cosinus function for which the cosinuses of successive values of @xmath23 have the" +"it is believed that the direct detection of gravitational waves ( gws ) will bring the era of gravitational wave astronomy . the interferometer detectors are now under operation and awaiting the first signal of gws @xcite . it is also known that pulsar timing arrays ( ptas ) can be used as a detector for gws @xcite . these detectors are used to search for very low frequency ( @xmath0 ) gravitational waves , where the lower limit of the observable frequencies is determined by the inverse of total observation time @xmath1 . indeed , the total observation time has a crucial role in ptas , because ptas are most sensitive near the lower edge of observable frequencies @xcite . taking into account its sensitivity , the first direct detection of the gravitational waves might be achieved by ptas . the main target of ptas is the stochastic gravitational wave background ( sgwb ) generated by a large number of unresolved sources with the astrophysical origin or the cosmological origin in the early universe . the promising sources are super massive black hole binaries @xcite , cosmic ( super)string @xcite , and inflation @xcite . previous studies have assumed that the sgwb is isotropic and unpolarized @xcite . these assumptions are reasonable for the primary detection of the sgwb , but the deviation from the isotropy and the polarizations should have rich information of sources of gravitational waves . recently , the cross - correlation formalism has been generalized to deal with anisotropy in the sgwb @xcite . result of this work enables us to consider arbitrary levels of anisotropy , and a bayesian approach was performed by using this formalism @xcite . on the other hand , for the anisotropy of the sgwb , the cross - correlation formalism has been also developed in the case of interferometer detectors @xcite . as to the polarization , there are works including the ones motivated by the modified gravity @xcite . we can envisage supermassive black hole binaries emit circularly polarized sgwb due to the chern - simons term @xcite . there may also exist cosmological sgwb with circular polarization in the presence of parity violating term in gravity sector @xcite . in this paper , we investigate the detectability of circular polarization in the sgwb by ptas . we characterize sgwb by the so called stokes @xmath2 parameter @xcite and calculate generalized overlap reduction functions ( orfs ) so that we can probe the circular polarization of the sgwb . we also discuss a method to separate the intensity ( @xmath3 mode ) and circular polarization ( @xmath2 mode ) of the sgwb . the paper is organized as follows . in section [ sec : stokes parameters for a plane gravitational wave ] , we introduce the stokes parameters for monochromatic plane gravitational waves , and clarify the physical meaning of the stokes parameters @xmath3 and @xmath2 . in section [ sec : formulation ] , we formulate the cross - correlation formalism for anisotropic circularly polarized sgwb with ptas . the basic framework is essentially a combination of the formalism of @xcite , and the polarization decomposition formula of the sgwb derived in @xcite . in section [ sec : the generalized overlap reduction function for circular polarization ] , we calculate the generalized orfs for the @xmath2 mode . the results for @xmath3 mode are consistent with the previous work @xcite . in section [ sec : separation method ] , we give a method for separation between the @xmath3 mode and @xmath2 mode of the sgwb . the final section is devoted to the conclusion . in appendixes , we present analytic results for the generalized overlap reduction functions . in this paper , we will use the gravitational units @xmath4 . let us consider the stokes parameters for plane waves traveling in the direction @xmath5 , which can be described by @xmath6 \ , \\ & & h_{xy}(t , z)=h_{yx}(t , z)={\rm re}[b_{\times}\mathrm{e}^{-iw(t - z ) } ] \ .\end{aligned}\ ] ] for an idealized monochromatic plane wave , complex amplitudes @xmath7 and @xmath8 are constants . polarization of the plane gws is characterized by the tensor , ( see @xcite and also electromagnetic case @xcite ) @xmath9 where @xmath10 take @xmath11 . any @xmath12 hermitian matrix can be expanded by the pauli and the unit matrices with real coefficients . hence , the @xmath13 hermitian matrix @xmath14 can be written as @xmath15 where @xmath16 by analogy with electromagnetic cases , @xmath17 and @xmath2 are called stokes parameters . comparing with , we can read off the stokes parameters as @xmath18= b_{+}^{\ast}b_{\times}+ b_{\times}^{\ast}b_{+},\\ v&=&-2{\rm i m } [ b_{+}^{\ast}b_{\times}]=i ( b_{+}^{\ast}b_{\times}- b_{\times}^{\ast}b_{+}).\label{stv}\end{aligned}\ ] ] apparently , the real parameter @xmath3 is the intensity of gws . in order to reveal the physical meaning of the real parameter @xmath2 , we define the circular polarization bases @xcite @xmath19 from the relation @xmath20 we see @xmath21 thus , we can rewrite the stokes parameters - as @xmath22 from the above expression , we see that the real parameter @xmath2 characterizes the asymmetry of circular polarization amplitudes . the other parameters @xmath23 and @xmath24 have additional information about linear polarizations by analogy with the electromagnetic cases . alternatively , we can also define the tensor @xmath25 in circular polarization bases @xmath26 where @xmath27 . note that the stokes parameters satisfy a relation @xmath28 next , we consider the transformation of the stokes parameters under rotations around the @xmath5 axis . the rotation around the @xmath5 axis is given by @xmath29 where @xmath30 is the angle of the rotation . the gws traveling in the direction @xmath5 @xmath31 transform as @xmath32 where we took the transverse traceless gauge @xmath33 after a short calculation , we obtain @xmath34 using and , the four stokes parameters ( [ sti])-([stv ] ) transform as @xmath35 as you can see , the parameters @xmath23 and @xmath24 depend on the rotation angle @xmath30 . this reflects the fact that @xmath23 and @xmath24 parameters characterize linear polarizations . note that this transformation is similar to the transformation of electromagnetic case except for the angle @xmath36 and can be rewritten as @xmath37 in this section , we study anisotropic distribution of sgwb and focus on the detectability of circular polarizations with pulsar timing arrays . we combine the analysis of @xcite and that of @xcite . in sec.[subsec : the spectral ] , we derive the power spectral density for anisotropic circularly polarized sgwb @xmath38 . then we also derive the dimensionless density parameter @xmath39 which is expressed by the frequency spectrum of intensity @xmath40 @xcite . in sec.[subsec : the signal ] , we extend the generalized orfs to cases with circular polarizations characterized by the parameter @xmath2 . for simplicity , we consider specific anisotropic patterns with @xmath41 expressed by the spherical harmonics @xmath42 . in the transverse traceless gauge , metric perturbations @xmath43 with a given propagation direction @xmath44 can be expanded as @xcite @xmath45 where the fourier amplitude satisfies @xmath46 as a consequence of the reality of @xmath43 , @xmath47 , @xmath48 is the frequency of the gws , @xmath49 are spatial indices , @xmath50 label polarizations . note that the fourier amplitude @xmath51 satisfies the relation @xmath52 where @xmath53 was defined by . the polarized tensors @xmath54 are defined by @xmath55 where @xmath56 and @xmath57 are unit orthogonal vectors perpendicular to @xmath58 . the polarization tensors satisfy @xmath59 with polar coordinates , the direction @xmath44 can be represented by @xmath60 and the polarization basis vectors read @xmath61 we assume the fourier amplitudes @xmath62 are random variables , which is stationary and gaussian . however , they are not isotropic and unpolarized . the ensemble average of fourier amplitudes can be written as @xcite @xmath63 where @xmath64 here , the bracket @xmath65 represents an ensemble average , and @xmath66 is the dirac delta function on the two - sphere . the gw power spectral density @xmath38 is a hermitian matrix , and satisfies @xmath67 because of the relation @xmath46 . therefore , we have the relations @xmath68 note that the stokes parameters are not exactly the same as the expression of , but they have the relation and characterize the same polarization . we further assume that the sgwbs satisfy @xmath69 we also assume the directional dependence of the sgwb is frequency independent @xcite . this implies the gw power spectral density is factorized into two parts , one of which depends on the direction while the other depends on the frequency . because of the transformations - , the parameters @xmath3 and @xmath2 have spin 0 and the parameters @xmath70 have spin @xmath71 @xcite . to analyze the sgwb on the sky , it is convenient to expand the stokes parameters by spherical harmonics @xmath72 . however , since @xmath70 parameters have spin @xmath71 , they have to be expanded by the spin - weighted harmonics @xmath73 @xcite . thus , we obtain @xmath74 in this paper , we study specific anisotropic patterns with @xmath41 for simplicity . therefore , we can neglect @xmath23 and @xmath24 from now on . thus , the gw power spectral density becomes @xmath75 where @xmath76 so , we focus on the parameters @xmath3 and @xmath2 . in what follows , we will use the following shorthand notation @xmath77 next , we consider the dimensionless density parameter @xcite @xmath78 where @xmath79 is the critical density , @xmath80 is the present value of the hubble parameter , @xmath81 is the energy density of gravitational waves , and @xmath82 is the energy density in the frequency range @xmath48 to @xmath83 . the bracket @xmath65 represents the ensemble average . however , actually , we take a spatial average over the wave lengths @xmath84 of gws or a temporal average over the periods @xmath85 of gws . here , we assumed the ergodicity , namely , the ensemble average can be replaced by the temporal average . using , , , as well as @xmath46 and @xmath86 , we get @xmath87 then we define @xmath88 hence , the dimensionless quantity @xmath39 in is given by @xmath89 where the spherical harmonics are orthogonal and normalized as @xmath90 using @xmath91 , we obtain @xmath92 without loss of generality , we normalize the monopole moment as @xmath93 so , becomes @xmath94 the time of arrival of radio pulses from the pulsar is affected by gws . consider a pulsar with frequency @xmath95 located in the direction @xmath96 . to detect the sgwb , let us consider the redshift of the pulse from a pulsar @xcite @xmath97 where @xmath98 is a frequency detected at the earth and @xmath96 is the direction to the pulsar . the unit vector @xmath44 represents the direction of propagation of gravitational plane waves . we also defined the difference between the metric perturbations at the pulsar @xmath99 and at the earth @xmath100 as @xmath101 the gravitational plane waves at each point is defined as @xmath102 for the sgwb , the redshift have to be integrated over the direction of propagation of the gravitational waves @xmath44 : @xmath103 we choose a coordinate system @xmath104 and assume that the amplitudes of the metric perturbation at the pulsar and the earth are the same . then becomes @xmath105 and therefore , reads @xmath106 where we have defined the pattern functions for pulsars @xmath107 note that our convention for the fourier transformation is @xmath108 therefore , the fourier transformation of can be written as @xmath109 in the actual signals from a pulsar , there exist noises . hence , we need to use the correlation analysis . we consider the signals from two pulsars @xmath110 where @xmath111 labels the pulsar . here , @xmath112 denotes the signal from the pulsar and @xmath113 denotes the noise intrinsic to the measurement . we assume the noises are stationary , gaussian and are not correlated between the two pulsars . to correlate the signals" +"as a common quantum phenomenon , the tunneling through a potential barrier plays a very important role in the microscopic world and has been studied extensively since the birth of quantum mechanics . one of the earliest applications of quantum tunneling is the explanation of @xmath0 decays in atomic nuclei . the quantum tunneling effect governs also many other nuclear processes such as fission and fusion . in particular , a lot of new features are revealed in sub - barrier fusion reactions which are closely connected with the tunneling phenomena @xcite . for most of the potential barriers , the penetrability can not be calculated analytically @xcite . among those potentials for which analytical solutions can be obtained , the parabolic potential @xcite is the mostly used in the study of nuclear fusion . by approximating the coulomb barrier to a parabola , wong derived an analytic expression for the fusion cross section @xcite which is widely adopted today in the study of heavy ion reactions ( see , e.g. , recent refs . the parabolic approximation works remarkably well both for the penetrability and for the fusion cross section at energies around or above the coulomb barrier @xcite . apparently the parabolic approximation breaks down at energies much smaller than the barrier height due to the long - range coulomb interaction . one may calculate the penetration probability numerically by using the path integral method or the wkb approximation . however , it is highly desirable to have an analytical expression for the barrier penetrability when one introduces an energy - dependent one - dimensional potential barrier @xcite or barrier distribution functions @xcite . in the present work , we derived a new barrier penetration formula based on the wkb approximation . the influence of the long coulomb tail in the barrier potential is taken into accout properly . therefore this formula is especially applicable to the barrier penetration with penetration energy much lower than the coulomb barrier . as a first attempt and a test study , we apply this new formula to evaluate @xmath0 decay half - lives of atomic nuclei . for the @xmath0 decay , the penetrability is usually calculated with the wkb approach @xcite , in other words , integrating numerically the wave number within two turning points at which the interaction potential is equal to the @xmath1-value of the @xmath0 decay . we will show that the present analytical formula reproduces the experimental results very well , especially for spherical nuclei . the paper is organized as follows . in sec . [ sec : formalism ] we present the new barrier penetration formula . the validity of the new formula is investigated and its application to @xmath0 decays are given in sec . [ sec : results ] . finally in sec . [ sec : summary ] we summarize our work . in the appendix , the detailed derivation of the new penetration formula is given . when the penetration energy is well below the coulomb barrier , the barrier penetrability formula derived from the wkb approximation reads , @xmath2 , \label{eq : wkb}\ ] ] where the potential usually consists of three parts , the nuclear , the coulomb , and the centrifugal potentials , @xmath3 @xmath4 and @xmath5 are the inner and outer turning points determined by the relation @xmath6 . by approximating @xmath7 to a parabola with the height @xmath8 and the width @xmath9 , eq . ( [ eq : wkb ] ) is reduced as @xmath10 , \label{eq : hw}\ ] ] which has been widely used in the study of heavy ion reactions . because of the long - range coulomb interaction , the coulomb barrier given in eq . ( [ eq : potential ] ) has a long tail and is asymmetric . thus for the penetration well below the barrier , the parabolic approximation is not valid . we may divide the potential barrier into two parts at the barrier position @xmath11 . the first part of @xmath7 with @xmath12 could still be approximated by half of a parabola and we need to evaluate the integration in eq . ( [ eq : wkb ] ) in the range @xmath13 only . for s wave , the integral in eq . ( [ eq : wkb ] ) is evaluated as , @xmath14 , \label{eq : x1x2}\ ] ] with @xmath15 under the parabolic approximation and @xmath16 \nonumber \\ & & \mbox { } + \frac { k a } { \sqrt { \tau - 1 } } \frac{v_0}{e } \ln [ 1 + e^ { ( r_0 - r_b ) / a } ] \label{eq : new } , \end{aligned}\ ] ] where @xmath17 and @xmath18 . the details of the derivation of eq . ( [ eq : new ] ) are given in the appendix . it should be mentioned that in the derivation of eq . ( [ eq : new ] ) , a woods - saxon form is used for @xmath19 . in this section , we use the new formula to study the typical barrier penetration problem , @xmath0 decays of atomic nuclei . the @xmath0 decay half - life is related to the decay width @xmath20 by @xcite @xmath21 the decay width @xmath20 is calculated as @xcite @xmath22 where @xmath23 is the assaults frequency of @xmath0 particle on the barrier , @xmath24 the spectroscopic or preformation factor and @xmath25 the penetrability with @xmath1 the @xmath0 decay q - value . for spherical nuclei , @xmath26 is parametrized as @xcite @xmath27 and the penetrability will be calculated with eqs . ( [ eq : x1x2 ] ) , ( [ eq : left ] ) , and ( [ eq : new ] ) . ( color online ) the barrier potential between the @xmath0 and the daughter nucleus for @xmath28po and @xmath29nd . the solid curve shows the exact potential @xmath7 and the dashed curve stands for the effective potential given in eq . ( [ eq : veff ] ) associated with the parabolic approximation eq . ( [ eq : left ] ) and the new barrier penetration formula eq . ( [ eq : new ] ) . note that the two curves are almost identical to each other . , title=""fig:"",scaledwidth=45.0% ] ( color online ) the barrier potential between the @xmath0 and the daughter nucleus for @xmath28po and @xmath29nd . the solid curve shows the exact potential @xmath7 and the dashed curve stands for the effective potential given in eq . ( [ eq : veff ] ) associated with the parabolic approximation eq . ( [ eq : left ] ) and the new barrier penetration formula eq . ( [ eq : new ] ) . note that the two curves are almost identical to each other . , title=""fig:"",scaledwidth=45.0% ] for the @xmath0-nuclear interaction , we adopt the coulomb and the woods - saxon potentials and parameters proposed in ref . @xcite , @xmath30 , & r \le r_m , \end{cases } \label{eq : coulomb}\ ] ] and @xmath31 } , \end{aligned}\ ] ] with @xmath32 and @xmath33 the mass and charge numbers of the daughter nucleus and @xmath1 the @xmath0 decay energy . the parameters in these potentials and given in eq . ( [ eq : prefomation ] ) were obtained by fitting @xmath0 decay half lives and cross section data for several fusion reactions . it can be easily verified that the position of the coulomb barrier @xmath11 is larger than @xmath34 thus the use of the coulomb force given in eq . ( [ eq : coul ] ) is valid . before the new formula is used to study alpha decays , we investigate in details its validity . first we examine how the effective potential connected with the new formula eq . ( [ eq : new ] ) is close to the exact one . two extreme examples are chosen for this purpose , @xmath28po which has a very short half - life @xmath35 s and @xmath29nd which has a quite long half - life @xmath36 s @xcite . the barrier potential @xmath7 is shown in fig . [ fig : potential ] for these two systems . the effective potential , @xmath37 is also shown for comparison . @xmath38 fm is the radial position outside of which the nuclear part of the @xmath0-nucleus potential could be neglected ( see the appendix for more details ) . in our calculations , the width of the parabolic potential is obtained by fitting the barrier potential from the inner turning point @xmath39 to the position of the barrier @xmath11 . unlike the full parabolic approximation , the effective potential is asymmetric and coincides with the exact potential very well , especially the outer side of the barrier which critically influences @xmath0 decays . .[tab : deviation ] comparison of the results for the barrier penetration probability for @xmath0 decays in po isotopes ( charge and mass numbers of the @xmath0 emitter are listed in the first and the second entries ) . the meaning of @xmath40 is given in eq . ( [ eq : x1x2 ] ) . the superscript `` wkb '' means the penetrability calculated from the wkb approach , `` para '' from the parabolic approximation in eq . ( [ eq : left ] ) , and `` new '' from the new formulas eq . ( [ eq : new ] ) . [ cols=""^,^,^,^,^,^,^"",options=""header "" , ] the deformation influences the @xmath0 decay life time both on the preformation mechanism and on the penetration process @xcite . in the present work , we have assumed the barrier potential to be spherical . in 68 of these 344 nuclei , the spherical potential assumption is met well ( with @xmath41 for the daughter nucleus @xcite ) . in table [ tab : spherical ] the calculated and experimental values of the @xmath0 decay half lives for these nuclei are given . the statistical summary is also shown in the last line of table [ tab : stati ] . it is found that the new formula gives very good results for these spherical nuclei . in most cases , the differences between the calculated and the experimental values of @xmath42 are smaller than 0.5 . the root mean square deviation between @xmath43 $ ] and @xmath44 $ ] is 0.34 . in the study of barrier penetration in nuclear physics , the parabolic approximation is usually adopted because an analytical solution exists for the penetrability of a parabola barrier potential . the parabola approximation works indeed well both for the penetrability and for the fusion cross section at energies around or above the coulomb barrier . but it fails at energies much smaller than the barrier height due to the long - range coulomb interaction . in the present work , we derived a new barrier penetration formula , eq . ( [ eq : new ] ) , based on the wkb approximation . we took into account the influence of the long coulomb tail in the barrier potential properly . therefore this formula is especially applicable to the barrier penetration with penetration energy much lower than the coulomb barrier . we have shown that the present analytical formula reproduces the wkb results very well . this new penetration formula is used to calculate @xmath0 decay half - lives of 344 nuclei with the @xmath0-nucleus potential given in ref . satisfactory agreement between the present calculation and the experiment is achieved . for spherical and even - even nuclei , the results are particularly good . therefore , the new formula could be used in the study of barrier penetration at energies much smaller than the barrier height . furthermore , we expect that the new formula will facilitate the study of the" +"for the hybrid monte carlo algorithm ( hmc)@xcite , often used to study quantum chromodynamics ( qcd ) on the lattice , one is interested in efficient numerical time integration schemes which are optimal in terms of computational costs per trajectory for a given acceptance rate . high order numerical methods allow the use of larger step sizes , but demand a larger computational effort per step ; low order schemes do not require such large computational costs per step , but need more steps per trajectory . so there is a need to balance these opposing effects . omelyan integration schemes @xcite of a force - gradient type have proved to be an efficient choice , since it is easy to obtain higher order schemes that demand a small additional computational effort . these schemes use higher - order information from force - gradient terms to both increase the convergence of the method and decrease the size of the leading error coefficient . other ideas to achieve better efficiency for numerical time integrators are given by multirate or nested approaches . these schemes do not increase the order but reduce the computational costs per path by recognizing the different dynamical time - scales generated by different parts of the action . slow forces , which are usually expensive to evaluate , need only to be sampled at low frequency while fast forces which are usually cheap to evaluate need to be sampled at a high frequency . a natural way to inherit the advantages from both force - gradient type schemes and multirate approaches would be to combine these two ideas . previously , we studied the behavior of the adapted nested force - gradient scheme for the example of the @xmath0-body problem @xcite and would like to learn more about their usefulness for lattice field theory calculations . due to the huge computational effort required for qcd simulations , it is natural to attempt an intermediate step first . we chose the model problem of quantum electrodynamics ( qed ) in two dimensions , the schwinger model @xcite , since it is well - suited as a test case for new concepts and ideas which can be subsequently applied to more computationally demanding problems @xcite . as a lattice quantum field theory , it has many of the properties of more sophisticated models such as qcd , for example the numerical cost is still dominated by the fermion part of the action . the fact that this model , with far fewer degrees of freedom , does not require such large computational effort makes it the perfect choice for testing purposes . we compare the behavior of numerical time integration schemes currently used for hmc @xcite with the nested force - gradient integrator @xcite and the adapted version introduced in @xcite . we investigate the computational costs needed to perform numerical calculations , as well as the effort required to achieve a satisfactory acceptance rate during the hmc evolution . our goal is to find a numerical scheme for the hmc algorithm which would provide a sufficiently high acceptance rate while not drastically increasing the simulation time . the paper is organized as follows . in section 2 we give a short overview of the hmc algorithm and numerical schemes for time integration , which are used in hmc . in section 3 we present the 2-dimensional schwinger model and introduce the idea of the force - gradient approach and the resulting novel class of numerical schemes . section 4 is devoted to the results of a comparison between widely used algorithms and the new approach and section 5 draws our conclusion . in this section we provide a general overview of the hmc algorithm @xcite to introduce our novel integrator . we also present some standard numerical time integrating methods used in hmc , as well state - of - the - art numerical schemes , which we later compare by applying them to the two - dimensional schwinger model . in the hybrid monte carlo algorithm , the quantum lattice field theory is embedded in a higher - dimensional classical system through the introduction of a fictitious ( simulation ) time @xcite . the gauge field @xmath1 is associated with its ( fictitious ) conjugate momenta @xmath2 , and the classical system is described by the hamiltonian , @xmath3 + { \mathcal{b}}[u],\ ] ] where @xmath4 $ ] and @xmath5 $ ] represent the kinetic and potential energy respectively . for a given configuration @xmath1 , a new configuration @xmath6 is generated by performing an hmc update @xmath7 , which consists of two steps : * * molecular dynamics trajectory : * evolve the gauge fields @xmath1 , elements of a lie group , and the momenta @xmath2 , elements of the corresponding lie algebra , in a fictitious computer time @xmath8 according to hamilton s equations of motions @xmath9 since analytical solutions are not available in general , numerical methods must be used to solve the system of eqn . . the discrete updates of @xmath1 and @xmath2 with an integration step @xmath10 are @xmath11 leading to a first - order approximation at time @xmath12 . since the momenta @xmath2 are elements of lie algebra , we have an additive update of @xmath2 . on the other hand , the links @xmath1 must be elements of the lie group , therefore an exponential update is used for @xmath1 to preserve the underlying group structure . * * metropolis step : * accept or reject the new configuration @xmath13 with probability @xmath14 where @xmath15 . in this paper we are concerned with numerical time integration schemes , which preserve the fundamental properties of geometric integration , time - reversibility and volume - preservation . all numerical schemes presented below possess these necessary properties . * basic schemes : * well - known , commonly used integration schemes in molecular dynamics are given by * the leap - frog method , a 3-stage composition scheme of the discrete updates defined above : @xmath16 * and a 5-stage extension widely used in qcd computations : @xmath17 * force gradient schemes : * force - gradient schemes increase accuracy by using additional information from the force gradient term @xmath18 , with @xmath19 defining lie brackets . the 5-stage force - gradient scheme proposed by omelyan et al @xcite is the simplest ; @xmath20 here we also test the modification of the force - gradient method proposed in @xcite , where the force - gradient term @xmath21 is approximated via a taylor expansion . an extension is given by the 11-stage decomposition @xcite , recently implemented as the integrator in the open source code openqcd as one of the standard options @xcite @xmath22where @xmath23 , @xmath24 , @xmath25 and @xmath26 are parameters from equation ( 71 ) in ref . @xcite . * nested schemes : * qed and qcd problems usually lead to hamiltonians with the following fine structure @xmath27 + { \mathcal{b}}_{1}[u]+ { \mathcal{b}}_{2}[u],\ ] ] where the action of the system can be split into two parts : a fast action @xmath28 such as the gauge action , and a slow part @xmath29 , for example , the fermion action . this allows us to apply the idea of multirate schemes ( an idea known as nested integration in physics literature)@xcite in order to reduce the computational effort . at first we consider the nested version of the leap - frog method @xmath30 where the inner cheaper system @xmath31+{\mathcal{b}}_{1}[u]$ ] is solved by @xmath32 with @xmath33 being a number of iterations for the fast part of the action . our main goal is to compare the above - mentioned methods with more elaborated nested schemes : in @xcite , a similar 5-stage decomposition scheme has been recently introduced : @xmath34 a nested version of , which has been used in @xcite reads @xmath35 where @xmath36 with @xmath37 and @xmath38 . in the limit @xmath39 we have @xmath40 . note that this approach uses force - gradient information at all levels , i.e. , the high computational cost of high order schemes appears at all levels . one may overcome this problem by using schemes of different order at the different levels without losing the effective high order of the overall multirate scheme . for the latter , we include appropriate force gradient information as we explain in the following for the case of two time levels , where the gauge action plays the role of the fast and cheap part , and the fermionic action plays the role of the slow and expensive part . the reasoning is as follows : if one uses the 5-stage sexton - weingarten integrator of second order for the slow action , and approximates the fast action by @xmath41 leap - frog steps of step size @xmath42 , the error of the overall multirate scheme will be of order @xmath43 . with the use of force gradient information only at the slowest level it is possible to cancel the leading error term of order @xmath44 . as @xmath45 usually holds in the multirate setting , the overall order is then given by the leading error term of order @xmath46 , i.e. , the scheme has an effective order of four . one example for such a scheme for problems of type is given by the 5-stage nested force - gradient scheme introduced in @xcite @xmath47 to summarize , the adapted scheme differs from the original one in two perspectives : * the force gradient scheme for the fast action is replaced by a leap - frog scheme . * only the part @xmath48 of the full force gradient @xmath49 is needed to gain the effective order of four . the numerical schemes - and - are second order convergent schemes . methods - and - have the fourth order of convergence . we do not consider integrators of higher order than four since the computational costs are too high . the schemes of the same convergence order differ from each other by the number of stages ( updates of momenta and links per time step ) . usually methods with more stages have smaller leading error coefficients and therefore have better accuracy , but higher computational costs . we would like to determine which integrator would represent the best compromise between high accuracy and computational efficiency . we will apply all these numerical integration schemes to the two - dimensional schwinger model . the most challenging task from the theoretical point of view is to derive the force - gradient term @xmath21 . in the next section we introduce the schwinger model and explain how to obtain the force - gradient term . the 2 dimensional schwinger model is defined by the following hamiltonian function @xmath50 = \frac{1}{2}\sum_{n=1,\mu=1}^{v,2 } p_{n,\mu}^2 + s_g[u ] + s_f[u].}\ ] ] with @xmath51 the volume of the lattice . unlike qcd , where @xmath52 and @xmath53 , for this qed problem , the links @xmath1 are the elements of the lie group @xmath54 and the momenta @xmath55 belong to @xmath56 , which represents the lie algebra of the group @xmath54 . this makes this test example very cheap in terms of the computational time . this together with the fact that the schwinger model also shares many of the features of qcd simulations , makes the schwinger model an excellent test example when considering numerical integrators : a fast dynamics given by the computationally cheap gauge part @xmath57 $ ] of the action demanding small step sizes , and a slow dynamics given by the computationally expensive fermion part @xmath58 $ ] allowing large step sizes . the pure gauge part of the action @xmath59 sums up over all plaquettes @xmath60 in the two - dimensional lattice with @xmath61 and is given by @xmath62 the links @xmath1 can be written in the form @xmath63 and" +"recently it was discovered that feynman integrals obey functional equations @xcite , @xcite . different examples of functional equations were presented in refs . @xcite , @xcite,@xcite . in these articles only one - loop integrals were considered . in the present paper we propose essentially new methods for deriving functional equations . these methods are based on algebraic relations between propagators and they are suitable for deriving functional equations for multi - loop integrals . also these methods can be used to derive functional equations for integrals with some propagators raised to non - integer powers . our paper is organized as follows . in sec . 2 . the method proposed in ref . @xcite is shortly reviewed . in sec . 3 . a method for finding algebraic relations between products of propagators is formulated . we describe in detail derivation of explicit relations for products of two , three and four propagators . also algebraic relation for products of arbitrary number of proparators is given . these relations are used in sec.4 . to obtain functional equations for some one- , as well as two- loop integrals . in particular functional equation for the massless one - loop vertex type integral is presented . also functional equation for the two - loop vertex type integral with arbitrary masses is given . in sec . another method for obtaining functional equations is proposed . the method is based on finding algebraic relations for ` deformed propagators ' and further conversion of integrals with ` deformed propagators ' to usual feynman integrals by imposing conditions on deformation parameters . to perform such a conversion the @xmath0- parametric representation for both types of integrals is exploited . the method was used to derive functional equation for the two - loop vacuum type integral with arbitrary masses . as a by product , from this functional equation we obtained new hypergeometric representation for the one - loop massless vertex integral . in conclusion we formulate our vision of the future applications and developments of the proposed methods . the method for deriving functional equations proposed in ref . @xcite is based on the use different kind of recurrence relations . in particular in refs . @xcite , @xcite , @xcite , generalized recurrence relations @xcite were utilized to obtain functional equations for one - loop feynman integrals . in general such recurrence relations connect a combination of some number of integrals @xmath1 corresponding to diagrams , say , with @xmath2 lines and integrals corresponding to diagrams with fewer number of lines . diagrams with fewer number of lines can be obtained by contracting some lines in integrals with @xmath2 lines . integrals corresponding to such diagrams depend on fewer number of kinematical variables and masses compared to integrals with @xmath2 lines . such recurrence relations can be written in the following form : @xmath3 where @xmath4 and @xmath5 are ratios of polynomials depending on masses @xmath6 , scalar products @xmath7 of external momenta , powers of propagators @xmath8 and parameter of the space time dimension @xmath9 . at the left hand - side of eq . ( [ nconnectr ] ) we combined integrals with @xmath2 lines and on the right hand - side integrals with fewer number of lines . in accordance with the method of ref . @xcite , to obtain functional equation from eq . ( [ nconnectr ] ) one should eliminate terms on the left hand - side by defining some kinematical variables from the set of equations : @xmath10 if there is a nontrivial solution of this system and for this solution some @xmath11 are different from zero then the right - hand side of eq . ( [ nconnectr ] ) will represent functional equation . for the one - loop integrals with @xmath2 propagators @xmath12 where @xmath13 different types of recurrence relations were given in refs . @xcite , @xcite . diagram corresponding to this integral is given in figure 1 . external legs ] in refs . @xcite , @xcite the following relation was derived : @xmath14 where the operators @xmath15 shift index of propagators by one unit @xmath16 , @xmath17 @xmath18 @xmath19 here @xmath20 are external momenta going through lines @xmath21 respectively , and @xmath22 is mass attributed to @xmath23-th line . gram determinant @xmath24 and modified cayley determinant @xmath25 are polynomials depending on scalar products and masses . it is assumed that these scalar products are made of @xmath9 dimensional vectors and @xmath24 and @xmath25 are not subject to any restriction or condition specific to some integer values of @xmath9 . ( [ reducedtod ] ) is written in the form corresponding to eq . ( [ nconnectr ] ) . to eliminate integrals with @xmath2 lines on the left hand - side of eq . ( [ reducedtod ] ) the following conditions to be hold : @xmath26 eq . ( [ reducedtod ] ) is valid for arbitrary kinematical variables and masses . solution of eqs . ( [ sharik ] ) can be easily done with respect to two kinematical variables or masses . starting from @xmath27 substitution of such solutions into eq . ( [ reducedtod ] ) gives nontrivial functional equations . the method for obtaining functional equations by eliminating complicated integrals from recurrence relations is quite general one . however for multi loop integrals , depending on several kinematical variables , derivation of equations like eq . ( [ reducedtod ] ) is computationally challenging . in the next sections we will describe easier and more powerful methods that can be used for deriving functional equations for multi - loop integrals . setting @xmath28 in eq . ( [ reducedtod ] ) and imposing conditions ( [ sharik ] ) leads to the following equation : @xmath29 in eq . ( [ fe_n_points ] ) integrands of @xmath30 are products of @xmath31 propagators depending on different external momenta , i.e. each term in this relation corresponds to the same function but with different arguments . in fact functional equations considered in refs . @xcite are of the same form as eq . ( [ fe_n_points ] ) . the question naturally arises : this relationship holds for integrals or it can be obtained as the consequence of a relationship between integrands ? by inspecting eq . ( [ fe_n_points ] ) , one can suggest the following form of the relation between products of propagators of integrands : @xmath32 where @xmath33 in what follows we will omit @xmath34 term assuming that all masses have such a correction . additionally we assume that vectors @xmath35 are linearly dependent , i.e. the gram determinant for the set of vectors @xmath36 is equal to zero . such a condition is valid for all examples considered in refs . @xcite , @xcite . now let s consider in detail implementation of our prescription for products of 2,3 and 4 propagators . at @xmath37 relation ( [ usual_props ] ) reads : @xmath38 where @xmath39 according to our assumption three vectors @xmath40,@xmath41,@xmath42 are linearly dependent . without loss of generality we may assume that @xmath43 furthermore , we assume that @xmath44 will be integration momentum and scalar quantities @xmath45,@xmath46 , @xmath47 , @xmath47 do not depend on @xmath44 . putting all terms in eq . ( [ 2prop_relation ] ) over a common denominator and then equating to zero the coefficients in front of various products of @xmath48 , @xmath49,@xmath50 yields the following system of equations : @xmath51 solution of this system of equations is : @xmath52 where @xmath53 is a root of the equation @xmath54 with @xmath55 this solution can be rewritten in an explicit form : @xmath56 where @xmath57 now let s find algebraic relation for the products of three propagators . at @xmath27 eq . ( [ usual_props ] ) reads : @xmath58 where @xmath59 , @xmath60 , @xmath61 are defined in eq.([p1p2p3 ] ) and @xmath62 in complete analogy with the previous case we can represent one momentum as a combination of other ones . without loss of generality we may write @xmath63 where @xmath64 for the time being are arbitrary coefficients . putting all terms in eq . ( [ 3prop_relation ] ) over a common denominator and then equating to zero the coefficients in front of various products of @xmath65 , @xmath66 , @xmath67 , @xmath68 yields the following system of equations : @xmath69 solving these equations for @xmath45 , @xmath46 , @xmath70 , @xmath71 , @xmath72 we have @xmath73 where @xmath74 is solution of the equation @xmath75 here @xmath76 let us now turn to the derivation of algebraic relation for the product of four propagators . at @xmath77 ( [ usual_props ] ) reads : @xmath78 where @xmath59 , @xmath60 , @xmath61,@xmath79 are defined in eqs . ( [ p1p2p3 ] ) , ( [ d4 ] ) , @xmath80 and @xmath81 is a linear combination of vectors @xmath40, ,@xmath82 , @xmath83 putting all terms in eq . ( [ 4prop_relation ] ) over a common denominator and then equating to zero the coefficients in front of different products of @xmath48 , @xmath84 yields system of equations : @xmath85 solving this system for @xmath45 , @xmath46 , @xmath70,@xmath86 , @xmath87 , @xmath88 we have @xmath89 where @xmath90 is a solution of the equation @xmath91 with @xmath92 eqs . ( [ 3prop_relation ] ) , ( [ 3prop_relation ] ) and ( [ 4prop_relation ] ) will be used in the next sections to derive functional equations for the propagator , vertex and box type of integrals . relations between products of five and more propagators can be easily derived in the same way as as it was done for products of two- , three- and four- propagators . from eq . ( [ usual_props ] ) one can derive system of equations and find its solution for arbitrary @xmath2 . multiplying both sides of eq . ( [ usual_props ] ) by the product of @xmath93 propagators @xmath94 yields @xmath95 or @xmath96 since we assume linear dependence of vectors @xmath97 , without loss of generality we may write : @xmath98 substituting ( [ pnp1 ] ) into eq.([ini_equ ] ) , collecting terms in front of @xmath48 , @xmath84 and terms without @xmath44 , equating them to zero after some simplifications yields the following system of @xmath99 equations : @xmath100 solving eq . ( [ sumy ] ) for one of the @xmath64 an substituting this solution into eq . ( [ kwadraticy ] ) gives quadratic equation for the remaining @xmath64 . this quadratic equation can be solved with respect to one of the parameters @xmath64 . thus the solution of the system of equations ( [ xequs ] ) , ( [ sumy ] ) , ( [ kwadraticy ] ) will depend on @xmath101 arbitrary parameters @xmath64 and one arbitrary mass @xmath102 . it is interesting to note that for any @xmath2 , functional equations for integrals with all masses equal to zero and functional equations for integrals with all masses equal are the same . in case of equal masses , two mass dependent terms in eq . ( [ kwadraticy ] ) cancel each other due to eq . ( [ sumy ] ) . in both cases systems of equations for @xmath103 , @xmath104 are the same and therefore arguments of integrals are the same . ( [ 2prop_relation ] ) is analogous to the equation for splitting propagators presented in ref . ( [ 3prop_relation ] ) is a generalization of eq . ( [ 2prop_relation ] ) . indeed , setting @xmath105 , canceling common factor @xmath61 on both sides of eq . ( [ 3prop_relation ] ) yields relation similar to ( [ 2prop_relation ] ) . in turn ( [ 4prop_relation ] ) is a generalization of ( [ 3prop_relation ] ) . multiplying algebraic relations ( [ 2prop_relation]),([3prop_relation ] )" +"one of the main goals of the search for periodic isolated sources of gravitational waves ( g.w . ) is to perform all sky surveys , based on `` blind searches '' , where the source parameters are unknown . in this case hierarchical procedures are applied , based on a sequence of increasing resolution steps . in this paper we study in details the problem of sensitivity loss due to discretization of parameters and to the needs to limit the computing cost , with hough procedures . in particular , we propose and study the characteristics of a frequency hough procedure , designed mainly to reduce the discretization problem , and we compare it with the sky hough procedure , which is actually used in the virgo collaboration . + the paper is organized as follows : in sect . 2 we present the basic scheme of the rome hierarchical procedure , based on the main idea of coincidences among subsets of data ; in sect . 3 we discuss the limits due to digitization of the sky hough procedure ; in sects . 4 , 5 we present the new frequency hough procedure , discussing details its implementation and its basic characteristics ; in sect . 6 we present the study of amplitude losses due to digitization , and thus efficiencies , for both the procedures . conclusions and comments are given in sect . hierarchical procedures , based on hough transform algorithms , are applied by various groups in the g.w . community . see , for example , references @xcite . there are various ways of implementing the hierarchical procedure and the hough transform . the hough transform is a linear transform that is used to recognize the parameters of the analytical description of a curve from the position of some points on it . it operates on an `` image '' of points , in our case the peakmap in the time - frequency plane . for each peak of this map we increase a set of bins of a multi - dimensional histogram ( in our case a two - dimensional histogram ) defined on the parameters space , called the hough map . in the old procedure , the parameter space was the position of the source , i.e. the celestial sphere , and we fixed the spin down value for each hough map . in the new one , the parameter space is the plane @xmath0 , and for each hough map , we fix the position of the source . the mapping ( i.e. which points of the hough map must be increased for a certain point in the peakmap ) can be done in different ways : we use always what we call the `` biunivocal mapping '' , i.e. a mapping in which every point in the hough map derive from a single point of the peakmap at a given time . it is easy to demonstrate that in this case the mapping is also uniform , i.e. in the case of uniformly distributed random dots in the peakmap , the expected value of the hough map @xmath1 is a constant ( for all parameter value ) . this value , depending on the number n of the spectra of the peakmap and on the mapping , defines the `` noise '' of the map . it is binomially distributed with parameters n and @xmath2 . we will refer here to the rome scheme , presently used in virgo data . [ fig : schema ] shows the basic scheme of the rome hierarchical procedure . details on the main aspects of the procedure are given in references @xcite . after data cleaning ( short time domain disturbances removal ) and `` short ffts data base '' ( sfdb ) creation , peakmaps are computed , using a very refined auto - regressive algorithm to equalize the spectral data by an appropriate follow - up of the noise . peakmaps are frequency vs time maps , obtained from equalized spectra by selecting all the local maxima above a chosen threshold . an accurate cleaning of peakmaps , by removing known noise lines and the more persistent lines , is needed and its implementation is critical for the next step analysis . on the cleaned peakmaps , methods of peaks detection are applied . that is , transformation from the input plane to the hough plane , thresholding and first order candidates selection . candidate parameters are defined by source frequency , celestial coordinates , first spin - down parameter . the need for coincidences among candidates obtained in different subsets of data ( two in the scheme of fig . [ fig : schema ] ) has been discussed in references @xcite . this method is very efficient to reduce the number of spurious candidates at a fixed threshold . thus , for a given false alarm probability , we can lower the threshold -with respect to the choice of not doing coincidences- gaining in detection efficiency . the method has a better efficiency when the data sets have similar sensitivities . after the coincidence , the survived candidates are analyzed coherently with longer ffts on corrected data . then the spectral filtering is used to take into account the spread of the power in five bands , as explained in reference @xcite . finally , second order candidates are produced . as stated before , the sky hough method shows amplitude losses , and thus loss of sensitivity , which are due to digitization of parameters . this effect shows up mainly for the complexity of the transform together with the need of reducing the computing cost : * the method is based on a transform between the time - frequency peakmap and the celestial sphere . it is not simple for the non linearity of the mapping ; * to reduce the computational effort , we need to use `` look - up tables '' which introduce further digitization errors ; * to reduce the computational effort , fast algorithms have been developed , which require the use of a rectangular grid to map the sky . compared to the `` optimal '' ( see later ) grid , the rectangular one has over - resolution in some regions of the sky . this leads also to a higher number of candidates . * the use of the celestial map as the space to spot the candidates is very prone to artifacts , see @xcite : some regions are always `` privileged '' , that is they have a higher candidates number with respect to the expectation . the problem arises because each hough map is constructed over the whole sky . hence , it seemed important the study of alternative procedures . given the observation that most of the problems are related to the complexity of the transformation , we exploit the possibility of the use of a different but simpler transformation . a part the simplicity of the transformation we obviously need to study a procedure which is less , or equivalently , computationally expensive . therefore we studied a procedure which has a better , or equivalent , sensitivity , at the same computational cost of the sky hough . the transformation we propose transforms the * time - observed frequency * plane into the * source frequency - spin down * plane . let s go into details . if @xmath3 is the frequency ( doppler corrected for a given sky direction ) , @xmath4 the source intrinsic frequency , @xmath5 the first spin - down parameter , @xmath6 the time at the detector and @xmath7 a reference time , we have that @xmath8 a straight line in the hough plane . we then get the following : @xmath9 each point in the input plane @xmath10 , that is a peak in the doppler shifted peakmap , is transformed into a straight line in the hough @xmath11 plane , with slope @xmath12 . the slope depends on the choice of the reference time . if we choose @xmath7 equal to the beginning time of the data we analyze , then the slope is always negative and inversely proportional to the time gap . + this is the choice we have done here . in addition , considering the width @xmath13 of the frequency bins in the input plane we notice that each peak is transformed into a stripe among two parallel straight lines @xmath14 it is a linear transformation . now the input plane is obtained from the original peakmap by correcting it for the doppler shift due to the earth revolution and rotation , for each point in the sky grid we need to analyze . thus `` time '' is the time at the detector and `` frequency '' the observed frequency , after the doppler correction . but , as each sfdb is short enough to not be affected by a time - varying doppler shift , then the doppler effect removal from the original peakmap , obtained from the collection of all the sfdb data , reduces to a very simple `` shifting '' procedure of the peakmap bins . in the analysis scheme , this bins shift is part of the hough procedure . + in the following , we give details on the construction of the map . the frequency hough map is constructed using the `` direct differential method '' , as is done with the sky hough . with this method , instead of building directly the hough map , one builds a map that , if `` integrated '' ( i.e. summed over bins from left to right ) , gives the hough map . this is important to minimize the number of floating point operations . as already explained , for each sky position , the input peakmap is got from the original one by shifting bins to correct for the doppler effect . the sky is sampled with a non uniform covering grid , which will be later discussed . here we explain in detail the technique , by giving the sequence of operations : * for each point in the sky grid , for each coordinate in the input plane @xmath10 and for each spin - down value @xmath15 , the map is incremented by 1 in the point @xmath16 and decremented by 1 in the point @xmath17 . hence , for each sky position , a differential map is constructed . the sum of the bins along the frequency direction is then performed to construct the final integral map . this two dimensional histogram is the frequency hough map . in the algorithm implementation we plan to divide the input peakmap into 10 hz bands , thus constructing , for each position in the sky , a different hough map every 10 hz . + in case there is the need to exploit higher order one spin down parameters , one ( or more ) loop(s ) has ( have ) to be added to the sequence of operations , to scan the discrete set of values of the new parameter(s ) . this clearly influences the computing cost , but does not change the basics of the method . let s first discuss two peculiar aspects of this new method , which are the basis of its appeal . from the given analysis scheme , it is easy to see that the frequency resolution for the estimation of the source frequency @xmath4 can be enhanced , with respect to the binning frequency @xmath13 , without relevantly affecting the computational effort . in fact , the use of a resolution @xmath18 with @xmath19 , affects only the size of the hough map . this has a computational cost only when summing over the bins to construct the integral map from" +"this review focuses specifically on what we have learned about the progenitors of core - collapse supernovae ( cc sne ) by examining images of the supernova ( sn ) sites taken prior to the explosion . by registering pre - sn and post - sn images , usually taken at high resolution using either space - based optical detectors , or ground - based infrared detectors equipped with laser guide star adaptive optics systems ( lgs - ao ) , about one dozen cc sn progenitors have now been directly detected ( i.e. , shown to be spatially coincident with the sn ) in pre - sn images , with roughly two dozen upper limits derived from non - detections @xcite . this field has come a long way in the last decade , and promises to advance rapidly as more and more nearby galaxies hosts of future cc sne have high - resolution images added to the archive . this review is organized as follows . following a brief summary of sn classification and stellar evolution theory ( 2 ) , one example from each of the following three categories of progenitor studies is provided ( 3 ; ordered from most - to - least common ) : ( 1 ) no progenitor star detected in pre - sn image(s ) ; ( 2 ) likely progenitor star identified via spatial coincidence in pre - sn and post - sn images ; ( 3 ) progenitor star detected in pre - sn image(s ) and subsequently confirmed by demonstrating its absence in images taken after the sn has faded beyond detection . a summary of overall results to date for each sn type is then given ( 4 ) , followed by a brief discussion of outstanding questions and areas in which future progress is likely ( 5 ) . note that discussion is limited to what the examination of images of sn sites taken prior to the explosion has taught us , and necessarily excludes ( or relegates to very brief comment ) such related investigations as sn environments ( e.g. , @xcite ; see also the article by elias rosa in this volume ) and sn progenitor `` forensics '' ( e.g. , @xcite ; see also the article by modjaz in this volume ) . for a comprehensive discussion of all such related areas , see the recent review by @xcite . it is typical to subdivide cc sne into at least five major categories ( see @xcite for a thorough review ) : ii - plateau ( ii - p ; hydrogen in spectrum and plateau in optical light curve ) , ii - linear ( ii - l ; hydrogen in spectrum , no plateau in optical light curve ) , iin ( hydrogen in spectrum and spectral and photometric evidence for interaction between sn ejecta and a dense circumstellar medium [ csm ] ) , iib ( hydrogen in spectrum initially , but transforms into a hydrogen - deficient spectrum at later times ) , and ib / c ( no evidence for hydrogen in spectrum at any time ) , where the ordering is a roughly increasing one in terms of inferred degree of envelope stripping prior to explosion ( i.e. , ii - p are the least stripped at the time of explosion , and ib / c are the most stripped ) . while most of this review focuses on the observational advances that have been made , theoretical input is critical to translate observed progenitor luminosity ( or limits ) into zero - age - main - sequence masses ( @xmath0 ) and stellar evolutionary states . among the most complete ( and accessiblestars . ] ) stellar evolution models at present are the metallicity - dependent models produced with the cambridge stellar evolution code , stars , the descendant of the code developed originally by @xcite and updated most recently by @xcite ( 2004 ; see also @xcite , and references therein ) , since they follow stellar evolution up to the initiation of core neon burning , which is likely to give an accurate indication of the pre - sn luminosity . the hertzsprung - russell diagram ( hrd ) of the stars evolutionary tracks are shown in figure 1 for stars ranging in initial mass from @xmath1 . comparison with other contemporary model grids ( e.g. , @xcite ; @xcite ) show that the endpoints for stars in the @xmath2 range differ by at most @xmath3 dex in luminosity among the codes @xcite , which gives some assurance that systematic uncertainties are not great , at least at the low - mass end for red supergiant ( rsg ) stars . two areas of uncertainty in need of better quantification ( or , at least , agreement within the community ) include the effects that stellar rotation and mass - loss might have on the observable characteristics of stars prior to core collapse . not surprisingly , when no progenitor star is actually detected at the sn location in pre - sn images , only an upper limit to the progenitor s luminosity and , hence , mass , can be derived . to illustrate the analysis process in such a situation , i consider sn 2006my , an sn ii - p that exploded in a galaxy @xmath4 mpc away ( nearly all sne with progenitor studies are within @xmath5 mpc , since source confusion becomes an increasing problem with distance ) . details for this particular event are provided by @xcite ; here i briefly outline the steps my colleagues and i took to derive an upper mass limit on its progenitor . the _ hubble space telescope _ ( _ hst _ ) imaged the site of sn 2006my using the wide - field and planetary camera 2 ( wfpc2 ) in 1994 ( pre - sn ) and again in 2007 ( shortly after explosion ) . we registered the two images and pinpointed the sn location to better than 30 milli - arcsec in the pre - sn frame ( figure 2a , b ) . such fine registration allowed us to rule out a nearby point source ( source ` 1 ' in figure 2a ) as the progenitor star with greater than @xmath6 confidence . ( note that this source had been previously identified by @xcite as the likely progenitor based on registration with lower - resolution ground - based optical post - sn images . ) we next set an @xmath7-band detection limit in the pre - sn frame by placing artificial stars of progressively fainter magnitude at the sn location and letting the photometry software ( in this case , hstphot , see @xcite ) attempt to detect them . the point at which the software no longer detected a point source then serves as the limiting upper magnitude for the progenitor star . to translate this single - filter detection limit into a luminosity , we assumed that the progenitor was a rsg ( given other sn ii - p progenitor detections this seems a reasonable assumption ; see 3.2 and 4 ) , and then determined the greatest bolometric magnitude it could have had while still remaining below our detection threshold . this is accomplished through : @xmath8 where @xmath9 is the distance modulus of the host galaxy ( ngc 4651 ) , @xmath10 the extinction to sn 2006my , @xmath7 the @xmath7-band detection threshold , @xmath11 the color range of rsg stars ( i.e. , spectral types @xmath12 ) , and @xmath13 the bolometric correction corresponding to each @xmath14 . upon adopting the most conservative values for each of the parameters ( i.e. , the ones that produce the least restrictive @xmath15 for the progenitor s upper luminosity limit ) , and allowing for a maximum systematic uncertainty of 0.2 dex in the theoretical stellar model endpoints ( see 2 ) , the limiting bolometric magnitude above which any rsg would have been detected in our pre - sn image , @xmath15 , is derived . we then compared this with the final luminosity of stars with @xmath16 predicted by the stars stellar evolution models ( figure 2c ) to derive an upper bound on the progenitor mass of @xmath17 . from this analysis , then , we conclude that any rsg progenitor with an initial mass greater than @xmath18 would have been detected using our analysis procedure . analyses similar to that described here for sn 2006my have been carried out on each of 22 non - detections in pre - sn images @xcite . as we shall see ( 4 ) , it is the sheer number of such progenitor non - detections that permits rather strong conclusions to be drawn about cc sn progenitors from this category of progenitor studies . next , we consider the individually more revealing situation where an object coincident with the transformed sn location is actually detected in the pre - sn image(s ) , a situation that exists now for 11 cc sne @xcite . as an outstanding example of the analytic power provided by having multi - filter pre - sn images available ( especially in the near infrared for rsg progenitors ) , we consider the recent work of @xcite on sn 2008bk , a very nearby ( @xmath19 mpc ) sn ii - p . in this case , pre - sn ground - based images in @xmath20 were registered with post - sn lgs - ao @xmath21-band images to yield solid progenitor star detections in @xmath22 , and upper luminosity limits in @xmath23 and @xmath24 . when compared with the known spectral energy distribution ( sed ) of rsg , a good match for the progenitor of sn 2008bk is found with a progenitor of spectral type m4i ( figure 3 ) . from comparison with the stars stellar evolutionary models an initial progenitor mass of @xmath25 is derived for this sn . similar studies on seven other detected sn ii - p progenitors have found stars consistent with rsg in all cases , providing nice agreement between theory and observation . as we shall see in 4 , however , the _ range _ of masses inferred for these rsg progenitors is somewhat unexpected . finally , we consider the most satisfying situation where images taken before , during , and long after the sn explosion exist that clearly show the progenitor star , the sn , and the absence of the progenitor star , respectively . such a sequence provides nearly conclusive proof of the progenitor star s identity . currently , such a time series exists for only two objects : sn 1987a ( e.g. , * ? ? ? * ) and sn 2005gl @xcite . because the case of sn 1987a is well - known , i present sn 2005gl as the example of this situation ; it also clearly demonstrates the investigative power provided by having a third observation , long after the sn has dropped below detection . as shown by @xcite , early spectra of sn 2005gl exhibited the classic features of a type iin event , showing narrow but resolved lines of hydrogen superposed on an intermediate - width component on an otherwise featureless continuum . analysis of the spectral features indicate ejecta interacting with a dense csm , whose properties suggest that the progenitor star exploded shortly after an lbv - like mass - loss episode . comparison of a pre - sn _ hst _ image with a post - sn image obtained from the ground using the lgs - ao at the keck ii telescope established a spatial coincidence between the sn and a very bright source possessing an estimated luminosity of over @xmath26 ( @xcite ; see figures 4a and 4b ) . the only single stars" +"single - transverse spin asymmetries ( ssas ) play a fundamental role for our understanding of qcd in high - energy hadronic scattering . they may be obtained for reactions in , for example , lepton - proton or proton - proton scattering with one transversely polarized initial proton , by dividing the difference of the cross sections for the two settings of the transverse polarization by their sum . there have been extensive experimental investigations of such asymmetries @xcite . these have initiated much theoretical progress , in particular within the last few years . a particular focus has been on a class of single - spin observables that are characterized by a large momentum scale @xmath1 ( for example , the virtuality of the photon in deeply - inelastic scattering ( dis ) ) and by a much smaller , but also measured , transverse momentum @xmath2 . in such a `` two - scale '' situation , single - spin asymmetries may arise at leading power , that is , not suppressed by an inverse power of @xmath1 . for some of these cases , factorization theorems have been established @xcite that allow to write the spin - dependent cross sections in terms of parton distribution functions and/or fragmentation functions , perturbative hard - scattering functions , and so - called soft factors . a crucial feature is that the distribution functions and the soft factor in this factorization are not integrated over the transverse momenta of partons , because these in fact generate the observed transverse momentum @xmath2 . among other things , the observables may therefore provide valuable insights into the dependence of parton distributions in nucleons on transverse momentum . this becomes particularly interesting when the nucleon is transversely polarized , because there may be correlations between the nucleon spin vector , its momentum , and the parton s transverse momentum . one particular correlation , known as the `` sivers effect '' and described by so - called `` sivers functions '' @xcite , is now widely believed to be involved in a variety of observed hadronic single - spin phenomena . closer theoretical studies have revealed that the sivers effect plays an important role in qcd , beyond giving rise to phenomenological functions to be used in the description of single - spin asymmetries . a particularly interesting feature is that the sivers effect is not universal in the usual sense , that is , it is not represented by universal probability functions convoluted with partonic hard - scattering cross sections . this might at first sight appear to make the study of these functions less interesting . however , the non - universality has in fact a clear physical origin , and its closer investigation has turned out to be an extremely important and productive development in qcd . in a nutshell , in order not to be forced to vanish because of the time - reversal symmetry of qcd , single - spin asymmetries require the presence of a strong - interaction phase . for the sivers functions this phase originates from the `` gauge links '' in their definition @xcite , which are path - ordered exponentials of the gluon field that make the functions gauge - invariant . in dis , the gauge link may be viewed as a rescattering of the parton in the color field of the nucleon remnant . that such a final - state rescattering may generate the phase required for a nonzero ssa in semi - inclusive hadron production in dis ( sidis ) was first discovered within a model calculation @xcite . depending on the hard - scattering process , the `` rescattering '' will however manifest itself in different ways . for example , for drell - yan lepton pair production in hadronic scattering , _ initial - state _ , rather than final - state , interactions are relevant . as a result , the phase provided by the gauge links is opposite , and the sivers functions for the drell - yan process have opposite sign @xcite . in more general terms , the nontrivial universality "" property of the sivers functions is the direct consequence of gauge interactions in quantum chromodynamics @xcite , and of the qcd factorization theorems applying to the relevant hard processes @xcite . it is a remarkable and fundamental qcd prediction that really tests all concepts we know of for analyzing hard - scattering reactions in strong interactions , and it awaits experimental verification . while measurements of ssas in sidis are now maturing and have established the presence of sivers - type contributions @xcite , it will still be a while until precise single - spin measurements in the relatively rare drell - yan process will become feasible at rhic @xcite or elsewhere @xcite . however , there are of course other hard - scattering reactions in hadronic collisions for which single - transverse spin asymmetries may be defined , and that may potentially be used in lieu of the drell - yan process for testing the nontrivial universality "" properties of the sivers functions . in @xcite , it was proposed to use the ssa in azimuthal correlations of two jets produced in @xmath0 collisions at rhic to learn about the sivers functions . to a first approximation , such dijets are produced by @xmath3 partonic qcd hard - scattering . with collinear kinematics , the jets are exactly `` back - to - back '' in the plane perpendicular to the initial beam directions and thus separated by @xmath4 in azimuthal angle in this plane . partonic transverse momenta will generate deviations from this topology , because they will lead on average to a non - vanishing net transverse momentum @xmath2 of the jet pair , much smaller than each of the jet transverse momenta @xmath5 individually . the observable is therefore of the `` two - scale '' type described above , and as was shown in @xcite , if one proton is polarized , a single - spin asymmetry may be defined that is in principle sensitive to the sivers functions . as a caveat , factorization of the spin - dependent cross section for this observable in terms of transverse - momentum - dependent ( tmd ) functions still remains to be established . unlike the relatively simple cases of sidis and the drell - yan process , where either final - state or initial - state interactions contribute to the sivers asymmetry , both are present for dijet production @xcite this complicates the analysis of the process - dependence of the sivers functions considerably , but at the same time it also makes it much more interesting from a theoretical point of view , because the interactions in this case are `` truly qcd '' , that is , they involve the detailed gauge structure of the theory , including for example its non - abelian nature . at the time of @xcite , the process - dependence had not yet been worked out for the case of the ssa in dijet production , so that phenomenological predictions had to remain qualitative , at best . over the last year , however , there has been extensive work on deriving and clarifying the structure of the gauge links for this and related processes in @xmath0 collisions @xcite . indeed , the resulting structure is far more complicated than that in sidis or the drell - yan process . however , it turns out that if one takes a certain weighted integral ( `` moment '' ) of the asymmetry , remarkable simplifications occur . this moment is defined by integrating the spin - dependent cross section with a factor @xmath6 , where @xmath7 is the azimuthal imbalance between the two jets ( @xmath8 if the jets are exactly back - to - back in azimuth ) . for each of the various contributing @xmath3 partonic channels , the gauge link then essentially collapses into a set of simple color factors that multiply contributions from color - gauge invariant subamplitudes to the given partonic process . one may , in fact , for convenience choose to absorb these factors into the hard - scattering functions , and _ define _ the sivers functions as the functions measured in the ssa in sidis . in this way , the net effect of the gauge links on the @xmath6-moment of the spin - dependent cross section is to generate new partonic hard - scattering functions that are different from the usual spin - independent ones , but that are actually similarly simple in structure . at the same time , taking the moment of the factorized spin - dependent cross section leads to a new expression that involves only a certain moment of the sivers functions in partonic transverse momentum @xmath9 , rather than the fully transverse - momentum dependent functions themselves . as was shown in @xcite , these @xmath9-moments of the sivers functions are directly related to twist - three quark - gluon correlation functions first introduced in @xcite to describe the ssa for single - inclusive hadron production in hadronic scattering . by now , quite some knowledge about these correlation functions has been gathered from phenomenological studies @xcite of the corresponding data . the upshot of all this is that it has now become possible for the first time to make predictions for the @xmath6-moment of the single - transverse spin asymmetry in dijet production at rhic that correctly take into account the process - dependence of the sivers functions and incorporate phenomenological information on some properties of the functions that is available from other measurements . this is the goal of this note . we study azimuthal correlations of two jets produced nearly `` back - to - back '' in a hadronic collision . more specifically , we are interested in situations in which the sum of the two jet transverse momenta , @xmath10 ( or a component or projection thereof ) , is measured and small , while both individual jet transverse momenta are large and similar . we will therefore approximate @xmath11 wherever possible . for the lengths of these momentum vectors we will simply write @xmath12 and @xmath13 . the differential cross section for the process with one transversely polarized hadron contains terms of the form @xmath14 where @xmath15 is a unit vector in the direction of the polarized proton , @xmath16 is the transverse spin vector of the polarized proton , and @xmath17 and @xmath18 are the pseudo - rapidities of the two jets . the first term in eq . ( [ sigma ] ) represents the unpolarized ( or spin - averaged ) cross section , while the second term is the single - transverse - spin dependent one . we note that the angular dependence of the spin - dependent term is @xmath19 , where @xmath20 is the so - called bisector - angle of the two jets , which ( approximately ) corresponds to the direction of @xmath21 . for this reason one may also choose to integrate the six - fold differential cross section in eq . ( [ sigma ] ) over @xmath22 , keeping @xmath21 fixed . as a generalization of the sidis and drell - yan cases @xcite , we can write down a factorization formula for the differential cross section at small imbalance ( @xmath23 ) of the jets , in terms of tmd parton distributions , soft factors , and hard - scattering functions @xcite . we remind the reader that such a factorization still remains to be proven . in this paper , we will not discuss the details of factorization issues related to the dijet correlations . as we mentioned above , significant simplifications occur when the imbalance of the two jets is integrated out by taking certain" +"kingman s coalescent is a random tree introduced by @xcite as the genealogy arising in large population genetic models . it has infinitely many leaves and is usually constructed from leaves to the root as follows : given that there are @xmath7 lines in the tree , after some exponential time with rate @xmath8 , two lines are chosen uniformly and merged to one line , leaving the tree with @xmath9 lines . due to the quadratic rate @xmath10 the tree immediately comes down from infinitely to finitely many leaves @xcite . since the seminal paper by @xcite this random tree has been generalized to other infinite trees arising in population genetics models . for the kingman coalescent some laws of large numbers and central limit theorems have been proved . they are nicely summarized in @xcite , chapter 4.2 ; see also proposition [ p:11 ] below . for @xmath11 let @xmath12 denote the number of lines time @xmath13 in the past . then , since the kingman coalescent immediately comes down from infinity , @xmath12 is finite . furthermore it is approximately @xmath14 . equivalently , the time @xmath0 it takes the coalescent to go from infinitely many lines to @xmath1 lines is approximately @xmath15 for large @xmath1 . going to the fine structure , at time @xmath0 the infinite population is decomposed in @xmath1 families ( whose joint distribution is exchangeable ) and every leaf in the tree belongs to exactly one of the @xmath1 families whose frequencies are denoted by @xmath16 . it is known that for large @xmath1 a randomly chosen @xmath3 is approximately exponentially distributed with mean @xmath17 . this translates into several laws of large numbers ; see e.g. ( 35 ) in @xcite . in particular the probability of picking ( from the initial infinite population ) two leaves that belong to the same family , given by @xmath18 , is approximately @xmath15 . the main goal of the present paper is to study the corresponding large deviations results . to the best of our knowledge , except for @xcite , cf . remark [ rem : angel ] , results in this direction are not present in the literature . we formulate our results in the next section . theorem [ t1 ] gives a full large deviation principle for the distributions of @xmath19 . the proof , given in section [ sec : proofs1 ] , is an application of the grtner - ellis theorem . as a byproduct , we derive a large deviation principle for the distributions of @xmath20 in corollary [ cor : tnt ] . large deviations of @xmath21 are considered in theorem [ t2 ] and exact rate functions for downwards and upwards deviations are given . the proof is given in section [ sec : proof - theorem - reft2 ] . for the upward deviations we use a variant of cramr s theorem for heavy - tailed random variables ; see e.g. @xcite . for the downward deviations we use a connection to self - normalized large deviations ; see @xcite . this connection was pointed out to us by alain rouault and nina gantert . since the rate function for downward deviations is hard to treat analytically we provide in theorem [ t3 ] a simple lower bound . the proof of that bound is given in section [ sec : proof - theorem3 ] . the kingman coalescent can be seen as a discrete graph , more precisely a discrete tree with infinitely many leaves . let @xmath22 be independent exponentially distributed variables with mean @xmath23 . then the kingman coalescent tree can be constructed from the root to the leaves as follows . 1 . start the tree with two lines from the root . 2 . for @xmath24 the tree stays with @xmath7 lines for the amount of time @xmath25 . after that time one of the @xmath7 lines is randomly chosen . this line splits in two so that the number of lines jumps from @xmath7 to @xmath26 . 3 . stop upon reaching infinitely many lines , which happens after ( the almost surely finite ) time @xmath27 . the random variable @xmath28 is the total tree height . alternatively , @xmath28 is the time to the most recent common ancestor ( mrca ) of the infinite population ( of leaves ) . counted from the top of the tree at time @xmath29 a random number @xmath12 of active lines in the kingman tree is present , i.e.@xmath30 at time @xmath0 every leaf belongs to one of @xmath1 disjoint families and all members of each such family stem from the same line at time @xmath0 . let us denote the frequencies of these families ( which exist due to exchangeability by definetti s theorem ) by @xmath16 . the following results are well known ( see @xcite for and and @xcite for ; proofs can also be found in @xcite . ) + let [ p:11 ] @xmath31 , @xmath32 and @xmath33 be as above . then @xmath34 we [ rem : interllnfe ] note that the left hand side of has the interpretation of a _ homozygosity by descent _ in the following sense : when picking two leaves from the tree at time @xmath35 , the probability that both share a common ancestor at time @xmath0 is @xmath36 . then , the law of large number states that the homozygosity by descent at time @xmath0 is approximately @xmath15 for large @xmath1 . in the present paper we are interested in large deviations results corresponding to the statements of proposition [ p:11 ] . we start with large deviations connected with . first we introduce some notation . for @xmath37 let @xmath38 denote the distribution of @xmath19 , i.e. @xmath39 . furthermore we denote by @xmath40 the borel @xmath41-algebra on @xmath42 and for @xmath43 we denote by @xmath44 the _ interior _ and by @xmath45 the _ closure _ of @xmath46 . for @xmath47 , let @xmath48 be the unique solution of the equation @xmath49 , where the continuous and increasing function @xmath50 is defined by ( see figure [ fig : t1 ] for a plot ) @xmath51 2 & : \ ; t=0 , \\[2ex ] \displaystyle\frac{2}{\sqrt{|t|}}\arctan\sqrt{|t| } & : \ ; t < 0 . \end{cases}\end{aligned}\ ] ] the proof of the following theorem is given in section [ sec : proof - theorem - reft1 ] . the sequence [ t1 ] @xmath52 satisfies a large deviation principle with scale @xmath1 and good rate function @xmath53 given by @xmath54 \infty & : \ ; x\leq 0 . \end{cases } \end{aligned}\ ] ] in other words , for any @xmath55 we have @xmath56 and @xmath53 from and , respectively.,title=""fig:"",width=226 ] and @xmath53 from and , respectively.,title=""fig:"",width=226 ] both , the function @xmath57 from and @xmath53 from are plotted in figure [ fig : t1 ] . the minimum of the rate function is attained at @xmath58 . this fact is clear from the law of large numbers , . in addition , @xmath59 for @xmath60 because @xmath61 almost surely . let us now have a closer look at the behaviour of @xmath62 for @xmath63 near @xmath35 and for large @xmath63 . since @xmath64 , we have that @xmath65 , and hence , @xmath66 . in this case , @xmath67 where the last equality follows from @xmath68 . to understand the behaviour for large @xmath63 , note that since @xmath69 for @xmath70 we have @xmath71 and in particular @xmath72 . it follows @xmath73 note that and are equivalent . indeed , @xmath74 ( this also holds with @xmath75 replaced by @xmath76 ) by construction , and @xmath77 as @xmath78 and @xmath79 as @xmath80 . hence , theorem [ t1 ] translates into a large deviation principle for @xmath20 . in the following we denote by @xmath81 the distribution of @xmath82 , i.e. @xmath83 . the proof of the next result is given in section [ sec : proof - coroll - refc ] ; see figure [ fig : cor1 ] for a plot of the rate function @xmath84 . for @xmath85 the family @xmath86 [ cor : tnt ] satisfies a large deviation principle with scale @xmath87 and good rate function @xmath84 given by @xmath88 \displaystyle \frac{\pi^2}{2 } & : \ , x=0 , \\[1.5ex ] \infty & : \ , x<0 , \end{cases } \end{aligned}\ ] ] with @xmath53 from . in particular , for @xmath89 we have @xmath90 from corollary [ cor : tnt ] . the figure on the right is a comparison of @xmath84 with the lower bound obtained from @xcite.,title=""fig:"",width=226 ] from corollary [ cor : tnt ] . the figure on the right is a comparison of @xmath84 with the lower bound obtained from @xcite.,title=""fig:"",width=226 ] the distributions @xmath91 ( as well as @xmath92 ) have been described explicitely in the literature . @xcite , section 6 , gives @xmath93 in principle , this formula must also give the large deviations for the measures @xmath81 , but this does not seem straight - forward . although [ rem : angel ] the main goal of @xcite was the analysis of spatial @xmath94-coalescents , they also provide some large deviations bounds on kingman s coalescent . these bounds are mainly based on markov inequality . precisely , in lemma 2.2 in @xcite it is shown that for @xmath95 @xmath96 and therefore @xmath97 in the neighbourhood of @xmath98 the last inequality translates easily into a bound for the rate function @xmath84 from ; see figure [ fig : cor1 ] . namely , for @xmath99 we have @xmath100 next , we state some large deviations results connected to . for @xmath101 we know from that @xmath102 holds almost surely . the proof of this result is based on the well - known fact ( see e.g. section 5 in @xcite ) that the distribution of @xmath103 can be derived using uniform order statistics : let @xmath104 be independent and uniformly distributed on @xmath105 $ ] , and @xmath106 be their order statistics . additionally , let @xmath107 be independent exponentially distributed random variables with mean @xmath23 . then , @xmath108 here the second equality in distribution is one of the well known representations of uniform spacings ; see e.g. section 4.1 in @xcite . it follows @xmath109 we will use this representation to obtain large deviations results for @xmath103 . in particular we show that upwards large deviations of @xmath103 are on the scale @xmath6 while downwards large deviations are on the scale @xmath1 . the proof is given in section [ sec : proof - theorem - reft2 ] . for [ t2 ] each @xmath110 , we have @xmath111 furthermore @xmath112 and for each @xmath113 , we have @xmath114 the function @xmath115 is positive for @xmath116 and is given by @xmath117 here @xmath118 is a function of the form @xmath119 with @xmath120 where @xmath121 denotes the distribution function of the one dimensional standard gaussian distribution . though the rate function in is exact it is hard to treat analytically . for this reason we provide in theorem [ t3 ] a much simpler lower bound for downwards large deviations of @xmath103 . for the proof we use the following lemma which provides another representation of @xmath103 in terms of exponential random variables ( see section [ sec : proofs2 ] for proofs ) . let [ l : wn ] @xmath122 be independent exponentially distributed random variables with mean @xmath23 . then , @xmath123 for [ t3 ] @xmath124 we have @xmath125 the main point in the proof of lemma [ l : wn ] is that @xmath103 does not depend on the order of the @xmath126 and hence we can as well order them according to their size . let us briefly explain how we will use in the proof of in . since @xmath103 is" +"rapid progress in the design and manufacture of optical fiber systems is a result of worldwide demand for ultra - high bit - rate optical communications . this explains the growing interest of the soliton community in soliton - based optical fiber communication systems . this area of research was considerably advanced in recent years @xcite . the most remarkable results include the application of the concept of the dispersion management to _ temporal optical solitons _ and soliton - based optical transmission systems , and the discovery of the so - called _ dispersion managed soliton_. high - speed optical communications require effective components such as high - performance broadband computer networks that can be developed by employing the concept of the bit - parallel - wavelength ( bpw ) pulse transmission that offers many of the advantages of both parallel fiber ribbon cable and conventional wavelength - division - multiplexing ( wdm ) systems @xcite . expanding development in the study of the soliton fiber systems has been observed in parallel with impressive research on their spatial counterparts , optical self - trapped beams or _ spatial optical solitons_. one of the key concepts in this field came from the theory of multi - frequency wave mixing and cascaded nonlinearities where a nonlinear phase shift is produced as a result of the parametric wave interaction @xcite . in all such systems , the nonlinear interaction between the waves of two ( or more ) frequencies is the major physical effect that can support coupled - mode multi - frequency solitary waves . the examples of temporal and spatial solitons mentioned above have one common feature : they involve the study of solitary waves in multi - component nonlinear models . the main purpose of this paper is to overview several different physical examples of multi - mode and/or multi - frequency solitary waves that occur for the pulse or beam propagation in nonlinear optical fibers and waveguides . for these purposes , we select three different cases : multi - wavelength solitary waves in bit - parallel - wavelength optical fiber links , multi - colour spatial solitons due to multistep cascading in optical waveguides with quadratic nonlinearities , and quasiperiodic solitons in the fibonacci superlattices . we believe these examples display both the diversity and richness of the multi - mode soliton systems , and they will allow further progress to be made in the study of nonlinear waves in multi - component nonintegrable physical models . because the phenomenon of the long - distance propagation of _ temporal optical solitons _ in optical fibers @xcite is known to a much broader community of researchers in optics and nonlinear physics , first we emphasize _ the difference between temporal and spatial solitary waves_. indeed , for a long time stationary beam propagation in planar waveguides has been considered somewhat similar to the pulse propagation in fibers . this approach is based on the so - called _ spatio - temporal analogy _ in wave propagation , meaning that the propagation coordinate @xmath0 is treated as the evolution variable and the spatial beam profile along the transverse direction in waveguides , is similar to the temporal pulse profile in fibers . this analogy is based on a simple notion that both beam evolution and pulse propagation can be described by the cubic nonlinear schrdinger ( nls ) equation . however , contrary to the widely accepted opinion , there is a crucial difference between temporal and spatial solitons . indeed , in the case of the nonstationary pulse propagation in fibers , the operation wavelength is usually selected near the zero point of the group - velocity dispersion . this means that the absolute value of the fiber dispersion is small enough to be compensated by a weak nonlinearity such as that produced by the ( very weak ) kerr effect in optical fibers which leads to a relative nonlinearity - induced change in the refractive index . therefore , nonlinearity in such systems is always weak and it should be well modeled by a cubic nls equation which is known to be integrable by means of the inverse - scattering technique . however , for very short ( e.g. , fs ) pulses the cubic nls equation describing the long - distance propagation of pulses should be corrected to include additional terms that would account for such effects as higher - order dispersion , raman scattering , etc . all such corrections can be taken into account with the help of the perturbation theory @xcite . thus , in fibers nonlinear effects are weak and they become important only when dispersion is small ( near the zero - dispersion point ) affecting the pulse propagation over large distances ( of order of hundreds of meters or even kilometers ) . the situation changes dramatically when we consider the propagation of multi - wavelength pulses with almost equal group velocities . the corresponding model is described by a nonintegrable and rather complicated system of coupled nls equations , which we briefly discuss below . in contrary to the pulse propagation in optical fibers , the physics underlying the stationary beam propagation in planar waveguides and bulk media is different . in this case an optical beam is generated by a continuous wave ( cw ) source and it is time independent . however , when the beam evolves with the propagation distance @xmath0 , it diffracts in the transverse spatial directions . then , a nonlinear change in the refractive index should compensate for the beam spreading caused by diffraction _ which is not a small effect_. that is why to observe spatial solitons as self - trapped optical beams , much larger nonlinearities are usually required , and very often such nonlinearities are not of the kerr type ( e.g. they saturate at higher intensities ) . this leads to the models of generalized nonlinearities with the properties of solitary waves different from those described by the integrable cubic nls equation . propagation distances involved in the phenomenon of the beam self - focusing and spatial soliton propagation are of the order of millimeters or centimeters . to achieve such large nonlinearities , one needs to use the optical materials with large nonlinearity - induced refractive index . one of the possible way to overcome this difficulty is to use the so - called _ cascaded nonlinearities _ of noncentrosymmetric optical materials where nonlinear effects are accumulated due to parametric wave interaction under the condition of the wave phase matching . such parametric wave - mixing effects generate novel classes of spatial optical solitons where resonant parametric coupling between the envelopes of two ( or more ) beams of different frequencies supports stable spatially localised waves even in a bulk medium ( see details in ref . it is this kind of multi - component solitary waves that we discuss below . a growing demand for high - speed computer communications requires an effective and inexpensive computer interconnection . one attractive alternative to the conventional wdm systems is bpw single - mode fiber optics links for very high bandwidth computer communications @xcite . they differ from the wdm schemes in that no parallel to serial conversion is necessary , and parallel pulses are launched simultaneously on different wavelengths . when the pulses of different wavelengths are transmitted simultaneously , the cross - phase modulation can produce an interesting _ pulse shepherding effect _ @xcite , when a strong ( `` shepherd '' ) pulse enables the manipulation and control of pulses co - propagating on different wavelengths in a multi - channel optical fiber link . to describe the simultaneous transmission of @xmath1 different wavelengths in a nonlinear optical fiber , we follow the standard derivation @xcite and obtain a system of @xmath1 coupled nonlinear schrdinger ( nls ) equations @xmath2 ) : @xmath3 { \displaystyle \qquad + \chi_j \left ( |a_j|^2 + 2 \sum_{m \neq j } |a_m|^2 \right ) a_j = 0 , } \end{array}\ ] ] where , for the @xmath4th wave , @xmath5 is the slowly varying envelope , @xmath6 and @xmath7 are the group velocity and group - velocity dispersion , respectively , and the nonlinear coefficients @xmath8 characterize the kerr effect . equations ( [ eq : nls_dim ] ) do not include the fiber loss , since the fiber lengths involved in bit - parallel links are only a small fraction of the attenuation length . we measure the variables in the units of the central wavelength channel ( say , @xmath9 ) , and obtain the following normalized system of the @xmath1 coupled nls equations , @xmath10 { \displaystyle \qquad + \gamma_j \left(|u_j|^2 + 2 \sum_{m\neq j } |u_m|^2\right ) u_j = 0 , } \end{array}\ ] ] where @xmath11 , @xmath12 is the incident optical power in the central channel , @xmath13 , @xmath14 , so that @xmath15 . for the operating wavelengths spaced @xmath16 nm apart within the band @xmath17 nm , the coefficients @xmath18 and @xmath19 are different but close to @xmath20 . initially , in eq . ( [ eq : nls ] ) , we omit the mode walk - off effect described by the parameters @xmath21 ( so that @xmath22 ) . this effect will be analysed later in this section . to analyze the nonlinear modes , i.e. localized states of the bpw model ( [ eq : nls ] ) , we look for stationary solutions in the form , @xmath23 and therefore obtain the system of equations for the normalized mode amplitudes , @xmath24 { \displaystyle \frac{1}{2 } \alpha_n \frac{d^2u_n}{dt^2 } + \gamma_n \left ( |u_n|^2 + 2\sum_{m \neq n } |u_m|^2 \right ) u_n = \lambda_n u_n , } \end{array}\ ] ] where @xmath25 , the amplitudes and time are measured in the units of @xmath26 and @xmath27 , respectively , and @xmath28 . system ( [ eq : nls_nn ] ) has _ exact analytical solutions _ for @xmath1 coupled components , the so - called _ bpw solitons_. indeed , looking for solutions in the form @xmath29 , @xmath30 , we obtain the constraint @xmath31 , and a system of @xmath1 coupled algebraic equations for the wave amplitudes , @xmath32 in a special symmetric case , we take @xmath33 , and the solution of those equations is simple @xcite : + @xmath34^{-1/2}$ ] . analytical solutions can also be obtained in the _ linear limit _ , when the central frequency pulse ( at @xmath35 ) is large . then , linearizing eqs . ( [ eq : nls_nn ] ) for small @xmath36 , we obtain a decoupled nonlinear equation for @xmath37 and @xmath38 decoupled linear equations for @xmath39 . each of the latter possess a localized solution provided @xmath40 , where @xmath41 ^ 2 $ ] . in this limit the central soliton pulse @xmath37 ( `` shepherd pulse '' ) can be considered as inducing an effective waveguide that supports a fundamental mode @xmath39 with the corresponding cutoff @xmath42 . since , by definition , the parameters @xmath43 and @xmath44 are close to @xmath20 , we can verify that the soliton - induced waveguide supports maximum of two modes ( fundamental and the first excited one ) . this is an important physical result that explains the effective robustness of the pulse guidance by the shepherding pulse . to demonstrate a number of unique properties of the multi - channel bpw solitons , we consider the case @xmath45 in more details . a comprehensive discussion of the case @xmath46 can be found in the preprint @xcite . we select the following set of the normalized parameters : @xmath47 , @xmath48 , and @xmath49 . solitary waves of this four - wavelength bpw system can be found numerically as localized solutions of eqs . ( [ eq : nls_nn ] ) . figure [ fig" +"entanglement @xcite in a composite system refers to certain implicit correlation between the subsystems arising from their interaction . it is the key resource of quantum computation and quantum information processing @xcite . due to recent advances in this field , entanglement has generated renewed interest . there have been different approaches to understand and to quantify entanglement @xcite . but so far the entanglement , only in a bipartite pure state has been investigated very extensively . the von neumann entropy @xcite of either of the subsystems provides a good measure of entanglement in this case @xcite . this is the quantum partner of the shannon s entropy @xcite in classical information theory and is defined as @xcite @xmath1 where @xmath2 . here , @xmath3 is the reduced density operator of the subsystem @xmath4 and is given by @xmath5 where @xmath6 is the density operator of the composite system under consideration and @xmath7 , @xmath8 . in general , the quantities @xmath9 satisfy the following inequality ( due to araki and lieb ) @xcite : @xmath10 where @xmath11 is the joint entropy of the composite system comprising @xmath12 and @xmath13 . the second part of the above inequality is known as subadditivity inequality @xcite . for a pure state , @xmath14 and thus @xmath15 . the equality sign in the above relation holds good if and only if the composite density matrix @xmath6 can be written as a tensor product of its two reduced density matrices @xmath16 and @xmath17 , i.e. , for a disentangled state . one can define the index of correlation @xmath18 given by the expression @xmath19 @xcite , which can also be interpreted as information entropy in quantum information point of view . we note that kim _ et al . _ have calculated the entropies of different kinds of pure states including two - mode fock states and squeezed states @xcite . further , the above relation for entropy has been studied in the context of entangled gaussian states @xcite . so far we have discussed about the measurement of entanglement in a bipartite pure state . if the composite system is in a mixed state ( defined by the density operator @xmath20 ) , the entanglement of formation @xmath21 can be defined in terms of the average von neumann entropies of the pure states of the decompositions @xcite . wootters has shown the quantity @xmath21 to be an explicit function of @xmath20 @xcite . he has introduced the notion of concurrence in this context . we further notice that from the schmidt decomposition of a pure bipartite state , one can properly identify the entanglement present in the state @xcite . this is also very useful to study bipartite continuous systems @xcite . on the other hand , for a mixed state @xmath20 , the separability criterion has been proposed @xcite to study entanglement . this is based on positive partial transpose mapping of @xmath20 . thus the negativity ( entanglement monotone ) of the eigenvalues of the partial transpose of @xmath20 could be a measure of entanglement in a mixed bipartite system @xcite . the concept of negativity as an entanglement measure has been used in context of interaction of atoms with thermal field @xcite . the separability criterion has been extended to continuous systems @xcite also . despite many approaches to define entanglement for a bipartite system , there have been only a few approaches to quantify entanglement in the composite systems of three or more particles @xcite . we note that a generalization of schmidt decomposition in multipartite systems in pure states has been introduced @xcite . @xcite proposed a measurement of entanglement in a tripartite system in terms of concurrences of the pairs of subsystems . this measure is invariant under permutations of the subsystems . an average entanglement in a four - partite entangled state has been defined in terms of von neumann entropies of the pairs of subsystems @xcite . very recently , yukalov has addressed the question more generally and quantified multipartite entanglement @xcite in terms of the ratio of norms of an entangling operator and of a disentangling operator in the relevant disentangled hilbert space . in this paper , we put forward a possible measurement of entanglement of a four - particle system by studying the entropy of the reduced three - particle system . as mentioned above , the von neumann entropy is a good measure for entanglement in a bipartite system . for a tripartite composite state , this entropy satisfies a strong subadditivity inequality ( ssi ) @xcite , which has many important implications in the subject of quantum information theory . in this paper , we study the properties of a four - particle entangled state through the three - particle entropy and the ssi . the structure of the paper is as follows . in sec . ii , we provide a brief discussion on strong subadditivity inequality from the quantum information point of view . in sec . iii , we describe a physical model and show the preparation of a four - particle entangled state . in sec . iv , we study the validity of the ssi in the present context and provide a physical explanation of the results . we conclude this paper by proposing a measurement of the corresponding four - particle entanglement . we have already mentioned that for a bipartite composite system of two particles @xmath12 and @xmath13 , the joint entropy @xmath11 satisfies the subadditivity inequality ( [ ineq ] ) . for a composite system of three particles a , b , and c , this inequality can be extended to the following form @xcite : @xmath22 this inequality is known as strong subadditivity inequality . the most obvious situation that the equality sign holds in ( [ lieb ] ) is when the composite density matrix @xmath23 can be written as the tensor product of its three reduced density matrices as @xmath24 , i.e. , when the system is in a disentangled state . however , the more stringent condition for this reads as @xcite @xmath25 there have been numerous implications of the above inequality ( [ lieb ] ) in quantum information theory @xcite . firstly , it refers to the fact that the conditioning on the subsystem always reduces the entropy , i.e. , @xmath26 , where , @xmath27 is the entropy of a conditional on knowing the state of b. secondly , the above inequality implies that discarding a quantum system never increases mutual information , i.e. , @xmath28 , where , @xmath29 is the mutual information of the subsystems a and b. thirdly , quantum operations never increase mutual information of two subsystems . this means that if the mutual information of the two subsystems a and b becomes @xmath30 after trace - preserving operation on b , then @xmath31 . further , this inequality ( [ lieb ] ) implies that the conditional entropy of the subsystems a , b , and c is also subadditive , i.e. , @xmath32 . to verify ssi , one needs to calculate the entropies like @xmath33 which clearly requires a three - particle mixed state which we can produce using a pure four - particle entangled state @xcite . in the next section , we discuss how one can prepare a pure four - particle entangled state so that we can study ssi for the first time for a system realizable using cavity qed methods . we consider two three - level atoms ( a and b ) with relevant energy levels in @xmath0-configuration ( see fig . [ fig1 ] ) interacting with a two - mode high quality optical cavity . the specified annihilation operators for the cavity modes are @xmath34 and @xmath35 . the atoms are interacting with the cavity mode @xmath34 in @xmath36 transition and with the mode @xmath35 in @xmath37 transition . the hamiltonian for the system under rotating wave approximation can be written as @xmath38\;,\ ] ] where , @xmath39 is the atomic transition frequency between the levels @xmath40 and @xmath41 , @xmath42 @xmath43 is the respective frequency of the cavity modes @xmath34 and @xmath35 , @xmath44 @xmath43 provides the atom - cavity coupling . we assume @xmath44 s to be real and function of time . we start with the initial state @xmath45 , where @xmath46 and @xmath47 are the initial numbers of photons in the cavity modes @xmath34 and @xmath35 , respectively and the two atoms are in @xmath48 state . the state of the system can be expanded in terms of the relevant basis states in the following way : @xmath49 from the schrdinger equation we find the following equations of the corresponding probability amplitudes : @xmath50\;,\\ \dot{d}_6&=&-i(\sqrt{\mu + 2}g_{2a}d_4+\sqrt{\mu + 2}g_{2b}d_7)\;,\nonumber\\ \dot{d}_7&=&-i(\sqrt{\mu + 1}g_{2a}d_5+\sqrt{\mu + 2}g_{2b}d_6+\delta d_7+\sqrt{n-1}g_{1b}d _ 8)\;,\nonumber\\ \dot{d}_8&=&-i(\sqrt{n-1}g_{1b}d_7+\sqrt{\mu + 1}g_{2a}d_9)\;,\nonumber\\ \dot{d}_9&=&-i(\sqrt{n}g_{1a}d_1+\sqrt{n-1}g_{1b}d_5+\sqrt{\mu + 1}g_{2a}d_8+\delta d_9)\;,\nonumber\end{aligned}\ ] ] where , we have used the following transformations : @xmath51 where , @xmath52 , @xmath53 is the one - photon detuning of the cavity modes for the @xmath54-th atom . here we have assumed that the cavity modes are in two - photon resonance and @xmath55 . writing these equations ( [ doteq ] ) in the matrix form @xmath56=-i[m][d_i]$ ] , we find that one of the eigenvalues of the matrix @xmath57 $ ] is zero . the corresponding eigenstate is @xmath58\ ; , \label{dark}\ ] ] where @xmath59 clearly , this state is an entangled state of four particles , namely , the atoms a and b , and the two modes @xmath34 and @xmath35 . using appropriate time - dependence of the pulses , the four - particle system can be prepared in this state , as discussed in the next section . recently , there have a few experimental demonstrations of preparation of four - particle entangled state @xcite and performance of a c - not gate @xcite . interestingly , the state @xmath60 is a two - atom two - mode multipartite coherent population trapping ( cpt ) state which is a counterpart of the well - known cpt state for a single atom interacting with two coherent fields @xcite . we next discuss how the state @xmath60 can be prepared by using raman adiabatic passage technique . we assume that both the atoms are initially in @xmath48 state . we further assume the time - dependence of the rabi frequencies @xmath44 of the two modes as @xmath61 here , @xmath62 ( @xmath63 ) is the amplitude of the respective pulse , @xmath64 and @xmath65 are the width and time - separation respectively , of the two pulses . note that the pulses are applied in counterintuitive sequence . under this condition , the atom - cavity system follows the evolution of the state @xmath60 adiabatically . this state is a zero eigenvalue eigenstate ( adiabatic state ) of the hamiltonian ( [ hamil1 ] ) . during this process , known as stimulated raman adiabatic technique ( stirap ) @xcite , the atom - cavity system remains in this state for all times . in the present case , at the end of the evolution , the population of both the atoms are simultaneously transferred to the state @xmath66 . however , if the atoms are not in one - photon resonance , i.e. , if @xmath67 , then this transfer process is not complete . this happens because the system does not remain confined in the null adiabatic state @xmath60 for @xmath67 @xcite . we now investigate the validity of ssi for any trio of quantum systems in the present process . we can express this inequality for any three particles , namely , atom a , atom b , and cavity mode @xmath34 with number @xmath46 of photons out of the four - particle system under consideration as @xmath68 here , @xmath69 defines the joint von neumann entropy of the relevant" +"slowly pulsating b - type supergiants ( spbsg ) have emerged as a new class of pulsating variables after saio et al . ( 2006 ) have detected pulsational frequencies in the most satellite data of the blue supergiant hd 163899 ( b2 ib / ii , klare & neckel 1977 , schmidt & carruthers 1996 ) . saio et al . ( 2006 ) identified 48 frequency peaks in the most light curve and attributed them to g- and p - mode pulsations . because so far only one object of this type is found , the spbsg class is not yet well defined as for the range of effective temperature and luminosity . also the evolutionary status of these pulsators remains unrevealed ; they may be either in the shell hydrogen burning phase as well as after core helium ignition . the finding of saio et al . ( 2006 ) has prompted a few groups ( godart et al . 2009 , daszyska - daszkiewicz , ostrowski , pamyatnykh . 2013 ; hereafter d2013 ) to reanalyse pulsation stability in models of b - type stars after the terminal age main sequence ( tams ) and to further studies of spbsg variables . the presence of g - mode pulsations in b - type post - main sequence stars has been explained by a partial reflection of some modes at an intermediate convective zone ( icz ) related to the hydrogen - burning shell or at a chemical gradient zone surrounding the radiative core . however , all studies of these objects published so far are based on the assumption that hd 163899 has not reached the phase of core helium ignition , i.e. , it is in the phase of shell hydrogen burning . this assumption might not necessary be fulfilled , because the blue loop can reach temperatures of early b spectral types . in this paper we calculate models which undergo core helium burning on the blue loop and compare them with models in the hydrogen shell burning phase . the structure of the paper is as follows . in section [ domains ] , we present the new instability domains which include pulsational instability on the blue loops . the effects of opacity , metallicity , overshooting , element diffusion and mass loss on the pulsational instability areas are studied . propagation diagrams and properties of instability parameter and kinetic energy of modes for representative models are described in section [ models ] . in section [ identification ] we construct photometric diagnostic diagrams for the b - type supergiant models and discuss a prospect for mode identification . an attempt to interpret the oscillation spectrum of hd 163899 is presented in section [ hd163899 ] . the last section contains conclusions . the evolutionary models were calculated with mesa evolution code ( modules for experiments in stellar astrophysics , paxton et al . 2011 , paxton et al . 2013 ) . mesa allows to follow the evolution of massive stars to the pre - supernova phase . our previous calculations ( d2013 ) were limited to the phase before core helium ignition due to the lack of helium burning in warsaw - new jersey evolution code we used . we considered the mass range of 13@xmath318 @xmath0 . all computed models have an initial hydrogen abundance of @xmath4 and agss09 metal mixture ( asplund et al . the initial metal abundance varies from @xmath5 to @xmath6 . opal ( iglesias & rogers 1996 ) and op opacity tables ( seaton 2005 ) were used . all effects of rotation were neglected . non - adiabatic pulsation analysis was performed using the code of dziembowski ( 1977 ) . in fig.[fig1 ] we present evolutionary tracks including various effects : opacity , metallicity , overshooting , mass loss and element diffusion . they will be discussed in detail in the following subsections . the convective zones are determined by the ledoux criterion . it seems to be more justified than the schwarzschild criterion because of a direct sensitivity of the chemical gradient to evolution . lebreton et al . ( 2009 ) argued that the use of the ledoux criterion leads to a narrower icz and hence to the smaller number of unstable modes . in case of our models , mesa produces the wide icz with both criterions and this effect is not significant . for the envelope , we adopted the parameter of the mixing length theory ( mlt ) of @xmath7 which is the higher value than usually used for massive stars . during the main sequence ( ms ) and hydrogen - shell burning phases , the value of @xmath8 has a negligible effect on structure of massive stars but on the red giant branch ( rgb ) a higher efficiency of convection is needed and hence we opted for the higher value of @xmath8 . we took into account convective overshooting from the hydrogen and helium core and inward overshooting from non - burning convective zones , using the exponential formula ( herwig 2000 ) : @xmath9 where @xmath10 is the diffusion coefficient derived from mlt at a user - defined location near the boundary of a convective zone , @xmath11 is the pressure scale height at that location , @xmath12 is the distance in the radiative layer away from that location , and @xmath13 is an adjustable parameter , which we set to @xmath14 for most of calculated models . this value of @xmath13 mimics the behaviour of step overshooting with @xmath15 . in our models the core helium ignition commences on the way towards the rgb but at this stage the energy produced from the helium burning is much lower than the energy produced from the hydrogen shell burning . the shell dominates the evolution up to the tip of rgb . at this point the energy produced in a helium core becomes comparable to the energy from the shell and the luminosity of a star drops . a star might eventually move towards higher effective temperatures and form a blue loop . the behaviour of the blue loops is still very poorly known and it is difficult to predict the effect of different parameters on their properties . we found that the convective overshooting has the most visible effect on their emergence , especially the inward overshooting from the non - burning zone . without that overshooting it is impossible to obtain blue loops in our models independently of metallicity , opacity , diffusion , etc . this effect is shown in fig.[fig2 ] , where we depicted two evolutionary tracks for the mass of 15 @xmath0 calculated with and without inward overshooting from the non - burning zone . the blue loop emerges if the @xmath16-gradient left by the evolution during ms is erased by the outer convective zone on the rgb . the range of this convective zone is increased by the inward overshooting . on the other hand , the overshooting from the hydrogen core generally acts against emerging of the blue loops . we show the effect of different values of the overshooting parameter on the evolutionary tracks in the central - left panel ( @xmath17 ) and in the bottom - left panel ( @xmath18 ) of fig.[fig1 ] . in both cases the blue loops are present but for the lower value of @xmath13 they have a larger extension . if we increase the overshooting only from the hydrogen core to @xmath18 and we leave @xmath17 for the helium core overshooting and the inward overshooting from non - burning zone , the blue loops still emerge but their extension is lower . this is caused mainly by the reduced overshooting from the helium core which decreases the amount of helium available to burn and hence leads to smaller extension of the blue loop . with ( solid line ) and without ( dashed line ) inward overshooting from the non - burning convective zone . opal opacity tables and metallicity @xmath19 were used.,width=325 ] the presented examples show that properties of mixing , especially the convective overshooting , have a huge impact on the behaviour of the blue loops . it is difficult to discriminate between different effects but generally it seems that the inward overshooting from the outer convective zone on the rgb is indispensable to obtain blue loops for the models in the studied range of masses . the overshooting from the hydrogen core suspends the emerging of the blue loops and the overshooting from the helium core has a slight effect on their extension . for the models considered in section2.1 , we computed pulsational instability for modes with the degrees @xmath20 . they are shown as thick lines in in fig.[fig1 ] . the top panels show models calculated with @xmath21 and opal ( the top - left panel ) and op opacity tables ( the top - right panel ) . the central panels depicts models calculated for @xmath22 and opal tables without and with mass loss ( the central - left and central - right panels , respectively ) . the bottom - left panel shows the models calculated with @xmath22 , opal tables and convective overshooting parameter @xmath18 . the bottom - right panel depicts models calculated with element diffusion . details of the used mass - loss models and implementation of diffusion are described later in this section . similarly to our previous results ( d2013 ) there is the p- and g - mode instability beyond tams for the models that undergo hydrogen shell burning . most of the unstable modes are non - radial , but the radial fundamental mode is also unstable in hotter models beyond main sequence . the main difference between our current and all previous calculations is the presence of unstable non - radial modes on the blue loops for more massive models ( @xmath23 and @xmath24 ) . the radial modes are stable in this evolutionary stage in all calculated models . the existence of pulsation instability on the blue loop , as well as the blue loops themselves , depend critically on the metallicity , @xmath25 . with lowering the metallicity the blue loops reach the higher effective temperatures which has a huge impact on pulsation instability . in models with the lower value of @xmath26 the driving layer related to the metal opacity bump is located too deep in the star to be effective . on the other hand , the lower value of metallicity the lower the @xmath25 opacity bump . this crucially weakens instability for the ms and h - shell burning models but it seems to have a negligible effect on the instability on the blue loops , especially when compared to the effect of the effective temperature . in models with @xmath27 the instability in the phase before core helium ignition is entirely quenched whereas there are still a lot of unstable modes in the models with very well developed blue loop . the pulsational instability on the blue loops vanishes at @xmath28 . the reason for that is a difference in the internal structure resulting from a presence of an inward overshooting from the nonburning zone in the blue - loop models . the main effect of this overshooting is visible during the evolution on the rgb , but there is also a thin zone of overshooting below the icz . that leads to enrichment of hydrogen in layers just below the icz , which causes a steep increase of the @xmath16-gradient in a thin zone . as a consequence the brunt - visl frequency , @xmath29 , increases as well , what makes trapping of pulsation modes more effective and some of them can be driven by the @xmath1-mechanism operating in the z - bump despite low metallicity . the opposite situation occurs for models" +"binary systems , whose behavior crucially depends on the underlying condition of immiscibility or miscibility @xcite , play a fundamentally important role in many areas of physics . in the case of immiscibility , a major effect is the formation of domain walls ( dws ) between regions occupied by immiscible components . commonly known are dws in media featuring a vectorial order parameter , such as ferromagnets @xcite , ferroelectrics @xcite , and liquid crystals @xcite . in self - defocusing optical media , dws separate regions occupied by electromagnetic waves with orthogonal circular polarizations of light haelt , me . similar interface patterns were predicted in arrays of nonlinear optical waveguides , modeled by discrete nonlinear schrdinger equations ( nlses ) @xcite . dws are known in superfluids too , where they are formed by immiscible binary bose - einstein condensates ( becs ) , as predicted theoretically @xcite and demonstrated in experiments @xcite . in the mean - field approximation @xcite , such settings are modeled by systems of nonlinearly coupled gross - pitaevskii equations ( gpes ) with the cubic self - repulsive nonlinearity , which are similar to coupled nlses describing the above - mentioned optical dws @xcite . in their stationary form , these equations coincide with coupled cubic ginzburg - landau equations modeling dws in dissipative patterns , such as interfaces between rolls with different orientations in large - area rayleigh - benard convection @xcite . the analysis of the dws in bec was extended for broader settings , including linear interconversion between the immiscible components ( this is possible when they represent two different hyperfine states of the same atom coupled by a resonant radiofrequency wave ) @xcite , dipolar @xcite and spinor ( three - component ) condensates @xcite , as well as the bec discretized by trapping in a deep optical - lattice ( ol ) potentials mering . furthermore , the study of the dws was recently extended for immiscible binary becs with three - particle collisions @xcite , in the case when the related losses may be neglected , the respective coupled gpes featuring the cubic - quintic repulsive nonlinearity @xcite . in the effectively one - dimensional ( 1d ) setting , ultracold bosonic gases with strong inter - atomic repulsion may be cast in the tonks - girardeau ( tg ) state , which emulates the gas of non - interacting fermions @xcite , provided that the energy of the repulsive interaction between bosons exceeds their kinetic energy , while the opposite situation corresponds to the becphase in the bosonic gas ( a review of the tg model was given in ref . the tg gas of hard - core bosons has been realized experimentally , using tight transverse confinement @xcite . in particular , a longitudinal ol potential was used to increase the effective mass in the trapped state , thus making the kinetic energy small enough @xcite . it is commonly known that gpes furnish very accurate description of the bec in atomic gases . a similar macroscopic model of the tg gas is offered by the nlse with the quintic self - repulsion term @xcite . in a rigorous form , the relevance of the corresponding sextic term in the free - energy density of the three - dimensional bosonic gas in its ground state , which reduces to the quasi-1d tg phase , was demonstrated in ref . @xcite , under condition @xmath0 , where @xmath1 , @xmath2 , and @xmath3 are , respectively , the inter - atomic repulsion strength , system s length , and the total number o atoms . the quintic model was used in various contexts , including shock waves @xcite , dark @xcite and gap - mode @xcite solitons , as well as bright solitons supported by dipole - dipole interactions @xcite , and , recently , dws in immiscible binary tg gases @xcite . further , oscillation frequencies derived from fermionic hydrodynamic equations , which apply to the hard - core tg gas , were found to be close to their counterparts predicted by the quintic nlse hydro . coupled quintic nlses also arise in works aimed at constructing the ground state of a binary tg mixture in the harmonic - oscillator potential by means of the density - functional method @xcite . on the other hand , this approach may not apply to tg gases beyond the framework of static configurations and hydrodynamic regimes . in particular , it fails for strongly non - equilibrium problems , such as merger of distinct gas clouds @xcite . as concerns the mixtures , it may be interesting to consider binary systems including the tg gas and another quantum - gas component . in particular , exact solutions were found for the ground state of tg - fermi mixtures minguzzi . the binary gas of impenetrable bosons is solvable too ctg - ba . the objective of the present work is to introduce basic nonlinear complexes , such as dws , bubble - drop ( bd ) modes ( bound pairs of two dws ) , and dark - bright solitons ( dbss ) , in an immiscible system of tg and bec gases . in the experiment , the system may be realized , in particular , as a bosonic gas composed of two atomic species under tight transverse confinement , with a longitudinal ol potential acing on ( being relatively close to a resonance with ) one species only . then , as the experimental setting presented in ref . @xcite suggests , a large effective mass of the near - resonant component will bring it into the tg state , while the other component may stay in the bec phase . as a model for this system , in section ii we adopt the cubic gpe for the self - repulsive bec component coupled by the cubic ( collisional ) repulsive term to the quintic nlse for the tg species . the use of the latter equation is appropriate , as we study only static configurations of the system . the same model may find a realization in optics as a model of colloidal waveguides . it has been recently demonstrated that , selecting the size of metallic nanoparticles in the colloid and their concentration , one can engineer desirable coefficients of the corresponding cubic and quintic nonlinearity @xcite . in particular , it is possible to design a waveguide which features a nearly pure quintic nonlinearity at a particular wavelength , while the cubic response dominates at a different wavelength . the copropagation of optical signals carried by these wavelengths will then emulate the tg - bec system . dws separating the bec and tg phases are addressed in section iii . we derive the respective immiscibility condition ( see eq . ( [ g < ] ) below ) , and then generate dw states in a systematic way , using both numerical solutions and the analytical thomas - fermi approximation ( tfa ) . the latter method makes it possible to obtain some dws in an explicit analytical form , as given below by eqs . ( [ exact ] ) - ( [ wtfa ] ) . db and dbs complexes are considered in sections iv and v , respectively , again using a combination of analytical and numerical methods . the analysis predicts that the db states exist solely in the form of the tg drop embedded into the bec background ( bubble ) , but not in the opposite case ; on the other hand , the dbs are predicted in either case of the bright tg soliton embedded into the bec dark soliton , or vice versa . these predictions are fully corroborated by numerical results . the paper is concluded by section vi . the system of coupled nlses with the cubic and quintic nonlinear terms for the bec and tg components , @xmath4 and @xmath5 , with respective scaled masses @xmath6 and @xmath7(i.e . , @xmath8 is the relative effective mass of tg components which , as said above , may be made larger than the actual atomic mass @xcite ) is @xmath9where real parameters @xmath10 and @xmath11 are strengths of the self - repulsion of the bec component , and repulsion between the bec and tg ones , respectively , while @xmath12 and the coefficient of the effective quintic self - repulsion of the tg component are scaled to be @xmath13 ( in the notation of ref . @xcite , the natural value of the latter coefficient is @xmath14 ) . substitution @xmath15makes it possible to further fix @xmath16 and @xmath17 , thus simplifying eq . ( [ first ] ) to a system with two free coefficients , @xmath8 and @xmath18:@xmath19 for the above - mentioned spatial - domain optical model ( with @xmath20 replaced by the propagation distance , @xmath21 , and transverse coordinate @xmath22 ) , the scaled propagation equations are derived , using the standard procedure @xcite , as@xmath23here @xmath24 and @xmath25 represent amplitudes of the copropagating electromagnetic waves with relative wavenumber and frequency @xmath26 and @xmath27 , cf . ( [ mmm ] ) . further , @xmath28 in eq . ( [ omega ] ) are the cubic and quintic spm coefficients for the two waves , while the cubic xpm coefficient is normalized to be @xmath13 . additional rescaling,@xmath29transforms eq . ( [ omega ] ) into the system of equations ( [ bec ] ) and ( [ tg ] ) , with @xmath30 . the hamiltonian corresponding to eqs . ( [ bec ] ) and ( [ tg ] ) is @xmath31 in addition to @xmath32 , the system preserves the norms ( scaled numbers of atoms in the ultracold gas , or total powers of the two waves , in terms of the optical model ) , @xmath33of the two components , and , for dynamical solutions , also the total momentum , @xmath34 , although , as mentioned above , the use of the quintic nls equation for the description of dynamics of the tg gas may be impugnable . stationary solutions to eqs . ( [ bec ] ) and ( [ tg ] ) with positive chemical potentials @xmath35 are looked for as @xmath36with real functions @xmath37 satisfying equations @xmath38(in the optical model , @xmath39 represent the propagation constants of the two waves ) . equations ( [ phi1 ] ) and ( [ phi2 ] ) , if considered as equations of the evolution along @xmath40 , conserve the formal hamiltonian,@xmath41cf . ( [ h ] ) . normalizing the stationary wave functions as@xmath42one may fix @xmath43 , which implies that the density of the uniform tg component is also fixed to be @xmath13 , see eq . ( [ bc ] ) below . numerical results for dws are presented in the following section chiefly for this case , while in sections iv and v other normalizations are used for bd and dbs states . solutions of stationary equations ( [ phi1 ] ) and ( [ phi2 ] ) for the domain wall ( dw ) separating semi - infinite domains occupied by the bec and tg components ( or the spatial domains occupied by the copropagating waves in the above - mentioned optics model ) are specified by the following boundary conditions ( b.c . ) , which include the respective asymptotic densities , @xmath44 and @xmath45 : @xmath46the condition that formal hamiltonian ( [ h ] ) must take the same values at @xmath47 and @xmath48 across the solution imposes a restriction on b.c . ( [ bc ] ) , which relates the two chemical potentials:@xmath49 in terms of the asymptotic densities , condition ( [ bc ] ) takes the form of@xmath50which actually implies the balance of the pressure applied to the dw" +"primordial black holes ( pbhs ) can form in the early universe via the collapse of large density perturbations @xcite . there are tight constraints on the abundance of pbhs formed from their present day gravitational effects and the consequences of their evaporation . these limits can be used to constrain the power spectrum of the primordial density , or curvature , perturbations . the pbh constraints on the curvature power spectrum are fairly weak , being many orders of magnitude larger than the measurements on cosmological scales . they do , however , apply over a very wide range of scales and therefore provide a useful constraint on models of inflation . peiris and easther @xcite have shown that there are single field inflation models , which are compatible with all cosmological observations , for which the perturbation amplitude on small scales is large enough to produce a significant density of pbhs . for scales which exit the horizon close to the end of inflation the standard ( stewart - lyth @xcite ) formulae for the amplitude of perturbations do not hold . leach and liddle @xcite carried out a numerical calculation of the evolution of perturbations for a quadratic inflationary potential . they found that the perturbations on scales which exit the horizon close to the end of inflation were roughly an order of magnitude larger than predicted by the stewart - lyth formula ( see also ref . @xcite ) . therefore to fully exploit the power of pbh constraints on inflation models , a numerical calculation of the amplitude of perturbations on small scales is required . it has recently been shown @xcite that pbhs can also form on scales which never leave the horizon . we do not consider this possibility here . in this paper we use a modified flow analysis to identify inflation models where the perturbations at the end of inflation may be large enough for primordial black holes to be overproduced . for these models we carry out a numerical evolution of the primordial perturbations and use the pbh constraints on the power spectrum to eliminate models which overproduce pbhs . we describe the modified flow analysis in sec . [ flow ] and the evolution of perturbations and the calculation of the power spectrum in sec . we apply the primordial black hole abundance constraints and present our results in sec . [ results ] and conclude with discussion in sec . [ discuss ] . we consider the hubble slow roll - parameters @xcite : @xmath0 where @xmath1 is the planck mass and @xmath2 denotes differentiation with respect to the scalar field , @xmath3 . the flow equations @xcite encode the variation of the slow - roll parameters in terms of the number of e - foldings from the end of inflation , @xmath4}$ ] and provide a method for stochastically generating inflation models : @xmath5(^l\lambda_h ) + ^{l+1}\lambda_h \ , , \\ & & \hspace{50 mm } l\ge 1 \nonumber \label{flowequations}\end{aligned}\ ] ] where @xmath6 and @xmath7 . following kinney @xcite we randomly chose ` initial ' values for the slow - roll parameters and @xmath8 , the number of e - foldings between cosmological scales exiting the horizon and the end of inflation , in the ranges : @xmath9 \ , , \\ \nonumber \epsilon_h&=&[0,0.8 ] \ , , \\ \nonumber \sigma_h&=&[-0.5,0.5 ] \ , , \\ \nonumber ^2\lambda_h \equiv \xi_h&=&[-0.05,0.05 ] \,,\\ \nonumber ^3\lambda_h&=&[-0.005,0.005 ] \ , , \\ \nonumber & ... & \\ ^{m+1}\lambda_h&=&0 \ , , \label{hierarchy}\end{aligned}\ ] ] truncating the hierarchy at @xmath10 . we then evolve the flow equations forward in time ( @xmath11 ) from @xmath12 until either @xmath13 or inflation ends with @xmath14 . in the former case we calculate the cosmological observables , the spectral index , @xmath15 , its running , @xmath16 , and the scalar to tensor ratio , @xmath17 , using the initial values of the slow - roll parameters @xcite : @xmath18 \ , , \\ r & = & \epsilon_h [ 1-c_1(\sigma_h+2\epsilon_h ) ] \ , , \end{aligned}\ ] ] where @xmath19 and @xmath20 . in the latter case we evolve the flow equations backward @xmath8 e - folds and calculate the cosmological observables at this point . in some cases inflation also ends when evolving backwards before @xmath8 e - folds are achieved . these models are incapable of supporting the required amount of inflation and are discarded . our algorithm differs from that originally proposed by kinney @xcite in how we handle models chosen from the initial hierarchy that are destined to inflate forever , @xmath21 , but do not reach this limit within @xmath8 e - foldings . in the original flow algorithm in this case the cosmological observables are calculated at the late - time fixed point i.e. the model is forced to evolve to its asymptotic limit . in this limit the running of the spectral index is negligible . therefore for models which are compatible with the wmap 7 year measurement of the spectral index , @xmath22 @xcite , the amplitude of the curvature perturbations can not be large on any scale and pbhs are never formed in significant numbers @xcite . following peiris and easther @xcite , we do not force these models to evolve to their asymptotic limit but instead terminate them once @xmath8 e - folds of inflation have occurred . at this point it is assumed that another mechanism , for example a second - field such as in hybrid inflation @xcite , terminates inflation . with this treatment some of these models are consistent with the wmap measurements of the spectral index and its running , but have perturbations on small scales which may be large enough to over - produce pbhs @xcite . the evolution of inflationary curvature perturbations , @xmath23 , is carried out using the mukhanov variable @xcite , @xmath24 , where @xmath25 the fourier modes , @xmath26 , evolve according to a klein - gordon equation with a time - varying effective mass : @xmath27 where @xmath28 is conformal time , @xmath29 , and @xmath30 \ , . \label{exactdespite}\end{aligned}\ ] ] at early times , @xmath31 , when a mode @xmath32 is well within the horizon , @xmath33 , the initial condition for @xmath34 , is taken to be the bunch - davies vacuum state , @xmath35 in the superhorizon limit , @xmath36 , eq . ( [ mukhanoveomtau ] ) has a growing mode solution @xmath37 , so that the curvature perturbation @xmath38 ` freezes out ' and becomes constant . the power - spectrum of the curvature perturbations can thus be calculated as @xmath39 eq . ( [ mukhanoveomtau ] ) can be solved exactly for the special case of power - law inflation . the commonly used stewart - lyth formula is found via a slow - roll expansion around this exact solution @xcite : @xmath40 ^ 2}{\pi\epsilon_h } \left(\frac{h}{m_{\rm{pl}}}\right)^2_{k = ah } \ , , \label{stewartlyth}\ ] ] where @xmath41 . this expression gives the power spectrum in the asymptotic superhorizon limit , @xmath42 , in terms of the hubble parameter and slow - roll parameters evaluated at horizon crossing @xcite . it is valid provided that the slow - roll approximation holds ( specifically that the slow - roll parameters are slowly varying around horizon crossing ) and the asymptotic limit is reached before inflation ends @xcite . for modes which exit the horizon close to the end of inflation the asymptotic limit will not be reached , and the slow - roll approximation may also be violated . leach & liddle @xcite investigated this for a simple quadratic chaotic inflation model . they found that for scales that exit the horizon very close to the end of inflation the power spectrum is roughly an order of magnitude larger than that found using the stewart - lyth expression . in other words , analytic calculations can significantly underestimate the amplitude of perturbations and hence the abundance of pbhs formed . therefore , a numerical calculation of the perturbation evolution is required to accurately compute the primordial power spectrum on the very smallest scales . we use a modified version of the inflation v2 module ( written by lesgourgues & valkenburg ) @xcite to carry out an accurate numerical calculation of the evolution of perturbations . fig . [ numericalenhancement ] shows the power spectrum of curvature perturbations of an example inflation model generated using the modified horizon flow formalism . the power spectrum on large scales is compatible with the wmap 7 year data , while the perturbations on small scales are sufficiently large that pbhs may be over - produced . the stewart - lyth calculation is in good agreement with the numerical calculation until the final few e - folds of inflation . on these small scales , the assumptions that are employed in the stewart - lyth calculation break down , and the numerical calculation finds a significant enhancement of the amplitude of the perturbations , @xmath43 and @xmath17 , for models generated using the modified flow algorithm described in the text . all models which sustain the required number of e - foldings of inflation are shown in the top two plots and those remaining once pbh constraints are applied are shown in the bottom plots.,title=""fig:"",width=154 ] , @xmath43 and @xmath17 , for models generated using the modified flow algorithm described in the text . all models which sustain the required number of e - foldings of inflation are shown in the top two plots and those remaining once pbh constraints are applied are shown in the bottom plots.,title=""fig:"",width=154 ] , @xmath43 and @xmath17 , for models generated using the modified flow algorithm described in the text . all models which sustain the required number of e - foldings of inflation are shown in the top two plots and those remaining once pbh constraints are applied are shown in the bottom plots.,title=""fig:"",width=154 ] , @xmath43 and @xmath17 , for models generated using the modified flow algorithm described in the text . all models which sustain the required number of e - foldings of inflation are shown in the top two plots and those remaining once pbh constraints are applied are shown in the bottom plots.,title=""fig:"",width=154 ] we use the modified flow algorithm described in sec . [ flow ] to generate a large ensemble ( 250,000 ) of inflation models . in fig . [ stochasticresults ] ( top row ) we plot the cosmological observables for all models which are able to sustain the required number of e - foldings of inflation , @xmath8 . in around @xmath44 of the models inflation ends naturally via @xmath45 and these largely populate the concentrated diagonal feature seen in the left hand plots as well as the @xmath46 line ( c.f . @xcite ) . in the remaining @xmath47 of models , @xmath48 and it is assumed , c.f . @xcite , that a secondary mechanism , such as hybrid inflation , acts to end inflation in these cases . large positive running is in principle allowed ( see top right plot ) , however these models may have large amplitude perturbations on small scales and hence overproduce pbhs . to apply the pbh constraints we use the stewart - lyth expression for the power spectrum , eq . ( [ stewartlyth ] ) , to identify inflation models where the amplitude of the perturbations on small scales which exit the horizon close to the end of inflation is large , and may lead to the over - production of pbhs . for these models , we then carry out an accurate numerical evolution of the primordial perturbations , as described in sec . [ pert ] . the pbh abundance constraints have recently been compiled and updated in refs . the resulting constraints on the amplitude of the power spectrum are" +"the flight management infrastructure ( fmi ) product is intended to keep the aircraft from interfering with preplanned observations on the sky . it predicts the ground tracks necessary to execute its mission , and corrects the plan for actual conditions while airborne . to support this , it contains both a planning component that can run on the ground and in the air , and an execution component that runs in the air . the planning component manages a set of ordered observations and optional aircraft repositioning requests . the execution component compares the plan to actual conditions in flight and requests headings ( indirectly ) from the autopilot . sofia mission planning differs from satellite or ground based observatory planning in a few key areas . most importantly , the observatory position is a function of observation target history , which prevents observations from being considered as time - slots alone . assignment of flight dates is also nontrivial targets can not be localized on the sky or the observatory will always fly in about the same direction ( requiring nearly equivalent dead time to return ) ; this suggests entire flight series should be considered at once , for greater target variety . flight planning and execution differs from conventional as well . all conventional aircraft fly from point to point along specified paths on the ground , and `` drift '' the aircraft to compensate for winds . typical drift angles ( course - heading ) exceed 3@xmath0 , and the worst possible case approaches 30@xmath0 , so sofia can not necessarily observe in this manner . expected winds can be planned for using a weather forecast . correcting course for _ unexpected _ winds can be accomplished by adjusting observation durations , by relocating the aircraft between observations , or by `` observation triage '' as a last resort . this requires an astronomically - aware airborne monitoring function to compare current conditions to plan . aircraft capabilities are a strong function of fuel weight , which argues against simple parametrizing by time , in favor of fuel . in addition to the geometrical and practical constraints described above , the sofia flight planning problem also has a number of external constraints , all of which prevent a truly automated , or even rigorously sequential , flight planning process . for instance , special use airspace ( sua ) incursions may require external approval , and it can not be known ahead of time whether such approval will be forthcoming in all cases . national airspace boundaries require international agreements . over - ocean operations are prohibited for safety reasons for the first flights ; for later flights , fairly complex fuel reserve constraints are required . gross takeoff weight has a hard limit of 700,000 pounds , which limits the duration of sofia missions . some science - driven constraints require interaction with scientists or detailed knowledge of the observations ; especially , trading off water vapor overburden estimates with altitude and duration , and for trading off observations against each other . prior to any particular mission , several iterations of flight planning are performed . this is expected to include fully integrated automated flight planning ( frank , gross , & krkl 2004 ) , routinely . manual choice of observation ( including order ) will occur subsequently . upon execution , replanning might occur if conditions are sufficiently different from assumptions . figure [ fig : sampleflight ] shows a color - processed screenshot of a simulated flight intended for april , 2008 , from palmdale , ca . actual conditions for the simulation shown differ from planned only by small timing errors of the order of several seconds between segments and at takeoff . as mentioned earlier , it is advantageous to consider entire flight series at once , in order to trade observations between flights . the data structure supporting this is shown in fig . [ fig : flightseries ] . fmi requires substantial input data in order to accurately predict a flight track and its constraints . weather forecast time - series are taken from the national center for environmental prediction global forecasting system , quadrilinearly interpolated . an alternative is required for dates more than several days in the future , since accurate forecasts are not available then ; we use a set of stacked monthly means for 19972001 ( the last years available ) from the european center for medium ranger weather forcasting 40 year reanalysis ( uppala et . al . 2005 ) also quadrilinearly interpolated . aircraft performance is interpolated from tables generated by boeing inflt runs , for cruising , thrust - limited climbs , and descents . planned flight track intersections with special use airspace ( sua ) boundaries ( including non - us zones , from the us national imagery and mapping agency ) are evaluated using a quadtree - based search on the 8000 + sua boundaries for each flight segment . observation segments are treated as initial value problems in cartesian coordinates , others may be boundary or initial problems , as appropriate . desired headings are calculated during execution from planned ( not actual ) sky coordinates and actual position ; direct steering by the telescope can not be allowed for safety reasons . in order to test fmi components and integrate other systems , as well as for training purposes , we use a simulation environment . this includes a medium - fidelity aircraft simulator , an automated pilot simulator , a method to set the time arbitrarily , and a telescope simulator ( brggenwirth , gross , nelbach , & shuping 2008 ) . while airborne , the fmi software components interact with the airborne data acquisition software to acquire the aircraft s position and attitude . while on the ground , the planner portion of fmi interacts with observers planning software and must support multiple simultaneous planning sessions . the airborne configuration is shown in fig . [ fig : dataflow ] ; the ground configuration is similar , except there is no flight executor nor mccs data ( except in testing configurations ) , and there is a connection to the observation planning database . sofia presents a unique flight planning problem due to the nature of astronomical observation . fmi provides a connection between scientific needs of an observatory with the practical constraints of operating an aircraft , without introducing excessive safety considerations or pilot workload , or planner effort . brggenwirth , s. , gross , m. a. k. , nelbach , f. j. , & shuping , r. y. 2009 , , 485 frank , j. , gross , m. a. k. , & krkl , e. 2004 , in proc . 16th conf . on innovative applications of artificial intelligence , ed . d. l. mcguinness & g. ferguson ( boston : mit press ) , 828 uppala , s. m. et al . 2005 , quart . j. r. meterol . soc.,131 , 2961" +"qcd at finite quark / baryon - number density at zero and at finite temperature describes nuclear matter . nuclear matter at high temperatures ( and possibly densities ) was certainly present in the early universe . neutron stars consist of dense cold nuclear matter . rhic and the cern heavy - ion program promise to produce hot nuclear matter in the laboratory . calculating the properties of high density nuclear matter could predict if and where strange matter could be produced . any method which can be used to determine the properties of nuclear matter could be adapted to nuclear physics calculations . finite quark - number density is best achieved by introducing a chemical potential @xmath0 for quark - number , and using the grand - canonical partition function . unfortunately , this renders the euclidean - time fermion determinant complex , with a real part which can change sign . standard lattice simulations , which rely on importance sampling , fail in this case . attempting to circumvent these problems by using canonical ( fixed quark number ) ensembles fail except at high temperatures @xcite because of sign problems . until a simulation method is found which avoids these difficulties , it is useful to study models which exhibit _ some _ of the properties of qcd at high @xmath0 . now it is expected that , at zero temperature , nuclear matter undergoes a phase transition at @xmath0 of order one third the mass of the nucleon . it has been proposed that at still higher @xmath0 the ground state is characterised by a diquark condensate @xcite . such a condensate would not only cause spontaneous breaking of baryon number , but would also spontaneously break colour . since colour is a gauge symmetry , such breaking is realized in the higgs mode . thus nuclear matter would become a colour superconductor at high @xmath0 . for this reason we have simulated 2-colour qcd , i.e. su(2 ) yang - mills theory with fermion matter fields ( ` quarks ' ) in the fundamental representation of @xmath4 , and finite @xmath0 . as well as having colour confinement this theory does exhibit diquark condensation as we shall demonstrate in this paper , but for @xmath5 , since the diquark ` baryons ' in the same multiplet as the pions , also have mass @xmath6 . for @xmath7 the phenomenon is describable as a rotation of the condensate from the chiral to the diquark direction as predicted by effective lagrangian analyses @xcite . unlike in true ( 3-colour ) qcd , the diquark condensates are colourless , and the broken symmetry is realized in the goldstone mode , and there is no colour superconductivity , but rather superfluidity , as in liquid @xmath8he . despite this , we shall later argue that this theory is more similar to 2-flavour qcd than one might think ( see section 4 ) . since 2-colour qcd has a non - negative determinant and pfaffian , even at non - zero @xmath0 , standard simulation methods can be used . we use the hybrid molelcular - dynamics method and simulate the theory with 4 flavours of staggered quarks @xcite . pfaffian simulations of a 4-fermion model including a diquark source term have been reported in @xcite . we have run simulations at a moderately large quark mass and an intermediate gauge coupling on @xmath1 and @xmath9 lattices , i.e. at zero temperature . we measured order parameters including the chiral and diquark condensates , the quark - number and energy densities , and the wilson line ( polyakov loop ) . the larger lattice allowed us to observe finite size effects and , more importantly to measure the scalar and pseudoscalar meson and diquark masses , which include all the potential goldstone bosons in the theory . preliminary results from these simulations were reported at lattice2000 , bangalore @xcite . the extension of these calculations to finite temperature was reported in a recent letter @xcite . this work builds on early work with 8 quark flavours which presented far less conclusive results @xcite . previous studies of diquark condensation in this model with various numbers of flavours have either used the approximation where @xmath10 in the updating algorithm @xcite ( as does @xcite ) , or been in the strong gauge - coupling regime @xcite . section 2 introduces the staggered - fermion lattice port of 2-colour qcd . the results of our simulation are presented in section 3 . section 4 gives our conclusions and indicates future avenues of research . because in 2-colour qcd fundamental quarks and antiquarks lie in the same representation of @xmath4 the flavour symmetry group for @xmath11 flavours is enlarged from @xmath12 to @xmath13 . the pattern of chiral symmetry breaking is @xmath14 rather than the usual @xmath15 @xcite . 3-colour qcd with 1 staggered quark ( 4 continuum flavours ) has a @xmath16 flavour symmetry . for 2 colours this is enhanced to @xmath17 @xcite . chiral or quark - number symmetry breaking ( the chiral and diquark condensates lie in the same u(2 ) multiplet ) occurs according to the pattern @xmath18 . the quark action for 2-colour qcd with one staggered quark is @xmath19\chi + \frac{1}{2}\lambda[\chi^t\tau_2\chi + \bar{\chi}\tau_2\bar{\chi}^t]\right\ } \label{eqn : lagrangian}\ ] ] where @xmath20 is the normal staggered covariant finite difference operator with @xmath0 introduced by multiplying the links in the @xmath21 direction by @xmath22 and those in the @xmath23 direction by @xmath24 . the superscript @xmath25 stands for transposition . note that we have introduced a gauge - invariant majorana mass @xmath26 which explicitly breaks quark - number symmetry . such an explicit symmetry breaking term is needed to observe spontaneous symmetry breaking on a finite lattice . we shall be interested in the limit @xmath27 . integrating out these fermion fields yields @xmath28 = \sqrt{{\rm det}({\cal a}^\dagger { \cal a } + \lambda^2 ) } \label{eqn : pfaffian}\ ] ] where @xmath29 we note that @xmath30 is positive definite for finite @xmath26 . hence the pfaffian never vanishes and thus , by continuity arguments never changes sign and can be chosen to be positive . note that @xmath31 has been shown to be positive in @xcite . denoting the @xmath32 matrix in equation [ eqn : pfaffian ] by @xmath33 we have seen that its determinant is the determinant of a positive definite matrix and thus can be used directly in our simulations . to do this we define @xmath34 by @xmath35 { \cal m } \left[\begin{array}{cc } \tau_2 & 0 \\ 0 & 1 \end{array}\right]\ ] ] so that @xmath36\ ] ] and @xmath37.\ ] ] we note that @xmath38 = \det[{\cal a}^\dagger { \cal a } + \lambda^2]$ ] . because we are now dealing with the matrix @xmath39 we can use the hybrid molecular dynamics method with ` noisy ' fermions @xcite to simulate this theory . here , although we generate gaussian noise with both upper and lower components , we keep only the upper components of the pseudo - fermion field to calculate @xmath40 $ ] , which means that we only need to invert @xmath30 at each update . keeping only half the components of the pseudo - fermion field is entirely analogous to keeping only the fermion fields on even sites in normal qcd simulations . the square root of equation [ eqn : pfaffian ] is obtained by inserting a factor of @xmath41 in front of the fermion term in the stochastic action in the standard manner . we now give a brief discussion of symmetry breaking in this model . this is covered in more detail in @xcite . at @xmath42 , the @xmath17 symmetry will break spontaneously . two directions in which it will choose to break are of particular interest . the first is where it breaks to give a non - zero chiral condensate @xmath43 . there will be 3 goldstone bosons corresponding to the 3 broken generators of @xmath17 . these states and their corresponding @xmath17 generators are @xmath44 @xmath45 remains unbroken . the second is where @xmath17 breaks to give a non - zero diquark condensate @xmath46 . this time the 3 goldstone bosons and corresponding generators are @xmath47 @xmath48 remains unbroken . when @xmath49 only 2 goldstone bosons remain , @xmath50 and @xmath51 . when in addition @xmath52 , only the latter state remains a goldstone boson . a more detailed study of the patterns of symmetry breaking can be performed in terms of an effective lagrangian for the goldstone modes as in @xcite . the only difference is that the effective field , denoted @xmath53 in that work , here belongs to a symmetric @xmath32 tensor representation of @xmath17 rather than to the antisymmetric @xmath54 representation of @xmath13 of the continuum case . one can see the remnant @xmath55 symmetry when @xmath27 by allowing @xmath26 to become complex . the majorana mass term in equation [ eqn : lagrangian ] then becomes @xmath56 $ ] . @xmath57 is replaced by @xmath58 in the pfaffian . although the 2-flavour theory would be of more interest in the continuum , we have chosen to simulate the 4-flavour theory because this represents a single staggered quark species and thus has well defined symmetries and a well defined spectrum at all lattice spacings . unlike the 8-flavour case simulated in @xcite it probably does have a sensible continuum limit . we have simulated 2-colour qcd with 1 staggered quark species ( 4 continuum flavours ) on @xmath1 and @xmath9 lattices . the simulations reported here are all at @xmath59 which is roughly the @xmath60 for the finite temperature transition on an @xmath61 lattice @xcite . this first set of simulations has been performed with quark mass @xmath62 in lattice units . these simulations are currently being repeated at @xmath63 , where the smaller pion mass will give a richer spectrum of goldstone and pseudo - goldstone bosons and where a larger portion of the relevant phase diagram should be described by effective lagrangians . ( we have also performed some zero temperature simulations at @xmath64 and @xmath65 . this has been reported in our finite temperature / finite @xmath0 letter @xcite . ) since we wished to take the limit @xmath27 , we needed @xmath66 . the values we chose were @xmath67 and @xmath68 for @xmath62 . ( at low @xmath0 s we also ran at @xmath10 . ) the smaller lattice was used to map out the interesting range of @xmath0 values , measuring order parameters including the diquark condensate @xmath69 , the chiral condensate @xmath70 , and the number density @xmath71 . in addition to measuring these quantities on the larger lattice , we also calculated the spectrum of potential goldstone bosons . the length of each ` run ' was 2000 molecular dynamics time units . @xmath72 had to be chosen as low as @xmath73 for @xmath67 and @xmath74 . in figure [ fig : pt2p ] we have plotted the diquark condensate as a function of @xmath0 at each @xmath26 for both lattice sizes . since we are interested in the limit where the symmetry breaking parameter @xmath27 , we have performed a linear extrapolation of the diquark condensate to @xmath10 . note that the effective lagrangian calculations @xcite suggest that linear extrapolations are the correct approach for @xmath26 sufficiently small , except at @xmath75 . the results of these extrapolations are plotted in figure [ fig : pt2p_0 ] . what we first notice is that for @xmath76 , the extrapolated diquark condensate is small enough that we can believe that it should be zero . for @xmath77 it is clearly non - zero . the points at @xmath78 would appear to show finite size rounding were it not for the fact that the @xmath1 and @xmath9 points are so close together . we think it more likely that @xmath78 is" +"the dipole - dipole interaction is ubiquitous in physics and for example responsible for the ever present van der waals force . it is also important for envisaged quantum computers based on atoms or ions in traps . considerable interest in the literature has also been aroused by its cooperative effects on the radiative behavior of atoms @xcite . in an as yet unexplained experiment @xcite with two and three ba@xmath0 ions , which exhibit macroscopic light and dark periods , a large fraction of double and triple jumps was reported , i.e. jumps by two or three intensity steps within a short resolution time . this fraction was orders of magnitudes larger than for independent ions . the quantitative explanation of such a large cooperative effect for distances of the order of ten wave lengths of the strong transition has been found difficult @xcite . experiments with other ions showed no observable cooperative effects @xcite , in particular none were seen for hg@xmath0 for a distance of about 15 wave lengths @xcite . more recently , an unexpected high number of simultaneous quantum jumps in a linear chain of trapped ca@xmath0 ions was reported @xcite while no such effects were found in another experiment @xcite using the same ion species and a similar setup . systems with macroscopic light and dark periods can provide a sensitive test for cooperative effects of the dipole - dipole interaction . these periods can occur for multi - level systems where the electron is essentially shelved for some time in a meta - stable state without photon emission @xcite . for two v systems with macroscopic light and dark periods the effect of the dipole - dipole interaction was investigated numerically in ref . @xcite and analytically in ref . @xcite and shown to be up to 30% in the double jump rate compared to independent systems . monitoring the dipole - dipole interaction of two v systems via quantum jumps of individual atoms was investigated in ref . the experimental systems of refs . @xcite are , however , not in the v configuration so that the results of ref . @xcite do not directly apply . the experiment of ref . @xcite used two hg@xmath0 ions , with the relevant three levels as in fig . [ dsystem ] , which we call a d configuration . from a theoretical point of view two such systems were studied in ref . @xcite for the special case @xmath1 , where @xmath2 is the distance and the wave lengths refer to the respective transitions of fig . [ dsystem ] , and for this case no cooperative effects were found . the general case will be treated explicitly further below . the cooperative effects found here are of similar magnitude as for v systems , and for distances of the above range the result of ref . @xcite is confirmed . our results are also in agreement with the experimentally observed absence of cooperative effects for distances of about 15 wave lengths @xcite . the levels of ba@xmath0 used in the experiment of refs . @xcite are depicted in fig . [ 5niveau ] ( a ) . the ground state @xmath3 and the two upper states @xmath4 and @xmath5 constitute a strongly driven fluorescing @xmath6 system which provides the light periods . only when the system is in the ground state can the weak incoherent driving of the @xmath3 - @xmath7 transition populate the meta - stable @xmath5 state , with ensuing dark period . therefore the details of the two upper states of the @xmath6 system play no significant role for the transition to a dark period , and therefore these two states are here replaced by an _ effective _ single level . this leads to the four - level configuration of fig . [ 5niveau ] ( b ) . the present paper is , to our knowledge , the first to theoretically investigate possible cooperative effects for two such four - level systems . surprisingly , these effects turn out to be much smaller than for two v systems for distances @xmath8 , and this shows that cooperative effects sensitively depend on how the meta - stable level is populated . our results for two four - level configurations are at odds with the experimental findings of ref . @xcite on the magnitude of double jump rates for two ba@xmath0 ions @xcite . the methods presented in this paper can be carried over to describe the ca@xmath0 experiments of refs . @xcite although this would of course require the use of a different level system . the plan of the paper is as follows . in section [ 2dpert ] we treat two dipole - dipole interacting d systems and explicitly calculate the transition rates between the various light and dark periods as well as the double jump rate . this is done by means of bloch equations . in section [ 4level ] the method is carried over to two four - level systems of fig . [ 5niveau ] ( b ) and the transition rates are calculated . in the appendix a direct quantum jump approach @xcite is outlined for two d systems . the d configuration , as displayed in fig . [ dsystem ] , is a model of the level system of @xmath9 used in the experiments of refs . @xcite . the transition @xmath10 is driven by a strong laser . level @xmath11 can also decay via a slow transition to the meta - stable level @xmath12 . for simplicity all transitions are treated as dipole transitions . in the following we will investigate two dipole - interacting d systems a fixed distance @xmath2 apart and calculate the transition rates between the three types of fluorescence periods . this will be done in this section by means of bloch equations . in the appendix the efficient quantum jump approach will be applied to two d systems , not only confirming the bloch equation result but also giving higher - order terms . for simplicity the laser direction will be taken as perpendicular to the line joining the two systems . rabi frequency and einstein coefficients satisfy @xmath13 it is convenient to use a dicke basis , @xmath14 in fig . [ 2dniveaus ] ( a ) the level configuration for two d systems is displayed in this basis , with the slow decays neglected , while in fig . [ 2dniveaus ] ( b ) only the slow decays are shown . from fig . [ 2dniveaus ] ( a ) it is seen that without slow decays ( i.e. for @xmath15 ) the configuration decouples into three independent subspaces , denoted by @xmath16 , with @xmath17 by means of the conditional hamiltonian , @xmath18 , and the reset operation , @xmath19 , the bloch equations can be written in the form @xcite @xmath20 + \mathcal{r}(\rho)~.\ ] ] for two d systems one finds by the same method as in refs . @xcite @xmath21 \nonumber \\ & & \hspace{0.4 cm } { } + \big(a_2+a_3 + 2\text{i}\delta_3\big)\big[2|e_3\rangle\langle e_3| \nonumber \\ & & \hspace{3.6 cm } { } + \sum_{j=1}^2|s_{j3}\rangle\langle s_{j3}| + |a_{j3}\rangle\langle a_{j3}| \big ] \nonumber \\ & & \hspace{0.4 cm } { } + \sum_{j=1}^2 c_j\big[|s_{jj+1}\rangle\langle s_{jj+1}| - |a_{jj+1}\rangle\langle a_{jj+1}|\big ] \nonumber \\ & & \hspace{1 cm } { } + c_3 \big[|s_{13}\rangle\langle s_{13}| - |a_{13}\rangle\langle a_{13}| \big ] \big\ } \nonumber \\ & & { } + \frac{\hbar}{2}\omega_3\big\{\sqrt{2}\big(|g\rangle\langle s_{13}| + |s_{13}\rangle\langle e_3| \big ) \nonumber \\ & & \hspace{1.5 cm } { } + |s_{12}\rangle\langle s_{23}| - |a_{12}\rangle\langle a_{23}| + \mbox{h.c . } \big\}\end{aligned}\ ] ] where @xmath22 is the detuning of the laser . the complex dipole coupling constants @xmath23 depend in an oscillatory way on the distance @xmath2 , @xmath24~,\end{aligned}\ ] ] with @xmath25 and @xmath26 the angle between the corresponding dipole moment and the line connecting the systems . for maximal effect we take @xmath27 in the following . the real part of @xmath23 leads to changes of the decay constants and the imaginary part to a level shift in the dicke basis , as seen from the expression for @xmath28 . the reset operation can be written in the form @xmath29 , \end{aligned}\ ] ] where @xmath30 to determine the transition rates we write eq . ( [ bloch ] ) in a liouvillean form as @xmath31 where the super - operator @xmath32 is a perturbation depending on the small parameters , and employ the following important property of the time development . starting with an initial state in one of the subspaces @xmath33 , the system will rapidly on a time scale of @xmath34 and @xmath35approach one of the quasi - stationary states @xmath36 . thereafter for times much larger than @xmath34 and @xmath35 , but much smaller than @xmath37 and @xmath38small populations in the other subspaces will build up until eventually , on a time scale of @xmath37 and @xmath38 , the true stationary state is approached . hence we consider a time @xmath39 with @xmath40 and calculate @xmath41 for initial @xmath42 . the quasi - invariant states are easily calculated from @xmath43 as @xmath44 \nonumber \\ \mbox{where } \qquad n & = & ( a_3 ^ 2 + 2\omega_3 ^ 2 + 4\delta_3 ^ 2)^2 \nonumber \\ & & \hspace{-1.5 cm } { } + ( a_3 ^ 2 + 4\delta_3 ^ 2)(|c_3|^2 + 2a_3\text{re}\,c_3 + 4\delta_3\text{im}\,c_3 ) \nonumber\end{aligned}\ ] ] as in ref . @xcite one has in perturbation theory @xmath45 but , unlike ref . @xcite , @xmath46 is not a superposition of just the eigenstates for nonzero eigenvalues of @xmath47 but also of the @xmath48 s . we therefore decompose @xmath46 into a superposition of all eigenstates ( matrices ) of @xmath47 , @xmath49 where @xmath50 contains the contributions from the eigenstates for nonzero eigenvalues of @xmath47 . for later use we note that these eigenvalues are of the order of @xmath51 and @xmath52 . the coefficients @xmath53 can easily be determined by means of the reciprocal ( or dual ) eigenstates where only those for eigenvalue @xmath54 of @xmath47 are needed . they are denoted by @xmath55 and are defined through @xmath56 @xmath57 the latter means @xmath58 , with the adjoint @xmath59 defined with respect to a scalar product given by @xmath60 . then one has @xmath61 the reciprocals @xmath55 are easily determined as follows . since the bloch equations conserve the trace one has @xmath62 for any @xmath63 . thus @xmath64 for any @xmath63 and therefore @xmath65 . now @xmath66 can be written as a sum of terms purely from @xmath67 , and @xmath68 and , since the subspaces are invariant under @xmath47 , these terms must be annihilated by @xmath59 individually . this yields @xmath69 since the sum of the right - hand sides indeed yields @xmath66 and the normalization condition of eq . ( [ norm ] ) is fulfilled . from eq . ( [ alpha ] ) one then obtains the @xmath53 . inserting now @xmath46 into eq . ( [ rhodeltata1 ] ) one obtains @xmath70 where for the @xmath50 term the upper integration limit can be extended to infinity since @xmath50 belongs to nonzero eigenvalues of @xmath47 and is therefore rapidly damped . now , @xmath71 is of the order of @xmath35 and @xmath34 on @xmath50 , and thus the last term in eq . ( [ rhotdeltata ] ) is of the order of @xmath72 which is much smaller than @xmath73 , by eq . ( [ rela3a1 ] ) . therefore the last term in eq . ( [ rhotdeltata ] ) can be neglected , and this equation then reveals that the @xmath53 s have the meaning of transition rates from subspace @xmath33 to @xmath74 , i.e. , @xmath75 the transition rates are now obtained from eqs . ( [ pij ] ) , ( [ alpha ]" +"a cluster category is a certain 2-calabi - yau orbit category of the derived category of a hereditary abelian category . cluster categories were introduced in @xcite in order to give a categorical model for the combinatorics of fomin - zelevinsky cluster algebras @xcite . they are triangulated @xcite and admit ( cluster-)tilting objects , which model the clusters of a corresponding ( acyclic ) cluster algebra @xcite . each cluster in a fixed cluster algebra comes together with a finite quiver , and in the categorical model this quiver is in fact the gabriel quiver of the corresponding tilting object @xcite . a principal ingredient in the construction of a cluster algebra is quiver mutation . it controls the exchange procedure which gives a rule for producing a new cluster variable and hence a new cluster from a given cluster . exchange is modeled by cluster categories in the acyclic case @xcite in terms of a mutation rule for tilting objects , i.e. a rule for replacing an indecomposable direct summand in a tilting object with another indecomposable rigid object , to get a new tilting object . quiver mutation describes the relation between the gabriel quivers of the corresponding tilting objects . analogously to the definition of the cluster category , for a positive integer @xmath0 , it is natural to define a certain @xmath1-calabi - yau orbit category of the derived category of a hereditary abelian category . this is called the _ @xmath0-cluster category_. implicitly , @xmath0-cluster categories was first studied in @xcite , and their ( cluster-)tilting objects have been studied in @xcite . combinatorial descriptions of @xmath0-cluster categories in dynkin type @xmath2 and @xmath3 are given in @xcite . in cluster categories the mutation rule for tilting objects is described in terms of certain triangles called _ exchange triangles_. by @xcite the existence of exchange triangles generalizes to @xmath0-cluster categories . it was shown in @xcite that there are exactly @xmath1 non - isomorphic complements to an almost complete tilting object , and that they are determined by the @xmath1 exchange triangles defined in @xcite . the aim of this paper is to give a combinatorial description of mutation in @xmath0-cluster categories . _ a priori _ , one might expect to be able to do this by keeping track of the gabriel quivers of the tilting objects . however , it is easy to see that the gabriel quivers do not contain enough information . we proceed to associate to a tilting object a quiver each of whose arrows has an associated colour @xmath4 . the arrows with colour 0 form the gabriel quiver of the tilting object . we then define a mutation operation on coloured quivers and show that it is compatible with mutation of tilting objects . a consequence is that the effect of an arbitrary sequence of mutations on a tilting object in an @xmath0-cluster category can be calculated by a purely combinatorial procedure . our definition of a coloured quiver associated to a tilting object makes sense in any @xmath1-calabi - yau category , such as for example those studied in @xcite . we hope that our constructions may shed some light on mutation of tilting objects in this more general setting . in section 1 , we review some elementary facts about higher cluster categories . in section 2 , we explain how to define the coloured quiver of a tilting object , we define coloured quiver mutation , and we state our main theorem . in sections 3 and 4 , we state some further lemmas about higher cluster categories , and we prove certain properties of the coloured quivers of tilting objects . we prove our main result in sections 5 and 6 . in sections 7 and 8 we point out some applications . in section 9 we interpret our construction in terms of @xmath0-cluster complexes . in section 10 , we give an alternative algorithm for computing coloured quiver mutation . section 11 discusses the example of @xmath0-cluster categories of dynkin type @xmath2 , using the model developed by baur and marsh @xcite . we would like to thank idun reiten , in conversation with whom the initial idea of this paper took shape . let @xmath5 be an algebraically closed field , and let @xmath6 be a finite acyclic quiver with @xmath7 vertices . then the path algebra @xmath8 is a hereditary finite dimensional basic @xmath5-algebra let @xmath9 be the category of finite dimensional left @xmath10-modules . let @xmath11 be the bounded derived category of @xmath10 , and let @xmath12 $ ] be the @xmath13th shift functor on @xmath14 . we let @xmath15 denote the auslander - reiten translate , which is an autoequivalence on @xmath14 such that we have a bifunctorial isomorphism in @xmath14 @xmath16 ) \simeq d{\operatorname{hom}\nolimits}(b,\tau a).\ ] ] in other words @xmath17 \tau$ ] is a serre functor . let @xmath18 $ ] . the @xmath0-cluster category is the orbit category @xmath19 $ ] . the objects in @xmath20 are the objects in @xmath14 , and two objects @xmath21 are isomorphic in @xmath20 if and only if @xmath22 in @xmath14 . the maps are given by @xmath23 . by @xcite , the category @xmath20 is triangulated and the canonical functor @xmath24 is a triangle functor . we denote therefore by @xmath25 $ ] the suspension in @xmath20 . the @xmath0-cluster category is also krull - schmidt and has an ar - translate @xmath15 inherited from @xmath14 , such that the formula ( [ ar ] ) still holds in @xmath20 . if follows that @xmath17 \tau$ ] is a serre functor for @xmath20 and that @xmath20 is @xmath1-calabi - yau , since @xmath26 $ ] . the indecomposable objects in @xmath14 are of the form @xmath27 $ ] , where @xmath28 is an indecomposable @xmath10-module and @xmath29 . we can choose a fundamental domain for the action of @xmath18 $ ] on @xmath14 , consisting of the indecomposable objects @xmath27 $ ] with @xmath30 , together with the objects @xmath31 $ ] with @xmath28 an indecomposable projective @xmath10-module . then each indecomposable object in @xmath20 is isomorphic to exactly one of the indecomposables in this fundamental domain . we say that @xmath32 $ ] has degree @xmath33 , denoted @xmath34 ) = d$ ] . furthermore , for an arbitrary object @xmath35 in @xmath36 , we let @xmath37 $ ] be the @xmath10-module which is the ( shifted ) direct sum of all summands @xmath38 of @xmath39 with @xmath40 . in the following theorem the equivalence between ( i ) and ( ii ) is shown in @xcite and the equivalence between ( i ) and ( iii ) is shown in @xcite . let @xmath41 be an object in @xmath20 satisfying @xmath42 ) = 0 $ ] for @xmath43 . then the following are equivalent * if @xmath44 ) = 0 $ ] for @xmath43 then @xmath45 is in @xmath46 . * if @xmath47 ) = 0 $ ] for @xmath43 then @xmath45 is in @xmath46 . * @xmath41 has @xmath48 indecomposable direct summands , up to isomorphism . here @xmath46 denotes the additive closure of @xmath41 . a ( cluster-)tilting object @xmath41 in an @xmath0-cluster is an object satisfying the conditions of the above theorem . for a tilting object @xmath49 , with each @xmath50 indecomposable , and @xmath51 an indecomposable direct summand , we call @xmath52 an almost complete tilting object . we let @xmath53 denote the @xmath5-space of irreducible maps @xmath54 in a krull - schmidt @xmath5-category @xmath55 . the following crucial result is proved in @xcite and @xcite . [ p : number ] there are , up to isomorphism , @xmath1 complements of an almost complete tilting object . let @xmath51 be an indecomposable direct summand in an @xmath0-cluster tilting object @xmath56 . the complements of @xmath57 are denoted @xmath58 for @xmath59 , where @xmath60 . by @xcite , there are @xmath1 exchange triangles @xmath61 here the @xmath62 are in @xmath63 and the maps @xmath64 ( resp . @xmath65 ) are minimal left ( resp . right ) @xmath63-approximations , and hence not split mono or split epi . note that by minimality , the maps @xmath64 and @xmath65 have no proper zero summands . we first recall the definition of quiver mutation , formulated in @xcite in terms of skew - symmetric matrices . let @xmath66 be a quiver with vertices @xmath67 and with no loops or oriented two - cycles , where @xmath68 denotes the number of arrows from @xmath13 to @xmath69 . let @xmath70 be a vertex in @xmath71 . then , a new quiver @xmath72 is defined by the following data @xmath73 it is easily verified that this definition is equivalent to the one of fomin - zelevinsky . now we consider coloured quivers . let @xmath0 be a positive integer . an @xmath0-coloured ( multi-)quiver @xmath71 consists of vertices @xmath67 and coloured arrows @xmath74 , where @xmath75 . let @xmath76 denote the number of arrows from @xmath13 to @xmath70 of colour @xmath77 . we will consider coloured quivers with the following additional conditions . * no loops : @xmath78 for all @xmath79 . * monochromaticity : if @xmath80 , then @xmath81 for @xmath82 * skew - symmetry : @xmath83 . we will define an operation on a coloured quiver @xmath71 satisfying the above conditions . let @xmath70 be a vertex in @xmath71 and let @xmath84 be the coloured quiver defined by @xmath85 in an @xmath0-cluster category @xmath20 , for every tilting object @xmath86 , with the @xmath50 indecomposable , we will define a corresponding @xmath0-coloured quiver @xmath87 , as follows . let @xmath88 be two non - isomorphic indecomposable direct summands of the @xmath0-cluster tilting object @xmath41 and let @xmath89 denote the multiplicity of @xmath90 in @xmath91 . we define the @xmath0-coloured quiver @xmath87 of @xmath41 to have vertices @xmath13 corresponding to indecomposable direct summands @xmath50 , and @xmath92 . note , in particular , that the @xmath93-coloured arrows are the arrows from the gabriel quiver for the endomorphism ring of @xmath41 . by definition , @xmath87 satisfies condition ( i ) . we show in section [ s : higher ] that ( ii ) is satisfied ( this also follows from @xcite ) , and in section [ s : symmetry ] that ( iii ) is also satisfied . the aim of this paper is to prove the following theorem , which is a generalization of the main result of @xcite . [ t : main ] let @xmath86 and @xmath94 be @xmath0-tilting objects , where there is an exchange triangle @xmath95 . then @xmath96 . in the case @xmath97 the coloured quiver of a tilting object @xmath41 is given by @xmath98 and @xmath99 where @xmath100 denotes the number of arrows in the gabriel quiver of @xmath41 . then coloured mutation of the coloured quiver corresponds to fz - mutation of the gabriel quiver . let @xmath6 be @xmath101 with linear orientation , i.e. the quiver @xmath102 . the ar - quiver of the 2-cluster category of @xmath103 is @xmath104 & & { i_3 } \ar[dr ] & & * + + [ o][f-]{p_3[1 ] } \ar[dr ] & & i_1[1 ] \ar[dr ] & & p_1[2]\ar[dr ] \\ p_2[2 ] \ar[ur ] \ar[dr ] & & { p_2 } \ar[ur ] \ar[dr ] & & * + [ o][f-]{i_2 } \ar[ur ] \ar[dr ] & & p_2[1 ] \ar[ur ] \ar[dr ] & & i_2[1]\ar[ur]\ar[dr ] & & p_2[2 ] \\ & { p_3 } \ar[ur ] & & * + [ o][f-]{i_1 } \ar[ur ] & & p_1[1 ] \ar[ur ] & & i_3[1]\ar[ur ] & & p_3[2 ] \ar[ur ] & & } \ ] ] the direct sum @xmath105 $ ] of the encircled indecomposable objects gives a tilting object . its coloured quiver is @xmath106 & i_2 \ar@<0.6ex>^{(0)}[r ] \ar@<0.6ex>^{(2)}[l ] & p_3[1 ] \ar@<0.6ex>^{(2)}[l ] } \ ]" +"this paper explores the phenomenology of the standard model s minimal supersymmetric @xcite extension with a continuous @xmath1 symmetry ( hereafter called the ` mr model')@xcite . this model of low - energy supersymmetry has a much smaller - dimensional parameter space than the minimal supersymmetric model with a discrete @xmath3-parity ( mssm @xcite ) . as a result , it has two attractive features . first , the mr model makes specific predictions of the values of a number of observables , such as the gaugino masses . in addition , the mr model is free of the superpotential term @xmath4 and the soft supersymmetry breaking terms @xmath5 that cause well - known theoretical difficulties in the mssm . we focus , in particular on the recent measurements of @xmath2 @xmath6 which yield a value @xmath7 @xcite that differs markedly from the one - loop standard model prediction @xmath8 @xcite . the oblique and qcd corrections to the @xmath9-quark and hadronic decay widths of the @xmath10 each largely cancel when the ratio is formed , making @xmath2 very sensitive to direct corrections to the @xmath11 vertex especially those involving the heavy top quark . our work complements some recent papers on susy models with discrete r - parity . the implications of the @xmath2 measurement for the mssm are discussed in refs . @xcite , @xcite and @xcite . a region of the mssm parameter space that has some phenomenology similar to that of the mr model is studied in @xcite . the following section describes the mr model in more detail . we then compute the vertex corrections to @xmath2 in the mr model and find that the result is within @xmath12 of the experimental value so long as the lighter top squark is light enough ( and the charged higgs boson is heavy enough ) . section 4 discusses additional constraints that place a lower bound on the mass of the lighter top squark . the information that future experiments may yield is studied in section 5 ; ongoing and upcoming experiments at fnal and lep should be capable of confirming or excluding the mr model . the last section briefly summarizes our findings . the model explored in this paper is the minimal supersymmetric extension of the standard model in which @xmath3-parity is extended to a continuous @xmath13 symmetry . the continuous @xmath3-symmetry is defined by assigning @xmath3 charges + 1 to the superspace coordinate @xmath14 , + 1 to matter superfields and 0 to higgs superfields . in terms of component fields , all ordinary particles carry zero @xmath3 charge while their superpartners have non - zero @xmath3-charge . the most general @xmath1-symmetric lagrangian is described by the superpotential @xmath15 where each term has @xmath16 , and the quark and lepton superfields @xmath17 @xmath18 have the usual @xmath19 gauge interactions . note the absence of a @xmath4 term which would violate the @xmath1 symmetry . the most general symmetry forbids majorana gaugino masses , the model contains an additional color octet chiral superfield to give a dirac mass to the gluino . this field appears only in the soft supersymmetry breaking potential . the gluino mass is relevant to this work in that it renders the 1-loop correction to @xmath2 from diagrams with internal gluinos and bottom squarks negligible compared to the effects of the diagrams considered here . we will therefore not mention the color octet superfield further . the effects of allowing the gluino to be extremely light in a @xmath1-symmetric model will be considered in future work . ] soft supersymmetry breaking potential consistent with our symmetries and a gim - like mechanism to naturally suppress flavor - changing neutral currents is : @xmath20 where we neglect small yukawa - suppressed corrections to the superpartners masses . note the characteristic absence of gaugino mass terms ( @xmath21 ) and trilinear scalar terms ( @xmath22 ) . for a more detailed description of the model we refer the reader to @xcite . the non - standard one - loop corrections to @xmath2 considered in this paper are of two kinds . one involves the charged - higgs / top / bottom vertex ; the other , the chargino / stop / bottom vertex . they therefore involve the following parameters : charged higgs mass @xmath23 , chargino masses @xmath24 , stop mass eigenvalues @xmath25 , stop mixing angle @xmath26 , and ratio of higgs vacuum expectation values @xmath27 . in the remainder of this section , we focus on those aspects of the model that are directly relevant to determining the above parameters . first we should discuss masses . the charged higgs mass is given in terms of the @xmath28 mass as @xmath29 which implies that @xmath30 is heavier than @xmath31 . the charginos masses are @xmath32 @xmath33 we will soon find that in this model the charginos are nearly degenerate with the @xmath31 bosons . as it is relevant to the limits we will ultimately set on the top squark masses , we also note that at the one - loop level , the light neutral higgs boson has a mass of of the @xmath34 term in the superpotential and the coefficient @xmath35 of the trilinear scalar operators in the supersymmetry breaking terms . those two coefficients vanish in the mr model because of the continuous @xmath1 symmetry . ] @xmath36 in the limit that @xmath37 , which allows bottom squark contributions to be neglected ; the reason this limit is preferred will become clear shortly . the values of the top squark masses are intimately connected to the physics of the lightest superpartner ( the photino ) . the photino is massless at tree level but , together with its dirac partner @xmath38 ( or @xmath39 in the notation of @xcite , acquires a dirac mass at one loop that is generated by the exchange of left- and right - handed top squarks@xcite @xmath40 from the cosmological point of view , the present mass density is bounded from above by @xmath41 . this implies a lower bound on the cross section for photino annihilation , @xmath42 . since @xmath42 grows as the square of the photino mass , the result is a lee - weinberg @xcite type of lower bound on the photino mass @xmath43^{-1 } ( \omega_{\tilde{\gamma}}h^2)^{-1}\ ] ] where @xmath44 runs over all squarks and sleptons of charge @xmath45 and mass @xmath46 such that the corresponding quarks and leptons are the possible final states of photino annihilation @xcite . since the photino can not be massless , equation ( [ photstop ] ) implies that the top squarks @xmath47 and @xmath48 can not be degenerate in the mr model . if one supposes @xmath48 to be lighter than @xmath47 , then , for a given mass of @xmath48 , one will find a lower bound on the mass of @xmath47 . for example , if @xmath49 gev , then @xmath50 gev . the top squark mass eigenstates @xmath51 and @xmath52 are related to @xmath48 and @xmath47 by @xmath53 which defines the mixing angle @xmath26 . we find that in order for the stop mass eigenvalues @xmath54,@xmath55 to be real , the stop mixing angle @xmath26 must be less than 10 degrees . thus , in the mr model , @xmath56 . finally , we need to discuss @xmath57 . we have already seen that the overall scale of @xmath58 is of the order of 1 gev . this makes the decay @xmath59 possible , which in turn makes the @xmath10 invisible width larger than it is in the standard model . the branching fraction of @xmath60 is suppressed by a factor of @xmath61 relative to the standard model branching fraction for one @xmath62 species , @xmath63 . thus we have @xmath64 the experimental limit on the number of light neutrino species @xcite , @xmath65 , therefore implies that at 95% c.l . @xmath27 lies very close which naturally appears in gut - inspired models with radiative electroweak symmetry breaking . ] to unity : @xmath66 the several parameters of the mr model are now essentially reduced to two . the stringent constraint @xmath67 forces the charginos to be approximately degenerate with the @xmath31 . the requirement that the photino not be massless forces the top squark mixing angle to be less than @xmath68 ; we take @xmath69 throughout our calculations . when @xmath69 , the superpartner of the right - handed top quark , @xmath48 is identical to the light top squark mass eigenstate @xmath51 ; since only @xmath48 enters the loop affecting the @xmath10 coupling to left - handed @xmath9 quarks , @xmath2 depends on @xmath54 but not @xmath55 . we are left with only two parameters on which @xmath2 will depend : @xmath23 and @xmath54 . in order to test the mr model , we can separate contributions to @xmath2 into those occurring in both the standard and mr models and those additional effects present only in the mr model . in the notation of refs . @xcite , @xmath70\\ \nonumber \\ { \nabla_b^{mr } } \equiv { \nabla_b}^{mr}(m_t ) -{\nabla_b}^{mr}(0)\nonumber \label{citr}\end{aligned}\ ] ] where @xmath71 is the one - loop level standard model prediction using a top quark mass of @xmath72 gev , @xmath73 is the standard model prediction assuming a massless top quark @xcite , and @xmath74 is the sum of the one - loop interference with the tree graph divided by the squared amplitude of the tree graph . in the mr model , there are two relevant types of non - standard one - loop vertex diagrams : those with internal charged - higgses and top quarks , and those with internal charginos and top squarks . their contributions to @xmath74 are proportional to @xmath75 ; the details of the calculation are presented in the appendix . another type of vertex diagram with internal neutralinos and bottom squarks makes contributions proportional to @xmath76 , which is negligible in the mr model because @xmath77 ; we omit these . -.5 in -2em -2em in figure 1 , we plot @xmath78 , the contribution from the @xmath79 t vertex diagrams to @xmath80 , as a function of @xmath81 , when @xmath27 is taken to be 1 , 0.9 or 1.1 . the overall sign is negative and the value of @xmath82 shifts by @xmath83 as @xmath27 varies from 1 to 1.1 or 0.9 . figure 2 shows the corresponding contribution from @xmath84 @xmath85 loops to @xmath86 , as a function of the light top squark mass @xmath54 when the mixing angle @xmath26 between top squarks is @xmath87 ( @xmath88 ) . the result is positive , and the deviation due to a 10@xmath89 shift in @xmath27 is negligible . thus the net shift in @xmath2 is due to a balance between the oppositely - signed contributions from the two types of loop diagrams . in figure 3 , we set @xmath90 gev and plot @xmath2 as a function of @xmath23 for a range of @xmath27 ; we can clearly infer a lower bound on the allowed value of @xmath23 at fixed @xmath54 . likewise , figure 4 shows the dependence of @xmath2 on @xmath54 for @xmath91 gev ; we can infer an upper bound on @xmath54 for fixed @xmath23 . in subsequent diagrams we plot results only for @xmath92 and keep in mind that an increase of 10% in @xmath57 corresponds to an increase of about 0.1% in @xmath2 for given @xmath23 and @xmath54 . -2em -2em figure 5 shows how the experimental 95% c.l . lower bound on @xmath2 separates the @xmath23 vs. @xmath54 parameter space into allowed and disallowed regions . recall that the @xmath93 loop gives negative corrections to @xmath2 , while the @xmath94 loop gives positive corrections . since the standard model prediction for @xmath2 lies well below the experimental lower bound , some positive contribution is required to bring the mr prediction for @xmath2 into agreement with experiment ." +"the classical method of adding two integers of @xmath1-bits takes @xmath2 bit operations but the classical method of multiplying them takes @xmath3 bit operations . complexity of addition is optimal in number of bit operations , whereas optimal multiplication algorithm for integers is an open problem . the classical approach to multiply two @xmath1-bit integers requires @xmath3 bit operations . karatsuba multiplication [ 9 ] uses divide - and - conquer technique to multiply two @xmath1-bit integers in @xmath4 bit operations(logarithms are to the base 2 unless otherwise specified ) by replacing some of the multiplication by less costly addition and subtraction . toom - cook algorithm further improves the above bound [ 3 ] . toom - cook method is the generalization of karatsuba method which split each number to be multiplied in multiple parts [ 12 ] . given two large integers , toom - cook splits up multiplicand and multiplier into @xmath5 smaller parts each of length @xmath6 , and performs operations on the parts . as @xmath5 grows , one may combine many of the multiplication sub - operations , thus reducing the overall complexity of the algorithm . for @xmath7 toom - cook reduces 9 multiplication to 5 , with asymptotic complexity of @xmath8 . schonhage - strassen integer multiplication algorithm [ 10 ] uses fast fourier transform ( fft ) by selecting the principal roots of unity as evaluation point to perform multiplication in @xmath9 bit operations . fft method employs a divide - and - conquer strategy by taking advantage of the special properties of the complex root of unity to perform multiplication of two polynomials in only @xmath10 arithmetic complexity [ 4 ] . in fact many multiplication algorithms can viewed as schemes for the evaluation of polynomials then multiplication of their values and followed by interpolation . currently , the asymptotically fastest algorithm for multiplication of two @xmath1-bit integers is by furer [ 7 ] which runs in @xmath11 . where @xmath12 is iterated logarithm function [ 5 ] defined as : @xmath13 furer algorithm uses arithmetic over complex number . same asymptotic bound can also be achieved using modular arithmetic [ 6 ] . + the schonhage - strassen algorithm and furer algorithm are asymptotically fast but they are suited for extremely large numbers . furer algorithm although asymptotically fastest , only achieves an advantage for astronomically large values and as such it is currently not used in practice . the crossover points between these algorithms are usually very high when the algorithms are implemented [ 8 ] . for small inputs even karatsuba algorithm runs slower than the classical multiplication algorithm because of recursion overhead . in this paper we use nikhilam sutra or method from vedic mathematics [ 11 ] to perform efficient multiplication for small inputs . nikhilam sutra performs large multiplication by converting it to small multiplication along with some addition and shifting operations . + this paper is organized as follows . section 2 describes background and motivation . section 3 presents our proposed work , the multiplication algorithm and its features . in section 4 , we present some applications . finally , section 5 contains conclusion . the simplest method to multiply two @xmath1-digit integers is using classical or long multiplication method which requires @xmath3 multiplication operations . whereas to add or subtract two @xmath1-digit integers using traditional method requires at most @xmath1 number of addition or subtraction which is optimal in terms of number of addition / subtraction operation performed . to improve the @xmath3 bound of multiplication , several algorithms have been discovered . the simplest one is karatsuba algorithm which is based on divide - and - conquer paradigm [ 1 ] . karatsuba algorithm is based on the fact that two - digit multiplication can be done with only three instead of four multiplications required by standard method . suppose we want to multiply two @xmath14-digit decimal numbers @xmath15 : 1 . compute @xmath16 2 . compute @xmath17 3 . compute @xmath18 4 . compute @xmath19 , here @xmath20 is equal to @xmath21 5 . result @xmath22 for large number of digits we can apply this method recursively by splitting the multiplicand and multiplier in two parts . the complexity of this method is @xmath23 . since multiplication operation is costly as compared to addition and shift , some constant number of addition and shift operations can be safely ignored . in this paper we assume that multiplicand and multiplier are having equal number of digits . + for example suppose we want to multiply @xmath24 . the standard method of long multiplication requires 4 one - digit multiplication along with some addition and shift . using karatsuba algorithm we can compute it as follows : 1 . compute @xmath25 2 . compute @xmath26 3 . compute @xmath27 ; @xmath28 4 . compute @xmath29 5 . result @xmath30 a schematic view of above multiplication is shown in fig . the three multiplication operations are enclosed in ellipse . in fact the total number of @xmath31-digit multiplication required in above example is 5 . note that to compute @xmath32 in step @xmath33 requires , three @xmath31-digit multiplication by applying this method one s more . using karatsuba method , width=264,height=151 ] nikhilam sutra is one of the 16 sutras of vedic mathematics [ 11 ] . it can be used to convert large - digits multiplication to small - digits multiplication with the help of few extra add , subtract and shift operations . in some cases two - digit multiplication can be performed using only @xmath31 one - digit multiplication instead of @xmath33 one - digit multiplication as required by karatsuba algorithm . suppose we have to perform same multiplication @xmath24 using this method . we can use the nikhilam sutra as follows : 1 . compute @xmath34 ; subtract the multiplicand from nearest base 2 . compute @xmath35 ; subtract the multiplier from the same base 3 . compute @xmath36 4 . compute @xmath37 5 . result @xmath38 in the fig . 2 , we can see that there is only one multiplication operation involved . using nikhilam method , width=264,height=151 ] above multiplication is also shown in table 1 . in this multiplication we have used @xmath31 multiplication , @xmath31 addition , @xmath33 subtraction and @xmath31 shift operation . this particular multiplication is more efficient than both standard multiplication and karatsuba method . suppose multiplicand is @xmath39 and multiplier is @xmath40 where @xmath41 is nearest base . we have : @xmath42 the general scheme of multiplication @xmath43 is shown in table 2 . .multiplication of @xmath44 [ cols=""^,^,^ "" , ] correctness of the nikhilamsquaring can be easily established using induction on the bit length of the input @xmath45 . note that in each column of table 8 , the partial result is , in fact multiplication of corresponding multiplicand and multiplier in that column . + * theorem 1 . * _ nikhilamsquaring algorithm computes square of the input @xmath45 . _ + * proof * : we prove this using induction on the bit length @xmath1 of @xmath45 . for @xmath46 , number @xmath45 has only one bit and @xmath47 when @xmath45 is @xmath31 and @xmath48 when @xmath45 is @xmath49 . therefore it works for @xmath46 . assume it is true for @xmath50 . now we show it for @xmath5 . assume @xmath51 , therefore @xmath52 . + case 1 : if @xmath5th bit is @xmath31 then @xmath53 , and the processing of @xmath5th step is @xmath54 also we have @xmath55 and therefore @xmath56 @xmath57 and hence @xmath58 , and the statement of theorem follows . + case 2 : if @xmath5th bit is @xmath49 , then the statement is trivial and @xmath59 , and theorem is proved . + nikhilammultiplication is described in algorithm 2 . it takes two binary numbers @xmath45 and @xmath60 as input and compute their multiplication@xmath61 as output . it performs two calls to nikhilamsquaring algorithm and using that , outputs the desired result . nikhilammultiplication uses only @xmath31 multiplication , @xmath31 division and @xmath62 add / subtract and shift operations for some constant @xmath63 . to show the correctness of nikhilammultiplication is trivial given the correctness of nikhilamsquaring . + * input * : @xmath64 * output * : @xmath65 @xmath66 * nikhilamsquaring * @xmath67 @xmath68 * nikhilamsquaring * @xmath69 @xmath70 * theorem 2 . * _ nikhilammultiplication algorithm computes the product of @xmath45 and @xmath60 . _ + * proof * : the statement of the above theorem follows from theorem 1 and the fact that : @xmath71 + since , asymptotically fast multiplication algorithms like schonhage - strassen and furer algorithms are only useful for extremely large numbers , for small to medium size numbers we can apply nikhilam multiplication . we can use nikhilam multiplication even in conjunction with some other fast algorithm like karatsuba . if @xmath72 is the threshold between classical multiplication and karatsuba algorithm then up to threshold limit @xmath72 we can use nikhilam multiply and beyond that limit we can use karatsuba multiply . we can write the karatsuba algorithm as given in [ 2 ] , with the only modification that if @xmath73 nikhilammultiplication is called . the corresponding pseudo code is given in algorithm 3 . karatsuba multiplication has relatively small threshold with the classical multiplication . the optimal threshold for karatsuba algorithm can vary from about ten to hundred words . nikhilammultiplication can also be used as a stand alone multiplication algorithm . + further optimization to nikhilammultiplication is also possible . least significant @xmath49 s can be truncated from input numbers , and in the end corresponding modification can be done in single operation . we can process the multiplicand and multiplier for consecutive @xmath49 s to skip some of the steps of the algorithm . the proposed algorithm is particularly efficient because multiplication operation is least involved in it . * input * : @xmath64 * output * : @xmath65 * nikhilammultiplication * @xmath74 @xmath75 @xmath76 mod @xmath77 div @xmath78 @xmath79 sign@xmath80 , @xmath81 sign@xmath82 @xmath83 * karatsubamultiplication * @xmath84 @xmath85 * karatsubamultiplication * @xmath86 @xmath87 * karatsubamultiplication * @xmath88 @xmath89 in this paper we have explored the possibility of applying the nikhilam sutra of vedic mathematics to binary number multiplication . we can take advantage of the fact that this sutra can convert large - digit multiplication to corresponding small digit multiplication . nikhilam method is particularly efficient when both multiplicand and multiplier are near to some base ( radix ) power . to take this advantage , we have first performed square operation in nikhilamsquaring and then we have used this to finally compute multiplication . future work can be to extend this method to large - digit multiplication and exploit it s properties to perform fast integer multiplications ." +"it has been known for a long time that the classical two - integral equilibrium theory in axisymmetric geometry is not sufficient to adequately describe the stellar discs of galaxies . in accordance with jeans theorem ( jeans 1915 ) , the phase space distribution function of a stellar system in a steady state depends only on the isolating integrals of the motion ; the binding energy @xmath0 and the vertical component of the angular momentum @xmath1 are isolating integrals in a stationary and axisymmetric system . it is a fundamental property of all two - integral distribution functions @xmath2 that the dispersion of the velocity in the radial direction equals the dispersion in the vertical direction : we know that , for example , the disc of the milky way does not have that property ( binney & merrifield 1998 ) . illustrations of other shortcomings of a two - integral model in a galactic context can be found in durand , dejonghe & acker ( 1996 ) . the introduction of a third integral of the motion helps to overcome these constraints : in that case , the velocity dispersions can be different in all the directions . numerical experiments show that a third isolating integral seems to exist for most orbits in realistic galactic potentials ( ollongren 1962 , innanen & papp 1977 , richstone 1982 ) . this third integral can be taken into account numerically in the models by using extensions of schwarzschild s ( 1979 ) orbit superposition technique ( cretton et al . 1999 , zhao 1999 , hfner et al . it is also possible to define an analytic third integral specific to particular orbital families ( de zeeuw , evans & schwarzschild 1996 , evans , hfner & de zeeuw 1997 ) or an approximate global third integral ( petrou 1983ab , dehnen & gerhard 1993 ) , but we choose to construct models with an exact analytic third integral by using a stckel potential ( stckel 1890 , de zeeuw 1985 ) . it is not quite obvious to define suitable global distribution functions @xmath3 that depend on three exact analytic integrals and that can somewhat realistically represent our ideas of a real stellar disc . for example , bienaym ( 1999 ) made three - integral extensions of the two - integral parametric distribution functions described in bienaym & schaud ( 1997 ) , but these ones were built to model the kinematics of neighbouring stars in the milky way only . dejonghe & laurent ( 1991 ) also defined the three - integral abel distribution functions , but these ones could not provide very thin discs in the two - integral approximation . robijn & de zeeuw ( 1996 ) constructed three - integral distribution functions for oblate galaxy models , but they also had problems to recover the two - integral approximation . in this paper we continue the work of batsleer & dejonghe ( 1995 ) , who constructed component distribution functions that are two - integral , but that can represent ( very ) thin discs when a judicious linear combination of them is chosen . we use these components as a basis for new component distribution functions that are three - integral , of which the batsleer & dejonghe components are a special case . in the next section , we outline some fundamentals of two - integral equilibrium systems and we show how to model discs with a finite extent in the vertical direction . in section 3 , we present some general facts about stckel potentials and we present new analytic three - integral distribution functions that can represent stellar discs . an analytical expression for the moments of these distribution functions is calculated in section 4 . in the next section , we discuss their physical properties and show their realistic disc - like character . finally , in section 6 , we show that these distribution functions can be used as basis functions in the modeling of a van der kruit disc . for the conclusions , we refer to section 7 . we denote the gravitational potential in cylindrical coordinates @xmath4 by @xmath5 . the two classical isolating integrals of the motion are the binding energy , @xmath6 , and the @xmath7-component of the angular momentum , @xmath8 . when we use the term orbit , we do not consider the information contained in the phases of the orbital motion : an orbit is thus shorthand for an orbital density . even with this definition , each pair @xmath9 represents a family of orbits ; to uniquely identify one particular orbit , we need the presence of a third effective integral of the motion ( i.e. we need a triple @xmath10 ) . the axisymmetric nature of the system implies we can focus on the motion in a meridional plane ( i.e. a plane with constant @xmath11 ) . for a position @xmath12 in the meridional plane , the expressions for @xmath0 and @xmath1 imply that all families of orbits that visit this position have isolating integrals of the motion @xmath9 that meet the requirement @xmath13 since we know that @xmath14 for given @xmath0 and @xmath1 , this relation restricts possible motion for the corresponding family of orbits to a toroidal volume in configuration space . in @xmath15-space , eq . ( [ eq : ele ] ) defines the region in which the points correspond to families of orbits passing through @xmath12 . the boundary line ( equality in eq . ( [ eq : ele ] ) ) contains orbits that reach the given position with zero velocity ( [ eq : mv ] ) in the meridional plane . keeping @xmath16 fixed while allowing @xmath17 to vary then gives us a family of such boundary lines , of which we denote the envelope by @xmath18 with the parametric equations ( batsleer & dejonghe 1995 , eq . 4 & 5 ) @xmath19 l_z^2 & = \displaystyle & - \varpi^3 \frac{\partial \psi}{\partial \varpi } ( \varpi , z_0 ) . \end{array } \right.\end{aligned}\ ] ] all points in integral space with @xmath20 represent families of orbits that will pass through @xmath21 at a certain @xmath17 . orbits for which @xmath22 also do reach the height @xmath23 , but can never go any higher . all points in integral space with @xmath24 represent families of orbits that can not reach @xmath25 . @xmath26 is thus the minimal binding energy of an orbit that can not bring a star higher than @xmath23 above the galactic plane . for every height @xmath27 we find a similar curve @xmath28 , with @xmath29 for every value of @xmath1 . similarly , the envelope for the orbits that can not go higher than @xmath30 is given by @xmath31 , which gives us all circular orbits in the galactic plane . orbits belonging to a disc with a maximum height @xmath23 are thus given by @xmath9 for which @xmath32 ( the shaded area in figure 1 ) . batsleer & dejonghe ( 1995 ) constructed disc - like component distribution functions with a finite extent in vertical direction by setting them equal to zero for @xmath20 . in order to fully understand the components that we present here , that paper should probably be considered as preparatory reading . [ fig : fig2int ] we will work in _ spheroidal coordinates _ , since these coordinates allow a simple expression for our ( axisymmetric ) stckel potential . spheroidal coordinates are given by @xmath33 , with @xmath34 and @xmath35 the roots for @xmath36 of @xmath37 and @xmath4 cylindrical coordinates . the parameters @xmath38 and @xmath39 are both constant and smaller than zero . a potential is of _ stckel form _ , if there exists a spheroidal coordinate system @xmath33 , in which the potential can be written as @xmath40 for an arbitrary function @xmath41 , @xmath42 . the function @xmath43 then represents the potential in the @xmath30 plane . for this kind of potential , the hamilton - jacobi equation is separable in spheroidal coordinates , and therefore the orbits admit three analytic isolating integrals of the motion . the third integral of galactic dynamics has the form @xmath44}\ ] ] more details can be found in de zeeuw ( 1985 ) and in dejonghe & de zeeuw ( 1988 ) . as mentioned before , we intend to create three - integral stellar distribution functions , for the construction of stellar discs : we want to achieve an exponential decline in the mass density for large radii , while we want to introduce a preference for ( almost ) circular orbits . it has been known for some time that two - integral models can describe very thin disc systems , with the restriction that both vertical and radial dispersions are equal ( jarvis & freeman 1985 ) . so we want to create three - integral distribution functions that can describe very thin discs in the two - integral approximation , unlike the abel distribution functions ( dejonghe & laurent 1991 ) . the fricke components ( fricke 1952 ) @xmath45 favour that part of phase space where stars populate circular orbits , so they could be taken as a starting point however , they can not be used in their basic form to model discs with a finite extent because they populate orbits which can reach arbitrary large heights : therefore , we will take as a starting point the components defined in batsleer & dejonghe ( 1995 , eq . 19 ) . in order to make the components depending on the third integral @xmath46 , we introduce the factor @xmath47 in which the parameter @xmath48 ( and @xmath49 ) will be responsible for the three - integral character of the components . the coefficients @xmath50 , @xmath51 , @xmath52 and @xmath48 can , in the most general case , be functions of @xmath1 . this leads us towards a general three - integral disc component of the form @xmath53 if @xmath54 the distribution function is identically zero in all other cases . the function @xmath55 is defined as @xmath56 the parameter @xmath57 is the rotation parameter ( the value of @xmath57 influences only the odd moments of @xmath58 , see section 4 ) . if @xmath59 , there is no rotation for the component , and if @xmath60 , @xmath58 represents a _ maximum streaming _ component with no counter - rotating stars . the requested exponential decline in the mass density with large radii is controlled by the parameter @xmath61 ( and to some extent by the parameter @xmath62 , see section 5 ) . the parameter @xmath63 is responsible for the favouring of almost circular orbits , i.e. orbits with a binding energy @xmath0 as close as possible to that of circular orbits in the galactic plane ( see section 5 ) . furthermore , if we want to favour ( almost ) circular orbits , we have to suppose the distribution function to be an increasing function of @xmath0 : this forces @xmath51 to be positive . since a large @xmath46 implies that the orbit can reach a large height above the galactic plane ( see de zeeuw 1985 for a complete analysis of the orbits in a stckel potential ) , the orbits with small @xmath46 s have to be favoured in order to describe thin discs : this forces @xmath48 to be negative . other constraints ( on @xmath50 , @xmath51 , @xmath52 , @xmath48 and @xmath63 ) will be imposed in section 4 , in order to enable the analytical calculations of the moments . the moments of a distribution function @xmath58 at the point @xmath33 of a spheroidal coordinate system are defined as @xmath64 with @xmath65 , @xmath66 , @xmath67 the components of the velocity in the @xmath34 , the @xmath11" +"the control and manipulation of single electrons in mesoscopic systems constitutes one of the key ingredients in nanoelectronics . the study of single - electron sources@xcite in the high - frequency regime has attracted a great interest due to their potential application in quantum electron optics experiments , in metrology , and in quantum information processing based on fermionic systems.@xcite in this work we study the time evolution of a quantum dot ( qd ) tunnel coupled to a single electronic reservoir , as depicted schematically in fig . [ fig_scheme](a ) . in the presence of some time - dependent voltage modulations , this system defines the building block of the typical single - electron source , namely the mesoscopic capacitor.@xcite in the linear - response regime , the relaxation behavior of such a mesoscopic capacitor has been extensively studied theoretically@xcite and experimentally,@xcite revealing the quantization of the charge relaxation resistance.@xcite on the other hand , the application of _ nonlinear _ periodic potentials to the mesoscopic capacitor yields the controlled emission and absorption of electrons at giga - hertz frequencies.@xcite from these experiments the average charge as well as current correlations@xcite after each cycle of the potential applied have been extracted . these results demonstrate the importance of investigating the dynamics of this kind of single - electron sources . in some of the recent realizations@xcite the coulomb interaction is weak ; however , in small - sized qds the coulomb blockade is , in general , strong and it is , therefore , desirable to include it in the theoretical analysis @xcite since it may even dominate time - dependent phenomena , see e.g. ref . . the time - evolution of interacting quantum dots after the coupling to the leads has been switched on , has , e.g. , been studied in refs . and references therein . , coupled to a normal lead with a tunneling strength @xmath0 . dot occupations can be measured via the current passing through a nearby quantum point contact ( qpc ) capacitively coupled to the dot . b ) qd attached to an additional superconducting contact . c ) qd coupled to a ferromagnetic lead . ] here we investigate the exponential relaxation of a qd towards its equilibrium state after its has been brought out of equilibrium by applying , e.g. , a voltage step pulse . we consider a voltage pulse that affects the occupation of only a single orbital energy level . the level can be spin split due to coulomb interaction . in an earlier work,@xcite some of the present authors investigated the decay of charge and spin of such a single level qd . it was found that the relaxation of charge and spin are given by rates which differ from each other due to coulomb repulsion . since the reduced density matrix of a qd with a single orbital level with spin is four dimensional , there are thus three rates which govern the relaxation of the diagonal elements of the density matrix towards equilibrium ( plus one which is always zero and corresponds to the stable stationary state ) . in addition to the rates that govern charge and spin there is a third rate that appears in the relaxation of a single level qd with spin and with interaction . this additional rate is the subject of this paper . interestingly , this additional time scale is independent of the interaction and of the dot s level position . it is shown to be related to two - particle effects and appears , e.g. , in the time - evolution of the mean squared deviations of the charge from its equilibrium value . we study in detail the perturbations leading to a relaxation of the system with the additional decay rate only , and find that it is indeed related to two - particle correlations . we also propose a procedure to separately read out the different relaxation rates occurring in the dynamics of the qd exploiting the sensitivity of a nearby quantum point contact to the occupation of the qd , see fig . [ fig_scheme ] ( a ) . in order to further clarify the properties of the additional time scale , we extend our study to two other setups : a qd proximized by an extra , superconducting electrode and tunnel coupled to a normal lead ; and a qd tunnel coupled to a ferromagnetic lead , see fig . [ fig_scheme ] ( b ) and ( c ) . we consider a quantum dot coupled to an electronic reservoir . we assume that the single - particle level spacing in the dot is larger than all other energy scales , so that only one , spin - degenerate level of the qd spectrum is accessible . at a certain time @xmath1 the system is brought out of equilibrium , e.g. by applying a gate potential , and afterwards relaxes to an equilibrium dictated by the hamiltonian @xmath2 . the hamiltonian @xmath3 of the decoupled dot @xmath4 contains the spin - degenerate level @xmath5 and the on - site coulomb energy @xmath6 for double occupation of the dot . the creation ( annihilation ) operator of an electron with spin @xmath7 on the dot is denoted by @xmath8 and @xmath9 is the corresponding number operator . the reservoir is modeled by the hamiltonian @xmath10 , in which @xmath11 creates ( annihilates ) an electron with spin @xmath12 and momentum @xmath13 in the lead . the coupling between the dot and the reservoir is described by the tunneling hamiltonian @xmath14 , where @xmath15 is a tunneling amplitude , which we assume to be independent of momentum and spin . by considering a constant density of states @xmath16 in the reservoir , the tunnel coupling strength @xmath0 is defined as @xmath17 . in the remainder of this paper , we focus on the relaxation behavior of the quantum dot to its equilibrium state and in particular on how this relaxation manifests itself in measurable quantities . we are not interested in the dynamics of the reservoir , thus the trace over its degrees of freedom is performed to obtain the reduced density matrix of the qd . the hilbert space is spanned by the four eigenstates of the decoupled dot hamiltonian , @xmath18 , where @xmath19 represents the unoccupied dot , the dot is in the state @xmath20 when being singly occupied with spin @xmath7 , and @xmath21 is the state of double occupation . the energies related to these states are @xmath22 and @xmath23 , where we set the electrochemical potential of the reservoir to zero . as we consider spin - conserving tunneling events , the off - diagonal elements of the reduced density matrix evolve independently of the diagonal ones ( which are the occupation probabilities ) . we can , therefore , consider these probabilities alone , which arranged in a vector are given by @xmath24 and fulfill the condition @xmath25 . the time evolution of the occupation probabilities is governed by the generalized master equation @xmath26 where the matrix elements @xmath27 of the kernel @xmath28 describe transitions from the state @xmath29 at time @xmath30 to a state @xmath31 at time @xmath32 . we consider now the dynamics of the system after being brought out of equilibrium at time @xmath1 . since for @xmath33 the total hamiltonian is time independent , the transition matrix elements depend only on the time difference @xmath34 , i.e. @xmath35 . furthermore , we are interested in the exponential decay towards equilibrium . to be more specific , we will therefore consider only the leading , time - independent , prefactor of the exponential functions . time - dependent corrections to the pre - exponential functions , that generally may appear,@xcite are disregarded . furthermore , when focussing on times @xmath32 distant from the switching time @xmath1 , such that the difference @xmath36 is hence much larger than the decay time of the kernel @xmath37 , we can replace the lower limit of the integral in eq . ( [ eq_master ] ) by @xmath38 . expanding the probability vector @xmath39 in eq . ( [ eq_master ] ) around the measuring time @xmath32 we find@xcite @xmath40 here we introduced the laplace transform of the kernel @xmath41 , with @xmath42 and the @xmath43-th derivative of the kernel with respect to the laplace variable @xmath44_{z=0}$ ] . the formal solution of eq . ( [ eq_masterexpand ] ) is given by @xmath45 which depends on the initial probability vector @xmath46 at @xmath47 , where the initial values for the system parameters are given by the ones just after the switching time @xmath1 . the matrix @xmath48 includes markovian and non - markovian processes.@xcite in the following , we consider the limit of weak coupling between quantum dot and reservoir and limit ourselves to a perturbation expansion up to second order in @xmath0 , which is valid for the regime where the tunnel coupling @xmath0 is much smaller than the energy scale set by the temperature @xmath49 . the perturbative expansion of @xmath48 is @xmath50 with @xmath51 and @xmath52 , where the number in the superscript represents the power of @xmath0 included in the transition matrix @xmath53 . notice that the first non - markovian correction , i.e. the term @xmath54 is present in second - order in the tunnel coupling . the evaluation of the kernel within a perturbative expansion can be performed using a real - time diagrammatic technique,@xcite which has been used in ref . in order to extract the exponential decay of spin and charge in the system studied here . considering eq . ( [ eq_exp ] ) , we see that the rates defining the decay of the state into equilibrium are found from the eigenvalues of the matrix @xmath48 , which turn out to be real and non - positive . the matrix @xmath48 is not hermitian , as expected since we deal with a dissipative system , and hence has different left and right eigenvectors , @xmath55 and @xmath56 . the time - dependent probability vector , @xmath57 , can be expressed in terms of the right eigenvectors of @xmath48 , each being related to a decay with a different rate . the left eigenvectors determine the observable that decay with a single time scale only , see also the appendix . + in the following we discuss the exponential relaxation towards equilibrium of the vector of occupation probabilities , in first order in the tunneling strength @xmath0 . we start by briefly discussing the simplest case of a single spinless particle . this limit is obtained , when a magnetic field much larger than the temperature is applied , @xmath58 . the hilbert space of the system is two dimensional and spanned by the states @xmath19 and @xmath59 for the empty and singly - occupied dot respectively , whose occupation probabilities are arranged in the vector @xmath60 . the decay to the stationary state is governed by matrix @xmath61 ( defined equivalently to @xmath62 but for the two - dimensional hilbert space for the problem at hand ) which contains a single relaxation rate , namely the tunnel coupling @xmath0 , as intuitively expected . we now include the spin degree of freedom but disregard interactions . the system is described by two independent hilbert spaces spanned by the states @xmath63 and @xmath64 with @xmath7 . the probability vector for each spin @xmath12 can be written in terms of the eigenvalues and eigenvectors of the matrix @xmath61 ( for the two - dimensional hilbert space ) as @xmath65 \label{eq_psigma}\ ] ] where the right eigenvector corresponding to the eigenvalue zero of @xmath61 defines the occupation probabilities for the equilibrium state , @xmath66 , with the fermi function @xmath67^{-1}$ ] and the inverse temperature @xmath68 . furthermore , @xmath69 is the vector representation" +"during the last two decades , a number of new paradigms for understanding complex living systems have emerged . these include , e.g. theory of dynamical systems , theory of complexity , nonlinear dynamics , evolutionary physics , and critical phenomena@xcite . among these , chaotic attractors , ( multi-)fractals , self - assemblies , dissipative structures and self - organization represent some of the most promising recent concepts . a particularly important testbed for a conceptualization of pattern formation in self - organizing systems is the b z reaction@xcite which belongs among the most extensively studied examples of chemical self - organization . however , despite decades of intensive research , there are still ongoing controversies over the actual chemical kinetics ( i.e. details of rates of chemical reactions involved ) and the mesoscopic dynamics ( i.e. exact nature and mechanism of patterns formation at the mesoscopic scale ) of the b z reaction@xcite . the b z reaction is considered as a textbook example of the so - called excitable medium@xcite . majority of available chemical models which aim to explain the chemical self - organization are based on the standard reaction - diffusion analysis and the law of mass action applied to a few selected reactions@xcite . on the other hand , self - organization is a hallmark of a far - from - equilibrium dynamics which appears difficult to reconcile with a common - sense chemical reaction scheme based on the law of mass action . turing patterns that appear in some reaction - diffusion models are often considered as a theoretical embodiment of the b z patterns@xcite . this is wrong for at least three reasons : turing patterns ( a ) can explain only wave b z patterns but not spirals@xcite , ( b ) appear only at specific parameter values in the reaction - diffusion equations , therefore they are unstable under fluctuations of parameters ( in contrast to experiments where patterns are observably robust ) , ( c ) are stable solutions of turing s reaction - diffusion equations while , in the experiment , we observe a dynamic system on a trajectory through the state space towards a limit cycle with alternating spirals and wave fragments . the mesoscopic description of the b z reaction is typically modeled with a cyclic cellular automaton which often generates patterns similar to the b z wave patterns found near to the final stage of the reaction . the morphological characterization of patterns is pivotal in these approaches while chemical aspects are often of a secondary interest . so far , mesoscopic studies of the b z reaction have been limited to a low - level cellular automata@xcite which can reasonably well account only for some of the observed b z wave patterns , while it is as yet unclear how to generalize these approaches to obtain a full - fledged evolution of wave patterns together with dynamics of spiral patterns . to the best of our knowledge , the influence of the number of levels has been systematically studied only in one case@xcite while most of the systematic studies in the literature have been confined to maximally 8 levels@xcite . in order to numerically implement a hotchpotch model , we have adopted an approach based on the version of wilensky netlogo model@xcite . in our case the model is limited to 200 achievable state levels and simulated on a square 50 @xmath0 50 grid . after a random setup of the space distribution of initial centers of @xmath1 $ ] as @xmath2 where @xmath3 is the maximally achievable number of levels of the cell state . the model at each time step @xmath4 may proceed in four possible ways : 1 . when a cell is at the @xmath5 , so - called _ quiescent _ , it may be `` infected '' by surrounding cells according to the equation @xmath6 where @xmath7 and @xmath8 is a number of cells at the @xmath9 and @xmath10 , respectively , @xmath11 and @xmath12 are characteristic constants of the process and @xmath3 is a maximum allowed level of state / excitation . when a cell is at the @xmath13 , its new state is calculated as @xmath14 where @xmath15 is a state of the @xmath16-th cell in the moore neighbourhood , which directly surrounds the examined cell , and @xmath17 is another arbitrary constant . for simplicity s sake , we denote in the following text @xmath18 and @xmath17 as 2a and 2b , respectively . 3 . when a cell is at the @xmath19 , then @xmath20 4 . when a cell achieves the @xmath21 , then @xmath22 here we posit that our improved stochastic version of the multilevel hotchpotch model not only faithfully represents the dynamics of wave - spiral patterns of the b z reaction but also provides insight into underlying chemical reactions in terms of the eyring activated complex theory@xcite . the emergence of correct spatial structures in our model depends on the ratio between the number of available states within the elementary time lag and on the rate of the internal increase in excitation process . at appropriate levels of noise , we observe a dynamical evolution of the system through circular waves up to the final stage spiral - wave interchange . this structure - stabilizing mechanism via the noise is a typical trademark of a mesoscopic description and is not simply attainable via microscopic deterministic rules . by the presence of the noise , we can explain many controversies in self - organization in the nature . the b z reaction is not easily comprehensible in terms of the standard law of mass action ( which represents the `` canonical method '' of interpretation of the chemical reactivity ) . this is due to the fact that the reaction space is separated into regularly evolving / travelling structures and that one has to consider a large number of interlocked chemical processes involved . in this work , we report on a new cellular - automaton based stochastic model of the b z reaction . the model retains some of the key features of the multi - level hotchpotch machine which , however , outperforms both in its ability to faithfully mimic the onset stage of the b z reaction and its potential to correctly describe the morphology of the interacting wave - spiral patters during their evolution . figure 1a compares a late stage of the b z reaction ( full data are accessible in supplementary material 1 ) in our least possible spatial constraining ( a 200-mm petri dish ) and roily conditions ( gentle mixing at 1400 rpm using an orbital mixer ) with simulation of the modified wilensky model of excitable medium@xcite . the structures are , for some parameter ranges , astonishingly similar . however , the most regular spirals and waves , best comparable to the model , are expected to arise in a very gently mixed , homogenous solution of thin layer in a vessel of the unlimited size which does not spatially constrain the evolution of waves . in order to achieve the manifest morphological similarity between the b z experiments and our simulation , we implemented the following changes into the wilensky model : 1 . the enlargement of the cellular grid to 1000 @xmath0 1000 , 2 . start from a very few points which enabled to analyze the behaviour of individual centers of emanation , 3 . a sequence of switching the values of cell states from natural to decimal numbers which extended the span of each cellular state , 4 . the addition of a uniform white noise to each automaton step which compensated for our limited knowledge of precise underlying mechanism , and 5 . the extension of the number of achievable states @xmath3 and rate of the internal cell excitation @xmath17 up to 2000 and 280 , respectively , to smooth the model waves . the first modification usage of the finer grid suppressed the influence of the nonidealities of the periodic boundaries on the evolution of the model system . the second intervention into the wilensky model was performed using random - exponential function for generation of the starting ( ignition ) points . multiplication of each cell state by the @xmath23 of the exponential distribution , i.e. @xmath24\ , , \ ] ] ensured that the simulation started with a small number of the ignition points . at this initial condition , we first tested the influence of the @xmath25 of natural numbers due to the rounding in processes 12 ( see eqs . ( [ eq2])-([eq3 ] ) ) , thus new states in time @xmath4 were calculated as @xmath26 and @xmath27 this modification , which was originally implemented to start the process from these few centers ( ignition points ) quite surprisingly increased the structural - patterns similarity between the b z experiment and the simulation . the results are shown in figure 1b c and supplementary materials 24 and were discussed in some detail in@xcite . in figure 1b , we present early simulation steps 2 , 4 , 14 , and 16 after the ignition in process 1 . for @xmath28 and @xmath29 , at least two non - zero points in a proper configuration @xmath7 , @xmath8 were required for the evolution of the waves in the simulation , since at least one addend in process 1 has to be equal to 1 . in this case , the early evolution gave octagons ( figure 1b , i ) and final state was formed by spirals ( figure 1c , i ) . in contrast , if @xmath30 and @xmath31 , then , e.g. @xmath32 and the non - zero cell was surrounded by evolving wave of 8 cells in @xmath33 . this early evolution resulted in squares with central circular objects ( figure 1b , ii ) which further led to the filamentous structures ( figure 1c , ii ) . the next step softened the definition of the state by allowing 1 decimal place in eqs . ( [ eq2])-([eq3 ] ) , i.e. @xmath34 and @xmath35 and kept @xmath28 and @xmath29 ( supplementary material 5 ) . if @xmath36 , the first layer of 8 cells in @xmath37 evolves in the moore neighbourhood . this modification provided the trajectory as observed for @xmath30 and @xmath31 with natural number states . more decimal places did not change the state space trajectory any more . this proves that the trajectory is determined by the ratio of the @xmath17 constant to the number of levels @xmath3 . the @xmath38 ratio close to 7 ( 28/200 ) showed the highest structural similarity to the experiment . there seems to be also a lower limit for the proper development of the system trajectory . in case of @xmath39 and @xmath40 , we observed evolution of square spirals and the simulation grid was never fully covered by spirals and waves . at the 2/14 ratio , the grid was already completely covered . at the 3/20 ratio , the circular structures similar to those observed in the experiment were firstly observed . at keeping the @xmath38 ratio , the next increase of the @xmath3 value smoothed only the edges of the structures . obviously , 7 state levels does not allow to cover the moore space with 8 neighbouring cells and 14 state levels are not yet sufficient enough to create an appropriate curvature . the course of the simulation and the type of the limit set ( late state ) depends on the type of the _ garden of eden _ as follows : a ) the emergence of the ignition point needs one or two neighbouring non - zero points and determines the overall type of the trajectory and b ) the number and distribution of ignition centers determines the duration" +"the cosmic ray energy spectrum is nearly featureless over ten orders of magnitude in energy , from @xmath0 ev to @xmath1 ev , with the differential flux falling approximately as @xmath2 . there are three small , though widely discussed , features : the `` knee '' , a hardening of the spectrum at @xmath3 ev ; the `` second knee '' , another hardening at about @xmath4 ev ; and the `` ankle '' , a softening of the spectrum at about @xmath5 ev . these features may represent changes in the sources , composition or dynamics of the cosmic rays . two often asked questions are : how do cosmic rays come to have such high energies ( a joule or more of kinetic energy in a proton or other sub - atomic particle ) , and does the spectrum continue above @xmath1 ev ? there are two types of models describing the sources of ultra - high energy cosmic rays ( uhecrs ) : astrophysical models ( `` bottom - up '' ) , in which cosmic rays are accelerated to very high energies by magnetic shock fronts moving though plasmas ; and cosmological models ( `` top - down '' ) , in which the cosmic rays are the result of the decays of super heavy particles which are relics of the big bang . i will only be discussing the former . one can evaluate the plausibility of various astrophysical sources by considering the magnetic field of the object and its size.@xcite the overall magnetic field contains the nascent cosmic rays during their acceleration and thus must be large enough to keep the cosmic rays within the object . smaller objects need larger fields ; larger objects , smaller fields . by this criterion we have several candidate sources : neutron stars , active galactic nuclei ( agn ) and clusters of galaxies among others . all these sources could plausibly , by the above argument , give cosmic rays at @xmath1 ev , but , in all cases , one is pushing the bounds of plausibility at the highest energies . if uhecrs are extragalactic , then they must traverse the intergalactic medium in order to be observed . this medium is filled with cosmic microwave background ( cmb ) photons , which should lead to a fourth , and not so small , feature of the uhecr spectrum . because of their large kinetic energies , uhecrs interact with the cmb to produce resonances ( in the case of protons ) or to dissociate ( in the case of nuclei ) . in the proton case , the resonance ( e.g. @xmath6 ) will decay quickly into proton or neutron and a meson ( e.g. @xmath7 ) . in either case , the result is a reduction in the energy of the leading particle . at somewhat lower energies , cosmic rays lose energy by creating electron - positron pairs in their interaction with the cmb . these energy loss mechanisms imply that there should be a sharp reduction in the uhecr flux above @xmath8 ev , assuming the uhecrs are protons and that they come from distances greater than a few tens of megaparsecs . nuclei should have an even lower energy threshold . this fact , first pointed out by greisen , zatsepin and kuzmin , has become known as the gzk cutoff.@xcite by measuring the shape of the uhecr spectrum and , crucially , modeling the spectrum at the source , one can hope to deduce which of the plausible sources listed above , if any , contribute to the uhecrs we see . if uhecrs are produced in our galaxy they are not subject to the gzk cutoff . however , there are no plausible astrophysical accelerators of uhecrs within our galaxy . any such object would appear as a point source in a map of the sky made with uhecrs , due to the short propagation distances and relatively weak magnetic fields . no such point source has been observed . uhecrs have a very low flux , so one must have a large collection area to obtain a reasonable event rate . this precludes direct observations of uhecr above the earth s atmosphere in satellite experiments . however , one may also use that atmosphere as a giant calorimeter , because uhecrs create extensive air showers ( eass ) when they encounter the atmosphere . this allows access to very large areas . there are two ways to instrument this atmospheric calorimeter : readout the particle multiplicities at the back end by putting arrays of detectors on the ground , or collect the light produced as the eas gives up its energy to the atmosphere . the former technique ( ground arrays ) has the advantage of 100% duty cycle : one can run at all times of the day . it has the disadvantage that one usually observes only the tail end of the eas and has to infer the properties of the primary particle rather indirectly . to illustrate , consider the lead - scintillator sandwich type calorimeter used in many fixed - target experiments at accelerators . one normally collects the light produced by the shower as it goes through the scintillator segments . the total light is proportional to the energy of the initial particle , and one can in principle measure the longitudinal development of the shower . now imagine throwing away the signals from all but the last scintillator segment and one can understand the difficulties faced by ground arrays . one must also make a trade - off between density of detectors on the ground and the total area over which one places detectors . collecting the fluorescence light from eass has complementary advantages and disadvantages . the main advantage is that one observes light from all stages in the development of the eas , and the amount of this light is directly proportional to the primary energy . the disadvantage is that one is subject to the optical changes inherent in the atmosphere and one can only run when and where it is dark and clear . as a counterpart to the example above , fluorescence detectors are like lead - glass calorimeters , where one collects light from the whole detector element . however , the glass may be somewhat smoky . the akeno giant air shower array ( agasa)@xcite is the largest , currently active example of a ground array . the agasa collaboration claims to see no evidence for the gzk cutoff,@xcite which has motivated a great deal of theoretical work on possible mechanisms by which the gzk cutoff could be avoided . the fly s eye experiment@xcite is an example of a fluorescence detector , and the experiment that has observed the highest energy cosmic ray ever detected at @xmath9 ev.@xcite the pierre auger observatory,@xcite currently under construction , will combine both a very large ground array and a fluorescence detector , in an effort to have the advantages of both types of detectors . the high resolution fly s eye experiment ( hires ) is a direct descendant of fly s eye , designed with bigger mirrors and finer pixels , to give a larger aperture by a factor of ten . it consists of two sites , separated by 12 km , in order to observe eass in stereo . stereo observation greatly reduces the uncertainty in the geometrical reconstruction of the eas . the sites are located on hills on the dugway proving grounds in the west desert of utah . the remote desert provides a dark , optically clean atmosphere , while the hills put the detectors above much of the remaining aerosols . each detector consists of mirror units viewing a @xmath10 patch of the sky with 256 photomultiplier tubes ( pmts ) , each of which views about @xmath11 , in a @xmath12 array . each mirror has an area of about 5 m@xmath13 . the hires - i site , the first of the two to be built , has one ring of mirrors covering from @xmath14@xmath15 and nearly the complete azimuth . the pmts are read out using a sample - and - hold technique , that gives the time and size of the signal for each tube . the hires - ii site has two rings of mirrors covering @xmath14@xmath16 . these pmts are read out using a flash adc ( fadc ) system , which samples each of the tubes every 100 ns . this provides the shape of the signal in each tube and allows one to combine the light from different tubes that were active at the same time . hires - i began operation in june of 1997 . hires - ii began in october of 1999 . the reader is referred to the published fly s eye@xcite and hires@xcite papers for details of the reconstruction techniques . only a brief summary will be given here . although hires was designed as a stereo experiment , there are two reasons for continuing to consider monocular analyses . first , since hires - i was running for two years before hires - ii came on - line , the largest uhecr data sample is the hires - i monocular sample . second , low - energy events are close to one or the other of the two sites , and trigger that site only . thus , the low - energy reach of the detector will always be in monocular mode . hires - ii is a better detector for reconstructing monocular events , due to its two rings : longer tracks lead to a better determination of the eas geometry . there are two tasks in determining the geometry of an eas : finding the shower - detector plane ( sdp ) and determining the angle of the shower within the sdp . the geometry of the shower within the sdp is determined by fitting the time of the tube signals @xmath17 for @xmath18 , @xmath19 and @xmath20 , where @xmath21 is the signal time in the @xmath22th tube , @xmath18 is the impact parameter , @xmath20 is the time the shower core reaches the @xmath18 point , @xmath19 is the angle of the eas in the sdp and @xmath23 is the viewing angle in the sdp of the @xmath22th tube . longer tracks make it easier to distinguish the tangent function from a straight line . hires - i tracks are often too short to resolve all the ambiguities from timing alone , and one must look to the reconstructed shower profile ( see below ) for assistance in determining the geometry . as an example , a picture of a 50 eev cosmic ray event from hires - ii , given in fig . [ fig : mirror - tvsa ] , shows the azimuthal and elevation angles of all the tubes in the mirrors that were part of the event . inactive tubes are shown as dots ; active tubes are shown as filled circles , where the radius is proportional to the tube signal . active tubes that are used in fitting the sdp are shaded according to the average time of the fadc measurements of the tube . the fitted sdp is also shown in the figure . the average time of the signal for each tube as a function of the angle ( @xmath23 ) in the sdp is also shown for the same event , including three fits to eq . [ eq : tvsa ] , one with @xmath24 ( light grey ) , one with @xmath25 ( dark grey ) and the best fit @xmath19 ( black ) . ev ) uhecr event , as seen on the mirrors / pmts of the detector ( left ) and in a time vs (" +"geometrical dynamics is a dynamics of elementary particles , generated by the space - time geometry . in the space - time of minkowski the geometrical dynamics coincides with the conventional classical dynamics , and the geometrical dynamics may be considered to be a generalization of classical dynamics onto more general space - time geometries . however , the geometric dynamics has more fundamental basis , and it may be defined in multivariant space - time geometries , where one can not introduce the conventional classical dynamics . the fact is that , the classical dynamics has been introduced for the space - time geometry with unlimited divisibility , whereas the real space - time has a limited divisibility . the limited divisibility of the space - time is of no importance for dynamics of macroscopic bodies . however , when the size of moving bodies is of the order of the size of heterogeneity , one may not neglect the limited divisibility of the space - time geometry . the geometric dynamics is developed in the framework of the program of the further physics geometrization , declared in @xcite . the special relativity and the general relativity are steps in the development of this program . necessity of the further development appeared in the thirtieth of the twentieth century , when diffraction of electrons has been discovered . the motion of electrons , passing through the narrow slit , is multivariant . as far as the free electron motion depends only on the properties of the space - time , one needed to change the space - time geometry , making it to be multivariant . in multivariant geometry there are many vectors @xmath1 , @xmath2, ... at the point @xmath3 , which are equal to the vector @xmath4 , given at the point @xmath5 , but they are not equal between themselves , in general . such a space - time geometry was not known in the beginning of the twentieth century . it is impossible in the framework of the riemannian geometry . as a result the multivariance was prescribed to dynamics . to take into account multivariance , dynamic variables were replaced by matrices and operators . one obtains the quantum dynamics , which differs from the classical dynamics in its principles . but the space - time conception remains to be newtonian ( nonrelativistic ) . multivariant space - time geometry appeared only in the end of the twentieth century @xcite . the further geometrization of physics became to be possible . it should note that there were numerous attempts of further geometrization of physics . they were based on the riemannian space - time geometry . unfortunately , the true space - time geometry of microcosm does not belong to the class of riemannian geometries , and approximation of real space - time geometry by a riemannian geometry can not be completely successful . in particular , the riemannian geometry can not describe such a property of real space - time geometry as multivariance . the multivariance of the space - time geometry was replaced by the multivariance of dynamics ( quantum theory ) . understanding of nature of elementary particles is the aim of the further geometr - ization of physics . this aim distinguishes from the aim of the conventional theory of elementary particles . let us explain the difference of aims in the example of history the chemical elements investigation . investigation of chemical elements reminds to some extent investigation of elementary particles . chemical elements are investigated from two sides . chemists systematized chemical elements , investigating their phenomenological properties . the results of these investigations were formulated in the form of the periodical system of chemical elements in 1870 . formulating this system , d.i.mendeleev conceived nothing about the atom construction . nevertheless the periodical system appears to be very useful from the practical viewpoint . physicists did not aim to explain the periodical system of chemical elements , they tried to understand simply the atom structure and the discrete character of atomic spectra . after construction of the atomic theory it became clear , that the periodical system of chemical elements can be obtained and explained on the basis of the atomic theory . as a result the `` physical '' approach to investigation of chemical elements appeared to be more fundamental , deep and promising , than the `` chemical '' one . on the other hand , the way of the `` physical '' approach to explanation of the periodical system is very long and difficult . explanation of the periodical system was hardly possible at the `` physical '' approach , i.e. without the intermediate aim ( construction of atomic structure ) . thus , using geometrization of physics , we try to approach only intermediate aim : explanation of multivariance of particle motion ( quantum motion ) and capacity of discrimination of particle masses . discrete character of masses of elementary particles can be understood , only if we understand the reason of the elementary particle discrimination . contemporary approach to the elementary particle theory is the `` chemical '' ( phenomenological ) approach . it is useful from the practical viewpoint . however , it admits hardly to understand nature of elementary particles , because the nature of the discrimination mechanism , leading to discrete characteristics of elementary particle , remains outside the consideration . the most general geometry is a physical geometry , which is called also the tubular geometry ( t - geometry ) @xcite , because straights in t - geometry are hallow tubes , in general . the t - geometry is determined completely by its world function @xmath6 , where @xmath7 is interval between the points @xmath8 and @xmath9 in space - time , described by the t - geometry . all concepts of t - geometry are expressed in terms of the world function @xmath0 . dynamics of particles ( geometric dynamics ) is also described in terms of the world function . the elementary particle is considered as an elementary geometrical object ( ego ) in the space - time . the elementary geometrical object @xmath10 is described by its skeleton @xmath11 and its envelope @xmath12 . the envelope @xmath12 is defined as a set of zeros of the envelope function @xmath13@xmath14the envelope function @xmath13 is a real function of arguments @xmath15 . any argument @xmath16 @xmath17 is a world function @xmath18 , @xmath19 . it is supposed that ego with skeleton @xmath20 is placed at the point @xmath5 . in t - geometry the vector @xmath21 is an ordered set of two points @xmath22 . the length @xmath23 of the vector @xmath4 is defined via the world function by means of the relation@xmath24 the scalar product @xmath25 of two vectors @xmath4 and @xmath1 is defined by the relation@xmath26equivalence @xmath4eqv@xmath1 of two vectors @xmath4 and @xmath1 is defined as follows . two vectors @xmath4 and @xmath1 are equivalent ( equal ) , if@xmath27 in the developed form we have@xmath28 skeletons @xmath20 and @xmath29 are equivalent ( @xmath30eqv@xmath31 , if corresponding vectors of both skeletons are equivalent@xmath32 the skeleton @xmath20 of ego at the point @xmath5 may exist as a skeleton of a physical body , if it may exist at any point @xmath33 of the space - time @xmath34 . it means that there is a solution for system of equations @xmath35for any point @xmath33 . further for brevity we take , that an existence of a skeleton means an existence of corresponding geometrical object . in the space - time of minkowski the problem of the skeleton existence is rather simple , because at given @xmath30 and @xmath3 the system ( [ c1.6 ] ) of @xmath36 algebraic equations has a unique solution , although the number of equations may distinguish from the number of variables to be determined . indeed , in the four - dimensional space - time the number of coordinates of @xmath37 points @xmath38 is equal to @xmath39 ( the point @xmath3 is supposed to be given ) . if @xmath40 the number @xmath36 of equations is larger than the number ( @xmath39 ) of variables . in the case of an arbitrary space - time geometry ( arbitrary world function @xmath0 ) existence of solution of the system ( [ c1.6 ] ) is problematic , and the question of existence of the skeleton as a skeleton of a physical body is an essential problem . on the contrary , if @xmath41 , the number of coordinates to be determined is less , than the number of equations , and one may have many skeletons @xmath42placed at the point @xmath3 , which are equivalent to skeleton @xmath30 , but they are not equivalent between themselves . this property is a property of multivariance of the space - time geometry . this property is actual for simple skeletons , which contain less , than four points ( @xmath41 ) . for instance , for the skeleton of two points @xmath43 , which is described by the vector @xmath4 , the problem of multivariance is actual . in the space - time of minkowski the equivalence of two vectors ( @xmath44 ) is single - variant for the timelike vectors , however it is multivariant for spacelike vectors . in the general space - time the equivalence relation @xmath44 is multivariant for both timelike and spacelike vectors . the problem of multivariance is essential for both existence and dynamics of elementary geometrical objects ( elementary particles ) . let us formulate dynamics of elementary particles in the coordinateless form . dynamics of an elementary particle , having skeleton @xmath11 , is described by the world chain @xmath45direction of evolution in the space - time is described by the leading vector @xmath4 . if the motion of the elementary particle is free , the adjacent links @xmath46 and @xmath47 are equivalent in the sense that @xmath48 relations ( [ c1.7 ] ) - ( [ c1.9 ] ) realizes coordinateless description of the free elementary particle motion . in the simplest case , when the space - time is the space - time of minkowski , and the skeleton consists of two points @xmath49 with timelike leading vector @xmath4 , the coordinateless description by means of relations ( [ c1.7 ] ) - ( [ c1.9 ] ) coincides with the conventional description . the conventional classical dynamics is well defined only in the riemannian space - time . the coordinateless dynamic description ( [ c1.7 ] ) - ( [ c1.9 ] ) of elementary particles is a generalization of the conventional classical dynamics onto the case of arbitrary space - time geometry . any geometry is constructed as a modification of the proper euclidean geometry . but not all representations of the proper euclidean geometry are convenient for modification . there are three representation of the proper euclidean geometry @xcite . they differ in the number of primary ( basic ) elements , forming the euclidean geometry . the euclidean representation ( e - representation ) contains three basic elements ( point , segment , angle ) . any geometrical object ( figure ) can be constructed of these basic elements . properties of the basic elements and the method of their application are described by the euclidean axioms . the vector representation ( v - representation ) of the proper euclidean geometry contains two basic elements ( point , vector ) . the angle is a derivative element , which is constructed of two vectors . a use of the two basic elements at the construction of geometrical objects is determined by the special structure , known as the linear vector space with the scalar product , given on it ( euclidean space ) . the scalar product of linear vector space describes interrelation of two basic elements ( vectors" +"the first detection of an extrasolar planet around a normal star ( mayor & queloz 1995 ) and subsequent deluge of similar discoveries by the radial velocity technique ( marcy , cochran & mayor 2000 ) , have taught us that @xmath05% of solar type stars harbor planetary systems very _ unlike _ our own . what remains to be determined is the abundance of planetary systems _ similar _ to that of the sun s ( eg . , terrestrial planets at @xmath00.5 - 2 au or jovian analogs at @xmath03 - 12 au ) and the frequency of planets around the most common stars in our galaxy , m dwarfs . microlensing is providing the first partial answers to these questions . microlensing occurs whenever a massive compact object ( such as a star , black hole , etc . ) passes very near the line - of - sight to a background luminous source . in the case of a single point lens , two images of the source are formed with a separation that scales with the angular radius of the einstein ring , @xmath1^{-1/2}$ ] , where @xmath2 , and @xmath3 , @xmath4 , and @xmath5 are the mass of the lens , its distance , and the distance to the source , respectively . for sources in the galactic bulge , this separation is @xmath01 mas , and thus generally too close to be resolved . the combined image brightness , however , can be observed and is a function of the changing projected distance between the lens and the observer - source line - of - sight . as the source moves through the axisymmetric magnification pattern generated by a single lens , a symmetric light curve results . this symmetry is destroyed for multiple lenses such as binary star systems or planetary systems . more complicated magnification patterns are formed , and the resulting light curve depends on the angle @xmath6 of the source trajectory . for binary lenses , the topology of the magnification map ( fig . 1 ) depends on only two parameters : the mass ratio @xmath7 of the lenses and their projected separation @xmath8 in units of the einstein ring radius . for typical galactic lenses , m dwarfs in the bulge or inner disk , the physical size of the einstein radius is @xmath9 au . because typical @xmath10 are comparable to the orbital radius of many solar system planets , microlensing is an excellent way to search for planets , as first suggested by mao & paczynki ( 1991 ) and further developed by gould & loeb ( 1992 ) . 0.0cm=12.5 cm -4.25 cm -0.5 cm figure 1 shows the differential magnification effect of binary lenses as a function of their mass ratio @xmath11 and separation @xmath12 . each panel covers an area @xmath13 on a side centered on the more massive primary lens . the brightness of an image is proportional to @xmath14 , where @xmath15 is the jacobian that describes the coordinate transformation between the image and source planes . the locus of points in the source plane for which @xmath16 is called the `` caustic curve . '' a source crossing the caustic will be highly magnified . -8.5 cm -0.5 cm -1 cm since most microlensing events are alerted in real time only when the source lies near or inside @xmath17 , a light curve will reveal the binarity of the lens ( via an anomaly @xmath18 ) only if the source trajectory passes over the contours shown in fig 1 . otherwise , the light curve will be indistinguishable from that due to a single isolated lens . figure 2 illustrates this effect ; two possible source trajectories are shown passing the same distance from the `` central '' caustic , but different distances from the two , outer `` planetary '' caustics ( all three caustics are caused by the lens - planet combination ) . the light curve associated with only one of these trajectories betrays the presence of the planet . since the deviation contours are most extended for @xmath11 and @xmath12 of order unity ( fig . 1 ) , these types of binary lenses will be the easiest to detect . even planets as small as the earth generate caustic structures as they orbit galactic lenses ; background sources passing over or near these caustics will experience a substantial additional microlensing effect due to the binarity of the lens . the cross section of the planetary caustic and thus the probability that a random trajectory will pass over or near it decreases slowly with mass ratio ( dominik 1999 ) . for this reason , microlensing unlike most other planet detection methods has _ sensitivity _ to terrestrial - mass planets . this sensitivity is limited primarily by the sampling rate and precision of the photometry required to see signals that are reduced in amplitude by finite source effects for @xmath19 . the _ efficiency _ with which planets of given @xmath11 and @xmath12 can be detected in a given light curve is a statistical quantity that depends on the photometric precision , sampling and duration of the photometric data and on the characteristics of the underlying event sampled , most notably its minimum impact parameter , @xmath20 , and the amount of blended non - lensed light in the same resolution element ( gaudi & sackett 2000 ) . determination of detection efficiencies for individual light curves allows non - detections to be translated into statistical upper limits for a given class of planet . in principle , the _ detection _ of a microlensing anomaly can be quantified statistically , but its clear identification with a planetary lens relies on the _ characterization _ of the planet through determination of @xmath11 and @xmath12 . since any given event will not repeat , characterization must be obtained at the time of detection , and will require better data . with sufficient data quality , both @xmath12 and @xmath11 can be determined from light curve modeling , although in some cases the well - known @xmath21 `` degeneracy '' ( griest & safizadeh 1998 ; dominik 1999 ) will prevent a unique identification . high magnification events are sensitive and reasonably efficient to the detection of small mass planets since their small @xmath20 brings them close to the central caustic generated by companions ( griest & safizadeh 1998 ) . unfortunately , such detections may be particularly difficult to characterize , since all planets orbiting the primary lens will distort the central caustic ( gaudi , naber & sackett 1998 ) ; more massive ones will have an effect over a larger range of @xmath12 . di stefano and scalzo ( 1999 ) point out that current programs typically halt intensive monitoring when @xmath22 ; extended high - precision monitoring may detect and characterize planets at larger separation from their host lenses . 0.25 cm -5.30 cm 5.25cm=5.5 cm -7.25 cm 8.9cm=8.5 cm -1.75 cm -0.2 cm of 21 light curves consistent with binary lenses analyzed by macho , two produced acceptable fits with companion masses as small @xmath23 ( alcock et al . the first suggestion of possible planetary - mass lenses ( bennett et al . 1997 ) came from macho survey data for macho 1994-blg-4 , which could be modelled as an m - dwarf/5@xmath24 pair , and macho 1995-blg-3 , a very short duration event modelled as an isolated 2@xmath24 lens . however , many alternate interpretations were allowed by the infrequently sampled light curves inherent to survey data ( which must sample @xmath0@xmath25 stars nightly ! ) ; no firm planetary detection was claimed in either case . the timescale @xmath26 ( @xmath27 is the relative proper motion of lens and source ) of typical galactic microlensing events is weeks to months ; whereas planetary ( @xmath28 ) anomalies would have durations of hours to days . the necessity of round - the - clock monitoring for detection and characterization of short - lived planetary deviations prompted the establishment of international collaborations such as mps ( rhie et al . 2000 ) and planet ( albrow et al . 1998 ) , which obtain sub - day to sub - hourly photometry on events discovered by the survey teams macho , ogle and eros . although tantalizing hints have been seen in some light curves ( see below ) , no clear _ planetary _ anomaly has been detected . 2.25 cm -4.0 cm -0.25 cm * macho 1997-blg-41 : * the very unusual event macho 1997-blg-41 caused a stir in the community : although clearly multiple lens microlensing , static stellar binary models did not fit the data . bennett et al . ( 1999 ) interpreted the double caustic structure as coming from a static triple system , a jovian planet orbiting a stellar binary . the planet team , modeling their own data , instead showed that the light curve could be fit as a normal stellar binary ( albrow et al . 2000a ) whose rotation brings one of the triangular caustics across the source trajectory ( fig . 3 ) . the proposed binary+jovian model was incompatible with planet data . * ogle 2000-bul-12 : * recently , yock et al . ( 2000 ) have suggested that a planet may be orbiting the primary lens of event ogle 2000-bul-12 , based on analysis of public domain ogle data ( udalski & szymanski 2000 ) that displayed a possible anomaly at peak . unpublished planet team data indicates no anomaly and much smaller scatter at the same temporal position ( fig . 4 ) . 0.5cm=6.5 cm -6.75 cm 6.75cm=6.75 cm -0.25 cm -0.25 cm * macho 1998-blg-35 : * although ruling out a large class of high - mass planets orbiting the lens of macho 1998-blg-35 ( 4.1 ) , the mps and moa groups ( rhie et al . 2000 ) noticed a weak anomaly near the peak of this high amplification event that they interpreted as intriguing evidence of a low - mass companion with @xmath29 . the signal fell below the formal mps / moa detection limit . planet team data for this event did not confirm this detection ; the planet light curve was consistent with an isolated point lens ( albrow et al . current microlensing planet searches have appreciable efficiency for the detection of companions with mass ratio @xmath30 , ie . , planets with masses of order @xmath31 . the lack of detected perturbations consistent with planets in this mass range allows constraints to be placed on the abundance of jovian analogs around typical stars ( ie , lenses ) in the milky way . the first published exclusion diagram ( fig . 5 ) for companions in an individual lensing system was presented by the mps / moa collaborations for macho 98-blg-35 ( rhie et al . 2000 ) . due to the high amplification of this event , the source would have passed very near any ( central ) caustic structure due to massive companions . since no anomaly consistent with jovian - mass companions was seen , exclusion contours could be derived as a function of @xmath11 and @xmath12 for this lensing system ( fig . the planet collaboration performed a similar analysis for another high amplification event , ogle 1998-bul-14 ( albrow et al . 1999b ) . when converted to parameters appropriate to a solar - type lens in the bulge and averaged over all orbital inclinations , the exclusion contours for jovian and super - jovian planets in the ogle 1998-bul-14 overlap the region of parameter space inhabited by current planet detections by the radial velocity technique ( fig . 5 ) . for the most part , however , microlensing is sensitive planets at larger orbital radii ( 1" +"the value of the circular orbital velocity at the sun s radius in the milky way is of considerable interest in galactic and extragalactic astrophysics . it is necessary to correct observed velocities of stars and galaxies for the motion of the sun around the galactic center . the circular velocity also plays a large role in characterizing the mass of the milky way in comparison with other spiral galaxies , placing it in a cosmological context , e.g. , when asking whether the milky way matches the tully fisher relation ( e.g. * ? ? ? * ; * ? ? ? * ) or what is its total star formation efficiency ( e.g. , * ? ? ? * ; * ? ? ? the circular velocity at the sun s radius has typically been established by measuring the sun s motion with respect to an object assumed to be at rest with respect to the galaxy ( sgr a@xmath2 : @xcite ; the stellar halo : @xcite ) , or by using a tracer population assumed to be angle - mixed , i.e. , having a uniform distribution of orbital phases , in a steady - state galaxy ( e.g. , * ? ? ? recently , a competitive estimate has been obtained by a different approach using a narrow stellar stream that is assumed to be tracing out an orbit @xcite . in this paper we re - analyze a new population of tracers of milky way dynamics : masers associated with star - forming regions ( * ? ? ? * r09 ) . using the very long baseline array ( vlba ) and the japanese vlbi exploration of radio astronomy ( vera ) , precise measurements of the parallaxes , proper motions , and line - of - sight velocities of masers have been made ( see r09 and references therein ) . these give accurate full six - dimensional phase - space information in the disk of the galaxy . since these massive star - forming regions are associated with spiral arms and their shocks , the dense molecular gas regions that produce masers do not lie on exactly circular orbits , nor are they detected at random points on their orbits . therefore , modeling approaches that assume a uniform distribution of the orbital phases of the tracer population can not give accurate determinations of the dynamics of the galaxy . for the existing maser data , the problem of non - random orbital phases is exacerbated by the sparseness of the sample only 18 masers with accurate six - dimensional phase - space information have been measured at present and by the spatially non - uniform selection of the current sample of masers . in this paper , we perform an analysis of the r09 maser data that deals simultaneously with the sparseness of the data , the spatial non - uniformity of the sampling , the non - random orbital phase distribution of masers , and prior information . assuming a flat rotation curve , @xmath7 constant , we use a simple model for the distribution of the maser velocities with respect to their local standards of rest : a mean offset from circular rotation @xmath8 and a general velocity dispersion tensor fixed in galactocentric cylindrical coordinates . in the probabilistic inference framework that we use described in @xmath9 [ sec : data]we can marginalize over the uncertainty in the inferred distribution function of masers , take prior information on the dynamics of the galaxy into account , use the sparse data set as efficiently as possible , and then ask what information on @xmath5 the maser data provide . our results presented in @xmath9 [ sec : results ] show that allowing for a finite velocity dispersion tensor in the model for the maser peculiar - velocity distribution function leads to lower values of @xmath5 than the large value reported in r09 , in whose analysis the maser velocity dispersion was ( implicitly ) assumed to vanish . adding in informative prior information about @xmath10 , inferred from monitoring stellar orbits around the black hole at the center of the galaxy @xcite and from the measurement of the proper motion of sgr a@xmath2 @xcite , we find that the best circular velocity estimate is @xmath3 km s@xmath1 , but that the current maser data set adds little information . we discuss this measurement and its limitations in the light of other recent determinations in @xmath9 [ sec : discussion ] . throughout the analysis that follows we use the standard cylindrical galactocentric coordinate frame @xmath11 , with associated unit vectors ( @xmath12 ) pointing toward the galactic center , in the direction of galactic rotation , and toward the north galactic pole , respectively . the data we analyze here consist of the galactic coordinates , parallaxes , proper motions , and line - of - sight velocities of 18 galactic masers , as well as their associated uncertainties , presented in table 1 of @xcite . following r09 , we add a 7 km s@xmath1 uncertainty in quadrature to the uncertainties in the velocity components of each maser to describe the random , virial motion in the massive star - forming region of the individual massive star associated with each maser . the line - of - sight velocities have been ` corrected ' by the radio observatories pipelines for the motion of the sun with respect to the local standard of rest ( lsr ) . this correction assumed a value of 20 km s@xmath1 toward @xmath13(b1900.0)= 18@xmath14 , @xmath15(b1900.0)=@xmath16 for the solar motion @xmath17 , although it is unclear whether all observatories used this standard value ( m. reid , private communication ) . we undo this correction , after which the currently accepted correction for @xmath17 can be applied ; however , as we will describe below , this correction will become part of our model and , therefore , the correction for @xmath17 does not occur during the preprocessing of the data . beyond these two corrections , no processing of the @xcite data has been done . parameter estimation in a probabilistic framework _ by necessity _ uses bayes s theorem to connect the probability of the model parameters given the data @xmath18 to the probability of the observed data given the model parameters ( e.g. , * ? ? ? this requires us ( 1 ) to identify all the parameters that need to be included in the model , ( 2 ) to write down the likelihood of the model and ( 3 ) to specify suitable priors for the model parameters . although the model space needs to be exhaustive , the probabilistic framework allows integration over uninteresting parameters . here we put forward a model for the maser kinematics in which the maser velocities are most easily modeled in galactocentric cylindrical coordinates . in order to go from the raw data described in @xmath9 [ sec : datasub ] to the velocity of each maser in galactocentric coordinates , we need to ( 1 ) correct the measured velocity for @xmath17 , ( 2 ) add to this velocity the circular velocity around the galactic center at the sun s radius , and ( 3 ) project this velocity onto the galactocentric coordinate frame ( the details of this transformation are described in the appendix of r09 ) . since the latter procedure includes geometrical projection factors depending on the distance @xmath10 of the sun from the galactic center , the model parameters need to include the three components of @xmath17 , @xmath10 , and @xmath5 . however , it is more practical to assume that sgr a@xmath2 is at rest with respect to the galaxy , and to use the proper motion @xmath19 of sgr a@xmath2 @xcite as a model parameter instead of the circular velocity , as @xmath19 is very tightly constrained independently of @xmath10 . these two parameters are related simply by multiplying the proper motion of sgr a@xmath2 by @xmath10 and correcting this for @xmath17 . the circular velocity then becomes a parameter derived from the actual model parameters , which is no problem in the probabilistic framework , where it is easy to propagate uncertainties correctly . as we will assume that the rotation curve is flat , no extra parameters to model the shape of the rotation curve need to be included in the model . if we had uniformly sampled the phase space of masers and full prior knowledge of the phase - space distribution function of massive star - forming regions , this would uniquely specify the likelihood of the model , as the probability of the measured position and velocity of each maser would simply be given by the distribution function of the masers convolved with the observational uncertainty . however , we have neither a uniform sample of masers nor much prior information about the distribution of masers throughout the galaxy . to account for the spatial non - uniformity of the sample we will focus on the distribution of velocities at the actually observed position of the maser , instead of using the full six - dimensional phase - space distribution function to evaluate the likelihood . for this distribution we will assume that it only depends on the peculiar velocity @xmath20 of the maser in galactocentric cylindrical coordinates . we will assume that this distribution of peculiar velocities is given by a gaussian distribution characterized by a mean , a 3-vector @xmath21 , the offset from circular motion , and a general velocity dispersion tensor , a symmetric @xmath22 tensor @xmath23 with six free parameters . since there have been no measurements of either the mean offset from circular motion of the masers or their velocity dispersion , we will use flat priors on these quantities . this model is essentially a generalization of the model used in @xcite where the velocity dispersion tensor was assumed to vanish ; this was a poor assumption as we will show below . the probability of a single maser is thus given by @xmath24|{\ensuremath{\overline{{{\boldsymbol{{\mathbf{v}}}}}}}},{\ensuremath{\mbox{\boldmath$\sigma$}}}\right)\otimes p({{\boldsymbol{{\mathbf{x}}}}},{{\boldsymbol{{\mathbf{v}}}}}|{{\boldsymbol{{\mathbf{x}}}}_i}^{\mathrm{obs}},{{\boldsymbol{{\mathbf{v}}}}_i}^{\mathrm{obs}})\,,\ ] ] where we have suppressed the dependence of @xmath25 on the dynamical parameters , and where the convolution with the observational uncertainty distribution @xmath26 has been included . the posterior distribution for the 14 model parameters is then given by @xmath27 where the first factor on the right - hand side is the prior probability distribution for these parameters and the product is the likelihood . we have used flat priors for @xmath21 and @xmath23 , which is why they do not appear explicitly . for @xmath19 we use a gaussian prior with a mean of 30.24 km s@xmath1 kpc @xmath1 and a standard deviation of 0.12 km s@xmath1 kpc@xmath1 @xcite . for @xmath10 we combine current state - of - the - art determinations of @xmath10 from galactic center orbits with equal weights : 8.0 @xmath28 0.6 kpc found by @xcite and 8.33 @xmath28 0.35 kpc found by @xcite . this prior is shown as the gray curve in [ fig : ro ] . for @xmath17 we use the value and uncertainties obtained from _ hipparcos _ data @xcite , although the clumpiness of the velocity distribution of nearby stars @xcite implies an uncertainty more on the order of a few km s@xmath1 in the value of @xmath17 ( j. bovy & d. w. hogg , in preparation ) . the implied prior for the circular velocity is shown as the thick gray curve in [ fig : thetao ] . to investigate how informative the maser measurements are about @xmath5 and @xmath10 , we will consider the effect of dropping ( some combination of ) these priors below . the framework described here can easily be generalized to more general descriptions of the distribution of the peculiar velocities of the masers" +"as has been pointed out previously by harney @xcite , finite vector analyzing powers @xmath3 arise in reaction processes only , if at least two different partial waves interfere . hence in case of an isolated @xmath4-channel resonance , which is formed by a single partial wave matching to spin and parity of the resonance , the analyzing powers in the resonance region will be vanishing small , if there is no sizeable interfering background from other reaction processes . recently , in the reaction @xmath5 a pronounced , narrow resonance structure corresponding to a mass of 2.38 gev and a width of about 70 mev has been observed in the total cross section near @xmath6 2.4 gev ( @xmath7 = 1.2 gev ) @xcite . its quantum numbers have been determined to be @xmath8 @xcite . the @xmath4-channel character of this resonance has been established recently by polarized @xmath9 scattering . inclusion of these new data into the said partial - wave analysis produces a pole in the coupled @xmath10-@xmath11 partial - waves at ( @xmath12 ) mev @xcite . since then this resonance is denoted by @xmath1 . the @xmath13 channel is the @xmath2 decay channel with the smallest amount of background from other reaction processes @xcite . nevertheless it has sizeable contributions from @xmath14-channel @xmath15 and @xmath16 excitations . both of them are very well known from the study of @xmath17-induced two - pion production @xcite . hence , due to the finite background amplitudes we may expect sizeable analyzing powers @xmath18 in the region of the @xmath2 resonance . also , they are expected to increase with increasing energy due to the increasing contribution of higher partial waves . since @xmath18 is composed only of interference terms of partial waves , it is sensitive to even small partial - wave contributions and therefore qualifies as a sensitive spectroscopic tool for the investigation of the @xmath2 resonance region . in order to investigate this issue in a comprehensive way we measured the basic _ isoscalar _ double - pionic fusion process @xmath0 exclusively and kinematically complete . the experiment was carried out with the wasa detector setup @xcite at cosy via the reaction @xmath19 using a polarized deuteron beam at the lab energy @xmath20 = 2.27 gev . since due to fermi motion of the nucleons in the beam deuteron the quasifree reaction proceeds via a range of effective collision energies , we cover the energy region 2.30 gev @xmath21 2.47 gev . the emerging deuterons as well as the fast , quasifree scattered spectator protons were detected in the forward detector of wasa and identified by the @xmath22e - e technique . gammas from the @xmath23 decay were detected in the central detector . that way the full four - momenta were determined for all particles of an event . since the reaction was measured kinematically overdetermined , kinematic fits with 6 overconstraints could be performed for each event . from the full kinematic information available for each event also the relevant total energy in the @xmath24 system could be reconstructed for each event individually . by just having a different trigger these measurements have been obtained in parallel to the ones for @xmath24 elastic scattering @xcite . the trigger used for the detection of the @xmath13 events required at least one hit in the forward detector and three neutral hits in the central detector . for details of the experiment , in particular also with respect to the determination of the beam polarization , checks for quasifree scattering and the procedure for deriving @xmath18 from the data , see ref . @xcite . for convenience the absolute normalization of the cross section data has been obtained just by relative normalization to the datum of the total cross section at @xmath25 = 2.38 gev published in ref . = 2.34 gev ( top ) , 2.38 gev ( middle ) and 2.42 gev ( bottom ) . the solid circles denote the experimental results of this work . the dotted lines give a 2-parameter fit to the data by use of eq . the solid lines show the fit results , if a @xmath26 term is added and the dashed lines a fit , if also a @xmath27 term is included , see eq . ( 2 ) . , title=""fig : "" ] = 2.34 gev ( top ) , 2.38 gev ( middle ) and 2.42 gev ( bottom ) . the solid circles denote the experimental results of this work . the dotted lines give a 2-parameter fit to the data by use of eq . the solid lines show the fit results , if a @xmath26 term is added and the dashed lines a fit , if also a @xmath27 term is included , see eq . ( 2 ) . , title=""fig : "" ] = 2.34 gev ( top ) , 2.38 gev ( middle ) and 2.42 gev ( bottom ) . the solid circles denote the experimental results of this work . the dotted lines give a 2-parameter fit to the data by use of eq . the solid lines show the fit results , if a @xmath26 term is added and the dashed lines a fit , if also a @xmath27 term is included , see eq . ( 2 ) . , title=""fig : "" ] scattering angle in the cm system . fits are shown for the 2- and 3-parameter options . , title=""fig : "" ] scattering angle in the cm system . fits are shown for the 2- and 3-parameter options . , title=""fig : "" ] scattering angle in the cm system . fits are shown for the 2- and 3-parameter options . , title=""fig : "" ] scattering angle in the cm system . , title=""fig : "" ] scattering angle in the cm system . , title=""fig : "" ] scattering angle in the cm system . , title=""fig : "" ] the analyzing powers @xmath18 extracted from this experiment are shown in figs . 1 - 3 in dependence of the center - of - mass ( c.m . ) scattering angles @xmath28 , @xmath29 and @xmath30 of emitted deuteron , @xmath23 and @xmath22 particles , respectively . the intermediate @xmath22 from the process @xmath31 has been reconstructed from the 4-momenta of its decay products @xmath23 and nucleon the latter by taking half the deuteron momentum , thereby neglecting the small correction due to fermi motion of the nucleons inside the deuteron . since the dalitz plot displayed in fig . 4 of ref . @xcite exhibits a @xmath22 excitation band sitting upon no substantial background , no cut on the @xmath22 mass appears to be necessary . the data have been binned into three energy bins as displayed in figs . 1 - 3 : @xmath25 = 2.30 - 2.35 gev with center of gravity at 2.34 gev , @xmath25 = 2.36 - 2.40 gev with centroid at 2.38 gev and @xmath25 = 2.41 - 2.47 gev centered at 2.42 gev . the middle one corresponds to the maximum cross section of the @xmath2 resonance , whereas the other two roughly correspond to its half maximum . at the lowest energy bin the analyzing power in dependence of the deuteron scattering angle is still small . however , substantial @xmath18 values are obtained at the two higher energy bins . in the following the description of the data is based on the formalism outlined in ref . @xcite . based on that work @xmath18 angular dependencies have been derived in ref . @xcite , which can be theoretically expected in @xmath17 induced , _ i.e. _ purely isovector two - pion production , if there are only relative @xmath4- and @xmath32- waves in the final channel : @xmath33 with the parameters a and b to be adjusted to the data . for the @xmath5 reaction the situation changes insofar as we deal here with a purely isoscalar channel . in addition @xmath34-waves have to be included , in order to allow the formation of @xmath1 . for simplicity we assume the @xmath35 system to be in relative @xmath4-wave . at least for the resonance formation this is well justified @xcite . applying the formalism presented in ref . @xcite to this situation @xcite we again end up with a formal description in terms of @xmath36 : @xmath37 due to the involvement of @xmath34-waves the sum runs now over 4 terms ( j = 1 , ... 4 ) from @xmath38 until @xmath39 . the weighting parameters @xmath40 ... @xmath41 to be adjusted to the data have now the following meaning : @xmath42 here @xmath43 denotes the momentum of the @xmath35 system relative to the deuteron and the strength parameters @xmath44 and @xmath45 stand for the transitions : @xmath46 where on the left - hand side the @xmath47 partial wave in the entrance channel is given by its spectroscopic nomenclature . the right - hand side denotes the partial wave of the deuteron together with its angular momentum relative to the @xmath35 system . the interference of these partial waves , which are abbreviated by @xmath4 , @xmath32 and @xmath34 , is indicated in brackets at the right - hand side of eq . note that in the entrance channel @xmath48 and @xmath49 as well as @xmath10 and @xmath11 are coupled partial waves . in principle , also the @xmath48 - @xmath49 coupled waves contribute to the @xmath50 configurations . however , for simplicity we omit this contribution , since it is expected to be small compared to the contribution of the @xmath2 resonance . in order to see how many terms in the expansion ( 3 ) are needed by the data , we performed fits with 2 , 3 and 4 terms as given in tables 1 - 3 and shown in figs . 1 - 3 by the dotted , solid and dashed lines , respectively . for the analyzing power in dependence of the deuteron scattering angle the latter two are very close together in the angular regions , which are well covered by data . this means that a 3-parameter fit is already appropriate for a proper description of the data . for the lowest energy , where the data are very close to zero throughout the measured angular range , already the 2-parameter fit is sufficient with providng a @xmath51 per degree of freedom ( ndf ) of unity the fact that already a 3-parameter fit is sufficient for an appropriate description of the data in the resonance region is in accordance with the new said solution , which exhibits the @xmath2 pole predominantly in the @xmath10 wave and only very weakly in @xmath11 . hence @xmath45 got to be small and @xmath41 negligible compared to @xmath52 . in fact , the resonance term @xmath52 is highly demanded by the data , as the comparison between dashed and dotted curves demonstrates . since @xmath52 enters also in @xmath40 , the latter is also requested by the fit , whereas @xmath53 turns out compatible with zero within uncertainties at resonance . therefore , the leading contribution to the analyzing power of the @xmath28 angular distribution turns out to be the interference of the resonant @xmath34 wave with the non - resonant @xmath32 wave . .results of the fits to the analyzing power data in dependence of the deuteron scattering angle by use of eq . ( 2 ) with two ( 2p ) , three ( 3p ) and four ( 4p ) terms . [ cols= "" < , < , < , < , < , < , < , < "" , ] + the @xmath43-dependence of the parameters makes it plausible that the analyzing power is smallest at the lowest energy @xmath25 = 2.34 gev and tends to level off as soon as the resonance maximum is reached . at" +"one of the most fundamental aspects of the stellar content of galaxies is the distribution by mass of newly formed stars , the initial mass function ( imf ) . evidence supporting or restricting variations in the imf for very low mass stars is of profound importance for an understanding of the mass content of the universe , the dynamical evolution of open and globular clusters , the chemical evolution of galaxies , and the physics of star formation . while developments in star formation theory ( e.g. shu 1991 ) and observations ( e.g. evans 1991 ) continue to increase our understanding of the complexities and processes involved in star formation , any understanding of how the imf does , or does not , depend on environment and metallicity is still elusive . for low mass stars , which are the subject of this paper , large surveys ( see reid & gilmore 1982 ; hawkins & bessell 1988 ; stobie , ishida & peacock 1989 ; bessell & stringfellow 1993 ) have provided a fairly well determined measure of the field star luminosity function near the sun . extensive modelling is required to derive the corresponding stellar initial mass function . however , there is reasonable agreement ( cf . et al . _ 1993 and tinney 1995 for recent references ) that the luminosity function shows a broad maximum near @xmath5 , while the underlying mass function ( mf ) breaks away from an approximate power - law increase below 0.5 m@xmath1 . star count surveys in the near - ir ( e.g. hu _ et al . _ 1994 ) and in the optical with hst ( bahcall _ et al . _ 1994 ; santiago , gilmore & elson 1995 ) , and most recently from the hubble deep field ( elson , santiago & gilmore 1996 ) , suggest that the field stars of the galactic thick disk and halo have a luminosity function which is not significantly distinguishable from that of the solar neighborhood down to masses near the hydrogen burning limit . this is a remarkable result , given that these stellar populations differ considerably in local density , and by a factor of forty in mean chemical abundance . field star analyses are , however , subject to many uncertainties , in particular imprecise distance determination ( kroupa _ et al . _ the derivation of an initial mass from a color and apparent magnitude of an object which may be an unresolved binary star of unknown age , distance , and metallicity remains a statistical goal , rather than a precise tool . by contrast , in clusters the primary uncertainties of differential ages , abundances and distances are removed . hence , extensive surveys of the open clusters near the sun have been undertaken ( e.g. pleiades : hambly & jameson 1991 ; hyades : reid 1993 ; praesepe : williams , rieke & stauffer 1995 ; hambly _ et al . _ such clusters are however primarily young , so that interpretation suffers from the limitation that evolutionary models for pre - main sequence stars of low mass are not yet well tested . ideally , one wants clusters older than perhaps 1 gyr , covering a wide range of metallicities . in the past year there has been a vast improvement in the quality and quantity of data on the low mass end of the stellar luminosity function ( lf ) from observations of globular clusters with the refurbished hst ( e.g. elson _ et al . _ 1995 ; de marchi & paresce 1995a , 1995b ; paresce , de marchi & romaniello 1995 ) . these four globular cluster studies have already provided good stellar lfs to @xmath6 ( @xmath2 0.2 m@xmath1 ) , and they will soon be supplemented by at least seven more hst globular cluster studies . in this paper we report deep hst observations of the lfs in two open clusters , which allow us to extend the metallicity range represented by these four globular clusters ( @xmath7 < -0.7 $ ] ) up to solar abundance . thus , for the first time we now have cluster luminosity functions extending to very low stellar masses and covering more than 2 dex in metallicity , and can therefore study the effect of metallicity on stellar luminosity functions . in this paper we search for a systematic dependence of the imf on some parameter to provide clues to the physics of star formation . we observed the open clusters ngc 2477 and ngc 2420 with hst on 1994 march 18 and 1994 may 18/19 , respectively , using the wfpc2 along with the f555w ( approximately v - band ) and f814w ( approximately i - band ) filters . our observations were taken 5.2 arc minutes sw of the cluster center ( 7:38:11.2 + 21:33:09.7 , j2000.0 ) for ngc 2420 and 2.7 arc minutes wsw of the cluster center ( 7:52:16.8 -38:35:40.1 , j2000.0 ) for ngc 2477 to avoid the brightest stars in each cluster . these fields still contain many very bright stars so we obtained the cumulative one hour exposures in each filter from nine 400s exposures in ngc 2477 and four 900s exposures in ngc 2420 . all data were acquired in the same manner and with the same filters , although the operating temperature of the ccds was @xmath8c during the march observations and @xmath9c during the may observations . the temperature change was made in order to decrease a charge - transfer efficiency ( cte ) problem which manifested itself as a position - dependent non - linearity of the wfpc2 ccds . the effect was found to be @xmath2 10% at @xmath8c and @xmath2 4% at @xmath9c ( holtzman _ et al . _ 1995b ) in a series of 40 second calibration exposures taken of a field in @xmath4 cen . elevated sky counts found in longer exposures such as ours are expected to decrease the cte problem ( holtzman _ et al . _ the lower operating temperature also resulted in far fewer ` hot pixels ' ; pixels with an elevated dark count lasting for hours or days . finally , an additional difference between our two cluster observations is that the sky level for the may data was five times higher than for the march data , owing to zodiacal light differences . the raw data were reprocessed using the iraf / stsdas software with the updated calibration frames that became available subsequent to the observations . this included the standard statistical corrections to the analogue to digital conversion , bias subtraction , dark count subtraction , flat fielding and geometric distortion correction . we also included the non - standard `` ramp correction '' for the march cte problem . the cte properties of the wfpc2 are still not entirely understood , but applying the correction reduced the significance of the cte effect to @xmath2 1% . the cte effect in the may data is expected to be @xmath10 1% because of the higher sky counts and the cooler ccds , so we did not attempt to apply a correction for these data . additionally we spent great effort trying to identify hot pixels as measured in the dark frames taken shortly before or after our observations , but were largely unsuccessful owing to the short life - times of these hot pixels . since hot pixels have counts which are independent of the filter in use , and thus have color equal to zero on the instrumental system , they appear in the same region of the color - magnitude ( cm ) diagram as the faintest white dwarfs . since the wfpc2 ccds are undersampled , hot pixels may appear like faint stars , especially two adjacent hot pixels or single hot pixels next to positive sky fluctuations . hot pixels thus decreased our limiting magnitude for white dwarfs ( von hippel _ et al . _ 1995 , hereafter paper i ) , but did not affect the limiting magnitude for the coolest main sequence stars , the subject of this paper . we performed aperture photometry using 1.5 pixel radius apertures with aperture corrections based on a detailed study of the many bright stars available in our fields . after some experimenting we did not employ point spread function ( psf ) fitting photometry as our fields were uncrowded and the psf was positionally dependent and not well characterized by our stars . unlike paper i , the photometry was directly transformed to the standard johnson - cousins vi system using the calibration from holtzman _ et al . _ ( 1995b ) . the photometry we present here is thus slightly different from that presented in paper i , but the differences are so small for the white dwarfs as not to modify the results of that study . the cm diagrams for all the stars in the fields of both our clusters , with galaxies removed , are presented in figures 1 and 2 . in order to characterize the completeness of our photometry we created synthetic stars using the tinytim hst psf generation package ( krist 1994 ) , added these stars to our data , and then tried to recover them using our standard finding and photometry procedure . the synthetic stars were created for both the f555w and f814w filters and were centered at 16 different sub - pixel positions and laid down in a grid of positions covering the whole of each ccd . this sub - pixel sampling was done since the psf locations affect the number of pixels under the psf , and thus the sky noise and read noise contributions per pixel cause the limiting magnitude to depend on the psf sub - pixel position . since this effect is based on noise changing systematically with psf position , it affects completeness , but not the measured magnitudes of objects bright enough to find . the resulting simulated noise - free stars were scaled and had noise added to them to mimic stars over a range of magnitudes . from this procedure we estimated our completeness levels , which are superimposed on figures 1 and 2 . these completeness levels lead to a limiting magnitude @xmath2 0.5 magnitudes brighter than initially expected for the refurbished hst , but this is now understood as due to the ccds leaking some charge between adjacent pixels ( holtzman _ et al . _ these estimates of completeness should be reasonably accurate for the redder stars where hot pixels are not a problem . we outline here the remaining sources of uncertainty in our photometry , although we emphasize that these are all small effects which do not affect our results . \1 ) the cte corrections are almost surely not perfect for the @xmath8c data and they have not been attempted for the @xmath9c data . the resulting uncertainties are @xmath2 1% and do not contribute to any important systematics . \2 ) the hst pipeline flats were taken at the gain=14 setting , whereas our data were taken at the gain=7 setting . the relative gains between these two settings are not identically 2.0 for all ccds . the appropriate gain ratios have been applied , but these are uncertain to @xmath2 1% each . this source of uncertainty should not cause systematic errors since all three wf ccds contain nearly equal portions of the cluster cm diagram . \3 ) the hst pipeline flats are good to a few percent , pixel - to - pixel , over most of the area of the ccds . \4 ) we applied a single aperture correction to all photometry for all wf ccds . in fact the relatively large number of bright but isolated stars in our images" +"the rationale for , capabilities of , and scientific context of the mid - infrared instrument ( miri ) on jwst are described in rieke et al . ( 2014 ; hereafter paper i ) and the overall optical , thermal , mechanical / structural electronic and control aspects of the design are summarized in wright et al . ( 2014 ; hereafter paper ii ) . this paper describes in more detail the miri medium resolution spectrometer ( mrs ) , which is an integral field unit ( ifu ) spectrometer that covers the wavelength range from 5 to 28.5 @xmath0 m at spectral resolving powers of a few thousand . the mrs consists of 4 channels that have co - aligned fields of view , simultaneously observing the wavelength ranges listed in table 1 with individually optimised ifus , collimators and gratings . section [ sec : optical ] of this paper provides a description of the optical design , including the rationale for choosing the ifu concept and its impact on how observations are carried out . section [ sec : measured ] then describes the expected on - orbit optical performance of the mrs as measured during cryogenic testing , and with a description of the procedure used to construct calibrated spectral data cubes from the raw measured images . the impact of particular characteristics of the mrs , including spectral fringing and straylight are also discussed here . an ifu based design was preferred to a long - slit design for the miri spectrometer for the following reasons . firstly , for point source observations , the need to centre the source in a narrow slit ( via a peak - up procedure ) is relaxed , simplifying and accelerating the target acquisition procedure . there is an additional benefit that there is no loss of light at the slices ( ` slit losses ' in a conventional long slit spectrometer ) . the mrs slice width is set to be less than or equal to the fwhm of the diffraction limited point spread function at the slicing mirror . an equivalent long - slit spectrometer would vignette the light outside this region , losing about 50% of the total . the amount of lost light could be reduced by making the slit wider , but doing so would in turn reduce the spatial and spectral resolution and could also decrease the signal to noise because of increased background radiation . second , from a scientific perspective , the wavelength range covered by the miri spectrometer is sufficiently broad ( a factor of nearly six ) that different emission mechanisms may dominate in different regions of the spectrum . in cases where these mechanisms do not share a common centre ( e.g. , stellar output compared with infrared re - emission in a starburst galaxy ) , a simple slit spectrograph poses a dilemma in placing the `` source '' on the slit . an ifu implements 3d spectroscopy , which solves this problem by giving accurately registered spatially resolved spectroscopy over the entire field . these considerations , combined with the wavelength coverage and resolving power requirements defined by the jwst mission science goals , and the mass , volume and electrical power limitations set by the jwst spacecraft environment , have resulted in a system with the characteristics summarised below and illustrated in block diagram form in figure 1 . as shown in the figure , the full 5 to 28.5 @xmath0 m wavelength range is divided within the spectrometer pre - optics ( spo ) into four simultaneous spectral channels @xcite , each with its own ifu @xcite and using a simple scheme of pass - band separation by dichroic filters whose design is described in hawkins et al . ( 2007 ) and wells et al . we denote the short and long wavelength limits of each channel as @xmath1 and @xmath2 . each channel serves an optimised spectrometer . this separation provides several benefits : ( 1 ) it enables the use of diffraction gratings in first order , allowing each to be used near peak efficiency around the blaze wavelength , and ( 2 ) it also allows the ifu slice widths to be tailored to the wavelength - scaled fwhm in each channel . electrical and thermal constraints limit the mrs to two 1024 x 1024 si : as detectors ( ressler et al . , 2014 , hereafter paper viii ) , resulting in the spectrometer being split into two sets of optics , each with its own detector array , one for the two short - wave channels and one for the two long - wave channels . in each case , the spectra of two wavelength channels are imaged simultaneously onto the left and right halves of a detector array . the product of spatial and spectral coverage that can be achieved in a single instantaneous exposure is ultimately set by the number of detector pixels . for the mrs , this results in a single exposure providing a spectral sub - band that covers only one third of each channel . full wavelength coverage then requires three exposures , with a pair of mechanisms being used to select the gratings and dichroics in each case . we refer to the short and long wavelength limits of each sub - band as @xmath3 and @xmath4 . this design choice allows the grating performance to be optimised over a narrow wavelength range ( @xmath4/@xmath5 @xmath61.2 ) . the gratings only have to work over 20% of the 1@xmath7 order near the blaze wavelength and the dichroics do not have to be used near the cross over between reflection and transmission . we will now step through the optical train as shown in figure 1 : the input optics and calibration ( ioc ) modules pick off the mrs fov from the jwst focal surface and pass it on to the spo . the spo spectrally splits the light into the 4 spectrometer channels and spatially reformats the rectangular fields of view into slits at the entrance of the spectrometer main optics ( smo ) . the smo comprises fixed optics that collimate the light for presentation to diffraction gratings mounted in the spo and then re - images the dispersed spectra onto the two focal plane arrays . key features of this optical system are described individually in the following subsections . the spectral and spatial coverage of the mrs is summarised in table 1 . the field of view of the mrs is adjacent to the miri imager field and picked off from the jwst focal surface using the miri pickoff mirror ( pom ) , which is common to both ( see paper ii ) . the sky and the jwst pupil are reimaged by the ioc so that there is a pupil image at the spo input and a sky image further on . a cold stop that is 5% oversized with respect to the jwst pupil is placed at the spo input pupil for straylight control . the light is directed towards the first dichroic filter via a fold mirror placed 10 mm beyond the pupil . the focal plane is formed 535 mm beyond the pupil , providing the long path length and narrow beam waist needed between the pupil and the inputs of the four integral field units ( ifus ) , for mounting a chain of dichroics to divide the light among the four spectral channels . a hole in the fold mirror , sized to be smaller than the footprint of the telescope central obscuration , acts as an aperture for the injection of light from the on - board spectrometer calibration unit ( scu ) , shown in figure 2 . the scu provides spatially and spectrally uniform blackbody illumination for flux calibration and pixel flat fielding functions , using as its light source a tungsten filament heated to a temperature of @xmath61000 k by the application of an 8 ma drive current . the filament is mounted inside a non - imaging flux concentrator that generates spatially uniform focal plane illumination at the exit port of a 25 mm diameter reflective hemisphere , ( described in glasse et al . , 2006 ) . two cadmium telluride lenses within the scu then re - image the exit port onto the ifu input focal planes . the lenses provide a pupil image that coincides with the hole in the input fold mirror . this hole is positioned to lie within the footprint of the central obscuration of the jwst primary mirror and so has no impact on the science beam . in this way , the scu can provide flood illumination of the full mrs field of view without any need for mechanisms or additional optical elements . the overall layout of the dichroic assembly is shown in figure 3 , with the input fold mirror and scu situated at the left - hand end ( but not shown ) . the three dichroics needed to divide the spectral band among the four spectrometer channels for one of the three sub - bands are indicated as d1 , d2 , and d3 in figures 1 and 3 . taking sub - band a as an example , the required reflective band for dichroic d1 is the wavelength range for sub - band a in channel 1 , while its transmission band needs to extend from the short end of sub - band a in channel 2 to the long end of sub - band a in channel 4 . the bands are listed in table 2 for all nine dichroics . in all cases , the mean reflectivity is above 0.95 and the mean transmission is above 0.74 . all of the gratings work in first diffractive order so additional blocking is needed to reject second and higher orders . because the dichroics work in series it is possible to use the combined blocking of dichroics 1 and 2 to remove the need for blocking filters in channels 3 and 4 . for channels 1 and 2 , dedicated blocking is provided by the fixed filters shown as bf1 and bf2 in figure 3 , with light traps lt1 and lt2 absorbing unwanted reflections . the path length required to reach the input of channel 4 is greater than the 535 mm discussed above , so the light transmitted by the final dichroic is re - imaged via an intermediate focal plane to the entrance of the channel 4 ifu . the 21 mm diameter dichroic filters are mounted on two wheels . first is the nine - sided wheel a containing the three channel 1 dichroic filters and three flat mirrors to direct the light towards channel 1 . the second , six - sided wheel , contains the six dichroics needed to divert the light into channels 2 and 3 . each dichroic filter is mounted onto a diamond machined facet on the wheel that provides the required alignment accuracy and reduces the magnitude of any print - through of surface form errors from the wheel to the filter substrate . the filters are held in place with a spring loaded bezel with a clear aperture of 17 mm compared with the coated area of 17.4 mm . the bezel prevents light from reaching the uncoated area of the filter , which might result in un - filtered light entering the optical path . the blocking filters are mounted directly to the spo chassis with a stand and bezel , similar to the mounting arrangement for the wheels . the mechanisms that carry the dichroic wheels also carry the corresponding wheels with diffraction gratings for each sub - band ( three per channel ) , as discussed in section 2.4 . by arranging for the" +"linear wave functions in quantum chemistry are fundamentally limited by their inability to compactly express wave functions in strongly correlated regimes , a difficulty that arises directly from the factorial growth of hilbert space in the quantum many - body problem . in practice , therefore , the field of quantum chemistry has long pursued sophisticated nonlinear forms for its approximate wave function ansatzes . @xcite a key challenge arises in this pursuit due to the difficulty of constructing an ansatz that is simultaneously size - consistent ( giving the same energy for independent systems when treated together or individually ) and variational ( giving an upper bound to the true energy ) while maintaining a cost that scales polynomially with system size . recently , wave function stenciling , wich is a generalization of gutzwiller s approach @xcite in which a nonlinear correlation factor removes unsuitable terms from an overabundant fermionic expansion , has been shown to achieve these three properties , @xcite and so appears to be a promising paradigm for future ansatz design . while the jastrow antisymmetric geminal power ( jagp ) in hilbert space is characteristic of this approach and has proven effective at capturing strong correlation during bond dissociations , @xcite it is much less effective for capturing the full range of dynamic correlation effects . one way to understand this difficulty is to consider that its number - operator - based jastrow factor , which is central to its stenciling strategy , @xcite can also be written as a very limited coupled cluster doubles operator . @xcite although sufficient for stenciling , this incomplete reproduction of the doubles operator only partially recovers dynamic correlation . in short , the hilbert space jastrow factor is effective at making large changes to the wave function through stenciling , but much less so at making the multitude of small changes demanded by dynamic correlation . in contrast , more traditional jastrow factors in real space , @xcite especially when working in tandem with diffusion monte carlo ( dmc ) , @xcite are renowned for their ability to capture dynamic correlation . indeed , this pairing has been employed as a reliable substitute for the `` gold standard '' coupled cluster with singles , doubles , and perturbative - triples ( ccsd(t ) ) @xcite in cases where the latter s higher cost scaling makes it untenable . @xcite this dichotomy between jastrow factors strengths in real space and hilbert space raises the natural question : what is preventing the development of a jastrow factor that can deliver both the large changes required for stenciling and the small changes for dynamic correlation ? further : can these obstacles be overcome in a way that maintains both low - order polynomial scaling as well as suitability for use as as a dmc guiding function in strongly correlated regimes , where the best current option is to rely on a factorial - cost determinantal expansion ? in this paper , we will present a real space formulation that answers these questions in the affirmative , explain why previous real space jastrows were not able to live up to this ideal , demonstrate that jastrow - based stenciling can be effective even when the stenciled wave function is a single slater determinant , and offer some thoughts on the requirements that should be satisfied in future by a general - purpose stenciling jastrow . the essential challenge to performing stenciling in real space is that any attempt to delete large portions of the wave function using a multiplicative jastrow factor will require its functional form to contain a high degree of curvature . such curvature is necessary , as any smooth function that asymptotes to a constant value at infinite distance ( as a jastrow factor should ) and contains little curvature will be similar to a constant , and multiplication by this nearly - constant function will not produce large changes in the wave function . unless the large curvature needed for stenciling can be hidden in some way , its tendency to raise the kinetic energy will lead the variational principle to eschew jastrow - based deletion of undesirable configurations , even in cases where the functional form could accommodate it . to address this challenge , we present a new form of four - body jastrow factor that is better - suited to hiding its curvature in regions of low wave function value ( where it will not affect kinetic energy ) and to counting electrons within local regions of space ( the mechanism by which hilbert space jastrows achieve stenciling ) . combined with traditional two - body jastrows , a slater determinant , and diffusion monte carlo , these real space number counting jastrow factors allow for an effective description of both static and dynamic correlation within a structure whose complexity is explicitly polynomial . let us begin by reviewing hilbert space jastrow factors ( hsjfs ) , which may be written in terms of a matrix @xmath0 and the second quantized number operators @xmath1 within an orthonormal ( and typically local ) one particle basis , @xmath2 note that these can be thought of as four - body e - e - n - n jastrow factors , as the indices @xmath3 and @xmath4 run over orbitals that are localized at or near the nuclei while the results of operating with the number operators tell us about the positions of up to two different electrons . as number operators are idempotent and overall constant factors irrelevant , @xmath0 can be chosen such that the hsjf contains any number of gaussian factors @xmath5 for use in wave function stenciling . application of one of these factors to a fermionic wave function effectively reweights each configuration in that wave function s expansion within this particular orbital basis according to a gaussian distribution in the total occupancy of an orbital subset @xmath6 . provided that the `` projection strength '' @xmath7 is sufficiently large , such a gaussian factor acts as a stencil , removing any configuration in which the set of orbitals @xmath6 contains an electron count differing from @xmath8 . given two or more molecular fragments , this effect can be used to eliminate any configurations in which a fragment possesses an unphysical charge ( an `` ionic configuration '' ) , which turns out to be sufficient for restoring size consistency to a geminal power @xcite . crucially , this factor does nothing to components of the wave function which do not deviate from the prescribed pattern of subsystem electron counts , thus preventing the hsjf from raising the kinetic energy of configurations that survive the stencil . unfortunately , a direct translation of the hsjf into real space is problematic for qmc methods due to the nonlocal nature of a number operator s real space form , @xmath9 efficient stochastic interrogations of a wave function in real space hinge on the ability to evaluate local wave function values @xmath10 , which is complicated by the number operators nonlocality . instead , we will seek a local function @xmath11 , associated with a region @xmath6 , enclosed within a jastrow factor of similar gaussian form @xmath12 that permits efficient local evaluation and , thanks to the sum over all the electron positions @xmath13 , maintains the bosonic symmetry required by the jastrow factor to keep the overall wave function correctly antisymmetric . in order to mimic the effects of a hsjf , we therefore desire that each real space gaussian component approximate the effects of its hilbert space counterpart as closely as possible at any sampled position of the electrons ; thus we want @xmath14 where @xmath15 is the fermionic wave function that is to undergo stenciling . when basis orbitals in @xmath6 are spatially separated from others in the system an ideal that is often approached in the localized physics of strong correlation it is sufficient to choose @xmath11 as a step function : @xmath16 in which @xmath17 is a region exclusively supporting the orbitals in @xmath6 . to preserve smooth wave function derivatives and allow for a gradual approach to step like behavior in cases where orbital subsets are partially overlapping in space , we relax the step discontinuity at the boundaries of @xmath17 by employing an analytical approximation to the heaviside function ( see section [ sec::ncjf_form ] ) . so long as the smoothed form of q rapidly approaches 0 as one moves away from the boundary of @xmath17 , the jastrow factor of eq . ( [ eqn : gauss_with_c ] ) retains the ability to precisely control the electron count on a subsystem that is spatially well - separated from other subsystems , as there is in this case ample room in between for the 1-to-0 switch to occur . thus , as with a hsjf , the real space form presented here can fully eliminate ionic terms between well - separated subsystems , allowing it to restore exact size consistency to geminal powers and to aid in the repair of restricted slater determinants . the key question now becomes whether we can construct functional forms for @xmath11 that permit useful demarcations of spatial regions while also ensuring that the curvature they introduce can be hidden in regions where its contribution to the kinetic energy , through the term @xmath18 is mitigated by small local wave function amplitudes @xmath19 . this is of course trivial when demarcating a region around a well - separated fragment , but becomes less so during dissociation events , where partial stenciling becomes beneficial long before the well - separated limit is reached . before detailing our proposed form for a stenciling - friendly 4-body jastrow factor , it is instructive to consider why existing 4-body forms are ill - suited for this task . begin by considering a previously used form @xcite for 4-body jastrows that closely mirrors that of a hsjf : @xmath20 by diagonalizing @xmath0 , choosing @xmath21 appropriately , and ignoring changes to wave function normalization , one may convert this jastrow into a product of gaussians , @xmath22 in which @xmath23 is the unitary matrix that diagonalizes @xmath0 . written this way , we may immediately identify the linear combination @xmath24 as one possible form for the counting function @xmath11 discussed in the previous section . we may evaluate the suitability of 4-body jastrows of the type given in eq . ( [ eqn:4body_form ] ) for use in hsjf - style stenciling by asking how easily these linear combinations can approximate a step function over a given region , and how much control they have over their curvature . by considering the task of controlling the electron count on a single atom well - separated from the remainder of whatever system is being modeled , the above analysis makes plain that the two common forms for the basis functions @xmath25 , atom - centered gaussians @xcite and symmetric polynomials @xcite , are not effective for wave function stenciling in hilbert space . in the same way that one requires many fourier components to converge to a square wave , small gaussian expansions or low - order polynomial expansions are unable to faithfully approximate the switching behavior required for our jastrow basis functions . indeed , gaussian functional forms contain significant curvature at and about the atom s center where the wave function is large in magnitude , and thus can not engage in the curvature hiding necessary to avoid a rise in kinetic energy when @xmath26 is large , i.e. in the strong stenciling regime . although it is true that in the infinite basis set limit , a complete set of functions ( such as the gaussian spherical harmonics ) can represent any smooth function , they will converge to the nearly steplike behavior required by @xmath11 only very slowly and so will retain appreciable curvature" +"the direct and precise measurement of the self - coupling between the electroweak gauge bosons in @xmath2-pair production will be a crucial step in testing the standard model of electroweak interactions and searching for physics beyond it . it will form an important part of the physics programme at lep2 and at a planned linear @xmath3-collider ( lc ) . as is well known there are three diagrams at tree level that contribute to the amplitude of @xmath4 in the standard model , one with @xmath5-channel neutrino exchange and the other two with a @xmath6 or @xmath7 in the @xmath8-channel , involving the vertices @xmath1 and @xmath0 . one can parametrise the corresponding vertex functions in order to quantify the couplings and to compare them with their form in the standard model . in the most general form respecting lorentz covariance each vertex involves seven complex form factors @xcite , three of which give couplings that violate @xmath9 symmetry . without further physical assumptions one is thus left with 28 real parameters whose simultaneous extraction in one experiment looks quite hopeless . given the limited event statistics expected at both lep2 and the lc one will only obtain meaningful errors on a reduced number of coupling parameters at one time . this may be achieved by imposing certain constraints on the full set of coupling constants ; various suggestions for such constraints based on symmetry considerations have been made in the literature @xcite . one must however keep in mind that experimental values or bounds on couplings that have been obtained with particular constraints can not be converted into results without constraints or with different ones ; the information lost by assuming relations between couplings can not be retrieved . although imposing such constraints is certainly legitimate and can be useful we stress that a data analysis with independent couplings will be valuable , both from the point of view of model independence and the capability to compare results of different experiments . we remark that of course one can also give ( reasonably small ) errors on _ single or few _ couplings in a multi - parameter analysis . in this paper we propose a parametrisation of the couplings which is well adapted to this end , the statistical errors on the different measured parameters being approximately uncorrelated . we will work in the framework of optimal observables , a way to extract unknown coupling parameters introduced for the case of one parameter in @xcite that has since been used for various reactions @xcite . general aspects of this method , in particular its extension to an arbitrary number of parameters , as well as its application to @xmath10 production were discussed in @xcite . in this paper we investigate again the reaction @xmath11 . we concentrate here on the decay channels , where one @xmath2 decays hadronically and the other into an electron or muon and its neutrino . calculated with the born level cross section of the standard model the statistics of these channels is about 3000 events for a collision energy of @xmath12 and @xmath13 integrated luminosity , which are typical planned lep2 parameters , and about 22000 events with @xmath14 at @xmath15 , which might be achieved at the lc . a complementary source of information is the integrated cross section , which is a quadratic function of the triple gauge couplings . the combination of information from the total event rate and from observables that make use of the detailed distribution in the final state has for example been used in @xcite , where @xmath9 violation in the decay @xmath16 was investigated . in sec . [ sec : method ] of this paper we will further develop some aspects of the method of optimal observables , in particular we will show how to apply it without the linear approximation in the coupling parameters that was used in @xcite . in sec . [ sec : diagon ] we then propose a parametrisation of the couplings that simultaneously diagonalises certain matrices connected with our observables and with the integrated cross section . these parameters achieve two goals : their quadratic contribution to the total cross section is a simple sum of squares and the covariance matrix of the corresponding optimal observables is diagonal . the methods which we use for this purpose are borrowed from the theory of small oscillations of a system with @xmath17 degrees of freedom ( cf . e.g. @xcite ) . our parameters correspond to `` normal coordinates '' and their use in an experimental analysis should in our view present several advantages . we give some numerical examples for @xmath2-pair production at lep2 and the lc in sec . [ sec : numeric ] and make some further remarks on how our proposal might be implemented in practice in sec . [ sec : practice ] . the last section of this paper gives a summary of our main points . the method of optimal observables has previously been presented in the approximation that the couplings to be extracted are sufficiently small to allow for a leading order taylor expansion of various expressions . here we show how to use it beyond this approximation . let us denote by @xmath18 the real and imaginary parts of the @xmath1 and @xmath0 form factors minus their values in the standard model at tree level . as the amplitude of our process is linear in these couplings we can write the differential cross section as @xmath19 where @xmath20 is a positive semidefinite symmetric matrix . @xmath21 collectively denotes the set of measured phase space variables . the integrated cross section is @xmath22 with the standard model cross section @xmath23 and coefficients @xmath24 the idea of using integrated observables is to define suitable functions @xmath25 of the phase space variables and to extract the unknown couplings from their measured mean values @xmath26 . let us give the details . from ( [ diffxsection ] ) and ( [ intxsection ] ) we obtain the expectation value @xmath27 $ ] of @xmath28 as @xmath29 - e_0[{{\cal o}}_i ] = \frac{\displaystyle \sum_{j } c_{ij } \ , g_j + \sum_{jk } q_{ijk } \ , g_j g_k}{\displaystyle 1 + \sum_{j } { \hat{\sigma}_{1,j } } \ , g_j + \sum_{jk } { \hat{\sigma}_{2,jk } } \ , g_j g_k}\ ] ] with the standard model expectation value @xmath30 = ( \int d\phi \ , { { \cal o}}_i s_0 ) / \sigma_0 $ ] and coefficients @xmath31 \ , { \hat{\sigma}_{1,j } } { \hspace{6pt},}\nonumber \\ q_{ijk } & = & \frac{1}{\sigma_0 } \int d\phi \ , { { \cal o}}_i s_{2,jk } - e_0[{{\cal o}}_i ] \ , { \hat{\sigma}_{2,jk } } { \hspace{6pt}.}\end{aligned}\ ] ] we remark in passing that the coefficients in ( [ expect ] ) can be written in a compact form as @xmath32 { \hspace{6pt},}\hspace{3em } q_{ijk } { \hspace{0.4em } = \hspace{0.4em}}v_0[{{\cal o}}_i \ , , \ ; s_{2,jk } /s_0 ] { \hspace{6pt},}\nonumber \\ { \hat{\sigma}_{1,j } } & = & e_0[s_{1,j } /s_0 ] { \hspace{6pt},}\hspace{4.4em } { \hat{\sigma}_{2,jk } } { \hspace{0.4em } = \hspace{0.4em}}e_0[s_{2,jk } /s_0 ] { \hspace{6pt},}\end{aligned}\ ] ] where @xmath33 = e_0[f g ] - e_0[f ] \ , e_0[g]$ ] is the covariance of @xmath34 and @xmath35 in the standard model . note that @xmath36 is symmetric and positive definite , whereas @xmath37 as a matrix in @xmath38 and @xmath39 is symmetric but in general indefinite . an estimation of the couplings can now be obtained by solving the system ( [ expect ] ) with @xmath27 $ ] replaced by the mean values @xmath26 , @xmath40 = \frac{\displaystyle \sum_{j } c_{ij } \ , g_j + \sum_{jk } q_{ijk } \ , g_j g_k}{\displaystyle 1 + \sum_{j } { \hat{\sigma}_{1,j } } \ , g_j + \sum_{jk } { \hat{\sigma}_{2,jk } } \ , g_j g_k } { \hspace{6pt},}\ ] ] provided of course one has @xmath41 observables for @xmath41 unknown couplings . when the system ( [ mean ] ) is linearised in the @xmath18 it is easily solved by inversion of the matrix @xmath42 . one is however not constrained to do so and can instead solve the exact set of equations ( [ mean ] ) . by multiplication with the denominator it can be rearranged to a coupled set of quadratic equations in the @xmath18 and will in general have several solutions . some of these may be complex and thus ruled out , but from the information of the @xmath43 alone one can not tell which of the remaining real ones is the physical solution . we will come back to this point . the measured mean values @xmath43 are of course only equal to the @xmath27 $ ] up to systematic and statistical errors . we only consider the latter here , which are given by the covariance matrix @xmath44 of the observables @xmath28 divided by the number @xmath45 of events in the analysis . to convert the errors on the observables into errors on the extracted couplings we use the quantity @xmath46 \right ) n v({{\cal o}})^{-1 } { } _ { ij } \left ( { \bar{{{\cal o}}}}_j - e[{{\cal o}}_j ] \right ) { \hspace{6pt},}\ ] ] which depends on the @xmath18 through the @xmath27 $ ] given in ( [ expect ] ) . solving ( [ mean ] ) is tantamount to minimising @xmath47 with @xmath48 , and a confidence region on the couplings is as usual given by @xmath49 with the constant determined by the desired confidence level . there are several possible choices for the covariance matrix @xmath50 in ( [ chi ] ) . it can be 1 . determined from the measured distribution of the observables @xmath28 , 2 . calculated from the differential cross section ( [ diffxsection ] ) , taking for the @xmath18 the values extracted in the measurement , 3 . calculated for vanishing couplings @xmath18 , 4 . calculated as a function of the couplings . choices 1 . and 2 . should lead to the same results in the limit of large @xmath45 where the statistical errors on the measured @xmath44 and @xmath18 become small . comparison of the covariance matrices obtained by these two methods might indeed be helpful to rule out unphysical solutions of ( [ mean ] ) . . in turn will be a good approximation of 2 . if the couplings are small enough . we consider possibility 4 . as the least practical one , except maybe for the case of one coupling . for several couplings the expression of @xmath44 as a function of the @xmath18 involves tensors of rank up to four and is even more complicated than the one for the expectation values ( [ expect ] ) , and the inverse matrix is yet more clumsy . for this reason we will discard choice 4 . in the following . in @xcite we considered an analysis at leading order in the @xmath18 , where one uses the linearised form of ( [ mean ] ) to estimate the couplings : @xmath51 \right ) { \hspace{6pt}.}\ ] ] correspondingly the linear approximation of ( [ expect ] ) is used in the expression ( [ chi ] ) of @xmath47 which then reads @xmath52 where @xmath53 is the inverse covariance matrix of the estimated couplings @xcite . as one works to leading order in the @xmath18 one can approximate @xmath50 by its value for zero couplings , i.e. choose possibility 3 . above . the confidence regions @xmath54 for the measured couplings are then ellipsoids in the space of the @xmath18 with centre at @xmath55 . the optimal observables @xmath56 discussed in @xcite have the property that to leading order the statistical errors on the estimated couplings are the smallest possible ones that can be obtained with _" +"the standard model is greatly successful but it still has many free parameters which must be small to describe nature . while its supersymmetric extensions , e.g. , the minimal supersymmetric standard model , are attractive scenarios , small couplings are also required to explain observed facts such as the fermion mass hierarchy and mixing angles . in recent years , extra dimensions have cast a new perspective on physics beyond the standard model . one of the important aspects of extra dimensional models is that bulk fields can be localized with finite - width wave - function profiles . this fact provides us with a geometrical explanation for small numbers . that is , with a configuration where some fields are separated from each other in the extra dimensional space , the couplings among them are generally suppressed . then how and where fields are localized is an issue to be considered . from this viewpoint , extra dimensional models with a curved background are interesting because fields could be localized depending on the shape of the background geometry . one of the most famous examples of curved geometries is the randall - sundrum ( rs ) model with the ads@xmath0 warped metric @xcite . field theories of vectors , spinors , and scalars have been studied on this background @xcite-@xcite . the localization behavior of zero - mode wave functions has interesting applications to phenomenology such as the suppression of unwanted operators . for example , hierarchical forms of yukawa couplings and proton decay were studied in @xcite . the localization of kaluza - klein ( kk ) excited modes also leads to interesting phenomena . for instance , the localization of higher kk gauge bosons could realize a composite scalar ( higgs ) condensation , which induces dynamical ( electroweak ) symmetry breaking on the brane where the kk gauge bosons localize @xcite . in addition , models on more complicated backgrounds where a warp factor oscillates generate bulk fields which localize at some points in extra dimensions @xcite . this type of localization might be useful in explaining the observed phenomena . however extra dimensional theories are generally nonrenormalizable and the calculations depend on the regularization scheme that one adopts . furthermore , extra dimensional theories are constrained by symmetries of higher dimensions . for example , in the supersymmetric case , bulk theories are constrained by @xmath5 supersymmetry in five dimensions . motivated by these facts , recently a four - dimensional ( 4d ) description of extra dimensional models was proposed @xcite . with this method , the phenomena of higher dimensional models are reproduced in terms of 4d theories , and several interesting models have been proposed along this line @xcite . in this paper , we present 4d gauge theories that describe physics on 5d curved geometries . as will be discussed below , taking generic values of gauge couplings and gauge - symmetry - breaking vacuum expectation values ( vevs ) , the models provide vector , spinor , and scalar fields on curved extra dimensions . as a good and simple illustration , we compare our 4d model with the rs one . we particularly focus on the `` localization '' behaviors of mass eigenstates in `` index spaces '' of gauge groups . it will be shown that the localization profiles and the exponentially suppressed massive spectrum are certainly reproduced . in addition , our formulation gives a localization mechanism even for massless vector fields . as a phenomenological application , hierarchical yukawa matrices are derived in our approach ; that is a hierarchy without symmetries in four dimensions . the localization behavior depends on the required conditions for gauge - symmetry - breaking vevs and gauge and other couplings . if these values are determined in the underlying theories , it may be said that the physics on warped backgrounds is dynamically generated within a four - dimensional framework . we consider several possibilities to realize the conditions by utilizing , for example , strongly coupled gauge theories . thus this could provide a purely 4d dynamical approach for small numbers . we will proceed with the argument as follows . in sec . [ sec : dwd ] , we describe our 4d gauge theories , which have generic ( nonuniversal ) values of gauge - symmetry - breaking vevs and couplings . the models provide vector , spinor , and scalar fields in warped extra dimensions . it is also shown that supersymmetry multiplets in flat 4d models generate supersymmetry multiplets on warped backgrounds . in sec . [ sec : ne ] , we then numerically determine with a finite number of gauge groups that the formulation given in sec . 2 certainly reproduces various properties of bulk fields on the rs background . in addition , a phenomenological application to quark mass matrices is also given . finally , we discuss possibilities of dynamically realizing the conditions required for curved geometries in sec . [ sec : ddwd ] . we conclude the discussion in sec . [ sec : conclusion ] . the appendix is devoted to a brief review of 5d bulk fields on a rs background . following refs . @xcite , we introduce @xmath6 gauge theories with gauge couplings @xmath7 ( @xmath8 ) , and scalar fields @xmath9 [ @xmath10 which are in bifundamental representations of @xmath11 . the system is schematized by the segment diagram in fig . [ fig : links ] . the gauge invariant kinetic term of the scalars @xmath9 is written by @xmath12 where the covariant derivative is given by @xmath13 . we assume that the scalar fields @xmath9 develop vevs proportional to the unit matrix , @xmath14 , which break the gauge symmetry to a diagonal @xmath15 . from the kinetic term ( [ eq : qkin ] ) , the mass terms for the vector fields @xmath16 are obtained : @xmath17 where the @xmath18 matrix @xmath19 is defined as @xmath20 the consequence of these mass terms is that we have a massless gauge boson corresponding to the unbroken gauge symmetry , which is given by the following linear combination : @xmath21 where @xmath22 and @xmath23 is the gauge coupling of the low - energy gauge theory @xmath15 . the profile of @xmath24 is independent of the values of @xmath25 . it is found from this that the massless vector field is `` localized '' at the points with smaller gauge couplings . if the gauge couplings take a universal value @xmath26 , the massless mode @xmath27 has a constant `` wave function '' along the `` index space '' of gauge groups . as seen below , this direction labeled by @xmath28 becomes the fifth spatial dimension in the continuum limit ( @xmath29 ) . the localization behavior can easily be understood from the fact that , for smaller gauge coupling @xmath7 , the symmetry - breaking scale @xmath30 of @xmath6 becomes lower , and hence the corresponding vector field @xmath16 becomes the more dominant component in the low - energy degree of freedom @xmath27 . it is interesting to note that this vector localization mechanism ensures charge universality . suppose that there is a field in a nontrivial representation of @xmath6 only . that is , it couples only to @xmath31 with strength @xmath7 . this corresponds to a four - dimensional field confined on a brane . if there are several such fields , they generally have different values of gauge couplings . however , note that these fields couple to the massless modes @xmath24 with a _ universal _ gauge coupling @xmath23 defined above . this is because , in the presented mechanism , the vector fields are localized depending on the values of the gauge couplings . as for massless eigenstates , the mass eigenvalues and wave functions are obtained by diagonalizing the mass matrix ( [ eq : diffop ] ) . the simplest case is the universal couplings @xmath32 in this case , one obtains the mass eigenvalues of @xmath19 as @xmath33 in the limit @xmath29 with @xmath34 fixed ( the limit to continuum 5d theory ) , the eigenvalues become @xmath35 these are the same spectrum as that of the bulk gauge boson in the @xmath36 extra dimension with radius @xmath37 . with generic values of vevs @xmath25 and gauge couplings @xmath7 , the situation is rather complicated . in this case , the mass term ( [ eq : gau - mass ] ) of the vector fields becomes @xmath38(a_\mu^{i+1})^2 \nonumber \\[1 mm ] & & + \frac{1}{2}v_n^2g_n(g_{n+1}-g_n)(a_\mu^n)^2 -\frac{1}{2 } v_1 ^ 2g_1(g_2-g_1)(a_\mu^1)^2 . \label{eq : gbbm}\end{aligned}\ ] ] the first term becomes the kinetic energy transverse to the four dimensions in the continuum limit . on the other hand , the second and third terms are bulk and brane mass terms , respectively . it should be noted that these mass terms vanish in the case of universal gauge coupling , which corresponds to a flat massless vector field in 5d theory as discussed above . in other words , nonuniversal gauge couplings generate bulk / brane mass terms and cause a localization of the wave function . first we consider the series of vevs @xmath25 and couplings @xmath7 that generates a vector field on the rs warped background , namely , the ads@xmath0 background . this model can be obtained by choosing a universal @xmath7 and by varying @xmath25 as @xmath39 substituting this and taking the continuum limit , eq . ( [ gkt ] ) becomes @xmath40 ^ 2 , \label{eq : contlimrs}\end{aligned}\ ] ] where @xmath41 represents the coordinate of the extra dimension : @xmath42 ( @xmath8 ) and @xmath43 , etc . it is found that eq . ( [ eq : contlimrs ] ) successfully induces the kinetic energy term along the extra dimension and mass terms for the vector field on the warped background metric @xmath44 where @xmath45 with @xmath46 . we here conclude that we can obtain the vector field on a rs warped background by varying only the vevs @xmath25 . in the following we will see that nonuniversal gauge couplings @xmath7 induce other interesting results beyond the effects from the background metric . now let us compare the 4d model with generic couplings ( [ eq : gbbm ] ) to extra dimensional ones . we define the dimensionless parameters @xmath47 and @xmath48 as @xmath49 first we restrict ourselves to the case that the gauge group is @xmath50 , namely , abelian theory with _ no vector self - couplings_. similarly substituting eq . ( [ eq : deffh ] ) and taking the continuum limit , eq . ( [ gkt ] ) becomes @xmath51\bigr]^2 . \label{eq : contlim}\end{aligned}\ ] ] equation ( [ eq : contlim ] ) induces the kinetic energy term along the extra dimension and mass terms for the vector field on the warped background metric : @xmath52 ^ 2 \eta_{\mu\nu}dx^\mu dx^\nu - dy^2 . \label{eq : generalbkg}\ ] ] the bulk and boundary mass terms are @xmath41 dependent and proportional to the derivatives of @xmath53 . this is also seen from the 4d model [ the second and third terms in eq . ( [ eq : gbbm ] ) ] . the above is a generic correspondence between our 4d case and continuum 5d theory . as an example , consider the following forms of the parameters : @xmath54 where @xmath55 is a positive constant with mass dimension @xmath56 . equation ( [ eq : contlim ] ) leads to @xmath57 -\frac{1}{2}\biggl[\zeta ke^{-2(\zeta+\eta)ky } ( a_\mu)^2\biggr]_0^{l/2}. \label{eq : wgmbbm}\end{aligned}\ ] ] the first term on the right hand side is the kinetic term of the gauge boson along the extra dimension with the warped background @xmath58 the second and third terms correspond to the bulk and boundary masses announced before . as easily seen , the above equation" +"the study of the formation and evolution of galaxies is one of the most important issues of present - day astronomy . the currently favoured models suggest that large galaxies such as the milky way formed through the hierarchical accretion of a number of smaller objects . one possible way to test this scenario is to focus on dwarf galaxies : in fact , it is reasonable to expect that their assembly was considerably less complicated than that of the milky way , and easier to understand . the nine dwarf spheroidal ( dsph ) satellites of the milky way are ideal targets in this respect : theoretically , they might be the `` fossil '' remnants of the `` building blocks '' which ended up inside the milky way ; observationally , they can be studied in much greater detail than more distant objects . for example , it has been possible to study their stellar populations , extracting informations about their star formation ( sf ) and chemical evolution histories ( see e.g. the review by mateo 1998 ) , which turned out to be quite varied . however , all of them contain a population of very old stars , and all of them exhibit low mean metallicities ( grebel & gallagher 2004 ) . large observational programs ( such as dart , i.e. dwarf abundances and radial - velocities team ) are measuring , for the first time , the stellar metallicity distribution in dsph galaxies ( tolstoy 2004 ; koch 2006 ; battaglia 2006 ) . despite the low average metallicities ( consistent with previous estimates ) , out of about 2000 stars which were observed in four different galaxies ( carina , fornax , sculptor , and sextans ) , none of them turned out to have a metallicity lower than [ fe / h]=-3 , which is quite surprising ( helmi 2006 ) . here , we use numerical simulations of chemical enrichment of dwarf galaxies in order to investigate whether this dearth of very metal poor stars ( vmpss , i.e. stars with @xmath0}\leq-3 $ ] ) is consistent with the simple hypothesis that the gas in the dwarf galaxies was completely self - enriched in metals ( i.e. that the gas metallicity when sf started in these galaxies was essentially 0 ) , and that the imf of these galaxies was always given by a salpeter power law extending from 0.1 to 100 @xmath1 . we modified the public sph code gadget ( springel 2001 ; springel 2005 ) in order to include the treatment of gas cooling , sf , supernova ( sn ) and stellar wind feedback , and metal enrichment of the inter - stellar medium . a complete description will be given in ripamonti 2006 . here it is sufficient to say that the gas cooling rate was taken from sutherland & dopita ( 1993 ) ( if @xmath2 ; otherwise it was assumed to be 0 ) , the sf recipe assumes a schmidt law ( see e.g. thacker & couchman 2000 ) , the stellar lifetimes are taken from the geneva evolutionary tracks ( e.g. schaller 1992 ) , and that sn energies and yields are from woosley & weaver ( 1995 ) . our simulations were aimed at reproducing the chemical properties of the sculptor dsph ( hereafter , scl ) , rather than those of the full sample of helmi ( 2006 ) . the reason for this choice is that the low metallicity tail of scl extends to slightly lower metallicities than those of the other three dsphs ( a fact which will strengthen our conclusions ) . furthermore , the sf history of scl appears to have lasted only a few gyr , and after this initial period it appears to have stopped , as no stellar population younger than about 10 gyr has been detected : such a simple history should be relatively easy to reproduce . the total mass of scl was quoted to amount to a few @xmath3 ( queloz 1995 ) , but more recent estimates ( battaglia 2006 ) have put it at a much higher value ( @xmath4 ) . here we report the results of simulations where its total mass was assumed to be @xmath5 : such a value is low when compared to recent measurements , but this should have only a small effect on the metallicity distribution of the stars in the galaxy . } \leq-3 $ ] ( thin solid ) , sf rate of stars with @xmath6}\leq-2.5 $ ] ( dashed ) , sf rate of stars with @xmath7}\leq-2 $ ] ( dotted ) . central panel : total mass of stars , and mass of stars in metallicity ranges ( symbols as in the top panel ) . bottom panel : maximum ( dotted ) , average ( solid ) , and median ( dashed ) of stellar metallicities . ] at the beginning of our simulations we assume that all the baryons are in gaseous form , and that both the gas and dm follow a nfw profile ( navarro 1997 ) with concentration @xmath8 and virial radius @xmath9 ( approximately coincident with the present - day tidal radius of scl ) . we place 20000 dm particles and 100000 gaseous particles within twice the virial radius . since we assume that a mass @xmath10 is entirely enclosed within @xmath11 , the total mass included in each simulation is about @xmath12 , of which a fraction @xmath13 is in the dm component , and a fraction @xmath14 is in the baryonic component ( @xmath15 , and @xmath16 are the cosmological density parameters of dm and baryons ; see spergel 2006 ) . the initial velocities were assigned according to the recipe for a spherical halo described in hernquist ( 1993 ) , and the gas particles were assumed to be cold . the main parameters of our simulations were related to sf and feedback . they include the typical mass of stellar particles ( @xmath17 ) , the sf efficiency @xmath18 ( which was varied in the range @xmath19 ; see e.g. thacker & couchman 2000 ) , the typical energy of a sn explosion which is transferred to neighbouring gas particles ( @xmath20 erg ) erg , the feedback completely stopped the sf after much less than one gyr , preventing the formation of more than a few @xmath21 of stars . ] , and the fraction @xmath22 of the metals ejected in a sn explosion which is retained by the galaxy ( we tested @xmath23 and @xmath24 ; this second value is justified by the results of mac low & ferrara 1999 , which found that metals from the sn ejecta can escape from the galaxy far more easily than the rest of the gas ) . and @xmath18 indicated in each panel . the dots ( whose size is comparable to the error bars ) show the metallicity distribution of 496 stars in scl . the leftmost point ( at @xmath0}=-3.5 $ ] ) actually groups together all the vmpss . values are normalized to the total number of stars . ] we ran a grid of simulations with different combinations of the above parameters ; each one was run for just 1 gyr , because in all of them we found that the formation of very low metallicity stars had essentially stopped before that time ( see fig . the mass of the stellar component was always much smaller ( typically , by a factor 3 - 10 ) than the stellar mass in scl , but sf in the simulated galaxy was still active , even if only for stars with @xmath0}\gtrsim-2.3 $ ] . this fact must be kept into account when comparing the observed scl metallicity distribution with those produced by the simulations , because the average stellar metallicity from the simulations is still growing . in fig . 2 we show such a comparison in four typical cases . it is apparent that the fraction of vmpss is always very high ; it is higher in models where a low value of @xmath22 and an high value of @xmath18 are assumed ( which is unsurprising because such assumptions correspond to a longer timescale for the metal enrichment of the gas ) . in all the cases the fraction of vmpss is difficult to reconcile with the observations , even when a `` dilution '' by a factor 3 - 10 ( due to the future formation of a large number of stars ) is introduced . furthermore , the models with @xmath23 , where this discrepancy is lower , suffer from another problem at the high metallicity end , since they produce an average metallicity which is too high , at least if @xmath25 . in fig . 3 we try to limit the effects of the unknown sf after the first gyr of evolution by looking just at the metallicity distribution of stars with @xmath0}\leq-2.3 $ ] , because in such metallicity range sf is essentially complete by the time the simulations are stopped . here the excess of vmpss appears less dramatic ; but this is mostly an artifact of the large error bars due to the low number ( 23 ) of observed stars in this metallicity range . furthermore , the _ shape _ of the distributions appear to be different : the models fail to reproduce the observed increase in the number of stars at @xmath0}\gtrsim-2.5 $ ] , and predict a very large number of essentially metal - free stars ( when @xmath23 is assumed , most of the vmpss have @xmath0}\leq-4 $ ] ) . and @xmath18 indicated in each panel . dots with error bars show the metallicity distribution of stars in scl . the two leftmost bins refer to stars with @xmath0}\leq-4 $ ] , and with @xmath26}\leq-3.5 $ ] . all the values are normalized to the number of stars with @xmath27/h\leq-2.3 $ ] . ] the metallicity distribution obtained in our simulations is quite different from the predictions of lanfranchi & matteucci ( 2004 ) , as they predict a quite sharp drop at low metallicity ( @xmath28}\lesssim-2.5 $ ] ) , in agreement with observations ( however , there is significant disagreement at @xmath0}\gtrsim-1.5 $ ] ) . this is probably due to their assumptions about the `` infall '' history of gas inside the galaxy ( which implies a very low sf rate at early times , when the vmpss should form ) , and about the complete mixing of gas ( so that there is no spread in the age - metallicity relation ) . instead , we have a large spread ( of the order of 1 dex ) in the metallicities of stars which form after the very early stages of our simulations ; furthermore , we do not need to assume an infall history for the gas , even if it can be argued that our initial conditions are not completely realistic because of the assumption that no star ever formed before the halo density profile reached a nfw shape . our simulations indicate that the dearth of observed vmpss in dsphs is problematic . apart from the hypothesis that observations are biased in some unidentified way against the detection of vmpss , possible solutions might involve a pre - enrichment of the gas up to the @xmath0}\sim-3 $ ] level ( see e.g. helmi 2006 ) , or a difference between the present and the primordial ( metal - free ) imf , such as a suppression of the sf rate of stars below @xmath29 in environments of very low metallicity ( see e.g. omukai 2005 ) . battaglia , g. , 2006 , a&a 459 , 423 grebel , e.k . , & gallagher , j.s . , 2004 apj ," +"the dynamical density matrix renormalization group ( dmrg ) @xcite and the closely related correction vector dmrg @xcite have been widely used in the last decade to compute the dynamical correlation functions and spectral functions of low - dimensional strongly correlated quantum systems . @xcite although more powerful dmrg approaches have been developed recently , @xcite dynamical dmrg ( ddmrg ) often remains the method of choice because it offers two practical advantages over the other approaches : it is simpler and it can be easily parallelized . for instance , it has been recently shown that ddmrg allows us to investigate features with small spectral weights such as power - law pseudo - gaps in luttinger liquids . @xcite the main drawback of ddmrg is that it always yields the convolution of the desired spectrum with a lorentzian distribution of finite width . therefore , the true spectrum can only be obtained through a deconvolution of the ddmrg spectrum . ( in principle , there are some methods to get around this problem @xcite but they are rarely used in practice . ) deconvolution is a typical ill - conditioned inverse problem , however . @xcite a direct solution of the deconvolution equation usually yields a very noisy and thus useless spectrum . nevertheless , various regularization methods have been successfully used to deconvolve ddmrg spectra for one - dimensional systems and quantum impurity problems . @xcite astonishingly , some of these deconvolution methods even allow us to bypass the finite - size scaling analysis and to obtain the piecewise smooth spectrum of an infinite systems directly from a broadened finite - system ddmrg spectrum . unfortunately , regularization also smooths out the sharp features of the true spectrum . this is a serious issue as the spectra of one - dimensional systems and quantum impurities often exhibit very interesting ( power - law ) singularities . in this paper we present a method , which allows us to determine sharp spectral features in the thermodynamic limit starting from a broadened finite - system ddmrg spectrum . for this purpose we consider the extrapolation to the thermodynamic limit and the deconvolution for the lorentzian kernel to be a single blind deconvolution , @xcite i.e. an inverse problem with an unknown kernel including both the lorentzian broadening and the finite - size effects . the key idea to preserve sharp spectral features in a piecewise smooth spectrum is to impose a minimal distance @xmath0 between extrema of the deconvolved spectrum . to illustrate our method we investigate the single - particle density of states ( dos ) of one - dimensional paramagnetic mott insulators represented by the half - filled hubbard model . @xcite we confirm that this dos has the step - like onset predicted by field - theoretical studies @xcite at least at weak to intermediate coupling up to @xmath1 . the hubbard model @xcite with on - site interaction @xmath2 and nearest - neighbor hopping @xmath3 is a basic lattice model for the physics of strongly interacting electrons , in particular the mott metal - insulator transition . @xcite at half filling ( i.e. , the number of electrons equals the number of sites @xmath4 ) the ground state is a mott insulator for strong interaction @xmath5 , while it is a fermi gas in the non - interacting limit @xmath6 . the hamiltonian of the hubbard model is defined by @xmath7 where the operator @xmath8 ( @xmath9 ) creates ( annihilates ) an electron with spin @xmath10 on the site @xmath11 , @xmath12 , and @xmath13 . the first sum runs over all pairs @xmath14 of nearest - neighbor sites while the other two sums run over all sites @xmath15 . here we will only consider half - filled systems and thus set the chemical potential @xmath16 to have electron - hole - symmetric spectra and a fermi energy @xmath17 . the bulk single - particle dos @xmath18 can be measured experimentally using photoemission spectroscopy or scanning tunneling spectroscopy . theoretically , it can be defined as the average of the local dos @xmath19 where the sum runs over both spins and all sites @xmath15 in the lattice , while @xmath20 is the local single - particle dos at site @xmath15 for spin @xmath10 and can be calculated using @xmath21 for @xmath22 and @xmath23 for @xmath24 . here @xmath25 denotes the eigenstates of the hamiltonian @xmath26 and @xmath27 their eigenenergies in the fock space . the ground state for the chosen number of particles corresponds to @xmath28 . the total spectral weight is @xmath29 we will consider only lattice geometry for which the hamiltonian ( [ eq : hamiltonian ] ) is invariant under the electron - hole transformation @xmath30 . therefore , for half filling the density of states is symmetric , @xmath31 . if the system is translation invariant , the bulk dos and the local dos are identical . for dmrg simulations , however , open boundary conditions are preferred to periodic boundary conditions . in this case , the bulk dos can be identified with the local dos on one of the two equivalent middle sites of the system , i.e. as far as possible from the system boundaries . inverse problems such as ( blind ) deconvolutions @xcite occur in many scientific fields and are among the most challenging numerical computations . experimental measurements and computer simulations often yield approximations of the true quantities which are measured or computed , respectively . it is often assumed that the deviations from exact results can be modelled by a convolution with a smoothing function and an additive noise due to the finite accuracy and resolution of the measurement or simulation process . a typical example of a blind deconvolution is the reconstruction of an original signal from a degraded copy using incomplete information about the degradation process . @xcite here we want to compute sharp spectral features in the piecewise smooth spectrum of an infinite system from a broadened finite - system spectrum calculated with ddmrg . in this section we first show that this task can be formulated as a blind deconvolution problem , then present an algorithm for solving it . let @xmath32 be a spectrum of a finite lattice model with @xmath4 sites . this spectrum is a dirac - comb ( a finite sum of dirac - peaks ) @xmath33 where the sum runs over all hamiltonian eigenstates @xmath25 which contributes to the spectrum , i.e. with a nonzero spectral weight @xmath34 . here @xmath35 denotes the corresponding excitation energies . this spectrum can be broadened with a lorentzian distribution of width @xmath36 @xmath37 to obtain a smooth spectral function @xmath38 with the ddmrg method we can calculate this spectrum for a discrete set of excitation energies @xmath39 . as numerical calculations are always affected by errors , ddmrg actually yields values @xmath40 which are related to the true spectral function by @xmath41 for @xmath42 , where @xmath43 represents the unknown errors . ( it should be noted that ddmrg errors @xmath43 include significant systematic contributions , for instance due to the variational nature of the procedure . @xcite ) in principle , one could determine the true spectrum , i.e. , the excitation energies @xmath35 and the corresponding weights @xmath44 , through this system of equations . in practice , however , this is an ill - conditioned problem except for simple discrete spectra . moreover , we are not interested in resolving the discrete peaks of small systems but in calculating the piecewise smooth spectra of macroscopic systems . the spectrum in the thermodynamic limit is given by @xmath45 note that , generally , the order of the two limits can not be exchanged . typically , the spectral function @xmath46 is piecewise smooth , i.e. , it exhibits one or more continua as well as isolated sharp features such as steps , power - law singularities or cusps . in principle , one should carry out several ddmrg simulations with varying system size @xmath4 and broadening @xmath36 and then extrapolate the numerical data to obtain @xmath46 . in most cases , a simultaneous extrapolation for @xmath47 and @xmath48 is possible @xcite using a constant value of @xmath49 . nevertheless , the computational cost of ddmrg simulations increases very rapidly with smaller @xmath36 and the overall cost of this approach is prohibitive for a full spectrum . indeed , this approach has been mostly used to study isolated spectral features in the thermodynamic limit such as power - law singularities and steps . @xcite as all operations used to define @xmath46 from @xmath50 are linear , the broadened spectrum of the finite system can also be written explicitly as a function of the infinite system spectrum @xmath51 the kernel @xmath52 includes both the finite - size effects and the lorentzian smoothing . its form is not known but it is clear that we must recover a pure lorentzian smoothing in the thermodynamic limit @xmath53 combining eqs . ( [ eq : deconv ] ) and ( [ eq : spec - inf ] ) we obtain a system of equations @xmath54 for @xmath55 , relating the ddmrg data set @xmath56 to the infinite system spectrum @xmath46 . determining @xmath46 from these equations is a so - called inverse problem . @xcite this kind of problem is also called blind deconvolution since our knowledge of the kernel is incomplete . [ strictly speaking , it is not a deconvolution because eq . ( [ eq : inverse - problem ] ) is not a convolution . however , as the kernel approaches the form @xmath57 in the thermodynamic limit , we will use the terminology of deconvolution problems . ] it should be obvious that this is an ill - posed problem . first , the errors @xmath43 and the kernel @xmath52 are not known . second , the problem is sorely underdetermined as we try to reconstruct the function of a continuous variable from a finite number @xmath58 of data points . finally , a convolution with a lorentzian is a smoothing operation and thus the corresponding deconvolution is an extremely ill - conditioned inverse problem : the solution will be extremely sensitive to small changes or errors in the input . various deconvolution methods have been used successfully to deduce piecewise smooth spectra from the broadened finite - system spectra calculated with ddmrg . they include , direct inversion at low resolution , @xcite linear regularization methods , @xcite fourier transform with low - pass filtering , @xcite nonlinear regularization methods such as the maximum entropy method , @xcite parametrization with piecewise polynomial functions , @xcite and a deconvolution ansatz for the self energy . @xcite however , this task has not been viewed as a blind deconvolution so far . instead , it has been considered as the deconvolution of a perfectly known kernel . the need for regularization or filtering techniques has been viewed as the consequence ill - conditioning and under - determination of the problem ( [ eq : inverse - problem ] ) with a lorentzian kernel . all of these methods offer some advantages for particular spectral forms . however , their common drawback is that they are ill - suited for sharp spectral features , such as steps or power - law singularities , within or at the edge of a continuum . either the regularization procedure smooths out true sharp features excessively or it allows the occurrence of deconvolution artifacts ( artificial sharp structures , rapid oscillations or negative spectral weight ) , especially in the vicinity of the true spectrum singularities . naturally , better results can be obtained if we can use _ a priori _ knowledge about the properties of the spectrum @xcite but , in practice , this is a rare occurrence . therefore , we need a better method for solving the inverse" +"non - hermitian hamiltonians are often employed to describe the open systems due to their features of complex - valued energy and non - preserved particle probability . recent observations show that a large families of non - hermitian hamiltonians can have all eigenvalues real , if the loss and gain are set in a balanced manner , being invariant under the combination of the parity ( @xmath1 ) and the time - reversal ( @xmath2 ) symmetry . a parity - time ( @xmath3 ) symmetric non - hermitian quantum theory has been well developed as the complex extension of conventional quantum mechanics @xcite . although the condition of the @xmath3 symmetry for a complete real spectrum is weaker @xcite , it still implies the underlying mechanism can be based on the balance of the loss and gain . however , such an intuitive consideration of the balance needs to be investigated precisely . the concept of the balance should not be simply understood as the conjugate relation of two non - hermitian subsystems arising from the @xmath3 symmetry . it can not provide physical explanation to the following features about exceptional point : ( i ) the @xmath3 symmetry of the system can not guarantee the balance of the loss and the gain , or the reality of the energy levels . ( ii ) the spontaneous symmetry broken states always appear in pairs . furthermore , this consideration is also related to the precise physical significance of the complex potential and non - hermitian coupling , which are basic elements for a discrete non - hermitian system . on the other hand , the purpose of this investigation is not only for the fundamental physics , but also for the application in practice due to the formal equivalence between the quantum schrdinger equation and the optical wave equation @xcite . furthermore , the @xmath3 symmetry breaking has been observed in experiments @xcite . in this paper , we investigate semi - infinite non - hermitian system without @xmath0 symmetry . based on this , we try to clarify the concept of balance in the non - hermitian discrete system in the framework of the quantum mechanics rather than a phenomenological description . we show an entirely real spectrum and study the exceptional point of a semi - infinite non - hermitian system from the dynamical point of view . we show that the wave function within the lead becomes a unidirectional plane wave at the exceptional point . this universal dynamical behavior is demonstrated as the self - sustained emission and reflectionless absorption of wave packets by two typical non - hermitian clusters containing the complex on - site potential and non - hermitian hopping amplitude . this paper is organized as follows . in section [ semi - infinite system ] we analyze the classification of possible solutions and solve two examples to illustrate our main idea . section [ relation with pt ] presents the connection between the semi - infinite systems and @xmath3-symmetric systems . section [ wavepacket ] is devoted to the numerical simulation of the wave packet dynamics to demonstrate the phenomena of the persistent emission and reflectionless absorption . section [ sec_summary ] is the summary and discussion . the discrete non - hermitian model , with the non - hermiticity arising from the on - site complex potentials as well as the non - hermitian hopping amplitude , is a nice testing ground to study the basic features of the non - hermitian system not only because of its analytical and numerical tractability but also the experimental accessibility . in recent years , fundamental aspects of non - hermitian continuum systems are studies by using discretization znojil , as well as the studies on quantum square wells @xcite . on the other hand , non - hermitian quantum models are also investigated , such as tight - binding systems @xcite , spin systems @xcite , and strongly correlated systems @xcite . besides the fundamental features of discrete @xmath3-symmetric quantum systems , theoretical research on the quantum dynamics and scattering behaviors in discrete non - hermitian networks are investigated in a series of papers @xcite . in experiment , light transport in large - scale temporal lattices is studied in @xmath4-symmetric fiber networks , it is also demonstrated that the @xmath3-symmetric network can act as a unidirectional invisible media @xcite . although many surprising features and possible applications of @xmath3-symmetric are revealed , they are mostly based on the finite systems . in this paper , we intend to study the infinite system . here we consider a semi - infinite lead coupled to a non - hermitian finite cluster . the hamiltonian is written as @xmath5it is noted that @xmath6 is non - hermitian , possessing the complex - valued eigen energy , while @xmath7 is hermitian , having complete spectrum @xmath8 , @xmath9 and the eigen state @xmath10 . to investigate the role of the lead in the non - hermitian @xmath11 , we will consider the whole solution of the hamiltonian @xmath12 and analyze its properties . the eigen state can be expressed as @xmath13 . the explicit form of the wave function @xmath14 depends on the structure of @xmath6 . generally speaking , the solution of @xmath15 can not be obtained exactly even the explicit form of @xmath6 is given . however , within the lead the wave function is always in the form @xmath16due to the semi - infinite boundary condition . the schrdinger equation has the explicit form@xmath17 \right ) & \notag\end{aligned}\]]within all the regions . the solutions of @xmath18 and @xmath15 depend on the structure of the system @xmath6 . nevertheless , the exclusive geometry of the lead will give some clues to the characteristics of the eigenvalues and eigenfunctions . in the framework of bethe ansatz method , all possible solutions within the lead can be classified into three types : \(1 ) scattering state wave , the wave function and energy are in the form @xmath19 \(2 ) monotonic damping wave , the wave function and energy are in the form@xmath20 \(3 ) oscillation damping wave , the wave function and energy are in the form @xmath21 .\end{aligned}\ ] ] in fig . [ fig1 ] , the concerned system and three types of possible solutions within the lead are illustrated schematically . for the case of a hermitian @xmath6 , the solutions are the form of @xmath22 and @xmath23 with @xmath24 or @xmath25 definitely . in the case of non - hermitian @xmath6 , @xmath26 may appear associated with the complex energy level . in case of absence of the solution @xmath27 , full real spectrum achieves , which shows the existence of the stationary states . it indicates that the lead acts as a channel to balance the gain or loss in the system @xmath6 . at certain points @xmath28 , the system makes transitions between wavefunctions @xmath29 and @xmath30 , as well as between @xmath31 and @xmath27 . the former transition is actually a switch between real and imaginary @xmath32 , preserving the reality of the eigen energy . then the transition point locates at @xmath33 , i.e.,@xmath34which usually occurs in the case of hermitian @xmath6 . the later transition only occurs in a non - hermitian system , eigen energy switching between real and complex values . in contrast to the above case , the transition point ( referred as exceptional point ) depends on the structure of the non - hermitian @xmath6 , i.e. , @xmath35it indicates that a unidirectional plane wave exists in the lead when an appropriate non - hermitian @xmath6 is connected . it has both fundamental as well as practical implications . this result reveals the exceptional point from an alternative way : it is the threshold of the balance between the non - hermitian subcluster and the lead . from a practical perspective , the unidirectional - plane - wave solution at the exceptional point can be used to realize the reflectionless absorption and persistent emission in the experiment . to characterize the probability generation ( negative in the case of the dissipation ) of the non - hermitian cluster , we introduce the current operator @xcite@xmath36where @xmath37 $ ] . for three types of wave functions @xmath38 , @xmath39 and @xmath40 , the corresponding currents can be obtained as @xmath41 } . \notag\end{aligned}\]]we can see that @xmath42 is time - independent and is conservative along the lead , representing a steady flow or the dynamic balance , while @xmath43 is non - periodically time - dependent , indicating the unbalance of the state . in other word , the mechanism of the reality of the spectrum is the balance between the source ( or drain ) and the channel of the probability flow . then the exceptional point is the threshold of such dynamic balance , corresponding to the unidirectional - plane - wave , i.e. , @xmath44 or @xmath45 . then the probability generation for the exceptional point is@xmath46which the sign indicates that the cluster is a source or drain , then it is referred as critical current in this paper . unlike the situation in traditional quantum mechanics , the magnitude of the current @xmath47 does not represent the absolute current in traditional quantum mechanics because the corresponding eigenstate is not normalized under the dirac inner product . we will demonstrate and explain these points through the following illustrative example . we would like to point out that , there is another type of the exceptional point , arising from the transition of two types of wave functions @xmath27 and @xmath48 , which is beyond our interest . in this subsection , we investigate two simple exactly solvable systems to illustrate the main idea of this paper . in order to exemplify the above mentioned analysis of relating the wavefunction within the lead and the eigenvalue , we take @xmath6 to be the simplest non - hermitian networks to construct two types of exemplified systems . type i is a uniform chain with a complex potential at one end and type ii is a uniform chain with a complex hopping at one end . in the following , we present the analytical results in the framework of above mentioned for the two models in order to perform a comprehensive study . the type i hamiltonian has the form @xmath49where @xmath50 is a complex number . according to bethe ansatz method , the wavefunction @xmath15 can be expressed as @xmath51 and the schrdinger equations for @xmath52 is @xmath53 f^{k}\left ( 1\right ) . \notag\end{aligned}\ ] ] submitting @xmath15 into the schrdinger equation , we have@xmath54which is the reflection amplitude for the scattering state . now we are interested in the wavefunction with complex eigen energy . the existence of the solution @xmath27 requires@xmath55which lead to @xmath56 with im@xmath57 . then we conclude that there is a unique complex solution within the region im@xmath58 and the system has full real spectrum if the potential is in the rest region . at the boundary , we have @xmath59which indicates a circle of radius @xmath60 in the complex plane . the phase diagram is sketched in fig . [ fig3 ] ( a ) . then the corresponding wavefunction has the form@xmath61which represents a unidirectional plane wave with energy@xmath62accordingly , the critical current is @xmath63which accords with the intuition that a positive imaginary potential can be a source and a negative imaginary potential can be a drain . however , unlike the situation in traditional quantum mechanics , the magnitude of the current @xmath47 does not represent the absolute current in traditional quantum mechanics because the eigenstate is not normalized under the dirac inner product . -symmetric networks : ( a ) two separable semi - infinite chains with the complex potential and ( b ) with the complex hopping at the end" +"there has been considerable recent interest on the general dynamics of the glass transitions in bulk polymer systems@xcite . a central experimental law which controls the rate of transition was long ago formulated by vogel , fulcher and tammann@xcite ; the empirical vft law of transition rates reads @xmath0 \right\ } , \label{intro1}\ ] ] wherein @xmath1 is the free energy of thermal activation . the vft thermal activation law is quite similar to the well known arrhenius@xcite thermal activation law except for the temperature singularity in the denominator on the right hand side of eq.([intro1 ] ) . the singularity occurs at a dynamical temperature @xmath2 which is somewhat lower than the thermodynamic glass transition temperature @xmath3 . the singularity is thereby never quite attained . nevertheless , the critical slowing down of the vft eq.([intro1 ] ) is experimentally well obeyed in bulk polymer glasses . there exist somewhat different physical views@xcite as to why the vft law might theoretically be true . nevertheless there is presently no agreed upon theory of eq.([intro1 ] ) . our purpose is to derive the vft thermal law through the following quite simple quantum mechanical considerations . the transition rate per unit time for an activated process involves an absolute squared transition amplitude ( matrix element ) times a density of final states . the logarithm of the density of final states represents the final entropy . thus , the quantum mechanical rule for computing transition rates is that @xmath4 , \label{intro2}\ ] ] wherein @xmath5 is the entropy of activation to a state with energy @xmath6 . the theoretical problem is to deduce the nature of the excitations@xcite and compute the entropy of activation from the the logarithm of the final state phase space magnitude @xmath7 the polymer glass excitation configurations@xcite pictured in fig.[fig1 ] are of two types : ( i ) there are - in the bulk of the polymer - closed chains of atoms referred to as _ closed _ strings . ( ii ) also , there are open polymer chains which begin and end on the boundary surfaces of the bulk polymer and are referred to as _ open _ strings . it will be shown below that the closed strings have an entropy obeying the vft thermal activation eq.([intro1 ] ) . on the other hand , the open string configurations with end points in the neighbourhood of surface boundaries obey shifted thermal activation laws . the distinction between the thermal activation properties of open and closed strings is crucial for an understanding of surface effects which are of importance for thin films@xcite . the vft thermal activation law holds only for the bulk polymer . by contrast , the dynamical sinularity temperature @xmath2 decreases as the ratio of boundary surface are to the bulk volume , @xmath8 , increases . consequently , the singularity temperature is sharply lowered@xcite when @xmath9 is decreased to a few nanometers . closed polymer chains in the form of `` polygons '' are treated as a self avoiding random polygons . the number of _ closed self avoiding polygon _ polymer chains containing @xmath10 links is thought to obey@xcite @xmath11 wherein @xmath12 denotes the connectivity . the de gennes scaling law@xcitein @xmath13 dimensions for the exponent @xmath14 is given by @xmath15 wherein @xmath16 is the fractal dimension of the complete closed chain configuration . in mean field theory@xcite we have @xmath17 if @xmath18 denotes the activation energy per link for a mobile closed chain ( closed string ) , then the energy @xmath19 determines the entropy via eqs.([intro3 ] ) , ( [ closed1 ] ) and ( [ closed4 ] ) according to @xmath20 wherein @xmath21 the activation entropy as a function of energy exhibits a minimum as shown in fig . [ fig2 ] . for stable entropy functions , the maximum entropy principle dictates upward convexity while metastable entropy functions exhibit downward convexity . since the density of final states @xmath22 , rates become slower as the minimum activation entropy is approached . in terms of the temperature @xmath23 , @xmath24 we have at @xmath2 the activated energy singularity @xmath25 . \label{closed8}\ ] ] eqs.([closed3 ] ) , ( [ closed5 ] ) and ( [ closed8 ] ) imply @xmath26 \nonumber \\ & \ & \ -(3-\alpha)k_b\ln \left[\frac{(t}{(t - t_0)}\right ] . \label{closed9}\end{aligned}\ ] ] using eqs.([intro2 ] ) , ( [ closed3 ] ) and ( [ closed9 ] ) , we may now complete the proof that the closed chain activation law has the vft form given by eq.([intro1 ] ) . explicitly , we have @xmath27^{2.8 } \nu_\infty e^{s_\infty /k_b}\ . \label{closed10}\end{aligned}\ ] ] in practice , the vft activation process is often observed by measuring viscosity , @xmath28 wherein @xmath29 is the mass density and @xmath30 is the length scale of the polymer links . in this regard , the prediction for the activation free energy @xmath31 is subject to an experimental test of the scaling critical index in eq.([closed2 ] ) . consider the problem of how much activation energy would be required to remove a given section of chain from the condensed matter piece of polymer . if the given section of chain were deep within the polymer , the removal would be quite difficult . for example , if one exerted a force on the given chain section , then it would become knotted with other polymer chain sections and would be rendered immobile . on the other hand , if the given section of chain was entirely located in the neighborhood of the surface boundary of the polymer , then it would be relatively easier to peel the chain off the surface . let us consider , in more detail , the activation energy to slide a section of polymer chain along a given path . such an activation energy has been denoted above as @xmath32 per link of the chain section . furthermore , let @xmath33 denote the distance from a chain link to the boundary surface . by the above physical arguments we expect @xmath34 to sharply decrease as @xmath35 . from eq.([closed6 ] ) we expect , for uniform connectivity ( @xmath36 ) , the dynamical singularity temperature to be a decreasing function of @xmath33 varying as @xmath37 in a local density theory@xcite , @xmath38 may be parameterized by @xmath39 in which the coherence length is related to the density @xmath40 the @xmath41 relation invalidates the vft eq.([intro1 ] ) for the case of very thin polymer films . a derivation has been provided for vft activated transition rates in bulk polymer glasses . our derivation depends on the micro - canonical counting of the number of closed polymer chain configurations within the bulk glassy system . the configuration counting is mapped into the self avoiding polygon problem . the activation energy @xmath18 per link determining the chain mobility also determines the dynamical glass transition temperature in the empirical vft law . the critical indices employed are calculated as in flory s theory . the chain movements also lend strong support to `` co - operative '' motion inside the bulk . it is also to be stressed that the dynamical glass transition temperature , @xmath42 , varies with the distance from the surface boundary through that a coherence length scale of about a few nanometers . this surface effect is due to the fact polymer strings localized near the surface boundary are more mobile than the polymer chains embedded in the bulk . for sufficiently thin films , the vft activation law thereby becomes modified as in eqs . ( [ se1 ] - [ se3 ] ) ." +"the principal limit in high precision measurements and optics communication is given by the quantum fluctuations of light . for several years , in order to beat the standard quantum limit , a number of methods consisting in generating squeezed states of light have been developed @xcite . in connection with quantum information technology the quantum features of the polarization of light has raised a lot of attention . the generation of polarization squeezing has been achieved experimentally by mixing an opo - produced squeezed vacuum with a coherent field @xcite , or more recently by mixing two independent opa - originated squeezed beams on a polarizing beamsplitter @xcite . several schemes using kerr - like media have also been proposed @xcite , and very recently , matsko et al . proposed to propagate a linearly polarized field through a self - rotative atomic medium to produce vacuum squeezing on the orthogonal polarization @xcite . the kerr - like interaction between cold cesium atoms placed in a high finesse optical cavity and a circularly polarized field has been studied in our group and a field noise reduction of 40% has been obtained @xcite . we recently observed experimental evidence of polarization squeezing when the incoming polarization is linear @xcite . in this paper , we present a theoretical investigation of polarization squeezing generated by an ensemble of x - like 4-level atoms illuminated by a linearly polarized field . to be as realistic as possible , the experimental parameters values of ref @xcite are taken as references . in the first part of the paper , we give a detailed study of the steady state and show that self - rotation is responsible for polarization switching and saturation leads to tristability . we derive simple analytical criteria for the existence of elliptically polarized solutions and the stability of the linearly polarized solution . this steady state study is essential to figure out the interesting working points for squeezing . in the second part , we focus on the case in which the polarization remains linear ( below the ps threshold ) and show that both the linearly polarized field mode and the orthogonal vacuum mode are squeezed . analytical spectra are derived in the low saturation limit and enable a clear discussion of the physical effects responsible for polarization squeezing ; in particular , we demonstrate that self - rotation is associated to strong atomic noise terms preventing vacuum squeezing at low frequency . on the other hand , saturation accounts for the squeezing on the mean field and crossed - kerr effect enables to retrieve vacuum squeezing at high frequency . the analytical results are compared with a full quantum calculation . finally , we derive the stokes parameters @xcite and relate their fluctuations to those of the vacuum field . the vacuum squeezing obtained is then equivalent to the squeezing of one stokes parameter , the so - called _ polarization squeezing _ @xcite . the system considered in this paper is a set of n 4-level cold atoms interacting in an optical cavity driven by a linearly polarized field as represented in fig [ fig1 ] . we denote @xmath0 the slowly - varying envelope operators associated with the @xmath1 components of the light @xcite . they are defined from the standard linear polarization components @xmath2 the atomic frequencies are both equal to @xmath3 . the field frequency is @xmath4 and the detunings from atomic resonance are equal on both transitions to @xmath5 . the 4-level system is described using collective operators for the n atoms of the ensemble , the optical dipoles being defined in the rotating frame associated to the laser frequency ( e.g. @xmath6 ) . the coupling constant between the atoms and the field is defined by @xmath7 , where @xmath8 is the atomic dipole and @xmath9 . with this definition , the mean square value of the field is expressed in number of photons per second . as in fig [ fig1 ] , the population of level 3 decays with rate @xmath10 on level 1 and with rate @xmath11 on level 2 , the dipole decay rate being @xmath12 . we consider the case of saturated optical pumping and neglect the relaxation rate of the ground states populations . this approximation is well verified for alkali cold atoms @xcite . with these conventions , the atom - field hamiltonian is @xmath13\ ] ] the atomic evolution is then governed by a set of quantum heisenberg - langevin equations @xmath14 note that we have not reproduced all the atomic equations , but only those of interest for the following . the langevin operators @xmath15 are @xmath16-correlated and their correlation functions are calculated via the quantum regression theorem @xcite . we consider a ring cavity with @xmath17 the transmission of the cavity coupling mirror , @xmath18 the cavity resonance frequency closest to @xmath4 and @xmath19 the cavity round - trip time . the cavity dephasing is @xmath20 . the incoming quantum fields are @xmath21 and the field equations read @xmath22 the atomic steady state is readily obtained by setting the time derivatives to zero and using the fact that a langevin operator mean value is zero . defining saturation parameters @xmath23 for both polarizations , @xmath24 the atomic steady state is given by @xmath25 @xmath26 are the rabi frequencies and @xmath27 is the coupling saturation parameter which plays a symmetrical role with respect to both polarization components . for an x - polarized field , @xmath28 is directly related to the intracavity field intensity . it is well known that such a coupled system may exhibit polarization switching when driven by a linearly polarized field @xcite . in fact , the intracavity field intensities depend on the atomic dephasings @xmath29 and absorptions @xmath30 @xmath31 with @xmath32 and @xmath33 the linear dephasing and absorption in the absence of saturation . these quantities depend in turn on the intensities to yield a complex coupled system . in order to derive analytical criteria for polarization switching , we follow the method given in @xcite and decompose dephasings and losses into their linear and non - linear parts , @xmath34 where @xmath35 and @xmath36 are the non - linear circular birefringence and dichroism , related to the ellipticity @xmath37 @xcite @xmath38 thus , as pointed out in the literature @xcite , the optical pumping induces non - linear self - rotation ( sr ) of elliptically polarized light . it will be shown in the next section that this effect is responsible for ps in a cavity configuration . let us first focus on the solution for the @xmath1 components . normalizing all the dephasings and absorptions by @xmath39 ( @xmath40 and @xmath41 ) , eqs ( [ aplus]),([amoins ] ) read in steady state @xmath42 with @xmath43 the maximal intracavity intensity in the absence of absorption . replacing ( [ spm ] ) in ( [ epsilon ] ) , we derive the equation for @xmath44 : non zero solutions correspond to elliptically polarized states . after straightforward calculations , we obtain @xmath45 the first trivial solution corresponds to the linearly polarized field . it follows from the second equation and ( [ phil]),([al ] ) that elliptically polarized states may exist as soon as the existence criterion @xmath46 is satisfied @xmath47 note that the absorption brings a positive contribution to the existence of asymmetrical solutions : this is due to the fact that non - linear circular dichroism produces `` self - elliptization '' of the field . however , this criterion gives no information on the stability of the solutions . in order to get some physical insight into this complicated problem it is useful to look at the evolution of the linearly polarized solution . in this section , we give a simple interpretation of ps as the threshold for laser oscillations . let us consider the linearly polarized solution along the x axis . the adiabatic elimination of the atomic variables leads to @xmath48 where @xmath49 is the intracavity field decay rate . in ( [ equationay2 ] ) all terms have zero mean value and are of order 1 in fluctuations ( @xmath50 ) . using @xmath51 , one obtains @xmath52 owing to sr the fluctuations of the orthogonal mode undergo a phase dependent gain . a similar equation has already been derived in previous theoretical works in a single pass scheme @xcite . in our configuration the presence of the cavity will lead to oscillations of this mode as soon as the phase sensitive gain is larger than the losses . this condition may be expressed as follows @xmath53 obviously , the linearly polarized solution is not stable when @xmath54 . however , the adiabatical elimination of the atomic variables does not _ a priori _ take all causes for instability into account . yet , we checked that this threshold analysis was consistent with a numerical calculation of the atom - field stability matrix . in the following we use @xmath55 as a stability criterion for the linearly polarized solution nevertheless , it does not yield information on the stability of the elliptically polarized solutions , which has been evaluated numerically . + besides , the ability of a system to produce squeezing being closely related to its static properties , the fluctuations of the vacuum field are expected to be strongly modified in the vicinity of the ps threshold . since eq ( [ equationay3 ] ) is similar to that of a degenerate optical parametric oscillator ( opo ) below the threshold @xcite , perfect squeezing could be obtained via sr . however , the atomic noise is not included in ( [ equationay3 ] ) and is to be carefully evaluated . , the cavity dephasing corresponding to ps is @xmath57 , close to @xmath58 as given by the ps criterion . when the cavity detuning is scanned from the right , the linear solution is stable until @xmath59 and unstable afterwards . then the elliptically polarized solutions , @xmath60 and @xmath61 , become stable for @xmath62 . we plot also the resonance peaks ( dashed line ) for the cavity with @xmath63 or @xmath64 atoms , in the absence of sr phenomenon.,width=377 ] ps is caused by a competition between the two @xmath1 optical pumping processes . we can understand the main features of this effect by restraining ourselves to the case where absorption and saturation are negligible : @xmath65 and @xmath66 . neglecting the excited state populations , the optical pumping equations for the ground state populations are @xmath67 so that the @xmath68 component tends to pump the atoms into level 2 , the @xmath69 into 1 , and , in steady state , @xmath70 and @xmath71 . the circular birefringence @xmath72 is proportional to the ground state population difference , and consequently , to the intensity difference @xmath73 [ see ( [ epsilon ] ) ] . this simple analysis allows for relating self - rotation to competitive optical pumping and will help us interpret the resonance curves . + under the previous conditions both criteria ( [ critereexistence ] ) and ( [ criterestabilite ] ) are equivalent and it follows that the linearly polarized solution bifurcates into an elliptically polarized state for @xmath74 . consequently , ps is observed as soon as the linear dephasing is greater than half the cavity bandwidth ( @xmath75 ) . this represents an easily accessible condition from an experimental point of view : in our cesium experiment using a magneto - optical trap @xcite , the number of atoms interacting with the light is @xmath76 . to find realistic experimental parameters , we assimilate each one of our x - model transitions to the transition @xmath77 of the @xmath78 line of @xmath79 , for which @xmath80 mhz . the square of the coupling constant @xmath81 is proportional to the ratio of the diffusion section at" +"the tensor model was originally considered in @xcite to generalize the matrix model , which describes the two - dimensional simplicial quantum gravity , to higher dimensional cases . while the matrix model is a successful tool to analyze the two - dimensional simplicial gravity , the tensor model has not been successful in this direction , partly because of the absence of analytical methods to solve it and of physically appropriate interpretations of its partition function . in ref . @xcite , a new interpretation of the rank - three tensor model was proposed . namely , theory of a dynamical rank - three tensor may be regarded as that of dynamical fuzzy spaces . this proposal is based on the fact that a fuzzy space is described by an algebra of functions , which can be characterized by a rank - three tensor that defines multiplication , @xmath0 . this reinterpretation of the tensor model provides a new practical manner of extracting physics from the tensor model . in the original interpretation , it is necessary to compute the tensor model non - perturbatively , since the large volume limit of spaces corresponds to the large loop - number limit of the feynman diagrams of the tensor model . on the contrary , under the new interpretation , the semiclassical treatment of the tensor model is physically meaningful ; its classical solutions can be regarded as background fuzzy spaces , and small fluctuations around solutions as field fluctuations on fuzzy spaces . another key difference from the original proposal is that rank - three is enough as the rank of tensor to describe fuzzy spaces with arbitrary dimensions . this property drastically simplifies the structures of the tensor model , since various dimensional cases can be treated in a common framework . the rank - three tensor model has mainly been analyzed in numerical manners by the present author @xcite . in particular , for the tensor models that possess a certain gaussian type of classical solutions , it has numerically been shown that the properties of low - lying long - wavelength modes of small fluctuations around such gaussian backgrounds are in remarkable agreement with the general relativity in all the dimensional cases having been studied so far ( @xmath1 ) @xcite . namely , the general relativity was found to emerge in the tensor model as an effective long - wavelength description of the tensor model around a particular class of classical background solutions . this is also expected to be true in any other dimensions , since the framework and the procedure of analysis are common . this paper gives a summary of the results obtained so far concerning the emergence of the general relativity in the tensor model . there exist various versions of the rank - three tensor model @xcite . the simplest is the one that has a real symmetric rank - three tensor as its only dynamical variable , and has the invariance under the orthogonal group . in this paper , this simplest one is considered . the dynamical variable is a real - valued rank - three tensor @xmath2 , each index of which takes integers , @xmath3 . the number @xmath4 is the total number of linearly independent functions on a fuzzy space , or can more physically be interpreted as the number of `` points '' forming a fuzzy space . the variable @xmath2 is assumed to be totally symmetric , @xmath5 the algebra of products defined by @xmath6 is commutative but nonassociative in general . therefore the tensor model in this paper is a theory of dynamical commutative _ nonassociative _ fuzzy spaces . the basis of functions @xmath7 can be changed by linear transformations . a simple choice of equivalence of the basis functions is to assume that bases related by the orthogonal transformations represent equivalent fuzzy spaces . correspondingly , the tensor model must be invariant under the orthogonal transformation @xmath8 where @xmath9 is an arbitrary element of the orthogonal group @xmath10 . the definition of the system is given by a partition function , @xmath11 where @xmath12 is an action with the variable @xmath2 , and must be invariant under the orthogonal group transformation ( [ eq : trans ] ) . the integration measure @xmath13 must also be invariant under ( [ eq : trans ] ) , and is defined from the invariant metric in the space of @xmath2 given by @xmath14 so far , the emergence of the general relativity in the tensor model has only been shown around a particular class of backgrounds in the tensor model . these backgrounds have certain gaussian forms , and the algebras defined by them represent certain simple kinds of commutative _ nonassociative _ fuzzy flat spaces with arbitrary dimensions @xcite . in this section , to describe such genuine gaussian backgrounds , the indices of @xmath2 are assumed to take continuous values , while they will take finite discrete values in the actual analyses of the following sections . the gaussian backgrounds have the form , @xmath15 , \label{eq : cx}\ ] ] where @xmath16 and @xmath17 are positive numerical constants , @xmath18 are @xmath19-dimensional continuous coordinates , @xmath20 , and @xmath21 . the algebra of functions @xmath22 defines a commutative _ nonassociative _ fuzzy @xmath19-dimensional flat space considered in @xcite . because of the translational symmetry of ( [ eq : cx ] ) , it is generally more convenient to describe it in the momentum basis . by applying fourier transformation to the coordinate indices , one obtains the expression in the momentum basis because of the reality condition of the tensor in the coordinate basis , and one needs also an additional symmetric tensor @xmath23 for contracting the indices . these details are essentially important in the mode analysis of the following sections . ] as @xmath24,\ ] ] where @xmath25 and @xmath26 are positive numerical constants . one of the motivations for considering such particular solutions is the ( partial ) computability due to the gaussian forms . another is that the fuzzy spaces are physically well - behaved , because the fuzziness is well localized and the spaces are invariant under the poincare transformation , representing fuzzy @xmath19-dimensional flat spaces . moreover , as shown in the next section , there exists a natural correspondence between the metric field in the general relativity and the tensor around the gaussian backgrounds in the tensor model . in fact , there exist infinitely many actions that have such gaussian backgrounds as their classical solutions . two explicit examples have been studied so far @xcite . unfortunately , the explicit forms of the actions are very complicated and unnatural . this is a serious problem , which must be investigated in future study . however , what is interesting and remarkable in these actions in common is that each of them contains all the dimensional gaussian fuzzy flat spaces as its classical solutions , as illustrated in figure [ fig : potential ] . this means that all the dimensional spaces can be treated with one action in a unified manner . thus , for example , it is in principle possible to study transitions between spaces with distinct dimensions in the tensor model . in the physical interpretation of the tensor model , a classical solution should be regarded as a background space , and fluctuations of tensor around such a classical solution as field fluctuations on a background space . the main interest of the present study is whether such fluctuations can be identified with the general relativity or not . to check this , the procedure carried out so far in @xcite assumes a correspondence between the tensor model around the gaussian backgrounds and the metric tensor field in the general relativity . this correspondence enables one to compute the expectations about the tensor model from the general relativity . if the expectations successfully agree with the numerical analysis of the tensor model , one may conclude that the general relativity is emergent around the gaussian backgrounds in the tensor model . generalizing the gaussian backgrounds ( [ eq : cx ] ) in a coordinate invariant manner , one can derive a natural correspondence between the metric tensor field in the general relativity and the tensor around the gaussian backgrounds as @xmath27,\end{aligned}\ ] ] where @xmath28 , and @xmath29 denotes the geometric distance between @xmath30 and @xmath31 . the main assumption in this correspondence is that the low - lying long - wavelength fluctuations of the tensor around the gaussian backgrounds in the tensor model are exhausted by the metric field in the general relativity in the manner given in ( [ eq : correspondence ] ) . it should be noted that this correspondence could be modified in higher orders of the fuzziness @xmath32 . for example , there could exist corrections such as @xmath33 in ( [ eq : correspondence ] ) . although it is certainly possible to directly use the correspondence ( [ eq : correspondence ] ) in the comparison between the tensor model and the general relativity , it is much more convenient to use a tensor with a smaller rank . let me define @xmath34 small fluctuations @xmath35 around a classical solution @xmath36 induces fluctuations of @xmath37 as @xmath38 on the other hand , if one assumes a gaussian background and puts the assumed correspondence ( [ eq : correspondence ] ) into ( [ eq : tensordk ] ) , one obtains in the lowest order @xcite @xmath39 where the momentum basis is used , and @xmath40 is the fourier transform of @xmath41 , which describes the fluctuations of the metric tensor field around a flat background . in later sections , the analysis of eigenvectors gives @xmath35 of each fluctuation mode in the tensor model . then one can compute @xmath42 of each mode by putting this @xmath35 and the background @xmath36 into ( [ eq : tensordk ] ) . this @xmath42 obtained from the numerical analysis of the tensor model can be compared with the fluctuation modes of the metric tensor field in the general relativity through ( [ eq : metricdk ] ) . another important fact which can be derived from ( [ eq : correspondence ] ) is that the measure which must be used in the analysis of the general relativity is uniquely determined from the measure ( [ eq : cmeasure ] ) in the tensor model . by putting the correspondence ( [ eq : correspondence ] ) into ( [ eq : cmeasure ] ) , one obtains the dewitt supermetric @xcite , @xmath43,\ ] ] in the lowest order @xcite . in this section , i will study the small geometric fluctuations on @xmath19-dimensional flat tori in the general relativity to prepare for the comparison with the tensor model . the important point in the analysis is that not all of the fluctuations of the metric tensor field are the fluctuations of geometry , because of the gauge symmetry ( local translation symmetry ) in the general relativity . the relevant modes are only those which are normal to the gauge symmetry @xcite . the measure to be used to define this normality condition is the dewitt supermetric given in ( [ eq : supermetric ] ) , since the numerical analysis of the tensor model uses the corresponding measure ( [ eq : cmeasure ] ) as shown in the following section . for small fluctuations around a flat metric @xmath44 , the supermetric ( [ eq : supermetric ] ) is given by @xmath45.\ ] ] on the other hand , the infinitesimal gauge transformation on a flat background is given in the momentum basis by @xmath46 where @xmath47 is the fourier transform of local translation vector . at the vanishing momentum sector @xmath48 ," +"the mystery of the dark energy / cosmological constant persists despite great efforts of particle physicists and cosmologists to find a convincing solution . since the famous article by s. weinberg , it is well known that candidate models should not only explain the smallness of the cosmological constant , if it is somehow related to quantum gravity , but also what is called the coincidence problem i.e. why does dark energy become dominant quite late in the history of the universe ? models inspired by string theory like 4-form gauge models can describe the smallness of the dark energy but not the coincidence problem . anthropical models explain the latter problem but it is very difficult to find a natural and convincing particle physics model for them . the same problem somehow exists for the alternative to a cosmological constant i.e. for quintessence models . even if tracker solutions make the model not very sensitive to the initial conditions , some fine tuning of the slope of the potential is necessary . it is also an open question if both inflation and quintessence behavior can be explained by the same field and if not , what is their relation and which type of particle physics can provide both of them specially in a natural way . + here we suggest an alternative to a primordial quintessence field . there are at least two motivations for the existence of a decaying dark matter ( ddm ) . if r - parity in susy models is not strictly conserved , the lsp which is one of the best candidates of dm can decay to standard model particles . violation of this symmetry is one of the many ways for providing neutrinos with very small mass and large mixing angle . another motivation is the search for sources of ultra high energy cosmic rays ( uhecrs ) . in this case , ddm must be composed of ultra heavy particles with @xmath2 . in a recent work we have shown that the lifetime of uhdm ( ultra heavy dark matter ) can be relatively short , i.e. @xmath3 where @xmath4 is the age of the universe ( astro - ph/0001137 ) . + if a very small fraction of the mass of primary ddm particles changes to a scalar field with proper self interaction potential , the gradual condensation of this field at late time behaves like a quintessential matter . the advantage of this model to others is that late time yield of this type of energy and its correlation with the amount of dark matter comes up naturally and the dominance of one with respect to the other at each epoch is automatically explained . + in the present work we only study the plausibility of this model . we postpone a more detailed study to elsewhere . the natural choice of cosmological parameters for this model is an initial @xmath5 where @xmath6 is an early time in the history of the universe . for the result presented here we consider it to be the time of decoupling of cmb photons ; @xmath7 . the remnants of the decay else than quintessence field mainly consist of very energetic particles which will contribute to the yield of hot dark matter . there is strict constraint on the amount of the latter from cosmological observations and the model must be consistent with observations . however , one should not forget that massive particles like proton / ant - proton and even electrons become colder with the expansion of the universe and at some point they are not any more considered as hot . in fact it can be shown that the whole effect on the equation of state of the universe is the reduction of the effective @xmath8 of the cosmological constant or a quintessence matter ( astro - ph/0002400 ) . + we summarize our preliminary results in two following figures . the first figure shows @xmath9 of the fit of quintessence models on the publicly available super - novae ia data . models with @xmath0 fit the data better than @xmath10 . + the second figure shows the evolution of density of various types of matter from decoupling of cmb photons to today for a typical selection of parameters . in one hand it shows that it is possible to obtain the present `` equivalent '' value of cosmological parameters without fine tuning of the suggested model . another conclusion is that the appearance of cosmological parameters as measured in the local universe is very recent i.e. the measurement of cosmological parameters at high redshift permits to distinguish between this model and other quintessence models . it is evident that the model presented here can not be believed before investigating many issues . the first and one of the most important ones is the condensation of the scalar field . one should determine the mass and the form of the potential and find the region of the parameter space that in a natural way can lead to a late condensation . the other issue is that the value of @xmath8 for this type of matter can not be constant . this can affect the evolution of halos , star formation rate , ionization of igm etc . and can be used to verify the model ." +"since the mid 1970 s the existence of heavy hadronic molecules ( composed by a pair of heavy hadrons instead of a pair of heavy quarks ) has been theorized@xcite . this assumption was made based on the similarities between the heavy meson - heavy antimeson system and the deuteron . however , it was not until the discovery of the @xmath0@xcite by the belle collaboration , in 2003 , that the first experimental data that could fit into that molecular scheme was found . since then , many other xyz states have been found , being the @xmath1 also natural candidates to have a molecular structure .. besides , the @xmath2 limit of qcd simplifies the theory so a set of symmetries are induced . probably , the most important symmetries induced in this limit are hqss , hfs , and hads . we make use of them , along with the assumptions of the @xmath0 and the @xmath1 to be heavy hadronic molecules , to obtain a family of heavy meson - doubly heavy baryons that could also be interpreted as triply heavy pentaquarks . this proceeding is organized as follows . first we briefly introduced our eft based on hqss and hfs that we will use in the analysis of the @xmath0 and the @xmath1 . second , we will discuss hads and its implications . finally , our results will be shown in table [ tab : predictions ] . in this work we are following the scheme described in @xcite where all sort of details can be found . at lowest order , hqss and hfs impose that the dynamics of the model does not depend on either the mass or the spin of the heavy quark . taking this into account , the most general potential that describes the dynamics of the heavy meson - antimeson pair depends only in four low energy constants or counter - terms ( lecs ) , up to corrections of the order @xmath3 : @xmath4 tr\left[{h}^{(\bar{q } ) } \bar{h}^{(\bar{q } ) } \gamma^{\mu } \right ] + \\ \nonumber { } & & + \frac{c_{a}^{\lambda}}{4}~ tr\left[\bar{h}^{(q)}_{a } \lambda^{i}_{ab } { h}^{(q)}_{b } \gamma_{\mu } \right ] tr\left[{h}^{(\bar{q})}_{c } \lambda^{i}_{cd}\bar{h}^{(\bar{q})}_{d } \gamma^{\mu } \right ] + \\ \nonumber { } & & + \frac { c_{b}}{4}~ tr\left[\bar{h}^{(q)}{h}^{(q ) } \gamma_{\mu } \gamma_{5 } \right ] tr\left[{h}^{(\bar{q } ) } \bar{h}^{(\bar{q } ) } \gamma^{\mu } \gamma_{5}\right ] + \\ & & + \frac{c_{b}^{\lambda}}{4}~ tr\left[\bar{h}^{(q)}_{a } \lambda_{ab}^{j}{h}^{(q)}_{b } \gamma_{\mu } \gamma_{5 } \right ] tr\left[{h}^{(\bar{q})}_{c } \lambda^{j}_{cd } \bar{h}^{(\bar{q})}_{d } \gamma^{\mu } \gamma_{5}\right]\end{aligned}\ ] ] being @xmath5 the gell - mann matrices and @xmath6 the meson ( antimeson ) field in the charm sector ( and viceversa in the bottom sector ) . moreover , the four lecs will be rewritten through a linear combination into @xmath7 , @xmath8 , @xmath9 and @xmath10 for notation . these four lecs will be fitted to reproduce some experimental data in our scheme . in this framework , bound states will be found by solving the lippmann - schwinger equation as they will appear as poles in the t - matrix : @xmath11 , and the ultraviolet divergences of the loop function are treated introducing a gaussian regulator in the propagator and in the potential such as : @xmath12 these assumptions determine three linear combinations of the lecs , that is : @xmath13 and @xmath14 which in turn are determined by the @xmath0 ( for more details , see @xcite ) and @xmath15 by the @xmath16 resonances [ @xcite ] . up to now , we have only established an eft that analyzes heavy meson - heavy antimeson molecules . in order to use this approach to different systems we will take advantage of the heavy antiquark - diquark symmetry ( hads ) . this @xmath17 limit symmetry , first introduced by savage and wise , states that a heavy diquark behaves as a heavy antiquark up to corrections of the order @xmath18 , , being v the velocity of the heavy quarks . furthermore , since the dynamics of our eft only depends on the light degrees of freedom , that are the same than in the heavy meson - heavy antimeson system , we can make use of some racah algebra ( similar to @xcite ) to obtain the potentials in every possible channels , which are displayed in table [ tab : potentials ] . the @xmath19 states are those where heavy quarks in the baryon are coupled to @xmath20 ( which is forbidden if the two quarks are the same because of the pauli s principle of exclusion ) . then we just have to solve the lippmann - schwinger equation in each channel using the lecs we have previously fitted to obtain the results of table [ tab : predictions ] . the isoscalar states are related to the @xmath0 . the isovector states are determined by the @xmath21 and the isovector component of the @xmath0 . the sources of error in the analysis are : the masses of the @xmath0 and @xmath22 resonances , the ratio of the @xmath0 amplitude decays ( calculated in @xcite ) and the two eft expansions used in this work . the errors for hqss are taken to be @xmath23 in the charm ( bottom ) sector and @xmath24 $ ] in the charm ( charm - bottom ) [ bottom ] sector for hads . then , an unique error is obtained by adding in quadratures all different sources . as a summary , we can conclude that our analysis based on several qcd symmetries in the @xmath17 limit predicts the existence of several heavy meson - doubly heavy baryon molecular partners of the @xmath0 and the @xmath1 . this same effective field theory approach could also be extended to study doubly heavy baryon - double heavy antibaryon molecular systems in the future . f .- k.g . acknowledges the theory division of ihep in beijing , where part of the work was done , for the hospitality . c. h .- d . thanks the jae - csic program . this work is supported in part by the dfg and the nsfc through funds provided to the sino - german crc 110 `` symmetries and the emergence of structure in qcd '' , by the nsfc ( grant no . 11165005 ) , by the spanish ministerio de economa y competitividad and european feder funds under the contract fis2011 - 28853-c02 - 02 and the spanish consolider - ingenio 2010 programme cpan ( csd2007 - 00042 ) , by generalitat valenciana under contract prometeo/2009/0090 and by the eu hadronphysics2 project , grant agreement no ." +"we are poised on the threshold of unprecedented technical growth in wide - field time domain astronomy , where ground - based observations yield very precise measurements of stellar brightness from high - volume data streams . so far , wide - field time - series surveys has been spearheaded by relatively small telescopes since they are supported by large field of view ( fov ) instruments operating with high duty cycle ( see @xcite for a summary of optical variability surveys ) . within the last decade , the advent of large mosaic ccds has facilitated the coverage of large sky area even for large - aperture telescopes ( e.g. , mmt megacam : @xcite ; eso very large telescope omegacam : @xcite ; subaru suprime - cam : @xcite ; chft megacam : @xcite ; iptf : @xcite ) . although these facilities are generally devoted to imaging surveys , researchers are attempting to utilize them for short- and long - term variability surveys with short - cadence exposures ( e.g. , @xcite ) . such wide - field imaging systems have enabled us to observe hundred of thousands of target stars simultaneously and also to detect various variability phenomena . a remarkable thing about these surveys is that the fraction of variable sources increases as the photometric precision of the survey improves . for this reason , it is important to improve the accuracy in photometry . another key issue in wide - field time - series photometry is the removal of temporal systematics from a single image frame or several consecutive image frames . it has recently become known that systematic trends in time - series data can be different and localized within the image frame when the fov is large . such spatially localized patterns may be related to subtle point spread function ( psf ) differences and sky condition within the detector fov ( e.g. , @xcite ) . as these patterns change in time , we can see how the temporal variations of systematic trends affect the brightness and shape of light curves directly . the time - scale of systematic variation is sometimes comparable to short - term variability , such as transits or eclipses , and in some cases even long - term variability . thus , it is often difficult to identify and characterize true variabilities . in this paper , we introduce a new photometry procedure , called multi - aperture indexing , which is suited to analyzing well - sampled wide - field images of non - crowded fields with a highly varying psf , such as those produced by wide - field mosaic imagers on large telescopes . we apply this procedure to archival imaging data from the mmt / megacam transit survey of the open cluster m37 ( hartman et al . 2008a ) , demonstrating a substantial improvement over the existing photometry . section 2 describes the mmt imaging database and identifies problems in the existing photometry which motivated the development of our new methods . section 3 describes the multi - aperture photometry that utilize newly defined contamination index and carefully tuned calibration procedures , including the results of the basic tests to validate our approach . section 4 gives an in - depth discussion about systematic trends in time - series data and suggests an efficient way for identifying , measuring , and removing spatio - temporal trends . section 5 describes the effects of new calibration on period search , and we summarize our main results in the last section . @xcite have conducted a study to find neptune - sized planets transiting solar - like stars in the rich open cluster m37 . the observing strategy was carefully designed for a transiting planet search by several considerations ( e.g. , the reliability of exposure time per frame , the effects of pixel - to - pixel sensitivity variations , and sensitivity of filter ) . their work did not reveal any transiting planets , but it did provide a rare opportunity to explore photometric variability at relatively high temporal resolution with 3090 s. @xcite discovered 1430 new variable stars , including very short - period eclipsing binaries ( e.g. , v37 , v706 , v1160 ) and @xmath1 sct - type pulsating stars ( e.g. , v397 , v744 , v1412 ) . we used the same data set on the open cluster m37 . a detailed discussion of the observations , original data reduction , and light curve production is described in @xcite . the data archive consists of approximately 5000 @xmath2-filter images taken over 24 nights with the wide - field mosaic imager ( megacam ) mounted at the @xmath3 cassegrain focus of the 6.5 m mmt telescope . note that megacam is made up of 36 2048 @xmath4 4608 pixel ccd chips in a @xmath5 pattern , covering a 24@xmath6@xmath424@xmath6 fov @xcite . this instrument has an unbinned pixel scale of @xmath7 , but it was used in @xmath8 binning mode for readout . the observation logs are summarized in table 1 of @xcite . in brief , the @xmath9-band time - series observations were undertaken between 2005 december 21 and 2006 january 21 , with a median fwhm of @xmath10 arcsec . exposure times are chosen to keep an @xmath11 mag star as close to the saturation limit , which is expressed as a function of seeing conditions . with an average seeing @xmath00@xmath12.89 on images , the quality of the images is good to achieve high - precision light curves ( less than 1% rms value ) down to 20 . in addition to the imaging data set , this database includes light curve data sets for a total of 23,790 sources detected in a co - added reference image . theses light curves are obtained by the image subtraction technique using a modified version of isis software ( @xcite ; @xcite ) . as shown in figure [ fig : fig1 ] , however , the raw light curves from the original image subtraction procedures exhibit many unusual outliers , and more than @xmath015% of data get rejected by a simple filtering algorithm after cleaning procedures . in practice , brutal filtering that is often applied to remove outlying data points can result in the loss of vital data , with seriously negative impact to short - term variations such as flares and deep eclipses . we also find that the image subtraction technique often resulted in measurement failures from several frames due to poor seeing or tracking problem . after removing these bad frames , it leads to loss of additional @xmath05% data points from most light curves . in order to overcome this problem , we have re - processed the entire image database with new photometric reduction procedures . 3-@xmath13 control limits ( dotted lines ) . these light curves contain outlier points that significantly increase the rms scatter of the raw light curves . ] we followed the standard ccd reduction procedures of the bias correction , overscan trimming , dark correction , and flat - fielding as described in @xcite . the individual ccd frames were calibrated in iraf , using the mosaic data reduction package megared . the first step is to correct the pixel - to - pixel zero - point differences that are usually described by the sum of a mean bias level and a bias structure . as the bias frames were not separately taken during the time of the observations , the mean bias level was subtracted from each image extension using an overscan correction and so we can not remove any remaining bias structure from all overscan - subtracted data frames . according to description in matt ashby s megacam reduction guide , the bias structure can be very significant in some small regions such as the portions of the arrays close to the readout leads . the dark currents are normally insignificant for megacam so that corrections are not needed even for long exposures . the next step is to correct pixel - to - pixel variations in the sensitivity of the ccd ; we used the program ` domegacamflat2 ` . this program determines the scaling factors to correct the gain difference between the two amplifiers of each chip by finding the mode in the quotient of pixels to the left and right of the amplifier boundary , and then flattens each of the frames with a master flat field frame . it is worth mentioning that the sky conditions were rarely photometric during the observing run , with persistent light cirrus for most of the nights . therefore it was only possible to obtain twilight sky flats on a handful of nights ( dome flats were not possible ) . we removed bad pixels using the megacam bad pixel masks distributed with the megared package . the values of bad pixels are replaced with interpolated value of the surrounding pixels using the iraf task ` fixpix ` . the numerous single pixel events ( cosmic - rays ) were identified and removed using the lacosmic package @xcite . the megacam data already have a rough world coordinates system ( wcs ) solution that is based on a single value of the telescope pointing . to update these with a more precise solution , we applied astrometric correction to each ccd in the mosaic using the wcstools imwcs program @xcite . the new solution is derived by minimizing the differences between the r.a . and decl . positions of sources in a single ccd chip and their positions listed in the 2mass point source catalog @xcite . the resulting astrometric accuracy is typically better than 0@xmath14.1 rms in both r.a . and decl . typically , a point or extended source detection algorithm is applied to each frame independently and it always requires criteria for what should be regarded as a true detection . in obtaining the pixel coordinates for all objects in the m37 fields , this procedure often misses some objects when the detection threshold approaches the noise level . also it needs a substantial effort to match the objects that are detected in only some of the frames . our approach is as follows : a complete list of all objects is obtained from a co - added reference frame , and then the photometry is performed for each frame using the fixed positions of the sources detected on the reference . since the relative centroid positions of all objects are the same for all frames in the time series , we can easily place an aperture on each target and measure the flux even for the stars at the faint magnitude end . we constructed the reference frame for each chip from the best seeing frames using the swarp software . benefiting from a highly accurate astrometric calibration of input frames , we were able to improve the quality of co - added images . in the swarp implementation , the pixels of each frame were resampled using the lanczos3 convolution kernel , then combined into the reference frame by taking a median or average . after this was done , sources were detected and extracted on the reference frame using the sextractor software @xcite . when configured with a lower detection threshold , sextractor extracts the number of spurious detections ( e.g. , diffraction spikes around bright stars , or outer features of bright galaxies ) . these false detections were removed by careful visual inspection for each chip . the final catalog contains a total of 30,294 objects including both point and extended sources . prior to the photometry , the initial centroid coordinates of the target objects for each frame were computed by using the wcstools sky2xy routine @xcite . the stored world coordinate system for each frame is used to convert the ( r.a" +"factorization of numbers into their prime factors is a hard non - polynomial problem for classical computers . it was shor @xcite who proposed a quantum algorithm which can solve the problem of factorization of numbers on a quantum computer with a tremendous speedup as compared to a classical computer . a practical demonstration of shor s algorithm has been carried out by factorizing the integer 15 @xcite , using nuclear magnetic resonance . however , quantum computers capable of implementing shor s algorithm for larger numbers have not been developed yet . several approaches to factorize numbers based on interference of multiple quantum paths have been proposed dowling , summhammer , merkel2006,mahesh , mehring , gilowski2008,bigourd2008,sadgrove2008,stefanak . those schemes do not use quantum entanglement and do not capitalize on quantum parallelism . as a consequence , these schemes scale exponentially with the number of digits of the factorized number . this is in contrast to shor s algorithm which requires only a polynomial number of operations . nevertheless , if the interference is implemented in a suitable way in a system , which does the factorization , then one can benefit because nature plays the role of a computer . as was pointed out by jones @xcite the proposed techniques for factorization based on gauss sums @xcite unfortunately do not provide useful methods to factorize numbers , because a precalculation of the factors is needed for the experiment . in spite of that , gauss sums would be useful if it is possible to avoid explicit precalculation stages of the algorithms . physical systems that can implement the gauss sums must be described by complex numbers . in the present paper we investigate how truncated fourier sum and its generalizations , like truncated gauss , kummer and exponential sums , could emerge from superposition of several oscillations . those sums can be used successfully to factorize numbers . due to the wide use of interferences and beats in optics , we shall keep our consideration close to optics and our examples are in wave optics too . however , the proposed implementation can be extended to virtually any physical system where superposition among several different oscillations appear , from the mechanical pendulum with several degrees of freedom , through the atomic and solid state systems and their analogs in quantum mechanics . in order to find the factors of a given number @xmath0 we use the following truncated sum : @xmath1where @xmath2 is an integer and @xmath3 is the number of terms in the sum . the argument @xmath4 scans through all integers between @xmath5 and @xmath6 for possible factors . the capability of the sum of eq . ( [ truncated sum ] ) to factor numbers originate from the fact that for an integer factor @xmath7 of @xmath0 with @xmath8 , all phases in @xmath9 are integer multiples of @xmath10 . consequently , the terms add up constructively and yield @xmath11 . when @xmath4 is not a factor , the phases oscillate rapidly with @xmath12 , and @xmath9 takes on small values . in this interference pattern , larger truncation parameter @xmath3 leads to better convergency . in principle , already the first several terms of the sum are sufficient to discriminate factors from non - factors . depending on the coefficient @xmath2 in eq.([truncated sum ] ) we distinguish several important cases : [ fourier , gauss and kummer ] @xmath13 the use of quadratic phases to factor numbers ( gauss sum ) has the advantage of fewer terms needed in the sum to distinguish factors from non - factors compared to the linear phase ( fourier sum ) , which is because of high quasi - randomness for the quadratic phase @xcite . in the very same way the kummer sum , and sums with nonlinear phases of higher order , has an advantage compared to the gauss sum @xcite . now we consider a system with @xmath3 different oscillation modes , with frequencies @xmath14 , phases @xmath15 and amplitudes @xmath16 @xmath17 using the superposition principle we can write the resulting oscillation as the sum of all oscillations : @xmath18 in the sum of eq . ( [ result oscilation ] ) we can vary the parameters @xmath19 , @xmath14 , @xmath15 and the time @xmath20 . in the next several sections we will show how truncated fourier , gauss , kummer and exponential sums could emerge when we fix three of the parameters for all oscillations , while changing the fourth parameter . first we consider the case when the parameters @xmath16 , @xmath14 , @xmath21 are equal for all oscillations in eq . ( [ individual oscillation ] ) @xmath22thus the only parameter that is left not fixed in eq . ( [ individual oscillation ] ) is the time @xmath20 . this can be easily realized in optics by interferometry , where the individual oscillations describe the electric field for the different arms of the interferometer as shown in fig.[four arms ] . from fig . [ four arms ] and eq . ( [ result oscilation ] ) we see that we have the following sums of electric fields in the detector@xmath23where @xmath24 is the phase accumulated in the @xmath12 arm of the interferometer due to the difference in travel time through each arm . suppose that each arm of the interferometer is with length @xmath25 the wave length of the light that we use in vacuum is @xmath26 and the corresponding frequency is @xmath27 , let the index of refraction in each arm of the interferometer is different and is denoted as @xmath28 . then the phase @xmath24 for the beam that travels through the @xmath12-th arm of the interferometer is given as@xmath29here @xmath30 is the time that light travel in the @xmath12-th arm of the interferometer to pass length @xmath31 and @xmath32 is the speed of light in that arm . the refraction index in arm @xmath12 of the interferometer is @xmath33thus @xmath34then the electric filed in the detector is @xmath35now if the index of reflection in the @xmath12 arm of the interferometer is @xmath36then @xmath37the detector registers the intensity,@xmath38various @xmath2 gives us a different type of truncated sum ( see eq . ( fourier , gauss and kummer ) ) . the number that we want to factorize is @xmath39 the trial factors are @xmath26 . each time when the trial factor @xmath26 is a factor of @xmath40 we will observe a maximum signal in the detector . the number of the terms in the sum can be controlled by doubling the elements in the interferometer fig . [ four arms ] . the numbers that could be factorized in this way are of order @xmath41 . now we consider a train of pulses , where the delay of the @xmath12 pulse compared to first pulse is given as@xmath42here @xmath12 takes the values @xmath43 , while @xmath44 can be set as a unit of time . we consider the case when all pulses have equal amplitudes @xmath45 and equal frequencies @xmath46 . then the electric field for the @xmath12 pulse is given by eq . ( [ individual oscillation ] ) and reads @xmath47let us make a different path way for every pulse in such a way that all pulses hit the same detector at the same time , this is equivalent to make @xmath48 at the place where all pulses collides . then the intensity that the detector registers is a result from the superposition among all electric fields , e.g the sum from eq . ( [ result oscilation]):@xmath49where @xmath50 . if one chooses the frequency @xmath51 as the number that we want to factorize ( @xmath0 ) and @xmath52 as a trail factor ( @xmath4 ) , then eq.([intensity ] ) reduces to the sum from eq . ( truncated sum ) . if we now consider a system that exhibits several oscillations with the same amplitude @xmath53 and the same initial phases ( @xmath54 ) , but with different frequencies @xmath14 , then the individual oscillations ( individual oscillation ) are described by @xmath55the resulting oscillation ( [ result oscilation ] ) is @xmath56where @xmath57 . we will observe beats when @xmath58 is a integer which could be used to find the factors of the number @xmath59 . one physical realization of the above idea could be a light with several high - harmonic generated frequencies brabec2000,gavrila1992 , chosen in the way that they present for example the odd terms in the fourier sum : @xmath60then in the detector the time of the detection play the role of the test factors and whenever there is a beat we observe a maximum of the signal , thus this time is a real factor . the last parameter that we can vary in eq . ( [ individual oscillation ] ) is the amplitude of the individual oscillation . for example if we work with laser light we can use the different polarization orientations of the electric field . the electric field is a vector in the polarization plane , which can be described by complex electrical field . let us consider the case when we have a linearly polarized light pulse , which is split in several parts and each part passes different pathways through faraday cells as shown in fig . [ faraday cells ] . applying different faraday rotation angles @xmath15 on each pathway and collecting all of the light at the same place ( at the detector ) the resulting electric field is the superposition:@xmath61where @xmath53 is the electrical field amplitude of the initial beam . the relation between the angle of polarization rotation due to the faraday effect @xmath15 and the magnetic field @xmath62 in a diamagnetic material @xcite is @xmath63 where @xmath31 is the length of each pathway and @xmath64 is the verdet constant for the material @xcite . for the amplitude of the resulted electric field we have:@xmath65if we now have a magnetic field @xmath62 for the @xmath12-th faraday cell , which is given as : @xmath66then the intensity in the detector is @xmath67here the number that we want to factorize is @xmath39 the trial factors are @xmath68 . we have shown how the factorization algorithm based on truncated fourier , gauss , kummer or exponential sums emerges naturally from superpositions of classical light waves . we have proposed a number of simple implementations in optics . these implementations can be extended to virtually any physical system where superpositions of several different oscillations appear . the factorization algorithms discussed in this paper are classical algorithms and thus their complexity scales exponentially with the number of digits . if an extension of this algorithm exists in entangled quantum systems , then a quantum computing parallelism would be involved with an exponential speedup of factorization . the present solutions therefore could be the first step to an alternative quantum factorization algorithm to the famous shor algorithm . this work has been supported by the eu tok project camel , the eu rtn project emali , the eu itn project fastquast , and the bulgarian national science fund grants no . wu-2501/06 and no . wu-2517/07 . the author is grateful to n. vitanov for stimulating discussions and critical reading of the manuscript . during the preparation of this paper , the author became aware of a related work by tamma et al ." +"suppose we are trying to learn a difficult classification problem : for example determining whether the given image contains a human face , or whether the mri image shows a malignant tumor , etc . we may first try to train a simple model such as a small neural network . if that fails , we may move on to other , potentially more complex , methods of classification such as support vector machines with different kernels , techniques to apply certain transformations to the data first , etc . conventional statistical learning theory attempts to bound the number of samples needed to learn to a specified level of accuracy for each of the above models ( e.g. neural networks , support vector machines ) . specifically , it is enough to bound the vc - dimension of the learning model to determine the number of samples to use @xcite . however , if we allow ourselves to change the model , then the vc - dimension of the overall learning algorithm is not finite , and much of statistical learning theory does not directly apply . accepting that much of the time the complexity of the model can not be a priori bounded , structural risk minimization @xcite explicitly considers a hierarchy of increasingly complex models . an alternative approach , and one we follow in this paper , is simply to consider a single learning model that includes all possible classification methods . we consider the unrestricted learning model consisting of all computable classifiers . since the vc - dimension is clearly infinite , there are no uniform bounds ( independent of the distribution and the target concept ) on the number of samples needed to learn accurately @xcite . yet we still want to guarantee a desired level of accuracy . rather than deciding on the number of samples a priori , it is natural to allow the learning algorithm to decide when it has seen sufficiently many labeled samples based on the training samples seen up to now and their labels . since the above learning model includes any practical classification scheme , we term it universal ( pac- ) learning . we first show that there is a computable learning algorithm in our universal setting . then , in order to obtain bounds on the number of training samples that would be needed , we consider measuring sample complexity of the learning algorithm as a function of the unknown correct labeling function ( i.e. target concept ) . although the correct labeling is unknown , this sample complexity measure could be used to compare learning algorithms speculatively : if the target labeling were such and such , learning algorithm @xmath0 requires fewer samples than learning algorithm @xmath1 "" . by asking what is the largest sample size needed assuming the target labeling function is in a certain class , we could compare the sample complexity of the universal learner to a learner over the restricted class ( e.g. with finite vc - dimension ) . however , we prove that it is impossible to bound the sample complexity of any _ computable _ universal learning algorithm , even as a function of the target concept . depending on the distribution , any such bound will be exceeded with arbitrarily high probability . the impossibility of a distribution - independent bound is entirely due to the computability requirement . indeed we show there is an uncomputable learning procedure for which we bound the number of samples queried as a function of the unknown target concept , independently of the distribution . our results imply that computable learning algorithms in the universal setting must waste samples "" in the sense of requiring more samples than is necessary for statistical reasons alone . there is comparatively little work in statistical learning theory on learning arbitrary computable classifiers compared to the volume of research on learning in more restricted settings . computational learning theory ( aka pac - learning ) requires learning algorithms to be efficient in the sense of running in polynomial time of certain parameters @xcite . that work generally restricts learning to very limited concept / hypothesis spaces such as perceptrons , dnf expressions , limited - weight neural networks , etc . the purely statistical learning theory paradigm ignores issues of computability @xcite . work on learning arbitrary computable functions is mostly in the learning in the limit "" paradigm @xcite , in which the goal of learning is to eventually converge to the perfectly correct hypothesis as opposed to approximating it with an approximately correct hypothesis . the idea of allowing the learner to ask for a varying number of training samples based on the ones previously seen was studied before in statistical learning theory @xcite . linial et al @xcite called this model dynamic sampling "" and showed that dynamic sampling allows learning with a hypothesis space of infinite vc - dimension if all hypotheses can be enumerated . this is essentially theorem [ thm : uncomputablealgorithm ] of our paper . however , the hypothesis space of all computable functions can not be enumerated by any algorithm , and thus these results do not directly imply the existence of a learning algorithm in our setting . our proof technique for establishing positive results ( theorem [ thm : learningalgorithmexists ] ) is parallel evaluation of all hypotheses , and is based on levin s universal search @xcite . in learning theory , levin s universal search was previously used by goldreich and ron @xcite to evaluate all learning algorithms in parallel and obtain an algorithm with asymptotically optimal computation time . the main negative result of this paper is showing the absence of distribution independent bounds on sample complexity for computable universal learning algorithms ( theorem [ thm : nobound ] ) . recently ryabko @xcite considered learning arbitrary computable classifiers , albeit in a setting where the number of samples for the learning algorithm is externally chosen . he demonstrated a computational difficulty in determining the number of samples needed : it grows faster than any computable function of the length of the target concept . in contrast , we prove that distribution - independent bounds do not exist altogether for computable learning algorithms in our setting . the _ sample space _ @xmath2 is the universe of possible points over which learning occurs . here we will largely suppose the sample space @xmath2 is the set of all finite binary strings @xmath3 . concept space _ @xmath4 and _ hypothesis space _ @xmath5 are sets of boolean - valued functions over @xmath2 , which are said to _ label _ points @xmath6 as @xmath7 . the concept space @xmath4 is the set of all possible labeling functions that our learning algorithm may be asked to learn from . in each learning scenario , there is some unknown _ target concept _ @xmath8 that represents the desired way of labeling points . there is also an unknown _ sample distribution _ @xmath9 over @xmath2 . the learning algorithm chooses a _ @xmath10 based on iid samples drawn from @xmath9 and labeled according to the target concept @xmath11 . since we can not hope to distinguish between a hypothesis that is always correct and one that is correct most of the time , we adopt the probably approximately correct "" @xcite goal of producing with high probability ( @xmath12 ) a hypothesis @xmath13 such that the probability over @xmath14 that @xmath15 is small ( @xmath16 ) . here we will mostly consider the concept space @xmath4 to be the set of all total recursive functions @xmath17 . we say that this is a universal learning setting because @xmath4 includes any practical classification scheme . we will mostly consider the hypothesis space to be the set of all partial recursive functions @xmath18 , where @xmath19 indicates failure to halt . from pac learning it is known that sometimes it helps to use different concept and hypothesis classes , if one desires the learning algorithm to be efficient @xcite . in a related way , allowing our algorithm to output a partial recursive function that may not halt on all inputs seems to permit learning ( e.g. theorem [ thm : learningalgorithmexists ] ) . abusing notation , @xmath8 or @xmath10 will refer to either the function or to a representation of that function as a program . similarly @xmath4 and @xmath5 will refer to the sets of functions or to the sets of representations of the corresponding functions . we assume all programs are written in some fixed alphabet and are interpreted by some fixed universal turing machine . if @xmath13 is a partial recursive function and @xmath20 then by convention @xmath21 for any partial recursive function @xmath22 ( even if @xmath23 also ) . we can now define what we mean by a learning algorithm : algorithm @xmath0 is a _ learning algorithm _ over sample space @xmath2 , concept space @xmath4 , and hypothesis space @xmath5 if : * ( syntactic requirements ) @xmath0 takes two inputs @xmath24 and @xmath25 , queries an oracle for pairs in @xmath26 , and if @xmath0 halts it outputs a hypothesis @xmath10 . * ( semantic requirements ) for any @xmath27 , for any concept @xmath8 , and distribution @xmath9 over @xmath2 , if the oracle returns pairs @xmath28 for @xmath29 drawn iid from @xmath9 , then @xmath0 always halts , and with probability at least @xmath12 outputs a hypothesis @xmath13 such that @xmath30 < { \varepsilon}$ ] . the always halting requirement seems a nice property of the learning algorithm and indeed the learning algorithm we develop ( theorem [ thm : learningalgorithmexists ] ) will halt for any concept and sequence of samples . however , relaxing this requirement to allow a non - zero probability that the learning algorithm queries the oracle for infinitely many samples does not change our negative results ( theorem [ thm : nobound ] ) , as long as a finite number of oracle calls implies halting . the fundamental notion in statistical learning theory is that of sample complexity . since the vc - dimension of our hypothesis space is infinite , there is no _ uniform bound _ @xmath31 on the number of samples needed to learn to the @xmath27 level of accuracy . we will consider the question of whether for a given learning algorithm there is a _ distribution - independent bound _ @xmath32 on the number of samples queried from the oracle where @xmath8 is the target hypothesis . in other words the bound is allowed to depend on the target concept @xmath11 but not on the sample distribution @xmath9 . such a bound may be satisfied with certainty , or satisfied with high probability over the learning samples . we first show that there is a computable learning algorithm in our setting . [ thm : learningalgorithmexists ] there is a learning algorithm over sample space @xmath2 of all finite binary strings , hypothesis space @xmath5 of all partial recursive functions , and concept space @xmath4 of all total recursive functions . in order to prove this theorem we need the following lemma . results equivalent to this lemma can be found in @xcite . [ lem : m ] let @xmath2 be any sample space and @xmath9 be any distribution over @xmath2 . fix any function @xmath33 . suppose hypothesis space @xmath5 is countable , and let @xmath34 be some ordering of @xmath5 . for any @xmath27 , let @xmath35 . suppose @xmath36 is an infinite sequence of iid samples drawn from @xmath9 . then the probability that there exists @xmath37 such that @xmath38 > { \varepsilon}$ ] , but @xmath39 agrees with @xmath11 on @xmath40 , is less than @xmath41 . the probability that a particular @xmath39 with error probability @xmath38 > { \varepsilon}$ ] gets @xmath42 i.i.d ." +"it is well known that in standard model ( sm ) the higgs quartic coupling has a landau pole for a sufficiently heavy higgs mass . the position of the pole is a function of the higgs boson mass . for light enough mass of the higgs boson , either landau pole is higher than the plank scale or it disappears , and the unitarity of sm is preserved . however very quickly as @xmath5 approaches @xmath6 the landau pole becomes close to the @xmath7 scale and as a consequence the perturbative unitarity is broken in longitudinal gauge boson scattering amplitudes . this is known as unitarity bound on higgs boson mass @xcite , which relates the higgs mass to the energy scale at which the unitarity is broken in sm . this scale , as a function of @xmath5 represents a scale at which either some new particles should come in and save unitarity , or otherwise , the sm becomes strongly coupled . note that in this paper we refer to unitarity of sm in the presence of the higgs boson , not to be confused with analysis of longitudinal gauge boson scattering in the absence of higgs boson , in which case unitarity is violated at much lower scales . in the standard analysis of unitarity bound on higgs mass for sm the equivalence theorem@xcite is used to relate the longitudinal gauge boson scattering amplitude to the corresponding scalar scattering , including unphysical goldstone boson modes in the @xmath8 gauge . at tree level and high energies these amplitudes are purely @xmath9waves , proportional to higgs self - coupling @xmath10 . naive analysis of loop contributions of su(2 ) and u(1 ) gauge bosons to say @xmath11 amplitude seems to give very small result , because couplings @xmath12 are small . however such amplitudes contain sudakov double logarithms@xcite-@xcite , and in a series of recent papers @xcite@xmath13@xcite it was shown how in the effective theory approach one can resum these large logarithms . the results of @xcite@xmath13@xcite are that at the @xmath7 scale such sudakov resummation leads to decrease in the cross section for processes like @xmath14 up to @xmath15 , a suppression factor that rapidly increases with the center of mass energy . in a recent paper @xcite it was shown that electroweak sudakov corrections play a significant role in top quark forward backward asymmetry . it is the purpose of this paper to go beyond the traditional tree level unitarity analysis of sm and study how higher order corrections , which are part of sm and can be calculated using existing techniques , modify the unitarity bound of sm . the paper is organized as follows : in section [ seq : theo ] we briefly review the approach developed in @xcite@xmath13@xcite to resum electroweak logarithms for high - energy processes . in section [ seq : ww ] we derive the effect of electroweak large logarithm resummation on the high energy behavior of longitudinal gauge bosons and higgs scattering amplitudes . we study the applications of derived corrections to the sm unitarity bound in section [ seq : unitarity ] . we conclude in section [ seq : concl ] . soft collinear effective theory ( scet ) @xcite@xmath13@xcite is an effective theory for highly energetic quarks and gluons . recently it has been extended in @xcite@xmath13@xcite to standard model to compute renormalization group improved amplitudes for sm including resummation of sudakov large double - logarithms from loops with su(2 ) and u(1 ) gauge bosons . the computation can be divided in three steps . first we integrate out the hard modes at the scale of center of mass energy @xmath16 for our scattering process . for @xmath17 process we match on four - particle contact operators in eft , which is referred to as @xmath18 with massless su(2 ) and u(1 ) gauge bosons . this leaves us with some basis of operators and wilson coefficients , which only contain @xmath19 and can be minimized by scale choice @xmath16 . next the effective operators in @xmath18 have to be evolved down to the weak scale @xmath20 . in order to relate the wilson coefficients at low scale to the ones obtained by matching on previous step at high scale one needs to exponentiate the anomalous dimension matrix , which consists from collinear and soft parts . this anomalous dimension has been studied and calculated to one loop order for any process in sm in @xcite@xmath13@xcite . finally at the low scale @xmath21 one has to match onto broken theory where gauge bosons have been removed . as a result one gets the effective amplitude for scattering of gauge bosons and quarks and leptons with resummed large logarithms . the corresponding amplitude in @xmath18 gets the following factorized form@xcite : @xmath22 \,p\exp\left(\int_{\mu_h}^{\mu_l}\frac{d\mu}{\mu}{\boldsymbol{\gamma}}(\alpha(\mu))\right)\nonumber\\ & & \qquad\,\,\,\times{\boldsymbol{c}}\left(\alpha(\mu_h),\left\{\ln\frac{p_i{\!\cdot\!}p_j}{\mu_h^2}\right\}\right),\label{mresummaster}\end{aligned}\ ] ] where @xmath23 is the column vector of wilson coefficients obtained from matching at high scale , @xmath24 is the anomalous dimension of effective operator , which is a matrix in the color space , and finally @xmath25 appears as a result of the low scale matching . the anomalous dimension for a general hard scattering process has the form @xmath26 , where collinear anomalous dimension is a sum of collinear anomalous dimensions associated with each leg and soft anomalous dimension has a non - trivial color structure but is universal in the sense that it only depends on light - cone directions and color flow . we derive in this section electroweak radiative correction contribution to the amplitude of longitudinal gauge and/or higgs boson scattering amplitude . the corresponding formalism has been developed in @xcite@xmath13@xcite and was briefly reviewed in section [ seq : theo ] . following these references we use the equivalence theorem to relate gauge boson amplitude to the corresponding unphysical scalar amplitude in @xmath8 gauge . this method was applied in refs . @xcite@xmath13@xcite to derive longitudinal gauge boson production at lhc to next - to - next - to - leading logarithmic order(nnll ) , except for scalar contribution at two loops that is missing for some parts . we work at next - to - leading logarithmic order ( nll ) . at the scale @xmath27 we integrate out hard modes and leave only collinear modes , corresponding to four external label momenta . for our purpose the higgs quartic coupling gives the biggest contribution to the matching . we neglect the gauge boson mediated interactions between the scalars , since they are suppressed by the ratio of weak coupling to higgs self - coupling @xmath28 . the tree level matching is given by higgs quartic term in the sm lagrangian , and is trivial : @xmath29 the higgs quartic coupling has a familiar landau pole at higher energies , and is given at one loop order : @xmath30 while @xmath31 . equation eq . is valid approximation for @xmath32 . for lower masses one has to include contribution of top quark yukawa coupling and the landau pole disappears . we come back to this case at the end of section [ seq : unitarity ] . from high scale the wilson coefficients must be evolved to the low scale @xmath34 which is of the order of the electroweak scale @xmath35 . this is achieved by calculating the anomalous dimension of the four particle operator in the effective theory @xmath18@xcite . the anomalous dimension for such process can be written as sum of process dependent collinear anomalous dimension , which is simply the sum over the corresponding terms for each leg , and the universal soft anomalous dimension @xcite , which only depends on kinematics and color structure , but is same for say scalars or fermions . thus the collinear part of anomalous dimension we know from @xcite@xmath13@xcite and the soft part of the anomalous dimension is same as in @xmath36 for @xmath37 and @xmath38 . for @xmath39 the soft anomalous dimension to one loop is known @xcite , it was derived for @xmath39 , @xmath37 and @xmath38 in refs . @xcite . since our effective operators are ( su(3))color singlets , the anomalous dimension gets contribution only from su(2 ) and u(1 ) gauge bosons . the result for the total anomalous dimension is : @xmath40\right)\nonumber\\ & & + \frac{\alpha_1}{\pi}2y_{\phi}^2 \left((t - u)-i\pi\right),\label{gammasoft}\end{aligned}\ ] ] where the mandelstam invariants are defined according to @xmath41 and @xmath42 where @xmath43 is the scattering angle in the center of mass frame , defined as angle between momenta of @xmath44 and @xmath45 in the cm frame . we will need the formula for the anomalous dimension in the universal form in terms of mandelstam variables @xmath46 , without assuming that @xmath47 as in eq . above . the corresponding analytic continuation looks as follows : @xmath48\right),\label{gtotanalytic}\end{aligned}\ ] ] where @xmath49 , @xmath50 @xcite . it is useful to have an analytical formula for ( matrix ) exponential of the integral from @xmath33 to @xmath34 of anomalous dimension in eq . that appears in the resummed amplitude in eq . : @xmath51 evaluation of @xmath52 requires standard tricks to switch integration from @xmath53 to @xmath54 using the beta - function as well as matrix exponentiation . the former has been analytically performed in the appendix a of ref . @xcite while the latter is a simple exercise for 2 by 2 matrices . rewriting the anomalous dimension in terms of cusp and non - cusp part : @xmath55 where @xmath56 and inex @xmath57 corresponds to @xmath38 and @xmath58 to @xmath37 parts of the sm gauge group and values for cusp and non - cusp parts are summarized in the table below note that the @xmath33 dependence in the non - cusp part of the anomalous dimension is cancelled exactly by same dependence in the log term in eq . and is introduced in order to use master formula from appendix a of ref . @xcite for the integral of the anomalous dimension . finally we get for the exponential factor in eq . a fully analytic expression : @xmath59 , \,\,\,\text{where}\\ & & \omega=\sum_{k=1}^2\frac{{\pi a_{1k}}\big[z_k\ln z_k+1-z_k\big]}{b_{0k}^2\,\alpha_k(\mu_l)}+\frac{a_{1k}b_{1k}}{4b_{0k}^3}\left[\ln z_k - z_k-\frac{1}{2}\ln^2{z_k}+1\right]+\frac{a_{2k}}{4b_{0k}^2}\left[z_k-\ln z_k-1\right]-\frac{\tilde{b}_{1k}}{2b_{0k}}\ln z_k,\label{omegadinasour}\\ & & w=\frac{2}{b_{02}}\ln z_2 , \qquad\qquad\delta=\sqrt{\frac{1}{4}\text{l}_{tu / s^2}^2+\frac{3}{4}\text{l}_{t / u}^2}.\end{aligned}\ ] ] in the equation above we defined @xmath60 , @xmath61 are the two lowest order beta - function coefficients for @xmath38 and @xmath37 and @xmath62 are the one and two - loop cusp anomalous dimension coefficients and one - loop non - cusp anomalous dimension coefficient . they are all summarized in the table below . note that @xmath63 is defined in such a way that it is same as @xmath64 for @xmath57 and is equal to part of @xmath65 which is proportional to unit matrix , i.e. omitting term @xmath66 , where @xmath67 is the matrix in the second term of the second line in eq . , which comes from soft anomalous dimension . the leading - logarithm ( ll ) expression is significantly simpler and is given by first term in the expression for @xmath68 in eq . : @xmath69}{b_{0k}^2\,\alpha_k(\mu_l)}}\right),\label{eq : gammall}\end{aligned}\ ] ] and unlike the nll expression , the ll one is proportional to unit matrix , has no angular dependance at fixed scales @xmath70 and does not depend on any momenta ( @xmath71 ) before setting the scale @xmath72 . [ cols=""<,^,>"",options=""header "" , ] at the low scale @xmath35 we integrate out @xmath73 and @xmath74 bosons , and match onto @xmath75 with only photons ( and of course gluons , but for our purpose they are irrelevant ) . at tree level we simply rewrite each doublet @xmath76 in our operator basis @xmath77 in terms of broken fields : @xmath78 where @xmath79 and @xmath80 and we omitted the higgs vev since we are interested in four - particle interactions only . writing the operators @xmath81 and @xmath82 in terms of four - particle operators involving fields @xmath83 is straightforward but contains a great number" +"the gaseous component of protoplanetary disks is crucial for understanding the planet formation process because it affects the structures and evolution of the disk via chemical reactions . theoretical studies have predicted that protoplanetary disks have multiple layers in their vertical direction due to stellar radiation . these include a relatively cool midplane , in which most of the molecules are depleted onto grains , a molecular - rich intermediate layer , and a hot surface layer ( e.g. , * ? ? ? * ) . because the physical environment differs among layers , gas phase abundances also vary significantly atomic carbon ( c ) is considered to be abundant in the disk surface where far - ultraviolet ( fuv ) photons drive the energy balance and gas chemistry , i.e. , the photon dominated region ( pdr ) . theoretical studies predict that in the pdr , fuv photons with energies less than the ionization energy of hydrogen ( 13.6 ev ) dissociate molecular hydrogen and carbon monoxide ( co ) and ionize c to yield ionized carbon ( c@xmath8 ) @xcite . when significant attenuation is achieved , a thin h / h@xmath9 transition layer should appear , beyond which hydrogen molecules dominate . because the ionization energy of c is 11.6 ev , c@xmath8 is dominant at the lower density regions of the pdr . deeper to the pdr , the carbon - ionizing radiation is attenuated , and co forms via various chemical reactions . as a result , for the uniform pdr , c exists in a thin layer sandwiched between the c@xmath8 and co layers . because photoevaporation at the disk surface is believed to govern the gas dispersal @xcite , observations of c are crucial for understanding disk dissipation . moreover , the observations of c are also important in terms of dust evolution in the disk because it affects the chemistry as a result of changes in the uv radiation field propagation and thus the intensity of the c line @xcite . however , detection of the submillimeter fine structure c lines has not been reported for protoplanetary disks thus far . although a few studies have attempted to detect the emission lines of c from protoplanetary disks around intermediate - mass stars , only upper limits have been obtained @xcite . in this paper , we present the results of [ c i ] @xmath0p@xmath1@xmath0p@xmath2 and @xmath10co @xmath3=43 observations with the band 8 qualification model receiver mounted on the atacama submillimeter telescope experiment ( aste ) , and report the first detection of [ c i ] emission from a protoplanetary disk . we estimate the optical depth of the emission to derive the column density of c , and discuss possible evolutionary trends in the total mass of atomic c. we performed [ c i ] @xmath0p@xmath1@xmath0p@xmath2 ( 492.161 ghz ) and co @xmath1143 ( 461.041 ghz ) observations toward three classical t tauri stars ( ttss ) , , , and , in november 2010 using the aste . target information is listed in table [ tab : info ] . in addition , we made [ c i ] observations toward two protostars ( pss ) in taurus , l1551 irs 5 and hl tau , to check the consistency of the observational data . we also used these data as a reference of the [ c i ] intensity during the ps phase of star formation . the observations were taken with an alma band 8 ( 400500 ghz ) qualification model heterodyne receiver ( band 8 qm ; * ? ? ? * ) mounted on the aste . the band 8 qm uses sideband separating receivers that detect two orthogonal polarizations and down - convert the sideband - separated intermediate frequency signals to 48 ghz . the half power beam width ( hpbw ) was @xmath12 and the main beam efficiency @xmath13 was estimated to be 45% from observations of jupiter . for the backend , we used mac , a 1024 channel digital auto - correlator , which has a band width of 128 mhz and a resolution of 125 khz , corresponding to 78 and 0.076 km s@xmath14 , respectively . the position switch method was employed and a single spectrum toward the source position was obtained for each target . because our tts targets are well known to be less affected by surrounding clouds , we selected off positions near the targets to effectively remove atmospheric fluctuations ; 28 , 15 , and 1 arcmin from the stellar positions of dm tau , lkca 15 , and tw hya , respectively . for the pss , we employed an off position of ( @xmath15 , @xmath16)=(4@xmath17 32@xmath18 6@xmath190 , 17@xmath20 48@xmath21 51@xmath220 ) , which was determined to avoid the co @xmath1110 emission of the l1551 cloud @xcite . the telescope pointing calibration was performed every 1.52 hours by observing o - cet and irc+10216 in the co @xmath1143 emission line , and the resulting pointing accuracy was @xmath233 . any time variation in intensity scale was checked by observing part of the orion horse - head nebula ( position a ; * ? ? ? * ) two or three times daily and was found to be less than @xmath2410% . the [ c i ] data were obtained under good sky conditions ( @xmath25 ) , whereas @xmath260.060.10 for the co observations . the single sideband system noise temperatures were typically 2100 k and 3100 k for [ c i ] and co , respectively . data reduction and analysis were performed using the common astronomy software applications ( casa ) version 3.3.0 software suite , in addition to its asap modules . it should be noted that we reduced only one polarization dataset because of a beam alignment problem during the observations . bad data were removed by the _ sdflag _ task , baseline fitting and subtraction of the baseline from the spectra were performed with the _ sdbaseline _ task , and the data sets were combined in each source with the _ sdaverage _ task . the final spectra were obtained after smoothing with a five pixel boxcar function along the channel axis by the _ sdsmooth _ task , corresponding to a velocity resolution of @xmath27 km s@xmath14 . ccccccccccccc dm tau & 04:33:48.72 & @xmath2818:10:10.0 & 140 & m1 & 0.5 & 4.3 & 2.4 & 890 & 34 & 0.32 & 1,4,5,6 + lkca 15 & 04:39:17.80 & @xmath2822:21:03.5 & 140 & k5 & 1.0 & 312 & 4.8 & 905 & 52 & 0.25 & 1,6,7 + tw hya & 11:01:51.91 & @xmath2934:42:17.0 & 54 & k7 & 0.8 & 10 & 3.4 & 215 & 7 & 0.15 & 2,8 + l1551 irs5 & 04:31:34.07 & @xmath2818:08:04.9 & 140 & & & & 5 & & & 1 & 1 + hl tau & 04:31:38.44 & @xmath2818:13:57.7 & 140 & & & & 6 & & & 1 & 1,3 [ tab : info ] figure [ fig : spec_tts ] shows the [ c i ] @xmath0p@xmath1@xmath0p@xmath2 and co @xmath1143 spectra toward the three t tauri star targets , and the derived spectral line parameters are listed in table [ tab : spec ] . we successfully detected [ c i ] emission with a peak intensity of @xmath30 k toward . the line profile is single peaked with a central velocity of @xmath316.1 km s@xmath14 , which is consistent with the systemic velocity of the circumstellar disk as estimated by molecular line observations ( 5.9 km s@xmath14 ; e.g. , * ? ? ? the emission appeared to be slightly asymmetric with a somewhat larger extent to redshifted velocities . this is similar to the spectral shape of the co @xmath1143 and other co transitions . @xcite . here , the emission component visible near @xmath32 km s@xmath14 was not analyzed because it most likely originates from the ambient cloud @xcite . for tw hya and lkca 15 , we did not detect any [ c i ] emission , and obtained only the 3@xmath33 upper limits shown in table [ tab : spec ] . to estimate upper limits to the total integrated intensity of the [ c i ] emission lines , we assumed velocity widths of 3 and 1 km s@xmath14 for lkca 15 and tw hya , respectively , the values obtained by single dish co observations @xcite . significant [ c i ] emission toward the pss l1551 irs 5 and hl tau was detected , as shown in figure [ fig : spec_ps ] . the spectral profiles are single - peaked at values close to their systemic velocities . the emission intensities are markedly higher than that of dm tau . emission in the co @xmath3=43 line was detected toward and . the peak velocities and line profiles are in good agreement with those of high-@xmath3 co spectra @xcite . the double - peaked profile of dm tau lies close to the systemic velocity . after correcting for the beam size and efficiency , the integrated intensity of co emission from tw hya was comparable to the marginal value reported by @xcite within the uncertainties . we derived the optical depth of the [ c i ] emission and thus the c column density using the equations reported by @xcite . the optical depth at the peak velocity , @xmath34}$ ] , is given by @xmath35 } = -\ln \biggr ( 1- \frac{t_\mathrm{a}^\ast/\eta_\mathrm{mb}}{f_\mathrm{disk } [ j(t_\mathrm{ex } ) - j(t_\mathrm{bg } ) ] } \biggl ) \mathrm{,}\ ] ] where @xmath36 is the beam filling factor of the source , @xmath37 is the excitation temperature , @xmath38 is the temperature of the cosmic background radiation , and @xmath3 is the radiation temperature defined by @xmath39 here @xmath40 is the planck constant , @xmath41 is the observed frequency , and @xmath42 is the boltzmann constant . the factor @xmath36 was derived from the ratio of the solid angle of the disk to that of the telescope s beam , @xmath43 . the solid angle @xmath44 was estimated by assuming that the extent of the [ c i ] emission is identical to that of the resolved co disk @xcite . the outer radius of the co disk and its inclination angle , in addition to the estimated @xmath36 , are listed in table [ tab : info ] . we employed @xmath45 for the pss because they were expected to be embedded in extended envelopes that extend over the beam area . for the ttss , we assumed a constant @xmath37 of 50 k , as suggested by theoretical studies of protoplanetary disks around typical t tauri stars that predict the c@xmath8/c / co transition layer to appear at regions with @xmath46 k @xcite . conversely , we assumed @xmath47 k for the pss , which is the accepted value for [ c i ] observations of a ps surrounded by an infalling envelope @xcite . assuming that local thermodynamic equilibrium ( lte ) applies , we derived the averaged c column density over the source via @xmath48^{-1 } \frac{\tau_\mathrm{[c~i]}}{1-\exp(-\tau_\mathrm{[c~i ] } ) } f_\mathrm{disk}^{-1 } \ \ \ \mathrm{.}\end{aligned}\ ] ] here , @xmath49 is the ground - state partition function for neutral atomic carbon , @xmath50 where @xmath51 and @xmath52 are the energies of the @xmath111 and 2 levels , respectively , and @xmath34}$ ] is the velocity - averaged optical depth of the [ c i ] emission . in this study , however , we used the optical depth at the peak velocity instead of the velocity - averaged optical depth , which gives an upper limit to the column density . it should be noted that we assumed the optically thin condition ( @xmath34}\ll1 $ ] ) for lkca 15 and tw hya because no [ c" +"in nature , there exists a variety of systems that involve chemical reactions . some are on a geographical - scale , while others on a nano - scale . chemical reactions are an integral part of life , including all living forms of life . to study the dynamics of reaction systems , we often adopt rate equations in order to observe the change in chemical concentrations . in rate equations , we regard the concentrations as continuous variables ; the rate of the reaction as a function of the concentrations . in macroscopic systems , there are a vast number of molecules ; thus , continuous representations are usually applicable . when the concentration of a certain chemical is small , fluctuations in the reactions or flow can be significant . we often handle such systems with the help of stochastic differential equations , in which we regard noise as a continuum description of the fluctuations @xcite . such an approximation is useful when the number of molecules is intermediate . the employment of stochastic differential equations led to some important discoveries such as noise - induced order @xcite , noise - induced phase transitions @xcite , and stochastic resonance @xcite . in stochastic differential equations , still quantities of chemicals are regarded as continuous variables . essentially , on a microscopic level , chemicals are composed of molecules . the number of molecules should be an integer ( @xmath0 , @xmath1 , @xmath2 , @xmath3 ) , which changes discretely . fluctuations are derivatives of discrete stochastic changes ; thus , continuum descriptions of fluctuations are not always appropriate and can be doubted . for chemicals with a small number of molecules of the order of @xmath1 , a single molecule is extremely significant ; therefore , the discreteness in the number is significant . biological cells appear to be a good example . the size of the cells is of the order of microns , in which nano - scale `` quantum '' effects can be ignored . however , in cells , some chemicals act at extremely low concentrations of the order of pm or nm . assuming that the typical volume of a cell ranges from @xmath1 to @xmath4 @xmath5 , the concentration of one molecule in the cell volume corresponds to @xmath6 pm@xmath6 nm . it is probable that the molecular numbers of some chemicals in a cell are of the order of @xmath1 , or sometimes reach @xmath0 . if such chemicals play only a minor role , we can safely ignore these chemicals . however , this is not always the case . in biological systems , chemical species with a small number of molecules may critically affect the behavior of the entire system . for example , there exist only one or a few copies of genetic molecules such as dna , which are important to characterize the behavior , in each cell . further , some experiments show that doses of particular chemicals at concentrations of the order of pm or fm may alter the behavior of the cells ( e.g. , @xcite ) . biological systems also include positive - feedback mechanisms such as autocatalytic reactions , which may amplify single molecular changes to a macroscopic level . the effects due to small molecular numbers in cells have been noticed only recently , both theoretically @xcite and experimentally @xcite . at present , we focus on the possible effects of molecular discreteness . to study such effects , we should adopt an appropriate method to handle molecular discreteness . some numerical methods to investigate reaction systems that take into account discreteness and stochasticity already exist ( we briefly review these methods ; see appendix ) . among the methods , we adopted gillespie s direct method , which is popular and frequently used . furthermore , some works related to molecular discreteness also exist . for example , blumenfeld et al . showed that the mass action law may breakdown in a small system @xcite . stange et al . studied the synchronization of the turnover cycle of enzymes @xcite . we regard it important to identify the phenomena for which molecular discreteness is essential . through stochastic simulations , we show that discreteness can induce transitions to novel states in autocatalytic systems @xcite , which may affect macroscopic chemical concentrations @xcite . we consider a simple autocatalytic network ( loop ) with @xmath7 chemicals . we consider @xmath8 chemicals and assume @xmath9 reactions between these chemicals ( @xmath10 , @xmath2 , @xmath3 , @xmath7 ; @xmath11 ) . all the reactions are irreversible . for the reactor , we assume a well - stirred container with volume @xmath12 . the set of @xmath13 , the number of @xmath8 molecules , determines the state of the system . the container is in contact with a chemical reservoir , in which the concentration of @xmath8 is fixed at @xmath14 . the flow rate of @xmath8 between the container and the reservoir is @xmath15 , which corresponds to the probability of the flowing out of a molecule per time unit is the diffusion rate across the surface of the container . here , we choose the flow proportional to @xmath12 , to have a well - defined continuum limit . one might assume the flow proportional to @xmath16 , considering the area of the surface . by rescaling @xmath17 , the model can be rewritten into the case with @xmath16 for finite @xmath12 . ] . we can consider the continuum limit as @xmath18 . in the continuum limit , the change of @xmath19 , the chemical concentration @xmath8 in the container , follows the rate equation @xmath20 where @xmath21 is the rate constant of the reaction @xmath22 , and @xmath23 . for simplicity , we consider the case with equivalent chemical species , given as @xmath24 , @xmath25 , and @xmath26 for all @xmath27 ( @xmath28 , @xmath17 , @xmath29 ) . by this assumption , the rate equation has only one attractor : a stable fixed point @xmath30 for all @xmath27 . for any initial condition , each @xmath19 converges to @xmath31 , the fixed point value . around the fixed point , @xmath19 vibrates with the frequency @xmath32 . if the number of molecules is finite but fairly large , we can estimate the dynamical behavior of the system using a langevin equation , obtained by adding a noise term to the rate equation . each concentration @xmath19 fluctuates and vibrates around the fixed point . an increase in the noise ( corresponding to a decrease in the number of molecules ) merely boosts the fluctuation . however , when the number of molecules is small , the behavior of the system is completely different . first , we investigate the case when @xmath33 , which is the smallest number of species to show the novel states described below . subsequently , we investigate the dynamical behavior of the system with a small number of molecules . in order to detect the phenomena for which the discreteness of the number of molecules is crucial , we employ stochastic simulations . here , we adopt gillespie s direct method . the frequency ( expected number per unit time ) * of the reaction @xmath22 is @xmath34 ; * of the outflow of @xmath8 is @xmath35 ; * of the inflow of @xmath8 is @xmath36 . in the continuum limit ( @xmath18 ) , these frequencies agree with the rate equation . we calculate these frequencies with the current @xmath13 , and stochastically decide when and which event will occur next . in this case , by an appropriate conversion of @xmath17 , @xmath12 , and @xmath37 , we can set @xmath28 and @xmath31 to be @xmath1 without loss of the generality ( @xmath38 and @xmath39 are the only independent parameters ) . we assume that @xmath40 and @xmath41 for the purpose of further discussion . the total number of molecules in the container , @xmath42 , is approximately @xmath43 on an average . by varying @xmath12 , we can control the average number of molecules without changing the continuum limit . first , we consider the case of a large @xmath12 , i.e. , both the number of molecules in the container and flow of molecules between the container and the reservoir are large . as expected , the behavior of the system is similar to that of the rate equation with noise . as shown in fig . [ fig : a-512 ] , each @xmath13 fluctuates and vibrates around the fixed point value @xmath44 ( i.e. @xmath45 ) . this is still in the realm of stochastic differential equations . however , when @xmath12 is small , we observe novel states that do not exist in the continuum limit . as shown in fig . [ fig : a-032 ] , continuous vibrations disappear . furthermore , two chemicals are dominant and the other two are mostly extinct ( @xmath46 ) . in fig . [ fig : a-032 ] , at @xmath47 , @xmath48 and @xmath49 dominate the system and @xmath50 for the most part . we call such a state the 1 - 3 rich state . reversely , at @xmath51 , @xmath52 and @xmath53 are large and usually @xmath54 . we call this state the 2 - 4 rich state . these states appear because of the following reason . in this system , the production of @xmath8 molecules requires at least one @xmath8 molecule as a catalyst . if @xmath8 becomes extinct , the production of @xmath8 halts . @xmath13 never regains before an @xmath8 molecule flows in . in the rate equation ( eq . ( [ eqn : tr1-rate ] ) ) , the concentration @xmath19 is a continuous variable , which can be an infinitesimal but positive value . the consumption rate of @xmath19 is proportional to @xmath19 itself ; thus , @xmath19 can not reach @xmath0 exactly within finite time , even if it can go to @xmath0 asymptotically as @xmath55 . in fact , the number of molecules must be an integer . transitions from @xmath56 to @xmath46 are probabilistic and may happen in finite time . for transitions to occur , it is important that the consumption rate of @xmath19 does not converge to @xmath0 at @xmath57 . the average interval of a molecule flowing in is @xmath58 for each chemical . if @xmath17 and @xmath12 are small enough to ensure that the inflow interval is longer than the time scale of the reactions , it is likely that the state of the system @xmath56 drops to @xmath46 before an @xmath8 molecule enters . when @xmath13 reaches @xmath0 , @xmath59 is also likely to become @xmath0 . for example , if we assume that @xmath60 , then @xmath48 is likely to increase because the consumption of @xmath61 halts ; @xmath49 is likely to decrease because the production of @xmath62 halts . thus , this results in @xmath63 . when @xmath63 , the consumption rate of @xmath64 is larger than the production rate of @xmath64 ; therefore , @xmath53 starts to decrease and often reaches @xmath0 . when @xmath50 , all the reactions stop . the system stays at @xmath50 for a long time as compared with the ordinary time scale of the reactions ( @xmath65 ) . this is the 1 - 3 rich state . in the 1 - 3 rich state , the system alternately switches between @xmath63 and @xmath66 . we consider that the system is in the 1 - 3 rich state with @xmath63 . one @xmath67 molecule flowing in may resume the reactions @xmath68 and @xmath69 . generally , the former is faster because @xmath63 ; hence , @xmath52 is likely to increase . since @xmath53 = 0 , the reactions are one - way ; @xmath48 decreases and @xmath49 increases" +"white dwarfs are the end points of all low- to intermediate - mass stars , which are the majority of stars in the universe . they are dense stellar remnants composed of electron degenerate cores surrounded by non - degenerate envelopes . these evolved stars provide key insight into galactic star formation and evolution . to use white dwarfs as tracers of galactic evolution , we must determine their basic physical parameters , such as effective temperatures ( @xmath3 ) , surface gravities ( @xmath4 ) and masses . more than 80percent of white dwarfs have hydrogen - rich atmospheres , known as da white dwarfs @xcite . spectroscopy has been a successful tool in obtaining da atmospheric parameters , yet it only provides a view of the outermost layers of the white dwarf , and it is subject to systematic problems that require correction if the star is cooler than roughly @xmath5k and the surface is convective @xcite . asteroseismology , however , can probe deep into the interior of a white dwarf and provide information on its composition , rotation period , magnetic field strength , mass , temperature and luminosity , by matching the observed non - radial @xmath6-mode pulsations to theoretical models ( see reviews by @xcite ) . as white dwarfs cool , they pass through instability strips depending on their outermost envelope composition , which coincides with the onset of a partial ionization zone . this zone efficiently drives pulsations , which cause periodic brightness variations of the white dwarf @xcite . the variable da white dwarfs ( davs ) , also known as zzceti stars , are the most commonly found and studied type of pulsating white dwarfs . their effective temperatures range between @xmath7k for a typical mass of m @xmath8 0.6@xmath9 , with pulsation periods ranging from @xmath10s @xcite . ground - based studies of zzceti stars have been carried out for decades , but very few have been observed long enough to resolve more than six pulsation modes . crucially , there are potentially nine free parameters in the asteroseismic modeling of pulsating white dwarfs @xcite , which has required holding fixed many parameters in order to constrain the internal properties of zzcetis . it is clear that fully constraining these free parameters and thus the internal white dwarf structure and evolution will require a larger sample of rich asteroseismic observations . considerable effort has been expended to obtain uninterrupted photometry from coordinated , multi - site , ground - based campaigns to study pulsating white dwarfs , especially through the whole earth telescope @xcite , which has been operating for more than two decades ( e.g. , @xcite ) . however , the _ kepler _ planet - hunting spacecraft offers a unique opportunity to obtain high - quality , space - based light curves of variable stars , white dwarfs included . unfortunately , few white dwarfs were known in the original _ kepler _ mission field , and only two pulsating white dwarfs were discovered within the first two years of the mission @xcite . in order to increase this sample , we began the search for all white dwarfs in the original field of the _ kepler _ mission , and more specifically any possible zzceti stars . we created the _ kepler_-int survey ( kis , @xcite ) in order to select white dwarf candidates using colour - colour diagrams , and report on that search here . in sections [ selection ] and [ spec ] , we describe the selection method of our white dwarfs and present their spectroscopic observations . in section [ astero ] , we focus on the nine new pulsating white dwarfs . we conclude in section [ conclusion ] . we selected our white dwarf candidates using @xmath0 , @xmath1 and @xmath11 , @xmath12 colour - colour diagrams using data from the _ kepler_-int survey ( kis ) , shown in fig . [ fig : colours ] . kis is a deep optical survey using the wide field camera on the 2.5-m isaac newton telescope ( int ) , taken through four broadband filters ( @xmath13 ) and one narrowband filter ( h@xmath14 ) , covering more than 97percent of the original _ kepler _ field down to @xmath1520@xmath16 mag @xcite . all magnitudes for the kis survey are expressed in the vega system . white dwarfs have bluer colours than main - sequence stars , and most single da white dwarfs also have strong h@xmath14 absorption lines , leading to @xmath17 ( see bottom panel of fig . [ fig : colours ] ) . we have integrated the atmospheric models of canonical - mass 0.6@xmath9 ( @xmath18 @xmath19 ) white dwarfs of @xcite with the various filter profiles to guide our colour cuts , similar to @xcite . our photometric selection recovered kic4552982 , the first zzceti star in the _ kepler _ field @xcite . we narrowed our selection to a small region around kic4552982 and to candidates close to the empirical ( @xmath3 , @xmath20 @xmath6 ) instability strip projected into @xmath21 space . this left more than 60 white dwarf candidates , 43 of which we were able to follow up spectroscopically ( table [ phot - summary ] ) . we were awarded a total of eight nights on the 4.2-m william herschel telescope ( wht ) in 2012 , 2013 , and 2014 , where we obtained intermediate resolution spectra of 43 of our candidates in order to confirm their identities as white dwarf stars and to characterize their atmospheric parameters , especially their effective temperatures and surface gravities . we used the intermediate - dispersion spectrograph and imaging system ( isis ) , with the r600r and r600b gratings on the red and blue arms , respectively . the slit widths were chosen close to the seeing of each night to maximize spectral resolution ( @xmath22 ) . a full journal of observations is included in table [ tab : specjour ] . the blue arm was centred at 4351 and the red arm at 6562 . the spectra covered a wavelength range from roughly @xmath23 in the blue ( see fig . [ spec - fit ] ) , and roughly @xmath24 in the red . however , since the higher - order balmer lines contain the most information about the atmospheric parameters ( e.g. , @xcite ) , we only used the blue arm for our balmer profile fits ( section [ sec : atmosparams ] ) . .journal of spectroscopic observations . [ cols=""<,^,^,^,^ "" , ] in addition to the confirmation of nine new zzceti stars , our ground - based photometry has put relatively strong limits on the lack of photometric variability in eight other white dwarfs with effective temperatures near the zzceti instability strip . those limits are quoted as a 3@xmath25 threshold in table [ astero - summary ] , and represented visually with a ft for each object in figure [ fig : ftnewnov ] . several of these non - variable white dwarfs have atmospheric parameters that place them within the empirical zzceti instability strip given their uncertainties , most recently updated by @xcite . it has been assumed that all white dwarfs in this region can foster a partial ionization zone and thus pulsate that the instability strip is pure but this claim is still under review @xcite , although there is good agreement between the observed and theoretical zz ceti instability strip ( e.g. , @xcite ) . we will not address that issue here , other than to say there are a number of reasons why these objects may appear not to pulsate . firstly , it is possible the white dwarfs really do vary , but at lower amplitudes than our detection limits allow ( e.g. , @xcite ) . additionally , it is possible that subtle issues in the flux calibration of our spectra have introduced unaccounted for systematic uncertainties in the derived atmospheric parameters , and the stars may have true temperatures outside the instability strip . given that the non - variable stars are more or less uniformly distributed in the ( @xmath3 , @xmath26 ) plane , it is likely that the low signal - to - noise of the time - averaged spectra is responsible for some interlopers , as demonstrated quantitatively by @xcite . the most interesting white dwarf not observed to vary in our sample is the ultramassive j1926 + 3703 , which sits in the middle of the empirical instability strip . at @xmath27@xmath9 , it would be the second - most - massive white dwarf known to pulsate , behind only gd518 @xcite . white dwarfs this massive likely have at least partially crystallized interiors . we did not detect photometric variability in this relatively faint target ( @xmath28mag ) to a limit of roughly 6.9ppt , but it is quite possible that this white dwarf pulsates at lower amplitude . for example , the two most massive known pulsating white dwarfs have low pulsations amplitudes , which rarely exceed 5ppt in a given night and are often far lower in amplitude @xcite . the _ kepler _ mission would have given at least an order - of - magnitude improvement on these nov limits , were these targets observed from space . for example , @xcite showed that j1909 + 4717 did not vary to at least an amplitude of 0.13ppt using just one month of _ kepler _ data in q4.1 . however , only the four known pulsating white dwarfs listed at the end of section [ sec : confirmationnewzzcetis ] were observed before the spacecraft had a failure of its second reaction wheel . we note that many white dwarfs with atmospheric parameters within the empirical instability strip remain unobserved , and we encourage additional follow - up to constrain pulsational variability in these white dwarfs . we especially encourage further monitoring of the ultramassive j1926 + 3703 . using photometric colour selection from the kis survey and subsequent medium - resolution spectroscopy from isis on the wht , we have discovered and characterized 42 new white dwarfs in the original _ kepler _ mission field . follow - up , high - speed photometry from ground - based telescopes confirmed that at least nine of these objects are zzceti stars . four were subsequently observed from space using the _ kepler _ space telescope , and @xcite report on the first zzceti found in this project , kic11911480 . asteroseismic inferences from the extended datasets on the other three will be presented in a forthcoming publication . unfortunately , the failure of the second and critical reaction wheel that kept _ kepler _ precisely pointed towards its original mission field occurred within months of our discovery of many of these new zzceti stars , and our sparse ground - based discovery light curves are so far the only time - series photometry for most of the targets here . at the end of its roughly four years pointed towards its original field , _ kepler _ observed a total of six pulsating white dwarfs . however , the two - reaction - wheel controlled _ k2 _ mission will cover a significantly larger footprint as it tours the ecliptic @xcite , and _ k2 _ will likely observe more than a thousand white dwarfs , dozens of them pulsating . already several important discoveries have come from these _ k2 _ observations of pulsating white dwarfs @xcite . the colour selection methods honed in this work have ensured that dozens of pulsating white dwarfs have been or will be observed by _ k2 _ for up to 80d at a time , using selection from a variety of multiwavelength photometric surveys . the authors acknowledge fruitful conversations with a. gianninas during the" +"speculations concerning the existence and frequency of brown dwarfs can be traced to before the introduction of the term @xcite . since then , wide - field surveys have uncovered hundreds of candidates in the field and revealed two new spectral types , the l and t dwarfs @xcite . yet the frequency of brown dwarfs compared to stars has remained a topic of confusion and debate . in a pioneering work , @xcite attempted the first census of the substellar initial mass function ( imf ) based on results from the two micron all sky survey @xcite . they presented evidence for a low - mass imf that was more shallow than a salpeter @xcite slope , suggesting that brown dwarfs were not a significant contributor to dark matter . @xcite used a bayesian approach to constrain the power - law slope below 0.08 @xmath2 to be in the range @xmath3 with a confidence level of 60% , where a salpeter slope is @xmath4 . these results indicate that , although brown dwarfs do not contribute significantly to the mass of typical stellar populations , they might still be as abundant as stars @xcite . the classical approach to deriving the mass function for stars and substellar objects is to take an observed luminosity function and apply a mass - luminosity relationship in order to derive the present - day mass function . then , corrections , based on the theory of stellar evolution , permit one to estimate an _ initial _ mass function from the present - day mass function ( see e.g. @xcite for complete descriptions of this process ) . the confounding variable in these analyses is the star formation history of the galactic disk , which is vital for substellar objects whose mass luminosity relationship evolves with time . a different approach is to use star clusters of known age as laboratories to measure the imf . open clusters are in principle good candidates because of their richness . yet they suffer from the effects of dynamical evolution , mass segregation , and evaporation ( e.g. * ? ? ? young ( @xmath5 10 myr ) embedded clusters are attractive alternatives as they are compact and rich ( from hundreds to thousands of stars within 0.31 pc ) , and yet to emerge as unbound ob / t associations , and the low mass objects are 101000 times more luminous than their older open cluster counterparts ( 0.116 gyr ) because they shrink and cool as they age . indeed , embedded clusters have been the targets of aggressive photometric and spectroscopic surveys in an attempt to search for variations in the imf as a function of initial conditions . @xcite found that the ratio of high - mass ( 110 @xmath6 ) to low - mass ( 0.11 @xmath6 ) stars for an ensemble of young clusters within 1 kpc was consistent with ( 1 ) each other and ( 2 ) having been drawn from the field star imf . more recent studies have pushed well into the substellar mass regime ( see @xcite for a recent review ) . there have been some claims for variations in the brown dwarf imf between nearby star - forming regions . @xcite argued that the low - density taurus dark cloud had a dearth of brown dwarfs compared to the rich orion nebula cluster ( onc ) . however , this preliminary result has been updated as additional data have become available and as the statistics improved for both clusters @xcite . here we use observations of seven nearby star clusters to constrain the combined brown dwarf imf . in section 2 , we describe the data , illustrate that there is no strong evidence for variation in the substellar imf between the star - forming regions , and outline our approach to constrain the low - mass imf . in section 3 we present our results , and in section 4 we discuss our results in the context of previous work as well as theories of star ( and substellar object ) formation . we have compiled the ratio of stars to brown dwarfs in nearby , well - studied young embedded clusters and the pleiades . the regions included in this study are described briefly below , where the ratio of stars ( 0.081.0 @xmath2 ) to brown dwarfs ( 0.030.08 @xmath2 ) is calculated . for all the regions , we consider the _ system _ imf , uncorrected for multiplicity within 200 au . the sample is focused on embedded clusters , in which spectroscopy has been used to determine the age of the cluster , field star contamination has been taken into account , and an extinction - limited sample has been defined . furthermore , we have included the pleiades , because it is one of the best - studied open clusters and bacause its substellar imf has been estimated . the break point at 0.08 @xmath2 has been adopted in accordance with the break point for the @xcite imf , similar to the characteristic mass in the @xcite single object imf . only a few of the clusters adopted here have the imf derived in an extinction - limited sample reaching 0.02 @xmath2 and we have opted for 0.03 @xmath2 as a lower mass limit to obtain a larger sample of clusters . _ @xcite imaged a 4 deg@xmath7 region of taurus that focused on the denser filaments , to identify cluster candidates . candidates were confirmed as cluster members , by use of follow - up intermediate - resolutionoptical spectroscopy , on the basis of their effective temperature , luminosity , and spectral features . in total , 112 objects were confirmed members with derived masses between 0.03 and 1.0 @xmath2 and extinctions a@xmath8 mag . some 96 objects were stars and 16 were brown dwarfs . thus , the ratio of stars to brown dwarfs in taurus was found to be @xmath9 where the errors are estimated using the method of @xcite . _ @xcite imaged a 42@xmath1028 region of the ic 348 cluster to identify cluster candidates . by the use of intermediate - resolution spectroscopy , most of the candidates were confirmed as cluster members , on the basis of their effective temperature , luminosity , and spectral features , which indicated that the objects were young . in total , @xcite found 168 cluster members with masses between 0.03 and 1.0 @xmath2 and extinctions a@xmath8 mag . the ratio of stars to brown dwarfs was found to be @xmath11 . _ _ @xcite imaged the central 1@xmath101 of the embedded cluster associated with mon r2 by utilizing the near - infrared camera andd multi - object spectrometer on board the _ hubble space telescope _ ( _ hst _ ) . an extinction - limited sample a@xmath12 mag was defined and a total of 19 objects were detected with masses between 0.03 and 1 @xmath2 . the ratio of stars to brown dwarfs was found to be @xmath13 . _ chameleon 1 . _ @xcite obtained an extinction - limited sample in chameleon 1 that was complete down to 0.01 @xmath2 for a@xmath14 mag , by use of observations of a 0.22@xmath100.28 region with the advanced camera for surveyes on board _ hst _ and a subsequent spectroscopic follow - up of cluster member candidates . the sub - sample from 0.03 to @xmath15 @xmath2 includes 24 objects and the ratio @xmath16 was found to be @xmath17 . _ pleiades . _ the pleiades is one of the best - studied open clusters , and numerous derivations of the imf have been published . here we focus on the survey by @xcite who covered a 6.4 deg@xmath7 region of the pleiades . the survey had a saturation limit of 0.48 @xmath2 . for higher masses , the survey was combined with a mass function built using the @xcite database . the pleiades suffer relatively low ( @xmath18 mag ) , mostly uniform , extinction , with negligible impact on the completeness of this sample , so we did not apply a reddening criterion . the ratio of stars to brown dwarfs was found to be @xmath19 . _ the orion nebular cluster . _ the onc has been the subject of extensive studies @xcite . we take the adopted ratio of stars to substellar objects from the study of @xcite . the total sample , covering the central 5.1@xmath105.1 , contains approximately 200 objects with masses between 0.02 and 0.6 @xmath6 and a@xmath20 mag . using their figure 14 , and extrapolating the slope from 0.080.6 to 1.0 @xmath6 ( one additional bin in their plot ) , we arrive at a ratio of stars to substellar objects of @xmath21 . _ ngc 2024 . _ the ratio of stars to brown dwarfs in ngc 2024 was found by @xcite from their photometric and spectroscopic study , covering the central 10@xmath1010 . they assigned masses to the photometric objects on the basis of the mass distribution in each magnitude bin , determined from the spectroscopic sample as in @xcite . the result was that a total of 148 objects in their survey area has masses between 0.02 and 1 @xmath6 and extinctions a@xmath22 15 mag . based on their figure 9 , we find that there are 27 objects between 0.03 and 0.08 @xmath6 resulting in a ratio of stars to substellar objects of @xmath23 . table [ results ] shows the ratio of stars to brown dwarfs for nearby embedded clusters and the pleiades , as described above , and the distribution of ratios is shown in fig , [ figure1 ] . the weighted mean of the ratios is found to be 4.3 , and the standard deviation of the weighted mean is 1.6 . all of the measurements presented are consistent with the weighted mean within 2@xmath24 . there is thus little evidence for variation in the low - mass imf between the different regions and we have adopted the hypothesis that the imf is universal . under this assumption , the complete set of imf determinations can be combined to place constraints that are stronger than for each of the individual measurements . for each cluster , we have calculated the probability of obtaining the observed ratio of stars to brown dwarfs for a given imf or greater . the ratio of stars to brown dwarfs drawn from a given sample size with an assumed imf is determined by the binomial theorem . the predicted distribution of ratios from both segmented power - laws and a ( * ? ? ? * @xmath25 , @xmath26 , @xmath27 ) lognormal imf for a cluster of 100 objects with unresolved binaries is shown in the lower panel in fig . [ figure1 ] . the peak mass in the lognormal is slightly higher , and the width is slightly more narrow than is presented in @xcite . the change in the best - fit parameters in @xcite is due to an updated luminosity function @xcite . a similar increase in the peak mass has been suggested by @xcite . the slope of the segmented power - law between 0.08 and 1.0 @xmath2 was chosen to be @xmath28 , and the slope has been varied below 0.08 @xmath2 in the range @xmath3 , which is the 60% confidence interval presented by @xcite . it is clear that the rising and flat imfs ( @xmath29 , and @xmath30 , respectively ) are difficult to reconcile with the observed distribution of ratios . we have quantitatively assessed the likelihood of obtaining the observed ratios from an assumed imf as follows . for each of the seven measurements , the probability of obtaining that ratio or higher , assuming an underlying imf , is calculated by adopting the binomial theorem . the product of" +"the study of spin dependent transport in low - dimensional systems has been largely dominated in the last few decades due to the rapid advancement in nano - scale science and technology @xcite . controlling electron s spin degree of freedom is extremely important for the development of quantum information processing as well as quantum computation @xcite . the spin - orbit ( so ) interaction which couples the electron s spin to the charge degree of freedom provides a much deeper insight for generating spin current and also its manipulation @xcite rather than the usual methodologies @xcite . earlier , people were mainly using @xcite ferromagnetic leads or external magnetic field to get spin filtering action though these are not very suitable especially for low - dimensional systems , since in one case a large resistivity mismatch is observed while in the other case the main difficulty appears for confining a huge magnetic field into a narrow region , like a nano - ring . depending on the sources , spin - orbit interaction is classified in two different categories : one is called extrinsic type which appears mainly due to magnetic impurities , while the other is defined as intrinsic type that appears as a result of lacking of inversion symmetry . in this category generally two kinds of spin - orbit interactions are taken into account . they are called as rashba and dresselhaus so interactions @xcite . the first one is associated with the inversion asymmetry of the structure and its strength can be regulated by means of external gate potential , and the second one is related to the bulk inversion asymmetry whose coupling strength depends on the material . considering the coupling of spin degree of freedom to the momentum of an electron , spin polarized currents in output terminals of a multi - terminal conductor can be achieved from a purely unpolarized electron beam injected to the input terminal @xcite . the existing literature suggest that a lot of theoretical progress has already been done to explore spin selective transmission through different model geometries . for example , a planar t - shaped conductor @xcite with a ring resonator exhibits polarized spin currents in outgoing leads in presence of rashba so interaction . in other work peeters _ et al . _ have shown how a ring - like geometry can be utilized as an electron spin beam splitter exploring the possible quantum interference effect in presence of so coupling @xcite . at the same time nikolic and his group @xcite put forward several key ideas in this particular field . in spite of the considerable volume of work available in this particular area , a practically unexplored issue is how does the curvature of a material which is clamped within input and output leads influence spin polarization . to the best of our knowledge , this part is unaddressed so far . in the present work we essentially focus towards this direction . we investigate the curvature effect on spin polarization by considering two simple geometries : a simple linear conductor and a ring - like geometry which is formed by bending the chain . the results are quite interesting . using a tight - binding ( tb ) framework and based on green s function formalism we show that for a ring shaped conductor spin polarized currents are obtained in output leads of a multi - terminal geometry from a completely unpolarized beam of electrons , while absolute zero spin polarization is obtained for the linear conductor . the rest of the paper is organized as follows . section ii illustrates two different models together with a brief theoretical description to obtain spin polarization in two output leads . section iii contains numerical results and discussion , and finally , in section iv we summarize our essential results . in this section we describe two different systems of our study and present a general theory for calculating spin polarization coefficient @xmath0 in two output leads based on green s function formalism . the three - terminal bridge setup is schematically shown in fig . [ model ] , where we take two different configurations of the same material . in one configuration we choose a finite one - dimensional ( @xmath1d ) chain , which is then bent to form a @xmath1d ring to generate another configuration . in both these two cases the material , subjected to rashba spin - orbit interaction , is connected with one input ( lead-1 ) and two output leads ( lead-2 and lead-3 ) . a tight - binding framework is given under the nearest - neighbor hopping approximation to describe the bridging material ( ring / chain ) and the side - attached leads . the tb hamiltonian of the entire system reads as , @xmath2 where three different terms in the right side correspond to the hamiltonians of three different regions of the bridge system those are elaborately explained below . the first term , @xmath3 , describes the hamiltonian of the conductor placed between the incoming and outgoing leads . depending on its geometry ( ring - like or chain - like ) the hamiltonian looks different . for a @xmath4-site linear conductor subjected to rashba so interaction the tb hamiltonian @xcite gets the form : @xmath5_z \mbox{\boldmath $ c$}_{n+1 } + h.c . \right ) \label{eq2}\end{aligned}\ ] ] where , + @xmath6 @xmath7 @xmath8 + @xmath9 + + in the above expression , @xmath10 and @xmath11 are the creation and annihilation operators , respectively , for an electron with spin @xmath12 at the @xmath13-th atomic site of the sample . @xmath14 is the on - site energy and @xmath15 measures the isotropic nearest - neighbor hopping integral . the parameter @xmath16 describes the rashba so coupling strength and the term @xmath17 gives the spin angular momentum of the electron . the unit vector @xmath18 describes the direction of the movement of an electron between the sites @xmath13 and @xmath19 . when this @xmath4-site linear conductor is bent to form a ring the hamiltonian becomes @xcite , @xmath20 where , + @xmath21 with @xmath22 . all the other symbols used in eq . [ eq3 ] carry their usual meanings . in our theoretical framework , three metallic leads are considered to be identical , semi - infinite and free from any kind of impurities and spin - orbit interaction . we can express them as , @xmath23 where @xmath24 for the three leads . in the absence of any so coupling @xmath25 takes the form : @xmath26 with @xmath27 and @xmath28 . + + where @xmath29 and @xmath30 are the site energy and nearest - neighbor hopping integral , respectively , in the @xmath31-th lead . other factors carry their usual meanings as stated earlier . out of these three leads , lead-1 is treated as the input terminal , while the other two are considered as the output terminals and all of them are coupled to the conductor through the hopping integral @xmath32 . here we assume that the lead-1 is always attached to site @xmath1 and the other two leads are coupled to the sites @xmath33 and @xmath34 , those are variables , of the conductor . following the same footing as above , we can write the tb hamiltonian to describe the conductor - to - lead coupling as , @xmath35 here , @xmath36 \label{eq7}\ ] ] with @xmath37 + the site @xmath38 corresponds to the boundary site of the lead , and it is coupled to the @xmath13-th site of the conductor , which is variable . the spin polarization coefficient in the output leads is defined as @xcite , @xmath39 where , @xmath40 gives the transmission probability of an injecting electron with spin @xmath41 which gets transmitted through the drain with spin @xmath42 . when @xmath43 we get pure spin transmission , while for the other case spin flip transmission is obtained . equation [ eq8 ] is the general expression of spin polarization coefficient between any two leads @xmath38 and @xmath44 , and , for our three - terminal system we call the polarization coefficients in two outgoing leads as @xmath45 and @xmath46 . in the present approach we select the quantization direction along the @xmath47 axis for simplification . to calculate transmission coefficient @xmath40 we use green s function formalism @xcite . in this framework the two - terminal transmission probability between the leads @xmath38 and @xmath44 is defined as @xmath48 $ ] . here @xmath49 and @xmath50 are the retarded and advanced green s functions , respectively , of the sample considering the effects of the electrodes . @xmath51 , where @xmath52 is the energy of an injecting electron , and @xmath53 s ( @xmath54 ) are the self - energies due to coupling of the conductor to the leads and @xmath55 s are their imaginary parts . in refs . @xcite the detailed calculations of self - energy matrices are available . based on the above theoretical framework we now analyze our numerical results . throughout the analysis we fix the electronic temperature of the system to absolute zero , and for simplification , we put @xmath56 . other common parameters are as follows : @xmath57 and @xmath58 . the rashba so coupling strength @xmath16 and all the energy scales are measured in unit of the hopping integral @xmath15 . before focusing to the central point i.e. , the curvature effect on spin polarization in a multi - terminal ( more than one output lead ) system in presence of rashba so interaction , we want to have a short glimpse on the system where a conductor subjected to so interaction is coupled to a single input and a single output lead i.e. , a two - terminal system . following our extensive numerical calculations we can conclude that irrespective of the curvature of the bridging material , only so interaction can not induce spin polarization in output lead of a two - terminal system . we verify it considering different geometrical shapes of the conductor , e.g. , circle , square , triangle , polygon , linear , etc . in few recent works @xcite it has also been shown that only so interaction is incapable of producing spin polarization . the reason is that , in presence of so coupling the time - reversal symmetry is still preserved , and therefore , it does nt break the kramer s degeneracy between the @xmath59 and @xmath60 states which results vanishing spin current in the output lead of a two - terminal system . the degeneracy gets removed when the system is subjected to any kind of magnetic impurity or external magnetic field . under this situation a two - terminal system with so coupling exhibits polarized spin currents @xcite . this phenomenon has already been established in the literature , but the essential issue of our present analysis the interplay between the curvature of the material and the multi - leads has not been addressed earlier . to explore it , in fig . [ ringpola ] we present the results for a three - terminal mesoscopic ring considering @xmath61 and @xmath62 . here , the two outgoing leads are attached symmetrically ( @xmath63 and @xmath64 ) with respect to the incoming lead , as shown schematically in fig . [ model](a ) . the upper panel of fig . [ ringpola ] corresponds to the energy dependence of spin polarization coefficient for the one output lead , while for the other output terminal it is shown in the middle panel of fig . [ ringpola ] , and , finally they are placed together in the lower panel of this figure to compare the polarization coefficients properly . from these spectra it is observed that finite spin polarizations , associated with the energy eigenvalues of the ring subjected to" +"the increasing possibilities and sophisticated ways to control larger and larger quantum systems require a thorough understanding of the dynamics of open quantum systems @xcite . as prime example , the phenomenon of decoherence is an effect of the environmental impact on quantum behavior of the system , leading to a sometimes rapid decay of its coherences in a certain basis @xcite . with respect to quantum information processing , decoherence is the main obstacle that needs to be overcome . however , the influence of the environment on an open quantum system is not always of disturbing nature . for example , an environment can also mediate quantum correlations between two qubits @xcite , which implies that in the process system and environment must get quantum mechanically correlated . it is an interesting question under which circumstances and how exactly those correlations develop . many interesting results about correlations and entanglement in quantum many body systems have been obtained in the last few years @xcite . the issue of system - environment correlations is also of importance for the quantum foundations of thermodynamics @xcite . although there are methods to detect the formation of system - environment correlations at the level of reduced dynamics @xcite , a detailed analysis of the role of _ quantum _ correlations in decoherence phenomena lies beyond such an approach . to gain deeper understanding one surely has to investigate the total ( sometimes thermal ) state of the composite quantum system , which in fact has been done for a couple of model systems @xcite . some of the authors find decoherence accompanied by system - reservoir entanglement , some of them report of certain conditions under which decoherence appears without . still , we lack a complete picture of entanglement _ dynamics _ including finite temperature environments and arbitrary system initial states . here we present an approach to this problem , based on a partial p - representation of the total state , investigating a purely decohering qubit . it enables us to make detailed , state and temperature dependent statements on the evolution of the correlations between system and environment , which we relate to the decoherence process . describing pure decoherence ( phase damping ) , we will assume a standard model @xcite @xmath0 , by coupling a qubit @xmath1 via @xmath2 non - dissipatively to a bath of harmonic oscillators @xmath3 @xcite . here @xmath4 denotes the transition frequency of the qubit and the coefficients @xmath5 describe the coupling strength between the qubit and each environmental mode of frequency @xmath6 . assuming the environment to be initially in the thermal state @xmath7/{\text{tr}}[\exp[-h_{\text{env}}/k_b t]]$ ] at temperature @xmath8 , and the total initial state to be the product @xmath9 , the following exact time local master equation for the reduced density operator @xmath10 $ ] follows @xmath11}-\frac{\gamma(t)}{2}\left(\rho_{\text{red}}-\sigma_z\,\rho_{\text{red}}\,\sigma_z\right ) . \label{equ : masterequation - decoherence}\ ] ] its solution reads @xmath12 with @xmath13 $ ] . here @xmath14 represents the _ initial _ state of the qubit , with bloch vector @xmath15 . for the following , it is essential to consider _ arbitrary _ ( mixed ) initial qubit states . this choice reflects experimental limitations in the preparation process , and also allows us to investigate decoherence and qubit - environment correlations in cases where the qubit is part of an entangled many qubit state @xcite . while pure initial qubit states will always lead to system - environment entanglement , even a slight decrease of initial purity may have a significant effect on the nature of the ensuing system - environment correlations . in ( [ equ : masterequation - decoherence ] ) and ( [ equ : solution - roh_red ] ) we have introduced the time dependent decoherence rate @xmath16 which by means of the spectral density of the environment @xmath17 can be written as @xmath18\cos[\omega s ] . \label{equ : decoherence_rate}\ ] ] for a time independent @xmath19 , qubit coherences decay on the decoherence time scale @xmath20 , sometimes referred to as `` @xmath21 '' . for the general case considered here , we define the decoherence time @xmath22 through the relation @xmath23 . the off - diagonal elements of the qubit have then decayed to a fraction @xmath24 of the initially present quantum coherences . indeed , a constant decoherence rate @xmath19 is obtained for an ohmic spectral density with a cut - off frequency @xmath25 , in the limit of high temperatures @xmath26 and large times @xmath27 . then eq . ( [ equ : masterequation - decoherence ] ) is of lindblad type , and the corresponding dynamics is markovian . for our studies we choose a sharp cut - off , @xmath28 @xcite , where @xmath29 parametrises the coupling strength between system and environment . accordingly , the asymptotic decoherence rate is given by @xmath30 . decoherence of qubits is sometimes modelled by random unitary dynamics @xcite . it is known that on the level of the reduced state , single - qubit decoherence can always be modelled that way , while for two qubits or more , there is genuine `` quantum '' decoherence i.e. there is decoherence that even on the reduced level can only be modelled by coupling the system to a quantum environment @xcite . considering a single qubit and its given quantum environment , this raises the question to what extent the total state involves any quantum correlations . in fact , the most general class of total initial states which allows for completely positive reduced dynamics is classically correlated , with zero discord @xcite . we emphasize that for our special choice of the spectral density , the map @xmath31 induced by ( [ equ : masterequation - decoherence ] ) is completely positive for all @xmath32 . this is due to the positivity of @xmath16 in our case , which also implies the `` markovianity '' of the reduced dynamics for all times in the sense of both works @xcite . for all these recent investigations it is relevant to gain a deeper understanding of the build - up of quantum correlations between system and environment . in this paper we investigate the correlation dynamics of the total state for a mixed initial product state and identify entangled and classically correlated regimes . it turns out that in general the dynamics of system - environment correlations can be markedly rich . let us provide the framework necessary to extract the desired information from the total state . we are interested in an exact expression for the total state @xmath33 , which we will represent in a coherent state basis . in a sense , our approach here is a mixed - state generalization of the _ non - markovian quantum state diffusion _ approach to open quantum system dynamics @xcite . we will combine the environmental coherent state labels into the vector @xmath34 of complex numbers and consistently make use of the notation @xmath35 ( see also @xcite ) . furthermore , introducing the average thermal occupation number @xmath36 of the @xmath37-th environmental mode , it is possible to expand the total state in terms of coherent states @xmath38 @xmath39 defining the matrix - valued partial p - function @xmath40 with values in the @xmath41 dimensional state space of the qubit . here we symbolically write @xmath42/{\overline{n}}:=\prod_\lambda\exp[-|\xi_\lambda|^2/{\overline{n}}_\lambda]/{\overline{n}}_\lambda$ ] . we find that expression ( [ equ : p - representation ] ) is a solution of the total von - neumann equation with initial @xmath43 if @xmath44 where @xmath45 $ ] and @xmath46\exp[b(t)-\left\{({b}(t)|\xi)-(\xi|b(t))\right\}]$ ] . here we have introduced the complex time dependent vectors @xmath47 and @xmath48 with scalar product @xmath49 and vector components @xmath50 furthermore , we use the abbreviations @xmath51\\ b(t)&=&2\,{\text{re}}{\hspace{-0.5ex}}\int_0^tds\int_0^sd\tau\left[\sum_\lambda\frac{2{\overline{n}}_\lambda+1}{{\overline{n}}_\lambda}|g_\lambda|^2e^{-i\omega_\lambda(t - s)}\right].\end{aligned}\ ] ] initially , @xmath52 and note that there are no approximations necessary to achieve the result ( [ equ : exact - solution ] ) and thus via ( [ equ : p - representation ] ) to obtain the exact state of the composite system . having the total state at hand we now want to draw conclusions on its separability . for this purpose we argue as follows : as long as the partial p - function is positive - semi - definite the total state @xmath33 in representation ( [ equ : p - representation ] ) is trivially separable . since one eigenvalue of @xmath53 is always positive , a good indicator for this circumstance is the determinant @xmath54 $ ] which in fact is independent of the coherent state labels @xmath55 and @xmath56 : @xmath57=e^{-2a(t)}\left[1-z^2\right]-e^{2b(t)}(x^2+y^2 ) . \label{equ : positive - p}\ ] ] recall that @xmath58 are the bloch coordinates of the _ initial _ state of the qubit . this expression is positive as long as the following condition is fulfilled @xmath59 . \label{equ : condition - sep}\ ] ] the quantity on the l.h.s . depends on the temperature of the surrounding heat bath via the thermal occupation numbers @xmath60 - 1)^{-1}$ ] , and reads @xmath61\cos[\omega(s-\tau ) ] . \end{split } \label{equ : s_t_continuum}\ ] ] with our special choice of @xmath62 , @xmath63 can be written in terms of known special functions . for a given initial qubit state with @xmath64 , condition ( [ equ : condition - sep ] ) defines an area in the @xmath65-plane , shown in fig . [ fig : sep - ent - dec_hightemp ] , within which the total state is necessarily separable . note that for a pure initial state the r.h.s . of ( [ equ : condition - sep ] ) is zero and the separable area vanishes . the qubit may decohere without becoming entangled to its environment despite an initial purity of @xmath66.,scaledwidth=47.0% ] it turns out that as @xmath67 , @xmath63 grows above all bounds for all temperatures and it becomes independent of temperature in the high temperature limit , @xmath68 . as a consequence , for any initial state and temperature , expression ( [ equ : p - representation ] ) of the total state at some point in time ceases to represent a proper mixture and thus , separability can no longer be concluded . let us stress that positivity of @xmath69 is a sufficient but not a necessary condition for separability . condition ( [ equ : condition - sep ] ) is visualized in fig . [ fig : sep - ent - dec_hightemp ] , where we relate our criterion for separability to the decoherence time @xmath22 introduced earlier . we resort to the _ weak coupling _ regime ( @xmath70 ) and choose a qubit initial state in the equatorial plane ( @xmath71 ) of the bloch sphere with purity @xmath72 ( recall that @xmath73 denotes the length of the bloch vector , i.e. , @xmath74 ) . while at low temperatures @xmath22 lies outside of our separability area , it is inside this area for temperatures of about @xmath75 . in the high temperature regime , when the dynamics is governed by a lindblad equation , decoherence of the qubit is thus complete , while the total state is still separable . this is especially striking because the initial state is so close to being the pure state @xmath76 . ) virtually all initial states decohere before any entanglement to the bath is built up.,scaledwidth=47.0% ] the question arises as to how many initial states , depending on temperature , meet the very same fate . in fig . [ fig : volumeofstates ] we display the relative volume of the set of states that are still separable at @xmath22 , i.e. after decoherence . remarkably , in the regime where the master equation ( [ equ : masterequation - decoherence ] ) is of lindblad form ( @xmath77 ) for practically all states decoherence has long happened before any entanglement between system an" +"the lab for adaptive optics ( lao ) currently has a testbed dedicated to the development of two key ao technologies for large telescopes ( called multi - conjugate ao ( mcao)@xcite and multi - object ao ( moao ) ) . both of these technologies take advantage of tomographic reconstructions using multiple guidestars ( a.k.a . reference sources)@xcite . in particular , mcao attempts to achieve a high strehl over a large field of view ( fov ) by accounting for anisoplanatism , using multiple deformable mirrors at optical conjugates . moao attempts to achieve very high strehls over small fovs embedded in larger uncorrected fields . first results from the testbed were shown in ammons 2006@xcite . recent results have demonstrated the effectiveness of tomography at finding the layers ofturbulence , and high strehls have been achieved with both mcao and moao . the testbed uses three optically addressed spatial light modulators ( slms ) from hamamatsu photonics . the slms allow us to have nearly 600,000 control elements , far more than any current mems . slms have been used with some success in the biological sciences ( for example , a demonstration is described in awwal 2003)@xcite . because their stroke is limited to approximately 1 wavelength deviation ( about 650 @xmath0 on the testbed ) and we would like to avoid phase - wrapping , we are incorporating a high stroke mirror into the testbed both to eliminate the need for the slms to phase wrap , and to test possible ao configurations for future systems called `` woofer - tweeter '' setups . taking an analogy from audio technology , the woofer - tweeter configuration in ao refers to the pairing of a higher resolution dm that has small stroke together with a high stroke ( and consequently low resolution ) dm called a woofer . though our testbed currently uses slms , woofer - tweeter combinations will also be useful for mems dms . in addition to our lab , similar architectures are being studied at u. victoria @xcite and at nui galway . [ cols=""^ "" , ] the particular alpao dm52 mirror we have in the lab has about a 133 @xmath0 @xmath1 focus shape when initially powered on but with no commands sent . in order to generate a flat shape we measured and inverted this wavefront and ran it through wooferfit to generate flattening commands . our first attempt at flattening the dm52 in open - loop resulted in a residual of approximately 11 @xmath0 @xmath1 of surface flatness deviation over the full clear aperture of the mirror . we then tried to fit a typical kolmogorov wavefront . the testbed uses etched glass kolmogorov phase plates as turbulence generators . the phase plates are meant to simulate a normal atmosphere s worth of wavefront aberration . we measured the wavefront using a set of shack - hartmann wavefront sensors . after doing a tomographic reconstruction of the estimated volume , there is a residual on the ground layer with approximately 250 @xmath0 @xmath1 tip / tilt removed wavefront error . we then fit this kolmogorov wavefront with the alpao dm52 using wooferfit . we compared the surface of the mirror as measured by a zygo interferometer to the wavefront generated by the tomography software . our comparison shows a 25 @xmath0 @xmath1 disagreement between the alpao dm52 and the wooferfit predicted shape over the clear aperture ( see fig . [ fig : fig3 ] above ) . the fit was noticeably better within the central portion of the mirror and when apertured down to 90% of the clear aperture the agreement was roughly 20 @xmath0 @xmath1 . it is important to note that these results are significant because they represent open - loop `` go - to '' control of the surface without the benefit of feedback from residual wavefront measurements . hence these results are applicable to systems which need to run open - loop like moao configurations mentioned earlier . we have tested the suitability of the alpao dm52 as a woofer dm and have shown it has promising open - loop characteristics . initial results look good for woofer - tweeter implementation in our mcao testbed . beckers j. m. _ eso conference on very large telescopes and their instrumentation _ , 693 ( 1988 ) . tallon , m. foy , r. _ a&a _ , * 235 * , 549 ( 1990 ) . ammons , s. m. laag , e. a. gavel , d. t. & kupke , r. _ proc . spie _ , * 6272 * ( 2006 ) . awwal , b. j. bauman , b. j. gavel , d. t. _ proc . spie _ , * 5169 * , 104 ( 2003 ) . keskin , o. hamptom , p. conan , r. bradley , c. hilton , c. & blain , c. _ proc . of the first nasa / esa conference on adaptive hardware and systems _ ( 2006 ) . the authors are grateful for funding from the gordon & betty moore foundation , whose generous gift enabled the construction of the laboratory for adaptive optics at the university of ca , santa cruz . the authors also acknowledge the generous support of the bachmann family . this work has been supported by the national science foundation science and technology center for adaptive optics , managed by the university of california at santa cruz under cooperative agreement no . ast - 9876783 ." +"gamma - ray bursts ( grb ) are cosmological explosions which produce an enormous amount of energy @xmath2erg within a few seconds to a few minutes by means of a highly relativistic jet . a grb light curve generally consists of a single or multiple broad pulses and rapid variability within the pulses on a timescale down to a few milliseconds.@xcite on the other hand , the spectrum is a continuum which is generally attributed to an optically thin synchrotron emission.@xcite interestingly , the spectrum generally shows a hard to soft evolution within the individual pulses.@xcite hence , pulses are important and should be considered independently . @xmath3 correlation : pulse - wise ( blue filled circles fitted with black solid line ) , burst average correlation of the same grbs ( orange open circles fitted with violet dot - dashed line ) and the same from nava catalog @xcite ( red dashed line with shaded @xmath4 data scatter ) . ( b ) the @xmath5 contours of the fit parameters of the pulse - wise correlation for two redshift bins . @xcite ] in recent works , @xcite we have given particular attention to the individual grb pulses and obtained the timing and spectral informations . we have then used the grb pulses to study grb correlations@xcite similar to the amati correlation@xcite . such studies are important due to several reasons : ( 1 ) as the correlation hold within the pulses it shows that the correlation is a pulse property , ( 2 ) it also shows that the correlation is real and not due to selection bias , ( 3 ) it provides a larger sample compared to the burst average studies . though pulse - wise grb correlation is powerful and indicates a basic mechanism of pulse generation , our pulse description is still empirical . here we review the results of our correlation studies and the possible improvements based on our new findings on the grb spectrum . we have developed a pulse model which describes a pulse simultaneously in energy and time domain.@xcite for this we use the spectral model as band function@xcite , lightcurve as norris model@xcite and spectral evolution as liang - kargatis model@xcite ( hereafter lk96 ) . our model is implemented in the x - ray spectral fitting package xspec as a table model with two parameters the peak energy at the beginning of a pulse ( @xmath6 ) and the characteristic evolution parameter ( @xmath7 ) . we apply this model on grb 090618 and generate the individual pulses . we derive various pulse properties e.g. , lightcurve and pulse width in various energies , spectral lag . a comparison with the data shows an excellent agreement . we then use this model for a set of _ fermi _ grbs with known redshift ( @xmath8 ) . we find that the @xmath6 bears a strong correlation with the energy ( @xmath9 ) within the individual pulses with a pearson coefficient , @xmath10 and a chance probability , @xmath11 . in a recent work,@xcite we have studied pulse - wise amati correlation for a set of 19 grbs with 43 pulses . we again obtain a good correlation ( see fig . [ grb_correlation]a ) . one of the major goal of grb correlation study is their application to constrain the cosmological parameters like matter and dark energy density at high redshifts , @xmath12 compared to that provided by the type ia supernovae ( @xmath13 in optical wavelengths ) . however , we need to investigate whether the grb correlation holds for different redshifts . in fig . [ grb_correlation]b , we plot the contours ( @xmath14 for single parameter and @xmath15 for two parameters ) of the correlation parameters for different @xmath8 bins , and we clearly see that they match within @xmath14 . hence , our correlation is stable with @xmath8 . the pulse model we have developed is an empirical one . it is worthwhile to mention that all grb correlations are empirical and shows considerable data scatter . this is also found in our pulse - wise correlation study ( fig . [ grb_correlation]a ) . hence , it is important to understand the physical mechanism of pulse emission and spectral characteristics . in some studies , the synchrotron origin of the spectrum has been challenged by observations of a spectral photon index higher than -1.5 ( or even higher than -2/3 ) , which is disallowed in the fast cooling ( slow cooling ) regime.@xcite in recent works it is found that the grb spectrum also contains a thermal component.@xcite in general the spectrum is a combination of the thermal and non thermal emission . however , the correct shape of the components is debatable , e.g. , a blackbody+powerlaw ( bbpl)@xcite , multi - colour blackbody+powerlaw ( mbbpl)@xcite , two blackbodies+powerlaw ( 2bbpl)@xcite , 2bb+cutoff powerlaw ( 2bbcpl)@xcite etc . moreover , the thermal emission is not always statistically significant . one way to find the correct model is to analyze the data with good spectral resolution e.g. , _ swift _ x - ray telescope ( xrt ) , _ nustar _ , _ chandra_. however , due to the focusing nature of these instruments such observations are rare . recently , we have found two such cases , grb 090618@xcite and grb 130925a.@xcite in fig . [ 2bbpl]a , we have shown the 2bbpl model fitted to the time resolved data of grb 090618 obtained from _ swift _ burst alert telescope ( bat ) and the xrt . in fig . [ 2bbpl]b the temperature and hardness evolution of this grb is compared with that found for grb 130925a observed with the xrt , the _ nustar _ and the _ chandra_. we see a remarkable similarity of the spectral evolution which denotes a common radiation mechanism . we note here that the pulse emission in grbs can have a wide variety . we have studied all such varieties and found a clear evidence of the two blackbodies in all cases , namely , ( 1 ) grbs with single pulse@xcite , ( 2 ) grbs with separable multiple pulses@xcite and ( 3 ) those having highly variable lightcurve@xcite . hence , the model appears to be a generic spectral shape . we suggest a spine - sheath jet structure to explain our observations ( see fig . [ jet]).@xcite such a structure is theoretically expected as the grb jet pierces through the envelop of the progenitor star . the two blackbodies are produced at the two photospheres of the jet , while the photons crossing the boundary layer of the spine and sheath are inverse - compotonized and form a cutoff powerlaw . in addition , internal shocks produced at larger radius will also contribute to the non - thermal emission . we are planning to pin down the mechanism by developing a spine - sheath jet model@xcite and then applying this model on a large set of grbs to obtain the physical parameters of the jet . the 2bbpl model is primarily found to be consistent with the data in kev mev or lower ( e.g. , the xrt ) energies . it is useful to apply this model to the prompt emission data in these energies and then investigate the predicted flux in other energies . in the following we perform such analysis to see how much we can explain the emission at very high energies ( gev ) based on the spectral model fitted to the lower energy data . the very high energy ( gev ) emission is detected in some grbs with _ fermi _ large area telescope ( lat ) . this emission is delayed compared to the prompt kev mev emission by a few seconds . it is well known that the band function can not capture the wide spectrum from kev to gev . also , the gev flux is found to be uncorrelated with the prompt kev mev flux . it is interesting to fit the kev mev data with the 2bbpl model and then compare with the flux at gev energies . analyzing a set grbs detected by the lat , we find a significant correlation of the gev photon fluence with that of the non - thermal ( powerlaw ) component of the 2bbpl model fitted to the kev mev data.@xcite also , the powerlaw flux of grbs with high gev emission tend to have a delayed onset , and this component lingers at the final phase of the prompt emission ( see fig . [ delayed_pl ] ) . remembering that the gev emission is delayed and long lasting than the kev mev emission , we strongly suggest that the powerlaw component of the 2bbpl model shares a common origin with the gev emission . in the framework of the spine - sheath jet model , this emission is produced at higher radius probably by synchrotron emission . on the other hand , the gev photons of grbs with low gev emission are probably produced due to inverse - compton of photons crossing the spine - sheath boundary . clearly such finding strongly validates the 2bbpl model . in future we shall test whether one or more spectral components of the 2bbpl model can be used to study the grb correlation . for example , in our pulse model we have assumed that the spectral evolution is given by the lk96 law . we have found that fitting the spectrum with an additional blackbody component leads to a similar evolution . now , the blackbody temperature shows a similar behaviour as shown by the @xmath16 ( see fig . [ lk96 ] ) . such findings give us hope to further improve the pulse description and finally obtain the fundamental grb correlation based on the physical spectral model . rb is a stipendiary of start program of the polish science foundation ( 2016 ) and supported by polish ncn grants 2013/08/a / st9/00795 , 2012/04/m / st9/00780 , 2013/10/m / st9/00729 , and 2015/18/a / st9/00746 ." +"neutrons stars are born in gravitational collapse of massive , degenerate stellar cores . newly born neutron stars are hot and lepton rich objects , quite different from ordinary low temperature , lepton poor neutron stars . in view of these differences , newly born neutron stars are called _ protoneutron _ stars ; they transform into standard neutron stars on a timescale of the order of ten seconds , needed for the loss of a significant lepton number excess via emission of neutrinos trapped in the dense , hot interior . in view of the fact that the typical evolution timescale of a protoneutron star ( seconds ) is some three orders of magnitude longer , than the dynamical timescale for this objects ( milliseconds ) , one can study its evolution in the quasistatic approximation ( burrows & lattimer 1986 ) . properties of static ( non - rotating ) protoneutron stars , under various assumptions concerning composition and equation of state ( eos ) of hot , dense stellar interior were studied by numerous authors ( burrows & lattimer 1986 , takatsuka 1995 , bombaci et al . 1995 , bombaci 1996 , bombaci et al . 1996 ) . the scenario of transformation of a protoneutron star into a neutron star could be strongly influenced by a phase transition in the central region of the star . brown and bethe ( 1994 ) suggested a phase transition implied by the @xmath0 condensation at supranuclear densities . such a @xmath0 condensation could dramatically soften the equation of state of dense matter , leading to a low maximum allowable mass of neutron stars . in such a case , the massive protoneutron stars could be stabilized by the effects of high temperature and of the presence of trapped neutrinos , and this would lead to maximum baryon mass of protoneutron star larger by some @xmath1 than that of cold neutron stars . the deleptonization and cooling of protoneutron stars of baryon mass exceeding the maximum allowable baryon mass for neutron stars , would then inevitably lead to their collapse into black holes . the dynamics of such a process was recently studied by baumgarte et al . it should be mentioned , however , that the very possibility of existence of the kaon condensate ( or other exotic phases of matter , such as the pion condensate , or the quark matter ) at neutron star densities is far from being established . recently , for instance , pandharipande et al . ( 1995 ) pointed out that kaon - nucleon and nucleon - nucleon correlations in dense matter raise significantly the threshold density for kaon condensation , possibly to the densities higher than those characteristic of stable neutron stars . in view of these uncertainties , we will restrict in the present paper to a standard model of dense matter , composed of nucleons and leptons . the calculations of the static models of protoneutron stars should be considered as a first step in the studies of these objects . it is clear , in view of the dynamical scenario of their formation , that protoneutron stars are far from being static . due to the nonzero initial angular momentum of the collapsing core , protoneutron stars are expected to rotate . on the other hand , the formation scenario involves compression ( with overshoot of central density ) and a hydrodynamical bounce , so that a newborn protoneutron star begins its life in a highly excited state , pulsating around its quasistatic equilibrium . in the present paper we study the rotation of protoneutron stars ; pulsations of protoneutron stars will be discussed in a separate paper ( gondek , haensel & zdunik , in preparation ) . some aspects of rapid uniform rotation of protoneutron stars have been recently studied in ( takatsuka 1995 , hashimoto et al . however , the calculations reported by takatsuka ( 1995 ) were actually done for static ( non - rotating ) protoneutron stars , and were then used to estimate the maximum rotation frequency of uniformly rotating protoneutron stars , @xmath2 , via an `` empirical formula '' . it should be stressed , that the validity of such an `` empirical formula '' , which expresses @xmath3 in terms of the mass and radius of the extremal _ static _ configuration with maximum allowable mass , had been checked only in the restricted case of _ cold _ neutron stars ( haensel & zdunik 1989 , friedman et al . 1989 , shapiro et al . 1989 , haensel et al . 1995 , nozawa et al . . only isentropic equations of state were considered by takatsuka ( 1995 ) . hashimoto et al . ( 1995 ) calculated the structure of stationary configurations of uniformly rotating protoneutron stars , using a two - dimensional general relativistic code . these authors restricted themselves to the case with zero trapped lepton number . they assumed a constant temperature in the hot interior of the star , and used a zero temperature ( cold ) eos for @xmath4 . it should be stressed , that the assumption of @xmath5 corresponds to an isothermal state in the newtonian ( flat space - time ) theory of gravitation . in general relativity , we will define isothermal state by @xmath6 ( where @xmath7 is the lapse function and @xmath8 is the lorentz factor , see section 3.1 ) , and the effects of the space - time curvature will turn out to be rather important for massive neutron stars . also , their choice for the low density edge of the hot interior can be questioned . finally , their criterion for finding maximally rotating configuration is actually valid only for cold ( @xmath9 ) or isentropic protoneutron stars : its use in the case of the @xmath5 hot interior is unjustified ( see section 3.2 for a correct statement of the stability criterion ) . in a recent paper , lai and shapiro ( 1995 ) have studied the secular evolution , secular `` bar instability '' , and the gravitational wave emission from the newly formed , rapidly rotating neutron stars . however , these authors used unrealistic ( polytropic ) equations of state of neutron star matter . moreover , the calculations were done within newtonian theory of gravitation . in view of this , the internal structure of their models of newly born neutron stars was quite different from that characteristic of the realistic models of protoneutron stars . the problem of the secular `` bar instability '' in rapidly rotating neutron stars was also studied , using general relativity , by bonazzola et al ( 1995 ) . however , numerical calculations were done only for realistic equations of state of _ cold _ neutron star matter . in the present paper we study the properties of uniformly rotating protoneutron stars , using exact relativistic description of the rapid , stationary rotation , combined with realistic equations of state of hot dense matter , used in the whole range of temperatures and densities relevant for protoneutron stars . in particular , we calculate the maximum frequency of uniform rotation of protoneutron stars and its dependence on their baryon mass , and on the thermal state and composition of stellar interior . it is clear , that uniform rotation represents only an approximation to the actual rotational state of a newly born protoneutron star . existing numerical simulations of gravitational collapse of rotating cores of massive stars produce differentially rotating protoneutron stars ( janka & moenchmeyer 1989a , b , moenchmeyer & mueller 1989 ) . however , it should be stressed that the initial rotational state of collapsing core is unknown , and this implies uncertainty concerning the rotational state of resulting protoneutron star . it is reasonable to say , that the actual degree of nonuniformity of rotation of a protoneutron star should be considered as unknown . in the present paper we will not address the question of the physical mechanisms that could `` rigidify '' the rotational motion within the protoneutron star interior . however , we will use the approximation of uniform rotation in order to limit the number the parameter space for our numerical calculation , and also because of the relative simplicity of the stability analysis in this specific , idealized case . within our simplified model , the `` neutrinosphere '' ( which has actually a deformed , spheroidal shape ) will separate hot , neutrino - opaque interior of a protoneutron star ( hereafter referred to as `` hot interior '' ) from a significantly cooler , neutrino - transparent envelope . the actual thermal state of the hot interior of protoneutron star is determined by its formation scenario , and is expected to be influenced by the dissipative processes ( damping of pulsations , viscous damping of differential rotation , neutrino diffusion ) . for simplicity , we will restrict ourselves to two limiting cases : an isothermal ( @xmath6 , see section 3 ) , and an isentropic ( entropy per baryon @xmath10 ) hot interior . we will also consider two limiting cases of the lepton composition of the protoneutron star interior . the first case , referring to the very initial state of protoneutron star , will correspond to a fixed trapped lepton number . in the second case , neutrinos will not contribute to the lepton number of the matter , which will correspond to vanishing chemical potential of the electron neutrinos ; such a situation will take place after a deleptonization of a protononeutron star . the position of the neutrinosphere will be located using a simple prescription based on specific properties of the neutrino opacity of hot dense matter . in all cases , the equation of state of hot dense matter will be determined using one of the models of lattimer and swesty ( 1991 ) . the plan of the paper is as follows . in section 2 we describe the physical state of the interior of protoneutron star , with particular emphasis on the eos of the hot interior at various stages of evolution . we explain also our prescription for locating the `` neutrinosphere '' of a protoneutron star , and we give some details concerning the assumed temperature profile within a protoneutron star . using simple estimates of the timescales relevant for various transport processes , we justify the approximation of stationarity which is used throughout this paper . in section 3 we give a brief description of the exact equations , used for the calculation of stationary configuration of uniformly rotating protoneutron stars . we discuss also stability of rotating configurations with respect to the axially - symmetric perturbations . the numerical method , used for the calculation of rapidly rotating configurations of protoneutron star , is briefly described in section 4 , where we also discuss numerical precision of our solutions . maximum rotation frequency , for various physical conditions prevailing in the hot stellar interior , calculated as a function of the baryon ( rest ) mass of protoneutron star , is presented in section 5 . then , in section 6 we show the validity of an empirical formula , which enables one to express with a surprisingly high precision the maximum frequency of rotating protoneutron stars in terms of the mass and radius of the maximum mass configuration of static ( non - rotating ) protoneutron stars with same eos . in section 7 we study the evolutionary transformation of a rotating protoneutron star into a cold neutron star . we show that , at fixed rest mass and angular momentum , maximum rotation frequency of protoneutron stars imposes severe constraints on the rotation frequency of solitary neutron stars . finally , section 8 contains discussion of our results" +"derived within linear response theory , the fluctuation dissipation theorem ( fdt ) predicts how the response function of a thermodynamic observable is related to correlation of thermal fluctuations at equilibrium . let us assume that an equilibrium system described by a hamiltonian @xmath0 is perturbed at time @xmath1 by an external force @xmath2 . the fdt predicts a response at a later time @xmath3 @xcite r^eq_a(t_2-t_1 ) = = a(t_2 ) [ -_h h(t_1)]_h=0_eq [ fdt - eq ] where the correlation is calculated at equilibrium corresponding to temperature @xmath4 with @xmath5 . the differential operator @xmath6 in the above relation denotes the scalar derivative evaluated at time @xmath7 . thus @xmath8 is the displacement conjugate to @xmath9 with respect to the hamiltonian . throughout this paper we use boltzman constant @xmath10 , unless otherwise stated . using the onsager regression hypothesis the fdt can be interpreted as follows the decay of a fluctuation is independent of how it has been created , under the influence of a small applied force or spontaneously by thermal noise . the fdt is violated away from equilibrium regime and this violation has been studied in context of glassy systems , granular matter , sheared fluid , stochastic processes , and biological systems @xcite . in a pioneering study back in 1972 @xcite , g. s. agarwal obtained a modified fluctuation - dissipation relation ( mfdr ) that related response functions around non - equilibrium steady states ( ness ) to correlations evaluated at steady state . for a system evolving with a statistical dynamics characterized by the fokker - planck ( fp ) equation @xmath11 , agarwal showed that a perturbation in the operator @xmath12 leads to a response that can be expressed in terms of a correlation function evaluated at the unperturbed steady state @xcite , r_a(t_2-t_1 ) = = a(t_2 ) m(t_1 ) where the _ agarwal term _ @xmath13/p_s$ ] with @xmath14 denoting the steady - state probability distribution . throughout this paper by @xmath15 we denote a steady - state average . over the last decade a formalism of stochastic thermodynamics has been developed that allows description of energy and entropy along fluctutating trajectories @xcite . various fluctuation theorems involving the distribution of entropy @xcite , and work theorems @xcite were discovered . recently , using an integral fluctuation theorem , a number of these relations were derived in a unified manner @xcite . important experimental tests include colloidal particles manipulated by laser traps @xcite , biomolecules pulled by afm or laser tweezer @xcite and autonomous motion of motor proteins @xcite . stochastic thermodynamics has also been used to derive several versions of mfdr around ness @xcite . some of these predictions were experimentally verified @xcite . in this paper , we present a unified derivation of a number of mfdrs based entirely on the agarwal formalism @xcite . thus the mfdrs we obtain are intrinsically equivalent to each other . we show that the agarwal term @xmath16 can be expressed as a velocity excess from a local mean velocity using both the _ continuum _ langevin and _ discrete _ master equation dynamics . this interpretation leads us to a modified einstein relation that has the same additive correction term for the two cases . finally we apply this framework to a flashing ratchet model of molecular motors @xcite to calculate the mfdr and the additive correction in einstein relation , which shows a non - monotonic variation with the asymmetry parameter of the ratchet . the structure of this paper is as follows . in sec . [ agarwal ] we review the derivation of the agarwal form of mfdr , that we use throughout this paper to calculate other versions of mfdr expressed in physically observable form . using this result , in sec . [ entropy - mfdr ] we present a simple and straightforward derivation of the mfdr in terms of stochastic entropy production , keeping in mind that this relation was used earlier to derive velocity - mfdr for a master equation dynamics @xcite . then , directly using the agarwal form , we derive the velocity - mfdr for a system evolving with continuum langevin dynamics in sec . [ lange - mfdr ] , and a discrete master equation in sec . [ master - mfdr ] . the velocity - mfdr is used in sec . [ einstein ] to derive a modified einstein relation at ness . in sec . [ ratchet ] , we study the velocity - mfdr , and the violation of the einstein relation in a flashing ratchet model of molecular motors . finally in sec . [ summary ] we summarise our main results and conclude . the probability distribution @xmath17 of finding a system at state @xmath18 at time @xmath19 evolves with time as _ t p(,t ) = ( , h ) p(,t ) [ eq1 ] where @xmath20 is a general time evolution operator that depends on external force @xmath2 . for weak @xmath9 , taylor expanding the operator we get ( , h ) = ( ) + h(t ) ( ) [ cl ] where @xmath21_{h=0}$ ] . the solution to eq . [ eq1 ] is p(,t ) = p_s + _ -^t de^(t- ) h ( ) p_s ( ) [ ps ] where @xmath14 denotes the steady - state distribution that obeys @xmath22 . then the response of any observable @xmath23 to a force @xmath2 is r_a(t_2-t_1 ) & = & = a ( ) + & = & a ( ) e^(t_2-t_1 ) p_s ( ) + & = & a ( ) e^(t_2-t_1 ) m ( ) p_s ( ) + [ resp ] where in the last step we used the agarwal term @xmath24/p_s$ ] . by definition , the two - time correlation function is @xmath25 , where @xmath26 is the joint probability distribution of finding the system at state @xmath27 at time @xmath28 and at state @xmath18 at time @xmath19 . one can express @xmath29 where @xmath30 is the transition probability . the time evolution @xmath11 can be solved to obtain the transition probability at steady state @xmath31 . thus the two - time correlation at steady state takes the form @xmath32 . therefore we can write eq . [ resp ] as r_a(t_2-t_1 ) = a(t_2 ) m(t_1 ) . this is the _ agarwal form _ of mfdr @xcite . the derivation presented here used a continuum notation of the phase space variable @xmath18 . however , the result is general , and can be derived similarly for a system that evolves through transitions between discrete states ( see eq . [ master - ag ] ) . the agarwal term in its operator form @xmath24/p_s$ ] requires detailed knowledge of the probability distribution at steady state . in the rest of this paper we focus on expressing this term in physically observable form the definition of non - equilibrium gibb s entropy @xmath33 has recently been used to get a definition of the stochastic entropy @xmath34 @xcite . for a master equation based discrete dynamics between states denoted by @xmath35 , the stochastic entropy can be written as @xmath36 . using this definition we obtain a simple interpretation of the agarwal term in terms of stochastic entropy m & = & p_s = . |_h=0 + & = & . |_h=0 = - _ t [ _ h s]_h=0 . in deriving the above relation we assumed that @xmath37 is linear in @xmath9 . we also used the fact that the steady state distribution @xmath38 . thus @xmath16 is expressed as time - evolution of a variable conjugate to the external force @xmath9 with respect to the stochastic system - entropy @xmath39 . in this sense , @xmath39 in ness plays the role similar to the hamiltonian in equilibrium fdt . we can now write the mfdr at ness as r_a(t_2-t_1)= a(t_2 ) [ -_h s(t_1 ) ] _ h=0 . [ mfdr - s ] ref . @xcite found this relation by considering a perturbation that takes the system to a final steady state . note that our simple and straightforward derivation does not require such an assumption , and thus the result is more general . the fdt at equilibrium can easily be derived from eq . [ mfdr - s ] . if , even in the presence of external perturbation the system remains at equilibrium , one can write down the probability distributions as @xmath40 $ ] where @xmath41 is the free energy . this distribution leads to the relation @xmath42_{h=0 } = \be [ ( \p_h f - \p_h h)p]_{h=0}$ ] . note that the equilibrium displacement evalutaed at @xmath43 is @xmath44_{h=0 } = 0 $ ] . thus we get the identity @xmath45_{h=0 } = -[(\p_h p)/p]_{h=0 } = \be [ \p_h h]_{h=0}$ ] , which leads to the equilibrium fdt eq . [ fdt - eq ] . let us consider a langevin system where the dynamics of a particle evolves by v = f + [ lange ] where @xmath46 is the particle velocity , @xmath47 is the mobility , and @xmath48 denotes total force imparted on the particle . the total force @xmath49 consists of a force due to interaction @xmath50 and an external time dependent force @xmath2 : @xmath51 . the last term @xmath52 denotes a thermal noise that obeys @xmath53 and @xmath54 with @xmath55 , the equilibrium einstein relation . the corresponding fp equation is _ t p(x , t ) & = & -_x j(x , t ) [ fp ] + with , j(x , t ) & = & ( f(x , t)-d_x ) p(x , t ) . the velocity form of mfdr for a langevin system was originally derived in ref . @xcite . here we briefly outline the derivation starting from the agarwal form . [ fp ] can be expressed as , _ t p(x , t ) = ( + h(t ) ) p(x , t ) , where , @xmath56 and @xmath57 thus the agarwal term @xmath58 and @xmath59 . the definition of the steady state current @xmath60 leads to the relation @xmath61 . defining a local mean velocity at steady state @xmath62 we can then rewrite @xmath63 . in this relation , using the langevin equation at initial steady state ( @xmath43 ) , we get @xmath64 . thus , the response function t r_a(t_2-t_1)= a(t_2 ) [ ( t_1 ) -v(t_1 ) + ( t_1 ) ] . [ lend ] note that in the langevin equation @xmath65 and @xmath66 have the same status , and @xmath67 can be regarded as a functional of noise history . then it can be shown that @xcite , t r_a(t_2-t_1)= d = a(t_2 ) ( t_1 ) . [ fdt - noise ] thus we can write eq . [ lend ] as r_a(t_2-t_1)= a(t_2 ) [ lange - va ] this is the _ velocity form _ of mfdr , which for velocity - response gives r_v ( t_2-t_1)= v(t_2 ) [ v(t_1 ) - ( t_1 ) ] . [ fdt - v2 ] note that the steady state average of @xmath68 is the same as the mean velocity : _ s = _ -l/2^l/2 dx p_s(x ) _ s(x ) = f - d [ p_s]_-l/2^l/2 = v_s . + [ nus_av ] the boundary term @xmath69_{-l/2}^{l/2 } = 0 $ ] either by a periodic boundary condition @xcite , or by taking the boundaries to infinity where the probabilities vanish . if the system is at equilibrium @xmath70 , and we get back the well - known equilibrium response , r^eq_v ( t_2-t_1)= v(t_2 ) v(t_1 ) _ eq . therefore the non - equlibrium mfdr eq . [ fdt - v2 ] can be viewed as the equilibrium fdt with an additive correction" +"given a discrete distribution @xmath0 on @xmath1 classes @xmath2 , we consider an index called _ polarization measure _ , defined by @xmath3 the polarization measure has been introduced in economics for real distributions by . the discrete version we consider here has been used in . the polarization measure has the following interpretation . let @xmath4 be i.i.d . @xmath5 and consider the indicator of _ exactly two equal _ @xmath6 then @xmath7 } = 3 \sum_{x=0}^n \pi_x^2(1-\pi_x ) = 3 { \operatorname{pol}\left(\pi\right)}$ ] . [ fig : polarization ] the polarization measure on the classes @xmath8 , as shown in fig . [ fig : polarization ] , has an unstable critical point at the uniform distribution , it is zero in the case of concentration in one class , and reaches its maximum 1/4 on distributions on two classes with equal probabilities . polarization measure was devised to be an index of the distance of a distribution from the three cases of maximal polarization . in fig . [ fig : polarization ] the simplex is represented as an equilateral triangle . in the following we shall use different sets of coordinates to represent the probability simplex , e.g. see fig . [ fig : gradpol - a ] ( left ) . we want to study the dynamics of this index , i.e. to characterise evolutions that maximise or minimise the index . this study requires tools from information geometry ( ig ) e.g. , . however , the following presentation is actually largely self - contained . the recourse to ig is not dispensable because the ordinary gradient flow of @xmath9 , as shown in fig . [ fig : gradpol - b ] ( left ) , does not lead to the extrema of interest on the border of the probability simplex . consequently , one wants to turn to a different way to compute the gradient , i.e. to the so - called amari s natural gradient . we use elementary fact of the theory of dynamical systems to characterise critical points of the gradient flow and refer to . the basics of ig are discussed in sec . [ sec : natural gradient ] . the application of ig to the polarization measure is described in sec . [ sec : pol ] . the possibility of a generalisation of such an index is shortly discussed in sec . [ sec : pols ] , while the reduction of the problem to the study of an exponential family is presented in sec . [ sec : polase ] . we suggest a possible application in sec . [ sec : app ] . further material , not directly related with the measure of polarization , but suggested by the methodology , is presented in the appendixes . differential equations on the probability simplex are well known in applications other then descriptive statistics . we briefly discuss the relations between these applications and our one in app . [ sec : replicator ] . in app . [ sec : hessian ] some issues related to the second order calculus are briefly discussed . we denote by @xmath10 the simplex of the probability function @xmath0 on @xmath11 . the interior of the simplex , @xmath12 , is the set of the strictly positive probability functions , @xmath13 the border of the simplex is the union of all the faces of @xmath10 as a convex set . we recall that a face of maximal dimension @xmath14 is called facet . a facet is a simplex of dimension @xmath14 . we define @xmath15 to be the vector space of random variables @xmath16 that are @xmath0-centered , @xmath17 } = 0 $ ] . in the geometry of @xmath18 , @xmath15 is the plane through the origin , orthogonal to the vector @xmath19 . 1 . the _ tangent bundle _ of the open simplex @xmath20 is the set @xmath21 2 . if @xmath22 is a one - dimensional statistical model , geometrically a curve , its _ score _ @xmath23 belongs to @xmath24 for all @xmath25 . as the score is a centered random variable , hence @xmath26 is a curve in the tangent bundle . in fact , @xmath27 is meant to represent a generic velocity vector through @xmath0 , see fig . [ fig : tangentbundle ] . the score is a representation of the velocity along a curve , because of a geometric interpretation of c. r. rao s classical computation : @xmath28= \frac d { dt } \sum_x u(x)p(x;t)= \sum_x u(x ) \frac d { dt } p(x;t)=\\ \sum_x u(x ) \frac d { dt } \log\left ( p(x;t)\right)p(x;t)= \sum_x \left(u(x)-e_t[u]\right ) \frac d { dt } \log\left ( p(x;t)\right)p(x;t)=\\ e_t\left[\left(u - e_t[u]\right ) \frac d { dt } \log\left ( p(t)\right ) \right]= { \left\langleu - e_t[u],d p(t)\right\rangle_{p(t)}}\end{gathered}\ ] ] we observe that the scalar product above is the scalar product on @xmath24 . a curve on the simplex is a parametric model . the probability @xmath0 is represented by a vector from @xmath29 to the point whose coordinates are @xmath30 . in fig . [ fig : tangentbundle ] , the velocity vectors are represented by arrows ; they are orthogonal to the vectors @xmath19 . [ fig : tangentbundle ] in our context , a _ vector field _ @xmath31 is a mapping such that @xmath32 , i.e. such that the couple @xmath33 belongs to the tangent bundle . @xmath34 for all @xmath0 . because of our geometrical construction , here we prefer to call @xmath35 a vector field , but we want to stress its statistical meaning of centered function of the distribution . a _ differential equation _ is an equation of the form @xmath36 . given a real function @xmath37 , its _ gradient _ is the vector field @xmath38 such that for all curves @xmath39 we have @xmath40 } , u , v \in b_\pi.\ ] ] the rao s computation in eq . is the prototypical gradient computation . the _ gradient flow equation _ is the differential equation @xmath41 along a solution of the gradient flow equation the value of @xmath42 is increasing because @xmath43 . actually the solution of the gradient flow equation is the curve of _ steepest ascent_. computations are usually performed in a _ @xmath44 @xmath45 being an open set in @xmath46 . the @xmath47-th coordinate curve is obtained by fixing the other @xmath14 components and moving @xmath48 only . the scores of the @xmath47-th coordinate curves are the random variables @xmath49 the sequence @xmath50 is a vector basis of the tangent space @xmath51 . the representation of the scalar product in such a basis is @xmath52 where the matrix @xmath53_{i , i=1}^n$ ] is the _ fisher information _ matrix . if @xmath54 is the expression in the parameters of a function @xmath55 , that is @xmath56 , and @xmath57 is the expression in the parameters of a generic curve @xmath58 , then the components of the gradient in are expressed in terms of the ordinary gradient by observing that @xmath59 as @xmath60 , we obtain from @xmath61 the _ natural gradient _ is a vector @xmath62 whose components are the coordinates of the gradient @xmath63 in its @xmath0-basis , that is @xmath64 by substitution of the expression in we obtain @xmath65 fig . [ fig : albero ] is an illustration for the function @xmath66 . the _ common parametrization _ of the ( flat ) simplex @xmath67 is the projection on the solid simplex @xmath68 , that is @xmath69 in which case @xmath70 , @xmath71 , is the random variable with values @xmath72 at @xmath73 , 1 at @xmath74 , 0 otherwise , hence @xmath75 and @xmath76 the element @xmath77 of the fisher information matrix is @xmath78 } = \\ \sum_x \pi(x,\bm\eta)^{-1}\left((x = j)(j = h)+(x = 0)\right ) = \eta_j^{-1}(j = h ) + \left(1 - \sum_k \eta_k\right)^{-1}\end{gathered}\ ] ] hence @xmath79_{i , j=1}^n.\ ] ] as an example we consider @xmath80 . the fisher information matrix , its inverse and the determinant of the inverse are , respectively , @xmath81 @xmath82 @xmath83 note that the computation of the inverse of @xmath84 is an application of the sherman - morrison formula and the computation of the determinant of @xmath85 is an application of the matrix determinant lemma . for general @xmath86 , we have the following proposition , whose interest stems from the definition of natural gradient , see eq . . [ prop : i-1 ] 1 . the inverse of the fisher information matrix is @xmath87 2 . in particular , @xmath85 is zero on the vertexes of the simplex , only . the determinant of the fisher information matrix is @xmath88 4 . the determinant of @xmath85 is zero on the borders of the simplex , only . 5 . on the interior of each facet , the rank of @xmath85 is @xmath14 and the @xmath14 liner independent column vectors generate the subspace parallel to the facet itself . 1 . by direct computation , @xmath89 is the identity matrix . 2 . the diagonal elements of @xmath85 are zero if @xmath90 or @xmath91 , for @xmath71 . if , for a given @xmath47 , @xmath90 , then the elements of @xmath85 are zero if @xmath92 , @xmath93 . the remaining case corresponds to @xmath91 for all @xmath47 . then @xmath94 on all the vertexes of the simplex . 3 . it follows from matrix determinant lemma . the determinant factors in terms corresponding to the equations of the facets . 5 . given @xmath95 , the conditions @xmath96 and @xmath97 for all @xmath98 , define the interior of the facet orthogonal to standard base vector @xmath99 . in this case the @xmath95-th row and the @xmath95-th column of @xmath100 are zero and the complement matrix corresponds to the inverse of a fisher information matrix in dimension @xmath14 with non zero determinant . it follows that the subspace generated by the columns has dimension @xmath14 and coincides with the space orthogonal to @xmath101 . consider the facet defined by @xmath102 , @xmath103 for all @xmath95 . for a given @xmath47 , the matrix without the @xmath47-th row and the @xmath47-th column has determinant @xmath104 . on the considered facet this determinant is different to zero and @xmath85 has rank @xmath14 and their columns are orthogonal to the constant vector . an other parametrization is the _ exponential parametrization _ based on the exponential family with sufficient statistics @xmath105 , @xmath71 , @xmath106 where @xmath107 some of the properties discussed in prop . [ prop : i-1 ] should actually be discussed under the exponential parametrization , see e.g. , but we do not do that here . we will discuss the exponential parametrization below in sec . [ sec : polase ] to show that polarization can be seen as an expectation with respect to an exponential family . we apply now the general theory of the natural gradient to the study of the dynamics of the polarization measure . our goal is to find the lines of the steepest ascent of the function @xmath9 . in the common parametrization we have @xmath108 and , for @xmath109 , @xmath110 with gradient @xmath111 the inverse of the fisher information matrix is @xmath112 the natural gradient is @xmath113 see in fig.s [ fig : gradpol - a ] and [ fig : gradpol - b ] the gradient fields . [ cols=""^,^ "" , ] to study the flow in the fixed points we consider the sign of the eigenvalues of the jacobian of the natural gradient , calculated in the fixed points , see @xcite . the jacobian of @xmath114 is @xmath115 $ ] where @xmath116 @xmath117 the jacobian calculated in the vertexes are @xmath118 and the two eigenvalues of the three jacobian are both positive . then , the fixed points" +"recently there has been a considerable interest in trying to obtain atomic decompositions of the space @xmath6 . these decompositions are usually obtained in terms of frames generated by a family of functions translated on a regular grid , and dilated by powers of a dilation matrix . the uniformity of the grid and the structure of the dilations can be exploited to obtain very sharp results . for irregular grids and unstructured dilations or if dilations are replaced by other transformations the situation is more complex and requires different techniques . one method is to use the regular case and try to obtain perturbations of the grid that preserve the frame structure . another possibility is to obtain irregular samples of the continuous transform , that have the required properties . in this article we study frame decompositions of the space @xmath4 using translations of a family of functions on irregular grids , and arbitrary dilations , and we even replace dilations by other transformations . our approach is different and very general , allowing quite general constructions . we prove the existence of smooth time - frequency frame atoms in several variables . the setting includes as particular cases , wavelet frames on irregular lattices and with a set of dilations or transformations that do not have a group structure . another particular case are non - harmonic gabor frames with non - uniform covering of the euclidean space . it also leads to new constructions of wavelet and gabor frames with regular lattice translates . one of the nice features of the proposed method is that it unifies different atomic decompositions . for the case of regular lattices guido weiss and his group @xcite developed a very fundamental program to characterize a large class of decompositions of @xmath4 through certain equations that the generators must satisfy . this is an important attempt to unify gabor and wavelets decompositions . other fundamental construction of mra wavelet frames on regular lattices can also be found in @xcite , @xcite , @xcite . our methods can be used to produce a substantial part of these systems . a set @xmath7 is a wavelet set if the inverse fourier transform of the characteristic function of the set is a wavelet . wavelet sets , frame wavelet sets and methods for constructing such sets have been studied recently @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite @xcite , @xcite . our methods give constructions of wavelet sets with translations on irregular grids . let @xmath8 and @xmath9 be countable index sets . we consider families of functions @xmath10 and discrete sets @xmath11 such that the collection @xmath12 form a frame for @xmath4 . the wavelet case is obtained when @xmath13 with a an expansive matrix and @xmath14 a fixed atom . we want to stress here that our constructions are much more general , allowing for example a different invertible ( not necessarily expansive ) matrix @xmath15 for each @xmath16 for the case of orthogonal wavelets , yang wang @xcite has recently considered wavelet sets associated with arbitrary families of invertible matrices and irregular sets of translates . he gave conditions for the existence of such wavelet sets and related them to spectral pairs . irregular wavelet and gabor frames also have been studied as perturbations of uniform ( lattice translate ) frames and also as sampling of the continuous wavelet/ gabor transform . see @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite,@xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite . the approach in this article can be considered in the spirit of the classic construction in 1 dimension of smooth regular tight frames done by daubechies , grossmann and meyer in @xcite . they found , for the case of uniform lattices , general conditions on a compactly supported smooth function @xmath17 , in order that it generates a tight gabor frame of @xmath18 . in the affine case they found necessary and sufficient conditions for a band limited function in order that it generates a smooth wavelet frame . see also @xcite . there were other related attempts to obtain atomic decompositions of functional spaces using very general systems . see for example @xcite , @xcite in the context of locally compact groups . this paper is organized as follows : section [ notation ] introduces the notation and some preliminaries . section [ wc ] presents a theorem on wavelet construction on arbitrary , sufficiently dense , but otherwise irregular grids and with arbitrary dilation or even invertible transformation matrices . specific constructions of such wavelets are obtained in section [ ew ] , first in the 1-d case and then in the multidimensional case . a general theory of frame atomic decomposition of @xmath4 is obtained in section [ gen - res ] . using the concept of outer frame , reconstruction formulas for these atomic decompositions are obtained in section [ rf ] . throughout the paper @xmath8 and @xmath9 will denote countable index sets , and @xmath19 will stand for the function @xmath20 we will use @xmath21 to denote the lebesgue measure of a measurable set @xmath22 . a set @xmath23 of measurable functions on @xmath24 is called a _ riesz partition of unity _ ( * rpu * ) , if there exist constants @xmath25 such that @xmath26 let @xmath27 be a family of measurable subsets of @xmath5 . a _ riesz partition of unity * associated to @xmath28 * _ , is a set @xmath23 of measurable functions , such that 1 . @xmath29 2 . there exist constants @xmath25 such that @xmath30 * if @xmath31 is a rpu , then @xmath32 is also a rpu . * if @xmath33 , we will say that @xmath31 is a _ regular partition of unity_. * if the sets in @xmath28 are essentially disjoint ( i.e. @xmath34 ) , the family @xmath35 will yield a regular partition of unity associated to @xmath28 . * every rpu @xmath31 can be normalized to obtain a regular partition of unity by considering @xmath36 * given a family @xmath37 of measurable sets on @xmath5 , define @xmath38 where @xmath39 is the cardinal of the set @xmath40 . the value @xmath41 is called the _ covering index _ of @xmath28 . we now recall the definition of frame for a given close subspace @xmath42 of @xmath4 . a set of functions @xmath43 is a _ frame _ for @xmath42 if @xmath44 and there exist constants @xmath45 , such that @xmath46 for a measurable set @xmath47 we will denote by @xmath48 the functions that have support in @xmath49 , and by @xmath50 the functions whose fourier transform has support in @xmath49 , i.e. @xmath51 we will need also the following definition . let @xmath52 be a hilbert space . a collection of vectors @xmath53 is an _ outer frame _ for a closed subspace @xmath42 of @xmath52 , if @xmath54 is a frame for @xmath42 , where @xmath55 is the orthogonal projection onto @xmath42 , or equivalently , there exist constants @xmath45 , such that @xmath56 related definitions to the concept of outer frames appear in @xcite , @xcite . throughout the paper , we will use the following immediate and very useful fact about frames : + if @xmath57 is a frame for @xmath48 , and @xmath58 , then @xmath57 is an outer frame for @xmath59 . our first results concerns the construction of wavelets @xmath60 with translates on the arbitrary irregular grid @xmath61 and with an arbitrary countable family of invertible @xmath2 matrices @xmath3 . [ wavelets ] [ wavelet ] let @xmath62 be a set of finite measure , @xmath17 a function in @xmath4 and @xmath63 a family of invertible matrices . for each @xmath64 set @xmath65 and let @xmath66 . assume that @xmath28 is a covering of @xmath5 , @xmath67 is a rpu with bounds @xmath68 and @xmath69 and that @xmath70 . consider @xmath71 such that for each @xmath64 , the set @xmath72 forms a frame for @xmath73 with lower and upper frame bounds @xmath74 and @xmath75 respectively . if @xmath76 and @xmath77 , then the collection @xmath78 is a wavelet frame of @xmath4 with bounds @xmath79 and @xmath80 , generated by a single function @xmath81 , where @xmath81 is the inverse fourier transform of @xmath17 . since for each @xmath64 we have that @xmath82 forms a frame for @xmath73 with lower and upper frame bounds @xmath74 and @xmath75 respectively , an application of part [ coro-2 ] of corollary [ transl ] for the matrix @xmath83 shows that @xmath84 forms a frame of @xmath85 with the same bounds . from the definition of @xmath86 , @xmath87 is then a frame for @xmath85 with frame bounds @xmath88 and @xmath89 . on the other side , if @xmath90 then @xmath67 is associated to @xmath91 . so , we can apply proposition [ genexpdil ] to @xmath92 and @xmath93 , to conclude that , @xmath94 forms a frame of @xmath4 with lower frame bound @xmath95 and upper frame bound @xmath96 . this gives that , @xmath97 forms a frame of @xmath4 with frame bounds @xmath79 ( or @xmath98 ) and @xmath80 . the theorem now follows from an application of the inverse fourier transform . 1 . the set of matrices @xmath99 can be arbitrary and need not have a group structure . the set @xmath100 can also be chosen to have a simple structure . for example , @xmath101 , @xmath102 where @xmath103 is a rotation and @xmath104 a dilation matrix , will be used to construct directional wavelets . an even simpler example is @xmath105 , @xmath106 , where @xmath107 is an invertible matrix which gives a construction of wavelet frames on @xmath5 . 3 . note that @xmath17 does not need to be compactly supported . we will use the theorem above to construct specific examples of wavelets , e.g. , directional wavelets , isotropic wavelets , etc . * interesting particular cases of theorem [ wavelet ] . * 1 . @xmath108 . + let @xmath109 be such that @xmath110 is a frame for @xmath73 with frame bounds @xmath111 and @xmath112 . then @xmath113 forms a wavelet frame of @xmath4 with bounds @xmath79 and @xmath80 . 2 . @xmath114 , with @xmath115 . + each of the following sets are wavelet frames of @xmath4 with bounds @xmath79 and @xmath80 : @xmath116 1 . if the set @xmath28 is a tiling of @xmath5 then the wavelets constructed above are shannon - like wavelets , thus not well localized in space . to obtain well localized space - frequency wavelets , @xmath117 must be constructed to be a smooth partition of unity , e.g. , at least @xmath118 as demonstrated in the examples in section [ ew ] , below reconstruction formulas for such wavelet frames are developed in section [ rf ] . to be able to use theorem [ wavelet ] to construct concrete examples of wavelet frames on irregular grids , we first need to construct exponential frames @xmath119 ( also called fourier frames ) for @xmath120 . exponential frames play a central role in sampling theory for paley - wiener spaces ( also known as spaces of band - limited functions ) . the density of a set @xmath121 and separateness of the points in @xmath122 play a fundamental role for finding exponential frames @xmath119 for @xmath120 . a sequence @xmath123 is separated if @xmath124 there are many notions for the density of a set @xmath122 . we start with three definitions that are due to beurling . 1 . a lower uniform density @xmath125 of a separated sequence @xmath126 is defined as @xmath127 where @xmath128^d}\right)$ ] , where @xmath129 denotes the cardinal of the set @xmath130 . an upper uniform density @xmath131 of a separated sequence @xmath122 is" +"our current hypothesis is that the galaxies and black holes observed today originated over 13 gyr ago , growing from seeds of primordial density perturbations . one can test this hypothesis by studying the star formation rate ( sfr ) history , from the epoch of reionization ( eor ) at redshifts @xmath21 , through the peak era at @xmath22 ( hopkins & beacom 2006 ) down to the present epoch . the feedback of ionizing radiation , kinetic energy , and heavy elements leaves imprints on early stars , supernovae , and galaxies , providing a fossil record "" that can be detected through abundances in galactic halo stars and the intergalactic medium ( igm ) and in the distributions of mass , metallicity , and luminosity of galaxies . determining when and how the universe was reionized by these early sources have been important questions for decades ( gunn & peterson 1965 ; sunyaev 1977 ; robertson et al . it has been suggested that igm reionization was complete by @xmath23 ( fan et al . 2001 ; gnedin & fan 2006 ; fan et al . 2006 ; hu & cowie 2006 ) , based on strong ly@xmath2 absorption from neutral hydrogen along lines of sight to qsos at @xmath24 . becker et al . ( 2007 ) and songaila ( 2004 ) used transmission of the ly@xmath2(and ly@xmath25 ) forest out to @xmath26 and @xmath27 , respectively , to suggest a smoothly decreasing ionization rate toward higher redshifts . recent surveys of high - redshift galaxies and ly@xmath2 emitters ( bouwens et al . 2011a ; ouchi et al . 2010 ; kashikawa et al . 2011 ; ono et al . 2012 ; schenker et al . 2012 ) infer an increasing igm neutral fraction from the declining populations between @xmath3 . further evidence for an increasing neutral fraction comes from the decreasing sizes of ionized near zones "" associated with quasars between @xmath28 and @xmath29 ( carilli et al . 2010 ) and from the ly@xmath2 damping wing in the transmission profile toward the newly discovered quasar at @xmath30 ( mortlock et al . these studies all suggest that the igm is becoming increasingly neutral between @xmath31 , marking the end of cosmic reionization when ionized regions overlap and percolate . whether the epoch of full reionization occurs at @xmath0 is still not ascertained . a contrasting estimate of the eor comes from the measured optical depth , @xmath32 , to electron scattering of the cosmic microwave background ( cmb ) in _ wmap-7 _ observations ( larson et al . 2011 ; komatsu et al . the error bars come from the central 68% in the marginalized cumulative distribution . using additional cosmological parameter constraints , they infer single - epoch reionization at @xmath33 . although such a high redshift could be explained with @xmath34cdm simulations and modeled sfr histories ( choudhury & ferrara 2005 ; trac & cen 2007 ; shull & venkatesan 2008 ) , the cmb observations are at variance with optical surveys that suggest late reionization , unless reionization is a process that extends to higher redshifts . for a fully ionized igm , including both h and he , the optical depth @xmath14 for @xmath35 ( see section 2.1 ) . in the cmb analysis ( larson et al . 2011 ) , marginalization of @xmath36 with other cosmological parameters allows the possibility of lower optical depth , with a reionization epoch as low as @xmath37 at 95% c.l . one can also invoke a partially ionized igm at @xmath38 , as discussed by many groups ( cen 2003 ; venkatesan et al . 2003 ; ricotti & ostriker 2004 ; benson et al . 2006 ; shull & venkatesan 2008 ) . however , even with the recent progress in finding high-@xmath12 galaxies , we still do not know whether galaxies are the sole agents of reionization . current observations of high-@xmath12 galaxies leave open several ionization scenarios , some involving simple hydrogen reionization at @xmath39 and reionization at @xmath40 , and others with more complex ionization histories ( bolton & haehnelt 2007 ; venkatesan , tumlinson & shull 2003 ; cen 2003 ) that depend on sfrs at @xmath41 . shull & venkatesan ( 2008 ) demonstrated how the cmb optical depth constrains the sfr and igm metallicity history at @xmath17 , and trenti & shull ( 2010 ) quantified the metallicity - driven transition from population iii ( metal - free stars ) to population ii ( stars formed from metal - enriched gas ) . several recent observations provide valuable constraints on the luminosity function of high-@xmath12 galaxies . the number density of galaxies appears to drop rapidly at @xmath17 ( bouwens et al . 2009 , 2010a , b , 2011a , b , c ) . with a comoving sfr density @xmath42 at @xmath43 ( gonzlez et al . 2010 ; bouwens et al . 2011a ) , the observed galaxies do not produce enough ionizing photons in the lyman continuum ( lyc ) to maintain a photoionized igm against recombinations . however , the luminosity function is steep , and the total lyc budget requires extrapolation to low - luminosity galaxies ( trenti et al . 2010 ; bouwens et al . moreover , the conversion from sfr to lyc production rate relies on insecure calibrations from theoretical models and comparison with high - mass , low - metallicity stars . we revisit the calculation of lyc photon production and assess the high-@xmath12 galaxy contribution to reionization . we also analyze several factors , such as the photon escape fraction ( @xmath11 ) , igm clumping factor ( @xmath44 ) , and electron temperature ( @xmath45 ) , which enter the calculation of the critical star formation rate "" ( @xmath46 ) necessary to maintain a photoionized igm . in section 2 , we calculate @xmath46 ( @xmath47 mpc@xmath48 ) in a filamentary igm , equating the production rate of lyman continuum ( lyc ) photons with the hydrogen recombination rate . the photoionization rate depends on the mass function of stellar populations , their evolutionary tracks and stellar atmospheres , and the escape fraction , @xmath11 of lyc photons away from their galactic sources . the recombination rate depends on the density and temperature of the igm , properties we explore with cosmological simulations . in section 3 , we give our results for the critical sfr at @xmath49 and present our new sfr simulator , a user - friendly interface for calculating @xmath50 and @xmath51 . in section 4 , we discuss the implications for the hydrogen eor . consistency between high - redshift galaxies and cmb optical depth appears to require @xmath0 and a partially ionized igm at @xmath17 . the peak signal from redshifted 21-cm emission would likely occur during the heating period between @xmath52 ( 145163 mhz ) when the hydrogen neutral fraction @xmath53 ( pritchard et al . 2010 ; lidz et al . we denote by @xmath1 ( @xmath54 ) the global star formation rate per co - moving volume . using a simple argument ( madau et al . 1999 ) , balancing photoionization with radiative recombination , we estimate the critical sfr to maintain igm photoionization at @xmath17 , assuming that the lyc photons are produced by populations of massive ( ob - type ) stars . because the mass in collapsed objects ( clusters , groups , galaxies ) is still small at high redshift , the igm contains most of the cosmological baryons , at mean density @xmath55 for a hubble constant denoted @xmath56 , we adopt the wmap-7 ( plus bao + @xmath57 ) parameters , @xmath58 and @xmath59 ( komatsu et al . 2011 ) relative to a critical density @xmath60 g cm@xmath48 . from the corresponding helium mass fraction @xmath62 ( peimbert et al . 2007 ) , we adopt a mean hydrogen number density , @xmath63 in a fully ionized igm , the cmb optical depth back to @xmath64 can be written as the integral of @xmath65 , the electron density times the thomson cross section along proper length , @xmath66 \ ; dz \ ; , \ ] ] for a standard @xmath34cdm cosmology ( @xmath67 ) with @xmath68^{1/2}$ ] . this integral can be done analytically ( shull & venkatesan 2008 ) , @xmath69 \left [ \ { \omega_m ( 1+z_{\rm rei})^3 + \omega_{\lambda } \}^{1/2 } - 1 \right ] \ ; .\ ] ] in the high - redshift limit , when @xmath70 , this expression simplifies to @xmath71 ( 1+z_{\rm rei})^{3/2 } \approx ( 0.0521 ) \left [ \frac { ( 1+z_{\rm rei})}{8 } \right ] ^{3/2}\ ] ] independent of @xmath72 to lowest order . the helium and electron densities are written @xmath73 and @xmath74 for singly ionized helium , where @xmath75 by number . to these formulae , we add @xmath76 , from electrons donated by reionized at @xmath77 ( shull et al . helium therefore contributes @xmath788% to @xmath36 , and a fully ionized igm produces @xmath14 , 0.060 , and 0.070 back to redshifts @xmath79 , 8 , and 9 , respectively . a comoving volume of 1 mpc@xmath80 contains @xmath81 hydrogen atoms . our simple ionization criterion requires a sfr density that produces a number of lyc photons equal to @xmath82 over a hydrogen recombination time , @xmath83^{-1}$ ] . the hydrogen case - b recombination rate coefficient ( osterbrock & ferland 2006 ) is @xmath84 , scaled to an igm temperature @xmath85 . for typical igm ionization histories and photoelectric heating rates , numerical simulations predict that diffuse photoionized filaments of hydrogen have temperatures ranging from 5000 k to 20,000 k ( dav et al . 2001 ; smith et al . these are consistent with temperatures inferred from observations of the ly@xmath2 forest at @xmath86 ( becker et al . 2011 ) . owing to gravitational instability , a realistic igm is inhomogenous and filamentary . semi - analytical models of the reionization of the universe often adopt a clumping factor "" , @xmath87 , to account for inhomogeneity in estimates of the enhanced recombination rate in denser igm filaments . the clumping factor therefore plays an important role in computing the critical sfr density needed to maintain the reionization of the universe . the clumping factor is also used in numerical simulations to implement `` sub - grid physics '' , in which changes in the density field occur on scales below the resolution of the simulation and are also approximated by the factor @xmath44 ( gnedin & ostriker 1997 ; madau et al . 1999 ; miralda - escud et al . 2000 ; miralda - escud 2003 ; kohler et al . 2007 ) . we correct the recombination time for density variations scaled to a fiducial @xmath88 , found in the simulations described below . at @xmath43 , the igm filaments have electron density @xmath89 ^ 3 c_h$ ] , and the characteristic times for hydrogen recombination and hubble expansion are , @xmath90^{-3 } \ ; , \\ t_{\rm h } & \approx & [ h_0 \omega_m^{1/2 } ( 1+z)^{3/2}]^{-1 } \approx ( 1.18~{\rm gyr } ) \left [ \frac { ( 1+z)}{8 } \right]^{-3/2 } \ ; . \end{aligned}\ ] ] in our calculations , we express the reionization criterion as @xmath91 , where @xmath46 is the critical sfr density ( @xmath54 ) and @xmath92 is the conversion factor from @xmath1 to the lyc production rate ( see section 2.2 ) . we define @xmath11 as the fraction of lyc photons that escape from their galactic sources into the igm ( dove & shull 1994 ) . recent statistical estimates ( nestor et al . 2011 ) suggest that @xmath93 for an ensemble of 26 lyman - break galaxies and 130 ly@xmath2 emitters at @xmath94 , and it could" +"analysis of large amounts of high - dimensional big data is of great interest since it illuminates the underlying phenomena . to cope with high - dimensional big data , it is sometimes assumed that there are some ( unobservable ) dependencies between the parameters of the multidimensional data points . mathematically , it means that the data is sampled from a low - dimensional manifold that is embedded in a high dimensional ambient space . dimensionality reduction methods , which rely on the presence of a manifold , map the data into a low - dimensional space while preserving certain qualities of the low - dimensional structures of the data . a broad class of dimensionality reduction methods are based on kernel - based methods . the kernel encapsulates a measure of mutual affinities ( or similarities ) between data points . particularly , if the kernel is semi - positive definite , it can be considered as gram matrix of inner products , which correspond to an implicit mapping of the data to a high dimensional space , typically refereed to as the feature space . depending on the chosen kernel , the new geometry of the data in feature space , represents important features of the data . kernel - pca is a technique that generalizes the well known principal component analysis ( pca ) @xcite . while the latter detects principal directions of data in euclidean space and then projects the data onto them , the former does the same in the feature space . it is resulted in a low dimensional euclidean representation ( embedding ) of the data that approximates the feature space geometry . the dimensionality of the embedding space is affected by the decay rate of the kernel s spectrum . examples of kernel methods are diffusion maps ( dm ) @xcite , local linear embedding ( lle ) @xcite , laplacian eigenmaps @xcite , hessian eigenmaps @xcite and local tangent space alignment @xcite . from a practical point of view , kernel methods have a significant computational drawback : spectral analysis of the kernel matrix becomes impractical for large datasets due to high computational complexity required to manipulate a kernel matrix . their global nature is also disadvantageous . furthermore , in many applications , the analysis process is dynamic due to data accumulation over time and , as a result , the embedding has to be modified once in a while . processing a kernel matrix in memory becomes impractical for large datasets due to their sizes . a general solution scheme embeds a subset of the source data that is usually referred to as a training dataset . then , the embedding is extended to any out - of - sample data point . the nystrm method @xcite , which is widely used in integral equations solvers , has become very popular as an out - of - sample extension method associated with dimensionality reduction methodology . for a review of spectral clustering and nystrm extension see section @xmath0 in @xcite . the nystrm extension scheme has three significant disadvantages : ( a ) it requires diagonalization of a matrix that costs @xmath1 operations @xcite . ( b ) it requires working with a matrix which may be ill - conditioned due to fast decay of its spectrum , and ( c ) it is unclear how to choose the length parameter @xmath2 since the output is sensitive to the choice of @xmath2 . some limitations of nystrm extension are overcome in @xcite . geometric harmonics ( gh ) @xcite is another out - of - sample extension method . it uses the nystrm extension of eigenfunctions of a kernel defined on the data . in order to avoid numerical instabilities , it uses only the significant spectral components . in that sense , the gh framework filters out high frequencies , which are determined by the kernel , rather than by the data this problem , additionally to the fixed interpolation distance problem , is treated in @xcite , where a multiscale interpolation scheme is introduced . another multiscale approach , which aims to solve the aforementioned limitations , was recently introduced in @xcite . both methods project the objective function on the eigencomponents of a series of kernels , which cover the complete spectrum of that function . the difference between these methods is in the extraction of principal components while the former is spectral and the latter is interpolative . all these methods use a kernel matrix ( or , perhaps , its low rank approximation ) as an interpolation matrix . this mechanism is strongly related to a variety of isotropic interpolation methods that employ radial basis functions ( rbf ) . such methods are used for scattered data approximation , where the data lies in a metric space . more details about rbf and scattered data approximation can be found in @xcite and @xcite , respectively . in this paper , we employ the manifold assumption to establish an anisotropic out - of - sample extension . we suggest a new anisotropic interpolation scheme that ascribes for each data point a likelihood neighborhood . this likelihood is based on geometric features from the dimensionality reduction map by using pca of the maps image . incorporation of such neighborhood information produces a linear system for finding the out - of - sample extension for this data point . this method also provides an abnormality measure for a newly - mapped data point . the paper has the following structure : section [ sec : setup ] introduces the problem and the needed definitions . the construction of the out - of - sample extension is described in section [ sec : alg_const ] . section [ sec : feature based variance ] establishes the geometric - based stochastic linear system on which the interpolant is based . three different interpolants are presented where each is based on different geometric considerations . in section [ sec : bound ] , an analysis of interpolations error is presented for the case of lipschitz mappings . computational complexity analysis of the scheme is presented in section [ sec : complexity ] . experimental results for both synthetic data and real - life data are presented in section [ sec : examples ] . let @xmath3 be a compact low - dimensional manifold of intrinsic dimension @xmath4 that lies in a high - dimensional ambient space @xmath5 ( @xmath6 ) , whose euclidean metric is denoted by @xmath7 . let @xmath8 be a smooth , lipschitz and dimensionality reducing function defined on @xmath3 , i.e. @xmath9 ( @xmath10 ) , where @xmath11 is a @xmath4-dimensional manifold . let @xmath12 be a finite training dataset , sufficiently dense sampled from @xmath3 , whose image @xmath13 under @xmath8 was already computed . given an out - of - sample data point @xmath14 , we aim to embed it into @xmath15 while preserving some local properties of @xmath8 . the embedding of @xmath16 into @xmath15 is denoted by @xmath17 . it is referred to as the extension of @xmath8 to @xmath16 . the proposed extension scheme is based on the local geometric properties of @xmath8 in the neighborhood of @xmath16 , denoted by @xmath18 . specifically , the influence of a neighbor @xmath19 on the value of @xmath17 depends on its distance from @xmath16 and the geometry of the image @xmath20 of @xmath18 under @xmath8 . this approach is reflected by considering @xmath17 as a random variable with mean @xmath21 and a variance @xmath22 that depends on both the distance of @xmath16 from @xmath23 and on some geometric properties of @xmath20 that will be detailedly discussed in section [ sec : tangent space ] . mathematically , @xmath24 where @xmath25 is a random variable with mean @xmath26 and variance @xmath27 that , as previously mentioned , depends on the local geometry of @xmath8 in the neighborhood @xmath18 of @xmath16 . thus , we get @xmath28 equations for evaluating @xmath17 , one for each neighbor @xmath19 . the optimal solution then , is achieved by the generalized least squares approach described in section [ sec : gls ] . in this section , we briefly describe the gls approach that will be utilized to evaluate @xmath17 . in general , the gls addresses the problem of a linear regression that assumes neither independence nor common variance between the random variables . thus , if @xmath29 are random variables that correspond to @xmath30 data points in @xmath31 , the addressed regression problem is @xmath32 where @xmath33 is an @xmath34 matrix that stores the data points as its rows and @xmath35 is an error vector . respectively to the aforementioned assumption , the @xmath36 conditional covariance matrix of the error term @xmath37 is not necessarily scalar or diagonal . the gls solution to eq . [ eq : regression ] is @xmath38 the mahalanobis distance between two random vectors @xmath39 and @xmath40 of the same distribution with conditional covariance matrix @xmath41 is @xmath42 [ obs : mahlanobis ] the mahalanobis distance in eq . [ eq : mahal_dist ] measures the similarity between @xmath39 and @xmath40 in respect to @xmath41 . if the random variables are independent , then @xmath41 is diagonal . then , it is more affected by low variance random variables and less by high variance variables . the gls solution from eq . [ eq : gls_solution ] , minimizes the squared mahalanobis distance between @xmath43 and the estimator @xmath44 , i.e. @xmath45 further details concerning gls can for example be found in @xcite . in our case , for a fixed out - of - sample data point @xmath14 with its @xmath46 neighbors , a linear system of @xmath30 equations , each of the form of eq . [ eq : basic_rv ] , is solved for @xmath17 . without loss of generality , we assume that @xmath47 . the matrix formulation of such a system is @xmath48 where @xmath49^t$ ] is the @xmath50 identity blocks matrix , @xmath51 is a @xmath52-long vector , whose @xmath53-th section is the @xmath54-long constant vector @xmath55 and @xmath56 is a @xmath52-long vector , whose @xmath53-th section is the @xmath54-long vector @xmath57 . the vector @xmath56 encapsulates the images of @xmath18 under @xmath8 such as the neighborhood of @xmath17 in @xmath11 . the corresponding covariance matrix is the @xmath58 blocks diagonal matrix @xmath41 , @xmath59 whose @xmath53-th diagonal element is @xmath60 . therefore , due to eq . [ eq : gls_solution ] , the gls solution to eq . [ eq : system_rv ] is @xmath61 and it minimizes the mahalanobis distance @xmath62 that measures the similarity ( with respect to @xmath41 ) between @xmath17 and its neighbors @xmath63 in @xmath11 , which are encapsulated in @xmath56 . once @xmath41 is defined as an invertible covariance matrix @xmath17 , as defined in eq . [ eq : psi_hat_solution ] , is well posed . the definition of @xmath41 depends on the definition of @xmath64 for any @xmath65 , which can be chosen subjected to the similarity properties to be preserved by @xmath8 . these properties are discussed in section [ sec : feature based variance ] . once eq . [ eq : psi_hat_solution ] is solved for @xmath17 , the mahalanobis distance from eq . [ eq : maha measure ] provides a measure for the disagreement between the out - of - sample extension of @xmath8 and @xmath16 with the surrounding geometry . thus , a large value of @xmath66 ( eq . [ eq : maha measure ] ) indicates that @xmath16 resides outside of @xmath3 and thus , in data analysis terminology , it can be considered as an anomalous data point . as mentioned in section [ sec : gls ] , the gls solution minimizes the mahalanobis distances between @xmath17 and its neighbors according to the stored" +"the concept of chiral symmetry breaking in strong interactions goes back to the pioneering work by nambu @xcite , and it has been widely explored and discussed since that time . restoration of chiral symmetry at high densities was proposed by lee and wick @xcite already in 1974 . theoretical procedures for studying chiral symmetry restoration at high temperatures were proposed on the same year by dolan and jackiw @xcite and by weinberg @xcite . qcd at finite temperature and density has attracted much interest . for latest studies of the qcd phase diagram see for instance @xcite . physical applications are to high energy heavy ion collisions @xcite and to the physics of the early universe @xcite . a review of lattice calculations can be found for instance in ref . the nambu - jona - lasinio model has been used under different approximations to obtain indications on the chiral transition ( see for instance @xcite ) . a number of peculiar features may emerge due to the chiral phase transition and recently much attention has been attracted by the possibility of disoriented chiral condensate formation ( see for instance @xcite ) . it is strongly suspected that a single transition occurs rather than separate transitions for deconfinement and chiral - symmetry . we had suggested a heuristic argument indicating that , at least for zero density , the critical temperature for chiral transition , @xmath3 , coincides with that for deconfinement , @xmath4 @xcite . the order parameters usually considered cover extreme and opposite ranges . the thermally averaged polyakov loop is suitable in the limit of infinite quark masses to describe the transition from the confined to the non - confined phase . the other extreme is the limit of vanishing quark masses , where the thermally averaged quark - antiquark bilinears are the typical order parameters for chiral symmetry transition . we shall deal here with the chiral transition , concentrating on the thermally averaged quark bilinears at finite temperatures as order parameters for chirality . for light massive quarks , such as @xmath5 and @xmath6 , rigorously , chiral symmetry is already broken in the lagrangian , but we can still retain the notion of phase transition , by looking at the region of @xmath7 where the condensate has a rapid variation . the current quark mass plays a role analogous to that of an external magnetic field in the ferromagnetic transition , as it explicitly violates the chiral symmetry whose restoration characterizes the phase transition . the analysis will be based on a composite operator formalism at finite temperature . the formalism makes use of an effective action for composite operators @xcite . actually the effective potential admits of a landau expansion around the critical point and thus the behaviour of the condensate is well reconstructed by knowing the coefficients ( which are infrared safe ) and the critical exponents . we shall compare with the results following from a landau expansion and show the general agreement . within the composite operator formalism we had already discussed the @xmath7 dependence of @xmath8 @xcite , in the whole range of temperatures up to @xmath3 . we shall here mainly deal with the ratio of the scalar to pseudoscalar mass @xmath9 at varying temperature . this ratio has a peculiar theoretical interest as a sensible indicator of the degree of chiral symmetry breaking . let us for the moment neglect the small @xmath5 and @xmath6 quark masses . when chiral symmetry is restored the two mesons are degenerate in mass . the ratio is then equal to unity . at zero temperature instead in the broken chiral phase the pion is a goldstone and has vanishing mass , while the sigma has a finite mass from the chiral condensation . thus one expects the mass ratio to decrease from @xmath10 to one at the chiral transition . quark masses will change this picture quantitatively leading to a decrease from a finite value to a value close to one . beyond some temperature , before approaching the critical value for the transition , the sigma will not have phase space left to decay into two pions . its instability will decrease when increasing the temperature , and the channel into two pions will finally be suppressed at some temperature in the vicinity but lower than the critical temperature . the decay channel into two photons will still be available and become the dominant channel @xcite . it is too early to say whether a possible experimental signature for the transition may be inferred from such behaviour . an accurate determination of the mass ratio versus temperature is in itself of theoretical interest as it constitutes a significant parameter for the degree of chiral symmetry breaking at finite temperature . this we shall do in this note in the composite operator formalism by making use of parameter values obtained from fits to zero temperature qcd . in section 2 we shall summarize the main results of the application of the composite operator formalism in qcd . in section 3 we determine the relevant qcd parameters and discuss the hadronic masses at non zero temperature . the temperature dependence of the observables is discussed in section 4 , where we also calculate the temperature at which the sigma can no longer decay via strong interaction . following ref . @xcite the zero temperature euclidean effective action for an @xmath11 qcd - like gauge theory is @xmath12 - { \rm tr}\left [ { \bf \sigma}{\bf s}\right ] -{\bf \gamma}_2({\bf s } ) + counterterms \label{effact}\ ] ] where @xmath13 , * m * is the bare quark mass matrix and @xmath14 is the sum of all the two - particle irreducible vacuum diagrams with fermionic propagator @xmath15 and @xmath16 . at two - loop level @xmath17 , where @xmath18 is the gauge boson propagator , so that @xmath19 , @xmath20 = 2{\bf \gamma}_2 $ ] and one can rewrite eq . ( [ effact ] ) in terms of @xmath21 @xmath22 + { \bf \gamma}_2({\bf \sigma } ) + counterterms\nonumber\\ & = & - { \rm tr}\ln\left[{\bf s}_0^{-1 } -{\bf \sigma } \right ] + { 1\over 2}{\rm tr}\left({\bf \sigma}\delta^{-1}{\bf \sigma } \right ) + counterterms \label{effact1}\end{aligned}\ ] ] here the variable @xmath21 plays the role of a dynamical variable . at the minimum of the functional action , that is when the schwinger - dyson equation is satisfied , @xmath21 is nothing but the fermion self - energy . a parametrization for @xmath21 , employed in @xcite was @xmath23 with a suitable ansatz for @xmath24 , and with * s * and * p * scalar and pseudoscalar constant fields respectively to be taken as the variational parameters . the effective potential one obtains from eq . ( [ effact1 ] ) ( see ref . @xcite ) is @xmath25-\nonumber\\ & & - n~{\rm tr}\ln\left[i\hat{k } - \left({\bf m}+{\bf \sigma}_s \right)-i\gamma_5{\bf \sigma}_p\right ] + \delta z~{\rm tr}({\bf m}~{\bf s } ) \label{effpot}\end{aligned}\ ] ] where @xmath26 is the quadratic casimir of the fermion representation ( for @xmath27 @xmath28 ) . furthermore @xmath29 , @xmath30 , @xmath31 ( @xmath32 , @xmath33 , @xmath34 gell - mann matrices , @xmath35 ) , @xmath36 is the gauge coupling constant and @xmath37 is the four - dimensional volume . in eq . ( [ effpot ] ) @xmath38 has a divergent part to compensate the leading divergence proportional to @xmath39 in the logarithmic term . we remark that both the current mass * m * and the self - energy @xmath21 are , in general , matrices in flavour space . however , as discussed in refs . @xcite if we neglect the mixing between different flavours originating , for instance , from terms such as the t hooft determinant @xcite , it follows that only the flavour diagonal elements of the fermion self - energy and mass can be different from zero at the minimum . with vanishing off - diagonal terms , the effective potential decomposes into the sum of @xmath40 contributions ( @xmath40 = number of flavours ) , one for each flavour . therefore , to study the minima of the effective potential , it is formally sufficient to consider a single contribution . of course , the choice of a given flavour number will reflect in the particular parameters assumed . in the present paper , as in ref.@xcite , we will take @xmath41 and a number of colour @xmath42 . the value of the parameters will be specified later on . as far as the choice for the function @xmath24 is concerned , in qcd , the operator product expansion suggests ( neglecting logarithmic corrections ) to take for @xmath24 a momentum behaviour as @xmath43 for large @xmath44 . we have chosen as a variational ansatz @xcite @xmath45 where @xmath46 is a momentum scale which is expected to be of the order of @xmath47 . to extend the zero - temperature theory to finite temperature we can still work with continuous energies by substituting for the sum over discrete energies @xmath48 ( where @xmath49 ) a sum of integrals over continuous energies by means of the poisson s formula @xcite @xmath50 this substitution corresponds to the imaginary - time formalism after using the poisson s formula and allows for an equivalent version af the dolan - jackiw finite temperature feynman rules @xcite . in conclusion the final form for the effective potential , for a quark of mass @xmath51 , is ( see ref . @xcite ) @xmath52-\nonumber\\ & & - 2n~\sum_{n=-\infty}^{n=+\infty}~(-)^{n}~\int{d^{4}k\over ( 2\pi)^{4}}~ \ln\left[k^2 + \left(m + \sigma_s\right)^2+\sigma^{2}_{p}\right ] + \delta z~ms \label{effpot1}\end{aligned}\ ] ] where @xmath53 and @xmath54 . let us now comment on the choice for the gauge coupling constant . as suggested by asymptotic freedom and renormalization - group considerations , we expect the strong forces to weaken at high temperature @xcite . we shall then assume that in the uv region the coupling constant @xmath55 depends logarithmically on the temperature @xmath7 . we take into account this assumption by writing @xmath56 where @xmath57 and we will discuss the parameters @xmath58 , @xmath46 and @xmath59 later on . at @xmath60 the effective potential does not acquire any extra divergence with respect to the @xmath61 case . the renormalization at @xmath61 can be performed by adding a counterterm and requiring that the derivative of the effective potential with respect to the term which breaks explicitly the chiral symmetry , evaluated at the minimum , satisfies for each flavour the renormalization condition @xcite @xmath62 the fermion condensate @xmath63 is related to the minimum @xmath64 of the effective potential , renormalized at the scale @xmath46 through the relation ( see ref . @xcite ) @xmath65 and @xmath66 . at finite @xmath7 we do not have any additional divergence with respect to the @xmath61 case ; nevertheless , in order to satisfy the generalization of the normalization condition ( [ normcond ] ) at finite @xmath7 we have to add a finite counterterm to that determined at @xmath61 @xcite . finally we recall that with the appropriate normalization for the pion field ( see next section ) , eq . ( [ normcond ] ) and its generalization at finite @xmath7 is also equivalent to the adler - dashen formula @xmath67 to compute the masses of the scalar and pseudoscalar mesons ( @xmath68 and @xmath69 respectively ) one has to take the second derivative of the effective potential ( [ effpot1 ] ) with respect to the scalar field @xmath70 and the pseudoscalar field @xmath71 , evaluated at the minimum ( for the sake of simplicity we are assuming that the up and down quarks are degenerate in mass and @xmath72 in eq . ( [ effpot1 ] ) ) . the actual values of the masses will be obtained by multiplying the second derivative by the appropriate factor @xmath73 that relates the physical fields @xmath74 (" +"quantum dots , their current and noise properties @xcite are widely investigated topics in today s nanophysics with a number of possible applications , the most revolutionary being a spin - based quantum computer @xcite . here , the spin of an electron in a quantum dot is used as a qubit , which serves as the basic building block of a quantum computer . a necessary ingredient for quantum processing is the possibility to couple at least two qubits and to understand and manipulate the various correlations . this is one of the motivations to study double quantum dots @xcite . in particular , it is required to create entangled electron states by the interaction of an electron inside the double dot with an electron tunneling onto the double dot . measuring this entanglement is an important experimental task and theoretical suggestions how to probe these states are needed . in this work , we will discuss the relation between zero - frequency current noise , coulomb correlations , and entanglement for the example of a double quantum dot . we will make use of the recent observation @xcite that noise measurements in the nonlinear coulomb - blockade regime can be used to obtain spectroscopic information of excited levels in a quantum dot . this scheme will be adapted to a double quantum dot and we will show that the important interaction parameter @xmath0 ( containing information about the entanglement ) @xcite enters the fano factor ( i.e. , the ratio of noise power to current ) in this regime . this kind of noise spectroscopy can be used to directly extract @xmath0 from experimentally observable quantities . we extend a previous discussion @xcite of the low - frequency shot noise of a double - dot system by an analysis of the full counting statistics of the transferred charge . this allows us to identify directly the interaction parameter by a noise measurement . one main result is obtained in the transport regime , in which predominantly only one electron occupies the lowest double dot level due to the coulomb interaction . thermal activation leads to tunneling events through excited two - electron states which result ( under the conditions discussed below ) in super - poissonian shot noise characterized by a fano factor @xmath1 hence , a measurement of the noise in this regime allows a direct determination of the interaction parameter @xmath0 . we now turn to a description of the model and the method . with maximally two electrons occupying the double dot and no magnetic field lifting the spin - degeneracy , the following hund - mulliken eigenstates of the double quantum dot are possible ( for a more detailed description see @xcite ) : the zero - electron state @xmath2 , two two - fold degenerate one - electron states @xmath3 ( symmetric ) and @xmath4 ( anti - symmetric ) , four two - electron states with one electron per dot , the singlet @xmath5 and the three - fold degenerate triplet @xmath6 . there are two other singlet states that have a significantly higher energy due to the large on - site coulomb interaction which do not have a physical effect in the regime studied ( but are included in the numerical calculations ) . we consider a ( longitudinal ) double dot coupled to leads , which are modeled as a fermi sea . the tunnel coupling leads to a tunneling amplitude @xmath7 , which measures the overlap between the orbital state and the lead wave function in terminal @xmath8 . we assume that @xmath9 is the applied bias voltage and that @xmath10 ( @xmath11 ) are the chemical potentials of the left and right leads . there is an additional lead with capacitive coupling to the double dot characterized by the gate voltage @xmath12 that shifts the potential on the dot . when one electron is on the dot , it can be in two possible states : its wave function is spread either symmetrically or anti - symmetrically over the two dots . the symmetric state has a lower eigenenergy , and the energy difference between the two one - electron states depends on the interdot tunneling amplitude @xmath13 , describing the potential barrier between the two dots . including the energy contribution of the gate voltage , the eigenenergies of these states can be calculated as @xmath14 . adding a second electron , we have first to overcome the gate voltage again , and additionally the repulsive coulomb interaction between the two electrons leads to a spin - dependent splitting of the eigenenergies . for the singlet state @xmath5 we obtain the energy @xmath15 , and for the ( three - fold degenerate ) triplet state @xmath16 the energy @xmath17 . here , @xmath18 is the ( inter - dot ) electron - electron repulsion and @xmath19 is the heisenberg exchange parameter that characterizes the heisenberg interaction between the two spins , @xmath20 ; @xmath21 is the on - site coulomb repulsion . because @xmath22 is positive , the singlet state has a lower energy than the triplet state . the singlet state can be expressed in terms of the creation operators @xmath23 , @xmath24 , which create an ( anti)-symmetric electron state @xmath25 the interaction parameter @xmath0 describes the competition between the kinetic - energy gain and the coulomb repulsion . in the hund - mulliken model @xmath26 is determined by the inter - dot tunneling amplitude @xmath13 and the on - site coulomb repulsion @xmath21 @xcite . in general , the dependence of @xmath0 on the microscopic parameters may have a different form , however we will always use this definition for the quantitative plots below . it is important to stress that the results obtained below are largely independent on the precise dependence of @xmath0 on the details of the quantum dot . hence , the noise features we find can be used as an additional test of the applicability of the model calculation of ref . @xcite to realistic quantum dots . we describe transport through the double dot in the sequential - tunneling approximation using the master equation @xmath27 here , @xmath28 and @xmath29 label the available states of the quantum dot , including the number of electrons on the dot , the orbital index , and the spin . @xmath30 is the occupation probability of state @xmath28 , and @xmath31 is the tunneling rate from state @xmath28 to state @xmath29 . the rates are given by @xmath32 here , @xmath33 is the bare tunneling rate to the left ( right ) terminal , and @xmath34 is the density of states in the leads . the matrix elements @xmath35 depend on the orbital and the spin state of the dot @xcite . the occupation in the leads is determined by the fermi functions @xmath36 $ ] , the direction of tunneling is defined by @xmath37 and the energy difference by @xmath38 . we note here , that the interaction parameter @xmath0 enters the calculations through the matrix elements @xmath35 of the singlet state . for a more detailed discussion of these tunneling rates we refer to @xcite . for later use we express the master equation ( [ emasteq ] ) in matrix form , @xmath39 , where @xmath40 for @xmath41 and @xmath42 . from the master equation , we obtain the noise @xcite . the quantity characterizing the current noise is the fano factor @xmath43 . it measures , how far the distribution of the tunneling events differ from the random , poissonian distribution : for poissonian noise , when the tunneling events are uncorrelated , @xmath44 . a fano factor @xmath45 can be due to anti - correlations ( e.g. the pauli principle ) . we will be mostly interested below in super - poissonian noise , @xmath46 , and we will show that here it is due to correlated transport cycles resulting from a blockade of open channels . by a transport cycle we mean the following process @xcite : suppose the system is initially in its ground state @xmath47 , and another state @xmath48 ( which would be available for tunneling according to its energy ) is blocked due to coulomb interaction . when this electron in @xmath47 tunnels out of the dot due to a thermal excitation , both the states @xmath47 and @xmath48 are available for electrons to tunnel into . a cycle is occurring , when a sequence of electrons tunnels through state @xmath48 before an electron enters the ground state @xmath47 and blocks the transport through the dot again . this cycle leads to a correlated transfer of a number of charges given by the number electrons tunneling through the excited state @xmath48 . hence , that effective charge transferred in one cycle is larger than one and leads to an increased fano factor . the above picture is based on the sequential - tunneling approximation . the parameters have to be chosen such that cotunneling processes can be neglected . this is experimentally possible , since the current due to cotunneling processes is generally of the order of @xmath49 , where @xmath50 is the tunneling amplitude and @xmath51 is the excitation energy in the virtual intermediate state . in our case the current in the most interesting regime is proportional to @xmath52 , where @xmath53 is exponentially small in @xmath54 . since the tunneling amplitude @xmath50 can in principle be made arbitrarily small , sequential tunneling becomes the dominant process . recently it was shown that noise spectroscopy deep inside the coulomb blockade regime is possible @xcite and in agreement with the sequential - tunneling description . the results of our calculation are summarized in fig . [ fbloccurfan ] , which shows the average current ( top panel ) and the fano factor ( bottom panel ) as a function of the bias voltage @xmath9 and the gate voltage @xmath12 . considering the current , the most visible feature is the coulomb blockade diamond ( green in fig . [ fbloccurfan ] ) . as long as the bias voltage is lower than the energy difference between the energetically lowest state and the next state with one electron more or less , i.e. , @xmath55 with @xmath28 and @xmath29 being two states differing by one electron , electron tunneling is exponentially suppressed . in our model , we have three such blockade regimes with 0 , 1 , and 2 electrons in the dot for zero bias voltage . the two parts of fig . [ fbloccurfan ] show the current and the fano factor for the most interesting of these blockade regions , the one - electron blockade regime . we will concentrate our discussion on this region , since most interesting features can be discussed here . we first look at the energies of the states in the blockade regime as a function of the gate voltage , see fig . [ fenplot ] . the capital letters in figs . [ fbloccurfan ] and [ fenplot ] correspond to these blockade regions , and we will now show that the features in the fano factor can be explained by the energy plot for the states in this region . we first consider the regions @xmath47 . they are both characterized by a fano factor @xmath44 , typical tunneling processes through a simple two - level system . indeed , fig . [ fenplot ] shows that the first excited states differ in electron number . in @xmath56 the excited state is @xmath2 and in @xmath57 @xmath5 . lowering the gate voltage , we come to region @xmath48 , where the first excited state is the state @xmath4 , i.e. , a state with one electron as well . thus , the description in terms of a single state , which can be occupied or not , does not hold any" +"the use of general principles to investigate systems whose microscopic makeup is unclear can be very rewarding . sometimes this method gives information on a whole class of systems . among such principles , thermodynamics , believed to be of universal applicability , stands out . an instructive example of its use is the application of the second law of thermodynamics to the problem of viscous flow , for which it permits the inference that the two viscosity coefficients must be positive without need to resort to microscopic expressions for the latter @xcite . in this work we use the generalization of the second law of thermodynamics holding in the presence of black holes ( the generalized second law gsl ) to reach further conclusions about the shear viscosity coefficient of an arbitrary fluid . we do this by describing a new paradox for ideal fluid flow in the presence of a black hole . this indicates that the correlation length of a real fluid can not be arbitrarily small . by implication the energy - momentum tensors describing systems which display macroscopic fluid behavior must be subject to a restriction : the shear viscosity , a function of the thermodynamic state of the system , can not be arbitrarily small . thereby the gsl opens an alternative macroscopic approach to the recently proposed lower bound on viscosity @xcite . the gsl is a unique law of physics that bridges thermodynamics and gravity . it is rooted in the understanding that a black hole , basically a pure gravity entity , is endowed with well defined entropy @xcite proportional to its surface area . the gsl @xcite then claims that the sum of the entropy of all black holes and the total ordinary entropy in the black holes exterior never decreases . while this formulation is reminiscent of the ordinary second law , the gsl is exceptional in that it relates ordinary entropy a rather elusive object from the mechanical viewpoint and the surface area of the black hole ( formally the area of its horizon ) whose evolution is quite mechanical in nature . from this point of view it is little surprise that the gsl has provided unexpected information on entropy . an example is the upper bound on the entropy of weakly self - gravitating thermodynamic systems ( the universal bound on entropy ube @xcite ) . while in particular cases the bound can be verified directly , it is the gsl which really makes understanding of the bound in generic situations easy . however , the gsl gives more than just a simpler way to see some results derivable by other means . at the microscopic level the gsl represents a piece of the yet to be established theory of quantum gravity . in particular , this law permits , in principle , to draw conclusions that from the microscopic viewpoint would only be derivable from a fundamental theory combining quantum mechanics with gravity . for example , the gsl gives an indication of the number of particle species in nature @xcite . in another example , the gsl reveals an _ a priori _ bound on the strength of the electromagnetic interaction @xcite . let us now describe the ideal fluid paradox revealed by invoking the gsl . we assume the existence of physical fluids with arbitrarily small shear viscosity @xmath0 at fixed values of some two thermodynamic variables , say the entropy and the energy densities , @xmath1 and @xmath2 , respectively . ( in this work we consider only simple fluids , so the values of @xmath1 and @xmath2 completely determine the thermodynamic state of the system . ) here physical "" means , among other things , that the fluid satisfies the gsl ; this could , in principle , be checked by considering the fluid at the microscopic level , but we shall not go into such detail . the assumption that the fluid has arbitrarily small viscosity allows us to describe its flow as ideal fluid flow , possibly with shocks ( the zero viscosity limit of a given flow can be non - trivial ; see refs . it turns out , as we shall show , that for sufficiently slow accretion of the fluid onto the black hole the overall entropy decreases and the gsl is violated . the realizability , in principle , of such slow accretion flows will be demonstrated , so that the small viscosity assumption engenders a paradox . of course , ideal fluid paradoxa exist already in non - relativistic physics , for example , the famous dalembert paradox . this maintains that an ideal fluid with no boundaries exerts no force whatsoever on a body moving through it with constant velocity . in particular , there is no lift force , so swimming or flying would be impossible in such a fluid . thus the established fact that swimming is possible in any fluid implies that every real fluid must have nonzero viscosity . there is however an essential difference between the dalembert paradox and the paradox described in this work . dalembert s paradox says nothing about the actual magnitude of @xmath0 . in contrast , our paradox implies , as we shall see , the existence of a lower bound on @xmath0 for given @xmath1 and @xmath2 . this conclusion is in concord with the recent ingenious conjecture of kovtun , starinets and son ( kss ) @xcite ( see also ref . @xcite ) . based on holographic calculations of the viscosity coefficient for certain strongly coupled quantum field theories with gravity duals , they suggested that the viscosity @xmath0 of a general , possibly non - relativistic , fluid is subject to the universal restriction @xmath3 currently this bound is considered a conjecture well supported for a certain class of field theories see the detailed discussion in ref . @xcite and the references therein . in the sequel we discuss the relation between the ideal fluid paradox presented in the next section and the kss bound . we also argue that a frequent objection to the validity of the kss bound is likely to be ruled out by the gsl . our paper is structured as follows . in sec . [ paradx ] we show explicitly that the slow accretion of a truly ideal fluid onto a schwarzschild black hole leads to a contradiction with the gsl . one escapes from the paradox by recognizing that every fluid must have a nonvanishing correlation length which restricts the range of applicability of the ideal fluid paradigm . in sec . [ kssp ] we obtain a lower bound on the correlation length and a generic estimate of the viscosity of real fluids , which together bound the viscosity to entropy density ratio from below . although this is not yet the kss bound , we consider there the connection between it and the ube , and argue that the gsl provides a natural frame for elucidation of the origin of the former . in the sec . [ summary ] we summarize our results and arguments . the realizability , in principle , of the slow accretion flow assumed in sec . [ paradx ] is demonstrated in the appendix . unless otherwise stated , we work in units with @xmath4 , where @xmath5 is speed of light and @xmath6 is boltzmann s constant . our metric signature is @xmath7 . in the present section we consider ideal fluid flow into a spherical black hole . for some flows , we demonstrate that it is possible for the gsl to be violated so that the total entropy of the system decreases . it follows that the assumption of a perfect continuum down to an arbitrarily small scale is not consistent with the gsl . consider a flow , not necessarily spherically symmetric , in which fluid is absorbed by the black hole . the rate of change of the total entropy @xmath8 of the system is the sum of the rate of change of the entropy of the black hole exterior , @xmath9 , and that of the black hole entropy @xmath10 : @xmath11 here and below we use schwarzschild coordinates @xmath12 , with @xmath13 where @xmath14 is the schwarzschild radius . we first calculate @xmath15 . let the fluid s proper entropy density be @xmath1 . since the fluid is assumed ideal , there is no dissipative contribution to the entropy current density which is thus purely convective , and must take the form @xmath16 , where @xmath17 is the fluid four - velocity . the fluid can carry entropy into the hole leading to a decrease of @xmath9 . the explicit expression for this comes from the entropy balance equation @xcite , @xmath18 where @xmath19 stands for the determinant of the schwarzschild metric @xmath20 . @xmath15 of the black hole exterior ( @xmath21 ) is thus @xmath22 we have not included a contribution from the outer boundary of the domain of integration because we intend to specialize to stationary flows . in any such situation the entropy flow into the hole per unit @xmath23-time is given by the r.h.s . of eq . ( [ exterior ] ) . the expression is non - positive because @xmath24 for infalling matter . we have assumed that the flow is differentiable , and that it contains no shocks ; otherwise there exists an additional contribution to @xmath15 associated with the entropy generation in the shocks @xcite . let us now consider the second term of the r.h.s . in eq . ( [ total ] ) . the absorption of the fluid by the black hole increases the latter s mass @xmath25 , producing an increase in the black hole entropy given through energy conservation by @xmath26 where @xmath27 is the black hole temperature , and @xmath25 is its mass . we shall now write down the flux of energy into the black hole . let @xmath28 be the killing vector associated with the stationarity of the black hole . then the energy - momentum tensor of the fluid , @xmath29 , must obey @xmath30 or equivalently @xmath31 since @xmath32 is _ minus _ the energy density of the fluid , @xmath33 the energy - momentum tensor of the ideal fluid is given by @xmath34 where @xmath2 is the energy density and @xmath35 is the pressure in the comoving frame . consider now the normalization condition @xmath36 , written as @xmath37.\ ] ] since @xmath38 and @xmath39 are physical velocity components , they should be bounded at @xmath40 . hence since @xmath41 is future and inwardly pointed , and @xmath42 as @xmath43 , we can infer from the last equation that @xmath44 at the horizon . combining all the above we find @xmath45 thus @xmath46 in harmony with hawking s area theorem @xcite . we observe from eqs . ( [ exterior ] ) and ( [ black ] ) that while the ( negative ) rate of change of @xmath9 is proportional to the first power of @xmath47 , the ( positive ) rate of change of the black hole entropy is proportional to the _ second _ power of @xmath47 . thus for sufficiently small @xmath48 , the total entropy of the system will _ decrease _ , in violation of the gsl . explicitly we have @xmath49,\ ] ] where we stress that at the horizon @xmath47 is never positive . we observe that when the accretion velocity @xmath50 ( the suitable mean value of @xmath51 over the horizon ) obeys @xmath52 the total entropy decreases and the gsl is broken . we now proceed to search for such flows . we first reconsider known explicit solutions . the above formulae apply for a generic , not necessarily spherically symmetric , accretion flow onto the black hole ; in particular it may have non -" +"when infrared dark clouds ( irdcs ) were originally identified as dark extinction features against the galactic background at mid - ir wavelengths @xcite , it was not clear what role , if any , they might play in the process of star formation . their high column densities ( @xmath4@xmath5 @xmath6 ) , together with their cold temperatures ( @xmath7 k ) suggest that if stars do form within irdcs , then irdcs must comprise an early phase in the process ; otherwise the embedded stars would have heated their surrounding gas and dust . recently , compact molecular cores within irdcs have been found to contain embedded young stars or protostars ( e.g. , @xcite ) . a few of these embedded young stellar objects will evolve into high - mass stars ( e.g. , @xcite ) . this star - formation activity , along with the similarity in size and mass between irdcs and cluster - forming molecular clumps , has led to the suggestion that irdcs are the birthplaces of all high - mass stars and clusters ( e.g. , @xcite ) . one striking feature of irdcs is their filamentary shape , evident in the images from mid - ir galactic surveys such as _ msx _ @xcite , glimpse @xcite , and mipsgal @xcite . similar filamentary structures are also found in familiar examples of associated high - mass star - forming molecular clouds , such as orion ( e.g. , @xcite ) . because these warmer clouds bear a striking resemblance to irdcs , the warm , star - forming filamentary clouds may represent a later evolutionary stage in the life of an irdc . indeed , filamentary clouds may play an important role in high - mass star formation because they allow for enhanced accretion rates onto cores @xcite . an extreme example of a filamentary irdc is the nessie "" nebula centered near @xmath8 . nessie is identified as a dark mid - ir extinction feature in the glimpse and mipsgal surveys ( figure [ figure1 ] ) . if the mid - ir extinction represents a single object , then this irdc has an unusually large aspect ratio of over 150:1 ( @xmath9 ) . nessie contains a number of extinction maxima which in other irdcs are typically associated with pre - stellar and protostellar cores with masses of order 100 @xmath10 ( e.g. , @xcite ) . if the formation of irdcs , perhaps due to the passage of a spiral shock , results in filaments , then these long , approximately cylindrical structures may produce the necessary conditions for the formation of dense molecular cores , and ultimately of clusters and high - mass stars . indeed , the theory of gravitationally bound gaseous cylinders predicts the formation of such dense cores , which due to the sausage "" or varicose "" fluid instability , fragment from the cylinder at roughly regular intervals ( e.g. , @xcite ) . this instability provides an attractive physical mechanism for high - mass star formation and cluster formation in filamentary irdcs . in this _ letter _ we report on molecular line mapping of the nessie nebula . we compare our results with the theory of self - gravitating fluid cylinders and show that the observations broadly conform to the expectations of the `` sausage '' instability . we speculate that this mechanism may be important in the formation of high - mass stars and star clusters . millimeter molecular line observations of the nessie nebula were taken on 2008 august with the australia telescope national facility ( atnf ) 22 m mopra telescope . the backend consisted of the wideband mops correlator configured to observe simultaneously 16 separate passbands covering the frequency range 86 to 93 ghz . each of these passbands was 137.5 mhz wide , with 4096 spectral channels , corresponding to a velocity resolution of 0.11 . we chose individual passbands to include molecular lines of interest . the brightest of the detected lines was ( 10)(90.66 ghz ) . although we detected a number of fainter molecular lines , these yield similar results and will be presented in a subsequent paper . the nebula was mapped in the `` on - the - fly '' mode , in which data are collected while the telescope scans in a raster pattern . the raster rows were chosen to be perpendicular to the galactic plane in order to avoid striping artifacts parallel to the nebula s long axis . the spacing between rows was 12 , or about 1/3 of the mopra beamwidth of 36 fwhm @xcite . flux calibration with a noise diode and an ambient temperature load was performed every 20 minutes . data reduction and analysis utilized the atnf livedata and gridzilla programs . the individual spectra were co - added and gridded onto a uniform 15 grid . linear baselines were removed from line - free channels . all spectra are presented on the antenna temperature ( @xmath11 ) scale . to convert to main - beam brightness temperatures , one should divide the antenna temperatures by the main - beam efficiency of 0.49 @xcite . system temperatures for the observations were @xmath12 k , which yielded a typical rms noise of @xmath13 k in each spectral channel . the mopra integrated intensity ( 10)maps closely correspond to the regions of mid - ir extinction ( figure [ figure1 ] ) . the map consists of fainter , uniform emission associated with the filament , upon which compact , brighter regions we call `` cores '' are superposed . gaussian fits to the ( 10)lines demonstrate that every position within nessie has essentially the same radial velocity , @xmath14 @xmath2 ( figure [ figure1 ] ) . if the clemens rotation curve is used , this velocity corresponds to a kinematic distance of 3.1 kpc @xcite . the molecular cores in nessie are often associated star - formation activity . specifically , many cores show the presence of excess 4.5 @xmath15 m emission called `` green fuzzies , '' which indicates shocked gas ( e.g. , @xcite ) , and bright 24 @xmath15 m point sources , which indicate an embedded protostar ( e.g. , @xcite ) . the cores do not appear to be randomly spaced within the filament , but instead have a characteristic spacing . the filament is thus reminiscent of a string with beads that are spaced sparsely but approximately uniformly along its length . we used the clumpfind2d algorithm with a threshold of seven times the rms noise and 2.5@xmath16 increments @xcite on the ( 10)integrated intensity map to identify 12 molecular cores ( see figure [ figure1 ] ) . the exact choice of clumpfind parameters will result in the identification of slightly more or fewer cores , but the resulting core spacing is quite insensitive to reasonable input parameters . since the cores are relatively isolated and well separated , clumpfind works well and identifies the cores that one would tend to select by eye . the positions and selected properties of the cores are listed in table [ coretable ] . columns 1 and 2 give the galactic coordinates of the position of peak integrated hnc intensity in each core , column 3 the peak hnc integrated intensity , columns 4 and 5 the angular size and physical extent , column 6 the lte mass ( see section [ discussion ] ) , and column 7 whether or not the core contains a 24 @xmath15 m point source . the mean projected spacing between cores is roughly 4.5 pc . although we prefer to use the molecular gas clumps as our indicator of core spacing , since we thereby include pre - stellar cores , another useful indicator of cluster - forming sites would be 24 @xmath15 m point sources , which indicate embedded high - mass stars or protostars . indeed , about half of the molecular cores contain 24 @xmath15 m point sources ( see table [ coretable ] ) . for all of the unresolved 24 @xmath15 m sources associated with the nebula , we find typical spacing of 4.1 pc , a value within 10% of the molecular core spacing . thus , both the spacing of gas clumps and of 24 @xmath15 m sources are in satisfactory agreement . the existence of cores that are spaced at approximately a characteristic spacing within a highly filamentary cloud is in broad agreement with the predictions of fragmentation of a self - gravitating fluid cylinder due to the sausage "" instability . the theory s original presentation by @xcite treated an incompressible fluid . later refinements included an isothermal , thermally supported cylinder with various magnetic field configurations @xcite . although the fragmentation due to the sausage "" instability of a self - gravitating fluid cylinder is similar to three - dimensional jeans collapse , there are important differences . in spherical gravitational jeans collapse , perturbations of all wavenumbers grow at the same rate , but in cylindrical gravitational collapse perturbations with certain wavenumbers grow more quickly than others . perturbations with the most unstable wavenumber will grow fastest , and hence overdensities ( cores ) will tend to form at a length scale whose wavenumber corresponds to this fastest growing mode . for a cylinder of infinite radius , this length scale is maintained even in the presence of a magnetic field parallel to the filament s axis @xcite . the theory thus predicts ( 1 ) that multiple cores should form within a filament , and ( 2 ) that the spacing between these cores should be roughly periodic , with a characteristic length scale equal to the wavelength of the fastest growing unstable mode of the fluid instability . for an incompressible fluid , this wavelength is @xmath17 where @xmath18 is the cylinder s radius @xcite . in an infinite isothermal gas cylinder , the relation is @xmath19 , where @xmath20 is the isothermal scale height given by @xmath21 , where @xmath22 is the sound speed , @xmath23 the gravitational constant , and @xmath24 the gas mass density at the center of the filament ( @xmath25 ) @xcite . for isothermal cylinders of finite radius @xmath18 surrounded by an external , uniform medium , the spacing depends on the ratio between the cylinder radius and the isothermal scale height , @xmath26 . for @xmath27 the core spacing approaches that for an infinite radius cylinder , @xmath19 , but for @xmath28 the spacing reduces to that of the incompressible case , @xmath17 . we now compare the observations of nessie to this theory under the assumption that nessie is well approximated by an isothermal cylinder . if nessie lies in the limit @xmath28 , the theory reduces to that of an incompressible fluid , and predicts cores spaced at a characteristic length scale @xmath29 . one can estimate the radius @xmath18 of nessie from the radial extent of the sharp extinction edges evident in the glimpse and mipsgal images . this suggests a radius of @xmath30 or @xmath31 pc at the kinematic distance of 3.1 kpc @xcite . thus , one would expect cores to form at a spacing of @xmath32 pc , in satisfactory agreement with the observations if the filament axis is mostly perpendicular to the line of sight . if nessie is treated as an isothermal gas cylinder with a central volume density @xmath33 @xmath34 and @xmath35 k , appropriate for cold , dense , molecular gas traced by ( 10)emission , then the isothermal scale height is @xmath36 pc . thus , nessie would be in the regime @xmath27 , and the theoretical spacing between cores should be @xmath37 pc . this is smaller than the observed spacing by about a factor of 5 . this discrepancy may arise from the fact that turbulent pressure dominates over" +"soon after the first experimental realization of graphene , a single - layer hexagonal form of carbon , the integral quantum hall effect ( iqhe)@xcite was observed by novoselov _ et al . _ and zhang _ _ et al.__@xcite at filling factors @xmath2 . the @xmath3 period is understood straightforwardly as a consequence of the four - fold ( near ) degeneracy of landau levels ( lls ) in graphene ; the zeeman energy is small in comparison to the interaction energy scale , and the pseudospin degree of freedom , which represents the two inequivalent dirac - cones at the corners of the brillouin zone , does not couple to external fields if the two sublattices are equivalent . the offset @xmath4 is a consequence of a dirac - like effective hamiltonian , which produces a linear dispersion for low energy electronic states @xcite . recently , zhang _ _ et al.__@xcite have observed quantum hall plateaus at @xmath5 . although external effects can surely lift the four - fold degeneracy of the low - lying lls , yang , das sarma and macdonald@xcite have shown that the exchange interaction can break the su(4 ) symmetry spontaneously , and the charged excitations are skyrmions @xcite in the @xmath6 landau levels at @xmath7 ( or , by particle - hole symmetry , at @xmath8 ) where @xmath9 is the filling factor within the landau level in question . this has been confirmed @xcite by exact diagonalization for @xmath10 with @xmath11 particles . although the fractional quantum hall effect@xcite ( fqhe ) has not yet been observed in graphene , it has been explored theoretically @xcite assuming an su(2 ) symmetry , as appropriate , for example , when the zeeman energy is sufficiently high that only the two - fold pseudospin degeneracy remains . in this situation , the graphene fqhe problem formally maps into the well studied problem of fqhe in gaas in the zero zeeman energy limit@xcite , with the pseudospin of the former playing the role of the spin of the latter . in the @xmath12 graphene ll , the interaction pseudopotentials@xcite are identical to those in gaas , so the mapping is perfect , and the earlier composite - fermion results of refs . carry over to graphene with minimal change ( spin replaced by pseudospin ) . in particular , it follows that fqhe occurs at fractional fillings given by @xmath13 , with pseudospin singlet states at even @xmath14 and pseudospin polarized states at odd @xmath14 ( fully pseudospin polarized for @xmath15 ) , terminating into a pseudospin singlet composite fermion fermi sea in the limit of @xmath16 ( @xmath17 ) . the effective interaction in the @xmath18 lls in graphene interpolates between those of the @xmath19th and @xmath20st lls for the quadratic dispersion ; the composite fermion formation@xcite , and therefore the fqhe , are found to be almost as strong in the @xmath21 ll in graphene as in the lowest ll of gaas @xcite . it is natural to wonder if fqhe with _ structure appears in graphene . for this purpose , we explore in this work fqhe including the full su(4 ) symmetry . by a combination of exact diagonalization and the cf theory , we find new fqhe states which result from an essential interplay between the spin and the pseudospin degrees of freedom ; such states occur at @xmath22 for @xmath1 . for other states , the energy spectrum of the su(4 ) problem matches with that of the su(2 ) problem , although the multiplicities are vastly different . we show by exact diagonalization that the su(4 ) symmetry is spontaneously broken at @xmath23 just as at @xmath7 , i.e. , the orbital part of the ground state is antisymmetric and the excitations are skyrmionic . at @xmath24 and @xmath25 , the orbital part of ground state is the same as in the su(2 ) symmetric system , but the state is now a highly degenerate su(4 ) multiplet . the outline of the paper is as follows . we review the methods in sec . [ methods ] . in sec . [ newstates ] we generalize the composite fermion theory to su(4 ) electrons , using fock s condition and constructing all possible wave functions of incompressible , filled @xmath26 level states of composite fermions . we also indicate which states have analogs in gaas and which do not . section [ onethird ] is concerned with exact diagonalization results for small systems , which are compared to the predictions of the cf theory . skyrmion - like excitations are also discussed . in sec . [ thermo ] we obtain thermodynamic energies using the cf theory to determine the thermodynamic ground states . section [ phasetrans ] discusses zero - temperature phase transitions and lists the cf predictions for the parameters where the new fqhe states should be observable . the paper is concluded in section [ conclu ] . the electronic structure of graphene is well described by a tight binding model@xcite , which gives a vaulted band structure with the valence and conductance bands touching in the symmetry protected dirac ( or fermi ) points at the six corners of the hexagonal brillouin zone . the low energy states , in particular , occupy double cones@xcite with apices at the corners . only two of these six double cones are inequivalent , giving rise to a pseudospin degree of freedom . denoting spin by @xmath27 and pseudospin by @xmath28 , the low energy states are described in the continuum approximation by an effective hamiltonian@xcite @xmath29 that acts on a 4-spinor hilbert space . here @xmath30 m / s is the fermi velocity , @xmath31 , @xmath32 is the on - site energy difference between the two sublattices , @xmath33 is the pseudospin operator , and @xmath27 is the spin . letting @xmath34 , measuring distance in units of the magnetic length @xmath35 , and using the symmetric gauge @xmath36 , this hamiltonian is diagonalized by the normalized eigenvectors @xmath37 where @xmath38 , @xmath39 , and @xmath40 is the eigenstate of the hamiltonian with quadratic dispersion in ll @xmath14 with angular momentum ( @xmath41 ) equal to @xmath42 : @xmath43 the corresponding energies are @xmath44 in the limit @xmath45 , the four vectors @xmath46 are degenerate , giving rise to an su(4 ) internal symmetry . the su(4 ) approximation is valid if @xmath47 and @xmath32 are small in comparison to the scale of the interactions , @xmath48 . while @xmath32 is not easy to estimate , it is generally believed to be much smaller than @xmath49 . one can check that @xmath50},\ ] ] where @xmath51 $ ] is the magnetic field in tesla . obviously , both @xmath52 and @xmath53 depend strongly on the interaction with environment in which the graphene sheet is placed . as two extremes , one can take @xmath54 and @xmath55 ( the graphite value ) . on the other hand , zhang _ et al . _ @xcite find @xmath56 . with these extreme values , assuming an extremely high field @xmath57 t , we get @xmath58 thus the su(4 ) symmetric approximation is typically valid unless @xmath52 happens to be close to the high end of the estimation . the interaction between eigenstates is conveniently described in terms of pseudopotentials@xcite , where the pseudopotential @xmath59 gives the energy of two electrons in relative angular momentum @xmath42 . as a consequence of eqs . ( [ lllpseudo ] ) and ( [ otherpseudo ] ) , the problem of interacting electrons in the @xmath14th ll of graphene can be mapped into a problem of interacting electrons in @xmath60 states with effective pseudopotentials@xcite @xmath61 where the form factor @xmath62 is @xmath63 the problem of interacting electrons is conveniently formulated in the spherical geometry , in which electrons move on the surface of a sphere and a radial magnetic field is produced by a magnetic monopole of strength @xmath64 at the center.@xcite here @xmath65 is the magnetic flux through the surface of the sphere ; @xmath66 , and @xmath67 is an integer according to dirac s quantization condition.@xcite for quadratic dispersion the single particle states are monopole harmonics@xcite @xmath68 , where @xmath69 is the angular momentum with @xmath70 being the ll index , @xmath71 is the @xmath72-component of angular momentum . the coulomb interaction is evaluated with the chord distance . the analogous solution for carriers with linear dispersion , described by the massless dirac s equation , is not known for the spherical geometry . we proceed to work in the basis of the monopole harmonics @xmath73 of the lowest ll , while using the effective pseudopotentials given in eq . ( [ effective ] ) . because we have @xmath74 , in the @xmath12 landau level the pseudopotentials derived by fano _ _ et al.__@xcite can be used . in other landau levels , however , we will use the effective pseudopotentials of the _ planar _ geometry ( eq . ( [ effective ] ) ) on the sphere . such an identification is obviously exact in the thermodynamic limit , but is usually reasonable also for finite systems . we neglect the finite thinkness of the two dimensional electron system , which is a much better approximation in graphene than in gaas heterostructures . the neglect of landau level mixing , also made below , is a more tricky assumption because both the ll separation ( c.f . ( [ landaulevels ] ) ) and the interaction energy scale as @xmath75 , and are of the same order . however , their relative strengths can be controlled by variation of other parameters ( fermi velocity , dielectric constant , etc . ) , and we will assume in the following that the ll separation is large enough to suppress ll mixing . we will compare the exact diagonalization results to the composite fermion theory @xcite , and also use this theory to explore the thermodynamic limit . ( exact diagonalization can be performed only for very small systems for su(4 ) symmetry . ) the composite fermion ( cf ) theory maps the strongly interacting system of electrons in a partially filled landau level to a system of weakly interacting particles called composite fermions , which are bound states of an electron and an even number of quantized vortices . the mapping consists of attaching @xmath76 quantized vortices of the many - body wave function to each electron . the quantized vortices produce berry phases that partly cancel the external magnetic field , and consequently composite fermions feel a reduced magnetic field @xmath77 . composite fermions in magnetic field @xmath78 fill quantized kinetic energy levels analogous to landau levels , called @xmath26 levels . if @xmath42 @xmath26 levels are filled , which corresponds to a filling factor @xmath79 , an incompressible quantum liquid state results . the fqhe is thus explained as the iqhe of composite fermions . according to the cf theory , the wave functions for correlated electrons in the lowest landau level at monopole strength @xmath64 are given by @xmath80 @xmath81 where @xmath82 is a wave function for @xmath83 non - interacting electrons at monopole strength @xmath84 , operator @xmath85 projects a state into the @xmath12 ll , and @xmath86 and @xmath87 . the procedure taking us from @xmath82 to @xmath88 is called composite - fermionization , "" which also converts electronic landau levels into @xmath26 levels of composite fermions . incompressible ground states are constructed by completely filling the lowest few @xmath26 levels in one or more spin bands . the explicit relation between the monopole strength @xmath64 , the filling factor @xmath89 and the particle number @xmath83 is given below in eq . ( [ mono ] ) . the above cf construction is valid for the orbital part of the wave function independent of whether the landau levels" +"central to a complete picture of galaxy evolution is the distribution of the interstellar matter ( ism ) within each galaxy and how that ism forms stars . given that the ism mass on galactic scales is dominated by molecular and atomic gas , observing the tracers of these gas components is necessary for measuring the ism distribution within the disks of spiral galaxies . accordingly , observations of the hi 21-cm line and the co @xmath9 2.6-mm line are often used as tracers of the atomic and molecular gas , respectively ( see , e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? while conversion of the velocity - integrated brightness temperature of the hi line , or @xmath10 , to atomic gas column density , @xmath11 , is usually straightforward ( though not always , e.g. , * ? ? ? * ) , the conversion of i(co ) to molecular gas column density @xmath12 is not quite so certain ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , especially given that the co @xmath9 line is known to be optically thick ( e.g. , see * ? ? ? * ; * ? ? ? * ; * ? ? ? recent observations @xcite suggest that the @xmath13 conversion factor , or x - factor , @xmath14 , is roughly constant within the disk of our galaxy , with @xmath15 , to be abbreviated as @xmath16 ; this or a similar value of @xmath14 is often called the `` standard '' value . this uniform x - factor value for our galaxy s disk now applies to the disks of external galaxies , where @xmath17 is inferred and , on average , is _ radially _ non - varying from the inner disk to a galactocentric radius of @xmath18 @xcite . the evidence for co - dark gas , both theoretically and observationally , is a further complication ( see , for example * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? it is thus advantageous to employ tracers other than co @xmath9 as independent checks on ism surface density variations to test recent physical models of @xmath14 ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) observed gas column and surface densities can then provide insights into large - scale star formation in galaxies . the schmidt - kennicutt ( s - k ) law , for example , states that star formation rate surface density , @xmath19 , is related to the gas surface density , @xmath20 , by @xmath21 with @xmath22 to @xmath23 ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? the index @xmath24 is appealing because the gas depletion time ( @xmath25 ) is constant thoughout the spiral disks . while there is some evidence that @xmath26 on size scales of @xmath27 ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , there is also evidence of non - linear and even non - universal slopes on such size scales ( see , e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , especially on the scales of individual giant molecular clouds ( gmcs ) @xcite . there is also strong evidence for an inside - out formation of galaxies ( e.g. * ? ? ? * ) , which is at odds with a constant gas depletion time and , therefore , with having @xmath28 . comparison between those results on the large ( i.e. , galactic ) scales with those on gmc scales is problematic . @xcite suggest that the schmidt law on the scales of gmcs are fundamentally different from the s - k law apparent on larger ( i.e. galactic ) scales ; the latter are not the `` result of an underlying physical law of star formation . '' many of the abovementioned results used observations of the optically thick co @xmath9 line and adopted a spatially constant @xmath14 . in contrast , millimetre ( mm ) , submillimetre ( submm ) , and far - infrared ( far - ir ) continuum observations sample optically thin continuum emission from the dust grains that pervade both the atomic and molecular gas . recently , there have been many papers of the far - ir / submm continuum emission of external galaxies from the _ planck _ and _ herschel _ missions ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? these papers find , for example , that the dust and stellar masses of galaxies are correlated @xcite and that spiral galaxies and dusty early type galaxies have @xmath29 to @xmath30 of dust @xcite . a major stumbling block to determining accurate surface densities from dust continuum emission is the unknown mass absorption coefficient , @xmath31 , at millimetre wavelengths . millimetre continuum emission is less temperature sensitive than that at submillimetre and far - ir wavelengths ; this provides an important constraint on dust mass and sometimes the spectral emissivity index , @xmath32 , can be constrained as well . observationally , the relevant quantity determined is the dust optical depth to gas column density ratio , @xmath33 . @xcite and @xcite have found that @xmath34 at 857@xmath0ghz ( wavelength of 350@xmath35 ) in the hi gas in the solar neighbourhood and @xmath36 at 250@xmath35 ( corresponding to @xmath37 at 857@xmath0ghz for @xmath38 ) in the hi gas in the taurus molecular complex . given that @xmath38 applies to the dust in our galaxy ( see , e.g. , * ? ? ? * ) and that the dust to _ hydrogen _ gas mass is about 0.01 , those observed @xmath33 correspond to @xmath39 to 0.5@xmath40 in the dust associated with hi . the dust associated with h@xmath41 , however , has @xmath33 double that in hi @xcite . consequently , estimating @xmath33 and @xmath31 from comparing the observed dust continuum emission against the hi gas emission alone , while useful , must be viewed with caution . the various estimates of @xmath31 suggest that determining the exact _ total _ mass of dust within a galaxy is uncertain by a factor of a few . in spite of the uncertain dust mass absorption coefficient , dust continuum emission can provide estimates of @xmath14 in our galaxy as well as in external galaxies ( see , e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? such observations have shown that while @xmath14 can be more or less spatially constant in some cases , like in the disk of our galaxy and other external galaxies ( see * ? ? ? * ; * ? ? ? * ) , there can be regions of `` dark '' gas , h@xmath41 with no co emission , both in our galaxy and other galaxies ( e.g. , see * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? therefore , observations of dust continuum emission provide a vital check on results inferred from co @xmath9 observations . even with the many recent advances mentioned above , there are many questions left unanswered . for example , do the inferred x - factor values ( i.e. * ? ? ? * ; * ? ? ? * ) apply to the outer disks of all galaxies ? also , are there systematic differences of the x - factor between arm and inter - arm regions ? can previous methods of observationally inferring the dust mass absorption coefficient at millimetre wavelengths be refined ? how do the answers to those questions influence the specific form of the observed s - k law in a given galaxy ? to address these questions and to better understand the gas and dust in spiral galaxies and their relationship to star formation , we observed the grand - design , face - on spiral galaxies m@xmath051 and m@xmath083with the bolometer - array camera , _ aztec _ ( aztronomical thermal emission camera ) , mounted on the 15-m jcmt in hawaii at a wavelength of 1.1@xmath0 mm . both of these galaxies are nearby with distances of less than 10@xmath0mpc ( see table [ tab1 ] for details ) and , hence , the spiral arms in both galaxies are resolved across the arms in the _ jcmt / aztec _ observations , which have a spatial resolution of 20@xmath42 . both galaxies have been studied extensively at numerous wavelengths ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? recent _ herschel _ observations of m@xmath051 and m@xmath083 at 70 , 160 , 250 , 350 , and 500@xmath35 have provided maps of the dust temperature , surface density , and even spectral emissivity index , @xmath32 @xcite , but with spatial coverage that is slightly more limited than those of the _ aztec _ 1.1@xmath0 mm continuum maps presented here ; the _ aztec _ images cover a few more kiloparsecs at the adopted distances given in table [ tab1 ] . as a result , these _ aztec _ 1.1@xmath0 mm continuum images extend both the spatial and the wavelength coverage of the dust emission in both m@xmath051 and m@xmath083 . this greater spatial coverage placed restrictions on the other wavelengths available for comparison with the _ aztec _ 1.1@xmath0 mm data ; there were no 250 , 350 , and 500@xmath35 data towards the outer disks of m@xmath051 and m@xmath083 . there are , however , _ spitzer _ 160@xmath35 data covering both of these galaxies . this wavelength is the longest of the _ spitzer _ data and , along with the _ aztec _ 1.1@xmath0 mm data , is the one most likely" +"general relativity and ordinary differential geometry should be replaced by non - commutative geometry at some point between the currently accessible energies of about 1 - 10 tev ( after starting the large hadron collider ( lhc ) at cern ) and the planck scale , which is @xmath2 times higher , where space - time and gravity should be quantized . this could occur either at the planck scale or below . quantum field theory on a non - commutative space - time ( ncqf ) could very well be an intermediate theory relevant for physics at energies between the lhc and the planck scale . it certainly looks intermediate in structure between ordinary quantum field theory on commutative @xmath3 and string theory , the current leading candidate for a more fundamental theory including quantized gravity . ncqft in fact appears as an effective model for certain limits of string theory @xcite . in joint work with r. gurau , j. magnen and f. vignes - tourneret @xcite , using direct space methods , we provided recently a new proof that the grosse - wulkenhaar scalar @xmath4 theory on the moyal space @xmath5 is renormalisable to all orders in perturbation theory . the grosse - wulkenhaar breakthrough @xcite was to realize that the right propagator in non - commutative field theory is not the ordinary commutative propagator , but has to be modified to obey langmann - szabo duality @xcite . grosse and wulkenhaar were able to compute the corresponding propagator in the so called `` matrix base '' which transforms the moyal product into a matrix product . this is a real _ tour de force _ ! they use this representation to prove perturbative renormalisability of the theory up to some estimates which were finally proven in @xcite . our direct space method builds upon the previous works of filk and chepelev - roiban @xcite . these works however remained inconclusive @xcite , since these authors used the right interaction but not the right propagator , hence the problem of ultraviolet / infrared mixing prevented them from obtaining a finite renormalised perturbation series . we also extend the grosse - wulkenhaar results to more general models with covariant derivatives in a fixed magnetic field @xcite . our proof relies on a multiscale analysis analogous to @xcite but in direct space . non - commutative field theories ( for a general review see @xcite ) deserve a thorough and systematic investigation , not only because they may be relevant for physics beyond the standard model , but also ( although this is often less emphasized ) because they can describe effective physics in our ordinary standard world but with non - local interactions . in this case there is an interesting reversal of the initial grosse - wulkenhaar problematic . in the @xmath4 theory on the moyal space @xmath5 , the vertex is sort of god - given by the moyal structure , and it is ls invariant . the challenge was to overcome uv / ir mixing and to find the right propagator which makes the theory renormalisable . this propagator turned out to have ls duality . the harmonic potential introduced by grosse and wulkenhaar can be interpreted as a piece of covariant derivatives in a constant magnetic field . now to explain the ( fractional ) quantum hall effect , which is a bulk effect whose understanding requires electron interactions , we can almost invert this logic . the propagator is known since it corresponds to non - relativistic electrons in two dimensions in a constant magnetic field . it has ls duality . but the interaction is unclear , and can not be local since at strong magnetic field the spins should align with the magnetic field , hence by pauli principle local interactions among electrons in the first landau level should vanish . we can argue that among all possible non - local interactions , a few renormalisation group steps should select the only ones which form a renormalisable theory with the corresponding propagator . in the commutative case ( i.e. zero magnetic field ) local interactions such as those of the hubbard model are just renormalisable in any dimension because of the extended nature of the fermi - surface singularity . since the non - commutative electron propagator ( i.e. in non zero magnetic field ) looks very similar to the grosse - wulkenhaar propagator ( it is in fact a generalization of the langmann - szabo - zarembo propagator ) we can conjecture that the renormalisable interaction corresponding to this propagator should be given by a moyal product . that s why we hope that non - commutative field theory is the correct framework for a microscopic _ ab initio _ understanding of the fractional quantum hall effect which is currently lacking . even for regular commutative field theory such as non - abelian gauge theory , the strong coupling or non - perturbative regimes may be studied fruitfully through their non - commutative ( i.e. non local ) counterparts . this point of view is forcefully suggested in @xcite , where a mapping is proposed between ordinary and non - commutative gauge fields which do not preserve the gauge groups but preserve the gauge equivalent classes . we can at least remark that the effective physics of confinement should be governed by a non - local interaction , as is the case in effective strings or bags models . in other words we propose to base physics upon the renormalisability principle , more than any other axiom . renormalisability means genericity ; only renormalisable interactions survive a few rg steps , hence only them should be used to describe generic effective physics of any kind . the search for renormalisabilty could be the powerful principle on which to orient ourselves in the jungle of all possible non - local interactions . renormalisability has also attracted considerable interest in the recent years as a pure mathematical structure . the work of kreimer and connes @xcite recasts the recursive bphz forest formula of perturbative renormalisation in a nice hopf algebra structure . the renormalisation group ambiguity reminds mathematicians of the galois group ambiguity for roots of algebraic equations . finding new renormalisable theories may therefore be important for the future of pure mathematics as well as for physics . that was forcefully argued during the luminy workshop `` renormalisation and galois theory '' . main open conjectures in pure mathematics such as the riemann hypothesis @xcite or the jacobian conjecture @xcite may benefit from the quantum field theory and renormalisation group approach . considering that most of the connes - kreimer works uses dimensional regularization and the minimal dimensional renormalisation scheme , it is interesting to develop the parametric representation which generalize schwinger s parametric representation of feynman amplitudes to the non commutative context . it involves hyperbolic generalizations of the ordinary topological polynomials , which mathematicians call kirchoff polynomials , and physicist call symanzik polynomials in the quantum field theory context @xcite . we plan also to work out the corresponding regularization and minimal dimensional renormalisation scheme and to recast it in a hopf algebra structure . the corresponding structures seem richer than in ordinary field theory since they involve ribbon graphs and invariants which contain information about the genus of the surface on which these graphs live . a critical goal to enlarge the class of renormalisable non - commutative field theories and to attack the quantum hall effect problem is to extend the results of grosse - wulkenhaar to fermionic theories . the simplest theory , the two - dimensional gross - neveu model can be shown renormalisable to all orders in their langmann - szabo covariant versions , using either the matrix basis @xcite or the direct space version developed here @xcite . however the @xmath6-space version seems the most promising for a complete non - perturbative construction , using pauli s principle to controll the apparent ( fake ) divergences of perturbation theory . in the case of @xmath7 , recall that although the commutative version is until now fatally flawed due to the famous landau ghost , there is hope that the non - commutative field theory treated at the perturbative level in this paper may also exist at the constructive level . indeed a non trivial fixed point of the renormalization group develops at high energy , where the grosse - wulkenhaar parameter @xmath8 tends to 1 , so that langmann - szabo duality become exact , and the beta function vanishes . this scenario has been checked explicitly to all orders of perturbation theory @xcite . this was done using the matrix version of the theory ; again an @xmath6-space version of renormalisation might be better for a future rigorous non - perturbative investigation of this fixed point and a full constructive version of the model . finally let us conclude this short introduction by reminding that a very important and difficult goal is to also extend the grosse - wulkenhaar breakthrough to gauge theories . one considers free electrons : @xmath9 where @xmath10 is the canonical conjugate of @xmath11 . the moment and position @xmath12 and @xmath13 have commutators @xmath14=0,\ \ [ r_i , r_j]=0,\ \ [ p_i , r_j]=\imath\hbar\delta_{ij } .\end{aligned}\ ] ] the moments @xmath15 have commutators @xmath16=-\imath\hbar\epsilon_{ij}eb,\ \ [ r_i , r_j]=0,\ \ [ \pi_i , r_j]=\imath\hbar\delta_{ij } .\end{aligned}\ ] ] one can also introduce coordinates @xmath17 , @xmath18 corresponding to the centers of the classical trajectories @xmath19 which _ do not commute _ : @xmath20=\imath\hbar\epsilon_{ij}\frac{1}{e b}},\ \ [ \pi_i , r_j]=0 . \end{aligned}\ ] ] this means that there exist heisenberg - like relations between quantum positions . one considers the string action in a generalized background @xmath21 where @xmath22 is the string worldsheet , @xmath23 is a tangential derivative along the worldsheet boundary @xmath24 and @xmath25 is an antisymmetric background tensor . the equations of motion determine the boundary conditions : @xmath26 boundary conditions for coordinates can be neumann ( @xmath27 ) or dirichlet ( @xmath28 , corresponding to branes ) . after conformal mapping of the string worldsheet onto the upper half - plane , the string propagator in background field is @xmath29 \ ; .\end{aligned}\ ] ] for some constant symmetric and antisymmetric tensors @xmath30 and @xmath31 . evaluated at boundary points on the worldsheet , this propagator is @xmath32 where the @xmath31 term simply comes from the discontinuity of the logarithm across its cut . interpreting @xmath33 as time , one finds @xmath34= i \theta^{\mu \nu } , \end{aligned}\ ] ] which means that string coordinates lie in a non - commutative moyal space with parameter @xmath31 . there is an equivalent argument inspired by @xmath35 theory : a rotation sandwiched between two @xmath36 dualities generates the same constant commutator for string coordinates . the recent progresses concerning the renormalisation of non - commutative field theory have been obtained on a very simple non - commutative space namely the moyal space . from the point of view of quantum field theory , it is certainly the most studied space . let us start with its precise definition . let us define @xmath37 and @xmath38 the free algebra generated by @xmath39 . let @xmath40 a @xmath41 non - degenerate skew - symmetric matrix ( wich requires @xmath42 even ) and @xmath43 the ideal of @xmath38 generated by the elements @xmath44 . the moyal algebra @xmath45 is the quotient @xmath46 . each element in @xmath45 is a formal power series in the @xmath47 s for which the relation @xmath48 holds . usually , one puts the matrix @xmath40 into its canonical form : @xmath49 sometimes one even set @xmath50 . the preceeding algebraic definition whereas short and precise may be too abstract to perform real computations . one then needs a more analytical definition . a representation of the algebra @xmath45 is given by some set of" +"the interior of cells is both highly structured and dynamical . active transport therefore plays a crucial role to target molecules to the various compartments of the cell as well as to maintain and reorganize the cell s structure . these tasks are accomplished by the cytoskeleton , a network of protein fibers , and the cytoskeletal motors , proteins which use the filaments of the cytoskeleton as highways or rails for directed transport . cytoskeletal motors are enzymes which catalyze the hydrolysis of adenosinetriphosphate ( atp ) and , at the same time , use the free energy released from this reaction to perform mechanical work and convert it into directed movements . these motor molecules have been studied extensively during the last decade , both experimentally and theoretically . the main emphasis has been on the properties of single motor molecules , their motor mechanisms , and their directed walks along filaments @xcite . the nanometer size and piconewton forces of the molecular motors imply that the typical binding energies are of the order of the thermal energy @xmath0 and that the motor filament binding can be overcome by thermal fluctuations . on large time and length scales ( @xmath1s and @xmath2 m ) , motors perform peculiar random walks , where periods of directed active movements along filaments alternate with periods of non - directed brownian motion in the surrounding fluid after unbinding from a filament @xcite . ( a related problem is the effective diffusion of an adsorbed particle along a surface via bulk excursions @xcite . ) in order to study these random walks , we have recently introduced a class of lattice models , which are , on the one hand generic in the sense that they are independent of the specific motor mechanisms , but which we can , on the other hand , also apply to describe specific motor molecules by adapting the model parameters to the observed transport properties @xcite . in addition , we can easily incorporate motor motor interactions such as the mutual exclusion from binding sites of the filaments , which leads to traffic jam-like density pattern and various kinds of phase transitions @xcite in the following , we will review our results for the motor s random walks obtained from these lattice models and present some new results from the corresponding continuum equations . the article is organized as follows : we introduce the lattice models in section [ sec : model ] . in section [ sec:2d3d ] , we summarize our analytical results for the random walks on a lattice without confining walls . compartments with confining walls which are experimentally accessible are studied in section [ sec : finitegeoms ] , where we summarize our numerical results and present new analytical results from a continuum description of the random walks . we have studied the random walks arising from many encounters with filaments by mapping them to random walks on a lattice @xcite . a line of lattice sites represents a filament . motors at these sites perform a biased random walk and move predominantly in one direction . per unit time , they make a forward step , a backward step and no step with probability @xmath3 , @xmath4 , and @xmath5 , respectively , where @xmath6 is the spatial dimension . with a small probability @xmath7 , they move to each of the adjacent non - filament sites and thus unbind from the filament . at the non - filament sites the motors perform simple symmetric random walks and move to each neighbor site with probability @xmath8 ( @xmath9 denotes the spatial dimension ) and rebind to the filament with probability @xmath10 when they reach again a filament site . confining walls are implemented as repulsive boundaries , at which all movements into the walls are rejected . consider a discrete time random walk on a two dimensional square lattice with lattice sites labeled by integer coordinates @xmath11 with the above transition probabilities . the master equation for this dynamics reads @xcite @xmath12 as initial condition we take an ensemble of particles at @xmath13 . note that , for simplicity , we have chosen the sticking probability @xmath14 . the fourier laplace transforms of the probability distribution along the filament @xmath15 and of the full distribution @xmath16 are defined as @xmath17 the master equations is reduced to an algebraic equation @xmath18p_{{\rm b}}(r , s ) } { s+1-\half\cos q-\half\cos r}. \end{aligned}\ ] ] where @xmath19 is the average speed on the line . by integrating this result over @xmath20 we also obtain @xmath21 on the left hand side . it thus satisfies a linear equation , that is easily solved . we end up with the distribution @xmath22^{-1 } \label{sold=2 } \end{aligned}\ ] ] for the motors bound to the filament , where @xmath23 . the distribution for the unbound motors follows from eq . ( [ p2= ] ) . _ survival fraction . _ we extract the transport properties of the motor s random walk from ( [ sold=2 ] ) . the value at @xmath24 gives the laplace transform @xmath25 of the probability @xmath26 that the motor is bound to the filament : @xmath27^{-1}\ ] ] for small times this implies @xmath28 which is a power series in @xmath29 . for @xmath30 , this is somewhat surprising : although the motors detach at times @xmath31 , the recurrent behavior of the random walk brings them mostly back to the filament , with half - integer powers in @xmath32 due to diffusion . for times @xmath33 we find @xmath34/ { \sqrt{\pi\,\epsilon^2\,t}}$ ] . the @xmath35 decay expresses that finally all motors unbind , and agrees with scaling arguments @xcite . _ average position and speed on the filament line . _ the expression ( [ sold=2 ] ) for @xmath21 contains much more information . at linear order in @xmath36 we may derive the average position of motor particles along the filament line , @xmath37 . we obtain for short times @xmath38 $ ] . the average position of the motors bound to the filament is given by @xmath39 and their average speed is @xmath40 , where @xmath41 is the average speed if the particles did not leave the line . for large times one gets @xmath42/{\epsilon } $ ] and @xmath43 , confirming the scaling @xmath44 @xcite . the effective motor velocity is reduced by a factor @xmath45 , i.e. , by the probability that a motor is in the bound state . the relation @xmath46 also applies to a simple two - state random walk , where motion is directed in one of the states only . in contrast to the simple two - state random walk , however , the probability @xmath47 is time - dependent . _ dispersion and diffusion coefficient on the filament line . _ from the second moment @xmath48 we may define the normalized second moment @xmath49 , the dispersion @xmath50 and the diffusion coefficient , @xmath51 . the results for the latter read at short @xmath32 @xmath52 and for large @xmath32 @xmath53 the limiting value of the diffusion coefficient , @xmath54 is large compared to the diffusion coefficient of the one - dimensional random walk along the filament , @xmath55 . this broadening of the distribution occurs since the unbound motors lag behind the bound ones , which implies that also the rebinding motors lag behind those that have been bound for some time . _ the density profile on the filament _ can be evaluated analytically for large @xmath56 and @xmath32 , @xmath57 the exponential decay for @xmath58 expresses the large probability of unbinding for @xmath59 . comparison with the results of monte carlo simulations shows very good agreement for times larger than about 8000 time steps @xcite . eventually every motor will unbind and diffuse in the surrounding fluid we now discuss the effects of the filament on the behavior of the unbound motors . _ position and longitudinal diffusion . _ one finds for the average velocity of unbound motors at small times @xmath60 and at large times @xmath61 $ ] . whereas each individual motor has zero average velocity in the fluid , the statistical velocity @xmath62 is non - zero , since it is driven by unbinding from the cloud of motors moving on the filament . the longitudinal diffusion coefficient behaves at large times as @xmath63+{1}/{4}$ ] . the order of magnitude @xmath64 tells us that , like on the line , longitudinal diffusion is strongly enhanced by the unbinding from and binding back to the line . the perpendicular diffusion coefficient is modified much less , @xmath65 at short times , while at large times @xmath66 . so the transverse diffusion starts out very small , and finally reaches its free space value . _ the spatio - temporal density profile of the unbound motors _ can also be derived , @xmath67 the presence of multiple tracks on microtubules can be modeled by internal states , which keeps the problem solvable @xcite . the same setup can be studied in @xmath68 @xcite . the fourier - laplace transformed density on the filament now reads @xmath69 \,i(r , s)}.\ ] ] with @xmath70 and @xmath71 and involving the complete elliptic integral @xmath72^{-1}$ ] . the main difference is now that the density of motors on the filament decays faster , as @xmath73 , because of a reduced return probability . lack of space prevents us to discuss this any further , but we will present some results from continuum equations for the three - dimensional case below . we have also studied these random walks in compartments with simple geometries which are accessible to _ in vitro _ experiments @xcite . in these geometries , a filament is immobilized to a surface , and the diffusion of unbound motors is restricted by confining walls . in the simplest case , the unbound motors can diffuse freely in the half space above the surface to which the filament is immobilized . by placing the filament in a quasi two - dimensional slab or in a rectangular or cylindrical tube , diffusion can be restricted along one or two dimensions perpendicular to the filament . we denote the linear extensions of the compartments by @xmath74 . scaling arguments and simulations show that , at large times with @xmath75 , when the motors experience the presence of the confining walls , these systems exhibit the same scaling behavior as systems with the same dimensionality , but without confining walls . for compartments with unconfined diffusion in @xmath76 dimensions perpendicular to the filament , the effective velocity is given by @xmath77 with @xmath78 . the continuum equations for the random walks of the motors can be solved in a similar way to the master equations of the lattice models . since boundary conditions are easily implemented in the continuum model , we use them to derive analytical solutions for the half space , slab and tube geometry , see also ref . we denote the coordinate parallel to the filament by @xmath79 and the coordinates perpendicular to it by @xmath80 . the continuum equations are given by @xmath81 \label{diff_gl1_3d}\\ \frac{\partial p}{\partial t } & = & -v_{{\rm b}}\frac{\partial p}{\partial x } + d_{{\rm b}}\frac{\partial^2 p}{\partial x^2}-\tilde\epsilon p + { \tilde\pi_{\rm ad}}p_0,\label{diff_gl2_3d}\end{aligned}\ ] ] with the bound - state velocity and diffusion coefficient @xmath82 and @xmath83 , the unbound diffusion coefficient @xmath84 , @xmath85 , @xmath86 , and @xmath87 . _ full three - dimensional space . _ let us start with the full three - dimensional space . we use the fourier laplace transformed form of eqs . ( [ diff_gl1_3d ] ) and ( [ diff_gl2_3d ] ) , @xmath88 with the momentum @xmath89 and with the same initial conditions as before . this leads to @xmath90 to obtain a convergent integral , we introduce a cutoff @xmath91 as" +"this paper is based on a talk given at a conference in naples @xcite . it is well known that if backward time travel could be implemented , or if the present could shape the past by some other means , then closed causal chains , or causal loops , could be formed . the possibility of causal loops must arise because changing , or rewriting , the past is not particularly meaningful . if these loops are not self consistent , paradoxes arise @xcite . the best known of these is the grandfather paradox : a man travels into the past to kill his grandfather before his grandfather meets his grandmother . if he succeeds then we have the paradox that the man is never born , thus the grandfather is not killed , thus the man is born and so on . a simpler and more direct example is autoinfanticide , whereby a man travels into the past and shoots himself as a baby . a different example is where a man travels back and introduces his parents to each other @xcite . here we have a paradox if he fails in his task . a more direct version of this latter type of paradox involves a robot , let us say , which enters a time machine in the present . when it emerges from the machine in the past it is sent through a rejuvenator which removes its memory and programs it to walk around until it enters the time machine in the present . a paradox occurs if something prevents the robot from entering the time machine in the present . sometimes the possibility of such paradoxes is taken as an argument against the possibility of backward time travel . it can , however , be argued that , because of continuity in nature , self - consistent loops or cycles in these situations always exist and it is only these cycles that nature allows @xcite . somehow the physics sorts things out so that the probability of inconsistent cycles is zero . we shall refer to this argument as the principle of self consistency @xcite . an example of a self - consistent solution to the autoinfanticide cycle is the scenario in which the man raises his rifle to shoot himself as a baby but , because of his bad shoulder , misses the baby s heart and hits it in the shoulder @xcite . if we accept that self - consistent loops are reasonable , the question arises as to the mechanism by which physics disallows inconsistent loops and ensures self consistency . in this paper we show that quantum mechanics may provide an answer to this question . quantum mechanics is essentially concerned with the preparation of a system and its subsequent measurement . the measurement device can be described mathematically by a probability operator measure ( pom ) @xcite . each element @xmath0 of the pom corresponds to a possible outcome event _ j _ of the measurement . all the pom elements are non - negative definite , that is , their expectation values for any state of the system are greater than or equal to zero . the pom elements sum to the unit operator , ensuring that the probability that there is some outcome of the measurement is unity . the pom elements themselves indicate the states the system can be `` found in '' . the preparation device can be described mathematically by a collection of preparation device operators ( pdo ) @xmath1 associated with possible preparation outcomes @xcite . these non - negative definite operators indicate the possible states the system can be `` prepared in '' . the _ a priori _ probability @xmath2 for a preparation event _ i _ is given by the trace tr@xmath1 . the trace of the sum of all the @xmath1 is unity , ensuring that the probability that there is some outcome of the preparation is unity . an essential feature of quantum mechanics , as opposed to classical mechanics , is that , even if there is no evolution of the system between the preparation and measurement events , the state the system is found in is not necessarily the state the system is prepared in . the usual formalism of quantum mechanics is predictive . between preparation and measurement we assign to the system a state on the basis of our knowledge of the preparation event . if we have no knowledge of the outcome of the preparation , the best we can do is to assign a density operator immediately after preparation equal to the sum of the pdo s . if , however , we know the outcome was the preparation event _ i _ , we assign the normalized density operator @xmath3 @xmath4tr@xmath1 immediately after preparation . this state evolves unitarily forward in time to become @xmath5 at the time of measurement . @xmath6 is the usual forward time unitary evolution operator . upon measurement there is a discontinuous change , or collapse , of the state to that corresponding to the pom element associated with the particular measurement outcome _ j_. the probability for the measurement outcome _ j , _ given the preparation outcome _ i , _ is given by @xmath7 . \label{e1}\ ] ] as the name indicates , the predictive formalism is particularly useful for predicting outcomes of measurement events based on knowledge of preparation events . we can use the formalism , in conjunction with bayes theorem , to retrodict outcomes of preparation events given measurement events@xcite . from bayes theorem we have @xmath8 when the known outcome _ i _ of the preparation device corresponds to a pure state @xmath9 , both @xmath1 and @xmath4tr@xmath1 are just @xmath10 . also when the known outcome _ j _ of the measurement device corresponds to a pure state @xmath11 both @xmath0 and @xmath12tr@xmath0 are just @xmath13 . it is simpler in such cases to work with the associated pure states instead of the pdo s and pom elements . expression ( [ e1 ] ) then becomes simply @xmath14 . an interesting situation arises when we have prepared two systems _ a _ and _ b _ in an entangled pure state , which evolves to , say , @xmath15 at the time of the measurement of system _ b _ , which is measured before system _ a_. if the measurement outcome is the pom element corresponding to state @xmath16 , then , in the predictive formalism , the measurement projects this state onto the entangled state , giving the state @xmath17 after normalization . this collapsed state continues to evolve forwards in time until system _ a _ is measured . a less usual , but equally valid , quantum mechanical formalism is the retrodictive formalism @xcite . here the state of a system between preparation and measurement is assigned on the basis of our knowledge of the _ measurement _ event . if we know the outcome was the measurement event _ j _ , we assign the normalized density operator @xmath18tr@xmath0 to the system immediately before measurement @xcite . this state evolves unitarily _ backwards _ in time to become @xmath19 at the time of preparation . upon preparation there is a discontinuous change , or collapse , of the state to that corresponding to the pdo associated with the particular preparation outcome _ i_. the probability for the preparation outcome _ i _ given the measurement outcome _ j _ is given by @xmath20}. \label{e4}\ ] ] the denominator ensures the probabilities for all possible preparation events sum to unity . it is not difficult to show , using the cyclic property of the trace , that this is the same as the formula for @xmath21 in ( [ e2 ] ) obtained from the predictive formalism plus bayes theorem . use of the retrodictive formalism for this purpose is more direct , however , which is why it is becoming useful for solving the basic quantum communication problem @xcite , in which bob measures the state of a quantum system sent by alice and has to retrodict the state she selected to send . our interest now , however , is the application of the retrodictive formalism to entangled systems . suppose the result of a measurement on two systems _ a _ and _ b _ corresponds to the pom element associated with the pure _ retrodictive _ entangled state which evolves backwards in time to @xmath15 at the time of the preparation of system _ b _ , which is prepared after system _ a _ is prepared . if the preparation outcome is the pdo corresponding to state @xmath22 , then we project this state onto the entangled state , renormalize , and obtain the state @xmath23 this collapsed retrodictive state continues to evolve backwards in time until the time of the preparation of system _ an even more interesting case arises when a retrodictive state from a measurement of system _ c _ at time @xmath24 evolves backwards to a state @xmath25 at the time @xmath26 of a preparation outcome that corresponds to the entangled state @xmath27 the projection of @xmath28 onto this state collapses it to @xmath29 , which can be associated with a predictive state evolving forwards in time from @xmath26 . a method of making predictive entangled states is to prepare the light in the input modes _ b _ and _ c _ of a beam splitter in the vacuum and one - photon states with preparation devices p0 and p1 respectively . we can then write the predictive input state as @xmath30 . to be specific , let the beam splitter , as shown in fig . 1(a ) , be symmetric and reflect as much light as it transmits . the action of the beam splitter can be represented by a unitary operator @xmath31 . it is possible to show that for this 50/50 beam splitter , the action of the beam splitter on the input state is to transform it to the entangled state @xcite @xmath32 in the output of the beam splitter . this shows that there is an equal chance for the photon to remain in mode _ c _ , that is to be transmitted , and for it to be reflected into mode _ b_. it is sometimes convenient to regard p0 , p1 and the beam splitter as a combined preparation device that generates the predictive state @xmath33 if the outcomes of p0 and p1 correspond to zero and one photons . this entangled state then propagates forward in time . if , at a later time @xmath24 , a measurement on the field in mode _ c _ shows that the photon is in mode _ c _ then , according to the usual description of the measurement process in the predictive formalism , the field instantaneously collapses at @xmath24 to @xmath34 after normalization . that is , the field in mode _ b _ changes suddenly to the vacuum simultaneously with the measurement of the field in mode _ c , _ even though this measurement event can take place an appreciable distance away . this , of course , is just an illustration of the well - known einstein - podolsky - rosen paradox involving instantaneous collapse over a large distance . the vacuum state @xmath35 , being a predictive state , continues to propagate forwards in time . and @xmath36 . in ( b ) photodetectors d1 and d0 detect one and zero photons in output modes @xmath37 and @xmath38.,scaledwidth=60.0% ] an entangled _ retrodictive _ state can be made as follows . photon detectors d1 and d0 are in the output ports _ b _ and _ a _ of a 50/50 beam splitter as shown in fig . if d1" +"in mesoscopic systems , the measurement of current and noise makes it possible to probe the effective charges which flow in conductors , and opens the possibility for studying the role of the statistics in stationary quantum transport experiments . this has been illustrated experimentally and theoretically in both cases where the interaction between electrons is less important@xcite or when it is more relevant@xcite . the present work deals with the study of photo - assisted shot noise in a specific one dimensional correlated system : a hall bar in the fractional hall regime , for which charge transport occurs via two counter - propagating chiral edges states . over the years , the attention has been focusing also on the transport properties of systems on which an external harmonic perturbation is acting . a fundamental step is first to study the current response . for instance , it is possible to generate a dc current by applying voltage gates on which an ac perturbation is acting @xcite . here we consider the superposition of a dc bias with a time dependent perturbation . for normal and superconducting systems , it has been shown@xcite that the photo - assisted shot noise allows to retrieve information on the finite frequency noise , which was computed for ballistic systems@xcite , and measured in diffusive metallic wires @xcite . such finite frequency measurements turn out to be challenging in practice . on the other hand , if an experiment is devoted to zero frequency noise , information on the finite frequency noise spectrum can be retrieved provided that the system has an added , external , finite frequency perturbation . in particular , the presence of a small , additional harmonic perturbation modifies the phase of the charge carriers ( reflection / transmission probabilities are affected to a lesser extent ) , and in some sense it acts as a probe to study the finite frequency noise spectrum of the conductor . note that the external modulation can either be imposed on a gate voltage , located in the vicinity of the conductor , which controls the transparency of the barrier . this corresponds to the gedanken experiment for the traversal time in tunneling@xcite and to the early proposals for photo - assisted shot noise@xcite . at the same time , the transport properties of an irradiated point contact@xcite have also been studied with this point of view . alternatively , the modulation can be imposed from the leads to which the system is connected , which may be simpler to achieve in experiments , because no additional gating is required . for non - interacting electrons , it has been shown@xcite that the derivative of the current noise with respect to the bias exhibits evenly spaced steps whose height is specified by bessel functions . this result which was derived using scattering theory has been generalized to diffusive metallic wires using known random matrix theory results and has been tested experimentally for normal diffusive metals@xcite and recently for ballistic samples in a point contact geometry@xcite . one then enquires whether electronic correlations will play an important role on the photo - assisted shot noise characteristics . in multichannel conductors described by a scattering theory , transport properties ( current and noise ) have been analyzed while taking into account screening in a self - consistent treatment@xcite . for a normal metal superconducting junction biased in the andreev regime , the correlations in the superconductor are responsible for a doubling of the electron charge in the shot noise @xcite . the noise derivative with respect to bias voltage then exhibits steps whose spacing contains the charge of a cooper pair , as confirmed by recent experiments@xcite . nevertheless , one can argue that ns systems are not so far from free electron systems , as these can be modeled by a scattering theory in which electrons are converted in hole and vice versa@xcite . another possible ground for studying the effect of interactions is to consider a one dimensional correlated electron system a luttinger liquid . reduced dimensionality is known to affect drastically the current - voltage characteristics @xcite . the finite frequency current response of a one dimensional wire has been discussed in ref . , while the effect of a localized time dependent perturbation on the conductance of a non - chiral luttinger liquid was addressed recently in ref . . the noise spectrum of a hall bar in the fractional hall regime was presented in ref . . here we choose the same model as the latter , mainly a simple fractional quantum hall fluid consisting of two edge states with a point contact . the potential difference between the two edges has both a dc and an ac component . the time average current flowing in this system has been discussed using a semi - classical approach in ref . . here , we concentrate on the shot noise in both the weak and strong backscattering regimes . it is expected that the step like behavior of non interacting electrons will be strongly modified when the electron filling factor @xmath2 deviates from @xmath3 . it is also expected that in the weak backscattering regime , the fractional charge @xmath4 probed by dc shot noise experiments@xcite should appear explicitly : the spacing between singularities in the shot noise should be given by the josephson frequency @xmath5 , where @xmath6 is the dc bias voltage . yet this remains to be shown in a first principles calculation . the paper is organized as follows . the model hamiltonian is presented in the next section , and the weak backscattering limit is considered in sec . 3 . results for the strong backscattering limit are collected in sec . 5 deals with the results using the refermionization procedure at filling factor @xmath1 . consider first a fractional quantum hall bar . the right and left moving chiral excitations are described by the hamiltonian @xcite : @xmath7 with @xmath8 for right and left movers . we adopt the simple , intuitive picture where depending on the strength of the impurity , either quasiparticles tunnel through the ( single ) quantum hall fluid , or the impurity is so strong that the fluid is split into two , and only electrons can tunnel from one fluid to the other@xcite . this picture has been sucessful in explaining the main features of transport in both regimes for the quantum hall bar@xcite . in the case of a weak impurity , the backscattering of quasiparticles is described by the tunneling hamitonian : @xmath9^{(\varepsilon)}~ , \label{tunneling_hamiltonian}\end{aligned}\ ] ] where the notation @xmath10 specifies the operator ( @xmath11 ) or its hermitian ( complex ) conjugate ( @xmath12 ) as in ref . . let @xmath13 be the bare tunneling amplitude , and @xmath14 be the total ( dc and ac ) potential drop at the junction . here , one has the choice of either including this voltage in the properties of the fractional edges , or to take this voltage into account using a gauge transformation . indeed , one can choose a gauge where the electric field at the junction is fully specified by a _ potential only . this procedure is called the peierls substitution . the quasiparticle field operator then acquires a phase which is tied to the gauge transformation function @xmath15 . the corresponding hopping amplitude thus becomes : @xmath16 note that the charge which appears in the phase factor is the fractional charge @xmath4 corresponding to edge state quasiparticles . this choice is justified in the weak backscattering regime , where quasiparticles tunnel through the quantum hall fluid . in addition , from the dc and ac voltage amplitudes , it is convenient to introduce new frequencies which include this anomalous charge : @xmath17 with this choice , the phase factor of the tunneling amplitude reads @xmath18 . in eq . ( [ tunneling_hamiltonian ] ) , @xmath19 is the quasiparticle field associated to the left ( @xmath20 ) or right ( @xmath21 ) movers . it can be expressed in term of the bosonic chiral field @xmath22 : @xmath23 where @xmath24 is the klein factor , which does not play any role in this lowest order calculation ( because @xmath25 ) , and @xmath26 is the short distance cutoff . 7 cm the backscattering current can be calculated using @xmath27 . the calculation method of the current follows closely that of refs . . for the voltage modulation , this means that the current operator reads : @xmath28^{(\varepsilon)}~,\end{aligned}\ ] ] for simplicity we set @xmath29 . using the keldysh formulation of non equilibrium transport , the average current is expressed as a time ordered contour : @xmath30 where @xmath31 is the keldysh index and the notation @xmath32 refers to the keldysh contour . expanding to lowest order in @xmath13 and taking into account quasiparticle conservation , the bosonized expressions for the quasiparticle fields are employed , together with the definition of the chiral green s function @xcite : @xmath33 and the backscattering current associated with an ( arbitrary ) time dependent perturbation becomes : @xmath34 assume now that the bias voltage is modulated by a harmonic perturbation . using the generating function of the bessel function as in ref . , @xmath35=\sum_{n=-\infty}^{+\infty}j_n(\omega_1/\omega)e^{in\omega t}$ ] , which is a signature of most photo - assisted processes , the tunnel amplitude is cast into an infinite sum : @xmath36 which gives : @xmath37 the change of variables @xmath38 with @xmath39 has been operated . note that only @xmath40 terms in eq . ( [ etaeta1 ] ) contribute to the first integral because of the symmetry properties of the green s function . on the contrary , only @xmath41 terms contribute to the second integral because such an integral does not depend on @xmath31 . using the expression for the green s function eq.([green ] ) , the current can thus be split into two contributions , with integrants containing either a sine or a cosine of @xmath42 . the time integral can be performed analytically and is expressed in terms of the gamma function @xmath43 ( see appendix [ appendixa ] ) . grouping the two contributions , we obtain : @xmath44 the fourier transform of the current , @xmath45 , yields : @xmath46 to zero order in the amplitude @xmath47 of the modulation , we recover the i - v characteristics of the pure stationary regime ( @xmath48 ) : @xmath49 expanding the current to first order with @xmath47 corresponds to @xmath50 and @xmath51 or to @xmath52 and @xmath53 : @xmath54~.\end{aligned}\ ] ] in the limit @xmath55 , eqs . ( [ ordre1 ] ) and ( [ ordre2 ] ) lead , at zero and first orders with @xmath47 , to the backscattering current : @xmath56 finally , one can analyze which dc contribution is provided by the ac modulation : the rectification property . this information is contained in the zero - frequency fourier transform : @xmath57 which is obtained to all orders in the modulation . also note that it can be re - expressed in terms of the dc current : @xmath58 a general relation which was noticed in ref . . first , note that the result of eq . ( [ real_time_current ] ) seems to blow up at @xmath1 . in this situation , the absolute value in the last term of this equation becomes independent of @xmath59 and the term proportional to @xmath60 vanishes at @xmath1 . consider now the case of arbitrary @xmath2 . for the present result to be valid , one should be consistent with the assumption of weak backscattering , and the differential conductance should thus be much smaller than the conductance quantum @xmath61 associated with the unperturbed fractional edge : @xmath62 first , consider the limit of a weak ac perturbation @xmath63 . in this case ," +"since davis & peebles ( 1983 ) first analyzed the anisotropy in the galaxy distribution from center for astrophysics ( cfa ) redshift catalog , it has been recognized that the peculiar velocity field of galaxies induces a significant systematic effect in statistics of observed galaxy distributions in redshift space . in particular , virialized random motion of galaxies produces an elongated pattern of galaxy distribution along the line of sight , called _ finger - of - god_. this effect significantly suppresses the amplitude of the two - point correlation function of galaxies in redshift space , especially on scales below @xmath0mpc . the proper account of this redshift - space distortion requires a detailed model for the pairwise velocity distribution function ( hereafter , pvdf ) of galaxies . davis & peebles ( 1983 ) discovered that the pvdf of the cfa galaxy sample is approximately described by an exponential distribution , instead of a gaussian : @xmath1 where @xmath2 is the separation length and @xmath3 denote the pairwise peculiar velocity between a pair of galaxy along the line - of - sight direction . the quantity @xmath4 is the peculiar velocity dispersion ( pvd ) . the exponential form of pvdf was confirmed also later by analyses of @xmath5-body simulations of dark matter particles and of other samples of galaxies ( e.g. , efstathiou et al . 1988 , fisher et al . 1994 , marzke et al . 1995 ) . theoretical models for the origin of the exponential pvdf of dark matter were put forward by sheth ( 1996 ) and diaferio & geller ( 1996 ) , and more recently by sheth & diaferio ( 2001 ) . they phenomenologically introduced a nonlinear model of pvdf using the press schechter formalism . to be more specific , they assume that any dark matter particle belongs to one of virialized clumps ( dark halos ) with the 1-point velocity distribution function being a maxwellian form . if one considers sufficiently small scales , the particle pairs of those separations are likely to be in the same halo , and then their pvdf is approximately given by @xmath6 where @xmath7 is the mass function of dark halos , @xmath8 is the pvdf of dark matter particles within a halo of mass @xmath9 . the quantity @xmath10 represents the statistical weight proportional to the number of particle pairs with separation @xmath2 in the halo : @xmath11 where @xmath12 is the density profile of the halo of mass @xmath9 , and @xmath13 is the dirac delta function . adopting the singular isothermal distribution as a particular choice of the dark halo profile , sheth ( 1996 ) showed that the scale - free model of @xmath14 with @xmath15 exactly reproduces the exponential pvdf ( [ eq : exp ] ) . while a perturbation theory ( seto & yokoyama 1998 ; juszkiewicz et al . 1998 ) also qualitatively explained why the gaussian initial models approach the exponential pvdf , the above model is much more successful quantitatively . further , a significant influence of the finger - of - got effect appears at small scale , where the perturbative approach can not be applied . therefore in the present paper , we attempt to improve the sheth ( 1996 ) model ( [ eq : shethp ] ) for the pvdf in several aspects ; first , we consider more popular cdm models instead of the scale - free power - spectra . second , we adopt a series of more realistic density profiles for dark halos ( hernquist 1990 ; navarro , frenk & white 1997 ; fukushige & makino 1997 , 2001a ; moore et al . 1998 ; jing & suto 2000 ) . third , we derive the one - point pvdf of dark matter particles in a halo directly from the abel integral of the above density profiles , instead of assuming the maxwellian form _ a priori_. this approach is important since we can incorporate the scale- and mass - dependence of the pvd in a consistent fashion unlike the previous modeling . finally we also apply the selection function following jing , brner & suto ( 2002 ) so as to phenomenologically attempt to predict the pvd of _ galaxies _ out of that of dark matter particles . this paper is organized as follows ; section 2 describes our improved modeling for the pvdf on the basis of the dark matter halo approach . in 3 , we present the resultant pvd in various cosmological models and discuss how the underlying halo profiles are sensitive to those results . we also provide a simple fitting formula of the pvd in the currently popular spatially - flat cdm model , which is useful in modeling the redshift - distortion effect . then we attempt to consider the effect of the spatial biasing of galaxies relative to the dark matter particles on the pvd by applying a phenomenological biasing scheme . finally section 4 is devoted to summary and conclusions . our present method to compute the pvdf is schematically shown in figure [ fig : pvdf_procedure ] . we will describe the details of the procedure below . throughout the paper , we consider the three representative cdm models parameterized by the density parameter @xmath16 , the dimensionless cosmological parameter @xmath17 , the amplitude of the mass fluctuation smoothed over the top - hat radius of @xmath18mpc , @xmath19 , and the hubble constant in units of 100 km / s / mpc @xmath20 ; standard cdm ( @xmath21 ; scdm ) , lambda cdm ( @xmath22 ; lcdm ) , and open cdm ( @xmath23 ; ocdm ) . those models are normalized to satisfy the x - ray cluster abundances ( kitayama & suto 1997 ) . ( 160mm,100mm)pvdf_procedure.eps the density profile of dark matter halos plays a key role in our method . following the recent suggestions from high - resolution numerical simulations , we adopt the following specific form : @xmath24 in the above , @xmath9 is the mass of the halo , @xmath25 is the mean density of the universe at @xmath26 , @xmath27 is the present critical density , @xmath28 is the characteristic density excess , and @xmath29 and @xmath30 indicate the virial radius and the scale radius of the halo , respectively . the virial radius is defined according to the spherical collapse model as @xmath31 we use the following expressions ( kitayama & suto 1996 ) for the critical over - density @xmath32 : @xmath33 where @xmath34 and @xmath35 are respectively given as @xmath36 and @xmath37 , in terms of the density parameter at the collapse time , @xmath38 . in practice , we focus on three specific profiles . ( i ) the original nfw profile with @xmath39 and @xmath40 ( navarro et al . 1997 ) , ( ii ) the modified nfw profile with @xmath41 indicated by higher - resolution simulations ( fukushige & makino 1997 , 2001a , b ; moore et al . 1998 ; jing & suto 2000 ) , ( iii ) the hernquist profile with @xmath39 and @xmath42 ( hernquist 1990 ) for which the analytic expression of the phase - space distribution function is known . the two parameters @xmath43 and @xmath44 are not independent , and are related in terms of the concentration parameter : @xmath45 the condition that the total mass inside @xmath44 is equal to @xmath9 relates @xmath46 to @xmath47 . therefore the halo mass - dependence of the above profiles is entirely specified by @xmath48 . in the case of the original nfw profile , we use the approximate fitting function from the simulation data of bullock et al . ( 2001 ) : @xmath49 for the other profiles , we first compute the amplitude of the two - point correlation functions of dark matter following the procedure of seljak ( 2000 ) and ma & fry ( 2000 ) , and then find the amplitude of the concentration parameter which reproduces the peacock dodds ( 1996 ) fitting formula . this calibration yield @xmath50 for the modified nfw profile ( oguri et al . 2001 ) , and @xmath51 for the hernquist profile , which we adopt throughout the analysis below . our next task is to compute the phase - space distribution function in a single halo from the given density profile ( [ eq : univ ] ) . while sheth ( 1996 ) and sheth et al . ( 2001 ) simply adopt the gaussian velocity distribution function , we eliminate this assumption and derive the velocity distribution function in a fully consistent manner . for this purpose , we make use of the jeans theorem which states that for a spherically symmetric and stationary system , the solution of the collisionless boltzmann equation can be expressed as a function of the specific binding energy , @xmath52 , alone . here we define @xmath53 as the minus of the gravitational potential satisfying the boundary condition of @xmath54 . one may wonder whether halos in hierarchical universes that should experience repeated merger and destruction continually are well approximated as stationary . nevertheless natarajan , hjorth & van kampen ( 1997 ) and hanyu & habe ( 2001 ) found that the phase - space distribution function directly estimated from their particle simulations agrees well with that derived from the jeans theorem . thus the above assumption is justified , at least empirically . then the phase - space distribution function @xmath55 in a single halo is directly computed from its given density profile @xmath12 as follows ( e.g. , binney & tremaine 1987 ) : @xmath56 figure [ fig : fe ] plots the dimensionless phase - space distribution function @xmath57 evaluated numerically from equation ( [ eq : abel ] ) , where @xmath58 is the characteristic mass of the halo and @xmath59 is the dimensionless specific energy . the hernquist model has an analytical solution for @xmath55 which is reproduced by our numerical result almost within an accuracy of 2% except for the tiny region @xmath60 , where the error reaches at 7% but the effect is safely negligible for later analysis . since the three halo profiles that we adopt have a central cusp , @xmath61 diverges at a corresponding value of @xmath62 . the modified nfw profile has @xmath61 which extends more broadly up to @xmath63 reflecting the stronger central concentration than that of the original nfw case . ( 80mm,80mm)fe.eps once the phase - space distribution function is given , one can also compute one - dimensional single - particle velocity distribution function along a particular direction by integrating over the other two components . assuming the isotropic velocity distribution , one has @xmath64 where we project along the direction of @xmath65 and the quantity @xmath66 is the corresponding binding energy . figure [ fig : f1v ] shows the dimensionless velocity distribution function @xmath67 at @xmath68 ( _ thin lines _ ) and @xmath69 ( _ thick lines _ ) , where @xmath70 is the scaling velocity . the figure indicates that the one - dimensional velocity distribution function in a halo can be reasonably approximated by the gaussian : @xmath71 although it has a sharp cutoff around the escape velocity of the halo , @xmath72 . in figure [ fig : f1v ] , the dashed lines indicate the gaussian - fit which has the same velocity dispersion evaluated from equation ( [ eq : f1 ] ) . it seems that the empirical gaussian approximation can reasonably reproduce the pvdf , and thus we use the approximation in the numerical integrations below so as to reduce the computational time . figure [ fig : svd ] plots the velocity dispersion @xmath73 computed from the best - fit gaussian , which clearly shows the scale - dependence that was" +"in the early days of general relativity there was a common belief that the universe had to be eternal and unchanging . following this concept , albert einstein introduced the first cosmological model , subsequently named after him . it consisted of a compact spatial hypersurface with positive curvature , the @xmath0-sphere @xmath1 , which did not change under the flow of time . in order to overcome the attraction force of matter and obtain a static configuration , a new term had to be introduced in the field equations the famous cosmological constant . although numerous observations have since excluded this kind of static models in favor of expanding ones , the einstein universe is still a very important explicit solution of the einstein equations , partly because of the conformal equivalence between ( a region of ) this model and minkowski s spacetime ( the standard background for quantum field theories ) . for example , since maxwell s equations are conformally invariant , one can think of any configuration of electromagnetic fields in the einstein universe as a configuration in flat spacetime . + the einstein universe is a particular case of , and conformal to , the closed friedmann - lematre - robertson - walker ( flrw ) models , where the assumption of staticity is relaxed by introducing a scale factor that allows the universe to expand or contract . using this relation , one can extend solutions of maxwell s equations in the einstein universe to the closed flrw models . in general , when one allows the spatial volume to change in time , the energy of the electromagnetic configuration will also change according to an appropriate power of the scale factor . + the common denominator of the models described above is the @xmath0-sphere @xmath1 . this manifold is an important example of a non - trivial fibre bundle , given by the hopf fibration , whose base is the usual @xmath2-sphere @xmath3 , and whose fibres are circles @xmath4 ( the clifford parallels ) . it is natural to look for solutions of the maxwell equations whose electric and magnetic fields , as measured by the static observers , are aligned with these fibres . such ansatz will be used in the first section to find a remarkable solution of maxwell s equations in the einstein universe , which will then be interpreted as a knotted , finite energy , radiating electromagnetic field in minkowski s spacetime . the extension of this solution to closed flrw models will be carried out in the second section . finally , the matter distribution that must be added to obtain a self - consistent solution of the einstein - maxwell equations will be determined in the third section . + we follow the conventions of @xcite ; in particular , we use the einstein summation convention and a system of units in which @xmath5 . we are interested in finding solutions of the maxwell equations in the cylinder @xmath6 with the standard lorentzian metric . this manifold represents a static universe with positive cosmological constant @xmath7 , called the einstein universe . by choosing the radius of this universe as our unit length we can assume , without any loss of generality , that @xmath8 is the product of @xmath9 by the unit sphere . + since @xmath10 is a lie group , so is @xmath8 . we can introduce the following left - invariant orthonormal tetrad of one - forms on this manifold : take @xmath11 to be the standard element of the holonomic basis on the cylinder , defining the cross section foliation . on each leaf , an orthonormal triad @xmath12 is chosen in such a way that being subscript or superscript . ] @xmath13 thus reproducing the @xmath14 lie algebra structure . in terms of the dual orthonormal vector tetrad , the choice of @xmath15 and relation ( [ eq : mcr ] ) can be written as @xmath16 = 2 \varepsilon_{ijk } x_k.\ ] ] we look for a solution of the maxwell equations in vacuum , @xmath17 with the faraday two - form @xmath18 written in this basis , they are @xmath19 the simplest nontrivial solution can be obtained from the assumption that the components @xmath20 and @xmath21 of the electric and magnetic fields @xmath22 and @xmath23 measured by the stationary observers depend only on time . using that ansatz , we arrive at the relations @xmath24 a solution of system ( [ eq : maxtime ] ) will include trigonometric functions with different initial phases and field strength factors . we choose the simplest one for the conformal analysis , @xmath25 because the results will not change qualitatively under more general assumptions . + recall that minkowski s spacetime is conformal to an open region of the einstein universe @xcite . more precisely , the minkowski metric @xmath26 can be written as @xmath27 where @xmath28 are the standard hyperspherical coordinates on the 3-sphere . in these coordinates , minkowski s spacetime corresponds to the region @xmath29 ( fig . [ fig : figure3 ] ) . since maxwell s equations are conformally invariant , we can interpret as an electromagnetic field in flat spacetime . the energy will of course change under the conformal transformation . its value will be given by the integral expression @xmath30 where @xmath31 is the energy - momentum tensor of @xmath32 , @xmath33 is @xmath34 normalized by the minkowski metric @xmath26 , and @xmath35 is the spacelike hypersurface corresponding to the hyperspherical cap @xmath36 of constant @xmath37 ( fig . [ fig : figure3 ] ) . note that @xmath35 is not a cauchy surface for minkowski s spacetime unless @xmath38 , as it approaches @xmath39 for @xmath40 and @xmath41 for @xmath42 . using @xmath43 and @xmath44 , we can reexpress the energy as an integral over the hyperspherical cap @xmath36 , @xmath45 it is straightforward to see that this quantity is finite . moreover , it is a decreasing function of the parameter @xmath42 , which indicates that the solution under consideration describes radiation fields . this can be seen by looking at the time dependence of the energy ( fig . [ fig : figure1 ] . ) , given , for @xmath42 , by the formula @xmath46 + the electromagnetic field is related to the simplest initial conditions given by raada in ( * ? ? ? * section 2 ) ( see also @xcite ) , where only the initial magnetic field is nonzero . in fact , the phase - shifted solution ( with @xmath47 ) @xmath48 is the cauchy development of initial conditions of that type . due to the fact that it is aligned along the clifford parallels , the hopf index @xmath49 is equal to one in our case . this fact can be confirmed using an integral expression for this quantity , namely @xmath50 where @xmath51 . in this section we turn our attention to the expanding models . consider a metric of the form @xmath52 where @xmath53 is the standard metric of @xmath1 with unit radius ; this corresponds to a closed flrw model , widely used in modern cosmology @xcite . + in analogy with the previous case , we introduce the tetrad @xmath54 , @xmath55 and the dual vector basis @xmath56 . + we are looking for a solution of the maxwell equations similar to , namely with a faraday tensor of the form @xmath57 where @xmath58 and @xmath59 depend only on time . substituting into the vacuum maxwell equations , , we have @xmath60 yielding @xmath61 the einstein universe case corresponds to @xmath62 . note that the @xmath63 component of the electromagnetic stress - energy tensor is @xmath64 indicating that the energy density of the solution is decaying with the fourth power of the radius of the universe . the solutions of maxwell s equations discussed in the last sections were derived under the assumption of a fixed background metric , satisfying the einstein field equations @xmath65 where @xmath66 is the einstein tensor , @xmath67 is the metric and @xmath68 is the total stress - energy tensor . one can ask what kind of matter has to be present for this configuration to be self - consistent . in order to answer this question , we consider the decomposition of the full stress - energy tensor into the parts coming from the electromagnetic field and matter , @xmath69 we already used the expression for the time - time component of @xmath70 when computing the energy of the solution ( [ eq : maxsol ] ) ; the full expression for this tensor is given by ( [ eq : setef ] ) . it is straightforward to see that it has diagonal form for any solution of the system ( [ eq : maxsoltime ] ) , @xmath71 , where in general @xmath72 . let us start from the assumption that matter can be described by a density @xmath73 and a principal pressure @xmath74 aligned with @xmath75 , @xmath76 a possible interpretation of this anisotropic pressure can be given by superimposing the stress - energy tensors of two pressureless fluids with the same mass density @xmath77 , moving in opposite directions along @xmath75 , with the same velocity with respect to the fundamental observers : @xmath78 another possible interpretation can be given by considering cosmic strings aligned with the clifford parallels , expanding and contracting with space while preserving the structure of the hopf fibration . because the metric in this model is similar to that of the closed flrw universe , we end up with a system analogous to the friedmann equations with the additional terms from electromagnetic stress - energy tensor , @xmath79 as it turns out , we can deal with system ( [ eq : freq ] ) using a similar procedure as in the standard case @xcite . the first equation is equivalent to @xmath80 after taking a time derivative of both sides and using the third equation from ( [ eq : freq ] ) , we find @xmath81 where @xmath82 is another integration constant . we can use now the second equation from ( [ eq : freq ] ) to obtain the pressure @xmath74 as @xmath83 note that the matter satisfies the weak , strong and dominant energy conditions if @xmath84 , as in this case @xmath85 . nevertheless , @xmath86 always approaches @xmath87 as @xmath88 tends to zero , indicating that the matter particles approach the speed of light near the big bang or the big crunch . in the limit case @xmath89 we have @xmath90 , meaning that the particles are actually moving at the speed of light . + the behavior of the scale factor @xmath88 can be derived from an effective potential formulation . using ( [ eq : fried1 ] ) and ( [ eq : friedrho ] ) we have @xmath91 we can think about each term as a kinetic part , an effective potential @xmath92 , and a conserved energy @xmath93 , respectively , @xmath94 the potential is a function of @xmath88 , but also depends on the three parameters @xmath7 , @xmath82 and @xmath95 . clearly we need a positive cosmological constant to have an ( unstable ) equilibrium point , so that we can reproduce the previous results concerning the einstein universe . in this case , @xmath92 will have the shape depicted on fig . [ fig : figure2 ] . depending on the values of the parameters , we can have expanding solutions , recollapsing solutions , de sitter - like bouncing solutions , and of course the unstable static solution and its asymptotes . note that in units for which the radius of the static solution is @xmath96 , we have @xmath97 ( hence we must have @xmath98 ) . finally , we note that except in the case" +"shape memory alloys [ sma ] are materials having many applications and attracting a lot of interest due to their unique properties of shape memory and pseudoelasticity , which stem from both temperature - induced and stress - induced martensitic phase transition . the mechanical behaviour of such materials is rather complex and arises from a strong interaction between thermal and mechanical phenomena . in fact , when these materials undergo the martensitic phase transition , the increase in temperature due to localised self - heating / self - cooling has been experimentally found to be anything but negligible @xcite . hence , the effects of heat transfer and of the heat dissipation towards the ambient are of primary relevance in the study of these materials @xcite and play a role in the rate - dependent behaviour of sma @xcite . in modelling the mechanical behaviour of a sma it is therefore important to account for mechanical and thermal aspects at the same time and to evaluate all the phenomena in their time evolution . in literature there exist many constitutive models for sma @xcite , which are derived following different approaches . some authors propose models developed within plasticity frameworks , which make use of one or even more internal variables to describe the pseudo - elastic behaviour @xcite . another group of constitutive models has been developed within a thermomechanic context ; in his work , tanaka @xcite proposed a macroscale model comprising an internal variable to quantify the extent of the phase transition , a dissipation potential and an assumed transformation kinetic . similarly , other models based on the same thermodynamic background but featuring different kinetic laws have been formulated @xcite , and a complete heat equation which accounts for the contribution of latent heat and of the dissipation connected with the phase transition was added to the framework @xcite . among others , chang et al . @xcite proposed a model comprising a strain - gradient elastic free energy and a chemical ( transitional ) free energy ; abeyaratne et al . @xcite developed a model including a non - convex helmholtz free energy function of the strain in order to describe the regions of stability of the different phases . in the context of using a non - convex free energy , it is not uncommon that micro - mechanical models are proposed @xcite ; muller and seelecke @xcite developed a microscale model based on statistical physics comprising a bulk free energy function of the lattice shear deformation . another approach to the description of the behaviour of sma consists in applying the ginzburg - landau theory for phase transitions . at a microscopic scale , falk @xcite developed a landau theory based on a shear strain order parameter . levitas and preston @xcite proposed a single - grain model based on the decomposition of the strain in an elastic and a transformational part , the latter being described by a pure order parameter which can assume different values to identify the different phases . in a similar fashion , wang and khachaturyan @xcite proposed a model in which the strain field depends on several order parameters , whose evolution is described by several time - dependent ginzburg - landau [ tdgl ] equations . nevertheless , attempts to handle the problem at a larger scale of observation have been made as well . among others , ahluwalia et al . @xcite and chen and yang @xcite proposed meso - scale models for the description of polycrystalline materials in which the order parameters account for the different orientations of each single grain ; in the same spirit , brocca et al . @xcite proposed a microplane model attempting to bridge the gap between micromechanics - based and macroscale models . berti et al . @xcite proposed a ginzburg - landau model which can be applied at the macroscale and encompasses mechanical as well as thermal effects by introducing the balance of linear momentum equation and the heat equation in a thermodynamically consistent framework ; the order parameter is related to the extent of the phase transition between austenite and the martensite variants and its evolution is regulated by a tdgl equation . owing to the presence of the heat equation , it is possible to describe the thermo - mechanical interactions which strongly influence the constitutive behaviour of a sma and to account for non - isothermal conditions . the model is presented both in a three - dimensional and a monodimensional setting ; the reduction to this latter case is still meaningful because in most engineering applications sma wires are employed . in this paper , we present a numerical study on the thermomechanical behaviour of a sma , with a particular focus on the rate - dependent response and on the influence of thermal conduction and heat transfer in the mechanical behaviour . starting from the models proposed in berti et al . @xcite and daghia et al . @xcite , we formulate a new free energy functional and give a proper expression for the relaxation parameter regulating the tdgl equation ; this gives the model the properties required to reproduce the symmetrical behaviour between the austenite - to - martensite and the martensite - to - austenite phase transitions observed experimentally . the ability of the model to quantitatively reproduce a variety of experimental evidences of a typical polycrystalline niti alloy is then demonstrated . the paper is organised as follows . in section [ sect : model ] , the theoretical model is described , starting from a suitable ginzburg - landau free energy whose properties are outlined in section [ sect : gl - pot ] . constitutive relations are given in section [ sect : constit ] , while the thermodynamic consistency of the model is shown in section [ sect : consistency ] and the complete differential system with appropriate boundary and initial conditions is provided in section [ sect : equations ] . in section [ sect : galerkin ] the galerkin formulation of the differential problem , suitable for the finite element implementation , is sketched . section [ sect : num - tests ] is the main part of the paper , where the numerical results of a number of simulated tensile tests on a bar specimen under different conditions are reported . after describing , in section [ sect : baseline ] , the effectiveness of the model in recovering the main experimental evidences in terms of stress - strain response , phase morphology and temperature evolution , in section [ sect : temp - test ] tensile tests performed at different values of the initial temperature are illustrated , while in section [ sect : max - def ] the stress - strain response under partial - loading conditions is depicted . the rate - dependent behaviour of the model is investigated in section [ sect : strain - rate ] , with a particular focus on the effects of the strain - rate on the domain nucleation , the hysteresis cycle and the energy dissipation . the influence of heat transfer phenomena on the mechanical response of the specimen is examined in section [ sect : environment ] . the last two aspects are considered jointly in section [ sect : env - rate ] . the paper ends drawing some conclusions in section [ sect : concl ] . the thermomechanical properties of sma stem from the nature of the martensitic phase transition ; here we will account for it by means of a ginzburg - landau approach @xcite . to this end we have to define a phase field , or order parameter , @xmath0 ; differently from the approach followed , among others , by falk @xcite , the order parameter is not identified with the uniaxial strain @xmath1 , but rather the phase field @xmath0 is used here as a macroscopic indicator of the phase ( martensite or austenite ) of the material at every point @xcite . strain is an independent field , though it is coupled with the order parameter . we assume that the martensite phase be present in only two relevant variants , @xmath2 , characterised by opposite uniaxial transformation strains with respect to the austenite phase [ a ] , namely @xmath3 , where @xmath4 is a fixed direction . the ginzburg - landau potential , whose properties will be described in detail in section [ sect : gl - pot ] , is expressly formulated to have ( at most ) three stable values of @xmath0 at values @xmath5 , corresponding to phases @xmath6 , respectively . we remark that , as a consequence of the _ first order _ character of the martensitic phase transition , intermediate values of @xmath0 do not represent any physically stable phase , but only transition layers between different stable or metastable physical phases . the model has to encompass evolution equations for the three basic fields : the order parameter ( @xmath0 ) , the strain ( @xmath7 ) and the temperature ( @xmath8 ) . the evolution of the phase field will be described by the tdgl equation @xmath9 the strain will be determined through the combination of the balance of linear momentum equation and a proper constitutive relation between strain , stress and order parameter , while the heat equation regulating the temperature evolution will arise from the balance of energy equation . for the formulation of the model , we consider a bar sample of sma occupying a bidimensional material domain @xmath10 . we indicate with @xmath11 the material coordinates and with @xmath12 the displacement vector field . relying on the small displacement approximation , we use the linearised strain tensor @xmath13 $ ] . following berti et al . @xcite , we assume a ginzburg - landau free energy in the form @xmath14},\end{aligned}\ ] ] where the temperature function @xmath15 is given by @xmath16 being @xmath17 the specific heat , @xmath18 a reference temperature for the specific heat , @xmath19 the compliance modulus , @xmath20 the stress tensor , @xmath21 the interface energy parameter regulating the interface width , and @xmath22 , @xmath23 , @xmath24 , @xmath25 material parameters related to the phase transition whose physical meaning will be explained in the following . the two potentials @xmath26 and @xmath27 are defined by @xmath28 } + \frac{1}{8 } { \left [ { 1 - \cos { \left ( { 2 \pi { \varphi } } \right ) } } \right]},\\ g({\varphi } ) & = & 1 - \cos { \left ( { \pi { \varphi } } \right)}.\end{aligned}\ ] ] [ cols=""^,^ "" , ] the stress - strain diagrams referring to the tests performed at different strain rates for the values of the heat transfer coefficient @xmath29 and @xmath30 are reported in figs . [ fig : stress - strain - rate - h5 ] and [ fig : stress - strain - rate - h20 ] , respectively , together with the maximum number of martensite nuclei originated during the loading stage . the behaviour is the same described in section [ sect : strain - rate ] for the case @xmath31 . a ginzburg - landau model that reproduces the most relevant macroscopic features of the behaviour of a shape memory alloy has been considered . the model encompasses a time - dependent ginzburg - landau equation for the evolution of the phase order parameter , the balance of linear momentum and the heat equation , in order to account for the interplay between the transitional , mechanical and thermal aspects which strongly influences the behaviour of sma . starting from the theoretical model described in berti et al . @xcite , a new free energy based on trigonometric functions has been formulated and a suitable form of the relaxation parameter of the tdgl equation has" +"we study surfaces in space @xmath0 such that through each point of the surface one can draw two circles fully contained in the surface . hereafter by a _ circle _ we mean either an ordinary circle in @xmath0 or a straight line . in this paper we reduce finding all such surfaces to the algebraic problem of finding all pythagorean @xmath1-tuples of polynomials . in a subsequent publication we are going to solve the latter problem . the problem of finding such surfaces traces back to the works of darboux from xixth century . basic examples a one - sheeted hyperboloid and a nonrotational ellipsoid are discussed in hilbert cohn - vossen s `` anschauliche geometrie '' . there ( and respectively , in a recent paper @xcite by nilov and the first author ) it is also proved that a smooth surface containing two lines ( respectively , a line and a circle ) through each point is a quadric or a plane . a torus contains @xmath2 circles through each point : a meridian , a parallel , and two villarceau circles . [ cols=""^ "" , ] all these examples are particular cases of a _ darboux cyclide _ , i.e. , a subset of @xmath0 given by the equation @xmath3 where @xmath4 and @xmath5 $ ] of degree @xmath6 do not vanish simultaneously ; see figure [ movie ] to the left . equivalently , a _ darboux cyclide _ is the stereographic projection of the intersection of the sphere @xmath7 with another @xmath8-dimensional quadric ( * ? ? ? * section 2.2 ) . almost each darboux cyclide contains at least @xmath9 circles through each point ( and there is an effective algorithm to count their actual number @xcite ) . conversely , darboux has shown that @xmath10 circles through each point guarantee that an analytic surface is a darboux cyclide . this result has been improved over the years : in fact already @xmath8 , or @xmath9 orthogonal , or @xmath9 cospheric circles are sufficient for the same conclusion ( * ? ? ? * theorem 3 ) , ( * ? ? ? * theorem 1 ) , ( * ? ? ? * theorem 20 in p. 296 ) , cf . hereafter two circles are called _ cospheric _ , if they are contained in one @xmath9-dimensional sphere or plane . recently there has been a renewed interest to surfaces containing @xmath9 circles through each point due to pottmann who considered their potential applications to architecture @xcite . pottmann noticed that the _ euclidean translational surface _ @xmath11 , where @xmath12 are two fixed generic circles in @xmath0 , contains @xmath9 circles through each point but is not a darboux cyclide ( * ? ? ? * example 3.9 ) . another example with similar properties was given by zub in 2011 : the stereographic projection of a _ clifford translational surface _ @xmath13 , where @xmath12 are now circles in the sphere @xmath14 identified with the set of unit quaternions . the projection itself is called a _ clifford translational surface _ as well ; see figure [ movie ] to the right . it may have degree up to @xmath15 . each degree @xmath15 surface in @xmath7 containing a _ great _ circle and another circle through each point is clifford translational ( * ? ? ? * corollary 2c ) . more examples can be obtained from these translational surfaces by _ mbius transformations _ , i.e. , compositions of inversions . euclidean and clifford translational surfaces are not mbius transformations of each other ( * ? ? ? * theorem 2b ) . for related transformations taking lines to circles see @xcite . we conjecture that the above ones are the only possible surfaces containing @xmath9 circles through each point . let us make this statement precise . we switch to a local problem involving a piece of a surface instead of a closed one and circular arcs instead of circles . by an _ analytic surface _ in @xmath16 we mean the image of an injective real analytic map of a planar domain into @xmath16 with nondegenerate differential at each point . we use the same notation for the map and the surface ; no confusion arises from this . a circle ( or circular arc ) _ analytically depending _ on a point is a real analytic map of an analytic surface into the variety of all circles ( or circular arcs ) in @xmath16 . analyticity is not really a restriction @xcite . [ mainthm ] if through each point of an analytic surface in @xmath0 one can draw two transversal circular arcs fully contained in the surface ( and analytically depending on the point ) then the surface is a mbius transformation of a subset of either a darboux cyclide , or euclidean or clifford translational surface . we hope to deduce main conjecture [ mainthm ] from the following 4-dimensional counterpart . the @xmath2-dimensional problem seems to be more accessible than the @xmath8-dimensional one because of nice approach using quaternions . in what follows identify @xmath17 with the skew field @xmath18 of quaternions , and @xmath0 with the set @xmath19 of purely imaginary quaternions . mbius transformations in @xmath17 are precisely the nondegenerate maps of the form @xmath20 and @xmath21 , where @xmath22 ; see @xcite for an exposition . circles in @xmath17 are precisely the nondegenerate curves having a parametrization of the form @xmath23 ( outside one point ) , where @xmath22 are fixed and @xmath24 runs . denote by @xmath25 $ ] the set of polynomials with quaternionic coefficients of degree at most @xmath26 in the variable @xmath27 and at most @xmath28 in the variable @xmath29 ( the variables commute with each other and the coefficients ) . denote @xmath30 . define @xmath31 , @xmath32 , and @xmath33 analogously . for each @xmath34 and real numbers @xmath35 ( but not quaternions ) the value @xmath36 is well - defined . thus the polynomial @xmath37 or a rational expression in such polynomials defines a surface in @xmath17 . [ 4dbconj ] assume that through each point of an analytic surface in @xmath17 one can draw two noncospheric circular arcs fully contained in the surface ( and analytically depending on the point ) . assume that for each point in some dense subset of the surface the number of circular arcs passing through the point and fully contained in the surface is finite . then some mbius transformation of the surface has a parametrization @xmath38 for some polynomials @xmath39 such that @xmath40 . conversely , almost each surface contains two circular arcs @xmath41 and @xmath42 through each point because the curves @xmath23 and @xmath43 are circular arcs for almost each @xmath22 . e.g. , @xmath44 is a clifford translational surface , and @xmath45 is a torus . the first result of this paper is the following assertions reducing the @xmath8-dimensional problem to the @xmath2-dimensional one . they are proved in section [ sec : proofs ] . [ prop21][prop:21-split ] if surface is contained in @xmath0 ( respectively , in @xmath7 ) then it is a subset of either an euclidean ( respectively , clifford ) translational surface or a darboux cyclide ( respectively , an intersection of @xmath7 with another @xmath8-dimensional quadric ) . [ cor-3d ] if a surface in @xmath0 is a mbius transformation of surface in @xmath17 then the former surface is a mbius transformation of a subset of either a darboux cyclide , or euclidean or clifford translational surface . surfaces containing two circles through each point are particular cases of surfaces containing two conic sections or lines through each point . the latter surfaces have been classified by brauner , schicho , and lubbes @xcite . in the particular case of so - called supercyclides a classification was given by degen @xcite . the schicho classification is up to a week equivalence relation , thus it does not allow automatically to find all surfaces containing two circles through each point . however the following parametrization result by schicho provides the first step toward the solution of our problem . the notions used in the statement are defined analogously to the above ; see section [ sec : proofs2 ] for details . [ schicho ] assume that through each point of an analytic surface in a domain in @xmath28-dimensional complex projective space one can draw two transversal conic sections intersecting each other only at this point ( and analytically depending on the point ) such that their intersections with the domain are contained in the surface . assume that through each point in some dense subset of the surface one can draw only finitely many conic sections such that their intersections with the domain are contained in the surface . then the surface ( possibly besides a one - dimensional subset ) has a parametrization @xmath46 for some @xmath47 such that the conic sections are the curves @xmath41 and @xmath42 . conversely , one can see immediately that almost each surface contains two conic sections @xmath41 and @xmath42 through each point . theorem [ schicho ] in particular implies that each surface containing two conic sections through each point is contained in an projective subspace of dimension at most @xmath15 and has the degree at most @xmath15 ( by standard elimination of variables ) . theorem [ schicho ] is proved completely analogously to ( * ? ? ? * theorem 11 ) , where the case when @xmath48 is considered ; see also ( * ? ? ? * theorem 17 ) . for convenience of the reader we give the proof in section [ sec : proofs2 ] . in comparison to @xcite we have added some details to make it accessible to nonspecialists . the main result of the paper is the following corollary also proved in section [ sec : proofs2 ] . [ haupt][param ] assume that through each point of an analytic surface in @xmath49 ( respectively , in @xmath16 ) one can draw two noncospheric circular arcs fully contained in the surface ( and analytically depending on the point ) . assume that through each point in some dense subset of the surface one can draw only finitely many circular arcs fully contained in the surface . then the surface ( possibly besides a one - dimensional subset ) has a parametrization @xmath50 where @xmath51 satisfy the equation @xmath52 ( respectively , the equation @xmath53 for some @xmath54 ) . this result reduces the above conjectures to solving the equation @xmath55 for `` pythagorean @xmath28-tuples '' in real polynomials . the resulting problem is hard but seems more accessible because of possible induction over the involved parameters ( @xmath28 , number of variables , degree ) . the problem has been solved for @xmath48 and @xmath2 in ( * ? ? ? * theorem 2.2 ) using that @xmath56 $ ] is a unique factorization domain ( ufd ) . in case of one variable a similar argument works for @xmath57 and @xmath1 because @xmath58 $ ] is still a ufd in a sense ( * ? ? ? * theorem 1 in chapter 2 ) , cf . @xcite , @xcite and conjecture [ conj-1-var ] below . the main difficulty of passing to two variables is that @xmath59 $ ] is _ not _ a ufd any more ; see example [ ex - beauregard ] below taken from @xcite . the case of two variables and @xmath60 arising in our geometric problem seems to be the simplest case not accessible by the methods available before . so far we give only one result in this direction , which is nice and interesting in itself , useful for the proof of the above conjectures and also for theorem [ prop21 ] above . the result is" +"bigravity is a theory of gravity with two independent _ dynamical _ metrics ( denoted by @xmath0 and @xmath1 ) . the action , first considered by isham - salam - strathdee @xcite , is @xmath2 & = & { 1 \over 16\pi g } \int \big[\ \sqrt{g } r(g ) + \sigma\ , \sqrt{f } r(f)- u(g , f ) \big]\end{aligned}\ ] ] where @xmath3 is an interaction potential depending both on @xmath4 and @xmath5 . the dimensionless parameter @xmath6 measures the relative strengths of both newton s constants . bigravity has received intermittent but consistent attention since it was first presented . for some recent work see @xcite . the first question one may ask is what is the physical metric determining the geometry of spacetime . this is the same as asking to what metric do particles couple to . we refer the reader to the literature for discussions on many different interpretations . in this work , we shall work entirely on vacuum space filled only by the two metrics . the problem we shall be concerned regularity of the black hole horizon is independent on the interpretation for the bigravity theory . the potential considered in @xcite was is replaced by @xmath7 which is consistent with diff invariance . we have set @xmath8 for simplicity , and to make contact with @xcite . ] @xmath9 where @xmath10 has dimensions of mass . flat space @xmath11 is a solution to the equations of motion . the linear theory around this solution @xmath12 describes @xcite a massless graviton because the action is diff invariant . ] @xmath13 plus a massive one @xmath14 with a pauli - fierz mass term . the mass is equal to @xmath15 and the effective newton s constant is @xmath16 . stability / unitarity of the linear theory then requires the two conditions @xmath17 the potential ( [ u1 ] ) breaks the original diff@xmath18diff symmetry down to the diagonal subgroup . the linear theory is nevertheless well - behaved because the mass term has the pauli - fierz form . [ see @xcite for a general non - go theorem forbidding cross interactions between @xmath19 gravitons preserving diff@xmath20 . ] the applications of bigravity to massive gravity has been extensively discussed in the literature and we shall omit here . our main goal is to discuss the properties of black holes . black hole thermodynamics in massive gravity ( with a different action ) has been studied in @xcite . the main goal of this paper is to study in detail the properties of black holes solutions to the action ( [ i ] ) . we shall argue in sec . [ issol ] that the solutions found in @xcite , associated to the potential ( [ u1 ] ) , do not have regular horizons and thus they can not represent black holes . there exists , however , a much larger class of potentials accepting exact solutions and having a unitary / stable linear theory @xcite . in sec . [ newu ] we consider a more general potential ( with two parameters ) and show that regular solutions do exist . we then compute the total energy , entropy , temperature and discuss the thermodynamical properties . we shall see that phase transitions exist when @xmath21 , which is allowed by unitarity / stability . soon after the action ( [ i ] ) was proposed , solutions with spherical symmetry of the form @xmath22 were discovered by isham and storey does not introduce conical singularities because these solutions are asymptotically ( a)ds , and have horizons . we thank r. mann for a useful conversation on this point . ] @xcite . for our purposes here is enough to mention that @xmath23 and @xmath24 have the schwarzschild - ads form @xmath25 @xmath26 and @xmath27 are independent integration constants and @xmath28 . the cosmological constants @xmath29 and @xmath30 are combinations of @xmath10 and @xmath27 . see @xcite for full details . a remarkable property of the solution , already noticed in @xcite , is that @xmath1 can also be brought to a schwarzschild form via a coordinate change @xmath31 , with a suitable @xmath32 . in the new coordinate system the metric @xmath1 takes the form , @xmath33 where @xmath34 is a constant . the zero s of @xmath24 then represent horizons for the metric @xmath1 . the full solution is then simply two schwarzschild metrics written in different coordinate system . the isham - storey solution fulfills another remarkable property . consider an arbitrary linear combination of both metrics @xmath35 since @xmath1 is off - diagonal , the metric @xmath36 is also off - diagonal . one can introduce a new time coordinate @xmath37 defined by @xmath38 , and again , for a suitable choice of @xmath39 the metric @xmath36 becomes diagonal . the remarkable property is that for _ any _ choice of @xmath40 this metric again has the schwarzschild form @xmath41 where @xmath42 are constants that depend on @xmath42 , and @xmath43 depend on all parameters @xmath44 . this metric represents a black hole with a new mass parameters that depends on the particular linear combination . in particular , the location of the horizon depends on @xmath40 . thus , for fixed values of @xmath45 , the isham - storey solution generates a whole family of black holes with horizons at arbitrary locations . summarizing , at first sight , the isham - storey configuration has ( at least ) two horizons -one for each metric- defined by the points where the functions @xmath23 and @xmath24 vanish . these ( candidate ) horizons are located at different and independent points in spacetime because the zeroes of @xmath23 and @xmath24 are defined by independent integrations constants @xmath46 and @xmath47 . this interpretation is however not correct . the isham - storey configuration is singular because , as we now show , there is no coordinate system where both horizons can be made regular simultaneously . as a first attempt to prove regularity , the metric @xmath0 can be put in eddington - flinkestein coordinates @xcite making it regular at its own horizon . remarkably , the metric @xmath1 becomes regular at that point as well . however , this can only be achieved for either ingoing or outgoing coordinates ( depending on the choice of sign for @xmath48 ) , but not for both simultaneously . as it is well - known @xcite , only half of the eddington - flinkestein coordinates is not enough to declare regularity . let us concentrate on the @xmath0 horizon defined by the condition @xmath49 if @xmath50 this equation has more than one positive solution . the argument that follows applies to all regular horizons . we assume , however , that the horizon is non - extremal , that is @xmath51 . the argument can be generalized to extreme horizons as well . defining a proper radial coordinate @xmath52 in a neighborhood of the horizon , the metric @xmath0 can be brought to the form @xmath53 where @xmath54 is a constant . the 1-form @xmath55 is singular at the horizon ( now located at @xmath56 ) but @xmath57 is regular . the metric ( [ a ] ) represents a regular spacetime written in singular hyperbolic polar coordinates . let us now look at the metric @xmath1 in the neighborhood of @xmath58 . the functions @xmath59 take finite values at that point and thus , naively , the metric @xmath1 looks regular , @xmath60 here @xmath61 and @xmath62 are non - zero for generic values of @xmath26 and @xmath27 . then , since the 1-form @xmath55 is singular at @xmath63 ( or @xmath64 ) , the metric ( [ fhor ] ) is actually singular there . a more geometrical way to see this is to note that the set of points @xmath65 with fixed angular variables correspond to a timelike one - dimensional curve in the metric @xmath1 , but a 0-dimensional point in the metric @xmath0 . this means that metric @xmath0 requires that the above set of points should be identified , while metric @xmath1 require them to be all independent . the only way to make this metric regular is to assume that @xmath24 and @xmath48 also vanish at @xmath63 ( with appropriate weights ) . a more explicit way to reach to the same conclusion is to put the metric ( [ a ] ) in regular cartesian coordinates . this can always be done in a neighborhood of its horizon . then one looks at the metric @xmath1 in this ( regular ) coordinate system . it follows that @xmath1 can be regular at the horizon of @xmath0 if and only if its own horizon is also located there . in summary , if @xmath58 and @xmath66 denote , respectively , the solutions to @xmath67 and @xmath68 we have concluded that @xmath0 is singular at @xmath66 , and @xmath1 is singular at @xmath69 . the only truly regular solution is one with @xmath70 . this solution does exist , but corresponds to a proportional case @xmath71 ( @xmath72 is a constant ) , where @xmath0 is the schwarzschild metric . this particular solution is the only regular black hole within the family of isham - storey solutions . it is instructive to recall the reissner - nordstrom black hole system having a non - zero coulomb field @xmath73 . the same arguments exhibited above imply that the potential @xmath74 must be zero at the horizon if one demands the 1-form @xmath75 to be regular there . for the reissner - nordstrom black hole , this can always be achieved via a suitable gauge transformation . the isham - storey exact solution associated to the potential ( [ u1 ] ) can not be interpreted as a black hole , but only as the exterior solution to some mass distribution in bigravity . we were motivated by the question of whether or not the singularity at the horizon was a generic property of bigravity , or a property of the particular isham - salam - strathdee potential ( [ u1 ] ) . the potential ( [ u1 ] ) is one member within the infinite dimensional family of potentials @xcite given rise to a unitary and stable linear pauli - fierz theory . it is then natural to ask whether or not other potentials may give rise to regular black holes . to answer this question ( in a simple way without trying to prove a general theorem ) we shall consider the 2-parameter family of potentials , @xmath76.\end{aligned}\ ] ] note that for all @xmath77 , this potential belongs to the pauli - fierz class as defined in @xcite , and that for @xmath78 we recover the potential ( [ u1 ] ) . see @xcite for a much larger class of potentials admitting exact solutions . we shall see that , for generic values of @xmath77 , regular , non - trivial ( i.e. , non - proportional ) black hole solutions do exist . since the condition @xmath79 represents an open set one can conjecture that , generically , the pauli - fierz family of potentials does accept regular black holes solutions . before displaying the exact solution to the potential ( [ u2 ] ) we mention that ( i ) the potential ( [ u2 ] ) also accepts the background @xmath80 . the linear spectrum contains a massless field plus a pauli - fierz massive theory . the mass is now , @xmath81 as in the previous case , @xmath82 must be positive to avoid ghosts . then , linear unitarity / stability holds for @xmath83 our goal is to prove that a regular solutions exist , not to classify all solutions , which is a hard task . we consider the family of potentials where" +"a new class of massive x - ray binaries has been recognized in the last few years , mainly thanks to observations carried out with the _ integral _ satellite . they are transient x - ray sources associated to o or b supergiant stars and characterized by short outbursts . these _ supergiant fast x@xmath0ray transients _ ( sfxts ) [ @xcite ; @xcite ] are remarkably different from the classical high mass x - ray binaries ( hmxbs ) with supergiant companions , that are bright persistent sources , and also differ from the be transients for their optical companions and shorter outbursts . the outbursts of sfxts involve a high dynamic range , spanning 3 to 5 orders of magnitudes , from a quiescent luminosity of @xmath1 erg s@xmath2 up to the peak luminosity of @xmath3 erg s@xmath2 . the outbursts typically last a few days and are composed of many short flares with duration of a few hours . besides these bright outbursts , the sfxts can display a fainter flaring activity with luminosity @xmath4 erg s@xmath2 @xcite . different mechanisms have been proposed to explain the sfxts properties ( see @xcite and references therein for a recent review ) . @xcite , proposed that sfxts outbursts are due to the presence of an equatorial wind component , denser and slower than the spherically symmetric wind from the supergiant , and possibly inclined with respect to the orbital plane of the system . the enhanced accretion rate occurring when the neutron star crosses this wind component can explain sfxts showing periodic outbursts , such as igr j11215@xmath05952 and also other sfxts , assuming different geometries for the outflowing equatorial wind . another possibility involves the gated mechanisms due to transitions across the centrifugal barrier @xcite.@xcite showed that a centrifugal or a magnetic barrier can explain the sfxts properties only if the supergiant wind is inhomogeneous , and the accreting neutron star has a strong magnetic field ( @xmath5 g ) and a long spin period ( @xmath6 s ) . @xcite proposed that the sfxts flares are produced by accretion of clumps of matter from the companion wind . in the framework of the clumpy wind model proposed by @xcite , @xcite and @xcite proposed that what distinguishes the sfxts from the persistent hmxbs with supergiant companions is their different orbital separation : in persistently bright sources the compact object orbits the companion at a small distance ( @xmath72 stellar radii ) where there is a high number density of clumps , while the transient emission in sfxts is produced by accretion of much rarer clumps present at larger distances . on the other hand , the monitoring with _ swift _ of a sample of four sfxts @xcite has demonstrated that these sources accrete matter also outside the bright outbursts , so any model should also account for this important observational property . the winds of o and b type stars are driven by the momentum transfer of the radiation field and @xcite showed that the dominant mechanism is the line scattering . the analytical formulation for line - driven winds has been developed by @xcite ( cak ) . in the cak theory the mass lost by the star is smoothly accelerated by the momentum transferred from the stellar continuum radiation , and forms a stationary and homogeneous wind . however , both observational evidence and theoretical considerations indicate that the stellar winds are variable and non homogeneous . changes in the uv line profiles , revealing wind variability , have been observed on time scales shorter than a day @xcite . the x - ray variability observed in 4u 1700@xmath0377 , vela x@xmath01 and other hmxbs can be explained in terms of wind inhomogeneity [ @xcite ; @xcite ] and further indications for the presence of clumps come from x@xmath0ray spectroscopy . for example , the x@xmath0ray spectrum of vela x@xmath01 during the eclipse phase shows recombination lines produced by a hot ionized gas and fluorescent k - shell lines produced by cool and dense gas of near - neutral ions @xcite . these authors proposed that the coexistence of highly ionized and near neutral ions can be explained with an inhomogeneous wind , where cool , dense clumps are embedded in a lower density , highly ionized medium . @xcite suggested that the wind acceleration is subject to a strong instability since small perturbations in the velocity or density distribution grow with time producing a variable and strongly structured wind . the first time - dependent hydrodynamical simulations of unstable line - driven winds were performed by @xcite and , more recently , by @xcite and @xcite . all these simulations show that the line - driven instability produces a highly structured wind , with reverse and forward shocks that compress the gas into clumps . moreover , the shock heating can generate a hot inter - clump medium into which the colder clumps are immersed @xcite . based on these considerations , we study in this work the expected variability and x@xmath0ray luminosity properties of neutron stars accreting from a clumpy wind . in the next two sections we describe our clumpy wind model and the assumptions for the mass accretion . in section [ application of the clumpy wind model ] we study the dependence of the parameters introduced in the previous sections . in sections [ study of the hmxb vela x-1 ] , [ study of the sgxb 4u 1700 - 377 ] and [ study of the sfxt igr j11215 - 5952 ] we compare the x - ray light curves predicted with our model to the observations of three high mass x - ray binaries , showing that it is possible to reproduce well the observed flaring behaviors . in our model , where the dynamical problem has not been treated , we assume that a fraction of the stellar wind is in form of clumps with a power law mass distribution @xmath8 in the mass range @xmath9 - @xmath10 . the rate of clumps produced by the supergiant is related to the total mass loss rate @xmath11 by : @xmath12 where @xmath13 is the fraction of mass lost in clumps and @xmath14 is the average clump mass , which can be computed from equation ( [ npunto ] ) . clumps are driven radially outward by absorption of uv spectral lines @xcite . from spectroscopic observations of o stars , @xcite suggest that clumps follow on average the same velocity law of a smooth stellar wind . we can then assume the following clump velocity profile without solving the dynamical problem : @xmath15 where @xmath16 is the terminal wind velocity , @xmath17 is the radius of the supergiant , @xmath18 is a parameter which ensures that @xmath19 km s@xmath2 , and @xmath20 is a constant in the range @xmath21@xmath22@xmath23 [ @xcite ; @xcite ] . assuming that the clumps are confined by the ram pressure of the ambient gas , their size can be derived by the balance pressure equation . following @xcite and @xcite , the average density of a clump is : @xmath24 where @xmath25 is the density profile of the homogeneous ( inter - clump ) wind , @xmath26 and @xmath27 are the inter - clump wind and the clump thermal velocity , respectively : @xmath28 and @xmath29 . @xmath30 is the boltzmann constant , @xmath31 and @xmath32 are the temperatures of the inter - clump wind and of the clumps , respectively , and @xmath33 is the mean atomic weight . the constant @xmath34 accounts for the confining effect of the bow shock produced by the ram pressure around the clump @xcite . @xmath35 is the relative velocity between the wind and the clump ( @xmath36 ) . adopting @xmath37 cm s@xmath2 , @xmath38 k , @xmath39 k and @xmath40 , we obtain : @xmath41 since the density radial profile @xmath25 of the homogeneous inter - clump wind ( obtained from the continuity equation @xmath42 ) is : @xmath43 where @xmath44 is a generic distance from the supergiant , from equations ( [ lucy_white ] ) , ( [ lucy_white_200 ] ) , ( [ legge_densita_vento_omogeneo ] ) , we obtain : @xmath45 where @xmath46 . @xcite analyzed the far - ultraviolet spectrum of o - type supergiants and found that clumping starts deep in the wind , just above the sonic point @xmath47 , at velocity @xmath48 km s@xmath2 . in the cak model the sonic point is defined as the point where the wind velocity is equal to the sound speed ( @xmath49 ) : @xmath50 adopting typical parameters for o supergiants , from equation ( [ sonicpoint ] ) we obtain that the clumping phenomenon starts close to the photosphere ( @xmath51 ) . assuming spherical geometry for the clumps and that the mass of each clump is conserved , it is possible to obtain the expansion law of the clumps from equation ( [ legge_densita_clump ] ) , with @xmath52 : @xmath53^{1/3}\ ] ] from equation ( [ legge_rcl_r ] ) we find that the clump size increases with the distance from the supergiant star . for the initial clump dimensions we tried two different distributions , a power law @xmath54 and a truncated gaussian function : @xmath55 where @xmath56 , and @xmath57 is a free parameter . for any given mass clump we derived the minimum and maximum values for the initial radii as follows . the minimum radius is that below which the clump is optically thick for the uv resonance lines . in this case gravity dominates over the radiative force causing the clump to fall back onto the supergiant . the momentum equation of a radiatively driven clump is : @xmath58 where @xmath59 is the mass of the supergiant , @xmath60 is the radiative acceleration due to the continuum opacity by electron scattering , @xmath61 is the radiative acceleration due to line scattering . while equation ( [ cak_equation ] ) is an approximation that ignores the pressure gradient , the solution of the momentum equation differs only slightly from the accurate solution derived by @xcite ; another assumption is that the photosphere has been treated as a point source @xcite . the radiative acceleration due to electron scattering is : @xmath62 where @xmath63 is the opacity for electron scattering , and is given by @xmath64 , where @xmath65 is the thomson cross section , @xmath66 is the number density of electrons , @xmath67 is the density of the clump and @xmath68 is the luminosity of the ob supergiant . @xcite found @xmath69 . assuming a constant degree of ionization in the wind both @xmath63 and @xmath60 are constant . the radiative acceleration due to the line scattering is : @xmath70 where @xmath71 @xmath72 g@xmath2 , @xmath30 , @xmath73 , @xmath74 are the force multiplier parameters , which are obtained with the calculation of the line radiative force @xcite . @xmath75 is the dimensionless optical depth parameter @xcite . according to the model of @xcite , we assume no velocity gradient inside the clump ( of size @xmath76 ) , then we utilize the dimensionless optical depth parameter for a static atmosphere @xmath77 . @xmath78 is the geometrical dilution factor @xcite , given by : @xmath79\ ] ] according to the equation ( [ legge_densita_clump ] ) , we find that the number density of electrons in each clump is given by : @xmath80 where @xmath81 such that : @xmath82 from equation ( [ cak_equation ] ) we obtain that the minimum radius of the clump is given by : @xmath83 where @xmath84 is the acceleration due to gravity . approximating @xmath75 as @xmath85 and assuming the force multiplier parameters calculated by @xcite , with @xmath86 km s@xmath2 and @xmath87 , we finally obtain the lower - limit for the clump radius : @xmath88 where : @xmath89 we found that for the interesting" +"it is convenient to split the problem of multiple populations in globular clusters ( gcs ) into two challenges or questions . first , what is producing the chemical abundance anomalies giving rise to observable features such as the na - o anti - correlation and multiple sequences in the colour - magnitude diagrams of gcs ( e.g. gratton et al . 2012 , piotto et al . 2012 ) ? but another important challenge is to understand how this polluted material makes its way into a large fraction of the cluster stars ( the observed enriched fraction is @xmath0 today ; see e.g. bastian & lardo 2015 ) . whether it is through multiple generations of star formation ( e.g. dercole et al . 2008 ) , via accretion onto low - mass pre - main sequence stars born as part of the same burst of star formation ( bastian et al . 2013 ) , or via a yet unknown alternative process ( as suggested by bastian et al . 2015 ) , the mechanism by which enriched material is incorporated into stars will dictate the initial configuration of the enriched ( i.e. polluted ) stars compared to the primordial ( i.e. normal ) stars . this will set the initial conditions for the long - term dynamical evolution of the cluster and its multiple populations , which is the focus of this contribution . because gcs are collisional systems , their long - term dynamical evolution leads to two phenomena that can affect the present - day kinematics and spatial distribution of subpopulations : phase - space mixing and mass segregation . due to two - body encounters , populations of stars with different initial phase - space distributions will exchange energy and angular momentum and gradually mix ( decressin et al . 2008 , vesperini et al . 2013 , hnault - brunet et al . the trend towards kinetic energy equipartition also leads massive stars and remnants to slow down and sink towards the centre of the cluster , effectively pushing the lower - mass stars outwards . because the two - body relaxation timescale ( on which these processes become important ) is inversely proportional to the local density ( e.g. spitzer 1987 ) , the importance of these processes will vary significantly between different regions of the cluster . in the outer regions , where the relaxation timescale is longer , there will be less mixing and we may expect to still see imprints of the initial conditions and formation process . in the inner regions , the shorter relaxation timescale leads to more mixing , potentially erasing any initial differences between subpopulations , and mass segregation can also proceed more efficiently and introduce differences in the spatial distribution and kinematics of different mass species . in the following sections , we review constraints on the formation of multiple populations imposed by their present - day kinematics and spatial distribution . n - body simulations of clusters with two subpopulations starting spatially segregated and with comparable numbers of stars have shown that complete spatial mixing is expected when about @xmath1 of the initial mass of the cluster has been lost due to two - body relaxation ( vesperini et al . this also applies to the distinct kinematics of different subpopulations , which will be erased on a similar timescale ( e.g. decressin et al . 2008 , hnault - brunet et al . given their current mass and galactocentric radius , a large fraction of galactic gc are expected to still be expanding within their tidal radius and to have lost less than 50% of their initial mass by relaxation - driven evaporation ( gieles et al . 2011 ) , so some memory of the initial configuration of subpopulations should be preserved in the outer parts of many gcs . and indeed , when looking at the spatial distribution of subpopulations in the outer regions of clusters ( from around the half - mass radius - @xmath2 - and beyond ) , a more centrally concentrated enriched population has been found in many clusters ( e.g. sollima et al . 2007 , bellini et al . 2009 , lardo et al . 2011 , milone et al . 2012 ) , suggesting that enriched stars formed more centrally concentrated . that said , evidence for a fully mixed cluster has also been reported ( ngc 6362 ; dalessandro et al . 2014 ) and full mixing may be more common than previously thought ( vanderbeke et al . 2015 ; although see their caveats about using horizontal branch stars as tracers ) . kinematic differences have been found in some cases in the outer regions of clusters , with the ( na ) enriched population having a lower velocity dispersion ( bellazzini et al . 2012 , kuinskas et al . the more centrally concentrated population is generally expected to be dynamically cooler ( see e.g. bekki 2011 ; mastrobuono - battisti & perets 2013 ; hnault - brunet et al . 2015 ) , regardless of its initial configuration ( flattened disc - like or spherical subsystem ) , so again this is consistent with an enriched population that started more centrally concentrated . using hubble space telescope ( hst ) proper motions of stars near @xmath3 in 47 tuc , richer et al . ( 2013 ) found that the presumably he - enriched stars ( bluer main - sequence stars ) have a more radially anisotropic velocity distribution . bellini et al . ( 2015 ) observed a similar behaviour for stars between @xmath4 and @xmath5 from hst proper motions in ngc 2808 , with stars coinciding with the presumably he - enchanced populations in the middle and blue main sequences showing a smaller tangential velocity dispersion than the populations corresponding to primordial stars , while no significant differences were found in the radial - velocity dispersion . we showed in hnault - brunet et al . ( 2015 ) that a more radially anisotropic velocity distribution for the polluted stars is also predicted if this population started more centrally concentrated and then diffused outward , and it is by no means a unique signature of any of the scenarios proposed . for example , whether gas collected into the core of the cluster to form a new generation of polluted stars ( possibly adopting a flattened initial distribution if the cluster had some net rotation ; e.g. dercole et al . 2008 , bekki 2010 ) , or if the polluted stars are the ones initially crossing the core of the cluster and preferentially on radial orbits ( e.g. as in the early disc accretion scenario of bastian et al . 2013 ) , any remaining present - day velocity anisotropy signature is expected to be very similar ( see fig . [ fig1 ] ) . ) as a function of radius ( in 3d ) for the polluted ( in blue ) and pristine ( i.e. primordial composition - in red ) stars as a function of time , for three different initial configurations : a spherical and isotropic subsystem of polluted stars embedded in a more extended spherical cluster ( model mgen0c - left ) , a flattened rotating subsystem of polluted stars embedded in a non - rotating spherical cluster ( model mgen1 - centre ) , a rotating cluster where the polluted stars are flagged as the ones with an orbit crossing the cluster core at @xmath6 ( model acc1 - right ) . the half - mass radius is indicated by grey dashed lines . for more details on these simulations see hnault - brunet et al . ( 2015 ) , from which this figure is adapted.,width=499 ] all the observational evidence collected so far in the outer parts of gcs points to an enriched population forming more centrally concentrated , but this does not help to discard or favour any particular formation mechanism since all current scenarios either predict such a trend or were designed to match these observational constraints . to make progress , we need to identify unique imprints that would allow to distinguish between various scenarios . for example , mastrobuono - battisti & perets ( 2013 ) proposed to look for morphological features such as a larger flattening of the enriched population , which is a possible outcome of a scenario with multiple generations of stars ( although this may prove challenging to measure ) . we recently suggested the differential rotation of subpopulations as a promising kinematic signature ( hnault - brunet et al . 2015 ) . given some net angular momentum initially , models for which a second generation forms from gas that collects in a cooling flow into the core of the cluster predict an initially larger rotational amplitude for the polluted stars compared to the primordial stars ( a consequence of angular momentum conservation ) . hypothetically removing @xmath7 of first - generation stars ( in order to alleviate the mass budget "" problem plaguing scenarios with multiple generations of star formation ) would also remove a large fraction of the angular momentum of the more extended primordial population ( see hnault - brunet et al . the opposite trend is expected from a scenario in which the polluted stars are the ones initially crossing the core of the cluster ( e.g. bastian et al . 2013 ) and preferentially on radial ( low - angular momentum ) orbits . in this case , the rotational amplitude of the polluted stars would be lower initially ( assuming the cluster has some net rotation ) . this is illustrated in fig . [ fig2 ] , where we also show that a differential rotation between the polluted and primordial stars of the order of 1 km s@xmath8 or larger can remain in the outer parts of a cluster after a hubble time of dynamical evolution ( the simulations shown are scaled to match the properties of 47 tuc ) . marginal evidence for differential rotation between subpopulations has been reported in a few clusters ( e.g. ngc 6441 and ngc 6388 ; bellazzini et al . 2012 ) , with polluted stars displaying a smaller rotational amplitude , but these are based on relatively small datasets and will need to be confirmed with more observations . : a flattened rotating subsystem of polluted stars embedded in a non - rotating spherical cluster ( model mgen1 - left ) , a rotating cluster where the polluted stars are flagged as the ones with an orbit crossing the cluster core at @xmath6 ( model acc1 - right ) . adapted from hnault - brunet et al . ( 2015).,width=374 ] larsen et al . ( 2015 ) found a surprising result when investigating the spatial distributions of subpopulations in m15 using hst / wfc3 photometry of red giants . unlike what is typically observed in the outer regions of clusters ( including m15 ) , they found that the giants with primordial composition are more centrally concentrated in the inner parts of the cluster ( within the half - light radius ) . they considered mass segregation as a possible culprit for the observed trend , but showed with @xmath9-body simulations that a significant mean mass difference would be needed , with primordial giants required to be @xmath10 m@xmath11 more massive than their enriched counterparts . if interpreted as a difference in helium content , this mean mass difference would imply extreme he enhancement ( @xmath12 ) , which is clearly incompatible with the colour - magnitude diagram of m15 . larsen et al . therefore concluded that the radial trends seen in m15 presumably reflect initial conditions , but we consider below another possibility . a larger binary fraction has been inferred for primordial stars compared to enriched stars ( @xmath13 vs." +"in most of the cosmological studies , dark matter particles are treated as collisionless particles . for instance , to describe the cosmological density evolution , collisionless boltzmann equation is adopted . in cosmological n - body simulations , a group of collisionless dark matter particles , are represented by a single collisionless particle in the computer from the coarse - grained point of view . in the treatment by the boltzmann equation , in which the distribution function is defined in a phase space , the particle mass and statistical weight are explicitly dealt with , although the dark matter particles are still regarded as classical particles without interaction except for gravity . in the coarse - grained view adopted by n - body simulations , there is no particle information and only the global mass density distribution is obtained . however , by adopting the assumption that dark matter particles are collisionless classical particles , we might have lost basic physics in some cases . at high number densities and relatively low temperature , low - mass elementary particles , experience quantum statistical degeneracy due to indistinguishability of identical particles . for instance , it used to be well known that the neutrino black body in the early universe was partially degenerate @xcite . neutrinos are fermions and the radiation pressure of the neutrino black body can be interpreted as the combination degeneracy pressure and thermal pressure . as we discuss later in this paper , massive relic neutrinos are likely to remain partially degenerate , after decoupling and even after they become nonrelativistic under adiabatic expansion . after nonlinear evolution of a high - density part of the universe , we might see a high concentration of dark matter particles around the center of a cluster of galaxies . if dark matter particles are composed at least partially of light fermions ( e.g. neutrinos ) , their degeneracy pressure may be large enough to support the density structure near the center of the cluster against gravity . a self - gravitating system supported by degeneracy pressure of fermions , such as a white dwarf or a neutron star , is known to have a flat - top density profile . this is our motivation to explore the possibility that recent results regarding the mass profiles of clusters of galaxies obtained by gravitational lensing @xcite might be explained by the degeneracy pressure of light fermionic dark matter particles . in this paper , using a phenomenological equation of state ( eos ) that describes the physical conditions between fully degenerate fermionic gas and the classical ideal gas , we integrate the equation of hydrostatic equilibrium , under the simple assumption that the local kinetic energy of a classical particle is equal to its gravitational energy determined by the 3d encircled mass . our model is expected to be valid only near the core of a cluster where dynamical equilibrium is possibly achieved . for pure fermions , the volume density profile is uniquely determined by three parameters , the central density , @xmath0 , and the properties of dark matter particles , namely , the mass , @xmath1 , and statistical weight , @xmath2 . to compare our model with observations , we smoothly connect our model volume density profile describing the inner region to a volume density profile derived from the observed column density profile by assuming spherical symmetry at a radius near the einstein radius . in this way our model column density profiles can be directly compared with strong lensing results . in reality , there are baryons and possibly other forms of dark matter such as massive cold dark matter particles . these general cases are dealt with by introducing another input parameter , the ratio of the total mass density and light fermion density , @xmath3 . a1689 studied by @xcite is the best studied cluster by both strong and weak lensing , for which column density profile is obtained from the core to radii greater than 1 mpc . as a case study , we apply our modeling to this cluster and constrain the possible combinations of particle properties . as a natural candidate for light fermions , we consider the case of massive neutrinos . the paper is organized as follows . we first obtain the volume density of a1689 from the observed column density profile of @xcite and show that ev fermions can be degenerate near the core of this cluster in 2 . our modeling procedure is described in 3 and the properties of input fermions are discussed in 4 , and then the results are presented in 5 . the moderate degeneracy of unbound relic neutrinos and the plausibility that they can fall into the cluster core , are discussed in 6 . recently broadhurst et al . @xcite reported a mass column density profile of the cluster of galaxies , a1689 , obtained from gravitational lensing . one of the important properties of the profile is that it has a flat top . we propose that this flat - top column density profile might be explained by the effects of degeneracy pressure of fermionic dark matter . here we analyze this proposal . first we briefly introduce the main results of @xcite . in their analysis , 1@xmath4 corresponds to 129 kpc @xmath5 . in @xcite , the central 250 kpc @xmath5 in radius of multi - color hst / acs images were analyzed . the mass column density profile , @xmath6 , is not expressed as a single power law of radius . the mass column density profile flattens toward the center with a mean slope of + @xmath7 within @xmath8250 kpc @xmath5 . inside the einstein radius ( @xmath9 ) , they obtained the slope of @xmath10 from the ratio between @xmath11 and the radius of the radial critical curve , @xmath12 . they fit their results with an inner region of an nfw profile @xcite with a relatively high concentration , @xmath13 . the mass column density , @xmath6 , is the integral of the volume density , @xmath14 , along the line of sight over the entire cluster scale of mpc . in order to study the possibility of fermion degeneracy near the center of the cluster , we need information on the volume density , @xmath14 , instead of the column density , @xmath6 . @xcite present the weak - lensing analysis of the wide field data obtained by subaru and obtained the column density profile at @xmath15 mpc @xmath5 . they fit the combined profile of hst / acs and subaru with an nfw profile with a very high concentration , @xmath16 , significantly larger than theoretically expected value of @xmath17 . they also fit the same observed column density profile with a power law profile with a core . they give this result in terms of the angular radius dependence of the convergence , @xmath18 , as @xmath19 @xmath20 and @xmath21 give the best fit although @xmath22 and @xmath21 are mutually dependent and a finite range of the combination ( @xmath22,@xmath23 ) gives equally good fits . in terms of @xmath24 and the degrees of freedom , this core power law profile fits the observation better than the best - fit nfw profile and we use this profile for further discussion . although @xcite do not claim so explicitly , the two facts that the best - fit nfw profile shows a much higher concentration than the value predicted by the cdm cosmology and the phenomenological profile , eq.([kappa ] ) , fits better than the best - fit nfw profile , may indicate some contradiction to the cdm cosmology . we start our analysis from this core power - law profile , eq([kappa ] ) , for further discussion . we convert ( [ kappa ] ) to a column density profile , @xmath6 , in physical units of length and mass using the relations , @xmath25 , @xmath26 0.95 @xmath27 , and the normalization of 2d encircled mass inside the einstein radius , @xmath28 , @xmath29 . the result is expressed as @xmath30 where @xmath31 kpc @xmath5 corresponds to @xmath32 , the value used in @xcite . the 2d encircled mass , @xmath33 , is analytically obtained and @xmath34 and @xmath35 respectively for @xmath36 and @xmath37 . therefore a high concentration of the mass is expected on the scale of @xmath28 . by assuming spherical symmetry , we wish to obtain the volume density @xmath14 by solving @xmath38 instead using a standard method like the abel transform , we assumed another power - law profile with a core radius for @xmath14 and obtained the best fit parameters , to see the changes of the core radius and the power law index . from now on , we fix @xmath39 @xcite , so that direct comparison between observations and models can be made . the range of integration in @xmath40 is from @xmath411.4mpc to @xmath421.4mpc , which correspond to the region with good weak lensing signals , since we need solid numbers on the scale of cluster core . the result is @xmath43 the best fit parameters somewhat depends on the range of integration . for instance , if we use the observed column density profile eq.([cpl ] ) out to @xmath442.8 mpc , regardless of the strength of weak lensing signals , the core radius in units of @xmath28 , and power - law index , change to 1.25 , and -3.71 , respectively . note that the power - law index of our choice , -3.41 , is closer to that of an nfw profile of -3 , than -3.71 . since our interest is in the inner region as we show later , and since the contribution of the outer region to the total mass is small , our choice should be justified . before proceeding to modeling of mass profiles , we first show that at the center of a1689 with volume densities of order of @xmath45 ( g@xmath46@xmath47 ) , nonrelativistic ev - mass fermions can become degenerate . since a mass of 1 ev corresponds to @xmath48 g , the number density , @xmath49 @xmath47 , and the mean inter - particle spacing is , @xmath50 cm . on the other hand , the de broglie wavelength for a 1 ev particle with a relative velocity @xmath51 is , @xmath52 cm . therefore for nonrelativistic particles with @xmath53 , the condition for high degeneracy , @xmath54 , is satisfied . we first formulate the modeling procedure of matter distribution for the case that the entire matter consists purely of fermionic dark matter and then , modify the formulation for the case that the fractional contribution of fermionic dark matter density to the total matter density is constant . first we provide our justification for introducing an equation of state and assuming hydrostatic equilibrium for the mixture of degenerate fermions and non - degenerate classical collisionless particles . a self - gravitating system composed purely of classical collisionless particles such as cold dark matter particles may be thermodynamically anomalous @xcite and the equation of state may be poorly defined . however , the effect of fermion degeneracy or introduction of repulsion due to pauli s exclusion principle is to make the mixture of degenerate fermions and classical collisionless particles a thermodynamically normal system and an analysis based on hydrostatic equilibrium valid . to deal with the general situations in which particle temperature is finite and degeneracy is partial , we need to know the equation of state ( eos ) , and have to determine the temperature profile along with the density profile . we adopt two major assumptions that simplify our analysis of fermionic dark matter distribution . first , we assume that the eos , or the pressure law , has the following form , @xmath55 where @xmath56 is the zero temperature" +"despite considerable progress obtained over the last century , astrophysicists are still far away from a thorough understanding on how magnetic fields are produced in the sun and other cool active stars ; the picture gets even worse when it comes to explain quantitatively how these fields generate the plethora of active phenomena observed both at their surface ( e.g. dark spots ) and in their immediate surrounding ( e.g. corona , wind ) . particularly interesting in this respect is the case of fully convective stars for which conventional dynamo processes ( supposed to concentrate mostly in the interface layer between the radiative interior and the convective envelope , i.e. the only place where the field can be stored for a time comparable to the period of the activity cycle ) can not be invoked to justify , not only the presence of a large - scale magnetic field ( e.g. johns - krull & valenti 1996 ) , but also their very intense activity level . the most recent observational results in this field , consisting of temporal series of magnetic maps obtained by indirect tomographic imaging from sets of rotationally modulated spectropolarimetric data ( donati et al . 1992 ; donati & cameron 1997 ; donati 1999 ; donati et al . 1999 ; donati et al . 2003 ; petit et al . 2003a , 2003b ) , are particularly intriguing and thus potentially very fruitful for providing new clues to what may be happening in the convective layers of these stars . all reconstructed magnetic maps to date indeed show the presence of large magnetic regions in the stellar photosphere where the field is mostly azimuthal ( i.e. parallel to the surface and oriented along parallels ) ; moreover , these regions are often observed to form partial , or even complete , rings of azimuthal field encircling the star at various latitudes , and are thus interpreted as the direct detection , at photospheric level , of the quasi - axisymmetric toroidal component of the large - scale dynamo field . these results suggest in particular that dynamos operating in very active stars are likely to be significantly different than that of the sun . the observations indeed reveal that such dynamos are able to produce large scale field ( and especially toroidal field ) very close to the surface ( since we would not observe toroidal field in the photosphere otherwise ) , and presumably even throughout the whole convective zone ; dynamo processes in these stars are therefore likely distributed within the convective envelope , rather than being confined at its base as in the sun . this conclusion raises however a number of subsequent , and yet unresolved , problems ; we can no longer understand , for instance , how the magnetic field can be stored within the convective zone for periods of time as long as decades . at the same time , it may provide new insight for a number of long standing mysteries , and in particular for our comprehension on how dynamos operate in fully convective stars . one of these mysteries concerns the long - term fluctuations observed in the orbital period of close binary stars in which one member is at least a cool active star ( e.g. hall 1990 ) , and occurring on a time scale of a few decades , i.e. much shorter than what would be required for tidal coupling between system components to operate ( zahn 1989 ) . the least unreasonable interpretation for this phenomenon remains that proposed by applegate ( 1992 ) ; he suggests that dynamo processes at work in one star of the binary system activate a periodic exchange between magnetic and kinetic energy within the convective zone of this star , and thus a cyclic fluctuation of its quadrupolar moment as well as of its gravitational field . given the amplitude of the observed fluctuations in orbital period , one can easily infer that such magnetic to kinetic energy exchanges specific to dynamo processes must occur throughout the whole convective zone and not only within a thin layer ( lanza et al . 1998 ; donati 1999 ) , i.e. that dynamo processes in these stars should indeed be distributed . if applegate s ( 1992 ) idea is true , it therefore implies that very active stars such as those found in close binary stars , but also young single stars that did not dissipate most of their angular momentum yet and still exhibit very energetic active phenomena , should feature a convective zone that globally undergoes such periodic exchanges between magnetic and kinetic energy . it means in particular that the internal velocity field within the convective zone of very active stars , and therefore both their radial and surface differential rotation profiles , should vary with time in a way correlated to the magnetic cycle . detecting such variations in the differential rotation of active stars thus appears as a very interesting observational challenge , as it would provide a definite confirmation of both applegate s ( 1992 ) mechanism and of the existence of distributed dynamos . it would also bring into a much wider astrophysical context the recent discovery that the solar angular rotation at the base of the convective zone is undergoing temporal fluctuations ( howe et al . 2000 ) as a probable consequence of the activity cycle . measuring surface differential rotation of very active stars is however a rather tricky task ; detecting changes of this differential rotation is even more difficult . several methods have been proposed to estimate surface differential rotation . some of them try to make use of the subtle changes that differential rotation induce in the profile of spectral lines ( brunning 1981 ; reiners & schmitt 2002 ) ; this method can however not be used for the stars we are interested in , the spectral lines of which being heavily distorted by the presence of cool spots at their surfaces . other methods ( e.g. donati & cameron 1997 ) propose to take advantage of these surface features , and use them as tracers to derive some information on how their rotation periods depend on latitude . the most recent of such techniques , that of cameron et al . ( 2002 ) , succeeded , not only in estimating surface differential rotation of one active star , but also in suggesting that temporal changes in the amount of differential rotation were indeed occurring in this star ( cameron & donati 2002 ) . in this paper , we propose to make use of yet another technique , first proposed by donati et al . ( 2000 ) to estimate the differential rotation of a young pre - main - sequence star , then by petit et al . ( 2002 , 2003a , b ) both for simulation purposes and application to spectropolarimetric data . the aim of this paper is to apply this method to the extensive spectropolarimetric data set that we collected in the last seven yr for three stars , namely the young ultra - fast rotator ab doradus , the young k0 star lq hydrae and the k1 subgiant of the rs cvn system hr 1099 , and from which yearly brightness and magnetic maps were obtained and published in the literature ( donati & cameron 1997 ; donati 1999 ; donati et al . 1999 , 2003 ) . in sect . [ sect : modelling ] , we recall the main aspects of both observational material and modelling tool , then describe its application to the three selected stars in sect . [ sect : diffrot ] ; after discussing at length the implication of our results for the understanding of the global dynamics of convective zones of cool stars ( in sect . [ sect : discussion ] ) , we finally conclude and propose in sect . [ sect : conclusion ] a few directions in which this work could be fruitfully extended . the data we use are the spectropolarimetric observations collected at the anglo - australian telescope ( aat ) with a visitor polarimeter mounted at cassegrain focus and fibre linked to the high resolution ucl echelle spectrograph ( ucles ) . this material , and in particular the observing logs , the observing procedures and the data reduction details , are described extensively in a series of published papers that present the results obtained up to now ( donati et al . 1997 ; donati & cameron 1997 ; donati 1999 ; donati et al . 1999 , 2003 ) . the data we use in this paper are all observations of ab dor , lq hya and hr 1099 collected since epoch 1995.9 , i.e. obtained in a similar spectrograph configuration . this makes a maximum amount of 7 data sets ( corresponding to epochs 1995.94 , 1996.99 , 1998.03 , 1999.00 , 1999.97 , 2000.93 and 2001.99 ) for each of the three stars ; we however anticipate that several of them ( and in particular those with very few data or collected over a timespan of no more than a few days , e.g. those at epoch 1999.97 ) will be unusable for our purpose , according to the conclusions of petit et al . note that all data were reprocessed with the newest version of the reduction software ( donati et al . 2003 ) to ensure the highest possible internal accuracy in radial velocity as well as the best level of homogeneity . all data were run through least - squares deconvolution ( lsd ) , a multiline tool developed by donati et al . ( 1997 ) found to extract successfully the average rotationally broadened shape of unpolarised or circularly polarised lines ( called stokes @xmath0 and @xmath1 lsd profiles in the following ) at each observed phase of the stellar rotational cycle , from the thousands of moderate to strong spectral features present in the recorded wavelength domain . as mentioned earlier , the method we chose to estimate surface differential rotation for the selected stars is that introduced by donati et al . ( 2000 ) , the validity of which was confirmed through an extensive sets of simulations by petit et al . recently , petit et al . ( 2003a , b ) applied it successfully to large data sets collected over several years on a different telescope and with a different ( though similar ) instrumentation for two different stars , one of them being our third object of interest ( the k1 subgiant of hr 1099 ) and the other a giant star of fk com type ( hd 199178 ) . this method consists in assuming a given surface differential rotation law ( that we implement in our indirect stellar surface imaging code ) and producing brightness or magnetic images of the stellar surface from all unpolarised or circularly polarised data available for this star at a given season ; we then take as most probable the differential rotation law that generates the images with lowest information content ( given a certain data fit accuracy ) , or equivalently the images that provide the best fit to the data ( given a certain image information content ) . in practice , both options yield very similar results ; the second one happens to be more convenient as it provides an easy way of estimating error bars on the differential rotation parameters ( see petit et al . 2002 ) . the stellar surface imaging code that we use is that of brown et al . ( 1991 ) and donati & brown ( 1997 ) , applied quite extensively to real data in the last decade ( the latest examples being donati et al . 2003 and petit et al . 2003a ," +"the existence and uniqueness of solutions to the differential equations of physics is seldom an issue . the very fact that these equations describe physical reality seems to argue that their solutions must exist and be unique . textbook examples of nonuniqueness , for example clairaut s equation ( ref . @xcite , p. 94 ) , seem like exceptional cases , which would not arise in physics in any case . there is , however , a system of differential equations , arising as a limiting case of a much studied physical problem , in which uniqueness fails for _ every _ solution at _ every _ time . the system is singular laplacian growth @xcite , @xcite . one might call this behavior `` maximally nonunique . '' it is so different from the usual behavior of differential equations that it hardly seems like a differential system at all . the way it occurs is the following : the theory of singular laplacian growth describes the motions of certain singularities of a conformal map , which are all located on the unit circle in the complex plane . they move on the circle , but they can also `` split , '' introducing new singularities , at any time . this behavior , which does not sound very remarkable , essentially implies the maximal nonuniqueness property . in ref . @xcite the term `` fragile '' was suggested for such a system , because its distinguishing feature is that its singularities can break apart . it is natural to ask if other physical systems might reduce to a fragile system in some limit , and if the fragile property manifests itself in the behavior of the system . turbulence is certainly a candidate to be a fragile system : like laplacian growth , turbulence is a phenomenon in which a differential equation has unexpectedly complex solutions . in this paper i argue that turbulence is a system that has a fragile ( maximally nonunique ) limiting case . the limiting case is the burgers equation . ( on rather different grounds a resemblance between the problems of turbulence and laplacian growth has been noted by hastings and levitov @xcite ) . the burgers equation @xcite , @xcite @xmath0 has played a shifting role in the problem of turbulence . it was first introduced as a one - dimensional zero pressure version of the navier - stokes equation ( with @xmath1 the viscosity ) in the hope that it might exhibit in its solutions some of the complexity of turbulence . by the hopf - cole trick , though , it was found to be equivalent to a linear diffusion equation , so that the initial value problem could be solved explicitly : one can write a formula for the solution ! that is surely too simple to be turbulent . attention was thus focussed on the only case which still seemed promising , the @xmath2 limit , the inviscid burgers equation , which is a conservation law for @xmath3 . in this limit the solution may develop discontinuities ( `` shocks '' ) . the distribution of shocks , and their development in time , for random initial data , is a problem called burgers turbulence . the reason that one should think of this as a @xmath2 limit , and not simply as a @xmath4 version of the equation , is that for @xmath4 the solution is ambiguous . to be sure , the solution of the inviscid equation is immediate by the method of characteristics : @xmath3 is constant along lines @xmath5 ( hence straight lines in the x - t plane ) . but if the characteristics cross , which they certainly will do in the case of random initial data @xmath6 , then one has multiple determinations of @xmath7 , as in fig . 1 . the resolution of this difficulty is to take the formula for @xmath7 in case @xmath8 , which is unambiguous , and let @xmath1 approach zero . the result is as shown in fig . 2 : a discontinuity forms at a definite location , separating one determination of @xmath3 from another . the same procedure shows that shocks interact in a definite manner , coalescing as shown in fig . 3 when one overtakes or collides with another . the rules for how these discontinuities form and interact were known long ago in the theory of compressible gas dynamics , where they are called the rankine - hugoniot jump conditions ( see ref . @xcite , pp . 488 - 90 , ref . @xcite , p. 596 ) . they are justified by appeal to the second law of thermodynamics : while @xmath3 is conserved , entropy must increase in the shock . that is what the argument with @xmath8 also does : we resolve the ambiguity in the inviscid burgers equation by putting in a dissipative term with the right sign . the second law of thermodynamics says mechanical energy should be dissipated in the shock , and not created . it is this condition which leads to the interaction rule illustrated in fig . now recall the suggestion of onsager , as emphasized by alexandre chorin , among others , that a statistical theory of the turbulent steady state should be characterized by a negative temperature ( see ref . @xcite , chapter 4 ) . what is meant is that there is a maxwell - boltzmann probability distribution @xmath9 which , instead of giving more weight to the low energy microstates in the ensemble description of the macrostate , as is usual , gives more weight to high energy microstates . ( this statistical `` temperature '' of turbulence has nothing to do with usual thermodynamic temperature , which is only weakly coupled to the mechanical degrees of freedom of interest . ) let us accept this idea for the moment . the second law says that entropy should increase , or perhaps better , in this more general situation , that information should be lost , in irreversible processes . stated in terms of the free energy @xmath10 ( and remembering @xmath11 ) this says that free energy should _ increase _ in the approach to the steady state . this is opposite to what is usual . putting onsager s idea together with the ideas of burgers turbulence thus requires that mechanical energy should be created in the shock rather than dissipated . we see that the limit in the inviscid burgers equation should be @xmath12 , i.e. , we should imagine the viscosity approaching zero through _ negative _ values , from _ below_. the inviscid burger s equation does not contain temperature or @xmath1 explicitly , of course , but the rules for how the shocks form and interact are now different . the following argument gives the simple idea which is at the heart of this paper . we do not try to give it an elaborate justification , since , like many simple ideas , it may contain some truth even if the arguments are wrong . the argument is that there is a symmetry of the ( general ) burgers equation , @xmath13 we can convert the @xmath14 inviscid burgers equation into the familiar @xmath8 inviscid burgers equation by reversing the signs of @xmath15 and @xmath16 , i.e. , reflecting graphs like fig . 3 through the origin . the result is fig . 4 , in which a single shock has spontaneously split into two , with no reference to initial conditions . this is the fragile property . if shocks can split at any time , as indicated , then the solutions to the differential equation are maximally nonunique . our aim in the previous section was to show that the equations which describe fluid flow , the navier - stokes equations , become maximally nonunique , or `` fragile , '' in some limit . this limit is rather far removed from physical reality , however . one naturally wonders how , if at all , the nonuniqueness property might manifest itself in a real system . the example of laplacian growth encourages one to think that real processes would not completely obscure the underlying `` fragile '' processes @xcite . the system we have imagined is characterized by two temperatures : a `` superhot '' negative temperature , which describes the ensemble of microscopic entities which make up the turbulent state , and the usual temperature , which describes the ensemble at the molecular level . these two ensembles interact only weakly , it has been argued , but , again by the second law of thermodynamics , to the extent that they interact , there must be a flow of energy from the first to the second , from the turbulent ensemble to the molecular ensemble . this picture is reminiscent of the kolmogorov cascade idea ( ref . @xcite , chapter 3 ) , and suggests identifying the turbulent ensemble with the `` energy range , '' ( a hypothetical range in @xmath17 space containing most of the energy ) , and the molecular ensemble with the `` dissipation range , '' ( a range in @xmath17 space , disjoint from the energy range , in which dissipation is important ) , i.e. , assigning a temperature gradient to the kolmogorov picture , with negative temperature at small @xmath17 and positive temperature at large @xmath17 . it is in the energy range , then , at small @xmath17 , that the fragile processes of nonuniqueness would occur . these processes extract mechanical energy from the negative temperature `` bath , '' and this energy must ultimately derive from the forces maintaining the turbulence . thus the onset of fragile processes would appear , on the macroscopic scale , as an increase in resistance to these applied forces . at a more microscopic level it would be the onset of nonuniqueness , allowing splitting and proliferation of microscopic entities as in fig . 4 . at a still more microscopic level , corresponding to the dissipation range , the usual picture would apply , and one would have dissipative processes like fig . 3 . in this view turbulence _ is _ the visible manifestation of nonuniqueness on the intermediate scale of the energy range , and the work done by external forces goes directly into the proliferation of singularities at that scale , and only indirectly into dissipation . in terms of modelling turbulence , it suggests that the proliferative processes of the energy range , which are still hypothetical , may be like the dissipative processes of the dissipation range , but time reversed ( and on a larger length scale ) . in this way the abstract picture suggested here might persist in a more realistic dynamics . the issue of nonuniqueness may also be relevant to cfd modelling of turbulence . the algorithms of differential equation solvers are not set up for equations which do not have unique solutions . experience with laplacian growth confirms that proximity to a nonunique model may indicate trouble for conventional numerical solutions . 99 r. courant and d. hilbert , _ methods of mathematical physics _ , vol 2 ( interscience publishers , 1962 ) . peterson , * phys 62 * , 284 ( 1989 ) . peterson , cond - mat/9710046 . hastings and l.s . levitov , cond - mat/9607021 . burgers , _ the nonlinear diffusion equation _ , ( riedel , dordrecht , 1974 ) . g. strang , _ introduction to applied mathematics _ , ( wellesley - cambridge press , wellesley ma , 1986 ) . chorin , _ vorticity and turbulence _ , ( springer , 1994 ) ." +"over the past decade , the search for sources of ultra - high energy cosmic rays ( uhecrs ) has begun to focus upon small scale anisotropy in event arrival directions . this refers to statistically significant excesses occurring at the scale of @xmath1 . the interest in this sort of anisotropy has largely been fueled by the observations of the akeno giant air shower array ( agasa ) . in 1999 @xcite and again in 2001 @xcite , the agasa collaboration reported observing what eventually became seven clusters ( six `` doublets '' and one `` triplet '' ) with estimated energies above @xmath2 ev . several attempts that have been made to ascertain the significance of these clusters returned chance probabilities of @xmath3 @xcite to 0.08 @xcite . by contrast , the monocular ( and stereo ) analyses that have been presented by the high resolution fly s eye ( hires ) demonstrate that the level of autocorrelation observed in our sample is completely consistent with that expected from background coincidences @xcite . any analysis of hires monocular data needs to take into account that the angular resolution in monocular mode is highly asymmetric . it is very difficult to compare the results of the hires monocular and agasa analyses . they are very different in the way that they measure autocorrelation . differences in the published energy spectra of the two experiments suggest an energy scale difference of 30% @xcite . additionally , the two experiments observe uhecrs in very different ways . the hires experiment has an energy - dependent aperture and an exposure with a seasonal variability @xcite . these differences make it very difficult get an intuitive grasp of what hires should see if the agasa claim of autocorrelation is justified . in order to develop this sort of intuition , we apply the same analysis to both agasa and hires data . the data set that we consider consists of events that were included in the hires - i monocular spectrum measurement @xcite . this set contains 52 events observed between may 1997 and february 2003 with measured energies greater than @xmath0 ev . the data set represents a cumulative exposure of @xmath4 km@xmath5sr@xmath6yr at @xmath7 ev . this data was subject to a number of quality cuts that are detailed in the above - mentioned papers @xcite . we previously verified that this data set was consistent with monte carlo predictions in many ways including impact parameter ( @xmath8 ) distributions @xcite and zenith angle distributions @xcite . for this study , we presumed an average atmospheric clarity @xcite . in order to calculate the autocorrelation function for this subset of data , we must first parameterize the hires - i monocular angular resolution . for a monocular air fluorescence detector , angular resolution consists of two components , the plane of reconstruction , that is the plane in which the shower is observed , and the angle @xmath9 within the plane of reconstruction ( see figure [ figure : picture ] ) . [ cols=""^ "" , ] we can see the result of these simulations . the observed hires - i signal corresponds to the 90% confidence upper limit with the inclusion of only 3.5 doublets beyond random background coincidence . if we repeat this analysis with first , a 7.5% reduction in the estimated angular resolution values and second , a 7.5% increase in the estimated angular resolution values , we obtain a range for the 90% confidence upper limit of @xmath10 $ ] doublets and a range for the 95% confidence upper limit of @xmath11 $ ] doublets . a final area of concern is the systematic uncertainty in the determination of atmospheric clarity . because hourly atmospheric observations are not available for the entire hires - i monocular data set , we have relied upon the use of an average atmospheric profile for the reconstruction of our data @xcite . while different atmospheric conditions have negligible impact on the determination of the arrival direction for events with measured energies this high , differing conditions can have an impact on energy estimation and thus the number of events that are included in our data set . over the @xmath12 error space for our estimation of atmospheric conditions , the total number of events in our data set fluctuates on the interval @xmath13 $ ] . the value of the observable , @xmath14}$ ] , has a fluctuation on the interval @xmath15 $ ] owing to addition and subtraction of events from the data set . note that in neither case does the value of @xmath14}$ ] exceed the mean value ( 0.99250 ) expected for a background set . we conclude that the hires - i monocular detector sees no evidence of clustering in its highest energy events . furthermore , the hires - i monocular data has an intrinsic sensitivity to global autocorrelation such that we can claim at the 90% confidence level that there can be no more than 3.5 doublets above that which would be expected by background coincidence in the hires - i monocular data set above @xmath0 ev . from this result , we can then derive , with a 90% confidence level , that no more than 13% of the observed hires - i events could be sharing common arrival directions . this data set is comparable to the sensitivity of the reported agasa data set if one assumes that there is indeed a 30% energy scale difference between the two experiments . it should be emphasized that this conclusion pertains only to point sources of the sort claimed by the agasa collaboration . furthermore , because a measure of autocorrelation makes no assumption of the underlying astrophysical mechanism that results in clustering phenomena , we can not claim that the hires monocular analysis and the agasa analysis are inconsistent beyond a specified confidence level . this work is supported by us nsf grants phy 9322298 , phy 9321949 , phy 9974537 , phy 0071069 , phy 0098826 , phy 0140688 , phy 0245428 , phy 0307098 by the doe grant fg03 - 92er40732 , and by the australian research council . we gratefully acknowledge the contributions from the technical staffs of our home institutions . we gratefully acknowledge the contributions from the university of utah center for high performance computing . the cooperation of colonels e. fisher and g. harter , the us army and the dugway proving ground staff is appreciated . p. g. tinyakov and i. i. tkachev , jetp lett . * 74 * , 1 ( 2001 ) [ pisma zh . * 74 * , 3 ( 2001 ) ] [ arxiv : astro - ph/0102101 ] . c. b. finley and s. westerhoff , accepted for publication in _ astroparticle physics _ [ arxiv : astro - ph/0309159 ] . r. u. abbasi _ et al . _ [ high resolution fly s eye collaboration ] , phys . lett . * 92 * , 151101 ( 2004 ) [ arxiv : astro - ph/0208243 ] . m. takeda _ et al . _ , phys . lett . * 81 * , 1163 ( 1998 ) [ arxiv : astro - ph/9807193 ] . t. abu - zayyad _ et al . _ [ high resolution fly s eye collaboration ] , submitted for publication in _ astroparticle physics _ [ arxiv : astro - ph/0208301 ] . y. uchihori , m. nagano , m. takeda , m. teshima , j. lloyd - evans and a. a. watson , astropart . * 13 * , 151 ( 2000 ) [ arxiv : astro - ph/9908193 ] . n. w. evans , f. ferrer and s. sarkar , astropart . * 17 * , 319 ( 2002 ) [ arxiv : astro - ph/0103085 ] ." +"interstellar gas in the solar neighborhood has a variety of thermal and chemical phases , including cold atomic gas inside or mixed with cold molecular clouds ( e.g. , sato & fukui 1978 ) , cool and warm atomic gas on the envelopes of molecular clouds ( chromey et al . 1989 ; andersson & wannier 1993 ; wannier et al . 1993 ) and in the diffuse , low density medium ( kulkarni & heiles 1987 ) , cold molecules in dark and dense clouds ( combes 1991 ) and in translucent clouds ( magnani , blitz & mundy 1985 ) , warm molecules in dense clouds near embedded luminous stars ( e.g. , cesaroni et al . 1994 ) , dense photo - ionized gas in the neighborhoods of o and b - type stars , low - density ionized gas between these stars ( walterbos & braun 1994 ; reynolds 1995 ; ferguson et al . 1996 ) , and hot , shock - heated gas near supernovae and windy stars ( ostriker & mckee 1988 ) . there is also considerable variety in the types of molecules that are present inside dark clouds , ranging from primarily h@xmath0 in translucent clouds ( spitzer & jenkins 1975 ; magnani et al . 1998 ) , with a possible trace of pah or long - chain molecules ( leger & puget 1984 ; tulej et al . 1998 ) , to a mixture of complex molecules in dense clouds ( e.g. , langer et al . 1997 ; see reviews by van dishoeck and thaddeus , this conference ) . the thermal and chemical states of the cold and cool gas have such a great variety because the clouds shield themselves to different levels from photodissociative radiation and radiant heating . this makes the molecular abundance and temperature depend on density , column density , metallicity , age , and local radiation field , all of which vary from cloud to cloud and with radius in the galaxy . the nature of cloud _ structure _ does not change this much , because it is largely the result of turbulence , self - gravity , and local explosions , which seem to act the same way everywhere . here we discuss the dominant processes that affect the molecular and thermal states of the gas , and we review the some of the aspects of cloud structure that are likely to arise from turbulence . interstellar clouds shield themselves from photo - dissociative radiation when the molecular formation rate ( in @xmath1 ) integrated over the cloud radius exceeds the molecular dissociation flux ( in @xmath2 ) from incident starlight ( jura 1975 ; federman , glassgold , & kwan 1979 ; van dishoeck & black 1988 ; sternberg 1989 ; hollenbach & tielens 1997 ) . this means that clouds determine their own molecular abundances for any particular radiation field , depending on their density , column density , and metallicity . dense clouds with only moderate column densities can have the same h@xmath0/h ratio as lower density clouds with larger column densities . as a result , _ regions with larger pressures tend to be more molecular _ , i.e. , higher pressures lead to higher densities and greater self - shielding at all cloud masses . one implication of this result is that most galaxies have a radial gradient in the molecular fraction outside the nuclear or barred region because the pressure is lower at larger radii ( elmegreen 1993 ; honma , sofue , & arimoto 1995 ) . the total ( turbulent+magnetic+thermal ) interstellar medium pressure varies approximately as @xmath3 for gas column density @xmath4 and total gas+star column density in the gas layer , @xmath5 . typically , @xmath6 , so @xmath7 . this means that as @xmath4 decreases exponentially with radius in a typical spiral galaxy , the total pressure decreases with radius too , and it has half the scale length . this corresponds to a rather rapid decrease of interstellar pressure with galactocentric radius . radial pressure gradients lead to the appearance of `` molecular rings '' in galaxies that have inner disk cutoffs from a bar or bulge . molecular rings are not true rings , like galactic resonance rings , but only molecular emission concentrations that result from smooth exponential disks with inner cutoffs . the rapid decrease of molecular fraction with increasing radius beyond the `` ring '' results primarily from large - scale pressure changes . high latitude clouds , shells , spiral - arm dust lanes , and other pressurized fronts should also have large molecular fractions compared to other clouds with the same column density . a good example of the influence of pressure on molecule formation is shown by the nearby l1457 cloud , which has h@xmath0 primarily in the southern part , where it was recently compressed ( moriarty - schieven , andersson & wannier 1997 ) . the _ thermal _ state in clouds is generally related to the _ molecular _ state , at least in the solar neighborhood , because once a cloud begins to shield itself in the h@xmath0 lines , it also becomes optically thick from dust . then it removes its principle quiescent heat source , which is the photoejection of electrons off grains ( de jong 1977 ; draine 1978 ; bakes & tielens 1994 ) . molecular clouds need not always be cold , though . different photons are involved with photodissocation , which is limited to spectral lines , and photoejection , which is a continuum process . besides , density and column density can vary separately . consequently , there are warm molecular clouds in the diffuse phase , i.e. , high density , low column - density clouds ( spitzer & cochran 1973 ) . these clouds tend to dominate the diffuse cloud population in the inner ( high pressure ) regions of bright galaxies ( polk et al . 1988 ; honma , sofue , & arimoto 1995 ) . there are also diffuse or dense molecular clouds in the high pressure regions of _ dim _ galaxies that are so cold they do not emit much co radiation ( allen et al . such temperature variations for molecular gas inversely affect the conversion factor from integrated co linewidth to molecular hydrogen . high temperature molecular clouds have proportionally less molecular matter per unit co emission than low temperature molecular clouds . figure [ fig : nn ] shows a schematic diagram of the cold and cool interstellar cloud phases in the parameter space that is defined by density and column density . the rising line that separates diffuse from self - gravitating gas comes from the relation @xmath8 for velocity dispersion @xmath9 . this is the threshold for strong self - gravity in a cloud . the falling line that separates molecular from atomic gas comes from the equation @xmath10 for metallicity @xmath11 and radiation field @xmath12 , normalized to solar neighborhood values . this relation is based on the balance between the h@xmath0 formation rate ( on dust , hence the @xmath11 dependence ) along a column of gas , @xmath13 , and the photodissociation rate per unit area , which is proportional to the absorbed photon flux , @xmath14 . the column density dependence in @xmath15 accounts for extra absorption in the line wings as @xmath16 increases ( federman , glassgold , & kwan 1979 ) . equation [ eq : mole ] was considered in more detail by sternberg ( 1989 ) , who included a temperature dependence for the molecule formation rate and dust extinction . sternberg also approximated the column density dependence of @xmath15 as @xmath17 for pure linewing absorption . according to sternberg , dust dominates molecules for the absorption of light in the shielding layer when @xmath18 , which translates to @xmath19\left[z / z_0\right]\right)^{1/2}}}>>1 . \label{eq : sternberg}\ ] ] ( this assumes sternberg s molecule formation rate , @xmath20 , and dust cross section , @xmath21 , both scale with metallicity , @xmath11 . ) if we scale the federman , glassgold & kwan ( 1979 ) result with @xmath22 instead of @xmath23 and add a @xmath24 dependence to the molecule formation rate ( from the thermal speed at which h atoms impact grains ) , then the equation of detailed balance implied by equation [ eq : mole ] , @xmath25 , gives a molecular column density for self - shielding of @xmath26 , and a corresponding dust opacity @xmath27 . the square root of this opacity is essentially the quantity @xmath28 in sternberg ( 1989 ) , to within a factor of 2 . the column density at this opacity limit is approximately @xmath29 @xmath30 for standard interstellar extinction , which means that points to the right of @xmath31 @xmath30 at high density @xmath32 in figure [ fig : nn ] are primarily shielded by dust , and points to the left are _ self_-shielded by molecules . in both cases , the clouds are molecular , as indicated . low density clouds are generally atomic except at very high column density , at which point they may turn molecular if the conditions are right . however , real clouds with very low densities are not likely to turn molecular at high column density if their spatial extent is so large that they include many field stars inside them . in that case , there is no proper boundary for self - shielding . such clouds will still make a transition from diffuse to self - gravitating at moderate column densities , however . this explains why the largest hi clouds in spiral galaxies can be self - gravitating , and conversely , why the largest self - gravitating clouds are often atomic ( elmegreen & elmegreen 1983 ; 1987 ; rand 1995 ) . figure [ fig : nn ] also suggests that high density clouds are generally molecular , except at very low column density . when the density is high because of a high pressure , molecular clouds can be diffuse . the internal density can also be high in a region with a low ambient pressure provided the cloud is self - gravitating ; this makes the cloud molecular again . in the solar neighborhood , most clouds make a transition from atomic and diffuse at low column density to molecular and self - gravitating at high column density , with relatively little total cloud mass in the form of molecular diffuse gas or atomic self - gravitating gas . however , in the spiral arms of our galaxy , atomic self - gravitating gas is prevalent in the form of giant hi cloud complexes ( @xmath33 m@xmath34 ) , which have relatively small molecular cores ( @xmath35 m@xmath34 ) that are also self - gravitating . such clouds are often regularly spaced along the spiral arms . in other galaxies such as m51 , these @xmath33 m@xmath34 spiral arm clouds are mostly molecular ( rand 1993 ) . this is a sensible result for m51 because it has a relatively high total gas column density , and therefore a high pressure ( @xmath36 ) . figure [ fig : nm ] makes these same points in a different way , showing the densities of diffuse and self - gravitating gas as functions of cloud mass . the larson ( 1981 ) relation between density and mass is used for the self - gravitating clouds . it comes from the two equations @xmath37 and @xmath38 . at low mass , both diffuse and self - gravitating states are possible , as in the usual two - fold solution to the virial equation with external pressure : @xmath39 in this equation , for masses less than @xmath40 , there are stable states with low density and" +"it has long been known that there is an @xmath0 supermultiplet which , with respect to @xmath1 supersymmetry , appears as a combination of one vector and one chiral multiplet @xcite . this supermultiplet is irreducible under @xmath0 supersymmetry and carries vanishing central charge . it is usually referred to as the vector supermultiplet . not long after its introduction , it was realized that there exists a variant , the vector - tensor multiplet , which , under @xmath1 supersymmetry , appears as a combination of one vector and one linear multiplet @xcite . this variant is irreducible under @xmath0 and , in contrast , carries non - vanishing central charge off - shell . on shell it is equivalent to the vector multiplet . this multiplet was originally constructed using component field techniques @xcite , and it and its properties have received little attention . recently , however , within the context of trying to understand the consequences of @xmath0 duality in superstrings , the vector - tensor multiplet has re - emerged . specifically , when heterotic string theory is reduced to an @xmath0 theory in four dimensions the dilaton and the antisymmetric tensor field lie in a vector - tensor multiplet @xcite . it is clear from this work that the vector - tensor supermultiplet is fundamental in heterotic theories and that elucidation of its properties , such as its behavior under duality transformations , is of importance . the coupling of the vector - tensor multiplet to supergravity has also recently been considered @xcite . it was shown that this requires the gauging of the central charge , leading to a chern - simons coupling between the vector - tensor multiplet and a vector multiplet . if one wants to fully understand the complete , off - shell structure of the tensor - vector multiplet , one powerful approach is to construct the appropriate @xmath0 superfield . it is the purpose of this paper to provide such a formulation . much of the interesting structure of the vector - tensor multiplet appears in its couplings to other multiplets @xcite . here , however , we will restrict ourselves to a superfield formulation of the free abelian case , leaving interacting generalization to future publications . since the vector - tensor supermultiplet has non - zero central charge , it is necessary to expand the usual superspace . the maximal central extension of the @xmath0 superalgebra has two central charges . consequently the corresponding superspace has two extra bosonic coordinates @xcite . working in this superspace , one can introduce superfields and covariant constraints . following the geometrical formulation of supergauge fields , we introduce a super - connection and the associated curvature . we then introduce the appropriate constraints , solve the bianchi identities and show how the component fields of the tensor - vector multiplet emerge . using superspace techniques we rederive the supersymmetry and central charge transformations and , after showing that there exist a lagrangian superfield in central charge superspace , the higher components of which are all total derivatives , we give the superfield and component actions . the existence of a superfield lagrangian is an example of a central - charge generalization of the superactions described in @xcite . it suggests that there is an even - dimensional submanifold of the central charge superspace naturally associated with the vector - tensor multiplet . central charge superspace has recently also been considered in @xcite and used to rederive the usual gauge supermultiplet . also , we want to point out that there is a strong relationship between the theory of @xmath1 supersymmetry in six dimensions and four - dimensional , @xmath0 central charge superspace . indeed , the superfield equations of motion in the six - dimensional theory motivated the choice of one important constraint equation in four - dimensional central charge superspace . in this sense , our constraint can be understood as a superfield realization of the dimensional reduction by legendre transformation discussed in @xcite . we start by briefly recapitulating the relevant formulae of @xmath0 superspace . throughout the paper we will use the conventions of @xcite . the @xmath0 supersymmetry algebra is obtained from the poincar algebra by adding four fermionic operators @xmath2 ( @xmath3 and @xmath4 ) and their anti - hermitian conjugates @xmath5 . moreover the algebra admits one complex `` central charge '' @xmath6 where @xmath7 and @xmath8 are hermitian . these operators satisfy the following anticommutation relations : @xmath9 where @xmath10 are the four - momenta and @xmath11 . the automorphism group of algebra is @xmath12 where the @xmath13 acts on the @xmath14 index in @xmath2 . the antisymmetric tensor @xmath15 with @xmath16 provides an invariant metric for raising and lowering the @xmath13 indices by @xmath17 and @xmath18 . @xmath0 superspace is a space with coordinates @xmath19 where @xmath20 , @xmath21 , and @xmath22 are commuting bosonic coordinates while @xmath23 and @xmath24 are anticommuting fermionic coordinates . a superfield @xmath25 is a function of the superspace coordinates , @xmath26 . taylor - series expansion of a general superfield @xmath25 in the @xmath27 coordinates terminates after a finite number of terms due to the anticommuting nature of @xmath27 . on the other hand , the expansion in @xmath21 and @xmath28 never ends . this means there are an infinite number of component fields ( functions of the spacetime coordinates @xmath20 ) in a general superfield . this infinite number of component fields can be reduced to a finite number either off - shell , by applying appropriate constraints , or on - shell , by choosing equations of motion which propagate only a finite number of component fields . translations in the superspace are generated by the supercovariant differential operators @xmath29 , @xmath30 , @xmath31 , and @xmath32 where @xmath33 . it is straightforward to compute the anticommutation relations for these operators . they are @xmath34 by construction @xmath35 and @xmath36 anticommute with @xmath37 and @xmath38 and so can be used to impose supersymmetric covariant conditions on superfields . the supervielbein @xmath39 of the @xmath0 superspace is defined as the matrix that relates the supercovariant derivatives @xmath40 and the ordinary partial derivatives @xmath41 the matrix @xmath42 is the inverse of @xmath39 . these two matrices define the geometry of the @xmath0 superspace . the torsion @xmath43 is defined as the exterior derivative of the supervielbein one - form @xmath44 , @xmath45 the non - vanishing components of the torsion are found to be @xmath46 in this section we give a geometrical superfield formulation of the vector - tensor multiplet . we begin by considering the usual geometrical form of super - gauge theory , though in superspace with central charge . we then find a suitable set of constraints on the superfield strength to reproduce the field content of the vector - tensor multiplet . restricting our attention to abelian gauge theories , let us introduce a hermitian connection @xmath47 . the hermiticity of the connection implies @xmath48 where @xmath49 is real , @xmath50 , and @xmath51 . the curvature two - form is defined as @xmath52 the coefficient functions @xmath53 comprise thirteen lorentz - covariant types . the ones that contain torsion terms are given by @xmath54 the curvature tensor @xmath55 is subject to the bianchi identities @xmath56 or equivalently @xmath57 each tensor component of the curvature tensor is an @xmath0 superfield which , in turn , has an infinite number of component fields . all but a finite number of these component fields must be eliminated by virtue of appropriate constraints . these constraints must be lorentz , gauge , and supersymmetric covariant . it is natural to adopt a set of constraints which set the pure spinorial part of the curvature tensor to zero . that is @xmath58 before imposing further conditions we would like to explore the consequences of . to do so we must solve the bianchi identities subject to these constraints . the result is that all the components of the curvature tensor @xmath59 are determined in terms of a single superfield @xmath60 and its hermitian conjugate @xmath61 . henceforth , we denote these superfields by @xmath62 and @xmath63 . in particular @xmath64 and @xmath65 furthermore , @xmath62 is constrained to satisfy @xmath66 } = - \epsilon^{\dot\alpha\dot\beta } \bar d_{\dot\alpha}^{[i } \bar w_{\dot\beta}^{j ] } , \label{3 } \\ & \epsilon^{\alpha\beta } d_\alpha^{(i } w_\beta^{j ) } = \epsilon^{\dot\alpha\dot\beta } \bar d_{\dot\alpha}^{(i } \bar w_{\dot\beta}^{j)}. \label{4}\end{aligned}\ ] ] let us explore the consequences of on the field content of @xmath62 . the expansion of @xmath62 in the anti - commuting coordinates has the general form @xmath67 it is obvious that conditions will not impose any restriction on @xmath68 . first we consider the implications of the lowest component of superfield constraints . condition implies that @xmath69 where @xmath70 and @xmath71 . conditions and further implies the reality condition @xmath72 and @xmath73 where @xmath74 . condition yields @xmath75 higher components of the superfield constraint imply further conditions on the fields @xmath76 , @xmath77 , and @xmath78 . one way to realize these conditions is to note that , from equations , , and , @xmath79 where @xmath80 and @xmath81 . the equations are the general solution of the bianchi identities subject to our constraints . three of the bianchi identities they satisfy are @xmath82 taking the lowest component of equation gives rise to @xmath83 so that @xmath84 is the field strength of a gauge field @xmath85 . that is @xmath86 the lowest components of and give @xmath87 } & = - \tfrac12 ( \partial_z + \partial_{\bar z } ) \mathscript f_{ab } , \\ \partial_{[a } h^i_{b ] } & = - \tfrac12 i ( \partial_z-\partial_{\bar z } ) \mathscript f_{ab } , \label{h1 } \\ \partial_a d & = - \tfrac14 i \left\ { ( \partial_z-\partial_{\bar z } ) h_a^r + i ( \partial_z + \partial_{\bar z } ) h_a^i \right\ } , \label{temp11}\end{aligned}\ ] ] where @xmath88 . this is as far as we can go using solely the constraints . so far we have the following component fields : an @xmath13 doublet of spinors @xmath89 , a real gauge field @xmath85 , a complex vector field @xmath90 , a real scalar @xmath78 and a real @xmath13 triplet of scalars @xmath91 . we would like to impose further constraints to reduce the number of fields to an irreducible multiplet . as we will show very shortly , it is possible to impose further constraints to ensure that the real and imaginary parts of @xmath90 are each field strengths , one of an anti - symmetric tensor and the other of a scalar . what about the fields @xmath78 and @xmath91 ? we will find that @xmath78 and @xmath91 play the role of auxiliary fields . note that the usual @xmath0 gauge multiplet has a triplet of auxiliary fields . hence , if we want to derive the usual gauge multiplet we are led to set @xmath78 to zero by promoting the constraint to the stronger one @xmath92 } = 0 , \qquad \epsilon^{\dot\alpha\dot\beta } \bar d_{\dot\alpha}^{[i } \bar w_{\dot\beta}^{j ] } = 0.\ ] ] on the other hand , if we want to derive the vector - tensor multiplet , which has a single auxiliary field , we must eliminate @xmath91 . this can be achieved by promoting condition to the stronger condition @xmath93 henceforth , we add condition as a further constraint on the theory . now let us proceed using conditions as well as the stronger version of , constraint . apart from eliminating @xmath91 , it can be shown that the consequences of imposing are @xmath94 we note that the conditions obtained so far on @xmath90 given in and are not sufficient to render the real and imaginary components of @xmath90 as field strengths . we would like , therefore , to impose yet another , and final , constraint that will achieve" +"the statistical toolkit @xcite was originally conceived as a statistical data analysis toolkit for the problem of comparing data distributions . its development follows the unified software development process @xcite . according to this approach , the life - cycle of the software is iterative - incremental , every iteration representing an evolution , an improvement , an extension in comparison with the previous one . iterations in the statistical toolkit development process are driven by the needs of its experimental applications ; practical use cases steer the implementations of new tests . the first development cycles of the statistical toolkit implemented a set of goodness - of - fit ( gof ) tests for the two - sample problem , i.e. for the comparison of two distributions . these developments were motivated by experimental requirements for regression testing , validation of simulation with respect to experimental data , comparison of expected versus reconstructed distributions , and more in general for the comparison of data from different sources . new requirements have been identified , based on the experience of using the statistical toolkit in several analyses for the validation of geant4 physics models . these projects highlighted the need for complementary functionality , beyond the problem of assessing the compatibility of two distributions . one of the problems faced in simulation validation ( and , more in general , in the comparison of experimental distributions ) , consists in the identification of possible systematic effects : tests of randomness address this requirement . another problem encountered in the experience with the simulation validation consists of the comparison not only of individual data distributions , but also of categories ( e.g. the evaluation of differences in the behaviour of two geant4 physics models with respect to a set of experimental test cases ) . goodness - of - fit tests quantify the compatibility of the agreement between a set of sample observations and the the corresponding values predicted from some model of interest , or between two ( or more ) sets of observations . the result of a goodness - of - fit test is expressed through a @xmath0-value , which represents the probability that the test statistic has a value at least as extreme as that observed , assuming the null hypothesis is true . the collection of tests implemented in the current version of the statistical toolkit is given in table [ old_tests ] ; extensive details can be found in @xcite . lll gof test & distribution type & ` < comparisonalgorithm > ` class + & & ` andersondarlingbinned ` + & & ` andersondarlingbinnedapproximated ` + & & ` andersondarlingunbinned ` + & & ` andersondarlingunbinnedapproximated ` + & & ` chi2 ` + & & ` chi2approximated ` + & & ` chi2integrating ` + & ` binned ` & ` cramervonmisesbinned ` + & ` unbinned ` & ` cramervonmisesunbinned ` + & ` unbinned ` & ` weightedcramervonmisesbuningunbinned ` + girone & ` unbinned ` & ` girone ` + goodman & ` unbinned ` & ` kolmogorovsmirnovapproximated ` + & & ` kolmogorovsmirnov ` + & & ` weightedadkolmogorovsmirnov ` + & & ` weightedbuningkolmogorovsmirnov ` + kuiper & ` unbinned ` & ` kuiper ` + & ` binned ` & ` tikubinned ` + & ` unbinned ` & ` tikuunbinned ` + watson & ` unbinned ` & ` watson ` + an effort has been invested to provide an effective software development environment , which exploits more modern tools and facilitates the use of the statistical toolkit in a variety of computing environments . for the new development cycle subversion ( svn ) @xcite has been selected as a tool in support of the configuration and change management discipline . the statistical toolkit code was moved to a svn repository . in order to facilitate using the statistical toolkit on a wide variety of operating systems , the build system has been moved to the cross platform make ( cmake ) @xcite system . the ` ctest ` testing tool , distributed as a part of cmake , is used for unit testing . to be as self - consistent as possible , the number of dependencies on external software systems has been minimized . the only essential external dependency is on the gnu scientific library @xcite . an additional user layer was implemented to facilitate the use of the statistical toolkit in analysis environment that are concerned neither with aida @xcite nor with root @xcite analysis objects , which are supported by the two user layers available in the current version . the new user layer allows the analyst to supply input data to the statistical toolkit in the form of comma - separated lists of values ( csv ascii files ) . if no external dependencies are specified , this user layer is built by default . otherwise , in properly set - up environments aida or root ( or both ) are found by ` cmake`and the corresponding user layer is built automatically . the statistical toolkit comes with an extensive set of ` unittests ` , which are meant to test the correct implementation of the statistical tests for each new version of the statistical toolkit . the new development cycle extends the functionality of the statistical toolkit with tests for randomness , one sample goodness - of - fit tests , i.e. comparing data to reference functions , and tests for categorical data . table [ new_tests ] lists the new tests . lll test & input data & class name + wald - wolfowitz & sequence of & ` waldwolfowitztwosamplesrunstest ` + runs test & signs ( -1/1 ) & ` waldwolfowitzonesamplerunstest ` + wald - wolfowitz & 1-dimensional & ` waldwolfowitzonesamplerandomnesstest ` + test of randomness & distribution & + mann - whitney @xmath1 test & 1-dimensional & ` mannwhitneytwosamplestest ` + & distribution & + fisher s exact test & @xmath2 matrix & ` fishersexact2x2test ` + @xmath3 contingency test & @xmath4 matrix & ` chi2contingencytabletest ` + @xmath3 paired test & paired values & ` chi2curvescomparisonalgorithm ` + randomness tests provide complementary information to the existing goodness of fit tests ( table [ old_tests ] ) : for instance , tests for randomness can highlight the presence of systematic effects in the distributions subject to comparison , which goodness of fit tests can not detect . a use case is illustrated in @xcite : goodness of fit tests confirm the compatibility of various geant4 proton elastic scattering models respect to reference data , nevertheless asymmetries in the distribution of differences between the results of the simulation and reference data hint to the presence of systematic effects associated with some of the geant4 physics models . the runs tests are statistical tests , used to test the hypothesis that the elements of the sequence are mutually independent or whether the data have some pattern . a run is defined as a series of values of the same type ( e.g. series of increasing / decreasing values , series of true / false values , etc ) , the number of consequent values of the same type being the length of the run . as an example consider tossing a coin and noting the outcome , which is either head ( @xmath5 ) or tail ( @xmath6 ) . a run in this example is each sequence of the same type of outcome . both too many runs ( as in case of cyclic pattern @xmath7 , which has the maximum possible number of runs for given number of observations ) and too few runs ( where heads and tails are clustered together @xmath8 ) exhibit evidence of a non - random relationship between the order of the experiments and the outcome . the wald - wolfowitz test from @xcite is the best known test that is based on the number of runs . it has been proposed as a test of whether two samples are from the same population , but as such has poor power @xcite and the mann - whitney test is preferable . the new version of the statistical toolkit ( to be released ) encompasses implementations of the the wald - wolfowitz runs test for one or two samples . when the test is used with two samples , the algorithm in @xcite is used to construct one ( binary ) sample , and results from the test for one sample are returned . to calculate the @xmath0-values , either the exact or an approximated formula can be used . the exact calculation of the two - tailed probability of the test statistics implemented in the statistical toolkit follows the description from @xcite , while the approximated formula takes into account that for large samples the distribution of the number of runs approaches a normal distribution . wilcoxon @xcite published a test for comparison of two samples , based on comparison of the general size of the two samples , ranking of the ( combined ) samples and then comparing the average ranks of separate ranks . the developments of the test followed fast and the first to publish it were mann and whitney @xcite . the new version of the statistical toolkit implements the mann - whitney @xmath1 test and an approximated formula for the @xmath0-value calculation , again assuming that the samples are large , hence the distribution of the ranks can be described with a normal distribution . categorical data analysis involves testing the significance of the association ( contingency ) between the groups . in practice the number of categories is usually small ( below 20 ) , although in principle the tests for categorical data could be used for any number of groups . the difference between the observed and the expected data , considering the given marginal and the assumptions of the model of independence , can be calculated using the @xmath3 test ( already available in the statistical toolkit ) ; however , the @xmath3 test gives only an estimate of the true probability value . the estimate might be inaccurate in case the marginal is very uneven or if there is a small value ( less than five ) in one of the cells of the contingency table . fisher s exact test for contingency tables @xcite is most widely known exact test for categorical data analysis . it is calculated by generating all tables that are more extreme than the table given by the user . to get the two - tailed @xmath0-value , the @xmath0-values of the tables that have @xmath0-values of the same size or smaller than the data table probability are added up to form the cumulative @xmath0-value , including the @xmath0-value of the data table itself . this method becomes computationally intensive already for moderately sized tables , since the number of table probabilities to be enumerated can easily reach billions . fisher s exact test for @xmath2 contingency tables is available in the new development version of the statistical toolkit . an algorithm to calculate the @xmath3 test with yates continuity correction has also been implemented as part of the new development cycle . the @xmath3 tests can be applied to general ( @xmath4 ) contingency tables , while due to computational reasons fisher s exact test is only implemented for @xmath9 tables . the new development cycle of the statistical toolkit comes with a more versatile build system and provides the user significant extensions in testing capabilities . the new tests extend the statistical toolkit capabilities with tests for randomness and tests for categorical data analysis . the new user layer component makes it possible to use the toolkit with many spreadsheet applications that allow exporting data directly to comma separated list of values . new tests , together with the new user layer , make the statistical toolkit" +"cognitive radio ( cr ) has been an important research area for its superiority in spectrum efficiency . generally , there are two categories in cr transmissions : underlay and overlay . in the underlay mode , the primary users ( pus ) and the secondary users ( sus ) can transmit in the same spectrum simultaneously with the guarantee that the sus transmissions should not affect the pus to a certain extent ( e.g. , the interference - signal - ratio at the pus should not exceed some constant ) . in the overlay mode , the sus sense the spectrum holes that the pus do not utilize periodically , and then transmit through these holes . recently , green ( i.e. , energy - saving and co2 emission reduction ) transmission becomes a vital consideration in communications system design due to severe energy shortage and environmental problems . under this circumstances , renewable energy , e.g. , solar , has been introduced into wireless communications . renewable energy or energy harvestingaided wireless communications becomes a hot research topic@xcite-@xcite . especially , the renewable energy aided cr network gains much interest because of its assemblage of spectrum efficiency and green energy advantages ( e.g. , eco - efficiency and potential energy - efficiency)@xcite . in @xcite , an upper bound on the theoretical achievable throughput of energy harvesting su has been obtained under overlay mode . in @xcite , the harvesting - sensing - throughput tradeoff is investigated for energy harvesting cr . an optimal single - slot spectrum sensing strategy for throughput optimization has been proposed . in @xcite , a hybrid underlay - overlay cognitive radio with energy harvesting is considered , and an access strategy for maximizing the long - term throughput of the system is derived by applying the partially observable markov decision process framework . in @xcite , a renewable energy aided cooperative cr system , where su receives unsuccessful packets transmitted by pu and relays them to pu rx , is considered . the stable throughput region is analyzed . in @xcite , the robust optimization is performed for energy harvesting cr with the channel and energy harvesting uncertainties . in the paper , we investigate a renewable energy powered cr , where a pu shares spectrum with an su . the pu transmits with constant power . the su transmitter ( tx ) is equipped with an energy harvester ( e.g. , a photovoltaic ) , and the harvested renewable energy is stored in a battery before usage . the generated data from application layer of the su tx is stored in a first - in - first - out ( fifo ) data buffer . in each transmission slot , the su tx allocates the stored renewable energy for transmitting some data to the su rx . to guarantee the pu s transmission qos , the isr at the pu rx should be less than a threshold ( i.e. , the su tx s transmitting power is constrained in each slot ) . as delay is an important qos merit ( delay - sensitive traffic such as the video increases sharply in wide - spectrum wireless networks , e.g. , lte networks ) , we focus on the average buffer delay minimization by scheduling the allocated renewable energy in each slot . accordingly , a constrained stochastic optimization problem is formulated . next , we analyze the constraints : in each slot , the allocated power , the transmitted data , and the pu s isr should not extend the corresponding battery power , the corresponding buffer data , and the isr threshold , respectively . based on activity of the constraints , we propose two algorithms . when the renewable energy constraint is inactive ( the data constraint or the isr constraint is active ) in all slots , we propose the optimal greedy algorithm . when the renewable energy constraint is active in all slots , we propose an optimal power re - allocation algorithm . generally , the two algorithms give the upper bound and lower bound , respectively . additionally , we explore the case that the pu s private information ( e.g. , the pu s channel gain ) is not accessible by the su . consider a cr network , where a pu co - exits with an su . slotted - time model is utilized in the paper , and each slot is with length @xmath0 . the channel power gains for pu tx @xmath1 pu rx , pu tx @xmath1 su rx , su tx @xmath1 su rx , and su tx @xmath1 pu rx during the @xmath2-th slot are denoted as @xmath3 $ ] , @xmath4 $ ] , @xmath5 $ ] , and @xmath6 $ ] , respectively . the pu transmits with a fixed power @xmath7 . the su tx is connected with a renewable energy harvester . the harvested renewable energy is stored in a battery before usage . the data are generated randomly in the application layer of the su tx , and wait in an fifo data buffer . in each slot , some data in the buffer are transmitted to the su rx . denote the transmitting power of su in the @xmath2-th slot as @xmath8 $ ] . to guarantee the pu s transmission , the interference - signal - ratio ( isr ) at the pu rx should be less than a given constant , @xmath9 , i.e. , @xmath10g_{21}[n]}{p_0 g_{11}[n]}\le \rho , \forall n.\end{aligned}\ ] ] let @xmath11 $ ] be the arrived renewable energy at the end of the @xmath2-th slot ( harvested renewable energy during the @xmath2-th slot ) . denote @xmath12 $ ] as the stored energy in the battery at the beginning of the @xmath2-th slot . assume that the battery capacity is large enough , we have @xmath13=e[n]-p[n]\tau+e_a[n]\end{aligned}\ ] ] assume that the additive white gaussian noise at the pu rx is with zero mean and variance @xmath14 . denote the transmitted data number ( in bit ) during the @xmath2-th slot as @xmath15 $ ] , then @xmath16=\log \big[\frac{p[n]g_{22}[n]}{p_0g_{12}[n]+n_0}+1\big]\end{aligned}\ ] ] denote the data buffer length at the beginning of @xmath2-th slot as @xmath17 $ ] , the arrived data at the end of the @xmath2-th slot ( generated data from application layer during the @xmath2-th slot ) as @xmath18 $ ] . we have @xmath19=q[n]-r[n]+d_a[n]\end{aligned}\ ] ] the objective is to minimize the average buffer delay over @xmath20 slots under the isr constraint by scheduling the renewable allocation in each slot @xmath21\right\}_{i=1}^{n}$ ] . accordingly , we have the following problem . @xmath22\right\}_{n=1}^{n } } \frac{1}{n}\sum\limits_{n = 1}^{n+1 } q[n]\end{aligned}\ ] ] ( [ isr constraint]),[isr constraint inproblem ] + 0p[n]e[n ] , n,[renewable constraint ] + 0r[n]q[n ] , n[rate constraint ] where ( [ isr constraint inproblem ] ) is the isr constraint , ( [ renewable constraint ] ) denotes the renewable energy constraint , and ( [ rate constraint ] ) is the rate constraint in each slot . in this section , the constraints in the formulated problem are analyzed . and two optimal algorithms ( referred to as the greedy algorithm and the pa algorithm ) for special scenarios are proposed thereafter . moreover , the two algorithms give the upper bound and lower bound respectively . although the bounds are not the exact solution , they give an important insight into the performance gap . the three constraints in ( [ optimization problem ] ) can be merged as$ ] is the function of the optimizing variable @xmath8 $ ] . ] @xmath23}\nonumber\\ & \le & \min\bigg\{\frac{e[n]}{\tau},\frac{\rho p_0 g_{11}[n]}{g_{21}[n]},\big(e^{q[n]}-1\big)\frac{p_0g_{12}[n]+n_0}{g_{22}[n]}\bigg\ } \nonumber\\ \\ & : = & \mathcal{c}[n]\end{aligned}\ ] ] _ remark : ( [ merged constraint ] ) reveals that the renewable energy constraint , the isr constraint , and the rate constraint can be equivalently transformed to three value - constraints on the allocated power in a slot . thus , in a slot , only one constraint among the three constraints is active . _ consequently , the su solves the following optimization problem to get the optimal renewable allocation . @xmath24\right\}_{i=1}^{n } } \frac{1}{n}\sum\limits_{i = 1}^{n+1 } q[i]\end{aligned}\ ] ] @xmath25\le \mathcal{c}[n ] , \forall n.\end{aligned}\ ] ] intuitively , we try to transmit as much data as possible , in one slot , so as to minimize the data queue length in data buffer . more data transmission corresponds to more renewable allocation . that is to say , allocate renewable as much as possible in each slot ( referred to as greedy renewable allocation ) is optimal for minimizing instant data queue length in a slot . formally , the greedy renewable allocation can be expressed as @xmath26=\mathcal{c}[n]\end{aligned}\ ] ] for @xmath27 then there is a natural question__is the greedy renewable allocation optimal over several slots in average sense?is the greedy renewable allocation optimal for the formulated problem ? _ _ with respect to the optimality of the greedy allocation , we have the following lemma . generally , the greedy renewable allocation is not optimal . when the renewable generation process , the data arrival process , and channel state variation are markov processes , the formulated problem ( [ optimization problem when private available ] ) corresponds to @xmath28 of lemma 10 in @xcite . thus , the greedy renewable allocation is not optimal in this case . thereafter , we arrive at the lemma . _ remark : although not optimal , the greedy renewable allocation is practically useful since its on - line feature and low - complexity . in addition , as the greedy allocation is a feasible solution of ( [ optimization problem when private available ] ) , it gives an upper bound of the optimal data queue length . _ the greedy renewable allocation is optimal in special circumstances . the following lemma characterizes the scenarios that greedy allocation is optimal . if @xmath29}{\tau}\ge \min\big\{\frac{\rho p_0 g_{11}[n]}{g_{21}[n]},\big(e^{q[n]}-1\big)\frac{p_0g_{12}[n]+n_0}{g_{22}[n]}\big\}\end{aligned}\ ] ] for @xmath30 , the greedy renewable allocation is optimal for ( [ optimization problem when private available ] ) . when ( [ sufficient condition for optimality of greedy ] ) holds , the constraint ( [ merged constraint ] ) can be reduced as @xmath31\le \min\big\{\frac{\rho p_0 g_{11}[n]}{g_{21}[n]},\big(e^{q[n]}-1\big)\frac{p_0g_{12}[n]+n_0}{g_{22}[n]}\big\}.\end{aligned}\ ] ] define @xmath32:=\log \big[\frac{\rho p_0 g_{11}[n]}{g_{21}[n]}\frac{g_{22}[n]}{p_0g_{12}[n]+n_0}+1\big].\ ] ] ( [ 1 ] ) is equivalent to @xmath15\le \min\big\{q[n],r_s[n]\big\}$ ] . ( [ optimization problem when private available ] ) becomes @xmath33\right\}_{i=1}^{n } } \frac{1}{n}\sum\limits_{i = 1}^{n+1 } q[i]\end{aligned}\ ] ] @xmath34\le \min\big\{q[n],r_s[n]\big\}.\end{aligned}\ ] ] the optimal solution is @xmath35=\min\big\{q[n],r_s[n]\big\};\ ] ] on the other hand , if ( [ sufficient condition for optimality of greedy ] ) is satisfied , the greedy renewable allocation becomes @xmath8=\min\big\{\frac{\rho p_0 g_{11}[n]}{g_{21}[n]},\big(e^{q[n]}-1\big)\frac{p_0g_{12}[n]+n_0}{g_{22}[n]}\big\}$ ] or @xmath15= \min\big\{q[n],r_s[n]\big\}$ ] equivalently . hence we reach the lemma . _ remark : ( [ sufficient condition for optimality of greedy ] ) gives a sufficient condition for the optimality of the greedy renewable allocation . it is a strong condition since ( [ sufficient condition for optimality of greedy ] ) should be satisfied for arbitrary @xmath36 $ ] . _ _ remark : @xmath37}{\tau}\ge \big(e^{q[n]}-1\big)\frac{p_0g_{12}[n]+n_0}{g_{22}[n]}$ ] means that the renewable energy is enough for emptying the data buffer in each slot . @xmath37}{\tau}\ge \frac{\rho p_0 g_{11}[n]}{g_{21}[n]}$ ] demonstrates that the available renewable energy is more than the isr upper bound on the su s transmitting power in each slot . alternatively , ( [ sufficient condition for optimality of greedy ] ) means that the renewable energy constraint is inactive in all slots . in either case , the greedy policy that transmits as much data as possible in each slot is optimal in average sense over slots . _ since @xmath17=q[1]+\sum\limits_{j=1}^{n-1}\big(d_a[j]-r[j]\big)$ ] , we have @xmath38=nq[1]+\sum\limits_{n = 1}^{n+1}\sum\limits_{j = 1}^{n-1}d_a[j]-\sum\limits_{n = 1}^{n+1}\sum\limits_{j = 1}^{n-1}r[j].\ ] ] then ( [ optimization problem when private" +"the origin of cosmic rays is an unsolved problem since the discovery in 1912 . the spectrum of cosmic rays has a break at the knee energy ( @xmath4 ev ) , and those below the knee energy are believed to have galactic origin . recently , the high energy stereoscopic system ( h.e.s.s . ) found more than 50 sources on the galactic plane in the very high energy ( vhe ; @xmath5 gev ) gamma - ray band ( @xcite ; @xcite ) . because vhe gamma - rays are produced either through inverse compton scattering of low energy photons by relativistic electrons , or through the decay of pions produced by collisions of relativistic protons with interstellar medium , high energy particles are surely present in the vhe gamma - ray sources . if relativistic electrons are present , they may be traced through the observations of synchrotron x - ray emission . however , in spite of extensive x - ray followup observations , a non - negligible fraction of the galactic vhe gamma - ray sources do not have an x - ray counterpart , and they are referred to as unidentified ( unid ) sources ( e.g. , @xcite ) . among identified galactic vhe gamma - ray sources , pulsar wind nebulae ( pwne ) represent the largest population @xcite . accordingly , one would expect that pwne are the first candidate of the origin of the unid vhe gamma - ray sources . however , identifying the vhe gamma - ray sources as pwne is not straightforward . the vhe gamma - ray emission region sometimes shows significant spatial offset from the x - ray emission region or a pulsar ( e.g. , @xcite ) . furthermore , the life time of x - ray emitting electrons through synchrotron emission may be shorter than that of vhe gamma - ray emitting electrons through compton scattering . this means that x - ray emission from the pwne can be much dimmer than the vhe gamma - rays if the pwne are old . finally , a pulsar is not always found in the vicinity of ( candidate ) pwne . hess j1427608 is one of the unid vhe gamma - ray sources located at @xmath6 @xcite , and is extended with @xmath7 . the flux is @xmath8 in the 110 tev band with a photon index of @xmath9 @xcite . no plausible counterpart is listed in the galactic supernova remnant ( snr ) catalog @xcite or in the simbad data base in the vicinity of hess j1427608 . we also looked for a possible counterpart in the atnf pulsar catalog @xcite . however , no energetic pulsar was found within from hess j1427608 . here , the definition of the energetic pulsar is those with @xmath10 erg s@xmath11 kpc@xmath12 , where @xmath13 is the spin - down energy and @xmath14 is the distance to the source . this search radius of is large enough compared to offsets of radio pulsars to vhe sources among known pwn systems , and virtually excludes the possibility of associating hess j1427608 with any known energetic radio pulsar . thus , hess j1427608 seems to be one of the most `` unlikely '' pwne among the vhe gamma - ray sources . in order to search for an x - ray counterpart , we observed hess j1427608 with suzaku , and also analyzed the xmm - newton archive data . we observed the sky region including hess j1427608 with suzaku ( @xcite ) from 2010 january 13 through 16 . the journal of the observation is listed in table [ tab : obslog ] . suzaku is equipped with two types of detectors : four sets of x - ray imaging spectrometers ( xis0xis3 : @xcite ) and a non - imaging hard x - ray detector ( hxd : @xcite ; @xcite ) . xis1 uses the back - illuminated ( bi ) ccd while the others the front - illuminated ( fi ) ccds . among the four sensors , xis2 is not operational and a part of xis0 ( corresponding to the off - source region in the latter analysis ) is not usable due to its anomaly . hereafter , unless otherwise mentioned , we used only xis1 and xis3 data for the current analysis . xis was operated in normal clocking mode without any window options . spaced - row charge injection ( @xcite ; @xcite ) was used to reduce the effects of radiation damage . we used version 2.4.12.27 of the processed data for hess j1427608 . the data was analyzed with the headas software version 6.10 and xspec version 12.6.0 . we used the cleaned event file created by the suzaku team . the resultant effective exposure was 104 ks . figure 1 shows xis images in the soft ( 0.52 kev ) and the hard ( 28 kev ) bands . the images were corrected for exposure using an exposure map generated by the ftool xisexpmapgen after subtracting non x - ray background ( nxb ) images generated by the ftool xisnxbgen @xcite . finally , the xis1 and xis3 images were added , and the resulting image was binned to a pixel size of and smoothed with a gaussian of @xmath15 . the position center and the extent of hess j1427608 are shown as a black cross and a yellow dashed circle , respectively . a few faint , point - like sources are seen in the soft band , while an apparently extended source is detected in the hard band . the position and apparent extension of the hard source match those of hess j1427608 . as will be shown in a later section , all the suzaku soft - band sources may be explained by the point - like sources in the xmm - newton archive data while the suzaku hard - band source seems to be a truly new source . we thus designate the central hard - band source suzaku j14276051 , and mainly focus on this source in the following analysis . because hess j1427608 and suzaku j14276051 are both extended , we evaluate the x - ray size of the source . for this purpose , careful estimation of the x - ray background is necessary since suzaku j14276051 is relatively faint . in particular , this region contains significant contribution from the galactic ridge x - ray emission ( grxe ) as well as the cosmic x - ray background ( cxb ) , both of which are subject to mirror vignetting effect resulting in a centrally - peaked spatial distribution . therefore , it is not appropriate to assume a flat background image defined at an off - source region within the field of view ( fov ) . instead , we estimated the grxe+cxb image in the source region through monte - carlo simulation . we explain details of the x - ray background estimation below . first , we estimated the surface brightness of the grxe and cxb assuming their uniform distribution in the sky . for this purpose , we analyzed the x - ray spectrum in the off - source annulus region shown in figure [ fig : xisspecreg ] . the region ( between and from the center of suzaku j14276051 ) was selected to minimize contamination from suzaku j14276051 . in other words , the off - source region contains only the grxe and the cxb after the subtraction of nxb . figure [ fig : xisanuspec ] shows the spectra extracted from the off - source region . the spectra were modeled by optically thin thermal three temperature plasma with neutral iron emission line plus the cxb following @xcite . in the course of model fitting , the hydrogen column density was fixed to @xmath16 determined by hi observations ( @xcite ) , the photon index of the cxb to 1.4 , and the surface brightness of the cxb to @xmath17 in the 210 kev band ( @xcite ) . we made the ancillary response file using the ftool xissimarfgen assuming a uniform emission in the sky . the model could reproduce the observed spectrum well . the best - fit parameters are listed in table [ tab : xisanuspec ] . next , we simulated the grxe+cxb event data assuming uniform emission with the best - fit spectrum model determined above using the ftool xissim @xcite . in order to avoid an extra ambiguity due to poor statistics , the exposure time for the simulation was set to 500 ks . then we extracted the grxe+cxb spectrum in the source region and added it to the nxb in the source region to obtain the total background spectrum , following the instruction in section 5.5.2 of the suzaku technical description . figure [ fig : xisspeccomp ] shows the simulated background spectra of the xis1 and xis3 respectively as well as the source and off - source spectra . as can be seen from the spectra , the source region contains significant emission above the grxe+cxb level . figure [ fig : xisprof ] shows the radial profiles of the nxb - subtracted image and the simulated grxe+cxb image in the 28 kev band . the difference is attributed to suzaku j14276051 . even if we consider the relatively broad half - power radius (; @xcite ) of the point spread function of suzaku mirror , suzaku j14276051 is clearly extended . in order to estimate the source extent , we compared the observed radial profile with that of a model calculation for an extended source having a 2d - gaussian distribution . instead of performing the @xmath18 fitting , we calculated @xmath18 for a set of @xmath19 , i.e. , , , , and . the simulated profiles were generated with xissim . it turned out that none of them gave an acceptable fit ; the radial profile of suzaku j14276051 has a core and a tail in comparison with the best - fit simulation data . we thus performed the @xmath18 test using only the core region ( @xmath20 ) . we then could obtain an acceptable fit ( @xmath21 for 3 degrees of freedom ) . the best - fit value obtained was @xmath0 with 90% confidence level . although suzaku j14276051 is extended , we tried to search for pulsations in the xis light curve as point sources may be hidden in the image . we extracted light curves of the source region in the 0.510 kev band and binned them to a time resolution of 16 sec . we calculated fourier power spectra every 2048 bin ( @xmath22 9.1 hour ) using the ftool powspec to obtain the ensemble - averaged power spectrum density ( psd ) . the psd of xis1 is dominated by the orbital period of the satellite and its higher harmonics , probably due to the contamination of earth albedo . thus we used only the psd of xis3 in the subsequent analysis . no significant peak was detected in the psd with an upper limit of @xmath23 ( poisson fluctuation level was normalized to 2.0 ) , which corresponds to an rms amplitude of 0.0064 count s@xmath11 . because the net count rate of the source is 0.021 count s@xmath11 , this corresponds to a relative amplitude of 31% . thus we conclude that no coherent pulsation is present in the light curves of suzaku j14276051 with an upper limit of 31 % between the pulse periods of 32 sec and 32768 sec . figure [ fig : xisspec ] shows the background - subtracted energy spectra of suzaku j14276051 . here , the background spectrum ( sum of grxe , cxb , and nxb ) was calculated with the method detailed in section [ subsec : xisimage ] . it is found" +"a wealth of information about the motion of microscopic particles can be gathered by scattering a well - controlled probe , typically light in the case of atoms with optical resonances . young s historic double slit experiment demonstrated that the probe light wave shows interference if it can propagate along more than a single path . interference fringes therefore can give sensitive information about the scatterers , as was shown by eichmann and coworkers @xcite by realizing young s double slits with two trapped atoms . on the other hand , the motional state of the probed particle gives information about the probe field , as recently discussed by eschner @xcite . as a commonly accepted rule , one can have either full interference contrast or full which - way - information at the same time . between these two extremes , there are interesting intermediate situations that can be quantified using general quantum duality relations derived by englert @xcite that have been used for instance in atom interferometers @xcite . in mesoscopic samples of weakly disordered clouds of cold atoms , coherent multiple scattering of light leads to enhanced backscattering @xcite . in this letter , we investigate coherent backscattering ( cbs ) of light by two atoms that are trapped in harmonic oscillators . this model system can describe how atomic motion destroys multiple scattering interference via recoil and doppler effects . we calculate the cbs interference visibility both at zero and finite temperature in shallow traps that allow to treat the limiting case of freely moving atoms . the cbs double scattering geometry realizes a two - way interferometer where the two mutually exclusive alternatives are the order in which the photon visits both atoms . which - way information is then present if one knows which of both atoms has been visited first . we calculate the which - way distinguishability proposed by englert and show how it is physically encoded . consider two atoms trapped in identical harmonic oscillators at fixed positions well separated from each other by many wavelengths of the probe light . a single incident photon with wave vector @xmath0 and polarization @xmath1 is then scattered by the atoms and detected in the backscattering direction @xmath2 with polarization analysis in the helicity - preserving channel @xmath3 . a photon scattered in the backscattering direction by a single atom with a non - degenerate ground state has the same polarization , but opposite helicity , and does not contribute to the detected intensity . since the atoms are far from each other , the probability for repeated scattering is very small . the detector then receives a photon that has been scattered exactly once by each atom , either along way a or along way b , see fig . [ twoways.fig ] . the total amplitude is the coherent superposition of both amplitudes . such an interference of counter - propagating multiple scattering amplitudes in the backscattering direction is known as coherent backscattering ( cbs ) @xcite . without interaction , the free electromagnetic field and the internal and external ( motional ) atomic degrees of freedom are described by the hamiltonian @xmath4 or @xmath5 the first term constitutes the standard hamiltonian for free photons @xcite . @xmath6 is the projector onto the degenerate multiplet @xmath7 of excited states with transition frequency @xmath8 from the non - degenerate ground state @xmath9 of atoms @xmath10 . the atomic motion is described by the number operators @xmath11 of excitations in the three - dimensional isotropic harmonic oscillators with frequency @xmath12 . the dipole interaction @xmath13 couples the photon field both to the electronic states and the motional degrees of freedom . @xmath14 is the electronic dipole transition operator for atom @xmath15 . the electric field operator @xmath16 is evaluated at the atomic center - of - mass position @xmath17 . the displacement operator @xmath18 from the trap s origin @xmath19 measures distance in units of the oscillator length @xmath20{\hbar/(2 m { { \omega_\ab{ho } } } ) } } $ ] . the vector joining the two atoms will be denoted @xmath21 , with a distance @xmath22 between the traps such that @xmath23 . of the first scatterer during the total scattering time @xmath24 is larger than the initial position uncertainty @xmath25 . , title=""fig:"",width=188 ] of the first scatterer during the total scattering time @xmath24 is larger than the initial position uncertainty @xmath25 . , title=""fig:"",width=151 ] [ atomicoverlap.fig ] since the atoms are well separated , the total double scattering process is described by the product of two individual scattering processes with free propagation inbetween . in the far - field photon propagator @xmath26 , we expand the absolute distance to linear order in the small relative displacement : @xmath27 . in the exponential , the zeroth - order contribution @xmath28 drops out from all interference quantities , whereas the linear term generates a phase difference between the amplitudes of @xmath29 and @xmath30 and must be kept . to this leading order , the denominator can be taken constant . the transition operator @xcite for way a takes a useful form in time representation and interaction picture where @xmath31 . up to irrelevant prefactors , @xmath32 read from right to left , it describes how the photon is scattered first by atom 1 , then propagates with @xmath33 , and is finally scattered by atom 2 . the transition operator @xmath34 of the reverse way b is obtained from @xmath35 by the substitution @xmath36 . the complex detuning @xmath37 of the probe frequency @xmath38 from the transition frequency includes the spontaneous decay rate or inverse lifetime @xmath39 . retardation times of order @xmath40 have been neglected in the time arguments of the operators . indeed , the photon scattering by two atoms defines two distinct time scales for the atomic motion : first , the total inverse detuning @xmath41 which is simply @xmath42 at resonance . second , the free propagation time @xmath40 from one atom to the other . for resonant atomic scatterers with @xmath43 of order @xmath44s or larger , and typical distances @xmath28 of 1@xmath45 mm or less , one has @xmath46 such that the scattering is resonance - dominated , and the free propagation time can be safely neglected . in all of the following , we have in mind the limit of quasi - free atoms and therefore consider the case of shallow traps @xmath47 in which the oscillation period of an atom is much larger than the time @xmath48 it takes to scatter a photon . the incident photon can choose between two _ a priori _ indistinguishable paths , way @xmath49 or @xmath50 . following englert s fashionable choice @xcite , we call this binary degree of freedom a qubit . let @xmath51 and @xmath52 denote the choice of way @xmath49 and @xmath50 . scattering entangles the qubit with the motional degrees of freedom . consequently , the atomic oscillator states can serve as a which - path detector . prior to scattering , the total initial state of qubit and detector is @xmath53 . the qubit is in the pure state @xmath54 , the symmetric superposition of equally probable ways . an external cooling laser field serves as a thermal bath for the trapped atoms . the detector is thus in a thermal state @xmath55 at inverse temperature @xmath56 with partition function @xmath57 . the total final state is then obtained by applying the transition operators associated with way @xmath49 and @xmath50 : @xmath58 in general , @xmath59 is not a unitary operator since it describes only the scattering amplitude around the backscattering direction . the factor @xmath60 guarantees , however , that @xmath61 is properly normalized . adapting englert s general definitions @xcite , we can express the _ visibility _ @xmath62 and the _ distinguishability _ @xmath63 obeying the fundamental _ duality relation _ @xmath64 as follows : @xmath65 the visibility is the ratio of interference contribution and background intensity @xmath66 and therefore equal to the cbs contrast . the distinguishability @xmath63 describes the maximum which - way information available in principle , i.e. , that can be extracted by the additional measurement of an optimal detector observable ; @xmath67 denotes the trace - class norm of the operator @xmath68 . another interesting quantity is the _ predictability _ @xmath69 the predictability measures the amount of which - way information available _ a priori _ , as for instance in unbalanced interferometers like young s double slits with different widths . for balanced interferometers @xmath70 , the predictability vanishes , @xmath71 . with the help of these quantities , we can quantify the breakdown of coherent photon backscattering by mobile atoms , both at zero and finite temperature . the distinguishability @xmath72 is difficult to evaluate in our case because it is defined via the trace - class norm of operators on the infinite - dimensional hilbert space of harmonic oscillators . on the contrary , visibility @xmath62 and predictability @xmath73 involve a thermal harmonic average of products like @xmath74 or @xmath75 . since the transition operator ( [ transitionoperatora ] ) contains only exponentials linear in the displacement , taking the trace amounts to gaussian integration . at zero temperature , the atoms are initially in their respective harmonic oscillator ground states . in other words , the detectors are prepared in pure states . setting @xmath76 in ( [ d_and_v ] ) permits to show that in this case the duality relation is always saturated : @xmath77 . thus , we can use the visibility @xmath62 , much easier to calculate than the distinguishability @xmath63 , in order to understand how much which - way information is present and how it is encoded . carrying out the thermal average , we find in the limit @xmath78 @xmath79 neglecting higher - order terms @xmath80 in the two relevant small parameters defined as follows : the influence of atomic recoil without harmonic trapping is encoded in the factor @xmath81 with @xmath82 the recoil energy , @xmath83 the probe detuning from the atomic resonance , and @xmath84 as before . the harmonic trap enters through the parameter @xmath85 it is worthwile to discuss the physical significance of both parameters . let us first consider a very shallow trap @xmath86 where the free recoil effect described by @xmath87 dominates . at least to order @xmath88 , we find @xmath89 . together with the general property @xmath90 ( read : the _ a priori _ information can not be larger than the total available information ) this implies that all which - way information is actually available _ a priori _ : @xmath91 . just as in the case of other asymmetric interferometers , this predictability is due to unbalanced scattering amplitudes . at perpendicular scattering @xmath92 , the situation is completely symmetric , and both paths are equally probable . but for the extreme case @xmath93 of atoms in line with the probe , the atom in front scatters either the incident probe photon at the laser frequency or the already scattered photon on its way out again , now at laser frequency minus twice the recoil . a different frequency generally implies a different scattering cross section such that the two paths have different probabilities . for a given position configuration , this information is known _ a priori _ without the necessity to perform any measurement . more quantitatively , the relative change in the resonant cross section @xmath94^{-1}$ ] under a small frequency change @xmath95 then is @xmath96 , one finds exactly @xmath97 . to this order , the predictability vanishes at exact detuning , since a small frequency change on the flat top of the resonance lorentzian has no effect . let us now interpret the influence of harmonic trapping at zero temperature . the predictability ( [ predzero ] ) contains no contribution in @xmath98 , which indicates" +"tracking and vertexing in a high multiplicity environment such as the lhc is a challenging task . in order to get a good secondary vertex resolution , one needs measurements as close to the interaction point as possible . to have acceptably low occupancies one needs a very fine segmented detector . the cms experiment uses a hybrid pixel detector with @xmath1m@xmath2 pixel size . the barrel part has three layers at mean radii of 4.4 , 7.3 and 10.2 cm . in the innermost layer the occupancy reaches @xmath3 at the full lhc luminosity of @xmath4s@xmath5@xmath6 . + the main purpose of the pixel detector is the reconstruction of secondary vertices ( mainly for b and @xmath7 physics ) and the generation of track seeds for the reconstruction in the full tracker . also tracks reconstructed with the pixel detector alone is the only available tracking information at the first stage of the higher level trigger ( hlt ) . here speed is more important than accuracy or efficiency . as pointed out in @xcite , pixel - only tracks can be reconstructed in less than 20ms ( 110ms ) per event for regional ( global ) track finder . the @xmath8 resolution is @xmath9[gev / c ] and the impact parameter can be measured with @xmath10 m for @xmath11gev / c rising to @xmath12 m for @xmath13 gev / c . the component of the vertex position along the beam line is measured at the hlt . the resolution depends on the physics channel ( number and momentum of tracks ) and is typically @xmath14 m with an efficiency of @xmath15 . the smallest independent unit of the barrel support structure is a half - shell . it is made out of 53 cm long and 0.25 mm thin carbon fiber ladders glued to aluminum cooling pipes with 0.3 mm wall thickness . to reach full spatial coverage ladders are mounted with overlap on alternating sides of the cooling tubes . this is shown in figure [ fig : mechanics ] on the left . since the ladders are not tilted , charge sharing is enhanced between pixels due to lorentz drift in the 4 t magnetic field and hence the spatial resolution through analog signal interpolation is increased . + eight modules are screwed onto each ladder using thermal grease to improve the heat transfer from the electronics components to the cooling tubes . this allows an easy removal of the mounted modules . + three half - shells are mounted together at the end flange building up half of the barrel detector . the left and right half barrels are mechanically separated . a six layer pcb is mounted on the end flange . it distributes power and signals to the individual modules . the pcb is equipped with lcds ( low current differential signal ) driver chips and is otherwise passive . about 10 cm long cables and cooling tubes connect the barrel support structure to the service half - cylinders . a sketch of the later is shown in figure [ fig : supply ] . the barrel layers are made out of two types of sensor modules . each layer has 32 half modules at the edges of the half - shells and 128 , 224 and 320 full modules for the three layers respectively . a sketch of a module is shown in figure [ fig : module ] . 16 ( 8) readout chips ( rocs ) are bump bonded to the full ( half ) sensors . a dedicated in bump bonding process has been developed at psi @xcite and the whole production is done in house . a three layer flexible high density interconnect ( hdi ) is glued on top of the sensor and wire bonded to the rocs and to the token bit manager chip ( tbm ) @xcite . it is then glued to si - nitride base stripes which give mechanical stability and reduces stress to the bump bonds due to an excellent cte match to si . details about the module assembly are described in these proceedings ( @xcite ) . the active area of a full ( half ) module sensor is 64.8@xmath1610.6 mm@xmath2 ( 64.8@xmath16 5.3mm@xmath2 ) . it is a double sided processed `` n+ on n '' design . this is a pixelated high dose n implantation in a lightly n - doped bulk material . the backside is p - doped forming the pn junction . the inter - pixel isolation is done with a moderated p - spray technique . there are mainly two reasons for this choice : ( i ) after irradiation , the bulk material will be type inverted . depletion will then begin at the structured n - side , allowing the device to be operated in a partially depleted mode and thus at a lower bias voltage . ( ii ) a multiple guard ring structure on the p - side controls the voltage drop from the large negative bias voltage towards the sensor edge and allows to put all sensor edges to ground potential . this enables a safe operation at very high bias voltages up to 600v . the readout chip ( roc ) is fabricated in a commercial @xmath17 m 5 metal layer cmos process . it s main purposes are * amplification and buffering of the charge signal from the sensor * zero suppression in the pixel unit cell . only signals above a certain threshold will be read out . this threshold can be adjusted individually for each pixel by means of four trim bits . the trim bits have capacitive protection against single event upset ( seu ) , which have shown to reduce seu by 2 orders of magnitude @xcite . a typical threshold dispersion after trimming at t=-10@xmath18c is 90 electron equivalents with a noise of 170 electrons . * level 1 trigger verification . hit information without a corresponding l1 trigger are abandoned . * sending hit information and configuration data out to the tbm chip * adjusting various voltage levels and offsets in order to compensate for chip - to - chip variations in the cmos device parameters the roc has 6 on chip voltage regulators . this makes it possible to operate the detector without voltage regulator boards inside the cms tracker volume , improves ac power rejection and strongly reduces intermodule cross - talk . more details about the roc can be found in @xcite . the module is readout in a daisy chained scheme . it is controlled by the token bit manager ( tbm ) chip . for each level 1 trigger the tbm generates a token bit which controls 8 or 16 rocs . one roc at a time sends its hit information through a lvds ( low voltage differential signal ) to the tbm chip where they are amplified and converted into a lcds ( low current differential signal ) . the later has been chosen because of its low voltage swing , in order to reduce cross - talk on the kapton signal cable to the supply tube . + there is one analog readout link running at 40mhz for each half module and each full module in the outermost layer and 2 such links for each full module in the two inner layers . in order to reduce readout time , the pixel address is sent in a digital coded analog signal , i.e. there exist 6 discrete address levels . the amplified sensor signal is sent purely analog . each hit pixel needs 6 clock cycles or 150ns to be read out . the address level separation has been measured with the entire system and was found to be @xmath1930 times the rms of the level width . thus , reliable address decoding is ensured . figure [ fig : signal ] shows a simplified diagram of the signal flow for the barrel pixel detector . the signal path in the middle shows the fast detector control link . the pixel front end controller ( pfec ) sends a clock signal with encoded fast control signals ( l1 trigger , reset , internal calibration and resynchronization signal ) to the detector . the pfec also downloads configuration data at run start and if necessary during runs via the industrial i@xmath2c protocol , modified to run at a higher clock rate of 40mhz . all connections between service tube and counting room are optical links . the doh ( digital opto hybrid ) does the conversion between optical and electrical signals . a pll chip regenerates the fast signals and restores the clock . a delay chip can adjust the phase for each signal separately . the gatekeeper chip blocks idle signals needed for automatic gain adjustment of the optical links from being transmitted to the module . finally there is a lvds to lcds level converter chip on the end flange print . + the path on the right shows the readout part . the tbm drives the analog signal all the way to the service tube . a level translator chip ( alt ) generates signal levels acceptable to the laser driver chips of the analog optical link . driver and optical transmitter are located on the analog opto hybrid ( aoh ) . the signal is received in the counting room by a vme front end driver unit ( pxfed ) @xcite . it converts back to electrical signals , does a baseline correction , determines all pixel addresses and digitizes the analog pulse height . it then passes this information to the cms daq system . + some of these components need to be programmed . this happens through a dedicated digital link via a standard i@xmath2c protocol . the boxes in gray show pixel specific full custom auxiliary asics developed at psi . barrel modules have been tested in a high rate 300 mev / c pion beam at psi . figure [ fig : effi ] shows the detection efficiency as a function of particle fluence for trigger rates of 10 and 100khz . three different methods have been used . for low trigger rates efficiencies are shown for tracks reconstructed with a beam telescope or using small scintillators only . the third method measures the efficiency for internal calibration signals which are superimposed on top of the beam induced data traffic . for comparison , triangles show the efficiencies as expected from simulations . at high trigger rates the data losses are dominated by readout related dead times . the agreement between data and simulation is excellent here . for low trigger rates the measurement shows @xmath20 higher inefficiency than expected from simulations . this can be understood by radiation damage of the sensor under test . + resolution studies have been made in @xcite . using pion beam test data together with simulations , one expects a resolution in @xmath21 between 10 and 20 @xmath22 m for sensors irradiated up to @xmath23n@xmath24cm@xmath2 , which corresponds to the first 4 years of operation in the innermost layer . the z resolution depends on the azimuthal angle @xmath26 and only weakly on the irradiation dose . for @xmath27 the resolution is @xmath28 m , increasing to 40 @xmath22 m at @xmath29 . an overview of the cms barrel pixel detector has been given . the design is finalized and all system components have been tested extensively . the device is still in the construction phase and will be delivered to cms in summer 2007 . first proton collisions are expected by the end of 2007 at the injection energy of 450gev per beam and at the full energy of 7tev in spring 2008 . the cms collaboration , cms tracker technical design report , cern / lhcc 98 - 6 the cms collaboration , cms physics technical design report" +"quantum phase transitions constitute a very active topic in theoretical physics @xcite , to which disorder and frustration of a quantum spin glass add considerable intricacies @xcite . although quantum effects were usually considered to be negligible in spin glasses at finite temperatures , diverse experiments @xcite have proved them to be highly relevant , leading to the first experimental realization of _ quantum annealing _ @xcite . one of the most widely employed theoretical approaches to the quantum spin - glass transition ( qsgt ) is the random couplings ising model in a transverse field ( ritf ) @xcite . within the analytical approach , a griffiths phase was found in the 1d case via an elegant rg procedure @xcite , while such a structure was proved to be absent from the infinite range case within the replica formalism @xcite . the 1d rg analysis was extended to study the presence of a certain number of long - distance links , proving the relevance of the perturbation @xcite . regarding numerical approaches , quantum monte - carlo ( qmc ) remains as the most suitable tool at @xmath0 . using it , a coherent picture was obtained in the 2d and 3d cases , showing that the griffiths phase is present in 2d but absent in 3d @xcite . classical spin glasses have been thoroughly analysed on bethe lattices @xcite . however , finite bethe lattices are dominated by boundary effects and present no frustration . a way out is to study random graphs with a fixed connectivity which , in the classical case , allow the application of the _ cavity approach _ @xcite . these random graphs present genuine frustration , since they have _ loops _ , and have no boundaries . on the other hand , the average size of the loops grows with the number of sites @xcite , thus making them resemble , _ locally _ , a bethe lattice ( see figure [ graph : fig ] ) . the density matrix renormalization group ( dmrg ) @xcite is known to be a highly accurate method to analyze @xmath1 ground state properties of 1d or quasi-1d quantum many body systems , including tree structures @xcite . we have extended the method in order to trace the behaviour of finite size samples of random graphs of fixed connectivity @xmath2 across the qsgt within the ritf model . given the high connectivity of these graphs , the applicability of the dmrg is highly non - trivial . it is remarkable that in the case of non - random couplings , we have found the number of retained states needed to ensure a good accuracy to be very high , rendering the application of the dmrg unfeasible . the careful analysis of _ pseudo-_critical points of finite size samples constitutes a powerful tool to study a qsgt . as a recent example , the work of igli and coworkers @xcite studies the distributions of , e.g. , the average entanglement entropy and the surface magnetization of finite size 1d samples . in this work we provide measurements of , among other observables , spin - glass susceptibilities , energy gaps , long distance spin - spin correlations and entanglement entropies , and use them to obtain insight on the mechanism of the transition . a full characterization of the qsgt , nonetheless , is not attempted in this work , since it would require to obtain statistics on a large number of disorder realizations . the rest of the paper is organized as follows : sec . [ model : sec ] presents the model , and sec . [ dmrg ] provides details on the application of dmrg . [ results ] shows the numerical dmrg results obtained . [ conclusions ] presents a discussion of the results and some concluding remarks . let us consider the random ising model in a transverse field ( ritf ) on a generic graph @xcite : @xmath3 where @xmath4 denotes pairs of neighboring sites @xmath5 and @xmath6 on the graph . the values of @xmath7 are uncorrelated random variables with a uniform probability density distribution in the interval @xmath8 $ ] . we will focus our study on randomly generated graphs , with @xmath9 sites and a fixed connectivity @xmath2 @xcite , i.e. , each site @xmath5 is connected to @xmath2 other ( randomly chosen ) sites @xmath6 . an example of such a graph , with @xmath10 sites , is shown in fig . [ graph : fig ] . it should be noticed that , locally and for large @xmath9 , such graphs resemble _ bethe lattices _ , as we have highlighted with thicker links in fig . [ graph : fig ] . nonetheless , the behaviour of finite bethe lattices is dominated by the boundary , unlike in our case , where there is none . moreover , trees have no loops and , therefore , present no _ frustration _ , while random graphs with fixed connectivity do contain loops and , therefore , have genuine frustration . it has been proved , nonetheless , that short loops become rare as @xmath11 : more precisely , the probability of finding a loop of any fixed size @xmath12 falls to zero when @xmath11 @xcite . the physics of classical spin glasses in these graphs has been studied using the cavity method by mzard and parisi @xcite . let @xmath13 be the absolute value of the disorder - averaged energy per site of the classical ground state . our numerical experiments show that it increases from @xmath14 at @xmath15 up to @xmath16 for larger @xmath9 , which is the theoretical limiting value for @xmath11 under the assumption that all links are satisfied . we will take the product of eigenstates of @xmath17 , for all @xmath5 , as the _ canonical basis _ for our problem . in this basis , we denote the state in which all spins point in the positive @xmath18-direction as @xmath19 . let us assume , for the moment , that @xmath20 for all @xmath5 . for @xmath21 , all the non - diagonal terms in the hamiltonian vanish . therefore , the ground state is given by the configurations with the classical minimum energy . disregarding accidental degeneracies , there are two such configurations , related by a simultaneous flip of all spins , @xmath22 for all @xmath5 . the transverse field @xmath23 may be considered as a _ kinetic energy _ coefficient , providing a hopping term among the classical configurations . in the @xmath24 limit the transverse field term dominates and the ground state tends to the state @xmath25 , with all the spins pointing in the positive @xmath18-direction , separated by a large gap @xmath26 from the first excited state . let us remark that all the components of the canonical basis have the same amplitude in the state @xmath25 . by decreasing @xmath23 there is a certain value @xmath27 for which the system undergoes a quantum spin - glass transition ( qsgt ) . for @xmath28 , the system is in a quantum paramagnetic phase , which presents no long - range order . below @xmath29 , the system is in a quantum spin - glass phase , presenting a hidden long - range order which may be detected by a number of observables . we will focus here on the divergence of the _ spin - glass susceptibility _ : @xmath30 i.e. , physically , a small longitudinal magnetic field @xmath31 , applied at site @xmath6 , generates a magnetization response on each site @xmath5 , which is measured ( and squared , so as to disregard its sign ) ; the results are summed over all sites @xmath5 and averaged over all sites @xmath6 . if the system is in a paramagnetic phase , the magnetization will be proportional to @xmath31 and short - ranged in space , so that the sum over @xmath5 and @xmath6 yields a finite value for @xmath32 . on the other hand , on approaching the spin - glass phase , an infinitesimally small longitudinal magnetic field @xmath31 , localized at a single site @xmath6 , will eventually induce a finite magnetization over a long - range of spins . this effect is at the origin of the divergence of @xmath32 . we shall now discuss the numerical approach we have used to study this system , and the results obtained . the density - matrix renormalization group ( dmrg ) has proved to be an accurate method to analyse the properties of 1d and quasi-1d systems @xcite . the dmrg may be described as a variational method within the matrix - product states ( mps ) , which constitute a low - dimensional subspace of the full hilbert space @xcite . a mps may be expressed as @xmath33 where each @xmath34 is a square matrix with dimension @xmath35 , which may be considered as the number of retained states per block when splitting the system into a left and right parts . the total number of variational parameters is less than @xmath36 . the success of the dmrg is related to the ability of these mps to reproduce faithfully the ground states of local 1d many - body problems for low values of @xmath35 @xcite . if @xmath37 , any state of the hilbert space may be exactly represented as a mps . the minimum number of retained states @xmath35 is related to the exponential of the von neumann entanglement entropy of the dmrg block @xcite . in a non - critical 1d system , this entropy is bounded for all sizes , while it grows as @xmath38 for a 1d critical system of length @xmath12 . it is believed that for a @xmath39-dimensional system out of criticality , the entanglement entropy scales as @xmath40 , where @xmath12 is the shortest spatial dimension of the system @xcite . this estimate is known as the _ area law _ and is believed to have logarithmic corrections at critical points . an important practical consequence is that , in order to study a 2d system , the number of retained states @xmath35 should grow as @xmath41 , thus making the dmrg very inefficient . our system , on the other hand , is defined on a random graph of fixed connectivity , @xmath2 . we will show that this poses no problem to the number of retained states @xmath35 , which appears to remain manageable even for @xmath42 as long as the couplings are random . however , the implementation of the dmrg on such a model has required the following technical refinements of the original method : * ( a ) path selection . * : : in a non-1d system , dmrg proceeds by converting the system into an effective 1d problem with long - range couplings . a path is chosen along the graph , which does not repeat sites , and is considered to be appropriate if the number of broken links between the left and the right blocks is kept low along a dmrg sweep . normally , the selection of a suitable path in a quasi-1d system ( e.g. ladders ) is done by geometrical intuition . in our implementation we have designed an automated procedure : a simulated annealing algorithm is employed in order to minimize the number of broken links . the full problem of finding the optimal path is computationally very hard . therefore , we do not aim at the exact optimum , but only to a reasonably good local minimum . we have noticed that our quasi - optimal path performs much better than a random path . * ( b ) perron - frobenius criterion . * : : the hamiltonian of the ritf on any graph fulfills , on the canonical basis , the" +"the idea of a statistical approach to hadron production in high energy collisions dates back to 50s @xcite and 60s @xcite and it has been recently revived by the observation that hadron multiplicities in collisions agree very well with a thermodynamical - like ansatz @xcite . this finding has also been confirmed in hadronic collisions and it has been interpreted in terms of a pure statistical filling of multi - hadronic phase space of assumed pre - hadronic clusters ( or fireballs ) formed in high - energy collisions , at a critical value of energy density @xcite . in this framework , temperature and other thermodynamical quantities have a statistical meaning which does not entail the existence of a thermalised hadronic system on an event - by - event basis . stated otherwise , statistical equilibrium shows up only when comparing many different events , whilst in each of them the gibbs law of equally likely multi - hadronic states applies . so far , this proposed statistical cluster hadronisation model has been mainly tested against measured abundances of different hadron species for a twofold reason . firstly , unlike momentum spectra , they are quantities which are not affected by hard ( perturbative ) qcd dynamical effects but are only determined by the hadronisation process ; indeed , in the framework of a multi - cluster model , they are lorentz - invariant quantities which are independent of the cluster s overall momentum . secondly , they are quite easy to calculate and provide a very sensitive test of the model yielding an accurate determination of the temperature . however , in order to establish the validity of this approach , it is necessary to test further observables and to assess their consistency with the results obtained for multiplicities . certainly , one of the best suited observables is the transverse momentum of identified hadrons , where transverse is meant to be with respect to beam line in high energy hadronic collision , and thrust or event axis in high energy collisions . indeed , such projection of particle momentum is supposed to be the most sensitive to hadronisation or , conversely , the least sensitive to perturbative qcd dynamics . + actually , it has been known for a long time that transverse momentum distributions are boltzmann - like in hadronic collisions and this very observation was pointed out by hagedorn as a major indication in favour of his statistical model of hadron production @xcite . it must be emphasized that the prediction of a thermal - like shape in principle only applies to particles directly emitted from the hadronising source , whereas measured spectra also include particles produced by decays of heavier hadrons . however , most analyses do not take into account the distortion of primordial hadronisation spectrum due the to hadronic decay chain and try to fit the data straight through it . this problem has been discussed in literature @xcite and an analytical calculation has been developed to take into account the effect of two and three body decays @xcite , which has then been used both for pp @xcite and heavy ion collision @xcite including most abundant resonances . in this paper we introduce a method allowing to rigorously and exhaustively determine the contribution of all particle decays . hence , by taking advantage of this technique , we have performed an analysis of many measured transverse momentum spectra of identified hadrons in a wide range of centre - of - mass energies for several kind of collisions . the statistical hadronisation model @xcite assumes that in high energy collisions , as a consequence of strong interaction dynamics , a set of colourless clusters ( or fireballs ) is formed having certain values of mass , volume , internal quantum numbers and momentum , the latter being inherited from the hard stage of the process . those clusters are assumed to give rise to hadrons according to a pure statistical law in the multi - hadronic phase space defined by their mass , volume and quantum numbers . this approach differs from another popular cluster hadronisation model @xcite mainly because it gives clusters a volume so that hadron production is ruled by the properly understood phase space rather than relativistic momentum space . in this framework , the use of statistical mechanics and thermodynamical quantities , such as temperature , which need spacial dimension besides momentum space in order to be meaningful , is allowed . we emphasize once more that the introduction of such quantities does not entail any thermalisation process of hadrons after their formation , nor the existence of a thermalised system event by event . + although many clusters with different momenta , volumes , masses and quantum numbers are formed , it can be shown that the average values of many observables , e. g. particle multiplicites , are the same as those relevant to one equivalent cluster having suitable values of volume ( namely the sum of all cluster volumes measured in the rest frame of the equivalent cluster itself ) , mass and quantum numbers ( namely the sum of all cluster quantum numbers ) . the proof of this statement @xcite , a lengthy one , requires the assumption of special probabilities governing the fluctuations of cluster masses and quantum numbers for a given set of volumes . if the volume ( or mass ) of the equivalent cluster is large enough , it is then reasonable to take a canonical approach ( i.e. introducing a temperature ) in order to calculate mean quantities , instead of carrying out an involved microcanonical calculation . therefore , even though actual clusters are small sized and microcanonical calculations would be needed to determine mean quantities within each of them , the choice of suitable mass fluctuation probabilities for the clusters allows one to calculate overall means dealing with only one large global structure and with much fewer parameters . arguing the other way around , it is not difficult to be convinced that the fluctuation probabilities to be chosen in order to achieve such reduction of the problem are exactly the same as those of obtaining a given set of masses by splitting a large cluster into a given number of clusters with volumes @xmath2 . this statement extends a reduction procedure to the microcanonical case which was proved in the canonical case @xcite , where , from the very beginning , clusters were given temperature and volume instead of mass and volume . nevertheless , it is not obvious how large the equivalent cluster should be for the canonical approximation to apply . for the present , we have adopted a simple - minded _ a posteriori _ method consisting in justifying the canonical framework by its capability of accordance with the data . a simple argument to support the canonical approximation even at moderate values of volumes is the very large number of states ( @xmath3 ) , i.e. hadrons and resonances , which can be excited in a hadron gas . + as far as single - particle transverse momentum spectra are concerned , a similar reduction theorem from many clusters to one equivalent cluster in the averaging procedure applies @xcite , though only approximately . in general , it can be shown that the _ primary _ spectrum of @xmath4 hadron species depends on transverse four - velocities @xmath5 with vanishing longitudinal component . ] of the @xmath6 clusters : @xmath7 \ ; f(u_{t1},\ldots , u_{tn } ) \nonumber \\ & & \times \ ; \sum_{i=1}^n \frac{\d n_j}{\d p_t}\vl_{i}(\ui ) \ , .\end{aligned}\ ] ] where @xmath8 is the transverse four - velocities distribution function . if one expands all single - cluster spectra @xmath9 in series of @xmath10 starting from a common value @xmath11 for all clusters , it can be proved that , at the zeroth order , the spectrum in eq . ( [ one ] ) becomes the same as that obtained for the aforementioned equivalent cluster , endowed with a tranverse four - velocity @xmath11 . this reduction possibly allows taking the canonical approach in order to calculate the transverse momentum spectrum since the equivalent cluster size is much larger than single cluster s : @xmath12 where @xmath13 , @xmath14 is the temperature , and @xmath15 , @xmath16 are modified bessel functions . ( [ two ] ) is the boltzmann limit of quantum statistics and it is a very good approximation for all hadrons except pions @xcite . for the zeroth order approximation in the @xmath10 expansion to be sufficiently accurate , the involved transverse four - velocities should be small , i.e. @xmath17 already for @xmath18 . since it is possible to choose the starting point @xmath11 of the series expansion to make the first order term vanishing @xcite , the largest neglected term turns out to be @xmath19 which is very small provided that the aforementioned condition on @xmath20 is met . the analysis presented in this paper assumes the validity of this approximation and primary spectra have been calculated according to eq . ( [ two ] ) . + even though eq . ( [ two ] ) looks like the spectrum from a thermalised source with a superimposed flow , a popular formula in the heavy - ion community , it is well worth emphasizing that in fact this formula has nothing to do with flow . indeed , the average transverse four - velocity @xmath11 is not meant to be the mean value of cluster velocity distribution in a single event ; rather , it is the average transverse four - velocity of all clusters over all collision events . in other words , @xmath11 may well arise from single clusters emitted at high @xmath21 in some events , e.g. following a hard parton scattering , and does not imply by any means a collective event - by - event expansion . gev @xcite . the measured @xmath22 spectra ( above ) have been normalised so as to have the same value at @xmath23 . while slopes of @xmath22 spectra are different , those of @xmath24 ( below ) are approximately the same for all identified particles . ] a peculiar prediction of a statistical picture in high energy collisions which is relevant to transverse momentum spectra is the so - called @xmath25 scaling : there should be an apparent common slope for @xmath26 spectra of identified hadrons at a given centre - of - mass energy . by looking at eq . ( [ two ] ) one can easily realize that this holds in the limit @xmath27 . in principle , @xmath25 scaling applies only to primary hadrons , namely those directly emitted from the hadronising source . on the other hand , as stated in sect . 1 , most observed or reconstructed particles in experiments arise from decays of heavier hadrons . those secondary decays may well distort the primary spectrum shape , thus spoling @xmath25 scaling . nevertheless , it can be seen in fig . ( [ mtslope ] ) that @xmath25 scaling apparently also holds for measured final hadrons , at least in the examined collision , implying seemingly little distortion from primary to final spectrum . settling this and other related issues demands a thorough analysis taking into account the effect of decays . therefore , measured @xmath21 spectrum of the @xmath4 hadron species should be compared with the sum of its primary spectrum and the contribution arising from all heavier hadrons decaying into it : @xmath28 whilst @xmath29 is given by eq . ( [ two ] ) , the calculation of the second term in the right hand side of eq . ( [ three ] ) within a statistical - thermal framework is a very complicated problem as the number of contributing resonances and decay modes is huge and" +"i would like to discuss in this talk three topics which superficially would look unrelated but in essence can be connected by the general theme of cheshire cat . i will first look at two - nucleon systems in terms of macroscopic variables of qcd , namely hadrons ; i will then go back to an elementary hadron , in particular the proton and examine its microscopic structure by punching "" a hole in the proton and then putting quarks and gluons of the appropriate quantum numbers inside and argue that there is a continuity in the descriptions in terms of hadronic variables and in terms of quark - gluon variables ; finally the continuity of quarks and hadrons at high density will be described in terms of qualitons quark solitons . many of my collaborators have contributed to the development discussed in this talk . among them are gerry brown , bengt friman , deog ki hong , kuniharu kubodera , kurt langfeld , hee - jung lee , dong - pil min , byung - yoon park , tae - sun park , vicente vento and ismail zahed . consider two nucleon interactions at very low energy . we are generically interested in the energy - momentum probe much less than the pion mass @xmath0 mev . at this energy , according to weinberg s theorem , "" the content of qcd can be phrased in terms of the nucleons and pions . in fact if we are probing a scale much less than the pion mass , we can even ignore the pions and work with the nucleons only . the corresponding framework is an effective field theory ( eft ) . much work has been done on this eft for two - nucleon systems @xcite ( see @xcite for recent reviews ) . there are two classes of observables to look at . one is scattering process and the other is response function to external fields . the two are of course complementary in revealing the physics involved . recent efforts have been put more on scattering than on response functions although more information has traditionally been gained from the latter in nuclear physics . both need to be treated simultaneously which i will do here . in the literature so far , there are broadly two approaches to eft in nuclear physics . one is the original weinberg approach @xcite where a systematic power counting is made only to the `` irreducible graphs , '' for which chiral perturbation theory ( with pions figuring crucially ) becomes applicable in organizing the expansion and the reducible graphs are summed to all orders with the irreducible graphs entering as vertices . this scheme used in ref.@xcite which in spirit is close to the original wilsonian eft but incurs possible errors in the power counting involves a scale @xmath1 as the counting is applied only to the irreducible terms . i will call this the @xmath2 counting . the other approach @xcite motivated to account more transparently for the large s - wave scattering lengths in two - nucleon scattering purports to do a systematic counting for the s - matrix as a whole which amounts to summing all graphs involving leading non - derivative four - fermi contact interactions while treating all others , including pion exchanges , as perturbation . this approach renders a more systematic accounting of the powers of @xmath3 where @xmath4 , @xmath5 as well as @xmath6 but at the expense of certain predictivity . this is referred to as @xmath7-counting scheme . there have been lots of hot debates as to whether one scheme is more powerful and or more consistent than the other , mainly in connection with the scattering @xcite . while the situation is not completely settled , i believe that it is fair to say that the two are both consistent with the tenet of eft and roughly equivalent in its power . eschewing the debate which seems somewhat academic , i will simply focus on the @xmath2-counting approach in this talk . in fact , in the processes that i will consider , i would claim that the @xmath2 counting is more adaptable to and more predictive in treating nuclear physics problems than the @xmath7 counting . one great advantage of the @xmath2 scheme is that it allows one to calculate precisely defined corrections to what can be obtained from so - called realistic potential models ( pm in short ) that have been developed by nuclear theorists since a long time , thus giving the realistic potential models ( pm ) a first - principle justification . it allows us to study processes involving not just few - body but also many - body systems . for instance , it is possible to calculate the hep "" process in the sun @xmath8 ( which is currently an exciting issue after the recent surperkamiokande neutrino data ) with an accuracy that can be controlled systematically . it has also been successfully applied to calculating axial charge transitions of heavy nuclei ( see @xcite ) with the additional ingredient of br scaling @xcite . while there is no definitive evidence that the @xmath2 scheme is fully justified for n - body systems with @xmath9 , it definitely works for @xmath10 systems . in ref.@xcite , it has been shown in a cutoff regularization ( with a finite cutoff as required by eft @xcite ) that the eft results of the leading order terms in all two - body observables at low energy @xmath11 are precisely reproduced by the potential model results . this is the case not only for scattering amplitudes but also all electroweak response functions . what eft brings in addition to what we get from the pm is a systematic procedure to compute corrections to the leading order results . for low - energy processes , this status of the pm can be understood by the fact that the tail of the wave functions is a physical quantity and the realistic potential models which are fit to experiments have the _ correct _ asymptotic properties in the wave function . this point has also been stressed and clarified by phillips and cohen in a recent important paper @xcite . considered to order @xmath12 where @xmath13 is the order in the @xmath2 counting ( which i will consider relative to the leading order term in the expansion of the irreducible graphs ) , the s - wave scattering amplitudes are accurately postdicted @xcite up to @xmath14 for @xmath10 and a cutoff appropriate to the number of pions exchanged ( one or two ) in the irreducible graphs . deuteron properties are also well understood within the same scheme @xcite . the scheme allowed the calculations to order @xmath15 and @xmath16 of the proton fusion process in the sun @xcite p+pd+e^+ + _ e[pp ] and of the threshold np capture @xcite with polarized projectile and target nucleons + d+.[np ] the process ( [ pp ] ) crucial for the solar neutrino problem is given in the scheme to an accuracy of @xmath17 percents ( the uncertainty here is due to the exchange current that appears at order @xmath16 ) . the unpolarized cross section for ( [ np ] ) has been computed to the accuracy of 1 percent in a complete agreement with the experiment . more significantly , the polarization observables @xmath18 ( circular polarization ) and @xmath19 ( anisotropy ) have been predicted _ parameter - free _ in ref.@xcite scheme was made by chen , rupak and savage @xcite . ] . this is a genuine prediction since there are no experimental data available . ( they are currently being measured in ill of grenoble @xcite . ) in all these postdictions and predictions , there is very little @xmath2 dependence as required by the tenet of eft . this is a clear indication that the scheme is fully consistent . one can go up in the momentum range by doing higher order calculations . phillips and cohen @xcite discuss how the two - body em form factors can be described in the @xmath2 scheme . pushing somewhat the validity of the scheme , one can calculate even the process e+de+n+p involving large momentum transfers @xmath20 gev . in fact this process measured in 1980 s at als of saclay and elsewhere is considered to be the _ unambiguous _ confirmation of meson - exchange currents in nuclei ( see @xcite ) . counting , everyone ( ! ) in the audience chuckled and said the process is completely out of reach for eft ( see @xcite ) . i grant that this may be true in the @xmath7 scheme at least for the moment but _ not _ in the @xmath2 scheme where it has worked stunningly , confirming the chiral filter hypothesis . "" _ voil _ the power of the @xmath2 scheme ! ] the nucleons that figured in the above section were color - singlet point - like fields that say nothing explicit about quarks and gluons . let me now imagine puncturing a hole of size of radius @xmath21 in the proton and populating the inside with the qcd degrees of freedom , quarks and gluons . how to do this consistently with qcd is known and the model involved is the chiral bag ( this is described extensively in @xcite ) which consists of a quark - gluon sector inside the bag and a color - singlet hadronic sector outside , with the two sectors connected by suitable boundary conditions . when constructed with relevant degrees of freedom and in consistency with the symmetries of qcd , the model gives what is now called cheshire cat . "" in short , the cheshire cat principle @xcite states that at low energy , physics involving hadrons should be independent of the bag size @xmath21 . it has been shown that this principle is operative semi - quantitatively in _ all _ properties of the nucleon @xcite _ except for _ the flavor - singlet axial charge ( fsac ) of the proton which is related to the proton spin . "" here i will briefly describe leaving the details to the paper by lee et al @xcite how this cheshire cat property can be recovered in the fsac when chiral symmetry and chiral anomaly are judiciously taken into account . it turns out that the interplay between the boundary conditions and casimir effects plays a crucial role . since the flavor - singlet axial current is not conserved because of the anomaly , the color can not be confined inside the bag unless a suitable boundary condition is put at the surface that cancels the outflow of the color @xcite . the boundary term that does this is proportional to the chern - simons current on the surface , i.e. , the chern - simons flux ( which is invariant under neither small nor large gauge transformation ) . this influences the fsac of the proton nontrivially . briefly , what happens is that the fsac contributed by the matter fields ( quarks inside the bag and @xmath22 outside the bag ) and the fsac contributed by the gauge field ( gluons inside the bag ) more or less ( or possibly exactly if treated rigorously ) cancel , leaving behind only the small contribution from the ( gauge field ) vacuum fluctuation which is effectively a casimir effect caused by the boundary with its color - anomalous boundary condition . the cancellation and the remnant small fsac are shown in fig . [ fsac ] . the upshot of the small result left over which is independent of the size @xmath21 provides yet another compelling evidence that the proton could be equivalently understood _ both _ in terms of quarks / gluons and in terms" +"magnetic reconnection is a fundamental process in astrophysical plasmas and is believed to be responsible for a wide range of solar phenomena , including solar flares ( for a review see * ? ? ? unfortunately , magnetic reconnection occurs on spatial scales that are too small to be resolved with current solar instrumentation and can not be observed directly . there is , however , considerable indirect evidence that magnetic reconnection plays a central role in solar flares . perhaps the most compelling piece of indirect evidence is the supra - arcade downflows that have been observed above many post - flare loop arcades ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? these downflows appear to be related to highly non - potential field lines that have reconnected and are propagating away from the current sheet . supra - arcade downflows have been observed with a number of instruments and their properties are summarized in the comprehensive review by @xcite . the downlows often appear as dark , collapsing features that look like small `` tadpoles '' ( voids with a trailing dark tail ) . some downflows have a loop - like appearance while others appear to evolve from voids into loops . the downflows generally begin at relatively high velocities ( 100200 km s@xmath1 is typical ) and then quickly decelerate to about 4 km s@xmath1 . observations at high spatial resolution give the impression that much of high temperature plasma in a flare is formed from collapsing loops @xcite , even when individual features can not be tracked . similar features are observed in the outer corona when the streamer belt is viewed face on ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? despite the extensive analysis of previous observations a number of questions remain regarding the downflows and their relationship to magnetic reconnection . the initial velocities measured for the downflows tend to be much smaller than the estimated alfvn speed in the lower corona ( @xmath01000 km s@xmath1 ) , the velocity expected for reconnection outflows . it is possible that the downflows are formed at large heights and are observed only after they have experienced some deceleration . in most models of solar flares the release of energy in the corona ultimately drives chromospheric evaporation and leads to the formation of hot , dense loops ( e.g. , * ? ? ? * ; * ? ? ? many of the downflows , however , are observed as dark features and it is not clear that all of the high temperature emission in the flare is formed from descending loops . finally , why some downflows appear as voids and while others appear as loops is unclear . it is possible that the observed morphology is strongly influenced by the viewing angle . the launch of the atmospheric imaging assembly ( aia ) on the _ solar dynamics observatory _ ( _ sdo _ ) provides a new opportunity to investigate the dynamics of newly reconnected flux tubes in solar flares . aia has several advantages over previous solar euv imagers , including a higher cadence ( 12s ) and more channels that observe at flare temperatures . the higher cadence allows us to create data sets optimized for observing the downflows at large heights . the aia 94 and 131 channels observe emission from and , respectively . these lines are formed close to 10mk , the temperature at which the flare emission measure generally peaks . observations from the twin _ stereo _ spacecraft @xcite can also be applied to this problem . during the 20102012 time frame the spacecraft are approximately 90@xmath2 from the earth - sun line , which allows flares to be observed simultaneously as limb events by aia and disk events by the euvi imagers on _ stereo_. in this paper we report new observations of supra - arcade downflows taken with aia and euvi . with the improved capabilities of aia we are able to track features at larger heights and in much weaker events than in previous studies . the combined aia and euvi observations provide compelling evidence that the downflowing voids and loops are manifestations of the same phenomenon observed along different lines of sight . we find , however , that the initial velocities are consistent with previous measurements and well below the estimated alfvn speed . the relationship between the brightest emission in the flare and the downflows is also not resolved . we find no evidence that the emission from the downflows rises with time , as would be expected from chromospheric evaporation . also , for these events the initial high temperature flare loops are observed to form almost `` in place '' with very little associated downward motion . these difficulties suggest that simple two - dimensional models of magnetic reconnection can not be applied directly to detailed observations of solar flares . the aia instrument on _ sdo _ is a multilayer imaging telescope . a full description of the instrument is given in @xcite . in brief , the aia instrument images the full sun in 10 different channels with 0.6 pixels at a typical cadence of 12s . there are 7 euv channels for imaging emission from the transition region and corona . the aia 94 , 131 , and 193 channels observe flare emission from , , and , respectively . each of the channels is also sensitive to emission formed at cooler temperatures . the 193 channel includes 195 , which is an intrinsically bright line and makes difficult to observe in smaller events . the lower temperature response for the 131 channel is primarily from emission lines that are much weaker than 195 , making the high temperature emission much easier to observe . the lower temperature lines in the 94 bandpass are largely unidentified , but they are also relatively weak . for a more complete description of the aia temperature response see @xcite . all of the aia data that we have analyzed are sub - fields of the full disk images obtained from the lmsal cutout service . the data has been processed using ` aia_prep ` to remove any energetic particle spikes and co - register the images from the different wavelengths to a common plate scale . for this work we consider three flares that occurred at the solar limb as viewed from earth : a c3.8 event that began at about 18:00 ut on 2011 march 16 , a c5.4 flare that began at about 20:30 ut on 2011 may 9 , and a c2.1 flare that begin at about 18:00 ut on 2011 may 18 . the soft x - ray light curves from the _ goes _ 15 spacecraft are shown in figure [ fig : goes ] . the _ goes _ light curves indicate that these flares are all long duration events that evolve over many hours . some representative aia 131 images are shown in figures [ fig : stereo0 ] , [ fig : stereo1 ] , and [ fig : stereo2 ] . all three events are clearly associated with a coronal mass ejection and have the classic morphology of a two - ribbon flare . each event shows a diffuse `` cloud '' of high temperature ( @xmath010mk ) plasma that rises with time . over time relatively narrow , lower temperature ( @xmath01mk ) loops form at the lowest heights and material is observed to drain back down to the surface of the sun along these loops . the temperatures that we give here are approximate and based on comparisons with previous work ( e.g. , * ? ? ? high temperature emission is observed only in the 94 and 131 channels while only low temperature loops are observed in channels such as 171 , which has a significant response only at low temperatures . very little emission is observed in the 193 channel images for these flares . the _ goes _ soft x - ray fluxes for these events are approximately 100 times smaller than was observed in the x - class flares considered previously ( e.g. , * ? ? ? * ; * ? ? ? * ) , so this is not surprising . movies of the data for each event show evidence for features forming at large heights and descending onto the accumulating post - flare loop arcade . these features are generally difficult to track in the raw intensity images . to eliminate the contribution of the more slowly varying emission it is useful to compute running difference images . with the high cadence of aia we have considerable flexibility in constructing these images . through trial and error we have found that averaging sets of 7 images taken 72s apart produced the best results . since the downflows move at relatively high velocities , too much averaging or too long an interval between frames blurs the features . averaging fewer frames or choosing a shorter interval between frames leads to noisier difference images . example running difference images are displayed in figures [ fig : stereo0 ] , [ fig : stereo1 ] , and [ fig : stereo2 ] . movies of the running difference images , which are available in the electronic version of the manuscript , show the downflows much more clearly than the raw intensity images . in general , the downflows appear as dark features in the running difference images , indicating that they are dark relative to the emission into which they are descending . in the march 16 event all of the downflows appear as elongated loop - like features . as illustrated in the example shown in figure [ fig : examples ] , when the loops first appear they are relatively broad but they are compressed as they descend . many of the descending loops that are the easiest to observe appear relatively late in the event ( after approximately 20:00 ut ) . at earlier times , 18:2019:00 ut for example , high temperature emission appears at relatively low heights very suddenly and does not appear to descend from larger heights . the loops that appear near 18:30 ut and are shown in the first column of figure [ fig : stereo0 ] illustrate this . there is , however , some downward motion after the emission appears , consistent with the shrinkage of post - reconnection loops ( e.g. , * ? ? ? * ) . some of the downflows in these events are observed as dark voids during the entirety of their descent . this is true for almost all of the downflows observed in the may 9 event . as with the loops observed in the march 16 event , the voids are relatively wide when they appear and are compressed in size as they descend . an example downflow is shown in figure [ fig : examples ] . the timing of the downflows is similar to that of the march 16 event , with many of the most easily observed downflows being observed somewhat later in the evolution of the flare . many downflows are observed after 21:15 ut , which is after the peak of the _ goes _ soft x - ray flux . in the may 18 event a mixture of descending voids and loops is observed . for this flare there are also some downflows that evolve from voids into loops . an example of a downflow that begins as a void and evolves into a loop is shown in figure [ fig : examples ] . the earliest high" +"a laser interferometer to detect gravitational waves , such as the laser interferometric gravitational wave observatory(ligo ) , virgo , geo600 , or tama300 , will be in operation within several years@xcite . it is one of the most urgent subjects for theoretical relativists to make a set of templates of gravitational waves . the direct detection of gravitational waves is very important not only as a new eye "" observing the universe ( gravitational wave astronomy ) but also as a new probe for fundamental physics . for example , we know that a neutron star , which is observed as a pulsar , has a mass @xmath1 and a radius @xmath2 @xmath3 . although we can guess its central region with some theoretical ansatz , we have no direct information from the inside of a neutron star because neither radiation nor a neutrino is transparent in the central region . the direct detection of gravitational waves may provide some information about the inside of a neutron star when it is formed , resulting in new observational facts or constraints about the equation of state for high density matter . one of the most promising astronomical sources for these ground - based detectors is a coalesced compact binary such as a neutron star binary . to complete a set of templates from such a source , many studies about the emitted gravitational waves have been done using various techniques . a numerical simulation without approximations ( numerical relativity ) is probably one of the best ways to calculate gravitational waves emitted from the compact binary system @xcite . although steady progress in numerical relativity has been achieved , there are still some difficulties which prevent us from finding the final results . instead , there are some powerful approximation methods to mimic the coalescence of a compact binary system . one such approximation is the perturbative approach . regge and wheeler @xcite and zerilli @xcite first formulated a method for metric perturbations in a schwarzschild black hole spacetime . then there are many works using such a black hole perturbation method in which we describe gravitational waves by metric perturbations in a black hole background spacetime and treat a companion of the binary as a test particle@xcite . this approximation for gravitational waves in a head - on collision of two black holes gives a good agreement with the results obtained by numerical simulation@xcite . thus , such a perturbative approach may provide a good approximation for gravitational waves from a compact binary as well . however , there are so far few works for neutron star perturbations . one may think that if we have two @xmath4 neutron stars , it will be a black hole after coalescence , when the ringing tail of the gravitational waves can be described by quasinormal modes of the black hole . the quasinormal modes of a neutron star may have nothing to do with the final stage of the coalescence . however , before black hole formation , we have to analyze the orbital evolution of the neutron star binary . therefore , we believe that a perturbation analysis for a neutron star is also important . for a nonradial pulsation of a spherically symmetric relativistic star , perturbation equations both for axial and polar modes were first derived by thorne and campolattaro @xcite . similar to the black hole perturbation , the axial mode for a spherical star is described by a second order differential equation . on the other hand , the polar mode was first described by a fifth order differential equation@xcite . however , because of the dynamical degrees of freedom of polar modes , i.e. , sound waves and gravitational waves , the basic equation can be reduced to a fourth order differential equation as shown by lindblom and detweiler @xcite . lindblom , mendell , and ipser @xcite also derived a couple of second order differential equations , which could be interpreted as those for sound waves and gravitational waves , respectively . as in the case of black hole perturbations , quasinormal modes , if they exist , will be important in the analysis of gravitational waves from a compact binary . for the polar mode , there are two types of quasinormal modes of a neutron star ; one is a fluid oscillation mode similar to the @xmath5 , @xmath6 , @xmath7 modes of a newtonian star ( cf . @xcite ) ; the other is a wave mode ( @xmath8 mode ) , which exists only in general relativity @xcite . even for the axial mode , chandrasekhar and ferrari@xcite illustrated that quasinormal modes exist if the effective potential has a minimal as that in an ultracompact star . kokkotas @xcite numerically calculated such axial quasinormal modes for various ultracompact stars . kojima @xcite extended it to a slowly rotating star , setting regge - wheeler gauge conditions . as for emitted gravitational waves from a binary system , kojima @xcite studied them for the case that a test particle is moving in a circular orbit around a polytropic star . for a circular orbit , the axial mode cancels from the orbital symmetry so that the polar mode was only taken into account . he showed that the resonance mode appears in the energy flux when the orbit reaches the radius where the orbital frequency coincides with that of the quasinormal mode . for the axial mode , recently , borrelli @xcite calculated energy spectra of gravitational waves emitted by a test particle spiraling into an ultracompact star . in his result , its energy spectrum shows many peaks , which correspond to axial quasinormal modes of the star . although it is important , since we are interested in a compact binary , a direct collision might show some different features from the binary case . we also do not know what will happen when a test particle reaches the surface of the star . to avoid such an unknown factor and to analyze the case of a compact binary , we first study gravitational waves emitted when a test particle is scattered by a neutron star in this paper . for a schwarzschild black hole , oohara and nakamura @xcite analyzed it and showed that the energy spectrum has no peak except for one which corresponds to the orbital frequency . here we consider a spherical star instead of a schwarzschild black hole . we study only the axial mode which does not exist in newton gravity . to discuss the dependence of the equations of state , we analyze two models : a uniform density star as in @xcite and a polytropic star . this paper is organized as follows . in secs . [ sec : linear]a and [ sec : linear]b , we briefly review the perturbation theory for a spherically symmetric relativistic star . we show our numerical results in sec . [ sec : gw ] . section [ sec : discussion ] is devoted to a discussion . some numerical techniques for calculating gravitational waves are summarized in the appendix . throughout this paper , we use units of @xmath9 and a metric signature of @xmath10 . we start with summarizing briefly the metric perturbation of a spherically symmetric relativistic star . a spherically symmetric background metric @xmath11 is described as @xmath12 @xmath13 where @xmath14 is a mass function inside a radius @xmath15 . we assume a perfect fluid as the stellar matter , i.e. @xmath16 where @xmath17 and @xmath18 are the total energy density and the pressure , respectively , which satisfy a barotropic equation of state , @xmath19 . using tolman - oppenheimer - volkov equations , we construct a stellar model and its spacetime metric numerically except for the constant density star case . the radius @xmath20 of a star is defined by a surface where the pressure vanishes , and the mass of the star @xmath21 is given by @xmath22 . for linearized einstein equations , we can decompose the perturbed metric into an axial mode @xmath23 and a polar mode @xmath24 : @xmath25 using regge - wheeler gauge conditions , we will integrate the interior and exterior regions of the linearized einstein equations , separately , and impose appropriate junction conditions at the surface @xmath20 to find the solution . in this paper , we only deal with axial mode perturbation . then , we write down the linearized einstein equation only for axial modes in the following subsections . in order to find the linearized einstein equations for axial modes , we expand the perturbed metric by tensor harmonics for polar angle @xmath26 and azimuthal angle @xmath27 @xcite , and proceed to a fourier transformation for the time coordinate @xmath28 . although there are ten independent components for the linearized metric , four of them are gauge freedoms of coordinate transformations , which are fixed by a choice of regge - wheeler gauge @xcite , resulting in two components belonging to axial modes , while the rest of the four correspond to polar modes . for axial mode perturbations , we can set @xmath29 where @xmath30 and @xmath31 are functions of the radial coordinate @xmath15 defined below , and @xmath32 is a spherical harmonics . the axial mode in the interior region of a star is described by a single wave equation for gravitational waves , because a rotation does not exist in a spherically symmetric background spacetime . that is , we have a single wave function @xmath33 , which determines the behaviors of axial modes as @xmath34 the equation for the wave function @xmath33 is derived from the linearized einstein equation for axial modes as @xmath35 where the `` tortoise '' coordinate @xmath36 and the effective potential @xmath37 are defined as @xmath38 respectively . as for the boundary condition , the wave function @xmath33 must be regular at the center of a star . expanding @xmath33 around the center @xmath39 , we find @xmath40 r^{l + 3 } + o(r^{l+5 } ) \right\ } , \label{eq : bc_x}\ ] ] where @xmath41 is an arbitrary constant , and @xmath42 , @xmath43 , and @xmath44 are the central density , pressure , and metric functions , respectively . apart from a free parameter @xmath41 , we obtain a solution @xmath33 by integrating eq . ( [ eq : inside_perturbation_equation ] ) with the boundary condition ( @xmath45 ) . further details of the numerical techniques constructing the wave function @xmath33 are given in the appendix , subsection [ subsec : app_interior ] . the background metric outside the star is the schwarzschild spacetime , i.e. , eq . ( [ eq : bgmetric ] ) , with @xmath46 as for the trajectory of a test particle , without loss of generality , we can assume that the particle moves on the equatorial plane ( @xmath47 ) . then , the equation of motion for the particle is described as @xmath48 where the particle trajectory is @xmath49 , and @xmath50 , @xmath51 , and @xmath52 are the mass , the normalized energy , and the normalized orbital angular momentum of the particle , respectively , with @xmath53 and @xmath54 . the normalized effective potential energy @xmath55 of the particle is given as @xmath56 in this paper , since we only consider the motion of a test particle scattered by a spherical star , the particle orbit is unbounded , i.e. , @xmath57 where @xmath58 is the maximum value of the potential . the perturbed metric outside a star only comes from an oscillation of spacetime , that is , gravitational waves . then , similar to the interior region , the linearized einstein equations for the metric @xmath59 and @xmath60 defined as eq . ( [ metric ] ) are reduced to a single wave equation for a new wave function @xmath61 defined by @xmath62 where @xmath63" +"in recent years , there has been a growing interest in the topic of consensus decision making in several fields including animal behaviour @xcite , social sciences @xcite and control theory @xcite . in this paper we use the paradigm of animal groups but we would like to stress already at this point that there is a considerable analogy between the decision - making processes in very different systems and we expect that our simple model should be applicable to a wider range of systems . our object of study is the phenomenon during which the animals moving in groups , seemingly make unanimous decisions on the choice and time of performing activities even in the absence of global leaders . it is expected that because of the heterogeneity in the attributes like the age , sex and social status of the animals in a group or the differences in their perception of external stimuli there will be differences in the motivations of the members at the time of making choices . however , in spite of the differences , synchronization is seen to take place . examples include takeoff of swarm of honeybees from nest sites @xcite , activity synchronization in sheep @xcite , collective movement in monkeys @xcite , group departures of domestic geese @xcite and departure of ants from a feeding site @xcite . the study of collective opinion formation in physics has mainly focused on human societies @xcite . parallels have been drawn between phase transitions in magnets and the opinion dynamics in populations . alternatively , the subject of collective motion of animal groups has been extensively modelled @xcite . here point - like particles , representing animals , move with constant speed , each tending to align with its immediate neighbours , for low noise levels , giving rise to a globally ordered state replicating the motion of flocks where all animals move in the same direction . in this report we model the process of landing of bird flocks performing foraging flights as a typical example of collective decision making . we view this phenomena as a shift of the average opinion of the flock from that of continuing horizontal flight about some preferred altitude to that of descent towards the surface below . we model the fact that birds land almost synchronously even in the presence of heterogeneity in motivations , along the lines of the random field ising model ( rfim ) @xcite . our approach is similar to that used in @xcite where the authors analyze ( among other cases ) the manner in which people in concert halls , initially joining the applause , stop clapping almost at the same time . in a very recent model @xcite for collective landing , birds are assumed to move under the action of different _ social _ forces . in addition , the internal state of each bird is characterized by a continuous variable called _ landing intent _ such that the internal state of each bird is directly coupled to the internal state of its neighbours . in contrast we allow motivation of individual birds to be influenced by only the observable variables of their neighbours , like position and velocity . in addition as a part of the model we introduce a method which enables us to work in open boundary conditions where the birds in flight move cohesively and do not spread out in the horizontal plane even in the presence of perturbations . with this model we investigate the level of synchronicity in collective landing across time and space and explore the nature of fluctuations close to the point in time when landing occurs . below we describe the two aspects of the model , _ viz . _ collective decision making and collective motion in detail . the birds in our model are represented by particles characterized by the dynamical variables of position @xmath0 and velocity @xmath1 in three dimensional space . the only _ natural _ boundary that we allow in the system is the @xmath2 plane which we consider to be the landing surface . the @xmath3-coordinate of a flying bird gives its height above the ground . we assign to each particle @xmath4 a variable @xmath5 such that we refer to a bird in the flying state as active ( @xmath6 ) and a bird in the landed state as inactive ( @xmath7 ) . this variable is updated at discrete times @xmath8 according to the condition : @xmath9 where @xmath10 is the time increment . once a bird @xmath4 has landed we keep its position unchanged till the end of the simulation . also , from here on we use the words `` bird '' and `` particle '' synonymously . first we focus on the variables @xmath11 and @xmath12 governing the cruising motion of the birds parallel to the landing surface . this motion is assumed to be essentially decoupled from the motion in the vertical direction and is modelled in the spirit of @xcite . a particle @xmath4 is assumed to move , with some uncertainty , in the average direction of motion of all neighboring particles @xmath13 whose separation @xmath14 from @xmath4 is less than a interaction radius @xmath15 . from now on we refer to the set of particles in this neighbourhood as @xmath16 with respect to a particle @xmath4 such that , the inactive particles and the particle @xmath4 are included as well . the expression for updating velocity at a time @xmath8 is given by @xmath17,\ ] ] where @xmath18 is the magnitude of the velocity , @xmath19 is the rotation matrix in two dimensions representing a random perturbation by an angle @xmath20 and @xmath21 denotes the unit vector @xmath22 . here @xmath20 is chosen with a uniform probability from the interval @xmath23 $ ] , where @xmath24 is the amplitude of the noise . we describe the force - like term @xmath25 below . we follow the standard version @xcite of the original spp model @xcite for the updating of positions : @xmath26 we mention here that it is a well - known problem with existing models of collective motion to maintain the cohesiveness of a moving flock in the presence of a finite amount of noise @xmath24 and with finite ranged ( as @xmath15 ) interaction between the members . a flock tends to break up into smaller sub - flocks which eventually move in independent directions . a periodic boundary condition ( pbc ) is used to prevent the flock from spreading out perpendicular to the direction of motion . however , in the problem of landing we find that the imposition of a pbc would be unrealistic in the sense that there will be a possibility of a particle that has become inactive and hence ceased to move , to continually exchange information with the rest of the moving flock . therefore , we introduce a new kind of `` comoving boundary '' condition where we imagine the motion of the particles on the @xmath27-plane to be governed by a circular bounding region with radius @xmath28 and the centre lying on the centre of mass ( _ com _ ) of all active particles ( mass of each assumed to be unity ) . this boundary therefore translates with the flock as the _ com _ is put into motion due to collective motion of the particles . when a particle which is inside the region tries to leave it , the particle is subjected to an attraction proportional to the distance from the boundary . the direction of this attraction is along the resultant of the direction towards the location of the _ com _ and the direction of motion of the _ com _ itself . for a particle located at @xmath29 at an instant of time , the attraction @xmath30 is given by : @xmath31\mathbf{c}\big(\mathbf{x^{\shortparallel}}\big ) & \mbox { if $ |\mathbf{x}^{\shortparallel}-\mathbf{\overline{x}}^{\shortparallel}| > r_\mathrm{b}$ } \\ 0 & \mbox { otherwise , } \end{array } \right.\ ] ] with @xmath32 where @xmath33 is the strength of the attraction , @xmath34 and @xmath35 are the position and the velocity of the _ com _ , respectively , parallel to the @xmath27-plane at that instant and @xmath36 is a parameter . the _ com _ and its velocity are calculated with respect to the active particles . in the figure [ field ] we plot @xmath25 when the motion of the _ com _ is in a direction parallel to the y - axis . similarly , we assume that the boundary adjusts itself to keep average separation between active particles constant . thus , in general @xmath28 is a function of time , given by , @xmath37 where @xmath38 is the fraction of the active particles at time @xmath8 and @xmath39 is the number of particles , initially active , per unit area of the @xmath27-plane . on the @xmath27-plane , defined through ( [ bound-1 ] ) for the value of @xmath40 . the direction of motion of the _ com _ is assumed to be along the y - axis , indicated by the arrow at the centre of the circle . the length of a vector is directly proportional to the distance from the boundary . , width=340 ] now we explain how the collective decision making process takes place in the flock and how it is related to the cohesion and eventual landing along the vertical direction . we characterize the decision of an individual bird as a binary choice problem @xcite . to each bird @xmath4 we assign an internal state variable @xmath41 such that when @xmath42 the bird continues to cruise above ground and when @xmath43 the bird decides to land . for the cruising state we assume that a bird likes to fly about an altitude @xmath44 on average without deviating too far above or below . however , we expect the elevation of a bird to fluctuate with time pertaining to factors like the noise in the medium and collision avoidance . thus when @xmath42 we consider the vertical motion of the particle to be essentially a random walk bounded by imaginary walls at @xmath45 and @xmath46 where @xmath47 is the thickness of the flock . in case the bird decides to land the vertical motion is directed towards the landing surface at @xmath2 . formally we define , @xmath48 & \textrm{if $ s_i(t)=1 $ and $ |\delta(t-\delta t)|>\delta z_0/2 $ } \\ -v & \textrm{if $ s_i(t)=-1 $ , } \end{array}\right.\ ] ] where @xmath49 takes values @xmath50 with equal probability and @xmath51 , is the amount of deviation from the height @xmath44 at time @xmath52 . to model the motivational differences in birds we assign to each bird @xmath4 , an inherent switching time @xmath53 @xcite such that if the bird begins an isolated flight at time @xmath54 , it would decide to land at time @xmath55 . we assume that the value of @xmath53 for the bird @xmath4 will in general depend on its energy reserves @xcite and thus in general will be different for different birds . we choose @xmath53 s from a gaussian distribution with a given standard deviation @xmath56 . the value of @xmath56 allows us to control the level of heterogeneity in a flock . although we assign _ a priori _ values of @xmath53 to birds , due to the randomness in the choice of these switching times , they can be thought to be additionally include the effect of the environment such as quality of foraging patches over which the flocks fly . for a particle in the flock , it will have a finite number of particles in its neighbourhood and therefore will be influenced by their actions while taking a decision . hence the internal state of a particle will be a function of two competing factors , ( i )" +"in the solar system , there are many small bodies such as asteroids and comets . since these small astronomical objects could keep the ancient information of the history of the solar system , a lot of efforts have been devoted to investigations of these objects so far ( e.g. , @xcite ) . for instance , the asteroid itokawa was explored by the japanese space craft _ hayabusa _ from september 2005 . the exploration uncovered the details of itokawa s surface terrain . itokawa is covered by various sizes of granular matter such as regolith , pebbles , and boulders @xcite . moreover , migrations and sorting of the regolith could occur on the surface of itokawa @xcite , although the surface gravity of itokawa is extremely low . impact craters located on the surface of itokawa were very subtle , i.e. , they show indistinct morphologies @xcite . this is probably due to the erasure of the craters by seismic shaking @xcite . in addition , tiny samples returned from itokawa allow us to analyze the detail of its history . @xcite revealed that itokawa s surface grains are relatively young in terms of cosmic - rays exposure . the estimated age is approximately eight million years . besides , using x - ray microtomography , @xcite found that some particles had rounded edges . all these facts suggest that the surface of itokawa would be active and continue to be renewed until recently . one possible explanation of such young surface is the regolith convection caused by impact - induced seismic shaking . although the direct measurement of the seismic wave has not been achieved , @xcite and @xcite studied the possibility of global seismic shaking of asteroid eros in order to explain its surface modification processes . they built a model of seismic shaking by considering the attenuating diffusion of the seismic wave . @xcite partially applied the model to the asteroid itokawa and showed that the global regolith convection might occur even by small - scale impacts . to unlock the regolith grains network supported by gravity , the maximum acceleration induced by the seismic shaking has to be greater than the gravitational acceleration . @xcite revealed that this criterion can be satisfied by a small - scale impact since the gravity on the surface of itokawa @xmath3 is very small , @xmath4 m / s@xmath5 @xcite . the value of @xmath3 is about five orders of magnitude smaller than the earth s gravitational acceleration , @xmath6 m / s@xmath5 . the evaluation is still qualitative since they only assessed the onset criterion of the regolith convection . while the quantitative assessment of the convective velocity is necessary to discuss the feasibility of the regolith convection , there have been very few such studies . granular convection can be generally observed in a granular matter under the mechanical vibration . when a granular matter is subjected to a steady vertical vibration , granular convection is readily induced . if the vibrated granular matter is polydisperse , the size segregation of grains occurs usually in vertical direction . this vibration - induced size segregation is called brazil nut effect ( bne ) . the bne can be caused by the granular convection @xcite . this means that the grains can be migrated and sorted simultaneously by vibration . although the regolith convection accompanied by migration and sorting seems to be a natural outcome of global seismic shaking , the scaling approach to the granular convective velocity is needed to discuss the consistency between regolith convection and observational data such as surface age of the asteroid . therefore , we experimentally measure and scale the velocity of granular convection in this study , as a first - step approach to this problem . fundamental nature of granular convection itself is an intriguing problem . the granular convection has long been studied both by experiments @xcite and numerical simulations @xcite . the onset of granular convection depends on the maximum acceleration of the applied vibration . if the maximum acceleration is less than the gravitational acceleration , any granular convection does not occur at all ( e.g. , @xcite ) . thus the dimensionless parameter @xmath7 , which represents the balance between the maximum vibrational acceleration and the gravitational acceleration @xmath1 , has been used to characterize the behavior of granular convection . @xmath7 is defined as , @xmath8 where @xmath9 is the vibration amplitude and @xmath10 is the frequency . in this study , the scaling method is applied to the analysis of granular convective velocity . we are interested in asteroidal - scale granular convection while the actual experiment is limited within the laboratory scale . in such a situation , the scaling is the only way to derive a meaningful quantitative relation . in the scaling analysis , dimensionless parameters such as @xmath7 are useful since they do not depend on the system of unit . the weak point of the scaling analysis is its arbitrariness . of course , @xmath7 is one of the most important dimensionless parameters to discuss the vibrated granular matter . however , the choice of the important dimensionless parameter is not unique . specifically , another dimensionless parameter called shaking parameter @xmath11 was firstly introduced by @xcite and recently used to describe the transitions among the granular leidenfrost , bouncing bed , undulations , convection , and so on @xcite . particularly , @xmath11 is relevant to characterize a strongly shaken shallow granular convection @xcite . @xmath11 is defined as , @xmath12 where @xmath13 is the constitutive grains diameter . @xmath11 denotes the balance between the squared vibrational velocity and the squared gravitational velocity . furthermore , @xmath11 can be also obtained by the natural non - dimensionalization of the granular - hydrodynamic model for the strongly shaken granular convection @xcite . using the aforementioned dimensionless parameters , we would like to find a useful scaling relation between granular convective velocity , the gravitational acceleration , and other parameters . therefore , we carry out a systematic laboratory experiments of the vibration - induced granular convection . this paper is constructed by following sections . in section [ sec : experiment ] , we explain the experimental setup and how to measure the convective velocity . section [ sec : results ] shows the characterization of some convective - roll patterns and the result of the scaling . in section [ sec : discussion ] , we discuss physical meaning and tentative implication of the scaling to the microgravity environment . section [ sec : conclusions ] contains a conclusions . a schematic illustration of the experimental apparatus is shown in fig . [ fig : setup ] . the experimental setup consists of a cylinder made by plexiglass of its height @xmath14 mm and inner radius @xmath15 ( @xmath16 , @xmath17 , or @xmath18 mm ) . glass beads are poured in the cylindrical cell to make a granular bed of the height @xmath19 , @xmath20 , @xmath21 , or @xmath22 mm . the system is mounted on an electromechanical vibrator ( emic 513-b / a ) and shaken vertically . the vibration frequency @xmath10 is varied from @xmath23 to @xmath24 hz and @xmath7 is varied from @xmath25 to @xmath26 . the grains used in this study are glass beads . most of experiments are carried out with glass beads of diameter @xmath27 mm ( as - one corp . bz08 ) and some of them are performed with glass beads of @xmath28 or @xmath25 mm ( as - one corp . bz04 , bz2 ) . size dispersion of glass beads is less than @xmath29% , and the true density of glass beads is @xmath30 kg / m@xmath31 . [ 0.9 ] to measure the granular convective velocity , particle imaging velocimetry ( piv ) method is utilized @xcite . motions of glass beads are filmed by a high - speed camera ( photoron sa-5 ) through a transparent side wall . to erase the memory effect of granular matter , one minute pre - vibration is applied before each experimental realization . this means that we measure the steady granular convection . while the actual impact - induced regolith convection might be transient , we have to concentrate on the steady convection to eliminate the memory effect . the frame rate is fixed at @xmath32 fps and spatial resolution of the image ranges from @xmath33 @xmath34m / pixel to @xmath35 @xmath34m / pixel depending on the experimental conditions . the high - speed images are acquired for @xmath36 s. since each image consists of @xmath37 pixels , the size of field of view ranges from @xmath38 to @xmath39 mm@xmath5 . raw data images are shown in backgrounds of figs . [ fig : vector_and_vertical_plot ] and [ fig : vectorplot ] . since it is hard to completely follow all the grains motion , we use piv method instead of the direct particle tracking . in the analyses of figs . [ fig : vector_and_vertical_plot ] and [ fig : vectorplot ] ( a ) , each instantaneous image is divided into @xmath40 boxes , i.e. , each box consists of @xmath41 pixels . note that the number of image partitioning depends on the experimental condition . then the velocity at each box is computed by detecting a peak of the cross - correlation between two different time snapshots . obtained ( time - averaged ) examples of the velocity field are shown by colored vectors in figs . [ fig : vector_and_vertical_plot ] and [ fig : vectorplot ] . an interval time to compute the velocity ( cross - correlation ) is kept constant so that it corresponds to a multiple of the period of vibration , i.e. , two cross - correlated images are kept in same phase . for instance , @xmath42 s time interval is used for @xmath43 hz vibration . if we use a full temporal resolution to calculate the velocity field , vibrational motion of individual grains can be captured just like @xcite measurement . however , we are mainly interested in the global convective motion rather than such microscopic vibration . therefore , we use phase - matching images to compute the velocity . as shown in fig . [ fig : vector_and_vertical_plot ] , convective - velocity vectors are decomposed into @xmath44 ( vertical ) and @xmath45 ( horizontal ) directions . they are averaged along the horizontal axis since we are mainly focusing on the axisymmetric convective flow ( like fig . [ fig : vector_and_vertical_plot ] ) for the reason mentioned later . then we obtain vertical and horizontal components of velocities as functions of @xmath44 , respectively as , @xmath46 and @xmath47 . in fig . [ fig : vector_and_vertical_plot ] , panels ( b ) and ( c ) respectively show @xmath46 and @xmath47 computed from the velocity field shown in panel ( a ) . the positive direction of @xmath44 axis is taken to downward , and @xmath48 corresponds to the top surface of the granular bed . @xmath49 is the center of container . above the surface of granular bed ( @xmath50 ) , saltations of grains are dominant and the measured velocity becomes random . this is the reason of large errors in @xmath51 and @xmath52 at @xmath50 ( fig . [ fig : vector_and_vertical_plot](b , c ) ) . first , we are going to focus on the global structure of the granular convective motion . we find that the global structure shows a transition from a single roll to a toroidal roll as @xmath10 increases . in the former state , grains rise up on the one side wall and fall down on the opposite side wall . thus , in this state , the resultant velocity field shows a certain circularity . due to this circularity" +"m. kac s classical paper can one hear the shape of a drum "" @xcite , triggered intensive research in two complementary aspects of this problem . on the one hand , a search for systems for which kac s question is answered in the affirmative was conducted , and , on the other hand , various examples of pairs of systems which are isospectral but not isometric were identified . in the present paper we shall focus our attention to quantum graphs and in the following lines will review the subject of isospectrality in this limited context . the interested reader is referred to [ 1 - 11 ] for a broader view of the field where spectral inversion and its uniqueness are discussed . spectral problems related to graphs emerge in two distinct ways . in the first , the spectrum of the connectivity ( adjacency ) matrix is considered . it represents a discrete version of the laplacian , and for finite graphs , the spectrum is finite . this set of problems is often referred to as combinatorial graphs . quantum ( metric ) graphs are obtained by associating the standard metric to the bonds which connect the vertices . the schrdinger operator consists of the one - dimensional laplacians on the bonds complemented by appropriate boundary conditions at the vertices ( see next section ) . the spectrum of quantum graphs is unbounded , and it displays many interesting features which made it a convenient paradigm in the study of quantum chaos @xcite . shortly after the appearance of kac s paper , m. e. fisher published his work on hearing the shape of a drum "" @xcite , where he addresses isospectrality for the discrete version of the laplacian . since then , the study of isospectral combinatorial graphs made very impressive progress . in particular , several methods to construct isospectral yet different graphs were proposed . a review of this problem can be found in @xcite . in particular , a method which was originally put forward by sunada @xcite to construct isospectral laplace - beltrami operators on riemann manifolds , was adapted for the corresponding problem in the context of combinatorial graphs . here we shall go one step further , and show that it can be also adapted for quantum graphs . the conditions under which the spectral inversion of quantum graphs is unique were studied previously . in @xcite it was shown that in general , the spectrum does not determine uniquely the length of the bonds and their connectivity . however , it was shown in @xcite that quantum graphs whose bond lengths are _ rationally independent _ can be heard "" - that is - their spectra determine uniquely their connectivity matrices and their bond lengths . this fact follows from the existence of an exact trace formula for quantum graphs @xcite . thus , isospectral pairs of non congruent graphs , must have rationally dependent bond lengths . the sunada method , which is based on constructing the isospectral domains by concatenating several copies of a given building block , automatically provides us with graphs with rationally dependent lengths . an example of a pair of metrically distinct graphs which share the same spectrum was already discussed in @xcite . in a previous report we have shown that all the known isospectral domains in @xmath0 @xcite have corresponding isospectral pairs of quantum graphs @xcite . here , we shall take the subject one step further , and propose that isospectral graphs can be resolved by counting their nodal domains . that is , the nodal counts of eigenfunctions belonging to the same spectral value are not the same . the idea that nodal counts resolve isospectrality was suggested in @xcite for a family of isospectral flat tori in 4-d , and was tested numerically . the present work offers both rigorous and numerical evidence to substantiate the validity of this conjecture in a few examples of isospectral graphs . for these examples the nodal counts differences ocur on a substantial fraction of the spectrum . the paper is organized in the following way . for the sake of completeness we shall give a short review of some elementary definitions and facts on quantum graphs . we shall then show how pairs of isospectral domains in @xmath0 can be reduced to isospectral pairs of quantum graphs , and discuss their spectra and eigenfunctions . finally , we shall study the nodal domains of these eigenfunctions and show that by counting nodal domains one can resolve the isospectral ambiguity of the graphs presented . we consider finite graphs consisting of @xmath1 _ vertices _ connected by @xmath2 _ bonds_. the @xmath3 _ connectivity matrix _ will be denoted by @xmath4 : @xmath5 when the vertices @xmath6 and @xmath7 are connected by @xmath8 bonds , and it vanishes otherwise . the group of bonds which emerge from the vertex @xmath6 form a star "" which will be denoted by @xmath9 . @xmath10 of a vertex is defined as the cardinality of the star @xmath9 and @xmath11 . vertices with @xmath12 belong to the graph _ boundary_. the vertices with @xmath13 belong to the graph _ interior_. the bonds are endowed with the standard metric , and the coordinates along the bonds @xmath14 are denoted by @xmath15 . the length of the bonds will be denoted by @xmath16 , and the total length of the graph is @xmath17 . the domain of the schrdinger operator on the graph is the space of functions which belong to sobolev space @xmath18 on each bond b and at the vertices they are continuous and obey boundary conditions as is mentioned in ( [ eq : bc ] ) . the operator is constructed in the following way . on the bonds , it is identified as the laplacian in 1-d @xmath19 . it is supplemented by boundary conditions on the vertices which ensure that the resulting operator is self adjoint . we shall consider in this paper the neumann and dirichlet boundary conditions : @xmath20 the derivatives in ( [ eq : bc ] ) are directed out of the vertex @xmath6 . _ comment _ : the neumann boundary conditions will be assumed throughout , unless otherwise stated . a wave function with a wave number @xmath21 can be written as @xmath22 where @xmath14 connects the vertices @xmath6 and @xmath7 , where the wave function @xmath23 takes the values @xmath24 and @xmath25 respectively . the form ( [ eq : wavefun ] ) ensures continuity . the spectrum @xmath26 and the corresponding eigenfunctions are determined by substituting ( [ eq : wavefun ] ) in ( [ eq : bc ] ) . the resulting homogeneous linear equations for the @xmath24 are written as @xmath27 and a non trivial solution exists when @xmath28 the spectrum @xmath29 , which is a discrete , positive and unbounded sequence is the zero set of the _ secular function _ @xmath30 . the secular functions of the type ( [ eq : secular ] ) have poles on the real @xmath21 axis , which renders them rather inconvenient for numerical studies . the secular function can be easily regularized in various ways , ( see e.g. , @xcite ) . it is easy to show that the complete wave function can be written down in terms of the vertex wave functions at the interior vertices with @xmath31 only . in the sequel we shall denote their number by @xmath32 . this reduces the dimension of the matrix @xmath33 above from @xmath1 to @xmath32 . the nodal domains of the eigenfunctions ( the connected domains where the wave function is of constant sign ) , are of two types . the ones that are confined to a single bond are rather trivial . their length is exactly half a wavelength and their number is on average @xmath34 . the nodal domains which extend over several bonds emanating from a single vertex vary in length and their existence is the reason why counting nodal domains on graphs is not a trivial task . the number of nodal domains in a general graph can be written as @xmath35\mathrm{sign}[\phi_j ] \right ) \right \ } -b + v \ . \label{eq : nnb2}\ ] ] where @xmath36 stands for the largest integer which is smaller than @xmath37 , and @xmath38 are the values of the eigenfunction at the vertices connected by the bond @xmath14 @xcite . ( [ eq : nnb2 ] ) holds for the case of an eigenfunction which does not vanish on any vertex : @xmath39 . recently schapotschnikow @xcite proved that sturm s oscillation theorem extends to finite tree ( loop - less ) graphs : the number of nodal domains of the @xmath40th eigenfunction ( ordered by increasing eigenvalues ) is @xmath40 . berkolaiko @xcite have shown that the number of nodal domains is bounded to the interval @xmath41 $ ] where @xmath42 is the minimal number of bonds which should be cut so that the resulting graph is a tree . nodal domains can be also defined and counted in an alternative way which makes use of the vertex wave functions @xmath43 ( see ( [ eq : wavefun ] ) ) exclusively : _ a nodal domain consists of a maximal set of connected interior vertices ( @xmath31 ) _ _ where the vertex wave functions have the same sign . _ this definition has to be modified if any of the @xmath24 vanishes . then , the sign attributed to it is chosen to maximize the number of nodal domains @xcite . we thus have two independent ways to define and count nodal domains . to distinguish between them we shall refer to the first as _ metric _ nodal domains , and the number of metric domains in the @xmath40th eigenfunction will be denoted by @xmath44 . berkolaiko s theorem states that @xmath45 . the domains defined in terms of the vertex wave functions will be referred to as the _ discrete _ nodal domains . the number of discrete nodal domains of the @xmath40th vertex wave function will be denoted by @xmath46 . the sequences of metric and discrete nodal domains counts @xmath47 and @xmath48 are the main objects of study of the present paper . the first pair of isospectral planar domains which was introduced by gordon , web and wolpert @xcite is a member of a much larger set which was discussed in @xcite . this was extended in @xcite to include domains which differ in the distribution of boundary conditions ( dirichlet or neumann ) along their boundaries . the common feature of these sets of pairs of isospectral domains is that they are constructed using the sunada method @xcite , and they share a few important and distinctive attributes : * the domains are constructed by concatenating an elementary building block "" in two different prescribed ways to form the two domains . a building block is joined to another by reflecting along the common boundary . the shape of the building block is constrained only by symmetry requirements , but otherwise it is quite general . * the eigenfunctions corresponding to the same eigenvalue are related to each other by a _ transplantation_. that is , the eigenfunction in a building block of one domain can be expressed as a linear combination of the eigenfunction in several building blocks in the other domain . the transplantation matrix is independent of the considered eigenvalue . * the construction of these pairs reflects an abstract algebraic structure which was identified by sunada @xcite . an example of an isospectral pair of domains in @xmath49 and its building block is given in figure ( [ fig:7 - 3](a ) ) . this is a pair whose construction is described in @xcite . it is denoted there by @xmath50" +"the ongoing heavy ion physics program with the star detector at rhic has accumulated the wealth of experimental data , stimulating important advances in the understanding of properties of hot strongly interacting matter @xcite . some of the focus areas currently under study are the thermodynamic and hydrodynamic properties of the matter created , in - medium effects on parton propagation , and hadronization mechanisms in qcd matter . uniform azimuthal acceptance and extended pseudo - rapidity coverage of the star detector is exceptionally suited for studies of jets and jet - medium interactions via triggered and non - triggered correlations . the data provided quantitative constrains on jet fragmentation and theoretical models of energy loss . systematic studies of medium effects are advanced by analysis of system size effects on tomographic probes . data collected with lighter cu ions have expanded those studies by providing additional control over the system size variations . complimentary data samples at lower beam energy of 62 gev have also allowed systematic studies as function of energy to be performed . star full capabilities for particle identification in a wide kinematic range have enabled new advances in more quantitative tests of qcd predictions . different detectors provide complimentary capabilities and coverage . pions , kaons , electrons and ( anti)protons are identified via their specific ionization energy loss in the time - projection chamber ( tpc ) material at low and high transverse momenta ( @xmath0 ) . in the intermediate momentum range tpc results are enhanced by the time - of - flight ( tof ) capabilities . muons can be identified in the muon telescope detector ( mtd ) prototype . photons at forward rapidities are measured using the photon multiplicity detector ( pmd ) . weakly decaying strange and multi - strange hadrons are identified geometrically by their decay vertices with the tpc and tof information on decay daughter particles . short - lived resonances are reconstructed combinatorially by the invariant mass technique . these capabilities have allowed measuring the yields and transverse momentum spectra addressing a variety of physics topics , including strangeness and heavy flavor production that are of topical interest for this conference . strangeness enhancement was long thought as one of the signatures for the quark - gluon plasma formation @xcite . early data suggested that strangeness equilibration is achieved at rhic and that initial collision geometry affects the strangeness systematics . in star studies of the collision geometry effects on strangeness production is being accomplished by comprehensive analysis of various strange species ( @xmath1,@xmath2 , @xmath3 , @xmath4 , @xmath5 , @xmath6 ) in light vs. heavy systems at all rhic energies . the latest update on those developments is reported in @xcite . new advances in heavy flavor sector afforded by star particle identification capabilities include the measurements of j/@xmath7 spectra and nuclear modification factors in cu+cu collisions , measurements of charm total cross - section for @xmath8 , d+au , au+au and cu+cu systems , new constrains on bottom contribution to heavy flavor from j/@xmath7-hadron and @xmath9-@xmath10 azimuthal correlation studies . these and other highlights on heavy quark measurements from star are reported in @xcite . the following two sections will focus on some of the new results from triggered and non - triggered correlation analyses . elliptic flow results have produced a lot of excitement from the beginning of rhic program . for the first time in heavy ion collisions the large @xmath11 values reported could be described by ideal hydrodynamics @xcite . theoretical calculations successful in description of flow results indicated the values of the shear viscosity over the entropy ratio consistent with the expectations for strongly interacting medium @xcite . although recent work seem to question the applicability of ideal hydro @xcite , most theories agree that the matter created at rhic is extremely dense , with the hydrodynamic description applicability limits extending to higher @xmath0 for more central collisions . flow results provide strong indications for partonic nature of the medium : constituent quark scaling observed for all measured hadron species ( including @xmath6 and @xmath5 with their small hadronic interaction cross - sections ) points on relevance of partonic degrees of freedom at hadronization @xcite . similar results are observed in the cu+cu collisions although the overall @xmath11 values are lower at a given centrality for the cu+cu compared to au+au at the same energy . new result reported recently by star on non - triggered two - particle correlations provide independent means to extract and cross - check azimuthal anisotropy parameters , but also to characterize other processes that induce relative angular correlations between the particles pairs . in this analysis di - hadron correlation formed with no transverse momentum restrictions on either hadron is used to study centrality evolution of characteristic structures in relative azimuth and pseudo - rapidity . it has been shown that the resulting correlation can be decomposed into a few structures , and information related to the individual sources can be extracted @xcite . per - particle pair densities for various centrality bins of 200 gev minimum bias au+au data sample are shown in figure 1 . minijet contribution , measured as the same - side two - dimensional gaussian correlation structure , was found to exhibit a threshold behavior . while approximate binary scaling is observed from @xmath8 and most peripheral au+au to mid - central collisions , a sharp transition is found for both 200 and 62 gev au+au data at about 55% and 40% event centrality , respectively . as shown in figure 2 , from this point the minijet peak amplitude exhibits rapid growth and the peak width in relative pseudo - rapidity broadens by more than a factor of 2 . here the transverse density , calculated as @xmath12 , where @xmath13 is initial collision overlap area s from glauber model , is used as a centrality measure . also shown in figure 2 is the total yield or `` volume '' of the minijet peak . it is estimated to include approximately one third of all produced particles in central collisions . novel features have been also observed by star in the triggered correlations . early results on the disappearance of away - side jet ( in certain kinematic range ) unambiguously established the presence of the jet quenching phenomena at rhic @xcite . experimental observations are found to be consistent with theoretical expectations for partonic energy loss @xcite , prompting more studies of the mechanisms of jet - medium interactions . two - dimensional study of the correlation structures for charged hadrons associated with a high-@xmath0 trigger shows shape modifications in both @xmath14 and @xmath15 dimensions compared to a @xmath8 reference . within a two - component approach the intermediate @xmath0 structure can be decomposed into a jet - like part , and the so - called `` ridge '' . the jet part appears similar in shape to the structures seen in @xmath8 data , while `` ridge '' resembles properties of the bulk medium . left panel of figure 3 illustrates the ridge - long range @xmath15 structure accompanying the jet peak in central 200 gev au+au collisions@xcite . jet - medium interaction is likely to be the origin of the ridge formation and modification of the jet - like peaks . di - hadron correlations with identified hadrons provide additional means to study parton propagation in the medium . measurements of identified particle spectra and ratios for associated hadrons in the jet cones and ridges could address the issues of color - charge dependence of energy loss , presence of meson / baryon effects and interplay between various hadronization scenarios . strong enhancement of baryon production at intermediate momentum range in inclusive measurements was theorized as an evidence for quark coalescence . however , in azimuthal correlations with the hyperon - triggers significant jet - like structures were observed for all species of hyperons ( including @xmath6 ) @xcite , which contradicts initial expectations from coalescence picture . associated hadron yields in ( multi)strange hadron correlations show no dependence on strangeness content . following those observations , a medium response to the propagating parton or `` phantom jet '' was proposed to accommodate the data within the coalescence picture @xcite . this theoretical explanation preserves the correlation in azimuthal space and produces ridge - like structure in pseudo - rapidity . to confront the models and further the understanding of physics mechanisms producing the ridge , it was essential to extend the correlation studies into @xmath15-@xmath14 space separately for baryons and mesons . preliminary star results show significant differences in strange ( central panel of figure 3 ) and non - strange ( figure 3 , right ) baryon to meson ratios measured in jet part around a 4 gev/@xmath16 triggers , with respect to the ridge part . the jet - part ratios for @xmath17 and @xmath18 are found to be significantly lower in central au+au collisions compared to non - triggered distributions , and are consistent with the inclusive ratios from 200 gev @xmath8 data @xcite . at the same time , the ridge ratios suggest relative baryon enhancement for both strange and non - strange species , which might be related to direct fragmentation of the gluons , radiated of the hard - scattered quark , or their subsequent recombination with the medium partons . higher statistics a+a data samples , expected to be collected in future runs , are required to address ridge hadro - chemistry in more details . -@xmath14 di - hadron correlation in 200 gev 12% central au+au collisions for hadronic triggers with @xmath19 gev/@xmath16 and associate hadrons with @xmath20 gev/@xmath16 . @xmath18 ( center ) and @xmath17 ( right ) ratios as function of @xmath0 for inclusive data , and ridge and jet parts in 200 gev a+a data . shown for comparison are the inclusive ratios from 200 gev @xmath8 and/or d+au collisions . , title=""fig:"",height=120 ] -@xmath14 di - hadron correlation in 200 gev 12% central au+au collisions for hadronic triggers with @xmath19 gev/@xmath16 and associate hadrons with @xmath20 gev/@xmath16 . @xmath18 ( center ) and @xmath17 ( right ) ratios as function of @xmath0 for inclusive data , and ridge and jet parts in 200 gev a+a data . shown for comparison are the inclusive ratios from 200 gev @xmath8 and/or d+au collisions . , title=""fig:"",height=120 ] -@xmath14 di - hadron correlation in 200 gev 12% central au+au collisions for hadronic triggers with @xmath19 gev/@xmath16 and associate hadrons with @xmath20 gev/@xmath16 . @xmath18 ( center ) and @xmath17 ( right ) ratios as function of @xmath0 for inclusive data , and ridge and jet parts in 200 gev a+a data . shown for comparison are the inclusive ratios from 200 gev @xmath8 and/or d+au collisions . , title=""fig:"",height=120 ] to add yet another dimension to the ridge studies , one can bring in additional particle to the correlation to explore internal structure of the observed peak . preliminary results of three - particle triggered correlation analysis for unidentified hadrons are presented in figure 4 for minimum bias d+au , peripheral and central au+au collisions at 200 gev . a jet - like peak is observed in all three correlations at small relative pseudo - rapidity values . in addition , a uniform distribution of associated yields is observed in au+au collisions , particularly , for most central events . this observation is quite puzzling for ridge phenomenology , contradicting to model predictions @xcite . specifically we note the absence of axial strips in the correlation structure . axial strips in three - particle correlation should be formed by associate hadron pairs , in which one of the hadrons is coming from the cone - part , and the other one - from the ridge . absence of these strips thus suggests complete decoupling of jet and ridge events . albeit the current" +"in june 2015 , the large hadron collider ( lhc ) has resumed its physics program with proton - proton ( pp ) collisions at @xmath4 = 13 tev . currently , this is the highest centre - of - mass energy reached in the laboratory . a full description of particle production in pp collisions can not be obtained from perturbative quantum chromodynamics and hence modelling efforts typically employ various empirical components that have to be adjusted based on experimental data . the measurement of light flavour particles production in pp collisions provides important input for event generators to model the soft parton interactions and the hadronization processes . furthermore , pp collisions are used as reference to isolate medium effects present in larger colliding systems . previous alice measurements @xcite , @xcite , @xcite on identified particles in pp collisions at lower energies show that the models usually give a fair description of the shapes of the @xmath1 spectra but fail on the description of the pion , kaon and proton yields . @xmath5 , k@xmath6 , p and @xmath7 are identified in the rapidity window @xmath8 0.5 using several particle identification ( pid ) techniques in the different alice sub - detectors : the inner tracking system ( its ) , the time projection chamber ( tpc ) , the time of flight detector ( tof ) and high momentum particle identification detector ( hmpid ) . the combined information of these detectors in different @xmath1 regions allows us to measure the particle production in the region starting from 150 mev/_c _ up to 20 gev/_c_. the @xmath9 and @xmath10 mesons are measured with invariant - mass analyses via the reconstruction of their hadronic decays . the combinatorial background is subtracted using either a like - sign or event mixing technique . the resulting invariant - mass distributions are then fitted . previous measurements by alice and details on the analysis procedure can be found in @xcite . the multi - strange @xmath11 , @xmath12 , @xmath13 , @xmath14 baryons are reconstructed via their weak hadronic decay products . candidates are selected with restrictions on the topology of the decay and the signal is extracted from the resulting invariant mass distributions . the full analysis procedure is described in @xcite . the @xmath1-dependent @xmath15 and @xmath16 ratios measured in central rapidity ( @xmath17 0.5 ) at @xmath4 = 2.76 , 7.0 and 13 tev are shown in fig . [ ratios ] . the comparison to pythia 8 @xcite ( monash-2013 @xcite ) for the different energies is also shown . within the systematic uncertainties the @xmath16 ratio is consistent for the three different energies . the @xmath15 ratio for the low - intermediate @xmath1 region shows a slight shift towards higher @xmath1 when increasing @xmath4 . within our systematic uncertainties the ratio is compatible for the three different energies in the @xmath1 region above 10 gev/_c_. this shift is also observed on the monte carlo predictions from the pythia 8 model . the origin of the peak in pythia 8 is attributed to the colour reconnection mechanism @xcite , and is expected to become more important at higher centre - of - mass energy . the @xmath1-integrated @xmath16 and @xmath15 ratios in pp collisions as a function of @xmath4 are shown in fig.[ratios_energies ] . results at different energies for different experiments are also shown . results from e735 at @xmath4 = 0.3 , 0.54 , 1.0 and 1.8 tev @xcite , @xcite , from phenix at @xmath4 = 62.4 and 200 gev @xcite and cms at @xmath4 = 0.9 , 2.76 and 7 tev @xcite are compared for both particle ratios . the last added point at 13 tev confirms the similar trend and saturation for @xmath18 900 gev observed in alice previous measurements . the hyperon - to - pion ratio as a function of @xmath4 measured in alice is shown in fig . [ hyperon_ratio ] . in comparison with the kaon- and proton - to - pion ratio the strange- and multi - strange - to - pion ratios show a hint of increase at 13 tev with respect to the lower collision energies . this enhanced production may be related to the enhancement observed as a function of multiplicity in pp collisions at @xmath4 = 7 tev @xcite , as the charged particle multiplicity density increases with the collision energy . the @xmath9 and @xmath10 meson production has been also measured in pp collisions at @xmath4 = 13 tev . the @xmath1-integrated @xmath19 and @xmath20 ratios are shown in fig . [ ratios_resonances ] . however , no energy evolution is observed in the range from rhic to the highest lhc energy . the @xmath1 dependence of the @xmath21 and @xmath16 is the same at lhc energies within our systematic errors . pythia 8 describes the shape but exhibits large deviations from the data for transverse momenta larger than 2 gev/_c_. above @xmath22 900 gev the @xmath21 and @xmath16 ratios are energy independent within systematic uncertainties . the relative production of strange resonances ( @xmath19 and @xmath20 ) remains constant within a wide range of centre of mass energy . multiplicity dependent studies in pp collisions at 13 tev will help disentangle the role of collision energy and event multiplicity in the identified particle production of pp collisions . 9 alice collaboration 2011 , _ eur . phys . j. c _ * 71 * 1655 . alice collaboration 2014 , _ phys . lett . b _ * 736 * 196 - 207 . alice collaboration 2015 , _ eur phys . j.c _ * 75 * 226 . alice collaboration 2012 , _ eur . j. c _ * 72 * 2183 . alice collaboration 2012 , _ phys . b _ * 712 * 309 - 318 . t. sjstrand , s. mrenna , and p. z. skands 2008 , _ comput . commun . _ * 178 * 852 - 867 . z. skands , s. carrazza , and j. rojo 2014 , _ eur . j. c _ * 74*. e735 collaboration , 1993 _ phys.rev . d _ * 48 * 984 - 997 . e735 collaboration 1992 , _ phys.rev . d _ * 46 * 2773 - 2786 . phenix collaboration 2011 , _ phys.rev . c _ * 83 * 064903 . cms collaboration 2012 , _ eur.phys.j . c _ * 72 * 2164 . alice collaboration 2016 , arxiv:1606.07424 [ nucl - ex ] ." +"hanle effect measurements ( bommier et al . 1994 ) have shown that quiescent ( non active - region ) filaments have `` inverse '' magnetic polarity , meaning that their transverse field component is opposite in sign to that of the coronal loops crossing high over the photospheric neutral line . the usual interpretation of this result is that the filament material is supported in the dipped or concave - upward portions of a twisted flux rope ( see , e.g. , van ballegooijen & martens 1989 ; rust & kumar 1994 ; low 1996 ; aulanier & dmoulin 1998 ; amari et al . 1999 ; lites 2005 ; gibson & fan 2006 ) . for this topology , it is natural to assume that one sign of helicity prevails throughout the flux rope and its overlying arcade . in an alternative scenario , the filament is regarded as a sheared arcade whose intermediate legs or `` barbs '' are rooted in minority polarity on the `` wrong '' side of the neutral line ( martin 1998 ) . in that case , the helicity of the filament itself would be opposite in sign to that of the overlying coronal loops , contrary to most theoretical models . possible support for this picture comes from the observation of continual flows along the spines and up and down the barbs of filaments ( zirker et al . 1998 ; wang 1999 ; kucera et al . 2003 ; lin et al . 2003 , 2005 ) ; such flows , which may be driven by chromospheric reconnection ( litvinenko & martin 1999 ; martin et al . 2008 ) , seem to obviate the need for static support within magnetic dips , one of the principal arguments in favor of a flux rope geometry . statistically ( and independently of the flux rope / sheared arcade question ) , it is found that filaments in the northern ( southern ) hemisphere are predominantly `` dextral '' ( `` sinistral '' ) , meaning that their axial fields point to the right ( left ) when viewed from the positive - polarity side of the photospheric neutral line ( martin 1998 ; pevtsov et al . 2003 ; yeates et al . 2007 ; yeates & mackay 2009 ) . dextral ( sinistral ) filaments have right - bearing ( left - bearing ) barbs but underlie arcades with left - handed ( right - handed ) helicity . the helicity sign of the overlying arcade can be inferred from the skew of the arcade loops relative to the polarity inversion line ( pil ) . although the magnetic topology of a stable filament / prominence remains a subject of debate , it is almost universally accepted that an erupting filament and its surrounding field have the structure of a twisted flux rope . in a three - dimensional system , the pinching - off of pairs of stretched , opposite - polarity field lines beneath the rising filament will necessarily give rise to a flux rope ; reconnections may occur among the legs / barbs of the filament , between the legs and the overlying arcade , and among the highly distended arcade field lines themselves . as the bright post - eruption arcade expands outward from the pil , the orientation of the reconnected loops ( seen projected against the photosphere ) will appear to rotate clockwise ( counterclockwise ) if the arcade has right - handed ( left - handed ) helicity ; this apparent rotation is due to the tendency for the loops rooted farther from the pil to cross it more nearly at right angles . the axes of the erupting filaments themselves are sometimes observed to rotate about the vertical direction . as viewed from above , this rotation is again usually clockwise if the post - event arcade has right - handed helicity , and counterclockwise if it has left - handed helicity ( for examples , see rust & labonte 2005 ; green et al . 2007 ; wang et al . 2009 ) . the sense of rotation is consistent with the conversion of field - line twist into writhe ( three - dimensional twisting of the axis itself ) , as predicted by mhd simulations of kink - unstable flux ropes ( linton et al . 1999 ; kliem et al . 2004 ; trk & kliem 2005 ) and of sheared arcades that have been converted into erupting flux ropes via reconnection ( lynch et al . it is reasonable to assume that the net helicity of the erupting structure is the sum of the helicity of the original filament and that of the surrounding field with which it has become entrained by reconnection ( see berger 1998 ) . if the barb system and the overlying coronal field have opposite helicity signs , as suggested by martin ( 1998 ) , then in most events the main contribution to the helicity of the erupting structure must come from the surrounding field ( compare also the discussion of ruzmaikin et al . however , the question arises as to whether the rotation ever occurs in the direction opposite to that implied by the helicity of the overlying arcade , thereby providing stronger support for the barb picture of martin . here we describe two events observed with the extreme - ultraviolet imaging telescope ( eit ; delaboudinire et al . 1995 ) on the _ solar and heliospheric observatory _ ( _ soho _ ) , in which the erupting quiescent filament appeared to rotate counterclockwise but the post - eruption arcade had right - handed helicity . the sequence of 19.5 nm images in figure 1 shows the eruption of a southern - hemisphere filament on 1999 september 20 . the dark filament in fact represents the western half of a longer structure that occupies a circular filament channel . the axis of the erupting feature undergoes a continual counterclockwise rotation between @xmath003:00 and @xmath005:00 ut . in order to exhibit this rotation more clearly , we have traced the filament spine at successive times and superposed these traces in figure 2 , after shifting them in longitude to correct for the average photospheric rotation . we note that the observed motions can not be interpreted simply as a straightening of the initially highly curved filament as it rises , which would require both the northern and southern portions of the filament to move eastward ; instead , the northern section moves eastward but the southern section moves westward , consistent with a counterclockwise rotation of the filament axis . subsequently ( after 04:48 ut ) , the rotation `` overshoots '' near both the northern and southern ends of the erupting filament , which thus kinks into a forward - s shape . as shown in figure 1 , the post - event arcade with its double row of footpoint brightenings begins to form after @xmath004:36 ut . in addition , in the images recorded between 04:36 and 05:12 ut , euv brightenings ( circled in figure 1 ) may be seen at the far endpoints of the erupting filament ; these brightenings occur as the filament threads , anchored well outside the filament channel itself , are jerked upward into a vertical orientation ( see wang et al . 2009 ) . from the slant of the post - eruption loops in the image taken at 06:00 ut , and from the apparent clockwise rotation of the loop orientation between 06:00 and 07:13 ut , we conclude that the overlying arcade has right - handed helicity , even though the filament rotates counterclockwise . the first post - eruption loops ( observed at 06:00 ut ) are located near the original pivot point of the filament rotation , where the traces approximately intersect in figure 2 , suggesting that the instability and rapid upward motion of the filament were initiated in this region . figure 3 shows the distribution of photospheric magnetic flux underlying the erupting filament . here , we compare a michelson doppler imager ( mdi ) line - of - sight magnetogram taken at 04:48 ut with the difference between the 19.5 nm images recorded at 04:48 and 04:36 ut . the magnetogram , saturated at @xmath150 g , represents a 5-minute average of higher - cadence data . the circular filament channel evidently encloses a positive - polarity region . since the northern ( southern ) end of the erupting filament is rooted in negative - polarity ( positive - polarity ) network flux , the axial field of the filament points toward the left as viewed from the positive - polarity region , and the filament is sinistral according to the chirality definition of martin ( 1998 ) . correspondingly , an h@xmath2 image taken on september 18 at the big bear solar observatory ( bbso ) shows left - bearing barbs ( figure 4 , top panel ) . as indicated by the 30.4 nm images in the left column of figure 5 , the filament re - forms immediately after the eruption ; however , its northern end now bends westward rather than eastward ( see also the h@xmath2 image in figure 4 , bottom panel ) . the mdi magnetograms in the right column of figure 5 suggest that this change in the shape of the filament , as well as the eruption itself , may have been associated with the emergence of a small magnetic bipole to the west of the original filament channel . the new bipole ( circled in the magnetograms taken at 06:27 and 13:19 ut ) appears to have altered the shape of the photospheric neutral line in the vicinity of the filament . in association with this filament event , the large angle and spectrometric coronagraph ( lasco ) on _ soho _ observed a faint halo coronal mass ejection ( cme ) with an average speed of 600 km s@xmath3 . the sequence of eit 30.4 nm images in figure 6 , taken at 6-hourly intervals , shows the disappearance of a high - latitude filament in the southern hemisphere on 2001 september 28 . in the frame recorded at 13:19 ut , during the eruption itself , the axis of the filament shows a pronounced counterclockwise rotation relative to its pre - eruption orientation . this kinking into a forward - s shape is seen even more clearly in figure 7 , where we have superposed four successive traces of the filament spine taken between 19:19 ut on september 27 and 13:19 ut on september 28 , after removing the effect of the photospheric differential rotation . the eruption is shown in more detail in the sequence of 19.5 nm running - difference images in figure 8 . the post - event arcade begins to form at 15:00 ut , with the appearance of a compact bundle of highly sheared loops that are almost aligned with the filament channel . from the mdi magnetogram ( fourth panel of figure 8) , we conclude that the western end of this narrow bundle of reconnected loops lies on the negative - polarity side of the photospheric neutral line , implying right - handed helicity . that the overlying arcade is indeed right - handed is confirmed by the subsequently forming loops ( bottom panel of figure 8) , which are rooted farther from the pil and are shifted clockwise relative to the earlier loops . h@xmath2 images recorded at bbso on september 27 show that the pre - eruption filament had left - bearing barbs ( see figure 9 ) , consistent with sinistral chirality . filaments are conventionally regarded as cool material supported inside the dips of a helical flux rope of a given `` handedness . '' if the flux" +"noncovalent functionalization of single - walled carbon nanotubes ( cnts ) with photoactive molecules is becoming a promising technique to explore functional materials for light - harvesting or optoelectronic applications . @xcite the coupling of the exceptional cnt transport properties with the optical properties of functional dyes , like porphyrins with a strong absorption in the near infrared and visible , make of cnt / dye complexes good candidates for sensitive nanoscale devices with potential applications in biomedical imaging , @xcite and hybrid organic - inorganic photovoltaic devices . @xcite however , the strength of the @xmath4-stacking interaction with respect to the cnt structural parameters , like the diameter and chirality , is still lacking . in addition , a better understanding of the cnt / dye optical properties considering changes in the dye structure due to the @xmath4-conjugation is needed . recently , the kinetics and thermodynamics properties of non - covalently bound cnt / porphyrin oligomers have been investigated by uv / visible spectroscopy and fluorescence titration.@xcite it was reported that the affinity of the cnts increases sharply with the porphyrin coverage , showing strongest binding energies for semiconducting cnts , particularly those with chiral indices ( 7,5 ) and ( 8,6 ) . in addition , others works have also investigated a supposed selective interaction of porphyrins towards semiconducting cnts , suggesting that the semiconducting and metallic cnts would have significantly different surface properties.@xcite these works have also suggested that noncovalent functionalization of a mixture of cnts with porphyrins may be an effective method for the separation of semiconducting cnts from metallic cnts . previously , we reported physisorption properties of iron porphyrin on both metallic and semiconducting cnts with similar diameters.@xcite our results showed a surprising strong @xmath4-stacking interaction , but with negligible energy differences . similar results were found for the physisorption strength of free - base and zinc porphyrins on the same semiconducting cnt,@xcite showing no clue on the suspected selectivity . considering the increasing interest in the noncovalent complexation of cnt - based materials for optoelectronic applications , we carry out an in - depth investigation on the stability and optical response of free - base tetraphenyporphyrin ( tpp ) molecules @xmath4-stacked on single - walled cnts with different chiralities and diameters , and also on graphene . our purpose is to give a theoretically insight into the binding strength and optical properties of these compounds as a function of the cnt structural parameters . our results show that the diameter instead chirality would be the relevant cnt parameter to explain the unusual strength of the tpp @xmath4-stacking interaction . in addition , the tpp binding energy on metallic and semiconducting cnts does not exhibit important differences that might suggest distinct interactions . regarding optical properties , we find that transition bands of the @xmath4-stacked tpp remain at almost the same energy position than those found in the isolated tpp , being independent of the cnt structural parameters . for the tpp physisorption on graphene , we find a very strong binding energy , of about 3.2 ev , providing an upper limit for the stability of cnt - tpp compounds . we also find a @xmath5-type doping on graphene induced by the tpp adsorption . our density functional theory ( dft ) calculations were performed using the siesta _ ab initio _ package,@xcite which employ norm - conserving pseudopotentials and localized atomic orbitals as basis set ( double-@xmath6 , singly polarized ) . the physisorption of tpp on both the cnt sidewall and graphene is assessed by van der waals density functional ( vdw - df ) as proposed by dion _ et al._@xcite this approach has been successfully applied to describe the dispersive interaction of aromatic molecules on the graphite surface , showing good agreement with available experimental data.@xcite in recent experiments , the functionalization of cnts with tpp molecules has been achieved by the micelle swelling methods in water suspension,@xcite where the cnt - tpp compound stays in the micelle core . because of the hydrophobic character of this core , it is not expected water molecules surrounding the compound , which can be considered close to a vacuum situation . in the present work we study the tpp physisorption 42 different cnt species , particularly those with chiral indices ( @xmath0,@xmath1 ) , with @xmath7 and @xmath3 . the cnt - tpp compounds are studied within the supercell approach , with periodic boundary conditions along the nanotube axis ( @xmath8 direction ) . we use unit cells with a volume of ( @xmath9 ) @xmath10 , where @xmath11 is cnt lattice constant and @xmath12 a factor to keep a minimum distance among tpp images along the cnts , chosen to be of 10 . this procedure results in supercell lengths ( @xmath13 ) between 22 - 57 , which can contain up to 754 atoms . a grid cutoff of 100 ry and the @xmath14 point were used for the real - space and @xmath15-space integration , respectively . for the optical calculations , we use a @xmath16 @xmath15-point mesh , for incident light polarized along the cnt axis . the accuracy of these parameters were tested considering larger grid cutoff ( 150 ry ) and @xmath15-point mesh ( @xmath17 ) . negligible variations in the total energies , optical spectra , and band structures were found , ensuring that our results are converged . for the tpp physisorption on graphene , we use a squared unit cell with @xmath18 periodicity and the @xmath14 point for the @xmath15-space integration . here , a vacuum region of 20 among graphene an their images was considered . for the optical response we use a @xmath15-point mesh of @xmath19 , for incident light polarized parallel to the graphene plane ( @xmath20 and @xmath21 directions ) . the tpp binding energy on the substrates is calculated by the energy difference between adsorbed and separated constituents , considering corrections due to the basis set superposition error . the complexes were fully relaxed by conjugate gradient minimization until the forces on the atoms were less than 0.05 ev / . the optical response of the functionalized cnts and graphene is obtained through first order time dependent perturbation theory , by calculating the imaginary part of the dielectric function ( @xmath22 ) . @xmath22 gives us a first approach for the optical absorption coefficient and it is calculated according to the equation : @xmath23 here @xmath24 is a constant that depends on the cell sizes ; @xmath25 and @xmath26 are the occupied and empty kohn - sham orbitals , respectively . the delta function represents the conservation of energy , which is described by a gaussian function with a smearing of 0.06 ev . it is important to note that dft calculations fail in describing electron - hole and electron - electron interactions , the so called many - body effects . these effects are responsible for the formation of excitons and the quasiparticle excitation . @xcite therefore , an accurate description of photoexcitations in cnts and graphene needs theories beyond dft , like those based on the gw - bethe - salpeter equation ( gw - bse).@xcite however , these calculations are not possible right now , considering the size of the systems under study . thus , @xmath22 can give us a first approach for the optical response of @xmath4-stacked tpp on cnts and graphene . the main difference of dft calculations with respect to gw - bse is a redshift in the absorption spectrum . for instance , in graphene this redshift is found to be about 0.6 ev.@xcite we first discuss different adsorption geometries for the tpp molecule on the cnts . figure [ f1 ] shows the equilibrium geometry of a tpp adsorbed on a ( 8,7 ) cnt . here , the n - h bonds of tpp are oriented perpendicular to the cnt axis , that we called position ( i ) . two other positions for tpp are likely to be found : with the n - h bonds parallel to the cnt axis ( ii ) , and with the n - h bonds forming an angle of 45@xmath27 with respect to the cnt axis ( iii ) . although position ( i ) is found to be the most stable , the other positions have total energies within 0.3 ev , suggesting that all three are equally probables . in the equilibrium geometry , the tpp phenyl groups exhibit a small rotation , which come with a molecular twisting . to compare the stability of different cnt - tpp complexes , only position ( i ) will be considered throughout this work . the adsorption distance is measured between the cnt surface and the n atoms of tpp , as shown in figure [ f1 ] . .adsorption distance ( @xmath28 ) , binding energy ( @xmath29 ) , and bandgap energy ( @xmath30 ) of cnt - tpp complexes . @xmath31 and @xmath32 are the cnt diameter and chiral angle , respectively . results for tpp on graphene ( g - tpp ) are also included . [ cols=""<,<,<,<,<,<"",options=""header "" , ] [ t1 ] table [ t1 ] lists tpp binding energies and binding distances for all the complex under study . we also include the dft bandgaps for the semiconducting complexes . those with small bandgaps ( @xmath330.1 ev ) are consistent with empirical model predictions of @xmath34 as well as with experimental data.@xcite we observe that binding energies and adsorption distances vary in ranges given by @xmath35 ev and @xmath36 , respectively . we note that stronger tpp @xmath4-stacking interactions result in larger adsorption distance . this can be understood by look at the tpp phenyl groups , whose h atoms become closer to the cnt surface for large diameter cnts , as can be seen in figure [ f1 ] . to estimate an upper limit for @xmath29 and @xmath28 , we calculate the tpp physisorption on graphene , which can be considered as a cnt with an infinite diameter . we find @xmath37 ev and @xmath38 . although the binding distance is similar to those found on cnts with @xmath39 , the binding energy is considerably larger , with almost twice the value found on the cnts . this can be understood because of the larger graphene - tpp overlap area , which tend to maximize the @xmath4-stacking interaction . figure [ f2 ] shows the cnt - tpp binding energy as a function of the cnt diameter . we observe an almost linear increase in the tpp attachment strength with the cnt diameter , which in some way confirms our assumption that larger cnt - tpp overlap area tends to increase the binding energy of the molecule . however , this general tendency is not followed in some cases , as can be seen in fig . for instance , ( i ) the larger tpp binding energy found for the ( 5,0 ) cnt ( @xmath40 ) with respect to the ( 6,0 ) cnt ( @xmath41 ) , by about 0.2 ev , and ( ii ) the abrupt changes in the tpp binding energy profile going from ( 6,0 ) to ( 6,1 ) , ( 7,5 ) to ( 7,6 ) , and ( 8,5 ) to ( 8,6 ) . we attribute these results to the particular atomic geometry of the cnt atoms just below the tpp molecule . we observe that the cnt - tpp binding distance tends to increase when the h atoms of the phenyl groups nearest neighbors to the cnt surface , lie exactly above nanotube c - atoms . this effect is due to the steric repulsion between them , which also explain the broad variation on the binding distances between the cnt surface and the tpp n - atoms , as shown in figure [ f3 ] ." +"monitoring the activity of large - scale neuronal ensembles during complex behavioral states is fundamental to neuroscience research . continued advances in optical imaging technology are greatly expanding the number and depth of neuronal populations that can be visualized . specifically , in vivo calcium imaging through microendoscopic lenses and the development of miniaturized microscopes have enabled deep brain imaging of previously inaccessible neuronal populations of freely moving mice ( @xcite ) . while these techniques have been widely used by neuroscientists , automatic methods for extracting cellular signals from this data are currently limited and suboptimal . the desired method should be able to ( 1 ) identify spatial footprints of all neurons , ( 2 ) denoise , demix and deconvolve the temporal signals ( @xcite ) . figure [ fig : example]a is an example frame from microendoscopic data , where the weak neuronal signals are submerged in the large background ( the raw video data can we watched here ) . for illustrative purposes , we draw two rois in the optical field and compute their mean fluorescence intensities ( figure [ fig : example]c , d ) . the red roi overlaps with one neuron and the green roi only has the background ( figure [ fig : example]b ) . thus the fluorescence in the red roi ( figure [ fig : example]c ) is a superposition of the background and the neuron s temporal activity , whereas the green ( figure [ fig : example]d ) provides an estimation of the background signal . by subtracting these two traces , we are able to roughly estimate the temporal activity of the neuron within the red roi ( figure [ fig : example]e ) . from this example , we can see that the background is an order of magnitude larger than the neural activity and its fluctuations are as fast as neuronal calcium transients . these features make it difficult to detect and demix cellular signals automatically from the raw video . our work is based on a matrix factorization approach , which can simultaneously segment cells and estimate changes in fluorescence in the temporal domain . this approach stems from the observation that spatiotemporal calcium activity can be approximated as product of two matrices : a spatial matrix that encodes the location of each neuron and a temporal matrix that characterizes the calcium concentration evolution for each neuron . it has several variations with different constraints , such as independent component analysis ( pca - ica , @xcite ) , nonnegative matrix factorization ( nmf , @xcite ) , sparse space - time deconvolution ( sstd , @xcite ) and constrained nonnegative matrix factorization ( cnmf , @xcite ) . in particular , pca - ica seeks spatiotemporal components that have reduced dependence . it is an inherently linear demixing method and can fail in the case when the neural components exhibit significant spatial overlaps ( @xcite ) . nonlinear methods like nmf , sstd and cnmf can deal with overlapping neural sources more effectively , and often outperform pca - ica . the main applications of these nonlinear methods are 2-photon or light - sheet imaging data , where the background is weak and has simple spatiotemporally separable structure . they usually model the background with a rank-1 nonnegative matrix . however , applying these nonlinear matrix factorization methods to the microendoscopic data faces two problems : ( 1 ) the background term is not well modeled by rank-1 nmf and its large residual could contaminate the extracted neuronal signals ; ( 2 ) the procedures of initializing the model parameters , especially spatial and temporal components of neurons , in these models do not work well because the strong and noisy background mixes with the weak neural signals . since the optimization problem in these methods are non - convex , without good initialization , it may lead to low - quality results or require excessive time for convergent results . in this paper , we extend the cnmf framework ( @xcite ) to address strong fluctuations in background fluorescence , and make it applicable to microendoscopic data . like the proposed cnmf in @xcite , our extended cnmf for microendoscopic data ( cnmf - e ) also has the capability of identifying neurons with low signal - to - noise ratio ( snr ) and simultaneously denoising , deconvolving and demixing large - scale microendoscopic data . to accomplish this : ( 1 ) we replace the rank-1 nmf approximation of the background with a more sophisticated approximation , which can better account the complex background and avoid absorbing cellular signals , and ( 2 ) we develop an efficient initialization procedure to extract neural activities with minimal influence from the background . the structure of the paper is as follows . in section [ sec : cnmf ] we briefly review the cnmf model and describe our modifications to the model . in section [ sec : fit_model ] , we develop our specialized model fitting procedure . in section [ sec : result ] we validate our new proposed cnmf - e on simulated and experimental data , and we also compare it with the widely used pca - ica method ( @xcite ) . * notation * a matrix @xmath0 represents the spatiotemporal activity of @xmath1 pixels in @xmath2 frames . the column vector @xmath3 is the observation of the whole frame in time - step @xmath4 . we use @xmath5 to refer the spatial location of one pixel , thus @xmath6 is the fluorescence intensity in @xmath4-th frame at location @xmath7 . for a column vector @xmath8 encoding the spatial information of @xmath1 pixels , @xmath9 indicates the value of @xmath10 at pixel @xmath7 . the video data we have are observations from the optical field for a total number of @xmath2 frames . the recorded data can be represented by a matrix @xmath11 , where @xmath1 is the number of pixels in the field . each neuron is characterized by its spatial ` footprint ' vector @xmath12 and ` calcium activity ' @xmath13 . here both @xmath14 and @xmath15 are forced to be nonnegative because of their physical interpretations . given @xmath16 of one neuron , its spatiotemporal activity is represented as @xmath17 . the background activity is represented by a matrix @xmath18 . suppose the field contains a total number of @xmath19 neurons , then the observation is a superposition of all neurons spatiotemporal activity , time - varying background and additive noise : @xmath20 where @xmath21 , c=[\mathbf{c}_1 , \cdots , \mathbf{c}_k]^t$ ] . the noise term @xmath22 is assumed to be gaussian and @xmath23 . @xmath24 is a diagonal matrix indicating that the noise is spatially and temporally uncorrelated . @xcite also explicitly model the calcium dynamics @xmath15 with a stable autoregressive process ( ar ) of order @xmath25 , @xmath26 where @xmath27 is the number of spikes that neuron fired at the @xmath4-th frame and it is sparse in the neural systems . the ar coefficients @xmath28 are different for each neuron and they are estimated from the data . estimating the model parameters @xmath29 in model ( [ eq : y])([eq : arp ] ) can give us all neurons spatial footprints and their deconvolved temporal activities . to fit the model , we also have to constrain the background term to have simplified structure , otherwise letting @xmath30 leads to the least reconstruction error . this framework is general and we use it in our new method as well . compared with the proposed implementation in @xcite , our method models the background term differently . in the work of @xcite , they model the background with a rank-1 nonnegative matrix @xmath31 , where @xmath32 and @xmath33 encode the background spatial and temporal structure respectively this is a good assumption for two - photon or light - sheet imaging data , but the background in microendoscopic data requires a more complex model . we also have to avoid the increased complexity from absorbing cellular signals into the background . thus the ideal model should explicitly model the background features that are distinct from neurons of interest . here we include two main features of the background into the model of @xmath34 : ( 1 ) the temporal component of each pixel has a constant large baseline and some slow trends ( see figure [ fig : example]d ) and ( 2 ) background is usually spatially smooth in a larger spatial range compared with neuron size ( figure [ fig : example ] ) , which means the background of all pixels within a neuron does not have large spatial gradients . this is because the fluctuations in the background reflects the out - of - focus fluorescence and they are significantly blurred . hence we model the background term as @xmath35 where @xmath36 and @xmath37 . @xmath38 explains the constant baselines and slow trends for all pixels ( figure [ fig : example]c ) and their temporal dynamics are much slower than calcium indicators . the second term @xmath39 models the fast fluctuation in the background and the spatial component @xmath40 has low spatial - frequency structure . the constraint of @xmath40 excludes cellular signals from the background term . in this section , we will describe our customized algorithm for fitting the model ( [ eq : y])([eq : arp])([eq : bg ] ) . we frequently use the pixel - wise formulation of model ( [ eq : y ] ) and ignore the noise term : @xmath41 our framework can be summarized into the following steps : 1 . initialize @xmath42 using the new initialization procedure . 2 . approximate the background @xmath43 using model ( [ eq : bg ] ) . update @xmath42 from data @xmath44 using constrained alternating matrix factorization . 4 . post - process the results automatically or manually : delete neurons , pick the missed neurons from the residuals , and merge neurons with high temporal correlations . repeat steps 2 , 3 , 4 until the results are biologically meaningful . our techniques differ from @xcite in the following aspects : ( 1 ) the initialization step for @xmath45 and @xmath46 here requires careful considerations of the background contaminations and our approach is totally new . ( 2 ) instead of updating the background term iteratively , we update the background independently in different iterations and the rank of the background model can be modified in each iteration . as a result , our algorithm has a better control of the residual levels in background . in the followings , we mainly describe our novel initialization step and briefly summarize the procedure of fitting the background term . as for steps ( 3 - 5 ) and discussions for scalability issue , we put them in the supplementary materials ( section [ supp : iterative_manual ] and [ supp : speed ] ) . , the initialized temporal activity of one neuron . d@xmath47 , raw data of the cropped small window ( green square in a and b ) . e@xmath47 , the estimated time - varying local backgrounds in the small cropped window . c@xmath48 , @xmath49 and @xmath50 are the re - ordered version of c@xmath47 , @xmath51 and @xmath52 . c@xmath53 is the temporal differencing of c@xmath48 and the result has been thresholded with its @xmath54 standard deviation . similarly , d@xmath53 is differencing result of d@xmath48 . f , the initialized spatial and temporal components of the neuron.,width=529 ] here we develop a robust procedure for initializing @xmath45 and @xmath46 without estimation of the background . this procedure utilizes the spatial smoothness feature in the background and removes it by spatial high - pass filtering of the raw data . we estimate the temporal component of one neuron @xmath15 from spatially filtered" +"an abelian cover is a finite morphism @xmath0 of varieties which is the quotient map for a generically faithful action of a finite abelian group @xmath1 . this means that for every component @xmath7 of @xmath2 the @xmath1-action on the restricted cover @xmath8 is faithful . the paper @xcite contains a comprehensive theory of such covers in the case when @xmath2 is smooth and @xmath3 is normal . the covers are described in terms of the _ building data _ consisting of branch divisors @xmath9 ranging over cyclic subgroups @xmath10 , and line bundles @xmath11 with @xmath12 ranging over the character group of @xmath1 . this collection must satisfy the _ fundamental relations_. here , we extend this theory to the case of singular varieties . namely , we allow @xmath3 and @xmath2 to be varieties satisfying serre s condition @xmath4 and having double crossing singularities in codimension 1 , which we abbreviate to g.d.c . for `` generically double crossings '' ( see [ ssec : ysmooth ] for the precise definition ) . our interest in this case lies in applications to the moduli theory . such non - normal abelian covers appear in our work @xcite where we explicitly construct compactifications of moduli spaces of some campedelli and burniat surfaces by adding stable surfaces on the boundary . `` stable surfaces '' here are in the sense of @xcite : they have slc ( semi log canonical ) singularities and ample canonical class . in this paper , we give a comprehensive treatment of the situation . in section [ ssec : ysmooth ] we show that the theory of standard covers of @xcite has a very natural extension to the case when @xmath2 is still smooth but @xmath3 is possibly g.d.c .. in section [ ssec : ynormal ] we extend it to the case of normal base by an @xmath4-fication trick . in section [ ssec : ynonnormal ] we prove that a cover with non normal @xmath2 can be obtained by gluing a cover over the normalization @xmath13 , and we spell out which additional data must be specified . in section [ sec : geometry ] we study the singularities of covers . we determine the conditions for @xmath3 to have slc singularities , to be cohen - macaulay , and we determine the index of the canonical divisor in the situations appearing in common applications . in section [ sec : z2-covers ] we treat in detail the special case when the group @xmath1 is @xmath14 and @xmath15 , as in @xcite . we restrict ourselves to the situation where the base @xmath2 is smooth or has two smooth branches meeting transversally , and the components of branch divisors and the double locus are smooth and have distinct tangent directions at the points of intersection , i.e. locally they look like a collection of lines in the plane . in this situation , we give a complete classification of the covers and the singularities of @xmath3 . the answer is contained in nine tables . some of these covers appear on the boundary of moduli of campedelli and burniat surfaces , but the full list is longer . @xmath1 denotes a finite abelian group . we work with equidimensional varieties defined over an algebraically closed field @xmath16 whose characteristic does not divide the order of @xmath1 . we denote by @xmath17 the group @xmath18 of characters of @xmath1 , and we write it multiplicatively . the abbreviations _ lc _ and _ slc _ stand for _ log canonical _ and _ semi log canonical_. ( cf . [ sec : geometry ] for the definitions ) . @xmath19 , @xmath20 , etc . denote the normalization of @xmath3 , @xmath21 , etc . we use the additive and multiplicative notation for line bundles and divisors interchangeably . linear equivalence will be denoted by @xmath22 . the first author was partially supported by nsf under dms 0901309 . the second author wishes to thank miles reid and angelo vistoli for several useful communications . we also thank the referee for many useful comments and corrections . part of this work was done while both authors were visiting msri in the spring of 2009 . this project was partially supported by the italian prin 2008 project _ geometria delle variet algebriche e dei loro spazi di moduli_. the second author is a member of gnsaga of indam . we recall some basic facts about serre s condition @xmath4 and the @xmath4-fication of a coherent sheaf . for a comprehensive treatment , the reader may consult @xcite , where the latter appears under the name `` @xmath23-closure '' . all varieties below are assumed to be reduced , equidimensional , but possibly reducible . let @xmath24 be a coherent sheaf on @xmath3 all of whose associated components are irreducible components of @xmath3 . then there exists a unique _ @xmath4-fication _ , or _ saturation in codimension 2 _ , a coherent sheaf defined by @xmath25 the sheaf @xmath26 is @xmath4 , and @xmath24 is @xmath4 iff the map @xmath27 is an isomorphism . in particular , for @xmath28 one obtains the @xmath4-fication @xmath29 , which is dominated by the normalization of @xmath3 . on a normal variety @xmath3 , an @xmath4-sheaf is the same as a _ reflexive sheaf _ , satisfying @xmath30 , see @xcite . further , reflexive sheaves of rank 1 are the same as _ divisorial sheaves _ , isomorphic to @xmath31 for some weil divisor @xmath32 , see e.g. ( * ? ? 1 ) . on a smooth ( or factorial ) variety weil divisors are the same as cartier divisors , and rank 1 @xmath4 sheaves are the same as invertible sheaves . let @xmath1 be a finite abelian group . an _ abelian cover _ with galois group @xmath1 , or _ @xmath1-cover _ , is a finite morphism @xmath0 of varieties which is the quotient map for a generically faithful action of a finite abelian group @xmath1 . this means that for every component @xmath7 of @xmath2 the @xmath1-action on the restricted cover @xmath33 is faithful . an _ isomorphism _ of @xmath1-covers @xmath34 , @xmath35 is an isomorphism @xmath36 such that @xmath37 . the @xmath1-action on @xmath3 with @xmath38 is equivalent to a decomposition : @xmath39 where @xmath1 acts on @xmath40 via the character @xmath12 . if @xmath41 is galois then each @xmath40 has rank 1 : if @xmath42 is a general closed point , then @xmath1 acts freely on @xmath43 , so it acts on @xmath44 as the regular representation . thus , @xmath45 is @xmath46-dimensional for every @xmath12 . when the sheaves @xmath40 are locally free , it is customary to write @xmath47 , with @xmath11 a line bundle . [ lem : flatness - and - cm ] 1 . the sheaf @xmath48 is @xmath49 for some @xmath50 iff every @xmath40 is @xmath49 . 2 . if @xmath51 is flat then @xmath3 is cm iff @xmath2 is cm . if @xmath2 is smooth and @xmath3 is @xmath4 then @xmath41 is flat and @xmath3 is cm . \(1 ) is clear by definition of depth . \(2 ) @xmath41 is flat iff every @xmath52-module @xmath40 is invertible . then each @xmath40 is cm iff @xmath52 is . \(3 ) on a smooth variety every divisorial sheaf is invertible , and so flat . now ( 2 ) applies . a @xmath1-cover @xmath51 , where @xmath3 and @xmath2 are @xmath4 varieties , is determined by its restriction to the complement of a closed subset of codimension @xmath5 : [ lem : remove - codim2 ] let @xmath2 be an @xmath4 variety , @xmath53 an open subset with @xmath54 , and @xmath55 a @xmath1-cover with @xmath56 an @xmath4 variety . then there exist a unique @xmath4 variety @xmath3 and a @xmath1-cover @xmath51 whose restriction to @xmath57 is @xmath58 . for the existence , we take @xmath59 , where @xmath60 is the inclusion . then @xmath61 , where each @xmath40 is a rank 1 @xmath4-sheaf . the algebra structure on @xmath48 is defined as follows . for an open set @xmath62 and sections @xmath63 , @xmath64 , their product is @xmath65 since @xmath66 and @xmath40 is saturated in codimension 2 . thus , @xmath67 is an @xmath4 variety with a finite morphism to @xmath2 . the @xmath17-grading on @xmath48 defines the @xmath1-action on @xmath3 . by construction , the eigenspace @xmath68 for the trivial character is @xmath69 . therefore , @xmath38 . uniqueness follows from the uniqueness of the @xmath4-fication . given a @xmath1-cover @xmath51 and an irreducible subset @xmath70 , we define the _ inertia subgroup _ @xmath71 of @xmath72 to be the subgroup of @xmath1 consisting of the elements that fix @xmath73 pointwise , or , equivalently since @xmath1 is abelian , that fix an irreducible component of @xmath73 pointwise . the _ branch locus _ @xmath74 of @xmath41 is the set of points of @xmath2 whose inertia subgroup is not trivial ( notice that we regard @xmath74 simply as a set , without giving it a scheme structure ) . if @xmath41 is flat , then @xmath74 is a divisor by ( * ? ? ? if @xmath75 is an irreducible divisor of @xmath2 such that @xmath3 is generically smooth along @xmath76 , then the natural representation @xmath77 of @xmath78 on the tangent space @xmath79 at the generic point of an irreducible component @xmath80 of @xmath76 is faithful , hence @xmath81 is cyclic ( cf . @xcite ) . notice that @xmath77 does not depend on the choice of the component @xmath80 of @xmath76 since @xmath1 is abelian . in this section we recall , in a form which is convenient for our later applications , the definition of standard abelian covers , a class of flat abelian covers that can be constructed from a collection of line bundles and effective divisors on the target variety ( cf . @xcite , @xcite ) . the prototypical example is the classical construction of a double cover of a variety @xmath2 from the data of an effective divisor @xmath32 on @xmath2 and a line bundle @xmath82 such that @xmath83 . let @xmath2 be a variety . a set of _ building data for a standard @xmath1-cover _ @xmath51 consists of the following : * irreducible effective cartier divisors @xmath84 ( possibly not distinct ) , * for each @xmath85 a pair @xmath86 , where @xmath87 is a cyclic subgroup of @xmath1 of order @xmath88 and @xmath89 is a generator of the group of characters @xmath90 , * line bundles @xmath11 , for @xmath91 . moreover we assume that these data satisfy the so called _ fundamental relations _ : @xmath92 where for a character @xmath12 we write @xmath93 , with @xmath94 , and we define @xmath95 $ ] . observe that @xmath96 is equal either to @xmath97 or to @xmath46 . we call the divisors @xmath85 , together with the pairs @xmath98 , the _ branch data _ of the cover . an equivalent way of describing the branch data , and therefore the building data , is to give for each pair @xmath99 , with @xmath100 a cyclic subgroup and @xmath101 a generator , the divisor @xmath102 . this is the notation used in @xcite . [ rem : branchdata ] if the group @xmath103 has no @xmath104-torsion , where @xmath105 , then the branch data determine the building data by ( * ? ? ? 2.1 ) . in general , the branch data are enough to determine the local geometry of the cover ( cf . proposition [ prop : bdata ] , ( 2 ) ) . when @xmath106 , it is enough to associate with every divisor @xmath85 a nonzero element @xmath107 , the generator of @xmath87 . also , the definition of @xmath108 is simpler : @xmath109 is equal to 1 if @xmath110 and it is equal" +"it is many years since the first description of how radio sources fueled by agn interact with and inject energy into the surrounding medium @xcite . now , largely due to _ chandra _ , we have many observational examples . x - ray signatures of the mechanisms involved are varied . gas cavities crafted by current or past radio lobes are common ( see * ? ? ? * for a review ) . agn - driven radio lobes are seen to shock the gas strongly , as in cena and pks b2152 - 699 @xcite or weakly , as in ngc4636 @xcite . while these phenomena mold the gas surface - brightness distribution , in other interactions it is the gas structures that shape the distribution of radio emission . this may be through the radio structures becoming buoyant , as in ngc326 @xcite or m87 @xcite , or because radio plasma is riding on a pressure wave of gas , as in 3c442a @xcite . moreover , as galaxies within groups and clusters interact with one another , their interstellar and intracluster media ( ism and icm ) get churned up through ram - pressure stripping , and wakes are observed as x - ray - gas density enhancements which are sometimes cooler and sometimes hotter than the surrounding gas ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? most of the best x - ray - studied cases are of radio galaxies of relatively low radio power hosted by the brightest central galaxy in the cluster or group environment , and less attention has been paid to cases where there are multiple radio galaxies in relatively close proximity . the radio galaxies hosted by ngc7016 and ngc7018 are a remarkable pair @xcite which reside in the central regions of the cluster abell3744 at @xmath3 @xcite and have escaped attention in recent years . they were mapped at high resolution in the radio with the vla by @xcite , and an image showing the salient features of figure [ fig : radio ] appears in @xcite in the context of rotation - measure modeling of ngc7018 . the radio source hosted by ngc7016 has asymmetric bent jets . lower - resolution radio data show a very long bent extension on the jet side one of the ` tendrils ' to which we refer later . on the counterjet side there is extreme looping , making a feature we refer to as the ` swirl ' . the radio source hosted by the eastern nucleus of the dumbbell galaxy ngc7018 is a classical double , of @xcite type ii ( fr ii ) morphology but unusual extended structure . we refer to the bright western extension from the southern lobe as the ` filament ' . at lower radio resolution , two long extensions ( tendrils ) are seen to the w and nw . ) and marking the ` filament ' and ` swirl ' referred to in this work . an unassociated radio source lies to the nw . ] while the complicated radio structures suggest interaction with the cluster atmosphere , little has been published on abell3744 s x - ray properties . it is detected in the rosat all - sky survey ( rass ) and is one of the 447 members of the reflex cluster catalog @xcite . however , it lies amongst the 12 per cent least luminous reflex clusters , with a cataloged 0.12.4-kev luminosity of only @xmath4 ergs s@xmath2 , and has not appeared in samples for deeper study . the rosat high resolution imager pointed at the field for 16.8 ks , and although investigation of the archival data shows a clear detection of the centers of both galaxies , the data are insufficiently sensitive for investigation of cluster substructure . in this paper we present new sensitive _ chandra _ observations of the system , together with new radio data obtained with the jansky very large array ( jvla ) . [ sec : obs ] describes the new observations and data processing . [ sec : cluster ] and [ sec : galaxies ] describe the cluster and galaxy / group x - ray features , respectively . in [ sec : rmorphs ] we highlight the fact that the two radio galaxies lie within the range of power that dominates jet - mediated feedback in the universe as a whole . after examining available galaxy velocity data in [ sec : velocities ] , with reference to the distribution of cluster gas and possible evidence for a merger , we discuss in [ sec : discussion ] relationships between the radio and x - ray structures and likely underlying causes . [ sec : summary ] summarizes our results . we adopt a luminosity distance for abell3744 of @xmath5 mpc ( appropriate for a hubble constant of 70 km s@xmath2 mpc@xmath2 ) , and 1 arcmin is equivalent to 45.3 kpc at the source . flux densities and spectral indices are related in the sense @xmath6 . we made a 75 ks observation of the system in full - window and vfaint data mode with the advanced ccd imaging spectrometer ( acis ) on board _ chandra _ on 2010 september 11 ( obsid 12241 ) . ngc7016 was positioned close to the nominal aimpoint of the front - illuminated i3 chip . the other three ccds of acis - i and the s2 chip of acis - s were also on during the observations , giving a frame time of 3.14 s. details of the instrument and its modes of operation can be found in the _ chandra _ proposers observatory guide . results presented here use ciao v4.5 and the caldb v4.5.6 calibration database . we re - calibrated the data to take advantage of the sub - pixel event reposition routine ( edser ) , following the software threads from the _ chandra _ x - ray center ( cxc ) , to make new level 2 events files . only events with grades 0,2,3,4,6 were retained . after screening to exclude intervals of high background at a threshold appropriate for use of the blank - sky background files , the calibrated dataset has an exposure time of 71.553 ks . since the cluster fills a large part of the detector array , background was measured from blank - sky fields following procedures described in the cxc software threads . after cleaning the background data using the same criteria as for the source data , and reprojecting to the same coordinate system , a small normalization correction was applied ( 2% ) so that the count rates matched in the @xmath7-kev energy band where particle background dominates . the ciao wavdetect task was used to find point sources with a threshold set to give 1 spurious source per field . their regions were subsequently masked from the data for the analysis of extended structure . all spectral fits are performed in xspec on binned spectra using @xmath8 statistics over the energy range @xmath9 kev . the models include galactic absorption of @xmath10 @xmath11 @xcite . parameter uncertainties are 90% confidence for 1 interesting parameter unless otherwise stated . we made sensitive , high - resolution , observations of the field containing ngc7016 and ngc7018 using the jvla in its a configuration at l ( 1.4 ghz ) and c ( 5 ghz ) bands ( table [ tab : vlatab ] ) . at the time of the observations , only part of the full bandwidth of the jvla correlator was available . the data were calibrated and flagged for extensive interference before being passed through the normal clean and gain self - calibration cycles in casa . for more diffuse structures we also downloaded archival l - band data taken in c configuration with the vla , and mapped them using standard procedures in aips . details of the heritage of the data sets and properties of the resulting maps are given in table [ tab : vlatab ] . for l to c - band spectral - index measurements we made a version of the c - band map with the same restoring beam as the l - band jvla map . lllllll ab1389 & 2011 jun 27 & 1.39 & jvla - a & @xmath12 & 0.066 & 1 + ab1389 & 2011 jun 27 & 4.96 & jvla - a & @xmath13 & 0.056 & 1 + ac105 & 1984 mar 31 & 1.525 & vla - c & @xmath14 & 0.16 & 2 + [ tab : vlatab ] from a map of our 1.4-ghz jvla data made with a restoring beam of @xmath12 arcsec . the outer lines mark the perimeter of the acis - i chip array . the white cross is at @xmath15 , the position adopted as the center of the cluster gas . ] figure [ fig : large ] is a smoothed , exposure - corrected 0.3 - 5 kev image of the _ chandra _ data , after removal of point sources but not the atmospheres of the three labeled ngc galaxies . 1.4-ghz radio contours are overlayed . the gaseous atmosphere of ngc7017 is seen in projection on the s jet of ngc7016 . the extended gas distribution very obviously deviates from spherical symmetry . interestingly , the filament and swirl ( fig . [ fig : radio ] ) both correspond to regions where the x - ray emission is less prominent . despite the lack of spherical symmetry , we have characterized the overall extent of the cluster atmosphere by fitting a @xmath16-model profile to a background - subtracted exposure - corrected radial profile centered on the position @xmath17 ( the approximate centroid of the diffuse emission contained within a circle of radius 227 arcsec ) shown as a cross in figure [ fig : large ] . the result is shown in figure [ fig : profile ] . we note the core radius of 220 arcsec inferred by @xcite based on earlier , less sensitive , rosat data falls within the @xmath18 error bound for @xmath19 . -model profile with the residuals ( shown as a contribution to @xmath20 ) in the lower panel . the best fit is for a core radius of @xmath21 arcsec and @xmath22 ( @xmath23dof = 84/69 ) . * right : * uncertainty contours ( @xmath18 , 90% and 99% for 2 interesting parameters ) of @xmath24 and @xmath16 for the radial - profile fit.,title=""fig : "" ] -model profile with the residuals ( shown as a contribution to @xmath20 ) in the lower panel . the best fit is for a core radius of @xmath21 arcsec and @xmath22 ( @xmath23dof = 84/69 ) . * right : * uncertainty contours ( @xmath18 , 90% and 99% for 2 interesting parameters ) of @xmath24 and @xmath16 for the radial - profile fit.,title=""fig : "" ] we have fitted the spectrum of the brightest extended emission in figure [ fig : large ] to a single - temperature thermal ( apec ) model absorbed by gas in the line of sight . emission from the three galaxy / group atmospheres has been excluded . we find very similar results for an on - source circle of radius 227 arcsec centered on @xmath25 as for a polygon of similar area tracing better a contour of constant surface brightness . the spectral contours for the circular extraction region and two outer annuli ( radii 227 and 300 arcsec , and 300 and 960 arcsec ) are shown in figure [ fig : clustertempabun ] . there is a weak trend for the best - fit temperature to decrease with increasing radius . the 90% confidence contour for the 227-arcsec - radius circle and" +"pseudodiffusive transmission refers to the @xmath1 scaling of the electrical current transmitted over a distance @xmath0 through a clean sheet of undoped graphene @xcite . the same @xmath1 scaling characterizes diffusion in a random potential , but now it applies in the absence of any disorder . there is a large number of theoretical @xcite and experimental @xcite studies of this phenomenon , which is understood as a general property of massless dirac fermions in the limit of vanishing excitation energy . the optical analogue in a photonic crystal with a dirac spectrum has been studied as well @xcite . layered superconductors with a _ d_-wave symmetry of the order parameter ( notably the high-@xmath2 cuprates @xcite ) form an altogether different system in which massless dirac fermions are known to exist @xcite . these are so - called nodal fermions , located in the two - dimensional brillouin zone near the intersections ( nodal points ) of the fermi surface with lines ( nodal lines ) of vanishing excitation gap . elastic mean free paths @xmath3 as large as @xmath4 have been reached in @xmath5 single - crystals @xcite , much larger than the superconducting coherence length @xmath6 . it is the purpose of this work to demonstrate theoretically the pseudodiffusive @xmath1 scaling of the transmission through a _ d_-wave superconductor over the range of lengths between @xmath7 and @xmath3 . this anomalous scaling was not noticed in earlier studies of similar systems @xcite . the problem is interesting from a conceptual point of view , because it highlights both the differences and similarities between dirac fermions produced by a bandstructure ( as in graphene or photonic crystals ) or produced by a _ d_-wave order parameter . in undoped graphene , the transmitted electrical current @xmath8 in response to a voltage difference @xmath9 scales as @xcite @xmath10 the length @xmath0 over which the current is transmitted should be large compared to the fermi wave length @xmath11 in the metal contacts , but small compared to the mean free path @xmath3 . the length @xmath0 should also be small compared to the transverse width @xmath12 of the graphene sheet ( to avoid edge effects ) . potential barriers ( smooth on the scale of the lattice constant ) at the interfaces between the metal contacts and the graphene sheet have no effect on the current , because of the phenomenon of klein tunneling @xcite . for the _ d_-wave superconductor , we find a transmitted electrical current per layer equal to @xmath13 for @xmath14 . here @xmath15 are the tunnel probabilities through the potential barriers at the two normal - metal superconductor ( ns ) interfaces . the dirac equation for nodal fermions is anisotropic @xcite , with different velocities @xmath16 and @xmath17 parallel and perpendicular to the nodal lines . this anisotropy ( with @xmath18 in @xmath5 ) increases the slope of the @xmath1 scaling . remarkably enough , the anisotropy does not introduce a dependence of the transmitted current on the angle @xmath19 between the direction of the current and the nodal lines . the result holds generically for any orientation , except for a narrow range of angles of order @xmath20 around @xmath21 . the tunnel barriers reduce the slope of the @xmath1 scaling of the transmitted electrical current , by a factor @xmath22 for small tunnel probabilities . this does not imply that the nodal fermions are only weakly transmitted , but rather that the transmission probabilities for transmission as an an electron or as a hole are almost the same for @xmath23 . indeed , we find that the electrical shot noise power @xmath24 as well as the transmitted thermal current @xmath25 ( both of which do not depend on the sign of the carriers charge ) remain finite in the limit @xmath26 . we interpret this result in terms of a resonant coupling via the nodal lines of the mid - gap states @xcite extended along the two ns interfaces . we also find , quite surprisingly , that the thermal conductivity is _ independent _ of the tunnel probabilities @xmath27 . the outline of this paper is as follows . in sec . [ nodalt ] we formulate the scattering problem and calculate the transfer matrix of the nodal dirac fermions through the _ d_-wave superconductor . the matching of wave functions at the interface with the metal electrodes is done in sec . [ wavematching ] , both for ideal ns interfaces and for interfaces containing a tunnel barrier . the transmission matrix of electrons and holes follows in sec . [ transmission ] . we then apply this result to the calculation of transport properties : the electrical current ( sec . [ electric ] ) , the thermal current ( sec . [ thermal ] ) , and the electrical shot noise ( sec . [ shotnoise ] ) . we conclude in sec . [ discuss ] with a discussion of our results and an outlook . geometry to measure the transmission of nodal fermions through a @xmath28-wave superconductor . a current @xmath29 is injected into the superconductor from metal contact @xmath30 ( at a voltage @xmath9 ) and drained to ground via the superconductor ( current @xmath31 ) or via a second metal contact @xmath32 ( current @xmath33 ) . if the separation @xmath0 of the metal contacts is large compared to the superconducting coherence length @xmath7 , the current @xmath33 is predominantly due to transmission parallel to the nodal lines @xmath34 or @xmath35 of vanishing excitation gap . ] we consider a two - dimensional spin - singlet superconductor ( s ) , connecting two normal metal contacts with parallel ns interfaces , separated by a distance @xmath0 . the transverse dimension @xmath12 of the superconducting strip ( in the @xmath36-@xmath37 plane ) is assumed to be large compared to @xmath0 , in order to avoid edge effects . the order parameter @xmath38 is assumed to have @xmath39 symmetry : it vanishes for wave vectors along two nodal lines , which are taken to be the @xmath36 and the @xmath37 axis . all our results also apply to @xmath40-superconductors , for our purposes , a simple @xmath41 rotation relates the two systems . to be specific , the @xmath36-@xmath37 plane can represent a single @xmath42 layer of a cuprate superconductor @xcite , with the @xmath43 $ ] direction at an angle @xmath41 . ellipsoidal equal - energy contours of low - energy excitations in the brillouin zone of a superconductor with @xmath39 symmetry . long and short axes have ratio @xmath44 . the contours are centered at the four nodal points ( solid dots ) , where the order parameter vanishes on the fermi surface . the normal @xmath45 to the ns interfaces is indicated . the dashed line , displaced from the nearest nodal point by @xmath46 , indicates points of constant wave vector component parallel to the interface . ] low - energy excitations in the superconductor are found in the brillouin zone near the four intersections @xmath47 , @xmath48 ) of the fermi surface with the nodal lines of the order parameter . ( these nodal points are labeled @xmath49 in fig . [ fig_brillouin ] . ) around these points , both the pair potential @xmath38 and the kinetic energy can be linearized : the dynamics of the nodal fermions is governed by an anisotropic dirac equation @xcite . for example , near node @xmath50 at @xmath51 this can be written in the form @xmath52 or more compactly with the help of pauli matrices , @xmath53\psi=\varepsilon\psi . \label{dirac2}\ ] ] we have set @xmath54 to unity , restoring units in the final expressions . the spinor @xmath55 contains the envelope wave functions of electron and hole excitations ( slowly varying on the scale of the fermi wavelength @xmath56 ) . the fermi velocity @xmath16 is larger than the velocity @xmath57 by a factor of order @xmath58 ( with @xmath59 the superconducting coherence length ) , which is in the range 1020 for cuprate superconductors . the equal - energy contours in the brillouin zone of the nodal fermions thus have an elongated ellipsoidal shape , @xmath60 as a function of the displacement @xmath61 of the wave vector from the nodal point . since the system is translation invariant along the ns interfaces , the component of the wave vector along these interfaces , @xmath62 , is a conserved quantity . here @xmath19 is the angle between the normal to the ns interface and the nodal line pointing to node @xmath50 , which we restrict to @xmath63 without loss of generality . moreover , since mirror reflection along the ns interface , followed by the transformation @xmath64 , while leaving all the other parameters unchanged , maps @xmath19 on @xmath65 , we can further restrict @xmath19 to @xmath66 . in all our formulas , to obtain the corresponding formulas for @xmath65 , replace @xmath46 by @xmath67 and @xmath68 by @xmath69 . we write @xmath70 , with @xmath71 the coordinate perpendicular to the ns interfaces and @xmath72 the coordinate parallel to them . we substitute @xmath73 into eq . and find that the spinor @xmath74 satisfies the wave equation @xmath75 \psi(s)=\varepsilon\psi(s ) , \label{dirac3}\ ] ] where @xmath76 is differentiation perpendicular to the ns interface , and @xmath77 and @xmath78 are the operators of particle current perpendicular and parallel to the ns interface , @xmath79 we note that the operator @xmath77 squares to a scalar , its magnitude giving the particle velocity @xmath80 perpendicular to the ns interface : @xmath81 to solve eq . , we multiply it by @xmath82 and rearrange to obtain @xmath83 with @xmath84 the solution to eq . can then be written as @xmath85 , \label{msdef}\end{aligned}\ ] ] where the second equation defines the _ transfer matrix _ @xmath86 . as expected , the particle current @xmath77 is conserved by eq . : @xmath87 = \psi^\dagger(s ) [ -i{\mathcal{a}}_0^\dagger { j}+i { j}{\mathcal{a}}_0 ] \psi(s)=0 $ ] . at the two ns interfaces the coupled electron - hole excitations in the superconductor are converted into uncoupled electrons and holes in the normal metal . we thus need to match , at @xmath88 and @xmath89 , the envelope wave functions @xmath55 of the nodal fermions in s to the bloch wave functions @xmath90 of free fermions in n. this is similar to the matching of dirac equation to helmholtz equation considered in the context of transmission through a photonic crystal @xcite . translational invariance parallel to the ns interfaces requires that the coupling conserve the wave vector component @xmath46 parallel to the interfaces . particle flux conservation imposes further constraints , as we determine here . at the surface of the superconductor , the order parameter @xmath91 attains its bulk value over a short length scale , the healing length @xmath92 . the two - component wave function on the s side of the interface ( at @xmath93 ) can be linked to that on the n side ( @xmath88 ) by an _ interface matrix _ @xmath94 , defined by @xmath95 in the normal metal , the operator of particle flux perpendicular to the ns interface can be written as @xmath96 with @xmath97 possibly different from @xmath98 because of a fermi energy mismatch . the requirement of particle flux conservation reads @xmath99 to derive the most general form of the interface matrix fulfilling this requirement , notice that a unitary rotation through angle @xmath100 , where @xmath101 , \label{theta_def}\end{aligned}\ ] ] transforms @xmath77 into @xmath102 up to a scalar factor : @xmath103 { j}\exp[-i\theta \sigma_y /2 ] . \label{jndef}\ ] ] this allows us to write the interface matrix as @xmath104 { \mathcal{m}}_0 , \label{mnsdef}\ ] ] where @xmath105 is a @xmath106 matrix fulfilling a generalized unitarity condition , @xmath107 eq . restricts @xmath108 to a three - parameter form @xmath109 ( ignoring an irrelevant scalar phase factor ) ," +"it is known , since the early days of quantum mechanics , that the low energy electronic properties of aromatic molecules are very sensitive to a magnetic field applied perpendicularly to their planes @xcite . the field breaks the time reversal symmetry and therefore induces an electronic current running around the circumference of the ring . this is the persistent current , arising due to aharonov - bohm effect @xcite . this is an equilibrium phenomenon , periodic in magnetic flux with period @xmath0 , the flux quantum @xcite . but , to be able to measure it requires systems with characteristic lengths in the nanoscopic or mesoscopic scale . indeed , on the one hand , the motion of the electrons has to stay coherent which is possible for systems smaller than the electronic coherence length . but , on the other hand , to cover a full period of magnetic flux requires rings with sufficiently large diameters . this is definitely not the case for the usual aromatic molecules where field as large as @xmath1 tesla are needed to observe the periodicity . however , nowadays , many man - made systems in the appropriate length scale , are available in various forms : isolated or ensemble of metallic or semiconducting rings @xcite and , more recently , carbon nanotubes which are large organic cylinders @xcite or , last , rings of carbon nanotubes @xcite . therefore , the study of persistent current have regained lot of interest during the last ten years . rings , made of usual metal or semiconductor , are studied intensively since the nineties and a few experiments , motivated by early theoretical prediction @xcite , have measured a sizable persistent current in some systems @xcite . but , neither the magnitude of the current - one or two orders of magnitude larger than expected - nor the diamagnetic sign of the response measured experimentally can be explained by existing theories . most of the theoretical efforts were devoted to the study of the interplay between disorder and coulomb interaction , but without convincing conclusions up to now @xcite . carbon nanotubes were discovered by iijima in 1991 @xcite . they are fascinating materials whose electronic properties are determined in a unique way by the topology of their lattice : they are rolled up strip of graphite sheet whose , depending on their diameter and chirality , can be either metallic or semiconducting @xcite . in any case , the electronic spectrum of these systems seems to be very sensitive to an applied magnetic field suggesting large orbital magnetic response @xcite . indeed , recently strong field effects have been seen in measurements of the tunnelling conductance of multiwall carbon nanotubes @xcite . magnetoconductance measurements of rings of carbon nanotubes have also been done @xcite . in order to better understand these experimental results , additional studies of electronic multichannel systems in presence of coulomb interaction are needed . this is clear for ballistic systems but , even for metallic rings which are in the diffusive regime , a proper understanding of the clean case should help to find a formalism able to treat disorder and interaction on equal footing . in this work , we consider cylindrical systems made of rolled square lattices ( multichannel systems ) , without disorder but with coulomb potential , long or short range . we are interested in how the coulomb potential can affect the ground state properties of these systems when a static magnetic field parallel to the cylindrical axis is tuned , and hence , on the behaviours of the persistent current . similar studies were done in the past but , either for pure 1d systems @xcite i.e. systems with only one electronic channel ( rings ) , or for multichannel systems ( cylinders ) but with strong disorder using first order perturbation theory or the hartree - fock approximation @xcite . the conclusions obtained here are not contained in these works . for cylinders , in the pure case and without electron - electron interaction , an axial magnetic field induces many level crossings at different values of the magnetic flux @xcite . at zero temperature , for a certain density of particles , the ground state energy shows also crossing points for particular values of the field where the ground state is degenerate . with the coulomb interaction , there exist interaction between these degenerate states resulting in avoided crossings ; in other words , at least at the vicinity of the crossing points the ground state becomes a true many - body state unable to be described by any mean field treatment . in this work , we propose a ` minimal ' variational wave function to deal with this particular problem , going beyond a simple hartree - fock calculation . as a result , we find , in addition to the avoided crossing formation , two others effects caused by repulsive interaction . ( i ) the positions of the ( avoided ) crossings points are shifted in magnetic field ; this effect is due to the non - equal hartree contributions of the different components of the interacting ground state . ( ii ) because of the presence of degeneracy , the hund s rule may drive the system to a triplet state : it follows sequences of singlet @xmath2 triplet @xmath2 singlet ground states which should be seen in various type of experiments such as measurements of the magnetoconductance , for instance . we believe the conclusions of this work rather general providing that the system under consideration is in the ballistic regime i.e. weakly disordered . indeed , all the effects described here , result from the degeneracy , or quasi - degeneracy , of the ground state induced by the magnetic field in the case without coulomb interaction . in principle , this always occurs for any cylindrical systems as carbon nanotubes , ring of carbon nanotubes or rings of usual semiconducting materials . the paper is organised as follows . in section ii , the model without coulomb interaction is presented and the origin of the crossing points induced by an applied magnetic field is described . in section iii , we introduce the model with coulomb interaction . in a first subsection , exact diagonalisation results are shown and the main interaction effects are discussed . in a second subsection , our variational ansatz is presented and some effects of the coulomb interaction are shown to be well reproduced by our approximation . last , in a third subsection , possible spin effects are analysed . the generic systems we consider along this work are rolled square lattices . in this section we start by neglecting the coulomb interaction to focus on orbital effects only . the electrons are then described by the following nearest - neighbour tight - binding model where an uniform magnetic field , @xmath3 , parallel to the cylindrical axis , is included via the peierls - london substitution @xmath4 where @xmath5 is the magnetic flux through the section of the cylinder in units of the flux quantum @xmath6 ( @xmath0 ) . the two indices @xmath7 , two integers , are the coordinates of the lattice sites : @xmath8 is the coordinate along the circumference , @xmath9 , and @xmath10 the one along the cylindrical axis , @xmath11 . the fermionic operator @xmath12 ( @xmath13 ) is the creation ( destruction ) operator of an electron at site @xmath7 with spin @xmath14 . the spectrum of the hamiltonian ( [ hcylinder ] ) , which depends continuously on the magnetic flux , is @xmath15 with @xmath16 and @xmath17 two integers such that @xmath18 and @xmath19 . we have applied open boundary conditions at the ends of the cylinder . note that the spectrum , and therefore every thermodynamic quantity , is periodic in flux , with periodicity @xmath20 @xcite . as the magnetic field is increased , the energy levels evolve and many level crossings appear @xcite ( cf . the details of the pattern of the crossing points is very complicated and depends on the geometry of the system and parameters of the model . at zero temperature , the ground state energy of the system with @xmath21 electrons is obtained by filling up successively the lowest energy levels according to the pauli principle . here , we restrict our study , almost exclusively , to the case of equal numbers of up and down spins i.e. @xmath22 , where the lowest @xmath23 levels are doubly occupied . the important variations of the energy levels with the magnetic field cause changes in the level occupation . as a consequence of that , at certain values of the magnetic field , @xmath24 , a former excited state may become the new ground state . such a switch of ground state are responsible for the appearance of cusps in the ground state energy curve . we can see an example in fig . 2a for a cylinder with @xmath25 and 80 electrons ; the ground state energy as function of the magnetic flux shows 5 different cusps . at these particular points , the ground state is changed from a state @xmath26 to a new one @xmath27 ( @xmath28 for ` _ in _ ' , and @xmath29 for ` _ out _ ' to do an analogy with scattering theory ) which are both a slater determinant built with the one - electron states , @xmath30 , eigenfunctions of the hamiltonian ( 1 ) . the two determinants differ only by the highest occupied level , @xmath31 and @xmath32 ( where the upperscript @xmath3 is for highest ) . one may see this orbital effect as a succession of scattering events where the time is replaced by the magnetic flux . the system of @xmath21 particles evolves freely until a particular ` time ' , @xmath24 , where the most energetic particle is scattered : @xmath33 . depending on the one - electron state exchanged , one should distinguish between * ` _ forward scattering _ ' ( fs ) where the two one - electron states , @xmath34 and @xmath35 , correspond to particles moving in the same direction along the circumference , * ` _ backward scattering _ ' ( bs ) where the two one - electron states , @xmath34 and @xmath35 , correspond to particles moving in the opposite direction along the circumference . in general , a fs corresponds to smaller change in momentum , @xmath36 ^ 2+[(q_i - q_o)\frac{\pi}{m+1}]^2)^{1/2}$ ] , than a bs . in fig 2a , only the cusp at @xmath37 is associated with a fs event , all the others are bs events . the persistent current ( pc ) is a thermodynamic quantity given , at zero temperature , in terms of the ground state energy @xmath38 by @xmath39 the second equality arises for free electrons only and in the case where @xmath22 . it can be shown that this derivative is proportional to the average of the current operator . this current yields an orbital magnetic moment which can be detected experimentally @xcite . obviously , the persistent current presents discontinuities for each value of the magnetic flux where the ground state energy shows cusps . 2b gives an example for the very same cylinder ( @xmath25 , @xmath40 ) . note that the persistent current in mesoscopic cylinders was studied with some details in the past . for instance , it was shown in @xcite that its intensity strongly depends on the shape of the fermi surface . this property has important consequences for carbon nanotubes @xcite . most of the other studies insist on the role played by disorder @xcite . as a remark , one may say that the orbital effect described above , works to reduce the persistent current : if" +"the twist of the solar magnetic field plays an important role in transient phenomena such as solar flares and coronal mass ejections , and in the dynamo processes that cause the 11-year solar activity cycle . the magnetic twist can be measured in various ways . magnetic helicity is an integral that quantifies topological complexity of field lines , such as linking , twist , or kinking ( @xcite , @xcite ) . for a closed magnetic system it is defined by @xmath0 , and alternative definitions have been developed for open systems @xcite . in this letter we consider current helicity , which we define as @xmath1 where @xmath2 is the magnetic field and @xmath3 is the current density . the quantity @xmath4 has the advantage that it describes the _ local _ distribution of twist and shear in the magnetic field , and that it is more readily determined from limited observational data than @xmath5 which requires global information . for a force - free field ( @xmath6 ) we have @xmath7 and @xmath4 , which may be a function of space , is a fundamental parameter that describes the torsion of the field lines around one another . note that we shall not consider the _ integral _ current helicity @xmath8 because unlike @xmath5 it is not a near - conserved quantity in mhd @xcite , and it does not even in general take the same sign as @xmath5 ( except for linear force - free fields where @xmath4 is constant in space and @xmath4 , @xmath9 , and @xmath5 all have the same sign , * ? ? ? there are two main techniques for estimating @xmath4 from observed vector magnetograms , which so far only cover a small region of the solar surface such as a single active region : 1 . compute @xmath10 and hence @xmath11 , which should give @xmath4 exactly for a force - free field @xcite . 2 . compute a linear force - free extrapolation from @xmath12 and choose the overall value , @xmath13 , which best reproduces the observed @xmath14 , @xmath15 distribution over the region @xcite . the studies by @xcite and @xcite show that both techniques are generally consistent . the key result of these observations is a robust hemispheric rule whereby the average @xmath4 value is negative in the northern hemisphere and positive in the southern hemisphere , although there is significant scatter including a mixture of signs of @xmath4 within single active regions . this hemispheric pattern in @xmath4 has also been found by @xcite who reconstructed the radial and toroidal components of the global magnetic field under simplifying assumptions . a trans - equatorial sign change in helicity is supported by numerous proxy observations such as h@xmath4 images of active region structure @xcite , _ in situ _ heliospheric measurements @xcite , differential rotation @xcite , and filament / prominence magnetic fields @xcite . using newly - developed simulations of the global coronal evolution , we have recently been able to reproduce the filament hemispheric pattern including exceptions ( with 96% agreement ) , in a comparison with 109 observed filaments @xcite . in this letter we describe the distribution of current helicity in a 30-month simulation , which we hope to compare with new magnetic observations from the sdo ( nasa solar dynamics observatory ) mission . our simulations of the 3d coronal field evolution @xcite use the coupled flux transport and magnetofrictional model of @xcite , in a domain extending from @xmath16 to @xmath17 in longitude , @xmath18 to @xmath19 in latitude , and @xmath20 to @xmath21 in radius . the coronal magnetic field @xmath22 evolves _ via _ the non - ideal induction equation @xmath23 in response to flux emergence and advection by large - scale motions on the photospheric boundary . rather than solve the full mhd system we approximate the momentum equation by the magnetofrictional method @xcite , setting @xmath24 this artificial velocity ensures evolution through a sequence of near force - free states . the second term is a radial outflow imposed only near to the upper boundary , where it simulates the effect of the solar wind in opening up field lines in the radial direction @xcite . the diffusivity @xmath25 consists of a uniform background term and an enhancement in regions of strong current density @xmath26 ( see * ? ? ? the photospheric boundary conditions are described in @xcite ; the surface flux transport model includes newly emerging magnetic bipoles based on active regions observed in synoptic normal - component magnetograms from nso , kitt peak . the emerging bipoles take a simple mathematical form , with properties chosen to match the location , size , tilt , and magnetic flux of the observed regions . they are inserted in 3d with a non - zero twist ( magnetic helicity ) , chosen to match the observed sign of helicity in each hemisphere . the simulation illustrated in this letter models 30 months of continuous evolution during the rising phase of cycle 23 ( from 1997 april 9 to 1999 october 10 , rotations cr1921 to cr1954 ) . from an initial potential field extrapolation , the photospheric and coronal fields were evolved forward continuously for 914 days with 396 new bipoles inserted during this time . two example snapshots of the simulated magnetic field are shown in figure [ fig : field ] . to illustrate the sources of current helicity in our simulation within an individual active region , figure [ fig : single ] zooms in to a bipole in the northern hemisphere which emerged on day 136 ( as measured from the start of the simulation ) . there are three main sources of coronal currents and helicity in our model : 1 . the new bipoles emerge twisted . this twist is initially concentrated low down in the centre of the bipole , as seen from the field lines in figure [ fig : single](a ) which are skewed as they cross the bipole s central polarity inversion line ( pil ) . the sigmoidal concentration of negative @xmath4 at the centre of the bipole is clearly seen on day 140 in figure [ fig : single](b ) . when the bipoles emerge they displace older fields and produce currents at the interface between old and new flux systems ( see * ? ? ? * ) . in figure [ fig : single](b ) this is visible at the nw edge of the new bipole where it adjoins a pre - existing bipole , and a layer of positive @xmath4 has developed . note that this is opposite in sign to that from the twist of the new region , as seen in figure [ fig : single](a ) . this corresponds to field lines that are oppositely skewed at this edge of the new bipole , as compared to those across the central pil . this is just one example of how both signs of @xmath4 may naturally be produced within a single active region , as found in observations . 3 . over time , surface motions shear the coronal field generating further currents . this is visible in figure [ fig : single](c ) , which shows the distribution of @xmath4 for the same region on day 190 , after 50 days evolution . there is a significant build - up of negative @xmath4 , particularly at the north and south ends of the bipole where helicity was initially low . this build - up is caused by differential rotation and convergence ( due to supergranular diffusion ) . in addition to these sources of current helicity , it may also be locally reduced by diffusive cancellation and reconnection . also , helicity is periodically removed through the top boundary of the domain when excessive build - up of twist leads to localised temporary losses of equilibrium , and the ejection of twisted flux ropes @xcite . the global distribution of current helicity , @xmath4 , is shown in figure [ fig : global ] at days 10 , 100 , and 910 of the simulation . from the initial potential field on day 0 ( with @xmath27 everywhere ) , a pattern of intermixed positive and negative @xmath4 has developed by day 10 , simply due to photospheric shearing this is before the first active region emergence . after about 100 days , a clear latitudinal trend in @xmath4 emerges , although there is still significant local variation in both strength and sign . this pattern persists for the rest of the simulation , and up to medium heights in the 3d corona ( nearer the top of the computational box high values of @xmath4 become localized to closed field regions , with @xmath28 where the field is open ) . in figures [ fig : global](a ) , ( e ) , and ( f ) , it can be seen how the mean @xmath4 at low latitudes ( @xmath16 to about @xmath29 ) develops into the observed hemispheric trend , although with considerable scatter as observed on the real sun . however , at high latitudes the sign of @xmath4 is reversed . these polar reversals correspond to the east - west pils at the polar crown boundaries , and move steadily poleward through the simulation as the polar crowns reduce in size towards polar field reversal ( we are approaching solar maximum ) . this opposite sign of @xmath4 is caused by differential rotation of the predominantly north - south field lines at this latitude , and is a well - documented problem for theoretical models @xcite . at lower latitudes , as was illustrated by figure [ fig : single](c ) , differential rotation of north - south pils produces the observed hemispheric sign of helicity @xcite . figure [ fig : global ] shows mean values of @xmath4 at active latitudes of the order @xmath30 . the actual maximum and minimum values recorded on day 910 of the simulation were @xmath31 and @xmath32 . a key result of this study is that these values are much higher than those estimated from linear force - free extrapolations . such solutions suffer a constraint on the maximum @xmath4 in order to obtain a decay with height @xcite , requiring that @xmath33 ( the `` first resonant value '' ) , where @xmath34 is the horizontal length of the periodic box . the linear force - free model of an observed filament by @xcite has @xmath35 , and for the solutions of @xcite this first resonant value was at @xmath36 . by contrast , studies using nonlinear force - free extrapolations from vector magnetograms using the grad - rubin type method @xcite find locally higher values of @xmath4 ( e.g. , * ? ? ? * ) . they are also more realistic because they allow variable @xmath4 within a single region , as in our simulations . for a particular active region , @xcite found maximum values of the order @xmath37 , consistent with the results of our simulations . in this letter we have shown how our 3d simulations of the global coronal magnetic field evolution are able to model the development and transport of current helicity , @xmath4 , over many solar rotations . we find a clear latitudinal pattern of @xmath4 that persists throughout the simulation , although locally within single bipoles there is significant scatter and intermixing of both signs of @xmath4 , in agreement with observations . local values may be much higher than those predicted by linear force - free extrapolations . with existing measurements of @xmath4 limited to vector magnetograms of individual active regions , robust observations of the latitudinal distribution of @xmath4 await full - disk vector magnetograms . these will shortly be available from the nasa solar dynamics observatory ( sdo ) satellite" +"secure multiparty computation is a fundamental cryptographic primitive in modern cryptography . it focuses on the studies of secure computation among the players that do not trust each other . in quantum cryptography , it is also studied extensively as secure multiparty quantum computation ( smqc ) . the smqc has been studied from two aspects : 1 ) the evaluation of classical function with quantum protocol , and 2 ) the evaluation of quantum transformation . lo @xcite studied one - sided two party computation of classical function , and proved that the task can not be realized securely with quantum protocols . later , refs . @xcite strengthened this impossibility result : two - sided secure two - party computation of classical function is also impossible with quantum protocols . secure multiparty computation of quantum circuit is also studied @xcite . @xcite presented a verifiable quantum secret sharing protocol , based on which constructed a smqc scheme . this construction of smqc can tolerate @xmath0 cheaters among @xmath1 players . this threshold was improved to @xmath2 in @xcite . dupuis et al . studied secure two - party quantum computation , and proposed a two - party protocol for secure evaluation of unitaries against specious adversaries @xcite , later the protocol was improved to securely compute any quantum operation against active adversaries @xcite . recently , ref . @xcite presented a quantum fully homomorphic encryption ( qfhe ) scheme , and described a smqc scheme of unitaries with trusted third party ( ttp ) based on qfhe scheme . this paper studies smqc without nonlocal measurements . the smqc task is reduced to secure two - party quantum computation of nonlocal cnot ( nl - cnot ) , and then the protocol presented in @xcite can be simplified . then the secure computation protocol of nl - cnot is reduced to bit commitment . firstly , the model of smqc studied in this paper is introduced here . suppose there are @xmath1 parties who jointly perform a computational task of quantum circuit . the input of the circuit is a @xmath3-qubit state . the @xmath1 parties are denoted as @xmath4 , whose inputs have @xmath5 qubits ( @xmath6 ) , respectively . through their local quantum computation and mutual communication , they accomplish the computational task , and each party can obtain the desired result . the quantum circuits are limited to be those containing no nonlocal measurements . in this model , any two of the @xmath1 parties are mutually distrusted , and each party may be dishonest . according to the possible cheating behaviors of dishonest participants , the smqc can have the different models , such as passive adversaries model , active adversaries model , or else . here , passive adversaries model refers that the dishonest parties merely gather information during the execution of smqc protocol , and the active adversaries model refers that the dishonest parties take active steps to disrupt the execution of multiparty protocol . in any multiparty protocol , each party may change its local input before even entering the execution of the protocol . this is also unavoidable when the parties utilize a trusted party . so , this is not considered a breach of security @xcite . @xcite constructed a smqc of unitaries with ttp based on qfhe . the scheme is described as follows : each party ( @xmath7 or @xmath8 ) preshares a secret key with ttp through quantum key distribution ( qkd ) ; then each party encrypts his data with his secret key , and sends the ciphertext to ttp ; using the preshared secret key , the ttp performs the quantum circuit on the encrypted data according to qfhe scheme ; the ttp sends back the ouputs to the corresponding parties , and then each party can decrypt the received state and obtain the desired result . this scheme is secure not only in the passive adversaries model but also in the active adversaries model . for some protocol @xmath9 and some protocol @xmath10 , we denote by @xmath11 the protocol where @xmath9 invokes instances of @xmath10 . * quantum universal composition ( uc ) theorem @xcite : * let @xmath10 , @xmath12 and @xmath9 be quantum polynomial time protocols . assume that @xmath10 quantum - uc - emulates @xmath12 . then @xmath11 quantum - uc - emulates @xmath13 . this theorem holds for both computational security and statistical security ( information - theoretical security or perfect security ) . quantum uc theorem ensures that if the quantum protocol @xmath10 can securely realize a functionality @xmath14 , then the protocol @xmath11 can securely realize a functionality @xmath15 . this section introduces the reduction from multiparty quantum computation to two - party quantum computation of nl - cnot . any unitary transformation can be decomposed into some cnot and single - qubit transformations , so any unitary transformation @xmath16 can be expressed by a quantum circuit @xmath17 that consists of only cnot and single - qubit gates . we consider @xmath1 parties @xmath4 participate in the joint computation of the quantum circuit @xmath17 . each of them @xmath18 has @xmath19 qubits as the inputs of the circuit , respectively . the circuit @xmath17 has @xmath6 qubits as its input . the @xmath3-qubit input of the circuit comes from all the @xmath1 parties . because the cnot gate is performed on two qubits , the cnot gates in the circuit can be classified into two kinds : ( 1 ) local cnot , which acts on the two qubits belonging to the same party , and ( 2 ) nl - cnot , which acts on the two qubits belonging to two different parties . for an arbitrary party @xmath18 , there are many single - qubit gates performing on his @xmath19-qubit input in the circuit . according to the computing sequence , these single - qubit gates are split into some small - scale quantum circuits by the nl - cnot gates in the circuit . the small - scale quantum circuit acts only on his @xmath19 qubits , so it is called local quantum circuit ( lqc ) . thus , the joint quantum circuit @xmath17 can be seen as a combination of some nl - cnot gates and lqcs . for example , any joint quantum circuit @xmath17 can be expressed similarly to this form in figure [ fig1 ] . quantum circuit to be computed jointly by @xmath1 parties . it can be seen as a combination of some nl - cnot gates and local quantum circuits ( lqcs).,width=302 ] because these lqcs are performed on their local qubits , the joint computation of the whole quantum circuit @xmath17 only requires the joint computation of every nl - cnot gate . according to quantum uc theorem @xcite , if the two - party computation of nl - cnot is secure , then there exists a smqc protocol for the unitary quantum circuit @xmath17 . thus , the smqc of unitary circuit is reduced to two - party quantum computation of nl - cnot . in general quantum circuit , there may be some quantum measurements . the measurements may be local or nonlocal . the local measurement means that it acts simultaneously on the qubits belonging to the same party . if the quantum circuit contains no nonlocal measurement , the smqc of quantum circuit can also be reduced to two - party quantum computation of nl - cnot . in order to implement ideal nl - cnot functionality by secure two - party protocol , we can still adopt the ttp in the similar way to the smqc presented in @xcite . the difference is that it is unnecessary to employ the qfhe scheme , while the qhe scheme of cnot is sufficient here . the detail is as follows . suppose alice and bob intend to compute a nl - cnot gate , they encrypt their qubits ( @xmath20 and @xmath21 ) using the secret key preshared with ttp separately , and send the two qubits to the ttp , then the ttp performs some quantum operation and sends back the result , finally alice and bob decrypt the received qubits separately and obtain the desired state @xmath22 . the @xmath1 parties intend to jointly compute a quantum circuit consists of some nl - cnots and lqcs ( the lqc may contain local measurements ) . the lqcs can be computed locally by themselves . once they have to jointly compute a nl - cnot gate , they call the ttp . the call procedure is described as above . because the secret key is needed during the call of ttp , they have to preshare some secret key through qkd , which is unconditionally secure . in this way , with the help of ttp , we can construct a smqc protocol for quantum circuit without nonlocal measurements . this protocol is just an improvement of the scheme presented in ref . @xcite . in this improved scheme , one computation of nl - cnot needs one call of ttp . so it is an interactive scheme , and each party does not interact with another party . moreover , the rounds of interaction depend on the number of nl - cnot gates in the quantum circuit . it can be concluded from the previous section that , nl - cnot plays a fundamental role in multiparty quantum computation . here the secure two - party computation of nl - cnot will be investigated as the key point . it will be reduced to bit commitment in the passive adversaries model and then a secure two - party quantum computation protocol of nl - cnot will be proposed . denote the four bell states as : @xmath23 , where @xmath24 , and @xmath25 . define quantum entanglement state @xmath26 this quantum state @xmath27 can be prepared using two copies of bell state @xmath28 and a cnot gate , e.g. @xmath29 . according to the implementation introduced in refs.@xcite , nl - cnot can be implemented as figure [ fig2 ] . this implementation involves an exchange of the two bits @xmath30 . if alice and bob do not send her / his bit ( @xmath31/@xmath32 ) simultaneously , there would leak information about her / his state . the analysis is referred to ref.@xcite . anyway , it is not secure to directly use this implementation of nl - cnot . the remote implementation of nl - cnot . the above / below of the dotted line expresses the local quantum operations of alice / bob . the dotted rectangle contains nonlocal computation.,width=302 ] based on the construction in figure [ fig2 ] , we should consider how to securely implement the computation of nl - cnot . it is obvious from the figure that , there are two nonlocal elements in this circuit : 1 ) the preparation of the entanglement state @xmath27 ; 2 ) the remote controlled operation in the dotted rectangle . the entanglement state @xmath27 can be prepared by any one party . after one party has prepared the 4-qubit state , he sends two qubits to the other party . it is secure in the passive adversaries model , because no additional information is revealed in the fixed state . in the part of the dotted rectangle , alice s local operation @xmath33 is controlled by bob s measurement result @xmath32 , and bob s local operation @xmath34 is controlled by alice s measurement result @xmath31 . so , in order to remotely implement nl - cnot . alice and bob must exchange their measurement results @xmath31 and @xmath32 . above all , in the passive adversaries model , the security of two - party quantum computation of nl - cnot depends on the security of exchanging two bits ( @xmath31 and" +"the concept of quantum entanglement plays a key role in the field of quantum information manipulation and processing@xcite . it describes the inseparability between parts of a given system in a given state . in the past decade , the close relation between quantum entanglement and the quantum correlation in many - body systems are discussed@xcite , especially in the context of condensed matter physics@xcite , cold atoms@xcite , and quantum chemistry@xcite , etc . one of the most interesting ideas is to employ the entanglement entropy as an indicator of quantum phase transition ( qpt)@xcite in both spin systems@xcite and the interacting fermion systems@xcite . for those quantum phase transitions that can not be described by landau s symmetry breaking paradigm , there is no well defined local order parameters . in such cases , the entanglement entropy may be a really useful concept for characterizing the quantum phase . one of such qpt is the mott metal - insulator transition , where a many - body system transits from a metallic state into an insulator , when the interaction strength between particles exceeds a critical value@xcite . experimentally , mott transition ( mt ) has been widely studied both in strongly correlated electron systems such as @xmath5@xcite and in cold atom systems@xcite . in the most strict sense of the mott transition , no symmetry breaking occurs at the transition and hence it belongs to the type outside the landau s paradigm . since 1960 s , mott transition has been one of the key issues in condensed matter physics . theoretically , intensive studies based on the hubbard - type models have been done in the past decades@xcite . the study of mt in terms of the quantum entanglement , especially using the entanglement entropy as a measure , appears for one - dimensional@xcite , two - dimensional@xcite , and infinite dimensional@xcite hubbard - like models . for fermionic lattice models , a connection has been established rigorously between the singularity of single - site entanglement entropy @xmath0 and the order of qpt , under certain conditions@xcite . this connection states that the discontinuity in the ( k - 1)-th order derivative of s gives a k - th order qpt . for one dimensional hubbard model , @xmath0 reaches a maximum at @xmath6 where mt occurs@xcite , due to equal population of all the local bases at the transition point@xcite . in two dimensions , study on finite size system does not disclose any singularity at @xmath3@xcite . in this paper , we focus on the single - site entanglement entropy @xmath0 near the mt in the fermionic hubbard model in infinite spatial dimensions . in this limit , the spatial fluctuations of electrons are suppressed while the local quantum fluctuation remains . the hubbard model can be solved exactly in this limit using the dynamical mean - field theory ( dmft)@xcite . recently , dmft is used to evaluate the relative entropy@xcite as a measure of correlation for the hubbard model as well as for a series of transition metal oxides@xcite . for the half - filled hubbard model , at low temperature , the fermi - liquid state in small @xmath7 regime is separated from the mott insulator state in large @xmath7 regime by a special second - order qpt@xcite . although this mott transition in large spatial dimensions has received considerable attention in the past years , no analysis has been carried out for the critical behavior of its entanglement properties . we expect that such analysis can help to deepen our understanding of the mt in general . the structure of this paper is as follows . in section @xmath8 , we introduce the single - site entanglement entropy @xmath0 and the method that we used to evaluate it for the hubbard model , _ i.e. _ , the dmft with exact diagonalization and the two - site dmft . in section @xmath9 , we present numerical as well as analytical results for @xmath0 near the mt . in section @xmath10 we end with a brief summary . the hamiltonian of the hubbard model reads @xmath11 @xmath12 here , @xmath13 is the hopping matrix element and @xmath7 is the on - site repulsion of electrons with opposite spin . @xmath14 and @xmath15 are annihilation and creation operators of the electron on site @xmath16 with spin @xmath17 , respectively . @xmath18 is the chemical potential . to study the local entanglement entropy , we divide the whole lattice into two parts , subsystem ( a ) ( a single site @xmath16 ) and the environment ( b ) ( the rest part of the lattice ) . for a given quantum state @xmath19 of the whole system , the reduced density matrix of the subsystem is @xmath20 the bipartite entanglement entropy between the subsystem and the environment is defined as ( setting @xmath21 ) @xmath22 from eq.(2 ) , one gets @xmath23 for any given operator @xmath24 of the system . taking @xmath25 , @xmath26 , @xmath27 , and @xmath28 for site @xmath16 , one gets 4 equations about the diagonal elements of @xmath29 under the basis set @xmath30 . here we study the symmetry unbroken ground state of hubbard model @xmath31 . the off - diagonal elements are all zero due to the @xmath32 and @xmath33 symmetries of hubbard model , i.e. , @xmath34 . we therefore obtain @xmath35 the averages are with respect to the ground state of hubbard model , and translation invariance is assumed here . for a half - filled lattice in the paramagnetic phase where the mott transition occurs , one has @xmath36 . the entanglement entropy thus reads @xcite @xmath37 here @xmath38 is the expectation value of the double occupancy . for the the ground state of the hubbard model in infinite spatial dimensions , this quantity can be readily evaluated from the converged self - consistent solution of dmft . the dmft is a well - developed theory for treating the hubbard - type strongly correlated models@xcite . in dmft , the hubbard model is first mapped into an effective anderson impurity model , @xmath39 + u c_{\uparrow}^{\dagger } c_{\uparrow } c_{\downarrow}^{\dagger } c_{\downarrow } -\mu \sum_{\sigma}c_{\sigma}^{\dagger } c_{\sigma}.\ ] ] here @xmath40 is the annihilation operator of bath site @xmath41 , and the the parameters of the electron bath @xmath42 determine the dynamical `` weiss field '' @xmath43 the impurity model is then solved to generate the impurity green s function @xmath44 on the matsubara frequency axis . finally , through the self - consistent equation @xmath45 together with @xmath46 , a new `` weiss field '' @xmath47 can be obtained and used to update the bath parameters @xmath48 . this process iterates and the converged solution of the impurity self - energy will be taken as the local self - energy of the lattice model , i.e. , @xmath49 . we adopt the semi - circular density of states @xmath50 @xmath51 is set as the energy unit . eq.(9 ) is the density of states of free electrons on the bethe lattice with infinite coordination number . it is widely used in the study of the mt because it simplifies the self - consistent equation while keeps the qualitative physics intact . we first solve dmft equations using the exact diagonalization ( ed ) method of caferral _ et al._@xcite . then , we resort to the two - site dmft@xcite for analytical results . at half filling , this theory is reduced to the linearized dmft@xcite . it is shown that it can produce rather accurate @xmath3 as well as physical quantities near the critical point . in the following , we present our results for @xmath52 and @xmath0 as a function of @xmath7 , both from dmft with ed and from the analytical two - site dmft formulism . it has been known@xcite that for finite temperatures @xmath53 , the metallic state for small @xmath7 is separated from the insulating - like state for large @xmath7 by a finite regime @xmath54 , in which the metal and the insulator phases coexist . the true first order phase transition occurs at @xmath55 ( @xmath56 ) where the free energies of the metallic and of the insulating solutions coincide . at zero temperature , @xmath57@xcite and @xmath58@xcite . the mott transition becomes a special second - order phase transition at @xmath59 : @xmath60 is continuous but the meta - stable solution of insulator extends from large u regime into the regime @xmath61 . in fig.1 , we show the double occupancy @xmath52 and entanglement entropy @xmath0 as functions of @xmath7 , obtained from dmft with ed for a very low temperature @xmath62 , which is practically same as zero temperature . as shown in fig.1(a ) , the double occupancy @xmath52 decreases linearly as @xmath7 increases up to the critical point @xmath63 . near @xmath63 , coexistence of two solutions and hysteresis in @xmath7-scanning are observed . from the solution of @xmath52 obtained by scanning from small @xmath7 to large @xmath7 ( solid circles in fig.1(a ) ) , we can identify a linear form in the @xmath64 regime after a non - singular term @xmath2 is subtracted , @xmath65 the other solution of @xmath52 ( empty squares in fig.1(a ) ) is obtained by scanning from large @xmath7 to small @xmath7 . it extends to @xmath66 and recovers the first solution through a finite jump . from the continuation of @xmath52 at @xmath63 in the second solution , we can infer that in the @xmath67 regime , a linear behavior with a much smaller slope must hold . therefore , we can summarize @xmath68 as @xmath69 with @xmath4 and having different values on two sides of the phase transition . this is consistent with the scenario of the special second - order mt@xcite in infinite dimensions : @xmath70 is discontinuous . our ed calculation gives @xmath71 and @xmath72 , in agreement with previous results of ed and projected self - consistent technique @xcite . there is a small but finite double occupancy @xmath73 at @xmath74 . this reflects that even at critical point and in the insulating state , there is residual local charge fluctuations . this has important consequence for the entanglement entropy in the insulating state . see below . in fig.1(b ) , the entanglement entropy @xmath0 is shown . at @xmath75 , @xmath76 comes from the equal population of electrons on the four local states . @xmath0 decreases monotonously with @xmath7 . after a inflection point at @xmath74 , it continues to decrease towards its strong - coupling limit @xmath77 , which comes from the spin two - fold degeneracy in the paramagnetic insulator phase . being consistent with @xmath52 , two solutions coexist in the regime @xmath78 and a hysteresis is observed . what is interesting is the nonzero critical value of the entanglement entropy @xmath79 . this reflects the residual entanglement between a single site and the others at the critical point and in the insulating phase . the critical behavior of @xmath0 may be easily obtained from eq.(8 ) and ( 5 ) : @xmath80 here @xmath4 and it has different values on two sides of mt . due to the finite @xmath81 , @xmath0 is not singular at @xmath74 but its derivative is discontinuous . this is the main result of this paper . here is the big difference between the static mean - field theory and the dmft . for static mean - field theories such as the weiss mean - field theory , the entanglement will become zero as soon as the system enters the long - range ordered phase , while it stays as a constant @xmath82 in the paramagnetic phase , arising from spin two - fold degeneracy . for dmft , although the short range spin - correlation is not taken into account , the local temporal fluctuations do" +"observations of galaxies in optical wavebands are strongly influenced by selective extinction which is hard to take into account due to inhomogeneous distribution of dust . by this reason the maps of color and brightness may give distorted picture of photometrical structure of galaxies and distribution of star - formation tracers . in paper @xcite it was proposed to use the combined color index @xmath1 whose value does nt depend on selective attennuation of light to trace the structure of galaxies . in general case for photometric bands a , b , c one can define combined index @xmath2 as @xmath3 to make it as far insensitive to extinction as possible . here @xmath4 is the ratio of color excesses . we have assumed its values for vbri system to be equal to standart values for our galaxy according to @xcite : @xmath5 = 0.840 , @xmath6 = 0.413 , @xmath7 = 2.033 , @xmath8 = 0.681 . as it was shown in @xcite , these ratioes do not depend practically on whether we observe the source through the dust screen or dust and stars are well mixed . similar approach was later used in @xcite to investigate the structure of m 51 . two spiral galaxies - and were observed in bvri colors ( cousins system ) 21 - 22 jan 1988 at 1-m reflector of special astrophysical observatory of russian academy of science . ccd camera 512x512 with scale 0.""37/pix was used . data processing was carried out with the help of midas package . asymmetric distribution of colors on the color maps of and gives evidence that they are dusty objects . combined colors indices do not describe neither `` real '' colors nor the value of the extinction . they may be considered as some conditional color indices free ( or nearly free ) of color excesses . the values of @xmath2 depend on stellar population , stellar abundances and , if r band is involved , on the presence of @xmath9 emission ( see @xcite ) . as an illustration , fig.1a shows how the values of @xmath10 , @xmath1 , @xmath0 and @xmath11 change when young stars formed in the single burst with the age t=0.1 gyr are overlapped onto the the old population ( t=13 gyr ) for different relative mass of young stars . the evolution program by + g.worthey ( see @xcite ) was used adopting salpeter imf and [ fe / h]=0 . fig.1b illustrates the dependence of q s on the burst ages for a fixed ( 1@xmath12 ) fraction of young stars . fig 1c shows a variation of q s with the adopted metallicity of the old population for the same parameters of burst as in fig 1b . as it follows from figures 1a - 1c , @xmath0 is the most sensitive to the fraction of young stars . the change of @xmath1 is less significant , but on the other hand this index should allow to localize giant emission regions where @xmath13 line locally increases r luminosity of the disk . in fig.2 and 3 the maps of @xmath0 and @xmath1 distribution for our galaxies are presented . maps are bounded by the ellipses whose major axes equal to @xmath14 . they appear to be much more symmetrically distributed than color indices . curiously a ring - like zone at about 15 "" ( 4.7 kpc for @xmath15 ) from the center appears in which is not noticeable at the color maps . it enables to consider this system as the galaxy , where star formation is enhanced in the ring . note that is absent in catalog of a ring galaxies by @xcite ) . @xmath1 map of reveals a clear 3-armed spiral - like structure where the values of @xmath1 have local maxima which may be explained by enhanced emission in @xmath13 ( local equivalent width @xmath16 100 @xmath17 ) . however blue stars do not form a clear spiral structure in this region as one can see from @xmath0 map of the galaxy . we can compare the relative intensity of star formation in different regions of a galaxy using @xmath0 @xmath1 diagram . the toy - model of a galaxy with exponential decreasing @xmath18 was developed using worthey s program ( from @xcite ) . the model values of q s which do not take into account recently formed stars ( t @xmath19 @xmath20 yr ) are shown by continious curve in fig.4 . dashed curve shows the values of the combined indices when the burst of sf is added to the previous model ( young population contains 30@xmath12 of the mass of the background population , has solar metallicity and the age of 0.1 gyr ) . the arrow in fig.4 . shows how @xmath21 emission shifts the point in the diagramm . the model curves show that the increasing of the fraction of young stellar population change mostly @xmath0 . on the other hand the @xmath22 shifts points horizontally . it enables to use the diagram as the diagnostic one for comparizon of star formation in different parts of a galaxy . as an example we put average values of q s for more than hundred points of central region ( diamond ) , regions of sf - ring ( triangle ) and outer regions ( square ) of on the diagram in fig.4 . mean errors of position of the points is about @xmath23 . regions in the center and in the sf - ring have the same @xmath0 which enables to conclude that they have similar fraction of young stars . the difference in @xmath1 may be explained by the presence of @xmath24 emission ( local @xmath25 ) . the outer regions of the galaxy contain a less amount of blue stars . these examples illustrate the ability to investigate structure and distribution of star formation tracers in dusty galaxies using optical broad - band photometry . combined photometrical indices @xmath0 and @xmath1 which are weakly affected by the selective extinction may be used successfully to restore the photometrical structure of galaxies with non - homogeneous dust distribution , even if their dust - free colors remain unknown . index @xmath0 depends on the presence of blue stars which enables to use it to localize regions of recent star formation . on the other hand , @xmath1 weakly depends on the light of blue stars but is sensitive to young star population through the emission in @xmath9 line . whereas color distribution is asymmetric in and due to internal absorption , their @xmath0 and @xmath1 maps are relatively symmetric and allow to reveal structure details hidden by the dust . in a ring - like region evidently related to active star formation is clearly visible at q - maps . in three armed spiral structure and active star formation reveal themselves in @xmath1 map of the galaxy . this research was suported by russian grants rfbr 98 - 02 - 17102 and federal program astronomy . d.b . very appreciates financial support of european space agency to participate to the 33rd eslab symposium ." +"the interaction between charged particles is known to be strongly affected by a background plasma . examples include dusty plasmas , where the screening of the dust - dust interaction is mainly determined by ions @xcite , and dense two - component plasmas @xcite , where the ions are screened by weakly coupled electrons . these plasmas are expected to occur in the interior of giant planets and white dwarf stars . while in the former case the degree of screening is determined by the ion debye length , the screening length in the latter is the thomas - fermi length , owing to the degeneracy of the electrons . the yukawa one - component plasma model is often used to describe the heavy plasma component while the light component determines the screening length . its static properties and collective excitations have been studied in several publications , e.g. @xcite . in many situations the plasma is neither homogeneous nor macroscopic . recently , it was shown @xcite that the density of a three - dimensional dusty plasma , where gravity is balanced by a thermophoretic force @xcite , is not homogeneous . the reason is the screened dust - dust interaction which produces an inhomogeneous density profile in a harmonic confinement . this is different from experiments with confined ions @xcite where the interaction is coulombic and the mean density is constant . in astrophysical plasmas the confinement is provided by gravity and may also influence the plasma properties . previous continuum theories @xcite for yukawa plasmas were limited to static properties . here we extend these results to a time - dependent theory and investigate the normal modes of a yukawa plasma in a spherical , harmonic confinement @xcite . this model is appropriate for the experiments of @xcite , for which the normal modes of rather small dust crystals have recently been measured @xcite . on the one hand , a fluid approach is expected to be accurate for long wavelength modes in a weakly coupled plasma . on the other hand , the agreement of theoretical predictions @xcite with experiments @xcite and simulations @xcite for confined ions turns out to be surprisingly good even in the strongly coupled phase . an analogous result for a confined one - component plasma with a screened interaction is still missing . open questions are the influence of screening on the normal modes and the eigenfrequencies . compared with the lagrangian description of ref . @xcite for the breathing mode , the present approach makes no assumption about the particular mode form . besides dusty plasmas and compact star interiors , we expect our results to be relevant for other systems as well , when screening and confinement are not negligible . this paper is organized as follows . the fluid equations are introduced and linearized in sec . [ sec : fluideq ] . in sec . [ sec : solution ] we explicitly consider an isotropic harmonic confinement . the density profile is reviewed and used to calculate the ground state potential and energy . further , the linearized poisson equation is solved and the eigenfrequency spectrum is derived . the normal modes are discussed in detail . we conclude with a discussion of the theory and an outlook on future work in sec . [ sec : conclusion ] . the fluid equations for a spatially confined one - component plasma read [ eqn : fluid ] @xmath6 & = -n\nabla u -\nabla\cdot { \mathbf{p } } -m n \nu { \mathbf{v}},\label{eqn : eomfluid}\end{aligned}\ ] ] where @xmath7 denotes the sum of the confinement potential @xmath8 and the potential @xmath9 induced by the particles . in the first ( continuity ) equation @xmath10 is the particle density and @xmath11 their mean velocity . the second equation is the momentum equation , where @xmath12 denotes the particle mass , @xmath13 their charge and @xmath14 the pressure tensor . a damping term with friction coefficient @xmath15 is included to account for collisions with neutral particles . the fluid equations are complemented by poisson s equation for the ( induced ) potential @xmath16 , @xmath17 where the screening of the interaction between the heavy particles by a polarizable background medium ( light charged components ) is explicitly taken into account . the range of the interaction is determined by the inverse of the screening parameter @xmath2 . a small perturbation of the plasma equilibrium is well described by linear response theory . this could be caused by an external perturbation ( e.g. laser manipulation of particles in a dusty plasma ) or by thermal effects . we are interested in strongly coupled plasmas and hence can neglect the pressure term ( cold fluid limit ) . ( [ eqn : fluid],[eqn : poisson ] ) are then linearized according to @xmath18 . products of first order terms are assumed negligible . the classical equilibrium density profile @xmath19 and the associated potential @xmath20 are determined from the zero order terms of eqs . ( [ eqn : eomfluid ] , [ eqn : poisson ] ) , [ eqn : groundstate ] @xmath21 which describe local force equilibrium and are equivalent to the energy minimization in @xcite ( we neglect the finite size factor @xmath22 , where @xmath23 is the particle number ) . first order quantities are determined by [ eqn : perturbed ] @xmath24 looking for normal mode solutions with a time dependence @xmath25 , e.g. @xmath26 , we obtain [ eqn : firstorder ] @xmath27 using eqs . ( [ eqn : firstorder ] ) we can rewrite ( [ eqn : pertpotential ] ) as @xmath28=\kappa^2 \hat{\phi}_1,\ ] ] where the plasma dielectric function is given by @xmath29 and @xmath30 denotes the local plasma frequency . @xmath31 and @xmath32 have been eliminated in favor of @xmath33 . ( [ eqn : poisson_diel ] ) is a self - contained equation for @xmath33 and will be solved in the following section for a special case . having found its solution , @xmath31 and @xmath32 follow from eqs . ( [ eqn : firstorder ] ) . so far our results are valid for arbitrary confinement . in order to make further progress let us now explicitly consider an isotropic harmonic confinement @xmath34 . the ground state density @xmath35 [ cf . ( [ eqn : groundstate ] ) ] is given by @xcite @xmath36 where @xmath37 is the wigner - seitz radius in the coulomb limit , @xmath38 . the normalized cluster radius is denoted by @xmath0 . for coulomb interaction the density is constant , @xmath39 , and @xmath40 , while for @xmath41 @xmath35 decreases parabolically towards the boundary . in this case @xmath42 must be determined from @xcite @xmath43=0,\ ] ] where @xmath44 is the inverse screening length normalized by the coulomb radius . for small @xmath45 the asymptotic solution of eq . ( [ eqn : radius ] ) is @xmath46 while for @xmath47 @xmath48 the relative error of these approximations is @xmath49 for @xmath50 and @xmath51 , respectively . the case @xmath52 is encountered if @xmath53 , i.e. if either @xmath54 and/or @xmath23 are large . this is why we will refer to @xmath4 as the macroscopic / strong screening limit . the plasma has a size of many screening lengths . the opposite case , @xmath55 , will be referred to as the coulomb limit , where the screening length is much larger than the plasma radius . it is straightforward to calculate the moments of the density , which are given by @xmath56 the ratio of two moments [ fig . [ fig : momentsenergy]a ] could help determine the unknown parameters @xmath3 and @xmath1 in experiments , where the particle positions are directly accessible . the moments can easily be calculated since the integral reduces to a sum over all particles as @xmath57 . the ground state potential @xmath58 is determined by eq . ( [ eqn : potential0 ] ) for which the yukawa potential is the associated green s function @xcite . thus , the solution is given by ( details can be found in appendix [ sec : appendixa ] ) @xmath59 ^ 2\right ] , & r\le r,\nonumber \\ r \exp(\xi-\kappa r)/r , & r > r . \end{cases}\end{aligned}\ ] ] since the confinement is parabolic the potential inside the plasma must decrease correspondingly to ensure force equilibrium . outside the cloud the potential behaves like that of a point charge placed at the origin . while for coulomb interaction the ( effective ) charge is @xmath60 , as expected from gauss s law , the result for yukawa interaction is @xmath61 $ ] . the ground state density and potential can further be used to calculate the total energy in mean - field approximation , @xmath62 , where @xcite @xmath63 using eqs . ( [ eqn : density0],[eqn : potential0sol ] ) we find after some algebra , @xmath64,\\ \frac{e_\text{int}}{q^2/a}&=\frac{(r / a)^5}{210}\left[\frac{126 + 147\xi+72\xi^2 + 18\xi^3 + 2\xi^4}{(1+\xi)^2}\right].\nonumber \end{aligned}\ ] ] the total energy then reads @xmath65,\ ] ] see fig . [ fig : momentsenergy]b . for small @xmath3 the interaction energy yields the dominant contribution to the total energy since the potential is only weakly screened . for large @xmath3 the cluster has a size of several screening lengths and the potential energy dominates . the critical point is at @xmath66 . for coulomb interaction ( @xmath67 ) the result is @xmath68 , which is the first ( mean - field ) term in the energy expansion of the shell model ( or the energy of the neutralizing background ) @xcite . in the opposite limit , @xmath52 , the asymptote is @xmath69 since @xmath70 [ leading order term in eq . ( [ eqn : radius_asy ] ) ] . in the limit @xmath71 we thus have @xmath72 for @xmath38 and @xmath73 for finite screening . -th to first density moment , and b ) ground state energy contributions.,scaledwidth=47.0% ] since the ground state density profile terminates in a finite step , cf . ( [ eqn : density0 ] ) , one has to solve ( [ eqn : poisson_diel ] ) separately for @xmath74 and @xmath75 . the dielectric function inside and outside the plasma reads @xmath76 where the constant term is given by @xmath77 and @xmath78 . accordingly we define a normalized plasma frequency @xmath79 . note that the plasma frequency @xmath80 only depends on the product @xmath81 , see eqs . ( [ eqn : plasmafreq],[eqn : density0 ] ) . ( [ eqn : poisson_diel ] ) must be supplemented by the boundary conditions [ eqn : boundarycond ] @xmath82 here @xmath83 and @xmath84 are unit vectors in the tangential and radial direction at the surface of the sphere with radius @xmath1 . these are the usual boundary conditions for the tangential component of the electric field @xmath85 and the radial component of @xmath86 . in order to solve eq . ( [ eqn : phi1 ] ) we use an expansion in spherical harmonics , i.e. @xmath87 since the spherical harmonics are eigenfunctions of the angular part of the laplacian , @xmath88 this leads to the following equation for the radial function @xmath89 , @xmath90&\\ -\left[x^2 + { \ell(\ell+1)}\epsilon(x,\omega)\right]\tilde f(x,\omega)&=0,\nonumber\end{aligned}\ ] ] after multiplying by @xmath91 . here we made a change of variables from @xmath92 to the dimensionless radius @xmath93 and introduced a new notation @xmath94 . in the remainder of this section we will separately solve ( [ eqn : radialx ] ) inside and outside the plasma . consider first the situation outside the plasma where the dielectric function is just a constant . here ( [ eqn : radialx ] ) reduces to @xmath95\tilde f(x)=0,\ ] ] the solutions of which are modified spherical bessel functions of the first and second kind , @xmath96 and @xmath97 , respectively @xcite . they are related" +"disordered systems of interacting localized particles have been extensively studied for over two decades . a characteristic feature of these systems is a complex many valley structure of the energy landscape of the state space @xcite . therefore , at sufficiently low temperatures , the system can not be considered to be in thermodynamic equilibrium : gibbs ensemble theory of statistical mechanics , which is based on the equivalence of time and ensemble averages , is not applicable . thus non - ergodic effects are important . the coulomb glass @xcite is a prominent example of such disordered systems . in heavily doped crystalline semiconductors , amorphous semiconductor - metal alloys , and granular metals , it plays an important role as a semiclassical model for systems of localized states . the dynamical behavior of the coulomb glass has been studied by several groups : schreiber et al.@xcite , as well as prez - garrido et al . @xcite determined numerically the transition probabilities between low - energy many - particle states , and studied the eigenvalues of the transition probability matrix . the former group directly diagonalized this matrix , whereas the latter developed a renormalization method to eliminate the transitions with large rates , what considerably simplifies the diagonalization . a broad distribution of relaxation times over several orders of magnitude was found in both cases . it reflects the glassy behavior of this system . moreover , wappler et al . @xcite used the damage - spreading algorithm to study the temporal evolution of the system , and found evidence for a dynamical phase transition . yu studied the time development of the coulomb gap considering a self - consistent equation for the density of states @xcite . she too observed that very long time scales are involved . the main aim of this work is to study numerically non - ergodic effects in the coulomb glass analyzing the transitions between many - particle states . we apply this procedure to the investigation of such effects in the specific heat . the paper is organized as follows : section ii introduces the coulomb - glass model . section iii describes how the low - energy many - particle states are obtained numerically . in sec.iv , we calculate the transition probabilities between these states , and map the dynamical behavior of the coulomb - glass sample to a graph . the nodes of the graph represent the many - particle states , and the edges the relevant transitions between them . analyzing the structure of this graph , we determine the value of a physical observable in dependence on the duration of its measurement . in sec . v , we use this method for the investigation of the non - ergodic effects in the specific heat : we study the influence of temperature , duration of measurement , disorder , and dimensionality . finally , in sec . vi we extract some conclusions . the classical impurity band ( cib ) model is the most realistic model for simulating an impurity band of localized states in a lightly doped semiconductor when quantum interference can be neglected @xcite . it is applicable if the following two conditions are fulfilled : ( i ) the mean nearest - neighbor distance is considerably larger than the localization radius of the wavefunction of an isolated impurity state . ( ii ) the temperature is so low that both the activation to the conduction band / from the valence band , and the formation of doubly charged donors / acceptors can be neglected . we consider a @xmath0-dimensional sample of an n - type , partially compensated semiconductor with donor concentration @xmath1 , and acceptor concentration @xmath2 . the degree of compensation @xmath3 can range from 0 to 1 . so donors are either occupied , that means neutral , or empty , that means positively charged . acceptors captured an electron each , and are negatively charged . the distribution of electrons between the donors is governed by the hamiltonian @xmath4 the donor occupation number @xmath5 equals 1 for occupied donors , and 0 for ionized donors . moreover , @xmath6 and @xmath7 , where the random positions of the donors are denoted by @xmath8 and @xmath9 , and those of the acceptors by @xmath10 . however , to minimize size effects , we impose periodic boundary conditions and use the minimum image convention @xcite . that means , in computing @xmath11 , we substitute the projection of @xmath11 onto each of the coordinate axis , @xmath12 with @xmath13 , by the smallest related value in a periodically repeated representation , @xmath14 with @xmath15 being the edge size of the sample . for numerical reasons , we construct the samples so that the nearest neighbor distance exceeds 0.5 , a well justified approximation for amorphous semiconductors , but not for crystalline systems . in this work , the unit of distance is defined by the donor density @xmath16 , and electron charge , dielectric constant , and boltzmann constant are taken to be unity . within the present study , most of the calculations are performed for a simplified version of this model . following refs . , see also , we consider a partially filled band of elementary charges ( particles ) localized on a regular lattice formed by the @xmath1 donor sites . here , the acceptors are substituted by background charges @xmath17 at each of the lattice sites , guaranteeing electro - neutrality on average . the disorder is simulated by a random potential @xmath18 . its values are uniformly distributed between @xmath19 and @xmath20 . thus , the influence of the randomness of the donor positions is ignored , as well as the correlations between the values of the acceptor potential at neighboring donor sites . moreover , the rectangular distribution of the @xmath18 is a simplification neglecting contributions from particular close pairs of donors and acceptors . this model is represented by the hamiltonian @xmath21 where @xmath22 denotes again the occupation number of site @xmath23 . as above , @xmath24 is the distance between sites @xmath23 and @xmath25 according to periodic boundary conditions . the lattice spacing is taken as unit of distance . a mixed form of both the models ( 1 ) and ( 2 ) is obtained in the following way : the sites are positioned at random , and the acceptor potential is substituted by a random on - site potential plus the potential of neutralizing charges @xmath17 at each site @xcite . this mixed form is more realistic than eq . ( 2 ) : it keeps the donor disorder as the hamiltonian ( 1 ) , but simplifies the disorder contribution from the acceptors . by means of @xmath18 , the influence of the random surroundings of host atoms in an amorphous semiconductor can be simulated . this model is in the following referred to as random - position - with - random - potential model . the relaxation procedures , which we use , alternatively simulate the sample to be isolated , or to be in contact with a particle reservoir @xcite . the latter means that , instead of @xmath26 , the grand canonical potential , @xmath27 , is minimized . the value of the chemical potential @xmath28 depends on @xmath3 , i.e. , it is fixed by the electro - neutrality condition . here , we first obtain @xmath28 performing a canonical simulation with reduced accuracy . then we calculate the set of low - energy states , as described below , taking into account particle exchange with the reservoir . for studying low - temperature properties treating correlations exactly , we need to know a set @xmath29 of almost all many - particles states in a certain energy interval above the ground state energy . if the occupation numbers are known , the energy of a state can easily and directly be determined from eq . ( 1 ) because we are treating a classical system . the problems , however , consist in the binomially large number of possible configurations , and in the existence of many local minima . thus it is a complicated task to obtain such a set of low - energy many - particle states . it has been approached by several methods : mochena and pollak @xcite developed an approximative renormalization - like procedure . schreiber and tenelsen @xcite used the metropolis algorithm to collect low - lying states which seems to be favorable in comparison to the previous method @xcite . mbius and pollak @xcite , and prez - garrido et al . @xcite used two - stage algorithms . in the first stage , they obtained sets of local minima by means of relaxation . for that , a complete search considering rearrangements of the site occupations including up to four sites , and an incomplete search concerning more complex rearrangements , built up of several low - energy one - electron hops ( shifts ) , were performed in refs . and , respectively . in the second stage , both groups completed the table of low - energy states by systematically investigating the neighborhood ( in the configuration space ) of each of these states . this neighborhood is defined via the accessibility within only one of the considered rearrangements . here , we find the set @xmath29 of @xmath30 low - energy many - particle states by means of a three - stage algorithm ; for a short preliminary description see ref . . in the first two stages , we create , and improve a `` backbone '' of @xmath29 , formed by metastable states , the number of which can be considerably smaller than @xmath30 . then , in the third stage , we complete @xmath29 by systematically investigating the neighborhood of the states found . our procedure , which includes sophisticated local search @xcite , and thermal cycling @xcite , is explained in detail in the following . in the first stage , creating the backbone of @xmath29 , we repeatedly start from states chosen at random , and simulate quenching the sample ( i.e. , a rapid relaxation ) by means of a local search procedure : in an iterative process , we search the neighborhood of the actual state for states of lower energy , and accept always the first such state found . the process stops when no lower neighboring state exists . our local search algorithm @xcite ensures stability with respect to rearrangements concerning one up to four sites . making use of the branch - and - bound idea in order to avoid unnecessary attempts to a large extent , it considers the following rearrangements : * transition of one electron between the sample and a reservoir , * arbitrary one - electron hops within the sample , * rearrangements by performing simultaneously an ( a ) and a ( b ) transition , and * arbitrary two - electron hops within the sample . to ensure high efficiency of the simulations , the searches in ( c ) and ( d ) have to be restricted to a certain number of neighbors . for one- , two- , and three - dimensional systems , we consider the first 4 , 8 , and 26 neighbors , respectively . ( though the number of possible rearrangements increases rapidly with the number of neighbors considered , the portion of long - range hops among the energy decreasing rearrangements is small due to the decreasing interaction strength . ) the second stage consists in extending , and improving this set of metastable states by thermal cycling @xcite . for that , a further set @xmath31 of metastable states is considered . initially , it equals a subset of @xmath29 , containing the states of lowest energy . we" +"cooperation among animals , either within or between species , is widespread throughout nature @xcite-@xcite . this presents a puzzle for darwinists since , according to darwin s theory , the rule among animals should be competition , not cooperation . attempting to understand the evolution of cooperation , maynard smith and price @xcite applied game theory to interactions between competing individuals of the same species that use different strategies for survival . they found that in situations like combat , in which each individual must decide whether or not to escalate the fight without knowing his opponent s decision , the interests of both combatants are best served if both decide not to escalate the fight . @xmath3 games ( 2 players making a choice between 2 alternatives ) , which showed their usefulness in economics and social sciences @xcite , constitute also a basic tool to model the conflict / cooperation situations in biology @xcite . furthermore , the marriage of game theory and darwinian evolution gave rise to a new branch of game theory , namely _ evolutionary game theory _ @xcite . in particular one of such games is the _ prisoner s dilemma _ ( pd ) , now well established as a useful tool for studying cooperative interactions among self - interested agents . the pd game comes from an experimental setup designed by the researchers at the rand corporation m. dresher and m. flood . the game refers to an imaginary situation in which two suspects are arrested near the scene of a crime . the police do nt have enough evidence to convict the pair on the principal charge . the two prisoners are held in separate cells and offered a deal : if one testifies implicating the other in the principal crime will go free , while the other , if remains silent , will receive 10 years in prison . if they both testify against each other , each will receive 5 years . finally , if they both remain silent , they will both be convicted by a minor crime and serve one year . what s the rational choice for each prisoner ? to remain silent ( cooperate with your partner ) or to confess ( not to cooperate ) ? the `` dilemma '' faced by the prisoners is that , whatever the other does , each is better off confessing than remaining silent . but the outcome obtained when both confess is worse for each than the outcome they would have obtained if both had remained silent . this puzzle illustrates a conflict between individual and group rationality . a group whose members pursue rational self - interest may all end up worse off than a group whose members act contrary to rational self - interest . formulated in its general form the pd game involves two players each confronting two choices : cooperate ( c ) or defect ( d ) and each makes his choice without knowing what the other will do . the possible outcomes for the interaction of both agents are : 1 ) they can both cooperate : ( c , c ) and get the reward `` for mutual cooperation @xmath4 , 2 ) they can both defect : ( d , d ) and get the punishment '' for mutual defection or 3 ) one of them cooperates and the other defects : ( c , d ) ; in that case the one who played c gets the `` sucker s payoff '' @xmath5 while agent who played d gets the `` temptation to defect '' @xmath6 . the following _ payoff matrix _ summarizes the payoffs for _ row _ actions when confronting with _ column _ actions : @xmath7 with the four payoffs obeying the inequalities : @xmath8 clearly it pays more to defect : if your opponent defects , and you cooperate you will end up with the worst payoff . on the other hand , even if your opponent cooperates , you should defect because in that case your payoff is @xmath6 which is higher than @xmath4 . in other words , independently of what the other player does , defection d yields a higher payoff than cooperation and is the _ dominant strategy _ for rational agents . nevertheless , reasoning that way both agents get @xmath9 which is worst than @xmath4 . a possible way out for this dilemma is to play the game repeatedly . in this iterated prisoner s dilemma ( ipd ) , in which condition ( [ eq : ine1 ] ) is supplemented with the condition : @xmath10 there are several strategies that outperform the dominant one - shot always d strategy and lead to some non - null degree of cooperation . the tournaments organized by axelrod @xcite , @xcite in the 80 were very illuminating . he invited researchers from different fields to contribute a strategy , in the form of a computer program , to play the prisoner s dilemma against each other and themselves repeatedly . each strategy specified whether to cooperate or defect based on the previous moves of both the strategy and its opponent . the programs were then ranked according to the total payoff accumulated . the winning program , was also the simplest : tit for tat ( tft ) , which plays c on the first move , and on all subsequent moves copies the choice of its opponent on the previous move . in an ecological approach @xcite , the scores from round two were used to calculate the relative frequencies of the strategies in a hypothetical population . the strategies were then submitted to each subsequent round in proportion to their cumulative payoff in the previous round . in the long run , tft outcompeted its rivals and went to fixation . axelrod and hamilton @xcite used these ecological competition between strategies as a basis for their analysis of the evolution of reciprocal altruism . this model is applicable in two opposite situations : on the one hand , in the case of higher animals , which can distinguish between their various opponents in order to reciprocate @xcite , discouraging thus defection . on the other hand , in the case of very simple organisms who have only one opponent in its lifetime . nowak and may @xcite found another way to escape from the dilemma : the incorporation of territoriality in evolutionary game theory favours cooperation . the authors proposed simple cellular automata ( ca ) for general ecological systems involving indiscriminating organisms who play against several opponents ( their neighbours ) . they neglected all strategical complexities or memories of past encounters considering _ unconditional _ cellular automata _ i.e. _ agents using unconditional strategies ( each cell is either in a c or d state ) , as opposed to the conditional ones like tft , the _ simpleton _ @xcite or pavlov @xcite `` win - stay , lose - shift '' , etc . cells simply play repeatedly with their neighbours and in the next round or generation adopt the state of the most successful cell of their neighbourhood ( the one that collected the highest score among the cell itself and its neighbours ) . coexistence of both states or behaviours were found for a simplified version of the pd in which the punishment @xmath9 is equal to the sucker s payoff @xmath5 , . ] implying then a `` weak dilemma '' ( maximum punishment _ i.e. _ the minimum possible value of @xmath9 ) . taking @xmath11 and @xmath12 allows to parameterise the payoff matrix in terms of just the parameter @xmath6 . szab and tke @xcite slightly modified the nowak - may ( n - m ) model with the addition of randomness : players are chosen to update their states randomly by copying the state of one of its neighbours with a probability depending on the payoff difference . they measured the fraction of cooperators @xmath13 for different values of the temptation to defect @xmath6 and found a continuous transition from @xmath14 to @xmath15 as @xmath6 increases . a problem with these simple spatial games is that if @xmath9 is augmented until it becomes non negligible compared with the reward @xmath4 then cooperation disappears and all the individuals end playing d. an alternative to go beyond weak dilemmas is to consider more sophisticated players , with @xmath16-steps memory and strategies involving conditional probabilities , as lindgren and nordahl @xcite did . they considered payoff matrices parameterised in terms of two parameters , @xmath17 and @xmath18 ( @xmath19 ) , and found the evolution of cooperation for payoff matrices beyond `` weak '' dilemmas . however , pursuing as much generality as possible without sacrificing the simplicity , which is part of the n - m model beauty , in this paper we explore a different approach . our starting point is realising that , interesting as it is , the n - m model lacks a fundamental ingredient , namely that of the stress exerted by the environment on the individuals . this is a crucial factor in order to explain the emergence of cooperation between self - interested individuals even when they are very simple ( without requiring long term memory nor distinguishing `` tags '' nor access to sophisticated strategies and , of course , no rational behaviour ) . the basic idea is that individuals need to collect , when playing with their @xmath20 neighbours , a payoff above certain threshold @xmath0 in order to prosper . in an ecosystem @xmath0 represents the minimal resources ( nutrients , energy , etc . ) without which organisms die ; in economics it may correspond to some threshold below which the business is no longer profitable , etc . thus , although d players are the most successful for @xmath21 large enough , when @xmath22 they can not achieve the critical payoff if surrounded by an entire neighbourhood of d s and so some of them will be replaced by c players . we use a normalized payoff matrix with @xmath11 and @xmath19 . besides the 3 parameters : @xmath0 , @xmath6 and @xmath9 we include a probability @xmath23 for players of adopting the behaviour that is the opposite of the one used by the most successful neighbour ( @xmath24 ) . in the simplest model version an individual has a probability of behaving different from the @xmath24 if the score of the @xmath24 is below @xmath0 . this simple recipe allows the evolution of cooperation even when the punishment @xmath9 is relatively soft i.e. when the sucker s payoff is much worse than the payoff for mutual defection ( @xmath25 ) . furthermore , it gives rise to states of universal cooperation . we also consider a more sophisticated hybrid model version in which the selective rule of copying the behaviour of the @xmath24 is supplemented with a `` win - stay , lose - shift '' criterion . that is , individuals also take into account if their own scores @xmath26 are below or above @xmath0 to update their behaviour . this version , although more complex , seems well - grounded since it is widely known that pavlovian strategies play a central role in animal behaviour @xcite-@xcite . moreover , the remarkable experiments conducted by milinski and wedekind @xcite,@xcite revealed that , humans engaged in social dilemma games use by far strategies of the kind of win - stay , lose - shift "" . for the different model versions , we explore a subspace of the space of parameters @xmath27 measuring the fraction of cooperators and quantities characterizing the resulting cluster structure . the players , which can adopt only two _ unconditional strategies _ or behaviours when playing with their neighbours : cooperate ( c ) or defect ( d" +"parton distribution functions , integrated and those that retain the partonic transverse degrees of freedom unintegrated , have to include wilson lines ( gauge links ) in order to render their definitions gauge invariant ( see , @xcite for a recent review ) . there are several ways to obtain the wilson - line structure of the parton distribution operator in deeply inelastic scattering ( dis ) . the most known procedure is the direct resummation of the collinear gluon radiation diagrams , see , e.g. , @xcite . this method can be applied to transverse momentum dependent ( tmd ) processes as well , and it allows to determine the appropriate configuration of wilson lines in the parton distribution functions ( pdfs ) that parameterize them @xcite . on the other hand , the geometry of the soft factor does not directly follow from the resummation procedure , but is rather related to the removal of rapidity singularities @xcite . a counterexample is the approach used in @xcite , based on the soft collinear effective theory ( scet ) , in which one can establish a tmd factorization theorem and explicitly derive the soft factor with the appropriate wilson lines . the drawback of the scet approach is that one can not really pass back to the original qcd fields , and , hence , a direct comparison of the operator expressions is questionable . in this note we want to discuss a procedure which allows one to reveal the geometry of the wilson lines in hard processes . although the presented method can not replace the exact proof of the tmd factorization theorem without additional specifications , it can serve as a demonstration of the universality and uniqueness of the soft - factor definition . the main idea is to use the freedom of the gauge redefinition of the fields in the qcd lagrangian and the fact that the choice of a particular gauge can be implemented by performing an explicit gauge rotation ( that will depend on the adopted configuration of the gluon fields ) . this gauge rotation allows us to freely pass from an operator defined in a particular gauge to a manifestly gauge - invariant definition . in conjunction with the kinematic constraints , it enables us to use the power of the scet approach within pure qcd to pick up the correct wilson - line geometry . for the sake of clarity , we start with a heuristic discussion to demonstrate this idea in the case of dis , and consider then the tmd factorization of the drell - yan ( dy ) process as an application of this technique . the details of the full - fledged analysis will be given in @xcite . the hadron tensor for the dis process reads @xmath0 where @xmath1 has the large virtuality @xmath2 , and @xmath3 is the electromagnetic current . it is well known ( see , e.g. , @xcite ) that the proof of the factorization theorem drastically simplifies if one uses a special reference frame , notably , the infinite - momentum frame ( with the spatial part of the hadron momentum taken along the third axis with a large component @xmath4 ) and imposing the lightcone gauge @xmath5 . here and below , we use the standard notation for the lightcone components @xmath6 , with @xmath7 and @xmath8 . the operator for the parton distribution in the lightcone gauge is just a bilocal quark operator : @xmath9 , where @xmath10 lies on the light - cone . note that we use the following four - vector notation : @xmath11 . for simplicity , we do not display these indices in the figures below . the general gauge independent expression is harder to derive . the derivation requires the complete resummation of the collinear gluon vertices see e.g. , @xcite and amounts to the insertion of a gauge link between the quarks depicting a contour that is compatible with the physical situation under study . this is done for a particular version of the eikonal approximation termed the soft approximation @xcite . in that case , the gauge contour can be taken to be a light ray . note that from the renormalization - group point of view , the particular contour of the gauge link is of minor importance as long as it is smooth , because only its endpoints create additional divergences that can be removed by dimensional regularization and minimal subtraction @xcite . contours with cusps and/or self - intersections deserve special care @xcite . the tmd case is more complicated and the proper wilson line has to be defined with prudence @xcite . in fact , it was first shown in @xcite , and later also in other works @xcite , that the ultraviolet ( uv ) divergences mix with the rapidity divergences that ensue from cusps in the wilson line which joins two points with a finite transverse separation . however , one can obtain the gauge - independent expression by a much simpler method . the essence of this method is the following : knowing the operator in the lightcone gauge , one can perform a gauge transformation of the quark fields from the lightcone gauge to a form that is manifestly gauge invariant . indeed , for every configuration of the gluon field , there exists a particular gauge transformation which fixes one or another gauge condition . the gauge transformation which neglects the `` plus''-component of the gluon field , and hence satisfies the light - cone gauge , can be found from the equation @xmath12 because the lightcone gauge is not exhausting the gauge freedom , we should also fix the boundary conditions imposed on the gluon propagator and adopt , say , the retarded boundary condition , @xmath13 . we denote the solution of equation ( [ uau = udu ] ) by @xmath14 : @xmath15 = { \left[}x,-\infty^+|\bar{n}^\mu{\right]}= \text{pexp}{\left(}-ig\int^0_{-\infty}~ d\sigma a_+(x^\mu+\bar{n}^\mu\sigma){\right)}\ , , \label{w_def}\end{aligned}\ ] ] where the gauge field @xmath16 here and below is a shorthand notation for @xmath17 . expression ( [ w_def ] ) describes a wilson line along the direction @xmath18 connecting the point @xmath19 with infinity , where the gluon field is supposed to vanish by virtue of the imposed boundary condition . in this way , the operator for the integrated parton distribution obtained in the lightcone gauge can be written in gauge - invariant form with the help of the gauge transformation in terms of the matrix @xmath14 , i.e. , @xmath20}q{\left(}0{\right)},~~(\xi^+=\xi_\perp=0 ) \ , . \label{dis_res}\end{aligned}\ ] ] this result ( illustrated in fig . [ fig:1 ] ) is well known and it can be obtained in a number of ways @xcite . it expresses the restoration of the geometry of the wilson line , starting from an expression that contains no wilson lines at all . the important point here is that this treatment picks up the route of the wilson line through infinity and not the direct one see fig . [ fig:1 ] ) . the latter would appear as the difference of two successive @xmath21 rotations first from @xmath22 to @xmath23 along @xmath24 , followed by a rotation from @xmath25 to @xmath23 . would one use another boundary condition , it would be possible to direct the wilson line to @xmath26 . a possible non - triviality might appear if one would impose a boundary condition that would allow the gluon field to be different from zero at lightcone infinity . then , in order to satisfy eq . ( [ uau = udu ] ) , one would have to multiply the solution by an additional boundary - dependent factor , viz . , the wilson line from the lightcone infinity to the point , where the gluon field vanishes . this factor would not depend on @xmath27 . the simplest solution would be to add a gauge link in the transverse direction , which can also be obtained by direct resummation as in @xcite , or be deduced from a scet analysis like in @xcite . , while the right one depicts the contour through infinity along the segments @xmath28 and @xmath29 that corresponds to the gauge transformation @xmath30.,scaledwidth=60.0% ] let us now consider processes that depend on unintegrated pdfs . the main difficulty in the description of such processes is the intensive exchange of soft gluons between the two initial ( final ) hadrons . these exchanges lead to a double logarithmic asymptotic behavior and constitute the main perturbative contribution of the factorized hard part . factorization reorganizes the singularity structure of the initial amplitude , leaving a trace in terms of the anomalous dimensions of the operators . in the case of the tmd factorization , the leading singularities amount to double logarithms . to collect and reorganize these singularities , an operator is necessary , termed the soft factor . it is composed of wilson lines which effectively accumulate all soft - gluon exchanges . presumably , different configurations of wilson lines may give rise to the same singularity structure in fixed - order perturbation theory . on the other hand , the initial object the hadron tensor does not contain any singularities so that it is up to us to define the soft factor and the parton density operators in a self - consistent way . let us now test our calculational scheme by applying it to the drell - yan process . the standard way to factorize this process can be found in @xcite . a perhaps simpler way to derive a factorized expression employs scet @xcite . recently , it was shown that these two approaches yield equivalent results @xcite , albeit the regularization of rapidity divergences is treated differently . the virtue of the scet approach is that the wilson - line geometry of the soft factor and that of the parton - distribution operators follows from the very structure of the scet electromagnetic currents . in contrast , in standard qcd the construction of the wilson - line geometry is , presumably , not uniquely defined . indeed , within the standard approach the soft factor is defined empirically with the aim to render the final expressions free of rapidity divergences . consistency checks of such procedures have not yet been established beyond the one - loop level . in order to show that the geometry of the wilson lines within the tmd factorization follows from the kinematics of the process , we will first rewrite the dynamics in factorized form using scet . subsequently , we will pass back to the original field degrees of freedom of qcd . this procedure will resemble the derivation of the wilson - line structure in the dis case , considered in the previous section . to this end , we are going to use for expedience the lightcone gauge and the so - called hadron frame @xcite together with scet - like variables and then express the fields in a general gauge using an @xmath21 rotation . the formal proof of factorization within this calculational scheme is beyond the scope of this short exposition . here , we only want to show the uniqueness of the gauge - link geometry of the hard processes obtained this way . in the hadron frame the two hadrons , involved in the dy scattering , move nearly on the light - cone in opposite directions : hadron @xmath31 along @xmath32 and hadron @xmath33 along @xmath34 . the large lightcone components of the hadron s momentum suggest the following decomposition of the spinor fields into `` large '' and `` small '' components @xcite , indicated by @xmath35 and @xmath36 labels , respectively : @xmath37 it is straightforward to show that the @xmath38(@xmath39 ) component of the field propagates mainly along the @xmath40(@xmath24 ) direction , and , therefore , according to the equation" +"molecular wires are molecules that bridge between metallic leads to form a nano - conductor whose current - voltage characteristic reflects the electronic structure of the molecule . the conductance may be controlled via its dependence on molecular properties . equally important is the use of such molecular junctions as capacitive elements in nano - electronics . understanding the behavior of such junctions under potential bias is a prerequisite for elucidating their transport properties . the importance of this issue for the conductance of molecular junctions was recently emphasized by datta and coworkers @xcite , who have shown , within a simple extended - hckel ( eh ) model for @xmath0,@xmath1-xylyl dithiol bridging between two gold leads , that the potential profile ( imposed on the molecule as input to the eh calculation ) had a profound effect on quantitative as well as qualitative aspects of the calculated current - voltage characteristic . the best fit to experimental results was obtained from a model that assumed ( a ) a flat potential profile in the interior of the molecular bridge , i.e. the potential drop occurs only at the molecule - lead contacts and ( b ) a symmetric distribution of the potential drop at the two contacts , i.e. for a total voltage @xmath2 the potential drops at each molecular edge by @xmath3 . this picture is supported by a recent model calculation by mujica _ et al . _ @xcite , where the schrdinger equation ( on the hartree level ) was solved in conjunction with the poisson equation to yield both the electronic structure and the spatial distribution of the electrostatic potential @xcite . it was found that beyond a screening distance of the order of 13 atomic lengths the potential is flat along the model molecular chain . ab initio calculations with open system boundary conditions reveal a different picture : lang and avouris @xcite have found for a chain of seven carbon atoms connecting between jellium leads that a substantial part of the voltage drop occurs along the carbon chain itself . et al . _ @xcite have obtained similar results for a chain of gold atoms as well as for a molecular wire phenyl - dithiol bridging between two gold electrodes @xcite . in an earlier work , pernas _ et al . _ @xcite have determined that the potential along a model molecular wire is flat in the absence of scattering centers , however these authors have derived the local potential from a questionable local charge neutrality condition . recently , weber _ et al . _ @xcite have considered the voltage profile across 9,10-bis((2-para - mercaptophenyl)-ethinyl)-anthracene coupled to two au@xmath4 clusters . their density functional theory calculations thus go beyond the assumption of a structureless metallic electrode and take into account the specific properties of the bond between the molecule and the gold atom in its local environment . on the experimental side , bachtold _ et al . _ @xcite have used scanned probe microscopy of both single - walled and multi - walled carbon nanotubes ( swnt and mwnt , respectively ) to measure the potential drop along such nanotubes connecting between two gold electrodes . they find an approximately linear drop of the potential in a mwnt of diameter 9 nm while for a metallic swnt bundle of diameter 2.5 nm the potential is flat beyond the screening regions at the tube edges . it should be emphasized that these experiments can not be related directly to the calculations discussed above . the nanotube length is a few microns and impurity and defect scattering may be effective as is most certainly the case in the mwnt measurement . the flat potential seen in the metallic swnt measurement is in fact a remarkable observation implying a very long mean free path ( @xmath5 m ) for electrons in these room temperature structures . it is clear from the studies described above that while the computational methodology for evaluating the potential distribution on a biased molecular wire is available , a complete understanding of the way this distribution behaves in different wires is lacking . in this respect simple models that focus on generic properties of conducting constrictions including molecular wires are useful . the calculations of pernas _ et al . _ @xcite provide such a model that is however hampered , as already stated by the restriction of local charge neutrality . the calculation of mujica _ et al . _ @xcite is also based on a generic molecular model , however , by using a 1-dimensional poisson equation for the electrostatic potential these authors tacitly assume a molecular bridge whose lateral dimension is much larger than the screening length . in view of the fact that the width of molecular wires is often just a few angstroms , such an assumption is overly restrictive . clearly , the magnitudes of the lateral width of the wire and the screening length should be important generic quantities for this issue . in this paper we present a simple model calculation that takes the relative magnitudes of these variables explicitly into account . we describe the model in section [ sec : model ] , present the calculation in section [ sec : potential ] and some results and discussion in section [ sec : results ] . the molecular wire is modeled as a cylinder of length @xmath6 and diameter of order @xmath7 ( the exact way in which @xmath7 enters into the model calculation is explained below ) , perpendicular to and connecting between two planar metal electrode surfaces . as depicted in fig . [ fig : geometry ] , the cylinder is oriented parallel to the @xmath8 axis , with its axis going through the origin in the @xmath9 plane . the two electrodes are assumed to be ideal conductors implying a constant potential on the entire surface of each electrode . we set the potentials at the left and right wire - electrode interface to be @xmath10 and @xmath11 , respectively . in view of ( [ eq : screening ] ) below , this guarantees a vanishing mean potential in @xmath8-direction and thus a neutral molecule . finally , we restrict the discussion of the potential profile to blocking junctions between electrodes and molecule so that no current is flowing . and diameter @xmath7 between two perfect conductors with potentials @xmath12 and @xmath13 . ] as in ref . @xcite we assume that the wire material does have screening capacity , and is characterized by a screening length @xmath14 . it should be noted that the existence , nature and size of such screening length in molecular systems is an open question with probably non - unique answer . molecules with large gaps between their highest occupied and lowest unoccupied molecular orbitals ( homo and lumo ) will obviously screen poorly , while highly conjugated molecules with low homo - lumo gap will screen relatively well . in the present discussion we assume that over the relevant length scales ( of order @xmath6 ) screening is described by a poisson equation @xmath15 according to the cylinder symmetry of the molecule , the charge density @xmath16 depends on the radial distance @xmath17 from the wire axis and the position @xmath8 along the wire . in transversal direction , the charge density is assumed to be determined by a given molecular electron distribution represented by a factor @xmath18 . the longitudinal part depends on the potential along the molecular axis . the screening is then described by @xmath19 which together with ( [ eq : poisson ] ) will allow us to determine the potential profile . any assumption about the functional form of @xmath18 is in fact an assumption about the confinement of the molecular charge distribution in the molecular cylinder and in our generic model it is sufficient to take a form that reflects the molecular thickness @xmath7 . other details of @xmath18 are expected to be of secondary importance . in the three - dimensional thomas fermi model for screening in a gas of electrons with charge @xmath20 and mass @xmath21 , the screening length @xmath14 of ( [ eq : screening ] ) is related to the electron density @xmath22 by @xmath23 with the fermi energy @xmath24 at metallic electron densities @xmath14 is typically of the order of 1 . to have efficient screening in a molecular system electrons ( or holes ) must occupy molecular states that are effectively delocalized over the length of the bridge . charge doping by transfer from the metal electrode to the molecular bridge may be one source of such electrons . their density is expected to be considerably lower than metallic , implying a larger characteristic screening length . we expect that a calculation based on ( [ eq : poisson ] ) and ( [ eq : screening ] ) that uses metallic electron density to estimate @xmath14 will provide an upper bound on the effective screening in a molecular wire . using the model described in the previous section , our problem is to solve the equation @xmath25 in the range @xmath26 subject to the boundary conditions @xmath27 it is convenient to decompose the full potential @xmath28 into a first term describing the bare potential @xmath29 in the absence of a molecule and a second term which reflects the additional potential @xmath30 satisfying the boundary conditions @xmath31 . the resulting differential equation @xmath32\ ] ] may be solved by the fourier ansatz @xmath33 after expressing the bare potential profile in terms of a fourier series one arrives at @xmath34}\hat f(k_{\parallel})\\ & \qquad\times\left[\delta\frac{1+(-1)^n}{\pi n } + \int\frac{d^2k_{\parallel } ' } { ( 2\pi)^2}\hat\phi_n(k_{\parallel}')\right ] \end{aligned } \label{eq : phift}\ ] ] where @xmath35 for the potential profile along the molecular axis , only the transversal integral over the fourier coefficients @xmath36 is needed which may easily be obtained from ( [ eq : phift ] ) . due to the symmetry of the bare potential only even fourier coefficients are found to contribute . we thus arrive at our main result describing the potential profile along the molecule @xmath37 the coefficients @xmath38 accounting for the influence of screening are given by @xmath39 where @xmath40 denotes a modified bessel function . in the limit of very small screening length , @xmath41 , it is possible to show by evaluating the sum in ( [ eq : phi00zf ] ) that the potential along the wire vanishes and the entire voltage drop occurs at the interface with the electrodes . for the following discussion , it is convenient to introduce a measure of the deviation of the voltage profile @xmath42 from the linear behavior ( [ eq : phi0 ] ) . since the integral over @xmath43 vanishes for a neutral molecule , we use instead @xmath44^{1/2}\;. \label{eq : deltadef}\ ] ] this quantity is normalized such that it equals 1 if the voltage drop occurs entirely at the ends of the molecule while it vanishes for a linear potential profile . employing ( [ eq : phi00zf ] ) , one may express @xmath45 in terms of the coefficients defined by ( [ eq : fn ] ) as @xmath46^{1/2}\;. \label{eq : delta}\ ] ] we now address the dependence of the potential profile on the width of the molecular wire and start with the limiting case of an infinitely thick molecule or , equivalently , a large number of molecules in parallel present between the two electrodes . then , @xmath47 and one finds from ( [ eq : fn ] ) @xmath48 using @xmath49 ( [ eq : phi00zf ] ) yields for the potential profile @xmath50 the deviation from the linear voltage drop can be quantified by inserting ( [ eq : fninf ] ) into ( [ eq : delta ] ) . evaluating the sum , one finds @xmath51^{1/2}\;. \label{eq :" +"one of the most fundamental problems in general relativity is the construction of exact solutions to the einstein equations ( or the einstein equations coupled to other equations associated with fundamental physical theories ) . an even more challenging problem is is to find solutions that might represent physically realizable systems that could possibly occur in nature . it is well known that of the many solutions to the systems of equations derived from the einstein equations lead to unphysical behaviour . in many cases , the spacetimes constructed may be truly singular even in the presence of matter or other fields . alternatively negative energy densities and/or negative pressures are often required in order to meet regularity conditions or boundary conditions that are imposed upon the metric or other geometric objects . in other cases where energy densities and pressures are positive , often one finds that the speed of sound violates causality by being greater than the speed of light . for example constant density configurations , where the pressure has a radial dependence to ensure that the interior solution remains static will lead to infinite sound speeds . charged dust solutions on the other hand have zero sound speed . they require such a fine balance between the mass and charge distributions that they are almost always unstable to any perturbations . they either undergo gravitational collapse or fly apart due to electrostatic repulsion . this paper will present a new solution to the spherically symmetric time independent einstein - maxwell system of equations that govern the behaviour of the space - time in the interior of a charged fluid sphere . at the outer boundary the solutions will be matched to the external vacuum solution for the field equations i.e. the reissner - nordstrm solution . it will be demonstrated that some of these solutions have parameter values that lead to physically realistic properties . while the total number of known exact interior solutions to the einstein - maxwell equations is much smaller than their uncharged counterparts , the number of solutions that can be said to be physically relevant is small . a review of such solutions has been provided by ivanov [ 1 ] and this makes a good starting place for understanding the different approaches that have been taken and the results obtained from those approaches . in some instances corrections to some of the original papers are provided . the most commonly used methods employ either isotropic coordinates ( where the problem was first discussed by papapetrou [ 2 ] and majumdar [ 3 ] ) or curvature ( i.e. schwarzschild - like ) coordinates . as mentioned in the introductory paragraph above , this paper will be primarily concerned with the construction of physically `` interesting '' solutions that might arise from regular initial conditions for charge and mass densities along with realistic pressure distributions . the motivations for this are to find compact charged fluid configurations that might represent realistic sources for the exterior vacuum reissner - nordstrm solutions . in particular one can ask whether it is possible to find realistic solutions for the extreme case where the total charge is equal to the total mass . a second motivation is to determine the possible end states for systems that have collapsed gravitationally but due to the repulsive nature of the electrostatic interaction are unable to form black holes and result in stable configurations . the approach to be taken here is to write the einstein - maxwell system in curvature coordinates . the einstein equations will yield three equations for two metric functions in terms of the mass density , the charge aspect and the fluid pressure . the maxwell equations simply state the the electrostatic maxwell field is just the coulomb field in a spherically symmetric space time . the solution will be given in terms of explicit closed - form functions of the radial coordinate for the two metric coefficients , a mass density , a charge aspect ( the integrated charge density ) and the pressure of the fluid . the review by ivanov outlines that various anstse that have been utilized to find exact solutions . essentially one gives two out of the five functions and uses the einstein - maxwell equations to construct the remainder . of course some methods of solution are easier than others , particularly if one is not concerned with ensuring that the solution have a physical interpretation . the simplest method is to give the functional dependence of the metric functions and construct the remaining variables from the derivatives on the `` left - hand - side '' of the differential equations . on the other hand giving the mass and/or charge distributions along with an equation of state of the form @xmath0 requires solving a set of nonlinear coupled differential equations . but the method has the advantage that there is some control over the physics . other methods use a combination of the two approaches . the requirements that make a solution physically relevant has had much discussion in the literature . ( see e.g. the reviews by delgaty and lake [ 4 ] and finch and skea [ 5 ] that analyze over one hundred known solutions for uncharged , spherically symmetric , fluid solutions in general relativity . ) those that we expect to meet are the following : 1 . the metric coefficients are regular everywhere including at the origin @xmath1 . the metric functions match to the reissner - nordstrm functions at the fluid - vacuum interface . the mass density is positive and decreasing outward toward the boundary . the integrated charge and mass increase outward to give the rn parameters at the boundary . 5 . the pressure @xmath2 is positive and finite everywhere inside the fluid 6 . the pressure vanishes at the fluid boundary with the vacuum . the speed of sound @xmath3 is causal ( @xmath4 ) . 8 . the speed of sound @xmath3 monotonically decreases with increasing @xmath5 . 9 . both the pressure and mass density are decreasing functions of @xmath5 : @xmath6 and @xmath7 . this list is not necessarily exhaustive but does include all of the requirements presented by delgaty and lake in their extensive review of exact fluid sphere solutions . supplementary conditions that define what finch and skea call `` interesting solutions '' have been reviewed in that manuscript . these extra conditions include : an explicit equation of state in the form @xmath0 , and non - numerical solutions to the differential equations that governing the behaviour of some of the dependent functions . while the latter condition will be met in what follows , the we have not succeeded in providing an equation of state outside of giving both the pressure and mass density in terms of functions of a radial coordinate . in comparing the behaviour of 127 known solutions against the requirements listed above , delgaty and lake found that only 9 of those satisfied all of the conditions . clearly such solutions are rare . many solutions have pathologies associated with negative pressures , and/or non causal sound speeds . as will be shown in what follows many of the new solutions also demonstrate such pathological behaviour . the outline for this manuscript is as follows : the next section introduces the coordinates , the line element , and the form of the einstein - maxwell equations to be solved . a strategy for solving for the unknown functions is then presented . section 3 then applies the method to obtain a general form of the solutions in terms of analytic functions . special cases are analyzed to determine which solutions and what parameters lead to physically relevant behaviour by meeting all of the conditions listed above simultaneously . finally , the last section concludes with some discussions . in curvature coordinates , the line element of a spherically symmetric , static spacetime can be written in the form : @xmath8 where @xmath9 is the metric on the unit two - sphere in terms of spherical polar angles @xmath10 and @xmath11 , and @xmath12 and @xmath13 are @xmath5-dependent functions . the coupled einstein maxwell equations can be written in the following form : @xmath14 & = & \kappa p + \frac{q^2}{r^4 } \label{fe3}\end{aligned}\ ] ] where the subscript ( @xmath15 ) represents a derivative with respect to @xmath5 and @xmath16 . in what follows , geometric units are used where @xmath17 . the charge function @xmath18 is obtained by integrating the charge density @xmath19 over a spherical proper volume : @xmath20 in what follows , it will be assumed that the charge function is known and this will be used to obtain the charge density once a solution for the metric function @xmath21 is determined . the spherical symmetry of the problem allows only a radial component to the electric field which can be computed from an electrostatic potential , @xmath22 . this leads directly to the one non - zero component of the maxwell field tensor : @xmath23 equation ( 2 ) provides a single equation for @xmath13 and since the the left - hand - side is a total derivative of the function @xmath24 multiplied by @xmath25 one introduces the mass aspect : @xmath26 which leads directly to an expression for @xmath21 : @xmath27 therefore if the mass density and the charge aspect are given as functions of @xmath5 one can find an expression for the mass aspect and therefore for the function @xmath28 . assuming that the metric function @xmath12 has been determined one can immediately obtain an expression for the pressure by taking a sum of the equations ( 2 ) and ( 3 ) . then one obtains : @xmath29 finally using equations ( 2 ) - ( 4 ) one can obtain the following equations by introducing the function @xmath30 : @xmath31 while the third equation ( 9 ) couples to equation ( 6 ) the first two equations are equivalent and lead to second order linear differential equations for the function @xmath32 . the procedure for constructing a solution is as follows : ( @xmath33 ) give the mass density and the charge aspect functions as explicit functions in the radial coordinate @xmath5 ; ( @xmath34 ) compute the mass aspect which leads to an explicit solution for the function @xmath28 ; ( @xmath35 ) obtain a solution for the function @xmath36 using the differential equation ( 7 ) or ( 8) ; ( @xmath37 ) finally solve for the pressure , @xmath38 using equation ( 6 ) . the advantages to this procedure are that one can begin with a radial dependence that guarantees that some of the requirements that the solution be physically significant are met from the very beginning . here it assumed that solutions for the conditions on the metric functions will follow if the input is physically motivated . given that there will be two constants of integration associated with the solution for @xmath32 and some free parameters associated with the choices for @xmath39 and @xmath40 , there should be enough freedom to ensure that the remaining equations are satisfied . of course the difficulty of solving the equations for @xmath36 depends on the choices that are made for @xmath41 and @xmath18 . in the remainder of this paper we present a choice that leads to some easily solvable equations after making the appropriate set of coordinate transformations . we then explore these solutions to determine whether or not they can meet the conditions for physical acceptability . one must begin with defining the mass density as a function of the radial coordinate and we choose : @xmath42 the charge function must also be given and in order to ensure that it is concentrated at the outer edge of the sphere it is given as a simple power function : @xmath43 with these" +"in the current picture of structure formation , inflation ends in reheating , which produces gaussian random field density fluctuations in the radiation , matter , and dark matter . as a gaussian random field , the density is described completely by its mean and 2-point correlation function ( 2pcf ) , which measures the probability of finding a certain value of the density at one point given the density at another . however , the subsequent evolution of the density field introduces additional correlations as gravity drives the convergence of overdense regions towards each other . in particular , a 3-point correlation function ( 3pcf ) is produced by this evolution ( bernardeau et al . 2002 or szapudi 2005 for reviews ) . since the evolution is itself sensitive to the cosmological parameters , measuring the 3pcf of galaxies offers an independent probe of these parameters . it is typically used to break the degeneracy between galaxy bias ( encoding the fact that galaxies do not trace the matter density field with perfect fidelity ) and the clustering on a given scale ( e.g. @xmath1 ) ( gaztaaga & frieman 1994 ; jing & borner 2004 ; guo et al . the 3pcf measurements also can probe primordial non - gaussianity ( desjacques & seljak 2010 ) ; while the constraints on this are currently dominated by cmb experiments such as planck , it is expected that the increasing quality and number of galaxy redshift surveys will provide interesting independent information . since the first measurement by peebles & groth ( 1977 ) , numerous studies have presented 3pcf measurements , summarized in kayo et al . ( 2004 ) , mcbride et al . ( 2011a , b ) , guo et al . ( 2014 ) and references therein . in this work , we present a new algorithm for measuring the 3pcf of galaxies through its multipole moments . this decomposition of the 3pcf was first advanced in szapudi ( 2004 ) and to a limited extent ( measurement of the monopole moment ) used in pan & szapudi ( 2005 ) on two - degree - field galaxy redshift survey ( 2dfgrs ) data . slepian & eisenstein ( 2015 ) ( hereafter se15 ) found this decomposition to be particularly useful for distinguishing linear and non - linear bias as well as isolating a possible relative velocity bias . current algorithms , such as that used for the mcbride et al . ( 2011 ) measurement ( presented in moore et al . 2001 , gray et al . 2004 , nichol et al . 2006 , and gardner et al . 2007 ) fundamentally scale as the number of possible triangles in a survey . if one wishes to measure the 3pcf out to some scale @xmath2 , there are @xmath3 relevant triangles , where @xmath4 is the number of objects in the survey , @xmath5 is the survey number density and @xmath6 . the algorithm presented in the series of references above , whose most recent incarnation is developed in march ( 2013 ) , uses multiple mrkd - trees . here `` mr '' means the kd - tree caches additional information , in this case the number of galaxies within each node of the tree as well as the bounding box of the node . this algorithm is faster than simply counting all triangles . it is particularly effective if the galaxies are close to each other , so that there are many triangles whose side lengths fall within a given combination of radial bins . however , typical galaxy surveys are sparse , particularly those mapping the largest volumes . for example , the baryon oscillation spectroscopic survey ( boss ) has an average separation of 13 @xmath7 , too large to permit many galaxies to be in the same bin . this means the algorithm will not be as fast for such large - scale measurements . the use case tested in march ( 2013 ) is triangles with three sides of @xmath8 mpc each , much smaller than the scales that are well - described by linear perturbation theory and hence most useful for cosmology . furthermore , even with the speed - ups coming from the multi - tree structure of the algorithm , it is still fundamentally scaling as the number of galaxies in the survey times the square of the number within @xmath2 ( march 2013 , figure 21 ) . in this paper , we present an algorithm that does better : it scales as the number of galaxies in the survey times the number within @xmath2 , and so by construction is significantly faster than any previous algorithm that is exact in angle . in brief , we write the opening angle dependence of the triangles about a given vertex in terms of legendre polynomials of @xmath9 , where these are two unit vectors describing two triangle sides . the dot product seems to require explicitly considering all pairs of galaxies about a given vertex ( i.e. third galaxy ) , but using the spherical harmonic addition theorem , this representation can be factored into a product of spherical harmonics each depending on only one unit vector . therefore from the spherical harmonic expansion of the radially binned density field one can obtain the multipole moments without ever needing to consider pairs about a given vertex . this is the central insight of this paper . in section [ sec : algorithm ] , we present the algorithm in more detail , and show in section [ sec : proj3pcf ] how this framework goes through to the projected 3pcf . section [ sec : edgecorrxn ] discusses edge correction , while section [ sec : implementation ] describes our implementation . section [ sec : covariance ] computes the covariance of this multipole decomposition in the gaussian random field limit , and section [ sec : mock_results ] presents the results of using the algorithm on the lasdamas sdss - ii data release 7 ( sdss - dr7 ) luminous red galaxy mock catalogs . we conclude in section [ sec : conclusions ] . in this paper , we parametrize triangle configurations by two side lengths , @xmath10 and @xmath11 , and the angle between them with cosine @xmath12 . we will decompose the 3pcf as a function of these three variables into a sum over legendre polynomials for the angular dependence times radial coefficients encoding the side length dependence , as @xmath13 szapudi ( 2004 ) first advanced this decomposition , and he puts a factor of @xmath14 in front of his analogous expansion coefficients ; we absorb this into @xmath15 . there are three major advantages to this decomposition . first , the shape of the 3pcf for fixed side lengths as a function of angle is smooth and slowly varying ( see e.g. bernardeau 2002 , figure 11 ) , without much fine structure . thus we expect that only a few multipoles will be required to capture the angle dependence . second , this decomposition provides a natural way to visualize the 3pcf for all triangle configurations ; one can make several panels for different @xmath16 , each with all @xmath10 and @xmath11 and amplitudes indicated by a colorbar , as in se15 . in contrast to many previous works , this allows immediate appraisal of the information in all triangles and not just a particular set of configurations ( e.g. isosceles , two - to - one , etc . ) third , as we will see , the multipole moments of the 3pcf can be obtained with much greater speed than other decompositions of the 3pcf . however , in contrast to other fast methods , such as tree methods that fix a critical angular scale below which they are approximate ( e.g. zhang & pen 2005 ) or fourier methods that choose a grid with some minimum spacing , we do not sacrifice accuracy to obtain this speed . our method is exact in angle . we will bin in side length , but even were speed of no concern this would be necessary to keep the covariance matrix to a reasonable size . the 3pcf describes the number of triangles of a given configuration whose vertices are the galaxies in a survey . while nine coordinates are required to completely describe any individual triangle connecting three galaxies , the 3pcf averages over both translations and rotations of the triangle configuration . the presumed losslessness of this averaging corresponds to the two usual cosmological assumptions of isotropy ( rotation - invariance about a given point ) and homogeneity ( translation - invariance ) . this ultimately reduces the 3pcf to a function of only three variables ; as indicated already , we will use two triangle sides and the angle between them . we will now show explicitly how to go from nine coordinates to three . we begin with averaging over rotations . we will show explicitly that legendre polynomials are an angular basis for the 3pcf after this averaging . to do so , we first step back and write an estimate ( denoted by a hat ) of the 3pcf for a triangle with sides @xmath17 extending from a vertex whose absolute position within the survey is @xmath18 . we have @xmath19 we now wish to average over all rotations of the triangle about @xmath18 . writing a rotation as @xmath20 ( simply a matrix involving the three euler angles ) , we have @xmath21 where subscript `` iso '' abbreviates `` isotropy . '' noting that @xmath22 , where @xmath23 is a wigner matrix ( e.g. arfken , weber & harris 2013 ( hereafter awh13 ) , equation ( 16.52 ) ) , we find @xmath24 the integral over wigner matrices is simply evaluated by orthogonality ( e.g. brink & satchler 1993 , appendix v ) as @xmath25 , @xmath26 the kronecker delta . using the spherical harmonic addition theorem ( awh13 , equation ( 16.57 ) ) @xmath27 and defining @xmath28 we find @xmath29 in what follows we drop the subscript `` iso '' as we will always be considering the isotropic 3pcf . we now move to averaging over translations . recalling that @xmath18 is the vertex of the triangle from which the two sides given by @xmath17 extend , the densities on a particular triangle of points will be @xmath30 . averaging over translations means allowing every point in the survey to serve as the vertex @xmath18 , so we must integrate over @xmath31 . we thus find that the @xmath32 radial coefficient of the 3pcf is @xmath33 where @xmath34 is the survey volume . our algorithm will bin radially ( denoted with a bar ) , so we seek @xmath35 with @xmath36 a binning function demanding that we are in the bin given by its second argument . binning averages the radial coefficient over some interval in each side length , and in that sense is not lossless . it is also necessary for the speed advantage of our algorithm , as will become clear shortly . we will not compute using equation ( [ eqn : binned_zeta ] ) . rather , we will bin radially around each possible origin @xmath18 _ before _ averaging over rotations and translations , so it will be useful also to define the binned estimator before translation - averaging as @xmath37 where @xmath38 is the radially binned density field about an origin @xmath39 . hence in practice we never compute @xmath40 using equation ( [ eqn : binned_zeta ] ) , but rather measure @xmath41 via equation ( [ eqn : binned_zetahat_l ] ) and then compute @xmath42 as the radially binned multipole coefficients of the 3pcf . a direct way to measure @xmath43 would be to" +"different dynamical mechanisms are commonly invoked to explain the architecture of the outer solar system and extrasolar planetary systems . in the solar system , scattering of small bodies ( planetesimals "" ) by the ice giants @xcite is thought to drive outward planetary migration and concomitant capture of pluto and other kuiper belt objects into resonance @xcite . the effects of planetesimal scattering on the gas giants are smaller but still significant , for example in the nice model "" @xcite where a divergent resonance crossing between jupiter and saturn triggers the late heavy bombardment . the presence of small bodies around other stars can be inferred from observations of debris disks @xcite , but as yet there is no evidence for a dynamical role of planetesimals in known extrasolar planetary systems . at radii where tidal effects are negligible ( roughly @xmath3 au ) the eccentricity distribution of extrasolar planets matches relatively simple models of gravitational scattering among a system of two or more massive planets that typically include neither planetesimals nor residual gas @xcite . the success of pure planet - planet scattering models does not imply that other dynamical processes can be ignored . the observed distribution of semi - major axes of extrasolar planets at small orbital radii requires the existence of an additional dissipative process @xcite , most probably gas disk migration @xcite , which will itself affect planetary eccentricity @xcite . at larger orbital radii simple arguments suggest that a dynamically significant external reservoir of planetesimals ought to be a common feature of young planetary systems . the formation of giant planets becomes increasingly difficult at large radii @xcite , and hence it is probable that disks of leftover debris surround the zone of giant planet formation in most young systems . the typical masses of planetesimal disks are unknown , but values of 30 - 50 @xmath4 that are comparable to those inferred for the early outer solar system are plausibly typical , since they are consistent with disk masses estimated from astronomical observations of the youngest stars @xcite . the dynamical effect of such disks on _ currently _ observed extrasolar planetary systems would be small , since radial velocity surveys preferentially detect planets that are either massive ( and hence largely immune to influence from planetesimal disks ) or orbit at very small radii where the mass of leftover debris is negligible . pooling knowledge from the solar system and extrasolar planetary systems motivates consideration of a model in which planet formation typically yields a marginally unstable system of massive planets in dynamical contact with both a residual gas disk and an exterior planetesimal disk . in this letter _ we ignore the gas disk and study the subsequent evolution under the combined action of planet - planet and planetesimal scattering . we do not attempt to model the full distribution of extrasolar planetary properties ( which would require the inclusion of hydrodynamic effects ) , but rather focus on how planetesimal disks affect the final eccentricity of extrasolar planets at moderately large orbital radii . we assume that the gas - dominated epoch of planet formation is sufficiently distinct from the subsequent phase of planet - planet and planetesimal scattering that it makes sense to study the latter with pure n - body simulations . we focus on two large ensembles of runs . the highmass set comprises 1000 integrations of three planet systems in which the masses of the planets are chosen randomly in the range @xmath5 , with a distribution , @xmath6 which matches that observed @xcite . the observed distribution is derived from an incomplete sample that represents ( in the context of our model ) the distribution _ after _ scattering , but these subtleties do not matter for our purposes . the lowmass set is identical except that we sample a wider swath of the mass function between @xmath7 and @xmath8 . the planets are initially placed in a marginally unstable configuration defined by circular , nearly coplanar orbits with a separation of 4 - 5 @xmath9 , where the mutual hill radius , @xmath10 here @xmath11 and @xmath12 are the planets semi - major axes , @xmath13 and @xmath14 their masses , and @xmath15 is the stellar mass . with this spacing the instability timescale is relatively long @xcite ( the median timescale before the first planet - planet encounter was 0.3 myr for the highmass integrations without disks ) . our initial conditions are only a small subset of the architectures predicted from giant planet formation models @xcite , though broadly consistent with scenarios in which giant planets are captured into mean - motion resonances during the late stages of gas disk evolution @xcite prior to being removed from resonance by turbulent perturbations @xcite . each integration is repeated twice , once with just the three planets and once with an external planetesimal disk whose inner radius of @xmath16 is 2 hill radii beyond the orbit of the outermost planet hill radii between neptune and the outer planetesimal disk is needed to match the timing of the late heavy bombardment @xcite . the spacing of 2 @xmath9 means that our models evolve on a somewhat shorter time scale . ] . the inner edge of the disk lies within the radius where a test particle in the restricted 3-body problem would be stable , so the disk is in immediate dynamical contact with the outer planet . the planetesimal disk is represented by 1000 bodies distributed between 10 and 20 au with a @xmath17 surface density profile and a total mass of @xmath18 . we integrate these systems using the mercury code @xcite for 100 myr . the integrator uses the symplectic wisdom - holman mapping @xcite for well - separated bodies , and the bulirsch - stoer method when objects are within @xmath19 mutual hill radii , where @xmath20 for our case . planets were removed if their orbital distances were smaller than 0.1 au ( `` hit sun '' ) or exceeded 100 au ( `` ejection '' ) . collisions were treated as inelastic mergers conserving linear momentum . a large ensemble of simulations includes some cases that are much harder to integrate accurately than the majority . to make the best use of our computational resources we adopted a default timestep ( 20 days ) that results in accurate integrations ( as measured by the fractional orbital energy conservation @xmath21 ) for the typical case . we then identified those runs ( about 10% ) in which energy was not adequately conserved and re - ran them with a smaller timestep . for runs without disks we re - ran cases with @xmath22 with a timestep of 5 days , while for the runs with disks we re - computed cases with @xmath23 with a timestep of 10 days . a small number of the re - run simulations ( typically 15 - 35 ) still did not meet our energy criterion and were discarded . in the absence of planetesimal disks our model planetary systems are typically unstable on myr time scales . there are also systems that are stable over the 100 myr duration of our runs . in our initial analysis we _ assume _ that the typical outcome of giant planet formation is a system that , in the absence of a disk , would be unstable . we therefore analyze the subset of disk - less simulations that are unstable , and compare the results to the matched set of simulations that include disks . this is not a perfect one - to - one comparison , since the chaotic nature of the evolution means that disk - less planetary systems can display different instability time scales in the presence of even negligible perturbations . nonetheless we _ do _ observe statistical differences between the evolution of systems ( with disks ) that correlate with the stability of the disk - free systems , and hence it makes sense as a first approximation to separately consider the results for stable and unstable cases . the results of our disk - less simulations agree with prior studies @xcite . scattering from initially unstable initial conditions frequently leads to the loss of one or more planets via ejection or collisions and sets up a broad eccentricity distribution @xcite . scattering among equal - mass planets produces larger eccentricities than scattering of unequal - mass planets @xcite . figure [ fig : ecum ] compares the final eccentricities obtained from the unstable highmass simulations and the observed distribution @xcite of extra - solar planets . they are in good quantitative agreement . the eccentricity distribution from the unstable lowmass simulations without disks is shifted toward lower values @xcite , and fits the observed distribution of extra - solar planets with @xmath24 @xcite . our model therefore exhibits evolution that is consistent with current observations of extrasolar planetary systems , which as we noted previously are mostly of systems at such small radii that planetesimal disks are dynamically unimportant . at larger radii we expect that both disks and planet - planet scattering will play a dynamical role . a wide range of outcomes is then possible . exchange of energy and angular momentum between the planets and the planetesimal disk leads to planetary migration @xcite , which can be either stabilizing or destabilizing . a low mass planet adjacent to the disk scatters planetesimals inward , resulting in divergent migration that is often stabilizing unless resonance crossing excites eccentricity to the point of triggering instability . alternatively , an outer massive planet interacting with the disk directly ejects planetesimals and migrates inward , compressing the system and leading to instability or resonant capture . an equally important effect is that the disk can act to recircularize the orbits of scattered planets _ after _ dynamical instabilities @xcite . to illustrate how significant recircularization can be we ran a small additional set of idealized experiments in which a single planet with mass @xmath25 on an orbit with @xmath26 and @xmath27 begins to interact with our _ initial _ planetesimal disk . for @xmath28 years ( longer for smaller @xmath25 ) , @xmath29 is damped roughly exponentially with a damping time scale @xmath30 , defined via , @xmath31 of @xmath32 years , independent of @xmath25 . the subsequent evolution was highly mass - dependent : for low - mass planets , @xmath29 continued to decrease on much longer timescales ( 0.36 , 0.63 , and 4.6 myr to reach @xmath33 for @xmath34 , and @xmath35 , respectively ) . massive planets disrupted the disk , halting dynamical friction . the total decrease in @xmath29 for @xmath36 was 0.15 or less , corresponding to an increase of 1.5 au or less in perihelion distance . figure [ fig : evol9 ] illustrates the diversity of outcomes from our simulations that include planetesimal disks . we split our simulations into three mass bins ( the solar system s giant planets fall into the middle bin ) and three stability categories . in stable "" systems there are no close encounters between planets and no large - scale change in system architecture ( the ordering of the planets is preserved and all planets survive ) . moderately stable "" systems experience substantial perturbations which may be due to resonance crossing in high - mass systems or close encounters in low - mass systems that are nonetheless insufficient to alter the architecture . unstable "" systems undergo close encounters leading to architectural change . subsets of our runs show dynamics analogous to that studied for the solar system and for extra - solar planetary systems . at high masses planetesimal disks stabilize about 30% of cases but planet - planet scattering leading to the loss of one or more planets is still common . quantitatively , the median eccentricity is reduced (" +"frictionless flow is one of the defining features of superfluidity @xcite . for a moving obstacle with velocity @xmath2 in a superfluid , the frictionless nature of the superfluid near the obstacle breaks down when @xmath2 exceeds a certain critical velocity @xmath1 . according to landau s criterion this critical velocity is estimated as @xmath3 $ ] , where @xmath4 is the excitation spectrum , @xmath5 is the planck constant , and @xmath6 is the wave vector , with @xmath7 , see refs . an object moving with a velocity above @xmath1 dissipates energy via the creation of elementary excitations , for example , vortices or phonons . superfluidity was first observed in liquid helium @xmath8 and helium @xmath9 . since then , superfluidity has been studied in quantum gas systems of bosons @xcite , fermions @xcite , as well as of bose - fermi mixtures @xcite . the phenomenon of superfluidity is closely related to the bose - einstein condensation ( bec ) of interacting gases . interestingly , a uniform two - dimensional ( 2d ) system can not undergo the bec transition because the formation of long - range order is precluded by thermal fluctuations @xcite . however , it forms a superfluid with quasi - long range order via the berenzinskii - kosterlitz - thouless ( bkt ) mechanism @xcite . the quasi - long range order of this state refers to the algebraic decay of the single - particle correlation function . the algebraic exponent of this correlation function increases smoothly with temperature . at the critical temperature , the superfluid density of the system undergoes a universal jump of @xmath10 , where @xmath11 is the de broglie wavelength . experiments on 2d bosonic systems , such as a liquid helium film @xcite , and trapped bose gases @xcite have shown indications of the bkt transition . furthermore , a trapped 2d system can form a bec due to the modified density of states @xcite and leads to an interesting interplay of the two phase transitions @xcite . quasi - long range order in 2d bosonic systems can be detected via interference and time - of - flight techniques @xcite . however , as a direct method , superfluidity of ultracold atomic gases was probed using a local perturbation , in particular via laser stirring . for example , superfluidity of 3d becs was tested via laser stirring in refs . @xcite . in the experiment @xcite , thermal relaxation of a perturbed 2d quasicondensate is studied . @xcite reported on stirring a trapped 2d bose gas of @xmath0rb atoms with a blue - detuned laser , moving on a circular path around the trap center . the circular motion ensures that the harmonically trapped 2d gas is probed at a fixed phase - space density . by choosing different radii of the circular motion , the superfluid transition was explored . in this paper , we provide a quantitative understanding of the experiment using a c - field simulation method . we demonstrate that a blue - detuned laser of intensity comparable to the mean - field energy causes dissipation due to the creation of vortex - antivortex pairs . this is in contrast to laser stirring with a red - detuned laser @xcite , where dissipation occurs via phonons @xcite . furthermore , we study the relaxation dynamics of the stirred gas following the stirring process , which shows a slow energy transport between the condensate and the thermal cloud . we identify the origin of this slow relaxation to be vortex recombination and diffusion . we show that this effect can explain quantitatively the shift of the measured critical phase - space density in the experiment . this paper is organized as follows . in sec . [ sec_sim_method ] we describe the simulation method that we use . in sec . [ sec_vc_sim ] we determine the critical velocity @xmath1 of the stirred gas , based on which we identify the superfluid to thermal transition . in sec . [ sec_mechanism ] we discuss the dissipation via vortex pairs . in sec . [ sec_comp_expt ] we compare the simulation results with the experiment . in sec . [ sec_nonequilibrium ] we analyze the relaxation of the stirred gas , and in sec . [ sec_conc ] we conclude . we simulate the stirring dynamics of a weakly interacting 2d bosonic system using the c - field simulation method that we used for a 3d system in ref . we describe this method in the following . we start out with the hamiltonian of the unperturbed system , @xmath12.\end{aligned}\ ] ] @xmath13 and @xmath14 are the bosonic annihilation and creation operator , respectively . the 2d coupling parameter @xmath15 is given by @xmath16 , where @xmath17 is the dimensionless interaction , @xmath18 is the atomic mass , @xmath19 is the 3d @xmath20-wave scattering length , and @xmath21 is the harmonic oscillator length of the confining potential @xmath22 in the @xmath23 direction . @xmath24 is the trap frequency along the @xmath23 direction . @xmath25 describes the external potential , which is a harmonic trap , @xmath26 . @xmath27 is the trap frequency in the radial direction and @xmath28 is the radial coordinate . we introduce a time - dependent term to describe laser stirring , @xmath29 where @xmath30 is the time - dependent stirring potential and @xmath31 is the density operator at the location @xmath32 . the stirring potential is a gaussian with a width @xmath33 and a strength @xmath34 , @xmath35 which is centered at @xmath36 . we move @xmath37 along a circular path as a function of time @xmath38 . we perform numerical simulations by mapping this system on a lattice system , which also introduces a short - range cutoff ; see appendix [ app_sim_heating ] . this short - range cutoff is of the order of the healing length @xmath39 , with @xmath40 being the density . we describe both the equations of motion and the initial state within a c - number representation , which corresponds to formally replacing the operators @xmath13 by complex numbers @xmath41 . furthermore , we approximate the initial ensemble by a classical ensemble , within a grand - canonical ensemble of temperature @xmath42 and chemical potential @xmath43 . we sample the initial states via a classical metropolis algorithm . the simulation setup consists of a disc - shaped 2d circular condensate of @xmath0rb atoms . this choice of the 2d circular condensate is inspired by the experimental setup of ref . @xcite . in the simulations we consider @xmath44 @xmath0rb atoms confined by the harmonic potential in both the radial and transverse directions . the trap frequencies are @xmath45 and @xmath46 . here the scattering length is @xmath47 , which yields @xmath48 . the temperature of the trapped gas is in the range @xmath49 . the simulation parameters that we use , are in the typical range of the experimental parameters of ref . @xcite . for simulations of a quasi- and a pure-2d trap geometry we use a lattice of @xmath50 and @xmath51 sites , with the lattice discretization length @xmath52 , respectively . we choose @xmath53 such that it is smaller than , or comparable to , the healing length @xmath54 and the de broglie wavelength @xmath55 , see ref . the trapped gas is in the pure-2d regime if @xmath56 . when @xmath57 and @xmath43 are comparable to @xmath58 , it is in the quasi-2d regime . after initializing the trapped system at temperature @xmath42 , we switch on the stirring potential described by eq . [ eq_stir_potential ] . in the experiment @xcite the trapped gas is stirred with a blue - detuned laser beam moving on a circular path around the trap center . for the circular motion of stirring we choose @xmath59 , where @xmath60 and @xmath61 are the stirring radius and frequency , respectively . for the stirring potential we use the strength @xmath62 and the width @xmath63 , in accordance with the experiment . the stirring sequence is the following : we linearly switch on the stirring potential over @xmath64 , let it stir the system for @xmath65 , and then switch it off over @xmath64 . this is again inspired by the experimental choices . we repeat this for various stirring velocities @xmath66 by changing both @xmath60 and @xmath61 . by choosing different @xmath60 we stir the different regimes of the trapped gas , the superfluid , the thermal , and the crossover regime . after stirring we calculate the total energy @xmath67 using the unperturbed hamiltonian in eq . [ eq_hamil ] , where we use @xmath41 instead of @xmath13 . from this energy we determine the equilibrium temperature @xmath68 of the stirred gas . we infer this temperature by numerically inverting the temperature dependence of the equilibrium state , @xmath69 . we elaborate on this in appendix [ app_sim_heating ] . from the temperature difference between the stirred and initial system , the heating @xmath70 is determined . we also calculate the local energy , as well as the vortex and anti - vortex distribution . we define the local energy as @xmath71 , where @xmath72 refers to the nearest neighbor sites . @xmath73 , @xmath74 , and @xmath75 are the complex - valued field , the density , and the trap potential at site @xmath76 , respectively . @xmath77 and @xmath78 are the bose - hubbard parameters , see appendix [ app_sim_heating ] . for the vortex distribution , we calculate the phase winding around the lattice plaquette of size @xmath79 , using @xmath80 , where the phase differences between sites is taken to be @xmath81 $ ] . @xmath82 is the phase field of @xmath41 . we identify a vortex and an antivortex by a phase winding of @xmath83 and @xmath84 , respectively . by counting all vortices and antivortices we determine the total number of vortices . we restrict this counting to the the superfluid region of the gas as we describe below . to study the superfluid behavior we stir a 2d quasicondensate with a repulsive gaussian potential . we prepare a trapped 2d quasicondensate of @xmath85 @xmath0rb atoms at temperature @xmath86 . we show the simulated density profile of the trapped gas in fig . [ fig_heating](a ) . we stir the gas with a circularly moving , repulsive stirring potential at stirring radius @xmath87 . as mentioned in sec . [ sec_sim_method ] , we use the strength @xmath62 and the width @xmath63 for the stirring potential . this strength @xmath34 is well above the local mean - field energy @xmath88 at the stirring location . after stirring we determine the induced heating @xmath89 from the equilibrium temperature @xmath90 of the stirred gas , [ sec_sim_method ] for details . by varying the stirring frequency @xmath61 we determine @xmath91 as a function of stirring velocity @xmath92 . we show @xmath93 determined for various @xmath2 in fig . [ fig_heating](b ) . the induced heating is almost negligible at low @xmath2 , its onset occurs at a velocity @xmath1 , and for @xmath94 it increases rapidly . we quantify the onset of heating using a fitting function , @xmath95 + b,\ ] ] which is discussed in ref . @xcite , with the free parameters @xmath96 , @xmath97 , and @xmath1 . for the simulated heating shown in fig . [ fig_heating](b ) , this function gives a critical velocity of @xmath98 . we compare this critical velocity to the bogoliubov estimate of the phonon velocity @xmath99 at the stirrer location . the bogoliubov velocity is determined by @xmath100 . the observed critical velocity is @xmath101 . this is notably different from the case of an attractive stirring potential , where @xmath102 @xcite . we explain this reduction of @xmath1 for a repulsive stirring potential in sec . [ sec_mechanism ] . by choosing different radii" +"flavor changing decays of heavy hadrons are of great interest in the heavy flavor physics due to their ability to provide useful information on the quark structure of the hadrons and reveal the nature of the weak interactions . in particular , the decay of the @xmath5-quark baryons can give us various charm related cabibbo - kobayashi - maskawa matrix elements , which are the main ingredients of the standard model . furthermore , a thorough understanding of the standard model itself needs a comprehension of the flavor changing dynamics . however , such a comprehension is difficult contemporarily since form factors characterizing those processes are nonperturbative quantities that need to be determined by some nonperturbative method . this paper aims to give a preliminary determination of the form factors of the exclusive semi - leptonic decay @xmath1 . in the calculation we will use the method of qcd sum rules on the light cone @xcite , which in the past has been successfully applied to various problems in heavy meson physics , see @xcite for a review . the light - cone sum rule ( lcsr ) is a non - perturbative method developed from the standard technique of the traditional qcd sum rules from shifman , vainshtein , and zakhavov(svz sum rules ) @xcite , which comes as the remedy for the conventional approach in which vacuum condensates carry no momentum @xcite . the main difference between svz sum rule and lcsr is that the short - distance wilson ope(operator product expansion ) in increasing dimension is replaced by the light - cone expansion in terms of distribution amplitudes ( das ) of increasing twist , which were originally used in the description of the hard exclusive process @xcite . in recent years there have been many applications of lcsr to baryons . the nucleon electromagnetic form factors were studied for the first time in refs . @xcite and later in refs . @xcite for a further consideration . several nucleon related processes gave fruitful results within lcsr , the weak decay @xmath6 was considered in both full qcd and hqet lcsr @xcite . the generalization to the @xmath7 transition form factor was worked out in ref . we have given the applications of lcsr on other @xmath8 octet baryons in refs . @xcite . in this paper we will make use of the lcsr approach to study the decay process @xmath1 , which has been preliminarily studied in the previous work @xcite . the improvement of the present paper is to use the renewed distribution amplitudes provided in ref . @xcite , and adopt two different kinds of interpolating currents to investigate the process . this transition had been studied in the literature by several authors , employing flavor symmetry or quark model or both in refs . there are also qcd sum rule description of the form factors @xcite , upon which the total decay rate are obtained . the paper is organized as follows : in sec . [ sec2 ] , we present the relevant @xmath0 baryon das . following that sec . [ sec3 ] is devoted to the lcsrs for the semi - leptonic @xmath1 decay form factors with two kinds of interpolating currents for the @xmath9 baryon . the numerical analysis and our conclusion are presented in sec . the das presented in this subsection is the same as that in our previous work @xcite and a part of the complete results in ref . herein we only give them out for the completeness of the paper . our discussion for the @xmath0 baryon das parallels with that for the nucleon in ref . @xcite , so we just list the results following from that procedure and it is recommended to consult the original paper for details . the @xmath0 baryon das are defined through the following matrix element : @xmath10 where @xmath11 designates the spinor for the @xmath0 baryon with momentum @xmath12 . since only axial - vector das contribute to the final sum rules of the process , we merely present this kind of structures for simplicity . the twist classification of those calligraphic das is indefinite , but they can be expressed by the ones with definite twist as @xmath13 the twist classification of @xmath14 is given in table . [ twist ] . to summarize , we have given an approved investigation on the semi - leptonic decay @xmath15 . the form factors characterizing the process are studied within the framework of the lcsr method . in the calculations we adopt both cz - type and ioffe - type current as interpolating field for the @xmath9 baryon . light - cone sum rules for the form factors are derived and used to predict the decay width , which is @xmath16 from cz - type interpolating current and @xmath17 from ioffe - type interpolating current . the results show that the adoption of the ioffe - type interpolating current is in better agreement with the experimental data . this is partly due to the fact that in the case when ioffe - type interpolator is used , terms proportional to the mass of the heavy quark appearing in the sum rules ( [ sr - ioffe ] ) can play an important role in the numerical analysis . in addition , the analyses also show that the higher twist contributions are important for the results so that they need to be included in the calculation . v. braun , light - 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light system . the paradigmatic example of this is the existence of exciton polaritons , hybrid matter - light particles formed by the strong interaction between excitons and photons @xcite . matter - light coupling can be engineered by confining light in optical cavities , so as to modify the density of states and the coupling to matter . for weak coupling , or a bad cavity , cavity losses are fast so one can eliminate virtual processes where photons are in the cavity . this gives fermi s golden rule , but with the cavity density of states modifying the emission rate , as first discussed by purcell @xcite . when coupling is strong , first order perturbation theory ( i.e. fermi s golden rule ) fails , as there can instead be coherent emission and reabsorption of photons before light leaks out of the cavity @xcite . a natural context in which strong matter - light coupling arises is between organic molecules and light in semiconductor microcavities . because of the existence of conjugated @xmath0 bonds in organic molecules , electronic transitions can acquire large dipole moments @xcite , leading to very strong coupling to light . when such molecules are placed in optical microcavities this leads to huge polariton splittings @xcite . these scales allow such experiments to be performed at room temperature , whereas for many inorganic materials , cryogenic temperatures are required . the polariton splitting is due to a collective phenomenon : the electronic transitions of many molecules couple to radiation , and as such the polariton splitting grows as the square root of the molecule density . in contrast , in weak coupling , the rate at which one molecule emits is independent of whether or not any other molecules are present @xcite . much of the recent work on organic microcavity polaritons ( see , e.g.ref . @xcite for a recent review ) has been focused on condensation and lasing @xcite , involving a strongly pumped system , and the appearance of macroscopic quantum coherence . there has however also been significant recent work on the effects of matter - light coupling in the vacuum state , i.e. without strong pumping . such work aims to understand how the physical and chemical properties of organic molecules are affected by strong coupling to electromagnetic modes . examples of this include modifying the rates of photochemical reactions @xcite , or modifying the transport properties of organic semiconductors @xcite . more recently , there has also been experimental @xcite and theoretical @xcite work on coupling the vibrational state of organic molecules to infra - red radiation , leading to molecular optomechanics . theoretical work @xcite has also studied how strong matter - light coupling to electronic states can suppress the effects of disorder and vibronic features in the polariton spectrum . of particular interest for the present paper is a recent work from the ebbesen group @xcite , in which the optical spectra of strongly - coupled organic microcavities were studied by varying molecular concentration and temperature , and paying particular attention to the relative weights of the resonant features in the absorption spectra : the two polariton peaks , and a third peak at the bare excitonic energy @xcite . our aim in this manuscript is to examine the behavior of such strongly - coupled organic microcavities starting from various microscopic models , allowing quantitative predictions of the extent to which a self - consistent adaptation of the molecular state , driven by coupling with light , may occur . to understand the variation of the optical spectra with both concentration and temperature the models which we consider all contain a variable degree of coupling to light . this is because a molecule that has strictly zero coupling to light is not visible in the absorption spectrum , while molecules with a small but non - zero coupling will lead to absorption at the bare molecular energy . in order that the coupling to light can vary self consistently ( in response to the rabi splitting ) , it must depend on some adaptable feature of the state or environment of the molecule . i.e. there must be some physical property that can vary , which determines the strength of matter - light coupling . we refer to this concept hereafter as `` self - consistent molecular adaptation '' . we refer to this process as `` self - consistent '' because the effective matter - light coupling depends on ( some aspect of ) the molecular state , and the molecular state is modified because of how its energy depends on the matter - light coupling . in the first part of this manuscript we investigate in detail two candidates that could lead to self - consistent adaptation : rotational and vibrational degrees of freedom , we also consider an extension of these models to generic ( classical ) aspects of the molecules physical or chemical state . while we do find a temperature dependence of the optical spectra , the involved energy scales turn out to be incompatible with the observation of ref . @xcite . in the final part of the present work , we examine how our model of vibrationally dressed polaritons naturally predicts an effect whose energy scale is of the right magnitude to explain the data . this effect does not involve the renormalization of the coupling strength , but instead involves the effect of vibrational replicas and their coupling to the excitonic transition on the optical spectra . our results thus show a first example of the rich , and presently poorly understood behavior that can stem from the interplay of strong matter - light coupling with strong coupling to vibrational / conformational modes of the molecules . we start by noting that the existence of a peak at the bare energy of the exciton , brought forward as evidence of novel physics in ref . @xcite , is not unexpected ; such a `` residual excitonic peak '' has been seen in many cases , for example ref . @xcite discussed theoretically , and demonstrated experimentally , the appearance of such a feature in a gaas / algaas heterostructure , containing quantum wells inside a dbr microcavity . while such a peak comes from the spectral weight of the exciton line , it is important to note that this peak _ can not _ be viewed simply as excitons which do not couple to light : if they did not couple , they would not be visible in the absorption or transmission spectrum . the origin of the peak can be understood physically as coming from the subradiant excitonic states due to inhomogeneous broadening . in a disordered system , the coupling to the photon mode picks out a specific superradiant state , which forms the polaritons , while the other states orthogonal to this superradiant state remain at the bare exciton energies . however , because of energetic disorder , the superradiant state is not an energy eigenstate , and a residual coupling between the superradiant and subradiant states exists , so that the spectral weight of the subradiant states is visible in the optical spectrum @xcite . a simple analytical treatment shows that the weight of this residual excitonic peak does decrease as the matter - light coupling increases . the existence of this peak is thus consistent with the behavior seen in @xcite . however , on its own this explanation can not account for the temperature dependence observed , as the residual excitonic peak should be unaffected by temperature , unless @xmath1 approaches optical energies , of the order of @xmath2 ( for comparison 300k@xmath3mev ) . one of the main goals of this paper is to address how this temperature dependence may occur . as will become clear in the following , to discuss the microscopic theory of such effects , it will be crucial to consider the physics of ultrastrong matter - light coupling @xcite , and the breakdown of the rotating wave approximation ( rwa ) . this requires retaining `` counter - rotating '' terms in the matter - light coupling hamiltonian . these terms , which involve simultaneous creation of pairs of excitations , are typically considered to be non - resonant and so are often neglected . however , if the matter - light coupling is a significant fraction of the bare exciton and photon energies , then these terms have a non - negligible impact . such behavior has been seen in both inorganic @xcite and organic @xcite systems , with a current record of a coupling strength @xmath4 of the bare oscillator frequency @xcite . our focus in this paper is on the more typical regime where such counter - rotating terms can not be neglected , but remain sufficiently small to be treated perturbatively . the rest of the paper is structured in two main sections . in section [ sec : rotational - freedom ] we consider how temperature dependence can arise due to self - consistent adaptation of the rotational and vibrational degrees of freedom of the molecules , via a mechanism very similar to that proposed in ref . @xcite . for the orientational degree of freedom , we consider both free molecules , and molecules with randomly pinned orientations as appropriate in a polymer matrix . we will see that in such systems we do predict a temperature dependence of the residual excitonic peak . however , while this effect could potentially be observed in other experimental realizations , the energy scales ( temperatures ) required and the scaling with molecular concentration are not compatible with the experimental observations reported in ref . @xcite . in section [ sec : vibrational - freedom ] we instead consider a different effect , arising from the interplay of vibrational modes with the matter - light coupling , which is able to reproduce similar behavior to that observed in experiments . specifically we find that vibrational excitations dress the residual excitonic peak in a strongly temperature dependent manner . moreover , the form of the vibrational dressed spectrum shows that the spectral feature at the exciton energy can have a more complex interpretation than that previously considered @xcite . a brief but self - contained account of the main theoretical methods used throughout this paper is given in the appendices . in this section we consider whether self - consistent molecular adaptation can enhance matter - light coupling by renormalizing the bare matter - light coupling strength . we consider models in which the effective matter - light coupling strength of a given molecule depends on the configuration of that molecule , such as its orientation , or its vibrational state . we then ask how this same matter - light coupling modifies the energy landscape for the auxiliary parameters describing the configuration . this leads to the idea of self consistency if strong coupling leads to a reduction of the ground state energy , the energy landscape is deformed so as to favor auxiliary parameters for which the effective matter - light coupling is as large as possible . our aim is to derive this from a microscopic model , and so quantify this effect . in the following we consider two potential scenarios involving adaptation of either orientational or vibrational degrees of freedom . if such a self - consistent enhancement of matter - light coupling occurs , then this can lead to a temperature dependent effective coupling , and thus to a temperature dependence of the residual excitonic peak . we show that such an effect exists , but that its strength is" +"the internal processes and morphological properties of solar active regions have been mostly subjects of case studies because of the earlier lack of detailed long term databases . several internal features of sunspot groups are of diagnostic importance about the development of active regions , their interaction with the surrounding velocity fields or the advancement of the dynamo mechanism . the investigation of these topics became possible with the appearance of new photospheric databases . the present report lists some of these new topics and presents some preliminary results . the more detailed analysis of these phenomena is under way and will be published in more extended works . the observational data are taken from the soho / mdi - debrecen sunspot data ( sdd ) , ( gyri et al , 2011 ) . this material is more detailed than the classic greenwich photoheliographic results ( gpr ) and its continuation , the debrecen photoheliographic data ( dpd ) . these latter sunspot catalogues are suitable and indispensable for long - term studies of the solar activity , the solar cycles and dynamo , however , they are much less suitable to investigate all internal finer details and processes within the sunspot groups . this is partly because of the daily sampling , the observations are taken on the ground . on the other hand , the internal structure is mostly determined by the magnetic polarity relations and these data are missing from the gpr and dpd . the sdd exploits the wealth of data provided by the soho / mdi instrument . the sunspot data are produced on an hourly basis , they comprise data of position , umbra - penumbra area and magnetic field for all observable sunspots and sunspot groups . currently this data structure allows the highest resolution in both space and time . the polarity distance of emerging bipolar active regions develops more or less parallelly with the sunspot area and it reaches a quasi - equilibrium state at the maximum phase of the active region . this equilibrium exists between the magnetic tension of the active region flux ropes and mechanical impacts on the emerged flux ropes . the upper panel of figure 1 shows the relationship between the total areas of sunspot groups and the distances between the centers of weight of their leading and following parts at the time of the largest total umbral area of the sunspot group . to ensure that in fact the time of maximum is considered only those sunspot groups are taken into account whose entire life - span was observed on the visible disc . this means a statistical sample of 272 active regions . the relationship is linear but fairly weak . this may indicate that the magnetic tension only plays a weak role in the formation of the active region size . the lower panel distinguishes the northern and southern hemispheres . apparently there is no significant difference between the two hemispheres . the emerged active regions usually exhibit a specific asymmetry : the leading and following subgroups are not equally compact . the left panel of figure 2 shows the relationship between the leading - following asymmetry indexes of spot numbers and mean spot areas . the data are computed at the time of the greatest total sunspot area of the active regions . the majority of the active regions belong to the upper left quarter of the diagram . this means that the typical configuration is characterized by smaller number and larger mean area of spots in the leading part . the right panel of figure 2 compares how dispersed are the leading - following parts . the emergence and decay of magnetic fields are important characteristics of the active region dynamics . they are related to different physical processes : the emergence is driven by buoyancy whereas the decay is the consequence of an erosion process caused by the turbulent environment of the flux ropes ( petrovay and van driel - gesztelyi , 1997 ; petrovay et al . , 1999 ) . nevertheless , these processes can be mixed during the development of the active region . the most recent relevant publication of hathaway and choudhary ( 2008 ) only refers to the development curve of the total area of a sunspot group from the gpr with daily resolution . the sdd opened the possibility to investigate the heading and trailing parts separately in hourly resolution . two active regions were selected to demonstrate the new possibilities . the selection was motivated by the aim to have area development curves with reasonably complete increasing and decreasing phases . development profiles of two active regions are plotted in figure 3 describing the history of active regions noaa 10988 and noaa 10311 . the heading and trailing parts are plotted separately along with the separation of their centers of weight . the fitted asymmetric gaussian is the following : @xmath0 where h and m are the value and position of maximum , d and a determine the width and asymmetry respectively . the detailed investigation of the emergence / decay process will need an extended sampling but some properties can be noticed from these two examples . the heading part is larger , it develops more rapidly but it reaches the maximum somewhat later that the trailing part in both cases . the magnetic axes of the active regions ( the axis is the line connecting the centers of weight of the areas of opposite polarities ) have certain tilts with respect to the azimuthal direction , the leading part tends to be closer to the equator than the following part , this is considered to be positive tilt in both hemispheres . this property is known as the joy s law . the underlying process is the winding up of the poloidal field to toroidal form , the process has been theoretically investigated by dsilva and choudhuri ( 1993 ) and caligari et al . . it should be noted , however , that the number of negative tilts can not be neglected . the present report investigates the rate of positive / negative tilts . the dpd and sdd catalogues also contain the tilt angles . the upper panel of figure 4 shows the numbers of positive and negative tilts at the times of the maximum areas of sunspot groups in both hemispheres in cycles 22 - 23 . the comparison of the curves of positive and negative tilts shows that in the developing phase the majority of positive tilts is significant , its number is higher than that of the negative tilts by a factor of 2 or more , but after the maximum the difference gradually disappears and at the end of the cycle the two directions are similarly frequent . the reason is obviously the gradual approach of the toroidal field to the azimuthal direction and at the end of the cycle the tilts are randomly varying between positive and negative values . this is demonstrated in the lower panel of figure 4 . the ratios of positive / negative tilt angles are plotted for cycles 22 - 23 and the beginning of cycle 24 for the two hemispheres separately . in all cases the positive / negative ratios are higher at the beginnings of the cycles and they are diminishing until the ends of cycles . to have an impression about the spatial and temporal distribution of tilts their positive and negative values have been plotted separately in the schwabe - diagram , see figure 5 . the size of the pixels are : a quarter of a year and @xmath1 in latitude , the data are averaged within these domains . the tilt data of dpd are determined for two objects , both for the umbrae and penumbrae and the diagram only takes into account those cases when the difference of these two data was smaller than @xmath1 , this restriction eliminates the most ambiguous cases . it is conspicuous that the highest mean values are found at the border of the butterfly diagram for both negative and positive angles , in the central region of the diagram the moderate mean positive tilts are overwhelming . the presented features are preliminary results of a series of ongoing investigations . the study of these topics became possible by the new detailed photospheric datasets . the leading - following differences have diagnostic importance about the dynamics of active regions . the role of polarity separation is studied by dsilva and choudhuri ( 1993 ) , the compactness asymmetry is analysed by fan et al . ( 1993 , 1994 ) , the sunspot decay is studied by petrovay et al . the best studied feature is the behaviour of active region tilts , an important ingredient of the flux transport dynamo models . recently , dasi - espuig et al . ( 2010 ) reports evidences for the role of the tilts in the preparation of the next cycle . the forthcoming extension of the above examinations will provide more empirical facts to these investigations . the research leading to these results has received funding from the european community s seventh framework programme ( fp7/2007 - 2013 ) under grant agreement no . * caligari , p. , moreno - insertis , f. , schssler , m. , 1995 , _ _ , 441 , 886 . * dasi - espuig , m. ; solanki , s. k. ; krivova , n. a. ; cameron , r. ; peuela , t. , 2010 , _ _ , 518 , 7 . * dsilva , s. ; choudhuri , a. r. , 1993 , _ _ , 272 , 621 - 633 . * fan , y. , fisher , g. h. & deluca , e. e. , 1993 , _ _ , 405 , 390 - 401 . * fan , y. , fisher , g. h. & mcclymont , a. n. , 1994 , _ _ , 436 , 907 - 928 . * gyri , l. , baranyi , t. , & ludmny , a. 2011 , iau symp . 273 , 403 . + see : http://fenyi.solarobs.unideb.hu/sdd/sdd.html * hathaway , d. & choudhary , d. p. , 2008 , _ _ , 250 , 269 - 278 . * petrovay , k. ; van driel - gesztelyi , l. , 1997 , _ _ , 176 , 249 - 266 . * petrovay , k. ; martnez pillet , v. ; van driel - gesztelyi , l. , 1999 , _ _ , 188 , 315 - 330 . *" +"the ( , ; hereafter , the ) is one of the first infrared sources discovered with an optical bipolar nebulosity @xcite . this object , usually referred to as a proto - planetary nebula ( @xcite ) , consists of the central star in the post - asymptotic giant branch ( post - agb ) phase and the physically - detached circumstellar shell , which is a consequence of mass loss during the preceding agb phase . while agb mass loss is qualitatively understood dust - driven , the exact physical mechanisms of the structure formation in the circumstellar shell are still not understood completely . the is known for its signature bipolar lobes and rather circular concentric arcs @xcite . while there are about a dozen sources with such arcs , the is known to possess the largest number of arcs ( @xmath4 ; @xcite ) . these concentric arcs are qualitatively perceived as manifestations of some kind of mass loss modulations that took place during the early agb phase . however , the deduced temporal intervals do not match with any of the known theoretical temporal intervals ( e.g. , thermal pulsing and surface pulsations of agb stars ; @xcite ) . one of the direct methods to understand the dynamics of the circumstellar structure formation is to perform a differential proper - motion analysis and _ measure _ the amount of relative translational motion of specific shell structures . we performed such an analysis for the bipolar lobes and the equatorial structures of the using nicmos imaging - polarimetry data taken with a 5.5-yr baseline and found that ( 1 ) the lobes expanded linearly ( i.e. , the expansion velocity linearly proportional to the distance to the expansion center ) , ( 2 ) the distance to the was @xmath5 pc , and ( 3 ) the object ( star and nebula ) itself experienced its own proper motion at ( @xmath6 , @xmath7 ) mas yr@xmath2 @xcite . however , we were unable to measure differential proper - motion of the concentric arcs because the nicmos field of view was too small and the surface brightnesses were too weak is in the near - ir . @xcite performed the latest attempt using acs / hrc and wfc3/uvis images with a 6.65-yr baseline . they reported ( 1 ) a uniform expansion of the bipolar lobes by 2.5% and ( 2 ) radial motion of the arcs by 007 . however , their analysis was limited to the central @xmath8 and lacked background reference sources to properly align multi - epoch images . hence , they were unable to confirm the bulk motion of the nebula and _ assumed _ that the shell structures expanded symmetrically . in this work , we performed differential proper - motion measurements of the concentric arcs using the archived imaging - polarimetry data from wfpc2 and acs / wfc , exploiting the data set s largest field of view , longest exposure time , and longest temporal baseline to overcome the deficiencies of the previous analyses . below , we describe the data set and reduction procedure ( 2 ) , present the reduced imaging polarimetry data , differential proper - motion measurements , and results of our analysis ( 3 ) , and summarize our finding ( 4 ) . we used the archived data of the in the f606w band with polarizers taken with wfpc2 ( gto / wf2 - 6221 ; pi : j. trauger ) on 1995 july 17 ( epoch 1 , hereafter ) and acs / wfc ( cal / acs-9586 ; pi : w. sparks ) on 2002 october 16 ( epoch 2 , hereafter ) , which provide a 7.25-yr baseline ( table [ obs ] ) . we reduced the data using the pyraf / stsdas multidrizzle package version 3.13 @xcite to process the multi - program data into a common frame of reference . after removing cosmic - ray hits from the pipeline - calibrated data using _ ( @xcite ; there was only one exposure with each of the three wfpc2 polarizers ) , we performed two rounds of multidrizzle processes to refine the image alignment by using background point sources as spatial anchors . in the end , we generated two sets of three polarizer images for a @xmath9 field at the @xmath10 pix@xmath2 scale centered at the catalog coordinates of the ( @xmath11 , @xmath12 ; @xcite ) . finally , these polarizer images were combined into two sets of stokes images via matrix transformations for each of the wfpc2 and acs polarizers as described by @xcite and @xcite , respectively . we measured the amount of shift for each background source and rejected those that shifted more than two-@xmath13 of the distribution : after this exercise 31 sources were adopted as stationary spatial anchors . because the was imaged near the center of the instrument arrays ( central @xmath14 for wfpc2/wf and @xmath15 for acs / wfc ) these anchors are not affected by the geometric distortion , which may contribute to false proper motions near the aperture edges . the accuracy of alignment was assessed by a residual vector root - mean - square offset computed from the gaussian centroid positions of these 31 spatial anchors and determined to be as good as 0.36 pix ( 0018 ) . the stokes _ i _ images ( figs . [ figimages]a , b ) are the total flux images at the broad v band in the ab magnitude system @xcite . these maps show the signature bipolar lobes plus the searchlight beams as well as the concentric arcs . the two - epoch aperture photometry revealed that the total integrated flux of the decreased by @xmath16 over 7.25 yrs , while the individual fluxes of the n and s lobes decreased by 34% and 41% , respectively ( table [ photom ] ) . @xcite reported similar but smaller flux variations , with the n lobe faded more than the s lobe ( by @xmath17 and @xmath18 , respectively ) , over 6.65-yr baseline immediately following ours . moreover , @xcite discovered that the integrated flux of the n lobe varies with a roughly 90-day period . these observations suggest that both n and s lobes vary their fluxes periodically with a phase lag , which is probably a manifestation of the pulsation of the central star modulated by the time - delay due to the line - of - sight path - length difference between the two lobes of the inclined nebula . the linearly - polarized - flux - only images , @xmath19 , were constructed with the stokes _ q _ and _ u _ images ( @xmath20 ; figs . [ figimages]c , d ) . in the single - scattering limit , @xmath19 images represent the cross - sections of the circumstellar shell because @xmath19 tends to be the strongest when the angle of scattering is close to @xmath21 . this uniqueness of @xmath19 had been used previously to probe the dust density structure in the evolve star circumstellar shells @xcite . contrary to our expectations , however , the bipolar lobes and searchlight beams appeared more prominently than the concentric arcs ( figs . [ figimages]c , d ) . this indicates that the nebula can not be approximated in the single - scattering limit ( as evidenced by the presence of the dust lane ) : the is therefore illuminated by a two - step process , in which starlight is first directed into the lobes and then scattered off from the lobes to the rest of the nebula . the polarization strength images , @xmath22 , display the relative strength of polarization more clearly ( figs . [ figimages]e , f ) . while stronger polarizations ( @xmath23 ) are seen in the lobes and searchlight beams , weaker polarizations ( @xmath24 ) are dominant along the equatorial plane except for the region of medium polarizations ( about 30 to @xmath25 , delineating the central @xmath26 region around the dust lane ( @xmath27 by @xmath28 au at 420 pc ) . this medium - polarization region appears to represent the surface of a marginal central dust concentration ( often referred to as a dust cocoon ; @xcite ) at which the line - of - sight optical depth at @xmath29 becomes greater than unity ( i.e. , dustsphere as in photosphere and molsphere ) . this dustsphere and the bipolar lobes are essentially brightly - lit surfaces that illuminate the rest of the nebula . hence , dust - scattered light from the rest of the nebula tends to be de - polarized , i.e. , weak in @xmath19 and @xmath30 . the structure of this central dust concentration is still unknown . @xcite reported the presence of a hollow co shell of @xmath31 radius expanding at @xmath32 km s@xmath2 at the position angle of @xmath33 ( coincident with the orientation of the 1.3 mm dust continuum ) . thus , this medium - polarization - strength region could represent the `` near - side surface '' of this central expanding co / dust shell . to better assess the geometry of the central material distribution , further investigations at higher spatial resolution at optically - thin bands are required . the polarization angle ( _ pa _ @xmath34 ) images show the position angle of the electric vector of the incident light ( figs . [ figimages]g , h ) . images for optically - thin nebulae typically show a pattern of an azimuthal gradient , which represents continuously changing polarization vector angles with respect to the position of the illumination source . however , our maps reveal roughly the same angle near the center generally aligned with the dust lane ( @xmath35 of e of n ) , indicating higher dust density around the dust lane at which the single - scattering approximation breaks down . for this reason , we were unable to pinpoint the location of the illumination source by back - tracing the polarization vectors ( e.g. , @xcite ) more accurately than a one-@xmath13 error ellipse of @xmath36 . as discussed above , the optical reflection nebulosity of the is caused by a two - step illumination process in rather de - polarized light . therefore , we reverted to the total intensity @xmath37 maps ( i.e. , to utilise all the flux available to us ) to follow the differential proper - motion of local shell structures using the same correlational method as in our previous analysis . briefly , this method measures the amount of translational shift of a given structure between two epochs via a cross - correlation analysis between cutouts of the two - epoch images ( e.g. , @xcite ) . we use our own idl script set created as part of our previous proper - motion investigations of the in the near - ir ( @xcite for details ) . to make the analysis more tractable with the @xmath37 maps , we edge - enhanced the shell structure while minimizing the background noise by processing the maps with the roberts cross operator @xcite . these maps are shown in fig . [ figroberts ] . because concentric arcs are azimuthally symmetric , the present correlational method is unable to break the azimuthal degeneracy and uniquely trace translational shifts of arc segments along the azimuthal direction . this prevented us from following the differential proper - motion of structures azimuthally away from the bipolar axis , and hence , from independently confirming the bulk motion of the nebula and location of the expansion center . thus , for the present analysis we adopted the previously discovered ( 1 ) bulk motion of the at a rate of ( @xmath6 , @xmath7 ) mas yr@xmath2 , (" +"optical dispersive and diffractive media with quadratic [ @xmath3 nonlinearity are well known for their potential to support various types of solitons , which have been a subject of intensive studies @xcite . in most cases , @xmath1 solitons are experimentally observed in the spatial domain , as the small size of available samples makes it difficult to accommodate the dispersion length of temporal solitons . nevertheless , using special techniques , such as tilted wave fronts , it is possible to induce a strong artificial dispersion and thus create temporal solitons in available @xmath1 optical crystals @xcite . another challenge for the experiment was creation of @xmath1 dark solitons ( dss ) and their two - dimensional counterparts ( optical vortices ) . for the first time , dss in @xmath1 models were considered in the cascading limit , which corresponds to a large phase mismatch between the fundamental - frequency ( ff ) and second - harmonic ( sh ) waves @xcite . in this limit , the @xmath1 model reduces to the nonlinear schrdinger ( nls ) equation with the kerr [ @xmath4 nonlinearity . beyond the cascading limit , a single analytical solution @xcite , and a continuous family of numerical solutions for fundamental and twin - hole dss @xcite were found . all these solitons are unstable in the spatial domain , due to the modulational instability ( mi ) of the cw ( continuous - wave ) plane - wave background which supports the ds . the only possibility to avoid the mi was found in the temporal domain , in the case when the group - velocity - dispersion coefficients have opposite signs at the ff and sh @xcite ( in fact , such a case is quite realistic in the temporal domain @xcite ) . nevertheless , effectively stable spatial - domain vortices , supported by a background of finite extension , were experimentally created in the case of negative phase mismatch between the ff and sh waves @xcite . in the latter case , the mi had the character of a convective instability , so that perturbations were carried away from the vortex s core faster than they grew due to the mi . additional possibilities for creation of solitons are offered by a combination of @xmath1 nonlinearity with bragg gratings ( bgs ) . the grating may be introduced in both the time - domain and spatial - domain models , but in the latter one it is a more realistic feature , amounting to a system of parallel scratches drawn on the surface of a quadratically nonlinear planar waveguide . in that case , the generic @xmath1 model is a four - wave one , as both the ff and sh components include two counter - propagating waves ( detailed descriptions of the model can be found in the reviews @xcite and @xcite ) . the mi of cw solutions was studied in the four - wave model , with a conclusion that they are unstable in most cases . stability regions for the cw states were also found , close to the transition to the nls limit , but only in a rather exotic case when the bg strength at the sh is larger than at the ff @xcite . a stable dark bi - soliton in this model was found numerically near the band edge @xcite . in this paper , our aim is to investigate the mi of cw states , and , in the case when they are stable , to find dss in a _ three - wave _ spatial - domain system , in which two ff components are linearly coupled through the resonant scattering on the bg . simultaneously , the quadratic nonlinearity couples the two ff components to the sh wave . the propagation direction @xmath5 is parallel to the scratches "" which form the bg . then , the above - mentioned couplings can be achieved by choosing ff carrier wave vectors to be of equal magnitude and making opposite angles with the @xmath5 axis , while the sh wave vector is parallel to it . thus , only the ff components are affected by the grating , while the sh wave is subject to diffraction . this model was introduced in ref . @xcite in the context of bright solitons . stable gap solitons , as well as bright _ embedded solitons _ ( which exist inside the continuous part of the system s linear spectrum @xcite ) have been found in this three - wave model . the paper is structured as follows . the model is formulated in section [ sec : model ] , where we also give an estimate for relevant values of the physical parameters . in section [ mi ] , we identify two types of cw solutions and analyze their modulational stability . it is shown that , on the contrary to other @xmath1 models in the spatial domain , in the present case one type of the cw solutions is _ stable _ in a broad range of parameters . dss supported by the stable cw background are considered in section [ dark ] . for stationary fundamental solitons , we find an approximate analytical and direct numerical solutions . _ tilted solitons _ ( with a slant relative to the propagation axis @xmath5 ) , as well as bound states of two dss , are found too . section [ stability ] presents results for the stability and interactions of the dss . it is shown that both the fundamental solitons and their bound states are _ stable _ in the whole region where the respective cw is modulationally stable . the work is concluded by section [ conclusions ] . we consider a quadratically nonlinear planar waveguide with a spatial bg in the form of scores directed parallel to the propagation direction @xmath5 . as shown in ref . @xcite , spatial evolution of two components @xmath6 and @xmath7 of the complex ff field , and the complex sh field @xmath8 obey the following system of normalized equations : @xmath9 here @xmath5 and @xmath10 are , respectively , the propagation and transverse coordinates , the subscripts stand for partial derivatives , the asterisk means for the complex conjugation , @xmath11 is the phase - mismatch parameter , and @xmath12 is an effective diffraction coefficient , defined with regard to the fact that bragg - reflectivity and @xmath1 constants are normalized to be @xmath13 . we notice that the complex conjugation applied to eqs . ( [ evolution ] ) , and the change of the notation @xmath14 , @xmath15 transforms @xmath12 to @xmath16 , therefore we may assume , without loss of generality , that @xmath12 is always positive ( while @xmath11 may be positive , negative , or zero ) . stationary solitary - wave solutions are looked for as @xmath17 where real @xmath18 and @xmath19 are the propagation constant and tilt of the corresponding optical beam in the @xmath20 plane , and complex functions @xmath21 are to be found from the equations @xmath22 with @xmath23 and the prime standing for @xmath24 . for symmetric ( untilted ) solutions with @xmath25 , one may set @xmath26 , @xmath27 , where the function @xmath28 is real , which yields a simplified system , @xmath29 in physical units , the same value of the power density of the cw background in the linbo@xmath30 planar waveguide that was used in the experiments with bright spatial solitons @xcite , i.e. , @xmath31 w/@xmath32 m at the pump wavelength @xmath33 @xmath34 m , may be assumed , in combination with the bg reflectivity @xmath35 @xmath36 , which is a typical value for weak gratings . then , the physical value of the wavenumber detuning corresponding to @xmath37 , i.e. , just above the upper edge of the spectral gap , which is shown below to be appropriate for dss , is about @xmath38 @xmath36 . the range of the parameters @xmath39 and @xmath12 relevant to the experiment can be determined as in ref . @xcite , where the normalized parameters of the model were related to physical ones . in particular , @xmath39 may take values in a wide range , @xmath40 . for example , the large phase mismatch used for the experimental generation of vortices in a @xmath1 media in ref . @xcite corresponds to @xmath41 . realistic values of the effective sh diffraction parameter are @xmath42 , depending on the angle between the ff wave vectors and the @xmath5 axis . the angle must be , however , small enough for the applicability of the paraxial approximation , which is implied in eqs . ( [ evolution ] ) . equations ( [ model ] ) give rise to two types of cw solutions . the first of them is a real one , with in - phase ff and sh components , @xmath43 which exists provided that @xmath44 . below , it will be referred to as a pr ( _ pure - real _ ) solution . in the other solution , the phase of the ff component is shifted by @xmath2 against the sh , @xmath45 this solution , with a _ purely imaginary _ ff field , will be accordingly called a pi one ( of course , the sh is real in it ) . the pi solution exists provided that @xmath46 . to investigate the modulational stability of the solutions , we consider a perturbed one in the form of @xmath47\exp ( ikz ) , \\ u_{2}=[u_{2}^{(0)}+a_{2}^{(0)}\exp ( -i\lambda z+i\omega x)+b_{2}^{(0)}\exp ( i\lambda ^{\ast } z - i\omega x)]\exp ( ikz ) , \\ u_{3}=[u_{3}^{(0)}+a_{3}^{(0)}\exp ( -i\lambda z+i\omega x)+b_{3}^{(0)}\exp ( i\lambda ^{\ast } z - i\omega x)]\exp ( 2ikz ) , \end{array } \label{perturbation}\ ] ] where @xmath48 stand for the amplitudes of the cw solutions defined above , @xmath49 , @xmath50 and @xmath51 are infinitesimal amplitudes and arbitrary real wavenumber of the perturbation , and @xmath52 is the eigenvalue to be found . substitution of these expressions into linearized equations ( [ evolution ] ) leads to a resolvability condition for @xmath53 , in the form of a cubic equation @xmath54 obviously , the stability requires that @xmath32 must be real and positive for all @xmath51 . we start the analysis for the case of @xmath55 . then , the coefficients in eq . ( [ cubic ] ) are @xmath56 for the cw solution of the pr type . for the pi - type solution , they are @xmath57 equation ( [ cubic ] ) was solved numerically ( an analytical solution is formally available , but it takes an intractably complex form ) . the result , in the form of the stability region of the pi solution , is displayed in fig . notice that the solution is always unstable if its wavenumber belongs to the gap of the ff subsystem , which is @xmath58 . the cw solutions of the pr - type solutions are always modulationally unstable . however , for large values of @xmath59 ( actually , in the case of large phase mismatch ) , the instability band of the perturbation wavenumber @xmath51 becomes very narrow . for example , it is @xmath60 for @xmath61 and @xmath62 . therefore , the instability generated by a random perturbation will grow very slowly in that case , and , for practical purposes , the cw state may be regarded stable . the above results pertain to @xmath55 in eqs . ( [ evolution ] ) . with other values of @xmath12 , we have found that , for the pi - type cws , the increase of @xmath12 results in shrinkage of the stability area , and the decrease of @xmath12 results in its expansion , see the dotted and dashed curves in fig . the pr -" +"statistical mechanics , be it for classical or quantum many - body systems , relies on the reasonable assumption that all microstates of a system in equilibrium are equally likely to be realized . in order to be correctly described by a statistical ensemble , a system must therefore be either coupled to an infinite thermal bath , or ( if isolated ) effectively display some form of ergodicity as per the eigenstate thermalization hypothesis @xcite , thereby allowing it to forget its initial state by ` relaxing ' towards a well - defined equilibrium state independent of the starting conditions . the existence of these relaxation processes is not usually questioned , but their precise mechanisms occur in a generally unspecified manner . for individual systems , classical mechanics distinguishes integrable and non - integrable cases , the former possibly having stable quasiperiodic orbits protected by the kam theorem @xcite , and therefore showing no true ergodicity . for non - integrable cases , ergodicity is taken for granted as a consequence of chaotic dynamics . in the quantum case , the question of equilibration has been the subject of many recent works , focusing in particular on the time evolution of a system after a quantum quench , at which a global parameter in the hamiltonian is suddenly changed @xcite - @xcite . this is equivalent to releasing a prepared state and letting it evolve unitarily in time according to the hamiltonian after the quench . such situations , some of which are experimentally realizable , lead to many interesting theoretical questions . under what circumstances is there a well - defined state at large times ( _ i.e. _ what , if anything , remains of the initial conditions for given quench situations ) ? can a general theory of relaxation based purely on the details of quantum dephasing be formulated ? are there different classes of systems ( _ e.g. _ integrable versus non - integrable , finite versus infinite , gapped versus gapless ) having different generic behaviour ? what remains of the usefulness of commonly used quasiparticle bases to understand the dynamics after the quench ? clearly , much progress remains to be done in order to have a full understanding of all these issues . it is our purpose here to consider a well - defined situation , which can be handled to a sufficient degree of exactness to provide some partial but reliable insights into some of these questions . the approach we will consider is based on the use of exact wavefunctions for the heisenberg magnet , and therefore exploits the integrability of this system . on the one hand , this renders some of our results non - generic . on the other hand , we are able to provide hard facts for finite as well as infinite systems , gapped versus gapless , and exclude some possible scenarios . since the theoretical understanding of the nonequilibrium dynamics of strongly - correlated systems is still in its infancy , such example cases will hopefully provide worthwhile reference points for later developments . the paper is organized as follows . in section 2 , we first define our nonequilibrium problem , and present the tools we will use to study it . we then discuss in section 3 the set of eigenstates we use to obtain quantitative results . section 4 considers the work probability distribution resulting from the quench for various system parameters . in section 5 , we study relaxation dynamics by concentrating on the loschmidt echo , which we compute . after a few words on the thermodynamic limit , we offer a discussion of our results and present our conclusions . all technical details for the computations are relegated to a series of appendices , which can safely be skipped by the reader only interested in the final results and conclusions . on the other hand , these appendices explain all calculations in sufficient detail to be reproduced by the specialist reader . we consider an isolated spin chain of @xmath2 sites , each occupied by a local spin-@xmath0 degree of freedom . for definiteness , we put the spins on a ring and impose periodic boundary conditions . the thought experiment we perform consists in preparing the quantum state of the system at @xmath3 as @xmath4 this state thus contains a magnetic domain wall between sites @xmath5 and @xmath6 , and another ( anti- ) domain wall between sites @xmath2 and @xmath7 ( in view of the periodic boundary conditions ) . this state can be prepared in different ways : we can view it as being created by an ising model with an appropriate position - dependent field , or as resulting from a sudden polarizing pulse applied on a section of an initially fully polarized chain . for times @xmath8 , we let this state evolve unitarily in time under the antiferromagnetic xxz hamiltonian @xmath9.\ ] ] note that the hamiltonian is rescaled by a factor of @xmath10 as compared to how it usually appears in the literature , in order the have a well - defined ising limit ( @xmath11 ) . for @xmath1 the spectrum of this theory is gapped , while for @xmath12 the system is in the quantum critical regime . we consider the case when the system is antiferromagnetic ( i.e. @xmath13 ) . in order to simplify the expressions and without loss of generality we put @xmath14 throughout the paper . the initial domain wall state ( [ domainwallstate ] ) is not an eigenstate of the xxz hamiltonian away from the ising limit @xmath15 . on the other hand , for any fixed value of @xmath16 , the exact eigenstates of this model form a basis in the hilbert space on which we can at least in principle decompose the initial domain - wall state to arbitrary accuracy . given this decomposition , the solution of the schrdinger equation becomes straightforward , and we obtain the exact time - dependent wavefunction after the quench as the linear decomposition @xmath17 eigenstates of @xmath18 at fixed total magnetization , and the complex amplitudes @xmath19 represent the overlaps ( vector of the quench matrix ) between the starting state and the exact eigenfunctions . since we always work with normalized wavefunctions , the coefficients @xmath19 should by definition satisfy the constraint @xmath20 this constraint will constitute an important sum rule , allowing to quantify the accuracy of our results by assessing how faithfully the resulting wavefunction is reproduced . all the complexity of the problem is therefore hidden in two places . first , wavefunctions @xmath21 and their energy @xmath22 must be known . this is standardly handled by the bethe ansatz ( see references @xcite - @xcite and references therein ; we provide a summary of the necessary details in appendices a and b ) . second , the overlaps @xmath19 must also be known . this is a problem of much greater complexity , which in the present situation finds its solution in the framework of the algebraic bethe ansatz . the derivation of these overlaps is given in appendices c and d. note that similar overlaps ( quench matrix entries ) were also recently calculated using the algebraic bethe ansatz for the case of the interaction - quenched richardson model @xcite . here , we also obtain these overlaps using integrability , but using a different method based on the explicit structure of the solutions to the bethe equations . despite being in possession of these two fundamental building blocks , one major difficulty remains . since the hilbert space is exponentially large in system size @xmath2 , the summation in ( [ timeevolphi ] ) is difficult to handle , and must in practice be truncated in order to reach sizes sufficiently large to allow the discrimination between finite- and infinite - size behaviour . we will show in the next section that this truncation is possible in the situation we consider . in particular , this puts us in position to study the long - time average of observables according to any prescription desired , a common one being @xmath23 and to make reliable observations on the relaxation / thermalization of the prepared state . the time evolution of this domain wall state has been studied in similar settings . for gapless spin chains this type of quench is studied in @xcite . an exact analysis has been carried out for the xx - chain in @xcite . the short time regime for the xxz chain is studied using tdmrg in @xcite , and an exact diagonalization was performed for the gapped xxz chain with open boundary conditions @xcite . we here offer a complement to these studies , consisting in results from integrability . the space of eigenstates of the xxz chain is spanned by bethe wavefunctions , each described by a set of rapidity parameters @xmath24 obtained as solution to the bethe equations . bethe wavefunctions are generically quite complicated objects , and can contain both unbound and bound magnons . we refer the reader to the standard literature @xcite as well as to our appendices for the basic detail . in summary , solutions of the bethe ansatz equations can be classified using strings ( see appendix [ a : bae ] for a discussion ) . an @xmath25string in a set of @xmath26 complex rapidities sharing the same real part and invariant under complex conjugation . these strings can be interpreted as bound states of ` mass ' @xmath26 . in the ising - limit it can be shown that an @xmath26-string corresponds to @xmath26 adjacent down spins . from a perturbative analysis , we expect at large anisotropy @xmath16 a well - defined hierarchy of states in terms of the importance of their overlap with the domain wall state . this hierarchy is presented in table [ tab : hierarchy ] . the most important states are those consisting of a single @xmath27string , which occupy a dispersionless line in the thermodynamic limit . they are followed by successively more complicated partitionings of the @xmath5 rapidities into more and more individual bound or unbound states , each partitioning representing a whole continuum of excitations . the number of particles in the state is defined here to be the number of elements in the partitioning . from a perturbative analysis it can be easily shown that for sufficiently large @xmath5 the system is insensitive to small changes of @xmath5 ( _ i.e. _ , of how distant the domain and anti - domain walls are from each other ) . this allows us to perform the calculation with an @xmath5 slightly below @xmath28 without loss of generality . the reason for this choice is that for these values the string hypothesis is better satisfied for the majority of string states . .the hierarchy of states , in order of importance of contributions to the normalization sum rule ( [ sumrule ] ) . each partitioning of @xmath5 rapidities into strings leads to an independent excitation class , only the few shown here being of relevance to the current setup . [ cols=""^,^,^,^"",options=""header "" , ] in this work we studied the relaxation dynamics of the gapped xxz chain after a quench from an initial domain wall state . the techniques that were used are based on the algebraic bethe ansatz for a finite chain . some of the results were extended to the thermodynamic limit . the key ingredient for studying this quench was deriving a numerically efficient expression for the overlap between the initial state and eigenstates of the xxz hamiltonian . overlaps for different ising states as initial state could be computed following the same logic , however in the general case of a finite density of domain walls this will become an intractable combinatorial problem . since the" +"the interaction between neutral objects is dominated by fluctuation forces due to the coordinated behavior of fluctuating charges or collective modes inside the objects . at zero temperature or at sufficiently small distances , the interactions result from quantum fluctuations . they are important on atomic scales as well as between macroscopic bodies . a prominent example for the latter is the casimir force between parallel metallic plates due to current or electromagnetic field fluctuations @xcite . during the last decade experimental verifications of this effect have been performed with increasing precision . these high precision measurements were enabled by the use of curved surfaces instead of parallel planar mirrors in order to avoid the problem of parallelism . the most commonly employed geometry is a sphere - plate setup that was used in the first high - precision tests of the casimir effect @xcite . this geometry has been successfully used ever since in most of the recent experimental studies of casimir forces between metallic surfaces @xcite . in order to keep the deviations from two parallel plates sufficiently small , spheres with a radius much larger than the surface distance have been used . the effect of curvature has been accounted for by the `` proximity force approximation '' ( pfa ) @xcite . this scheme is assumed to describe the interaction for sufficiently small ratios of radius of curvature to distance . however , this an uncontrolled assumption since pfa becomes exact only for infinitesimal separations , and corrections to pfa are generally unknown . at the other extreme , the interaction between a planar surface and objects that are either very small or at asymptotically large distance is governed by the casimir - polder potential that was derived for the case of an atom and a perfectly conducting plane @xcite . this limit has been probed experimentally with high precision for a bose - einstein condensate that was trapped close to a planar surface @xcite . recently , there have been first attempts to go beyond the two extreme limits of asymptotically large and small separations by measuring the casimir force between a sphere and a plane over a larger range of ratios of sphere radius to distance @xcite . so far , no theoretical prediction is available that can describe the electromagnetic casimir interaction between a compact object and a planar surface at all distances , including the important sphere - plate geometry . until recently , progress in understanding the geometry dependence of fluctuation forces was hampered by the lack of practical methods that are applicable at all separations . conceptually , the effect of geometry and shape is difficult to study due to the non - additivity of fluctuation forces . explicit consequences of this non - additivity and also non - monotonic changes in the force have been recently predicted for a pair of cylinders next to planar walls @xcite . this behavior has been interpreted in terms of collective charge fluctuations inside the bodies @xcite . for some decades , there has been considerable interest in the theory of casimir forces between objects with curved surfaces . two types of approaches have been pursued . attempts to compute the force explicitly in particular geometries and efforts to develop a general framework which yields the interaction in terms of characteristics of the objects like polarizability or curvature . within the second type of approach , balian and duplantier studied the electromagnetic casimir interaction between compact perfect metals in terms of a multiple reflection expansion and derived also explicit results to leading order at asymptotically large separations @xcite . for parallel and partially transmitting plates a connection to scattering theory has been established which yields the casimir interaction of the plates as a determinant of a diagonal matrix of reflection amplitudes @xcite . for non - planar , deformed plates , a general representation of the casimir energy as a functional determinant of a matrix that describes reflections at the surfaces and free propagation between them has been developed in ref . later on , an equivalent representation has been applied to perturbative computations in the case of rough and corrugated plates with finite conductivity @xcite . functional determinant formulas have been used also for open geometries that do not fall into the class of parallel plates with deformations . for the electromagnetic casimir interaction between a planar plate and infinitely long cylinders , a partial wave expansion of the functional determinant has been developed @xcite . the same results have been reobtained and used to compute corrections to the pfa for the cylinder - plate geometry in ref . kenneth and klich identified the inverted green s function in the functional determinant as a t - matrix and derived a formal result for the casimir interaction in terms of this matrix in the case of scalar fields in a medium with a space and frequency dependent speed of light @xcite . recently we described a new method based on a multipole expansion of fluctuating charges that makes possible accurate and efficient calculations of casimir forces and torques between any number of compact objects @xcite . the method applies to electromagnetic fields and dielectrics as well as perfect conductors . it also applies to other fields , such as scalar and dirac , and to any boundary conditions . in this approach , the casimir energy is given in terms of the fluctuating field s scattering amplitudes from the individual objects , which encode the effects of the shape and boundary conditions . an equivalent partial wave expansion has been applied to a scalar model for dielectrics @xcite . casimir interactions due to scalar field fluctuations serve as a simplified model for the full electromagnetic interaction . this model is usually easier to analyze and provides an important tool in developing conceptually new approaches and in estimating geometry dependencies . for the sphere - plate geometry with dirichlet boundary conditions bulgac _ _ obtained the casimir interaction over a wide range of separations from a modified krein trace formula @xcite . most notably in the context of scalar fields , a versatile numerical world - line algorithm based on monte carlo methods has been developed and applied to a number of interesting geometries , including the here studied sphere - plate interaction @xcite . in this work , we extend our approach developed in refs . @xcite to describe the interaction of compact objects in the presence of a plane mirror . our general result holds for scalar and electromagnetic fields . in the electromagnetic case the mirror is assumed to be perfectly conducting but the compact objects can be dielectrics or perfect conductors . the derivation of the general result for the casimir interaction , see eqs . and , is given in section [ sec : derivatiobn ] by combining a functional integral approach and the method of images . in section [ sec : plate - sphere ] we apply our approach to compute the interaction of a sphere with a plane mirror over a wide range of separations for the scalar dirichlet and neumann problem and for the electromagnetic field that is most relevant to applications . we provide a large distance expansion of the interaction , generalizing the casimir - polder potential to include higher order multipole polarizabilities . for small separations , we compute the two leading correction terms to the pfa . in this section we first review the functional integral formulation of casimir interactions between compact objects for a scalar field and the electromagnetic field . the fluctuating field is integrated out in order to obtain an effective action for the fluctuating sources on the objects . then we show that the interaction of compact objects with an infinite plane mirror can be described by the equivalent problem of the interaction of compact objects with their mirror images in otherwise empty space , i.e. , without the plane mirror . this equivalence holds for dirichlet or neumann boundary conditions ( at the mirror and the objects ) for a scalar field and for a perfectly conducting mirror plane and arbitrary dielectric objects in the case of electromagnetic fluctuations . we first consider a real quantum field @xmath0 in order to introduce the method of images in the path integral formulation of casimir interactions . we assume that the space is divided into two half spaces by a mirror plane at @xmath1 . @xmath2 fixed closed surfaces @xmath3 , @xmath4 , are located in the right half space ( @xmath5 ) . these surfaces are regarded as the boundaries of objects on which either dirichlet or neumann boundary conditions are imposed . the action of the unconstrained field in minkowski space is @xmath6 = \frac{1}{2}\int dt \int _ > d{{\bf x}}\left\ { \frac{1}{c^2 } ( \partial_t \phi)^2 - ( \nabla\phi)^2\right\ } \ , .\ ] ] here the @xmath7-integration runs over the right half space , indicated by @xmath8 . the free energy @xmath9 of the constraint field @xmath0 at inverse temperature @xmath10 is represented by the euclidean functional integral @xmath11_{{\mathcal c}}\exp\left ( -s_e[\phi]/\hbar \right ) \ , , \ ] ] where the euclidean action @xmath12 follows from eq . after the wick rotation @xmath13 , @xmath14 with @xmath15 . the functional integral is over all fields that are periodic in the @xmath16-interval from @xmath17 to @xmath18 and that obey the boundary conditions at the surfaces , indicated by the subscript @xmath19 . the surfaces are fixed and the boundary conditions are time independent . hence each fourier component of the field with respect to @xmath20 obeys the constraints at the surfaces separately . to make use of this property , we expand @xmath21 as @xmath22 with matsubara frequencies @xmath23 and @xmath24 . the functional integral splits into independent functional integrals over the @xmath25 and the logarithm of @xmath26 can be written as the sum @xmath27_{{\mathcal c}}\exp \left[-\frac{\lambda}{2\hbar c } \int _ x}}\left\ { \kappa_n^2 |\phi_n|^2 + |\nabla \phi_n|^2 \right\}\right ] \nonumber\ , .\end{aligned}\ ] ] in the following we are interested in the limit of zero temperature . then @xmath28 , and the sum over @xmath29 can be replaced by the integral @xmath30 and @xmath25 is replaced by @xmath31 . combining positive and negative @xmath32 , we get @xmath33 with @xmath34_{{\mathcal c}}[{{\mathcal d}}\phi^*({{\bf x}},\kappa)]_{{\mathcal c}}\exp \left[-\frac{\lambda}{\hbar c } \int _ x}}\left\ { \kappa^2 |\phi|^2 + |\nabla \phi|^2 \right\}\right ] \ , .\ ] ] the ground state energy is obtained from @xmath26 as @xmath35 the casimir energy is the difference between the ground state energy of the surfaces at their actual distance and the sum of the ground state energies of the separate surfaces which is obtained by removing the surfaces to infinite separation , @xmath36 where @xmath37 is the partition function for the surfaces with infinite separation . in the following we suppress the label @xmath32 . next , the constraints at the objects are implemented by functional @xmath38-functions @xcite . for dirichlet boundary conditions , @xmath39 , on the surfaces @xmath3 , the constraint functional integral can be expressed in terms of an unconstrained integral by using @xmath40_{{\mathcal c}}[{{\mathcal d}}\phi^*]_{{\mathcal c}}= \\ & & \!\!\!\!\!\int \!\!{{\mathcal d}}\phi { { \mathcal d}}\phi^ * \prod_{\alpha=1}^n \int \!\!{{\mathcal d}}\varrho_\alpha { { \mathcal d}}\varrho^*_\alpha \exp\left [ i\!\!\int_{\sigma_\alpha}\!\!\!\!\ ! d{{\bf x}}\,\left\{\varrho_\alpha^*({{\bf x } } ) \phi({{\bf x } } ) + { { \mbox{c.c.\,}}}\right\ } \right ] , \nonumber\end{aligned}\ ] ] where the @xmath38-functions at each position of the surfaces have been written as an integral over a source field @xmath41 that is non - zero on the surfaces @xmath3 only . when we use this representation of the constraints in eq . , the now unconstrained functional integral over @xmath42 is gaussian and yields @xmath43 \nonumber\\ & \equiv & { \mathcal z}_0 \prod_{\alpha=1}^n\int { { \mathcal d}}\varrho_\alpha{{\mathcal d}}\varrho^*_\alpha e^{-(\hbar c/\lambda ) \tilde s[\varrho]}\ , , \end{aligned}\ ] ] where @xmath44 is the partition function of the" +"the search for a plausible model of fermion masses is a continuing quest in particle physics . in particular , the quark sector is a fertile ground to test various models since it is there that one has the largest amount of information : quark masses , ckm angles , cp phase , and it is in this sector that most models turn their attention to . two of us have recently constructed a model of fermion masses @xcite in which the mass matrix is almost of the pure phase form and is constructed out of four plus two extra compact spatial dimensions . as shown in @xcite , one extra compact spatial dimension was needed to give a democratic mass matrix and another one was needed to make its matrix elements complex . in @xcite , an almost pure phase mass matrix was found to take the form @xmath3 with @xmath4 , @xmath5 , and @xmath6 , although ref . @xcite contains a more general result . our motivation for that work was based on an attempt to give a theoretical basis for the so - called pure phase mass matrix ( ppmm ) ansatz ( similar to the previous form but with @xmath7 ) of ref.@xcite which , at the time of its construction , was quite successful in fitting the various angles and masses . in so doing , we arrived at a mass matrix which contains the pure phase form as a particular limit . as we shall see below , the general result of ref . @xcite allows us to be able to fit the latest determination of the ckm elements @xcite . along the way , as stipulated in ref . @xcite , we found a special region , in the allowed parameter space that fits the ckm matrix , where the parameter @xmath0 of the famous strong cp problem can be found to satisfy the experimental bound @xmath8 . this result is somewhat surprising since it is not at all evident that solutions of our model that fit the mass spectrum and the ckm matrix could also give values of @xmath0 below the experimental bound . this connection between weak and strong cp is certainly very intriguing and will be the subject of our focus at the end of the paper . the organization of the paper will be as follows . we first briefly review the construction of a democratic mass matrix ( dmm ) in five dimensions . we then summarize the salient points of the model of ref . @xcite : its construction in six dimensions and the resulting quark mass matrices . next we enumerate and describe the parameters used in the numerical analysis of the mass matrices which is carried out in the section that follows . there we will show the allowed region in our parameter space where solutions are found to fit both the mass spectrum and the ckm matrix . finally , we discuss a subspace in the allowed region where the bound @xmath8 is obeyed . in particular , we present some thoughts on the possible physics which might be responsible for this behaviour . before discussing the results of ref . @xcite , let us first review how a democratic mass matrix ( dmm ) @xcite arises in the case with one extra compact dimension . a dmm is a special case of an almost ppmm with @xmath9 , namely one in which all matrix elements are unity , apart from a common factor , and hence the name `` democratic '' . as described in @xcite , in order to obtain a democratic mass matrix and to avoid unwanted flavour - changing neutral current processes ( fcnc ) , we imposed the following permutation symmetries on the action : @xmath10 , with @xmath11 , @xmath12 and @xmath13 . @xmath14 are the five - dimensional dirac fields whose left - handed zero modes are given respectively by @xmath15 , @xmath16 , and @xmath17 . ( for convenience , left - handed fields are used throughout @xcite and in this paper with the last two fields representing actually the two quark @xmath18 singlets . ) the extra dimension is compactified on an @xmath19 orbifold . the action which obeys this permutation symmetry is the sum of two terms , @xmath20 and @xmath21 , where @xmath22 @xmath23 in eq . ( [ s0 ] ) @xmath24 is the covariant derivative . ( the gauge fields are supposed to be uniformly spread along the fifth dimension @xmath25 inside the thick brane . ) @xmath26 is the vacuum expectation value vev for the background scalar field @xmath27 . the attractive proposal of @xcite to localize chiral zero modes at different points along the extra dimension @xmath25 was adopted in @xcite . as a result , @xmath28 and @xmath29 are the five dimensional `` masses '' which determine the locations of @xmath16 and @xmath17 along @xmath25 . ( as pointed out in ref . @xcite , in order to have an invariant `` mass term '' under the @xmath30 symmetry , one has to require a `` mass reversal '' @xmath31 . the behaviour of @xmath32 under @xmath30 could come for example in a model where the `` masses '' are generated by the radiative corrections to the vev @xmath33 , @xmath34 with @xmath35 being independant of @xmath25 . because @xmath36 under @xmath30 symmetry , at the same time @xmath37 originating in this `` mass reversal '' . ) in eq . ( [ syuk ] ) @xmath38 and @xmath39 are the yukawa couplings in five dimensions which have been chosen real and flavor independant and @xmath40 is the five dimensional sm doublet higgs field whose zero mode @xmath41 is assumed to be uniformly spread along @xmath25 inside the thick brane . here @xmath42 is the charge conjugation operator in five dimensions . for the purpose of keeping track of the dimensionalities of various objects , let us remind ourselves that , in five dimensions , the yukawa coupling @xmath38 has a ( mass ) dimension @xmath43 . a scalar field , in five dimensions , has a dimension @xmath44 . the zero mode of the sm higgs field can be written as @xmath45 where @xmath41 is the usual 4-dimensional higgs field with dimension @xmath46 , and therefore the constant @xmath47 has a dimension @xmath48 . in dimensionally reducing the above action to four dimensions , the following dimensionless combination appears in the yukawa term : @xmath49 the effective action for the yukawa term of the up sector in four dimensions can now be written as @xmath50 where a similar expression holds for the down sector . as stressed in ref . @xcite , since all the @xmath51 s are located at the same place inside the brane , and similarly for all the @xmath52 s . the wave function overlap @xmath53 is independant of @xmath54 . the yukawa action now becomes @xmath55 where @xmath56 is given by @xmath57 and similarly for the down sector @xmath58 from eq . ( [ syukeff2 ] ) one obtains the democratic mass matrix ( dmm ) @xmath59 which has eigenvalues @xmath60 , with @xmath61 . the dmm of eq . ( [ dmm1 ] ) does not reproduce the right mass spectrum and the right ckm matrix . what has been shown in ref . @xcite is that by adding another compact extra dimension one can obtain a viable scenario represented by an almost - ppmm . the main idea of ref . @xcite is that by introducing a sixth compact extra dimension , and by requiring that the background scalar field couples to the fermions through a yukawa interaction which is non - local along that extra dimension , one can obtain an oscillatory behavior for the fermion wave function along the sixth dimension . fermions are delocalized along the sixth dimension , in contrast with the fifth dimension , and the oscillatory behavior of the wave functions , together with the breaking of family symmetry , has the effect of producing phases in the mass matrix . let us now summarize the main results obtained in ref . we first rewrite more compactly the action given in ref . @xcite which is the sum of @xmath20 and @xmath21 where @xmath62 \ , , \label{s0six}\end{aligned}\ ] ] and @xmath63 where @xmath64 is the charge conjugation in six dimensions . ( the gamma matrices in six dimensions can be obtained in ref . @xcite . ) in eq . ( [ s0six ] ) we expressed the dependance from @xmath65 only for the non - local interaction terms . the important point here is that while these interactions will produce an oscillatory behavior for the fermion wave functions along the sixth dimensions , the local terms , which are built using @xmath66 , are found to be responsible for localizing the fermions along the fifth dimension . the above actions are invariant under the family permutation symmetry @xmath10 . the vacuum expectation values ( vev ) for the background scalar fields @xmath67 and @xmath68 are given by @xmath69 and @xmath70 as in ref . @xcite , the family symmetry is broken by the background scalar field @xmath71 and by introducing different non - local `` mass terms '' @xmath72 , @xmath73 and @xmath74 for each family . to break the family symmetry together with the left right symmetry along the sixth dimension will allow us to reproduce the right mass spectrum and the right ckm matrix . as shown in ref . @xcite , the absence in eq . ( [ s0six ] ) of local interactions of the form @xmath75 , which will localize the fermions wave function along the sixth dimension , is obtained by introducing the discrete symmetry q @xmath76 as pointed out in ref . @xcite the realization of the q - symmetry of eq . ( [ qsym ] ) implies that the introduced orbifold for the compactification is @xmath77 instead of @xmath19 . this also implies that the physical space is @xmath78 $ ] instead of the initial support @xmath79 $ ] . the non - local terms of eq . ( [ s0six ] ) and the local terms containing @xmath66 are invariant under the above q - symmetry . from the yukawa action of eq . ( [ syuksix ] ) one can now obtain the effective action in four dimensions @xmath80 where we considered only the up sector , but equal considerations hold for the down sector . using eqs . ( [ syukeff2 ] ) and ( [ gyu ] ) one can rewrite @xmath81 as @xmath82 where @xmath83 \label{aijused}\end{aligned}\ ] ] in eq . ( [ aijused ] ) we have used for @xmath84 and @xmath85 respectively @xmath86 \label{wavesixq}\ ] ] @xmath87 \label{wavesixu}\ ] ] which correspond to a vev @xmath88 with @xmath89 . as pointed out in ref . @xcite , @xmath90 is now a generic symbol for the length of the physical space , which is @xmath91 for the orbifold @xmath92 . from eq . ( [ syukeff6 ] ) one obtains the mass matrix @xmath93 following ref . @xcite , if one now uses the linear approximation for the kink , which is valid for @xmath94 , all domain wall thiknesses along @xmath65 are of the size of the compact dimension , one can obtain for the elements @xmath95 the form @xmath96 with @xmath97 and @xmath98 . in the linear approximation for the kink one obtains the following expressions for @xmath95 @xmath99 \ , , \ ] ] where @xmath100 @xmath101 as shown in ref . @xcite , one can explicitly carry out the integration and obtain @xmath102 now if @xmath103 and @xmath104 one can expand eq . ( [ aij ] ) giving @xmath105 which has the desired almost - ppmm form . it has to be stressed here that the expression for the mass matrix" +"the aim of this paper is to investigate an optimal stopping problem under partial observation for piecewise - deterministic markov processes ( pdmp ) both from the theoretical and numerical points of view . pdmp s have been introduced by davis @xcite as a general class of stochastic models . they form a family of markov processes involving deterministic motion punctuated by random jumps . the motion depends on three local characteristics , the flow @xmath1 , the jump rate @xmath2 and the transition measure @xmath3 , which selects the post - jump location . starting from the point @xmath4 , the motion of the process @xmath5 follows the flow @xmath6 until the first jump time @xmath7 , which occurs either spontaneously in a poisson - like fashion with rate @xmath8 or when the flow hits the boundary of the state space . in either case , the location of the process at @xmath7 is selected by the transition measure @xmath9 and the motion restarts from @xmath10 . we define similarly the time until the next jump and the next post - jump location and so on . one important property of a pdmp , relevant for the approach developed in this paper , is that its distribution is completely characterized by the discrete time markov chain @xmath11 where @xmath12 is the @xmath13-th post - jump location and @xmath14 is the @xmath13-th inter - jump time . a suitable choice of the state space and local characteristics provides stochastic models covering a large number of applications such as operations research @xcite , reliability @xcite , neurosciences @xcite , internet traffic @xcite , finance @xcite . this list of examples and references is of course not exhaustive . in this paper , we consider an optimal stopping problem for a partially observed pdmp @xmath5 . roughly speaking , the observation process @xmath15 is a point process defined through the embedded discrete time markov chain @xmath11 . the inter - arrival times are given by @xmath16 and the marks by a noisy function of @xmath17 . for a given reward function @xmath18 and a computation horizon @xmath19 , we study the following optimal stopping problem @xmath20,\ ] ] where @xmath21 is the @xmath22-th jump time of the pdmp @xmath5 , @xmath23 is a stopping time with respect to the natural filtration @xmath24 generated by the observations @xmath15 . in some applications , it may be more appropriate to consider a fixed optimization horizon @xmath25 rather than the random horizon @xmath21 . this is a difficult problem with few references in the literature , see for instance @xcite where the underlying process is not piecewise deterministic . regarding pdmp s , this problem could be addressed using the same ideas as in @xcite . it involves the time - augmented process @xmath26 . although this process is still a pdmp , its local characteristics may not have the same good properties as those of the original process leading to several new technical difficulties . a general methodology to solve such a problem is to split it into two sub - problems . the first one consists in deriving the filter process given by the conditional expectation of @xmath27 with respect to the observed information @xmath28 . its main objective is to transform the initial problem into a completely observed optimal stopping problem where the new state variable is the filter process . the second step consists in solving this reformulated problem , the new difficulty being its infinite dimension . indeed , the filter process takes values in a set of probability measures . our work is inspired by @xcite which deals with an optimal stopping problem under partial observation for a markov chain with finite state space . the authors study the optimal filtering and convert their original problem into a standard optimal stopping problem for a continuous state space markov chain . then they propose a discretization method based on a quantization technique to approximate the value function . however , their method can not be directly applied to our problem for the following main reasons related to the specificities of pdmps . firstly , pdmps are continuous time processes . although the dynamics can be described by the discrete - time markov chain @xmath11 , this optimization problem remains intrinsically a _ continuous - time _ optimization problem . indeed , the performance criterion is maximized over the set of stopping times defined with respect to the _ continuous - time _ filtration @xmath29 . consequently , our problem can not be converted into a fully discrete time problem . secondly , the distribution of a pdmp combines both absolutely continuous and singular components . this is due to the existence of forced jumps when the process hits the boundary of the state space . as a consequence the derivation of the filter process is not straightforward . in particular , the absolute continuity hypothesis * ( h ) * of @xcite does not hold . thirdly , in our context the reformulated optimization problem is not standard , unlike in @xcite . as already explained , this reformulated optimization problem combines _ continuous - time _ and _ discrete - time _ features . consequently , this problem does not correspond to the classical optimal stopping problem of a discrete - time markov chain . moreover , it is different from the optimal stopping problem of a pdmp under complete observation mainly because the new state variables given by the markov chain @xmath30 are not the underlying markov chain of some pdmp . therefore the results of the literature @xcite can not be used . finally , a natural way to proceed with the numerical approximation is then to follow the ideas developed in @xcite namely to replace the filter @xmath31 and the inter - jump time @xmath14 by some finite state space approximations in the dynamic programming equation . however , a noticeable difference from @xcite lies in the fact that the dynamic programming operators therein were lipschitz continuous whereas our new operators are only lipschitz continuous between some points of discontinuity . we overcome this drawback by splitting the operators into their restrictions onto their continuity sets . this way , we obtain not only an approximation of the value function of the optimal stopping problem but also an @xmath0-optimal stopping time with respect to the filtration @xmath29 that can be computed in practice . our approximation procedure for random variables is based on quantization . there exists an extensive literature on this method . the interested reader may for instance consult @xcite and the references within . the quantization of a random variable @xmath32 consists in finding a finite grid such that the projection @xmath33 of @xmath32 on this grid minimizes some @xmath34 norm of the difference @xmath35 . roughly speaking , such a grid will have more points in the areas of high density of @xmath32 . as explained for instance in @xcite , under some lipschitz - continuity conditions , bounds for the rate of convergence of functionals of the quantized process towards the original process are available , which makes this technique especially appealing . quantization methods have been developed recently in numerical probability or optimal stochastic control with applications in finance , see e.g. @xcite . the paper is organized as follows . section [ section - def ] introduces the notation , recalls the definition of a pdmp , presents our assumptions and defines the optimal stopping problem we are interested in , especially the observation process . the recursive formulation of the filter process is derived in section [ section - filtre ] . in section [ section - dynamic ] , we reduce our partially observed problem for the pdmp @xmath5 to a completely observed one involving the process @xmath36 for which we provide the dynamic programming equation and construct a family of @xmath0-optimal stopping times . then , our numerical methods to compute the value function and an @xmath0-optimal stopping time are presented in section [ section - quantif ] where we also prove the convergence of our algorithms after having recalled the main features of quantization . finally , an academic example is discussed in section [ section - example ] while technical results are postponed to the appendices . in this first section , let us define a piecewise - deterministic markov process ( pdmp ) and introduce some general assumptions . for any metric space @xmath37 , we denote @xmath38 its borel @xmath23-field , @xmath39 the set of real - valued , bounded and measurable functions defined on @xmath37 and @xmath40 the subset of functions of @xmath39 that are lipschitz continuous . for @xmath41 , denote @xmath42 and @xmath43 . let @xmath37 be an open subset of @xmath44 . let @xmath45 be its boundary and @xmath46 its closure and for any subset @xmath47 of @xmath37 , @xmath48 denotes its complement . a pdmp is defined by its local characteristics @xmath49 . * the flow @xmath50 is continuous . for all @xmath51 , @xmath52 is an homeomorphism and @xmath53 is a semi - group : for all @xmath54 , @xmath55 . for all @xmath56 , define the deterministic exit time from @xmath37 : @xmath57 we use here and throughout the convention @xmath58 . * the jump rate @xmath59 is measurable and satisfies : @xmath60 * finally , @xmath3 is a markov kernel on @xmath61 which satisfies : @xmath62 from these characteristics , it can be shown @xcite that there exists a filtered probability space @xmath63 on which a process @xmath64 is defined . its motion , starting from a point @xmath65 , may be constructed as follows . let @xmath66 be a nonnegative random variable with survival function : @xmath67 where for @xmath65 and @xmath68 $ ] , @xmath69 one then chooses an @xmath37-valued random variable @xmath70 with distribution @xmath71 . the trajectory of @xmath72 for @xmath73 is : @xmath74 starting from the point @xmath75 , one selects in a similar way @xmath76 the time between @xmath7 and the next jump time @xmath77 , as well as @xmath78 the next post - jump location and so on . davis showed @xcite that the process so defined is a strong markov process @xmath79 with jump times @xmath80 ( @xmath81 ) . the process @xmath82 where @xmath83 is the @xmath13-th post - jump location and @xmath84 ( @xmath85 ) is the @xmath13-th inter - jump time is clearly a discrete - time markov chain . the following non explosion assumption about the jump - times is standard ( see for example @xcite ) . [ hyp - tk_goes_to_infty ] for all @xmath86 , @xmath87<+\infty$ ] . it implies that @xmath88 a.s . when @xmath89 . moreover , we make the following assumption about the transition kernel @xmath3 . we assume that there exists a finite set @xmath90 such that for all @xmath65 , one has @xmath91 . in other words , for all @xmath92 , @xmath12 may only take its values in the finite set @xmath93 . this assumption ensures that the filter process , defined in the next section , has finite dimension . this is required to derive a tractable numerical method in section [ section - quantif ] . when this assumption does not hold , one may consider a preliminary discretization of the transition kernel to introduce it . [ hyp - ts - bounded ] we assume that the function @xmath94 is bounded on @xmath93 i.e. for all @xmath95 , we assume that @xmath96 . [ def - ts - order ] for all @xmath95 , denote @xmath97 and assume that @xmath98 , , @xmath99 are numbered such that @xmath100 @xmath101 . moreover , let @xmath102 . for any function @xmath103 in @xmath39 , introduce the following notation @xmath104 for any lipschitz continuous function @xmath103 in @xmath40 , denote @xmath105 $ ] its lipschitz constant @xmath106=\sup_{x\neq y \in e}\frac{|w(x)-w(y)|}{|x - y|}.\ ] ]" +"nova outbursts are thermonuclear runaway events on white dwarfs . depending on the binary parameter such as the mass accretion rate , composition of the envelope and the white dwarf mass , nova outbursts shows a wide variety of the recurrence period , its light curve , the duration time and expanding speed of gaseous matter and so on . classical nova shows enhancement of carbon and oxygen or other white dwarf material in its ejecta . the recurrence period is as long as ten thousand of years or so and we can observe only one outburst for one nova binary . on the other hand , recurrent novae repeat outbursts every several to several - tens of years and its ejecta shows no enhancement of white dwarf material . after the onset of shell flash , the white dwarf rapidly brightens up and the envelope greatly extend to a giant size and the strong wind mass - loss begins to blow the envelope mass . after the star reaches the optical maximum the photospheric radius reduces with increasing effective temperature , which causes the decay of visual light curve . the mass loss during nova outburst is a radiation - driven wind which is accelerated deep inside the photosphere ( friedjung 1966 ) . such a wind is called as the optically thick wind . the decay phase of nova outbursts is followed by a quasi - evolution theory ( summarized in kato & hachisu 1994 ) which is to make a sequence of optically thick wind solutions of expanding envelope . figure 1 ( left ) shows the run of the opacity throughout an envelope of a classical nova model . the opal opacity has a strong peak owing to iron lines at @xmath1 which locates deep inside the photosphere . this opacity peak blocks radiative flux to accelerate the wind mass - loss . as shown in the right figure the wind velocity increases quickly at the temperature region corresponding to this opacity peak . the wind velocity already reaches the terminal velocity at the photosphere . in the optically thick wind the mass - loss rate is very large , because the acceleration occurs deep inside where the density is high . it is naturally understood that the velocity and the mass - loss rate of winds are larger for larger metallicity , i.e. , larger in population i than in population ii novae . the evolutionary course of the decay phase in h - r diagram is plotted in figure 2 . the decay phase of the classical nova and the recurrent nova with different composition is similar to the curves in figure 2 ( see kato 1997 for classical novae , kato 1999 for recurrent novae ) . at the optical peak the star reaches the maximum radius which point locates somewhere in the right side of each curve . as the strong wind blows out the envelope mass , the photospheric radius moves inward and the effective temperature rises , thus the star moves leftward . the wind mass - loss occurs in the dashed parts . after the wind stops , the star still goes leftward until nuclear burning extinguishes at the small dot . in less massive stars , the acceleration is not enough to cause the optically thick wind . in massive white dwarfs , the evolutionary speed is short mainly because of the small envelope mass which is blown off within a short time by the wind . therefore , the nova outburst is fast in massive white dwarfs and slow in less massive stars . in a lowest limit of white dwarfs , the acceleration is weak to cause the optically thick wind . the wind acceleration also depends on the metallicity as shown in the left figure . the larger iron content , the stronger peak of the opacity that causes a strong wind . in @xmath2 , shell flashes do not occur or very weak in @xmath3 white dwarf for classical novae , and @xmath4 for recurrent / symbiotic novae . in @xmath5 , shell flashes do not occur or very weak in @xmath6 for classical nova , and @xmath7 for recurrent / symbiotic nova . the decay phase of nova outburst is followed by the optically thick wind theory . the method of light curve fitting of nova is firstly established in nova cygni 1978 ( kato 1994 ) . the wind mass - loss rate depends strongly on the white dwarf mass , therefore , we can determine the white dwarf mass from the light curve fitting . in case of nova cygni 1978 , the two independent fittings of optical and uv light curves give the same values of white dwarf mass of @xmath8 and the distance to the star . nova cygni 1978 is a moderately fast nova . more rapid evolution is predicted only in more massive white dwarfs . light curve fittings of several classical novae show a fast classical nova corresponds to a very massive white dwarf ( @xmath9 ) , moderately classical nova such as nova cyg 1978 , correspond a moderately massive white dwarf ( @xmath10 ) , and slow evolution of slow novae , the less massive white dwarf(@xmath11 for nova mus 1985 ) . it is very interesting that the fastest limit of classical nova corresponds to the massive limit of the white dwarf , and the slowest one the lowest limit . recurrent nova and symbiotic nova can be treated as a same subgroup of nova , that shows no white dwarf material enhancement . the difference between the two is in the white dwarf mass and the contribution of the companion and the accretion disk . the similar relation to classical nova , i.e. , the relation between the evolutionary speed of light curves and white dwarf mass , also stands in these novae . most rapid evolution of some recurrent novae corresponds very massive white dwarf close to the upper limit ( @xmath12 as shown above ) and slow evolution the moderately massive white dwarfs ( e.g. , @xmath13 for t pyx ) . very long duration of some symbiotic novae corresponds low - mass white dwarfs ( @xmath14 for symbiotic nova rx pup ) . using binary models composed by a white dwarf , an accretion disk and a companion , we have calculated theoretical light curve of recurrent novae . in the first phase , the envelope largely expand to about several tens of the binary size , and the companion are deeply embedded by the envelope . as the strong wind carries away most of the expanding envelope , the photospheric radius moves inward , and in the later phase , we can see the companion and the accretion disk again . the early phase of the light curve is determined by the wind mass - loss rate . in the following plateau phase the accretion disk and the partly irradiated companion contribute the visual magnitude . therefore , in this stage , we have calculated visual flux summing up of three component , of the white dwarf photosphere , the irradiated accretion disk , and the partly irradiated companion that is shadowed by the accretion disk . we divided their surfaces into 9000 small areas and calculated emission flux from each areas to sum up . the recurrent nova u sco , v394 cra , ci aql , and v2487 oph are members of the subclass of u sco type that have a slightly - evolved main - sequence companion . u scorpii is one of the well observed recurrent novae , characterized by the shortest recurrence period @xmath15 yr , the fastest decline of its light curve 0.6 mag per day , its extremely helium - rich ejecta he / h@xmath16 by number . the latest outburst in 1999 was well observed from the rising phase to the cooling phase by many observers including eclipses which provide us a unique opportunity to construct a comprehensive model for u sco during the outburst . we have reproduced the light curves by binary model as shown in figure 3 . to fit the early linear decay phase ( @xmath17 days after maximum ) , we have calculated total 140 @xmath18-magnitude light curves with various wd mass , hydrogen content the envelope , where the heavy element content @xmath19 is fixed , and companion mass . we choose @xmath20 as a limiting mass just before the sn ia explosion in w7 model ( @xmath21 ) of nomoto , thielemann , & yokoi ( 1984 ) . the early 7 days light curve hardly depends on the chemical composition or the companion mass but mainly depends on the white dwarf mass . the @xmath22 light curve is in much better agreement with the observations than the other wd masses . in the middle plateau phase , the irradiated accretion disk mainly contributed to @xmath18 light , because the white dwarf photosphere shrinks to a small size and shadowed by the accretion disk . to fit the cooling phase ( @xmath23 days after maximum ) , we must adopt very small hydrogen content of @xmath24 among other values . this is because the hydrogen content , @xmath25 , determines the period of hydrogen steady shell burning , i.e. , the period of the mid - plateau phase . in our model , the optically thick wind stops at @xmath26 days , and the steady hydrogen shell - burning ends at @xmath27 days . in the evolutional course of the outburst , the visual magnitude drops and uv and soft x - ray fluxes increases . it is because the photospheric temperature increases after the optical peak , because the main emitting region moves blueward ( to uv then to soft x - ray ) . this picture is very consistent with the bepposax supersoft x - ray detection @xmath28 days after the optical peak ( kahabka , et al . in the strong wind phase we can not expect much of supersoft x - rays because of self - absorption by the wind itself . in this way , the light curve fitting gives us an estimate for binary parameters , such as the white dwarf mass and chemical composition of the envelope , and if orbital period is available , we further know the mass transfer rate and the growth rate of the white dwarf mass . v394 cra is a twin system that shows very similar light curves . in the same way as in u sco , we have reproduced light curve of v394 cra and determined the white dwarf mass to be 1.37 @xmath0 and @xmath24 with @xmath19 as shown in figure 4 ( hachisu & kato 2000b ) the light curve analysis of ci aql and v2487 oph is separately reported in detail in this conference proceedings ( hachisu et al . for v2487 oph , hachisu & kato for ci aql ) . the white dwarf mass of these two recurrent novae are also massive , 1.2 @xmath0 for ci aql and 1.35 @xmath0 for v2487 oph . rs oph , t crb , v745 sco and v3890 sgr are a subclass of recurrent nova with a red giant companion . as the companion substantially contributes the light curve in later phase , we have calculated huge number of binary models with different parameters and choose a configuration which gives the best fitted light curve . figure 5 ( left ) shows the binary configuration of t crb selected in this way . the cool component ( right ) is a red giant filling up its inner critical roche lobe . its hemisphere is heated up by the hot component ( @xmath29 white dwarf , left ) . the surface of the accretion disk is also heated up . the light curve fitting is shown in" +"stars form in dense and cool molecular clouds . when the local density is high enough , the matter can gravitationally collapse and form a young stellar object ( yso ) . in the early phases , the thick envelope dominates the emission from the yso and hides what is going on within ( class i ) . eventually , the envelope flattens out to a circumstellar accretion disk . this disk still causes an infrared ( ir ) excess above the level of a stellar photosphere ( class ii or classical t tauri star - ctts ) , which can be used to distinguish those objects from main - sequence stars , for example using the _ spitzer _ space telescope @xcite infrared array camera ( irac , * ? ? ? * ) . when the disk is cleared , the ir colors of the yso match those of main - sequence stars ( class iii or weak - lined t tauri star - wtts ) . in addition to the circumstellar absorption , many ysos are embedded in the molecular cloud , so that even class iii objects can appear reddened . the accretion disk does not reach down to the central star . instead , the inner edge of the gas disk is truncated by the stellar magnetic field . the inner radius of the optically thick dust in the disk is larger than the inner radius of the gas disk and mostly given by the dust - sublimation temperature . some of the mass in the circumstellar disk condenses into planets , some is blown out by accretion - driven disk and stellar winds , and is accreted onto the central star . this accretion can happen via magnetically confined accretion funnels ( e.g. , * ? ? ? * ) or via some magneto - hydrodynamical instability ( e.g. , * ? ? ? t tauri stars ( tts ) were originally identified by their variability @xcite long before anybody realized that tts are indeed pre - main sequence stars . the dominant timescale in the optical is the stellar rotation period , typically a few days to a week or more . ysos can have cool spots caused by magnetic activity similar to our sun and also hot spots which mark the impact points of the accretion funnels onto the stellar surface ( see , e.g. , review by * ? ? ? this impact happens at free - fall velocities up to 500 km s@xmath1 ; thus , the accretion shock heats the accreted mass to x - ray emitting temperatures . in the optical , the accretion region appears as emission that often is approximated as a blackbody with temperature @xmath2 k ( @xcite , but see also @xcite who argue that line emission contributes to the veiling in addition to a continuum ) . variability in the mass accretion rate can lead to changes in the hot spot signatures . the dynamical timescale that controls the accretion is the keplerian period of the inner disk where the accretion funnels start . the inner disk radius is found close to the co - rotation radius leading to a typical timescale of a few hours for typical masses and rotation periods of ysos . indeed optical variability with amplitudes around 0.1 mag is often observed in ctts on this timescale @xcite . another source of variability related to the accretion could be oscillations of the accretion shock on timescales of seconds . this has been predicted theoretically ( e.g. , * ? ? ? * ) , but is not observed so far , possibly because the accretion spot separates into many small funnels that oscillate independently at different phases and frequencies . however , @xcite find indications that strong accretion in v1647 ori could excite radial pulsations of the star itself . one of the largest classes of short timescale ( @xmath3 days ) optical and ir variability in ysos is that due to variable extinction events @xcite . these come in three categories - aa tau - type variables ( stars with broad , periodic flux dips , whose amplitudes can be up to a magnitude or more in the optical ) , presumably due to our line of sight passing through a warp in the inner circumstellar disk ; stars with similar or narrower flux dips that have no obvious periodicity - presumably due to stars where our line of sight passes close to the disk and where disk instabilities can levitate dust high enough above the plane to intersect our line of sight briefly ; and stars with narrow , periodic flux dips - perhaps where our line of sight is being intersected by dust entrained in material accreting onto the star in a funnel flow . about 20% of the ysos in ngc 2264 fall into one of these categories in the sample of @xcite . ysos can also vary on much longer timescales . variability on the timescales of years could be caused by changing circumstellar extinction for a keplarian disk around a solar - mass yso this timescale translates to a radius of a few au ) or by massive accretion events when a significant fraction of the disk mass drains onto the yso @xcite . in this case the accretion luminosity can outshine the yso by orders of magnitudes and it takes months to years ( in the case of exor outbursts , * ? ? ? * ) or even centuries until the accretion decays back down to the original level . in any lightcurve , several of the processes dicussed above can contibute to the observed variability at the same time and it depends on the properties of each object which one dominates and if secondary effects can be detected in the lightcurve . for example , cool spots , hot spots , absorption , and massive accretion events can all influence the same optical light curve . another case are x - rays , where the flux and the spectrum can change due to periodic absorption , variability in the accretion rate ( tw hya , * ? ? ? * ) or coronal activity similar to what is seen on the sun . in most ysos , the last point is dominant and x - ray lightcurves often show the fast rise in flux and temperature and a slower decay characteristic of coronal activity ( see , e.g. , the _ chandra _ monitoring of the orion nebular cluster , * ? ? ? * ; * ? ? ? * ) . the spectral energy distribution ( sed ) of ysos in the optical is dominated by the stellar photosphere and the accretion spot . thus , optical monitoring is very effective for understanding the stellar rotation and the accreting spot . however , the disk radiates mostly at longer wavelengths , which are probed in the ir observations presented in this article . depending on the mass of the disk and the size of the inner hole , the disk will start to dominate the sed at the @xmath4 band or in the irac bands at @xmath5 m and @xmath6 m . simple disk models still treat the disk as a static and axisymmetric structure , but observationally it now seems that the disk is in fact `` a bubbling , boiling , wrinkled , dented , warped mass of gas and dust '' @xcite , see also @xcite . this paper is part of the ysovar ( young stellar object variability ) project , which has monitored the ( onc ) and eleven smaller star forming regions with irac in @xmath5 m and @xmath6 m to understand the mid - ir variability of ysos . first results on the onc are published in @xcite . more details of the observing strategy and an overview of the data can be found in @xcite ( from now on `` paper i '' ) . comparing data from all clusters , paper i defines certain cut - off values for the data reduction , e.g. how much variability in a lightcurve is required to reliably identify an object as variable . in the analysis , paper i concentrates on variability in the ir on timescales of years . in this article , we present a _ spitzer_/irac monitoring campaign of the star forming region l1688 in the mid - ir to characterize the variability timescales and amplitudes as well as the color changes in the mid - ir in much more detail for the objects in l1688 than paper i on timescales up to two years . the structure of this paper is as follows : first , we introduce l1688 , the star forming region targeted by these observations ( section [ sect : thestarformingregionl1688 ] ) . in section [ sect : observationsdatareductionandauxiliarydata ] we introduce the data reduction and discuss source lists and stellar properties obtained from the literature . section [ sect : midirvariability ] classifies all sources according to their variability . section [ sect : resultsanddiscussion ] presents our results and discusses physical models to explain the observed features in the lightcurves . we end with a summary and some conclusions in section [ sect : summary ] . lynds 1688 ( l1688 ) is a sub - cloud of the @xmath7 ophiuchus star forming region , one of the best - studied young clusters in the sky ( see e.g. review by * ? ? ? the central region of l1688 is very dense and deeply embedded ( @xmath8 mag , see figure [ fig : map ] ) . thus , all surveys of the regions necessarily miss some cluster members . an extinction limited , spectroscopic survey @xcite finds an average age of 3.1 myr for a 6.8 pc@xmath9 region centered on l1688 and no significant deviation from the initial mass function . earlier studies concentrated on the deeper embedded core and found a much younger age of 0.3 myr . some , but not all , of this difference is due to the specific reddening laws or pre - main sequence evolutionary tracks used in these studies ( see discussion in * ? ? ? @xcite present photometric and spectroscopic monitoring for five ysos in l1688 nearly simultaneous with the _ spitzer _ observations discussed here . they do not see any correlation between the hydrogen emission lines that are usually considered accretion indicators and the features in the ir lightcurves of their targets , indicating that the relatively modest variability they observed is not caused by changes in the accretion rate . additional notable objects with well - sampled nir lightcurves are @xcite and , which show eclipses with periods of 131 and 93 days , respectively . these sources can be interpreted as multiple systems , where one or more components are eclipsed by a warped circumstellar disk . thus far , the most comprehensive study of near - ir variability of ysos in l1688 is @xcite ( see references therein for other ir variability studies ) , who make use of a two micron all sky survey ( 2mass * ? ? ? * ) calibration field that overlaps l1688 so each source has up to 1584 datapoints in @xmath10 , @xmath11 , and @xmath4 spanning 2.5 years . they find 79% of the known ysos to be variable . in total , 32 sources are periodic ( including cool starspots , hot accretion spots and 6 systems with eclipses ) , 31 sources show a long - term trend and 40 sources vary aperiodically on shorter timescales . the new data presented in this article complements the @xcite study with observations at longer wavelengths . in this section we briefly describe the data reduction for the _ spitzer _ and _ chandra _ observations . a" +"chaos in ordinary language means disorder , randomness , absence of law , and unpredictability . it played the major role in philosophy of ancient greeks . already empedocles ( cca.490430 b.c . ) viewed the real world , , as a combination of the world of perfect order , ( today we may tentatively translate it as ) , and the world of complete disorder , . since chaos seemed to be too elusive for any kind of rigorous description , the attention of science has for long been focused only to sphairos . this has changed over the past decades when numerous explorations have shown that chaos is not as lawless as originally thought . at present , the term _ chaos theory _ belongs to the common speak @xcite . in both classical and quantum physics @xcite is built on very sophisticated mathematics . it sticks on the original idea of randomness , but at the same time it creates a new type of universality in the representation of reality . the universality of chaos is based on ergodic character of motions and implies high efficiency of the statistically oriented description . since majority of systems in nature are chaotic , at least to a considerable extent , this type of description is often the ultimate one . the routes to more deterministic descriptions may exist but they are usually impassable . chaos thus belongs to very fundamental subjects in physics . among the physical systems that materialize the signatures of chaos in nature , an important place is held by atomic nuclei . already the fact that even more than 80 years after the discovery of their composition we are not able to present a satisfactory microscopic theory of nuclear structure is a good reason to think that nuclei are indeed chaotic objects par excellence . it is not an accident that nuclei were at dawn of the field named quantum chaos . however , atomic nuclei not only show well recognized signs of chaos , they also provide a variety of models that can be used to better understand the rules of chaos in a more general context . such a path is followed in this text . our aim is not to draw an exhaustive map of the overlap between physics of chaos and physics of nuclei such reviews exist @xcite and we may only recommend to read them . instead , we want to make a passage through selected topics of classical and quantum chaos using models taken from the description of nuclear collective dynamics . before diving into the ocean of chaos , we have to briefly introduce the models we will be playing with . these are the old ( and the good ) geometric collective model ( below abbreviated as gcm ) and the newer and more sophisticated interacting boson model ( ibm ) of nuclei . both these models attempt to describe nuclear collective motions vibrations and rotations assuming only the quadrupole type of nuclear deformations . the number of degrees of freedom associated with both gcm and ibm is five . two degrees of freedom correspond to the quadrupole deformation of the nucleus in the body - fixed frame ( one can think of an ellipsoid with a fixed volume ) ; their dynamics therefore represents vibrational motions . the other three degrees of freedom correspond to the orientation of the whole nucleus in the laboratory frame they describe rotations . in the following we will mostly consider only the non - rotational case , i.e. , fix the angular momentum ( which is an integral of motions ) to zero . in this case , we will be left just with two vibrational degrees of freedom , opening a direct link to other @xmath0 systems famously studied in the context of chaos . we will see that nuclear vibrations represent a rather rich specimen of chaos in two dimensions . the gcm , introduced already in 1952 by a.bohr ( for the review see @xcite ) , treats the nucleus as structureless drop described by quadrupole shape variables @xmath1 and rotation euler angles @xmath2 . these 5 generalized coordinates are associated with a particular parametrization of the rank-2 tensor @xmath3 ( real , symmetric , and traceless in the cartesian form ) , describing the quadrupole deformation of the nucleus in the laboratory frame . the deformation tensor @xmath3 can be introduced via the expansion of the nuclear radius @xmath4 to spherical harmonics @xmath5 , or alternatively via multipole moments of the nuclear mass ( charge ) distribution @xmath6 . in the first case , the @xmath7 spherical component of the deformation tensor ( @xmath8,@xmath9,@xmath10 ) is associated with the coefficient ( up to complex conjugation ) at the @xmath11 term of the radius expansion . in the second case , the deformation tensor is obtained via the following integral ( up to a scaling factor ) of the mass ( charge ) density : @xmath12 . any variables describing the shape of the nucleus must be invariant under rotations of the nucleus as a whole . there are just two independent building blocks for all rotational invariants made of the quadrupole deformation tensor namely the quadratic and cubic couplings of the quadrupole tensor to zero total angular momentum . the shape variables @xmath13 and @xmath14 can be defined as a certain parameterization of these two elementary couplings:^{(\lambda)}$ ] of rank-@xmath15 and -@xmath16 spherical tensors @xmath17 and @xmath18 to the resulting spherical tensor of rank @xmath19 ( the definition is analogous to the elementary angular momentum coupling ) . scalar product of spherical tensors is defined for @xmath20 as @xmath21^{(0)}$ ] . ] @xmath22^{(0)}=\tfrac{1}{\sqrt{5}}\ \beta^2 \ , \qquad [ [ \alpha^{(2)}\times\alpha^{(2)}]^{(2)}\times\alpha^{(2)}]^{(0)}=-\sqrt{7}\ \beta^3\cos 3\gamma \label{bega } \,.\ ] ] alternatively , @xmath13 and @xmath14 can be derived from the eigenvalues of @xmath3 , which read as @xmath23 $ ] , @xmath24 , @xmath25\bigr)$ ] . these values are the only components of the deformation tensor in the intrinsic frame ( if ) of the nucleus ( the frame connected with the principal axes of the quadrupole deformation ) , where the deformation tensor is diagonal . the transformation between the if and laboratory frame ( lf ) is expressed in terms of the euler angles @xmath2 , describing the orientation of the deformed nucleus in lf . ) with the same choice of parameters . adapted from ref.@xcite . ] note that @xmath1 can be considered as radial coordinates in the cartesian plane @xmath26 . while the radius @xmath13 quantifies the degree of deformation of the nucleus ( @xmath27 for spherical shape ) , the angle @xmath14 parameterizes the type of the deformed shape . the plane is divided into six equivalent angular sectors , which follow from an inherent discrete symmetry of the problem , given by the dynamical equivalence of three possible orientations of the deformed shape in the if ( along @xmath28 ) and two deformation types ( prolate , oblate ) . the @xmath29 , @xmath30 , and @xmath31 axially symmetric prolate or oblates shapes are located at @xmath14 equal to @xmath32 , @xmath33 , and @xmath34 , respectively , while the intermediate @xmath14 values correspond to the related triaxial shapes . note that these conclusions are consistent with the above - given form of the deformation tensor in the intrinsic frame . to become more familiar with the formalism ( which , as one has to agree , looks rather tough as the first sight ) , the reader is encouraged to consult specialized literature , e.g. , ref.@xcite . the plane of deformation coordinates with the basic sample of shapes is depicted in fig.[begafi ] . the momenta associated with the coordinates @xmath13 and @xmath14 are denoted as @xmath35 and @xmath36 , respectively . in the non - rotational case , as noted above , the euler angles @xmath2 are fixed , rendering zero values of the associated rotational momenta . the resulting vibrational hamiltonian therefore contains just the shape variables @xmath1 and the corresponding momenta @xmath37 . our analysis is performed mostly with the hamiltonian which contains purely quadratic momentum term of the kinetic energy , and quadratic , cubic and quartic coordinate terms of the potential energy : @xmath38}_{t_{\rm vib}}+\underbrace{a\beta^2+b\beta^3\cos 3\gamma+c\beta^4}_{v_{\rm vib}}\ , . \label{hgcm}\ ] ] @xmath39 and @xmath40 are adjustable parameters satisfying physical constraints @xmath41 ( kinetic energy is positive ) and @xmath42 ( the potential is confining ) . the geometric hamiltonian ( [ hgcm ] ) is closely related to the famous hnon - heiles hamiltonian , which was originally introduced in the context of stellar dynamics in galaxies and became a paradigmatic example of chaos in the classical domain @xcite . the hnon - heiles hamiltonian is a special case of eq.([hgcm ] ) with @xmath43 . in this contribution ( as in ref.@xcite ) we claim that the inclusion of the confining @xmath44 term generates even much richer structures than those obtained in the @xmath43 case . the coexistence of regular and chaotic types of classical motions generated by the full geometric hamiltonian at high energies is illustrated in fig.[begafi ] . the two trajectories shown in this figure were calculated for the same model parameters and energy , but represent very dissimilar species of collective motions . the regular orbit corresponds to a moderate , highly organized vibration , localized in a relatively small region around an axially symmetric equilibrium shape ( above the potential well to which the nucleus with given parameters drops in the low energy limit ) . in contrast , the chaotic orbit represents some large - amplitude vibrations , which rather disorderly wander through small , medium and large oblate deformations with all three intrinsic orientations . a generalization of the simple hamiltonian ( [ hgcm ] ) can be achieved by considering higher - order terms in kinetic or potential energy . we consider two extensions of the kinetic energy , particularly @xcite : @xmath45 \,,\qquad t_{\rm vib}^{(ii)}=\frac{1}{2m(1+\kappa\beta^2)}\left[p_\beta^2+\left(\frac{p_\gamma}{\beta}\right)^2\right ] \ , , \label{halt}\ ] ] both based on some specific deformation - dependent effective mass ( @xmath46 is an additional model parameter ) . such or similar extensions of the effective mass are relevant for the description of nuclear rotational bands since they modify the behavior of nuclear moments of inertia . here we consider them to probe the sensitivity of the vibrational measures of chaos to the general form of the hamiltonian kinetic term . another extension of the above hamiltonian is the inclusion of rotational terms , containing the intrinsic components of angular momentum and the corresponding moments of inertia . this however leads beyond the 2d description and makes the analysis much more difficult . we follow this line only in rather a restricted manner considering only rotations around a fixed axis @xmath31 @xcite . this can be done by introducing a third collective coordinate , angle @xmath47 , and the associate momentum @xmath48 , which coincides with the angular momentum of the nucleus around @xmath31 in both laboratory and intrinsic frames . the quadrupole deformation tensor @xmath49 in the laboratory frame is obtained from the diagonal form @xmath50 in the intrinsic frame ( see above ) via rotation by angle @xmath51 around the @xmath31-axis . this identifies @xmath47 as a variable connected with the if @xmath52 lf transition . the rotational energy reads as : @xmath53 which has to be added to the vibrational hamiltonian in eq.([hgcm ] ) to get the total hamiltonian @xmath54 . details can be found in ref.@xcite . an important feature of the geometric hamiltonian is related to its scaling properties the fact that dynamics of the system must be invariant under scale transformations affecting the units of relevant quantities , i.e. , energy , coordinate , and momentum . let us return now to the bare vibrational hamiltonian ( [ hgcm ] ) . since the scale" +"understanding the physics of the hubbard model continues to be a fundamental issue in strongly correlated systems . this model captures the transition between a metallic state and a correlated insulator ; how this transition takes place has been investigated by many workers in the past , with differing approaches emphasizing the formation of hubbard bands , @xcite the increasing mass of the quasiparticles @xcite and the proximity to antiferromagnetism . @xcite significant progress has been made in recent years by the development of dynamical mean - field theory ( dmft ) . @xcite here a set of equations exact in the limit of infinite dimensions is derived which maps the problem onto an interacting impurity model to be solved self - consistently . this method has revealed a mott transition that is a synthesis of the pictures of mott and brinkman rice : formation of hubbard bands in parallel with a large mass quasiparticle . the absence of momentum dependence in correlations within dmft means that this method does not account for variations in quasiparticle properties across the brillouin zone . this is likely to be important if the mott transition has an antiferromagnetic aspect . building on the success of dynamical mean - field theory , extensions to the theory are being actively studied . one such extension combines it with density - functional theory to improve the treatment of local correlations . @xcite another considers intersite correlations via so called cluster dmft . @xcite it is also often important to include multiple local orbitals when modeling real materials such as the correlated oxides . in all of these extensions the task of solving the resulting self - consistent equations becomes increasingly problematic : the equations require the solution of impurity models with an increasing number of local degrees of freedom , which often demand high - performance computing resources and sophisticated approximation schemes to extract the low energy physics . yet in contrast to these computationally intensive approaches , potthoff @xcite demonstrated that much of the mott transition physics could be captured with a drastic approximation of the non - interacting bath of electrons that couples to the impurity in dmft . whereas in one computational scheme for tackling the dmft equations , the bath is modeled by up to twelve coupled sites ( the exact diagonalization method @xcite ) , potthoff used just a single site to represent the bath . the self - consistency conditions were constructed to ensure that the quasiparticle properties and band filling were matched . solving them yielded a successful description of the mott transition showing , for example , the narrowing of the quasiparticle resonance and the formation of the hubbard bands . a value of the critical hubbard interaction , @xmath1 , was obtained comparable to the best calculations . in this paper we present an extension of potthoff s `` two - site '' approach to treat cluster dmft . we use our method to investigate the approach to the mott transition for a single band hubbard model on a two - dimensional square lattice with nearest neighbor hopping , @xmath2 . the hamiltonian is @xmath3 where @xmath4 $ ] . we study this model as an example case , although our method is readily extended to more complicated hamiltonians . the method allows us to quickly investigate the zero temperature phase diagram across a large range of parameter space using a desktop computer . the efficacy of our approach is reinforced by our results which are consistent with other results in the literature for the magnetic phase diagram . moreover we can go beyond existing work to study the quasiparticle properties in momentum space : seeing , for example , how an electron - like metal ( well away from half - filling ) becomes a hole - like doped mott insulator near half - filling . some of our results are suggestive of the physics of the cuprate superconductors with the appearance of pseudogap regions and `` arc - like '' fermi surfaces brought about , in our case , by the combination of antiferromagnetism and proximity to a van hove point . we also observe a fermi surface distortion resulting from a pomeranchuk instability also reported elsewhere in the literature.@xcite physically , this is due to the proximity of the fermi surface to the van hove point , but the tendency will be exaggerated in our model due to the reduced symmetry of our cluster ( see later ) . we begin with a summary of dmft together with potthoff s `` two - site '' approach . we then discuss how dmft can be extended to a cluster of sites , and describe our application of potthoff s approach to a cluster consisting of a pair of sites . we then demonstrate this method on the 2d hubbard model and present our results . we conclude with a discussion of the physics behind these results and future extensions of our method . the dmft procedure @xcite can be described as follows . we focus on a single site of the hubbard model , and notionally integrate out all the other sites . this gives an effective action for the remaining site of the form @xmath5 the function @xmath6 completely encapsulates the dynamics of electrons entering and leaving the site from the rest of the lattice ; however it is not known _ a priori _ since we can not in practice integrate out the other sites . with this action we could determine the interacting green s function @xmath7 , and extract a local self - energy from the dyson s equation @xmath8 the dmft ansatz , exact in infinite dimensions , is to use this local self - energy as a spatially homogeneous ( but frequency - dependent ) self - energy for the full lattice problem : @xmath9 the self - consistency requirement that the on - site green s function of the extended lattice ( containing the self - energy ) is the same as the local green s function we started with , _ i.e. _ @xmath10 provides the constraint on the unknown initial function @xmath11 , thereby completing the self - consistency loop . [ dmftseff ] is the effective action of a single interacting impurity coupled to a continuum bath , but the procedure described above can not be achieved exactly because the single site impurity problem with an unrestricted bath is still intractable . one must approximate and use a model that is practically solvable ; for example , a finite - sized impurity model for exact diagonalization , @xcite or a discretized effective action for quantum monte carlo methods . @xcite this means that only limited functional forms of @xmath11 can be represented , and also that the final self - consistency condition can not be implemented precisely . in the `` two - site '' realization of dmft introduced by potthoff , @xcite the local model is an impurity site together with a bath consisting of _ a single site only _ , with a hamiltonian : @xmath12 where the electron creation operators @xmath13 and @xmath14 are for the impurity site and the bath site respectively . diagonalizing the non - interacting ( @xmath15 ) model yields @xmath16 $ ] ( where we are now considering zero temperature real frequency green s functions ) . the two - site model allows a minimal frequency dependence in @xmath6 . by exactly diagonalizing the many particle hamiltonian of eq . [ impham ] , the local on - impurity - site interacting green s function @xmath17 can be constructed from the lehmann representation , and the self - energy @xmath18 is extracted ( _ c.f . _ eq . [ dmftsigma ] ) using : @xmath19 the full functional self - consistency of eq . [ dmftsc ] can not be achieved within such a restricted representation so it is necessary to decide how best to implement a self - consistency requirement . potthoff chose two physically motivated features , taking advantage of the analytic simplicity of the two - site impurity model . firstly , the electron fillings given by the green s functions must be equal for the impurity model and the lattice model . secondly , features of the central quasiparticle peak are matched : the self - energy is reduced to the low energy form @xmath20 , and terms of the resulting `` coherent '' impurity and lattice green s functions at high energy are matched ( see ref . for more detail ) . in effect , the shape of the central quasiparticle peak is analyzed by the size of its high energy tails , isolated from other parts of the spectrum . the resulting self - consistency conditions for the four bath parameters ( @xmath21 ) are : @xmath22 where the quasiparticle residue @xmath23 and we have assumed that @xmath24 . solving these equations produces results for the mott transition which compare well with the full dmft , and properties of the fermi liquid which are consistent with exact results ( see ref . ) . it is hard to imagine a simpler model which can do this ; it succeeds because of the physical motivation of its self - consistency conditions , namely the filling and properties of the quasiparticle peak . it is a useful approach for calculations on extended models such as multiple bands @xcite and , as we shall demonstrate , clusters . we now consider an extension of this method to cluster dmft : @xcite instead of starting with a single site , self - consistency conditions are derived for a cluster of sites , which allows a momentum dependence in the self - energy . the geometry of the lattice becomes important and hence different types of magnetic order can be investigated , and spectral information varies non - trivially in @xmath25-space , unlike conventional dmft . a number of studies have been reported . @xcite we describe here a cluster dmft for the case where the cluster consists of just a pair of sites . we then detail how to implement potthoff s two - site method to solve cluster dmft . this can be contrasted with the exact diagonalization formulation of conventional dmft , @xcite where a single impurity site with multiple bath sites is used ; instead , we use multiple impurity sites in a cluster and include correlations in the simplest way via potthoff s scheme for single bath sites . below , we derive the self - consistency conditions for the pair - cluster ( each of the two cluster sites is connected to a single bath site ) . implementing a cluster dmft is fundamentally ambiguous , as recently noted by biroli _ et al . _ ; @xcite the approach we adopt is `` cdmft '' within their classification , which is arguably the simplest scheme appropriate for broken symmetry states . one of the strengths of conventional dmft is that it is exact in the limit of infinite dimensions . in contrast , our cluster approach is not a systematic @xmath26 correction , though it is of course exact in the limit of infinite cluster size when the self - consistent bath is merely a sophisticated boundary condition . @xcite in cluster dmft we imagine integrating out all sites except those in the cluster . an electron can in general now leave from and arrive back at any of the sites within the cluster : the function @xmath6 must become a matrix , coupling together the dynamics of the cluster sites . the resulting action ( _ c.f . _ eq . [ dmftseff ] ) is : @xmath27 where the summations are over the cluster sites . solving this local problem now yields a matrix @xmath28 and a matrix self - energy . different approaches to" +"magnetic skyrmions are topological protected textures of the magnetization @xcite , that have been observed experimentally in various magnetic materials , in both bulk systems and thin magnetic layers @xcite . as a topological object , the skyrmion is stable and possesses a peculiar particle - like nature , which makes it suitable for the application as an information carrier . indeed , a number of theoretical and numerical works have demonstrated that magnetic skyrmions could be essential components for future magnetic and spintronic devices for data storage and computation @xcite . the position of an isolated magnetic skyrmion can be manipulated by an external driving force . a spin - polarized electric current has been reported to be an effective driving force for the motion of magnetic skyrmions in confined geometries @xcite . in addition , the scattering of a propagating spin wave has been demonstrated to generate a momentum - transfer resulting in a skyrmion or domain wall motion @xcite . in the absence of boundaries , the skyrmion will be driven towards the magnon source , i.e. , the skyrmion velocity posses a component antiparallel to the magnon current @xcite . in confined geometries , the boundary acts as a potential barrier and its repulsive force can also result in an effective motion parallel to the magnon current @xcite . in this paper , we study in detail the motion and dynamics of an isolated magnetic skyrmion in a magnetic nanowire driven by spin waves travelling longitudinal or transverse to the wire . as the magnon current decays on a length scale set by the gilbert damping , the longitudinal driving is only viable for short wires . for transverse driving , a steady - state skyrmion motion is obtained with a characteristic velocity - current relation . we find that it is determined by an interplay of the magnonic driving and the repulsive potential arising from the edge of the wire . for large magnon currents , however , the skyrmion is pushed into the driving layer , that generates the spin waves , leading to a breakdown of the skyrmion velocity . our results provide a guide for future experimental studies on skyrmion motion in confined geometries driven by magnonic spin - transfer torques . we consider a magnetic wire with a surface - induced dzyaloshinskii - moriya interaction that stabilizes magnetic skyrmions , see appendix [ sec : methods_1 ] for details . the motion of an isolated magnetic skyrmion is investigated that is driven by spin waves propagating longitudinal and transverse to the wire . we first discuss the resulting skyrmion trajectories and then turn to a discussion of the relation between the driving current and the skyrmion velocity in the steady state . we first present results for the skyrmion trajectories obtained with the help of micromagnetic simulations . as shown in figs . [ fig1 ] and [ fig2 ] , we consider a nanowire consisting of a magnetic layer with a length @xmath4 nm in the @xmath5-direction and various different widths @xmath6 and @xmath7 nm in the @xmath8-direction corresponding to panels ( a)-(d ) , respectively . the thickness of the magnetic layer in the @xmath9-direction is fixed at @xmath10 nm . the initial magnetization profile of the magnetic layer corresponds to a magnetization pointing along the @xmath11-direction except at the center of the sample , where the skyrmion is initially located , and at the sample edges , where the magnetization is tilted due to the dzyaloshinskii - moriya interaction . two setups with longitudinal and transverse driving are considered , figs . [ fig1 ] and [ fig2 ] , respectively . the driving is generated by a locally applied oscillating magnetic field , that is , a radio frequency ( rf ) field . it is applied only within a narrow strip of width @xmath12 nm that is either located on the left - hand side of the sample for longitudinal driving or at the top of the nanowire for transversal driving . we consider a rf field @xmath13 with amplitude @xmath14 mt and frequency @xmath15 ghz . it possesses a longitudinal polarization with @xmath16 for fig . [ fig1 ] and @xmath17 for fig . more details on the simulation and material parameters are given in appendix [ sec : methods_1 ] . we first discuss the situation of _ longitudinal driving_. figure [ fig1](a1 ) shows the case of a square - shaped thin film where @xmath18 nm at time @xmath19 . the panels ( a2)-(a4 ) show snapshots at later times after the driving field has been switched on . the rf field at the left edge produces spin waves traveling towards the right , along the length direction of the sample . since the magnetic skyrmion is far away from the sample edges , we observe a nearly pure skew scattering between the propagating spin wave and the magnetic skyrmion , which is in good agreement with that reported in ref . . indeed , the spin wave - skyrmion scattering leads to a backwards motion of the magnetic skyrmion . it can be seen that the magnetic skyrmion basically moves against the propagation direction of the spin wave , and reaches the left edge in a finite time . in addition , the skyrmion gets slightly dragged towards the upper edge . the width in figs . [ fig1](a ) is sufficiently large so that the skyrmion reaches the magnon source before it touches the upper edge of the wire . the situation changes when the track is narrower . in figs . [ fig1](b ) the width is @xmath20 nm and the skyrmion still has not reached the upper edge at a time @xmath21 ns . however , for even narrower wires with @xmath22 nm and @xmath23 nm , see figs . [ fig1](c ) and [ fig1](d ) , it reaches the edge after a short time . close to the edge , the skyrmion changes the direction of its motion . instead of approaching the driving layer , the skyrmion moves along the edge away from it . this evading motion along the edge is also much faster than the attractive motion towards the magnon source . for the _ transverse driving _ we observe similar effects . the rf field is applied on the upper edge of the nanowire , see fig . [ fig2 ] , in the same wire geometries as for the parallel driving . due to the oscillating magnetic field , magnons are excited and propagate downwards along the @xmath24-direction . the interaction with magnons pushes the skyrmion towards the upper edge of the wire with a slight side - shift to the right - hand side . this can be particularly well seen for the wide wire in figs . [ fig2](a ) . this setup is however too wide to observe the effects from the sample edge within the simulated time span . in contrast to the longitudinal driving mechanism , the skyrmion is now driven faster towards the upper edge , which becomes apparent for the narrower wires shown in figs . [ fig1](b)-(d ) . when the skyrmion arrives at the edge , it speeds up dramatically and moves along the upper edge towards the right - hand side . it reaches the end of the wire in a much shorter time than for longitudinal driving . , @xmath25 , @xmath26 , @xmath27 , @xmath28 for both plots and @xmath29 and @xmath30 for the parallel driving ( a ) and @xmath31 and @xmath32 for the transverse driving ( b ) . , scaledwidth=47.0% ] , @xmath25 , @xmath26 , @xmath27 , @xmath28 for both plots and @xmath29 and @xmath30 for the parallel driving ( a ) and @xmath31 and @xmath32 for the transverse driving ( b ) . , scaledwidth=47.0% ] the skyrmion trajectories observed by our micromagetic simulation can be understood in the framework of an effective thiele equation of motion for the skyrmion @xcite . within this description , the skyrmion coordinate @xmath33 is governed by the equation @xmath34 where @xmath35 is the gyrocoupling vector with @xmath36 , which is related to the topological winding number of the skyrmion , @xmath3 is the gilbert damping , and @xmath37 the dissipative tensor which can be approximated to be diagonal , @xmath38 . the force on the right - hand side is attributed to the magnon driving and the edge of the sample , @xmath39 . close to the edge , the dzyaloshinskii - moriya interaction leads to a twist of the magnetization @xcite that acts as a repulsive potential for the skyrmion @xcite . to a good approximation , this potential falls off exponentially with the distance to the edge @xcite . we thus describe the repulsive force by the edges of a nanostrip of width @xmath40 by a superposition of edges at positions @xmath41 and @xmath42 : @xmath43 where @xmath44 parametrizes the strength of the potential and @xmath45 the penetration depth of the magnetization twist . the momentum - transfer from the magnon current to the skyrmion also results in a force , @xmath46 where @xmath47 is the two - dimensional magnon - current density , and @xmath48 is the wavevector of the spin wave with @xmath49 and @xmath50 . it was shown in refs . @xcite that the force is determined by the two - dimensional transport scattering cross section of the skyrmion , @xmath51 and @xmath52 , longitudinal and transverse to the flow direction @xmath53 of the magnon current . in general , they depend in a non - trivial manner on the magnon frequency . in the high - frequency limit or , equivalently , for large magnon wavevectors @xmath54 @xcite , the transversal transport scattering cross section is universal @xmath55 and @xmath56 so that @xmath57 . we also accounted for the decay of the magnon current on a length scale set by the gilbert damping , @xmath58 where @xmath59 is the magnon mass and @xmath60 is the frequency of the wave . the solution of the thiele equation is plotted in fig . [ fig3 ] for some set of parameters . for longitudinal driving in panel ( a ) , the wire can be divided into two different areas . the skyrmion trajectories belonging to the red shaded area , on the one hand , will end up at the driving layer ( red line ) . when the skyrmion starts within the blue shaded area , on the other hand , it will be driven away from the driving layer . the interplay between the magnon and edge forces dominates the motion . as the magnon current decays exponentially on the length scale @xmath61 with increasing distance to the driving layer , the magnon force that keeps the skyrmion close to the edge also decays so that eventually the skyrmion slowly approaches the center of the wire . the red and blue shaded areas are separated by a critical skyrmion trajectory ( white line ) . in any case , the longitudinal driving setup will not produce a steady state . in case of transversal driving in fig . [ fig3](b ) , a skyrmion initially positioned at the center of the wire gets attracted towards the driving layer at the top of the wire . at the same time , it gets repelled by the edge twist of the magnetization and if the driving is not too strong the skyrmion reaches a steady state with @xmath62 and a constant velocity , @xmath63 , along the edge . within the thiele approximation , this saturated velocity is given by @xmath64 it depends on the steady state distance to the edge , @xmath8 , which is in turn governed by the driving amplitude @xmath0 . the last equation applies in the high - frequency limit @xmath55 and , in addition , @xmath65 ." +"popularity plays a major role in the dynamics of online systems . public attention can suddenly concentrate on a web page or application @xcite , a youtube video @xcite , a trending topic in twitter @xcite , or on a story in the news media @xcite , sometimes even in absence of an apparent reason . typically , after an initial increase of attention , the focus will move elsewhere leaving as a trace a characteristic activity profile . such popularity peaks are not only of great relevance for the monetization of online content , but also pose scientific challenges related to understanding the mechanisms ruling their dynamics @xcite . in particular , specific features of the popular item under consideration can now be related to its activity profile by means of semantic analysis and natural language processing of the messages exchanged by the users @xcite . here we use data from the twitter micro - blogging system to investigate the relation between activity profiles over time and content . there are several reasons for selecting twitter : it is one of the most popular online social networks , part of its message stream is programmatically accessible to the public @xcite , and the content of the messages is short , making it amenable to automated processing . twitter is used as an hybrid between a communication media and an online social network @xcite and hosts real - time discussion of current topics of popular interest . we take advantage of the practice introduced by twitter users of attaching `` hashtags '' to their messages as a way of explicitly marking the relevant topics . twitter has incentivated this practice by supporting hashtags in their web interface and in their programmatic api , turning them into lightweight social annotations of the information streams users consume . here we focus our analysis on those hashtags that exhibited a popularity peak during our observation period , and systematically analyze the corresponding messages ( `` tweets '' ) by grounding the words they contain in a semantic lexicon . this paper is structured as follows : section [ sec : background ] reviews the literature on twitter and in particular the literature on temporal patterns of twitter activity . section [ sec : data ] describes the twitter dataset we used and the techniques we applied to select popular hashtags and their usage patterns . in section [ sec : classes ] we identify dynamical classes of hashtag usage and relate them to the semantics of the corresponding tweets . in section [ sec : spreading ] we relate the same dynamical classes to the spreading properties of hashtags over the underlying social network . section [ sec : discussion ] summarizes our findings and points to applications and further research directions . several aspects of twitter have been extensively investigated in the literature , including its network topology @xcite , the relations and types of messages between users @xcite , the internal information propagation @xcite , the credibility of information @xcite , and even its potential as an indicator of the state of mind of a population @xcite . the possibility that popular trends or hashtags could be classified in groups have been discussed in refs . @xcite , and the effect of semantic differences on the persistence of a hashtag have also been considered @xcite . the shape of peaks in popularity profiles has been used to classify the events in groups @xcite . the hypothesis that both the increase and decrease of public attention follow a power - law - like functional shape whose exponents define universality classes , in parallel to what occurs with phase transitions in critical phenomena , has been explored @xcite . this approach , however , is difficult to apply to twitter : the fast timescales involved and the highly reactive nature of twitter make the time series very noisy and pose the challenge of characterizing activity dynamics in a way which is both robust and scalable . the causes that underlie the existence of distinct classes of popularity are thought to be a combination of all the mechanisms that drive public attention . news regarding a popular item can propagate either over the social network of the users of a given system a so - called endogenous process or it can be injected through mass media ( exogenous driving ) . the duality between exogenous and endogenous information propagation has permeated the analysis of popularity in several recent studies @xcite , even though it is not always clear how to distinguish between them based solely on the shape of the respective popularity profiles @xcite . our dataset comprises about @xmath0 million twitter messages or _ tweets _ posted between november @xmath1 , @xmath2 and may @xmath3 , @xmath4 . the data were collected at indiana university thanks to their temporary privileged access to the twitter data stream @xcite . each tweet includes textual content , an author , the time at which it was posted , whether or not it was in reply to another tweet , and additional metadata . the collected tweets come from about @xmath5 million unique user accounts . in order to build a representation of the social network over which hashtag diffusion takes place , we queried the twitter rest api for the complete list of followers and friends of @xmath6 million users . we collected neighbor information for @xmath7 million of them , the discrepancy being accounted for by users with a private profile . using this information we constructed a directed follower network , where each edge takes on the direction in which information flows : if user a follows user b , the respective social link points from b to a , as a can see b s status updates . for the identification of topics , we extracted all the hashtags contained in the twitter messages ( by matching the tweet content to the pattern # [ a - za - z0 - 9 _ ] * ) . our dataset includes about @xmath8 distinct hashtags ( see table [ tab : data ] ) . we selected the most popular topics by restricting our data to the hashtags used by at least @xmath9 distinct users and to the messages containing at least one of such hashtags . based on this selection , we used for the following analysis about @xmath10 million tweets and @xmath11 popular hashtags . .general statistics about the dataset [ tab : data ] [ cols= "" < , > "" , ] like most systems driven by human actions , twitter exhibits bursty activity , circadian rhythms , and in general the full temporal complexity of a large - scale social aggregate . because of this , there is no single natural scale for investigating its temporal behavior , and the choice of a time scale is not neutral with respect to the phenomena one can study at that scale . here we choose to investigate activity at the scale of days , i.e. , we do not study human dynamics at the level of minutes and seconds , nor phenomena driven by the circadian cycle , nor slower trends that develop over several weeks of months . we analyze daily activity levels , and focus on events that are meaningful at that scale , such as the wait for a scheduled social event . at the daily scale the popularity profile of hashtags can look very different . on visual inspection the individual temporal profiles of hashtag usage display behaviors that typically fall into one of the following three categories : continuous activity , periodic activity , or activity concentrated around an isolated peak . continuous - activity profiles are those for which a rather constant level of daily activity is maintained by the user community ( e.g. , ` music ` ) . hashtags with periodic activity profiles display series of spikes spaced by one or more weeks , or months ( e.g. , ` followfriday ` ) . finally , activity profiles with an isolated peak are characteristic of hashtags associated with a unique event to which a user community pays attention for a limited span of time ( e.g. , ` oscars ` ) . in the following we will concentrate on this class of hashtags . to identify activity peaks , for every hashtag @xmath12 we compute the time series of daily activity , where the activity @xmath13 on day @xmath14 is defined as the number of tweets containing @xmath12 . in the following we will write @xmath15 to indicate the activity level of a generic hashtag . we use a sliding window of @xmath16 days ( @xmath17 ) centered on day @xmath18 , @xmath19 $ ] , and let @xmath18 slide along the activity time series for the hashtag . within this window we evaluate the baseline hashtag activity as the median @xmath20 of @xmath21 . then , we define the outlier fraction @xmath22 of the central day @xmath18 as the relative difference of the hashtag activity @xmath23 with respect to the median baseline @xmath20 : @xmath24 / \max(n_b , n_{\mbox{\tiny min}})$ ] . here @xmath25 is a mininum activity level used to regularize the definition of @xmath22 for low activity values . we say that there is an activity peak at @xmath18 if @xmath26 , where @xmath27 is an arbitrary threshold value that in the following we set as @xmath28 . we checked that different values of the threshold do not change significantly our results , and that the same peaks can be identified by using different peak - detection techniques . of course it may happen that for a given hashtag @xmath12 the time series @xmath13 exhibits more than one peak . since we are interested in isolated popularity bursts , we ignore all peaks that are separated from other peaks by less than one week . finally , for every hashtag we select the peak ( if any ) with the highest @xmath22 and we offset the day index so that for all hashtags the activity peak occurs on day @xmath29 , as shown in fig . [ activity ] . using this method we select @xmath30 peaks of daily hashtag activity : the corresponding hashtags are listed in appendix [ appendix - usage ] , together with manual annotations about their meaning and a coarse classification . to correlate the temporal activity patterns with content , we perform a simple semantic grounding of the tweets by using the wordnet @xcite semantic lexicon . for each tweet , we pre - process the text by removing user mentions ( ` @username ` ) , hashtags , urls and a standard set of english stop words . then , for each word we perform stemming ( with the standard porter algorithm ) , lemmatization , and we finally attempt to look up in wordnet the corresponding ( i.e. , the basic node of the wordnet lexicon , a set of synonyms that refer to a single concept ) . from now on we will refer to wordnet synsets as _ concepts_. words for which no concept can be looked up in wordnet are ignored . if few or no terms are successfully looked up in wordnet as english words , we attempt to identify the tweet language : we run the textcat @xcite language categorization algorithm on the text and we discard the tweet if english is not included in the top @xmath31 most likely languages identified by textcat . overall , the above analysis identifies about @xmath32 distinct concepts that are associated with the hashtags under study . typical examples of the activity profiles for the selected hashtags are shown in figure [ activity ] . the curves are centered around the day on which the popularity reaches its maximum ( day @xmath29 ) . the displayed time window spans one" +"the fragmentation of molecular clouds ( mcs ) induced by supersonic turbulence is a fundamental aspect of the star formation process . recent models of the star formation rate @xcite and of the stellar initial mass function @xcite are based on the statistics of turbulent fragmentation , such as the probability density function ( pdf ) of gas density and the scalings of velocity and density fluctuations . so far , these statistics have been derived almost exclusively from numerical simulations with rather idealized setups , including periodic boundary conditions , driving by a random volume acceleration , isothermal equation of state , or no self - gravity ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? these simulations do not address important issues related to the coupling of the internal dynamics of mcs with the turbulence on larger scales , such as the ( large - scale ) origin of the turbulence and its role in the formation and dispersion of mcs and the cloud s finite lifetime . to study mc turbulence in a more realistic larger - scale context , and specifically to test the idea that mc turbulence is driven primarily by sn explosions , we have carried out a magneto - hydrodynamic ( mhd ) adaptive - mesh - refinement ( amr ) simulation of sn - driven turbulence with the ramses amr code @xcite . the numerical method and setup were discussed extensively in @xcite paper i hereafter and are only briefly summarized in the next section . although still somewhat idealized ( e.g. periodic boundary conditions and no vertical stratification ) , this simulation represents a major advance relative to previous statistical studies of supersonic turbulence : it allows us i ) to test the effect of a realistic and physically motivated driving force , such as sn explosions , ii ) to see the development of mc turbulence as an integral part of the process of cloud formation and dispersion , iii ) to select a very large sample of mcs , forming _ ab initio _ from the large scale turbulence with realistic initial and boundary conditions ( and realistic statistical distributions of such conditions ) . in paper i we demonstrated that clouds selected from the simulations have mass and size distributions , and velocity - size and mass - size relations in agreement with the observations . using tracer particles , we also studied their evolution and found that they form and disperse in approximately four dynamical times . we also studied the velocity scaling in the whole volume and within individual mcs , showing that the turbulence , driven purely by sn explosions , is efficiently injected into mcs , with a realistic velocity dispersion in the dense gas . in this work , we focus on a specific aspect of direct interest to the modeling of star formation , that is the compressive ratio ( the ratio of powers in compressive and solenoidal motions ) of mc turbulence and its relation to the statistics of density fluctuations ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? besides sne , galactic gas infall , large - scale disk instabilities and spiral arm shocks are also sources of large - scale turbulence ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , but it is generally accepted that sn explosions dominate the energy budget of star - forming galaxies at mc scales ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? because the primary goal of this work is to study the compressive ratio of the turbulence in mcs , we focus on the driving by sne . prior to our work , large - scale sn - driven turbulence in the multi - phase ism has been studied with fully - periodic volumes without stratifications ( e.g. * ? ? ? * ) , or with vertically extended , stratified galactic - fountain simulations ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? these works demonstrated that sne can drive ism turbulence with an outer scale of @xmath2 pc , and derived its velocity scaling laws and gas density pdfs . however , they did not reach the necessary spatial resolution to study mc properties , particularly the cascade of sn - driven turbulence in their interior . more recent simulations in periodic boxes @xcite or stratified galactic - fountains @xcite have significantly lower spatial resolution than earlier works , and do not tackle the problem of mc turbulence either . with resimulations of a kpc - size region from a global disc - galaxy simulation , @xcite achieved a large enough dynamic range to study the formation and disruption of mcs . in these simulations , mc turbulence is generated with various prescriptions for sn feedback , resulting in mcs with realistic velocity dispersion . however , the feedback is instantaneously inserted in any region of converging flows as the gas density reaches a threshold value of 500 @xmath3 , so the ability of sn feedback to drive the turbulence within mcs is assumed rather than demonstrated . the statistical properties of sn - driven turbulence from these simulations are not discussed . this paper is structured as follows . in section 2 , we give a brief description of the simulation setup , and in section 3 we summarize our recent findings concerning the compressibility of sn - driven turbulence . section 4 derives the overall expansion / contraction and rotation of the mcs selected from our simulation . section 5 analyzes the statistics of the compressive ratio of the turbulence within those mcs . the density variance - mach number relation and the density probability distribution in the mcs are explored in sections 6 and 7 , respectively . our conclusions are summarized in section 8 . we simulate a cubic region of size @xmath4 pc , with a minimum cell size of @xmath5 pc ( a maximum resolution equivalent to a mesh of @xmath6 cells ) , periodic boundary conditions , a mean density of 5 @xmath3 ( corresponding to a total mass of @xmath7 m@xmath8 ) and a core - collapse sn rate of 6.25 myr@xmath9 . we distribute sn explosions randomly in space and time ( see discussion in paper i in support of this choice ) , so our sn rate could also be interpreted as the sum of all types of sn explosions . individual sn explosions are implemented with an instantaneous addition of 10@xmath10 erg of thermal energy and 15 m@xmath8 of gas , distributed with an exponential profile in a spherical region of radius @xmath11 pc , which guarantees numerical convergence of the sn remnant evolution @xcite . besides the pdv work , and the thermal energy introduced to model sn explosions , our total energy equation adopts uniform photoelectric heating up to a critical density of 200 @xmath3 , and parametrized cooling functions from @xcite . the simulation is started with zero velocity , a uniform density @xmath12 @xmath3 , a uniform magnetic field @xmath13 @xmath14 g and a uniform temperature @xmath15 k. the first few sn explosions rapidly bring the mean thermal , magnetic and kinetic energy to approximately steady - state values , with the magnetic field amplified to an rms value of 7.2 @xmath14 g . we have run the simulation for 45 myr without self - gravity and then continued with self - gravity for 11 myr . the interested reader is referred to paper i for further details about the numerical setup . before analyzing the compressive ratio of the turbulence within mcs , we briefly summarize our recent results on the overall compressibility of sn - driven turbulence ( see details in paper i ) . in our discussion , we shall make a strict distinction between the driving acceleration , @xmath16 , for the turbulent velocity and the driving force , @xmath17 , for the flow momentum . as in previous works on supersonic turbulence , we are more concerned with the effective driving acceleration , @xmath16 , rather than the driving force , @xmath18 , because the compressibility of the velocity field is directly related to that of the driving acceleration , not the force . all studies of the compressibility of interstellar turbulence decompose the velocity , @xmath19 , rather than the momentum , @xmath20 , into solenoidal and compressive modes , and refer to the compressibility of the driving acceleration , rather than that of the driving force ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . in our simulation , the sn explosion energy is deposited as thermal energy in small , randomly - selected spheres , so it is initially injected via the pressure term in the navier - stokes equation . denoting as @xmath21 the pressure source due to sn explosions , the effective driving force and acceleration can be written as @xmath22 and @xmath23 , respectively . although the effective force , @xmath22 , is purely compressive , the driving acceleration , @xmath23 , is not so , in general . clearly , the divergence and the curl of this effective acceleration , @xmath23 , are given , respectively , by @xmath24 and @xmath25 . the latter , known as the baroclinic effect ( e.g. * ? ? ? * ; * ? ? ? * ) , is nonzero in general . in particular , considering random density and pressure fluctuations outside a sn - explosion sphere , the baroclinic term is always nonzero at the boundary of such a sphere . therefore , the effective acceleration for sn driving is neither purely compressive nor purely solenoidal , rather it consists of a mixture of solenoidal and compressive modes . if the direction of @xmath26 is random with respect to @xmath27 , the divergence and curl of @xmath23 are comparable , suggesting similar amounts of solenoidal and compressive modes in the effective acceleration . with the expansion of the remnant , solenoidal motions generated around the pressure sources "" are transferred to larger scales . for example , a single sn remnant leads to an energy spectrum that peaks at a wavenumber @xmath28 , with @xmath29 the remnant radius ( see paper i ) . we find that , at large scales , the solenoidal and compressive modes in our simulation are roughly in equipartition , supporting the above picture . ( unshaded histogram ) , and contraction velocity , @xmath30 ( solid - line shaded histogram ) , normalized to the rms velocity in the cloud , for a sample of 507 clouds selected before the introduction of gravity . the dashed - line shaded histogram shows the probability distribution of mean cloud contraction velocity for a sample of 802 clouds selected after gravity is included in the simulation . this histogram has been normalized to the same total probability as the other two histograms . ] while the remnant expansion brings the velocity power to large scales , the nonlinear advection term causes cascades of both solenoidal and compressive modes towards small scales . if the sn rate is not too high and there is sufficient time in between sn events to allow the flow to fully develop , a dynamically quasi - relaxed state is reached" +"the development of a statistical mechanics for granular matter and other jammed materials presents many difficulties . first , the macroscopic size of the constitutive particles forbids equilibrium thermalization of the system . second , the fact that energy is constantly dissipated via frictional interparticle forces further renders the problem outside the realm of equilibrium statistical mechanics . in the absence of energy conservation laws , a new statistical approach is needed in order to describe the system properties . along this line of research , edwards @xcite has proposed to replace the energy by the volume as the conservative quantity of the system . then a canonical partition function of jammed states can be defined and a statistical mechanical analysis ensues . while it is always possible to measure the total volume of the system , it is unclear how to treat the volume fluctuations at the microscopic level . thus , it is still an open problem the definition of an analogous `` hamiltonian '' that describes the microstates of jammed matter . such a `` hamiltonian '' is called the volume function @xcite , denoted @xmath0 . the idea is to partition the granular material into @xmath1 elements and associate an additive volume function to them , @xmath2 , such that the total system volume , @xmath0 , is @xmath3 from a theoretical perspective , initial attempts to define the volume function involved modelling under mean - field approximations proposed by edwards @xcite not taking into account the contact network . the necessary definition in terms of the internal degrees of freedom has been pursued by ball and blumenfeld @xcite who have shown by an exact triangulation method that the volume defining each grain can be given in terms of the contact points using vectors constructed from them . the method consists of defining shortest loops of grains in contact with one another , thus defining the void space around a central grain . a simpler version for the volume function was also given by edwards as the area in 2d or volume in 3d encompassing the first coordination shell of the grains in contact @xcite . the resulting volume is the antisymmetric part of the fabric tensor , the significance of which is its appearance in the calculation of stress transmission through granular packings @xcite . this definition is only an approximation of the space available to each grain since there is an overlap of volumes for grains belonging to the same coordination shell . thus , it overestimates the total volume of the system : @xmath4 @xcite . furthermore , both definitions of @xmath2 in @xcite are proportional to the coordination number of the grain . this is in contrast to expectation since the free volume available to a grain should decrease as the number of contacts increase . indeed , this observation is corroborated by experimental studies of jammed granular matter using x - ray tomography @xcite to determine the volume per grain versus coordination number . based on the idea that the volume function represents a free volume available per grain , we introduce a new `` hamiltonian '' to describe the microstates of jammed matter . we analytically calculate the volume function and demonstrate that it is equal to the voronoi volume associated to each particle , partitioning the space into a set of regions , associating all grain centroids in each region to the closest grain centroid . even though the voronoi construction successfully tiles the system , its drawback in its use as a volume function was that , so far , there was no analytical formula to calculate it . our approach provides this formula in terms of the contact network . furthermore we introduce a theory of volume fluctuations to calculate a coarse - grained average volume function defined at the mesoscopic level that reduces the degrees of freedom to only the coordination number @xmath5 . we find that the volume function is inversely proportional to @xmath5 in agreement with the tomography experiments of @xcite . our analysis also provides an equation of state , relating volume with coordination number in the limit of fully random system . indeed , it predicts with good accuracy the limiting cases of random loose and random close packing fractions . our results allow construction of a statistical partition function from which macroscopic observables can be calculated . this case is treated in more detail in the second part of this work : jamming ii @xcite . this paper is the first installment in a series of papers devoted to different aspects of jammed matter and is the main theoretical contribution for the subsequent statistical mechanics approach . the present paper is an extended version of the supplementary information section i in @xcite . the outline is as follows : section [ hamiltonian ] details the development of the microscopic volume function in terms of the particle coordinates . the relation of this form with the voronoi volume of each particle is discussed in section [ voronoi - formula ] . section [ proba ] discusses the statistical theory to calculate the probability distribution of the voronoi volumes leading to the average mesoscopic volume function discussed in section [ meso ] . section [ test ] tests the assumptions of the theory and we finish with the outlook in section [ outlook ] . we start by defining a volume function for rigid spherical grains of equal size in terms of particle positions . the volume function represents the available volume to the particle with the constraint of fixed total system volume . since we are dealing with rigid jammed particles , the available free volume is in principle zero since the particle by definition can not move . however , we allow the particle to move by introducing a soft interparticle potential and then taking the limit of particle rigidity to infinity . the resulting volume is well - defined , representing the free volume associated with each grain in the jammed packing . we consider a rigid particle of radius @xmath6 jammed at position @xmath7 in contact with another particle at position @xmath8 such that @xmath9 ( see fig . [ volumea ] ) . in order to calculate the volume associated with such a particle we allow it to move by introducing a generic interparticle soft - potential , @xmath10 , determined by an exponent @xmath11 governing the rigidity of the particles ( see below ) . a small energy threshold @xmath12 is introduced in order to drive the particle in a certain direction @xmath13 as indicated in fig . [ volumea ] . a small displacement @xmath14 of particle @xmath15 along the @xmath16 direction results in an increase of energy @xmath17 between particles @xmath15 and its neighbors : @xmath18 where the sum is taken over all the neighbors of particle @xmath15 . the soft pair potential @xmath10 can be any repulsive function provided it approaches the hard sphere limit when the control parameter @xmath19 , implying @xmath20 [ a possible function is simply @xmath21 , the case @xmath22 corresponds to the hertz potential ] . this condition implies that @xmath23 and therefore from eq . ( [ e ] ) , we obtain : @xmath24 we define the available volume to a grain , @xmath25 , under the energy threshold @xmath12 as : @xmath26 ds,\ ] ] where @xmath27 is the dimension of the system , @xmath28 is an infinitesimal solid angle in @xmath27 dimensions , and the available volume @xmath25 is averaged over all the directions of the @xmath27 dimensional solid angle . the integration over @xmath29 can be simplified when @xmath30 since for a fixed direction @xmath16 we have : @xmath31 & \\ = \lim_{\alpha\rightarrow\infty } \int_0^\infty \theta[\epsilon - f_\alpha(\max_{\s\cdot\drij > 0}(\s\cdot&\drij)\dr ) ] \dr^{d-1 } d[\dr ] \\ \propto & \min_{\s\cdot\drij > 0}(\s\cdot\drij)^{-d}. \end{split}\ ] ] thus , we obtain : @xmath32 equation ( [ va ] ) can be interpreted as follows : for each direction @xmath16 , the available volume is determined by the particle position whose projection of the distance to particle @xmath15 in the @xmath16 direction is minimal . the total volume is then the average over all directions @xmath16 . the proportionality constant in eq . ( [ va ] ) can be determined because @xmath25 is equal to the volume of the grains , @xmath33 , when the coordination number @xmath34 , suggesting that , in this limit , @xmath35 for any @xmath16 . that is , @xmath36 for mono - disperse spherical particles , @xmath37 . thus , we have @xmath38 where we have replaced @xmath39 for nearest neighbors in the last equation . this allows us to generalize the volume formula to satisfy additivity and relate it to the voronoi volume as shown below . equation ( [ vi ] ) is not additive , and is different from the voronoi volume since only contacting particles are considered in the calculation . strictly speaking , only at the limit when the coordination number @xmath34 , and all the geometrical constraints come from contacting particles , the volume function eq . ( [ vi ] ) converges to the voronoi volume . however , the formula becomes additive when considering all particles rather than the nearest neighbors in the calculation of the minimum integrand in eq . ( [ vi ] ) . this approach is justified since non - contact particles may contribute to the energy of deformation in eq . ( [ energy ] ) . further , if the minimum in eq . ( [ vi ] ) is taken over all the particles in the packing , @xmath25 is exactly equal to the voronoi volume , which is obviously additive . in turn we provide a formula for the calculation of the voronoi volume in terms of particle positions , as shown next . first , we recall the definition of a voronoi cell as a convex polygon whose interior consists of all points which are closer to a given particle than to any other . formally , the volume of the voronoi cell of particle @xmath15 can be calculated as ( see fig . [ volumeb ] ) : @xmath40 where @xmath41 is the distance from particle @xmath15 to the boundary of its voronoi cell in the @xmath16 direction . note that this definition is valid whether the particle @xmath42 is in contact with @xmath15 or not . if we denote the distance from particle @xmath15 to any particle @xmath42 at @xmath16 direction as @xmath43 then @xmath41 is the minimum of @xmath44 over all the particles @xmath42 for any @xmath45 ( see fig . [ volumeb ] ) . this leads to @xmath46 substituting into eq . ( [ vor0 ] ) , we prove that the voronoi volume is indeed the volume available per particle as calculated in eq . ( [ vi ] ) : @xmath47 formula ( [ vor1 ] ) can be rewritten as @xmath48 where we define the orientational volume for the @xmath15 particle in the @xmath16 direction as : @xmath49 let us recapitulate and recall the three volumes defined so far which are interrelated : the voronoi and the available volume which satisfy @xmath50 , and the orientational volume which satisfies @xmath51 . all the quantities are additive , thus they provide the total volume of the system : @xmath52 for isotropic packings , @xmath53 ( without the average over @xmath16 ) is also additive since the choice of orientation @xmath16 is arbitrary . thus , we obtain : @xmath54 this property reduces the calculations , since there is no need for an orientational average . we define the orientational free volume function as : @xmath55 and the reduced orientational free volume function @xmath56 with its average value , @xmath57 , over the particles , @xmath15 , for isotropic systems as : @xmath58 this average orientational volume" +"the study of the effect of strong magnetic field on dense stellar plasma is one of the oldest branches of physics . it has gotten a new life after the discovery of a few magnetars- the strange stellar objects , with unusually high surface magnetic fields @xcite . these stellar objects are believed to be strongly magnetized young neutron stars . the surface magnetic fields are observed to be @xmath1 g . then it is quite possible that the field strength at the core region may go up to @xmath2 g . the exact source of this strong magnetic field is of course yet to be known . these objects are also supposed to be the possible sources of anomalous x - ray and soft gamma emissions ( axp and sgr ) . if the magnetic fields are really so strong , in particular at the core region , they must affect significantly most of the important physical properties of such stellar objects and the physical processes , e.g. , weak and electromagnetic interactions taking place at the core region . which means , the presence of strong quantizing magnetic field at the core region should modify , both qualitatively and quantitatively the equation of state of dense neutron star matter , and as a consequence the gross - properties of neutron stars @xcite , e.g. , mass - radius relation , moment of inertia , rotational frequency etc . should also change significantly . in the case of compact neutron stars , the phase transition from neutron matter to quark matter at the core region , if any , will also be affected by strong quantizing magnetic field . it has been shown that a first order phase transition initiated by the nucleation of quark matter droplets is absolutely forbidden if the magnetic field @xmath1 g at the core region @xcite . however a second order phase transition is allowed , provided the magnetic field strength @xmath3 g . this is of course too high to achieve at the core region . the elementary processes , in particular , the weak and the electromagnetic processes taking place at the core region of a neutron star are strongly affected by such ultra - strong magnetic field @xcite . since the cooling of neutron stars are mainly controlled by neutrino / anti - neutrino emissions , the presence of strong quantizing magnetic field should affect the thermal history of strongly magnetized neutron stars . further , the electrical conductivity of neutron star matter which directly controls the evolution of neutron star magnetic field will also change significantly . in another kind of work , the stability of such strongly magnetized rotating objects are studied . it has been observed from the detailed general relativistic calculation that there are possibility of some form of geometrical deformation of these objects from their usual spherical shapes @xcite . in the extreme case such objects may either become black strings or black disks . in the non - extreme case , however , it is also possible to detect gravity waves from these deformed rotating objects . in a recent study on microscopic model of dense neutron star matter , we have observed that if most of the electrons occupy the zeroth landau level , with spin anti - parallel to the direction of magnetic field and very few of them are with spin along the direction of magnetic field and landau quantum number @xmath4 , then either such strongly magnetized system can not exist or such a strong magnetic field is just impossible at the core region of a neutron star @xcite . motivated by the problems as mentioned in preceding two sections , in this paper we shall study the effect of strong quantizing magnetic field on the transport coefficients of dense stellar electron - proton plasma . we shall follow an exact formalism @xcite which is applicable for a wide range of magnetic field strengths and obtain the transport coefficients from the relativistic version of boltzmann kinetic equation by linearizing the distribution function and using relaxation time approximation . we shall obtain the relaxation time from the rates of standard electromagnetic processes taking place inside electron - proton plasma and make necessary modification in the rate calculation due to the presence of strong quantizing magnetic field . we have noticed that the electrical conductivity of the medium becomes extremely small in presence of ultra - strong magnetic field ( @xmath5 g ) . the magnetic field at the core region of a magnetar must therefore decay very rapidly ( time scale @xmath6 a few mins . ) and becomes moderate or low enough . as a consequence there will be in principle no problem on the existence of magnetars ( with very low or moderate core magnetic field ) . the formalism we have developed to obtain rates of electromagnetic processes or the relaxation time is also applicable to evaluate neutrino emissivity and mean free path in presence of strong quantizing magnetic field . in presence of strong quantizing magnetic field , since the momentum component in the transverse plane with respect to the external magnetic field gets quantized , whereas the component along the field direction varies continuously ( from @xmath7 to @xmath8 ) , the momentum space volume element becomes @xmath9 ( we have assumed @xmath10 ) where we have chosen the gauge @xmath11 , so that the constant magnetic field @xmath12 is along z - direction . we have considered the simplest possible picture of neutron star matter with @xmath13 out of thermodynamic equilibrium and the neutrinos are assumed to be non - degenerate . the baryonic components are interacting via @xmath14 meson exchange type mean field and the electrons are assumed to be freely moving particles . in this article , we shall first calculate the transport coefficients of electron gas . then it is very easy to obtain the transport coefficients for proton matter just by replacing mass , chemical potential etc . of electrons by protons and taking into account the proper modification in presence of @xmath14 meson exchange type mean field @xcite . spinor solutions for electrons in presence of strong quantizing magnetic fields are then given by @xmath15^{1/2 } } \times\left ( \begin{array}{c}(\varepsilon_{\nu}^{(e)}+m_e ) i_{\nu;p_y}(x)\\ 0\\p_z i_{\nu;p_y}(x)\\-i(2\nu e b_m)^{1/2}i_{\nu-1;p_y}(x ) \end{array } \right)\ ] ] and @xmath16^{1/2 } } \times\left ( \begin{array}{c } 0\\(\varepsilon_{\nu}^{(e)}+m_e)i_{\nu-1;p_y}(x)\\ i(2\nu e b_m)^{1/2}i_{\nu;p_y}(x)\\-p_z i_{\nu-1;p_y}(x ) \end{array } \right)\ ] ] where @xmath17 and @xmath18 represent up and down spin states respectively , @xmath19 h_{\nu } \left [ \sqrt{e b_m}\left ( x- \frac{p_y}{e b_m } \right ) \right],\ ] ] with @xmath20 the hermite polynomial of order @xmath21 and @xmath22 the energy eigen value with @xmath23 the landau quantum numbers . for neutron we consider the usual spinor solutions . since the temperature of the system is @xmath24 electron chemical potential , we have not considered the negative energy spinor solutions , in the energy eigen value @xmath25 is the transverse component of electron momentum . to overcome the serious problem on the mechanical stability and hence the existence of magnetars , we have studied the variation of transport coefficients , in particular the electrical conductivity of electron gas / proton matter in presence of strong quantizing magnetic field and try to show whether the electrical conductivity which is solely responsible for the evolution of neutron star magnetic field , becomes sufficiently small in presence of ultra strong magnetic field . the paper is organized in the following manner . in section 2 , we have developed the relativistic version of boltzmann kinetic equation for fermions in presence of strong quantizing magnetic field and obtain the expressions for transport coefficients following de groot @xcite . we shall use the relaxation time approximation for the collision term . in section @xmath26 we shall evaluate the the relaxation time from the rates of standard electromagnetic processes taking place at the core region . we shall incorporate the necessary changes in the rate calculation due to the presence of strong quantizing magnetic field ( or the effect of quantized landau levels ) . in the last section we shall discuss importance of the results . the relativistic version of boltzmann transport equation is given by @xcite @xmath27 where the second and the third terms are coming from electromagnetic and gravitational ( general relativistic ) interactions respectively and @xmath28 is the collision term . since we have considered the flat space - time geometry and noticed that there is no contribution of external magnetic field , only the induced electric field arising from local charge non - neutrality , causes an induced current in the system will contribute in the electromagnetic interaction term and the curvature term is neglected . to obtain the shear and bulk viscosity coefficients , heat conductivity and electrical conductivity of dense electron gas we make the relaxation time approximation , given by @xmath29 where @xmath30 i.e. , the system is assumed to be very close to the local equilibrium configuration . here @xmath31 is the relaxation time and @xmath32 is the ( local ) equilibrium distribution ( fermi distribution ) function , given by . we shall now follow the general technique to obtain the perturbed part @xmath34 as a linear sum of driving forces . following the formalism developed in the book by de groot @xcite , we express the four derivative as the sum of a space like part and a time like part , given by @xmath35 with @xmath36 the hydrodynamic velocity , @xmath37 is the convective time derivative and @xmath38 is the gradient operator , with @xmath39 some kind of projection operator , @xmath40 the metric tensor . then using the eqns.(6)-(9 ) , the decomposition of @xmath41 and the equations of motion , given by @xmath42 we obtain the perturbative part @xmath34 , given by @xmath43 } p_\nu e^\nu ( 1- f^{(0)})\end{aligned}\ ] ] where @xmath44 is the driving force for bulk - viscosity , @xmath45 is the driving force for heat conduction , @xmath46 is the driving force for shear viscosity and @xmath47 is the driving force for electric current ( @xmath47 for @xmath48 are the components of electric field vector ) . the quantity @xmath49 is given by @xmath50 with @xmath51 , @xmath52 and @xmath53 are the equilibrium local kinetic pressure and number density respectively . for a non - relativistic boltzmann gas @xmath54 , the local temperature of the system and finally @xmath55 , the enthalpy per particle with @xmath56 the local energy density and @xmath57 the ratio of specific heats at constant pressure and constant volume respectively . now from the definition , the heat flow four current is given by @xmath58 where the first term is the equilibrium contribution , which is identically zero . then omitting the symbol @xmath59 , we have the irreversible term @xmath60 again using the definition @xmath61 we have the heat conductivity coefficient @xmath62 now from the definition , the energy - momentum tensor is given by @xmath63 which can also be written as @xmath64 , with the equilibrium value @xmath65 and the non - equilibrium part @xmath66 which is a symmetric second rank tensor . now we consider a model in which a flow of electron gas with cylindrical symmetry is assumed . then considering @xmath67 , @xmath68 , we have from the definition @xmath69 hence the shear viscosity coefficient is given by @xmath70 where @xmath71 , the transverse component of electron momentum . then it is quite obvious that in presence of ultra strong magnetic field , for which @xmath72 , the shear viscosity coefficient vanishes . here @xmath73 is the maximum value of quantum number of the landau levels occupied by electrons for a given density and temperature . for @xmath74 , @xmath75,\ ] ] where @xmath76 $ ] indicates the nearest integer less than the actual value . to obtain an expression for bulk viscosity coefficient , we next consider the" +"in our previous paper @xcite , we extended the notion of vassiliev invariant and other invariants associated with chern simons theory to the context of spin networks @xcite . we showed that these invariants are loop differentiable in the sense of distributions and we defined an infinitesimal generator of diffeomorphisms in terms of the loop derivative . the generator correctly annihilates diffeomorphism invariant states . in this paper we will introduce a hamiltonian constraint based on the loop derivative . we will limit the discussion to invariants of trivalent vertices and will only concentrate on the `` euclidean '' part of the hamiltonian constraint in the sense of barbero @xcite and thiemann @xcite . limiting ourselves to trivalent intersections is clearly unphysical since the volume operator identically vanishes on such states . however , the essence of most calculations is already present with trivalent intersections and the calculational difficulty is significantly lower than with four or higher valent intersections . we will come back to this issue in the discussion section where we will highlight which results are quite plausibly going to survive when one goes to higher valent intersections . we will then extend the space of invariants through the construction of `` habitats '' such that the resulting states are not diffeomorphism invariant . based on these states we will check the consistency of the quantum commutator algebra of diffeomorphisms and hamiltonian . we will show that there are no anomalies , therefore constituting a consistent theory of canonical quantum gravity . we will start in the next section by introducing the hamiltonian constraint of quantum gravity in terms of the loop derivative . this derivation will be `` generic '' in the sense that we will motivate it through formal manipulations of the loop transform and therefore will not make specific assumptions about the quantum state in the connection representation on which the operator is acting upon . without being more precise about the space of states upon which it acts , we can not guarantee that the operator is well defined . we will show that on several spaces related to the vassiliev invariants the operator is indeed well defined . the results obtained will be later applied in specific `` habitats '' in which we will show that the operators exist and we can compute correctly the commutators . this we will discuss in section iii . the need to introduce new ( non - diffeomorphism - invariant ) `` habitats '' is based on the fact that the spaces we have considered in the companion paper are all diffeomorphism invariant and therefore one can not explore in a non - trivial way commutators involving the diffeomorphisms . we will introduce an explicit example of such a habitat in detail , the `` functions with marked vertices '' . in the end we will see that we will be able to recover the classical poisson algebra at the level of quantum commutators , but there will be subtle issues involved in the definition of the right hand side of the commutator of two hamiltonians , which we will discuss in detail . the last section will be devoted to discussing the implications of the level of consistency achieved by the theory . we wish to introduce a quantum version of the hamiltonian constraint of canonical general relativity . following thiemann @xcite , one can construct this operator introducing the real version of the ashtekar variables first discussed by barbero @xcite . in this formulation , the canonical pair consists of a set of ( densitized ) triads @xmath0 and as conjugate variables real - valued @xmath1 connections @xmath2 . the hamiltonian constraint of canonical , real , lorentzian general relativity in this framework consists of two terms , @xmath3 where @xmath4 in these expressions , @xmath5 is the newton constant and in ( [ k ] ) @xmath6 means that the smearing function @xmath7 is unity . this remarkable formulation implies that the hamiltonian constraint is composed by two terms . the first one , @xmath8 , coincides with the hamiltonian constraint one would obtain in a canonical formulation of general relativity on a manifold of euclidean signature . the lorentzian theory is therefore attained through the addition of an extra term . both terms are given as expressions involving the poisson bracket of a connection with the volume of the space @xmath9 and with the function @xmath10 . the latter can be in turn obtained as a poisson bracket of the euclidean part of the hamiltonian constraint with the volume . in this paper we will only concentrate on realizing at a quantum mechanical level the euclidean part of the hamiltonian . if the reader wishes , we are considering canonical quantum gravity in the euclidean context . however , it should be noticed that the additional term in the hamiltonian is obtained by successive commutators of the operator we will consider , with the volume operator . this suggests that one could generalize our construction to the lorentzian case rather straightforwardly , but this has not been studied in detail . the work of thiemann also shows that similar structures arise if one couples the theory to matter . we will in this paper only concentrate on the vacuum case but again one does not see a priori impediments to extend our treatment to general relativity coupled to matter . to implement the hamiltonian constraint we will partially use the same procedure proposed by thiemann . we will not describe it again in full detail here , we just list some of the salient features . one starts by writing the classical expression ( [ hame ] ) as @xmath11 f_\epsilon(y , x)\ ] ] where @xmath12 is a regularization of the dirac delta function , i.e. @xmath13 . strictly speaking , this expression is only gauge invariant in the limit , so to preserve gauge invariance in the regularization procedure we will `` join '' the @xmath14 with the connection using an infinitesimal piece of holonomy @xmath15 along an arbitrary path @xmath16 going from @xmath17 to @xmath18 , which tends to the null path in the limit @xmath19 . to unclutter the notation we will therefore denote @xmath20 , @xmath21 f_\epsilon(y , x ) \label{uno}\ ] ] in order to prepare the classical expression for quantization , we triangulate the space - like hypersurface @xmath22 in terms of elementary tetrahedra @xmath23 . the triangulation has the following properties : we select a finite set of distinct points of @xmath22 , denoted as @xmath24 . at each of these points we choose three independent directions @xmath25 and construct the eight tetrahedra with vertex @xmath26 and edges @xmath27 , with @xmath28 . the eight tetrahedra saturating @xmath26 define a closed region @xmath29 of length scale @xmath30 . the remaining region @xmath31 is triangulated by arbitrary tetrahedra @xmath32 . the motivation for this peculiar discretization is that when we promote the classical expression to a quantum operator , we will adapt the triangulation to the spin network of the state in question by choosing the points @xmath26 to coincide with the vertices of the spin network . in terms of this triangulation of space we can write equation ( [ uno ] ) in the form , @xmath33 f_\diamond(y)\,,\label{hamt}\ ] ] where the regions @xmath34 indicate either a box @xmath29 or a tetrahedron @xmath32 , and @xmath35 is any point interior to @xmath34 . conventionally we will choose for the boxes @xmath36 , and for the tetrahedra @xmath37 will represent one of its vertices . to discretize the integral we have introduced the volume of each region @xmath38 , @xmath39 where @xmath40 if @xmath41 , and @xmath42 if @xmath43 . in this last case , the @xmath44 s represent the edges of the tetrahedra @xmath32 adjacent to @xmath37 . we also have adapted the regularization of the dirac delta function to the tetrahedral decomposition by defining , @xmath45 where @xmath46 is one if @xmath47 and zero otherwise . we now replace in ( [ hamt ] ) the @xmath48 using formula ( [ vol ] ) and we represent @xmath49 using a holonomy in the fundamental representation along the edge @xmath50 of the triangulation , @xmath51f_\diamond(y)\ , , \label{classham}\ ] ] and we retraced the path described by the holonomy to preserve gauge invariance . it should be noticed that this retracing does not contribute to the expression at leading order in @xmath30 ( the scale parameter of the regions @xmath34 ) . we will now proceed to study the quantization of the last expression . for that we need to `` adapt '' the triangulation we introduced to a spin network state @xmath52 @xcite . let @xmath53 be the set of vertices of the spin network and let @xmath54 be the triples of non - coplanar edges incident at @xmath55 ( @xmath56 , being @xmath57 the number of such triples ) . to adapt the triangulation to the spin network state we perform two operations : first we identify the points @xmath26 of the boxes @xmath29 with the vertices @xmath55 and second , given a triple of edges @xmath54 incident at @xmath55 , we orientate the three unit vectors @xmath58 along the tangents of the edges at @xmath55 . then we can write , @xmath59 to simplify the notation we identify from now on @xmath60 . as in the previous paper , we assume we are acting on a state given by a loop transform , @xmath61 w_a[s]\ , , \label{states}\ ] ] and we realize the hamiltonian operator over the spin network wavefunctions by promoting the classical expression ( [ classham ] ) as an operator acting on the wilson net appearing in the loop transform , very much as we did in the companion paper when we discussed the diffeomorphism operator , @xmath62 \right)f_{\box_v}(y ) w_a(s)\,.\nonumber\end{aligned}\ ] ] a first observation is that the volume operator has non - vanishing contributions only at the vertices of the spin net , so we replace the sum in the hamiltonian over all @xmath34 s by a sum over all the vertices of the spin net . the second observation is that , for an n - valent vertex , we have taken the average over all the non - coplanar triples of edges associated with this vertex . finally notice that only one of the terms in the commutator contributes , that with the volume operator on the left . the one with the volume operator on the right vanishes since it is proportional to the trace of the lie algebra element @xmath63 . let us now consider a generic @xmath64valent vertex and study the action of the operator on the wilson net . we assume that the holonomies are all outgoing from @xmath26 . schematically , we are trying to represent the action of @xmath65 , with @xmath66 a generic edge of spin @xmath67 incident at @xmath26 . an @xmath64valent vertex is characterized by an intertwiner that can be represented through a vector @xmath68 of @xmath69 of irreducible representations . the factor @xmath70 acts by adding a line of spin @xmath71 ingoing from the vertex @xmath26 and parallel to the line @xmath66 , @xmath72 notice that the insertion of the holonomy leaves a wilson net that is not gauge invariant anymore , we represent this by keeping the group indices @xmath73 in the diagram . if one was acting on an @xmath64valent vertex characterized by an intertwiner @xmath68 , this leaves an @xmath74valent vertex characterized by intertwiners @xmath75 ; @xmath67 being in the diagram the spin of the line connecting the original vertex to the point ( infinitesimally nearby ) where the holonomy was inserted . notice that @xmath67 coincides with the spin of the original line @xmath66 . we denote that the line is infinitesimally close by the dashed circle . we now act with the volume operator . for that we" +"differential analysis is based on studying the time evolution of the distance between trajectories emanating from different initial conditions . a dynamical system is called contractive if any two trajectories converge to one other at an exponential rate . this implies many desirable properties including convergence to a unique attractor ( if it exists ) , and entrainment to periodic excitations @xcite . contraction theory proved to be a powerful tool for analyzing nonlinear dynamical systems , with applications in control theory @xcite , observer design @xcite , synchronization of coupled oscillators @xcite , and more . recent extensions include : the notion of partial contraction @xcite , analyzing networks of interacting agents using contraction theory @xcite , a lyapunov - like characterization of incremental stability @xcite , and a lasalle - type principle for contractive systems @xcite . a contractive system with added diffusion terms or random noise still satisfies certain asymptotic properties @xcite . in this respect , contraction is a robust property . in this paper , we introduce three forms of generalized contractive systems ( gcss ) . these are motivated by requiring to take place only after arbitrarily small transients in time and/or amplitude . indeed , contraction is usually used to prove _ asymptotic _ properties , and thus allowing ( arbitrarily small ) transients seems reasonable . in some cases as we change the parameters in a contractive system it becomes a gcs just before it looses contractivity . in this respect , a gcs is the analogue of marginal stability in lyapunov stability theory . we provide several sufficient conditions for a system to be a gcs . these conditions are checkable , and we demonstrate their usefulness using examples of systems that are _ not _ contractive with respect to any norm , yet are gcss . we begin with a brief review of some ideas from contraction theory . for more details , including the historic development of contraction theory , and the relation to other notions , see e.g. @xcite . consider the time - varying system [ eq : fdyn ] = f(t , x ) , with the state @xmath0 evolving on a convex set @xmath1 . we assume that @xmath2 is differentiable with respect to @xmath0 , and that both @xmath2 and @xmath3 are continuous in @xmath4 . let @xmath5 denote the solution of at time @xmath6 with @xmath7 ( for the sake of simplicity , we assume from here on that @xmath5 exists and is unique for all @xmath8 and all @xmath9 ) . we say that is _ contractive _ on @xmath10 with respect to a norm @xmath11 if there exists @xmath12 such that [ eq : contdef ] @xmath13 and all @xmath14 . in other words , any two trajectories contract to one another at an exponential rate . this implies in particular that the initial condition is `` quickly forgotten '' . recall that a vector norm @xmath15 induces a matrix measure @xmath16 defined by @xmath17 where @xmath18 is the matrix norm induced by @xmath19 . a standard approach for proving is based on bounding some matrix measure of the jacobian @xmath20 . indeed , it is well - known ( see , e.g. @xcite ) that if there exist a vector norm @xmath19 and @xmath12 such that the induced matrix measure @xmath21 satisfies [ eq : jtc ] ( j(t , x ) ) -c , for all @xmath13 and all @xmath22 then holds . ( this is in fact a particular case of using a lyapunov - finsler function to prove contraction @xcite . ) it is well - known ( * ? ? ? 3 ) that the matrix measure induced by the @xmath23 vector norm is [ eq : muqdef ] _ 1(a)=\{c_1(a ) , , c_n(a ) } , where [ eq : ccstac ] c_j(a):=a_jj+ _ |a_ij| , i.e. , the sum of the entries in column @xmath24 of @xmath25 , with non diagonal elements replaced by their absolute values . the matrix measure induced by the @xmath26 norm is [ eq : mat_meas_inf ] _ ( a)=\{d_1(a ) , , d_n(a ) } , where [ eq : dstac ] d_j(a):=a_jj+ _ |a_ji| , i.e. , the sum of the entries in row @xmath24 of @xmath25 , with non diagonal elements replaced by their absolute values . often it is useful to work with scaled norms . let @xmath27 be some vector norm , and let @xmath28 denote its induced matrix measure . if @xmath29 is an invertible matrix , and @xmath30 is the vector norm defined by @xmath31 then the induced matrix measure is @xmath32 one important implication of contraction is _ entrainment _ to a periodic excitation . recall that @xmath33 is called _ @xmath34-periodic _ if @xmath35 for all @xmath36 and all @xmath22 . it is well - known that if is contractive and @xmath37 is @xmath34-periodic then for any @xmath38 there exists a unique periodic solution @xmath39 of , of period @xmath34 , and every trajectory converges to @xmath40 . entrainment is important in various applications ranging from biological systems @xcite to the stability of a power grid @xcite . note that for the particular case where @xmath37 is time - invariant , this implies that if @xmath10 contains an equilibrium point @xmath41 then it is unique and all trajectories converge to @xmath41 . the remainder of this paper is organized as follows . . section [ sec : main ] details sufficient conditions for their existence , and describes their implications . the proofs of all the results are detailed in section [ sec : proofs ] . we begin by defining three generalizations of . [ def : qcont ] the time - varying system is said to be : * _ contractive after a small overshoot and short transient _ ( sost ) on @xmath10 w.r.t . a norm @xmath11 if for each @xmath42 and each @xmath43 there exists @xmath44 such that @xmath45 for all @xmath46 and all @xmath14 . * _ contractive after a small overshoot _ ( so ) on @xmath10 w.r.t . a norm @xmath11 if for each @xmath42 there exists @xmath47 such that @xmath48 for all @xmath46 and all @xmath14 . * _ contractive after a short transient _ ( st ) on @xmath10 w.r.t . a norm @xmath11 if for each @xmath43 there exists @xmath49 such that @xmath50 for all @xmath46 and all @xmath14 . the definition of sost is motivated by requiring contraction at an exponential rate , but only after an ( arbitrarily small ) time @xmath51 , and with an ( arbitrarily small ) overshoot @xmath52 . however , as we will see below when the convergence rate @xmath53 may depend on @xmath54 a somewhat richer behavior may occur . the definition of so is similar to that of sost , yet now the convergence rate @xmath55 depends only on @xmath54 , and there is no time transient @xmath51 ( i.e. , @xmath56 ) . in other words , so is a uniform ( in @xmath51 ) version of sost . the third definition , st , allows the contraction to `` kick in '' only after a time transient of length @xmath51 . it is clear that every contractive system is sost , so , and st . thus , all these notions are generalizations of contraction . also , both so and st imply sost and , as we will see below , under a mild technical condition on and sost are equivalent . figure [ fig : graphbn2 ] on p. summarizes the relations between these gcss ( as well as other notions defined below ) . the motivation for these definitions stems from the fact that important applications of contraction are in proving _ asymptotic _ properties . for example , proving that an equilibrium point is globally attracting or that the state - variables entrain to a periodic excitation . these properties describe what happens as @xmath57 , and so it seems natural to generalize contraction in a way that allows initial transients in time and/or amplitude . the next simple example demonstrates a system that does not satisfy , but is a gcs . [ exa : scalarsys ] consider the _ scalar _ time - varying system [ eq : scals ] x(t)=-(t)x(t ) , with the state @xmath0 evolving on @xmath58 $ ] , and @xmath59 is a class k function ( i.e. @xmath40 is continuous and strictly increasing , with @xmath60 ) . it is straightforward to show that this system does not satisfy w.r.t . _ any _ norm ( note that the jacobian @xmath61 satisfies @xmath62 ) , yet it is st , with @xmath63 , for any given @xmath43 . the next section presents our main results . the proofs are placed in section [ sec : proofs ] . the next three subsections study the three forms of gcss defined above . just like contraction , sost implies entrainment to a periodic excitation . to show this , assume that the vector field @xmath37 in is @xmath34 periodic . pick @xmath64 . define @xmath65 by @xmath66 . in other words , @xmath67 maps @xmath68 to the solution of at time @xmath69 for the initial condition @xmath70 . then @xmath67 is continuous and maps the convex and compact set @xmath10 to itself , so by the brouwer fixed point theorem ( see , e.g. ( * ? ? ? * ch . 6 ) ) there exists @xmath71 such that @xmath72 , i.e. @xmath73 . this implies that admits a periodic solution @xmath74 with period @xmath34 . assuming that the system is also sost , pick @xmath75 . then there exists @xmath44 such that @xmath76 for all @xmath77 and all @xmath78 . taking @xmath79 implies that every solution converges to @xmath80 . in particular , there can not be two distinct periodic solutions . thus , we proved the following . [ prop : st_entrain ] suppose that the time - varying system , with state @xmath0 evolving on a compact and convex state - space @xmath81 , is sost , and that the vector field @xmath37 is @xmath34-periodic . then for any @xmath82 it admits a unique periodic solution @xmath83 with period @xmath34 , and @xmath84 converges to @xmath80 for any @xmath85 . since both so and st imply sost , proposition [ prop : st_entrain ] holds for all three forms of gcss . [ def : nc ] system is said to be _ nested contractive _ ( nc ) on @xmath10 with respect to a norm @xmath19 if there exist convex sets @xmath86 , and norms @xmath87 , where @xmath88 $ ] , such that the following conditions hold . a. @xmath89 } \omega_\zeta=\omega$ ] , and [ eq : setsinc ] _ _ 1 _ _ 2 , _ 1 _ 2 . b. for every @xmath90 there exists @xmath91 $ ] , with @xmath92 as @xmath93 , such that for every @xmath77 and every @xmath94 [ eq : enter ] x(t , t_1,a ) _ , tt_1 + , and is contractive on @xmath95 with respect to @xmath96 . c. [ item : cc ] the norms @xmath96 converge to @xmath97 as @xmath98 , i.e. , for every @xmath99 there exists @xmath100 , with @xmath101 as @xmath102 , such that @xmath103 eq . means that after an arbitrarily short time every trajectory enters and remains in a subset @xmath95 of the state space on which we have contraction with respect to @xmath96 . [ thm : qcon ] if the system is nc w.r.t . the norm @xmath19 then it is sost w.r.t . the norm @xmath19 . the next example demonstrates theorem [ thm : qcon ] . it also shows that as we change the parameters in a contractive system , it may become a gcs when it hits the" +"exact solutions of the einstein equations are associated to highly idealized physical systems that have some exceptional geometrical properties . in some cases with a simple exact solution one can capture a significant part of the physical properties of non trivial systems . also , in nonlinear theories like general relativity and fluid dynamics the exact solutions play an important role in numerical analysis . these solutions can be used to test numerical codes and its outcomes . also they can be employed as initial conditions to describe more realistic situations , e.g. , a static solution can be used as part of the initial conditions for a full dynamical simulation . since the natural shape of an isolated self - gravitating fluid is axially symmetric , the solutions of einstein s field equations with this symmetry play a particularly important role in the astrophysical applications of general relativity . in particular disk like configurations of matter are of great interest , since they can be used as models of galaxies or accretion disks . also these disks can be used as starting point to represent more realistic models in which the bulge and halo of the galaxy are considered . solutions for static thin disks without radial pressure were first studied by bonnor and sackfield @xcite , and morgan and morgan @xcite , and with radial pressure by morgan and morgan @xcite . the first solution represent disks made of pressureless dust whereas the second disks with azimuthal pressure but without radial pressure . and the third a disk made of an anisotropic fluid with nonzero radial pressure . the bonnor - sackfield disk has a singular rim . these disks are finite . several classes of exact solutions of the einstein field equations corresponding to static @xcite and stationary @xcite thin disks have been obtained by different authors , with or without radial pressure . thin disks with radial tension @xcite , magnetic fields @xcite and magnetic and electric fields @xcite have been also studied . the non linear superposition of a disk and a black hole was first considered by lemos and letelier @xcite . this solution and its generalizations has been studied in some detail in @xcite . recently the stability of circular orbits of particles moving around black holes surrounded by axially symmetric structures have been considered in @xcite . for a recent survey on relativistic gravitating thin disks , see @xcite . except for the pressureless disks all the other disks have as source matter with azimuthal pressure ( tension ) different from the radial pressure ( tension ) . however , in some cases these disks can be interpreted as the superposition of two counter - rotating perfect fluids . a detailed study of the counter - rotating model for the case of static thin disks is presented in @xcite . recently , more realistic models of thin disks and thin disks with halos made of perfect fluids were considered in @xcite . in all the disks mentioned above an inverse style method was used to solve the einstein equations . the metric representing the disk is guessed and then it is used to compute the source ( energy - momentum tensor ) . this method was named by synge as the g - method @xcite in contrast to the t - method or direct method in which the source is given and the einstein equations are solved . the t - method , has been used to generate disks by the jena group @xcite . essentially , they are obtained by solving a riemann - hilbert problem . these solutions are highly non trivial , but they deserve special attention because of their clear physical meaning . in the solutions obtained by the g - method the well known `` displace , cut and reflect '' method is used . the idea of the method is simple . given a solution of the vacuum einstein equations , a cut is make above all singularities or sources . the identification of this solution with its mirror image yields relativistic models of disks . in general , these disks are of infinite extension and finite mass . the aim of this paper is to consider disks beyond the thin disk limit to add a new degree of reality to these geometric models of galaxies . even though in first approximation the galactic disks can be considered to be very thin , e.g. , in our galaxy the radius of the disk is 10@xmath0 and its thickness is 1@xmath0 . in a more realistic model the thickness of the disk need to be considered . also it is well known in fluid mechanics that the addition of a new dimension can make dramatic changes in the dynamics of the fluid . in principle , this new dimension will also change the dynamical properties of the the disk source , e.g. , its stability . in this paper we generalize the `` displace , cut and reflect '' method in order to obtain thick disks models from vacuum solutions of einstein equations . we shall replace the surface of discontinuity of the metric derivatives with a `` thick '' shell in such a way that the matter content of the disk will be described by continuous functions with continuous first derivatives . this generalization can be named `` displace , cut , _ fill _ and reflect '' method . the disks obtained with this method , in general , will be of infinite extension and finite mass . also as in the case of thin disks , the matter that form the thick disks will not obey simple equations of state and in some regions of the disk the pressure can change sign given rise to tensions . although the energy condition will be fulfilled . the models of thick disks presented can be considered as generalizations of models of thin disks studied in references @xcite and @xcite . the article is divided as follows . in sec . ii we present , in some detail , the main idea of the `` displace , cut , _ fill _ and reflect '' method in newtonian gravity . the method is then applied , in sec . iii , to construct relativistic thick disks in weyl coordinates . we also study the general expression for the energy - momentum tensor of the disks . the method is illustrated by taking two simple weyl solutions that lead to thick disks in agreement with all the energy - conditions . in sec . iv we apply the method to the schwarzschild solution in isotropic cylindrical coordinates . the disk obtained also satisfy all the energy conditions , this disk have equal azimuthal and radial pressures and different vertical pressure . finally , in sec . v , we summarize our main results . @xmath1 @xmath2 @xmath3 the newtonian gravitational potential of a thin disk can be obtained by a simple procedure , the `` displace , cut and reflect method '' , due to kuzmin @xcite . the method can be divided in the following steps : first , choose a surface that divides the usual space in two parts : one with no singularities or sources an the other with the sources . second , disregard the part of the space with singularities . third , use the surface to make an inversion of the nonsingular part of the space . the result will be a space with a singularity that is a delta function with support on @xmath4 . this procedure is depicted in fig . [ fig : thind ] . in order to obtain a thick disk we need to modify the above procedure . we essentially need to replace the surface of discontinuity with a `` thick '' shell in such a way that the matter content of the disk be described by continuous functions . now method has an additional step and can be named `` displace , cut , _ fill _ and reflect '' . after we disregard the part of the space with singularities , we put a thick shell below the surface . then we use the bottom surface of the shell to make the inversion . the procedure is illustrated in fig . [ fig : thickd ] . mathematically the method is equivalent to make the transformation @xmath5 , where @xmath6 is a constant and @xmath7 an even function of @xmath8 . in newtonian gravity , the potential @xmath9 is a solution of the laplace equation @xmath10 where @xmath11 are the usual cylindrical coordinates . after we make the transformation @xmath12 , the above equation leads to @xmath13 \phi_{,hh } , \label{eq : laph}\ ] ] where primes indicate differentiation with respect to @xmath8 . for the case of thin disks we take @xmath14 . note that @xmath15 and @xmath16 where @xmath17 is the heaveside function and @xmath18 the usual dirac distribution . by using ( [ eq : laph ] ) , the poisson equation leads to a mass density given by @xmath19 we have a surface distribution of matter located in the plane @xmath4 . in fig [ fig : figh ] , with dashed lines , we plot @xmath7 an its derivatives . for the case of thick disks the function @xmath20 must be selected in such a way that @xmath21 and its first derivatives be continuous across the plane @xmath22 . let us take a function @xmath7 defined as @xmath23 hence , by taking the function @xmath20 above defined we can generate disks of thickness @xmath24 located in the region @xmath25 . in fig . [ fig : figh ] we plot @xmath7 an its derivatives ( solid lines ) . when @xmath26 the function @xmath7 is a linear function of @xmath8 such that @xmath27 . hence , its second derivative is zero . then the mass density vanish outside the disk . since the first derivative is continuous at @xmath28 ( see fig . [ fig : figh ] ) and the second derivative piecewise constant we have that the mass density , @xmath29 , will be well defined inside the disk , @xmath30 for @xmath31 and @xmath32 for @xmath33 . as a simple example we can consider the usual potential for a mass point , written in cylindrical coordinates as @xmath34 by doing the transformation @xmath12 in the previous potential , we obtain the mass densities @xmath35 for a thin disk ( kuzmin - toomre disk @xcite ) , and @xmath36}{8 \pi a^2 { \rm r}^3 } \nonumber \\ & & \label{thicknden}\\ & + & \frac{3m(a^2 - z^2)(z^2 + 2ab)^2}{16 \pi a^4 { \rm r}^5 } , \nonumber \end{aligned}\ ] ] where @xmath37 , for a thick disk . when @xmath38 , the mass density will be positive everywhere . the function @xmath20 presented in ( [ eq : funh ] ) is the simplest function that have the desired properties . the part of the function in the domain @xmath39 can be changed by superposition of even functions of @xmath8 . in @xmath28 this new function need to be matched continuously with linear functions of @xmath8 such that @xmath27 , like in ( [ eq : funh ] ) . in this case the mass density can depend on the variable @xmath8 in a more general way . it is instructive to obtain the surface thin disk density ( say @xmath40 ) associated to ( [ thinnden ] ) , @xmath41 as a limit of the thick disk volume density ( [ thicknden ] ) . to obtain the surface density of the thin disk from the volume density ( [ thinnden ] ) we first do @xmath42 now to perform the thin disk limit we put @xmath43 and @xmath44 ( @xmath45 and @xmath46 artitrary constants ) in @xmath47 and we take the limit @xmath48 this limit is" +"although this is a meeting on aspherical planetary nebulae ( pne ) , which are the descendants of intermediate / low - mass stars , i d briefly like to shift gears and discuss massive stars . in the nebulae around massive stars , like pne , we see a wide variety of non - spherical geometries with a common theme of bipolar shapes in the ejecta . for most of the more stunning examples of massive star nebulae , one can usually find a pn with nearly identical appearance , at least superficially . some of the more familiar comparisons are @xmath0 car to hb 5 , mz 3 , or even the red rectangle ( soker 2007 ) , as well as the similar multiple rings seen around sn 1987a , the luminous blue variable ( lbv ) star hd 168625 ( smith 2007 ) , the red square ( tuthill & lloyd 2007 ) , and he 2 - 104 ( corradi et al . 2001 ) , or the peculiar double rings around ry scuti ( smith et al . 2002 ) and abel 14 , to name a few . not surprisingly , discussions of the shaping mechanisms for massive stars and pne share common themes : binaries / mergers vs.interacting winds vs. rotating ejections . for massive stars , though , magnetic fields still seem to be mostly taboo for the time - being . also , like lower mass stars during the agb phase , it seems to be the case that massive stars shed most of their mass in a brief post - ms evolutionary phase , either as a rsg or an lbv . this was not always thought to be the case : for very massive stars , the relative importance of lbv eruptions vs. steady winds has been appreciated fairly recently because of the revised lower mass - loss rates estimated for o stars on the main sequence , and because of the very high masses of lbv nebulae ( see smith & owocki 2006 ) . despite vastly different amounts of mass and energy , the compelling similarities between massive star nebulae and pne make it worthwhile to ask if conclusions gleaned from massive stars can inform the shaping mechanisms of pne , and vice versa . in the interest of being provocative , then , i ll mention some results for eta carinae and a few other massive stars that have been studied in detail , which challenge some familiar ideas developed from the study of pne . but first , some general comments on winds . a fast wind sweeping into a slower and denser wind is a natural avenue to pursue for shaping nebulae , and such models have had varying degrees of success in reproducing pne shapes ( there are dozens of potential references to cite here , including many in these proceedings ) . a similar process may occur in _ some _ massive stars if they pass through a very slow - wind phase as a rsg and then evolve through a faster wind phase as a bsg / lbv or a wolf - rayet ( wr ) star . this can and does produce a wind - blown bubble around the wr star in some cases . a key point , though , is that in the case of massive stars we have some problems if we want interacting winds to account for most bipolar nebulae . first , the slower nebulae around rsgs and yellow hypergiants are generally not axisymmetric . they are often asymmetric or chaotic , but they almost never have clear signs of organized axisymetry ( see , e.g. , vy cma [ smith et al . 2001 ] ; nml cyg [ schuster et al . 2006 ] ; irc+10420 [ humphreys et al . 2002 ] ) . second , the resulting wind - blown bubbles around wr stars are _ not _ bipolar ! this lack of axisymmetry occurs despite the apparent fact that massive stars have high binary fractions . what does that mean ? if binary mergers and jets blown by binaries are dominant shaping mechanisms , should nt we see signs of axisymmetry at all stages ? why is it the case that the only bipolar / pinched - waist nebulae around massive stars are those seen around blue supergiants such as lbvs and b[e ] supergiants ? a critical point , i think , is that _ in these blue supergiants , their escape speeds , observed ejecta / wind speeds , and surface rotation speeds are all comparable_. they are around 100200 km s@xmath1 , as opposed to 1020 km s@xmath1 for rsgs and 1000 - 2000 km s@xmath1 for wr stars . i suspect that this is an important clue that for many nebulae around massive stars , intrinsically aspherical ejection from the surface of a rotating star is a prime agent in shaping their nebulae ( see smith & townsend 2007 ) . in the context of interacting winds , then , i suspect that a very interesting avenue to pursue is an aspherical fast wind interacting with a slow spherical wind or thin shell . in fact , due to the sporadic nature of episodic mass loss from massive stars , thin shells rather than steady winds is probably where most of the circumstellar mass resides . now , that discussion of interacting winds was for massive stars that go through a slow - wind rsg phase followed by a fast wind phase in their evolution ... but that only occurs up to initial masses of about 40 m@xmath2 . stars with higher initial mass ( like eta car and most lbvs ) never pass through a rsg phase . so for these stars , _ ejection as an lbv is the slowest the wind speeds ever get ... but it is precicesly those lbv nebulae that are observed to be bipolar_. how can this be ? this means that they ca nt be shaped by interacting winds , because a slow dense wind blowing into a faster rarefied wind does nt produce much interaction . instead , the slow dense wind that follows the fast wind needs to be shaped on its own ; this is discussed and amplified below . despite the lack of interaction between the fast and slow wind , they produce shapes very similar to some pne a fact worth considering . eta carinae is a key object for trying to understand the shaping of bipolar nebulae , partly because is it bright and so well - observed , and partly because we have caught it so soon ( only 160 yr ) after its violent mass ejection , before its shape has been corrupted by interaction with the ism . despite its status as the most luminous and most massive star known , there is considerable overlap with some topics in pne research , as i will highlight here . studies of the mass , kinematics , and detailed structure have led to the following basic results ( summarized from smith 2006 ; smith et al.2003 ) : \1 . the nebula follows a hubble - like expansion law , with the same age for the equatorial and polar ejecta . the walls of the nebula are very thin , indicating that the duration of mass ejection was less than 10% of the time elapsed since ejection . essentially all the mass is in the thin molecular shell , formed from material ejected by the star in the outburst , not in swept - up material . the large mass , momentum , and kinetic energy came from a single exlposive event , and could not have been driven by radiation pressure alone or by the stellar wind that has blown after the eruption . all these clues point to a single violent bipolar explosion that ejected the nebula seen today . interestingly , all these same basic conclusions were inferred by alcolea et al . ( 2007 ) from a similar detailed study of the pn m 1 - 92 . in the case of eta carinae , though , the difficulties for an interacting winds scenario are compounded further . the mass as a function of latitude has been measured in the bipolar lobes around eta car , showing that most of the mass comes from high latitudes near the pole ( smith 2006 ) . this rules - out the familiar type of interacting - wind scenario where a spherical wind plows into a disk or torus ( e.g. , frank et al . 1995 ) , because in that scenario , the pinched waist is essentially the result of mass loading at low latitudes ( note that the bipolar nebula formed in a merger model is a variation of this ) . similarly , a different type of interacting winds scenario where a fast aspherical wind plows into a slower wind does nt work either ( frank et al . 1998 ; gonzalez et al.2004 ) . this is because we can observe the stellar wind that has been blowing after the 19th century eruption , potentially inflating and shaping the nebula . however , it is about 1000 times too weak to shape the polar lobes ( like a light breeze blowing on a brick wall ) , and besides , the post - outburst wind speed is almost the same as that of the nebula , so the winds are not interacting anyway ! there seems to be little way to escape the conclusion that the bipolar shape of the homunculus nebula around eta car resulted from an intrinsically bipolar ejection by the star itself , and not from any sort of interacting winds scenario . a possible avenue to pursue is discussed after the next section . i d like to diverge for a moment to talk about the detailed ionization structure in the walls of the nebula around eta car , as opposed to its overal bipolar shape , where additional similarities to some pne can be seen . eta car s nebula has a distinct double - shell structure , with a thin outer shell composed of molecular gas and cool dust , and a thicker inner shell of partially - ionized atomic gas and warmer dust ( smith 2006 ; smith et al . in high - resolution spectra and images of h@xmath3 2.122 @xmath4 m and [ fe ii ] 1.644 @xmath4 m , this structure is almost identical to that seen in some pne , most notably in m 2 - 9 ( hora & latter 1994 ; smith et al . . these near - ir h@xmath3 and [ fe ii ] emission lines are usually taken as signposts for shock excitation ( shull & hollenbach 1978 ) because they are seen in supernova remnants , and the double - shell structure is reminiscent of a forward / reverse shock structure that one might expect for interacting winds ( e.g. , chevalier 1982 ) . however , they can also arise from dense atomic and molecular gas that is heated radiatively in a dense pdr ( e.g. , sternberg & dalgarno 1989 ) . using cloudy simulations , smith & ferland ( 2007 ) demonstrated that the observed ir emission tracers , ionization structure , and the observed dust temperatures can arise naturally from radiative heating if the two shells contain roughly the amount of mass inferred from studies of the dust ( smith et al . in fact , in the case of eta car , radiative heating dominates the energy budget compared to shock heating . this is comforting , because as noted earlier , the post - eruption wind speed is very similar to that of the nebula ejected in the eruption , so" +"according to greek mythology the goddess of wisdom , pallas athene , emerged clad in full armor after hephaestus split open zeus s head . in much the same way the local group sprang forth suddenly , and almost complete , in chapter vi of the realm of the nebulae ( hubble 1936 , pp . 124 - 151 ) . hubble describes the local group as `` a typical small group of nebulae which is isolated in the general field '' . he assigned ( in order of decreasing luminosity ) m31 , the galaxy , m33 , the large magellanic cloud , the small magellanic cloud , m32 , ngc205 , ngc 6822 , ngc 185 , ic 1613 and ngc 147 to the local group , and regarded ic 10 as a possible member . in the 2/3 century since hubble s work , the number of known local group members has increased from 12 to 36 ( see table 1 ) by the addition of almost two dozen low - luminosity galaxies . recent detailed discussions of individual local group galaxies are given in mateo ( 1998 ) , grebel ( 2000 ) and van den bergh ( 2000a ) . hubble ( 1936 , p. 128 ) pointed out that investigations of the local group were important for two reasons : [ 1 ] `` [ t]he members have been studied individually , as the nearest and most accessible examples of their particular types , in order to determine the[ir ] internal structures and stellar contents '' . in the second place [ 2 ] , `` the [ g]roup may be examined as a sample collection of nebulae , from which criteria can be derived for further exploration '' . small galaxy groups , like the local group , are quite common . from inspection of the prints of the _ palomar sky survey _ van den bergh ( 2002a ) has estimated that 16% of nearby galaxies are located in such small groups . hubble ( 1936 , p. 128 ) emphasized that `` the groups [ such as the local group ] are aggregations drawn from the general field , and are not additional colonies superposed on the field '' . from its observed radial velocity dispersion of 61 @xmath0 8 km @xmath1 the local group is found to have a virial mass of ( 2.3 @xmath0 0.6 ) x @xmath2 m@xmath3 ( courteau & van den bergh 1999 ) . the zero - velocity surface of the local group has a radius of 1.18 @xmath0 0.15 mpc , but @xmath480% of the local group members are actually situated within 0.4 mpc of the barycenter of the local group , which is located between m31 and the galaxy . from its virial mass , and the integrated luminosity of group members of 4.2 x 10 @xmath5 l@xmath3 , the dynamical mass - to - light ratio of the local group is found to be @xmath6 = 44 @xmath0 12 in solar units . such a high m / l value is an order of magnitude larger than the mass - to - light ratio in the solar neighborhood of the galaxy . this supports the conclusion by kahn & woltjer ( 1959 ) that the mass of the local group is dominated by invisible matter . the local group is situated in the outer reaches of the virgo supercluster . the nearest neighbor of the local group is the small antlia group ( van den bergh 1999a ) . this tiny cluster is located at a distance of only 1.7 mpc from the barycenter of the local group , i.e. well beyond the zero - velocity surface of the group . the antlia group has a mean radial velocity of + 114 @xmath0 12 km s@xmath7 . the number of galaxies brighter than m@xmath8 = -11.0 in the local group is 22 , compared to only four such objects in the antlia group . however , because the antlia group contains no supergiant galaxies like m31 and the milky way system , its integrated luminosity is @xmath4150 times smaller than that of the local group . since the local group is a relatively small cluster , this result suggests that clusters of galaxies have a range in luminosities ( and masses ? ) that extends over at least four orders of magnitude . the centaurus group ( van den bergh 2000b ) , at a distance of @xmath43.9 mpc , which contains m 83 ( ngc 5236 ) and centaurus a ( ngc 5128 ) , is the nearest massive cluster . if one assumes ngc 5128 and ngc 5236 to be members of a single cluster one obtains a total virial mass of 1.4 x 10@xmath9 m@xmath3 and a zero - velocity radius of 2.3 mpc for the centaurus group . in other words the zero - velocity surfaces of the centaurus group and the local group would almost touch each other . however , karachentsev et al . ( 2002 ) conclude that the galaxies surrounding ngc5128 and m83 , respectively , actually form dynamically distinct clusterings . if that is indeed the case then the total mass of these clusters is reduced to only 3 x 10@xmath10 m@xmath3 , and the radius of the zero velocity surface around cen a is less than 1.3 mpc . a second massive nearby cluster contains ic342 and the highly obscured elliptical maffei 1 . mccall ( 1989 ) concluded that `` it is likely that ic342 and maffei 1 had a significant impact on the past dynamical evolution of the major members of the local group '' . more recently fingerhut et al . ( 2003ab ) have , however , found that the galactic absorption in front of maffei 1 is lower than was previously believed . as a result the distances to maffei 1 , and its companions , are too large for these objects to have had significant dynamical inetractions with individual local group members since the big bang . if the peculiar velocities of galaxies are induced by gravitational interactions , then one might have expect massive field galaxies to have a lower velocity dispersion than dwarfs . data on the nearby field ( whiting 2003 ) do not appear to support this expectation . whiting finds the mean radial velocity dispersion among field galaxies within 10 mpc to be 113 km s@xmath7 . a much lower dispersion of @xmath430 km s@xmath7 for the local hubble flow has , however , been found by karachentsev et al . it is noted in passing that the former value appears to be significantly larger than the radial velocity dispersion of 61 @xmath0 8 km @xmath1 that courteau & van den bergh ( 1999 ) found within the local group itself . to first approximation the local group is a binary system with massive clumps of galaxies centered on m31 and on the galaxy . van den bergh ( 2000 , p. 290 ) estimates a mass m(a ) = ( 1.15 - 1.5 ) x 10@xmath10 m@xmath3 for the andromeda subgroup of the local group , compared to m(g ) = ( 0.46 - 1.25 ) x 10@xmath10 m@xmath3 for the galactic subgroup . more recently sakamoto , chiba & beers ( 2003 ) have given somewhat higher mass estimates . if leo i is included they find m(g ) = ( 1.5 - 3.0 ) x @xmath2 m@xmath3 , compared to m(g ) = ( 1.1 - 2.2 ) x 10@xmath10 m@xmath3 if it is assumed that leo i is not a member of the galactic subgroup . recent proper motion observations by piatek et al . ( 2002 ) suggest that the fornax dwarf spheroidal galaxy may not , as had previously been thought , be a distant satellite of the galaxy . instead the data appear to indicate that fornax is a free - floating member of the local group that is presently near perigalacticon . within each of the two main local group subclusters there are additional subclumps such as the m31 + m32 + ngc205 triplet , the ngc147 + ngc185 binary , and the lmc + smc binary . for the entire local group one finds , at the 99% confidence level , that low - luminosity early - type dsph galaxies are more concentrated in subclumps than are late - type dir galaxies . in other words most dir galaxies appear to be free - floating members of the local group , whereas the majority ( but not all ) dsph galaxies seem to be directly associated with either m31 or the galaxy . it is not yet clear if the mean ages of the stellar populations in dsph galaxies are themselves a function of location . van den bergh ( 1995 ) has tentatively suggested that there is some evidence to suggest that star formation in dsph galaxies in the dense regions close to m31 and the galaxy might typically have started earlier than star formation in remote dsph galaxies . the data that are shown in table 2 show a strong correlation between the morphological types of faint galaxies with @xmath11 ( i.e. objects fainter than m32 ) and their environment . this dependence was first noticed by einasto et al . almost all sph + dsph galaxies are seen to be associated with the two dense subclusters within the local group , whereas most ir galaxies appear to be more - or - less isolated group members . it seems quite possible possible ( cf . skillman et al . 2003 ) that the faint dir and dsph galaxies have similar progenitors , and that the differences between them that are observed now are due to environmental factors that favored gas loss from those dwarfs that occurred in dense environments , i.e. near giant galaxies . within the local group the m31 , m32 , m33 subgroup has a total luminosity l@xmath8 = 3.0 x 10@xmath5 l@xmath3 , which is significantly greater than that of the subgroup centered on the milky way system which has l @xmath8 = 1.1 x @xmath12 l@xmath3 . these luminosities of the m31 and galactic subgroups account for 71% and 24% of the total local group luminosity , respectively . it should , however , be noted that some uncertainty in the luminosity ratio of m31 , to that of the galaxy , is introduced by the fact that both of these systems are viewed edge - on . as a result the internal absorption corrections ( which may be quite large ) are uncertain . nevertheless , the notion that m31 is more massive than the galaxy receives some support from the observation that m31 appears to have 450 @xmath0 100 globular clusters , compared to only 180 @xmath0 20 such clusters associated with the galaxy ( barmby et al . 2000 ) . furthermore ( freeman 1999 ) the bulge mass of m31 is 3.6 x 10@xmath5 m@xmath3 , which is almost twice as large as the 2 x 10@xmath5 m@xmath3 mass of the galactic bulge . on the basis of these results one might have expected the total mass of the m31 subgroup of the local group to be two or three times larger than that of the galaxy subgroup . surprisingly this does not appear to be the case evans & wilkinson ( 2000 ) . using radial velocity observations evans et al . ( 2000 ) conclude that `` there is no dynamical evidence for the widely held belief that m31 is more massive - it may even be less massive '' . more recently gottesman et al . ( 2002 ) have also concluded from dynamical arguments that the mass of m31 `` is unlikely to be as great as that of our own milky way '' . these" +"during the last decades we have witnessed a rapid development of methods of geometrical quantization . it was triggered by the discovery of the integration measure over two - dimensional geometries which was applied in calculations of quantum amplitudes in string theory @xcite . in practice , it turned out that the geometrical quantization of strings works only for either non - physical dimensions @xmath12 @xcite , or in the critical dimension @xmath13 where the world - sheet degrees of freedom of the string decouple from the theory @xcite . the case of non - critical strings with @xmath12 was also independently formulated in terms of a matrix model which is equivalent to the dynamical triangulations approach @xcite . this method allows for calculating different topological contributions in the double scaling limit @xcite . however , both the polyakov conformal field approach and the matrix model calculations break down at @xmath14 . the problems that turn up at this point , also known as the ` @xmath14 barrier ' , are attributed to instabilities of the conformal mode . whether it is possible to stabilize the conformal mode for surfaces embedded in physical dimensions is not yet clear . some attempts to solve this problem have been made within the conformal field formalism @xcite . another idea is to extend dynamical triangulations to the sypersymmetric case , and to attack the problem directly in physical dimensions . by introducing supersymmetry one hopes to avoid the instabilities of bosonic surfaces that manifest as the degeneration of the world - sheet geometry into branched polymers @xcite . disrectization of supersymmetric surfaces is known to be a difficult problem . a discretization of the world - sheet supersymmetry , for example , inherits all the difficulties which appear arleady on regular lattices @xcite and on top of this it introduces new problems related to the fact that the symmetry must be local @xcite . supersymmetry is broken explicitly by the lattice , and it is not clear how to ascertain whether it gets restored in the continuum limit . one encounters similar problems for the green - schwarz type of surfaces where one has to preserve the @xmath15-symmetry , which is a local world - sheet symmetry @xcite . one also attempted to introduce supersymmetry into the surfaces models indirectly by considering models with effective actions with extrinsic curvature terms obtained by integrating out fermions from the supersymetric theory @xcite . such discretized surfaces have been extensively studied ( see e.g. @xcite ) , but it is not clear what is nature of the critical point observed in the discretized theory and whether it can be directly related to the original supersymetric theory of continuum surfaces . in this paper we study a model of supersymmetric surfaces that constitutes a sort of classical limit of the ikkt matrix model @xcite obtained by sending the matrix size @xmath0 to infinity @xcite . the attractive feature of the surface model is that the supersymmetry is introduced in such a way that in principle the model can be straightforwardly discretized . by re - writing the iib string action in the schild gauge @xcite , one avoids the problems related to the proper treatment of the local @xmath15-symmetry in the discretization . the action that results from this procedure has no redundant degrees of freedom left , and no local symmetry . we investigate this model by means of the dynamical triangulation approach . some preliminary studies in this direction were already done in @xcite . we perform monte - carlo simulations of surfaces embedded in a 4dimensional target space . we find a theoretical picture that explains the numerical results for @xmath16 , and allows us to make some predictions for the behaviour of the ten dimensional version of the model . the results presented here give an insight into typical geometrical features of surfaces that play an important role in the ensemble generated by the ikkt matrix model @xcite . the paper is organized as follows . first we shortly recall the model and describe the discretization scheme . then we discuss singularities of the purely bosonic model and show that they are removed by adding fermions . for the model with fermions we estimate the large @xmath17 behaviour of the partition function by assuming that it is dominated by tube like configurations . we present the results of the @xmath18 simulations to show that tubes do indeed dominate in the ensemble . we conclude the paper with a short discussion , concerning in particular the relation of the results to the matrix model @xcite . the action for iib strings can be cast into the following form @xcite : @xmath19 here @xmath20 is the metric tensor on the world - sheet ; @xmath21 are bosonic co - ordinates in the @xmath22-dimensional target space ; @xmath23 and @xmath24 are @xmath25-dimensional spinors ; and @xmath26 are @xmath27 dirac matrices . for @xmath13 , the dimensionality of the spinor representation is @xmath28 , and @xmath29 are majorana - weyl spinors . for @xmath30 , we have @xmath31 , and @xmath29 are weyl spinors . the poisson brackets in are defined as @xmath32 based on this action the authors of @xcite introduced a matrix model which was then interpreted as a constructive definition of superstring theory . the matrix model is obtained from by substituting fields @xmath33 and @xmath34 by @xmath35 traceless hermitean matrices , and the poisson brackets by commutators @xmath36 $ ] . the resulting theory @xmath37 ^ 2 + \frac{1}{2 } \bar{\phi } \gamma_\mu [ a^\mu , \phi ] - \lambda \mathbbm{1 } \right ) \label{maction}\ ] ] is quantized by the feynman integral @xmath38 with the standard integration measure for traceless hermitean matrices . this procedure defines a kind of third quantization of string theory , which is supposed to reproduce in a double scaling limit the sum over all topological and geometrical excitations of the world - sheet of strings @xcite . the original model @xcite was defined in ten dimensions . here we will discuss the semiclassical limit of @xmath39 , in which the model reduces to the string theory on a fixed topology @xcite with the partition function @xmath40 where the action is given by . we will concentrate for now on the case @xmath30 , where we can most easily perform numerical simulations . we use the dynamical triangulation approach to regularize the integration measure @xmath41 . the partition function is then given by @xmath42 where @xmath43 the sum runs over equilateral , oriented triangulations @xmath44 with @xmath0 triangles and @xmath45 vertices . @xmath46 is the symmetry factor of a given @xmath44 , and @xmath47 is the discretized action on this particular triangulation . primes on the products indicate that the zero modes were removed ( see the following discussion ) . the fields @xmath48 and @xmath49 are now located on the vertices of @xmath44 . the action has one parameter , namely the cosmological constant @xmath50 . the continuum limit is taken by adjusting @xmath50 in the grand - canonical partition function @xmath51 to its critical value and sending the lattice spacing @xmath52 to zero . alternatively , if one prefers to work with the ensemble of canonical partition functions @xmath53 , one can take the continuum limit by simultaneously sending @xmath0 to infinity and @xmath52 to zero while holding the physical area of the worldsheet @xmath54 fixed . this latter approach is the one we will choose here . the discretized action consists of two terms , a purely bosonic part @xmath55 and a fermionic part @xmath56 . following the suggestions in @xcite , these are : @xmath57 in contrast to the action presented in @xcite , here @xmath58 are weyl fermions . the first sum runs over all triangles of the triangulation , the second over all links . the constant in is set to @xmath59 . the operation @xmath60 , when acting on an oriented link @xmath61 , gives that neighbour of @xmath62 that comes after @xmath63 when going counterclockwise around @xmath62 . in other words , if we denote two neighbouring oriented triangles by @xmath64 and @xmath65 , then @xmath66 and @xmath67 ( see figure [ omega ] ) . two neighbouring , oriented triangles @xmath64 and @xmath65 , connected by the link @xmath61 . the ` outer ' vertices @xmath25 and @xmath68 can be accessed by the operation @xmath60 as defined in the text , with @xmath66 and @xmath67.,height=188 ] two things should be noted about this action . firstly , the bispinors @xmath58 in the target space have a handedness , _ i.e. _ @xmath69 and @xmath70 . using the chiral representation of the dirac matrices in the euclidean sector , @xmath71 where @xmath72 are the pauli matrices and @xmath73 is the @xmath74 unity matrix , we can parametrize the chiral bispinors @xmath23 and @xmath24 in terms of two - component spinors @xmath75 : @xmath76 thus , we can re - write the fermionic part of the action as @xmath77 \psi_j \label{sf}\ ] ] where @xmath78 are real numbers that are antisymmetric in @xmath62 and @xmath63 , @xmath79 . secondly , the action has a zero mode related to the translational invariance in the bosonic sector , @xmath80 . as a remnant of the original supersymmetry , there is also a similar symmetry in the fermionic sector : @xmath81 , @xmath82 @xcite . this might be not evident at first sight , but the change in the action is indeed zero , @xmath83 because for each vertex @xmath62 the sum of the @xmath84 over all its neighbours @xmath63 is zero : @xmath85 . these zero modes have to be divided out in the measure . in practice , this can be done by inserting a delta function @xmath86 and an additional product @xmath87 which acts like a delta function for the grassmann variables @xmath88 for one vertex . taking all this into account , the canonical partition function for the four dimensional model now reads @xmath89 where @xmath90 integration over the fermions results in the appearance of a factor @xmath91 , where @xmath92 is a @xmath93 matrix that is obtained from @xmath94 by crossing out the two rows and columns that correspond to the vertex @xmath68 . the determinant @xmath95 is a non - negative function of bosonic coordinates @xmath96 , a feature that is essential for the mc simulations . it follows from the structure of the matrix @xmath92 , which has pairs of complex conjugated eigenvalues @xmath97 . ( more specifically , if @xmath98 is an eigenvector to the eigenvalue @xmath50 , then @xmath99 is an eigenvector to the eigenvalue @xmath100 . ) the final form of the partition function is now @xmath101 where for convenience we introduced an additional parameter @xmath102 . for @xmath103 we have the purely bosonic model ; @xmath104 is the case considered in @xcite ; and @xmath105 corresponds to our partition function . as we will see , the model with @xmath105 , for which the number of bosonic and fermionic degrees of freedom is susy balanced , is the only interesting one , because only in this case is the partition function well - defined . the behaviour of the partition function for the purely bosonic model @xmath106 has already been discussed in the context of the quantization of the nambu - goto string @xcite , where it was shown that this partition function is in general not integrable . namely , one can explicitly construct triangulations for which the integral over bosonic fields is divergent . the source of this divergence can be intuitively explained as follows . the bosonic part of the action is the sum of all triangle areas squared , with the areas measured in the target space . thus , as long as the areas of all triangles stay constant , we can change their shape without changing the action . as an example , let us pick an" +"phenix @xcite is a large , widely spread collaboration where many organizations from many countries participate ( 12 nations , 57 institutions , about 400 collaborators , about 1/4 pb is planned to be produced in the current year ) . the collaboration is in third year of data taking . distributed data ( experimental and simulated ) , distributed computing facilities and distributed users is our reality . before discussing technical decisions we have to emphasize a range of common things and features in grid computing for hep which are important for further discussion . first of all we paid attention that many systems for physics analysis are already in developing or prototyping stage @xcite . we recognized that using the globus tools @xcite is now standard de facto for distributed systems in hep . the last thing was emphasized many times on chep2003 @xcite . in more detail we could see the following common components ( on all projects ) : * using globus security infrastructure ( gsi ) ; * using the replica / file catalog for files distributed around the globe , however different projects use different cataloging engines : globus replica catalog @xcite , other types of file catalogs ; * using the gridftp over wan in conjunction with other data moving protocols @xcite ; * job submission with globus tools ; * using the concept of virtual organization . that is not surprising because every collaboration ( phenix is not exclusion ) needs several common tools : * data moving over wan ; * job submission from distributed users to distributed computing clusters ; * monitoring tools . on other hand the character of using globus middleware is different in different projects . if someone tries to see in deeper details - a lot of differences between collaborations could be discovered . those differences are rooted in the style of physics measurements which in turn depends on the details of the physics experiment , style of collaboration work , existing computing resources , prehistory of computing infrastructure and many other details . in other words there is no evidence that concrete large and sophisticated system built on top of grid middleware might be used in a different collaboration without reasonable adaptation or redesigning . that means we have to discuss briefly phenix computing environment for physics analysis . phenix has several computing facilities for physics analysis : * rhic computing facility - rcf @xcite - main computing facility for phenix ; * cc - j @xcite ; * midrange cluster at sunysb @xcite ; * also there is a range of other computing facilities which is used for phenix physics analysis at several member institutes of phenix . it is assumed phenix will have more computing facilities in future . by taking a look at phenix member list it is clear that data distribution inside collaboration is not trivial . even limited task to know the files are ( in which site and location ) is not possible without file / replica catalog ( or file catalog ) . in general file catalog is required to keep locations of all data files in the collaboration . there was a range of various decisions @xcite concerning file catalog . architecturally we tested two level _ file cataloging engine _ : distributed phenix file catalog @xcite is located at bnl and at remote universities and local sunysb file catalog based on magda @xcite . all instances of the catalog are interconnected by special replication process . technical description for central phenix file catalog was available in a different presentation on chep-2003 @xcite . at the same time it was recognized that remote universities need some cataloging facilities for internal use . an adapted version of magda @xcite was implemented and used at sunysb as local ( at sunysb ) cataloging facility @xcite . with time , it became clear that it is suitable and important to keep the information about many files ( physics data and other type of files : scripts , papers , etc . ) . part of this information ( information about files with physics data ) is propagated to the central phenix file catalog . there are several tools on top of adapted magda at sunysb which are most interesting for end users . first of all there are web pages @xcite with detailed information where and which files are available . another tool is the set of scripts to link locally available data files to the local directory . as described before , sunysb magda catalog has replicated subset of central phenix file catalog . periodically cronjob starts the scripts to transfer the information about part of the files from central phenix file catalog to magda catalog and back , part of information from magda catalog is to be copied to central phenix file catalog . in this way it is possible to keep detailed information about files which are interesting for sunysb . in this context we mean that commands below create the soft link for locally available files . also information about linked files can be seen at the web pages @xcite if the panel _ used files _ will be clicked . * ` ma_linklocalfile ` _ lfn _ - to link locally available file _ lfn _ otherwise special completion code will be returned ; * ` ma_linkfilelist ` _ list _ - to link locally available files from the _ list _ ; * ` ma_linkfilesubstr ` _ substring _ - to link all files which names are containing the _ substring _ ; * ` ma_showlinkedfiles ` - to display all files linked by current user ; * ` ma_releasefile ` _ lfn _ - to release the file _ lfn _ ; * ` ma_releaseherefiles ` - to release all files in current directory ; * * ` ma_releaseallfiles ` * - to release all files earlier linked by current user . when data file names are released the following steps are performed for every file : * the appropriate soft link is deleted ; * the appropriate record is deleted from the magda database ; that means this record will not appear anymore in output of the command ` ma_showlinkedfiles ` and in statistics delivered on the web pages . the information to the catalog magda is coming from special spider scripts which are running on required _ sites _ ( in our case there are 3 sites where spiders are running ) . on most sites a spider is started once a day or even once a week if the information is not changed often . file moving over wan is done at sunysb through use of adapted magda and through an alternative way - by a script . with magda user could go to the web site @xcite and describe required _ site _ , _ host _ , _ location _ ( actually the exact directory path ) and _ collection _ ( collection of files ) . after that it is possible to describe the _ task _ for data transfer ( with web pages on @xcite ) . real data moving is possible after activating the _ task _ by using the web pages @xcite . at night cronjob will perform all the activated _ tasks_. for the user convenience the script * gcopy * was developed to copy the files over wan . the script uses cluster descriptions which is discussed in chapter _ job submission _ of this paper . the usage of the script : * gcopy * _ fromsite_:_fromlocation _ _ tosite_:[_tolocation _ ] ` \ ` [ _ substring _ ] the parameters _ fromsite _ and _ tosite _ are names of globus gateways . _ fromlocation _ and _ tolocation _ are exact directory paths . the parameter _ substring _ with wild - cards may be used to select file names in directory _ fromlocation _ to be copied . technically the file transfer is performed with gridftp protocol ( command * globus - url - copy * ) . the feature _ third party transfer _ is used the feature because the host where the file transfers are started is not the part of any computing cluster . default number of threads for data transfer is 5 . due to a range of network routers ( 6 or so ) between sunysb and bnl and due to other causes we see a significant difference in network connectivity speed during a day ( a factor of 2 ) . the best throughput we saw was about 7 mbytes / sec . this maximum throughput could be reached with different number of transfer threads and different size of network window at different time . taking into account those facts we conclude that it is difficult to predict what time the data transfer between bnl and sunysb will take . this is true for relatively large portion of data ( 0.2 tb and more ) . finally , it is much better to be sure that your data are available locally on the computing cluster where you plan to submit the jobs before job submission . in a distributed environment , it is often effective to use several computing clusters in different sites to get enough computing power or to load available clusters more evenly . we have to emphasize that nobody in the collaboration needs computing power as it is . physicists have a need to use * _ qualified _ * computing power . that means such a computing cluster where all phenix software is already installed and ready to be used . in further discussion we will assume the following : * all required application software has been installed ; * required physics data are already locally available or if you plan to do a simulation you have enough disk space for the output simulated data ; * all globus tools have been deployed ; * users have already the certificates to use globus secure infrastructure ( gsi ) as well . as already mentioned , the use of globus infrastructure for job submission is common place now . at the same time till last autumn ( 2002 ) we had some difficulties with globus toolkit ( gt ) ( especially with data transfer ) . it was decided to create a light weight testbed with minimum functionality of gt , with minimum efforts , and with minimum time for implementation which could be tested in real environment where conditions are close to production reality . to do that a simple set of scripts was developed . our script set ( set of wrappers on top of gt 2.2.3 ) for job submission and job output retrieval is deployed at client side . about 30 scripts were developed with total number of lines about 2000 . several of them are most significant for users . * * gparam * - script to describe the configuration : number of computing clusters , names of globus gateways , other information ; in addition the script $ home/.gsunyrc ( same meaning as * gparam * ) is used to keep local values for current account ; * * gproxw * - to create globus proxy for a week ; * * gping * - to test availability of all clusters described in * gparam * ; * * gping-*_m _ to test availability of a desired cluster ( here _ m _ is suffix to denote a cluster : * s * - for cluster at sunysb @xcite , * p * - for phenix at bnl @xcite , * unm * for cluster at university of new mexico @xcite ) ; * * grun-*_m _ to perform one command ( script ) on a desired cluster ( see remark to * gping-*_m _ ) ; * * gsub-*_m _ _" +"a variety of transition metal materials such as the cuprates @xcite , ru - oxides @xcite , and fe - pnictides @xcite has been proposed to harbour an electronic nematic phase @xcite . electronic nematic phases are broadly characterized by the presence of spontaneously broken rotational symmetry and viewed as the quantum counterpart of nematic classical liquid crystal phases . the theoretical proposal of nematic quantum liquid crystals became more concrete when experiments on ultra - pure bilayer ruthenate ( sr@xmath0ru@xmath10@xmath2 ) samples subjected to a magnetic field along the c - axis revealed an unusual phase characterized by a pronounced residual resistivity in place of a putative meta - magnetic quantum critical point ( qcp ) @xcite . interestingly , sr@xmath0ru@xmath1o@xmath2 was initially viewed as a prototype for the study of quantum phase transitions , exhibiting a striking non - fermi liquid resistivity thought to originate from the putative magnetic field tuned qcp @xcite . the unusual phase found in ultra - pure samples is delimited by two consecutive first order meta - magnetic transitions at low temperature and , remarkably , exhibits a significant in - plane magnetoresistive anisotropy when the external field is slightly tilted towards one of the in - plane crystal axes @xcite . these observations strongly imply the formation of an anisotropic metallic , i.e. electronic nematic , phase in the bilayer ruthenate compound . based at first on the two consecutive metamagnetic transitions , an electronic nematic phase was proposed and generic features of nematic phase formation were theoretically explored early on @xcite . it was found that the transition between the isotropic and nematic phase is generally first order , and that nematic order typically develops near a van hove singularity ( vhs ) to avoid a lifshitz transition . varying the chemical potential , the nematic phase is bounded at low and high values by two isotropic phases , while the concomitant first order transitions lead to jumps in the electron density . when a magnetic field is applied ( and the chemical potential is held fixed at , say , some low value ) , zeeman coupling acts as a spin - dependent chemical potential term . tuning the zeeman field increases the volume of , e.g. , the spin - up species which then enters the nematic phase near the vhs , resulting in a jump in the spin - up density at the isotropic - nematic transition . in contrast , the spin - down fermi volume continuously decreases without passing a van hove point . such behavior gives rise to meta - magnetism , i.e. a sudden jump in the difference of up- to down - spin density at the isotropic - nematic transition @xcite . using more realistic band structures , microscopic models were suggested and the above conclusion was found to be robust @xcite . despite this mechanism of nematic phase formation , the origin of the critical signatures remains mysterious and recent thermodynamic data revealed additional complexity that requires new insight into the nematic theory @xcite . for over a decade in temperature @xmath3 , the resistivity behaves nearly perfectly linear @xcite , while the specific heat coefficient ( @xmath4 ) varies as @xmath5 over the same range @xcite . this behaviour resembles quantum criticality observed in a variety of other correlated materials , suggesting the existence of an unidentified qcp related to the nematic phase . how can one reconcile the first order nature of the isotropic - nematic transition and the critical behavior associated with a second order transition ? /t$ ] . the meta - nematic transition ( marked by the arrow ) and the qcp ( marked by @xmath6 ) are shown . ( b ) the corresponding absolute entropy landscapes with ( @xmath7 ) and without ( @xmath8 ) nematic ordering ( for details see main text ) . [ fig1 ] ] in this paper , we present a way to resolve this puzzle by introducing two nematic order parameters relevant for multi - orbital systems , and investigate as to how their interplay leads to interesting physics . while the current work is motivated by the bilayer ruthenate , our study on the isotropic - nematic transition is generally applicable to a t@xmath9-orbital system . we show that in the presence of moderate spin - orbit ( so ) coupling the multi - orbital nature of the system is a key property for turning a nematic first order transition into a qcp . we also show that the nematic qcp is accompanied by a nearby jump in nematicity , dubbed here meta - nematic transition , which obscures the qcp at low temperature . this finding is in contrast to the current wisdom that a qcp is hidden under the nematic dome . figure [ fig1 ] ( a ) shows the finite temperature phase diagram of such a multi - orbital system , including the contour plot of the entropy difference between the nematic and the isotropic phase . the nematic qcp marked by @xmath6 is found on the right low temperature phase boundary . note also that the entropy inside the nematic phase near the meta - nematic transition indicated by the arrow is higher than in the isotropic phase . while the separation between the continuous and the meta - nematic transition depends on the underlying band structure and the so coupling strength , thermodynamics and transport at finite temperature will be governed by the qcp aside from singular density of states ( dos ) effects , which may be relevant for the phenomena observed in sr@xmath10ru@xmath11o@xmath12 @xcite . a more detailed discussion will be presented below . theoretical progress has recently been made in developing microscopic models for nematic phase formation in sr@xmath0ru@xmath1o@xmath2 . one approach suggested that the nematic phase is a spontaneous fermi surface ( fs ) distortion arising from a band with strong d@xmath13 character and a vhs near the fermi level @xcite , while another proposed that it originates from orbital ordering , i.e. , the density difference between d@xmath14 and d@xmath15 orbitals , ignoring the d@xmath13 orbital @xcite . both scenarios lead to broken x - y symmetry . to distinguish both types of ordering in the present paper , we call the former nematic and the latter orbital order . although the underlying microscopic driving mechanisms are distinct , both approaches have noted the importance of so coupling , which is in line with the results of angle resolved photoemission spectroscopy ( arpes ) @xcite . however , they failed to locate a qcp . thus , given that all t@xmath9 orbitals are coupled via so interaction , we explore here a broader notion of x - y symmetry breaking in a multi - orbital system . to understand the origin of nematicity and its consequences , we start from a tight - binding model , which reproduces the fs of sr@xmath0ru@xmath1o@xmath2 @xcite and was introduced in @xcite . the model is based on the ru 4d t@xmath16 orbitals and includes moderate so coupling @xmath17 . we also incorporate a staggered lattice potential @xmath18 with @xmath19 to account for the effect of the staggered rotation of the ruo@xmath20 octahedra , which doubles the real space unit cell @xcite . in principle , the lattice potential can be momentum dependent ( e.g. @xmath21 as in @xcite ) but here we assume a constant value @xmath22 as the results do not depend on its momentum structure . the tight - binding band structure then has the form @xmath23 where @xmath24 consists of electron operators creating an electron with spin @xmath25 in one of the t@xmath9-derived orbitals @xmath26 . the orbital dispersions are given by @xmath27 , @xmath28 , while the hybridization between the quasi-1d orbitals is @xmath29 . in the following the underlying band structure parameters are @xmath30 , @xmath31 , @xmath32 , @xmath33 , @xmath34 , @xmath35 , @xmath36 and @xmath37 ( if not stated otherwise ) , while the chemical potential @xmath38 serves as a tuning parameter . all energies throughout the paper are expressed in units of the intra - orbital nearest neighbour hopping integral @xmath39 . ) and orbital ( @xmath40 ) order parameters over the @xmath3-@xmath38 plane , respectively . note the small magnitude of @xmath40 . ( iii ) shows the qualitative changes of the fs in half of the original brillouin zone at selected points in the phase diagram for @xmath41 . in order of increasing @xmath38 these are taken just before and after the nematic transition at @xmath42 ( a & b , respectively ) , at @xmath43 ( c ) , just before and after the meta - nematic jump at @xmath44 ( d & e , respectively ) , and at the continuous transition at @xmath45 ( f ) . [ fig2 ] ] since the nematic phase reported in sr@xmath10ru@xmath11o@xmath12 arises from a metallic state , it is reasonable to assume that long - range interactions are well screened , leaving moderately weak ( compared with the bandwidth ) on - site and nearest neighbour interactions . the microscopic interaction hamiltonian is then @xmath46 with @xmath47 the density operator for electrons in orbital @xmath48 at site @xmath49 and spin @xmath50 . here , @xmath51 , @xmath52 , and @xmath53 represent repulsive intra - orbital on - site , inter - orbital on - site , and intra - orbital nearest neighbour interactions , respectively . we assume that @xmath54 is finite along nearest neighbour x(y)-bonds , while @xmath55 is finite along all four nearest neighbour bonds , and that @xmath56 . different instabilities compete within @xmath57 . most natural candidates are spin density wave and ferromagnetic instabilities . however , it was shown in @xcite that orbital ordering between d@xmath15 and d@xmath14 orbitals dominates when the inter - orbital interaction is significant between the two quasi-1d orbitals in the presence of so coupling . this important observation , however , did not take into account the 2d d@xmath13 orbital , which dominates the @xmath58 fs sheets of sr@xmath10ru@xmath11o@xmath12 as observed by arpes @xcite . in particular , the @xmath59 sheet possesses a vhs near the fermi level implying that it is most susceptible to an instability . reference @xcite indeed suggests that nematic ordering in the xy dominated bands is the leading instability when the nearest neighbour interaction is taken into account . since these theories imply that ferromagnetic and antiferromagnetic spin density wave instabilities are suppressed by so coupling , we focus here on the interplay of nematic and orbital ordering . introducing nematic and orbital order parameters , @xmath60 and @xmath61 , respectively , one arrives at the following hamiltonian @xmath62 \nonumber \\ & & - v_{{\mathrm{n } } } \sum_{{\bf k } , \sigma } \big [ \delta^{\sigma}_{{\mathrm{n } } } ( \cos{k_x}-\cos{k_y } ) n^{xy}_{{\bf k } \sigma } + \frac{1}{2 } \left(\delta^{\sigma}_{{\mathrm{n}}}\right)^{2 } \big ] , \end{aligned}\ ] ] where the effective interactions are given by @xmath63 and @xmath64 . note that the on - site intra - orbital interaction @xmath51 hinders orbital ordering ( favouring magnetic ordering instead ) , but does not interfere with nematic ordering . on the other hand , the inter - orbital interaction @xmath65 favours orbital ordering , while the nearest neighbour intra - orbital interaction @xmath66 favours nematic over orbital order . ( dotted lines visualize discontinuities ) . note that the first order transition at the right phase boundary becomes continuous for @xmath67 . the results in figure [ fig1 ] and [ fig2 ] are based on @xmath37 . very recent unpublished transport data @xcite in fact bear a strong qualitative resemblance to this @xmath37 plot . the resistivity has a pronounced shoulder for fields higher than those of the two first - order transitions , and within this shoulder becomes anisotropic under the application of small in - plane magnetic fields . [" +"microwave cavities and resonators are important scientific tools used in many physical , chemical , biological and engineering applications to boost system performance . for physical science applications , various cavities are used as sensors@xcite , clocks@xcite , spectroscopy@xcite , probes of fundamental physics@xcite and as building blocks of future quantum systems@xcite . these applications utilise the whole range of microwave cavities , either of one- , two- or three - dimension , metallic or dielectric , fabry - prot type or whispering gallery depending on whether on not each of these cavity types meet particular requirements such as : high quality factors , high tunability , energy density in a small volume , separation of magnetic and electric fields , required frequency spectrum , etc . each of these cavities have advantages and disadvantages with respect to these requirements . in this work we present a new approach to cavity design based on the recently proposed multi - post re - entrant cavity@xcite that is flexible enough to meet all these criteria simultaneously together with extra new features . multi - post re - entrant cavities are generalisation of well known one - post reentrant cavities@xcite characterised by high mechanical tunability@xcite and potentially high quality factors for superconducting realisation@xcite . they are widely used as ultra - sensitive transducers for example in gravitational wave antennas@xcite , microwave enhanced chemistry@xcite , dielectric measurements@xcite , gas and liquid characterisation@xcite , etc . in the following discussion , we deal with closed metallic cavities having metallic rods from the top surface to the bottom . these rods are referred as posts , and a possible small distance between the rod and the bottom surface is called the gap . each post equipped with a finite gap can be viewed as a lumped harmonic oscillator with the post body being an equivalent inductance and the gap being the equivalent capacitance . posts located in the vicinity of each other also have some mutual inductance that introduces coupling between the corresponding ho . the posts may be arranged in different two dimensional patterns or lattices . for this reason , the lattice is referred to as 2d though the original one - post re - entrant resonator is a cavity that belongs to the class of 3d cavities . indeed , when a multi - post generalization is constructed , it is done in only two dimensions since the dimension along posts is vacuous and is essentially different from the other two . the same logic is used for the designation of , for example , microstrip circuits as 2d systems : although they are embedded into 3d structure , one of the dimensions is different in nature and the circuit design is made in two dimensional space . for this reason , all cavities in this work are shown only in two dimensions depicting the working plane . the multipost re - entrant cavity has much in common with both the 3d cavities and lumped component resonators . having the advantage of high quality factors specific to 3d closed cavities , it has the advantages of discrete lumped circuits such as high concentration of the electric energy and high tunability . moreover , it has been demonstrated that these cavities may be used to achieve high concentrations of the magnetic field@xcite that is useful for many spectroscopy applications . the uniqueness of the cavity is due to the discreteness of its elementary parts ( metallic posts ) . indeed , if the cavity is made of a good conductor , each post may be assigned with the specific direction of the current at each moment of time . combinations of these directions distinguishes different modes of the cavity . as a result , the cavity design is reduced to an arrangement of posts on a two dimensional lattice and investigation of the cavity properties with respect to different 2d arrangements . the purpose of this work is to demonstrate various aspects of the 2d structures of posts and establish intuition for such cavity design as well as draw analogies with existing physical systems . for this reason , the work describes mode polarisation and frustration phenomena as well formation of discrete whispering gallery and fabry - perot modes . additionally , we describe one of the main features of re - entrant cavities namely mechanical tuning applied to multi - post structures and its consequences for a typical optomechanical problem . then , we give an example of a multipost structure that may be used as a quantum memory , and , finally , we introduce an idea of programmable cavity arrays as a generalisation of the cavity design approach . a multipost cavity can be regarded as a system of coupled harmonic oscillators ( ho ) . indeed , each post represent an electrical ho with the gap playing the role of a capacitor and the post itself being an inductor . the cavity exhibits a number of resonance frequencies corresponding to the number of posts @xmath0 . each resonance is uniquely identified with a pattern of current directions ( at the same instance of time ) giving a unique magnetic field distribution@xcite . fo example , a two post cavity@xcite exhibits two re - entrant modes : a dark mode ( @xmath1 mode ) with the both posts having the same direction and a bright mode ( @xmath2 mode ) with the opposite direction of currents at any instance of time . the same logic and description may be applied to more complicated cases . although , more generally the result depends on the cavity symmetries . in the case of a cavity with @xmath3 arranged in a rectangle ( d@xmath4 symmetry ) the modes are organised in the following order starting from the lower to higher frequency : @xmath5 - @xmath6 - @xmath7 - @xmath8 . since all posts are identical , the second and the third modes are identical in frequency since they are related via a symmetry operation ( @xmath9 rotation ) . the comparison between two @xmath3 objects with different symmetries is shown in fig . [ d4d2 ] . it should be mentioned here that objects with the same symmetry type but different geometry can exhibit different field patterns . in some cases a situation arises when for symmetry reasons it is not possible to decide on the pattern of the current for some modes . for instance in the case of a three post cavity with the d@xmath10 symmetry , the cavity s two higher frequency modes can not be identified with any possible current pattern . indeed , if two posts have @xmath2 current direction , the third node can not be associated with any direction due to symmetry reasons and one post can not sustain two current directions simultaneously as well . regardless the choice , the system has an asymmetric solution . the same holds true if one chooses @xmath2 as a pattern for first two posts . such modes we label as frustrated modes or modes exhibiting current frustration in analogy with spin frustration@xcite well known in condensed matter physics . table [ t1 ] summarises these properties for some low order cases . it has to be underlined that in practice , the current frustration can not be achieved . the reason is due to unavoidable symmetry breaking arising from any cavity imperfections . moreover , even for finite element modelling ( fem ) , the symmetry is broken by small asymmetries of the mesh . although , in this case , this property can be easily controlled by the mesh size . .classification of some cavities and corresponding modes . 0 is the canceled ( for symmetry reasons ) current . ? denotes frustrated current . the last column demonstrates wether the system has degenerate modes or not . [ cols="">,^,^,^,^"",options=""header "" , ] [ t1 ] and different symmetries . the colour shows the direction of the electric field in the gap along the cavity height.,scaledwidth=40.0% ] many of the resonant system may be subdivided into two groups : fabry - prot ( fp ) and whispering gallery mode ( wgm ) resonators . the first type have their largest wave - vector situated on a segment of a line . experimentally , the segment is formed by two boundary conditions limiting the wave propagation medium . the second cavity type is characterised by a wave - vector defined on a circle with the rotational symmetry in the ideal case . the wave is formed due to full internal reflection form the media boundary . it has been demonstrated@xcite that arrays of posts can make media for fabry - prot type resonances with both optical and acoustic branches of a dispersion relation . in the same manner , for @xmath11 , d@xmath12 cavities may be considered as discrete wgm resonators . for a resonator defined on a 1d structure ( circle or segment ) of posts , one can introduce a wave length @xmath13 as a number of posts covered by one complete variation of currents ( see @xcite for illustrations in the case of a segment ) . though the system is defined on a discrete set @xmath13 can be fractional . for instance if a resonator is constructed of @xmath0 posts , its mode numbers @xmath14 should run from 1 to @xmath15 . obviously , not all these numbers are integers . fractional wavelengths correspond to frustrated modes discussed above . in the case of the broken symmetry , the fractional wavelength modes appear as modes with variable wavelength . similarly to traditional wgm devices , for discrete wgms , one can introduce a wave number along the circle containing the corresponding regular polygon . moreover , because of the rotational symmetry of the system , the multiple post cavities demonstrate so - called doublets@xcite . wgm doublets are often observed in high @xmath16-factor cylindrical resonators such as sapphire single crystals@xcite or nonuniform circular dielectric resonators@xcite . figure [ doublet ] illustrates this property of a fem approximation to the d@xmath17 cavity resonator . this type of the wgm cavity shows eight doublet modes where four modes have variable wavelengths . two more modes @xmath18 ( @xmath19 ) and @xmath20 ( @xmath21 ) are identical under all cavity symmetry operations . cavity . the colour shows the direction of the electric field in the gap along the cavity height . modes are characterised by the mode number @xmath14 and wave length @xmath13 . @xmath22 are actual wavelengths.,scaledwidth=40.0% ] another feature of the discrete wgm cavity is associated with its symmetry . since the cavity does not have the continuous rotational symmetry , the sine and cosine components of the doublet are not equivalent by default . this property is clearly seen for the first doublet in fig . [ doublet ] . generalising these results , the re - entrant cavity modes for an d@xmath12 system perform an arithmetic expansion of the integer @xmath0 . the expansion is made by the cavity wavelengths because of the fact that @xmath0 is constructed by @xmath14 wavelengths ( mode order ) of length @xmath13 . when @xmath0 is not devisable by @xmath14 , @xmath13 is variable and made by a set of different numbers @xmath22 . generally , the sum of all wavelengths @xmath22 is @xmath0 . this principle is demonstrated for d@xmath17 in fig . [ doublet ] , where the cavity reveals 9 of such expansions ( the first mode with all currents in the same direction may be understood as a 0-order mode with the infinite wavelength ) . note that these expansions are not all expansions of @xmath0 into a sum of integers , but only those with terms smaller than @xmath15 . in other words , the cavity performs division of an integer @xmath0 by @xmath23 . it has been already demonstrated@xcite that one" +"the prototypical hollow nanoparticle is the buckyball c@xmath4 , which crystallizes into _ fullerite_. many other morphologies for carbon sheets have been found since the early 1990s , including fullerenes c@xmath5 of varying size , multi - walled fullerenes ( _ carbon onions _ ) , and single- and multi - walled carbon nanotubes . closed structures of carbon are formed in order to avoid dangling bonds at the edges of finite sized carbon sheets . this mechanism is generic for anisotropic layered material of finite size , and up to now more than 30 other materials have been prepared as hollow nanoparticles ( see the reviews @xcite and references therein ) . this includes the metal dichalcogenides mex@xmath0 ( me = w , se , x = s , se ) , bn , and gan . usually _ inorganic fullerenes _ like ws@xmath0 and mos@xmath0 are multi - walled . in fig . [ tem ] we show transmission electron micrographs of mos@xmath0-particles which were synthesized by solid - gas reaction . control of size and shape is rather difficult , as evidenced by the irregularly faceted shapes . however , the methods used for the synthesis of hollow nanoparticles are developing very rapidly , and it is to be expected that control of size , thickness and shape will become much better in the future . [ cols=""^,^ "" , ] hollow nanoparticles combine covalent in - plane strength with flexible out - of - plane bending of thin films , which results in high mechanical stability . they interact by van der waals ( vdw ) forces , which for example determine the material properties of fullerite @xcite and the phase behavior of buckyballs @xcite . vdw interactions become even more important for larger fullerenes , carbon onions and inorganic fullerenes ; these materials , therefore , feature a large degree of non - specific adhesion . in particular , vdw adhesion can lead to deformation of the hollow nanoparticles . for example , it has been found that carbon nanotubes adhering to each other or to flat surfaces show observable deformations for radii as small as 1 nm @xcite . in the presence of local surface features like crystal steps , adhering nanoparticles will have spacially varying electronic properties due to spacially varying deformation . hollow nanoparticles may lead to new applications in nanoelectronics and -optics . in contrast to filled nanoparticles , they can also be used for storage and delivery systems . they show superior mechanical properties , like high flexibility , high tensile strength and light weight , which will lead to applications as ultra - strong fibers . larger fibers can be produced using the cohesiveness provided by vdw interactions . inorganic fullerenes have also been shown to offer favorable tribological properties @xcite . detailed investigations with the surface force apparatus demonstrated that low friction and wear is caused by material transfer onto the sliding surfaces @xcite . for these applications , a good theoretical understanding of the physical properties of hollow nanoparticles is important . here we discuss structural properties of spherical hollow nanoparticles in a continuum approach that allows us to focus on unusual generic properties which result mainly from geometrical effects . in particular , we address mechanical properties , van der waals interaction , thermodynamic behavior and deformation by adhesion . in this paper , we focus on the main results of our work ; more details can be found elsewhere @xcite . during recent years , mechanical properties of fullerenes and carbon nanotubes have been extensively studied at the level of molecular calculations , that is by first principles , tight binding and force field techniques . the advantage of molecular models is that they can provide detailed quantitative predictions . for larger systems like multi - walled nanoparticles , their implementation becomes difficult due to computer time requirements . here we use classical continuum elasticity theory , which is asymptotically correct for large systems and allows us to treat all these systems using the same framework . the large advantage of this approach is that it provides insight into the generic properties of these systems . molecular calculations for carbon nanotubes have shown that the predictions of continuum elasticity theory persist well into the limit of radii smaller than 1 nm @xcite . recently this observation could be verified also for bn and mos@xmath0 nanotubes @xcite . the layered material discussed here usually has a hexagonal lattice structure , for which elasticity theory @xcite predicts that there are only two in - plane elastic constants and the sheet is elastically isotropic . its deformation energy consists of stretching and bending terms . for single - walled carbon sheets , the in - plane stretching modulus @xmath6 erg/@xmath7 and the out - of - plane bending rigidity @xmath8 erg . for both mos@xmath0 and ws@xmath0 , @xmath9 is smaller by a factor @xmath10 and @xmath11 is larger by a factor @xmath12 . for multi - walled nanoparticles , the elastic constants scale with thickness @xmath2 as @xmath13 and @xmath14 , where @xmath15 is the largest in - plane elastic constant of the corresponding layered material @xcite . the values for @xmath15 are @xmath16 , @xmath17 and @xmath18 erg/@xmath19 for c , mos@xmath0 and ws@xmath0 , respectively . stretching can be avoided completely by bending the sheet into a cylindrical nanotube . however , this is not possible for spherical nanoparticles , which we discuss here . the same holds true for saddle - like structures , and in general for all surfaces with non - zero gaussian curvature . on a microscopic level , the requirement for non - zero gaussian curvature also means that a flat sheet can not be bent into a sphere without introducing defects . continuum elasticity approaches to fullerenes therefore explicitly treated the 12 pentagonal defects necessary to close a sheet of carbon hexagons @xcite . in order to avoid this complication , here we assume that the curvature generating defects are distributed in a homogeneous manner and result in a vanishing internal strain ( like for a ping - pong ball ) . in this case , the hollow nanospheres can be modeled as elastic shells with thickness @xmath2 and prefered radius @xmath1 . mechanical collapse in tribological applications is likely to be caused by either direct forces or high pressure . in the latter case , an inward buckling instability occurs , since the pressure energy scales with a higher power of indentation @xmath20 than the restoring elastic energy ( @xmath21 versus @xmath22 ) @xcite . mechanical collapse is expected when indentation @xmath20 becomes of the order of radius @xmath1 . the critical pressure for collapse can then be estimated to be @xmath23 . for buckyballs and typical inorganic fullerenes , this yields values of 15 and 2 gpa , respectively . for nanoparticles , the corresponding forces are in the nn - range . since vdw interactions are very difficult to treat on a molecular level , a continuum approach is even more useful in this case . it is well known from colloid science that vdw interactions strongly depend on the geometry of the system under investigation . geometrical aspects of vdw interactions are well treated in the hamaker approach , in which an atomic lennard - jones interaction is summed in a pairwise manner over the relevant geometry and the molecular details of the interaction are lumped into the effective lennard - jones parameters @xmath24 and @xmath25 . for carbon , @xmath26 and @xmath27 erg @xcite . the corresponding hamaker constant @xmath28 is in the order of @xmath29 erg . for two buckyballs , the hamaker approach for thin sheets leads to the _ girifalco potential _ @xcite , which is considerably shorter ranged than a lennard - jones potential . since a small range of attraction leads to the disappearance of the gas - liquid coexistence from the phase diagram @xcite , it has been suggested that buckyballs constitute the first non - colloidal system for which the gas - liquid critical point does not appear in the phase diagram . however , large scale simulations have shown that buckyballs indeed do show a gas - liquid coexistence , which extends roughly from 1900 to 2000@xmath30c @xcite . for hollow nanoparticles in general , the effect of a finite thickness @xmath2 becomes important . however , for nanoparticles in a crystal or adhering to a flat substrate or to each other , the distance of closest approach @xmath31 between interacting particles is on an atomic scale . under such conditions , the vdw interaction saturates on the atomic scale @xmath31 with increasing thickness @xmath2 . for example , the surface energy for the interaction with a halfspace scales as @xmath32 and @xmath33 for thin films and halfspaces , respectively , with the crossover occuring for @xmath34 . since @xmath35 in our case , the surface energy is @xmath33 independently of @xmath2 and no significant scaling with thickness is expected . for a more detailed investigation , one has to consider the general case of two nanospheres of finite thickness interacting in a pairwise manner by a lennard - jones potential @xcite . the interaction energy can be written as @xmath36 , where @xmath37 is the interaction energy between two filled balls of radii @xmath38 and @xmath39 , respectively , which can be calculated analytically for a lennard - jones potential . in order to predict phase behavior , three quantities characterizing the resulting potential are especially important : the hard core diameter @xmath40 sets the density scale , the potential depth sets the temperature scale , and the interaction range determines if a gas - liquid coexistence occurs ( compare fig . [ tem ] ) . our full analysis has shown that for hollow nanoparticles of radius @xmath1 and thickness @xmath2 , the potential depth and interaction range scale linearly and inversely with @xmath1 . both quantities depend only weakly on @xmath2 . in fig . [ interactionrange ] we show our numerical results for the interaction range as a function of @xmath1 and @xmath2 . recent work for the double - yukawa potential suggests that the gas - liquid coexistence disappears for an interaction range smaller than @xmath41 @xcite . our analysis predicts that this happens for @xmath42 and @xmath43 for single- and multi - walled nanoparticles , respectively . for larger @xmath1 , the critical point will disappear from the phase diagram . we consider the case where a spherical hollow nanoparticle is indented a distance @xmath20 due to adhesion to a flat substrate . the vdw energy gained on adhesion can be estimated to be @xmath44 where @xmath28 is the hamaker constant and @xmath31 an atomic cutoff @xcite . the energy of deformation can be estimated to be @xmath45 . with increasing @xmath1 , deformation becomes more likely , since both the vdw energy and deformability increase . however , deformability decreases rapidly with increasing thickness @xmath2 , since @xmath46 . solving for the indentation @xmath20 and using the values given above , it is found that for hollow carbon nanoparticles with few walls , @xmath20 can be in the nm - range @xcite . however , for typical inorganic fullerenes deformations are suppressed by the larger shell thickness @xmath2 . finally we briefly discuss a nanotube adhering to a flat substrate . as explained above , nanotubes can be bent without being stretched . on deformation , one has to pay a bending energy per length of @xmath47 . the gain in vdw energy scales as @xmath48 . it follows that for carbon nanotubes with small thickness @xmath2 , the indentation @xmath20 can be in the nm - range for even smaller values of radius @xmath1 than for hollow carbon nanoparticles . it is a pleasure to thank r. tenne for many stimulating discussions . uss was supported by the" +"thin thickness structures exist widely in nature . many things such as eggs , snails , airplanes and so on in our daily life are covered with solid shells that play protective roles . in the realm that we can not see with naked eyes , virus usually have protein shells , and eukaryotic cells are enclosed by cell membranes that consist of lipids , proteins and carbohydrates etc . a lipid molecule has a polar hydrophilic head group and one or two hydrophobic hydrocarbon tails . when a quantity of lipid molecules disperse in water , they will assemble themselves into a lipid bilayer in which the hydrophilic heads shield the hydrophobic tails from the water surroundings because of the hydrophobic forces . solid shells and lipid bilayers are , respectively , in the categories of hard condensed matter and soft one . their mechanical properties have attracted much attention for a long time @xcite . the significant difference between solid shells and lipid bilayers is that the former can endure the in - plane shear stress but the latter can not . due to this difference , solid shells and lipid bilayers have different forms of deformation energy . under the assumption of homogenous and isotropic bulk materials and in the limit of thin thickness , the elastic free energy per unit area of a solid shell is expressed as @xcite : @xmath0\nonumber\\ & + & \frac{c}{2(1-\nu^2)}\left[(2j)^2 - 2(1-\nu)q \right ] , \end{aligned}\ ] ] where @xmath1 and @xmath2 are bending rigidity and in - plane stiffness of the shell . @xmath3 , @xmath4 and @xmath5 are , respectively , the young s modulus , the poisson ratio and the thickness of the shell . @xmath6 and @xmath7 are the trace and determinant of the in - plane strain tensor , respectively . for a spherical solid shell with radius @xmath8 , the critical osmotic pressure ( i.e. , the pressure difference between the outer surface and inner one of the shell , above which the shell loses its stability ) is @xcite : @xmath9 in 1973 , helfrich @xcite recognized that the lipid bilayer was just like liquid crystal in smectic a phase at room temperature . based on the elastic theory of liquid crystal @xcite , he proposed the curvature energy per unit area of the bilayer @xmath10 where @xmath11 and @xmath12 are elastic constants ; and @xmath13 , @xmath14 and @xmath15 are mean curvature , guassian curvature and spontaneous curvature of the lipid bilayer , respectively . for phospholipid bilayers at room temperature @xmath16 , the persistence length is usually much larger than the size of the membranes and the effect of shape fluctuations is negligible @xcite because of @xmath17j@xmath18 @xcite , where @xmath19 is the boltzmann factor . the free energy of a closed bilayer under the osmotic pressure @xmath20 is written as @xmath21 , where @xmath22 is the area element and @xmath23 the volume enclosed by the closed bilayer . @xmath24 is the surface tension of the bilayer . the first order variation of @xmath25 gives the shape equation of closed bilayer @xcite:@xmath26for a spherical lipid bilayer with radius @xmath8 , the critical osmotic pressure for stability is @xcite : @xmath27 it follows that @xmath28 because the typical value of @xmath29 is about 1 . therefore , lipid bilayer is , indeed , much softer than solid shell . are there membranes intermediate in the state between helfrich s fluid lipid bilayers and classical solid shells ? the polymer vesicles discussed below may be as a example . in the last decade , decher invented the layer - by - layer assembling technique @xcite . following this technique , caruso _ _ made spherical polyelectrolyte capsules by the step - wise adsorption of polyelectrolytes onto charged colloidal templates and then decomposition of the templates @xcite . the capsules composed of about 10 layers of alternating polystyrene sulfonate and polyallylamine hydrochloride . the thickness @xmath5 of capsules was about tens of nanometers which was remarkably less than their radii @xmath8 ( several micrometers ) . _ @xcite found that the spherical polyelectrolyte capsule lost its stability and changed its shape abruptly above some threshold of osmotic pressure @xmath30 which was proportional to @xmath31 and @xmath32 . in their experiment , the thickness dependence of @xmath30 might not be exact because the polyelectrolyte capsule with more than 10 layers was chemically instable as they claimed . they also explained their results through the stability theory of classical elastic solid shells @xcite . but it is well known that the classical theory is based on the assumption of homogenous and isotropic bulk materials which entirely ignores the characteristic of the polyelectrolyte capsule consisting of many polymers . if considering the polymer structures of spherical polyelectrolyte capsule , can we still derive @xmath33 ? in this paper , we will answer above questions . to do that , we derive the entropy of a polymer confined in a curved surface and the elastic free energy of a membrane consisting of polymers by scaling analysis . it is found that the elastic free energy of the polymer membrane has the form of the in - plane strain energy plus helfrich s curvature energy . the elastic constants in the free energy are obtained by discussing two simplified models : one is the polymer membrane without in - plane strains and asymmetry between its two sides , which is the counterpart of quantum mechanics in curved surface @xcite ; another is the planar rubber membrane with homogeneous in - plane strains . the equations to describe equilibrium shape and in - plane strains of polymer vesicles by osmotic pressure are derived by taking the first order variation of the total free energy containing the elastic free energy , the surface tension energy and the term induced by osmotic pressure . the critical pressure , above which a spherical polymer vesicle will lose its stability , is obtained by taking the second order variation of the total free energy . it is found that the in - plane mode also plays important role in the critical pressure because it couples with the out - of - plane mode . these theoretical results reveal that polymer vesicles possess the mechanical properties being intermediate between helfrich s fluid membranes and classical solid shells . the following contents of this paper are organized as below : in sec . [ frgsec ] , we derive the free energy of polymer membrane by using the scaling concepts @xcite . in sec . [ shsteqsec ] , we obtain the shape and in - plane strain equations of closed polymer vesicles by using the surface variation theory developed in ref.@xcite . in sec . [ stabsec ] , we discuss the mechanical stability of the spherical polymer vesicle by taking the second order variation of the free energy . in sec.[conclusion ] , we give a brief summary and discussion . the polymer membrane concerned in this paper is one or a few thin layers consisting of cross - linking polymer structure like rubber @xcite at molecular levels . it can be represented as a mathematical surface with curvature and strains . it is hard to derive its free energy in a strict way . but we can drive it by using scaling concepts in polymer physics proposed by de gennes @xcite . in the following contents , we take de gennes convention : the entropy @xmath34 is a dimensionless quantity and boltzmann factor @xmath19 is implicated in temperature @xmath16 . if we take the gaussian chain model @xcite , the root of mean square end - to - end distance of a polymer is @xmath35 , where @xmath36 is segment length of the polymer and @xmath37 is the number of segments . assume that the principal radii of the surface are much larger than @xmath38 . if the in - plane strain tensor of the surface is denoted by @xmath39 which is assumed to be a small quantity , the entropy of the polymer confined the surface must be the function of @xmath40 , @xmath41 , @xmath6 and @xmath7 because it is a dimensionless invariant quantity under the transformation of coordinates , where @xmath13 , @xmath14 , @xmath42 and @xmath43 are the mean curvature of the surface , the gaussian curvature of the surface , the trace of strain tensor and the determinant of strain tensor , respectively . thus we can expand it as @xmath44 up to the second order terms , where @xmath45 are constants . in this expression , an unimportant constant term is neglected . moreover , one must notice that generally we have @xmath46 and @xmath47 . additionally , there is no first order term of @xmath6 in the expression of the entropy because we expect that @xmath48 plays the same role as @xmath39 in the entropy . it is useful to write the entropy in another equivalent form @xmath49 where @xmath50 is a constant , so called spontaneous curvature , which is expected to satisfy @xmath51 . in fact , @xmath15 vanishes if there is no asymmetric factor between two sides of the surface because @xmath13 turn into @xmath52 if we change the normal direction of the surface . assume @xmath5 to be the membrane thickness and @xmath53 the number of polymers per volume . additionally , we neglect the the entanglement of polymers . consequently , the free energy per unit area of a membrane consisting of polymers has the following form @xmath54+\frac{k_{c}}{2}(2h+c_{0})^{2}-\bar{k}k,\label{elastic}\end{aligned}\ ] ] where @xmath55 , @xmath56 , @xmath57 , @xmath58 . obviously , eq.([elastic ] ) is degenerated to helfrich s curvature energy of fluid membranes if @xmath59 , and to the elastic energy of classical solid shells if @xmath60 , @xmath61 , @xmath62 , @xmath63 and @xmath64 . @xmath65 , @xmath66 , @xmath11 and @xmath12 are unknown universal constants independent of the detailed shape and the small in - plane strains of the polymer membrane . if only discussing the closed polymer vesicles in this paper , we need not to know @xmath12 because the integral of @xmath67 is an unimportant constant . to determine @xmath65 , @xmath66 and @xmath11 , we will discuss two ideal cases : one is the cylinder polymer membrane without any strain and asymmetry between its two sides ; another is the planar membrane with the homogenous in - plane strains . in the former case , we denote @xmath68 the radius of the cylinder . on the one hand , ( [ elastic ] ) is simplified as @xmath69 on the other hand , we know there is a 1 - 1 correspondence relation between polymer statistics and quantum path integral method @xcite as shown in table [ correspond ] . in 1971 , jensen and koppe dealt with the quantum mechanics of a particle constrained in a curved surface and obtained a nontrivial conclusion @xcite : the constraint would induce an effective potential @xmath70 $ ] in shrdinger equation , where @xmath71 is the particle mass . in terms of the correspondence rules in table [ correspond ] , there will be an effective potential @xmath72 $ ] for a polymer confined in curved surface . especially , @xmath73 for the cylinder with radius @xmath68 . we must pay more attention to the fact that there is a minus symbol in the potential term when we use the correspondence rules . in fact , yaman _ _ overlooked this fact in recent literature @xcite . but this flaw can not diminish the value of their pioneer work in the study of polymer confined in curved surface . thus their results can be safely transplanted only if we change the sign . consequently , we obtain the free energy of the cylindrical membrane consisting of @xmath74 polymers per unit area @xmath75 if neglecting the entanglement between polymers . comparing eq.([cylinder1 ] ) with eq.([cylindf ] ) ," +"the number density of galaxy clusters as function of mass and redshift is a well known probe of cosmological parameters @xcite . several methods now exist to calibrate the cluster mass ( optical dynamics , galaxy infall , x - ray , sunyaev zeldovich , and weak or strong gravitational lensing ) each of which have their own advantages and drawbacks . of particular interest to future optical imaging surveys is weak lensing which uses the shape distortion of background galaxies induced by the gravity of a foreground cluster to measure the cluster mass . this lensing distortion is especially useful since it is independent of the dynamical state of the cluster and allows the cluster halo to be probed out to very large radii . much progress has been made in cluster lensing studies since its initial detection @xcite , however surprisingly a recent compilation estimates that only @xmath2 individual clusters have been studied with weak lensing @xcite . typically these clusters are imaged deeply to obtain a sufficient lensing signal but usually only cover a limited area around each cluster , probing the cluster halo in the inner few mpc s . at low redshift in particular weak lensing has not been well studied since this requires imaging an area of @xmath3 or more around each cluster @xcite . studying a large sample of clusters with weak lensing at low redshift allows for a direct comparison to other methods of mass calibration which have been well studied in the low redshift regime . to date the largest area imaging survey is the sloan digital sky survey ( sdss ) @xcite . previous studies in the sdss have measured weak lensing by stacking clusters @xcite in the redshift range @xmath4 . in spite of the shallow imaging , weak lensing of _ individual _ clusters in the sdss is also possible @xcite provided the clusters lie at low redshift . in the low redshift limit @xmath5 the lensing shear signal is @xmath6 where @xmath7 and @xmath8 are the angular diameter distances of the lens and source , and @xmath9 is the angular diameter distance between the lens and source . the lensing noise is @xmath10 so the lensing signal - to - noise ratio is equal to a constant . therefore by taking advantage of the large imaging area provided by the sdss and `` going wide '' @xcite weak lensing can be used to probe the mass of low redshift galaxy clusters . using the sdss we recently reported a weak lensing measurement of the coma cluster @xcite which is the lowest redshift cluster ( @xmath11 ) ever measured with weak lensing . since this study we have begun a program to measure other nearby , low redshift clusters in the sdss . in this letter we present the first results from our campaign using clusters selected from two publicly available spectroscopic galaxy cluster catalogs in the sdss : the c4 catalog of @xcite and the @xcite catalog . for our study we use data from the sdss , an 8000 @xmath12 imaging and spectroscopic survey using a dedicated 2.5 m telescope @xcite at apache point observatory in new mexico . imaging is obtained in a time - delay - and - integrate ( or drift scan ) mode in five filters @xmath13 @xcite using the sdss imaging camera @xcite . the astrometric calibration of the sdss is described in detail in @xcite and the photometric calibration pipeline is described in @xcite and @xcite . targets for the sdss spectroscopic survey are selected using automated algorithms described in @xcite and spectra are obtained using two fiber - fed double spectrographs . the main spectroscopic galaxy sample is complete to a magnitude of @xmath14 . in our lensing analysis we use galaxies drawn from the sdss data release six @xcite . shape measurement is performed using the photo pipeline @xcite which measures the shapes of objects using adaptive moments @xcite . we correct for the effects of the point spread function ( psf ) using the linear psf correction algorithm described in @xcite . source galaxies used in our lensing analysis are required to be detected in each of the @xmath13 bands , classified by photo as galaxies ( type=3 ) , and have extinction corrected model magnitudes @xcite in the range @xmath15 . other lensing studies in the sdss have used more sophisticated star - galaxy classifiers @xcite , however similar to @xcite we use the photo classification and restrict the sample to larger galaxies with a resolution factor @xmath16 ( or @xmath17 ) . here r is given by @xmath18 where @xmath19 and @xmath20 are the sum of the second order moments ( in the ccd row and column directions ) of the object and psf respectively . our catalog is further restricted in that we only use shape measurements from the @xmath21 band which is the filter that typically has the best seeing @xcite . photometric redshifts are drawn from the sdss photoz2 table @xcite and we restrict our sample to galaxies between @xmath22 with error @xmath23 . we have selected low redshift clusters in the sdss from two publicly available spectroscopic catalogs : ( 1 ) the c4 cluster catalog of @xcite and ( 2 ) the @xcite catalog . the public c4 catalog is based on the sdss data release two @xcite and contains 748 clusters in the redshift range @xmath24 over a 2600 @xmath12 region . the c4 algorithm searches for clusters in a seven dimensional parameter space which includes position ( @xmath25,decl . ) , redshift , and four colors ( @xmath26,@xmath27,@xmath28,@xmath29 ) . the use of galaxy colors in this algorithm is found to minimize cluster projection effects @xcite . the public c4 catalog contains three different cluster centers which include the peak in the c4 density field , a luminosity - weighted mean centroid , and the position of the bcg ( brightest cluster galaxy ) . the berlind catalog uses the friends - of - friends algorithm of @xcite to search for groups and clusters in the sdss nyu value added galaxy catalog ( nyu - vagc ) @xcite which is equivalent to the sdss data release three @xcite . the berlind sample consists of three volume limited catalogs and we use the mr20 ( absolute r magnitude brighter than @xmath30 ) catalog to search for clusters since it extends over the broadest redshift range @xmath31 . for each system the berlind catalog measures several cluster parameters including an unweighted group centroid , a mean redshift , and a richness estimate . for this study we select five of the richest clusters from the c4 catalog and two rich clusters from the berlind catalog , described further in @xmath32 . the lensing shear due to a cluster is given by @xmath33 where @xmath34 is the average projected mass density within a radius r , @xmath35 is the projected mass density at r , and @xmath36 is the critical surface mass density @xcite . we fitted the data for each cluster to a navarro , frenk , & white profile ( nfw ) @xcite which has been found in numerical simulations to provide an excellent description of dark matter halos , ranging from galaxy to cluster sized haloes . from this mass profile a virial mass @xmath37 can be determined from @xmath38 where the virial radius @xmath39 is defined as the radius where the density reaches a value of 200 times @xmath40 ( the critical density of the universe at the redshift of the cluster ) . the virial radius is related to the halo concentration ( @xmath41 ) by @xmath42 where @xmath43 is the scale radius , the radius where the density profile changes shape @xcite . the expression for the tangential shear due to an nfw halo is given in @xcite . to measure the shear in each cluster we use an unweighted shear estimator given by @xmath44 where @xmath45 is the tangential ellipticty and n is the number of galaxies measured in logarithmically spaced annuli relative to the center of each cluster . our use of an unweighted estimator is valid since our source galaxies are in the magnitude and size range where the shape measurement error in each galaxy is small compared to the intrinsic shape noise . we scaled the tangential ellipticity to a tangential shear in each bin using the shear responsivity @xmath46 , where we assume a fixed value of @xmath47 in all of our measurements @xcite . to fit the data to an nfw model we adopt a likelihood approach . we define a binned likelihood given by @xmath48 where @xmath49 and @xmath50 are @xmath51 here @xmath52 is the mean tangential ellipticity and @xmath53 is the standard deviation of the mean tangential ellipticity . in figure [ fig : contours ] we show lilkelihood plots in @xmath54 vs. @xmath41 for five c4 clusters ( a2048 , a1767 , a2244 , c4 1003 , and c4 3156 ) and two clusters from the berlind catalog ( a1066 and a2199 ) . the corresponding value of @xmath55 is also shown on the right panels in the figure . the maximum likelihood value for each cluster is indicated as the large white dot and contours represent the @xmath56 ( blue ) , @xmath57 ( green ) , and @xmath58 ( yellow ) confidence regions . for all of the clusters the halo concentration is not well constrained , which is in general typical of weak lensing measurements of clusters . for both sets of clusters we find that the shear is maximized when centered on the cluster bcg . for the c4 clusters we use the reported bcg center in the catalog but for the berlind clusters we re - center on the cluster bcg by hand . all cluster centers reported in table [ tab : cluster ] indicate the position of the cluster bcg used in the lensing analysis . mass model parameters for our sample of clusters are summarized in table [ tab : cluster ] . the weak lensing masses of our cluster sample varies from @xmath59 with the cluster redshifts ranging from @xmath60 . because of the very wide area imaging available in the sdss the shear field due to each cluster can be measured out to large separation . with this sample we are finding that the error in the mass is slightly reduced when extending the outer radius out to @xmath61 , and this is the outer cutoff radius used in our analysis . beyond this radius the mass determination does not appear to improve , and may be subject to the effects of large scale structure ( see @xmath62 . stacked measurement of galaxy clusters have measured the mean shear field out to @xmath63 @xcite , but this is the first time we know of that the shear field of individual clusters have been measured out to this large of a separation . we briefly comment on two clusters in our sample below : * abell 2199 * is a known supercluster which also contains the cluster abell 2197 . @xcite measured the mass of this cluster using the galaxy infall method and obtained a central mass of @xmath64 which is within @xmath65 of our measurement . our imaging data is not deep enough to separate the contributions of a2199 and a2197 therefore our mass should be interpreted as an estimate of mass of the combined system . * abell 2244 * has a relatively small separation on the sky @xmath66 and in redshift @xmath67 to the cluster abell 2245 . because of the relative proximity of these two clusters we also can not separate out the individual contributions and report only an estimate of the combined mass for the system . in our calculation of the weak lensing mass we have assumed the redshift of abell 2244 ( @xmath68 ) . because weak lensing relies on" +"interactions between neutral dielectric bodies are traditionally viewed as being due predominantly to electromagnetic field fluctuations , or equivalently , dipole fluctuations that give rise to van der waals ( vdw ) fluctuation - induced interactions between them @xcite . these interactions are attractive between identical bodies in vacuum or in a polarizable medium , such as water or an aqueous electrolyte ( or coulomb fluid ) . they contribute one of the two key ingredients of the classical derjaguin - landau - verwey - overbeek ( dlvo ) theory of colloidal stability , the other one being the mean - field electrostatic interaction , which is repulsive for like - charged colloidal surfaces @xcite . recent works have , however , highlighted the role of image - induced , ion - depletion effects in this scenario ( see , e.g. , refs . @xcite and references therein ) , leading to depletion of mobile solution ions from the vicinity of dielectric interfaces and , therefore , to an additional attractive force between apposed dielectric boundaries . this is because most dielectric surfaces in the context of bio- and soft materials have a lower ( static ) dielectric constant than that of water and , therefore , solution ions experience repulsion from their same - sign image charges in the proximity of dielectric boundaries @xcite . the recent advances in the study of image - induced , ion - depletion effects follow on the trail of the onsager - samaras framework formulated originally in the context of the surface tension problem of electrolytes @xcite . such non - mean - field effects , which belong to the general class of depletion interactions @xcite , arise due to the discrete nature of mobile ions neglected in the collective mean - field description based on the standard poisson - boltzmann theory @xcite . the studies of image - induced , ion - depletion effects have been focused exclusively on the case of strictly neutral ( charge - free ) dielectric surfaces . in this case , the ion - depletion interactions can be amplified in the presence of mobile multivalent ions in the solution @xcite due to stronger ion - image repulsions for these ions , even when the multivalent ions are present at small bulk concentrations around just a few mm @xcite . in this paper , we revisit the problem of interaction between neutral dielectric surfaces in a coulomb fluid by adding to it a novel feature : we relax the constraint of _ strict _ electroneutrality of surface boundaries , considered so far in the literature , by assuming that the surfaces are neutral only _ on the average _ , while microscopically they carry a _ quenched _ ( fixed ) random distribution of positive and negative charges . we show that this seemingly simple generalization leads to significant qualitative changes in the distribution of ions and , consequently , also in the effective interactions between dielectric surfaces , especially when the intervening coulomb fluid contains mobile multivalent ions . disordered charged systems are abundant in soft matter with examples ranging from polycrystalline surfaces with patchy surface potentials @xcite , dielectric contact surfaces @xcite , vapor - deposited amorphous films on solid substrates @xcite , surfactant - coated surfaces @xcite , dna microarrays @xcite , intrinsically disordered proteins @xcite , patchy colloids @xcite and random polyelectrolytes and polyampholytes @xcite . surface charge disorder in these examples can exhibit highly random distributions as well as patchy and heterogeneous patterns , originating from different sources including specific electronic and/or structural properties of materials involved , surface grafting or adsorption of charged molecules and/or contaminants , synthetic and fabrication processes , etc . the surface charge disorder can be highly sample specific and , at the same time , can depend strongly on the method of preparation . it may be set and quenched for each sample ( which is the case of interest in this paper ) , annealed ( in which case the surface charges are mobile and in thermal equilibrium with the rest of the system ) , or partially quenched or partially annealed @xcite . motivated by these examples , study of charge disorder and , in particular , effective interactions between random charge distributions has witnessed growing attention from theoreticians over the last several years @xcite , as well as from the simulation side where initial steps have been taken to include the effects of charge heterogeneity and disorder @xcite . disorder effects have been studied extensively in the context of electromagnetic fluctuation - induced interactions between two apposed , randomly charged surfaces in vacuum @xcite , where they have been associated with anomalously long - ranged surface interactions observed in recent experiments @xcite . they have also been studied in situations where a weakly coupled coulomb fluid , containing , e.g. , monovalent cation and anions , intervenes between the bounding surfaces @xcite . this however leaves out the case of asymmetric coulomb fluids containing both monovalent ions and multivalent ( counter- ) ions . these kinds of systems are in fact quite common in experiments within the biological context as in the case of viruses , dna condensates or other charged biopolymer aggregates @xcite and are expected to behave very differently since multivalent ions are known to couple strongly with fixed surface charges . strong - coupling behavior of multivalent counterions at uniformly charged surfaces or surfaces with regular charge patterns has been studied extensively over the last decade and its connection to exotic phenomena such as like - charged attraction has been throughly discussed ( for recent reviews and a more exhaustive list of references , see refs . @xcite ) . in disordered charged systems , such strong - coupling phenomena have been considered only in a few cases so far @xcite by assuming that bounding surfaces carry a _ finite _ mean surface charge density , to which multivalent counterions can couple strongly , in the same sense as considered in the context of uniformly charged surfaces as noted above . yet , the presence of charge randomness on bounding surfaces was shown to give rise to novel phenomena such as strong surface attraction of multivalent counterions , characterized by a density profile that diverges at the surface , in clear violation of the contact - value theorem established for uniformly charged surfaces . this kind of behavior originates from a singular , attractive , single - ion potential , which is created by the randomness in the distribution of surface charges and , as such , depends on the surface charge variance . consequently , one can also show that the thermal entropy of counterions is diminished upon introducing a finite degree of charge randomness on the boundaries . in other words , the system becomes more ` ordered ' as a direct outcome of the interplay between the thermal entropy of ions and the configurational entropy of charge randomness , entering through an ensemble average over various realizations of the disordered charge distribution . this peculiar disorder - induced effect , which stands at odds with what one may expect intuitively , has been referred to as _ antifragility _ @xcite . our analysis in this paper is focused on yet another facet of the disorder - induced effects by assuming , in a system of two plane - parallel dielectric slabs , that the randomly charged surfaces of the slabs bear _ no net charge_. this eliminates the direct strong coupling between multivalent ions and the mean surface charge and , thereby , also the ensuing strong - coupling interactions , considered in our previous papers @xcite , that would otherwise completely mask the vdw and image - induced , ion - depletion interactions between the slabs in an asymmetric coulomb fluid . this allows us to address the question of how the presence of surface charge disorder affects the standard picture for the interaction of neutral bodies based on the vdw and ion - depletion effects . the surface charge disorder has several different implications : first , it contributes a _ repulsive _ interaction between the slabs , which comes from self - interactions of disorder charges on the bounding surfaces with their image charges ; this contribution counteracts the _ attractive _ vdw interaction as discussed thoroughly elsewhere @xcite . then , as noted above , the individual ions in the coulomb fluid experience an attractive disorder - induced potential , which strongly attracts them toward the bounding surfaces . this effect counteracts the ion - image repulsions that tend to deplete ions from the slit region between the slabs and form the basis of the image - induced , ion - depletion mechanism for attraction between strictly neutral slabs . thus , randomly charged bounding surfaces tend to accumulate more mono- and multivalent ions in the slit . the system , however , responds differently to the increased number of ions : while the osmotic pressure due to monovalent ions increases and even becomes _ repulsive _ , consistent with the standard mean - field picture , the osmotic pressure due to multivalent ions , becomes ever more _ attractive _ ! this behavior is rooted in the combined effect of the surface charge disorder and the presence of mobile multivalent ions , with the latter creating strong inter - surface attractions upon further accumulation in the slit . as a result , the effective total interaction pressure between randomly charged , net - neutral dielectric surfaces can differ qualitatively from what one expects based on the standard vdw @xcite and image - induced , ion - depletion interactions in the case of strictly neutral surfaces ( see , e.g. , refs . @xcite and references therein ) . the net effect due to the interplay between disorder , mono- and multivalent - ion contributions yields a qualitatively different behavior for the effective surface - surface interactions , depending on the strength of disorder as quantified by the _ disorder coupling ( or strength ) parameter _ @xcite . this feature bears some conceptual resemblance to the strong - weak coupling dichotomy that exists for net - charged surfaces , dependent on the _ electrostatic coupling parameter _ in that case @xcite . in weakly disordered systems , corresponding to a small disorder coupling parameter , one then discerns a distinct non - monotonic behavior for the interaction pressure as a function of the separation between the slabs , with a pronounced repulsive hump at intermediate separations ; conversely , in strongly disordered systems , corresponding to a large disorder coupling parameter , the effective interaction pressure becomes strongly attractive , with a range and magnitude larger than that of the vdw or the image - induced , ion - depletion interaction pressure as found between strictly neutral surfaces . the organization of the paper is as follows : in section [ sec : model ] , we introduce our model and , in section [ sec : general ] , we briefly discuss the theoretical background and present the general results for the two - slab system . the results of our analysis for the density profile of multivalent ions and the effective interactions between the slabs are presented in section [ sec : results ] . we conclude our discussion in section [ sec : conclusion ] . and randomly charged inner surfaces are immersed in a bathing ionic solution of dielectric constant @xmath0 . the solution contains a mixture of monovalent and multivalent salts . multivalent ions are confined in the slit region and are shown by large spheres ; monovalent salt anions and cations are shown by small red and blue spheres . the slabs are assumed to be neutral on the average and their thickness is taken to be infinite.,width=321 ] our model consists of two plane - parallel" +"the optical properties of metal nanoparticles ( nps ) @xcite represent a topic of active research in several areas , like nano - optics @xcite , solid - state physics @xcite , biology @xcite and photonics @xcite . what makes them particularly attractive is their ability to sustain an electromagnetic resonance yet being much smaller than the incident wavelength . this peculiar feature originates from the existence of an electron - density mode that can couple to external radiation giving rise to a localized surface - plasmon - polariton resonance ( spr ) @xcite . in the experimental practice , metal nps have been often studied close to interfaces and under both wide - field and tight illumination @xcite . nevertheless , since the np is very small compared to the wavelength , the measured plasmon spectrum is usually only compared to theory based on plane wave ( pw ) illumination @xcite . while the effect of supporting films and substrates has been extensively investigated @xcite , to the best of our knowledge , there is no detailed study on the spectrum of metal nps under tight illuminations @xcite . the electromagnetic problem of a linearly - polarized pw scattered by a spherical particle dates back to the work of mie @xcite . after the invention of the laser , the availability of narrow band and collimated beams has posed new theoretical issues on the scattering of light by particles . morita et al . @xcite , and tsai and pogorzelski @xcite were the first to study the case of spherical particles illuminated by a gaussian beam whose waist is smaller or larger than the particle size . a decade later , barton et al . @xcite extended the study from the far field to the near and internal fields . other authors have also considered the scattering properties of objects under gaussian illumination @xcite . in summary , all works have found that there is a significant deviation from the case of pw illumination if the particle size is larger than the beam waist . less attention has been given to the case of a high - numerical - aperture ( high - na ) beam incident upon a metal np @xcite . trk et al . @xcite and challener et al . @xcite have described the high - na beam by pw expansion @xcite . subsequently , the scattering problem was solved using classical mie theory @xcite or the finite - difference time - domain method @xcite . although the pw expansion provides an accurate description of the electromagnetic field at the focus , it does not provide an easily accessible physical insight on the effect of strong focusing . moreover , in the mentioned studies , only selected wavelengths were considered and the modification of the plasmon spectrum was not taken into account . the aim of this work is to study the interaction of a high - na beam with metal nps in more detail and compare it with the case of pw illumination . by solving the scattering problem using a multipole - expansion approach @xcite , we gain intuition on the np s optical response both in the far and near field . we show that even when the np is smaller than the focal spot , the difference in the multipole content of a high - na beam compared to a pw causes a modification of the plasmon spectrum , especially when the metal np exhibits resonances of order higher than the dipolar one . the paper is organized as follows . in sec . [ theory ] we present the analytical solution of generalized mie theory @xcite for a high - na beam incident on a spherical np placed at the focus . we also derive formulae for the scattering and extinction cross sections and for the average intensity enhancement in the near field . in sec . [ results ] we present and discuss results for gold and silver nps with a 100 nm diameter . the generalized mie theory of a high - na beam incident on a spherical np placed at the focus is carried out by expanding the electromagnetic field in multipoles . the inset to fig . [ multipole ] sketches the layout of the problem . a pw polarized along @xmath0 and propagating along @xmath1 is focused by a high - na aplanatic system @xcite . it can be shown that the incident field components at the reference sphere in the image space are @xcite @xmath2 in the spherical coordinates ( @xmath3 , @xmath4 , @xmath5 ) . here @xmath6 is the pw amplitude and @xmath7 is the wavevector . the parameter @xmath8 represents the illumination angular weighting factor and @xmath9 is the lens focal length . the factor @xmath10 is added to ensure phase agreement with the electric field computed by pw expansion @xcite . for a system satisfying the sine condition one finds @xmath11 @xcite . the multipole - expansion coefficients of the incident field in the image space are obtained by enforcing the boundary conditions set by eqs . ( [ esph1]-[esph3 ] ) @xcite . the @xmath5 dependence in these equations already tells us which multipoles can properly represent the incident field , namely @xmath12,\ ] ] where the sum over @xmath13 extends from 1 to infinity and @xmath14 , @xmath15 are the vector spherical harmonics defined in ref . . the explicit dependence of the electromagnetic field on ( @xmath16 ) is omitted in the following expressions for the sake of brevity . furthermore , we choose the spherical hankel function of the second kind ( @xmath17 ) @xcite in the multipoles so that the incident field is an incoming wave . using the asymptotic expression @xmath18/\rho$ ] and matching the far fields of eq . ( [ eincexp ] ) to eqs . ( [ esph1]-[esph3 ] ) , we obtain the conditions @xmath19 and @xmath20= kfe_0a(\theta),\ ] ] where @xmath21 are associated legendre functions @xcite and @xmath22 . using the procedure described in ref . , the expansion coefficients are found to be @xmath23 \sin\theta\mathrm{d}\theta.\ ] ] the parameter @xmath24 is the angular semi - aperture of the lens and is determined by the formula na=@xmath25 , where @xmath26 is the refractive index of the background medium . the regularity of the electromagnetic field at the focus requires that eq . ( [ eincexp ] ) contains also outgoing multipoles represented by spherical hankel function of the first kind ( @xmath27 ) @xcite , with the same amplitude of the incoming ones , i.e. no sources at the origin @xcite . that implies @xmath28 , where @xmath29 is the spherical bessel function of the first kind @xcite . we use the notation @xmath30 and @xmath31 for multipoles with @xmath29 and include the factor 2 into @xmath32 to eliminate it from eq . ( [ eincexp ] ) . relative strength of the multipole coefficients for the expansion of a pw @xmath33 and a high - na beam ( @xmath34 and @xmath35 ) @xmath36 . inset : a pw polarized along @xmath0 and propagating along @xmath1 is focused by a high - na lens and scatters on a metal np positioned at the focus . @xmath24 is the angular semi - aperture of the lens.,width=313 ] when a spherical np of radius @xmath37 is placed at the focus , we have to solve for a boundary value problem involving the incident field @xmath38 , the scattered field @xmath39 and the internal field @xmath40 . the sum of incident and scattered fields builds up the total field @xmath41 in the background region@xcite . the symmetry of the problem implies that the np will not excite multipoles except those present in the incident field . therefore , we can formally write the solution as a linear superposition of multipoles @xmath42 where the notation @xmath43 and @xmath44 means @xmath27 in the multipoles since the scattered field must be an outgoing wave . the magnetic field @xmath45 is simply obtained from maxwell s equations and from the properties of spherical vector harmonics @xcite . fulfilling the boundary conditions at the np surface @xmath46 leads to an expression for the expansion coefficients that reads @xmath47 where @xmath48 and @xmath49 are riccati - bessel functions , @xmath50 is the size parameter and @xmath51 is the relative refractive index @xcite , if @xmath52 is the wavevector inside the np . similar expressions hold for the coefficients of the internal field @xmath53 notice that the coefficients of eqs . ( [ miea]-[mied ] ) have exactly the same expression as the mie coefficients for an incident pw @xcite . once they are known , we simply use eqs . ( [ einc]-[eint ] ) to compute the electromagnetic field inside and outside the np analytically . the interaction of light with material particles is usually investigated by considering far - field cross sections . the scattering and absorption cross sections , @xmath54 and @xmath55 , represent how strongly a particle scatters or absorbs light , respectively , for a given incident intensity . the total amount of power that is removed from the incident beam via scattering and absorption is proportional to the extinction cross section @xmath56 @xcite . since the radial component of every multipole vanishes in the far field , the scattered power @xmath57 reads @xmath58 where @xmath59 and @xmath60 represent the scattered field . after performing the integration over the angles and exploiting the orthogonality of the angle - dependent functions @xmath61 and @xmath62 @xcite , eq . ( [ wsca ] ) simplifies to @xmath63 where @xmath64 is the background medium impedance . likewise , the extinguished power @xmath65 is defined as @xmath66 where @xmath67 and @xmath68 refer to the incident field . after integration eq . ( [ wext ] ) reduces to @xmath69 notice that eqs . ( [ wscas ] ) and ( [ wexts ] ) have the same dependence on mie coefficients as for a pw @xcite . since the intensity of a pw is homogeneous , the cross sections are easily obtained by dividing the scattered or extinguished powers by the illumination intensity . however , for a high - na optical system the intensity at the focus is inhomogeneous , and introducing a cross section is not straightforward . nevertheless , in order to be able to compare our results with that of a pw @xcite , we define the cross section by dividing eq . ( [ wscas ] ) and ( [ wexts ] ) by the incident intensity @xmath70 , @xmath71 here we compute the poynting vector along @xmath1 and take its average over the np @xmath72 circular section of area @xmath73 at the focal plane . far - field quantities like the cross sections do not provide information on the near field . to further compare the optical response of a np illuminated by a high - na beam with a pw , we would like to consider a parameter similar to the cross section as an estimate of the complex structure of the near field . messinger et al . @xcite have defined the near - field quantity @xmath74 by computing the scattering cross section at @xmath46 , including the radial field component , and dividing it by the np area . they also considered a similar quantity , called @xmath75 , by taking only the radial component of the scattered field . they found that @xmath75 is very close to @xmath74 because in the near - field the radial component is quite large . however , to study the near - field more precisely , one has to take into account both the incident and the scattered fields . thus we evaluate the total field intensity @xmath76 , average it over the np surface and then normalize it by the intensity at the focus to obtain an enhancement factor , @xmath77" +"one interesting phenomenon occurring in ultracold atomic gases trapped in periodic potentials is the possibility to localize matter in states which can stay for a long time due to an interplay between nonlinearity , dispersion and periodicity . such states ( also called gap - solitons ) have been observed in bose - einstein condensates ( bec ) and in arrays of nonlinear optical waveguides @xcite . for attractive atomic interactions in bec and in absence of a periodic potential , stable localized solutions are possible only in a one - dimensional ( 1d ) setting since in two ( 2d ) and three ( 3d ) dimensions the phenomenon of collapse appears @xcite . more precisely , one observes that when the number of atoms exceeds a critical threshold , the solution collapses in a finite time ( blow - up ) while for number of atoms below the critical threshold there is an irreversible decay of the state into background radiation . for the higher dimensional nonlinear schdinger ( nls ) equation , however , it is known that there exists an unstable localized solution , the so called townes soliton @xcite , which separates decaying solutions from collapsing ones . townes soliton , however , exists only for a single value of the number of atoms , being unstable against fluctuations around it ( for slightly overcritical or undercritical number of atoms the solution collapses or decays , respectively ) . the situation is drastically changed in presence of an optical lattice ( ol ) . to this regard , it has been shown that stable 2d and 3d solitons can exists in ols both in bec and nonlinear optics contexts @xcite . moreover , it is known that while the periodic potential can only marginally shift the critical value for collapse , it can substantially move the delocalizing transition curve , thereby increasing the soliton existence range in parameter space from a single point to a whole interval @xcite . the typical situation with 2d and 3d bec solitons in ols is therefore the following : in the parameter space the stable localized solutions are confined from above by the collapse curve and from below by the delocalizing transition curve , thus , in contrast with the one dimensional case where there are no limits for the existence of localized states , strict limitations for soliton existence appear in multidimensional cases . from this point of view it is clear that for possible experimental observation of multidimensional bec solitons the parameter design becomes very important . since the collapse curve is only marginally affected by the periodic potential , to enlarge existence ranges of solitons it is of interest to give a full characterization of the delocalizing curve in parameter space . the aim of this paper is just devoted to this , i.e. we characterize 2d and 3d delocalizing curves of gap - solitons in terms of an unstable solution of the multidimensional gross - pitaeviskii equation ( gpe ) , which we call gap - townes soliton . this solution can be viewed as a separatrix ( it separates gap soliton states from extended ( bloch ) states ) and reduces to the known townes soliton when the strength of the ol goes to zero . similar solutions were found also for the 1d nls equation with higher order nonlinearities in @xcite , where they were called gap - townes solitons , and in @xcite where they were termed townes solitons . conditions for the occurrence of the delocalizing transition phenomenon of one - dimensional localized modes of several nonlinear continuous periodic and discrete systems of the nonlinear schrdinger type were also recently discussed in @xcite . for the periodic multidimensional gpe the delocalizing curve has been characterized in @xcite as the critical threshold for the existence of one bound state in an effective potential . the characterization given here , however , is more general since it is valid also for 1d nls with higher order nonlinearities . to this regard we remark that in absence of confining potential the 2d and 3d gpe behaves similarly to the 1d nls with quintic and septic nonlinearities , respectively . the interplay between dimensionality and nonlinearity has been used to investigate collapse in lower dimensional nls on the basis of pure dimensional arguments . in particular , the critical condition for collapse has been characterized as @xmath0 , where @xmath1 is the order of the nonlinearity in the equation and @xmath2 is the dimensionality of the system @xcite . in the following we take advantage of this interplay to construct approximate gap - townes soliton solutions of the gpe with multidimensional separable ols , in terms of products of exact gap - townes solutions of the 1d nls with higher nonlinearities . remarkably , we find that , except for strengths of the optical lattices very small , our approach produces very accurate gap - townes solutions of multidimensional gpe with ol , thus giving an evident computational advantages . the results obtained in this paper can be seen as a generalization of the existence of gap - townes solitons in the quintic nls discussed in @xcite to the case of the multidimensional gross - pitaeviskii equation . we finally remark that the obtained results can also be applicable for photonic lattices with kerr type of optical nonlinearity where the existence of a critical threshold for the lattice solitons has been observed @xcite . the paper is organized as follows . in section ii we introduce the model equations and discuss the link between multidimensional gpe with a separable trapping potential and the corresponding 1d nls equation with higher order nonlinearity . we use a self consistent approach to approximate gap - townes solitons of the gpe with products of exact gap - townes soliton of the corresponding 1d nls equation with higher order nonlinearity . in section iii we discuss the existence of localized solutions in the multidimensional gpe with ol by means by a variational approach and compare 2d and 3d results with those obtained from the va applied to the quintic and septic nls , respectively . in section iv we perform a numerical investigation of the existence ( delocalizing ) threshold for gap - townes solitons of the 2d and 3d gpe . finally , in the last section we briefly summarize our main results . let us consider the following gross - pitaevskii equation in d - dimensions ( @xmath3 ) as a model for a bec in an optical lattice@xcite @xmath4\psi + \gamma|\psi|^{2}\psi=0 , \label{gpe}\ ] ] where @xmath5 denotes the d - dimensional laplacian , @xmath6 denotes a square optical lattice with strength @xmath7 , @xmath8 is the coefficient of nonlinearity , and @xmath9 for @xmath10 , respectively . here we will be mainly interested in cases @xmath11 and @xmath12 . the existence of localized solutions of the multidimensional gpe with periodic potential and positive and negative nonlinearities ( atomic scattering lengths ) , has been previously investigated both by variational analysis and by direct numerical simulations . in the following we concentrate on a topic which was not discussed in previous works , namely the existence of gap - townes solitons in the multidimensional gpe and its link to the phenomenon of delocalizing transition . due to the instability properties of these solutions it is difficult to find them without an analytical guide . to this regard we take advantage of the fact that the periodic potential is separable and in spite of the nonlinearity of the system we look for factorized stationary solutions of the form @xmath13 in 2d case ( @xmath11 ) the substitution of the factorized ansatz into eq . ( [ gpe ] ) gives : @xmath14 + \gamma |\phi_1|^2|\phi_2|^2=-\mu.\ ] ] this equation can also be written as @xmath15 . by assuming @xmath16 and adopting a diagonal coordinate @xmath17 we have that eqs . ( [ separable ] ) become equivalent to the following 1d eigenvalue problem @xmath18 . the above equations can be easily extended to the 3d gpe with periodic potential . in this case ( [ quintic ] ) will be replaced by the following 1d nls equation with septic nonlinearity @xmath19 . it is appropriate to mention that a factorized solution of the form ( [ factorized ] ) with the components solutions of the nonlinear eigenvalue problem ( [ quintic ] ) can not be an exact solution of the 2d or 3d gpe , since , due to the nonlinearity , the problem is obviously not exactly separable . on the other hand , by imposing the coincidence of the solutions along the diagonal axis may be a constraint for a reasonable approximate solutions of the 2d and 3d problems , especially when the nonlinearity is small . , @xmath20 . the critical number of atoms in normalized units for the gap - townes soliton is @xmath21 . the gap soliton and the bloch state in the lower panel are obtained for slightly overcritical ( n=0.4347 ) and undercritical ( n=0.4176 ) values , respectively . ] -.2 cm , @xmath20 . the critical number of atoms in normalized units for the gap - townes soliton is @xmath21 . the gap soliton and the bloch state in the lower panel are obtained for slightly overcritical ( n=0.4347 ) and undercritical ( n=0.4176 ) values , respectively.,title=""fig:"",width=173,height=173 ] , @xmath20 . the critical number of atoms in normalized units for the gap - townes soliton is @xmath21 . the gap soliton and the bloch state in the lower panel are obtained for slightly overcritical ( n=0.4347 ) and undercritical ( n=0.4176 ) values , respectively.,title=""fig:"",width=173,height=173 ] in analogy with the 1d nls with quintic nonlinearity investigated in ref . @xcite we expect that the delocalizing curve coincides with the existence curve of gap - townes solitons for which it was shown that the critical number of atoms decreases with increasing the strength of the ol . this means that in a deep ol the effective nonlinearity required for the existence of a gap - townes soliton is smaller and the problem may become effectively close to separable . to check the correctness of this argument we construct factorized solutions ( [ factorized ] ) of the 2d gpe by means of a self - consistent method which allows to solve the 1d quintic nls eigenvalue problem exactly ( similar results can be obtained for the 3d case ) . in the top panel of fig . 1 we show a 2d gap - townes soliton obtained from the product ansatz using exact ( self - consistent ) gap - townes solitons of the corresponding quintic nls equation in eq . ( [ quintic ] ) . the lower left and right panels show , respectively , the gap soliton and the extended bloch state found at energy slightly below and slightly above ( bottom of the lowest band ) the one of the gap - townes soliton . to check the reliability of the factorized ansatz we have computed the time evolution under the original 2d gpe equation using the factorized solution as initial condition . this is shown in fig . 2 where the time evolution of the gap - townes soliton in fig . 1 ( central panel ) and the ones obtained for slightly overcritical and undercritical numbers of atoms are shown . we see that while the product solution constructed from the quintic nls remains localized for a long time , a slight increase or decrease of the number of atoms produces shrinking or decay of the solution , respectively . this clearly shows the existence and role of gap - townes solitons of the 2d gpe with optical lattice in characterizing the delocalizing threshold . the existence of localized states in multidimensional gpe with ol and in 1d nls with higher order" +"four - dimensional conformal field theories have attracted much attention in the last decade , mainly because of their relevance in the context of the ads / cft correspondence and its developments as well as its applications in completely different fields of which condensed matter is an example . the conformal symmetry imposes stringent constraints on the theory @xcite . in the case of two dimensions , for example , where scale invariance implies conformal invariance , the symmetry is enough to solve the theory @xcite . in four and higher dimensions , this is in general not true @xcite , since examples are known of theories with scale but not conformal symmetry @xcite , but meaningful statements can be made as well ( e.g. @xcite for the four - dimensional case ) . moreover , in the presence of supersymmetry , superconformal invariance puts restrictions on the operator scaling dimensions , independently of the space - time dimensionality @xcite . for these theories , a great deal of information can be obtained from the conformal group , that in four dimensions is @xmath3 and that acts non - linearly on the coordinates , due to the presence of operations such as the inversion and the special conformal transformations . however , it has been long known that it is possible to formulate the theory in such a way that the conformal group will act linearly on the coordinates , in the same fashion as the angular momentum does . in addition , correlation functions automatically exhibit manifest conformal symmetry and any results written in terms of the embedding coordinates are valid not just in minkowski space but in any conformally flat space - time . this approach goes back to @xcite and had applications to m / string theory branes @xcite as well as to more complicated conformal field theories in @xcite ( in particular @xcite generalizes the construction from scalars to more generic tensor fields ) . moreover , embeddings of chiral conformal superspaces were considered in @xcite , in terms of off - shell twistors @xcite , while @xcite and @xcite review the general ( chiral and non - chiral ) case . in particular , using the twistor notation , @xcite gives the two - point correlators between chiral and anti - chiral superfields for arbitrary @xmath2 . in some cases , @xmath4-point correlators have been calculated for various values of @xmath4 ( see for example @xcite where @xmath5 and the primaries are not chiral superfields ) . the supertwistor approach was also used in @xcite to study the superconformal structure of 4d @xmath6 compactified harmonic / projective superspace . the results presented here ( as well as in @xcite ) are equivalent to those obtained with twistor calculations . in the embedding method , one introduces two additional coordinates and embeds the four - dimensional space - time into a larger six - dimensional space with signature @xmath7 . in this space the conformal group generators act as angular momenta . the four - dimensional space is recovered by constraining the six - dimensional coordinates on the projective light - cone . the group @xmath3 is isomorphic to @xmath8 . as a consequence , one can re - express everything in spinor indices and introduce gamma matrices for the basis change from @xmath3 to @xmath8 . in @xcite , the authors generalize the embedding methods to @xmath0 superconformal field theories . the superconformal group is @xmath9 and the six - dimensional complex superspace is constructed out of the coordinates @xmath10 , which contain the standard space - time @xmath11 , one fermionic direction @xmath12 and an additional bosonic coordinate @xmath13 . @xmath14 transforms linearly under a superconformal transformation . upon projecting on the projective light - cone , the four - dimensional superspace @xmath15 is recovered . moreover , scalar and holomorphic fields are considered and it is shown that they correspond to four - dimensional @xmath0 chiral superfields whose @xmath16 component is an @xmath0 chiral primary operator @xcite . in this paper we generalize the embedding method to extended supersymmetry where the superconformal group is @xmath17 . most of the arguments are similar to the ones in @xcite and analogue results are obtained by considering more fermionic coordinates @xmath18 , with @xmath19 . automatically , more bosonic variables @xmath20 also appear in the six - dimensional superspace , which will then be removed once the light - cone constraint is imposed . we define such a set - up in section [ section : conformal and superconformal group ] , where the generators as well as the necessary representations are introduced . in section [ section : superspace ] we construct the @xmath2-extended four - dimensional superspace . this is done as a coset construction , achieved by applying translations and supersymmetry transformations to a reference origin . the resulting space is invariant under the superconformal and lorentz groups . in section [ section : the chiral sector ] we consider representations of the superconformal algebra in terms of superfields . in particular , we generalize the arguments of @xcite to @xmath2-extended chiral superfields , find their transformation rules under the @xmath21 symmetry subgroup of the superconformal algebra as well as under generic superconformal transformations . we also study in detail the case of chiral superfields in @xmath1 extended supersymmetry . as an aside result of our calculations , we have discovered an interesting connection between the number of component fields of a given kind in an @xmath2-extended supermultiplet and the so - called pascal s pyramid at layer @xmath2 . this aspect of number theory seems not to be mentioned explicitly in the literature . one can use it as a check that superfield expansions are correct . throughout this paper we use the conventions of @xcite and @xcite . in particular , the various definitions for the spinor indices and the gamma matrices are the same as in @xcite . in the appendix we give some details of the calculations as well as our notation . in particular , in appendix [ explicit su(2,2 ) transformations ] we compute explicitly the @xmath8 transformations of the coordinates @xmath11 . in appendix [ appendix useful identities ] we give our notation for the spinorial indices and show some identities that will be useful in our computations . in appendix [ 4d superspace barred ] we provide the necessary for computing the coordinates of the 4d barred superspace . in appendix [ appendix pascal pyramid ] we define the pascal pyramid , with some of its properties and symmetries , construct the @xmath5 chiral multiplet and relate it to the pyramid at layer @xmath22 . the superconformal group in four dimensions has fifteen generators that satisfy the @xmath3 algebra . it includes the poincar generators ( @xmath23 for translations and @xmath24 for lorentz transformations ) as a subalgebra . in addition there are the generators @xmath25 for special conformal transformations as well as the dilatation generator @xmath26 . special conformal transformations can be thought of as an inversion , followed by a translation and then by another inversion and act non - linearly on the coordinates @xmath27 . schematically : @xmath28 with real parameters @xmath29 , @xmath30 , @xmath31 and @xmath32 . here indices are raised and lowered by the four - dimensional metric @xmath33 . the conformal group @xmath3 is identical to the lorentz group in a space with six dimensions and signature @xmath7 . one can use this observation to make the conformal transformations act linearly on the coordinates . define new variables @xmath34 , with @xmath35 . under @xmath3 , @xmath34 transforms linearly : @xmath36 infinitesimally , @xmath37 , the conformal transformation @xmath38 is generated by the @xmath3 differential operators @xmath39 in order to recover the four - dimensional space , one has to demand that the coordinates @xmath34 are constrained on the projective light - cone : @xmath40 since the conformal group @xmath3 is equivalent to @xmath8 , we can transform everything into spinor notation . @xmath8 is the group of four by four special matrices that are unitary with respect to a fixed invariant matrix of signature @xmath41 . the connection is realized by using gamma matrices to transform the vector index @xmath42 into an anti - symmetric pair of spinor indices ( @xmath43 ) . a spinor @xmath44 of @xmath8 transforms as @xmath45 the @xmath8 index @xmath46 has an undotted component transforming in the fundamental representation of @xmath47 and a dotted component transforming in the complex conjugate representation , @xmath48 , with @xmath49 and @xmath50 ( e.g. @xcite ) . the vector @xmath34 becomes an anti - symmetric tensor @xmath51 , with each index transforming as in ( [ su(2,2 ) spinor transformation ] ) : @xmath52 with @xmath53 the light - cone constraint is written as @xmath54 with @xmath55 . similarly , one can express the @xmath3 generators @xmath56 in spinor notation . the result is @xmath57 , @xmath58 , with @xmath59 being the @xmath8 generators . the @xmath2-extended superconformal group in four dimensions is @xmath17 consisting of matrices of the form @xmath60 this is a block matrix , with the indices running in the range @xmath61 and @xmath62 . the diagonal blocks are commuting , while the off - diagonal ones are anti - commuting . an @xmath17 vector in the fundamental representation is written as @xmath63 where the @xmath44 component is fermionic and the @xmath2 @xmath64 fields are bosonic . indices are raised and lowered with the invariant matrix @xmath65 where @xmath66 is the @xmath8 invariant metric . in order to be an element of @xmath17 , the matrix @xmath67 must have unit superdeterminant : @xmath68 it must also satisfy @xmath69 where @xmath70 . one can introduce the @xmath17 generators @xmath71 as @xmath72 hence : @xmath73 with @xmath74 , @xmath75 , @xmath76 and @xmath77 . from the superdeterminant , it follows that @xmath71 have vanishing supertrace : @xmath78 where @xmath79 is the trace of @xmath80 , @xmath81 . from ( [ definition of su(2,2|n ) ] ) , it follows that @xmath82 hence , explicitly * for @xmath83 : @xmath84 , which implies that @xmath85 is a @xmath86 generator * for mixed indices : @xmath87 ( equivalently @xmath88 ) * for @xmath89 : @xmath90 ( equivalently @xmath91 ) , which states that @xmath80 is hermitian and hence @xmath92 is unitary , @xmath93 , as it should be since @xmath80 is the @xmath94-symmetry generator . in order to make @xmath85 an @xmath8 generator ( and hence @xmath95 ) , one can subtract its trace and replace @xmath71 by @xmath96 in the fundamental representation . by defining supercharges according to @xmath97 v_a\,,\ ] ] one has @xmath98 similarly , the @xmath94-symmetry generator is a non - abelian matrix @xmath99 which contains the @xmath100 block of the extended supersymmetry . many concepts here are similar to those presented in @xcite . if @xmath101 transforms in the fundamental representation , @xmath102 and @xmath103 in the anti - fundamental , @xmath104 then the product @xmath105 transforms as a tensor @xmath106 the singlet representation is given by its supertrace , @xmath107 where @xmath108 which , due to the property of the supertrace @xmath109 , is invariant under @xmath17 transformations . the adjoint representation is given by the part of @xmath110 with vanishing supertrace , @xmath111 tensors @xmath14 and @xmath112 transform ] ] as the products @xmath113 and @xmath114 : @xmath115 this implies that the product @xmath116 transforms as @xmath110 and hence the scalar product @xmath117 is @xmath17 invariant . the tensor @xmath14 contains the superspace components of six - dimensional conformal group . explicitly : @xmath118 where @xmath11 is anti - symmetric , @xmath119 are fermionic variables and @xmath120 is a symmetric matrix of bosonic coordinates . in order to use the invariant scalar product ( [ invariant scalar product ] ) , we need the conjugate of @xmath121 , @xmath112 , with components @xmath122 defining @xmath123 and @xmath124 , and using" +"emergent phenomena is one of the most profound topics in modern science addressing the ways that collectivities and complex patterns appear from multiplicity of components and simple interactions . ensembles of random hamiltonians allow one to explore the emergent phenomena in a statistical way , and thus to establish generic relations and rules . to study the many - body physics of interest we adopt a shell model approach with a two - body interaction hamiltonian . the sets of the two - body interaction strengths are selected at random resulting in the two - body random ensemble ( tbre ) . symmetries , such as rotational , isospin , and parity , entangled with complex many - body dynamics result in surprising regularities discovered recently in the low - lying spectrum . patterns exhibited by the random ensembles are remarkably similar to those observed in real nuclei . the high probability for the ground state spin to be zero is the most astounding feature of the tbre discovered in ref . signs of almost every collective feature seen in nuclei , namely , pairing superconductivity , deformation , and vibration , have been observed in random ensembles @xcite . while the systematics of the ground state quantum numbers is almost not sensitive to the short - range pairing matrix elements , the probability to find a coherent paired structure in the wave - functions of low - lying states is enhanced @xcite . the presence of rotational features in the spectra is another unexpected result seen in the tbre @xcite . the goal of this work is to study the emergence of collective mean - field dynamics in ensembles with random interactions . the discussion is organized as follows : in sec . [ sec : collectivity ] we briefly define the tbre , introduce signatures of collective motion , and discuss ways to detect them . in sec . [ sec : single_level ] we present our study of collectivities in single@xmath0 level models . more complex models are explored in secs . [ sec : two_levels ] and [ sec : realistic - model - space ] . we summarize our results in sec [ sec : summary ] with a discussion of the quadrupole - quadrupole hamiltonian which appears to be responsible for most of the observed phenomena . in the spirit of the traditional shell model approach , we define a model configuration as @xmath1 where @xmath2 nucleons occupy a set of single particle levels labeled by their angular momentum @xmath0 . in this work we assume that the single particle energies are degenerate . we examined other models for which this was not the case and the results are similar . the hamiltonians in the tbre are defined with a set of two - body matrix elements which are selected at random . the distribution of the matrix elements is gaussian so that , within a given symmetry class , the ensemble of hamiltonian matrices for two particles coincides with gaussian orthogonal ensemble . the presence of rotational symmetry and , where relevant , of parity and isospin symmetries is assumed . the typical number of random realizations was between @xmath3 and @xmath4 for all ensembles presented in this work . in the tbre the number of realizations where the ground state spin @xmath5 is disproportionally large . aiming at collective phenomena we select realizations with @xmath5 . with the exception of the ground state , labeled as @xmath6 , we denote the low - lying states by the value of their spin with an identifying subscript . the subscript is given in bold font if it refers to the absolute position of a given state in the spectrum . throughout the paper we give probabilities of finding realizations with certain features , these probabilities are always quoted in percent relative to the size of the ensemble ; however , all probability distribution plots are normalized to unit area . in order to identify and to analyze manifestations of collective phenomena in the spectra we use a set of observables . the goal is to choose a finite number of spectral observables that are likely to convey the most information about possible collective structures in a scale - independent way and with minimal model dependence . these quantities and the logic behind their selection are discussed in what follows . the geometry of the nuclear mean field is described by the multipole density operators @xmath7 with multipolarity @xmath8 and magnetic component @xmath9 . the structure of the multipole operators depends on the valence space , for each model it is addressed separately . the reduced transition rate from an initial state @xmath10 to a final state @xmath11 @xmath12 is one of the observables . here @xmath10 denotes a many - body state with angular momentum @xmath13 and magnetic projection @xmath14 the total transition strength from a state @xmath13 is given by the sum rule @xmath15 which provides a convenient normalization to assess the _ fractional collectivity _ of the transition @xmath16 the shape of a state is described by its multipole moments specified by the expectation value @xmath17 for a non - spherical system this moment describes the shape of a deformed nucleus measured in the lab frame . the intrinsic shape is characterized by the body - fixed ( intrinsic ) multipole moments @xmath18 a rotational spectrum ( band ) emerges for every fixed intrinsic shape . in a rigid rotor these intrinsic moments are the same for all states in the band and they determine the lab - frame observables in eqs . ( [ eq : be ] ) and ( [ eq : qlab ] ) . for the ground state band of interest , the intrinsic moments determine the total transition strength @xmath19 . in the axially symmetric case the quantum number @xmath20 , a projection of the angular momentum onto the body - fixed symmetry axis , is conserved . then for each rotational @xmath20-band the relations between the observables in the lab frame and in the intrinsic frame are expressed via clebsch - gordan coefficients @xmath21 and @xmath22 this limit of an axially symmetric rotor provides a convenient normalization to examine the multipole moments . in this work instead of @xmath23 we quote a normalized intrinsic moment @xmath24 which is computed as if the state is a member of the @xmath25 rotational ground state band . in this paper we only briefly touch the subject of collectivities other than quadrupole , see sec . [ sub : higher - multipole - collectivity ] ; thus for convenience the subscript @xmath8 is omitted for @xmath26 . the relation between the lab - frame moment of the @xmath27 state and its intrinsic moment is @xmath28 for the axially symmetric rotor the quadrupole transition sum rule for the @xmath6 is saturated by a single transition @xmath29 the quadrupole moment is @xmath30 for prolate or @xmath31 for oblate _ _ shapes . we normalize the total transition strength @xmath32 to its maximum possible value for a given valence space . taking the @xmath26 case as an example , we define the quadrupole - quadrupole ( qq ) hamiltonian as @xmath33 the eigenstate energy of the qq hamiltonian coincides with the total transition strength for that state : @xmath34 . thus , the absolute value of the ground state energy of the qq hamiltonian @xmath35 is the maximum possible value of the total transition strength @xmath36 for a given model space and for a given structure of the quadrupole operator . we therefore define a _ relative transition strength _ as@xmath37 to summarize , in our study we use the dimensionless variables defined in eqs . ( [ eq : b ] ) , ( [ eq : q ] ) , and ( [ eq : s ] ) . to shorten notations we define @xmath38 and @xmath39 for collective models of pairing , rotations , and vibrations @xmath40 we refer to a realization with @xmath41 as _ collective _ and with @xmath42 as _ non - collective_. the quadrupole moment @xmath43 allows one to separate different collective modes : @xmath44 for rotations and @xmath45 for vibrations and for paired states . in what follows we allude to collective realizations with @xmath46 as _ prolate _ and those with @xmath47 as _ oblate . _ for rotations the relative transition strength @xmath48 is proportional to the square of the intrinsic moment , and thus it is associated with the hill - wheeler deformation parameter @xmath49 . within elliot s su(3 ) model @xcite the relative transition strength @xmath48 can be thought to represent the expectation value of the casimir operator which identifies the irreducible representation . in cases where @xmath50 the ground state band structure is close to that of the qq hamiltonian . the collective structure is further analyzed using the following @xmath51 state . the types of collective modes can be classified by the ratio of the excitation energies measured relative to the energy of the @xmath6 state @xmath52 this ratio is close to @xmath53 for pairing , 2 for vibration , and 10/3 for rotation . the ratio of deexcitation rates@xmath54 is another measure . it is nearly 0 for pairing , 2 for vibrational mode , and 10/7 for rotational motion . typically , for models with the qq hamiltonian @xmath55 and @xmath56 are close to the rotational values , see summary in tab . [ tab : qq ] . a comprehensive review of different collective models , their analytic predictions , and comparisons with rotational spectra observed in real nuclei can be found in the textbooks @xcite . we begin our presentation with single @xmath0 level models . starting from the original paper @xcite the single @xmath0 level with identical nucleons has been at the center of numerous investigations ; a good summary may be found in the following reviews @xcite . with many issues understood and with still unanswered questions , the single @xmath0 model remains an important exploratory benchmark . the model , while simple , has a number of particularly attractive features which can be of both advantage and disadvantage @xcite : the hamiltonian is defined with a small number of parameters ; apart from an overall normalization constant , the multipole operators are uniquely defined ; a special role is played by the quasispin su(2 ) group ; and the particle - hole symmetry is exact . in fig . [ fig : jl19n6 ] the system with 6 nucleons in a single @xmath57 level is examined , we refer to this system as @xmath58 . here we select 10.4% of random realizations where the @xmath6 state is followed by the @xmath59 state . the distribution of the fractional collectivity @xmath60 in fig . [ fig : jl19n6](a ) points to highly collective nature of the quadrupole transition @xmath61 most realizations with @xmath6 and @xmath59 are collective @xmath62 , their fraction is 7.8% of the total number of samples . these realizations are shaded in red . this collectivity is not a statistical coincidence . the system @xmath58 has 1242 spin - states , among them there are 10 states with @xmath63 and 23 states with @xmath64 . thus , statistically the chance for the @xmath65 spin sequence to occur among all other possible outcomes is only 0.015% . the large fractional collectivity for the transition between these two states is even more unlikely , given that the transition strength is shared among 23 @xmath64 states , the chances for @xmath66 are of the order of 1 in @xmath4 . there are two peaks in the distribution of the quadrupole moment in fig . [ fig : jl19n6](b ) , they reflect prolate and oblate deformations . for most of the collective realizations , which are shaded in fig . [ fig : jl19n6 ] , the magnitude of the quadrupole" +"the one - dimensional ( 1d ) bose and fermi gases with zero - range interactions are celebrated examples of exactly solvable many - body problems @xcite . ultracold atoms offer the stupendous possibility to achieve these systems in the degenerate regime by using highly elongated cigar traps @xcite . moreover , using magnetic feshbach resonances and/or tuning the trap parameters make it possible to study 1d systems in strongly correlated regimes . this way , the tonks - girardeau and the super tonks - girardeau phases have been achieved @xcite . in addition , the existence of confinement induced resonances and resonances shifts have been confirmed @xcite . analogously to the three - dimensional ( 3d ) case @xcite , it has been shown recently that considering a large 1d effective range parameter permits one to enrich the phase diagram of the bose and fermi 1d degenerate gases @xcite . for bosons , this regime is achieved for narrow resonances i.e. , in the limit of small feshbach coupling between atoms and diatomic molecules @xcite . for fermions , the @xmath0-wave scattering resonance is intrinsically narrow and this regime can be easily reached @xcite . as in 3d systems , for small energy processes , the regime of large effective range can be studied in the limit where the actual radius of the interacting potentials is formally zero whereas the effective range and the scattering length of the model are finite . using a contact model ( cm ) , it was shown for one - component fermions in ref . @xcite and for identical bosons in ref . @xcite that the eigenstates of these systems are given by the bethe ansatz ( ba ) and are thus integrable in the limit of large effective range @xcite . this result is in strong contradiction with the mcguire - yang - baxter criterion which when applied in this regime shows diffractive effects in multiple scattering @xcite . hence integrability is inherently not possible . in this paper , we consider the three - body problem , which is intimately related to the integrability issue @xcite . to this end we use a hamiltonian two - channel model ( htcm ) , which encapsulates the feshbach mechanism . whereas the cm and the htcm are strictly equivalent at the two - body level , in the three - body problem the htcm gives large deviations with respect to the predictions based on the ba . we show that in the limit of the contact of three particles , all the solutions of the htcm have the same type of singularity not satisfied by the ba . the behavior of the wave function in the limit where the three particles fall one on top of the other appears then as a key ingredient in the violation of the integrability . we show that equivalence of the cm and of the htcm can be achieved at the three - body level by imposing continuity conditions on the wave function . our modeling of the system is based on a parameterization of the two - body 1d asymptotic scattering states including the effective range term . for an incoming wave of relative wave number @xmath1 and relative coordinate @xmath2 , we write it as @xmath3 e^{ik_0|z| } . \label{eq : scattering}\ ] ] in eq . , @xmath4 is the sign function and @xmath5 ( @xmath6 ) is the scattering amplitude in the even ( odd ) sector , parameterized as @xmath7 for ultracold atoms in a 1d waveguide , the scattering lengths @xmath8 and the effective range parameters @xmath9 in eq . can be expressed as a function of 3d scattering parameters in the homogeneous space @xcite . in what follows , we consider only positive values of the effective range parameter @xmath10 , an assumption justified in the limit of narrow resonances @xcite . from the analyticity of the scattering amplitude , one finds a single bound state , i.e. , a dimer @xmath11 of energy @xmath12 in the even sector for all values of @xmath13 and in the odd sector only for positive values of @xmath14 @xmath15 \times \sqrt{\frac{\kappa_\eta}{1 + 2{b}_\eta \kappa^{3 - 2\eta}_\eta } } \times e^{-{\kappa_\eta } |z| } . \label{eq : dimer}\ ] ] in eq . @xmath16 is the heaviside function and in the odd sector @xmath17 , one recognizes the sign function @xmath18 . the dimer binding wave number @xmath19 in eq . is the positive root of @xmath20 we now come to the integrability issue for a system of @xmath21 one - component bosons ( fermions ) where the two - body scattering occurs only in the even ( in the odd ) sector @xcite . integrability means that the eigenstates are given by the ba and there is thus no diffractive scattering i.e. , the wave numbers of the particles are globally conserved after multiple collisions in the system @xcite . the expressions of the transmission @xmath22 and reflection @xmath23 coefficients in the scattering of two identical particles are thus particularly relevant . they are defined by an alternative expression of the asymptotic scattering state in eq . where the interaction occurs only in one of the sectors @xmath24 or @xmath25 : @xmath26 from eq . , considering a pair of particles @xmath27 of wave numbers @xmath28 , the transmission and reflection coefficients are related to the exchange of momentum between the scattering particles with : @xmath29 a necessary condition for integrability is given by the mcguire - yang - baxter criterion , which follows from the absence of diffractive scattering in the three - body integrable problem @xcite : @xmath30 for @xmath24 this last equality is verified if and only if @xmath31 ( lieb liniger model ) and for @xmath25 if and only if @xmath32 or @xmath33 i.e. , in the fermi tonks - girardeau ( ftg ) regime @xcite . this is in strong contradiction with the results of refs . @xcite where the ba was used as an eigenstate of contact models in regimes where eq . is not satisfied . to understand this discrepancy , in the rest of this paper we focus on the three - body problem which has the advantage of the simplicity while being a cornerstone of the integrability we first use a cm which includes the effective range as a straightforward generalization of the lieb liniger model and introduced in refs . it is analogous to the one used in the context of narrow feshbach resonances for atoms in the three dimensional space @xcite . for convenience we introduce the shorthand notations @xmath34 for the @xmath21 coordinates of the system and @xmath35 for the relative coordinate of the pair of particles @xmath27 : @xmath36 the center of mass of the pair @xmath27 is denoted @xmath37 , and the relative distance between the pair and the particle @xmath38 is denoted @xmath39 : @xmath40 the cm is defined as follows : firstly , for all the configurations where @xmath41 , @xmath42 , the wave function @xmath43 verifies the schrdinger equation without any interaction between particles ; secondly , for each pair of interacting particles @xmath27 the wave function verifies the contact conditions @xmath44 where for @xmath24 ( for @xmath25 ) the operator @xmath45 symmetrizes ( antisymmetrizes ) the state @xmath46 in the exchange of the particles @xmath47 and @xmath48 : @xmath49 . \label{eq : symmetrization}\end{gathered}\ ] ] in eq . , the positions @xmath50 and @xmath51 ( where @xmath52 ) are kept fixed @xcite . one can verify that the exact expressions of the scattering amplitudes in eq . are deduced from the contact conditions of eq . by using the wave - function of eq . . another equivalent way to implement the contact model is to include directly the contact condition in the schrdinger equation by using the @xmath53 potentials @xmath54 for each pair of interacting particles @xmath27 . for a pair of particles of reduced mass @xmath55 , in the even sector of the interaction : @xmath56 \langle ( z)_n | \hat{\pi}^{ij}_{0 } | \psi \rangle \label{eq : vpseudo_even}\end{gathered}\ ] ] and in the odd sector of the interaction : @xmath57 in eqs . and , @xmath58 is an arbitrary parameter , i.e. , the action of the pseudo - potential on exact eigenstates do not depend on the value of @xmath58 @xcite . in the regime where a dimer exists and if the system is integrable , then the ground state for three identical particles of mass @xmath59 is a trimer of energy @xmath60 given by the ba @xcite @xmath61 . \label{eq : ba_bound}\ ] ] following the standard method in refs @xcite , one considers the contact condition in eq . for each pair @xmath27 in configurations where the third particle @xmath62 is distinct from the center of mass @xmath50 ( i.e. , @xmath63 ) . for instance , in the case where @xmath64 : @xmath65 applying the contact condition for the pair @xmath66 on eq . gives @xmath67 . the same reasoning for the other configurations give the same result . moreover , the wave function in eq . is a solution of the free schrdinger equation almost every where excepted at the contact of two or three particles . thus surprisingly , the ba for the trimer appears as an eigenstate of the cm with the binding wavenumber @xmath68 , in deep contradiction with the mcguire - yang - baxter criterion . the consistency of the cm is thus puzzling and to go further we now use a htcm which is a more conventional approach . in this model , the scattering process between two particles is only due to the coherent coupling between the pair of particles and a molecular state of mass @xmath69 . for a plane wave of wave number @xmath70 , we choose the convention @xmath71 and we denote the creation operator in the open channel @xmath72 , where @xmath24 for bosons and @xmath25 for fermions . the creation operator for molecules in the closed channel is denoted by @xmath73 , where the index @xmath74 permits one to distinguish the composite boson ( i.e. , the molecule ) made of two fermions , from the molecule made of two bosons . we consider only pure systems with identical particles and for each system ( @xmath24 or @xmath25 ) , the hamiltonian is @xmath75\\ + \biggl [ \frac{\hbar^2 \lambda_\eta}{m } \int \frac{dkdk}{(2\pi)^2 } \langle k|\delta^\eta_\epsilon\rangle \hat{a}_{\eta,\frac{k}{2}+k}^\dagger \hat{a}_{\eta,\frac{k}{2}-k}^\dagger \hat{b}_{\eta , k } + { \rm h.c . } \biggr ] \label{eq : hamiltonian-2channel}\end{gathered}\ ] ] in eq . @xmath76 is the single particle kinetic energy , @xmath77 is the strength of the coherent coupling between the two channels and @xmath78 is the internal energy of the molecular state . the function @xmath79 in the second line of eq . is a cut - off for the inter - channel coupling @xmath80 physically , the short - range parameter @xmath81 represents the length scale below which the collisional properties have a 3d character . for atoms moving in the monomode regime of a 1d harmonic waveguide of atomic frequency @xmath82 , it is typically of the order of the transverse length @xmath83 . at this scale the 1d effective model of eq . is no more relevant . this explains the fundamental interest of considering the zero - range limit ( @xmath84 ) which permits one to capture the universal 1d properties for energies much smaller than the level spacing in the waveguide i.e. , @xmath85 . in the zero - range limit , the scattering lengths and the effective range parameters of the htcm are given by @xmath86 the molecular energy in the odd sector @xmath87 is a bare parameter which diverges in the zero - range limit in such a way that @xmath14 keeps a desired finite value , whereas the parameters @xmath88 and @xmath77 stay finite in this limit . in the htcm , a three" +"attractors play a key role in the study of non - conservative dynamics . the description of attractors and the properties of their basins help predict the future behaviour of the orbits of a system . in this work we deal with physical measures i.e. an ergodic measure @xmath0 is physical if its basin of attraction has positive volume ( see section [ sec : preliminaries ] for precise definitions ) . we will think these measures as the attractors of our systems . in many cases , basins are ( essentially ) open sets and it is clear that if a point belongs to certain regions its trajectory goes , almost surely , to an attractor that is well determined . for instance , uniformly hyperbolic diffeomorphisms exhibit a finite number of physical measures and the union of their basins cover lebesgue almost every point the ambient manifold . moreover , each one of their basins is an open set ( modulo a set of null volume ) and then , we can clearly distinguish one attractor from the others . outside the uniformly hyperbolic world , this kind of behaviour of the basins of attractors is no longer true . open sets of diffeomorphisms of manifolds with boundary may have attractors with intermingled basins . more specifically , two or more basins are dense in the same open set . it was i. kan @xcite ( see also @xcite for a description of the example in terms of the partial hyperbolicty and lyapunov exponents ) who showed for the first time the existence of examples of partially hyperbolic endomorphisms defined on a surface and exhibiting two hyperbolic physical measures whose basins are intermingled . moreover , he showed that such phenomenon is robust among the maps preserving the boundary . we refer the reader to @xcite for a rigorous proof of kan example and @xcite for a generalization of the kan example and its relation with the sign of the schwarzian derivative . in @xcite the authors shown that the set of points that are not attracted by either of the components in the kan s example has hausdorff dimension less than the dimension of the phase space itself . following the same type of arguments , it is possible to construct a partially hyperbolic diffeomorphism defined on a 3-manifold with boundary exhibiting two intermingled physical measures , and such phenomenon still can be made robust . furthermore , it is well known that it is possible to extend such example to the 3-torus , but in this case it is no longer robust . we describe these examples in section [ sec : examples ] . the existence of these examples rise the question of how robust are the intermingled basins phenomenon for diffeomorphisms defined on boundaryless manifolds . in this work we show that partially hyperbolic diffeomorphisms on the 3-torus having hyperbolic physical measures with intermingled basins are not robust . in a recent work , okunev @xcite , studied attractors in the sense of milnor in the most restrictive case of @xmath1 partially hyperbolic skew products on @xmath2 with an anosov dffeomorphisms acting on the base @xmath3 . the author obtains results with the same flavour as ours without any explicit hypotheses about lyapunov exponent in the central direction . we are interested in diffeomorphisms defined on a 3-dimensional manifold @xmath4 , in particular we put our focus on @xmath5 . we give some basic definitions necessary to formulate the results , but the reader can find the precise definitions , properties and more detailed information in section [ sec : preliminaries ] and the references therein . a diffeomorphism @xmath6 is _ partially hyperbolic _ if the tangent bundle splits into three non trivial sub - bundles @xmath7 such that the strong stable sub - bundle @xmath8 is uniformly contracted , the strong unstable sub - bundle @xmath9 is uniformly expanded and the center sub - bundle @xmath10 may contract or expand , but this contractions or expansions are weaker than the strong expansions and contractions of the corresponding strong sub - bundles . it is known that there are unique foliations @xmath11 and @xmath12 tangent to @xmath9 and @xmath8 respectively @xcite but in general , @xmath10 , @xmath13 , and @xmath14 do not integrate to foliations ( see @xcite ) . the system is said to be _ dynamically coherent _ if there exist invariant foliations @xmath15 and @xmath16 tangent to @xmath17 and @xmath18 respectively . of course , if this is the case , there exists an invariant foliation tangent to @xmath10 obtained just by intersecting @xmath15 and @xmath16 . we will study dynamically coherent diffeomorphism with compact center leaves . as we mentioned above these diffeomorphisms are not always dynamically coherent although there are some results providing this property . just to mention one result , brin , burago , and ivanov have shown that every absolute partially hyperbolic system ( see subsection [ ssec : ph ] for the definition ) on the 3-torus is dynamically coherent @xcite . a set @xmath19 is _ @xmath20-saturated _ if it is the union of complete strong unstable leaves . the diffeomorphism @xmath21 is _ accessible _ if every pair of points @xmath22 can be joined by an arc consisting of finitely many segments contained in the leaves of the strong stable and strong unstable foliations . assuming that the center bundle is one - dimensional , k. burns , f. r. hertz , j. r. hertz , a. talitskaya and r. ures @xcite proved that the accessibility property is open and dense among the @xmath1-partially hyperbolic diffeomorphisms ( see also @xcite ) . our main theorem is the following . [ mteo : a ] let @xmath23 , @xmath24 , be partially hyperbolic , dynamically coherent with compact center leaves . let @xmath0 be a physical measure with negative center lyapunov exponent . assume that @xmath25 is a compact , @xmath21-invariant and @xmath20-saturated subset such that @xmath26 . then , @xmath27 contains a finite union of periodic 2-dimensional @xmath28-tori , tangent to @xmath29 . in particular @xmath21 is not accessible . we say that two physical measures @xmath0 and @xmath30 with disjoint supports have _ intermingled basins _ @xcite if for an open set @xmath31 we have @xmath32 and @xmath33 for any open set @xmath34 . [ mcor : b ] the set of dynamically coherent partially hyperbolic @xmath1-diffeomorphisms defined on @xmath2 , @xmath24 , exhibiting intermingled hyperbolic physical measures has empty interior . moreover , if @xmath35 is isotopic to a hyperbolic automorphism , there do not exist hyperbolic physical measures with intermingled basins . closely related , hammerlindl and potrie @xcite showed that partially hyperbolic diffeomorphisms on @xmath36-nilmanifold admit a unique @xmath20-saturated minimal subset . then , @xmath21 has a unique hyperbolic physical measure ( see section [ ssec : metric ] for more details ) and thus , it is not possible to have the intermingled basins phenomenon . we have as corollary of their work : [ mcor : c ] if @xmath4 is a @xmath36-nilmanifold , then there does not exist hyperbolic physical measures with intermingled basins . this paper is organized as follows . section [ sec : preliminaries ] is devoted to introduce the main tools in the proof : partial hyperbolic diffeomorphisms , physical measures , @xmath20-measures and lyapunov exponents . a toy example as well as kan - like examples are revisited in section [ sec : examples ] . proofs of theorem [ mteo : a ] and corollary [ mcor : b ] are developed in section [ sec : proofs ] . throughout this paper we shall work with a _ partially hyperbolic diffeomorphism _ @xmath21 , that is , a diffeomorphism admitting a nontrivial @xmath37-invariant splitting of the tangent bundle @xmath38 , such that all unit vectors @xmath39 ( @xmath40 ) with @xmath41 satisfy : @xmath42 for some suitable riemannian metric . @xmath21 also must satisfy that @xmath43 and @xmath44 . we also want to introduce a stronger type of partial hyperbolicity . we will say that @xmath21 is _ absolutely partially hyperbolic _ if it is partially hyperbolic and @xmath45 for all @xmath46 . for partially hyperbolic diffeomorphisms , it is a well - known fact that there are foliations @xmath47 tangent to the distributions @xmath48 for @xmath49 . the leaf of @xmath50 containing @xmath51 will be called @xmath52 , for @xmath49 . in general it is not true that there is a foliation tangent to @xmath10 . sometimes there is no foliation tangent to @xmath10 . indeed , there may be no foliation tangent to @xmath10 even if @xmath53 ( see @xcite ) . we shall say that @xmath21 is _ dynamically coherent _ if there exist invariant foliations @xmath54 tangent to @xmath55 for @xmath49 . note that by taking the intersection of these foliations we obtain an invariant foliation @xmath56 tangent to @xmath10 that subfoliates @xmath54 for @xmath57 . in this paper all partially hyperbolic diffeomorphisms will be dynamically coherent . we shall say that a set @xmath58 is _ @xmath59-saturated _ if it is a union of leaves of the strong foliations @xmath60 for @xmath61 or @xmath62 . we also say that @xmath58 is @xmath63-saturated if it is both @xmath64- and @xmath20-saturated . the accessibility class of the point @xmath41 is the minimal @xmath63-saturated set containing @xmath51 . in case there is some @xmath41 whose accessibility class is @xmath4 , then the diffeomorphism @xmath21 is said to have the _ accessibility property_. this is equivalent to say that any two points of @xmath4 can be joined by a path which is piecewise tangent to @xmath8 or to @xmath9 . in this section we consider @xmath65 be a diffeomorphism , not necessarily partially hyperbolic , defined on the riemannian manifold @xmath4 . we denote by @xmath66 the normalized volume form on @xmath4 . a point @xmath67 is _ birkhoff regular _ if the birkhoff averages @xmath68 @xmath69 are defined and @xmath70 for every @xmath71 continuous . we denote by @xmath72 the set of birkhoff regular points of @xmath21 . birkhoff ergodic theorem @xcite , implies that the set @xmath72 has full measure with respect to any @xmath21-invariant measure @xmath73 . when @xmath73 is an ergodic measure , @xmath74 for every @xmath75 in a @xmath73-full measure set @xmath76 . if @xmath73 is an @xmath21-invariant measure , the _ basin _ of @xmath73 is the set @xmath77 if @xmath73 is an @xmath21-invariant ergodic measure , then @xmath78,and so @xmath79 has full @xmath73-measure . an @xmath21-invariant probability measure @xmath0 is _ physical _ if its basin @xmath80 has positive lebesgue measure on @xmath4 @xcite . a physical measure is said to be _ hyperbolic _ if all its lyapunov exponents are nonzero @xcite . in the setting of partially hyperbolic diffeomorphims defined on a 3-dimensional manifold , a physical measure is hyperbolic if @xmath81 a point @xmath41 is _ lyapunov regular _ if there exist an integer @xmath82 , numbers @xmath83 and a decomposition @xmath84 into subspaces @xmath85 such that @xmath86 , and for every @xmath87 @xmath88 denote by @xmath89 the set of lyapunov regular points . the numbers @xmath90 are called the _ lyapunov exponents _ of @xmath51 . the splitting is called _ oseledets decomposition _ and the subspaces @xmath85 are called _ oseledets subespaces _ at @xmath51 . s theorem @xcite guarantee that the set @xmath89 has full measure with respect any invariant measure . in general the functions @xmath91 , @xmath92 , @xmath93 and @xmath94 are measurable . nevertheless , if @xmath73 is an ergodic invariant measure for @xmath21 , there is a subset @xmath95 , such that @xmath96 and there exist an integer @xmath97 , subspaces @xmath98 , numbers @xmath99 such that for every @xmath100 , we have * @xmath101 ; * @xmath102 , for every @xmath103 ; * @xmath104 , for every @xmath103 ; an ergodic measure @xmath73 is _ hyperbolic _ if" +"atom interferometry has opened new frontiers in precision metrology . highly sensitive gravimeters , gravity gradiometers , and gyroscopes have been constructed , and promising work has been done to integrate these sensors into a robust apparatus that can operate outside the laboratory with applications in inertial navigation and geodesy @xcite . moreover , atom interferometers have been used to make competitive measurements of the fine structure constant @xcite . since atom interferometric measurements of the fine structure constant do not assume the validity of quantum electrodynamics ( qed ) , while determinations of the fine structure constant based on measurements of the electron magnetic moment do make this assumption , comparison between the results of these two methods provides a stringent test of qed @xcite . in addition , an experiment to test einstein s equivalence principle with unprecedented precision is underway @xcite , and atom interferometric gravitational wave detectors offer the possibility to study gravitational radiation in frequency ranges complementary to ligo and lisa @xcite . atom interferometers have traditionally relied on matter gratings or light pulses to act as beam splitters and mirrors for matter waves , with atomic wave packets traveling freely between these interaction zones . light - pulse schemes using either raman pulses ( where the internal state of the atom is changed ) or bragg pulses ( where the internal state of the atom remains unchanged ) have been implemented , such as those described in @xcite . for a number of applications of light - pulse atom interferometers , such as measurements of gravity and rotation , the sensitivity is proportional to the separation in momentum that can be attained between the two arms @xcite . in measurements of the fine structure constant , the sensitivity scales as the square of this separation @xcite . therefore , significant efforts have been devoted to the development of large momentum transfer ( lmt ) beam splitters . lmt beam splitters achieving momentum splittings of @xmath0 using multi - photon bragg pulses have recently been demonstrated @xcite . however , the required laser intensities to make significant improvements on this result may prove to be prohibitive @xcite . in contrast , lmt beam splitters that use several two - photon bragg pulses or a multi - photon bragg pulse of relatively small order to separate the two arms of the interferometer in momentum space , followed by the acceleration of one of the arms with an optical lattice , could potentially provide multiple order of magnitude increases in attainable momentum separations with relatively modest laser intensity requirements . an atom interferometer that uses this method has been successfully operated in a proof of principle experiment ( with a maximum demonstrated momentum splitting of @xmath1 ) @xcite . in a separate experiment , an atom interferometer with @xmath2 lmt beam splitters has been realized using a similar technique @xcite . alternatively , both arms of the interferometer could be simultaneously accelerated in opposite directions by two different optical lattices after the initial splitting . using this second scheme , an interferometer with @xmath0 lmt beam splitters that achieves 15@xmath3 contrast and an individual beam splitter that provides an @xmath4 momentum separation have been demonstrated @xcite . the utility of atom interferometry hinges upon the ability to precisely calculate the phase accumulated along the different arms of an interferometer @xcite , of which the phase acquired during interactions of the atoms with light is an important component . indeed , the phase obtained by an atom during a raman or bragg pulse is well - understood @xcite . analogously , in order to take full advantage of the potential of lattice beam splitters , we must have a detailed understanding of the phase evolution of an atom in an optical lattice . in this paper , we provide a rigorous analytical treatment of this problem . to our knowledge , such a treatment has not been previously presented in the literature . based on this analysis , we propose atom interferometer geometries in which optical lattices are used to continuously guide the atoms , so that the atomic trajectories are precisely controlled for the duration of the interferometer sequence , with a different lattice guiding each arm of the interferometer ( as illustrated in fig . [ fig : guidedinterf ] ) . we point out here a distinction in terminology between a lattice waveguide and a lattice beam splitter . here , a lattice waveguide is the use of a lattice to continuously control the trajectory of an arm of an atom interferometer . we note that two separate lattice waveguides can independently control the two arms of an interferometer , or a single lattice waveguide can simultaneously control both arms . in contrast , a lattice beam splitter is an interaction of relatively short time ( in comparison to a waveguide ) with the primary purpose of splitting the arms of the interferometer in momentum space rather than providing continuous trajectory control . the underlying physics behind lattice waveguides and lattice beam splitters is the same , and they can be treated with a common formalism . a single lattice waveguide that simultaneously transfers @xmath5 of momentum to the two arms of a ramsey - bord interferometer has been previously achieved in @xcite . however , to our knowledge , our idea of using optical lattice waveguides to create a fully confined atom interferometer has not been previously considered . our analysis indicates that these lattice interferometers will offer unprecedented sensitivities for a wide variety of applications and that they will be able to operate effectively over distance scales previously considered too small to be studied by precision atom interferometry . for example , one particularly interesting configuration involves using two optical lattice waveguides to continuously pull the two arms of the interferometer apart , subsequently holding the two arms a fixed distance from each other in a single lattice waveguide that is common to the two arms , and then using two lattice waveguides to recombine the arms . such a configuration could be used , for instance , as a gravimeter . the sensitivity of lattice interferometers is illustrated by the fact that , given the experimental parameters stated in @xcite ( @xmath6 atoms / shot and @xmath7 shots / s ) , a shot noise limited lattice gravimeter whose arms are separated by 1 m for an interrogation time of 10 s has a sensitivity of @xmath8 @xmath9/hz@xmath10 . we perform phase shift calculations for these lattice interferometers using the theoretical groundwork formulated in this paper , and we discuss how lattice interferometers can both exceed the performance of conventional atom interferometers in many standard applications and expand the types of measurements that can effectively be carried out using atom interferometry . the paper is organized as follows . ii . describes the hamiltonian for an atom in an optical lattice in the different frames we use in the paper . iii . discusses the phase evolution of an atom in an optical lattice under the adiabatic approximation . iv . introduces the formalism of perturbative adiabatic expansion to calculate corrections to the adiabatic approximation , and sec . v. applies this formalism to calculate phase corrections to a lattice beam splitter . vi . proposes a number of interferometer geometries that make use of lattice manipulations of the atoms . the main results of the paper are eqs . ( [ eqn : phasecorrection ] ) and ( [ eqn : phasecorrectionref ] ) , which show how to obtain analytical corrections to the lowest order phase shift estimates . these corrections are surprisingly large , and understanding them is vital to realizing the full accuracy of the sensor geometries proposed in sec . vi . , as well as other geometries utilizing optical lattice manipulations of the atoms . for example , the gravitational wave detector proposed in @xcite will likely make use of lattice beam splitters and/or waveguides . previously , the phase evolution induced by lattice manipulations was not sufficiently well - understood to allow for a detailed design of the atom optics system or an estimation of the corresponding systematic effects . an optical lattice is a periodic potential formed by the superposition of two counter - propagating laser beams . atoms can be loaded into the ground state of the lattice by ramping up the lattice depth adiabatically , and the lattice can then be used to impart momentum to the atoms and/or to control the atoms trajectories . optical lattices are thus a useful tool for atom optics . we begin our discussion of the lattice - atom interaction by finding a useful form for the hamiltonian . as is typical for many applications of atom interferometry , to minimize decoherence we assume that we work with atomic gases dilute enough so that the effects of atom - atom interactions are negligible . we first consider the hamiltonian in the lab frame , where for now we assume a vertical configuration with constant gravitational acceleration @xmath9 so that we have a gravitational potential given by @xmath11 . we expose the atom to a superposition of an upward propagating beam with phase @xmath12 and a downward propagating beam with phase @xmath13 , which couples an internal ground state @xmath14 to an internal excited state @xmath15 . the two - photon rabi frequency is @xmath16 , where we let @xmath17 denote the single - photon rabi frequency of the upward propagating beam , @xmath18 denote the single - photon rabi frequency of the downward propagating beam , and @xmath19 denote the detuning from the excited state . we depict the physical setup in fig . [ fig : setup ] . making the rotating wave approximation and adiabatically eliminating the excited state as is standard procedure @xcite , we obtain the following hamiltonian where the periodic term in the potential arises from a spatially varying ac stark shift and where @xmath20 is the magnitude of the wave vector of the laser beams @xcite : @xmath21+mg\hat{x}\ ] ] note that where the difference between the frequency of the upward propagating beam and the frequency of the downward propagating beam is denoted by @xmath22 , we will have the relation @xmath23 . for a given @xmath24 , the lattice standing wave will be translated by @xmath25 in the @xmath26 direction from the origin . thus , the velocity of the lattice in the lab frame is : @xmath27 and we rewrite the lab frame hamiltonian as : @xmath28+mg\hat{x}\ ] ] in order to most readily describe the dynamics of an atom in an accelerating optical lattice , it is useful to work in momentum space . the @xmath29 term that appears in the lab frame hamiltonian makes such an approach difficult , especially when considering non - adiabatic corrections to the phase shift . however , we can change frames by performing a unitary transformation in order to obtain a hamiltonian that is easier to handle analytically . in the end , we will see that approaching the problem from the point of view of dressed states provides a convenient hamiltonian for our purposes . we consider the transformation procedure from the lab frame to the dressed state frame in appendix a , where we also introduce an intermediate frame that freely falls with gravity ( which we call the freely falling frame ) . we note that the general form of the unitary transformations considered in appendix a as well as the specific transformations to the different frames we consider can also be found in the appendix of @xcite . and the lasers are detuned from the transition between the atom s internal ground state and excited state so that the atom s external momentum states are coupled through two - photon transitions , creating an effective lattice potential.,width=672 ] it is convenient to absorb the initial velocity" +"deformed quantum field theories have been subject to renewed attention in recent years due to their natural appearance in string theory . initial investigations focussed on theories on non - commutative spacetime in which the commutators of the spacetime co - ordinates become non - zero . more recently@xcite , non - anticommutative supersymmetric theories have been constructed by deforming the anticommutators of the grassmann co - ordinates @xmath2 ( while leaving the anticommutators of the @xmath3 unaltered ) . consequently , the anticommutators of the supersymmetry generators @xmath4 are deformed while the remainder are unchanged . it can be shown that this structure arises in string theory in a background with a constant graviphoton field strength . a graviphoton background @xmath5 couples to the field @xmath6 which is the string worldsheet field corresponding to the supercharge @xmath7 ( and also to its worldsheet conjugate ) in berkovits formulation of the superstring@xcite . upon eliminating @xmath8 and its conjugate using their equations of motion , one obtains an effective contribution to the lagrangian l_= f^-1_^ ^ , where @xmath9 is the worldsheet conjugate of @xmath10 . this leads to a propagator = ^2f^ ( - ) . with standard open string coupling arguments , this implies \{^,^}=^2f^ c^ , where @xmath11 is usually referred to as the `` non - anticommutativity parameter '' . we then find \{_,_}=&-4 c^^_^ _ , y^=&x^+i^^ _ ^. ( more details of this derivation can be found in refs . it is straightforward to construct non - anticommutative versions of ordinary supersymmetric theories by taking the superspace action and replacing the ordinary product by the moyal @xmath12-product@xcite which implements the non - anticommutativity . non - anticommutative versions of the wess - zumino model and supersymmetric gauge theories have been formulated in four dimensions@xcite and their renormalisability discussed@xcite , with explicit computations up to two loops@xcite for the wess - zumino model and one loop for gauge theories@xcite . even more recently , non - anticommutative theories in two dimensions have been constructed@xcite , and their one - loop divergences computed@xcite . in ref . @xcite we returned to a closer examination of the non - anticommutative wess - zumino model ( with a superpotential ) in four dimensions , and showed that to obtain correct results for the theory where the auxiliary fields have been eliminated , from the corresponding results for the uneliminated theory , it is necessary to include in the classical action separate couplings for all the terms which may be generated by the renormalisation process ; and in ref . @xcite we extended this analysis to the gauged @xmath13 case . there are obstacles to obtaining a renormalisable @xmath0 theory with a trilinear superpotential in the case of adjoint matter ( in the case of matter in the fundamental representation , only a mass term is allowed anyway)@xcite . the requirements of @xmath0 invariance and renormalisability impose the choice of gauge group @xmath1 ( rather than @xmath14 or @xmath15)@xcite , @xcite . in the adjoint case with a trilinear superpotential , the matter fields must also be in a representation of @xmath1 . the problem is that the superpotential contains terms with different combinations of @xmath14 and @xmath13 chiral fields which mix under @xmath0 supersymmetry , but for which the yukawa couplings renormalise differently . however , recently an elegant solution to this problem has been found@xcite in which the kinetic terms for the @xmath13 chiral fields are modified , in such a way that the @xmath14 and @xmath13 chiral fields ( and consequently their yukawa couplings ) renormalise in exactly the same way . in ref . @xcite we confirmed the conclusions of ref . @xcite in a component version of their superspace calculation . the results of refs . @xcite imply that the non - anticommutativity parameter ( @xmath16 ) which specifies the superspace deformation in @xmath0 supersymmetry is unrenormalised at one loop . it is clearly interesting to ask whether this feature persists at higher orders . a full two - loop calculation would be extremely complex , and the results we present here are only partial in two respects . firstly we only check the renormalisation of one , judiciously chosen , term in the action ( of course if different terms in the action required different renormalisations of @xmath16 , this would represent a violation of @xmath0 supersymmetry ) ; and secondly , we only check the terms in the two - loop renormalisation constant for @xmath16 which include the yukawa coupling , omitting the purely gauge - coupling dependent term . our conclusion is that there are no yukawa dependent terms in the renormalisation constant for @xmath16 through two loops , and we consider it likely that @xmath16 is unrenormalised at this order . in this section we present the classical form of the adjoint @xmath0 action with a superpotential in the component formalism , including the modifications suggested in ref . the adjoint action was first introduced in ref . @xcite for the gauge group @xmath15 . however , as we noted in refs . @xcite , @xcite , at the quantum level the @xmath15 gauge invariance can not be retained since the @xmath14 and @xmath13 gauge couplings renormalise differently ; and we are obliged to consider a modified @xmath0 invariant theory with the gauge group @xmath1 . in the adjoint case with a yukawa superpotential , it turns out that the matter fields must also be in the adjoint representation of @xmath1 . the classical action with a superpotential may be written s_0&=&d^4x \{e^ab(-14f^af^b_-i^a^ ( d_)^b+12d^ad^b)&&-12ic^d^abce^adf^d_^b^c&&+f - i^d_-d^d_+d_f+ i2(_f-_f)&&+c^ ( 2d__d_+if_d f)&&+ ( -1)&&+12(yd^abc^a^b f^c -yd^abc^a^b^c + d^abc^a^b ^c -d^abc^a^b^c)&&+13ic^f^abcd_^a d_^b^c -ic^d^abed^cde f^d_^a^b^c&&+_12c^d^abc(^a^b _ d_^c + d_^a^b_^c+i^af_^b f^c)&&+_22c^d^ab0(^0^a _ d_^b + _ ^0^a_^b + i^0f_^af^b)&&+_32c^d^ab0(^a^b _ _ ^0 + d_^a^b_^0 + i^af_^bf^0)&&+_42c^d^0ab(^a^0 _ d_^b + d_^a^0_^b + i^af_^0 f^b)&&+_52c^d^000(^0 ^ 0 _ _ ^0 + _ ^0 ^ 0_^0 + i^0f_^0 f^0)}. [ sadj ] where _ f&=&^a^a,(^a)^bc = if^bac,_d&=&^a ^a,(^a)^bc = d^abc , [ lamdef ] ( similarly for @xmath17 , @xmath18 ) , and we have d_&=&_+ia^f_,f_^a&=&_a_^a-_a_^a - f^abc a_^ba_^c , [ dmudef ] with similar definitions for @xmath19 , @xmath20 . if one decomposes @xmath15 as @xmath1 then our convention is that @xmath21 ( for example ) are the @xmath14 components and @xmath22 the @xmath13 component . of course then @xmath23 unless all indices are @xmath14 . we note that @xmath24 , @xmath25 . we also have e^ab=,e^00= , e^0a = e^a0=0 . [ etensor ] compared with our previous work such as ref . @xcite , we have absorbed a factor of @xmath26 into our definitions of the fields in the gauge multiplet . we have omitted terms which are @xmath0 supersymmetric on their own ( such as terms involving only @xmath27 , @xmath28 and/or @xmath29 ) , which will have no relevance for our current discussion . they were considered in full in refs . @xcite ; and indeed we included them ourselves in refs . @xcite , @xcite . we have , however , included some additional sets of terms ( those multiplied by @xmath30 ) which are required for renormalisability of the theory . each of these sets of terms is separately @xmath0 invariant . it is easy to show that eq . ( [ sadj ] ) is invariant under a^a_&= & -i^a _ , ^a_&= & i_d^a+(^)_,^a_=0,d^a&= & -^d_^a,&= & 2,=0,^&= & 2^ f,_=-i2(d _ ) ( ^)_,f^a&= & 0,^a&= & -i2d_^a^-2i(^f)^a + 2c^d_(^b _ ( ^d)^ab ) . [ newsusy ] in eq . ( [ sadj ] ) , @xmath31 is related to the non - anti - commutativity parameter @xmath11 by c^=c^ _ ^_^ , [ cmunu ] where ^&=&14(^^- ^^),^&=&14(^^- ^^ ) . [ sigmunu ] our conventions are in accord with @xcite ; in particular , ^^=-^+2^. [ sigid ] properties of @xmath16 which follow from eq . ( [ cmunu ] ) are c^&&=12^ ( ^)_^c _ , c^_&&=c_^ ^_,c^_^&&=-c^ _ ^. [ cprop ] we use the standard gauge - fixing term s_gf=1d^4x e^ab(.a)^a(.a)^b [ gafix ] with its associated ghost terms . the vector propagator is given by ^ab_v=-1 ( _ + ( -1)p_p_)(e^-1)^ab . [ gprop ] the scalar propagator is _ ^ab =- p^ab [ sprop ] where p^ab=^ab , p^00= , p^0a = p^a0=0 , the fermion propagator is ^ab_= p_^_p^ab , [ fprop ] where the momentum enters at the end of the propagator with the undotted index , and the auxiliary propagator is _ f^ab = p^ab . [ aprop ] the bare action will be given as usual by replacing fields and couplings by their bare versions , shortly to be given more explicitly . note that in the @xmath0 supersymmetric case , fields and their conjugates may renormalise differently . we found in refs . @xcite , @xcite that non - linear renormalisations of @xmath32 and @xmath33 were required ; and in a subsequent paper@xcite we pointed out that non - linear renormalisations of @xmath29 , @xmath33 are required even in ordinary @xmath34 supersymmetric gauge theory when working in the uneliminated formalism . the renormalisations of the remaining fields and couplings are linear as usual ( except for @xmath35 , @xmath30 , see later ) and given by ( in the case of the @xmath14 fields ) ^a_b = z_^12^a , a^a_b = z_a^12a^a _ , & & ^a_b = z_^12^a,^a_b = z_^12^a,^a_b = z_^12^a , ^a_b = z_^12^a , & & g_b = z_gg , y_b = z_yy , c_b^=z_cc^ , ( -1)_b&=&z_(-1 ) , _ 1 - 5b = z_1 - 5 . [ bare ] the corresponding @xmath13 gauge multiplet fields @xmath36 etc are unrenormalised ; so is @xmath37 . the renormalisation constants for the @xmath13 chiral fields will be denoted @xmath38 etc and discussed later . in eq . ( [ bare ] ) , @xmath39 are divergent contributions ; in other words we have set the renormalised couplings @xmath30 to zero for simplicity . the anomalous dimensions @xmath40 etc , and the renormalisation constants for the couplings @xmath26 , @xmath41 , @xmath16 and @xmath42 , start with tree - level values of 1 . ( the slightly non - standard definition of @xmath43 is once again to make our results correspond more closely with those of ref . @xcite . ) the anomalous dimensions for the gauge - multiplet fields and hence the gauge @xmath44-functions are the same as in the standard @xmath34 theory . since our gauge - fixing term in eq . ( [ gafix ] ) does not preserve supersymmetry , the anomalous dimensions @xmath45 and @xmath40 for @xmath46 and @xmath47 are different ( and moreover gauge - parameter dependent ) , as are those ( @xmath48 and @xmath49 ) for @xmath21 and @xmath50 . moreover , neither @xmath48 nor @xmath49 coincide with @xmath51 , the chiral superfield renormalisation constant . we have assigned the same coupling @xmath41 to all the three - point interactions ; for instance , both @xmath52 and @xmath53 . this is by no means guaranteed a priori . from the non - renormalisation theorem , one expects z_y = z_^-32 [ nonren ] and so consistency requires @xmath51 and @xmath54 to be equal . this is arranged by a judicious choice of @xmath43 ( a change in @xmath43 alters @xmath51 while leaving @xmath54 unchanged ) . at one loop we find , writing @xmath55 for the @xmath56-loop contribution to @xmath57 , z^(1)_&=&[-ny+2g^2(1-)n]l , z^(1)_&=&[-ny-2g^2(1+)n]l , z^(1)_f&=&-nyl , z^(1)_y&=&-32z_^(1),z_^(1)&=&[-ny+4g^2n]l , z_g&=&1 - 2g^2nl , [ zchi ] where ( using dimensional regularisation with @xmath58 ) l=1 and n=n+(1- ) . [ ndef ] the remaining renormalisation constants will not be required but the one - loop results can be found in ref . the difference between @xmath51 and @xmath48 , @xmath49 is due solely to the choice of a non - supersymmetric gauge ; the gauge - independent terms are the same , and since" +"compact binary ( neutron star - neutron star , ns@xmath1 , or black hole - neutron star , bh - ns ) mergers are prime sources of gravitational radiation . the gw detectors ligo @xcite , virgo @xcite and geo600 @xcite are designed to optimally detect merger signals . these detectors have been operational intermittently during the last few years reaching their nominal design sensitivity @xcite with detection horizons of a few dozen mpc for ns@xmath1 and almost a hundred mpc for bh - ns mergers ( the ligo - virgo collaboration adopts an optimal canonical distance of 33/70mpc ; @xcite ) . both ligo and virgo are being upgraded now and by the end of 2015 are expected to be operational at sensitivities @xmath2 times greater than the initial ligo @xcite , reaching a few hundred mpc detection horizon for ns@xmath1 mergers and a gpc for bh - ns mergers ( 445/927 mpc are adopted by the ligo - virgo collaboration as canonical values ; @xcite ) . understanding the observable em signature of compact binary mergers has several observational implications . first , once the detectors are operational it is likely that the first detection of a gw signal will be around or even below threshold . detection of an accompanying em signal will confirm the discovery , thereby increasing significantly the sensitivity of gw detectors @xcite . second , the physics that can be learned from observations of a merger event through different glasses is much greater than what we can learn through em or gw observations alone . finally , even before the detectors are operational , detection of em signature will enable us to determine the expected rates , a question of outmost importance for the design and the operation policy of the advanced detectors . the current constraints on the rates are rather loose . the last ligo and virgo runs provided only weak upper limits on the merger rates : 8700 myr@xmath3(@xmath4 corresponding to @xmath5 yr@xmath3 gpc@xmath6 for ns@xmath1 and @xmath7 myr@xmath3 ( @xmath4 ( @xmath8 ) for bh - ns @xcite . estimates based on the observed binary pulsars in the galaxy are highly uncertain , with values ranging from @xmath9 @xcite . it has been suggested @xcite that short gamma - ray bursts ( grbs ) arise from neutron star merger events . the estimated rate of short grbs are indeed comparable to binary pulsar estimates @xcite . however , while appealing , the association is not proven yet @xcite . if correct , the observed rate of short grbs , @xmath10 , provides a lower limit to the merger rate . the true rate depends on a poorly constraint beaming angle , resulting in an uncertainty of almost two orders of magnitude . there are no direct estimates of bh - ns mergers , as no such system has ever been observed , and here one has to relay only on a rather model dependent population synthesis ( e.g. , * ? ? ? * ; * ? ? ? possible em signals from coalescence events were discussed by several authors . there are several suggestions @xcite of a prompt ( coinciding with the gw signal ) short lived em signals , mostly in low radio frequencies , whose amplitudes are highly uncertain . @xcite suggested that the radioactive decay of ejected debris from the merger will drive a short lived supernova like event . @xcite calculated the radioactive heating during this process self - consistently . they find that if @xmath11 is ejected then the optical emission from a merger at @xmath12 mpc peaks after @xmath13 day at @xmath14 . if the mass ejection is lower then the optical emission will be even fainter . finding , and especially identifying the origin of , such rare and faint events in the crowded variable optical sky is an extremely challenging task , even for current and future optical searches like ptf @xcite , panstarr , and lsst @xcite . an intriguing possibility is that mergers produce short grbs @xcite . however , short grbs are expected to be beamed , and only rarely this em signal will point towards us . a beamed grb that is observed off - axis will inevitably produce a long lasting radio orphan "" afterglow @xcite . a key point in estimating the detectability of grb orphan afterglows is that the well constrained observables are the _ isotropic _ equivalent energy of the flow and the rate of bursts that point towards earth . however , the detectability of the orphan afterglows depends only on the _ total _ energy and _ true _ rate , namely on the poorly constraint jet beaming angle . @xcite have shown that while large beaming increases the true rate it reduces the total energy , and altogether reduces the detectability of radio orphan afterglows . this counterintuitive result makes the detectability of late emission from a decelerating jet , which produced a grb when it was still ultra - relativistic , less promising . however , regardless of amount of ulrtra - relativistic outflow that is launched by compact binary mergers , and of whether they produce short grbs or not , mergers are most likely do launch an energetic sub - relativistic and mildly - relativistic outflows . the interaction of these outflows with the surrounding matter will inevitably produce blast waves and possibly stronger radio counterparts than that of ultra - relativistic outflows . below we first discuss ( in 2 ) the current estimates of mass and energy ejection from compact binary mergers . in 3 we calculate the radio emission resulting from the interaction of this ejecta ( sub - relativistic , mildly relativistic and off - axis relativistic ) with the surrounding interstellar matter ( ism ) . the calculations follow to a large extent models of radio ib / c supernovae @xcite and long grb radio afterglows @xcite . the success of radio supernova ( sn ) modeling , where the observations are superb , indicates that the microphysics is well constrained ant that equipartition parameters describe well the physical conditions . hence the main uncertainty in the predicted radio signal is in the amount of matter ejected from the merger event and its velocity . luckily the estimates of this important quantity can be significantly improved even using existing numerical models . we discuss the observational implications for detectability of merger remnants in 4 . we estimate the expected rates of detection of different outflows in 4.1 . we devote in 4.2 a special attention to short grb orphan afterglows that are a special case of our model , in which the outflow is launched relativistically , but the radio emission peaks only during its mildly relativistic phase . the estimates of orphan afterglows detectability is independent of whether they are the products of binary mergers or not . in 4.3 we examine possible other radio transients that may hinder the identification of merger remnants . finally in 4.4 we examine blind transient searched done in the past and we identify rt 19870422 as a possible and even likely merger remnant . we conclude in 5 . numerical simulations of compact binary mergers have been carried out by various groups with two different approaches . some ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) use newtonian dynamics ( modified to allow for gravitational radiation back - reaction ) with detailed microphysics . others ( e.g. , * ? ? ? * ; * ? ? ? * ) use full general relativistic dynamics with different levels of approximate microphysics , with or without mhd . in almost all ns@xmath1 simulations one finds an accretion disk surrounding a rapidly rotating massive object that eventually collapses to a black hole . an exception is the recent general relativistic simulations of @xcite who find no disks in some configurations . the system lifetime is at least a few dozen milliseconds and possibly longer . the fate of an accretion disk in a bh - ns merger is expected to depend on the mass ratio , the bh spin and the ns compactness . in some cases the disk is very small while in others it is substantial ( e.g. , * ? ? ? * ; * ? ? ? all simulations find some form of relativistic or sub - relativistic mass ejection . first , matter is ejected as tidal tails during the first stages of the merger . in bh - ns mergers the ejected energy can be very high and its velocity is mildly relativistic . for example @xcite find @xmath15 c ejecta with @xmath16 erg , where c is the light speed . in a ns@xmath1 mergers a lower , but yet significant , amount of energy can be ejected ( e.g. , @xcite find @xmath17 erg ) at a lower velocities of @xmath18 c. this mass ejection is expected also if no significant disk is formed . disk formation leads to several additional outflow sources . first , neutrino heating drives a wind from the disk surface ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? the energy in this wind is substantial with predictions ranging between @xmath19 erg and @xmath20 erg for 0.01 - 0.1 m@xmath21 disk . the outflow velocity is @xmath22 c from the outskirts of the disk and it is increasing , possibly up to relativistic velocities , for wind that is ejected from close to the central object . the mass ejection becomes even stronger when neutrino heating shuts - off and the wind is driven by viscous heating and by he - synthesis @xcite , leading to an ejection of @xmath23 of the initial disk mass at @xmath18 c. additional energy source is neutrino - antinuetrino annihilation above the disk , which can deposit up to @xmath24 erg , into an amount of mass that is not well constrained , leading possibly to a relativistic outflow . finally , more speculative , but yet very plausible , source of outflow are em processes that tap the rotational energy of the central object , such as the blandford - znajek mechanism @xcite . these are likely to produce relativistic outflows with an energy that can be as high as @xmath25 erg , and are the most probable engines of short grbs , if those are produced by compact binary mergers . the conclusion is that a significant mass and energy ejection is a prediction of almost all compact binary merger modelings . in ns@xmath1 mergers an ejection of @xmath26 erg at @xmath18 c is a fairly robust prediction . faster ejecta ( relativistic or mildly relativistic ) with energy @xmath27 is also quite likely from inner parts of the 0.01 - 0.1 m@xmath21 disk that is typically found in simulations . the outflow from bh - ns mergers was explored only by a few authors , but it is also seems to be significant and potentially even more energetic and at faster velocities than the outflow from ns@xmath1 mergers . consider a spherical outflow with an energy @xmath28 and an initial lorentz factor @xmath29 , with a corresponding velocity @xmath30 , that propagates into a constant density , @xmath31 , medium . if the outflow is not ultra relativistic , i.e. , @xmath32 it propagates at a constant velocity until , at @xmath33 , it reaches radius @xmath34 , where it collects a comparable mass to its own : @xmath35 and @xmath36 where we approximate @xmath37 and ignore relativistic effects . here and in the following , unless stated otherwise , @xmath38 denotes the value of @xmath39 in c.g.s . units . at a radius @xmath40 the flow decelerates assuming the sedov - taylor self - similar solution , so the" +"the leading optical flow algorithms to date , with few exceptions , are not end - to - end deep learning . while some of them employ deep matching scores for estimating the best match in image i for every location in image i , almost all methods employ multiple steps that do not involve learning . with the current affinity toward end - to - end deep learning solutions , the existence of large training datasets , and many concurrent contributions in the field of deep optical flow and related fields , one may wonder why this is the case . out of the four steps of modern optical flow pipelines : matching , filtering , interpolation and variational refinement , we focus on the third . in this step , a sparse list of matches is transformed into dense optical flow maps . it is one of the most crucial steps and without the availability of the epicflow method @xcite , which currently dominates this step , a large number of sparse matching techniques would not have been competitive enough to gain attention . epicflow is extremely effective and is built on top of solid computer vision foundations . however , despite using sophisticated heuristics for improved runtime , it is still rather slow and as a non - learning method , it is bounded in the performance it can deliver . replacing epicflow by a deep learning method is harder than it seems at first glance . feedforward neural networks excel in analyzing image information , but neuroscience tells us that in biological networks , lateral and top - down feedback loops are involved in solving cases where the information is missing or corrupted at random locations . artificial feedback networks are slower than feedforward networks , harder to train , and have not proven themselves in the practice of computer vision . we note that feedback networks with a predefined number of feedback iterations can be unrolled into deep feedforward networks with one major caveat while in most feedforward networks , the supervision flows from the top down , in feedback networks , the supervision occurs at each iteration . to resolve this , we equip our network with supervision at every layer . inspired by neuroscience , we also suggest a loss involving lateral dependencies . here , too , we replace the process of lateral feedback during run - time with additional supervision during training . in this way , the feedforward network learns how to mimic a network with lateral feedback loops by utilizing the training labels . taken together , our contributions are : ( a ) we propose , for the first time , to the best of our knowledge , a neural network based sparse - to - dense interpolation for optical flow . our network performs better than the current state of the art , it is robust and can be adjusted to different matching algorithms and serve as the new default interpolation method in optical flow pipelines . ( b ) we introduce a new lateral dependency loss , embedding the correlations between neighbors into the learning process . ( c ) we define a novel architecture involving detour networks in each layer of the network . the new architecture provides a substantial increase in performance . ( d ) we solidify the importance of motion boundaries in learning dense interpolation for optical flow . [ [ interpolation - in - the - visual - cortex . ] ] interpolation in the visual cortex . + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + the visual system often receives a noisy and missing input . however it is known to robustly denoise and fill - in the gaps in the input image . this phenomenon termed - perceptual filling - in @xcite , was reported to occur for occlusions @xcite , illusory contours and surfaces @xcite , in the `` blind spot''@xcite and in visual scotomas @xcite . different features in the visual stimulus are filled in , including brightness@xcite , color@xcite , texture and motion@xcite . the neurophysiological mechanism underlying perceptual filling - in is still under debate . however many have found evidence for the existence of a neuronal filling - in mechanism @xcite . in this mechanism , neurons that are retinotopically mapped to visible or salient parts of an image ( such as the edges ) are activated first . this initial activation is followed by a later spread to neurons that are mapped to the missing parts , resulting in a complete representation of the image @xcite . this activation spread is mediated by both lateral connections within areas in the cortex as well as top down connections @xcite . it was also shown to be very sensitive to edges in the image , usually originating in edges and stops when encountered with edges @xcite . finally , neuronal filling - in was found to take place in multiple areas in the visual cortex hierarchy , from v1 and v2 @xcite via v4 @xcite and in higher areas @xcite . we designed our interpolation network to incorporate three concepts inspired by neuronal filling - in : the interactions between neighbor neurons , multi - layer supervision and the importance of edges . neighbor neurons interactions can be modeled by recurrent connections within a layer , such as the model suggested by liang and hu @xcite . while the anatomic resemblance of such models to the cortex is appealing , in reality , they are unfolded to a feedforward network with shared weights . we , therefore , preferred to utilize the loss to force the interaction between neighbor neurons while using more simple , strictly feedforward networks , which were shown to perform extremely well for vision tasks while excelling in training time and simplicity . [ [ interpolation - for - optical - flow . ] ] interpolation for optical flow . + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + most current optical flow approaches are based on a four phase pipeline . the first phase matches pixels between the images in the image pair , based on nearest neighbor fields or feature matching techniques ( hand engineered or learned ) @xcite . the second phase filters matches with low confidence producing a noisy and missing flow map@xcite . the missing pixels usually undergo large displacements , a significant shift in appearance , or are occluded in one of the images . therefore , a third phase is needed to interpolate the missing parts and reduce the noise . a fourth and final phase applies refinement to the interpolated dense map from phase 3 . the best and most used algorithm for optical flow interpolation ( the third phase ) is currently epicflow @xcite . epicflow computes the flow of each pixel using a weighted sum of the pixel s local environment . locality is defined by a geodesic distance function based on the image edges that correspond to the motion boundaries . this edges aware approach yields good interpolation results for occluded pixels and large displacement . epicflow excels in interpolation . however it is less robust to noisy matches , especially in the vicinity of large missing regions , as displayed in their figure 8 . this sensitivity to noise is increased by the fact that the noise produced by each matching algorithm displays slightly different patterns . to overcome these difficulties , a trained algorithm like ours that learns the noise patterns is more suitable . we suggest a new interpolation method based on a deep convolutional neural network . the method is applied in a feedforward manner and leads to an improvement in both accuracy and speed over the epicflow method . finally , it is noteworthy that some of the new optical flow methods do not rely on the aforementioned pipeline @xcite . one interesting example is presented by dosovitskiy et al . @xcite in their flownet model . they present an end to end convolutional neural network for optical flow that outputs a dense flow map . while their method does not reach the state of the art performance , it runs in real - time and demonstrates the power of feedforward deep learning in optical flow estimation . the optical flow dense interpolation problem is defined in the following way : given a sparse and noisy set of matches between pixels @xmath0 , we want to approximate the dense flow field @xmath1 between a source image @xmath2 and a target image @xmath3 . to solve this problem , we use a fully convolutional network with no pooling . the main branch of the network consists of ten layers each applying a 7x7 convolution filter followed by an elu @xcite non - linearity ( fig . [ fig : net_arch ] ) . we use zero - padding to maintain the same image dimensions at each layer of the network . the input to our algorithm is a set of sparse and noisy matches @xmath4 . these matches can be produced by any third party matching algorithm . in our experiments , we used several of the leading matching algorithms : flowfields ( ff ) @xcite , cpm - flow ( cpm ) @xcite , discreteflow ( df ) @xcite , and finally deepmatching ( dm ) @xcite . from the matches , we produce a sparse flow map of size @xmath5 where @xmath6 and @xmath7 are the height and width of the image pair . each pixel is initialized with the displacement to its match in the x and y axis . missing pixels are filled with zeros . apart from the sparse flow map , we add two additional matrices as guiding inputs to the networks : a binary mask of the missing pixels , and the edges map ( fig . [ fig : net_arch ] ) . we create a binary mask of all the missing pixels to indicate their position to the network ( since zero can be a valid displacement value ) . it was shown by others @xcite to enhance performance in deep neural networks for inpainting . the last input to the network is an edges map of one of the images in the image pair for which the flow is computed . the contours of an image was shown to be a key feature in image processing in the early visual cortex @xcite . epicflow @xcite already showed the benefit of the image edges as motion boundaries for optical flow estimation . in our work , we show evidence that a learning system also benefits from receiving the edges as input ( see fig . [ fig : edges ] ) . we used an off - the - shelf edges detector - the `` structured edges detector '' ( sed ) @xcite - the same one used by epicflow . all the inputs are stacked together and downsampled by 8 to form an @xmath8 matrix . rather then a simple stacking , we also considered different ways of introducing the edges map into the network . among others , we have tried feeding the edges to all layers in the deep network , feeding the map to a different network and combining its output with the main branch in a deeper layer as well as constructing different networks to deal with pixels around the edges and far from the edges . however , we found that the simplest approach used here produced the best results . to optimize the network results , we used the epe (" +"within the shubnikov phase of type ii superconductors the applied magnetic field enters the sample in the form of flux lines . the standard mean - field type calculation@xcite shows that in an isotropic material two straight vortices repel at all distance scales , with an interaction strength @xmath1 , @xmath2 being the basic energy scale in the vortex matter , @xmath3 is the zero - order modified bessel function , @xmath0 is the inter - vortex distance , and @xmath4 the magnetic penetration length ( @xmath5 denotes the flux quantum ) . however , it has recently been shown @xcite that in layered and strongly anisotropic superconductors the thermal fluctuations of the flux lines give rise to a long range attraction @xmath6 of the van der waals type between the vortices , where @xmath7 denotes the temperature and @xmath8 is the interlayer separation . the strongly fluctuating and layered high temperature superconductors are particularly well suited to exhibit this attractive component in the vortex - vortex interaction . alternatively , the attraction is induced through static vortex distortions due to an underlying pinning landscape , an effect recently studied by mukherji and nattermann@xcite and by volmer _ et al._@xcite following a suggestion of nelson@xcite , the statistical mechanics of vortices can be mapped to the imaginary time quantum mechanics of two - dimensional ( 2d ) bosons . the particular interaction between the flux lines renders the bosons charged ( with a charge screened on the scale of the london penetration depth @xmath4 ) . this type of long range interaction can be formulated in terms of a massive gauge field theory@xcite . within the resulting 2d massive electrodynamics , the vortex matter acts as a dielectric medium and we can define a casimir problem , see fig . 1 : under the vortex @xmath9 boson mapping two half - spaces of vortices separated by a gap of width @xmath0 act as two dielectric planar media which attract each other via a casimir force . = 8.5 cm in the present work , we determine the casimir force between two dielectric half planes of charged bosons . for dilute media , the macroscopic casimir force can be related to the microscopic van der waals force between the media s constituents via pairwise summation . here , we present a derivation of the van der waals force between vortex lines via this alternative route , calculating first the casimir force between two dielectric planar media in the boson picture and then reconstructing the van der waals force in the reductionist way . since the discovery of the casimir effect@xcite in 1948 , several hundred papers have dealt with this phenomenon , disseminating its fascination into many branches of physics @xcite . casimir forces between macroscopic bodies are a quantum effect caused by a shift in the zero - point energy of gauge field fluctuations such as the electromagnetic one . the casimir effect is bound to a number of system properties , such as topology and dielectric permittivity , and the reduction to an analogous van der waals interaction is not always possible . however , the interpretation in terms of a van der waals attraction is possible for the case of rarefied media and appropriate geometries , such as the parallel plate setup@xcite . in our derivation of the van der waals force from the casimir effect we will make use of these special conditions . in the following , we discuss the relationship between the casimir effect and the van der waals interaction within a path integral formulation ( sec . ii ) before deriving the appropriate action for the 2d charged bosons from the london functional describing the vortices ( sec . iii ) . in section iv , we briefly review the derivation of the van der waals force in the original vortex language and then proceed with the calculation of the 2d casimir effect in section v , the main section of the paper containing the new results . we consider two parallel material slabs made from fluctuating dipoles and separated by a vacuum gap . summing pairwise over all microscopic van der waals interactions between the dipoles provides the macroscopic casimir interaction between the slabs . on the other hand , we can determine the dielectric properties of the individual slabs as produced by the fluctuating dipoles . the specific boundary conditions due to the dielectric properties of the slabs influence the spectrum of the electromagnetic field confined in between . the change in the spectrum as a function of the separation of the slabs produces the casimir force . this analogy between the casimir and the van der waals force is transparently brought out within a path integral formulation , see fig . 2 : assume the system under consideration can be described by an action @xmath10 $ ] depending on the gauge field @xmath11 and a particle current @xmath12 . carrying out the partial integration in the partition function @xmath13{\cal d}[{\bf j}]\ , e^{-{\cal s } [ { \bf j},{\bf a}]/\hbar}$ ] over the matter field @xmath12 or over the gauge field @xmath11 , we obtain an effective action @xmath14 describing the conjugate field alone : from the effective action @xmath15 $ ] describing the gauge field we can derive the casimir effect , while the interaction of the particle currents as described by @xmath16 $ ] will give us the van der waals attraction . the casimir- and van der waals forces then can be related to one another via the pairwise summation of the interparticle forces@xcite : consider two @xmath8-dimensional homogeneous macroscopic dielectric bodies of density @xmath17 with parallel interfaces separated by a distance @xmath0 . the two bodies attract one another due to a microscopic particle - particle interaction @xmath18 , @xmath19 , of the van der waals type . the interaction energy can be written in the form @xmath20 where @xmath21 is a hypercube of size @xmath22 parallel to the interface and @xmath23 , with @xmath24 the @xmath25 dimensional in - plane coordinate , while @xmath26 is the coordinate along the direction perpendicular to the plane . we then find for the casimir force density@xcite @xmath27 the result @xmath28 } { \gamma(\alpha/2 ) } \frac{1}{\alpha - d } \frac{1}{r^{\alpha - d}}. \label{f_of_r}\end{aligned}\ ] ] the result ( [ f_of_r ] ) then allows to infer the parameters @xmath29 and @xmath30 , characterizing the van der waals interaction @xmath31 , from the macroscopic casimir force density @xmath32 . ( 8.5,5 ) ( 0.1,0.1)(8.3,4.7 ) ( 2.25,2)(0,-1)0.75 ( 6.25,2)(0,-1)0.75 ( 4.25,0.75)(-1,0)1 ( 4.25,0.75)(1,0)1 ( 3.5,4)(-1,-1)1 ( 5,4)(1,-1)1 ( 3.8,4.25)@xmath10 $ ] ( 1.8,2.4)@xmath33 $ ] ( 5.9,2.4)@xmath16 $ ] ( 0.75,0.7)casimir effect ( 0.75,0.35)in dielectrics ( 5.75,0.7)van der waals ( 5.75,0.35)attraction ( 3.4,0.35)summation ( 3.6,1)pairwise ( 0.9,3.75)integrate ( 0.9,3.4)over @xmath12 in @xmath34 ( 6,3.75)integrate ( 6,3.4)over @xmath11 in @xmath34 after mapping the thermally fluctuating vortex matter to a system of 2d quantum charged bosons , we will arrive at an action @xmath35 $ ] with two gauge fields @xmath11 and @xmath36 , see eq . ( [ edr ] ) . the casimir effect we are interested in here is the one produced by the fake gauge field @xmath11 : the integration over the matter field @xmath12 will produce the dielectric properties of the media , while the integration over the physical gauge field @xmath37 renders the fake field massive and hence will always exponentially confine the casimir force to finite distances . we start from the london free energy in an isotropic superconductor@xcite @xmath38 = \frac{1}{8\pi}\int { \rm d}^3r \ , [ { \bf b}^2 + \lambda^2(\nabla \times { \bf b})^2 ] , \label{london}\ ] ] with @xmath39 the magnetic field and @xmath4 denoting the london penetration depth . in order to acquaint for the vortices , we add the current term @xmath40 with @xmath41 where @xmath42 , @xmath43 , the coordinates @xmath44 denote the position , the vectors @xmath45 the direction of the vortex lines , and @xmath5 is the unit of flux . ignoring screening , the interaction between the vortex lines is long ranged and thus can conveniently be expressed through a mediating gauge field @xmath11 . as usual , we introduce the gauge field @xmath11 as an auxiliary field such that @xmath46 ) = \exp(-\beta { \cal f})$ ] , with @xmath47 the inverse temperature@xcite ( we set the boltzmann constant @xmath48 to unity and fix the gauge through the condition @xmath49 ) , @xmath50 & = & \int { \rm d}^3{x } \ , \left[i{\bf a}\cdot\left({\bf j}-\frac{1}{\phi_0}(\nabla\times{\bf a})\right ) \right . \label{fprime } \\ & & \quad + \left . \frac{1}{8\pi}(\nabla \times { \bf a})^2 + \frac{1}{2g^2}(\nabla \times { \bf a})^2 \right ] , \nonumber\end{aligned}\ ] ] where @xmath51 and the line energy @xmath52 is the basic energy scale in the problem . in ( [ fprime ] ) , we have accounted for screening by introducing back into the model the real gauge field @xmath37 . the anisotropy of uniaxial layered materials is most conveniently introduced through a rescaling of the scalar fake magnetic field @xmath53 @xcite , @xmath54 where the anisotropy factor @xmath55 is determined through the effective masses perpendicular ( @xmath56 ) and parallel ( @xmath57 ) to the @xmath58-plane ( the fake electric field @xmath59 remains unchanged ; the subscript ` @xmath60 ' identifies the planar component of a vector , @xmath61 ) . we map the statistical mechanics of the vortex system to the imaginary time quantum mechanics of 2d bosons through the replacements@xcite @xmath62 ( imaginary boson time ) , @xmath63 ( the boson s planck constant ) , @xmath64 ( the boson action ) , and @xmath65 ( the light velocity in the boson system ) . the boson partition function is given by @xmath66 { \cal d}[{\bf a}]{\cal d}[{\bf a } ] e^{-{\cal s}[\{{\bf r}_\mu\},{\bf a},{\bf a}]/\hbar^{\scriptscriptstyle b } } , \label{zzz}\ ] ] with @xmath67 and @xmath68 = \int \!\ ! { \rm d}\tau \sum_\mu \left[\frac{m}{2 } \left(\partial_\tau { \bf r}_\mu ( \tau)\right)^2 - \mu^{\scriptscriptstyle b } \right],\label{plm}\\ & & { \cal s}_{\rm int } [ \{{\bf r}_\mu\},{\bf a},{\bf a } ] = \int \!\ ! { \rm d } \tau { \rm d}^2 r \left[i{\bf a}\cdot \left({\bf j}-\frac{1}{\phi_0 } ( \nabla \times { \bf a})\right ) \right . \label{edr } \\ & & \quad + \left . \frac{1}{8\pi } ( \nabla \times { \bf a})^2 + \frac{1}{2g^2}\left((\nabla\times{\bf a})_{xy}^2 + \frac{1}{\varepsilon^2 } ( \nabla\times { \bf a})_\tau^2\right ) \right ] . \nonumber\end{aligned}\ ] ] here , @xmath69 is the chemical potential of the bosons , @xmath70 is the boson density , and @xmath71 is the boson mass ( we have introduced a term @xmath72 to account for the external magnetic field @xmath73 producing the vortices in the superconductor ; @xmath74 denotes the planar coherence length ) . in the thermodynamic limit , we have @xmath75 , corresponding to @xmath76 , i.e. , we are interested in the ground state physics of the boson system . note that the free boson action @xmath77 contains the bare mass @xmath78 due to the vortex core energy . the retarded self - interaction of the bosons via their gauge fields then produces the mass renormalization @xmath79 , where @xmath80 is the dispersive line tension@xcite of the vortex lines . to set the stage , we briefly review the derivation of the van der waals interaction as presented in ref . ; this will allow us to fix some flaws in the previous derivation and will provide us with a check on the results for the casimir force derived later . for a simple qualitative analysis we consider two vortices in a layered superconductor ( with layers separated by the distance @xmath8 ) . ignoring the coupling between the layers , the fluctuating pancake vortices interact via a logarithmic potential @xmath81 . second order perturbation theory then provides us with a van der waals interaction @xmath82 , the energy scale" +"in some of the popular puzzles one is supposed to take a ring off a rope which is usually tangled with the rigid part of the puzzle . typically , such puzzles possess ingenious solutions which , if considered carefully enough , lead to interesting problems in low - dimensional topology . this phenomenon can be observed in the chinese rings which are shown below . the purpose of the puzzle is to take the loose ring off the rope . although this puzzle was for a long time a toy of the first author s children , we become seriously interested in it only after l. kauffman pointed to us some interesting mathematical aspects of it , @xcite . the history of the chinese rings can be found in @xcite . the goal of this paper is to prove that a particular solution of the chinese rings puzzle is the simplest possible , as conjectured in @xcite . if you have not thought about this puzzle before , then we suggest that you try to solve it now in order to gain an appreciation for this beautiful problem . do not be discouraged by the initial difficulty in finding a solution . indeed it is almost impossible to see all the necessary moves to be performed on the rope just by staring at the picture above . however , it is easy to see that a solution exists : imagine for a moment that the toy is made out of a flexible material and press the longer columns down so that all columns have the same length , as shown in figure 1 . figure 1 . now the solution becomes obvious ! since now the rope is completely separated from the columns , it can also be untangled in the original puzzle . ( actually , we need to be sure that the rope is long enough for this theoretical solution to be correct ; this can be confirmed by direct experimentation ) . the above solution shows how a simple topological idea can yield a beautiful solution to what seems to be a complicated problem . the same idea shows that the chinese rings can be presented in a somewhat more regular form : figure 2 . note that we replaced the rope by another column with an attached ring . the problem now is to separate the loose ring ( which is assumed to be infinitely elastic ) from the solid part of the puzzle . the problem addressed in this paper is to find the simplest solution to this puzzle . as we will see soon , the solution to this problem involves an inductive argument in the number of columns . for that reason we consider a more general version of the puzzle of fig . 2 composed of an arbitrary number of columns ( all but one with an attached ring at the top ) . a precise answer to our problem requires an objective measure of the complexity of possible solutions to the puzzle . for that , imagine an arc @xmath0 drawn below with a dashed line , joining the highest column of the toy with the base . the complexity of a solution for the puzzle is the minimal number of times the elastic ring passes through the arc @xmath1 in the process of that solution . figure 3 . the minimal complexity of a solution for the chinese rings with @xmath2 columns presented at fig 3 is @xmath3 this result was conjectured by l. kauffman in @xcite , who wrote : "" this problem in the topology of the chinese rings is a useful test case for questions that can arise in applications of knot theory to natural structures where there is always a mixture of topology and mechanical / geometrical modeling . a solution to the ring conjecture will probably involve the discovery of new techniques for understanding topology of graph embeddings in three - dimensional space . it is fun to be able to take a classical puzzle as fascinating as the chinese rings and find within it a significant topological problem . let us find the solution ! "" * habiro moves * there is a surprising connection between the chinese rings ( known for hundreds of years ) and a very recent theory of vassiliev invariants of knots , @xcite . k. habiro @xcite proved that two knots can not be distinguished by vassiliev invariants of order @xmath4 if and only if they are related by a sequence of moves ( called habiro moves ) presented below : + + + + note that the habiro move corresponds exactly to the operation of untangling the loose ring in the version of chinese rings presented in figure 3 ! the solution of the puzzle presented at the beginning of the paper requires that we first untangle the rings attached to the columns . note that as a result of this deformation of the puzzle , the arc @xmath1 will assume the form presented below . figure 4 . because we can now remove the ring by passing through the @xmath5 strands of @xmath0 the complexity of this algorithm is obviously at most @xmath3 we are going to show that this is the simplest solution to the chinese rings ; i.e. the complexity of any other solution is not less than @xmath3 for the purpose of the proof we are allowed to relax the conditions of the problem and consider it in a topological setting by allowing arbitrary deformations of the dimensions and the shape of the toy . moreover we add a point at infinity to the ambient three - space and hence consider the problem in @xmath6 these assumptions make the problem simpler and surely do not increase the complexity of the minimal solution . the body of the chinese rings with @xmath2 columns ( and with the loose ring excluded ) is a handlebody @xmath7 of genus @xmath8 embedded in the standard way into @xmath6 its complement , @xmath9 is also a handlebody of genus @xmath10 the loose ring is contractible in @xmath9 and this is the reason for which the puzzle has a solution . the arc @xmath1 assumes a complicated position in @xmath11 which can be deduced from fig . 4 , see fig . 5 figure 5 : complement of the puzzle @xmath12 if we remove the arc @xmath1 from @xmath11 then the loose ring , @xmath13 will no longer be contractible . recall that the complexity of a solution for the puzzle is the minimal number of passes of the ring through @xmath1 necessary for contracting the ring to a point in @xmath14 we need to show that this number is at least @xmath3 unfortunately , the position of the ring @xmath15 in @xmath16 is very complicated ; try to figure it out by yourself to see that , indeed , it is not an easy problem ! in order to avoid this problem we use three tricks : first , we take a dual approach : we fix the ring @xmath15 in @xmath11 and count the number of times the arc @xmath1 has to pass through @xmath15 in order to make @xmath15 contractible in @xmath14 second , we slightly relax the conditions of the puzzle , by assuming that @xmath1 can be deformed by an arbitrary homotopy fixing its endpoints . we assume that the endpoints of @xmath1 are at some @xmath17 therefore we consider @xmath1 as an element of @xmath18 our intention is to prove that under these relaxed conditions the complexity of the puzzle is at least @xmath3 this will surely imply that the complexity of the puzzle under original assumptions is also at least @xmath3 third , we modify the puzzle by attaching the loose ring to the base of the puzzle by an additional column , and we try to untangle @xmath1 in the modified puzzle . this seems to be a more difficult problem , but actually it is not . observe that the modified puzzle is homeomorphic to a handlebody of genus @xmath19 and that its complement is homeomorphic also to a handlebody , @xmath20 notice also that we have an embedding @xmath21 corresponding to the fact that the modified toy differs from the original only by an additional column . one can prove using van - kampen s theorem that the map @xmath22 induces an isomorphism of the fundamental groups , @xmath23 therefore the additional column does not create any new obstacle for @xmath1 ! ( recall that we consider the arc @xmath1 up to homotopy only . ) the benefit of this trick is that the modified puzzle is much easier to solve because it does not have any loose ring . observe that the arc @xmath1 lies in @xmath24 in the pattern presented in figure 6 . figure 6 . denote the loops going around the holes in @xmath24 in the manner presented below by @xmath25 + figure 7 . @xmath26 is the free group on generators @xmath27 we want to determine the presentation of the element @xmath28 representing the arc @xmath1 given as in fig . 6 , with say an anti - clock orientation . the presentations of @xmath29 and @xmath30 are as follows : + figure 8 : @xmath31 and @xmath32 observe that @xmath33 can be built inductively from @xmath34 by replacing the @xmath2-th hole in @xmath24 by two holes and twisting them @xmath35 see fig 6 . this operation corresponds to replacing all @xmath36 in the presentation of @xmath34 by @xmath37 therefore @xmath38 note that each such presentation is reduced , i.e. none of the words @xmath34 has a subword of the form @xmath39 indeed , this is true for @xmath40 in general , if this is true for some @xmath2 then it is also true for @xmath41 suppose that @xmath34 is reduced . the only difference between @xmath34 and @xmath33 is that @xmath42 in @xmath34 is replaced by @xmath43 therefore , @xmath33 can not contain @xmath44 for @xmath45 hence , if @xmath33 was not reduced , it would have to have a reduction in @xmath46 s . that is , it would have to contain a subword composed of @xmath47 and its inverse . but this is impossible , since this would mean that @xmath34 contains the subword @xmath48 observe also that the number of appearances of @xmath36 in @xmath34 is @xmath3 this can also be proved by induction : @xmath49 appears once in @xmath50 and @xmath46 appears in @xmath33 twice as many times as @xmath42 in @xmath51 therefore we proved the following [ 1.1 ] the above inductively defined presentation of @xmath28 is reduced and @xmath36 appears @xmath5 times in it . recall that we are supposed to count the minimal number of times the the ring @xmath15 has to pass through the arc @xmath1 ( in the original puzzle ) in a process of contracting it to a point . equivalently , we can calculate the number of times the arc @xmath1 has to pass through the @xmath2-th hole in @xmath24 in order to be placed inside @xmath52 ( in the situation in which the modified puzzle is considered ) . we claim that this number is at least @xmath3 whenever @xmath1 passes through the @xmath2-th hole , @xmath53 is inserted in a word representing @xmath1 or deleted from it . intuitively , since @xmath36 appears @xmath5 times in @xmath34 one has to repeat this process @xmath5 times . this may seem as an obvious fact at first , but after a closer look one can realize that it requires a proof . we will see in the next section that this problem is a special case of an interesting problem in the combinatorial group theory . in order to finish our proof we need the following fact . [ 1.2 ] if letters @xmath54 form a reduced word @xmath55 then the minimal" +"as is well known , the standard model , with an elementary higgs doublet field , suffers from the problem of quadratic divergences when radiative corrections , due to the loops of fermions , the top quark in particular , to the mass of the higgs boson is calculated . this problem is often referred to as the hierarchy problem , as we require an artificial fine tuning between the induced radiative mass , which is of the order of the cut - off scale , e.g. , @xmath9 , and the counterterm to produce a mass of the order of the electroweak scale . this tempts us to speculate that the higgs boson may in fact be composite . the simplest implementation of this idea is top - quark condensation @xcite . it turns out , however , that this compositeness by itself is not sufficient to remove the problem of quadratic divergences , and fine tuning is still required in the simpler approaches to top - quark condensation . the problem of divergences can only be artificial , because the same loop corrections , applied to the mass of the goldstone bosons , produce a similar quadratic divergence , whereas the goldstone theorem guarantees that spontaneous symmetry breaking results in massless goldstone bosons . this suggests that these quadratic divergences are an artifact , and will vanish if the condition of current conservation is implemented properly . for example , the approach of chesterman , king and ross @xcite uses the vanishing of the mass of the goldstone boson as a consistency check , and is able to obtain sensible values for the mass of the higgs boson . a more direct investigation into this point regarding current conservation was made by gribov in ref . @xcite , and his results are in quantitative agreement with ref . @xcite . in that paper , he implemented the symmetry condition , somewhat by force , by requiring that the goldstone - boson self - energy vanishes in the soft limit . the mass of the higgs boson is then obtained by subtracting off the goldstone - boson self - energy , leading to the following pagels stokar - type equation for the mass of the higgs boson : @xmath10 this gives the mass @xmath11 gev for the higgs boson using the top - quark mass @xmath12 gev and @xmath13 as input . gribov s cut - off @xmath14 is given by the u(1)@xmath3 landau pole , @xmath15 gev , but the results are relatively insensitive to the value of the cut - off scale . this value of @xmath0 is not far from the recent lhc results @xcite which suggest @xmath16 gev . it is worth noting here that eqn . ( [ eqn_gribov_higgs_mass ] ) is general and is independent of the physics that causes the cut - off . our questions are the following . first , what may be the justification for this procedure , in particular the mechanism for the cancellation of the divergences ? second , whether there may be correction terms due to the loops of goldstone and higgs bosons in eqn . ( [ eqn_gribov_higgs_mass ] ) . concerning the first question , we shall show in this paper that the quadratic divergences are proportional to the tadpole and therefore vanish when the vacuum is stable . although this statement must be independent of the basis , it is most easily verified by defining the goldstone bosons as the divergence of the weak current so that derivative couplings do not arise . our analysis is quite general in the sense that no new interactions are introduced up to the uv cut - off scale . this procedure has the well - known phenomenological disadvantage that the mass @xmath5 of the @xmath17 boson is predicted to be too low for fixed @xmath6 or , equivalently , @xmath6 is predicted to be too large for fixed @xmath5 . this is partially alleviated by taking large @xmath14 such as , as in gribov s scenario , the u(1)@xmath3 landau pole . even this is not sufficient and , as remarked in ref . @xcite , more uv contribution is required , which may be , one would naturally guess , due to strong dynamics at near and above the cut - off . the methods of our analysis are analogous to those in ref . @xcite that are worked out in the context of anti - ferromagnetism . the second of the questions above is also addressed within this framework , and we find that the correction to eqn . ( [ eqn_gribov_higgs_mass ] ) is large and negative . as an explanation of our framework , we implement current conservation by requiring the vanishing of the ward takahashi identities . this fixes the bosonic three - point and four - point couplings . in other words , the shape of the higgs potential is fixed by current conservation , and this turns out to be of the same form as that of the standard model . we then implement the vacuum - stability condition , namely that the higgs @xmath18 one - point function , or the tadpole , vanishes . note that the cancellation of the tadpole , which is imposed as the cancellation among the top - quark , goldstone - boson and higgs - boson loops , is by itself an independent condition on the symmetry - breaking parameters . this yields @xmath19 which implies @xmath4 gev in the u(1)@xmath3 scenario , if we only include the qcd part of the running . this is very close to the lhc value , but this remarkable success should not be taken too seriously , because this condition will be affected by the renormalization , due to the u(1)@xmath3 interaction , of the top - quark mass at near the landau pole . it should be noted that this extra condition on the higgs mass , in principle , completely fixes the symmetry - breaking parameters . that is , all three masses , @xmath5 , @xmath6 and @xmath0 , are fixed for given values of the cut - off scale and gauge couplings . this provides a natural solution to the hierarchy problem and , indeed , we obtain a large hierarchy that is comparable with the actual hierarchy between the uv and ewsb scales . the form of the uv theory does not affect our analysis at the present level of approximation , so long as the symmetry is spontaneously broken by a uv condensate which exists only at high energies . this requires a supercritically strong uv interaction , and a natural candidate is gribov s u(1)@xmath3 scenario . we discuss the physics of this scenario . tadpole cancellation in bosonic self - energy was , in part , discussed by gribov himself in the context of chiral symmetry breaking in ref . however , he imposes tadpole cancellation there by introducing a boson boson quark quark term ( e.g. , eqn . ( 132 ) of ref . @xcite ) to cancel the anomalous term in the ward takahashi identity associated with compton scattering . one problem in doing so is that this will lead to the necessity of introducing an infinite number of @xmath20-boson quark quark couplings . in ref . @xcite , and in the context of anti - ferromagnetism , we proposed a more economical mechanism which also seems to us to be more natural . here , only the three - point and four - point couplings among the goldstone and higgs bosons are needed , and these couplings are fixed by symmetry conditions such as the ward takahashi identities . we shall demonstrate that the couplings are consistent with the standard - model - like quartic higgs potential . in the low - energy effective theory , the phenomenology is identical to that of the standard model , at least insofar as the couplings to the bosons and the top quark are concerned . as for the other fermionic yukawa couplings , it is natural to assume that they are as given by the standard model though , strictly speaking , other possibilities can not be ruled out . let us start with the fermionic vertex function for the left - handed su(2 ) current . as discussed in ref . @xcite , ward takahashi identity is satisfied by the following modified vertex : @xmath21 here , the small blob stands for the unmodified vertex @xmath22 and the two - point function ( @xmath23 in gribov s notation ) which follows from that , and the asterisk stands for the vertex that is modified by the inclusion of the goldstone - boson contribution . the dashed line stands for one of the three goldstone bosons @xmath24 , @xmath25 . takahashi identity , applied to the modified vertex , fixes the @xmath26 coupling to fermions to be , for example , @xmath27 where @xmath28 , the goldstone - boson form factor , is defined by the two - point function of eqn . ( [ eqn_modified_vertex ] ) . @xmath29 , where @xmath30 is the usual ` vacuum - expectation value of the higgs field ' . note that the feynman rules are , as usual , given by @xmath31 . this will apply to all couplings that appear in the following . the same exercise may be repeated for the bosonic vertex : @xmath32 the unmodified vertex is necessarily proportional to @xmath33 ( momenta flows left to right , or more generally @xmath26 to @xmath34 ) in order to satisfy the ward takahashi identity , and the normalization is fixed by the ward takahashi identity applied to the amplitude shown in fig . [ fig_fermion_boson_current_amplitude ] . the three diagrams whose sum must satisfy the ward takahashi identity.,title=""fig : "" ] the three diagrams whose sum must satisfy the ward takahashi identity.,title=""fig : "" ] the three diagrams whose sum must satisfy the ward takahashi identity . ] this fixes the @xmath35 coupling to be : @xmath36 when the yukawa coupling of the higgs boson to fermions is given by @xmath37 four diagrams whose sum must satisfy the ward takahashi identity . not all diagrams are present for all combinations of @xmath26,title=""fig : "" ] four diagrams whose sum must satisfy the ward takahashi identity . not all diagrams are present for all combinations of @xmath26,title=""fig : "" ] four diagrams whose sum must satisfy the ward takahashi identity . not all diagrams are present for all combinations of @xmath26,title=""fig : "" ] four diagrams whose sum must satisfy the ward takahashi identity . not all diagrams are present for all combinations of @xmath26,title=""fig : "" ] next , we consider the ward takahashi identity in the set of amplitudes that are described by fig . [ fig_triple_boson_current_amplitude ] . this allows us to work out the goldstone - boson quartic couplings : @xmath38 four diagrams whose sum must satisfy the ward takahashi identity.,title=""fig : "" ] four diagrams whose sum must satisfy the ward takahashi identity.,title=""fig : "" ] four diagrams whose sum must satisfy the ward takahashi identity.,title=""fig : "" ] four diagrams whose sum must satisfy the ward takahashi identity.,title=""fig : "" ] we then turn to the set of amplitudes that are described by fig . [ fig_triple_boson_current_amplitude_second ] , and obtain @xmath39 note that the higgs - boson self - coupling is not fixed by current conservation conditions but either by loops or by the symmetry between goldstone and higgs bosons . as noted in ref . @xcite , these turn out to be the same as the couplings of the standard model : @xmath40 this implies @xmath41 we notice that the effective lagrangian for the multi - boson interaction terms can be written as @xmath42 ^ 2.\ ] ] in terms of the standard - model higgs -" +"the shapes of the surfaces between molecular clouds and the hii regions around massive stars typically feature elongated structures , commonly referred to as pillars , columns , spikes , or elephant trunks @xcite . the surface is a photoionization front driven by the strong uv radiation from the ob stars . one well - known example is the eagle nebula which has three large , molecular pillars near a small group of o stars @xcite . although a number of theoretical and numerical studies have been done , the formation mechanism is still not fully understood . the ob stars are hot , with photospheres at temperature of a few tens of thousands of kelvins @xcite , and give off high intensity uv photons . these uv photons irradiate the molecular cloud which surrounds the ob stars and photoevaporation occurs , resulting in a stratified structure . the photoevaporative flow ( ablated plasma ) velocity is normal to the molecular surface @xcite . the region between the ob stars and the molecular cloud surface is the hii region in which the hydrogen gas is almost fully ionized and the photoionization and recombination to neutral atomic hydrogen occurs in steady state . the if is a very thin layer because of the short mean free path for the incident photons on the cloud surface . at this cloud surface all the photons above the lyman limit are absorbed . the photons below the ionization limit but above 11.2 ev can not ionize the hydrogen atom in the ground state but can penetrate the if and dissociate the molecular hydrogen in the underlying layers . the thickness of the dissociation front differs with each cloud . the last layer in the stratified structure is the molecular gas . because of strong radiative cooling , the molecular cloud temperature is typically a few tens of kelvin @xcite . the dynamics of such irradiated molecular clouds is thought to play a role in star formation @xcite . consequently , the outflow dynamics from the molecular cloud into the hii regions is of considerable , general interest @xcite . the pillars in m16 , popularly known as the eagle nebula , are at a distance of @xmath0 kpc ( @xcite ) . it is estimated that half of the ionizing radiation comes from a single o3 - 4 star and the rest mostly comes from the three other nearby stars ( o5 - 6 ) @xcite . the orientation of this system can be seen in fig . [ poundeagle ] ( taken from @xcite ) . the total ionizing flux is estimated to be @xmath1 . the temperature in the hii region near the molecular cloud surface is 9500 k and the ionized hydrogen number density is @xmath2 @xcite . the thickness of the photodissociation region ( pdr ) is relatively thin because the large hydrogen number density ( @xmath3 ) provides high optical depth . as measured by co line observations , the velocity gradients along the long axes of the pillars ( from `` head '' to `` tail '' ) are between -20.7 and + 6.7 @xmath4 , with an average magnitude of 8.3 @xmath4 . furthermore , the pillars are not in the same plane in the sky ; the differing signs of the velocity gradients indicate inclination towards ( positive gradient ) or away ( negative gradient ) from the observer . predictions of the classical rayleigh - taylor ( rt ) instability theory with regard to the velocity gradient @xcite are incompatible with the observed gradient , at least for constant acceleration @xcite . another formation mechanism should be considered . the formation mechanism of pillars beside massive stars has been discussed by a number of authors . there are two classes of models for their formation . one is that the pillars are formed due to dense , pre - existing cores in the molecular cloud ( e.g. @xcite ; @xcite ; @xcite ; @xcite ) . in a interesting variation on this idea , @xcite also simulated the result of a radiatively driven , pre - existing , short pillar with the same density as the background molecular cloud ( their case ii ) . even in this case , the pillar grows . another possibility is that the pillars are caused by hydrodynamic instabilities . @xcite proposed a model based on the rt instability occurring at the contact discontinuity between the dense molecular cloud and the lower density , hot , photoevaporated plasma . he suggested that the pillars in the eagle nebula were the result from the nonlinear stage of the rt instability . @xcite estimated the time scale of the instability to be less than @xmath5 years . @xcite showed observations of several nebulae and estimated the age of the pillars by the rt model , assuming small initial amplitude of the perturbations . @xcite found another type of instability at the if in a non - accelerating frame , the so - called if instability , which , in his analysis , was present in the case of non - normal incident radiation . he derived a dispersion relation for perturbations growing by this process . @xcite extended it to include recombination , which plays a crucial role in the hii region . the recombination in the ionized gas works to smooth the surface when the wavelength of the perturbation is much larger than the recombination length . @xcite showed robust development of photoionized pillars with an isothermal model , although they considered a semi - infinite cloud and a non - accelerating if . @xcite derived a dispersion relation for the if with a non - normal incident radiation field including the effect of recombination in the ionized gas . @xcite found unstable modes with non - normal radiation for an accelerating if , but did not include recombination . most studies have assumed a semi - infinite molecular cloud and non - accelerating if . instabilities at an accelerating if were studied numerically by mizuta et al . ( 2005 , hereafter paper i ) . they show that , for imposed perturbations with small initial amplitude , i.e. in the linear regime , there was no significant growth . large growth of a classical rt instability is observed when recombination in the hii region is not included . we study here in more depth the dynamics of an accelerating if . the existence of the acceleration at the if is quite different than most previous models . this paper is organized as follows . the numerical method and conditions are described in sec . [ model ] . the results and discussions are given is sec . [ discussion ] , and the conclusion is given in sec [ conc ] . the same physics and computational method used in paper i are included in this study . the energy balance and magnetic pressure to prevent radiative collapse for the molecular cloud are considered . the equations we numerically solve are : @xmath6 where @xmath7 is mass density , @xmath8 is pressure , @xmath9 is unit tensor , is the velocity vector , and @xmath10 is the specific internal energy . the equations ( [ e - massconserv])-([e - energyconserv ] ) are mass , momentum and energy conservation with energy sources . the energy source terms due to recombination in the ionized region , absorption of the uv radiation from ob stars , and cooling in the molecular gas are @xmath11 , respectively . these energy sources are evaluated as @xmath12 , \\ n_{mol } & = & n~(1-f)/2 , \\ \rho \epsilon & = & 3 ( nf ) k t + 2.5 n_{mol } k t , \ ] ] where @xmath13 is the temperature in kelvins @xmath14 is the proton mass , @xmath15 is the boltzmann constant , and @xmath16 and @xmath17 are atomic hydrogen and molecular hydrogen number density . we ignore metal line cooling for simplicity , since its cooling power has the same dependence as that of recombination ( proportional to ionized hydrogen number density ) . the dissociation heating in the neutral region and other radiative processes are also ignored for simplicity . the heating function is @xmath18 erg which corresponds to the average energy deposited into the gas per absorbed ionizing photon , and leads to produce an isothermal temperature of @xmath19 k in the ionized gas as an equilibrium state of photoionization heating and recombination cooling . the case b recombination coefficients , which are summation of all recombination coefficients of hydrogen except the recombination to the ground state , are assumed constant @xmath20 and @xmath21 ( at @xmath19 k from @xcite ) , where @xmath22 includes the thermal velocity dependence of the rates of recombination and free - free collisional cooling . the equation of state ( eq . [ e - eos ] ) includes a magnetic pressure term for dense gas to prevent radiative collapse @xcite , where @xmath23 is the ionization fraction , @xmath24 is the ionized hydrogen volume density , @xmath25 and @xmath26 are constant values . the index @xmath27 ( @xmath28 ) is also constant . numerically , we do not take into account the atomic hydrogen state , assuming the dissociation front is thin as in the eagle nebula . equations ( [ e - fevolution ] ) and ( [ e - radtransport ] ) describe the evolution of @xmath29 and the transport of the incident radiation , where @xmath30 is the photoionization cross - section of hydrogen , and @xmath31 is the number flux of ionizing photons , i.e. , photons @xmath32 . since we use the `` on - the - spot approximation '' ( i.e. , photons emitted in recombination to ground state are immediately reabsorbed , whereas the photons emitted in recombination to second or higher levels are assumed to escape from the system ) , we do not consider the diffusive photon emission and transport . the 2d computational domain is ( @xmath33 ) = ( 0.46 pc@xmath343 pc ) . uniform grid points ( @xmath35 pc ) are used . periodic boundary conditions are employed ( @xmath36 and @xmath37 pc ) . the other boundary conditions are open boundary which means zero gradient . an incident photon flux ( @xmath38 ) is imposed from one boundary ( @xmath39 pc ) , where @xmath40 is the unit vector of the @xmath41 axis . the rays are parallel to the @xmath41 axis . a cloud of initial thickness of a quarter pc , and density of @xmath42 is set 0.5 pc away from the boundary where the incident photons come in . a very dilute gas @xmath43 is imposed in the other regions . initially , the gas at @xmath44 pc is in pressure equilibrium , and the gas at @xmath45 pc is isothermal ( 40 k ) . the constant parameters in the equation of state , such as , @xmath26 and @xmath25 , are the mass density and thermal pressure , of the initial molecular cloud , respectively . we impose the perturbation in the cloud in three different ways . the first is a density perturbation in a layer of 0.125 pc thickness along the surface of the cloud , with the form @xmath46)$ ] , where @xmath47 is the amplitude of the perturbation and @xmath48 . we assume a wavelength of @xmath49 pc , and consider amplitudes @xmath50 ( model d2 ) , 0.3 ( d3 ) , 0.4 ( d4 ) and 0.5 ( d5 ) . the second method is a 30% amplitude perturbation in the incident photon number flux of form @xmath51)$ ] , starting at 98 , 102 , 106 , or 108 kyr and ending at 110 kyr . these are models p098 , p102 , p106 , p108 , respectively . this is similar to the" +"in recent work we considered the properties of cumulants of time - integrated quantities in closed quantum systems , focusing in particular on the case of the time - integrated transverse magnetisation in the quantum ising chain @xcite . the aim was to highlight the importance of time - integrated operators , as opposed to time - local ones , as appropriate observables for the characterisation of real time dynamics of many - body quantum systems . the reason is that very often many - body systems , both classical and quantum , display collective dynamical behaviour of a more complex nature that what is suggested by their structural or stationary properties . glass forming systems are a typical example of this @xcite . for such systems time - integrated observables , in particular those which are extensive in both system size and time , serve as dynamical order parameters , as their higher moments can encode the full range of dynamical fluctuations . this is essentially the idea behind full - counting statistics ( fcs ) both in mesoscopics @xcite and in quantum optics @xcite , and of the thermodynamics of trajectories formalism in stochastic systems @xcite . the main point of @xcite was to show that by considering time - integrated observables it is possible to uncover the existence of distinct `` dynamical phases '' delimited by singularities of their cumulant generating function ( cgf ) . these transitions are the closed system equivalent of the `` trajectory transitions '' of open classical and quantum systems @xcite , i.e. , singularities in the cgf of time - integrated dynamical observables indicative of far - from - gaussian behaviour of their corresponding probability distributions ( analogous to the singularities of free - energies and the non - gaussian behaviour of order parameter distributions at equilibrium phase transitions ) . for time - integrated observables of closed quantum systems there is in general no associated probability distribution , but the cgf does exist , and it can be non - analytic in the long time limit as a function of its argument ( the `` counting '' field ) @xcite . these singularities are in general extensions of static quantum phase transition points , and share many similarities with them ; for example if one quenches across these phase boundaries the echo dynamics can display `` dynamical phase transitions '' @xcite similar to the ones found for quenches across static critical points @xcite . the cgf of a time - integrated observable is obtained from the spectrum of a non - hermitian perturbation of the hamiltonian of the system @xcite . in particular , the long - time cgf is related to the complex eigenvalue of this non - hermitian hamiltonian with the largest imaginary part . singularities in the cgf then emerge due to the closing of a gap in this complex energy spectrum . recently there has been a growing interest around a special class of operators which , while non - hermitian , do have a real spectrum ( and thus could be the actual hamiltonians of physical quantum systems)@xcite . that such operators can display a real spectrum is due to an associated @xmath0-symmetry @xcite . when this @xmath0 symmetry is broken these non - hermitian operators in general have complex eigenvalues @xcite , but when the symmetry is unbroken the spectrum is real . in this paper we explore the connection between the cumulants of time - integrated observables of a closed quantum system and the @xmath0-symmetry properties of the non - hermitian hamiltonian from which their cgf is derived . in certain cases , and for certain observables , the non - hermitian hamiltonian can display regimes of broken and of unbroken @xmath0-symmetry , and these regimes then correspond to distinct dynamical phases of the system . we apply this analysis to study the behaviour of the time - integrated longitudinal magnetisation in the one - dimensional transverse field ising model ( tfim ) . we show that the static disordered phase of the tfim belongs to a @xmath0-symmetric regime , so that the cgf of the time - integrated magnetisation is vanishing ( implying that all its cumulants are sub - linear in time ) . in contrast the static ordered phase belongs to a regime where @xmath0 is spontaneously broken , and where the cumulants of the time - integrated magnetisation grow superlineraly with time . the paper is organized as follows . in sec . [ sec : theo ] we provide the necessary theoretical background , both summarizing the method of ref . @xcite for studying time - integrated observables , and briefly reviewing known results on @xmath0-symmetries in spin models . in sec . [ sec : single ] we present a warm up example to illustrate our approach , that of the time - integrated magnetisation of a single spin system and its connection to @xmath0-symmetry breaking . our main results on the behaviour of the cumulants of the time - integrated longitudinal magnetisation in the tfim are described in sec . [ sec : ising ] . finally , in sec . [ sec : conc ] we give our conclusions . we consider a closed quantum system which evolves unitarily under a hamiltonian @xmath1 ( note we set @xmath2 ) , and we focus on a general time - integrated dynamical observable whose moments ( and cumulants ) we are interested in : @xmath3 where @xmath4 is some static system observable , and @xmath5 is written in the heisenberg picture with @xmath6 . the cumulants of @xmath7 encode information on the dynamical fluctuations of the system . in order to obtain the cumulants , we first need to define the moment generating function ( mgf ) and its associated non - unitary evolution operator @xmath8 @xcite , @xmath9 where we deformed @xmath1 to a non - hermitian hamiltonian @xmath10 . with this modified evolution operator one can show that the mgf is given by @xcite @xmath11 from these definitions it is easy to demonstrate that the moments of @xmath7 are obtained via differentiation , @xmath12 . the cgf is given by the logarithm of the mgf , @xmath13 , such that @xmath14 , where @xmath15 indicates cumulant . these quantities define the fcs @xcite of the observable @xmath7 in this system , where in contrast to the usual approach used in studying fcs we consider the parameter @xmath16 to be real . to study the analytic properties of this generating function in the long - time limit it is useful to consider the scaled form of the cgf , @xmath17 for extensive systems , such as the tfim studied below , we also want to scale the function in order to define the large size limit , such that @xmath18 . it is convenient also to define the `` order parameter '' @xmath19 , i.e. , the long - time average of the observable @xmath7 , per unit time , that one would obtain by controlling @xmath16 ( rather than the actual dynamical average which corresponds to when @xmath20 ) , and the associated susceptibility @xmath21 , which help to characterise the dynamical phases delimited by singularities of @xmath22 @xcite . in standard formulations of quantum mechanics there is a strict requirement of hermiticity of the hamiltonian ( @xmath23 ) which ensures the existence of a real energy spectrum . recently , after the seminal work of bender et al . @xcite , the has been much interest in the study of non - hermitian hamiltonians which may still have a real spectrum provided they are invariant under a space - time reflection @xcite . representing the parity operator by @xmath24 , and time reversal by @xmath25 , this space - time symmetry is called @xmath0-symmetry , and a @xmath0 symmetric hamiltonian is defined as @xmath26 the operator @xmath0 satisfies @xmath27 , and @xmath25 is an antilinear operator @xcite . these properties , together with condition allow for a formulation of a physical theory of quantum mechanics without violating any of the original axioms . the condition ensures that the @xmath0 operator commutes with the hamiltonian . a conventional @xmath0 operator acts as a combination of a spatial reflection ( say , @xmath28 ) and a time reversal , usually corresponding to complex conjugation . this operator is not linear , hence the eigenstates of @xmath1 may differ from those of @xmath0 . consider an eigenstate @xmath29 of @xmath0 corresponding to the eigenvalue @xmath30 . using only the properties of the operators @xmath0 and @xmath25 one can readily show that @xmath31 this means that @xmath30 is a phase , and can be written as @xmath32 , with @xmath33 . if we consider that @xmath29 is also an eigenstate of the hamiltonian @xmath1 with energy @xmath34 it is easy to show from the fact that @xmath1 and @xmath0 commute that @xmath35 as @xmath30 is nonvanishing it follows that @xmath34 is real . this conclusion breaks down when the eigenstates of @xmath0 are _ not _ the same as the eigenstates of the non - hermitian hamiltonian @xmath1 . in this case we say that the @xmath0-symmetry of @xmath1 is _ broken _ , and conversely we refer to the case where the spectrum is real as the _ unbroken _ case . it is important to note that the exact form of the operator @xmath0 is not important in our discussion . when examining the spectrum of a non - hermitian hamiltonian , provided there is some antilinear operator @xmath0 such that @xmath36 and eq . holds , then the spectrum is real or complex depending on whether or not the symmetry is broken . in this section we discuss a simple single spin hamiltonian as a toy example of our approach of relating @xmath0-symmetry to cumulants of time - integrated observables . consider a single - spin system with hamiltonian @xmath37 where @xmath38 denote the usual pauli spin operators . the operator of interest is the time - integrated magnetisation in a given direction in the @xmath39 plane , i.e. , as in eq . with @xmath40 following the prescription of sec . [ sec : form ] , the associated operator becomes @xmath41 this non - hermitian hamiltonian , discussed in a different context in ref . @xcite , has eigenvalues @xmath42 the @xmath0 operator in this case is defined as the composition of @xmath43 , and of @xmath25 , the operator indicating complex conjugation . consider first the case of the transverse magnetisation in the @xmath44 direction , i.e. , @xmath45 . in this case @xmath10 is invariant under the joint action of @xmath24 and @xmath25 . the eigenvalues simplify to @xmath46 provided @xmath47 , the eigenvalues are real and we are in the @xmath0 _ unbroken _ regime . in this case one can use eq . to show that the cumulants of the time - integrated magnetisation in the @xmath44 direction oscillate in time , and are therefore sublinear at long times , as indicated by the fact that @xmath48 . when the @xmath0-symmetry is _ broken _ @xcite , that is when @xmath49 , the eigenvalues form a complex conjugate pair , and the mgf takes the form @xmath50 the coefficients @xmath51 are determined by the overlaps of the initial state with the eigenstates of @xmath52 . in the long - time limit the mgf is dominated by the imaginary part of either @xmath53 or @xmath54 , the choice of which depends on the sign of @xmath16 . in fact a change of the sign of @xmath16 is equivalent to performing hermitian conjugation on @xmath52 . from eq . one can easily see in this regime the cgf will scale linearly with @xmath55 as @xmath56 , and @xmath22 will be finite . this behaviour is illustrated in fig . [ fig : fig1](a ) which shows both @xmath22 and @xmath57 as" +"the crab nebula pulsar ( b0531 + 21 ) intermittently produces single pulses having intensity orders of magnitude greater than those of the normal periodic emission @xcite . these giant pulses ( gps ) consist of complex superpositions of nanosecond- and microsecond - scale impulses @xcite and have been observed over many octaves of the radio spectrum @xcite . the details of the gp emission mechanism remain mysterious . because the intrinsic duration of crab gps is much less than the pulse broadening due to the host nebula and the interstellar medium ( ism ) along the line of sight , crab gps are also potentially of great value as a probe of the electron density of those regions . studies of crab gps are often limited to frequencies above 100 mhz where the emission is relatively strong and/or existing large radio telescopes are available ; see for example @xcite ; @xcite ; @xcite ; @xcite ; @xcite ; @xcite ; and @xcite . studies of crab gps below 100 mhz have historically been limited by the lack of suitable large telescopes and the difficulties imposed by strong and diverse radio frequency interference ( rfi ) at these frequencies . observations of crab gps have been reported at 40 and 60 mhz by @xcite and more recently at 23 mhz by @xcite . a search of 14 hours of data collected in a 2.5 mhz bandwidth around 38 mhz by the 10-dipole eight meter - wavelength transient array ( eta ) experiment revealed 11 gp candidates , but these proved difficult to confirm due to the low sensitivity ( @xmath2 for the strongest pulse candidate of @xmath3 kjy ) and difficulties with rfi @xcite . detection of crab gps by lofar in the frequency ranges 3280 mhz and 139187 mhz has been reported but further details are not provided @xcite . in this paper we report the detection and characterization of crab gps in the frequency range 2084 mhz by the recently - completed long wavelength array station 1 ( lwa1 ) radio telescope . lwa1 consists of a pseudorandom array of 256 dual - polarized broadband dipoles within a 110 m @xmath4 100 m elliptical footprint , m from the center of the array and are used for array calibration and power spectrum measurement . ] and is capable of nyquist - rate acquisition of beam outputs covering its entire tuning range of 10 - 88 mhz simultaneously . this facilitates high - signal - to - noise ratio detection of crab gps at a rate of several per hour ; also , the large instantaneous bandwidth provides the ability to study variations in flux density and pulse broadening with frequency on a pulse - by - pulse basis . the large bandwidth also facilitates improved methods for the recognition and mitigation of the effects of rfi . this paper is organized as follows : section [ sida ] describes lwa1 and the methods used for data collection , data reduction , identification of crab gps , pulse characterization , and flux density calibration . section [ sresults ] summarizes the findings of the study including statistics of pulse amplitude and pulse broadening . section [ sdisc ] includes a brief description of ongoing and planned follow - up work . lwa1 is collocated with the very large array ( vla ; @xmath5 w , @xmath6 n ) in central new mexico . the telescope consists of a primary array of 256 pairs of dipole - type antennas whose outputs are individually digitized and formed into beams . a detailed technical description of the instrument , including performance characterization , can be found in @xcite . lwa1 provides 4 independently - steerable dual - polarization beams . each beam provides two separate passbands with independently - selectable center frequencies . each passband consists of nyquist - rate time - domain output at sample rates up 19.6 million samples per second ( msps ) per passband with @xmath7 mhz usable bandwidth , in 4-bits real ( `` i '' ) plus 4-bits imaginary ( `` q '' ) format . the beam main lobe width varies with frequency and pointing direction , but ranges from about @xmath8 full width at half - maximum ( fwhm ) at @xmath9 mhz to about @xmath10 fwhm at @xmath11 mhz for observations of the crab pulsar within about 1 hour of upper culmination . the system equivalent flux density ( sefd ) varies as a function of frequency , pointing relative to zenith , and ( because the system temperature is strongly dominated by galactic noise ) pointing in celestial coordinates . sefd estimates for the flux density calibration specific to the present work are developed in section [ sfc ] ; however sefd is typically found to be in the range 617 kjy for high - elevation pointings over most of the frequency range . frequency range can be understood by noting that the collecting area of a dipole decreases as the square of frequency , whereas the galactic noise - dominated antenna temperature decreases with frequency at about the same rate . ] this corresponds to a @xmath12 sensitivity @xmath13 jy assuming both polarizations , 17 mhz bandwidth , and 25 ms integration . a description of lwa1 early science results ( including first pulsar observations ) can be found in @xcite . to date lwa1 has detected 13 known pulsars and has several on - going programs dedicated to survey , monitoring , and characterization of pulsars @xcite . data for the present work were collected in 10 1-hr observations in fall 2012 , each centered on the transit of the crab pulsar , as detailed in table [ tobs ] . in each observation , two beams were used together to track the pulsar ( i.e. , both beams pointing in precisely the same direction ) . the center frequencies of the passbands of the first beam were 76 mhz and 60 mhz , whereas the center frequencies for the second beam were 44 mhz and 28 mhz . since the usable bandwidth is @xmath14 mhz per passband , this scheme yields contiguous frequency coverage from 20 mhz to 84 mhz . the total volume of data collected in this fashion was @xmath15 tb ; relatively large since the data are recorded as raw voltage streams without channelization or other `` on the fly '' processing . this format provides the maximum flexibility for both initial processing and subsequent reprocessing of the data at later time using other search parameters or techniques . although the instrument is capable of tracking sources to very low elevation angles , we have restricted the observations to 1 hour each day around upper culmination in order to ( 1 ) limit the extent to which change in the beam characteristics over the track can manifest as variations in estimated flux density , ( 2 ) distribute the observations more evenly over the expected range of source conditions , and ( 3 ) reduce the tempo of data acquisition to a manageable pace . concerning ( 2 ) , a parameter of interest in the present work that is known to vary significantly over timescales of weeks to months is pulse broadening @xcite ; in fact , such variations can occur even on timescales of minutes @xcite . because this study involved the use of a new instrument and new data analysis procedures , we performed simultaneous observations of the bright pulsar b0329 + 54 using the remaining two beams , using the same synchronized - tracking four - passband scheme employed for crab gp observing . this allowed an independent check of the instrument and data reduction procedures using a well - known object , as well as providing an `` off pointing '' ( separated by @xmath16 h in right ascension ) for confirmation of crab gp detections as well as for identification of rfi through anticoincidence techniques . the data were analyzed using custom incoherent dedispersion software developed by one of us ( s.e . ) , designed specifically for rapid analysis of periodic and single - pulse emission of dispersed astrophysical signals in raw lwa1 beam data . the steps in data reduction for one passband of one beam were as follows : first , any samples having @xmath17 ( that is , the magnitude of the complex - valued sample equal to or greater than maximum encodable real or imaginary magnitude ) were assumed to be due to rfi and set to zero ; typically 0.1% to 1% of samples were zeroed in this process . next , data were partitioned into blocks of length @xmath18 ( center frequency - dependent ) and divided into channels using the fast fourier transform ( fft ) . values of @xmath18 and the associated time and frequency resolutions are shown in table [ tfft ] . these values were chosen to make the residual dispersion negligible relative to the width of the scatter - broadened pulse after incoherent dedispersion . the raw linear polarizations were incoherently combined at this point . time - frequency pixels associated with the outer 10% of frequency channels were discarded and the inner 90% were `` flattened '' ; that is , variations in frequency and time ( attributable to the instrument or to ionospheric effects ) within the time span of the spectrogram ( typically 1050 s ) were removed . finally , all pixels in frequency bands containing persistent rfi , or rfi which was intermittent but frequently observed , were discarded ; additional details about this procedure are given in section [ sigp ] . in addition to the amplitude variation , the ionosphere imparts both refraction and dispersion to received signals . for the purposes of the present work , these additional effects are negligible and may be safely ignored : the worst - case ionospheric refraction is on the order of arcminutes ( see e.g. @xcite ) and thus is a tiny fraction of the narrowest beam width in the present work . the worst - case ionospheric contribution to the total dispersive delay over 2084 mhz is @xmath19 ms @xcite , corresponding to an apparent error in dispersion measure ( dm ) @xmath20 pc @xmath21 . this is at least two orders of magnitude less than the error in assumed dm used for dedispersion , which is described below and shown to be insignificant . following rfi mitigation , the result was incoherently dedispersed assuming dm @xmath22 56.791 pc @xmath21 @xcite . although coherent dedispersion would be preferable from a sensitivity perspective , the residual dispersion after application of incoherent dedispersion at the time - frequency resolutions identified above is less than than the observed width of the scatter - broadened pulses by more than two orders of magnitude ; thus the penalty in the present work is negligible . in addition to having a large advantage in terms of computation burden , the frequency - domain interference mitigation procedure described below ( section [ sigp ] ) is easily implemented in the incoherent dedispersion framework , but much less straightforward to implement as part of a coherent dedispersion scheme . the dedispersed time series was averaged to obtain an integration time and effective time resolution of approximately 25 ms for the 76 mhz and 60 mhz passbands , and either 33 ms or 50 ms for the 44 mhz and 28 mhz passbands . note that there is no subsequent adjustment to the assumed dm of 56.791 pc @xmath21 in our processing . in particular , we did not perform a search over dm . as explained in section [ spb ] , refinement of the dm used for dedispersion proves to be unnecessary because the resulting bias in estimated pulse parameters turns out to be negligible . the products saved from this procedure were ( 1 ) the dedispersed and" +"neutron stars can be considered as resonators where various oscillation modes can be excited . these oscillations are attracting much attention because , in principle , they can be used to study the internal structure of neutron stars . some of them ( for instance , r - modes ) can be accompanied by gravitational radiation . because neutron stars are relativistic objects , their oscillations must be studied in the framework of general relativity . the relativistic theory of oscillations was developed in a series of papers by thorne and coauthors @xcite . in particular , the rapid ( @xmath6 s ) damping of p - modes with multipolarity @xmath7 by gravitational radiation was demonstrated by @xcite . an exact treatment of general - relativistic effects is complicated , but in many cases it is possible to use the relativistic cowling approximation @xcite . an analysis of various oscillation modes and mechanisms for their dissipation was carried out by @xcite . let us also note the review paper by @xcite , which contains an extensive bibliography . as a rule , one considers neutron star oscillations with low values of @xmath8 . although neutron stars are objects at the final stage of stellar evolution , they can be seismically active for many reasons . possible mechanisms for the generation of oscillations have been widely discussed in the literature ( see , e.g. , @xcite and references therein ) . recently , much attention has been paid to r - modes vortex oscillations that can be generated in rapidly rotating neutron stars and accompanied by powerful gravitational radiation . in addition , oscillations can be excited in neutron stars , for example , during x - ray bursts ( nuclear explosions in outermost layers of accreting neutron stars ) , bursting activity of magnetars ( anomalous x - ray pulsars and soft gamma - ray repeaters ; see , e.g. , @xcite ) , and glitches ( sudden changes of spin periods ) of ordinary pulsars . in this paper we focus of high - frequency ( @xmath2 khz ) pressure oscillations ( p - modes ) with high multipolarity @xmath9 localized in neutron star envelopes ( crusts ) . in our previous paper @xcite we have studied these oscillations for @xmath10 . in that case p - modes are localized in the outer envelope ( before the neutron drip point , at densities @xmath11 g @xmath12 ) , where the equation of state ( eos ) of stelar matter is relatively smooth . accordingly , the oscillation spectrum is simple and well established . in the present paper we extend our analysis to p - modes with lower @xmath8 . these oscillations penetrate into the inner envelope of the star , where the eos undergoes considerable softening due to neutronization and becomes more complicated ( essentially different for ground - state and accreted matter ) . we show that the neutron drip affects strongly the oscillation spectrum . if detected , this spectrum would give valuable information on the eos in neutron star envelopes and also on global parameters of neutron stars ( their masses and radii ) . following @xcite we study oscillations localized in a thin neutron star envelope . it is convenient to use the approximation of a plane - parallel layer , and write space - time metric in the envelope as @xmath13 where the local time @xmath14 and local depth @xmath15 are related to the schwarzschild time @xmath16 and circumferential radius @xmath17 by @xmath18 @xmath19 is the circumferential radius of the stellar surface , @xmath20 and @xmath21 are spherical angles , @xmath22 is the gravitation radius , and @xmath3 is the gravitational mass of the neutron star . the metric ( [ metric ] ) is locally flat and allows us to use the newtonian hydrodynamic equations for a thin envelope with the gravitational acceleration @xmath23 the pressure in the envelope is primarily determined by degenerate electrons and neutrons ( in the inner envelope ) , being almost independent of temperature @xmath24 . accordingly , we can use the same zero - temperature eos for the equilibrium structure of the envelope and for perturbations . employing this eos , we neglect the buoyancy forces and study p - modes . the linearized hydrodynamic equations ( for a non - rotating star ) can be rewritten as ( see , e.g. , the monograph by * ? ? ? * ) @xmath25 where @xmath26 is the velocity potential and @xmath27 is the squared sound speed . the velocity potential can be presented in the form @xmath28 where @xmath29 is an oscillation frequency , and @xmath30 is a spherical function ( see , e.g. , @xcite ) . an unknown function @xmath31 obeys the equation @xmath32 the boundary condition at the stellar surface is @xmath33 . it comes from the requirement of vanishing lagrange variation of the pressure at the surface . the formal condition @xmath34 in the stellar interior should be imposed to localize oscillations in the envelope . of course , the actual variable @xmath15 is finite and the real depth of oscillation localization will be controlled in calculations . the eos of matter in neutron star envelopes contains a sequence of first - order phase transitions associated with changes of nuclides with growing density . these phase transitions are relatively weak ( the density jumps do not exceed 20 per cent ) . we should add boundary conditions at all phase transitions within the envelope . these are two well known conditions at a plain boundary of two liquids @xcite . the first condition can be written as @xmath35 it ensures equal radial velocities at both sides of the boundary . the second condition is @xmath36 it comes from the requirement of pressure continuity at the boundary . note , that the boundary conditions ( [ bound1 ] ) and ( [ bound2 ] ) provide a source of buoyancy which leads to the density discontinuity of g - modes ( see , e.g. , * ? ? ? oscillations of a plane - parallel layer for a polytropic eos ( @xmath37 , @xmath38 being the polytropic index ) were studied analytically by @xcite . in this case , the squared sound speed is @xmath39 . the solution for eigenfrequencies is @xmath40 and eigenmodes are given by @xmath41 where @xmath42 is a generalized laguerre polynomial @xcite , and @xmath43 is the number of radial nodes . note , that the mode with @xmath44 does not have any radial nodes ; its properties are independent of the polytropic index @xmath38 . this mode corresponds to the vanishing lagrangian variation of the density ( incompressible motion ) . adding the condition @xmath45 to eq . ( [ phi ] ) , one can easily show that the mode with the frequency @xmath46 and the eigenfunction @xmath47 , defined by eq . ( [ fk ] ) , is the proper mode for a wide class of eoss . note , that the boundary conditions ( [ bound1 ] ) and ( [ bound2 ] ) are automatically satisfied for this mode , and it is continuous at phase transitions . the oscillation frequency redshifted for a distant observer is @xmath48 the frequency @xmath49 will be used to normalize eigenfrequencies of other p - modes . the number of radial nodes @xmath50 will be used to enumerate the modes . let us use the equation of hydrostatic equilibrium @xmath51 and transform eq . ( [ f ] ) taking the equilibrium pressure @xmath52 as an independent variable , @xmath53 the boundary conditions ( [ bound1 ] ) and ( [ bound2 ] ) can be written as @xmath54 therefore , eq . ( [ fp ] ) with the boundary conditions ( [ bound1 p ] ) , ( [ bound2 p ] ) and with regularity requirement can be treated as the equation for an eigennumber @xmath55 containing the scaling parameter @xmath56 ( with @xmath57 for @xmath58 ) . accordingly , the eigenfrequencies can be written as @xmath59 here , @xmath60 and @xmath61 are functions which can be calculated numerically . they are universal for all neutron stars with a given eos in the envelope . the velocity potentials @xmath62 are also universal functions of @xmath52 . therefore , p - mode oscillations in stellar envelopes are self - similar and can be easily rescaled to a neutron star with any radius and mass . in principle , this can be used to determine @xmath4 and @xmath3 ( see sec . [ subsec_eigenfrec ] ) . numerical results are presented for a `` canonical '' neutron star model , with the mass @xmath63 and the radius @xmath64 km . for this model , we have @xmath65 cm s@xmath66 , @xmath67^{1/4 } \,\mbox{s}^{-1}\ ] ] and ( for a distant observer ) @xmath68^{1/4}\mbox{~s}^{-1}.\ ] ] oscillation frequencies have been determined via a series of iterative trials , checking the coincidence of the mode number and the number of radial nodes . we employ two models of matter in neutron star envelopes , the accreted and ground - state matter . for the accreted matter , we use the eos of @xcite ( hz ) . it was derived by following transformations of atomic nuclei ( beta captures , emission and absorption of neutrons , pycnonuclear reactions ) in an accreted matter element with increasing the pressure . the eos was calculated for the densities from @xmath69 g @xmath12 to @xmath70 g @xmath12 . for lower densities , we have taken the matter composed of @xmath71 and the eos of degenerate electrons with electrostatic corrections . for higher densities , we use the eos of the ground - state matter presented by @xcite ( bps ) because , as remarked by @xcite , the hz eos becomes very similar to the bps eos at @xmath72 g @xmath12 . we have also considered envelopes composed of the ground - state ( cold catalyzed ) matter . in the outer envelope we use the eos of @xcite ( hp ) and the recent eos of @xcite ( rhs ) . for the inner envelope , we employ the eos of @xcite . phase transitions in these eoss have been treated carefully using the boundary conditions ( [ bound1 ] ) and ( [ bound2 ] ) at any phase transition . for comparison , we have also employed the model of the outer envelope composed of ground - state matter with a smoothed composition ( the smooth composition model scm ) . in the latter case we have included only a large density jump at the neutron drip boundary between the inner and outer envelopes . the squared sound speed @xmath73 as a function of depth @xmath15 for all these eoss is shown in fig . [ fig_cs2 ] . the solid line is for the accreted envelope ; the dashed , dotted and dash - and - dot lines are for the hp , rhs and scm eoss of the ground - state matter . the different versions of the ground - state eos show approximately the same sound speed profiles , but the profile in the accreted envelope is significantly different . the depth of the accreted envelope ( up to the density @xmath74 g @xmath12 , which is the largest density in the envelope , where the atomic nuclei are present , for the bps eos ) is @xmath75 m. for all models of the ground - state matter , the largest density in the envelope has been taken @xmath76 g @xmath12 ; the envelope depth is @xmath77 m. figures [ fig_omegaccreted ] and [ fig_omegground ] show squares of dimensionless eigenfrequencies @xmath78 versus multipolarity @xmath8 for accreted and ground - state envelopes of the canonical neutron star . because of the scaling ( [ scaling ] ) the figures can be easily transformed to a" +"the standard paradigm is that active regions form when a coherent flux tube from deep in the convection zone reaches the surface , typically modeled using the thin flux tube approximation @xcite . @xcite have shown how important the actual convective motions are to the rise of magnetic flux . recent simulations of active region formation have started from a coherent semi - torus of magnetic field placed in the surface layers of a model solar convection zone @xcite . our simulations show that such a coherent structure is not necessary for the formation of an active region . the action of magneto - convection itself produces rising flux tubes , which when they reach the surface can produce an active region . we use the stagger code @xcite to simulate magneto - convection in a domain 48 mm wide by 20 mm deep . this depth is 10% of the geometric depth of the solar convection zone , but contains two thirds of its pressure scale heights . horizontal directions are periodic and the vertical boundaries are open with plasma and magnetic field moving through them . because of the large domain dimensions the coriolis force from the solar rotation begins to have some effect , so we include f - plane rotation at a lattitude 30 deg north . the initial state was a snapshot of hydrodyanamic convection which had been relaxed for several turnover times ( about 2 days at 20 mm depth ) . we then started advecting minimally structured , uniform , untwisted , horizontal magnetic field into the domain by inflows at the bottom . the initial field strength was 200 g ( weak enough to have little dynamic effect ) , which was slowly increased with a 5 hour e - folding time until it reached 1 kg strength and thereafter held constant . the incoming field is at 30 deg to the east - west axis . the active region is not affected by the horizontal boundaries : first , because its size is 25 mm inside a 48 mm wide box , second , because it is spreading very slowly with time and , third , because the top boundary is close by ( at the temperature minimum ) so the magnetic field does not have room to spread out much in the atmosphere and interact with the mirror active regions produced by the horizontal periodicity . 1.7 kg , but the actual range is @xmath0 3 kg . the x - axis is the east - west axis . the field entered in the upflows at the bottom at an angle 30@xmath1 to the x - axis . the ar approximately maintains this orientation . the separation of the pores is approximately the size of the supergranule scale convective cells near the bottom of the domain . , title=""fig:"",scaledwidth=25.0% ] 1.7 kg , but the actual range is @xmath0 3 kg . the x - axis is the east - west axis . the field entered in the upflows at the bottom at an angle 30@xmath1 to the x - axis . the ar approximately maintains this orientation . the separation of the pores is approximately the size of the supergranule scale convective cells near the bottom of the domain . , title=""fig:"",scaledwidth=25.0% ] 1.7 kg , but the actual range is @xmath0 3 kg . the x - axis is the east - west axis . the field entered in the upflows at the bottom at an angle 30@xmath1 to the x - axis . the ar approximately maintains this orientation . the separation of the pores is approximately the size of the supergranule scale convective cells near the bottom of the domain . , title=""fig:"",scaledwidth=25.0% ] 1.7 kg , but the actual range is @xmath0 3 kg . the x - axis is the east - west axis . the field entered in the upflows at the bottom at an angle 30@xmath1 to the x - axis . the ar approximately maintains this orientation . the separation of the pores is approximately the size of the supergranule scale convective cells near the bottom of the domain . , title=""fig:"",scaledwidth=25.0% ] as the magnetic field enters the computational domain , convective upflows immeadiately begin to drag portions toward the surface , while convective downflows immeadiately pull other portions down , thus creating magnetic loops . magnetic field begins to reach the surface after about 20 hours . smaller scale convective patterns nearer the surface produce smaller scale crenulations in the magnetic loops , giving them a serpentine structure with small loops riding piggy - back "" on larger ones . the field first emerges as small bipoles with mixed polarity over a confined region of 25 mm square . at about 40 hours , a large flux bundle begins to emerge with rate of 2 - 4@xmath210@xmath3 mx / hr ( figure [ fig : arform1 ] ) . the area of major flux emergence is confined by the convective up- and down - flows and does not fill the entire domain . flux emergence in the remainder of the domain is much smaller . the field first emerges horizontally over granules and then vertical field appears in the intergranule lanes at the ends of the horizontal field . the vertical legs of the bipoles quickly separate . initially , granules become elongated transverse to the magnetic field . in later emergence events the granules are elongated parallel to the horizontal field ( figures [ fig : arform2 ] and [ fig : arform3 ] ) . opposite polarity field migrates to unipolar clusters , sometimes colliding and cancelling in the process ( figure [ fig : arform1 ] ) . the horizontal components of the emerging field pass through the upper boundary , leaving behind their nearly vertical legs . individual flux concentrations collect . the leading spot is more compact and rotating and the follow spots more diffuse and non - rotating ( figure [ fig : arform1 ] ) . the unsigned vertical flux in the active region is a little more than @xmath4 mx and a similar amount is in the remainder of the domain . this active region has not formed penumbra . as found by @xcite and upper boundary condition forcing a more horizontal field at the surface is needed to form penumbra . the emerging flux and active region here covers a region of supergranule scale , similar to the sizes of the convective cells at the bottom of the simulation domain . the orientation of the active region is approximately the 30 deg orientation of inflow field at the bottom . the magnetic field lines that emerge are an undulation on a larger , subsurface magnetic structure spanning most of the domain . eventually , the rate of new flux emergence slows and the space between the spots has little horizontal field ( figure [ fig : arform3 ] ) . . the actual range is [ 0.2,2.5 ] . in the initial emergence the granules are elongated transverse to the honrizontal field . thereafter the granules appear elongated along the magnetic field direction . , title=""fig:"",scaledwidth=25.0% ] . the actual range is [ 0.2,2.5 ] . in the initial emergence the granules are elongated transverse to the honrizontal field . thereafter the granules appear elongated along the magnetic field direction . , title=""fig:"",scaledwidth=25.0% ] . the actual range is [ 0.2,2.5 ] . in the initial emergence the granules are elongated transverse to the honrizontal field . thereafter the granules appear elongated along the magnetic field direction . , title=""fig:"",scaledwidth=25.0% ] . the actual range is [ 0.2,2.5 ] . in the initial emergence the granules are elongated transverse to the honrizontal field . thereafter the granules appear elongated along the magnetic field direction . , title=""fig:"",scaledwidth=25.0% ] these simulations show that magneto - convection itself can produce the flux tubes that give rise to active regions . the action of up and downflows on an initial supergranule size patch of horizontal field can keep the major portion of the magnetic flux confined to emerge at the surface in a similar supergranule size region . interesting work for the future will be to investigate the evolution of larger scale magnetic structures , such as those in the flux emergence simulations of @xcite and @xcite , as they pass through the upper convection zone . the calculations were performed on the pleiades cluster of the nasa advanced supercomputing division . rfs is supported by nasa grants nnx12ah49 g and nnx08ah44 g and nsf grant ags-1141921 . this support is greatly appreciated ." +"in the minimal supersymmetric standard model ( mssm ) , the ( susy ) particles must be produced in pairs . the phase space is largely suppressed in pair production of susy particles due to the important masses of the superpartners . the r - parity violating ( ) extension of the mssm contains the following additional terms in the superpotential , which are trilinear in the quarks and leptons superfields , @xmath7 where @xmath8 are flavour indices . these couplings offer the opportunity to produce the scalar particles as resonances @xcite . although the coupling constants are severely constrained by the low - energy experimental bounds @xcite , the resonant superpartner production reaches high cross sections both at leptonic @xcite and hadronic @xcite colliders . the resonant production of susy particle has another interest : since its cross section is proportional to a power @xmath9 of the relevant coupling , this reaction would allow an easier determination of the couplings than the pair production provided the coupling is large enough . as a matter of fact in the pair production study , the sensitivity on the couplings is mainly provided by the displaced vertex analysis of the lightest supersymmetric particle ( lsp ) decay which is difficult experimentally , especially at hadronic colliders . neither the grand unified theories ( gut ) , the string theories nor the study of the discrete gauge symmetries give a strong theoretical argument in favor of the r - parity violating or r - parity conserving scenarios @xcite . hence , the resonant production of susy particle through couplings is an attractive possibility which must be considered in the phenomenology of supersymmetry . the hadronic colliders have an advantage in detecting new particles resonance . indeed , due to the wide energy distribution of the colliding partons , the resonance can be probed in a wide range of the new particle mass . this is in contrast with the leptonic colliders for which the center of mass energy must be fine - tuned in order to discover new narrow width resonances . at hadronic colliders , either a slepton or a squark can be produced at the resonance respectively through a @xmath10 or a @xmath11 coupling constant . in the hypothesis of a single dominant coupling constant , the resonant scalar particle can decay through the same coupling as in the production , leading to a two quark final state for the hard process @xcite . in the case where both @xmath10 and @xmath12 couplings are non - vanishing , the slepton produced via @xmath10 can decay through @xmath12 giving rise to the same final state as in drell - yan process , namely two leptons @xcite . however , for reasonable values of the coupling constants , the decays of the resonant scalar particle via gauge interactions are typically dominant if kinematically allowed @xcite . + the main decay of the resonant scalar particle through gauge interactions is the decay into its partner plus a gaugino . indeed , in the case where the resonant scalar particle is a squark , it is produced through @xmath11 interactions so that it must be a right squark @xmath13 and thus it can not decay into the @xmath14-boson , which is the only other possible decay channel via gauge interactions . besides , in the case where the resonant scalar particle is a slepton , it is a left slepton produced via a @xmath10 coupling but it can not generally decay as @xmath15 or as @xmath16 . the reason is that in most of the susy models , as for example the supergravity or the gauge mediated models , the mass difference between the left charged slepton and the left sneutrino is due to the d - terms so that it is fixed by the relation @xmath17 @xcite and thus it does not exceed the @xmath14-boson mass . nevertheless , we note that in the large @xmath18 scenario , a resonant scalar particle of the third generation can generally decay into the @xmath14-boson due to the large mixing in the third family sfermion sector . for instance , in the sugra model with a large @xmath18 a tau - sneutrino produced at the resonance can decay as @xmath19 , @xmath20 being the lightest stau . + the resonant scalar particle production at hadronic colliders leads thus mainly to the single gaugino production , in case where the decay of the relevant scalar particle into gaugino is kinematically allowed . in this paper , we study the single gaugino productions at tevatron run ii . the single gaugino productions at hadronic colliders were first studied in @xcite . later , studies on the single neutralino @xcite and single chargino @xcite productions at tevatron have been performed . the single neutralino @xcite and single chargino @xcite productions have also been considered in the context of physics at lhc . in the present article , we also study the single superpartner productions at tevatron run ii which occur via @xmath0 processes and do not receive contributions from resonant susy particle productions . the singly produced superpartner initiates a cascade decay ended typically by the decay of the lsp . in case of a single dominant @xmath11 coupling constant , the lsp decays into quarks so that this cascade decay leads to multijet final states having a large qcd background @xcite . nevertheless , if some leptonic decays , as for instance @xmath21 , @xmath22 being the chargino and @xmath23 the neutralino , enter the chain reaction , clearer leptonic signatures can be investigated @xcite . in contrast , in the hypothesis of a single dominant @xmath10 coupling constant , the lsp decay into charged leptons naturally favors leptonic signatures @xcite . we will thus study the single superpartner production reaction at tevatron run ii within the scenario of a single dominant @xmath2 coupling constant . in section [ theoretical ] , we define our theoretical framework . in section [ discussion ] , we present the values of the cross sections for the various single superpartner productions via @xmath2 at tevatron run ii and we discuss the interesting multileptonic signatures that these processes can generate . in section [ analysis1 ] , we analyse the three lepton signature induced by the single chargino production . in section [ analysis2 ] , we study the like sign dilepton final state generated by the single neutralino and chargino productions . our framework throughout this paper will be the so - called minimal model ( msugra ) which assumes the existence of a grand unified gauge theory and family universal boundary conditions on the supersymmetry breaking parameters . we choose the 5 following parameters : @xmath24 the universal scalars mass at the unification scale @xmath25 , @xmath26 the universal gauginos mass at @xmath25 , @xmath27 the trilinear yukawa coupling at @xmath25 , @xmath28 the sign of the @xmath29 parameter ( @xmath30 , @xmath31 denoting the running scale ) and @xmath32 where @xmath33 and @xmath34 denote the vacuum expectation values of the higgs fields . in this model , the higgsino mixing parameter @xmath35 is determined by the radiative electroweak symmetry breaking condition . note also that the parameters @xmath26 and @xmath36 ( @xmath37 wino mass ) are related by the solution of the one loop renormalization group equations @xmath38 with @xmath39 , where @xmath40 are the beta functions , @xmath41 is the at @xmath25 and @xmath42 $ ] , @xmath43 $ ] corresponding to the gauge group factors @xmath44 . we shall set the unification scale at @xmath45 and the running scale at the @xmath46-boson mass : @xmath47 . we also assume the infrared fixed point hypothesis for the top quark yukawa coupling @xcite that provides a natural explanation of a large top quark mass @xmath48 . in the infrared fixed point approach , @xmath18 is fixed up to the ambiguity associated with large or low @xmath18 solutions . the low solution of @xmath18 is fixed by the equation @xmath49 , where @xmath50 for @xmath51 . for instance , with a top quark mass of @xmath52 @xcite , the low solution is given by @xmath53 . the second important effect of the infrared fixed point hypothesis is that the dependence of the electroweak symmetry breaking constraint on the @xmath54 parameter becomes weak so that @xmath35 is a known function of the @xmath24 , @xmath26 and @xmath18 parameters @xcite . finally , we consider the extension of the msugra model characterised by a single dominant coupling constant of type @xmath2 . at hadronic colliders , either a sneutrino ( @xmath55 ) or a charged slepton ( @xmath56 ) can be produced at the resonance via the @xmath2 coupling . as explained in section [ intro ] , for most of the susy models , the slepton produced at the resonance has two possible gauge decays , namely a decay into either a chargino or a neutralino . therefore , in the scenario of a single dominant @xmath2 coupling and for most of the susy models , either a chargino or a neutralino is singly produced together with either a charged lepton or a neutrino , through the resonant superpartner production at hadronic colliders . there are thus four main possible types of single superpartner production reaction involving @xmath2 at hadronic colliders which receive a contribution from resonant susy particle production . the diagrams associated to these four reactions are drawn in fig.[graphes ] . as can be seen in this figure , these single superpartner productions receive also some contributions from both the @xmath57 and @xmath58 channels . note that all the single superpartner production processes drawn in fig.[graphes ] have charge conjugated processes . we have calculated the amplitudes of the processes shown in fig.[graphes ] and the results are given in appendix [ formulas ] . in this section , we discuss the dependence of the single gaugino production cross sections on the various parameters . we will not assume here the radiative electroweak symmetry breaking condition in order to study the variations of the cross sections with the higgsino mixing parameter @xmath59 . first , we study the cross section of the single chargino production @xmath60 which occurs through the @xmath2 coupling ( see fig.[graphes](a ) ) . the differences between the @xmath61 , @xmath62 and @xmath63 production ( occuring respectively through the @xmath64 , @xmath65 and @xmath66 couplings with identical @xmath67 and @xmath68 indices ) cross sections involve @xmath69 lepton mass terms ( see appendix [ formulas ] ) and are thus negligible . the @xmath60 reaction receives contributions from the @xmath70 channel sneutrino exchange and the @xmath57 and @xmath58 channels squark exchanges as shown in fig.[graphes ] . however , the @xmath57 and @xmath58 channels represent small contributions to the whole single chargino production cross section when the sneutrino exchanged in the @xmath70 channel is real , namely for @xmath71 . the @xmath57 and @xmath58 channels cross sections will be relevant only when the produced sneutrino is virtual since the @xmath70 channel contribution is small . in this situation the single chargino production rate is greatly reduced compared to the case where the exchanged sneutrino is produced as a resonance . hence , the @xmath57 and @xmath58 channels do not represent important contributions to the @xmath72 production rate . the dependence of the @xmath72 production rate on the @xmath54 coupling is weak . indeed , the rate depends on the @xmath54 parameter only through the masses of the third generation squarks eventually exchanged in the @xmath57 and @xmath58 channels ( see fig.[graphes ] ) . similarly , the dependences on the @xmath54 coupling of the rates of the other single gaugino productions shown in fig.[graphes ] are weak . therefore , in this article we present the results for @xmath73 . later , we will discuss the effects of large @xmath54 couplings on the cascade decays which are similar to the effects of large @xmath18 values ." +"in contemporary neural computing , an active branch of research is the nature - inspired algorithms with diverse applications in engineering optimization . most of these algorithms are based on the so - called swarm intelligence , and usually involve some form of non - deterministic , stochastic components , which often appear in terms of random walks . such random walks can be surprisingly efficient when combined with deterministic components and elitism , as this has been demonstrated in many modern metaheuristic algorithms such as particle swarm optimization , firefly algorithm and other algorithms @xcite . recent studies in nature - inspired algorithms have shown promising results with divers algorithms , including new algorithms such as accelerated particle swarm optimization @xcite , bat algorithm @xcite , krill herd algorithm @xcite , flower algorithm @xcite , and other algorithms @xcite . a comprehensive review can be found in @xcite . in all these algorithms , different degrees of randomization , exploration and exploitation have been used so as to maintain a good degree of solution diversity in the solution population , which helps to enhance the performance of these algorithms . applications of modern nature - inspired algorithms have been very diverse with promising results @xcite . in order to gain insight into the working mechanism of a stochastic algorithm , mathematical analysis of the key characteristics of random walks is necessary . though there are some extensive studies of random walks with solid results in the statistical literature , most of these results are based on rigorous assumptions so as to obtain theoretical results using markov chain models and/or markov chain monte carlo methods @xcite . consequently , such results may be too theoretical , and thus have not much practical implications for designing optimization algorithms . in addition , it is necessary to translate any relevant theoretical results in the right context so that they are truly useful to the optimization communities . the current work has extended our earlier work extensively @xcite . therefore , the aims of this paper are two - folds : to introduce the random walks and lvy flights in the proper context of metaheuristic optimization , and to use these results in the framework of markov theory to analyze the iteration process of algorithms such as step sizes , efficiency and the choice of some key parameters . the rest of the paper is organized as follows : section 2 briefly introduce the eagle strategy ( es ) . section 3 introduces the fundamentals of random walks and discusses lvy flights , as well as their links to optimization via markov chain theories . section 4 analyzes the choice of step sizes , stopping criteria and efficiency . section 5 presents four case studies for engineering optimization applications . finally , we briefly draw the conclusions in section 6 . eagle strategy developed by xin - she yang and suash deb @xcite is a two - stage method for optimization . it uses a combination of crude global search and intensive local search employing different algorithms to suit different purposes . in essence , the strategy first explores the search space globally using a lvy flight random walk ; if it finds a promising solution , then an intensive local search is carried out by using a more efficient local optimizer such as hill - climbing and downhill simplex method . then , the two - stage process starts again with new global exploration followed by a local search in a new region . the main steps of this method can be represented as the pseudo code as outlined in fig . [ eagle - fig-50 ] . the advantage of such a combination is to use a balanced tradeoff between global search which is often slow and a fast local search . some tradeoff and balance are important . another advantage of this method is that we can use any algorithms we like at different stages of the search or even at different stages of iterations . this makes it easy to combine the advantages of various algorithms so as to produce better results . it is worth pointing out that this is a methodology or strategy , not an algorithm . in fact , we can use different algorithms at different stages and at different time of the iterations . the algorithm used for the global exploration should have enough randomness so as to explore the search space diversely and effectively . this process is typically slow initially , and should speed up as the system converges , or no better solutions can be found after a certain number of iterations . on the other hand , the algorithm used for the intensive local exploitation should be an efficient local optimizer . the idea is to reach the local optimality as quickly as possible , with the minimal number of function evaluations . this stage should be fast and efficient . ' '' '' objective function @xmath0 + initialization and random initial guess @xmath1 + * while * ( stop criterion ) + global exploration by randomization ( e.g. lvy flights ) + evaluate the objectives and find a promising solution + intensive local search via an efficient local optimizer + ( a better solution is found ) + update the current best + + update @xmath2 + * end * + ' '' '' for the local optimizer in this paper , we will use the accelerated particle swarm optimization ( apso ) @xcite which is a simple but efficient variant of particle swarm optimization . the apso essentially has one updating equation _ i^t+1 = ( 1- ) _ i^t + * g*^ * + _ t , where @xmath3 is the current best solution among all the solutions @xmath4 at iteration @xmath5 . @xmath6 is a parameter , and @xmath7 is the scaling factor . here @xmath8 is a random number drawn from a standard normal distribution @xmath9 . as the typical scale @xmath10 of a problem may vary , @xmath11 should be linked to @xmath10 as @xmath12 where @xmath13 should decrease as the iterations proceed in the following form _ t = _ 0 ^t , where @xmath14 and @xmath15 . from our previous parametric study , we will use @xmath16 , @xmath17 , and @xmath18 @xcite . in almost all nature - inspired algorithms , two conflicting and yet important components are exploration and exploitation , or diversification and intensification . the balance between these components are very important to ensure the good performance of an algorithm @xcite . in other words , a good degree of diversity should be maintained in the population of the solutions so that exploration and exploitation can be reflected in the evolving population . if the population is too diverse , it is good for global exploration , but it may slow down the convergence . on the other hand , if the diversity is too low , intensive local exploitation may lead to premature convergence , and thus may loose the opportunity of finding the global optimality . however , how to maintain good balance is still an unsolved problem , and different algorithms may have different ways of dealing with this issue . in most algorithms such as the particle swarm optimization , exploration and diversity can be considered as the steps by using random numbers , while intensification and exploitation are by the use of current global best . however , there is no direct control on how to switch between these components . even in the accelerated particle swarm optimization ( aspo ) , diversity is mainly controlled by a random - walk - like term , while the control is indirectly carried out by an annealing - like reduction of randomness . on the other hand , eagle strategy provides a direct control of these two stages / steps in an iterative manner . first , solutions are sampled in a larger search space , and these solutions often have high diversity . these solutions are then fed into the apso for evolution so that a converged state can be reached , and at the converged state , solution diversity is low . then , a new set of samples are drawn again from the larger search space for another round of intensive apso iteration stage . in this way , both exploration and exploitation have been used to main a good degree of diversity in the overall population , which also allows the system to converge periodically towards global optimality . as we will see in the late analysis of random walks and search strategies , randomization techniques are often used for exploration to increase the diversity of the solutions , while the selection of good solutions and evolution of an algorithm tend to lead to convergence of the system . however , their role is subtle . for example , in memetic algorithms , the balance is even more subtle @xcite . it can be expected that the analysis in the rest of the paper can provide some insight into the working mechanisms and subtlety of random walks and randomization techniques in maintaining the good diversity of solutions in different algorithms . in modern stochastic optimization algorithms , especially those based on swarm intelligence , there are often a deterministic component and a stochastic component , though traditional algorithms such as the steepest descent method are purely deterministic . randomness is now an essential part of the stochastic search algorithms . randomization techniques such as random walks have become an integrated part of a search process in stochastic algorithms . however , how to achieve the effective randomization remains an open question . the exact form of randomization may depend on the actual algorithm of interest . one of the objective of this paper is to analyze and discuss the main concepts of random walks and lvy flights , and their role in metaheuristic optimization . in essence , a stochastic search process involves the use of a random process to generate new solutions in the search space so that the solutions can sample the landscape appropriately . however , the effectiveness of this sampling process depends on the random process used and the actual way of generating new solutions / samples . if the search space is treated as a black box ( thus no knowledge or assumption about the modality is made ) , a random walk is one of the most simplest ways to carry out the search for optimality . briefly speaking , a random walk is a random process which consists of taking a series of consecutive random steps @xcite . that is , the total moves @xmath19 after @xmath20 steps are the sum of each consecutive random step @xmath21 : s_n=_i=1^n x_i = x_1 + ... + x_n = _ i=1^n-1 x_i + x_n = s_n-1 + x_n , where @xmath22 is a random step drawn from a random distribution such as a normal distribution . depending on the perspective , the above relationship can also be considered as a recursive formula . that is , the next state @xmath19 will only depend on the current existing state @xmath23 and the move or transition @xmath24 from the existing state to the next state . in other words , the next state will depend only on the current state and the transition probability , and it has no direct link to the states in the past . from the markov theory , we know that this is typically the main property of a markov chain , to be introduced later . it is worth pointing out that there is no specific restriction on the step sizes . in fact , the step size or length in a random walk can be fixed or varying . random walks have many applications in physics , economics , statistics ," +"cosmic shear shows great promise for testing the cosmological model and measuring cosmological parameters . it measures the gravitational bending ( lensing ) of light by all the intervening mass in the universe . in cosmic shear , distant ( background ) galaxies provide a convenient screen of objects with potentially simple statistical properties , from which the light bending can be inferred . the distortion depends on the lens geometry and thus on the curvature and expansion history of the universe ; it also depends on the distribution of matter , which itself depends on most aspects of the cosmological model . cosmic shear was first detected in 2000 @xcite and has been used to constrain cosmological parameters in subsequent surveys ( recently * ? ? ? cosmic shear has the potential to become the most powerful probe of cosmology because it observes a non - gaussian three dimensional field in the local universe , where the mysterious dark energy dominates . however a number of details inevitably remain to be investigated further whilst planning for future experiments . the simplest statistic is the two point angular correlation function ( or integrals of this quantity such as the power spectrum or aperture mass , * ? ? ? if the background galaxies can be separated into populations at different redshifts the power of this statistic is greatly increased by cross - correlating galaxies in different redshift bins @xcite . this technique will dominate for future surveys which aim to measure the equation of state of the dark energy , or determine a new gravitational theory . cosmic shear is particularly simple if distant background galaxies can be assumed to have random orientations . the distortion by gravitational lensing can then be extracted statistically , for example by averaging over galaxy orientations in a given patch of sky . unfortunately it is unlikely to be straightforward since when galaxies form they tend to align pointing towards dark matter concentrations due to tidal interactions . this leads to two complicating effects : ( i ) neighbouring galaxies at a given redshift are intrinsically aligned @xcite and ( ii ) a pair of galaxies at two different redshifts have correlated observed ellipticities because a dark matter concentration close to the nearer object may tidally align the nearer object _ and _ simultaneously gravitationally lens the more distant object @xcite . these intrinsic alignment effects are complicated because they require an understanding of tidal alignments of galaxies , however they do have a distinctive signature and can therefore be removed without requiring a detailed understanding of galaxy formation @xcite . in this paper we present another complicating effect which is much simpler than the intrinsic alignment effects : cross - correlation of a pair of galaxies at different redshifts produces a contribution to the usual cosmic shear two - point statistic even if there are no tidal effects . this is because the nearer galaxy will gravitationally lens the more distant galaxy ( galaxy - galaxy lensing ) . this effect produces a net anti - correlation in the realistic case when the nearer galaxy ( i ) is not circularly symmetric and ( ii ) has a correlation between the asymmetry of the light and the mass . in this paper we present this new factor and quantify its effect for elliptical dark matter halos for which mass and light have the same ellipticity and orientation . first we review ellipticity and shear correlation function notation . we then illustrate the galaxy - galaxy lensing contribution to the ellipticity correlation function and calculate the effect due to a population of galaxy lenses at a fixed redshift . we investigate how this effect depends on the source and lens redshift . finally we compare this to the size of the tomographic cosmic shear cross - correlation signal . the two - point correlation function of the shear field @xmath2 at positions separated by an angle @xmath3 on the sky is given by @xmath4 , averaging over all pairs of angular separation @xmath3 ( we use complex notation for shears @xmath5 and similarly for ellipticities . ) for a concise introduction to cosmic shear see @xcite ; see also @xcite and @xcite . cosmic shear aims to measure this correlation function by measuring observed ellipticities of distant galaxies @xmath6 and taking into account how intrinsic ( pre - shear ) ellipticities @xmath7 are modified by shear . for small shears this reduces to @xmath8 ; we define @xmath9 throughout . an estimate of the shear two point correlation function is obtained from the observed ellipticity correlation function @xmath10 where @xmath11 is the observed ellipticity of a distant galaxy @xmath12 and @xmath13 is that of a nearer galaxy @xmath14 . therefore we can expand the correlation functions to find @xmath15 , where the shear - ellipticity correlation is given by @xmath16 if we ignore intrinsic alignments ( @xmath17 ) and use @xmath18 . @xcite calculated the shear - ellipticity correlation function numerically using n - body simulations . the aim of that work was to quantify the intrinsic alignment - shear correlation presented by @xcite . their results should in fact contain a mixture of the intrinsic alignment - shear correlation and the galaxy - galaxy lensing signal we present here . however , they do not discuss the distinction between the two effects , or specifically state that the galaxy - galaxy lensing contribution might be significant . here we present simple analytical and numerically integrated results to quantify only the galaxy - galaxy lensing contribution . we assume a concordance @xmath19cdm cosmology throughout , with parameters taken from @xcite : hubble constant @xmath20 km s@xmath21 mpc@xmath21 , @xmath22 , @xmath23 , @xmath24 , @xmath25 , dark energy equation of state @xmath26 except where otherwise stated . we assume a flat universe with a scale invariant primordial power spectrum . in this section we calculate the galaxy - galaxy lensing contribution to @xmath27 , given by @xmath28 , as discussed above . to estimate this quantity we first calculate the signal for a single elliptical lens averaged over background galaxies at a fixed angular distance , and then average over a population of lenses . we assume that the lens light has the same ellipticity and orientation as the lens mass . by default we consider an nfw @xcite mass profile , calculating the projected mass from the equations given in @xcite and @xcite . we use @xmath29 , the mass enclosed within the radius at which the density is 200 times the mean density of the universe , for consistency with simulations . we derive the concentration parameter , @xmath30 , as a function of @xmath29 using eq . 12 of @xcite with @xmath31 , as appropriate for an nfw model . we calculate the shear for an elliptical mass distribution using the equations in @xcite and @xcite . note that this is not the same as calculations using elliptical potentials , which give dumbbell shaped mass distributions ( e.g. , * ? ? ? . the projected mass distribution is squashed and stretched to have elliptical isodensity contours a factor @xmath32 smaller ( larger ) along the minor ( major ) axes , as compared to the corresponding spherical mass distribution . the shear map for an elliptical nfw lens of ellipticity @xmath33 aligned along the @xmath34 axis is shown in fig . [ fig : map ] . the shading and contours show the convergence map ( projected mass density in units of the critical lens density ) . the overlaid shear sticks show two particularly interesting features : ( i ) the shear on the major axis of the lens is larger than that on the minor axis , for a given angular separation from the lens center ; ( ii ) the shear 45 degrees around from the major axis is approximately tangential to the center of the lens . these two features do depend on the details of the mass profile , but are general for relevant radii for an elliptical nfw profile , and also for a singular isothermal ellipsoid ( sie ) ( for which the shear is always exactly tangential and its amplitude follows the mass , see * ? ? ? * ; * ? ? ? these two characteristics point towards our main result : that there is a net anti - correlation between lens ellipticity and the resulting shear of background galaxies . this arises because ( i ) the shears on the major and minor axes cancel out , but only partially , leaving a shear which is perpendicular to the major axis of the lens ; ( ii ) the shear sticks in - between the major and minor axes do not remove this anti - correlation ( for example this could have happened had the shear sticks been aligned along iso - density contours ) . this is quantified in detail in fig . [ fig : map_angle ] , which shows the shear - ellipticity correlation for a lens at @xmath35 with a background source at @xmath36 , but as a function of @xmath3 around the lens center ( consider moving around a concentric circular annulus in fig . [ fig : map ] ) . the integral under this curve shows the net effect of averaging over galaxies . the shape of the curve is non - trivial , but on average is below zero , as shown by the dashed lines . the larger amplitude oscillation is for the elliptical nfw shown in fig . [ fig : map ] , and the smaller oscillation is for an sie with the same @xmath29 . they both show the same qualitative effect at the radius used for the figure ( 0.1 arcmin ) . at larger radii , for the sie , the average shear - ellipticity correlation remains a similar fraction of the maximum due to the scale independence of the sie . for the nfw profile , the average becomes a smaller fraction of the maximum due to the steepening of the nfw profile with radius . the middle dashed line in fig . [ fig : cf cosmic shear ] shows this average quantity as a function of angular separation for a single lens of mass @xmath37 and ellipticity @xmath38 . the other dashed lines show how the effect depends on lens mass . so far we have shown that for a single foreground lens there is an anti - correlation between shear and lens ellipticity . we now compare the cosmic shear tomographic cross correlation ( @xmath39 ) with the average of @xmath28 over all foreground lenses . qualitatively : the shear - ellipticity correlation for a single lens is a scalar quantity , and therefore is independent of the angle of the coordinate system . as a result , on averaging over many isolated lenses at different angles to each other , the anti - correlation will be preserved : we average many negative numbers ( @xmath40 for each lens ) together and still obtain a negative number . this assumes that the foreground lenses are isolated from each other , and that there is no additional lensing from structures the foreground lenses are aligned with ( i.e. ignores the intrinsic alignment shear correlation ) . we now quantify the effect of averaging over many isolated lenses at a given redshift . first we assume all lenses have the same mass and consider just the variety of ellipticities . we average over a population of lens ellipticities , drawing each ellipticity component from a gaussian of width 0.16 , and calculating the absolute ellipticity . we find that the shear - ellipticity correlation scales roughly as the square of the lens ellipticity . this implies that the mean shear scales with lens ellipticity . the shear - ellipticity correlation function , after" +"trapping and controlling small numbers of neutral atoms has , in recent years , emerged as one of the most active and productive areas in physics research @xcite . such systems allow to perform experiments to answer fundamental questions in quantum mechanics @xcite and hold great potential for use in quantum information processing @xcite . advances in the technology of optical lattices and micro - traps have allowed for substantial progress in this area @xcite and various concepts have been developed to prepare and process the states of single atoms . while techniques for controlling and preparing the internal states of atoms using appropriate electromagnetic fields are well developed , only a few concepts exist for achieving the same control over the spatial part of a wavefunction @xcite . such control would complement currently existing techniques and allow for the complete engineering of a particle s quantum state . one area where control over the spatial part of the wavefunction is important is the challenge of devising techniques for controlled movement of atoms between different regions in space . in optical lattices this corresponds to moving between discrete lattice sites and in waveguide settings this would allow transfer from one guide to another . direct tunneling is a coherent process that can achieve this , however rabi - type oscillations make it experimentally very hard to reach high fidelities @xcite . recently it was pointed out that systems consisting of three separated centre - of - mass modes allow for the use of stirap - like processes to achieve robust transfer of atoms from one position to another with high fidelity @xcite . the process of stimulated raman adiabatic passage ( stirap ) is well known in three - level - optics , where it refers to the technique of applying a counter - intuitive sequence of laser pulses to achieve a transition of an electron between the two ground states in a @xmath0-system @xcite . in the atom trap scenario the energy levels are replaced by spatially separated trap ground states and the laser interaction is replaced by the coherent tunneling interaction . one advantage of adiabatic techniques is their large robustness against experimental uncertainties as long as the whole process is carried out mostly adiabatically @xcite . however , this also means that a resonance between the asymptotic eigenstates has to exist , which is a condition that for many realistic situations is hard to ensure . suggestions for and examinations of realistic systems in which the stirap process could be observed for cold atomic gases are therefore currently very rare . in this work we will focus on atom - chip systems and investigate their suitability to observe this adiabatic process . these micro - fabricated chips , on which surface mounted , current carrying wires provide guiding potentials for matter waves , can be loaded with ultracold atom gases at low densities . as opposed to traditional experimental setups , these systems allow reaching smaller dimensions and the wire geometry , and therefore the waveguide geometry , can be chosen almost at will @xcite . the first investigation into adiabatic techniques in waveguides was presented by eckert _ @xcite , who showed that a cpt - like process which acts like a 50:50 beam splitter could be realised with a large degree of fidelity . while the initial state for a numerical evolution can be prepared with a large degree of localisation , one of the problems following the subsequent evolution inside the waveguide is that the wavefunction disperses along the guide . this makes it hard to exactly measure the final state of the system and put a quantitative number on the efficiency of the adiabatic process . here we will introduce a simple harmonic potential along the longitudinal direction of the trap , which will allow us to perfectly measure the fidelity of the process . it is also worth mentioning that stirap in optical waveguides with classical light has been observed recently @xcite . in the next section we will first remind the reader by briefly reviewing the idea of stirap and its translation into the realm of waveguides . after that , in section [ sec : model ] , we will examine a model waveguide potential in which the resonance condition is fulfilled throughout the whole process and show that the dispersion of the wavefunction in the longitudinal direction has no significant effect on the fidelity of the process . in section [ sec : atomchips ] we describe a realistic situation by examining three waveguides created on top of an atom chip . we show that even though the resonance condition is not fulfilled at all times , a counter - intuitive approach will lead to larger transfer and can clearly be distinguished from a direct tunneling approach . finally we conclude . in this section we will briefly review the basic idea of stirap , which is a technique originally developed for transitions in optical @xmath1-systems and which makes use of a two - photon raman process . by applying the pump and the stokes pulse in a counter - intuitive time - ordered way it leads to population transfer directly from one of the ground states to the other without any population ever being in the excited transitional state . in optical systems this inhibits spontaneous emission and is therefore often referred to as a dark - state technique . the basic idea can be understood in the simple model of a three state system described by the hamiltonian @xmath2 where we have set the energies of the three asymptotic eigenstates to zero and the rabi frequencies of the pump and the stokes pulses are given by @xmath3 and @xmath4 , respectively . this hamiltonian can be diagonalised and the eigenstate which is of interest to us here is the so - called dark state given by @xmath5 where the mixing angle @xmath6 is given by @xmath7 . this angle describes how the the population is distributed between the two states @xmath8 and @xmath9 and it can be chosen by varying the strength of the pump and the stokes pulse with respect to each other in time . in particular , if the intensity of the stokes pulse increases before that of the pump pulse ( counter - intuitive coupling scheme ) , one finds that all initial population in @xmath8 will be transferred to @xmath9 . the fact that this process can be observed for trapped atoms was first pointed out by eckert _ the asymptotic eigenstates of the hamiltonian ( [ eq : hamiltonian ] ) are then the spatial modes the atoms occupy and the time - dependent coupling is given by the tunneling strength between these modes . while the time - dependence of the tunneling strength can be achieved by temporally changing the distance or the barrier height between the individual states , an atom moving in a waveguide can also experience this as a function of travelled distance @xcite . in the next section we will examine an example of this . the schrdinger equation for the evolution of a wave - packet in a two - dimensional waveguide structure is given by @xmath10 where @xmath11 is the mass of the atom . as the third dimension does not significantly contribute to the dynamics we are aiming to observe , the restriction of the above hamiltonian to two dimensions is justified . in this section we will first examine the stirap process using an idealised potential in which the condition of resonance between the individual waveguides is fulfilled at any point . this will help us to illustrate the basic process and in particular highlight the influence of the longitudinal dimension . in section [ sec : atomchips ] we will compare these results to realistic atom chip scenarios in which we will have to relax the resonance condition . the assumption we make to guarantee that the ground state energy in all three waveguides is the same everywhere is that we can construct our potential @xmath12 by stitching three independent waveguides together . in a realistic situation the potentials creating each guide would influence each other and lead to non - symmetric situations between pairs . we assume each guide to have the potential @xmath13 ^ 2\ ] ] where @xmath14 determines the height , @xmath15 the width and @xmath16 the position of the minimum along the @xmath17-axis . the overall potential is then assumed to be given by the minimum value of each of the three potentials at any point in space . a schematic view of the area in which the guides approach most closely is shown in fig . [ fig : schematic ] . the eigenstates of matter waves propagating in two - dimensional waveguides at different distances have recently been explored by jskelinen and stenholm @xcite . they determined the conditions under which the movement of a matter wave can be considered adiabatic in a curved waveguide and developed a formalism based on localised and de - localised basis states . here we will take a more straightforward approach and present a numerical solution to the process , which will show that despite the existence of velocity - dependent potentials due to the curvature of the waveguides @xcite the stirap process can be observed with high fidelity . our simulations start with a well - localised wave - packet far away from the coupling area . in time , however , this packet will disperse along the waveguide , making it hard to quantify the success of the transfer process . to overcome this problem we introduce an additional harmonic potential of frequency @xmath18 along the @xmath19-axis , which will lead to a refocussing of the wave - packet in the longitudinal direction after a time of @xmath20 . the initial state of our wave - packet is given by the ground state of an isotropic trap of the transverse frequency of the waveguide and its movement along the guide is induced by the harmonic potential as well . in fig . [ fig : intuitive ] we show the evolution of the wavefunction at different times throughout the process for a counter - intuitive arrangement of the waveguides . starting with the wave - packet located in the lower guide , one can clearly see that a majority of the probability is transferred into the upper guide . the evolution of the same initial state in an intuitive arrangement of waveguides ( see fig . [ fig : intuitive ] ) shows significantly less transfer . ] the amount of transfer varies as a function of several parameters . the first one is the distance between the two points of closest approach of the outer waveguides to the middle one , @xmath21 . we show the amount transfered as a function of this quantity in fig . [ fig : rho ] on the left hand side . the full line ( blue ) represents the counter - intuitive case and a maximum at a finite value of @xmath21 is visible . the broken line shows the same quantity for the intuitive setting , clearly indicating that direct tunneling does not lead to high fidelities . the second parameter that plays an important role is the degree of adiabaticity of the process . for a waveguide system this translates into the velocity with which the atom moves or alternatively the length of the coupling area . here we keep the velocity effectively constant and show on the right hand side of fig . [ fig : rho ] the variation of the maximum amount transfered as a function of the overall length of the coupling area . making the overall structure longer also corresponds to decreasing the curvature of the waveguides and thereby reducing the velocity - dependent couplings introduced by it @xcite . as" +"the special relativity theory ( srt ) introduces an universal fundamental constant , the speed of light in space , it is constant in all frames . hence all reference frames are completely equivalent and an ether rest frame is superfluous . the experimental basis of the srt has been pointed out by t. roberts @xcite , where a lot of experimental tests done by many authors are summarized . following this article we found several experiments about round - trip test of light speed isotropy ( two - way light path ) , from the traditional michelson - morley to modern laser / maser tests , as well as , about one - way light path test of light speed isotropy . in all cases , the experiments have been mounted in earth s surface on a rotating table or fixed to the earth , in this last case it is looked for effects due to the earth s rotation . only the upper limits have been found and they are in agreement with a null effect , all results confirm the prediction of the srt , or in other words , the srt has not been refuted by any experiment . however , recently there are evidences suggesting that the propagation of light over cosmological distances has anisotropy characteristics@xcite , this means that the speed of light is not a true constant , it depends on direction and polarization . this is a further indication in favor of the existence of a preferred reference frame . this picture is in agreement with the interpretations of the cobe@xcite measurements giving the earth s `` absolute '' velocity in relation to the uniform cosmic microwave background radiation(cmbr ) . of course , there are also interpretations claiming that the cobe measurements only give a velocity for the `` relative '' motion between the earth and the cmbr @xcite . for instance , it is possible to remove the earth motion to obtain a `` virtual '' image , where an isotropic distribution of cmbr with small fluctuations ( @xmath2 ) can be seen . on the other hand , the big bang cosmology is well described by the robertson - walker - friedmann metric@xcite , the time in this metric called as the `` cosmological time '' has an absolute beginning and it coincides with the begin of the big bang , in other word , it is possible to estimate the absolute age of the universe . in short , the cobe measurements of the earth motion relative to the `` cmbr rest frame '' on an inflationary scenario , described by the robertson - walker - friedmann metric , lead to the concept of absolute space - time , because in this scenario it is not possible to remove the earth s motion without altering the robertson - walker - friedmann metric@xcite . the consequences of an absolute space - time assumption are the breakdown of the symmetry - energy and symmetry - momentum ( linear and angular ) conservation laws . the extension of the effects of the violation of these symmetries is still not known . so far , we know that probably they are relevant only in cosmological scale . in fact , in 1999 , coleman and glashow began to wonder , if lorentz s symmetry is certainly an exact symmetry of the nature , in the region close to the plack s scale energy . the lorentz symmetry violation may be correlated to the existence of an absolute reference frame created by the big - bang . the main objective of this paper is to present experimental results on an `` one - way light path '' laser diffraction experiment mounted in the shell of the tupi muon telescope @xcite and that shows clearly that the speed of light depends on the propagation direction . the effect is observed as a amplified doppler shift in the diffraction images as function of the laser beam alignment relative to the earth s velocity vector . the experiment is an improved version about light diffraction suggested by c. m. g. lattes @xcite in 1980 . the results are well described by the the so called ether gauge theory ( egt ) , and it is an extension of the lorentz s ether theory . the gauge of the length is : the moving rods undergo the shortening by lorentz factor and the gauge of the time is : the moving clocks undergo the slowdown by lorentz factor . the egt scenario satisfies the cosmological time boundary condition ( see next section ) and leads naturally to a non - isotropic `` one - way '' light propagation relative to the earth frame and where there is a preferred direction . the assumption of a preferred frame agree also with a previous analysis made by brans and stewart @xcite where a description of the topology of the universe has imposed a preferred state of rest so that the principle of special relativity , although locally valid , is not globally applicable . the analysis of the global positioning system ( gps ) carried out by hatch @xcite provides also strong indirect evidence for the presence of an ether - drift velocity . we presents here a straightforward analysis about light propagation on the basis of the ether gauge theory ( egt ) formalism based upon a modification of the lorentz ether theory in order to include the cosmological time constraint . this exigency is satisfied by tangherlini @xcite and selleri @xcite transformation . this scenario admit an absolute referential frame @xmath3 called hereafter as the hubble s frame @xcite and it is linked with the `` cmbr rest frame '' . the hubble s frame is defined as : + ( a ) the frame where the cmbr is isotropic and + ( b ) the frame where light propagation is isotropic . for simplicity and without loss of generality , only a bi - dimensional analysis is made . the tangherlini - selleri transformation from @xmath3 to @xmath4 in motion relative to @xmath3 with velocity parameter @xmath5 and where we choose the @xmath6 and @xmath7 as the direction of the relative motion has been found to be @xmath8 where @xmath9 . the main difference between the egt transformation ( tangherlini - selleri transformation ) and the srt transformation ( lorentz transformation ) , constitutes the transformation of the time , the tangherlini - selleri time transformation satisfied the cosmological constraint ( synchronization of clocks ) , if @xmath10 then @xmath11 . the main consequence of this scenario is that , in the @xmath4 frame , the axis - x ( direction of @xmath12 ) behaves as a preferred direction . the transformation equations for the velocity of a moving point can be found differentiating eq.(1 ) with respect to @xmath13 . @xmath14 now , if we denote @xmath15 , @xmath16 and @xmath17 , the speed of light components in the @xmath4 frame are @xmath18 and the module of this velocity can be obtained as @xmath19 the last equation means that in the @xmath4 frame the speed of light is not a constant , but it depends on @xmath20 . fig.1 shows the space - time diagram ( light cone ) in the @xmath4 frame . it is possible to see that the axis - x ( direction of @xmath21 ) behaves as a preferred direction . the cone of light is symmetric in relation to the y - axis , while it is asymmetric in relation to the x - axis . the slope of the lines is proportional to the inverse value of the speed of light . for illustrative purpose , a large value for @xmath22 in this diagram has been used . the effect , for instance , due to the earth motion relative to the cmbr rest frame is tiny ( @xmath23 ) . from this picture , it is possible to see that there is a resulting vector speed of light , and it is represented as @xmath24 in fig.1 , and hereafter it will be called as the emission vector . the emission vector points in opposite direction of the vector @xmath25 and , following eq.(4 ) , the emission vector has a module given by @xmath26 with amounts to @xmath27 . the effect due to the earth motion gives @xmath28 . on the other hand , the one - way ( forward and backward ) speed of light in the earth frame ( @xmath4 ) are defines as @xmath29,\\ c_e^b = c_h\;\gamma^2[1-\beta \cos ( \theta_h+\pi)],\end{aligned}\ ] ] under this conditions , the one - way speed of light `` dipole '' anisotropy is defined as @xmath30 where @xmath31 is the average values as @xmath32 with eq.(6 ) and eq.(7 ) , eq.(8 ) becomes @xmath33 thus the egt scenario predicts a `` dipole '' speed of light anisotropy with an amplitude @xmath34 , which coincides with the value of the dipole temperature anisotropy ( @xmath35 ) of the cmbr as observed by cobe . fig.2 summarized the situation , where the dependence of the `` dipole '' speed of light anisotropy is plotted as function of @xmath20 . following fig.2 , it is possible to see that in earth - based experiments , the choice of the direction of the light beam is essential , an random choice for the light beam direction , as in experiment mounted on a rotating table , can easily lead to ambiguous results . in order to compensate the change of direction due to the earth rotation , the earth - based experiments must be mounted like a optical telescope using an equatorial ensemble , for intance . the tupi muon telescope is installed on the campus of the universidade federal fluminense , niteri , rio de janeiro - brazil at sea level . the position is : latitude : @xmath36 s , longitude : @xmath37 w. the tupi muon telescope has an equatorial assembly and a servo - mechanism which allows the axis of the telescope to be pointed so as to accompany a given source @xcite . on the other hand , the bigger temperature anisotropy in the cosmic background radiation is represented by a dipole with an amplitude of @xmath38 which arises from the motion of the solar system barycenter with a velocity @xmath39 ( @xmath40 ) at 68%cl , relative to the so called `` cmbr rest frame '' and towards a point whose equatorial coordinates are @xmath41)@xcite . this direction points for the crater constellation . a laser light diffraction experiment has been mounted in the shell of the tupi muon telescope , as is represented in fig.3 . the layout of the diffraction device is shows in fig.4 , the experiment permits us to obtain the variations of the diffraction line positions , @xmath42 , as a function of the laser beam alignment , @xmath20 , relative to the earth s velocity vector , obtained by cobe . this experiment is an improved version of an experiment accomplished in 1980 in campinas brazil and suggested by c. m. g. lattes ( with unpublished results ) . just as in the modern version of the michelson - morley experiment @xcite , where anisotropies are sought in the light ( radiation ) propagation due the earth rotation , the lattes version tried to measure variations of the positions ( @xmath42)(see fig.4 ) of the diffraction lines due to the earth s rotation . this requires to make measurements over long time of at least several days to weeks , and it is necessary to take into account the atmospheric pressure and temperature variations among others , because the daily atmospheric variations may mask the effect . in the tupi laser diffraction experiment , a complete set of measurements is made in only ten minutes . in addition , just" +"the progenitor stars of core - collapse supernova explosions form in giant molecular clouds . since these massive stars have a short lifetime many of them end their lives while the parental clouds are still nearby and may even still harbor small star forming regions that produce stars of lower mass . according to in galaxies like ours about 70% of all supernova explosions are of type ii and should explode close to the dense clouds from which they were formed . after these stars explode , strong shocks are driven into the clouds , heating , compressing , dissociating , and accelerating the gas leading to a large variety of observable effects . a picture book example is the galactic supernova remnant ( snr ) ic 443 on which most studies of snr - molecular cloud interactions have been focused . but recently more and more snrs have been discovered interacting with molecular clouds , e.g. w28 , w44 , 3c 391 ( e.g. , * ? ? ? * ; * ? ? ? * and references therein ) , and many others , among them the galactic snr ctb 109 ( g109.11.0 ) . ctb 109 was first discovered as an snr in x - rays with _ einstein _ @xcite and in radio in the 610 mhz galactic plane survey @xcite . it has a semi - circular morphology in both the x - ray and the radio and is located next to a giant molecular cloud ( gmc ) complex in the west . this semi - circular morphology suggests that the snr shock has been stopped entirely by the gmc complex , and that the appearance is not simply due to absorption . a linear feature in co ( ` co arm ' ) extends from the gmc complex to the local x - ray minimum in the northern half implying that a part of the gmc complex extends in front of the remnant ( see fig.[chandraco ] ) . the cold interstellar medium in which the remnant is embedded has been studied in detail by @xcite . the most puzzling x - ray morphological feature in ctb 109 is the bright , extended interior region known as the ` lobe ' . the x - ray spectrum from the lobe obtained with _ xmm - newton _ is completely thermal @xcite . the lobe could be the result of a hole in the gmc allowing the x - ray emission through with little or no absorption or it could be the result of intrinsically brighter emission due to an interaction between the shock and the cloud . in order to investigate the later hypothesis we obtained new high resolution x - ray and co data . observations of the @xmath1co and @xmath5co ( j=@xmath6 ) spectral lines , at 45 resolution , were obtained using the five college radio astronomy observatory ( fcrao ) 14 m antenna in march 2003 . the telescope was equipped with the 32 element sequoia focal plane array @xcite . the data were acquired through on - the - fly mapping , in which the telescope was scanned continuously across the sky while reading out the spectrometers at regular intervals of 1125 . calibration to the @xmath7 scale was done using the chopper wheel method @xcite , and the data were converted to the radiation temperature scale ( @xmath8 ) by correcting for forward scattering and spillover losses ( @xmath9 = 0.7 ) . the 1024-channel spectrometers were set to a total bandwidth of 25 mhz ( @xmath10 ) centered on @xmath11 . following recording of the data , the spectra were converted onto a regular grid of 225 pixel spacing using the fcrao _ otftool _ software . the new data have higher sensitivity than the cgps data @xcite and are fully nyquist sampled . the higher sensitivity and the full sampling allow us to detect the faint clouds around the lobe and study them in great detail . the _ xmm - newton _ observations have shown that the x - ray bright lobe is thermal and seem to indicate an interaction between the shock wave and a molecular cloud @xcite . therefore , we proposed an additional deep observation with _ chandra _ to probe the shock - cloud interaction region at higher angular resolution . the observation was performed using the advanced ccd imaging spectrometer ( acis ) in full - frame , timed - event mode with an exposure of 80 ksec ( obsid 4626 ) . the data were taken in the energy band of @xmath12.03em0.3 10.0 kev . the acis - i array covered the northeast part of the snr and the northern tip of the lobe was observed at the aimpoint . the data are analyzed with ciao 3.2.2 and caldb 3.1.0 . the complete analysis of these data including a detailed spectral analysis of the whole area will be presented in a different paper . here , we present the high - resolution x - ray image of the lobe of ctb 109 obtained with _ chandra _ the image is binned with a size of 4 pixels ( 1 pixel = 0.492 ) and smoothed with a gaussian with a sigma of 2 pixels ( the original pixels binned by 4 ) . x - ray spectra which are extracted at regions corresponding to co clouds are also discussed , in order to obtain the absorbing foreground hydrogen column density ( ) . the spectra are binned with a minimum of 50 counts per bin and analyzed using the x - ray spectral analysis tool xspec . to fit the spectra , we use a model for a thermal plasma in non - equilibrium ionization with variable abundances ( vnei ) and hydrogen column density , , for the foreground absorption ( phabs ) . in figure [ chandraco ] we display the distribution of molecular gas in the vicinity of the x - ray lobe . in the left image , the co arm discovered by is shown . the anti - correlation of the co emission with the _ chandra _ image nicely demonstrates that this molecular cloud is located in the foreground and absorbs the x - ray emission from ctb 109 coming from behind it . in the right panel we averaged the co emission over a velocity range more negative than that of the co arm . we can identify three small molecular clouds surrounding the eastern part of ctb 109 s x - ray lobe with the brightest to the galactic east ( on the left side of the lobe in fig.[chandraco ] , hereafter east ) , a fainter one to the galactic north ( above the lobe , hereafter north ) , and another one in the galactic south ( below the lobe , hereafter south ) which is not fully covered by our observations . the noise level in the image is @xmath12.03em40 mk . assuming the progenitor star exploded at or close to the current position of the anomalous x - ray pulsar 1e2259 + 586 , the location of these clouds is suggestive of an interaction of the snr shock wave with those molecular clouds resulting in the x - ray lobe . most of the molecular clouds are rather faint in the @xmath5co line , which is why we can not perform a detailed comparison with the @xmath1co measurements . however , we can estimate an average brightness ratio for each of the clouds ( see table [ cotab ] ) . the value for the southern cloud is a bit difficult to interpret since it is not fully covered by our observations and it seems to consist of a number of small clouds . we find brightness ratios between 3.5 in the dense part of the co arm and 13 in the southern clouds . according to @xcite , at the galactocentric radius of ctb 109 the @xmath1c to @xmath5c isotope ratio @xmath13 should be about 63 . this indicates that we miss some of the @xmath1co emission and this line is optically thick . in the following we assume local thermodynamic equilibrium and the same excitation temperature for both isotopic species and all molecules along the line of sight in each cloud . we determine an average optical depth for each cloud in both lines by the following procedure : we use the @xmath1co to @xmath5co ratio for each cloud to determine how much @xmath1co emission we are missing by assuming the @xmath5co line is optically thin . this can be translated to a first iteration for the optical depth @xmath14 . if both species have the same excitation temperature the @xmath1co to @xmath5co brightness temperature ratio @xmath13 can be written as : @xmath15 . from this we determine a first iteration for the optical depth @xmath16 of the @xmath5co line . this is again used to determine a better value for the missing @xmath1co emission and so on . this iterative procedure converges usually after just a few iterations . the results for @xmath14 and @xmath16 are listed in table [ cotab ] . to integrate the @xmath5co column density we actually use the @xmath1co data scaled to @xmath5co by the brightness ratios for each individual cloud since the signal to noise ratio is higher in our @xmath1co data . the @xmath5co column density is then scaled by @xmath17 to determine the column density of the h@xmath18 molecules @xcite . we also estimate h@xmath19 number densities and masses of the clouds ( table [ cotab ] ) . while the northern cloud , the southern cloud , and the faint eastern tail of the eastern cloud have comparable h@xmath18 column densities ( @xmath20 @xmath3 ) , the bright part of the eastern cloud that overlaps the lobe has a higher @xmath2 @xmath3 . it is interesting to note that we calculated a peak h@xmath19 column density of @xmath21 @xmath3 for the co arm , which compares nicely with the value of @xmath22 @xmath3 determined by . in order to compare with these results , we extract spectra from the _ chandra _ data in regions corresponding to the co clouds and derive the atomic h column density in the foreground by fitting the spectrum with a model including a thermal non - equilibrium ionization model and a foreground absorption . for the northern cloud , we obtain = 6.3 ( 5.6 7.0 ) @xmath23 @xmath3 ( 90% confidence range in parentheses ) . for the larger eastern cloud , the foreground absorption of the part inside the lobe is = 4.5 ( 4.2 4.9 ) @xmath23 @xmath3 , outside the lobe , we get = 5.9 ( 5.5 6.4 ) @xmath23 @xmath3 , and in the eastern tail the foreground absorption is = 5.0 ( 4.2 5.4 ) @xmath23 @xmath3 . although the column density is largest in the bright part of the eastern cloud , the foreground is the lowest . therefore , the eastern cloud is not located in front of the lobe . the foreground absorption in the region of the southern cloud is = 6.8 ( 5.8 7.3 ) @xmath23 @xmath3 . the x - ray absorption is significantly higher in the regions corresponding to the northern cloud and the southern cloud than in the eastern tail of the eastern cloud . it seems that these two clouds are located in front of the remnant and absorb some of the x - ray emission . as the snr is believed to be located next to the gmc , we assume that both have a systematic velocity of @xmath24 . the three clouds ( radial velocities between @xmath25 and @xmath26 ) are slightly blue - shifted from the gmc to the west , indicating that these clouds are moving towards us relative to the gmc complex . as the bright" +"it was shown in ref . @xcite that mg atoms can be magneto - optically trapped . this offers many possible applications of cold mg atoms for ultra high resolution spectroscopy , new frequency standards and collective quantum effects . a magnesium clock has already been developed by ref . the most abundant isotopes of mg have a single electronic ground state without hyperfine interactions , which opens a road to simpler theoretical modeling of ground state atomic collisions as compared to the modeling of , say , alkali - metal atom collisions@xcite . magnesium is not the only alkaline earth species that can be magnetically and optically manipulated . ingenious cooling schemes exist for ca@xcite and sr@xcite . for sr ref . @xcite have nearly reached the quantum degeneracy regime . optical clocks based on the ultra - cold calcium have been constructed for mg@xcite and ca@xcite . the first experimental photoassociation spectra were reported for calcium@xcite while photoassociation spectroscopy for alkaline earth atoms has been studied theoretically in ref . @xcite the coldest temperatures in dilute atomic gases are obtained by a process called evaporative cooling . ground state collisions are crucial for evaporative cooling . elastic collisions during this process lead to a thermalization of atoms and under the right conditions formation of a bose condensate . elastic collision rates at ultra cold temperatures can be described by a single parameter , the scattering length _ a_. formation of bose - einstein condensates is determined by the nonlinear coupling parameter in the condensate schrdinger equation , which in turn depends on the sign and value of the scattering length . inelastic collisions , which change the internal state of the atoms , can eject trapped atoms . examples of inelastic processes are , for example , spin - exchange , spin - depolarization , and penning and associative ionization , where the first two have been observed in alkali - metal gases@xcite and the latter have been observed in metastable rare gas samples@xcite . for alkaline - earth atoms the electronic ground state is solely composed of closed shells and is a @xmath3 state . consequently , no inelastic atom - atom collisions can occur . this opens a pathway to more efficient evaporative cooling . in this paper we present our calculation of the ground state mg@xmath4 scattering length and cross - section as a function of the collision energy , using a potential constructed from high resolution spectra of the magnesium dimer measured by balfour and douglas @xcite . at temperatures below 5 mk ground state mg collisions are in the s - wave scattering regime and the _ = 0 phase shift determines the cross - section and , at zero collision energy , the scattering length . this phase shift can be found by matching the numerically evaluated scattering wavefunction of the interaction potential to free scattering wavefunctions at large internuclear separation _ r_. slight changes to the inner part of the potential can generate significant changes in the phase shift and the scattering length . we will discuss several ways to obtain the interaction potential of ground state mg@xmath4 . firstly , a rydberg - klein - rees ( rkr ) potential curve has been constructed in ref . @xcite from their measurement of the rovibrational levels ( @xmath5 = 0 - 12 , @xmath6 = 10 - 76 ) of ground state mg@xmath4 . secondly , vidal and scheingraber @xcite have reevaluated the molecular constants of ref . @xcite and improved upon the rkr analyses by applying a variational procedure based on the inverted perturbation approach ( ipa ) . finally , there exist a large number of theoretical electronic structure calculations @xcite of the ground state mg@xmath4 potential . this paper briefly describes our _ ab initio _ multiconfiguration valence bond ( mvb ) calculation of the ground state potential . although , as we will show , the theoretical uncertainty in the shape of the potential is too large to predict the scattering length we nevertheless compare scattering data for our _ ab initio _ potential and the most recently published theoretical potential by czuchaj _ @xcite to those for the rkr and ipa potential . this will give us a feeling for the state of the art in molecular electronic structure calculations of interacting two electron atoms . this paper is set up as follows . in section [ exp ] we describe the existing experimental data and the potentials that have been constructed from the data . section [ abinitio ] presents the theoretical calculations in the existing literature as well as a new calculation using the multiconfiguration valence bond method . section [ lr ] describes the long - range behavior of the potentials and connects this to the short - range potentials obtained in sections [ exp ] and [ abinitio ] . finally , section [ vib ] discusses how well bound states of the four potentials that have been constructed reproduce the experimental bound state energies , and determines the scattering properties for the best of these four potentials . the rkr potential of ref . @xcite and the ipa potential constructed in this work from data published in ref . @xcite are shown in fig . [ all_pot ] . for the rkr potential we use a dissociation energy d@xmath7 = 424(5 ) @xmath1 ( 1 @xmath1 = 29.9792458 ghz ) , defined as the energy difference between the bottom of the potential and the asymptotic energy . reference @xcite did not provide a tabulated ipa potential but expressed the potential in terms of dunham coefficients y@xmath8 . we have constructed a potential from the y@xmath8 for _ l _ = 0 - 3 , @xmath9 = 0 - 5 provided in table iv of ref . @xcite by applying the rkr procedure . we will call this potential the ipa potential . we will show lateron by solving the schrdinger equation for the rkr and ipa potentials that the ipa potential reproduces the term values significantly better than the rkr potential of ref . @xcite . for the ipa potential we take the dissociation energy d@xmath7 to be 431.0(1.0 ) @xmath1 in accordance with fit of ref . @xcite to the last outer turning points of the potential . the 1.0 @xmath1 uncertainty is based on the sensitivity of the fit with the order of the long - range dispersion expansion . the rkr and ipa potential are only known over a limited region of internuclear separation , 6 @xmath10 to 14 @xmath10 . this range is determined by the inner and outer turning point of the most - weakly - bound measured rovibrational level . for a scattering calculation the potential must be known for all internuclear separations . therefore we have connected the repulsive short range of the rkr potential to the repulsive wall of our mvb potential which will be discussed in section iii . the repulsive short range wall of the ipa potential is a linear extrapolation from the attractive region as our mvb potential could not be smoothly connected to the ipa potential . both rkr and ipa potentials suffer from a well known `` short range turnover '' in the potential inherent to the rkr inversion procedure . we simply removed those inner turning points from the data set before extrapolation . the extrapolation of the rkr and ipa potential to longer @xmath11 is discussed in section iv . the ground state mg@xmath4 molecule is formed from two closed shell atoms , each of which is described by the configuration 1s@xmath122s@xmath122p@xmath133s@xmath12 . this might suggest that theoretical modelling will be easy . instead , numerous computational efforts have proven the opposite . the first dramatic complication arises at the hartree - fock level , because it predicts a purely repulsive ground state potential . the binding of the magnesium dimer is created by the correlation energy only . there are inter- and intrashell correlations affecting the potential , that , apparently , have a strong dependence on internuclear separation . the question becomes how well a computational approach can incorporate these correlations . there are a large number of methods @xcite which have been tested for the computation of the correlation corrections . in a pioneering publication stevens and krauss @xcite calculated the ground state potential of mg@xmath4 using a nonrelativistic multiconfiguration self - consistent field method . their work shows the importance of the ability to simultaneously incorporate both the long - range atomic and short - range molecular correlations . many - body perturbation theory can provide an alternative to the configuration interaction approach to model correlation effects in the mg@xmath4 molecule . double excitation type diagrams were applied by purvis and bartlett @xcite to significantly improve the molecular binding energy . in ref . @xcite a combination of a coupled - cluster method with single and double excitations and perturbative triple excitations is used to reach a good agreement with the rkr potential of ref . the potential curve of ref . @xcite is shown in fig . [ all_pot ] . for this paper we have used the multiconfiguration valence bond ( mvb ) method to calculate the ground state mg@xmath4 potential . a detailed description of the computational approach is given in ref . we create a nonorthogonal basis set from self - consistent dirac - fock atomic orbitals belonging to the [ 1s@xmath12 ] 2s@xmath12 2p@xmath13 3s@xmath12 configuration and additional sturmian orbitals labeled 3p , 3d , 4s , 4p , 5s , and 5p . the closed shells 1s@xmath12 + 1s@xmath12 form the core of the molecule and no excitations from 1s@xmath12 + 1s@xmath12 will be allowed . the 2s@xmath12 , 2p@xmath13 and 3s@xmath12 orbitals are valence orbitals and single and double excitations from these orbitals occur . various covalent and ionic configurations are constructed by distributing electrons from the optimized valence orbitals in all allowed ways over the 3p , 3d , 4s , 4p , 5s , and 5p orbitals . in total , there are 1041 molecular configurations in our configuration interaction . we have performed two kinds of nonrelativistic calculations . the first kind is aimed at calculating the best possible short - range potential by first perturbatively estimating the correlation energy of each molecular configuration excited from the ground state configuration . if the estimate falls below a threshold this configuration is not included in the configuration interaction procedure . this truncation of the configurations is necessary because inclusion of all configurations in the configuration interaction procedure is not computationally possible . the second kind of calculation gives the best possible long - range potential by excluding ionic configurations and switching off the exchange interaction in the hamiltonian in order to reduce the size of the matrix and to accelerate the calculation . the two calculations are connected between 13 @xmath10 and 14 @xmath10 , because at these internuclear separations the difference between the total energy of the two kinds of calculations , and thus the exchange energy , is less than 5% of the binding energy . figure [ all_pot ] shows our ground state @xmath15 potential of mg@xmath4 . the dissociation energy is d@xmath7 = 410 @xmath1 . the long - range dispersion potential of the mg@xmath4 ground state has attracted considerable attention over the past few decades . mg@xmath4 was the first alkaline earth van der waals molecule for which a high accuracy rkr potential was obtained and thus allowing a comparison with , or extraction of , the long - range potential . stwalley @xcite and li and stwalley @xcite constructed a dispersion potential using the form @xmath16 from the frequency - dependent atomic dipole polarizability and the rkr curve . the dipole - dipole dispersion coefficient @xmath2 was determined from the atomic polarizability while both @xmath17 , the energy difference between the @xmath18 rovibrational level and the asymptotic" +"in most barred galaxies , gas is concentrated on the leading side of the bar ( e.g. , * ? ? ? * ) , which is reproduced in numerical simulations ( e.g. , * ? ? ? * ) . then , the bar gravity torques make gas lose angular momentum , which initiates a gas inflow and fuels a central mass concentration ( cmc ) . the bar is weakened by the cmc growth , because of escaping orbits @xcite . @xcite , @xcite and @xcite report the dissolution of galactic bars with cmcs of mass 0.5 to 2 % of the disk mass . to explain the large fraction of barred galaxies observed both at @xmath0 ( e.g. , * ? ? ? * ) and at @xmath1 @xcite , we have proposed that bars are dissolved and reformed ( * ? ? ? * hereafter paper i ) : our n - body simulations showed that bars are dissolved in 14 gyrs in most galaxies , which we had attributed to the cmc growth . yet , whether bars are really transient is still debated . resonant rings are often observed in barred galaxies , which implies that gravitational torques are much larger than viscous torques ( e.g. , * ? ? ? * ) . for a long time , gaseous simulations were too limited in resolution , induced too large viscous torques , so that such rings did not form . if viscous torques are still over - estimated , this may induce unrealistic inflows of gas , so that cmcs are more massive and/or fueled more rapidly , and the life - time of bars may be much under - estimated @xcite . moreover , even if the cmc fueling is realistic , the effects of the cmc may not be enough to fully dissolve the bar : recent simulations with more spatial resolution by @xcite that do not include the whole gas response have shown that bars are more robust against the growth of cmcs than what was believed before . thus , the limited lifetime of bars found in paper i and other works could be an artifact of viscous torques or an over - estimation of the effects of the cmc . in this letter , we show that the gas inflow in our simulations is actually initiated by gravitational torques , that are much larger than viscous torques . while most existing works had focused on the effects of the cmc growth , we show that another phenomenon can also lead to the destruction of galactic bars in a few gyrs : the torques between the stellar bar and the gaseous arms also disturb the bar and can dissolve it . we then find that galactic bars are transient , even when the gas infall and the effects of the cmc are correctly treated and do not destroy the bar themselves : the growth of the cmc is not the only factor of bar dissolution . we employ the n - body fft code described in paper i , including star formation . the gravitational potential is computed on a cartesian grid of size @xmath2 . the softening length and cell size are 75 pc , and the number of particles is @xmath3 for each component ( gas and stars ) . the dissipative dynamics of the ism is modeled by the 3-d sticky - particles code described in paper i ( we use an elasticity parameter for cloud - cloud collisions @xmath4 in this paper ) . star formation and stellar mass - loss are also included . we use a visible ( stellar and gaseous ) mass of @xmath5 m@xmath6 . the disk truncation radius is @xmath7 kpc and its scale - height is 1.2 kpc . the bulge and dark halo are plummer spheres of radial scale - lengths 2 and 36 kpc respectively . the bulge - to - disk mass ratio is 0.25 , and the dark - to - visible ratio inside the disk radius is 0.6 . the initial gas mass is @xmath8 m@xmath6 ( 7.25 % of the visible mass ) . at @xmath9 gyr , during the bar dissolution , the remaining mass of gas is @xmath10 m@xmath6 ( 5.5 % of the visible mass ) . we also run a control simulation without gas . we compute the bar strength @xmath11 as the maximum over radius of the @xmath12 angular component of the gravitational torques , following the definition given in paper i , where this parameter was denoted @xmath13 ( see eq . 27 in paper i ) . the response of gas to the stellar bar is shown in fig . [ snap ] . inside the corotation radius ( cr , 6kpc ) , gas is concentrated on the leading side of the bar . then , as shown in fig . [ fig2 ] , the bar gravity torques make gas lose 1015% of its angular momentum over one rotation , while the shear viscosity torques are much smaller : the gas inflow in our simulations is really initiated by the bar gravity torques , contrary to the hypothesis raised by @xcite . the bar - driven gas inflow fuels a central mass concentration ( cmc ) : we show in fig . [ fig1 ] the increase in the mass inside radii 100 and 250 pc . at @xmath14 gyr , the mass radial profile shows a central peak of stars and gas that can be fitted by a plummer cmc of mass @xmath15 m@xmath6 and radial scale - length 90 pc . according to @xcite , such a cmc can not fully dissolve the bar . yet , while the gravitational softening length and the number of particles we used are close to that of @xcite , the bar is here fully dissolved in less than 2 gyrs : the residual values of @xmath16 correspond to a weak oval distortion and spiral arms , but no bar is present . a surprising point shown in fig . [ fig1 ] is that the cmc growth occurs after the bar is already significantly weakened . the increase of the mass included inside radius 250 pc occurs between @xmath17 and @xmath18 gyr . the bar strength is then smaller than 40% of its maximal value . as for the increase in the mass inside radius 100 pc , it occurs at the very end of the bar dissolution , from @xmath19 to @xmath18 gyrs . at the opposite , the bar weakening is already significant at @xmath20 gyr : at this time , no strong increase in the mass has occurred , excepted at large scales of more than 1kpc , but mass concentrations at such scales are totally inefficient to dissolve bars . it thus seems that the cmc growth is not the only factor that is responsible for the destruction of the bar . furthermore , the bar dissolution is not an artifact of a too long time step : we have divided the time step by factor 8 , and found a similar result ( see fig . [ fig1 ] ) . the dashed line represents the bar major axis , defined as the major axis of the most eccentric ellipse in an ellipse - fitting model of the stellar density . gas is concentrated on the leading side of the bar inside the cr radius ( 6 kpc ) , with a shift of several degrees.,width=207 ] , as a function of radius ( in units of the cr radius at @xmath21 myr ) . the curves labeled g show the effects of the gravitational torques ; they are mean values over periods of 100 myr around @xmath22 ( dotted line ) , 900 ( solid line ) , and 1000 myr ( dashed line ) . the curve labeled v shows the effects of viscous torques , that are negligible with respect to gravity torques . inside the cr radius , gas loses 1015 % of its momentum in one period . torques are positive between the cr and the outer lindblad resonance ( olr ) . because of the bar slowing - down , the cr and olr radii increase with time . the thin solid line shows the comparison with an sph simulation with the same initial conditions at @xmath21 myr . gravity torques are of the same order with this different code . , width=283 ] to confirm that the cmc growth is not the only phenomenon responsible for the bar dissolution , we have run a purely stellar simulation with the same initial conditions , and added an analytical cmc . this model is similar to that used by @xcite . the final cmc is a plummer sphere corresponding to the cmc we had fitted in the complete simulation ( see previous section ) . its radial scale - length is 90 pc , and its mass is grown up to @xmath15 m@xmath6 following the variations of m(100pc ) shown in fig . [ fig1 ] . in this model , the bar is not fully dissolved , but only partly weakened ( see fig . [ p2a ] ) . this is in agreement with the conclusion of @xcite that the bar can survive to the growth of such a cmc . we have also run a simulation in which we include the gas response , but suppress artificially the growth of the cmc : every gas particle that is found below radius 100 pc , with a velocity inferior to the circular velocity at this radius , is artificially suppressed , unless already present at @xmath23 . we do not suppress particles that are just crossing the central 100 pc with a large velocity , but only those that have definitively fallen in this region . as shown in fig . [ p2a ] , the bar is dissolved , and the evolution is very similar to that of the complete simulation . this result definitively proves that a phenomenon different from the cmc growth intervenes in the dissolution of the bar . this phenomenon is related to the gas response , since it is not observed in the purely stellar simulation ( fig . [ p2a ] ) . inside the cr , the bar has been shown to exert important gravitational torques on the ism . in the same time , the leading arms of gas exert torques on the stellar bar . the mean torque undergone by stars inside the bar is positive , but the real torques vary with radius and azimuth . this could be the reason why the bar is dissolved in the simulation where the cmc has been artificially suppressed : gravitational torques between the stellar bar and gaseous arms are still present in this model . to confirm the role of gravity torques , we have run a purely stellar simulation in which gravitational torques exerted by gas have been artificially added . to this aim , in the complete simulation , we compute the amplitude @xmath24 and phases @xmath25 of the tangential forces @xmath26 exerted by gas in the fourier decomposition @xmath27 where @xmath28 is computed in the frame of the bar . we record the mean values @xmath29 and @xmath30 between 0.8 and 1 gyr . then , in a purely stellar simulation , we analytically add the gravity torques given by @xmath31 where @xmath28 in still computed in the frame of the stellar bar . the amplitude of these torques is realistic , since @xmath29 and @xmath30 are given by the complete simulation , even if they do not follow any temporal evolution . we apply no torques before 800 myr and increase them progressively up to their final amplitude between 800 and 900 myr . in this model , that only" +"following classical protocols , quantum information protocols were initially formulated in terms of qubits that are manipulated unitarily in order to realize computational and communication tasks that may over perform their classical analogs @xcite . a different , but widespread approach to process quantum information involves using continuous variables ( cv ) @xcite . among the most important advances in the field of cv quantum information are the realization of quantum teleportation @xcite , as well as quantum cryptography protocols , which rely on states defined in a continuous variables representation @xcite . universality for manipulation of continuous variables quantum states was defined in ref . @xcite , and subsequently measurement based quantum computation was generalized from the discrete to the continuous realm @xcite . manipulating quantum information in continuous or discrete variables , on its usual circuit based formulation , involves the application of unitary gates . while such gates , in the discrete variable ( dv ) case can be expressed in terms of su(2 ) transformations , a general unitary in cv is composed by polynomials of conjugate operators with a continuous unbounded spectrum , such as position and momentum of a particle , or the electromagnetic field quadratures . even though , in the general case , a direct correspondence between universal operations in dv and cv has not been established , it was shown by gottesman , kitaev and preskill ( gkp ) in ref . @xcite , that such a correspondence exists for a family of states that , while being defined in cv , can be used to encode a qubit . moreover , the gkp encoding is also at the heart of the demonstration showing that fault - tolerant measurement - based quantum computation with cv cluster states is possible @xcite . a drawback of this encoding is that it relies on non - physical states . furthermore , physical states that are close to them are of extremely challenging experimental realization with optical field quadratures . in addition , the gkp encoding has the specific purpose of quantum computation applications . in the more general context of quantum mechanics , quantum computing presents the particular aspect of requiring measurements realized in the computational basis only . however , a number of important quantum mechanics or quantum information related tasks , such as bell inequalities violation @xcite , quantum state tomography @xcite , and fundamental tests of quantum mechanics @xcite , rather rely on the recovery of binary information through the measurement of different mutually unbiased bases . for these applications , one should build a formalism offering an analogy of pauli matrices in phase space not only from the operational point of view , as proposed in @xcite , but also from a measurable perspective . moreover , in order to build a complete toolbox to manipulate and measure discrete quantum information encoded in cv , one should also define how to perform rotations between different measurement bases . in the present article we create a framework to manipulate and measure binary quantum information encoded in continuous variables using the formalism of modular variables ( mv ) @xcite , which allows us to naturally identify discrete structures in continuous variable states . we further introduce adapted operations and observables which enable us to manipulate and readout the encoded discrete quantum information in terms of the corresponding cv logical states . our formulation shows that , if one is interested in recovering quantum information by measuring binary observables defined in cv , one can loosen the requirements imposed on the gkp states . our results have immediate experimental impact which we demonstrate by applying them to the transverse degrees of freedom of single photons . the structure of this paper is as follows . in the next section we give an introduction to the modular variables formalism , including the definition of the modular position and momentum operators and the resulting representation in terms of their common eigenstates . in sec . [ sec : qipframework ] we present our main results and show how to process discrete quantum information encoded in logical states expressed in the modular variables representation . further on , measurements of judiciously chosen modular variables are revealed to enable the readout the encoded discrete quantum information from the corresponding logical states . section [ sec : expproposal ] is devoted to the discussion of an experimental implementation of our ideas using the transverse degrees of freedom of single photons . finally , we conclude in sec . [ sec : conclusion ] . in the modular variables ( mv ) formalism , pairs of canonically conjugate observables are expressed in terms of modular and integer parts , respectively . in the case of the position and momentum operators this leads to @xcite : @xmath0 where @xmath1 , @xmath2 ( @xmath3 ) has integer eigenvalues , and @xmath4-\ell/4 $ ] ( @xmath5-\pi/\ell$ ] ) is the modular position ( momentum ) operator with eigenvalues in the interval @xmath6 ( @xmath7 ) ( see fig . [ fig_1 ] ( a ) and ( b ) ) . the center of the domains containing modular variables @xmath8 and @xmath9 is not of further importance and was chosen for future convenience . and @xmath10 , respectively , and of ( b ) the bounded spectra of the modular position and momentum operator . the red arrows indicate the displacements implementing the logical pauli operators @xmath11 , @xmath12 , and @xmath13 . ( c ) representation of the transverse distribution of a single photon created in a source s with a gaussian wave function which is transformed into a periodic diffraction pattern by passing through a grating with slit distance @xmath14 . in experiments , such a diffraction grating can be implemented easily using a spatial light modulator ( slm ) . ] the separation ( [ eq : defmodvar ] ) , in modular and integer parts , proved itself useful for the detection of entanglement in spatial interference patterns @xcite . furthermore , measurements of more general modular variables , namely periodic functions of position and momentum operators , have been used recently in proposals to test the clauser - horne - shimony - holt ( chsh ) @xcite , the leggett - garg @xcite and noncontextuality inequalities @xcite . later on , in sec . [ sec : readoutmodvar ] , we provide a general framework suitable to deal with measurements of such modular variables based on the above introduced modular representation . further on it can be shown that the modular position and momentum operators , @xmath15 and @xmath16 , commute @xcite : @xmath17=0 $ ] , which leads to the definition of the modular basis @xmath18 , consisting of the common eigenstates of the these two modular operators . consequently , in terms of the modular basis we can write @xmath19 , with a normalized wave function @xmath20 written in the modular representation . the modular representation is especially convenient when dealing with periodically symmetric states , _ e.g. _ the gkp states . as a matter of fact , using the definition of @xcite and the notation @xmath21 for the logical gkp qubits , one has simply that , in the modular basis : @xmath22 and @xmath23 , showing that the gkp states naturally emerge from the modular basis . a formal definition of the modular basis and related expressions , as well as an example of @xmath20 will be discussed in the next section . formally , the modular eigenstates @xmath24 can be defined as superposition of position or momentum eigenstates ( distinguished by subscripts @xmath25 and @xmath26 , respectively ) : @xmath27 fulfilling the completeness and the orthogonality relation : @xmath28 where @xmath29 and @xmath30 are dirac @xmath31 functions defined on the intervals @xmath32 and @xmath7 , respectively ( for brevity , we will omit in the following the superscripts @xmath33 and @xmath10 ) . inversely , we can define the position and momentum eigenstates in terms of the new modular eigenstates , as : @xmath34 hence , an arbitrary state in position representation @xmath35 transformed to the modular representation , reads : @xmath36 where @xmath37 is called modular wave function of @xmath38 . the same representation was introduced by j. zak in 1967 under the term @xmath39-representation @xcite . the modular variables representation is particularly well suited for wave functions that obey a certain periodicity in position or momentum space . for example , the state @xmath40 , representing a comb of @xmath31 functions with distance @xmath14 in position space , becomes in the modular representation @xmath41 , namely a single @xmath31 peak at the origin , if we set @xmath42 . this state , together with @xmath43 , are examples of the logical qubit state introduced in the gkp paper @xcite . instead , a more physical state can be obtained if we replace the @xmath31 comb by a comb of finitely squeezed gaussian spikes with width @xmath44 and a gaussian envelope with width @xmath45 ( see fig . [ fig_2](b ) ) . the wave function of such a state in position representation , reads : @xmath46 with a normalization factor @xmath47 . in the limit @xmath48 and @xmath49 , of a large envelope and sufficiently thin spikes , respectively , the latter can be approximated by @xmath50 . then , transforming eq . ( [ app : eq : approxgkp ] ) to the modular representation with the help of eq . ( [ app : eq : modvareigenstates ] ) , yields : @xmath51 where @xmath52 and @xmath42 . to obtain the above result we used that according to the poisson sum formula we have @xmath53 , and that in the limit of large gaussian envelopes we can approximate @xmath54 . a possible experimental platform allowing for the production of such periodic states is given by the transverse degrees of freedom of single photons , as illustrated in fig . [ fig_1](c ) . labeling quantum states using bounded continuous variables enables the definition of two disjoint sets of equal size for each one of the variables . such a splitting can be done in infinitely many ways , and in order to illustrate the principles of our ideas we discuss in detail the splitting of the domain of the variable @xmath8 into two subintervals @xmath55 and @xmath56 . as a consequence , we obtain a continuum of two - level systems spanned by the states @xmath57 in terms of which we can express a general state @xmath38 as : @xmath58 where @xmath59 with a complex function @xmath60 such that @xmath61 and two real functions , @xmath62 and @xmath63 , defined on @xmath64 . the mathematical expressions allowing to switch back and forth between the position and modular representation can be found in appendix [ app : logicalqubits ] . equation ( [ eq : generalstate ] ) can be seen as a weighted continuous superposition of pure qubit states @xmath65 for each subspace with fixed @xmath8 and @xmath9 . we stress that , so far , no approximation has been made , and state ( [ eq : generalstate ] ) is simply an alternative way of writing an arbitrary state expressed in a continuous basis . note that the choice of @xmath33 is also arbitrary , and modifying it for a given state modifies the definition of the functions appearing in ( [ eq : generalstate ] ) and ( [ eqn : continuousqubit ] ) . in the following , in order to encode discrete quantum information in cv states , we assume that @xmath66 and @xmath67 are constant functions such that eq . ( [ eq : generalstate ] ) becomes @xmath68 with logical qubit states , defined as : @xmath69 the logical qubit states ( [ eq : logical0 ] ) and ( [ eq : logical1 ] ) reflect a dichotomization of" +"particle tracking velocimetry ( ptv ) is a method to measure particle velocities @xcite with video camera recording . in experiments , the particles are small solid objects that can scatter enough light to be imaged separately . the velocity is calculated based on measured positions of particles . among the algorithms used to calculate velocities @xcite , the most common is simply to divide the difference in a particle s position in two consecutive video frames by the time interval between the frames @xcite . although ptv may allow tracking individual particles for many frames , for this algorithm it is only necessary to track for two frames . particle tracking velocimetry has been widely used for many years in topics in various fields , such as cell motion in biology @xcite , flow in granular materials @xcite , and kinetic temperature in dusty plasmas @xcite . small particles of solid matter can be added as tracers in a gas or liquid to study convection @xcite and turbulence @xcite in fluid mechanics . many dynamical quantities can be calculated using velocities measurements with ptv , for example velocity profiles in a shear flow @xcite , mean - square velocity fluctuations @xcite , velocity distribution functions @xcite , and velocity autocorrelation functions @xcite . some of these uses for ptv , such as velocity profiles , can also be accomplished with particle image velocimetry ( piv ) @xcite . compared to piv , ptv provides a measurement of velocity at the location of a particle , without requiring an averaging over a grid . recently , many experimenters using ptv have taken advantage of the abundance of high - speed cameras now offered for commercial sale . they may be unaware , however , that velocities determined using the ptv method can have errors that become more severe as the camera frame rate is increased . for example , we show that when determining kinetic temperature by calculating the mean - square velocity fluctuation for random motion , the result will have an exaggerated value that worsens at higher frame rates , due to one of the two kinds of errors studied here . we identify two kinds of velocity errors in ptv according to their source . one kind arises from acceleration of the particle during the time interval between measurements of its position . the other arises from errors in the position measurements themselves . while the former is made less severe by using a faster frame rate , the latter is actually made worse . therefore , a faster frame rate is not always best for ptv . an error arises from acceleration , whether due to a change in a particle s speed or its direction . this error occurs for all kinds of acceleration , for example a particle accelerating along a straight line , moving in a circle at a steady speed , or colliding with another particle . it is impossible to eliminate this error when the motion is unknown during the sampling interval between frames . the only information available in ptv are the particle positions determined at the times that a video image was recorded , i.e. , the video frames . the size of this error also depends on the algorithm for calculating velocity from data for the particle positions . the simplest and most common algorithm is to assume that the particle moves with zero acceleration between two consecutive frames . in this two - frame tracking method , the particle is assumed to move in a straight line at a steady speed between the positions in two frames . thus , the velocity is calculated simply as the difference in positions divided by the time interval between frames . using two position measurements @xmath0 , denoted by @xmath1 and @xmath2 separated by a time @xmath3 , the velocity at a time halfway between them is calculated as @xmath4 the camera s frame rate is @xmath5 if no frames are skipped . we use upper - case symbols like @xmath6 and @xmath7 to indicate quantities that are _ computed _ from the positions that are measured in a single frame . if the particle actually undergoes acceleration , for example if it has a curved trajectory , the simple algorithm of eq . ( [ 2-frame - velocity ] ) will obviously lead to errors in the velocity @xmath8 . alternatively , one could use an algorithm using more than two position measurements , which can sometimes better account for acceleration . a spline fit @xcite could reduce the error arising from acceleration , but it is more computationally expensive than two - frame tracking . to illustrate how errors in @xmath8 arise from acceleration and how these errors diminish with a higher frame rate , we consider the motion during a coulomb collision of a pair of identical electrically - charged particles . the largest acceleration in this case will occur when the particles are closest and the direction of motion is changing most rapidly . this highly curved portion of a trajectory can be approximated as a circular arc . this motivates us to choose uniform circular motion as a simple instructive example of velocity errors arising from acceleration , fig . suppose the particle s position is measured accurately at each frame , as indicated by the dots in fig . the simple two - frame tracking method , which assumes zero acceleration between measurements , will describe the motion as a polygon instead of the ideal circle . at a fast frame rate , the polygon has more sides and more closely approximates the ideal circle . another error in velocity arises from uncertainties in the particle positions from which the velocity is computed . particle positions are uncertain for at least two reasons : random noise in the camera sensor , and the finite size of pixels in the sensor . the latter leads to the phenomenon of pixel locking , where particles are wrongly identified as being located at favored positions such as the corner or middle of pixels . while it is possible to design an experiment to reduce these particle - position uncertainties @xcite , they can never be eliminated . suppose that all measured particle positions contain an uncertainty @xmath9 . we can use propagation of errors to estimate the uncertainty of the calculated velocity @xmath8 , arising from the uncertainties in the particle positions , for any given algorithm . choosing the algorithm used in the simple two - frame tracking method , eq . ( [ 2-frame - velocity ] ) , the uncertainty in the calculated velocity @xmath8 is @xmath10 importantly , this source of error becomes larger , not smaller , as the time interval between measurements @xmath3 is decreased . this is seen in eq . ( [ 2-frame - error ] ) , where the denominator diminishes with an increasing frame rate but the numerator does not vary with frame rate at all . thus , this error in velocity is @xmath11 . now that high frame - rate scientific cameras have become more easily available , this error in ptv probably occurs more commonly . to illustrate the combined effect of both types of errors , those due to acceleration and due to uncertainties in particle position , consider the sketch in fig . 1(b ) for a particle undergoing uniform circular motion . the uncertainty in particle positions is indicated in fig . 1(b ) by shading around the true positions . uncertainties in particle position cause the measurements to fall on the vertices of a polygon that is deformed , as compared to fig . 1(a ) without particle - position uncertainties . here we are interested primarily in errors in the velocity @xmath8 . in fig . 1(b ) , the length of the edges of the distorted polygon is an indication of velocity . comparing this thick irregular polygon to the original ideal circle , it is obvious that the velocity vector will have errors in its direction . the magnitude of the velocity will also have errors , as we discuss next . to demonstrate the combined effect of both sources of error in velocity , we present a simple simulation . a single particle is assumed to perform uniform circular motion with a radius @xmath12 and period @xmath13 . a time series of a particle s @xmath14 and @xmath15 coordinates is recorded at intervals @xmath3 . the simulation duration is 1000 circular periods . to simulate a measurement error , we add a random error chosen from a gaussian distribution to the true position . the probability of an error @xmath16 in this gaussian distribution is @xmath17 $ ] , and the same for the @xmath15 direction . we then calculate a time series @xmath18 , for the particle s velocity using the simple two - frame tracking method , eq . ( [ 2-frame - velocity ] ) . we use @xmath18 to calculate a time series for the kinetic energy , @xmath19 , where the mass @xmath20 will cancel in our final results . we average over the entire time series yielding @xmath21 , which we compare to the true kinetic energy @xmath22 in fig . 2 . we indicate the discrepancy between @xmath23 and @xmath22 as a single data point in fig . 2 . we vary the size of the position error @xmath24 and the sampling interval @xmath3 , yielding all the data points shown in fig . 2 . figure 2 shows the total error in @xmath23 due to both sources combined . for @xmath25 , fig . 2 also shows the error due to acceleration only , as indicated by circles . this error due to acceleration is always negative , and it is most severe for large @xmath3 , i.e. , for a slow frame rate . the total error in @xmath23 , however , can be either positive or negative , as shown by the other data points in fig . 2 . the total error is positive at small @xmath3 due mainly to the contribution of particle - position uncertainty , and it becomes negative at large @xmath3 due mainly to acceleration . in between , the total error in @xmath23 has its smallest magnitude , which for this simulation occurs at at a sampling interval of about 3% of the circular period , i.e. , @xmath26 . this observation suggests that it may be possible to choose a best frame rate to minimize errors , as we discuss next . in an actual experiment , one can not independently measure the two sources of error in velocity , or in quantities such as @xmath27 that are calculated from the velocity . in most physical systems , the true motion of one particle will differ from that of another particle , and their accelerations will vary with time , unlike the idealized circular motion simulation in fig . 2 . nevertheless , examining fig . 2 suggests a possible scheme for choosing a @xmath3 that has some promise to reduce the total error . the scheme we suggest for reducing the total error for a quantity ( such as @xmath23 ) computed from velocities is as follows . the experimenter can record motion at a high frame rate , and then analyze the data not only at the frame rate , but also at larger @xmath3 by skipping one frame to double @xmath28 , two frames to triple @xmath3 , and so on . plotting the average of ke vs. sampling interval @xmath3 will yield a graph similar to fig . if the graph exhibits a nearly _ flat spot _ at a particular value of @xmath3 , that value is a candidate to consider as the best value for computing ke . in sec . iii b" +"arguably , newton s problem of the body of minimal resistance is the original variational problem with convexity constraints . it consists of finding the shape of a solid that encounters the least resistance when moving through a fluid . this is equivalent to finding a convex function from a convex domain ( originally a disk ) in @xmath0 to @xmath1 that minimizes a certain funtional ( see section [ problem ] ) . original solution "" assumed radial symmetry . this turned out to be false , as shown by brock , ferone and kawohl in @xcite , which sparked new interest to the study of variational problems with convexity constraints . one can also find these kinds of problems in finance and economics . starting in 1978 with the seminal paper of mussa and rosen @xcite , the study of non - linear pricing as a means of market screening under adverse - selection has produced a considerable stream of contributions ( @xcite,@xcite,@xcite , ... ) . in models where goods are described by a single quality and the set of agents is differentiated by a single parameter , it is in general possible to find closed form solutions for the pricing schedule . this is , however , not the case when multidimensional consumption bundles and agent types are considered . although rochet and chon @xcite provided conditions for the existence of an optimal pricing rule and fully characterized the ways in which markets differentiate in a multidimensional setting , they also pointed out that it is only in very special cases that one can expect to find closed form solutions . the same holds true for models where the set of goods lies in an infinite - dimensional space , even when agent types are one - dimensional . this framework was first used , to our knowledge , by carlier , ekeland and touzi @xcite to price financial derivatives traded over - the - counter "" . it was then extended by horst and moreno @xcite to model the actions of a monopolist who has an initial risky position that she evaluates via a coherent risk measure , and who intends to transfer part of her risk to a set of heterogenous agents . in both cases the authors find that only very restrictive examples allow for explicit solutions . given that a great variety of problems , such as product lines design , optimal taxation , structured derivatives design , etc . can be studied through the scope of these models , there is a clear need for robust and efficient numerical methods that approximate their optimal pricing schedules . note that this also provides an approximation of the optimal products "" . most of the papers mentioned above eventually face solving a variational problem under convex constraints . this family of problems have lately been studied under different scopes . carlier and lachand - robert @xcite have studied the @xmath2 regularity of minimizers when the functional is elliptic and the admissible functions satisfy a dirichlet - type boundary condition . their results can be extended to of our examples . lachand - robert and pelletier @xcite characterize the extreme points of a functional depending only on @xmath3 over a set of convex functions with uniform convex bounds . in this paper we provide several variants of an algorithm , based on the idea of approximating a convex function by an affine envelope , to solve these types of problems . this deviates from previous work by chon and herv @xcite and carlier , lachand - robert and maury @xcite , where the authors use finite element methods . in the former case , a conformal ( interior ) method is used and a non - convergence result is given . as a consequence , the latter uses an exterior approximation method , which is indeed found to be convergent in the classical projection problem in @xmath4 lachand - robert and oudet present in @xcite and algorithm for minimizing functionals within convex bodies that shares some similarities to ours . for a particular problem , they start with an admissible polytope and iteratively modify the normals to the facets in order to find an approximate minimizer . we estimate the minimizers for several problems with known , closed form solutions as a means of comparing the output of our method to the true solutions . these are taken from @xcite and @xcite . finally , we provide an example in which we approximate the solution to a risk - minimization problem similar to the one presented in @xcite . this is still based on the affine - envelope idea , but requires some additional methodology , since it involves solving a non - standard variational problem . the remainder of this paper is organized as follows . in section [ problem ] we state our problem and provide some classical examples . our algorithm and a proof of its convergence are presented in section [ descriptionconvex ] . in section [ examples ] we show the solutions obtained via our algorithm to several problems found in the literature . since these problems share a common microeconomic motivation , we include a brief discussion on the latter . the examples include the well known rochet - chon "" problem , a one dimensional example from carlier , ekeland and touzi and the risk transfer case for a principal who offers call options with type - dependent strikes and evaluates her risk via the short fall "" of her position . this section is followed by our conclusions . finally a section devoted to technical results and all our codes are included in the appendix . the aim of this paper is to present a numerical algorithm to approximate the solutions of some variational problems subject to convexity constraints . a classical example of the latter is newton s problem of the body of minimal resistance , which , given @xmath5 a smooth subset of @xmath6 consists of minimizing @xmath7=\int_{\t}\frac{d\t}{1+|\nabla v|^2},\ ] ] over the set of convex functions @xmath8 we use the following notation throughout : * @xmath9 are convex and compact sets , * @xmath10 where @xmath11 is strictly convex and @xmath12 * @xmath13 * @xmath14:=\int_{\theta}l(\t , f(\t ) , \nabla f(\t))d\t.$ ] our objective is to ( numerically ) estimate the solution to @xmath15\ ] ] we assume @xmath11 is such that ( [ eq : problem ] ) has a unique solution ( see , for example , @xcite ) . given the properties of @xmath16 and @xmath17 we immediately have the following [ zerov ] assume @xmath18 solves @xmath19 then there is @xmath20 in @xmath5 such that @xmath21 let @xmath22 ( recall @xmath5 is compact)and define @xmath23 then @xmath24=\int_{\t}\u(\t)-\t\cdot\nabla\u(\t)+c(\nabla\u(\t))d\t = i[\v]-\|\t\|\v_0.\ ] ] this would contradict the hypothesis of @xmath18 being a minimizer of @xmath25 over @xmath26 unless @xmath27 it follows from proposition [ zerov ] that we can redefine @xmath26 to include only functions that have a root in @xmath28 this , together with the compactness of @xmath29 implies the following proposition , which we will use frequently . [ zerov2 ] there exists @xmath30 such that @xmath31 for all @xmath32 in @xmath33 it follows from proposition [ zerov2 ] and the restriction on the gradients that for each choice of function @xmath34 problem @xmath35 has a unique solution , since the functional @xmath25 will be strictly convex , lower semi continuous and the admissible set is bounded ( see @xcite ) . our algorithm will still work with more general @xmath16 s as long as one can prove that the family of feasible minimizers is uniformly bounded . from this point on , whenever we use supscripts we refer to vectors . for example @xmath36 on the other hand a subscript indicates a function to be evaluated over some closed , convex subset of @xmath37 of non - empty interior , ie , @xmath38 is a sequence of functions @xmath39 for some @xmath40 contained in @xmath41 we will consider @xmath42^n.$ ] to find an approximate solution to @xmath19 we proceed as follows : 1 . we discretize the domain @xmath5 in the following way : we partition it into @xmath43 which consists of @xmath44 equal cubes of volume @xmath45 the elements of @xmath46 will be denoted by @xmath47 @xmath48 now define @xmath49 as the set of centers of the @xmath50 s . the elements of @xmath49 will be denoted by @xmath51 the choice of a uniform partition is done for computational simplicity . we denote @xmath52 and associate such weight with @xmath53 3 . we associate to each element @xmath54 of @xmath49 a non - negative number @xmath55 and an n - dimensional vector @xmath56 the former represents the value of @xmath57 and the latter @xmath58 4 . we solve the ( non - linear ) program + @xmath59 + over the set of all vectors of the form @xmath60 and all matrices of the form @xmath61 such that : 1 . @xmath62 ( non - negativity ) , 2 . @xmath63 for @xmath64 ( feasibility ) , 3 . @xmath65 ( convexity ) . + if the problem in hand includes dirichlet boundary conditions these can be included here as linear constraints that the @xmath66 s corresponding to points on the boundary "" of @xmath49 must satisfy . let @xmath67 be the solution to @xmath68 we define @xmath69 where + @xmath70 6 . @xmath71 yields an approximation to the minimizer of @xmath72 [ rem : constraints ] the constraints of the non - linear program determine a convex set . [ rem : pwafine ] 4 ( c ) guarantees that @xmath73 is a supporting hyperplane of the convex hull of the points @xmath74 note that @xmath71 is a piecewise affine convex function . under the assumptions made on @xmath75 the problem @xmath76 has a unique solution . the function @xmath77 is strictly convex . it follows from proposition [ zerov2 ] that any acceptable vector - matrix pair @xmath78 must lie in @xmath79^k\times q^k,$ ] which together with remark [ rem : constraints ] implies @xmath76 consists of minimizing a strictly convex function over a compact and convex set . the result then follows from general theory . [ pr : conv ] there exists @xmath80 such that : 1 . the sequence @xmath81 generated by the @xmath76 s has a subsequence @xmath82that converges uniformly to @xmath83 2 . @xmath84=i[\overline{v}].$ ] the bounded ( proposition [ zerov2 ] ) family @xmath85 is uniformly equicontinuous , as it consists of convex functions with uniformly bounded subgradients . by the arzela - ascoli theorem we have that , passing to a subsequence if necessary , there is a non - negative and convex function @xmath86 such that @xmath87 by convexity @xmath88 almost everywhere ( lemma [ pr : vprime ] ) ; since @xmath89 belongs to the bounded set @xmath29 the integrands are dominated . therefore , by lebesgue dominated convergence we have @xmath90=i[\v ] .\ ] ] let @xmath91 be the maximizer of @xmath92 $ ] within @xmath93 our aim is to show that @xmath81 is a minimizing sequence of problem @xmath19 in other words that @xmath90=i\left[\u\right ] .\ ] ] we need the following let @xmath91 be such that @xmath94=i[\u].$ ] given the lattice @xmath95 we define : 1 . @xmath96 2 . @xmath97 3 . @xmath98 and 4 . @xmath99 notice that @xmath100 is also constructed as the convex envelope of a family of affine functions . the inequalities @xmath101 @xmath102\ge i[\u]\ ] ] follow from the definitions of @xmath103 @xmath71 and @xmath104 as does the following [ pr : conv ] let @xmath91 and @xmath105 be as above , then @xmath106 uniformly as @xmath107 [ pr : conv2 ] for each @xmath108 there exist @xmath109 and @xmath110 such that @xmath111\right|\le\epsilon_1(k)\ ] ] @xmath112\right|\le\epsilon_2(k)\ ] ] and @xmath113 as @xmath107 we will show ( [ eq" +"the yokonuma hecke algebras ( of type gl ) , denoted @xmath1 , have been used by j. juyumaya and s. lambropoulou to construct invariants for various types of links , in the same spirit as the construction of the homflypt polynomial from usual hecke algebras . we refer to @xcite and references therein . in particular , the algebras @xmath1 provide invariants for classical links and the natural question was to decide if these invariants were equivalent , or not , to the homflypt polynomial . this study culminated in the recent discovery @xcite that these invariants are actually topologically stronger than the homflypt polynomial ( _ i.e. _ they distinguish more links ) . in @xcite , another approach to study invariants coming from yokonuma hecke algebras was developed . the starting point was the fact that the algebra @xmath1 is isomorphic to a direct sum of matrix algebras with coefficients in tensor products of usual hecke algebras . this allowed an explicit construction of markov traces on @xmath2 from the known markov trace on hecke algebras ( on hecke algebras , there is a unique markov trace up to normalisation , and it gives the homflypt polynomial ) . in addition to its usefulness for the construction of markov traces , the approach via the isomorphism also helps to study the resulting invariants . indeed some properties of the invariants follow quite immediately from a precise understanding of the isomorphism ( see paragraph * 4 * below ) . independently of which approach is used , another ingredient was added in @xcite : a third parameter in the invariants . while the first two parameters come from the algebra @xmath1 , this third parameter @xmath3 has its origin in the framed braid group , and corresponds to a certain degree of freedom one has when going from the framed braid group to the algebra @xmath1 . more precisely , we can deform the standard surjective morphism from the framed braid group algebra to its quotient @xmath1 into a family of morphisms ( depending on @xmath3 ) respecting the braid relations and the markov conditions . another way of interpreting the parameter @xmath3 is that it modifies the quadratic relation satisfied by the generators of @xmath1 . its existence explains ( or is reflected in ) the fact that different presentations for @xmath1 were used before . lambropoulou invariants correspond to certain specialisations of this parameter @xmath3 , depending on the chosen presentation . so the parameter @xmath3 unifies every possible choices and yields more general invariants . it is indicated in ( * ? ? ? * remark 8.5 ) that changing the presentation seems to give a non - equivalent topological invariant . .2 cm * 2 . * in this paper , we consider the affine yokonuma hecke algebras ( of type gl ) , denoted @xmath4 . they were introduced in @xcite in connections with the representation theory and the jucys murphy elements of the classical yokonuma hecke algebras . our main goal here is to generalise for @xmath4 the whole approach to link invariants via the isomorphism theorem . the invariants are in general for links in the solid torus . the classical links are naturally contained in the solid torus links and , restricted to them , the obtained invariants correspond to the invariants obtained in @xcite from @xmath1 ( naturally seen as a subalgebra of @xmath4 ) . specialising the parameter @xmath3 , we identify the juyumaya lambropoulou invariants among them . for those invariants , we emphasize that we recover some known results @xcite by a different method and furthermore obtain some new results already in this particular case . we start with an isomorphism between the algebra @xmath4 and a direct sum of matrix algebras with coefficients in tensor products of affine hecke algebras . as done in @xcite , the isomorphism can be proved repeating the same arguments as for @xmath1 ( see @xcite where the proof for @xmath1 is presented , as a particular case of a more general result by g. lusztig @xcite ) . here we sketch a short different proof for @xmath4 using the known result for @xmath1 . we also prove the analogous theorem for the cyclotomic quotients of @xmath4 ( with ariki koike algebras replacing affine hecke algebras ) . useful for concrete use , the formulas for the generators are simple and given explicitly . concerning links , s. lambropoulou constructed invariants , analogues of the homflypt polynomial , for links in the solid torus from affine hecke algebras @xcite . then , it was explained in @xcite how to obtain invariants for those links from the algebras @xmath4 , unifying the methods of j. juyumaya and s. lambropoulou for @xmath1 and the construction of s. lambropoulou for affine hecke algebras . due to the recent results of @xcite , it is expected that the invariants obtained from @xmath4 are stronger than the ones obtained from affine hecke algebras . here we follow the alternative approach which uses the isomorphism to construct markov traces on the family of algebras @xmath5 . to sum up , the markov traces are constructed and can be calculated with the following steps : for an element of @xmath4 , apply first the isomorphic map to obtain an element of the direct sum of matrix algebras ; then , for each matrix , apply the usual trace which results in an element of a tensor product of affine hecke algebras ; finally apply a tensor product of markov traces on affine hecke algebras . our result consists in obtaining the compatibility conditions relating the markov traces appearing in different matrix algebras so that the preceding procedure eventually results in a genuine markov trace on @xmath5 . with the definition used here , for a given @xmath6 , the set of markov traces on @xmath5 forms a vector space . from the isomorphism , a set of distinguished markov traces appears naturally , which spans the set of all markov traces constructed here . thus , our study of markov traces ( and of invariants ) is reduced to the study of these basic "" markov traces ( and of the corresponding basic "" invariants ) . it turns out that these basic markov traces are indexed , for a given @xmath6 , by the non - empty subsets @xmath7 together with a choice , denoted formally by @xmath8 , of @xmath9 arbitrary markov traces on affine hecke algebras . we note that if we restrict to @xmath1 , the parameter @xmath8 disappears and the basic markov traces on @xmath2 are indexed , for a given @xmath6 , only by the non - empty subsets @xmath7 . this recovers a result of @xcite . .2 cm * 3 . * throughout the paper , we intended to give in details the connections between the two approaches , so that one would be able to pass easily from one to the other . this will allow in particular to specialise and translate all our results on the invariants to juyumaya lambropoulou invariants as well . roughly speaking , j. juyumaya and s. lambropoulou constructed invariants from @xmath1 in two steps @xcite . the same approach was followed in @xcite for @xmath4 . first a certain trace map , analogous to the ocneanu trace and satisfying a certain positive markov condition , was constructed . then a rescaling procedure was implemented , in order to produce genuine invariants . the rescaling procedure amounts to two things : a renormalisation of the generators and a renormalisation , depending on @xmath10 , of the trace . in the approach presented here , the first step is included from the beginning in a more general quadratic relation for the generators . the second step is already included in the definition of a markov trace , namely that it is a family , on @xmath10 , of trace maps satisfying the two markov conditions . as a consequence , to obtain invariants here , one directly applies the markov trace and no rescaling procedure is needed . for the comparison , our first task is to explain that juyumaya lambropoulou approach is equivalent to considering certain markov traces ( with the definition used here ) and to relate their variables with the parameters considered here . then we need to identify these markov traces in terms of the ones constructed via the isomorphism theorem . we obtain finally the explicit decomposition of these markov traces in terms of the basic markov traces indexed by @xmath7 and @xmath8 as above . in particular , for @xmath1 , this results in an explicit formula for the juyumaya lambropoulou invariants , as studied in @xcite , in terms of the basic invariants constructed here . we note that , in this case , the parameter @xmath8 is not present , and that juyumaya lambropoulou invariants are also parametrised , for a given @xmath6 , by non - empty subsets of @xmath11 . nevertheless , they do not coincide with the basic invariants and the comparison formula is not trivial ( see formulas ( [ compare2 ] ) in section [ sec - inv ] ) . in general , for @xmath4 , we obtain the expression of the invariants constructed in @xcite in terms of the basic invariants constructed here . concerning the third parameter @xmath3 , we recall that it was not present in the previous approach . actually , one need to specialise it to a certain value in our invariants to recover the juyumaya lambropoulou invariants . the two different presentations of @xmath1 that were used , as in @xcite , correspond to two different values of @xmath3 that we give explicitly . similarly , for @xmath4 , the invariants constructed in @xcite correspond to a certain specialisation of @xmath3 . .2 cm * 4 . * we conclude this introduction by describing the main properties obtained for the invariants . as explained before , they follow quite directly from a precise understanding of the isomorphism , and are expressed easily in terms of the basic invariants defined here . the main results are : * for @xmath6 and a non - empty subset @xmath7 , the corresponding invariants coincide with invariants corresponding to @xmath12 and the full set @xmath13 . therefore , we only have to consider the full sets @xmath11 for different @xmath6 . * further , given a number @xmath0 of connected components of a link , the invariants corresponding to @xmath11 are zero if @xmath14 . so , given @xmath0 , we only have to consider @xmath15 . moreover , with the comparison results explained in paragraph * 3 * , it is easy to deduce the similar properties for invariants obtained via juyumaya lambropoulou approach . the first item remains true as it is . the second item results in an explicit formula expressing , if @xmath14 , the invariants corresponding to @xmath11 in terms of the invariants corresponding to @xmath13 with @xmath16 . specialising @xmath17 to the appropriate values and restricting to classical links , we recover with the first item a result of @xcite . the second item in this case was proved only for @xmath18 also in @xcite . let @xmath19 and @xmath20 and @xmath21 be indeterminates . we work over the ring @xmath22 $ ] . the properties of the affine yokonuma hecke algebras recalled here can be found in @xcite . we use @xmath23 to denote the symmetric group on @xmath10 elements , and @xmath24 to denote the transposition @xmath25 . the affine yokonuma hecke algebra @xmath4 is generated by elements @xmath26 subject to the following defining relations ( [ def - aff1])([def - aff3 ] ) : @xmath27 g_ig_{i+1}g_i & = & g_{i+1}g_ig_{i+1 } & & \mbox{for $ i=1,\ldots , n-2$,}\\[0.1em ] x_1\,g_1x_1g_1 & = & g_1x_1g_1\,x_1 & & \\[0.1em ] x_1g_i" +"_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ since all men have imperfections + hanging bones inside their closets + that they trust no one will notice + absent tips on where to find them , + it will shock no one to learn that + even mighty hiawatha + famous chief of myth and legend + did some things he was not proud of + while a brother in a frat house + with a surly reputation + at an unknown little college + that his father helped to finance + so that he would get admitted + by the shores of gitche - gumee . + _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ far from loving fields and flowers + and the odor of the forest + as one reads in all the textbooks + hiawatha hated woodlands + and the animals one finds there , + whom he felt were always pooping , + and the plants the critters fed on + down in dank and swampy bottoms , + nearly perfect grounds for breeding + mighty hordes of great mosquitoes + who were always lean and hungry + and equipped with maps and radar + could detect where you were hiding + to inflict their bites and torments , + with their sneaky friends the black flies , + and their angry friends the green flies , + and the rocks ensnared by tree roots + that existed just to trip you + and would look improved as concrete + in foundation for a condo . + _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ thus the kindly , thoughtful image + of a noble man of nature + was a total fabrication + of a team of gifted spin docs + hired later for this purpose . + he was really just a tech nerd + who cared only for equations + and explaining all behavior + from the basic laws of physics + armed with only mathematics . + _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ hiawatha hated woodlands . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ thus , instead of lakes and forests , + hiawatha worshipped newton , + whose account of kepler s orbits + built on rules that galileo + had inferred from observation + plus the innocent assumption + of a law of gravitation + was a cosmic inspiration ; + and the brilliant sadie carnot , + whose insightful laws of heat flow + were deduced from working engines + absent microscopic theories ; + and the tragic ludwig boltzmann + who ascribed these laws to counting + but fell victim to depression + when he found no one believed him + and so killed himself by jumping + from an adriatic tower . + hiawatha saw that maxwell s + guessing missing laws of motion + needed for predicting light waves , + was the most transcendent genius , + as was albert einstein s insight + that the speed of light being constant + must mean time was not consistent + and that mass could be converted + into heat and vice versa . + just as clear was that the planck law + must imply debroglie s wavelength + was in force in any matter + so that sharp atomic spectra + and distinct atomic sizes + and the laws of bond formation + came from quantum interference . + _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ thus it was that hiawatha + came to be infatuated + with the laws of quantum matter , + which means liquid noble gases , + neutrons in a burnt - out star core , + or just rocks so cryogenic + they can not get any colder , + even with improved equipment , + like the state of too much sliding + on the ice of gitche - gumee + after dark in dead of winter + in an inexpensive loincloth . + pain and danger notwithstanding + quantum matter s simple structure + makes the eager physics tyro + quite unable to resist it . + hiawatha learned how atoms + self - assemble into crystals , + how electrons move right through them , + waving past the rigid ions + thereby making them metallic + in the absence of a bandgap + which arises from diffraction + and prevents the charge from moving + thereby causing insulation , + but by means of wires and doping + with atomic imperfections + when the bandgap is a small one + can be used to make transistors . + in addition to the basics + he learned how electric forces + like those seen in clinging woolens + cause some things to be magnetic + up until the lowly phonon , + quantum particle of sound wave , + storing heat the way that light does + mediates a strong attraction + that can pair up two electrons + causing them to move together + overcoming all resistance + and producing other magic + such as quantum oscillations . + _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ they were little more than con men . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ at this quite untimely moment + of his fragile student history + when his mind was most suggestive + our poor hapless hiawatha + had the terrible misfortune + to fall in with wicked people + who were little more than con men + and advanced in their profession + making theories of such matter + that were not at all deductive + but instead used mathematics + as a way to sow confusion + so that no one would discover + that their stuff was pure opinion + spiced with politics and chutzpah + so it looked somewhat like science + even though it really was nt . + _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ how they did this was ingenious + for it s not a simple matter + to produce concrete equations + that are absolutely hokum + and escape without detection + when they represent relations + of some quantities one measures + written down as abstract symbols + that could easily be tested . + what they did was deftly prey on + prejudicial ways of thinking + that their colleagues thought were reasoned + but were simply misconceptions , + generated during training + they had all received as students , + that the properties one wanted + were completely universal + so details did not matter . + but the data did not say this + and , moreover , had they done so + there would have been no good reason + to think any more about it . + so , while everyone was watching , + they swapped in some new equations + that they said would solve the problem + on account of being much simpler + but in fact described a system + very different from the first one + and , moreover , was unstable , + balanced at competing phases , + so that nobody could solve it + thus betraying the deception . + _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ adding to the dazzling brilliance + of this coldly thought - out swindle + they declared it _ fundamental _ + so that all the strange creations + made by people trying to solve it + and quite clearly not succeeding + proved it was a fount of deepness + one should struggle to unravel + even if it took a lifetime . + as a nifty added bonus + any hint you dropped in public + that it might have no solution + simply meant you were nt a genius , + told the world that you were stupid , + that you were a hopeless failure + who should not command a pencil . + no one wanted to admit this + so they d cover up their failure + and pretend that they had solved it + even though they clearly had nt . + this succeeded , for the most part , + but in one respect it did nt , + for their desperate need to publish + and thereby maintain their funding + caused a massive flood of papers , + each quite different from the others , + to descend upon the journals + and to overwhelm and clog them . + this would have been very funny + had it not been so pathetic . + _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _" +"we are entering a golden age for milky way astronomy . the european space agency ( esa ) s @xmath4 mission @xcite , which launched @xmath5 december 2013 , has recently published its first data release @xcite , giving us a new window on our galaxy , and in particular , the solar neighbourhood . the primary astrometric catalogue in _ gaia_-dr1 is the tycho-@xmath4 astrometric solution ( tgas , * ? ? ? * ; * ? ? ? * ) , which uses data from the @xmath6 - 2 catalogue @xcite , to provide a baseline of approximately 30 years upon which to calculate astrometric values for stars in common between @xmath6 - 2 and @xmath4 . there is also significant overlap between stars in the tgas catalogue and stars observed by the radial velocity experiment ( rave , e.g. * ? ? ? * ) , enabling the full 6-dimensional phase space information to be known for over 200,000 stars in the solar neighbourhood . this enables us to explore local dynamics in unprecedented detail . many aspects of the structure and dynamics of the milky way are difficult to measure , owing to our position within the galaxy , and complex observational selection effects such as dust extinction . thus , many of the fundamental parameters of the milky way carry significant uncertainty . one such parameter is the velocity at which the sun rotates around the galaxy , for which plausible values span the range from @xmath7 to @xmath8 ( e.g. , * ? ? ? * ; * ? ? ? * ) and are dependent on the data set and technique used . @xcite proposed that the rotation velocity of the sun may be measured by searching for a lack of stars exhibiting zero angular momentum . stars with zero angular momenta are expected to plunge into the galactic nucleus and subsequently experience scattering onto chaotic orbits with a high scale height , henceforth spending the majority of their time in the stellar halo @xcite . if stars with very low angular momentum are indeed not present in the solar neighbourhood , the tail of the tangential velocity distribution will exhibit a dip centred at the solar reflex value . this method for measuring the solar velocity is attractive because it should depend only on the existence of low angular momentum orbits within the milky way s disk . with 6-dimensional phase space measurements for nearby stars it becomes possible to calculate the tangential velocity distribution with respect to the sun , and thus we can test this prediction by searching for a dearth of stars around the assumed value of the negative of the solar motion . this paper is constructed as follows . in section [ sec : observation ] we discuss our treatment of the data , and the feature observed in the resulting velocity distribution . in section [ sec : modeling ] we present simulated models which can explain the feature and make predictions for the size and shape of the observed feature . in section [ sec : detection ] we fit our model to the data and present our measurement of @xmath9 . finally , in section [ sec : conclusion ] we discuss the implications of the detection and look forward to future measurements . we cross match the tgas catalogue @xcite and the rave dr5 data @xcite to add rave line - of - sight velocities to the tgas astrometric data . where available , we employ the rave spectrophotometric distance estimates , because estimating distances from the tgas parallax is non - trivial ( e.g. * ? ? ? however , where no rave distance is available , we naively invert the tgas parallax @xmath10 to obtain distance estimates for the remaining stars , removing any star with @xmath11 to avoid large distance uncertainties . the resulting sample consists of 216,201 stars with 6-dimensional phase - space measurements . then , we convert the velocities from equatorial coordinates to standard galactic cartesian coordinates centred on the sun , @xmath12 , with @xmath13 positive in the direction of the galactic centre ( toward galactic longitude @xmath14 ) and @xmath15 positive in the direction of galactic rotation ( toward @xmath16 ) , both measured with respect to the sun . ( img ) for stars observed to be within 700 pc of the sun . the sun s velocity has @xmath17 . the low - velocity tail of the distribution displays a clear dip in the range between @xmath18 and @xmath19 that is marked with an arrow and overlaid with an exponential for illustration . * bottom panel : * normalised kde of the above distribution clearly showing the dip.,title=""fig:"",scaledwidth=49.0% ] ; ; ; ; figure [ fig : disp ] shows the distribution of @xmath15 for stars within 700 pc as a histogram ( top panel ) and with kernel density estimation ( e.g. , @xcite ; bottom panel ) using a gaussian kernel with bandwidth 9 . we chose 700 pc as a balance between quantity of stars , and quality of data . there is a clear underdensity of stars in the approximate region of @xmath18 to @xmath19 , marked with an arrow ( see also the top panel of figure [ fig : fit ] ) . although there are only @xmath20 stars per bin at these velocities , this dip in the distribution is clear across @xmath21 bins . we defer a discussion of the significance of the dip until section 4 where we fit a model for the dip obtained from simulations . furthermore , in the two - dimensional distribution of @xmath22 , we find a lack of stars with both positive @xmath13 and large negative @xmath15 . that is , there are very few stars observed on disk orbits ( @xmath23 and @xmath24 ) plunging towards the galactic centre . quantitatively , there are 24 stars with @xmath25 in the range @xmath26 and 34 stars with @xmath27 . these rates are inconsistent with being drawn from the same distribution at @xmath28 . our analysis does not explicitly take into account the uncertainties on the distance or velocity estimates . propagating the uncertainties through the coordinate transformation results in an uncertainty of approximately 10 per cent on the measured cartesian velocities . at the @xmath15 range of the dip , this corresponds to uncertainties of approximately @xmath29 . because the width of the dip feature appears to be approximately @xmath30 we can neglect the uncertainties in this initial investigation . a likely explanation for these missing stars , as mentioned in section [ sec : intro ] , is that they have been scattered onto chaotic orbits with larger scale heights by interaction with the galactic nucleus . this is expected for disk stars with approximately zero angular momentum as discussed in @xcite . thus , as these stars would then spend the majority of their orbits far from the galactic plane , it is very unlikely that they would be observed in the solar neighbourhood at any one given time . in galactocentric coordinates , such stars have tangential velocities @xmath31 , corresponding to heliocentric @xmath32 , minus the solar tangential velocity measured in the galactocentric frame . @xcite performed an analysis of this effect and matched models of the dip constructed within an analytic potential to data from local stellar catalogues complete to 25 pc . they found the dip to be centred at @xmath33 , with a depth greater than 80% . however , they are careful to note that there are only 18 stars with @xmath34 and that a larger sample will improve the measurement . the tgas+rave sample used here has 374 stars with @xmath35 , allowing far greater confidence in our subsequent analysis of the feature . firstly , we make a fresh prediction of the feature which we expect to observe in the tgas data , similar to @xcite , but with an updated potential , and drawing the distribution of initial positions , radial , and vertical velocities from the observed data to tailor the prediction to the current data set . it is challenging to construct an @xmath36-body model with sufficient resolution to predict the high velocity tail in the local neighbourhood . thus , we integrate test particles in a milky - way like potential , and observe the resulting orbits . for our milky - way potential we use ` mwpotential2014 ` from ` galpy ` @xcite . ` mwpotential2014 ` consists of a power - law spherical bulge potential with an exponential cut - off , a miyamoto - nagai disk potential , and a nfw halo potential . the parameters of this potential have been fit to a wide variety of dynamical data in the milky way ; the full parameters are given in @xcite . to model the hard galactic nucleus that is not included in ` mwpotential2014 ` , we also include a plummer potential @xmath37 , where @xmath38 @xmath39 and @xmath40 pc . note that we do not include a non - axisymmetric bar potential in this initial work , which may affect the feature slightly . this should be considered when applying this technique to future @xmath4 data releases . ( img ) exhibiting chaotic behaviour . * middle panel : * example orbit of a particle with @xmath41 . * bottom panel : * example orbit of a particle with @xmath42 . orbits that penetrate the galactic nucleus are scattered onto non - disk orbits that spend little time in the solar neighborhood.,title=""fig:"",scaledwidth=49.0% ] ; ; ; ; ; ; figure [ fig : orbits ] displays the orbits of three stars integrated for 2 gyr . the top panel shows the orbit of a star with @xmath43 , which exhibits chaotic behaviour upon interaction with the galactic nucleus . the middle and lower panels show the orbits of stars with @xmath41 and @xmath42 , respectively , which exhibit well - behaved disk orbits . the star with no angular momentum spends little of its orbital period near the galactic plane , whereas the two stars which do not approach the nucleus remain within a few hundred parsecs of the plane . without an ab - initio model for the disc , it is difficult to predict how many stars are expected to be missing near zero angular momentum and what the exact profile of the dip should be . therefore , we use the fraction of the orbital period of the test - particle stars that they spend near the mid - plane of the disc as a proxy for whether it has been scattered to a much higher scale height . we integrate many orbits with positions , radial , and vertical velocities drawn from the tgas+rave sample and from an initial , uniform distribution in @xmath15 covering the low - velocity tail . we then re - weight the stars using the fraction of time they spend near the plane and construct the dip profile by dividing this weighted , final @xmath15 distribution by the initial , uniform distribution . figure [ fig : dips ] shows the computed dip profiles for velocities within @xmath44 of @xmath45 . the top panel shows the results of 7 simulations with reflex solar motion , @xmath9 , of @xmath46 , @xmath47 , @xmath48 , @xmath49 , @xmath50 , @xmath51 and @xmath52 , assuming @xmath53 pc as the criterium ` close to the disc plane ' . it is clear that the shape and depth of the overlaid distributions are very similar and thus not dependent on the value of the solar motion . the dip profile is not entirely symmetric around zero @xmath54 , because the spatial distribution of the tgas+rave sample is asymmetric around the sun . the middle panel of figure [ fig : dips ] displays the" +"the merger of two white dwarfs has received considerable interest during the last years because it is thought to be at the origin of several interesting astrophysical phenomena . in particular , the coalescence of two white dwarfs is one of the possible scenarios the so - called double - degenerate scenario to account for type ia supernova outbursts ( webbink 1984 ; iben & tutukov 1984 ) . moreover , it is thought as well that the merger of two degenerate cores could lead to the formation of magnetars ( king , pringle & wickramasinghe 2001 ) . also , three hot and massive white dwarfs members of the galactic halo could be the result of the coalescence of a double white - dwarf binary system ( schmidt et al . 1992 ; segretain et al . 1997 ) . additionally , hydrogen - deficient carbon and r corona borealis stars ( izzard et al . 2007 ; clayton et al . 2007 ; longland et al . 2011 ) are thought to be the consequence of the merging of two white dwarfs . also , the large metal abundances found around some hydrogen - rich white dwarfs with dusty disks around them could also be explained by the merger of a carbon - oxygen and a helium white dwarf ( garca berro et al . last but not least , the phase previous to the coalescence of a double white - dwarf close binary system has been shown to be a powerful source of gravitational waves that would be eventually detectable by lisa ( lorn aguilar et al . 2005 ) . here we show that the merger of two degenerate cores can also explain the presence of very high magnetic fields in some white dwarfs a result previously anticipated by wickramasinghe & ferrario ( 2000 ) but not yet quantitatively proved . high - field magnetic white dwarfs have magnetic fields in excess of 10@xmath0 g and up to 10@xmath1 g ( schmidt et al . surprisingly , very few belong to a non - interacting binary system ( kawka et al . 2007 ) , and moreover they are more massive than average ( silvestri et al . 2007 ) . one possibility is that these white dwarfs descend from single stars , so the magnetic field is a fossil of previous evolution ( angel et al . 1981 ) . however , this scenario can not explain why these stars are massive , and why they are not found in non - interacting binary systems . recently , it has been suggested ( tout et al . 2008 ) that strong magnetic fields are produced during a common envelope episode in a close binary system in which one of the components is degenerate . during this phase , spiral - in of the secondary induces differential rotation in the extended convective envelope , resulting in a stellar dynamo which produces the magnetic field however , the magnetic field produced in this way does not penetrate in the white dwarf , and decays rapidly when the common envelope is ejected ( potter & tout 2010 ) . in this paper we show that the hot , differentially rotating , convective corona resulting from the merger of two degenerate cores produces strong magnetic fields , which are confined to the outer layers of the resulting remnant , and which do not decay for very long timescales . the paper is organized as follows . in sect . [ dynamo ] we explain the precise mechanism that produces the required magnetic fields , and we show that these fields are confined the outer layers of the remnant of the coalescence and do not decay for very long timescales . sect . [ mc ] is devoted to analyze if our model can account for the number of high - field magnetic white dwarfs in the solar neighborhood , while in sect . [ conc ] we summarize our findings and we present our conclusions . the merger of two degenerate cores is the final destiny of the evolution of a sizable fraction of binary systems . three - dimensional simulations of the merger process ( guerrero et al . 2004 ; yoon et al . 2007 ; aguilar et al . 2009 ) indicate that the remnant of the coalescence of two white dwarfs consists of a central white dwarf which contains all the mass of the primary . on top of it a hot corona , which is made of approximately half of the mass of the disrupted secondary , can be found . finally , surrounding this compact remnant a rapidly rotating keplerian disk is formed , containing nearly all the mass of the secondary which has not been incorporated to the hot corona . according to these calculations little mass ( @xmath2 ) is ejected from the system during the merger . the structure of the remnant of the coalescence is illustrated in fig . 1 . the existing simulations show that the temperature gradient in the hot corona is high , and consequently the corona is convective . we computed the boundaries of the convective region using the schwarzschild criterion , and we found that the inner and outer edges of the convective region are located at radii @xmath3 , and @xmath4 , respectively , and that the total mass inside this region is @xmath5 ( see fig . 1 ) . moreover , this region rotates differentially , and is prone to magneto - rotational instability . assuming energy equipartition , the resulting @xmath6 dynamo produces a magnetic field @xmath7 . for the typical values found in the simulations of lorn aguilar et al . ( 2009 ) , the magnetic field amounts to @xmath8 g. thus , the energy available in the convective corona is sufficiently large to produce strong magnetic fields . we note that even in the case in which only 0.1% of the total energy of the convective shell is invested in magnetic energy the fields produced in this way are of the order of @xmath9 g , a value typical of high - field magnetic white dwarfs . we also note that there are very few white dwarfs with magnetic fields larger than @xmath10 g , and that when these fields are observed , these are confined to spots on their surfaces . for this mechanism to be efficient at producing the observed magnetic fields , the dynamo must work for several convective turnovers before the energy of the hot corona is radiated away . the temperature of the corona is so high that is preferentially cooled by neutrino emission . the neutrino luminosity of the corona is @xmath11 , while the total thermal energy of the non - degenerate material in the corona is @xmath12 erg . hence , the convective shell lasts for @xmath13 yr . the convective turnover timescale is @xmath14 , where @xmath15 cm is the pressure scale height and @xmath16 cm / s is the convective velocity . thus , @xmath17 s , and during the lifetime of the hot corona the number of convective cycles is sufficiently large . consequently , the @xmath6 mechanism is able to produce a strong magnetic field . we also note that if the duration of the convective shell is substantially smaller than that estimated here , large magnetic fields can still be produced . specifically , even assuming durations @xmath18 times smaller than that previously estimated , the number of convective cycles would still be enough to produce magnetic fields comparable to those observationally found in high - field magnetic white dwarfs . we thus conclude that the stellar dynamos produced in the aftermath of the merger of two degenerate cores can produce magnetic fields of the order of @xmath9 g. from now on we adopt this value ( typical of high - field magnetic white dwarfs ) as a fiducial value for the rest of the calculations . [ corona ] once the magnetic field is established we need to know if it can diffuse outwards , to the surrounding disk , or inwards , to the degenerate primary . to this end we solved the diffusion equation ( jackson 1998 ; wendell et al . 1987 ) : @xmath19 being @xmath20 the magnetic conductivity , for which we used the most up - to - date prescription ( cassisi et al . 2007 ) , while the rest of the symbols have their usual meaning . we first integrated the diffusion equation for the surrounding disk using cylindrical coordinates , adopting the velocity field and density and temperature profiles resulting from our sph simulations ( lorn aguilar et al . the initial condition adopted here is @xmath21 , while we also imposed the boundary condition @xmath22 at the outer edge of the disk . we used a crank - nicolson integration scheme with variable coefficients ( dautray & lions 2000 ) which turns out to be stable . we found that the timescale for diffusion of the magnetic field across the disk is @xmath23 yr . we did the same calculation , this time using spherical coordinates , to estimate the penetration of the magnetic field in the dense , degenerate primary . the use of spherical coordinates is perfectly justified because the departures of the compact primary from sphericity are very small . for this calculation we followed the procedure outlined in wendell et al . ( 1987 ) . in this case the electrical conductivity is totally dominated by degenerate electrons , and depends on the adopted temperature of the isothermal white dwarf . if a temperature @xmath24 k is taken ( lorn aguilar et al . 2009 ) the diffusion timescale turns out to be @xmath25 yr . since this timescale depends on the adopted initial temperature we computed , using an up - to - date stellar evolutionary code ( renedo et al . 2010 ) , a cooling sequence for a white dwarf of the mass , @xmath26 , and chemical composition of the remnant , a carbon - oxygen core . the time to cool from @xmath27 k to a value typical of field white dwarfs ( say @xmath28 k ) is very short , @xmath29 yr . hence , we can safely assume that as the white dwarf cools , the rapid increase of the electrical conductivity does not allow the magnetic field to penetrate in the degenerate core of the primary , and remains confined to the surface layers . our model naturally predicts that the masses of high - field magnetic white dwarfs should be larger than average and that they should be observed as single white dwarfs , as observationally found see , for instance , valyavin & fabrika ( 1999 ) . however , high - field magnetic white dwarfs are generally found to be slow rotators ( wickramasinghe & ferrario 2000 ) . this apparent contradiction of the model can be easily solved . if the rotation and magnetic axes are misaligned , magneto - dipole radiation rapidly spins down the white dwarf see , however , timokhin ( 2006 ) and spitkovsky ( 2006 ) , where the time evolution of magnetospheres for axisymmetric and oblique rotators is described in detail . the evolution of the rotational velocity when both axes are misaligned ( benacquista et al . 2003 ) is : @xmath30 where @xmath31 is the moment of inertia of the white dwarf , @xmath32 is the angle between the magnetic and rotation axes and @xmath33 . thus , the spin - down timescale is simply @xmath34 . adopting the values resulting from our sph simulations ( lorn aguilar et al . 2009 ) we obtain @xmath35 yr , for a field strength @xmath36 g. hence , if both axes are perfectly aligned the remnant of the coalescence will be" +"in this paper we study the optimal stopping problems in an uncertain environment . the classical solution to the optimal stopping problems based on the dynamic programming principle assumes that there is a unique subjective prior distribution driving the reward process . however , for example , in incomplete financial markets , we have to deal with multiple equivalent martingale measures not being sure which one underlies the market . in fact under the presence of the multiple possible distributions , a solution of the optimal stopping problem by maximization with respect to some subjective prior can not be reliable . instead , it is reasonable to view the multitude of possible distributions as a kind of _ model uncertainty risk _ which should be taken into account while formulating an optimal stopping problem . here one may draw on concepts from the theory of risk measures . as the established generic notion for static risk assessment at present time @xmath14 , convex risk measures are specific functionals @xmath15 on vector spaces of random variables viewed as financial risks ( see @xcite and @xcite ) . they typically have the following type of robust representation @xmath16 - \gamma_{0}({\mathrm{q}})\bigr\},\end{aligned}\ ] ] where @xmath17 denotes the set of probability measures which are absolutely continuous w.r.t . a given reference probability measure @xmath18 and @xmath19 is some penalty function ( see e.g. @xcite and @xcite ) . in this way , model uncertainty is incorporated , as no specific probability measure is assumed . moreover , the penalty function scales the plausibility of models . turning over from static to dynamic risk assessment , convex risk measures have been extended to the concept of conditional convex risk measures @xmath20 at a future time @xmath21 which are specific functions on the space of financial risks with random outcomes ( see @xcite , @xcite and @xcite ) . under some regularity conditions , they have a robust representation of the form ( see e.g. @xcite , @xcite or ( * ? ? ? 11 ) ) @xmath22-\gamma_t({\mathrm{q}})\bigr\},\end{aligned}\ ] ] where @xmath23 is a ( random ) penalty function and @xmath24 consists of all @xmath25 with @xmath26 as in ( [ rhostatic ] ) , the robust representation mirrors the model uncertainty , but now at a future time @xmath8 in recent years the optimal stopping with families @xmath27}$ ] of conditional convex risk measures was subject of several studies . for example , the works @xcite and @xcite are settled within a time - discrete framework , where in addition the latter one provides some dual representations extending the well - known ones from the classical optimal stopping . optimal stopping in continuous time was considered in @xcite , @xcite , @xcite , @xcite . all these contributions restrict their analysis to the families @xmath27}$ ] satisfying the property of time consistency , sometimes also called recursiveness , defined to mean @xmath28 hence the results of the above papers can not be , for example , used to solve optimal stopping problems under such very popular convex risk measure as average value at risk . the only paper which tackled the case of non time - consistent families of conditional convex risk measures so far is @xcite , where the authors considered the so - called distorted mean payoff functionals . however , the analysis of @xcite excludes the case of average value at risk as well . moreover , the class of processes to be stopped is limited to the functions of a one - dimensional geometric brownian motion . the main probabilistic tool used in @xcite is the skorokhod embedding . in this paper we consider a rather general class of conditional convex risk measures having representation with @xmath29 $ ] for some lower semicontinuous convex mapping @xmath1.$ ] the related class of risk measures @xmath15 known as the class of _ divergence risk measures _ or _ optimized certainty equivalents _ was first introduced in @xcite , @xcite . any divergence risk measure has the representation @xmath30\ ] ] with @xmath31,\ , y\mapsto\sup_{x\geq 0}(xy - \phi(x)).\ ] ] ( cf . @xcite , @xcite , @xcite , or appendix [ appendixaa ] ) . here we study the problem of optimally stopping the reward process @xmath32 where @xmath9}$ ] is an adapted nonnegative , right - continuous stochastic process with @xmath33 } y_t$ ] satisfying some suitable integrability condition . we do not assume any time - consistency for the family @xmath34 and basically impose no further restrictions on @xmath35 . our main result is the representation @xmath36\right\},\end{aligned}\ ] ] which allows one to apply the well known methods from the theory of ordinary optimal stopping problems . in particular , we derive the so - called additive dual representation of the form : @xmath37}\big(\phi^{*}(x+ y_{t } ) - x - m_{t}\big)\right],\end{aligned}\ ] ] where @xmath38 is the class of adapted martingales vanishing at time 0 . this dual representation generalizes the well - known dual representation of rogers , @xcite . the representation together with can be used to efficiently construct lower and upper bounds for the optimal value by monte carlo . the paper is organised as follows . in section [ setup ] we introduce notation and set up the optimal stopping problem . the main results are presented in section [ main_results ] where in particular a criterion ensuring the existence of a saddle - point in is formulated . section [ discussion ] contains some discussion on the main results and on their relation to the previous literature . a monte carlo algorithm for computing lower and upper bounds for the value function is formulated in section [ mc ] , where also an example of optimal stopping under average value at risk is numerically analized . the crucial idea to derive representation is to consider the optimal stopping problem @xmath39 where @xmath40 denotes the set of all randomized stopping times on @xmath11.$ ] it will be studied in section [ optimalrandomizedstoppingtimes ] , where in particular it will turn out that this optimal stopping problem has the same optimal value as the originial one . finally , the proofs are collected in section [ proofs ] . let @xmath41 be a probability space and denote by @xmath42 the class of all finitely - valued random variables ( modulo the @xmath4-a.s . equivalence ) . let @xmath43 be a young function , i.e. , a left - continuous , nondecreasing convex function @xmath44 $ ] such that @xmath45 and @xmath46 . the orlicz space associated with @xmath43 is defined as @xmath47<\infty~ \mbox { for some $ c>0$}\big\}.\ ] ] it is a banach space when endowed with the luxemburg norm @xmath48\leq 1\right\}.\ ] ] the orlicz heart is @xmath49<\infty~ \mbox { for all $ c>0$}\big\}.\ ] ] for example , if @xmath50 for some @xmath51 then @xmath52 is the usual @xmath53space . in this case @xmath54 where @xmath55 stands for @xmath53norm . if @xmath43 takes the value @xmath56 , then @xmath57 and @xmath58 is defined to consist of all @xmath59essentially bounded random variables . by jensen inequality , we always have @xmath60 in the case of finite @xmath61 we see that @xmath62 is a linear subspace of @xmath63 which is dense w.r.t . @xmath64 ( see theorem 2.1.14 in @xcite ) . let @xmath65 and let @xmath66 be a filtered probability space , where @xmath67}$ ] is a right - continuous filtration with @xmath68 containing only the sets with probability @xmath14 or @xmath69 as well as all the null sets of @xmath70 . furthermore , consider a lower semicontinuous convex mapping @xmath1 $ ] satisfying @xmath71 for some @xmath72 @xmath73 and @xmath74 its fenchel - legendre transform @xmath75 is a finite nondecreasing convex function whose restriction @xmath76 to @xmath77 is a finite young function ( cf . lemma [ optimizedcertaintyequivalent ] in appendix [ appendixaa ] ) . we shall use @xmath78 to denote the orlicz heart w.r.t . @xmath79 then we can define a conditional convex risk measure @xmath80}$ ] via @xmath81- { \mathbb{e}}\left[\left.\phi\left(\frac{d{\mathrm{q}}}{d{\mathrm{p}}}\right)\right |{\mathcal f}_{t}\right]\right)\ ] ] for all @xmath82 where @xmath83 denotes the set of all probability measures @xmath3 which are absolutely continuous w.r.t . @xmath4 such that @xmath84 is @xmath59integrable and @xmath5 on @xmath6 note that @xmath85 is @xmath59integrable for every @xmath86 and any @xmath87 due to the young s inequality . consider now a right - continuous nonnegative stochastic process @xmath88 adapted to @xmath89 furthermore , let @xmath10 contain all finite stoping times @xmath90 w.r.t . @xmath89 the main object of our study is the following optimal stopping problem @xmath91 if we set @xmath92 for @xmath93 and @xmath94 otherwise , we end up with the classical stopping problem @xmath95.\ ] ] it is well known that the optimal value of the problem may be viewed as a risk neutral price of the american option with the discounted payoff @xmath96}$ ] at time @xmath97 however , in face of incompleteness , it seems to be not appropriate to assume the uniqueness of the risk neutral measure . instead , the uncertainty about the stochastic process driving the payoff @xmath98 should be taken into account . considering the optimal value of the problem ( [ stoppproblem ] ) as an alternative pricing rule , model uncertainty risk is incorporated by taking the supremum over @xmath83 where the penalty function is used to assess the plausibility of possible models . the more plausible is the model , the lower is the value of the penalty function . let us illustrate our setup in the case of the so called average value at risk risk measure . the average value at risk risk measure at level @xmath990,1]$ ] is defined as the following functional : @xmath100 where @xmath101 and @xmath102 denotes the left - continuous quantile function of the distribution function @xmath103 of @xmath104 defined by @xmath105 for @xmath990,1[$ ] . note that @xmath106 $ ] for any @xmath107 moreover , it is well known that @xmath108\quad\mbox{for}\ , x\in l^{1},\ ] ] where @xmath109 is the young function defined by @xmath110 for @xmath111 and @xmath112 otherwise ( cf . * theorem 4.52 ) and @xcite ) . observe that the set @xmath113 consists of all probability measures on @xmath70 with @xmath114a.s .. hence the optimal stopping problem ( [ stoppproblem ] ) reads as follows @xmath115 the family @xmath116}$ ] of conditional convex risk measure associated with @xmath109 is also known as the conditional av@r @xmath117}$ ] at level @xmath118 ( cf . * definition 11.8 ) ) . [ entropicriskmeasure ] let us consider , for any @xmath119 the continuous convex mapping @xmath120 } : [ 0,\infty[\rightarrow{\mathbb{r}}$ ] defined by @xmath120}(x ) = ( x\ln(x ) - x + 1)/\gamma$ ] for @xmath121 and @xmath120}(0 ) = 1/\gamma.$ ] the fenchel - legendre transform of @xmath120}$ ] is given by @xmath120}^{*}(y ) = ( \exp(\gamma y ) - 1)/\gamma$ ] for @xmath122 in view of lemma [ optimizedcertaintyequivalent ] ( cf . appendix [ appendixaa ] ) the corresponding risk measure @xmath123}}$ ] has the representation @xmath124}}(x ) = \inf_{x\in{\mathbb{r}}}{\mathbb{e}}\left[\frac{\exp(\gamma x - \gamma x ) - 1}{\gamma } - x\right ] = \frac{\ln\big({\mathbb{e}}[\exp ( - \gamma x)]\big)}{\gamma}\ ] ] for @xmath125}^{*}}.$ ] this is the well - known entropic risk measure . optimal stopping with the entropic risk measures is easy to handle , since it can be reduced to the standard optimal stopping problems via @xmath126}}(-y_{\tau } ) = \frac{1}{\gamma}\cdot\ln\big(\sup_{\tau\in{\mathcal t}}{\mathbb{e}}\big[\exp(\gamma y_{\tau})\big]\big).\ ] ] [ polynomial ] set @xmath127 } = x^{p}/p$ ] for any @xmath1281,\infty[,$ ] then the set @xmath129},0}$ ] contains all probability measures @xmath3 on @xmath70 with @xmath130 and @xmath131}}(x ) = \sup\limits_{{\mathrm{q}}\in { \mathcal q}_{\phi^{[p]},0}}\left({\mathbb{e}}_{{\mathrm{q}}}[- x ] - \frac{1}{p}~{\mathbb{e}}\left[\left(\frac{d{\mathrm{q}}}{d{\mathrm{p}}}\right)^{p}\right]\right)\quad\mbox{for}~x\in l^{p/(p - 1)}.\ ] ] let @xmath132 denote the topological interior of the effective domain of the mapping @xmath1.$ ] we shall assume @xmath133 to be a lower semicontinuous convex function satisfying @xmath134 the following theorem is our main result ." +"unlike the optical spectra of hot cspn , which are characterized by lines of hydrogen , helium and some light metals , the ultraviolet spectra are dominated by fe and ni lines ( schnberner & drilling 1985 ) . their observed strengths show large variations between different objects suggesting a possible spread in abundances . iron group lines are ideal temperature indicators ( fig.1 ) , which is important to set up a reliable temperature scale for the hottest cspn . effective temperatures of the hottest central stars are known with low accuracy only . as a temperature indicater one usually takes the relative strength of neutral and ionized helium lines in optical spectra , however , at very high temperatures neutral helium lines disappear . the sample of stars in our study includes seven very hot hydrogen - rich cspn . these are the same objects that are investigated by traulsen et al . ( these proceedings ) to derive temperature and gravity by utilizing uv lines from light metals , namely c , n , and o. this sample covers the hottest phase of post - agb evolution ( @xmath0@xmath170000k ) and includes four objects , which have been observed with fuse _ and _ hst / stis . the fuse spectra cover the range 9101180 with a resolution of about 0.1 . fig.2 displays a section of the available spectra . they are ordered by increasing effective temperature ( starting from ngc1360 with 97000k , up to ngc6853 with 126000k ) which becomes obvious in the shift of the iron ionisation balance . only lines of fevi and fevii are labeled in this figure , and the numbers next to the identification bars are the respective log__gf _ _ values . we also detect lines of c , n , o and of other elements of the iron group . as yet unidentified spectral lines are possibly absorptions of covi ( 1139.4 ) , nivi ( 1096.6 , 1121.9 , 1125.4 , 1141.9 , 1145.0 , 1148.9 ) and mnvi ( 1088.7 , 1128.5 ) . in addition to the fuse observations , fig.2 displays a model spectrum which is plotted over the spectrum of ngc1360 . the model has solar abundances , and includes , besides h and he , lines from fevi and fevii . temperature and gravity of the model ( @xmath0 @xmath2 95000 k and log__g _ _ @xmath2 5.50 ) are close to those derived from the cno analysis mentioned above . note the h@xmath3 contamination of the fuse spectra other than ngc1360 . the very broad troughs in lss1362 are h@xmath3 lines , and one can see the matching ( relatively weak ) absorption in ngc7293 . a large fraction of the absorption features in ngc6853 are from warm h@xmath3 , which will have to be deblended to obtain the photospheric spectrum . the spectra are analyzed using nlte metal line blanketed model atmospheres in order to determine @xmath0 , surface gravity , and chemical composition . for model calculations we use the tbingen nlte model atmosphere package tmap ( werner & dreizler 1999 ) and the atomic data files of the iron group ions were prepared with the iron opacity interface `` ironic '' ( rauch & deetjen 2003 ) . the large number of iron lines calls for a statistical treatment of opacities . we include data from kurucz s ( 1991 ) line list . the final synthetic spectra contain only lines whose wavelength position is accurately known from laboratory measurements ( so - called pos tables of kurucz ) . so far , all models have solar abundances and include h and he , plus lines from fevi , and fevii . the possibility of using the fevi / fevii ionisation equilibrium as a temperature indicator can be seen by the disappearance of fevi lines and the increasing strength of fevii lines in the spectra of models with increasing effective temperature ( fig.1 ) . the decrease of the fevii line strengths in the hottest model is explained by a shift of the ionization balance from fevii to feviii . ( all models have log__g _ _ = 7 . ) our first calculations seem to confirm that the temperature of ngc1360 is indeed lower than previously thought . the study of cno lines arrived at a similar result . the iron abundance in ngc1360 is apparently close to solar . kurucz , r. l. 1991 , in stellar atmospheres : beyond classical models , ed . l.crivellari , i.hubeny , d.g.hummer , nato asi ser . c 341 , kluwer , dordrecht , p.441 rauch , t. , & deetjen , j. l. 2003 , in stellar atmosphere modeling , eds . i. hubeny , d. mihalas , & k. werner , asp conference proceedings , 288 , 103 schnberner , d. , & drilling , j. s. 1985 , apj , 290 , l49 werner , k. , & dreizler , s. 1999 , in computational astrophysics , eds . h.riffert & k.werner , journal of computational and applied mathematics , 109 , 65" +"the modified newtonian dynamics ( mond ) is an empirically - based modification of newtonian gravity or inertia in the limit of low accelerations ( @xmath1 ) suggested by milgrom ( 1983 ) as an alternative to cosmic dark matter . in addition to explaining galaxy scaling relations ( tully - fisher , faber - jackson , fundamental plane ) , this simple algorithm allows one to accurately predict the shapes of spiral galaxy rotation curves from the observed distribution of gaseous and stellar matter . mond also accounts for the kinematics of small groups of galaxies ( milgrom 1998 ) and of superclusters , as exemplified by the perseus - pisces filament ( milgrom 1997 ) without the need for unseen mass . these well - documented phenomenological successes ( sanders & mcgaugh 2002 and references therein ) challenge the cold dark matter ( cdm ) paradigm and provide some support for the suggestion that the current theory of gravity and inertia ( general relativity ) may need revision in the limit of low accelerations or field gradients . however , problems do arise when one attempts to apply mond to the large clusters of galaxies . the and white ( 1988 ) first noted that , to successfully account for the discrepancy between the observed mass and the traditional virial mass in the coma cluster , the mond acceleration parameter , supposedly a universal constant , should be about a factor of four larger than the value implied by galaxy rotation curves . with mond , the dynamical mass of a pressure supported system at temperature t is @xmath2 ; therefore , the the and white result could also be interpreted as an indication that the mond dynamical mass is still larger than the detectable mass in stars and gas . in astronomical tests involving an individual extragalactic object , such as the coma cluster , a contradiction is not necessarily a falsification . one can always argue that the peculiar aspects of an object , such as deviations from spherical symmetry or incomplete dynamical relaxation , exempt that particular case . however , gerbal et al . ( 1992 ) , looking at a sample of eight x - ray emitting clusters , noted that the problem is more general : although mond reduced the newtonian discrepancy by a factor of 10 , there is still a need for dark matter , particularly in the central regions . later , considering a large sample of x - ray emitting clusters , i found that the mass predicted by mond remains , typically , a factor of two or three times larger than the total mass observed in the hot gas and in the stellar content of the galaxies ( sanders 1998 ) . more recently , aguirre , schaye & quataert ( 2001 ) pointed out that mond is inconsistent with the observed temperature gradient in inner regions of three clusters for which such data is available . again , the problem can be remedied by additional non - luminous mass , primarily in the inner regions , of order two or three times the observed gas mass . this discrepancy is also evident from strong gravitational lensing in the central regions of clusters the formation of multiple images of background galaxies . here , mond does not apply because accelerations are newtonian , and the implied surface density greatly exceeds that of visible matter and hot gas ( sanders 1998 ) . so , although mond clearly reduces the classical newtonian mass discrepancy in clusters of galaxies , there still remains a missing mass problem , particularly in the cores . here i consider the issue of the remaining missing mass in clusters and whether or not this a fundamental problem for mond . first i calculate the structure and x - ray surface brightness distribution of mond isothermal gas spheres . except for the very central regions , the structure of these objects is self - similar ; the finite mass is primarily determined by the temperature and is very weakly dependent upon the central density . thus there exists a mass - temperature relation ( @xmath3 ) which is absolute ; this implies a gas mass typically 5 to 10 times larger than that observed in x - ray emitting clusters of the same temperature . moreover , for central electron densities in the range of 0.001 to 0.01 , there is a well - defined x - ray luminosity - temperature relation which is less steep ( @xmath4 ) and lies well above the observed luminosity - temperature relation for clusters ( @xmath5 ) . looking at individual objects , the radial dependence of x - ray surface brightness does not reproduce that typically observed in x - ray emitting clusters observations which are well - fit by the traditional @xmath0-model "" ( sarazin 1988 ) . the conclusion is that self - gravitating mond isothermal gas spheres are not good representations of clusters of galaxies . gas spheres with a density distribution described by a @xmath0-model are not isothermal in the context of mond . a central or boundary temperature must be specified to determine the run of temperature in such objects , but those models with the lowest temperature gradients have large core radii and are again over - massive and over - luminous with respect to observed clusters of the same temperature . these problems may be solved by postulating the existence of a second rigid component in the mass distribution : a constant density core having a radius about twice that of the @xmath0 model core and a central surface density comparable to @xmath6 . here , by rigid i mean a component with a fixed density distribution which does not respond to the gravitational field of the hot gas or galaxies . the presence this additional component in the coma cluster is implied by the mond hydrostatic gas equation for cumulative mass . if this component is generally present in clusters , it contributes to the gravitational force in the inner regions and reduces the core radius at a given temperature . in this way the observed luminosity - temperature and mass - temperature relations for clusters may be reproduced . about 40 individual clusters have been considered in terms of such a two - component model ; i.e. , the observed surface - brightness distributions and mean temperatures are fit by specifying the density of the non - luminous component which is assumed to extend to two gas core radii . the total mass of this additional component varies between a few times @xmath7 and @xmath8 m@xmath9 and the implied mass - to - light ratio is typically 50 in solar units . therefore , the required rigid component is not a standard stellar population ; as noted previously , mond requires dark , or heretofore undetected , matter in the central regions of rich clusters . although the total discrepancy between dark and detectable mass is reduced by , on average , a factor of four over that implied by newtonian dynamics , it is clear that there remains a dark matter problem for mond . i discuss the issue of whether or not this is a contradiction . i speculate on the possible nature of this non - luminous component and argue that neutrinos of finite mass are a possible candidate . the structure of isotropic isothermal spheres may be determined by solving the equation of hydrostatic equilibrium : @xmath10 with the pressure @xmath11 given by @xmath12 where @xmath13 is the one - dimensional velocity dispersion ( constant for an isothermal sphere ) , @xmath14 is the density . the gravitational acceleration , @xmath15 , in the context of mond , is given by @xmath16 where @xmath17 is the usual newtonian gravitational acceleration , @xmath18 @xmath19 is the critical acceleration below which gravity deviates from newtonian ( found to be about @xmath20 cm / s@xmath21 from fits to galaxy rotation curves ) , and @xmath22 is a function which interpolates between the newtonian regime ( @xmath23 when @xmath24 ) and the mond regime ( @xmath25 when @xmath26 ) . a function having this asymptotic form , @xmath27 works well for galaxy rotation curves and is also used here . milgrom ( 1984 ) demonstrated that mond isothermal spheres have a finite mass and a density which falls of as @xmath28 where @xmath29 at large radii . in the outer regions , where @xmath30 = constant , it follows immediately from eqs . 1 and 2 that @xmath31 which means that the mass is uniquely determined by the specified velocity dispersion or temperature . for an isothermal gas sphere this relation becomes @xmath32 where @xmath33 is the mean atomic weight ( @xmath34 for an fully ionized gas with solar abundances ) and @xmath35 is the proton mass . this would be , in effect , the extension of the faber - jackson relation to clusters of galaxies ( sanders 1994 ) . however , the observational definition of such a relation is ambiguous because the total gas mass defined by the @xmath0-model is typically divergent . if one considers the mass inside a fixed radius ( sanders 1994 ) , or within a radius where the density falls to some fixed value ( mohr , mathiesen & evrard 1999 ) , a relationship of this form ( eq . 4 ) is observed for clusters . however , the mass at a given temperature is typically a factor of 5 to 10 below that implied by eq . is shown in fig . 1 where the mond mass - temperature relation for isothermal gas spheres ( dashed line ) is compared to the observed gas mass - temperature relation for 42 clusters listed in table 1 . here the observed gas mass is given by the @xmath0-model ( eq . 7 below ) extrapolated to a radius where the gas density has fallen to about @xmath36 g/@xmath37 , or 250 times the mean cosmological density of baryonic matter . the characteristic scale of mond isothermal gas spheres is @xmath38 ( sanders & mcgaugh 2002 ) . given that the x - ray luminosity due to free - free emission is @xmath39 ; then , eqs . 4 and 5 above would imply an x - ray luminosity - temperature relation of the form @xmath4 . the observed luminosity - temperature relation ( e.g. , ikebe et al . 2002 ) is significantly steeper , @xmath5 , than that of mond isothermal spheres . to pursue this in more detail , i calculated the x - ray luminosity for mond isothermal spheres with electron densities and temperatures similar to those of the x - ray emitting clusters of galaxies . i assume a central electron density of 0.006 @xmath40 as being typical of clusters , and , for a given temperature , numerically integrate eqs . 1 and 2 from the center outward . the optically thin free - free radiation for the entire sphere is then calculated from the run of electron density . the resulting luminosity - temperature relation is shown by the dashed curve in fig . 2 . compared to the observations by ikebe et al . ( 2002 ) scaled to h=0.7 . in both cases , this is the radiation emitted in the band 0.2 to 2.4 kev where the x - ray flux is typically measured by satellites such as asca and rosat . not only is the theoretical dependence shallower than observed , the predicted luminosities are an order of magnitude larger than actual clusters at the same temperature . on the basis of these scaling relationships , it would seem that mond isothermal spheres are not good representations of clusters of galaxies . this conclusion is reinforced when we consider the surface brightness distribution of a mond isothermal" +"the abundance patterns of extremely metal - poor ( emp ) stars are useful in studying nucleosynthesis in massive supernovae ( sne ) . population ( pop ) iii stars are usually considered to be massive stars . some of them might become black holes without supernova explosions , but some should have exploded as supernovae to initiate the first metal enrichment in the early universe . the stars born from the gas enriched by the pop iii sne are pop ii stars with low metallicity . low - mass pop ii stars have long lifetimes and might be observed as extremely metal poor ( emp ) stars with [ fe / h ] @xmath0 . ( here , [ a / b ] = @xmath1(@xmath2/@xmath3 ) - @xmath1(@xmath2/@xmath3)@xmath4 , where the subscript `` @xmath5 '' refers the solar value and @xmath2 and @xmath3 are the abundances of elements a and b , respectively . ) therefore , a emp star may reflect the nucleosynthetic result of a pop iii sn and constrain properties of the pop iii sn . there have been attempts to actually fit the abundance patterns of emp stars with the supernova nucleosynthesis models . for example , using the mixing - fallback model proposed by umeda @xmath6 nomoto ( 2002 ) ( hereafter un02 ) and umeda @xmath6 nomoto ( 2003 ) ( hereafter un03 ) mimicking aspherical explosion effects ( e.g. , tominaga 2009 ) , they showed that the abundance patterns of the elements from c to zn of carbon - normal emp stars and carbon - rich emp stars can be successfully reproduced by energetic core - collapse sn ( `` hypernova '' , hereafter hn ) , models and faint sn models , respectively ( un02 ; un05 ; tominaga et al . 2007 ) , while those of very metal poor ( vmp ) stars ( @xmath7 [ fe / h ] @xmath8 ) can be reproduced by normal core - collapse sn models or the imf - integration of hypernova and normal core - collapse sn models ( tominaga et al . it is important to note that the observed emp stars are so far all explained by the pollutions by core - collapse sne with initial stellar masses 11@xmath9 and no evidence of pair instability sne with initial stellar masses 140@xmath10 ( un02 , see also chieffi @xmath6 limongi 2002 ; un03 ; umeda @xmath6 nomoto 2005 , hereafter un05 ; heger @xmath6 woosley 2002 , 2008 ) . these previous sn models do not eject elements heavier than zn in a sizeable amount , and this is consistent with the abundance of some emp stars . however , there are also emp stars showing enhancements of neutron - capture elements . some of them show abundance patterns almost identical to the solar system r - process pattern for sr and heavier elements ( e.g. , sneden et al . 2000 ; hill et al . one example of such a star is cs22892 - 052 and called as a main `` r - process star '' ( sneden et al . the process producing heavy neutron capture elements ( @xmath11ba - u ) is referred to as `` main '' r - process ( e.g. , truran et al . 2002 ; wanajo & ishimaru 2006 ) . on the other hand , there are other emp stars that require another neutron - capture process referred sometimes as `` lepp '' ( lighter element primary process ) or `` weak r - process '' ( travaglio et al . 2004 ; wanajo @xmath6 ishimaru 2006 ) . travaglio et al . ( 2004 ) reported emp stars with abundances of sr , y , and zr which can not be explained by the s - process or main r - process . in the weak r - process stars , the elements with intermediate mass ( 37@xmath12z@xmath1247 , i.e. , from rb to ag ) elements show moderate enhancements with respect to heavy ones ( z@xmath1356 , i.e. , heavier than ba ) . more recently francois et al . ( 2007 ) showed several other examples of the weak r - process stars . there are evidences of the existence of weak r - process but its origin is unknown . several possible mechanisms to produce the weak r - process elements are proposed . wanajo et al . ( 2001 ) presented calculations of r - process nucleosynthesis in neutrino - driven winds from a proto - neutron stars . they showed that the abundance pattern of weak r - process is reproduced when the main r - process nucleosynthesis is failed . the nucleosynthesis in neutrino - driven winds was also studied in hoffman et al . ( 1996 ) by taking the electron fraction @xmath14 of the wind matter as a free parameter . they showed that weak r - process elements may be synthesized for low @xmath14 ( @xmath150.47 ) . although the production of weak r - process elements in neutrino - driven winds was suggested , it is difficult to give a detailed yield because the physical conditions and ejected mass depend on unknown supernova explosion mechanisms . explosive nucleosynthesis in low @xmath14 matter was also studied in the context of multi - dimensional explosion models ( janka et al . 2003 ; pruet et al . they showed that small amounts of low @xmath14 ( @xmath160.46 ) matter as well as high @xmath14 ( @xmath170.56 ) matter are ejected from a hot bubble just outside a proto - neutron star . the high @xmath14 ( @xmath170.56 ) matter is suggested to be ejected even in the one - dimensional cases ( e.g. , frlich et al . 2006 ) . on the other hand , the ejection of low @xmath14 matter is driven by the convection in the hot bubble , and thus essentially the multi - dimensional phenomenon . janka et al . ( 2003 ) suggested that the low @xmath14 matter contains the weak r - process elements ( sr , y and zr ) to explain the galactic abundances , but a detailed nucleosynthesis calculation did not confirm the production of these elements ( pruet et al . 2005 ) . in this paper , we investigate the physical conditions to produce sufficient amounts of the weak r - process elements ( sr , y and zr ) and discuss whether core - collapse sne with a slight modification can be compatible with the observed abundances of the weak r - process elements in the emp stars . in order to do this , we assume that small amount of low @xmath14 matter is ejected by the multi - dimensional effects , which may be driven by the convection in a hot bubble ( janka et al . 2003 ) or jets in a jet - like explosion ( e.g. , maeda @xmath6 nomoto 2003 ) or a collapsar model ( e.g. , pruet et al . 2003 , 2004 ; popham , woosley @xmath6 fryer 1999 ) . the entropy of the low @xmath14 matter flow may depend on the ejection mechanism . we assume that the matter flow has the same entropy as the supernova shock wave . jet - like explosion or collapsar models may describe hne . however , they contain many unknown parameters , and the innermost @xmath14 of the ejecta depends on those parameters . on the other hand , the simulations of janka et al . ( 2003 ) contain less input parameters , so the obtained @xmath14 profile is more reliable , though their simulations are about normal sne . we are interested in the emp stars , and their progenitor may be more massive and explode energetically , i.e. , may become hne . therefore , we vary @xmath14 beyond the range given by the simulation in janka et al . although we have multi - dimensional effects in mind , we only perform one - dimensional calculations in this paper , because it is often useful to make a large parametric search to disclose the essence of physics . in @xmath18 2 , we show observational trends of [ sr , y , zr / fe ] . in @xmath18 3 , we describe our progenitor and explosion models . in @xmath18 4 , we present weak r - process nucleosynthesis and specify conditions mention our assumption applying to our models in order to reproduce reproducing the observational [ sr , y , zr / fe ] . we also compare our yields with 4 emp stars which have peculiarly high [ sr , y , zr / fe ] . in @xmath18 5 , summaries and discussions are given . since we are interested in the weak r - process elements in the emp stars , we select stars with [ fe / h ] @xmath19 from cayrel et al . ( 2004 ) and use their data from carbon to zinc . observations of [ sr , y , zr / fe ] are taken from honda et al . ( 2006 ) for hd122563 and francois et al . ( 2007 ) for the other stars . taking the previous works on the weak r - process into consideration , we use two abundance ratios as a diagnostic to distinguish `` main r - process stars '' and `` weak r - process stars '' . they are relative numbers of sr and ba , sr / ba , and y and eu , y / eu . we use @xmath20 from anders @xmath6 grevesse ( 1989 ) . a main r - process star cs22892 - 052 has [ sr / ba ] = -0.57 and [ y / eu ] = -1.16 . therefore , if a emp star has [ sr / ba ] @xmath21 and [ y / eu ] @xmath22 , we consider the star as a weak r - process star , otherwise as a main r - process star ( see also aoki et al . figure 1 shows [ sr / fe ] , [ y / fe ] , and [ zr / fe ] vs. [ fe / h ] of the weak r - process stars . among 21 selected stars , 20 stars are with @xmath23 [ sr , y , zr / fe ] @xmath24 . the calculation method and other assumptions are the same as described in umeda et al . 2000 ( hereafter unn00 ) , un02 , un05 and tominaga et al . 2007 , except for the size of the nuclear reaction networks . in this paper , we adopt the pop iii progenitors as in un05 and apply the model with @xmath25 = 13 @xmath26 and @xmath27 = 1.5 ( hereafter model-1301 ) , the one with @xmath25 = 25 @xmath26 and @xmath27 = 1 ( hereafter model-2501 ) , and the one with @xmath25 = 25 @xmath26 and @xmath27 = 20 ( hereafter model-2520 ) . model-1301 and model-2501 are normal sn models , and model-2520 is a hn model . detailed nucleosynthesis is calculated as a postprocessing after the hydrodynamical calculation with a simple @xmath28-network . the isotopes included in the post process calculations are 809 species up to @xmath29pd ( see table 1 ) . we note that a neutrino process during explosive burning ( yoshida et al . 2008 ; woosley @xmath6 weaver 1995 ) is not taken into account . the abundance distributions after the sn explosion for model-1301 , model-2501 and model-2520 are shown in figure 2 . we obtain the final yields by setting the inner boundary of the ejected matter , a mass - cut ( @xmath30 ) as we describe in the next section . in this section we summarize the abundance pattern of sn ejecta" +"since the discovery of 51 peg b ( mayor & queloz 1995 ) , over a hundred gaseous planets have been discovered in orbit around g , k , and m stars . these discoveries have opened a new domain of research in astronomy , at the crossroad between stellar and planetary physics . many ground - based and space - based missions are planned for the coming years to search for more of these objects , and the next decade will probably see the first direct detection of an extrasolar planet . these projects require a robust theoretical background to accurately understand the properties of these objects and to provide reliable guidance for observations . the vast majority of these planets have a projected mass , @xmath4 , of about one jupiter mass ( @xmath5 ) but are found to orbit much closer to their parent star than jupiter , with a pile - up around @xmath6 au . as such , these planets experience strong irradiation from their parent star . observations of objects that transit their parent star provide information crucial to understanding these so - called hot - jupiters . the transit light curve or photometry , supplemented by radial velocity measurements of the star , yields the absolute mass and average radius of the planet . together with an estimate of the age of the parent star from stellar evolution models , the radius and mass provide stringent constraints on the evolution of the internal and atmospheric properties of strongly irradiated planets . the correct description of these properties has been questioned recently by the detection of the transit planet @xmath0 ( brown et al . no consistent model can adequately reproduce the observationally determined mass and radius of the planet ( @xmath7 ) ( cody & sasselov 2002 ) without stretching these determinations beyond their error bars ( guillot & showman 2002 , baraffe et al . 2003 , burrows et al . this led to the suggestion that an important part of fundamental physics might be missing in the description of irradiated planets and has motivated several authors to propose possible shortcomings of the theory . in the present letter , the theory developed in baraffe et al . ( 2003 ) for non - irradiated and irradiated planets is applied to various cases of hot - jupiters , with special focus on the case of the second observed transit , @xmath1 . the theory adequately reproduces the observed radius of the planet , for the proper age of the system and the more recent mass determination ( torres et al . 2003 ) . the comparison of the present predictions for the evolution of hot - jupiters with forthcoming transit detections will allow the unambiguous verification or rejection of the present theory for a planet in close orbit around its parent star , the strong incident stellar radiation substantially modifies not only the emergent spectrum but also the evolution of the irradiated planet , as shown initially by guillot et al . these effects are examined below . under strong irradiation conditions , the solution of the transfer equation , which determines the atmospheric thermal structure of the planet , must include the incoming incident stellar flux in the source function . such calculations were first conducted for hot - jupiters by seager & sasselov ( 1998 ) , using a limited set of opacities , and have subsequently been improved by barman , allard & hauschildt ( 2001 ) and sudarsky , burrows & hubeny ( 2003 ) . figure [ f1.eps ] compares the thermal structures of irradiated and non - irradiated planets with surface gravity @xmath8 ( cgs units ) and intrinsic temperatures @xmath9 k and @xmath10 k , respectively , orbiting a g2 main sequence star at 0.023 au or 0.046 au . the atmosphere models were produced using the same cloud - free opacity setup described by allard et al . ( 2001 ) and barman , allard & hauschildt ( 2001 ) . as examined below , this @xmath11 sequence corresponds to an age sequence of @xmath123@xmath13 yr to @xmath129@xmath14 yr for @xmath1 . the irradiated thermal profile is shown to be strongly modified with respect to the non - irradiated one . as stressed in baraffe et al . ( 2003 ) , the differences between irradiated and non - irradiated temperature profiles clearly demonstrate the necessity to do _ consistent _ calculations that combine the irradiated atmosphere profile and interior profile . matching arbitrarily the inner profile to an atmospheric profile defined by the equilibrium temperature of the planet yields severely flawed results . note that the present calculations assume that all the incident flux is concentrated on the day - side of the planet . such an assumption maximizes the effect of irradiation and might overestimate the flux deposit . the present nearly isothermal irradiated profiles , however , are consistent with the 2@xmath15 m observed spectrum of @xmath0 ( richardson , deming & seager 2003 ) . future calculations will include the latitude dependence of the incoming radiation but it is certainly interesting to verify whether the present calculations , with minimal assumptions , adequately reproduce the radius of new observed transiting planets . consistent evolution calculations of irradiated planets have been conducted only recently by baraffe et al . ( 2003 ) and burrows et al . the calculations presented here proceed as described in chabrier & baraffe ( 1997 ) for the non - irradiated case . a grid of irradiated atmospheric structures is computed for various @xmath16 conditions , for a given orbital distance @xmath17 , and interpolation between these structures yield the unique boundary condition with the internal structure , at large enough optical depth ( @xmath18 ) . as shown initially by guillot et al . ( 1996 ) , irradiation pushes the radiative - convective boundary deeper into the interior and , under strong irradiation conditions , may force the boundary between the atmospheric and internal structure to lie in a radiative layer . to insure consistency between the atmosphere and internal thermal structures , we have computed the rosseland mean of the atmospheric opacities and used this value to calculate the radiative gradient for the interior structure . the evolution of the planet obeys the usual first and second principles of thermodynamics . the energy balance , however , must include the incoming stellar radiative flux @xmath19 , where @xmath20 and @xmath21 denote the parent star flux and radius , respectively . the total emergent flux of the planet @xmath22 now reads : @xmath23 where @xmath11 denotes the intrinsic effective temperature of the planet , @xmath24 its bond albedo , and the first term on the r.h.s . of eqn.([evolir ] ) describes the reflected part of the spectrum . note that the albedo @xmath24 is not a free parameter in our calculations but is calculated consistently with the radiative transfer equation . for both transit cases , the models predict @xmath25 . the total luminosity thus reads : @xmath26 where @xmath27 denotes the specific entropy of the planet . whereas the total flux @xmath28 or luminosity @xmath29 is the quantity accessible to observation , only the last term on the right hand side of eqn.([evolirrad ] ) concerns the evolution of the planet intrinsic luminosity @xmath30 . the first term , which defines the bond albedo , illustrates the fraction of the stellar luminosity reflected by the planet atmosphere . the second term defines its equilibrium temperature , i.e. the temperature the planet would reach in the absence of any internal source of energy ( @xmath31 ) . figure [ f2.eps ] compares the emergent flux calculated for @xmath1 and @xmath0 at their present ages . in both cases , the infrared part of the spectrum ( @xmath32 m ) is dominated by the re - radiation of the absorbed incident stellar flux . indeed , under the conditions of interest , this contribution largely dominates the intrinsic contribution of the planet ( @xmath33 k @xmath34100 k for @xmath1 , and @xmath35 k @xmath34100 k for @xmath0 ) . for @xmath0 , the short wavelength part of the spectrum ( @xmath36 m ) is mostly due to reflection of stellar light by h@xmath37 rayleigh scattering . however , in @xmath1 the high equilibrium temperature , @xmath38 k , leads to a lower concentration of h@xmath37 . consequently , reflection is less significant and the majority of the spectrum of @xmath1 is thermal radiation . figure [ f3.eps ] displays the evolution of the radius for different strongly irradiated planet conditions , with masses 0.69 @xmath39 and 1.5 @xmath39 , orbiting a g2 star ( @xmath40 k ) at different orbital distances , namely @xmath410.046 au and @xmath410.023 au . at a given orbital distance , the less massive the planet the larger the effect of irradiation . this was expected from figure [ f1.eps ] , showing the larger modification of the inner atmosphere profile with larger stellar / planet flux ratio . in all cases , however , irradiation substantially slows down the contraction of the planet , in particular at the early stages of evolution , when degeneracy effects in the interior are smaller . the case @xmath42 and @xmath410.023 au ( thick solid line ) corresponds to @xmath1 , for its recently revised mass , @xmath43 , and radius @xmath44 ( torres et al . 2003 ) . the age of the system was derived from the evolution of the parent star for its observed extinction - corrected magnitude and effective temperature ( sasselov 2003 ) . we derive @xmath45 , @xmath46 gyr to reproduce the observations , in excellent agreement with sasselov ( 2003 ) . the striking result is the very good agreement , within the error bar , between the present calculations and the observations . a prediction of the theory is that irradiation from a g2 star yields less than about @xmath47 increase of the planet radius after @xmath48 gyr , compared with the non - irradiated case , with all radii merging within the @xmath49 - 1.15 @xmath50 range at this stage . a key test for the theory , however , would be the observation of young @xmath51 yr ) transits , where radii of irradiated planets are predicted to vary rapidly with time and to depend substantially on the orbital distance . the case of @xmath0 thus becomes a puzzle . as discussed at length in baraffe et al . ( 2003 ) , no consistent evolution calculation can reproduce the observed radius . note that our calculations take into account the extension of the atmosphere , which we find to be of the order of @xmath52 ( at optical wavelengths ) for the age of this object . given the remaining uncertainties in the opacities of these planets , including for example non - equilibrium processes or day - night temperature gradients , we can not exclude larger extensions . it is very unlikely , however , that different opacities modify the internal adiabat strongly enough to increase the planet radius by 30% and thus solve the aforementioned discrepancy between theory and observation for @xmath0 . such a modification requires a drastic change of the energy deposited at the top of the internal adiabat , which essentially determines the radius ( baraffe et al . 2003 , guillot & showman 2002 ) . molecular absorption , however , will prevent incident photons from penetrating that deep ( @xmath53 k near the top of the internal adiabat , see figure [ f1.eps ] ) . as discussed in 4.3 of baraffe et al . ( 2003 ) , dynamical processes such as tidal dissipation or synchronization are unlikely to provide the extra source of energy , for these timescales are at most of the order of @xmath54 yr . an interesting alternative scenario involves" +"molecular polymorphism , the observation of different crystal structures made up of the same molecules , has been a central problem standing in the way of affordable and reliable crystal structure prediction ( csp ) which would greatly accelerate the development of new materials for applications in solid state chemistry , material science and pharmaceutical science @xcite . the key challenges for ab initio csp of molecular crystals can be summarized as * i ) * the computational cost of thermodynamical exploration of a rich polymorphic phase space , * ii ) * the accuracy needed to resolve similarly - low energies among polymorphs @xcite , and * iii ) * the fact that kinetic factors may control the crystallization procedure rather than thermodynamic ones @xcite . the past decade witnessed these challenges being tackled by the scientific community and the progress can be followed through the blind tests organized yearly by the cambridge crystallographic data centre @xcite . the exponential growth in the hardware performance and new , efficient algorithms tailored for molecular crystals have allowed a wider region of the phase space to be explored . the increased computational performance also enabled a transition from empirical interatomic potentials to more accurate but time consuming quantum mechanical techniques , mainly density functional theory ( dft ) . this transition did not guarantee however an increase in predictive power in all cases @xcite : the standard dft functionals do not describe properly van der waals ( vdw ) interactions , which forces csp studies to employ approximate semi - empirical corrections . these approximations to vdw interactions strongly affect the energy ordering of explored structures , which is a core information in predicting polymorphism . hence , to render csp predictions reliable , a fully ab initio method , able to obtain an accurate lattice energy including the vdw interactions , has been highly desirable . recently a breakthrough in the description of vdw interactions in dft has been made : many new non - local functionals that accurately describe the dispersion interactions have been proposed and demonstrated unprecedented success in a wide range of systems from molecules , molecular crystals to layered materials , with a computational cost comparable to that of standard functionals @xcite . it has been recently shown that even in difficult cases such as glycine crystals , where polymorphs show energy differences as little as 1 kcal / mol , new non - local functionals can yield the correct stability ordering as well as accurate pressure evolution @xcite . encouraged by these results we combine this critical progress in dft with recent developments in evolutionary csp @xcite , specifically adapted for molecular structure search @xcite , and perform a fully ab initio csp search on glycine crystals , without semi empirical corrections in the energy description , using neither information on cell geometry nor the symmetry of the experimentally observed polymorphs . we thus assess whether state - of - the - art ab - initio csp can pass the challenging blind test of exploring the phase space of polymorphic glycine . glycine , nh@xmath2ch@xmath2cooh , the smallest aminoacid , is an excellent test case for csp studies as its already rich polymorphism under ambient conditions is amplified and becomes less understood at higher pressure ( see fig.[fig1 ] ) . , with indicated @xmath3 molecules in unit cell , the form readily obtained by evaporation of aqueous solutions is @xmath1-glycine , which for long was believed to be the most stable phase instead of the later discovered ground - state phase @xmath4 . pressure evolution of ambient pressure phases show that while @xmath4 and @xmath5 phases quickly lose single crystal nature or undergo a phase transition within a few gpa , @xmath1 phase stays stable up to 23 gpa , the highest pressure reached in experiments . a reversible , hysteresis - free single - crystal to single - crystal transition occurs from @xmath5 to @xmath6 phase at 0.76 gpa . single crystals of the @xmath4 phase instead undergo an extended polymorphic transformation in the wide range of 2.7 - 7.6 gpa , to a high - pressure polymorph , the @xmath7 phase , accompanied with the fragmentation of single crystals into powder . upon decompression , the @xmath7 phase is stable down to 0.62 gpa , where a new , irreversible phase transition occurs to the @xmath0 phase , a new polymorph which is reported to be stable at ambient conditions for at least three days.,scaledwidth=47.0% ] a clear example to this is the @xmath0 phase , which is reported to be stable at ambient conditions for at least three days @xcite . interestingly , despite its stability , and at least three csp studies devoted to glycine so far @xcite , a decade after its observation , the @xmath0 phase has not been structurally resolved yet . the complex polymorphism of glycine highlights the importance of performing an extensive search in phase space , while practical concerns limit any csp study to explore primarily the lowest energy structures . in this study we use evolutionary algorithms ( ea ) as implemented in the uspex package to address this interplay efficiently @xcite . we perform three test suits with z=2 , 3 or 4 glycine molecules in the crystal unit cell . at the first generation , we start with a population of 30 random structures . this population evolves through generations where only the thermodynamically most stable members are allowed to procreate. the procreation operations are cross - overs of parent structures , and mutations that involve variation of the molecular position and orientation . the diversity of the population is guaranteed by addition of new random structures at each generation . the highest computational cost in this workflow is due to the ab initio geometry optimization of each structure considered . to keep this cost well within the capacity of modern high - performance computing technologies and within the budget of academic as well as industrial research , we limit the evolution to 20 generations at most ( see methods for details ) . we use ea as implemented in the uspex package to search for the low - energy structures of glycine with z=2 , 3 or 4 molecules in the unit cell . at the first generation , 30 structures are created randomly . after energy ordering , the @xmath8 of the population that is energetically least favorable is discarded . among the remaining , a fingerprint analysis is performed and potential parents whose fingerprint is within a threshold distance of 0.01 from any lower energy structure are discarded as well . the so - determined unique structures are eligible as parents and are allowed to procreate . the 30 new structures of the next generation are created from parents through the following operations : heredity ( cross - over of two structures ) ( @xmath9 ) , softmutation ( translation and rotation based on estimate of soft vibrational modes ) ( @xmath8 ) , rotation of the molecule ( @xmath8 ) , and random structure generation ( @xmath8 ) . in addition , the three best parents are directly cloned to the next generation . in all simulations , the maximum number of generations was 20 . for every structure generated by uspex , the geometry and cell relaxation is performed using vdw - df functional @xcite which was implemented in the quantum espresso package @xcite . a kinetic energy cutoff of @xmath10 ryd and a charge density cutoff of @xmath11 ryd are used . the brillouin zone sampling resolution was gradually increased in three steps during relaxation : resolution of @xmath12 , @xmath13 and @xmath14 respectively . energies and geometries of the last step with the densest k - point are used throughout the study . paw pseudopotentials are taken from the pslibrary project@xcite . by using this setup all structures are fully relaxed within a convergence of less than 0.1 mry for absolute total energy , @xmath15 mry / a.u . for the forces on atoms and less than @xmath16 gpa for the stress tensor . the cluster analysis is performed by using single linkage clustering , where two structures with fingerprint distance less than distance threshold @xmath17 are considered to belong to the same cluster . since uspex definition of fingerprint does not include any information on the enthalpy of the structure , a constraint is added such that two structures with enthalpy difference more than 0.5 kj / mol are not allowed to form a cluster . this constraint is found necessary only when the clustering analysis is performed for all the encountered structures , while limiting the analysis to low enthalpy region , such constraint was not necessary as each cluster was successfully identified with distance only . the results of csp can be visualized through the distribution of energy as a function of volume for the structures encountered during the search . despite the exploration of a wide region in phase space ( see left panel of fig.[fig2 ] ) , phase . as shown in the _ inset _ of the z=4 panel , crowding around each polymorph , when compared with its equation of state , is compatible with numerical noise due to incomplete relaxation . the distance - based clustering techniques adopted here are however well suited to separate and identify the different low lying polymorphs even in presence of noise . , scaledwidth=47.0% ] about 40% of all the structures lies within 4 kj / mol of the experimentally known ground state structure , @xmath4 . focusing on this region of the energy landscape as shown in the right panels of fig.[fig2 ] , we see structures forming islands with varying size and shapes . this feature illustrates the added complication in the case of molecular csp with respect to standard inorganic solids where a well - defined , isolated minimum would be observed for each phase . the shape and finite size of the islands can be understood considering that glycine is very soft , therefore structures that are far off from the equilibrium lattice parameters are thermodynamically penalized only slightly as demonstrated in the inset of fig.[fig2 ] . this effect , combined with the numerical noise in geometry optimization , as well as an increased number of degrees of freedom in molecular crystals , is enough to give rise to crowding around each polymorphic minimum . nevertheless islands are well separated and a clear assignment of polymorphs can be made for most of them . this is in stark contradiction with a very recent csp study for glycine with empirical corrections for intermolecular interactions , which reported that the obtained energy - volume points were not separated well enough to clearly identify each polymorph , thus underlining the challenge of polymorphism for csp @xcite . in this study instead the separation between several islands are well represented down to very small energy differences ( inset of fig.[fig2 ] ) . we believe this stems from the leap in accuracy and precision reached by the use of fully ab initio energetics together with last generation evolutionary algorithm tools . ssibility of machine learning the polymorphs reliable energetics from ab initio calculations is necessary but not sufficient to guarantee a reliable structure classification in csp . more than one polymorph can be present within a given extended island ; or what appears to be two adjacent islands due to insufficient sampling and/or relaxation , may actually correspond to the same packing order . indeed the most human - time consuming part of a csp procedure is known to be the stage where the output structures are comparatively examined in order to successfully separate the essential data from the crowd of repetitions @xcite . although not utilized to their full extent within csp , concepts from data mining , mainly clustering techniques , can be of great help" +"barely fifteen years after the invention of the laboratory maser in 1953 which required a population inversion in the ammonia molecule to be carefully _ engineered _ interstellar masers were _ discovered _ as a remarkable and naturally - occurring phenomenon . the @xmath3 transition of water vapor , with a frequency near 22 ghz , was among the first masing transitions detected from an astrophysical source ( the orion molecular cloud ; cheung et al . 1969 ) , and has proven to be an extraordinarily useful probe in environments as diverse as interstellar shock waves , circumnuclear gas in active galactic nuclei ( agn ) , and the envelopes of evolved stars ( elitzur 1992 ; lo 2005 ; and references therein ) . with brightness temperatures that often exceed @xmath5 k and in extreme cases can exceed @xmath6 k ( e.g. garay , moran & haschick ( 1989 ) , and with linewidths that are often extremely narrow , 22 ghz water masers can be observed with very long baseline interferometry ( vlbi ) . the very high angular resolution of such vlbi observations enables proper motion studies of the kinematics of gas outflowing from proto- and evolved stars . moreover , trigonometric and geometric / rotational parallaxes can be determined , yielding the distances and motions of star forming regions in our galaxy , in local group galaxies , and in more distant agn ( e.g. brunthaler et al . 2007 ; braatz et al . such observations have led to revised estimates of the size , shape and kinematics of the milky way ( e.g. reid et al . 2009 ) , as well as the best evidence yet obtained for the existence of supermassive black holes ( e.g. miyoshi et al . 1995 ) . masers directly probe extreme environments ( of density and temperature ) , whose properties can often only be inferred indirectly from other lines . over the 40 years since the first detection of interstellar water maser emission in the 22 ghz transition , several additional interstellar maser transitions have been detected at higher frequencies , some in response to a specific prediction of a population inversion ( menten et al . 1990a ) . in the case of pure rotational emissions , these comprise the 183 ghz ( waters et al . 1980 ) , 321 ghz ( menten et al . 1990b ) , 325 ghz ( menten et al . 1990a ) , 380 ghz ( phillips et al . 1980 ) , 439 ghz ( melnick et al . 1993 ) and 471 ghz ( melnick et al . 1993 ) lines , associated respectively with the @xmath7 , @xmath8 , @xmath9 , @xmath10 , @xmath11 , and @xmath12 transitions . these transitions are shown in the energy level diagram in figure 1 . in addition , several water transitions within the the @xmath131 and 2 vibrationally - excited states have been observed toward the circumstellar envelopes of evolved stars , as have the 437 ghz @xmath14 and 475 ghz 5@xmath15 pure rotational transitions ( melnick et al . 1993 ; menten et al . 2008 ) . the detection of multiple masing transitions has been crucial in elucidating the pumping mechanism responsible for the population inversions and the physical conditions in the masing gas . understanding the latter , of course , is crucial to the astrophysical interpretation of maser observations . while the interpretation of the emission observed in a single line ( e.g. the 22 ghz transition ) is very geometry dependent , because the non - linear amplification of the radiation strongly favors those sight - lines that happen to possess the greatest velocity coherence , the interpretation of multiline observations is more robust and permits important constraints to be placed upon ( 1 ) the excitation mechanism and ( 2 ) the conditions of temperature and density in the emitting gas . the pattern of pure rotational maser transitions observed from interstellar sources appears to confirm an excitation model ( e.g. neufeld & melnick 1991 ) in which collisional pumping , combined with spontaneous radiative decay , leads to the inversion of exactly those transitions that are observed to mase . in evolved stars , however , the additional presence of the 437 ghz @xmath14 maser transition suggests that collisional pumping is not the entire story and that radiative pumping by dust continuum radiation is also important . quantitative measurements of maser line ratios provide additional constraints . for example , the predicted dependence of a maser line ratio upon the temperature and density of the masing gas was used by melnick et al . ( 1993 ) to derive a lower limit of 1000 k upon the gas temperature in several observed sources ; this value argued against a model ( elitzur , hollenbach & mckee 1989 ) in which the masers were excited in 400 k material behind a dissociative shock wave , and favored a model ( kaufman & neufeld 1996 ) in which non - dissociative magnetohydrodynamic shocks were the source of the emission . the analysis makes the assumption that the maser beam angle is similar for the two transitions that are being compared . prior to the launch of the _ herschel space observatory _ ( pilbratt et al . 2010 ) , the observational data on pure rotational water masers had been limited to transitions of frequency less than 500 ghz , largely because of atmospheric absorption . the hifi spectrometer on _ herschel _ ( de grauuw et al . 2010 ) , however , provides the opportunity of expanding the available data set by the addition of higher frequency transitions that promise to increase our leverage on the pumping mechanism and the physical conditions in the maser - emitting gas . to date , _ herschel _ observations of oxygen - rich evolved stars have led to the detection of two additional water maser transitions : ( 1 ) the @xmath0 transition at 620.701 ghz ( detected toward vy cma by harwit et al . 2010 , and toward w hya , ik tau and irc+10011 by justtanont et al . 2012 ) ; and ( 2 ) the @xmath16 transition at 970.315 ghz ( detected toward w hya and ik tau by justtanont et al . to our knowledge , neither maser has previously been observed from interstellar gas . in this paper , we report the first detection of 621 ghz water maser emission from _ interstellar _ gas , obtained with _ herschel_/hifi in mapping observations of the orion - kl region . in addition , we report the detection of 621 ghz water maser emission obtained serendipitously in single pointings toward the w49n star - forming region and the orion south molecular cloud . our _ herschel _ observations of orion - kl were carried out on 2011 march 11 as part of the `` orion small maps '' subprogram within the hexos guaranteed time key program ( gtkp ; p.i . , e. bergin ) . we used the `` heterodyne instrument for the infrared '' ( hifi ) , in `` on - the - fly mapping '' ( otf ) mode , to obtain a nyquist - sampled map consisting of a 6 by 8 rectangular array of pointings spaced by @xmath17 in r.a . and the map center was located at offset ( @xmath18 relative to orion - kl . ( all offsets given in this paper are relative to @xmath19 ( j2000 ) , the position we adopt for orion - kl . ) the reference position for the otf mapping observations , at offset @xmath20 , was chosen to be devoid of known molecular emission . the observations were carried out in the upper sideband of mixer band 1b , using the wbs spectrometer , which provides an oversampled channel spacing of 0.5 mhz ( 0.27 km / s at a frequency of 621 ghz ) , roughly one - half the effective resolution . the absolute frequency calibration is accurate to 100 khz ( roefsema et al . the beam size was 34@xmath21 ( hpbw ) , and the absolute pointing accuracy is @xmath22 . two concatenated astronomical observation requests ( aors ) were used to obtain two separate maps , with a small relative offset ( @xmath23 ) chosen to make the center of the h polarization beam for one map coincident with the center of the v polarization beam for the other map . as discussed in 3 , the goal of acquiring two separate maps in this manner was to obtain a measurement of any linear polarization in the maser feature . as summarized in table 1 , the total duration of each aor was 1987 s , with an on - source integration time of 420 s , which yielded individual spectra with an r.m.s . noise of 62 mk ( on the scale of antenna temperature and for a 1.1 mhz channel width ) . the _ herschel _ data on orion - kl were reduced using standard methods in the herschel interactive processing environment ( hipe ; ott 2010 ) , version 10.0 on 2011 march 21 , ten days after the _ herschel _ observations of orion - kl were performed , we used the effelsberg 100 m telescope to carry out observations of the 22.23508 ghz @xmath3 transition , with the goal of determining the 621 ghz / 22 ghz line flux ratio as a constraint upon models for the maser emission mechanism . here , we obtained a map , centered at offset @xmath24 , consisting of a 9 by 9 square array of pointings spaced by @xmath25 in r.a . and the beam size was 41@xmath21 ( hpbw ) , and the frequency resolution was 6.1 khz , corresponding to a velocity resolution of 0.082 km / s . the observations were performed using the k - band receiver at the prime focus of the 100 m telescope , with an observing time of 1.0 min per position . in calibrating the spectra , we applied corrections for the atmospheric attenuation and for the dependence of the telescope gain on the elevation . the calibration factor was determined by the observation of suitable calibration sources like ngc7027 and 3c286 ( taking into account the significant linear polarization of the latter ) . in addition to the mapping observations of orion - kl that are the primary subject of this paper , we have also identified two additional _ spectra that show narrow and/or time variable 621 ghz features suggestive of maser action . our observations of high - mass star - forming region w49n were carried out at three separate epochs , as part of the prismas gtkp ( p.i , m. gerin ) . these observations had the primary goal of measuring foreground absorption in nearby spectral lines of @xmath26 , but included the 621 ghz line within the bandpass . for each epoch , the relevant data were acquired in 3 aors obtained with slightly different lo settings . the aor numbers , dates of observation , beam center position , duration of the observations , and rms noise achieved are listed in table 1 . the data reduction methods that we adopted within the prismas gtkp have been described , for example , by neufeld et al . our observations of the hot core in the orion south molecular cloud were performed as part of a spectral line survey in the hexos gtkp . the data of present interest were acquired in a full spectral scan of band 1b , in which the 621 ghz transition was observed ( in either the upper or the lower sideband ) at 19 separate lo settings . the data reduction methods that we adopted for spectral scans within the hexos gtkp" +"general relativity concerns a geometrical formulation of gravity and has as a tenet a pseudo - riemannian geometry for the manifolds taken in consideration . however , this is an arbitrary choice and is intended to preserve scalar products between vectors and , consequently , their lengths when parallel transported along an arbitrary path on the manifold . nevertheless , considering that in this theory the characterization of space - time is made by rulers and clocks based on light rays emission and reception , ehlers , pirani and schild@xcite ( eps ) , followed by woodhouse,@xcite have shown that the pseudo - riemannian geometry represents a restriction among the possibilities those measuring tools allow . that is , starting from axioms concerning light rays and trajectories of freely falling particles you get , necessarily , a weyl geometry as the most general one . this , in turn , differs from the pseudo - riemannian one by allowing vectors to change their modulus when paralel transported along any curve . weyl s motivation was to geometrize electromagnetism , with the intend to unify it with gravitation , and the length variation of vectors was associated with the electromagnetic potential.@xcite being so , it suffered some criticisms that made it be abandoned . however , the axiomatic characterization of space - time by eps and woodhouse bring weyl geometry to light once again . this time there is no association of length variation with any known physical field . the vector field that performs such a variation , which we will call @xmath0 , is purely geometrical , and thus the objections raised before are transcended . in sec . [ sec - propriedades ] are presented the main properties of weyl geometry . from them , preserving the postulate that test particles travel through time - like geodesics , it is verified that those should be different from the pseudo - riemannian case of general relativity ( gr ) . the @xmath0 field appears giving extra contributions to the trajectories of material particles and thus influencing on an observable of the theory . this is one of the motivations to study einstein gravity in weyl geometry : as a way to determine how or to what extent one can use the new geometric field to make the theory more consistent . in the following section it is made a brief study of congruences of curves in weyl . it is defined the concept of physical distance between neighboring curves and it is shown that their evolution is given by a linear transformation . next , the matrix of this transformation is decomposed in their irreducible parts , which are the corresponding expressions for the expansion , shear and rotation from gr . in sec . [ sec - form varia e acopl ] we restrict the weyl geometry to its integrable version , where @xmath1 . in this case , variations of length depend only on the starting and ending points of the trajectory . variational formulations are presented for both obtaining gravitation in this geometry and for particles to follow geodesics . it is established how other physical fields are coupled with the new geometric one and it is observed that the coupling used endows our theory with a gauge symmetry inducing a conformal invariance . as discussed in ref . , since dirac@xcite raised the question about the gravitational constant be , in fact , a constant , this problem has been a challenge for theoretical physics . however , it is argued that this can be solved by taking into account the principle that all fundamental equations of physics must be invariant under local transformations of scale , as proposed by weyl@xcite and hoyle and narlikar.@xcite it is therefore of great theoretical interest to examine a conformal invariant version of gravitation . other versions of a non - conformal model for the gravitational interaction in weyl integrable space - times ( wist ) were already developed@xcite and applications were made in cosmology@xcite and in spherically symmetric configurations for modeling stars.@xcite besides that , the wist geometry has been used to describe the quantum behavior of a particle in an external potential in the non - relativistic@xcite and the relativistic@xcite regime . nevertheless , none of them has formulated the theory in this gauge invariant way . carrying on with the reformulation of the theory , it remained to redefine the observables of gr within this formalism . in sec . [ sec - red - shift ] this is done for the red - shift and in sec . [ sec - verif inv conf ] it is shown that it preserves the gauge symmetry of the theory , as expected . moreover , in sec . [ sec - inv conf em mod cosmo ] it is shown that for cosmological models the conformal invariance opens the possibility that observations may no longer indicate a curvature nor an evolution to the metric . all observations and conclusions from the red - shift in gr being fully described in terms of the @xmath2 field . we conclude that this reformulation of einstein s gravitation in the more general and axiomatic context of weyl geometries turns out to acquire a gauge symmetry that , although it represents a theoretical advance , introduces an indeterminacy of their objects which needs to be solved , for consistency . weyl s geometry differs from that of riemann by allowing vectors to also change their modules when parallel transported along a closed path . this can be summarized by the following expression for the covariant derivative of the metric:@xcite @xmath3 this implies a connection given by @xmath4 where symbols with hat refer to their equivalent in the riemannian case . from it , we can also conclude that for any vector @xmath5 we have : @xmath6 then , the most general geodesic equation is given by : @xmath7 where @xmath8 is the tangent vector of the geodesic and @xmath9 is the parameter which describes it . we consider a congruence of curves @xmath10 , @xmath11 , which in a local coordinate system @xmath12 , have coordinates @xmath13 and we take the parameter @xmath14 so that @xmath15 two neighboring points , @xmath16 and @xmath17 , define a new vector which we will call _ connection vector_. their components are @xmath18 and it is associated with the distance , on the manifold , between the points @xmath19 and @xmath20 . the physical distance , locally determined by an observer at rest in relation to what has the curve @xmath21 as world line , is given by @xmath22 , which we will call _ relative position vector _ , where @xmath23 makes the projection of any vector in the space perpendicular to @xmath8 . introducing the notation @xmath24 to any vector @xmath5 , the relative velocity between two neighboring particles in the congruence is given by @xmath25 and is related to @xmath26 by the following equation : @xmath27 by the property @xmath28 , we can simplify the result to @xmath29 where we have defined @xmath30 . this shows that the velocity of separation between neighboring particles is related to the relative position vector by a linear transformation . it can be easily verified that @xmath31 , then we have their irreducible parts : @xmath32 } \end{array}\right\}\;\rightarrow\ ; v_{\alpha\beta } = \omega_{\alpha\beta } + \sigma_{\alpha\beta } + \frac{1}{3}\theta h_{\alpha\beta } \ , . \label{decomp irredutivel para v}\ ] ] where @xmath33 and @xmath34}$ ] are their symmetric and antisymmetric parts respectively . although we are not with the riemannian connection anymore , the parameter we have defined is such that @xmath35 , @xmath36 and @xmath37 are still related to the expansion , shear and rotation of the congruence respectively.@xcite in order to make this geometric description compatible with a variational principle for the dynamics of a particle in a gravitational field,@xcite we will restrict ourselves to a particular case of weyl geometry which is called weyl integrable space - time ( wist ) in what follows . this is done simply by restricting the field @xmath38 to a gradient . that is , from now on we will consider only @xmath39 this kind of geometry is easily obtained by performing a palatini approach to the action @xmath40 where @xmath41 is the ricci scalar and we follow the sign conventions of ref . . variation of the connection gives precisely ( [ conexao de weyl ] ) with ( [ omega em wist ] ) , what is necessary and suficient to give ( [ deriv da metrica em weyl ] ) ensuring we are in wist . variation of the metric and @xmath2 gives respectively : @xmath42 where @xmath43 is the einstein tensor . we see that variation of @xmath2 gives a redundant equation , since ( [ variacao de omega - vacuo ] ) is the same as the trace of ( [ variacao da metrica - vacuo ] ) . such equality implies in a freedom to one of the functions to be determined . soon it will be shown what this freedom can imply in turn . for test particles to obey the geodesic equation ( [ eq geodesica em weyl ] ) , we first note that in wist we have @xmath44 so , the equation becomes @xmath45 moreover , according to refs . and , in order to characterize a good clock for the observer who follows this geodesic , we should choose such a parameter in which the right hand side of the above equation is zero . this is achieved by precisely that same parameter @xmath14 defined before , in ( [ parametro afim ] ) . this equation is obtained by the following action for a test particle with mass @xmath46 : @xmath47 if we now notice that @xmath48 that is , the connection is just like the riemannian one ( christoffel symbol ) written with @xmath49 , we see that things work much like they were in riemann , but with @xmath49 instead of @xmath50 whenever it appears . that is exactly what happened in the action ( [ acao para part teste em wist ] ) and hence in the geodesic equation ( [ eq geodesica em wist ] ) . specially if we take the parameter @xmath51 defined in sec . [ sec - congruencia de curvas ] , which is again another case of replacing @xmath50 by @xmath49 in the definition of the affine parameter in the riemannian case . moreover , the situation is the same in ( [ acao para weyl - vacuo ] ) : since we have @xmath52 , the einstein - hilbert action becomes @xmath53 now we have made these considerations , it is quite clear that the most natural choice for coupling other fields with @xmath2 is by keeping this same recipe . that is , we take any other lagrangian of the form @xmath54 , in gr , and write it as @xmath55 . then , we will have for our wist action : @xmath56\sqrt{-\tilde{g}}d^4x \ , . \label{acao inv conf wist}\ ] ] variation of the connection gives us wist . variation with respect to the metric gives @xmath57 e^{\omega}\sqrt{-\tilde{g } } = 0 \quad \rightarrow \nonumber \\ \rightarrow \quad & g_{\mu\nu}(\tilde{g}^{\mu\nu } ) = -t_{\mu\nu}(\tilde{g}^{\mu\nu } , ... ) \;\ ; \therefore \;\ ; r(\tilde{g}^{\mu\nu } ) = t(\tilde{g}^{\mu\nu } , ... ) \ , , \label{eq einstein inv conforme}\end{aligned}\ ] ] where we have defined @xmath58}{\delta \tilde{g}^{\alpha\beta } } \ , . \label{tensor momento energia wist}\ ] ] varying @xmath2 we have @xmath59 e^{\omega}g^{\mu\nu}\sqrt{-\tilde{g } } = 0 \quad \rightarrow \nonumber \\ \rightarrow \quad & r(\tilde{g}^{\mu\nu } ) = t(\tilde{g}^{\mu\nu } , ... ) \ , , \label{dinamica p omega wist}\end{aligned}\ ] ] which is a redundant equation , since it is equal to ( [ eq einstein inv conforme ] ) ." +"in the field of microarrays it has traditionally been difficult to compare new methods to methods in published papers as the many methods available for pre - processing , summarizing and filtering make it almost impossible to work with the exact same data , even when the raw data is made available . that is why we consider reproducible research fundamental as it will facilitate easy 1 ) revision of papers , 2 ) access to data and results , 3 ) communication to other researchers and 4 ) comparison between different methods . reproducible research is gaining relevance among the scientific community as shown by the number of papers published on the subject during the last years @xcite . _ showed that the results of only 2 out of 18 published microarray gene - expression analyses were completely reproducible @xcite . this is why some authors demand that documentation and annotation , database accessions and url links and even scripts with instructions are made publicly available @xcite . journals like biostatistics have even appointed an associate editor for reproducible research , but still treat it as a desirable goal "" rather than a requirement @xcite . setting up a framework for reproducible research necessarily implies working with free and open - source software as for example r / bioconductor @xcite . additionally , using sweave @xcite ( a tool for embedding ` r ` code in latexdocuments @xcite ) , enables automatic reports that can be updated with output from the analysis . the main tool in this paper will be the bioconductor package ` aroma.affymetrix ` @xcite that can analyse all affymetrix chip types with a ( .cdf ) chip definition file . the number of arrays ( samples ) that can be simultaneously analysed by ` aroma.affymetrix ` is virtually unlimited as the system requirements are just 1 gb ram , for any operating system @xcite . this package is freely available and can easily be installed into ` r ` . the aroma.affymetrix website www.aroma-project.org is conceived as reference for all the possible microarrays that can be analysed with ` aroma.affymetrix ` , and does not focus specifically on the analysis of the genechip human exon 1.0 st array ( or exon array in short ) . portable scripts for a fast and basic analysis can be obtained on request to ` aroma.affymetrix ` s authors . the analysis of exon array data in ` r`/bioconductor is not yet standard . there are several packages available , and it can be a tremendous effort for a newcomer to maneuver between them , and to overcome the numerous challenges associated with these packages . this paper aims to make this task easier and to provide a quick reference guide to ` aroma.affymetrix ` s documentation . we also explain how to extract data for different statistical analyses and propose a method for gene annotation and for gene profile visualization . for this last step , we use the packages ` biomart ` and ` genomegraphs ` to annotate and visualize the transcripts in a genomic context . the analysis workflow presented in this paper is carried out solely in ` r`/bioconductor , and the paper is available as a sweave ( .snw ) document that will allow the reader to reproduce our exact results . the .snw document can also be converted into an ` r ` script and executed . the workflow starts by reading in the data , followed by background correction and quantile normalization . we then explain how to obtain transcript cluster - , probeset - , and probe - level estimates . afterwards , different methods for the statistical analysis of differential splicing or differential gene expression are reviewed . finally , we make a suggestion on how to annotate transcript clusters to genes in the lists obtained from the statistical analyses , and how to plot the data including genomic information . to exemplify the use of the workflow , an example dataset @xcite is analysed along the way . splicing is the post - transcriptional process that generates mature eukaryotic mrnas from pre - mrnas by removing the non - coding intronic regions and joining together the exonic coding regions . for many genes , two or more splicing events take place during maturation of mrna molecules resulting in a corresponding number of alternatively spliced mrnas . these mature mrnas translate into protein isoforms differing in their amino acid sequence and ultimately in their biochemical and biological properties @xcite . alternative splicing is one of the main tools for generating rna diversity , contributing to the diverse repertoire of transcripts and proteins @xcite . it is known that 92 - 94% of multi - exon human genes are alternatively spliced and that 85% of those have a minor isoform frequency of at least 15% @xcite . in our case we will focus on the detection of differential splicing between groups , as for instance tissue types , or healthy vs. diseased samples . the exon array was presented in october 2005 as a tool for the analysis and profiling of whole - transcriptome expression @xcite . to interrogate each potential exon with at least one probeset , the exon array contains about 5.6 million probes grouped into more than 1.4 million probesets ( most probesets consisting of 4 probes ) , which are further grouped into 1.1 million exon clusters , or collections of overlapping exons . finally , exon clusters are grouped into over 300.000 transcript clusters to describe their relationship , as for example shared splice sites or overlapping exonic sequences . each gene is covered , on average , by 40 probes interrogating regions located along the entire gene @xcite . this probe positioning aims at providing better estimates of gene expression levels than previous arrays , and allows for the study of differential splicing @xcite and differential gene expression based on summarized exon expression . the exon array has three levels of annotation for the interrogated transcript clusters : _ core , extended _ and _ full _ @xcite . core transcript clusters are supported by the most reliable evidence such as refseq transcripts and full - length mrnas @xcite and a core transcript cluster is roughly a gene @xcite ; the extended level contains the core transcript clusters plus cdna - based annotations @xcite and the full level contains the two previous levels plus _ ab - initio _ , or algorithmic , gene predictions @xcite . it is worth noting that ` aroma.affymetrix ` enables the analysis at the three levels of annotation mentioned above , and also that it provides intensity estimates for probes , probesets and transcript clusters , allowing for a variety of options for the analysis . our workflow for the analysis of exon array data starts setting up the required folder structure for ` aroma.affymetrix ` . the data is then preprocessed and summarised at transcript cluster and/or probeset level . next , transcript clusters are analysed with several statistical models to detect differential expression or splicing and the transcripts of interest are annotated and visualised at the end , see figure [ fig : flowchart ] . in the code , places where user input is needed are marked by * * * "" , and places where the user can choose whether to modify parameters are marked by * * "" . to exemplify the use of the tutorial we have used affymetrix s colon cancer data set @xcite , consisting of a collection of paired samples of colon tumour tissue and adjacent normal tissue from 10 patients and available at http://www.affymetrix.com/support/technical/sample_data/exon_array_data.affx . according to affymetrix s website , the rna samples are from a commercial source . this dataset has been used in a number of papers to evaluate the performance of different analysis methods @xcite and a number of genes have been validated to present differential splicing or not @xcite . the analysis was done in ` r ` version 2.15.1 ( 32 bit ) . start by installing and loading ` aroma.affymetrix ` in ` r ` and loading the other libraries required : .... > source(""http://aroma - project.org / hblite.r "" ) > hbinstall(""aroma.affymetrix "" ) > require(aroma.affymetrix ) > require(biomart ) > require(genomegraphs ) .... this section corresponds to steps 1 . and 2 . in figure [ fig : flowchart ] . the first step is to create the folder structure : under a main folder of our choice - ` myworkingdirectory ` "" - we will create the ` rawdata ` "" and ` annotationdata ` "" folders , which will be common to all ` aroma.affymetrix ` projects . inside ` annotationdata ` "" , the subfolder ` chiptypes ` "" will contain one subfolder per chip type , with the exact name of the .cdf file provided by affymetrix , ` huex-1_0-st - v2 ` "" in our case . inside this folder we will save any library and annotation files that might be needed . besides , the ` mydataset ` "" folder will be created under ` rawdata ` "" to store .cel files . these files are the output of a microarray experiment and contain the result of the intensity calculations per probe or pixel . note that the microarray experiment produces one .cel file per array and that one array analyses one sample . affymetrix sometimes refer to their microarrays as chips "" . note also that we need one ` mydataset ` "" folder per experiment and that ` mydataset ` "" will be added as a tag at the end of the ` aroma.affymetrix ` output . .... > # * * * user - defined working directory > wd < - "" myworkingdirectory "" > # * * * user - defined data set name > ds < - "" mydataset "" .... in the second step we save our library ( chip definition file ( .cdf ) in our case ) and .cel files in the corresponding folders . affymetrix s unsupported .cdf files can be downloaded from http://www.affymetrix.com/auth/support/downloads/library_files/huex-1_0-st-v2.cdf.zip , note that registration is needed . for the exon array , elizabeth purdom has created a number of binary .cdf files based on affymetrix s text .cdf file @xcite that are faster to query and more memory efficient . such binary .cdf files for core , extended and full sets of probesets can be downloaded from http://aroma-project.org/node/122 . in the example below we use the custom aroma file for core transcript clusters , which might be updated in the future . our original .cel files will be copied from the user - specified ` mycelfiledirectory ` "" into the exon ` rawdata ` "" subfolder ( the code is part of the .snw version of this paper ) . the desired output folder specified in ` output.folder ` "" should exist in advance . .... > # * * download user - defined library file > library.file < - + paste(annotation.data.exon , + "" huex-1_0-st - v2,corer3,a20071112,ep.cdf "" , + sep = "" / "" ) > download.address < - + "" http://bcgc.lbl.gov/cdffiles/ "" > file < - paste(""huex-1_0-st - v2,a20071112,ep "" , + "" huex-1_0-st - v2,corer3,a20071112,ep.cdf "" , + sep = "" / "" ) > custom.cdf < - + paste(download.address , file , sep = "" "") > download.file(url = custom.cdf , + destfile = library.file , + mode = "" wb "" , quiet = false ) > # * * * user - defined directory containing .cel files > cel.directory < - "" mycelfiledirectory "" > # * * * user - defined output folder > output.folder < - "" output.folder "" .... besides , the sample information should be saved in a tab separated file with column names ` celfile ` , ` replicate ` , and ` treatment ` containing .cel file name" +"the so - called @xmath0-cdm cosmology @xcite , in which the universe is dominated by dark energy and cold dark matter ( cdm ) , accurately describes the large scale properties and evolution of the cosmos . on the scale of the halos of large galaxies , this model predicts copious cdm sub - structures , the most massive of which are identified with the dwarf satellite galaxies that are observed to inhabit such regions @xcite . numerical simulations that adopt this framework @xcite generally reveal that the sub - halos that could host visible dwarf galaxies are distributed roughly spherically about the large galaxy . observationally however , the distribution of dwarf galaxies within the local group appears to be more complicated . @xcite and @xcite first noted that several prominent dwarf galaxies are correlated with streams of emission , and suggested that the outer halo globular clusters of the milky way may represent ` ghostly ' indicators of ancient accretions @xcite . more recent analyses @xcite that include the faint dwarf galaxies detected during the past decade in the sloan digital sky survey ( sdss ) support the earlier results , although concerns remain about the spatial selection biasses given the sdss sky coverage . interestingly , the satellites appear to be rotationally stabilized , orbiting within the plane defined by their spatial alignment @xcite . it has been claimed that the proposed planes of satellites are not predicted within @xmath0-cdm , and can not simply represent a memory of past coherent accretion , although other studies dispute this conclusion @xcite . in a previous contribution we showed that our nearest large companion , the andromeda galaxy , possesses an immense , kinematically coherent , thin plane of dwarf galaxies , representing @xmath2 of the total dwarf population of andromeda ( @xcite ; see also @xcite ) , confirming previous studies @xcite that had hinted at potential spatial correlations of dwarfs in m31 . a scenario that has been proposed to explain these alignments is that the present - day satellites are the remnants of tidal dwarf galaxies formed in ancient major mergers @xcite . this explanation is problematic , however , as it requires that the dwarfs are not dark matter dominated . it is in this context that ( * ? ? ? * hereafter bb14 ) recently analyzed the millennium - ii simulation @xcite , to investigate the incidence of satellite alignments in that large @xmath3 volume of a @xmath0-cdm universe . they concluded that due to the spatial correlation between satellites in @xmath0-cdm , structures similar to that observed are relatively common , arising in approximately 2% of the halos they investigated . the aim of the present paper is to examine the validity of the bb14 analysis , and to extend our earlier analysis to make better use of the accurate kinematic information available for the real satellites . in section [ sec : sample_selection ] , we discuss how the samples were selected from the simulation . section [ sec : results ] presents the analysis and results , and conclusions are drawn in section [ sec : conclusions ] . we select sub - halos from the millennium - ii simulation , using the @xcite catalog which was scaled to the wmap year 7 analysis . the semi - analytic recipes that were applied to the dark matter simulation provide a wealth of predicted physical properties for galaxies that reside within the dark matter halos . since we are interested in selecting systems similar to m31 , we follow bb14 and pick all halos in the redshift @xmath4 snapshot that have virial masses between @xmath5 and @xmath6 , mass - weighted age @xmath7 , and whose neighbors within @xmath8 have a baryonic component less massive than @xmath9 . ( we define the baryonic mass to be the sum of the stellar and cold gas components ) . a total of 1141 such hosts are found . in addition to those bb14 selection criteria , we apply the following three criteria to select hosts that are reasonably similar to m31 . we require that the hosts have baryonic masses in the range @xmath10@xmath11 ( this leaves 1024 galaxies ) , and we require that the group that the host galaxy resides in should have mass @xmath12 , a 95% upper limit to the mass of the local group @xcite ( leaving 885 galaxies ) . to ensure that the m31 analog , as in reality , is the dominant galaxy within the survey region , we finally reject hosts that have a companion within @xmath8 that possesses @xmath13 of their baryonic mass . these cuts yield a sample of 679 host galaxies within the millennium - ii simulation . figure [ fig : observations]a shows the observed distribution of the 15 satellites of m31 that are confined to a narrow plane . it can be immediately appreciated that the plane lies almost perfectly edge - on from our viewing point . the side view is displayed in figure [ fig : observations]b , using the most likely value of the line of sight distances measured by @xcite . the arrows mark the measured line of sight velocity @xcite , with the red arrows showing those satellites that have the same sense of rotation . to reproduce the observational configuration , we place ourselves in the simulation at a random position @xmath14 distant from the host galaxy ( equivalent to the milky way - m31 distance , @xcite ) , with a random camera angle . we initially select all the sub - halos within the millennium - ii simulation that lie within @xmath8 of the chosen host and that have stellar mass @xmath15 ( as proposed by bb14 ) , to which we then apply the pandas spatial selection function . within the pandas area shown in figure [ fig : observations]a , 27 satellites are known ( beyond @xmath16 ) , of which 15 are narrowly aligned in the thin plane discussed by @xcite . to approximate this observed sample , we select in the simulation the brightest 27 satellites that are visible within the pandas field of view . if there are less than 27 satellites within this field of view , we discard the viewing position and draw a new one . using exactly the same procedure as was applied to the real data in @xcite , we calculate the pole of the plane that has the lowest perpendicular rms dispersion ( i.e. the thinnest plane ) for any sub - sample of 15 satellites . in a coordinate system where @xmath17 points east , @xmath18 points north and @xmath19 points along the line of sight vector to m31 ( i.e. as shown in figures [ fig : observations]b and [ fig : observations]d ) , the pole of the observed structure points towards @xmath20 . if the pole of the lowest rms plane , as seen from the randomly - chosen viewpoint , lies within @xmath21 of the pole of the real plane , we store this host and its sample of satellites ; otherwise a new viewing position is randomly drawn . if no sample is found after @xmath22 random draws of the viewing position , we discard the host . this procedure is repeated 12 times , so as to obtain ( in the best cases ) 12 different views of each of the 679 host galaxies . cases where a new viewing position of the same host coincided within @xmath23 to one previously calculated were discarded , as we considered such configurations to be `` repeats '' of the previous solutions ) of satellites , meaning that different sub - samples are selected from different viewing positions . while our procedure gives rise to identical satellite sub - samples in 1.2% of the random draws , the @xmath24 separation requirement still means that these provide different line of sight velocity projections ( used in figure [ fig : angular_momentum ] ) . in 76% of the draws more than @xmath25 of the satellites are different . hence the multiple views help build up better statistics . ] . in figures [ fig : observations]c and [ fig : observations]d we overplot all the sub - samples of 15 satellites found around the host galaxies in the way described above . the samples have been rotated so that the viewpoint lies at @xmath26 . by construction , the random samples have the same orientation as the data . our main motivation to force the alignments to be edge - on was to be able to compare the radial velocity information on the satellites directly to the simulations , but this also automatically corrects for the inclination - dependent detection bias in pandas @xcite , and it also avoids the issue that rotation of a structure aligned perpendicular to the line of sight would not have been detected . nevertheless , tests show that forcing this orientation does not substantially alter the results below . the semi - analytic modeling of @xcite differentiates normal galaxies from `` orphans '' ; the latter being systems whose parent subhalo is no longer resolved . it is possible that many of these orphans are tidally disrupted , and that they are hence not directly comparable to the observed dwarf galaxies . despite these concerns , we will first assume that the orphan satellites represent structures that can be reliably compared to real dwarf galaxies ( this is an assumption that bb14 considered ) . however , we noticed that in the millennium - ii simulation , many of the orphans are spatially clustered around massive sub - halos . we decided to reject all the orphan satellites that were next to a massive , non - orphan , satellite , closer than twice the radius of the stellar disk of the non - orphan satellite . this is justified on the grounds that in reality it is unlikely that such objects would have been identified ( they would be very hard to distinguish from their companion ) . additionally , we reject orphan satellites that are both closer than @xmath27 ( which corresponds approximately to the line of sight distance uncertainty for the best measured dwarf galaxies ) and that have space velocities @xmath28 from a non - orphan satellite , since observationally we would consider such objects to be tidal debris . this is the sample that was displayed previously in figures [ fig : observations]c and [ fig : observations]d . one notices immediately from a visual comparison of panels ( b ) and ( d ) that the sample of simulated satellites that includes orphans is significantly more centrally - concentrated than the real satellites , so clearly the extent of the plane is an important property to attempt to reproduce , in addition to its thinness . bb14 decided to parametrize the radial extent via the rms dispersion within the plane ( `` rms parallel '' ) , which we calculate as the sum of the squares of the distances in the plane _ from the host galaxy_. in figure [ fig : parameters]a we show this parameter plotted against the plane thickness ( `` rms perpendicular '' ) . let us define `` condition 1 '' to be the requirement that the simulated systems should be thinner than the observed structure ( @xmath29 ) , `` condition 2 '' that they should be spatially more extended than the observations ( @xmath30 ) , and `` condition 3 '' that 13 or more out of the subsamples of 15 satellites share the same sense of rotation . we find that 2% of the systems @xmath31 conform to conditions 1 and 2 ( crosses in panel ( a ) ) , but only 3 out of 7757 simulated systems ( 0.04% ) conform to conditions 1,2 and" +"it has been shown that a cooperative communication can provide more reliable communication by reducing the error probability , while the required power remains the same . the concept of cooperation in the communication has a long history going back to @xcite where an information theoretic aspect view of cooperative communication in a multiple access channel ( mac ) is defined . although this work was based on the concept of feedback , it can be seen as a beginning of the notion of cooperation in communication . this concept have then been further extended in the information theoretic framework in several seminal works in @xcite . the initial spark started in @xcite then lead to a fundamental context of network coding ( nc ) , as a method for achieving capacity of wired networks , introduced in 2000 @xcite . thereafter , there have been a vast number of researches on this idea where different advantages of using nc have been addressed . owing to the cooperative nature of network coding , in @xcite , it was shown that using nc over a wireless network can provide diversity , where it is called cooperative diversity in nc , similar to its previous counterparts @xcite . it then lead the researchers in wireless communication also to become interested in nc , either in ad - hoc or cellular networks @xcite . moreover , implementing nc , as an alternative method of routing , in which the nodes in the network process their received packets , can help to increase the multiplexing gain of such networks . a very simple example of a cooperative system is a multiple access relay channel ( marc ) . although there is no direct cooperation between the users , sharing the relay node can be seen as a cooperative behavior . a relay node can be utilized conventionally , where at each time slot the relay only serves for one of the users . on the other hand , if the relay can process the received data from the users and aggregate these data and then send the new aggregated data to the destination , it would be possible to achieve diversity . one instance of such doing can be found in @xcite , where an xoring scheme was considered as a simple way of implementing nc in a wireless network in order to provide diversity in the network . the authors in @xcite have proposed a scheme in a marc in which the users send the log - likelihood ratio ( llr ) of their coded messages to the destination in a noisy channel , and they have shown that their proposed scheme improves the bit error probability ( bep ) of the system . practical analogue nc for cooperation in the physical - layer of marc has not been considered yet , and it has prompted us to consider this method of cooperative scheme here . in this paper , we propose a cooperative scheme based on a simple addition of the received signals in the relay node . we loosely call this scheme as an instance of analogue nc . to this end , we consider a system which uses decode and forward ( df ) for relay cooperation , and after modulating the users re - encoded packets , simply adds the packets for transmission in the relay . we assume that each node has a single antenna . also we assume that each user has a power limitation of @xmath0 , but the power limitation of the relay node in @xmath1-user marc will be @xmath2 which is logical . we propose a detection method in the end - node , i.e. destination , being based on v - blast model in a multiple - antenna system @xcite . we derive a tight upper bound on the system s bep for both uncoded and coded transmissions , from which we show that using v - blast detection technique , we can achieve full - order diversity , being two in a two - user marc setting . simulation results indicate that the bounds are tight enough . moreover , results show that the proposed scheme can achieve a diversity order of two for any number of users and only one relay node , in contrast to the traditional methods ( e.g. alamouti scheme ) in which each user must have two antennas for transmission . the paper is organized as follows . in section [ sec : systemdescription ] , we briefly describe the system and the proposed transmission protocol . in section [ sec : detection ] we introduce the detection algorithm . the performance analysis is presented in section [ sec : perfanal ] . numerical experiments are shown in section [ sec : numexp ] . we finally finish the paper with the concluding remarks in section [ sec : conc ] . notation and abbreviations in the paper are as below . boldface lower case letters denote column vectors . concatenation of several vectors is also denoted by a boldface lower case letter . @xmath3 element of the vector @xmath4 is denoted by @xmath5 . boldface upper case letters are used to denote matrices . @xmath6 denotes transpose operators . the cadinality of a set @xmath7 is shown by @xmath8 . @xmath9 denotes the probability of event @xmath10 when dealing with random variable , @xmath11 , we use @xmath12 , @xmath13 , and @xmath14 to denote the cumulative distribution function ( cdf ) , probability density function ( pdf ) , and characteristic function , respectively . finally , the notation @xmath15 $ ] is used to denote taking expectation of @xmath16 with respect to the subscript @xmath11 . for the simplicity of presentation , we consider marc with two users a and b , and one relay r , and the destination d. the results can be generalized for more than two users sharing one relay . figure [ fig : marc - view ] shows a two - user marc used throughly in this paper . in what follows , we model the received signals at the destination and relay node . the transmitted signal by the relay node is considered in the next subsection . let @xmath17 denote the channel gain between nodes @xmath18 and @xmath19 , where @xmath20 and @xmath21 . the channel gains are assumed to be independent zero mean complex gaussian random variables with the powers of @xmath22 and @xmath23 , for the link between the user ( @xmath24 or @xmath25 ) and the relay ( @xmath26 ) , and the link between node ( @xmath24 , @xmath25 , or @xmath26 ) and the destination , respectively . that is , we have considered different qualities for user - relay and user ( relay)-destination channels . we assume a block fading in which the channel ( gain ) coefficient is constant during each block transmission @xcite . moreover , we assume that each user sends a codeword @xmath27 . for all the wireless communication links shown in figure [ fig : marc - view ] , we consider an additive white gaussian noise ( awgn ) with one - sided power spectral density ( psd ) of @xmath28 . then , knowing the fact that @xmath29 s are normally distributed with the powers mentioned above , the instantaneous signal to noise ratio ( snr ) of the link between user @xmath30 and the relay node @xmath26 is given by @xmath31 being distributed exponentially as follows @xmath32 furthermore , the received signals at the destination from two users can be modeled as @xmath33 whereas @xmath34 and @xmath35 are the received additive ( vector - valued ) white gaussian noises at the destination side . the @xmath36 and @xmath37 , the vectors of dimension @xmath1 , denote the transmitted blocks from users @xmath24 and @xmath25 , respectively , with the following power constraints : @xmath38 where @xmath1 is the number of bits in each block . similarly , the received signals at the relay node are given by @xmath39 where @xmath40 and @xmath41 are the noises received at the relay node through user @xmath24 and @xmath25 , respectively . since , in this paper we aim at proposing a cooperative protocol while sharing a single relay node by two nodes , we propose to divide the time as shown in figure [ fig : timeslot ] . in figure [ fig : timeslot ] the transmission time slots are allocated based on time division multiple access ( tdma ) scheme . as illustrated in figure [ fig : timeslot ] , in the first two time slots , users a and b transmit their blocks . then , the relay , based on its received signals @xmath42 and @xmath43 , decodes the received blocks . depending on whether or not the relay can correctly decode the received blocks , which can be recognized by a error - detecting code ( e.g. , crc codes ) , the relay decides upon cooperation with the two transmitters in the third slot , as shown in figure [ fig : timeslot ] leading to four possible scenarios summarized in table [ table : relayscenarios ] . .four possible states at the relay node . [ cols=""^,^,^"",options=""header "" , ] as can be inferred from table [ table : relayscenarios ] , relay cooperation can be categorized into four states : first , corresponding to @xmath44 , the relay will be silent , and as a result the destination only receives the direct block transmissions from two users . hence , the bit error probability is the same as that of a direct transmission with power @xmath45 . second , corresponding to @xmath46 and @xmath47 , the relay node only cooperates in transmission of one of the users . thereby , only one of the users benefits a second order diversity transmission . denoting this user by @xmath48 ( @xmath49 ) , the received signal at the destination from the relay will be @xmath50 where @xmath51 and @xmath52 are relay s estimate of user s signal and additive noise at the destination , respectively . in this case , the bit error probability for the assisted user is equal to that of a maximum ratio combining ( mrc ) receiver , @xcite , with two independent receptions of the transmitted signal , and for the other user , it is similar to the first state . lastly , for @xmath53 , the relay can successfully decode both users blocks . then , the relay encodes and modulates these signals separately , and transmits the sum of the modulated analog signals . thus , the destination node will receive the following signal @xmath54 in this section , we propose a method for detection at the destination node . first , we assume that the destination knows fading coefficients , e.g. by acquiring transmitting pilot symbols , and also knows the state of cooperation at the relay , e.g. it can be implemented by sending 2 bits encoding four states . for @xmath55 in table [ table : relayscenarios ] , both users have interference - free direct transmission , and , as stated above , the conventional receiver is used . for @xmath56 ( @xmath57 ) , the user which is able to utilize relay resource , the destination uses mrc of the two received signals , one from the user and the other from the relay . in the last state , we propose a novel method for detection relying on the basis of v - blast detection . first , from equations - , we rewrite the three received signals in three time slots ( see figure [ fig : timeslot ] ) at the destination in a following matrix format given by @xmath58 without loss of generality , we focus on detecting user @xmath24 s" +"the field of _ computational learning theory _ deals with the abilities and limitations of algorithms that learn functions from data . many models of how learning algorithms access data have been considered in the literature . among these , two of the most prominent are via _ membership queries _ and via _ random examples_. membership queries are `` black - box '' queries ; in a membership query , a learning algorithm submits an input @xmath9 to an oracle and receives the value of @xmath10 . in models of learning from random examples , each time the learning algorithm queries the oracle it receives a labeled example @xmath11 where @xmath9 is independently drawn from some fixed probability distribution over the space of all possible examples . ( we give precise definitions of these , and all the learning models we consider , in section [ sec : jprelim ] . ) in recent years a number of researchers have considered quantum variants of well - studied models in computational learning theory , see e.g. @xcite . as we describe in section [ sec : jprelim ] , models of learning from quantum membership queries and from fixed quantum superpositions of labeled examples ( we refer to these as _ quantum examples _ ) have been considered ; such oracles have been studied in the context of _ quantum property testing _ as well @xcite . one common theme in the existing literature on quantum computational learning and testing is that these works study algorithms whose only access to the function is via some form of quantum oracle such as the quantum membership oracle or quantum example oracles mentioned above . for instance , @xcite modifies the classical harmonic sieve algorithm of @xcite so that it uses only uniform quantum examples to learn @xmath12 formulas . @xcite considers the problem of quantum property testing using quantum membership queries to give an exponential separation between classical and quantum testers for certain concept classes . @xcite studies the information - theoretic requirements of exact learning using quantum membership queries and probably approximately correct ( pac ) learning using quantum examples . many other articles such as @xcite could further extend this list . as the problem of building large scale quantum computers remains a major challenge , it is natural to question the technical feasibility of large scale implementation of the quantum oracles considered in the literature . it is desirable to minimize the number of quantum ( as opposed to classical ) oracle queries or examples required by quantum algorithms . thus motivated , in this paper we are interested in designing testing and learning algorithms with access to both quantum and classical sources of information ( with the goal of minimizing the quantum resources required ) . all of our positive results are based on a quantum subroutine due to @xcite , which we will refer to as an @xmath2 ( fourier sample ) oracle call . as explained in section [ sec : jprelim ] , a call to the @xmath2 oracle yields a subset of @xmath13 ( this set should be viewed as a subset of the input variables @xmath14 of @xmath3 ) drawn according to the fourier spectrum of the boolean function @xmath3 . as demonstrated by @xcite , such an oracle can be implemented using @xmath15 uniform quantum examples from a uniform distribution quantum example oracle . in fact , all of our algorithms will be purely classical apart from their use of the @xmath2 oracle . thus , all of our algorithms can be implemented within the ( uniform distribution ) quantum pac model first proposed by @xcite . this model is a natural quantum extension of the classical pac model introduced by valiant @xcite , as described in section [ sec : jprelim ] . we emphasize that no membership queries , classical or quantum , are used in our algorithms , only uniform quantum superpositions of labeled examples , and we recall that such uniform quantum examples can not efficiently simulate even classical membership queries in general ( see @xcite ) . our approach of focusing only on the @xmath2 oracle allows us to abstract away from the intricacies of quantum computation , and renders our results useful in any setting in which an @xmath2 oracle can be provided to the user . in fact , learning and testing with @xmath2 oracle queries may be regarded as a new distinct model ( which may possibly be weaker than the uniform distribution quantum example model ) . we are primarily interested in the information theoretic requirements ( i.e. the number of oracle calls needed ) of the learning and testing problems that we discuss . we give upper and lower bounds for a range of learning and testing problems related to _ @xmath0-juntas _ ; these are boolean functions @xmath16 that depend only on ( an unknown subset of ) at most @xmath0 of the @xmath1 input variables @xmath14 . juntas have been the subject of intensive research in learning theory and property testing in recent years , see e.g. @xcite . our first result , in section [ sec : testjuntas ] , is a @xmath0-junta testing algorithm which uses @xmath17 @xmath2 oracle calls . our algorithm uses fewer queries than the best known classical junta testing algorithm due to fischer _ @xcite , which uses @xmath18 membership queries . however , since the best lower bound known for classical membership query based junta testing ( due to chockler and gutfreund @xcite ) is @xmath19 , our result does not rule out the possibility that there might exist a classical membership query algorithm with the same query complexity . to complement our @xmath2 based testing algorithm , we establish a new lower bound : any @xmath0-junta testing algorithm that uses only a @xmath2 oracle requires @xmath6 calls to the @xmath2 oracle this shows that our testing algorithm is not too far from optimal . finally , we consider algorithms that can both make @xmath2 queries and also access classical random examples . in section [ sec : learnjuntas ] we give an algorithm for learning @xmath0-juntas over @xmath20 that uses @xmath7 @xmath2 queries and @xmath21 random examples . since any classical learning algorithm requires @xmath22 examples ( even if it is allowed to use membership queries ) , this result illustrates that it is possible to reduce the classical query complexity substantially ( in particular , to eliminate the dependence on @xmath1 ) if the learning algorithm is also permitted to have some very limited quantum information . moreover most of the consumption of our algorithm is from classical random examples which are considered quite `` cheap '' relative to quantum examples . from another perspective , our result shows that for learning @xmath0-juntas , almost all the quantum examples used by the algorithm of bshouty and jackson @xcite can in fact be converted into ordinary classical random examples . we show that our algorithm is close to best possible by giving a nearly matching lower bound . in section [ sec : jprelim ] we describe the models and problems we will consider and present some useful preliminaries from fourier analysis and probability . section [ sec : testjuntas ] gives our results on testing juntas and section [ sec : learnjuntas ] gives our results on learning juntas . in keeping with standard terminology in learning theory , a _ concept _ @xmath3 over @xmath23 is a boolean function @xmath24 , where @xmath25 stands for true and @xmath26 stands for false . concept class _ @xmath27 is a set of concepts where @xmath28 consists of those concepts in @xmath29 whose domain is @xmath30 for ease of notation throughout the paper we will omit the subscript in @xmath28 and simply write @xmath31 to denote a collection of concepts over @xmath20 . the concept class we will chiefly be interested in is the class of _ @xmath0-juntas_. a boolean function @xmath32 is a @xmath0-junta if @xmath3 depends only on @xmath0 out of its @xmath1 input variables . we are interested in the following computational problems : pac learning under the uniform distribution : : : given any _ target concept _ @xmath33 , an _ @xmath34-learning algorithm for concept class @xmath31 _ under the uniform distribution outputs a _ hypothesis _ function @xmath35 which , with probability at least @xmath36 , agrees with @xmath37 on at least a @xmath38 fraction of the inputs in @xmath30 this is a widely studied framework in the learning theory literature both in classical ( see for instance @xcite ) and in quantum ( see @xcite ) versions . property testing : : : let @xmath3 be any boolean function @xmath39 . a _ property testing algorithm for concept class @xmath31 _ is an algorithm which , given access to @xmath3 , behaves as follows : + * if @xmath33 then the algorithm outputs accept with probability at least @xmath36 ; * if @xmath3 is _ @xmath34-far _ from any concept in @xmath31 ( i.e. for every concept @xmath40 , @xmath3 and @xmath41 differ on at least an @xmath34 fraction of all inputs ) , then the algorithm outputs reject with probability at least @xmath36 . + the notion of property testing was first developed by @xcite and @xcite . quantum property testing was first studied by buhrman _ et al . _ @xcite , who first gave an example of an exponential separation between the query complexity of classical and quantum testers for a particular concept class . note that a learning or testing algorithm for @xmath31 `` knows '' the class @xmath31 but does not know the identity of the concept @xmath3 . while our primary concern is the number of oracle calls that our algorithms use , we are also interested in _ time efficient _ algorithms for testing and learning ; for the concept class of @xmath0-juntas , these are algorithms running in poly@xmath42 time steps . in order for learning and testing algorithms to gather information about the unknown concept @xmath3 , they need an information source called an _ oracle_. the number of times an oracle is queried by an algorithm is referred to as the _ query complexity_. sometimes our algorithms will be allowed access to more than one type of oracle in our discussion . in this paper we will consider the following types of oracles that provide classical information : membership oracle @xmath43 : : : for @xmath3 a boolean function , a _ membership oracle _ @xmath44 is an oracle which , when queried with input @xmath9 , outputs the label @xmath10 assigned by @xmath3 to @xmath45 uniform random example oracle @xmath46 : : : a query @xmath47 of the random example oracle returns an ordered pair @xmath48 where @xmath9 is drawn uniformly random from the set @xmath49 of all possible inputs . clearly a single call to an @xmath43 oracle can simulate the random example oracle @xmath46 . indeed @xmath46 oracle queries are considered `` cheap '' compared to membership queries . for example , in many settings it is possible to obtain random labeled examples but impossible to obtained the label of a particular desired example ( consider prediction problems dealing with phenomena such as weather or financial markets ) . we note that the set of concept classes that are known to be efficiently pac learnable from uniform random examples only is rather limited , see e.g. @xcite . in contrast , there are known efficient algorithms that use membership queries to learning important function classes such as @xmath12 ( disjunctive normal form ) formulas @xcite . we will consider the following quantum oracles , which are the natural quantum generalizations of membership queries and uniform random examples respectively . quantum membership oracle @xmath50 : : : the quantum membership oracle @xmath51 is the quantum oracle whose query acts on the computational basis states" +"smc 3 is one of the symbiotic systems in the magellanic clouds . the system contains a wd and an m giant with an orbital period of 4.5 years ( eg . it is a supersoft x - ray source powered by a steady hydrogen burning on the surface of the white dwarf ( orio _ et al . _ 2007 ) . because the system contains a massive white dwarf ( m@xmath01.18 m@xmath1 ; orio _ et al . _ @xcite ) with a high accretion rate ( @xmath2 m@xmath1/yr ; kahabka @xcite ) it is considered as one of the most promising supernova ia progenitors among the known symbiotic population . to estimate the mass of the red giant we used the fact that it pulsates with a period of 110 days ( kahabka @xcite ) . smc 3 lies on the sequence b in the k - log(p ) plane ( wood 2000 ) which suggests the first overtone pulsation . assuming the pulsation constant of q=0.04 we derived the mass of 2.3@xmath3 m@xmath1 . to carry out our analysis we used the startrack population synthesis code ( belczyski _ et al . _ the code includes the wind accretion through bondi - hoyle mechanism , roche - lobe overflow , @xmath4 roche - lobe overflow and @xmath5 roche - lobe overflow . as initial conditions we adopted the current parameters of the system and then we modeled its future evolution . we assumed @xmath6=1.44 m@xmath1 and , since we studied the system in the sn ia context , a co wd . for all of our models the system went trough a common envelope ( ce ) after @xmath7 yrs and for none of the models system wd managed to accumulate enough matter to become a type ia supernova . the orbital separation after the ce was relatively big ( a@xmath8r@xmath1 ) , which makes a merger in the hubble time unlikely . the obtained parameters of the system are presented in fig . we predict that the system will not become a type ia supernova in contrary to what was suggested in the literature ( orio _ et al . _ the caveat is that our predicted mass transfer rate is somewhat lower then the one expected for the steady hydrogen burning on the surface of the white dwarf ( nomoto _ et al . _ a lower @xmath9 then expected could be due to the fact that our model underestimates the rg mass loss trough wind by treating it as in the single star scenario , whereas there is a strong observational evidence that this wind is significantly enhanced due to tidal interactions in syst ( mikoajewska _ et al . _ large roche lobe filling factor suggests ellipsoidal variability in the system . 99 belczyski k. 2008 , apjs , 174 , 223 kahabka p. , 2004 , a&a , 416 , 57 kato m. 2013 , apj , 763 , 5 nomoto k. 2007 , apj , 663 , 1269 mikoajewska j. 2002 , adspr , 30 , 2045 orio m. 2007 , apj , 661 , 1105 wood p.r . , 2000 , pasa , 17 , 18" +"this article proposes an approach to inferring the causal impact of a market intervention , such as a new product launch or the onset of an advertising campaign . our method generalises the widely used difference - in - differences approach to the time - series setting by explicitly modelling the counterfactual of a time series observed both before and after the intervention . it improves on existing methods in two respects : it provides a fully bayesian time - series estimate for the effect ; and it uses model averaging to construct the most appropriate synthetic control for modelling the counterfactual . the ` causalimpact ` r package provides an implementation of our approach ( http://google.github.io/causalimpact/ ) . inferring the impact of market interventions is an important and timely problem . partly because of recent interest in big data , many firms have begun to understand that a competitive advantage can be had by systematically using impact measures to inform strategic decision making . an example is the use of `` a@xmath0b experiments '' to identify the most effective market treatments for the purpose of allocating resources [ @xcite ] . here , we focus on measuring the impact of a discrete marketing event , such as the release of a new product , the introduction of a new feature , or the beginning or end of an advertising campaign , with the aim of measuring the event s impact on a response metric of interest ( e.g. , sales ) . the causal impact of a treatment is the difference between the observed value of the response and the ( unobserved ) value that would have been obtained under the alternative treatment , that is , the effect of treatment on the treated [ @xcite , @xcite ( @xcite ) ] . in the present setting the response variable is a time series , so the causal effect of interest is the difference between the observed series and the series that would have been observed had the intervention not taken place . a powerful approach to constructing the counterfactual is based on the idea of combining a set of candidate predictor variables into a single `` synthetic control '' [ @xcite ] . broadly speaking , there are three sources of information available for constructing an adequate synthetic control . the first is the time - series behaviour of the response itself , prior to the intervention . the second is the behaviour of other time series that were predictive of the target series prior to the intervention . such control series can be based , for example , on the same product in a different region that did not receive the intervention or on a metric that reflects activity in the industry as a whole . in practice , there are often many such series available , and the challenge is to pick the relevant subset to use as contemporaneous controls . this selection is done on the _ pre - treatment _ portion of potential controls ; but their value for predicting the counterfactual lies in their _ post - treatment _ behaviour . as long as the control series received no intervention themselves , it is often reasonable to assume the relationship between the treatment and the control series that existed prior to the intervention to continue afterwards . thus , a plausible estimate of the counterfactual time series can be computed up to the point in time where the relationship between treatment and controls can no longer be assumed to be stationary , for example , because one of the controls received treatment itself . in a bayesian framework , a third source of information for inferring the counterfactual is the available prior knowledge about the model parameters , as elicited , for example , by previous studies . ) with an intervention beginning in january 2014 . two other markets ( @xmath1 , @xmath2 ) were not subject to the intervention and allow us to construct a synthetic control [ cf . @xcite ] . inverting the state - space model described in the main text yields a prediction of what would have happened in @xmath3 had the intervention not taken place ( posterior predictive expectation of the counterfactual with pointwise 95% posterior probability intervals ) . the difference between observed data and counterfactual predictions is the inferred causal impact of the intervention . here , predictions accurately reflect the true ( gamma - shaped ) impact . a key characteristic of the inferred impact series is the progressive widening of the posterior intervals ( shaded area ) . this effect emerges naturally from the model structure and agrees with the intuition that predictions should become increasingly uncertain as we look further and further into the ( retrospective ) future . another way of visualizing posterior inferences is by means of a cumulative impact plot . it shows , for each day , the summed effect up to that day . here , the 95% credible interval of the cumulative impact crosses the zero - line about five months after the intervention , at which point we would no longer declare a significant overall effect . ] [ fig : intro : illustration ] we combine the three preceding sources of information using a state - space time - series model , where one component of state is a linear regression on the contemporaneous predictors . the framework of our model allows us to choose from among a large set of potential controls by placing a spike - and - slab prior on the set of regression coefficients and by allowing the model to average over the set of controls [ @xcite ] . we then compute the posterior distribution of the counterfactual time series given the value of the target series in the pre - intervention period , along with the values of the controls in the post - intervention period . subtracting the predicted from the observed response during the post - intervention period gives a semiparametric bayesian posterior distribution for the causal effect ( figure [ fig : intro : illustration ] ) . as with other domains , causal inference in marketing requires subtlety . marketing data are often observational and rarely follow the ideal of a randomised design . they typically exhibit a low signal - to - noise ratio . they are subject to multiple seasonal variations , and they are often confounded by the effects of unobserved variables and their interactions [ for recent examples , see @xcite , @xcite ( @xcite ) ] . rigorous causal inferences can be obtained through randomised experiments , which are often implemented in the form of geo experiments . many market interventions , however , fail to satisfy the requirements of such approaches . for instance , advertising campaigns are frequently launched across multiple channels , online and offline , which precludes measurement of individual exposure . campaigns are often targeted at an entire country , and one country only , which prohibits the use of geographic controls within that country . likewise , a campaign might be launched in several countries but at different points in time . thus , while a large control group may be available , the treatment group often consists of no more than one region or a few regions with considerable heterogeneity among them . a standard approach to causal inference in such settings is based on a linear model of the observed outcomes in the treatment and control group before and after the intervention . one can then estimate the difference between ( i ) the pre - post difference in the treatment group and ( ii ) the pre - post difference in the control group . the assumption underlying such _ difference - in - differences _ ( dd ) designs is that the level of the control group provides an adequate proxy for the level that would have been observed in the treatment group in the absence of treatment [ see @xcite ] . dd designs have been limited in three ways . first , dd is traditionally based on a static regression model that assumes i.i.d . data despite the fact that the design has a temporal component . when fit to serially correlated data , static models yield overoptimistic inferences with too narrow uncertainty intervals [ see also @xcite , @xcite ( @xcite ) , @xcite ] . second , most dd analyses only consider two time points : before and after the intervention . in practice , the manner in which an effect evolves over time , especially its onset and decay structure , is often a key question . third , when dd analyses _ are _ based on time series , previous studies have imposed restrictions on the way in which a synthetic control is constructed from a set of predictor variables , which is something we wish to avoid . for example , one strategy [ @xcite ] has been to choose a convex combination @xmath4 of @xmath5 predictor time series in such a way that a vector of pre - treatment variables ( not time series ) @xmath1 characterising the treated unit before the intervention is matched most closely by the combination of pre - treatment variables @xmath6 of the control units w.r.t . a vector of importance weights @xmath7 . these weights are themselves determined in such a way that the combination of pre - treatment outcome time series of the control units most closely matches the pre - treatment outcome time series of the treated unit . such a scheme relies on the availability of interpretable characteristics ( e.g. , growth predictors ) , and it precludes nonconvex combinations of controls when constructing the weight vector @xmath8 . we prefer to select a combination of control series without reference to external characteristics and purely in terms of how well they explain the pre - treatment outcome time series of the treated unit ( while automatically balancing goodness of fit and model complexity through the use of regularizing priors ) . another idea [ @xcite ] has been to use classical variable - selection methods ( such as the lasso ) to find a sparse set of predictors . this approach , however , ignores posterior uncertainty about both which predictors to use and their coefficients . the limitations of dd schemes can be addressed by using state - space models , coupled with highly flexible regression components , to explain the temporal evolution of an observed outcome . state - space models distinguish between a state equation that describes the transition of a set of latent variables from one time point to the next and an observation equation that specifies how a given system state translates into measurements . this distinction makes them extremely flexible and powerful [ see @xcite for a discussion in the context of marketing research ] . the approach described in this paper inherits three main characteristics from the state - space paradigm . first , it allows us to flexibly accommodate different kinds of assumptions about the latent state and emission processes underlying the observed data , including local trends and seasonality . second , we use a fully bayesian approach to inferring the temporal evolution of counterfactual activity and incremental impact . one advantage of this is the flexibility with which posterior inferences can be summarised . third , we use a regression component that precludes a rigid commitment to a particular set of controls by integrating out our posterior uncertainty about the influence of each predictor as well as our uncertainty about which predictors to include in the first place , which avoids overfitting . the remainder of this paper is organised as follows . section [ sec : theory ] describes the proposed model , its design variations , the choice of" +"the nonequilibrium properties of strongly correlated electron systems are a challenging subject in need of a better understanding . while experimental studies in this area face difficulties in the solid state context , ultracold quantum gases provide a controlled way to address this difficult issue . for this reason , recent experiments employing out - of - equilibrium cold atom gases in optical lattices , which allows the realization of model hamiltonians for strongly correlated particles ( for a review , see , e.g. , ref . @xcite ) , have attracted considerable attention @xcite . among the fundamental questions recently addressed in these experiments is the issue of thermalization in isolated quantum systems @xcite . in the transient regime , quantum quenches have been shown to induce a collapse and revival of coherence properties @xcite , and transport measurements in different lattice systems have unveiled the intriguing consequences of strong correlations @xcite . the important effects of interactions have been observed in the expansion of bosons in one - dimensional ( 1d ) lattices as well @xcite . in the expansion from a mott insulator ( mi ) state , quasi - condensates at finite momenta emerge @xcite , while in the hard - core regime , the expansion from a superfluid state leads to the dynamical fermionization of the bosonic momentum distribution function ( mdf ) @xcite . the latter is a generic feature of the expansion of harmonically trapped hard - core bosons in the absence of a lattice @xcite . in addition , it has been shown in ref . @xcite that , independently of the initial interaction strength , a freely expanding lieb - liniger gas always enters a strongly correlated ( hard - core like ) regime . the expansion dynamics of strongly correlated fermions , which due to the spin - degree of freedom is expected to be richer , has not yet been addressed , and it is the objective of this work . concretely , we study the expansion of two - component interacting fermions in a 1d lattice . the ground state physics of these systems is characterized by a tomonaga - luttinger ( tl ) state with power - law decaying correlations at any incommensurate filling . at half - filling , a charge gap opens and the system exhibits quasi long - range antiferromagnetic correlations @xcite . here , we wish to elucidate how the initial state of the system , being either mi or tl , affects the expansion process . identifying distinctive features for the mi is of much interest to experimentalists in the search for the fermionic mi state . however , our main objective is to shed light on the relation , if any , between these out - of - equilibrium systems and their equilibrium counterparts . as the main result of this work , we provide evidence that correlations measured in nonequilibrium are quantitatively described by appropriately chosen equilibrium reference systems . the outline of the paper is the following . first , we describe the model and the numerical procedure in sec . [ sec : model ] . section [ sec : mdf ] contains our results on the time - evolution of density profiles and the momentum distribution function for both tl and mi initial states . in sec . [ sec : gs ] , we investigate what the possible relation to equilibrium system is , and we present a comparative analysis of spin and charge correlation functions . we also comment on the validity of our findings in other models , such as the hubbard chain with a nearest - neighbor repulsion , which renders the model nonintegrable . we conclude with a summary of our results contained in sec . [ sec : sum ] . the nonequilibrium dynamics is analyzed using the adaptive time - dependent density - matrix renormalization group method ( tdmrg ) @xcite . we consider the 1d hubbard model with nearest - neighbor hopping @xmath1 and an on - site coulomb repulsion @xmath2 : @xmath3 @xmath4(@xmath5 ) is a fermion creation(annihilation ) operator acting on site @xmath6 , with ( pseudo-)spin index @xmath7 , @xmath8 is the corresponding density operator , and we define @xmath9 . @xmath10 denotes the number of sites , @xmath11 is the lattice constant , and open boundary conditions are imposed . we prepare an initial state with a filling @xmath12 that is non - vanishing in only a portion of the system by applying a confining box - potential @xmath13 . hence , we have @xmath14 , with @xmath15 for @xmath16 and @xmath17 otherwise . at time @xmath18 , we turn off @xmath19 . @xmath20 is given in units of @xmath21 , we set @xmath22 to unity . in our tdmrg runs we use a third - order trotter - suzuki time - evolution scheme with a time step of @xmath23 . the discarded weight during the time - evolution is kept below @xmath24 . to simulate the longest time scales possible on a given system size before the particles are reflected at the boundaries , we select an asymmetric set - up and , hence , particles can only expand into one direction . we have checked that the same overall picture is observed in symmetric set - ups ( see also ref . @xcite ) . = @xmath25 ; main panel : mdf ; inset : density ) ; ( b ) tl ( @xmath12=@xmath26 ) ; both at @xmath27 and plotted at times @xmath28 . note that at @xmath29 and before the right boundary is reached , the mdf exhibits only small changes . dotted line in ( b ) : mdf of a reference system ( see text in sec . [ sec : gs ] a for details ) with @xmath30 . inset in ( b ) : decay of one - particle correlations during the expansion of the mi . the @xmath20=@xmath31 curve is for a @xmath10=@xmath32 system at half - filling . dotted vertical lines in ( a ) and ( b ) denote @xmath33.,scaledwidth=45.0% ] we first discuss the properties of the mdf @xmath34 , computed from @xmath35 , where @xmath36 is the one - particle density matrix . in fig . [ fig : nk_fermi](a ) , we show the evolution of @xmath34 ( main panel ) and the density @xmath37 ( inset ) for an initial mi state . the main panel reveals a peculiar behavior of @xmath34 : as the mott insulator melts , a peak develops at a finite momentum @xmath38 . we further find that , for @xmath2 larger than the band - width @xmath39 , @xmath38 closely approaches @xmath40 . this behavior resembles that of hard- and soft - core bosons @xcite . qualitatively , we understand this in terms of an energy argument : in the mi state with @xmath41 , the total kinetic energy is close to zero . hence , particles emitted into an empty lattice have a small average kinetic energy corresponding to a momentum @xmath40 . as the fermi statistics prohibits quasi - condensation into a single momentum state , @xmath34 becomes a broad function around @xmath42 . while the initial mi state is characterized by an exponential decay of one - particle correlations , _ i.e. _ , @xmath43@xmath44@xmath45 , @xmath46=const , we find that during the expansion , the system develops power - law correlations . in the inset of fig . [ fig : nk_fermi](b ) , we compare the @xmath43 of a mi in equilibrium with the correlations that emerge during its expansion , measured within the moving cloud . the inset reveals the weak decay of correlations during the expansion , consistent with a power law . one may associate the dynamical emergence of this power law with a _ metallization _ of the moving cloud , which , after the melting of the mi , starts behaving as an inhomogeneous metal . as of now , our numerical analysis is restricted to a small number of particles and time scales of @xmath47 only , which prevents us from extracting , _ e.g. _ , exponents of the power laws . note , though , that in the case of free fermions expanding from an insulating state with @xmath48 , _ i.e. _ , a state with no off - diagonal correlations , the emergence of power laws has been established for a large number of particles and hence over substantially larger distances than in the present work @xcite . in the main panel of fig . [ fig : nk_fermi](b ) , we show the evolution of the mdf starting from a tl state with @xmath49 . in this case , the initial state has a well - defined fermi momentum and a power - law decay of correlations @xcite . such decay is preserved during the expansion . moreover , @xmath34 also exhibits a peak , but at a momentum @xmath50 ( @xmath38 increases as @xmath51 ) . another property of this peak , distinguishing it from the peak formed after the melting of the mi , is that it exhibits a much sharper edge at the large momentum side , reminiscent of a fermi edge . from the previous analysis , we conclude that if @xmath34 could be experimentally studied during the expansion in the strongly correlated regime , then the emergence of peaks at @xmath52 in the fermionic mdf would serve to identify the presence of a mott insulator in the initial state . the experimental challenge is to independently control the trapping potential and the lattice @xcite . this has been achieved in the experimental study of disordered ultracold bose gases in both 1d optical lattices @xcite and homogeneous 1d systems @xcite . at this point we would like to emphasize that the physics of our expanding system is different from the one found in theoretical studies of strongly correlated systems in 1d lattices undergoing a relaxation following a quantum quench @xcite . in the latter , correlations have been found to decay faster than with a power law ( sometimes clearly exponentially ) @xcite , while in our moving clouds we find power - law decaying correlations [ inset of fig . [ fig : nk_fermi](b ) ] . in addition , after the relaxation to a steady state , one can ask the question of what statistical ensemble may best describe physical observables , but here we are solely concerned with the transient regime , _ i.e. _ , a regime in which statistical ensembles do not provide us with insights into the behavior of physical observables . our results thus far have singled out a noticeable property of these systems during their expansion : independently of the initial ground state , power laws are observed in the nonequilibrium dynamics . in 1d systems in equilibrium , power - law correlations are only seen in the ground state , as finite temperatures introduce a cut - off at large distances , followed by an exponential decay @xcite . hence , one may wonder whether a system out of equilibrium can in some way resemble the ground state of a system in equilibrium . a natural choice for such a reference state is the ground state of a system that has exactly the same density distribution as the time evolving state , _ i.e. _ , @xmath53 for all sites @xmath6 . hence , a reference system has to be determined at each given time . we construct such reference states by self - consistently computing a set of onsite energies @xmath54 in @xmath55 with @xmath56 from eq . ( [ eq : ham ] ) such that at a desired time , the density profile @xmath57 is reproduced , while keeping @xmath1 and @xmath2 fixed . once the density has converged within an error of" +"nonuniform growth is inherently present in a broad class of phenomena including the development of biological populations , communication networks or economic systems like incomes of persons or companies @xcite . in many cases it is obvious to assume that in a system consisting of groups or clusters of units the attachment of a new entity to one of the groups depends on the already achieved strength or size of that particular group . simon @xcite analysed a simple model of this kind where the growth probability was proportional to the cluster size and he gave exact results for the time dependent size distribution . referring to the examples of words in a book or personal incomes simon derived a power law distribution of cluster sizes . recently , in the search for an explanation of the widely observed scale invariance of large networks like the www @xcite , the internet or power networks @xcite , scientific citation @xcite the idea of preferential growth has been applied to evolving graphs @xcite . it turned out that such graphs behave remarkably : they have `` small world '' properties @xcite and the distribution of the strength of vertices ( number of edges from or to a vertex ) is scale free , provided that the probability of linking a vertex with a new one is proportional to its strength @xcite this class of models represent a new mechanism for `` self - organized criticality''@xcite . the idea of preferential growth seems to be essential in economic systems too where clustering of companies , e.g. , according to their market seem to follow such a pattern @xcite . these models have been treated by different tools including simulations , continuum or mean field theories @xcite and exact calculations @xcite by which information has been accumulated about the asymptotic behavior and the time dependence of the global distribution functions . however , much less attention has been paid to the full time - dependent solution of the problem . the aim of the present work is to give such a solution of a particular model . the paper is organized as follows . in section ii we define the model and the quantities of interest as well as we present the basic master equation . in section iii the main steps of the full time dependent analytic solution is given and the consequences for the steady state and the integrated distributions are drawn . section contains the analysis about the asymptotics and scaling . in section v we present a discussion of our results . the paper terminates with two appendices containing some details of the calculations . we model a growing system which consists of groups of different sizes . at the beginning ( @xmath5 ) we have one group with one element in it . at each time step we add a new element to the system . with probability @xmath6 it will belong to one of the existing groups . the probability that it joins the @xmath2-th group is proportional to the size of the group ( @xmath7 ) , see fig [ fig_explain ] . ( the number of elements is equal to the time , @xmath8 , because the system size is rising by one in each time step . ) with probability @xmath9 the new element will belong to a new group . the process can be described by the following master equation : [ master ] _ i(k , t ) & = & p(k-1 ) t-1 _ i(k-1,t-1 ) + p(1-k t-1 ) _ i(k , t-1 ) + + & & + ( 1-p ) _ i(k , t-1 ) + ( 1-p ) _ i-1(t-1 ) _ k,1(1-_i,1 ) , where @xmath1 is the probability that at time @xmath3 there are @xmath4 elements in the group @xmath2 , and @xmath10 is the probability that at time @xmath3 there are @xmath2 groups in the system : [ boxprob ] _ i(t ) = t-1 i-1 p^t-1-(i-1 ) ( 1-p)^i-1 . in the following we introduce some important quantities and their definitions . given the size distribution of the individual groups , @xmath1 , the size distribution of the total system can be calculated as their average : [ def_p_k , t ] ( k , t ) = 1 t _ i=1^t _ i(k , t ) . in the long time limit this quantity approximates to a stationary value : @xmath11 . the mean of the @xmath2-th group size : [ def_mean ] ( t ) = _ k=1^t - i+1 k _ i(k , t ) . the reason that the upper limit of the above sum is not infinity is that @xmath12 if @xmath13 . in the first step we calculate the group size distribution in the asymptotic case , @xmath14 . the exact analytic formula for @xmath14 was already calculated in @xcite , we present it here to see the dependence of the exponent on the parameter @xmath6 . if we sum up eq . ( [ master ] ) for @xmath15 , we get : [ recurs_p ] t ( k , t ) = ( t-1-pk ) ( k , t-1 ) + p(k-1 ) ( k-1,t-1 ) + ( 1-p)_k,1 , since : _ i-1(t-1 ) ( 1-_i,1 ) & = & 1 , + _ i(k , t-1 ) = _ i=1^t-1 _ i(k , t-1 ) & = & ( t-1 ) ( k , t-1 ) . the stationary behavior of @xmath16 , mentioned in the previous section , can be checked from eq . ( [ recurs_p ] ) . replacing the stationary quantity @xmath14 into eq . ( [ recurs_p ] ) one gets : ( k ) = -pk(k ) + p(k-1)(k-1 ) + ( 1-p ) _ k,1 , which can be solved for @xmath14 : [ p_k , inf ] ( k ) = ( k)(2 + 1 p ) ( k+1 + 1p ) 1-p 1+p_k k^-1 - 1/p . [ fig_p_k , inf ] in the model the first group has an accentuated role since it always has at least one element because of the initial conditions . therefore the master equation ( [ master ] ) for the first group ( @xmath17 ) has the following simpler form : [ i1_master ] _ 1(k , t ) = _ 1(k , t-1 ) - p t-1 k _ 1(k , t-1 ) + ( k-1 ) _ 1(k-1,t-1 ) . for @xmath18 in the above equation on the r.h.s the last term vanishes so the probability @xmath19 can be calculated easily : _ 1(1,t ) = ( t - p ) ( t ) ( 1-p ) . for @xmath20 one can prove ( see appendix [ sec_sum ] ) that the following equality holds : [ k>1_i1_biz ] _ k=1^l ( -1)^k-1 l-1 k-1 _ 1(k , t ) = ( t - lp ) ( t ) ( 1-lp ) . the analytic form of @xmath21 can be received from eq . ( [ k>1_i1_biz ] ) by multiplying both sides with @xmath22 and summing up for @xmath23 , [ pm_1,k ] _ 1(k , l=1^k ( -1)^l-1 k-1 l-1 . in the case of @xmath24 we have to look at the hole master equation ( [ master ] ) . in this case the equality ( [ k>1_i1_biz ] ) does nt hold because of the last factor in ( [ master ] ) . our assumption is that the probability @xmath1 will have a modified form : [ pm_i , k , t ] _ i(k , t ) = ^_1(k , t ) . the validity of the above form can be checked by replacing it back in eq . ( [ master ] ) , see appendix [ sec_i>1 ] . replacing the analytic formula ( [ pm_i , k , t ] ) into ( [ def_mean ] ) one gets : ( t ) = _ k=1^t - i+1 k _ l=1^k ( -1)^l-1 k-1 l-1 ( t - lp ) ( t)(1-lp ) , the two sums can be transposed @xmath25 , and @xmath26 so the mean value will have the following form : [ mean - k , t ] ( t ) = _ l=1^t - i+1 ( -1)^l-1 l t - i+2 l+1 ( t - lp ) ( t)(1-lp ) _ b = i^t ( b)(1-lp ) ( b - lp ) b-2 i-2 p^b - i ( 1-p)^i-1 . in sec . [ sec_p_k , inf ] we calculated the stationary group size distribution directly from the master equation . now we are interested in its dynamic . in order to compute that , we start from the definition ( [ def_p_k , t ] ) of @xmath16 , and replace the solution we got for @xmath1 in the previous sections ( [ pm_i , k , t ] ) . [ p_k , t _ _ ] ( k , t ) & = & 1 t _ l=1^k ( -1)^l-1 k-1 l-1 ( t - lp ) ( t)(1-lp ) transposing the two sums : @xmath27 , and taking into account that : @xmath28 one finally arrives at the time dependent distribution : [ p_k , t ] ( k , t ) = _ ( k , ) + p+lp 1+lp ] in the long time limit we will get back our result ( [ p_k , inf ] ) since the second term in @xmath29 $ ] decays for large @xmath3 values with @xmath30 , and the sum transforms into : ( k , ) = 1-p 1+p ( k)(2 + 1/p ) ( k+1 + 1/p ) . we study the @xmath31 limes of @xmath1 and @xmath32 . in the analytic formula for @xmath1 , see . ( [ pm_i , k , t ] ) , there are two components , @xmath33 and @xmath34 , that depend on the time . [ beta_pm_i , k , t ] _ i(k , t ) = ( 1-p)^i-1 _ l=1^k ( -1)^l-1 k-1 l-1 _ a(l , p , t ) _ b(i , l , p , t ) the limes of the first term , @xmath33 , can be easily calculated _ t a(l , p , t ) = 1 ( 1-lp ) t^-lp the second term in the long time limit @xmath35 will converge to a hypergeometric sum : _ t b(i , l , p , t ) = ( i , l , p ) = ( i ) ( 1-lp ) ( i - lp ) _ 2f_1(i , i-1;i - lp;p ) . for large time values the only time dependent term in ( [ beta_pm_i , k , t ] ) will be @xmath36 which in case of large @xmath3 is a fast decaying function of @xmath37 . so in the case of @xmath38 we can assume that only the first term of the sum gives non - negligible component for @xmath1 . [ pm_i , k , inf ] _ t _ i(k , t ) = t^-p ( 1-p)^i-1 ( i ) ( i - p ) _ 2f_1 ( i , i-1;i - p;p ) + o(t^-2p ) for large @xmath2 values the above formula simplifies further , because in that case @xmath39 , and @xmath40 : [ pm_inf , k , inf ] _ i(k , t ) = ( i t ) ^p to study the asymptotic behavior of @xmath41 we start from the fact , that for small @xmath4 values , @xmath42 , the individual group size distribution , @xmath1 , can be described by the first term of the sum , see eq . ( [ pm_i , k , inf ] ) , and for larger values @xmath43 it has a" +"on scales larger than a few megaparsecs , pressure forces in the baryonic matter in the universe are negligible , so the evolution of dark and baryonic matter is mainly determined by gravity . on small scales pressure becomes important and may segregate between the evolution of baryonic and dark matter . pressure forces , cooling of gas , and star formation feedback , are key ingredients in galaxy formation . these ingredients combine to cause differences between the distributions of galaxies and dark matter ( biasing ) , even on large scales where these effects are not directly important ( e.g. , kaiser 1984 , dekel & rees 1987 , kauffmann , nusser & steinmetz 1997 , benson et . al . 2000 ) . on scales smaller than the jeans length of the photo - heated intergalactic medium ( igm ) , pressure forces dominate gravity and can prevent the collapse of gas into dark haloes below a certain mass threshold . for haloes massive enough the temperature of the igm can be neglected and the gas falls into the halo . the mean free path for collisions between gas particles inside a halo is @xmath12 where @xmath13 is the overdensity inside the virial radius and @xmath14 is a typical cross section for collisions in units of @xmath15 . this is smaller than the virial radius of a typical halo by a few orders of magnitude . therefore , on its infall into the halo , the gas is likely to form shocks and transform its kinetic energy into heat . the hot dense gas can then cool to form stars which explode and inject energy into the halo gas . detailed study of these processes under general conditions is not feasible . one can aim at a global parameterization based on general physical requirements which match observational data ( kauffman , white , guiderdoni 1993 , somerville & primack 1999 , cole et . al . 1994 ) . another route would be to study special aspects which can be treated by either numerical or analytical methods . here we focus on the collapse of the baryonic gas in an einstein - de sitter universe , ignoring the gas initial temperature , cooling and heating processes . we assume that the collapse initiates from a symmetric scale free density peak , and that the velocity of each shell in the peak is taken to match the general expansion of the universe . the energy of each shell is negative and it will expand up to a maximum distance before it starts falling towards the center of the perturbation . the maximum distance is termed the turnaround radius . shell crossing is not allowed and the collapse can proceed in two distinct ways , either a shock wave forms , or shells accumulate at the center . which of these possibilities actually occurs , depends on the physical conditions at the center . if the velocity vanishes at the center than a shock wave forms . if on the other hand physical conditions allow a non vanishing velocity at the center then the shells accumulate at the center ( bertschinger 1985 ) . inner boundary conditions can be arranged so that a shock is accompanied by the accumulation of central mass , but a proper stability analysis is needed to determine whether or not this is possible ( bertschinger 1985 ) . in this paper we focus on shocked collapses without the formation of a central mass . since the initial gas pressure is negligible , the collapse eventually develops in a self - similar way where the only relevant scale at any time is the radius of the shell at maximum expansion . bertschinger ( 1985 ) , and forcada - miro & white ( 1997 ) have studied similarity solutions in spherically symmetric perturbations with initial relative mass excess @xmath16 , and @xmath17 , respectively . here we derive similarity solutions in planar , cylindrical , and spherical geometries , for the collapse of a perturbation with @xmath18 for any @xmath19 and adiabatic index @xmath2 . in section [ equations ] we write the equations of motion for symmetric perturbations in planar , cylindrical , and spherical geometry . in section [ asymptotic ] we discuss the asymptotic behaviour of the fluid variables near the center , in the case of shocked collapse . in section [ numerical ] we present results of numerical integrations of the equations . in section [ asymptotic : dm ] we derive asymptotic behaviour of the fluid variables in a universe dominated by collisionless dark matter . in section [ discussion ] we conclude with a discussion of the results and their potential astrophysical consequences . we write the newtonian equations of motion governing the adiabatic collapse of symmetric perturbations in a collisional fluid ( gas ) of adiabatic index @xmath6 and zero initial pressure . except section [ asymptotic : dm ] , we restrict the analysis here and throughout to the collapse in a flat universe containing collisional gas only . the initial gas pressure is zero , so the expansion scale factor of the universe is @xmath20 , the hubble function is @xmath21 , and the background density is @xmath22 . denote by @xmath23 and @xmath24 the physical position and velocity of a gas shell , where @xmath25 is the symmetry center of the perturbation . further , let @xmath26 and @xmath27 be the gas density and pressure at @xmath23 . as in fillmore & goldreich ( 1984 ) define the mass within a distance @xmath23 from the symmetry center by @xmath28 , where @xmath29 , and 3 refer , respectively , to planar , cylindrical , and spherical perturbations . the mass within a fixed shell varies with time like @xmath30 , because of the hubble expansion along @xmath31 of the axes . in this notation , the equations of motion are , the continuity equation , @xmath32 euler , @xmath33 adiabatic condition , @xmath34 and the relation , @xmath35 these equations are satisfied everywhere except at the shock where the fluid variables are described by jump conditions obtained from mass , momentum , and energy conservation . the initial conditions leading to self - similar collapse are specified at an early time close to zero , @xmath36 , as @xmath37 where @xmath38 is the mean density contrast interior to @xmath23 , and @xmath10 . for cosmological initial conditions the initial density contrast must be tiny , so we will be interested in the solution in the region @xmath39 . a perturbation with @xmath40 can be realized by placing a high narrow positive density peak at the center ( @xmath41 ) of a symmetric void with local density contrast @xmath42 . the condition ( [ inivel ] ) means that a gas shell at @xmath23 moves initially with the general universal expansion . this condition can be relaxed to allow for a non vanishing initial zero peculiar velocity according to late time linear theory ( e.g. , peebles 1980 ) . however , this does not affect the details of the collapse ( peebles 1980 , bertschinger 1985 ) , so we use ( [ inivel ] ) which is commonly adopted in the literature . bertschinger ( 1985 ) and white & forcada ( 1997 ) , respectively , considered the collapse of spherical perturbations with @xmath43 , and @xmath44 . the equations of motion ( [ eom1][eom4 ] ) together with the initial conditions ( [ inid][inip ] ) are insufficient to completely determine the evolution of the perturbation . still missing is an inner boundary condition specifying the velocity and mass at @xmath45 , for @xmath46 . for a shock to develop without the accumulation of a central mass ( a black hole for @xmath47 ) we must have @xmath48 and @xmath49 . relaxing the condition @xmath50 leads to a non - vanishing central mass with or without the presence of a shock . in a critical density universe ( @xmath51 ) the only length scale relevant to the collapse is the scale of non - linearity . at any time , @xmath52 , this scale can be defined as the distance of the shell at the maximum expansion , i.e. , the shell with @xmath53 ( gunn 1977 , fillmore & goldreich 1984 , bertschinger 1985 ) . this radius is termed the current turnaround radius , @xmath54 . starting from tiny initial density contrast , the mean overdensity ( density in units of @xmath55 ) interior to @xmath54 is a fixed number independent of time . for time @xmath56 , when shells with @xmath39 reach their turnaround , the collapse develops a self - similar behaviour that depends on @xmath23 and @xmath52 through the combination @xmath57 . the turnaround radius @xmath54 is given by ( e.g. , fillmore & goldreich 1984 ) , @xmath58 where , @xmath59 for @xmath60 and 3 , respectively . the turnaround radius grows faster than the scale factor @xmath61 . this is because the mass , @xmath62 , interior to @xmath63 must grow with time while the mass , @xmath64 , inside a fixed shell in a homogeneous universe is constant . for @xmath65 the turnaround radius grows faster than @xmath52 reaching the horizon scale in finite time . when this happens relativistic description must be used and @xmath63 ceases to be the only scale in the problem ( fillmore & goldreich 1984 ) . the equations can be cast into a non - dimensional form using the scaled variables @xmath66 , @xmath67 , @xmath68 , and @xmath69 defined by ( bertschinger 1985 ) , @xmath70 expressed in terms of these variables , the equations ( [ eom1]-[eom4 ] ) become , respectively , @xmath71 @xmath72 @xmath73 @xmath74 where the prime symbol denotes derivatives with respect to @xmath75 . we will mainly be concerned with solutions for shocked collapse with vanishing mass at the center . the inner boundary condition appropriate for this collapse are vanishing mass and velocity at @xmath76 , i.e. , @xmath77 self - similarity implies that the shock appears at fixed @xmath78 , so the physical radius of the shock @xmath79 and its non - dimensional speed is @xmath80 . at the surface of the shock the fluid variables satisfy the jump conditions obtained from mass , momentum , and energy conservation . in terms of the non - dimensional fluid variables , the jump conditions appropriate for an adiabatic shock are , @xmath81 where the superscripts of the minus and plus signs refer to pre- and post - shock quantities . in employing energy conservation we have taken @xmath82 as the non - dimensional internal energy per unit mass . in section [ numerical ] we will find numerical solutions satisfying the requirements for shocked collapse without a central mass . except spherical perturbations with @xmath83 only one value @xmath84 can yield solutions satisfying these requirements . spherical perturbations with @xmath83 allow a range of values for @xmath84 . before presenting the numerical solutions we derive in the next section the asymptotic behaviour of the fluid variables near the center , and two integrals of motion which will be used as a check on the numerical solutions . solutions to ( [ a1][a4 ] ) with the appropriate jump and boundary conditions for all @xmath85 will be found by numerical integration . we present here an analytic treatment of the equations to derive the asymptotic behaviour of the fluid variables near @xmath45 , and two integrals of motion ( e.g. , bertschinger 1983 , 1985 ) . we restrict the analysis shocked collapses satisfying the inner boundary condition ( [ innerb ] ) . all fluid variables can be expressed in terms of an auxiliary function @xmath86 as follows . @xmath87 where @xmath88 and @xmath89 are constants . the fluid variables in ( [ b6][b5 ] ) satisfy the non -" +"the orientation of electronic spins in semiconductors by electrical means along with the possibility to convert the electron spin polarization into an electric signal are the focus of active research and motivate studies in several directions . a lot of efforts are aimed at realizing the electrical spin injection from a ferromagnetic metal contact into a semiconductor @xcite . the second field of research concerns mutual transformation of charge and spin currents and the spin accumulation at the sample edges @xcite . the third possibility of coupling between spin and electric current , without magnetic materials and role of the sample edges , arises in noncentrosymmetric systems allowing the spin - orbit interaction linear in the electron wave vector @xcite . the effect of spin orientation of free carriers by a passage of electric current was first predicted for gyrotropic crystals @xcite and observed in bulk tellurium as a current - induced optical activity @xcite , see also @xcite , and strained ingaas epitaxial layers @xcite . the theory was extended on two - dimensional ( 2d ) systems lacking a center of inversion @xcite and experimentally proved @xcite , see also chap . 9 in the book @xcite , ref . @xcite and references therein . summarizing the theoretical consideration , the spin polarization @xmath2 ( per particle ) created by the electric - current flow can in general be estimated as @xmath3 where @xmath4 is a dimensionless coefficient of the order of unity , @xmath5 and @xmath6 are the root - mean - squares of the group velocity and the quasimomentum referred to the extremum point in the brillouin zone , @xmath7 is the electron drift momentum in the electric field @xmath8 , and @xmath9 is a coefficient ( in units of velocity ) relating the spin - orbit energy with the electron quasimomentum . a value of the induced spin @xmath2 can be increased by increasing the ratios @xmath10 and ( or ) @xmath11 . the first ratio is large and has an order of unity in strongly spin - orbit coupled systems , like @xmath6-type bulk te , the ( 111 ) surface of topological insulator bi@xmath12se@xmath13 @xcite and new classes of noncentrosymmetric systems that emerged recently @xcite . however , in this case the spin is tightly bound to the quasimomentum and loses the degree of freedom . in conventional semiconductor 2d systems with a weak spin - orbit coupling , like gaas- or inas - based heterostructures , and for comparatively weak fields @xmath14 kv / cm , each of the two ratios are smaller than @xmath15 resulting in a value of @xmath16 . this linear dependence of the induced spin on the electric field is presented by curve 1 in fig . [ fig_spin_vs_e ] for a degenerate electron gas with the typical parameters : @xmath17 mev@xmath18 , the transport scattering time @xmath19 s , the electron effective mass @xmath20 ( @xmath21 is the free - electron mass ) , and 2d concentration @xmath22 @xmath23 . ) ; the dotted curve 2 is an intuitive extrapolation of eq . ( [ s_low_field ] ) for the increasing electric field ; curve 3 presents the result of calculation in the streaming regime . ] in such a system the current - induced spin can be increased only via the second ratio , @xmath11 . an application of the increasing field leads to a transformation from the linear dependence of drift momentum upon @xmath8 to saturation . if the interparticle collisions play a minor role in the kinetics , the electron momentum - space distribution in strong electric fields becomes extremely anisotropic , or as they say , _ each electron accelerates quasiballistically in the `` passive '' region until reaching the optical - phonon energy @xmath24 and the quasimomentum @xmath25 . then it loses its energy by emitting an optical phonon and starts the next period of acceleration . neglecting spin effects , the streaming distribution has been analyzed for the three - dimensional ( 3d ) plasma @xcite as well as for 2d electron gas @xcite . it is obvious that in this case the ratio @xmath11 lies in the range of 0.5 . a naive extrapolation of eq . ( [ s_low_field ] ) for the moderate electric fields is shown by the dashed curve 2 in fig . [ fig_spin_vs_e ] . however , in this work we argue that the spin reaches a value remarkably larger than @xmath26 given by eq . ( [ s_low_field ] ) for @xmath27 . we will show that , actually , in this case the generated spin can be estimated by @xmath28 where @xmath29 is an electron charge and @xmath30 is the optical phonon emission time in the `` active '' energy region . an explicit behavior of the spin orientation in the streaming regime is shown by curve 3 in fig . [ fig_spin_vs_e ] for the same value @xmath17 mev@xmath18 . one can see that the spin polarization is saturated at the high value @xmath31 in the fields @xmath32 kv / cm . at the higher fields the spin slightly decreases . in the present work we develop a theory of spin orientation by the electric current in the streaming regime . simultaneously we theoretically study relaxation and dynamics of the electronic spin polarization in this regime . the paper is organized as follows . in sec . [ sec : distr ] , we summarize the spin - independent theory of the streaming - like transport . in sec . [ sec : dp ] , we propose a theory of spin - dependent high - field transport . sections [ sec : el_spin_orient ] and [ sec : strong ] are devoted to the spin orientation by electric field . in sec . [ sec : disc ] we discuss the related aspects of the spin - dependent streaming and conclude the paper . in the streaming regime realized in an appropriate range of the dc electric field , the electron distribution in the momentum space has a steaming - like , or needle - like , form spread between the @xmath33-point @xmath34 and the point @xmath35 , where @xmath36 is the unit vector in the direction opposite to the electric field @xmath37 . the formation of such an anisotropic electron distribution requires the following hierarchy of times @xmath38 here @xmath30 is the time of optical phonon emission by an electron in the active energy region , @xmath39 is the travel time through the passive region of the momentum space , @xmath40 is the momentum relaxation time due to electron scattering by acoustic phonons or static imperfections , and @xmath41 is the electron - electron collision time . the electron - electron scattering tends to convert the anisotropic distribution to the shifted maxwellian distribution with an effective electron temperature and a drift velocity @xmath42 . the corresponding time can be estimated by @xmath43 , where @xmath44 is the electron 2d density and @xmath45 is the dielectric constant . before proceeding with the spin orientation by the electric current in a strong electric field we remind the main steps in description of the spin - independent streaming distribution @xcite . we assume the electric field @xmath37 to be directed antiparallel to the in - plane axis @xmath46 and satisfy the inequalities ( [ tauee ] ) . the two regions are selected in the momentum space , namely , passive with @xmath47 and active with @xmath48 and positive @xmath49 . the electron distribution function @xmath50 defined within the passive and active regions is indicated by @xmath51 and @xmath52 , respectively . the kinetic equation for @xmath50 breaks up into the two equations @xmath53 here @xmath54 is the probability rate for the longitudinal - optical ( lo ) phonon emission in the electron transition @xmath55 , with @xmath56 ; it is given by fermi s golden rule @xmath57 where @xmath58 is the electron energy @xmath59 , @xmath30 is the inverse total emission rate @xmath60 , it also enters the inequality ( [ tauee ] ) , @xmath61 is the matrix element for emission of the lo phonon with the in - plane wave vector @xmath62 and the vertical component @xmath63 . in bulk zinc - blende - lattice semiconductors , one has for the frhlich electron - phonon interaction @xmath64 , where @xmath65 is the polar - optical interaction constant @xcite , @xmath66 is the crystal volume and @xmath67 are the 3d electron quasimomenta . in a quantum well , the frhlich coupling is renormalized as follows @xmath68 where @xmath69 is the electron size - quantized envelope wavefunction . after the summation over @xmath63 one obtains @xmath70 the two branches of the distribution function found by solving the first and second equations ( [ kinetic_eq ] ) are sewed at the circle @xmath71 by the continuity boundary condition @xmath72 . the solution normalized to the 2d concentration @xmath44 reduces to @xcite @xmath73 where @xmath74 , @xmath75/2 $ ] , @xmath76 , and @xmath77 . note that , strictly speaking , in the second equation ( 12 ) of ref . @xcite the difference @xmath78 should be replaced by @xmath79 with @xmath80 equal to @xmath81 rather than merely @xmath82 . one can see from eq . ( [ spin_independ ] ) that the penetration @xmath83 into the active region and the width @xmath84 of the distribution in the transverse direction @xmath85 are given by @xmath86 and @xmath87 . thus , the needle - like distribution is formed provided @xmath88 which establishes the upper limit for the electric field strength . in this case the function @xmath89 can be approximated by the heaviside function @xmath90 and @xmath91 by @xmath92 . it is also worth to mention that the relative number of particles in the active and passive regions given by @xmath93 coincides with the ratio @xmath94 of the times spend by electrons in these regions . let us present estimations of the characteristic times for gaas - based structures where @xmath95 , @xmath96 mev , @xmath97 @xmath98 , and @xmath99 s. in this case the condition @xmath88 , or equivalently @xmath100 , is met if @xmath101 kv / cm . on the other hand , the condition @xmath102 with a typical value @xmath103 s of the momentum relaxation time requires @xmath104 kv / cm . in the field @xmath105 kv / cm one has @xmath106 , @xmath107 , @xmath108 , and the travel time @xmath109 s is longer than @xmath30 but shorter than @xmath40 . for the time @xmath110 we obtain an estimation @xmath111 which means that the condition @xmath112 is satisfied at @xmath113 @xmath23 similarly to gan - based structures @xcite . another restriction on the density @xmath44 is imposed from the requirement @xmath114 which allows to exclude the pauli blocking of the electron acceleration in the passive region . this requirement is equivalent to the inequality @xmath115 , where @xmath116 is the number of states in the needle , i.e. , in the rectangular area of the 2d quasimomentum space with the sides @xmath117 and @xmath84 . it is also met for @xmath118 @xmath23 . note that in the experiment @xcite the above conditions are not fulfilled . the spin - dependent kinetic theory operates with the electron spin density matrix @xmath119 describing the electron distribution both in the quasi - momentum and spin spaces . this @xmath120-dependent 2@xmath1212 matrix may conveniently be presented as @xmath122 where @xmath123 ( @xmath124 ) are the pauli spin matrices , the distribution function @xmath125 is the average occupation of the two spin states with the same @xmath120 , and @xmath126 is the average spin of an electron occupying the point @xmath120 of the quasi - momentum space . the 2d electron concentration and spin polarization per particle are given by @xmath127 , @xmath128 . in addition to the parabolic term @xmath129 , we include in the effective electron hamiltonian the spin - dependent contribution @xmath130" +"strangeness production has been extensively studied in relativistic heavy - ion collisions . its measurement represents an important tool to investigate the properties of the strongly interacting system created in the collision , as there is no net strangeness content in the initially colliding nuclei . in these proceedings we briefly discuss the technique used to identify k@xmath0 , , and and to measure their transverse momentum ( @xmath2 ) spectra . then we describe the main results about baryon anomaly , strangeness nuclear modification factor and strangeness enhancement . the alice detector was designed to study heavy - ion physics at the lhc . at mid - rapidity , tracking and vertexing are performed using the inner tracking system ( its ) , consisting of six layers of silicon detectors , and the time projection chamber ( tpc ) . the two innermost layers of the its and the v0 detector ( scintillation hodoscopes covering the forward pseudo - rapidity region on either side of the interaction point ) are used for triggering . the v0 is also used to estimate centrality in collisions as well as multiplicity in collisions . a complete description of the alice sub - detectors can be found in @xcite . the single - strange ( k@xmath0 and @xmath3 ) and multi - strange ( @xmath4 and @xmath5 ) particles are reconstructed via their characteristic weak decay topologies into two and three particles , respectively . tracks reconstructed by the tpc and the its are combined to select candidates satisfying a set of geometrical criteria . in addition , particle identification is performed by a selection on the specific energy loss in the tpc for the daughter tracks . particle yields as a function of @xmath2 are determined , in various multiplicity / centrality intervals , using an invariant mass analysis . acceptance and efficiency corrections are calculated using monte carlo simulations . for more details , we refer to @xcite . transverse momentum spectra for k@xmath0 , , and have been published in @xcite for collisions and in @xcite for collisions . in both systems the hardening of the spectral shape from low- to high - multiplicity collisions has been observed . moreover , in the context of blast wave model , it has been shown that spectra for k@xmath0 and @xmath3 are well predicted using parameters from a simultaneous fit to @xmath6 , k@xmath7 and p spectra in high multiplicity and collisions . this is also true for @xmath4 and @xmath5 in collisions , while in collisions they can not be described in a common freeze - out scenario , as they would require a lower mean transverse flow velocity and a higher kinetic freezeout temperature to be described properly . the @xmath2-differential ( @xmath3+@xmath8)/k@xmath0 ratio is shown in fig . [ fig-0 ] in the highest and a low - multiplicity class for and collisions . the shape and the multiplicity dependence are qualitatively similar in the two collision systems . in collisions this phenomenon has been interpreted as a redistribution of baryons and mesons in momentum , when centrality increases , a consequence of the increased radial flow @xcite . the flattening of the ( @xmath9+@xmath10)/@xmath11 ratio as a function of @xmath2 in the 0 - 10% central collisions is further evidence supporting an hydrodynamical evolution of the system . in addition this data can also be described by parton recombination models @xcite . + @xmath8)/k@xmath0 as a function of @xmath2 in the highest and a low - multiplicity class in ( left ) and ( right ) collisions . open boxes are total systematic uncertainties and shaded boxes represent the uncorrelated - over - multiplicity component . ] the nuclear modification factor is defined as the ratio of the @xmath2 spectra in ( @xmath12 ) or ( @xmath13 ) and in pp collisions scaled by the number of nucleon - nucleon collisions . it has been shown that the strong suppression of hadron production at high @xmath2 observed at the lhc in collisions is not due to an initial - state effect but may be due to jet quenching in hot qcd matter @xcite . in fig . [ fig-2 ] the @xmath12 as a function of @xmath2 for multi - strange baryons in central ( 0 - 10% ) collisions is shown and compared with those for lighter hadrons ( @xmath14 , k and p ) . @xmath12 for @xmath4 is similar to the one for p , especially at high @xmath2 , while @xmath14 and k at low @xmath2 follow a clearly different trend , which can be interpreted as a consequence of having different masses in a radial flow scenario . @xmath12 for @xmath5 is above unity , which might be the result of the larger strangeness enhancement compared to @xmath4 @xcite . in the right canvas of the same figure , the @xmath13 as a function of @xmath2 in minimum - bias collisions is shown for the same particles . in this case , there is no suppression for @xmath14 , k and p at high @xmath2 ( @xmath15 6 gev/_c _ ) , as verified for unidentified particles @xcite . in the so - called cronin region ( 2 @xmath16 @xmath2 @xmath16 6 gev/_c _ ) an increase of the @xmath13 with the mass and the strangeness content of the particles is visible . in collisions ( left ) and @xmath12 in 0 - 10% most central collisions ( right ) as a function of @xmath2 for @xmath14 , k , p , @xmath4 and @xmath5 particles . open boxes are total systematic uncertainties.,title=""fig : "" ] in collisions ( left ) and @xmath12 in 0 - 10% most central collisions ( right ) as a function of @xmath2 for @xmath14 , k , p , @xmath4 and @xmath5 particles . open boxes are total systematic uncertainties.,title=""fig : "" ] the strangeness enhancement is known as one of the proposed signatures for the qgp formation in relativistic heavy - ion collisions . rafelski and mller s expectation , first proposed in 1982 @xcite , is that qgp formation should lead to a higher abundance of strangeness per participating nucleon than in pp interactions . this phenomenon has been actually observed at sps @xcite , rhic @xcite and the lhc @xcite , and has been found to increase with centrality and with the strangeness content of the particle , and decrease as the centre - of - mass energy increases . statistical hadronization models based on a grand - canonical approach have been demonstrated to be able to predict particle yield ratios in heavy - ion collisions over a large energy scale @xcite . in this description , the energy dependence of strangeness enhancement has been understood as the consequence of a suppression of strangeness production due to the reduced phase - space volume in reference pp collisions ( canonical suppression ) @xcite . at sps and rhic the strangeness enhancement has been studied looking at the ratio between the yield in collisions and those in pp interactions at the same energy normalized to the mean number of participants ( @xmath17 ) . it has been shown that this is not the ideal way to isolate the enhancement component due to strangeness content , since the production rates of charged particles do not scale linearly with @xmath18 @xcite . a better observable is the ratio to pion yields , shown in fig . [ fig-3 ] for @xmath3 , @xmath4 and @xmath5 as a function of @xmath19/d@xmath20 for , and pp collisions . in the case of multi - strange baryons , the ratio is shown to increase by up to a factor of about 2 - 3 going from pp collisions to collisions and is more pronounced for the @xmath5 ; for the @xmath3 a possible increase is not significant within the systematic uncertainty . it is shown that the predictions from statistical hadronization models using a chemical freezeout temperature of 156 mev @xcite are comparable with the ratios measured in the most central collisions for all the three particles . looking at the data , an increase of the ( multi-)strange baryon - to - meson ratios with multiplicity is observed . the increase is seen to be more pronounced for particles with a larger strangeness quantum number . in particular ( @xmath21)/@xmath6 and @xmath22/@xmath6 ratios slightly exceed the saturation limit observed for , while the @xmath23/@xmath6 ratio is not higher than the one observed in peripheral . comparison of hyperon - to - pion ratios as a function of pion multiplicity to the trends observed in statistical hadronisation models , where the local conservation of the strangeness is required ( as in a canonical ensemble ) , indicates that the behaviour is qualitatively consistent with the lifting of canonical suppression with increasing multiplicity @xcite . /d@xmath20 for ( filled blue cross ) and ( filled red square ) collisions . open boxes are total systematic uncertainties and shaded boxes show the uncorrelated - over - multiplicity component . lines represent predictions from statistical hadronization models @xcite ( continuous ) and @xcite ( dashed).,title=""fig : "" ] /d@xmath20 for ( filled blue cross ) and ( filled red square ) collisions . open boxes are total systematic uncertainties and shaded boxes show the uncorrelated - over - multiplicity component . lines represent predictions from statistical hadronization models @xcite ( continuous ) and @xcite ( dashed).,title=""fig : "" ] /d@xmath20 for ( filled blue cross ) and ( filled red square ) collisions . open boxes are total systematic uncertainties and shaded boxes show the uncorrelated - over - multiplicity component . lines represent predictions from statistical hadronization models @xcite ( continuous ) and @xcite ( dashed).,title=""fig : "" ] the production of ( multi-)strange particles was measured in and collisions with the alice detector . the multiplicity dependence of the ( @xmath3+@xmath8)/k@xmath0 ratio and the hardening of the spectra with increasing multiplicity point to similar collective behaviour . as observed for unidentified particles , @xmath12 for @xmath4 is clearly suppressed at high @xmath2 , while @xmath13 does not show any suppression . the fact that relative strangeness production in not only increases with multiplicity but also bridges pp and collision values is an important recent observation in the study of strangeness production 15 aamodt k _ et al . _ ( alice collaboration ) 2008 _ jinst _ * 3 * s08002 abelev b _ et al . _ ( alice collaboration ) 2014 _ phys . b _ * 728 * 216 - 227 abelev b _ et al . _ ( alice collaboration ) 2014 _ phys . _ b * 728 * 25 - 38 adam j _ ( alice collaboration ) 2016 _ phys . _ b * 758 * 389 - 401 abelev b _ ( alice collaboration ) 2013 _ phys . lett . _ * 111 * 222301 abelev b _ et al . _ ( alice collaboration ) 2015 _ phys . _ c * 91 * 024609 abelev b _ et al . _ ( alice collaboration ) 2013 _ phys . lett . _ * 110 * 082302 rafelski j and mller b 1982 _ phys . lett . _ * 48 * 1066 antinori f _ et al . _ ( na57 collaboration ) 2006 _ j. phys . _ g * 32 * 427 - 441 abelev b _ et al . _ ( star collaboration ) 2008 _ phys . _ c * 77 * 044908 stachel j , andronic a , braun - munzinger p and redlich k 2014 _ j. phys . ser . _ * 509 * 012019 hamieh s , redlich k and tounsi a 2000 _ phys . _ b * 486 * 61 - 66 aamodt k _ et al . _ ( alice collaboration ) 2011 _ phys . lett . _ *" +"aging is a key aspect of the dynamics in a host of complex glassy systems @xcite . its main characteristics are a slow , sub - linear drift of macroscopic averages with the age @xmath0 of the system , i.e. the time elapsed after an initial thermal quench , and a concomitant age dependence of the correlation and response functions . the latter shows that a quasi - stationary fluctuation regime for short observation times @xmath1 is followed by off - equilibrium dynamics for @xmath2 . this behavior can be attributed to an increasing degree of thermal stability of the dynamically relevant attractors or landscape valleys as the age @xmath0 grows @xcite . within each valley , the pseudo - equilibrium fluctuations are determined by the free energy . however , the inter - valley non - equilibrium dynamics could be practically irreversible , and hence qualitatively different . adopting the simplified view that the selection is truly irreversible allows us to formulate a theoretical description of large non - equilibrium rearrangements , or ` quakes ' , which borrows from studies of non - thermal models @xcite and which supplies a basis to the striking similarity of complex dynamics seen in very different systems with multiple metastable states . the key feature is dynamical invariance to shifts in the _ logarithm _ of time . this implies that the time spent in thermally metastable attractors is power - law distributed with an exponent @xmath3 . furthermore , the distribution has a @xmath4 aging behavior , often called full or pure aging . the exponent @xmath3 depends on the system size but not on the temperature . the further assumption that the memory of the initial configuration decays as @xmath5 with the number @xmath6 of quakes leads to a power - law decay and a @xmath4 form of the correlation function for @xmath7 . the corresponding non - equilibrium exponent @xmath8 is jointly determined by @xmath3 and @xmath9 . these theoretical results are checked through extensive numerical simulations of short ranged spin glass systems . while direct experimental evidence is not yet available , possibly related large - scale irreversible rearrangements similar to quakes have recently been identified in aging colloidal gels @xcite . beyond its original macro - evolutionary context , the concept of ` punctuated equilibrium ' @xcite is applicable to any stochastic dynamics where long periods of stagnation are dotted by fast irreversible changes . this occurs e.g. in micro - evolution @xcite and in certain driven dissipative models @xcite . within a population evolving in a fitness landscape @xcite , fitness _ records _ achieved by an individual through random mutations are amplified to the macroscopic level by darwinistic selection and trigger punctuations . since the same statistics describes both punctuations and records , the analytical description available for the latter @xcite can be applied to the former . below , we discuss how thermal noise may similarly induce large and irreversible quakes in glassy systems . to summarize the basic ideas of record statistics @xcite , consider times @xmath10 and @xmath11 , and independently draw for each integer time a random number from any fixed distribution not supported on a finite set . the attempts whose outcome exceeds all previous outcomes are marked as records . for large times , the probability that @xmath6 such events occur in @xmath12 $ ] is then @xmath13^k \left [ \frac{t_w + t}{t_w } \right]^{-\alpha } , \label{logpoisson}\ ] ] where @xmath14 for a single sequence of attempts . the total number of records produced by @xmath15 independent sequences is a sum of log - poisson variables , and hence itself log - poisson distributed , with @xmath16 . equation ( [ logpoisson ] ) can be recognized as a poisson distribution with @xmath17 replacing the linear difference @xmath18 between the time arguments , or , for short , a log - poisson distribution , but the generalization to the propagator @xmath19 is straightforward and completely analogous to the standard case . ] . equation ( [ logpoisson ] ) implies that the rate of events decays as @xmath20 , while the logarithmic rate of events approaches the constant value @xmath3 for @xmath21 . glossing over the discreteness of the time arguments , we can now pick thermal noise as the ( arbitrary ) source of randomness producing the records . since landscape induced correlations are negligible if records are intercalated by long intervals spent dwelling near a local energy minimum , the number of energy records observed in a fixed time interval is expected to be proportional to a log - poisson variable @xcite . the same applies if energies are measured relative to the current lowest energy minimum , producing the energy difference henceforth referred to as a ` barrier ' . with this definition , not all barrier crossings carry physical significance . however , if quakes are log - poisson distributed , they are naturally associated with the crossing of barriers of record magnitude . two special landscape features sketched in fig.[land_sketch ] would allow barrier records to induce quakes : i ) the stability of the attractors successively selected , as gauged by e.g. an exit barrier , must only increase marginally @xcite , i.e. in principle by an infinitesimal amount . this requires that shallow attractors be predominant , and implies that the actual magnitude of the records generating the quakes is immaterial . ii ) a large and negative energy change associated to a quake , ensures its irreversibility . such changes are observed in both atomistic glass models @xcite and spin glasses @xcite , the only adjustable quantities in this landscape cartoon are the parameter @xmath3 and the form of the quake induced decorrelation . the noise independence of the statistics restricts @xmath3 to be a temperature independent quantity . an interesting increase with system size can arise in spatially extended systems , where sufficiently distant regions can evolve independently . in the sequel , we first deal with some theoretical consequences of the marginal stability of the attractors and irreversibility of the quakes . to make contact with experiments , we then summarize an empirical way to identify quakes in glassy systems @xcite and apply it to spin glasses . the distribution of the residence or trapping time @xmath22 in valleys of an energy landscape has been considered theoretically @xcite , but has not previously been measured . let @xmath23 mark the occurrence of the @xmath6th event in a log - poisson process with logarithmic rate @xmath3 . in perfect analogy to the usual poisson process , the ` log - waiting time ' @xmath24 has the exponential distribution @xmath25 which is mathematically equivalent to the event distribution given in eq . ( [ logpoisson ] ) . we now consider the distribution of the residence time @xmath26 for traps entered at @xmath27 . as @xmath28 , we find @xmath29 which corresponds to full aging behavior . equation . ( [ an_scaling ] ) with @xmath30 is plotted ( circles ) in the main panel of fig . [ residence_t ] , together with spin glass data ( lines ) . these are scaled in a slightly different manner , to account for a small but systematic deviation from full aging . the power - law form of eq . ( [ an_scaling ] ) was suggested by bouchaud @xcite , with the added and crucial assumption of an infinite average residence time . in our case , the average residence time @xmath31 is equal to @xmath32 which is finite and @xmath33 for the observed @xmath34 . as a consistency check , we note that the largest relaxation time @xmath35 in a valley must be smaller than @xmath36 , for local equilibration to apply . when the latter is of order @xmath0 , @xmath37 follows . in the lack of special symmetries @xcite , @xmath38 , where @xmath39 characterizes the short time decay of correlation functions , either as a cut - off parameter or directly as the time constant of an exponential decay . hence @xmath40 as expected . additional information on the effect of the quakes enters the calculation of thermally averaged correlations functions . let @xmath41 be the configurational overlap between the lowest energy configurations in valley @xmath42 and @xmath43 . with probability @xmath44 , @xmath42 and @xmath43 are the ` current ' attractors at times @xmath0 and @xmath45 , whence the _ non_-equilibrium part of the configurational autocorrelation function is given by @xmath46 of special interest is @xmath47 , the average overlap between the first and the ( @xmath48th valley . this is the sole contribution to eq . ( [ two - point ] ) for @xmath49 , in which case @xmath50 additionally describes the magnetization decay of the fully polarized configuration of a spin glass @xcite . the exponential form @xmath51 anticipates the results in fig . [ correlation ] . an exponential decay means that each event induces the same relative change , and leads to @xmath52 where the non - equilibrium exponent @xmath53 is given by @xmath54 equation ( [ expos ] ) thus links a dynamical exponent to the landscape geometry . the second approximate equality given in eq . ( [ expos ] ) is only justified for @xmath55 . the further assumption that @xmath41 is altogether independent of @xmath42 amounts to translational invariance with respect to @xmath42 , and hence with respect to additive shifts in the logarithm of @xmath0 . these are equivalent to a multiplicative rescaling of @xmath0 . not surprisingly , eq . ( [ two - point ] ) yields the scale invariant and full aging form @xmath56 how should valleys and quakes be concretely defined given a time sequence of data ? one approach is the protocol developed @xcite for numerical data describing isothermal relaxation after a deep quench . the basic observation is that at sufficiently low @xmath57 pseudo - equilibrium fluctuations repeatedly visit the same local energy minimum . hence , the attainment of an energy value lower than all previous values implies a non - equilibrium event , i.e. an ongoing quake . several closely spaced minima records will often occur as a quake slides downhill among which the one preceding a barrier record is likely to be the most physically significant , as it ideally coincides with a new local minimum . by the same token , in a series of barrier records corresponding to an uphill climb , the last record preceding a low energy record is most significant , as it marks the access to a new local minimum , and hence the start of a quake . the times at which the above types of event occur provide an empirical definition of both valleys and quakes . this procedure yields a null result if i ) only a single energy minimum is present ; or ii ) the initial condition is the ground state irrespective of the number of local minima present ; or iii ) all the minima and/or barriers are equal . also , iv ) if the trajectories can bypass the energy barriers and edge their way into states of lower energy through ` entropic barriers ' , the number of valleys discovered remains less or equal to one at all times . the actual outcome is very different , as illustrated in fig . [ no_valleys ] , where the estimated average and variance of the number @xmath58 of valleys visited is plotted versus the logarithm of time . an equality between variance and average is a key feature of poisson distributions . if we neglect the initial curvature , the estimated quantities are very nearly proportional to @xmath59 , indicating that @xmath58 itself is proportional to a log - poisson variable through a constant of order one . we emphasize that log - poisson statistics is an idealized low @xmath57 description ," +"recently , a paradigm has appeared to emerge according to which black - hole binaries in the hard state show weak both compton reflection ( i.e.backscattering of x - rays from a surrounding cold medium ) and associated fluorescent fe k@xmath0 lines ( as found by gierliski et al . 1997 ; ycki , done & smith 1997 , 1998 ; zdziarski et al . 1998 ; ebisawa et al . 1996 ) whereas seyfert-1 agns would universally show stronger reflection ( nandra & pounds 1994 ) and strong and broad fe k@xmath0 lines ( nandra et al . 1997 ) . if this were correct , it would certainly be of importance for our understanding of the physics of x - ray sources in accreting compact objects . we critically examine this paradigm based on available data . we concentrate on the continuum spectral properties , deferring an analysis of a more complex issue of the fe k@xmath0 fluorescent emission to a future work . here , we study the strength of compton reflection as a function of the intrinsic spectral slope . a correlation between these quantitites has originally been found in observations of gx 3394 ( ueda , ebisawa & done 1994 ) . in this work , we consider seyferts , radio galaxies , and x - ray binaries containing either black holes or weakly - magnetized neutron stars . our seyfert sample consists of ( makino et al . 1987 ) spectra ( extracted from the leicester database ) of radio - quiet ( hereafter rq ) seyfert 1s and narrow emission - line galaxies . the latter are seyferts intermediate between type 1 and 2 showing moderate x - ray absorption ( e.g. smith & done 1996 ) . this sample is basically the same as that of the classical study of spectra of seyferts of nandra & pounds ( 1994 ) . however , here we exclude 3 radio - loud agns , as there are hints that their nature is different from that of rq ones ( woniak et al . 1998 ) . on the other hand , we include some late observations of seyfert 1s not listed in nandra & pounds ( 1994 ) , which gives us 61 observations of 24 rq seyferts . we further include 2 observations of 4u 0241 + 61 , a low - redshift agn ( @xmath1 ) , which we find to be of rq type after correcting its @xmath2 magnitude for galactic extinction . finally , we include an observation of ngc 4151 contemporaneously by both and the osse detector on board of _ cgro _ , which latter data allow a determination of the strength of reflection in this strongly - absorbed bright seyfert ( zdziarski , johnson & magdziarz 1996 ) . we compare the data for seyferts with those for 4 x - ray binaries in the hard ( also called low ) state . two of them , cyg x-1 and gx 3394 , are black - hole candidates , and two , gs 1826238 and 4u 1608522 , are x - ray bursters ( thus containing weakly - magnetized neutron stars ) . for cyg x-1 , we use 5 , 3 and 4 observations from 1987 , 1990 and 1991 , respectively ( ebisawa et al . 1996 and references therein ; gierliski et al . 1997 ) . for gx 3394 , we use 5 observations out of 6 ones of ueda et al . ( 1994 ) ( excluding one in an off state ) . a spectrum of gs 1826238 ( strickman et al.1996 ) and 2 spectra of 4u 1608522 from 1990 and 1991 ( yoshida et al . 1993 ) have been extracted from the database . we use spectra from both the top ( @xmath320 kev ) and mid ( @xmath420 kev ) layers of the lac ( turner et al . 1989 ) , to which data we add a systematic error of 0.5 per cent per channel . inclusion of the mid - layer data significantly increases the effective area above 10 kev , allowing to measure the hard x - ray spectra much more accurately than with the top layer alone ( see woniak et al . 1998 ; magdziarz et al . we further select only the data with no systematic differences between the top and mid - layer spectra above 10 kev , which reduces the number of usable seyfert observations by 10 . we fit the data ( using xspec , arnaud 1996 ) with a continuum model consisting of an e - folded power law ( unless stated otherwise ) and a component due to its compton reflection ( magdziarz & zdziarski 1995 ) at a normalization , @xmath5 . in the case of an isotropic primary source and no obscuration of either the source or the reflector , @xmath6 , where @xmath7 is the solid angle subtended by the reflector . we initially assume the reflector is neutral with the abundances of anders & ebihara ( 1982 ) , but allow for its ionization and/or a free fe abundance when it is statistically required . we fix the e - folding energy at 400 kev ( zdziarski et al . 1995 ) and the reflector viewing angle of seyferts at @xmath8 ( nandra et al . ( for @xmath9 , the fits below would typically give @xmath5 higher by @xmath10 per cent . ) we model the fe k@xmath0 line as a gaussian with the line flux as a free parameter , independent of reflection . this allows for resonant absorption and/or additional line components due to either matter in the line of sight ( makishima 1986 ) , scattering of a part of the primary continuum by an ionized medium ( krolik & kallman 1987 ) and/or emission of a thomson - thin torus surrounding an agn nculeus ( e.g. woniak et al . 1998 ) . then we carefully treat the low - energy part of the spectra . for each object , we initially model absorption of the above continuum by a neutral medium at the redshift of the source ( in addition to a fixed local absorber with the galactic column density ) . we then test for the effect of either replacing the neutral absorber by an ionized one , ignoring some low - energy channels , or using a broken power - law incident continuum . this is to assure that the hard x - ray power - law photon index , @xmath11 , is properly measured and not affected by either the presence of a soft excess or by complex absorption . in the case of ngc 4151 , we assume @xmath12 and fit the /osse data with a dual absorber model ( zdziarski et al . 1996 ) and a thermal - comptonization continuum model ( misra et al . , in preparation ) . the above procedure gives us @xmath5 and @xmath11 with their error contours . for seyferts , some detections are rather weak and yield very large error contours . since our main goal is to study the dependence @xmath13 , we have eliminated from the sample observations for which the 1-@xmath14 ( @xmath15 ) error contour has @xmath16 . inclusion of such data would only weakly affect our fitted dependences ( see section 3 ) but would confuse our graphical representation of the results . this criterion eliminates , in particular , all the observations of mcg 6 - 30 - 15 and mkn 335 . to improve statistics in those cases , we have coadded multiple observations of each of those objects . in the case of mkn 335 , the resulting @xmath17 was still @xmath18 , and thus we kept it out of the sample . for mcg 6 - 30 - 15 , we coadded 4 ( out of 5 ) observations that were performed in the standard mode with all the lac detectors operating , which then resulted in data with an acceptable @xmath19 . [ fig : cor ] = 17.6 cm the procedures outlined above give us 47 data sets for 23 rq agns : 4u 0241 + 61 , akn 120 , fairall 9 , ic 4329a , mcg 2 - 58 - 22 , mcg 5 - 23 - 16 , mcg 6 - 30 - 15 , mkn 509 , mkn 841 , ngc 2110 , ngc 2992 , ngc 3227 , ngc 3783 , ngc 4051 , ngc 4151 , ngc 4593 , ngc 526a , ngc 5506 , ngc 5548 , ngc 7172 , ngc 7213 , ngc 7314 and ngc 7469 . 1a shows their best - fit points in open symbols , and the corresponding 1-@xmath14 confidence contours are shown in thin solid line . for clarity , the inset shows the best - fit points ( except that of mcg 6 - 30 - 15 ) without the contours . the open circles denote rq seyferts from the sample of nandra & pounds ( 1994 ) , and the open square and triangles , ngc 4151 and 4u 0241 + 61 , respectively . we see an extremely strong correlation . at the hard end , objects with @xmath20 have almost no reflection . the reflection strength then increases with increasing @xmath11 . reflection appears to saturate at @xmath21 as our softest seyfert , mcg 6 - 30 - 15 , has @xmath21 at the best - fit @xmath22 , somewhat below an extrapolation of the trend for objects with harder spectra . we also see that ngc 4151 and 4u 0241 + 61 show rather average values of @xmath11 and @xmath5 . we checked in section 3 below that the correlation is not an artefact of our fitting procedure . indeed , although there are intrinsic @xmath5-@xmath11 correlations due to finite measurement errors for each observation , we clearly see in fig . 1a that their extents are much less ( especially for data with good statistics ) than the extent of the global correlation . objects with hard power laws and significant reflection would have reflection easily measured by due to their high count rate at @xmath23 kev . also , soft power laws without reflection would also have been measured as such by , albeit with relatively large errors . the absence of such objects in the sample strongly supports the physical reality of the correlation . we note that a similar @xmath13 correlation has been observed for ngc 5548 ( magdziarz et al . we show the contours for this object alone in fig . 1b , including one contour omitted in fig . 1a [ due to our criterion of @xmath24 , which also obeys the correlation . we also find an @xmath13 correlation for mkn 509 . we then consider hard - state x - ray binaries , for which fit results are shown by heavy contours and filled symbols in fig . the 12 filled squares correspond to cyg x-1 ( at assumed @xmath8 ) . we see that cyg x-1 has typically _ more _ reflection than average for seyferts with the same @xmath11 ( although its contours are still within the area covered by seyferts ) . although the presence of an @xmath13 correlation can not be proven from these data alone , done & ycki ( 1999 ) found such a correlation in observations by and . the filled circles in figs . 1a , c correspond to the data for gx 3394 . we fit the data as in zdziarski et al . ( 1998 ) , assuming @xmath9 . we see that the contours show a highly significant correlation themselves , as found before by ueda et al . ( 1994 ) , and that their correlation is consistent with that for average seyferts" +"the possible exploration of chemical composition of planets and extraterrestrial materials @xcite by analysis of gamma spectra emitted from the surface , renewed the interest for gamma ray production cross sections in stable nuclei @xcite . the energy level structure of the stable @xmath2 has been studied extensively in the past via _ inelastic neutron scattering _ ( ins ) @xcite , and pertinent cross sections for the gamma ray production exist @xcite . however , secondary neutrons produced by primary cosmic rays have much higher energies compared to reactor ones and cross sections for gamma ray production by the use of neutrons with energies up to 150 mev were studied recently @xcite . despite @xmath3 nuclear reaction being well - explored , few publications @xcite report on relative intensities of gamma lines induced by ins on @xmath2 nuclei . pre - world war ii iron is widely used as a passive shield and 846.8 kev gamma line , induced by inelastic scattering of neutrons produced by cosmic muons , is a well - known feature in background spectra @xcite . even though detailed knowledge of all possible sources of radiation could be of crucial importance in numerous low - background experiments , the gamma radiation due to excitation of @xmath2 nuclei by inelastic scattering of muon - produced neutrons received little attention . reliable experimental studies @xcite of cross sections for @xmath3 reaction have indicated that detected intensities of gamma lines depend on incident neutron energy , and it is to be expected that the same holds for _ relative _ intensities . indeed , for incident neutron energies between 6.3 mev and 14.2 mev , relative intensity of 1238.3 kev gamma line changes by almost 80% @xcite . there are several muon - stimulated mechanisms of neutron production with significant contributions to the background @xcite : muon capture , muon - induced spallation reactions , muon - induced hadrons cascades , and photonuclear reactions ( high energy photons from a muon - induced electromagnetic cascade ) . at the earth s surface and shallow depths , the dominant neutron production mode is negative muon capture . this process occurs by stopping muons and plays a significant role @xcite because the mean energy of surface muons is about 4 gev . on the other hand , the energies of neutrons emitted after muon capture do not exceed several mev @xcite . high energy muons , also present at earth s surface in much lower arrival numbers , penetrate to the larger depths . it has been demonstrated through several background measurements in underground laboratories @xcite that the hard muon component may create neutrons with energies up to several hundred mev . the goal of this paper is to identify characteristic @xmath2 gamma lines in background spectra registered by a iron - shielded hpge detector . the relative intensities of measured gamma transitions are assessed against published results on the same gamma transitions detected in neutron beam scattering experiments . we use @xmath4 source to get the qualitative information about the average energy of muon - created neutrons in the iron shield and to infer relative intensities of gamma lines associated with scattering of muon - induced neutrons and fission neutrons . the hpge detector used in experiments is located in the low - background laboratory of the department of physics in novi sad ( 80 m amsl ) . the detector is placed inside a cube chamber made of pre - world war ii iron with a useful cube - shaped inner volume of @xmath5 . iron walls are 25 cm thick and the total mass of the shield is about 20 tons . no other passive shields were used throughout the measurements . the distance between the top of the iron shield and 30 cm thick concrete roof construction is about 3 m. iron chamber is placed on concrete base over 2 m away from walls made of bricks and wood . relative efficiency of hpge detector is 25% with the active detection volume of ge crystal being located in the center of the inner volume of the iron cube chamber . the integral background count rate for energies ranging from 20 kev to 2 mev was about 1 count per second . to get experimental evidence about relative intensities of gamma lines following de - excitation of @xmath2 nuclei after inelastic scattering of fission neutrons , @xmath4 source ( having stable neutron emission rate of @xmath6 into @xmath7 sr ) was placed at several different positions inside the iron chamber . to attenuate gamma radiation originating from @xmath4 fission products accumulated in source , solid angle of detector as seen from the californium source was screened by a layer of iron . measurements were done with uncovered @xmath4 source , as well as with the source packed in 2 cm of paraffin . in order to explore the gamma radiation produced by the interaction of neutrons with surrounding iron , long time spectra was obtained by the summing a number of background spectra , thus amounting to a total observation time of @xmath8 . the strongest gamma transition in fig . [ fig:1 ] is due to 846.8 kev background line with the measured intensity of @xmath9 . intensities of the remaining three gamma lines in fig . [ fig:1 ] have been normalized to that of 846.8 kev line and are summarized in table [ tab:1 ] . variations in detection efficiency , due to different penetration abilities of gamma photons in iron and detector itself , were accounted for at each observed energy with the help of geant4 simulations @xcite . in the first approximation , it was considered that gamma photons are emitted uniformly from a complete volume of the iron shield . however , simulations also take into account attenuation of the emitted radiation originating from the part of the iron shield that is shaded by the dewar vessel . it is interesting to note that @xmath10 gamma transition in fig . [ fig:1 ] occurs at energy that coincides with the background line of @xmath11 ( @xmath12 series member ) at 1238.1 kev . hence , intensity of @xmath2 1238.3 kev gamma line was inferred by proper decoupling and subtraction of @xmath11 contribution . namely , nine @xmath11 gamma lines in the energy interval between 609.3 kev and 1764.6 kev were used for proper efficiency calibration of our detector and for deconvolution of the 1238.1 kev @xmath11 portion from the nearby @xmath2 1238.3 kev line profile . we further note that isolated @xmath2 1810.8 kev gamma line appeared relatively weak in background spectra , whereas another line of interest at 1037.9 kev remained absent . it is the flat part of the background spectra at the place of the missing 1037.9 kev gamma line that was used in resolving the upper limit for its intensity reported in table [ tab:1 ] . .[tab:1 ] relative intensities ( in % ) of gamma transitions depopulating excited states in @xmath2 . gamma lines were detected both in the background and by the use of californium source ( see text for details ) . [ cols=""^,^,^,^,^ "" , ] similar procedure was repeated in the case of spectra recorded with @xmath4 source located inside of the iron chamber . namely , two types of additional measurements were performed : one with uncovered californium source and the other with the source enclosed in 2 cm thick paraffin container . paraffin moderator was used primarily to reduce the mean energy of fission neutrons emitted by @xmath4 . the outcome of these measurements showed that relative intensities of @xmath2 gamma lines originating after inelastic neutron scattering do not depend on @xmath4 source position in the chamber . characteristic times of both measurements were about @xmath13 . in this relatively short period of time , intensities of background @xmath11 lines were much lower than the intensity of lines emitted from @xmath2 excited nuclei and there was no need to subtract a possible contribution due to 1238.1 kev background line . relative intensities of all three gamma lines of interest obtained in these measurements are also presented in table [ tab:1 ] . part of the energy level scheme of @xmath2 with gamma - ray lines investigated in this work . ] due to slow - down of neutrons in the paraffin , intensities of the observed gamma lines became significantly lower , however , relative intensities remained similar to those obtained with uncovered @xmath4 source . figure [ fig:2 ] juxtaposes the relative intensities of 1037.9 kev , 1238.3 kev , and 1810.8 kev gamma lines measured in our iron shield with those from neutron beam experiments . the solid squares denote results of relative intensities of gamma lines obtained in the standard neutron beam experiments . data for 6.3 mev and 7.3 mev neutrons were published by lachkar _ et al _ @xcite and 14.2 mev data are due to xiamin _ et al _ @xcite . our result acquired by the use of uncovered californium source is also given in fig . [ fig:2 ] at the adopted mean energy of 2.3 mev for @xmath4 fission neutrons . the solid horizontal lines in fig . [ fig:2 ] represent the values of the relative intensities of gamma lines measured in the background spectra whereas the dashed lines denote a 1-@xmath14 uncertainty corridor . relative intensities of gamma lines detected both in the background spectra and the spectra measured by the use of @xmath4 source . results of pertinent gamma transitions obtained in neutron beam measurements at 6.3 mev , 7.3 mev , and 14.2 mev @xcite are shown in solid squares ( see text for details ) . ] another possible source of gamma radiation emitted from the excited @xmath2 nucleus is the @xmath15 reaction where muon capture occurs without the emission of neutrons . heisinger _ et al _ @xcite estimated that about 15.7% of the overall number of muon captures in iron take place through this channel . the product of the muon capture , @xmath16 , decays to the @xmath2 and we report the relative intensities of three gamma lines of interest in the last column of table [ tab:1 ] . very weak 1238.3 kev gamma radiation emitted in the decay of @xmath16 suggests that almost all 1238.3 kev photons come from ins at @xmath17 nuclei . relatively strong gamma line of 1810.8 kev is emitted in decay of @xmath16 and it is possible that both processes , inelastic neutron scattering and decay of @xmath16 , contribute jointly to the total count rate under 1810.8 kev gamma peak in the background spectra . the evidence about possible @xmath16 involvement in measured gamma lines in the background spectra can be obtained by analysis of its high energy part . one of the strongest gamma lines in decay scheme of @xmath16 has 14.3% intensity and comes from the 2113.2 kev transition depopulating the 2959.9 kev level . the neutrons created by cosmic muons have insufficient energy to excite the 3122.9 kev level in @xmath17 , and 1037.9 kev gamma line remains unobserved in the background spectra . one can draw similar conclusion for radiative depopulation of nearby 2959.9 kev level ( not shown in fig . [ fig:2 ] ) . recent measurements by castaneda _ et al _ @xcite showed that cross sections for neutron induced 1037.9 kev and 2113.2 kev gamma ray production from iron have similar values in broad energy range . the cross sections for both transitions appear much lower compared to the cross section for production of 846.8 kev gamma transition . for example , the cross section for 846.8 kev gamma transition at the neutron energy of 6.5 mev is almost fifty times larger than the cross section for the 1037.3 kev and the 2113.2 kev transitions . in this case , the 2113.2 kev gamma line in the" +"inflation in the early universe @xcite is now an indispensable ingredient of modern cosmology not only to explain the global properties of homogeneous and isotropic space with a vanishingly small spatial curvature but also to account for the origin of the primordial curvature perturbation that seeded cosmic structure formation @xcite . at present , despite the significant progress in the state - of - the - art precise measurements of the cosmic microwave background radiation ( cmb ) by wmap @xcite and planck @xcite missions , there is no single observational result in conflict with the single - field inflation paradigm @xcite . in particular , the anti - correlation of the temperature and the e - mode polarization anisotropies on large scales observed by the wmap mission strongly supports the superhorizon perturbations suggested by inflation @xcite . in other words , once inflation sets in , virtually all the available cosmological observation data can be explained simultaneously irrespective of the initial condition of the universe this does not mean that we may be indifferent to the initial condition of the universe before inflation . on the contrary , in order to achieve complete understanding of the cosmic history , we must work out the very beginning of the universe that may smoothly evolve into the inflationary phase . as is well known , as long as the null energy condition ( nec ) is satisfied in the expanding phase , the hubble parameter and the energy density of the universe increase backward in cosmic time . so , it is often claimed that , if one tries to discuss what happened before inflation and/or how inflation started , one needs to know the information of very high energy physics , and challenge the initial singularity problem @xcite in terms of quantum gravity . but , this is not always the case . recently , it was recognized that , if an action includes higher derivative terms of a scalar field like the galileon terms , the nec can be violated without encountering ghost nor gradient instabilities . see , e.g. , ref . @xcite for a recent review and ref . @xcite for a subtle issue of nonlinear instabilities . if the nec is violated , the energy density can grow as time proceeds , contrary to the conventional wisdom . in the nec violating theories , the universe can therefore start from the static zero - energy state described by the minkowski spacetime from infinite past @xcite , and the universe starts expansion with the increase of the energy density . such a picture of the emergence of the universe was first proposed by creminelli _ et al . _ @xcite with the name galilean genesis . in their model , however , the hot big bang state was postulated to be realized after the effective field theory description breaks down as the energy density blows up beyond its realm of validity . therefore , the theory to describe the most important epoch of the early universe is lacking there . nevertheless , since their original idea is so interesting that a number of extension has been made in a wider class of scalar field theories @xcite and various aspects of the genesis scenario have been explored in the literature @xcite , such as avoidance of the superluminal propagation of perturbations and absence of primordial tensor perturbations . they have been unsuccessful , however , to realize transition from the genesis phase to the hot big bang state within their model lagrangians . in this paper , we take a different approach , namely , to make use of the galilean genesis to explain the initial condition of the universe before inflation and smoothly connect it to the inflationary phase , thereby solving the initial singularity problem @xcite and the trans - planckian problem @xcite ( see also @xcite ) in inflationary cosmology . in fact , such an approach has also been put forward by pirtskhalava _ et al . _ @xcite recently . their model lagrangian , however , gives rise to gradient instability as it is , although it has been argued there that higher - order structure of the effective field theory for perturbations possesses enough freedom to cure the gradient instability . discussion on termination of inflation and reheating is not presernted there , either . in the present paper , we construct a specific model free from any catastrophic instabilities and with subluminal velocities of primordial perturbations . in our setup the universe starts from the minkowski spacetime from infinite past and is smoothly connected to the inflationary phase followed by the graceful exit . for this purpose , we provide a generic lagrangian capable of describing the background and perturbation evolution in all the above phases instead of choosing the effective field theory approach because the latter can not capture the evolution of the background and perturbations from pre - inflationary genesis to the exit from inflation with the same single lagrangian . although we start with asymptotically minkowski space at the past infinity for aesthetic beauty , it has been shown that the galilean genesis solution is an attractor for a variety of initial conditions including those with a negative hubble parameter and/or finite curvature , provided that the time derivative of the scalar field has the right sign @xcite . the horndeski theory @xcite or the generalized galileon @xcite , whose mutual equivalence was first shown in @xcite , is known to be the most general scalar - tensor tensor theory with the second - order field equations , and thereby avoid ostrogradski instabilities in spite of having higher derivative terms in the action . the theory can be generalized to have second - order field equations only in a specific gauge while maintaining the number of propagating degrees of freedom . this possibility was realized recently by gleyzes _ et al . _ @xcite ( see also ref . @xcite ) and was extended further by gao @xcite . the number of propagating degrees of freedom in these theories is indeed shown to be the same as that of the horndeski theory @xcite . in this paper , we use the subclass of gao s framework as a concrete realization of the unified scenario starting from galilean genesis through inflation to the graceful exit . this paper is organized as follows . in the next section , we give a framework of our model and derive the background equations of motion and the quadratic actions of cosmological perturbations . in sec . iii , a concrete lagrangian is constructed to describe our scenario beginning from the genesis phase through the inflationary one to the graceful exit , and such a background dynamics is presented explicitly . in sec . iv , we discuss the stability during each phase based on the quadratic actions of cosmological perturbations . in sec . v , a concrete realization of our scenario is given . the final section is devoted to our conclusions and discussion . let us start with describing the general framework to construct and study our explicit realization of the early - time completion of inflation . we would like to consider theories composed of a metric @xmath0 and a single scalar field @xmath1 , and hence it will be appropriate to work in the horndeski theory . the lagrangian of the horndeski theory is of the form @xmath2,\label{horndeski - l}\end{aligned}\ ] ] where @xmath3 , @xmath4 is the four - dimensional ricci scalar , and @xmath5 is the four - dimensional einstein tensor . we have four arbitrary functions of @xmath1 and @xmath6 in the horndeski theory . this is the most general lagrangian having second - order field equations . nevertheless , it will turn out that this framework is insufficient for our purpose , and hence we have to go beyond the horndeski theory . one can generalize the horndeski theory to possess higher order field equations while maintaining the number of propagating degrees of freedom @xcite . the first step to do so is to perform an adm decomposition by taking @xmath7 const hypersurfaces as constant time hypersurfaces . in the adm language , the metric is written as @xmath8 by definition @xmath1 is a function of only @xmath9 , @xmath10 , and @xmath11 , where a dot denotes differentiation with respect to @xmath9 , so any function of @xmath1 and @xmath6 can be regarded as a function of @xmath9 and the lapse function @xmath12 , provided that @xmath13 and @xmath14 never vanish . then , the horndeski lagrangian ( [ horndeski - l ] ) can be written in terms of the adm variables as @xmath15 with @xmath16 where @xmath17 and @xmath18 are the extrinsic and intrinsic curvature tensors on the constant time hypersurfaces , and @xmath19 , @xmath20 , @xmath21 , and @xmath22 are subject to the relations @xmath23 variation of the above lagrangian with respect to @xmath12 gives a second - class constraint that eliminates only one degree of freedom , as opposed to general relativity . the key trick to generalize the horndeski theory is to notice that this property remains the same even if one liberates @xmath19 and @xmath20 from the restriction imposed by eq . ( [ ab - constraint ] ) @xcite . we thus arrive at the so called glpv theory that is more general than horndeski but has the same number of propagating degrees of freedom . one can move back to a covariant form of the lagrangian by introducing the unit normal to the constant time hypersurfaces as @xmath24 , writing the extrinsic curvature tensor in terms of @xmath25 , and using the gauss - codazzi equations . since there are six arbitrary functions of @xmath9 and @xmath12 in the adm form , the resultant covariant lagrangian has six arbitrary functions of @xmath1 and @xmath6 . the above idea has been pushed forward by gao @xcite , who proposed a unified framework to study single scalar - tensor theories beyond horndeski . one can write a general lagrangian in the adm form as @xmath26,\end{aligned}\ ] ] where the coefficients @xmath27 , @xmath28 , ... are arbitrary functions of @xmath9 and @xmath12 . the hamiltonian depends nonlinearly on @xmath12 as in the glpv theory , giving rise to a single scalar degree of freedom on top of the traceless and transverse gravitons @xcite . in this paper , we will employ the lagrangian @xmath29 with @xmath30 where @xmath31 , @xmath32 , and @xmath33 are constant parameters of the theory . this is a deformation of the glpv lagrangian and belongs to a subclass of gao s framework . the generalization to this level is sufficient for the purpose of the present paper . the glpv theory is recovered by taking @xmath34 . given the lagrangian ( [ ourlag ] ) in the adm form , one can restore the scalar degree of freedom @xmath1 to write its covariant expression in the same way as in the glpv theory . however , it will be more convenient for our purpose to use the explicitly time - dependent lagrangian , because by doing so one can easily design the lagrangian so as to admit the desired cosmological evolution . before specifying the suitable form of @xmath35 , @xmath36 , ... to construct our early universe model , let us derive the general equations governing the background and perturbation dynamics of cosmologies based on the lagrangian ( [ ourlag ] ) . the adm variables are given by @xmath37 where @xmath38 is the curvature perturbation in the unitary gauge and @xmath39 is the transverse and traceless tensor perturbation . a spatially flat background has been assumed and the spatial diffeomorphism invariance was used to write @xmath40 in the above form . in the following , the background value of the lapse function is denoted by @xmath12 where there is" +"plasmonic nanostructures and optical metamaterials have emerged as promising candidates for controlling light - matter interactions at subwavelength from terahertz to near infrared . owing to their interesting physics and exotic properties , engineering spectral properties of light such as absorption , transmission , reflection and emission has been widely realized by manipulating amplitude , phase and polarization of independent electric and magnetic waves responses @xcite . such structures provide improved performance in established technologies such as photodectors @xcite , thermophotovoltaic solar energy conversion @xcite , thermal emitters @xcite , and biochemical sensing @xcite . in all aforementioned modern technologies , perfect black body as the main part which soaks up electromagnetic waves with arbitrary wavelength , polarization and incident angle is much more desirable @xcite . as a result , investigating novel approaches to significantly boost the absorption efficiency of black bodies trapping wideband , angle independent and polarization insensitive light has been a major concern for many researchers @xcite . amongst advanced light trapping methods , bodies based on resonant cavities have demonstrated dramatic promise , including fabry - perot cavities which can be designed by multilayer thin - film coatings to yield resonant enhancement @xcite . however , there is a trade - off between their operational bandwidth and absorption efficiency . in addition , their angle dependent optical response necessitate tracking systems in specific applications such as solar cells to maximize achieving energy @xcite . using metallic subwavelength structures supporting surface plasmons ( sps ) , i.e. , light induced collective surface electron density fluctuations at the interface between metal and dielectric , have been approved as a promising method for high efficiency energy harvesting systems @xcite . by proper structuring metalic nanoparticles @xcite , grating arrays @xcite and subwavelength slits @xcite , light can be concentrated into a thin semiconductor in the form of both localized and propagative surface plasmon polaritons . although progress in fabrication technologies at nanoscale in the past few years has facilitated the development of optical nanoantennas with various characterization such as size , shape and thickness , sharp resonance response with high quality factor nature of sps impose narrow operating bandwidths which strongly depends on the incident polarization @xcite . accordingly , to achieve a broadband optical response , several pseudo - random , periodic , and aperiodic plasmonic nanostructures have recently been proposed @xcite . in this paper , in order to achieve wideband , polarization insensitive , and angle - independent absorber over solar spectrum , we investigate absorption mechanism of an inspired fractal pattern , namely sierpinski carpet . in scattering theory , reflected , refracted or diffracted phenomena is strongly dependent on the size of scaterrer relative to the wavelength of spectrum . due to the self - similarity of fractals , different scales within the same structure are replicated resulting in multiple - band spectral response which is useful in broadband applications such as multiband antennas @xcite . moreover , fractal structures might have a larger perimeter - to - footprint ratio than its basis shape leading to reduced spaced resonant elements and compact devices @xcite . our proposed configuration consists of an array of silver nanobricks on top of a thin silicon dioxide platform . the proposed experimentally feasible metallo - dielectric super absorber is capable of absorbing light in the visible spectrum ( @xmath3-@xmath4 nm ) with a simulated average absorption more than @xmath5% . performing three - dimensional ( 3d ) simulations based on finite integration technique ( fit ) , we theoretically investigate the effect of propagative and localized plasmon modes and localized magnetic and electric dipole resonances on enhancing the efficiency of proposed light trapping structure . these results suggest alternative schemes for design and improvement of subwavelength high performance optical absorbers , sensors and thermal emitters . a schematic image of our proposed broadband absorber is shown in fig . as it is observed , each unit cell consists of a three - layer metal - dielectric - metal ( mdm ) thin - film where a silicon dioxide substrate with thickness @xmath6 is settled on a thick silver backreflector with thickness @xmath7 needed to reflect the incident light back and extends the absorption thickness . the top plasmonic layer is formed in a way that a fractal - like pattern of silver nanobricks is appeared . this pseudo - similar geometrical shape , namely sierpinski carpet , is constructed with a square of side width @xmath8 and height @xmath9 ( fig . [ fig2](a ) ) ; then divided into a grid of @xmath10 smaller cuboids with width of @xmath11 and height of @xmath12 , and only the central sub - square is remained(fig . [ fig2](b ) ) . the same procedure is then recursively applied to the eight side squares . we continue this process up to the second iteration as shown in fig . [ fig2](c ) in which all dimensions are compatible with the current nanotechnology fabrication limitations . the dielectric function of silver and refractive index of silicon dioxide are taken from experimental results @xcite , respectively , and inserted into the cst microwave studio commercial software package . periodic boundary conditions are applied in @xmath13 and @xmath14 directions , and the ports at the front and back surfaces of the unit cell are set for the optical ray incidence , reflection and transmission . furthermore , to consider strong interactions between metal and silicon dioxide , an extremely refined mesh is constructed for the whole structure . we first perform numerical computations to investigate the relationship between the absorption spectrum , lattice constant and dielectric spacer thickness . due to the nature of fractal - like structures , the optimal width of all metal nanocuboids will be achieved automatically by obtaining the optimum lattice constant . other design parameters are chosen in a manner to be subwavelength and practicable . it is notable that sensitivity of the absorption response to these parameters can also be readily explored . now , consider a plane wave impinges toward the structure shown in fig . [ fig1](b ) at normal incidence . [ fig3 ] presents the optical extinction spectrum of the structure for verious values of @xmath8 and @xmath6 while other geometric parameters are chosen as @xmath15 , @xmath16 nm , @xmath17 nm and @xmath18 . optical extinction is defined by @xmath19 in which @xmath20 and @xmath21 are frequency - dependent total transmittance and reflectance from the mdm absorber , respectively . it is notable that using an optically thick silver backreflector hinders light transmission and approximately reduces the optical extinction to @xmath22 . obviously , the lower the amount of the @xmath21 and @xmath20 , the higher the performance of the absorber . it should be noted that reflectance @xmath21 can be readily obtained from the @xmath23-parameters @xmath24 . moreover , since the operating wavelength window is at least @xmath25 times larger than the lattice constant of the unit cell , no higher order diffraction is considered due to the subwavelength characterization of each unit cell . an optimal thickness of the dielectric layer exists which maximizes the extinction . with the aforementioned geometry parameters , when @xmath26 nm , the reflectance has its minimum values in most wavelengths resulting in higher average absorption . for the present geometry , absorption is mainly attributed to metal losses and plasmon coupling between the silver nanocuboids and the backreflector . by increasing the thickness of the dielectric layer , coupling strength will be enhanced first until reaching its maximum value , then decreases thereafter @xcite . when the nanocuboids array resides far away from the silver backreflector , the optical extinction of such system is dominantly determined by the dielectric layer properties @xcite . to investigate the electromagnetic wave trapping in the dielectric layer and plasmonic fractal , we first break down the fractal - like structure into two base - periodicity patterns as shown in fig . [ fig4 ] . by exploring the underlying mechanism of these two simple individual patterns , physical analysis of the main complex unit cell can readily be revealed . the corresponding calculated extinction spectra over the wavelength window ( @xmath0 nm ) are depicted in fig . [ fig4 ] . to disclose the physical origin of the absorption , the electromagnetic field distributions for these resonant modes should be first presented . as fig . [ fig4 ] shows , two distinct peaks observed for the first base - periodicity pattern : one is around the wavelength @xmath27 nm and the other is about @xmath28 nm . these peaks are attributed to the electric / magnetic dipolar resonances and the presence of surface plasmon modes ; although , contribution of parasitic absorption of silver nanocuboids and backreflector plays an important role in enhancement of optical extinction . for the absorption peak at @xmath29 , the electric displacement vectors are represented by the arrows in both of nanocuboids and the backreflector ( fig . [ fig6](a ) ) . this opposite electric displacement generates circulating currents between the top and bottom plasmonic layers . such circulating current , namely magnetic resonance leads to an artificial magnetic moment that interacts significantly with the magnetic field of the incident light @xcite . as a result , an intense enhancement of the localized electromagnetic fields is emerged between the two plasmonic layers as shown in fig . [ fig6](b ) by surface colormap . furthermore , the electric field distribution amplitude and polarization plotted in fig . [ fig6](c ) and fig . [ fig6](d ) imply that the accumulated charges at the both sides of nanocuboids which couple to their image charges in the silver backreflector generate strong electric dipole resonances . as a result , such strong resonances trap and confine incident electromagnetic energy efficiently to the intermediate dielectric spacer and provide enough time to be dissipated as heat due to the ohmic losses within the plasmonic section . the feature of enhanced absorption is further illustrated with the time - averaged resistive loss density for the absorption peaks . [ fig6](e ) depicts that a large portion of incident power is absorbed by the plasmonic nanocuboids and the silver backreflector . the absorption peak at @xmath30 is related to the excitation of sp modes at the interface between the silicon dioxide dielectric spacer and the ground mirror due to the coupling effect of periodic top silver nanocuboids . the main advantage of sp modes is their tunability by adjusting the the shape and size of subwavelength plasmonic structures . it is worth mentioning that at larger periods , the metal nanocuboids array will excite lower - energy modes by providing smaller momenta @xcite . [ fig6](f ) and fig . [ fig6](g ) depict that the magnetic and electric fields are mainly confined at the silicon dioxide / silver interface which confirms the typical feature of interface - bounded sp modes . furthermore , as shown in figs . [ fig6](h ) , high electric field intensity around the metal edges implies the existence of localized surface plasmon mode . such an anti - phase electric field distribution is induced by the accumulation of opposite charges at the tips of silver nanopatterns . due to the strong coupling of resonant electric modes excited at sharp corners of nanocuboids , electric field is significantly boosted between the gap of adjacent metallic nanoparticles . [ fig6](i ) illustrates that power dissipation due to resistive loss almost occurs in the nanocubids . for the case of @xmath10 small nanocuboids array shown in fig . [ fig4 ] , two peaks are emerged at @xmath31 nm and @xmath32 nm . as fig . [ fig8](a ) and fig . [ fig8](b ) depict , cavity mode which comes from the interaction between the incident light and the reflected light from silver back reflector is appeared at @xmath33 . such a cavity" +"neutrinos have masses , the tiny masses far below the range of the masses of the quarks and charged leptons . maybe due to the non - zero masses , neutrinos oscillate among themselves , giving rise to a lepton - flavor violation ( lfv ) . neutrino masses and neutrino oscillations may be regarded as one of the most important experimental facts over the last thirty years @xcite . certain lfv processes such as @xmath0 @xcite and @xmath1 are closely related to the most cited picture of neutrino oscillations so far @xcite - they also occur , however tiny , if neutrinos oscillate . in this note , i wish to point out that the cross - generation or off - diagonal neutrino - higgs interaction may serve as the detailed mechanism of neutrino oscillations , with some vacuum expectation value ( vev ) of the new higgs field(s ) . presumably just like other building blocks of matter such as quarks and charged leptons , we could treat these neutrinos as point - like dirac particles . then , neutrino oscillations are fundamental and deep , certainly deeper than oscillations in other composite systems - such as oscillations in the @xmath2 system . thus , it would be natural to describe the reaction as @xmath3 with some vev for the family higgs field @xmath4 , where @xmath5 and @xmath6 are family - triplet dirac fields . here the curl - dot product is to be explained later . the existence of this unique story for neutrino oscillations is amazing . for over half a century , we have the outstanding question why there are three generations in the minimal standard model @xcite . and , for the last decade , another outstanding puzzle emerges that the dark - matter world is about five times the visual ordinary - matter world ( the latter described by the minimal standard model ) . besides the role in the minimal standard model , neutrinos may be able to tell us something in the dark - matter world which our neutrinos are capable of talking to ( or interacting with ) . indeed , there is room left for something very interesting . remember that the right - handed neutrinos never enter in the construction of the minimal standard model @xcite . the message that the right - handed neutrinos seem to be `` unwanted '' could be telling us something . now , the fact that neutrinos have tiny masses suggests that `` more naturally '' they would be four - component dirac particles , and unlikely to be the two - component majorana particles . the room left for the right - handed neutrinos is that they are `` unwanted '' in the minimal standard model and that they could form some multiplet(s ) under a new ( dark - matter ) gauge group besides the minimal standard model . we have some candidate from the symmetries - the family symmetry that there are three generations in the building blocks of ( ordinary ) matter , and so far only three . the puzzle so well - known that we no longer question ourselves why or why not ! we have seen this fact , but we do nt know why - let s speculate that it could be the story associated with the dark - matter world . it arises naturally the so - called family gauge theory @xcite . note that the right - handed neutrinos do not appear in the minimal standard model . so , we could make a massive @xmath7 gauge theory completely independent of the minimal standard model , including the particle content . we could treat @xmath8 as a triplet under this @xmath7 - so to give rise to a family gauge theory . this completes the derivation of the family gauge theory @xcite . the @xmath7 is by definition the massive gauge theory - all the involved particles , except the neutrinos , are massive dark - matter particles . so , the question becomes : can we construct the overall consistent theory based on the group @xmath9 , i.e. , to add an extra @xmath7 to the minimal standard model ? the answer is an amazing `` yes '' . the first step is to decide what our `` basic units '' ( out of the building blocks of matter ) are and how many they are . for instance , the right - handed neutrino triplet @xmath8 ( @xmath10 - @xmath7 triplet and @xmath11 singlet ) would be a `` basic unit '' . in hwang and yan @xcite , we assign three @xmath7 fermion triplets - @xmath12 , @xmath13 , and @xmath14 ( charged ) . all quarks are singlets under @xmath7 . as the major second step , we have to check whether the complicated higgs mechanisms would work out . this is the `` amazing '' part of the story . in the extended standard model @xcite , we have three scalar / higgs fields : the standard - model higgs @xmath15 , the family higgs triplet @xmath16 , and the mixed family - triplet and @xmath11-doublet scalar / higgs @xmath17 . in the u - gauge , the standard - model higgs picks out the neutral component ( one degree of freedom ) , which in turn projects out the neutral components in @xmath17 such that the neutral part has the spontaneous symmetry breaking ( i.e. the `` projected - out higgs mechanism '' ) but the charged part remains to be massive . the neutral part of @xmath17 and the family higgs @xmath16 make the eight gauge bosons very massive , leaving four real family higgs . using this language @xcite , we can write the mass term of the neutrinos : @xmath18 which is an off - diagonal matrix ( in @xmath7 ) . although it is trivial , the operation does not belong to the mathematics of the matrix . that is , @xmath19 would transform into @xmath20 or into @xmath21 , @xmath20 would into @xmath21 or @xmath19 , and so on . this is interesting in view of neutrino oscillations , since it could be regarded as the underlying interaction ( mechanism ) for neutrino oscillations ( which we are talking about @xcite ) . an oscillation occurs in a way similar to the decay by way of creating a new species plus the vacuum expectation value ( or , changing the vacuum ) . in quantum mechanics , this may be so far the only way how an oscillation can occur . to illustrate the point further , we calculate the golden lepton - flavor - violating decay @xmath0 as the celebrated example . we show in figures 1(a ) , 1(b ) , and 1(c ) three leading basic feynman diagrams . here the conversion of @xmath20 into @xmath19 is marked by a cross sign and it is a term from our off - diagonal interaction given above with the higgs vacuum expectation values @xmath22 and @xmath23 . here the higgs masses are assumed to be very large , i.e. , greater than a few @xmath24 , as in @xmath7 . the only small number ( coupling ) is @xmath25 , explaining the tiny masses of neutrinos . .,width=384 ] using feynman rules from wu and hwang @xcite , we write , for fig . 1(a ) , @xmath26 with @xmath27 . on the other hand , feynman rules yield , for fig . 1(b ) , @xmath28 and a similar result for fig . the four - dimensional integrations can be carried out , via the dimensional integration formulae ( e.g. ch . 10 , wu / hwang @xcite ) , especially if we drop the small masses compared to the w - boson mass @xmath29 in the denominator . in this way , we obtain @xmath30 it is interesting to note that the wave - function renormalization , as shown by figs . 1(b ) and 1(c ) , yields @xmath31 noting that @xmath32 and @xmath33 would make the contribution from figs . 1(b ) and 1(c ) to be the same as , but opposite in sign , that from fig . this is a manifestation of `` gauge invariance '' . in a normal treatment , one ignores the wave - function renormalization diagrams 1(b ) and 1(c ) in the treatment of the decays @xmath0 , @xmath34 , and @xmath35 . thus , one may ignore some important cancelation , if any . comparing this to the dominant mode @xmath36 @xcite , we could obtain the branching ratio . the decay rate for @xmath37 , as would be obtained here , would be of the order @xmath38 , which is extremely small . the off - diagonal mass matrix would be modified by the self - energy diagram since the neutrinos form a triplet under @xmath7 . it is presumed that these self - energy diagrams , after the ultraviolet divergences get subtracted , lead to masses of the right order . the four family higgs have to belong to two triplets - the neutral part of @xmath17 and the purely family higgs @xmath16 . if it is two - two divided such as that addressed in @xcite , then the situation would be as follows : if the off - diagonal mass matrix is diagonalized alone , the three roots would be two negative and one positive , adding up to zero . this seems like one ordering in the masses of neutrinos - one up and two downs . of course , it could be three - one divided as well . besides the golden decay @xmath37 ( much too small ) and neutrino oscillations ( already observed ) , violation of the @xmath39 universality is also anticipated and might be observed . as the baryon - antibaryon asymmetry is sometime attributed to the lepton - antilepton asymmetry , the current scenario for neutrino oscillations @xcite seems inadequate for this purpose . if we take the hints from neutrinos rather seriously , there are so much to discover , even though the minimal standard model for the ordinary - matter world would , by and large , remain to be intact . of course , the standard - model higgs has now been discovered . the direct search for the family higgs and the massive family bosons in the @xmath24 range would be too costly . so , the searches for some lepton - flavor - violating decays and for violation of the @xmath39 universality would be alternative for the moment . to sum up , if we treat neutrinos as `` point - like '' dirac particles , the curl - dot product as in eq . ( 1 ) would be the way to go . it is the way to connect neutrino oscillations with the lepton - flavor - violating decays or reactions . the curl - dot products are _ not _ the matrix operations ( in the mathematics sense ) ; it represents a new way to introduce renormalizable interactions and so expands the horizon of quantum field theory . we believe that , in the dark - matter world , the dark - matter particles are also species in the extended standard model . most of reactions happening among dark - matter particles , even involving neutrinos , can not be detected in the ordinary - matter world . it is clear that the minimum extended standard model would be the extended standard model to be based on the group @xmath40 , since this model is rather unique ( and economical ) . the issue is whether our standard model would close up our world - that is , all particles in our world are accounted for . in a slightly different context @xcite , i propose" +"the sdss ( york et al . 2000 ) consists of four major components : a dedicated 2.5 m telescope at apache point , new mexico , along with a separate 50 cm telescope used to monitor the extinction and to provide calibration patches for the main telescope ; a large format imaging camera ( gunn et al . 1998 ) containing 30 @xmath0 ( 13@xmath113 arcmin ) photometric ccds with @xmath2 filters and 24 @xmath3 astrometric and focus ccds ; two 320-fibre - fed double spectrographs , each with two @xmath0 ccds ; and lots and lots of software , with contributions from most of the sdss institutions ( listed in the acknowledgments ) . the primary goals of the project are to survey the northern galactic cap ( @xmath4 square degrees ) in five bands to ( psf ) limits of 22.3(u ) , 23.3(g ) , 23.1(r ) , 22.3(i ) , and 20.8(z ) , and to carry out a spectroscopic survey of @xmath5 galaxies , @xmath6 qsos , and a few @xmath7 stars . the sdss is now in operational mode , and as of this writing ( late january 2001 ) has imaged some 1600 @xmath8 and obtained about 120,000 spectra as part of its commissioning and initial operations phases . these data have allowed dramatic new astronomical discoveries to be made , discoveries that we shall not further discuss here ( e.g. blanton et al . 2001 , fan et al . 2000 , 2001 , fischer et al . 2000 , ivezi et al . 2000 , leggett et al . the sdss took an early decision to use public domain software wherever possible ; in practice this has largely been applied to our infrastructure rather than scientific codes . our software engineering tools are entirely public domain ( with the exception of compilers ) . we adopted as a source code manager and have been pleased with its performance . we currently have about 1.7gby in our cvs repository ( including at least one version of iraf ) . we have found that , after an initial period of distrust , scientists have found cvs to be extremely useful ; in at least some cases , people sitting next to each other at the observatory in new mexico have communicated via a cvs repository in illinois . while cvs allows us to control individual pieces of software , it does not provide a means of controlling complete systems . we have used a fermi national accelerator laboratory ( fnal ) utility called which allows us to associate a set of _ dependent products _ with a piece of our software . for example , version ` v5_2_10 ` of the image processing pipeline depends upon ` v7_15 ` of our infrastructure routines . this enables us to guarantee that at any time in the future we can reconstruct an entire system , using exactly the same bits and pieces . the particular versions ( e.g. ` v5_2_10 ` ) correspond to tags in the cvs repository . we have adopted a procedure that stable versions of our pipelines correspond to _ branch tags _ in cvs ; this has allowed us to proceed with development while giving us the ability to fix bugs found in the stable , delivered , code . we have used as our problem report and bug database . since july 1998 we have acquired 1799 entries in the database ; the last thousand have been filed since february 2000 . we use a heavily enhanced version of tcl 7.4 ( actually , of tclx ) as our command language . much of the work developing this system ( known as _ dervish _ , n _ shiva _ , sergey et al . 1996 ) was carried out at fnal . in addition to what now appear to be basically cosmetic changes ( which we regret ) , the major enhancements that we made were : * memory tracing / defragmentation / debugging + a common problem with programs that make heavy use of dynamically allocated memory is that the memory acquired from the operating system becomes _ fragmented _ , or that the program forgets to free resources . both of these problems can be resolved by adding a layer above ` malloc ` , and we have done so . figure [ figmemtrace ] shows that the total memory used in the steady state by the frames pipeline ( see below ) is well controlled . * support for c datatypes at tcl level . + we wrote a processor that scans the c include files ( ` .h files ' ) and generated a description of the schema of all the types declared therein . this was originally used to implement a primitive persistent store , but proved more useful in making the c data elements available at the tcl prompt ; this greatly increased the power and flexibility of our command language , allowing us to build the command - and - control parts of our pipelines in tcl rather than having to use compiled c. for example , where a ` handle ' is an address and a datatype . * easy(ish ) bindings from c to tcl . + we implemented a set of library calls that made it possible to bind c commands to tcl in a way that , if not simple , at least required no thought and could be handled by pasting appropriate boiler - plate code . saoimage we gratefully adopted ` saoimage ` , and added a facility to overlay bitmasks . slatec pgplot if we were starting this problem today , we would probably not use tcl ( maybe python in its pyraf incarnation ? ) , and we would certainly make greater efforts to use _ vanilla _ , up - to - date , versions of our chosen system . the sdss has quite a large number of pipelines which must be run in order to fully process the data ; we shall not discuss the spectroscopic reductions or the operational and scientific databases . * ` astroline ` + on the mve167 processors ( running vxworks ) used to archive the raw data on the mountain , we also run a pipeline that processes the pixels before they re written to disk / tape . we generate star cutouts ( ` postage stamps ' ) and column quartiles ; this is all that we save from the 22 astrometric ccds . * ` mt ` pipeline . + process the photometric telescope camera data . this consists of a set of staring - mode observations of fields of standard stars , used to define the extinction and photometric zero - points for the 2.5 m scans . * ` serial stamp collecting ` ( ssc ) pipeline . + reorganise the data stream , cut a more complete set of postage stamps . * ` astrometric ` pipeline . + process the centroids of stars from ` astroline`/`ssc ` and generate the astrometric transformations from pixels to @xmath9 and between bands . * ` postage stamp ` pipeline ( psp ) . + estimate the flat field vectors , bias drift , and sky levels , and characterise the psf for each field . * ` frames ` pipeline . + process the full imaging data , producing corrected frames , object catalogues , and atlas images . * calibration . + take the outputs from ` mt ` pipeline and ` frames ` , and convert counts to fluxes . one major gain from splitting responsibilities in this way is that once we get to the ` frames ` pipeline , fields ( 10arcmin@xmath114arcmin patches on the sky ) may be processed independently and in any order . the sdss imaging piplelines employ a number of novel and even interesting algorithms , which are slowly being written up for publication ; for example the image deblender ( lupton 2001 ) . here we shall only discuss a couple of features connected to handling the point spread function ( psf ) and the related problem of star / galaxy separation . even in the absence of atmospheric inhomogeneities the sdss telescope delivers images whose fwhms vary by up to 15% from one side of a ccd to the other ; the worst effects are seen in the chips furthest from the optical axis . if the seeing were constant in time one might hope to understand these effects ab initio , but when coupled with time - variable seeing the delivered image quality is a complex two - dimensional function and we chose to model it heuristically using a karhunen - love ( kl ) transform . the description of the psf ( as derived in the next subsection ) is critical for accurate psf photometry , i.e. for all faint object photometry if the psf varies so does the aperture correction . we also need to accurately know the psf in order to be able to separate stars from galaxies ; after all , the _ only _ valid discriminant that is nt based on colours or priors is that galaxies do nt look like stars . a good knowledge of the local psf is also needed for all studies that measure the shapes of non - stellar objects ( e.g. weak lensing studies , fischer et al . 2000 ) . the first step is to identify a set of reasonably bright , reasonably isolated stars from our image . we then use these stars to form a kl basis , retaining the first @xmath10 terms of the expansion : @xmath11 where @xmath12 is the @xmath13 psf star , the @xmath14 are the kl basis functions , and @xmath15 are pixel coordinates relative to the origin of the basis functions . in determining the @xmath14 , the @xmath12 are normalised to have equal peak value . once we know the @xmath14 we can write @xmath16 where @xmath17 are the coordinates of the centre of the @xmath13 star , @xmath18 determines the highest power of @xmath19 or @xmath20 to include in the expansion , and the @xmath21 are determined by minimising @xmath22 note that all stars are given equal weight as we are interested in determining the spatial variation of the psf , and do not want to tailor our fit to the chance positions of bright stars . for each ccd , in each band , there are typically 15 - 25 stars in a frame that we can use to determine the psf ; we usually take @xmath23 and @xmath24 ( i.e. the psf spatial variation is quadratic ) . we need to estimate @xmath10 kl basis images , and a total of @xmath25 @xmath26 coefficients , and at first sight the problem might seem underconstrained . fortunately we have many _ pixels _ in each of the @xmath12 , and thus only the number of spatial terms ( @xmath27 , i.e. 6 for @xmath24 ) need be compared with the number of stars available . in fact , rather than use only the stars from a single frame to determine that frame s psf , we include stars from both proceeding and succeeding frames in the fit . this procedure has several advantages : the spatial variation is better constrained at the leading and trailing edges of the frame ; the psf variation is smoother from frame to frame ; and the psf is determined from more stars . we have found that optimal results are obtained by using a range of @xmath28 frames to determine the kl basis functions @xmath14 and @xmath29 frame to follow the spatial variation of the psf . if we try to use a larger window we find that variation of the @xmath30 coefficients is not well described by the polynomials" +"the computational effort needed to deal with large combinatorial structures considerably varies with the task to be performed and the resolution procedure used@xcite . the worst case complexity of a task , more precisely an optimization or decision problem , is defined as the time required by the best algorithm to treat any possible inputs to the problem . for instance , the sorting problem of a list of @xmath0 numbers has worst - case complexity @xmath1 : there exists several algorithms that can order any list in at most @xmath2 elementary operations , and none with asymptotically less operations . unfortunately , the worst - case complexities of many important computational problems , called np - complete , is not known . partitioning a list of @xmath0 numbers in two sets with equal partial sums is one among hundreds of such np - complete problems . it is a fundamental conjecture of theoretical computer science that there exists no algorithm capable of partitioning any list of length @xmath0 , or of solving any other np - complete problem with inputs of size @xmath0 , in a time bounded by a polynomial of @xmath0 . therefore , when dealing with such a problem , one necessarily uses algorithms which may takes exponential times on some inputs . quantifying how ` frequent ' these hard inputs are for a given algorithm is the question answered by the analysis of algorithms . in this paper , we will present an overview of recent works done by physicists to address this point , and more precisely to characterize the average performances , called hereafter complexity , of a given algorithm over a distribution of inputs to an optimization problem . the history of algorithm analysis by physical methods / ideas is at least as old as the use of computers by physicists . one well - established chapter in this history is , for instance , the analysis of monte carlo sampling algorithms for statistical mechanics models . in this context , it is well known that phase transitions , _ i.e. _ abrupt changes in the physical properties of the model , can imply a dramatic increase in the time necessary to the sampling procedure . this phenomenon is commonly known as critical slowing down . the physicists insight in this problem comes mainly from the analogy between the dynamics of algorithms and the physical dynamics of the system . this analogy is quite natural : in fact many algorithms mimick the physical dynamics itself . a quite new idea is instead to abstract from physically motivated problems and use statistical mechanics ideas for analyzing the dynamics of algorithms . in effect there are many reasons which suggest that analysis of algorithms and statistical physics should be considered close relatives . in both cases one would like to understand the asymptotic behavior of dynamical processes acting on exponentially large ( in the size of the problem ) configuration spaces . the differences between the two disciplines mainly lie in the methods ( and , we are tempted to say , the style ) of investigation . theoretical computer science derives rigorous results based on probability theory . however these results are sometimes too weak for a complete characterization of the algorithm . physicists provide instead heuristic results based on intuitively sensible approximations . these approximations are eventually validated by a comparison with numerical experiments . in some lucky cases , approximations are asymptotically irrelevant : estimates are turned into conjectures left for future rigorous derivations . perhaps more interesting than stylistic differences is the _ point of view _ which physics brings with itself . let us highlight two consequences of this point of view . first , a particular importance is attributed to `` complexity phase transitions '' _ i.e. _ abrupt changes in the resolution complexity as some parameter defining the input distribution is varied@xcite . we shall consider two examples in the next sections : * random satisfiability of boolean constraints ( sat ) . in @xmath3-sat one is given an instance , that is , a set of @xmath4 logical constraints ( clauses ) among @xmath0 boolean variables , and wants to find a truth assignment for the variables which fulfill all the constraints . each clause is the logical or of @xmath3 literals , a literal being one of the @xmath0 variables or its negation e.g. @xmath5 for 3-sat . random @xmath3-sat is the @xmath3-sat problem supplied with a distribution of inputs uniform over all instances having fixed values of @xmath0 and @xmath4 . the limit of interest is @xmath6 at fixed ratio @xmath7 of clauses per variable@xcite . * vertex cover of random graphs ( vc ) . an input instance of the vc decision problem consists in a graph @xmath8 and an integer number @xmath9 . the problem consists in finding a way to distribute @xmath9 covering marks over the vertices in such a way that every edge of the graph is covered , that is , has at least one of its ending vertices marked . a possible distribution of inputs is provided by drawing random graphs @xmath8 _ la _ erds - reny _ i.e. _ with uniform probability among all the graphs having @xmath0 vertices and @xmath10 edges . the limit of interest is @xmath11 at fixed ratio @xmath12 of edges per vertex . the algorithms for random sat and vc we shall consider in the next sections undergo a complexity phase transition as the input parameter @xmath13 ( @xmath14 for sat , @xmath15 for vc ) crosses some critical threshold @xmath16 . typically resolution of a randomly drawn instance requires linear time below the threshold @xmath17 and exponential time above @xmath18 . the observation that most difficult instances are located near the phase boundary confirms the relevance of the phase - transition phenomenon . secondly , a key role is played by the intrinsic ( algorithm independent ) properties of the instance under study . the intuition is that , underlying the dramatic slowing down of a particular algorithm , there can be some _ qualitative _ change in some structural property of the problem e.g. the geometry of the space of solutions . while there is no general understanding of this question , we can further specify the above statements case - by - case . let us consider , for instance , a local search algorithm for a combinatorial optimization problem . if the algorithm never increases the value of the cost function @xmath19 where @xmath20 is the configuration ( assignment ) of variables to be optimized over , the number and geometry of the local minima of @xmath19 will be crucial for the understanding of the dynamics of the algorithm . this example is illustrated in sec . [ gradxor ] . while the `` dynamical '' behavior of a particular algorithm is not necessarily related to any `` static '' property of the instance , this approach is nevertheless of great interest because it could provide us with some ` universal ' results . some properties of the instance , for example , may imply the ineffectiveness of an entire class of algorithms . while we shall mainly study in this paper the performances of search algorithms applied to hard combinatorial problems as sat , vc , we will also consider easy , that is , polynomial problems as benchmarks for these algorithms . the reason is that we want to understand if the average hardness of resolution of solving np - complete problems with a given distribution of instances and a given algorithm truly reflects the intrinsic hardness of these combinatorial problems or is simply due to some lack of efficiency of the algorithm under study . the benchmark problem we shall consider is random xorsat . it is a version of a satisfiability problem , much simpler than sat from a computational complexity point of view@xcite . the only but essential difference with sat is that a clause is said to be satisfied if the exclusive , and not inclusive , disjunction of its literals is true . xorsat may be recast as a linear algebra problem , where a set of @xmath4 equations involving @xmath0 boolean variables must be satisfied modulo 2 , and is therefore solvable in polynomial time by various methods e.g. gaussian elimination . nevertheless , it is legitimate to ask what are the performances of general search algorithms for this kind of polynomial computational problem . in particular , we shall see that some algorithms requiring exponential times to solve random sat instances behave badly on random xorsat instances too . a related question we shall focus on in sec . [ codesection ] is decoding , which may also , in some cases , be expressed as the resolution of a set of boolean equations . the paper is organized as follows . in sec . [ dpllsection ] we shall review backtracking search algorithms , which , roughly speaking , work in the space of instances . we explain the general ideas and then illustrate them on random sat ( sec . [ dpllsatsection ] ) and vc ( sec . [ dpllvcsection ] ) . in sec . [ dpllflucsection ] we consider the fluctuations in running times of these algorithms and analyze the possibility of exploiting these fluctuations in random restart strategies . in sec . [ localsection ] we turn to local search algorithms , which work in the space of configurations . we review the analysis of such algorithms for decoding problems ( sec . [ codesection ] ) , random xorsat ( sec . [ gradxor ] ) , and sat ( sec . [ walksatsection ] ) . finally in the conclusion we suggest some possible future developments in the field . in this section , we briefly review the davis - putnam - loveland - logemann ( dpll ) procedure @xcite . a decision problem can be formulated as a constrained satisfaction problem , where a set of variables must be sought for to fulfill some given constraints . for simplicity , we suppose here that variables may take a finite set of values with cardinality @xmath21 e.g. @xmath22 for sat or vc . dpll is an exhaustive search procedure operating by trials and errors , the sequence of which can be graphically represented by a search tree ( fig . [ trees ] ) . the tree is defined as follows : * ( 1 ) * a node in the tree corresponds to a choice of a variable . * ( 2 ) * an outgoing branch ( edge ) codes for the value of the variable and the logical implications of this choice upon not yet assigned variables and clauses . obviously a node gives birth to @xmath21 branches at most . * ( 3 ) * implications can lead to : * ( 3.1 ) * a violated constraint , then the branch ends with @xmath20 ( contradiction ) , the last choice is modified ( backtracking of the tree ) and the procedure goes on along a new branch ( point 2 above ) ; * ( 3.2 ) * a solution when all constraints are satisfied , then the search process is over ; * ( 3.3 ) * otherwise , some constraints remain and further assumptions on the variables have to be done ( loop back to point 1 ) . a computer independent measure of computational complexity , that is , the amount of operations necessary to solve the instance , is given by the size @xmath23 of the search tree _ i.e. _ the number of nodes it contains . performances can be improved by designing sophisticated heuristic rules for choosing variables ( point 1 ) . the resolution time ( or complexity ) is a stochastic variable depending on the instance" +"ultracold atoms provide a unique toolbox to study many - particle physics under very clean and well - defined conditions . the precise control over their interactions and their trapping potentials allows to study the dynamics of phase transitions as well as the preparation of strongly correlated quantum states @xcite . while so far the majority of experiments is carried out with ground state atoms , exploiting the unique properties of highly excited states is gradually moving into the focus of experimental and theoretical efforts . atoms in highly excited states can interact strongly , i.e. , the interaction strength can be of the order of several tens of mhz at a distance of several micrometers . the corresponding quantum dynamics takes place on a microsecond timescale and thus is orders of magnitude faster than the atoms external dynamics . such scenario is usually referred to as frozen gas @xcite . a number of experimental groups have studied the excitation dynamics of such system using rydberg states of alkali metal atoms @xcite which were excited from an ultracold gas . here a dramatic reduction of the fraction of excited atoms was observed once the atomic density was too high or the interaction between excited states was too strong @xcite . this is a manifestation of the so - called rydberg blockade @xcite effect that is responsible for the collective character @xcite of rydberg excitations in dense gases . very recently the power of rydberg states to establish a controlled interaction of single atoms trapped in distant traps has been demonstrated in a series of impressive experiments @xcite . strongly supported by these results , highly excited atoms nowadays are believed to have a manifold of applications ranging far beyond traditional atomic physics . indeed , exploiting the properties of atoms in rydberg states permits the study of spin systems at criticality @xcite , the quantum simulation of complex spin models @xcite , the investigation of the thermalization of strongly interacting many - particle systems @xcite and also the implementation of quantum information protocols @xcite . in a recent work ( ref . @xcite ) we showed that the unique properties of rydberg atoms allow the creation of entangled many - particle states on a one - dimensional ring lattice on a short time scale . finding simple ways for creating entangled many - particle states is of importance , since such states have a number of applications , e.g , they serve as resource for the creation of single - photon light sources @xcite , for improving precision quantum measurements @xcite and for measurement based quantum information processing . in this paper we will go into depth and largely expand on our previous study . we show that excited many - particle states of a laser - driven gas of rydberg atoms on a ring lattice can be obtained analytically in the limit of strong laser driving . we give a detailed derivation of the system s hamiltonian in sec . [ sec : system ] . the construction of the many - body excitations , their eigenenergies and their correlation properties are analyzed in sec . [ sec : states ] . in sec . [ sec : how_address ] we discuss thoroughly how these states can be excited in an experiment . we conclude with a summary and outlook in sec . [ sec : conclusion ] . we study a gas of bosonic ground - state atoms confined to a deep large spacing optical or magnetic @xcite ring lattice with periodicity @xmath0 ( see fig . [ fig : lattice ] ) . the wannier functions @xmath1 are localized at the @xmath2-th site with a width @xmath3 . we assume the external dynamics of the atoms to be frozen , i.e. , no hopping and hence no particle exchange between the lattice sites is present . this is well justified as the internal ( electronic ) dynamics - in which we are interested here - takes place on a much shorter timescale , of the order of hundred nanoseconds . we consider two electronic levels which are denoted by @xmath4 and @xmath5 . here @xmath5 is a rydberg @xmath6s - state which - due to its quantum defect - is well isolated from any other electronic level . it is coupled to the ground state @xmath4 via a laser with rabi frequency @xmath7 and detuning @xmath8 . within the rotating wave approximation , the hamiltonian describing the coupling of the atoms to the laser field reads ( with @xmath9 ) @xmath10 where @xmath11 and @xmath12 ( @xmath13 and @xmath14 ) represent the creation ( annihilation ) of a ground and a rydberg state , respectively , and @xmath15 stands for the number of atoms in state @xmath5 at the @xmath2-th site . being much larger than the extension @xmath16 of the wannier functions ( deep lattice ) . the internal atomic degrees of freedom at each site are described by the ( collective ) states @xmath17 and @xmath18 , coupled by @xmath19.,width=264 ] we will consider throughout this paper the case where each lattice site is occupied by the same number of atoms , @xmath20 . this is achieved , for example , if the system is initialized in a mott - insulator state . the interaction between the rydberg atoms is given by the van - der - waals potential @xmath21 , that is quickly decaying with the distance @xmath22 between atoms . nevertheless , as @xmath23 scales with the eleventh power of the principal quantum number @xmath6 , the interaction can strongly affect the excitation dynamics of atoms that are separated by several micrometers . this strong interaction gives rise to the so - called blockade effect @xcite . we consider a scenario in which the simultaneous excitation of two or more atoms to the rydberg state on a single lattice site is blockaded . thus , on each lattice site @xmath2 , only the two states @xmath24_1\otimes\dots\left[\left|g\right>_k\right]_{n_0}\\ \left|r\right>_k&=&\frac{1}{\sqrt{n_0}}{\cal s } \left\{\left[\left|r\right>_k\right]_1\otimes\left[\left|g\right>_k\right]_2\otimes\dots\left[\left|g\right>_k\right]_{n_0}\right\},\end{aligned}\ ] ] are accessible , where @xmath25 is the symmetrization operator . the effective rabi frequency for the laser coupling between these so - called ( super)atom states ( see fig . [ fig : lattice ] ) is given by @xmath26 . taking all this into account , in eq . ( [ eqn : laser_ham ] ) we can replace @xmath27 $ ] , where @xmath28 and @xmath29 are the pauli spin matrices . since @xmath3 ( see fig . [ fig : lattice ] ) we can rewrite the van - der - waals potential between two ( super)atoms in the state @xmath30 located @xmath31 sites apart as @xmath32 , where @xmath33 is the separation between those sites . as already pointed out , @xmath34 is quickly decaying with the distance . in particular , the next - nearest neighbor interaction is a factor of @xmath35 smaller than the nearest neighbor one ( @xmath36 ) . we will thus only focus on the nearest neighbor interaction which is well - justified for large enough lattices . the interaction hamiltonian for the entire atomic ensemble , with @xmath37 , then reads @xmath38 with the rydberg number operator @xmath39/2 $ ] and the boundary condition @xmath40 . in summary , the complete hamiltonian that drives the dynamics of our system can be written as @xmath41.\ ] ] the system can be described as a periodic arrangement of spin-@xmath42 particles , where the two spin states , corresponding to the two internal states of the ( super)atoms , @xmath17 and @xmath18 , interact via an ising - type potential . in this picture , the rabi frequency @xmath19 and the combination of @xmath43 can be effectively interpreted as perpendicular magnetic fields . hence , the relevant parameters in our system will be : a ) the ones related to the laser , i.e. , the single - atom rabi frequency @xmath7 and detuning @xmath8 , which can be time - dependent and b ) the interaction between rydberg atoms represented by @xmath44 . throughout this paper , we consider the regime where the detuning is much smaller than both the collective rabi frequency ( laser driving ) and the interaction strength , i.e. , @xmath45 . as a consequence , the behavior of the system will be determined by the ratio of the latter two parameters . here we focus on the limit @xmath46 , i.e. , the laser coupling is much stronger than the interaction between atoms . in this regime the first term of the hamiltonian ( [ eqn : working_hamiltonian ] ) is the dominant one and it is convenient to make it diagonal by means of a rotation of the basis . this is achieved by the unitary transformation @xmath47 which brings @xmath48 and @xmath49 . when applied to our hamiltonian ( [ eqn : working_hamiltonian ] ) , it yields @xmath50 with @xmath51\label{eqn : h_xy}\\ h_1&=&\frac{\delta}{2}\sum_{k=1}^l\left(1-\sigma_{x}^{(k)}\right)\label{eqn : h_1}\\ h_2&=&\frac{\beta}{4}\sum_{k=1}^l \left[\left(\sigma_{+}^{(k)}\sigma_{+}^{(k+1)}+\sigma_{-}^{(k)}\sigma_{-}^{(k+1)}\right)-2\sigma_x^{(k)}\right]\label{eqn : h_2},\end{aligned}\ ] ] where @xmath52 is the famous @xmath53-model of a spin chain with a transverse magnetic field . let us now analyze the importance of the individual contributions of @xmath54 . as we can see in fig . [ fig : spectrum ] , the spectrum of @xmath54 decays into manifolds of states which are separated by gaps whose width is approximately @xmath55 . this is caused by the dominant first term of @xmath52 , i.e. , @xmath56 . the eigenstates of @xmath57 are - in terms of the ( super)atom states - given by @xmath58\ ] ] with @xmath59 . thus , each of the manifolds that determine the coarse structure of the spectrum is spanned by a set of product states that have the same number of ( super)atoms in the state @xmath60 . in fig . [ fig : spectrum ] , these manifolds are denoted by @xmath61 , which is the eigenvalue of the states with respect to the operator @xmath62 . the second term of @xmath52 conserves the total number of @xmath60 ( super)atoms . in other words , it couples only states that belong to the same @xmath61-manifold and that are nearly degenerate . as a consequence , the strength of these intra - manifold couplings due to @xmath63 is proportional to @xmath44 . conversely , @xmath64 and @xmath65 couple states that belong to manifolds with different number of ( super)atoms in the state @xmath60 . in particular , @xmath64 and the last term of @xmath65 flip one of the ( super)atoms from @xmath60 to @xmath66 or viceversa . thus , the coupled states belong to different manifolds with @xmath67 , energetically separated by @xmath55 . the two first terms of @xmath65 drive a similar process , flipping always two contiguous ( super)atoms in the same state simultaneously , i.e. , @xmath68 or @xmath69 . as a result , these terms connect states with eigenvalue @xmath61 to those with @xmath70 , which are separated roughly by @xmath71 . these features are reflected in fig . [ fig : spectrum ] . and @xmath72 . the spectrum splits into manifolds which can be labeled by the quantum number @xmath61 of the operator @xmath73 . for sufficiently large @xmath19 , the coupling between manifolds that is established only by @xmath64 and @xmath65 can be neglected . the ( constrained ) dynamics inside the @xmath61-subspaces is then determined by @xmath52.,width=188 ] the transition rates between @xmath61-manifolds corresponding to @xmath64 and @xmath65 can be estimated by second order perturbation theory to be of the order @xmath74 and @xmath75 , respectively . hence , for sufficiently strong driving @xmath46 , their contribution can be neglected and the system s dynamics is constrained to the @xmath61-manifolds . as a consequence , the hamiltonian that drives the intra - manifold dynamics , @xmath52 , _ effectively drives the dynamics of the entire system in this parameter regime_. this hamiltonian is analytically solvable , and we thus have" +"loop quantum cosmology ( lqc ) has become in the past years an interesting candidate for a quantum description of the early universe via homogeneous cosmological models @xcite . based on the same quantization methods of loop quantum gravity @xcite , it has also become a testing ground for different conceptual and technical issues that arise in the full theory . it is perhaps not surprising that the model was first fully understood is the spatially flat @xmath0=0 frw cosmological model coupled to the simplest kind of matter , namely a mass - less scalar field that serves as an internal time parameter @xcite . it was shown numerically that the big bang singularity is replaced by a quantum bounce @xcite , that connects an early contraction phase of the universe with the current state of expansion . by means of an exact solvable model , this bounce was then understood to be generic and present for all states of the theory , and the energy density was shown to be absolutely bounded by a critical density @xmath1 of the order of the planck density @xcite . it was then shown that semiclassical states after the bounce have to come from states that were also semiclassical well before the bounce @xcite . this results have also benefited from uniqueness results that warranties the physical consistency of the theory @xcite . the same quantization methods were applied to other isotropic models with and without a cosmological constant . thus , a closed @xmath0=1 was extensively studied in @xcite and @xcite , while the open @xmath0=-1 was considered in @xcite . a detailed study of singularity resolution for these models was recently completed in @xcite , extending previous results for the flat case @xcite . for the flat model , a cosmological constant was included in @xcite and a massive scalar field in @xcite , where singularity resolution was also shown to emerge as a feature of the theory . an extension of this consistent quantization method was successfully implemented for the simples anisotropic cosmology , namely a bianchi i spacetime in @xcite . it was soon realized that , for anisotropic models with a nontrivial spatial curvature , this quantization method based on considering holonomies along closed loops was no longer applicable . the operator associated to the field strength was no longer well defined on the kinematical hilbert space of the theory used so far . the proposal put forward in @xcite was to consider _ open _ holonomies to represent the connection , and then define the curvature out of the resulting operator . as it turns out , this quantization method has some resemblance to the quantization procedure known as ` polymerization ' @xcite . for the quantization of bianchi ix cosmological models , it was also noted that this ` connection quantization ' could be successfully implemented @xcite , and the singularity could also be resolved . a natural issue that one would like to investigate are the physical consequences of this ` new ' loop quantization . do we have the same qualitative behavior as in the holonomy based quantization ? this question has been satisfactorily ( but trivially ) answered in some cases where both quantizations are available . when the spatial curvature vanishes , as is the case of the @xmath0=0 frw and bianchi i models , both quantization methods coincide @xcite ( once one appropriately fixes a free parameter ) . it is then quite natural to ask whether the same feature is present in other models where the intrinsic spatial curvature in non - trivial . is there an important effect that the spatial curvature carries ? in this respect , the @xmath0=1 frw model is unique to answer this question since , ( to our knowledge ) it is the only such model for which both loop quantizations exist . the purpose of this paper is to explore this issue in detail . more precisely , we shall develop the _ connection based _ quantum theory for a @xmath0=1 frw model and explore its more important features by using an effective description of the dynamics . we shall then compare this description with that from the standard holonomy based loop quantization explored in @xcite , where the effective description has been show to correctly capture the dynamics of semiclassical states @xcite . perhaps somewhat surprisingly , what we find is that in the new connection based quantum theory , the corresponding cyclic universe undergoes a series of bounces and recollapses , but now _ there are two different kind of bounces_. in the cosmic evolution , the universe alternates between these two bounces where both the density and minimum volume differ . interestingly , for universes that grow to become ` large ' before the expansion stops , the two bounces become more similar to each other , so that for a large universe like ours , they become almost indistinguishable . the structure of this manuscript is the following : in sec . [ sec:2 ] we recall the classical @xmath0=1 model , introducing some new notation . in sec . [ sec:3 ] we recall the effective description of the holonomy based quantization and explore some of its consequences . section [ sec:4 ] is the main section of the paper . in the first part , we develop the loop quantization of the model , and in the second part we consider its effective description . we analyze then some of its consequences . we end in sec . [ sec:5 ] with a discussion . in the appendix we summarize our conventions and the computation of closed holonomies . the spacetimes under consideration are of the form @xmath2 , where @xmath3 is a topological three - sphere @xmath4 . it is standard to endow @xmath3 with a fiducial basis of one - forms @xmath5 and vectors @xmath6 . the fiducial metric on @xmath3 is then @xmath7 , with @xmath8 the killing - cartan metric on su(2 ) . here , the fiducial metric @xmath9 is the metric of a three sphere of radius @xmath10 . the volume of @xmath3 with respect to @xmath9 will be denoted by @xmath11 . we also define the quantity @xmath12 . it can be written as @xmath13 , where the quantity @xmath14 will appear in many expressions . the isotropic and homogeneous connections and triads can be written in terms of the fiducial quantities as follows , a_a^i = c_0^o^i_a;e^a_i = p^2_0^oe^a_i . here , @xmath15 is dimension - less and @xmath16 has dimensions of length - squared . the metric and extrinsic curvature can be recovered from the pair @xmath17 as follows , q_ab=|p|^2_0^oq_abk_ab=(c-_02)|p|^2_0^oq_ab note that the total volume @xmath18 of the hypersurface @xmath3 is given by @xmath19 . the poisson bracket for the phase space variables @xmath17 is given , as in the @xmath0=0 case by , \{c , p } = 8g3 , with @xmath20 the barbero - immirzi parameter . from here , one can calculate the curvature @xmath21 of the connection @xmath22 on @xmath3 as , f^k_ab = c^2 - 2c^2_0^k^o^i_a^o^j_b the only relevant constraint is the hamiltonian constraint that has the form , _ = _ ^3xwhere @xmath23 , and @xmath24 is the extrinsic curvature . by means of the relation @xmath25 , with @xmath26 the spin - connection compatible with the triad , we can re - express the second term of the hamiltonian constraint as , e^a_ie^b_jk^i_[ak^j_b]=12 ^ 2^ij_ke^a_i e^b_j(f_ab^k-_ab^k ) . here @xmath27 is the curvature of the spin - connection @xmath26 . the advantage of this substitution is that for this model , this expression has a simple form , _ ab^k=-1a_0 ^ 2_ij^k ^o^i_a^o^j_b with this , the gravitational constraint can be reduced to , _ = -38g^2it is convenient to introduce new variables @xcite : @xmath28 and @xmath29 . the quantity @xmath18 is just the volume of @xmath3 and @xmath30 is its canonically conjugate , \{,v } = 4gwe can then compute the evolution equations of @xmath18 and @xmath30 in order to find interesting geometrical scalars . then , = \{v , h_}= 3(v - v^2/3 ) from which we can find the standard friedman equation using the constraint equation @xmath31 and @xmath32 , h^2:=(3v)^2= - . [ class - frid ] we can now compute @xmath33 , : = -32 + 4gp[dot - theta - clas ] where we have used the standard definition of pressure as @xmath34 . we can readily find the time evolution of the expansion parameter @xmath35 as , = 4 g ( - 3p)- 3 ^ 2v^2/3 from eq . ( [ class - frid ] ) we can see that the condition for a turnaround point , namely when @xmath36 is that the density satisfies @xmath37 . this is the point where the hubble parameter vanishes . from ( [ dot - theta - clas ] ) we see that , if @xmath38 then @xmath39 at the turnaround point , which means that there is a transition from an expanding phase ( where @xmath40 ) to a contracting phase ( where @xmath41 ) , so it corresponds to a point of _ re - collapse_. this section has two parts . in the first one , we recall the effective equations for the quantization of the @xmath0=1 model as developed in ref.@xcite , and explore some of its consequences for arbitrary matter content . in the second part we restrict our attention to the case of a mass - less scalar field . the basic strategy of loop quantization is that the effects of quantum geometry are manifested by means of holonomies around closed loops that carry the information about the field strength of the connection . as is shown in detail in the appendix , the curvature takes then the form , ^f_ab^k= ^k^o^i_a^o^j_b where @xmath42 . in terms of the new variables @xmath43 and @xmath19 , it can be written as , ^f_ab^k = v^2/3 ^ 2 ^ 2_0^k^o^i_a^o^j_b where we have defined @xmath44 . with this form of the curvature as defined by closed holonomies , and neglecting the so called inverse triad corrections , one can arrive at the form of the effective hamiltonian , _ = -v+v we can now compute the equations of motion from the effective hamiltonian as , @xmath45 from here , we can find the expansion as , = = ( -d)(-d)=2(-d)[exp-1 ] . from the above equation we can see that the absolute value of expansion has an absolute upper limit equal to @xmath46 . we can now compute the modified , _ effective friedman equation _ , by computing @xmath47 , h^2 & = ( + ^2d-(1+^2)d^2 ) ( 1 - -^2d+(1+^2)d^2 ) + & = ( -_1)(1- ) [ eff - frid-1 ] where @xmath48 $ ] and @xmath49 is the _ critical density _ of the @xmath50 frw model . we can immediately note from eq . ( [ eff - frid-1 ] ) that there are two points where the hubble parameter @xmath51 vanishes and the universe has a turnaround . the first one corresponds to the point @xmath52 . note that @xmath53 , in the limit @xmath54 , tends to @xmath55 , which is the classical value for re - collapse as given by eq . ( [ class - frid ] ) . thus , in the limit of large volumes one expects @xmath53 to represent the density at re - collapse . the second value for density where the hubble parameter vanishes is given by @xmath56 . note that these densities , where there is a turnaround , is not an universal constant for all trajectories as was the case for the @xmath0=0 model ( for the bounce at @xmath57 ) . instead , the quantity @xmath53 is a function of volume and depends on each individual trajectory . the second density for turnaround is bounded" +"in a variety of cosmological models based on fundamental theory , exotic astrophysical objects which have not been observed are often predicted . conversely , an observational evidence for an exotic object would stimulate creative theoretical discussions . probing these exotic objects and detecting them will give us significant progress of research in fundamental physics . even if we can not detect it , giving a constraint on the abundance of the exotic objects is one of powerful means of investigating the nature of our universe . generally , the interaction between such unobserved exotic objects and well known matters is very weak or not well established . thus , only the gravitational interaction would cause reliable observational phenomena . one of the most direct measurements of gravitational effects of an exotic object is gravitational lensing . for instance , massive compact halo objects are probed by using micro - lensing@xcite . cosmic strings are also targets for probing by using gravitational lensing phenomena@xcite . in this paper , we propose a way to probe ellis wormholes@xcite by using lensed spectra of astronomical sources . the ellis wormhole was first introduced by ellis as a spherically symmetric solution of einstein equations with a ghost massless scalar field . the dynamical stability of the ellis wormhole is discussed in ref . @xcite and the possible source to support the ellis geometry was proposed in ref . . gravitational lensing by the ellis wormhole was studied in refs . @xcite and recently revisited by several authors@xcite . so far , it has been suggested that ellis wormholes can be probed by using light curves of gamma - ray bursts @xcite , micro - lensing @xcite ( see also refs . @xcite ) and imaging observations @xcite , while our proposal is the use of spectroscopic observations to probe ellis wormholes . in order to fully investigate the lensed spectrum of a point source , the wave effect in gravitational lensing must be taken into account . the wave effect for the point mass lens is discussed in refs . wave effects in gravitational lensing by the rotating massive object@xcite , binary system@xcite , singular isothermal sphere@xcite and the cosmic string@xcite have been considered . in sec . [ waveform ] , we calculate the amplification factor of gravitational lensing by the ellis wormhole taking the wave effect into account . the geometrical optics limit is analytically presented in sec . the difference in the amplification factor between the point mass lens and the ellis wormhole lens is discussed in sec . [ obs ] based on observables . in sec . [ obsconst ] , possible observations to probe ellis wormholes are listed . [ summary ] is devoted to a summary . in this paper , we use the geometrized units in which the speed of light and newton s gravitational constant are both unity . the line element in the ellis wormhole spacetime can be written by the following isotropic form : @xmath2 where @xmath3 corresponds to the throat and we simply call @xmath4 the throat radius in this paper . , our definition of the throat radius is half the areal radius of the throat . ] assuming the thin lens approximation is valid , we consider the wormhole lens system shown in fig . [ thinlens ] . on the lens plane @xmath5 . @xmath6 is the intersection of the line ao and the plane @xmath7 . @xmath8 is the position vector of the point b on the plane @xmath7 . ] we use the position vector @xmath9 in the flat space . then , the coordinate @xmath10 is given by @xmath11 , where @xmath12 is the lens position . we set @xmath13-axis as the perpendicular direction to the lens plane and the source plane . @xmath14 , @xmath15 , and @xmath16 denote the distances from the observer plane to the source plane , from the observer plane to the lens plane , and from the lens plane to the source plane , respectively . in the geometrical optics limit , we consider light rays emanated from the source . the vector @xmath17 on the lens plane @xmath5 in fig . [ thinlens ] specifies the light ray which is deflected once at @xmath18 . since @xmath19 can be regarded as the closest approach of the light ray , as is shown in ref . @xcite , the deflection angle @xmath20 is given by @xmath21 as a result , the einstein radius @xmath22 for the ellis wormhole is given by @xmath23 where @xmath24 since we are interested in the wave effect , that is , the deviation from the geometrical optics limit , we need to treat the wave equation rather than light rays . neglecting the polarization effect , we consider the scalar wave equation with the frequency @xmath25 . the wave equation for the monochromatic wave @xmath26 is given by @xmath27 = -4\pi a ~\delta(\vec x-\vec x_{\rm s}),\ ] ] where @xmath28 is the position vector of the point source and @xmath29 in the source term is a constant which specifies the amplitude . without the wormhole , we obtain the wave form @xmath30 at the observer o as follows : @xmath31 = \frac{a}{{d_{\rm s } } } \exp\left[i\omega { d_{\rm s}}\left(1+\frac{\eta^2}{2{d_{\rm s}}^2 } + \mathcal o\left(\left(\frac{\eta}{{d_{\rm s}}}\right)^4\right)\right)\right],\ ] ] where @xmath32 and @xmath33 and we consider the case @xmath34 in this paper . our assumptions to calculate the wave form at o are summarized as follows(see ref . @xcite ) : * the geometrical optics approximation is valid between the source plane and the plane @xmath7 in fig . [ thinlens ] . * thin lens approximation is valid and a ray from the source is deflected once on the lens plane @xmath5 . * assuming @xmath35 , we use a non - dimensional parameter @xmath36 defined by @xmath37 , which gives the typical scale of the deflection angle . then , we assume @xmath38 and @xmath39 . * on the plane @xmath7 , the gravitational potential of the lens object is negligible and @xmath40 , where @xmath41 is the distance between the planes @xmath5 and @xmath7 . on the assumptions made above , we calculate the wave form on the plane @xmath7 up to the leading order for the amplitude and next leading terms for the phase part . applying the kirchhoff integral theorem between the plane @xmath7 and the observer , we calculate the approximate wave form at o. the vector @xmath17 specifies the light ray which is deflected once on the plane @xmath5 at @xmath18 and reaches the plane @xmath7 . the deflection angle is fixed by @xmath17 and the background geometry . the point a in fig . [ thinlens ] denotes the deflected point . we label the intersection of the deflected light ray and the plane @xmath7 as b , while @xmath6 in the fig . [ thinlens ] denotes the intersection of the line ao and the plane @xmath7 . as will be mentioned at the end of this section , the dominant contribution to the wave form at o comes from rays which satisfy @xmath42 , where @xmath43 . therefore we consider @xmath44 as @xmath45 hereafter . first , we consider the following ansatz for @xmath46 in the region between the source plane and the plane @xmath7 : @xmath47 on the plane @xmath7 , the amplitude @xmath48 is given by @xmath49 in the geometrical optics approximation , the phase @xmath50 satisfies the eikonal equation given by @xmath51 at the point b , the phase based on the source position s is given by the following integral @xmath52 where we have introduced the optical path length @xmath53 defined as @xmath54 since , in the geometrical optics approximation , we find @xmath55 the integral is given by @xmath56 after the calculations explicitly shown in appendix [ dereq ] , we finally obtain the following expression : @xmath57 . \label{sourceint3}\ ] ] this expression for the phase and eq . for the amplitude can be used for any value of @xmath17 , that is , we have obtained an approximate wave form on the plane @xmath7 . applying the kirchhoff integral theorem@xcite and neglecting the contribution from the infinity , we express the wave form @xmath58 at o by the following integral : @xmath59 where @xmath60 is the waveform at b. since we are interested in only the leading order of the amplitude , we obtain @xmath61 \int { \mathrm{d}}\xi^2 \exp\left[i\omega\left\ { + \frac{{d_{\rm l}}{d_{\rm s}}}{2{d_{\rm ls}}}\left(\frac{\vec\xi}{{d_{\rm l}}}-\frac{\vec\eta}{{d_{\rm s}}}\right)^2 + \frac{\pi a^2}{\xi}\right\}\right],\ ] ] where we have used the following approximations : @xmath62 defining the amplification factor @xmath63 by @xmath64 , we obtain @xmath65,\ ] ] where @xmath66 @xmath67 gives the optical path difference between the lensed trajectory and the unlensed one in the geometrical optics limit for @xmath68 . introducing a polar coordinate , we rewrite this integral as @xmath69\int^{2\pi}_0{\mathrm{d}}\varphi \exp\left[-2i\omega d xy \cos\varphi\right ] \label{intxphi } \\ & = & -2i\omega d{{\rm e}}^{i\omega dy^2}\int^\infty_0{\mathrm{d}}x x\exp\left[i\omega d\left(x^2+\frac{2}{x}\right)\right ] j_0(2\omega dxy ) . \label{intx}\end{aligned}\ ] ] the integrand is divergent at the infinity on the real axis . this is caused by our approximation associated with @xmath36 , and not real . if we write down the integrand in a precise form without any approximation , we do not have any divergence . actually , in the precise form , the contribution from the integral in the region @xmath70 is negligible due to the cancellation of the quasi - periodic integration . for the same reason , the contribution from the integration in the region @xmath71 is also negligible . since the approximate expression of eq . is valid in the region @xmath72 , we can obtain a reliable result by neglecting the contribution from the region @xmath70 in the integral . practically , to make this integral finite , it is convenient to consider the analytic continuation to the complex plane and take the path of the integral as shown in fig . [ path ] . then , this integral can be numerically performed . in this section , we derive an approximate form of the amplification factor @xmath63 . in the expression , we apply the stationary phase approximation to the integral with respect to @xmath73 . then we obtain @xmath74 , \label{geointx}\ ] ] where @xmath75 and @xmath76 satisfies @xmath77 note that eq . has only one positive root as a function of @xmath78 . in eq . , we again perform the stationary phase approximation in the integral with respect to @xmath78 , and we obtain @xmath79\cr & & + \frac{x_-^3}{\sqrt{(x_-^3 + 2)(1-x_-^3)}}\exp\left[i\omega d\frac{-x_-^3 + 4}{x_- } -\frac{i\pi}{2}\right]\biggr ) , \end{aligned}\ ] ] where @xmath80 satisfies @xmath81 note that @xmath82 and @xmath83 . if we define @xmath84 and @xmath85 as @xmath86 @xmath87 can be expressed as @xmath88 @xmath84 is the magnification factor for each image in the geometrical optics approximation . as an observable , we focus on @xmath89 in this paper . in the geometrical optics approximation , we obtain @xmath90 with @xmath91 being the following : @xmath92 where note that the definition of @xmath93 can be written in terms of @xmath80 , which is a function of @xmath94 . @xmath89 and @xmath95 are depicted as functions of @xmath25 for each value of @xmath94 in fig . [ waveformwh ] . and @xmath95 for the wormhole lens , where @xmath96 . , title=""fig : "" ] and @xmath95 for the wormhole lens , where @xmath96 . , title=""fig : "" ] and @xmath95 for the wormhole lens , where @xmath96 . , title=""fig : "" ] and @xmath95 for the wormhole lens , where @xmath96 . , title=""fig : "" ] in this paper , we assume the following situations for the observation : * we can observe the spectrum of a source . * the unlensed spectrum shape is well known . note that , in our analysis , knowledge about the luminosity" +"in the current paradigm of galaxy formation within cdm cosmology , baryons accrete , dissipate , and settle to the centers of dark matter halos . gas with a non - negligible angular momentum will form an ` disk ' with typical surface densities exceeding @xmath10 ( or column densities , @xmath11 ) . various processes ( e.g. merger induced shocks , secular evolution ) inspire the formation of molecular clouds that cool , fragment , and initate star formation . finally , stellar feedback ( e.g. winds , supernovae ) , agn activity , galaxy interactions , and even magnetic fields @xcite may inhibit star formation , perhaps driving the gas from the galaxy . the disks of galaxies , therefore , serve as a barometer of recent star formation activity and a record of prior processing . the mass , metallicity , velocity field , surface density profile , etc.reflect both the underlying dark matter potential and also the star formation history of the galaxy . in the local universe , disks are mapped in the 21 cm line with radio telescopes . these data reveal the mass , surface density profiles , and kinematics of modern disks ( e.g. * ? ? ? * ; * ? ? ? * ) . with current facilities , unfortunately , it is impossible to survey disks in 21 cm emission at high redshift . such analysis awaits the construction of facilities like the proposed square kilometer array . in lieu of 21 cm observations , one may observe gas through electronic transitions , e.g. the lyman , balmer , and paschen series . although these lines can be studied in emission , they arise in ionized gas via recombination processes . furthermore , detectable fluxes require a strong ( i.e. local ) excitation / ionization source and one tends to map special , isolated regions of the galaxy . to study the bulk of an disk , one may instead probe the gas in absorption via the lyman series @xcite . at the characteristic column densities of disks , the ly@xmath1 transition is damped and astronomers refer to the observed profiles as damped ly@xmath1 systems ( dlas ; * ? ? ? these dla profiles are mainly revealed in the spectra of distant quasars , yet they also manifest in the spectra of grb afterglows ( e.g. * ? ? ? unfortunately , these intrinsically luminous sources cover only a small fraction of the sky such that one rarely intesects a given disk with multiple sightlines ( e.g. * ? ? ? therefore , disks at high @xmath12 must be studied statistically through the observation of thousands of quasars across the sky . this experiment has been realized over the past few years as an unintended consequence of the sloan digital sky survey ( sdss ) of high redshift quasars ( * ? ? ? * ; * ? ? ? * ; hereafter phw05 ) . in this letter , we report on the results for a survey of the sdss data release 5 ( sdss - dr5 ; * ? ? ? we place new constraints on the projected column density distribution , total covering fraction , and integrated mass density of disks at @xmath13 . we search for evolution in these quantities from @xmath14 to 4 and also compare the measurements with disks from the local universe @xcite . these results offer new insight on the evolution of disks and their role in the processes of galaxy formation . throughout the letter , we adopt a @xmath15cdm cosmology with @xmath16 , @xmath17 , and @xmath18 . we have surveyed damped ly@xmath1 systems at @xmath19 using the database of quasar spectroscopy from the sdss - dr5 . we have implemented the algorithms developed in phw05 to search for dla candidates , measure the survey path , eliminate strong bal quasars , and to fit voigt functions to candidate dlas . tables and figures for the ly@xmath1 fits are provided online ( http://www.ucolick.org/@xmath20xavier/sdss ) . the full statistical sample now comprises 738 dlas with @xmath21 over a total redshift path @xmath22 , each located at velocity @xmath23 from the background quasar . in figure [ fig : fnhi]a we present the @xmath24 frequency distribution @xmath0 of the full statistical sample . this measure describes the projected column density distribution of gas in galaxies at high @xmath12 per comoving absorption pathlength @xmath25 . similar to our previous results ( phw05 ) , @xmath0 is well described by a power - law at low @xmath24 values @xmath26 with @xmath27 , but transitions to a steeper function at @xmath28 . this break in @xmath0 is required to yield a finite mass density , @xmath29 . following the formalism in phw05 , we fitted a double power - law to @xmath0 ; the best - fit model is overplotted on the data in figure [ fig : fnhi]a and tabulated in table [ tab : newsumm ] for a series of redshift intervals . the table also lists the zeroth and first moments of @xmath0which give the line density @xmath30 and values respectively . the former quantity represents the covering fraction per @xmath25 for the integrated population of disks at a given epoch . the latter quantity is the comoving mass density of gas in high @xmath12 galaxies . lccccccccccc @xmath312.2,5.5]&10872.8 & 3082.5 & 739&3.05&@xmath32&@xmath33&@xmath34&@xmath35&@xmath36&@xmath37 + @xmath312.2,2.4 ] & 1652.7 & 514.4 & 79&2.31&@xmath38&@xmath39&@xmath40&@xmath41&@xmath42&@xmath43 + @xmath312.4,2.7 ] & 2405.8 & 717.5 & 132&2.57&@xmath44&@xmath45&@xmath46&@xmath47&@xmath48&@xmath49 + @xmath312.7,3.0 ] & 2539.7 & 723.7 & 169&2.86&@xmath50&@xmath51&@xmath52&@xmath53&@xmath54&@xmath55 + @xmath313.0,3.5 ] & 2702.5 & 732.2 & 227&3.22&@xmath56&@xmath57&@xmath58&@xmath59&@xmath60&@xmath61 + @xmath313.5,4.0 ] & 1139.2 & 291.3 & 86&3.70&@xmath62&@xmath63&@xmath64&@xmath65&@xmath66&@xmath67 + @xmath314.0,5.5 ] & 432.8 & 103.6 & 46&4.39&@xmath68&@xmath69&@xmath70&@xmath71&@xmath72&@xmath73 + a principal result of our survey is that the shape of the distribution function does not evolve . figure [ fig : fnhi]b shows the cumulative @xmath0 distributions for a series of redshift intervals from @xmath2 to 5 . we have performed a series of two - sided kolmogorov - smirnov test comparisons and find that the null hypothesis can not be ruled out at greater than 90% confidence for any pair . table [ tab : newsumm ] also reveals that the parameters of a double power - law fit to the data show no significant ( @xmath74 ) variations with redshift . in figure [ fig : fnhi]b , we also present the cumulative @xmath0 function for disks in the local universe , as estimated from 21 cm observations @xcite . remarkably , the @xmath75 distribution function is a near perfect match to the high @xmath12 universe . this is a stunning result noted first and independently by @xcite and phw05 . although the universe and the galaxies within it have evolved substantially over the @xmath8gyr interval from @xmath76 to today , the combined distribution of surface densities is invariant . stated differently , the population of galaxies at any epoch shows a self - similar projected surface density distribution . assuming a @xmath15cdm cosmology . the mass density is observed to decline by @xmath77 from @xmath6 to 2.2 , an interval spanning less than 2gyr . the red band shows the estimate of at @xmath78 from 21 cm surveys of local disks @xcite . _ lower : _ the line density of dlas per comoving absorption length @xmath25 . this quantity can be visualized as the integrated covering fraction per comoving pathlength for disks . folowing the mass density , the covering fraction decreases by 50% from @xmath79 to 2 where it reaches the present - day value ( red band ) as estimated from 21 cm observations @xcite . taken together , the results argue that disks have not evolved significantly over the past @xmath8gyr . , width=336 ] although the shape of @xmath0 is invariant , its normalization decreases with time . this is revealed in figure [ fig : moments ] where we present @xmath30 and from @xmath80 to 2 . both the co - moving covering fraction and the mass density of disks decreases by 50@xmath81 in this @xmath5gyr interval . this sharp decline in both @xmath30 and is a surprising and profound result . before discussing its origin , we emphasize that the evolution must occur at all column densities of the dlas such that the shape of @xmath0 remains invariant . therefore , one should focus on processes that affect the inner and outer regions of disks together . the results of the previous section have far reaching implications for the nature and role of disks and for the processes of galaxy formation . let us begin with the invariance in the shape of @xmath0 . in terms of statistical power , the shape of @xmath0 is dominated by systems with low @xmath24 values and the primary result is that the ` faint - end slope ' of @xmath0 is invariant . in the local universe , low @xmath24 sightlines correspond to the outer regions of disks . we draw the inference that galaxies have self - similar surface density profiles in the outer disk at all cosmic times . in the most straightforward , analytic models of galaxy formation ( e.g. * ? ? ? * ) , @xmath0 is determined by the radial surface density profiles , which in turn are set by the total mass of the system , the angular momentum distribution of the galaxy , the gas mass fraction , etc . this simple picture is modified by spiral density waves , warps , galaxy mergers , the detailed nature of ism clumping , molecular cloud formation , and feedback from supernovae and/or agn activity . all of these processes are expected to vary with time , especially the characteristic mass of galaxies . the results presented in figure [ fig : fnhi]b suggest that the outer regions of disks are not especially sensitive to these processes nor to the underlying dark matter halo mass . we note that this is actually a prediction of viscous models of galactic disk formation @xcite . we await explorations of this topic witin the context of cosmological simulations of galaxy formation ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? secular and feedback processes may be expected to have greater effect on the gas toward the inner regions , i.e. at the highest surface densities . we have also searched for variations in @xmath0 at large @xmath24 , but identify none . at the 95@xmath81 c.l . , all of the redshift intervals have @xmath0 distributions consistent with a break column density of @xmath82 . furthermore , restricting the frequency distributions to @xmath83 , all give satisfactory ks - test probabilities . we conclude there is no evolution at these column densities , but caution that the full sample includes only 105 dlas . the data also reveal , for the first time , that @xmath0 is steeper than @xmath84 beyond the break . this can not be attributed to projection alone ( which predictes @xmath84 ; see * ? ? ? * ) , but we associate the steeper drop to the conversion of atomic gas to molecules @xcite . now consider the sharp decrease in the total comoving covering fraction and mass density from @xmath6 to 2 ( figure [ fig : moments ] , table [ tab : newsumm ] ) . one s initial reaction may be to interpret this decline in terms of active star - formation , i.e. the conversion of the gas in dlas to stars via _ in situ _ star formation . this interpretation is problematic for several reasons . first , one expects star formation to mainly influence gas at high surface densities ; this is revealed , in part , by the form of the schmidt law , @xmath85 , where @xmath86 is the sfr per unit area and @xmath87 is" +"since its inception , it has been clear that general relativity has many striking similarities to gauge theories . both are based on the idea of local symmetry and therefore share a number of formal properties . nevertheless , their dynamical behavior can be quite different . while maxwell electrodynamics describes a long - range force similar to the situation with gravity , the non - abelian gauge theories used to describe the weak and strong nuclear forces have rather different behaviors . quantum chromodynamics , which describes the strong nuclear forces , for example , exhibits confinement of particles carrying the non - abelian gauge charges . certainly , there is no obvious corresponding property for gravity . moreover , consistent quantum gauge theories have existed for a half century , but as yet no satisfactory quantum field theory of gravity has been constructed ; indeed , there are good arguments suggesting that it is not possible to do so . the structures of the lagrangians are also rather different : the non - abelian yang - mills lagrangian contains only up to four - point interactions while the einstein - hilbert lagrangian contains infinitely many . despite these differences , string theory teaches us that gravity and gauge theories can , in fact , be unified . the maldacena conjecture @xcite , for example , relates the weak coupling limit of a gravity theory on an anti - de sitter background to a strong coupling limit of a special supersymmetric gauge field theory . there is also a long history of papers noting that gravity can be expressed as a gauging of lorentz symmetry @xcite , as well as examples of non - trivial similarities between classical solutions of gravity and non - abelian gauge theories @xcite . in this review a different , but very general , relationship between the weak coupling limits of both gravity and gauge theories will be described . this relationship allows gauge theories to be used directly as an aid for computations in perturbative quantum gravity . the relationship discussed here may be understood most easily from string perturbation theory . at the semi - classical or `` tree level , '' kawai , lewellen and tye ( klt ) @xcite derived a precise set of formulas expressing closed string amplitudes in terms of sums of products of open string amplitudes . in the low - energy limit ( _ i.e. _ anywhere well below the string scale of @xmath1 gev ) where string theory effectively reduces to field theory , the klt relations necessarily imply that similar relations must exist between amplitudes in gravity and gauge field theories : at tree - level in field theory , graviton scattering must be expressible as a sum of products of well defined pieces of non - abelian gauge theory scattering amplitudes . moreover , using string based rules , four - graviton amplitudes with one quantum loop in einstein gravity were obtained in a form in which the integrands appearing in the expressions were given as products of integrands appearing in gauge theory @xcite . these results may be interpreted heuristically as @xmath2 this remarkable property suggests a much stronger relationship between gravity and gauge theories than one might have anticipated by inspecting the respective lagrangians . the klt relations hold at the semi - classical level , _ i.e. _ with no quantum loops . in order to exploit the klt relations in quantum gravity , one needs to completely reformulate the quantization process ; the standard methods starting either from a hamiltonian or a lagrangian provide no obvious means of exploiting the klt relations . there is , however , an alternative approach based on obtaining the quantum loop contributions directly from the semi - classical tree - level amplitudes by using @xmath0-dimensional unitarity @xcite . these same methods have also been applied to non - trivial calculations in quantum chromodynamics ( see _ e.g. _ refs . @xcite ) and in supersymmetric gauge theories ( see _ e.g. _ refs . @xcite ) . in a sense , they provide a means for obtaining collections of quantum loop - level feynman diagrams without direct reference to the underlying lagrangian or hamiltonian . the only inputs with this method are the @xmath0-dimensional tree - level scattering amplitudes . this makes the unitarity method ideally suited for exploiting the klt relations . an interesting application of this method of perturbatively quantizing gravity is as a tool for investigating the ultra - violet behavior of gravity field theories . ultraviolet properties are one of the central issues of perturbative quantum gravity . the conventional wisdom that quantum field theories of gravity can not possibly be fundamental rests on the apparent non - renormalizability of these theories . simple power counting arguments strongly suggest that einstein gravity is not renormalizable and therefore can be viewed only as a low energy effective field theory . indeed , explicit calculations have established that non - supersymmetric theories of gravity with matter generically diverge at one loop @xcite , and pure gravity diverges at two loops @xcite . supersymmetric theories are better behaved with the first potential divergence occurring at three loops @xcite . however , no explicit calculations have as yet been performed to directly verify the existence of the three - loop supergravity divergences . the method described here for quantizing gravity is well suited for addressing the issue of the ultraviolet properties of gravity because it relates overwhelmingly complicated calculations in quantum gravity to much simpler ( though still complicated ) ones in gauge theories . the first application was for the case of maximally supersymmetric gravity , which is expected to have the best ultra - violet properties of any theory of gravity . this analysis led to the surprising result that maximally supersymmetric gravity is less divergent @xcite than previously believed based on power counting arguments @xcite . this lessening of the power counting degree of divergence may be interpreted as an additional symmetry unaccounted for in the original analysis @xcite . ( the results are inconsistent , however , with an earlier suggestion @xcite based on the speculated existence of an unconstrained covariant off - shell superspace for @xmath3 supergravity , which in @xmath4 implies finiteness up to seven loops . the non - existence of such a superspace was already noted a while ago @xcite . ) the method also led to the explicit construction of the two - loop divergence in eleven - dimensional supergravity @xcite . more recently , it aided the study of divergences in type i supergravity theories @xcite where it was noted that they factorize into products of gauge theory factors . other applications include the construction of infinite sequences of amplitudes in gravity theories . given the complexity of gravity perturbation theory , it is rather surprising that one can obtain compact expressions for an arbitrary number of external legs , even for restricted helicity or spin configurations of the particles . the key for this construction is to make use of previously known sequences in quantum chromodynamics . at tree - level , infinite sequences of maximally helicity violating amplitudes have been obtained by directly using the klt relations @xcite and analogous quantum chromodynamics sequences . at one loop , by combining the klt relations with the unitarity method , additional infinite sequences of gravity and super - gravity amplitudes have also been obtained @xcite . they are completely analogous to and rely on the previously obtained infinite sequences of one - loop gauge theory amplitudes @xcite . these amplitudes turn out to be also intimately connected to those of self - dual yang - mills @xcite and gravity @xcite . the method has also been used to explicitly compute two - loop supergravity amplitudes @xcite in dimension @xmath5 , that were then used to check m - theory dualities @xcite . although the klt relations have been exploited to obtain non - trivial results in quantum gravity theories , a derivation of these relations from the einstein - hilbert lagrangian is lacking . there has , however , been some progress in this regard . it turns out that with an appropriate choice of field variables one can separate the space - time indices appearing in the lagrangian into ` left ' and ` right ' classes @xcite , mimicking the similar separation that occurs in string theory . moreover , with further field redefinitions and a non - linear gauge choice , it is possible to arrange the off - shell three - graviton vertex so that it is expressible in terms of a sum of squares of yang - mills three - gluon vertices @xcite . it might be possible to extend this more generally starting from the formalism of siegel @xcite , which contains a complete gravity lagrangian with the required factorization of space - time indices . this review is organized as follows . in section [ section : traditional_approach ] the feynman diagram approach to perturbative quantum gravity is outlined . the kawai , lewellen and tye relations between open and closed string tree amplitudes and their field theory limit are described in section [ section : klt_relations ] . applications to understanding and constructing tree - level gravity amplitudes are also described in this section . in section [ section : einsteinhilbert ] the implications for the einstein - hilbert lagrangian are presented . the procedure for obtaining quantum loop amplitudes from gravity tree amplitudes is then given in section [ section : trees_to_loops ] . the application of this method to obtain quantum gravity loop amplitudes is described in section [ section : gravity_loops ] . in section [ section : divergence_properties ] the quantum divergence properties of maximally supersymmetric supergravity obtained from this method are described . the conclusions are found in section [ section : conclusions ] . there are a number of excellent sources for various subtopics described in this review . for a recent review of the status of quantum gravity the reader may consult the article by carlip @xcite . the conventional feynman diagram approach to quantum gravity can be found in the les houches lectures of veltman @xcite . a review article containing an early version of the method described here of using unitarity to construct complete loop amplitudes is ref . excellent reviews containing the quantum chromodynamics amplitudes used to obtain corresponding gravity amplitudes are the ones by mangano and parke @xcite and by lance dixon @xcite . these reviews also provide a good description of helicity techniques which are extremely useful for explicitly constructing scattering amplitude in gravity and gauge theories . broader textbooks describing quantum chromodynamics are refs . chapter 7 of _ superstring theory _ by green , schwarz , and witten @xcite contains an illuminating discussion of the relationship of closed and open string tree amplitudes , especially at the four - point level . a somewhat more modern description of string theory may be found in the book by polchinski @xcite . applications of string methods to quantum field theory are described in a recent review by schubert @xcite . scattering of gravitons in flat space may be described using feynman diagrams @xcite . the feynman rules for constructing the diagrams are obtained from the einstein - hilbert lagrangian coupled to matter using standard procedures of quantum field theory . ( the reader may consult any of the textbooks on quantum field theory @xcite for a derivation of the feynman rules starting from a given lagrangian . ) for a good source describing the feynman rules of gravity , the reader may consult the classic lectures of veltman @xcite . # 1#21.0#1 the momentum - space feynman rules are expressed in terms of vertices and propagators as depicted in fig . [ figure : gravityfeynman ] . in the figure , space -" +"experiments on single photons coupled strongly to single ( artificial ) atoms @xcite allow for in - depth studies of photon - atom interactions on a single particle level . this has first been demonstrated with individual atoms coupled to microwave @xcite and later optical cavity fields @xcite . in solids , strong coupling has been achieved with quantum dots @xcite and superconducting circuits @xcite . despite the diversity of physical realizations the coherent exchange of energy between photons and atoms can be described in all these systems by a generic model named after jaynes and cummings @xcite . in circuit quantum electrodynamics experiments , superconducting quantum circuits are coupled to single microwave photons in a planar transmission line cavity @xcite . in this configuration , coupling strengths exceed decay rates by two orders of magnitude , and strong resonant coupling between a microwave cavity and a single @xcite or multiple @xcite superconducting qubits has been observed . in the case of finite detuning between a single qubit and a resonator mode , energy exchange between the individual systems is strongly suppressed due to energy conservation . in this dispersive regime , a residual interaction mediated via virtual photons induces a finite lamb @xcite and ac - stark shift @xcite of the energy levels . for two qubits coupled to a common cavity field , the same mechanism leads to an interaction mediated by virtual photons @xcite as experimentally demonstrated @xcite . this coupling is similar to the j - coupling of interacting nuclear spins as observed in nuclear magnetic resonance experiments ( e.g.@xcite ) . it is also a dominant interaction of double quantum dots , where the exchange splitting between spin singlet and spin triplet state can be used to control a logical qubit state encoded in a two - electron spin - state @xcite . in contrast to these local interactions , and also opposed to the direct coupling of superconducting quantum circuits @xcite , the coupling mediated via virtual resonator photons allows for a long - range interaction between two or more distant superconducting qubits . in the context of quantum information processing , it can be used to realize two - qubit gates @xcite with superconducting qubits @xcite . in this paper we measure the exchange coupling as a function of detuning of two qubits from a single or multiple resonator modes and characterize the symmetry properties of the coupled system . in section [ sec : jcoupling ] the inter - qubit coupling mechanism and its spectroscopic measurement is outlined . in section [ sec : singlemode ] the coupling near a single resonator mode is analyzed . in section [ sec : multimode ] higher harmonic modes of the transmission line resonator are included in the analysis . section [ sec : darkstate ] and [ sec : twophoton ] describe the formation of a dark state at the avoided level crossing and the observation of a two - photon transition from the ground to the doubly excited state that is allowed only at qubit resonance . in our experiments two superconducting qubits are dispersively coupled to a microwave cavity , see fig . [ fig : setup ] . the quantum circuits are realized as weakly anharmonic transmon qubits @xcite and the cavity is formed by a @xmath0 coplanar - waveguide resonator supporting several harmonic modes @xcite . to input and output transmission lines . two transmons are capacitively coupled to the resonator at its ends ( @xmath1 ) . additional ac - signal lines are capacitively coupled to the qubits ( not used in the experiments ) . ( b ) optical micrograph of a transmon qubit . ( c ) schematics of the measurement setup . the state of the qubit is determined by measuring the transmission of the rf signal through the transmission line cavity modeled as an lcr oscillator . when a spectroscopy signal ( spec ) is resonant with a qubit transition , the resonance frequency of the cavity is shifted and the change in transmission amplitude is recorded at the analog - digital converter ( adc ) after down - conversion with a local oscillator ( lo ) @xcite . the qubit frequencies can be tuned independently with superconducting coils ( sc coil 1/2).,width=325 ] in the dispersive regime , the detuning @xmath2 is larger than the coupling strength @xmath3 of both qubits ( @xmath4 ) to each resonator mode @xmath5 . the relevant hamiltonian @xmath6 is obtained by adiabatically eliminating the direct qubit - resonator interaction of the qubits for each harmonic mode @xmath7 in the jaynes - cummings hamiltonian @xcite . the first term denotes the qubit hamiltonian with lamb - shifted transition frequencies @xmath8 from the ground to the first excited state . higher transmon levels do not play a role in our experiments and are therefore neglected . the second term in eq . ( [ eq : hj ] ) describes the resonator modes with frequencies @xmath9 , integer multiples of the fundamental frequency @xmath10 , shifted by the cavity pulls @xmath11 @xcite . finally , the third term describes the effective qubit - qubit coupling , also called j - coupling or transverse exchange coupling , @xmath12 a flip - flop interaction mediated by virtual photon exchange . the transverse exchange coupling in eq . ( [ eq : j ] ) leads to an avoided level crossing of the excited qubit states @xcite . at qubit - resonance , where @xmath13 , the size of the splitting is @xmath14 . the new eigenstates are the symmetric triplet states @xmath15 , @xmath16 and @xmath17 , as well as the anti - symmetric singlet state @xmath18 , see fig . [ fig:2qsplitting](a ) . in the maximally entangled states @xmath19 a single excitation is shared between the two qubits . more generally , for @xmath20 the eigenstates of the hamiltonian in eq . ( [ eq : hj ] ) can be parametrized as @xmath21 with the mixing angle @xmath22 determined by @xmath23 and @xmath24 . the separable qubit states @xmath25 and @xmath26 are asymptotically realized , @xmath27 and @xmath28 , for large qubit - qubit detunings ( @xmath29 ) , as indicated in fig . [ fig:2qsplitting](b ) . we have performed two sets of experiments using samples with different parameters listed in table [ tab : parameters ] . in these experiments , the energy spectrum of the coupled qubits is probed by monitoring the transmission through the resonator while applying a second spectroscopy tone @xcite at frequency @xmath30 . for the spectroscopy measurement shown in fig . [ fig:2qsplitting](b ) , the first qubit is kept at a fixed frequency @xmath31 and the second qubit frequency @xmath32 is swept across the avoided crossing by changing its flux bias using external coils . the value of @xmath33 can be extracted from a fit of the upper and lower branch of the avoided crossing to the function @xmath34 where @xmath35 is in this parameter regime an approximately linear function of the flux @xmath36 threading the second qubit loop . the fit parameters are the transition frequency @xmath37 of the first qubit and the coupling strength @xmath33 . both are determined with a precision of typically better than @xmath38 . in this particular example we find @xmath39 and @xmath40 . + two additional features are observed in fig . [ fig:2qsplitting](b ) . first , a third spectroscopic line centered between the upper and the lower branch appears at higher drive powers . this is a signature of a two - photon transition from the ground state ( @xmath15 ) to the doubly excited state ( @xmath16 ) of the coupled qubit system that is only allowed directly at the anti - crossing . this is discussed in section [ sec : twophoton ] . second , the upper branch shows a transition to a dark resonance at the avoided crossing , which can be explained by the symmetry of the states with respect to the spectroscopic drive , see section [ sec : darkstate ] . according to eq . ( [ eq : j ] ) the coupling @xmath41 scales inversely with the detuning @xmath42 , considering only a single resonator mode . we have recorded the avoided crossing between the two qubits at different detunings @xmath43 from the fundamental mode of the resonator using a spectroscopic measurement performed on sample a. the corresponding parameters are listed in table [ tab : parameters ] . the measured values of @xmath33 shown in fig . [ fig:2qsplitting](c ) are determined for each detuning from a fit as described in section [ sec : jcoupling ] . .parameters of samples a and b as determined from independent measurements . @xmath44 denotes the fundamental frequency , @xmath45 the cavity decay rate , @xmath46 the charging energy , @xmath47 the maximum josephson energy and @xmath48 the coupling strength to the fundamental cavity mode of qubits @xmath49 and @xmath50 . [ cols=""<,<,<"",options=""header "" , ] ) . ( b ) spectroscopic measurements of the anti - crossing in the regions labeled a , b , c and d in ( a).,width=325 ] the spectroscopic line between upper and lower branch of the avoided level - crossing in fig . [ fig:2qsplitting](b ) is a two - photon transition from the ground state @xmath15 to the doubly excited state @xmath16 . similarly , this transition has also been observed in a phase qubit coupled coherently to a two level fluctuator in the tunnel barrier of the josephson junction comprising the qubit @xcite and in molecular spectroscopy of two nearby molecules @xcite . it becomes visible only at the center of the avoided level crossing , again a manifestation of the symmetry properties of the system . the rate of the corresponding two - photon transition @xcite @xmath51 is given by a sum over the intermediate states @xmath52 . off the avoided crossing the qubits are effectively decoupled . in this case the intermediate states are @xmath53 . the transition is then prohibited due to destructive interference between the two possible paths , @xmath54 or @xmath55 , connecting the ground to the doubly excited state . due to the opposite sign of the detunings @xmath56 , the two terms in the sum cancel and the transition rate @xmath57 . with the qubits at resonance , the intermediate states are @xmath58 and one term in the sum vanishes due to the forbidden transition to the dark state . with only one possible path connecting the @xmath59 to the @xmath60 state , no interference takes place and the transition becomes allowed . the enhanced transition rate can be employed for directly creating the maximally entangled state @xmath61 . we have analyzed the coupling between two distant qubits mediated by the harmonic modes of a resonator . we have observed an overall increase of the exchange coupling with frequency as expected from a model including higher - harmonic modes of the coplanar waveguide resonator . good qualitative agreement over a wide frequency range between the dispersive model and experimental data is obtained when taking spurious resonances of the coplanar waveguide in addition to the coplanar waveguide modes into account . hence , measurements of the transverse inter - qubit coupling can be employed to detect and investigate spurious global coupling channels between distant qubits , complementary to measurements of single qubit spectra used to detect spurious local resonances @xcite . how many higher harmonic modes to include in the theory , i. e. where to set a high - frequency cut - off , can , however , not be decided on the basis of current measurements . in addition , we have observed dark states and enhanced two - photon absorption at the avoided level crossing in spectroscopic measurements . these characteristic features are based on the relation between the symmetry of the drive and the singlet and" +"the time - dependent properties of semiconductor nanostructures and their response to electric pulses are currently being studied through transient current measurements and in a pump - and - probe configuration.@xcite along with these experimental developments theoretical schemes for the description of time - dependent transport emerged . the methods include the non - equilibrium keldysh - green function formalism,@xcite scattering theory , @xcite and more recently the generalized master equation ( gme ) adapted for electronic transport.@xcite these methods were used mostly for studying the transient currents generated by a time - dependent potential applied on the sample or by a time - dependent coupling between the leads and the sample . an example in the first category is the time dependent pumping of electrons through a small open system.@xcite in the second category we mention the transient currents and the geometrical effects imposed by the lateral confinement of the sample.@xcite in another recent work we investigated the modulation of the drain current when a sequence of square pulses is applied to the source probe connected to a quantum dot and a short quantum wire described within lattice model.@xcite that study was motivated by the experiments of naser _ et al_.@xcite in the present work we further exploit the gme method and study the transport properties of a quantum wire operating in a turnstile regime . the turnstile pump is a single - electron device where the sample is periodically connected and disconnected with the left and right lead respectively , but with a relative phase shift . it was experimentally created by kouwenhoven _ et al._@xcite by modulating in time the two tunneling barriers between a quantum dot and two leads . the electrons were driven by a finite bias between the leads . this setup is different from a quantum pump where a current is generated by asymmetric external oscillations , but without a bias . in the experiment of kouwenhoven _ the barrier heights oscillate out of phase in the following sense : on the first half - cycle electrons enter from the source probe in the system but there is no current in the drain probe because the corresponding tunneling barrier is high enough to prevent this . in the second half - cycle the source is disconnected , the drain contact opens , and a discharge of the dot follows . it was found that an integer number of electrons are transmitted through the structure in each pumping cycle . more recently , due to the general interest in applications of nanoelectronic devices , more complex turnstile pumps have been studied by numerical simulations , like one - dimensional arrays of junctions @xcite or two - dimensional multidot systems . @xcite in the present paper we predict that the turnstile operation can also be performed in a quantum wire sample and in an external magnetic field as well . our results are obtained using a parabolic lateral confinement model both for the quantum wire and for the leads . we put a special effort on describing the lead - sample contacts . in a previous work we studied the turnstile transport through a sample described by a lattice ( tight - binding ) model . the sample was a one - dimensional system with two or three sites and the transport calculations were done using nonequilibrium keldysh - green functions.@xcite the quantum wire considered in this work is much more complex . we start from the single - particle hamiltonian of a two - dimensional wire of length @xmath0 parabolically confined along the @xmath1 direction and with hard - wall conditions at @xmath2 . the eigenfunctions of the hamiltonian were described in detail in ref . and will not be repeated here . the material is organized as follows : in section [ model ] we briefly review the main equations of the model and of the gme method , section [ calc ] is devoted to the numerical results for zero magnetic field ( [ beq0 ] ) , in the presence of a magnetic field ( [ bne0 ] ) , and to the edge states ( [ es ] ) . the conclusion are given in section [ conc ] . we consider an isolated finite quantum wire of length @xmath3 nm , extended in the @xmath4-direction . the width of the wire is defined by a parabolic confinement potential in the @xmath1-direction with the characteristic energy @xmath5 mev . the quantum wire is terminated at @xmath2 with hard wall potentials . in addition , we have two semi - infinite leads , one extended from @xmath6 to @xmath7 , and the other one from @xmath8 to @xmath9 . both have a parabolic confinement in the @xmath1 direction with an energy of 0.8 mev , and are also terminated at @xmath2 with hard walls . the leads and the finite quantum wire , or the system , are all subjected to an external constant magnetic field @xmath10 . the length of the wire , @xmath0 , and the magnetic length modified by the parabolic confinement @xmath11 , with @xmath12 and the cyclotron frequency @xmath13 , are convenient length scales in the calculations . we assume the gaas effective mass , @xmath14 . the many - electron hamiltonian of the system composed by the semi - infinite leads and the finite quantum wire , but isolated from each other , is : @xmath15 where an electron in the system is created ( annihilated ) by the operators @xmath16 ( @xmath17 ) , and in the leads by @xmath18 ( @xmath19 ) . @xmath20 are the energies of the single - electron states labeled with @xmath21 in increasing order , @xmath22 is the energy spectrum of the left and right leads , labeled as @xmath23 and @xmath24 respectively , and @xmath25 representing a discrete label of subbands and a continuous quantum number labeling states within each subband . at @xmath26 the system is coupled to the leads with the hamiltonian @xmath27 with @xmath28 describing the time - dependence of the coupling , such that @xmath29 , and @xmath30 describing the coupling strength of state @xmath31 and @xmath25 in the system and the leads , respectively . the coupling is defined by a nonlocal overlap integral of the two states in the region of contact around @xmath2 . the coupling coefficients are defined phenomenologically with the tensor @xcite @xmath32 where a nonlocal - overlap of the wave functions in the system and the leads is modeled by @xmath33}\nonumber\\ & \exp{\left(\frac{-|e_a-\epsilon^l(q)|}{\delta_e^l}\right)}. \label{gl}\end{aligned}\ ] ] the strength of the coupling between the leads and the sample is defined by the parameter @xmath34 , which captures the tunneling rate at the contact between each lead and the sample , and also by the parameters @xmath35 , @xmath36 and @xmath37 which adjust the spatial overlap of lead and sample wave functions in the contact region . since all we have from our model are the wave functions derived for the uncoupled subsystems , this intuitive ansatz , eqs . ( [ t_aq ] ) and ( [ gl ] ) , is a convenient way of describing the coupling . in our calculations these coupling parameters will be the same for both leads and hence the label @xmath38 will be omitted . the system can be subjected to a bias @xmath39 and in order to reduce the number of many - electron states ( mes ) to a reasonable number in the following calculations we limit the number of single - electron states ( ses ) for the particular calculation by selecting a window of relevant states around the bias window , i.e. @xmath40 $ ] , such that the transport properties are not changed significantly by extending the window . we consider these states relevant for the transport , or `` active '' , while all the other states are `` frozen '' , being either permanently occupied or permanently empty . in addition to the electrons frozen in the states below the active window ( which are not included in the transport calculation ) , we also assume the lowest active state occupied at the moment @xmath26 _ i. e. _ when the contacts begin to operate . in this way the transient phase is shorter than if we would assume an empty active window , and we can spend less computing time until the system reaches the periodic state . the time - evolution of the total system - finite wire and leads - after the coupling at @xmath26 , can be described by the liouville - von neumann equation for the statistical operator @xmath41 . the evolution of the finite wire itself can be captured by the reduced density operator @xmath42 ( rdo ) , _ i. e. _ by averaging over the the lead variables . from the resulting integro - differential equation we retain only the lowest order ( quadratic ) terms in @xmath43 and obtain @xcite @xmath44\\ & -&\frac{1}{\hbar^2}\sum_{l=\mathrm{l , r}}\int dq\:\chi_l(t ) ( [ { \cal t}_l,\omega_{ql}(t)]+h.c . ) , \label{gme}\end{aligned}\ ] ] where we have introduced two operators to compactify the notation @xmath45 with @xmath46 , and a scattering operator @xmath47 acting in the many - electron fock space of the system @xmath48 with the rdo it is possible to calculate the statistical average of the charge operator @xmath49 for the coupled system @xmath50q_\mathrm{s } \}\\ & = & { \rm tr}_\mathrm{s}\{\rho(t)q_\mathrm{s } \ } = e\sum_{a,\mu } i^{\mu}_a \ , \langle\mu | \rho(t ) | \mu\rangle , \end{aligned}\ ] ] with the traces assumed over the fock space . the average time - dependent spatial distribution of the charge can also be obtained , @xmath51 the net current flowing into the sample is @xmath52 the total current in eq . ( [ current ] ) is given by the left hand side of the gme , eq . ( [ gme ] ) , and the partial currents associated to each ses and each lead correspond to the terms of the sum on the right hand side ( the trace of the commutator of @xmath53 and @xmath54 is zero ) . the functions which modulate the coupling between the leads and the quantum wire are built in the following way : for @xmath55 we use the fermi - like function @xmath56 , with @xmath57 ps@xmath58 , and we define @xmath59 , where @xmath60 is the lead index . then , for @xmath61 , @xmath28 become step - like functions alternating between 0 and 1 , both with the same period @xmath62 , but with a delay of @xmath63 . in this way we mimic the on / off contact switching done in the turnstile experiments . we choose @xmath64 , which means we first switch off the left contact while the right one is still on . then the left is turned on again while the right is turned off , and so on . the energy spectrum of the leads and of the sample are shown in fig.[elev ] . the leads have parabolic subbands while the sample has discrete levels . the maximum energy for each subband shown in the graph indicates the corresponding maximum wave vector in the @xmath65-integration of the gme . the chemical potentials in the leads defining the bias window ( bw ) are shown with the dashed horizontal lines . we consider two bw s : bw1 with chemical potentials @xmath66 mev and @xmath67 mev , and bw2 with @xmath68 mev and @xmath69 mev respectively . in both cases the applied bias is @xmath70 mev . in the numerical calculations of the reduced statistical operator we also include the sample states with energy outside the bw , between the limits @xmath71 and @xmath72 with @xmath73 mev . the first active window contains 4 sess and the second one contains 5 sess . in fig . [ occup1 ] we show the" +"galactic globular clusters ( gcs ) are dense and old ( @xmath1 gyr ) stellar systems containing up to @xmath2 stars , orbiting the milky way halo and bulge . their study is crucial to understand the dynamical evolution of collisional systems ( e.g. * ? ? ? * ; * ? ? ? * ) and the interplay between dynamics and stellar evolution ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? their high central densities provide the ideal ground to the formation of exotic objects like blue straggler stars , cataclysmic variables , low - mass x - ray binaries and millisecond pulsars ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . in this respect , remarkable is the case of m71 , which is a low - density gc located at a distance of about 4 kpc from earth . it has a quite high metallicity ( [ fe / h]@xmath3 ) , a color excess @xmath4 ( * ? ? ? * edition ) and a total mass of about @xmath5 @xcite . x - ray observations revealed that it hosts a large population of x - ray sources , most likely consisting of stellar exotica . surprisingly , as discussed in @xcite , the number of x - ray detections in m71 is significantly larger than what is expected from its present - day mass and its collisional parameter ( which is a characteristic indicator of the frequency of dynamical interactions and thus of the number of stellar exotica in a gc ; e.g. @xcite ) . however , it is worth noticing that m71 is located at a low galactic latitude ( @xmath6 ) , likely on a disk - like orbit @xcite . hence , it could have have lost a substantial fraction of its initial mass , due to heavy interactions with the galactic field and to shocks caused by encounters with molecular clouds and/or spiral arms . moreover the structural parameters of this cluster have been estimated from shallow optical images @xcite , and therefore need to be re - determined more accurately . hence , the value of the collisional parameter , which directly depends on the cluster structural parameters @xcite , could be biased . by taking advantage of two epoch of observations obtained with the _ hubble space telescope _ ( hst ) and wide - field near - infrared and optical datasets for m71 , here we present the determination of : _ ( i ) _ the stellar proper motions ( which allow us to distinguish cluster members from galactic contaminants ) , _ ( ii ) _ the absolute pm of the system ( from which we estimate its orbit within the galaxy during the last 3 gyr ) , and @xmath7 the cluster gravitational center and structural parameters . in section [ obs ] we describe the procedures adopted for the data reduction and analysis . sections [ pm ] and [ abspm ] are devoted to the determination of relative stellar proper motions ( pms ) , and of the cluster absolute pm and orbit , respectively . in section [ clust ] we present the new determination of cluster gravity center , density profile and structural parameters from near - infrared data and we study how the latter change if optical observations are used instead . we also provide an estimate of the initial mass of the system . finally , in section [ conclu ] we summarize the results and discusse the x - ray source abundance discrepancy in light of the new values of the cluster structural parameters and the initial mass estimate . the present work is based on two different datasets . their characteristics and the adopted data reduction procedures are described in the following . _ high - resolution dataset _ this has been used to determine the stellar pms . it consists of two sets of images acquired with the wide field channel ( wfc ) of the advanced camera for surveys ( acs ) mounted on hst ( see figure [ mappafov ] for a map of the fields of view - fovs - covered by these observations ) . this camera provides a fov of @xmath8 with a pixel scale of @xmath9 . the first epoch data have been collected under go10775 ( p.i . : sarajedini ) on 2006 july 1 , and consist of a set of ten dithered images , five in the f606w filter ( with exposure times : @xmath10 s ; @xmath11 s ) and five in the f814w filter ( @xmath10 s ; @xmath12 s ) . the second epoch is composed of proprietary data obtained under go12932 ( p.i . : ferraro ) on 2013 , august 20 . it consists of a set of ten deep images acquired through the f606w filter ( @xmath13 s ; @xmath14 s ; @xmath15 s ) and nine images in the f814w filter ( @xmath16 s ; @xmath17 s ; @xmath18 s ) . the photometric analysis has been performed on the -flc images ( which are corrected for flat field , bias , dark counts and charge transfer efficiency ) following the procedures described in detail in @xcite . briefly , both the epochs have been analyzed with the publicly available program img2xym_wfc.09x10 , which uses a pre - determined model of a spatially varying point spread function ( psf ) plus a single time - dependent perturbation psf ( to account for focus changes or spacecraft breathing ) . the final output of this process are two catalogs ( one for each epoch ) with instrumental magnitudes and positions for all the sources above a given threshold . star positions were corrected in each catalog for geometric distortion by adopting the solution provided by @xcite . by using the stars in common with the public catalog of ( * ? ? ? * see also @xcite ) , instrumental magnitudes have been calibrated on the vegamag system and instrumental positions have been reported on the absolute right ascension and declination coordinate reference system ( @xmath19 and @xmath20 , respectively ) . the final color - magnitude diagrams ( cmds ) are shown in figure [ cmd ] for the two different epochs . ) . the grey dots highlight the stars in common are between the two datasets , which has been used to measure the stellar proper motions . the solid circle marks the core radius of the cluster as derived in this work ( @xmath21 ; see section [ density ] ) . , width=321 ] _ wide - field dataset _ to determine the cluster gravitational center and structural parameters , we used ground - based near - infrared images ( prop i d : 11ad90 ; pi : thanjavur ) obtained with the wide field imagers wircam mounted at the canada - france - hawaii telescope ( cfht ) . to study the effect of differential reddening , we also made use of optical wide - field images ( prop i d : 04ac03 , 03ac16 ; pi : clem ) acquired with megacam at the same telescope . the wircam camera consists of a mosaic of four chips of 2040@xmath222040 pixels each , with a pixel scale of @xmath23 , providing a total fov of @xmath24 . we analyzed seven images obtained with the @xmath25 and @xmath26 filters , with exposure times of 5 s and 24 s , respectively . a dither pattern of few arcseconds was applied to fill the gaps among the detector chips . the megacam camera consists of a mosaic of 36 chips of 2048@xmath224612 pixels each , with a pixel scale of @xmath27 providing a fov of @xmath28 . a total of 50 images have been acquired , both in the g and in the r bands , with exposure times of 250 s each . a dither pattern of few arcseconds was adopted for each pointing , thus allowing the filling of most of the interchip gaps , with the exception of the most prominent , horizontal ones . figure [ mapground ] shows the map of the wide - field dataset . for both these sets of observations , the images were pre - processed ( i.e. bias and flat - field corrected ) by means of the elixir pipeline developed by the cfht team and the photometric analysis has been performed independently on each chip by following the procedures described in @xcite . briefly , by means of an iterative procedure , an adequate number ( @xmath29 ) of isolated and bright stars has been selected in each chip and filter to model the psf . hence , the psf model has been applied to all the stellar - like sources at about 4@xmath30 from the local background by using daophot and the psf - fitting algorithm allstar @xcite . for each filter and chip , we matched the single - frame catalogs to obtain a master list . each master list includes the instrumental magnitudes , defined as the weighted mean of the single image measurements reported to the reference frame of the transformation , and the error , which is the standard deviation of the mean . instrumental magnitudes have been reported to the sdss photometric system for the megacam catalog , and to the 2mass system for the wircam catalog . finally the instrumental positions have been reported to the absolute coordinate reference frame by using the stars in common with the 2mass catalog . the cmds for these datasets are shown in figure [ cmd2 ] for stars located at less than @xmath31 from the center . as can be seen from both fig . [ cmd ] and fig . [ cmd2 ] , the standard evolutionary sequences are well defined . however , they are also heavily contaminated by foreground objects , as expected from the location of m71 close to the galactic disk . ) .,width=321 ] from the center are plotted . , width=321 ] to study the pms of m71 , we used the high resolution datasets . these are separated by a temporal baseline of 7.274 years and because of their different orientation , pointing and magnitude limit , the pm analysis could be performed only on the @xmath32 stars in common , located in the overlapping fov ( see figure [ mappafov ] ) and having magnitudes @xmath33 ( corresponding to magnitudes @xmath34 ) . we adopted the procedure described in ( * ? ? ? * see also @xcite ) . briefly , we used six parameters linear transformations to report the coordinates of the stars in each exposure to the distortion - free reference catalog of @xcite . since we are interested in the stellar pms relative to the cluster frame , these transformations have been determined by using a sample of @xmath35 stars that , in the reference catalog , are likely cluster members on the basis of their cmd position ( i.e. stars located along the main sequence ) . moreover , the transformations have been determined independently on each detector chip in order to maximize the accuracy . at the end of the procedure , for each of the @xmath32 stars we have up to ten position measurements in the first epoch catalog and up to nineteen in the second epoch catalog . to determine the relative pms , we computed the mean x and y positions of each star in each epoch , adopting a @xmath36 clipping algorithm . the star pms are thus the difference between the mean x , y" +"the distant globular cluster palomar 13 has been found to have a very high m / l ratio of @xmath0 and its profile can be well fitted either by a king profile with a power - law tail or a nfw model [ 1 ] with scale radius @xmath1pc and central density @xmath2 . a possible explanation is that this distant cluster @xmath3 is one of the numerous dark clumps predicted by cdm scenarios , which was not destroyed by the galactic tidal field . it may be a disrupted cluster as well , out of dynamical equilibrium . here we assume that the nfw profile is the signature of a halo made of cold particles . physics beyond the standard model could be supersymmetry . the lowest massive supersymmetric particle , i.e. the neutralino , is a natural candidate for cdm . if r - parity is conserved the neutralino is stable , is its own antiparticle and has a very small cross - section for annihilation . we assume that the halo of palomar 13 is made of neutralinos and calculate the flux in high energy @xmath4-rays due to their annihilation . theoretical physics beyond the standard model is reviewed by j. ellis in this book . the susy benchmark models have been proposed to provide a common way of comparing the discovery potential of future accelerators [ 2 ] . these scenarios correspond to 13 configurations of the 5 msugra parameters with the trilinear coupling parameter @xmath5 set to 0 . the models fulfill the conditions imposed by lep measurements , @xmath6 result and relic density constraint @xmath7 . we calculate the @xmath4 fluxes for the benchmark models bcgil in the `` bulk '' region with our current mc simulation programs : darksusy [ 3 ] and suspect [ 4 ] . the simultaneous use of the suspect and darksusy package allows to perform the rge evolution from the gut scale to the ewsb scale . the fluxes ( in @xmath8 ) obtained by varying the threshold energy and integrated within @xmath9 are shown in the following figure . the main points are that we need to work at low energy threshold and very low flux @xmath10 . these fluxes are not out of reach but ground - based ongoing instruments will have to be improved by one order of magnitude for that purpose . an array of 5 hesses ( each including four 15-m class telescopes like in hess ) , operating in adjacent areas at 5000 m altitude , would reach a flux limit of @xmath11 at 25 gev in 400 h. * with that flux limit most of the neutralino parameter space in the galactic center could be explored . this is roughly the instrument needed to demonstrate or disprove supersymmetry in astrophysics . * p. cot , s.g . djorgovski , g. meylan , s. castro , j.k . mccarthy , 2002 astro - ph/0203410 j. ellis , j.l . feng , a. ferstl , , k.t . matchev , & k. olive , 2001 , astro - ph/0110225 http://www.physto.se/~ edsjo / darksusy/ http://www.lpm.univ - montp2.fr:7082/~ kneur / suspect.html" +"over the past two decades , the utility of type ia supernovae ( sne ia ) as standardizable candles to trace the expansion history of the universe has been underscored by the increasing resources dedicated to optical / near - ir discovery and follow - up campaigns ( @xcite ; @xcite ) . at the same time , the nature of their progenitor system(s ) has remained elusive , despite aggressive studies to unveil them ( see e.g. @xcite ) . the second nearest ia sn discovered in the digital era , sn 2011fe @xcite located at @xmath6 @xcite , represents a natural test bed for a detailed sn ia progenitor study @xcite . ] . the best studied type ia sn at early times before sn 2011fe , sn 2009ig , demonstrated how single events can provide significant insight into the properties of this class of explosions @xcite . the fundamental component of sn ia progenitor models is an accreting white dwarf ( wd ) in a binary system . currently , the most popular models include ( i ) a single - degenerate ( hereafter , sd ) scenario in which a massive wd accretes material from a h - rich or he - rich companion , potentially a giant , subgiant or main - sequence star , ( @xcite ; @xcite ) . mass is transferred either via roche - lobe overflow ( rlof ) or through stellar winds . alternatively , ( ii ) models invoke a double sub-@xmath7 wd binary system that eventually merges ( double degenerate model , dd ; @xcite , @xcite ) . in sd models , the circumbinary environment may be enriched by the stellar wind of the donor star or through non - conservative mass transfer in which a small amount of material is lost to the surroundings . winds from the donor star shape the local density profile as @xmath8 over a @xmath9 parsec region encompassing the binary system . theoretical considerations indicate that the wind - driven mass loss rate must be low , since an accretion rate of just @xmath10 is ideal for the wd to grow slowly up to @xmath7 and still avoid mass - losing nova eruptions ( steady burning regime , @xcite ) . strong evidence for the _ lack _ of a wind - stratified medium and/or the detection of a constant local density ( with a typical interstellar medium density of @xmath11 ) may instead point to a dd model . arising from the interaction of the sn shock blast wave with the circumbinary material , radio and x - ray observations can potentially discriminate between the two scenarios by shedding light on the properties of the environment , shaped by the evolution of the progenitor system ( see e.g. @xcite , @xcite ) . motivated thus , several dozen sne ia at distances @xmath12 mpc have been observed with the very large array ( vla ; @xcite ; @xcite ; soderberg in prep . ) , the chandra x - ray observatory @xcite , and the swift x - ray telescope ( @xcite ; russel & immler , in press ) revealing no detections to date . these limits were used to constrain the density of the circumbinary material , and in turn the mass loss rate of the progenitor system . however these data poorly constrain the wd companion , due in part to the limited sensitivity of the observations ( and the distance of the sne ) . the improved sensitivity of the expanded very large array ( evla ) coupled with a more detailed approach regarding the relevant radio and x - ray emission ( and absorption ) processes in type ia supernovae , has enabled the deepest constraints to date on a circumbinary progenitor as discussed in our companion paper on the recent type ia sn2011fe/ ptf11kly ( @xcite . see also @xcite ) . here we report a detailed panchromatic study of sn2011fe bridging optical / uv and gamma - ray observations . drawing from observations with the _ swift _ and chandra satellites as well as the interplanetary network ( ipn ; @xcite ) , we constrain the properties of the bulk ejecta and circumbinary environment through a self - consistent characterization of the dynamical evolution of the shockwave . first we present optical / uv light - curves for the sn , indicating that the object appears consistent with a `` normal '' sn ia . next we discuss deep limits on the x - ray emission in the month following explosion . we furthermore report gamma - ray limits ( 25 - 150 kev ) for the shock breakout pulse . in the appendix we present an analytic generalization for the the inverse compton ( ic ) x - ray luminosity expected from hydrogen poor sne that builds upon previous work by @xcite and @xcite but is broadly applicable for a wide range of shock properties , metallicity , photon temperatures , and circumstellar density profiles ( stellar wind or ism ; see appendix [ sec : iclum ] ) . we apply this analytic model to sn2011fe to constrain the density of the circumbinary environment , and find that our limits are a factor of @xmath13 10 deeper than the results recently reported by @xcite . observations are described in sec . [ sec : obs ] ; limits to the sn progenitor system from x - ray observations are derived and discussed in sec . [ sec : xray ] using the ic formalism from appendix [ sec : iclum ] . we combine our radio @xcite and x - ray limits to constrain the post - shock energy density in magnetic fields in sec . [ sec : epsilonb ] , while the results from the search of a burst of gamma - ray radiation from the sn shock break - out is presented in sec . [ sec : gammaray ] . conclusions are drawn in sec . [ sec : conc ] . -0.0 true cm region around the sn is marked with a white box . _ inset : _ _ chandra _ 0.5 - 8 kev deep observation of the same region obtained at day 4 since the explosion . no source is detected at the sn position ( white circle ) . , title=""fig : "" ] sn 2011fe was discovered by the palomar transient factory ( ptf ) on 2011 august 24.167 ut and soon identified as a very young type ia explosion in the pinwheel galaxy ( m101 ) ( @xcite ) . from early time optical observations @xcite were able to constrain the sn explosion date to august 23 , @xmath14 ( ut ) . the sn site was fortuitously observed both by the _ hubble space telescope _ ( hst ) and by _ chandra _ on several occasions prior to the explosion in the optical and x - ray band , giving the possibility to constrain the progenitor system ( @xcite ; @xcite ) . very early optical and uv photometry has been used by @xcite and @xcite to infer the progenitor and companion radius and nature , while multi - epoch high - resolution spectroscopy taken during the evolution of the sn has been employed as a probe of the circumstellar environment @xcite . limits to the circumstellar density have been derived from deep radio observations in our companion paper @xcite , where we consistently treat the shock parameters and evolution . here we study sn 2011fe from a complementary perspective , bridging optical / uv , x - ray and gamma - ray observations . _ swift _ observations were acquired starting from august 24 , @xmath15 days since the onset of the explosion . _ swift_-xrt data have been analyzed using the latest release of the heasoft package at the time of writing ( v11 ) . standard filtering and screening criteria have been applied . no x - ray source consistent with the sn position is detected in the 0.3 - 10 kev band either in promptly available data ( @xcite ; @xcite ) or in the combined @xmath16 ks exposure covering the time interval @xmath17 days ( see fig . [ fig : x - rays ] ) . in particular , using the first 4.5 ks obtained on august 24th , we find a psf ( point spread function ) and exposure map corrected @xmath18 count - rate limit on the undetected sn @xmath19 . for a simple power - law spectrum with photon index @xmath20 and galactic neutral hydrogen column density @xmath21 @xcite this translates into an unabsorbed 0.3 - 10 kev flux @xmath22 corresponding to a luminosity @xmath23 at a distance of 6.4 mpc @xcite . collecting data between 1 and 65 days after the explosion ( total exposure of @xmath16 ks ) we obtain a @xmath18 upper limit of @xmath24 ( @xmath25 , @xmath26 ) . finally , extracting data around maximum light ( the time interval 8 - 38 days ) , the x - rays are found to contribute less than @xmath27 ( @xmath18 limit , total exposure of 61 ks ) corresponding to @xmath28 , @xmath29 . we observed sn 2011fe with the _ chandra _ x - ray observatory on aug 27.44 ut ( day 4 since the explosion ) under an approved ddt proposal ( pi hughes ) . data have been reduced with the ciao software package ( version 4.3 ) , with calibration database caldb ( version 4.4.2 ) . we applied standard filtering using ciao threads for acis data . no x - ray source is detected at the sn position during the 50 ks exposure @xcite , with a @xmath18 upper limit of @xmath30 in the 0.5 - 8 kev band , from which we derive a flux limit of @xmath31 corresponding to @xmath32 ( assuming a simple power - law model with spectral photon index @xmath33 ) . @xmath18 upper limits from _ swift _ and _ chandra _ observations are shown in fig . [ fig : ic ] . the sn was clearly detected in _ swift_-uvot observations . photometry was extracted from a @xmath34 aperture , closely following the prescriptions by @xcite ( see fig . [ fig : ic ] ) . pre - explosion images of the host galaxy acquired by uvot in 2007 were used to estimate and subtract the host galaxy light contribution . our photometry agrees ( within the uncertainties ) with the results of @xcite . with respect to @xcite we extend the uvot photometry of sn 2011fe to day @xmath35 since the explosion . due to the brightness of sn 2011fe , u , b and v observations strongly suffer from coincidence losses @xcite around maximum light ( see @xcite for details ) : supernova templates from @xcite were used to fit the u and b light - curves and infer the sn luminosity during those time intervals in the u and b bands . for the v - band , it was possible to ( partially ) recover the original light - curve applying standard coincidence losses corrections : however , due to the extreme coincidence losses , our v - band light - curve may still provide a lower limit to the real sn luminosity in the time interval @xmath36 days since explosion . in fig . [ fig : ic ] we present the _ swift_-uvot 6-filter light - curves , and note that the re - constructed v - band is broadly consistent with the nugent template . we adopted a galactic reddening of @xmath37 @xcite . in the case of the `` golden standard '' ia sn 2005cf ( which is among the best studied ia sne ) , the v band is found to contribute @xmath38 to the bolometric luminosity @xcite , with limited variation" +"the first of the four veritas telescopes has been in routine operation since january 2005 at the basecamp of the fred lawrence whipple observatory at mt . hopkins , arizona . the site is 1275 m above sea level . several tev gamma ray sources have been detected @xcite and the construction of the other telescopes is underway . a detailed description of the first veritas telescope , called _ telescope 1 _ in the following , can be found in @xcite , a full description of the veritas project in @xcite . for the following comparison of data with monte carlo simulations , gamma - ray candidates are extracted from observations of the crab nebula ( 3.9 h on source ) and mrk 421 ( 4.2h on source ) in march and april 2005 . the data is taken in on - off mode at elevations above 60@xmath4 and in good weather conditions . images are parameterized using standard second moment analysis @xcite . image pixels are selected by a two level cut on the charge per pixel . picture and boundary thresholds are pedestal plus four respective two times the pedestal variance . the cuts on image parameters to select gamma - rays are @xmath5 , length / size @xmath6 , length @xmath7 , @xmath8 width @xmath9 , and @xmath10 distance @xmath11 . alpha is the orientation angle of the image ellipse relative to the direction of the source position . length and width describe the shape of the image , and distance the location of the image centroid with respect to the source position . only events with at least five image pixels are taken into account . these cuts results in a combined significance of about 21.7@xmath12 and roughly 900 gamma - ray candidates for the observations of the crab nebula and mrk 421 . the crab data set is statistically limited due to the fact that the observation started very late in the season . a complete chain of monte carlo simulations has been developed . it consists of air shower simulations with corsika @xcite and a detailed simulation of the telescope response @xcite . corsika version 6.20 is used with the hadronic interaction models qgsjet for primary energies above 500 gev and fluka below . simulated hydrogen , helium , and oxygen nuclei induced air showers are produced in an energy range from 10 gev ( 150 gev for oxygen ) to 50 tev at different elevations . spectral indices are taken from fits to balloon measurements @xcite . the shower cores are distributed randomly on a circular area with a radius of 1000 m around the telescope . the isotropic distribution of the cosmic ray incident angles is simulated by randomizing the shower directions in a cone of radius 3.5@xmath4 around the pointing direction of the telescope . primary gamma - rays are simulated with a crab - like spectrum in an energy range from 10 gev to 10 tev on a circular area at the ground with radius 450 m . scatter areas are chosen according to the lateral cherenkov light distributions of hadronic and gamma - ray showers . measurements of the atmospheric properties at the current site of telescope 1 and the final one at kitt peak are currently in progress . the calculations described here use the u.s . standard atmosphere , which does not always reflect the properties of the atmosphere in southern arizona . atmospheric extinction values are estimated by modtran 4 @xcite assuming 50 km visibility at 550 nm at ground level . the photo - electron rate per pmt is measured to be 100 - 200 mhz . this corresponds to a night sky background rate of @xmath13 photons @xmath14 m@xmath2 s@xmath3 sr@xmath3 , which is used in the simulations . the telescope simulations consist of two parts , the propagation of cherenkov photons through the optical system and the response of the camera and electronics . the geometrical properties of the optical system is fully implemented in the simulation . misalignment of the mirrors and their surface roughness is taken into account . the camera configuration is that of april 2005 , i.e. a 499 pixel camera with 1 1/8 phototubes without light cones . the field of view of the camera is 3.5@xmath4 . the response of the pmts to single photons has been measured ; the single photo - electron pulse has a rise time of 3.3 ns and a width of 6.5 ns @xcite . in the simulations a signal in a pmt is created by adding up single photo - electron pulses with appropriate amplitude and time jitters applied . electronic noise and all efficiencies , including mirror reflectivities , geometrical , quantum , and collection efficiencies , and losses due to signal transmission have been modeled . the pulses are digitized into 2ns samples with a trace length of 24 samples reflecting the properties of the fadc system . the trigger simulation utilizes a simplified model of the constant fraction discriminator , which is the first stage of the veritas multi - level trigger , and a full realization of the pattern trigger , requiring three adjacent pixels above threshold in a time window of 5 ns . the currently used trigger threshold of 70 mv corresponds to about 6.7 photoelectrons . the output of the telescope simulations , i.e. fadc traces for all pmts , are written to disk in the veritas raw data format . the analysis steps , which include pedestal calculation , image cleaning , image parametrisation , and source reconstruction , are exactly the same for simulated and real data . comparison of image parameter distributions from observation data ( closed symbols ) and monte carlo calculations ( open symbols).,title=""fig:"",scaledwidth=41.0% ] comparison of image parameter distributions from observation data ( closed symbols ) and monte carlo calculations ( open symbols).,title=""fig:"",scaledwidth=41.0% ] comparison of image parameter distributions from observation data ( closed symbols ) and monte carlo calculations ( open symbols).,title=""fig:"",scaledwidth=41.0% ] comparison of image parameter distributions from observation data ( closed symbols ) and monte carlo calculations ( open symbols).,title=""fig:"",scaledwidth=41.0% ] the raw trigger rate of telescope 1 with trigger conditions as described above is between 140 and 150 hz , mainly depending on elevation . dead time losses due to readout are @xmath1510% , the corrected trigger rate is consequentially @xmath15150 - 160 hz . the simulation of the cosmic ray background results in trigger rates of 101 hz from air showers induced by protons , 26 hz from helium nuclei , and @xmath155 hz from nuclei of the cno group for an elevation of 70@xmath4 . the monte carlo calculations reproduce the observed trigger rate with an accuracy of @xmath1515% , which is acceptable , taking into account an estimated uncertainty in the cosmic ray fluxes of @xmath1525% and various systematic uncertainties in the modeling of the telescope . second moment image parameters are the standard tool in analyzing data from iacts . the suppression of the hadronic and muonic background as well as the estimation of the primary energy depends strongly on the correct predictions of the image parameters from monte carlo calculations . fig.[fig1 ] shows a comparison of image parameter distributions from real data and simulations . the alpha , distance , length , and width distributions show very good agreement and proof the validity of the simulations . the described cuts on image parameters are chosen to extract a sample of gamma ray candidates with very little contamination from background events . about 10% of all gamma ray showers are accepted with these cuts , rejecting @xmath1599.9% of all cosmic ray showers . these hard cuts are necessary for data from a single telescope to reject the large background due to local muons . ( telescope arrays are insensitive to such single muons and can be run and analyzed with looser cuts . ) left : effective area of telescope 1 after @xmath0-selection cuts ( filled circles ) and extended supercuts ( filled triangles ) . right : energy spectrum of the crab nebula compared with earlier results from whipple @xcite and hegra @xcite.,title=""fig:"",scaledwidth=41.0% ] left : effective area of telescope 1 after @xmath0-selection cuts ( filled circles ) and extended supercuts ( filled triangles ) . right : energy spectrum of the crab nebula compared with earlier results from whipple @xcite and hegra @xcite.,title=""fig:"",scaledwidth=41.0% ] the effective area of telescope 1 after cuts is shown in fig.[fig2 ] ( left ) . most of the high - energy events fail the hard @xmath0-selection cuts due to the cut on distance . this is different for the application of extended supercuts @xcite , which do not result in a similar good rejection of background events , but take the dependence of the image parameters on image size into account . the maximum effective area after extended supercuts is @xmath16 m@xmath17 . the measured gamma ray rate from the observation of the crab nebula is @xmath18 @xmath0s / min . using the crab spectra reported in @xcite results in a simulated gamma ray rate from the crab nebula of 2.2 @xmath0s / min . the energy threshold of a cherenkov telescope is conventionally defined as the position of the peak of the energy spectrum of the source convoluted with the effective area curve of the detector . according to this definition , the threshold is 150 gev at trigger level , 160 gev after applying extended super cuts , and 370 gev after applying the hard cuts described earlier . the right - hand side of fig.[fig2 ] shows the reconstructed energy spectrum of the crab nebula after applying extended supercuts to the data set . a power law fit to the data points results in a spectral index of @xmath19 and a flux constant of @xmath20 m@xmath2s@xmath3tev@xmath3 ( statistical errors only ) . this agrees well with earlier measurements by other telescopes . the agreement of the monte carlo simulations with observational data shows that we have a good understanding of the first veritas telescope and that the design performance is being met . the final configuration of veritas with four telescopes will have a significant higher sensitivity and an energy threshold of 110 gev @xcite . this research is supported by grants from the u.s . department of energy , the national science foundation , the smithsonian institution , by nserc in canada , by science foundation ireland and by pparc in the uk . gernot maier acknowledges the support as a feodor lynen fellow of the alexander von humboldt foundation . j. holder et al . , _ status and performance of the first veritas telescope _ , 29th icrc , pune ( 2005 ) t. weekes et al . , astroparticle physics , 17 , 221 ( 2002 ) a. m. hillas , proc . 19th int . cosmic ray conf . , 3 , 445 ( 1985 ) d. heck et al . , report fzka 6019 , forschungszentrum karlsruhe ( 1998 ) c.duke & s.lebohec , http://www.physics.utah.edu/gammaray/grisu/ j. hrandel , astroparticle physics , 19 , 193 ( 2003 ) kneizys et al . , _ the modtran 2/3 report and lowtran 7 model _ , technical report , ontar corporation ( 1996 ) g. mohanty et al . , astroparticle physics , 9 , 15 ( 1998 ) a.m. hillas et al.,the astrophysical journal , 503 , 744 ( 1998 ) f. aharonian et al . , the astrophysical journal , 614 , 897 ( 2004 ) s. fegan , proc . 28th int . cosmic ray conf . , 2847 ( 2003 )" +"despite the fact that the galaxy is one unique system , understanding its formation holds important clues to study the broader context of galaxy formation . wide field spectroscopic surveys play a particularly important role in analysis of the milky way : spectroscopy enables us to measure the radial velocity , which in turn allows us to study the details of galactic dynamics . spectroscopy also permits to measure the abundance of chemical elements in a stellar atmosphere which holds important clues on the initial chemical composition and its subsequent metal enrichment . despite this importance , ten years ago wide - field spectroscopic surveys of the milky way was still limited to the geneva copenhagen survey ( cgs , nordstrm et al , 2004 ) , which only covered a sphere of about 100 pc radius around the sun ( the so - called hipparcos sphere ) . the situation has fundamentally changed over the past decade , with several wide - field spectroscopic surveys underway : sdss - segue and rave being completed in terms of data taking , lamost , apogee and hermes well underway , and some massive campaigns such as 4most , weave and desi in the making , each of the latter delivering spectroscopic data for some 10 million stars . the gaia mission will also not only provide exquisit distances and proper motions for up to 1 billion stars , it also will deliver spectra for some 100 million stars . the rave survey can play a particular role in the preparation of the gaia era , as the spectral range , signal to noise and spectral resolution of rave spectra is similar to those expected from the gaia - rvs . rave began observations in 2003 , and since then has released four data releases ( noted dr hereafter ) : dr1 in 2006 ( steinmetz 2006 ) , dr2 in 2008 ( zwitter 2008 ) , dr3 in 2011 ( siebert 2011 ) , and dr4 in 2013 ( kordopatis 2013a ) . rave is a magnitude - limited survey of stars randomly selected in the southern celestial hemisphere . the original design was to only observe stars in the interval @xmath0 but owing to the ir based selection function , some stars that are brighter and fainter can be found . the spectra are obtained from the 6df facility on the 1.2 m australian astronomical observatory s uk - schmidt telescope in siding spring , australia , where three field plates with up to 150 robotically positioned fibres are used in turn . the effective resolution of rave is @xmath1 and the wavelength range coverage is around the infrared ionised calcium triplet ( ir caii , @xmath2 ) , one of the widely used wavelength ranges for galactic archaeology . it is also the wavelength range in which the gaia rvs is operating . rave overall has amassed 574 630 spectra for 483 330 unique stars , 425 561 of these targets are included in dr4 . band for which radial velocity measurements are available . each panel shows a different magnitude bin . grey - scale coding represents the ratio of rave observations to 2mass stars . ( from dr4 ) , scaledwidth=90.0% ] dr4 s completeness with respect to 2mass is shown for various magnitude bins in the aitoff projections shown in figure [ fig : completeness_maps ] . each 6df field set - up only selects targets from one of the following four magnitude bins : @xmath3 ( @xmath4 for the new 2mass input catalogue ) , @xmath5 , @xmath6 and @xmath7 mag . this minimizes the magnitude range within any one 6df field set - up to be within a bin , meaning exposure times can be scaled more appropriately for all the targets in the same field . each field set - up is a random selection of unobserved targets within these bins ( apart from designed repeat observations ) . any spectrum within a 6df field set - up can be adjacent to any other in the same set - up on the ccd but the bins limit the magnitude difference , which also minimizes fibre cross - talk . figure [ fig : completeness_maps ] also shows that while for the brighter magnitudes bins , high rates of completeness have been achieved ( with some individual fields reaching close to 100% compared to 2mass ) , rave has not exhausted the input catalogue for fainter targets , in particular for @xmath8 . radial velocities ( rv ) are obtained using a standard cross - correlation in fourier space on the continuum subtracted spectra ( see dr3 for details ) in a two - step procedure : first an estimate of the rv is determined using a subset of 10 template spectra . this first estimate gives an rv estimate with an accuracy better than 5 km s@xmath9 and is used to shift the spectrum to the zero velocity frame . using the full template database then a new template is constructed using a penalized chi - square technique ( see dr2 ) , which then in turn is used to derive a the more precise rv published in the data base . the histograms of the internal error of the rvs in dr1 , dr2 , dr3 and dr4 is shown in fig . [ f : internal ] . it can be seen that 68% of the targets have an internal rv error better than 1.4 km s@xmath9 in dr4 ( see left frame of figure 2 ) . error estimates derived from repeat observations and from comparison with external reference stars give values consistent with the numbers quoted above . . for dr4 , the number of stars per bin is divided by 15 to compensate for the increase in sample size . * bottom left : * the cumulative distributions , where the dotted lines mark 50 , 68 and 95% of the samples . * middle : * comparison of the reference values found in the literature and the derived effective temperatures . dotted diagonal lines represent offsets from unity of @xmath10 k. the mean offsets ( @xmath11 ) and the dispersions ( @xmath12 ) are indicated in the upper left corner of each plot . * right : * same for @xmath13 , dotted diagonal lines represent offsets from unity of @xmath14 dex.,title=""fig:"",scaledwidth=30.0% ] . for dr4 , the number of stars per bin is divided by 15 to compensate for the increase in sample size . * bottom left : * the cumulative distributions , where the dotted lines mark 50 , 68 and 95% of the samples . * middle : * comparison of the reference values found in the literature and the derived effective temperatures . dotted diagonal lines represent offsets from unity of @xmath10 k. the mean offsets ( @xmath11 ) and the dispersions ( @xmath12 ) are indicated in the upper left corner of each plot . * right : * same for @xmath13 , dotted diagonal lines represent offsets from unity of @xmath14 dex.,title=""fig:"",scaledwidth=29.0% ] . for dr4 , the number of stars per bin is divided by 15 to compensate for the increase in sample size . * bottom left : * the cumulative distributions , where the dotted lines mark 50 , 68 and 95% of the samples . * middle : * comparison of the reference values found in the literature and the derived effective temperatures . dotted diagonal lines represent offsets from unity of @xmath10 k. the mean offsets ( @xmath11 ) and the dispersions ( @xmath12 ) are indicated in the upper left corner of each plot . * right : * same for @xmath13 , dotted diagonal lines represent offsets from unity of @xmath14 dex.,title=""fig:"",scaledwidth=29.0% ] the wavelength region @xmath2 is very attractive for galactic archaeology purposes , as it features relatively few telluric absorptions , but exhibits many iron and @xmath15-element lines , in particular the prominent ca triplet , which allows relatively easily radial velocity measurements and metallicity estimations for any type of spectrum . however , spectra with a resolution @xmath16 suffer from spectral degeneracies that , if not appreciated , can introduce serious biases in spectroscopic surveys that use automated parameterization pipelines . these degeneracies are mostly important for cool main - sequence stars and stars along the giant branch ( see kordopatis 2011 for a discussion ) . in matching observed spectra to templates in a library , decision - tree methods have been shown to perform better compared to other algorithms , like the projection methods ( e.g. : principal component analysis ) or the ones trying to solve an optimization problem ( e.g. : minimum @xmath17 ) , in particular when the snr is low . the rave dr4 pipeline therefore employs a hybrid of a decision - tree algorithm called degas ( bijaoui 2012 ) and a projection method called matisse ( recio - blanco 2006 ) which improves the interpolation between the grid points . a comparison with a set of reference stars ( see middle and right frame of figure 2 ) shows a satisfactory dispersion of about 400k for the derived t@xmath18 ( considerable less for a high s / n subsample ) , while the @xmath13 determination is still suffering from the aforementioned degeneracies in the ca triplet region ( see table 1 and 2 in dr4 ) . abundances for individual chemical elements are determined for the elements mg , al , si , ti , ni and fe based on a curve of growth analysis using the atmospheric parameters of the previous section as input values for t@xmath18 and @xmath13 ( boeche 2011 ) . the chemical pipeline relies on an equivalent widths ( ews ) library which contains the expected ews of the lines visible in the rave wavelength range ( 604 atomic and molecule lines ) . these ews are computed for a grid of stellar parameters values covering the range [ 4000,7000 ] k in t@xmath18 , [ 0.0,5.0 ] dex in @xmath13 and @xmath19 $ ] dex in @xmath20}$ ] and five levels of abundances in the range @xmath21 $ ] dex . the chemical pipeline constructs on - the - fly spectrum models by adopting the effective temperatures and surface gravities obtained by the dr4 atmospheric parameters pipeline . it then searches for the best fitting model by minimizing the @xmath17 between the models and the observational data . the estimated errors in abundance , based on a comparison with reference stars , depend on the element and range from 0.17 dex for mg , al and ti to 0.3 dex for ti and ni . the error for fe is estimated as 0.23 dex . distances are estimated for spectra with snr@xmath22 pixel@xmath9 by projecting the atmospheric parameters onto a the padova set of theoretical isochrones and obtaining the most likely value of the absolute magnitude of the stars . dr4 employs an algorithm based on the bayesian distance - finding method presented in binney ( 2014 ) , and takes into account the interstellar extinction , as well as kinematic correction factors obtained by the method of schnrich ( 2012 ) . testing using hipparcos stars indicates that the inverse of the expectation value of the parallax is the most reliable distance estimator . compared to a subset of hipparcos stars , the method results in an over - estimation of less than 10% for the dwarfs and less than 20% for the giants . the method has also been tested on the open cluster spectra , delivering very satisfactory distances , provided a cluster - specific age prior is used . @xmath23{median_vphi } & \includegraphics[width=0.47\linewidth , angle=0]{median_meta } \end{array}$ ] based on the currently available proper motions ( ucac4 ) , radial velocities derived from rave spectra and distances derived from matching rave stellar" +"astro - f ( murakami 1998 ) is the second japanese space mission for infrared astronomy , following the first successful mission irts ( infrared telescope in space , murakami et al . 1996 ) . the astro - f is designed as the second - generation survey mission . the previous all sky survey by the infrared astronomy satellite ( iras ) ( neugebauer et al . 1984 ) was a great success . many new phenomena , such as infrared galaxies and vega - like stars , were found in the survey , and the iras survey catalogues have been essential tools in many fields of astronomy . however , the spatial resolution ( a few arcminutes ) and the sensitivity ( about 1 jy ) of the iras survey are not good enough , compared to those of the surveys at other wavelengths . hence we plan the next generation infrared sky survey with astro - f by taking the advantage of the recent development of detector technology . .specifications of astro - f [ cols= "" < , < "" , ] astro - f has a 67 cm telescope cooled to 5.8 k , and covers wide wavelength range from k - band to 200 @xmath0 m with two focal plane instruments : far - infrared surveyor ( fis ) and infrared camera ( irc ) . fis will perform the all - sky survey with 4 photometric bands at the wavelength range of 50 200 @xmath0 m using two - dimensional ge : ga detector arrays . the sensitivity and the spatial resolution of the astro - f / fis all sky survey are much better than those of the iras survey . irc is for the near- and mid - infrared ranges , and large - format arrays are employed for deep sky surveys in selected sky regions . the scientific targets of the astro - f range from distant galaxies to near - by objects in the solar system . the results of the new infrared survey by astro - f will serve as valuable input catalogues for large - aperture space telescopes such as first ( pilbratt 2000 ) and also for 810 m class ground - based telescopes . figure 1 shows a picture of the thermal test model of the astro - f satellite , figure 2 shows a diagram of astro - f in the observation configuration , and table 1 shows the specifications of astro - f to reduce the total weight of the cryostat , we employed a hybrid cryogenics design ; the telescope and focal plane instruments are to be cooled by liquid helium with the help of mechanical cryocoolers . figure 3 shows a cross - sectional view of the astro - f cryostat with the 67 cm telescope installed . the outer shell of the cryostat is thermally isolated from the spacecraft and is cooled below 200 k by radiation . the cryostat has two vapor - cooled shields ( vcs ) . the inner vcs is cooled not only by evaporated helium gas but also by two sets of 2-stage stirling - cycle coolers . this additional cooling power provided by the coolers increases the life time of the liquid helium by a factor of two . although the amount of liquid helium is small ( 170 liter ) , the expected hold time of liquid helium in orbit is as long as 550 days due to the cryocoolers . one more advantage of using mechanical coolers is that , as long as the mechanical coolers work properly , we can continue observations at least in the near - infrared even after liquid helium runs out . the cryocoolers are now under extensive tests , and the expected life time of the coolers is longer than 2 years . the telescope and most of the focal - plane instruments are cooled by the evaporated helium gas , and the expected temperature is 5.8 k. far - infrared detector arrays require lower temperatures , and are cooled to 1.8 k by the direct thermal connection to the helium tank . astro - f telescope is a ritchey - chretien system with a effective aperture size of 67 cm . figure 4 shows the whole telescope assembly , which is to be cooled down to 5.8 k. the goal of the image quality is diffraction - limited performance at the wavelength of 5 @xmath0 m , including the aberration of the camera optics at the focal plane . in order to reduce the total weight of the telescope system , we have employed silicon carbide ( sic ) for mirror material because of its large young s modulus and high thermal conductivity . both the primary and secondary mirrors have a sandwich structure which consists of porous sic ( 3 mm thick ) as a core and cvd coat of sic ( 0.5 mm thick ) on surfaces . porous sic can be easily machined for light - weight structures , and cvd sic coat is dense and strong enough for smooth polishing . this structure reduces the weight of the primary mirror to 11 kg . the mirrors are coated with au for good reflectivity with zns overcoat for protection . we plan to measure the surface figure of the primary mirror and the whole telescope assembly both at ambient temperature and at liquid helium temperature . please see onaka , sugiyama & miura ( 1998 ) and kaneda , onaka & yamashiro ( 2000 ) for details of the astro - f telescope and its developing program . astro - f has two focal instruments : far - infrared surveyor ( fis ) for far - infrared and infrared camera ( irc ) for near- and mid - infrared . these two instruments share the focal plane as shown in the left figure of figure 5 . the vertical arrow shows the scan direction . irc consists of three channels , but the nir and the mir - s channels share the same entrance aperture , and there are only two apertures in total for irc . fis has two detector modules , and they also share the same entrance aperture . two sets of fsts ( focal plane star sensor ) are used for pointing reconstruction during the survey mode . the goal of the pointing reconstruction is to determine the telescope direction with the uncertainty less that @xmath5 , which is required for the identification of observed infrared sources at other wavelengths . fis ( kawada 2000 , takahashi et al . 2000 ) is designed primarily to perform the all - sky survey in 4 photometric bands at wavelength of 50 - 200 @xmath0 m . fis also has spectroscopic capability as a fourier - transform spectrometer . figure 6 shows the optical layout of fis . the incident beam from the telescope comes from the entrance aperture below the bending mirror . the incident beam is paralleled by the collimator mirror . this parallel beam goes to the filter wheel . this filter wheel determines the mode of operation , i.e. scanner ( = photometric imager ) or spectrometer . in the scanner mode , the incident filter on the filter wheel is just a hole . the parallel beam goes through the hole and reflected by the flat mirror . then the beam is divided into two in the spectral domain by a dichroic beam splitter on the same filter wheel ( but at the opposite side ) . the radiation longer than 110 @xmath0 m goes through the filter and is concentrated onto the long wavelength detector module . the shorter wavelength radiation is reflected by the dichroic beam splitter and is focused on the short wavelength detectors module . each detector module consists of two detector arrays . another set of filters just in front of the detector arrays determines the effective photometric bands . table 2 lists the four photometric bands . the optical efficiency of each band is about 40 @xmath6 . [ hbt ] cccc ' '' '' band & wavelength & pixel fov & array + ' '' '' & ( @xmath0 m ) & ( arcsec ) & + ' '' '' n60 & @xmath7 & 30 & @xmath8 + ' '' '' wide - s & @xmath9 & 30 & @xmath10 + ' '' '' wide - l & @xmath11 & 50 & @xmath12 + ' '' '' n170 & @xmath13 & 50 & @xmath14 + for the spectrometer mode of fis , we use a polarized michelson interferometer ( martin - puplett type ) . we need three polarizing filters : input , beamsplitter , and output . the input and output polarizing filters are on the filter wheel and are to be selected for the spectrometer mode . in this mode , the parallel beam is reflected by the input polarizing filter . then the polarized beam goes into the interferometer , and are divided by the polarizing beam splitter whose polarizing direction is rotated 45@xmath15 against the polarity of the incident beam . two beams divided by the beam splitter are reflected by two sets of roof - top mirrors . we move one set of the mirrors to change the optical path difference between the two beams . the two beams are combined again on the beam splitter , and the combined beam goes onto the output polarizing filter . by the output polarizing filter , the beams are divided in the polarity domain , and concentrated by the camera mirrors on each detector module . the maximum optical path difference is about 50 mm , which corresponds to a spectral resolution of 0.2 @xmath16 . the big advantage of the spectrometer mode of fis is that it is an imaging spectrometer suitable for spectroscopic mapping observations of extended sources . each detector module consists of two bands , and fis have four bands in total as is shown in table 2 . the detector arrays for wide - s and n60 are ge : ga detector array which is connected to the cryogenic readout electronics ( hirao et al . 2001 ) directly by indium ( hiromoto et al . 1998 ) . for the detector arrays of wide - l and n170 , we use compact stressed ge : ga detector arrays ( doi et al . 2000 ) . the pixel size of each detector array is comparable with the size of the diffraction pattern of the main mirror at each band . hence if we scan the sky with the detector array whose minor axis is parallel to the scan direction , the sampling frequency in the cross - scan direction is below the nyquist sampling frequency . in other words , the spatial resolution in the cross - scan direction is worse than that of the diffraction limited size . hence , we tilted the detector array by 26.5@xmath15 as shown in the right figure of figure 5 , to increase the sampling frequency and thereby to improve the spatial resolution in the cross - scan direction . this tilt guarantees the nyquist sampling for each scanning observations , which is critical requirement to achieve the diffraction limited spatial resolution . [ htb ] cccc ' '' '' channel & wavelength & pixel fov & array + ' '' '' & ( @xmath0 m ) & ( arcsec ) & + ' '' '' nir & @xmath17 & 1.46 & @xmath18 insb + ' '' '' mir - s & @xmath19 & 2.34 & @xmath20 si : as + ' '' '' mir - l & @xmath21 & 2.34 & @xmath20 si : as + irc ( watarai et al . 2000 , onaka et al . 2000 ) is another focal - plane instrument onboard astro - f ." +"the recent experimental developments in ultracold fermi gases and in particular the experimental realization of the bec - bcs crossover through feshbach resonance @xcite have arised in a field where theoretical investigations started a long time ago . indeed fairly soon after the publication of the bardeen - cooper - shrieffer ( bcs ) theory @xcite , the extension to the neutral fermi liquid @xmath4he was considered @xcite . although the case of liquid @xmath4he is more complex than the one of ultracold gases , it is nevertheless analogous to the situation found on the bcs side of the crossover , in the strong interaction regime . similarly the possibility of bose - einstein condensation ( bec ) of composite bosons was considered quite early for excitons in semiconductors @xcite , where the composite nature of these bosons is expected to be an essential physical feature . this is the situation met in the bec range of the bec - bcs crossover . deep theoretical investigation of this last situation was made not long afterwards by keldysh and kozlov @xcite , following a seminal work by popov @xcite which considered a physical model with short range potentials , much closer to the ultracold gas case . in both cases , due to the formal similarity between the bogoliubov and the bcs frameworks , the theoretical treatment relied on the fact that in the dilute limit the formalism leads directly to the schrdinger equation for the molecular state corresponding to the composite boson . this provided an anticipation of the study of the whole bec - bcs crossover . independently eagles @xcite , in the course of a study of superconductivity in doped semiconductors ( where the electron gas has a low concentration compared to standard metals ) , was led to investigate the extrapolation of the simple bcs formalism toward the dilute regime where pair formation would take place , due to the attractive interaction , and bose condensation of these pairs should occur at lower temperatures . in the context of cold gases , the physics of the crossover was considered by leggett @xcite , who stressed the physical interest of considering cooper pairs as giant molecules , emphasized the change of physical regime when the chemical potential goes through zero , and introduced the scattering length in the bcs formulation . the matter was taken up by nozires and schmitt - rink @xcite who studied the smooth evolution of the critical temperature in the crossover within the simplest @xmath5matrix approximation , showing in particular how the critical temperature of the ideal bose gas is recovered in the strong coupling limit . s de melo , randeria and engelbrecht @xcite addressed the crossover with the functional integral formalism . as it has often been stressed , the physical situation found in this bec - bcs crossover is extremely interesting since ( at least for wide feshbach resonances @xcite ) the scattering length @xmath6 of the different fermions with mass @xmath7 is enough to fully describe their interaction , while one has still to deal with the full complexity of a strongly interacting system . as a result the theoretical problem has not been solved exactly and one has to rely on various approximate schemes @xcite , the simplest one being the straight bcs formalism ( often called bcs - mf ) which is known to give a correct description at zero temperature in both the extreme bec and bcs limits @xmath8 . the imperfections of the approximate treatments are clearer in the bec regime . indeed if one wants to describe properly the departure from the ideal bose gas of dimers , one has to provide a correct description of the dimer - dimer interaction , in order to find the expected physics of a weakly interacting bose gas . as stressed by keldysh and kozlov @xcite the composite nature of the dimers has already to be properly taken into account at this stage in order to obtain correct results . a first step in this direction for the specific case of short range interactions , relevant for cold gases , was made by haussmann @xcite who obtained , both in the normal and in the superfluid state ( where this can be found naturally out of the bcs ansatz ) , that the dimer - dimer scattering length @xmath1 is related to the fermion scattering length @xmath6 by @xmath9 . this result was also obtained in ref.@xcite in the superfluid state by other methods . the level of approximation corresponding to this result turns out to be the born approximation for the dimer - dimer scattering . at the same level of approximation pieri and strinati @xcite derived quite recently the gross - pitaevskii equation from the bogoliubov - de gennes equations . however this level of approximation was markedly improved by pieri and strinati @xcite who performed the calculation at the level of a @xmath5matrix approximation and found @xmath10 . nevertheless their calculation does not include all the processes resulting from the existence of the fermions making up these composite bosons . the exact numerical result was obtained recently by petrov , salomon and shlyapnikov @xcite who basically solved the relevant schrdinger equation for the four - body problem and found for this dimer - dimer scattering length @xmath11 . thereafter it was shown @xcite how this same problem could be exactly formulated and solved within the methods of quantum field theory , with naturally exactly the same result . this last work is quite relevant to the present paper , and represents the basis out of which we will work . this is naturally linked to the fact that field theoretic methods are a convenient , and probably necessary , framework for an exact formulation and solution of this superfluid strong coupling problem raised by the bec - bcs crossover . in this paper , we provide an exact approach to the bec - bcs crossover problem from the bec side by presenting an exact fermionic theory of a bec superfluid of composite bosons in the low density range . the two interacting fermion species we deal with are actually the two lowest energy hyperfine states used experimentally @xcite in ultracold gases of @xmath12li or @xmath13k , and as it is usually done we will for convenience refer to them as `` spin up '' and `` spin down '' states . specifically working in the low density range means that we proceed basically to an expansion in powers of the gas density . otherwise our framework is completely general . in the present paper we deal with the lower orders in this expansion , but nothing in principle prevents our approach to be extended to higher orders , although admittedly this will require much more work . similarly we will restrict ourselves to the @xmath14 situation , which brings strong simplifications as we will see because in this case there are no fermions at all in the normal state . however it is quite possible to extend our approach to non zero temperature . finally we deal here with thermodynamics , but our framework allows us naturally to calculate dynamical quantities . as we mentionned our approach is in principle a low density expansion . however the density @xmath0 is not a convenient basic parameter since it rather appears in the formalism as the result of a calculation . on the other hand it is known ( and we will see it explicitely below ) that in the simple bcs approximation for the bec limit , which as mentionned above corresponds to a born approximation at the level of the mean field term , the density @xmath0 is proportional to @xmath15 , where @xmath16 is the gap parameter of the bcs theory . hence a convenient way to proceed effectively to a low density expansion is rather to expand in powers of @xmath16 . however this quantity is specific of the bcs approximation , which has no general validity . but it is directly related to the anomalous self - energy @xmath17 ( where @xmath18 is an energy - momentum four - vector ) which is a completely general microscopic quantity characteristic of a superfluid system . hence our method will specifically be an expansion of the general equations in powers of the anomalous self - energy @xmath17 . here we will calculate the equation of state , or more precisely the dependence of the chemical potential @xmath19 on the density @xmath0 ( a short account of our calculation has already been published @xcite ) . actually this is rather the reciprocal of this function which comes naturally out of the calculation , since @xmath19 enters the green s functions while @xmath0 is obtained at the end of the calculation , after elimination of @xmath17 which comes in the intermediate steps . the lowest order term in the expression of @xmath19 , beyond the trivial term of half the molecular binding energy @xmath20 , is the mean - field term . one has to note that , even at this stage , the composite nature of the bosons we deal with is entering as noted by keldysh and kozlov @xcite . however in our case it is lumped into the full dimer - dimer scattering length @xmath1 . this result is physically natural since , beyond the zeroth order term @xmath20 in the chemical potential @xcite corresponding to an isolated molecule , we expect in a density expansion to find the physics of two coexisting molecules , which should be fully describable by @xmath1 for its static properties , corresponding to the zero energy scattering properties . nevertheless , as far as we know , this quite reasonable result has always been in the literature more or less taken for granted or cursorily obtained , but not fully explicitely derived from a microscopic theory for composite bosons . hence our first step will be to obtain this fully explicit derivation . however we are naturally essentially interested by the next order term , at which we will also limit our present calculation . from the theory of weakly interacting elementary bosons this term is proportional to @xmath2 , as first obtained by lee and yang @xcite . we refer to this term as the lhy term . this term has then been rederived by beliaev @xcite making use of field theoretic methods . naturally it is reasonable to expect that a similar term arises for composite bosons . what is however less clear is that the coefficient is just the same as for elementary bosons , i.e. that it can be simply expressed in the same way in terms of @xmath1 . indeed it is clear that , at some stage in the expansion , the composite nature of the bosons will enter by other quantities than those describing the physics of elementary bosons . this is quite obvious physically since , by going to higher densities ( which corresponds to take into account higher order terms in the expansion ) , we will go toward unitarity and find physical properties linked to the existence of fermi seas . obviously this can not be obtained from the physics of elementary bosons . hence it is conceivable that additional processes contribute to the @xmath2 term for composite bosons . nevertheless we will find at the end of our paper that the @xmath2 term is indeed identical to the lhy term provided the dimer - dimer scattering length is used . the fact that this is not obvious is immediately realized from the number and the complexity of our steps , which do not map systematically on the elementary boson derivation . on the other hand this result makes sense physically when it is realized that the lhy term is directly linked to the existence of the gapless collective mode . a standard perturbation expansion should produce" +"one possible classification of evolutionary games @xcite is to those that are governed by pairwise interactions and to those that are governed by group interactions . the prisoner s dilemma and the snowdrift game @xcite , as well as the stag - hunt game @xcite , are classical examples of evolutionary games that are governed by pairwise interactions . the public goods game , on the other hand , is a typical example of an evolutionary game that is governed by group interactions . similarly as by the transition from two - body to many - body interactions in many branches of physics , in evolutionary games too the transition from pairwise to group interactions leads to a substantial increase in complexity . for example , reciprocity @xcite , _ i.e. _ the act of returning favor for a favor , is straightforward in games governed by pairwise interactions . as there are only two players involved at each instance of the game , it is relatively easy to decide what to do based on what the opponent has done in the past @xcite . in games governed by group interactions , however , it is much more difficult to keep track of actions of all the other players , and hence it is difficult to reciprocate . the same argument is valid for punishment @xcite , where unlike returning positive actions , the goal is to identify those that inflict harm or act antisocial and sanction them accordingly . regardless of the distinction between pairwise and group interactions , the central theme of evolutionary game theory is the successful evolution of cooperation . according to darwin , natural selection favors the fittest and the most successful individuals , which implies an innate selfishness that greatly challenges the concept of cooperation @xcite . to cooperate namely means to sacrifice some fraction of personal benefits for the sake of social welfare . the opposite strategy is defection , implying that players who defect will always try to maximize their fitness regardless of the consequences this might have for the society . since the focus here is on games governed by group interactions , we may use the definition of the public goods game to illustrate the key difference between cooperation and defection as follows . in a group consisting of @xmath0 players , those that cooperate will contribute @xmath1 to the public good , while those that defect will contribute nothing . note that on a larger scale , the contribution of cooperators can be considered as a contribution to society , which will typically contain a large number of such groups . all the contributions will then be multiplied by a factor @xmath2 , which is typically larger than @xmath1 to take into account synergetic effects of collaborative efforts , and subsequently the resulting amount will be shared amongst all the group members irrespective of their initial contribution . from this definition it follows that defectors acquire an evolutionary advantage over cooperators by withholding the initial contribution to the public good , and from the viewpoint of each individual defection is thus clearly the rational strategy to choose . from the viewpoint of the group and the society as a whole , however , cooperation is the optimal strategy as then the multiplication factor @xmath2 will have the biggest impact and accordingly the welfare of the society will be maximized . the fact that defection maximizes individual payoffs while cooperation maximizes social prosperity , and thus that what is best for an individual is opposite to what is the best for society , is traditionally refereed to as a social dilemma . failure to maintain cooperation in such a case leads to the so - called `` tragedy of the commons '' @xcite , where nobody contributes to the public good ( everybody defects ) and the society is therefore destined to go bankrupt . rather surprisingly , and in fact contradictive to the darwinian concept of acting so as to maximize personal fitness , economic experiments on public goods games indicate that humans cooperate much more in such situations than expected @xcite , and in so doing these experiments call for the identification of mechanisms that can explain the successful evolution of cooperation . introducing additional strategies besides cooperation and defection has proven to be very effective . for example , if players are given the chance to abstain from the public goods game by not contributing but also by not taking part in the distribution of accumulated payoffs , cooperation may be promoted by means of the spontaneous emergence of cyclic dominance between the three competing strategies @xcite . the introduction of peer - punishers , _ i.e. _ those that are willing to bare additional costs in order to sanction defectors , has also proven to be effective for the promotion of cooperation @xcite , as was the introduction of pool - punishers that contribute to the establishment of sanctioning institutions @xcite . rewarding cooperative players instead of punishing defectors has also been considered as an additional strategy that may promote cooperation @xcite , and the emerging `` stick versus carrot '' dilemma ( whether to sanction defectors or reward cooperators ) has recently received ample attention @xcite . interestingly , random explorations of these additional strategies , termed conveniently as exploration dynamics "" @xcite , may also substantially elevate the level of cooperation in a society . driven by the application of methods from statistical physics ( see @xcite for a comprehensive review ) , as well as by the fascinating complexity arising from the evolutionary competition between the strategies , physicists have also made important contributions to the understanding of the successful evolution of cooperation . foremost , research published in recent years has made it clear that heterogeneities amongst players play a crucial role by the evolution of cooperation . scale - free networks , for example , have been recognized as very potent promoters of cooperative behavior @xcite . in fact , evolutionary games on complex and coevolving networks @xcite in general tend to promote cooperation past the boundaries imposed by regular lattices @xcite . similarly , heterogeneities in strategy adoption probabilities can also enhance cooperation @xcite , especially if the strategy adoption is favored from the more influential players @xcite . heterogeneities can also be introduced directly to payoffs in terms of noise @xcite or quenched diversity @xcite , whereby cooperators are promoted as well provided the uncertainties are adequately adjusted and distributed . while the majority of previous works aimed at disentangling the impact of heterogeneity on the evolution of cooperation focused on games governed by pairwise interactions , recent results indicate @xcite that cooperation within the public goods game is also susceptible to the same mechanism of promotion . however , if payoffs are evaluated from public goods games in multiple groups , the indirect linkage of players due to their membership in the same groups may result in qualitatively different behavior @xcite as reported previously for games governed by pairwise interactions @xcite . this motivates us to examine to what extent strongly heterogeneous states do in fact promote the evolution of cooperation in games governed by group interactions . for this purpose , we study the evolution of cooperation in the public goods game on three types of regular graphs , namely on the square lattice , the triangular lattice , and the random regular graph ( rrg ) . these are characteristic for interaction graphs with ( square and triangular lattice ) and without ( rrg ) spatial structure , as well as for interaction graphs with zero ( square lattice and rrg ) and a high ( triangular lattice ) clustering coefficient , thus covering a broad plethora of properties that are known to vitally affect the evolution of cooperation @xcite . heterogeneity is then introduced by means of either a uniform or an exponential distribution of payoffs amongst the players , thereby violating the traditional assumption of equally distributed public goods amongst all group members . according to the statistical properties of the two considered distributions , exponentially distributed public goods give rise to strongly heterogeneous states , while uniformly distributed public goods correspond to moderate heterogeneities affecting the evolution of cooperation . unexpectedly , we find that moderate heterogeneities promote cooperation better than strongly heterogeneous states , which is not in agreement with results obtained previously for evolutionary games governed by pairwise interactions @xcite . the remainder of this paper is organized as follows . in the next section we describe the employed evolutionary public goods game and the interaction graphs , while in section 3 we present the results . lastly , we summarize our findings and compare them with those reported earlier for evolutionary games governed by pairwise interactions . assuming structured interactions defined by either the square lattice , the triangular lattice , or the random regular graph , as schematically depicted in figure [ graphs ] , @xmath3 players are arranged into overlapping groups of size @xmath0 such that every player is surrounded by its @xmath4 neighbors . accordingly , each individual belongs to @xmath5 different groups . initially each player on site @xmath6 is designated either as a cooperator ( @xmath7 ) or defector ( @xmath8 ) with equal probability . cooperators contribute a fixed amount ( here considered being equal to @xmath1 without loss of generality ) to the public good while defectors contribute nothing . the sum of all contributions in each group is multiplied by the factor @xmath2 and the resulting public goods are distributed amongst all the group members . if @xmath7 the payoff of player @xmath6 from every group @xmath9 is @xmath10 and if @xmath8 the payoff is @xmath11 , where @xmath12 is the number of cooperators in group @xmath9 while @xmath13 is the scaling factor by means of which the heterogeneity in the distribution of public goods is introduced . the scaling factors are drawn randomly from either the uniform distribution @xmath14 or the exponential distribution @xmath15 . here @xmath16 are uniformly distributed random numbers from the unit interval , and @xmath17 in all cases , so that the average @xmath18 over all the players is zero . moreover , @xmath19 scales the magnitude of heterogeneity and will , together with @xmath2 , be considered as the key parameter affecting the evolution of cooperation . naturally , @xmath20 returns the traditional version of the game , while large @xmath19 lead to segregation of players , which may be additionally amplified by considering exponential rather than uniformly distributed @xmath13 . it should be noted that heterogeneity is here not quantified explicitly ( _ e.g. _ by means of standard deviation of @xmath13 ) , but rather it refers to the diversity of players in the sense of to what extend they can differ from one another . since the exponential distribution segregates the players much more than the uniform distribution , the former is referred to as being substantially more heterogeneous ( see also @xcite for explicit shapes of the two distributions and alternative ways of interpretation ) . related to this setup , it is important to note that quenched heterogeneities introduced via @xmath13 may evoke the existence of the griffiths phase @xcite , which has recently attracted considerable attention @xcite , also in studies concerning the evolution of cooperation @xcite . the essence of the problem of quenched heterogeneities for the extinction processes has been well described in @xcite , where it was shown that such systems are frequently characterized by patches of different sizes , providing better conditions for one of the strategies ( or species ) to survive . due to the localization , the subordinate strategy can die out very slowly on the separated ( or weakly interacting ) patches , with an average lifetime increasing with the patch size . noest @xcite demonstrated that for suitable conditions ( determined" +"a particle moving freely inside a square box and specularly reflecting off the boundary in accordance with the snell s law defines a square billiard . we consider the situation where the box is rotating about a vertical axis passing through one of its corners while the particle moves freely . the billiard problem thus posed breaks time reversal invariance . this aspect makes the system even more interesting for a quantum mechanical study . the motivation to study this problem in detail is in its intimate , direct relation to the physics of rotating nuclei . rotating nuclei have been studied in a great detail , beginning from the cranking model by inglis @xcite , and the later work by bohr and mottelson @xcite . the latter work was brought to conclusion by jain et al . @xcite where they showed that there were three regimes classified by the solutions of the duffing equation in the angular momentum space . these results have been subsequently used in understanding several aspects of superdeformed nuclei @xcite . classical and quantum billiards with a rotating boundary was first studied by fairlie and siegwart @xcite and also by frisk and arvieu @xcite . they showed that the phase space portraits exhibited regular to chaotic motion transition with change in perturbation parameter . more studies along these lines were carried out later @xcite . the billiards considered are related , with respect to the time reversal invariance , to chaotic billiards in the presence of magnetic field . for these systems , the spectral fluctuations belong to the gaussian unitary ensemble of random matrices @xcite . in this paper , we study the classical and quantum signatures of chaos in a square billiard rotating about one of its corners . we study poincar surface of section of classical phase space and show that this system goes from regular to chaotic with change in rotational frequency . quantum signatures of chaos are studied in the nearest - neighbour level spacing distribution and in the nature of wavefunctions . wavefunction statistics shows transition from regular to chaotic motion and also reveals the time reversal symmetry breaking . we consider a square billiard rotating about the axis perpendicular to the billiard plane and passing through one of its corners . if we take this corner to be the origin of the coordinate system , then in the rotating frame of the billiard , the hamiltonian will be @xmath3 @xmath4 is the hard wall potential of the billiard ( we consider square billiard with walls at @xmath5 ) and @xmath1 is the rotational frequency of billiard . the classical dynamics of the system is governed by the parameter @xmath6 where @xmath7 is the energy of the particle . for larger values of @xmath2 , the system exhibits more regular behavior . as the value of @xmath2 decreases , the chaotic region in phase space increases as can be seen in fig . [ fig : poincare ] . here canonically conjugate variables @xmath8 and @xmath9 are plotted for different values of @xmath2 which are related to the position of the particle and its momentum when it strikes the wall . @xmath8 and @xmath9 are the birkhoff coordinates on the walls . @xmath10 is the fractional distance along the wall the particle strikes increasing in counter - clockwise direction . @xmath11 is the normalized canonical conjugate momentum of @xmath10 . @xmath12 @xmath13 , @xmath14 and @xmath15 . the kam tori disappear as @xmath2 decreases.,title=""fig:"",width=188 ] , @xmath14 and @xmath15 . the kam tori disappear as @xmath2 decreases.,title=""fig:"",width=188 ] , @xmath14 and @xmath15 . the kam tori disappear as @xmath2 decreases.,title=""fig:"",width=188 ] it is seen from phase space plots shown in fig . [ fig : poincare ] that with small rotational perturbation , small kam islands form near the points satisfying nonlinear resonance conditions . as the perturbation increases with decrease in parameter @xmath2 , number of kam islands decreases and the chaotic area increases . therefore with change in the value of parameter @xmath2 , the system goes from regular to chaotic with mixed phase space for intermediate values of @xmath2 . the signature of the onset of chaos can be seen in the nearest neighbor spacing ( nns ) distribution calculated for the first 1000 energy levels of the system . these energy levels are calculated by writing the hamiltonian in eqn . [ eq : ham ] in particle in box wavefunction basis and numerically diagonalizing the resulting hamiltonian matrix . as we can see from fig . [ fig : level_spacing ] that as the value of @xmath1 increases the level spacing distribution changes from poisson to wigner like distribution . this is expected from our classical analysis where decrease in @xmath2 leads to more chaotic motion . since the classical dynamics of the system depends on the parameter @xmath6 , therefore we expect that the level spacing distribution will show different dynamics for different energy levels . therefore , in fig . [ fig : high_low_comparison ] we show the level spacing distribution computed from 1000 lowest energy states and for 8000th to 9000th energy levels for @xmath16 . we can clearly see that for the lower energy levels , the spacing distribution shows departure from poisson distribution whereas for the higher energy levels , the level spacing distribution is still poisson . this is because the parameter @xmath2 for the @xmath17 level is 32 and for the lowest level in the higher energies shown , @xmath18 . since the energy level sequence of a square box goes to infinity , the level spacing distribution for a very large number of levels will always be poisson . = 10 , 30 and 50 . the parameter @xmath2 for the highest energy level ( @xmath19 state ) is 129 , 13.8 and 4.7 for @xmath20 10 , 30 and 50 respectively . the average value of @xmath2 for the 1000 levels is 65.2 , 6.6 and 2 . the distribution changes from poisson to wigner as @xmath2 decreases with increase in @xmath1.,title=""fig:"",width=188 ] = 10 , 30 and 50 . the parameter @xmath2 for the highest energy level ( @xmath19 state ) is 129 , 13.8 and 4.7 for @xmath20 10 , 30 and 50 respectively . the average value of @xmath2 for the 1000 levels is 65.2 , 6.6 and 2 . the distribution changes from poisson to wigner as @xmath2 decreases with increase in @xmath1.,title=""fig:"",width=188 ] = 10 , 30 and 50 . the parameter @xmath2 for the highest energy level ( @xmath19 state ) is 129 , 13.8 and 4.7 for @xmath20 10 , 30 and 50 respectively . the average value of @xmath2 for the 1000 levels is 65.2 , 6.6 and 2 . the distribution changes from poisson to wigner as @xmath2 decreases with increase in @xmath1.,title=""fig:"",width=188 ] .,title=""fig:"",width=226 ] .,title=""fig:"",width=226 ] as seen above , the transition from regular to chaotic dynamics is governed by the parameter @xmath2 which depends on the energy and rotation frequency . this is evident from the classical phase space as well as from the study of level spacing distribution for lower and higher energy levels at a fixed @xmath1 . to get a clearer picture of this transition , wavefunction statistics is important . the reason for the importance for the statistics of wavefunctions is their complexity and analytical intractability . for fully chaotic wavefunctions , it is expected that their amplitude distributions will be well approximated by a normal distribution @xcite . in fig . [ fig : histogram_of_wavefunction ] , the probability distribution function of @xmath21 and @xmath22 averaged over ten states near 1000th state are plotted for @xmath23 @xmath24 , @xmath25 @xmath26 and @xmath27 @xmath28 . @xmath21 gradually becomes gaussian distributed and @xmath22 becomes poisson distributed as @xmath1 increases from 0.1 to 10.0 . both the statistics of @xmath21 and @xmath22 become chaotic at @xmath29 which is consistent with the classical dynamics shown in fig . [ fig : poincare ] . the poisson distribution of @xmath22 brings out the possibility of breakdown of time reversal symmetry due to rotation for large @xmath30 . one may recall that rotation has similar effect as that of a magnetic field on a charged particle - both correspond to breaking of time reversal . therefore , the wavefunction statistics shows transition to gue statistics corresponding to chaotic dynamics with time - reversal symmetry breaking . another interesting observation is that the probability distribution function of @xmath22 appears to be a sum of porter - thomas like distribution with a very sharp decay near zero and a poisson like distribution with linear profile in log scale . this may be indication of mixed gue and goe like dynamics in the rotating billiard system which needs to be further studied in more detail . wavefunction at different values of @xmath1 . the inset in left panel shows the magnified view of the same graph from @xmath31 to @xmath32 . the inset in the right graph shows the intensity distribution for @xmath33 0 to 3.,title=""fig:"",width=287 ] wavefunction at different values of @xmath1 . the inset in left panel shows the magnified view of the same graph from @xmath31 to @xmath32 . the inset in the right graph shows the intensity distribution for @xmath33 0 to 3.,title=""fig:"",width=287 ] in this paper , we show that the classical phase space of a particle in a rotating square billiard shows transition from completely regular state to chaotic state as the parameter @xmath2 decreases . the corresponding behaviour is seen in quantum analogue of this system . as we increase the rotational frequency @xmath1 , the level spacing distribution shows transition from poisson distribution to wigner like distribution . wavefunction statistics also captures these features along with a strong indication towards the breakdown of time - reversal symmetry with an increasing @xmath1 . 99 d. r. inglis , phys . rev . * 96 * ( 1956 ) , 1059 . a. bohr and b. r. mottelson , phys . * 22 * ( 1980 ) , 461 . s. r. jain , a. k. jain , and z. ahmed , phys . lett . b*370 * ( 1996 ) , 1 . a. k. jain and s. r. jain , _ superdeformed bands _ ( 1996 ) , in s. n. chintalpudi , a. k. jain ( eds . ) , _ nuclear structure physics _ , pp . 57 . s. r. jain and a. k. jain , _ cranking model _ ( 1996 ) , in s. n. chintalpudi , a. k. jain ( eds . ) , _ nuclear structure physics _ , pp . s. r. jain and a. k. pati , phys . * 80 * ( 1998 ) , 650 . d. b. fairlie and d. k. siegwart , j. phys . a * 21 * ( 1988 ) , 1157 . d. k. siegwart , j. phys . a * 22 * ( 1989 ) , 3357 . h. frisk and r. arvieu , j. phys . a * 22 * ( 1989 ) , 1765 . s. borgan and r. c. johnson , phys . lett . a * 262 * ( 1999 ) , 427 . m. v. berry , proc . lond . a*413 * ( 1987 ) , 183 . m. v. berry , j. phys . a*10 * ( 1977 ) , 2083 ." +"space - borne cosmic ray experiments require the capability to measure the energies of particles with lorentz factors @xmath1 with detectors that are relatively large yet lightweight . nasa s proposed advanced cosmic ray composition experiment for space science ( access ) mission @xcite , for example , requires a transition radiation detector ( trd ) capable of measuring the energies of cosmic rays up to 100 tev / nucleon for particles with charge @xmath3 . such experiments require that the range of existing trds must be extended upward by an order of magnitude or more , requiring designs modified for use at these higher energies . transition radiation ( tr ) is produced when a charged particle crosses the interface between two materials with different dielectric constants , resulting in the rapid rearrangement of the particle s electric field as it passes from one material to the next @xcite . for highly relativistic particles ( @xmath4 ) the radiation is emitted at x - ray frequencies . the spectrum produced depends on the plasma frequencies and thicknesses of the two materials as well as the energy of the particle . typically , the materials used are a low atomic number solid such as plastic with plasma frequency @xmath5 , and a gas or vacuum with plasma frequency @xmath6 . radiation is emitted up to a frequency @xmath7 , beyond which the spectrum is suppressed . in the usual case , where @xmath8 , the total intensity produced from a single interface is proportional to @xmath9 , where @xmath10 is the atomic number of the incident particle . the intensity from a single interface is weak . therefore , in practical applications , a radiator is constructed with a large number @xmath11 ( typically @xmath12 ) of thin foils of thickness @xmath13 separated by a distance @xmath14 ( or fiber or foam radiators with equivalent average @xmath15 and @xmath16 ) with radiation produced at each of the @xmath17 interfaces . interference effects from the superposition of the amplitudes produced at each interface give rise to pronounced minima and maxima in the spectrum , with the last ( highest frequency ) maximum near @xmath18 where @xmath19 is 1 for a metal and 0 for a nonconductor . as the particle energy increases , the total radiated intensity increases up to a lorentz factor @xmath20 above which saturation sets in due to the interference . we have included here the possibility of a nonzero conductivity which introduces an imaginary part to the wave vector and leads to an effective plasma frequency @xmath21 @xcite . the saturation energy and characteristic frequency can be tuned by varying the radiator foil material , thickness , and separation . an x - ray detector appropriate for absorbing the tr x - rays must be placed after the radiator . the radiation is emitted at an angle @xmath22 with respect to the incident particle direction , so for high lorentz factors the x - rays are spatially inseparable from the ionization energy deposited in the detector by the particle itself . therefore , in conventional applications , the detector must be made thin in order to minimize the ionization signal , yet with sufficient stopping power to absorb the x - rays . for @xmath23 less than about 40 kev , gaseous detectors ( e.g. xenon - filled wire chambers ) are typically employed . in order to improve statistics and provide redundancy , a complete trd consists of multiple layers of radiators and x - ray detectors . such trds have been used successfully both at accelerators and in space . in most cases , the trd is employed as a threshold device to identify particle types : for example , a meson or hadron may be accompanied by a small tr signal , while an electron of the same energy but larger @xmath24 is characterized by a large signal . in the case of the space shuttle crn experiment @xcite , a fiber trd was used to measure the energies of cosmic ray nuclei with @xmath25 . ref . @xcite gives an extensive review of tr applications and radiator configurations . a brief listing of cosmic ray experiments incorporating trds is given in @xcite . in order to increase the maximum particle energy @xmath26 , one must increase the plasma frequency ( or equivalently , density ) , thickness , and/or spacing of the foils ( eq . [ eq : saturation ] ) . in a space instrument , the overall thickness will be constrained , putting a limit on @xmath27 ( assuming @xmath28 ) . increasing @xmath5 by using metal foils instead of plastic , for example , and/or @xmath13 results in a hardening of the x - ray spectrum produced ( eq . [ eq : omega_max ] ) . metal foils have been used in early accelerator tests @xcite , and in particular lithium foils have been used in order to minimize the absorption at low x - ray frequencies @xcite . in the case of very high energies , though , with @xmath29 and a typical spacing @xmath30 cm , @xmath31 can be in excess of several hundred kev . gas detectors are then no longer efficient in detecting these hard x - rays . although @xcite describes the use of gas detectors near @xmath29 by optimizing the radiator design , scintillators such as nai or csi provide an efficient alternative at these lorentz factors and corresponding high x - ray energies . the higher density of the scintillators leads to an increase in the ionization energy deposited by the particle as it traverses the detector . however , as the tr spectrum hardens , compton scattering in the radiators becomes important , becoming the dominant photon interaction above @xmath32 kev . a significant portion of the x - rays produced are scattered out of the path of the incident particle . thus , a detector that is segmented or positioned outside of the beam can efficiently detect the tr signal spatially separated from the ionization . we describe here the test of a scintillator - based compton scatter trd for high lorentz factor particles , including the use of metal foils , based on the results of accelerator measurements with high energy electrons at the cern sps . comparisons of the measured results with detailed simulations will also be presented . a scintillator - based compton scatter trd was designed to investigate the predicted increase in saturation energy obtained by using thick , dense radiator materials including mylar ( @xmath33 g/@xmath34 ) , teflon ( @xmath35 g/@xmath34 ) , and aluminum ( @xmath36 g/@xmath34 ) . metal foils are of particular interest because of the characteristic enhancement in the signal expected due to the nonzero conductivity @xcite . , width=326 ] [ cols=""<,^,^,^,^,^,^ "" , ] for the plastics , radiators of @xmath37 foils were constructed by attaching 19.1 cm @xmath38 18.4 cm plastic foils to 3.4 mm thick wood frames and stacking them together . for the aluminum , each radiator consisted of seven 2.7 cm thick honeycomb panels bundled together and aligned with the cells perpendicular to the particle beam . the honeycomb was a composite material chosen both for its dimensions and its adaptability as a combined detector - plus - structure for a space instrument ( fig . [ fig : honeycomb ] ) . particles passing through the structure passed through either 1 ) a section of foils perpendicular to the beam in which two 3 mil sheets glued together form a foil with an effective @xmath39 mil , @xmath40 mm , and @xmath41 foils along the particle trajectory or 2 ) a section of foils at a @xmath42 angle with respect to the particle beam , resulting in an effective foil thickness @xmath43 mil , @xmath14 ranging from 0 to 5.2 mm , and @xmath44 . the yield from a composite material ( e.g. , a foam ) with average values @xmath45 , @xmath46 , and @xmath47 has been shown to be essentially the same as from a regular foil radiator with the same @xmath13 , @xmath14 , and @xmath11 @xcite . we therefore calculate the al honeycomb effective parameters as averages of configuration 1 weighted by 46% ( to account for the fraction of the area perpendicular to the beam covered by configuration 1 ) and configuration 2 weighted by 54% . the resulting average honeycomb radiator parameters are given in table [ tab : rad_par ] , along with the parameters of the plastic radiator configurations tested . the total length of each radiator was 19 cm . each radiator was viewed by three x - ray detectors , each consisting of a 19 cm @xmath38 19 cm @xmath38 5 mm thick nai(tl ) crystal hermetically sealed between a 6.4 mm thick glass optical window on one flat face and a 0.75 mm thick aluminum entrance window on the other face . an ultraviolet transmitting lucite lightguide was coupled to the glass window using optical grease , reducing the aperture to a 13 cm diameter circle . an electron tubes 9390 kb 130 mm photomultiplier tube with a standard bialkali photocathode was mated to the lightguide with optical grease . the lightguide was wrapped in aluminum foil and the whole assembly wrapped with black tape to make it light tight . six identical modules were constructed , with each module containing a radiator and the three nai(tl ) detector assemblies , one on each side of the radiator and one above the radiator outside of and parallel to the beam ( fig . [ fig : schematic ] ) . the modules were positioned one behind the other along the beam and aligned such that the particle beam travelled down the center of the modules . only x - rays scattered at large angles away from the beam were then detected . , width=432 ] for the first accelerator run , the 18 pmt signals were fed into camac - based , 11-bit caen c205a charge adcs and read out with the cern cms h2a daq computer . for the second accelerator run , the signals from the pmts were fed into custom - built 8-channel front end modules which contained a charge integrator , peak detect and hold circuit , and gain - adjustable amplifier . analog - to - digital conversion was performed with a 64-channel , 12-bit national instruments pci-6071e daq board running in a pc and controlled under labview 6i . the instrument was exposed to high energy electrons at the cern sps h2a test beam site in august / september 1999 and again in august / september 2001 . beam energies ranged from 7 to 150 gev , covering the range of lorentz factors @xmath48 . a set of scintillators in the beam upstream of the trd provided event triggering . the trigger rate was kept to about 1 khz to avoid deadtime in the daq system . beam definition scintillators in front of and behind the trd ( s1 and s2 in fig . [ fig : schematic ] ) flagged events for which the electrons showered within the radiator stacks . a pb shower counter ( s3 ) was placed downstream of s2 to flag pions present as a contaminant in the higher energy beams . energy calibration runs were performed both immediately before and after the beam runs using radioactive @xmath49ba ( 81 , 303 and 356 kev ) and @xmath50cs ( 662 kev ) x - ray sources . in order to account for bremsstrahlung and other background produced by the electrons in passing through the radiators and upstream material , a background run was performed for each radiator configuration in which the radiators were replaced by solid blocks with the same material and thickness ( in g/@xmath51 ) as the radiators . ) represent the calculated spectrum for module 1 ." +"during 19971998 the number of x ray pulsars found in the small magellanic cloud ( smc ) rapidly increased from three ( smcx1 , rxj0053.87226 , and 2e0050.17247 ; lucke et al 1976 ; hughes 1994 ; israel et al . 1997 ) up 14 ( for a review see yokogawa et al . 1998 ) thanks to sensitive observations of the large area detectors on board the _ r_xte and asca satellites . the majority were found to be associated with massive be spectral type stars showing intense h@xmath7 emission lines . only smcx1 , which is associated with a super giant b0 spectral type star in a 3.9d orbital period binary system , is a persistent ( although moderately variable ) x ray pulsar . for all the remaining x ray pulsars pronounced variability ( a factor @xmath850 ) or , more often , transient behaviour has been definitively proven . the source 2e0101.57225 was detected at a nearly constant flux level in all the _ einstein _ , _ rosat _ and _ asca _ pointings which surveyed the relevant region of the smc ( see hughes & smith 1994 ) , but pulsations were not found due to poor statistics . based on the accurate position obtained with the _ rosat _ hri , these authors found that 2e0101.57225 is very likely associated with a be spectral type star ( r.a.=01@xmath903@xmath101386 , dec.=7209141 ; equinox j2000 ) . 2e0101.57225 is located near the optical limb of the supernova remnant snr010172.4 . hughes & smith ( 1994 ) present several arguments that make the be / x ray binary snr association unlikely . in this _ letter _ we report the discovery of 345s pulsations from the source saxj0103.27209 during a _ beppo_sax observation of the smc . the comparison with the data of past x ray missions allows us to conclude that saxj0103.27209 and 2e0101.57225 are the same object , a persistent source with moderate variability ( within a factor of 510 ) . we also report the results of the timing analysis of a recent public _ chandra _ observation and discuss optical observations carried out at eso . the smc field including the position of the 2e0101.57225 was observed by the narrow field instruments ( nfis ) on board the _ beppo_sax satellite ( boella et al . 1997a ) on 1998 july 2627 ( effective exposure time of 40320s ) . we used data from the medium energy ( mecs ; boella et al . 1997b ) and low energy ( lecs ; parmar et al . 1997 ) instruments . a bright x ray source ( @xmath03.7@xmath210@xmath11cts@xmath4 , 110kev ) was detected on axis in the mecs , at r.a.=01@xmath903@xmath1013@xmath12 , dec.=720916 ( j2000 ; 90% confidence uncertainty radius of 30 ) . the mecs event list and spectrum were extracted from a circular region of 4 radius ( corresponding to an encircled energy of @xmath090% ) around the x ray position . a 4 extraction radius ( @xmath085% encircled energy ) was also used for the lecs in order to minimize the contamination from the soft x ray emission of the bright nearby source 2e0102.37217 . the local background was measured in a region of the mecs and lecs images far from any detected field sources . the arrival times of the @xmath01500 photons were corrected to the barycenter of the solar system and background subtracted light curves were accumulated in 0.5s bins . a single power spectrum was calculated over the entire time span covered by the observation in order to maximize the sensitivity to coherent pulsations . significant power spectrum peaks were searched for using the algorithm described in israel & stella ( 1996 ) . a highly significant peak ( @xmath09.4@xmath13 based on the fundamental only ; see upper left panel of fig.1 ) was found at a frequency of 0.002889hz , corresponding to a period of 345.2s . an accurate determination of the period was obtained by fitting the phases of the modulation over 4 different intervals of @xmath016000s each . the scatter of the phase residuals was consistent with a strictly periodic modulation at the best period of 345.2@xmath140.3s ( 90% confidence ) . a comparison of the 14kev ( panel s in fig.1 ) and 410kev ( panel h ) folded light curves provides marginal evidence for an energy dependent pulse profile : nearly sinusoidal at low energies , while double horned above 4kev . however the pulsed fraction ( semi amplitude of modulation divided by the mean source count rate ) of @xmath045% is constant over the two energy intervals considered . a spectral analysis was performed in the 0.76.5 and 1.610kev energy ranges for the lecs and mecs , respectively . the spectra were rebinned to have at least 20 counts in each energy channel , such that @xmath15 fitting techniques could be used . no single component model was found to fit the data well ( a power law gave a @xmath16=41/15 ; where @xmath17 is the degree of freedom ) . among double component models , an absorbed power law plus a black body gave the best fit ( @xmath16=15/15 ) for a photon index of 1.0@xmath18 , n@xmath19@xmath203.8@xmath21@xmath210@xmath22cm@xmath11 , and a black body temperature of 0.11@xmath140.03kev ( uncertainties refer to 1@xmath13 ) . the observed flux in the 210 kev energy band was 2.7@xmath210@xmath24ergs@xmath4 cm@xmath11 ( the soft component accounts for @xmath015% of the total ) corresponding to an unabsorbed 210kev x ray luminosity of 1.2@xmath210@xmath3ergs@xmath4 assuming a distance of 62kpc ( laney & stobie 1994 ) . after the discovery of 345s pulsations in 2e0101.57225 ( israel et al . 1998 ) , yokogawa & koyama ( 1998 ) found a signal at a period of 348.9s during a 1996 may _ asca _ observation ( absorbed luminosity of 5@xmath210@xmath5ergs@xmath4 ; 210kev ) implying a period derivative ( with respect to _ beppo_sax ) of 1.7syr@xmath4 . the source was also detected by _ asca _ on 1993 may 12 and 1997 november 14 at an absorbed luminosity level of 6 and 5@xmath210@xmath5ergs@xmath4 , respectively . a re analysis of the latter _ asca _ datasets allowed us to infer an upper limit ( 3@xmath13 confidence ) in the 6080% range on the pulsed fraction for a period of @xmath0345s . to better constrain the absorption we used archival data from the _ rosat _ satellite ( pspc ; 0.12kev band ) which observed the field of 2e0101.57225 between 1991 october 8 and 1992 april 28 ( sequence 600195 ; effective exposure time 26630s ) . assuming that the source showed the same flux and spectrum during the two observations , we fitted the _ rosat _ and _ beppo_sax data together . we found that the two component model derived above again gave the best fit ; a @xmath16=23/25 was obtained for a photon index of 1.1@xmath140.1 with n@xmath19 of 3.9@xmath25@xmath210@xmath22cm@xmath11 and a black body temperature of 0.12@xmath26kev corresponding to an equivalent black body radius r@xmath27 in the 260 km range ( see fig.2 ; 1@xmath13 uncertainties ) . the corresponding power spectrum shows no significant ( 3@xmath13 confidence ) peak in the 339359s period interval with a @xmath060% upper limit on the pulsed fraction . the field including 2e0101.57225 was observed by the nasa advanced x ray astrophysics facility satellite _ chandra _ on 1999 august 23 with the imaging spectrometer ( acis ; garmire et al . 1992 , bautz et al . 1998 and references therein ) in the high resolution imaging mode for an effective exposure time of 19551s . the source was detected at an off axis angle of about 9 in the s4 ( front illuminated ) ccd of the acis s detector with a count rate of @xmath09@xmath210@xmath11 ct s@xmath4 ( in the 0.510kev energy range ; see fig.3 left panel ) . the source shows two emission peaks separated by @xmath05 . however the size of the emission region is comparable with the 90% encircled energy region of a source at 9 off axis angle . we extracted a 3.24s binned light curve of the source from a region within 8 from the center of the emission : r.a.=01@xmath903@xmath101406 , dec.=72091525 ( equinox j2000 ) . the statistical uncertainty radius is only @xmath00.5 but at this stage the uncertainty in the absolute positioning at such an off axis angle might be as large as 90 . however the detection of the pulsations clearly associates the _ chandra _ source with that of _ beppo_sax . we also note that the _ chandra _ coordinates are consistent with the _ rosat _ hri uncertainty circle and differ by less than 2 from those of the proposed optical counterpart ( see below ) making the association very likely . according to the _ chandra _ source naming convention we designated it as cxoj010314.1720915 . a single power spectrum was calculated over the entire observation . the search was performed over a period interval around that detected by _ beppo_sax and assuming a maximum @xmath28p@xmath28 of @xmath03 s yr@xmath4 which translates into a search over only two fourier frequencies ( see fig.1 lower panels ) . a peak was detected at a significance level of 7.5@xmath13 . a refined period was determined by means of the phase fitting technique ; this gave a value of 343.5@xmath140.5s ( see table1 ) . we note that the _ chandra _ data were not corrected to the barycenter of the solar system . however , for a relatively long period pulsar in the direction of the smc , the effect of the spacecraft and of the earth motion , would cause a maximum correction of a factor of 10 smaller than the statistical uncertainty of the period given above . the pulse profile is sinusoidal ( over the whole _ chandra _ energy band ) and the pulsed fraction is @xmath045% ( see fig.1 ) . this result implies that the pulsar is continuing to spin up at a constant rate of 1.7syr@xmath4 since 1996 ( see fig.1 ; right panel ) . in order to further address the issue of the double peaked _ chandra _ image ( see fig.3 ) , we extracted two separate light curves for each of the two peaks . we found that the signal at 343.5s was present with a similar pulsed fraction in both light curves ; this result is consistent with the hypothesis of a point like source . an independent confirmation was also obtained through a raytracing simulation , encompassing a monochromatic source ( 1.49kev ) and models for the mirror assembly and acis detector . the results indicate that expected psf at an off axis angle of 9 is artificially elongated in the direction connecting the two peaks detected in the chandra image around the position of 2e0101.57225 ; the two peaks are probably artefacts resulting from the small number of x rays in the image . we conclude that the source is consistent with being point like . optical images ( h@xmath7 and h@xmath7 red continuum ; 200s each ) of the _ beppo_sax error circle of saxj0103.27209 were obtained on 1998 july 24 at the danish 1.5 m telescope with the danish faint object spectrometer camera ( dfosc ) at la silla ( chile ) in order to search for emission line stars . the data were reduced using standard eso midas procedures for bias subtraction , flat field correction , aperture photometry and one dimensional stellar and sky spectra extraction . within the _ beppo_sax position circle we found only one h@xmath7 active object : this is the o9b1iii ve m@xmath6=14.8 star originally suggested as the optical counterpart of 2e0101.57225 ( hughes & smith 1994 ) . a 10a resolution 38008500a spectrum ( 20 slit ) of this star was obtained with the same instrument on 1998 october 20 . strong h@xmath7" +"periodic arrangements are quite ubiquitous in various physical systems . from naturally occurring crystal structures in solid state systems , to artificially made periodic arrangements such as photonic crystals and optical lattices , both theoretical and experimental research in these systems has provided us with an understanding of fundamental physical phenomena , as well as with the possibility of achieving technological applications . there has been a growing interest in recent years in understanding the fundamental properties of photonic crystals @xcite and of optical lattices @xcite , particularly concerning their possible applications in quantum optics and condensed matter systems . photonic crystals are periodic arrays of dielectric media in which light propagates linearly in various ways , depending on the geometry of the system . on the other hand , optical lattices are periodic arrays of electromagnetic field arising from the interference pattern of concurrent laser fields . in this case , ultracold atoms propagate nonlinearly in ways which depend also on the specific geometry of the system . both systems share important properties , namely the band structure of their energy spectrum as well as the possibility of producing confined and extended modes of light in photonic crystals @xcite and of matter in optical lattices@xcite . however , there are important physical differences which render each system unique . interaction between atoms in optical lattices has led to research into the nature of nonlinear matter waves in these systems , revealing a vast spectrum of nonlinear behaviour(see e.g. @xcite ) . by contrast , light waves in photonic crystals obey maxwell s equations and , hence , always satisfy the superposition principle . it is of conceptual importance to understand how light and matter waves in these two systems are comparable , and to investigate the possibility of using the light fields in photonic crystals to control the matter waves in optical lattices . such a study can be carried out in two regimes : in the high - particle - density and coherent regime ( in the case of photonic crystals , we mean photons , and in the case of optical lattices , we mean atoms ) , a description using a classical field in both systems is appropriate ; on the other hand , in the low particle density regime , quantum phenomena arise , and the description of both systems will require a microscopic study ( for photonic crystals see , @xcite , and for optical lattices , see @xcite ) . in the present paper , we address the first regime of high particle density . we focus on two interesting connected possibilities : first , one particular type of wave manipulation , namely the generation of confined modes produced by defects in both periodic structures ; and second , the propagation of nonlinear matter waves in the presence extended light fields produced in photonic crystals . we will see that , although defects are just one example of wave manipulation that would be interesting to implement experimentally to create elaborate optical lattices , there are technical difficulties that have to be met before a successful realization . the present paper is organized as follows : first , we review some important properies of defects in photonic crystals and in optical lattices . second , we explain how an optical lattice can be induced by extended modes in photonic crystals . finally , we exemplify this new way of obtaining optical lattices by using a photonic crystal with a two - dimensional square geometry . we conclude by suggesting the potential of using defect modes of photonic crystals to manipulate nonlinear matter waves embedded in them , and comment on the difficulties that must be resolved before realizing it experimentally . photonic crystals ( pc ) are periodic arrays of different dielectric materials whose dispersion relation presents bandgaps depending on specific structural parameters . this is their most important feature , because it allows us to control the flow of light through the material with low energy loss . the dielectric contrast of a photonic crystal is what produces a gap in the energy spectrum , for a given value of the propagation vector @xmath0 of the light field that propagates in the structure . periodicity allows us to use the bloch theorem to obtain with ease the band diagram and electric and magnetic field modes . @xcite by introducing defects , it is possible to confine a single mode of the electromagnetic field in a very narrow space of the lattice . furthermore , we can introduce an active medium , such as a quantum dot or a two level atom , inside the defect , thus making it possible to analize radiation - matter interactions @xcite . in order to obtain an analytical solution for the master equation , use is made of maxwell s equations in free space in cartesian coordinates for a square array of dielectric rods embedded in air ; only the linear term in the electric displacement is taken into account . the solution consists on diagonalizing the resulting matrix which is obtained when we expand the dielectric function and the electric field in a basis of plane waves and introducing them in the corresponding maxwell equation . the dielectric function has the form @xmath1 where the @xmath2 are the expansion coefficients of the dielectric function . these contain the information about the geometrical distribution of the dielectric rods and have the form @xmath3 where @xmath4 is the diameter of the rods , @xmath5 is the dielectric constant and @xmath6 is the length of the supercell ( @xmath7 is its area ) ; @xmath8 is the number of layers around the defect . we have obtained equation ( [ a1 ] ) analytically . the unitary cell for @xmath9 is shown in fig.([diel1 ] ) . the electric field has the form @xmath10 where @xmath11 is the periodic function that takes into account the periodicity of the field in the @xmath12 plane and the @xmath13 are the reciprocal vectors of the square array . the periodic function has the form @xmath14 introducing eq.([die21 ] ) and eq.([ezp ] ) in maxwell s equations we obtain the resulting eigenvalue equation @xmath15=k^{2}\sum_{p , q}{\alpha_{nm}\beta_{n - p , m - q}},\label{auto2}\ ] ] where the @xmath16 are the expansion coefficients of the electric field . we can note that this is a generalized eigenvalue problem whose eigenfunctions correspond to the expansion coefficients of the electric field with eigenvalues that correspond to the allowed energies for a fixed pair @xmath17 and @xmath18 . with this solution , we construct the band diagram of the pc with a defect and we analyze the effect of introducing it in the crystal . ultracold atoms in optical lattices are described in three different regimes depending on the particle density in the system @xcite . we focus on the limit of high - particle - density , in which the system remains in a macroscopic superfluid state . in this limit , we can make use of a classical field to describe the macroscopic coherent state of the atoms in the optical lattice , which is reminiscent of the classical field that describes light in photonic crystals . however , as has been noted , there is a marked difference between both systems : in the case of ultracold atoms , the waves behave nonlinearly , due to the interparticle interaction , whereas light always propagates linearly . this nonlinear description of the atomic case can be modeled using the well - known gross - pitaevskii ( gp ) equation : @xmath19\psi(\mathbf{r})=\mu \psi(\mathbf{r}),\ ] ] where @xmath20 denotes the nonlinear coupling . this equation can be derived using a hartree - type ansatz to minimize the energy of the system , asuming @xmath21wave scattering between the atoms . the wavefunction @xmath22 describes a macroscopic coherent state . in the case of optical lattices , the periodic potential is given by @xmath23 where @xmath24 is proportional to the intensity of the laser light . such a periodic potential can be generated by setting up standing waves with two lasers at perpendicular angles . the two - dimensional nature of this optical lattice can be achieved by setting up a tightly confining field in the third perpendicular direction , thus eliminating to a large extent the corresponding degree of freedom . the gp equation was numerically integrated with a procedure consisting of two stages . first , we perform a pseudospectral interpolation of the gp equation without the nonlinearity , i.e. of the schr@xmath25dinger single - particle equation . since the usual bloch argument concerning periodic lattices in solid state physics applies also in optical lattices , we make use of the bloch form of the wave function . once we obtain the solution in @xmath26-space we reconstruct the spatial wave function as a superposition of plane waves , which amounts to making the plane - wave expansion that what was done in the photonic crystal case . afterwards , we propagate this single - particle wavefunction in imaginary time , using the gp equation . the evolution in imaginary time generates a superposition of eigenstates of the gp equation with exponentially decaying coefficients . by using this procedure , the term in the superposition with the lowest energy , i.e. the ground - state , will be the least suppressed in the evolution and , thus , will be predominant after some time has passed . in this way we will have obtained the gp ground state . it is important to notice that , because the gp equation is determined by the spatial density of the system , we need to normalize the wave function continuously in the time evolution . otherwise , the system will not evolve with the correct effective gp hamiltonian . using this same procedure , we can introduce a gaussian defect in the optical lattice . such defects have been studied in one - dimensional optical lattices , and have been shown to exhibit transport properties with dynanic solitonic behaviour due mainly to the nonlinearity inherent in the system @xcite . however , here we focus mainly on the ground state of the system . it should be noted that there is an important difference between defects in optical lattices and in photonic crystals concerning confined states . in experimental setups in optical lattices , it is the ground state which can be achieved by lowering the temperature of the system . as a result , in the band diagram of the optical lattice , we always choose the point of lowest energy . this contrasts to what is done in photonic crystals , where the interest focuses on confined modes that have an energy in the bandgap of the spectrum . in this case , it is not the lowest energy state which is chosen in order to confine light waves , but rather a higher energy state . as we have discussed previously , optical lattices are stationary periodic light fields . such lattices are usually generated through the use of interfering laser fields . however , it is not necessary to use laser fields . what matters is that we have a light field that couples to the atoms we are using through an effective external dipole potential . such a dipole potential is proportional to the intensity as @xmath27 where @xmath28 denotes the field intensity . in particular , photonic crystals are suitable structures in which various types of distributions can be generated . as we reviewed in the previous section , by a suitable combination of geometry , it is possible to mold the field distribution by making use of , for example , defects . if we could take advantage of the vast set of intensity distributions in photonic crystals , we could achieve much more exotic behaviour than what has been achieved up until" +"this paper describes our computer program speden that reconstructs the density from the diffraction patterns of individual particles . speden is of interest for three reasons . diffractive imaging promises to improve the resolution , sensitivity , and practical wavelength range in x - ray microscopy , for three - dimensional objects that are tolerant to x - rays . a few examples are defects in semiconductor structures , phase separation in alloys , nano - scale machines and laser fusion targets . a long - term vision is the possibility of high - resolution reconstruction of diffraction patterns of single bio - molecules . of broad theoretical interest is speden s unique approach to the reconstruction of scatterers - a difficult mathematical problem . in the rest of this section we expand on these three topics . reconstruction of the electron density from non - uniformly sampled , three - dimensional diffraction patterns is of wide interest and applicability with present - day sources . in radiation - tolerant samples , x - ray diffraction and diffraction tomography are capable of higher resolution than ( straight- or cone - beam ) tomography alone . in tomography , resolution is limited by the quality of the incident beam and by the spatial resolution of the detector ; in diffraction the resolution can be as fine as the wavelength of the incident radiation . experimentally , diffraction imaging has already produced x - ray images at higher resolution than possible with available x - ray optics ( miao et al . , 1999 , and he et al . , 2002 ) . the price to be paid for these benefits is the intrinsic difficulty of the reconstruction . nevertheless , several successful reconstructions from experimental x - ray data , using the iterative hybrid input - output version of the gerchberg - saxton - fienup ( gsf ) algorithm , have been reported recently ( miao et al . , 2002 , and marchesini et al . , 2003 ) . the first successful application of this algorithm to electron diffraction data was reported in 2001 ( weierstall et al . , 2002 ) , and it has been used more recently to produce the first atomic - resolution image of a single carbon nanotube ( zuo et al . , 2003 ) . in biology , the use of the gsf has recently been shown to dramatically reduce the number of images needed for tomographic cryoelectronmicroscopy of protein monolayer crystals , so that phasing can be based mainly on the three - dimensional diffraction data ( spence et al . , 2003 ) . the development of speden was also prompted by the promise of new ways to image bio - molecules . free - electron lasers can , in principle , provide x - ray pulses of tens to hundreds of femtoseconds in length and brightness up to ten orders of magnitude greater than synchrotron radiation . it was predicted that , under such circumstances , it should be possible to dispense with crystals and reconstruct the electron density of single biological particles from their diffraction pattern ( neutze et al . , 2000 ) . in proposed experiments , a large number of single particles will be injected into the x - ray beam in random orientation and their diffraction patterns will be recorded , each in a single shot of the free - electron laser . such diffraction patterns will be very noisy and their resolution will be limited by the signal to noise ( s / n ) ratio . the measured diffraction patterns that correspond to different orientations of the particle will be classified into a number of mutually exclusive classes . the images within each class will then be averaged and the class averages assembled into a three - dimensional diffraction pattern by finding their mutual orientation relationships . finally , the three - dimensional diffraction pattern will be reconstructed to yield the electron density of the molecule . we have worked on the analysis of all three steps of such an experiment . the essence of the first analysis is that the maximum x - ray intensity at a given pulse length is limited by the requirement that the molecule stay intact during the pulse , even though it eventually disintegrates ( hau - riege et al . , the second analysis discusses the division of noisy diffraction patterns into a number of distinct classes . if the images are divided into too few classes , the available resolution is not realized . if the patterns are divided into too many classes , the class averages will be poor and the pattern quality suffers . the individual class averages , each corresponding to a well - defined orientation of the particle , will be assembled into a three - dimensional diffraction pattern . the result will be a three - dimensional diffraction pattern that is measured at a limited number of orientations . it will be , therefore , sparse , irregular and will have a limited signal to noise ratio ( huldt et al . , 2003 ) . the program speden , described in this paper , provides a way to optimally determine the electron density from such a three - dimensional ensemble of continuous diffraction patterns . we first give an analysis of their properties and discuss the methods and the expected difficulties of reconstructing a `` sensible '' electron density from them . we then describe how speden adapts the holographic method ( szoke et al . , 1997a ) in crystallography to deal with continuous diffraction patterns as opposed to discrete bragg spots ; this will be discussed in the next section . we then report quantitative results of preliminary tests for verifying the correctness of our method . these tests use computed and measured diffraction patterns from samples of inorganic particles . the reconstruction of the density of scatterers from its diffraction pattern is an `` inverse problem '' . other , well - studied inverse problems are those of computed tomography , image deblurring , phase recovery in astronomy , and crystallography . in tomography , for example , an inversion algorithm ( e.g. filtered back projection ) is used to recover the density of scatterers from the measured tomograms . it is widely recognized that the reconstructed density is very sensitive to inaccuracies in the measurement . small errors in the diffraction pattern cause large errors in the reconstruction . this property is called ill - posedness or ill conditioning . the reconstruction of the electron density from x - ray diffraction patterns is indeed ill conditioned . it also has two _ additional _ difficulties . first , in contrast to tomography , there are no direct inversion algorithms not even approximate ones . second , the reconstructed electron density at any sample point is influenced strongly by the electron densities of all sample points , as opposed to a limited number of them . therefore , errors in density are non - local and `` propagate '' far . fortunately , very good fundamental discussions of these subjects are provided in the books of daubechies ( daubechies , 1992 ) , bertero and boccacci ( bertero et al . , 1998 , bertero , 1989 ) and natterer ( natterer , 1996 , natterer and wbbeling , 2001 ) . in somewhat simplified terms , the reconstruction of the electron density is similar to finding the inverse of an ill - conditioned non - square matrix , a subject thoroughly discussed in golub and van loan ( golub et al . , 1996 ) . we consider these mathematical properties to be essential for understanding the successes and limitations of reconstruction algorithms ; we will try to be fully cognizant of them in the discussion that follows . the crystallographic phase problem is a good starting point for further discussion . it was first realized by sayre ( sayre , 1952 ) that the number of observable complex structure factors , limited by the bragg condition , is equivalent to a critical sampling of the electron density in the unit cell of the crystal . the sampling theorem of whittaker and shannon teaches us that , if the amplitudes and phases of all the diffraction peaks were accurately measured , the electron density could , in principle , be reconstructed everywhere ( bricogne , 1992 ) . unfortunately , only the amplitudes of the bragg reflections are measured , not their phases . therefore there is not enough information in the diffraction pattern for a unique reconstruction of the electron density . sayre proposed ( sayre , 1980 ) that if we could measure the diffraction amplitudes `` in between '' the bragg peaks , we should have enough information to reconstruct the electron density , or to `` phase '' the diffraction pattern . this is exactly the situation in diffraction from a single particle . nevertheless , it is still difficult to reconstruct the electron density , even from a well `` oversampled '' diffraction pattern . one corollary of critical sampling is that the amplitudes and phases of the bragg reflections of a crystal are independent of one other , but any structure factor in between them depends on the surrounding ones to some extent . therefore , too much oversampling does not help to obtain independent data , although it does improve the s / n ratio by reducing the noise . ill posedness is still with us , although with oversampling , the error propagates less . an additional difficulty with diffraction patterns from a set of discrete orientations of a particle is that at low resolution the diffraction pattern is well oversampled while at high resolution the sampling is sparse . a fundamental property of diffraction is that the position and the handedness of the electron density are undetermined , resulting sometimes in stagnation of the algorithm and drift in the position of the results ( stark , 1987 ) . there are two well - known , necessary remedies for the lack of information and for the ill posedness of the reconstruction problem . the more important one is the need for more information . for example , one way to include _ a priori _ knowledge is to accept reconstructed electron densities only if they are `` reasonable '' . the second remedy is to use `` stabilized '' or pseudo - inversion algorithms . in the next section we introduce our version of a real space reconstruction algorithm ; we will argue that our algorithm deals with all these problems optimally , at least in some sense . we return to the comparison of our algorithm with other methods for phase - recovery in section 2.3 . subsectionspeden , a real - space algorithm in this section we outline the workings of our reconstruction program , speden . speden uses a real - space method for reconstruction ; its acronym stands for single particle electron density . for computational efficiency the particle to be recovered is put into a _ fictitious _ unit cell that is several times larger than the particle itself . all reconstruction algorithms use this artifice in order to be able to calculate structure factors by fast fourier transform techniques . the resulting similarity with crystallography enables the use of many crystallographic concepts . in fact , the recognition of this similarity enabled us to write a program , speden , based on our crystallographic program , eden , with relatively small modifications . the most significant difference between the two programs is that in crystallography the bragg condition restricts the reciprocal lattice vectors to integer values , while the continuous diffraction pattern can be - and usually is - measured at arbitrary , non - integer values of" +"most of the compact objects currently investigated and modeled in astrophysics are observable `` because of the presence of some matter or radiation around them ( we will often term them as central objects '' below ) . at the lowest order of approximation , the associated gravitational field can be described by the spherically symmetric schwarzschild solution , when shape deformation and rotation effects of the source can be neglected , and matter can be considered as a collection of test particles moving along geodesics . however , this is only an idealized situation which is likely not to represent any real astrophysical system . the dynamics of a body orbiting a compact object is indeed strongly influenced by the combined effect of the overall gravitational field , the surrounding matter and in turn the radiation distribution associated with high energy processes arising thereby . a typical example is represented by a luminous compact object surrounded by orbiting matter , such as accretion discs around a neutron star or a black hole . the most luminous and persistent sources of electromagnetic radiation in the universe are the active galactic nuclei ( agn ) , which are believed to be powered by mass accretion onto black holes . their emitting range is from @xmath0 erg s@xmath1 ( e.g. , the nuclei of some nearby galaxies ) to more than @xmath2 erg s@xmath1 ( distant quasars ) , which is far beyond the eddington luminosity ( about @xmath3 erg s@xmath1 ) . therefore , the x - ray variability in agns and the disc emission lines might contain imprints of the radiation drag effects . in a series of papers we have studied the dynamics of test particles in a given gravitational background while subject to a thomson - type interaction with a superimposed test radiation field , namely the so called poynting - robertson ( pr ) effect @xcite . we modeled the radiation flux as made of photons emitted all along a common direction from a point - like source , leading to an effective drag force to be added to the gravitational force . more realistic descriptions would take into account the finite size of the radiating source and allow for photons to be emitted in any direction . however , the computation of the radiation force in this case usually requires complicated numerical ray - tracing calculations for null geodesics in the background spacetime . the general relativistic stress - energy tensor associated with such a more general scenario was constructed for the first time in the pioneering work of @xcite , who considered the special case of test bodies radially moving in the spacetime of a spherically symmetric non - rotating radiation source with finite radius to model jets and solar winds . they studied the radial equilibrium solutions in which the test particle remains at rest under the combined inward gravitational attraction and the outward photon pressure ( the eddington sphere ) . the stability of this equilibrium configuration has been recently investigated by @xcite , who have also discussed its implications for hoyle - lyttleton accretion onto a luminous star ( see also @xcite ) . @xcite , @xcite and @xcite have then analyzed the effects of a luminosity variation on the eddington sphere , especially in view of the possible occurrence of coronal ejection from the system . within this framework , leaving the spherical symmetry makes the problem very difficult to be addressed . the generalization of the abramowicz et al . approach to the case of an arbitrary particle motion in the equatorial plane of a rotating source is due to @xcite , but in the limit of slow rotation only . their model was then used by @xcite to study the existence of equilibrium solutions . following the original robertson approach , we have considered so far different spacetime solutions of astrophysical interest endowed with reflection symmetry with respect to the equatorial plane , like black hole solutions ( schwarzschild and kerr ) @xcite or radiating spacetimes ( vaidya ) @xcite . we have also discussed the effect of coupling with additional properties of test particles ( like intrinsic spin ) @xcite . the main result of our previous analysis is that particles moving on the symmetry plane ( which do not escape ) are definitely attracted to a certain critical radius where they orbit the central source maintaining equilibrium . in general , the critical radius is not unique for sufficiently large values of the impact parameter of the photons as well as of the strength of the radiation field . here we explore the case of a central source having a quadrupolar structure as described by the erez - rosen solution . this is an exact solutions to the vacuum einstein s field equations which generalizes the schwarzschild spacetime to the case of a gravitational source endowed with an arbitrary mass quadrupole moment , and hence it is specified by two parameters , the mass @xmath4 and the quadrupole parameter @xmath5 . this situation has a strong astrophysical motivation and represents a natural generalization of previous results , even if rotational effects are neglected . in fact , also the kerr solution possesses a non - vanishing quadrupole moment , but the latter is induced by the spacetime rotation . here , the quadrupole parameter @xmath5 describes a genuine mass quadrupole moment directly related to the shape deformation of the source . for instance , the supermassive objects hosted in galaxy centers are generally expected to be also endowed with a non - negligible mass quadrupole moment , which may affect the dynamics of stars moving in the region very close to the central object @xcite . besides rotation , torques from the source s quadrupole moment cause in general precession of the stellar orbital planes , which can be measured by high - precision astrometry . this is the case of the compact cluster of stars orbiting the center of the milky way galaxy at milliparsec distances , monitored since many years @xcite . taking into account quadrupolar deformations is also important when considering the spacetime region around neutron stars , which can assume a pronounced oblate configuration . neutron stars can be part of low mass x - ray binaries ( lmxbs ) , where they are spun up by matter that accretes from a companion , which is typically either a low mass star or a white dwarf . for a dynamically negligible magnetic field , the accretion disc of lmxbs can extend down to the star s surface , where curvature effects dominate . therefore , the observed flux emitted in the inner part of the disc may contain the signatures of a more complicated structure of the source , which can be inferred from available x - ray data . however , significant quadrupolar deformations are mainly due to rotation , as in the case of kerr black holes or rapidly rotating neutron stars . hence , an accurate description of the above systems would need also the inclusion of rotation , which is but beyond the scope of the present analysis , mostly motivated to better understand the role of the quadrupole . the main outcome of this work is the analysis of the effects induced on the equilibrium solutions by the quadrupolar deformation of the source . this is a typical feature of particles undergoing pr effect already discussed in previous works , as already mentioned . we will show that the presence of the quadrupolar structure of the source of the gravitational field may affect the conditions for equilibrium in a significant way , introducing an additional degree of freedom with respect to spherically symmetric sources represented by the quadrupole parameter . this feature can in principle give rise to observable effects . we use geometrical units ( @xmath6 ) and follow notations and conventions of @xcite . the metric signature is @xmath7 . latin indices run from 1 to 3 , greek indices from 0 to 3 . the gravitational field of a nonrotating mass with a quadrupole moment can be described by the erez - rosen solution @xcite . it belongs to the static weyl class of solutions with the line element written in prolate spheroidal coordinates ( @xmath8 ) , with @xmath9 and @xmath10 , as follows @xcite [ metric_weyl ] s^2=-ft^2+\{e^2(x^2-y^2)(+)+(x^2 - 1)(1-y^2)^2 } , where @xmath11 is a constant and the quantities @xmath12 and @xmath13 are functions of @xmath14 and @xmath15 only . the metric functions are given by @xmath16 \,,\end{aligned}\ ] ] where @xmath17 and @xmath18 are legendre polynomials of the first and second kind , respectively ( see appendix a ) , and @xmath5 is the dimensionless quadrupole parameter . positive values of @xmath5 correspond to prolate configurations , i.e. , the mass is mostly concentrated along the axes @xmath19 , whereas negative values to oblate ones . when @xmath20 , the metric ( [ metric_weyl ] ) reduces to the schwarzschild solution provided that @xmath11 be identified with the mass of the source , namely @xmath21 . transition of this metric form to the more familiar one associated with standard schwarzschild - like coordinates is accomplished by the following coordinate transformation @xmath22 and @xmath23 . furthermore , the above solution reduces to the well known hartle - thorne spacetime @xcite with vanishing rotation parameter when linearized with respect to the quadrupole parameter . a suitable family of fiducial observers is that of the so called static observers , with unit timelike four velocity @xmath24 aligned with the timelike killing vector @xmath25 . they are accelerated with acceleration @xmath26 . an orthonormal frame adapted to the static observers is thus given by e_t = n , e_x=1_x , e_y=1_y , e_=1_. the four acceleration as well as the curvature vectors @xmath27 , where @xmath28 , associated with the diagonal metric coefficients @xcite only have nonzero components in the @xmath14-@xmath15 2-plane of the tangent space , i.e. , @xmath29 we limit our analysis to the symmetry plane @xmath30 . therefore , both the acceleration and the curvature vectors are directed along the @xmath31axis , which hereafter will be referred to as the radial direction . let a pure electromagnetic radiation field be superposed as a test field on the gravitational background described by the metric ( [ metric_weyl])([metdef ] ) , with the energy - momentum tensor [ ten_imp ] t^=^2 k^k^ , k^k_=0 , where @xmath32 is assumed to be tangent to an affinely parametrized ( ingoing / outgoing ) null geodesic in the symmetry plane , i.e. , @xmath33 with @xmath34 . we then have [ kdef ] k = e(n)[n+(k , n ) ] , ( k , n)= e_x+ e _ , where e(n)= - k n = is the relative energy of the photons and [ cosbeta ] = . the constant @xmath35 denotes the photon impact parameter defined in terms of the conserved energy @xmath36 and angular momentum @xmath37 associated with the timelike and azimuthal killing vectors , respectively . the case @xmath38 corresponds to outgoing photons ( increasing radial distance from the central source ) and @xmath39 to incoming photons ( decreasing @xmath14 ) . since @xmath32 is completely determined , the coordinate dependence of the quantity @xmath40 then follows from the conservation equations @xmath41 , and will only depend on @xmath14 in the symmetry plane . from eq . ( [ ten_imp ] ) using the geodesic condition for @xmath32 , these can be written as [ flux_cons ] 0=_(^2 k^ ) = _ ( ^2 k^ ) , implying that @xmath42 . therefore , we find @xmath43 , leading to ^2=_0 ^ 2 = _ 0 ^ 2 . in the limit @xmath44 corresponding to photons in radial motion the flux simplifies as ^2=_0 ^ 2 . the photon motion in the symmetry plane has been investigated by @xcite through the analysis of the associated" +"the dimension 2 gluon condensate @xmath0 in pure yang - mills theory has been proposed in @xcite , and it has been investigated in different ways since then @xcite . in @xcite an analytical framework for studying this condensate has been developed , based on work carried out in the gross - neveu model @xcite . different problems had to be overcome . first of all there is the gauge invariance of this condensate . in order to make the operator @xmath1 gauge invariant , one can take the minimum of its integral over the gauge orbit . since @xmath2 , with @xmath3 , is positive , this minimum will always exist . in a general gauge , however , the minimum is a highly nonlocal and thus hard to handle expression of the gauge field . a minimum is however reached in the landau gauge ( @xmath4 ) , though , so that working in this gauge reduces the operator to a local expression . secondly adding a source @xmath5 , coupled to @xmath1 , makes the theory nonrenormalizable at the quantum level . to solve this , a term quadratic in the source must be added , which in turn spoils the energy interpretation of the effective action . one way around this is to perform the legendre inversion , but this is rather cumbersome , especially so with a general , spacetime dependent source . one can also use a hubbard - stratonovich transform , which introduces an auxiliary field ( whose interpretation is just the condensate ) and eliminates the term quadratic in the source . details can be found in @xcite . the result was that the yang - mills vacuum favors a finite value for the expectation value of @xmath1 . the precise renormalization details of the procedure proposed in @xcite were given in @xcite . recently , chernodub and ilgenfritz @xcite have considered the asymmetry in the dimension two condensate . they performed lattice simulations , computing the expectation value of the electric - magnetic asymmetry in landau gauge , which they defined as @xmath6 at zero temperature , this quantity must of course be zero due to lorentz invariance . necessarily it can not diverge as divergences at finite @xmath7 are the same as for @xmath8 , hence this asymmetry is in principle finite and can be computed without renormalization , for all temperatures . a first remark concerns the visibility of the ( de)confinement phase transition in the value of the asymmetry@xcite . at temperatures lower than the critical one , the asymmetry goes from zero at zero temperature to a positive value , which reaches a maximum at the critical temperature . at higher temperatures , the asymmetry decreases and becomes negative when @xmath9 . the two transition points the phase transition temperature and the symmetric point where the asymmetry goes through zero divide the temperature range in three regions . these seem to coincide with those associated with the condensed , liquid , and gaseous states of the magnetic monopoles , whose dynamics are closely related to confinement and deconfinement ( see , for example , @xcite ) . at yet higher temperatures , one would expect the perturbative behavior to kick in , which goes like @xmath10 at lowest order . however , lattice artifacts prohibit lattice computations at sufficiently high temperatures to see this @xcite . at low temperatures , from thermodynamical arguments one would expect an exponential fall - off with the lowest glueball mass in the exponent , @xmath11 . instead , the authors of @xcite found an exponential with a mass @xmath12 significantly smaller than @xmath13 . so far , there is no explanation for this behavior . in @xcite , the authors and collaborators have extended the framework from @xcite to include the asymmetry @xmath14 . in that article , the potential was computed for @xmath8 , and no non - trivial value for the asymmetry was found as is necessary for lorentz invariance . in this paper we extend the computations in order to include finite temperature effects , with the aim of shedding more light on the results of @xcite . in section [ prel ] we give a short review of what was found in @xcite , which is then continued by a computation of the finite temperature effective action in section [ tr ] . in section [ min ] we find and discuss the minima of the potential , the values of the different condensates and their temperature dependence . section [ conc ] concludes the paper . in @xcite the effective action in the presence of a dimension two condensate and of an asymmetry was computed . since the starting point for the calculations when @xmath15 are identical , we shortly review the steps taken in @xcite . the starting point to compute the effective potential is the following lagrangian density : @xmath16 where the following couplings have been introduced : @xmath17 to one - loop order . the vacuum expecation values of the @xmath18 and @xmath19 fields are @xmath20 in order to simplify notations , we set @xmath21 which denote an effective mass and an effective mass matrix . with these notations , the condensates as defined with the conventions of @xcite are @xmath22 where the latin index denotes the space components . with these givens it is possible to compute the effective action for a space - time independent @xmath23 and @xmath24 using the background field formalism . we separate the two fields into a classical part and quantum fluctuations , after which the fluctuations can be integrated out . expanding the resulting path integral over @xmath25 to one - loop order gives @xmath26 + \frac{n^2 - 1}2 \operatorname{tr}\ln \left ( -\partial^2\delta_{\mu\nu } + \left(1-\frac1\xi\right)\partial_\mu\partial_\nu + \delta_{\mu\nu } g\sigma ' + m_{\mu\nu}\right ) \;,\ ] ] where the limit @xmath27 is implied , as we work in the landau gauge . as we are interested in the asymmetry , we parametrize the mass matrix as @xmath28 i.e. we preserve rotational invariance in the spatial part . with this form , the @xmath29 in the effective potential can be split into different parts , and in the limit @xmath27 we get @xmath30 + \frac{n^2 - 1}2\operatorname{tr}\ln ( -\partial^2 ) + \frac{n^2 - 1}2(d-2 ) \operatorname{tr}\ln\left(-\partial^2+m^2-\frac { a}{d-1}\right ) \nonumber \\ & & + \frac{n^2 - 1}2\operatorname{tr}\ln\left(-\partial^2+m^2 + a\left(1-\frac{d}{d-1}\frac{\partial_0 ^ 2}{\partial^2}\right)\right ) \;.\end{aligned}\ ] ] at finite @xmath7 and in euclidean space - time , the spectrum of @xmath31 is discrete the eigenvalues are @xmath32 where @xmath33 are the matsubara frequencies and @xmath34 is the momentum in the spacelike directions . it happens to be convenient to take the second and the last terms of together ( mark that @xmath35 in dimensional regularization does not vanish for finite @xmath7 , but it gives a constant contribution to the energy ) , so that we have to compute the following traces : [ beginnetje ] @xmath36 the sums can be computed using standard techniques . in order to have convergent sums , one first writes ( for concreteness , consider the first sum ) : @xmath37 then the sum can be computed , for example using a formula derived from the product representation for the sine function : @xmath38 where we have taken the logarithm of both sides of the first identity , and subsequently taken the derivative with respect to @xmath39 . applying this to our sum and performing the indefinite integral in @xmath40 , we find @xmath41 where @xmath42 is a constant of integration . by considering the @xmath43 limit , one can show that it must be equal to @xmath44 . this gives the result that @xmath45 this can be split into the @xmath8 contribution and a finite temperature correction : @xmath46 where we have set @xmath47 in the temperature correction . the second expression can be computed in an analogous way , except that the numerator in the sum is a fourth - order polynomial , and it is thus necessary to split the fraction in partial fractions . we find the temperature correction to the trace to be equal to @xmath48 where we have used the short - hand notations @xmath49 and @xmath50 . from @xcite we already know the zero - temperature effective potential . if we add the temperature correction found above , we can start the work of searching for minima . as the expressions involved are pretty much unhandleable , we use two strategies : expanding in series gives some analytical insight in the low- and high-@xmath7 behavior , and numerical minimization gives a global view of the temperature dependence . for the numerical part , we have used @xmath51 , the value of @xmath52 in the non - perturbative minimum at zero temperature@xcite , and @xmath53 . it is possible to have @xmath54 shift as @xmath52 gets modified at finite temperature ; this , however , does not significantly change the results . plotting and visually inspecting the potential reveals only one minimum , which coincides with the already known non - perturbative minimum at @xmath8 . one would expect the zero - temperature perturbative solution to become a saddle - point of the potential at finite @xmath7 , but it turns out that this saddle - point can only be found from @xmath55 onwards . for lower temperatures it seems that the saddle - point is located in a region of the parameter space where the effective potential has an imaginary part . for slightly higher temperatures , the saddle - point and the non - perturbative minimum merge and from a temperature of @xmath56 onwards no solutions to the gap equation can be found anymore . we will say more about this in paragraph [ hoget ] . the values of the condensates in the non - perturbative minimum are plotted in figure [ eerstefiguur ] . in this figure we have used the sign and prefactor conventions of @xcite instead of those from @xcite , which means that the value of @xmath0 , being the opposite of @xmath18 , is negative . we see that the absolute value of @xmath0 is slightly lowered by raising the temperature . the asymmetry is positive and rising , just as was found on the lattice in @xcite . our value for the asymmetry seems to be slightly lower , but as we have only done a one - loop calculation , one can not expect the results to have very high accuracy . condensate ( full line ) and the asymmetry @xmath14 ( dashed line ) as functions of the temperature , in units @xmath57 . [ eerstefiguur],width=264 ] in figure [ elem ] the values of the electric part and the magnetic part are plotted separately . at @xmath8 both are , naturally , equal . when increasing the temperature , the electric component goes up , while the magnetic component remains approximately constant . this is also what has been found on the lattice@xcite . similar conclusions for correlations in the gluon condensate were also found in @xcite . condensate as function of the temperature . ( the magnetic component has been divided by three to be able to compare with the electric component . ) [ elem],width=264 ] analytically , the limit @xmath58 can be considered . in order to find the dominant behavior , we proceed as follows : first , the exponentials in the integrals are small for small @xmath7 , meaning that @xmath59 . then , we expand the square roots for small @xmath60 . the expansion of the square root will only be valid up to a certain value of @xmath60 , but this is still a legitimate step as the greater values of @xmath60 hardly contribute due to exponential suppression . in the expansion we only keep the terms up to the first non - trivial order of @xmath60 ," +"the rsp game @xcite is a game where players take their move simultaneously , each choosing a hand from the rock ( r ) , the scissors ( s ) and the paper ( p ) . the cyclic strength relation of the three hands determines the win and the loss ; the rock crushes the scissors , the scissors cut the paper and the paper wraps up the rock . the cyclic competition of the rsp game can mimic various relations in reality , particularly in the population dynamics ; _ e.g. _ a colony of three competing mutations of _ e. coli _ @xcite and a three - morph mating system of a lizard @xcite . the present study proposes a model of the rsp game on lattices . each player on a lattice point chooses the next hand from the hand of the neighboring player with the maximum point . ( we refer to such a player as a copy player . ) we found interesting spatial patterns , such as vortices and sinks , appearing particularly on the triangular lattice . the spatial pattern with vortices and sinks appears as a coexisting steady state on the triangular lattice . as far as we know , the previous studies considered the rsp game either on the square lattice @xcite or on various networks @xcite . it is , however , easy to imagine that triangles appear in the population dynamics in reality , _ e.g. _ clusters in complex networks . it is also known that elementary properties can be very different in many - body systems on non - bipartite lattices and on bipartite lattices . the vortex pattern that we observe in the present study is , in fact , due to the frustration of the triangular lattice ( fig . [ fig1 ] ) , a three - sided situation where each of the three players around a triangle chooses the rock , the scissors and the paper , respectively . ( hereafter , we refer to the three hands simply as the hands 2 , 1 and 0 , respectively . ) the existence of vortices was pointed out by some studies in the past @xcite . we here stress the importance of the frustration as the cause of the stationary vortex pattern . we show that the stationary vortex pattern does not appear on the square lattice nor on the honeycomb lattice . the paper is organized as follows . in sec . [ sec2 ] , we introduce the new model and discuss its elementary properties . we show that pairs of vortices and sinks can appear as spatial patterns . we also argue that players close a vortex core scores a high point while players close to a sink scores a low point . we report the results of our simulation on the triangular lattice in sec . [ sec3 ] and on the square and honeycomb lattices in sec . we confirm that the spatial pattern with vortices and sinks is stationary on the triangular lattice , while it is not on the square nor honeycomb lattices . in sec . [ sec5 ] , we introduce a random player , who chooses its hand randomly . we show that a random player can be a source in the spatial pattern . we propose a model where players residing on lattice points repeatedly play the rsp game with the nearest neighbors . we hereafter consider the triangular lattice , the square lattice and the honeycomb lattice , with an emphasis on the triangular lattice , whose frustration generates stationary vortices in the course of the rsp game . all players on the lattice points make their moves all at once , which constitutes one time step . a move is either 0 , 1 or 2 . the hand 1 wins over the hand 0 , the hand 2 wins over the hand 1 , and the hand 0 wins over the hand 2 . a win , a draw or a loss are determined between each pair of the nearest neighbors of the lattice . each player scores one point for a win , zero point for a draw and minus one point for a loss . hence , a player can score @xmath0 points at most and minus @xmath0 points at least in each time step , where @xmath0 is the number of the nearest neighbors on the lattice ( @xmath1 for the triangular lattice , @xmath2 for the square lattice and @xmath3 for the honeycomb lattice ) . this is a zero - sum game ; that is , the sum of the scores of all the players is always zero . particularly on the triangular lattice , we define the frustration and its sign ( fig . [ fig1 ] ) . we refer as a positive frustration to the situation where the hands 2 , 1 , and 0 appear in this order when we circle around a triangle counterclockwise . on the other hand , a negative frustration is the situation where the hands 0 , 1 , and 2 appear in this order when we circle around a triangle counterclockwise . we will argue in the next subsection that a positive frustration generates a counterclockwise vortex , whereas a negative frustration generates a clockwise vortex . all the players choose their hands at random in the initial time step with an equal probability . each player adopts the copy strategy or the random strategy afterwards . the copy strategy is to choose a hand of the player who , of all the nearest neighbors and the player itself , marked the highest score in the last time step . we refer to a player adopting the copy strategy as a copy player hereafter . if there are more than a player of the highest score with different hands , a copy player chooses a hand from their hands randomly . the random strategy is to choose a hand at random . we refer to a player adopting the random strategy as a random player . in the present study , we consider only the case where each player is either a copy player or a random player all through the game . we mostly consider copy players hereafter . we show that copy players on the triangular lattice exhibit vortex structure . in sec . [ sec5 ] , we discuss an impact of random players on the structure as impurities . before showing the simulation results , let us argue that two spatial patterns typically appear . one is a vortex and the other is a sink . they are logical consequences of the combination of the rsp game and the copy strategy . note first that copy players tend to form domains of the same hands . a copy player well inside a domain of , say , the hand 0 , will keep the hand 0 in the next time step because all its neighbors are of the hand 0 and their scores are all zero ; hence the bulk of the domain is stable . copy players on the boundary of a domain , on the other hand , may change their hands in the next time step , and hence the boundary moves . let us argue how the boundary moves in the following two cases . the three domains of the hands 0 , 1 and 2 can have either the topology of fig . [ fig2 ] ( a ) or ( b ) . ( a ) ( b ) + ( c ) in the topology of fig . [ fig2 ] ( a ) , there is a negative frustration around the point a and a positive frustration around the point b. a copy player of , say , the hand 0 , located just outside the domain of the hand 1 , tends to choose the hand 1 in the next time step because the neighbors with the hand 1 get high scores . thus the boundary between the domains of the hand 0 and the hand 1 moves onto the the domain of the hand 0 , so that the domain of the hand 1 expands . likewise , the boundary between the domains of the hand 1 and the hand 2 moves onto the domain of the hand 1 and the boundary between the domains of the hand 2 and the hand 0 moves on to the domain of the hand 2 . hence the boundaries rotate clockwise around the negative frustration at the point a and counterclockwise around the positive frustration at the point b. we will indeed show below in section [ sec3 - 2 ] that the boundaries take a configuration schematically illustrated in fig . [ fig2 ] ( c ) . that is , the topology of fig . [ fig2 ] ( a ) generates a pair of vortices of moving boundaries . ( a similar argument for a different model can be found in refs . @xcite . ) we refer to the counterclockwise vortex as a positive vortex and the clockwise vortex as a negative vortex . in short , a positive frustration of a configuration generates a positive vortex of moving boundaries and a negative frustration generates a negative vortex . in the topology of fig . [ fig2 ] ( b ) , on the other hand , the circular boundaries shrink toward the center ; the players with the hand 0 just inside the boundary mimic the players with the hand 1 just outside the boundary . the central domain of the hand 0 collapses eventually . then the domain of the hand 1 becomes the central domain and will collapse after a while . thus the topology of fig . [ fig2 ] ( b ) generates a sink . finally , a source does not appear when there are only copy players , because a new domain is never generated inside a domain . it is spontaneously generated only when some players adopt strategies other than the copy strategy . specifically , a random player can be a source as is shown in sec . [ sec5 ] . we here argue that the scores of the players near a vortex core are high , while those near a sink are low . both in fig . [ fig2 ] ( b ) and ( c ) , the boundaries are not straight . near the vortex cores in fig . [ fig2 ] ( c ) , the boundary is convex from the viewpoint of the winners ( the hand 2 in fig . [ fig3 ] ( a ) ) and concave from the viewpoint of the losers ( the hand 1 fig . [ fig3 ] ( a ) ) . near the sink in fig . [ fig2 ] ( b ) , on the other hand , the boundary is convex from the viewpoint of the losers ( the hand 1 in fig . [ fig3 ] ( b ) ) and concave from the viewpoint of the winners ( the hand 2 in fig . [ fig3 ] ( b ) ) . ( c ) and ( b ) : ( a ) a bend around the frustration a of fig . [ fig2 ] ( c ) ; ( b ) a bend around the sink of fig . [ fig2 ] ( b ) . ( c ) a simple case of two subsequent steps.,title=""fig : "" ] ( a ) ( c ) and ( b ) : ( a ) a bend around the frustration a of fig . [ fig2 ] ( c ) ; ( b ) a bend around the sink of" +"the itinerant ferromagnetism has been one of the most fundamental problems in condensed matter physics , and we are still some way from a full understanding of the problem . for the ferromagnetism in the hubbard model , a simplest possible model for interacting itinerant electrons , there are various studies , which are pioneered by gutzwiller@xcite , hubbard@xcite , and kanamori@xcite . for the hubbard model on finite - size systems , it recently extended to rigorous proofs that spin - independent coulomb interaction can indeed result in fully - polarized ferromagnetic ground states without degeneracy for appropriate conditions and/or appropriate models@xcite . apart from these , there is a body of numerical studies for finite systems , where various authors have shown that finite hubbard models with appropriate band fillings and boundary conditions have fully - polarized ferromagnetic ground states@xcite . on the other hand , for infinite systems , the itinerant nature of electrons makes the problem interesting and subtle . the most important reason is the existence of the spiral - spin(sp ) state , a _ spin - singlet _ state that has the spin - spin correlation length as large as the sample size@xcite , which is known to accompany the fully - polarized ferromagnetic(f ) state in various finite - size itinerant models . by accompanying we mean sp and f states are close in energy in finite systems , where the ground state changes between them when the boundary condition is twisted . the sp state does not seem to be an accident of the hubbard model , since sp states are found not only in electron systems with strong charge - charge interactions , but also in those with spin - dependent interactions such as double - exchange@xcite or kondo lattice@xcite models . so we believe that it is a general feature of strongly correlated systems for the f state to be accompanied by the sp state . it is rather surprising , since the latter has the total @xmath0 while the former has @xmath1 . thus it is desirable to resolve this question to understand the ferromagnetism in itinerant systems in the thermodynamic limit . thus the problem we have to clarify is the relation between the sp and f states in the thermodynamic limit ( do those states degenerate or coalesce , etc ) , which we address in this paper . first , we show that the sp state is eligible as the ground state ( i.e. , degenerate with the f state in energy in the thermodynamic limit ) when the f state is the ground state . we check this for one - dimensional ( 1d ) @xmath2-@xmath3 hubbard model with infinitely large coulomb interaction taken as a typical example and calculate the energies of the sp and f states as a function of the inverse system size with the density matrix renormalization group ( dmrg ) method . next , we discuss whether the symmetry of the sp state is broken in the thermodynamic limit , following the arguments by koma and tasaki@xcite on symmetry breaking and finite - size effects in quantum many - body systems on a lattice . we show that ( i ) the sp state possesses a kind of order parameter , ( ii ) although the state does not break the global su(2 ) symmetry in the finite system , it does so in the thermodynamic limit by making a linear combination of other states that are degenerate in that limit . we have studied excitation spectrum of the sp state by calculating one - particle spectral function , dynamical spin and charge susceptibilities for the sp state in various finite - size models , including 1d @xmath2-@xmath3 hubbard model , tasaki s flat band model , and hubbard ladder . we have found that the excitation spectrum of these two states in the finite size system are almost identical . the present results suggest that we should regard the sp state as identical with the f state although they have the total spins in the opposite extremes ( @xmath0 for the sp state , @xmath1 for f ) in the finite size system . these properties can be exploited to determine the magnetic phase diagram from the calculation of the total spin of the finite - size system in an unambiguous fashion . otherwise we have to worry about not only the total spin , but the spin - spin correlation to identify sp states in determining the phase diagram . the paper is organized as follows . in sec . ii , we first confirm that the sp and f states have degenerate energy for @xmath4 : sample size ) in that the energy per site is identical between them . dmrg is used to calculate the difference in the total energy , @xmath5 , between the sp state and the f state as a function of system size @xmath6 for the @xmath2-@xmath3 hubbard model with @xmath7 as a typical example . the extrapolate @xmath8 is always finite ( or zero depending on the boundary condition even in the thermodynamic limit ) , i.e. , @xmath9 per site does indeed vanish . it implies that when the f state is the ground state , the sp state is also eligible as the ground state if these states are translation invariant . then we move on to the discussion on symmetry breaking of the sp state along the koma - tasaki s argument . in sec . iii , we calculate the single - particle spectral function and dynamical spin and charge susceptibilities for various models . our results suggest that the sp state and the f state are identical state in the thermodynamic limit . in sec . iv , we take an appropriate combination of the boundary condition and the number of electrons to make the sp state higher in energy than the sf state , and the phase diagram for the one - dimensional @xmath2-@xmath3 hubbard model , tasaki model , and 2-leg hubbard ladder model is obtained with exact diagonalization of small systems . we have found that the phase boundaries rapidly converge to those for larger systems obtained with dmrg . we may expect that it can be exploited to the determination of the phase diagram of 2d or higher dimensional systems . a summary of the present study is given in sec . 1d @xmath2-@xmath3 hubbard model is one of the simplest models that is thought to exhibit ferromagnetism for sufficiently strong electron - electron interaction . mller - hartmann suggested that in the low - density limit the ground state of @xmath2-@xmath3 hubbard model is ferromagnetic@xcite . daul and noack@xcite have carried out highly accurate dmrg calculation to conclude that there is an extensive ferromagnetic phase in the phase diagram . since the @xmath2-@xmath3 hubbard model is numerically tractable , we study the energy difference of the sp and f states by taking this model with @xmath7 as an example . the @xmath2-@xmath3 hubbard hamiltonian is given by @xmath10 where @xmath11 creates an electron at site @xmath12 with spin @xmath13 , @xmath2 is the nearest - neighbor hopping , and @xmath3 the next nearest - neighbor hopping , @xmath14 the hubbard repulsion , and @xmath15 . in this section we take @xmath16 , @xmath17 and @xmath7 . as we can check by a simple exact diagonalization , the ground state of the system has always @xmath18 for any value of @xmath14 at least for system sizes up to 12 sites when a periodic boundary condition(pbc ) is adopted . this is to be contrasted with the phase diagram obtained by daul and noack with an open boundary condition(obc ) , in which a wide ferromagnetic region is found for @xmath17 and large @xmath14 . let us first confirm that the sp and f states are degenerate in the sense that their difference in the total energy behaves as @xmath19 i.e. , the energy per site vanishes , @xmath20 where @xmath21 is the lowest energy within the @xmath18 sector , namely the energy of the sp state . we take obc , because the dmrg becomes most accurate for this condition . as daul and noack showed@xcite , the ground state of @xmath2-@xmath3 hubbard model is ferromagnetic for @xmath17 and @xmath22 in obc at least up to 50 sites . to estimate @xmath9 , we must calculate the energy of the ground state of the @xmath18 sector which has higher energy than the ferromagnetic ground state . therefore , we add the term @xmath23 to the original hamiltonian ( [ eqnttj ] ) to selectively shift the states with higher total spin to higher energies by turning on @xmath24 , while conserving the su(2 ) symmetry . here we set @xmath25 . in fig . [ dmrgspin ] , we show the spin correlation function , @xmath26 ( @xmath27 ) of the spin singlet state for @xmath28 sites , @xmath29 as an example . we can see that the spin correlation wave length is as large as the system size . namely , the spin singlet state is the sp state . since dmrg is a variational procedure , the energy of the sp state is an upper bound , while the energy of the f state is calculated exactly because the f state does not feel the on - site coulomb interaction . hence we overestimate @xmath9 . to minimize this overestimation , we must calculate the energy of the sp state as accurately as possible . this is the reason why we have set @xmath7 and @xmath17 . namely , the exclusion of double occupancies reduces the hilbert space drastically , while a small value of @xmath30 reduces the truncation error . using the finite - size algorithm in dmrg , we calculated up to @xmath31 for the density of electrons @xmath32 , sweeping the system about 20 times to improve the wave function . we store the density matrix at each step to construct good initial vector for each super - block diagonalization . we have kept up to @xmath33 states per block at each step , where the convergence is checked by comparing the results for @xmath34 . the truncation error is smaller than @xmath35 , which is small enough to enable us to extrapolate @xmath8 . in fig . [ dmrgene](solid line ) , we show the results for @xmath5 as a function of inverse system size @xmath36 for electron density @xmath32 . we can see that all the points for @xmath37 fall upon a linear dependence on @xmath36 , from which we can extract @xmath8 . for all the densities studied , @xmath8 indeed remains finite ( @xmath38 ) . in order to check whether the result is not an accident for @xmath7 , we can introduce the effect of large but finite @xmath14 as an ( antiferromagnetic ) exchange interaction @xmath39 , @xmath40 added to the @xmath7 @xmath2-@xmath3 hubbard model . here @xmath41 is the spin operator , where @xmath42 is the pauli matrices and @xmath43 denotes the gutzwiller projection operator . in fig . [ dmrgene ] the results for @xmath44 are superposed . we can see that @xmath9 does not change drastically even if we introduce the effect of finite @xmath14 . this kind of @xmath9 may depend on the boundary condition , which can be indeed the case with finite systems . for instance , kusakabe and aoki@xcite have shown for a finite two - dimensional hubbard model that nagaoka s ferromagnetic state ( one hole in the half - filled band with @xmath7 ) alternate with an sp state as the boundary condition is changed from periodic to anti - periodic . in other words a level crossing takes place between the two states as an aharonov - bohm magnetic flux is introduced to twist the boundary condition . such a" +"the large hadron collider ( lhc ) at cern will open a new frontier in particle physics due to its higher collision energy and luminosity as compared to the existing accelerators . the general - purpose atlas and cms experiments at the lhc will employ precision tracking , calorimetry and muon measurements over a large solid angle to identify and measure electrons , muons , photons , jets and missing energy accurately . therefore , they have great physics potential in discovering many possible new particles . among them are the standard model ( sm ) higgs boson , supersymmetric ( susy ) and other new particles beyond the sm . all of them can have masses in a very large range up to the tev scale . the significance calculation in searching for and observation of a physics signal with known location and shape is no longer valid when either the location or the shape of the signal is unknown . this will be the case for many of the possible new physics signals at the lhc . in section 2 , we give a short review of the significance calculation and current analysis strategy in high energy physics ( hep ) and at the lhc . using a signal with known shape but unknown location as an example , we discuss in detail in section 3 the problems of the current significance calculation . we then describe general procedures for significance calculation and comparing different search schemes in section 4 . in section 5 , we describe a new analysis method and compare it with the current `` sliding - window '' approaches following these procedures . detailed comparison results are also given in this section . summary and discussion are given in section 6 . in this note we limit ourselves to the significance calculation and analysis method used in searching for an individual decay mode of new physics signals . in the field of hep , a common strategy to detect a physics signal is to search for an excess of events in a certain region of a kinematic observable . the observation probability is given by poisson statistics : @xmath0 where @xmath1 is the number of the expected events to be observed in the region , and @xmath2 is the number of the observed events in this region . when @xmath1 is large ( over 25 , for instance ) , the significance of an observation can be approximated well by @xmath3 of gaussian statistics , where @xmath4 . in hep , the significance of an observation is defined by the probability that such an observation is due to statistical fluctuation of background events . when we claim an observation has a significance of @xmath5 @xcite , the common criterion for a hep discovery , the probability that the claimed discovery is due to statistical fluctuation of background events , known as the type i error rate in statistics , needs to be less than @xmath6 . the background fluctuation probabilities which define the 1@xmath7 to 5@xmath7 significances in hep are shown in table [ tab : sig - def ] . .the definition of significance in hep and the corresponding background statistical fluctuation probabilities . [ cols=""^,^,^,^,^,^"",options=""header "" , ] [ result30 ] the work and results for 5 , 10 , 15 , 20 , 25 , 30 and 35 signal events embedded with gaussian means at 42.00 , 46.00 , 48.00 , 49.00 , 49.50 , 49.75 , 49.90 and 50.00 are shown in ref . the results for 10 , 20 , and 30 signal events embedded are shown in tables [ result10 ] , [ result20 ] and [ result30 ] . we can see that the number of signal embedded experiments successfully found with a certain significance is much lower than what expected from @xmath3 calculations . this is a price we have to pay for not knowing the exact location of the signal . furthermore , for the `` sliding - window '' method , the sensitivity strongly depends on the exact location of the embedded signal . if the step size is greater than 1 , the embedded signals are totally missed for the worst - case scenarios . for step size of 1 or less , there are still significant differences in the sensitivities between the best - case and worse - case scenarios , depends on the step size of the `` sliding - window '' used to scan the kinematic range . in comparison , the new analysis method is independent of the exact location of the gaussian mean of the embedded signal events . this is because the new method scans the entire parameter space for the best fit to the entire experiment . the maximum @xmath3 from `` sliding - window '' approaches with step sizes of 16 , 4 , 1 , and 0.1 for the best - case scenario mc experiments each with 20 signal events embedded are shown in figure [ fig : sw-20-best ] . similarly , the maximum @xmath3 from `` sliding - window '' approaches with step sizes of 16 , 4 , 1 , and 0.1 for the worst - case scenario mc experiments each with 20 signal events embedded are shown in figure [ fig : sw-20-worst ] . the maximum likelihood output of the best fits for mc experiments with 5 , 10 , 20 and 30 signal embedded are shown in figure [ fig : ml - signal ] . compared to `` sliding - window '' approaches with a step size small enough not to miss the worst - case scenarios , the sensitivity of the new analysis method is significantly higher . this means that the new analysis approach is a significantly better and more sensitive scheme to search for new physics signals at the lhc than the current `` sliding - window '' method . = 0.90 = 0.90 the analysis method described above performs a scan of the entire parameter space using unbinned maximum likelihood fits at every small interval of the parameter space . it is very cpu - intensive . the 13.45 million background - only and 630,000 signal embedded mc experiments were generated and analyzed over several months with about 10 dual - cpu servers . we have examined the significance calculation and analysis methods in searching for an individual decay mode of a new physics signal at the lhc . unlike the search for a physics signal with known location and shape , the significance calculation for new physics signals with unknown location or shape strongly depends on the details of the search scheme and the situation it applies to . using a signal with known shape but unknown location as an example , we have demonstrated that the significance calculation using the current `` sliding - window '' method at the lhc is over - estimated . this is because we search for an excess of events over multiple narrow windows , but the significance is still calculated according to an individual narrow window . the significance and sensitivity of the `` sliding - window '' method strongly depends on the specifics of the method and the situation it applies to , e.g. the step size of the `` sliding - window '' used to scan the available kinematic range , the total available kinematic range to search for the new physics signal , and the exact location of the new physics signal , etc . we describe general procedures for significance calculation and comparing different search schemes . we have applied the procedures and compared the current `` sliding - window '' approaches with a new analysis method . the proposed new analysis method uses maximum likelihood fits with floating parameters and scans the parameter space for the best fit to the entire sample . we find the results of the new analysis method is independent of the location of the new physics signal and significantly more sensitive in searching for new physics signal than the current `` sliding - window '' approaches . while the lhc experiments have great potential in discovering many possible new physics signals , we need to be extremely careful in evaluating the significance of an observation from the real lhc data . because possible new physics can show up in many kinematic observables , over a very large kinematic range , the fluctuation probability of background events will be much higher . for individual decay modes of new physics signals , the expected significances in observing the new physics signal will be much smaller than current expectations @xcite . combining independent decay modes of the same new physics signal will be essential to establish the discovery of the new physics signal . significant observations of the same new particle in independent decay modes at consistent locations will be the most effective way to establish the discovery of this new particle . careful evaluation of the observation significance in each individual decay mode following the general procedures described in this paper is the starting point , before we can evaluate the significance of the observations of independent decay modes . the authors would like to thank the members of the smu hep group for their encouragements and useful discussions . this work is supported by the u.s . department of energy under grant number de - fg02 - 04er41299 ." +"long - range forces , namely gravitation and electromagnetic interactions , are difficult to treat exactly in many - particle systems . in condensed matter , biological and solid state physics , there is considerable interest in the simulation of charged and polar molecules embedded in a slab in which the particles are replicated periodically in two directions . the applications range widely to include soap bubbles , cell membranes and electrochemistry . surprisingly ewald and other rapidly convergent methods for computing long - range interactions in infinitely periodic systems are computationally more demanding when the system is periodic in only one or two of the three spatial dimensions because of the breaking of spatial symmetry . several `` two - dimensional ewald '' ( * ew2d * ) methods have already been proposed@xcite . the most successful is that introduced by parry@xcite and others@xcite . this method can be used to obtain accurate results but is limited to small systems ( i.e. @xmath1 to @xmath2 charges ) . this springs from the fact that the pair separations , @xmath3 , are no longer separable in the fourier summation because of the necessary decoupling of the aperiodic @xmath4 component from the periodic @xmath5 and @xmath6 components . therefore it appears that the complexity ( scaling of time with number of charges ) of this method can be no better than quadratic . also the one dimensional ewald method@xcite suffers from the same problem . a promising alternative to ewald summation is possible using a convergence - factor technique@xcite . the basic coulomb pair interaction is multiplied by one with the factor @xmath7 . it is crucial to prove that the limit can be taken outside of the summation and now the modified potential is more readily susceptible to analysis . in a recent study,@xcite arnold and holm derive a two - dimensional version of this method with complexity @xmath8 along with accurate error formulas . this method is particularly attractive when extremely high accuracy is desired . we will use this method , abbreviated as * mmm2d * and the * ew2d * algorithm mentioned above as reference methods . one idea , used several times to study water interfaces , introduces a spatial constraint within the simulation cell . if the box has dimensions @xmath9 , the particles may have @xmath4-coordinates on @xmath10 , while the space within @xmath11 ( the gap size ) remains empty @xcite . the primary cell is , as usual , replicated in all three directions periodically . the effect of this is to create a `` primary layer '' and an empty layer followed by an infinite array of intercalated image and empty layers . figure [ periodicity ] summarizes the essential geometrical considerations in this problem . while this idea seems trivially to be correct , it has one flaw . the flaw can be realized by attempting to reproduce the results of an * ew2d * calculation using a three dimensional ewald summation ( * ew3d * ) as just described . one will find that the results always differ by a dipole - moment dependent constant . this fact , although at first thought to be merely a slow convergence issue , was noticed by spohr @xcite . the * ew3d * formula contains a shape dependent dipole - term whose origin was mathematically proven in the 1980 s @xcite , that reflects the naturally chosen spherical order of summation in the conditionally convergent coulomb sum . for the case of layers , however , it is necessary to use a _ slab - wise summation order_. this was realized by yeh and berkowitz@xcite , who applied a theory due to e. r. smith @xcite for infinite crystals of various shapes in order to obtain the correct dipole term for a slab - wise summation order . another complication arises , if the periodic supersystem is surrounded by some medium with a different dielectric constant . this medium has a polarizing effect on the particles in the simulation cell no matter how large the supersystem is . for the remainder of this paper we consider only the simple case of zero contrast for which the dielectric constant is the same inside and outside the supersytem . this is often referred to as the vacuum boundary condition . one of the advantages of using this method from a practical point of view is that any standard ewald program may be used with only minor modification . it is easy to show numerically that the use of this new dipole term and sufficient spacing ( @xmath12 ) , yields the same result as two - dimensional `` brute force '' , * mmm2d * and * ew2d * summation methods . as explained in a previous paper , referred to here as `` paper i''@xcite , errors introduced due to the image layer effects decay exponentially with the size of the gap . this method is sometimes referred to as a corrected three - dimensional ewald sum ( * ew3dc*)@xcite . like the original ewald method it has a complexity of @xmath13 and the equations can be discretized onto a mesh yielding an @xmath14 complexity . in paper i @xcite , we derived an analytic electrostatic layer correction term , called * elc*-term , that subtracts the interactions of the unwanted slab replicas . this term can be evaluated linearly in @xmath15 , and has full error control . the use of the * elc * term and the change of summation order , shortly called the * elc * method , enables us to adapt any 3d summation method , such as the non - ewald convergence - factor@xcite and multipole expansion@xcite methods , to slab geometries . the latter of these , though in possession of a slightly better scaling , has such a considerable amount of overhead that it is useful only for much larger systems than normally used@xcite . the abbreviations and complexities of some of the two - dimensional methods available at present are summarized in table [ tab1 ] , where the ending lc always denotes the use of the * elc * method . in this terminology the * ew3d * algorithm plus the * elc * method is called * ew3dlc * and so on . .methods for slab geometry . [ cols=""^,^,^"",options=""header "" , ] [ tab2 ] the results of this analysis are displayed in table [ tab2 ] . under these conditions , the * ew3dlc * method is only slightly ( 30% ) faster . the reason is that much of the work in these calculations is performed in the real - space and therefore the extra amount of reciprocal - space required by * ew3dc * due to the enlarged gap is not a major issue . in fact it is almost compensated by the time used by layer correction term . for larger @xmath15 , * ew3dlc * should become faster than * ew3dc * since the reciprocal - space time becomes much longer than the layer correction time . the same is true about higher accuracy conditions as is observable from the analytical error estimates ( eqs . [ real_error]-[fourier_error ] ) . moreover , in a mesh implementation , the same comparison should yield a more substantial advantage to the layer correction since more of the computational effort is expended in reciprocal space . we have presented and tested a method with broad applicability and low computational cost for computing the electrostatic forces or energy of a cell of charges with two - dimensional periodicity . this method has a complexity that is virtually linear when applied to a mesh , so that only minor further improvements in computation time can be attempted through a reduction of computational overhead . the algorithm differs from * ew3dc * only by the effort to program the * elc*-term , but once this is done the errors are easier to control and there is a greater degree of freedom in choosing the box edges . this makes it easy to apply to cubic versions of the * p3 m * algorithm ( which was one of our initial motivations ) . for larger systems and better accuracy as may be required in monte carlo and some molecular dynamics simulations the method should be considerably faster than * ew3dc*. it is interesting to estimate the largest system tractable with modern computing . the * p3 m * algorithm can be optimized to be at least twice as fast as the version presented here , so an @xmath16 calculation could be carried out in approximately . 2 seconds . a 100-node parallel computer with a 90% scale factor could handle a system of 0.45 million particles in 1 second which is sufficient for a many molecular dynamics and monte carlo simulations . finally we can draw attention to several issues suitable for further research . most importantly we have not treated the case of dissimilar dielectric materials at the slab surfaces . because of the symmetry of the consequent charge reflections there could be a way to handle the problem efficiently within the current framework . another topic is the clarification of the dipole term for slab - wise summation for different dielectric constants at the interface between the periodic supersystem and the surroundings . the authors thank zuowei wang and florian mller - plathe for helpful discussions . financial support from the dfg `` schwerpunkt polyelektrolyte '' is gratefully acknowledged . for quick reference the force and pressure formulas for the layer correction are given here . the layer correction force on particle @xmath17 is @xmath18 , \nonumber \\ & & \sum_{j}q_{i}q_{j}\bigl[\;2\sum_{k_{x},k_{y}>0}\frac{k_{y}\cosh ( k_{\parallel } z_{ij})}{k_{\parallel } ( e^{k_{\parallel } l_{z}}-1)}\cos ( k_{x}x_{ij})\sin ( k_{y}y_{ij})+ \nonumber \\ & & \sum_{k_{y}>0}\frac{\cosh ( k_{y}z_{ij})}{(e^{k_{y}l_{z}}-1)}\sin ( k_{y}y_{ij})\bigr ] , \nonumber \\ & & -\sum_{j}q_{i}q_{j}\bigl[\;2\sum_{k_{x},k_{y}>0}\frac{\sinh ( k_{\parallel } z_{ij})}{(e^{k_{\parallel } l_{z}}-1)}\cos ( k_{x}x_{ij})\cos ( k_{y}y_{ij})+ \nonumber \\ & & \sum_{k_{x}>0}\frac{\sinh ( k_{x}z_{ij})}{(e^{k_{x}l_{z}}-1)}\cos ( k_{x}x_{ij})+\sum_{k_{y}>0}\frac{\sinh ( k_{y}z_{ij})}{(e^{k_{y}l_{z}}-1)}\cos ( k_{y}y_{ij})\bigr]\biggr).\end{aligned}\ ] ] the diagonal components of the pressure tensor can be obtained from the partition function . for example the normal component is @xmath19 . this yields @xmath20 where @xmath21 for one of the parallel components we find @xmath22 \cos ( k_{x}x_{ij})\cos ( k_{y}y_{ij})+ \nonumber \\ \sum_{k_{x}>0 } & & \nu ( k_{x})\cos ( k_{x}x_{ij})+ \nonumber \\ \sum_{k_{y}>0 } & & \frac{1}{k_{y}l_{z}}\frac{\cosh ( k_{y}z_{ij})}{(e^{k_{y}l_{z}}-1)}\cos ( k_{y}y_{ij})\biggr).\end{aligned}\ ] ] obviously this is cumbersome since after decomposing the trigonometric and hyperbolic terms to obtain a formula that can be evaluated linearly in @xmath15 the expanded version will contain over 80 terms . if rapid pressure calculations are not demanded one can omit this term and increase @xmath23 . one third of the trace of this tensor will as usual yield the scalar pressure , @xmath24 . another consideration in obtaining the pressures is the treatment of the dipole term . fortunately , a shear or distortion on the system does not result in a distortion in the shape of the supersystem . this is in contrast to the treatment of standard ewald summation because the spherical summation order requires a complex analysis of the consequences of a distorted sphere.@xcite the summation order of the layer correction is implicitely cylindrical . it probably does not matter whether the summation procedes along the radius of the cylinder first and then along its axis ( as written ) or vice versa . but they may not proceed simultaneously ." +"it is commonly accepted that the present globular cluster ( gc ) population in the milky way represents the survivor of an initially more numerous one , depauperated by many disruptive processes @xcite . + the observational results obtained in the last decade have clearly confirmed the role played by the milky way environment on the gc evolution . up to now , about @xmath2 galactic gcs show evidences of star depletion due to the tides caused by the field of the galaxy . + the first evidence of the existence of tails surrounding gcs were achieved by @xcite . using colour - magnitude selected star counts in a dozen of galactic gcs , these authors showed that in the outer parts the stellar surface density profiles exceeded significantly the prediction of king models , extending also outside the tidal radius . they identified this surrounding material as made up of stars in the act of being tidally stripped from the cluster field and pointed out the importance of defining the large - scale distribution of extra - tidal stars on the sky to obtain constraints and traces for the gc orbits . more recently , other works confirmed and enlarged grillmair et al.s findings @xcite giving evidence of the existence of many gcs surrounded by haloes or tails . for m92 , @xcite found , also , that the extratidal material is not randomly distributed , being the density profile in the tails shallower for bright stars than for fainter ones . + this was the state of the art until the spectacular findings of two tidal tails emanating from the outer part of the palomar 5 globular cluster and covering an arc of 10 degrees on the sky , corresponding to a ( projected ) length of 4 kpc at the distance of the cluster @xcite , obtained in the framework of the sloan digital sky survey ( see also _ http://www.sdss.org_ ) . the stellar mass in the tails of this sparse , low - mass , halo cluster ( with an estimated concentration parameter @xmath3 ) adds up to 1.2 times the mass of stars in the cluster , estimated in the range between @xmath4 and @xmath5 . more recently , @xcite , still using sdss data , have detected a continuation of pal 5 s trailing tidal stream out to almost 19 degrees from the cluster . combining this with the already known southern tail of pal 5 yields a stream some @xmath6 kpc long on the sky . + substantial tidal streams have recently been found associated with another low - mass and low - concentration gc in the sdss area : ngc 5466 . for this cluster @xcite reported giant tails extended for about 1 kpc in length and @xcite , still using sdss data , suggested that a @xmath7 kpc tidal stream of stars , extending from bootes to ursa major , could also be associated with this system . + together with the so - called sagittarius stream @xcite , which emerges from a dwarf galaxy that is currently being accreted by the milky way , palomar 5 and ngc 5466 represent outstanding examples of ongoing tidal erosion of stellar systems in the milky way , being , up to now , also the only two globulars known for which such extended stream - like structures have been detected in the galactic halo . + one of the first numerical investigations of the role played by a galactic tidal field on spherical stellar systems was that of @xcite , who studied the effect of realistic , time - varying tidal fields on the stellar orbits in a star cluster . they numerically integrated the equations of motion of three - bodies in models of spherically symmetric clusters which , in turn , move in eccentric orbits in the field of a model galaxy . one of the main conclusions of this work , which extended previous investigations made by @xcite , was that star clusters rotating in a retrograde sense are more stable in a tidal field than clusters with either direct rotation or no rotation due to the contribution of the coriolis acceleration , acting in the same direction as the gravitational attraction for retrograde motion . + more recent works on weak tidal encounters based on a fokker - planck approach @xcite and self - consistent n - body techniques @xcite confirmed that the interaction with external tidal field , combined with two - body relaxation in the core of the cluster and following replenishment of stars near the tidal radius , causes a flow of stars away from the cluster . the stripped stars remain in the vicinity of the cluster for several orbital periods , migrating either ahead of the cluster or falling behind , giving rise to a slow growth of the tidal tails . + a semi - analytic study of the development of tidal streams in galactic satellites was done by @xcite , who gave estimates for the rate of growth of tidal tails . the effects of a realistic galactic tidal field ( including both bulge , halo and disk ) on gcs were investigated few years later by @xcite . the main findings of the work were the following : stars escaped from the system go to populate two giant tidal tails along the cluster orbit ; these tails present substructures , or clumps , attributed to strong shocks suffered by the cluster , and are preferentially formed by low mass stars . + @xcite performed n - body simulations of gcs orbiting in a two - component galaxy model ( with bulge and halo and no disk ) , using the direct - summation nbody6 code @xcite and focusing their attention , in particular , to the correlation between tidal tail elongation ( described by mean of a position angle , defined as the angle between the direction of the tail and the galactic center direction ) and the cluster orbit . they found that , on circular orbits , tidal tails mantain an almost constant position angle ( @xmath8 ) , while gcs on non circular orbits show a variation of the position angle , according to orbital path and phase . the position angle increases when the cluster heads for perigalacticon . on the other hand , it tends to decreases when the cluster heads for apogalacticon . finally , some authors investigated also the dynamical evolution of some globular clusters in the tidal field of the galaxy . in this context @xcite modelled the disruption of the globular cluster pal 5 by galactic tides . pal 5 is remarkable not only for its extended and massive tidal tails , but also for its very low mass and velocity dispersion . in order to understand these extreme properties , they performed many simulations aiming at reproducing the pal 5 evolution along its orbit across the milky way . they explained the very large size of pal 5 as the result of an expansion following the heating induced by the last strong disk shock about 150 myr ago . the clumpy substructures detected in the tidal tails of pal 5 are not reproduced in their simulations , so that they argued that these overdensities have been probably caused by interaction with galactic substructures , such as giant molecular clouds , spiral arms , and dark matter clumps , which were not condsidered in their modeling . these simulations also predict the destruction of pal 5 at its next disk crossing in about 110 myr , suggesting that many more similar systems have once populated the inner parts of the milky way but have been transformed into debris streams by the galactic tidal field . + in this context , it may be interesting mentioning the recent numerical work devoted to the study of smaller size systems ( open clusters ) in the mw tidal field @xcite , which confirms already known results in the case of the external part of gc tidal tails ) about the alignement of stars of the tidal stream around a common orbit in the external field @xcite . in the above sketched theoretical and observational background , this work which is inserted in a wider study on the dynamics of globular clusters in external tidal fields @xcite is devoted to clarifying the connection among tidal tails and cluster orbit . we will describe and discuss the mechanisms that determines the tails morphology and how they depend on cluster trajectory and orbital phase . + for this purpose , we performed detailed @xmath9body simulations ( with @xmath10 ) of gcs moving in a realistic three - components ( bulge , disk and halo ) milky way potential . + the paper is organized as follows : in sect.[cluster ] the galaxy ( sect.[galaxy ] ) and cluster ( sect.[cluster1 ] ) models adopted are presented , so as the numerical approach used ; in sect.[results ] we deal with the main results of our work , showing the formation and development of tidal tails around the cluster ( sect . [ tails ] ) , giving a qualitative approach for describing the tail morphology ( sect.[qualit ] ) , presenting the numerical procedure adopted to fit tails direction ( sect.[fit ] ) and , finally , discussing the tail - orbit alignement and its dependence on the orbital phase . in sect.[concl ] , all the results are summarized and discussed . the model adopted for the galactic mass distribution is that of @xcite . it consists of a three component system : a spherical central bulge and a flattened disk , both of @xcite form , plus a massive spherical halo . the gravitational potential is time indipendent , axysimmetric and given in an analytical form which is continuous together with its spatial derivatives . + choosing a reference frame where the ( _ x , y _ ) plane coincides with the mw equatorial plane , the three components of the potential have , in cylindrical coordinates , the form : @xmath11^{100}_r,\\\end{aligned}\ ] ] where square brackets indicate the difference of the function evaluated at the 100 kpc and the generic @xmath12 extremes . the parameters in the formulas above are listed in table [ tbl1 ] . the total initial mass of the cluster was chosen @xmath13 m@xmath14 , i.e. a value compatible with masses of galactic globular clusters lying inside 4.5 kpc from the mw center ( see @xcite and @xcite ) . the stellar mass spectrum of our cluster initial model was chosen as a kroupa imf sampled in the range @xmath15 and `` evolved '' ( in the sense of accounting for mass loss on the base of stellar evolution , according to @xcite ) up to @xmath16 gyr ( which corresponds to our assumed cluster age ) . in this interval of time all masses greater than @xmath17 m@xmath18 go into the @xmath19 range . as in @xcite , we sampled this mass function into 12 mass classes , equally spaced in a linear scale , whose space and velocity distribution were evaluated by the adoption of a multimass king distribution @xcite . + obviously , the choice of @xmath10 as total number of cluster stars , together with the given value of @xmath20 and of the above described mass function implied a rescaling of the star masses . finally , to investigate the role played by the degree of cluster concentration , we considered clusters with two different values for the king concentration parameter @xmath21 ( listed in table [ tbl2 ] ) . + the clusters move on the @xmath22 coordinate plane ( the ( @xmath23 ) plane corresponds to the galactic disk ) , along orbits of different eccentricity , defined as @xmath24 being @xmath25 and @xmath26 , respectively , the gc pericentric and apocentric orbital" +"several recent papers have shown that a surprisingly tight correlation exists between the masses of supermassive black holes and the velocity dispersions of the bulges which host them . ferrarese & merritt ( 2000 ) re - analyzed published samples of black hole mass estimates , showing that if the analysis is restricted to 12 galaxies with reliable black hole mass measurements , the correlation is extremely good , with @xmath4 . gebhardt et al . ( 2000a ) report a similar relation with a somewhat shallower slope , @xmath5 , and a scatter of only 0.3 dex , based on a sample of 26 galaxies , including 13 new black hole mass estimates derived using hubble space telescope spectra . in a second paper , gebhardt et al . ( 2000b ) demonstrate that black holes with reverberation mapping mass estimates also fall on the same relation . the tightness of this new correlation greatly increases confidence in the accuracy of the observed black hole mass estimates . it also strengthens theoretical arguments that spheroid formation and the growth of black holes are closely linked ( richstone et al . 1998 ; cattaneo , haehnelt & rees 1999 ; kauffmann & haehnelt 2000 ( kh2000 ) ; monaco , salucci & danese 2000 ; cavaliere & vittorini 2000 ) . cattaneo et al . ( 1999 ) and kh2000 demonstrated that the @xmath6 relation and the scatter reported by kormendy & richstone ( 1995 ) and magorrian et al . ( 1998 ) is well reproduced in phenomenological models of galaxy formation in hierarchical cosmogonies . in this letter , we analyze the relation between black hole mass and bulge velocity dispersion in the kh2000 model . we assume a @xmath7cdm cosmology with @xmath8 , @xmath9 , @xmath10 , @xmath11 throughout . in cold dark matter ( cdm)-like cosmologies , galaxies form in a hierarchy of merging halos ( e.g. white & rees 1978 ; white & frenk 1991 ) . the formation and evolution of galaxies in such a picture has been studied in considerable detail using monte - carlo realizations of the hierarchical growth of structure , which include simple prescriptions to describe gas cooling , star formation and supernova feedback ( see kauffmann et al 1999 ; somerville & primack 1999 ; cole et al 2000 for a selection of recent results ) . below we summarize the main features of the model described by kh2000 , who constructed a unified model for the formation and evolution of galaxies , supermassive black holes and qsos . in their model , the quiescent accretion of cooling gas from a halo results in the formation of a disk . the fraction of cold gas in the disk that forms stars over one dynamical time is assumed to scale with redshift as @xmath12 . this assumption was required in order to fit the observed decline in the total content of cold gas in galaxies towards low redshift inferred from observations of damped lyman - alpha systems ( storrie - lombardi et al . if two galaxies of comparable mass merge , a spheroid forms and the remaining gas is transformed into stars in a `` starburst '' . the same major mergers are responsible for the formation and fuelling of black holes in galactic nuclei . during the merger the central black holes of the progenitors coalesce and a fraction of the available cold gas is accreted by the black hole . the accreted fraction is assumed to scale with the circular velocity @xmath13 of the surrounding dark matter halo as @xmath14 ( this scaling was adopted in order to fit the slope of the @xmath15 relation of magorrian et al ( 1998 ) . ) the only change in this letter compared to kh2000 is a reduction by a factor of three in the fraction of gas assumed to accrete onto the black hole . this is needed because the mass estimates of black holes from the new data are significantly smaller than those of magorrian et al ( 1998 ) . in the kh2000 model , black holes grew in mass only during major mergers . as pointed out previously , it is certainly possible that supermassive black holes have more complicated accretion histories ( see haehnelt , natarajan & rees 1998 and haehnelt & kauffmann 2000 for a detailed discussion ) . other accretion modes could easily be incorporated into the model . we note , however , that the recent reduction in the estimated total mass density in black holes makes arguments for accretion modes other than those traced by optical- and infrared - bright qsos less compelling . fig . 1a shows scatterplots of black hole mass versus bulge velocity dispersion in our models . we do not have a dynamical model for computing @xmath1 for the bulges in our simulations . for simplicity , we have assumed a constant ratio @xmath16 , where @xmath13 is the circular velocity of the halo in which the bulge found itself after its last major merger . it is easy to show that any well - mixed population of stars orbiting within an isothermal potential must satisfy @xmath17 . following kauffmann & charlot ( 1998 ) , we choose the ratio of @xmath18 to reproduce the zero point of the observed faber - jackson relation ( see fig . 2 ) . to fit the observations , we require @xmath19 . the thick solid line in fig . 1a ( @xmath20 ) shows the relation derived by gebhardt et al . ( 2000a ) , which is reproduced very well . in the models , the total mass of gas that cools in a halo scales roughly as @xmath21 . feedback effects steepen the relation to approximately @xmath22 , but feedback would have to be more extreme in order to obtain a correlation as steep as @xmath23 ( ferrarese & merritt 2000 ) . the scatter in the relation is 0.2 dex , somewhat smaller than the 0.3 dex reported by gebhardt et al . which include measurement errors . 1b shows the black hole mass bulge luminosity correlation compared with the observed relation in the gebhardt et al . sample . for the simulated galaxies , the scatter is about a factor two larger and again agrees well with the observational data . the large scatter in the relation in fig . 1b is a consequence of the large dispersion in the relation between the luminosities and velocity dispersions of bulges . this is illustrated in in fig 2a where we plot the @xmath24 ( faber - jackson ) relation for the elliptical galaxies in our model . elliptical galaxies are defined as those objects with a ratio of bulge to total luminosity greater than 0.4 in the b - band . in the next section , we study the origin of the scatter in these relations and explain why the scatter in the @xmath2 relations is significantly smaller than that of the @xmath25 or @xmath26 relations . previous work has demonstrated that hierarchical galaxy formation models succesfully reproduce the faber - jackson ( @xmath28 ) and the magorrian ( @xmath15 ) relations ( kauffmann & charlot 1998 , kh2000 ) . the slopes of these correlations are determined by how much gas is able to cool and forms stars or is funneled to the centre in a dark matter halo of given mass or circular velocity . this is set by the assumed balance between gas cooling , star formation , supernova feedback and accretion in the halos . the correlations are tight for bulges that form at fixed epoch , but the scatter increases substantially if the galaxy population as a whole is considered . this is demonstrated by fig . 2b , where we plot the residuals in our `` faber - jackson '' relation as a function of the age of the bulge . age is defined as the time elapsed since the bulge had its last major merger . as can be seen , the residuals in the faber - jackson relation correlate strongly with age : young bulges of fixed velocity dispersion are brighter than old bulges . our results are in good agreement with those of forbes & ponman ( 1999 ) , who study residuals in the faber - jackson relation for a sample of 88 nearby ellipticals with ages determined from absorption line spectroscopy . kh2000 showed that a similar effect is expected for the @xmath15 relation . young bulges of fixed luminosity contain less massive black holes than older bulges . this prediction was recently confirmed by merrifield , forbes & terlevich ( 2000 ) . why does the @xmath2 relation exhibit such small scatter ? in fig . 3a , we show how the gas and the stellar masses of bulge progenitors vary as a function of the formation redshift of the bulge . results are shown for bulges with @xmath29 km s@xmath30 and @xmath31 km s@xmath30 . the cold gas masses of the progenitors of bulges of given velocity dispersion _ are essentially independent of redshift _ , whereas their stellar masses decrease at high redshift . as discussed by kh2000 , this decrease in the ratio of gas mass to stellar mass in galaxies is crucial for explaining the observed rapid decline of the qso activity at late times , as well as the decrease in the total content of cold gas in galaxies inferred from damped ly@xmath32 systems ( storrie - lombardi et al . 1996 ) . in our model the amount of gas available for accretion onto a black hole during a major merger depends only on the velocity dispersion of the bulge and not on redshift . this together with our assumption that a fixed fraction of this gas is accreted by the black hole accounts for the small scatter in the @xmath2 relation for bulges forming in gas - rich mergers . what about gas - poor mergers , where gas accretion contributes little to the growth of the black hole ? such gas - poor mergers are important for massive bulges forming at late times ( kh2000 ) . figure 3b shows `` evolutionary tracks '' in the @xmath33 plane for 20 black holes in our model with masses @xmath34 . these black holes typically form in 3 - 5 merging events spaced quite widely in redshift . at late times , the host galaxies of these black holes have rather small cold gas fractions . nevertheless , it is clear from our plot that black holes always move along the correlation as they merge , even for massive systems at late times . the latter can be understood as follows . let us consider the case where black holes grow only by merging and therefore have masses that scale in proportion to those of their host halo . for halos of constant characteristic density , the velocity dispersion @xmath1 scales @xmath35 . with decreasing redshift the characteristic density decreases and the velocity dispersion grows more slowly with increasing mass : @xmath36 . in cdm - like cosmogonies the characteristic mass of typical dark matter haloes scales as @xmath37 , where @xmath38 is the effective slope of the dm fluctuation spectrum . at galaxy scales @xmath39 . this gives a scaling @xmath40 . we have demonstrated that the model of kh2000 where supermassive black holes are formed and fuelled during major mergers produces a tight correlation between black hole mass and bulge velocity dispersion very similar to that observed by gebhardt et al . ( 2000a ) . the model also reproduces the observed relation between black hole mass and bulge luminosity , as well as the relation between bulge luminosity and bulge velocity dispersion . in the model , the slopes of these relations are determined by how much gas cools , forms stars or is" +"gauge theories in three spacetime dimensions typically possess solitonic disorder operators that strongly affect the physics at long distances . a classic example is polyakov s proof that monopoles in a pure @xmath2 gauge theory lead to confinement even at weak coupling @xcite . that emit magnetic flux . we will give a more careful definition in section 2 , where we will also explain what we mean by monopole states in three dimensions . for a general review of basic properties of monopoles and their relation to other solitons in various dimensions , see e.g. @xcite . ] effects of gauge theory disorder operators on the phase structure of many other three - dimensional models have been analyzed in e.g. @xcite . the primary question concerning these operators is whether they cause confinement ; if not , as is often the case , the next order of business is to understand the ir fixed point . identifying disorder operators in such a nontrivial cft is often a daunting task . using various classical limits , their quantum numbers have been calculated in the ir of qed with many fermion flavors @xcite , in the critical @xmath3 model at large @xmath4 @xcite , in the ir of qcd with many fermion flavors and with various gauge groups @xcite , and in the infinite - level limit of conformal chern - simons - matter theories @xcite . disorder operators also feature prominently in supersymmetric theories , where their dimensions and intricate duality mappings can often be understood using holomorphy and localization @xcite . understanding disorder operators in the ir of non - abelian theories without supersymmetry is generally difficult . even in the planar limit , no results at finite t hooft coupling were available unless the number of matter flavors was much larger than the number of colors . however , recent progress in studying the t hooft limit of chern - simons ( cs ) theories coupled to matter @xcite makes it possible to elegantly compute the scaling dimensions of an interesting class of disorder operators in conformal cs - fermion theories with only one fermion flavor . we perform this computation in this brief note . our main result is that the lowest - dimension disorder operators with @xmath5 units of magnetic flux have dimension where @xmath6 is the yang - mills - regulated cs level . this result is valid at all t hooft couplings . our presentation starts with a technical definition of disorder operators in section 2 . in section 3 we obtain the advertised result by computing the thermal partition function of all cs - fermion states with a given magnetic flux on a two - sphere , and along the way we clarify certain aspects of the path integral computation given in @xcite . in section 4 we conclude by discussing implications of our findings for the bosonization duality between cs - fermion and cs - boson theories . we are interested in local operators @xmath7 that create magnetic flux in a theory with gauge group @xmath8 . a state created by a such a disorder operator at @xmath9 has flux that can be gauge - fixed into the form where @xmath10 is any two - sphere enclosing @xmath11 , @xmath12 is the gauge field strength in the theory , @xmath13 are the anti - hermitian cartans of @xmath8 , and @xmath14 are the gauge - invariant gno charges that index different monopole states in four spacetime dimensions @xcite . the quantization of gno charges is most easily demonstrated in the path integral language , where configurations with a disorder operator at the origin can be depicted ( in a suitable gauge ) as fluctuations around wu - yang gauge field configurations @xcite ( note that the field strength associated to the above connection gives @xmath15 when integrated over an @xmath16 centered at the origin . ) this is an allowed configuration if the gauge fields on the south and north hemispheres differ by a gauge transformation . fixing @xmath17 for convenience , the difference between north and south at @xmath18 is @xmath19 , and so the appropriate gauge transformation is enacted by the group element @xmath20 . this object must be well - defined as we circle the equator of the @xmath16 by letting @xmath21 . this condition , @xmath22 , is only satisfied for a discrete set of @xmath14 s . there are reasons to believe that not all gno charges correspond to different disorder operators . first , even if the wu - yang backgrounds are classical saddles , they need not all be stable in the quantum theory @xcite . second , the operators defined via eq . need not be eigenstates of the dilatation operator in the ir cft , and so they might not all be independent . third , the gno monopoles are not all topologically protected . topological charges exist only if the gauge group has a nontrivial fundamental group @xmath23 , e.g. for @xmath24 but not for @xmath25 @xcite . however , even though the gno classification may be too refined , we will find disorder operators with small amounts of flux in the planar limit that appear to have well - defined scaling dimensions with no indication of instabilities . this means that the situation is similar to the one found in many - flavor qcd @xcite , where large classes of gno charges were shown to correspond to stable monopoles even though there was no a priori reason for them to do so . so far we did not assume that the theory was conformal , and the operators @xmath7 were instantonic in character . these instantons represent transitions to / from states with magnetic flux that we will call monopoles . analyzing the spectrum of such states in general qfts is hard , but progress was made in the supersymmetric context in @xcite . things are simpler in a conformal theory , where each disorder operator corresponds to a monopole state @xmath26 on @xmath27 , a two - sphere of radius @xmath28 . in the path integral these states correspond to configurations with background fields @xmath29 on @xmath30 . in a yang - mills theory coupled to matter , disorder operators are defined in a gauge - invariant way using eq . . their scaling dimensions are determined , via the state - operator correspondence , as casimir energies of the fluctuations around wu - yang monopoles on @xmath31 , when these are good saddles . is given by a constant times the area form . if there is a reason to break the rotational invariance in the theory , it may happen that the true saddles are large deformations away from eq . for which the magnetic flux is not uniformly distributed across the sphere . in that case , all comments we make apply to fluctuations around these new backgrounds . spherical symmetry will never be broken in our examples , so we will work with fluctuations around uniform flux backgrounds . ] the fluctuations in question must be gauge - invariant themselves . in the case of yang - mills theory this means that no operators with electric charge may be present . this picture changes if a chern - simons term at level @xmath6 is present in the action . the wu - yang configuration in this case has electric charge @xmath32 , and the gauss law requires that matter fields compensate for this charge @xcite . this means that gauge - invariant disorder operators in cs - matter theories do not merely create magnetic flux ; they also create enough matter to dress themselves into an electric singlet . this dressing may introduce large corrections to the casimir energy due to matter self - interactions @xcite . for instance , in a cs - fermion theory at @xmath33 ( or at zero t hooft coupling in the planar limit ) , the matter fields can be heuristically treated as noninteracting fermions in a background magnetic field that fill up a fermi sea until they reach @xmath34 units of charge ; the landau levels are separated by gaps of order @xmath35 , giving a total fermi energy of @xmath36 @xcite . ( see also @xcite . ) we will show that this holds at all t hooft couplings . our approach to calculating disorder operator dimensions is the following . we focus on the conformal cs - fermion theory , radially quantized with a wu - yang background on the spatial two - sphere , and we compute the path integral over all gauge field and matter fluctuations around this background . if the euclidean spacetime is taken to be @xmath37 , the result is a thermal partition function of all monopole states with the given set of gno charges ( with matter dressing automatically taken care of ) . in the low temperature ( @xmath38 ) limit , the result must take the form @xmath39 , with @xmath40 being the desired energy ( or flat - space scaling dimension ) of the lightest disorder operator in this gno class . we will calculate this @xmath40 in the t hooft limit by using several subtle tricks that we carefully explain in the following section . consider the conformal @xmath0 chern - simons theory coupled to dirac fermions in the fundamental representation . the thermal partition function is given by the path integral on @xmath41 , with the two - sphere volume @xmath42 and temperature @xmath43 . the euclidean action is we normalize @xmath44 , and in particular we choose @xmath45 to be a matrix whose only nonzero entry is @xmath46 at the @xmath47th place on the diagonal . ( this choice means that gno charges have values @xmath48 for @xmath49 . ) we are interested in the planar limit , where @xmath4 and @xmath6 are taken to infinity with the t hooft coupling @xmath50 fixed . in dimensional regularization , the theory is unitary only for @xmath51 @xcite . the cs level @xmath6 is quantized by demanding invariance under large gauge transformations ; in order to offset the parity anomaly of the fermions , @xmath52 should take on values in @xmath53 @xcite , but in the t hooft limit this is immaterial and we may think of @xmath6 as being a ( large ) integer . at @xmath54 we recover the singlet fermion model @xcite , and as @xmath55 approaches unity the theory approaches pure cs theory @xcite . a subtlety ( pointed out by o. aharony ) arises here because we regulate the above theory using dimensional reduction , but the preceding discussion of disorder operators in cs theory assumed regularization using a yang - mills term . the cs levels in the two regularizations are related by @xmath56 . in dimensional reduction this shift arises because we must regulate the monopoles by giving them a core of nonzero size . this uv regularization effectively acts as an edge of the system , and the electric charge of the monopoles gets shifted by the @xmath4 edge states of cs theory . the operator content is simple to describe : cs has no dynamical degrees of freedom and the only operators with @xmath57 energies are products of @xmath58 `` single - trace '' singlets built out of two matter fields and covariant derivatives . these single - trace operators are the scalar operator @xmath59 and conserved currents @xmath60 ; they have protected ( @xmath61-independent ) scaling dimensions in the planar limit , and they are conjectured to be holographically dual to higher - spin fields of the vasiliev system in ads@xmath62 @xcite . if the gauge group is @xmath63 , the theory also contains baryons @xmath64 whose energies are @xmath65 @xcite . for any gauge group , there are also disorder operators defined in section 2 , and if the group is not simply connected ( e.g." +"on 15 february 2013 at about 03:20 utc 17-meter asteroid entered the earth s atmosphere and exploded while travelling at a speed of 19 km / s . the body became a superbolide meteor , which was seen over the southern ural region . at the moment of maximum brightness , which occurred near the city of chelyabinsk , the meteor was brighter than the sun . the several small fragments of meteorite ( ordinary chondrite ) were quickly found on the west of chelyabinsk , with the largest fragment of total mass of 654 kg raised from the bottom of the chebarkul lake on 16 october 2013 ( popova et al . 2013 , brown et al . 2013 , borovicka et al . 2013 , kohut et al . 2014 ) . about 16 hours after chelyabinsk fireball occurrence the 45-meter asteroid 367943 duende ( 2012 da14 ) approached the earth and missed it by about 27 700 km . this was striking coincidence but subsequent analysis of the data clearly indicated the two objects could not have been related because they had widely different orbits ( wlodarczyk 2012 , moskovitz et al . 2013 ) what is more interesting similar situation occurred over two years earlier . on the night of 2010 oct 9/10 , mt . lemmon survey reported a discovery of a new 20-meter apollo type asteroid designated as 2010 tb54 ( hergenrother 2010 ) . the asteroid has been expected to pass only 6.1 lunar distance ( 0.011 au ) from the earth . over 11 hours earlier sky over central poland was illuminated by @xmath0 magnitude fireball . what is even more interesting these both bodies , contrary to chelyabinsk meteorite parent body and duende asteroid , seem to be related . in this paper we report an analysis of the multi - station observations of the pf131010 fireball made by cameras of the _ polish fireball network_. both the trajectory and orbit are calculated indicating that the fireball was related to 2010 tb54 asteroid . even closer resemblance of orbits is found for 2010 sx11 asteroid . the _ polish fireball network ( pfn ) _ is the project whose main goal is regularly monitoring the sky over poland in order to detect bright fireballs occurring over the whole territory of the country ( olech et al . 2005 , odek et al . 2007 , 2009 , winiewski et al . 2012 ) . it is kept by amateur astronomers associated in _ comets and meteors workshop ( cmw ) _ and coordinated by astronomers from copernicus astronomical center in warsaw , poland . currently , there are over 20 fireball stations belonging to _ pfn _ which operate during each clear night . the pf131010 ciechanw fireball was observed by five _ pfn _ video stations ( table 1 ) : two of the recordings allowed us to determine the trajectory of the phenomenon , one recording includes observations made from a distance of over 400 km , another one features an initial part of the trajectory , and the last one noticed a bright reflection on clouds layer only . the most detailed and valuable recording comes from the pfn37 station in nowe miasto lubawskie , positioned 80 km north - east of toru ( see fig . 1 ) . a camera with a 70-degree field of view registered its path in the southern direction diagonally through the field of view . the bolide appeared between the constellations of orion and the gemini as a point - like structure of about 2 magnitude . the brightness of the meteor increased quickly , and after 1.2 seconds the wake appeared . until about 3 seconds the bolide continued its luminous path as an object of about @xmath5 magnitude . the fireball started to lose its brightness in the middle of the visible trajectory , reaching a local minimum at about 4.6 second of the flight . [ cols=""<,<,^,^,^,<,<"",options=""header "" , ] the observed final velocity of 5.8 km / s at the height of 29 km ( which most probably could descend even lower ) indicates a possible meteorite fall near grabowo , south of ostoka . an estimated impact point of the single meteorite weighing about 2 kilograms is about 22 kilometers of the final trajectory point , about 3.5 km to the left of the trajectory axis ( see fig . the exact coordinates of the impact point are @xmath6 n , @xmath7 e. calculations have been performed with assumption that only one fragment survived the ablation . the dynamic mass has been calculated using parameters observed at the end of the visible trajectory . the mass is given for chondrite body with bulk density of 3.7 @xmath8 and calculated using standard formulas ( ceplecha 1987 ) . because of huge trajectory uncertainties concerning the parameters observed in the final part of the trajectory the precision in determining the final place of impact amounts to about 3 km . an atmosphere profile , obtained during atmospheric probing performed on october 13 , 2010 at 00:00 ut ( the legionowo meteorological station located 65 km south of the terminal point ) , was used for the computations . a searching expedition was launched soon after the first rough estimates of results was determined , but their efforts were fruitless . after another manual measurement of the meteor position there was a new result ( presented here ) , slightly different from the previous one . the second expedition took place at the end of march 2015 , though without positive results either . the area ( with active agriculture ) is not easy to search , with at least half of it not easily accessible . based on the observational data we were able to determine the radiant of ciechanw fireball , its geocentric velocity and orbital parameters of the meteoroid which entered the earth s atmosphere . the orbital parameters are listed in the first row of table 3 * * , * * and the diagram showing orbit of the fireball in the inner solar system is displayed in fig . the orbit of ciechanw fireball is located almost in the ecliptic plane and has low eccentricity . the meteoroid hit the earth less than two months before perihelion passage which was expected on december 4 , 2010 at distance of @xmath9 au . comparison of the orbit of ciechanw fireball to orbits of near earth objects ( neo ) allowed us to select several asteroids with drummond criterion @xmath10 ( drummond 1979 ) . two of them are especially interesting . the 2010 tb54 asteroid has @xmath11 criterion value as small as 0.058 . what is more interesting this object passed within the distance of only 0.016 au from the earth on october 13 , 2010 at 14:14 ut , i.e. only 11.4 hours before the occurrence of the ciechanw fireball . this asteroid has been discovered by mount lemnon survey on october 9 , 2010 , its observing arc is 3 day long and based on 30 optical measurements . 2010 tb54 has absolute magnitude @xmath12 magnitude , and its diameter is less than 29 meters . even lower drummond criterion value ( @xmath13 ) was noted for 2010 sx11 asteroid . the close encounter with this body occurred on october 11 , 2010 at 13:10 ut at the distance of 0.025 au . in this case the time difference amounts to 37.7 hours . 2010 sx11 is a larger body , with absolute magnitude @xmath14 magnitude and diameter between 33 and 73 meters . observing arc span is 21 days , 33 optical measurements were used to determine orbital elements . uncertainties of orbital elements for both asteroids are similar but slightly smaller for 2010 sx11 . our results indicate the possibility that in period of october 11 - 13 there is an activity of meteor shower of asteroid origin with radiant located in the border of pisces and aries constellations . a numerical integration of the orbital parameters backwards in time has been performed in order to test the link between the fireball ciechanw and two neos : 2010 sx11 and 2010 tb54 . for the integrations of the asteroids and test particles representing fireball , the radau integrator in the mercury software was used ( chambers 1999 ) . the model of the solar system used in integrations included : 8 planets , four asteroids ( ceres , pallas , vesta , and hygiea ) , and the moon as a separate body . the positions and velocities of the perturbing planets and the moon were taken from the de406 ( standish 1998 ) . the initial orbital elements of asteroids 2010 sx11 and 2010 tb54 were taken from jpl horizons website . together with initial orbital elements of asteroids , the test particles were integrated to the same epoch of the beginning of the integration . next , the backward integration was continued for 5000 yr . during the evolution , the ascending and descending nodes of theoretical particles are dispersed within heliocentric distances from 0.8 to 1.8 au , with a concentration around earth s orbit . the generated stream has been widely dispersed in longitude , mostly by perturbation from the earth . therefore , application of a conventional similarity functions : @xmath15 ( southworth and hawkins 1963 ) , @xmath11 ( drummond 1981 ) , or @xmath16 ( jopek 1993 ) , would be strongly influenced in the longitude term in the d - criterion . due to it , we used ( steel 1991 ) criterion , @xmath17 , where the longitude term is not included . figures 7 and 8 show that the evolution of the @xmath17 criterion reveals a link between the ciechanw fireball and neos , with the values of @xmath17 being less than 0.15 through the whole integration time ( except one test particle when we compare orbits with 2010 tb54 and 2010 sx11 , respectively ) . the theoretical geocentric radiants of the asteroids has been determined using fortran code which is able to calculate radiant coordinates and theoretical stream orbit ( neslusan et al . theoretical radiants of asteroids and ciechanw meteoroid does nt match if calculated from present orbital elements . however similarity of the radiant is visible for back integrated orbital elements . distance between 2010 sx11 radiant and ciechanw radiant was close to 8.5 degrees 5000 years ago . also the theoretical radiant of 2010 tb54 was located in the same sky area , 7.5 degrees from the ciechanw radiant . five thousands years ago all theoretical radiants were closer than 10 degrees each other with geocentric discriminants @xmath18 for 2010 sx11 , @xmath19 for 2010tb54 and @xmath20 for ciechanw . change of radiant distances in time may suggest that age of possible stream is probably larger than 10000 years . in this paper we presented an analysis of the multi - station observations of a bright fireball which occurred over eastern poland . our main conclusions are as follows : * the meteor appeared on 2010 oct 12/13 at 02:52:32 ut over the eastern part of poland was detected by five video stations of _ polish fireball network _ , * the maximum brightness of the fireball reached @xmath21 mag and was observed at height of @xmath22 km over ciechanw city , * the entry velocity was only @xmath1 km / s and after three seconds of flight the meteoroid was significantly decelerated with the rate of @xmath23 resulting with final velocity of only @xmath3 km / s , * low value of final velocity indicates a possible 2 kg meteorite fall near grabowo , south of ostoka , * the low eccentric orbit of the fireball , positioned almost in the ecliptic plane , is similar to orbits of 2010 tb54 and 2010 sx11 asteroids" +"almost a century ago , in their pioneering research @xcite , kaluza and klein ( kk ) proposed unification of four dimensional gravity and electromagnetism in a five dimensional gravity framework . this proposal raised a fair amount of curiosity , interest and research activity among theoretical physicists , on the physics of extra dimensions . the idea of extra spatial dimensions appeared in a new incarnation with the advent of superstring theories @xcite . the theoretical existence of branes in string theory eventually motivated the hypothesis that we may be living on an embedded , timelike submanifold ( the brane ) of a higher dimensional ( @xmath0 ) lorentzian spacetime ( warped or unwarped ) , as assumed in the so - called arkani - hamed dvali dimopoulos ( add ) @xcite and randall sundrum ( rs ) @xcite braneworld models . the seminal work of randall and sundrum ( rs ) @xcite on warped braneworlds , published more than a decade ago , refers to the idea of the scale of the extra dimension being spacetime dependent , while addressing the issue of stability , in a two - brane scenario . in a single brane scenario or from a purely higher dimensional bulk perspective , the space - time dependence of the metric function(s ) associated with the extra dimensional coordinate(s ) basically imply that the scale of the extra dimension depends on the on - brane ( four dimensional ) spacetime coordinates . except for a brief discussion on rs type models , we shall , in this article , mostly work with the single brane scenario and a five dimensional bulk . in earlier papers @xcite , geodesics in warped spacetimes have been investigated in detail . however , such a study of geodesics alone can not tell us about the overall local behavior of a family of test particles , as observed in the neighbourhood of a freely falling observer . this motivates us to study the evolution of geodesic congruences . since the appearance of _ raychaudhuri equations , in 1955 @xcite , relativists have discussed and analysed its implications in various contexts . in its original incarnation , the raychaudhuri equations provided the basis for the analysis of spacetime singularities in gravitation and cosmology @xcite . for example , the equation for the expansion and the resulting theorem on geodesic focusing , is a crucial ingredient in the proofs of penrose - hawking singularity theorems @xcite . the kinematics of geodesic congruences is characterised by three kinematical quantities : isotropic expansion , shear and rotation ( henceforth referred as esr ) @xcite , which evolve along the flow according to the raychaudhuri equations . though mostly quoted and used in the context of gravity , these equations by virtue of their geometric nature , have a much wider scope in studying geodesic as well as non - geodesic flows in nature , which may possibly arise in diverse contexts ( see @xcite for some open issues ) . two of the authors here have recently used these equations to investigate the kinematics of geodesic flows in stringy black hole spacetimes @xcite and flows on flat and curved deformable media ( including elastic and viscoelastic media ) in detail @xcite . in this article , we attempt to understand the kinematics of geodesic flows in five dimensional warped bulk spacetimes with and without branes . in section ii we quickly recall the background spacetime geometries and geodesics . section iiia analyses flows in the rs geometry with and without branes . the esr , as obtained from definitions , for a background with a thick brane are discussed in section iiib . numerical solutions of the geodesic and raychaudhuri equations are presented in iiic . finally , section iv contains our conclusions and comments . the bulk spacetimes we work with are given by the line element @xcite ( @xmath1 is the conformal time ) , @xmath2 + b^2(\eta ) d\sigma^2 . \label{eq : cmetric}\ ] ] table [ tab : models ] , shows the chosen functional forms of @xmath3 ( the warp factor ) , the cosmological [ @xmath4 and extra dimensional [ @xmath5 scale factors ( following @xcite ) . .the four possible combinations of @xmath3 , @xmath6 and @xmath7 . [ cols=""^,^"",options=""header "" , ] we began by considering geodesic flows in the rs background . without branes congruence singularities always occur whereas with two branes , the expansion profile indicates how focusing / defocusing can occur in the spacetime between the branes . later , we analyse geodesic flows in a bulk geometry with a thick brane . using first integrals of geodesic motion , analytic expressions for the kinematic variables are obtained . we show how differences arise as we change the warp factor from growing to decaying or when we do not have any warping but retain the time - evolving cosmological and extra dimensional scales . further , we numerically solve the raychaudhuri and geodesic equations to obtain the expansion , shear , rotation and demonstrate the role of initial conditions on their evolution . with @xmath8 , a growing warp factor leads to a finite @xmath1 ( and @xmath9 ) congruence singularity whereas for a decaying warp factor , geodesics are focused at @xmath1 ( and @xmath9 ) @xmath10 . for a de sitter universe , a decaying warp factor may fail to focus the geodesics ( due to the large negativity of the curvature term in the raychaudhuri equation ) , though this is not the case with a growing warp factor . when the curvature effect is relatively small , a congruence singularity can still arise but for high enough negative initial expansion . the effect of initial rotation , on the esr profiles , especially the expansion scalar , is found to be quantitative . focusing without and with initial rotation yields similar results , though with large initial rotation , geodesics tend to spread for a while ( focusing at larger @xmath11 value ) . all our conclusions are summarised in table [ summary - table ] . for a visual perspective , we have shown snap - shots of the evolution of a square element orthogonal to a geodesic congruence , from a local observer s point of view . the evolution of the expansion , shear and rotation , along the congruences become more explicit through these figures . the effect of @xmath7 seems to be largely quantitative since , in our models , as @xmath11 evolves @xmath7 tends to a static value with a deceleration . it may be asked what relevance , if any , does a congruence singularity have in the context of realistic scenarios ? after all , congruence singularities are not real spacetime singularities where curvatures diverge . here , we are tempted to draw an analogy from null geodesic congruences , for which congruence singularities are nothing but the well - studied caustics where optical intensities get magnified immensely . similarly , in the case of timelike geodesics , we may end up with accretion like effects resulting out of matter accumulation in the neighborhood of a point . for instance , our visualisation analyses do show how the square elements change shape , get rotated because of variations in the metric functions . we may contemplate such accretion effects for flows around brane world black holes @xcite and in such situations , it will become necessary to pursue a line of thought very similar to what we have followed in this article . sg thanks council for scientific & industrial research ( csir ) , india for providing financial support and centre for theoretical studies , iit kharagpur , india for allowing him to use its research facilities . m. s. green , j. h. schwarz and e. witten , _ superstring theory _ ( cambridge university press , uk , 1987 ) ; j. polchinski , _ string theory _ ( cambridge university press , uk , 1997 ) . i. antoniadis , phys . lett . b * 246 * ( 1990 ) 377 . n. arkani - hamed , s. dimopoulos , g. dvali , phys . b * 429 * , 263 - 272 ( 1998 ) ; n. arkani - hamed , s. dimopoulos , g. dvali , phys . d * 59 * , 086004 ( 1999 ) . i. antoniadis , n. arkani - hamed , s. dimopoulos and g. r. dvali , phys . b * 436 * ( 1998 ) 257 [ arxiv : hep - ph/9804398 ] . l. randall and r. sundrum , phys . 83 * , 3370 ( 1999 ) . t. c. scott and r. b. mann , _ general relativity and quantum mechanics : towards a generalization of the lambert w function _ , aaecc ( applicable algebra in engineering , communication and computing ) , vol . 6 , ( 2006 ) [ arxiv : math - ph/0607011v2 ] ." +"in recent years , much research has been dedicated to developing vision - based advanced driver assist systems ( adas ) . these systems help drivers in controlling their vehicle by , for instance , warning against lane departure , hazardous obstacles in the vehicle path or a too short distance to the preceding vehicle . as these systems evolve with more advanced technology and higher robustness , they are expected to increase traffic safety and comfort . a key component of adas is free - space detection , which provides information about the surrounding drivable space . in this work , we employ a fully convolutional network ( fcn ) for this task and explore _ online _ training in a _ self - supervised _ fashion , to increase the robustness of the free - space detection system . figure [ fig : scheme ] provides a schematic overview of our proposed framework , which will be described in detail in the __ section . neural nets with deep learning are becoming increasingly successful and popular for image analysis . in the field of intelligent vehicles , many of the recent state - of - the - art algorithms rely on neural nets , mostly on convolutional neural nets ( cnns ) . they excel in a wide variety of adas applications , such as stereo disparity estimation @xcite , object detection for cars and pedestrians @xcite and road estimation @xcite@xcite . in literature , training a neural net typically requires many data samples for proper convergence of the large amount of parameters and proper generalization of the classifier . different strategies are adopted throughout the field to handle this . in image recognition and object detection problems in natural environments , a common method is to start with a net that is trained on a large and generic dataset , in either a supervised @xcite or unsupervised manner @xcite@xcite@xcite . to apply it to a new task , one can remove the last layer of the net , which provides class confidences , and train a new one for the problem at hand . this exploits the observation that these pre - trained nets are a compact and yet rich representation of the images in general , since they are trained extensively on a broad visual dataset @xcite@xcite@xcite . an extension of this concept is not just retraining the last classification layer of a pre - trained net , but to also fine - tune a larger part or even the complete net with task - specific data @xcite@xcite@xcite@xcite . scene labeling , in contrast to scene or object recognition , requires a per - pixel classification . several strategies have been developed to go from global object detection to fine - grained segmentation , such as classification of sliding windows @xcite or image region proposals @xcite , multi - scale cnns combined with superpixels @xcite , or recurrent cnn architectures , which are a compact , efficient version of a multi - scale approach @xcite . recently , fully convolutional networks ( fcns ) , have been employed for pixel - level segmentation @xcite@xcite . fcns have several attractive properties in comparison to the aforementioned methods for scene parsing . for example , fcns have no constraints on the size of their input data and execute inference in a single pass efficiently per image , instead of a single pass per superpixel , window or region @xcite . consequently , they do not require concepts like superpixel , region or multi - scale pre- or post - processing @xcite . in the field of image segmentation , an additional interesting approach of training is weak supervision , where a limited set of related annotations are exploited for training . for example , the authors of @xcite train cnns for pixel - level segmentation on image - level labels , since labels for the latter are more abundant than for the former . even though weakly- or unsupervised training methods of cnns are improving , they are currently still outperformed by fully supervised methods @xcite@xcite . together with the fact that creating large amounts of pixel - accurate training labels is inherently much work , we propose a middle - way in this paper : self - supervised training . if training labels can be generated automatically , the amount of supervised training data available becomes practically unlimited . however , this leads to a paradox , since it requires an algorithm that can generate the labeling , which is exactly the issue that needs to be solved . therefore , we propose to rely on an algorithm based on traditional ( non - deep learning ) computer vision methods . this algorithm needs not to be perfect but at least sufficiently good to generate weak training labels . the goal is then that the fcn , trained with these weak labels , outperforms the traditional algorithm . for next - generation adas , stereo cameras and multi - view cameras are an increasingly used sensor configuration . stereo cameras provide insight into the geometry of the scene by means of the stereo disparity signal , which is valuable information for free - space detection . a state - of - the - art algorithm to distinguish free space and obstacles is the disparity stixel world @xcite . it performs very well under favourable lighting conditions where the stereo estimation works reliably , but the algorithm is shown to have trouble under adverse conditions such as dim or very bright light @xcite@xcite@xcite . we will use this algorithm to generate free - space masks and exploit these as weak training labels . we will rely on the generalization power of fcns to deal with the errors in the weak labeling . in essence , we use a stixel - based disparity vision system to train a pixel - accurate free - space segmentation system , based on an fcn , and refer to this as self - supervised training . as a further contribution , our proposed self - supervised training is enhanced by combining it with the aforementioned strategies of task - specific fine - tuning of neural nets . since traffic scenes come in a wide variety ( urban versus rural , highway versus city - center ) , with varying imaging conditions ( good versus bad weather , day versus night ) , adas have to be both flexible and robust . a potential strategy is to train many different classifiers and to select the one that is most relevant at the moment ( for instance , based on time and geographical location ) , or train a complex single classifier to handle all cases . in contrast , we show in this paper that it is feasible to fine - tune a relatively simple , single classifier in an online fashion . this is obtained by using the same self - supervised strategy as for offline learning , namely , based on generally correct segmentation by the disparity stixel world . this results in automatically improved robustness of the free - space detection , as the algorithm is adapted while driving . although our system does not yet operates in real - time , we deem this to be feasible in the near future , as the stixel world system can execute in real - time and our fcn is relatively small , which allows for both fast training and fast inference . considering the overall approach , our work is also related to @xcite , where automatically generated labels are exploited to train a cnn for road detection , which is applied as a sliding - window classifier . they also have an online component , which analyzes a small rectangular area at the bottom of the image ( assumed road ) and calculates a color transform to boost the uniformity of road appearance . the results of offline and online classifications are combined with bayesian fusion . our proposed work differs in several key points . firstly , we do not need to assume that the bottom part of a image is road in the online training step , which is often an invalid assumption in stop - and - go traffic , since we exploit the stereo disparity as an additional signal . secondly , their offline and online method is a hybrid combination of supervised and hand - crafted features , whereas our method can be trained and tuned in a fully end - to - end fashion , using a single fcn , while avoiding an additional fusion step . thirdly , we do not require a sliding window in our inference step , since we use an fcn and not a cnn . the remainder of this paper is structured as follows . our self - supervised and online training strategies are described in more detail in section __. our validation procedures are provided in section __ , with a corresponding __ section . finally , our research findings are briefly summarized in the __ section . in the following sections we will first explain the baseline fcn algorithm for image segmentation . after this , we will introduce our self - supervised and the corresponding online training strategies of the fcn in more detail . the color - based segmentation algorithm used as a basis of our work is an fcn @xcite . an fcn is a convolutional neural network , where all fully connected layers are replaced by their equivalent convolutional counterparts . this adaptation transforms the net into a deep filter that preserves spatial information , since it only consists of filtering layers that are invariant to translation . therefore , an fcn can process inputs of any size @xcite . a challenge with this approach is that fcns also typically contain several subsampling layers , so that the final output is smaller or of coarser resolution than the input image . to address this issue , the authors of @xcite introduce skip - layers that exploit early processing layers , which have a higher resolution , to refine the coarse results in the final layer . in this way , the output resolution matches that of the input for pixel - level labeling . for our experimentation , we have relied on the cn24 framework as described in @xcite . its extension to fully convolutional networks is shortly introduced in @xcite . provided that the context ( road detection ) and data ( images captured from within a vehicle @xcite ) are comparable to our research , we adopt their network architecture and their recommendations about the optimal training strategy . the network consists of several convolutional , max pooling and non - linear layers : conv ( @xmath3 ) ; maxp ( @xmath4 ) ; relu ; conv ( @xmath5 ) ; relu ; full ( @xmath6 ) ; relu ; full ( @xmath7 ) + spatial prior ; relu ; full ( @xmath8 ) + tanh . the fully connected layers are interpreted and executed as convolutional layers by the cn24 library . the special feature of this network is the spatial prior , which is trained in the learning process as an integral part of the net , using the normalized positions of training patches . this spatial prior exploits the spatial bias that is certainly present in road or free - space segmentation in traffic scenes . we employ the recommended settings for training , based on image patches and without using dropout . note that our current work is not meant to offer an exhaustive test on optimizing the network architecture or the hyper parameters of the training process . we acknowledge the fact that our results may be improved by investigating that more properly , but the focus in this paper is to show the feasibility of" +"the concepts of observability and controllability , introduced first by kalman @xcite , play an important role in modern control theory . in fact , these properties often govern the existence of a solution to an optimal control problem . observability and controllability of discrete - time systems have also been treated in the literature in a generalised form . a survey of the main results for discrete system sampled nonuniformly can be found in @xcite . in general , both concepts have been characterised by criteria mutually independent , but , in this work , it is demonstrated that , if certain conditions not very restrictive are imposed on the continuous system , then the characterisations of observability and controllability for the discrete system can be unified . there is an important problem which arises in discrete - time systems but not in continuous - time systems . a linear system which is completely observable and controllable may lose these properties after the introduction of sampling . this stresses the importance of the sampling sequence to guarantee the above - mentioned internal properties . there are restrictions on the aperiodic sampling sequence , stronger than in the periodic case . at any rate , this partial freedom in the choice of the sampling instants can be conveniently used to obtain a rather well conditioned system , a reduction in the propagation of measuring and/or rounding errors etc . further interesting applications of these ideas , e.g. the sensitivity of system observability and controllability , are treated by exploiting an adequate geometric structure . in this way , the familiar analytical techniques @xcite can be presented in a more intuitive form . this discussion is restricted to : \a ) linear time - invariant single - input / single - output differential systems of finite order @xmath0 \b ) continuous - time systems completely controllable and observable in the sense given by kalman @xcite \c ) systems whose transfer function is a strictly proper rational function . consequently , their impulse response @xmath1 will be a particular solution of an _ _ n__th - order homogeneous linear differential equation with constant coefficients of the form @xmath2 therefore @xmath3 where @xmath4 are constant coefficients . @xmath5 is the fundamental system of solutions of eqn . [ eq:1 ] . in the state space , the systems considered can be described by the following equations @xmath6 @xmath7 where @xmath8 denotes the state - vector and @xmath9 are the scalar input and output , respectively . the matrices @xmath10 are of appropriate orders and constant . canonical realisations in the state space obtained from the impulse response will be used . in particular , \(i ) _ observability canonical form _ @xmath11 : @xmath12 is a @xmath13 bottom - companion matrix with @xmath14 in the last row , @xmath15 ( denotes the transpose ) where @xmath16 correspond to the _ n_-first markov parameters of the impulse response @xmath1 and @xmath17 \(ii ) _ controllability canonical form _ @xmath18 : @xmath19 @xmath20 @xmath21 all minimal realisations are related by similarity transformations and , in each particular problem , the most adequate one will be selected . the observability ( controllability ) of a discrete system depends on the observability ( controllability ) of the continuous - time system , plus some additional conditions on the sampling sequence . the problem of observing ( controlling ) the state of any realisation by means of the sampling can be reduced to the task of solving a system of linear equations . consequently , an adequate choice of the sampling instants guarantees the compatibility of this system . the question of the controllability will be discussed first . the corresponding results for the observability will be given later . finally , a joint characterisation of both internal properties will be presented . let @xmath22 be an arbitrary minimal realisation of order @xmath0 for the kind of systems under study . the system considered will be completely _ n_-controllable ( controllable in @xmath0 steps ) @xcite , @xcite if , for any initial state @xmath23 of eqn . [ eq:3 ] , the system can be directed to @xmath24 by means of @xmath0 impulse inputs applied at @xmath0 consecutive sampling instants . the solution of the state - space equation for the system eqn . [ eq:3 ] at time @xmath25 can be written as @xmath26 @xmath27 \left [ \begin{array}{c } u_{n-1 } \\ $ \vdots$ \\ u_0 \\ \end{array } \right]\ ] ] where @xmath28 @xmath29 is the length of the sampling interval between two consecutive sampling instants . the scalar input is @xmath30 @xmath31 being the value of the impulse input at the sampling instant @xmath32 . to consider the transference from an initial state to a final state in @xmath0 steps , we study the rank of the matrix @xmath33 $ ] . indeed , @xmath34 where @xmath35 is the jordan canonical form of matrix @xmath36 and @xmath37 is the invertible matrix of the change of basis : @xmath38 therefore , we must compute the value of @xmath39\ ] ] or briefly , @xmath40 \qquad ( m = 0 , \ldots , n-1)\ ] ] with @xmath41 by similarity transformations @xmath42 where @xmath43 is the matrix of the change of basis of @xmath44 to the jordan canonical form . then we denote the components of @xmath45 by @xmath46 @xmath47 being the multiplicity of the @xmath48 different eigenvalues of matrix @xmath36 with @xmath49 . it is easy to see @xcite that , for the controllability canonical form , @xmath50 with @xmath51 defined as in eqn . 2 ; thus making use of the laplace s expansion by minors , the determinant eqn . 17 can be factorised as follows : @xmath52= n_1 n_2 \ , det[\,\varphi_i(\alpha_m)\,]\ ] ] @xmath53 @xmath54 & \ , & \ , \\ \ , & \ddots & \ , \\ \ , & \ , & \left[\begin{array}{ccc } y_1^r & \ldots & y_{mr}^r \\ \vdots & { \mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu\raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu } } & \ , \\ y_{mr}^r & \ , & \ , \\ \end{array}\right ] \\ \end{array}\right]\ ] ] note that @xmath55 will be non null if , and only if , @xmath56 which is guaranteed , according to the previous significance of the components of @xmath45 , because only minimal realisations are considered . finally , @xmath57 \ ; ( i = 1 , \ldots , n ; \ ; m = 0 , \ldots , n - 1)]$ ] is an @xmath13 matrix of the form @xmath58\ ] ] @xmath59 being the fundamental system of solutions of eqn . 1 . the value of @xmath60 $ ] will depend on the choice of the sampling instants . let us now consider one special aspect here , because it can be the source of some terminological problems . the nonsingularity of the matrix @xmath33 $ ] is a necessary and sufficient condition to ensure that any initial state @xmath23 can be taken to an arbitrary state @xmath61 in @xmath0 steps : this is called _ n_-reachability . if the state @xmath61 coincides with the origin , then the above condition is sufficient to insure that any initial state @xmath23 can be taken to the origin in @xmath0 steps : this is called _ n_-controllability . n_-reachability is a more restrictive condition than the _ n_-controllability . in fact , the _ n_-reachability implies _ n_-controllability , but the converse may not be true . from eqn . 23 and the previous considerations , the following result is derived : _ lemma 1 : _ the realisation @xmath22 is completely _ n_-reachable ( reachable in @xmath0 steps ) if , and only if , @xmath0 consecutive sampling instants are chosen in such a way that @xmath62\neq 0 \qquad ( i = 1 , \ldots , n;\ ; \ , m = 0 , \ldots , n-1)\ ] ] _ proof : _ the proof is evident from the factorisation of the expression 23 . note that , for this kind of system , the _ n_-reachability depends on the characteristic modes of the continuous system and on the choice of the sampling instants . we remark that the hypothesis _ ( b ) _ in section 2 is necessary , because , if this condition is not verified , then the canonical realizations obtained from the impulse response would not be actual realisations in the state space for the system considered . consequently , the above result would not be true . in eqn . 14 , the scalar input is defined as impulse inputs at the sampling instants . in practice , a control of the form @xmath63 is generally used . for technical reasons , @xmath64 must be generated with the aid of a filter , so that the equations of the device which generates @xmath64 can be included in eqn . 1 . the results are completely analogous . the observability problem can be discussed without loss of generality putting @xmath65 . for the same arbitrary minimal realisation @xmath22 the observability question is studied . the system considered will be completely _ n_-observable ( observable in @xmath0 steps ) @xcite , @xcite , if any initial state @xmath23 of eqn . 3 can be calculated from @xmath0 values of the output taken at @xmath0 consecutive sampling instants . therefore , according to eqn . 3 and for the same values @xmath66 as before , the following system of linear equations is set : @xmath67 in mathematical terms , the condition of _ n_-observability means that @xmath68=n \qquad ( m = 0 , \ldots , n - 1)\ ] ] the linear system eqn . 30 can be rewritten as @xmath69 where @xmath35 and @xmath37 are defined as before @xmath70 now , we study the value of @xmath71 \qquad ( m = 0 , \ldots , n - 1)\ ] ] by similarity transformations @xmath72 where @xmath73 is the matrix of the change of basis of @xmath12 to the jordan canonical form . it is known @xcite that , for the observability canonical form , @xmath74 where @xmath75 is the multiplicity of the eigenvalues of matrix @xmath36 , with @xmath49 . thus , making use of the laplace s expansion by minors , the determinant eqn . 14 can be factorised as follows : @xmath76 = m_1 m_2 \ , det [ \varphi_i(\alpha_{m})]\ ] ] where @xmath77 @xmath78\ ] ] with @xmath79 identity matrix of dimension @xmath80 . finally , @xmath81 \ ; ( i = 1 , \ldots , n ) , \,(m = 0 , \ldots , n - 1)$ ] is the same matrix as the one defined in eqn . 27 . now , from the expression 37 , the following result is derived : _ lemma 2 : _ the realisation @xmath22 is completely _ n_-observable ( observable in @xmath0 steps ) if , and only if , @xmath0 consecutive sampling instants are chosen in such a way that @xmath82 \neq 0 \qquad ( i = 1 , \ldots , n ; \;\ , m = 0 , \ldots , n-1)\ ] ] _ proof : _ the proof is evident from the factorisation of the expression 37 . note that , for this kind of system , the _ n_-observability depends on the characteristic modes of the continuous system and on the choice of the sampling instants . we remark that the result is analogous to that of the preceding subsection . the results obtained in the two preceding subsections can be summarised as follows : _ theorem : _ a system verifying the conditions _ ( a ) _ , _ ( b ) _ and _ ( c ) _ in section 2 , is jointly _ n_-reachable and _ n_-observable , if , and only if , @xmath0 consecutive sampling instants are chosen in such a way that @xmath83 \neq 0" +"the signatures of the strong interactions in the quark - gluon matter were found in heavy ion collisions experiments @xcite . there are proposals @xcite suggesting that color - magnetic monopoles contribution can explain this rather unexpected property . these proposals inspired a number of publications devoted to the properties and possible roles of the monopoles in the quark - gluon phase @xcite . lattice gauge theory suggests a direct way to study fluctuations contributing to the euclidean space functional integral , in particular , the color - magnetic monopoles can be studied . in a number of papers the evidence was found that the nonperturbative properties of the nonabelian gauge theories such as confinement , deconfining transition , chiral symmetry breaking , etc . are closely related to the abelian monopoles defined in the maximally abelian gauge @xmath3 @xcite . this was called a monopole dominance @xcite . the drawback of this approach to the monopole studies is that the definition is based on the choice of abelian gauge . there are various arguments supporting the statement that the abelian monopoles found in the mag are important physical fluctuations surviving the cutoff removal : scaling of the monopole density at @xmath4 according to dimension @xmath5 for infrared @xmath6 cluster @xcite ; abelian and monopole dominance for a number of infrared physics observables ( string tension @xcite , chiral condensate @xcite , hadron spectrum @xcite ) ; monopoles in the mag are correlated with gauge invariant objects - instantons and calorons @xcite . it has been recently argued that the mag is a proper abelian gauge to find gauge invariant monopoles since thooft - polyakov monopoles can be identified in this gauge by the abelian flux , but this is not possible in other abelian gauges @xcite . most of these results were obtained for @xmath0 gluodynamics but then confirmed for @xmath7 theory and qcd @xcite . listed above properties of abelian monopoles survive the continuum limit and removal of the gribov copy effects . it is worth noticing that removal of gribov copy effects changes numerical values of monopole characteristics quite substantially @xcite . in this paper we are studying thermal monopoles . it was shown in ref . @xcite that thermal monopoles in minkowski space are associated with euclidean monopole trajectories wrapped around the temperature direction of the euclidean volume . so the density of the monopoles in the minkowski space is given by the average of the absolute value of the monopole wrapping number . in @xcite another approach to study thermal monopole properties in the quark - gluon plasma phase based on the molecular dynamics algorithm was suggested and implemented . the results for parameters of inter - monopole interaction were found in agreement with lattice results @xcite . first numerical investigations of the wrapping monopole trajectories were performed in @xmath0 yang - mills theory at high temperatures in refs . @xcite and @xcite . a more systematic study of the thermal monopoles was performed in ref . it was found in @xcite that the density of monopoles is independent of the lattice spacing , as it should be for a physical quantity . the density density spatial correlation functions were computed in @xcite . it was shown that there is a repulsive ( attractive ) interaction for a monopole monopole ( monopole antimonopole ) pairs , which at large distances might be described by a screened coulomb potential with a screening length of the order of @xmath8 fm . in ref . @xcite it was proposed to associate the respective coupling constant with a magnetic coupling @xmath9 . in the paper @xcite trajectories which wrap more than one time around the time direction were investigated . it was shown that these trajectories contribute significantly to a total monopole density at @xmath10 slightly above @xmath1 . it was also demonstrated that bose condensation of thermal monopoles , indicated by vanishing of the monopole chemical potential , happens at temperature very close to @xmath1 . however , the relaxation algorithm applied in @xcite to fix the mag is a source of the systematic errors due to effects of gribov copies . it is known since long ago that these effects are strong in the mag and results for gauge noninvariant observables can be substantially corrupted by inadequate gauge fixing @xcite . for the density of magnetic currents at zero temperature it might be as high as @xmath11 . for nonzero temperature the effects of gribov copies were not investigated until recently . in a recent paper @xcite this gap was partially closed . it was shown that indeed gauge fixing with sa algorithm and @xmath12 gauge copies per configuration gives rise to the density of the thermal monopoles @xmath13 to @xmath14 lower ( depending on the temperature ) than values found in @xcite . large systematic effects due to effects of gribov copies found in ref . @xcite imply that results obtained in earlier papers @xcite for the density and other monopole properties can not be considered as quantitatively precise and need further independent verification . the quantitatively precise determination of such parameters as monopole density , monopole coupling and others is necessary , in particular , to verify the conjecture @xcite that the magnetic monopoles are weakly interacting ( in comparison with electrically charged fluctuations ) just above transition but become strongly interacting at high temperatures . in this paper we use the same gauge fixing procedure as in refs . @xcite to avoid systematic effects due to gribov copies . the careful study of the finite volume and finite lattice spacing effects was made in @xcite . we fix our spatial lattice size to @xmath15 which was shown in ref . @xcite to be large enough to avoid finite volume effects . we check finite lattice spacing effects comparing results obtained on lattices with @xmath16 and 6 at two temperatures . let us emphasize that our studies are computationally much more demanding in comparison with studies undertaken in refs . @xcite , since we produce @xmath12 gribov copies per configuration to avoid gribov copies effect . for this reason our check of the continuum limit is not as extensive as it was in refs . @xcite . the important contribution of this work to the thermal monopole studies is a check of universality . in studies of magnetic currents at zero temperature it was found @xcite that the density of the infrared magnetic currents is different for different lattice actions with difference as large as @xmath14 . the conclusion was made that the ultraviolet fluctuations contribute to the infrared density and this contribution has to be removed . partial removal was made by the use of the improved action . in present paper we use the improved lattice action - tadpole improved symanzik action and compare our results for the density and other quantities with results obtained with the wilson action @xcite . we find that the universality holds for monopoles which do not form short range ( ultraviolet ) dipoles . we also want to point out that in this work we use more natural procedure of computing monopole correlators in comparison with papers @xcite and @xcite . it was mentioned in ref . @xcite that monopole trajectories had a lot of small loops attached to them which were uv noise . presence of such loops do not allow to determined monopole spatial coordinates unambiguously for all time slices . this problem was bypassed in @xcite by using only one time slice . we remove the small loops attached to thermal monopole trajectories and thus we are able to determine the monopole coordinates in every time slice unambiguously . then we use all time slices to compute the correlators what allows us to decrease the statistical errors substantially . we studied the @xmath0 lattice gauge theory with the tadpole improved symanzik action : parameter @xmath22 is the input tadpole improvement factor taken here equal to the fourth root of the average plaquette p = @xmath23 . we use the same code to generate configurations of the lattice gauge field as was used in ref . our calculations were performed on the asymmetric lattices with lattice volume @xmath24 , where @xmath25 is the number of sites in the time ( space ) direction . the temperature @xmath10 is given by : where @xmath27 is the lattice spacing . to determine the values of @xmath22 we used results of ref . @xcite either directly or to make interpolation to necessary values of @xmath28 . the critical value of the coupling constant for @xmath29 is @xmath30 @xcite . for @xmath29 the ratio @xmath31 was obtained using data for the string tension from ref . @xcite again either directly or via interpolation . for @xmath32 ratio @xmath31 was taken to be equal to the ratio for @xmath29 multiplied by factor @xmath33 . in table [ tab : lattice_size ] we provide the information about the gauge field ensembles and parameters used in our study . we apply the simulated annealing ( sa ) algorithm which proved to be very efficient for this gauge @xcite as well as for other gauges such as center gauges @xcite and landau gauge @xcite . to further decrease the gribov copy effects we generated @xmath12 gribov copies per configuration starting every time gauge fixing procedure from a randomly selected gauge copy of the original monte carlo configuration ." +"with their characteristic period - luminosity ( pl ) and period - luminosity - color ( plc ) relations , classical cepheids play a relevant role as distance indicators for the definition of the extragalactic distance scale . the application of a large magellanic cloud ( lmc)-based pl relation to external galaxies observed with the hubble space telescope ( hst ) , has led to the calibration of secondary distance indicators and in turn to an estimate of the hubble constant ( @xmath4 , see e.g. * ? ? ? * ; * ? ? ? * ) . the theoretical explanation for the observational evidence of a pl relation for classical cepheids relies on the assumption that intermediate mass stars undergoing central helium burning are characterized by a mass - luminosity ( ml ) relation , as predicted by stellar evolution models . the ml relation is significantly dependent on several physical and numerical assumptions adopted in stellar evolution models , thus the comparison between observations and cepheid evolutionary / pulsation models provides a unique insight into the stellar evolution and pulsation physics . an important issue still under debate is the universality of the cepheid pl relations , and , in turn , the possibility of applying lmc - calibrated cepheid pl relations to infer the distance of any galaxy containing cepheids , independently of its chemical composition . in the last decade many efforts were devoted to investigate the dependence of the cepheid properties on metallicity , since a metallicity effect could produce significant systematic errors in the evaluation of the extragalactic distance scale and in turn on @xmath4 . however , no general consensus has been reached yet . on the theoretical side , linear non adiabatic models mostly suggest that a variation in chemical composition produces negligible effects on the pl relations ( see e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , while nonlinear convective pulsation models @xcite predict a significant metallicity effect on the cepheid instability strip ( hereinafter is ) topology and on the pl relations . for instance , @xcite and @xcite find that the synthetic pl relations become shallower as the metallicity increases , and the size of the effect depends also on the photometric band , with a decreasing sensitivity as wavelength increases from optical to near infrared ( nir ) bands . consequently , metal - rich pulsators with periods longer than five days have fainter optical magnitudes than metal - poor pulsators . this scenario is further complicated by the theoretical finding that the helium mass fraction @xmath5 also plays a role at the highest metallicities ( @xmath6 ) , with the slope of the linear pls increasing as @xmath5 increases at fixed @xmath7 @xcite . in turn , the metallicity correction to the predicted distance moduli varies with the assumed @xmath8 , showing a sort of turnover around solar metallicity . in particular , for p @xmath9 20 days and [ o / h ] @xmath9 0.2 dex , as measured in several spiral galaxies observed by the hst key project @xcite , the average predicted metallicity correction varies from @xmath100.2 mag to @xmath11 + 0.25 mag , as @xmath8 increases from 2.0 to 3.5 . on the empirical side , several authors suggest that metal - rich cepheids are , at fixed period , brighter than metal - poor ones , either over the entire period range @xcite , or at least for periods shorter than @xmath12 25 days @xcite . @xcite by comparing distances based on cepheids and on the tip of the red giant branch ( trgb ) method for a selected sample of spiral galaxies , found that the metallicity effect , usually expressed in the form @xmath13 , is equal to @xmath140.25 mag dex@xmath15 . however , the revised trgb distances by @xcite no longer support a @xmath16 value of @xmath140.25 mag dex@xmath15 and are in better agreement with the theoretical results ( see * ? ? ? * for details ) . other empirical results that seem to support the nonlinear theoretical scenario were obtained by @xcite , on the basis of spectroscopic [ fe / h ] measurements for galactic and magellanic cloud cepheids . using only their spectroscopic abundances for galactic cepheids with published distances , @xcite found that the metallicity correction is in qualitative agreement with the model results , and shows the same kind of turnover around solar metallicity as predicted by nonlinear pulsation theory . more recently , using direct high resolution metallicity measurements for a total of 68 galactic and magellanic cepheids , @xcite found that metallicity affects the @xmath17-band cepheid pl relation , with metal - rich cepheids appearing to be systematically fainter than metal - poor ones , in agreement with the theoretical predictions by @xcite and @xcite , and independently of the adopted distance scale for galactic and lmc cepheids . on the other hand , direct empirical tests of the metallicity effect based on the observation of cepheids in the outer and inner fields of m101 @xcite , in ngc4258 @xcite , and , recently , in m33 @xcite , should be taken with caution . indeed , in m101 the presence of blended cepheids could have affected the results of the test ( see * ? ? ? * ) , while in the case of ngc4258 there is evidence against the assumed metallicity gradient , as both the comparison with pulsation models and the most recent hii abundance measurements @xcite suggest a rather constant lmc - like metal - content for the cepheids observed in the two selected fields ( see * ? ? ? * for details ) . in m33 , @xcite adopted the [ o / h ] gradient by @xcite and conclude that blending can not account for the difference in distance modulus between the two fields . however , as also pointed out by @xcite , these results are always based on indirect measurements of the metallicity , assumed to be that corresponding to the oxygen nebular abundances of hii regions at the same galactocentric distance of the cepheids . finally , there are also recent empirical results in favour of the universality of the pl slope : distance estimates based on the `` near - infrared surface brightness '' ( isb ) technique ( * ? ? ? * and references therein ) and the hst parallaxes @xcite for ten galactic cepheids seem to indicate a vanishing metallicity effect between galactic and magellanic cepheids . similar suggestions have been put forward by several authors ( see e.g. * ? ? ? * ; * ? ? ? * ) for cepheids in galaxies with metallicities significantly lower than the lmc , but no theoretical predictions are available in the literature for the metallicity effect on the properties of cepheids in this range of abundances or at lower z. the identification and study of cepheids in very metal - poor galaxies , is a challenging perspective . these galaxies represent the closest analog to primordial galaxies in the early universe and , as such , offer the best place where to study star formation and stellar evolution in a ( almost ) pristine environment . some of these galaxies have also been claimed to be primordial systems just forming in the local universe due to lack of detection of faint red stars on the red giant branch tip ( trgb , stars older than @xmath111 gyr ) . however , the lack of these stars may also be due to a much larger distance of these systems that does not allow to resolve the faint trgb stars . a precise determination of the distance of these galaxies through cepheids allows us to verify or confute their nature of young nearby galaxies . in the context of the hst acs go program 10586 ( pi : a. aloisi ) we have identified three classical cepheids in the blue compact dwarf galaxy izw18 , having respectively periods of 8.71 , 125 and 130.3 days . a new estimate of the distance , and , in turn , of the age of the galaxy stellar populations were obtained both from the classical cepheids and from the galaxy s trgb , which allowed us to rule out the possibility that izw18 is a truly primordial galaxy of recent formation in the local universe @xcite . at the same time this project also provided a first sample of ultra - low metallicity ( @xmath18 ) classical cepheids @xcite , thus representing an important benchmark for the pulsation models . in this paper we investigate theoretically the pulsation properties of cepheids at this very low metallicity ( z=0.0004 ) , in order to probe the metallicity effect at z @xmath19 0.004 , and to provide a theoretical scenario for the classical cepheids recently detected in izw18 @xcite . the organization of the paper is as follows : in sect . 2 we present the new set of pulsation models ; in sections 3 and 4 we show our results for the topology of the is and the behaviour of the light curves , while the multi - filter plc , period - wesenheit and pl relations are presented and discussed in sect . 5 . finally , in sect . 6 we discuss the comparison with the cepheids observed in izw18 and the implications for the cepheid distance scale . conclusions are summarized in sect . using the same pulsation code ( see * ? ? ? * for details ) adopted in our previous investigations of more metallic cepheids @xcite , we investigated for the first time the full amplitude behaviour of metal - poor cepheid models . to this purpose we fixed the metal and helium abundances at @xmath1 , @xmath2 and selected model stellar masses in the range from 4 to 13 @xmath20 . two luminosity levels ( see table 1 ) were assumed for most of the selected stellar masses corresponding to canonical and mild overshooting ( noncanonical ) evolutionary predictions , respectively . the canonical scenario is provided by the pisa evolutionary library ( pel ) for @xmath21 and discussed in @xcite we extrapolated the ml relation obtained for lower masses taking into account the evidence that , for higher metal content , models with 13 @xmath20 follow the same ml relation as lower mass models . ] , while the noncanonical luminosity level is obtained by adding 0.25 dex ( in @xmath22 ) to the canonical value , according to the prescriptions by @xcite . for each mass and luminosity , an extensive range of effective temperatures was explored for pulsation instability , in order to derive the location of the blue and red edges of the is in the hertzsprung - russell ( hr ) diagram . for canonical models , we also explored the effect of varying the mixing length parameter @xmath23 , adopted in the code to close the nonlinear system of dynamical and convective equations ( see * ? ? ? * ; * ? ? ? * for details ) , in the range from the standard value of 1.5 to 2.0 . in the following two sections we discuss the results obtained for the topology of the is , and for the morphological properties of the bolometric light curves , respectively . for each selected mass and luminosity , the effective temperatures of the hottest pulsating fundamental model , increased by 50 k ( fundamental blue edge , hereafter fbe ) , and of the coolest pulsating fundamental model , decreased by 50 k ( fundamental red edge , hereafter fre ) are reported in the third and fourth columns of table 1 , respectively . the adopted uncertainty of 50 k in the location of the is boundaries stems" +"an axion is a strongly motivated particle for a dark matter candidate . the axion was originally introduced to solve the strong cp problem in quantum chromodynamics ( qcd ) @xcite . axion - like particles ( alps ) also appear naturally in string theory @xcite . the topological complexity of string theory compactifications can provide a plenitude of light alps spanning many orders of magnitude in mass , known as the string axiverse scenario @xcite . in principle there is no lower limit to the alp mass in this scenario , though the lower limit of relevance for dark matter is the hubble scale , @xmath4 ev . recent gamma - ray data from blazars suggests the existence of cosmological magnetic fields stronger than @xmath5 g in large voids @xcite . such magnetic fields can be accounted for by primordial magnetic fields , which are generated in the early universe ( for recent reviews , see refs . @xcite ) . since alps generally couple with electromagnetic fields , one can expect a conversion between cosmic microwave background ( cmb ) photons and alps in the presence of primordial magnetic fields . such a conversion produces observable distortions in the cmb spectrum @xcite . @xcite has studied the resonant conversion between cmb photons and alps . they obtained the photon - alp mixing constraint from the far infrared absolute spectrophotometer ( firas ) data of the cosmic background explorer ( cobe ) @xcite . since the cobe firas constraint on the resonant conversion probability @xmath6 corresponds to @xmath7 , they provided a constraint @xmath8 for alp masses between @xmath9 ev and @xmath10 ev , where @xmath0 is the coupling constant and @xmath1 is the spatially averaged magnetic field strength at the present epoch . their result suggests that , if primordial magnetic fields have a strength close to the current upper limit , the cmb distortion constraint gives a stronger constraint on @xmath0 than the solar and astrophysical bounds @xcite . recently , pixie @xcite and prism @xcite have been proposed to provide precision measurements of the cmb frequency spectrum . measuring cmb distortions form the blackbody spectrum is a good probe to access the thermal history of the universe ( see refs . @xcite for recent reviews ) . the current goal of these sensitivities to cmb distortions is set to be a factor @xmath11 improvement on the cobe firas . here , we revisit cmb distortions due to resonant photon - alp conversions , and make a forecast about the feasibility of future constraints from pixie / prism . we also expand the constraint to smaller alp masses , @xmath12 ev , than in ref . such small - mass alps naturally arise in the axiverse scenario and have diverse phenomenology in the cmb , large scale structure , and black hole astrophysics that can constrain them independently of their couplings to the visible sector @xcite . however , when the coupling to photons is present such alps can go through resonant conversions with cmb photons due to plasma effects in the cosmic dark age and be constrained independently of their contribution to dark matter . we evaluate cmb distortions due to small - mass alps , taking into account multiple resonant conversions . this paper is organized as follows . we briefly review the resonant conversion between photons and alps in the cosmological scenario in sec . we also derive the analytical form of the resonant conversion in both strong and weak coupling limits at the resonant epoch . in sec . iii , we calculate the resonant conversion probability numerically and evaluate the pixie / prism constraints on the alp coupling and primordial magnetic field strength . iv is devoted to our conclusions . throughout this paper , we adopt natural units where @xmath13 , @xmath14 and the boltzmann constant @xmath15 . we use cosmological parameters for a flat @xmath16cdm model , @xmath17 , @xmath18 , and @xmath19 . alps couple to electromagnetic fields through a two photon vertex . in the existence of external magnetic fields , electromagnetic fields in the alp interaction terms can be decomposed into the dynamical part of photons and the external magnetic field part . as a result , the interaction term of an alp and a photon with external magnetic fields is given by @xmath20 where @xmath21 is the photon frequency , @xmath22 is the component of the external magnetic field perpendicular to the propagation of photons , and @xmath23 is the component of a photon parallel to the @xmath22 component . due to this interaction , the propagation eigenstates of the photon - alp system @xmath24 are different from the interaction eigenstates with external magnetic fields . therefore , conversion between @xmath25 and @xmath26 occurs in the same way as for massive neutrinos of different flavors . the mixing angle of @xmath24 in vacuum is given by @xcite @xmath27 where @xmath28 is the alp mass . this mixing angle produces photon - alp oscillations with a wavenumber @xmath29 in the cosmological plasma , the photon dispersion relation is modified due to plasma effects . this modification can be parametrized by an effective photon mass @xmath30 . among the various plasma effects , the scatterings off free electrons and neutral atoms make negative and positive contributions to the effective photon mass , respectively . due to these effects , the effective mass can be given as @xcite @xmath31 , \label{eq : m_gamma}\ ] ] where @xmath32 is the plasma frequency @xmath33 with the fine structure constant @xmath34 , the electron mass @xmath35 and the free electron number density @xmath36 . the refractive index of neutral hydrogen @xmath37 is set to @xmath38 in normal conditions @xcite . in eq . ( [ eq : m_gamma ] ) , we ignore the contributions of helium and magnetic fields , because these effects are negligibly small @xcite . the effective photon mass depends on the evolution of the ionization fraction @xmath39 through the neutral hydrogen and free electron number densities . ionized hydrogen recombines with free electrons at @xmath40 and is reionized around @xmath41 @xcite . we calculate @xmath39 with recfast @xcite , adopting a toy model for reionization which is given by a @xmath42 function , @xmath43 $ ] with @xmath44 and @xmath45 . we plot the evolution of the effective photon mass in fig . [ fig : mg2 ] with cmb temperature @xmath46 . the effective mass squared has positive and negative contributions from scattering off free electrons and neutral atoms , respectively . as a result , the effective mass becomes negative for high frequencies in the dark ages where negative contributions dominate positive ones . the effective photon mass modifies photon - alp oscillations through the lagrangian . this effect arises as the effective mixing angle @xmath47 @xcite , @xmath48 where the parameter @xmath49 controls the significance of the plasma effects , @xmath50 as shown in fig . [ fig : mg2 ] , the effective mass at early universe can be much larger than the alp mass and @xmath51 . in this case , the conversion between @xmath25 and @xmath26 is suppressed . however , as the universe evolves , the effective mass equals an alp mass and @xmath49 reaches unity . at this time , the effective mixing angle becomes @xmath52 and the resonant conversion occurs between photons and alps with this mass . this is in analogy to `` resonant '' neutrino oscillations known as mikheyev - smirnov - wolfenstein ( msw ) effect @xcite . , @xmath53 , @xmath54 and @xmath55 with cmb temperature @xmath46 . for @xmath56 the photon mass is always positive and the minimum alp mass that experiences resonant conversion is @xmath57ev , with multiple resonance for @xmath58ev ( horizontal line ) . since @xmath30 passes through zero and back for high @xmath21 , these will be most relevant for light alps and multiple resonances . , width=302 ] the conversion probability for the resonance is given by @xcite @xmath59 where @xmath60 is the level crossing probability , @xmath61 and @xmath62 are the effective mixing angles at the photon production ( @xmath63 ) and detection points ( @xmath64 ) , respectively . at the photon production point ( i.e. at reheating ) , since the redshift is very high , @xmath49 is large . hence we approximate @xmath65 throughout this paper . the level crossing probability @xmath60 indicates the non - adiabaticity of the conversion . while @xmath60 becomes zero in the limit of the adiabatic conversion , @xmath60 reaches unity in the extremely non - adiabatic case . in order to obtain the level crossing probability , we make the approximation that @xmath30 varies linearly in the resonance regime , and make a taylor - series expansion at the resonance position , neglecting the second- and higher - derivative terms . in this approximation , the level crossing probability is given by applying the landau - zener result @xcite , @xmath66 , \label{eq : landau}\ ] ] where @xmath67 and @xmath68 are respectively the oscillation wavelength and vacuum mixing angle at the resonance epoch , and @xmath69 is a scale parameter to be evaluated at the location where a resonance occurs @xcite , @xmath70 where @xmath71 refers to the time at the resonance . for small @xmath28 ( @xmath72 ev ) , we expected from fig . [ fig : mg2 ] that multiple resonances occur . the conversion probability can be calculated in a manner similar to the single resonance case . following the classical probability result , we obtain the probability for the double resonant case by replacing @xmath60 by @xmath73 , where @xmath74 and @xmath75 are the probabilities for the first and second resonances , respectively @xcite . similarly to the double resonant case , the probability for more multiple resonances can be calculated . resonant photon - alp conversions depend on the component of external magnetic fields perpendicular to the propagation direction of photons , @xmath22 . generally , primordial magnetic fields have structures which depend on the generation mechanisms of these fields . therefore , the resonant conversion probability is possibly anisotropic due to these structures and depends on the ratio of the magnetic field coherent scale to the resonant scale . in this paper , we focus on the monopole component of cmb distortions to the black - body spectrum . before calculating resonant conversion probabilities numerically , it is worth estimating them analytically for two cases , @xmath76 and @xmath77 where @xmath78 is the effective photon mass at the detection point ( @xmath64 ) . in the case of @xmath76 , the resonant conversion probability has been studied in ref . the mixing angle at the detection point is expressed by that in the vacuum state given by eq . ( [ eq : theta0 ] ) . since we are interested in the weak mixing limit , @xmath79 , we can approximate @xmath80 . in this case , the resonant conversion happens only once . therefore the conversion probability is provided by eq . ( [ eq : g - p - eq - heavy ] ) , and the sky - averaged conversion probability can be approximated by @xmath81 in order to satisfy the cobe firas limit , @xmath82 , a strong non - adiabatic resonance , @xmath83 , is required . for the single resonance case , @xmath60 is given by eq . ( [ eq : landau ] ) . a strong non - adiabatic condition , @xmath84 , leads the level crossing probability to @xmath85 accordingly , in the weak coupling limit , the conversion probability at a comoving frequency @xmath21 can be provided by @xcite @xmath86 where the redshift factor comes from the dependence of both magnetic fields and cmb physical frequency on the resonant epoch . for @xmath87 , cmb photons suffer multiple resonances . since photons are still detected in vacuum , we" +"magnetars , comprising soft gamma repeaters ( sgrs ) and anomalous x - ray pulsars ( axps ) , have been brought to great attention because they are likely to have super strong surface magnetic fields reaching @xmath8 g @xcite . this exceeds the critical field strength @xmath9 g , where @xmath10 , @xmath11 , @xmath12 , and @xmath13 are the electron mass , the light velocity , the electron charge and the reduced planck constant , respectively . to understand radiation processes in such an environment , it is necessary to fully take into account non - perturbative effects in quantum electrodynamics . outstanding properties of magnetars include burst activity , observed from all sgrs and some axps . a typical `` short burst '' has a duration of @xmath1100 ms , and a 2100 kev energy release by 10@xmath14 erg ( e.g. , @xcite ) . among a variety of burst activities , the most energetic ones are the giant flares , which were so far detected from sgr0526@xmath1566 ( e.g. , @xcite ) , sgr1900@xmath014 ( e.g. , @xcite ) , and sgr1806@xmath1520 ( e.g. , @xcite ) . x - ray spectra of short bursts provide useful diagnostics of their emission mechanism . wide - band spectra of short bursts from sgr1806@xmath1520 and sgr1900@xmath014 , detected by high energy transient explorer 2 ( hete-2 ; @xcite ) , are generally described by a photoelectrically absorbed two - blackbody ( 2bb ) model @xcite , even though this could be a phenomenological description . spectra of bursts @xcite and intermidiate flares @xcite from sgr 1900@xmath014 also favor the 2bb modeling . in addition , bursts from the new magnetar sgr0501@xmath04516 , detected by suzaku @xcite and swift @xcite , also exhibited 2bb - type spectra ( @xcite , hereafter paperi ; @xcite ) . in terms of this modeling , these short bursts all exhibit an interesting scaling as @xmath16 @xcite , where @xmath17 and @xmath18 are the higher and lower temperatures of the 2bb model , respectively . it has long been known that sgrs and axps show not only burst activities but also persistent emission in energies below @xmath110 kev , of which the spectra are generally reproduced by two phenomenological models ; 2bb ( e.g. , @xcite ) or a photoelectrically absorbed blackbody plus power law model ( bb@xmath0pl ; e.g. , @xcite ) . moreover , recent studies of sgr0501@xmath04516 and other objects propose a `` blackbody plus comptonized blackbody '' model ( @xcite , hereafter paperii ) and a resonant cyclotron scattering model @xcite as alternative possibilities . although the spectral modeling is thus ambiguous , the persistent x - ray emission interestingly shows the same @xmath16 relation as those of the bursts @xcite if we employ the 2bb representation . this suggests a common radiation mechanism between the bursts and persistent emission , further leading to a possibility that the persistent x - ray emission may consist of numerous micro bursts @xcite . recent studies using integral ( e.g. , @xcite ) and suzaku ( @xcite ; paperii ; @xcite ) revealed an extremely hard x - ray component above @xmath110 kev in persistent emission spectra of a significant fraction of sgrs ( including sgr0501@xmath04516 : paperii ) and axps . the hard x - ray component , which is thought to be distinct from the blackbody - like soft component , can be reproduced by a power law ( pl ) model with an extremely hard photon index of @xmath19 . as reported in paperii for sgr0501@xmath04516 and in @xcite for some other sources , the 2100 kev luminosity of the hard x - ray component is often comparable to that of the soft blackbody component . considering these properties , as well as a clear dependence of the hardness ratio between the hard and soft luminosities on the characteristic age as revealed with suzaku @xcite , the hard x - ray component is expected to provide an important clue to the nature of magnetars . theoretically , the hard x - ray production mechanism is extensively discussed @xcite , but it is not yet conclusive . if there is a common radiation mechanism between the bursts and persistent emissions , the hard x - ray component may also be seen in burst spectra . however , short bursts of magnetars so far studied , with fluence @xmath20 erg @xmath3 , generally have @xmath21715 kev ( e.g. , @xcite ) . as a result , their 2bb spectra , extending well up to @xmath22 kev , would mask any hard x - ray component . this raises a possibility that bursts with considerably lower fluence , which have remained not much studied , may have lower values of @xmath17 , e.g. , close to those found in the persistent emission ( e.g. , @xmath210.43.9 kev ; @xcite ; paperii ) , and would allow more sensitive searches for the hard - tail component . considering this , we focus on wide - band spectroscopy of low - fluence bursts . observations with suzaku are suitable for this purpose , because of its high sensitive over a broad energy band , realized by the x - ray imaging spectrometer ( xis ; 0.212 kev ; @xcite ) and the hard x - ray detector ( hxd ; 10600 kev ; @xcite ) . we have hence revisited the suzaku data of sgr0501@xmath04516 , acquired during its 2008 august activity . as a third publication ( after paperi and paperii ) from this observation , the present paper reports on our successful detection of a hard component , in an hxd spectrum which sums over 31 short bursts from this new magnetar . the new soft gamma repeater sgr0501@xmath04516 was discovered on 2008 august 22 by the burst alert telescope on - board swift , when it displayed sgr - like burst activity @xcite . soon after the discovery , a spin period of @xmath23 was reported based on an observation by the rossi x - ray timing explorer @xcite . as described in paperi and paperii , we triggered a suzaku target - of - opportunity ( too ) observation , which started at 00:05 on 2008 august 26 and ended at 08:25 on 2008 august 27 ( ut ) . the xis was operated with a 1/4 window option which yields a 2 s time resolution , while the hxd was operated in the standard mode . the acquired data were already utilized in paperi and paperii ; the former described a strong short burst and persistent soft x - ray emission , while the latter focused on the detection of a hard component in the persistent emission . the present paper , utilizing the same too data , deals with broad - band spectra of 31 smaller short bursts . the distance to sgr0501@xmath04516 , though estimated to be 1.5 kpc based on its directional proximity to the young supernova remnant hb9 @xcite , is actually very uncertain . in this paper , the distance is hence assumed to be 4 kpc , which is similar to the value of @xmath15 kpc employed by @xcite . the reduction of the xis and hxd event data ( v2.2 ) were made using heasoft6.6.1 software . the latest calibration database ( caldb:20090402 ) was applied to unfiltered xis event data using _ xispi _ ( v2008 - 04 - 10 ) . then , using _ xselect _ ( v2.4a ) , we extracted a new set of filtered xis events with the standard criteria and a grade selection `` grade = ( 0,2 - 4,6 ) '' . after that , hot and flickering pixels were removed using _ cleansis _ ( v1.7 ) . telemetry - saturated time intervals , estimated by _ xisgtigen _ ( v2007 - 05 - 14 ) , were removed from the xis data using _ xselect_. we created light curves and spectra from the cleaned xis event data using _ xselect_. response matrix files were generated by _ ( v2007 - 05 - 14 ) , and ancillary response function files by _ xissimarfgen _ ( v2008 - 04 - 05 ) . the obtained net exposure is @xmath160 ks . using _ hxdpi _ and _ hxdgrade _ ( v2008 - 03 - 03 ) , we applied the latest calibration database ( caldb:20090902 ) to the unfiltered hxd event data . cleaned pin and gso events were extracted from these newly calibrated data with the standard criteria using _ xselect_. again , we created light curves and spectra using _ xselect_. dead time corrections were applied to the spectra using _ hxddtcor_. response matrix files of version 2008 - 01 - 29 were used . this yielded a net exposure of @xmath24 ks for the hxd data . as shown in figure1 of paperi , a number of visually obvious bursts are found in a 0.212 kev xis light curve with 2-s resolution , obtained by summing the data from the two fi sensors ( xis0 and xis3 ) and the one bi sensor ( xis1 ) . at least three of them , including the strongest one analyzed in paperi , were also noticed in the 1020 kev hxd - pin light curve with a 500 ms time resolution . following our preliminary attempt in paperi , we conducted a quantitative burst search using the 0.212 kev light curve of the xis . after visually eliminating 8 obvious bursts which have @xmath25 cts(2s)@xmath26 , the light curve was converted to a count - rate ( per 2s ) histogram as shown in figure [ fig : xis_hist ] ; this includes the background , the persistent signal emission , and short bursts . the histogram has an average of @xmath27 and a standard deviation of @xmath28 , both in units of cts(2s)@xmath26 , where the quoted errors refer to 90% confidence levels , and can be approximated by a poissonian distribution . we searched the xis count - rate histogram for those 2-s bins where the count rate exceeds @xmath29 cts(2s)@xmath26 . this selection has yielded 35 time bins with significant excess counts . regarding a set of consecutive such bins as representing a single burst , we thus detected 32 short bursts altogether . among them , the strongest one was already analyzed in paperi . below , we therefore analyze the remaining 31 bursts , which are summarized in table [ tab : burst_summary ] . they are hereafter identified sequentially as # 01 , # 02 , @xmath30 , and # 31 . these 31 short bursts are considered to be free from event pile - up effects in the xis , because their count rates were less than 107 cts(2s)@xmath26xis@xmath26 above which the effect becomes significant . light curves of typical short bursts ( # 03 , # 13 , # 14 , # 22 and # 23 ) are presented in figure [ fig : burst_lc ] . among them , two ( # 03 and # 14 ) are accompanied by significant emissions in the hxd - pin and/or hxd - gso energy bands . since the present paper puts its focus on burst spectra , we must subtract the persistent emission of sgr0501@xmath04516 , as well as the non x - ray background and the cosmic x - ray background . for each burst , we therefore accumulate the xis and hxd data over a time region ( see below ) containing the burst , and subtract the corresponding background spectra which are acquired before and after the burst period . the on - burst and background data of the xis were both extracted from box regions with sizes of ( detx , dety ) = ( @xmath31 , @xmath32 ) for xis1 , and ( @xmath32 , @xmath31 ) for xis0 and" +"nanotechnology , as well as biology , biophysics and chemistry are using or studying setups and objects which are smaller and smaller . in these systems , one is usually interested in mean values , but thermal fluctuations play an important role because their amplitude are often comparable to the mean values . this is for example the case for quantities such as the energy injected in the system or the energy dissipated by the system . these fluctuations can lead to unexpected and undesired effects : for instance , the instantenous energy transfer can be reversed by a large fluctuation , leading energy to flow from a cold source to a hot one . these events , although rare , are quantitatively studied by the recent fluctuations theorems ( fts ) . these theorems give fluctuation relations ( frs ) that quantify the probability of these rare events in systems which can be arbitrarily far from equilibrium . fts have been demonstrated in both deterministic systems @xcite and stochastic dynamics @xcite . experiments searching for frs have been performed in dynamical systems @xcite , but interpretations are very difficult because a quantitative comparison with theoretical prediction is impossible . other experiments have been performed in stochastic systems described by a first order langevin equation : a brownian particle in a moving optical trap @xcite and an out - of - equilibrium electrical circuit @xcite in which existing theoretical predictions @xcite were verified . interesting comments on the langevin equation can be found in @xcite . in the present article , we study a thermostated harmonic oscillator described by a second order langevin equation . we experimentally search frs for the work done by an external operator and for the heat dissipated by the system , and present analytical derivations of fts based on experimental observations . this paper is organized as follows . in section [ sec : system : description ] , we present the experimental system , write its energy balance to define the work given to the system together with the heat dissipated . we then introduce the fluctuation relations ( frs ) and the fluctuation theorems ( fts ) . in sections [ sec : tftexp ] , [ sec : ssftrampexp ] and [ sec : sinusexp ] , we present experimental results on the fluctuations of first the work and then the heat . a short discussion on experimental results in given in [ sec : expconc ] . then , in sections [ sec : worktheo ] and [ sec : heattheo ] , we present some analytical derivations of fts based on hypothesis inspired by experimental observations . we compare these analytical predictions to the experimental observations and finally conclude in section [ sec : conc ] . our system is a harmonic oscillator and we measure the non - equilibrium fluctuations of its position degree of freedom . the oscillator is damped due to the viscosity of a surrounding fluid that acts as a thermal bath at temperature @xmath0 . our oscillator , depicted in fig . [ fig : pendulum]a , is a torsion pendulum composed of a brass wire ( length @xmath1 @xmath2 , width @xmath3 @xmath2 , thickness @xmath4 @xmath5 ) and a glass mirror glued in the middle of this wire ( length @xmath6 @xmath2 , width @xmath7 @xmath2 , thickness @xmath8 @xmath2 ) . the elastic torsional stiffness of the wire is @xmath9 @xmath10 . it is enclosed in a cell filled by a water - glycerol mixture at @xmath11 concentration . the system is a harmonic oscillator with resonant frequency @xmath12 @xmath13 and a relaxation time @xmath14 @xmath15 . @xmath16 is the total moment of inertia of the displaced masses ( _ i.e. _ the mirror and the mass of displaced fluid ) @xcite . the damping has two contributions : the viscous damping @xmath17 of the surrounding fluid and the viscoelasticity of the brass wire which can be neglected here . the angular displacement of the pendulum @xmath18 is measured by a differential interferometer @xcite . the measurement noise is two orders of magnitude smaller than thermal fluctuations of the pendulum . @xmath19 is acquired with a resolution of @xmath20 bits at a sampling rate of @xmath21 @xmath13 , which is about 40 times @xmath22 . we drive the system out - of - equilibrium by forcing it with an external torque @xmath23 by means of a small electric current @xmath24 flowing in a coil glued behind the mirror ( fig . [ fig : pendulum]b ) . the coil is inside a static magnetic field . the displacements of the coil and therefore the angular displacements of the mirror are much smaller than the spatial scale of inhomogeneity of the magnetic field . so the torque is proportional to the injected current : @xmath25 ; the slope @xmath26 depends on the geometry of the system . the angular displacement @xmath18 of this harmonic oscillator is very well described by a second order langevin equation : @xmath27 where @xmath28 is the thermal noise , delta - correlated in time of variance @xmath8 and @xmath29 the boltzmann constant and @xmath0 the temperature of the system which is the one of the surrounding fluid . the fluctuation dissipation theorem ( fdt ) gives a relation between the amplitude of the thermal angular fluctuations of the oscillator at equilibrium and its response function . for a harmonic oscillator , the equilibrium thermal fluctuation power spectral density ( psd ) is : @xmath30 where @xmath31 . using fdt ( eq . [ eq : fdt ] ) , we measure the coefficient @xmath26 and test the calibration accuracy of the apparatus which is better than @xmath32 . more details on the set - up can be found in @xcite . when the system is driven out of equilibrium using a deterministic torque , it receives some work and a fraction of this energy is dissipated into the heat bath . multiplying eq . ( [ eq : langevin_oscillator ] ) by @xmath33 and integrating between @xmath34 and @xmath35 , we obtain a formulation of the first law of thermodynamics between the two states at time @xmath34 and @xmath35 ( eq . ( [ eq : energy_conservation ] ) ) . the change in internal energy @xmath36 of the oscillator over a time @xmath37 , starting at a time @xmath34 , is written as : @xmath38 where @xmath39 is the work done on the system over a time @xmath37 : @xmath40 and @xmath41 is the heat given to the system . equivalently , @xmath42 is the heat dissipated by the system . @xmath36 , @xmath39 and @xmath41 are defined as energy in @xmath43 units . the internal energy is the sum of the potential energy and the kinetic energy : @xmath44^{2 } + \frac{1}{2 } c \theta(t)^2 \right\}. \label{eq : udef}\ ] ] the heat transfer @xmath41 is deduced from equation ( [ eq : energy_conservation ] ) ; it has two contributions : @xmath45^{2}{\mathrm{d}}t ' + \frac{1}{k_b \ t } \int_{t_i}^{t_i+\tau } \eta(t ' ) \frac{{\mathrm{d}}\theta}{{\mathrm{d}}t}(t ' ) { \mathrm{d}}t ' . \label{eq : qdef}\end{aligned}\ ] ] the first term corresponds to the opposite of viscous dissipation and is always negative , whereas the second term can be interpreted as the work of the thermal noise which have a fluctuating sign . the second law of thermodynamics imposes @xmath46 to be positive . we rescale the work @xmath39 ( the heat @xmath41 ) by the average work @xmath47 ( the average heat @xmath48 ) and define : @xmath49 ( @xmath50 ) . the brackets are ensemble averages . in the present article , @xmath51 , respectively @xmath52 , stands for either @xmath53 or @xmath54 , respectively @xmath39 or @xmath41 . there are two classes of fts . the _ stationary state fluctuation theorem _ ( ssft ) considers a non - equilibrium steady state . the _ transient fluctuation theorem _ ( tft ) describes transient non - equilibrium states where @xmath37 measures the time since the system left the equilibrium state . a fluctuation relation ( fr ) examines the symmetry of the probability density function ( pdf ) @xmath55 of a quantity @xmath51 around @xmath56 ; @xmath51 is an average value over a time @xmath37 . it compares the probability to have a positive event ( @xmath57 ) versus the probability to have a negative event ( @xmath58 ) . we quantify the fr using a function @xmath59 ( symmetry function ) : @xmath60 the _ transient fluctuation theorem _ ( tft ) states that the symmetry function is linear with @xmath51 for any values of the time integration @xmath37 and the proportionality coefficient is equal to @xmath8 for any value of @xmath37 . @xmath61 contrary to tft , the _ stationary state fluctuation theorem _ ( ssft ) holds only in the limit of infinite time ( @xmath37 ) . @xmath62 the questions we ask are whether fluctuation relations for finite time satisfy the two theorems and what are the finite time corrections . in a first time , we test the correction to the proportionality between the symmetry function @xmath63 and @xmath51 . in the region where the symmetry function is linear with @xmath51 , we define the slope @xmath64 : @xmath65 . in a second time we measure finite time corrections to the value @xmath66 which is the asymptotic value expected by the two theorems . to the applied torque @xmath67 . ] for the transient fluctuation theorem , we choose the torque @xmath67 depicted in fig . [ fig : lineartorque]a ) . it is a linear function of time : @xmath68 with @xmath69 @xmath70 and @xmath71 @xmath72 . the value of @xmath73 is chosen such that the mean response of the oscillator is of order of the thermal noise , as can be seen in fig . [ fig : lineartorque]b ) where @xmath19 is plotted during the same time interval of fig . [ fig : lineartorque]a ) . the system is at equilibrium at @xmath74 ( @xmath75 pn.m and @xmath76 pn.m @xmath77 ) . in this section the starting time @xmath34 of integration of all quantities defined before ( @xmath39 , @xmath36 and @xmath41 ) is @xmath74 . so the work is : @xmath78 @xmath79 , @xmath80 @xmath81 and @xmath82 @xmath83 plotted as a function of @xmath37 . b ) pdfs of @xmath53 for various @xmath84 : 0.31 @xmath79 , 1.015 @xmath81 , 2.09 @xmath83 and 4.97 @xmath85 . continuous lines are theoretical predictions with no adjustable parameters . c ) corresponding functions @xmath86 . the straight continuous line is a line with slope @xmath8 . d ) pdfs of @xmath80 for two values of @xmath84 : 4.97 @xmath79 and 8,96 @xmath81 . e ) corresponding pdfs of @xmath54 . continuous lines are gaussian fits . f ) corresponding functions @xmath87 . the straight continuous line is a line with slope @xmath8 . ] in fig . [ fig : tft]a ) , we represent the time average ( @xmath88 ) of the power injected into the system , the internal energy difference @xmath89 and the time average ( @xmath88 ) of the power dissipated by the system . @xmath88 and @xmath89 are linear in @xmath37 after some short relaxation time @xmath90 defined in the langevin equation : for @xmath84 smaller than @xmath8 , some oscillations around the linear behavior can be seen . the average value of work @xmath47 is therefore quadratic in @xmath37 and is equal to @xmath91 @xmath43 for @xmath92 . the difference between @xmath47 and @xmath93 corresponds to the mean value of dissipated heat @xmath46 ( eq . ( [ eq : qdef ] ) ) . as can be seen in fig.[fig : tft]a ) , @xmath94 is larger than @xmath93 for all times @xmath37 . the average of the dissipated power ( @xmath95 ) is therefore positive for all times @xmath37 as" +"the formal expressions of equilibrium statistical mechanics strictly apply only to ergodic systems that are in thermodynamic equilibrium . thus these expressions only strictly apply to systems which are at the global free energy minimum given the system hamiltonian and the macroscopic thermodynamic state variables ( number of particles , temperature and pressure or density ) . for such systems gibbsian equilibrium statistical mechanics provides an exact prescription for how to calculate the various thermodynamic quantities @xcite . however , these prescriptions are routinely applied to systems that are not in true thermodynamic equilibrium ( for example to metastable liquids @xcite , glasses @xcite , polymorphs @xcite and allotropes ) . it is often observed empirically that within experimental uncertainties many expressions for thermodynamic quantities yield consistent results . in the present paper we provide arguments for why many of the results of equilibrium statistical mechanics can be applied to such time independent nondissipative nonequilibrium systems . we also point out some of the limits inherent in the application of the formulae of equilibrium statistical mechanics to such systems . we choose to study the isothermal isobaric ensemble @xcite ( externally regulated pressure and temperature ) . the methods and reasoning we use here can be directly transferred to other ensembles such as the canonical ( fixed volume and externally regulated temperature ) . the gibbs free energy @xmath0 , which is the thermodynamic potential for the isothermal isobaric ensemble , is related to the partition function @xmath1 by the equation @xmath2 and the partition function is given by the integral@xmath3,\label{del0}\ ] ] where @xmath4 is the phase space vector describing the coordinates @xmath5 and momenta @xmath6 , of all the @xmath7 particles in the system , @xmath8 is the thermodynamic pressure , and @xmath9 where @xmath10 is boltzmann s constant and @xmath11 is the temperature . the integration domain @xmath12 provides limits for both integrals and extends over all the available phase space @xmath13 . this is @xmath14 for every component of the generalized momentum , @xmath15 for the volume @xmath16 , and over the volume for the cartesian coordinates of the particles . since the system hamiltonian @xmath17 is single valued , so too is the partition function and in turn the free energy . if we require the distribution function of a single thermodynamic phase it is necessary that other phases do not contribute significantly to the partition function . the full integration domain @xmath12 may include states that are characteristic of crystalline states or fluids states . in the thermodynamic limit this does not cause problems because , as we shall see , the partition function will be _ completely _ dominated by those microscopic domains that have the lowest free energy . however the application of these formulae to allotropes or metastable systems does present a problem . the standard equilibrium statistical mechanical expressions for variables such as the enthalpy @xmath18 , the average volume @xmath19 and second order quantities such as the specific heat at constant pressure @xmath20 may all be computed from a knowledge of the partition function eq . [ del0 ] or equivalently the thermodynamic potential eq . [ g0 ] . if other phases of lower free energy exist this computation ( from eq . [ del0 ] as written ) will strictly speaking be incorrect . it is well known that the formulae for thermal properties such as entropy , free energy , temperature and specific heat do _ not _ hold for _ dissipative _ nonequilibrium systems outside the linear response regime @xcite . in this paper we examine the question of whether they are correct for any _ nondissipative _ nonequilibrium systems such as allotropes , metastable systems or history dependent glasses . we provide a statistical mechanical theory of time independent , nondissipative , nonequilibrium systems . the theory is based on the fact that these systems are nonergodic and individual sample systems comprise ergodic domains that do not span all of phase space . we show that if these domains are robust with respect to small changes in thermodynamic state variables , a successful statistical mechanical treatment of these nonequilibrium systems can be given . we provide direct evidence , from molecular dynamics simulations on a model glass former , that the resulting statistical mechanical formulae are satisfied within empirical errors . finally we provide an independent test of the two key elements of our theory : boltzmann weights within the phase space domains and the robustness of those domains . it happens that these two elements are the necessary and sufficient conditions for the application of the transient fluctuation relation to finite thermodynamic quenches ( in temperature or pressure ) for such systems @xcite . while the application of thermodynamics to a single time averaged system is usually straightforward the application to a ensemble , whose members may be locked in different phase space domains , can require modification to the standard formulae . in the case of glasses our treatment has some similarities with the energy landscape approach of stillinger and weber @xcite . however there are significant differences ; our treatment makes no reference to the inherent structure and imposes no a priori knowledge of the inter - domain relative population levels . the energy landscape approach has been extended to account for the phenomena of ageing or history dependence by the addition of a fictive parameter @xcite . sciortino has convincingly shown that the addition of a single fictive parameter is inadequate to deal with glasses , which may have different properties at the same temperature and pressure if they are prepared by a different protocol ( different history dependence ) @xcite and poses the challenge to recover a thermodynamic description `` by decomposing the ageing system into a collection of substates '' . the treatment we present here succeeds in doing just that by providing a rigorous development of equilibrium statistical mechanics and thermodynamics for ensembles of systems where the phase space breaks up into ensembles of domains whose inter - domain dynamics is nonergodic and whose inter - domain population levels may not be boltzmann weighted . a dynamical system in equilibrium has the properties that it is nondissipative and that its macroscopic properties are time independent . thus the n - particle phase space distribution function , @xmath21 , must be a time independent solution to the liouville equation @xcite,@xmath22 where @xmath23 is the phase space compression factor @xcite obtained by taking the divergence of the equations of motion ( see eq . [ phase - space - compression ] ) and @xmath24 is the extended phase space vector which consists of @xmath25 and may include additional dynamical variables such as the volume @xmath16 . since the system is assumed to be nondissipative both the ensemble average @xmath26 and the time average @xmath27 of the phase space compression factor ( which is directly proportional to the rate at which heat is exchanged with the fictitious thermostat ) are zero . the time independent solution to eq . [ liouville - eq0 ] depends on the details of the equations of motion . equilibrium solutions to eq . [ liouville - eq0 ] for the equations of motion , suitable for use in molecular dynamics simulations , are compatible with gibbsian equilibrium statistical mechanics @xcite . microscopic expressions for mechanical properties like the pressure , the internal energy , the enthalpy and the volume can be derived without reference to gibbsian statistical mechanics and indeed can be proved to hold for nonequilibrium systems including nonequilibrium dissipative systems . there are two ways in which the formulae derived from gibbsian equilibrium statistical mechanics can break down . the most obvious way is that the relative weights of microstates may be non - boltzmann and the exponential factor @xmath28 $ ] , may be replaced by some other function ( either the exponential function itself may be modified as in tsallis statistics @xcite or the hamiltonian may be modified to some new function @xmath29 ) . in either circumstance the standard expressions for the thermal quantities derived from equilibrium gibbsian statistical mechanics will not be valid . this certainly happens in dissipative nonequilibrium systems where the distribution function is not a time independent solution to eq . [ liouville - eq0 ] . in deterministic nonequilibrium steady states the phase space may break down into ergodically separated domains ( each of which will be fractal and of lower dimension than the ostensible phase space dimension . this is a consequence of dissipation . ) however for these steady states , the domains are always exquisitely sensitive to macroscopic thermodynamic parameters since they are strange fractal attractors @xcite . often a deterministic _ nonequilibrium _ steady state approaches a unique fractal attractor . as time progresses the distribution function collapses ever closer to ( but never reaching ) the steady state attractor . the second way that these expressions may fail is that the system may become nonergodic . in this case three things happen . a ) most obviously time averages no longer equal full ( domain @xmath12 ) ensemble averages . b ) if we take an initial microstate the subsequent phase space trajectory will span some phase space domain @xmath30 where the initial phase is labeled @xmath31 . in this case for nondissipative nonequilibrium systems where the domains are robust ( i.e. small changes in thermodynamic state parameters , to leading order do not change the domain ) the standard equations of equilibrium statistical mechanics may continue to be valid but in a slightly modified form . we will examine this in some detail below . c ) given robust domains the population densities between each domain may well depend on the history of the system . macroscopic _ history can be expected to condition the ensemble s set of initial _ microstates _ @xmath32 from which the macroscopic material is formed . this in turn can be expected to condition the set of nonergodic domains @xmath33 that characterize the ensemble . for a macroscopic sample spanning a single ergodic domain @xmath30 , the free energy @xmath34 then satisfies only a local extrema principle and thus looses much of its thermodynamic meaning . we use the constant pressure nos - hoover equations of motion by combining the nos - hoover feedback mechanism with the so - called sllod or dolls equations of motion , which are equivalent for dilation . it is known that these equations of motion do not produce artifacts in the systems linear response to an external field and that to leading order the effect on the dynamical correlation functions is at most @xmath35 , where @xmath7 is the number of particles @xcite . the equations of motion are,@xmath36 where @xmath37 is the position , @xmath38 is the momentum and @xmath39 is the force on the @xmath40 particle , @xmath41 is the particle mass , @xmath42 is the barostat time constant , @xmath43 is the thermostat time constant , @xmath11 is the input temperature , @xmath8 is the input ( thermodynamic ) pressure and the instantaneous ( mechanical ) pressure is given by @xmath44 . because these equations of motion have additional dynamical variables the extended phase space vector is @xmath45 . in order to obtain the equilibrium distribution function we first define the hamiltonian , in the absence of any external fields , dilation @xmath46 or thermostats @xmath47 , as @xmath48 , where @xmath49 is the total inter - particle potential energy . to proceed further we identify the extended hamiltonian as @xmath50 and then obtain the phase space compression factor@xmath51 where the index @xmath52 sums over the components of the cartesian position and momentum vectors . using the heisenberg streaming representation ( rather than the more usual schrdinger representation eq . [ liouville - eq0 ] ) of the liouville equation@xmath53=-\lambda\left({\mbox{\boldmath $ \gamma$}}^{\prime}(t)\right),\label{liouville - streaming}\ ] ] we can obtain the particular time independent" +"gas cooling plays a key role in galaxy formation . according to the hierarchical structure formation model , galaxies form in gravitationally collapsed dark matter halos . the dissipative baryonic matter cools by emitting radiation and condenses into halos to form galaxies @xcite . subsequently stars form through the radiative cooling of interstellar medium ( ism ; e.g. , * ? ? ? the cooling rate of gas varies with its chemical abundance , because different atoms and molecules have different cooling rates . the chemical abundance of cosmic gas evolves as a function of time and environment . in the early universe , the primordial gas consists of mainly hydrogen ( mass fraction of @xmath3 ) and helium ( mass fraction of @xmath4 ) with a negligible amount of light metals ( e.g. * ? ? ? * ) . throughout this paper , all the elements heavier than helium are collectively called ` metals ' . most metals are produced inside stars and spread out to the space by galactic winds driven by supernova ( sn ) explosions . in the metal - enriched gas , the total cooling rate is significantly enhanced relative to that of the primordial gas by the atomic emission lines from recombination of ionised metals . metals may influence galaxy formation in two different ways . firstly , the sf efficiency is increased owing to the shorter gas cooling time . star formation generally takes place in dusty metal - enriched ism , therefore , the enhanced cooling rate by metals would boost up the sf efficiency . however , the energy / momentum feedback by sne may suppress the subsequent star formation after the initial starburst by heating up the ambient gas . this complicates the situation , and it is not clear whether the net effect of metal cooling and sn feedback would be negative or positive . the feedback process is highly nonlinear , therefore , a direct numerical simulation would be a useful tool to explore the effects of feedback and metal cooling . secondly , the metals dispersed into the igm by sn feedback also enhance the cooling of igm . this can lead to the increase of igm accretion onto galaxies , because colder gas can sink into galaxies more easily . both of the above two effects may affect the galaxy growth and cosmic sf history significantly . therefore it is essential to include the effects of metal cooling and chemical enrichment by feedback in the studies of galaxy formation and evolution , and capture the complex two - way interactions between galaxies and igm . in addition , metal enrichment also affects the equation of state by altering the mean molecular weight of gas , which influences the hydrodynamic calculation of gas thermal state . cosmological hydrodynamic simulations are widely used in the studies of galaxy formation and cosmic sf history ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? most of these works included the treatments of radiative cooling by h & he , star formation , and sn feedback . however , some of the simulations did not include the effects of metal cooling and/or chemical enrichment by galactic wind . furthermore , the effects of metal cooling on galaxy growth and cosmic sf history has not been explored in detail using cosmological hydrodynamic simulations and presented in the literature , as it is costly to run large cosmological simulations with and without the effect of metal cooling . in this paper , we investigate the effects of metal cooling and metal enrichment on galaxy growth and cosmic sf history using a series of cosmological hydrodynamic simulations with and without metal cooling . the aim of this paper is to single out the effects of metal cooling among our simulations . this work can be regarded as our initial step towards the long - term goal of developing more complete cosmological hydrodynamic code with physically motivated models of star formation and feedback . the paper is organised as follows . in [ sec : method ] , we describe our simulation method focusing on how we implement the metal cooling . in [ sec : global ] , we study the metal cooling effects on the global properties , such as cosmic sfr , phase space ( @xmath5 vs. @xmath6 ) distribution of gas , and the evolution of four phases ( hot , warm - hot , diffuse , and condensed ) of baryons . we then study the galaxy mass functions ( [ sec : mf ] ) and gas mass fractions ( [ sec : gasfrac ] ) . finally , we discuss and summarise our findings in [ sec : summary ] . we use the updated version of the tree - particle - mesh ( treepm ) smoothed particle hydrodynamics ( sph ) code gadget-2 @xcite for our cosmological simulations . the gravitational dynamics is computed by a treepm algorithm , which uses a particle - mesh method @xcite for the long - range gravitational force and a tree method for the short - range gravitational force @xcite . this hybrid algorithm makes the gravitational force calculation faster than a tree method and allows better force resolution than a pm method in dense regions . the gas dynamics is computed by an sph method . the sph is particularly useful if the simulation needs to resolve large dynamical range , which is an inevitable requirement for the study of galaxy formation in a cosmological context . therefore a treepm - sph simulation can provide a fast and high resolution calculation for both gravitational dynamics and hydrodynamics . the gadget-2 code adopts the entropy - conservative formulation @xcite , which alleviates the overcooling problem that previous sph codes suffered from . our basic simulations include radiative cooling and heating processes for hydrogen and helium using a method similar to @xcite . an external uv background radiation is treated as a spatially uniform photoionising radiation @xcite , and modified to match the ly@xmath7 forest observations @xcite . implementing star formation and feedback from first principles is not feasible in current cosmological simulations , because the spatial & mass - scales of molecular clouds are not resolved . star formation and sn feedback are represented by the subgrid multiphase ism model developed by @xcite . in the multiphase scheme , a single gas particle represents both hot and cold gas . the stars are formed in the cold portion when the density exceeds a given threshold , @xmath8 , which is derived self - consistently within the multiphase ism model . the related parameters , such as the normalisation of gas consumption time and evaporation efficiency of cold gas , are set to satisfy the empirical kennicutt - schmidt law @xcite . the sn feedback returns some fraction of the cold gas to the hot phase , and increases the thermal energy of the hot gas . as an extension to the multiphase ism model , the simulation includes a phenomenological model for sn - driven galactic wind @xcite . the galactic wind is particularly important for distributing the metals produced by sne into the igm . we use the strong kinematic wind with a velocity of 484kms@xmath9 . it has been shown that this model produces favourable results for the luminosity function of lyman - break galaxies at the bright - end @xcite and the hi column density distribution function @xcite at @xmath1 , when compared to the runs without the wind . however , @xcite pointed out the problems of this galactic wind model by comparing with the observations of civ absorption lines in quasar spectra , and suggested that the momentum - driven wind model @xcite is a more viable model , which can carry more metals with lower wind velocities . in this paper we choose not to modify our galactic wind model in order to single out the effects of metal cooling , and to allow direct comparisons to the previous works @xcite . here we focus on the effects of metal cooling on galaxy growth , while @xcite focused on the civ statistics of the igm . the metallicity of gas particles are also tracked by the code , assuming a closed box model for each gas particle . the yield ( @xmath10 ) of 0.02 is assumed . in principle , there could be a time delay between sn explosions and chemical enrichment of the ambient gas . unfortunately , current cosmological simulations do not have sufficient resolution to track the detailed mixing process of metals . in our simulations , we ignore this time delay and assume an instantaneous mixing within each gas particle . this assumption is reasonable , because the overall time step of the simulations is longer than the mixing time - scale on small scales . ideally we would like to track individual metals and compute the cooling rate of each element at each time - step of the simulation . this approach has been used to study the evolution of individual galaxies @xcite . for cosmological simulations , it requires a large memory to track individual metals and the computation becomes exceedingly expensive ( but see * ? ? ? * ; * ? ? ? * for such an attempts ) . our simulations collectively track the total mass fraction of metals ( @xmath11 ) as the measure of metallicity . we obtain the chemical abundance and cooling rates for a given @xmath12 and temperature by interpolating the table given in ( * ? ? ? * hereafter sd93 ) for the standard collisional ionisation equilibrium model , and create a lookup table . metal cooling is implemented in the full range of metallicity in the table from sd93 , from [ fe / h]=-3 to [ fe / h]=1 . in addition , the metal cooling outside of this range is computed by extrapolating the table . we require that the extrapolation does not go lower than the primordial cooling rate . the primordial abundance pattern is used where [ fe / h ] @xmath13 @xcite , and the solar abundance pattern is used where [ fe / h ] @xmath14 @xcite . for @xmath15 [ fe / h ] @xmath16 , the abundance pattern is computed by interpolating between the primordial and solar abundance patterns . note that , [ fe / h ] = @xmath17 - @xmath18 , where @xmath19 is the number density . figure [ fig : xyz_table ] shows the relationships between the metal parameters ( [ fe / h ] , @xmath20 , @xmath21 , and @xmath22 ) and the total metallicity @xmath12 . because the abundance pattern" +"there is considerable current interest in studying the collision of two black holes , since these events could be primary sources of gravitational waves for interferometric gravitational wave detectors currently under construction . the mathematics describing such events consists of the nonlinear partial differential equations of general relativity , einstein s theory of gravitation . these equations are very difficult to solve especially in the case of two merging holes , or of the highly distorted final hole that is formed by the merger . limited ( in resolution and evolution time ) full numerical simulations of grazing collisons of black holes are being done now @xcite , but long term stable evolutions are still distant in the future . it is therefore of interest to have at hand approximate results which in certain regimes could be used to test and possibly even complement the full numerical evolutions . among such approximation methods is the close - limit "" approximation in which spacetime of a black hole collision is represented as a single distorted black hole and evolutions are done with simple linear perturbative equations . in the past , this method has been applied to the case of a head - on collision of two boosted holes @xcite and the case of slow inspiral @xcite with considerable success . in both these cases , the black holes considered had no spin . in this work , we will consider the collision of spinning holes . since we are attempting a linear , first order perturbative calculation , it is sufficient to study the coalescence of two spinning holes with zero initial linear momentum . this is because , to obtain the results for the inspiral of spinning holes , one can simply do a linear superposition of these results with those from our past work @xcite . however , the first order perturbative treatment imposes several restrictions on the physical scenarios we can treat . in addition to the close - slow limitations , we can only easily analyze cases in which the spins of the two black holes are equal and opposite . this happens because , to lowest order , the ( perturbative ) extrinsic curvature of a black hole with spin @xmath0 and a conformal distance @xmath1 from the origin is of order @xmath2 . superposing another hole with parallel and equal spin and at @xmath3 will yield a situation with zero perturbation in extrinsic curvature , which is not a case of interest . so in the following , we shall present two cases that are exhaustive . _ case i _ , when the two spins are equal and opposite and aligned along the common axis of the two holes . specifically , we place the two holes at @xmath4 and have their spins parallel and anti - parallel to the x - axis . _ case ii _ , when the two spins are equal and opposite and perpendicular to the common axis of the two holes . here , we place the two holes at @xmath4 and have their spins parallel and anti - parallel to the y - axis . these cases have no net angular momentum . so we expect zerilli and teukolsky formalisms to agree exactly ( kerr parameter @xmath5 ) . we , therefore report calculations and results from the teukolsky formalism only . part of this work , in the context of the zerilli formalism can be found in this reference @xcite . to evolve a spacetime in general relativity , one needs to provide initial data , a 3-geometry @xmath6 and an extrinsic curvature @xmath7 , that solve einstein s equations on some starting hypersurface ( i.e. , at some starting time ) . these initial value equations have the form , @xmath8 where @xmath6 is the spatial metric , @xmath7 is the extrinsic curvature and @xmath9 is the scalar curvature of the three metric . if we propose a 3-metric that is conformally flat @xmath10 , with @xmath11 a flat metric , and @xmath12 the conformal factor , and we use a decomposition of the extrinsic curvature @xmath13 , and assume maximal slicing @xmath14 , the constraints become , @xmath15 where @xmath16 is a flat - space covariant derivative . to solve the momentum constraint , we start with a solution that represents a single hole with spin @xmath0 @xcite , @xmath17\ .\ ] ] in this expression for the conformally related extrinsic curvature at some point @xmath18 , the quantity @xmath19 is a unit vector , in the `` base '' flat space with metric @xmath20 , directed from a point representing the location of the hole to the point @xmath18 . the symbol @xmath21 represents the distance , in the flat base space , from the point of the hole to @xmath18 . it is straightforward to show that the solution of the hamiltonian constraint corresponding to eq . ( 5 ) corresponds to a spacetime with adm angular momentum @xmath22 . the next step is to modify this to represent holes centered at @xmath4 in the conformally flat metric . since the momentum constraint is linear , we can simply add two expressions of the above form , @xmath23 we will choose in further expressions to use a polar coordinate system in the flat space determined by @xmath20 centered in the mid - point separating the two holes and label the polar coordinates as @xmath24 . so @xmath25 will be the distance in the flat space from the midpoint between the holes . to solve the hamiltonian constraint [ hami ] , we introduce an approximation , ( the slow approximation ) which we will show is enough for our purposes . in fact , in this approximation the solution for the conformal factor turns out to be the familiar misner @xcite solution if one chooses the topology of the slice to have a single asymptotically flat region , or the brill lindquist @xcite solution if there are three asymptotically flat regions . we assume that the black holes are initially close , and that the initial spins @xmath0 are small . we denote by @xmath26 and @xmath27 the normal vectors corresponding , respectively , to the one hole solutions at @xmath28 and at @xmath29 , and we recall @xmath25 to be the distance to a field point , in the flat conformal space , from the point midway between the holes . for large @xmath25 , the normal vectors @xmath26 and @xmath27 almost cancel . more specifically @xmath30 . a consequence of this is that the total initial @xmath31 is first order in @xmath32 . it scales linearly with the spin @xmath0 as well . thus the source term in the hamiltonian constraint is quadratic in @xmath0 . if we choose to find a solution to the conformal factor to first order in @xmath0 ( which should give us a good approximation in the case of slowly spinning holes ) , we can ignore this quadratic source term . so now , the hamiltonian constraint looks like the one for zero momentum , which is simply the laplace equation . a well known solution to this , is the misner solution @xcite . this solution , is characterized by a parameter @xmath33 which describes the separation of the two throats . we can relate this parameter to the conformal distance @xmath1 in the following way @xcite , @xmath34 we must now map the coordinates of the initial value solution to the coordinates for the schwarzschild ( kerr with @xmath5 ) background . to do this , we interpret the @xmath25 as the isotropic radial coordinate of a schwarzschild spacetime , and we relate it to the usual schwarzschild radial coordinate @xmath21 by @xmath35 . from this we arrive at the following expressions for the components of the metric and extrinsic curvature . following the construction as outlined in the last section , we get the following expressions for the initial spatial metric and extrinsic curvature : @xmath36\ .\ ] ] the metric has a form , identical to the misner solution @xcite . now , we use the methodology and expressions in @xcite , to find the initial data for the teukolsky function , @xmath37 , where @xmath38 . for the azimuthal modes @xmath39 we get these expressions , @xmath40 @xmath41 and for the azimuthal mode @xmath42 we get , @xmath43 @xmath44 to all these expressions , we also need to add metric contributions . they have the same form as the ones in @xcite , therefore we will not list them here . again , following the construction as outlined in the last section , and using the close - slow approximation , we arrive at the following expressions for the initial spatial metric and extrinsic curvature : @xmath45\ .\ ] ] the metric again has a form , identical to the misner solution @xcite . using the methodology and expressions we discussed in @xcite , the initial data for the teukolsky function , is : for the azimuthal modes @xmath39 we get , @xmath46 @xmath47 and for the azimuthal mode , @xmath42 the initial data are identically zero . to all these expressions we need to add the metric contributions , that have a form identical to the ones in our past work @xcite . given the cauchy data from the last section , the time evolution is obtained from the teukolsky equation @xcite , @xmath48 \partial_{tt}- \frac{4 m a r}{\delta}\partial_{t\varphi } + 4\left[r+ia\cos\theta-\frac{m(r^2-a^2)}{\delta}\right]\partial_t \nonumber\\ & & + \,\delta^{2}\partial_r\left(\delta^{-1}\partial_r\right ) + \frac{1}{\sin\theta}\partial_\theta\left(\sin\theta\partial_\theta\right ) + \left[\frac{1}{\sin^2\theta}-\frac{a^2}{\delta}\right ] \partial_{\varphi\varphi}\\ & & -\ , 4 \left[\frac{a ( r - m)}{\delta } + \frac{i \cos\theta}{\sin^2\theta } \right ] \partial_\varphi -\left(4 \cot^2\theta + 2 \right)\biggr\}\psi=0,\end{aligned}\ ] ] where @xmath49 is the mass of the black hole , @xmath50 its angular momentum per unit mass ( which is zero in our case ) , @xmath51 , and @xmath52 . evolving the initial data we just calculated , with this equation will enable us to extract gravity wave waveforms that correspond to the late stage merger of spinning holes . we can also estimate the energy carried away by these gravitational waves . the radiated energy is given by @xcite , @xmath53 note that the angular momentum radiated in the cases we consider is zero . in this section we show waveforms and plots for energy radiated from the collision of two spinning holes . recall that the two holes have equal mass and equal and opposite spin , and we are considering two cases , _ case i _ in which the spins are aligned along the common axis of the two holes , and _ case ii _ in which the two spins are perpendicular to the common axis of the two holes . the waveforms that follow , are for a collision of two black holes that were initially separated by a conformal distance of @xmath54 and had an individual spin of @xmath55 in units of adm mass . in figure [ waveformi ] we show the @xmath56 mode of the teukolsky function for a _ case i _ collision . we see the typical quasi - normal ringing , in both the real and imaginary parts of the function . in figure [ waveformii ] we plot the @xmath56 mode of the teukolsky function for a _ case ii _ collision . note that the initial data is purely real for this case , hence the imaginary part of the waveform is identically zero . quasi - normal ringing is self - evident here as well . this is the type of signal that gravity wave observatories like ligo , will detect if they happen to witness a collision of the kind we are considering . let us turn now to the evaluation of the radiated energies for these two cases . figure [ energy ] shows the radiated energy as a" +"the dynamics of a non - equilibrium system often results in highly complicated domain structures ( microstructures ) . typically , as time proceeds , the average size of these structures grows as a direct consequence of free - energy reduction : the interface is eliminated resulting in an increase in the size of homogeneous regions . traditional non - equilibrium dynamics usually deals with the equilibrium states that are spatially uniform @xcite , i.e. , the stable phases are characterized by homogeneous values for the appropriate intensive thermodynamic variables . classic , albeit quite simple , examples of models governing the evolution of such systems are the cahn - hilliard ( ch ) equation for conserved systems @xcite and allen - cahn ( ac ) equation for non - conserved systems @xcite . examples are found in polymer mixtures @xcite , alloys @xcite , liquid - crystals @xcite , and in cosmology @xcite . a model that has generated considerable recent interest is the phase field crystal ( pfc ) equation @xcite , which is a conservative form of the familiar , non - conserved , swift - hohenberg ( sh ) equation @xcite . these systems differ from the ch and ac systems in that the stable phase is periodic . for sh models , the order parameter is viewed as capturing the inhomogeneities in a fluid associated with rayleigh - bnard convection . in the case of the pfc model , which is a simple version of more elaborate density functional theories of liquid / crystal interfaces @xcite , the model captures features at the atomic scale , and thus contains highly detailed physical information about the system s structure . such models can describe many of the basic properties of polycrystalline materials that are realized during non - equilibrium processing . the equations of motion governing these non - equilibrium phenomena are non - linear partial differential equations that can not generally be solved analytically for random initial conditions . therefore , computer simulations play an essential role in our understanding and characterization of non - equilibrium phenomena . the standard euler integration is known to be unstable for time step @xmath0 above a threshold fixed by lattice spacing @xmath1 @xcite . in ch and ac systems , to maintain an interfacial profile , the lattice spacing must be smaller than the interfacial width @xmath2 , and in pfc and sh systems , @xmath1 must smaller than the periodicity selected by the system . thus , the euler update is inefficient , and in practice it is computationally costly to use to evolve large systems . various computational algorithms @xcite have been developed by increasing @xmath3 compared to the simplest euler discretization . however , these methods still require a fixed time step , so they eventually become inefficient . recently , unconditionally stable algorithms @xcite were developed to overcome this difficulty for ch and ac equations . these algorithms are a class of stable algorithms free of the fixed time step constraint for equations with a mix of implicit and explicit terms . while these algorithms allow for an increasing time step in ch systems as time proceeds , only a finite effective time step is possible for ac systems . a recent study @xcite , based on this unconditionally stable algorithm , demonstrated analytically that one can use an accelerated algorithm @xmath4 to drive the ch equation , with the accuracy in correlation controlled by @xmath5 . in this manuscript we apply this unconditionally stable algorithm to the pfc and sh equations ( section @xmath6 ) . in section @xmath7 we establish the effectiveness of this approach through numerical studies of the algorithm , demonstrating that the algorithm is both efficient and accurate for solving pfc equation . finally , in section @xmath8 we provide some concluding remarks . in this section , we develop a class of unconditionally stable time stepping algorithms ( @xmath3 taken arbitrarily large without the solution becoming unstable ) to the pfc and sh equations . although the main purpose of this section is to study unconditionally stable algorithms for the pfc equation , we include a parallel discussion of the sh equation , as the methodology applies to both equations with only trivial differences . both the pfc and sh equations start from a free energy functional that describes the configurational cost of periodic phases in contact with isotropic phases , and can be expressed as @xmath9=\int d\vx \left\{\frac{1}{2 } \phi\left[r + ( 1 + \nabla^2)^2\right]\phi + \frac{\phi^4}{4}\right\ } , \label{eq : pfcbasic}\ ] ] where the periodic order parameter @xmath10 has the wave number @xmath11 in equilibrium , and @xmath12 characterizes the quench depth . for the pfc equation , @xmath13 is proportional to the deviation of the temperature from the melting temperature @xmath14 . in the pfc model the order parameter ( the density ) is conserved , and thus the equation of motion is in the form of a continuity equation , @xmath15 , with current @xmath16 , where @xmath17 is the mobility . absorbing @xmath17 into the time scale , we obtain the dimensionless form of the pfc equation @xmath18\phi + \phi^3\right\}. \label{eq : eq_of_motion : pfc}\end{aligned}\ ] ] for the sh equation , on the other hand , the order parameter is not conserved by the dynamics , and its evolution is postulated to have the the form @xmath19\phi - \phi^3 . \label{eq : eq_of_motion : sh}\end{aligned}\ ] ] eq . ( [ eq : eq_of_motion : sh ] ) has a simple dissipative form , where the rate of change of @xmath20 is proportional to the gradient ( with an an @xmath21 inner product in functional space ) of the free energy . in order to obtain an unconditionally stable algorithm , we now follow methods previously developed for the ch and ac equations @xcite , and work out in some detail how to semi - implicitly parameterize the equation of motion . we begin by `` splitting '' the linear terms in the equation of motion into `` forward '' and `` backward '' pieces , both for eq . ( [ eq : eq_of_motion : pfc ] ) : @xmath22 \nonumber \\ = & & \phi_t+\dt \grad^2 \left[a_1(r+1 ) \phi_t+2a_2 \nabla^2 \phi_t+a_3\nabla^4 \phi_t + \phi_t^3 \right ] , \label{eq : semi_implicit : pfc}\end{aligned}\ ] ] and for eq . ( [ eq : eq_of_motion : sh ] ) : @xmath23 \nonumber \\ = & & \phi_t-\dt \left[a_1(r+1 ) \phi_t+2a_2 \nabla^2 \phi_t+a_3\nabla^4 \phi_t + \phi_t^3 \right ] . \label{eq : semi_implicit : sh}\end{aligned}\ ] ] the constants @xmath24 , @xmath25 and @xmath26 control the degree of splitting . in order to find the constraints on these parameters that yield an unconditionally stable algorithms , a standard von neumann linear stability analysis on eq . ( [ eq : semi_implicit : pfc ] ) and eq . ( [ eq : semi_implicit : sh ] ) may be performed . the procedures are quite similar and the results are identical for these two equations . we will only show the details for the pfc model in next subsection . as was found in the analysis of vollmayr - lee and rutenberg @xcite for the ch equation , the pfc equation will be linearly unstable to perturbations for legitimate physical reasons . specifically , the isotropic phase @xmath27 can be metastable or unstable to the stable periodic ( crystalline ) phase @xcite if the system is an undercooled liquid . this situation ( which is precisely what we are interested in modeling ) is established when @xmath28 . this _ physical instability _ complicates our standard von neumann stability analysis , as we wish to predict when our numerical methods will cause an instability that is unrelated to the physical instability resulting from the thermodynamic . we can investigate the physical instability by a linear stability analysis on the equation of motion eq . ( [ eq : eq_of_motion : pfc ] ) . we let @xmath29 , where @xmath27 is a constant phase and @xmath30 is a small perturbation , and linearize the pfc equation eq . ( [ eq : eq_of_motion : pfc ] ) in @xmath30 to get @xmath31\eta_t . \end{aligned}\ ] ] this can be fourier transformed to find @xmath32 \eta_{\vk , t}.\end{aligned}\ ] ] the physical instability for the above equation occurs for @xmath33<0 , \label{eq : physical_instability}\end{aligned}\ ] ] which reduces to @xmath28 with @xmath34 in the stable phase , as we indicated above . now we can proceed to analyze the _ numerical stability _ and determine the constraints for the splitting parameters . we linearize the general step eq . ( [ eq : semi_implicit : pfc ] ) by substituting @xmath29 and get @xmath35 \nonumber \\ = & & \eta_t+\dt \grad^2\left[a_1(r+1 ) \eta_t+2a_2 \nabla^2 \eta_t+a_3\nabla^4 \eta_t + 3\bar{\phi}^2 \eta _ t \right],\end{aligned}\ ] ] the fourier transform of the above equation results in @xmath36 \nonumber \\ = & & \eta_{\vk , t}\left[1-\dt k^2 \ { a_1(r+1)-2a_2 k^2+a_3 k^4 + 3\bar{\phi}^2 \ } \right].\end{aligned}\ ] ] this can be re - expressed as @xmath37=\eta_{\vk , t}[1+\dt \mathcal{r}_\vk].\end{aligned}\ ] ] note that @xmath38 . while we want to avoid numerical instability , the physical instability is to be expected during the dynamics , and will not lead to numerical problems . but , as we indicated above , both of the instabilities will be captured by a general von neumann stability analysis . one manner of dealing with this is to recognize that a proper unconditionally stable algorithm will be stable if and only if @xmath39 and should be unstable if and only if @xmath40 . the von neumann stability criterion is @xmath41 ^ 2 & > & \left[1+\dt\mathcal{r}_\vk\right]^2 \quad\mathrm{for}\ \mathbf{r_k}>0 \nonumber\\ \left[1+\dt \mathcal{l}_\vk\right]^2 & < & \left[1+\dt\mathcal{r}_\vk\right]^2 \quad\mathrm{for}\ \mathbf{r_k}<0.\end{aligned}\ ] ] the above inequalities can be rewritten as @xmath42&>&0 \quad\mathrm{for}\ \mathbf{r_k}>0 \nonumber\\ \mathbf{r_k}\left[2+\dt(\mathcal{l}_\vk+\mathcal{r}_\vk)\right]&<&0 \quad\mathrm{for}\ \mathbf{r_k}<0 \nonumber , \label{eq : von_neumann}\end{aligned}\ ] ] which , dividing by @xmath43 can be reduced to a single inequality , @xmath44 , which implies @xmath45 for arbitrarily large @xmath3 , and we obtain @xmath46,\end{aligned}\ ] ] which can be satisfied using the mode independent restrictions ( and @xmath47 ) @xmath48 these are the constraints on the parameters @xmath24 , @xmath25 and @xmath26 for unconditionally stable algorithms for all modes , for quenches in the range @xmath49 . with these choices there is no threshold for @xmath3 in order to maintain numerical stability . the quantity @xmath3 is termed the _ algorithmic time step_. we note that unconditional stability does not mean that the user of such algorithms may simply take as large a time step as is desired . indeed , to obtain accurate physical results , there are additional restrictions on how large @xmath3 may be . to determine how large a time step we may take , and still maintain an accurate solution , we calculate the fourier space `` effective time step '' , as will be described below . we first note that when @xmath50 , eq . ( [ eq : semi_implicit : pfc ] ) corresponds to the traditional euler update @xmath51\phi_t + \phi_t^3\right\ } , \label{eq : pfc - euler - update}\end{aligned}\ ] ] where @xmath52 denotes the field obtained after an euler update on a previous field @xmath53 , while we use the unprimed @xmath54 to denote the field obtained by unconditionally stable algorithm on @xmath53 throughout . we now define the spatial fourier transform of @xmath55 . in fourier space , writing @xmath56 , the euler update becomes @xmath57\phi_{\vk , t } + ( \phi^3)_{\vk , t}\right\ } , \label{eq : pfc - euler - fourier}\end{aligned}\ ] ] where @xmath58 . in fourier space , the unconditionally stable algorithms eq . ( [ eq : semi_implicit : pfc ] ) can be written in a form that is analogous to eq . ( [ eq : pfc - euler - fourier" +"early - type galaxies in clusters exhibit a linear color - magnitude ( cm ) relation indicating that bright galaxies are systematically redder than their faint cluster companions ( visvanathan & sandage 1977 ) . this remarkable relation shows very small scatter ( @xmath3 magnitude ) in high precision photometry of local clusters such as coma and virgo ( bower , lucey & ellis 1992a , 1992b , hereafter ble92 ) and can be extended to clusters at medium - to - high redshift ( @xmath4 ) ( ellis et al 1997 , stanford , eisenhardt & dickinson 1998 ) . a first attempt at explaining the universality of the cm relation involves using the age of each galaxy as the main determinant of its color . ageing stellar populations redden progressively as stars with decreasing initial mass evolve off the main sequence . therefore , if the colors of cluster galaxies are purely controlled by age , the small scatter about the cm relation implies a nearly synchronous star formation process for all galaxies of a given mass , while the slope of the cm relation implies systematically older ages for more massive galaxies . as shown most recently by kodama & arimoto ( 1997 ) , such a picture is highly unlikely because it does not preserve the slope nor the magnitude range of the cm relation in time . another important factor that affects the colors of stellar populations is metallicity . at fixed age , a more metal - rich stellar population will appear redder and fainter than a more metal - poor one ( e.g. , worthey 1994 ) . hence , increasing metallicity at fixed age has a similar effect on colors as increasing age at fixed metallicity . this is usually referred to as the _ age - metallicity degeneracy _ ( worthey 1994 ) . several studies have shown that cm relation of cluster elliptical galaxies could be primarily driven by metallicity effects ( larson 1974 ; matteuci & tornamb 1987 ; arimoto & yoshii 1987 ; bressan , chiosi & tantalo 1996 ; kodama & arimoto 1997 ) . the physical mechanism usually involved is that of a galactic wind : supernovae - driven winds are expected to be more efficient in ejecting enriched gas , and hence in preventing more metal - rich stars from forming , in low - mass galaxies than in massive galaxies with deeper potential wells . although age is generally assumed to be the same for all galaxies in these studies , this has not been proven to be an essential requirement . in fact , scenarios in which e / s0 galaxies progressively form by the merging of disk galaxies ( schweizer & seitzer 1992 ) in a universe where structure is built via hierarchical clustering also predict that the cm relation is driven primarily by metallicity effects ( kauffmann & charlot 1998 ) . moreover , age effects could be important if , for example , there is sufficiently strong feedback from early galaxy formation to bias the luminous mass distribution of subsequent generations of galaxies by the heating of intergalactic gas . in this paper we present a new , more model - independent approach for evaluating the full range of ages and metallicities allowed by the spectro - photometric properties of early - type galaxies in clusters . the method is based on the construction of age - metallicity diagrams constrained by the colors of early - type galaxies in the nearby coma cluster and in 17 clusters observed with the _ hubble space telescope _ ( _ hst _ ) at redshifts up to @xmath5 ( stanford et al . such an analysis has hitherto been hindered because of the lack of both accurate stellar libraries for different metallicities and reliable morphological information on cluster galaxies at medium - to - high redshifts . our results can subsequently be reframed into specific theories of galaxy formation , since they will be indispensable for any model that seeks to produce galaxies resembling those actually observed . in 2 we present the spectral evolution models used in this paper . the cluster sample is described in 3 . in 4 we construct the age - metallicity diagrams allowed by the observations , and in 5 we compute the corresponding ranges in mass - to - light ratio and in several commonly used spectral indices . we discuss our main conclusions in 6 . we compute the spectral evolution of early - type galaxies using the latest version of the bruzual & charlot ( 1998 ) models of stellar population synthesis . these span the range of metallicities @xmath6 and include all phases of stellar evolution , from the zero - age main sequence to supernova explosions for progenitors more massive than @xmath7 , or to the end of the white dwarf cooling sequence for less massive progenitors . in addition , the models predict the strengths of 21 stellar absorption features computed using the worthey et al . ( 1994 ) analytic fitting functions for index strength as a function of stellar temperature , gravity and metallicity . this constitutes the standard `` lick / ids '' system that is often used as a basis for spectral diagnostics in early - type galaxies . the resulting model spectra computed for stellar populations of various ages and metallicities have been checked against observed spectra of star clusters and galaxies ( bruzual et al . 1997 ; bruzual & charlot 1998 ) . the uncertainties in the models are discussed in charlot , worthey & bressan ( 1996 ) . these can reach up to 0.05 mag in rest - frame @xmath8 , 0.25 mag in rest - frame @xmath9 and a 25% dispersion in the @xmath10-band mass - to - light ratio . with these uncertainties in mind , we will concentrate more on understanding the trends seen in the observations than on inferring absolute age and metallicity values . it is worth noting that the most massive elliptical galaxies exhibit [ mg / fe ] ratios in excess of that found in the most metal - rich stars in the solar neighborhood ( by @xmath11 dex ; see worthey , faber , & gonzalez 1992 ) . while this may limit the accuracy of the predicted mg@xmath12 indices of bright elliptical galaxies , the recent models of bressan et al . ( 1998 ) convincingly show that an enhancement in light elements at fixed total metallicity has virtually no effect on the other spectrophotometric properties of model stellar populations . we approximate model early - type galaxies by instantaneous - burst stellar populations . the reason for this is that we aim at constraining the age and metallicity ranges of stars dominating the light of early - type galaxies , whose photometric properties are well represented by instantaneous - burst populations . in fact , this is true even if the galaxies underwent subsequent small amounts of star formation or if the epoch of major star formation was extended over several billion years ( e.g. , fig . 1 of charlot & silk 1994 ) . the predicted colors of our models at fixed age and metallicity agree well with the results of more refined calculations including the effects of infall and galactic winds for corresponding values of the mean age and metallicity ( kodama & arimoto 1997 , bressan , chiosi & tantalo 1996 ) . for example , adopting metallicities matching the luminosity weighted metallicities @xmath13 in table 2 of kodama & arimoto yields @xmath14 and @xmath9 colors that agree to better than 0.05 mag with the results from these authors at an age of 15 gyr . such a discrepancy is well within the errors of current population synthesis models ( charlot et al . 1996 ) . in the remainder of the present paper , the initial mass function ( imf ) is taken from scalo ( 1986 ) and is truncated at 0.1 and 100@xmath15 . we use the above models to compute the locations in the age metallicity diagram of stellar populations satisfying specified spectro - photometric properties . figure 1 shows four such age metallicity diagrams corresponding to imposed values of the @xmath14 and @xmath9 colors and mg@xmath16 and h@xmath17 spectral indices . these quantities are chosen here because they can be constrained by many observations of early - type galaxies ( 3 and 5 ) . in each panel , the models satisfying the same value of the spectro - photometric property of interest are related by a continuous line , different lines corresponding to different imposed values . with this definition , the slope of a line in the age metallicity diagrams indicates the relative sensitivity of the color or index under consideration to age and metallicity . vertical lines would correspond to a sensitivity purely to age , and horizontal lines to a sensitivity purely to metallicity . figure 1 then shows immediately that the @xmath14 and @xmath9 colors and mg@xmath16 index depend more strongly on metallicity than on age , while the h@xmath17 index depends more strongly on age than on metallicity . we will return to this point in 4 and 5 . the relative dependence of the spectro - photometric properties of instantaneous - burst populations on age and metallicity has been previously investigated by worthey ( 1994 ) . he used the parameter @xmath18 at fixed color or index to represent the ratio of the change @xmath19 in age needed to counterbalance a change @xmath20 in metallicity in order to keep that color or index unchanged . the difference between worthey s and our approach is that he computed a single effective value of @xmath18 for each spectro - photometric property , while the different lines in figure 1 show the behavior of the @xmath18 slope for different values of the color or index under consideration . for comparison , the arrow in each panel of figure 1 indicates the @xmath21 vector obtained by worthey ( 1994 ) . in each case , the general agreement with the mean slope of the lines is good . table 1 gives a more quantitative comparison between worthey s ( 1994 ) and our results . we computed linear fits to all lines in figure 1 and then a linear fit between the derived slopes and their corresponding color or index value . the slopes and zero points of these relations for each spectro - photometric property are listed in columns ( 2 ) and ( 3 ) of table 1 . we then evaluated @xmath18 for four values of the @xmath14 and @xmath9 colors ( and corresponding model predictions for the mg@xmath16 and h@xmath17 indices ) matching the properties of early - type galaxies at four magnitudes @xmath22 , @xmath23 , @xmath24 and @xmath25 along the local cm relation ( ble92 ; see 3 ) . the agreement with worthey s ( 1994 ) predictions is seen to be of the order of @xmath26 % . it is worth noting that our generalized fits deviate significantly from worthey s `` 3/2 rule '' which takes the @xmath27 ratio to be 1.5 for any color . c|cc|cccc|c property & slope & zero point & @xmath28= 17.5 & @xmath28= 19.0 & @xmath28= 20.5 & @xmath28= 22.0 & worthey + [ @xmath14 ] & 0.444 & 0.653 & 1.19 & 1.24 & 1.30 & 1.35 & 1.5 [ @xmath9 ] & 0.886 & @xmath311.004 & 1.59 & 1.69 & 1.79 & 1.89 & 1.9 [ mg@xmath16 ] & 0.118 & 0.976 & 1.33 & 1.36 & 1.40 & 1.45 & 1.7 [ h@xmath17 ] & @xmath310.092 & 0.645 & 0.47 & 0.48 & 0.49 & 0.50 & 0.6 observational constraints on the photometric properties of early - type galaxies are taken from the recent sample of stanford , eisenhardt & dickinson ( 1998" +"the imaginary time path integral @xcite has provided a useful framework suitable for numerical analyses of quantum statistical - mechanical systems . most of the static properties of quantum systems can be calculated by means of the path integral monte carlo ( pimc ) or path integral molecular dynamics ( pimd ) technique @xcite . however , it is not straightforward to apply the pimc / pimd methods to computing dynamical properties such as the real time quantum correlation function @xmath2 . this is because it is nontrivial to construct real time quantities from a finite number of imaginary time data obtained numerically @xcite . to overcome such difficulty , a number of promising methods of numerical analytic continuation based on the maximum entropy method have been proposed and applied to various many - body systems @xcite . recently , the centroid molecular dynamics ( cmd ) method @xcite , the ring polymer molecular dynamics ( rpmd ) method @xcite , and the effective potential analytic continuation ( epac ) method @xcite have been proposed as new quantum dynamics methods to calculate real time quantum correlation functions at finite temperature . both the cmd and the rpmd are the methods to calculate the canonical ( kubo - transformed ) correlation function @xcite @xmath3 by means of molecular dynamics techniques . on the other hand , the epac is a method to obtain the real time quantum correlation function @xmath2 by means of the effective action formalism @xcite and an analytic continuation procedure @xcite . it has been shown analytically that all these methods are exact in harmonic systems for the real time quantum correlation functions of a linear function of the position operator , @xmath4 @xcite . however , for nonlinear operators such as @xmath5 , it is nontrivial whether these quantum dynamics methods yield the exact result even in harmonic systems @xcite . this is the _ nonlinear operator problem _ in quantum dynamics methods . from a practical point of view , the nonlinear operator problem is a quite important subject to be tackled . in many problems of chemical interest , the real time correlation functions of nonlinear operators are often needed for the calculation of various dynamical properties @xcite . for example , the cmd has been applied to the calculation of the transport coefficients such as thermal conductivity , shear viscosity , and bulk viscosity of quantum liquid parahydrogen @xcite . here it is found that the calculated transport properties are in good agreement with the experimental data . however , there is no rigorous theoretical basis for applying the cmd method to such properties represented by means of the correlation functions involving operators nonlinear in @xmath0 ( or momentum operator @xmath6 ) . therefore we need , in general , a quantum dynamics method which is theoretically valid even for the time correlation functions of nonlinear operators . the present status of the nonlinear operator problem in the three quantum dynamics methods , cmd , rpmd , and epac , is summarized as follows . for the cmd method , _ have argued this problem in their pioneering paper to conclude that a cmd correlation function involving nonlinear operators corresponds to a higher - order kubo - transformed correlation function @xcite . on the other hand , craig and manolopoulos have shown that the rpmd is exact for all the operators involving @xmath0 in the limit @xmath7 @xcite . as for our epac method , the nonlinear operator problem has not been examined yet . in addition to these three methods , a theoretical approach based on the quantum mode - coupling theory has been applied to study the dynamical properties involving nonlinear operators in quantum liquids @xcite . in the present paper , we develop the method of the epac for the calculation of the real time quantum correlation function involving the nonlinear operator @xmath5 . as a simple example , at first we show the epac correlation function @xmath8 for a harmonic oscillator comparing with the results of the cmd and the rpmd . next we calculate @xmath8 numerically in an asymmetric anharmonic system . we also propose a simplified epac method to reduce the computational cost required in the epac calculation . in sec . ii , we summarize the effective action formalism and present how to calculate the epac correlation function involving nonlinear operators . the results for a harmonic oscillator are given in sec . numerical results for an anharmonic oscillator are shown in sec . iv . in this section we also present the simplified epac method . the conclusions are given in sec . hereafter we treat the real time quantum autocorrelation function of the nonlinear operator @xmath9 , @xmath10 . in principle , this can be obtained from the imaginary time green function @xmath11 via an analytic continuation procedure @xcite . here @xmath12 represents a time - ordered product . on the other hand , it is known that the green function @xmath11 is given as a special case of @xmath13-point imaginary time green function @xmath14 , which can be constructed from the standard effective potential @xmath15 appearing in the effective action formalism @xcite . consequently , the real time quantum correlation function @xmath16 should be obtained by means of the effective action formalism and the analytic continuation . a series of these procedures is the epac method for the nonlinear operator @xmath9 , which we newly show in this section . as the simplest example , we present the epac calculation of the autocorrelation function of the quadratic operator @xmath17 , @xmath18 , in secs . iia and iib . we begin with the effective action formalism @xcite . consider a quantum system where a quantum particle of mass @xmath19 moves in a one - dimensional potential @xmath20 at inverse temperature @xmath21 . the quantum canonical partition function of this system is expressed in terms of the imaginary time path integral @xmath22&=&\int^{\infty}_{-\infty}dq \int^{q(\beta\hbar)=q}_{q(0)=q}{\cal d}q ~\!\exp\left [ -s_{e}/\hbar + \int^{\beta\hbar}_{0}d\tau j(\tau)q(\tau)/\hbar \right ] , \label{2}\end{aligned}\ ] ] where @xmath23 is the euclidean action functional @xmath24=\int^{\beta\hbar}_{0}d\tau \left[~\!\frac{1}{2}~\!m ~\!\dot{q}^2 + v(q)~\!\right ] , \label{3}\end{aligned}\ ] ] and @xmath25 is an external source . the generating functional @xmath26 $ ] is defined as @xmath27 & = & \hbar \log { \cal z}_{\beta}[j ] .\label{4}\end{aligned}\ ] ] the functional derivative of @xmath26 $ ] with respect to @xmath25 produces the quantum statistical - mechanical expectation value of the operator @xmath0 in the presence of @xmath28 , @xmath29}{\delta j(\tau ) } & = & \langle \hat{q}(\tau)\rangle_{\beta}^{j } \equiv q(\tau ) .\label{5}\end{aligned}\ ] ] the effective action @xmath30 $ ] is defined by the legendre transform of @xmath26 $ ] , @xmath31&=&-w_{\beta}[j ] + \int^{\beta\hbar}_{0}d\tau j(\tau)q(\tau ) , \label{6}\end{aligned}\ ] ] which satisfies the quantum - mechanical euler - lagrange equation @xmath32/\delta q(\tau)=j(\tau)$ ] . the exact quantum statistical - mechanical expectation value @xmath33(@xmath34 ) is obtained as a solution of the equation @xmath35}{\delta q(\tau)}=0 .\label{8}\end{aligned}\ ] ] note that the expectation value @xmath33 is independent of imaginary time @xmath36 in thermal equilibrium . the @xmath37-point connected green function @xmath38 is generated by the @xmath37th - order functional derivative of @xmath26 $ ] with respect to @xmath25 @xcite . for example , the two - point connected green function is given by @xmath39}{\delta j(\tau_{1})\delta j(\tau_{2 } ) } \right|_{j=0 } \nonumber \\ & = & \langle t \hat{q}(\tau_{1})\hat{q}(\tau_{2})\rangle_{\beta } -\langle \hat{q}(\tau_{1})\rangle_{\beta } ~\!\langle \hat{q}(\tau_{2})\rangle_{\beta } .\label{9}\end{aligned}\ ] ] then we obtain the two - point green function @xmath40 the procedure in eqs . ( [ 2])-([10 ] ) has been described in ref . . in a similar way , the three- and four - point green functions can be explicitly expressed as @xmath41 } { \delta j(\tau_{1})\delta j(\tau_{2})\delta j(\tau_{3 } ) } \right|_{j=0 } \nonumber \\ & & + q_{s}(\tau_{1 } ) \langle t \hat{q}(\tau_{2})\hat{q}(\tau_{3})\rangle_{\beta } + ( 1\leftrightarrow 2)+(1\leftrightarrow 3 ) \nonumber \\ & & -~2~q_{s}(\tau_{1})q_{s}(\tau_{2})q_{s}(\tau_{3 } ) , \\ \label{11 } \langle t \hat{q}(\tau_{1})\hat{q}(\tau_{2})\hat{q}(\tau_{3 } ) \hat{q}(\tau_{4})\rangle_{\beta } & = & \hbar^{3}\left.\frac{\delta^{4 } w_{\beta}[j ] } { \delta j(\tau_{1})\delta j(\tau_{2})\delta j(\tau_{3})\delta j(\tau_{4 } ) } \right|_{j=0 } \nonumber \\ & & \!\!\!\!\!\!\!\!\!\!\!\!\!\!\ ! + \hbar^{2}q_{s}(\tau_{1})\left.\frac{\delta^{3 } w_{\beta}[j ] } { \delta j(\tau_{2})\delta j(\tau_{3})\delta j(\tau_{4 } ) } \right|_{j=0 } + ( 1\leftrightarrow 2)+(1\leftrightarrow 3)+(1\leftrightarrow 4 ) \nonumber \\ & & \!\!\!\!\!\!\!\!\!\!\!\!\!\!\ ! + \langle t \hat{q}(\tau_{1})\hat{q}(\tau_{2})\rangle_{\beta } \langle t \hat{q}(\tau_{3})\hat{q}(\tau_{4})\rangle_{\beta } + ( 2\leftrightarrow 3)+(2\leftrightarrow 4 ) \nonumber \\ & & \!\!\!\!\!\!\!\!\!\!\!\!\!\!\ ! -~2~q_{s}(\tau_{1})q_{s}(\tau_{2})q_{s}(\tau_{3})q_{s}(\tau_{4 } ) , \label{12}\end{aligned}\ ] ] respectively . here @xmath42 denotes the interchange of @xmath43 with @xmath44 . on the other hand , the @xmath37th - order functional derivative @xmath45 is connected with the @xmath37th - order functional derivative of the effective action @xmath46 @xcite , @xmath47}{\delta j(\tau_{1})\delta j(\tau_{2 } ) } \right|_{j=0 } & = & \left(\left . \gamma_{\beta}[q]}{\delta q(\tau_{1})\delta q(\tau_{2 } ) } \right|_{q = q_{s}}\right)^{-1 } , \label{13 } \\ \left . \frac{\delta^{3 } w_{\beta}[j ] } { \delta j(\tau_{1})\delta j(\tau_{2})\delta j(\tau_{3 } ) } \right|_{j=0 } & = & -\frac{1}{\hbar^{3 } } \int^{\beta\hbar}_{0}\!\!\!\!\!ds_{1 } \int^{\beta\hbar}_{0}\!\!\!\!\!ds_{2 } \int^{\beta\hbar}_{0}\!\!\!\!\!ds_{3 } \nonumber \\ & & \times g_{\beta}^{c}(s_{1}-\tau_{1 } ) g_{\beta}^{c}(s_{2}-\tau_{2 } ) g_{\beta}^{c}(s_{3}-\tau_{3 } ) \nonumber \\ & & \times\left . \frac{\delta^{3 } \gamma_{\beta}[q ] } { \delta q(s_{1})\delta q(s_{2})\delta q(s_{3 } ) } \right|_{q = q_{s } } , \label{14}\\ \left . \frac{\delta^{4 } w_{\beta}[j ] } { \delta j(\tau_{1})\delta j(\tau_{2})\delta j(\tau_{3})\delta j(\tau_{4 } ) } \right|_{j=0 } & = & -\frac{1}{\hbar^{4 } } \int^{\beta\hbar}_{0}\!\!\!\!\!ds_{1 } \int^{\beta\hbar}_{0}\!\!\!\!\!ds_{2 } \int^{\beta\hbar}_{0}\!\!\!\!\!ds_{3 } \int^{\beta\hbar}_{0}\!\!\!\!\!ds_{4 } \nonumber \\ & & \times g_{\beta}^{c}(s_{1}-\tau_{1 } ) g_{\beta}^{c}(s_{2}-\tau_{2 } ) g_{\beta}^{c}(s_{3}-\tau_{3 } ) g_{\beta}^{c}(s_{4}-\tau_{4 } ) \nonumber \\ & & \times\left . \frac{\delta^{4 } \gamma_{\beta}[q ] } { \delta q(s_{1})\delta q(s_{2})\delta q(s_{3})\delta q(s_{4 } ) } \right|_{q = q_{s } } \nonumber \\ & & \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\ ! + \frac{1}{\hbar^{5 } } \int^{\beta\hbar}_{0}\!\!\!\!\!ds_{1 } \int^{\beta\hbar}_{0}\!\!\!\!\!ds_{2 } \int^{\beta\hbar}_{0}\!\!\!\!\!ds_{3 } \int^{\beta\hbar}_{0}\!\!\!\!\!ds_{4 } \int^{\beta\hbar}_{0}\!\!\!\!\!du \int^{\beta\hbar}_{0}\!\!\!\!\!dv \nonumber \\ & & \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\ ! \times g_{\beta}^{c}(s_{1}-\tau_{1 } ) g_{\beta}^{c}(s_{2}-\tau_{2 } ) g_{\beta}^{c}(u - v ) g_{\beta}^{c}(s_{3}-\tau_{3 } ) g_{\beta}^{c}(s_{4}-\tau_{4 } ) \nonumber \\ & & \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\ ! \times\left . \frac{\delta^{3 } \gamma_{\beta}[q ] } { \delta q(s_{1})\delta q(s_{2})\delta q(u ) } \right|_{q = q_{s } } \!\!\!\!\cdot~\left . \frac{\delta^{3 } \gamma_{\beta}[q ] } { \delta q(v)\delta q(s_{3})\delta q(s_{4 } ) } \right|_{q = q_{s } } \nonumber \\ & & \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\ ! + ( 2\leftrightarrow 3)+(2\leftrightarrow 4 ) .\label{15}\end{aligned}\ ] ] using eqs . ( [ 9])-([15 ] ) , we can construct the imaginary time green functions in terms of the effective action @xmath30 $ ] . now we employ the local potential approximation ( lpa ) to the effective action , @xmath31&=&\int^{\beta\hbar}_{0}d\tau\left [ v_{\beta}(q)+\frac{1}{2}~\!m~\!\dot{q}^{2 } \right ] , \label{16}\end{aligned}\ ] ] where @xmath15 is the standard effective potential , i.e. , the leading order of the derivative expansion of @xmath30 $ ] @xcite . for the case @xmath33 is @xmath36 independent , eq . ( [ 8 ] ) becomes the stationary condition @xmath48 , which determines the expectation value @xmath33 as the standard effective potential minimum @xmath49 . then the functional derivatives of the effective action @xmath46 become @xmath50}{\delta q(\tau_{1})\delta q(\tau_{2 } ) } \right|_{q = q_{s } } & = & \left(-m\frac{d^{2}}{d\tau^{2}}+ \left . \frac{\partial^{2 } v_{\beta}}{\partial q^{2 } } \right|_{q = q_{\rm min } } \right)\delta(\tau_{1}-\tau_{2 } ) , \label{17}\\ \left . \frac{\delta^{3 } \gamma_{\beta}[q ] } { \delta q(\tau_{1})\delta q(\tau_{2})\delta q(\tau_{3 } ) } \right|_{q = q_{s } } & = & \left . \frac{\partial^{3 } v_{\beta}}{\partial q^{3 } } \right|_{q = q_{\rm min } } \delta(\tau_{1}-\tau_{2})\delta(\tau_{1}-\tau_{3 } ) , \label{18}\\ \left . \frac{\delta^{4 } \gamma_{\beta}[q ] } { \delta q(\tau_{1})\delta q(\tau_{2})\delta q(\tau_{3})\delta q(\tau_{4 } ) } \right|_{q = q_{s } } & = & \left . \frac{\partial^{4 } v_{\beta}}{\partial q^{4 } } \right|_{q = q_{\rm min } } \delta(\tau_{1}-\tau_{2})\delta(\tau_{1}-\tau_{3})\delta(\tau_{1}-\tau_{4 } ) .\label{19}\end{aligned}\ ] ] if we expand @xmath51 around the minimum @xmath52 , @xmath53 then the derivatives of @xmath51 appearing in eqs . ( [ 17])-([19 ] ) are given" +"the structure , properties and reactions of nuclei and nuclear matter depend on the dynamics of the nucleons @xcite . this is the reason why the derivation of the nuclear forces is probably the most important problem of nuclear physics . after the discovery of quantum chromodynamics ( qcd ) the fundamental theory of strong interactions a solid theoretical understanding of the nuclear force should be grounded on qcd , either directly or indirectly . lattice qcd represents the direct , computational derivation : the interaction of quarks and gluons is not analytically solvable at the distances that are characteristic for nuclear physics but it is numerically solvable at the expense of huge computational resources . recent progress in this front is exciting @xcite . the indirect derivation requires to explain the nuclear interaction without explicitly solving qcd . yet qcd must enter indirectly in the picture . otherwise we will end up with a phenomenological description instead of a theoretical explanation . physics as a science depends to a great extent on the existence of scale separation in nature . one can describe the properties of atoms without explicit knowledge of the composite nature and internal structure of the nuclei within . the nucleus is indeed much smaller than the atom containing it , i.e. there is an excellent separation of scales . analogously , one can describe the dynamics of nucleons and pions without knowing the details of the strong interaction of the quarks and gluons inside them . however the average distance of nucleons in a nucleus about @xmath0 is not that different from the size of the nucleon or the wavelength of the quarks and gluons inside , maybe @xmath1 . without a clear separation of scales the development of satisfactory theoretical explanations to physical phenomena becomes more difficult . as a consequence the description of nuclei is less clear and more involved than that of atoms . effective field theories ( efts ) are the standard theoretical tool to exploit the separation of scales of a physical system with the intention of building the most general description of it at low energies @xcite . if we call the low energy scale @xmath2 and the high energy scale @xmath3 , an eft provides a power expansion in terms of @xmath4 of all the physical quantities of a system . for that one considers first all the possible interaction terms in the lagrangian that are compatible with the low energy symmetries of the system . then one orders the infinite feynman diagrams obtained in the previous step according to their expected size . the method by which we estimate the size of the diagrams is called power counting . while writing the diagrams is trivial , their power counting is not . the connection of the eft to the fundamental theory at the scale @xmath3 is provided by renormalization , the core idea of eft . in its standard formulation renormalization deals with ultraviolet ( uv ) divergences in the feynman diagrams of the eft . to remove the divergences one includes an uv cut - off and allows the couplings in the lagrangian to depend on the cut - off . if the calculation of the observable quantities of the eft is independent of the cut - off then the eft is renormalizable . power counting is decided according to how we have to arrange calculations to remove the divergences at each order in the expansion . wilsonian renormalization @xcite provides an alternative but equivalent formulation . here the starting point is the independence of observables with respect to the cut - off . in this case it is the calculation of the couplings under the assumption of cut - off independence that leads to the size of these couplings at low energies and to their power counting @xcite . this is referred to as renormalization group : the focus is on the evolution of the couplings as the cut - off changes , not on the divergences . in wilsonian renormalization the cut - off runs from the high to the low energy scale , from @xmath3 to @xmath2 . this is counterintuitive from the standard point of view , where the cut - off runs from @xmath2 to @xmath3 with the purpose of finding out whether there are uv divergences . yet they are equivalent . the cut - off can either run to the ultraviolet or the infrared ( ir ) . as far as the observables are independent of the cut - off we end up with identical power countings . the starting point in wilsonian renormalization can be either an eft or the fundamental theory . the advantage in the first case is that power counting can be determined without a complete order - by - order calculation of observables . in the second case there is the possibility of evolving a fundamental theory from @xmath3 to @xmath2 , which amounts to uncovering the eft by means of a concrete calculation . of course this is only possible in the few cases where the fundamental theory is known or easily solvable ( a nice example can be found in ref . ) . this manuscript is dedicated to wilsonian renormalization in nuclear eft @xcite : even though it is less well - known than the standard idea of removing divergences , it can provide a clearer interpretation of power counting and the role of the cut - off in eft . in nuclear physics the eft usually contains nucleon and pion fields that are constrained by chiral symmetry , a low energy symmetry of qcd that is exact in the limit of massless @xmath5 , @xmath6 and sometimes @xmath7 quarks . the problem is that historically renormalization has been only well understood in the case of systems that are perturbative @xcite . this is the case in hadron physics for processes involving at most one baryon , where chiral perturbation theory ( chpt ) @xcite , the standard eft for low energy hadronic processes , is used . but in nuclear physics the existence of the deuteron and the virtual state ( the @xmath8 singlet ) , not to mention the few thousand known nuclei , indicates that the nuclear force is non - perturbative . besides there is the additional problem that eft entails nuclear forces that are strongly divergent at short distances . thus it is not a surprise that progress in nuclear eft has been full of unexpected turns and controversies . recently we have begun to have a solid grasp of the non - perturbative renormalization of the eft potentials @xcite and how to organize the power counting in this situation @xcite , but even these advances have been the subject of debate @xcite . here we will review power counting from the perspective of the renormalization group . historically events have unfolded in a zig - zag pattern . weinberg made the first proposal for a nuclear eft @xcite , which includes the iteration of the eft potential ( at least at lowest order ) . this serves to capture the non - perturbative character of nuclear interactions but in exchange requires non - perturbative renormalization . as previously said , this has been the source of a few surprises . kaplan , savage and wise ( ksw ) discovered a subtle but nonetheless serious inconsistency with the weinberg proposal @xcite . these authors also developed a new formulation of nuclear eft , the ksw counting @xcite , which is free from that inconsistency . however the convergence of the ksw counting in the triplet partial waves happened to be unsatisfying to say the least @xcite . the community turned back to the weinberg proposal in search for phenomenological success @xcite . but later nogga , timmermans and van kolck @xcite discovered that the weinberg proposal contains a new , more conspicuous inconsistency at the lowest order : it is not renormalizable in some p- and d - waves . new developments about renormalizability followed @xcite that made finally possible a consistent nuclear eft with good convergence properties @xcite . despite these advancements , there is an ongoing debate about whether these problems are relevant and whether it would be simply more sensible to reinterpret renormalizability for non - perturbative problems in a different way @xcite . we will not discuss these new developments , except for a brief comment . here we are mostly concerned about the derivation of eft power counting from a specific set of renormalization tools , which happen to be more than enough to make nuclear eft work at the theoretical level . from this perspective the previous ideas , though interesting , do not appear to be totally necessary . this manuscript is organized as follows : in sect . ii we introduce wilsonian renormalization for the particular case of non - relativistic scattering of two particles . part of it is general and part of it is specific to nuclear physics . we also discuss the relationship of power counting with the anomalous dimension of couplings and the relationship between wilsonian renormalization and the more standard approach of removing ultraviolet divergences . in sect . iii we extend the results beyond the two - nucleon system , in particular to the deuteron electroweak reactions and to the three - body problem . finally we summarize our conclusions . we also include an appendix discussing the derivation of a particular equation in this manuscript . here we illustrate how wilsonian renormalization works for non - relativistic s - wave scattering @xcite . the starting point is a `` fundamental theory '' . for a non - relativistic two - body system the equivalent of a fundamental theory is the non - relativistic potential @xmath9 . to obtain the scattering amplitudes we solve the schrdinger equation at finite momentum @xmath10 @xmath11 where @xmath12 is the reduced wave function , @xmath13 the reduced mass , @xmath10 the center of mass momentum and @xmath14 the underlying potential , which we assume to be known at all distances . as we are considering s - wave scattering there is no centrifugal term . we solve this equation with the regular boundary condition at the origin @xmath15 finally the phase shift can be extracted from the asymptotic wave function @xmath16 wilsonian renormalization works as follows . in a first step we include a cut - off @xmath17 as a separation scale @xmath18 we will consider that the physics at distances shorter than the cut - off @xmath19 is unknown . of course if we cut the potential for @xmath19 the physical observables will change . we want to prevent this from happening . in a second step we include a new piece in the potential that counteracts the loss of information from having a cut - off and keeps the observables unchanged . this extra piece is the contact - range potential , which can take many parametrizations . for simplicity we choose the following form for the contacts @xmath20 that is , an energy - dependent delta shell potential . now we solve the schrdinger equation with the `` renormalized '' potential @xmath21 for distances below @xmath17 we have a free schrdinger equation @xmath22 with the regular solution @xmath23 for distances above @xmath17 we have the original schrdinger equation , i.e. eq . ( [ eq : schro - fundamental ] ) . finally at @xmath24 the delta - shell potential @xmath25 generates a discontinuity in the first derivative of the wave function that takes the form @xmath26 where @xmath27 refers to @xmath28 , with @xmath29 . a derivation can be found in [ app : delta ] . this is the renormalization group equation ( rge ) for the contact - range coupling @xmath30 . the rge we have written above is exact : the starting point is the full potential @xmath9 and" +"demand for large - scale networks consisting of multiple agents ( i.e. , nodes ) with different objectives is steadily growing due to their increased efficiency and scalability compared to centralized distributed structures @xcite . a wide range of problems in the context of distributed and parallel processing can be considered as a minimization of a sum of objective functions , where each function ( or information on each function ) is available only to a single agent or node @xcite . in such practical applications , it is essential to process the information in a decentralized manner since transferring the objective functions as well as the entire resources ( e.g. , data ) may not be feasible or possible @xcite . for example , in a distributed data mining scenario , privacy considerations may prohibit sharing of the objective functions @xcite . similarly , in a distributed wireless network , energy considerations may limit the communication rate between agents @xcite . in such settings , parallel or distributed processing algorithms , where each node performs its own processing and share information subsequently , are preferable over the centralized methods @xcite . here , we consider minimization of a sum of unknown convex objective functions , where each agent ( or node ) observes only its particular objective function via the stochastic gradient oracles . particularly , we seek to minimize this sum of functions with a limited number of gradient oracle calls at each agent . in this framework , we introduce a distributed online convex optimization algorithm based on the sgd iterates that efficiently minimizes this cost function . specifically , each agent uses a time - dependent weighted combination of the sgd iterates and achieves the presented performance guarantees , which matches with the lower bounds presented in @xcite , only with a relatively small excess term caused by the unknown network model . the proposed method is comprehensive , in that any communication strategy , such as the diffusion @xcite and the consensus @xcite strategies , are incorporated into our algorithm in a straightforward manner as shown in the paper . we compare the performance of our algorithm respect to the state - of - the - art methods @xcite in the literature and present the outstanding performance improvements for various well - known network topologies and benchmark data sets . distributed networks are successfully used in wireless sensor networks @xcite , and recently used for convex optimization via projected subgradient techniques @xcite . in @xcite , the authors illustrate the performance of the least mean squares ( lms ) algorithm over distributed networks using different diffusion strategies . we emphasize that this problem can also be casted as a distributed convex optimization problem , hence our results can be applied to these problems in a straightforward manner . in @xcite , the authors consider the cooperative optimization of the cost function under convex inequality constraints . however , the problem formulation as well as the convergence results in this paper are significantly different than the ones in @xcite . in @xcite , the authors present a deterministic analysis of the sgd iterates and our results builds on them by illustrating a stronger convergence bound in expectation while also providing msd analyses of the sgd iterates . in @xcite , the authors consider the distributed convex optimization problem and present the probability-@xmath4 and mean square convergence results of the sgd iterates . in this paper , on the other hand , we provide the expected convergence rate of our algorithm and the msd of the sgd iterates at any time instant . similar convergence analyses are recently illustrated in the computational learning theory @xcite . in @xcite , the authors provide deterministic bounds on the learning performance ( i.e. , regret ) of the sgd algorithm . in @xcite , these analyses are extended and a regret - optimal learning algorithm is proposed . in the same lines , in @xcite , the authors describe a method to make the sgd algorithm optimal for the strongly convex optimization . however , these approaches rely on the smoothness of the optimization problem . in @xcite , a different method to achieve the optimal convergence rate is proposed and its performance is analyzed . on the other hand , in this paper , the convex optimization is performed over a network of localized learners , unlike @xcite . our results illustrate the convergence rates over any unknown communication graph , and in this sense build upon the analyses of the centralized learners . furthermore , unlike @xcite , our algorithm does not require the optimization problem to be sufficiently smooth . distibuted convex optimization appears in a wide range of practical applications in wireless sensor networks and real - time control systems @xcite . we introduce a comprehensive approach to this setup by proposing an online algorithm , whose expected performance is asymptotically the same as the performance of the optimal centralized processor . our results are generic for any probability distribution on the data , not necessarily gaussian unlike the conventional works in the literature @xcite . furthermore , our performance bounds are optimal in a strong deterministic sense up to constant terms . our experiments over different network topologies , various data sets and cost functions illustrate the superiority and robustness of our approach with respect to the state - of - the - art methods in the literature . our main contributions are as follows . 1 . we introduce a distributed online convex optimization algorithm based on the sgd iterates that achieves an optimal convergence rate of @xmath0 after @xmath1 gradient updates , for each and every node on the network . we emphasize that this convergence rate is optimal since it achieves the lower bounds presented in @xcite up to constant terms . we show that the average sgd iterate achieves a msd of @xmath3 after @xmath1 gradient updates . our analyses can be extended to analyze the performances of the diffusion and consensus strategies in a straightforward manner as illustrated in our paper . we illustrate the highly significant performance gains of the introduced algorithm with respect to the state - of - the - art methods in the literature under various network topologies and benchmark data sets . the organization of the paper is as follows . in section [ sec : prob ] , we introduce the distributed convex optimization framework and provide the notations . we then introduce the main result of the paper , i.e. , a sgd based convex optimization algorithm , in section [ sec : main ] and analyze the convergence rate of the introduced algorithm . in section [ sec : sim ] , we demonstrate the performance of our algorithm with respect to the state - of - the - art methods through simulations and then conclude the paper with several remarks in section [ sec : conc ] . throughout the paper , all vectors are column vectors and represented by boldface lowercase letters . matrices are represented by boldface uppercase letters . for a matrix @xmath5 , @xmath6 is the frobenius norm . for a vector @xmath7 , @xmath8 is the @xmath9-norm . here , @xmath10 ( and @xmath11 ) denotes a vector with all zero ( and one ) elements and the dimensions can be understood from the context . for a matrix @xmath5 , @xmath12 represents its entry at the @xmath13th row and @xmath14th column . for a convex set @xmath15 , @xmath16 denotes the euclidean projection onto @xmath15 , i.e. , @xmath17 . we consider the problem of distributed strongly convex optimization over a network of @xmath2 nodes . at each time @xmath18 , each node @xmath13 observes a pair of regressor vectors and data , i.e. , @xmath19 and @xmath20 , where the pairs @xmath21 are independent and identically distributed ( i.i.d . ) for all @xmath22 , which is a common framework in the conventional studies in the literature @xcite . here , the distributions of the data pairs can differ from one node to another and we do not have any information on the underlying distributions . in such a framework , the aim of each node is to minimize a strongly convex cost function @xmath23 over a convex set @xmath15 . however , @xmath23 s are now known and each node accesses to its @xmath23 only via a stochastic gradient oracle , which given some @xmath24 , produces a random vector @xmath25 , whose expectation @xmath26 is a subgradient of @xmath27 at @xmath28 . using these stochastic gradient oracles , each node estimates a parameter of interest @xmath29 on a common convex set @xmath15 and calculates an estimate of the output as @xmath30 i.e. , by a first order linear method . after observing the true data at time @xmath18 , node @xmath13 suffers a loss of @xmath31 , where @xmath32 is a strongly convex loss function . as an example , our cost function can be defined as follows @xmath33 where @xmath34 is a lipschitz - continuous convex loss function with respect to the first variable , where is extensively studied in the literature @xcite as a strongly convex loss function involving regularity terms . nodes , where each agent communicates with a set of nodes in its neighborhood.,title=""fig : "" ] + here , the aim of each node is to minimize its expected loss over the convex set @xmath15 . to continue with our example in , the aim of each node is to minimize @xmath35 where we drop the notational dependency of @xmath36 to the time index @xmath18 since the data pairs are assumed to be independent over time . we emphasize that the formulation in covers a wide range of practical loss functions . as an example , when @xmath37 , we consider the regularized squared error loss and when @xmath38 , we consider the hinge loss . since we make no assumptions on the loss function @xmath39 other than strong convexity , one can also use different loss functions with their corresponding gradients and our results still hold . in this framework , at each time @xmath18 , after observing the true data @xmath20 , each node exchanges ( i.e. , diffuses ) information with its neighbors in order to produce the next estimate of the parameter vector @xmath40 . for example , in fig . [ fig : network ] , we have a distributed network consisting of @xmath41 nodes , where each node communicates with its neighbors . although the aim of each node is to minimize its expected loss in , the ultimate goal of the distributed network is to minimize the total expected loss , i.e. , @xmath42 for each node @xmath13 , with at most @xmath18 stochastic gradient oracle calls at each agent , where @xmath2 is the number of nodes in the distributed network . here , we emphasize that the expected total loss in is defined with respect to the data statistics at every node , whereas the parameter vector is trained using the gradient oracle calls at @xmath13th node and the information diffusion over the distributed network . thus , our aim is to minimize a global , strongly convex cost function at each node over a distributed network , where each learner is allowed to use at most @xmath18 calls to the gradient oracle until time @xmath18 . in this section , we present the main result of the paper , where we introduce an algorithm based on the sgd updates that achieves an expected regret upper bound of @xmath0 after @xmath1 iterates . the proposed method uses time dependent weighted averages of the sgd updates at each node together with the adapt - then - combine diffusion strategy @xcite to achieve this performance . however , as later explained in the paper ( i.e. , in section [" +"molten salts are liquid mixtures of ionic species at high temperatures . they receive much attention due to their diverse but promising applications that range from metal production @xcite , the pyrochemical treatment of nuclear waste @xcite , primary or secondary coolants in several concepts of generation iv fission @xcite and fusion @xcite nuclear reactors , and electricity storage devices @xcite . in the context of nuclear applications , the nuclear reactions produce rare earth elements in the core . from the neutronic point of view , these have a poisoning effect and must therefore be eliminated . one of the advantages of most of the concepts of reactors based on molten salts , including the promising thorium - fueled molten salt fast reactor ( msfr ) is that their fuel is dissolved in the primary coolant ( which is the molten salt ) @xcite . such liquid state fuel allows for the elimination and reprocessing of several fission products and rare earth elements during the reactor operation , via chemical or electrochemical methods @xcite . one drawback is the complex handling of the molten salt fuel inside the ( recycling ) circuit : important care must be taken for controlling the physico - chemical conditions@xcite , and additional efforts have to be made on the development of adapted structure materials @xcite . the knowledge on molten fluoride salts chemistry has long remained fragmented and limited to a few experimental techniques ( mainly electrochemical ones ) due to experimental hindrances . one has to deal with high temperatures ( from 500 k to 1800 k ) and to control the corrosive properties by setting up original experiments . many efforts have been made towards this direction and several experimental techniques have been adapted to the study of molten salts . the development of new cells has unlocked the study of molten fluorides by exafs spectroscopy @xcite , which , coupled to other spectroscopic methods such as nuclear magnetic resonnance ( nmr ) @xcite or raman @xcite , is able to provide a view of the local structure in these melts . as for the dynamic properties , similar improvements have been made and the self - diffusion coefficients can be measured up to 1500 k by pulsed field gradient nuclear magnetic resonance ( pfg - nmr ) @xcite . such measurements are important since the diffusion coefficients provide an information on the _ individual _ dynamics of the ions , complementing the viscosity or electrical conductivity measurements which inform about the _ collective _ dynamics of the macroscopic system . during the past decade , these experimental efforts have been accompanied by the development of simulation tools adapted to the study of molten fluorides and chlorides , namely density functional theory @xcite , thermodynamic modeling @xcite and molecular dynamics ( md ) @xcite . among those , the latter has proven to be efficient for the study of the structure and dynamics of the system at the microscopic scale , allowing the interpretation of experimental results @xcite and the prediction of quantities that hitherto remained unknown @xcite . the simulations are based a polarizable ion model , which has strong physical grounds @xcite and can efficiently be parameterized from first - principles @xcite , _ i.e. _ , without having empirically recourse to any experimental data . in this work , we combine state - of - the - art experimental and simulation tools to study a series of lif - yf@xmath2 molten salts of varying compositions . we first describe shortly the methodological aspects . then , we compare measured and calculated self - diffusion coefficients and electrical conductivity to show that md simulations are in quantitative agreement with experiments , which allows for further use of the simulations to discuss the interplay between the microscopic structure of the electrolytes and their dynamic properties . mixtures of lif and yf@xmath0 salts ( purity @xmath3 % ) were prepared in a glove box under argon in order to avoid h@xmath4o and o@xmath4 contamination of the samples . we use boron nitride ( bn ) crucibles to confine the salts , and to prevent them from any chemical reaction . the amount of salt in each crucible is _ ca_. 50 mg . the bn crucible is heated by a symmetrical irradiation with two co@xmath4 lasers . the laser power is increased progressively until the target temperature is reached . the high temperature pfg nmr spectra were recorded using a bruker avance wb 400 mhz operating at 9.40 t. an argon stream prevents oxidation of the bn at high temperature . the 10 mm liquid nmr probe is specially designed by bruker and adapted in cemhti to work up to 1500 k. it is equipped with a gradient coil providing 5.5 g@xmath5@xmath6a@xmath7 that is combined with a gradient amplifier of 10 a. we use a nmr pulse sequence combining bipolar gradient pulses and stimulated echo@xcite . it is repeated with 8 gradients of linearly increasing strength . measurements were performed using the following nmr parameters : durations of radiofrequency magnetic field application for @xmath8 pulses @xmath9 @xmath10s ( @xmath11f ) and @xmath12 @xmath10s ( @xmath13li ) , gradient strength @xmath14 was varied from 0 to 50 g / cm , gradient application time @xmath15 between 1 and 5 ms . for @xmath13li measurements , we used a pre - saturation cycle before the diffusion sequence because of the long relaxation time @xmath16 of this nucleus ( 25 s in pure molten lif ) . finally , the self - diffusion coefficients were obtained by nonlinear least - square fitting of the echo attenuation@xcite . the experimental setup used for measuring the electrical conductivity is described in details in reference @xcite ; the conductivity cell configuration was derived from the one proposed by hives and thonstad @xcite . the conductivity was measured for lif - yf@xmath0 mixtures with compositions ranging from @xmath17 = 0.00 to 0.18 , at several temperatures . here we report the results obtained for the 1130 k isotherm . all the details are given in the supplementary material document no.1 @xcite . we use molecular dynamics ( md ) to compute static and dynamic properties of the molten salt at the atomic scale . the md simulations used therein rely on interatomic interaction potentials parameterized from first principles . the parameterization procedure is described elsewhere @xcite . they are of _ ab initio _ accuracy and have been successful in reproducing accurately the electrical conductivity , the heat capacity , the viscosity , etc , of various ionic materials ( mainly molten fluorides and solid oxides@xcite ) . in the case of molten fluorides , the interaction potential is best described as the sum of four different components : charge - charge , dispersion , overlap repulsion , and polarization . the detailed description of the potential is given in the supplementary material document no.1 @xcite . we studied 11 concentrations ranging from @xmath17 = 0.10 to 0.60 by steps of 0.05 . each system was simulated along two isotherms . the first one at 1130 k allows for comparison with experimental data . the other one at 1200 k allows for comparison with previous works on fluorozirconates @xcite . for both temperatures , ( i ) the equilibrium volume was determined from a simulation in the isothermal isobaric ( npt ) ensemble with a target pressure of 1 atm , using the method described by martyna _ et al . _ @xcite ; ( ii ) production runs were then performed in the canonical ( nvt ) ensemble , @xcite with a time step of 1.0 fs . the total simulation time was of 4 ns for the production runs for each system . the relaxation time of the thermostat was set to 20 ps . the simulation cell parameters and the number of atom of each species are summarized for each composition and temperature in the supplementary material document no.1 @xcite . the cut - off distance for the real space part of the ewald sum @xcite and the short range potential was set to half the length ( @xmath18 ) of the cubic simulation cell . the value of the convergence parameter in the ewald sum was set equal to @xmath19 and 8@xmath20 @xmath21-vectors were used for the reciprocal space part calculation of the forces and potential energy . the self - diffusion coefficients of fluoride , lithium and yttrium ions along the 1130 k isotherm are presented in fig . [ fig : diffusion_coef ] as a function of the salt concentration . both experimental and molecular dynamics results are presented for f@xmath22 and li@xmath23 . for y@xmath1 , the self - diffusion coefficient can only be measured from molecular simulations , due to the nmr characteristics of @xmath24y ( low gyromagnetic ratio and long relaxation time up to 45 min ) . the self - diffusion coefficient @xmath25 of species @xmath26 is extracted from molecular dynamics simulations using einstein s relation , _ i.e. _ , from the long - time slope of mean squared displacement : @xmath27 where @xmath28 is the position of atom @xmath29 of type @xmath26 at time @xmath30 . the brackets denote an ensemble average over all trajectories and atoms @xmath29 of type @xmath26 . the self - diffusion of li@xmath23 is about 60 % higher than that of f@xmath22 , whatever the concentration . excellent agreement is found between experiments and simulations . we can therefore be confident in the md simulation results for y@xmath1 . the latter value is about one third of the diffusion coefficient of li@xmath23 over the whole range of compositions . all self - diffusion coefficients decrease at the same rate with the increase in yttrium fluoride concentration . at @xmath31 k as a function of the mole fraction in yf@xmath0 . full ( open ) symbols indicate experimental ( molecular dynamics ) data[fig : diffusion_coef ] . dashed and dotted lines are just guides for the eyes . ] the electrical conductivities measured at a temperature of 1130 k are presented in fig . [ fig : conductivity ] for different salt concentrations in yf@xmath0 and compared to experimental results@xcite . in molecular dynamics simulations , the electrical conductivity is calculated from @xmath32 where @xmath33 with @xmath34 the boltzmann constant , @xmath35 is the elementary charge , @xmath36 the volume of the cubic simulation cell of length @xmath18 , and @xmath37 is the net displacement of all the ions of species @xmath26 and charge @xmath38 in time @xmath30 . there are @xmath39 species here . the error bars associated to our calculations of the electrical conductivity from eq . [ eq : conductivity ] are estimated to 10 % . such high values are due to the collective nature of @xmath40 . it is not averaged over both the time steps and all the atoms of a given species , as self - diffusion coefficients are , and consequently require long simulations runs . the true electrical conductivity of eq . [ eq : conductivity ] is thus often approximated by the nernst - einstein formulae , which relates @xmath40 to the individual diffusion coefficients of the various species in the liquid . surprisingly , we find the electrical conductivity calculated from the nernst - einstein formulae to be overestimated by only 10 to 20 % . larger differences , typically 40 % , are usually observed for such salts@xcite . margulis et al . showed that the nernst - einstein relation always overestimates the conductivity in molten salts and ionic liquids because of conditions in the momentum balance that contraint the motion of ions of same charge to be anticorrelated@xcite . the real electrical conductivity , as calculated from md using eq . [ eq : conductivity ] , is plotted in fig . [ fig : conductivity ] . again , good agreement is found with experiments . the electrical" +"there is a growing amount of experimental and numerical evidence indicating that two - dimensional ( 2d ) turbulence at moderate to low reynolds number is dominated by the existence of coherent structures@xcite . this observation is more or less independent of whether the turbulence maintains an energetically steady state with a fully developed inverse energy cascade or merely coarsens with time as in decaying 2d turbulence . coherent structure dominance and the unique aspects of the 2d dual cascade picture , _ i.e. _ an inverse cascade moving energy from small to large length scales and a direct cascade moving mean - squared vorticity , or enstrophy , from large to small length scales , clearly distinguishes 2d turbulence from its three - dimensional ( 3d ) counterpart . an emphasis in the study of 2d turbulence is to understand what impact these structures have on the statistics of turbulence . recent numerical and experimental results demonstrate that statistical quantities display different behavior in regions around locally hyperbolic points in the velocity field ( saddles ) and within vortices ( centers)@xcite . the existence of coherent structures is expected to play an important role in the turbulent dispersion ( mixing ) of passive scalars@xcite . in particular , centers , if long lived , should act as trapping regions that prevent scalar advection over their encircling manifolds . on the other hand , saddles should quite effectively enhance the dispersion by the stretching of fluid elements into thin filaments along the saddle s unstable manifold . it is this picture that underlies the description of trajectories of fluid elements in 2d turbulence in terms of successive trapping and flight events , i.e. , levy flights@xcite . although there is little evidence supporting this idea , the proposal highlights the importance of accounting for coherent structures in any mixing model . how coherent structures affect the mixing properties of 2d turbulent flows can have profound impact on real world problems . an example of geophysical significance is the antarctic circumpolar vortex which , during the winter months , prevents ozone - depleted air over the south pole from mixing with ozone - rich air at mid latitudes@xcite . also , the possibility that 3d turbulence may not be as dominated by coherent structures as is 2d turbulence does not mean that coherent structures do not play an important role in 3d mixing@xcite . understanding how coherent structures influence mixing in 2d may aid in the understanding of 3d mixing . the mixing problem is generally approached by applying statistical treatments to fluid - element ( or particle ) trajectories , i.e. , to the lagrangian dynamics of the fluid . classical descriptions of lagrangian dynamics involve the statistical properties of both single trajectories ( @xmath0 ) following the work of g.i . taylor@xcite and relative displacement of two trajectories ( @xmath1 ) following the work of richardson@xcite . in this manuscript , the effects of coherent structures on mixing in 2d turbulence will be quantified by measuring their effects on these classical quantities . recently there has been important theoretical and numerical work on the evolution of fluid `` patches '' ( groups of @xmath2 fluid elements with @xmath3)@xcite . this approach is interesting and could include the effects of coherent structures on the evolution of fluid patches but is beyond the scope of the present work . following the discussion in @xcite , the classical descriptions of particle motion in 2d fluids start from the observation that the lagrangian trajectory , @xmath4 , of a fluid element or non - inertial particle embedded in the fluid is governed by the stochastic equation : @xmath5 in eq . [ eq : stochasticequation ] , @xmath6 is the incompressible fluid velocity at position @xmath7 at time @xmath8 , @xmath9 is the molecular diffusivity and @xmath10 represents standard brownian motion . since our system is in a regime dominated by turbulent advection and not by thermal fluctuations , @xmath9 will be set to zero . for single - particle trajectories , the important statistical property is the distance a particle has traveled , on average , over a given time interval @xmath11 . defining @xmath12 one can show that @xmath13 which , upon performing an ensemble average and assuming @xmath14 is statistically stationary , becomes an equation for the second moment of the single particle displacement @xmath15 the behavior of @xmath16 depends on how @xmath17 compares with the lagrangian correlation time @xmath18 . if @xmath19 then @xmath20 so that the term within the integral of eq . [ eq : singlepointintegral ] simply becomes @xmath21 . in this case @xmath22 , _ i.e. _ ballistic motion . if , on the other hand , @xmath23 then the integral in eq . [ eq : singlepointintegral ] reduces to @xmath24 yielding brownian walk behavior for the single particle displacement : @xmath25 . these limits follow simply from the properties of the velocity autocorrelation . for intermediate times the behavior of @xmath16 depends on the nature of the inertial turbulent fluctuations and not much is known about its scaling in 2d turbulence@xcite . for two - particle trajectories , the quantity of interest is the statistics of the relative displacement of particles in a turbulent flow . defining the relative displacement of two trajectories @xmath26 , eq . [ eq : stochasticequation ] implies that @xmath27 as in the case of the single trajectories , an equation for @xmath28 can be obtained ( dropping the subscripts for simplicity ) : @xmath29 if @xmath30 is small , @xmath31 should be linearly proportional to @xmath30 , _ i.e. _ , the first term in a taylor series . this linear behavior yields exponential growth in time for @xmath28 . on the other hand , if @xmath30 is within the inertial energy range one expects that @xmath32@xcite . this yields @xmath33 where @xmath34 is the trajectory spacing at time @xmath35 . under the assumption that @xmath34 is small compared to the scales of interest we get @xmath36 , the famous @xmath37 law derived by richardson@xcite . a richardson range was reported in both 2d@xcite and 3d experimental systems@xcite . our work on 2d lagrangian statistics and coherent structures begins with a description and characterization of the experimental apparatus and measurement techniques in sec . [ sec : experimental ] . section [ sec : lagrangian ] presents the basic single trajectory and two trajectory lagrangian statistics . in sec . [ sec : coherentstructures ] the quantities presented in sec . [ sec : lagrangian ] are conditioned on the presence of coherent structures to elucidate the role that such structures play in the mixing process . finally , in sec . [ sec : conclusions ] , the implications of and future opportunities for these lagrangian measurements of turbulence in 2d systems are discussed . section [ subsec : system ] describes the stratified electromagnetically forced layer that was the quasi 2d fluid used in this set of experiments , as well as the technique used for obtaining velocity and trajectory information , namely particle tracking . in sec . [ subsec : bphk ] the technique for identifying coherent structures within the flow is established . finally , sec . [ subsec : characterization ] presents basic statistical properties of the turbulence produced in the layer . the two - point prediction of @xmath38 obtained in sec . [ sec : introduction ] requires the presence of an inverse energy cascade where @xmath39 scales as @xmath40 ( as we will see this is not a strict requirement ) . for 2d , or more pointedly quasi-2d , turbulence this implies that the turbulence must be continuously forced . one method for continuously forcing the body of a fluid , originally pioneered by dolzhansky in 1979 @xcite , is to subject a current carrying fluid to external magnetic fields . this method of forcing has since evolved into the stratified electromagnetic layer@xcite which has become one of the more common systems for the study of 2d turbulence . schematic illustration of the stratified layer 2d turbulence experiment . see sec . [ subsec : system ] for detailed description.,width=336 ] the stratified electromagnetic layer is comprised of a dense salt water layer , typically of order @xmath41 cm deep and @xmath42 cm @xmath43 @xmath42 cm square , underneath a less dense solution of roughly the same depth . a current is passed in the plane of the layer and the layers are subject to a spatially varying magnetic field penetrating them vertically . the resultant lorentz force drives fluid motion . the evolution of the stratified layer system is expected to approximate the forced / damped 2d navier - stokes equation , @xmath44 supplemented by the incompressibility condition @xmath45 . as usual , @xmath14 is the fluid velocity field , @xmath46 is the density normalize pressure , @xmath47 is the external electromagnetic forcing , @xmath48 is the fluid kinematic viscosity , and einstein summation is used throughout . the linear term with coefficient @xmath49 represents the effects of frictional drag owing to the container bottom . in the set of experiments presented here , the system described above is modified slightly by replacing the lower layer of fluid with fluorinert fc-75 and the upper layer by a dense salt water solution of @xmath42% by mass nacl with a small amount of liquid detergent added to lower surface tension and help with dissolution of tracer particles . the fluorinert is used because it has a density @xmath50 times that of water with near the same viscosity , which allows for much stronger stratification than in the case of two salt water solutions . it is also a strong dielectric so the lower layer is completely passive and only the upper salt water layer is electromagnetically forced . finally , and perhaps most importantly , the fluorinert and water are immiscible . these combined features allow the fluorinert system to maintain stratification indefinitely , allowing the salt water layer to be driven harder than in previous systems @xcite . raw particle tracks obtained from the stratified layer over four consecutive frames ( @xmath51 s).,width=336 ] the experimental apparatus , shown schematically in fig . [ fig : apparatus ] , consisted of a @xmath41 cm thick layer of salt - solution suspended over a @xmath41 cm thick layer of fluorinert . the layers were contained in a @xmath52 cm @xmath43 @xmath42 cm box with reservoirs at each end across which copper electrodes were placed in the fluid . for the results reported in this paper an alternating square - wave current with frequency @xmath53 hz and amplitude @xmath54 amps was driven through the salt solution . a set of @xmath55 cm diameter rare - earth magnets of approximately @xmath56 t residual field strength were arranged with alternating field direction in a @xmath42 cm @xmath43 @xmath42 cm square array with a period of @xmath57 cm and oriented at @xmath58 with respect to the current direction . the combination of the current and the magnetic field produces a kolmogorov - like forcing@xcite of alternating shear bands with the shear direction along @xmath59 and periodicity @xmath60 cm in the @xmath61 direction ( which implies @xmath62 rad / cm ) . using the layer depths of @xmath41 cm yields an approximation of @xmath63 hz for the frictional coupling assuming a simple linear shear in the fluorinert . also , the salt solution upper layer has a viscosity around @xmath64 that of water . to obtain velocity information as well as trajectory information used in generating lagrangian statistics , the upper salt - solution layer was seeded with polycrystalline powder with mean diameter @xmath65 @xmath66 and density @xmath67 gm / cc . images of the particle fields , illuminated using several xenon short - arc flash lamps , were obtained with a @xmath68 @xmath43 @xmath69 pixel ccd camera at a frame rate of" +"in active galactic nuclei various physical processes such as particle acceleration , emission of high energy photons , and so on , take place . accretion of matter onto the central black holes is thought to be the energy source of these processes . when a fraction of matter is ejected from the accretion disks , relativistic jets of plasmas are formed . the relativistic jets are thought to explain intense and variable emission from blazars . the beaming effect amplifies the radiation from jets depending on the opening angle of the jets , bulk lorentz factor , @xmath4 , and the angle between the line of sight and the jet axis , @xmath5 . some blazars are known to emit very high energy @xmath6-rays in the tev energy band . they are , for example , pks 2155304 , mrk 421 , and mrk 501 ( e.g. , * ? ? ? recent observations of tev @xmath6-rays have found remarkably short time variability of tev blazars . in 2006 july pks 2155304 with redshift @xmath7 showed an outburst of tev @xmath6-rays . the average flux during the outburst was more than 10 times typical values observed from the object @xcite . during this period x - rays were also monitored by _ swift_. in the 0.310 kev energy band the x - ray flux increased by a factor of 5 @xcite . the observations by the high energy stereoscopic system ( h.e.s.s . ) report that the timescale of variation is a few minutes @xcite . the well - resolved burst of the tev @xmath6-ray flux from pks 2155304 varied on timescales only @xmath8 s. recently magic also observed short time variation in mrk 501 @xcite . when the size of the emission region in the comoving frame of the jet is denoted by @xmath9 , the observed timescale of the variability sets a limit on @xmath9 , i.e. , @xmath10 , where @xmath11 is the speed of light and @xmath12^{-1}$ ] is the beaming factor with @xmath13 . @xcite argued that @xmath14 60 - 120 @xmath15 is required to explain @xmath16 min , where @xmath17 is the schwarzschild radius with @xmath18 and @xmath19 being the gravitational constant and the central black hole mass , respectively . such large values of @xmath20 are also suggested by @xcite recently , based on the requirements of radiative cooling time and optical depth for @xmath6-rays due to electron - positron pair production . the emission spectra of blazars are characterized by two peaks in the @xmath21-@xmath22 representation , where @xmath23 is the differential energy flux . the lower energy peak is located in the optical x - ray bands and the higher energy peak is located in very high energy @xmath6-ray bands . the lower energy peak is most probably by synchrotron radiation of nonthermal electrons / positrons . radiation mechanisms of high energy @xmath6-rays are thought to be inverse compton scattering off soft photons in the leptonic models ( e.g. , * ? ? ? * ) and hadronic interaction of relativistic particles and photons in the hadronic models ( e.g. , * ? ? ? * ; * ? ? ? the soft photons of the leptonic models are supplied by synchrotron radiation by relativistic electrons / positrons in the jet ( synchrotron self - compton model ) or by the external sources such as accretion disks @xcite and disk radiation scattered around the jet @xcite . these emission models assume that the emission region is one zone . observations of tev @xmath6-rays of blazars have revealed that large values of @xmath24 are required to fit the emission spectra of very high energy @xmath6-rays by inverse compton scattering ( e.g. , * ? ? ? on the other hand , the observations of the apparent velocity of vlbi knots show that parsec - scale jets are subrelativistic or at most mildly relativistic @xcite . to reconcile the discrepancy between these values of @xmath4 , the deceleration of jets is considered . @xcite assumed that tev @xmath6-rays are produced by inverse compton scattering off synchrotron photons that are emitted by decelerated jet components . @xcite , on the other hand , proposed a spine - layer model . in this model they assumed that a fast moving emission region is surrounded by a slow moving sheath . gamma - rays are then produced by inverse compton scattering off the photons emitted in the spine and the sheath . although various emission models of jets with multiple radiation zones have been proposed as mentioned above , a simple synchrotron self - compton ( ssc ) model is still worth use in obtaining physical parameters of the emission regions in jets . in this paper we show that a simple ssc model can explain the tev @xmath6-rays and x - rays of pks 2155304 . pks 2155304 is an interesting source because of its strong tev @xmath6-ray emission and the short time variability of tev emission . since the redshift of pks 2155304 is 0.116 , the absorption of tev @xmath6-rays by extragalactic background light ( ebl ) is effective ( e.g. , * ? ? ? this is an ideal object to test ebl models as well as emission models . in [ sec : model ] we describe the parameters of our numerical calculations and in [ sec : results ] the values of the parameters are determined by fitting the observed data . finally discussion is given in [ sec : sum ] . the emission region is assumed to be a sphere with radius @xmath9 moving relativistically with bulk lorentz factor @xmath4 . below we assume @xmath25 , i.e. , @xmath26 . we solve kinetic equations of electrons and photons in the emission region @xcite . here we assume that the plasmas and radiation in the emission region are in a steady state . electrons are continuously injected in the emission region at rate @xmath27 . the injection spectrum is given by @xmath28 where @xmath29 , @xmath30 , and @xmath31 are parameters , and @xmath32 is the normalization constant determined by @xmath33 the electrons escape from the emission region by advection on timescale @xmath34 , where @xmath35 is a dimensionless parameter . the cooling processes of the electrons are synchrotron radiation and inverse compton scattering . we assume that the emission region has randomly oriented magnetic field @xmath36 . photons are assumed to escape from the emission region on timescale @xmath37 . we also include the absorption of @xmath6-rays in the emission region by @xmath38 production due to photon - photon collisions . this effect is found to be negligible for @xmath6-rays with observed energy less than 10 tev in our numerical results . parameters in our model are @xmath4 , @xmath9 , @xmath36 , @xmath27 , @xmath29 , @xmath30 , @xmath31 , and @xmath35 . the dependence of solutions on @xmath35 is weak and we set @xmath39 . in addition to the above parameters , the cosmological parameters such as hubble constant @xmath40 and the density parameters of matter @xmath41 and cosmological constant @xmath42 are needed to calculate the luminosity distance and the optical depth for @xmath6-ray absorption by ebl . we assume @xmath43 km s@xmath44 mpc@xmath44 , @xmath45 , and @xmath46 . it is known that tev @xmath6-rays emitted by distant sources are absorbed by ebl . this was first pointed out by @xcite and detailed calculations were performed by @xcite and @xcite . later @xcite proposed that the ebl spectrum is estimated by considering the absorption of tev @xmath6-rays from blazars . since then various models of ebl have been proposed ( see * ? ? ? * for review ) . the redshift of pks 2155304 is 0.116 and the optical depth of tev @xmath6-rays is greater than unity for @xmath6-rays with energy greater than 1 tev . in our previous work @xcite , we used models by @xcite to fit the emission spectrum from h1426 + 428 . there we found that model lll of @xcite is applicable in the ssc model . in this paper we use the same ebl model to calculate the deabsorbed tev spectrum . h.e.s.s . observed a @xmath6-ray outburst from pks 2155304 on 2006 july 28 ( mjd 53944 ) @xcite . almost simultaneous observation by _ swift _ was performed in the x - ray band on july 29/30 @xcite . the observed emission spectra are shown in figure [ fig : photonspec1 ] . the tev data in 2006 july are from h.e.s.s . the tev spectrum is corrected with an ebl model , lll , of @xcite for absorption by @xmath38 production through photon - photon collisions . the x - ray spectrum of 2006 july 29 and 30 is shown by a thick dashed line . this spectrum is a log - parabolic model fit given by @xcite . other x - ray , optical , and radio data are not simultaneous with the tev data . the x - ray data except those of _ swift _ are from _ bepposax _ and radio data are from ned . 2mass data are also plotted . the tev emission spectrum observed in 2003 july @xcite is shown for comparison . our models are shown in figure [ fig : photonspec1 ] by solid and dashed lines for 2006 july and 2003 july , respectively . we did not fit the emission spectra below @xmath47 hz , assuming this emission is from different regions , possibly from extended regions far away from the central black hole . the values of the parameters for the flare in 2006 july are the following : @xmath48 , @xmath49 g , @xmath50 cm , @xmath51 , @xmath52 , and @xmath53 ( model a in table [ tbl-1 ] ) . the value of @xmath9 is @xmath54 , if @xmath55 . from these parameters , the timescale of variability is @xmath56 s. we also obtained the parameter values which give @xmath57 s. those are shown in table [ tbl-1 ] ( models b and c ) . when @xmath57 s is assumed , the spectral energy distribution ( sed ) of 2006 july is fitted well if @xmath4 is in the range @xmath58 . when @xmath59 , the fluxes in the tails of the lower and higher peaks of the sed are too high . on the other hand , when @xmath60 , the tail of the lower peak ( the x - ray band ) is too steep . seds for models a , b , and c are shown in figure [ fig : photon - abc ] . in table [ tbl-1 ] the parameters given in other papers such as @xcite and @xcite are also listed . note that @xmath61 h is assumed in @xcite and that @xcite did not perform the spectral fitting . in figure [ fig : photon - tev ] various deabsorbed tev spectra are compared with our models . the deabsorbed spectra are calculated with different ebl models given by @xcite . when ebl models other than lll , lhh , llh , and lhl are applied ( llh and lhl are not shown in the figure ) , the tev spectrum has a peak at @xmath62 hz . such a spectrum is difficult to produce by the one - zone ssc model , if the x - rays are emitted in the same region as tev @xmath6-rays . in particular the klein - nishina effect suppresses the emission in the tev band . in our simulations , small numbers of nonthermal electrons and synchrotron photons are initially injected and time evolution is followed until a steady state is attained . because of this initial condition , the sed takes longer time than the observed timescale to attain a steady state . the time evolution of the sed of model a is shown in figure [ fig : photon - evolv" +"x - ray emission from agn is thought to be produced in the very central regions of accretion flow , close to the black hole , since this is where most of the gravitational potential energy is dissipated . observational evidences for this come from results of modeling of spectral features , often showing distortions consistent with those caused by doppler effects and gravitational redshift . in particular , broad profiles of the fe k@xmath0 line are currently the best evidences for the very central x - ray generation and reprocessing . geometrical models of x - ray emitting accretion flows are of two kinds : the accretion disk with a corona scenario , and a hot flow scenario . these were extensively studied in the context of x - ray binaries , where the wealth of data enables putting stronger constraints on the geometry of accretion flow than in the case of agn . in the former scenario the standard keplerian accretion disk extends to the last stable orbit and the hard x - rays are produced by an active corona above the disk . this is motivated mainly by the solar corona where magnetic flares are thought to be powered by differential rotation of the sun s interior . the hot flow scenario is based on an alternative solutions of accretion flow , where the flow is optically thin and hot , most likely two - temperature , with proton temperature reaching the virial value . both the observational data and the theoretical arguments suggest that the two solutions operate in different ranges of mass accretion rate . presence of spectral features from x - ray reprocessing by cold optically thick plasma , with strong relativistic distortions obviously implies that the disk has to extend to the last stable orbit . this is the situation in , e.g. , the seyfert 1 galaxy mcg6 - 30 - 15 , which is currently the best example of effects of strong gravity in x - ray spectra . in this contribution we study some of the consequences of the relativistic effects on the variability of x - ray emission . assume that the hard x - rays are produced by magnetic flares co - rotating with the keplerian disk . assume further that durations of the flares are consistent with the flare avalanche model of @xcite , so that there is a broad distribution of the durations ( superposition of flare profiles of different durations explains the slope of the power spectrum ) . then , the natural association of a flare time scale with the keplerian time scale ( so that longer flares are produced further away ) , results in the radial x - ray emissivity increasing with radius , which is clearly inconsistent with the dissipation rate of gravitational energy @xcite . abandoning this association leads to a possibility of long flares occurring at small distances ( @xmath1 ) . the x - rays source can then participate in the keplerian motion , possibly for a number of @xmath2 , which produces a periodic modulation of emission due to doppler boost . the strength of the resulting quasi - periodic signal in the pds depends on the black hole spin , inclination angle and other details of the radial distribution of flares . for parameters appropriate for the seyfert galaxy mcg6 - 30 - 15 , where @xmath3 and @xmath4 , the strength of the predicted signal is high enough for the signal , if present , to be detected in the _ xmm - newton _ data @xcite . however , the data @xcite do _ not _ reveal such a signal . this would suggest that the x - rays can not be produced by co - rotating flares , but rather by a structure not participating in the keplerian rotation , e.g. , the base of a jet . on the other hand , a number of observations show periodic variability of the energy of a narrow fe k@xmath0 line , suggesting line production in localized regions co - rotating with the disk ( t. j. turner , these proceedings ) . if the two properties no qpo signal in the primary emission and a periodic modulation of the fe line turn out to be universal , this will clearly suggest a non - trivial geometry of the x - ray source . the reprocessed component ( fe k@xmath0 line and the compton reflected continuum ) show rather weaker variability than , and uncorrelated with , the variability of the primary emission ( e.g. , * ? ? ? this is observed on a time scale of @xmath5@xmath6 sec , i.e. , _ longer _ by a factor of @xmath7100 than the keplerian timescale at the inner disk ( assuming @xmath8 ) . such a reduction of variability is rather surprising , since in the simplest model the reprocessed component should respond to primary variations on the light travel timescale . the latter is very short , if indeed the reprocessing takes place close to the center , as evidenced by the broad profiles of the fe k@xmath0 line . the light bending model , formulated by ( * ? * hereafter mf ) , postulates that the de - coupling of variations is due to changing amount of relativistic effects , in particular bending of light trajectories from the source to the accretion disk , as the location of the source changes . in its basic form the model assumes that the intrinsic emission is constant , and the observed variability is solely due to changing location of the primary source . the variability of the reprocessed component is reduced because reprocessing takes place in a more extended area . @xcite demonstrate that in the simple geometry of an off - axis source moving vertically , the model predicts reduction of line variability of a factor of @xmath9 , as the source height changes from 1 to @xmath10 . we have extended the mf model to consider a number of geometrical scenarios : in addition to the basic model ( c the same as in mf ) , where the source is located off - axis , at projected radial distance @xmath11 , and moves vertically , we considered an on - axis source ( model a ) moving vertically and a source located very low above the disk surface , moving _ radially _ ( model s ) . photon transfer in the kerr metric was computed with the code described in detail in @xcite . we first computed time averaged profile of the fe k@xmath0 line in order to find the range of parameters where the profile match that observed in mcg6 - 30 - 15 . then , we computed variability of the line vs. that of the primary emission , as the source location changes . details are presented in niedwiecki & ycki ( in preparation ) . our results are somewhat different than those of mf . for @xmath12 and @xmath13 , in model c ( with @xmath14 ) , we find that the observed line profile requires a very low height of the source , @xmath15 . the profile computed for @xmath16 ( as in mf ) has a rather weak red wing , certainly not compatible with what is observed in mcg6 - 30 - 15 ( see fig . [ zyckifig : kaprof]a ) . similar profiles can be obtained in model s , where the source _ radial _ position changes around 23@xmath17 ( fig [ zyckifig : kaprof]b ) . we then addressed the problem of reduced variability of the k@xmath0 line and we computed the luminosity of the primary source vs. that of the fe k@xmath0 line , as the source position is changed . our results are plotted in fig . [ zyckifig : ff ] for a number of models . in model c we find no reduction of variability of the line in contrast to results of mf , especially for source height @xmath18 . this is most likely caused by differences in the assumed value of the outer disk radius : @xmath19 in our case compared to @xmath20 in mf computations . this latter value is too small for the line to be computed correctly when the height of the source is @xmath21 . we find a significant reduction of line variability in model s , for a source moving radially very low above the disk surface . source position changing between @xmath22@xmath23 produces line flux changes by a factor of @xmath9 compared to a factor of @xmath24 for the continuum . this is primarily a result of light bending to the equatorial plane , beyond @xmath25 , where a relatively constant blue horn is then produced ( niedwiecki & ycki , in preparation ) . note , though , that model s would predict the strong signal in pds ( on keplerian timescale ) which is not observed ( sec [ zyckisec : qpo ] ) . miniutti , g. , fabian , a. c. 2004 , mnras , 349 , 1435 poutanen , j. , & fabian , a. c. 1999 , mnras , 306 , l31 vaughan , s. , fabian , a. c. 2004 , mnras , 348 , 1415 vaughan , s. , fabian , a. c. , nandra , k. 2003 , mnras , 339 , 1237 ycki , p. t. , niedwiecki , a. 2005 , mnras , 359 , 308 ycki , p. t. 2002 , mnras , 333 , 800" +"scattering experiments are amongst the most powerful tools to obtain information on the microscopic structure of matter . in solid state physics , conventional elastic scattering of photons , electrons , and neutrons are the standard methods to study the precise spacing and the location of atoms in solids . one obtains this information by measuring the angular distribution of the diffracted particles which depends on the microscopic lattice structure of the studied solid . in conventional x - ray and electron diffraction experiments , the incident particles interact with all the electrons in the sample and , since the majority of the electrons is located close to the nucleus , these experiments yield the averaged position of the atoms . the situation is very similar for neutron diffraction , for which scattering occurs from the nuclei directly . in addition to the sensitivity to the lattice structure , neutron and non - resonant x - rays also interact with the magnetic moments and therefore information on the magnetic structures in solids can be derived . however , in many of the currently most intensively studied systems not only the behaviour of lattice and spins needs to be studied . also the charge and orbital degrees of freedom often play an essential role . in some materials a collective electronic ordering of spins , charges , and orbitals occurs which typically only affects a small fraction of the valence electrons . these phenomena can lead to novel exciting ground states . for instance , complex electronic phenomena involving the cooperative ordering of various electronic degrees of freedom are discussed intensively in relation with such outstanding phenomena like high - temperature superconductivity in cuprates@xcite or the colossal magneto - resistance in manganites@xcite . as we will describe later on , charge and orbital orders are very difficult to observe with the aforementioned traditional scattering techniques . a new experimental probe , which enables to observe complex electronic order was therefore urgently needed . resonant ( elastic ) soft x - ray scattering ( rsxs ) provides exactly this : a highly sensitive probe for spacial modulations of spins , charges , and orbitals in complex materials . this unique sensitivity is achieved by merging diffraction and x - ray absorption spectroscopy ( xas ) into a single experiment , where the scattering part provides the information of spatial modulations and the xas part provides the sensitivity to the electronic structure . more precisely , rsxs close to an absorption edge involves virtual transitions from core levels into unoccupied states close to the fermi level and these virtual transitions depend strongly on the spin , charge and orbital configuration of the resonant scattering centers . the ordering of spins , charges , and orbitals typically results in electronic superlattices with periodicities of several nanometers , which matches very well with the wavelengths of soft x - rays lying between between @xmath0 6 to 0.6 nm corresponding to photon energies between @xmath0 200 ev to 2000 ev . moreover , since the virtual excitations in rsxs are related to specific core level excitations , the excitation energy of which changes from element to element , the method is element specific like xas . thus rsxs , different from magnetic neutron scattering can probe magnetic structures related to specific elements . the price paid for the unique sensitivity offered by rsxs is a very limited ewald sphere and a rather short photon penetration depth limiting studies to only the topmost 100 atomic layers or , depending on the resonance used , even less . but these limitations are very often compensated by the gain in sensitivity , which is extremely important when turning to magnetic and electronic properties of samples characterized by a very small amount of contributing material , i.e. , for studying thin films , nanostructures as well as surfaces and interfaces . as a consequence of the broken translational symmetry at the surface , nanosystems can show ordering phenomena which differ locally or macroscopically from those of the respective bulk systems , and even completely new phenomena can arise . for such systems , rsxs has been established as a very powerful and unique tool to study complex electronic ordering phenomena on a microscopic scale . the need for such studies has strongly increased within the last decade since the fabrication of high quality samples with macroscopic properties tunable by composition , strain , size and dimensionality has become possible , raising the hope for future multifunctional heterostructures characterized by so far unexpected and unexplored novel material properties and functionality . although rsxs offers many important ingredients to study condensed matter , it has only recently developed its full power . the reason for this is that intense soft x - ray sources with tunable energy only became available with the advent of 2nd and 3rd generation synchrotron radiation facilities . furthermore those soft x - rays are absorbed in air and therefore the diffraction stations have to operate in vacuum , which poses another complication and made the development of rsxs challenging . finally , as mentioned above , the penetration depth into the solids is of the order of nanometers which means that surface effects may become important . thus in many surface sensitive systems the surfaces should be prepared under ultra - high vacuum ( uhv ) conditions or at least should be kept under uhv during the measurements . this review covers the recent progress in rsxs and gives a survey of the application of the technique . after the introduction , the principles of rsxs are presented , followed by a description of the experimental development . the main part is then devoted to the application of rsxs in the study of magnetic structures , charge order , and orbital order in thin layers , artificial structures , interfaces , and correlated systems . the review concludes with a summary and an outlook . elastic resonant x - ray scattering combines x - ray spectroscopy and x - ray diffraction in one single experiment . roughly speaking , x - rax diffraction provides the information about the spatial order , while the spectroscopic part provides the sensitivity to the electronic states involved in the ordering . a first qualitative understanding of this strongly enhanced sensitivity to electronic order can be gleaned from the schematic illustration of the resonant scattering process shown in figure[fig : rsxs_scheme ] : the incoming photon virtually excites a core electron into the unoccupied states close to the fermi level , thereby creating the so - called intermediate state @xmath1 of the resonant scattering process . this virtual transition depends very strongly on the properties of the valence shell and , therefore , results in the tremendously enhanced sensitivity of resonant x - ray scattering to electronic ordering . the state @xmath1 then decays back into the ground state @xmath2 and a photon with the same energy as the incoming one is re - emitted . this combination of spectroscopy and diffraction will be described in the following . in this section , aspects of the diffraction of x - rays by a crystal will be summarized . for more detailed and extensive descriptions of this topic the reader is referred to the literature@xcite . + + in the following we will consider a crystal that is formed by a perfectly periodic arrangement of lattice sites , which act as scattering centers for the incident x - ray field . the scattering from site @xmath3 in the crystal is described in terms of a scattering length @xmath4 , which is also called the form factor , and can be represented as@xcite @xmath5 the first two terms @xmath6 and @xmath7 represent the non - resonant charge and magnetic scattering , respectively , where the scattering described by @xmath6 , which is proportional to the total number of electrons of the scatterer , is called thomson scattering . @xmath8 denotes the so - called dispersion correction , which is not only a function of the photon energy @xmath9 , but also of the polarisation of the incoming ( @xmath10 ) and scattered beam ( @xmath11 ) . this correction becomes very important close to absorption edges and describes the resonant scattering processes illustrated in figure[fig : rsxs_scheme ] . and @xmath12 , respectively . the whole crystal can be described by discrete translations of the unit cell with its basis . the relative phase of x - rays scattered by the two sites of the basis is @xmath13 ( right panel).,width=283 ] physically the scattering length @xmath4 describes the change in amplitude and phase suffered by the incident wave during the scattering process : a scatterer with scattering length @xmath4 exposed to an incident plane wave @xmath14 causes a scattered radial wave @xmath15 , which , far away from the scattering center , can be approximated by a plane wave . in order to calculate the intensity of the total scattered wave field with wave vector @xmath16 , all the radial waves have to be summed with the correct relative phases . as illustrated in figure[fig : scatter_scheme ] , the geometric relative phase of two scatterers is given by @xmath17 , where @xmath18 is the scattering vector and @xmath19 is the difference in position . the total intensity detected in a distant detector is therefore @xmath20 where @xmath21 is the vector pointing to the origin of unit cell @xmath22 and @xmath23 is the position of the scatterer @xmath4 measured from that origin . @xmath24 is called the unit cell structure factor and describes the interference of the waves scattered from the different sites within a unit cell . the lattice sum @xmath25 is due to the interference of the scattering from the different unit cells at @xmath21 . its @xmath26-dependence therefore provides information about the number of sites scattering coherently , i.e. , it is related to the correlation length of the studied order . for an infinite number of coherently scattering unit cells , @xmath27 , where @xmath28 represents the reciprocal lattice . this corresponds to the well - known laue condition , which states that a reflection can only be observed if @xmath29 is a reciprocal lattice vector . the treatment described above is known as the kinematic approximation . this approximation is valid as long as the intensity of the scattered wave is much weaker than that of the incidence wave , which means that the interaction between the incoming and outgoing waves or multiple scattering events can be neglected . since in resonant x - ray diffraction experiments one usually deals with weak superlattice reflections , this approximation is valid in most cases . if , however , the scattered wave becomes too strong , then one has to resort to the so - called dynamical theory of diffraction . this description will not be presented here and the interested reader is referred to the literature@xcite . and @xmath16 , is vertical in this example . incoming and outgoing polarisations are denoted as @xmath30 and @xmath31 , respectively , where @xmath32 indicates a polarisation perpendicular to the scattering plane and @xmath33 refers to a polarisation parallel to the scattering plane . the polarisation of the scattered radiation can be determined using the polarisation analyzer . @xmath34 define the reference frame in which the polarisations , wave vectors and spin - directions will be expressed.,width=283 ] + + a typical geometry of a resonant scattering experiment is shown in figure[fig : exp_scheme ] . an incoming photon beam with defined wave vector @xmath35 impinges on the sample and is scattered elastically into the direction defined by @xmath16 , corresponding to a scattering vector @xmath18 . in the so - called specular geometry the incoming and the outgoing beam are at an angle @xmath36 with the sample surface . in this case , the scattering angle between @xmath35 and @xmath35 is" +"the theory about the structure of space and time has been discussed from very long time not only among philosophers but also among physicists . it is very well known the correspondence between newton s disciple s. clark and leibniz about the absolute or relational character of space and time @xcite . the laws of mechanics and electromagnetism were written with the hypothesis of an absolute space and time but relational theories were unable to construct a consistent model of physical world and were abandoned . with the invention of the special theory of relativity the old arguments of relational theories were renewed but only in the phenomenological level . einstein himself recognized the atractive ideas of leibniz as a pioneering work in the theory of relativity @xcite . in this century the controversy among the physicists who defend the absolute or relational theory of space and time has increased in great amount from different reasons @xcite . the experimental and theoretical development of general relativity and cosmological models have forced to review the concepts of space and time . the revision of the foundations of quantum mechanics has moved some physicists to reduce the structure of space and time to some properties of quantum processes @xcite . finally , the study of fundamental axioms of geometry ( in the mathematical as well in the physical sense ) has introduced new light into the discussion about the primitive or derived character of space and time . we do nt want to go again in the arguments given by the two positions . instead we will expand some recent relational theories of space and time to prove that the basic assumption common to all of them is that there exists some fundamental objects out of them the structure of space and time is constructed . we will identify those objects as events , processes , yes - no experiments , monads ( following leibniz s ideas ) and so on . therefore the conceps of space and time are for these authors derived concepts in the logical as well in the ontological level . his model starts with objects and the interrelations between objects . an object is thus `` located '' either directionally or positionally in terms of its relations with other objects . `` one does not really need a space to begin with . the notion of space comes out as a convenience at the end '' . the physical objects consist of some units with definite spin acting among themselves giving rise to a n - unit with a total spin representing a direction . the interaction of two n - units es interpreted as the angle between the two directions . they consider the notion of space - time continuum as an illusion of low energy dynamics . quantum systems are defined without the notion of space . the @xmath0 variables have to be replaced by the labels for quantum degrees of freedom . bose and fermi fields satisfy the canonical commutation relation , where the quantum degree of freedom play the role of site variable . @xmath1 = -i\delta_{\ell m},\left\{\psi_{\alpha } ^+ \left(\ell\right),\psi_\beta \left(m\right)\right\}=\delta_{\alpha \rho}\delta_{\ell m}\ ] ] the hamiltonian incorporates link fields @xmath2 and @xmath3 to boson and fermion fields , satisfying @xmath4=-i\delta _ { \ell \ell ' } \delta_{mm'}\delta _ { \alpha \alpha ' } \delta_{\beta \beta ' } \ ] ] the hamiltonian is constructed out of such fields . @xmath5\ ] ] all the fields are labelled by integer indexes , that is , they are connected among themselves as a finite network , with the structure of 1-simplex , ( where each field is acting with all the other fields ) and the different 1-simplices are interacting with other 1-simplices giving rise to n - simplex of more complicated structure . this is called a generalized slac lattice , which underlies the continuum space - time . @xcite . this author , after classifying the relational theories of space and time , proposes a set - theoretical model of space and time in which the primitive concepts are preparticles as the most basic components of a physical system . using the membership relation of set theory he construct the elementary particles as subsets of the power set of preparticles . inclusion relations among preparticles and interaction among them gives rise to the temporal and spatial structure of the world out of which reference frames and motions are described . @xcite proposes a relational theory of physical space . the world is constituded by things such as elementary particles and fields and physical systems are composed out of these things . the concept of space is a derived one , therefore these things are not located in the space . these things are acting among themselves , the result of these interactions are called processes or events . space is nothing more that the collections of these individual things and their relations . @xcite starts from the set of concrete physical events @xmath6 , or , the set of space - time points that are actually occupied by material objects or processes . there is a relationalist s ontology by which the ( 3 + 1)-dimensional continuum is nothing more than a construction out of the set @xmath6 of physical events . @xcite offers a relational theory of minkowski space - time . suppose that there are a finite number of point particles and the mutual spatial relations among the particles obey the axioms of euclidean geometry . any talk about space is to be analyzed according to the representations of the interparticle relations . of course these theories must recover the field - theoretical models out of the individual events that are finite in number . a real challenge for the relational theories . @xcite has introduced the concept of pregeometry to understand the laws of euclidean and non - euclidean geometry . the objects in the pregeometry are logical in character . space and time are not physical entities but conceptions created by man , to keep track of the order of things . time and space must be derived in the classical limit from the universe of our discrete elements ( or bits ) of information . @xcite have develope wheeler s ideas in some model of curved space time using spin - network , the elementary structure of which are the @xmath7-simbols for 3 particles of spin 1/2 acting among themselves . the structure of a curve 2-dimensional surface is described by the closed interaction of half - integral spin particles whose diagramatic representation is given by a closed finely triangulated 2-surface with @xmath8 triangles and @xmath9 edges . the fineness of the diagram , determined by @xmath10 , can be used to derive a correspondence law between the basic pregeometry and the continuous limit of physical geometry . the ponzano - regge model has been developped by modern authors in the study of quantum gravity . in the last section we have reviewed some modern theories in which the concepts of space and time are derived from the relations among fundamental objects ( building blocks ) . the underlying structure should be compared with the properties of the physical space and time . we want to develope now some pregeometry in which the axioms are given by mutual relations of these building blocks . given some reticular network of fundamental objects we can postulate from purely logical properties ( in the sense of wheeler s pregeometry ) a n - dimensional cubic lattice . the difference between hilbert s axiomatic formulation and our approach is the following : hilbert @xcite presuposes the concepts of points , lines and surfaces , and the axioms are constructed with these objects . in our approach the points , lines and surfaces are derived from the relational character of the lattice , but the logical consecuences of the lattice are equivalent to the set of axioms in hilbert s formulation . a _ principal straight line _ is a indefinite set of points in the lattice , such that each of them is contiguous to other two , and the minimal path between two arbitrary points of this line is always unique . from these two theorems we can define cartesian ( discrete ) coordinates and an euclidean space . this structure of 2-dimensional space can be easily generalized to 3-dimensional cubic lattice . with the help of cartesian coordinates we can define a ( non principal ) straight line passing through two arbitrary points . 1 . there is a unique straight line through any two different points . any straight line contains at least two points . there are three non - colinear points . 2 . given three points a , b , c of a straight line if b is between a and c , a , b , c are three distinct points , and b is between c and a. given two points a and c , there exists one point b over the straight line ac such that c is between a and b. given three points on a straight line there is only one between the other two . 3 . given two points a , b of a straight line , and a point @xmath13 of the same or different line there exists a point @xmath14 in the same line as @xmath13 such that the segment @xmath13@xmath14 is congruent with ab . if two segments are congruent with a third one , they are congruent one to another . 4 . given a straight line and a point exterior to it , there exists one and only one straight line that incides in the point and does not cross the first one . for more complicated lattice we can follow the `` skeleton '' geometry of wheeler used to describe the topological properties of curved space - time , that where developped by regge and recently by many other authors . @xcite `` angular momentum : an approach to combinatorial space - time '' in _ quantum theory and beyond _ ( t. bastin ed . ) cambridge 1971 ; `` newton , quantum theory and reality '' in _ three hundred years of gravitation _ ( s.w . hawking and w. israel ed . ) cambridge 1987 ." +"since the mid-1990s we built visual interactive maps of bibliographic and database information at strasbourg astronomical observatory , and some of these , with references , are available at murtagh [ 2006d ] . the automated annotation of such maps is not easy . at the time of writing zdnet and the bbc ( british broadcasting corporation ) use interactive annotated maps to support information navigation . in zdnet s case , some prominent terms are graphically presented and can be used to carry out a local search ; and in the bbc case , terms relating to downloadable radio programs are displayed in moving sizes and locations . in the work described in this article , we adopt a different approach : we select the terms of interest in a manual or semi - automated way . this not only represents expert user judgement but also allows for inclusion of rare or very frequent terms . in one of our three case studies , we use an automated way to select such terms . for selected terms , we use their inter - relationships to build a hierarchy and use this as a central device for summarizing information and supporting navigation . `` ontologies are often equated with taxonomic hierarchies of classes ... but ontologies need not be limited to such a form '' [ gruber 2001 ] . gruber is cited in gmez - prez et al . [ 2004 ] as characterizing an ontology as `` an explicit specification of a conceptualization '' . in wache et al . [ 2001 ] , ontologies are motivated by semantic heterogeneity of distributed data stores . this is also termed data heterogeneity and is counterposed to structural or schematic heterogeneity . ontologies are motivated by wache et al . [ 2001 ] `` for the explication of implicit and hidden knowledge '' , as `` a possible approach to overcome the problem of semantic heterogeneity '' . so , ontologies may help with integration of diverse , but related , data ; or they may help with clarifying or disambiguating distinctions in the heterogeneous data . ontologies are likely to be of immediate help in supporting querying . for example , the query model may be based on the ontology ( or ontologies ) used . there is extensive activity on standards and software , relating more to the above - mentioned schematic rather than semantic heterogeneity , and a useful survey of this area is denny [ 2004 ] . denny takes an ontology in a broad - ranging view as a knowledge - representation scheme . a short review of some recent approaches in this area follows . ahmad and gillam [ 2005 ] develop a semi - automated approach using text with no markup . multiword expressions are determined , and frequency of occurrence information is used to point to term or phrase importance . a stop list is used to avoid irrelevant words . part of speech analysis is not used . a semantic net is formed to allow development of the ontology elements . abou assali and zanghi [ 2006 ] use syntactic part of speech tagging to determine the nouns . these authors retain sufficiently frequent nouns . they apply the notion of weak subsumption : if for the most part a word is in a text that another is in , and not vice versa , then this leads to a hierarchical relationship . chuang and chien [ 2005 ] assert that multiway trees are appropriate for concept hierarchies , whereas binary trees are built using hierarchical clustering algorithms . hence they modify the latter to provide more appropriate output . ( a formal approach for mapping a binary hierarchical classification tree onto a multiway hierarchy is described in murtagh [ 2006b ] . ) a hierarchical clustering has often been used to represent an ontology . note that this is usually not a concept hierarchy . a concept hierarchy is based on a subsumption relationship between terms , whereas a hierarchical clustering is an embedded set of clusters of the term set . later in this article ( section [ secorientree ] ) , we show a way to derive a concept hierarchy , involving subsumption of terms , from a hierarchic clustering . a hierarchic clustering is typically a binary , rooted , terminal labeled , ranked tree , and a concept hierarchy is typically a multiway , rooted , terminal and non - terminal labeled , ranked tree . by starting with the former ( binary ) tree representation , we have an extensive theoretical and formal arsenal at our disposal , to represent the main lines of what we need to do , and to help to avoid ad hoc , user parameter - based , `` engineering '' approaches . as seen later in this work , we start by laying the foundations of our perspective by basing this on binary trees , and later proceed to the multiway tree . an alternative approach can be found in ganesan et al . [ 2003 ] , where similarities or distances on trees are redefined and re - axiomatized for the case of multiway trees . an alternative representation for an ontology is a lattice , and formal concept analysis ( fca ) is a methodology for the analysis of such lattices . if we have a set of documents or texts , @xmath0 , characterized by an index term set @xmath1 , then as janowitz [ 2005 ] shows , hierarchical clustering and fca are loosely related . hierarchical clustering is based on pairwise distances or dissimilarities , @xmath2 ( @xmath3 is the set of non - negative reals ) . fca is based on partially ordered sets ( posets ) such that there is a dissimilarity @xmath4 ( @xmath5 is the power set of the index terms , @xmath1 ) . other approaches ( rule - based ; machine learning approaches , etc . ; layered , engineering , approaches with maintenance management see maedche [ 2006 ] ) are also available . one difficulty with such `` engineering '' approaches is that there is an ad hoc understanding of the problem area , and often there is dependence on somewhat arbitrary threshold and selection criteria that do not generalize well . our approach formalizes the problem area the information space in terms of its local or global topology . where we do have selection criteria , such user interaction is at the application goal level . visualization is often an important way to elucidate semantic heterogeneity for the user . visual user interfaces for ontological elucidation are discussed in murtagh et al . [ 2003 ] , with examples that include interactive , responsive information maps based on the kohonen self - organizing feature map ; and semantic network graphs . a study is presented in murtagh et al . [ 2003 ] of client - side visualization of concept hierarchies relating to an economics information space . the use of `` semantic road maps '' to support information retrieval goes back to doyle [ 1961 ] . motivation , following murtagh et al . [ 2003 ] , includes the following : ( i ) visualization of the semantic structure and content of the data store allows the user to have some idea before submitting a query as to what type of outcome is possible . hence visualization is used to summarize the contents of the database or data collection ( i.e. , information space ) . ( ii ) the user s information requirements are often fuzzily and ambiguously defined at the outset of the information search . hence visualization is used to help the user in his / her information navigation , by signaling the relationships between concepts . ( iii ) ontology visualization therefore helps the user before the user interacts with the information space , and during this interaction . it is a natural enough progression that the visualization becomes the user interface . this article is organised as follows . to begin with , in section [ sect2 ] , we table the issue of whether or not there is inherent hierarchical structure in a text , or a collection of texts . in section [ sect3 ] we show how we can rigorously determine the extent of inherent hierarchical structure in a text . this quantifying of inherent hierarchical structure is then used in subsections [ sect41 ] , [ sect42 ] , [ sect52 ] and [ sect7 ] . a text provides both global and linear semantics , and how we can process these two different perspectives on a given text is discussed in section [ sect4 ] . a central aspect of our approach is a new distance or metric , which we have recently introduced and exemplified on another data analysis problem . this new distance is described in subsection [ sect5 ] . in section [ sect6 ] we apply what we have described in earlier sections to the selection of salient and characteristic pairs and triplets of terms , and also the selection of pertinent terms . our motivation is not just the traditional view of phrase counting ( even though we incorporate this view ) but rather the characterization of text content using its internal ( local hierarchical ) structure . a natural approach to defining a concept hierarchy lies in use of a hierarchical clustering algorithm . however , the latter forms an embedded sequence of clusters , so that a hierarchy of concepts must somehow be derived from it . in section [ secorientree ] we first of all show that `` converting '' any hierarchical clustering into a hierarchy of concepts is relatively straightforward . however we do have to face the problem of a unique , and beyond that best , solution . we show how we can admirably address this need for a unique solution . our innovative approach is based on the foundations laid in sections [ sect2 ] and [ sect4 ] of this article . we analyze three different data sets in this work : firstly a set of documents , with some degree of heterogeneity , to illustrate our key goal ; secondly a homogeneous text , partitioned into successive textual segments ; and thirdly a small homogeneous text , partitioned at the sentence level , proxied by lines of text . we select terms , indeed nouns , in a partially automated way , since this crucial aspect of ontology design may benefit from being user - driven , and may have scalability advantages . in later sections we address the issue of finding and presenting structure in text . we link such structure with the textual content . consequently a key , initial question is to know whether or not there is structure present , and to what extent . a first problem to be addressed is whether or not the document has any hierarchical structure to begin with . as input , we have possibly a fully tagged document ( based , e.g. , on part - of - speech tagging , schmid [ 1994 ] ) . however in this work , we start with free text , because it is the most generally available and applicable framework . additional information provided by part - of - speech tagging can be of use to us , as we will show later . next we consider the issue of whether or not a document has sufficient inherent hierarchical structure to warrant further investigation . we could approach this problem by fitting a hierarchy , and there are many algorithms for doing so ( such as any hierarchical clustering algorithm ; de soete [ 1986 ] describes a least squares optimal fitting approach ) . however departure from inherent hierarchical" +"one - dimensional electronic systems are characterized by the increased role of interactions and the formation of gapless collective modes , that breaks down the fermi liquid theory . instead , a state of matter is formed that is described as the luttinger liquid @xcite . it has become experimentally accessible in the quantum hall ( qh ) effect systems , where the edge states act as one - dimensional ( 1d ) chiral conductors . some of the recent exciting experiments worth mentioning would include : electronic mach - zehnder ( mz ) interferometry , in which the observed behavior of the interference oscillations has demonstrated the inapplicability of the single - electron description @xcite ; energy relaxation along the qh edge channels with some unexplained losses in the energy transfer @xcite ; a demonstration of coherence and indistinguishability of independently emitted electrons @xcite ; and coulomb interaction of a localized state , quantum dot ( qd ) , with qh edge states @xcite , which presents a situation that potentially contains very interesting physics in the strong coupling regime . however , the latter experimental work @xcite has considered the system only in thermal equilibrium , where , due to the detailed balance , the whole range of implications of strong coupling has remained obscured . . the quantum dot with the single relevant level at @xmath0 close to the fermi energy is coulomb interacting ( waved lines ) with the surrounding channels @xmath1 , with coupling strengths @xmath2 , and has a weak tunnel coupling with amplitudes @xmath3 with the inner channels ( dotted lines ) . voltage bias @xmath4 is applied to one of the outer channels , which creates nonequilibrium excitations after the left partitioning quantum point contact ( labeled @xmath5 ) with transparency @xmath6 . the visibility of the interference pattern with respect to the aharonov - bohm phase @xmath7 is observed after the right qpc . , scaledwidth=35.0% ] in this work we extend the discussion to the case far from equilibrium , where the tunneling transitions recharging the qd are stimulated by the nonequilibrium processes in the edge channels . the cooperation of the two factors , the nonequilibrium excitations in the channels and the backaction of the quantum fluctuations of the fermi sea due to perturbation by an event of tunneling , is manifested in the strong coupling regime by the orthogonality catastrophe , leading to the fermi edge singularity ( fes ) @xcite in the transition rates , and by their asymmetry with respect to the sign of the dissipative component of current . this is because the strong coupling negates the limitations of the _ central limit theorem _ , therefore giving access to the non - gaussian fluctuations of the charge current that break the charge symmetry , while commonly they are small @xcite and difficult to observe @xcite . an equivalent system at zero temperature has been considered in the previous initiative by rosenow and gefen @xcite . however , we must clearly indicate that in the specific regime defined above , our results are in sharp contradiction . particularly , we believe that thoroughly accounting for the effects of strong coupling might have been an issue in their case , while they assumed that the coupling is finite ( not weak ) and is even maximum possible in the most interesting case . in this respect , our results can also be contrasted with the results of some earlier works , in which the transition rates between a lead and a quantum dot interacting with noisy 1d conductors were studied , e.g. , refs . @xcite . in levinson s work @xcite the interaction between the qd and a qpc ( analogous to the 1d edge channels in our case ) was assumed to be weak . this assumption narrows the effects to the gaussian noise , and allowed a perturbative expansion in the interaction strength to the lowest order . in turn , @xcite , although using strong coupling , has adopted an assumption about the structure of the scattering matrix , that the mixing of the states arriving from different reservoirs is weak . this led to a substantially reduced effect of nonequilibrium noise , which only appeared as a small correction to the power - law exponent in the transition rates . the differences between the assumptions and the findings of these works and ours essentially highlight the exceptionality of the situation where strong coupling is combined with the non - gaussian noise . it should be also noted that a number of exact solutions of the fes problem exist in various systems @xcite , but they all require the use of highly complex methods that may obscure the physics , such as in ref . @xcite in which the distinctive nonequilibrium phenomenon of charge symmetry breaking in the strong coupling limit has been overlooked . in 1d systems , however , the complexity can be largely overcome by employing the recently developed nonequilibrium bosonization technique @xcite . this approach naturally accounts for the interactions and allows us to reduce the problem of finding electron correlation functions to the calculation of the full counting statistics ( fcs ) of a 1d current @xcite , which can then be calculated analytically for asymptotically low transmission or reflection , or numerically in a general case . the experimental setup is constructed by embedding the 1d channel as an arm of an electronic mz interferometer at @xmath8 @xcite , as shown schematically in fig . [ fig : setup ] . then the electron correlation function in the channel can be investigated by measuring the phase shift @xmath9 of the aharonov - bohm ( ab ) oscillations of the current @xmath10 and the visibility @xmath11 . the quantum dot charge fluctuates due to tunneling to some of the additional channels nearby . voltage bias @xmath4 applied before the partitioning quantum point contact ( qpc ) with transparency @xmath6 creates nonequilibrium excitations in the arms of the interferometer . the operating regime of the setup is determined by the interplay of the principal energy scales : the temperature @xmath12 of the environment , the quantum level broadening widths @xmath13 due to the tunnel coupling , and the classical level broadening @xmath14 due to the nonequilibrium noise - induced transitions , where @xmath15 is the fermi density of states and @xmath3 are the tunneling amplitudes . in the essentially quantum case , when @xmath13 is the dominant energy scale , the interferometer is found close to its ground state , where the interference pattern does not sustain any loss of visibility . assuming the low - energy limit , where the relevant energies : @xmath16 , the voltage bias @xmath4 , and the detuning @xmath0 of the quantum dot level from the fermi energy are much smaller than the inverse time of flight through the interferometer , the internal dephasing in the channels can be neglected , and therefore the loss of coherence is solely due to the interaction with the localized state . when the latter is occupied , the interference pattern acquires an additional shift compared to the empty state . this shift corresponds to the phase of scattering @xmath17 on the localized charge . due to the transitions , this pattern is averaged with the occupation probabilities @xmath18 , @xmath19 of the quantum dot , which gives the visibility @xmath20 and the phase shift @xmath9 as @xmath21 \label{visibility def } , } \ ] ] where the constant prefactor @xmath22 is arbitrary , and without loss of generality we will further refer to the normalized value of the visibility @xmath20 in the sense of assuming @xmath23 . the experiment by weisz _ at al . _ @xcite has been realized in thermal equilibrium with @xmath16 being the largest energy scale . in that case the transition rates at the impurity satisfy the detailed balance equation , and therefore the dot occupation probability @xmath24 is boltzmannian . this yields the result for the visibility @xmath25 @xcite . in the limit of strong coulomb interaction and symmetric coupling @xmath26 ( see fig . [ fig : setup ] ) , complete loss of visibility is observed , respectively , accompanied by the @xmath27-valued jump of the phase shift of the ab oscillations when the energy level of the dot crosses the fermi level . throughout the rest of this paper we assume the low - temperature limit @xmath28 , where the charge fluctuations at the impurity are activated by the partitioning noise of the @xmath29 . the low - energy physics of a qh system shown in fig . [ fig : setup ] can be conveniently described by the bosonized hamiltonian ( see , _ e.g. _ , refs . @xcite ) @xmath30 where the coulomb interaction potential @xmath31 of the charge densities @xmath32 at different points of channels @xmath33 and @xmath34 governs the propagation of the excitations along the edge channels ; the bosonic fields @xmath35 satisfy the commutation relations @xmath36 = 2i\pi \delta_{a b}\delta(x - y)$ ] , and indexes @xmath37 enumerating the fields take values @xmath38 on the corresponding channel to the left of , to the right of , up from , or down from the quantum dot . the bare level energy of the quantum dot @xmath39 is determined by the applied gate voltage , which is the key controllable parameter of the system . the quantum dot charge @xmath40 interacts with the charge densities on the channels via the coulomb potentials @xmath41 . the amplitudes of tunneling from channel @xmath42 are denoted by @xmath43 , and @xmath44 are the annihilation operators of an electron at @xmath45 , chosen at the location of the quantum dot . when the quantum level broadening is smaller than the classical broadening @xmath46 , tunneling between the channels and the dot can be taken into account perturbatively . the remaining part of the hamiltonian can be diagonalized by eliminating the coulomb interaction term with the help of a standard unitary transformation @xmath47 , where @xmath48 the functions @xmath49 are chosen with the aim to cancel the interaction part @xmath50 of the hamiltonian by the term produced after the transformation of the first line in eq . ( [ hamiltonian ] ) . this requirement is expressed by the integral equation @xmath51 on the other hand , the coulomb potential along channel @xmath33 , created by the impurity charge and the arbitrary charge density distribution @xmath52 on channel @xmath34 , is @xmath53 from which it follows that the solution @xmath54 of eq . ( [ integral equation ] ) is nothing but the charge density @xmath55 , accumulated on the grounded channels @xmath56 , screening the charge present on the quantum dot , i.e. , when @xmath57 . these densities are , naturally , localized in the interaction region around the quantum dot at @xmath45 . the total charges @xmath58 can be expressed in terms of the zero - frequency fourier components of the potentials @xmath41 . in absence of other metallic objects in proximity of the dot , the electroneutrality principle implies that @xmath59 . this relation repeats the statement of the friedel sum rule @xcite via the direct connection between the additional phase @xmath60 acquired by an electron passing by the dot and the charges @xmath61 . as a result of the transformation , the tunneling part of the hamiltonian is rendered in the form @xmath62 where the fields @xmath63 have been approximated by their value @xmath64 at @xmath45 since in the low - energy limit the fields change on distances longer than the size of the interferometer and thus are almost constant in the region of interaction . the transformation also shifts the parameter @xmath39 , which determines the time evolution of the annihilation operator @xmath65 by the static self - interaction energy of the accumulated charge density @xmath66 . the physical quantities" +"the properties of hadrons and their masses at finite density and temperature are extremely important to study the phase transition from the hadronic phase to the quark gluon plasma . generally speaking , the nonperturbative calculations at finite temperature and/or density support the idea that hadronic masses change as a function of temperature and density . the nucleon mass is found to depend substantially on temperature variations of the quark condensate and interaction process . as the condensate disappears smoothly with chiral - symmetry restoration so does the nucleon mass@xcite . recently , baryons have been studied in the context of bethe - salpeter equation ( bse ) . the baryon is considered as a bound state of the confined constituent diquark and quark interacting via an exchange quark . despite the simplicity of the model , it has been used to study the intermediate energy physics successfully @xcite . furthermore , it has been some attempts to extend bse to study mesons at finite temperature@xcite . however , the dressed quark propagator and the variation of the constituent quark mass with temperature are essential to study the bound states in a hot bath . the schwinger - dyson equation ( dse ) is used to study the quark propagator at finite temperature@xcite . the dse with qcd potential can be solved numerically at finite temperature @xcite . furthermore , the constituent quark mass and its variation with temperature is studied using the lattice - qcd - based schwinger - dyson equation . spontaneously broken chiral symmetry is found to be restored at the critical temperature@xcite . the linear confinement dissociates smoothly with temperature@xcite . from dse , it is expected that the dressed quark mass to decrease with temperature in the same order of the linear confinement dissociation . the condensate is found also to disappear smoothly at the same order . in sec . ii , we shall derive the bse for a quark - diquark bound state at finite temperature . the modification of the interaction with temperature is approximated using a mixed representation of the imaginary time formalism and then we adopt the adiabatic ( instantaneous ) approximation . in this approximation , we set the time component to zero after evaluating the matsubara sums not before . the constituent scalar - diquark and quark substructures are effectively taken into account and their masses are taken momentum and temperature dependent based on the lattice - qcd . in sec . iii , we briefly review the mit bag model for nucleon and then we extend it to finite temperature case by taking on the considerations the dissociation of the nucleon bag pressure with temperature . finally in sec . v , we present our results and conclusions . the baryon is considered as a bound state of confined constituent diquark and quark interacting via quark exchange . the bse for the diquark and quark bound states is given by @xmath4\chi_p(p'),\end{aligned}\ ] ] where @xmath5 we have taken @xmath6 where @xmath7 is the quark - diquark vertex coupling @xmath8 and @xmath9 is the exchange quark propagator and @xmath10 . the scalar diquark propagator reads @xmath11 } \nonumber \\ & = & \left(\frac{1}{z_d}\right ) \frac{i}{2\epsilon_1}\left [ \frac{1}{p_0+m_1-\epsilon_1+i\delta } - \frac{1}{p_0+m_1+\epsilon_1-i\delta } \right],\end{aligned}\ ] ] and the fermion quark propagator reads @xmath12\beta,\end{aligned}\ ] ] where @xmath13 and @xmath14 refers to the scalar diquark while @xmath15 refers to the quark and @xmath16 and @xmath17 . we have chosen the proper choice @xmath18 . in the center of mass frame we have @xmath19 . the fermion positive and negative energy projections read @xmath20 where @xmath21 . it is possible to take @xmath22 and @xmath23 with a good approximation . in principle , these functions can be considered in the calculations by adopting smearing functions in the propagators@xcite . in the present calculations , we shall assume these functions are absorbed by the quark - diquark vertex coupling @xmath24 . the constituent diquark and quark masses are given by @xmath25 and @xmath26 for the diquark and quark , respectively . in the adiabatic approximation , the temperature response is separated from the momentum dependent and the constituent diquark and quark masses reduce to @xmath27 and @xmath28 . the dynamical chiral - symmetry breaking ( dcsb ) is one of the most nonperturbative qcd feature . based on the lattice qcd at the quenched level and landau gauge and the lattice data in the chiral limit , the quark mass function at zero temperature is reproduced by @xmath29 } , \label{qconstit}\end{aligned}\ ] ] where @xmath30 870 mev , @xmath31 , the current mass @xmath32 mev and @xmath33 is the momentum in euclidean space . using the lattice - qcd - based gap equation ( dse ) at finite temperature , it is found that @xmath34 has a chiral symmetry restoration phase transition at the critical temperature @xmath35 . the quark and diquark acquire their constituent masses from the linear confinement . these masses can be computed using dse to calculate the self - energy correction . however the linear confinement constant @xmath36 in the configuration space is found to dissociate thermally spontaneously to @xmath37 . the linear confining is a nonperturbative effect and it is believed to generate the major contribution to the self - energy correction for the current quark mass to acquire its constituent value . it is reasonable to take the self - energy correction and mass variation with respect to the temperature at the same order of the spontaneous linear confinement dissociation @xmath38 where @xmath39 for @xmath40 and @xmath41 for @xmath42@xcite . since the constituent diquark is assumed as a weekly quark - quark bound state , it is reasonable to assume @xmath43 . furthermore , we assume the diquark substructure takes the same quark formula substructure given in eq.([qconstit ] ) . in the adiabatic approximation , euclidean momentum @xmath33 in the quark substructure is reduced to three dimensional momentum where @xmath44 . however , in the imaginary time formalism , we can write @xmath45 where @xmath46 and we can take @xmath47 to the first order approximation . to be consistent with the adiabatic approximation considered in our calculations , we have adopted @xmath44 in our calculations . furthermore , we have shown that the first order approximation effect is small . in an adiabatic approximation , the bound state equation at finite temperature is derived as follows @xmath48 \int \frac{d^3 p'}{(2\pi)^3 } \left[-k(q_0,{\bf q};t)|_{q_0=0}\int \frac{d p'_0}{(2\pi)}\chi_p(p')\right].\end{aligned}\ ] ] at zero temperature , the adiabatic approximation is reduced to the instantaneous approximation . however , as we shall show below , a special attention must be paid for the interaction potential in the adiabatic approximation . the kernel interaction is taken as an exchange quark between the diquark and quark , @xmath49 where @xmath10 . the bse propagator is reduced to @xmath50 where @xmath51\left[1+n_b\left(\epsilon_{-1}\right ) -n_f\left(\epsilon_{-2}\right)\right ] \nonumber \\ & + & \frac{1}{2\epsilon_1}\left [ \frac{1}{m+(\epsilon_1-\epsilon_2 ) } \right ] \left[n_b\left(\epsilon_{+1}\right ) + n_f\left(\epsilon_{-2}\right)\right ] \nonumber \\\end{aligned}\ ] ] and @xmath52 \left[1+n_b\left(\epsilon_{+1}\right ) -n_f\left(\epsilon_{+2}\right)\right ] \nonumber \\ & + & \frac{1}{2\epsilon_1}\left [ \frac{1}{m-(\epsilon_1-\epsilon_2)}\right ] \left[n_b\left(\epsilon_{-1}\right ) + n_f\left(\epsilon_{+2}\right)\right],\end{aligned}\ ] ] where @xmath53 . the thermal distribution functions for quark and scalar diquark @xmath54 and @xmath55 are the fermi - einstein and bose - einstein distribution functions , respectively , and @xmath56 . at zero temperature , the bse propagator given by eq.([bs_propg1 ] ) is reduced to @xmath57.\end{aligned}\ ] ] it is a wonderful to write the thermal distribution function of bse propagator in a proper way to discuss thermal reaction processes . the thermal distribution function for the positive energy solution is written as follows @xmath58= \left[1+n_b(\epsilon_{-1})\right]\left[1-n_f(\epsilon_{-2})\right ] + n_b(\epsilon_{-1})n_f(\epsilon_{-2}).\end{aligned}\ ] ] it corresponds to the difference between the virtual decay and creation rates via the virtual reaction processes @xmath59 and @xmath60 , respectively . it is interested to note that the constituent diquark and quark chemical potentials @xmath61 and @xmath62 , respectively , are always less than their relativistic energies and @xmath63 and @xmath64 to preserve the confinement condition . this guarantees the creation rate is always larger than the decay rate . furthermore , the additional ` landau damping ' term @xmath65 = n_b(\epsilon_{+1})\left[1-n_f(\epsilon_{-2})\right ] + \left[1+n_b(\epsilon_{+1})\right]n_f(\epsilon_{-2}),\end{aligned}\ ] ] corresponds the virtual decay and creation processes via the reaction scattering @xmath66 and @xmath67 , respectively . this corresponds particles disappear or are created through the scattering in the bath , and not via the process which are available at zero temperature . the thermal distribution function for the negative energy solution corresponds to @xmath68 and @xmath69 for the decay and creation processes , respectively . on the other hand , the ` landau damping ' term in the negative energy solution reduces to the creation and decay processes @xmath70 and @xmath71 , respectively . the exchange quark propagator is decomposed as follows @xmath72.\end{aligned}\ ] ] hence the kernel interaction reads @xmath73.\end{aligned}\ ] ] when we substitute @xmath74 , we get @xmath75.\end{aligned}\ ] ] however , this choice is not adequate in the adiabatic approximation . in the adiabatic assumption , we shall consider the instantaneous approximation after evaluating the matsubara frequencies sum in the mixed representation for the imaginary time formalism . the fourier transformation of the kernel interaction to the mixed representation reduces to @xmath76 \beta\lambda_{+}(-{\bf q } ) + e^{\epsilon_q\tau } \left[n_f\left(\epsilon_q\right)\right ] \beta\lambda_{-}(-{\bf q } ) \right ] . \nonumber \\\end{aligned}\ ] ] the inverse transformation of the mixed representation with an adiabatic approximation reads @xmath77 \beta\left[\lambda_{+}(-{\bf q})+\lambda_{-}(-{\bf q})\right ] , \nonumber\\ & = & -g^2_{dq}\frac{1}{\epsilon_q}\left[1 - 2n_f\left(\epsilon_q\right)\right]\beta,\end{aligned}\ ] ] where @xmath78 . it is worth to note here that in the adiabatic approximation we have substituted @xmath74 in the mixed representation after evaluating the matsubara frequencies sum . we have introduced in bse the following interaction potential @xmath79 where @xmath80 $ ] . the bse reduces to @xmath81 the bse wavefunction decomposes as dirac wavefunction for positive parity @xmath82 the bse wavefunction reads @xmath83 where @xmath84 is the spinor and the quantum numbers are suppressed . the decompositions of the bse wave function with respect to the positive and negative energy components read @xmath85\eta({\bf p'})- i\hat{\bf p}\times\hat{\bf p'}\cdot\vec{\sigma}]\zeta({\bf p ' } ) , \\ \sigma\cdot\hat{\bf p}\left[-|{\bf p}|\eta({\bf p'})+ [ \epsilon_2-m_2][\hat{\bf p}\cdot\hat{\bf p'}+ i\hat{\bf p}\times\hat{\bf p'}\cdot\vec{\sigma}]\zeta({\bf p'})\right ] \end{array}\right)\chi,\end{aligned}\ ] ] and @xmath86\eta({\bf p ' } ) + |{\bf p}|[\hat{\bf p}\cdot\hat{\bf p'}+ i\hat{\bf p}\times\hat{\bf p'}\cdot\vec{\sigma}]\zeta({\bf p ' } ) \\ p}\left [ |{\bf p}|\eta({\bf p'})+ [ \epsilon_2+m_2][\hat{\bf p}\cdot\hat{\bf p'}+ i\hat{\bf p}\times\hat{\bf p'}\cdot\vec{\sigma}]\zeta({\bf p'})\right ] \end{array}\right)\chi.\end{aligned}\ ] ] we have taken @xmath87 where @xmath88 and @xmath89 , @xmath90@xcite , @xmath91 mev and @xmath92 mev for the diquark and quark , respectively . the nucleon is assumed as mit bag of the confined quarks@xcite . the quark field @xmath93 inside the nucleon bag of radius @xmath94 satisfies the dirac equation @xmath95\psi_{q}(\vec{r},t)=0 , \label{dirac } % ( 2.1)\end{aligned}\ ] ] where @xmath96 is the current mass of a quark of flavor @xmath97 . the current quark masses are taken @xmath98 for the up and down flavor quarks . the single - particle quark energy is given by @xmath99 where @xmath100 for a given value of the bag radius @xmath94 , the quark momentum @xmath101 is determined by the confinement boundary condition at the bag surface which , for quarks of flavor @xmath97 in a spherical bag , reduces to @xmath102 , where @xmath103 and @xmath104 are spherical bessel functions of order zero and one , respectively . the bag energy is given by @xmath105 where @xmath106 is the total constituent quarks kinetic energy inside the bag and @xmath107 term is the zero - point energy for quarks and @xmath108 is the bag parameter . the spurious center - of - mass energy is subtracted to obtain nucleon mass , @xmath109 where @xmath110 the bag radius @xmath94 is obtained through the minimization of the baryon mass with respect to its bag radius @xmath111 the bag parameter @xmath108 is taken as @xmath112 corresponding to its value for a" +"studying structures and energetics of small palladium clusters is of great importance as the first step toward understanding their catalytic properties . in ref . @xcite , the structures and physical properties of small palladium clusters pd@xmath0 ( @xmath115 ) and several larger clusters have been studied using density functional theory ( dft ) calculation . they have investigated their isomeric structures extensively and found many energetically nearly degenerate isomers . in ref . @xcite , based on the lowest energy structures of pd@xmath0 ( @xmath19 ) found in ref . @xcite , the role of small palladium clusters in catalyzing dissociative chemisorption of molecular hydrogen has been studied by dft calculation . the results include the structures of the pd clusters under full hydrogen saturation . as for pd@xmath9 cluster , they have reported detailed analysis of sequential h@xmath10 dissociative chemisorption starting from bare pd@xmath9 cluster to pd@xmath9h@xmath11 cluster . their conclusion of this work is that the capacity of small pd clusters to adsorb h atoms is substantially smaller on average than that of pt clusters , indicating that pd nanoparticles are less efficient than pt nanoparticles in catalyzing dissociative chemisorption of h@xmath10 molecules . although this may be not so industrially encouraging result for the pd clusters , the obtained structures have interesting features from the viewpoint of chemical bonds . our paper is a follow - up study of these papers to learn more about nature of chemical bonds in pd@xmath0 ( @xmath19 ) and their hydrogen - saturated versions using the electronic structures obtained by quantum chemical calculation . in our analysis of chemical bonds , we use the electronic stress tensor . this method is based on the regional density functional theory ( rdft ) and rigged quantum electrodynamics ( rqed ) @xcite and has been applied to several molecular systems @xcite . our method includes recently proposed bond orders @xcite which are defined using the electronic stress tensor . one of our purposes is to show their usefulness in the pd clusters . as far as metallic clusters are concerned , our analysis had been only applied to pt clusters @xcite and al@xmath12 cluster @xcite so the present analysis can be useful basis for further research using our stress tensor based analysis . special interest in these pd clusters is that there seems to be h - h bonds within the clusters . some of these h - h bonds are considered to form after hydrogen molecules are dissociatively adsorbed to the pd clusters @xcite . it would be intriguing to investigate whether these h atoms are bonded from the viewpoint of electronic stress tensor and , if bonded , how the bonding nature differs from that of the free h@xmath10 molecule . this paper is organized as follows . in the next section , we briefly explain our quantum chemical computation method . we also describe our analysis method based on the rdft and the rqed , including the definition of our bond orders . in sec . [ sec : results ] , we discuss our results . in sec . [ sec : bo ] , we analyze the chemical bonds of the hydrogenated pd clusters using our bond orders . in sec . [ sec : stress ] , we discuss the chemical bond using the stress tensor with special emphasis on the pd h bonds associated with h atom with high coordination number and the bonds between h atoms . in sec . [ sec : bes ] we discuss a way to improve our bond order definition by integrating energy density over some area . we summarize our paper in sec . [ sec : summary ] . we perform ab initio quantum chemical calculation for pd clusters and their hydrides . in this work , calculations are performed by program package @xcite using density functional theory ( dft ) with perdew - wang 1991 exchange and correlation functional ( pw91 ) @xcite . the 6 - 31 g * * basis set with polarization functions @xcite has been used for hydrogen atoms and lanl2dz effective core potential @xcite for pd atoms . optimization was performed without imposing symmetry . in the following section , we use quantities derived from the electronic stress tensor to analyze chemical bonds of bare and hydrogenated pd clusters . this method based on rdft and rqed@xcite provides useful quantities to investigate chemical bonding such as new definition of bond order @xcite . we briefly describe them below . ( for other studies of quantum systems with the stress tensor in a slightly different context , see refs . see also refs . @xcite for related discussion on energy density . ) the basic quantity in this analysis is the electronic stress tensor density @xmath13 whose components are given by @xmath14 , \label{eq : stress}\end{aligned}\ ] ] where @xmath15 , @xmath16 is the electron mass , @xmath17 is the @xmath18th natural orbital and @xmath19 is its occupation number . by taking a trace of @xmath13 , we can define energy density of the quantum system at each point in space . the energy density @xmath20 is given by @xmath21 we note that , by using the virial theorem , integration of @xmath20 over whole space gives usual total energy @xmath22 of the system : @xmath23 . regional chemical potential @xmath24 @xcite is calculated approximately using @xmath20 @xcite . @xmath25 where @xmath26 is the ordinary electron density at @xmath27 . since electrons tend to move from high @xmath24 region to low @xmath24 region , the distribution of @xmath24 maps the chemical reactivity . now , we define bond orders as @xmath20 or @xmath24 at lagrange point "" @xcite . the lagrange point @xmath28 is the point where the tension density @xmath29 given by the divergence of the stress tensor @xmath30 , \label{eq : tension}\end{aligned}\ ] ] vanishes . namely , @xmath31 . @xmath29 is the expectation value of the tension density operator @xmath32 , which cancels the lorentz force density operator @xmath33 in the equation of motion for stationary state @xcite . therefore , we see that @xmath29 expresses purely quantum mechanical effect and it has been proposed that this stationary point characterizes chemical bonding @xcite . then , our definitions of bond order are @xmath34 and @xmath35 one should note normalization by the respective values of a h@xmath10 molecule calculated at the same level of theory ( including method and basis set ) . we use molecular regional dft ( mrdft ) package @xcite to compute these quantities introduced in this section . some part of the visualization is done using pymol molecular viewer program @xcite . the optimized structures for hydrogenated pd clusters pd@xmath10h@xmath10 , pd@xmath36h@xmath10 , pd@xmath12h@xmath37 , pd@xmath38h@xmath39 , pd@xmath9h@xmath11 , pd@xmath40h@xmath41 , pd@xmath37h@xmath41 and pd@xmath42h@xmath43 are shown in fig . [ fig : be ] . in the figure , atoms are connected when the lagrange point ( sec . [ sec : rdft ] ) is found between them and the bond is colored to show the magnitude of the bond order @xmath44 ( eq . ) . [ fig : bmu ] shows the exactly the same structures with the different bond order @xmath45 ( eq . ) . these structures are obtained by re - optimizing the structures reported in ref . we performed optimization with multiplicity of 1 , 3 and 5 for each cluster and adopted the one with the lowest energy , which turned out to be singlet for all the clusters . we did not find much difference between the structures in ref . @xcite and our re - optimized ones . for later use , we report that we performed similar procedure for bare pd clusters pd@xmath0 ( @xmath19 ) starting with the structures obtained in ref . @xcite . in this case triplets have the lowest energy for all the clusters . to show features of the chemical bonds in those clusters collectively and to exhibit usefulness of our bond order definitions , we plot bond orders against the bond length for all the bonds in the bare and hydrogenated pd clusters in fig . [ fig : dist_bo_compare ] . in addition to our bond orders @xmath44 and @xmath45 , we plot using conventional bond orders : the wiberg bond index @xcite , atom - atom overlap - weighted natural atomic orbital ( nao ) bond order @xcite and the mayer s bond order @xcite . it is apparent that our bond orders have better correlation than the other conventional bond orders . therefore , we only show our bond orders for the following analysis . in figs . [ fig : dist_be ] and [ fig : dist_bmu ] , we re - plot the bond order v.s . bond length for @xmath44 and @xmath45 respectively , this time distinguishing between different types of bonding . the types we consider are pd pd , terminal pd h , two - fold pd - h , three - fold pd h , four - fold pd h and h h . here , two - fold pd - h bond is associated with the h atom bridging two pd atoms like pd h pd and , similarly , three-(four-)fold pd - h bond with the h atom bonded to three ( four ) pd atoms . each type of bonding is plotted by different marks in figs . [ fig : dist_be ] and [ fig : dist_bmu ] and number of each type for each cluster is shown in table [ tab : bond_type ] . we note that some of the h atoms which we classified as having two - fold and three - fold pd h bonds have a bond with h atom in addition . in detail , h(12 ) and h(13 ) in pd@xmath38h@xmath39 and h(10 ) and h(21 ) in pd@xmath40h@xmath41 are bonded to each other in addition to two pd atoms , which results in having three bonds from each h. similarly , h(10 ) and h(11 ) in pd@xmath9h@xmath11 are bonded to each other in addition to three pd atoms , making four bonds from each h. from figs . [ fig : dist_be ] and [ fig : dist_bmu ] , we see that bonds in the pd clusters can be classified by the different slopes on the bond order v.s . bond length plane . there are a slope that corresponds to the pd pd bonds and two slopes for pd h bonds . there are three outliers that correspond to h h bonds . the fact that pd pd bonds , whether they are in hydrogenated clusters or in bare clusters , are on a single slope indicates that the character of the bonding is not affected much by the hydrogenation . they on average become longer and weaker upon hydrogenation but the relation between the bond order and bond length is unchanged . pd h bonds may be classified in two groups . one has shorter bond length ( @xmath46 ) and higher inclination to which terminal pd h bond and two - fold pd some bonds in three - fold and four - fold pd h also belong to this group . another group has longer bond length ( @xmath47 ) and lower inclination and consists only of three - fold and four - fold pd h . for convenience , we call the former group a "" and the latter b "" . closer inspection of these h atoms with high - coordination numbers tells that there is no h atom which has only group b bonds . the bonds stem from h atoms consist of those of group a or mixture of a and b. see table [ tab : bond_type_2 ] for the detail . it is interesting that there are pd h bonds which are longer than some of the pd" +"tremendous progress has been realized in the last decades concerning the theoretical foundation of quantum optics in dielectric media . while the historical approach proposed by jauch and watson @xcite was already based on the standard canonical quantization formalism for fields , it neglected dispersion and dissipation which are intrinsic properties of any causal dielectric media satisfying kramers krnig relations . since then several important studies were devoted to the extension of the method to inhomogeneous and artificially structured media which are central issues in modern micro and nano photonics @xcite . furthermore , theoretical approaches adapted to transparent but dispersive media with negligible losses have been also developed based on different techniques such as the slowly varying envelope approximation @xcite or the quasi modal expansion method which is valid near resonance for polaritons @xcite . more recently , losses were included in the theory by adding phenomenologically some optical dissipation channels in the light propagation path @xcite . such a method was successfully used for the modeling of casimir forces in dissipative media @xcite and surface plasmon polaritons @xcite . + moreover , the most fundamental progress was probably done when huttner and barnett , and others @xcite proposed a self - consistent canonical quantization procedure for an homogeneous and causal dielectric medium by coupling photonic degrees of freedom with mechanical oscillator variables acting as thermal baths . the method , based on the pioneer works by fano and hopfield @xcite ( see also ref . @xcite ) , was subsequently extended to several inhomogeneous systems including anisotropic and magnetic properties @xcite . in parallel to these theoretical works based on the standard canonical quantization method , a different and powerful axis of research appeared after the work by gruner and welsch @xcite ( see also ref.@xcite ) based on the quantum langevin noise approach used in cavity qed ( i.e. , quantum electrodynamics ) @xcite . the method is also known as the green tensor method @xcite since it relies on efficient green dyadic techniques used nowadays in nano - photonics and plasmonics @xcite . this ` langevin - noise ' approach , which actually extends earlier ` semi classical ' researches based on the fluctuation - dissipation theorem by lifshitz and many others in the context of casimir and optical forces @xcite , was successfully applied in the recent years to many issues concerning photonics @xcite and nano - plasmonics where dissipation can not be neglected @xcite . in this context the relationship between the huttner - barnett approach on the one side and the langevin noise method on the other side has attracted much attention in the last years , and several works attempted to demonstrate the validity of the langevin noise method from a rigorous hamiltonian perspective which is more in a agreement with the canonical huttner - barnett approach @xcite . + the aim of this work is to revisit these derivations of the equivalence between the langevin noise and hamitonian method and to show that some unphysical assumptions actually limit the domain of validity of the previous attempts . more precisely , as we will show in this work , the analysis and derivations always included some hypothesis concerning causality and boundary conditions which actually lead to circularity in the deductions and are not applicable to the most general inhomogeneous systems used in nano - optics . specifically , these derivations , like the fluctuation - dissipation reasoning in lifshitz and rytov works @xcite , give too much emphasis on the material origin of quantum fluctuations for explaining macroscopic quantum electrodynamics in continuous media . however , as it was already pointed out in the 1970 s @xcite , one must include with an equal footings both field and matter fluctuations in a self consistent qed hamiltonian in order to preserve rigorously unitarity and causality @xcite . while this does nt impact too much the homogeneous medium case considered by huttner and barnett @xcite it is crucial to analyze further the inhomogeneous medium problem in order to give a rigorous foundation to the gruner and welsch theory @xcite based on fluctuating currents . this is the central issue tackled in the present work . + the layout of this paper is as follows : in section ii we review the lagrangian method developed in our previous work @xcite based on an alternative dual formalism for describing the huttner - barnett model . in this section we summarize the essential elements of the general lagrangian and hamiltonian model necessary for the present study . in particular we present the fundamental issue about the correct definition of hamiltonian which will be discussed at length in this article . in section iii we provide a quantitative discussion of the huttner - barnett model for an homogeneous dielectric medium . we discuss a modal expansion into plane waves and separate explicitly the electromagnetic field into classical eigenmodes and noise related langevin s modes . we show that both contributions are necessary for preserving unitarity and time symmetry . we consider limit cases such as the ideal hopfield - fano polaritons @xcite without dissipation and the weakly dissipative polariton modes considered by milonni and others @xcite . we discuss the physical interpretation of the hamiltonian of the whole system and interpret the various contributions with respect to the langevin noise method and to the loss - less hopfield - fano limit . in section iv we generalize our analysis to the inhomogeneous medium case by using a green dyadic formalism in both the frequency and time domain . we demonstrate that in general it is necessary to keep both pure photonic and material fluctuations to preserve the unitarity and time symmetry of the quantum evolution . we conclude with a discussion about the physical meaning of the hamiltonian in presence of inhomogeneities and interpret the various terms associated with photonic and material modes . in ref . @xcite we developed a new lagrangian formalism adapted to qed in dielectric media without magnetic properties . here we will use this model to derive our approach but a standard treatment based on the minimal coupling scheme @xcite or the power - zienau @xcite transformation would lead to similar results . we start with the dual lagrangian density : @xmath0 where @xmath1 and @xmath2 are the magnetic and displacement fields respectively . in this formalism the usual magnetic potential @xmath3 , defined such as @xmath4 , is replaced by the dual electric potential @xmath5 ( in the ` coulomb ' gauge @xmath6 ) defined by @xmath7 implying @xmath8 the material part @xmath9 of the lagrangian density in eq . [ 1 ] reads @xmath10 with @xmath11 the material oscillator fields describing the huttner - barnett bath coupled to the electromagnetic field . the coupling depends on the polarization density which is defined by @xmath12 where the coupling function @xmath13 defines the conductivity of the medium at the harmonic pulsation @xmath14 . from eq . [ 1 ] and euler - lagrange equations we deduce the dynamical laws for the electromagnetic field @xmath15 with the electric field @xmath16 . similarly for the material oscillators we have : @xmath17we point out that the lagrangian density in eq . [ 1 ] includes a term @xmath18 which is necessary for the derivation of the dynamical laws for the material fields @xmath19 @xcite . furthermore , to complete the qed canonical quantization procedure of the material field we introduce the lowering @xmath20 and rising @xmath21 operators for the bosonic material field from the relation @xmath22 . as explained in ref . @xcite by using the equal time commutation relations between the canonical variables @xmath11 and @xmath23 , we deduce the fundamental rules @xmath24=\delta(\omega-\omega')\delta^3(\mathbf{x}-\mathbf{x'})\textbf{i}. \label{33}\end{aligned}\ ] ] ( with @xmath25 the unit dyad ) and @xmath26=[\mathbf{f}^\dagger_\omega(\mathbf{x},t),\mathbf{f}^\dagger_{\omega'}(\mathbf{x}',t)]=0 $ ] allowing a clear interpretation of @xmath20 and @xmath27 as lowering and rising operators for the bosonic states associated with the matter oscillators . + moreover , eqs . [ 5],[8 ] can be formally integrated leading to @xmath28 where @xmath29 is an initial time and where @xmath30 is a fluctuating dipole density distribution defined by : @xmath31 \nonumber\\ \label{35}\end{aligned}\ ] ] with @xmath32 and where by definition @xmath33 . we therefore have @xmath34 which is reminiscent of the general linear response theory used in thermodynamics @xcite . we point out that the term @xmath35 can be seen as an induced dipole density . however , as we will show in the next section the electric field itself is decomposed into a purely fluctuating term @xmath36 and a scattered field @xmath37 which depends on the density @xmath38 . therefore , the contribution @xmath35 to @xmath39 is also decomposed into a pure photon - fluctuation term @xmath40 and an induced term @xmath41 related to material fluctuations @xmath38 . + importantly , the linear susceptibility @xmath42 which is defined by @xmath43 characterizes completely the dispersive and dissipative dielectric medium . we can show that the permittivity @xmath44 is an analytical function in the upper part of the complex plane @xmath45 , i.e. , @xmath46 , provided @xmath42 is finite for any time @xmath47 . from this we deduce the symmetry @xmath48 and it is possible to derive the general kramers - krnig relations existing between the real part @xmath49\equiv\widetilde{\varepsilon}'(\mathbf{x},\omega)$ ] and the imaginary part @xmath50\equiv\widetilde{\varepsilon}''(\mathbf{x},\omega)$ ] of the dielectric permittivity . therefore , the huttner - barnett model characterized by the conductivity @xmath51 is fully causal and can be applied to describe any inhomogeneous dielectric media in the linear regime . + the central issue of the present paper concerns the definition of the hamiltonian @xmath52 in the huttner - barnett model . we remind that in ref . @xcite we derived the result : @xmath53 with @xmath54 where @xmath55:$ ] means , as usually , a normally - ordered product for removing the infinite zero - point energy . inserting the definition for @xmath20 obtained earlier we get for the material part @xmath56 which has the standard structure for oscillators ( i.e. , without the infinite zero - point energy ) . + however , hutner and barnett @xcite after diagonalizing their hamiltonian found that the total evolution is described in the homogeneous medium case by @xmath57 while as we will see this is actually a correct description ` for all practical purpose ' in a homogeneous dissipative medium for large class of physical boundary conditions , this is in general not acceptable in order to preserve time - symmetry and unitarity in the full hilbert space for interacting matter and light . the general method based on langevin forces and noises avoided quite generally mentioning that difficult point . we emphasize that while the conclusions presented in refs . @xcite is accepted by more or less all authors on the subject @xcite they have been some some few dissident views ( see refs . @xcite ) claiming , that in the context of an input - output formalism , the langevin noise formalism is not complete unless we consider as well fluctuations of the free photon modes ( see also the replies with an opposite perspective in refs . @xcite ) . in the present work we will generalize and give a rigrous qed like hamiltonian foundations to the prescriptions of refs . @xcite and we will show that it is actually necessary to include a full description of photonic and material quantum excitations in order to preserve unitarity . in order to appreciate this fact further we will first consider the problem associated with quantization of the electromagnetic field . we first introduce the paradigmatic homogeneous medium case considered initially by huttner and barnett @xcite , i.e. , with @xmath58 . we start with faraday s law : @xmath59 rewritten according to eq . [ 21 ] as : @xmath60 inserting eq . [ 4 ] and using the coulomb ( transverse ) gauge condition we get : @xmath61 we use the modal expansion method developed in ref" +"the study of the time - evolution of a non - relativistic charged particle in homogeneous magnetic and electric fields has a long history in physics . in a quantum context , the treatment of the problem goes back to darwin @xcite , who considered the evolution of a gaussian wave - packet in a magnetic field , and fock @xcite who obtained the eigenenergies and eigenstates of a charged particle in an isotropic harmonic potential , subjected to a magnetic field normal to the plane of motion . if one takes a particle of charge @xmath0 and mass @xmath1 , moving in the @xmath2 plane in an harmonic potencial of frequency @xmath3 and subjected to a magnetic field @xmath4 , the hamiltonian describing the system is given , in the symmetric gauge where @xmath5 , by @xmath6+\frac{1}{2}\,m\,\omega_0 ^ 2\,(\hat{x}^2 + \hat{y}^2)\ , , \label{eq1}\ ] ] where the operators @xmath7 obey the canonical commutation relations . this simple problem has applications in the context of the quantum hall effect @xcite , where disorder and the coulomb interaction also play a crucial role . another field for which the study of this hamiltonian has proved fruitful is that of quantum dots , where the simple hamiltonian given by ( [ eq1 ] ) seems to give a good account of the @xmath8 curves obtained when a gate voltage is applied to the quantum dot @xcite , with corrections due to the assymetry of the confining potential and to the coulomb interactions also playing a role . for some types of quantum dots , such as inas / gaas quantum dots , the agreement between the theoretical and experimental results seems to hold for magnetic fields up to 15 t @xcite . the study of the evolution of gaussian wave packets also goes back to the first days of quantum mechanics . this study was first undertaken by schrdinger @xcite , kennard @xcite and also by darwin @xcite in the context of the harmonic oscillator , of a free particle and of a particle in constant electric and magnetic fields . this problem continues to attract attention to the present day in many contexts , see the review by dodonov @xcite . schrdinger considered the time - evolution of a minimal uncertainty state , i.e. a coherent state of the harmonic oscillator , in the terminology of glauber @xcite . these states have a wide range of applications in quantum optics ( see e.g. @xcite ) , where they act as the quasi - classical states of the em field , and in quantum field theory , where they are the basis of the phase - space path integral @xcite . such states and their derivatives have become important in quantum information processing in recent years , in the context of the manipulation of cold atoms in traps . it has become possible to reconstruct the wigner function of a coherent state of the center - of - mass of an harmonically bound ion @xcite . kennard has on the other hand considered the evolution of a more general wavepacket of the harmonic oscillator , what is now known as a squeezed state . important early contributions are those of husimi @xcite and infeld and plebaski @xcite . these later authors introduced the so - called squeezing operator and established a relation between the evolution of initial states for which the time - evolution is known ( unsqueezed states ) and states which are derived from such initial states by the application of the squeezing operator ( squeezed states ) . the generalisation of this relation to the fd hamiltonian in an homogeneous time - dependent electric field is the main result of the present paper . stoler @xcite proved that squeezed - coherent states are unitarily equivalent to coherent states , thus being minimal uncertainty states , but that their minimal character is not preserved by time - evolution , although the uncertainty periodically assumes the minimum value compatible with heisenberg s uncertainty relation . he also showed that the squeezing operator as currently written in terms of quadratures operators is exactly of the form given by infeld and plebaski . squeezed states play a proeminent role in quantum optics , see again @xcite . recently , they have also become important in quantum information processing both in a quantum optics context and also through the manipulation of cold atoms @xcite . see in particular reference @xcite for an up - to - date report of the state of quantum information processing using cold atoms and photons . besides the paper of darwin already referred , the time - evolution of states of a non - relativistic particle in homogeneous electric and magnetic fields was also considered by malkin , manko , trifonov and dodonov @xcite , who considered the dynamics of a particle in an homogeneous electromagnetic field in terms of coherent states , obtaining an explicit representation of the green s function , and studied the invariants of the system ; by lewis and riesenfeld @xcite , who also considered the invariants of such a system ; by kim and weiner @xcite , who considered the evolution of gaussian wave - packets in a magnetic field , subjected to an isotropic harmonic potential ( i.e. the fd hamiltonian ) , but also to sadle - point potentials , which are relevant for tunnelling problems . the structure of this paper is as follows : in the next section , we review the notion of squeezing operator and generalise the relation of infeld and plebaski to states evolving under the fock - darwin hamiltonian . in section [ secc ] , with a view to applications in the manipulation of cold atoms , we use the relation obtained to establish a relation between the wigner function of different states and apply it to the special case of squeezed - coherent states . in section [ secd ] , we present our conclusions . in appendix [ appendixa ] , we present a derivation of the finite frequency permitivity and conductivity of the fd hamiltonian that uses the same operator methods that are used in the main text but which lies somewhat outside of the scope of the main text . finally , in appendix [ appendixb ] , we derive the original infeld - plebaski relation through elementary means . we consider the time - evolution of the state @xmath9 , that obeys the time - dependent schrdinger equation @xmath10 , where @xmath11 , with @xmath12 being given by equation ( [ eq1 ] ) and where the interaction hamiltonean @xmath13 of the charge with the external electric field is given , in the schrdinger picture , by @xmath14 . if one now expands the squares and groups the different terms of ( [ eq1 ] ) , one obtains @xmath15 where @xmath16 is the giration frequency and @xmath17 , with @xmath18 being the angular momentum component along the @xmath19 axis . one should note that one can write @xmath20 , where @xmath21 is the hamiltonean of the isotropic harmonic oscillator with frequency @xmath22 , and also that @xmath23=0 $ ] . given the state vector @xmath9 , one can define the corresponding state vector @xmath24 , in the interaction representation , such that the two vectors coincide at @xmath25 . this state vector evolves acording to the hamiltonian @xmath26 , which given that @xmath21 and @xmath27 in @xmath12 commute , one can also write as @xmath28 if one now applies the time - dependent rotation , encoded by @xmath27 to @xmath13 , followed by the dynamics of the isotropic harmonic oscillator , encoded in @xmath21 , one obtains for @xmath29 : @xmath30+\,e_{y}'(t)\left[\,\hat{y}\,\cos(\omega_r t)+\hat{p}_y\,\sin(\omega_r t)\,\right]\right\ } , \label{eq3}\end{aligned}\ ] ] where @xmath31 are the components of the electric field in the rotated frame . the wave equation for @xmath32 can be formally integrated in terms of time - ordered products of the integral of @xmath29 , i.e. @xmath33 . now , since the commutator of the operators @xmath34 at different times is a c - number , one can write the time ordered operator above as @xmath35\right)\ , , \label{eq3_1}\end{aligned}\ ] ] where the second term on the rhs is a phase factor . collecting the several terms , one obtains for the evolution of @xmath9 @xmath36\ , \,[e_x'(u)e_x'(v)+e_y'(u)e_y'(v)]\right)\nonumber\\ & & \mbox{}\times \exp\left(-\frac{i\omega_lt}{2\hbar}\,\hat{l}_z\right)\ , \exp\left(-\frac{i}{\hbar}\,\hat{h}_0\,t\right)\,\exp\left(-\frac{i}{\hbar } \,\int_{0}^{t}\,du\,\hat{h}_1^{int}(u)\right)\ , { \mbox{$ \mid \overline{\psi}_0\ , \rangle$}}\ , . \label{eq4}\end{aligned}\ ] ] one now assumes , following infeld and plebaski @xcite , that the initial state @xmath37 is related to a certain initial state @xmath38 , for which the time - evolution under the isotropic harmonic oscillator hamiltonian @xmath21 is known , by @xmath39 where the first operator is a translation operator in phase space , with @xmath40 being arbitrary real constants , and the second operator is the squeezing operator , with @xmath41 being a real constant that indicates the degree of squeezing . substituting equation ( [ eq5 ] ) in ( [ eq4 ] ) one can combine the operators @xmath42 and @xmath43 , since the commutator of their exponents is a c - number . this operation merely generates a phase factor , coming from the commutator . one can then commute the resulting operator to the left - hand side , through @xmath44 , using the time - evolution of @xmath45 under @xmath21 and under the time - dependent rotation around the @xmath19 axis . combining the resulting phase factors and operators , we obtain @xmath46\right)\ , \exp\left(\frac{i}{\hbar}(\,p^c_x(t)\hat{x}+p^c_y(t)\hat{y } -x_c(t)\hat{p}_x - y_c(t)\hat{p}_y\,)\right)\nonumber\\ & & \mbox{}\times \exp\left(-\frac{i\omega_lt}{2\hbar}\,\hat{l}_z\right)\ , \exp\left(-\frac{i}{\hbar}\,\hat{h}_0\,t\right)\ , \exp\left(\frac{i}{2\hbar}\,r\,(\hat{{\mbox{${\boldsymbol p}$}}}\cdot\hat{{\mbox{${\boldsymbol r}$}}}+ \hat{{\mbox{${\boldsymbol r}$}}}\cdot\hat{{\mbox{${\boldsymbol p}$}}})\right)\,{\mbox{$ \mid \psi_0\ , \rangle$}}\ , . \label{eq6}\end{aligned}\ ] ] where @xmath47 , @xmath48 , @xmath49 and @xmath50 are the classical solutions of the equations of motion for the fock - darwin problem with initial positions @xmath51 and @xmath52 and initial momenta @xmath53 and @xmath54 . these solutions are given by @xmath55\,\cos(\omega_rt)\nonumber\\ & & \mbox{}+\frac{1}{m\omega_r}\,\left[\,p_x^0 \cos\left(\frac{\omega_l}{2}t\right)-p_y^0 \sin\left(\frac{\omega_l}{2}t\right)\,\right]\,\sin(\omega_rt)\nonumber\\ & & \mbox{}-\frac{e}{2m\omega_r}\,\int_0^t\,du\ , \left\{e_x(u)\,\left[\sin(\omega_+(t - u))+\sin(\omega_-(t - u))\right]\right . \nonumber\\ & & \mbox{}\left.+e_y(u)\,\left[\cos(\omega_+(t - u))-\cos(\omega_-(t - u))\right]\right\}\ , , \label{eq7}\end{aligned}\ ] ] @xmath56\,\cos(\omega_rt)\nonumber\\ & & \mbox{}+\frac{1}{m\omega_r}\,\left[\,p_x^0 \sin\left(\frac{\omega_l}{2}t\right)+p_y^0 \cos\left(\frac{\omega_l}{2}t\right)\,\right]\,\sin(\omega_rt)\nonumber\\ & & \mbox{}-\frac{e}{2m\omega_r}\,\int_0^t\,du\,\left\{-e_x(u)\,\left[\cos(\omega_+(t - u))-\cos(\omega_-(t - u))\right]\right . \nonumber\\ & & \mbox{}\left.+e_y(u)\,\left[\sin(\omega_+(t - u))+\sin(\omega_-(t - u))\right]\right\}\ , , \label{eq8}\end{aligned}\ ] ] and @xmath57\,\cos(\omega_rt)\nonumber\\ & & \mbox{}-m\omega_r\,\left[\,x_0 \cos\left(\frac{\omega_l}{2}t\right)-y_0 \sin\left(\frac{\omega_l}{2}t\right)\,\right]\,\sin(\omega_rt)\nonumber\\ & & \mbox{}-\frac{e}{2}\,\int_0^t\,du\,\left\{e_x(u)\,\left[\cos(\omega_+(t - u))+\cos(\omega_-(t - u))\right]\right . \nonumber\\ & & \mbox{}\left .- e_y(u)\,\left[\sin(\omega_+(t - u))-\sin(\omega_-(t - u))\right]\right\}\ , , \label{eq9}\end{aligned}\ ] ] @xmath58\,\cos(\omega_rt)\nonumber\\ & & \mbox{}-m\omega_r\,\left[\,x_0 \sin\left(\frac{\omega_l}{2}t\right)+y_0 \cos\left(\frac{\omega_l}{2}t\right)\,\right]\,\sin(\omega_rt)\nonumber\\ & & \mbox{}-\frac{e}{2}\,\int_0^t\,du\,\left\{e_x(u)\,\left[\sin(\omega_+(t - u))-\sin(\omega_-(t - u))\right]\right . \nonumber\\ & & \mbox{}\left.+e_y(u)\,\left[\cos(\omega_+(t - u))+\cos(\omega_-(t - u))\right]\right\}\ , . \label{eq10}\end{aligned}\ ] ] one can read the classical dielectric permitivity of the system from equations ( [ eq7],[eq8 ] ) and one obtains the same results as in appendix [ appendixa ] , which shows that the quantum and classical results are identical , as one would expect for a linear system . the classical velocities @xmath59 can be easily computed by derivation of ( [ eq7],[eq8 ] ) with respect to time or , using the relations @xmath60 and @xmath61 , from equations ( [ eq7 ] ) to ( [ eq10 ] ) . one can then read the classical conductivity of the system from the resulting expression and this result again coincides with that of appendix [ appendixa ] , i.e. the classical and quantum results are the same . finally , one can also show , after derivation of the velocity expressions with respect to time , that the solution given by ( [ eq7 ] ) and ( [ eq8 ] ) obeys the classical equations of motion in two dimensions @xmath62 , with @xmath63 . the left most operator in equation ( [ eq6 ] ) is again a translation operator in phase phase . if one considers the wave - function in the coordinate representation , @xmath64 , and one applies this translation operator to" +"quantitative electronic structure theories are essential to the understanding and designing of novel materials and devices . it is now generally accepted that transport properties of nanoscale devices depend on both the intrinsic electronic structure of the active channel , as well as its interfacial properties with contacts and other scattering centers . a particular challenge in this respect is to incorporate both long and short range correlations within the same framework , such as the bulk bandstructure of periodic solids as well as the local chemical properties of clusters , surfaces , and interfaces . for instance , simulating scanning tunneling spectra ( sts ) of molecules on silicon substrates requires an accurate description of the silicon bulk bandstructure that quantitatively captures not just the bandgap responsible for the onset of negative differential resistance , @xcite but also the multiple effective masses which determine the contact density of states and injection velocities , and the strain parametrizations that capture atomic reconstruction and relaxation near the surface and their bonding with molecular components.@xcite in addition , one needs to describe the electrostatics responsible for band - bending in the silicon depletion layer , the molecular transport levels and their transmission under bias , and finally the electronic properties of the scanning tip and the intervening vacuum layer , all within the same formalism . it is no surprise therefore that under these circumstances , standard electronic structure techniques developed by quantum chemists for simulating molecules are usually incompatible with those developed by solid - state physicists for bulk bandstructure , making it important to develop a common formalism that addresses both domains of interest and also maintains a good compromise between computational accuracy and practicality . while sophisticated methods exist for equilibrium geometry and bandstructure , comparable success has yet to be achieved for transport problems , partly because of the lack of universally accepted experimental standards , but mainly because quantum transport inherently involves solving a complicated nonequilibrium open boundary problem for which electronic structure theories are not benchmarked . a proper quantitative understanding of correlation effects in transport is still evolving and it is not yet clear if mean - field approaches that work at equilibrium are at all capable of handling the profusion of electronic excitations that often dominate in nanoscale conduction.@xcite even aside from such correlation issues , one needs to worry about heterointerfaces since current flow involves charge transport across two intrinsically different material systems a multimoded contact consisting of a highly conductive material externally maintained at thermal equilibrium , and a sparsely moded device region that is readily driven away from equilibrium and acts as the active transport channel . in this paper , we employ a semi - empirical approach to electronic structure that can be adopted for electronic conduction through complex hybrid systems by combining it with the nonequilibrium green s function ( negf ) technique for quantum transport . our theoretical parameters are tailored to salient features of the bulk bandstructure , while the employment of non - orthogonal basis sets resembling linear combinations of underlying atomic orbitals seems to make them fairly transferrable to surfaces as well , as observed in the past.@xcite in addition , the presence of explicit basis sets opens up the possibility of ` stitching ' together disparate regions@xcite by matching the interfacial green s function , which is the _ only _ quantity through which the diverse regions communicate with each other quantum mechanically . the modularity of our approach also allows us to conveniently separate the problems of determining the optimized interfacial geometry and the interfacial transmission ( we are ignoring current - induced forces ) , the former depending on the total energy of the system while the latter depends only on a few relevant single - electron levels near the fermi energy . in other words , _ given a particular atomistic configuration of the contact - channel - contact heterostructure , we seek to determine its transport properties by coupling our electronic structure approach with quantum transport using negf . _ the outline of the paper is as follows : section ii explains the strengths of eht over other traditional bandstructure methods . in section iii we briefly summarize the negf aproach used to calculate density of states and transmission of cnts ; we then specify the model hamiltonian and describe the details of eht used to determine the bandstructure . the numerically calculated bandstructure data for nanotubes are then compared in section iv with experimental scanning tunneling spectroscopy experiments along with other theoretical approaches . in section v we investigate the changes in the dispersion of a semi - conducting cnt under large lateral deformations as well as with a co molecular attachment to its surface that allows it to function as a molecular sensor . we summarize our work and discuss future extensions in the last section . a particular trade - off in any bandstructure theory is between flexibility and rigor . while empirical , orthogonal tight - binding ( otb ) methods are quick and practical , they are benchmarked for specific geometries and are usually not very transferable to other environments involving significant structural deformations beyond a few percent . tight binding basis - sets are commonly assumed to be both orthogonal and short - ranged,@xcite while atomic wavefunctions are not , meaning that otb basis sets do not resemble eigenstates of an atomic hamiltonian . efforts at improving tight - binding theories involve going beyond nearest neighbor techniques , using higher virtual orbital bases for increased completeness,@xcite and employing power laws for parameter transfer under small ( @xmath0 ) strain.@xcite nevertheless these models are likely to miss important chemical details involving properties varying on an interatomic length scale , in particular near deformed surfaces and interfaces where a drastic reconstruction of the atomic structure is expected.@xcite at the other end of the spectrum are accurate , but computationally expensive first - principles techniques developed by quantum chemists and solid state physicists , such as configuration interaction ( ci ) and density functional theories ( dft ) in various atomic or plane wave basis sets or combinations thereof . structural deformations are naturally captured by such total energy calculations by solving a one electron schrdinger equation in a suitable self - consistent potential approximating the electron - electron interaction.@xcite such codes are typically based on rigorous variational theorems and are quantitatively quite accurate , at least for equilibrium properties . their extension and practical implementation to transport beyond the linear response regime is continuously evolving,@xcite and a topic of current research.@xcite conceptually , it is not clear if any self - consistent potential approach can quantitatively describe the rich spectrum of many - body transitions that are often experimentally accessed in strongly correlated transport in weakly coupled systems.@xcite we aim for a practical compromise between these two limits by using a semi - empirical technique motivated by extended - hckel calculations popular in the chemistry community . such theories , widely used in the past to describe the equilibrium properties of isolated molecules,@xcite have recently been applied to molecular conduction @xcite and also extended to solids using transferable atomic - orbital basis sets ( ao ) for calculating the electronic structure of various compounds benchmarked with detailed dft calculations within the local density ( lda ) or generalized gradient ( gga ) approximations.@xcite given a geometry , one uses the explicit eht basis functions to calculate a non - orthogonal overlap matrix @xmath1 , which along with separately fitted onsite hamiltonian matrix elements yields the corresponding off - diagonal hopping elements of the hamiltonian . within the standard hckel prescription , structural changes are simply accounted for by re - calculating the overlap and hopping elements , but leaving the basis sets and onsite elements unchanged . in the following , we apply this eht parametrization scheme@xcite by benchmarking it to a two - dimensional graphene sheet@xcite and extending it to obtain the bandstructure , density of states and electronic transmission of carbon nanotubes ( cnt ) of varying chiralities . we show that the same bulk - optimized eht - parameters ( onsite energies and ao - basis functions ) are transferable to small diameter cnt bandstructures , capturing even curvature - induced bandgap effects for larger than @xmath2 tube deformation , in quantitative agreement with sts data . furthermore , surface chemical effects are examined through the study of nanotube based carbon - monoxide sensors whose alteration of electronic structure upon molecular adsorption compares favorably with ab - initio calculations of da silva _ et al._.@xcite in our follow - up paper , we will demonstrate a similar transferability between bulk silicon , various silicon surfaces , apply the eht - methodology to unreconstructed silicon nanowires . taken together , the wide variety of these examples illustrates the range of transferability of eht parameters , which we believe makes extended hckel theory a useful practical tool for electronic structure and quantum transport . simulating conduction through a heterostructure involves combining suitable bandstructures for the channel and contact materials with self - consistent electrostatics and quantum transport . while the formulation of correlated transport is itself an active area of research , our aim here is to develop a minimal model that would capture quantum chemistry , surface physics , bandstructure and electrostatic effects that are all crucial for different prominent aspects of nanoscale conduction . the ingredients needed for a proper simulation are the hamiltonian and potential matrices describing the device bandstructure and electrostatics , and the contact self - energies that effectively open up the system and allow us to add or remove charge under nonequilibrium conditions . the eht prescription gives us a practical way to calculate these ingredient matrices for a given atomistic structure , and then connect them with a non - equilibrium green s function ( negf ) formulation of quantum transport , which we briefly summarize below.@xcite the retarded green function of the device is given by @xmath3^{-1}~,\ ] ] where @xmath1 and @xmath4 describe the overlap and hamiltonian matrices of the device unit cell calculated according to the hckel prescription eq.([eht_rule ] ) . the matrix elements @xmath5 are self - energies that provide open boundary conditions to the device with the left and right semi - infinite contacts . the self - energy @xmath6 incorporates the coupling matrix @xmath7 describing the contact - device bonding , while @xmath8 is the surface green function of the left / right contact calculated by means of a recursion technique.@xcite in a non - orthogonal tight - binding scheme the density of states ( dos ) is given by @xmath9 where @xmath10 denotes the spectral function . finally , in the phase - coherent limit the zero - bias transmission through the unit cell reads @xmath11 $ ] , where @xmath12 are the broadening matrices which specify the time an electron resides within the device . in this paper , we will study infinite nanotubes so that the active device is just one cnt unit cell and the left and right contacts extend that cell to infinity in either direction . the bandstructure of a nanotube with chirality @xmath13 is calculated employing the non - orthogonal slater - koster scheme and solving for the generalized eigenvalue problem@xcite @xmath14 where @xmath15 denotes the eigenvector of the @xmath16 subband , and @xmath17 is a bloch wavevector within the first brillouin zone . the size of the overlap and hamiltonian matrices are determined by the chosen basis set , i.e. , the number of atoms within the unit cell multiplied by the number of orbitals per atom . in our case , using four @xmath18-orbitals per atom , the size of these matrices is @xmath19 for an armchair @xmath20 tube as sketched in fig . [ fig_3dtubestructure ] . the overlap- and hamilton matrices @xmath21 and @xmath22 representing the structure in reciprocal space" +"a clear understanding of nuclear structure beyond the valley of @xmath4-stability requires detailed spectroscopic investigations . direct reactions , such as single - nucleon transfer reactions are established probes of the single - particle nuclear shell structure and have provided considerable insight into the properties of stable nuclei in the past . with the on - going increase in radioactive nuclear beam intensities , such as those achieved at the spiral facility , this kind of reaction is now feasible . the inverse kinematics of such reactions leads , however , to significant constraints on the experimental apparatus @xcite . one of the main obstacles to overcome is to reach good energy resolution in the kinematically reconstructed excitation energy given that the energy spread of the secondary beam may be relatively large , the target - like residue can be emitted over a large angular range and that thick targets are often required to compensate for the relatively low intensities of the beams @xcite . already , pioneer detectors such as must @xcite and the active target maya @xcite have been build to tackle some of these obstacles and , the detector tiara described here proposes a new alternative to these other apparatus . the tiara array is designed and built specifically to study direct reactions with radioactive beams and addresses the challenge of the excitation energy resolution by employing the technique of @xmath1-ray tagging . this has the advantage of providing , in principle , a final excitation energy resolution limited only by doppler broadening . the tiara array was commissioned at the ganil laboratory through a study of the d(@xmath2n , p)@xmath3n reaction @xcite with coincident @xmath1-ray detection . the results are reported here together with a full description of the array . the tiara array @xcite has been designed with the ultimate goal of performing nucleon transfer and other direct reaction studies in inverse kinematics using radioactive ion beams @xcite . the array is used to identify the binary reaction channels and to determine the excitation energies of the populated states . this task is achieved by providing position and deposited energy measurements of the light charged target - like residue , which can be emitted over a wide angular range . tiara consists of a set of single - layer silicon detectors manufactured by micron semiconductor @xcite which covers 85@xmath5 of 4@xmath0 ( fig . [ fig : tiaracoverage ] ) . the set includes a large annular double sided silicon strip detector ( sihyball ) , eight resistive charge division silicon detectors forming a `` barrel '' around the target , and two smaller `` cd - type '' silicon strip detectors ( s1 and s2 ) . eight resistive charge division detectors based on 6-inch silicon wafer technology form an octagonal barrel around the beam axis and surrounding the target . each of the detectors presents an active area 94.6 mm long and 22.5 mm wide with a thickness of 400 @xmath6 m . the junction side facing the target is divided into 4 longitudinal resistive strips obtained by p@xmath7 implantation on n - type silicon . each 4k@xmath8-resistive strip has a 5.65 mm pitch while the inter - strip gap is 100 @xmath6 m . the strips provide for measurement and pixellation of the azimuthal angle in 32 bins of approximately 9.5@xmath9 . the pcb board around the silicon has been minimised and bevelled so that the dead area between the detectors as well as between the barrel and annular detectors , is minimised . at one end of the ohmic side of the detector , the pcb board is extended by @xmath1015 mm in order to gather all the output signal tracks : the 8 position signals ( 2 signals per strip ) and the connection of the ohmic side to ground . miniature junkosha coaxial cables of 1 mm diameter and 30 cm length were chosen for their favourable vacuum properties to transmit the signals from the detector to the vessel feed - throughs . once assembled ( fig . [ fig : photohybbar ] right ) , the barrel presents an octagonal cross section of 27.6 mm side length and 33.3 mm inner radius . from the centre , the angular range spans 36@xmath9 to 144@xmath9 . for the commissioning measurements described later , the centre of the barrel was mounted 1 mm forward of the target position leading to an angular coverage of 35.5@xmath9 to 143.5@xmath9 . the measurement of the position along the strip is achieved by resistive charge division and , with alpha particles of 5.5 mev , the position resolution along the longitudinal axis is determined to better than 0.5 mm ( fwhm ) . the resulting polar angle is thus deduced with a precision better than 1@xmath9 . the energy of the particle is obtained simply by summing the signals from the two strip ends . figure [ fig:3alphas ] was obtained using a mixed source of @xmath11pu , @xmath12am and @xmath13 cm with alpha energies of 5156 , 5484 and 5805 kev respectively . it illustrates the correlation between the signals from the ends of the strips ( fig [ fig:3alphas](a ) ) . with a shaping time of 1@xmath6s the barrel suffers slightly from ballistic deficits which result in a non - linear dependence of the energy sum , measured at each end of a strip , as a function of the position . nevertheless , this dependence is easily described with a second - order polynomial function and a corresponding corrective factor can be applied to the energy sum . the resolution for one strip is @xmath1070 kev ( fwhm ) for 5.5 mev alphas ( fig [ fig:3alphas](b ) ) . s shaping time . ( c ) : same as ( b ) for the 4 strips of a barrel detector.,width=453,height=264 ] as noted earlier , in order to enhance the angular coverage of the tiara array , double - sided dc annular silicon - strip detectors are mounted at both ends of the barrel . for these detectors the annular rings on the entrance face ( junction side ) were fabricated by p@xmath7 implantation on n - type silicon . the forward angles are covered by two 500 @xmath6 m thick annular detectors based on 4-inch wafer technology . the smallest of the two ( s2-design ) was positioned 150 mm downstream of the target position covering the polar angular range [ 3.8@xmath9,13.1@xmath9 ] . the active area is delimited by a disk of 11 mm inner radius and 35 mm outer radius . the detector is divided into 48 rings of 0.5 mm pitch at the front ( target side ) and 16 azimuthal sectors at the back . however , for the present measurements , the number of channels to instrument was reduced by linking the rings in threes giving effectively 16 rings of 1.5 mm pitch . the second forward annular detector ( s1 design ) was mounted 92 mm downstream of the target position to cover the polar angular range [ 12.6 @xmath9,27.5@xmath9 ] . its active area is divided into 4 quadrants of 20.5 mm inner and 48 mm outer radii . although each quadrant has 16 front rings ( 1.65 mm pitch ) and 4 azimuthal back sectors , for the experiment reported here the four quadrants were combined to form two semi - circles to reduce the total number of rings from 16@xmath154 to 16@xmath152 . the backward angles from 137.0@xmath9 to 169.4@xmath9 are covered by a 400 @xmath6 m thick double - sided silicon - strip detector ( dsssd ) based on 6-inch wafer technology and positioned 150 mm upstream of the target position . this detector is composed of six individual wedges ( fig . [ fig : photohybbar ] ) originally developed at oak ridge for the sihyball forward array @xcite . each wedge is divided into 16 strips facing the target and 8 azimuthal back sectors . the active area of a wedge is delimited by inner and outer radii of 28.11 mm and 140 mm , respectively , and spans approximately 55@xmath9 of the total azimuthal angle . the pitch of the rings is 5.3 mm and the polar angular range is close to 2 degrees per strip . the energy resolution , illustrated in fig . [ fig:3alphas]b , is typically @xmath1070 kev ( fwhm ) for 5.5 mev alpha particles . one of the critical features of the tiara array is the target changing mechanism ( fig . [ fig : target ] ) . the design of this mechanism has been chosen to maximise the solid angle coverage of the array . positioned upstream , just behind the sihyball , it offers the possibility to use four different targets during a run without breaking vacuum . the mechanism consists of a target storage wheel with 4 positions and a rod parallel and slightly offset to the beam axis . a set of clamps , four on the storage wheel and one at the extremity of the rod ( fig . [ fig : target ] ) are used to hold the target frames . the rod is driven along the beam axis via a ball screw . it first picks up a target from the wheel and continues its motion along the beam axis through the inner hole of the sihyball detector until the target position in the barrel is reached . the target frame is 3@xmath153 @xmath16 in area with a central hole of 20 mm diameter . it can only be positioned perpendicular to the beam axis , introducing some shadowing at 90@xmath9 in the barrel detector ( section 3.3 ) . the whole mechanism is controlled remotely and the position of both the wheel and the rod is monitored by optical readouts . four feed - throughs on the vacuum vessel are used for the target control system . the reaction chamber of tiara is made of aluminium and is some 56 cm long ( excluding the target mechanism ) . figure [ fig : photosetup ] shows the vessel in position in front of the vamos spectrometer and in the middle of the exogam support structure . the vessel presents a longitudinal diabolo shape with a central cylindrical section of 85 mm outer diameter housing the barrel and two 500 mm diameter cylindrical sections at each end housing the annular detectors . two aluminium end plates accommodating fischer dbpe 105-series feed - throughs ( 27 pins each ) and supporting kinematics plates for detector alignment complete the chamber . while one of the end - plates can accommodate up to 17 feed - throughs , the other one , which also includes two pipes for additional pumping , can accommodate up to 15 of them . given that 4 feed - throughs are already used for the target mechanism , a total of 28 feed - throughs can be used for the transmission of the detector signals . the tiara reaction chamber has been designed to allow a gamma - ray array such as exogam to be placed as close as possible to the target . as such , the thickness of the walls of the central section has been limited to 2 mm in order to reduce the @xmath1-ray attenuation to a minimum . for a photon energy of 1 mev , the linear attenuation coefficient in aluminium is 0.166 @xmath17 . this leads to an attenuation of 3.3@xmath5 in a 0.2 cm layer compare to 8@xmath5 in a 0.5 cm layer . there are 8@xmath152@xmath154 channels to be instrumented for the octagonal barrel , ( 16 rings + 8 sectors)@xmath156 channels for the sihyball detector , ( 16 rings + 8 sectors)@xmath152 channels for the s1 detector and ( 16 rings + 16 sectors ) channels for the s2 detector , resulting in a total of 288 channels" +"in a recent paper miller - jones et al . ( 2010 , here after m2010 ) present a detail study of an outburst of the x - ray binary ( xrb ) aquila x-1 ( aql x-1 ) . aql x-1 is a binary system of a k7v star and a neutron star ( ns ) that experiences repeated outbursts . m2010 discuss the outburst properties in the context of the transition from the hard state to the soft state and back , and plot the evolution of aql x-1 on the hardness - intensity diagram ( hid ) commonly used for outbursts of accreting black hole ( bh ) . during the canonical hard state of a bh xrb outburst , a steady optically thick compact jet is expected . during the hard to soft state transition ( and sometimes back the other way ) a major radio flare , brighter than the compact jet , occurs , and optically thin jet ejecta are often observed or inferred to be launched when the `` jet line '' is crossed ( e.g. , fender et al . 2009 ) . it is still not known whether the compact jet exist during the soft state . m2010 notice two significant differences between the outburst of aql x-1 and outbursts of bhs . these are the flat radio spectrum between 5 and 8 ghz , and the absence of bright , optically thin , relativistically moving knots . a major radio outburst is observed to occur during the hard - soft transition in the outburst of aql x-1 . however , during this transition , its spectrum is flat and no jet ejecta are seen . g2010 argue that during this transition only the compact jet is being observed . the presence of a compact jet in this transition may or may not be consistent with bh xrbs . it is the lack of transient , optically thin jet emission in this transition that is different from other bh xrb outbursts . in light of these differences and some similarity with solar flares , i speculate on an alternative interpretation to the radio and soft x - ray emissions ( but not to the hard x - ray emission preceding these two ) based on magnetic flares . the alternative interpretation of magnetic activity was discussed for an accreting white dwarf by soker & vrtilek ( 2009 ) . soker & vrtilek ( 2009 ) suggested that the radio emission from an outburst of the dwarf nova ss cyg reported by krding et al . ( 2008 ) originated from magnetic activity that formed a corona similar to coronae found in magnetically active stars , rather than from jets . soker & vrtilek ( 2009 ) based their claim on the results of laor & behar ( 2008 ; hereafter lb2008 ) , who found that when the ratio between radio and x - ray fluxes of accretion disks in radio - quiet quasars is as in active stars , @xmath0 , then most of the radio emission might come from coronae . in lb2008 , the radio luminosity is @xmath1 , usually at around 6 cm , while @xmath2 is the integrated x - ray luminosity in the range @xmath3 . jets might still occur . if the magnetic activity in erupting accreting disks is similar to that in active stars , then mass ejection , is expected . the presence of coronae above accretion disks ( e.g. , galeev et al . 1979 ; done & osborne 1997 ; wheatley & mauche 2005 ) , and the connection between coronae and jets ( e.g. , fender et al . 1999 ; markoff et al . 2005 ; rodriguez & prat 2008 ) has already been proposed . however , the results of ishida et al . ( 2009 ; also lb2008 ) put the presence of coronae in accretion disks on a solid ground , and further suggest that magnetic activity similar to that in active stars occur in these coronae . the speculative interpretation in the present letter ( section [ sec : flare ] ) is based on three properties of the november 2009 outburst of aql x-1 ( m2010 ) . i emphasize that i do not propose an alternative explanation to the hard ( @xmath4 ) x - ray peak , and in any case postpone its detail study for a future paper . in x - ray transients the hard x - ray peak can generally be accounted for by a disk instability as studied by dubus et al . ( 2001 ) . in the present case , the hard x - ray peak has a triangular shape ( see definition in chen et al . 1997 ) for @xmath5d . the radio peak appears during the decay phase of the hard x - ray emission . the soft ( rxte asm ; @xmath6 ) x - ray emission appears with the hard x - ray emission , but its large and rapid rise starts only after the radio peak ( see below ) . the two peaks , one in the hard x - ray followed by one in the soft x - ray , can be seen for another flare of aql x-1 in yu et al . ( 2003 ) , but they do not have radio observations . the two x - ray peaks do not resemble at all the secondary peaks discussed for x - ray novae by chen et al . ( 1997 ) , and must be explained by a different process . among xrb systems the double peak structure of the outburst is common , like xte j1859 + 226 ( brocksopp et al . 2002 ) in which the radio peak occurs at the start of the extended soft x - ray peak ; the hard x - ray peak occurs before the peaks of the radio and of the soft x - ray emissions ( brocksopp et al . such a structure is seen in solar flares as well . in the magnetic flare model the hard x - ray peak is related to the event that rapidly amplifies the magnetic field . this field later powers the radio and soft x - ray emissions . the appearance of the hard x - ray and soft x - ray peaks one after the other is quite similar to that seen in bh xrb systems , but it is not at all similar to the delay in rise to maximum between the optical and extreme uv and x - ray emissions in dwarf novae ( mauche et al . 2001 ; wheatley et al . 2003 ) . in aql the two peaks are separated , while in dwarf novae their behavior with time is more or less similar , with a relatively short delay . the disk instability can account for the delay in dwarf novae ( schreiber et al . 2003 ) , but here a different explanation is required . many solar flares , as well as of similar stars such as uv ceti ( gdel et al . 1996 ) , show the neupert effect ( neupert 1968 ) . this effect is a behavior where the integration of the radio flux ( and in many cases the non - thermal hard x - ray emission ) is proportional to the x - ray flux at rise . in some cases , the radio peak comes at the beginning of the x - ray rise . in figure [ fig : flare ] , i compare the behavior of one specific solar flare as compiled by gdel et al . ( 1996 ; more detail in cliver et al . 1986 , dennis & zarro 1993 , and benz & gdel 1994 ) , with the november 2009 outburst of aql x-1 ( m2010 ) in radio and soft x - ray emissions . the solar flare is a gradual hard x - ray burst ( ghb ) of april 26 , 1981 ( cliver et al . 1986 ) . in many cases ghbs are preceded by coronal mass ejection and with a hard x - ray peak . the flux units are in relative units , while each time unit is 1 hour for the solar flare , and 7.1 weeks for aql x-1 . namely , a ratio of 170 in the time scale . radio fluxes are in thin lines and x - ray fluxes are in thick lines . aql x-1 is depicted by a blue dashed line , while the solar flare is shown with a red solid line . note that the aql x-1 radio intensity was multiplied by 600 , as the ratio @xmath7 is @xmath8 times weaker in aql x-1 as in the solar flare that is shown . + 3.5 cm ) fluxes in relative units of aquila x-1 november 2009 outburst ( from m2010 ; blue dashed line ) , and a solar flare from april 26 , 1981 as compiled by gdel et al . ( 1996 ; red solid line ; @xmath9 ) . for aql x-1 there are three radio segments , where the left one is only an upper limit . the ratio of radio to x - ray in aql x-1 is @xmath8 times smaller than that in the solar flare . in the plot , the aql x-1 radio flux was multiplied by 600 . each time unit is one hour for the solar flare and 7.1 days for aql x-1 . , title=""fig : "" ] i note the following similarities between the bursts in these two vastly different systems : 1 . the general shape of the radio ( 3.6 cm-6 cm ) and the soft ( @xmath6 ) x - ray emissions is similar , with a ratio of @xmath10 in time scale between the two systems . the beginning of the soft x - ray emission appears before the radio . part of this early rise might be a contribution from the hard x - ray component . however , from the different behavior of the two components , some of the early rise is part of the soft x - ray component itself . however , the steep rise in x - ray flux comes only after the radio peak . the rise to maximum in radio flux is slightly faster than the decline . 5 . in the 1981 april 26 solar ghb there is a hard x - ray peak preceding the radio peak ( fig . 1 in cliver et al . 1986 ; fig . 7 in dennis & zarro 1993 ) . this is similar to the hard x - ray peak preceding the radio peak in aql x-1 . however , i do not claim the same explanation for the hard x - ray peaks in the two systems . i only claim that the hard x - ray emission is connected to the process that powers the radio and soft x - ray peaks that follow . there is a weaker second radio peak in the light curve of aql x-1 . the popular accretion disc - radio jet paradigm ( the spectral state transition paradigm ) predicts reflaring in radio as the source hardens . the magnetic flare interpretation proposed here , on the other hand , requires the presence of a second flare . indeed , the small radio peak precedes a major x - ray flare that has its x - ray peak 24 days after the second radio peak ( swift / bat hard x - ray transient monitor home - page ) . it is possible that a larger radio peak was presence closer to the second x - ray peak , but no radio data" +"my keynote talk was similar in content to a recent talk at a sacramento peak workshop celebrating the 70th birthday of robert f. stein . this written version builds to a large extent on that writeup @xcite , but it is updated and some sections have been expanded . before discussing models of the solar chromosphere it is worthwhile discussing the very definition of the term `` chromosphere '' . the name comes from the greek words `` @xmath0 '' ( color ) and `` @xmath1 '' ( ball ) alluding to the colored thin rim seen above the lunar limb at a solar eclipse . the color comes mainly from emission in the balmer h@xmath2 line . this is thus one possible definition the chromosphere is where this radiation originates . at an eclipse this region has a sharp lower edge , the visible limb , but a fuzzy upper end with prominences protruding into the corona . the nature of this region is difficult to deduce from eclipse observations since we see this region edge on during a very short time span and we have no way of telling whether it is homogeneous along the line of sight or very inhomogeneous in space and time . it was early clear that the emission in h@xmath2 must mean an atmosphere out of radiative equilibrium without extra heating the temperature will not be high enough to have enough hydrogen atoms excited to the lower or upper levels of the transition . early models were constructed to explain observations in h@xmath2 and in resonance lines from other abundant elements with opacity high enough to place the formation in these regions even in center - of - disk observations ( lines like the h and k resonance lines from singly ionized calcium ) . these early models were constructed assuming one dimensional plane - parallel geometry and they resulted in a temperature falling to a minimum around 4000k about 500 km above the visible surface , a temperature rise to 8000k at a height of about 2000 km and then a very rapid temperature rise to a million degree corona . these plane - parallel models have led to a common notion that there is a more or less homogeneous , plane - parallel region between these heights that is hotter than the temperature minimum . in such a picture the chromosphere may be defined as a region occupying a given height range ( e.g. between 500 and 2000 km height over the visible surface ) or a given temperature range . we may also use physical processes for our definition : the chromosphere is the region above the photosphere where radiative equilibrium breaks down and hydrogen is predominantly neutral ( the latter condition giving the transition to the corona ) . this discussion shows that there is no unique definition of the term `` chromosphere '' , not even in a one - dimensional , static world . it is even more difficult to agree on a definition of the `` chromosphere '' that also encompasses an inhomogeneous , dynamic atmosphere . as mentioned above , the first models of the chromosphere were constructed with a large number of free parameters to match a set of observational constraints . since some equations are used to restrict the number of free parameters ( not all hydrodynamical variables at all points in space and time are determined empirically ) we call this class of models _ semi - empirical _ models . typically one assumes hydrostatic equilibrium and charge conservation but no energy equation . the temperature as function of height is treated as a free function to be determined from observations . in the other main class of models one tries to minimize the number of free parameters by including an energy equation . such theoretical models have been very successful in explaining radiation from stellar photospheres with only the effective temperature , acceleration of gravity and abundances as free parameters . in the chromosphere , an additional term is needed in the energy equation e.g. energy deposition by acoustic shocks or energy input in connection with magnetic fields ( e.g.currents or reconnection ) . it is thus clear from observations that the chromosphere is not in radiative equilibrium there is a net radiative loss . this loss has to be balanced by an energy deposition , at least averaged over a long enough time span , if the atmosphere is to be in equilibrium . this is often called the problem of chromospheric `` heating '' . it is important to bear in mind , though , that the radiative losses may be balanced by a non - radiative energy input without an increase in the average temperature . the term `` chromospheric heating '' may thus be misleading since it may be interpreted as implying that the average temperature is higher than what is the case in a radiative equilibrium atmosphere . in the following we will use the term `` heating '' in a more general sense : a source term in the energy equation , not necessarily leading to an increased temperature . chromospheric heating is needed not only for the quiet or average sun but also in active regions , sunspots and in the outer atmospheres of many other stars . i will in the following mainly discuss the quiet sun case . the outline of this paper is as follows : in section 2 we discuss semi - empirical models of the chromosphere . in section 3 we discuss theoretical models ; first we elaborate on 1d hydrodynamical models , then we discuss the role of high frequency acoustic waves for the heating of the chromosphere and finally we describe recent attempts to model the chromosphere in 3d including the effects of magnetic fields . semi - empirical models can be characterized by the set of observations used to constrain the model , the set of physical approximations employed and the set of free parameters to be determined . spectral diagnostics used to constrain chromospheric models must have high enough opacity to place the formation above the photosphere . the continuum in the optical part of the spectrum is formed in the photosphere so the only hope for chromospheric diagnostics lies in strong spectral lines in this region of the spectrum . candidates are resonance lines of dominant ionization states of abundant elements and lines from excited levels of the most abundant elements ( hydrogen and helium ) . most resonance lines are in the uv but the resonance lines of singly ionized calcium ( caii ) , called the h and k lines , fulfill our criteria . these lines originate from the ground state of caii , the dominant ionization stage under solar chromospheric conditions , and the opacity is therefore given by the density directly and the optical depth is directly proportional to the column mass ( i.e. to the total pressure in hydrostatic equilibrium ) . also the source function has some coupling to local conditions even at quite low densities ( in contrast to the strongly scattering resonance lines of neutral sodium ) . other chromospheric diagnostic lines in the optical region are the hydrogen balmer lines and the helium 1083 nm line . they all originate from highly excited levels and thus have very temperature sensitive opacity . the population of he1083 is also set by recombination such that its diagnostic potential is very difficult to exploit . with the advent of space based observatories , the full uv spectral range was opened up . continua shortward of the opacity edge from the ground state of neutral silicon at 152 nm are formed above the photosphere and can be used to constrain chromospheric models . together with observations in ly-@xmath2 , such uv continuum observations were used by @xcite in their seminal series of papers on the solar chromosphere . the val3 paper @xcite is one of the most cited papers in solar physics ( 1072 citations in ads at the time of writing ) and the abstract gives a very concise description of the models and the principles behind their construction : `` the described investigation is concerned with the solution of the non - lte optically thick transfer equations for hydrogen , carbon , and other constituents to determine semi - empirical models for six components of the quiet solar chromosphere . for a given temperature - height distribution , the solution is obtained of the equations of statistical equilibrium , radiative transfer for lines and continua , and hydrostatic equilibrium to find the ionization and excitation conditions for each atomic constituent . the emergent spectrum is calculated , and a trial and error approach is used to adjust the temperature distribution so that the emergent spectrum is in best agreement with the observed one . the relationship between semi - empirical models determined in this way and theoretical models based on radiative equilibrium is discussed by avrett ( 1977 ) . harvard skylab euv observations are used to determine models for a number of quiet - sun regions . '' the val3 models are thus characterized by them using ly-@xmath2 and uv - continuum observations for observational constraint , hydrostatic equilibrium and non - lte statistical equilibrium in 1d as physical description and temperature as function of height as free function . to get a match with observed line - strengths , a depth - dependent microturbulence was also determined and a corresponding turbulent pressure was added . the number of free parameters to be determined by observations is thus large in principle the number of depth - points per depth - dependent free function ( temperature and microturbulence ) . in practice the fitting was made by trial and error and only rather smooth functions of depth were tried thus decreasing the degrees of freedom in the optimization procedure . the models have a minimum temperature around 500 km above the visible surface ( optical depth unity at 500 nm ) , a rapid temperature rise outwards to about 6000k at 1000 km height and thereafter a gradual temperature increase to 7000k at 2000 km height with a very rapid increase from there to coronal temperatures . the caii lines were not used in constraining the val3 models and the agreement between the model representing the average quiet sun , val3c , and observations of these lines was not good . an updated model with a different structure in the temperature minimum region was published in @xcite ( where the main emphasis was on similarly constructed semi - empirical models for sunspot atmospheres ) . a peculiar feature with the val models was a temperature plateau introduced between 20000 and 30000k in order to reproduce the total flux in the lyman lines . this plateau was no longer necessary in the fal models where the semi - empirical description of the transition region temperature rise was replaced by the balance between energy flowing down from the corona ( conduction and ambipolar diffusion ) and radiative losses @xcite . one goal of semi - empirical models is to obtain clues as to the non - radiative heating process . from the models it is possible to calculate the amount of non - radiative heating that is needed to sustain the model structure . for the val3c model this number is 4.2 kwm@xmath3 with the dominant radiative losses in lines from caii and mgii , with ly-@xmath2 taking over in the topmost part . the models described so far do not take into account the effect of the very many iron lines . this was done in modeling by @xcite . instead of using the temperature as a free parameter and observations as the constraints , they adjusted the non - radiative heating function until they obtained the same temperature structure as in the val3c model ( arguing" +"after the well known leading paper by morris and thorne @xcite , considerable attention has been devoted to the study of traversable lorentzian wormholes @xcite . such kind of geometries would connect two regions of the same universe , or of two universes , by a traversable throat . if they actually exist , they would present some features of particular interest as , for example , the possibility of using them for time travel @xcite . however , the flare - out condition @xcite to be satisfied at the throat requires the presence of exotic matter , that is , matter which violates the null energy condition ( nec ) @xcite . however , it was shown in ref . @xcite that the amount of exotic matter necessary for the existence of a wormhole can be made infinitesimally small by suitably choosing the geometry . after this , special attention has been devoted to quantifying the amount of exotic matter @xcite ; in particular , this amount has been pointed as an indicator of the physical viability of a traversable wormhole @xcite . besides , for a wormhole to be considered traversable , the geometry must be such that the magnitude of tidal forces are admissible for an hypothetic traveller ; this has also been analyzed for most physically meaningful configurations studied in the literature . of course , no unstable solution of the equations of gravitation could be of interest as a candidate for a traversable wormhole . thus , besides the characterization of static solutions , their stability under perturbations must always be explored . in particular , this has been thoroughly studied for the case of small perturbations preserving the symmetry of the original configuration . a class of wormholes for which poisson and visser @xcite developed a straightforward approach for analyzing this aspect are thin - shell ones , that is , wormholes which are mathematically constructed by cutting and pasting two manifolds to obtain a geodesically complete new manifold @xcite . in these wormhole configurations the exotic matter lies in a shell placed at the joining surface ; so the theoretical framework for dealing with them is the darmois israel formalism , which leads to the lanczos equations , that is , the einstein s equations projected on the joining surface @xcite . once an equation of state for the exotic matter in the shell is provided , the solution of the lanczos equations gives the dynamical evolution of the wormhole . such a procedure has been subsequently followed to study the stability of more general spherically symmetric configurations ( see , for example , refs . @xcite ) . according to present day theoretical developments , a scenario in which the fundamental building blocks of nature are extended objects instead of point objects should be considered quite seriously . in particular , 1dimensional objects ( strings ) are the most popular candidate for such fundamental objects . the study of the gravitational effects of matter in the form of clouds of both cosmic and fundamental strings has then deserved considerable attention ; see for example refs . we are interested in the viability of wormholes ; so within this framework any reasonable configuration including more parameters and thus allowing for improving its features as : amount of exotic matter , pressure , traversability and stability , deserves to be analyzed . in the present work we start from the metric proposed in the leading paper by letelier @xcite to address the study of thin - shell wormholes associated to a string cloud ( and also a global monopole ; see below ) . we study in detail the amount of exotic matter required for the construction , the traversability and also the stability of the configuration under perturbations preserving the original symmetry . as we shall see , comparing with the schwarzschild case , the string cloud allows for more freedom in the choice of the configurations to be stable , and also allows to reduce the amount of exotic matter without increasing the pressure . because recently certain attention was devoted to exotic matter fulfilling the chaplygin gas equation of state , in appendix a we explicitly impose it on the shell matter to obtain its time evolution beyond a perturbative approach . in appendix b we discuss a possible extension of the analysis to a related geometry . throughout the paper we set units so that @xmath0 . the action of a string evolving in spacetime is given by @xmath1 where @xmath2 is a constant characterizing each string , @xmath3 , @xmath4 are a timelike and a spacelike parameter , and @xmath5 is the determinant of the induced metric on the string world sheet : @xmath6 introducing the bivector @xmath7 with @xmath8 the two - dimensional levi civita symbol , the lagrangian density @xmath9 can be put as @xmath10 with this notation , a cloud of strings is described by the energy - momentum tensor @xmath11 where @xmath12 is the proper density of the cloud . the quantity @xmath13 is gauge invariant , and is called the _ gauge invariant density _ of the cloud @xcite . in the case of a static spherically symmetric cloud , we have @xmath14 with @xmath15 a positive constant . the general solution to einstein s equations for a string cloud with spherical symmetry in ( 3 + 1)-dimensional spacetime , that is with density given by ( [ rho0 ] ) , takes the form @xcite @xmath16 where @xmath17 this metric represents the spacetime associated with a spherical mass @xmath18 centered at the origin of the system of coordinates , surrounded by a spherical cloud of strings . besides , it can also be understood as the metric associated to a global monopole , which increases the interest of starting from it to construct a wormhole ( for the details see refs . @xcite , and for a related work involving a traversable wormhole see ref . the event horizon of this metric is placed at @xmath19 where @xmath20 . if @xmath15 is less than unity we have that the cloud of strings enlarges the schwarzschild radius of the mass by the factor @xmath21 . when @xmath22 the metric represents a homogenous spacetime . the cloud of strings alone @xmath23 does not have horizon ; it only presents a naked singularity at @xmath24 . in fig . 1 we show where the event horizon is located and how this changes with the parameter @xmath15 . when @xmath25 we recover the schwarzschild radius and for @xmath15 close to unity the event horizon radius tends to infinity . is shown . we can see how the position of the event horizon changes when the parameter @xmath15 varies within the range @xmath26,height=377 ] now we build a spherically symmetric thin - shell wormhole starting from the generic geometry ( [ 1 ] ) ( see fig . we take two copies of the string cloud spacetime and remove from each manifold the four - dimensional regions described by @xmath27 the resulting manifolds have boundaries given by the timelike hypersurfaces @xmath28 then we paste or identify these two timelike hypersurfaces to obtain a geodesically complete new manifold @xmath29 with a matter shell at the surface @xmath30 , where the throat of the wormhole is located . this manifold is constituted by two asymptotically _ locally _ flat regions connected by a traversable lorentzian wormhole . and @xmath31 , for @xmath32 when @xmath25 . after the boundaries are identified we get a geodesically complete new manifold with a matter shell at @xmath30.,height=302 ] to study this class of wormhole we use the standard darmois israel formalism @xcite . the wormhole throat is placed at the surface @xmath33 . this is a synchronous timelike hypersurface . we can introduce coordinates @xmath34 in @xmath33 , with @xmath35 the proper time on the throat . in order to be able to perform a quite general analysis ( for example , to study the mechanical stability of the configuration ; see below ) , we allow the radius of the throat be a function of the proper time , @xmath36 . this is strictly right because the existence of a generalized birkhoff theorem for the string cloud @xcite ensures that the metric of the embedding remains the same independently of the motion of the throat , as long as the spherical symmetry is preserved . so , the boundary hypersurface reads : @xmath37 the second fundamental form ( extrinsic curvature ) at the two sides of the throat is given by @xmath38 where @xmath39 are the unit normals ( @xmath40 ) to the surface @xmath33 in @xmath29 . defining the jump in the extrinsic curvature as @xmath41={k}^{+}_{il}-{k}^{-}_{il}$ ] and its trace as @xmath42)$ ] we obtain the so - called lanczos equations : @xmath43+{k}g_{il}=8\pi{s_{il}}\ ] ] where @xmath44 is the surface stress - energy tensor of the shell placed at the throat . the non vanishing components of the extrinsic curvature are : @xmath45 @xmath46 where the dot means derivation with respect to the proper time @xmath35 , and a prime stands for a derivative with respect to @xmath47 . then , from eqs . ( 8) , ( 9 ) and ( 10 ) we get a formal expression for the pressure @xmath48 and the energy density @xmath49 in terms of @xmath50 , first and second derivatives of @xmath50 , and the function @xmath51 which depends on the parameters of the system @xmath52 : @xmath53 @xmath54 where the prime means derivation with respect to @xmath47 . as it was to be expected , the energy density is negative , indicating the existence of exotic matter at the shell . we shall focus on this aspect of the wormhole in the next section . it is easy to see from eqs . ( 11 ) and ( 12 ) that the energy conservation equation is fulfilled : @xmath55 where @xmath56 is the area of the wormhole throat . the first term in eq . ( 13 ) represents the internal energy change of the shell and the second the work by internal forces of the shell . the dynamical evolution of the wormhole throat is governed by the lanczos equations and to close the system we must supply an equation of state @xmath57 that relates @xmath58 and @xmath59 . in section 4 we shall develop this point in a perturbative approach , while in the appendix we shall obtain the dynamical evolution of the throat for a particular equation of state . many authors ( see for instance refs . @xcite ) have proposed to quantify the amount of exotic matter as a way to characterize the viability of a traversable wormhole . here we shall analyze the energy conditions and evaluate the total amount of exotic matter for the wormholes built in section 2 , in the case of static configurations , i.e. , @xmath60 . in this case , the energy density and pressure are @xmath61 @xmath62 the _ weak energy condition _ ( wec ) states that for any timelike vector @xmath63 it must be @xmath64 ; the wec also implies , by continuity , the _ null energy condition _ ( nec ) , which means that for any null vector @xmath65 it mus be @xmath66 @xcite . in an orthonormal basis the wec reads @xmath67 , @xmath68 , while the nec takes the form @xmath69 . in the case of the wormhole constructed in section 2 we have that the radial pressure is zero , @xmath70 , and the energy density verifies @xmath71 , so that both energy conditions are violated . the transverse pressure is @xmath72 and the sign of @xmath73 is not fixed by this conditions , but it depends on the values of the parameters of the system . there have been several proposals for quantifying the amount of exotic matter in wormholes . in" +"nearest neighbor search in very large databases is becoming increasingly important in machine learning , computer vision , pattern recognition , and multimedia retrieval along with many applications in document , image , audio , and video retrievals @xcite . however , it becomes difficult to efficiently store and search huge collections when the dataset size gets larger and larger ( e.g. millions or even billions ) . the idea of mapping real - valued vectors to compact codes @xcite provides a very attactive way to solve this problem . there have been many recent methods on developing hashing methods for compressing data to compact binary strings @xcite , or vector quantization based methods @xcite that compress data to compact codes . vector quantization ( vq ) was actively studied for source coding / signal compression under real - time constraints dating back to decades ago @xcite . recently , the problem of how to apply vq techniques to efficient approximate nearest neighbor ( ann ) search has attracted a lot of attension @xcite . while many structured vq models can be found @xcite , in this paper , we restrict our attention to product quantization ( pq ) and residual quantization ( rq ) , which both have been successfully applied to fast nearest neighbor search @xcite . product quantization works by grouping the feature dimensions into groups , and performs quantization to each feature group . in particular , it performs a @xmath0-means clustering to each group to obtain sub - codebooks , and the global quantization codebook is generated by the cartesian products of all the small sub - codebooks . in this way , it can generate a huge number of landmark points in the space , which guarantees low quantization error ; it has achieved state of the art performance on approximate nearest neighbor search @xcite , and can also provide a compact representation to the vectors . inspired by the success of pq , some latest works have extended pq to a more general model by finding an optimized space - decomposition to minimize its overall distortion @xcite . a very recent work @xcite has deployed this optimized pq within residual clusters . while it maximizes the strength of locality , it also uses extra space for multiple transformations as well as pq codebooks . different from pq , rq works by performing quantization to the whole feature space , and then recursively apply vq models to the residuals of the previous quantization level , which is a stacked quantization model . in particular , it performs a @xmath0-means clustering to the original feature vectors , and construct @xmath0 clusters . for points in each cluster , it computes the residuals between points and the cluster centers . in the next level , it aggregates all the residual vectors for all points , and performs another clustering to these residual vectors . this process is recursively applied ( stacked ) for several levels . in this way , rq produces sequential - product codebooks . a comprehensive survey of earlier rq models can be found in barnes et al . recent works have shown the effectiveness of rq to perform both indexing @xcite and data compression @xcite tasks in ann search problems . however , it has been observed that the effectiveness of rq might be limited to a very small number of levels @xcite , and the randomness of residual vectors increases very quickly when we stack more and more rq layers . this results in increasingly noisy residual vectors of each level , and effective quantization at higher rq levels becomes more difficult . in other words , the layer - wise learning in rq models provides suboptimal sub - codebooks in that each sub - codebook is learned without consideration to subsequent layers . thence several global optimization approaches have been proposed by jointly learning sub - codebooks over all layers @xcite . different from seeking out joint optimization solutions , we here look for specific transformations to each of the residual clusters to make the resulting vectors more aligned , in order to directly address the problem of cluster misalginment and noise increase over each level after the first and improve overall quantization accordingly . to this end , we propose a novel approach to optimizing the rq model that is motivated by the noise and shape in the residual space , as shown in figure [ figure : orq - example ] . we find that the residual vectors for each cluster have significantly different directions , which make quantization at the next level much harder . a natural idea is to align these residual vectors for each cluster , which can potentially reduce quantization error in the next level . thus , we propose to learn one rotation matrix for each residual cluster , and use them to align the residual vectors in each cluster , so as to reduce the global quantization error . then we alternate between learning rotation matrices and the residual quantization to minimize its distortion , which is mainly inspired by `` iterative quantization ( itq ) '' @xcite ; very recently itq has been successfully applied to the pq models @xcite . different from itq and the optimized pq ( opq ) , which learn a global rotation , both ours and the locally optimized pq ( lopq ) @xcite learn one projection matrix per residual cluster . in stead of independent learning in lopq , however , all local transformations in our method are learned associatively with a shared codebook . in this way , we successfully reduce the memory overheads about codebook usage in lopq . this offers a great flexibility to use reasonable larger codebooks in potential . we have found that by doing this iterative alignment and quantization , we can achieve significantly smaller quantization error than both vanilla rq and opq methods . in addition , we also propose a hybrid ann search method which is based on the proposed trq and pq . experimental results on several large - scale datasets have clearly demonstrated the effectiveness of our proposed methods , in particular have shown that the extra transformations only introduced very limited computation overheads when integrated with advanced indexing structures , e.g. the inverted mutli - index @xcite . therefore , our method is able to achieve very significant gain over other state of the art methods in terms of trade - off among memory usage , search quality and speed . in this section , we review related background on two types of structured vector quantization , i.e. product quantization and residual quantization . to accurately quantize large number of points in a high dimensional space , we need a large number of landmark points ( or centroids ) . for example , if we use the @xmath0-means clustering method to find such quantizers , when the number of cluster centers @xmath0 becomes huge ( e.g. millions or even more ) , performing @xmath0-means becomes prohibitively expensive . structured vector quantization make special assumptions about the data distribution , and try to explore such structure to generate large number of landmark points to increase the quantization accurateness @xcite . pq and rq are two structured vq families with different assumptions about data distribution . we here present discussions on structural codebook constructions and objective function formulations of the related vq models following a brief introduction of the unstructured vq . vector quantization ( vq a.k.a . @xmath0-means ) without any structure constraints is probably one of the most widely used vector quantization method . given a dataset @xmath1 , vq is a mapping : @xmath2 where @xmath3 is a quantizer and @xmath4 is a _ centroid _ or a _ center _ from the codebook @xmath5 . according to lloyd s optimality conditions , an optimal quantizer satisfies the nearest neighbor condition : @xmath6 here @xmath7 is the distance between two vectors and euclidean distance is used in this paper . for each centroid , a set of data points will be assigned to it , and forms a cluster . according to the second optimal condition , a centroid is computed as : @xmath8 we estimate the codebook centers to minimize the objective function : the mean squared error ( mse ) @xmath9 while the globally optimal solution of the above problem is np - hard , it can be solved by heuristic alternatives . the best known approach is the @xmath0-means algorithm @xcite , in which the above two conditions are optimized alternatively . product quantization assumes that certain groups of features are independent with each other , and explores this assumption to generate a large number of landmark points by grouping the feature space into @xmath10 groups ( each group is a subspace ) . by quantizing each of the subspaces separately using sub - quantizer @xmath11 , it produces an implicit codebook as a cartesian product of @xmath10 small sub - codebooks , @xmath12 . in this case , codebook @xmath5 can provide an exponentially large number of cluster centers while retains a linear size of storage . given a data point @xmath13 , it estimates the globally nearest center by concatenating all its nearest sub - centers from the sub - codebooks as @xmath14 . the mse of this product quantizer can be estimated as : @xmath15 the degradation of pq performance can be severe if there are substantial statistical dependences among the feature groups @xcite ; recent works have shown that such dependences could be reduced , to some extent , by more careful space - decomposition @xcite . their works extended the idea from iterative quantization @xcite to the pq scheme that learn an rotation to transform the data to reduce the dependences between feature groups . for example , the work from @xcite jointly seeks a whole space rotation @xmath16 and pq codebooks @xmath5 by minimizing @xmath17 @xmath18 residual quantization ( rq ) has a different assumption in that it does not assume the features are independent , but assumes the quantization residuals of the first level quantizer can be further quantized . thus , it is a stacked quantization model . for the first level , rq simply uses a @xmath0-means clustering to quantize the data , and assign them to @xmath0 centers . for each data point , by subtracting from the assigned centroid , we can collect their residual vectors as @xmath19 . then @xmath20 will be used as the input to the next level , and we again use @xmath0-means - means is a basic choice . ] to quantize the residual vectors . by repeating this for @xmath21 times , we can have a sequential product codebook @xmath22 . given an input vector @xmath13 , by computing the nearest center at each level , we can get a sequence of indexes @xmath23 . the globally nearest center for @xmath13 here becomes a direct sum of all the sub - centers @xmath24 . simply considering one level , we represent @xmath13 at level @xmath25 as @xmath26 where @xmath27 . then the residual vector from level @xmath25 is @xmath28 the mse for a @xmath21-level rq is @xmath29 the most important advantage of rq is that it does not make the unrealistic assumption that the features are statistically independent . in addition , it holds a non - increasing property , that is , adding a level will always reduce the mse error . as discussed above , residual quantization recursively performs quantization on residual vectors from previous levels . in other words , all the residual vectors from different clusters are collected and fed into the same quantizer in the next level . as shown in figure [ figure : orq - example ] ( b ) , the residual clusters can have different shapes , orientations , or scales , which makes" +"the large area telescope ( lat ) , on board the _ fermi _ gamma - ray space telescope @xcite , is a pair - conversion @xmath0-ray telescope , sensitive to photon energies from about 20 mev up to @xmath1 gev . the lat consists of a tracker ( two sections , front and back ) , a calorimeter and an anti - coincidence system to reject the charged - particle background . _ fermi _ lat , working in all - sky survey mode , is an optimal hunter for high - energy flares , transients and new gamma - ray sources , and is an unprecedented monitor of the variable @xmath0-ray sky , thanks to the large peak effective area , wide field of view ( @xmath2 sr ) , improved angular resolution and sensitivity . 0.0 cm 0.3 cm this all - sky monitoring is complemented by the flare advocate ( a.k.a . gamma - ray sky watcher , fa - gsw ) duty , a scientific service belonging to the lat instrument science operations and devoted to quicklook inspection and daily review of the gamma - ray sky observed by _ lat , performed with continuity for all the year through weekly shifts . 0.0 cm the fa - gsw service points out basic facts and information about the @xmath0-ray sky of potential interest for the lat internal science groups , through a day - by - day inspection and review of the all - sky photon count maps collected and of the quicklook science pipeline results . summaries about the sky surveyed and monitored by _ fermi _ lat , transients , flaring and new sources on six - hour and 1-day time intervals are communicated along with any relevant news to the external multiwavelength ( mw ) astrophysical community using the lat - mw mailing - list . furthermore astronomer s telegrams ( atels ) , automatic burst gcns and special gcns for blazar flares are distributed in addiction to weekly summary reports in the `` fermi sky blog '' ( fig . [ fig : fermiskyblog ] ) . thanks to this service joined with the public distribution of lat data at the fssc the _ fermi _ lat collaboration is therefore able to promote and increase the rate of multifrequency collaborations and observations , maximizing the scientific return and rate of international scientific cooperation of the _ fermi _ mission . first seeds for variability and mw follow - up and studies are often triggered by the fa - gsw activity ( see the lat mw coordinating group and @xcite ) . this activity is based on the automated quicklook data analysis of level 2 ( l2 ) at the _ fermi _ lat instrument science operation center ( isoc ) of slac - stanford ( fig . [ fig : schemeblocks.eps ] ) . l2 processing ( instrument monitoring pipeline , background monitoring , and quick look science analysis ) is triggered by the first availability of level 1 ( l1 ) processed data and performed on longer time intervals ( six hour , 1 day and 1 week ) referred therefore as automated science processing ( asp ) . the asp analysis pipeline running on the final astrophysical science data ( photon event files ft1 , and spacecraft data files ft2 fits files ) is composed of several scientific tasks ( fig . [ fig : schemeblocks.eps ] , and @xcite ) : 0.0 cm .the 159 atels posted divided for topics . [ cols=""<,^"",options=""header "" , ] [ table : ateltypes ] * automatic analysis of gamma - ray bursts ( impulsive transients ) through refinement of parameters for lat - detected grbs , detection and characterization of grbs not detected onboard , search and analysis of delayed high - energy afterglow emission ; * flux history monitoring based on maximum - likelihood method ( gtlike science tool ) of predefined list of sources ( called data release plan , drp , sources ) with subsequent addictions of publicly announced sources ( like flaring blazars subject of atels ) ; * blind guess - detection on all - sky photon counts maps accumulated in 6-hours , 1-day , 1-week intervals , through a fast method based on two - dimensional mexican hat wavelet transform , thresholding and sliding cell algorithms @xcite ; * transient and flare identification based on variability test ; * interactive lat source catalogs ; * multi - mission / multifrequency tools and archives ( like the error circle explorer and the spectral energy distribution builder ) linked to asp and provided by the asi science data center ( asdc , roma ) . 0.0 cm * gamma - ray flare advocate task . flaring sources approaching a daily flux of @xmath3 photons @xmath4 s@xmath5 deserves attention ( detection , localization , flux , photon index checked , photon counts maps and exposure maps are outlooked ) . internal / public notes , atels , target of opportunity ( too ) are submitted , mw observing campaigns are organized when needed . * gamma - ray sky watcher task . results from the lat automated science processing ( asp ) pipeline in 1-day and 6-hour time intervals are checked , searching for transients , increasing / decrasing brightness trends , and new @xmath0-ray source candidates and spatial associations . fa - gsws discovered new gamma - ray blazars before the release of _ fermi _ catalogs , discovered several bright flares and outbursts from blazars , some transient from low galactic latitude source , observed the emission of the quiet - sun and the flaring - sun emission . in multifrequency science fa - gsws triggered several targets of opportunity ( toos ) with the _ swift _ satellite ( about a dozen per year ) and involved the radio - astronomy community in joint observing programs . mw observing campaigns on several blazar and galactic source targets were also performed . in table [ table : ateltypes ] and fig.[fig : atelstastistics ] basic statistics about the 159 astronomical telegrams ( atels ) published on behalf of the fermi lat collaboration from july 24 , 2008 ( atel#1628 ) to august 24 , 2011 ( atel#3580 ) are illustrated . the average rate of published atels is about one per week / shift . more in detail the substantial menu of discoveries triggered by the fa - gsw service is : many flares from @xmath0-ray blazars ( the extraordinary outbursts of 3c 454.3 fig . [ fig:3c454 ] and @xcite large flares of pks 1510 - 089 , 4c 21.35 , pks 1830 - 211 , ao 0235 + 164 , pks 1502 + 106 , fig . [ fig : pks1502 ] , 3c 279 , 3c 273 , pks 1622 - 253 , 3c 66a , etc . ) ; short / long activity duty cycles of bright @xmath0-ray blazars ; unidentified transients near the galactic plane ( like j0910 - 5041 , j0109 + 6134 , galactic center region ) or associated to galactic sources ( like the crab nebula , the nova v407 cyg fig . [ fig : v407cyg ] and @xcite , the microquasar cyg x-3 , the binary star system 1fgl j1018.6 - 5856 ) , intense mev emission from the quiet and active sun . the all - sky variability monitor of _ fermi _ and the continuous day - by - day service performed by fa - gsws represents the liaison between the fermi lat collaboration and the mw astrophysical / astroparticle community , always invited to observe fermi lat sources and to propose mw collaborations ." +"the study of the velocity gradient tensor in fully developed turbulence has lead to interesting findings and has contributed to improved understanding of many statistical and geometrical properties of turbulent flows . in particular , recent progress has been made in the study of the lagrangian dynamics and modeling of the velocity gradient tensor ( see ref . @xcite for an overview of the subject ) . this tensor is given by @xmath1 , where * u * is the velocity vector . taking a spatial gradient of the navier - stokes equations , the following transport equation for * a * is obtained : @xmath2 where @xmath3 stands for the lagrangian time derivative , @xmath4 is the kinematic viscosity and @xmath5 is the pressure hessian . the first term @xmath6 is the self - stretching term . the restricted euler ( re ) approximation , which assumes an isotropic pressure hessian @xmath7 and neglects viscous effects , leads to an autonomous set of coupled ordinary differential equations @xcite . the intrinsic dynamics of the re system leads to a finite time divergence of the components of * a * during which the vorticity @xmath8 gets aligned with the eigenvector of the rate of strain , @xmath9 , associated with the intermediate eigenvalue , as often observed in real turbulence @xcite . to prevent the development of unphysical finite time singularities , both the anisotropic part of the pressure hessian and the viscous diffusion term have to be modeled this was the subject of former works @xcite . in particular , closures were proposed in ref . @xcite for @xmath10 and @xmath11 in terms of the local value of * a*. the local closures of ref . @xcite , when inserted into the dynamics generated by eq . ( [ eq : nsa ] ) under the action of a stochastic forcing term , lead to stationary statistics of * a * along lagrangian trajectories which compare well with those obtained from direct numerical simulations ( dns ) of the navier - stokes equations at moderate reynolds numbers @xcite . at higher reynolds numbers , predictions of the stochastic model proposed in refs . @xcite turn out to become unrealistic , mainly because of the weakness of the closure for the anisotropic part of the pressure hessian . indeed , the pressure hessian is related to the spatial distribution of the velocity gradient using singular integral operators @xcite according to : @xmath12 above , the integral is understood as a cauchy principal value ( p.v . ) and @xmath13 is the hessian of the green s function for the laplacian operator , namely @xmath14 one can see from eq . ( [ eq : soph ] ) that only the isotropic part of the pressure hessian is purely local ( the first term on the right - hand side ( rhs ) of eq . ( [ eq : soph ] ) ) . all the nonlocal effects of pressure hessian enter through the anisotropic part ( or deviatoric part corresponding to the second term in the rhs of eq . ( [ eq : soph ] ) ) . hence , in this view , the re approximation can be understood as the neglect of all the nonlocal effects implied by the incompressibility condition ( or pressure field ) . in order to quantify the precise action of pressure in numerical turbulent flows , it was proposed , in ref . @xcite , to study the probability current associated with pressure in the plane spanned by the two highly relevant invariants of @xmath15 , @xmath16 and @xmath0 ( the so - called @xmath17-plane ) . one of these invariants , defined as , @xmath18 quantifies the net balance , or competition , between enstrophy and dissipation . the other important invariant , defined as @xmath19 quantifies the competition between enstrophy production and strain skewness ( i.e. dissipation production ) . as it will be recalled in the following , in terms of the velocity gradient evolution in statistically stationary turbulence , pressure has two important roles . first of all , pressure counteracts the development of the singularity implied by the self - stretching term . this feature is found to be well reproduced by existing closures @xcite . the other important pressure action is the redistribution of probabilities towards enstrophy production dominated regions ( i.e. towards @xmath20 ) . this is not reproduced well by existing closures . as discussed in refs . @xcite , a related deficiency of the closures is that they all predict that the pressure hessian is proportional to @xmath0 . in the @xmath21 plane dynamics , this implies that when @xmath22 , the effect of pressure hessian also vanishes . for real turbulence , there is no such vanishing of pressure hessian effects when @xmath22 @xcite . in this article , we investigate whether these particular features of pressure ( redistribution of probabilities towards enstrophy production , and non - vanishing action even when @xmath22 ) is inherent to true navier - stokes turbulence , or can also be observed in various approximations , namely synthetic turbulent velocity fields . various types of synthetic fields are considered . the first type of synthetic field considered is gaussian fields obtained by superposing random - phase fourier modes with prescribed spectra . the second type is called ` multifractal ' @xcite , and consists of a gaussian field whose vorticity field is amplified by means of the ` fluid deformation closure ' and made consistent with multifractality s long - range correlations in physical space @xcite . the third type of synthetic field is generated using the lagrangian mapping technique @xcite . it also relies on random - phase gaussian fields but then applies a multi - scale deformation of fluid particles using a simple lagrangian mapping . for each of these synthetic velocity fields , a pressure field is obtained numerically by means of the pressure poisson equation . as will be seen , unlike the local closures discussed above , these synthetic fields reproduce many correct features of the pressure hessian . in particular , they will be shown to reproduce the redistribution of probability towards enstrophy production , as well as displaying non - vanishing action , even when @xmath22 . the second part of the paper studies to what degree spatial locality is important in determining these properties of the anisotropic part of the pressure hessian . as can be seen from the expression for the pressure hessian ( eq . ( [ eq : soph ] ) ) , the anisotropic part of the pressure hessian is also the part that is spatially nonlocal , i.e. the part that requires knowledge of @xmath23 at positions @xmath24 . arguably , the more non - local effects are important , the more challenging it is to formulate closures in terms of local quantities . in order to examine the degree of locality , in the second part of this paper we decompose the space integration in eq . ( [ eq : soph ] ) into two parts , a local part given by the integration over a small ball of radius given by the kolmogorov length scale @xmath25 , and the remainder being the ` nonlocal ' portion . we will show that neglecting the second non - local contribution leads to an expression that models the anisotropic part of the pressure hessian in terms of the hessian of the invariant @xmath0 . using dns data , this expression is compared with the true pressure hessian . we follow the approach used in refs . @xcite , based on a fokker - planck equation for the dynamics of @xmath16 and @xmath0 . to summarize the approach , we remark that it can be shown that the time evolution along a lagrangian trajectory of the non - dimensional invariants @xmath26 and @xmath27 is given by @xmath28 @xmath29 where @xmath30 is the strain variance , and @xmath31 is the non - dimensional time . also , @xmath32 stands for ( minus ) the deviatoric part of the pressure hessian , i.e. @xmath33 and @xmath34 is the viscous term ( recall that in the re approximation , @xmath35 ) . the fokker - planck equation describing the time evolution of the joint density @xmath36 may be written as : @xmath37 where the divergence of the _ probability current _ @xmath38 controls the time variations of the joint probability density @xmath39 . the probability current can be written in terms of conditional averages as @xmath40 and can be decomposed into @xmath41 , where the probability currents @xmath42 , @xmath43 and @xmath44 are associated , respectively , to the effects on the lagrangian evolution of the invariants @xmath0 and @xmath16 ( eqs . ( [ eq : dynq ] ) and ( [ eq : dynr ] ) ) of the restricted euler term @xmath6 , of ( minus ) the pressure hessian @xmath45 and of diffusivity @xmath46 entering in eq . ( [ eq : nsa ] ) . in this article , we will focus on the probability current associated with the pressure hessian @xmath43 . it can be written as @xmath47 more details are provided in ref . @xcite . in the following , we will make extensive use of data from standard direct numerical simulation ( dns ) of the navier - stokes equations , for a taylor - based reynolds number of order @xmath48 . dns is based on a pseudo - spectral method with 2nd - order accurate adams - bashforth time stepping ; the computation box is cubic ( size @xmath49 ) with periodic boundary conditions in the three directions and spatial resolution @xmath50 . statistical stationarity is maintained by an isotropic external force acting at low wavenumbers in order to ensure a constant energy - power supply . it provides , in the units of the simulation , a constant energy injection rate @xmath51 . the kinematic viscosity of the fluid is @xmath52 . the kolmogorov s scale is @xmath53 so that @xmath54 , since @xmath55 . we display in fig . [ fig : vectamprq](a ) the vector plot and streamlines of the probability current @xmath43 associated with the pressure hessian ( eq . ( [ eq : wp ] ) ) in the @xmath56-plane , as it was done in ref . three main remarks can be made at this stage : ( i ) first , the pressure hessian counteracts the development of the finite time singularity along the right tail of the vieillefosse line implied by the re term , ( ii ) probabilities are found to be very low in the dissipation production dominated region ( i.e. @xmath57 and above the vieillefosse tail ) meaning that pressure does not play there a significant role , and ( iii ) pressure redistributes the probabilities towards the enstrophy production dominated region ( i.e. the flux is directed to the left , towards @xmath58 ) . as far as the restricted euler term is concerned , as is well known @xcite , the deterministic @xmath59 probability current pushes probabilities toward the right tail of the vieillefosse line ( data not shown ) . this result helps create a picture of the time evolution of velocity gradients along lagrangian trajectories in stationary flows : the re term `` pushes '' the probabilities towards the right tail towards and along the vieillefosse line , while the pressure regularizes the implied finite time singularity and redistributes the probabilities towards the left part of the plane such that , in turn , the re term can act again , etc . to that picture should be added the viscous diffusion effects , @xmath44 pushes the probabilities toward vanishing @xmath16 and @xmath0 not only along the vieillefosse line but also everywhere else , and stochastic forcing , such that the full" +"looking at people ( lap ) is a challenging area of research that deals with the problem of automatically recognizing people in images , detecting and describing body parts , inferring their spatial configuration , performing action / gesture recognition from still images or image sequences , often including multi - modal data . any scenario where the visual or multi - modal analysis of people takes a key role is of interest within the , so called , field of looking at people @xcite . because of the huge configuration space of human bodily structure , posture , and movement , human analysis is a difficult problem for computer vision and machine learning , which involves dealing with numerous distortion factors , including : illumination changes , partial occlusions , changes in the point of view , rigid and elastic deformations , or high inter and intra - class variability . despite the high difficulty of the problem , modern computer vision and machine learning techniques have advanced greatly the state - of - the - art and therefore deserve further attention . our selection of tasks when organizing new events is motivated both by academic interest and by potential applications , such as tv production , home entertainment ( multimedia content analysis ) , education purposes , sociology research , surveillance and security , improved quality live by means of monitoring or automatic artificial assistance , etc . academic interest in illustrated by new burgeoning subareas of lap , such as affective computing , social signal processing , human behavior analysis , and social robotics , providing us with opportunities to make connections with other domains and expose the computer vision and machine learning community to new problems of high practical and societal interest . these objectives were first illustrated in 2011 when chalearn lap organized its first event on one - shot multi - modal gesture recognition from rgb - depth data sources . since then , chalearn lap has organized over 10 international challenges in the field of lap , including face analysis , body posture , action / gesture analysis , including still images , image sequences , and multi - modal data sources , and focusing in cutting edge trends in computer vision and pattern recognition , like explainable computer vision , personality analysis , and collaborative competitions ( a.k.a . _ coopetitions _ ) . in this paper we briefly review the events organized so far , which are not limited to challenges , but also include , workshops , special issues , and book series . we also introduce the new chalearn lap platform , which contains all information and resources from previous and current events , including programs , papers , codes , and data , among others . finally , we discuss about near future plans within chalearn lap series . chalearn http://chalearn.org is a non - profit organization with vast experience in the organization of academic challenges . chalearn is interested in all aspects of challenge organization , including data gathering procedures , evaluation protocols , novel challenge scenarios ( e.g. , coopetitions ) , training for challenge organizers , challenge analytics , results dissemination and , ultimately , advancing the state - of - the - art through challenges . since 2003 , chalearn has been organizing a number of challenges in several interrelated fields , including machine learning , computer vision , pattern recognition , causality and bioinformatics . the first challenge we organized was the nips 2003 feature selection challenge , and currently several challenges are running ( please visit chalearn s website for update information on ongoing and past challenges http://chalearn.org ) . chalearn lap is a division of chalearn that focuses in challenges in the fields of computer vision and pattern recognition . this section reviews the historic of chalearn lap events . we split them into challenges and their associated workshops , special issues , and challenges in machine learning ( ciml ) springer book series . table [ tablesummary ] summarizes the list of challenges and their associated workshops and special issues . next , we briefly review the organized competitions in the period 2011 - 2016 . kinect revolutionized in 2010 the field of gesture recognition , and had a broad impact into other lap areas . it i a valuable resource as it provides a variety of data modalities , including rgb image , depth image ( using an infrared sensor ) , and audio . for this reason the first three challenges organized by chalearn lap relied on the use and exploitation of such rich information . first , we organized a challenge on gesture and sign language recognition from video , mostly focusing on hand and arm gestures , although facial expressions and whole body motion may enter into account @xcite , with funding from darpa , nsf , and the pascal2 eu network of excellence , and prizes donated by microsoft xbox and texas instrument . we used the kaggle platform . applications include recognizing signals for man - machine communication , translating sign languages for the deaf to hearing people , and computer gaming . the challenge focused in one - shot gesture recognition ( i.e. , learning models from a single example ) , and included qualitative and quantitative tracks . a large user - independent "" dataset ( of over 60000 gestures ) covering a high number of domains and gesture categories was released @xcite , and the leveinstein metric was used as a quantitative measure for ranking participants . dozens of participants joined the competition that lasted more than one year . although the impulse for the design of this challenge and part of the funding was given by the darpa deep learning program , _ no deep learning method _ was applied ! rather , more conventional combinations of ad hoc feature extraction methods and hidden markov models dominated the methodology of top ranking participants . the _ no deep learning revolution _ caught up right after this first challenge ! chalearn lap organized in 2013 a challenge and workshop on multi - modal gesture recognition from 2d and 3d video data using kinect @xcite . in this challenge and all following ones , we used the codalab platform running on microsoft azure , with the support of microsoft research . new in this competition was the user independent aspect capturing applications of gesture recognition genuinely important in many multi - modal interaction and computer vision applications , including image / video indexing , video surveillance , computer interfaces , and gaming . user - independent recognition of continuous , natural signing is very challenging due to the multimodal nature of the visual cues ( e.g. , movements of fingers and lips , facial expressions , body pose ) , as well as technical limitations such as spatial and temporal resolution and unreliable depth cues . we ran a competition containing a dataset with more than 13000 gesture samples from a dictionary of 20 italian sign gesture categories . for the first time in video lap challenges deep learning methods won ! an interesting finding from this challenge was that the audio modality was very helpful for recognizing gestures . chalearn organized in 2014 three parallel challenge tracks on human pose recovery on rgb data , action / interaction spotting on rgb data , and gesture spotting on rgb - depth data @xcite . + the challenge featured three quantitative tracks : + * track 1 : human pose recovery . more than 8,000 frames of continuous rgb sequences are recorded and labeled with the objective of performing human pose recovery by means of recognizing more than 120000 human limbs of different people . * track 2 : action / interaction recognition . 235 performances of 11 action / interaction categories are recorded and manually labeled in continuous rgb sequences of different people performing natural isolated and collaborative actions randomly . * track 3 : gesture recognition . more than 14000 gestures are drawn from a vocabulary of 20 italian sign gesture categories . the emphasis of this third track is on multi - modal automatic learning of a set of 20 gestures performed by several different users , with the aim of performing user independent continuous gesture spotting . during this challenge , the state of the art was significantly advanced in the three tracks , where solutions based in deep learning obtained the best results . after the boom of kinect and the fact that human - level performance was reached in several tasks / challenges involving kinect - recorded data , chalearn lap started to look at open challenges in relevant fields that have to do with still and sequences of rgb images . chalearn organized in 2015 parallel challenge tracks on rgb data for human pose recovery , action / interaction spotting , and cultural event recognition @xcite . the challenge featured three quantitative tracks : * track 1 : human pose recovery . more than 8,000 frames of continuous rgb sequences are recorded and labeled with the objective of performing human pose recovery by means of recognizing more than 120,000 human limbs of different people . * track 2 : action / interaction recognition . 235 performances of 11 action / interaction categories are recorded and manually labeled in continuous rgb sequences of different people performing natural isolated and collaborative actions randomly . * track 3 : cultural event recognition . more than 10000 images corresponding to 50 different cultural event categories will be considered . in all the categories , garments , human poses , objects and context will be possible cues to be exploited for recognizing the events , while preserving the inherent inter- and intra - class variability of this type of images . examples of cultural events will be carnival , oktoberfest , san fermin , maha - kumbh - mela and aoi - matsuri , among others . chalearn organized for iccv2015 two parallel quantitative challenge tracks on rgb data @xcite . * track 1 : apparent age estimation . 5000 images each displaying a single individual , labeled with the apparent age . each image has been labeled by multiple individuals using a collaborative facebook implementation . the votes variance is used as a measure of the error for the predictions . this is the first state of the art dataset for apparent age recognition rather than real age recognition . * track 2 : cultural event recognition . near 30000 images corresponding to 100 different cultural event categories will be considered . in all the categories , garments , human poses , objects and context will be possible cues to be exploited for recognizing the events , while preserving the inherent inter- and intra - class variability of this type of images . chalearn organized for cvpr2016 three parallel quantitative challenge tracks on rgb face analysis @xcite . * track 1 : apparent age estimation . an extended version of the previous iccv2015 challenge dataset . it contains 8,000 images each displaying a single individual , labeled with the apparent age . each image has been labeled by multiple individuals , using a collaborative facebook implementation and amazon mechanical turk . the votes variance is used as a measure of the error for the predictions . this is the first state of the art dataset for apparent age recognition rather than real age recognition . * track 2 : accessories classification . the aim of this track is to detect and classify complements and accessories worn by the subjects . it uses a fraction of the faces of the world dataset , a challenging dataset consiting of 8000 images , each displaying a single individual , labelled with the accessories they are wearing . * track 3 : smile and gender classification . in this track , participants will have" +"very large volume neutrino telescopes ( vlv@xmath0ts ) provide a unique window to the high - energy universe @xcite , because they allow for the detection of high - energy neutrinos which can reach the earth after having travelled from far galactic or extra - galactic sources , almost undeflected by cosmic magnetic fields and insensitive to electromagnetic and strong forces . in this respect neutrinos propagate quite differently with respect to charged cosmic rays ( crs ) , and are thus precious messengers capable of providing direct information on the regions of the universe where they are produced . a first detection of high - energy leptonic events up to an energy of a few pev was reported by the icecube collaboration . the initial evidence from the first two - year data analysis @xcite was subsequently strenghtened by increased statistics in the three and four - year analyses @xcite . so far , more than 50 high - energy starting events have been recorded . the discussion on the origin of these events is quite lively , and a number of hypotheses concerning the possible sources has been formulated . although it is believed that most of the neutrino events detected so far have an extraterrestrial origin , theoretical calculations predict the existence of a terrestrial component due to the decays of the unstable hadrons produced by the interactions of high - energy and ultra - high - energy crs with the earth s atmosphere @xcite . this terrestrial component should be properly taken into account as a background and subtracted in any astrophysical analysis . the terrestrial component is usually separated into two contributions : the conventional neutrino flux , coming from the decay of @xmath1 and @xmath2 mesons , and the prompt neutrino flux , originating from the decay of heavier mesons and hadrons , in particular those including charm quarks as valence quarks in their composition . the prompt component is supposed to become dominant with respect to the conventional one only at energies high enough . several computations of conventional neutrino fluxes exist ( see e.g. ref . @xcite ) , together with experimental evidence . on the other hand , no experimental evidence for the existence of a prompt flux has emerged so far . it is thus important to provide precise and refined theoretical predictions of prompt neutrino fluxes , to understand if the lack of detection is just due to the still low statistics of the vlv@xmath0 t experiments at high energy , or if the methodologies and/or theories used so far to predict these fluxes have some flaws . in ref . @xcite we have recently computed prompt neutrino fluxes making use of qcd , with microscopic interactions described by event generators including up - to - date information from the qcd theory community working at hadron colliders . as shown in the following , we have used the same generators adopted in our astrophysical study , to produce predictions which can be compared with experimental data recently collected at the large hadron collider ( lhc ) . nowadays , state - of - the - art tools for predicting many differential distributions at the lhc are represented by shower monte carlo ( smc ) codes , matched with hard - scattering processes evaluated in perturbative qcd including next - to - leading - order ( nlo ) radiative corrections at least @xcite . for a few selected processes , calculations at the differential level involving the resummation of different kinds of large logarithms to all orders , or next - to - nlo ( nnlo ) qcd radiative corrections , start to be available as well . however , this is not yet the case for the processes involving charm quarks we are interested in in this paper . interfacing hard scattering amplitudes including radiative corrections with the parton shower algorithms ( ps ) embedded in the smcs requires a careful matching , to avoid double counting effects and to ensure a proper coverage of the whole phase space available for light parton emissions . at present , one of the most widely used nlo qcd + ps matching schemes is powheg @xcite , which has been automated in dedicated tools , like e.g. the ` powhegbox ` @xcite . at nnlo the situation is even more complicated , and efforts to extend matching schemes with ps at this level of accuracy are ongoing , as well as those for pushing the accuracy of ps far beyond the present one . in this paper we consider @xmath3 @xmath4 @xmath5-hadron + @xmath6 hadroproduction evaluated by means of ` powhegbox ` + ` pythia 6 ` @xcite . this allows to generate differential distributions for the hadroproduction of different kinds of charmed mesons and hadrons at nlo qcd + ps accuracy . the ps ensures at least leading logarithmic ( ll ) accuracy in all collinear qcd emissions following the first light partonic one accompanying @xmath3 , which is instead evaluated by ` powhegbox ` with nlo accuracy . theoretical predictions for @xmath7 hadroproduction by ` powhegbox + pythia 6 ` compared to lhcb data at 7 tev . transverse momentum distributions in different rapidity bins are shown in different panels . the green and violet bands refer to scale and mass variation , respectively , summed in quadrature in the blue band . central values for all input parameters are fixed as explained in the text . , title=""fig:"",scaledwidth=44.0% ] theoretical predictions for @xmath7 hadroproduction by ` powhegbox + pythia 6 ` compared to lhcb data at 7 tev . transverse momentum distributions in different rapidity bins are shown in different panels . the green and violet bands refer to scale and mass variation , respectively , summed in quadrature in the blue band . central values for all input parameters are fixed as explained in the text . , title=""fig:"",scaledwidth=44.0% ] theoretical predictions for @xmath7 hadroproduction by ` powhegbox + pythia 6 ` compared to lhcb data at 7 tev . transverse momentum distributions in different rapidity bins are shown in different panels . the green and violet bands refer to scale and mass variation , respectively , summed in quadrature in the blue band . central values for all input parameters are fixed as explained in the text . , title=""fig:"",scaledwidth=44.0% ] theoretical predictions for @xmath7 hadroproduction by ` powhegbox + pythia 6 ` compared to lhcb data at 7 tev . transverse momentum distributions in different rapidity bins are shown in different panels . the green and violet bands refer to scale and mass variation , respectively , summed in quadrature in the blue band . central values for all input parameters are fixed as explained in the text . , title=""fig:"",scaledwidth=44.0% ] theoretical predictions for @xmath7 hadroproduction by ` powhegbox + pythia 6 ` compared to lhcb data at 7 tev . transverse momentum distributions in different rapidity bins are shown in different panels . the green and violet bands refer to scale and mass variation , respectively , summed in quadrature in the blue band . central values for all input parameters are fixed as explained in the text . , title=""fig:"",scaledwidth=44.0% ] this computation requires to fix some input . to establish the central values of the renormalization and factorization scales @xmath8 and @xmath9 , of the charm mass @xmath10 and a set of parton distribution functions ( pdfs ) suitable for the calculation of prompt neutrino fluxes , taking into account that a broad range of center - of - mass energies @xmath11 are involved , including both energies much lower and much higher than those explored so far at colliders , we have studied the behaviour of the total @xmath3 hadroproduction cross - section at different orders / degrees of accuracy we have compared predictions including lo , nlo and nnlo qcd corrections , as well as the behaviour of the cross - sections when adopting the @xmath12 scheme as an alternative to the on - shell one in the renormalization of the charm quark mass . the procedure leading to our choice of the central values of these parameters and of their range of variation , useful to determine the associated uncertainties , is detailed in ref . @xcite . here we summarize our choices . the central @xmath8 and @xmath9 scales were fixed to @xmath13=@xmath14 , and allowed to vary in the range ( @xmath8 , @xmath9 ) @xmath15 ( 0.5 , 0.5 ) , ( 2,2 ) , ( 0.5 , 1 ) , ( 1 , 0.5 ) , ( 1 , 2 ) , ( 2,1 ) @xmath13 . we did not include the variations ( 0.5 , 2 ) and ( 2 , 0.5 ) @xmath13 , as suggested in ref . the central charm mass value was fixed to @xmath16 = 1.4 gev in the on - shell scheme and allowed to vary in the range @xmath17 0.15 gev . we have used the abm11 pdfs @xcite at nlo including the pdf and @xmath18 variations . we emphasize that the choice of all these parameters was uniquely derived by theoretical considerations , taking into account in particular the convergence of the perturbative series of radiative corrections , and the behaviour of different sets of pdfs already available in the ` lhapdf 6.1.5 ` interface @xcite in an extended bjorken-@xmath19 range , also covering the region of low @xmath19 . no comparison with any recent experimental data was used to tune these parameters or retune other parameters entering ` pythia 6 ` , for which we have adopted one of the most recent already available perugia tunes @xcite , ensuring a transverse - momentum ordered ps . our predictions for ( @xmath20 + @xmath21 ) fluxes as a function of @xmath22 . uncertainties due to scale variation around the central value @xmath8 = @xmath9 = @xmath23 , are shown in panel 2.a ( upper - left ) , considering all possible ( @xmath8 , @xmath9 ) scale combinations ( 0.5 , 0.5 ) , ( 2 , 2 ) , ( 1 , 2 ) , ( 2 , 1 ) , ( 0.5 , 1 ) and ( 1 , 0.5 ) @xmath13 , and in panel 2.b ( upper - right ) by disregarding the non - diagonal contributions ( 0.5 , 1 ) and ( 1 , 0.5 ) @xmath13 . the addition in quadrature of the uncertainties in panel 2.a ( 2.b ) with those due to @xmath10 and pdf variation gives rise to the qcd uncertainty band in panel 2.c ( 2.d ) . in each panel , different colors refer to fluxes computed with different primary cr all - nucleon spectra , including power - law and four different variants of gaisser cr spectra @xcite . see text for more detail.,title=""fig:"",scaledwidth=44.0% ] our predictions for ( @xmath20 + @xmath21 ) fluxes as a function of @xmath22 . uncertainties due to scale variation around the central value @xmath8 = @xmath9 = @xmath23 , are shown in panel 2.a ( upper - left ) , considering all possible ( @xmath8 , @xmath9 ) scale combinations ( 0.5 , 0.5 ) , ( 2 , 2 ) , ( 1 , 2 ) , ( 2 , 1 ) , ( 0.5 , 1 ) and ( 1 , 0.5 ) @xmath13 , and in panel 2.b ( upper - right ) by disregarding the non - diagonal contributions ( 0.5 , 1 ) and ( 1 , 0.5 ) @xmath13 . the addition in quadrature of the uncertainties in panel 2.a ( 2.b ) with those due to @xmath10 and pdf variation gives rise to the qcd uncertainty band in panel 2.c ( 2.d ) . in each panel , different colors refer to fluxes computed with different primary cr all - nucleon spectra , including power - law and four different" +"access to large data sets on human activities and interactions has long been limited by the difficulty and cost of gathering such information . recently , the ever increasing availability of digital traces of human actions is widely enabling the representation and the analysis of massive amounts of information on human behavior . the representation of this information in terms of complex networks @xcite has led to many research efforts because of the naturally interlinked nature of these new data sources . tracing human behavior in a variety of contexts has become possible at very different spatial and temporal scales : from mobility of individuals inside a city @xcite and between cities @xcite , to mobility and transportation in an entire country @xcite , all the way to planetary - scale travel @xcite . mobile devices such as cell phones make it possible to investigate mobility patterns and their predictability @xcite . on - line interactions occurring between individuals can be monitored by logging instant messaging or email exchange @xcite . recent technological advances further support mining real - world interactions by means of mobile devices and wearable sensors , opening up new avenues for gathering data on human and social interactions . bluetooth and wifi technologies give access to proximity patterns @xcite , and even face - to - face presence can be resolved with high spatial and temporal resolution @xcite . the combination of these technological advances and of heterogeneous data sources allow researchers to gather longitudinal data that have been traditionally scarce in social network analysis @xcite . a dynamical perspective on interaction networks paves the way to investigating interesting problems such as the interplay of the network dynamics with dynamical processes taking place on these networks . in this paper , we capitalize on recent efforts @xcite that made possible to mine behavioral networks of face - to - face interactions between individuals , in a variety of real - world settings and in a time - resolved fashion . we present an in - depth analysis of the data we collected at two widely different events . the first event was the infectious exhibition @xcite held at the science gallery in dublin , ireland , from april @xmath0 to july @xmath0 , 2009 . the second event was the acm hypertext 2009 conference @xcite hosted by the institute for scientific interchange foundation in turin , italy , from june @xmath1 to july @xmath2 , 2009 . in the following , we will refer to these events as sg and ht09 , respectively . intuitively , interactions among conference participants differ from interactions among museum visitors , and the concerned individuals have very different goals in both settings . the study of the corresponding networks of proximity and interactions , both static and dynamic , reveals indeed strong differences but also interesting similarities . we take advantage of the availability of time - resolved data to show how dynamical processes that can unfold on the close proximity network such as the propagation of a piece of information or the spreading of an infectious agent unfold in very different ways in the investigated settings . in the epidemiological literature , traditionally , processes of this kind have been studied using either aggregated data or under assumptions of stationarity for the interaction networks : here we leverage the time - resolved nature of our data to assess the role of network dynamics on the outcome of spreading processes . at a more fundamental level , simulating simple spreading processes over the recorded interaction networks allows us to expose several properties of their dynamical structure as well as to probe their causal structure . the paper is organized as follows : first , we briefly describe the data collection platform and our data sets in section [ data ] ; in section [ static - properties ] we discuss the salient features of the networks of interactions aggregated on time windows of one day . these networks are static objects , carrying only information about the cumulative time that daily each pair of individuals has spent in face - to - face proximity . section [ dynamic - properties ] analyzes the dynamical properties of face - to - face interactions between conference participants and museum visitors . section [ resilience ] further characterizes the aggregated network structures by investigating the effect of incremental link removal . finally , section [ information - diffusion ] investigates the role played by causality in information spreading along the proximity network , and section [ conclusions ] concludes the paper and defines a number of open questions . the data collection infrastructure uses active radio - frequency identification devices ( rfid ) embedded in conference badges to mine face - to - face proximity relations of persons wearing the badges . rfid devices exchange ultra - low power radio packets in a peer - to - peer fashion , as described in refs . exchange of radio packets between badges is only possible when two persons are at close range ( @xmath3 to @xmath4 m ) and facing each other , as the human body acts as a rf shield at the carrier frequency used for communication . the operating parameters of the devices are programmed so that the face - to - face proximity of two individuals wearing the rfid tags can be assessed with a probability in excess of @xmath5 over an interval of @xmath6 seconds , which is a fine enough time scale to resolve human mobility and proximity at social gatherings . false positives are exceedingly unlikely , as the ultra - low power radio packets used for proximity sensing can not propagate farther than @xmath4-@xmath7 m , and a sustained excess of packets is needed in order to signal a proximity event . when a relation of face - to - face proximity ( or `` contact '' , as we will refer to it in the following ) is detected , the rfid devices report this information to receivers installed in the environment ( rfid readers ) . the readers are connected to a central computer system by means of a local area network . once a contact has been established , it is considered ongoing as long as the involved devices continue to exchange at least one radio packet for every subsequent interval of @xmath6 seconds . conversely , a contact is considered terminated if an interval of @xmath6 seconds elapses with no packets exchanged . for a detailed description of the sensing platform and some of its deployments , see refs.@xcite . the deployments at the science gallery in dublin @xcite and at the ht09 conference in turin @xcite involved vastly different numbers of individuals and stretched along different time scales . the former lasted for about three months and recorded the interactions of more than @xmath8 visitors ( more than @xmath9 face - to - face contacts recorded ) , whereas the latter took place over the course of three days and involved about @xmath10 conference participants ( about @xmath11 contacts ) . behaviors are also very different : in a museum , visitors typically spend a limited amount of time on site , well below the maximum duration permitted by the museum opening hours , they are not likely to return , and they follow a rather pre - defined path , touching different locations that host the exhibits . in a conference setting , on the other hand , most attendees stay on - site for the entire duration of the conference ( a few days ) , and move at will between different areas such as conference room , areas for coffee breaks and so on . the coverage of the community was different in both settings . at the science gallery , visitors were equipped with a rfid tag upon entering the venue , as part of an interactive exhibit , and therefore almost the totality of them were tracked . on the other hand , at ht09 , about 75% of the participants volunteered to being tracked . this sampling may introduce some biases in the results . sampling issues are also commonly encountered in the study of static complex networks @xcite . reference @xcite has shown that for a broad variety of real - world deployments of the rfid proximity - sensing platform used in this study , the behavior of the statistical distributions of quantities such as contact durations is not altered by unbiased sampling of individuals . on the other hand , we can not completely rule out that a systematic bias is introduced by the selection of volunteers , if volunteers and non - volunteers have different behavioral patterns . accurately checking this point would require monitoring an independent data source for face - to - face contacts , and because of scalability issues this would be feasible only for small control groups . issues regarding the effect of missing data and incomplete sampling on the properties of dynamical processes unfolding on the networks also deserve attention and will be the subject of future investigations . we start by analyzing aggregated networks of interaction obtained by aggregating the raw proximity data over one day . this aggregation yields a social graph where nodes represent individuals , and an edge is drawn between two nodes if at least one contact was detected between those nodes during the interval of aggregation . therefore , every edge is naturally weighted by the total duration of the contact events that occurred between the tags involved , i.e. , by the total time during which the corresponding individuals have been in face - to - face proximity . the choice of daily time windows seems quite natural in our settings . it would represent , for instance , a typical time scale for a description of articulated social networks based on surveys , in which each participant would ( ideally ) declare who s / he has encountered during the course of the day . such a choice for the duration of the time - window , albeit natural , is by no means unique @xcite . for instance , it is possible to aggregate the data over longer periods of time ( weeks or months ) to investigate the stationarity of the collected data @xcite . shorter aggregation times of the order of a few minutes are also useful , for instance , to resolve circadian activity patterns at the venue under investigation . figure [ aggregated - networks ] displays the aggregated contact networks for june 30@xmath12 at the ht09 conference ( top left ) , and for three representative days for the sg museum deployment . despite the large variation in the number of daily museum visitors , ranging from about @xmath13 to @xmath14 , the chosen days illustrate many features of the sg aggregated networks , in particular the presence of either a single or two large connected components ( cc ) in the network . days with smaller numbers of visitors can also give rise to aggregated networks made of a larger number of small isolated clusters . as shown in fig . [ nclusters ] , depending on the number of visitors the number of cc can in fact vary substantially . for a large number of visitors , typically only one cc is observed . for a low number of visitors , on the other hand , many clusters are formed . overall one also notices that the network diameter ( highlighted in all the plots of fig . [ aggregated - networks ] ) is considerably longer for sg than for ht09 aggregated networks , reflecting the different behavioral patterns in these settings . the small - world nature or lack thereof of the aggregated networks can be investigated statistically by introducing a proper null model . to this end ," +"the problem of the study and measurement of t - odd distributions in hadron - hadron scattering has recently acquired a certain relevance and quite a few related experiments have been thought or scheduled for the next ten years@xcite . in particular several studies and models have been proposed for the sivers distribution function@xcite . its possible existence as a leading - twist distribution was demonstrated@xcite recently , and related@xcite to previously studied t - odd mechanisms@xcite . some phenomenological forms for its dependence on @xmath0 and @xmath2 have been extracted@xcite from available data@xcite . while studies of general properties@xcite of t - odd functions relate these functions with a wide spectrum of phenomena , quantitative models mostly follow the general scheme suggested in @xcite . a known quark - diquark spectator model@xcite is extended by including single particle ( meson or gluon ) exchange@xcite . in the case of @xcite the unperturbed starting model was a bag model . the class of processes i want to consider here is the one of single spin asymmetries in collisions between an unpolarized hadron and a transversely polarized proton . in particular , azimuthal asymmetries in drell - yan dilepton production and hadron semi - inclusive production , where in both cases one of the colliding hadrons is normal - polarized . i consider phenomena that may be present in the beam energy range 10 - 300 gev ( so , not necessarily leading twist effects ) . the present work uses phenomenological schemes that are not typical of perturbative qcd , but rather of high - energy nuclear physics . it is inspired by previous works on t - odd structure functions in high - energy nuclear physics@xcite , by a previous work on nuclear - target induced polarization in drell - yan@xcite , and by the results from the theory and phenomenology of spin - orbit interactions in high - energy hadron - hadron exclusive processes ( see e.g. @xcite and references therein ) . the goal is not to reproduce precisely some phenomenology . rather , it is to establish whether scalar and spin - orbit interactions dominated by their absorption part are able to build a nonzero sivers - like asymmetry with a reasonable shape , possibly of higher - twist nature . for this reason , the model for both the initial `` intrinsic '' state of a quark in the proton , and for initial state interactions is built in such a way to be as simple as possible . all the necessary functions have been chosen in gaussian form and the parameter number has been reduced to the minimum necessary to explore the interesting independent physical situations . contrary to the ordinary treatment of the problem , where one works on a two - point correlation operator deriving from a set of squared one - point amplitudes , i develop most of the work at the level of one - point amplitudes , square them and then sum over the relevant states . i imagine , for a hadron with a given spin projection @xmath3 @xmath1 @xmath4 , a two - component quark spinor @xmath5 , with @xmath6 associated with the transverse quark spin . in this scheme , the @xmath7trace normally calculated on the correlation operator simply corresponds to the sum @xmath8 . this quantity is the final goal of the calculation , and the distribution functions associated to an unpolarized quark , including sivers one , are extracted from it . concerning the initial , `` intrinsic '' state of a quark in the hadron , i assume that the relevant quantity defining this state is the quark total angular momentum @xmath9 in the hadron rest frame . in this state a nonzero correlation @xmath10 @xmath11 @xmath12 is present . in other words , the quark @xmath9 coincides with the parent hadron spin . this may be realized both in s - wave and in p - wave , with spin - spin correlation @xmath13 @xmath11 @xmath14 . a nonzero correlation between the hadron and the quark angular momentum is necessary in any model , since a spin - related effect is impossible if a quark transports no information on the parent hadron spin . clearly , we have different effects in the s and p - wave cases . this correlation alone would not produce a single - spin asymmetry of naive time - odd origin because of global invariance rules . initial state interactions between the two hadrons , or between the quarks of one hadron and the quarks of the other one , must be introduced@xcite . i reproduce these interactions in eikonal approximation @xmath15 , where @xmath16 is a 2x2 space - time dependent matrix reproducing a mean field acting on the projectile quark , and @xmath17 is a light - cone coordinate . then the full matrix element , affected by this operator , is calculated in space - time representation . although it may seem more natural to adopt a mean field treatment for problems where a projectile is subject to multiple soft scattering@xcite , there is also a tradition for such recipes in hadronic problems dominated by a single or at most double hard scattering event , when the scatterer belongs to a composite structure the way it is used here , the above eikonal approximation is only a short - wave approximation , that alone does not support the persistence of initial state interaction effects at very large energies . this derives from the fact that we do not know the asymptotic properties of the operator @xmath16 ( see below ) . in addition , the above eikonal approximation does not support automatically factorization , since it is applied at single point amplitude level . the added initial state interactions ( the @xmath16 matrix ) consist of two terms : ( i ) anti - hermitean scalar mean field , ( ii ) anti - hermitean spin - orbit mean field . hermitean terms have been tested and they affect the results . alone , these terms do not produce t - odd distributions ( by definition , since they they are intrinsically t - even ) and do not change the main qualitative features of the presented results . not to overload this work with a many - parameter phenomenology , i have limited myself to terms that are not intrinsically t - even . a remark is important : strong and electromagnetic interactions are t - even and hermitean . as well known in nuclear physics@xcite , relevant anti - hermitean terms originate in the projection of hermitean interactions on a subspace , including only a part of all those degrees of freedom that are able to exchange energy / momentum within a characteristic interaction time relevant for the problem . if one were able to include all the relevant degrees of freedom in the formalism , there would be no room for anti - hermitean interactions ( see @xcite for a long discussion about these points ) . the results of this calculation show that also most of the considered anti - hermitean terms are not effective , for the purpose of a sivers asymmetry . the key interaction term is one of the three components of the spin - orbit scalar product . a chain of qualitative arguments presented in section iii relates imaginary spin - orbit terms to the high - energy hadron - nucleon analyzing power and recoil polarization . these observables are nonzero at as large beam energies as 300 gev ( for the case of quasi - forward scattering@xcite ) or 25 - 30 gev ( for the case of large transferred momenta up to 7 gev / c , see e.g.@xcite ) . their behavior at larger energies is not known , and there is no commonly accepted model that allows for an extrapolation@xcite . this has two consequences . on the one side , at energies @xmath11 100 gev we face the possibility of relevant sivers - like asymmetries with this origin . on the other side , it is impossible to decide whether this is a leading twist effect . for this reason , as above anticipated , it is impossible to decide whether the @xmath16 operator appearing in the rescattering factor @xmath15 is nonzero at very large energies . because of this , in the following the terms `` sivers asymmetry '' and `` sivers effect '' are preferred to `` sivers function '' . the latter is appropriate in the case of a leading twist contribution . experimentally , it may be impossible to distinguish between the two at the presently available energies . where not differently specified , all variables will refer to the center of mass of the colliding hadrons . let @xmath18 @xmath1 @xmath19 , be the quark impact parameter and @xmath20 @xmath1 @xmath21 the transverse momentum conjugated with it . let @xmath22 be the large light - cone component of the hadron momentum , so that @xmath23 is the quark @xmath24 momentum conjugated with @xmath25 . i substitute @xmath25 with the rescaled coordinate @xmath26 not to work with a singularity of the fourier transform in the infinite momentum limit @xmath22 @xmath27 @xmath28 . since the inclusive process is described here in terms of squared amplitudes , and these amplitudes are calculated before being squared , @xmath17 is not bound to be positive , as it happens in the ordinary treatment based on a two - point correlator with intermediate real states . in that case @xmath17 has the meaning of the difference between the light - cone positions of two points . here it describes the light - cone position of one of the two only . i represent the initial `` unperturbed '' quark state in the form @xmath29 so our hadron consists in a coherent superposition of plane wave states with given @xmath0 , @xmath20 and transverse spin , each with amplitude @xmath30 or @xmath31 . i suppose that the parent hadron has @xmath32polarization @xmath4 , and that one initial state only contributes to the final distribution function . the expected distribution has the form is the sivers function . since this work refers to energies @xmath11 10@xmath33300 gev , i will speak of `` sivers asymmetry '' referring to the full second term @xmath34 . ] @xmath35 the sivers asymmetry can of course be isolated by subtracting two terms like the previous one , corresponding to opposite hadron polarizations . here i limit myself to searching for @xmath36asymmetric terms in the above @xmath37 unpolarized quark distribution corresponding to one assigned hadron transverse polarization . to introduce initial state interactions , i identically write @xmath38 as a twice iterated fourier transform , and in the intermediate stage i substitute each plane wave spinor by a spinor that contains the distortion due to the initial state interactions . writing only the @xmath39dependence for simplicity , it means that in the undistorted plane wave @xmath40\vec f_{pw}(x')\ ] ] ( where @xmath41 is the identity matrix and in the last passage i have only highlighted the piece to be modified ) the free field operator @xmath42 is substituted by the more general matrix operator @xmath43 reproducing a field subject to the action of initial state interactions : @xmath44 more precisely , initial state interactions in eikonal approximation affect the quark light - cone path starting from @xmath17 @xmath1 @xmath45 and reaching the hard interaction point @xmath17 , along fixed impact parameter lines ( see the discussion in refs.@xcite and @xcite , and compare the figures describing final state interactions for deep inelastic scattering in ref.@xcite with those for initial state interactions in drell - yan in ref.@xcite ) . these initial state interactions are here averaged by an effective mean field containing absorbing and spin orbit terms . so , each plane wave is substituted by a wave with" +"ever since mark kac posed the question `` can one hear the shape of a drum ? '' @xcite , there has been a great deal of interest in finding relations between the geometry of a manifold or a graph and spectral properties of the laplacian defined on it . the impressive works @xcite , which have been chosen by way of example , witness the steady progress achieved in recent years and provide further references . whereas laplacians on manifolds dominated the scene in the earlier years , the rise of spectral graph theory @xcite in the late 1980s and 90s has contributed to deepen our understanding of the discrete case . spectral theory of random graphs , however , is still a widely open field . the very recent contributions @xcite take a probabilistic point of view to derive heat - kernel estimates for laplacians on _ supercritical _ bernoulli bond - percolation graphs in the @xmath0-dimensional hyper - cubic lattice . on the other hand , traditional methods from spectral theory are used in @xcite to investigate the integrated density of states of laplacians on _ subcritical _ bond - percolation graphs . depending on the boundary condition that is chosen at cluster borders , two different types of _ lifshits asymptotics _ at spectral edges were found @xcite . for example , the integrated density of states of the neumann laplacian behaves as @xmath1 at the lower spectral edge for bond probabilities @xmath2 below the percolation threshold @xmath3 . we have put quotation marks here , because , strictly speaking , one should take appropriate logarithms on both sides . the lifshits exponent @xmath4 in is independent of the spatial dimension @xmath0 . this was explained by the fact that , asymptotically , @xmath5 is dominated by the smallest eigenvalues which arise from very long _ linear clusters _ in this case . in contrast , for the dirichlet laplacian and @xmath6 , it was found that @xmath7 we note that @xmath8 . the lifshits exponent in comes out as @xmath9 , because the dominating small dirichlet eigenvalues arise from large _ fully connected cube- or sphere - like clusters_. thus , depending on the boundary condition ( and the spectral edge ) different geometric graph properties show up in the integrated density of states . we refer to the literature cited in @xcite for a discussion of other spectral properties of these and closely related operators , for the history of the problem and what is known in the physics literature . lifshits asymptotics for a neumann laplacian on erds rnyi random graphs are studied in @xcite . in this paper we pursue the investigations of @xcite and ask what happens to and in the _ supercritical phase _ of bond - percolation graphs . clearly , one would not expect the contribution of the finite clusters to alter the picture completely . but for the infinite percolating cluster , the story may be different . indeed , we will prove that the percolating cluster produces a _ van hove asymptotics _ @xmath10 in the neumann case for @xmath11 . there is also an additional lifshits - tail behaviour due to finite clusters , but it is hidden under the dominating asymptotics . loosely speaking , is true because the percolating cluster looks like the full regular lattice on very large length scales ( bigger than the correlation length ) for @xmath11 . on smaller scales its structure is more like that of a jagged fractal . the neumann laplacian does not care about these small - scale holes , however . all that is needed for to be true is the existence of a suitable @xmath0-dimensional , infinite grid . in contrast , the dirichlet laplacian does care about holes at all scales so that continues to hold for @xmath12 , as we shall prove . low - lying dirichlet eigenvalues require large fully connected cube- or sphere - like regions , and this is a large - deviation event . closely related large - deviation results for laplacians on percolation graphs have been obtained in @xcite . to be precise , @xcite refer to the pseudo - dirichlet laplacian @xmath13 in the sense of our definition [ deltadef](ii ) below . considering both site- and bond - percolation graphs , and using a discrete version of the method of enlargement of obstacles , antal @xcite derives the long - time asymptotics for the mean ( i.e. annealed ) hitting - time distribution of the set of absent sites ( resp . bonds ) for the random walk generated by @xmath13 . biskup and knig work in the setting of the parabolic anderson model , which contains @xmath13 on _ site_-percolation graphs as a special case . in particular , they establish a lifshits tail for the corresponding integrated density of states , see also remark [ bikorem ] . this paper is organised as follows . in the next section we give a precise statement of our results in theorems [ lifshits ] and [ hove ] . section [ lifshitsproof ] is devoted to the proof of theorem [ lifshits ] . in this proof we follow the strategy laid down in @xcite , see also @xcite . the goal there was to establish lifshits tails in the context of random schrdinger operators . finally , section [ hoveproof ] contains the proof of theorem [ hove ] , where we apply the recent deep heat - kernel estimates from @xcite . to set up the mathematical arena , let us first recall some notions from bernoulli bond percolation . for @xmath14 , a natural number , we denote by @xmath15 the ( simple hyper - cubic ) lattice in @xmath0 dimensions . being a graph , the lattice @xmath16 has the _ vertex set _ @xmath17 and the _ edge set _ @xmath18 given by all unordered pairs @xmath19 of nearest - neighbour vertices @xmath20 , that is , those vertices which have euclidean distance latexmath:[$|x - y| : = \bigl(\sum_{\nu=1}^{d } @xmath17 are canonically represented as @xmath0-tuples @xmath22 with entries from @xmath23 . next , we consider the probability space @xmath24 , which is endowed with the usual product sigma - algebra , generated by finite cylinder sets , and equipped with a product probability measure @xmath25 . elementary events in @xmath26 are sequences of the form @xmath27 , and we assume their entries to be independently and identically distributed according to a bernoulli law @xmath28 with _ bond probability _ @xmath290,1[$ ] . to a given @xmath30 , we associate an edge set @xmath31 . a _ bond - percolation graph in @xmath17 _ is the mapping @xmath32 with values in the set of subgraphs of @xmath15 . given @xmath33 , the _ vertex degree _ @xmath34 counts the number of edges in @xmath35 which share @xmath36 as a common vertex . [ deltadef ] the random operators @xmath37 , respectively @xmath38 , are called vertex - degree operator , respectively adjacency operator , of bond - percolation graphs in @xmath17 . their realisations , @xmath39 , respectively @xmath40 , act on the hilbert space of complex - valued , square - summable sequences indexed by @xmath17 according to @xmath41 for all @xmath42 , all @xmath33 and all @xmath30 . with these definitions , we introduce _ laplacians on bond - percolation graphs _ for three different `` boundary conditions '' at non - fully connected vertices + [ cols= "" > , < , < "" , ] here @xmath43 stands for the identity operator on @xmath44 . the motivation and origin of the terminology for the different boundary conditions are discussed in @xcite together with some basic properties of the operators . [ genergodic ] the random self - adjoint laplacians are ergodic with respect to @xmath17-translations . hence , their spectra and the spectral subsets arising in the lebesgue decomposition are all equal to non - random sets with probability one . in particular , the spectrum is @xmath25-almost surely given by @xmath45 $ ] for all @xmath46 , as was shown in @xcite . next , we define the quantity of our main interest for this paper , the integrated density of states of @xmath47 . to this end let @xmath48 be the sequence which is concentrated at the point @xmath33 , i.e. @xmath49 and @xmath50 for all @xmath51 . moreover , @xmath52 stands for the heaviside unit - step function , which we choose to be right continuous , viz . @xmath53 for all real @xmath54 and @xmath55 for all real @xmath56 . [ ndef ] for every @xmath290,1[$ ] and every @xmath46 we call the function @xmath57 with values in the interval @xmath58 $ ] the _ integrated density of states of _ @xmath47 . the integrated density of states @xmath59 is the right - continuous distribution function of a probability measure on @xmath60 . the set of its growth points coincides with the @xmath25-almost - sure spectrum @xmath61 $ ] of @xmath47 . it is shown in @xcite that the laplacians are related to each other by a unitary involution , which implies the symmetries @xmath62 for their integrated densities of states for all @xmath63 . the limits on the right - hand sides of ensure that the discontinuity points of @xmath59 are approached from the correct side . [ fininf ] by ergodicity , definition [ ndef ] of the integrated density of states coincides with the usual one in terms of a macroscopic limit of a finite - volume eigenvalue counting function . more precisely , let @xmath64 stand for bounded cubes centred at the origin with volume @xmath65 . for every @xmath46 let @xmath66 be the finite - volume restriction of @xmath47 to @xmath67 introduced in def . 1.11 in @xcite . then there exists a set @xmath68 of full probability , @xmath69 , such that @xmath70\ ] ] holds for all @xmath71 and all @xmath72 , except for the ( at most countably many ) discontinuity points of @xmath59 , see lemma 1.12 in @xcite . in section [ lifshitsproof ] we will construct another finite - volume restriction of @xmath13 , for which holds , too . let @xmath73 denote the critical bond probability of the percolation transition in @xmath17 . we recall that @xmath74 for @xmath75 , otherwise @xmath760,1[$ ] , see e.g. @xcite . despite the title of this paper , our first main result covers the non - percolating phase @xmath770,p_{c}[$ ] and the critical point @xmath78 , too . [ lifshits ] assume @xmath79 and @xmath290,1[$ ] . then the integrated density of states @xmath59 of the laplacian @xmath47 on bond - percolation graphs in @xmath17 exhibits a _ lifshits tail _ at the lower spectral edge @xmath80 and at the upper spectral edge @xmath81|}{\ln ( 4d -e ) } = -\ ; \frac{d}{2 } \qquad \mathit{for } \quad \mathrm{x } \in \{\mathrm{n } , \widetilde{\mathrm{d}}\ } \,.\ ] ] the theorem follows directly from the upper and lower bounds in lemma [ liflemma ] below , together with the subsequent remark [ lifrelate ] . in fact , the bounds of lemma [ liflemma ] provide a slightly stronger statement than theorem [ lifshits ] . [ lifrelate ] the lifshits tails at the upper spectral edge are related to the ones at the lower spectral edge by the symmetries . in the non - percolating phase , @xmath770,p_{c}[$ ] , the content of the theorem is known from @xcite , where it is proved by a different method . the method of @xcite , however , does not seem to extend to the critical point or the percolating phase , @xmath82p_{c},1[$ ] . the lifshits asymptotics of theorem [ lifshits ] are determined by those parts of the percolation graphs , which contain large , fully - connected cubes . this" +"neutral hydrogen gas ( ) on the edges of spiral galaxies is only very loosely gravitationally bound . therefore , when spiral galaxies interact , the outer can be easily disturbed ( hibbard & van gorkom 1996 ) . during a merger , the may be heated and ionised , or may cool into molecular ( @xmath4 ) clouds within the remnant ( hibbard & van gorkom 1996 ) . it may be tidally driven into the centre of the galaxy and converted into molecular gas , or it could be turned into stars when tidal streams collide and become compressed . the gas may also escape the interacting system and disperse , becoming too diffuse to detect , or perhaps ionised . this paper re - examines the evidence for deficiency in compact groups of galaxies using a new survey , the parkes all sky survey . compact groups of galaxies are excellent places to look for interactions and mergers between ( spiral ) galaxies . a compact group is defined as having several galaxies with similar redshifts within a small area of the sky , which are also isolated from surrounding galaxies . this ensures that the cores of clusters are excluded from the definition . a compact group generally has a low velocity dispersion , @xmath5250 km s@xmath6 ( hickson 1997 ) , and a crossing time much smaller than the hubble time , meaning interactions and mergers are very likely . although the fraction of spirals in the field is higher ( @xmath580% ) , the fraction of compact group galaxies which are spirals is still @xmath550% ( hickson 1997 ) . although interactions are thought to be common in compact groups , the star - formation rate ( sfr ) , and the amount of molecular gas in the galaxies in the compact groups , are only weakly enhanced in comparison to field galaxies ( leon et al . they concluded that only compact groups with a very small mean separation of @xmath730 kpc had a strong @xmath4 enhancement . verdes - montenegro et al . ( 1998 ) also showed that while 20% of compact groups had an apparent deficiency of co emission , the rest had co and fir properties similar to isolated galaxies . both leon et al . ( 1998 ) and verdes - montenegro et al . ( 1998 ) concluded that tidal interactions in compact groups were very important in the groups evolution . the aim of this paper is to determine the extent to which the in compact groups has been affected by the environment . this has been investigated previously by williams & rood ( 1987 , hereafter wr87 ) , huchtmeier ( 1997 , hereafter h97 ) and verdes - montenegro et al . ( 2001 ) , all of whom observed subsamples of the hickson compact groups ( hcgs , hickson 1982 ) . their results indicated that the average amount of in the groups was between 40% and 50% of the mass expected by summing the mean mass in comparable field galaxies . williams & rood ( 1987 ) compared the content of the compact groups with that of a reference sample of loose groups ( rlg ) , and with a sample of 204 spiral galaxies in the rc2 ( de vaucouleurs et al . 1976 ) . in the south , wr87 observed hcgs 3 , 14 , 16 , 19 , 22 , 23 , 25 , 26 , 30 , 31 , 40 , 62 , 64 , 67 , 88 , 89 and 97 . the comparison loose groups were selected to have the same number of galaxies as the compact groups , and to have the same joint distribution of galaxy luminosity , hubble morphological type . the expected masses therefore were a function of the luminosity of the galaxies . twenty - seven of the 34 detected compact groups had less than the comparable loose group . a similar procedure was used by huchtmeier ( 1997 ) , using an explicit relation between the integrated blue luminosities of the groups and the expected masses of the groups . the groups observed in the south were hcgs 4 , 14 , 19 , 21 , 22 , 24 , 25 , 26 , 30 , 40 , 42 , 48 , 62 , 67 , 87 , 91 and 97 . in comparison to four nearby groups , a reference sample of 146 galaxies ( huchtmeier & richter 1988 ) , and to the virgo cluster spirals , several compact groups appeared to have a very low mass - to - blue luminosity ratio . these authors did not consider how the mass of the compact groups related to the distribution of masses in the comparison samples . instead , only the average values of the sample galaxy masses were used . however , any two galaxies with identical optical measurements ( eg . diameter , morphology , luminosity ) will not necessarily have the same mass . there may be a dependence of the mass on these observables , but the scatter in this correlation is significant . verdes - montenegro et al . ( 2001 ) compiled the data from wr87 and h97 , and added vla imaging of 16 hcgs ( 2 , 16 , 18 , 23 , 26 , 31 , 33 , 40 , 44 , 49 , 54 , 79 , 88 , 92 , 95 , 96 ) . using all 72 groups from the combined sample , verdes - montenegro et al . ( 2001 ) calculated the mean `` deficiency '' to be def@xmath8 , where def@xmath9 - \log[{\rm m(hi)}_{\rm observed}]$ ] . a comparison sample from haynes & giovanelli ( 1984 ) was used . this comparison sample is also used in this paper and is described in section [ estimators ] . calculated values of def@xmath10 suggested that compact groups contained only 40% of the mass of comparable field galaxies . verdes - montenegro et al . ( 2001 ) also deduced that an evolutionary sequence for hcgs could be followed , beginning with being associated with individual galaxies , through to the gas enveloping the entire group , to a group having no detectable . this paper compares the content of the galaxies in compact groups with estimated values of mass for field galaxies . the distribution of mass in the reference field galaxies will be specifically included in the comparison . thus it is possible to identify groups with masses outside the expected range . the upper limits of the non - detected groups are also taken into account using the statistical methods of buckley & james ( 1979 ) . this paper first deals with the selection of the group sample ( section [ samplesel ] ) , and then with the observations , reduction and the derived parameters ( section [ obsresults ] ) . the mass estimation methods are described in section [ estimators ] , as well as the estimated content of the groups . section [ discussion ] compares the relative contents of the compact groups and the reference sample . for this paper , h@xmath11 mpc@xmath6 compact groups were selected from the optical catalogues of hickson ( 1982 , hereafter h82 ) and prandoni et al . ( 1994 , hereafter p94 ) . the sample included all compact groups which had a declination @xmath12 , and a velocity @xmath13 km s@xmath6 . a total of 62 groups satisfied these criteria , and are the primary sample of this paper . hipass covers the entire southern sky up to a declination of @xmath14 , over the velocity range @xmath15 km s@xmath6 ( barnes et al . 2001 ) . using the 13-beam multibeam instrument on the parkes radio telescope , the survey was completed in march 2000 . the velocity resolution of the survey is 18.0 km s@xmath6 , and the rms noise per channel is typically 13 mjy . the hickson compact groups ( h82 ) - for which a complete catalogue of properties of the constituent galaxies is available ( hickson 1993 ) - were selected so that a direct comparison with previous results could be made . the southern compact groups ( scgs , p94 ) were selected by an automatic routine , and therefore have the potential to be a more complete and less biased sample ( p94 ) . however , there has not been a published follow - up survey of the member galaxies , and thus the scgs do not have complete redshift information . h82 selected groups from the red palomar observatory sky survey ( poss ) plates by eye , with each of the groups satisfying specific criteria . firstly , the groups needed to be compact and isolated . specifically , there needed to be at least 4 galaxies within 3 magnitudes of the brightest galaxy , all within a circle of angular radius @xmath16 , the group radius . the isolation criteria specified that there should be no galaxies within 3 magnitudes of the brightest galaxy within @xmath17 of the group centre . the magnitude concordance was used to select physically associated groups without any redshift information , while the isolation criteria ensured that the cores of clusters , and associations in clusters were not identified as compact groups . p94 selected groups in the same way as h82 , except that the search was on cosmos scans of plates taken with the united kingdom schmidt telescope ( ukst ) , and the search algorithm was machine implemented . the miriad task * mbspect * was used to inspect the hipass spectrum for each group , which was made by averaging over a region of 5@xmath185 pixels , centered on the optically determined position of the group . each hipass pixel is 4 arcminutes on a side . this 20@xmath1920@xmath20 averaging area ensures that all flux coming from the groups is accounted for , as the largest group in the sample has an optical diameter of @xmath21 . the spectra were examined by eye for emission lines , and groups with evidence of emission were selected for reobservation . the hcg spectra were searched at each group s known optical velocity ( hickson 1993 ) . the scgs however , do not have comprehensive velocity information for all their member galaxies , and thus the entire velocity range of hipass was examined at each scg position on the sky . in total , 19 hcgs and 21 scgs showed possible emission . twelve hcgs and ten scgs were clear non - detections . the primary sample for this paper is shown in table [ basicdata ] . column ( 1 ) gives the name of the compact group , and columns ( 2 ) & ( 3 ) give the position of the group in j2000 coordinates . .basic observational data for the compact group sample and pointed observations using the mx mode . descriptions of the quantities in each column are given in the text . [ cols=""^,^,^,^,^,^,^ "" , ] finally , this result can be contrasted to that found by solanes et al . ( 2001 ) who studied the deficiency in spiral galaxies found in clusters . they found that within 1 abell radius ( 1 r@xmath22 ) of the cluster centre , spiral galaxies show strong deficiency , while in the outer parts of the cluster , the contents were similar to those found in the field . as the galactic densities of compact groups can approach that of the cores of rich clusters ( h82 ) , it is interesting then that compact groups do not show the same deficiency . solanes et al . ( 2001 ) concluded that hydrodynamical effects caused by the interaction of the with the hot" +"the plasma membrane is a complex fluid where lipids and proteins continuously interact and generate signaling platforms in order to communicate with the outside world . one of the key mechanisms by which membrane molecules search reaction sites is based on lateral diffusion . quantitative imaging methods , such as single - particle tracking @xcite , spatiotemporal image correlation spectroscopy @xcite , fluorescence correlation spectroscopy ( fcs ) @xcite , and sted - fcs @xcite , show that the dynamics of proteins and lipids in the plasma membrane often deviate from normal diffusion . in particular , the mean square displacement ( msd ) does not grow linearly in time as expected for brownian motion @xcite . this behavior suggests processes that hinder diffusion . since the formation of protein complexes is governed by diffusion - mediated encounters , hindered diffusion plays fundamental roles in cell function . unveiling the underlying mechanisms leading to the observed anomalous diffusion on the cell membrane is critical to understanding cell behavior . anomalous diffusion in the plasma membrane can be caused by macromolecular crowding @xcite , transient binding @xcite , heterogeneities @xcite , and membrane compartmentalization by the underlying cytoskeleton @xcite . in recent years it has become evident that a single mechanism can not account for the complex dynamics observed in the plasma membrane @xcite . we have shown that interactions with clathrin coated pits ( ccps ) cause anomalous diffusion and ergodicity breaking @xcite . however , it was observed that this process coexisted with a different anomalous diffusion mechanism attributed to diffusion within a fractal topology . experimental evidence for the organization of the plasma membrane by the cortical actin cytoskeleton has been provided by measurements in cell blebs , spherical protrusions that lack actin cytoskeleton @xcite , and in the presence of actin - disrupting agents @xcite . the picket - fence model explains these observations by postulating that the mobility of membrane - bound molecules is hindered by the actin - based cytoskeleton in close proximity to the plasma membrane , leading to transient confinement @xcite . confinement and segregation of membrane components can have important physiological consequences by allowing the formation of functional domains on the cell surface . however , in spite of the vast evidence that has accumulated over the last two decades , a direct observation of the dynamic compartmentalization of membrane proteins by underlying actin fences is challenging due to the spatial and temporal resolutions required for its visualization . here we employ superresolution imaging and single - particle tracking of membrane proteins to elucidate the compartmentalization of the plasma membrane by intracellular structures . while tracking individual voltage - gated potassium channels as described in our previous studies @xcite , we found that these membrane proteins exhibited anomalous diffusion on the cell surface . we now report that the anticorrelated dynamics are best modeled by obstructed diffusion instead of fractional brownian motion and we directly visualize the transient confinement of potassium channels by cortical actin in live cells . in order to characterize the cortical actin meshwork , we employ stochastic optical reconstruction microscopy ( storm ) to obtain superresolution images in fixed cells . we find a non - integer fractal dimension for the actin cortex and a broad distribution of compartment sizes as expected for a self - similar structure . these observations consistently explain the anticorrelated subdiffusive motion of membrane proteins and provide new insights on the hierarchical organization of the plasma membrane . voltage - gated potassium channels kv1.4 and kv2.1 were expressed in human embryonic kidney ( hek ) cells , labeled with quantum dots ( qds ) @xcite , and imaged using total internal reflection fluorescence ( tirf ) microscopy at 50 frames / s , so that individual molecules could be detected on the cell surface . kv1.4 and 2.1 are similar in size , 654 and 853 amino acids , respectively , but share less than 20% overall amino acid identity @xcite . they are placed into distinct gene subfamilies because of this low identity . they are most similar within a central core domain composed of six transmembrane alpha helices and the ion conducting pore . in contrast , they share no amino sequence identity within the cytoplasmic n- and c - terminal regions ; each kv1.4 subunit has 402 cytoplasmic amino acids while the kv2.1 subunits have 624 . both channels exist as homotetrameric structures giving the functional channel 24 membrane spanning domains and a total of either 1608 or 2496 cytoplasmic amino acids . figure [ fig : turn](a ) shows representative trajectories of kv1.4 channels . the motion of the ion channels was initially evaluated in terms of their time - averaged msd , @xmath0 where @xmath1 is the total experimental time , @xmath2 the particle position , and @xmath3 the lag time , i.e. , the time difference over which the msd is computed . when a particle displays brownian diffusion , the msd is linear in lag time , i.e. , @xmath4 . in contrast , anomalous diffusion is characterized by a different msd scaling , namely msd @xmath5 , where @xmath6 is the anomalous exponent . anomalous diffusion is classified as subdiffusion when @xmath7 and superdiffusion when @xmath8 . figure [ fig : turn](b ) shows the msd of 20 individual trajectories . the msds of kv1.4 as well as kv2.1 channels show subdiffusive behavior , albeit with large apparent fluctuations . figures [ fig : turn](c ) and [ fig : turn](d ) show the msds averaged over 1,312 kv1.4 ( @xmath9 cells ) and 6,385 kv2.1 ( @xmath10 cells ) trajectories , respectively , @xmath11 . throughout the manuscript we employ overlines to denote time averages and brackets to denote ensemble averages . the anomalous exponent @xmath6 of kv1.4 was found to be 0.89 and that of kv2.1 was 0.74 , indicating subdiffusion in both cases . several distinct mathematical models lead to subdiffusion @xcite . among the most well - accepted types of subdiffusion in biological systems , we encounter ( i ) obstructed diffusion , ( ii ) fractional brownian motion ( fbm ) , and ( iii ) continuous time random walks ( ctrw ) . both fbm @xcite and obstructed diffusion @xcite are models for subdiffusive random walks with anticorrelated increments that have been extensively used in live cells . fbm describes the motion in a viscoelastic fluid @xcite , which can be caused by macromolecular crowding @xcite . fbm is a generalization of brownian motion that incorporates correlations with power - law memory . it is characterized by a hurst exponent @xmath12 that translates into an anomalous exponent @xmath13 . obstructed diffusion describes the motion of a particle hindered by immobile ( or slowly moving ) obstacles , e.g. , percolation . as the concentration of immobile obstacles increases , the availability of space decreases . near a critical concentration known as percolation threshold , the obstacles form a fractal with dead ends in all length scales . in particular , the reduction of the available space results in anomalous diffusion with a recurrent exploration pattern . a ctrw is a generalization of a random walk where a particle waits for a random time between steps @xcite . when the waiting times are asymptotically distributed according to a power law such that the mean waiting time diverges , the ctrw is subdiffusive . these three models describe very distinct physical underlying mechanisms but they can yield similar sublinear msd scaling , particularly in obstructed diffusion and fbm models . thus the msd analysis is insufficient to elucidate the type of random walk . different tests beyond the msd have been employed to distinguish among types of subdiffusive random walks , including _ p_-variations @xcite , first passage probability distribution @xcite , mean maximal excursion @xcite , gaussianity @xcite , and fractal dimensions @xcite . here we employ the distribution of directional changes , i.e. , the turning angles , a tool that probes correlations in the particle displacements and has been shown to contain information on the complexity of a random walk @xcite . figure [ fig : turn](e ) illustrates the construction of turning angles from a particle trajectory . in simple brownian motion , the turning angles are uniformly distributed . contrastingly , when the steps are correlated the distribution of turning angles is not uniform @xcite . figures [ fig : turn](f ) and [ fig : turn](g ) show the distribution of turning angles of kv1.4 and kv2.1 for different lag times ( 1,312 kv1.4 tracks , 10 cells and 6,385 kv2.1 tracks , 14 cells ) . both distributions peak at @xmath14 indicating the particles are more likely to turn back than to move forward . in other words , kv channels have a preference to go in the direction from where they came rather than to persist moving in the same direction . this property is a fingerprint of subdiffusive random walks with anticorrelated increments . besides the shape of the distribution , the dependence on lag time bears valuable information . strikingly , we observe that the distribution is independent of lag time , i.e. , we measure the same distribution of directional changes whether the lag time is 20 ms or 1 s. we examined numerical simulations of fbm and obstructed diffusion and found that they have distinctive attributes in their distribution of directional changes . figure [ fig : turn](h ) shows the distribution of directional changes for subdiffusive fbm simulations with hurst exponents @xmath15 and @xmath16 . even though the distributions peak at @xmath17 , the probability density function is different from the experimental data [ figs . [ fig : turn](f ) and [ fig : turn](g ) ] . in our experimental data , the turning angle distributions increase sharply as @xmath18 approaches @xmath17 and most of the deviations from a uniform distribution are above @xmath19 . however , fbm gives rise to a gradual increase that takes place mainly in the range @xmath20 . further , the turning angles of fbm reach a plateau , in contrast to our measurements . conversely , obstructed diffusion , strongly resembles our experimental results . figure [ fig : turn](i ) shows the turning angle distribution for obstructed diffusion simulations in a square lattice with obstacle concentrations @xmath21 and @xmath22 @xcite . note that @xmath22 is slightly above the percolation threshold . these results show that the motion of kv channels in the plasma membrane is better modeled by percolation , i.e. , obstructed diffusion , rather than motion in a viscoelastic medium , i.e. , fbm . potential obstacle candidates for obstructed diffusion in the plasma membrane are the cortical cytoskeleton , lipid rafts , and extracellular glycans . by evaluating the msd and turning angle distribution of @xmath3c318 , a mutant in which the last 318 amino acids of the c - terminus of kv2.1 channel had been deleted @xcite , we found that the anticorrelated diffusion originates from interactions with intracellular structures . we observed that @xmath3c318 channels diffuse freely in the plasma membrane , @xmath23 with a diffusion coefficient @xmath24/s [ fig . [ fig : turn](j ) , n=3114 tracks , 5 cells ] . further , the distribution of turning angles of @xmath3c318 was flattened , as expected for brownian diffusion [ fig . [ fig : turn](k ) ] , indicating the intracellular c terminal domain of kv2.1 plays a key role in the anticorrelations within the particle trajectory . even though the distribution of turning angles in the @xmath3c318 mutant is close to that in brownian motion , a small peak is still noticeable at @xmath17 suggesting additional complexities in the plasma membrane . in contrast to kv1.4 , which is homogeneously distributed on the cell membrane , a subpopulation of kv2.1 channels forms micron - sized clusters that localize to endoplasmic" +"we would like to know if agn really have accretion disks . predictions of the spectral energy distribution ( sed ) are hard to make , and model dependent , and so are not a robust test . instead , i consider effects that test the generic idea of blackbody emission at a range of temperatures from a flat surface . from a tilted flat surface , we should see a standard @xmath0 dimming plus whatever atmospheric limb darkening effects might apply . for superluminal sources we can derive a fairly accurate viewing angle to the jet . for a sample of 21 such sources rokaki _ et al _ ( 2002 ; see also these proceedings ) have measured the @xmath1 equivalent width ( ew ) , which gives the relative continuum brightness if the face on ew is always the same . the results show two separate effects . at small angles ew has a steep @xmath2 dependence , presumably due to relativistic jet beaming . at larger angles , ew declines more gently with @xmath2 , and the simplest model , with @xmath0 dimming and standard thin disk limb darkening , fits extremely well . the data are not good enough to distinguish rival disk models , but the general idea of a flat tilted emitter is strongly endorsed . the seds of luminous quasars peak in the uv , roughly as expected for blackbody emission from around a billion solar mass black hole . ( actually , observed seds are a little cooler than expected .. ) . the spectral index curves slowly from @xmath3 in the optical , through @xmath4 near the peak , and finally steepening to @xmath5 in the far - uv and onwards through the soft x - ray excess . ( elvis _ et al _ 1994 ) . however lower luminosity seyfert galaxies often have @xmath6 , and dwarf agn have @xmath7 ( e.g. ho filippenko and sargent 1996 ; ho , these proceedings ) . in fact @xmath8 and @xmath9 change slowly and systematically with luminosity ( mushotzky and wandel 1989 ; zheng and malkan 1993 ; puchnarewicz _ et al _ 1996 ; see fig . this change is consistent with the big blue bump ( bbb ) shifting to lower frequency with lowering luminosity , from blue bump to green bump to red bump , in a manner reminiscent of a cooling blackbody . of course accretion disks are not single blackbodies , but the sum of blackbodies . one can show that if an sed @xmath10 is made of the sum of blackbody emitting areas , and that each sub - area changes temperature by the same factor @xmath11 , then the new sed can be expressed in terms of the old one by the scaling formula @xmath12 ( lawrence 2002 in preparation ) . one expects accretion discs to behave just this way when varying accretion rate or central heating rate , and roughly this way when varying black hole mass , as long as one considers emission coming well away from the inner boundary . as a result , if one has a template sed , then one can use the scaling formula to predict all other seds without having to know how the sed was made - i.e. whether it was from a thick disk , donut , flared disk , etc . the scaling simply tests the idea that the sed is made from the sum of blackbodies . -0.2 cm -0.2 cm i took two template seds - 3c273 , from kriss _ et al _ 1999 , and h1946 + 786 from kuhn _ et al _ 1995 - and calculated the expected @xmath8 vs luminosity track . the result is shown in fig . 1 and shows an impressive agreement remembering that this prediction has no adjustable parameters . it starts to break down at the low end , but this could easily be due to boundary conditions , or the effect of reddening etc . the extreme ends of the diagram require the controlling parameter , e.g. accretion rate , to vary by something like a factor of a million . seyfert galaxy optical - uv variations show the bbb getting bluer when brighter . do these variations also follow the sum - of - blackbodies scaling law ? 1 indicates the low and high states of ngc 5548 , from peterson _ et al _ 1991 . clearly the colour variations are far too strong . a single black body track is almost this steep , but the wide range of temperatures needed to explain the sed produces a far flatter track . a possible explanation is that the colour changes result from mixing a variable blue component of approximately fixed shape with a static red component . perhaps then the @xmath13 locus we see in fig . 1 represents a kind of baseline stable state for agn accretion discs heated by gravity / viscosity , with the thickness of the correlation caused by various degrees of mixing of a second variable component that has a different heating source . from the point of view of accretion disc models , or indeed any models where the energy is generated through an extended structure , there are two problems with seyfert galaxy optical - uv variations . ( i ) the timescale - months - is far shorter than the viscous timescale expected for stable accretion discs , which is hundreds of years . ( ii ) variations occur simultaneously at different wavelengths , whereas emission at different wavelengths should arise at very different radii . fluctuations travelling at sound speed should then produce delays of order months . et al _ ( 1991 ) proposed that much of what we see is reprocessed radiation , so that fluctuations co - ordinate at light speed . that paper discussed optical fluctuations driven by uv , but most authors since have assumed that the variable uv itself is driven by variations in the observed x - ray source . the reprocessing idea seems to have been dramatically confirmed by observations of ngc 7469 , which shows that there _ are _ delays , but on a timescale of hours to days , and with delay varying as @xmath14 exactly as expected for a simple centrally heated disc model ( collier _ et al _ 1998 , wanders _ et al _ 1997 ) . so accretion discs score well on the brightness - angle test , and on the luminosity - colour test , but fail to match observed variations , unless we drop the idea of local gravitational heating and instead have a second heating source , which dominates in the uv regions , and which communicates across the disk at light speed . for some years the second heating source has generally been identified with the observed x - ray source . however , the x - ray heating model has two serious problems . first , simultaneous uv and x - ray observations of n7469 have not shown the expected correlation , with the x - ray emission if anything _ trailing _ the uv ( nandra _ et al _ 1998 ) . second , the x - ray luminosity is substantially less than the uv luminosity - by a factor of a few in low luminosity seyferts , and by a factor of twenty in quasars . we arrive then at the strange conclusion that agn accretion disks seem to be externally heated , but by an agent that we do not see . furthermore this mystery agent must carry most of the primary energy in agn . this then is the _ ghost in the machine_. what else could heat the observed variable uv source ? if we require external heating at light speed , there would be seem two possibilities - an unseen radiation source , or particles . the most obvious radiation source is euv emission from the very inner disk . in observed terms there is just enough energy - essentially we are talking about the right hand side of the bbb heating the left hand side . however in flat discs , and even in flared discs , it is hard for the outer disc to see enough of the inner disc . ( gravitational bending helps , but probably not enough ) . particles are an interesting and under - explored possibility . we want such particles to deposit their energy in the disc as heat before radiating , so protons are a much better bet than electrons . if they are not to cool on local electrons before hitting the disk , then they are probably high energy protons . one such possibility is virialised protons at @xmath15k from a two - temperature inner region , if a thin cold disc can co - exist with it . this possibility has been considered by spruit and hardt ( 2000 ) , although they assume that such protons heat an x - ray corona , which in turn heats the disc , rather than heating the cold disc itself . a second source of high energy protons could be from a standing shock near the black hole ( e.g. kazanas and ellison 1986 ) . it could well be that much of the accretion energy is generated in the `` plunging region '' inside 3@xmath16 , with most of the mass disappearing , but a large fraction of the energy being channelled into ultrarelativistic particles that escape . as these will follow field lines it is likely that most of these particles will end up in the disc . however they may lose most of their energy on the way , or at the skin of the disc , producing more gamma - rays than we observe . finally , bombardment by such particles may significantly alter abundances in the disc . skibo ( 1997 ) has in fact already argued that features in the wings of the x - ray fe line can be attributed to emission from just such enhanced abundances produced by cosmic rays . the above discussion assumes that the disc is _ externally _ heated , persuaded by the consistency of the time - delay versus wavelength result with the expected light - travel time . however the near - simultaneity of variations more generally drives us to drop the idea of distributed local heating . another possibility then is that much of the energy is generated near the black hole in some unknown form , and transmitted through the _ interior _ of the disc , perhaps by fast shocks , emerging at a larger radius as ( approximately ) nice simple black - body radiation . this makes an agn seem more like a star , but with a nastier geometry . probably in fact we need both local and central energy generation . collier , s. , _ et al_. : 1998 , apj , 500 , 162 . elvis , m. _ et al_. : 1994 , apjsupp , 95 , 1 . kazanas , d . , and ellison , d.c . : 1986 , apj , 304 , 178 . kriss , g.a . , _ et al_. : 1998 , apj , 527 , 683 . krolik , j.h . , _ et al_. : 1991 , apj , 371 , 541 . kuhn , o. , _ et al_. : 1995 , apj , 438 , 643 . ho , l.c . , filippenko , a.v . , and sargent , w.l.w . : 1996 , apj , 462 , 183 . mushotzky , r.f . , and wandel , a. : 1989 , apj , 339 , 674 . nandra , k. , _ et al_. : 1998 , apj , 505 , 594" +"the magnetic field evolution in plasmas such as the solar corona and the earth s magnetosphere often follows an ideal evolution in which all topological features of the field remain unchanged over time . this invariance provides a motivation to investigate topological properties of the magnetic field such as magnetic null points , flux surfaces and periodic field lines . some of these topological features , particularly magnetic null points , are surprisingly stable and turn out to be conserved not only under an ideal plasma dynamics but also for a wide range of non - ideal flows . mathematically this is reflected in the existence of an index theorem ( greene , 1992 ) for magnetic null points which allows only a small number of bifurcation processes to either generate or destroy magnetic null points . this underlines the importance of magnetic null points and their properties for the structure and dynamics of astrophysical plasmas . generic magnetic null points ( i.e. null points where all eigenvalues of the linearisation of the magnetic field at the null have non - zero real part ) are associated with certain distinguished field lines and flux surfaces , namely spines ( or @xmath0 lines in the terminology of lau & finn , 1990 ) and fan surfaces ( or @xmath1 surfaces ) as well as , sometimes , magnetic separators , the intersection lines of two fan surfaces . combined , these features are sometimes termed the magnetic skeleton ( e.g. priest & titov , 1996 ) . in dynamical systems terminology , null points are hyperbolic fixed points of a volume preserving ( divergence - free ) vector field and the spine and fan of a null are stable or unstable invariant manifolds . a null whose fan surface corresponds to a stable manifold and the spine line to an unstable manifold is designated as type a while the converse is known as type b. the magnetic separator is a heteroclinic intersection of fan surfaces , lying in the fan plane of both a type a and type b null as shown in figure [ fig : initialstate2 ] . conservation of topology has important implications for the plasma evolution , limiting the evolutions that may occur and the amount of free magnetic energy bound in the configuration . however , even for plasmas which are largely ideal , the frozen - in condition can be violated in localised regions ( such as current sheets ) where non - ideal effects become important . the key requirement for such a process to change the topology is to have a non - zero electric field component in the direction parallel to the magnetic field ( hesse & schindler , 1988 ) . such a component ( for further details see sections 4 and 5 ) enables a change in connectivity of the magnetic field lines and so a change of topology , the process being known as magnetic reconnection . reconnection may allow for significant magnetic energy release , both locally at the reconnection site and globally in the previously topologically bound energy . historically , models of magnetic reconnection were solely two - dimensional . theoretical considerations show that in two - dimensions reconnection can only occur at a hyperbolic ( x - type ) null - point of the field ( for details see e.g. hornig , 2007 ) . such null - points , lying at the intersection of four topologically distinct flux domains , are also likely sites of current sheet formation . the resultant reconnection is now fairly well understood ( for reviews see , e.g. biskamp 2000 , priest & forbes 2000 ) , although modelling still required to fully determine the importance of the complete physics including kinetic effects ( birn & priest 2007 ) . in three - dimensions , the typical situation in astrophysical plasmas , there are no fundamental restrictions on where reconnection occurs , the only requirement being the presence of a localised non - ideal term in ohm s law ( hesse & schindler , 2007 ; schindler _ et al . _ 1988 ) . accordingly , reconnection may take place wherever such non - ideal terms become important . three - dimensional null - points are thought to be one such location ( klapper _ et al . _ various forms of reconnection can occur at 3d nulls ( for a review see priest & pontin 2009 ) and the nature of the reconnection has been analysed in some detail ( e.g. pontin _ et al . _ 2004 , 2005 ; galsgaard & pontin 2011 ) . current sheets may also form away from null points ( e.g. titov _ et al . _ 2002 ; browning _ et al . _ 2008 ; wilmot - smith _ et al . _ models for the local reconnection process here ( e.g. hornig & priest 2003 , wilmot - smith _ et al . _ 2006 , 2009 ) show that , just as in the 3d null case , there are many distinct 3d characteristics of reconnection , some of which we discuss below . one topologically distinguished location where current sheets may form away from nulls is at separators which , like the 2d null point , lie at the intersection of four flux domains . it is this characteristic that has been used to argue why separators should be prone to current sheet formation ( lau & finn 1990 ) . the minimum energy state for certain field configurations has the current lying along separators ( longcope 1996 , 2001 ) and current sheet formation at separators has been observed in numerical simulations ( e.g. galsgaard & nordlund , 1997 ; haynes _ et al . _ 2007 ) . reconnection taking place at separators is known as separator reconnection . a recent series of papers ( including galsgaard & parnell 2005 ; haynes _ et al . _ 2007 ; parnell _ et al . _ 2008 ; parnell _ et al . _ 2010a ) examine the reconnection taking place in a ` fly - by ' experiment where two magnetic flux patches on the photosphere are moved past each other and the resultant evolution in the corona is followed . the authors find strong current concentrations and therefore reconnection around each of a number of separators ( up to five in some time frames , haynes _ et al . _ these separators are created in the reconnection process and connect the same two nulls ( see also longcope & cowley , 1996 ) . magnetic flux is found to evolve in a complex manner , being reconnected multiple times through these distinct reconnection sites ( parnell _ et al . _ 2008 ) . separators were also found to be important in a simulation of magnetic - flux emergence into the corona ( parnell _ et al . _ 2010b ) where current sheets between the emerging and pre - existing coronal field were shown to be threaded by numerous separators , a feature of complex magnetic fields suggested by albright ( 1999 ) . et al . _ ( 2010b ) found the regions of highest integrated parallel electric field to be at or in association with the separators , so arguing that reconnection occurs at the separators themselves . separator reconnection also appears to be a key process at the magnetopause where magnetic nulls or even clusters of nulls appear in the northern and southern polar cusp regions ( dorelli _ et al . _ 2007 these nulls are linked by a separator along the dayside magnetopause which will therefore be involved in reconnection with the interplanetary magnetic field . indeed reconnection in such a configuration has been implied by observations from the cluster spacecraft ( xiao _ et al . _ 2007 these studies partially motivate the present work where we want to investigate how and why multiple separators can be involved in reconnection . although separator configurations have been analysed for some time ( e.g. chance _ et al . _ 1992 ; craig _ et al . _ 1999 ) , there remain several unanswered basic questions surrounding the nature of separator reconnection , particularly involving the way magnetic flux evolves , i.e. exactly how the changes in field line connectivity occur . there have been suggestions that the reconnection involves a ` cut and paste ' of field lines at the separator itself in a manner similar to the 2d null case ( e.g. lau & finn 1990 ; priest & titov 1996 ; longcope _ et al . _ however , previous detailed investigations into the nature of individual 3d reconnection events both at and away from null points have shown the flux evolution to be quite distinct from the 2d picture ( hornig & priest 2003 ; pontin _ et al . _ 2004 , 2005 ) and , in the light of these models , such a simple flux evolution would be surprising . indeed a number of key features of 3d reconnection are now known which show many of its features are quite distinct to the 2d case . accordingly it would appear useful to re - examine the fundamental nature of separator reconnection and consider whether it has its own particular distinguishing characteristics . in doing so we also wish to address a conclusion of parnell et al . ( 2010a ) who suggested that separator reconnection does not appear to involve the nulls that lie at both ends of the separator as well as the recent findings ( parnell _ et al . _ 2010b ) of very large numbers of separators sometimes appearing in numerical mhd experiments . accordingly the aim of the present work is to describe in detail the nature of an isolated 3d reconnection event in the vicinity of a separator . we do so using a simple analytical model which is described in detail in section [ ref : themodel ] . the model allows us to consider typical magnetic field connectivities resulting from separator reconnection in section [ sec : bif ] and the nature of the magnetic flux evolution in section [ sec : evolve ] . we consider how reconnection rates may be determined in separator configurations in section [ sec : rates ] before discussing our findings and concluding in sections [ sec : discussion ] & [ sec : conc ] . a fully self - consistent model for reconnection must incorporate a dynamic evolution which generates current sheet(s ) as well as the reconnection that takes place at those current sheets and changes the magnetic field topology . an example in the solar corona is the emergence of a magnetic flux tube from the convection zone and reconnection with the pre - existing coronal magnetic field . inherent in such events is an enormous separation of scales between the global dynamic process and the local reconnection events . accordingly , a typical approach to model reconnection itself is to start with a local magnetic field configuration that is considered susceptible to current sheet formation ( such as , in two dimensions , an x - type null point of the field ) . in simulations the magnetic field is then confined to a finite region and the boundaries driven in such a manner as to initiate a reconnection event which can then be studied in detail . determining physically realistic boundary conditions is just one of the obstacles in this modelling technique . here we also take a simplified approach to consider the local reconnection process , aiming to model the effect of reconnection on the field topology in a three - dimensional magnetic separator configuration . as discussed in section 1 , such configurations are thought to be likely sites for current sheet formation and associated reconnection" +"the aim of the present work is twofold . firstly , we study here the effect of introducing small pressure perturbations in an otherwise pressure - free gravitational collapse which was to terminate in a black hole final state . for such a purpose , spherically symmetric models of black hole and naked singularity formation for a general matter field are considered , which undergo a complete gravitational collapse under reasonable physical conditions while satisfying suitable energy conditions . secondly , we investigate the genericity and stability aspects of the occurrence of naked singularities and black holes as collapse endstates . the analysis of pressure perturbations in known collapse models , inhomogeneous but otherwise pressure - free , shows how collapse final states in terms of black hole or naked singularity are affected and altered . this allows us to examine in general how generic these outcomes are and we study in the initial data space the set of conditions that lead the collapse to a naked singularity and investigate how ` abundant ' these are . while it is known now for some time that both black holes and naked singularities do arise as collapse endstates under reasonable physical conditions , this helps us understand and analyze in a clear manner the genericity aspects of occurrence of these objects in a complete gravitational collapse of a massive matter cloud in general relativity . the physics that is accepted today as the backbone of the general mechanism describing the formation of black holes as the endstate of collapse relies on the very simple and widely studied oppenheimer - snyder - datt ( osd ) dust model , which describes the collapse of a spherical cloud of homogeneous dust @xcite , @xcite . in the osd case , all matter falls into the singularity at the same comoving time while an horizon forms earlier than the singularity , thus covering it . a black hole results as the endstate of collapse . still , homogeneous dust is a highly idealized and unphysical model of matter . taking into account inhomogeneities in the initial density profile it is possible to show that the behaviour of the horizon can change drastically , thus leaving two different outcomes as the possible result of generic dust collapse : the black hole , in which the horizon forms at a time anteceding the singularity , and the naked singularity , in which the horizon is delayed thus allowing null geodesics to escape the central singularity where the density and curvatures diverge , to reach faraway observers @xcite-@xcite . it is known now that naked singularities do arise as a general feature in general relativity under a wide variety of circumstances . many examples of singular spacetimes can be found , but their relevance in models describing physically viable scenarios has been a matter of much debate since the first formulation of the cosmic censorship hypothesis ( cch ) @xcite . in particular , the formation of naked singularities in dynamical collapse solutions of einstein field equations remains a much discussed problem of contemporary relativity . the cch , which states that any singularity occurring in the universe must be hidden within an event horizon and therefore not visible to faraway observers , has remained at the stage of a conjecture for more than four decades now . this is also because of the difficulties lying in a concrete and definitive formulation of the conjecture itself . while no proof or any mathematically rigorous formulation of the same exists in the context of dynamical gravitational collapse ( while some proofs exist for particular classes of spacetimes that do not describe gravitational collapse , as in @xcite and @xcite ) , many counterexamples have been found over the past couple of decades @xcite-@xcite . many of these collapse scenarios are restricted by some simplifying assumptions such as the absence of pressures ( dust models ) or the presence of only tangential pressures @xcite-@xcite . it is well - known that the pressures can not be neglected in realistic models describing stars in equilibrium . it seems natural therefore that if one wishes to study analytically what happens during the last stages of the life of a massive star , when its core collapses under its own gravity thus forming a compact object as a remnant , pressures must be taken into account . therefore , further to early works that showed the occurrence of naked singularities in dust collapse , much effort has been devoted to understanding the role played by pressures @xcite-@xcite . the presence of pressures is a crucial element towards the description of realistic sources as we know that stars and compact objects are generally sustained by matter with strong stresses ( either isotropic or anisotropic ) . at first it was believed that the naked singularity scenario could be removed by the introduction of pressures , thus implying that more realistic matter models would lead only to the formation of a black hole . we now know that this is not the case . the final outcome of collapse with pressure is entirely decided by its initial configuration and allowed dynamical evolutions and it can be either a black hole or a naked singularity . furthermore it is now clear that within spherical collapse models ( be it dust , tangential pressure or others ) the data set leading to naked singularities is not a subset of ` zero measure ' of the set of all possible initial data . despite all this work we can still say that much more is to be understood about the role that general pressures play during the final stages of collapse . perfect fluid collapse has been studied mostly under some simplifying assumptions and restrictions in order to gain an understanding , but a general formalism for perfect fluids described by a physically valid equation of state is still lacking due to the intrinsic difficulties arising from einstein equations . considering both radial and tangential pressures is a fundamental step in order to better understand what happens in the ultra - dense regions that forms at the center of the collapsing cloud prior to the formation of the singularity . for this reason , perfect fluids appear as a natural choice since these are the models that are commonly used to describe gravitating stars in equilibrium and since it can be shown that near the center of the cloud regularity implies that matter must behave like a perfect fluid . in the present paper we use a general formalism to analyze the structure of collapse in the presence of perfect fluid pressures . this helps to understand better realistic collapse scenarios and their outcomes and brings out clearly the role played by pressures towards the formation of black holes or naked singularities as the endstate of collapse . we examine what are the key features that determine the final outcome of collapse in terms of a black hole or a naked singularity when perfect fluids , without any restriction imposed by the choice of an equation of state , are considered . the reason we do not assume an explicit equation of state here is that the behavior of matter in ultra - dense states in the final stages of collapse is unknown . on the other hand , having regularity and energy conditions satisfied provides a physically reasonable framework to study collapse endstates . we find that not only naked singularities are not ruled out in perfect fluid collapse scenarios but also that the separation between the black hole region and the naked singularity region in the space of all possible evolutions has some interesting features . in particular , we show that the introduction of small pressures can drastically change the final fate of the well - known pressureless models . for example , we see that adding a small pressure perturbation to an inhomogeneous dust model leading to a black hole can be enough to change the outcome of collapse to a naked singularity , and viceversa . further to this , we investigate here the space of initial data and collapse evolutions in generality , in order to examine the genericity of naked singularities in collapse . to study small pressure perturbations as well as the genericity and stability aspects , we use the general formalism for spherically symmetric collapse developed earlier @xcite , @xcite in order to address the basic problem of how generic is a given collapse scenario which leads to the formation of naked singularities . given the existence of an increasing number of models describing collapse leading to a naked singularity , the issue of genericity and stability of such models in the space of initial data has become the crucial ingredient in order to decide whether the cosmic censorship hypothesis in its present form should be conserved , modified or dropped altogether . it should be noted , however , that the concepts such as genericity and stability are far from well - defined in a unique manner in general relativity , as opposed to the newtonian gravity . a major difficulty towards such a task is the non - uniqueness of topology , or the concept of ` nearness ' itself in a given spacetime geometry @xcite . one could define topology on a space of spacetime metrics by requiring that the metric component values are ` nearby ' or also additionally requiring that their @xmath0-th derivatives are also nearby , and in each case the resulting topologies will be different . this is in fact connected in a way with the basic problem in arriving at a well - formulated statement of the cosmic censorship itself . there have been attempts in the past to examine the genericity and stability of naked singularities in special cases . for example , in @xcite it was shown that for certain classes of massless scalar field collapse the initial data leading to naked singularity has , in a certain sense , a positive codimension , and so the occurrence of naked singularity is unstable in that sense . on the other hand , it was shown in @xcite , @xcite that naked singularity occurrence is stable in the sense of the data sets leading to the same being open in the space of initial data . but these need not be dense in this space and so ` non - generic ' if we use the definition of ` genericity ' in the sense given in the dynamical systems theory ( where a set of initial data leading to a certain outcome is said to be generic if it is open and dense within the set of all initial data ) . in that case , however , both black hole and naked singularity final states turn out to be ` non - generic ' . therefore , in the following we adopt a more physical definition of ` genericity ' in the sense of ` abundance ' , and we call generic an initial data set that has a non - zero measure , and which is open ( though not necessarily dense ) in the set of all initial data . with this definition , the results obtained in @xcite and @xcite would mean that both black hole and naked singularity are generic collapse endstates . we note that we do not deal here with the self - similar models , or scalar fields , which is a somewhat special case . therefore , the issue of genericity and stability of naked singularities in collapse remains wide open , for spherically symmetric as well as non - spherical models and for different forms of matter fields . our consideration here treats in this respect a wide variety of physically reasonable matter fields for spherically symmetric gravitational collapse . in section [ einstein ] , the general structure" +"with the recent appearance of the internet and the world - wide web , understanding the properties of growing networks with popularity - based construction rules has become an active and fruitful research area @xcite . in such models , newly - introduced nodes preferentially attach to pre - existing nodes of the network that are already `` popular '' . this leads to graphs whose structure is quite different from the well - known _ random graph _ @xcite in which links are created at random between nodes without regard to their popularity . this discovery of a new class of graph theory problems has fueled much effort to characterize their properties . one basic measure of the structure of such networks is the _ node degree _ @xmath5 defined as the number of nodes in the network that are linked to @xmath0 other nodes . in the case of the random graph , the node degree is simply a poisson distribution . in contrast , many popularity - driven growing networks have much broader degree distributions with a stretched exponential or a power - law tail . the latter form means that there is no characteristic scale for the node degree , a feature that typifies many networked systems @xcite . power laws , or more generally , distributions with highly skewed tails , characterize the degree distributions of many man - made and naturally occurring networks @xcite . for example , the degree distributions at the level of autonomous systems and at the router level exhibit highly skewed tails @xcite . other important internet - based graphs , such as the hyperlink graph of the world - wide web also appear to have a degree distribution with a power - law tail @xcite . these observations have spurred a flurry of recent work to understand the underlying mechanisms for these phenomena . a related example with interest to anyone who publishes , is the distribution of scientific citations @xcite . here one treats publications as nodes and citations as links in a citation graph . currently - available data suggests that the citation distribution has a power - law tail with an associated exponent close to @xmath6 @xcite . as we shall see , this exponent emerges naturally in the _ growing network _ ( gn ) model where the relative probability of linking from a new node to a previous node ( equivalent to citing an earlier paper ) is strictly proportional to the popularity of the target node . in this paper , we apply tools from statistical physics , especially the rate equation approach , to quantify the structure of growing networks and to elucidate the types of geometrical features that arise in networks with physically - motivated growth rules . the utility of the rate equations has been demonstrated in a diverse range of phenomena in non - equilibrium statistical physics , such as aggregation @xcite , coarsening @xcite , and epitaxial surface growth @xcite . we will attempt to convince the reader that the rate equations are also a simple yet powerful analysis tool to analyze growing network systems . in addition to providing comprehensive information about the node degree distribution , the rate equations can be easily adapted to analyze both heterogeneous and directed networks , the age distribution of nodes , correlations between node degrees , various global network properties , as well as the cluster size distribution in models that give rise to independently evolving sub - networks . thus the rate equation method appears to be better suited for probing the structure of growing networks compared to the classical approaches for analyzing random graphs , such as probabilistic @xcite or generating function @xcite techniques . in the next section , we introduce three basic models that will be the focus of this review . in the following three sections , we then present rate equation analyses to determine basic geometrical properties of these networks . we close with a brief summary . the models we study appear to embody many of the basic growth processes in web graphs and related systems . these include : * the _ growing network _ ( gn ) @xcite . nodes are added one at a time and a single link is established between the new node and a pre - existing node according to an attachment probability @xmath7 that depends only on the degree of the `` target '' node ( fig . [ network ] ) . + + [ network ] * the _ web graph _ ( wg ) . this represents an extension of the gn to incorporate link directionality @xcite and leads to independent , dynamically generated in - degree and out - degree distributions . the network growth occurs by two distinct processes @xcite that are meant to mimic how hyperlinks are created in the web ( fig . [ io - growth ] ) : * * with probability @xmath8 , a new node is introduced and it immediately attaches to an earlier target node . the attachment probability depends only on the in - degree of the target . * * with probability @xmath9 , a new link is created between already existing nodes . the choices of the originating and target nodes depend on the out - degree of the former and the in - degree of the latter . + * the _ multicomponent graph _ ( mg ) . nodes and links are introduced _ independently _ @xcite . ( i ) with probability @xmath8 , a new _ unlinked _ node is introduced , while ( ii ) with probability @xmath9 , a new link is created between existing nodes . as in the wg , the choices of the originating and target nodes depend on the out - degree of the former and the in - degree of the latter . step ( i ) allows for the formation of many clusters . because of its simplicity , we first study the structure of the gn @xcite . the basic approaches developed in this section will then be extended to the wg and mg models . we first focus on the node degree distribution @xmath5 . to determine its evolution , we shall write the rate equations that account for the change in the degree distribution after each node addition event . these equations contain complete information about the node degree , from which any measure of node degree ( such as moments ) can be easily extracted . for the gn growth process in which nodes are introduced one at a time , the rate equations for the degree distribution @xmath10 are @xcite @xmath11 the first term on the right , @xmath12 , accounts for processes in which a node with @xmath13 links is connected to the new node , thus increasing @xmath5 by one . since there are @xmath14 nodes of degree @xmath13 , the rate at which such processes occur is proportional to @xmath15 , and the factor @xmath16 converts this rate into a normalized probability . a corresponding role is played by the second ( loss ) term on the right - hand side ; @xmath17 is the probability that a node with @xmath0 links is connected to the new node , thus leading to a loss in @xmath5 . the last term accounts for the introduction of new nodes with no incoming links . we start by solving for the time dependence of the moments of the degree distribution defined via @xmath18 . this is a standard method of analysis of rate equations by which one can gain partial , but valuable , information about the time dependence of the system with minimal effort . by explicitly summing eqs . ( [ nk ] ) over all @xmath0 , we easily obtain @xmath19 , whose solution is @xmath20 . notice that by definition @xmath21 is just the total number of nodes in the network . it is clear by the nature of the growth process that this quantity simply grows as @xmath22 . in a similar fashion , the first moment of the degree distribution obeys @xmath23 with solution @xmath24 . this time evolution for @xmath25 can be understood either by explicitly summing the rate equations , or by observing that this first moment simply equals the total number of link endpoints . clearly , this quantity must grow as @xmath26 since the introduction of a single node introduces two link endpoints . thus we find the simple result that the first two moments are _ independent _ of the attachment kernel @xmath7 and grow _ linearly _ with time . on the other hand , higher moments and the degree distribution itself do depend in an essential way on the kernel @xmath7 . as a preview to the general behavior for the degree distribution , consider the strictly linear kernel @xcite , for which @xmath27 coincides with @xmath28 . in this case , we can solve eqs . ( [ nk ] ) for an arbitrary initial condition . however , since the long - time behavior is most interesting , we limit ourselves to the asymptotic regime ( @xmath29 ) where the initial condition is irrelevant . using therefore @xmath30 , we solve the first few of eqs . ( [ nk ] ) directly and obtain @xmath31 , @xmath32 , _ etc_. thus each of the @xmath5 grow linearly with time . accordingly , we substitute @xmath33 in eqs . ( [ nk ] ) to yield the simple recursion relation @xmath34 . solving for @xmath35 gives @xmath36 returning to the case of general attachment kernels , let us assume that the degree distribution and @xmath27 both grow linearly with time . this hypothesis can be easily verified numerically for attachment kernels that do not grow faster than linearly with @xmath0 . then substituting @xmath33 and @xmath37 into eqs . ( [ nk ] ) we obtain the recursion relation @xmath38 and @xmath39 . finally , solving for @xmath35 , we obtain the formal expression @xmath40 to complete the solution , we need the amplitude @xmath41 . using the definition @xmath42 in eq . ( [ nkgen ] ) , we obtain the implicit relation @xmath43 which shows that the amplitude @xmath41 depends on the entire attachment kernel . for the generic case @xmath44 , we substitute this form into eq . ( [ nkgen ] ) and then rewrite the product as the exponential of a sum of a logarithm . in the continuum limit , we convert this sum to an integral , expand the logarithm to lowest order , and then evaluate the integral to yield the following basic results : @xmath45 , & $ 0\leq\gamma<1$;\cr k^{-\nu } , \quad \nu>2 , & $ \gamma=1$;\cr { \rm best\ seller } & $ 1<\gamma<2$;\cr { \rm bible } & $ 2<\gamma$.}\end{aligned}\ ] ] thus the degree distribution decays exponentially for @xmath46 , as in the case of the random graph , while for all @xmath47 , the distribution exhibits robust stretched exponential behavior . the linear kernel is the case that has garnered much of the current research interest . as shown above , @xmath48}$ ] for the strictly linear kernel @xmath49 . one might anticipate that @xmath50 holds for all _ asymptotically _ linear kernels , @xmath51 . however , the situation is more delicate and the degree distribution exponent depends on microscopic details of @xmath7 . from eq . ( [ nkgen ] ) , we obtain @xmath52 , where the exponent @xmath53 can be tuned to _ any _ value larger than 2 @xcite . this non - universal behavior shows that one must be cautious in drawing general conclusions from the gn with a linear attachment kernel . , out - degree @xmath54 , and total degree 9.,scaledwidth=25.0% ] [ degrees ] as an" +"complex networks have been the focus of the study of dynamical properties of complex systems in nature and society in the last decade @xcite . usually all nodes are assumed to belong to one population or class , and the interactions between two distinct populations have been reported just recently @xcite . the dynamical properties of two interacting populations , extroverts and introverts were recently studied using dynamical network evolution model @xcite . buldyrev et al @xcite developed a framework for understanding the robustness of interacting networks . using the generating functions method they present the exact analytical solutions for the critical fraction of nodes , which upon removal , will lead to a complete fragmentation into interdependent networks . the focus of the current approach in understanding the formation and evolution of terrorist networks is on middle - range perspective as opposed to the micro - level approach that considers individual terrorist and macro - level analysis of the root causes of terrorism @xcite . in particular , the interest is in placing the relationships between individuals in the context of ( i ) their interactions with each other , ( ii ) how they are influenced by ideas originating from their environment , ( iii ) their interactions with people and organizations outside of their group @xcite . motivated by this description which conceptually refers to a complex system and because networks provide a fruitful framework to model complex systems @xcite , we introduce a network model that aims to describe the interactions between potentially terrorist and non - terrorist populations . our goal is to present a model of a social network that contains two types of agents which demonstrate different affinities in establishing connections within their own population versus connections with the other population . we also aim that the model is simple enough to allow the derivation of approximate analytical expressions of the basic characteristics of the network . the latter can be achieved in the general framework of rate equation theory in the mean field approximation which has been introduced to study fundamental characteristics of growing network models @xcite . within this framework we introduce the rate equations that are specific to our model , solve them and obtain analytical expressions that predict the growth dynamics of the degree of individual vertices . , the initial contact @xmath2 and the secondary contact @xmath3 . ( a)-(d ) show the connections when the new node is an @xmath1 node . ( e)-(h ) show the connections when the new node is a @xmath0 node . empty symbols ( @xmath4 ) mark an @xmath1 node while full symbols ( @xmath5 ) mark a @xmath0 node . full lines represent links between nodes of the same type , e.g. friends , such as @xmath6 or @xmath7 . dashed lines represent links between nodes of different types such as @xmath8 , e.g. enemies . ] while the probability to create initial connections is easily defined , the probability for the secondary contacts between nodes is difficult to derive because of the interactions between the two types of nodes . as a first approximation , we assume that the initial and secondary contacts form edges with the same probabilities . to include a more precise contribution of both the initial and the secondary contacts in the rate equations we empirically obtain their functional dependences . this leads to an improved agreement between analytical and numerical simulation results . from the functional dependence of the degree of a node as a function of time using the mean - field arguments , we derive the degree distribution for each of the two types of nodes . we also derive analytical expressions of the structural , three - point correlations between nodes to study the clustering properties of the networks . the network models are broadly classified into two categories : the network evolution models in which addition of new edges depends on the local structure of the network , and nodal attribute models in which the existence of edges is determined solely by the attributes of the nodes ( for review see @xcite ) . the network evolution models can be further categorized into growing network evolution models and dynamical network evolution models . in the former the network growth starts with a small seed network and nodes and links are added according to specific rules until the network reaches a predetermined size . dynamical network evolution models start with an empty network and edges are added and deleted according to specific rules until statistical properties of the network stabilize . in this paper , we propose a model that incorporates a growing network evolution process with nodal attributes which could be thought of as a new class of model . the model has five free parameters , three describing the growing network evolution process and two describing nodal attributes . the parameters of the growing network evolution process are the number of nodes @xmath9 , the average number of nodes selected at random as initial contacts @xmath10 , and the average number of nodes selected as secondary contacts @xmath11 among the neighbors of each initial contact @xcite . two parameters quantify the type and amount of nodes , non - violent @xmath1 or potentially violent @xmath0 nodes and the type of interactions between them which are as follows : ( i ) nodes are randomly marked as non - violent @xmath1 with probability @xmath12 and potentially violent @xmath0 with probability @xmath13 ; ( ii ) when establishing initial contacts , nodes connect with probability @xmath14 if the nodes are of the same type , such as @xmath0 with @xmath0 or @xmath1 with @xmath1 , or with probability @xmath15 if the nodes are of different types such as @xmath1 with @xmath0 nodes . the secondary contacts are established with nodes among the neighbors of the initial contacts . the model combines the random attachment of initial contacts with the implicit preferential attachment of the secondary contacts . in that , the model represents a generalization with two types of node attributes of growing models such as @xcite . the definition of establishing edges can be thought of as creating links between friends ( solid lines in fig . [ fig1 ] ) or between enemies ( dashed lines ) . by varying the value of @xmath14 , we can generate different strengths of friendliness or animosity . the possible configurations of triads that arise in social networks in such a context are : ( a ) three friendly interactions ; ( b ) one friendly and two unfriendly connections ; ( c ) two friendly interactions and one unfriendly ; ( d ) three unfriendly interactions @xcite . according to the strong formulation of structural balance theory in social sciences , configurations ( a ) and ( b ) are considered stable while ( c ) and ( d ) are unstable and likely to break apart @xcite . in their empirical large - scale verification of the long - standing structural balance theory , the authors of @xcite find that the unstable triads , especially formation ( c ) are extremely underrepresented in an online social system in comparison to a null model . our model produces correctly the stable configurations ( a ) ( fig . [ fig1]a , e ) and ( b ) ( fig . [ fig1]b - d , f - h ) but can not produce the unstable configurations ( c ) and ( d ) in accordance with the strong formulation of the structural balance theory @xcite . the model algorithm consists of the following steps : ( 1 ) start with a seed network of @xmath16 connected nodes among which some are @xmath1 and some are @xmath0 , depending on @xmath12 ; ( 2 ) at each time step add a new node , which has probability @xmath12 to be a non - violent and @xmath13 to be a violent node ; ( 3 ) select on average @xmath17 random nodes as initial contacts . the probability to connect the same type of nodes is @xmath14 while @xmath15 is the probability for initial contacts if they are of different types . ( 4 ) select on average @xmath18 nodes among the neighbors of each initial contact as secondary contacts . connecting the new node with the secondary contacts is done without checking if it is the same type of node or not . there are two reasons for this choice . ( i ) because the probability to establish inter - population connections ( @xmath14 ) is higher than the probability to connect nodes intra - population ( @xmath19 ) , it is more likely that the first contact and its neighbors ( potential secondary contacts ) are of the same type than of different types . therefore the secondary contacts will be more likely to be intra - population contacts even without explicitly modifying their probability to connect based on the type . ( ii ) the secondary contacts are meant to mimic the ` friend - of - a - friend ' type of contacts in the real world , and we think that the implicit preferences given by the existing network connections would more accurately describe the nature of such contacts without including an explicit separate probability . apply steps ( 2 ) to ( 4 ) until the network reaches the necessary size . we start with constructing the rate equations that describe the change of the degree of a node on average during one time step of the network growth process for each of the non - violent @xmath1 and violent @xmath0 nodes . the degree of a node grows via two processes . one is the random attachment of connecting a new node to @xmath10 nodes that are its initial contacts . the second process is when the new node is further connected to the @xmath11 nodes among the neighbors of the initial contacts . in the following we assume that the probability of this second process is linear with respect to the degree of the node which leads to implicit preferential attachment . the rate equations are : @xmath20 @xmath21 where @xmath22 is the degree of node @xmath3 and we assumed that @xmath23 and @xmath24 . all possible combinations of triads of a new node @xmath25 , the initial contact @xmath2 , and the secondary contact @xmath3 are schematically shown in fig . [ fig1](a - h ) and presented by the third through the sixth terms in eq . ( [ n ] ) and eq . ( [ v ] ) for an @xmath1 and @xmath0 node , respectively . for example , the fifth term in eq . ( [ n ] ) describes the rate of change of the degree of vertex @xmath3 ( which is an @xmath1 node ) due to establishing the configuration of contacts shown in fig . the fifth term contains four factors . the first factor is the average number of secondary contacts which is @xmath26 . @xmath27 is the probability that the new node created at time step @xmath28 is a @xmath0 node . @xmath14 is the probability that the newly created node connects to the initial contact which is a node of the same type . finally , @xmath29 is the probability that the node selected for initial contact ( node @xmath2 in fig . [ fig1]c ) shares an edge with the node @xmath3 . this is a standard expression for preferential attachment except for the complications induced by having two distinct populations . the nominator @xmath30 is the degree of the @xmath3 node if we count only the links to different types of nodes ( in this case @xmath0 nodes ) . the denominator is the sum of all possible links which the type of node selected for initial contact ( in" +"molecular clouds are observed through the emission of a number of molecular transitions that provide a wealth of information about their chemical composition , gas temperature and density , magnetic field strength , fractional ionization , structure and kinematics . this information is essential to our understanding of the process of star formation . the interpretation of molecular emission line maps is not always unique . the main source of uncertainty is the absence of the third spatial dimension ( along the line of sight ) in the observational data . statistical properties of the velocity and density distributions along the line of sight are difficult to disentangle . furthermore , the components of the gas velocity on the plane of the sky are unknown . two dimensional images of molecular clouds are usually converted into three dimensional `` objects '' using the radial velocity instead of the third spatial dimension . this method can be useful to separate individual mass condensations from each other , since it is conceivable that their relative velocity is larger than their internal one . however , velocity blending or the lack of well defined condensations along the line of sight may cause significant uncertainties ( issa , maclaren & wolfendale 1990 ; adler & roberts 1992 ; ballesteros paredes , vazquez semadeni & scalo 1999 ; pichardo et al . 2000 ; ostriker , stone & gammie 2001 ; lazarian et al . 2001 ; ballesteros paredes & mac low 2002 ) . due to the difficulty of a direct interpretation of the observational data , a `` forward approach '' that starts from a rather general theoretical model and synthesizes its observational properties can be more instructive . different models may sometimes satisfy the same set of observational constraints , but they should also provide guidance for further observational studies that could help select the correct model . ideally , numerical models to be compared with observed spectral line data cubes should be based on the numerical solutions of the mhd equations , in the regime of highly super sonic turbulence , and on radiative transfer calculations . in some works , stochastic fields are used instead of the solution of the mhd equations and in most studies the radiative transfer calculation is omitted , in favor of density weighted velocity profiles . the first large synthetic spectral maps of molecular transitions computed by solving the non lte radiative transfer through the density and velocity data cubes obtained as the numerical solution of the mhd equations were presented by padoan et al . ( 1998 ) , based on juvela s radiative transfer code ( juvela 1997 ) , and were used in a number of works ( e.g. padoan et al . 1999 , 2000 , 2001 ) . another new radiative transfer code has also been used more recently to generate synthetic spectral maps from mhd simulations ( ossenkopf 2002 ) . a number of statistical methods have been proposed to compare numerical models of turbulence with large spectral maps of molecular clouds ( see for example scalo 1984 ; kleiner & dickman 1985 , 1987 ; stutzki & gusten 1990 ; gill & henriksen 1990 ; houlahan & scalo 1992 ; hobson 1992 ; langer , wilson , & anderson 1993 ; williams , de geus & blitz 1994 ; miesch & bally 1994 ; miesch & scalo 1995 ; lis et al . 1996 ; blitz & williams 1997 ; heyer & schloerb 1997 ; stutzki et al . 1998 ; miesch , scalo & bally 1999 ; falgarone et al . 1994 ; padoan et al . 1999 ; mac low & ossenkopf 2000 ; bensch , stutzki & ossenkopf 2001 ) . in this work we apply the spectral correlation function ( scf ) method , proposed by rosolowsky et al . ( 1999 ) and further developed in padoan , rosolowsky & goodman ( 2001 ) , to a number of observational and synthetic spectral maps . we show that the slope and normalization of the scf of observational maps correlate with the spectral line width . theoretical models of molecular clouds should therefore yield synthetic spectral maps reproducing such correlations , but not all of them can . in the next section we briefly define the scf , and in 3 we present the observational data used in this work . the computation of the theoretical models and synthetic spectral maps is presented in 4 . results from numerical models are compared with the observational data in 5 and are discussed in 6 . conclusions are drawn in 7 . the spectral correlation function ( scf ) measures the spatial correlation of spectral line profiles within a spectral map . it is sensitive to the properties of both the gas mass distribution and the gas velocity field ( rosolowsky et al . 1999 ; padoan , rosolowsky & goodman 2001 ; padoan et al . 2001 ; ballesteros paredes , vazquez semadeni & goodman 2002 ) . let @xmath2 be the antenna temperature as a function of velocity channel @xmath3 at map position @xmath4 . the scf for spectra with spatial separation @xmath5 is : @xmath6 where the average is computed over all map positions @xmath4 . @xmath7 is the scf uncorrected for the effects of noise , @xmath8 ^ 2 } { \sigma_vt(\vecr , v)^2+\sigma_vt(\vecr+\vecdr , v)^2 } } \right\rangle _ { \vecdr } , \label{2}\ ] ] where the average is limited to separation vectors @xmath9 with @xmath10 , and @xmath11 is the scf due to noise alone , @xmath12 and @xmath13 is the `` spectrum quality '' ( see discussion in padoan , rosolowsky & goodman 2001 ) . @xmath13 is defined as the ratio of the rms signal within a velocity window @xmath14 and the rms noise , @xmath15 ( over all velocity channels ) , @xmath16 where @xmath17 is the width of the velocity channels . in the present work we compute the scf of both observational and synthetic spectral maps , obtained by computing the radiative transfer through the three dimensional density and velocity fields of numerical simulations of super sonic mhd turbulence . the result is typically a power law for @xmath18 that extends up to a separation @xmath5 comparable to the map size , reflecting the self similarity of super sonic turbulence ( padoan , rosolowsky & goodman 2001 ) . the power law behavior is sometimes interrupted at an intermediate scale , possibly suggesting the presence of a physical mechanism limiting the inertial range of turbulence . an example of a scf that defines an intermediate scale is the scf of the hi survey of the large magellanic cloud ( lmc ) by kim et al . ( 1998 , 1999 ) . padoan et al . ( 2001 ) have recently been able to map the gas disk thickness of the lmc , assuming it is related to the intermediate scale defined by the break in the scf power law . the absolute value of @xmath18 at any @xmath19 and the slope of the @xmath18 power law for any given region depends on which molecular tracer is used ( padoan , rosolowsky & goodman 2001 ) . transitions probing higher gas density produce more fragmented integrated intensity maps than transitions probing lower gas density , and their scf is therefore steeper . in order to compare the scf of observational and synthetic maps it is therefore important to solve the radiative transfer through the model density and velocity fields accurately for the same molecular transition that is observed . in this work our aim is to compute the scf of observational data in order to provide constraints for theoretical models . the best constraints come from computing the scf of spectral maps of a specific molecular transition over a large range of line width and linear size . observationally , small scale and narrow line width objects are usually mapped out with high density tracers , while larger objects are instead usually probed with lower density tracers . @xmath0co provides a good compromise , since it is the only molecule for which very large maps containing thousands of spectra have been obtained with a significant range of resolution . in this work we have therefore chosen to use observational and synthetic maps of the j=10 line of @xmath0co . we have used 11 @xmath0co maps . for each map , we have listed in table 1 the approximate size , the distance , the rms velocity computed as the standard deviation of the line profile averaged over the whole map , the telescope beam size , the spatial sampling , the width of the velocity channels and the spectral quality defined in the previous section . smaller maps have been obtained from portions of the maps of the taurus , perseus and rosette molecular cloud complexes and the scf has been computed for each of them . the position of these smaller maps within the molecular cloud complexes is shown in figures 1 and 2 . they have been called t1 to t7 in taurus , p1 to p5 in perseus , r1b in the rosette molecular cloud map by blitz & stark ( 1986 ) and r1 and r2 in the rosette molecular cloud map by heyer et al . ( 2001 ) . the scf of each map has been approximated with a power law , over the range of spatial separations where a power law fit is relevant . for each power law fit we compute its slope , , and its absolute value at 1 pc , : @xmath20 the values of , , @xmath1 ( the line of sight rms velocity ) and the galactic coordinates of the center of each map are given in table 2 . the scf of maps of molecular cloud complexes and some smaller regions are shown in figure [ fig5 ] . we solve the compressible mhd equations in a staggered mesh of @xmath21 computational cells , with volume centered mass density and thermal energy , face centered velocity and magnetic field components , edge centered electric currents and electric fields and with periodic boundary conditions . the code uses shock and current sheet capturing techniques to ensure that magnetic and viscous dissipation at the smallest resolved scales provide the necessary dissipation paths for magnetic and kinetic energy . a more detailed presentation of the numerical method can be found elsewhere . ( padoan & nordlund 1999 ) . for the purpose of the present work we have computed numerical solutions of the mhd equations using an isothermal equation of state , and a random driving force . in all experiments , the initial density is uniform , and the initial velocity is random . we generate the velocity field in fourier space , and we give power , with a normal distribution , only to the fourier components in the shell of wave - numbers @xmath22 . we perform a helmholtz decomposition , and use only the solenoidal component of the initial velocity . however , a compressional component of the velocity field develops almost immediately due to the flow compressibility . the external driving force is generated on large scales in the same way as the velocity field . the initial magnetic field is uniform , and is oriented parallel to the @xmath23 axis : @xmath24 . because of the limited numerical resolution we have chosen not to model the collapse of turbulent density fluctuations . gravity has therefore been neglected . we have recently started to compute turbulent self gravitating flows with a numerical mesh of 500@xmath25 cells . results of the analysis of these larger simulations including self gravity will be presented in future works . we have run a number of mhd simulations in a @xmath21 computational mesh , with periodic boundary conditions . the simulations are intended" +"quantum tensor networks are a competitive tool to study strongly correlated quantum systems on a lattice . their history begins with the density matrix renormalization group ( dmrg ) @xcite - an algorithm to minimize the energy of a matrix product state ( mps ) ansatz in one dimension ( 1d ) , see ref . @xcite for a comprehensive review of mps algorithms . in the last decade mps was generalized to a 2d `` tensor product state '' widely known as a projected entangled pair state ( peps ) @xcite . another type of tensor network is the multiscale entanglement renormalization ansatz ( mera ) @xcite , and the branching mera @xcite , that is a refined version of the real space renormalization group . being variational methods , the quantum tensor networks do not suffer form the notorious fermionic sign problem , and thus they can be applied to strongly correlated fermions in 2d @xcite . a possible breakthrough in this direction was an application of the peps ansatz to the t - j model @xcite , which is a strong coupling approximation to the celebrated hubbard hamiltonian of the high temperature superconductivity @xcite . an energy of the ground state was obtained that could compete with the best variational monte - carlo results @xcite . the tensor networks also proved to be a powerful tool to study topological spin liquids ( tsl ) . the search for realistic models gained momentum after white demonstrated the spin - liquid nature of the kagome antiferromagnet @xcite . this result was obtained by a _ tour de force _ application of a quasi-1d dmrg . the dmrg investigation of tsl s was elevated to a higher degree of sophistication in ref . unfortunately , the mps tensor network underlying the dmrg suffers from severe limitations in two dimensions , where it can be used for states with a very short correlation length only . in contrast , the peps ansatz in fig . [ figpeps ] is not restricted in this way . its usefulness for tsl has already been demonstrated . in ref . @xcite it was shown how to represent the rvb state with the peps ansatz in an efficient way . in ref . @xcite peps was used to classify topologically distinct ground states of the kagome antiferromagnet . finally , in ref . @xcite peps demonstrated a tsl in the antiferromagnetic @xmath1 model . in contrast to the ground state , finite temperature states have been explored so far mostly with the mps @xcite . in a way that can be easily generalized to 2d , the mps is extended to finite temperature by appending each lattice site with an ancilla @xcite . a thermal state is obtained by an imaginary time evolution of a pure state in the enlarged hilbert space starting from infinite temperature . however , the thermal states are of more interest in 2d , where they can undergo finite temperature phase transformations . a thermal peps with ancillas was considered in ref . @xcite , where a finite temperature phase diagram of the 2d quantum ising model in a transverse field was obtained . this approach is further developed in this paper to a fermionic thermal peps , with a benchmark application to a 2d spinless hubbard model . before we proceed , let us note that the peps with ancillas is not the only way to attack the strongly correlated thermal states . a very interesting alternative was developed in a series of papers @xcite where , instead of the imaginary time evolution , a tensor network representing the partition function is contracted by subsequent tensor renormalizations in the imaginary time and space dimensions . yet another interesting alternative , presented in ref . @xcite , is based on linear optimization of local density matrices at finite @xmath2 . finally , alternative representations for fermionic states are also developed @xcite . the paper is organized as follows . in section [ tpeps ] we introduce fermionic peps with ancillas at finite temperature and outline the algorithm in most general terms . in brief section [ hubbard ] the hubbard model for spinless fermions on a square lattice is introduced with a hoping term , a symmetry breaking term , and a nearest - neighbor ( nn ) attraction . the following section [ suzuki ] introduces the imaginary time evolution operator , its second order suzuki - trotter decomposition for the spinless hubbard model , and their diagrammatic representation in terms of the tensor network . the peps tensors require renormalization / truncation of their bond indices after every suzuki - trotter gate . the renormalization procedure is described in section [ renormalization ] , where it is illustrated with a series of diagrams . it is a variation on the corner matrix renormalization @xcite . in section [ results ] we report benchmark results of the algorithm in the spinless hubbard model . we conclude in section [ summary ] . we consider spinless fermions on an infinite square lattice with a hamiltonian @xmath3 . every site has two fock states numbered by their fermionic occupation number @xmath4 . every site is accompanied by a fermionic ancilla with fock states @xmath5 . the enlarged hilbert space is spanned by fock states @xmath6 , where the ordered product runs over all lattice sites @xmath7 . the infinite temperature state @xmath8 is obtained from a pure state in the enlarged space by tracing out the ancillas , ( 0 ) = tr_a|(0)(0)| , where |(0 ) = _ s ( every site with its ancilla . the state @xmath9 at a finite @xmath10 is obtained from | ( ) e^-12h |(0 ) u ( ) |(0 ) after an imaginary time evolution . for an efficient simulation of the evolution we represent @xmath11 by a peps on the checkerboard lattice , see fig . [ figpeps ] . the lattice has two sublattices , @xmath12 and @xmath13 , with the same tensor , @xmath14 and @xmath15 respectively , at every site of the sublattice . here @xmath16 and @xmath17 are fermion and ancilla indices respectively , and @xmath18 are bond indices to contract the tensor with its nearest neighbors . the tensors are parity preserving : only the tensor elements with an even sum @xmath19 can be non - zero . by construction , the ansatz is translationally invariant with respect to diagonal moves , but when the tensors @xmath12 and @xmath13 are the same ( up to a gauge transformation on bond indices ) it gains full translational invariance . the state is | ( ) = _ \{a_s , i_s } _ a , b[\{a_s , i_s } ] _ s|a_s , i_s . here the sum runs over all indices @xmath20 at all sites . the amplitude @xmath21 $ ] is the tensor contraction in fig . . the initial product state ( [ psi0 ] ) can be represented by a^ia_ltrb = b^ia_ltrb = ^ia r0 _ b0 [ a0 ] with the minimal bond dimension @xmath22 . and @xmath23 . in ( b ) , the amplitude @xmath24 $ ] with all bond indices connecting nearest - neighbors tensors contracted . the index contraction is represented by a line connecting two tensors . each crossing between two lines implies a fermionic swap factor : when the indices on both lines are odd , then their contribution to the contraction is multiplied by @xmath25 . the inclusion of this swap gate follows the strategy proposed by corboz _ the tensors make a checkerboard lattice with sublattices @xmath12 and @xmath13 . the ansatz becomes translationally invariant when the tensors @xmath26 ( modulo a gauge transformation on the bond index ) . ] we proceed with the spinless hubbard hamiltonian & = & - _ s_a , s_b c_s_a^c_s_b + h.c . + + & & - _ s_a , s_b c_s_a c_s_b + h.c . + + & & - g _ s_a , s_b ( n_s_a-12)(n_s_b-12 ) + & & h_ba + h_ab + h _ [ calh ] here the index @xmath27 ( @xmath28 ) runs over the sublattice @xmath12 ( @xmath13 ) , @xmath29 is a fermionic annihilation operator , and @xmath30 is the occupation number . the @xmath31-term is an explicit @xmath32 symmetry breaking @xmath0-wave pairing , and the @xmath33-term is a nearest - neighbor attraction . we define elementary infinitesimal evolution operators : u_ab(d ) & & e^-12d h_ab = _ s_a , s_b ( 1 + 12 d c_s_b^c_s_a ) , + u_ba(d ) & & e^-12d h_ba = _ s_a , s_b ( 1 + 12 d c_s_a^c_s_b ) , + u_(d ) & & e^-12d h _ = _ s_a , s_b ( 1 + 12 d c_s_a c_s_b ) , + u_g(d ) & & e^-12d h_g + & & _ s_a , s_b , where @xmath34 . each of the evolution operators is a product of @xmath35-site gates . they are the building blocks for the second order suzuki - trotter decomposition . on the tensors @xmath12 and @xmath13 , compare with eqs . ( [ a],[b ] ) . here each crossing between two lines implies a fermionic swap factor @xmath36 . the operator @xmath37 when its bond index @xmath38 , or @xmath39 when @xmath40 . notice that the tensor @xmath41 is parity preserving : the sum of its three indices is even . notice also that when more than one index @xmath40 the contraction is zero : a creation / annihilation operator can not be applied more than once . ] the action of the hopping operator , say , @xmath42 maps the tensors @xmath12 and @xmath13 to new tensors : & & ( a)^ia_i(l , s_l),i(t , s_t),i(r , s_r),i(b , s_b ) = [ a ] + & & _ s,0 a^ia_ltrb+ + & & _ s,1 s_s_tls_s_tas_s_las_s_rb _ j i |c| j a^ja_ltrb , + & & ( b)^ia_i(l , s_l),i(t , s_t),i(r , s_r),i(b , s_b ) = [ b ] + & & _ s,0 b^ia_ltrb+ + & & _ s,1 s_s_tls_s_tas_s_las_s_rb _ j i |c^| j b^ja_ltrb , see the diagrams in figure [ figaprime ] . here the gate indices @xmath43 and @xmath44 . an odd @xmath40 means a transfer of one fermion along the bond @xmath45 . @xmath46 is an invertible parity - preserving index function . @xmath36 is a fermionic swap factor : @xmath47 when both @xmath17 and @xmath48 are odd and @xmath49 otherwise . equations ( [ a],[b ] ) are an exact map , but the new tensors @xmath50 and @xmath51 have the bond dimension @xmath52 instead of the original @xmath53 . the same is true for the action of @xmath54 , see the diagrams in figure [ figadelta ] , & & ( a)^ia_i(l , s_l),i(t , s_t),i(r , s_r),i(b , s_b ) = [ adelta ] + & & _ s,0 a^ia_ltrb+ + & & _ s,1 s_s_tls_s_tas_s_las_s_rb _ j i |c| j a^ja_ltrb , + & & ( b)^ia_i(l , s_l),i(t , s_t),i(r , s_r),i(b , s_b ) = [ bdelta ] + & & _ s,0 b^ia_ltrb+ + & & _ s,1 s_s_tls_s_tas_s_las_s_rb ( -1)^s_b+s_r _ j i |c| j b^ja_ltrb , just as for the action of @xmath55 , the same for both @xmath12 and @xmath13 , ( a)^ia_i(l , s_l),i(t , s_t),i(r , s_r),i(b , s_b)= ^s/4 ( i-12)^s/2 a^ia_ltrb . [ ag ] since @xmath55 does not transfer fermions between different sites , in eq . ( [ ag ] ) the gate indices @xmath56 are even and @xmath46 is preserving the parity of @xmath45 . on the tensors @xmath12 and @xmath13 , ( [ adelta],[bdelta ] ) . the factors @xmath57 and @xmath58 are represented here by the self - crossing loops . ] after every gate @xmath59 , the new bond dimension @xmath52 has to" +"all different brane solutions in eleven - dimensional supergravity are the classical solitons of m - theory , so there has been lot of interest and achievement in constructing and classifying the brane solutions of eleven - dimensional supergravity @xcite-@xcite . these solutions generate the p branes and the solitons of string theory that in turn make a way to understand the quantum theory of black holes . the black hole structure can be considered as some wrapped specific p branes around some compact manifoldes . moreover the supergravity brane solutions are the systems that provide evidence for the bulk - boundary holography duality @xcite-@xcite . one other important feature of the solutions is whether they are stable supersymmetric solutions or not . it turns out that in general , orthogonal intersecting system of m2 and m5 branes preserve some number of supersymmetry and are stable systems @xcite . it is also a well known fact that for supersymmetric solutions of supergravity , the metric functions can be obtained in terms of harmonic functions @xcite-@xcite . the harmonic functions are on the transverse space to brane systems and related to the saturated bps bound of the brane systems . as long as the near core region of supersymmetic bps solutions of brane sysytems is of importance in bulk - boundary duality , numerous solutions of orthogonal intersecting m branes have been constructed @xcite-@xcite , @xcite-@xcite . however , to find the brane solutions that are not restricted to the near core region of d4 , d5 or d6 branes , one can lift the corresponding brane to an embedded self - dual ( or anti - self - dual ) space in eleven - dimensional supergravity @xcite . upon dimensional reduction , the m - brane solutions with self - dual ( or anti - self - dual ) transverse space yield systems of p branes that are not restricted to the near core of d4 , d5 or d6 branes . instead the solutions are on near core of lower dimensional branes , such as d2 where its world - volume theory enjoys remarkable properties such as renormalizability . moreover , the lower dimensional brane is always fully localized in the world volume of higher dimensional brane and the system preserves some suspersymmetries . the method works very well for a single m2 or m5 brane , as by assuming an ansatz for the eleven dimensional metric , the supergravity equations of motion reduce to one partial differential equation that can be solved mainly by numerical methods after imposing the proper boundary conditions @xcite-@xcite . in this paper , we consider a system of two intersecting m2 branes and find a class of exact analytic solutions to supergravity equations of motion . the equations of motion consist of two coupled partial differential equations . the equation of motion for the metric function of one membrane depends on the metric function of second membrane in the system . upon dimensional reduction , we get a system of three d branes in type iia supegravity . we explicitly calculate the number of preserved supersymmetries by finding the solutions to the killing spinor equation and show the system of two m2 branes preserves four supersymmetries . the outline of the article is as follows . in section [ sec : supergravitysolutions ] , we briefly discuss the eleven dimensional supergravity equations of motion and the ansatz for the eleven - dimensional metric . in section [ sec : tn ] , we present our exact analytical solutions to the two coupled differential equations for the metric functions of two m2 branes . we find a second set of solutions to the equations of motion by analytically continuing the separation constant that appear in the first exact analytical solutions . in sections [ sec : bianchi ] , we consider the four dimensional triaxial bianchi ix space as a part of the overall transverse space to two membranes . although it is very unlikely to find an analytical solutions to equations of motion , however we find approximate analytical solutions for the membrane metric functions . in section [ sec : supersymmetry ] , we find the explicit solutions to the killing spinor equation for the system of two m2 branes . we show all of the solutions presented in sections [ sec : tn ] and [ sec : bianchi ] preserve four supersymmetries . in section [ sec : summary ] , we wrap up the article by concluding remarks and future possible research directions . the equations of motion for the bosonic fields of @xmath0 supergravity are given by @xcite @xmath1 , \label{gmingg}\\ \nabla_{m}f^{mnpq } & = -\frac{1}{576}\varepsilon^{m_{1}\ldots m_{8 } npq}f_{m_{1}\ldots m_{4}}f_{m_{5}\ldots m_{8 } } , \label{df}\end{aligned}\ ] ] where @xmath2}$ ] is the field strength of the three form gauge field @xmath3 . the solutions to equations of motion ( [ gmingg ] ) and ( [ df ] ) may preserve partial supersymmetry if there exists non - trivial killing spinors that satisy the killing spinor equation . the killing spinor equation indicates that the supersymmetric variation of the gavitino field vanishes . we consider a system of two m2 branes in which the branes are located in @xmath4 and @xmath5 with the metric @xcite @xmath6 where @xmath7 and @xmath8 . moreover , we consider the dependence of the metric functions on transverse coordinates as @xmath9 and @xmath10 , so the metric functions @xmath11 and @xmath12 depend on the overall transverse coordinates @xmath13 while @xmath11 depends also on the relative transverse coordinates @xmath14 . this means the first brane is completely localized on transverse directions while the second brane is delocalized along the relative transverse directions . we notice that the delocalization of a brane in a brane configuration is necessary for the decoupling limit of the theory living on the other brane worldvolume @xcite . we also show ( in section [ sec : supersymmetry ] ) the presence of self - dual ( or anti - self dual ) space @xmath15 in transverse space to both m2 branes implies partial preserved supersymmetry for the system . in this regard , in section [ sec : tn ] , we consider the four dimensional self - dual transverse space @xmath15 in ( [ ds11genm2 ] ) as @xmath16 where @xmath17 and @xmath18 . the range of coordinates are , @xmath19 , @xmath20 and @xmath21 where @xmath22 . in section [ sec : bianchi ] , we consider the system of two m2 branes ( [ ds11genm2 ] ) in background of self - dual triaxial bianchi ix space @xmath23 where the @xmath24 invariant one forms @xmath25 s are [ sigma.b.0 ] @xmath26 and @xmath27 in ( [ fbianchi ] ) , @xmath28 are three arbitrary constants that can be chosen as @xmath29 , @xmath30 and @xmath31 . the constant @xmath32 is positive and @xmath33 . we notice @xmath34 and coordinate @xmath35 always should be greater than or equal to @xmath36 . moreover , we consider the four - form field strength @xmath37 in terms of metric functions @xmath11 and @xmath12 as @xmath38 dimensional reduction of the metric ( with components @xmath39 ) together with the four - form field strength ( [ 4field ] ) to @xmath40 along one of the compact spatial coordinates in the transverse space ( e.g. @xmath41 ) yields type iia supergravity solutions . the fields of type iia supergravity could be read from the relations @xmath42 , @xmath43 and @xmath44 , where @xmath45 and @xmath46 take values in ten dimensions . the winding number @xmath47 , shows how many times the membrane wraps around the compact dimension @xcite . in the following sections , we set @xmath48 . the type iia rr four - form @xmath49 and nsns three - form field strength @xmath50 are related to ( [ 4field ] ) by @xmath51 where @xmath52 is the radius of circle parameterized by @xmath41 . the metric and the four - form field strength ( [ 4field ] ) satisfy the equations of motion ( [ gmingg ] ) and ( [ df ] ) contingent on functions @xmath11 and @xmath12 satisfy the following set of coupled differential equations @xmath53 @xmath54 the solutions to equation ( [ laph1 ] ) for the first membrane metric function @xmath11 depend on the solutions to equation ( [ laph2 ] ) for the second membrane metric function @xmath12 . we can find the solutions to the first differential equation by separating the coordinates as @xmath55 where @xmath56 is the charge of m2 brane . this separation of variables gives an exact solution for @xmath12 in the near core region of second m2 brane . the equation reduces to two ordinary decoupled differential equations for @xmath57 and @xmath58 that are given by @xmath59 @xmath60 where @xmath61 is the separation constant . the solutions to are given by @xmath62 in terms of modified bessel functions @xmath63 and @xmath64 and @xmath65 , @xmath66 are two constants . to have a finite solution far away from the branes , we have to choose the constant @xmath67 . moreover , the solutions to ( [ odef2c ] ) are given by @xmath68 where @xmath69 stands for the kummer function of type @xmath70 and @xmath71 , @xmath72 are two constants . in what follows in the present section , we show the first and second term of ( [ odef2cs ] ) by @xmath73 and @xmath74 respectively . figure [ fig : figure1 ] shows the behaviour of solution @xmath73 , where the solution vanishes at infinity . the near horizon limit of @xmath74 ( equation ( [ limit2 ] ) ) requires that we choose the constant @xmath75 in ( [ odef2cs ] ) . vanishes far away from the branes . the constants @xmath61 and @xmath76 are set to @xmath77.,scaledwidth=50.0% ] the general solution for the metric function @xmath78 is a superposition of different solutions given by ( [ odef1cs ] ) and ( [ odef2cs ] ) for different values of @xmath61 , @xmath79 where @xmath80 is an arbitrary function of the separation constant @xmath61 . to determine and fix the function @xmath80 , we consider the limits [ limitflat ] @xmath81 in which the transverse space to m2 branes approaches to @xmath82 @xmath83 where @xmath84 . to obtain ( [ sixdimlimits ] ) , we consider @xmath85 and the coordinate @xmath41 is redefined to @xmath86 by @xmath87 . in the limits ( [ limitflat ] ) where the transverse space to m2 branes is flat , the metric function @xmath78 must approach to @xmath88 . the proper choice of @xmath80 in the general solution ( [ mh2cs ] ) leads to the required behaviour of the metric function @xmath78 in the limits ( [ limitflat ] ) . in the limits ( [ limitflat ] ) , the differential equation ( [ odef2c ] ) for @xmath58 can be simplified to @xmath89 the solutions to ( [ odef2capp ] ) are given by @xmath90 in terms of bessel functions where @xmath91 and @xmath92 are two constants . comparing with , one can show @xmath93 hence the metric function in the limits ( [ limitflat ] ) becomes @xmath94 we choose @xmath75 in integrand of ( [ limith1 ] ) since in the limits ( [ limitflat ] ) , the radial function @xmath95 diverges . the solution to integral equation ( [ limith2 ] ) for @xmath80 is given by @xmath96 . so the general solution for the second membrane metric function @xmath78 reads as @xmath97 furnished with the general solution for @xmath78 , we can find the general solution to the second differential equation for the first membrane metric function @xmath98 . the differential equation ( [ laph1 ] ) is separable if we separate the coordinates by @xmath99 where @xmath100 is the charge of first m2 brane . substituting ( [ h1metricfunction ] ) in" +"sato et al . ( 2005 ) recently presented the discovery of a planetary companion to the bright g0 iv star hd 149026 . the star exhibits a time - variable doppler shift that is consistent with a sinusoid of amplitude @xmath8 m s@xmath9 and period @xmath10 days , which would be produced by the gravitational force from an orbiting planet with @xmath11 @xmath12 . furthermore , at the predicted time of planet - star conjunction , the star s flux declines by 0.3% in the manner expected of an eclipse by a planet of radius @xmath13 @xmath14 ( given an estimate of the stellar radius , 1.45 @xmath15 , that is based on the stellar parallax and effective temperature ) . sato et al . ( 2005 ) observed three such eclipses . this discovery is extraordinary for at least two reasons . firstly , the occurrence of eclipses admits this system into the elite club of bright stars with detectable planetary transits . of all the previously - known transiting systems , only hd 209458 ( charbonneau et al . 2000 ; henry et al . 2000 ) and tres-1 ( alonso et al . 2004 ; sozzetti et al . 2005 ) have parent stars brighter than @xmath16 , and therefore only they are amenable to a number of fascinating measurements requiring a very high signal - to - noise ratio . among these studies are ( i ) the search for satellites and rings ( brown et al . 2001 ) , ( ii ) the search for period variations due to additional companions ( wittenmyer et al . 2005 ) , ( iii ) the detection of ( or upper limits on ) atmospheric absorption features in transmission ( charbonneau et al . 2002 ; brown , libbrecht , & charbonneau 2002 ; deming et al . 2005a ) , ( iv ) the characterization of the exosphere ( bundy & marcy 2000 ; moutou et al . 2001 , 2003 ; vidal - madjar et al . 2003 , 2004 ; winn et al . 2004 ; narita et al . 2005 ) , ( v ) the measurement of the angle between the sky - projected orbit normal and stellar rotation axis ( queloz et al . 2000 ; winn et al . 2005 ) , and ( vi ) the search for spectroscopic features near the times of secondary eclipse ( richardson et al . 2003a , 2003b ) , and ( vii ) the direct detection of thermal emission from the planet ( charbonneau et al . 2005 ; deming et al . charbonneau ( 2004 ) reviews these techniques and related investigations . secondly , the planet is the smallest and least massive of the 8 known transiting extrasolar planets . this makes hd 149026b an important test case for theories of planetary structure . sato et al.(2005 ) argued that , once the effects of stellar insolation are included , the small planetary radius implies that the planet has a large and dense core . in particular , assuming a core density @xmath17 , their models predict a prodigious core mass of 78 earth masses , or 74% of the total mass of the planet . this , in turn , would seemingly prove that the planet formed through core accretion , as opposed to direct collapse through a gravitational instability . a system of such importance should be independently confirmed , and the determination of its basic parameters should be refined through multiple observations . with this as motivation , we performed photometry of hd 149026 on two different nights when transits were predicted by sato et al . these observations and the data reduction procedures are described in 2 . the model that we used to determine the system parameters is described in 3 , and the results are discussed in 4 . our data are available in digital form in the electronic version of this article , and from the authors upon request . we observed hd 149026 ( @xmath18 , @xmath19 ) on ut 2005 june 6 and ut 2005 july 2 with the 48-inch ( 1.2 m ) telescope of the f. l. whipple observatory ( flwo ) located at mount hopkins , arizona . we used minicam , an optical ccd imager with two @xmath20 chips . in order to increase the duty cycle of the observations , we employed @xmath21 binning , which reduced the readout and overhead time to 20 s. each binned pixel subtends approximately @xmath22 on the sky , giving an effective field of view of about @xmath23 for each ccd . fortunately , there exists a nearby object of similar brightness and color ( hd 149083 ; @xmath24 , @xmath25 , @xmath26 @xmath27 , @xmath28 ) , which we employed as an extinction calibrator . we selected the telescope pointing so that both stars were imaged simultaneously . we defocused the telescope so that the full - width at half - maximum ( fwhm ) of a stellar image was typically 15 binned pixels ( 9@xmath29 ) , and we used automatic guiding to ensure that the centroid of the stellar images drifted no more than 3 binned pixels over the course of the night . in addition to enabling longer integration times , this served to mitigate the effects of pixel - to - pixel sensitivity variations that were not perfectly corrected by our flat - fielding procedure . on ut 2005 june 6 , we gathered 5.5 hrs of sdss @xmath0-band observations with typical integration times of 8 s and a cadence of 28 s. the conditions were photometric , and the frames span an airmass from 1.01 to 1.74 . on ut 2005 july 2 , we gathered 4.4 hrs of sdss @xmath2-band observations with integration times of 6 s and a median cadence of 26 s. the field appeared to remain free of clouds for the duration of the observations , which spanned an airmass range of 1.01 to 1.43 , although occasional patches of high cirrus could be seen in images from the mmt all - sky camera . we converted the image time stamps to heliocentric julian day ( hjd ) at mid - exposure . the images were overscan - subtracted , trimmed , and divided by a flat - field image . we performed aperture photometry of hd 149026 and the comparison star hd 149083 , using an aperture radius of 15 binned pixels ( 9@xmath29 ) for the ut 2005 june 6 data , and an aperture radius of 20 binned pixels ( 12@xmath29 ) for the ut 2005 july 2 data . we subtracted the underlying contribution from the sky for both the target and calibrator by estimating the counts in an annulus exterior to the photometric aperture . the relative flux of hd 149026 was computed as the ratio of the fluxes within the two apertures . normalization and residual extinction corrections are described in 3 . tophat is an automated telescope located on mt . hopkins , arizona , which was designed to perform multi - color photometric follow - up of transiting extrasolar planet candidates identified by the hat network ( bakos et al . since tophat has not previously been described in the literature , we digress briefly to outline the principal goals and features of the instrument . wide - field transit surveys must contend with a large rate of astrophysical false positives , which result from stellar systems that contain an eclipsing binary and precisely mimic the single - color photometric light curve of a jupiter - sized planet transiting a sun - like star ( brown 2003 ; charbonneau et al . 2004 ; mandushev et al . 2005 ; torres et al . although multi - epoch radial velocity follow - up is an effective tool for identifying these false positives ( e.g. latham 2003 ) , instruments such as tophat and sherlock ( kotredes et al . 2004 ) can be fully - automated , and thus offer a very efficient means of culling the bulk of such false positives . tophat is a 0.26 m diameter f/5 commercially - available baker ritchey - chrtien telescope on an equatorial fork mount developed by fornax inc . a 1@xmath3025-square field of view is imaged onto a 2k@xmath312k peltier - cooled , thinned ccd detector , yielding a pixel scale of 2@xmath322 . the time for image readout and associated overheads is 25 s. well - focused images have a typical fwhm of 2 pixels . a two - slot filter - exchanger permits imaging in either @xmath1 or @xmath33 . the components are protected from inclement weather by an automated asymmetric clamshell dome . we observed hd 149026 on ut 2005 july 2 , the same night as the flwo 1.2 m @xmath2 observations described above . in order to extend the integration times and increase the duty cycle of the observations , we broadened the point spread function ( psf ) by performing small , regular motions in ra and dec according to a prescribed pattern that was repeated during each 13 s integration ( see bakos et al . 2004 for details ) . the resulting psf had a fwhm of 3.5 pixels ( 7@xmath327 ) . we gathered 4.8 hrs of @xmath1 observations with a cadence of 68 s , spanning an airmass range of 1.01 to 1.45 . we converted the time stamps in the image headers to hjd at mid - exposure . we calibrated the images by subtracting the overscan bias and a scaled dark image , and dividing by an average sky flat from which large outliers had been rejected . we evaluated the centroids of the target and the three brightest calibrators in each image . for each star , we summed the flux within an aperture with a radius of 8 pixels ( 17@xmath326 ) , and subtracted a local sky estimate based on the median flux in an annulus exterior to the photometric aperture . we divided the resulting time series for the target by the statistically - weighted average of the time series for the three calibrator stars . the resulting relative flux time series was then corrected for normalization and residual extinction effects as described in the following section . we attempted to fit simultaneously ( i ) the 3 photometric time series discussed above , ( ii ) the @xmath34 photometry of 3 transits presented by sato et al . ( 2005 ) , and ( iii ) the 7 radial velocities that were measured by sato et al . ( 2005 ) when the planet was not transiting . we did not attempt to fit the 4 radial velocities measured during transits , which would have required a model of the rossiter - mclaughlin effect ( queloz et al.2002 ; ohta , taruya , & suto 2004 ; winn et al . 2005 ) . we modeled the system as a circular keplerian orbit . following sato et al . ( 2005 ) , we assumed the stellar mass ( @xmath35 ) to be @xmath36 and the stellar radius ( @xmath37 ) to be @xmath38 . the free parameters were the planetary mass ( @xmath39 ) , planetary radius ( @xmath40 ) , orbital inclination ( @xmath41 ) , orbital period ( @xmath42 ) , central transit time ( @xmath43 ) , and the heliocentric radial velocity of the center of mass ( @xmath44 ) . we included 2 free parameters for each of our 3 photometric time series : an overall flux scaling @xmath45 ; and a residual extinction coefficient ( @xmath46 ) to correct for differential extinction between the target star and the comparison object , which have somewhat different colors . these are defined such that the relative flux observed through an airmass" +"statistical mechanics of random networks gained recently many applications in interdisciplinary sciences . the list of references is already very rich ; in almost each year new monographies appear @xcite . in theory , the promising challenge is to investigate collective phenomena in networks @xcite . more than often it is useful to decorate nodes @xmath7 with additional variables , as ising spins @xmath8 . properties of such networks are of interest for theory of computations , as inference problems , but also for the theory of disordered magnetic systems . here we are interested in the spin - glass phase of the small - world random networks . + for trees , where closed loops are absent , there is a consistent theory of ising magnetism , i.e. the bethe theory @xcite . once the loops appear in the system , the bethe theory becomes an approximation . in our system , small loops are introduced when we enhance the clustering coefficient @xcite . still , the results of the bethe theory are useful as a point of reference . as it was demonstrated in @xcite , the accordance of the numerical results with this theory was deteriorated when @xmath0 increases . on the other hand , there is at least one periodic two - dimensional ising lattice when all bonds are antiferromagnetic , the density of frustration is high and the transition temperature is positive ; this is one of the archimedean lattices @xcite . the ground state of this system is highly frustrated , but at least some of the energy barriers between different states remain finite . although at zero field the net magnetization is zero , there is no disorder in the system ; therefore it is hard to speak about the spin - glass phase . then , the @xmath9 ) archimedean lattice can be compared to our system in the case where @xmath0 is maximal . + recently we investigated the transition from the paramagnetic to the spin - glass phase in the random erds - rnyi network with enhanced clustering coefficient @xmath0 @xcite . the enhancement is introduced by adding new links between neighbours of the same sites @xcite . in this way , @xmath0 varied from almost zero to about 0.3 . the main result was the transition temperature @xmath10 dependence on the clustering coefficient @xmath0 . however , in the numerical plots the transition was partially hidden by the contribution of spins which could flip with zero energy cost . that is why here we investigate the same transition in the regular random network , where the degree of each node is an odd number - here it is equal to three . in such systems no spin can flip at zero energy cost in zero external magnetic field . + in the next section we show the method and the numerical results . in section iii the transition temperature @xmath2 is compared with the predictions of the bethe theory . short discussion closes the text . initial form of the constructed network is prepared as an even number @xmath11 of unlinked nodes . the system is divided into two equal parts . three dangling links are assigned to each node . then , the links of one part of nodes are randomly joint to links of the second part . in this way , initially the system is bipartite , with the clustering coefficient @xmath0 equal to zero provided that the number of nodes is large enough . next step is performed for each node with the probability @xmath12 : the node is substituted by a group of three nodes , mutually linked . after this substitution , three previous neighbours of the node are linked to the nodes of the group . in this way , the degree of each node remains exactly three . as the ising interaction is exclusively antiferromagnetic , the frustration is purely geometrical . when @xmath3 , there is no frustration . the density of frustrated bonds increases with @xmath0 . if @xmath13 , the clustering is maximal and for each node , two out of its three neigbours are linked to each other ; then @xmath14 . the final number of nodes is @xmath15 ; for each @xmath12 the amount @xmath11 is chosen as to get approximately the same @xmath16 . + the heat - bath monte carlo algorithm is applied to investigate the magnetic properties : the susceptibility @xmath17 , the specific heat @xmath18 and the edwards - anderson order parameter @xmath1 . @xmath17 can be calculated from the field derivative of the magnetization @xmath19 or from the variance of the spectrum of @xmath20 . similarly @xmath18 can be obtained from the temperature derivative of energy or from the variance of the energy fluctuations . the parameter @xmath1 is calculated from the formula @xcite @xmath21 ^ 2\ ] ] the antiferromagnetic exchange integral @xmath22 is set to -1 . as a rule , the calculations are performed for @xmath16 equal at least @xmath23 spins . the time of calculation - after a necessary transient - was usually @xmath24 steps , where one step is equivalent to probing @xmath16 spins in random order . the results are limited to temperature @xmath25 , where the transient time for relaxation of energy was smaller than @xmath26 timesteps . + in fig . 1 we show the magnetic susceptibilities @xmath27 for different values of the clustering coefficient @xmath0 . the temperature is expressed in energy units @xmath28 . the finite size effect is checked for @xmath3 and @xmath29 ; the differences between @xmath30 and @xmath31 are invisible . as a rule , the plots obtained from the field derivative of the magnetization coincide with those from the variance of the magnetization at zero field above the transition temperature . below @xmath2 , the curves split for intermediate values of @xmath0 ( between 0.1 and 0.29 ) . the plots for the magnetic specific heat obtained from the variance of energy ( figs . 2 and 3 ) and from its thermal derivative coincide in most cases , even below @xmath2 and for intermediate values of @xmath0 . however , the data from the maxima of the specific heat are known to provide an evaluation of the upper limit of the transition temperature @xmath2 rather than @xmath2 itself . the results on @xmath2 obtained by different methods are compared in fig . as we see , there is a systematic split between @xmath2 obtained from @xmath32 and @xmath2 obtained from @xmath18 , but the character of the curve @xmath33 is preserved . in fig . 4 we show the data on @xmath2 obtained from the thermal dependence of the edwards - anderson order parameter @xmath1 . these data also show a decrease of @xmath2 with @xmath0 . however , this decrease persists till @xmath34 , where our numerical results are less reliable . + for @xmath3 the network is bipartite . although the interaction is antiferromagnetic , the system is equivalent to a ferromagnet . to see this , we have to flip spins at half of nodes and to invert simultaneously the sign of all exchange integrals @xmath22 from -1 to + 1 . the formula for the curie temperature ( @xmath35 ) for the regular bethe lattice with the coordination number @xmath36 is @xcite for @xmath39 the system contains loops and it is no more equivalent to a ferromagnet . on the other hand , the network is no more a regular bethe lattice . the number of second neighbours decreases gradually with @xmath12 from 6 when @xmath40 to 4 when @xmath13 . the latter case is , however , in some sense more regular than the one with smaller @xmath12 , because all nodes have again the same number of the second neighbours . then the nel temperature ( @xmath38 ) between the paramagnetic and the antiferromagnetic phase is to be found from where @xmath43 is the average branching parameter , i.e. @xmath44 , where @xmath45 ( @xmath46 ) is the average number of first ( second ) neighbours @xcite . + although the data from the specific heat fit better to the bethe theory , it is known that the position of the maximum of @xmath18 is rather the upper bound of the transition temperature than this temperature itself . + the numerical results indicate , that for @xmath3 the low - temperature phase is antiferromagnetic . they also suggest that for @xmath47 and @xmath48 the system becomes a spin glass . however , the identity of this phase remains not clear . for @xmath14 the system can be compared to the @xmath49 archimedean lattice @xcite with random rewiring . we can expect that the ground state is degenerated in the same way as in this archimedean lattice . however , the condition is that the rewiring does not destroy the small triangles introduced when @xmath0 is enhanced . in this way the frustration is not altered by rewiring : the frustration remains local . then , there is frustration and disorder , but the disorder does not influence the frustration . on the other hand , the energy barriers between the local energy minima remain finite , because the system can move from one minimum to another by flipping a finite amount of spins . although the system behaves as a spin glass , some ingredients of this mysterious phase are missing . + to summarize , our intention was to compare the numerical results on the transition temperature @xmath2 with the results of the bethe approximation . in ref . @xcite , distinct departures have been found between the bethe theory and the numerical experiment . here the departure is smaller and quantitative rather than qualitative . as a rule , the transition temperature is overestimated by the bethe approximation . most important difference between the system considered in this text and the system discussed in ref . @xcite is the degree distribution . this suggests , that the qualitative departure of the results of ref . @xcite from those of the bethe approximation is due to the variance of the degree distribution . + 88 a .- barabasi , _ linked : how everything is connected to everything else and what it means for business , science , and everyday life _ , plume books , new york 2003 . s. n. dorogovtsev and j. f. f. mendes , _ evolution of networks : from biological nets to the internet and www _ , oxford up , oxford 2003 . , eds . s. bornholdt and h. g. schuster , wiley - vch , berlin 2003 . r. pastor - satorras and a. vespignani , _ evolution and structure of the internet : a statistical physics approach _ , cambridge up , cambridge 2004 . r. durrett , _ random graph dynamics _ , cambridge up , cambridge 2006 . g. caldarelli , _ scale - free networks _ , oxford up , oxford 2007 . s. n. dorogovtsev and a. v. goltsev , _ critical phenomena in complex networks _ , rev . mod . phys . * 80 * ( 2008 ) 1275 . s. katsura and m. takizawa , _ bethe lattice and bethe approximation _ , prog . * 51 * ( 1974 ) 82 . r. j. baxter , _ exactly solved models in statistical mechanics _ , academic press , london 1982 . j. m. mooij and h. j. kappen , _ on the properties of the bethe approximation and loopy belief propagation on binary networks _ , j. stat . mechanics : theory and experiment ( 2005 ) p11012 . p. holme and b. j. kim , _ growing scale - free networks with tunable clustering _ , e * 65 * ( 2002 ) 026107 . a. maka , k. malarz and k. kuakowski , _ clusterization , frustration and collectivity" +"the realization of rovibrationally stable dense samples of ultracold diatomic molecules remains one of the major goals in the field of atomic and molecular physics . while cooling diatomic alkali molecules was seen as a logical next step following the optical cooling of atoms , many of the possible applications currently under investigation extend beyond atomic and molecular physics . testing fundamental symmetries based on high - precision spectroscopy of ultracold molecules @xcite or the attempts to detect the time variation of fundamental constants @xcite are examples of such applications . another one is ultracold chemistry , where the interacting species and products are in a coherent quantum superposition state and could be realized by controlling reactive collisional processes @xcite . important insights about new phases of matter could be gained from strong anisotropic dipole - dipole interaction between ultracold dipolar molecules @xcite . finally , ultracold polar molecules could also represent an attractive platform for quantum computation @xcite . many of those applications require dense samples of ultracold polar molecules in the lowest rovibrational state that makes them collisionally stable and long - lived . translationally ultracold ( 100 nk - 1 mk ) molecules are produced from an ultracold atomic gas by photoassociation ( pa ) @xcite or magnetoassociation ( ma ) @xcite . in a typical pa scheme , a pair of colliding atoms is photoassociated into a bound electronically excited molecular state that spontaneously decays , forming molecules in the electronic ground state . in magnetoassociation , a magnetic field is adiabatically swept across a feshbach resonance , converting two atoms in a matching scattering state into a molecule . both techniques produce weakly bound molecules in highly excited vibrational states of the ground electronic potential . such molecules have to be rapidly transferred to deeply bound vibrational states before they are lost from the trap due to inelastic collisions . stimulated raman adiabatic passage ( stirap ) @xcite has recently attracted significant interest as an efficient way to produce deeply bound molecules , starting from feshbach molecules @xcite . it allows to realize high transfer efficiency and preserve the high phase - space density of an initial atomic gas . in stirap , the laser pulses , coupling an initial and a final state to an intermediate excited state , are applied in a counter - intuitive sequence where a pump pulse is preceeded by a stokes pulse . during the transfer , the system stays in a `` dark '' state , _ i.e. _ , a coherent superposition of initial and final states , preventing any losses that would otherwise occur from the excited state . by adiabatically changing amplitudes of the laser pulses , the `` dark '' state evolves from the initial to the final state , resulting in nearly 100% transfer efficiency @xcite . efficient adiabatic passage from the continuum requires laser pulses shorter than the coherence time of the continuum @xcite . the adiabaticity condition of stirap , @xmath4 , where @xmath5 is the transfer time , therefore implies a large effective rabi frequency @xmath6 for the pulses . in addition , dipole matrix elements between the continuum and the bound state are usually small , and so the pump pulse that couples the continuum and the excited state would require a very high intensity , which proves impractical . thus the previous stirap experiments @xcite , being restricted by the very short coherence time of the continuum , used a feshbach molecular state as an initial state . the small continuum - bound dipole matrix elements can be dramatically increased by photoassociating atoms in the vicinity of a feshbach resonance . it has been shown , both theoretically and experimentally , that the photoassociation rate increases in the presence of a feshbach resonance by several orders of magnitude @xcite . this can be explained by considering that delocalized scattering states acquire some bound - state character due to admixture of a bound level associated with a closed channel , resulting in a large increase of the franck - condon factor between the initial scattering state and the final excited state . the recently proposed feshbach optimized photoassociation ( fopa ) technique @xcite relies on this enhancement to directly reach deeply bound ground state vibrational levels from the scattering continuum . consequently , photoassociation in the vicinity of a feshbach resonance is expected to increase molecular formation rate up to @xmath7 molecules / s @xcite . in the present work , we combine the approach used in fopa with stirap for reducing the required pulse intensity . we predict highly efficient transfer of an entire atomic ensemble into the lowest rovibrational level in the molecular ground state . the paper is organized as follows . in section ii , we derive a theoretical model of a combined atomic and molecular system . fano theory is used to describe the interaction of a bound molecular state with the scattering continuum , represented as closed and open channel , respectively . the resulting continuum states are coupled by two laser fields to the vibrational target state in the ground state via the intermediate excited molecular electronic vibrational state . in section iii , we present the results of numerical solutions of the model for several alkali dimers . we find optimal rabi frequencies and profiles of stirap pulses for those systems . finally , we conclude in section iv . we consider a three level system as represented in figure [ levels ] . the ground level labeled @xmath8 is the final product state to which a maximun of population must be transfered . typically , this level will be the lowest virational level ( @xmath9 ) of a ground molecular potential . this ground level is coupled to an excited bound level @xmath10 of an excited molecular potential via a stokes pulse depicted by the blue down - arrow in figure [ levels ] . this level @xmath10 is itself coupled via a pump pulse ( red up - arrow ) to an initial continuum of unbound scattering states @xmath11 of energies @xmath12 ( grey area in figure [ levels ] ) . if we denote @xmath13 , @xmath14 and @xmath15 the time dependent amplitudes associated to the final , intermediate , and initial states @xmath8 , @xmath10 , and @xmath11 , respectively , then the total wave function @xmath16 of the system is given by : @xmath17 is transferred to a final target state @xmath8 via an intermediate state @xmath10 . both @xmath11 and @xmath8 are coupled to @xmath10 by a pump and a stokes pulse , respectively labeled @xmath18 and @xmath19 . a bound level @xmath20 corresponding to a closed channel can be imbedded in the continuum.,scaledwidth=70.0% ] no restriction applies to the definition of the continuum state @xmath11 as it can be associated to either a single - channel or a multi - channel scattering state . in this work , we consider the multi - channel case in which a bound level @xmath20 associated to a closed channel is embedded in the continuum of scattering states @xmath21 of an open channel . when the energy of @xmath21 coincides with that of @xmath20 , a so - called feshbach resonance @xcite occurs . these are common in binary collisions of alkali atoms due to hyperfine mixing and the tuning of the zeeman interaction by an external magnetic field , hence the possibility to control interatomic interactions with a magnetic field . following the fano theory presented in ref . @xcite , the scattering state @xmath11 can be expressed as : @xmath22 with @xmath23 and @xmath24 here , @xmath25 is the phase shift due to the interaction between @xmath20 and the scattering state @xmath26 of the open channel . we assume @xmath27 $ ] . the width of the feshbach resonance , @xmath28 , is weakly dependent on the energy , while @xmath29 is the interaction strength between the open and closed channels . the position of the resonance , @xmath30 , includes an interaction induced shift from the energy of the bound state @xmath31 . if we label @xmath32 the energy of the state @xmath33 , the total hamiltonian @xmath34 is given by : @xmath35 the light - matter interaction hamiltonian @xmath36 takes the form : @xmath37 where @xmath38 are the pump and stokes laser fields of polarization @xmath39 , respectively , while @xmath40 and @xmath41 are the dipole transition moments between the states @xmath10 and @xmath8 , and @xmath10 and @xmath11 , respectively . in this form the hamiltonian already takes into account mixing between the bound state of the closed channel and scattering states of the open channel . the schrdinger equation describing stirap conversion of two atoms into a molecule is : @xmath42 for simplicity , we set the origin of the energy to be the position of the ground state @xmath8 , and use the rotating wave approximation with @xmath43 , @xmath44 , and @xmath45 . the schrdinger equation becomes : @xmath46 where @xmath47 , @xmath48 , and @xmath49 is the dissociation energy of the ground electronic potential with respect to the state @xmath8 . the rabi frequencies of the fields are @xmath50 ( assumed real ) , @xmath51 . the previous system of three equations can be reduced into a two - equation system by eliminating the continuum amplitude @xmath52 in eq.([eq : cont - ampl ] ) . introducing a solution in the form of @xmath53 into eq.([eq : cont - ampl ] ) , we get @xmath54 where @xmath55 is some moment before the collision of the two atoms . the resulting continuum amplitude is @xmath56 inserting this result into eq . ( [ eq : c2 ] ) , we obtain a final system of equations for the amplitudes of the bound states : @xmath57 + the third term of eq . ( [ eq : c2-new ] ) , labelled @xmath58 , corresponds to the back - stimulation term , whereas the last term , labelled @xmath59 , corresponds to the source function . in this source term , the initial amplitude of the continuum wave function @xmath60 describing a collision at @xmath61 of two atoms with relative energy @xmath62 has been discussed in various contributions @xcite . a gaussian wavepacket provides the most classical description of a two - atom collision characterized by a minimal uncertainty relation between the energy bandwidth @xmath63 of the wavepacket and the duration of the collision : @xmath64 futhermore , the rabi frequency of the field coupling continuum states @xmath11 to the state @xmath10 is given by @xcite @xmath65 where @xmath66 is the dipole matrix element between an unperturbed scattering state @xmath26 and the state @xmath10 , and @xmath67 is the fano parameter , expressed as : @xmath68 where @xmath69 is the polarization vector of the pump field , and @xmath70 is the dipole matrix element between bound states @xmath10 and @xmath20 . the @xmath67 factor is essentially the ratio of the dipole matrix elements from the state @xmath10 to the bound state @xmath20 ( modified by the continuum ) and to an unperturbed continuum state @xmath26 . this factor can be made much larger than unity , and as will be shown below , the total dipole matrix element from the continuum can be enhanced by this factor in the presence of the resonance . the magnitude of @xmath67 can be controlled by the choice of the vibrational state @xmath10 . selecting a tightly bound excited vibrational state will increase the bound - bound and decrease the continuum - bound dipole matrix elements , resulting in larger @xmath67 . on the contrary , choosing a highly excited state close to a dissociation threshold decreases @xmath67 . using the expressions given in eqs.([s_epsiton_t0 ] ) , ( [ eq : rabi - fr ] ) , and ( [ eq : q ] ) for the initial amplitude of the continuum wave" +"in recent years , mapreduce has emerged as a computational paradigm for processing large - scale data sets in a series of rounds executed on conglomerates of commodity servers @xcite , and has been widely adopted by a number of large web companies ( e.g. , google , yahoo ! , amazon ) and in several other applications ( e.g. , gpu and multicore processing ) . ( see @xcite and references therein . ) informally , a mapreduce computation transforms an input set of key - value pairs into an output set of key - value pairs in a number of _ rounds _ , where in each round each pair is first individually transformed into a ( possibly empty ) set of new pairs ( _ map step _ ) and then all values associated with the same key are processed , separately for each key , by an instance of the same reduce function ( simply called _ reducer _ in the rest of the paper ) thus producing the next new set of key - value pairs ( _ reduce step _ ) . in fact , as already noticed in @xcite , a reduce step can clearly embed the subsequent map step so that a mapreduce computation can be simply seen as a sequence of rounds of ( augmented ) reduce steps . the mapreduce paradigm has a functional flavor , in that it merely requires that the algorithm designer decomposes the computation into rounds and , within each round , into independent tasks through the use of keys . this enables parallelism without forcing an algorithm to cater for the explicit allocation of processing resources . nevertheless , the paradigm implicitly posits the existence of an underlying unstructured and possibly heterogeneous parallel infrastructure , where the computation is eventually run . while mostly ignoring the details of such an underlying infrastructure , existing formalizations of the mapreduce paradigm constrain the computations to abide with some local and aggregate memory limitations . in this paper , we look at both modeling and algorithmic issues related to the mapreduce paradigm . we first provide a formal specification of the model , aimed at overcoming some limitations of the previous modeling efforts , and then derive interesting tradeoffs between memory constraints and round complexity for the fundamental problem of matrix multiplication and some of its applications . the mapreduce paradigm has been introduced in @xcite without a fully - specified formal computational model for algorithm design and analysis . triggered by the popularity quickly gained by the paradigm , a number of subsequent works have dealt more rigorously with modeling and algorithmic issues @xcite . in @xcite , a mapreduce algorithm specifies a sequence of rounds as described in the previous section . somewhat arbitrarily , the authors impose that in each round the memory needed by any reducer to store and transform its input pairs has size @xmath0 , and that the aggregate memory used by all reducers has size @xmath1 , where @xmath2 denotes the input size and @xmath3 is a fixed constant in @xmath4 . the cost of local computation , that is , the work performed by the individual reducers , is not explicitly accounted for , but it is required to be polynomial in @xmath2 . the authors also postulate , again somewhat arbitrarily , that the underlying parallel infrastructure consists of @xmath5 processing elements with @xmath5 local memory each , and hint at a possible way of supporting the computational model on such infrastructure , where the reduce instances are scheduled among the available machines so to distribute the aggregate memory in a balanced fashion . it has to be remarked that such a distribution may hide non negligible costs for very fine - grained computations ( due to the need of allocating multiple reducer with different memory requirements to a fixed number of machines ) when , in fact , the algorithmic techniques of @xcite do not fully explore the larger power of the mapreduce model with respect to a model with fixed parallelism . in @xcite the same model of @xcite is adopted but when evaluating an algorithm the authors also consider the total work and introduce the notion of work - efficiency typical of the literature on parallel algorithms . an alternative computational model for mapreduce is proposed in @xcite , featuring two parameters which describe bandwidth and latency characteristics of the underlying communication infrastructure , and an additional parameter that limits the amount of i / o performed by each reducer . also , a bsp - like cost function is provided which combines the internal work of the reducers with the communication costs incurred by the shuffling of the data needed at each round . unlike the model of @xcite , no limits are posed to the aggregate memory size . this implies that in principle there is no limit to the allowable parallelism while , however , the bandwidth / latency parameters must somewhat reflect the topology and , ultimately , the number of processing elements . thus , the model mixes the functional flavor of mapreduce with the more descriptive nature of bandwidth - latency models such as bsp @xcite . a model which tries to merge the spirit of mapreduce with the features of data - streaming is the mud model of @xcite , where the reducers receive their input key - value pairs as a stream to be processed in one pass using small working memory , namely polylogarithmic in the input size . a similar model has been adopted in @xcite . mapreduce algorithms for a variety of problems have been developed on the aforementioned mapreduce variants including , among others , primitives such as prefix sums , sorting , random indexing @xcite , and graph problems such as triangle counting @xcite minimum spanning tree , @xmath6-@xmath7 connectivity , @xcite , maximal and approximate maximum matching , edge cover , minimum cut @xcite , and max cover @xcite . moreover simulations of the pram and bsp in mapreduce have been presented in @xcite . in particular , it is shown that a @xmath8-step erew pram algorithm can be simulated by an @xmath9-round mapreduce algorithm , where each reducer uses constant - size memory and the aggregate memory is proportional to the amount of shared memory required by the pram algorithm @xcite . the simulation of crew or crcw pram algorithms incurs a further @xmath10 slowdown , where @xmath11 denotes the local memory size available for each reducer and @xmath12 the aggregate memory size @xcite . all of the aforementioned algorithmic efforts have been aimed at achieving the minimum number of rounds , possibly constant , provided that enough local memory for the reducer ( typically , sublinear yet polynomial in the input size ) and enough aggregate memory is available . however , so far , to the best of our knowledge , there has been no attempt to fully explore the tradeoffs that can be exhibited for specific computational problems between the local and aggregate memory sizes , on one side , and the number of rounds , on the other , under reasonable constraints of the amount of total work performed by the algorithm . our results contribute to filling this gap . matrix multiplication is a building block for many problems , including matching @xcite , matrix inversion @xcite , all - pairs shortest path @xcite , graph contraction @xcite , cycle detection @xcite , and parsing context free languages @xcite . parallel algorithms for matrix multiplication of dense matrices have been widely studied : among others , we remind @xcite which provide upper and lower bounds exposing a tradeoff between communication complexity and processor memory . for sparse matrices , interesting results are given in @xcite for some network topologies like hypercubes , in @xcite for pram , and in @xcite for a bsp - like model . in particular , techniques in @xcite are used in the following sections for deriving efficient mapreduce algorithms . in the sequential settings , some interesting works providing upper and lower bounds are @xcite for dense matrix multiplication , and @xcite for sparse matrix multiplication . the contribution of this paper is twofold , since it targets both modeling and algorithmic issues . we first formally specify a computational model for mapreduce which captures the functional flavor of the paradigm by allowing a flexible use of parallelism . more specifically , our model generalizes the one proposed in @xcite by letting the local and aggregate memory sizes be two independent parameters , @xmath11 and @xmath12 , respectively . moreover our model makes no assumption on the underlying execution infrastructure , for instance it does not impose a bound on the number of available machines , thus fully decoupling the degree of parallelism exposed by a computation from the one of the machine where the computation will be eventually executed . this decoupling greatly simplifies algorithm design , which has been one of the original objectives of the mapreduce paradigm . ( in section [ sec : preliminary ] , we quantify the cost of implementing a round of our model on a system with fixed parallelism . ) our algorithmic contributions concern the study of attainable tradeoffs in mapreduce for several variants of the fundamental primitive of matrix multiplication . in particular , building on the well - established three - dimensional algorithmic strategy for matrix multiplication @xcite , we develop upper and lower bounds for dense - dense matrix multiplication and provide similar bounds for deterministic and/or randomized algorithms for sparse - sparse and sparse - dense matrix multiplication . the algorithms are parametric in the local and aggregate memory constraints and achieve optimal or quasi - optimal round complexity in the entire range of variability of such parameters . finally , building on the matrix multiplication results , we derive similar space - round tradeoffs for matrix inversion and matching , which are important by - products of matrix multiplication . the rest of the paper is structured as follows . in section [ sec : preliminary ] we introduce our computational model for mapreduce and describe important algorithmic primitives ( sorting and prefix sums ) that we use in our algorithms . section [ sec : intromatrix ] deals with matrix multiplication in our model , presenting theoretical bounds to the complexity of algorithms to solve this problem . we apply these results in section [ sec : applications ] to derive algorithms for matrix inversion and for matching in graphs . our model is defined in terms of two integral parameters @xmath12 and @xmath11 , whose meaning will be explained below , and is named . algorithms specified in this model will be referred to as _ mr - algorithms_. an mr - algorithm specifies a sequence of _ rounds _ : the @xmath13-th round , with @xmath14 transforms a multiset @xmath15 of key - value pairs into two multisets @xmath16 and @xmath17 of key - value pairs , where @xmath16 is the input of the next round ( empty , if @xmath13 is the last round ) , and @xmath17 is a ( possibly empty ) subset of the final output . the input of the algorithm is represented by @xmath18 while the output is represented by @xmath19 , with @xmath20 denoting the union of multisets . the universes of keys and values may vary at each round , and we let @xmath21 denote the universe of keys of @xmath15 . the computation performed by round @xmath13 is defined by a _ reducer _ function @xmath22 which is applied independently to each multiset @xmath23 consisting of all entries in @xmath15 with key @xmath24 . let @xmath2 be the input size . the two parameters @xmath12 and @xmath11 specify the memory requirements that each round of an mr - algorithm must satisfy . in particular ," +"in a recent paper @xcite , one of us ( sla ) analyzed the consequences of introducing gravitation into the framework of trace dynamics pre - quantum mechanics @xcite , assuming the metric to be described as usual by a classical field . the focus of @xcite was on deriving an induced effective action describing trace dynamics modifications to gravitation , applying it to the cosmological robertson - walker metric , and beginning an application to the spherically symmetric case . the purpose of the present paper is to continue the latter , with a detailed investigation of modifications to spherically symmetric vacuum solutions . before proceeding with this , however , we give a brief introduction to the basic ideas of trace dynamics pre - quantum mechanics . a book - length exposition of trace dynamics is given in [ 2 ] , with a synopsis as section 2 of [ 1 ] ; readers wanting more detail than given here can refer to these references . the fundamental idea of trace dynamics is to set up a pre - quantum theory , based on non - commuting matrix- or operator- valued dynamical variables which have no a priori commutation relations ; for example , canonical coordinates @xmath2 at different spatial points are not assumed to commute . the lagrangian for this system is taken as the trace of an operator lagrangian constructed as a polynomial in the @xmath2 and their time derivatives , and using just cyclic permutation under the trace , one finds that the euler lagrange equations for the trace lagrangian are operator equations of motion , without invoking canonical quantization . this system is more general than the usual quantum field theory , and the rest of the trace dynamics program shows that with certain approximations ( basically a decoupling of high energy from low energy degrees of freedom ) , quantum field theory with unitary state evolution emerges as the thermodynamics of the underlying trace dynamics system . in trace dynamics , state vector reduction in measurement is a physical process , and is the only low energy non - local and non - unitary remnant of the underlying operator dynamics . in the discussion of the book [ 2 ] , gravity was not included . in the paper [ 1 ] , gravity was included in the form of a classical background metric @xmath9 , and a trace dynamics - induced correction to the usual einstein action was defined as the average of the trace dynamics pre - quantum variable action over the canonical ensemble . the structure of this correction was analyzed under the assumption that the pre - quantum matter fields are massless , and so admit a weyl scaling invariance when the metric is rescaled . this , together with three space rotational and general coordinate invariance , implies that the induced correction to the einstein action for has the following form for non - rotating metrics , to zeroth order in the derivatives of the metric , @xmath10 with @xmath11 a constant and with @xmath12 . a salient feature of this effective action is that it picks a preferred frame , and thus violates lorentz invariance . the traditional statement of the principle of relativity is that all inertial frames are physically equivalent , and that there is no way to measure the absolute velocity of an inertial observer . we now know , since the discovery of the cosmic microwave background ( cmb ) radiation , that this statement needs modification . the cmb provides a reference inertial frame , and by measuring the dipole component of the angular variation of the cmb , an observer with a radiometer can infer her absolute velocity with respect to this frame . such measurements @xcite show that the solar system is moving with a velocity of 369 km / s relative to the cmb . empirically , we know that the cmb is highly isotropic , to an accuracy of one part in @xmath13 . thus , it is natural to identify the preferred frame picked out by the trace dynamics canonical ensemble , and by the action of eq . , with the cmb rest frame , since identification with any frame moving with a finite velocity with respect to the cmb rest frame would violate rotational symmetry and spatial isotropy . calculations using the effective action of eq . must be carried out in the cmb rest frame , with predictions for frames moving with a finite velocity with respect to the cmb frame obtained by applying an appropriate boost to the results of the cmb rest frame calculations . none of this implies that the physical laws underlying trace dynamics are lorentz violating they are not but only reflects the rest frame of the underlying pre - quantum `` fluid '' , the dynamics of which is averaged over by the trace dynamics canonical ensemble . our assertion , motivated by rotational invariance , is that this rest frame is the same as the rest frame of the cmb , as well as the rest frame of the background galaxies . there has been an extended discussion in the literature of possible lorentz violating effects , and experimental bounds on them , but to our knowledge these do not take the form of a lorentz violating effective action of the form of eq . . thus , one motivation of this paper is to study further implications of a new form of preferred frame effect , based on the two assumptions which are used in @xcite but which are more general than the trace dynamics program : ( 1 ) the preferred frame effective action , as a function of the metric , is three space general coordinate invariant ( but not four space general coordinate invariant ) , and ( 2 ) the preferred frame effective action is invariant under weyl rescalings of the metric and matter fields . we can then rewrite @xmath22 of eq . as @xmath23 which is to be added to the standard einstein - hilbert action @xmath24 to give the total gravitational action @xmath25 varying this action with respect to the spatial metric components @xmath26 gives the modified equations of motion for the spatial components @xmath27 of the einstein tensor ; as discussed in @xcite and as elaborated on below , the equations of motion of the remaining components of the einstein tensor can be inferred by conserving extension using the bianchi identities . by construction , for the rw metric the modified action of eq . gives the usual equations of the standard cosmological model . but for other metrics , it implies different physics than is implied by the usual interpretation of `` dark energy '' as a consequence of a `` bare '' cosmological term , and this offers the possibility of distinguishing between the two interpretations of `` dark energy '' . in particular , for the schwarzschild metric solution of the einstein equations obtained from the usual einstein - hilbert action , the effective action @xmath28 diverges as @xmath29 near the schwarzschild radius @xmath30 , suggesting that including this term and solving the resulting modified einstein equations may substantially affect the horizon structure . thus , a second motivation of this paper is to study places where the two interpretations of dark energy , either as a `` bare '' cosmological constant arising from lorentz invariant vacuum physics , or as a frame - dependent effect of pre - quantum matter fluctuations , give different results . the natural place to start such a study is in the well - defined arena of spherically symmetric metrics , which was initiated in @xcite . our aim in the present paper is to continue the analysis of the spherically symmetric case , both for static and time dependent metrics , by deriving and solving the differential equations governing spherically symmetric schwarzschild - like solutions in the preferred rest frame for the effective action . we proceed now to give an outline of the paper , and a brief summary of the principal results . in sec . ii we analyze the equations in standard polar coordinates , marshalling both analytic and numerical results . in sec . iii we study the related equations that describe the schwarzschild - like solutions in isotropic coordinates . in sec . iv we extend our results to the time - dependent case , focussing on the mcvittie ansatz which , as in the static case , can be analyzed by solving ordinary differential equations in a radius - like variable . in sec . v we discuss the relevance of our results to outstanding issues in black hole physics . notational conventions and extensions of our discussion are given in appendices . our results show that , as anticipated , the effective action of eq . substantially changes the horizon structure . at macroscopic distances @xmath31 cm from the nominal horizon ( with @xmath32 the black hole mass in solar mass units ) the solutions closely approximate the standard schwarzschild form until cosmological distances are reached . hence we do not expect significant consequences for the astrophysics of stellar and galactic structure . within @xmath33 cm from the nominal horizon , the behavior of @xmath0 changes , with @xmath0 remaining non - vanishing until the internal singularity is reached ; this could have consequences , still to be explored , for discussions of the black hole `` information paradox '' . we can conclude little from the internal singularity itself , since here the approximation of neglecting metric derivatives in the effective action of eq . breaks down . at cosmological distances , the static solutions have a physical ( not a coordinate ) singularity , which may be a consequence of using the static metric assumption in a cosmological regime where it does not apply . introducing time dependence significantly alters the form of the spherically symmetric solutions . time - dependent solutions in the mcvittie ansatz are very sensitive to initial values and integration details , but subject to uncertainties which we discuss , there may be solutions which have similar horizon behavior to the static case , but in which the large distance physical singularity is pushed out to super - cosmological distances for black hole masses of astrophysical interest . the standard form for the static , spherically symmetric line element is @xmath34 corresponding to the metric components @xmath35 since we have @xmath36 , we can use the simplified form of the induced action given in eqs . . substituting @xmath37 , we get @xmath38 varying the spatial components @xmath26 of the metric , while taking @xmath39 , and writing @xmath40 we find from eq . that the spatial components @xmath41 are given by @xmath42 adding this to the variation of the einstein action @xmath43 of eqs . and , and equating the total variation to zero , we get the modified einstein equations for @xmath44 and @xmath45 , @xmath46 with the equation for @xmath47 proportional to that for @xmath45 . proceeding in an analogous way , one can derive the modified equations for a general axially symmetric metric . these are given ( but not solved ) in appendix d of the arxiv version of this paper ( arxiv:1308.1448v3 ) . before proceeding to study eqs . , we first examine the analogous equations that would be obtained from an ordinary cosmological constant ( that is , eq . with @xmath17 interpreted as the observed cosmological constant @xmath19 ) , which correspond to replacing @xmath62 by unity in eqs . . this gives the einstein equations @xmath63 as is well known , this system of equations can be solved by making the ansatz @xmath64 , with @xmath65 a constant , which implies that @xmath66 . substituting this , the @xmath45 equation reduces to @xmath67 and the" +"the recent advance in modern cosmology due to new and improved telescopes and techniques seems to overthrow the long - lasting paradigm or hope of an einstein - de sitter ( eds ) universe . from the cosmic microwave background ( cmb ) @xcite , along with studies of large scale structure ( lss ) , @xcite and the lyman @xmath1 forest @xcite ( ly@xmath1 ) etc . it is inferred that the universe consists of roughly 30 % matter ( cold dark matter , cdm and ordinary matter ) and 70 % dark energy . furthermore , measurements of the apparent magnitude of type ia supernovae ( sne ) have been used by two collaborations @xcite to estimate the values of the total matter energy density @xmath2 , which includes cdm , and the density in dark energy , e.g. @xmath3 . type ia sne are believed to be so - called standard candles , i.e. they show a very small scatter in intrinsic luminosity after empirical corrections @xcite , and by measuring the apparent magnitudes , the cosmology - dependent luminosity distance can be inferred . the supernovae look fainter than they would in an eds universe favouring both a non - zero @xmath3 and @xmath4 . combined with cmb data from boomerang and maxima @xcite , they end up at approximately the same values as the above - mentioned cmb , lss and ly@xmath1 measurements . however , there is a number of potential systematic errors that can contaminate the measurements . first , inter- and/or intra - galactic dust may obscure the light from the sne and make them look fainter . this has been investigated in e.g. @xcite . it is also still unclear whether there is any evolution of the sn brightness with redshift . many potential sources of evolution have been proposed , such as differing progenitor composition @xcite or host galaxy morphology ( and thereby redshift ) dependence @xcite just to name a few . furthermore , if photons can oscillate into axions , the sne will also look fainter due to the reduced number of received photons . this has been addressed e.g. in reference @xcite . a fourth possible contaminant is magnification or de - magnification by gravitational lensing . having a large sample of sne this can be corrected for statistically @xcite , but when studying single sne , the lensing effects need a careful treatment . this was the case with the farthest known sn so far , sn1997ff , at a redshift of 1.7 . the vicinity of the line - of - sight to this sn was unusually dense in galaxies and modelling of the individual lens galaxies was required . this was done by @xcite who conclude a large possible magnification depending on the lens masses and concentrations . bentez et al . @xcite conclude a magnification of 0.34@xmath50.12 mag . in this paper we present the well - known multiple lens - plane method applied to the calculation of the magnification of any point- or extended source . section [ sec : lensing ] describes this method in a general way . furthermore , we model the lenses as spherically symmetric navarro - frenk - white ( nfw ) or singular isothermal sphere ( sis ) halos and the lensing properties of these are described in sections [ subs : nfw ] and [ subs : sis ] . for more information on under which circumstances each halo type is appropriate , see e.g. reference @xcite . the method and models are manifested in a ` fortran 77 ` program , q - let , obtainable from the author upon request or it can be downloaded at ` http://www.physto.se/~cg/qlet/qlet.htm ` . the program is described in the text in section [ sec : program ] . in reference @xcite , an early version of q - let was used to estimate the magnification of the abovementioned sn1997ff . section [ sec : ramone ] describes the application of the code to the recently discovered supernova sn2003es . this section introduces the multiple lens - plane method and gives the important equations needed in the study of multiple light deflection . for more details , see reference @xcite . we also describe the lensing properties of the nfw and sis halo profiles . we start by projecting the mass of each massive object ( e.g. galaxy ) onto a plane at the respective object redshift . in the @xmath6:th plane , this gives a surface mass density @xmath7 , where @xmath8 is the impact parameter of the light - ray in each plane ( see figure [ fig : mullens ] ) . the justification for this projection is that the light is deflected only in the very vicinity of the lens in most cases and then travels practically unimpeded until it reaches the observer or another lens , situated far away from the preceding one . from figure [ fig : mullens ] , where most quantities are defined , we see that the position of the light - ray in each plane can be obtained recursively from the observed position @xmath9 through @xmath10 where @xmath11 is the angular diameter distance between redshifts @xmath12 and @xmath13 , @xmath14 and @xmath15 . with @xmath16 lens - planes we find the source position as @xmath17 . for convenience we use , in each plane , dimensionless quantities defined by @xmath18 where @xmath19 is an arbitrary scale length in the @xmath6:th plane which , if chosen as @xmath20 , makes @xmath21 the angular impact parameter in each plane . furthermore , the _ convergence _ is @xmath22 where ( in geometrised units ) @xmath23 is called the _ critical density _ due to its relation to the ability of a lens to produce multiple images . if we also define @xmath24 , the _ scaled deflection potential _ @xmath25 , needed for the magnification and defined through @xmath26 becomes @xmath27 in these units where @xmath28 is the source position , the lens equation is given by @xmath29 we now want to find the magnification as a function of image position . let @xmath30 denote the jacobian matrix of the lens equation @xmath31 furthermore we need @xmath32 @xmath33 where @xmath34 @xmath35 , @xmath36 and @xmath37 . this gives @xmath38 as @xmath39 where @xmath40 is the 2@xmath412 unit matrix . the @xmath42:s can be found by recursion and by noting that @xmath43 ; @xmath44 finally , the magnification is given by @xmath45 negative values of @xmath46 indicates images of reversed parity relative to the unlensed image . the use of the navarro - frenk - white model calls for a brief description of its lensing properties . before projection onto the lens plane , the nfw profile is given by @xmath47 where @xmath48 and @xmath49 are scale parameters that can be determined once e.g. the mass is specified , @xmath50 is the radial co - ordinate . the projected surface mass density will be circularly symmetric and we no longer need vector notation on the impact parameter but instead choose @xmath51 as the radial co - ordinate with the origin at the lens centre . if we choose @xmath52 ( cf . equation ( [ eq : dimless1 ] ) ) and define @xmath53 , then @xmath54 where @xmath55 and @xmath56 . the deflection angle is @xmath57 where @xmath58 and the magnification will be given by @xmath59^{-1}. \label{eq : mag5}\ ] ] a flaw of this model is that the total mass diverges when integrated out to infinity . however , this is not too serious since the deflection angle only is sensitive to the mass inside the impact radius , and the magnification is sensitive to this mass and the convergence at this point ( for circularly symmetric lenses ) . thus all mass outside the impact radius is unimportant . a single nfw halo gives either one or three images , where the primary image has @xmath60 , the secondary @xmath61 and the tertiary @xmath62 . the singular isothermal sphere model , also used here , is based on the assumption that the dark matter in the halo behaves as particles in an ideal gas trapped in their gravitational potential . the gas is assumed to be in thermal equilibrium and the resulting density profile before projection ( in geometrised units ) is @xmath63 where @xmath64 is the line - of - sight velocity dispersion of the particles . if we choose @xmath65 the equations for convergence , deflection angle , intrinsic source position and magnification become very simple for this model : @xmath66 @xmath67 and @xmath68 and @xmath69 as with the nfw model , the sis will give an infinite mass when integrated to infinity but the argument above regarding deflection angle and magnification also holds here . when considering a single sis halo it can give either one or two images depending on the impact parameter . primary images have @xmath60 and secondary have @xmath61 . the quick lensing estimation tool , q - let is a ` fortran 77 ` code written in order to quickly be able to estimate the lensing effects on a point source or an extended object . the structure of the code is as follows * read the input datafile and sort the planes * check if parameter values are allowed * present a choice between a point- or an extended source with elliptical image shape , alternatively a square grid ( see section [ subs : output ] ) * compute magnifications and positions of light rays * present a choice of how to output the results a used supplied datafile contains the cosmological parameters , the source redshift and position and the lenses redshifts , positions , velocity dispersions _ or _ masses and finally their halo type . the mass should be @xmath70 , i.e. the mass within the radius ( @xmath71 ) within which the average energy density is 200 times the critical density at the lens redshift . a point source must be put at the origin . for the case of an elliptical image , the origin will be put at the source centre and the ellipse will be centered at user specified co - ordinates which should be taken as ( 0,0 ) if an elliptical image only is studied . the possibility of putting the ellipse off - origin is useful to study e.g. a sn that is offset from its host galaxy centre and the galaxy shape is to be investigated . the sn is put at the origin and the host galaxy central co - ordinates are given as input . if a square grid ( see section [ subs : output ] ) is used , it will be centered at @xmath72 . the angular positions of the lensing galaxies should of course be assigned with respect to this origin and should be given in arcseconds . the velocity dispersions and masses should be given in @xmath73 and @xmath74 respectively . see section [ subs : input ] for an example of an input file . if only @xmath70 is given for a sis lens , this mass will be used to calculate the corresponding velocity dispersion since @xmath75 is the parameter used to determine the lensing strength for this halo type . if , on the other hand , only @xmath75 is given for a nfw lens , this velocity dispersion will be used to calculate the corresponding @xmath70 for a * sis * lens and assuming @xmath76 is the same for the nfw halo for a discussion of the validity of this . ] . this is done since the lensing properties of the nfw halo depends upon @xmath70 in our calculations . if , for some reason , both the mass and velocity dispersion are given , the mass ( velocity dispersion ) will be" +"@xmath3 after totally geodesic @xmath4-spheres , clifford tori represent the next simplest minimal embeddings of closed surfaces in the round unit @xmath1-sphere @xmath5 . in fact marques and neves @xcite , in their proof of the willmore conjecture , have identified clifford tori as the unique area minimizers among all embedded closed minimal surfaces of genus at least one , and brendle @xcite has shown they are the only embedded minimal tori , affirming a conjecture of lawson . the first examples of higher - genus minimal surfaces in @xmath5 were produced by lawson himself @xcite , and further examples were found later by karcher , pinkall , and sterling @xcite . both constructions proceed by solving plateau s problem for suitably chosen boundary and extending the solution to a closed surface by reflection . in this article we carry out certain constructions by using gluing techniques by singular perturbation methods . one begins with a collection of known embedded minimal surfaces . these ingredients are then glued together to produce a new embedded surface , called the initial surface , having small but nonvanishing mean curvature introduced in gluing . the construction is successful when the initial surfaces are close to a singular limit . the construction is then completed by perturbing the surface to minimality without sacrificing embeddedness . of course the size of the mean curvature and the feasibility of perturbing the surface so as to eliminate it both depend crucially on the design of the initial surface . gluing methods have been applied extensively and with great success in gauge theories by donaldson , taubes , and others . in many geometric problems similar to the one studied in this article obstructions appear to solving the linearized equation . an extensive methodology has been developed to deal with this difficulty in a large class of geometric problems , starting with @xcite , @xcite and with further refinements in @xcite . we refer to @xcite for a general discussion of this gluing methodology and @xcite for a detailed general discussion of doubling and desingularization constructions for minimal surfaces . in this article , however , we limit ourselves to constructions of unusually high symmetry ( except in section [ further ] ) and this way we avoid these difficulties entirely . the first desingularization construction by gluing methods for minimal surfaces with intersection curves which are not straight lines was carried out in @xcite and serves as a prototype ( see for example @xcite ) for desingularizations of rotationally invariant surfaces with transverse intersections without triple or higher points . ( an independent construction by traizet @xcite has straight lines as intersections . ) for one earlier application of the gluing methodology in the context of minimal surfaces in @xmath5 see @xcite , where a `` doubling '' construction of the clifford torus is carried out ; this work has been extended in @xcite for `` stackings '' of the clifford torus and in @xcite for doublings of the equatorial two - sphere . the present construction also glues tori , but by desingularization rather than doubling . the idea of a desingularization construction for intersecting minimal surfaces in a riemannian three - manifold is to start with a collection of minimal surfaces intersecting along some curves and to produce a single embedded minimal surface by desingularizing the curves of intersection . assuming transverse intersection , this is accomplished , at the level of the initial surface , through the replacement of a tubular neighborhood of each component curve of the intersection set by a surface which on small scales approximates a minimal surface in euclidean space desingularizing the intersection of a collection of planes along a single line . in prior desingularization constructions the appropriate models for these desingularizing surfaces were furnished by the classical scherk towers of @xcite , which desingularize the intersection of two planes . one novelty of the present article is our use of the more general karcher - scherk towers , introduced in @xcite , which come in families desingularizing any number of intersecting planes and so accommodate curves of intersection whose complements , in small neighborhoods of the curves , contain more than four components . note that although having more than two minimal surfaces intersect along a curve is not a generic situation , it can happen in rotationally invariant cases as for example in the case of coaxial catenoids . extending the results of @xcite to such situations for example is an interesting but difficult problem because one would have to use the full family of karcher - scherk towers as studied in @xcite . a motivation for our construction is the observation ( * ? ? ? * section 2.7 ) that lawson s surfaces may be regarded as desingularizations of a collection of great @xmath4-spheres intersecting with maximal symmetry along a common equator . in this article we pursue analogous constructions with tori instead of spheres as proposed in ( * ? ? ? * section 4 , page 300 ) . pitts and rubinstein have described one class of surfaces ( item 10 on table 1 of @xcite ) , similar to some of our surfaces , to be obtained by min - max methods . recently choe and soret @xcite have produced examples by solving plateau s problem for a suitably selected boundary , in the spirit of @xcite . their examples resemble the simpler examples we construct . ( to prove they are the same one would have to prove that the solution of the plateau problem is unique ; see remark [ r : unique ] ) . our construction has been developed independently and is more general in ways we describe below , and our strategy is quite different , based as we already mentioned on gluing techniques by singular perturbation methods . on the other hand our methods work only for high - genus surfaces . to outline , we construct two infinite families of embedded minimal surfaces in @xmath5 . the first family consists of desingularizations of a configuration @xmath6 ( see [ e : wk ] ) of @xmath7 clifford tori intersecting symmetrically along a pair of disjoint great circles @xmath8 and @xmath9 which lie on two orthogonal two - planes in @xmath10 . the second family consists of desingularizations of a configuration @xmath11 ( see [ e : wk ] ) which is the previous one augmented by the clifford torus which is equidistant from @xmath8 and @xmath9 . in both cases the construction is based on choosing `` scaffoldings '' , that is unions of great circles contained in the given configuration , and which we demand to be contained in the minimal surfaces we construct . moreover , reflections with respect to the great circles contained in the scaffoldings are required to be symmetries of our constructions . we denote the scaffoldings we choose by @xmath12 or @xmath13 ( see [ scaff ] ) . to construct the initial surfaces we replace tubular neighborhoods of the intersection circles with surfaces modeled on appropriately scaled and truncated maximally symmetric karcher - scherk towers . towers with @xmath14 ends are used along @xmath8 and @xmath9 , while classical scherk towers with @xmath15 ends are used along other circles of intersection ( present only in @xmath11 ) . the replacements are made so that each initial surface is closed and embedded , contains the applicable scaffolding , and is invariant under reflection through every scaffold circle ( see definition [ initsdef ] ) . these initial surfaces are perturbed then to minimality in a way which respects the reflections , so the surfaces produced are closed embedded minimal and still contain the scaffolding ( see the main theorem [ mainthm ] ) . note that lawson s approach also makes use of a scaffolding . our approach , however , gives much more freedom in the number of handles we include in the fundamental domain , while in lawson s method the fundamental domain is a disc so that plateau s problem can be solved . this makes no difference when considering the original construction of lawson in @xcite : we expect that the construction with more handles in the fundamental domain will still produce a lawson surface even though it does not a priori impose all the symmetries of the surface . when there are more than two circles of intersection involved , however , we can choose different numbers of handles on each of them and this gives a plethora of new surfaces as in the present constructions ( see the main theorem [ mainthm ] ) . it seems also rather daunting to try to construct even the simplest of our surfaces desingularizing @xmath11 by lawson s method . the present constructions motivate two important new directions for further study . first , what other similar desingularization constructions can be carried out in cases where there are obstructions due to less symmetry ? one has to deal then with the obstructions in the usual way by introducing smooth families of initial surfaces with the parameters corresponding to the obstructions as in earlier work ( see @xcite ) . we discuss this question in section [ further ] and we provide some partial answers . second , as remarked in the end of ( * ? ? ? * section 4.2 ) , there are various natural questions about rigidity and uniqueness for the surfaces presently constructed which are similar to those asked ( * ? ? ? * questions 4.3 , 4.4 and 4.5 ) about the lawson surfaces . in particular we are currently working to prove that the surfaces desingularizing @xmath6 can not be smoothly deformed to surfaces desingularizing @xmath2 clifford tori still intersecting along @xmath8 and @xmath9 but with different angles ( that is they can not `` flap their wings '' ) . more precisely we hope to prove that even with reduced symmetries imposed so `` flapping the wings '' is allowed , there are no new jacobi fields on our surfaces . @xmath3 as we have already mentioned the main difficulty of this construction as compared to earlier results is proving that under the symmetries imposed there is no kernel on the karcher - scherk towers . as for the classical singly periodic scherk surfaces ( @xmath16 ) @xcite , this is achieved by subdividing the surface suitably and applying the montiel - ros approach @xcite . our approach is also somewhat different than usual in some other aspects and we employ the high symmetry we have available . @xmath3 in section 2 we study in sufficient detail the maximally symmetric karcher - scherk towers using the enneper - weirstrass representation and following @xcite . in section 3 we study the geometry of the clifford tori and the initial configurations we will be using later , their symmetries , and the symmetries and scaffoldings we will impose in our constructions later . in section 4 we discuss in detail the construction of the initial surfaces and we study their geometry . in section 5 we provide estimates for the geometric quantities on the initial surfaces . in section 6 we study the linearized equation and estimate its solutions on the initial surfaces . we finally combine these results to establish the main theorem in section 7 . finally in section 8 we discuss further results using more technology . given an open set @xmath17 of a submanifold immersed in an ambient manifold endowed with metric @xmath18 , an exponent @xmath19 , and a tensor field @xmath20 on @xmath17 , possibly taking values in the normal bundle , we define the pointwise hlder seminorm @xmath21_\alpha(x ) = \sup_{y \in b_x } \frac{{\left\lvertt(x)-\tau_{yx}t(y)\right\rvert}_g}{d(x , y)^\alpha},\ ] ] where @xmath22 denotes the open geodesic ball , with respect to @xmath18 , with center @xmath23 and radius the minimum of @xmath24 and the" +"foams are studied both as unique industrial materials and also as a paradigm for complex fluids in general . in addition , many properties of foam arise from the collective effects of soap film interactions , which in turn derive from the chemistry and physics of static and flowing surfactant layers . thus , both microscipic and macroscopic properties can be probed in foam experiments . in particular , two dimensional ( 2d ) foams allow easy access to many properties of bubbles and foam since each bubble and each soap film interaction can be observed and analyzed @xcite . a series of studies by cantat and coworkers @xcite probes the relationship between the elastic and rheological properties of mono- and bi - disperse foams by studying the behavior of isolated large bubbles in a flowing monodisperse background field . under certain conditions a large bubble will flow faster than the surrounding bubbles , pushing its way thorough the background flow . cantat et al . explained their observations by including the effects of both the frictional drag on individual soap films and the elastic stress in the background flow . the elastic energy ultimately drives the bubble rearrangements necessary to let the large bubble through . debregeas et al . , the first to study shear banding in foam , used couette flow to generate shear stresses in a two dimensional foam @xcite . the shear bands in their experiments are formed and maintained by topological rearrangements at band interfaces that relax local stress . since the shear is quantifiable , these experiments allow one to study the energy dissipated via topological rearrangements ( e.g. t1 and t2 ) as well as their time scales . unlike these previous experiments which couple frictional dissipation to topological dissipation , our configuration largely eliminates topological dissipation . we generated extended parallel shear bands by injecting air into a background flow . the injected air parted the background flow producing three bands : two bands of background flow surrounding a central band with a different bubble structure and flow rate ( figs . [ raw ] , [ injection ] , and supplemental material ) . although severe topological rearrangements necessarily occur as the background flow is pushed aside ( fig . [ injection ] ) , stable coexistence of the shear bands incurs little topological cost . in a strict sense , a t1 transition occurs each time a soap film separating two large bubbles in the channel passes by a border between two small bubbles in the background flow . however , by the symmetry of the configuration , these transitions superimpose only a small periodic perturbation onto the overall dissipation . we consistently reproduced the shear bands over a range of experimental parameters such as background flow rate , air injection rate and foam thickness . simple geometric analysis reveals that the experimental parameters are insufficient to predict the relative size of the shear band . we hypothesize that the size emerges spontaneously to minimize drag dissipation in the system . by including both the drag between soap films and the glass plates and the drag of one soap film against another , we successfully predict the shear band height selection . furthermore , we obtain an estimate of the ratio of film - glass drag to film - film drag : @xmath0 . although many theoretical and experimental efforts have studied the film - glass drag ( see appendix a ) , this paper is the first , to our knowledge , to compare it to film - film drag . we hope our result leads to further experimental and theoretical study . our setup consists of a bubble generator and a hele - shaw cell ( hsc ) . the hsc consists of two sheets of 1/2 plate glass which we separated by one to three metal shims ( 0.8 mm ) creating a flow cell approximately 15.5 cm wide and 71 cm long . the hsc is sealed to the bubble generator at one end and open at the other . approximately 30 cm from the bubble generator , the top hsc plate has a 1 mm hole centered side to side . we injected air into the background flow through this port to generate the shear band . the bubble generator consists of a small tank ( @xmath11 liter ) made of polycarbonate sheet . we generated bubbles by injecting air into the soap solution ( 85 % distilled water , 10 % joy dish soap , 5 % glycerol ) through a submerged manifold with four independent heads to which we can attach standard syringe needles ( 0.24 @xmath2 i.d . to 0.58 @xmath2 i.d . ) . the size of the bubbles each needle produces is very sensitive to the rate of air flow , so we controlled the rate of foam generation ( and therefore the rate of foam flow through the cell ) with the size and number of active needles rather than the rate of air . one difficulty in generating foam with multiple needles driven by the same air supply is maintaining the identical pressure drop in each needle . to handle this , we passed air from a high pressure high volume source through a fine needle valve , and then distributed this low pressure high volume air to each needle , independently , via a four - valve fish tank manifold . we also controlled the air to the air injection port with a fine needle valve . we began each trial by adjusting needle size and flow rate to form a stable , monodisperse foam flow throughout the hsc with bubble size @xmath3 . then we began passing air through the air injection port . small bubbles in the background flow inflated as they passed under the injection port , and these inflated bubbles formed a band of large bubbles flowing down the center of the hsc ( figs . [ raw ] , [ injection ] ) . we took images of this channel under 45 different conditions in which we manipulated three mechanical parameters : the distance between the plates ( 0.8 @xmath2 , 1.6 @xmath2 , and 2.4 @xmath2 ) , the background foam flow rate ( 0.5 @xmath4 to 3.5 @xmath4 ) , and the air injection rate ( 0 to 0.1 @xmath4 ) . for each of the 45 configurations we recorded movies using a 1024x1044 pixel ccd camera at the fastest rate the camera would shoot ( @xmath5 30 fps ) for 200 frames . we post - processed the images with matlab scripts to track individual bubbles and calculate bubble flux . although in the experiments we controlled the rate of bubble generation and air injection rate , we were not able to simultaneously measure these rates . however , the volume flow rate of air ( both to the bubble generator and the air injection port ) directly correspond to the volume flux of bubbles produced . we measured the areas ( @xmath6 ) and velocities ( @xmath7 ) of bubbles via image analysis , and then calculated the volume flux of bubbles @xmath8 where @xmath9 is the separation between the hsc plates.because the inflated bubbles formed band of relatively stable width , one bubble wide , these `` bubbles '' actually took the form of individual soap films spanning a channel between two regions of background flow . the velocity of the central band was always in the same direction as the background flow , and the speed was always equal to or greater than that of the background flow . as in cantat s experiments @xcite , below a threshold value of air injection , the central band moved in unison with the background flow ( i.e. at the same speed ) . above this threshold it moved faster . in this case , the single soap film separating large bubbles in the channel remained in contact with the soap films of the bubbles bounding the channel , though on average perpendicular to these films , as it moved along them ( see fig . [ raw ] and online movie ) . intermittently , a line of bubbles perpendicular to the flow would take the place of the single soap film , however , we do not consider this as part of the phenomenon we analyzed in this study . if we injected air still faster , we passed another threshold above which the channel became unstable and fingered into the background flow . due to the narrow width of our channel , we have not yet investigated this fingering . although it would be interesting to investigate , following cantat et al . , the orgin of the threshold behavior , our chief question was how the width of the channel is determined by the parameters we experimentally controlled : channel depth ( number of spacers ) , background foam flux ( bubble generation rate ) and channel bubble flux ( air injection rate ) , size of background bubbles , and the width of the hsc . our theoretical analysis suggested that the channel width was really only a function of the ratio of the two fluxes with a single fitting parameter , the ratio of film - film drag to film - glass drag . the control variables determine the volume flux of channel bubbles in a strictly geometric manner . but this flux can occur in a narrow , fast channel or a wide , slow one . we hypothesize that the system selects this width in some optimal way . we make the following simplifications : we model the drag force on an element of bubble wall as a linear response that arises independently from components of velocity proportional to and perpendicular to the element of bubble wall , and we model the bubbles in the foam as squares and rectangles with sides oriented parallel and perpendicular to the flow ( fig . [ cartoon ] ) . based on these assumption , which we elaborate in appendix a , we express the power dissipated by a soap film of length @xmath10 parallel and perpendicular to the direction of bubble flow as @xmath11 and @xmath12 respectively . to calculate the power dissipated by the background flow , we consider a block of width @xmath13 of small background flow bubbles , where @xmath14 is the width of the channel bubbles . the height of the flow on either side of the channel is @xmath15 where @xmath16 is the number of bubbles . each small bubble contributes one parallel and one perpendicular film . considering the drag these generate , we write @xmath17 for the power dissipated by this block of bubbles . the power dissipated by a large bubble is the power dissipated by the motion of a single soap film which is perpendicular the flow . the height of the soap film is @xmath18 , it moves at a velocity @xmath19 , and has a depth @xmath9 , which is the distance between the plates . the drag generated by contact with the glass plates dissipates a power @xmath20 while the drag generated by the relative motion of this film against the bubbles bounding the channel is @xmath21 where @xmath22 is the drag coefficient ( per unit length ) for one soap film moving across another such as at the interface where a film separating channel bubbles meets the idealized continuous film that defines the central channel . the power flux is the power dissipated per unit distance along the hsc . we calculate this by dividing the total power by the width @xmath14 of our hypothetical block . combining equations [ backgroundblock],[pchannel1 ] , [ prelative ] and making the associations @xmath23 , @xmath24 and @xmath25 , we express the power flux as @xmath26 since we experimentally control fluxes" +"the calice ( _ _ * cal*__orimeter for a _ _ * li*__near _ _ * c*__ollider _ _ * e*__xperiment ) collaboration performed tests of new calorimeter technologies for the planned international linear collider ( ilc ) . several prototypes were investigated during the testbeam phase at desy ( 2006 ) , cern ( 2006 & 2007 ) and fnal ( 2008 & 2009 ) . the analog hadron calorimeter ( ahcal , @xcite ) has been successfully used in all five test - beams . it is a sampling calorimeter with a size of @xmath0 with 38 layers using 2 cm of steel as absorbing material , resulting in a depth of approximately @xmath1 ( @xmath2 for pions ) . the active layers have a very granular structure , using scintillator tiles from @xmath3 up to @xmath4 . each scintillator tile is read out with a silicon photomultiplier . r0.5 this granular structure allows for identification of tracks generated by minimum ionizing particles ( mip ) passing through ( parts of ) the detector . this capability is an excellent tool for detector calibration@xcite and provides the possibility for detailed studies of the shower substructure . this article presents an algorithm for the identification of mip - like track segments within hadronic showers ( see section [ sec : tracking ] ) . a few examples of identified mip tracks are displayed in figure [ fig : typicalevent ] . as one can see , the tracks provide information on the 3d substructure of hadronic showers . this information is used for confronting monte carlo simulations with data ( section [ sec : mcdata ] ) . to provide a clean sample of tracks by minimum ionizing particles in the environment of a hadronic shower , which includes regions of high local particle density , specific selections criteria for the calorimeter cells used by the tracking algorithm are necessary . a sample of the detector cells very likely being traversed only by a single particle is selected by imposing an isolation criterion , illustrated in figure [ fig : isolationcriterion ] . a hit is called isolated if there is no direct neighbour cell with a hit within the same layer . the tracking algorithm will only use hits fulfilling this criterion . as there is no magnetic field in the calice experiment , the presented algorithm was optimized for finding straight tracks . the tracking algorithm used for identification of single particle tracks is a local search method working layer by layer . a track is followed from the beginning to the end . the algorithm has the following steps : 1 . search for isolated hits in all layers using the introduced isolation criterion . a cell is called hit if the energy deposited exceeds @xmath5mip . a mip is defined as the most probable energy deposition of a single passing minimum ionizing particle . 2 . use the isolated hits as start point ( seed ) , starting from the first layer in beam direction . for each of these points : 1 . increment by one layer in beam direction and search for unused isolated hits that can continue the current track . the search window is @xmath6 cells in @xmath7 and @xmath8 ( when @xmath9 is beam axis ) , resulting in 9 checked cells . for a 1d illustration see figure [ fig : trackingalgorithm ] . 2 . repeat last step until the end of the detector is reached or no continuation hit can be found . the algorithm allows for gaps , i.e. maximum one consecutive layer with no hit . 3 . once the track is completed , start over with the remaining isolated hits in the detector to find more tracks . as the algorithm works layer - wise for each track there is a maximum of one hit per layer . with the isolation criterion it is then very likely that the found track was generated by a single particle . the characteristics of mip - like tracks reflects the spatial structure of hadronic showers . by comparing to simulation the shower modeling provided by the different physics lists can be validated . here , the two following parameters were chosen : track angle and track length . the comparison was done using these physics lists from mokka / geant4@xcite : + ` qgsp_bert ` , ` qgsp_bert_trv ` , ` qgs_bic ` , ` lhep ` , ` ftf_bic ` , ` ftfp_bert ` the comparison of the actual distribution is done for @xmath10 data at an energy of @xmath11gev . for energies in the range from @xmath12gev up to @xmath13gev the mean value was used for comparison . the track angle is sensitive to the scattering angle of secondary particles created in hadronic showers and hence the shower structure . the comparison for the angle distribution of the tracks is shown in figure [ fig : mcdata:25gev : trackangle ] for @xmath11gev . the distribution shows many tracks at angles @xmath14 lower than @xmath15 ( @xmath16 of all tracks ) . as in every event the incident particle is not inclined , the initial track of the incoming particle is major contributor to those at low angles . if we go to higher angles , the number of tracks found decreases until it vanishes for @xmath17 . this is not necessarily due to the shower shape but the incapability of the used algorithm to identify tracks at very large angles . all physics lists considered with the exception of ` lhep ` and ` qgs_bic ` provide an angular distribution of tracks that is similar to the one observed in data . the tracks produced by ` lhep ` and ` qgs_bic ` have too low average angles . this can be seen as well when comparing the mean value for the complete energy range shown in figure [ fig : mcdata : all : trackangle ] . ` lhep ` is significantly below the data over the whole energy range , while ` qgs_bic ` performs better but is still too low . the remaining physics lists are again quite close together and reproduce the result from data better , while they all tend to produce tracks at lower angles than testbeam data , especially for higher energies . + the track length gives the distance a particle travels before participating in a hadronic interaction , in units of ahcal layers : @xmath18 the slope of the distribution is sensitive to high energy cross sections , especially for secondary particles created in or after the first hadronic interaction . the results of the comparison can be seen in fig . [ fig : mcdata : tracklength ] . for the mean value for all energies ( figure [ fig : mcdata : all : tracklength ] ) the physics lists all show good agreement with the testbeam data . especially for energies higher than @xmath19gev the difference between simulation and test beam data is at the order of 1% , with a slight tendency towards longer tracks in the simulation . noise hits can influence the isolation criterion which can lead to tracks being aborted early . if the amount of noise is not added correctly during the digitization phase of the simulated data , this will lead to a constant offset between all physics lists and the testbeam data . the track length for the @xmath11gev run in figure [ fig : mcdata:25gev : tracklength ] shows the exponential fall - off expected from the hadronic interaction of particles passing through matter . the peak at @xmath20layers is coming from punch through hadrons and from muons coming from @xmath21 decays . the amount of muons and punch - through pions is well reproduced by the simulation . to be able to study tracks coming from the incoming beam particle ( `` primary '' tracks ) and tracks being created in hadronic interaction ( `` secondary '' tracks ) individually , the histogram from figure [ fig : mcdata:25gev : tracklength ] is split into two : for the primary tracks a histogram containing only tracks starting in layer 1 or 2 ( figure [ fig : mcdata:25gev : tracklengthfirstlayer ] ) and for the secondary tracks a histogram containing tracks starting in layer 3 or later . the histogram containing the secondary tracks can be seen in figure [ fig : mcdata:25gev : tracklengthafterfirstlayer ] . those tracks are created mainly by secondary particles coming from the shower core and hence is sensitive to the correct modeling of high energy cross sections within the physics list . here the difference between testbeam data and simulation is below 10% , with the simulation producing less shorter tracks , but on average all physics lists produce tracks that are longer than the ones from testbeam data , which can be seen as well in figure [ fig : mcdata : all : tracklength ] . the fluctuations at the end are due to insufficient statistics ( compare with statistical error indicated by the gray area , here shown for the ` lhep ` physics list ) . the exponential decrease is reproduced well by all physics lists , demonstrating a good description of the cross sections in the models . the punch - through particles can be seen as well in figure [ fig : mcdata:25gev : tracklengthfirstlayer ] showing the primary tracks . all physics lists recreate the peak around the full detector length of @xmath20layers . this indicates a good understanding of the simulation of the beamline , including the decay of pions to muons and the trigger . the exponential fall is interrupted for track lengths around 28 - 30 layers . this is due to the change in the geometry of the ahcal from fine to coarse after the first 30 layers . two particles resolved in the fine granularity might become unresolved and give non - isolated hits , therefore ending the track . hence many tracks will stop in layer 30 , leading to the observed length distribution for tracks starting at the front face of the ahcal . this discontinuity in track length can be seen both for testbeam data as well as for all simulations . however , the discontinuity is more pronounced in all considered physics lists compared to testbeam data , indicating potential problems in the digitization , i.e. in the simulation of the optical crosstalk which might differ for different tile sizes and hence creates a different number of fake hits , changing the number of isolated hits . a simple tracking algorithm has been developed that is capable of identifying tracks created by minimum ionizing particles in hadronic showers . the algorithm relies on isolated hits and works on a layer - by - layer basis . the intrinsic track properties track angle and track length are used as parameters in a comparison between testbeam data and simulations created with various physics lists . for the given data the four physics lists ` qgsp_bert ` , ` qgsp_bert_trv ` , ` ftf_bic ` and ` ftfp_bert ` all give results that are close together and comparable to testbeam data , with a slight advantage in favor of the ` qgsp_bert(_trv ) ` lists ." +"topological insulators ( tis ) are amongst the most actively investigated systems in condensed matter physics @xcite . in reality , there is evidence for their existence in two @xcite and three @xcite spatial dimensions . due to bulk - boundary correspondence , non - trivial topological states of matter have edge states at their boundaries with peculiar transport and optical properties . for instance , the two - dimensional ( 2d ) , time - reversal symmetric quantum spin hall state that is realized in hg(cd)te quantum wells ( qws ) is known to come along with helical edge states that are protected against elastic backscattering of non - magnetic impurities @xcite . however , not only the edge state physics of these systems is interesting but also the 2d bulk physics bears exciting novelties . the low - energy excitations of hg(cd)te qws are described by a model the bernevig - hughes - zhang ( bhz ) model @xcite that interpolates between the limiting cases of schrdinger and dirac fermions . this interplay between schrdinger and dirac physics constitutes an opportunity for new phenomena to emerge . we have , for instance , recently discovered collective charge excitations at zero doping , i.e. intrinsic plasmons , in this system which are absent in both separate limits @xcite . in this article , we complement our study of the screening properties and the collective charge excitations of hg(cd)te qws on the basis of random phase approximation ( rpa ) , and hence present a comprehensive analysis of its polarization function in the static and full dynamic limit , at zero and finite doping . continuously tuning the parameters of the bhz model , we reproduce the limits of pure dirac and pure schrdinger fermions and explore intermediate regimes , in order to understand how analogies and differences emerge . we support our numerical calculations of the polarization functions with analytical expressions derived by f - sum rules . in the static limit , we calculate the screening properties due to the intrinsic system and at finite doping , analyzing the induced charge density ( with friedel oscillations ) in response to a charged impurity . different to the dirac fermion system graphene , where static screening in the intrinsic limit is momentum independent and can therefore be absorbed into an effective dielectric constant @xcite , the bhz model shows a significant momentum dependence that translates into a finite extent of the induced charge density . in the dynamic limit , we are particularly interested in a better understanding of the plasmon excitations of this system away from zero doping where we previously found a new plasmon due to the interplay between schrdinger and dirac fermion physics @xcite . at finite doping , under certain conditions specified below that are e.g. applicable to hg(cd)te qws , we find a coexistence between this novel ( interband ) plasmon and an ordinary ( intraband ) plasmon . both plasmons can be rather weakly damped by single - particle excitations and should therefore be observable . interestingly , the two plasmons respond to the topology of the bandstructure with a distinctive behavior . they seem to merge one into the other in a normal insulating phase , while they remain clearly resolved when the system realizes a topological insulator . generally , rpa is known to provide reliable predictions at large densities and in systems with a large number of fermionic degrees of freedom . while its validity was indeed questioned for the intrinsic dirac limit , where the system is unable to screen the coulomb interaction and strong renormalization effects are expected @xcite , rpa has been shown to yield a quantitative description of many - body effects in graphene @xcite . it has been widely used for the study of plasmons in the dirac model , including various forms of ( multilayer ) graphene and ti surface states , see ref . for a comprehensive review . closely related to our work , the intraband plasmons of black phosphorous have been studied on the basis of rpa and an extended version of the bhz model including anisotropy @xcite . a similar study has been done for mos@xmath0 @xcite . our article is organized as follows . in sec . [ sec_model ] , we introduce the bhz model and present the general formalism we employ to calculate the static and dynamical dielectric function and the induced charge density . the nature of the nontrivial pseudospin , the origin of possible interband plasmons , experimentally relevant parameters and the different contributions to the f - sum rule are also discussed here . subsequently , in sec . [ sec_undoped ] , we present the static screening properties , the dynamical excitation spectrum ( new interband plasmon ) and the f - sum rule in the undoped regime . here we revisit and go beyond the results from ref . . [ sec_doped ] , this analysis is extended to the case of finite doping where inter- and intraband excitations equally matter . we begin by discussing the ability of the bhz model to interpolate between dirac and schrdinger physics . afterwards , we have a closer look at parameters which are experimentally relevant for hg(cd)te qws , see sec . [ sec : hg(cd)te quantum wells ] . in this limit , we find a coexistence of inter- and intraband plasmons occuring for energies and momenta which are suitable for raman or electron loss spectroscopy . we close this chapter by investigating the influence of a non - trivial topology on the plasmonic excitation spectrum . finally , in sec . [ sec_con ] , a conclusion and a brief outlook are given . the bhz hamiltonian @xcite for a two - dimensional electron gas ( 2deg ) near the @xmath1-point has the form @xmath2 here @xmath3 are the pauli matrices associated with the band - pseudospin degree of freedom ( band @xmath4 and @xmath5 in hg(cd)te quantum wells ( qws ) ) , @xmath6 , @xmath7 with @xmath8 . the system possesses time - reversal symmetry and @xmath9 is block diagonal in the kramer s partner or spin degree of freedom . restricting ourselves to the block @xmath10 , the results can be extended to the other one by applying the time reversal operator . @xmath10 describes fermions with intermediate properties between a dirac and a conventional 2deg system . the off - diagonal term ( @xmath11 parameter ) is typical for a dirac system ( @xmath12 in graphene ) , with @xmath13 the dirac mass ( corresponding to a gap of @xmath14 ) . we consider positive and negative masses , where the latter one corresponds to an inversion of the bandstructure and the system is topologically non - trivial @xcite . for simplicity , we restrict ourselves to a bandstructure with a minimum at the @xmath1-point , which limits the mass to @xmath15 . in analogy to a 2deg , the diagonal elements bear kinetic energy elements which preserve ( @xmath16 parameter ) and break ( @xmath17 parameter ) particle - hole ( p - h ) symmetry ( @xmath18 for schrdinger fermions with @xmath19 the quasi - particle mass ) . the eigenstates of eq . ( [ eq : hamiltonian ] ) are described by the following dispersion and pseudospin @xmath20 with @xmath21 for valence and conduction band . note that we consider electrons to be perfectly localized on the 2d x - y plane and therefore we neglect the real shapes of the envelope functions due to the quantum confinement along @xmath22 direction @xcite . the bhz model is characterized by intrinsic scales for momentum , @xmath23 , and energy , @xmath24 , which reflect the interpolating character of the model between dirac ( @xmath11 parameter ) and schrdinger ( @xmath16 parameter ) system . fermi momentum @xmath25 and chemical potential @xmath26 provide externally tunable momentum and energy scales , which we call fermi scales in the following . we expect the ratio between fermi and intrinsic scales to govern the physics of this system . we therefore define the dimensionless quantities @xmath27 where we set @xmath28 in the following . @xmath29 is defined to be the energy to the wave vector @xmath30 , such that @xmath31 if @xmath32 . for @xmath33 , we therefore expect intermediate physics , while in the limit @xmath34 ( @xmath35 ) the dirac ( 2deg ) physics should be recovered . the linear response of an homogeneous system to an external applied potential is described by the density - density generalized susceptibility or retarded polarization function @xmath36 . this response comprises two main phenomena : screening , described by the real part @xmath37 $ ] , and dissipation by single - particle excitations ( spes ) , given by the imaginary part @xmath38 $ ] . the polarization function in rpa yields the expression @xmath39 with @xmath40 , @xmath41 a positive infinitesimal , @xmath42 for spin degeneracy , @xmath43 and @xmath44 the fermi - dirac function with @xmath45 and @xmath46 the boltzmann constant . in the following we will assume zero temperature , @xmath47 . the overlap factor is given by @xmath48.\label{eq : f factor}\ ] ] eq . ( @xmath49 ) implies that @xmath50 is only a function of the reduced dimensionless variables @xmath51 and @xmath52 and parametrically depends on @xmath53 , @xmath54 and @xmath30 . in the massless dirac limit ( @xmath55 ) , eigenspinors are characterized by their helicity and consequently the overlap factor @xmath56 only depends on the angle @xmath57 between @xmath58 and @xmath59 . it is strictly one ( zero ) for states with the same ( opposite ) helicity . in the bhz model , the quadratic terms have the effect of turning the pseudospin of the eigenstates out of plane in opposite directions for conduction and valence bands at large @xmath51 , see fig . [ fig : overlap ] . , and a ti phase ( b ) , @xmath60 . the bands are separated by an additional @xmath61 for better illustration of the pseudospin . [ fig : overlap],title=""fig:"",width=158 ] , and a ti phase ( b ) , @xmath60 . the bands are separated by an additional @xmath61 for better illustration of the pseudospin . [ fig : overlap],title=""fig:"",width=158 ] this results in a decay of the overlap factor down to @xmath62 in the limit of a conventional 2deg system ( @xmath63 or @xmath64 ) . a finite mass @xmath65 has a similar effect , but in the limit of @xmath66 . the pseudospin turns in the same ( opposite ) direction as for the quadratic term for positive ( negative ) mass , see fig . [ fig : overlap ] . this has the direct consequence that for a normal insulator ( ni ) phase the interband overlap factor is reduced , while it is increased for a ti phase . on the contrary , a positive ( negative ) mass enhances ( diminishes ) the intraband overlap factor . this picture is also confirmed in section [ f - sum rule introduction ] by calculating the f - sum rule . the bare coulomb interaction @xmath67 in an electron gas is modified by screening into the effective interaction @xmath68 . there , screening is described by the dynamical dielectric function . employing dimensionless units , it acquires the form @xmath69 where we have introduced the interaction strength parameter @xmath70 ( effective dirac fine structure constant @xcite ) and the dimensionless function @xmath71 @xmath72 in graphene one finds @xcite @xmath73 , while in hg(cd)te qws it is of the order @xmath74 @xcite . here , @xmath75 is the background dielectric constant , accounting for screening of internal electronic shells , while @xmath76 gives the dynamic screening due to electrons in the low energy bands . zeros of @xmath77 describe a density - density ( longitudinal ) perturbation of" +"braneworld models have been shown to be extremely rich in phenomena leading to modifications of general relativity ( gr ) at both low and high energies @xcite . when the four - dimensional description of branes is considered , massless scalar degrees of freedom -the moduli- appear mediating the gravitational interaction together with the usual 4d graviton . the presence of these moduli is commonly related to the geometry of the entire system and plays a significant role in the phenomenology of extra - dimensions . at low energies , for instance , braneworld models are best described by scalar - tensor theories @xcite . within this framework , the gravitational couplings become functions of the moduli and standard gr predictions get modified in ways that can be tightly constrained by present astrophysical observations . current tests on gravity allow us to measure relativistic corrections to newton s law at the first post - newtonian level ( @xmath0 ) with great precision @xcite . at this order , the predictions of scalar - tensor theories can be parameterized by two `` weak field '' quantities , @xmath1 and @xmath2 , the post - newtonian parameters introduced long ago by eddington @xcite . when solar - system tests are taken into account these parameters are observed to be very close to 1 ( gr corresponds to @xmath3 ) . for example , the time delay variation of the cassini spacecraft near the solar conjunction @xcite has given the result @xmath4 , whereas the lunar laser ranging experiment @xcite shows that @xmath5 . another source of constraints on @xmath1 and @xmath2 , qualitatively different from solar - system tests , comes from the observation on binary pulsars systems @xcite . in this case , the `` strong field '' conditions generated by the compactness of neutron stars allow the analysis of nonperturbative effects caused by the moduli , implying tight bounds on the eddington parameters . in this paper the low energy regime of braneworld models is considered . we show that solar - system and binary - pulsar tests can be used to discriminate between different 5d braneworld models and to shed light on their extra - dimensional configuration . for this , we have chosen a rather general setup , bps - braneworlds , of which the randall - sundrum model @xcite and dilatonic braneworlds @xcite are just particular examples . the model consists of a 5d space - time bounded by two 3-branes with tensions @xmath6 and @xmath7 . a scalar field @xmath8 lives in the 5d bulk and is dominated by a bulk potential @xmath9 . at the same time , the brane tensions are functions of the scalar field boundary values , @xmath10 and @xmath11 , of the form : @xmath12 and @xmath13 , where @xmath14 is the brane potential . in order to stay close to gr and acceptable phenomenology @xcite , a special condition ( the bps condition ) exists between the scalar field potential @xmath9 and the brane potential @xmath14 : @xmath15 this condition ensures supersymmetry to be preserved near the branes @xcite and the existence of static vacuum solutions in the absence of matter fields . additionally , it allows the system to be described by a simple and attractive bi - scalar - tensor theory , where the moduli ( @xmath10 and @xmath11 ) are related to the positions of the branes on the 5d background . deviations from the bps condition can also be included in the formalism , resulting in the presence of dark energy . this article is organized as follows : in sec . [ s2 ] we review bps braneworlds and introduce their low energy effective description . we also discuss some relevant aspects of these models , such as its extra - dimensional geometry and the presence of singularities . in sec . [ s3 ] we deduce the system s equations of motion and analyze the cosmological evolution of the branes . there we find that the negative tension brane is generally expected to evolve towards a state where its warp factor becomes null . for late time cosmology this result implies that both branes end up interacting only weakly . in sec . [ s4 ] , the first post - newtonian level parameters are introduced and computed for the model . it will be found that they depend on the shape of @xmath14 and on the positions of the branes in the background . then we explore the way in which solar - system and binary - pulsar tests constrain the 5d configuration for this class of models . finally , in sec . [ s5 ] we provide some concluding remarks . in this section we introduce bps - brane models in some detail and provide their low energy effective theory . let us consider a 5d manifold @xmath16 with topology @xmath17 , where @xmath18 is a fixed 4d lorentzian manifold without boundaries and @xmath19 is the orbifold constructed from the one - dimensional circle with points identified through a @xmath20-symmetry . @xmath16 is bounded by two branes located at the fixed points of @xmath19 . let us denote the brane surfaces by @xmath21 and @xmath22 respectively and the space @xmath16 bounded by the branes as the bulk space . in this model there is a bulk scalar field @xmath8 with a bulk potential @xmath9 and boundary values @xmath10 and @xmath11 at the branes . the brane tensions are @xmath23 and @xmath13 where @xmath14 is the brane potential ( sometimes called the superpotential ) . additionally , we consider the existence of matter fields @xmath24 and @xmath25 localized at the branes ( see fig . [ f1 ] ) . with a bulk potential @xmath9 . additionally , the bulk - space is bounded by branes , @xmath21 and @xmath22 , with tensions @xmath26 and @xmath27 respectively.,scaledwidth=45.0% ] the total action of the system is given by @xmath28 where @xmath29 is the action for the bulk fields , including the gravitational field and the bulk scalar field @xmath30.\end{aligned}\ ] ] here , @xmath31 is the determinant of the five dimensional metric of signature @xmath32 and @xmath33 its ricci scalar . the term @xmath34 of eq . ( [ s2 : tot - act ] ) is the action for the boundary fields given by @xmath35 where @xmath36 is the gibbons - hawking boundary term , and @xmath37 and @xmath38 are the brane tensions terms of the form @xmath39 finally , the last term in eq . ( [ s2 : tot - act ] ) corresponds to the action for the matter fields at the branes . it is given by : @xmath40 + s_{2}[\psi_{2},g_{\mu \nu}^{(2)}],\end{aligned}\ ] ] where @xmath24 and @xmath25 denote the matter fields at each brane , and @xmath41 and @xmath42 are the respective 4d induced metrics . to conclude , let us recall the bps condition between the bulk potential @xmath43 and the superpotential @xmath44 : @xmath45 relation ( [ s2 : bps - cond ] ) is of the utmost importance ; it allows the construction of static vacuum solutions in which the branes can be located anywhere in the background ( bps states ) . when @xmath44 is a constant the randall - sundrum model is recovered with a negative bulk cosmological constant @xmath46 . suppose that @xmath47 is the matter energy density of the braneworld universe , then , the low energy regime for this type of system is characterized by the condition @xmath48 . in the rest of this paper we assume that this is the case . we now study the 5d geometry of the present setup . as already mentioned , in the absence of matter , condition ( [ s2 : bps - cond ] ) allows the construction of static vacuum solutions . this can be outlined as follows : let us assume without loss of generality that the 5d infinitesimal - metric @xmath49 is given by @xmath50 here , the extra - dimension is parameterized by the coordinate @xmath51 and @xmath52 is the scalar component of the 5d metric from the four - dimensional point of view ( it will be related to one of the moduli on the branes ) . @xmath53 , on the other hand , is the induced 4d metric at each @xmath51-slice parallel to the branes ( the branes are located at orbifold fixed points @xmath54 and @xmath55 ) . now , consider the following factorization of @xmath53 : @xmath56 where @xmath57 is a 4d metric satisfying the vacuum einstein s equation @xmath58 ( here @xmath59 is the einstein tensor constructed out of @xmath60 ) . then , condition ( [ s2 : bps - cond ] ) allows us to find a static vacuum solution to the entire system provided that the following differential equations are fulfilled : @xmath61 in this solution the branes can be localized anywhere in the 5d background without modifying the geometry around them . in what follows we deduce a few important results out of relations ( [ s2 : match1 ] ) and ( [ s2 : match2 ] ) . an immediate consequence of eq . ( [ s2 : match1 ] ) is the following : if @xmath44 is not a constant function of @xmath8 then we can parameterize the coordinate @xmath51 in terms of @xmath8-values : @xmath62 note that this parameterization depends heavily on the shape of @xmath14 . in particular , observe that as @xmath63 approaches a local maximum or minimum , the @xmath51-coordinate tends to infinity . this implies that @xmath64 can not change signs in the entire bulk space . this observation simplifies much of the analysis on the braneworld geometry . without lost of generality we may assume @xmath65 everywhere in @xmath16 , thus @xmath8 becomes an increasing monotonic function of @xmath51 ( otherwise we can perform the change of variables @xmath66 ) . observe from eq . ( [ s2 : match2 ] ) that the 5d geometry profile is dictated by the shape of @xmath44 ; if @xmath68 ( @xmath69 ) then the warp factor @xmath67 is a decreasing ( increasing ) function of @xmath51 . in sec . [ s3 ] we shall see that in order to have consistent dynamics at the branes , @xmath44 must have the same sign everywhere in the bulk . in general , this implies that the brane tensions @xmath6 and @xmath7 must have opposite signs ( as in the randall - sundrum model ) . again , without lost of generality , we may assume that @xmath68 everywhere in the bulk ( otherwise , we can invert the positions of the branes ) . fig . [ f2 ] shows the generic behavior for @xmath67 and @xmath8 as functions of @xmath51 . and the scalar field @xmath8 as functions of @xmath51 . we can always choose @xmath8 to increase and @xmath67 to decrease in the @xmath51-direction.,scaledwidth=45.0% ] putting eqs . ( [ s2 : match1 ] ) and ( [ s2 : match2 ] ) together , @xmath70 can be solved and expressed in terms of @xmath71 in an @xmath52-independent way : @xmath72 , \label{s2 : omega } \\ \alpha(\phi ) & = & \frac{1}{\sigma } \frac{\partial \sigma}{\partial \phi}. \label{alpha def}\end{aligned}\ ] ] here @xmath73 is an arbitrary constant value for @xmath8 . if we define @xmath74 and @xmath75 , then the induced metrics to the first and second branes are @xmath76 and @xmath77 respectively . furthermore , both metrics are conformally related by the warp factor @xmath78 . \label{s2 : warp}\end{aligned}\ ] ] the parameter @xmath79 defined in eq . ( [ alpha def ] ) will have an important role in the rest of the paper . finally , consider the possibility of having singularities at a finite position in the bulk . singularities appear in the bulk either if @xmath80 or @xmath81 . thus , eq ." +"the distribution of stellar metallicities in the halo of the galaxy has been intensively studied for many years , especially since it was recognized in the early 1980 s that the halo contains field stars with [ fe / h ] lower than that of the lowest metallicity globular clusters . the central difficulty of this enterprise is that low - metallicity stars , especially those with [ fe / h ] @xmath1 , are extremely rare in the solar neighborhood , comprising no more than @xmath2% of the stars within a few kpc of the sun . as a direct consequence , knowledge of the form of the metallicity distribution function ( mdf ) , in particular the shape of its low - metallicity tail , has long been limited by small - number statistics . the difficulty of isolating a `` fair '' sample of halo stars based on in - situ studies has left astronomers with little choice but to identify likely halo stars based on their motions . spectroscopic follow - up of stars selected from proper - motion surveys has allowed the determination of at least a reasonably accurate picture of the global shape of the halo mdf . the studies of ryan & norris ( 1991 ) and carney et al . ( 1996 ) were able to demonstrate that the mdf of halo stars peaks at a metallicity [ fe / h ] @xmath3 , including tails extending up to the solar metallicity on the high side , and to metallicities at least down to [ fe / h ] = @xmath4 , or slightly below , on the low side . both suggested mdfs are consistent with one another , and with the predictions of the so - called `` simple model '' ( e.g. hartwick 1976 ) . the actual shape of the mdf at the lowest metallicities , and its precise cutoff , is limited by the small numbers of stars in these samples . even taken together , these surveys only include some 250 very metal - poor stars with [ fe / h ] @xmath5 , and but a handful with [ fe / h ] @xmath6 . recent kinematically unbiased surveys for metal - poor stars have revealed the presence of at least two hyper metal - poor ( hmp ) stars , with [ fe / h ] @xmath7 ( christlieb et al . 2002 ; frebel et al . the presence of these two stars raise several additional questions concerning the nature of the mdf , including : * what is the shape of the low - metallicity tail of the halo mdf , and in particular , is it continuous ? * does there exist a sharp cutoff of the halo mdf , and if so , at what metallicity does it occur ? * is the halo mdf constant throughout the halo , or does it vary with distance ? the answers to these , and other questions about the nature of the halo mdf , can only be obtained from much larger samples of very metal - poor stars , ideally chosen in - situ in the halo of the galaxy , well outside the solar neighborhood . fortunately , due to the collective efforts of many of the astronomers present at this conference , we have arrived at the point where the results of the large - scale objective prism surveys ( the hk survey of beers and colleagues ; beers et al . 1985 , 1992 , beers 1999 , and the he s of christlieb and colleagues ; christlieb 2003 ) can now begin to shed light on at least some of these questions . below we summarize the present picture of the low - metallicity tail of the halo mdf as obtained by these two efforts . we then consider the information provided by the large numbers of very metal - poor stars contained in the most - recent public data release of the sloan digital sky survey ( york et al . 2000 ) , and its planned extension , sdss - ii , which includes the segue program . the hk survey ( formerly known as the preston - shectman survey ) was initiated over 25 years ago . during the course of the survey , a total of some 300 objective - prism plates covering 2800 deg@xmath8 in the northern hemisphere and 4100 deg@xmath8 in the southern hemisphere were obtained . the selection of candidate metal - poor stars was accomplished based on visual inspection with a binocular 10 x microscope . since the visual inspection was performed without the benefit of the stellar colors ( hence temperatures ) it was expected that the hk - survey candidates would carry a rather severe temperature - related bias . the potential bias becomes less of a problem at the lowest metallicities , below [ fe / h ] @xmath9 , where the caii k lines of even quite cool stars are difficult to detect at the resolution of the survey . medium - resolution ( 1 - 2 ) spectroscopic and broadband photometric follow - up of candidate metal - poor stars from the hk survey has been underway for two decades . for the majority of this period , the spectroscopic follow - up was conducted with single - slit spectroscopy using 1.5m-2.5 m telescopes at a variety of observatories . most recently , the use of the 6df multiplexed spectrograph on the uk schmidt telescope made it possible to obtain more than one hundred such spectra simultaneously , hence the pace of this effort was sped up considerably . table 1 lists the total number of spectra of hk survey candidates ( including large numbers of field horizontal - branch and other a - type stars in addition to the metal - poor candidates ) obtained to date . this table also lists the numbers of hk survey stars with available spectroscopy that have had optical broadband photometry ( primarily @xmath10 ) measured thus far . near - ir @xmath11 from the 2mass point source catalog ( cutri et al . 2003 ) is also available for over 90% of the hk - survey stars with available spectroscopy . the he s objective - prism survey provides the opportunity to greatly increase the number of very metal - poor stars identified by the hk survey . it reaches about two magnitudes deeper than the hk survey ( @xmath12 vs. @xmath13 ) and also covers regions of the southern sky not sampled by the hk survey ; a total of about 8225 deg@xmath8 of the sky above @xmath14 is presently available from the he s . another 1275 deg@xmath8 covered by the he s is now being scanned and analyzed for candidates . the selection of metal - poor candidates from the he s database of digital objective - prism spectra is performed using quantitative criteria including automatic spectral classification ( christlieb , wisotzki , & grasshoff 2002 ) . the strength of the caii k line is determined using the @xmath15 line index ( beers et al . 1999 ) , as measured directly from the objective - prism spectra . due to the broad wavelength range covered by the he s spectra it is also possible to determine @xmath16 directly from the prism spectra , with an accuracy on the order of @xmath2 mag . stars that have caii k lines weaker than expected for their estimated @xmath16 colors and an approximate metallicity of [ fe / h ] @xmath17 are selected as low - metallicity candidates . medium - resolution spectroscopic follow - up of candidate metal - poor stars from the he s has been underway for the past five years , primarily with 2.5m-4 m class telescopes . the use of larger telescopes and substantially more efficient spectrographs than were available for much of the hk survey follow - up results in a much faster assembly of this information . the he s has also benefitted from multiplex follow - up with the 6df instrument . table 1 summarizes the numbers of he s targets ( including stars other than metal - poor candidates ) with available medium - resolution spectroscopy obtained to date . broadband optical photometry ( primarily @xmath18 ) is only now being obtained for the metal - poor he s candidates ( beers et al . , in preparation ) ; about 80% of the stars with available spectroscopy have @xmath11 from 2mass . all of the sdss stars discussed below have available @xmath19 photometry . .[tab : observations ] observational follow - up of surveys [ cols=""<,>,>,>,>"",options=""header "" , ] many astronomers may not be aware that the publicly available medium - resolution ( 2.5 ) spectroscopy and @xmath19 photometry from the sdss includes substantial numbers of stars in the milky way . at present , through the dr3 release , these total over 70,000 stars . analysis pipelines have been developed ( and are presently being refined ) , and value added catalogs that summarize best estimates of atmospheric parameters ( t@xmath20 , log g , [ fe / h ] ) , as well as radial velocities , distance estimates , and proper motions , are now being assembled ( beers et al . 2004 ) . by the time the final data from the main sdss are released ( presently anticipated to be june 2006 ) , the number of stars with similar data should be well over 100,000 . most stars contained in the sdss database were not targeted specifically to be metal - poor halo objects , and indeed they represent a complex assembly of objects selected for calibration and reddening determinations , directed studies of various classes of stars ( e.g. horizontal - branch stars , carbon stars , white dwarfs , late - type k and m dwarfs , etc ) , as well as objects originally targeted as quasars that turned out to be stars . in spite of its rather inhomogeneous assembly , the sdss stellar database does provide a useful means for sampling the tail of the halo mdf ( though one of course must be open to the issues of selection bias ) . the abundance calibration of beers et al . ( 1999 ) is used to obtain estimates of [ fe / h ] for the hk and he s stars . this method relies on the variation of the caii @xmath15 index with @xmath21 color as a function of [ fe / h ] . this approach works well , obtaining abundance errors on the order of @xmath22 dex over the color range @xmath23 and for stars with abundances @xmath24 } \le -0.5 $ ] . near the red end of the color range , and near the high - metallicity end as well , saturation of the caii k lines becomes more of an issue ; at these extremes this method tends to underestimate the true metallicity of a given star . at the very lowest metallicities , below [ fe / h]@xmath25 , the approach could _ over_-estimate the true metallicity , as a result of contamination of the caii k line by interstellar caii , or by molecular carbon features in the spectra of carbon - enhanced metal - poor stars . in fact , both of these situations arose in the cases of the medium - resolution discovery spectra of the two known hmp stars he 0107 - 5240 and he 1327 - 2326 . not all of the hk / hes objects have available @xmath21 colors at present . thus , we have developed techniques that can be used to estimate this color , based on a calibration of the strength of the balmer h@xmath26 line . previous tests indicate that the colors estimated in this" +"the basic method of studying very high energy cosmic rays ( cr ) is the air shower technique , which amounts to investigate nuclear - electro - magnetic cascades extensive air showers ( eas ) induced by energetic cosmic ray particles in the atmosphere . contemporary eas experiments resemble to a large extent their accelerator counterparts in the sense that in both cases one applies sophisticated simulation procedures to obtain a good understanding of the measurements and to interprete the data . in cr experiments an unavoidable complication is that one deals with particle interactions at energies significantly in excess of those of present colliders . in particular , this is a severe problem for the description of the backbone of air showers the hadronic cascade , as the corresponding microscopic theory perturbative quantum chromodynamics ( pqcd ) is inapplicable for the treatment of general hadronic collisions and the data on secondary particle production in the fragmentation region , being of crucial importance for the description of eas development , are rather scarce , especially , for scattering on nuclear targets . the situation can be improved by employing phenomenological hadronic monte carlo ( mc ) models , e.g. dpmjet @xcite , qgsjet @xcite , sibyll @xcite , or the new qgsjet - ii @xcite and epos @xcite models . being based on some underlying theoretical approaches , they relate different interaction characteristics to each other and allow one to extrapolate the interaction picture to different kinematic regions and for different types of colliding particles , within particular model framework . correspondingly , they are characterized by a restricted number of adjustable parameters , which can be fitted with available data . however , any model is only a model , its microscopic content being restricted by only a number of possible physics mechanisms . thus , one can not exclude the possibility that something important is missing , especially , concerning the very high energy range . on the other hand , even the underlying theoretical ideas may appear to be wrong . this explains the need for alternative model approaches and for continuing tests of model validity , using both accelerator and cosmic ray data . meanwhile , the spread in model predictions may give some feeling on the corresponding uncertainties @xcite . it is presently commonly accepted that high energy hadronic ( nuclear ) collisions are mediated by multiple parton cascades , proceeding in parallel . at not too high energies all parton branchings in a cascade are characterized by a small 4-momentum squared @xmath0 transferred , the processes generally referred to as non - perturbative soft ones . by the uncertainty principle , at each step the newly emitted parton is separated from its parent by a non - small distance @xmath1 in the transverse plane . as a consequence , the interaction region widens with energy , remaining at the same moment rather dilute , with a small parton density per unit area . on the other hand , with the energy increasing one observes a sizable contribution of so - called semi - hard processes , where some parton emissions proceed with a comparatively large momentum transfer @xmath2 , @xmath3 being some cutoff for pqcd being applicable , and result in the production of observed hadron jets of high @xmath4 . the smallness of the strong coupling @xmath5 , characteristic for such processes , is compensated by large logarithmic factors and by high number of partons in the cascade @xcite . such hard parton branchings proceed with a negligible displacement in the transverse plane , leading to a rapid rise of parton densities . thus , one can to a some extent separate hadronic collisions at large and small impact parameters . the former are characterized by low parton densities and mainly proceed via non - perturbative soft processes . the latter are more and more dominated with increasing energy by the contribution of semi - hard processes ; one deals there with large numbers of partons being closely packed , which results in significant non - linear effects : different cascades fuse together , preventing parton densities from further increase @xcite . how this picture transforms in the very high energy limit ? there , dominant semi - hard contributions look as follows . first , the underlying parton cascade develops in the soft low virtuality region , with small @xmath6 partons diffusing towards larger impact parameters . then , hard parton branchings become efficient ; new partons are produced without sizable transverse displacements , contributing to the overall parton density increase at a given point . as the result , the black high density region extends to larger and larger impact parameters . on the other hand , the dilute peripheral region always persists outside the black one , being formed by purely soft parton cascading . in general , one expects that with increasing energy the parton density in the black region is saturated up to comparatively high values of parton virtualities and the relevant processes can , in principle , be described within the perturbative formalism @xcite , while the peripheral region remains governed by non - perturbative physics . according to present data , the relative sizes of the dense and the dilute areas remain comparable in the collider energy range @xcite , the peripheral collisions thus giving an important contribution to observed quantities . in reality , the discussed separation of central and peripheral collisions is rather crude , as the average parton densities rise gradually with decreasing impact parameter . thus , there exists an important transition region of moderately large impact parameters , characterized by large but not yet saturated parton densities , where the contributions of both soft and semi - hard processes are of equal importance , and where non - linear parton effects provide sizable corrections . in fact , it is the treatment of such non - linear interaction contributions in the dense and in the transition regimes which is the main challenge for contemporary hadronic interaction models . the qgsjet model , being based on the pomeron phenomenology @xcite , describes hadronic multiple scattering processes as multiple exchanges of composite objects pomerons , corresponding to independent microscopic parton cascades . for the soft low virtuality cascades a phenomenological soft pomeron amplitude is employed , whereas semi - hard scattering processes are treated as exchanges of semi - hard pomerons , the latter composed of a piece of qcd parton ladder sandwiched between two soft pomerons @xcite ; the soft pomerons and the ladder describing correspondingly the low and high virtuality parts of the underlying parton cascade . the principal feature of qgsjet - ii is the treatment of non - linear parton effects described as pomeron - pomeron interactions , based on all order re - summation of the corresponding reggeon field theory diagrams @xcite . the basic assumption of the scheme is that pomeron - pomeron coupling is dominated by non - perturbative parton processes and can be described by means of phenomenological multi - pomeron vertices . the approach allows one to obtain a consistent description of various hadronic cross sections and structure functions , including diffractive ones , for a fixed , energy - independent @xmath7-cutoff @xcite . presently it is the most advanced model for the description of hadronic interactions in the peripheral and the transition regimes . however , in central collisions one may expect sizable corrections to come from hard ( high @xmath0 ) pomeron - pomeron coupling , which is neglected in qgsjet - ii . a reasonable agreement of the model predictions for central nucleus - nucleus collisions with the data of rhic collider indicates the smallness of such effects @xcite . nevertheless , the situation may change at much higher energies . sibyll 2.1 @xcite also employs pomeron formalism for the description of soft processes , while semi - hard ones are treated in the framework of the mini - jet approach @xcite , which is qualitatively similar to the above - discussed semi - hard pomeron scheme ( the differences between the two approaches are discussed in @xcite ) . the treatment of non - linear effects in that model is essentially orthogonal to the one in qgsjet - ii , being based on the parton saturation approach @xcite . namely , it is assumed that semi - hard processes result in the production of partons of transverse momenta larger than some effective energy - dependent saturation scale , @xmath8 , for which the double leading - log ansatz @xcite is used . however , the correlation between actual parton densities and the saturation scale holds in the model only in average sense , i.e. it reflects the increase of the average density with energy ; the same scale is used both for dense central and for dilute peripheral collisions . on the other hand , non - linear effects are neglected for the soft interaction component . the latter is partly cured in dpmjet - iii @xcite , taking into consideration lowest order diagrams for pomeron - pomeron interactions . the epos model , being the successor to nexus @xcite , employs the above - discussed soft and semi - hard pomeron scheme and , in contrast to all other mc generators , takes into account energy - momentum correlations between multiple re - scatterings @xcite ( see also @xcite for a qualitative discussion ) . the description of non - linear effects is based on an effective treatment of lowest order pomeron - pomeron interaction graphs , with the corresponding parameters being adjusted from comparison with rhic data . a big advantage of the model is an excellent calibration to available accelerator data . however , its extrapolation towards very high energies may depend on the adopted empirical parameterizations for non - linear interaction contributions . although the spread in contemporary model predictions for eas characteristics is much more moderate than ten years ago @xcite , it is still quite significant . among the most model - dependent quantities is the shower maximum position , which depends on the corresponding results for total inelastic and diffractive cross sections and for the inelasticity of proton - air interactions . the predicted inelastic cross sections of different models stay in reasonable agreement at collider energy range and sizably diverge at highest cr energies , the largest values coming from the sibyll model . on the other hand , model predictions for the inelasticity of proton - air interactions and for the rate of diffraction processes differ significantly at all energies . in general , both cross sections and inelasticities are likely to be dominated by the contribution of hadronic collisions in the peripheral and the transition regimes , for which qgsjet - ii provides a more elaborate description , compared to other mc generators . an important test of model predictions will be provided by the lhcf experiment @xcite , which will measure leading neutron spectra in proton - proton collisions . this observable appears to be sensitive both to the average inelasticity and to projectile proton diffraction dissociation ; there are almost an order of magnitude differences in model predictions for the forward neutron spectra , which can be well discriminated by the experiment @xcite . on the other hand , the high energy behavior of the total proton - proton cross section will be reliably fixed by the corresponding lhc measurement . an important topic are model predictions for the cr muon component . here one has to distinguish between the results for inclusive muon spectra and for eas muon content for a given primary energy . the former are dominated by single interactions of primary protons of energies in average only an order of magnitude higher than the ones of measured muons . due to the steepness of the primary cr spectrum , the corresponding results are very" +"in euv images of the solar corona , coronal loops appear as long graceful arcs of bright plasma that trace magnetic field lines through the atmosphere . these loops can be preferentially illuminated because localized heating and inefficient cross - field diffusion lead to hot plasma spreading along individual field lines . despite the obvious magnetic nature of these structures , it has proven challenging to measure through spectroscopic means the magnetic - field strength within the corona . of course measuring the magnetic - field strength is equivalent to measuring the energy density , and is therefore a key constraint in the modeling of energetic and eruptive phenomena such as flares and cmes . coronal loops are sometimes observed to vacillate back and forth with a regular frequency . the identification of these oscillations as resonant mhd kink waves , trapped between the loop s footpoints ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , launched the field of coronal loop seismology . coronal seismology promises the opportunity to measure the magnetic - field strength along the loop through inversion of the kink - mode eigenfrequencies ( e.g. , * ? ? ? however , before such inversions can be performed the ability to construct stable , curved coronal loop models with realistic density and magnetic profiles is needed . the state of the art in the modeling of static coronal loops is nonlinear force - free field ( nlfff ) models . typically such models have used vector magnetograph measurements in the photosphere as an observational constraint . a substantial weakness to such an approach is that the force - free assumption is rather inappropriate within the chromosphere and the low corona @xcite ; thus , the region in which the force - free assumption is valid and the region in which the observational constraint is applied are disjoint . this leads to a substantial mismatch between the model field and the actual magnetic field @xcite . more recent work has partially overcome this difficulty by applying additional constraints higher in the corona . these constraints have taken the form of euv images of bright coronal loops from instruments such as stereo and the _ atmospheric imaging assembly _ ( aia ) . initially , multiple such euv images were used , each taken from a different vantage point either using simultaneous images from the two stereo spacecraft or using solar rotation to view the presumably static magnetic structure from different angles . solar stereoscopy was then used to reconstruct the 3-d curve traced by a loop ( see the reviews of * ? ? ? * ; * ? ? ? * ) . however , recent attempts to deduce the 3-d shape of a loop from just a single high - resolution euv image ( such as those from aia ) and a coeval photospheric magnetogram have had intriguing success @xcite . despite the achievements that the nlfff models have made in reconstructing the geometry of the magnetic field , the force - free assumption decouples the thermodynamic variables from the magnetic field . certainly , if the dynamic timescales are significantly shorter than the cooling times , hydrostatic balance along field lines is still valid . however , deducing the mass density and gas pressure requires either the specification of the temperature by fiat , or the inclusion of an energy equation that models the heating and cooling of the loop ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? here we constrain the mass density within the loop in a different manner . in essence , we find an equilibrium solution by considering deviations from a force - free state . this deviation only occurs within the loop and appears as a change in the field strength without a concomitant change in the field s direction . such a field strength perturbation produces both magnetic buoyancy and a small lorentz force , both of which depend intimately on the shape or geometry of the loop and which oppose each other in equilibrium . the establishment of this equilibrium requires that the mass along the loop redistributes itself with a timescale shorter than the cooling time . thus , accounting for the buoyancy of the loop allows one to directly connect the mass density and other thermodynamic variables ( such as the temperature ) to the shape of the loop and the magnetic - field strength within the loop . we will show that the temperature profile of the loop is not a function that can be freely specified , but instead has a functional form that is a direct consequence of the geometry of the loop . our goal here is to self - consistently include curvature and buoyancy in the equilibria of coronal loops and to develop models of the temperature , density , and field strength with the geometry of the loop as the primary input . in order to permit analytic solutions we treat coronal loops as slender magnetic fibrils and adopt the thin - flux - tube approximation when deriving the force balance . the balance of forces is characterized by a magnetic bond number which is the dimensionless ratio of the buoyancy force to the lorentz force . the shape and curvature of the loop is succinctly expressed in terms of the magnetic bond number , which may be a function of position along the loop . in 2 we will derive the equation that describes the balance of forces and from this equation we identify the magnetic bond number . then , assuming that the shape of the loop is provided by observations , we derive the temperature and mass density profiles that are consistent with this shape . in 3 we present a simple equilibrium solution for an embedded fibril which has a uniform magnetic bond number . we discuss the atmospheric properties that are consistent with a constant magnetic bond number and derive the resulting coronal magnetic field . in 4 we demonstrate another simple solution corresponding to a semi - circular fibril with a uniform radius of curvature . finally , in 5 we discuss the implications of our findings and summarize the results . we will model a coronal loop as a curved , magnetic fibril embedded in a larger coronal magnetic structure . we will further assume that the fibril is compact and thin . by _ thin _ we mean that the radius of the fibril is small compared to any other relevant length scale . even though the thin - tube approximation may not apply to all coronal loops , it is an appropriate approximation for many . recent high - spatial - resolution observations of the solar corona in the fe xiii 19.5 nm line by the hi - c instrument have enabled a resolution of about 150 km , sufficient to resolve the cross - section of most coronal loops . using these observations , @xcite examined brightness cross - sections for 91 loops in the solar corona and found a distribution of radii sharply peaked at 270 km . by examining the pixel - to - pixel brightness fluctuations across loop cross - sections , @xcite have argued that coronal loops are unlikely to be structured on a finer unresolved spatial scale . since the corona s pressure and density scale heights are generally a hundred times larger than this spatial scale and the lengths of loops a thousand times larger , the thin - flux - tube approximation appears to be quite relevant for a substantial fraction of coronal loops . we also assume that the external corona is magnetically dominated and its magnetic field is a force - free field . we adopt the notation that quantities evaluated in the external corona have a subscript ` e ' , while those within the fibril lack a subscript . thus , the external magnetic field is @xmath0 ; whereas , the internal magnetic field of the fibril is just @xmath1 . one way to envision the fibril is to select a bundle of field lines within the coronal magnetic field and uniformly increase or decrease the field strength within that bundle by a constant factor , @xmath2 . we call the constant @xmath3 the field - strength deviation and it can be positive or negative depending on whether the fibril is strongly or weakly magnetized compared to its surroundings . we consider only loops that are small deviations from the force - free state . thus , the field - strength deviation will be a small quantity , @xmath4 . the constant @xmath3 was chosen such that it represents the constant of proportionality between the exterior magnetic pressure and the magnetic - pressure contrast ( the difference in the magnetic pressure between the inside and outside of the fibril ) , @xmath5 the field - strength deviation @xmath3 must be constant along the fibril . otherwise the fibril and surrounding corona would not have a common flux surface where they join . since the internal magnetic field is proportional to the external magnetic field , the internal field is also force free . however , because of the discontinuity in the field strength at the edge of the fibril , there exists a current sheath that surrounds the fibril . we neglect the spherical geometry of the solar atmosphere and assume that the corona can be treated as a plane - parallel atmosphere with constant gravity @xmath6 . we employ a cartesian coordinate system , with the @xmath7@xmath8 plane corresponding to the photosphere and the @xmath9 coordinate increasing upwards ( i.e. , @xmath10 ) . we restrict our attention to coronal loops that are symmetric about the origin and that are confined to the @xmath7@xmath9 plane . such loops lack torsion . in addition to the cartesian coordinate system , both within the fibril and within the external corona we will employ the local frenet coordinates for a field line ( illustrated in figure 1 ) . the direction tangent to the magnetic field will be denoted with the unit vector @xmath11 ( thus @xmath12 ) , and the longitudinal coordinate @xmath13 is the pathlength along a field line measured from the photosphere ( @xmath14 corresponds to the footpoint intersecting the photosphere in the region @xmath15 ) . the curvature vector for the field line is indicated by @xmath16 , and points in the direction of the principle normal @xmath17 with a modulus equal to the reciprocal of the local radius of curvature @xmath18 of the field line . the direction of the unit vector in the binormal direction will be indicated with @xmath19 and the torsion of the field line with the variable @xmath20 . in the equilibrium considered here , the loop itself lacks torsion , @xmath21 , and its binormal uniformly points in the @xmath8-direction , @xmath22 . however , the exterior coronal magnetic field may be 3-d ( with spatial symmetries near the loop ) . therefore , for completeness and to aid follow - up work we consider the more general case for the moment and specialize only as necessary . the standard geometrical relations between these coordinate vectors , i.e. , the frenet - serret formulae , are given below for reference , assuming that the position vector of a field line is given by @xmath23 , @xmath24 notice the lack of ` e ' subscripts on the frenet vectors . for a sufficiently thin tube the frenet vectors will be nearly constant across the fibril with the same value as the surrounding corona . therefore , we avoid appending subscripted labels to the" +"there is a significant interest in constructing simple stochastic models with avalanches reflecting properties of various natural phenomena , but only part of them have the advantage of being solvable . one way to make models analytically tractable is to use the mean - field approximation . however , requirements of exact results can force further simplifications in a model . for example , in terms of self - organized criticality , in spite of the fact that the mean field theory of such critical phenomena was already proposed @xcite , dhar made further simplifications for distinguished btw model @xcite ( a unified view of mean - field picture of stochastic self - organized critical models is presented in @xcite ) . we point out also that considering structure of abelian algebras leads to analytical results in some sand - pile and related stochastic models @xcite . solvable simple models can also be constructed in the field of directed percolation ; for an extremely simple one , see @xcite . another way towards solvability is to consider stochastic properties as non - essential and study deterministic models ; see such an approach for sand - pile in @xcite . in the context of deterministic cellular automata , an analytic approach related to solvability is investigated as part of the theory of integrable systems and may employ sophisticated methods . we underline that construction of integrable cellular automata is definitely not an easy task . our aim here is to follow the ideas of analytic approach and apply them to construction of _ stochastic _ automata . in the article we propose and analyse in a direct elementary way the random domino automaton ( rda ) - a new slowly driven systems exhibiting avalanche phenomena . we prefer here an elementary self - contained approach to the description of the automaton and we make no use of applicable markov processes terminology . we stress here , all results , except of equation ( see @xcite for details ) , have elementary derivation in the text below . on the other hand , in spite of its simple formulation and being analytically tractable , automaton covers wide range of behaviours depending on the choice of the parameters . the application of the rda model for studying ito equation is investigated in our parallel papers @xcite . an inspiration for defining the rule for the domino automaton comes from very simplified view of earthquakes . it corresponds to two tectonic plates moving with relative constant velocity . the wedge may be irregularly rough , and relative motion can be locked in some places , producing stress accumulation . beyond some threshold of stress , a relaxation took place . the size of relaxation depends on the nearby accumulated stress . rda is inspired by earthquakes ; however , a direct reproducing of realistic - like behaviour of such complicated phenomena is obviously beyond its scope in the present form . nevertheless , construction and analysis of models is one of primary aims in geosciences @xcite . there are many very simplified cellular automata models focusing on specific features of the investigated behaviour in the field . here we point out a sequence of papers @xcite , where some interesting cellular automata models were presented . finally , as an unexpected property we mention an interesting link between stochastic cellular automata and integer sequences ( see @xcite or the on - line encyclopedia of integer sequences ) . it is known , how to obtain catalan numbers out of the bond directed percolation on a square lattice @xcite . our cellular automaton in specific case leads to motzkin numbers ( for details see @xcite ) . plan of the article is as follows . in section [ sec : autdef ] we introduce a definition of random domino automaton with rebound parameters . section [ sec : eqs ] contains full combinatorial derivation of equations for the distribution of clusters , which describes stationary state of the automaton . several exact formulas - balance relations , average size of clusters and avalanche , general formula for all moments - are displayed . we finish with introducing special form of rebound parameters , which leads to two distinguished special cases studied in details in next section [ sec : speccases ] . these cases correspond to exponential and inverse - power distributions as shown below . the obtained analytical results are compared with simulations . section [ sec : concl ] gives a resume of results presented in the article as well as directions for future work . appendix [ app : empty_cl_derv ] contains derivation of complementary set of equations , describing empty clusters of the automaton . in the random domino automaton model , the space consists of discrete number @xmath0 of cells on a line , and we assume periodic boundary conditions . each cell may be in one of two states : empty state , when it is empty , or occupied state , when contains a ball . the evolution of the automaton is given by the following update procedure performed in each discrete time step . a ball is added to the system to the randomly chosen cell and we assume each cell to be equally possible . if the chosen cell is empty , there are two possibilities : it becomes occupied with probability @xmath1 or the ball is rebounded with probability @xmath2 leaving the state of the automaton unchanged . if the chosen place is already occupied , there are also two possibilities : the ball is rebounded with probability @xmath3 or with probability @xmath4 the incoming ball triggers a relaxation . by relaxation we mean : balls from the chosen cell and from all its adjacent occupied cells are removed . thus , the relaxation produces an avalanche of size equal to the number of cells changing their state . then the update procedure repeats in the next time step . all possibilities are shown schematically on the diagram below . [ cols=""^,^,^,^,^,^,^,^,^,^,^,^,^ "" , ] the average size of a cluster is the same as the average size of an avalanche , because any cluster , regardless of its size , has the same chance to become an avalanche . hence , both balance equations lead to the same result @xmath5 table [ tab : table2 ] contains values of average density and average cluster / avalanche size obtained from equations and simulation in an exemplary case where @xmath6 . the size of lattice is set to @xmath7 in order to avoid restrictions for size of avalanches , which are relatively bigger comparing to the previous case . a simple form of @xmath8 together with balance equations and alows to reduce the set of equations - to the solvable recurrence . the formulas for @xmath9s are rational functions of @xmath10 and @xmath0 only . the explicit form of solutions and relation to the motzkin numbers is presented in @xcite . figure [ fig : figb ] presents exact values of @xmath9s compared in log - log scale with the simulation result in the exemplary case described above . the slope of the distribution of @xmath9 approximates inverse - power distribution in the middle part of a range of sizes @xmath11 ; for bigger values of @xmath11 , values of @xmath9 decrease quicker . this property agrees with convergence of moments of @xmath9 we use above . for value of @xmath10 closer to @xmath12 the straight part of the plot extends for bigger values of @xmath11 . in the limit case @xmath13 , the distribution is given by the following power law @xcite @xmath14 we proposed and studied properties of simple stochastic cellular automaton with avalanches inspired by an extremely simplified model of earthquakes . the main goal was to construct a simple model with `` transparent '' mathematical structure , which would enable obtaining exact results yet covering a wide range of behaviours . the rule of the automaton allows to derive from the first principles ( using elementary combinatorics ) the set of equations describing the average values of the model parameters . these equations leads to equations for moments and to neat formulas for average cluster and avalanche sizes in terms of the zero and the first moments . after analysis of moment equations , we considered in detail two cases which differ by the form of parameter @xmath15 responsible for triggering of avalanches . we obtained exponential type and inverse - power type distributions of clusters within uniform framework . ( the distribution of avalanches @xmath16 is easily obtained from the formula @xmath17 . ) the quasi - equilibrium assumption seems to be justified by simulation results . the exponential case @xmath18 is not fully analytically solvable ; nevertheless , the closed set of equations leads to several exact relations . moreover , an approximate formula for @xmath9 was derived , and intimate relation to percolation was pointed out . hence , the proposed approach can be regarded as an extension of percolation approximation results , and can provide basis for exact treatment of other models . the automaton rule clearly states that there is a `` coupling '' between the adjacent cells , since the relaxations takes out the whole cluster , so treating cluster not cells as independent is a substantial improvement in the presented case . the case @xmath19 is fully solvable , and all variables are expressed as rational functions of ratio @xmath20 of rebound parameters only . the shape of the distribution of clusters @xmath9 approximate an inverse - power distribution in the various ranges of variable @xmath11 , depending on chosen parameters . in the limit case , distribution tends to @xmath21 . the critical density is equal to @xmath22 . the limit case of the presented automaton reduces the set of equations to the recurrence , which leads to known integer sequence - the motzkin numbers ( see @xcite ) . this result establishes a new , remarkable link between the combinatorial object and the stochastic cellular automaton . the first application of rda - related to ito equation - is already studied in our parallel papers @xcite . the model serves as a fully controlled stochastic `` phenomenon '' and an applicability of the reconstruction of the ito equation from generated time series was tested . due to its simplicity , it allows to derive exactly the suitable ito equation , and analytical results were compared with histogram method . the obtained results are part of broader studies of the privilege concept and its role for appearance of inverse - power distributions @xcite . the model posses also some properties which may be used in seeking of applications to natural phenomena and checking their adequacy . for example , in the context of earthquakes , the discrete nature of the model makes possible an adjustment of positions and sizes of cells to the geological structure of a fault . bending and shrinking of the 1-d grid have no influence on equations ; the only important feature is an order of cells . in this context , relations describing average size of cluster @xmath23 and avalanche @xmath24 may be interpreted as relations giving their dependence on the density of energy on the wedge . the model establishes one - to - one correspondence between distribution of avalanches ( i.e. observable quantity ) and respective parameter @xmath25 responsible for triggering avalanches , as it was illustrated in two cases considered above . we emphasize that the relation works in both directions . fixing rebound parameters leads to various distributions of avalanches , but also , for any distribution @xmath9 , one can easily find unique values of rebound parameters @xmath25 by simple use of the set of equations - . thus , within the proposed model , one can infer about triggering properties from `` observed" +"the formation of planets in protoplanetary disks is strongly tied to the existence of dust which makes up about 1% of the total mass of the disk @xcite . the basic collisional growth model assumes that , as a first step toward planet formation , kilometer - size planetesimals are formed by sticking collisions of dust particles which are only held together by surface forces @xcite . there are some issues in planetesimal formation which are not yet understood . somewhat problematic is inward drift especially of meter - size bodies . in a standard disk the pressure is supposed to decrease with distance from the star @xcite . the gas is therefore supported by a pressure gradient and rotates with sub - keplerian velocity . small solids couple to the gas and thus also rotate more slowly than keplerian . however , solid bodies are not supported by the pressure gradient . this leads to an inward drift of the solid bodies which for a meter size body in a minimum mass nebula can be as large as 1 au in 100 years @xcite . such an inward mass transport of solids leads to a redistribution of matter : the outer part of the disk becomes depleted in solids , while the inner part becomes enriched . the physics of the inner 1 au of protoplanetary disks strongly depends on the fate of this incoming matter : it might contribute to the local planet formation process and add mass to forming planetary bodies , it might evaporate and be accreted by the star , or it might be recycled in some more complex way . as the physics in the inner part of the disk is complex the evolution of solid bodies is still an open question . to address this problem , we started to investigate a mechanism of particle recycling which is especially active in this inner region of a protoplanetary disk and , more specifically , close to the inner edge of a disk within the inner 1 au . there is a growing number of observations which show that , in some phases , protoplanetary disks contain inner gaps which are optically thin but still contain gas , while the outer part is still dense and optically thick @xcite . in other words , solids at the inner edge of a disk are embedded in a gaseous environment and are illuminated by the star . + @xcite first described a mechanism that significantly erodes dusty bodies to small particles under very general conditions , e.g. by mere illumination and at low gas pressure ( kw m@xmath2 of intensity and mbar gas pressure ) . @xcite showed that this erosion process also works under the conditions of transitional disks . there will most likely be a small shell at the inner edge of a disk where the conditions for particle erosion are met @xcite . every dusty body which enters this zone and which is too small to hold its dust by gravity ( sub - planetesimal ) is subject to erosion by this process . different scenarios are possible as to how this contributes to the evolution of the disk . the dust might , for example , be transported upward and outward over the disk by photophoresis . such a model has been suggested by @xcite . at later times or throughout the optical thin inner parts the dust might also be transported by photophoresis in the midplane @xcite . @xcite showed that the erosion process is a suitable mechanism to explain the existence of small dust particles which are observed in protoplanetary disks over their entire lifetime . the dust might also be recycled locally and added probably more efficiently than by the original larger bodies to existing large planetesimals or protoplanetary bodies to boost their growth . these aspects are speculative and not the main focus of this paper which reports on experiments that analyze the gravity dependence of the light induced erosion mechanism providing basic input for future modeling . + acts on the surface particles . when this force overcomes gravity and cohesion , the surface particles are lifted . a crater is formed where again temperature gradients develop . if the illuminated spot is limited in size , the developing crater might prevent further release of particle . ] a sketch of the light induced erosion mechanism is shown in figure [ fig : fig1 ] : the illumination of a dusty surface first leads to a solid - state greenhouse ( ssg ) effect . this effect is known to exist for ice and comets @xcite . it means that visible light enters a porous body and is absorbed over some depth , but as the body is opaque to infrared radiation only the top surface can cool by thermal emission . therefore , the maximum temperature is below the surface . in recent years it was shown that this is also true for purely dusty surfaces @xcite . if temperature gradients across a particle exist as in the case of an ssg profile , and if the particle is embedded in a gaseous environment , a photophoretic force acts on the particle from the warm to the cold side . hence , the surface particles of an illuminated dust bed are subject to a lifting force . if this force is stronger than gravity and cohesion , aggregates are ejected . the ssg and photophoresis are the basis for light induced erosion of dusty bodies . the physics behind this has been studied in a number of works @xcite . + in protoplanetary disks , dust particles on dusty sub - planetesimals are bound by cohesion and gravity . however , the gravitational force is small due to the small mass of the objects . therefore photophoretic forces acting on the particles have to overcome less gravity and the effect of dust erosion induced by illumination is more intense compared to larger bodies or laboratory experiments . in the first microgravity experiments @xcite showed that the threshold light flux for particle erosion indeed depends on the gravity level . at low gravity cohesion eventually becomes the dominant opposing force . the erosion rate was not measured in the experiments of @xcite : however , this is important in determining how rapidly a body can be eroded or what mass flux it might provide in small particles if it crosses the erosion zone in a protoplanetary disk . + to quantify the effect of light induced erosion for application to ( sub)-planetesimal recycling we carried out low gravity experiments and determined the gravity dependence of the erosion rate . the experiments were carried out during the first _ joint european partial - g parabolic flight _ campaign . on this campaign , over 3 days , 13 parabolas at 0.16@xmath0 , 12 parabolas at 0.38@xmath0 and 6 parabolas at 0@xmath0 ( @xmath0 @xmath3 9.81 m s@xmath2 ) were provided . we also developed a preliminary model which agrees well with the experimental results . a sketch of the experimental setup is shown in figure [ fig : fig2 ] . four separate chambers are placed in one vacuum chamber . each chamber contains a dust sample with a depth of 2 cm covering a total area of 6 @xmath4 . for the campaign reported here the chambers were filled with basalt powder with a broad size distribution between @xmath5 and @xmath6 @xmath7 m . we consider this dust particle size range suitable to simulate the dust in protoplanetary disks . they include micron - size particles discussed @xcite with reference to the matrix in chondrites ( typically a few microns but occasionally up to about 20 @xmath7 m @xcite ) . the constituents in interplanetary dust particles or cometary material are smaller , on the order of 0.1 @xmath7 m @xcite which might not be adequatley represented in our experiment sample . on the other hand , chondrites largely consist of chondrules of submillimeter size , so the larger grain fraction in our sample might correlate with these dimensions . certainly , the size dependence of the erosion mechanism should be considered in more detail in the future . + the dust samples were dried at about 500 k for 24 hr and were stored in a desiccator until they were placed in the vacuum chamber just before the experiments . the ambient pressure of air in the vacuum chamber was then set to @xmath8 @xmath1 0.9 mbar for all experiments . + during each experimental run one sample was illuminated by a diode laser of 2 w optical output at 655 @xmath1 10 nm . the laser profile was homogenized by coupling the laser to an optical fiber and projecting the fiber outlet onto the sample surface with a size of 25 @xmath1 4 mm@xmath9 . the average intensity was 12 kw m@xmath2 which varied by 17 % within the spot . this corresponds to the inner regions of a protoplanetary disk @xmath10 0.4 au where the light flux for a star similar to the sun is @xmath11 kw m@xmath2 . an accelerometer was used to measure the residual gravity acting on the experiment . the experimental chamber was supported by vibrational attenuators to prevent any influence of airplane vibrations , which might reduce the cohesion between the dust particles . released aggregates were observed from the side by a camera at 60 images per second . + measurements ( images ) were taken for 1@xmath0 , the acceleration phase at 1.7@xmath0 and the low - gravity phase at 0.16@xmath0 ( moon level ) or 0.38@xmath0 ( mars level ) . to confine the dust within the individual chambers , they were enclosed in a glass cylinder . this cylinder and the chambers were independently rotatable by a rotational feedthrough from the outside . after each parabola , and hence before every new experiment , the inside of the rotating glass cylinder was cleaned by a small strip of foam . this ensured that the laser and the camera view were not affected by dust . rotating the inner , dust containig part of the chambers ensures that for every new experiment a fresh spot of the dust surface was illuminated . this prevented selection effects , e.g. , that all ejectable particles ( e.g. of a certain size fraction ) were already released . after removing the background noise of the camera images the average gray scale value was taken as a relative measurement for the ejected mass or particle number . this assumed that the ejected particle distribution stays constant with time , that averaging is done over a significantly large number of particles and that the image is not saturated with particles . as we provide new spots for each experiment , observe well separated aggregates and take an average over a large number of aggregates in typically 900 images for a given @xmath0-phase , we consider the gray value as a suitable measure . shows an overlay of 100 images of the ejected aggregates at different g - levels . the number of ejected aggregates clearly increases with lower gravitational acceleration . + a parabolic flight has the advantage that different gravity levels can be tested with the same dust sample in a short period of time . however , the effects of the transitions between the different @xmath0-levels have to be filtered out . they induce a higher erosion rate during the transitions from high-@xmath0 to low-@xmath0 . this is due to the release of gravitational and photophoretic tension from the dust bed , as higher gravity levels require a steeper temperature gradient for erosion . it takes a certain time before the new equilibrium temperature profile is established at which aggregates are ejected regularly . shows which data were selected to determine the number of ejected aggregates in the different phases" +"currently there is an international `` community '' of the first generation laser interferometric gravitational wave ( gw ) detectors @xcite ( ligo in usa @xcite , virgo in italy @xcite , geo-600 in germany @xcite , tama-300 in japan @xcite and aciga in australia @xcite ) . the development of the second - generation gw detectors ( advanced ligo in usa @xcite , lcgt in japan @xcite ) is underway . the ultimate sensitivity of laser gw detectors is restricted by the standard quantum limit ( sql ) a specific sensitivity level where the measurement noise of the meter ( photon shot noise ) is equal to its back - action noise ( radiation pressure noise ) @xcite . the sensitivity of gw detectors is also limited by classical displacements noises of various nature : seismic and gravity - gradient noise at low frequencies ( below @xmath4 hz ) , thermal noise in suspensions , bulk and coatings of the mirrors ( @xmath5 hz ) . in 2004 s. kawamura and y. chen put forward an idea of so called displacement - noise - free interferometer ( dfi ) which is free from displacement noise of the test masses as well as from optical laser noise @xcite . the most attractive feature of dfi is the ability to achieve sub - sql sensitivity ( no sql since radiation pressure noise is canceled ) not accompanied by the necessity to build complicated optical schemes for quantum - non - demolition ( qnd ) measurements @xcite . the possibility to separate gw signal from displacement noise of the test masses is based on the _ distributed _ character of interaction between gw and light wave unlike the localized influence of mirrors positions on the light wave , taking place only at the moments of reflection . the `` price '' for this separation is the decreased detector response to gws , especially at low frequencies where the so called long wave approximation is valid , that is when the distance @xmath1 separating test masses is much less than the gravitational wave length @xmath6 , i.e. @xmath7 or @xmath8 ( @xmath9 is the light travel time between test masses , @xmath10 is the speed of light and @xmath11 is the gw frequency ) . in particular , the analysis presented in @xcite for double mach - zehnder interferometer showed that in long wave approximation the shot - noise limited sensitivity to gws turns out to be limited by @xmath12-factor for 3d configurations and @xmath13-factor for 2d configurations . for signals centered at @xmath14 hz and for interferometers with size of @xmath15 km ( @xmath16 s ) , dfi sensitivity of the ground - based detector is @xmath17 times worse than that of a conventional single round - trip laser detector . another approach to the displacement noise cancellation was presented in @xcite where a single detuned fabry - perot cavity pumped through both of its movable , partially transparent mirrors was analyzed . in this paper we investigate model originated from a simple toy model @xcite of the gw detector . our model consists of two double pumped fabry - perot cavities positioned in line . each cavity is pumped through both partially transparent mirrors . by properly combining the signals of output ports of the cavity an experimenter can remove the information about the fluctuations of the mirrors displacements and laser noise from the data . the `` price '' for isolation of the gw signal from displacement noise in our case is the suppression of sensitivity by factor of @xmath12 ( resonance gain partially compensates it ) as compared with conventional interferometers it is larger than limiting factor @xmath18 of the double mach - zehnder 2d configuration @xcite . this paper is organized as follows . in sec . [ simple ] we analyzed simplified round trip model ( without any fabry - perot cavities ) . in sec . [ sec_fp_cavity ] we derive the response signals of a single double pumped fabry - perot cavity to a gravitational wave of arbitrary frequency and introduce their proper linear combination which cancels the laser noise and the fluctuating displacements of one of the mirrors . in sec . [ sec_2fp_cavities ] we analyze configuration of two double - pumped fabry - perot cavities which allows to calcel displacement noise of all mirrors completely . finally in sec . [ conclusion ] we discuss the physical meaning of the obtained results and briefly outline the further prospects . for clear demonstration we start from analysis of the simplest toy model @xcite consisting of @xmath19 platforms @xmath20 , @xmath21 and @xmath22 positioned in line as shown on fig . gw propagates perpendicularly to this line . we assume that lasers , detectors and mirrors are rigidly mounted on each platform which , in turn , can move as a free masses . we also assume that mean frequency @xmath23 of each laser is equal to others . in this section we do not take into account laser noise yet paying attention only on displacement noise and gw signal . we restrict ourselves to the case when radiation emitted from the laser on some platform is registered ( after reflection ) by detector on the same platform so called round trip configuration . actually detectors are homodyne detectors measuring the phase of incident wave . strictly speaking , in order to describe detection of light wave we have to work in the reference frame of detector , i.e. in accelerated frame . however , in our model detector is mounted on the same platform as laser which radiation detector registers and we can work in inertial laboratory frame as it was demonstrated in @xcite . moreover , in this case of round trip configuration we can use transverse - traceless ( tt ) gauge considering gw action as effective modulation of refractive index @xmath24 by weak gw perturbation metric @xmath25 . it is worth noting that in the opposite case , when laser and detector are mounted on different platforms , we should use the local lorentz ( ll ) gauge see details in @xcite . . gw propagates perpendicularly to line consisting of three platform.,scaledwidth=35.0% ] we denote the phase of the wave emitted , for example , from platform @xmath20 , reflected on platform @xmath22 and detected on platform @xmath20 as @xmath26 and so on . let us measure phase @xmath27 ( of the wave emitted from and detected on platform @xmath20 after reflection from platform @xmath21 ) and phase @xmath28 ( see also fig . [ dl3 ] ) @xmath29 , \\ \label{phi_aba } \phi_{aba}(t ) & = \psi_h(t)+ k\big[2x_b(t-\tau ) -x_a(t ) - x_a(t-2\tau)\big],\\ \label{phi_bab } \phi_{bab}(t ) & = \psi_h(t)+ k\big[-2x_a(t-\tau ) + x_b(t ) + x_b(t-2\tau)\big],\\ \label{psi } \psi_h ( t ) & \equiv\frac{\omega_0}{2}\int_{t-2\tau}^{t}h(t')dt',\end{aligned}\ ] ] here @xmath30 is the wave vector of light emitted by laser , @xmath31 is bouncing time and @xmath25 is perturbation of dimensionless metric originated by gw , @xmath10 is the speed of light . obviously , we can exclude information on displacement @xmath32 of platform @xmath20 in the following combination @xmath33 : @xmath34.\nonumber\end{aligned}\ ] ] exclusion of information on displacements of platforms @xmath20 in combination @xmath33 means that we effectively convert platform @xmath20 into ideal ( i.e. displacement noise free ) test mass for gw detection . by similar way measuring phases @xmath35 and @xmath36 @xmath29 , \\ \phi_{cbc}(t ) & = \psi_h(t)+ k\big[-2x_b(t-\tau ) + x_c(t ) + x_c(t-2\tau)\big],\nonumber\\ \phi_{bcb}(t ) & = \psi_h(t)+ k\big[2x_c(t-\tau ) -x_b(t ) - x_b(t-2\tau)\big],\nonumber\end{aligned}\ ] ] we can exclude information on displacement @xmath37 of platform @xmath22 in combination @xmath38 : @xmath39\nonumber \end{aligned}\ ] ] comparing ( [ cc1 ] ) and ( [ cc2 ] ) we see that position @xmath40 makes contributions into @xmath33 and @xmath38 with opposite signs in contrast to the gw signal . so we should just sum @xmath33 and @xmath38 in order to exclude _ completely _ information on positions of all platforms : @xmath41 it is useful to rewrite this formula in frequency domain : @xmath42 in long wave approximation ( @xmath43 ) we have in time and frequency domain correspondingly @xmath44 we see that in our simplest model the payment for separation of gw signal from displacement noise is decrease of gw response , which in long wave approximation is about @xmath45 . now we can analyze model with two fabry - perot cavities . we start from single double pumped fabry - perot cavity presented on fig . [ t1t2onefp ] . pump waves in different input ports are assumed to be orthogonally polarized in order the corresponding output waves to be separately detectable and to exclude nonlinear coupling of the corresponding intracavity waves . to simplify our model we assume that mirrors and lasers with detectors of each cavity are rigidly mounted on two movable platform ( see fig . [ t1t2onefp ] ) ( in contrast to scheme analyzed in @xcite with four platforms ) . laser @xmath46 with its detectors and mirror with amplitude transmittance @xmath47 are rigidly mounted on movable platform @xmath48 . in other words , we assume that all the elements on the platform do not move with respect to each other . laser @xmath46 pumps the cavity from the left and we assume that the wave transmitted through the cavity is redirected to platform @xmath48 by reflecting mirror @xmath49 as shown on fig [ t1t2onefp]a . so waves , emitted by this laser , are finally registered by detectors positioned on the same platform as laser . the mirror with amplitude transmittance @xmath50 and laser @xmath51 pumping cavity from the right with its detectors are rigidly mounted on platform @xmath52 . we assume that amplitude transmission coefficients of mirrors are small : @xmath53 . we put mean distance between the mirrors to be equal to @xmath1 . without the loss of generality we assume the cavity to be lying in the plane perpendicular to direction of gw and along one of the gw principal axes . it is convenient to represent the electric field operator of the light wave as a sum of ( i ) the `` strong '' ( classical ) plane monochromatic wave ( which approximates the light beam with cross - section @xmath54 ) with amplitude @xmath20 and frequency @xmath23 and ( ii ) the `` weak '' wave describing quantum fluctuations of the electromagnetic field : [ e ] @xmath55e^{-i(\omega_0t\mp k_0x)}+{\textrm{h.c.}},\\ a(x , t)&=\int_{-\infty}^{+\infty } a(\omega_0+\omega)e^{-i\omega\left(t\mp x / c\right)}\,\frac{d\omega}{2\pi},\nonumber\end{aligned}\ ] ] with amplitude @xmath56 ( heisenberg operator to be strict ) obeying the commutation relations : @xmath57&=0,\\ \bigl[a(\omega_0+\omega),a^\dag ( \omega_0+\omega')\bigr]&=2\pi\delta(\omega-\omega').\end{aligned}\ ] ] for briefness throughout the paper we denote @xmath58 this notation for quantum fluctuations @xmath59 is convenient since it coincides exactly with the fourier representation of the classical fields . and we omit the @xmath60-multiplier . for convenience throughout the paper we denote mean amplitudes by block letters and corresponding small additions by _ the same _ small letter as in ( [ e ] ) . in ideal case the input laser wave is in coherent state ( it means that fluctuational amplitude @xmath56 describes vacuum fluctuations ) . in more realistic case small amplitudes @xmath61 describes technical laser fluctuations . but fluctuational wave incoming into cavity through the non - pumped port ( denoted by @xmath62 or @xmath63 on fig . [ t1t2onefp ] ) is always in vacuum state . through the left port is shown only . pump laser with both detectors and input mirror are assumed to be rigidly mounted on moveable platform @xmath64 . transmitted wave is redirected by additional mirror @xmath49 to platform @xmath48 . transmitted and reflected wave are detected by detectors on platform @xmath48 . end and additional mirror @xmath49 are assumed to be rigidly mounted on movable platform @xmath65 . b ) pump by laser @xmath51 through the right port of the same" +"one of the main issues in multi - obstacle , multi - agent environments is the collision avoidance assessment . usually the avoidance constraints have to be considered both between an agent and fixed obstacles and between any two agents . the problem is intensively studied , yet actual , in the literature but is usually tilted towards heuristic approaches or online validations . the first usually lacks stability and performances guarantees and the later is easily boggled into numerical issues @xcite . an alternative approach is to solve offline the difficult trajectory generation part of the overall problem , online only a straightforward trajectory tracking is employed . this reduces significantly the online computations and allows stability and performance analysis . the caveat is that the trajectory to be computed has to respect the dynamics of the agent and to validate the collision avoidance constraints at all times @xcite . an interesting implementation is represented by flat trajectory design which guarantees that the corresponding system dynamics are respected ( with the caveat that state and input constraints are not easily accounted for @xcite ) . this construction shifts the state and input constraints into constraints over the flat output . to handle this , usually , the flat output is project over some basis functions which means that only the coefficients of the projections need to be found . in this sense , b - spline functions represent an ideal choice since they have enough flexibility @xcite and nice theoretical properties ( of which we will make extensive use throughout the paper ) . the present work builds on results sketched in @xcite and further advances the topic in several directions . foremost , we provide exact and sub - optimal formulations of the collision avoidance problems between an agent and the obstacles and between any tho agents . in both cases we make use of the geometrical properties of the b - spline functions which allow to bound locally the trajectories obtained through them . hence , the collision problems become separation problems between sets of consecutive points . in the exact case , these constraints lead to nonlinear formulation where both the control points and the separation hyperplanes are variables . a simplified ( and hence sub - optimal approach ) is to select the separation hyperplanes from the support hyperplanes of the obstacles therefore reducing the problem to a mixed integer formulation . both methods make use of a multi - obstacole framework and are tested and compared over extensive simulations . the rest of the paper is organized as follows : tackles flat output and b - spline characterizations , discusses flat trajectory generation and presents the main results of the paper which are then illustrated in . draws the conclusions . the minkowski sum of two sets , @xmath0 and @xmath1 is denoted as @xmath2 . @xmath3 denotes the convex hull of set generated by the collection of points @xmath4 . the problem of designing reference trajectories in a multi - agent multi - obstacle environment is in general a difficult one . a popular approach is to parametrize them through flatness constructions @xcite . in this section we will describe some of the basics of flat trajectory and their parametrization via b - spline basis functions . a nonlinear time invariant system : [ eq : contsys ] ( t)=f(x(t),u(t ) ) , where @xmath5 is the state vector and @xmath6 is the input vector is called differentially flat if there exists the flat output @xmath7 : [ eq : flat_out ] z(t)=(x(t),u(t),(t ) , , u^(q)(t ) ) such that the states and inputs can be algebraically expressed in terms of @xmath8 and a finite number of its higher - order derivatives : [ eq : diff_a ] x(t)&=&(z(t),(t ) , , z^(q)(t ) ) , + u(t)&=&(z(t),(t),,z^(q)(t ) ) . [ rem : flatinput ] for any system admitting a flat description , the number of flat outputs equals the number of inputs @xcite . in the case of linear systems @xcite the flat differentiability ( existence and constructive forms ) is implied by the controllability property . within the multi - agent framework , the most important aspect of construction is that it reduces the problem of trajectory generation to finding an adequate flat output . this means choosing @xmath8 such that , via mappings @xmath9 , various constraints on state and inputs are verified . since the flat output may be difficult to compute under these restrictions , we parametrize @xmath8 using a set of smooth basis functions @xmath10 : [ eq : paramflat ] z(t)=_i=1^n_i ^i(t ) , _ i . parameter @xmath11 depends on the number of constraints imposed onto the dynamics @xcite . there are multiple choices for the basis functions @xmath10 . among these , _ b - spline _ basis functions are well - suited to flatness parametrization due to their ease of enforcing continuity and because their degree depends only up to which derivative is needed to ensure continuity @xcite . a b - spline of order @xmath12 is characterized by a _ knot - vector _ @xcite [ eq : knot_vector ] t=\{_0,_1 _m } , of non - decreasing time instants ( @xmath13 ) which parametrizes the associated basis functions @xmath14 : @xmath15 for @xmath16 and @xmath17 . considering a collection of _ control points _ [ eq : control_points ] p=\{p_0,p_1 p_n } , we define a _ b - spline curve _ as a linear combination of the control points and the b - spline functions [ eq : bspline_curve ] z(t)=_i=0^n b_i , d(t)p_i = pb_d(t ) where @xmath18 and @xmath19 . this construction yields several interesting properties @xcite : 1 . [ p:1 ] @xmath8 is @xmath20 in any @xmath21 and @xmath22 in any @xmath23 ; 2 . [ p:3 ] at a time instant @xmath24 , @xmath8 depends only on the b - splines @xmath25 ; consequently , the b - spline curve @xmath8 lies within the union of all convex hulls formed by all @xmath12 successive control points ; 3 . [ p:5 ] the ` r ' order derivatives of b - spline basis functions can be expressed as linear combinations of b - splines of lower order ( @xmath26 with matrices @xmath27 of appropriate dimensions and content ) ; 4 . taking the first and last @xmath12 knot elements equal ( @xmath28 and @xmath29 ) leads to a _ clamped b - spline curve _ where the first and last control points coincide with the curve s end points . let us consider for exemplification the b - spline basis functions defined by parameters @xmath30 and @xmath31 with the knot vector of length @xmath32 and with components equally sampled between @xmath33 and @xmath34 . using these elements we construct the b - spline curve which we depict in . note that the convex - hulls determined by all @xmath31 consecutive control points ( property [ p:3 ] ) contain the curve : z(t)_i=3 5\{p_i-3,p_i-2,p_i-1,p_i } , t. in particular , the patterned shape depicted in the figure denotes region @xmath35 which contains the curve @xmath8 for any @xmath36 $ ] . let us consider a collection of @xmath37 way - points and the time stamps associated to them : [ eq : wt ] w=\{w_s } t_w=\{t_s } , for any @xmath38 . the goal is to construct a flat trajectory which passes through each way - point @xmath39 at the time instant @xmath40 ( or through a predefined neighborhood of it @xcite ) , i.e. , to find a flat output @xmath8 such that [ eq : xconstr ] x(t_s)=(z(t_s), z^(r)(t_s))=w_s , s=0 n . [ rem : waypoints ] note that here we assume that the way - points are defined over the entire state . arguably there might be situations where only a subspace of the state is of interest ( e.g. , only the position components of the state ) . making use of the b - spline framework we provide a vector of control points and its associated knot - vector such that is verified ( parameter @xmath12 is chosen such that continuity constraints are respected ) : [ eq : flatconstraints ] ( b_d(t_s),p)=w_s , s=0 n , where @xmath41 is constructed along property [ p:5 ] . let us assume that the knot - vector is fixed ( @xmath42 , @xmath43 and the intermediary points @xmath44 are equally distributed along these extremes ) . then , we can write an optimization problem with control points @xmath45 as decision variables whose goal is to minimize a cost @xmath46 along the time interval @xmath47 $ ] : [ eq : flatcost ] p=&_p _ t_0^t_n||(b_d(t),p)||_qdt + & with @xmath48 a positive symmetric matrix . the cost @xmath49 can impose any penalization we deem necessary ( length of the trajectory , input variation , input magnitude , etc ) . in general , such a problem is nonlinear ( due to mappings @xmath50 and @xmath51 ) and hence difficult to solve . a nonlinear mpc iterative approach has been extensively studied @xcite . with these tools at hand we can propose various methods for collision avoidance in a multi - agent multi - obstacle environment . let us consider a collection of polyhedral obstacles [ eq : obstacles ] o=\{o_1 o_n_o } and assume that the k - th agent follows a trajectory @xmath52 during the interval @xmath53 $ ] , generated as in through a collection of control points @xmath54 and the associated knot vector @xmath55 . consequently , the collision avoidance conditions mentioned earlier can be formulated as follows : 1 . collision avoidance between the k - th agent and l - th obstacle : [ eq : real_avoidance_ao ] r_k(t)o_l , t , 2 . collision avoidance between the @xmath56-th and @xmath57-th agents ( for any @xmath58 : [ eq : real_avoidance_aa ] r_k_1(t)r_k_2(t ) , t. the distinctive feature of conditions is that they require a continuous time interval ( @xmath47 $ ] ) validation ( i.e. , imposing constraints at discrete time instants @xmath59 along the interval is not deemed sufficient ) . consequently , we make use of property property [ p:3 ] which allows to bound the continuous b - spline parametrized curve by its control points . coupling this with the _ separating hyperplane theorem _ ( a well - known construction @xcite which states that for any two disjoint convex objects there exists a separating hyperplane ) several results are attainable . first , we provide a slight reformulation of proposition 1 from @xcite . [ prop : avoid ] the k - th agent is guaranteed to avoid obstacles , i.e. , to verify , if there @xmath60 s.t . [ eq : avoidance ] _ j\{i - d+1 i}(c_il^k)^p_j^k_x^-1(o_l ) ( c_il^k)^x , for @xmath61 and @xmath62 . condition states that there exists a hyperplane defined by its normal @xmath63 which separates the points @xmath64 from the obstacle @xmath65 . since , according to property [ p:3 ] , the curve is contained in @xmath66 it follows that is a sufficient condition to verify . in note the use of mapping @xmath67 . this appears because the obstacle avoidance constraint is the state - space whereas is in the control point space . a similar reasoning is employed for the inter - agent collision condition . [ prop : avoid_inter ] the pair ( @xmath68 ) of agents , with @xmath69 , is guaranteed to avoid collision , i.e. , to validate , if there @xmath70 s.t . : [ eq : avoid_inter ] _ i_2}(c_i_1i_2^k_1k_2)^p_j^k_2 , for all possible pairs @xmath71 which validate [ eq : intersection_aa_indices ] \{(i_1,i_2 ) : [ _ i_1^k_1,_i_1 + 1^k_1]}. recall that ( as per property [ p:3 ] ) a region @xmath72 contains the b - spline curve in" +"analyses of the impulsive phase of solar flares detected in various electromagnetic wavelength ranges are important for understanding the acceleration and propagation of particles . the accelerated electrons reveal their presence e.g. in hard x - ray and radio emissions , and cause rapid heating of the chromosphere and subsequent emission in the hydrogen h@xmath1 line . one of the key questions is the form of the accelerated electron distributions . their determination from the hard x - ray spectra depends not only on the emission mechanism but also on the processes affecting the propagation of the particles . as suggested by brown , emslie , and kontar ( 2003 ) , it is the mean electron flux distribution @xmath3 depending only on the bremsstrahlung cross section that should be used as a reference for both observational hard x - ray spectral analyses and theoretical models of electron acceleration and propagation . the mean electron flux distribution can be determined either by inverting the photon spectra ( johns and lin , 1992 ; piana et al . , 2003 ) or by a forward fitting method usually assuming a power - law form of @xmath3 ( holman et al . , 2003 ) . observed hard x - ray spectra also contain a contribution of photons backscattered in the photosphere and this will modify the calculated @xmath3 ( bai and ramaty , 1978 ; alexander and brown , 2002 ) . besides the x - ray emission , numerous types of radio emission in the metric and decimetric range are usually observed during flares . they provide further information about the acceleration and propagation of the electron beams and plasma parameters in the emission region ( karlick , 1997 ) . according to standard solar flare models ( e.g. dennis and schwartz , 1989 ) , the accelerated electrons provide one of the mechanisms for the flare energy transport from the release site to the lower atmospheric layers . as the accelerated electrons propagate along the magnetic field lines toward the photosphere , they lose their kinetic energy mainly via coulomb collisions ( brown , 1971 ) in the lower corona and chromospheric layers . the chromospheric response to the beam energy deposition determines the characteristics of optical and uv emission from the flare loops . numerical models of chromospheric response to pulsed electron beam heating ( e.g. canfield and gayley , 1987 ; heinzel , 1991 ) predict the time correlation of hard x - ray and h@xmath1 emission recently analysed e.g. by trottet et al . ( 2000 ) and wang et al . their results show that hard x - rays and h@xmath1 intensities in some flare kernels exhibit time correlations in the time range from subseconds to @xmath210 s. some flare models ( e.g. heyvaerts , priest , and rust , 1977 ; cargill and priest , 1983 ) and observations ( czaykowska et al . , 1999 ) suggest that h@xmath1 kernels are located between the upflows of the beam heated plasma and the downflows of the cool plasma in the loops disconnected from the reconnection site . the leading edges of the h@xmath1 emission close to the newly reconnected loops are supposed to be also heated by the accelerated particles , which are detectable e.g. as the hard x - ray sources . comparison of the spatial distribution of yohkoh hard x - ray sources and h@xmath1 flare kernels was done by e.g. asai et al . they found that many h@xmath1 kernels brighten successively during the evolution of the flare ribbons , but only a few radiation sources were seen in the hard x - ray images . they suggest that this discrepancy may be the result of the low dynamic range capability of the yohkoh hard x - ray telescope . in this paper , we analyse the impulsive phase of the august 20 , 2002 solar flare , which is characterised by a very flat photon spectrum at the x - ray burst maximum ( spectral index @xmath4 ) . similar flat spectra have been reported , e.g. by nitta , dennis , and kiplinger ( 1990 ) and frnk , hudson , and watanabe ( 1997 ) . the event presented here is the first such flat spectrum spectrum observed with the high energy resolution of the reuven ramaty high energy solar spectroscopic imager ( rhessi ) ( lin et al . , 2002 ) . we show the influence of photons backscattered in the photosphere on the determination of the mean electron flux distribution and compare results obtained by inversion and forward fitting methods . we also study the spatial correlation of h@xmath1 emission and its time changes with hard x - ray sources . in section 2 we describe the global behaviour of the event with regard to hard x - ray and radio fluxes . sections 3 and 4 present the rhessi , h@xmath1 and magnetic field observations , methods , and results . finally , the results are discussed in section 5 and the conclusions are given in section 6 . the analysed flare is well suited for a multi - wavelength study of the electron propagation because its observations provide a set of simultaneous data of comparable time and spatial resolution in the wavelengths directly related to the accelerated particles : rhessi hard x - ray spectra and images , h@xmath1 images ( kanzelhhe observatory ) , and radio and microwave fluxes ( bern , ondejov , and zrich facilities ) . the flare was detected by goes satellites on august 20 , 2002 . it started at 08:25 ut and reached its maximum at 08:26 ut as an m3.4 flare . the 1b h@xmath1 flare was reported in noaa ar 0069 at s10w38 , starting at 08:25 ut , peaking at 08:26 ut , and ending at 08:37 ut . from the fluxes at 4299 mhz ( ondejov ) and 988 mhz ( zrich ) . attenuators states a0 , a1 , and a3 and the time interval in which the derivative of h@xmath1 intensity was analysed are indicated by the lines at the top of the rhessi data plot . the abrupt changes in rhessi flux in the 12 - 25 kev energy band at @xmath2 08:25:17 ut and @xmath2 08:25:41 ut are caused by the attenuator changes ( a0 @xmath5 a1 and a1 @xmath5 a3 , respectively ) at these times.,scaledwidth=94.0% ] a global overview of the flare evolution in dm / m radio waves and rhessi x - rays is shown in figure [ fig_hsi_radio ] . the rhessi flare was first detected at 08:24:32 ut with the increase in flux in the 12 - 25 kev energy band . then , with some time delays ( at @xmath2 08:24:45 ut ) , bursts in higher and higher energy bands followed . during the starting phase of the x - ray emission at 08:24:30 - 08:25:08 ut , no radio bursts were observed in the dm / m range . the first weak and narrowband emission ( nbe ) in the dm - range was registered at 08:25:08 ut in the 2000 - 2200 mhz frequency range , followed by the type iii burst below 500 mhz at 08:25:16 ut . the most energetic part of this flare occurred during the time interval 08:25:15 - 08:25:50 ut , when significant hard x - ray emission was detected up to 7 mev ( see also data from the song instrument on board coronas - f ; myagkova , priv . comm . ) and microwave emission up to 89.4 ghz . the turn - over frequency between optically thick and thin part of the radio emission was shifted to values between 19.6 and 50 ghz . at that time the radio emission in the dm - range also reached the maximum and a very fast drifting ( @xmath2 -4000 mhz s@xmath6 ) and short - lasting ( @xmath2 0.1 s ) type iiid burst ( relativistic type iii burst - see poquerusse , 1994 ) was observed in the 400 - 1000 mhz range at 08:25:31.8 ut . in the decimetric range ( 2000 - 4500 mhz ) this phase was characterised by broadband pulsations . rhessi x - ray data were analysed with the rhessi data analysis software ( hurford et al . , 2002 ; schwartz et al . , 2002 ) . during the flare , different attenuators were automatically placed in front of all detectors to absorb soft x - rays and reduce pulse pile - up . the attenuator states a0 , a1 , and a3 ( no attenuator , thin attenuator , and both thick and thin attenuator , respectively ) are indicated on figure [ fig_hsi_radio ] . corrections for the effects of the different attenuator states are available for all times except when the attenuators are moving , a period of @xmath2 1 s. image reconstruction was performed with both the clean and the pixon algorithms using data from the front segments of the detectors . detector 7 was used only for the images in the energy bands above 7 kev due to its energy threshold of about 7 kev . detector 1 and 2 mainly added noise to the images indicating that there was no significant source structure with an angular scale finer than @xmath2 4 arcsecond . therefore , these detectors were excluded . the clean algorithm was used for obtaining morphology and time evolution of x - ray sources , see sections [ spatial ] and [ tder ] , figures [ fig_ha_hsi_mdi_low ] , [ fig_ha_hsi_mdi_high ] , and [ fig_haderiv_hsi ] . since there was no source component as large as or larger than fwhm of the detector 8 ( 107 arcsec ) , the imaging fields of view in all clean images were set smaller than this fwhm and consequently detectors 8 and 9 were also not used in the clean image reconstruction . the pixon algorithm ( puetter and pia 1994 ; metcalf et al . , 1996 ) is known to suppress spurious sources and to have high photometric accuracy ( metcalf et al . , 1996 ; alexander and metcalf , 1997 ) . we have used the pixon imaging technique for imaging spectroscopy at the burst maximum , see section [ flatspectrum ] . we analysed data summed over the eight front segments . detector 2 was excluded since its energy threshold is about 20 kev and its energy resolution is about 10 kev . the data were corrected for pulse pile - up and decimation . full 2d detector response matrices , each corresponding to the applied attenuator state , were used to convert input photon fluxes to count rates . the response matrix accounts for the efficiency and resolution of the detectors , the absorption by the attenuators , grids , and all other material above the detectors , and all other known instrumental effects ( smith et al . , 2002 ) . the time bin for rhessi spectra was 2 s ( @xmath7 a half rotation ) , which ensures that the rapid modulation produced by the grids does not have any distorting effect on the spectra . the rhessi spectra were analysed in the time interval 08:25:10 - 08:26:00 ut and were fitted from 8 kev up to typically 400 kev , depending on the signal - to - noise ratio . rhessi data of this flare were contaminated by an electron precipitation starting at 08:16 ut and detected up to 300 kev . therefore , a special care was taken to estimate the background due to the electron precipitation in the 12 - 300 kev energy range while standard techniques were used at other energies . in the 12 - 40 kev energy range , the background was estimated using count rates from the onboard charged particle detector" +"globular star clusters ( gcs ) are spectacular residents of our galaxy s halo and beyond , yet there are long standing mysteries as to how , when , and where they formed . these mysteries expanded with the recent discoveries of ultra - compact dwarfs ( ucds ) , which began to bridge the classical gap between galaxies and star clusters and raised questions of how to differentiate between these two classes of stellar system . while studies of gcs in the milky way ( mw ) are focusing on remarkable clues about their origins from multiple stellar populations , another important window is to examine the extragalactic populations of gcs and ucds to provide additional context , statistics , and opportunities for witnessing formation in action . here we discuss briefly three areas of novel discovery and insight emerging recently from extragalactic studies . the first is new constraints on gc origins in a cosmological context ( [ sec : cosmo ] ) , the second is more extensive mapping of the parameter space of compact stellar systems ( [ sec : css ] ) , and the third concerns observations of tidally stripped nuclei ( [ sec : inform ] ) . gcs are thought to trace ancient phases of star and galaxy formation , but many of the particulars are murky . the mw provides important clues through the _ bimodality _ of its gc system , which consists of a roughly spherical , non - rotating , metal - poor `` halo '' component , and a flattened , rotating , metal - rich , `` bulge / thick - disk '' component . this configuration suggests a early , chaotic assembly through infalling dwarf galaxies ( e.g. , ( * ? ? ? * searle & zinn 1978 ) ) , followed by intense star - forming activity in the main part of the galaxy . a similar pattern is seen in other galaxies , including the giant ellipticals and lenticulars ( e / s0s ) , which commonly show color bimodality ( blue and red gcs ; e.g. , ( * ? ? ? * zepf & ashman 1993 ) ; ( * ? ? ? * larsen et al . 2001 ) ) . despite some controversies about interpreting the colors , bimodality in metallicity has now been confirmed through spectroscopic efforts with keck / deimos as part of the sluggs survey ( brodie et al . 2012 , 2014 ; usher et al . 2012 ) , with supporting evidence from kinematics ( pota et al . 2013 ) . adding to this picture is recent , deep _ hubble space telescope _ ( _ hst _ ) imaging in the outer halo of a nearby s0 galaxy , which detected the elusive second peak of metal - poor red - giant - branch ( rgb ) stars corresponding to the metal - poor gc peak ( figure [ fig : bimod ] ; ( * ? ? * peacock et al . 2015 ) ) . this observation supports the view that blue gc subpopulations trace underlying metal - poor stellar halo populations and that gc bimodality implies two distinct , fundamental modes of early star formation . the different relative peak heights require a higher gc formation efficiency or survival rate in the metal - poor population , for reasons that remain undetermined ( see harris & harris 2002 ) . 5060 kpc , and the gcs from subaru / suprime - cam photometry at comparable radii ( spectroscopic metallicities at smaller radii show similar results ) . the stellar histograms have been arbitrarily renormalized for comparison to the gcs . peaks are apparent in both tracers at [ @xmath3/h ] @xmath4 and @xmath5 , providing the first demonstration beyond the mw that gc bimodality is reflected in the underlying stellar halo . , width=432 ] a clearer view of gc origins could be obtained through estimates of their ages , but even in the mw , the best current methods are still uncertain at the @xmath6 2 gyr level which is the difference between forming at @xmath7 and @xmath8 . this conundrum motivates an alternative approach where gc metallicities @xmath3 are used as a proxy for age , after recognizing that metals build up in galaxies like clockwork ( ( * ? ? ? * shapiro et al . 2010 ) ; ( * ? ? ? * spitler 2010 ) ) . thus the gcs can be connected to the observed galaxy mass metallicity redshift relation in order to thereby infer both their epochs and their sites of formation . we have applied this `` metallicity matching '' method to gc spectroscopic data for a sample of e / s0s from sluggs ( ( * ? ? ? * forbes et al . 2015 ) ) . as figure [ fig : metal ] shows , for each gc subpopulation , there is a range of possible average formation epochs : for example , the metal - poor gcs could have been formed very early in massive galaxies , or later in dwarf galaxies . this degeneracy is broken by invoking plausible growth curves for the gc host galaxies : one curve for the main progenitor galaxy , and one for a typical 1:10 mass - ratio accreted satellite . assuming that the metal - rich gcs are a predominantly in situ population , they appear to have formed in the range @xmath9 24 . if the metal - poor gcs are primarily accreted , then they formed at @xmath9 45 . in high - mass galaxies , and metal - poor gcs at @xmath10 in dwarfs . , width=432 ] this relatively recent birth date for the metal - poor gcs would make them a post - reionization population an important conclusion since it has been proposed that reionization either produced a hiatus between the two gc subpopulations , or was caused by the gcs themselves ( e.g. , ( * ? ? ? * beasley et al . 2002 ) ; ( * ? ? ? * katz & ricotti 2013 ) ) . on the other hand , there are significant caveats . one is that the galactic metallicity relation is not well constrained at redshifts above @xmath11 . another is that there may have also been an earlier , in situ phase of metal - poor gc formation in the main galaxy , which is reflected in some problems of crafting a self - consistent pure - accretion model ( e.g. , ( * ? ? ? * spitler et al . 2012 ) ) ) . the inferred metal - rich gc birth date is more secure , and raises intriguing possibilities for further progress since the universe at @xmath0 is becoming well studied , as the `` high noon '' of cosmic star formation . we can now see directly where and how the intense bursts of star formation activity occurred that must have formed the bulk of the metal - rich gc populations . the answer is remarkable : rather than the gas - rich major mergers that dominated the thinking about gc and galaxy formation for many years , high-@xmath12 star formation is seen to concentrate in extended , turbulent , gas - rich galactic disks ( e.g. , ( * ? ? ? * genzel et al . 2008 ) ) . these disks host supergiant clumps of gas and young stars that seem natural spawning sites for gcs ( shapiro et al . 2012 ; kruijssen 2015 ) . this consolidation of observations at low and high redshifts motivates a new generation of theoretical models for the assembly of gc systems in a cosmological context . the models should include violent disk instabilities ( e.g. , ( * ? ? ? * porter et al . 2014 ) ) , and should respect the full range of chemo - dynamical constraints : not only the numbers , ages , and metallicities of gcs ( ( * ? ? ? * tonini 2013 ) ; ( * ? ? ? * li & gnedin 2014 ) ) , but also their spatial and orbital distributions which have so far posed severe theoretical challenges ( see brodie et al . 2014 , section 5.4 , for more discussion ) . ucds were discovered serendipitously through spectroscopic surveys ( ( * ? ? ? * hilker et al . 1999 ) ; ( * ? ? ? * drinkwater et al . 2000 ) ) . they appear similar to gcs but typically have larger sizes ( half - light radii @xmath13 1040 pc rather than @xmath6 24 pc ) and higher luminosities ( up to @xmath14 ) . their formation mechanisms may include merging super star clusters and tidal stripping of galactic nuclei . however , their distributions in basic parameter space and in galactic environments are not clear . two major efforts to map out the properties of ucds more systematically include sluggs ( [ sec : cosmo ] ) and the archive of intermediate mass stellar systems project ( aimss ; ( * ? ? ? * norris et al . 2014 ) ) . -band absolute magnitude for distance - confirmed hot stellar sytems . larger red circles mark objects discovered in the past 2 years . the black square and circle show ngc 2419 and @xmath2 cen , respectively . ] these surveys revealed that ucds are _ not _ synonymous with being very luminous : the family of large-@xmath15 objects also extends to lower luminosities and meets up with the `` faint fuzzies '' or extended clusters ( ( * ? ? ? * brodie et al . 2011 ) ; ( * ? ? ? * forbes et al . 2013 ) ) this expansion of classification boundaries means that the unusual mw object ngc 2419 is the nearest ucd . at the other end of the spectrum , record - breaking dense stellar systems have been found ( ( * ? ? ? * strader et al . 2013 ) ; ( * ? ? ? * sandoval et al . 2015 ) ) , with these novel extremes of high- and low - surface brightness demonstrating the pivotal role of selection effects in shaping our conceptions of stellar systems . an additional uncharted area of parameter space is the gap between ucds and compact ellipticals , which is now seen to be filled in with ce ucd transition objects ( see size luminosity diagram in figure [ fig : size ] ) . this steadily growing menagerie of diverse compact stellar systems compounds the need to decipher their interrelations and origins . the ucds probably include more than one underlying subpopulation , and recent cosmological models conclude that most of them are unusually large star clusters , with only a minority being stripped nuclei ( ( * ? ? ? * pfeffer et al . 2014 ) ) . tests of these claims are needed from in - depth observational studies of the ucds . some cases of stripped nuclei are obvious , based on an overmassive central black hole , or on an extended star formation history ( ( * ? ? ? * seth et al . 2014 ) ; ( * ? ? ? * norris et al . 2015 ) ) . metallicity is another useful diagnostic , as ces and the highest - mass ucds were found to be relatively metal - rich , in a probable reflection of stripped nuclei origins ( ( * ? ? ? * janz et al . 2016 ) ) . further hereditary clues may come from kinematics and dynamics ( ( * ? ? ? * brodie et al . 2011 ) ; ( * ? ? ? *" +"in this paper , we propose a clustering - based iterative algorithm to solve certain optimization problems in machine learning when data size is large and thus it becomes impractical to use out - of - the - box algorithms . we rely on the principle of data aggregation and then subsequent disaggregations . while it is standard practice to aggregate the data and then calibrate the machine learning algorithm on aggregated data , we embed this into an iterative framework where initial aggregations are gradually disaggregated to the extent that even an optimal solution is obtainable . early studies in data aggregation consider transportation problems @xcite , where either demand or supply nodes are aggregated . zipkin @xcite studied data aggregation for linear programming ( lp ) and derived error bounds of the approximate solution . there are also studies on data aggregation for 0 - 1 integer programming @xcite . the reader is referred to rogers _ et al _ @xcite and litvinchev and tsurkov @xcite for comprehensive literature reviews for aggregation techniques applied for optimization problems . for support vector machines ( svm ) , there exist several works using the concept of clustering or data aggregation . evgeniou and pontil @xcite proposed a clustering algorithm that creates large size clusters for entries surrounded by the same class and small size clusters for entries in the mixed - class area . the clustering algorithm is used to preprocess the data and the clustered data is used to solve the problem . the algorithm tends to create large size clusters for entries far from the decision boundary and small size clusters for the other case . et al _ @xcite developed screening rules for svm to discard non - support vectors that do not affect the classifier . et al _ @xcite and doppa _ et al _ @xcite proposed a second order cone programming ( socp ) formulation for svm based on chance constraints and clusters . the key idea of the socp formulations is to reduce the number of constraints ( from the number of the entries to number of clusters ) by defining chance constraints for clusters . after obtaining an approximate solution by solving the optimization problem with aggregated data , a natural attempt is to use less - coarsely aggregated data , in order to obtain a finer approximation . in fact , we can do this iteratively : modify the aggregated data in each iteration based on the information at hand . this framework , which iteratively passes information between the original problem and the aggregated problem @xcite , is known as _ iterative aggregation disaggregation _ ( iad ) . the iad framework has been applied for several optimization problems such as lp @xcite and network design @xcite . in machine learning , @xcite used hierarchical micro clustering and a clustering feature tree to obtain an approximate solution for support vector machines . in this paper , we propose a general optimization algorithm based on clustering and data aggregation , and apply it to three common machine learning problems : least absolute deviation regression ( lad ) , svm , and semi - supervised support vector machines ( s@xmath0vm ) . the algorithm fits the iad framework , but has additional properties shown for the selected problems in this paper . the ability to report the optimality gap and monotonic convergence to global optimum are features of our algorithm for lad and svm , while our algorithm guarantees optimality for s@xmath0vm without monotonic convergence . our work for svm is distinguished from the work of yu _ et al _ @xcite , as we iteratively solve weighted svm and guarantee optimality , whereas they iteratively solve the standard unweighted svm and thus find only an approximate solution . on the other hand , it is distinguished from evgeniou and pontil @xcite , as our algorithm is iterative and guarantees global optimum , whereas they used clustering to preprocess data and obtain an approximate optimum . et al _ @xcite and doppa _ et al _ @xcite are different because we use the typical svm formulation within an iterative framework , whereas they propose an socp formulation based on chance constraints . our data disaggregation and cluster partitioning procedure is based on the optimality condition derived in this paper : relative location of the observations to the hyperplane ( for lad , svm , s@xmath0vm ) and labels of the observations ( for svm , s@xmath0vm ) . for example , in the svm case , if the separating hyperplane divides a cluster , the cluster is split . the condition for s@xmath0vm is even more involved since a single cluster can be split into four clusters . in the computational experiment , we show that our algorithm outperforms the current state - of - the - art algorithms when the data size is large . the implementation of our algorithms is based on in - memory processing , however the algorithms work also when data does not fit entirely in memory and has to be read from disk in batches . the algorithms never require the entire data set to be processed at once . our contributions are summarized as follows . 1 . we propose a clustering - based iterative algorithm to solve certain optimization problems , where an optimality condition is derived for each problem . the proposed algorithmic framework can be applied to other problems with certain structural properties ( even outside of machine learning ) . the algorithm is most beneficial when the time complexity of the original optimization problem is high . we present model specific disaggregation and cluster partitioning procedures based on the optimality condition , which is one of the keys for achieving optimality . 3 . for the selected machine learning problems , i.e. , lad and svm , we show that the algorithm monotonically converges to a global optimum , while providing the optimality gap in each iteration . for s@xmath0vm , we provide the optimality condition . we present the algorithmic framework in section 2 and apply it to lad , svm , and s@xmath0vm in section 3 . a computational study is provided in section 4 , followed by a discussion on the characteristic of the algorithm and how to develop the algorithm for other problems in section 5 . we start by defining a few terms . a _ data matrix _ consists of _ entries _ ( rows ) and _ attributes _ ( columns ) . a machine learning optimization problem needs to be solved over the data matrix . when the entries of the original data are partitioned into several sub - groups , we call the sub - groups _ clusters _ and we require every entry of the original data to belong to exactly one cluster . based on the clusters , an _ aggregated entry _ is created for each cluster to represent the entries in the cluster . this aggregated entry ( usually the centroid ) represents one cluster , and all aggregated entries are considered in the same attribute space as the entries of the original data . the notion of the _ aggregated data _ refers to the collection of the aggregated entries . the _ aggregated problem _ is a similar optimization problem to the original optimization problem , based on the aggregated data instead of the original data . _ declustering _ is the procedure of partitioning a cluster into two or more sub - clusters . we consider optimization problems of the type @xmath1 where @xmath2 is the number of entries of @xmath3 , @xmath4 is @xmath5 entry of @xmath3 , and arbitrary functions @xmath6 and @xmath7 are defined for every @xmath8 . one of the common features of such problems is that the data associated with @xmath3 is aggregated in practice and an approximate solution can be easily obtained . well - known problems such as lad , svm , and facility location fall into this category . the focus of our work is to design a computationally tractable algorithm that actually yields an optimal solution in a finite number of iterations . our algorithm needs four components tailored to a particular optimization problem or a machine learning model . 1 . a _ definition of the aggregated data _ is needed to create aggregated entries . 2 . _ clustering and declustering procedures ( and criteria ) _ are needed to cluster the entries of the original data and to decluster the existing clusters . an _ aggregated problem _ ( usually weighted version of the problem with the aggregated data ) should be defined . an _ optimality condition _ is needed to determine whether the current solution to the aggregated problem is optimal for the original problem . the overall algorithm is initialized by defining clusters of the original entries and creating aggregated data . in each iteration , the algorithm solves the aggregated problem . if the obtained solution to the aggregated problem satisfies the optimality condition , then the algorithm terminates with an optimal solution to the original problem . otherwise , the selected clusters are declustered based on the declustering criteria and new aggregated data is created . the algorithm continues until the optimality condition is satisfied . we refer to this algorithm , which is summarized in algorithm [ algo_aid ] , as _ aggregate and iterative disaggregate _ observe that the algorithm is finite as we must stop when each cluster is an entry of the original data . in the computational experiment section , we show that in practice the algorithm terminates much earlier . create clusters and aggregated data * do * solve aggregated problem check optimality condition * if * optimality condition is violated * then * decluster the clusters and redefine aggregated data * while * optimality condition is not satisfied in figure [ fig : ex_decluster ] , we illustrate the concept of the algorithm . in figure [ fig : ex_decluster_1 ] , small circles represent the entries of the original data . they are partitioned into three clusters ( large dotted circles ) , where the crosses represent the aggregated data ( three aggregated entries ) . we solve the aggregated problem with the three aggregated entries in figure [ fig : ex_decluster_1 ] . suppose that the aggregated solution does not satisfy the optimality condition and that the declustering criteria decide to partition all three clusters . in figure [ fig : ex_decluster_2 ] , each cluster in figure [ fig : ex_decluster_1 ] is split into two sub - clusters . suppose that the optimality condition is satisfied after several iterations . then , we terminate the algorithm with guaranteed optimality . figure [ fig : ex_decluster_3 ] represents possible final clusters after several iterations from figure [ fig : ex_decluster_2 ] . observe that some of the clusters in figure [ fig : ex_decluster_2 ] remain the same in figure [ fig : ex_decluster_3 ] , due to the fact that we selectively decluster . we use the following notation in subsequent sections . 1 . @xmath9 : index set of entries , where @xmath2 is the number of entries ( observations ) 2 . @xmath10 : index set of attributes , where @xmath11 is the number of attributes 3 . @xmath12 : index set of the clusters in iteration @xmath13 4 . @xmath14 : set of clusters in iteration @xmath13 , where @xmath15 is a subset of @xmath16 for any @xmath17 in @xmath18 5 . @xmath19 : last iteration of the algorithm when the optimality condition is satisfied the multiple linear least absolute deviation regression problem ( lad ) can be formulated as @xmath20 where @xmath21 \in \mathbb{r}^{n \times m}$ ] is the explanatory variable data , @xmath22 \in \mathbb{r}^{n}$ ] is the response variable data ," +"the search for the last unobserved particle of the standard model ( sm ) , the higgs boson , has been a major goal of high energy physics for many years , and is a central part of fermilab s tevatron program . direct searches at the cern lep collider have set a 95% c.l . limit on the higgs boson mass of @xmath6 gev @xcite . taking into account this limit , precision electroweak measurements indirectly constrain the sm higgs boson mass to be lower than 190 gev at the 95% c.l . @xcite , which is within reach of the fermilab tevatron collider experiments . previous cdf and results on higgs searches were combined in the tevatron higgs combination presented in april 2008 @xcite . both cdf and have recently reported new and updated searches for the sm higgs boson @xcite-@xcite and their combination @xcite . in this note , we combine the most recent results of all such searches in collisions at which are sensitive to a high mass ( 155 - 200 gev / c@xmath3 ) higgs : the searches for a sm higgs boson decaying to @xmath7 pairs ( the @xmath8 s then decaying leptonically ) and produced through gluon - gluon fusion ( ) , vector boson fusion ( vbf ) , or in association with vector bosons ( and @xmath9 with hadronic @xmath10 decays ) in data corresponding to integrated luminosities of 3.0 at cdf and 3.0 at d . to simplify their combination , the searches are separated into mutually exclusive final states ( see table [ tab : cdfacc ] and [ tab : dzacc ] ) referred to as `` analyses '' in this note . selection procedures for each analysis are detailed in refs . @xcite , and are briefly described below . event selections are similar for the corresponding cdf and d analyses . for the analyses , a large and two opposite - signed , isolated leptons ( any combination of electrons or muons ) are selected , defining three final states ( @xmath11 , @xmath12 , and @xmath13 ) for d . cdf separates the events into five non - overlapping samples , first by separating the events by jet multiplicity ( 0 , 1 or 2 ) , then subdviding the 0 and 1 jet samples in two , one having a low signal / bacgkround ( s / b ) ratio , the other having a higher one . the presence of neutrinos in the final state prevents reconstruction of the higgs boson mass , so other variables have to be used for separating signal from background . in these analyses , the final discriminants are neural - network outputs based on several kinematic variables @xcite . these include likelihoods constructed from matrix - element probabilities as input to the neural network , for cdf . all analyses in these channels have been updated with more data and analysis improvements compared to our previous combination @xcite . the cdf and d experiments also contribute analyses , where the associated @xmath8 boson and the @xmath8 boson from the higgs boson decay which has the same charge are required to decay leptonically , thereby defining like - sign dilepton final states ( @xmath14 , @xmath15 , and @xmath16 ) containing all decays of the third @xmath8 boson . in these analyses , cdf derive the limits from a counting experiment , while for dthe final variable is a likelihood discriminant formed from several topological variables . higgs boson signals ( gluon - gluon fusion , vector boson production , or associated production with vector bosons ) are simulated using pythia @xcite , and cteq6l @xcite parton distribution functions at leading - order ( lo ) . the signal cross sections are normalized to next - to - next - to - leading order ( nnlo ) calculations @xcite , and branching ratios from hdecay @xcite . the @xmath17 production cross section is also corrected for two - loop electroweak corrections @xcite . for both cdf and d , events from multijet ( instrumental ) backgrounds ( `` qcd production '' ) are measured in data with different methods , in orthogonal samples . for cdf , backgrounds from other sm processes were generated using pythia , alpgen @xcite , mc@nlo @xcite and herwig @xcite programs . for d , these backgrounds were generated using pythia , alpgen , and comphep @xcite , with pythia providing parton - showering and hadronization for all the generators . background processes were normalized using either experimental data or next - to - leading order calculations from mcfm @xcite . integrated luminosities , and references to the collaborations public documentation for each analysis are given in table [ tab : cdfacc ] for cdf and in table [ tab : dzacc ] for d . the tables include the ranges of higgs boson mass ( @xmath18 ) over which the searches were performed , but the combination presented in this note is performed only for search of higgs bosons with mass of 155 gev / c@xmath3 or above . we also show in figure [ fig : combollr-2 ] the 1-@xmath22 distribution as a function of the higgs boson mass , which is directly interpreted as the level of exclusion of our search . for instance , both our observed and expected results exclude a higgs boson with @xmath23 165 gev/@xmath5 at @xmath24 92% c.l . cdf collaboration , `` search for higgs boson production in association with w boson with 2.7 '' , + cdf conference note , http://www-cdf.fnal.gov/physics/new/hdg/hdg.html cdf collaboration , `` search for the standard model higgs boson in the missing et and b - jets signature '' , + cdf conference note , http://www-cdf.fnal.gov/physics/new/hdg/hdg.html cdf collaboration , `` search for zh in 2.4 fb-1 '' , + cdf conference note , http://www-cdf.fnal.gov/physics/new/hdg/hdg.html cdf collaboration , `` search for @xmath26 production using 3.0 fb@xmath25 '' , + cdf conference note , http://www-cdf.fnal.gov/physics/new/hdg/hdg.html cdf collaboration , `` combined upper limit on standard model higgs boson production '' , + cdf conference note , http://www-cdf.fnal.gov/physics/new/hdg/hdg.html collaboration , `` combined upper limits on standard model higgs boson production from the d0 experiment with 1.1 - 2.4 fb@xmath25 '' d conference note 5756 . a. djouadi , j. kalinowski and m. spira , `` hdecay : a program for higgs boson decays in the standard model and its supersymmetric extension , '' comput . commun . * 108 * , 56 ( 1998 ) [ arxiv : hep - ph/9704448 ] . t. junk , nucl . instrum . meth . a434 , p. 435 - 443 , 1999 , a.l . read , `` modified frequentist analysis of search results ( the @xmath38 method ) '' , in f. james , l. lyons and y. perrin ( eds . ) , _ workshop on confidence limits _ , cern , yellow report 2000 - 005 , available through cdsweb.cern.ch ." +"recent discoveries of red - skewed iron lines in spectra of neutron star ( ns ) sources serpens x-1 @xcite , 4u 1820 - 30 , gx 349 + 2 ( * ? ? ? * c08 hereafter ) and 4u 1636 - 536 @xcite show that the phenomenon of red - skewed lines is not restricted to black hole ( bh ) sources . in this paper we report on the discovery of the asymmetric iron line in the _ suzaku _ spectrum of the ns source cygnus x-2 ( cyg x-2 ) . therefore , cyg x-2 is the fifth ns source which shows strongly asymmetric iron line profile . this indicates that the red - skewed lines in ns sources may be as common as in bh sources . more generally , asymmetric emission lines appear to be abundant in both types of accretion powered x - ray sources . it is crucial to correctly identify the physical origin of the red - skewness of these lines because they can be potentially used to study the properties of the accretion close to accreting objects as well as to constrain the fundamental characteristics of compact objects . c08 interpreted the @xmath1 iron line profiles in terms of relativistically red - shifted emission due to reflection off the accretion disk very close to a compact object . this scenario is commonly accepted as an explanation of strongly red - skewed iron lines in bh sources @xcite . the main motivation for applying the relativistic line formation scenario to the ns case was the fact that the inner radius of the accretion disk , which was predicted by the relativistic line model was consistent with the interpretation of the highest observed kilohertz quasi - periodic oscillation ( khz qpo ) frequency in this sources as a keplerian frequency at this radius . a red - skewed profile of emission lines can be also produced by repeated electron scattering in a diverging outflow as proposed by @xcite , lt07 hereafter , see also references therein . in the framework of the wind model the fluorescent iron line k@xmath2 is formed in the partly ionized wind as a result of illumination by central source . electron scattering of the iron k@xmath0 photons within the ionized expanding flow leads to a decrease of their energy ( redshift ) . this photon redshift is an intrinsic property of any outflow for which divergence is positive . recently @xcite confirmed using multidimensional monte - carlo simulation that for sufficiently high wind densities , moderate fe k@xmath2 emission lines can be formed and that electron scattering in the flow may cause these lines to develop extended red wings . we examine the red - skewed line profile observed in cyg x-2 both in terms of the relativistic paradigm and in the framework of the wind downscattering . the main obstacle in analyzing the high spectral resolution data with the wind model is that analytical solution is not available for the general formulation of this problem . lt07 used monte carlo ( mc ) simulations to model the line profiles produced in the wind environment . in the presented work we provide a consistent analysis of the line profile with the wind model by introducing the lt07 mc code into xspec astrophysical data analysis package . we find that the wind outflow model is able to reproduce the red - skewed line profile with the fit quality similar to that shown by the relativistic reflection models . therefore , in order to distinguish between these two models one has to consider their consistency in a broader phenomenological context . for example , c08 proposed to look for high frequency quasi - periodic oscillations ( hf qpos ) as an additional evidence of a keplerian disk existence close to a ns , which then would necessitate the presence of the reflection components in energy spectra . in contrast , the presence of the opaque wind in the system would result in smearing the signal coming from the central region . this smearing effect leads to a suppression of the fast variability of x - ray emission . unfortunately , high time resolution observations by _ rossi x - ray timing explorer _ ( _ rxte _ ) , simultaneous with the _ suzaku _ observations analyzed in this paper , are not available . thus , we resort to a study based on the _ rxte _ data set with similar spectral characteristics . our comparative analysis indicates that the source was in low variability state during these observations which is more consistent with the wind / outflow scenario . description of _ suzaku _ and supporting _ rxte _ observations as well as details of our spectral fitting are presented are presented in 2 . we discuss implications of the relativistic and wind outflow red - skewed line formation scenarios in cyg x-2 in 3 . conclusions follow in 4 . cyg x-2 is a low mass x - ray binary ( see * ? ? ? * for review ) which exhibits a z - shape color - color diagram @xcite . the observations of thermonuclear x - ray bursts @xcite identified the nature of the compact object in cyg x-2 as a neutron star . @xcite used the _ rxte _ burst data to estimate the ns mass to be about 1.4 solar masses and radius to be about 9 km . @xcite reported the simultaneous detection of twin khz peaks at 500 and 860 hz and highest single khz qpo at 1007 hz . cyg x-2 was observed by _ @xcite on may 16 , 2006 for a total exposure of 39 ksec ( observation i d : 401049010 ) . however , during more than a half of the observation the satellite were operating in the medium telemetry mode which led to the telemetry saturation and resulted in data unusable for scientific analysis . during intervals when the high telemetry setting were utilized the foreground illuminated xis detectors ( i.e. xis 0 , 2 and 3 ) operated in 3@xmath33 event editing mode with burst clock and 1/4 window settings . the 3@xmath33 event editing mode is not available for the xis 1 for this observation . we therefore used data from xis 0 , 2 , and 3 collected when high telemetry rate was utilized . we reduce the _ suzaku _ xis and hxd data using the _ xselect _ data analysis tool following the guidelines given by _ suzaku _ data analysis guide . the xis images indicate that strong pile - up in the center of the source point spread function ( psf ) leads to a characteristic `` crater '' . in order to remove piled - up data we extracted xis spectra from the annulus regions with the outer radius set to the maximum allowed by the xis detector field of view ( @xmath4 arcsec ) and the inner radius was manually selected to excise the most piled - up inner core of psf ( @xmath5 arcsec ) . the spectra and corresponding responses were extracted by _ xselect _ extractor and _ xisresp _ , _ xisrmfgen _ tools . spectra and responses for individual detectors were then added using _ mathpha _ and _ addrmf _ ftools . we linearly rebin xis spectral and response data to obtain 1024 spectral channels . hxd / pin spectrum was corrected for non - x - ray and cosmic x - ray background . we fit xis and pin spectra jointly in xspec using 0.7 - 9.0 kev energy range for xis data and 15.0 - 40.0 kev range for pin data fixing the cross - normalization factor between xis and pin spectra at unity . due to large calibration uncertainties we also ignore 1.5 - 2.5 kev range for xis spectrum . for the continuum spectra we choose the sum of thermal ( bbody ) and comptonized ( comptt ; * ? ? ? * ) components , modified by interstellar photoelectric absorption according to @xcite . when we directly fit the data with this model we observe three distinct narrow features in the residuals ( see figure [ line_res ] , left panel a ) . first , we see a line signature at 6 - 7 kev , which is the primary target of our investigation . we also observe a weak excess around 3.2 kev and a prominent line at 1 kev . the feature at 3.2 kev is probably an instrumental artifact . the line at 1 kev was reported previously from cyg x-2 @xcite and presumably belongs to the source spectrum . both features are well represented by gaussian shape ( see residuals on panel b of figure 1 ) . in addition to these narrow lines we observe a building - up excess towards higher energies in xis spectrum . this indicates a presence of a residual pile - up in the regions close to the excised central part of the psf . to mitigate this effect we utilize the xspec pileup convolution model designed to model pile - up effect in ccd detectors . the xspec implementation of the pile - up model was initially designed to describe this effect in _ chandra _ data . however , the model , developed in @xcite , is valid for _ suzaku _ xis detectors also . _ suzaku _ psf of xis ccds is broader and spreads around larger number of pixels . therefore , pile - up model for the xis spectra would require larger number of regions to be considered for pile - up . to model pile - up in xis detectors we used the following parameter settings for the _ pileup _ xspec model : 2 second time frame , maximum of 10 photons to pile up , unity for grade correction and morphing parameter and 5% of psf to consider for pile - up . the number of detector regions to consider independently for pile - up was allowed to change which led to the best fit value of 38 regions . this is consistent with the number of 3@xmath33 pixel regions close to excised central core of psf . this approach successfully removed the hard excess due to the pile - up effect . finally , we excluded 4.5 - 7.5 kev energy range where the line emission is expected to be significant and fit the spectrum again to obtain the fit quality of @xmath6 . the result is shown in panel d of fig . [ line_res ] . the final best - fit parameters for the continuum model are following : hydrogen column @xmath7 @xmath8 for wabs ; seed photons temperature @xmath9 kev , electron temperature @xmath10 kev , optical depth @xmath11 for comptt and _ bbody _ temperature @xmath12 kev . the energy , sigma and equivalent width ( @xmath13 ) for gaussians used to fit lines are @xmath14 kev , @xmath15 kev , @xmath16 ev and @xmath17 kev , @xmath18 kev , @xmath19 ev . when we include the iron k@xmath0 emission region ( 4.5 - 7.5 kev energy band ) and fit the spectrum with the relativistic and wind line models the parameter ranges of the above continuum parameters change insignificantly ( see table 1 ) . this indicates that continuum model weakly depends on the assumed line model . it is worth noting that the values of the continuum parameters imply that during this _ suzaku _ observation cyg x-2 was in the `` high / soft '' state characterized by high opacity of geometrically thin configuration . panel e in fig . [ line_res ] shows the residuals of the best - fit model with iron region noticed in the data . the apparent line profile is broad and red - skewed . in fact , the fit" +"there are many kinds of networks including probably the most influential network of all , the world wide web @xcite . this network is a popular one to analyze because of its size and easy accessibility for statistical analysis . however , there are many other networks that share some of the properties of the web and some that do not . among these networks we find social networks @xcite , collaboration nets @xcite , industrial and business related networks @xcite , transportation nets @xcite and many biological related nets such as food , ecological , and protein interaction networks @xcite and neural networks @xcite . the mathematical description of networks started with the fundamental works of erds and rnyi @xcite , which in the absence of reliable data on large networks were rarely compared to real networks . recently , the computational boom has provided us an increasing number of types of networks and more data on these networks . one of the most exciting discoveries is the scale - free structures of certain evolving networks @xcite . these nets have power law degree distribution , where only a few vertices have many connections to the others and the rest of the graph is rarely connected . to explain the origin of this scale free structure of networks barabsi _ et al_. @xcite suggested the mechanism of preferential attachment and emphasized the key role of growth . in their model the probability of a new node connecting to an existing node is proportional to the degree of the target node . variations on this model include networks where there is aging of nodes , nonlinear attachment probabilities , and re - wiring are allowed . probably the most obvious feature of real networks that is missing from most of the models studied by mathematicians and physicists are characteristics of individual nodes in real networks which influence the connection probability . thus , if the nodes represent individual persons , it is obvious that in many circumstances two people are more likely to become connected in some form of relationship because of the nature of their individual characteristics . our model is motivated by the need to incorporate this idea . a similar idea was used in a preferential attachment model by bianconi and barabsi @xcite who assigned to each new node a fitness parameter . in their model a larger fitness parameter may overcompensate the smaller probability of attachment . in our study we propose a simple model of growing networks whose statistical properties are identical to a more complicated model containing nodes with distinct characteristics . we will calculate the edge distribution of the growing network , the distribution of cluster sizes and the emergence of a giant cluster . we will also show how the number of attempted connections made when a new node is added determines the position and type of the phase transition as well as the cluster size distribution . we first consider a social network model where each node has individual characteristics or traits . each node that is added to the network is assigned a permanent set of random traits which could be coded as an ordered binary string or vector of length @xmath8 . when a node is added it chooses randomly @xmath9 possible partners from the already existing nodes , or if there are less then @xmath10 ( because the simulation has not yet reached time step @xmath11 ) it chooses all the existing nodes as possible partners . a trait distance between the new node and one of its possible partners is calculated based on their trait vectors ( @xmath12 , @xmath13 ) using a distance measure , @xmath14 , such as the hamming distance . then a connection is formed between the two nodes with a probability determined from a given probability distribution over the distance function @xmath15 . different functions , @xmath16 , correspond to different soicopsychological situations . thus , if we wish to model the case where people are more likely to link together if they have similar traits , then @xmath16 would be a monotonically decreasing function of @xmath17 . for this case , the simplest @xmath16 would be to form a link if @xmath17 is below some threshold . this procedure is repeated for each possible partner of the new node . thus , each new node can have initially up to @xmath18 links with the other existing nodes . existing nodes can have more than @xmath18 links as more nodes are added to the network and link up with the existing nodes . there are no multiple links between pairs of nodes . because each node is given a random trait vector , and the nodes to link to are also chosen randomly , many properties of the network simply depend on the probability @xmath19 , that two chosen nodes will link together : @xmath20 where @xmath21 is the probability of the distance @xmath17 between two nodes , and the sum is over all possible distance values . thus , the model is reduced to the following procedure . at each time step we add a node to the network , and attempt to link with @xmath18 existing nodes which are chosen at random . an actual connection is made with a probability @xmath19 . the asymptotic behavior of the network in the limit of large time @xmath22 , does not depend on the initial condition of starting with a single isolated vertex . although frequently structural properties of a network of nodes with trait vectors depends only on @xmath19 , there are other properties which will depend on the detailed form of @xmath16 and the nature of the trait vectors . examples of such properties include the distribution of traits in different parts of the network and the correlation of traits with distance in the network . for example , one can imagine a very simple network of nodes representing men and women . in one network the probability of forming a link is independent of sex , and in the other persons prefer to link up with members of the opposite sex . as long as the mean probability of two chosen nodes linking together is the same in the two scenarios the structural properties of the two networks will be the same , but the distribution of men and women within the network will be quite different in the two cases . in this paper we confine ourselves to the structural properties of networks and are considering these other non - structural properties in our current research . the expected number of edges at a node is approximately @xmath23 where @xmath24 is the time - step when it was created , ( the smaller @xmath25 is , the older the node is ) @xmath22 is the total simulation time , @xmath1 is the probability that two nodes form a connection , @xmath26 is the maximum number of initial connections of a newly created node , and @xmath27 is the @xmath28 harmonic number given by the formula @xmath29 for @xmath30 , and @xmath31 . this equation shows that the number of edges of a node heavily depends on the age of the node . equation ( [ eq : kn ] ) slightly overestimates the number of connections for the oldest nodes in the network in two respects . first , the above formula assumes that a node always has @xmath2 possible initial connections . however , multiple connections between a pair of nodes are not allowed , and there are less than @xmath2 available partners for the initial connections of a node created before or in the @xmath32 time step ( overestimation of initial connections ) . second , the term for the late connections assumes that a node has a @xmath33 chance of being selected as the partner of the @xmath34 node ( which chooses @xmath2 possible partners out of @xmath35 already existing nodes ) . however , for a node created in time step @xmath36 , this term yields a probability of being chosen greater than @xmath37 between time steps @xmath38 and @xmath2 ( where @xmath39 ) that is unacceptable again because multiple connections between a pair of nodes are not allowed ( overestimation of late connections ) . below is the formula correcting these errors , but will use the simpler , uncorrected formula in the remaining part of our paper because the errors are negligible . @xmath40 & \textrm{if } n\leq k+1\\ \delta k\left ( \alpha _ { t}-\ln \left ( n-1\right ) -\frac{1}{2\left ( n-1\right ) } \right ) & \textrm{if } n > k+1\ , , \end{array}\right . \end{array}\ ] ] using @xmath41 , where @xmath42 is the euler - mascheroni constant @xcite , and @xmath43 . note that the first @xmath10 nodes are expected to have the same number of connections ( because @xmath44 does not depend on @xmath45 in their case ) , and the edge number starts breaking down exponentially for nodes created after time step @xmath10 ( fig . [ fig : kn_ca ] and [ fig : kn_si]_a _ ) . this means that this growth mechanism is identical to that where the first @xmath46 nodes are created in the same time step . we now wish to determine the edge distribution , @xmath47 , equal to the probability that a node picked at random has on average @xmath48 edges . we return to eq . ( [ eq : kn ] ) ignoring the correction term in eq . ( [ eq : kn_c ] ) , and write the formula for @xmath49 in the simpler form ( fig . [ fig : kn_ca ] and [ fig : kn_si]_a _ ) : @xmath50 where @xmath51 is the same used in eq . ( [ eq : kn_c ] ) . using eq . ( [ eq : kn_a ] ) , neglecting the term @xmath52 in eq . ( [ eq : kn_a ] ) for @xmath25 large enough , and knowing that the age distribution of nodes is uniform , we analytically approximate the edge distribution of the network with the following exponential @xmath53 we used the standard transformation rule for random variables , @xmath54 with @xmath55 . for sufficiently large @xmath22 , due to the definition of @xmath51 , this can be effectively approximated by a distribution which is independent of @xmath22 ( fig . [ fig : kn_ca ] and [ fig : kn_si]_b _ ) : @xmath56 we can also determine a slightly different degree or edge distribution which is the percentage of nodes with @xmath57 edges . denote by @xmath58 the expected number of nodes with degree @xmath59 at time @xmath22 . the number of isolated nodes , @xmath60 , will increase by @xmath61 , which is the probability of the addition node not connecting to any existing node , and decrease on average by @xmath62 : @xmath63 the formula for the expected number of nodes of degree @xmath64 is a bit complicated . for ( @xmath65 ) there are two ways to increase @xmath66 : either selecting degree @xmath35 nodes for connection with the new node or the new node having exactly @xmath59 edges . for ( @xmath67 ) , the new node can not contribute to @xmath68 . the decrease will be proportional to the probability of choosing a degree @xmath59 node for attachment . these equations are correct as @xmath70 , and numerical simulations show that @xmath71 . substituting this form into the equations for @xmath72 we obtain @xmath73 this degree distribution @xmath74 decays exponentially consistent with our previous result for @xmath47 . in some network models , such as the preferential attachment models , all the nodes belong to a single cluster . for such models the focus is on the degree distribution and the distance between nodes in the network . however , our network can" +"the equilibrium ( thermodynamic ) isotope effect ( eie ) is defined as the effect of isotopic substitution on the equilibrium constant . denoting an isotopolog with a lighter ( heavier ) isotope by a subscript _ ( _ h _ ) , the eie is defined as the ratio of equilibrium constants@xmath6 where @xmath7 _ _ _ _ and @xmath8 are molecular partition functions per unit volume of reactant and product . we study a specific case of eie - the equilibrium ratio of two isotopomers . in this case , the eie is equal to the equilibrium constant of the isotopomerization reaction , @xmath9 where superscripts _ r _ and _ p _ refer to reactant and product isotopomers , respectively . usually , equilibrium isotope effects are computed only approximately:@xcite in particular , effects due to indistinguishability of particles and rotational and vibrational contributions to the eie are treated separately . furthermore , the vibrational motion is approximated by a simple harmonic oscillator and the rotational motion is approximated by a rigid rotor . in general , none of the contributions , not even the indistinguishability effects can be separated from the others.@xcite however , at room temperature or above the nuclei can be accurately treated as distinguishable , and the indistinguishability effects can be almost exactly described by symmetry factors . on the other hand , the effective coupling between rotations and vibrations , anharmonicity of vibrations , and non - rigidity of rotations can in fact become more important at higher temperatures . for simplicity , from now on we denote these three effects together as anharmonicity effects and the approximation that neglects them the harmonic approximation ( ha ) . in some cases the effects of anharmonicity of the born - oppenheimer potential surface on the value of eie can be substantial.@xcite ishimoto _ _ have shown that the isotope effect on certain barrier heights can even have opposite signs , when calculated taking anharmonicity effects into account and in the ha.@xcite our goal is to describe rigorously equilibria at room temperature or above . therefore , two approximations that we make are the born - oppenheimer approximation and the distinguishable particle approximation ( we treat indistinguishability by appropriate symmetry factors ) . the error due to the born - oppenheimer approximation was studied for h / d eie by bardo and wolfsberg,@xcite and by kleinman and wolfsberg,@xcite and was shown to be of the order of 1 % in most studied cases . since we assume that nuclei are point charges , the born - oppenheimer approximation implies that the potential energy surface is the same for the two isotopomers . the differences of born - oppenheimer surfaces due to differences of nuclear volume and quadrupole of isotopes can be important for heavy elements@xcite , but these are not studied in this work . symmetry factors themselves result in an eie equal to a rational ratio , which can be computed analytically . in order to separate the symmetry contributions from the mass contributions to the eie , it is useful to introduce the reduced reaction free energy,@xmath10 where @xmath11 and @xmath12 are the symmetry factors discussed in more detail in sec . [ sec : examples ] . to include the effects of quantization of nuclear degrees of freedom beyond the ha rigorously we use the feynman path integral representation ( pi ) of the partition function . the quantum reduced reaction free energy can then be computed by thermodynamic integration with respect to the mass of the isotopes . to compute the derivative of the free energy efficiently , we use a generalized virial estimator . the advantage of this estimator is that its statistical error does not increase with the number of imaginary time slices in the discretized path integral . as a consequence , converged results can be obtained in a significantly shorter simulation than with other estimators . the ultimate goal would be to combine the path integral methodology with _ ab initio _ potentials . however , since millions of samples are required , the computational expense results in the following compromise : first , the equilibrium isotope effects are computed using _ ab initio _ potentials , but as usual , within the ha . then all anharmonicity corrections are computed using the pi methodology , but with semiempirical potentials . in other words , we take advantage of the higher accuracy of the _ ab initio _ potentials to compute the harmonic contribution to the eie and then make an assumption that the anharmonicity effects are similar for _ ab initio _ and semiempirical potentials . after describing theoretical features of the method , we apply it to hydrocarbons used in experimental measurements of isotope effects on [ 1,5 ] sigmatropic hydrogen transfer reactions . two of them were recently used by doering _ @xcite who reported equilibrium ratios of their isotopomers . this allows us to validate our calculations as well as to discuss the apparent discrepancy in measurements of doering _ et al . _ from a theoretical point of view . the outline of the paper is as follows : in sec . [ sec : method ] , we describe a rigorous quantum - mechanical methodology to compute the eie . section [ sec : examples ] presents the [ 1,5 ] sigmatropic hydrogen shift reactions on which we test the methodology , explains how _ ab initio _ methods can be combined with the pi to compute the eie , and discusses in detail symmetry effects in these reactions . section [ sec : computational - details ] explains the implementation of the method in amber 10 and describes details of calculations and error analysis of our pimd simulations . results of calculations are presented and compared with experiments in sec . [ sec : results ] . section [ sec : discussion - and - conclusions ] concludes the paper . eie can be calculated by a procedure of thermodynamic integration@xcite with respect to the mass . this method takes advantage of the relationship@xmath13,\label{eq : ti}\ ] ] where @xmath14 is the ( quantum ) free energy and @xmath15 is a parameter which provides a smooth transition between isotopomers @xmath16 and @xmath17 . this can be accomplished , e.g. , by linear interpolation of masses of all atoms in a molecule according to the equation @xmath18 in contrast to the partition function itself , the integrand of eq . @xmath19 is a thermodynamic average and therefore can be computed by either monte carlo or molecular dynamics simulations . classically , the eie is trivial and eq . can be evaluated analytically . when quantum effects are important , this simplification is not possible . to describe quantum thermodynamic effects rigorously , one can use the path integral formulation of quantum mechanics.@xcite in the path integral formalism , thermodynamic properties are calculated exploiting the correspondence between matrix elements of the boltzmann operator and the quantum propagator in imaginary time.@xcite in the last decades , path integrals proved to be very useful in many areas of quantum chemistry , most recently in calculations of heat capacities,@xcite rate constants,@xcite kinetic isotope effects,@xcite or diffusion coefficients.@xcite let @xmath20 be the number of atoms , @xmath21 the number of spatial dimensions , and @xmath22 the number of imaginary time slices in the discretized pi ( @xmath23 gives classical mechanics , @xmath24 gives quantum mechanics ) . then the pi representation of the partition function @xmath25 in the born - oppenheimer approximation is @xmath26,\label{eq : pi_qr}\\ c & \equiv\left(\frac{p}{2\pi\hbar^{2}\beta}\right)^{npd/2}\prod_{i=1}^{n}m_{i}^{pd/2}.\label{eq : pi_prefactor}\end{aligned}\ ] ] where @xmath27 is the set of cartesian coordinates associated with the @xmath28@xmath29 time slice , and @xmath30 is the effective potential @xmath31 the @xmath22 particles representing each nucleus in @xmath22 different imaginary time slices are called `` beads . '' each bead interacts via harmonic potential with the two beads representing the same nucleus in adjacent time slices and via potential @xmath32 attenuated by factor @xmath33 with beads representing other nuclei in the same imaginary time slice . by straightforward differentiation of eq . we obtain the so - called thermodynamic estimator ( te),@xcite @xmath34 a problem with expression is that its statistical error grows with the number of time slices . a similar behavior is a well known property of the thermodynamic estimator for energy,@xcite where the problem is caused by the kinetic part of energy . of imaginary time slices in the path integral . all results obtained by 1 @xmath35 long simulations ( with the time step 0.05 @xmath36 ) of compound * 1 - 5,5,5-__d__@xmath37 * ( @xmath38 ) using gaff force field , normal mode pimd , and nos - hoover chains of thermostats . [ fig : gve_te_values ] ] of imaginary time slices in the path integral . all results obtained by 1 @xmath35 long simulations ( with the time step 0.05 @xmath36 ) of compound * 1 - 5,5,5-__d__@xmath37 * ( @xmath38 ) using gaff force field , normal mode pimd , and nos - hoover chains of thermostats . note that the rmse of the gve is not only non - increasing ( as expected from theory ) , but in fact decreases slightly with increasing @xmath22 , which is due to the decrease of correlation length.[fig : gve_te_errors ] ] the growth of statistical error of the thermodynamic estimator for energy is removed by expressing the estimator only in terms of the potential and its derivatives using the virial theorem.@xcite in our case , a similar improvement can be accomplished , if a coordinate transformation , @xmath39 is introduced into eq . prior to performing the derivative . here , the `` centroid '' coordinate is defined as @xmath40 in other words , first the `` centroid '' coordinate @xmath41 is subtracted , and then the coordinates are mass - scaled . resulting generalized virial estimator ( gve)@xcite takes the form @xmath42 . \label{eq : gve}\ ] ] its primary advantage is that the root mean square error ( rmse ) of the average , @xmath43 , is approximately independent on the number of imaginary time slices @xmath22,@xmath44 in this equation @xmath45 denotes the length of the simulation and @xmath46 is the correlation length . the convergence of values and statistical errors of both estimators as a function of number @xmath22 of imaginary time slices for systems studied in this paper is discussed in section [ sec : computational - details ] . as expected , up to the statistical error they give the same values as can be seen in fig . [ fig : gve_te_values ] . nevertheless , when quantum effects are important , and a high value of @xmath22 must be used , the gve is the preferred estimator since it has much smaller statistical error and therefore converges much faster than the te ( see fig . [ fig : gve_te_errors ] ) . thermodynamic average in eq . can be evaluated efficiently using the path integral monte carlo ( pimc ) or path integral molecular dynamics ( pimd ) . in pimc , gradients of @xmath47 in eq . result in additional calculations since the usual metropolis monte carlo procedure for the random walk only requires the values of @xmath47 . this additional cost can be , however , reduced either by less frequent sampling , or by using a trick in which the total derivative with respect to @xmath15 ( not the gradients ! ) is computed by finite difference.@xcite in case of pimd , the presence of gradients of @xmath47 in eq . does not slow down the calculation since forces are already computed by a propagation algorithm . although in principle , a pimc algorithm for a specific problem can always be at least as efficient as a pimd algorithm , in practice it is much easier to write a general pimd algorithm" +"the polarization bell states of a pair of quantized spatiotemporal electromagnetic modes @xmath0 and @xmath1 are @xmath2 and @xmath3 where @xmath4 and @xmath5 , for @xmath6 , denote single - photon states of horizontal and vertical polarization , respectively . these states form a maximally - entangled basis for the two - qubit hilbert space of single - photon states for modes @xmath0 and @xmath1 . as such , they are extremely important for applications such as quantum teleportation @xcite , quantum superdense coding @xcite , and quantum key distribution @xcite , as well as their fundamental role in the clauser - horne - shimony - holt ( chsh ) inequality @xcite . the standard approach to generating these states is to post - select the biphoton output from spontaneous parametric downconversion ( spdc ) @xcite , and the standard approach to verify their entanglement behavior is via quantum - interference measurements @xcite . recently , chen _ et al . @xcite reported an experiment that mimicked the quantum - interference behavior seen with an spdc entanglement source using two independent pseudothermal light beam obtained by passing laser light through a rotating ground - glass diffuser . their experiments were carried out in the low - flux regime using photon - coincidence counting , and they provided a quantum - mechanical explanation that ascribed their observations to two - photon interference , just as is the case for spdc light . _ it has long been known that the semiclassical theory of photodetection in which light is treated as a classical electromagnetic wave and the fundamental photodetection noise is the shot noise arising from the discreteness of the electron charge produces quantitatively identical predictions to those obtained from quantum photodetection theory when the illumination is in a classical state , i.e. , a coherent - state or a statistical mixture of such states . see @xcite for a detailed review of this topic . except for any excess noise it may carry , laser light is coherent - state light . moreover , its propagation through ground - glass diffusers , free space , optical fibers , and beam splitters are all linear transformations , for which classical - state inputs yield classical - state outputs . it follows that there must be an explanation for the experiments reported in @xcite that relies on semiclassical photodetection theory , i.e. , one that only needs classical electromagnetic waves . our purpose in this paper is to present that explanation . furthermore , although we will begin with a treatment that applies to low - flux operation using photon - coincidence counting , our approach readily extends to high - flux operation using photocurrent cross - correlation . the remainder of the paper is organized as follows . in sec . 2 we describe the modified mach - zehnder interferometer with photon - coincidence counting in the low - flux regime that was employed in @xcite . in sec . 3 we introduce our classical - light model for this interferometer , and use it to derive the singles and coincidence rates as functions of the interferometer s differential time delay and its polarization - analysis angles . here we will show that our results explain the observations reported in @xcite . finally , in sec . 4 , we indicate how our theory can be extended to high - flux operation with photocurrent cross - correlation , and we provide some concluding remarks about the implications of our work . the configuration for the experiment from @xcite is shown in figure 1 . a continuous - wave mode - locked ti : sapphire laser operating at @xmath7 nm wavelength with 78mhz pulse - repetition frequency and a @xmath8fs pulse duration illuminated an interference filter , to somewhat increase the pulse duration , followed by a rotating ground - glass diffuser , to render the light spatially incoherent . the diameter @xmath9 mm output beam from the diffuser was divided by the 50 - 50 beam splitter bs1 , with the resulting output beams propagating @xmath10 mm ( from the diffuser ) to collection planes , one of which could be offset , longitudinally , by @xmath11 . each collection plane contained the tip of a single - mode fiber , whose transverse coordinates , @xmath12 and @xmath13 , satisfied @xmath14 , where @xmath15 m is the correlation length of the speckles cast in these planes . the fibers routed the light they collected to polarizers p1 and p2 , set for orthogonal polarizations that we shall take to be @xmath16 and @xmath17 , respectively , before entering the 50 - 50 beam splitter bs2 . the outputs from bs2 then underwent polarization analysis , by analyzers a1 and a2 set for angles @xmath18 and @xmath19 with respect to @xmath16 , prior to single - photon detection . computer processing completed the experiment by averaging the detector outputs over many pulses to obtain the singles rates @xmath20 and @xmath21 and the coincidence rate @xmath22 . is the nominal ground - glass to fiber - tip propagation distance , and @xmath11 is a variable offset in one arm . p1 and p2 are polarizers that select orthogonal polarizations that we shall take to be @xmath16 and @xmath17 , respectively . a1 and a2 are polarization analyzers set for angles @xmath18 and @xmath19 , respectively . @xmath23 and @xmath24 are single - photon detectors , width=360 ] chen _ et al . used quantum - mechanical analysis to show that @xmath22 consisted of a background term plus a quantum interference term that is proportional to @xmath25 when @xmath26 . their background term arises from what in a related prior experiment @xcite they called `` self - intensity correlations . '' these correlations can be measured by summing the coincidence rates when a beam block is placed in front of the fiber tip at @xmath12 and when a beam block is placed in front of the fiber tip at @xmath13 . subtracting the self - intensity correlations from the full coincidence rate obtained at @xmath26 then yields , according to theory , a unity - visibility quantum interference pattern . that background - subtracted quantum - interference pattern can then be used to obtain a violation of the chsh inequality , in the same manner that is done @xcite for the polarization - entangled signal and idler obtained from an spdc source . the experimental data from @xcite bears out this theory : the authors report @xmath27% visibility in their background - subtracted quantum - interference pattern at @xmath26 . _ chen _ et al . do not attempt to explain their experiments with a classical - light model , i.e. , with semiclassical photodetection theory . in their previous work on a related anticorrelation experiment @xcite , they claimed there was no classical - light explanation for their results . we , however , have shown that such is not the case @xcite . in particular , we reported a straightforward classical - field analysis that reproduced the essential characteristics of the anticorrelation observed in @xcite . our demonstration is especially important for the following reason . were chen _ @xcite correct in asserting that their anticorrelation measurement could not be explained in this manner it would present quantum optics with a major conundrum : either laser light that has undergone linear transformation is _ not in a coherent state or a random mixture of coherent states , or the quantum and semiclassical theories of photodetection _ can make different quantitative predictions for the measurement statistics of classical - state light . in the present paper , we shall extend our scalar - wave model from @xcite to provide a classical - light explanation for the simulated bell - state reported in @xcite . the linear velocity of the ground - glass diffuser where it was illuminated in @xcite was @xmath280.8 m/s , so that for the @xmath29fs and @xmath30fs post - if pulse durations considered therein it is fair to say that the ground glass was completely stationary while a single laser pulse propagated through it . we shall assume that to be the case for the experiments in @xcite . the differential time delay @xmath31 corresponding to the longitudinal variation @xmath11 was @xmath32ps in @xcite and we will assume that the photodetectors employed therein had the same @xmath33ns coincidence gate as in @xcite . hence , with @xmath34ps , we have that @xmath35 . because the fibers are single mode , and because their transverse coordinates have been set to ensure that the light beams they collect are uncorrelated , we will assume ( cf . @xcite ) that @xmath36 and @xmath37 , the positive - frequency _ classical fields emerging from polarizers p1 and p2 , respectively , are given by @xmath38 and @xmath39 here : @xmath40 and @xmath41 are independent , identically distributed , zero - mean , isotropic , complex - valued gaussian random variables with common mean - squared strength @xmath42 representing constant - in - time speckle ; @xmath43 is a transform - limited gaussian pulse normalized to satisfy @xmath44 with @xmath45 being the post - if pulse duration ; and @xmath46 , @xmath47 are orthogonal unit vectors along the @xmath16 and @xmath17 directions . note that in ( [ eplus ] ) and ( [ eminus ] ) we have chosen @xmath48 units , so that the average energy in either field is @xmath49 , i.e. , @xmath50 is their average photon number . _ _ et al . used photon - coincidence counting , their experiment was necessarily in the low - brightness regime wherein @xmath51 prevails . as a result , we can say that the singles rates ( counts / gate ) and the coincidence rate ( coincidences / gate ) obey @xcite @xmath52 and @xmath53 in these expressions : @xmath54 is the photodetectors quantum efficiency ; the complex envelopes of the fields that illuminate detectors @xmath23 and @xmath24 are @xmath55 and @xmath56 where we have suppressed all propagation delays except for the interferometer s differential delay @xmath57 . using the statistics of @xmath40 and @xmath41 , along with the disparities between @xmath45 , @xmath57 , and @xmath58 , it is easy to evaluate the singles rates and the coincidence rate . _ the statistical independence of the @xmath40 and @xmath41 , and their mean - squared strengths , immediately gives us @xmath59 & + & \left . \langle |v_-|^2\rangle \sin^2(\theta_k)\int_{-t/2}^{t/2}\!dt\,|f(t-\delta t/2)|^2\right ) \\[.05 in ] & \approx & \frac{\eta n}{2 } , \quad \mbox{for $ k = a , b$},\end{aligned}\ ] ] where the approximation follows from @xmath60 . similarly , for the coincidence rate , the statistical independence of @xmath40 and @xmath41 leads to @xmath61 & + & c_a^2s_b^2\langle |v_+|^2\rangle \langle |v_-|^2\rangle \int_{-t/2}^{t/2}\!dt\,|f(t_+)|^2\int_{-t/2}^{t/2}\!du\,|f(u_-)|^2 \nonumber \\[.05 in ] & + & c_b^2s_a^2\langle |v_+|^2\rangle \langle |v_-|^2\rangle\int_{-t/2}^{t/2}\!dt\,|f(t_-)|^2\int_{-t/2}^{t/2}\!du\,|f(u_+)|^2 \nonumber \\[.05 in ] & -&2c_ac_bs_as_b\langle |v_+|^2\rangle \langle |v_-|^2\rangle\int_{-t/2}^{t/2}\!dt\!\int_{-t/2}^{t/2}\!du\,{\rm re}[f^*(t_+)f^*(u_-)f(t_-)f(u_+ ) ] \nonumber \\[.05 in ] & + & \left.s_a^2s_b^2\langle |v_-|^4\rangle \int_{-t/2}^{t/2}\!dt\,|f(t_-)|^2\int_{-t/2}^{t/2}\!du\,|f(u_-)|^2\right),\end{aligned}\ ] ] where @xmath62 and @xmath63 , for @xmath64 , @xmath65 , for @xmath66 , and the first and last terms on the right are the self - intensity correlations . following @xcite , we shall suppress these self - intensity correlations they can be found by first measuring the coincidence rate with @xmath36 blocked and then measuring the coincidence rate with @xmath37 blocked by subtracting them from @xmath22 and focus our attention on @xmath67 & + & c_b^2s_a^2\int_{-t/2}^{t/2}\!dt\,|f(t_-)|^2\int_{-t/2}^{t/2}\!du\,|f(u_+)|^2 \nonumber \\[.05 in ] & -&\left.2c_ac_bs_as_b\int_{-t/2}^{t/2}\!dt\!\int_{-t/2}^{t/2}\!du\,{\rm re}[f^*(t_+)f^*(u_-)f(t_-)f(u_+ ) ] \right),\end{aligned}\ ] ] where we have used the mean - squared values of @xmath40 and @xmath41 . now , by exploiting @xmath68 and some trigonometric identities , we can reduce the preceding expression to @xmath69 . \label{ctilde}\ ] ] at this point we are ready to compare our classical - light theory with the experimental results from @xcite . there it is shown that @xmath70 leads to" +"the gammev chameleon afterglow search ( chase ) reported seeing an anomalous afterglow in their apparatus after having shone a high - power pulsed laser into the bore of a cryogenic vacuum chamber immersed in a magnetic field @xcite . the experiment was designed to produce a population of chameleon particles ( scalar or pseudoscalar particles with possible couplings to matter and electromagnetic fields ) via induced photon - chameleon oscillations within the magnetic field . after turning off the laser , this chameleon population would diminish as individual particles re - convert into photons and escape the apparatus @xcite . this afterglow of photons would indicate the presence of chameleon particles , provided that the properties of the regenerated photons matched the predictions from the chameleon field theory . the fact that an afterglow signal was observed ( hereafter called the `` orange glow '' for reasons described shortly ) was troubling as various properties of the orange glow were not consistent with theoretical predictions . chameleon theory predicts an afterglow with specific dependence on the laser polarization and the magnetic field strength , as well as equivalent ingoing and outgoing photon energies . by contrast , the orange glow had none of these properties , being independent of both laser polarization and magnetic field , having outgoing photons at a variety of wavelengths dominated by contributions in the orange and red portions of the spectrum ( hence the name ) , and having an unanticipated dependence on the temperature of the vacuum chamber . in this article we present all of our data that pertains materially to the characterization of the orange glow signal . we do not claim any specific explanation of the source or cause of the orange glow , though the dependence upon temperature suggests strongly that the effect is due to some chemical or material property that is excited by the input laser . indeed , some of the general properties of the orange glow match luminescent behavior seen in some vacuum products @xcite , though the details differ . the ultimate sensitivity of the chase experiment was not limited by the presence of the orange glow , though some modifications to the data analysis software and to the science operations were needed in order to achieve the design goals . the data and discussion presented here may be useful for the design of future experiments that use high intensity light sources in conjunction with single photon detectors in a cryogenic environment . this paper is organized as follows . we discuss the design of the chase apparatus ( [ design ] ) followed by multiple sections presenting data used to characterize the orange glow including some of our initial observations ( [ oddruns ] ) , data taken using broadband optical filters ( [ color ] ) , our initial characterization data and science data ( [ sciruns ] ) , and different vacuum chamber temperatures ( [ tempruns ] ) . all of this information is presented in roughly the order that it was gathered . we discuss potential implications of the orange glow and a comparison with previously observed luminescence from @xcite in the discussion ( [ discussion ] ) . the chase apparatus comprises a laser / optical system , a superconducting magnet , vacuum system , and a single photon detector . a schematic of the apparatus is shown in figure [ schematic ] . the laser is a continuum surelite i-20 nd : yag laser , frequency doubled to 532 nm . it provides approximately 3 watts of green light in 5ns pulses at a rate of 20 hz . the laser was shone into the bore of a superconducting tevatron dipole magnet . the laser light passed through two anti - reflection coated 1 bk7 glass windows held within the bore of the magnet by two brass clips attached to an aluminum support rod . after passing through the magnet , the beam was deflected by a `` pick - off mirror '' into a power meter used to monitor the laser performance . the magnet itself was energized with fields up to 5 tesla ( currents up to 5040 amps ) and as low as 0.05 tesla for science operations . several calibration runs were conducted with no magnetic field . when operating , the @xmath0 cm diameter bore of the magnet cools to 4 kelvin from the liquid helium circulating near the magnet coils ( within the magnet itself the bore has a slightly square - shaped cross section , but that is of little consequence here ) . cryo - pumping by the cold walls of the chamber in conjunction with three ion pumps yielded a vacuum pressure at or below @xmath1 torr . when operating at room temperature the pressure maintained by the ion pumps would occasionally rise slowly by a factor of a few but remained below @xmath2 torr . the photodetector was a hamamatsu h7422p-40 photo multiplier tube ( pmt ) that had @xmath3 hz of dark rate noise . the pmt was housed inside a separate , dark `` pmt box '' and was optically isolated from the laser , magnet bore , and power meter by a gate valve . during operations , the edges of the pmt box were taped closed with metal tape and a dark shroud was laid over the box in order to prevent stray light from the environment from contaminating the measurements . ultimately , when the pmt was exposed to the entire apparatus up to , but not including the `` laser box '' that housed the laser and steering optics there was a @xmath4hz excess of photons due in part to electromagnetic discharge from the ion pumps @xcite . a typical science run consisted of shining the laser through the bore of the magnet and onto the power meter while the pmt was isolated by the `` pmt gate valve '' . following laser operations , a second `` laser gate valve '' located near the laser box was closed , the pmt gate valve was opened , and the pick - off mirror was retracted from the beam path by a pneumatic piston . any photons streaming from the magnet bore and vacuum system were focused onto the pmt photocathode by a lens with a 4 focal length . a custom - made aluminum shutter located between the lens and the pmt was cycled open and closed at intervals of a few seconds ( nominally 15 seconds open and 15 seconds closed , though these times were adjusted frequently during the investigation of the orange glow ) . these optical components are shown in figure [ schematic ] . a final note on the apparatus was the presence of four gate valves . the two optical gate valves ( pmt and laser ) have been mentioned and were used essentially as optical elements to independently isolate the laser and pmt from each other and from the bore of the magnet . two other `` vacuum gate valves '' were located on either side of the magnet bore and were used to isolate the magnet bore from the rest of the vacuum system when needed . two residual gas analyzers ( rgas ) were connected to the apparatus , but were not powered during any of the operations studied herein . these vacuum gate valves , rgas , and pressure gauges are not shown in figure [ schematic ] . the orange - colored afterglow was first seen during a test run of the full apparatus . the magnet was cold but not energized , and all other components were configured for science operations . immediately after observing the glow we ran a series of tests to diagnose its source and cause . checking the seals and materials inside the pmt box and conducting several test runs using the laser and manipulating the different vacuum gate valves showed that the orange glow originated within the bore of the magnet . we ran a series of tests to determine how much illumination was required in order to saturate the orange glow signal including several runs with increasingly shortened laser operations and some where the q - switch timing on the laser was changed in order to reduce its output power . visual inspection of the pmt output showed no noticeable difference between operating the laser for a full 15 minutes and operating it for as little as 15 seconds ( roughly the limit of the operation software ) . adjusting the q - switch until the average power was reduced to 0.2 watts with an exposure time of 100 seconds finally produced a noticeable drop in the orange glow amplitude . .list of relevant parts . [ cols=""<,<,<"",options=""header "" , ] we ran a series of tests of the different materials that may have had some residue inside the magnet bore , as well as some spare optical elements . these elements as well as some of the optical filters that we used to diagnose the color content are shown in table [ parts ] . placing either an additional interior window ( identical to the 1 "" windows located inside the magnet ) or an additional vacuum window in the beam path inside the pmt box showed no increase in the orange glow . had the orange glow come from the windows we would have expected a @xmath5 increase in the signal . samples of kimwipes , apiezon - l o - ring grease , ball vac kote 44147 , and leybold he-175 roughing pump oil all vacuum materials that are commonly used with the tevatron magnets were placed in the pmt box near the power meter and pick - off mirror ( but not directly in the beam itself ) and illuminated with scattered laser light from the pick - off mirror . we observed no qualitative increase in the orange glow . an important note , however , is that the pmt box is at room temperature . no tests of these vacuum materials or the 1 , interior window were done at temperatures near 4 k. nevertheless , the vacuum windows are always at room temperature and can therefore be ruled out as the orange glow source . following science operations we noted a significant temperature dependence of the orange glow . previous studies of the luminescence of vacuum products ( particularly apiezon products ) have shown such temperature dependence @xcite . however , there are some slight differences between the effects reported in @xcite and the orange glow which may indicate that the orange glow is either a somewhat different effect , comes from a different material , or that it is produced in a somewhat different manner . we discuss these differences in the observations below , but first present what we know about the orange glow signal . we conducted a series of tests using several optical filters inserted between the focusing lens and the pmt . the expected chameleon afterglow signal would be at the same 532 nm green wavelength of the incident laser . our first test used a 10nm - wide filter centered at 530 nm , where the chameleon signal was expected . following that test we used 40nm - wide filters centered at 550 nm , 600 nm , 650 nm , and 700 nm as well as a short - pass filter that nominally transmits visible light with wavelengths shorter than 550 nm . the part numbers for these filters are given in table [ parts ] . for each color test we operated the laser for three minutes after which afterglow data were aquired for roughly two minutes . the data reduction and calculation of errors is done following the procedures outlined in @xcite . the resulting time series for each of the six filters is shown in figure" +"scale - free networks have been widely studied during the recent years , mainly because of their connection to a plethora of real - world structures @xcite . these networks are made by nodes connected to each other via links , which may be directed or undirected ( in the present work we only deal with undirected links ) . studies of their structure show that most of them possess the small - world property , i.e. the mean path length is extremely small and every node can be reached by following a path consisting from a very small number of nodes , as compared to the case of lattice systems . a special feature , though , that distinguishes this class of networks is the fact that the probability distribution for a node to have @xmath5 links to other nodes obeys a power law : @xmath6 where @xmath7 is a parameter that measures how densely connected a network can be . there is a wide range of real - life networks @xcite that have been shown to follow this power - law form in their connectivity , including networks in nature , such as the cell , metabolic networks and the food web , artificial networks such as the internet , the www and power grids , or even social networks , such as sexual partnership networks . the scale - free networks , termed after the absence of a characteristic typical node connectivity , exhibit many unusual properties as compared to simple lattice models , random graphs , or even small - world ( watts - strogatz @xcite ) networks . this scale - free character results in the existence of a small number of nodes which are connected to a large number of other nodes . these super - connected nodes ( termed ` hubs ' ) have been shown to have a central place in the interpretation of many of the network properties . a lot of work has been devoted in the literature to the study of static properties of the networks , while interest is growing for dynamical properties on these networks . recently @xcite , we presented results for the absence of kinetic effects in reaction - diffusion processes taking place on scale - free networks . in this work , we study a number of random walk properties , including mean - squared displacement , network coverage , and trapping processes on scale - free networks of varying connectivities . trapping has been considered in the past as a model for energy transfer , but also in a more general frame in the context of networks , as a model for the probability of reaching targets located on the network in a given concentration via random moves @xcite . it is of interest , thus , to study the mechanism , the effects of connectivity , concentration , size , etc on such structures that exhibit these unique properties . our results refer to small to moderate time regimes , where we are still far from the asymptotic limit . this limit has been known to be very hard to reach in regular lattices , too , and can not be predicted by direct simulation techniques . one of the most basic quantities in the random walk theory is the mean - squared displacement @xmath8 of a particle diffusing in a given space , which is a measure of the distance @xmath9 covered by a typical random walker after performing @xmath2 steps . in most cases , this quantity is described by an expression of the form : @xmath10 the value of the parameter @xmath11 classifies the type of diffusion into normal linear diffusion ( @xmath12 ) , sub - diffusion ( @xmath13 ) , or super - linear diffusion ( @xmath14 ) . of course , when we consider distinct time steps and nearest neighbor lattice hops the maximum value of @xmath11 can be 2 , i.e. a completely biased walk where the random walker continuously moves away from the origin . recently @xcite , the mean squared displacement was studied in small world networks , where it was shown that diffusion is linear and results were found to collapse under a proposed scaling . the behavior of a random walk is also characterized by the coverage of the space , as expressed by the average number of distinct sites visited @xmath15 after @xmath2 steps . in regular euclidean lattices this quantity follows a power law with the number of steps , except in the case of two dimensions , where logarithmic corrections appear in the denominator ( @xmath16 ) . in one dimension @xmath17 , and in dimensions higher than two @xmath18 , and the number of sites visited grows linearly with the number of steps @xmath2 , since the random walker practically visits at each step a new site . in infinite dimensions , of course , the number @xmath15 of visited sites is equal to @xmath2 , since there is no revisitation of sites during the walk , and the walker covers the largest possible area . in small - world networks a scaling ansatz was proposed @xcite , which was verified by simulations , and @xmath15 shows a transition from a slope 0.5 ( one - dimensional behavior ) to a slope 1 ( @xmath19 behavior ) . an important process related to random walk theory is trapping @xcite . trapping reactions have been widely studied in the frame of physical chemistry , as part of the general reaction - diffusion scheme . the general idea includes two different species a and b , which diffuse freely in a given space and upon proximity they react according to a+b@xmath20b . many different variations describe a plethora of physical phenomena . in this paper we deal with the special case of the trapping problem where b particles are immobile . the simplest mean - field analytical treatment predicts a simple exponential decay in the density of a s , while the earlier contributions to the subject go back to smoluchowski @xcite , who was the first to attempt to relate the macroscopic behavior with the microscopic picture by taking into account local density fluctuations . however , over the years a lot of work @xcite has been devoted to the trapping problem which , even in its simplest form , was shown to yield a rich diversity of results , with varying behavior over different geometries , dimensionalities and time regimes . the main property monitored during such a process is the survival probability @xmath1 , which denotes the probability that a particle a survives after performing @xmath2 steps in a space which includes traps b with a concentration @xmath0 . it is well - known that @xmath21 behaves differently in different dimensions , as well as in different time - regimes . the problem was studied in regular lattices and in fractal spaces@xcite , and , recently , in small - world networks by blumen and jasch @xcite . the simplest treatment of the trapping problem on a lattice assumes that when a random walker has performed @xmath2 steps and has visited @xmath22 different lattice sites at least once , the probability that it has not yet been trapped is equal to @xmath23 , where @xmath0 is the trap concentration . when this quantity is averaged over all different possible walks and trap configurations the resulting survival probability will be equal to @xmath24 where @xmath25 a simplification of this equation was first proposed by rosenstock @xcite and simply substitutes the above expression with the typical value of the distribution , i.e. @xmath26 this approximation has the advantage that the mean value of the number of sites visited @xmath27 is well known @xcite for practically all dimensionalities ( including e.g. fractal ones ) . notice that the rosenstock approximation does not necessarily imply a simple exponential decay , except in the case where @xmath28 . the formula predicts simple exponential decay of the survival probability with the number of steps @xmath2 only for @xmath29 , and exponential dependence on @xmath30 in @xmath31 . in 2 dimensions the predicted behavior is rather complex , with logarithmic corrections in the exponent . the applicability of eq . ( [ rosen ] ) is limited to short - times and/or not too large trap concentrations . when the survival probability becomes low enough , this expression deviates significantly from the correct behavior . a significant improvement was possible by the use of averaged quantities , known as cumulants , where the averaged quantity of eq . ( [ exact ] ) can be written as a function of the cumulant generating function @xcite : @xmath32 where @xmath33 are the cumulants , which are associated to the moments of @xmath22 , e.g. @xmath34 , @xmath35 , etc . the expression ( [ exact ] ) for the survival probability then simply becomes @xmath36 improved accuracy can be obtained upon increasing the truncation order @xmath37 . in theory , the knowledge of all the moments ( @xmath38 ) for the @xmath22 distribution is required for the use of ( [ cum_gf ] ) . these moments are known analytically only in one - dimensional lattices , while for @xmath39 usually the first 2 - 4 moments are used . a detailed analytical treatment of the problem was performed by donsker and varadhan @xcite , who were able to predict the asymptotic behavior of the survival probability as @xmath40 the positive constant @xmath41 depends only on the dimensionality and the structure of the lattice . this asymptotic expression does not provide any information on when the asymptotic limit is reached . since it has been observed that the rosenstock approximation describes quite well the high-@xmath21 regime , it is obvious that a crossover to the donsker - varadhan behavior will take place . the location of this crossover has been studied in detail @xcite , and it was shown that only with indirect methods it is possible to reach the asymptotic limit . this asymptotic behavior has also been explained via heuristic arguments . the slow relaxation of @xmath21 at long times is due to an interplay of two different factors . first , mean - field treatments assume a uniform trap distribution over the entire space . this is not strictly true , though , and for large enough sizes it is possible to find very extended trap - free regions . a random walker in such a region will survive for extremely long times compared to walkers in normal regions and will thus determine the asymptotic behavior . the second factor is due to unusually ` compact ' random walks , which revisit many times the same sites , and thus result to a very small value of @xmath22 , even at longer times . recently , a number of papers were published concerning trapping on a version of the small - world networks @xcite . these networks , first proposed as a model by watts and strogatz @xcite , are one - dimensional rings where additional links are inserted between two random sites with a given probability . it was shown that the results represent a fine interplay between pure order and pure disorder statistics . initially , the walkers feel only the presence of the one - dimensional lattice , but at longer times the behavior of the survival probability follows that of an open tree structure . the decays of the survival probability were clearly not exponential , and the cumulants description did not yield accurate coincidence with the numerical results in all of the studied cases . in this work , we extend the above mentioned random walk problems ( mean - squared displacement , coverage , and trapping ) in the case where the underlying structure is a scale - free network , obeying a power -" +"the reidemeister torsion is an invariant for a cw - complex and a representation of its fundamental group . in other words , this invariant associates with the local system for a representation of the fundamental group . originally the reidemeister torsion is defined if the local system is @xmath4 , i.e. , all homology groups vanish . however we can extend the definition of the reidemeister torsion to non - acyclic cases @xcite . in this paper , we focus on the non - acyclic cases . it is known that the fox calculus plays important roles in the study of the reidemeister torsion @xcite . the many results were obtained by using the fox calculus for the acyclic reidemeister torsion . in particular , there are important results related to the alexander polynomial in the knot theory @xcite . the fox calculus is also important for non - acyclic cases @xcite . it is related to the cohomology theory of groups . this paper contributes to the study of the non - acyclic reidemeister torsion by using the fox calculus . our purpose is to apply the fox calculus for the acyclic cases to the study of the non - acyclic reidemeister torsion by using a relationship between the acyclic reidemeister torsion and the non - acyclic one . our main theorem says that the non - acyclic reidemeister torsion for a knot exterior is given by the differential coefficients of the twisted alexander invariant of the knot . the twisted alexander invariant of a knot is the acyclic reidemeister torsion and expressed as a one variable rational function @xcite . a conjecture due to j. dubois and r. kashaev @xcite will be solved in @xcite by using our main theorem . in the latter of this paper , we apply this relationship to study the reidemeister torsion for the pair of a @xmath3-bridge knot and @xmath1-representation of its knot group . we give an explicit expression of the non - acyclic reidemeister torsion associated to @xmath5 knot . this is a new example of calculation of the non - acyclic reidemeister torsion . furthermore , we investigate where the non - acyclic reidemeister torsion associated to a @xmath3-bridge knot has critical points . note that the non - acyclic reidemeister torsion is parametrized by the representations of a knot group . moreover this reidemeister torsion turns into a function on the character variety of the knot group . we will see that the critical points of the non - acyclic reidemeister torsion associated to a @xmath3-bridge knot are binary dihedral representations and these representations are related to the geometry of the character variety of a @xmath3-bridge knot group . this paper is organized as follows . in section [ review_twisted_torsion ] , we review the reidemeister torsion . in particular , we give the notion of the non - acyclic reidemeister torsion of knot exteriors @xcite . section [ main_theorem ] includes our main theorem on a relationship between the non - acyclic reidemeister torsion and the twisted alexander invariant for knot exteriors . we give a formula of the non - acyclic reidemeister torsion for a knot exterior by using a wirtinger presentation of a knot group . in section [ applications ] , we apply the results of section [ main_theorem ] to study the non - acyclic reidemeister torsion for a @xmath3-bridge knot group and @xmath1-representation of its knot group . in this paper , we use the following notations . * @xmath6 is the field @xmath7 or @xmath8 . * @xmath9 is the lie group @xmath1 ( resp . @xmath10 if @xmath6 is @xmath7 ( resp . @xmath8 ) . the symbol @xmath11 denotes the lie algebra of @xmath9 . * @xmath12 denotes the adjoint action of @xmath9 to the lie group @xmath11 . * @xmath13 is a product on the @xmath11 , which is defined by @xmath14 * @xmath15 denotes an @xmath16-dimensional vector space over @xmath6 . * for two ordered bases @xmath17 and @xmath18 in a vector space , we denote by @xmath19 the base - change matrix from @xmath20 to @xmath21 satisfying @xmath22 . we write simply @xmath23 $ ] for the determinant @xmath24 of @xmath19 . we deal with ordered bases in this paper . we recall the definition of the torsion . let @xmath25 be a chain complex over @xmath6 . for each @xmath26 let @xmath27 denote the kernel of @xmath28 , @xmath29 the image of @xmath30 and @xmath31 the homology group @xmath32 . we say that @xmath33 is _ acyclic _ if @xmath31 vanishes for every @xmath26 . let @xmath34 be a basis of @xmath35 and @xmath36 be the collection @xmath37 . we call the pair @xmath38 a _ based chain complex _ , @xmath36 the preferred basis of @xmath33 and @xmath34 the preferred basis of @xmath35 . let @xmath39 be a basis of @xmath31 . we construct another basis as follows . by the definitions of @xmath27 , @xmath29 and @xmath31 , the following two split exact sequences exist . @xmath40 @xmath41 let @xmath42 be a lift of @xmath43 to @xmath35 and @xmath44 a lift of @xmath31 to @xmath27 . then we can decompose @xmath35 as follows . @xmath45 we choose @xmath46 a basis of @xmath29 . we write @xmath47 for a lift of @xmath46 and @xmath48 for a lift of @xmath39 . by the construction , the set @xmath49 forms another ordered basis of @xmath35 . we denote simply this new basis by @xmath50 . then the definition of @xmath51 is as follows . @xmath52^{(-1)^{i+1 } } \in { { \mathbb f}}^*.\ ] ] it is well known that @xmath51 is independent of the choices of @xmath53 , the lifts @xmath54 and @xmath55 . we also define the torsion @xmath56 with the sign term @xmath57 as follows @xcite @xmath58 here @xmath59 where @xmath60 and @xmath61 . let @xmath62 be a finite connected cw - complex and @xmath63 its universal covering with the induced cw - structure . since the fundamental group @xmath64 acts on @xmath63 by the covering transformation , the chain complex @xmath65 has a natural structure of a left @xmath66$]-module . we denote by @xmath67 a homomorphism from @xmath64 to @xmath9 . we regard the lie group @xmath68 as a right @xmath66$]-module by @xmath69 . we use the notation @xmath70 for @xmath11 with the right @xmath66$]-module structure . following @xcite , we introduce the following notations . set @xmath71 where @xmath72 is @xmath73 and @xmath74 is a surjective homomorphism from @xmath64 to the multiplicative group @xmath75 . note that @xmath76 . we call @xmath77 _ the @xmath70-twisted chain complex _ and @xmath78 _ the @xmath79-twisted chain complex _ of @xmath62 . we also denote by @xmath80 the @xmath6-module consisting of the @xmath64-equivalent homomorphisms from @xmath81 to @xmath11 , i.e. , a homomorphism @xmath82 satisfies @xmath83 for @xmath84 . we call @xmath80 _ the @xmath70-twisted cochain complex _ of @xmath62 . @xmath85 and @xmath86 denote the homology and cohomology groups of the @xmath70-twisted chain and cochain complexes . we keep the notation of the previous subsection . let @xmath87 be the set of @xmath26-dimensional cells of @xmath62 . we take a lift @xmath88 of the cell @xmath89 in @xmath63 . then , for each @xmath26 , @xmath90 is a basis of the @xmath66$]-module @xmath91 . let @xmath92 be a basis of @xmath11 . then we obtain the following basis of @xmath93 : @xmath94 when @xmath95 is a basis of @xmath96 , we denote by @xmath97 the basis @xmath98 of @xmath99 . then @xmath100 is well defined . furthermore adding a sign - refinement term into @xmath101 , we define _ the reidemeister torsion _ of @xmath102 as a vector in some @xmath103-dimensional vector space as follows . let @xmath104 be the basis over @xmath7 of @xmath105 . choose an orientation @xmath106 of the real vector space @xmath107 and provide @xmath108 with a basis @xmath109 such that each @xmath39 is a basis of @xmath110 and the orientation determined by @xmath111 agrees with @xmath106 . let @xmath112 be either @xmath113 or @xmath114 according to the sign of @xmath115 . then we define the reidemeister torsion @xmath116 by @xmath117 where @xmath118 and @xmath119 here @xmath120 means the dual space of a vector space @xmath15 and the dual basis of @xmath118 is @xmath121 where @xmath122 is the dual element of @xmath123 . we made some choices in the definition of @xmath116 . however the following well - definedness is known @xcite : * the sign of @xmath116 is determined by the homology orientation @xmath106 i.e. , if we choose the other homology orientation , then the sign of @xmath116 changes ; * @xmath116 does not depend on the choice of the lift @xmath124 for each cell @xmath89 ; * @xmath116 does not depend on the choice of the basis @xmath97 in @xmath125 . we also have the following well - definedness . if the euler characteristic of @xmath62 is equal to zero , then @xmath116 does not depend on the choice of the basis of @xmath11 . this follows from the definition . similarly we define the reidemeister torsion of the twisted @xmath79-chain complex . we define @xmath126 by @xmath127 @xmath126 has the indeterminacy of @xmath128 where @xmath129 . this indeterminacy is caused by the choice of the lifts @xmath130 and the action of @xmath74 . it is also known that the sign refined torsion @xmath131 has the invariance under simple homotopy equivalences , and that it satisfies the following _ multiplicativity property_. suppose we have the following exact sequence of based chain complexes : @xmath132 where these chain complexes are based chain complexes which consist of vector spaces with bases . here we denote bases of @xmath133 by @xmath134 and a lift of @xmath135 to @xmath33 by @xmath136 . for each @xmath26 , fix the volume forms on @xmath137 by using given bases and choose volume forms on @xmath138 and @xmath139 . there exists the long exact sequence in homology associated to the short exact sequence @xmath140 : @xmath141 we denote by @xmath142 this acyclic complex . note that this acyclic complex is a based chain complex . [ m_property ] we have @xmath143 where @xmath144 \in { { \mathbb z}}/2{{\mathbb z}}.\end{aligned}\ ] ] let @xmath145 be a finitely generated group and we denote by @xmath146 the space of @xmath9-representations of @xmath145 . we define the topology of this space by compact - open topology . here we assume that @xmath145 has the discrete topology and the lie group @xmath9 has the usual one . a representation @xmath147 is called _ central _ if @xmath148 . a representation @xmath67 is called _ abelian _ if its image @xmath149 is an abelian subgroup of @xmath9 . a representation @xmath67 is called _ reducible _ if there exists a proper non - trivial subspace @xmath150 of @xmath151 such that @xmath152 for any @xmath153 . a representation @xmath67 is called _ irreducible _ if it is not reducible . we denote by @xmath154 the subset of reducible representations and by @xmath155 the subset of irreducible ones . note that all abelian representations are reducible . the lie group @xmath9 acts on @xmath146 by conjugation . we write @xmath156 $ ] for the conjugacy class of @xmath157 , and we denote by @xmath158 the quotient space @xmath159 . if @xmath9 is @xmath1 , then one can see that the reducible representations are exactly abelian ones . note that this does not hold for the case of @xmath2-representations . the action by conjugation of @xmath1 on @xmath160 factors through @xmath161 . this action is free on the @xmath162 . we set @xmath163 . if @xmath9 is @xmath2 , then the quotient space @xmath164 is not hausdorff in general . following @xcite , we will focus on the _ character variety _ @xmath165 which is the set of @xmath166 of @xmath145 . associated to the representation @xmath167 , its character @xmath168 , defined by @xmath169 . in some sense , @xmath170 is the" +"deformations of the bosonic heisenberg algebra by parameters have known successful achievements in mathematical physics @xcite-@xcite and in nonlinear physics ( e.g. nonlinear quantum optics ) @xcite-@xcite . one of the simplest deformation of the bosonic algebra , a one parameter @xmath0-deformation , was introduced by arik and coon @xcite and is defined by @xmath10 clearly , one recovers the ordinary fock algebra of the harmonic oscillator at the limit @xmath11 , with then @xmath12=\mathbb{i}$ ] . the most of studies pertaining to such deformations are made with the parameter @xmath130,1]$ ] . however , in @xcite , a study was performed even for complex values of @xmath0 . concerning the issue of convergence , infinite products and deformed exponential series require at least that the modulus @xmath14 . this leads to the consideration that @xmath15 , with @xmath16 the unit complex disc but the zero . keeping in mind these last remarks , nothing prevents to perform the following limit @xmath17 reminiscent of a fermionic algebra @xcite-@xcite . it then raises many natural questions . is it possible to understand the generators associated to this limit as fermions ? then , in the case of a positive answer , is there a mapping from the bosonic operators ( defined for @xmath18 ) to fermionic ones ( defined for @xmath19 ) , i.e. a kind of supersymmetry ? recent years , many investigations on @xmath0-deformed algebras and supersymmetry have been undertaken dealing with @xmath0-deformed supersymmetric factorization @xcite or differential representation , intertwining properties and coherent states @xcite ( and more references therein ) . nevertheless , as far as we can establish , none of them focuses on the complete study of the product of these deformed algebras for different parameters @xmath0 . so doing , one will immediately generate a full deformed universal algebra of all different deformed generators acting on a unique representation hilbert space . we propose to investigate how the notions of @xmath1 grassmann grading and supersymmetry can be extended to this multi - deformed enveloping algebra . in this paper , we introduce the notion of @xmath0-deformed grading on the enveloping algebra generated by all products in different deformed heisenberg algebras . this notion generalizes the ordinary grassmann grading and , moreover , by defining a generalized @xmath0-graded bracket , one is able to recover , in each subalgebra , the correct structure for bosonic , fermionic , @xmath1 graded and basic deformed bosonic algebras . the extension of grassmann parity affords us to understand ordinary associative superalgebras and their @xmath1 graded structure ( the usual framework of supersymmetry ) as limit algebras when the parameter @xmath20 . we then determine the modified supersymmetric hamiltonian and its deformed supercharges mapping some deformed fermions on deformed bosons . the paper s outline is as follows . the following section is dedicated to the definition and basic properties of the @xmath0-deformation of the heisenberg algebra in the sense of arik and coon , for complex parameter @xmath0 , and its representation . the limit @xmath2 is clarified . afterwards , section 3 addresses the algebraic settlement of the deformed structure producing the general @xmath0-deformed grading . the particular case of ordinary grassmann parity is discussed . section 4 investigates the extended notion of supersymmetry on the enveloping algebra . the specific limit @xmath21 , producing a modified version of the ordinary supersymmetry , is also discussed . the paper ends by some remarks in section 5 and an appendix provides useful identities and illustrations . let us consider the arik and coon deformation of the heisenberg algebra @xcite @xmath22 with parameter a complex number @xmath0 . if we regard @xmath23 as the adjoint of @xmath24 , it follows that , by hermitian conjugation of ( [ qdef0 ] ) , @xmath25 . by simple substraction of these equations , one ends with @xmath26 from the positivity of @xmath27 . hence , @xmath0 should be a real parameter . however , introducing a new operator @xmath28 , let us reconsider the same kind of deformed structure , namely @xmath29 and relax the previous condition of adjoint property between @xmath24 and @xmath28 . then , nothing can be said , _ a priori _ , on the parameter @xmath0 . we will place ourself in this general situation such that , @xmath30 , @xmath31 . all the following main equations are again valid outside the unit disc . only the notion of convergence of functions series and infinite products involved in deformed special function theory has to be reconsidered . we are not dealing with these ideas here , but we want , as much as possible , to have a theory with interesting properties for the theoretician community . ] @xmath320,1],\;\ ; \varphi_q \in [ 0,2\pi[.\end{aligned}\ ] ] in order to define the power function of @xmath0 , namely @xmath33 , one uses the complex form of the exponential function @xmath34 , where @xmath35 stands for the principal branch of complex logarithm . a realization of the algebra ( [ qdef ] ) is also well known . to construct it , one starts with the ordinary bosonic operators @xmath36 and @xmath37 , fulfilling @xmath12=\mathbb{i}$ ] with the number @xmath38 , generating the ordinary number operator in the fock hilbert space @xmath39 . then we define @xmath40_q}{n+1}}a|n\rangle,\quad a_q^\natural |n\rangle=\sqrt{\frac{[n]_q}{n}}a^\dagger|n\rangle,\quad [ n]_q = \frac{1-q^n}{1-q},\end{aligned}\ ] ] where one refers to @xmath41_q$ ] as the @xmath0-basic number of the theory . note that @xmath41_q$ ] is not necessarily self - adjoint . indeed , @xmath42_q)^\dag=[n]_{\bar q}$ ] , which is not @xmath41_q$ ] unless @xmath0 is real . the adjoint of the operator @xmath24 can be expressed as @xmath43_{\bar q}}{n}}a^\dagger \label{adjoi}\end{aligned}\ ] ] from which it appears possible to define naturally a self - adjoint deformed number operator as @xmath44_{\bar q}[n]_q}}$ ] . from ( [ adjoi ] ) , a relation between @xmath45 and @xmath28 can be inferred : @xmath46 we are then in position to define properly the unary operation @xmath47 which is the adjoint operation composed with the complex conjugation . the operator @xmath48 , viewed as a matrix , can be understood as the transpose of @xmath24 . moreover , it can be checked that @xmath49 , therefore @xmath47 is an involution ; we also have @xmath50 . for a real parameter @xmath0 , the definitions of @xmath23 and @xmath51 coincide . let us briefly mention the limit @xmath52 . the corresponding basic number @xmath41_0 $ ] proves to be the constant operator @xmath53 . this implies that @xmath54 and @xmath55 are mutually inverse in the fock space without the vacuum @xmath56 . as a result of the triviality of the @xmath57-commutator , the @xmath57-deformed algebra is again a lie algebra . then the enveloping algebra over @xmath58 becomes a division algebra ( other relations concerning division algebras built over the heisenberg generators are available in @xcite ) . let us focus now on the limit @xmath2 of the algebra ( [ qdef ] ) . this limit can be written as @xmath59 a prime remark would be that , recalling that @xmath31 , the above limit could be performed only by avoiding the forbidden value @xmath60 ; this can be done by varying continuously @xmath0 along a straight line if @xmath0 does not belong to the segment @xmath610,1]$ ] . in the case @xmath130,1]$ ] , then the same limit can be only made by choosing a contour through the complex plane . noting that , in any state @xmath62 , @xmath63_{-1}|n\rangle = \lim_{q\to -1 } [ n]_q |n\rangle = \frac{1-(-1)^n}{2 } |n\rangle = \left\{\begin{array}{cc } 0 , & { \rm if}\ ; n=2p \\ 1\,|n\rangle , & { \rm if}\ ; n=2p+1 \end{array}\right . \label{limn}\end{aligned}\ ] ] then we infer the following representation for the operators @xmath64 let us recall that a fermionic algebra is usually defined by a set of algebraic relations @xmath65 the anticommutation rule is already satisfied by the pair @xmath66 . checking , that for any @xmath67 , @xmath68_q[n]_q}|n-2\rangle$ ] , @xmath69_q[n+2]_q}|n+2\rangle$ ] , one infers from ( [ limn ] ) that , indeed , for any state , @xmath70 and @xmath71 . thus , the pair @xmath66 is close to what one usually refers to as a fermionic algebra . for this reason , we will refer henceforth to these operators to fermions and to their algebra , to a fermionic algebra . here , more rigorously , the operators @xmath66 are fermionic operators with an infinite dimensional representation space which is a direct sum of ordinary two dimensional fermionic representation spaces . the notion of @xmath1 grassmann grading for associative complex superalgebras @xcite will find , in the next lines , an extension according to the present @xmath0-deformed study . but before , for the sake of rigor , let us put in algebraic terms the definition of the deformation of the heisenberg algebra ( [ qdef ] ) . * building a @xmath0-grading on the enveloping algebra . * for all @xmath67 , we introduce the deformed complex heisenberg algebra with its three generators and deformed commutator as the pair @xmath72_q\right ) . \label{hesdef}\end{aligned}\ ] ] some remarks are in order at this stage . first , the deformed heisenberg algebra @xmath73 is not a lie algebra unless that one considers the limit points @xmath74 . the jacobi identity fails to be satisfied in the general situation when @xmath75 . note also that these algebras are not disjoint since @xmath76 , for @xmath77 . the data of the pair ( [ hesdef ] ) are equivalent to the data of a complex vector space @xmath73 and a constraint ( equivalence relation ) @xmath78_q=\mathbb{i}$ ] on the tensor algebra built out of its generators . next , let us give the definition of the @xmath0-grading of generators of any @xmath73 and find an extension for any element of the enveloping algebra spanned by all @xmath73 s , @xmath67 . this concept will be introduced by the data of two attributes related to the parameters @xmath0 : the `` degree '' , denoted by @xmath79 , and the `` radius '' , denoted by @xmath80 . by convention , elements of @xmath81 are of degree @xmath82 and we define the degree of the generators of @xmath73 as @xmath83 given a generator of @xmath73 , its degree becomes a real parameter in the segment @xmath84 which can be viewed as the normalized phase of the deformation parameter @xmath0 . for instance , the degree of an ordinary ( heisenberg ) boson is @xmath85 , while the degree of the operators @xmath86 reproducing a well defined notion of @xmath1 grassmann parity for these limit . we will characterize the generators of @xmath73 , by another quantity that we will refer to as its `` radius '' or `` length '' which is nothing but @xmath87 given the modulus @xmath88 of the deformation parameter @xmath0 . at this stage , the following deformed bracket for elementary generators can be defined @xmath89_{q , q'}:= x_{q}\,y_{q ' } - g(q , q')y_{q'}\,x_{q},\qquad g(q , q'):=e^{i\pi|x_{q}||y_{q'}|}\ell(x_{q})\ell(y_{q ' } ) . \label{gradef}\ ] ] a quick verification , using ( [ deg ] ) and ( [ leng ] ) , yields the following limits @xmath90_{1,1 } = [ a_{1},a^\dag_{1}]_{q=1}= a_{1 } a^\dag_{1 } - a^\dag_{1 } a_{1 } = \mathbb{i } , & & \label{com}\\ { \rm ( fermion)}\;\ , g(-1,-1)=-1 : \;\,[a_{-1},a^\dag_{-1}]_{-1,-1 } = [ a_{-1},a^\dag_{-1}]_{q=-1}= a_{-1 } a^\dag_{-1 } + a^\dag_{-1 } a_{-1 } = \mathbb{i } , & & \label{antic}\\ { \rm ( q - def . ) } \;\,g(q , q)=q : \;\,[a_{q},a^\dag_{q}]_{q , q } = [ a_{q},a^\dag_{q}]_{q}= a_{q } a^\dag_{q } - qa^\dag_{q } a_{q } = \mathbb{i}.&&\end{aligned}\ ] ] another interesting property of the deformed bracket ( [ gradef ] ) is that it reproduces the @xmath1 graded bracket between fermion and bosons . in other words , in addition to ( [ com ] ) and" +"control refers to the ability to steer a dynamical system from an initial to a final state with a desired accuracy ; optimal control does so with minimum expenditure of effort and resources . a famous example is the apollo space mission where optimal control was used to safely land the spacecraft on the moon . the essence of this control task can be stripped down to a textbook example where students calculate the change in acceleration , that is , the rate of burning fuel , required to reach the moon s surface with zero velocity . this example highlights the central role of optimal control in any type of engineering , its importance being rivaled only by feedback , a subject not covered in this review . in _ quantum _ optimal control @xcite , newton s equations governing the motion of the spacecraft are replaced by the quantum mechanical laws of motion , of course . in contrast , the control , corresponding for example to a radio - frequency ( rf ) amplitude or the electric field of a laser , is assumed to be classical . quantum optimal control represents one variant of quantum control @xcite and is closely related to coherent control @xcite . the latter requires exploitation of quantum coherence , i.e. , matter wave interference . in contrast , quantum control could also refer to inducing a desired dynamics , for example by amplitude modulations that avoid driving certain transitions , without matter wave interference . despite of its prominence in mathematics and engineering @xcite , optimal control was introduced to nmr spectroscopy @xcite and to the realm of matter wave dynamics @xcite only in the 1980s . in the latter case , the idea was to calculate , via numerical optimization , laser fields that would steer a photoinduced chemical reaction in the desired way @xcite . it was triggered by the advent of femtosecond lasers and pulse shaping capabilities that opened up seemingly endless possibilities to create intricate laser pulse trains . while a controlled breaking of chemical bonds was indeed demonstrated soon after @xcite , the pulses were obtained by closed - loop optimizations in the experiments @xcite rather than from theoretical calculations . in experimental closed - loop optimization , a shaped pulse is applied to the sample , and the outcome is measured . based on the outcome , the pulse shape is modified , typically by a genetic algorithm . however , even for a chemical reaction as simple as breaking the bond in a diatomic alkali molecule , the calculated optimized laser field can not directly be used in the experiment @xcite . the reason for this is two - fold : the way how the optimized laser fields are obtained is rather different in theory and experiment . whereas the field in calculations is shaped as a function of time @xcite , experiments employ spectral shaping @xcite . as a result , calculated pulses are often incompatible with experimental pulse shaping capabilities . second , the theoretical modeling is simply not accurate enough . this results in pulses which are optimal for the wrong dynamics and which can therefore not directly be applied in the experiments . these obstacles are not present , or at least much less severe , in other fields of application @xcite . once the timescale of the relevant dynamics is nanoseconds or slower , pulse shaping in the experiment is also done in time domain @xcite . while device response might still be an issue @xcite , the overall approaches in theory and experiment are similar in spirit . moreover , hamiltonians and relaxation parameters may be known much more accurately than is currently the case in photoinduced chemical reactions . a prominent example is nmr where the development of optimal control in theory and experiment went hand in hand , yielding beautiful results , for example on arbitrary excitation profiles @xcite , or robust broadband excitation @xcite . given these observations , quantum information processing ( qip ) and related technologies offer themselves as an obvious playground for quantum optimal control : in these applications , typically the quantum system to be controlled is well characterized , and timescales are sufficiently slow to use electronics for pulse shaping . not surprisingly , quantum optimal control has attracted much interest in these fields over the last decade . this included the adaptation of optimal control tools , for example to gate optimization @xcite , creation of entanglement @xcite , or measurement @xcite . gate optimizations were carried out for almost all qip platforms , notably comprising ions @xcite , atoms @xcite , nitrogen vacancy ( nv ) centers in diamond @xcite , and superconducting qubits @xcite . other qip tasks , such as state preparation @xcite , transport @xcite , and storage @xcite , have also been the subject of optimal control studies . these tasks are not only relevant for quantum computing and communication but also for related applications that exploit coherence and entanglement , for example quantum sensing or quantum simulation . protocols derived with optimal control have by now reached a maturity that allows them to be tested in experiments . examples include the crossing of a phase transition studied with trapped , cold atoms @xcite ; the improvement of the imaging capabilities of a single nv center @xcite ; and the creation of spin entanglement @xcite , quantum error correction @xcite and matter wave interferometry @xcite . all of these examples share a generic feature that is typical for quantum engineering : control over the system , which inevitably also brings about noise , needs to be balanced with sufficient isolation of the desired quantum features . this sets the theme for controlling open quantum systems . traditionally , a quantum system is defined to be open when it interacts with its environment @xcite . this interaction results in loss of energy and phase information . it can be modeled phenomenologically within the semigroup approach or microscopically , by embedding the system in a bath . besides coupling to a bath , the dynamics of a quantum system becomes effectively dissipative also when the system is subject to measurements or noisy controls . dissipative processes pose a challenge to quantum control . at the same time , desired dissipation may act as an enabler for control . we will review control strategies in both cases and then explain how optimal control theory can be used to adapt them to more complex quantum systems . this topical review is organized as follows : section [ sec : oqs ] briefly recalls the basic concepts in the theory of open quantum systems , introducing the distinction between markovian and non - markovian dynamics in sec . [ subsec : marknonmark ] and addressing the issue of gauging success of control for open quantum systems in sec . [ subsec : success ] . the problem of analyzing controllability of open quantum systems , an important prerequisiste to synthesizing control fields , is introduced in sec . [ subsec : controllability ] . progress in the control of open quantum systems is reviewed in sections [ subsec : strategies ] and [ sec : oc - oqs ] with sec . [ subsec : strategies ] dedicated to control strategies that were constructed with analytical methods and sec . [ sec : oc - oqs ] covering numerical optimal control . in sec . [ subsec : oct ] , the numerical methodology is explained in detail for a simple example , followed by a discussion of the modifications required to adapt it to more advanced control targets . the remainder of sec . [ sec : oc - oqs ] reviews applications of numerical optimal control to open quantum systems , starting with examples for fighting or avoiding decoherence in sec . [ subsec : fighting ] . control strategies that rely on the presence of the environment are discussed in secs . [ subsec : cooling ] and [ subsec : exploiting ] . section [ sec : concl ] concludes . the state of an open quantum system is described by the density operator @xmath0 which is an element of liouville space . any theory that aims at the control of an open quantum system is faced with two basic prerequisites the ability to calculate the system s dynamics , @xmath1 , and the ability to quantify success of control . formally , the time evolution of any open quantum system can be described by a dynamical map , @xmath2 which is completely positive and trace preserving ( cptp ) @xcite . the dynamical map is divisible if it can be written as the composition of two cptp maps @xmath3 @xmath4 . if the dynamical map is divisible , the open system s time evolution is memoryless and called markovian . various scenarios can lead to markovian dynamics , weak coupling between system and environment together with a decay of environmental correlations much faster than the timescales of the system dynamics being the most common case @xcite . however , open systems often exhibit pronounced memory effects , in particular in condensed matter experiments , which reflect characteristic features of the environment . the dynamics are then called non - markovian . memory effects are caused by structured spectral densities , nonlocal correlations between environmental degrees of freedom and correlations in the initial system - environment state @xcite . in the markovian case , the dynamics can be described by a master equation in lindblad form @xcite . in general , it needs to be solved numerically to determine @xmath5 . this can be done with arbitrarily high precision @xcite . however , the computational effort may quickly become challenging due to the exponential scaling of the size of hilbert and liouville space . to date , room for improvement seems to be limited @xcite . the situation is worse for non - markovian dynamics , where a unified framework such as the master equation in lindblad form does not exist . a variety of methods has been developed @xcite , each with different assumptions and hence a different range of applicability . they include time - local non - markovian master equations @xcite , stochastic unravellings @xcite , and an auxiliary density matrix approach @xcite . a common feature of these methods is their ability to correctly describe thermalization of the system . slightly different in philosophy are methods which attempt to solve the dynamics of both system and environment @xcite . key is to account only for that part of the environment that is relevant for the system s dynamics , i.e. , for the effective modes , which can be spins or harmonic oscillators . the underlying idea is that of quantum simulation on a classical computer @xcite , where the true environment is replaced by a surrogate one that generates the same dynamics . if one is interested in short times , the number of modes in the surrogate hamiltonian can be truncated with a prespecified error @xcite . longer propagation times than those computationally affordable with exact dynamics of system and environment become possible by separating the environment into two baths , one that is responsible for the memory effects and that is modeled by effective modes as explained above , and a second one that by itself would lead to markovian dynamics only . the secondary bath can be accounted for in terms of a markovian master equation in lindblad form @xcite or via a stochastic unravelling using a single secondary bath mode @xcite . a more comprehensive overview over methods to tackle non - markovian dynamics is found in ref . @xcite . understanding the influence of memory effects requires the ability to quantify them . an obvious way to define a measure of non - markovianity is" +"video streaming applications have become over the past few years the dominant applications in the internet and generate the prevalent part of traffic in today s ip networks ; see for instance guillemin et al . @xcite for an illustration of the application breakdown in a commercial ip backbone network . video files are currently downloaded by customers from large data centers , like google s data centers for youtube files . in the future , it is very likely that video files will be delivered by smaller data centers located closer to end users , for instance cache servers disseminated in a national network . it is worth noting that as shown in guillemin et al . @xcite , caching is a very efficient solution for youtube traffic . while this solution can improve performances by reducing delays , the limited capacity of those servers in terms of bandwidth and computing can cause overload . one possibility to reduce overload is to use bit rate adaptation . video files can indeed be encoded at various bit rates ( e.g , small and high definition video ) . if a node can not serve a file at a high bit rate , then the video can be transmitted at a smaller rate . it is remarkable that video bit rate adaptation has become very popular in the past few years with the specification of mpeg - dash standard where it is possible to downgrade the quality of a given transmission , see schwarz et al . @xcite , sieber et al . @xcite , aorga et al . @xcite , vadlakonda et al . @xcite and fricker et al . adaptive streaming is also frequently used in mobile networks where bandwidth is highly varying . in this paper , we investigate the effect of bit rate adaptation in a node under saturation . we assume that customers request video files encoded at various rates , say , @xmath3 for @xmath4 , with @xmath5 . jobs of class @xmath6 require bit rate @xmath3 . the total capacity of the communication link is @xmath0 . if @xmath7 is the state of the network at some moment , with @xmath8 being the number of class @xmath9 jobs , the quantity @xmath10 has to be less than @xmath0 . the quantity @xmath11 is defined as the _ occupancy _ of the link . the algorithm has a parameter @xmath1 and works as follows : if there is an arrival of a job of class @xmath12 , * if @xmath13 then the job is accepted ; * if @xmath14 then the job is accepted but as a class @xmath15 job , i.e. it has an allocated bit rate of @xmath16 and service rate @xmath17 ; * if @xmath18 , the job is rejected . for @xmath19 , jobs of class @xmath9 arrive according to a poisson process with rate @xmath20 and have an exponentially distributed transmission time with rate @xmath21 additionally , it is assumed that @xmath22 to study this allocation scheme , a scaling approach is used . it is assumed that the server capacity is very large , namely scaled up by a factor @xmath23 . the bit rate adaptation threshold and the request arrival rates are scaled up accordingly , i.e. @xmath24 _ performances of the algorithm . _ our main result shows that , for the downgrading policy and if @xmath25 is chosen conveniently , then 1 . the equilibrium probability of rejecting a job converges to @xmath26 as @xmath23 goes to infinity ; 2 . the equilibrium probability of accepting a job without downgrading it converges to @xmath27 as @xmath23 goes to infinity . see theorem [ theoeq ] and corollary [ corol ] . the above formula gives an explicit expression of the success rate of this allocation mechanism . the quantity @xmath28 , the probability of downgrading requests , can be seen as the `` price '' of the algorithm to avoid rejecting jobs . the scaling has been introduced by kelly to study loss networks . see kelly @xcite . the transient behavior of these networks under this scaling has been analyzed by hunt and kurtz @xcite . this last reference provides essentially a framework to establish convenient convergence theorems involving stochastic averaging principles . this line of research has been developed in the 1990 s to study uncontrolled loss networks where a request is rejected as soon as its demand can not be accepted . when the demand can be adapted to the state of the network , for controlled loss networks , several ( scarce ) examples have been also analyzed during that period of time . one can mention bean et al . @xcite , zachary and ziedins @xcite and zachary @xcite for example . our model can be seen as a `` controlled '' loss networks instead of a pure loss network . controlled loss networks may have mechanisms such as trunk reservation or may allocate requests according to some complicated schemes depending on the state of the network . in our case , the capacity requirements of requests are modified when the network is in a `` congested '' state . contrary to classical uncontrolled loss networks , as it will be seen , the markov process associated to the evolution of the vector of the number of jobs for each class is not reversible . additionally , the invariant distribution of this process does not seem to have a closed form expression . kelly s approach @xcite is based on an optimization problem , it can not be used in our case to get an asymptotic expression of some characteristics at equilibrium . for this reason , the equilibrium behavior of these policies is investigated in a two step process : 1 . transient analysis . we investigate the asymptotic behavior of some characteristics of the process on a finite time interval when the scaling parameter @xmath23 goes to infinity . 2 . equilibrium . the stability properties of the limiting process are analyzed , we prove that the equilibrium of the system for a fixed @xmath23 converges to the equilibrium of the limiting process . for our model , the transient analysis involves the _ explicit _ representation of the invariant distribution of a specific class of markov processes . it is obtained with complex analysis arguments . as it will be seen , this representation plays an important role in the analysis of the asymptotic behavior at equilibrium . it should be noted that related models have recently been introduced to investigate resource allocation in a cloud computing environment where the nodes receive requests of several types of resources . we believe that this domain will receive a renewed attention in the coming years . see stolyar @xcite and fricker et al . @xcite for example . in some way one could say that the loss networks are back and this is also a motivation of this paper to shed some light on the methods that can be used to study these systems . we consider a system in overload . because of bit rate adaptation , requests may be downgraded but not systematically rejected as in a pure loss system . as it will be seen , the stability properties of this algorithm are linked to the behavior of a markov process associated to the occupation of the link . under exponential assumptions for inter - arrival and service times , this process turns out to be , after rescaling by a large parameter @xmath23 , a bilateral random walk instead of a reflected random walk as in the case of loss networks . using complex analysis methods , an explicit expression of the invariant distribution of this random walk is obtained . with this result , the asymptotic expression of the probability that , at equilibrium , a job is transmitted at its requested rate ( and therefore does not experience a bit rate adaptation ) is derived . this paper is organized as follows : in section [ model ] , we present the model used to study the network under some saturation condition . convergence results when the scaling factor @xmath23 tends to infinity are proved in section [ secmod ] . the invariant distribution of a limiting process associated to the occupation of the link is computed in section [ secinv ] by means of complex analysis techniques . applications are discussed in section [ app ] . * acknowledgments * + the authors are very grateful to an anonymous referee for pointing out a gap in the proof of theorem [ theoeq ] in the first version of this work . one considers a service system where @xmath29 classes of requests arrive at a server with bandwidth / capacity @xmath0 . requests of class @xmath9 , @xmath30 , arrive according to a poisson process @xmath31 with rate @xmath20 . a class @xmath9 request has a bandwidth requirement of @xmath3 units for a duration of time which is exponentially distributed with parameter @xmath21 . for the systems investigated in this paper , there is no buffering , requests have to be processed at their arrival otherwise they are rejected . without any flexibility on the resource allocation , this is a classical loss network with one link . see kelly @xcite for example . this paper investigates allocation schemes which consist of reducing the bandwidth allocation of arriving requests to a minimal value when the link has a high level of congestion . in other words the service is downgraded for new requests arriving during a saturation phase . if the system is correctly designed , it will reduce significantly the fraction of rejected transmissions and , hopefully , few jobs will in fact experience downgrading . we introduce @xmath1 , the parameter @xmath2 will indicate the level of congestion of the link . it is assumed that the vector of integers @xmath33 is such that @xmath34 . the condition @xmath16 is used to simplify the presentation of the results and to avoid problems of irreducibility in particular but this is not essential . if the network is in state @xmath7 and if the occupancy @xmath11 is less than @xmath2 , then any arriving request is accepted . if the occupancy is between @xmath2 and @xmath35 , it is accepted but with a minimal allocation , as a class @xmath15 job . finally it is rejected if the link is fully occupied , i.e. @xmath36 . it is assumed that @xmath37 , for @xmath19 , i.e. class 1 jobs are served with the smallest service rate . mathematically , the stochastic model is close to a loss network with the restriction that a job may change its requirements depending on the state of the network . this is a controlled loss network , see zachary and ziedins @xcite . it does not seem that , like in uncontrolled loss networks , the associated markov process giving the evolution of the vector @xmath38 has reversibility properties , or that its invariant distribution has a product form expression . related schemes with product form are trunk reservation policies for which requests of a subset of classes are systematically rejected when the level of congestion of the link is above some threshold . see bean et al . @xcite and zachary and ziedins @xcite for example . concerning controlled loss networks , mathematical results are more scarce . one can mention networks where jobs requiring congested links are redirected to less loaded links . several mathematical approximations have been proposed to study these models . see the surveys kelly @xcite and zachary and ziedins @xcite . in our model , in the language of loss networks , the control is on the change of capacity requirements instead of a change of link . the invariant distribution being , in general , not known , a scaling approach" +"it is well known that radio waves propagating in the interstellar medium ( ism ) are scattered by the irregularities in the galactic electron density . the scattering in turn gives rise to a number of observable phenomena . among others , these include angular broadening and intensity fluctuations ( both in time and frequency ) of compact radio sources . while a nuisance in many radio astronomical observations , these phenomena can be used to investigate the nature of the irregularities in the interstellar plasma density . these density irregularities are in turn believed to follow the fluctuations in the interstellar kinetic and magnetic energies . ideally one would like to invert observations of radio scintillation and scattering to determine the statistics of the plasma density . as noted by narayan ( 1992 ) this inverse problem is not well posed and one must rely on modeling methods . a complete prediction of scintillation observables requires an _ a priori _ knowledge of both the form of the spatial power spectrum of the electron density fluctuations and the distribution of the scattering material along the line of sight . for a given profile of the distribution of the scattering material , one may compare observations and predictions and so constrain the functional form of the spectrum . the power spectrum provides useful insight into the physics of the plasma irregularities . hence a knowledge of the form of the density spectrum becomes central in both predicting scintillation phenomena and understanding the physics of the interstellar plasma . in this paper , we revisit the investigation of the form of the density spectrum . a commonly used model for the density spectrum has been based on a power - law model with a large range between `` inner '' and `` outer '' scales ( e.g. rickett 1977 ) : @xmath1 \ , \mbox{. } \label{eq : extpowerlaw } \ ] ] here @xmath2 is the magnitude of the three - dimensional wavenumber @xmath3 . @xmath4 denotes the strength of fluctuations ( with a weak dependence on distance @xmath5 ) . @xmath6 is the spectral exponent , and @xmath7 and @xmath8 are the inner and outer scales respectively . for @xmath9 , we obtain the _ simple _ power - law model : @xmath10 . armstrong , rickett , & spangler ( 1995 ) have constructed an empirical density spectrum by combining radio scintillation observations in the local ism ( @xmath11 1 kpc ) with measurements of the differential faraday rotation angles and large - scale electron density gradients . they have shown the power spectrum to be consistent with a simple kolmogorov power - law model ( @xmath12 ) over an astronomical 10 orders of magnitude in wavenumber scale ( @xmath13m@xmath14m@xmath15 ) . the kolmogorov spectrum in density suggests a turbulent cascade in the magnetic and kinetic energies . this has lead to several theoretical investigations of the generation and maintenance of hydromagnetic turbulence in the ism ( e.g. pouquet , 1978 ; higdon 1984 & 1986 ; biskamp , 1993 : sridhar & goldreich 1994 ; goldreich & sridhar 1995 and 1997 ) . however , the armstrong et al . study combined observations from many lines of sight and the scatter among them leaves a substantial uncertainty in the exponent @xmath6 . a list of symbols is given in table 3 . in spite of the positive evidence for the simple kolmogorov spectrum , substantial observational inconsistencies remain . for instance , long - term refractive intensity scintillations of some pulsars have modulation indices as much as a factor of 2 larger than predicted by the simple kolmogorov model ( cf.gupta , rickett , & coles 1993 ) . other discrepancies are revealed in the diffractive dynamic spectra of pulsars . on some occasions , periodic fringes are observed , which are not predicted by the simple kolmogorov model ( cf . roberts & ables 1982 ; cordes & wolszczan 1986 ; rickett , lyne , & gupta 1997 ; gupta , bhat & rao , 1999 ) ; in addition , sloping bands in the dynamic spectra often persist longer than predicted by the model ( cf.gupta , rickett , & lyne 1994 ; bhat , rao & gupta , 1999b bhat , gupta & rao , 1999c ) . further for some pulsars , the decorrelation bandwidth has larger amplitude variations than predicted for the kolmogorov spectrum ( bhat , gupta & rao , 1999c ) . such anomalies suggest the presence of large refractive structures giving rise to the focusing and defocusing of the scattered ray bundles . the interference of the ray bundles can also explain the occasional fringes observed in the dynamic spectra of some pulsars . given the relatively frequent occurrence of such events , one can ask whether they can be considered as mere occasional anomalies or should be considered as a widespread phenomenon intrinsic to the spectrum on a grand scale . the observational inconsistencies suggest the need for an enhancement in the power on the large `` refractive '' ( 10@xmath16 m to 10@xmath17 m ) spatial scales relative to the power on the small `` diffractive '' ( 10@xmath18 m to 10@xmath19 m ) scales . there are several means by which this ratio may be enhanced . one is to include the inner scale cut - off in the density spectrum , which reduces the power at small scales ( coles et al . 1987 ) ; these authors proposed inner scales of @xmath20 m. , though this does not correspond to any obvious physical scale . physically , the inner scale corresponds to the scale at which the turbulent cascade dissipates and becomes a source of heating for the plasma ( spangler , 1991 ) . the value of the inner scale is largely unknown . using different methods , spangler & gwinn ( 1990 ) , kaspi & stinebring ( 1992 ) , and gupta et al . ( 1993 ) have reported values for the inner scale ranging from @xmath21 to @xmath22 meters . in proposing the smaller values , spangler & gwinn ( 1990 ) argued that the inner scale is the larger of the ion inertial length , @xmath23 ( where @xmath24 is the alfvn speed , and @xmath25 is the ion cyclotron frequency ) , and the ion larmor radius , @xmath26 ( where @xmath27 is the ion thermal speed ) ; they obtained parameters for the warm ionized medium in reasonable agreement with observations . in a recent discussion , minter & spangler ( 1997 ) have suggested ion - neutral collisional damping and wave - packet steepening as possible dissipation mechanisms for the turbulence in the diffuse ionized gas , which would make the mean - free path for ion - neutral collisions a possible value for the inner scale . however , this is thought to be larger than the maximum values proposed to explain the observations , making it a less convincing dissipation mechanism . observationally , the kolmogorov model with a large inner scale predicts refractive modulation indices consistent with pulsar measurements ( gupta et al . it has also been proposed to explain the occasional periodic fringes , with an inner scale on the order of the fresnel scale ( cordes , pidwerbetsky , & lovelace 1986 ; goodman et al . . however , rickett et al . ( 1997 ) reported a fringe event for the pulsar b0834 + 06 that could not be explained as the effect of a large inner - scale spectrum . the event requires similar conditions to those needed to explain the extreme scattering events ( fiedler et al . 1987 ) . another way to enhance the ratio of the power between the refractive and diffractive scales in the spectrum is to steepen the spectrum with spectral exponents @xmath28 ( blandford & narayan 1985 ; goodman & narayan 1985 ; romani , narayan , & blandford 1986 ) . while power - law spectra with @xmath29 11/3 have a turbulence connotation , spectra with @xmath30 might involve some forms of turbulence , but are also consistent with a distribution of non - turbulent structures with a range of spatial scales . such steep spectra with @xmath31 predict refractive modulation indices close to unity ( goodman & narayan 1985 ) , which is substantially larger than the range 30 to 40 % observed from the nearby pulsars . on this basis rickett & lyne ( 1990 ) and armstrong et al . ( 1995 ) have rejected spectra steeper than 4 for the interstellar plasma . however , the special case of @xmath32 has been given little attention . we can conceive of a power - law model with spectral exponent @xmath32 given by : @xmath33 hereafter , we refer to this model as the `` @xmath32 model . '' blandford & narayan ( 1985 ) briefly discussed this special case without including a cut - off at low wavenumbers . it is interesting to note that even though the kolmogorov spectral exponent @xmath12 is very close to 4 , the @xmath32 model has a very different physical implication . its physical origin has been rarely discussed , and it has not been formally compared with observations . physically , this spectrum suggests the random distribution in location and orientation of discrete discontinuous objects across the line of sight . an `` outer '' scale , @xmath34 , is included to account for the typical size of such objects . the `` inner '' scale here would correspond to the scale of the sharpness of a typical discontinuity . we assume the `` inner '' scale to be smaller than the diffractive scale of scintillations , and hence has no significant effect on the scintillations . the @xmath32 model could characterize stellar wind boundaries , supernova shock fronts , sharp boundaries of hii regions at the strmgren radius , or any plasma `` cloud '' with sufficiently sharp boundaries ( transition regions shorter than the diffractive scintillation scale ) which may cross the line of sight . note that , though turbulence is not necessarily implied by the model , strong turbulence which has steepened to form shocks would also be described by the @xmath32 model . in these models a single discrete object crossing the line of sight could also explain the `` extreme scattering events '' observed in the flux density variations of extra - galactic sources ( e.g. fiedler et al . we note that the analysis of such events have been primarily based on geometrical optics involving a single `` cloud '' ( goodman et al . 1987 ; cordes et al . 1986 ; cordes & wolszczan 1986 ; roberts & ables 1982 ; ewing et al . 1970 ) . our analysis of the @xmath32 model includes the `` wave optics '' effects when the line of sight passes through very many such clouds . the ism is assumed to consist of a random assembly of discrete structures with abrupt density steps which may be independent of each other . if the @xmath32 model were compatible with all of the scintillation observations , it would remove the implication of interstellar plasma turbulence with an inertial range spanning as much as 10 orders of magnitude in scale , which has become the canonical model for iss phenomena . it would , however , still be consistent with turbulence that has steepened into shocks . we start with a simple derivation of the @xmath32 model in section [ sec : deriv ] . in section [ sec : structfn ] , we give equations for the wave structure function for the @xmath32 model and compare predictions in section [ sec : decbw ] , the variation of the diffractive decorrelation bandwidth with frequency is used to test the @xmath32 model against the simple" +"a data base has been created combining 1100 days of observations with batse , from jd 2448387 to 2449480 ( to ) . it includes observations of fast variability ( 0.010.488 hz ) as well as flux measurements ( ) and energy spectral fits . the goal of this work is to look for correlations between various parameters derived from power spectral , flux , and energy spectral measurements . this work is part of a larger on - going project to systematically study the power spectral behavior of all black - hole candidate sources observed with batse . in section 2 we describe the methods used for creating the power spectra and the results of the occultation analysis . in section 3 we show that correlations occur between several quantities derived from the energy spectral and power spectral fits , and briefly discuss these results . the batse occultation analysis technique has been described elsewhere ( harmon et al . @xcite ) . for this study , the corrected detector count rates for have been fit to a power law in the energy range 45140 kev , and a total flux ( photons @xmath0 ) has been calculated for the same energy band . typically 1530 measurements are made each day . from these data we produced daily averaged flux and photon spectral to quantify the rapid variability , we have created power spectra from the 1.024 second time resolution large area detector ( lad ) count rate data , using two energy channels covering the range 2050 and 50100 kev . these data were filtered to eliminate bursts , then searched for segments with 512 contiguous time bins ( 524.288 seconds without gaps ) when the source was above the earth s limb . each segment was fit to a quadratic polynomial and the fit residuals converted to a power density spectrum ( pds ) using standard fast fourier transform techniques . the pds was normalized to squared fractional amplitude per unit frequency , according to the method described by miyamoto et al . ( @xcite ) , using the raw daily averaged detector count rates in the 20100 kev energy band obtained from the occultation analysis . interference from other black hole candidate sources ( e.g. , , and ) was eliminated by selection of only those detectors in which these sources did not appear . using similar 524.288 second intervals obtained when the source was occulted by the earth , we have determined that the quadratic detrending of the raw data yields a background ( source occulted ) power level consistent with a pure poisson process for frequencies between 0.01 hz and the nyquist frequency ( 0.488 hz ) . the results obtained are consistent with those obtained using a full background model developed by rubin et al . ( @xcite ) . = 6.5 cm = 6.5 cm it is well known that the power spectrum of has a characteristic shape ( belloni & hasinger @xcite ) ; the spectrum is flat below a break frequency , @xmath1 , and has a power law form above @xmath2 . we have attempted to parameterize the shape of these spectra by fitting to a function , p , of the form @xmath3 here @xmath4 is the amplitude of the low frequency part of the spectrum , @xmath5 , and @xmath6 is related to the slope of the power spectrum just above the break frequency . figure 1 shows three randomly selected spectra and the fits obtained using this functional form . we also calculated the fractional amplitude from the power spectral density for the frequency range . the three power spectral fit parameters ( @xmath4 , @xmath7 , @xmath8 ) , the fractional amplitude , the the total flux , and photon power - law index were plotted against one another to study the relationships between these quantities . some of the results are shown in figs . 2 and 3 . the strongest correlation is observed between the break frequency @xmath2 ( @xmath7 ) and the amplitude ( fig . the fractional amplitude monotonically decreases as the @xmath2 increases . these observations are similar to the results of belloni & hasinger ( @xcite ) based on 13 observations from the exosat archive at lower energies ( @xmath9 220 kev ) . figure 3 shows a plot of fractional amplitude vs. spectral index of a power law fit in the 45140 kev band . a correlation is also seen in these data . the energy spectrum generally becomes softer as the amplitude decreases . the fractional amplitude is in the range 830% during these observations . the origin of this effect is not well understood . a more detailed study of the type presented here is in preparation . this project was performed within nasa grant nag5 - 2560 and supported in part by the netherlands organization for scientific research ( nwo ) under grant fvdh acknowledges support by the netherlands foundation for research in astronomy with financial aid from nwo under contract number . jvp acknowledges support from nasa grant nag5 - 2755 . belloni , t. & hasinger , g. , 1990 , a&a 227 , l33 harmon , b.a . 1993 , in : friedlander , m. , gehrels , n. , macomb , d. , aip conf . 280 , compton gamma - ray observatory . aip press , new york , p. 313 miyamoto , s. et al . , 1994 , apj 435 , 398 rubin , b.c . 1993 , in : friedlander , m. , gehrels , n. , macomb , d. , aip conf . 280 , compton gamma - ray observatory . aip press , new york , p. 1127" +"muons have been undispensible probes in fundamental ( and applied ) physics for a long time . their completely unexpected discovery is ascribed to anderson and neddermeyer.@xcite muons have already been seen earlier by kunze@xcite albeit without claiming detection of a new particle . actually muons were until the 1940s mostly considered to be the predicted and searched for pions . in 1960 muonium ( mu ) , the hydrogen - like bound state of a positive muon and an electron ( @xmath2e@xmath3 ) , was unambiguously detected by hughes and coworkers.@xcite muons and mu continue to play a role of utmost importance in precision tests of the standard model of particle physics as well as in the search for new physics beyond it . they can be produced in comparatively large quantities , they live long enough for many applications and they decay sufficiently fast in a parity violating , self polarization - analyzing weak process ( @xmath4 ) which makes them most versatile . actually , the discovery of parity violation ( pv ) in nuclear @xmath5 decay@xcite was instantaneously followed by the demonstration of pv in muon decay.@xcite later it has been shown that the v - a structure of the standard model weak interaction follows already solely from muon decay experiments , including inverse muon decay.@xcite the reader will find an excellent review on fundamental muon physics@xcite and many references concerning the important role of low momentum muons , pions and neutrons in precision physics in ref . . below , a brief status update on muon activities at psi is presented without explicitly connecting to the standard - model extension ( sme ) and its coefficients.@xcite however , given the fact that all precision experiments acquire time stamped data sets , a wealth of opportunities exists for corresponding analyses . psi s hipa complex with its unique beam power provides the largest intensities of low momentum pions , muons and ultracold neutrons to fundamental physics experiments . the arrangement of the pion production targets as part of the beam optics of the proton beam onto the continuous spallation neutron source sinq at psi guarantees a highly efficient pion and muon production . the full proton beam intensity can be used while about 70% of the beam continues with only a small energy loss to the spallation target of sinq . most of the recent particle physics experiments used low momentum beams of both polarities ( @xmath2 , @xmath6 ) for measurements with stopped muons in low mass targets . prime examples of such efforts yielded ( i ) the new limit of @xmath7 ( 90% c.l . ) for the charged lepton flavor violating decay @xmath8 by the meg collaboration,@xcite using @xmath9/s @xmath2 of about 28mev / c ( 4mev kinetic energy ) stopping after some degrader in an about 200@xmath10 m thick polyethylene target and ( ii ) the measurements of 2s-2p lamb shift transitions in muonic hydrogen and deuterium by the crema collaboration,@xcite stopping about 600/s @xmath6 of only 3kev kinetic energy in a 20 cm long target filled with about 1hpa of h@xmath11 or d@xmath11 , respectively , and determining the nuclear rms charge radii of both proton and deuteron to about @xmath12 precision . these two experiments were conducted at hipa s @xmath13e5 beamline ( see the beamline overview map@xcite ) which presently is the world s highest intensity low momentum muon beam for particle physics . even slightly higher intensities are obtained at the @xmath10e4 beam@xcite which is usually dedicated to condensed matter studies with muon spin rotation ( @xmath10sr ) but has recently also been applied to study mu production into vacuum.@xcite a very successful series of experiments was conducted by the mulan,@xcite mucap,@xcite and musun@xcite collaborations , initially in the @xmath13e3 and later in the @xmath13e1 beam areas.@xcite the 1ppm measurement of the positive muon lifetime by mulan resulted in a 0.5ppm determination of the fermi coupling constant @xmath14 . mucap measured the @xmath6 lifetime in a high - purity protium target and determined the singlet capture rate to 1% and by that the weak pseudoscalar coupling @xmath15 of the proton to 7% . musun is under way to determine the muon capture rate on deuterons by the same technique . various new muon experiments are under way and progress has recently been reported at psi s annual particle physics users meeting.@xcite the meg ii experiment aims at a sensitivity to @xmath8 of @xmath16 . the mu3e collaboration pursues a search for the charged lepton flavor violating decay @xmath17 in two phases , first aiming at @xmath18 and later @xmath19 at the new himb . studies for himb already benefit conventional meson target designs.@xcite himb will provide @xmath20/s below 30mev / c to the phase-2 mu3e experiment . the beamline will open up new possibilites for statistically limited muon experiments in general . the muse collaboration will compare muon and electron scattering on hydrogen at the @xmath13m1 beamline@xcite and decisively test the difference in rms charge radii obtained so far by electron scattering and ordinary hydrogen spectroscopy versus the muonic atom result.@xcite the crema collaboration has meanwhile finished data taking on the 2s-2p lamb shift transitions in @xmath21he and is now turning to the laser spectroscopy of the ground state hyperfine splitting in h and @xmath22he . also spectroscopy of heavy muonic atoms is regaining interest , e.g. , the mux collaboration is setting out to measure the charge radii of @xmath23ra and other heavy , radioactive isotopes . a lot of progress is also being made by the mucool collaboration with the development of a very high brightness beam of slow @xmath2.@xcite together with ref . this development will allow for an improved measurement of the mu 1s-2s transition@xcite and pave the way for a test of the free fall of mu,@xcite the mass of which is dominated by the antimatter , second generation lepton . illuminating discussions with colleagues , especially at cpt16 , and continued support of psi s accelerator and beam line groups and psi / eth technical services , the swiss national science foundation ( 200020_159754 ) and the eth zrich ( eth-35 14 - 1 ) are gratefully acknowledged ." +"graphene systems , which are composed of one or a few carbon monatomic layers , have attracted much attention due to their unusual electronic properties even at room temperature , such as a high carrier mobility , thermal and structural stabilities , low spin orbit , hyperfine interactions , long spin relaxation length , and gate - tunable spin transport , and their potential for applications in nanoelectronic and spintronic devices @xcite.currently , there is a continuous interest in blg properties , both theoretically and experimentally . a bilayer graphene consists of two single graphene layers and has two different stacking arrangements : ab ( bernal ) and aa . energy band gap in blg nanoribbon and nanoflake could be controlled by substrate properties and the applied vertical electric field , so these structures could be used as a channel material in carbon - based transistors @xcite . moreover , several studies have been performed , both theoretically and experimentally , on transport properties in blg structure @xcite . interestingly , blg field - effect - transistors with high on / off current ratios at room temperature have been reported @xcite . in blg nanoribbons with zigzag edges , electronic transport is dominated by edge - states similar to those of single - layer graphene @xcite . these states are expected to be spin - polarized and make zigzag - edge blg nanoribbons junctions attractive for spin - polarized transport @xcite . on the other hand , long spin relaxation length in bilayer graphene nanoribbons and few - layer graphene flakes was observed at room temperature @xcite . moreover , spin - filtering and spin - dependent transport properties of blg with ferromagnetic electrode and gate , external magnetic field , and exchange field have been investigated theoretically and experimentally @xcite . another important feature of graphene in spintronic devices is its magnetoresistance . giant magnetoresistance ( gmr ) in graphene junction with ferromagnetic electrodes @xcite and magnetic states of zigzag edges have been extensively investigated @xcite . but there has been a little attention to the magnetoresistance effects in blg junction @xcite . in this paper , we studied the coherent magnetic transport properties of a blg nanoflake connected to two single - layer zigzag graphene nanoribbon ( zgnr ) electrodes . the results showed that the application of a magnetic field only on blg as a channel changes the spin configuration and conductivity of the blg zigzag edge and induces a perfect spin - polarized conductance in the ab- stacked blg structures . moreover , we studied the magnetic transport properties by changing blg width and length connected between zgnr electrodes . finally , we found a gmr up to @xmath0 and suggested that the gmr could be tuned by varying blg width and length . we simulated the system depicted in fig . 1a using a @xmath1-orbital tight - binding model and hubbard repulsion treated in the mean - field approximation . this formalism that includes @xmath2 interaction in blg induces localized magnetic moments in zigzag - edge atoms . we wrote the mean - field hamiltonian in the ab - stacked blg as follows @xcite : @xmath3 where @xmath4 ( @xmath5 ) stands for the creation ( annihilation ) operator of an electron with spin @xmath6 located on site . the tight - binding parameters @xmath7 were fixed to their bulk values equal to @xmath8 for the in - plane nearest neighbors of i and j and @xmath9 for the interlayer hopping parameter @xcite , and @xmath10 is the on - site coulomb interaction . the greens function of the junction is expressed as @xmath11^{-1}.\ ] ] where @xmath12 , @xmath13 are the self - energy matrices due to the connection of right and left zgnr electrodes to the channel , respectively . the spin - dependent density of states ( dos ) of the blg in the presence of electrodes is given by @xmath14 accordingly , the magnetic moment at each atomic site can be expressed as @xmath15 according to the landauer - buttiker formalism @xcite the spin - dependent conductance and currents can be written as @xmath16.\ ] ] using @xmath17 , the coupling matrices @xmath18 can be expressed as @xmath19 $ ] . also , the spin - dependent currents can be written as @xmath20 where @xmath21 is the fermi@xmath22dirac distribution function and consider the effect of temperature . we calculate the magnetoresistance of each device as @xmath23 we solved equation 1 - 3 self consistently by an iteration method . by choosing anti - ferromagnetic ( afm ) and ferromagnetic ( fm ) spin configurations as initial conditions in blg nanoflake , different spin configurations of afm and fm were achieved , respectively . moreover , the effect of single - layer graphene nanoribbon as an electrode on blg was added via self - energies , and the green function of blg was subsequently calculated . finally , the new expectation values of number operators were replaced in the hamiltonian , and this process was repeated until convergence was achieved@xcite . note that in the bilayer graphene nanoflake , the upper single - layer graphene was only connected to the lower one through single - band tight binding model in the first nearest neighbors approximation . the effect of electrodes on the upper monoatomic sheet was indirectly added through the hopping parameter between two monatomic sheets in blg nanoflake . modulation of hopping parameter between electrodes and blg could broaden electron energy level and consequently lead to the decrease of edge magnetism in blg nanoflakes@xcite . and length @xmath24 attached between semi - infinite zgnr electrodes , ( b ) ( top view ) and ( c ) ab - stacked blg as a channel with afm and fm spin configurations on zigzag edges , respectively . open ( red in online version ) and filled ( blue in online version ) circles represent spin - down and spin - up densities , respectively . the magnetic moments are within [ -0.25:0.25 ] @xmath25 and [ -0.05:0.25 ] @xmath25 in cases b and c , respectively . ] and @xmath24 ) with afm ( a and c ) and fm ( b and d ) spin configurations . ( a ) and ( b ) show the density of states , and ( c ) and ( d ) show the transmission coefficient of the blg junction . the solid ( dashed ) line is for minority- ( or majority- ) spin electrons . ] we considered ab - stacked blg as a channel connected between two semi - infinite single - layer zgnr electrodes . a similar junction ( monolayer - bilayer junction ) was proposed in previous works and its electronic and transport properties were investigated even under applied biases @xcite . the number of armchair rows along x direction , @xmath26 , defines a blg length and the number of zigzag rows along y direction , @xmath27 , defines a blg width . thus , blg length and width are @xmath28 and @xmath29 , respectively , with a=2.42(fig . anti - ferromagnetic ( afm ) spin configuration of ab - stacked blg ( see fig . 1b ) is more stable than other spin configurations . however , in the presence of an external magnetic field , the edge spin orientations become parallel and blg structure would have ferromagnetic ( fm ) spin configuration along all zigzag edges , similar to monolayer graphene nanoribbons and flakes @xcite ( see fig . we considered two different spin configurations in blg junction . rectangular blgs with afm spin configuration along zigzag edge have a zero net magnetic moment according to the lieb s theorem @xcite . due to external magnetic field applied perpendicular to blg , it has a fm spin configuration and a net magnetic moment in the channel . consequently , the degeneracy between up- and down - spin electrons breaks . according to the prediction of density functional theory , the spin - correlation length limits long - range magnetic order to 1 nm at room temperature@xcite , therefore in our calculation the semi - infinite zgnrs do not include edge magnetism and all spin - dependent scatterings are induced by the localized magnetic moments in blg . in other words , the effect of edge magnetic moments on the zigzag - shaped edges in these zgnr electrodes was intentionally not included in our calculations in order to emphasize on the role of magnetic field in blg geometry and its magnetic edge - states in generating spin - polarized currents and gmr . we showed in fig . 2 the spin - dependent destiny of states and conductance as some functions of energy for the device depicted in fig . 1 with afm and fm spin configurations in blg . by comparing density of states and conductance for afm an fm cases , it is clear that due to the influence of external magnetic field on the edge - states in the blg nanoflake , the conductance and density of states of the blg junction do not vanish at the band center . therefore , the electronic structure and conductance strongly change with the spin orientation of the zigzag edge - state . moreover , the density of states and conductance for the two spin sub - bands are non - degenerate in fm case ( see figs . 2b and 2d ) . hence , in the fm case , conductance and energy spectra around the fermi energy indicate a high conductivity and a spin - polarized behavior . generally , magnetic transport properties of zgnr / ab - stacked blg / zgnr junction are strongly dependent on the magnetization of the zigzag edge - states in blg . in fm case , when the electron conduction through the nonmagnetic zgnr as electrodes arrives at blg nanoflake , different scatterings occur for majority- and minority - spin electrons . hence , the transmission coefficients for spin - up and spin - down electrons are different . for more clarification , we plotted spin polarization ( @xmath30 ) as a function of energy and with @xmath24 and four different widths in fig . 3 . interestingly , a high spin polarization near the fermi energy and in a large energy region could be obtained for the ab - stacked blg junction with different widths . it is clear that , the spin polarization depends on the blg width . for example , in blg of widths @xmath31 and @xmath32 , the spin polarization through the junction will be different from that of a blg of widths @xmath33 and @xmath34 . in summary , blg of widths @xmath31 and @xmath32 shows a perfect spin polarization in a large energy region . as width increases , some non - spin - polarized local density is produced around the fermi energy due to the effect of non - magnetic edge state of zgnr as electrodes , and spin polarization values are therefore strongly modulated by increasing width near the fermi energy . and fm spin configuration . ] in order to see the sensitivity of the device to a switching magnetic field , we plotted the zero - bias magnetoresistance as @xmath35 as a function of blg length for four widths , as shown in fig . 4a . the junction , made entirely of carbon , produces a giant magnetoresistance ( gmr ) up to @xmath36 . 4a shows the zero - bias magnetoresistance changes in a wide range from @xmath37 to @xmath36 . our results showed that the gmr in the junction is sensitive to the width and length of blg nanoflakes . moreover , we can produce a higher magnetoresistance in blg junction by using a longer blg nanoflake . interestingly , for a blg longer than 1 nm , gmr increases as channel length increases and its" +"the sunspot number series was introduced in the 1860s by rudolf wolf of zrich and became the most commonly used index of long - term solar variability ever since . the sunspot number series is longer than 400 years , including the maunder minimum ( ) , and is composed of observations from a large number of different observers . since they used different instruments and different techniques for observing and recording sunspots , it is unavoidable that data from different observers need to be calibrated to each other to produce a homogeneous dataset . the first inter - calibration of data from different observers was performed by rudolf wolf in the mid-19th century . he proposed a simple linear scaling between the different observers ( the so - called @xmath0factors ) so that the data ( count of groups and sunspots ) from one observer should be multiplied by a @xmath0factor to rescale it to another reference observer . the value of the correction @xmath0factor is assumed to be rigidly fixed , as found by a linear regression , for each observer , and it characterizes the observer s quality in a relative way with respect to the reference observer . since then , this method has always been used until very recently ( ) . the @xmath0factor approach utilizes the method of ordinary linear least square regression forced through the origin . this method is based on several formal assumptions which are usually not discussed , but their violation may lead to incorrect results : 1 . _ linearity _ , _ i.e. _ the relation between two variables @xmath4 and @xmath5 can be described as linear in the entire range of the @xmath4-values . this assumption is invalid for the sunspot ( group ) numbers , as shown by or and discussed here , because of the essential nonlinearity . 2 . _ random sample _ , _ i.e. _ the pairs of @xmath4- and @xmath5-values are taken randomly from the same population and have sufficient lengths . this assumption is valid in this case . zero conditional mean _ , _ i.e. _ normality and independence of errors , implying that all errors are normally distributed around the true values . this assumption is also invalid since the errors are asymmetric and not normal ( ) . _ constant variance ( homoscedasticity)_. this assumption is violated since the variance of the data is not constant but depends on the level of solar activity so that the variance of the data points is much larger for periods of high activity than around solar minima . x - values are supposed to be known exactly without errors . this assumption is invalid since data from the calibrated observer ( x - axis ) can be even more uncertain than those by the reference observer ( y - axis ) . 6 . additionally , forcing through the origin is assumed for the @xmath0factors . this assumption is also invalid as shown by , since no spot reported by an observer does not necessarily mean that an observer with a better instrument would not see some small spots . we do not discuss here the issue of collinearity , since this assumption is not directly applied to the regression problem considered here . accordingly , five out of six assumptions listed above are invalid in the case of sunspot numbers making the linear scaling calibration by @xmath0factor formally invalid . this method was reasonable in the mid-19th century for interpolations to fill short gaps in observations , but now we aim to develop a more appropriate method for a direct calibration of different observers to each other . several indirect methods of solar - observer calibration have been introduced recently ( ) but here we focus on a direct inter - calibration based on modern statistical methods . it was proposed recently ( ) that the `` quality '' of a solar observer can be quantified not by a relative @xmath0factor but by the observational acuity threshold , _ i.e. _ the minimum size of a sunspot group the observer can see considering the used instrumentation , technique and eyesight . this quantity [ @xmath1 ( in millions of the solar disc , msd ) has a clear meaning all sunspot groups bigger than @xmath3 are reported while all the groups smaller than @xmath3 are missed by the observer . we note that weather conditions and age or experience may lead to variations of the actual threshold for a given observer in time , but here we consider that the threshold is constant in time . this is also assumed in the @xmath0factor methodology . the threshold would be consistent with the @xmath0factor if the fraction of small ( @xmath6 ) groups on the solar disc was roughly constant and independent on the level of solar activity . however , as many studies imply ( ) , the fraction of small groups varies with solar activity : it is large around solar minima and decreases with the level of solar activity . accordingly , the use of the linear @xmath0factor method may lead to a distortion of the calibrated sunspot numbers ( ) . in this article we study the relation between sunspot group counts by a `` poor '' observer and those by the reference `` perfect '' observer , using the reference dataset described in section [ sec : data ] . in section [ sec : dist ] we study the distribution of sunspot group sizes and its dependence on the level of solar activity . its effect on observations by solar observers of different quality and their inter - calibrations are discussed in section [ sec : obs ] . we propose the use of a new nonlinear @xmath2factor to calibrate data from a `` poor '' observer to the reference conditions depending on the level of solar activity , in a more realistic manner than that offered by the traditionally used linear @xmath0factor . we base our analysis on the royal greenwich observatory ( rgo ) data series of sunspot groups with their areas . this series is referred to as the reference dataset throughout this article . although the rgo data series starts in 1874 , there are indications that its quality might be variable before 1900 ( ) or even before 1915 ( ) due to the `` learning '' curve , although other studies did not find this effect or attributed it only to the very early part of the rgo record before 1880 ( ) . to stay on the conservative safe - side , we consider here rgo data only for the period 19161976 when the data series is homogeneous in quality . we have checked that the result remains qualitatively the same if the period of 18741915 is included into the analysis . since the rgo series was terminated in 1976 , we also stop our reference dataset at that time , not extending it with data from the _ solar observing optical network _ ( soon ) because of a possible transition inhomogeneity ( ) . to make the results compatible with the direct observations , we used in our analysis the uncorrected ( for foreshortening ) whole area of sunspot groups , _ i.e. _ as it is seen from earth . we consider sunspot groups , not individual spots , since several closely located spots indistinguishable by the observer can be seen as one blurred spot even with a poor telescope and thus are more representative for the actual data . from the reference rgo data series we compiled files of daily numbers of sunspot groups with different observational acuity thresholds [ @xmath1 quantified as the group areas in msd , so that a group is counted ( observed ) if its uncorrected total area is not smaller that the threshold value in msd . the corresponding daily number of groups is denoted as @xmath7 where the subscript @xmath8 denotes the value of the threshold in msd . for example @xmath9 denotes the number of groups with area @xmath10 msd for each day . the number of groups without applying any threshold ( @xmath11 , _ i.e. _ the total number of groups in the reference dataset irrespectively of their size ) is called the reference series @xmath12 . for the analysis of data by rudolf wolf and alfred wolfer ( section [ sec : ww ] ) we used the daily number of sunspot groups as presented in the database of here we investigated how size of sunspot groups changes with solar activity . this is usually studied using the mean size of sunspot groups ( ) but this may be confusing because the size distribution of spots is highly asymmetric and the mean value is not a robust feature . figure [ fig : map]a depicts the cumulative distribution function ( cdf ) of sunspot - group sizes ( uncorrected total area in msd ) for the reference dataset ( section [ sec : data ] ) . cdf(@xmath3 ) is defined as the fraction of the sunspot groups with area not smaller than the given value of the area threshold [ @xmath1 . by definition cdf(0 ) is equal to unity ( each group has a non - zero size ) . the black curve shows the global cdf for all the sunspot groups ( about 119300 groups ) in the reference dataset . the blue dotted line represents the cdf for 920 groups ( 46 days ) for high activity days with 20 groups ( @xmath13 ) reported . the red dashed curve depicts the cdf for 2781 days with low activity ( only one group reported , @xmath14 ) . one can see that there is a significant fraction of large groups even for low - activity days : @xmath1510% of groups have area greater than 500 msd . the group - size distribution changes with the level of solar activity : while the cdf for low - activity days is lower than the global cdf , the distribution for high - activity days is significantly higher . for example , as one can see from figure [ fig : map]a , the relative contribution of large sunspot groups ( @xmath16 msd ) doubles for high - activity days ( @xmath13 ) with respect to low - activity days ( @xmath14 ) . this implies that the rise of activity is mostly due to the emergence of large sunspot groups , indicating that the sunspot - group size distribution changes with the level of solar activity . to generalize the study of the cdf dependence on the level of solar activity , we plotted in figure [ fig : map]b a contour plot of the cdf as a function of the activity level ( quantified in @xmath17 ) and the group size ( quantified in msd ) . all the cdf were normalized to that at the low - activity level ( @xmath14 , see red dashed line in figure [ fig : map]a ) so that cdf(@xmath14 ) is unity for all @xmath3 . one can see that the shape of cdf changes with the level of solar activity so that the fraction of large spots is growing , while the fraction of small spot decreases with activity . for example , the brown spot in the top - right corner implies that the relative fraction of groups with area @xmath18 msd is nearly doubled for high - activity days ( @xmath13 ) compared to low - activity days ( @xmath14 ) , as discussed above for figure [ fig : map]a . in the subsequent section we study how the fact that the size distribution of sunspot groups changes with the level of solar activity affects solar observers of different quality and their mutual inter - calibration ." +"relative dispersion of passive particles in turbulent flows is one of the fundamental problems in turbulence research . it characterizes the transport and mixing properties of turbulence and is important from both theoretical and practical points of view . reflecting universal behavior of turbulent fluctuations , relative dispersion also has some universal properties because of its locality - in - scale nature @xcite . in particular , the dispersion process exhibits anomalous dispersion in the inertial range . this is first observed by richardson ( 1926 ) @xcite , and since then , a number of theoretical , experimental , and numerical investigations have been devoted to understand and model relative dispersion process @xcite . however , comprehensive understanding has not been obtained yet . recently , a few works focusing on underlying mechanism of the anomalous dispersion were reported . in the inertial range , the mean free path , @xmath2 , the mean length for persistent expansion of relative separation without changing its moving direction , is an order of relative separation itself , @xmath0 : @xmath3 @xcite . here , @xmath4 is a non - dimensional constant called the persistent parameter . in two - dimensional inverse cascade turbulence ( 2d - ic ) , @xmath4 is estimated as @xmath5 @xcite . this means separating motions are not purely diffusive but composed of an appreciable amount of persistent motions . in addition , it was also reported that there is a relation between stagnation - point structures and richardson s law @xcite , and that dispersion process is described by persistent streamline topology @xcite . from these results , it is expected that coherence of turbulent field , which must share its origin with fine coherent vortical structures such as worms in three - dimensional navier - stokes ( 3d - ns ) turbulence , has a significant role in turbulent relative dispersion . the correlations in turbulence are characterized in scale - space due to their self - similarity , and are not made disappear by coarse graining in real space . reflecting these correlations , relative separation moves persistently to some extent , so that , unlike the brownian motion , relative separation process should not be described only by random collision motions even as an approximation@xcite . in other words , the characteristic length can not be defined because the mean free path , @xmath2 , varies depending on the spatial scale . whereas there are several experiments and numerical simulations of which results are rather close to the prediction of richardson s diffusion equation @xcite that closely relates to random collision motions . thus , these results raise a question ; how are the effects of persistent motions wiped out ? in the previous paper @xcite , we have introduced a self - similar telegraph model of turbulent relative dispersion , and showed that the separation pdf can be close to the prediction of richardson s diffusion equation for slowly separating particle pairs even in the presence of persistent motions . in the present paper , we check the consistency of the physical picture of the self - similar telegraph model by carrying out direct numerical simulations ( dns ) of 2d free convection ( 2d - fc ) turbulence instead of 3d - ns turbulence . this is because ( i ) dns of 3d - ns turbulence requires extremely large computer resources , so that it is difficult to track particles for a long time , which is necessary to investigate dynamical properties of relative dispersion process , and ( ii ) 2d - fc turbulence has both statistical and dynamical characteristics similar to those of 3d - ns turbulence ( see appendix a ) @xcite . among them , the existence of coherent structures , which are approximated by the burgers t - vortex layer , is notable . this is a crucial difference from coherent structures in 2d - ic turbulence that are nested cat s eye vortices @xcite . therefore , comparing the results of the 2d - fc case with those of the 2d - ic case , we can investigate the effects of coherent structure on turbulent relative dispersion . this comparison gives a physical meaning of the drift term of the self - similar telegraph model . the inertial range achieved by our dns is not so wide that the relative motions of particle - pairs in the dissipation , the inertial , and the energy containing scales are not sufficiently resolved by usual fixed time statistics . in order to investigate the scaling natures of relative dispersion in such a narrow and limited inertial range , we utilize exit - time statistics introduced into research of turbulent relative dispersion by boffetta and sokolov ( see appendix b ) @xcite . by detailed investigation of the pdf of exit - time , we show that the pdf is divided into two region , the region - i and -ii , corresponding to persistent expansion and random transition between expansion and compression of relative separation , respectively . this result agrees with the picture of the self - similar telegraph model . in addition , we provide a method for estimation of the parameters of the self - similar telegraph model by using exit - time pdf . in the following sections , first we provide a brief review of the self - similar telegraph model in 2 . section 3 presents a summary of the numerical scheme and parameters of our dns of 2d - fc turbulence . some of the results by the fixed - time and the exit - time statistics are provided and discussed in 4 . concluding remarks are made in 5 . in addition , some properties of 2d - fc turbulence and exit - time statistics are presented in appendix a and b , respectively . in the previous paper @xcite , we have introduced a self - similar telegraph model for turbulent relative dispersion , which is a model describing the evolution of the pdf of relative separation of particle pairs in the inertial range . the relative separation of two particles , @xmath6 is defined as follows : @xmath7 where @xmath8 and @xmath9 are the lagrangian positions of the particles . the model is based on sokolov s model @xcite and consists of persistent expansion and compression of relative separation , @xmath0 , according to the relative velocity , @xmath10 , where @xmath11 and @xmath12 are a dimensional constant and a scaling exponent , respectively : @xmath13 for kolmogorov scaling and @xmath14 for bolgiano - obukhov scaling . the transition rate from expansion to compression and that from compression to expansion are given by @xmath15 and @xmath16 , respectively . here @xmath17 is a characteristic time scale at a spatial scale @xmath0 , @xmath18 , and @xmath19 are the inverses of persistent parameters , @xmath20 for expansion and @xmath21 for compression . introducing @xmath22 and @xmath23 , the evolution equation of the separation pdf , @xmath24 , is derived as follows : @xmath25 \\ + \sigma\frac{{\partial}}{{\partial}r } \left[v(r)p\right ] , \label{eq : t - model } \end{aligned}\ ] ] where @xmath26 is richardson s diffusion coefficient , @xmath27 , and @xmath28 . the parameters of the model are @xmath29 and @xmath30 : @xmath29 represents the strength of persistency of moving directions , and @xmath30 does the difference in persistency between expansion and compression . therefore , @xmath29 and @xmath30 reflect the strength and structure of coherence of the flow , respectively . for slowly - separating particle pairs , i.e. , in the case of @xmath31 , the first term of the l.h.s . ( [ eq : t - model ] ) can be neglected and the approximated equation is given by @xmath32 + \sigma\frac{{\partial}}{{\partial}r } \left[v(r)p\right ] . \label{eq : palm - eq}\ ] ] this form of the equation was first derived by palm @xcite and is also the same as the diffusion equation of goto - vassilicos model @xcite . we call eq . ( [ eq : palm - eq ] ) palm s equation . the similarity solution of eq . ( [ eq : palm - eq ] ) is @xmath33 where @xmath34 is the normalization factor . because the tail of the exit - time pdf , @xmath35 , consists of slowly - separating particle pairs , it is calculated from palm s equation ( [ eq : palm - eq ] ) with the method used by boffetta and sokolov @xcite . the asymptotic form of @xmath35 is given by @xmath36 where @xmath37 is the @xmath38-th zero of the @xmath39-th order bessel function and @xmath40 is the mean exit - time from @xmath0 to @xmath41 : @xmath42 note that the mean exit - time calculated from the self - similar telegraph model , eq . ( [ eq : t - model ] ) , is the same as eq . ( [ eq : avetime - palm ] ) . this is because the mean exit - time is calculated from a steady solution of the equation @xcite , and the solution of eq . ( [ eq : t - model ] ) is the same as that of eq . ( [ eq : palm - eq ] ) . by comparing the tail of the exit - time pdf obtained by dns and eq . ( [ eq : palm - etime ] ) , we can estimate the value of @xmath30 . the last term of the r.h.s . of eq . ( [ eq : t - model ] ) is a drift term consistent with the scaling law , and the direction of the drift is determined by @xmath43 . the parameter @xmath43 consists of two parts , the `` scaling - determined '' one , @xmath44 , and the `` dynamics - determined '' one , @xmath30 . in order for eq . ( [ eq : palm - eq ] ) to recover richardson s equation , the drift term has to disappear , which means @xmath45 . we call this case the richardson case or the zero - drift case , where the parameters of the model reduce to one , @xmath46 ; @xmath47 is determined by the relation @xmath48 . rescaled energy and entropy spectrum @xmath49 and @xmath50 obtained by dns at resolution @xmath51 ( nv10 ) and @xmath52 ( nv11 ) . the straight lines refer to the bolgiano - obukhov scaling : @xmath53 , @xmath54 . , width=332 ] .[table : dnsparms ] parameters used in the present dns . [ cols=""^,^,^,^,^,^"",options=""header "" , ] in this section , we explain the method of dns used in the present work and show basic properties of turbulent fields produced by our simulation . we generate turbulent field by dns of the vorticity equation with a large - scale friction term @xmath55 and the temperature equation with a large - scale forcing term @xmath56 : @xmath57 where @xmath58 , @xmath59 , @xmath60 , @xmath39 , @xmath61 , @xmath62 , and @xmath63 represent the vorticity field , the temperature field , the velocity field , the kinematic viscosity , the thermal diffusivity , the thermal expansion coefficient , and the gravitational acceleration , respectively . the large - scale forcing term used here is @xmath64 where @xmath65 is a constant . the large - scale friction term is written in the fourier space as @xmath66 where @xmath67 , @xmath68 , @xmath69 , and @xmath70 are a constant , the wave number vector , the fourier mode of the friction term , and the fourier mode of the vorticity field , respectively . our dns is performed on a @xmath71 domain with the doubly periodic boundary conditions at resolutions @xmath72 : @xmath51 ( nv10 ) and @xmath73 ( nv11 ) . we employ a pseudo - spectral method for" +"in recent years , uv and optical photometry and spectroscopy of nearby elliptical galaxies has suggested that these galaxies , which have a reputation for being old , red , and dead , may not be quite as dead as previously assumed . between a few percent to 30% of local ellipticals appear to be experiencing low levels of ongoing star formation activity @xcite . the star formation is not intense enough to affect the galaxies morphological classification , as it only amounts to a few percent of the total stellar mass . however , this disk growth inside spheroidal galaxies may be a faint remnant of a process that was more vigorous in the past and may have played a role in establishing the range of galaxy morphologies we observe today . star formation , of course , requires cold gas , so interpreting the uv and optical data in terms of star formation activity has important implications both for the early - type galaxies and for a general understanding of the star formation process . it is not obvious that star formation should `` work '' the same way inside spheroidal galaxies as it does inside disks , with the same efficiency , the same dependence on the gas surface density , or the same regulatory mechanisms . for example , it has been hypothesized that even if there is a molecular disk inside an elliptical or lenticular galaxy , the disk would probably be stabilized by the galaxy s steep gravitational potential @xcite . thus it is of interest to probe the relationships between molecular gas and star formation activity in early - type galaxies . it is not as straightforward , however , to measure star formation rates in early - type galaxies as it is in spirals . nebular line emission is common in ellipticals @xcite , but it is usually not thought to be associated with star formation . its distribution is generally smooth , centrally peaked , and sometimes filamentary @xcite ; its morphology and line ratios suggest ionization sources such as agn activity , evolved stars , or cooling from the hot gas phase rather than star formation . far - ir ( fir ) and cm - wave radio continuum emission are also commonly used as tracers of star formation activity in gas - rich spirals , but agns and the evolved stellar population have been identified as the sources of mid - ir ( mir ) and fir emission in most elliptical galaxies @xcite . here we investigate evidence for and against star formation activity in a sample of elliptical and lenticular galaxies that have unusually large molecular gas contents . we make use of matched - resolution images of the molecular gas distribution , the cm - wave radio continuum and the 24 intensity . the properties of more typical , co - poor early - type galaxies are reviewed so that they can provide a comparison sample for the co - rich early - type galaxies . we then present the morphology of the 24 emission , with simple parametric fits and comparisons to molecular gas , radio continuum , and optical images that show dust disks in silhouette . the mid - ir and far - ir flux densities of the co - rich galaxies are presented along with discussion of the 24 to 2 flux density ratios and the fir / radio flux density ratios as diagnostics of whether the mid- to far - ir emission has a circumstellar or star formation origin . the results are mixed ; in some cases it is clear that the 24 emission is primarily associated with star formation , and in other cases heating by the evolved stellar population or even by an agn are inferred . thus , the results are at least qualitatively consistent with the suggestions that present - day star formation activity may be occurring in substantial numbers of local early - type galaxies . the isocam and isophot instruments aboard the _ infrared space observatory _ provided some insight into the variety of processes that contribute to the mid - ir and far - ir emission of early - type galaxies . for example , a handful of elliptical and lenticular galaxies found their way into the _ iso _ atlas of bright spiral galaxies and are discussed by @xcite with particular reference to the rate and distribution of star formation activity . the 12 images show very little emission beyond their galaxies nuclei . in @xcite , enhanced mir and fir to @xmath1 flux density ratios are used as star formation indicators . it is not at all obvious that this interpretation is accurate for early - type galaxies , but in most of these cases the ratios are consistent with interstellar radiation fields due to the old stellar population so little if any star formation activity is inferred . there are a minority of e - s0/a galaxies whose fir/@xmath1 flux density ratios ( within a 15 aperture ) are as high as the median values for sb - scd spirals , suggesting the possibility of star formation activity . @xcite fit the spectral energy distributions ( seds ) and compared 15 images to optical and near - ir images for a sample of 18 ellipticals , dwarf ellipticals , and lenticulars . in two cases they found no evidence for excess 15 emission over the stellar photospheric emission ; in most of the rest of the sample there is such an excess and it is smoothly distributed , more or less following the stellar distribution . a few targets show thermal emission at 15 from the dust that is visible in silhouette in the optical images , and two show agn emission ( a nuclear point source and even some synchrotron radiation from the jet in m87 ) . thus , in early - type galaxies the stellar photospheres , circumstellar dust , silhouette dust lanes or disks , agn , and ( possibly ) star formation all contribute in the mid - ir images . fourteen galaxies classified as e , s0 , or s0/a were observed as part of the spitzer infrared nearby galaxies survey ( sings ; * ? ? ? eleven of these were detected up to 160 and the 24 morphologies of these galaxies are discussed by bendo et al . ( 2007 ) . with a couple of exceptions , such as ngc 1316 ( which has asymmetric extended emission over 2 ) and ngc 5866 ( which contains an edge - on disk ) , these early - type galaxies tended to have only poorly resolved nuclear emission at 24 . six of the 11 also have published co observations @xcite , and four of the six are detected . ngc 5866 is notably co - rich , as a large amount of molecular gas ( 4.4 ) is very clearly detected by @xcite . however , maps of the molecular gas distributions in most of these galaxies are not currently available . mips observations of more typically co - poor elliptical galaxies have also been published by @xcite and @xcite . of the 19 galaxies analyzed by @xcite , 13 have been searched for co emission and none have been detected @xcite . @xcite show that the 24 emission from their ellipticals follows the @xmath2 near - ir surface brightness profiles very closely . the 24 emission even has the same effective radius as in @xmath1 ; the ratio of two radii is found to be 0.96 with a dispersion of 0.20 . in addition , @xcite have shown that the 24 emission globally tracks the optical luminosity in elliptical galaxies as there is a tight linear correlation between the 24flux density and the @xmath3-band flux density . this 24 emission is interpreted to be circumstellar dust from the mass loss of post main sequence stars . in short , several processes may contribute to mir emission from early - type galaxies . in the majority of the elliptical galaxies that are not co - rich the 24 emission seems to either follow the stellar photospheric emission or a nuclear source . extended 15 and 24 emission has been observed from a few early - type galaxies that are very rich in molecular gas or that exhibit silhouetted dust . until now , however , it has been rare to be able to compare the distribution of possible star formation activity in early - type galaxies to that of the molecular gas , the raw material for the star formation . most early surveys for molecular gas in early - type galaxies were strongly biased towards fir - bright targets , with a typical selection criterion having an iras 100 flux density @xmath4 1 jy @xcite . more recent co searches are not fir - biased , but they still find significant molecular gas contents . @xcite reached a surprisingly high co detection rate of @xmath5 in a volume - limited sample of nearby field lenticular galaxies , and @xcite detected co emission in @xmath6 of a similar sample of field ellipticals . @xcite also detected co emission in @xmath7 of the early - type galaxies in the sauron survey @xcite , a representative sample that uniformly fills an optical magnitude apparent axis ratio space . thus , the co detection rates in ellipticals and lenticulars are high enough to support the uv - inferred incidence of star formation activity ( if that gas does indeed engage in star formation ) . the cold gas masses are highly variable in these detections , with @xmath8 in the range @xmath9 to @xmath10 and lower . since we are interested in morphology as a means of distinguishing the origin of the mir , fir , and radio emission , we have selected for this project some of the relatively few elliptical and lenticular galaxies with maps resolving their molecular gas distribution @xcite . because of the way galaxies were selected for co mapping , the targets were already known to be fir - bright and to have concentrations of molecular gas in their centers ( as opposed to their outskirts ) . we also apply a criterion on the angular extent of the molecular gas to be able to test the correspondence between the molecular gas and 24 emission . if the 24 emission arises in star formation activity , we expect it to trace the molecular gas . if the 24 emission is related to agn activity , we expect it to be a point source , and if it comes from circumstellar dust , it should trace the stellar distribution . thus , we required the targets to have molecular gas in structures on the order of 20 to 30 or more in diameter . corresponding dust emission , if present , should be resolved in the 24 images . the targets distances range up to 80 mpc and optical luminosities are in the range @xmath11 ( table [ sampletable ] ) . observations of ugc 1503 , ngc 807 , ngc 2320 , ngc 3032 , ngc 3656 , ngc 4476 , and ngc 5666 were made with the mips instrument at 24 , 70 , and 160 in project 20780 of cycle go-2 . the data were taken in photometry mode using the large field size in all cases . relatively short exposures were used to avoid saturation on these bright sources in medium - high background regions . exposures were made in four cycles of 10 seconds at 24 , with sky offsets of 300 , and in 8 cycles of 3 seconds at 160 . observations at 70 were made in the fixed cluster - offsets mode with offsets @xmath12 80 , and 8 cycles of 3 seconds . to maximize the morphological information recoverable at 70 the fine" +"the identification of high proper motion stars is an important tool to identify neighboring stars . the lhs catalog @xcite listed over four thousand stars with proper motions near or above half an arcsecond per year but only 73 stars with motions above two arcseconds per year . digitized photographic sky surveys and the more recent digital optical and near - infrared sky surveys have allowed many new proper motion stars to be identified . currently , the simbad database lists some 108 stars ( including white dwarfs and brown dwarfs ) with motions above two arcseconds per year . nevertheless , high proper motion stars remain to be identified . at low galactic latitudes , crowding makes it difficult to correctly pair stars , even though important progress has been made to bring the completeness in the galactic plane to at least 90% @xcite and perhaps as high as 99% @xcite . @xcite also estimate that incompleteness sets in at @xmath0 for low galactic latitudes ( @xmath1 ) but @xmath2 at high latitudes , and remark that independent surveys are needed to fully assess completeness of their catalog . unfortunately , the vast number of reddened background stars makes it difficult to identify cool , nearby objects by photometry alone . a second potential source of incompleteness is that for very large motions , the stars may move so far that automated pairing programs fail . the relatively recent discovery of such objects as a white dwarf moving at 2.55 `` /yr @xcite and an m6.5 dwarf moving at 5.05 ' ' /yr @xcite , both detectable on the photographic plate surveys , are illustrative . third , cooler objects , particularly brown dwarfs , are too faint for photographic plates , though these can often be selected by infrared colors alone . these problems can be addressed with a new infrared sky survey . the wide - field infrared survey explorer ( wise ) has surveyed the entire sky in four mid - infrared filters @xcite , allowing a comparison with the near - infrared two micron all - survey ( 2mass ) @xcite , even in the galactic plane . the wise explanatory supplement demonstrates that the matching of the two surveys is good to 0.2 `` for high signal - to - noise stars , and that 99.9% of wise stars match 2mass sources to within 3 arcseconds . the time baseline is approximately a decade , so objects with @xmath3 ' ' /yr are expected to move out of the matching window . the high reliability and completeness of wise and 2mass allow us to search for previously unidentified proper motion stars . in this _ , we report on two particularly important sources . our strategy is based on the fact that nearby hydrogen - burning stars should appear as relatively bright , high signal - to - noise sources in both wise and 2mass . we initially obtained a list of possible proper motion stars by querying the wise preliminary source catalog for stars with @xmath4 that lacked 2mass pairings within three arcseconds . we then matched this list with the @xcite catalog of stars with motions greater than 0.15 arcseconds per year . we found that nearly all lspm stars had @xmath5 and @xmath6 ( with the exception of a few very bright stars affected by saturation ) , and so we applied these color cuts to the sample . this selection for initial analysis , it should be noted , is intended to select main sequence stars and will likely exclude white dwarfs and brown dwarfs . we furthermore excluded known stars by requiring no simbad sources within 12 arcseconds and no matches to the ppmxl catalog @xcite . this left only 118 sources , each of which were examined in the digitized sky survey , 2mass and wise images . because we had made no additional cuts based on wise source quality , this list included many bright star artifacts , as expected in the preliminary processing . however , we also found we recovered a number of known proper motion stars , such as the 5 "" /yr star so 025300.5 + 165258 @xcite [ wisep j025303.27 + 165214.2 ] which move quickly enough that they were not excluded by the simbad query , as well as previously unknown stars . we extended this analysis to @xmath7 without difficulty . for yet lower galactic latitudes , @xmath8 , we found we could exclude most of the bright star artifacts , and none of the proper motion stars , by requiring that the source not be extended ( @xmath9 ) in wise . we also had to drop the w3 color cuts , because the 12 micron data do not reach as deep in regions of high background . no matches at the lowest latitude to ppmxl were attempted given its potential unreliability in crowded fields . the resulting 492 sources were also examined by eye , and 229 appear to be genuine proper motion objects . the main sources of false matches in the plane were apparently real but non - moving sources whose 2mass detections were masked or flagged due to nearby bright stars in the crowded fields . as expected , most of the genuine high proper motion stars were listed by @xcite or more recent publications @xcite . complete details and a full list of detected stars will be presented in a future publication , where we will assess completeness and reliability . only one previously unknown source with motion above two arcseconds per year was detected in the 58% of the sky in the preliminary release that is , we are able identify pairings for all other bright wise stars , as we define them above . wisep j191239.91 - 361516.4 is at @xmath10 and lies in a moderately crowded field . we also discuss a second source , wisep j190648.47 + 401106.8 , with a proper motion of 0.48 "" /yr at @xmath11 . further analysis of the other proper motion stars detected and the effect of relaxing the color constraint is ongoing and will be reported in a later paper . we identify wisep j191239.91 - 361516.4 with 2mass j19123922 - 3614555 , denis 191239.2 - 361455 , and usno - b 0537 - 0751534 . a finder chart is shown in figure [ fig0 ] . the wise and 2mass photometry and astrometry are listed in table 1 , and in addition , @xmath12 from denis @xcite and @xmath13 from usno - b @xcite . the wise observations are from 1 april 2010 to 7 april 2010 and the 2mass observations are from 25 june 1999 . since the wise positions are tied directly to the 2mass positions , we can compute the proper motion of 2.09 `` /yr directly . the reported wise-2mass positional uncertainties of 0.2 '' lead to an uncertainty of the proper motions of 0.02 `` /yr . ( we can also directly compare wise-2mass proper motions to those reported in the lspm catalog , and we find that the standard deviation of the differences is 0.013 ' ' /yr in each coordinate , which can be attributed primarily to the wise-2mass uncertainties . ) the photometry is consistent with a mid - m ( @xmath14 m4 ) dwarf . the photometry and a 3200k model atmosphere @xcite are plotted in figure [ fig1 ] . comparing to the parallax sample of @xcite , we expect @xmath15 for @xmath16 for a disk main sequence dwarf . this suggests a distance of 13 parsecs and @xmath17 km / s , but if the star is metal - poor , it would be closer with a lower velocity , and a distance within 10 parsecs is possible . ( if an equal - luminosity binary , it may be more distant . ) a trigonometric parallax is needed . according to simbad , it is the 103rd fastest proper motion star known . we identify wisep j190648.47 + 401106.8 ( hereafter w1906 + 40 ) with 2mass j19064801 + 4011089 and sdss j190648.29 + 401107.6 @xcite . the ten photometric observations are shown in figure [ fig1 ] , with @xmath18 , @xmath19 , @xmath20 , and @xmath21 . the wise observations are from 16 april 2010 to 22 april 2010 and the 2mass observations are from 23 may 1998 . a finder chart is shown in figure [ fig3 ] . both @xmath22 and @xmath23 are consistent with a late - m or an early - l type @xcite . a low - resolution irtf spex @xcite spectrum was obtained on 19 april 2011 and processed using spextool @xcite . it is shown in figure [ fig2 ] . we classify w1906 + 40 as spectral type l1 . the source may be a hydrogen - burning star or a brown dwarf . according to the relations of @xcite , the distance is @xmath24 parsecs and the tangential velocity is @xmath25 km / s , but again , a trigonometric parallax is needed . the most compelling property of this nearby l dwarf is that it lies in the kepler mission field @xcite , as kepler i d 4996077 , making it the coolest dwarf known in the field . it was not on the kepler observing list , but examination of the kepler full field images ( ffi ) shows that w1906 + 40 is detected . ddt monitoring with kepler will provide a unique time series for an ultracool dwarf , which are known to have large flares with a duty cycle of @xmath26% @xcite . we have identified two nearby proper motion stars at low galactic latitudes , demonstrating the value of an infrared proper motion survey based on the wise and 2mass catalogs . @xcite note that an important wise mission objective is to identify unknown , nearby low - luminosity brown dwarfs . proper motion selection using wise promises to also contribute to the solar neighborhood _ stellar _ census over the entire sky , including the galactic plane . the objects detected here are consistent with the evidence @xcite that the vast majority of high proper motion hydrogen - burning stars have been detected . @xcite , however , estimates that a third of nuclear - burning stars within 33 parsecs remain unidentified but have motions below 0.15 "" /yr . wise and 2mass photometry and astrometry appear to be accurate enough to allow many of these to be identified , even at low galactic latitudes , although optical follow - up will be required . this publication makes use of data products from the wide - field infrared survey explorer , which is a joint project of the university of california , los angeles , and the jet propulsion laboratory / california institute of technology , funded by the national aeronautics and space administration . this publication makes use of data products from the two micron all sky survey , which is a joint project of the university of massachusetts and the infrared processing and analysis center / california institute of technology , funded by the national aeronautics and space administration and the national science foundation . this research has made use of the nasa/ ipac infrared science archive , which is operated by the jet propulsion laboratory , california institute of technology , under contract with nasa . this research has made use of the vizier catalogue access tool , cds , strasbourg , france . this research has made use of the simbad database , operated at cds , strasbourg , france . the digitized sky surveys were produced at the space telescope science institute under u.s . government grant nag w-2166 . the images of these surveys are based on photographic data obtained using the oschin schmidt telescope on palomar mountain and the uk schmidt telescope . the plates" +"the kagome lattice structure , which consists of corner - sharing triangles , is notorious for supporting exotic states of matter . for instance , the possible experimental realization of quantum spin - liquids based on spin-1/2 kagome lattices has generated in the past intense research efforts on herbertsmithite and similar frustrated antiferromagnets @xcite . recently , the kagome lattice has also received plenty of attention for quasiparticle excitations with non - trivial topology @xcite . from topologically non - trivial electronic bands , effects such as the quantum spin hall effect ( qshe ) @xcite and the quantum anomalous hall effect ( qahe ) @xcite can emerge , also in kagome lattices @xcite . a quantum spin hall insulator in two dimensions , also known as a topological insulator , is a topological state of matter , present in a system with spin - orbit coupling , where symmetry protected dissipationless spin - polarized currents counterpropagate on the sample edges , while the bulk of the sample remains insulating ( fig . [ fig : halleffects]a ) . this phenomenon has received considerable attention because majorana bound states have been predicted to appear at interfaces between qshe materials and superconductors @xcite . employing these majorana zero modes for topological quantum computation is a rapidly developing field @xcite . in contrast to the qshe , in a quantum anomalous hall insulator only one spin species propagates around the sample edge due to the presence of intrinsic magnetization in the sample ( fig . [ fig : halleffects]b ) . this state of matter offers a direct realization of _ intrinsic _ topological properties in a material through the combination of spin - orbit coupling and magnetism @xcite . due to the dissipation - free , spin - polarized edge currents in the absence of external magnetic fields , realizations of the qahe are also intensively sought for , especially for application in new energy - efficient spintronic devices @xcite . so far , in electronic systems the qahe has only been observed in thin films of chromium - doped ( bi , sb)@xmath0te@xmath1 at a temperature of @xmath2 @xcite , the main limitation being the low curie temperature of the material involved . lately , it has been proposed that the qahe can be realized in some other compounds using , for instance , manipulated surfaces or exfoliated monolayers @xcite . another interesting approach is design from scratch of organometallic networks with topological bandstructures @xcite . a good strategy for designing qahe compounds based on existing materials with favorable energy scales that are adequate for applications is however currently lacking . here , we propose a new approach to create materials with non - trivial band topology and large curie temperatures , exploiting the electronic properties of doped mott insulators on a kagome lattice . a quick look at the one - electron properties ( bandstructure ) of the kagome lattice with nearest neighbor hoppings ( fig . [ fig : purekagomedosfilling ] ) shows huge potential for the realization of possible exotic states by only varying the electron filling . at half - filling the fermi level lies near a van hove singularity and inclusion of many - body correlation effects renders the system a mott insulator @xcite . at a filling of @xmath3 , however , the mott transition is absent @xcite and the fermi level is at the dirac point , where non - trivial band effects may be expected upon consideration of spin - orbit coupling . the spin - orbit coupling opens a gap at the position of the dirac point and the non - trivial topology of electrons on the kagome lattice leads to surface states of both spin species that traverse the bulk band gap opened by relativistic effects and , the qshe is realized . even more interesting is the filling of @xmath4 with the fermi level right at the flat band . it was recently suggested @xcite that if a nearly flat band is partially filled , a proper combination of spin - orbit coupling , ferromagnetism and geometric frustration will give rise to the fractional quantum hall effect at high temperatures . along these lines , we exploit here as a key ingredient for topological non - trivial states , the tendency towards ferromagnetism @xcite of a filled flat band in hole - doped transition - metal - based kagome lattices . at @xmath4 the ferromagnetic instability combined with correlation effects is expected to gap out one spin - channel and move the fermi level of the other spin - channel exactly to the dirac point . when spin - orbit coupling ( soc ) is considered , we have the same situation as for the filling of @xmath3 but only for one spin species . in such a situation , the qahe with fully spin - polarized dissipation - free surface states is realized . to demonstrate this new strategy of finding qshe and qahe materials by doping mott insulators , we investigate which possible modifications of the natural mineral herbertsmithite -a mott insulator with spin - liquid behavior- leave the perfect kagome motif undistorted and realize different electronic fillings . herbertsmithite crystallizes in the centrosymmetric space group @xmath5 and its structure is based on layers of cu@xmath6 ( @xmath7 ) ions building a perfect two - dimensional half - filled frustrated kagome lattice separated by layers of zn@xmath6 ions ( fig . [ fig : dopingenergies]a ) . the cu atoms are in a square planar crystal field environment of oxygen ions so that the orbitals near the fermi level are correlated @xmath8 states . evaluating density functional theory ( dft ) total energies , we show that single crystals of materials obtained by following various doping choices in herbertsmithite can in principle be synthesized . further , we prove that the magnetic ground state of hole - doped herbertsmithite at filling @xmath9 is ferromagnetic , which validates that the flat band physics of the pure kagome lattice carries over to realistic situations . finally , we demonstrate the presence of topologically non - trivial surface states of doped herbertsmithite using a state - of - the - art wannier function technique based on fully relativistic dft calculations . we prepared hypothetical materials starting from the experimental crystal structure of herbertsmithite @xcite , substituting zinc ( zn@xmath6 ) atoms between the copper kagome layers ( see fig . [ fig : dopingenergies ] ) by monovalent @xmath10=li@xmath11 , na@xmath11 ( hole - doping ) and trivalent al@xmath12 , ga@xmath12 , in@xmath12 , sc@xmath12 , y@xmath12 ( electron - doping ) . we refer to these compounds as @xmath10-herbertsmithite , @xmath10cu@xmath1(oh)@xmath13cl@xmath0 . experimental and hypothetical crystal structures were fully relaxed using dft in the projector augmented wave ( paw ) formulation @xcite implemented in gpaw @xcite with a plane - wave cutoff of @xmath14 and the gga exchange - correlation functional @xcite . we optimized the stoichiometric structures using @xmath15 @xmath16-points ( @xmath17 @xmath16-points for non - stoichiometric structures ) until forces were below @xmath18 . for each of the substituted structures with perfect copper kagome layer we also constructed a defect structure , where we lowered the symmetry of the unit cell and exchanged the substituent @xmath10 with a copper atom from a kagome lattice site . as the chemical composition of these defect structures is identical to the defect - free structures , energy differences can be evaluated directly within dft . in case the defect structure has lower energy , the kagome lattice is likely to be destroyed and the phenomena of interest here will not arise in the target compound . total energies , electronic bandstructures and magnetic exchange interactions of the relaxed structures were then evaluated using _ ab - initio _ dft calculations within an all - electron full - potential local orbital ( fplo ) @xcite basis . for the exchange - correlation functional we employed the generalized gradient approximation ( gga ) @xcite , as well as dft+u @xcite functionals . the latter was necessary in order to treat the correlated nature of cu 3@xmath19 orbitals . the hubbard repulsion on the cu 3@xmath19 orbitals was set to @xmath20 and hund s rule coupling to @xmath21 . although we concentrate our investigation on the cu @xmath8 orbitals close to the fermi level , the interactions were included in the entire cu 3@xmath19 shell , which is spread out over a large range of energies due to the interaction with the ligands . additionally , we investigated the effect of spin - orbit coupling on the electronic bandstructure employing the fully relativistic version of the fplo code . total energies , electronic bandstructures , tight - binding and heisenberg models were extracted from calculations converged using @xmath22 , @xmath23 , @xmath24 and @xmath15 @xmath16-point grids respectively . to demonstrate the existence of surface states , we constructed bulk tight - binding models for the copper states @xmath25 from fully relativistic dft calculations using projective wannier functions @xcite . employing a method based on green s functions @xcite , we calculate the states on the surface of herbertsmithite . the spectral function is obtained from the green s function as @xmath26 . by performing exhaustive dft calculations we identified as the limiting factor for modifying herbertsmithite the tendency of certain ions towards substituting copper sites in the kagome layer . in fig . [ fig : dopingenergies]b we plot the energy difference ( tabulated in the supplemental information ) between substitution at the kagome site and substitution at the interlayer site for herbertsmithite as a function of the substituent ionic radius @xcite . in herbertsmithite , sodium ( na@xmath11 ) and yttrium ( y@xmath12 ) prefer to occupy a site in the kagome layer , which generates a monoclinically distorted crystal structure with no perfect kagome lattice . if the substituent atom occupies the interlayer site , the perfect kagome motif is preserved . in terms of substitution energies , lithium ( li@xmath11 ) is the most promising candidate for synthesis of hole - doped herbertsmithite . on the electron - doped side , aluminum ( al@xmath12 ) , gallium ( ga@xmath12 ) and scandium ( sc@xmath12 ) are the most promising candidates for substitution . formation of the substituted materials is found to be energetically favorable compared to the formation of the parent compound clinoatacamite , cu@xmath0(oh)@xmath1cl . all herbertsmithite - based materials investigated are stable against formation of vacancies and copper impurities , as opposed to full substitution , on the interlayer site . we also investigated fractional substitution of zn@xmath6 by ga@xmath12 and found that the doping series ga@xmath27zn@xmath28cu@xmath1(oh)@xmath13cl@xmath0 should be stable in a broad range of ga : zn ratios ( see supplemental information ) . , @xmath29 , @xmath30 , @xmath31 ) in the brillouin zone . ( b ) fm bandstructure without soc . the spin down channel is gapped , while the dirac point of the spin up channel is located exactly at the fermi level . the path through the brillouin zone is shown in the supplemental information . ( c ) fully relativistic fm bandstructure close to the dirac point . soc opens a gap . ] in the analysis of the electronic and magnetic properties we concentrate here on the hole - doped materials ( @xmath4 , as defined in fig . [ fig : purekagomedosfilling ] ) where the fermi level lies in the region of the flat band of the kagome lattice and a strong ferromagnetic instability is to be expected . [ fig : holedopedherbertsmithitebands]a displays the fully relativistic non - spin - polarized electronic bandstructure of li - herbertsmithite , where the parities of the three ( dominantly cu @xmath8 ) bands closest to the fermi level are also indicated . due to the bulk nature of the system , the ideal kagome flat band acquires some dispersion ." +"modelling of the nucleosynthesis of the heavy elements ( e.g. in the astrophysical r- and p - processes ) requires knowledge of the rates of thousands of reactions . in lack of experimental data , the reaction rates are usually obtained from statistical model calculations . statistical models utilize different input parameters which strongly influence the calculated cross sections and hence the reaction rates . besides the astrophysical conditions , inaccurate nuclear input parameters used in the reaction rate calculations can be responsible for the fact that the nucleosynthesis models are not able to reproduce well the heavy element abundances observed in nature @xcite . therefore , the measurement of the relevant reaction cross sections is of high importance to check the results of statistical model calculations and to help choose the best input parameters . it has been found that the results of statistical model calculations strongly deviate from the measured cross section values in the case of reactions involving alpha particles . the reason of this discrepancy is that the calculated cross sections show a strong dependence on the alpha - nucleus optical potential and this potential is ambiguous at the astrophysically relevant low energies ( see e.g. @xcite ) . therefore , the need for experimental cross sections is more pronounced in the case of alpha - induced reactions . realizing this need , the cross sections of the @xmath0eu(@xmath5)@xmath6 tb and @xmath0eu(@xmath1,n)@xmath2 tb reactions have been measured at astrophysically relevant energies using the activation technique . in this method , the cross section is deduced from the off - line measurement of the reaction products , @xmath6 tb and @xmath2 tb . the half - life of the reaction products enter into the calculation of the cross section , and thus the uncertainty of the half - life values directly contributes to the uncertainty of the obtained cross sections . @xmath6 tb does not have any long lived isomer and the half - life of its ground state is relatively well known : 5.32@xmath40.06d @xcite . the situation for @xmath2 tb is , however , more complicated @xcite . its ground state decays by @xmath7 emission and electron capture to @xmath2gd with a half - life of t@xmath8=21.5@xmath40.4h . @xmath2 tb is has two long - lived isomeric states with unknown excitation energies but well established level ordering . the m1 isomer decays both by internal transition to the ground state and by @xmath7 and electron capture to @xmath2gd with a half - life of t@xmath9=9.4@xmath40.4h . the m2 isomer decays almost exclusively by @xmath7 and electron capture to @xmath2gd ; there is only a weak internal transition to the m1 state . one can note that the half - life of the m1 isomer has an unusually large uncertainty of more than 4% . this is because ambiguous data can be found in the literature . the measurements can be grouped into two categories . in the first group three half - life values of about 10h can be found by vylov et al . ( 9.9@xmath40.1h @xcite ) , by berkes et al . ( 9.8@xmath40.3h @xcite ) and by nedovesov et al . ( 9.9@xmath40.4h @xcite ) . in the second group , two less precise and lower half - life values can be found by lau and hogan ( 9.0@xmath40.5h @xcite ) and sousa et al . ( 9.0@xmath41.0h @xcite ) . in the compilation @xcite , a recommended value of 9.4@xmath40.4h is given with a remark : _ an unweighted average was chosen because the two more precise values are also the highest and may include an unaccounted for contribution from the 22.7 h isomer . _ if one accepts that some of the available half - life measurements involve a hidden systematic error , the half - life of the m1 isomer can have an uncertainty of up to 10% . since the preliminary analysis of the @xmath0eu(@xmath1,n)@xmath2 tb cross section measurement shows that the m1 isomer is by far the most strongly populated state in @xmath2 tb , the uncertainty of the m1 isomer half - life substantially influences the obtained cross section of the @xmath0eu(@xmath1,n)@xmath2 tb reaction . therefore , a high precision experiment has been carried out aiming at the determination of the m1 isomer half - life . in section [ sec : experimental ] the details of the experiment are presented . section [ sec : analysis ] shows the data analysis and the results are presented in section [ sec : results ] . @xmath2 tb sources have been produced by the @xmath0eu(@xmath1,n)@xmath2 tb reaction . the targets have been prepared by evaporating eu@xmath10o@xmath11 enriched to 99.2% in @xmath0eu onto thin al foils . the use of enriched @xmath0eu target was necessary because the ( @xmath1,n ) reaction on the heavier eu isotope leads to @xmath12 tb ( t@xmath3=5.35@xmath40.1d ) and the decay of this isotope is followed by a strong @xmath13-radiation with similar energy to the one from @xmath2 tb used in the analysis ( see sec . [ sec : gammacounting ] ) . a thin ( @xmath14 10@xmath15g/@xmath16 ) al protective layer has been evaporated onto each target in order to prevent the produced @xmath2 tb nuclei from diffusing out of the source during the half - life measurement . .[tab : sources ] details of the source preparation [ cols=""<,^,^,^,^ "" , ] a number of possible systematic uncertainties may influence the obtained half - life results . first of all , any change of the detection efficiency in the course of the measurement leads to the alteration of the measured half - life . such a change can be caused either by geometrical effect ( e.g. changes in the source detector distance ) or instabilities of the intrinsic efficiency of the detector . this possibility can be tested by comparing the results of several measurements . as can be seen in table [ tab : results ] the results of the five measurements are in perfect agreement , the standard deviation of the points is as low as 0.1% . however , to give a conservative estimation , the difference between the highest and the lowest value , 0.24% , has been adopted for the detection efficiency systematic uncertainty . the reliable dead - time determination of the data acquisition system is also of high importance . the five sources have been measured under different conditions regarding the initial dead - time of the system and gave consistent results . nevertheless , the dead - time provided by the multichannel analyzer has been tested using a pulse generator . the signals from the pulse generator have been fed into the counting system using the test input of the detector preamplifier . the observed number of pulser signals in the spectrum has been compared with the sent signals ( measured by a counter ) and from the ratio the dead - time could be calculated . it was found that the dead - time provided by the acquisition system was precise within about 0.3% in the dead - time range encountered in the present experiment . this 0.3% uncertainty translates into less than 0.1% uncertainty of the half - life value , therefore 0.1% has been adopted for the dead - time determination systematic uncertainty . the effect of detection efficiency changes and dead - time determination can also be studied using a reference source with precisely known half - life . the half - life of the reference source should preferably be close to that of the investigated isotope . the backing of the eu targets contained some copper impurity . during @xmath1-bombardment the @xmath17cu(@xmath1,n ) reaction takes place with high cross section producing @xmath18ga . the half - life of this isotope is 9.49h@xmath40.07h @xcite , similar to that of @xmath2tb@xmath19 . the decay of this isotope could well be seen in all but one samples . the half - life of @xmath18ga was determined by measuring the 1039kev @xmath13-radiation following its decay . the obtained results are also listed in table [ tab : results ] . the values obtained on the different sources are again in good agreement , and their weighted average is in agreement with the literature value . this independently supports the findings about the efficiency and dead - time related systematic uncertainties . in the case of @xmath2 tb a very important source of uncertainty in the m1 isomer half life is the possible contribution of the m2 isomer and the ground state leading to decays through the 540kev transition . the m2 isomer is known to decay by isomeric transition to the m1 state providing a continuos feeding of that state . the m2 decay branching ratio to the m1 state is , however , only 1.8%@xmath40.6% @xcite . on the other hand , the m2 isomer is only very weakly populated by the @xmath0eu(@xmath1,n)@xmath2 tb reaction . gavriljuk et al . @xcite found that the cross section ratio to the m2 and m1 states is @xmath20=0.019@xmath40.003 at 15.6mev @xmath1-energy . we have also calculated this ratio by measuring and comparing the characteristic @xmath13-radiations for the two isomers . we found @xmath20 values in the range between 1.2% and 2.7% for the measured 5 different @xmath1-energies . the combination of the low cross section ratio and the low isomeric transition decay ratio results in a maximum of 0.08% feeding of the m1 state by the m2 decay ( here a conservative upper limit of two sigma deviation from the isomeric transition literature value was taken ) . this feeding influences the determined m1 half - life by at most 0.1% and therefore this value is taken as the systematic uncertainty from the m2 feeding . our half - life determination was based on the assumption that the 540.2kev @xmath13-radiation comes exclusively from the m1 decay , as measured by e.g. sousa et al . @xcite . a small contribution of the ground state decay to this @xmath13-line can , however , not be excluded . this is especially important because our analysis shows that the ground state is strongly populated not only by the decay of the m1 state but also directly by the ( @xmath1,n ) reaction ( typically @xmath21@xmath220.3 ) . to test this possibility , a chi square analysis has been performed . a hypothetical ground state decay contribution to the 540.2kev @xmath13-line has been assumed and the goodness - of - fit was checked by the reduced chi square value as a function of the ground state decay contribution . the results of this test can be seen in fig . [ fig : chisquare ] . the minimum of the chi square curve is at zero ground state contribution to the 540.2kev @xmath13-line . this confirms the result of @xcite that this line can be associated solely with the m1 isomer . at the point where the reduced chi square increases by one , the obtained half life changes by 0.27% . this value is taken for the systematic uncertainty from ground state decay contribution . the adopted value for the half - life of the @xmath2tb@xmath19 isomer and its statistical uncertainty is calculated as the weighted average of the five measured samples . this gives 9.994h@xmath40.006h . the total uncertainty is the quadratic sum of the statistical uncertainty and the following partial systematic uncertainties : detection efficiency ( 0.24% ) , dead - time determination ( 0.1% ) , m2 isomer feeding ( 0.1% ) and ground state decay contribution ( 0.27% ) . the final result is t@xmath3=9.994h@xmath40.039h with a total uncertainty of 0.4% . the half - life value obtained in the present work is significantly higher than the recommended value in the literature ( 9.4h@xmath40.4h @xcite ) and its uncertainty is one order of magnitude lower . it should be pointed out that our value is in agreement with the results of" +"the normally ordered form of an expression involving ladder or , more generally , field operators is defined as one in which all annihilation operators are moved to the right using the appropriate commutation rules . such expressions play an important role wherever the fock space representation is used . in field theory and in many body quantum mechanics , normal order enters the formalism through the wick theorem @xcite . this enables us to represent field theoretical @xmath3point green functions or statistical @xmath3point correlation functions ( both defined as the vacuum mean values of products of the field operators ) by expressions within which all initially taken operators are contracted . another advantage of the normally ordered operators is seen if their matrix elements are calculated in the coherent states representation @xcite . if the coherent states are introduced as eigenstates of the annihilation operators such matrix elements automatically become functions of the complex variables and provide us the fock bargmann representation of quantum mechanical quantities . quantum optics is one branch of quantum physics where this approach is a basic tool widely used in numerous applications . the intersection between the boson normal ordering problem and combinatorics was discovered more than thirty years ago . the first seminal result @xcite was that , for both bosons and fermions , ordering a general string ( _ i.e. _ , a product of nonnegative integer powers ) of the canonical creation and annihilation operators results in an expansion in which the coefficients are combinatorial numbers called _ rook numbers_. the second seminal result @xcite expressed the boson string @xmath4 , where @xmath5=1 $ ] , as @xmath6 that is in terms of classical combinatorial numbers known as _ stirling numbers of the second kind_. both results , especially the second one , being the `` physicists version '' of the relation @xmath7 known to mathematicians much earlier , have inspired investigations which lead one to conclude that the relation between the normal ordering problem and combinatorics is not accidental . generalizations of ( [ katriel1 ] ) to the normally ordered expressions being more complicated than @xmath4 , @xcite@xcite , have led to the introduction of new classes of combinatorial numbers , whose properties were elucidated using standard methods of combinatorial analysis recurrences , generating functions and graph representations . normal ordering for noncanonical operators has also been investigated , in particular @xmath8-bosons , leading to @xmath8generalizations of stirling and bell numbers @xcite , @xcite , @xcite . this work has also revealed the relation between matrix elements taken in the coherent states representation and the bell numbers , @xcite , @xcite , @xcite , @xcite . as noted above , all these results indicate a fundamental connection between the general normal ordering problem and combinatorics . most of field theoretical calculations employ operator expressions reduced to the normally ordered form . this leads one to believe that the methods of combinatorial analysis will be useful in understanding and solving problems of quantum physics . our main goal in this work is to justify this statement . we shall provide the reader with a general method for constructing normally ordered expressions and shall explain how to link them to well - known combinatorial problems . we shall also present analogies between our methods and those of standard field theory , in particular feynman diagrams . finally , we will illustrate this approach using examples arising in one mode boson normal ordering . let @xmath9 and @xmath10 be two formal power series , also called the exponential generating functions ( egf ) of sequences @xmath11 and @xmath12 , respectively . then @xmath13 which is a straightforward consequence of the elementary relation @xmath14 reducing the usual cauchy product of series to the point wise hadamard product . if we apply this result to a function @xmath15 of an operator @xmath16 then for any indeterminate @xmath17 @xmath18 on taking the normal form @xmath19 $ ] of the both sides @xmath20=\left.f\left(\lambda\frac{\d}{\d x}\right){\cal n}(\e^{x\hat{w}})\right|_{x=0}\,.\ ] ] we emphasize that on the left hand side above the functional and operator aspects are mixed while on the right hand side they are distinct . the functional aspects are given by a ( formal ) series in usual derivatives while the operator aspects are described by an universal expression namely the normally ordered exponential of @xmath16 , in general a _ word _ @xmath21 in terms of the operators @xmath0 , @xmath1 . this means that ( [ prod4 ] ) , which we shall call the _ product formula _ , enables us to reformulate the general normal ordering problem into a normal ordering of @xmath22 . to calculate it explicitly still remains a non - trivial mathematical task but the problem is tractable for a large class of physically interesting examples . in this note we shall consider the cases where @xmath21 is either a product of positive powers of @xmath0 and @xmath1 , or a power of @xmath23 . applying the _ double exponential formula _ requires some effort . it is easy to see that it works effectively if we deal with monomials in both exponentials but leads to rather tedious calculations in more complicated cases . it is more practical to expand both exponents as formal power series ; a general method for this is the theory of _ multivariate bell polynomials _ @xcite , @xcite . multivariate bell polynomials arose from the question of constructing the taylor maclaurin expansion of the composite function @xmath38 . for any @xmath39 and @xmath40 given as formal power series one gets @xmath41(x)=\sum_{n=1}^\infty f_n[f;g]\,\frac{x^n}{n!}\,,\ ] ] where @xmath42=\sum_{k=1}^nb_{nk}(g_1,g_2,\dots , g_{n - k+1})f_k\,.\ ] ] the coefficients @xmath43 are certain polynomials in the taylor coefficients @xmath44 called multivariate bell polynomials , or sometimes more simply but unprecisely , _ i.e. _ , as polynomials which coefficients are the stirling numbers of the second kind and @xmath45 are the bell numbers . ] , bell polynomials . the multivariate bell polynomials are closely related to combinatorial numbers . they satisfy @xmath46}\ , g_1^{\nu_1}g_2^{\nu_2}\dots g_{n - k+1}^{\nu_{n - k+1}}\,,\ ] ] where the summation @xmath47 is over all possible non - negative @xmath48 which are partitions of an integer @xmath49 into sum of @xmath50 integers , _ _ , @xmath51 from ( [ bell3 ] ) and ( [ bell4 ] ) one may show that the multivariate bell polynomials satisfy , for @xmath0 and @xmath52 arbitrary constants , the homogeneity relation @xmath53 recalling ( [ prod10 ] ) one expects that the multivariate bell polynomials of especial use to us are those from exponential generating functions @xmath54\frac{x^n}{n!}\,,\\[6pt ] y_n[g]&=&\disty\sum_{k=1}^n b_{nk}(g_1,g_2,\dots , g_{n - k+1})\ , , \end{array}\ ] ] obtained from ( [ bell1 ] ) and ( [ bell2 ] ) for @xmath55 , @xmath56 . it may also be seen from ( [ bell3 ] ) and ( [ bell4 ] ) that @xmath57 are the stirling numbers of the second kind . in such a case ( [ bell2 ] ) gives @xmath58 and @xmath59 with @xmath60 denoting the bell numbers . the second useful case is @xmath61 , _ i.e. _ , the case when only two g s do not vanish . we have @xmath62 h_n^{(m)}(g_1,g_{m})=n!\disty\sum_{r=0}^{[n / m ] } \frac{g_1^{n - mr}g_{m}^r}{(n - mr)!r!(m!)^r}\ , , \end{array}\ ] ] where @xmath63 are called the two variable hermite kamp de friet polynomials . they are generalizations of the standard hermite polynomials , @xcite . another important property is the _ inversion formula_. this states that the following two expressions @xmath64=\sum_{k=1}^n b_{n , k}(g_1,\dots , g_{n - k+1})\ ] ] and @xmath65,\dots , y_{n - j+1}[g]\bigr)\,,\ ] ] are inverse to each other if this notion is understood in the following way : an arbitrary series @xmath66\}_{n=1}^\infty$ ] can be obtained in the form ( [ bell5 ] ) if we choose the series @xmath67 only as in ( [ bell6 ] ) . it means that we are really able to change the double exponential formula into power series and _ vice versa_. many other properties of the multivariate bell polynomials are also known , together with their explicit forms for some basic ( elementary ) functions . as mentioned in the introduction using the coherent states representation of the normally ordered strings of @xmath0 and @xmath1 allows us to dispense with operators and deal with functions of a complex variable @xmath68 and its conjugate @xmath69 . taking the coherent states mean value of the _ double exponential formula we get @xmath70\bigr|z\bigr>= \left.\exp\biggl(\sum_{m=1}^\infty\frac{l_m}{m!}\,\lambda^m \frac{\d^m}{\d x^m}\biggr)\cdot \exp\biggl(\sum_{n=1}^\infty v_n^{(\hat{w})}(z , z^*)\frac{x^n}{n!}\biggr)\right|_{x=0}\,,\ ] ] which , for the case @xmath71 and for @xmath72 , becomes @xmath73\bigr|1\bigr>= \left.\exp\biggl(\sum_{m=1}^\infty\frac{l_m}{m!}\ , \lambda^m\frac{\d^m}{\d x^m}\biggr)\cdot \exp\biggl(\sum_{n=1}^\infty n^{(\hat { w } ) } \frac{x^n}{n!}\biggr)\right|_{x=0}\,,\ ] ] identical with the _ counting formula _ of @xcite , used there in order to enumerate the feynman type diagrams in zero dimensional analogues of the field theoretical models . the field theoretical analogy may be pushed further on recalling the functional formalism of the field theory , @xcite . a basic quantity which defines any field theory model is the generating functional of the green functions . physically it is interpreted as the vacuum vacuum transition amplitude of the time ordered exponential of the quantum field operator in the heisenberg picture @xmath74 coupled to an external current @xmath75 @xmath76 from which the @xmath3point green functions are got as the @xmath3th functional derivatives with respect to @xmath77 . passing to the interaction picture one obtains @xmath78 where @xmath79 is an interaction lagrangian density . rewriting @xmath80 in terms of a functional integral @xmath81\exp\left(\i\left(s_0+s_{\mathrm{int}}+{\phi}j\right)\right),\ ] ] with @xmath82 and @xmath83 denoting free ( bilinear ) and interaction action functionals for the field @xmath84 , and @xmath85 , respectively , one notes that @xmath80 is an analogue of the partition function of statistical mechanics . another expressions for the generating functional of the green functions are those given using functional differential operators @xmath86\right ) \big|_{\phi=0}=\\[12pt ] & = & \disty\exp\left[\i s_{\mathrm{int}}\left(-\i\frac{\delta } { \delta j}\right)\right]\cdot \exp\left[-\frac12\,j\delta j\right ] , \end{array}\ ] ] where @xmath87 is the causal green function of the free field equation generated by a free action , @xmath88 is , as previously , an interaction action and we use abbreviations @xmath89 j\delta j&=&\disty \int\d^{d}x\,\d^{d}yj(x)\delta(x , y)j(y)\,,\\[9pt ] j\phi & = & \disty\int\d^{d}xj(x)\phi(x)\ , . \end{array}\ ] ] equivalence of both formulas of ( [ coh3 ] ) comes from the identity @xmath90\right|_{\phi=0}\ ] ] satisfied by arbitrary functionals @xmath91 and @xmath92 having formal taylor expansions around zero @xcite . here we remark that while in the derivation of the first equality of ( [ coh3 ] ) the normal ordering is extensively used , the second equality , as well as ( [ coh5 ] ) , may be obtained by manipulating the functional integral representation of the green functions generating functional . although much simpler that the standard advanced field theoretical methods , our approach give essentially the same formulae , which are directly applicable to the time evolution operator or to the _ partition function integrand _ @xcite . this we consider as a strong argument in favour of the present method . in the effort to understand the meaning of perturbation expansions in quantum physics , both in quantum mechanics and in quantum field theory , it is important to know their large order behaviour . solving the problem for the coupling constant perturbation series one finds that the number of the feynman diagrams , contributing order by order to the perturbation series coefficients , grows factorially , @xcite , @xcite , @xcite . the factorial growth occurs because of the combinatorial reasons which ( at least qualitatively and for the large orders asymptotics ) explain why such a behaviour does not essentially depend on details of the model if one disregards the problem of _ _ renormalons__. enumeration of diagrams for more complicated models is echoed by that of their zero dimensional" +"the parameter estimation is one of most important ingredients in various fields of both the classical and quantum worlds metrology06prl , metrology11np . the task of quantum estimation is not only to determine the value of unknown parameters but also to give the precision of the value . it is a vital issue on how to improve the estimation precision which is closely related to the quantum cramr - rao inequality and quantum fisher information ( qfi ) fisher , jiliangxuejiuchan , jiliangxuejiuchan2,wangxiaoguangzongshu , xiaomin , xiangguoyong , kexue , pra2012 that determines the bound of the parameter s sensitivity theoretically by @xcite @xmath0where @xmath1 means the time of experiments , and @xmath2 is the qfi with the symmetric logarithmic derivative @xmath3 defined by @xmath4 . ( [ crbound ] ) implies that the larger qfi means higher sensitivity of the parameter estimation . the pioneer work on the quantum parameter estimation were proposed by caves @xcite who showed that the precision of phase estimation can beat the shot - noise limit ( standard quantum limit ) . later , lots of jobs with the similar aims are proposed , such as based on maximally correlated states winelind , n00n states @xcite , squeezed states @xcite , or generalized phase - matching condition @xcite , and so on . in practical scenarios , it is inevitable for a quantum system to interact with environments , the precision of quantum estimation will be influenced by different extents @xcite . in recent years , enormous effects have been devoted to how to improve the precision of parameter estimation in the case of open systems . for example , the precision spectroscopy using entangled state in the presence of markovian dephasing @xcite and non - markovian noise @xcite are investigated ; the qfi under decoherence channels @xcite or in a quantum - critical environment @xcite are analyzed ; the qfi measured experimentally with photons and atoms are reported @xcite ; it is also reported that the qfi subject to non - markovian thermal environment @xcite could show revival and retardation loss ; the parameter - estimation precision in noisy systems could be enhanced by dynamical decoupling pulses tigao - wangxiaoguang , redesigned ramsey - pulse sequence @xcite or error correction @xcite are also shown ; noisy metrology beyond the standard quantum limits is possible when the noise is concentrated along some spatial direction @xcite . however , if the environment we considered is a squeezed reservoir , how the qfi is influenced by the reservoir s parameters ? the squeezed reservoir has been widely studied in quantum information processing . for example , the squeezed light ( reservoir ) @xcite or finite - bandwidth squeezing @xcite for inhibition of the atomic phase decays and its application in microscopic fabry - prot cavity @xcite . in addition , some other considerations of the squeezing reservoir were also discussed , such as the quantum entanglement dynamics @xcite , heat engine recycle @xcite , geometric phase observable @xcite , etc . the physical realization of the squeezed reservoir has also been proposed both in theory and in experiment based on various techniques such as the four - wave mixing @xcite , the parametric down conversion wulingan , the suitable feedback of the output signal corresponding to a quantum nondemolition measurement of an observable @xcite , control the parameter of the driven laser @xcite , quantum conversion of squeezed vacuum states @xcite or energy - level modulation @xcite , the atomic systems in cavity qed @xcite or dissipative optomechanics system @xcite and so on . the reduction of the radiative decay of the atomic coherence in squeezed vacuum has been realized in the superconducting circuit and microwave - frequency cavity system @xcite . in this paper , we will investigate the effects of reservoir squeezing on the qfi based on the non - perturbation processing @xcite . we consider a phase estimation scheme which a two - level system with an imposed unknown phase interacts with a squeezed reservoir before the final optimal measurements . to find the influences induced by the reservoir , we derive the non - perturbative master equation by the path integral method lujingjifen . in terms of the master equation , we obtain the exact analytic expression of qfi which is related to the precision of parameter estimation . it can be found that the qfi depends on the estimated parameter and the decay of qfi can be reduced by the squeezed reservoir compared with thermal ( vacuum ) reservoir . in particular , if the appropriate squeezing phase matching condition is satisfied , the decay of qfi can be prevented prominently by the reservoir squeezing . this paper is organized as follows . in sec . [ sec2 ] , the parameter estimation scheme is introduced and the non - perturbation master equation is obtained . in sec . [ sec3 ] , the exact analytic expression of qfi for the estimated parameter is obtained and the effects of reservoir squeezing on the qfi are investigated . the conclusion are given in the end . the setup of the parameter estimation is sketched in fig . [ scheme ] . the input state is a two - level superposed state @xmath5 . after the phase gate ( @xmath6 ) is operated on the input state @xmath7 , the output state is given by @xmath8let the system ( @xmath9 ) interacts with a squeezed reservoir , the quantum fisher information ( qfi ) of the final state can be obtained via optimal measurement . the inverse of square root of the qfi is related to the precision of parameter estimation according to eq . ( [ crbound ] ) regardless of the experiment times @xmath10 . the initial state of the squeezed reservoir coupled to the system is given by @xmath11 where the squeezed operator @xmath12 and the thermal state @xmath13 are given by @xmath14here @xmath15 is the squeezed parameter , @xmath16 is the reference phase of squeezed field and the parameter @xmath17 with @xmath18 and @xmath19 denoting the boltzsman constant and temperature , respectively . noting that the thermal state @xmath13 will become the vacuum state @xmath20 if the temperature @xmath21 , whilst the environment will become the squeezed vacuum reservoir @xmath22 @xcite . the total hamiltonian of the system and reservoir reads @xmath23with @xmath24where @xmath25 denotes the transition frequency of the two - level system , @xmath26 is the raising / lowering operators of the system , @xmath27 is the creation ( annihilation ) operators of the squeezed reservoir and @xmath28 is the strength of coupling between the system and environment . in order to get the master equation for the reduced system , we would like to employ the non - perturbative master equation which can be given , in the schrdinger picture , by path integral method @xcite as @xmath29where @xmath30 denotes the reduced density matrix of the system , @xmath31 denotes the partial trace of squeezed reservoir and @xmath32 , @xmath33 , @xmath34 are the super operators defined by@xmath35 , \\ { l_{0}}\rho & = & [ { h_{s}}+{h_{bath}},\rho ] , \\ { l_{int}}\rho & = & [ { h_{int}},\rho ] .\end{aligned}\ ] ] assuming the initial state of system plus reservoir is product state @xmath36 , through tedious but straightforward derivation , the non - perturbative master equation in the interaction picture can be given by @xmath37where the coefficients @xmath38 and @xmath39 are represented by @xmath40with @xmath41 denoting average photon number . in this paper , the structure of squeezed reservoir is supposed as the lorentz form @xmath42where @xmath43 is the spectral width of the reservoir and connects with the reservoir correlation time as @xmath44 , @xmath45 is the decay of the system and determines the relaxation time scale as @xmath46 . performing the continuum limit of the bath mode , the time correlation function can be expressed as @xcite @xmath47 and the coefficient @xmath48 in the master equation ( [ eq - master ] ) is @xmath49 one can prove that the non - perturbative master equation ( [ lujingjinfen ] ) coincides with the second - order time - convolutionless ( tcl ) master equation for the two - level system interacting with a thermal reservoir breuer , lujingjifen . because no markovian approximation is used , it will lead to non - markovian dynamics for a qubits coupling to a ( squeezed ) thermal reservoir intuitively . however , just like the second - order tcl master equation for the two - level system interacting with vacuum reservoir , the phenomenon of temporary backflow of information @xcite can not be revealed . if the markovian limit is considered , the characteristic correlation time of reservoir @xmath50 is sufficiently shorter than the system s @xmath51 , i.e , @xmath52 , so the lorentz spectrum will become a flat form , i.e. , @xmath53 , and the coefficient @xmath54 . thus , the widely used markovian master equation scully , breuer can be easily obtained from the eq . ( [ eq - master ] ) , @xmath55 for the initial system state ( [ rhoout ] ) , the solution of the master equation given by ( [ eq - master ] ) can be solved straightforward , which reads @xmath56where the elements of density matrix are @xmath57 , \notag \\ \rho _ { s}^{01}(t ) & = & \rho _ { s}^{10}(t)^{\ast } , \rho _ { s}^{00}(t)=1-\rho _ { s}^{11}(t ) . \label{zhongjian}\end{aligned}\]]here , the parameters @xmath58 are given by @xmath59it is worth noting that the solution of markovian master equation ( markovian ) can be obtained by just replacing the parameter @xmath60 by @xmath61 in eq . ( [ canshu ] ) . and @xmath62 ( @xmath63 ) . panel ( a ) is under the condition @xmath64 , and panel ( b ) is under @xmath65 . for both panels , @xmath66 , @xmath67 and @xmath68 . ] the explicit expression of the qfi for the estimated parameter @xmath69 is given by @xcite @xmath70where @xmath71 are the eigenvalues of estimated state and @xmath72 are the corresponding eigenvectors . for pure states , the qfi can be simplified as @xmath73 . substituting the estimated state ( [ rhos ] ) into the formula of qfi ( [ fisher1 ] ) , the first term of eq . ( [ fisher1 ] ) is @xmath74 $ ] with @xmath75 $ ] and the second term is @xmath76% + 2b_{1}^{2}b_{2}^{2}\right\}/m$ ] . summing the two terms , we can obtain he analytic expression of qfi for the estimated parameter @xmath69 @xmath77where the parameters @xmath78 , @xmath79 , @xmath80 are given in eq . ( [ canshu ] ) . from the analytic qfi ( [ fisher ] ) , one can obviously find that the qfi depends on the estimated parameter @xmath69 and squeezed phasing parameter @xmath81 . it varies as @xmath69 with the periodicity @xmath82 , and as @xmath83 with periodicity @xmath84 . a vivid illustrations of such relations are given by fig . [ various ] . with various temperatures without squeezing . panel ( a ) is based on the master equation ( [ eq - master ] ) with @xmath66 and panel ( b ) respects to the markovian master equation ( [ markovian ] ) . here we set @xmath85 ( blue dotted line ) , @xmath86 ( black dotted - dashed line ) , @xmath87 ( red dashed line ) , 2@xmath87 ( green line ) , respectively . ] in order to show the effects of the reservoir squeezing , we will first give a brief demonstration of the behavior of qfi without squeezing . that means we consider the reservoir as a standard thermal reservoir . in this case , the qfi given in eq . ( [ fisher ] ) can be simplified as @xmath88the dynamics of @xmath89 with different temperatures are plotted in" +"lmc x-1 is one of four extremely luminous ( @xmath1 ergs s@xmath2 ) x - ray binaries in the large magellanic cloud . the source has long been known to show a rather soft x - ray spectrum ( @xmath3 kev ; markert & clark 1975 ) and irregular x - ray variability by at least a factor of three ( griffiths & seward 1977 , johnston , bradt , & doxsey 1979 ) . however , its optical identification was uncertain for many years . the source lies within the bright emission nebula n159 ( henize 1956 ) containing many early - type stars ( see finding chart of region in cowley , crampton , & hutchings 1978 ) . based on the rather uncertain x - ray position , it was originally thought that the b5 supergiant r148 ( @xmath4 ) was the optical counterpart , although the peculiar o7 iii star ( star # 32 of cowley et al . ) @xmath5 away could not be ruled out . recent analysis of @xmath6 high - resolution imager data has confirmed that star # 32 ( @xmath7 ) is the most probable identification ( cowley et al . spectroscopic studies of this star reveal an orbital period near 4 days and a probable mass for the compact star of @xmath8 ( hutchings , crampton , & cowley 1983 , hutchings et al . 1987 ) , making it a strong black - hole candidate . because lmc x-1 is so luminous , its x - ray properties were studied even with the earliest x - ray detectors . white & marshall ( 1984 ) discussed the complex character of its x - ray spectrum , showing that it could not be described by a simple model because of the high - energy excess above 3 kev . thus a two - component model with a soft thermal spectrum and plus a hard high - energy tail was needed . they pointed out the similarity in spectral properties of lmc x-1 to another black - hole candidate , lmc x-3 , and they were the first to recognize that an unusually soft x - ray spectrum may be a reliable signature of a black - hole candidate . using _ ginga _ data , ebisawa , mitsuda , & inoue ( 1989 ) also found a two - component model was needed to fit the spectrum : an ultrasoft blackbody ( @xmath9 kev ) and a hard power law ( photon index @xmath102.5 ) . later , schlegel et al . ( 1994a , 1994b ) modeled the spectrum , based on broad band x - ray telescope ( bbxrt ) data , finding results similar to those of ebisawa et al . ebisawa et al . undertook a timing analysis of their _ ginga _ data and found quasi - periodic oscillations ( qpo ) with a peak frequency of 0.0751 hz in one of the observations . they concluded that the qpo came from the hard - tail component , which was unusually bright at the time in comparison to the thermal component . qpo were not found in the bbxrt data ( schlegel et al . ) , confirming the transient nature of these aperiodic signals . since the presence of qpo might be related to the spectral state of the system , we undertook a series of observations with rossi x - ray timing explorer ( @xmath0 ) over a period of nine months to search for qpo and to further define their origin . a series of nine observations were made between 1996 february and 1996 october . table 1 lists the details of the observational data , in reverse time order , following the numbering system of the @xmath0 science data center . only data from the proportional counter array ( pca ) were analyzed due to the very low net count rate for events with energies @xmath1116 kev . each observation was broken into two or three segments due to earth occultations or passages through the south atlantic anomaly . in 1996 march , two proportional counter units ( pcu ) were found to be discharging , making it necessary to shut them down periodically . the result was that some observations were made with only three of the five pcu operating ( observations # 4 , # 6 , and # 7 ) , as noted in table 1 . observation # 3 experienced a shutdown of two pcu during the second half of the exposure , so it was necessary to analyze this observation in two parts ( # 3a and # 3b ) . background - subtracted light curves , using 16-s time bins , were derived for the 25.9 kev and 5.915.9 kev energy ranges . the spectral hardness within each bin was found by calculating the ratio of counts , @xmath12 ( 5.915.9 kev)/(25.9 kev ) . typical values for the hardness ratio are @xmath100.10.2 ; mean values for each observation are listed in table 1 . the light and @xmath13 curves for observations # 2 , # 3b and # 4 are shown in fig . 1 . the selected observations span a wide range of source intensity and hardness . in observation # 3b ( ` average ' count rate ; lowest @xmath13 ) lmc x-1 was in a quiescent mode with minimal flickering , while in both # 2 ( second highest count rate ; highest @xmath13 ) and # 4 ( lowest count rate ; ` average ' @xmath13 ) the source varied rapidly on a time scale of minutes . examination of all of the observations reveals no dependence of the source s flickering characteristics on either the count rate or hardness . however , for each observation the plot of hardness ratio is similar to that of the high - energy count rate , implying the ratio is driven primarily by the number of 5.915.9 kev counts . @xmath14 data for the black hole candidate gx339@xmath154 in its very high state ( miyamoto et al . 1991 ) show the same behavior ( see their fig . 2 ) . while in this very high state , the source is 23@xmath16 more intense and shows significantly enhanced variability ( on timescales of minutes ) compared to when it is in a ( relatively quiescient ) high state ( makishima et al . although the @xmath0 observations also show various degrees of short - term variability , there is no clear indication that lmc x-1 enters a very high spectral state . to test the dependence of @xmath13 on the source count rate , we used data from all observations to construct the hardness - intensity diagrams shown in fig . 2 . the plot of @xmath13 versus low - energy count rate has no significant relationship between the parameters however , the plot of @xmath13 versus 5.915.9 kev count rate exhibits a very strong correlation which is also present in each of the individual observations . this dependence confirms the trend inferred from examination of the simple light and hardness - ratio curves . we examined the data for time lags between high and low - energy photons by calculating the cross - correlation of the two light curves . a small positive lag , in the sense that high - energy photons tend to arrive after their low - energy counterparts , was found for all observations . however , the mean lag time in each case was comparable to the 0.025-s step used in the calculations , so that the results are not conclusive . to further investigate the temporal variations , power density spectra ( pds ) were constructed using the background - subtracted data , rebinned at 0.125-s resolution . within an observation , the fourier transformation was calculated for each 512-s data segment ( 4096 points ) , covering the frequency range 0.0024 hz . typically , each pds represents the average of @xmath1011 individual transforms . two sets of pds were made , one covering the entire pca energy range ( 260 kev ) and the other restricted to primarily those photons in the hard spectral tail ( 5.915.9 kev ) . no significant differences between these were found . in fig . 3 we present the power density spectrum ( 5.915.9 kev ) for observation # 7 . the power density increases at low frequency ( i.e. , red noise ) and can be modeled in terms of a power law plus a constant ( i.e. , power @xmath17 , where @xmath18 is the power index ) . fitted values of the power index , for both the 5.915.9 kev and 260 kev pds , are listed in table 2 . the average indices are @xmath19 and 0.87 for the restricted and full energy ranges , respectively . there is no significant dependence of the modeled power index with either the hardness ratio or the source count rate . for comparison , ebisawa et al . ( 1989 ) measured an index of 0.81 in a @xmath14 observation taken when lmc x-1 was in an x - ray bright state . if present , quasi - periodic oscillations would appear as a broad peak in the pds . none of our observations shows this signature , although ebisawa et al . found strong qpo near 0.0751 hz in some of the @xmath14 data , with weaker qpo around 0.142 hz . ( most likely , this other peak is the second harmonic . ) upper limits for the amplitude of qpo signals in the @xmath0 observations were found by calculating the percent r.m.s . variation of the average excess power ( after subtracting the fitted model ) between 0.05 and 0.10 hz . typical 3@xmath20 limits are @xmath100.8% for the 260 kev pds , as listed in table 2 . for comparison , the amplitudes of the primary and secondary @xmath14 qpo peaks were 2.9% r.m.s . and 1.8% r.m.s . , respectively . hence , the power found in the @xmath14 qpo was much larger than the upper limits placed on the @xmath0 data . clearly , the appearance of qpo in lmc x-1 is a transient phenomenon , as further documented by the lack measurable qpo in bbxrt observations of this source ( schlegel et al . 1994a , 1994b ) . the x - ray energy spectrum of lmc x-1 was separately fit by two multi - component models over the energy range 3.615.9 kev . the soft thermal component was represented by both a blackbody and by a multicolor disk model ( mitsuda et al . 1984 ; makishima et al . 1986 ) , while the high - energy excess was always accounted for using a simple power law . within limitations imposed by an uncertain background subtraction at low energies in the @xmath0 data , both combinations yield acceptable fits . the intervening hydrogen absorption was fixed at @xmath21 @xmath22 in all cases , since the derivation of @xmath23 as a free parameter is very sensitive to errors in background subtraction . mean values for the fitted parameters , which are similar to those of ebisawa et al . ( 1989 ) and schlegel et al . ( 1994a ) , are summarized in table 3 . since the hardness ratio depends on source intensity , further modeling was performed on data selected by pca count rate count ( i.e. , 130140 cnts s@xmath2 , 140150 cnts s@xmath2 , etc . ) . the results of this fitting for the blackbody plus power - law model are shown in fig . 4 . within each observation , we find a trend for an increasing ` scale ' of the power law ( i.e. , comparable to intensity provided the photon index is constant ) with increasing source count" +"from the atmospheric and solar neutrino data , there is increasing evidence for neutrino oscillations@xcite . if this is a correct interpretation , the standard model ( sm ) has to be extended to incorporate the small masses of the neutrinos suggested by data . there have been several ideas proposed in literature to generate small neutrino masses . the zee - model is one of such attempts@xcite . in this model , all flavor neutrinos are massless at the tree level , and their small masses are induced radiatively through one - loop diagrams . for such a mass - generation mechanism to work , it is necessary to extend the higgs sector of the sm to contain at least two weak - doublet fields and one weak - singlet charged scalar field . although some studies have been done to examine the interaction of the leptons and the higgs bosons in the zee - model@xcite , the scalar ( higgs ) sector of the model remains unexplored in detail . in this paper we study the higgs sector of the zee - model to clarify its impact on the higgs search experiments , either at the cern lep - ii , the run - ii of the fermilab tevatron , the cern large hadron collider ( lhc ) , or future linear colliders ( lc s ) . experimental search for the higgs boson has been continued at the cern lep and the fermilab tevatron experiments . in the lep - ii experiments , the higgs boson with the mass less than about 110 gev has been excluded if its production cross section and decay modes are similar to those of the sm higgs boson@xcite . run - ii of the tevatron can be sensitive to a sm - like higgs boson with the mass up to about 180 gev , provided that the integrated luminosity of the collider is large enough ( about @xmath2)@xcite . furthermore , the primary goal of the cern lhc experiments is to guarantee the discovery of a sm - like higgs boson for its mass as large as about 1 tev@xcite , which is the upper bound of the sm higgs boson mass . ( for a higgs boson mass beyond this value , the sm is no longer a consistent low energy theory . ) when the higgs boson is discovered , its mass and various decay properties will be measured to test the sm and to distinguish models of new physics at high energy scales . for example , the allowed mass range of the lightest cp - even higgs boson ( @xmath0 ) can be determined by demanding the considered theory to be a valid effective theory all the way up to some cut - off energy scale ( @xmath3 ) . for @xmath4 gev ( i.e. , the planck scale ) , the lower and upper bounds of the sm higgs boson masses are 137 gev and 175 gev , respectively @xcite . the higgs mass bounds for the two - higgs - doublet - model ( thdm ) were also investigated@xcite with and without including the soft - breaking term with respect to the discrete symmetry that protects the natural flavor conservation . it was found in ref . @xcite that the lower bound of the lightest cp - even higgs boson is about 100 gev in the decoupling regime where only one neutral higgs boson is light as compared to the other physical states of higgs bosons . the higgs sector of the zee - model is similar to that of the thdm except for the existence of an additional weak - singlet charged higgs field , so that the physical scalar bosons include two cp - even , one cp - odd and two pairs of charged higgs bosons . in this paper , we shall first determine the upper and lower bounds for the lightest cp - even higgs boson mass ( @xmath5 ) as a function of the cut - off scale @xmath6 of the zee - model , using renormalization group equations ( rge s ) . we show that the upper and lower mass bounds for @xmath0 are almost the same as those in the thdm . we also study the possible range of the higgs - boson self - coupling constants at the electroweak scale as a function of @xmath6 . by using these results , we examine effects of the additional loop contribution of the singlet charged higgs boson to the partial decay width of @xmath7 . we show that , by taking @xmath8 gev , the deviation of the decay width from the sm prediction can be about @xmath920% or nearly @xmath1010% for @xmath11 between 125 gev and 140 gev when the mass of the isospin singlet charged higgs boson is taken to be around 100 gev . the magnitude of the deviation becomes larger for lower cutoff scales and smaller masses of the singlet charged higgs boson . if we choose @xmath12 gev and the singlet charged higgs boson mass to be 100 gev , the positive deviation can be greater than @xmath1030% ( @xmath1040% ) for @xmath13 gev ( @xmath14 gev ) . such a deviation from the sm prediction could be tested at the lhc , the @xmath15 lc and the @xmath16 option of lc@xcite . we also discuss phenomenology of the singlet charged higgs boson at present and future collider experiments , which is found to be completely different from that of the ordinary thdm - like charged higgs bosons . to detect such a charged higgs boson at lep - ii experiments , experimentalists have to search for their data sample with @xmath17 or @xmath18 plus missing energy , in contrast to the usual detection channels : either @xmath19 or @xmath20 decay modes . this paper is organized as follows . in sec . [ sec : zeemodel ] , we introduce the higgs sector of the zee - model and review the neutrino masses and mixings in this model which are consistent with the atmospheric and solar neutrino observations . numerical results on the possible range of the mass and coupling constants of the higgs bosons are given in sec . [ sec : rge_analysis ] . in sec [ sec : h-2gamma ] , we discuss the one - loop effect of the extra - higgs bosons in the zee - model to the partial decay width of @xmath7 and its impacts on the neutral higgs - boson search at high - energy colliders . the phenomenology of the charged higgs boson that comes from the additional singlet field is discussed in sec . [ sec : charged ] . in sec . [ sec : conclusion ] , we present additional discussions and conclusion . relevant rge s for the zee - model are given in the appendix . to generate small neutrino mass radiatively , the zee - model contains a @xmath21 singlet charged scalar field @xmath22 , in addition to two @xmath21 doublet fields @xmath23 , and @xmath24 . the zee - model lagrangian is written as : @xmath25 where @xmath26 @xmath27 where @xmath28 ( @xmath29 are the generation indices , and @xmath30 \nonumber \\ & & + \sigma _ { 1}\left| \omega^{-}\right| ^{2}\left| \phi _ { 1}\right| ^{2}+ \sigma _ { 2}\left| \omega^{-}\right| ^{2}\left| \phi _ { 2}\right| ^{2}+ \frac{1}{4}\sigma _ { 3}\left| \omega^{-}\right| ^{4 } \ , . \label{higgs_potential } \end{aligned}\ ] ] in the above equations , @xmath31 is the left - handed quark doublet with an implicit generation index while @xmath32 and @xmath33 denote the right - handed singlet quarks . similarly , @xmath34 and @xmath35 denote the left - handed and right - handed leptons in three generations . the charge conjugation of a fermion field is defined as @xmath36 , where @xmath37 is the charge conjugation matrix ( @xmath38 ) with the super index @xmath39 indicating the transpose of a matrix . also , @xmath40 and @xmath41 with @xmath42 . without loss of generality , we have taken the anti - symmetric matrix @xmath43 and the coupling @xmath44 to be real in the equations ( [ fij_int ] ) and ( [ higgs_potential ] ) . in order to suppress flavor changing neutral current ( fcnc ) at the tree level , a discrete symmetry , with @xmath45 , @xmath46 , @xmath47 , is imposed to the higgs sector of the lagrangian , which is only broken softly by the @xmath48 term and the @xmath49 term . under the discrete symmetry there are two possible yukawa - interactions ; that is , for type - i @xmath50 and for type - ii , @xmath51 where @xmath52,@xmath53,@xmath54 are diagonal yukawa matrices and @xmath55 is the cabibbo - kobayashi - maskawa ( ckm ) matrix . later , we shall only keep the top yukawa coupling constants @xmath56 in our numerical evaluation of the rge s . ] . in that case , there is no difference between the yukawa couplings of the type - i and the type - ii models . finally , for simplicity , we assume that all @xmath57 and @xmath58 are real parameters . let us now discuss the higgs sector . the @xmath59 symmetry is broken to @xmath60 by @xmath61 and @xmath62 , the vacuum expectation values of @xmath63 and @xmath64 . ( they are assumed to be real so that there is no spontaneous cp violation . ) the number of physical higgs bosons are two cp - even higgs bosons ( @xmath65,@xmath66 ) , one cp - odd higgs boson ( @xmath67 ) and two pairs of charged higgs boson ( @xmath68 , @xmath69 ) . we take a convention of @xmath70 and @xmath71 . in the basis where two higgs doublets are rotated by the angle @xmath72 , with @xmath73 , the mass matrices for the physical states of higgs bosons are given by @xmath74 \,,\ ] ] for cp - even higgs bosons , @xmath75 for cp - odd higgs boson , and @xmath76 \,,\ ] ] for charged higgs bosons . here , @xmath77 and @xmath78 . the vacuum expectation value @xmath79 ( @xmath80 gev ) is equal to @xmath81 . mass eigenstates for the cp - even and the charged higgs bosons are obtained by diagonalizing the mass matrices ( [ neutralmassmatrix ] ) and ( [ chargedmassmatrix ] ) , respectively . the original higgs boson fields , @xmath63 , @xmath64 , @xmath22 , can be expressed in terms of the physical states and the nambu - goldstone modes ( @xmath82 and @xmath83 ) as @xmath84 where the angle @xmath85 and @xmath86 are defined from the matrices which diagonalize the @xmath87 matrices @xmath88 and @xmath89 , respectively . namely , we have @xmath90 where @xmath91 and @xmath92 . the mixing angles @xmath93 and @xmath94 then satisfy @xmath95 which show that @xmath93 and @xmath94 approaches to @xmath96 and zero , respectively . ] , when @xmath97 is much greater than @xmath98 , @xmath99 and @xmath100 ; i.e. , in the decoupling regime . in this limit , the massive higgs bosons from the extra weak - doublet are very heavy due to the large @xmath101 so that they are decoupled from the low energy observable . although neutrinos in this model are massless at the tree level , the loop diagrams involving charged higgs bosons , as shown in fig . [ fig : neutrino_mass ] , can generate the majorana mass terms for all three - flavors of neutrinos . it was shown @xcite that at the one - loop order , the neutrino mass matrix , defined in the basis where the charged lepton yukawa - coupling constants are diagonal in the lepton flavor space , is real and symmetric with vanishing diagonal elements . more explicitly , we have @xmath102 with @xmath103 where @xmath104 @xmath105 is the charged lepton" +"the detection of stellar orbits @xcite close to sgr a * has proven that the galactic center ( gc ) hosts a massive black hole ( mbh ) with a mass of @xmath1 . sgr a * appears rather dim in all wavelengths , which is explained by accretion flow models @xcite . in the near infrared ( nir ) it was detected after diffraction limited observations at the 8-m class telescopes had become possible @xcite . usually the emission is not detectable . however , every few hours sgr a * flares in the nir , reaching up to @xmath2mag . a first flare spectrum was obtained by @xcite , showing a featureless , red spectrum ( @xmath3 with @xmath4 ) . we observed the gc on 2005 june 18 from 2:40 to 7:15 ut with sinfoni @xcite , an adaptive optics ( ao ) assisted integral field spectrometer which is mounted at the cassegrain focus of eso - vlt yepun ( ut4 ) . the field of view was 0.8@xmath50.8 for individual exposures , mapped onto 64@xmath532 spatial pixels . we observed in k - band with a spectral resolution of fwhm @xmath6 nm . the first 12 integrations lasted @xmath7min each . during those we noticed nir activity of sgr a * and we switched to 4 minute exposures . we followed sgr a * for another 32 exposures . in total we interleaved nine integrations on a specifically chosen off field ( 712 w , 406 n of sgr a * ) . the seeing was @xmath80.5 and the optical coherence time @xmath9ms , some short - time deteriorations excluded . the ao was locked on the closest optical guide star ( @xmath10 , 10.8 e , 18.8 n of sgr a * ) , yielding a spatial resolution of @xmath11mas fwhm , close to the diffraction limit of ut4 in k - band ( @xmath12mas ) . our detection triggered immediate follow - up observations with visir , a mid - infrared ( mir ) instrument mounted at eso - vlt melipal ( ut3 ) . from 5:25 ut onwards visir was pointing to the gc . at the position of sgr a * no significant flux was seen . a conservative upper limit of 40@xmath13mjy ( not dereddened ) at 8.59@xmath14 m is reported ( lagage et al . , in prep ) . the reduction of the sinfoni data followed the standard steps : from all source data we subtracted the respective sky frames to correct for instrumental and atmospheric background . we applied flatfielding , bad pixel correction , a search for cosmic ray hits , and a correction for the optical distortions of sinfoni . we calibrated the wavelength dimension with line emission lamps and tuned on the atmospheric oh - lines of the raw frames . finally we assembled the data into cubes with a spatial grid of 12.5@xmath13mas / pix . for all 44 cubes we extracted a collapsed image ( median in spectral dimension ) of a rectangular region ( 0.25@xmath50.5 ) centered on sgr a * and containing the three s - stars s2 , s13 , and s17 . we determined the flux of sgr a * from a fit with five gaussians to each of these images . four gaussians with a common width describe the four sources . the fifth gaussian ( with a width @xmath15 wider , typical for the halo from the imperfect ao correction ) accounts for the halo of the brightest star s2 ( @xmath16mag ) . the halos of the weaker sources ( all @xmath17mag ) could be neglected for the flux measurement . we fixed the positions of all sources ( known a - priori from a combined cube ) and the amplitude ratios for the stars . five parameters were left free : an overall amplitude , the background , the width , the flux ratio halo / s2 , and @xmath18 , the flux ratio sgr a*/s2 . this procedure disentangles real variability from variations in the background , the strehl ratio , and the seeing . as a crosscheck we determined @xmath18 in a second way for all images ; for both sgr a * and s2 we measured the flux difference between a signal region centered on source and a reasonable , symmetric background region . the such determined values agreed very well with the fits . for further analysis we used the fitted ratios and included the difference between the two estimates in the errors . the value of the spectral power law index @xmath19 crucially depends on the background subtraction . subtracting too much light would artificially make the signal look redder than it is . hence , a reasonable choice for the background region excludes the nearby sources s2 and s17 . furthermore , the background flux is varying spatially . actually sgr a * lies close to a saddle point in the background light distribution , caused by s2 and s17 ( see fig . [ adb ] ) . in the east - west direction the background has a maximum close to sgr a * and in the north - south direction a minimum . a proper estimate of the background can be achieved in two ways : a ) working with small enough , symmetric apertures , and b ) subtracting from the signal an off state obtained at the position of sgr a * from cubes in which no emission is seen . we used the first method as well as two variants of the second . + * small apertures : * the local background at a position @xmath20 can be estimated by averaging over a small , symmetric region centered on @xmath20 . given the background geometry we have chosen a ring with inner radius @xmath21pix and outer radius @xmath22pix . the circular symmetry was only broken since we explicitely excluded those pixels with a distance to s17 and s2 smaller than 3 and 7 pixels respectively . unfavorable of this method is that the local background is only approximated , since a sufficiently large region has to be declared as signal region . + * off state subtraction : * the local background can be extracted from cubes in which no signal is seen . since the seeing conditions change from cube to cube , one still has to correct for the varying amount of stray light in the signal region . we estimate this variation by measuring the difference spectrum between signal and off cube in a stray light region . the latter must not contain any field stars and should be as far away from the nearby sources as sgr a*. we used two stray light regions to the left and to the right of sgr a * , between 5 and 10 pixels away . the disadvantage of this method is that one needs a suitable off state . the latter point is critical for our data . even though sgr a * has not been detected directly in the first three cubes , the light at its position appears redder than the local background . assuming that this light is due to a very dim , red state of sgr a * , we would subtract too much red light and artificially make the flare too blue . in this sense , this method yields an upper limit for @xmath19 . + * constant subtraction : * the off state method can be varied to obtain a lower limit for @xmath19 . assuming that the true off state spectrum has the color of s2 , one can demand that it is flat after division by s2 . in our data , the s2 divided off state spectrum is rising towards longer wavelengths . hence , in this third method we estimate the background at blue wavelengths and use that constant as background for all spectral bins . we obtained spectra as the median of all pixels inside a disk with radius @xmath21pix centered on source minus the median spectrum of the pixels in the selected off region . in order to correct for the interstellar extinction we then divided by the s2-spectrum ( obtained in the same way as the signal ) . next the temperature of s2 is corrected by multiplying by the value of @xmath23 of a blackbody with @xmath24k . after binning the data into 60 spectral channels it is finally fit with a power law @xmath25 . with this definition , red emission has @xmath26 . the error on @xmath19 is obtained as the square sum of the formal fit error and the standard deviation in a sample of 20 estimates for @xmath19 obtained by varying the on and off region selection . we observed a strong ( flux density up to @xmath27mjy or @xmath28ergs / s ) , long ( more than 3 hours ) flare which showed significant brightness variations on timescales as short as 10 minutes ( fig . [ lightcurve ] , top ) . while the data is not optimal for a periodicity search ( poorer sampling than our previous imaging data ) , it is worth noting that the highest peak in the periodogram ( significance of @xmath29 ) lies at a period of @xmath30min this is also the timescale found by @xcite , who identify the quasi - periodicity with the orbital time close to the last stable orbit ( lso ) of the mbh . we divided the data into three groups : a ) the cubes of the first peak near @xmath31min ( `` preflare '' ) , b ) the cubes at @xmath32min with @xmath33@xmath34 0.25 ( `` dim state '' ) , and c ) the cubes at @xmath32min with @xmath33@xmath35 0.25 ( `` bright state '' ) . for the three sets we created combined cubes in which we determined @xmath19 , using all three background estimates . in all cases we obtained the correct spectral index @xmath36 for s17 ( a star with a spectrum similar to s2 but a flux comparable to sgr a * ) . for sgr a * we get : + [ cols="">,^,^,^"",options=""header "" , ] + the values obtained from the small apertures lie between the values from the other two methods , consistent with the idea that they yield upper and lower limits . the absolute values vary systematically according to the chosen background method . however , independent from that , it is clear that the preflare is redder than the dim state which in turn is redder than the bright state . an obvious question then is whether flux and @xmath19 are directly correlated . hence , we applied the spectral analysis to the individual cubes . we kept the data in which sgr a * is detected , the error @xmath37 and the spectral index for s17 does not deviate more than @xmath38 from the expected value . the resulting spectral indices appear to be correlated with the flux ( fig . [ lightcurve ] , [ corr ] ) . the values match the results in @xcite and @xcite . bright flares are indeed bluer than weak flares , as suspected by @xcite and consistent with the earlier multi - band observations of @xcite . our key new result is that this even holds within a single event . for all three background methods it is clear that the main event was preceded by a weak , red event . for the small apertures and the constant subtraction method instantaneous flux and spectral index are correlated . for the off state subtraction method one could instead group the data into a preflare at the beginning and a bluer , brighter main event . we checked our data for contamination effects . if stray light would affect the flare signal , @xmath19 should" +"recently @xcite a semiempirical shell model mass equation ( ssme ) based on proton magic number z = 126 @xcite was shown to have a high predictive power in the interior of major shell regions beyond lead n @xmath1 and with 126 @xmath2 n @xmath2 184 . we refer to them respectively as region a and region b , like in refs . [ 1,2 ] . ] . the equation has been proposed as a substitute inside the above regions for the previous ssme @xcite which is based on z = 114 as the highest proton magic number and it stops there . tabulated masses with separation and decay energies for both regions are available @xcite . in the present work the predicted masses ( eq . ( 1 ) of ref . @xcite , referred to as eq . ( 1 ) in the sequel , and table b of ref . @xcite ) are applied to the results of recent superheavy elements ( she ) experiments . we first address the smoothness of the predictions and their overall agreement with @xmath3 systematics . then we test the agreement of the equation with the data observed in several recent fusion - evaporation she experiments where the produced nuclei are identified by their decay ties to known daughter isotopes . finally we address the interpretation problem in some recent hot fusion experiments where the observed decay chains do not connect the parent to a known daughter , and several reaction channels are in principle possible . inside a shell region the mass surface predicted by eq . ( 1 ) is smoother than the empirical surface and does not account for fine structure effects . this is illustrated in fig . 1 showing q@xmath4 systematics for the heaviest n @xmath5 140 even - z nuclei from pu through z = 110 @xcite . respective full and empty circles denote experimental values and values estimated from systematics . the small circles connected by thin lines show the predictions of eq . ( 1 ) . as a rule both the experimental and the predicted isotopic lines show similar negative trends when n increases , and they shift upwards rather uniformly when z increases . for the experimental lines , though , this regular pattern breaks down for nuclei in the vicinity of the deformed doubly submagic nucleus ( n@xmath6 , z@xmath6 ) @xmath7fm ( n@xmath6 = 152 , z@xmath6 = 100 ) , and presumably even more so near @xmath8hs ( n@xmath6 = 162 , z@xmath6 = 108 ) @xcite ( see also fig . 5 . ) . in these neighborhoods the trend of isotopic lines between n = n@xmath6 and n = n@xmath6 + 2 is positive , and the vertical distance between isotopic lines with z = z@xmath6 and z = z@xmath6 + 2 for n @xmath9 n@xmath6 is larger than for other z values . none of these submagic number effects is shown by the predicted thin lines systematics . ( see also refs . @xcite . ) in the ssme non - smooth abrupt local changes , which are associated with subshell and deformation effects , are assumed to have been smoothed out by configuration interaction ( eq . ( 4 ) of ref . @xcite ) , and the mass equation describes a smooth surface representing their average . the deviations from the average are mostly small , though , resulting in the above mentioned overall high - quality predictive power . for the 57 experimental @xmath3 values measured in region b after the equation was adjusted @xcite the respective average deviation @xmath10 and rms deviation @xmath11 of the predicted values from the data are @xmath128 and 220 kev ( table ii of ref . ( for all the 115 data points shown in fig . 1 , both experimental and estimated from systematics , the corresponding values are @xmath1233 and 214 kev . ) we now address the agreement of the equation with @xmath0-decay energies observed in the cold fusion production experiments of elements 107 - 112 @xcite ( see also refs . @xcite and @xcite ) . figs . 2 - 5 show the measured and the predicted @xmath3 values , assuming that the decays go through or near the g.s . fig . 5 shows as well the @xmath3 values observed in hot fusion experiments producing @xmath13sg @xcite and @xmath14bh @xcite , where in refs . @xcite and @xcite the @xmath0-chains were studied after chemical separation of the recoiling evaporation residue ( evr ) parent , leading to chemical identification . the figures show as well the @xmath15 and @xmath16 values for the plotted data points . on the whole they are not large , with @xmath16 values compatible with the above quoted 220 kev value from table ii of ref . the respective overall @xmath15 and @xmath16 values for all the 32 data points in figs . 2 - 5 are 86 and 337 kev . the largest individual deviations occur for z = 107 , 108 and 110 in fig . 5 , with respective values of 659 , 712 and @xmath12605 kev . these seem to be too large for the above quoted value of 220 kev , and they correspond to a kink observed in the @xmath17112 @xmath3 chain at z = 108 . if this kink is a genuine submagic number effect due to the crossing of n = 162 on the way from z = 108 to z = 110 @xcite , then fig . 5 illustrates the oversmoothness of the predicted masses as compared to the empirical data with its discontinuities in the vicinity of doubly submagic nuclei . ( see sect . the pertinent submagic numbers in the present case are n@xmath6 = 162 and z@xmath6 = 108 . closer scrutiny of figs . 1 and 5 reveals stronger magicity of @xmath8hs as compared to @xmath7fm . in hot fusion - evaporation she experiments , when the compound nucleus ( cn ) is produced at a sufficiently high excitation energy ( e@xmath18 ) , there are often several conceivable open emission channels for forming the parent , which would lead to different observable @xmath0-decay chains . when the @xmath0-decay chain starting from the evr parent nucleus does not connect to a known daughter isotope , comparing different predictions to the observed data might facilitate the choice between different conceivable interpretations . we consider from this point of view some recent she experiments @xcite . in refs . @xcite a @xmath19 cm target was bombarded by 240 mev @xmath20ca ions . three observed three - members @xmath0-decay chains are assigned to the nuclide @xmath21116 and its sequential decay down to @xmath22110 . the cn formed in the reaction is @xmath23116 at e@xmath24 27 mev obtained from the cm and ca masses @xcite and the predicted mass of the cn @xcite . at this higher energy more channels for particle emission might be open than in the cold fusion experiments considered in sect . iii , including up to @xmath25 and also @xmath26 or @xmath0 emission . four conceivable evr parents in addition to the assigned parent @xmath21116 are considered in table i. their corresponding formation channels , the estimated values of their excitation energies ( e@xmath27 ) in tables i and ii are obtained from the kinematics of the reactions assuming that the evaporated neutrons have zero kinetic energy and the evaporated charged particles ( @xmath26 and @xmath0 ) have a kinetic energy which is equal to their potential energy at the top of the coulomb barrier . higher kinetic energies of the evaporated particles would reduce the estimates given in the tables . this is the case for the @xmath28 channels , with an average c.m . neutron kinetic energy of about 1 mev per neutron @xcite . ] when formed , and the deviations @xmath15 and @xmath16 from the data of the corresponding predicted @xmath3 values , assuming that the @xmath0-decays go through or near the g.s . , are given in the table . for the @xmath29 formation channel assigned by the authors the estimated e@xmath27 value of the parent nucleus @xmath30 is too low ( less than 2 mev ) to have a reasonable production cross section . moreover , the 758 kev @xmath16 value of the predicted @xmath3 values is too large . on the other hand , for the @xmath31 channel leading to the evr parent @xmath32 the corresponding estimated e@xmath27 value and the value of @xmath16 are @xmath214 mev and 466 kev which are reasonable . this might lend support to a scenario based on the @xmath31 ( and possibly also @xmath25 ) channel . the last two members of the @xmath0-decay chains seen in this experiment agree with the two - members @xmath0-decay chains observed before in a z = 114 experiment @xcite . if they are the same , a formation of the present z = 116 parent by @xmath31 ( or @xmath25 ) emission would imply the same formation channel for the z = 114 evr parent in ref . @xcite , rather than the assigned @xmath29 channel . 6 compares the experimental @xmath3 values with the predictions of eq . ( 1 ) for assumed @xmath31 , @xmath25 and @xmath29 evaporation channels . the improvement when going from @xmath29 to @xmath31 is clear . as a second example we consider the experiment reported in ref . a @xmath33pu target was bombarded by 236 mev @xmath20ca ions . an observed three - members @xmath0-decay chain is considered a good candidate for originating from the parent @xmath34114 and its sequential decay down to @xmath17hs ( z = 108 ) . for the @xmath25 formation channel assigned by the authors , leading to the evr parent @xmath35 , the respective estimated e@xmath27 value and the @xmath16 value are @xmath29 mev and 905 kev . the @xmath16 value is too large . if the assignment of the authors is confirmed this might indicate that the decay chain does not proceed through levels in the vicinity of the g.s . on the other hand , for the @xmath26 or @xmath0 channels , leading to the respective evr parents @xmath36113 or @xmath37112 , the respective e@xmath27 and @xmath16 values are 8 or 9 mev and 414 or 363 kev . this might lend some support to scenarios based on the @xmath26 or @xmath0 evaporation channels . 7 compares the experimental @xmath3 values with the predictions of eq . ( 1 ) for assumed @xmath38 and @xmath0 evaporation channels . the advantage of the @xmath26 or @xmath0 assignments over @xmath25 and @xmath31 is obvious . .conceivable evr parents of the @xmath0-decay chain [ 25,27 ] with their formation channels , their estimated values of e@xmath27 , and the deviations @xmath15 and @xmath16 from the data of the corresponding predicted @xmath3 values . [ cols=""<,^,^,^,^ "" , ]" +"while the earth s magnetism has been studied for centuries starting with the first scientific monograph of gilbert ( 1600 ) , the question of the magnetism of other planets had received scant attention until recently because of the lack of relevant observations . only in 1955 clear evidence for the existence of a planetary magnetic field other than the geomagnetic one was obtained through the observation of the jovian decametric radio waves ( burke and franklin , 1955 ) . since it had been more or less accepted until the end of the 19-th century that geomagnetism arises from the remnant magnetization of the earth similar properties may have been assumed for the other terrestrial planets and the moon this view lost its appeal , however , when it became evident that the curie - temperature is exceeded in the earth below a depth of about 30 km . ferromagnetic materials in the earth s crust could thus explain only magnetic fields with a relatively short wavelength . the current period of intense research on the magnetism of planets other than that of the earth started with the first detailed measurement of jupiter s magnetic field by the pioneer 10 space probe in 1973 and the discovery of mercury s magnetism by mariner 10 in 1974 . in the early seventies also the development of the theory of magnetohydrodynamic dynamos had started in which the reaction of the lorentz force of the generated magnetic field is taken into account in physically realistic configurations ( childress and soward , 1972 ; busse , 1973 ; soward , 1974 ) . until that time dynamo theoreticians had focused their attention on the kinematic problem in which the possibility of growing magnetic fields driven by somewhat arbitrarily chosen velocity fields is considered . it must be remembered that only a few years earlier it had been demonstrated by backus ( 1958 ) and herzenberg ( 1958 ) in a mathematically convincing way that the homogeneous dynamo process of the generation of magnetic fields in a singly connected domain of an electrically conducting fluid is indeed possible . doubts about the feasibility of this process which had first been proposed by larmor ( 1919 ) had persisted after cowling ( 1934 ) had proved that purely axisymmetric fields could not be generated in this way . the complexity of the magnetohydrodynamic dynamo problem described by the nonlinearly coupled navier - stokes equations and the equation of magnetic induction had prevented progress in understanding planetary dynamos through analytical solutions . only the advent of powerful enough computers in the 1990-ies has allowed to solve numerically the coupled three - dimensional partial differential equations through forward integration in time . even today and for the foreseeable future the limits of computer capacity will permit the exploration of only a small fraction of the parameter space of interest for the understanding of planetary dynamos . in view of the difficulties of a rigorous theory of planetary dynamos , many attempts have been made to obtain simple similarity relationships which would fit the observed planetary magnetic moments as function of certain properties of the planets . some early proponents have gone as far as claiming the existence of a `` magnetic bode s law '' corresponding to a relationship between the magnetic moment and size or angular momentum of a planet in analogy to the titius - bode law for the radii of the orbits of the planets . just as in the latter case , however , attempts to derive a magnetic bode s law from basic physical principles have failed . other proposals have taken into account physical forces . since a common ingredient of planetary dynamos is the existence of a fluid part of the core with a sufficiently high electrical conductivity the latter parameter together with the core radius and the angular velocity of the planetary rotation usually enter the similarity relationships such as those proposed by hide ( 1974 ) , busse ( 1976 ) , jacobs ( 1979 ) and dolginov ( 1977 ) . malkus ( 1968 , 1996 ) has argued for the precession of the earth as the cause of geomagnetism and he and vanyo ( 1984 ) have demonstrated through laboratory experiments that precession and tides may cause turbulent motions in fluid planetary cores . dolginov ( 1977 ) proposed a scaling law for the precessional origin of all planetary magnetic fields . while a dynamo driven by turbulent flows caused by precession and tides can not be easily excluded in the case of the earth ( tilgner , 2005 ) , it is much less likely in the case of other planets such as uranus for which precessional torques are rather minute . just as a common precessional origin of planetary magnetism is not regarded as feasible , so have all other proposed similarity relationships lost in appeal and are no longer seriously considered . we shall return , however , to scaling relationships based more directly on the basic equations in section 6 . since the proposal of the geodynamo as the cause of the earth s magnetism had been in doubt for a long time before 1958 , numerous alternative proposals had been made in the literature . among these only the possibility that thermoelectric currents may generate a planetary magnetic field is still discussed in the case of mercury ( stevenson , 1987 ; giampieri and balogh , 2002 ) . for a discussion of the failings of the various proposals for non - dynamo origins of planetary magnetic fields we refer to the papers of bullard ( 1949 ) and stevenson ( 1983 ) . although the dynamo hypothesis of the origin of planetary magnetism is not without difficulties , it is the only one considered seriously at the present time with the possible exception of the just mentioned case of mercury . dynamos generally convert mechanical energy into magnetic one . in contrast to the technical dynamo which is characterized by a multiply connected region of high electrical conductivity , i.e. it depends on an appropriate wiring , planetary dynamos are referred to as homogeneous dynamos since they operate in a singly connected domain of high electrical conductivity . since flows in planetary cores with active dynamos are usually turbulent the small scale structure of the magnetic field is correspondingly chaotic . the large scale structure , however , can be quite regular . one distinguishes `` steady '' and oscillatory dynamos . the most famous example of the latter kind is the solar dynamo which exhibits a well defined period of about 22 years . the geodynamo , on the other hand , is a `` steady '' dynamo , even though it varies in its amplitude by a factor of two or more on the magnetic diffusion time scale and reverses its polarity on a longer time scale . a measure of the magnetic diffusion time is given by the decay time , @xmath0 , of the magnetic field in the absence of fluid motions . here @xmath1 and @xmath2 refer to the electrical conductivity and the magnetic permeability of the planetary core of radius @xmath3 . in the case of the earth the decay time is of the order of 20 000 years , but it may vary between a few hundred and a million years for other examples of planetary dynamos . the theory of homogeneous dynamos is based on maxwell s equations for the magnetic flux density @xmath4 , the electric current density @xmath5 and the electric field @xmath6 in the magnetohydrodynamic approximation in which the displacement current is neglected . this approximation is highly accurate as long as the fluid velocity is small compared to the velocity of light which is certainly the case for all planetary applications . these equations together with ohm s law for a moving conductor are given by @xmath7 where @xmath2 is the magnetic permeability of the fluid and @xmath1 is its electrical conductivity . these `` pre - maxwell '' equations have the property that they are invariant with respect to a galilei transformation , i. e. the equations remain unchanged in a new frame of reference moving with the constant velocity vector @xmath8 relative to the original frame of reference . indicating the variables of the new frame by a prime we find @xmath9 this invariance is the basis for the combination in mhd of equations ( 1 ) with the equations of hydrodynamics in their usual non - relativistic form . it is remarkable that this invariance does not only hold with respect to a galilei transformation , but with respect to a transformation to a rotating frame of reference as well . in that case @xmath8 is replaced by @xmath10 in equations ( 2 ) , but when @xmath11 is operating on any vector @xmath12 the term @xmath13 must be added on the right hand side , since even a constant vector field becomes time dependent when seen from a rotating frame unless it is parallel to @xmath14 . elimination of @xmath6 and @xmath5 from equation ( 1 ) yields the equation of magnetic induction @xmath15 which for a solenoidal velocity field @xmath16 and a constant magnetic diffusivity @xmath17 can be further simplified , @xmath18 this equation has the form of a heat equation with the magnetic field line stretching term on the right hand side acting as a heat source . this interpretation is especially useful for the dynamo problem . in order that a magnetic field @xmath4 may grow , the term on the right hand side of ( 4 ) must overcome the effect of the magnetic diffusion term on the left hand side . using a typical velocity @xmath19 and a typical length scale @xmath20 , the ratio of the two terms can be estimated by the magnetic reynolds number @xmath21 , @xmath22 only when @xmath21 is of the order one or larger may growing magnetic fields become possible . in the following we shall first consider the mathematical formulation of the problem of convection driven dynamos in rotating spherical shells in a simple form in which only the physically most relevant parameters are taken into account . before discussing dynamo solutions in section 5 we shall briefly outline in section 4 properties of convection it the absence of a magnetic field . applications to various planets and moons will be considered in section 6 of this article and some concluding remarks are given in section 7 . a sketch of the geometrical configuration that will be considered is shown in figure 1 . for the equations describing convection driven dynamos in the frame rotating with the angular velocity @xmath23 we use a standard formulation which has also been used for a dynamo benchmark ( christensen _ et al . but we assume different scales and assume that a more general static state exists with the temperature distribution @xmath24 where @xmath25 denotes the ratio of inner to outer radius of the spherical shell and @xmath20 is its thickness . @xmath26 is the temperature difference between the boundaries in the special case @xmath27 . in the case @xmath28 the static temperature distribution @xmath29 corresponds to that of a homogeneously heated sphere with the heat source density proportional to the parameter @xmath30 . the gravity field is given by @xmath31 where @xmath32 is the position vector with respect to the center of the sphere and @xmath33 is its length measured in units of @xmath20 . in addition to @xmath20 , the time @xmath34 , the temperature @xmath35 and the magnetic flux density @xmath36 are used as scales for the dimensionless description of the problem where @xmath37 denotes the kinematic viscosity of the fluid , @xmath38 its thermal diffusivity and @xmath39 its density . the boussinesq approximation is used in that @xmath39 is assumed to be constant except in the gravity term where its temperature" +"entanglement , an essential feature of the quantum mechanics , has been introduced in many fields of physics . in the field of quantum information , the entanglement has played a key role . the study of entanglement properties in many - body systems have attracted much attention @xcite-@xcite . the heisenberg chains , widely studied in the condensed matter field , display rich entanglement features and have many useful applications such as in the quantum state transfer @xcite . most of the systems considered in previous studies are spin - half systems as there exists a good measure of entanglement of two spin - halves , the concurrence @xcite , which is applicable to an arbitrary state of two spin halves . on the other hand , the entanglements in mixed - spin or higher spin systems are not well - studied due to the lack of good operational entanglement measures . there are several initial studies along this direction @xcite , however these works are restricted to the case of two particles . for the case of higher spins , a non - entangled state has necessarily a positive partial transpose according to the peres - horodecki criterion @xcite . in the case of two spin halves , and the case of ( 1/2,1 ) mixed spins , fortunately , a positive partial transpose is also sufficient . thus , the sufficient and necessary condition for entangled state in ( 1/2,1 ) mixed spin systems is that it has a negative partial transpose . this allows us to investigate entanglement features of the mixed spin system . the peres - horodecki criterion give a qualitative way for judging whether the state is entangled or not . the quantitative version of the criterion was developed by vidal and werner @xcite . they presented a measure of entanglement called negativity that can be computed efficiently , and the negativity does not increase under local manipulations of the system . the negativity of a state @xmath0 is defined as @xmath1 where @xmath2 is the negative eigenvalue of @xmath3 , and @xmath4 denotes + the partial transpose with respect to the first system . the negativity @xmath5 is related to the trace norm of @xmath3 via @xmath6 where the trace norm of @xmath3 is equal to the sum of the absolute values of the eigenvalues of @xmath3 . in this paper , we will use the concept of negativity to study entanglement in ( 1/2,1 ) mixed - spin systems . as shown in most previous works , models with the nn exchange interactions are considered and it is not easy to have pairwise entanglement between the nnn spins @xcite . it is true that there exist some quasi - one - dimension compounds offering us systems with nnn interactions . bose and chattopadhyay @xcite and gu et al . @xcite have investigated entanglement in spin - half heisenberg chain with nnn interactions . in our paper here , we study entanglement properties not only in the ( 1/2,1 ) mixed - spin systems only with nn interactions , but also in the system with nnn interactions . entanglement in a system with a few spins displays general features of entanglement with more spins . for instance , in the anisotropic heisenberg model with a large number of qubits , the pairwise entanglement shows a maximum at the isotropic point @xcite . this feature was already shown in a small system with four or five qubits @xcite . so , the study of small systems is meaningful in the study of entanglement as they may reflect general features of larger or macroscopic systems . also , due to the limitation of our computation capability , we only concentrate on small systems such as 4 , 5 and 6-spin models . the paper is organized as follows . in sec . ii , we study the systems with only nn interactions . the analytical results of negativity for the cases of two and three spins are given . the relation between entanglement and the macroscopic thermodynamical function , the internal energy is revealed . also we numerically compute the negativity in more general mixed - spin models up to eight spins , and consider the effects of magnetic fields in this section . in sec . iii , the system with nnn interaction is discussed . for the four - spin case , we analytically calculate the eigenenergy of the system from which we get the analytical results of the negativity of the nn spins . we numerically study negativities versus nnn exchanging coupling , and the case of finite temperature is also considered . for larger system up to eight - spin system , we get some numerical results . the conclusion is given in sec . we study entanglement of states of the system at thermal equilibrium described by the density operator @xmath7 , where @xmath8 , @xmath9 is the boltzmann s constant , which is assumed to be one throughout the paper , and @xmath10 is the partition function . the entanglement in the thermal state is called thermal entanglement . we consider two kinds of spins , spin @xmath11 and @xmath12 , alternating on a ring with antiferromagnetic exchange coupling . the hamiltonian is given by @xmath13 where @xmath14 and @xmath15 are spin-1/2 and spin-1 operators , respectively . the exchange interactions exist only between nearest neighbors , and they are of the same strength which are set to one . we adopt the periodic boundary condition . in fig . 1 , we give the schematic representation of the above hamiltonian . next , we first consider the models with two and three spins , and aim at getting analytical results of entanglement . for the two - spin case , the hamiltonian ( [ h01 ] ) reduces to @xmath16 . to have a matrix representation of the hamiltonian , we choose the following basis @xmath17 where @xmath18 is the eigenstate of @xmath19 and @xmath20 with the corresponding eigenvalues given by @xmath21 and @xmath22 , respectively . in the above basis , the hamiltonian can be written as a block - diagonal form with the dimension of each block being at most @xmath23 . thus , the density matrix @xmath24 for the thermal state is obtained as @xmath25 with the partition function and the matrix elements given by @xmath26 after the partial transpose with respect to the first spin - half subsystem , we can get @xmath27 @xmath28 which is still of the block - diagonal form , and computation of its eigenvalues is straightforward . there are only two eigenvalues which are possibly negative . the negativity is thus given by @xmath29\nonumber\\ + & \frac{1}2\max\big[0,\sqrt{(a_5-a_6)^2 + 4b_1 ^ 2}-a_5-a_6\big].\label{n}\end{aligned}\ ] ] substituting eqs . ( [ para1])([para2 ] ) leads to the analytical result of negativity @xmath30\nonumber\\ = & 2\max[0,a_2 - 2a_1]\nonumber\\ = & \frac{1}{3}\max\big[0,\frac{e^\beta-4e^{-\frac{1}{2}\beta } } { e^\beta+2e^{-\frac{1}{2}\beta}}\big],\label{n1}\end{aligned}\ ] ] where the second equality follows from eq . ( [ para2 ] ) . we can see that the negativity is a function of the single parameter @xmath31 . in the limit of @xmath32 , the negativity becomes 1/3 and the ground state is entangled . from eq . ( [ n1 ] ) , it is direct to check that the negativity is a monotonically decreasing function when temperature increases . after a certain threshold value of the temperature , the entanglement disappears . this threshold value @xmath33 can be obtained as @xmath34 for a ring of spin - half particles interacting via the hisenberg hamiltonian , it was shown that the pairwise thermal entanglement is determined by the internal energy @xcite . it is natural to ask if similar relations exist in the present mixed - spin system . the internal energy can be obtained from the partition function as @xmath35 substituting eq . ( [ para1 ] ) into the above equation leads to @xmath36 from eqs . ( [ n1 ] ) and ( [ u ] ) , we obtain a quantitative relation between the negativity and the internal energy @xmath37.\label{u1}\ ] ] the above equation builds a connection between the microscopic entanglement and the macroscopic thermodynamical function , the internal energy . the internal energy completely determine the thermal entanglement . from the equation , we can also read that the thermal state becomes entangled if and only if the internal energy @xmath38 . since @xmath39 , we have @xmath40,\label{u2}\ ] ] which is consistent with the result obtained in ref . @xcite by the group - theoretical technique . we now consider the three - spin case and the schematic representation of the corresponding hamiltonian is given by fig . 1 . in this situation , there are two types of pairwise entanglement , the entanglement between spin 1/2 and spin 1 and the entanglement between two spin halves . the eigenvalue problem can be solved analytically , and after tracing out the third spin - half system the reduced density matrix @xmath24 is still of the same form as in eq . ( [ rho ] ) with matrix elements given by @xmath41 substituting the above equations to eq . ( [ n ] ) leads to the negativity @xmath42/z.\ ] ] it is evident that the negativity becomes 1/3 in the limit of @xmath32 . from the expression of the negativity , the threshold value of temperature after which the entanglement vanishes can be estimated as @xmath43 to examine the entanglement between two spin halves , we trace out the spin 1 system and get the reduced density matrix @xmath44 as follows @xmath45 with the matrix elements given by @xmath46 after taking the partial transpose , we can get @xmath47 @xmath48 then , the negativity is readily obtained as @xmath49.\ ] ] it is straightforward to check that the negativity is always zero . or , from another way , all the eigenvalues of the matrix @xmath47 are obtained as @xmath50 obviously the negativity vanishes here , in other words there is no entanglement between the two spin halves . the ground - state negativity @xmath51=1/3 and @xmath52=0 , here @xmath53 denotes the negativity between the @xmath54 and @xmath55 spin on the chain and @xmath56 denotes the one between the @xmath54 and @xmath57 spin . the equation above can be obtained from the non - degenerate ground state given by : @xmath58 it is interesting to see that the ground - state entanglement between the spin half and spin 1 in the three - spin case is the same as that in the two - spin case . due to the su(2 ) symmetry in our system , there are following relations between correlation functions and negativities @xcite @xmath59 where we have removed the max function in the negativity , implying that the negative value of @xmath5 indicates no entanglement . then , we have the relation between the internal energy and the negativities @xmath60 the second equality follows from the exchange symmetry , namely , the hamiltonian is invariant when exchanging two spin halves . so , for the three - spin case , the internal energy is related to two negativities . to apply the above result , we consider the the ground - state properties ( @xmath61 ) . the hamiltonian can be rewritten as @xmath62.\ ] ] then , by the angular momentum coupling theory , the ground - state energy is obtained as @xmath63 . substituting the ground - state energy and @xmath64 to eq . ( [ relation ] ) , we obtain @xmath65 , indicating that there exists no entanglement between two spin halves . next , we consider more general situations , i.e. , the case of even @xmath66 sites . except for the su(2 ) symmetry in the system , there exists exchange symmetry for the case of even spins . for instance , in the four" +"one of the most active topics in current electromagnetics research is the study of artificial structures where permittivity @xmath0 and permeability @xmath1 are engineered . this allows them to have values not available in natural materials , or which can not normally be obtained at the desired operating frequency . a particularly interesting example is materials having a permittivity of zero at some frequency @xcite . in such structures the wavelength becomes infinite , and wave propagation over distances much larger than the free space wavelength can be treated as quasi - static . since this qualitative behavior is still observable even when the complex permittivity is close to but not identically zero , the term epsilon - near - zero ( enz ) has been coined to describe it . as one interesting application of enz materials , it has been shown theoretically that a narrow enz channel would support complete transmission of a signal incident from a larger waveguide @xcite , despite the large geometric mismatch . this was subsequently demonstrated experimentally in systems where the enz response was engineered via a surface pattern @xcite , and also using the natural dispersion characteristics of a rectangular waveguide near its cut - off frequency without the use of any composite structure @xcite . using the cut - off waveguide approach , it is straightforward to tailor the center - frequency and bandwidth of this transmission effect by modifying the geometry of the waveguide . it has also been shown that the enz tunneling frequency is sensitive to a dielectric cavity included within the waveguide , thus it can be used for sensing @xcite . this paper aims to demonstrate experimentally that the tunneling effect can be dynamically controlled by placing a tuning element within the waveguide . this allows for efficient control of the enz transmission , with potential applications in tunable slow - light structures . we also demonstrate that the introduction of nonlinearity into the system allows the enz resonance to be controlled by the incident wave itself . the structure under consideration is presented in fig . [ fig : structure](a ) , where rectangular waveguides of width @xmath2 and height @xmath3 feed a signal through a narrow section of width @xmath2 , height @xmath4 , and length @xmath5 , which exhibits the enz property at microwave frequencies . since the enz tunneling occurs at the cut - off frequency of the fundamental te@xmath6 mode of the narrow section , the feeding sections of waveguide are made from a material with a higher dielectric constant to ensure that their te@xmath6 mode is propagating . in refs . an equivalent circuit model was given for the structure , with the feeding waveguides , enz channel and dielectric cavity represented by sections of transmission line , as shown in fig . [ fig : structure](b ) . the reactances at the transition due to the excitation of evanescent higher - order modes @xcite have previously been shown to have a negligible effect on the enz tunneling . equation was then derived as the condition for full transmission of an enz system including a cavity with a different dielectric constant from the rest of the enz channel : @xmath7 here @xmath8 , @xmath9 , @xmath10 , @xmath11 and @xmath12 represent the impedance and wavenumber of each section and @xmath13 . the subscript @xmath14 refers to the enz channel , and @xmath15 to the dielectric cavity within it , and all relevant dimensions are given in fig . [ fig : structure](a ) . equation has one solution associated with enz tunneling , and an infinite number of solutions corresponding to the fabry - perot resonances along the channel . it can be used to show how the enz transmission frequency will change due to a change in dielectric constant of the cavity , which could potentially include the whole length of the enz section . this could be used in a sensing configuration where the cavity is filled with some material of unknown dielectric constant , or alternatively for tuning if the dielectric constant can be controlled externally . at microwave frequencies , tuning is much more readily achieved using lumped nonlinear components , as illustrated in fig . [ fig : lumped_structure](a ) . this can be regarded as a limiting case of a dielectric inclusion of small cross - section , however it is much more convenient to include the lumped elements into the equivalent circuit model , as shown in fig . [ fig : lumped_structure](b ) we are most interested in capacitive lumped inclusions , however the insertion of a narrow conducting element between the top and bottom of the waveguide will also result in some additional inductance in the equivalent circuit model @xcite , due to the excitation of higher - order evanescent modes . thus we consider here a series inductance @xmath16 and capacitance @xmath17 with a shunt connection between the transmission line section , noting that the values in the equivalent circuit model also include the effect of parasitics and the excitation of higher - order modes . the resultant expression for complete transmission is : @xmath18 this also has solutions for the enz and fabry - perot resonances , and generalizes the dielectric sensing and tunability of this structure to include lumped elements . thus the study of lumped nonlinear inclusions can yield much insight into the broader behavior of nonlinear enz systems . it should be noted that the impedance @xmath11 of a waveguide mode is not uniquely defined @xcite , however for consistency with the circuit model of fig . [ fig : lumped_structure ] we are required to use the following definition : @xmath19 we have confirmed numerically that the introduction of a lumped linear capacitance can be used to tune the frequency of the enz response . figure [ fig : tuning_ideal ] shows the transmission response with @xmath20nh as @xmath17 is varied , calculated using our equivalent circuit model . ] it can be seen that the maximum magnitude of the transmission is not changed , but the resonant frequencies are shifted and the quality factor is increased by the additional capacitance . the electric field within the channel at the enz transmission frequency was analyzed in the commercial electromagnetics solver cst microwave studio @xcite for a channel loaded with a 4pf capacitor . it was found that a phase variation of only 4@xmath21 occurred over the length of the channel , which is one third of the free space wavelength . the complete transmission and low phase variation confirm that the essential features of the enz coupling have been maintained . to confirm the tunability , we use an experimental configuration and parameter retrieval procedure similar to that described in ref . , with @xmath22 mm , @xmath23 mm and @xmath24 mm . the input and output waveguides consist of ptfe ( teflon ) beams covered in conductive tape , fed by a coaxial connector attached to a probe . smaller probes are placed within these waveguides to measure the amplitudes of the modes propagating inside the waveguide and to find the transmission and reflection parameters of the enz channel . the transmission through the system is measured at 1601 frequency points using a network analyzer , and by measuring the amplitude and phase of all the incident and reflected waves within the feeding waveguides , we are able to solve for the scattering parameters of the enz channel . the enz channel itself is fabricated from brass sheet and blocks . to introduce a tunable capacitance , we use an smv1231 varactor diode , with capacitance tunable between 0.45 - 2.35pf . this is soldered to a small piece of circuit - board introduced into the enz channel . as shown in fig . [ fig : lumped_structure](a ) there is a direct electrical connection at one end and a small inductor - capacitor network at the other to allow dc biasing whilst still maintaining a low impedance rf connection to the channel wall . figure [ fig : tuning_narrow](a ) shows the measured transmission as a result of tuning the dc voltage and hence the diode capacitance . the observed frequency shift is similar to that predicted by the equivalent circuit model , as shown in fig . [ fig : tuning_ideal ] , although there is as a reduction in the transmission amplitude and quality factor for higher capacitance values . the discrepancy is due to the parasitic capacitance , inductance and resistance of the diode , the inductance due to the interruption in the waveguide , as well as the influence of the circuit board and biasing components . however , it is clearly shown that high transmission can still be achieved for a substantial tuning range , and that for quite reasonable values of voltage the enz resonance can effectively be switched on and off by the control signal . ] the numerical results obtained from cst microwave studio are shown in fig . [ fig : tuning_narrow](b ) for comparison , corresponding to the diode capacitance for each voltage in fig . [ fig : tuning_narrow](a ) . by adding a parasitic inductance of 3.5nh and a parasitic capacitance of 0.1pf due to the circuit board and biasing circuit , we are able to achieve reasonable agreement with experiments . we note that exact agreement is difficult due to the high sensitivity of the channel resonance to small variations in component values and to minor geometrical imperfections . ] the equivalent circuit results presented in ref . show that the sensitivity of the channel to the dielectric change is independent of the height of the enz waveguide section . defined in eq . scales as @xmath25 . we see that the right hand side of the equation remains constant , since @xmath26 and @xmath27 scale proportionally and inversely with @xmath4 respectively . in the fraction on the right hand side , the terms @xmath28 and @xmath29 both scale as @xmath30 , thus it also remains unchanged . in practice there would be a small frequency change due to the shunt susceptance at the discontinuities which we neglect here . ] in contrast , the sensitivity to a lumped capacitance is strongly dependent on the height of the waveguide , since this modifies @xmath27 , but has only a small effect on @xmath16 and @xmath17 due to evanescent higher - order modes . to demonstrate this effect we have repeated the experimental and numerical results with a another channel , as shown in fig . [ fig : tuning_wide ] . it can be seen that the increase in the channel height improves the tunability of the structure . to achieve agreement with experimental results , the parasitic inductance was changed to 2.6nh , to reflect the necessarily different dimensions of the biasing structure in this experimental configuration . ] as this structure is strongly resonant and exhibits a high phase velocity , it is clear that it should have a correspondingly low group velocity . since the enz tunneling theory is also applicable in plasmonic systems @xcite , a nonlinear enz channel coupled to external waveguides could be used as a tunable slow - light structure . in order to demonstrate this effect and to analyze the response of this system to a signal with finite bandwidth , we have calculated the group delay from the experimentally measured transmission . the effective group index , calculated as @xmath31 , is shown in fig . [ fig : tuning_delay ] . it should be noted that this quantity is calculated for the finite structure rather than an infinite enz channel , as discussed in ref . . the effective group index can reach 25 for the measured structures , and the maximum delay corresponds to the transmission peak as expected . to put these results in context , we consider" +"spiral arms in disc galaxies can be classified into three categories : grand - design , multiple - arm , and flocculent spirals @xcite . grand - design spiral arms are large - scale coherent , symmetric , two - armed patterns ( e.g. ngc 628 ) , whose number fraction is more than @xmath3 in nearby spiral galaxies @xcite . observations show that grand - design spirals are associated with bars or companions @xcite , suggesting that a bar or companion is essential in forming a grand - design spiral in a disc galaxy . in barred spiral galaxies , the grand - design spirals extend from the ends of the bars . furthermore , although some studies found little or no correlation between bar strengths and spiral arm strengths @xcite , other studies have found correlations @xcite . these observations , therefore , suggest that bars drive grand - design spirals with the _ same _ pattern speed as the bars . this ` bar - driven spiral hypothesis ' has been promoted by the ballistic closed - orbit theory , which is based on non - self - gravitating hydrodynamic simulations in fixed barred potentials ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? this theory explains the physical mechanism responsible for the formation of the spirals in barred galaxies in terms of closed orbits of the gas ( see also * ? ? ? * ) : the spiral arms in barred galaxies are regarded as _ kinematic _ density waves ( i.e. crowding of gaseous closed orbits ) driven by an external barred potential . however , spiral arms in observed barred galaxies are composed of not gas but stars ; therefore , theories based on stellar dynamics are required for investigating the origin of spiral arms in barred galaxies . on the other hand , the ` invariant manifold theory ' is another bar - driven spiral theory @xcite and has been developed from stellar orbital theories in fixed barred potentials @xcite . essentially , the back - bones of barred spirals are bunches of untrapped stars escaped from unstable lagrangian points @xmath4 and @xmath5 close to the ends of the bar . this means that stars should _ move along _ the arms rather than across the arms @xcite . this behaviour is completely different from the quasi - stationary density wave theory , which predicts that stars should _ traverse _ the arms but would stay longer in the arm than in the inter - arm region @xcite . furthermore , the manifold theory predicts a rigidly rotating spiral arm with a similar pattern speed to that of the bar ( i.e. @xmath6 ) and that stronger bars should have more open spirals compared to weaker bars @xcite . recently , @xcite extended the classical epicyclic orbit approximation to the ` p - ellipse ' orbit approximation @xcite and proposed that ensembles of eccentric resonant orbits excited in lindblad zones can provide a backbone for generating kinematic bars and spiral waves . furthermore , @xcite showed that some resonant eccentric orbits have a similar appearance to invariant manifold orbits . the manifold theory and eccentric resonant orbits theory , however , do not consider the self - gravity of stars , despite the fact that the self - gravity of stellar discs plays an essential role in the dynamical evolution of spirals via the ( non - linear ) swing amplification mechanism @xcite . the swing amplification mechanism , proposed by toomre in @xcite , operates through a combination of three aspects , i.e. the shearing flow , epicyclic motions , and the disc self - gravity , in disc galaxies - body simulations of galactic discs partly supported this mechanism @xcite . however , @xmath0-body simulations of galactic discs suggested the importance of nonlinearity , such as mode - mode coupling and radial migration of stars @xcite , in the dynamical evolution of spiral arms . ] . because the amplification is most efficient around the corotating radius ( e.g. * ? ? ? * ) , prominent spiral arms tend to have differentially rotating patterns , which almost follow the galactic rotation at every radius ( @xmath7 ; * ? ? ? besides , the pitch angles are expected to depend on the shear rates of galactic discs @xcite . for investigating the origin of grand - design spirals in barred galaxies , @xmath0-body and @xmath0-body / hydrodynamic simulations are required , and several preliminary numerical studies have been proposed . however , the studies have not reached a consensus about the dynamics of barred spirals . some numerical simulations of barred spiral galaxies have shown that the bar and spiral arm are rigidly rotating patterns with _ different _ pattern speeds , and they are independent patterns @xcite or are coupled via non - linear interactions @xcite . recently , @xcite performed @xmath0-body simulations of pure stellar barred spiral galaxies and analysed the spiral rotation frequency from _ selected _ snapshots where the spiral amplitude is above 70% of the maximum amplitude ; they concluded that the spiral rotation frequency approaches the bar s rigid body rotation in barred galaxies with the increment of bar strength . on the other hand , @xcite performed @xmath0-body / hydrodynamic simulations of a barred spiral galaxy and suggested that the spiral arms are not rigidly rotating patterns but transient recurrent patterns ( i.e. dynamic spirals ) , and these results are similar to those obtained from multiple arm spiral galaxies @xcite . @xcite also found that spiral arms in barred galaxies are dynamic patterns whose rotation frequencies decrease with the radius in such a way that the rotation frequency is similar to the rotation of stars . in this study , to address the short - term ( e.g. a few hundred million years ) behaviour of grand - design spirals in barred spiral galaxies , we performed a three - dimensional ( 3d ) @xmath0-body / hydrodynamic simulation of a milky - way - like barred spiral galaxy . this paper is organized as follows . we describe the galaxy model and our numerical simulation methodologies in section [ sec : method ] . in section [ sec : results ] , we present our results concerning the short - term behaviour of grand - design spirals in the barred galaxy and effects of the bar on spiral dynamics . finally , we summarize our results in section [ sec : summary ] . long - term ( e.g. @xmath8 gyr ) behaviour of spirals in barred galaxies , as well as effects of a ` live ' dark matter ( dm ) halo , will be presented in a forthcoming paper ( m. s. fujii et al . in preparation ) . we performed a 3d @xmath0-body / hydrodynamic simulation of a milky way - like galaxy with an @xmath0-body / smoothed particle hydrodynamics ( sph ) simulation code asura-2 @xcite . in this study , we focus on the dynamical evolution of spiral arms in a simulated barred spiral galaxy , while detailed studies on spatial distributions of the interstellar medium ( ism ) around spiral arms as well as the structures of the ism / clouds and their galactic environmental dependences are separately discussed in baba , morokuma - matsui & egusa ( @xcite ) and baba , morokuma - matsui & saitoh ( @xcite ) , respectively . the self - gravities of stars and sph particles were calculated by tree with the gravity pipe ( grape ) method @xcite . the tree method allows us to reduce the number of particle pair interactions that must be computed by dividing the volume into cubic cells , so that particles in distant cells are treated as a single large particle centred at the cell s centre of mass . the grape tool is a special - purpose hardware for calculating gravitational forces . in this study , we used a software emulator of grape , known as phantom - grape @xcite . radiative cooling and heating , star formation , and stellar feedback from type ii supernovae and @xmath9 regions were also included . the radiative cooling of the gas was solved assuming an optically thin cooling function for a wide temperature range of @xmath10 @xcite . star formation from cold , dense gas and feedback models was based on the simple stellar population ( ssp ) approximation with the salpeter initial mass function . these were implemented in a probabilistic manner @xcite . the @xmath9-region feedback was implemented using a stromgren volume approach @xcite . we generated the initial axisymmetric model of a stellar and gaseous discs with a classical bulge embedded in a dm halo . [ fig : initrc ] shows the initial circular velocity curves of each component in the model . the stellar disc follows an exponential profile : @xmath11 where @xmath12 , @xmath13 , and @xmath14 are the total mass , scale - length , and scale - height of the stellar disc , respectively . using hernquist s method @xcite , the velocity structure of the stellar disc in cylindrical coordinates is approximately determined by a maxwellian approximation . we set the reference radial velocity dispersion by assuming that toomre s @xmath15 at @xmath16 equals @xmath17 ( see section 2.2.3 of * ? ? ? the gas disc also follows an exponential profile with a total mass of @xmath18 , scale - length of @xmath19 , and scale - height of @xmath20 . the gas disc was truncated at @xmath21 . the initial temperature was set to @xmath22 k , and the initial velocity dispersion was @xmath23 everywhere . the classical bulge follows the hernquist profile : @xmath24 where @xmath25 and @xmath26 are the total mass and scale - length of the bulge @xcite , respectively . following @xcite , we generated the classical bulge from the distribution function with an energy cutoff ( see equation ( 10 ) of * ? ? ? * ) . here , we set @xmath27 of that equation to be 0.21 . for simplicity , we assumed the dm halo to be a static potential , whose density profile follows the navarro - frenk - white profile : @xmath28 where @xmath29 , @xmath30 , and @xmath31 are the total mass , virial radius , and concentration parameter of the of the dm halo , respectively @xcite , and @xmath32 . as shown in fig . [ fig : initrc ] , the contribution from the stellar disc to the total circular velocity in the galaxy model surpasses that from the dm haloes in the regions of @xmath33 kpc . in this case , the galaxy satisfies the criteria for the bar instability @xcite and spontaneously develops a stellar bar . note that a static halo omits dynamical friction on the bar ( e.g. * ? ? ? * ; * ? ? ? * ) ; however , dynamical friction will be weak because the central density of the dm halo in this study is low . we will investigate effects of a ` live ' dm halo on the dynamical evolution of barred spirals in a future study . the initial numbers of stars and sph particles were @xmath34 million and @xmath35 million , respectively , and the particle masses of stars and sph particles were about @xmath36 and @xmath37 , respectively . we used a gravitational softening length of @xmath38 pc . following the above procedures , we generated a galaxy model in a near - equilibrium state and then subsequently allowed the galaxy to evolve for @xmath39 rotational periods under the constraint of axisymmetry @xcite . this equilibrium state was used as the initial condition for the numerical simulation . the quantities that characterize the spiral" +"in the past decades , raman spectroscopy@xcite techniques were successfully applied to carbon compounds , such as graphite ( see ref . and references therein ) and carbon nanotubes.@xcite upon the discovery of graphene,@xcite raman spectroscopy has proven to be a powerful tool to identify the number of layers , structure , doping , disorder , and to characterize the phonons and electron - phonon coupling.@xcite so far , most of the attention was focused on the position and width of the raman peaks . here we present a detailed calculation of the _ intensities _ of the multiphonon raman peaks in graphene . raman scattering involves an electron - hole pair as an intermediate state ; we show that the multiphonon raman peaks are strongly sensitive to the dynamics of this electron - hole pair . thus , raman scattering can be used as a tool to probe this dynamics . writing the low - energy hamiltonian of the interaction of electrons with the crystal vibrations and the electromagnetic field from pure symmetry considerations , we describe the system in terms of just a few independent coupling constants , considered to be parameters of the theory . the electron scattering rate is introduced phenomenologically as another parameter . the results of the present calculation are used to extract information about these parameters from the raman peak intensities , measured experimentally . as shown below , the raman intensities strongly depend on the electron scattering rate ; moreover , the electron - phonon and electron - electron contributions to this rate can be separated . this is especially important as there are very few techniques giving experimental access to electron scattering rates , which , in turn , determine the transport properties of graphene samples . besides , the quasiclassical character of the process imposes a severe restriction on the electron and hole trajectories which can contribute to the two - phonon raman scattering : upon the phonon emission the electron and the hole must be scattered backwards . this restriction results in a significant polarization memory : it is almost three times more probable for the scattered photon to have the same polarization as the incidend photon than to have the orthogonal polarization . also , the raman intensities depend on electron - phonon coupling constants ; to reproduce the experimental results , one has to take into account renormalization of these coupling constants by electron - electron interaction . this renormalization is missed by local or semi - local approximations to the density - functional theory , typically used for the _ ab initio _ calculation of the coupling constants . since graphene is a non - polar crystal , raman scattering involves electronic excitations as intermediate states : the electromagnetic field of the incident laser beam interacts primarily with the electronic subsystem , and emission of phonons occurs due to electron - phonon interaction . the matrix element of the process can be schematically represented as @xmath0 here @xmath1 is the initial state of the process ( the incident photon with a given frequency and polarization , and no excitations in the crystal ) , @xmath2 is the final state ( the emitted photon and @xmath3 phonons left in the crystal ) , while @xmath4 , @xmath5 , label the intermediate states where no photons are present , but an electron - hole pair is created in the crystal and @xmath6 phonons have been emitted . @xmath7 and @xmath8 , @xmath5 are the energies of these states , and @xmath9 is the inverse lifetime of the electron ( hole ) due to collisions . @xmath10 and @xmath11 stand for the terms in the system hamiltonian describing interaction of electrons with the electromagnetic field and with phonons , respectively . in the calculations we do not include the phonon broadening , assuming the phonon states to have zero width . first , this approximation is consistent with the available experimental information : the phonon width is about @xmath12 at most,@xcite while the electronic broadening is at least an order of magnitude higher ( see the discussion below , sec . [ sec:2intensities ] ) . second , this approximation is irrelevant provided that we calculate the integrated intensities of the raman peaks , since they are determined by the total spectral weight of the phonon state which does not depend on the phonon broadening . ( color online ) . schematic representation of the role of electron dispersion ( dirac cones , shown by solid lines ) in the one - phonon ( a , b ) and two - phonon raman scattering ( c , d ) . vertical solid arrows represent interband electronic transitions accompanied by photon absorption or emission ( photon wave vector is neglected ) , dashed arrows represent phonon emission , the horisontal dotted arrow represents the impurity scattering.,width=264 ] the photon wave vector is negligible , so momentum conservation requires that the sum of the wave vectors of emitted phonons must vanish ( provided that the impurity scattering is neglected ) . for the same reason raman scattering on one intervalley phonon must be impurity - assisted [ process ( b ) in fig . [ fig : res ] , giving rise to the so - called @xmath13 raman peak ] . @xmath13 peak is absent in the experimental raman spectrum of graphene,@xcite showing that impurity scattering is indeed negligible in these samples . looking at the intermediate electronic states involved in the raman scattering ( fig . [ fig : res ] ) , we notice that for one - phonon scattering [ processes ( a ) , ( b ) ] at least one intermediate state must be virtual , since energy and momentum conservation can not be satisfied simultaneously in all processes . thus , at least one of the factors in the denominator of eq . ( [ ramanmatrixelement= ] ) must be of the order of the phonon frequency @xmath14 [ for the impurity assisted scattering one of the electron - phonon matrix elements in the numerator of eq . ( [ ramanmatrixelement= ] ) should be replaced by the electron - impurity matrix element ] . for the two - phonon scattering [ process ( c ) ] all intermediate states can be real , so that all energy mismatches in the denominator of eq . ( [ ramanmatrixelement= ] ) can be nullified simultaneously and the result is determined by the electron scattering rate @xmath9 . we emphasize the qualitative difference between the _ fully resonant _ process ( c ) and the double - resonant@xcite process ( b ) , where one intermediate state is still virtual . we also note the analogous difference between the two - phonon processes ( c ) and ( d ) in fig . [ fig : res ] : only the process ( c ) is fully resonant , the other one involves an energy mismatch of @xmath15 . as a result , its amplitude will be smaller by a factor @xmath16 . obviously , these arguments can be extended to all multi - phonon processes with odd and even number of phonons involved : in order to annihilate radiatively , the electron and the hole must have opposite momenta ; if the total number of emitted phonons is odd , the electron and the hole must emit a different number of phonons , which is incompatible with energy conservation in all processes . our main focus will thus be on even - phonon processes , as their intensities are determined by the electronic scattering . the full resonance picture presented above assumes the mirror symmetry between the electron and the hole spectra . the electron - hole asymmetry can be included as a correction to the dirac spectrum : the electron and the hole energies can be written as @xmath17 , where @xmath18 is the momentum counted from the dirac point , @xmath19 is the dirac velocity , and @xmath20 is the asymmetry parameter . the energy scale @xmath21 , quantifying the role of the asymmetry in the raman scattering is defined as @xmath22 , where @xmath23 and @xmath24 are the frequencies of the incident and the scattered photon ( the details are given in secs . [ sec : warping ] , [ sec : intdev ] ) . namely , the arguments of the previous paragraph hold if @xmath25 . in the opposite case , it is @xmath21 that determines the smallest value of the denominators in eq . ( [ ramanmatrixelement= ] ) . we will always assume that both @xmath26 . in the real space , the typical size of the region of space probed by the electron - hole pair in the fully resonant two - phonon raman scattering , is @xmath27 . for the doubly resonant defect - induced one - phonon scattering , the inverse energy mismatch @xmath28 determines the time duration of the process by virtue of the uncertainty principle , so the length scale of the process in the real space is @xmath29 . although this length scale is much shorter than @xmath30 , it is still much greater than the lattice constant or the electron wavelength @xmath31 . the fully resonant raman scattering , where the energy is conserved in each of the elementary scattering processes , admits a simple quasiclassical description , described qualitatively in this subsection , and justified rigorously in secs . [ sec:2raman],[sec:4raman ] . let us denote by @xmath32 the energy of the electron and the hole in the photoexcited pair . initially , it is given by the half of the excitation frequency @xmath23 , @xmath33 . after the emission of @xmath3 phonons it is decreased by @xmath34 ; assuming @xmath35 , we neglect this decrease in the qualitative considerations . thus , during all the time taken by the raman scattering , electron and hole can be viewed as wave packets of the size @xmath36 , propagating across the crystal along classical trajectories . the electron and the hole are created in the same region of space of the size @xmath36 around some point @xmath37 at the moment of the arrival of the excitation photon . at this initial moment they have opposite momenta @xmath38 , and opposite velocities @xmath39 ( if the electron - hole asymmetry is taken into account , the two velocities will have slightly different magnitude ) , so they move along the straight lines , their positions being @xmath40 , @xmath41 . after a typical time @xmath42 they undergo some scattering processes ( e. g. , phonon emission ) , where their momenta and ( generally speaking ) energies are changed . each such elementary scattering process occurs during a short time @xmath43 . thus , the trajectories of the electron and the hole after their creation are represented by broken lines , with the typical segment length @xmath44 ( the electron mean free path ) . the crucial point is that in order to recombine radiatively and contribute to raman signal , the electron and the hole should meet again within a spatial region of the size @xmath36 , and have opposite momenta . the latter condition automatically implies that the number of the phonons emitted by the electron and the hole is the same . these considerations are illustrated by fig . [ fig : trajectories ] . in the presence of a significant electron - hole asymmetry , @xmath45 , the described picture is modified . namely , one of the segments of either the electron or the hole trajectory has the length @xmath46 instead of @xmath30 , the corresponding time travelling being restricted by the phase mismatch rather than by collisions . ( color online ) . ( a ) an example of a quasiclassical electron - hole trajectory contributing to the four - phonon raman scattering . (" +"superconducting films are candidate substances for the improvement of electronics technology in a myriad of applications . while the low resistance is very attractive in this regard , it has proved difficult to control the nonlinear behaviour of such materials in response to electromagnetic field@xcite . when a magnetic field is strong enough to penetrate into a superconductor in the form of quantised magnetic flux tubes , the vortex state obtains as a mixed state of superconducting phase punctuated by the vortices themselves . vortices are surrounded by a supercurrent and can be forced into motion by the current resulting from an applied field . as a topological defect , a vortex is not only stable under perturbations@xcite but can not decay . the collection of vortices in a type - ii superconductor forms what is called vortex matter , and it is this which determines the physical properties of the system rather then the underlying material properties , in particular driving phase transitions@xcite . in the mixed state , a superconductor is not perfect ; it exhibits neither perfect diamagnetism nor zero electrical resistance . the transport current @xmath0 generates a lorentz force @xmath1 on the vortex and forces it into motion , dissipating energy . in reaching thermal equilibrium , energy is transferred via interactions between phonons and quasiparticle excitations . small - scale imperfections such as defects scatter the quasiparticles , affecting their dynamics . in _ superconductors , impurities are plentiful and vortices experience a large friction . this implies a fast momentum - relaxation process . in contrast is the _ clean _ limit , where impurities are rare and no such relaxation process is available . it is in this situation of slow relaxation that the hall effect appears . generally , the @xmath2-@xmath3 phase diagram@xcite of the vortex matter has two phases . in the _ pinned phase _ vortices are trapped by an attractive potential due to the presence of large - scale defects , thus resistivity vanishes . this phase contains what are known as glass states . there is then the _ unpinned phase _ in which vortices can move when forced and so a finite resistivity appears . this phase is also known as the flux - flow region and can be of two types . one type is a liquid state where vortices can move independently ; the other type is a solid state in which vortices form a periodic abrikosov lattice@xcite resulting from their long - range interacton . one model for the transition between the pinned and unpinned phases appears in @xcite . in the unpinned phase , the system is driven from equilibrium and experiences a relaxation process . there are several ways to describe such a system . a microscopic description@xcite invoking interactions between a vortex and quasi - particle excitations at the vortex core provides a good understanding of friction and sports good agreement with experiments in the sparse - vortex region @xmath4 . there is also a macroscopic description , the london approach , where vortices are treated either as interacting point - like particles or an elastic manifold subject to a pinning potential , driving force and friction@xcite . in the small - field region , vortices behave as an array of elastic strings . in the dense - vortex region @xmath5 , where the magnetic field is nearly homogeneous due to overlap between vortices , ginzburg - landau ( gl ) theory , which describes the system as a field , provides a more reasonable model . in dynamical cases , time - dependent gl ( tdgl ) theory is appropriate@xcite ; in gl - type models , additional simplification can come from the lowest landau level ( lll ) approximation which has proven to be successful in the vicinity of the superconducting - normal ( s - n ) phase transition line @xmath6 . this has been pursued in the static case@xcite ( without driving force ) and in the dynamic case with a time - independent transport current@xcite . it may be noted that in the glass state , zero resistance within the lll approximation can not be attained@xcite . based on tdgl theory , we will study the dynamical response of a dense vortex lattice forced into motion by an alternating current induced by an external electromagnetic field . vortices are considered which are free from being pinned and thermally excited , which in addition to thermal noise would produce entanglement and bending . we assume the vortices can transfer work done by an external field to a heat bath . experimentally , a low - temperature superconductor far away from the clean limit is the best candidate for attaining these conditions . we do not consider thermal fluctuation effects specific to high - temperature superconductors . in a dissipative system driven by a single - harmonic electric field @xmath7 , long after its saturation time we can expect the system to have settled into steady - state behaviour , where the vortices are vibrating periodically with some phase . the tdgl model in the presence of external electromagnetic field is analysed and solved in . the dynamical s - n phase transition surface @xmath8 is located in @xmath9-space . this surface coincides with the mean - field upper - critical field @xmath10 in the absence of the applied field , and with the phase - transition surface in the presence of the constant driving field considered by hu and thompson@xcite . we will provide an analytical formalism for perturbative expansion in the distance to @xmath11 , valid in the flux - flow region . the response of vortex matter forced into motion by the transport current is studied in . the current - density distribution and the motion of vortices are treated in . in analysing the vortex lattice configuration in , a method is utilised whereby the heat - generation rate is maximised . next are discussed power dissipation , generation of higher harmonics , and the hall effect . an experimental comparison is made in with far - infrared ( fir ) measurement on nbn . finally , some conclusions are made in . let us consider a dense vortex system prepared by exposing a type - ii superconducting material to a constant external magnetic field @xmath12 with magnitude @xmath13 . we also select the @xmath14 axis of the superconductor to be in the @xmath15 direction . let the superconductor carry an alternating electric current along the @xmath16 direction , generated by an electric field @xmath17 as shown in . such a system when disturbed from its equilibrium state will undergo a relaxation process . for our system , the tdgl equation@xcite is a useful extension of the equilibrium gl theory . in the dense - vortex region of the @xmath2-@xmath3 phase diagram , vortices overlap and a homogeneous magnetic field obtains . describing the response of such a system by a field , the order parameter @xmath18 in the gl approach , is more suitable than describing vortices as particle - like flux tubes , as is done in the london approach@xcite . a strongly type - ii superconductor is characterised by its large penetration depth @xmath19 and small coherence length @xmath20 , @xmath21 . the difference between induced magnetic field and external magnetic field is @xmath22 . in the vicinity of the phase - transition line @xmath10 vortices overlap significantly , and @xmath23 making @xmath24 small . in this case , the magnetic field may be treated as homogeneous within the sample . we will have in mind an experimental arrangement using a planar sample very thin compared with its lateral dimensions . since the characteristic length for inhomogeneity of electric field@xcite @xmath25 is then typically large compared with sample thickness , this implies that the electric field may also be treated as homogeneous throughout@xcite , eliminating the need to consider maxwell s equations explicitly . in equilibrium , the gibbs free energy of the system is given by@xcite @xmath26&=&\int\td { \bf r } \bigg\ { \frac{\hbar^2}{2m_{ab}}|{\bf d}\psi|^2 + \frac{\hbar^2}{2 m_c}|\partial_z \psi|^2 \nonumber\\ & & { \ \ \ \ } -\alpha ( \tnst - t)|\psi|^2+\frac{\beta}2 |\psi|^4 \bigg\}\end{aligned}\ ] ] where @xmath27 is the critical temperature at zero field . covariant derivatives employed here preserve local gauge symmetry and are two - dimensional ; @xmath28 and @xmath29 . governing the dynamics of the field @xmath18 is the tdgl equation @xmath30 this determines the characteristic relaxation time of the order parameter . microscopic derivation of tdgl can be found in @xcite in which the values of @xmath31 , @xmath32 and @xmath33 are studied . in the macroscopic case , these are viewed simply as parameters of the model . at microscopic scale , disorder is accounted for by @xmath33 , the inverse of the diffusion constant ; the relation of @xmath33 to normal - state conductivity is discussed in . in standard fashion , @xmath34 while @xmath35 . our set of equations is completed@xcite by including ampre s law , writing for the total current density @xmath36 as we shortly make a rescaling of quantities , we have written @xmath37 subscripts here for clarity . the first term is the normal - state conductivity . the second term can be written using a maxwell - type equation relating the vector - potential with the supercurrent , @xmath38 .\end{aligned}\ ] ] this is a gauge - invariant model ; we fix the gauge by considering the explicit vector potential @xmath39 and @xmath40 , corresponding to an alternating transport current . each vortex lattice cell has exactly one fluxon . we do not assume the electric field and the motion of vortices are in any particular direction relative to the vortex lattice , by way of rendering visible any anisotropy . for convenience , we define some rescaled quantities . the rescaled temperature and magnetic field are @xmath41 and @xmath42 . @xmath43 denotes the mean field upper - critical field , extrapolated from the @xmath27 region down to zero temperature . in the @xmath44-@xmath45 plane of the crystal we make use of _ magnetic length _ @xmath46 . we define @xmath47 where @xmath48 . the scale on the @xmath14-axis is @xmath49 with @xmath50 . the coordinate anisotropy in @xmath15 is absorbed into this choice of normalisation , as can be seen in . the order parameter @xmath18 is scaled by @xmath51 . the time scale is normalised as @xmath52 . therefore , frequency is @xmath53 . note that @xmath54 is then inversely proportional to @xmath45 . the amplitude of the external electric field is normalised with @xmath55 so that @xmath56 . after our rescaling the tdgl equation takes the simple form @xmath57 where the operator @xmath58 is defined as @xmath59 with our specified vector potential , covariant derivatives are @xmath60 , @xmath61 and @xmath62 . we define @xmath63 for convenience . the tdgl equation is invariant under translation in @xmath15 , thus the dependence of the solution in the @xmath15 direction can be decoupled . @xmath58 is not hermitian ; @xmath64 where the conjugation is with respect to the usual inner product , defined below . we will make extensive use of the eigenfunctions of @xmath58 and @xmath65 in what follows . the eigenvalue equation @xmath66 defines the set of eigenfunctions of @xmath58 appropriate for our analysis ; this can be seen in . the convention is that @xmath67 when and only when @xmath68 . taking corresponding in @xmath58 and switches it in the resulting @xmath69 to get the ` corresponding ' eigenfunction @xmath70 for @xmath65 . ] eigenfunctions of @xmath65 to be @xmath71 , the orthonormality @xmath72 may be chosen , so long as @xmath73 . shown in , crystal structure determines linear combinations of these basis elements with respect to @xmath74 ; the resulting @xmath75 functions are then useful for expansion purposes below . the inner product is @xmath76 where the brackets @xmath77" +"over the last decades , numerous data on hot giant electric dipole resonance ( gdr ) parameters have been accumulated . since the field seems to have matured , it might be useful at this point to gather all present data in one comprehensive compilation in a uniform format . the introduction is organized in the following way : first , we give some theoretical motivation why gdr parameters might be dependent on temperature , hence what question the present compilation tries to address . then , in subsection [ sect : exp ] , we give an overview over typical experimental techniques used for measuring hot gdr parameters ; in subsection [ sect : smc ] we describe different ways of how hot gdr parameters are extracted from such experiments by means of statistical - model calculations . although we have not attempted to extract any gdr parameters from such calculations ourselves , we believe it is helpful for the reader to get a general impression of the experimental and data - analysis part of the compiled works . in subsection [ sect : data ] we explain how different sets of gdr parameterizations from the original articles were brought onto a common footing . finally , we end the introduction with a statement regarding our policy and a note on references . a first good understanding of statistical @xmath0 emission was gained from the works of brink @xcite and axel @xcite who realized that average electric - dipole ( @xmath1 ) transition strengths in different energy regimes can be described in a unified fashion by assuming that the gdr can be built on any excited state , and that the gdr properties do not depend on the temperature of the excited state in question . this so - called brink - axel hypothesis has been refined in the past to allow for temperature- and spin - dependent widths . a model to motivate such a modification takes into account shape fluctuations of the nucleus . since the ground - state gdr splits into two components for a nucleus with static deformation , and the splitting depends on the degree of deformation @xcite , it is reasonable to assume that at finite temperatures , when the nucleus can explore a large volume in deformation space , the gdr response will be an average over different deformations and hence , different splittings . the result within this adiabatic damping model will be a more diffuse and certainly wider gdr than the ground - state gdr . quantitatively , assuming a fermi - gas level density , one can write the nuclear entropy in the microcanonical ensemble as @xmath2 , where @xmath3 is some potential energy proportional to the square of the deformation @xmath4 . the entropy is trivially maximized for @xmath5 ; expanding @xmath6 for small @xmath7 yields @xmath8 . with @xmath9 , the probability distribution to find a nucleus with energy @xmath10 and deformation @xmath11 becomes @xmath12 where the second factor represents a gaussian distribution of deformations around @xmath5 and a width of @xmath13 . assuming that the splitting of the gdr into two components is roughly proportional to the nuclear deformation , the shape - fluctuation model predicts an increase in width of the gdr roughly proportional to @xmath14 . moreover , there is also a potential spin dependence of the gdr width which stems from the possibility of spin - induced deformation . finally , orientation fluctuations of the nucleus and nuclear - structure effects such as pairing can influence the temperature dependence of the gdr in different energy regimes . several groups have calculated temperature - dependent gdr widths along these lines @xcite and a simple scaling law has emerged @xcite . investigations of the low - energy tail of the gdr have also yielded indications for a temperature - dependent gdr width . it was , e.g. , noted by popov @xcite in @xmath15 experiments on sm nuclei that the @xmath0 strength function tends to approach a finite value for @xmath16 for @xmath0 transitions in the quasicontinuum ( below the neutron separation energy ) . this experimental observation led kadmenski , markushev , and furman ( kmf ) to propose a @xmath0 strength - function model for spherical nuclei with a temperature - dependent width @xcite based on the effect of in - medium nucleon - nucleon collisions . the proposed temperature dependence was derived within migdal s theory of fermi liquids and has the form @xmath17 . the model was later improved by sirotkin @xcite who included the pauli exclusion principle , and it was extended to deformed nuclei within the framework of the generalized lorentzian model by kopecky and uhl @xcite and by inclusion of a coupling term between the @xmath1 operator and the quadrupole deformation according to mughabghab and dunford @xcite . the kmf model ( taken at constant temperatures ) and its extensions have been successfully applied to improve @xmath0 and isomeric production cross sections @xcite and they have been used for direct fits of measured low - energy @xmath0 strength functions @xcite . the connection of collisional - damping models with hot gdr parameters has been made in @xcite . unlike the measurement of the gdr by ground - state photo - absorption cross - section measurements @xcite , measurements of hot gdr parameters can be performed in many different ways . one of the simplest ways is by fusion - evaporation reactions where only @xmath0 rays are detected @xcite . such measurements are the most inclusive reactions , since the high - energy @xmath0 yield which competes with particle and especially neutron evaporation is representative for a range of different product nuclei , excitation energies , and spins . moreover , it is not necessarily guaranteed that all detected @xmath0 rays stem from fusion - evaporation reactions . other reactions such as inelastic or deep inelastic scattering can compete and yield @xmath0 rays from target or projectile - like fragments . to improve the sensitivity of such experiments to the fusion - evaporation reaction channel , typical gates such as , e.g. , @xmath0-multiplicity filters @xcite , detection of heavy evaporation residues @xcite , and detection of evaporated , light charged particles such as protons or @xmath18 particles @xcite can be performed . the resulting @xmath0-ray spectra are more exclusive , not only in terms of the product nuclei from which high - energy @xmath0 rays are emitted , but also in terms of the spin and the excitation - energy range investigated . for example , a gate on different @xmath0 folds translates rather directly into certain spin regions of the investigated product nucleus @xcite . a gate on evaporated light charged particles will not only reduce the average charge and mass of the product nucleus , but it will also reduce its average excitation energy , since the evaporated particles will carry away some part of the initial excitation energy of the compound nucleus @xcite ; hence applying such a gate will test the gdr at somewhat lower temperatures than the fully inclusive experiment . in the same way , gating on the @xmath0 sum energy @xcite or on specific product nuclei by means of detecting in coincidence discrete , known low - energy @xmath0 transitions @xcite will also influence the average spin and excitation - energy region from which the high - energy @xmath0 rays are emitted , since one effectively biases the competition between high - energy @xmath0 decay and neutron evaporation in one or the other direction . other , more rarely used gating conditions are , e.g. , the isomeric @xmath0 decay by discrete transitions @xcite or the @xmath18 decay of a product nucleus @xcite , both of which have similar implications for the average spin and excitation - energy range from which prompt high - energy @xmath0 rays are observed . for heavy nuclei , an added difficulty is the possibility of fission of the compound nucleus . typically , for low spins , the production of an evaporation residue dominates while for high spins fission will become the dominant exit channel @xcite . hence , by gating on evaporation residues or fission fragments , one effectively selects a spin region from which high - energy @xmath0 emission is observed @xcite . in the case of the fission exit channel , one also observes high - energy @xmath0 emission from the fission fragments themselves @xcite , though typically at significantly higher @xmath0 energies owing to the much lower mass of the fission fragments . another complication is the fact that high - energy @xmath0 emission can occur from the compound nucleus ( which is desired ) , or during the saddle - to - scission motion after the nucleus has passed the fission barrier @xcite . also , for the heaviest nuclei investigated , it is not clear whether a true compound nucleus forms which is confined by some fission barrier or whether one observes direct fission or just the formation of a mononucleus . where we suspect the latter as in , e.g. , @xcite , the extracted data do not enter the present compilation . in some cases , one employs inelastic ( see , e.g. , @xcite ) or deep inelastic scattering @xcite to excite the target or projectile nucleus . by measuring the kinetic energy of at least one of the products , one can reconstruct the reaction kinematics event by event and it is possible to obtain initial excitation - energy indexed coincident high - energy @xmath0 spectra with only one beam energy . otherwise , the excited nucleus can be treated in the same way as a compound nucleus which is formed in a fusion - evaporation reaction . high - energy @xmath0 spectra are typically analyzed using a statistical - model calculation . in the first step , total fusion cross sections and maximum @xmath19 or average @xmath20 angular momenta are determined . typically , total fusion cross sections can be verified by experiment ; maximum angular momenta are calculated by the theory of either winther @xcite or swiatecki @xcite . average angular momenta can then be determined by @xmath21 . in the next step , the decay of the highly excited compound nucleus is modeled . in many cases , this simply involves a hauser - feshbach - type theory @xcite into which particle and @xmath0 transmission coefficients ( sometimes including higher - than-@xmath1 multipolarities ) as well as nuclear level densities enter . typically , particle transmission coefficients are not discussed in great detail in the compiled works . the level - density models are either the phlhofer model @xcite ( the default in the statistical - model code cascade @xcite ) or the reisdorf model @xcite . the phlhofer model relies on the local dilg _ parameterization @xcite for excitation energies up to and slightly above the nucleon separation energy , while it interpolates then to a regime where the level - density parameter @xmath22 becomes proportional to the nuclear mass number @xmath23 . the reisdorf approach builds on the generalized superfluid model by ignatyuk _ @xcite , but it uses a global parameterization for the asymptotic level density parameter @xmath22 . in one case @xcite , the level - density model by fineman _ @xcite is used in the data analysis . _ _ _ statistical - model calculations are often adapted to different experimental situations . for light compound nuclei near the @xmath24 line , an isospin - dependent formalism is often used @xcite . also , the wigner energy @xcite is sometimes included in the level - density parameterization @xcite . for large excitation energies , pre - equilibrium emission due to direct and semi - direct reaction mechanisms are often taken into account ( see , e.g. , @xcite ) . especially the peqag2 code @xcite has been developed for this purpose . in the case of fissile" +"one of the key questions in the field of nanoelectromechanical systems ( nems ) @xcite is the effect of mechanical motion on the electric properties of the systems . it is equally important for undestanding of fundamental questions such as behavior of non - equilibrium , dissipative , driven systems and for the prospects of nems practical applications , such as switches , relays , and actuators . electron motion in both external ac electromagnetic fields ( see _ e.g. _ ref . @xcite ) and subject to time - dependent noise @xcite have been extensively studied in the past . the new feature brought by nems is that not only electrons move in the field created by the mechanical vibrations ( for brevity , phonons ) , but also the phonons are created by the electron motion through the nems device . the phonons are generally driven out of equlibrium thus creating the feedback for the electron motion . in this article , we concentrate on nems operating in the single electron tunneling ( set ) regime . these include experimental realizations based on single molecules @xcite , semiconductor beams @xcite , and suspended carbon nanotubes @xcite . in set regime a nems can be represented as a set device coupled to a mechanical ( harmonic ) oscillator . the coupling is provided by a force ( typically of electrostatic origin , see _ e.g. _ ref . @xcite ) acting on the oscillator . the value of the force depends on the charge state of the set device , providing the feedback . this feedback can be strong even if the electron - phonon coupling is weak : indeed , if one consideres an set next to the coulomb blockade threshold , only two charge states , say , @xmath0 and @xmath1 , with @xmath2 being the number of electrons at set , are important . the occupation of set above the coulomb blockade threshold fluctuates between zero and one , providing a force which is a random telegraph signal . the signal swings an underdamped oscillator to large amplitudes , which in their turn affect the transport properties of the set device by modifying the tunnel matrix elements and the energy difference between the two charge states . the transport properties of nems devices depend on a number of parameters . one is the coupling strength @xmath3 , defined as the square of the ratio of the displacement of the oscillator center under the action of the force at the amplitude of the zero - point motion , @xmath4 , where @xmath5 and @xmath6 are the mass and the frequency of the oscillator , and @xmath7 is the difference of the forces acting on the oscillator in the charge states @xmath1 and @xmath8 . in is important that the planck constant is in the denominator , and thus strong coupling actually means quantum regime . other parameters determining the behavior are given by ratios of various energy scales characterizing the nems device . the most relevant one is the ratio between the typical tunnel rate @xmath9 and the oscillator frequency @xmath6 . surprisingly , the strong - coupling ( quantum regime ) is more extensively studied in the literature . assuming the oscillator is underdamped , for @xmath10 and @xmath11 , the behavior of the system is dominated by franck - condon physics . the tunnel rates are modified due to emission of phonons in the course of electron tunneling @xcite . for the coupling to a single mode , this leads to the steps in the current as the function of the applied bias voltage , the height of the step is determined by the coupling constant @xcite . for @xmath12 the electron level width becomes bigger than the distance between the steps , and franck - condon structure disappears . however , in this regime the motion of the oscillator is much slower than the electron tunneling , and one can use born - oppenheimer approximation , considering electrons in the quasi - stationary field potential provided by the oscillator . in this situation , the oscillator may become bistable , and the electron tunneling is dominated by switching events between the two states of the oscillator @xcite . all these phenomena are the manifestation of strong mechanical feedback . similar effects have been studied in ref . @xcite in the context of superconducting nems . it is less obvious that strong feedback is also possible at weak coupling @xmath13 . this is the classical regime , where boltzmann equation serves as the starting point @xcite . ref . @xcite studied the low - frequency case @xmath12 . the oscillator motion in this case is described by fokker - planck equation with effective diffusion and effective damping ( originating from the electron tunneling out of the set device ) , both determined by the energy dependence of the tunnel rates . it turns out that the strong feedback regime is feasible , but the behavior of the current strongly depends on the energy dependence of the tunnel rates . for instance , in the two most commonly investigated cases electron tunneling through a single level and electron tunneling through a continuum of levels with the constant density , like in a single electron transistor , the strong feedback does not appear . four distinct regimes have been identified : ( i ) no phonons generated ; ( ii ) the oscillations are generated with the fixed finite amplitude ; ( iii ) the oscillator is bistable , one state has the oscillations with zero amplitude , and another one the oscillations with a finite amplitude ; ( iv ) the system is bistable , with the two states representing the oscillations with two different amplitudes . in the regimes ( ii ) , ( iii ) , and ( iv ) current is strongly modified with respect to the case when the phonons are not generated . a quantity even more sensitive to the oscillations is the current noise . the natural measure of the current noise in set devices is poisson value of the zero - frequency spectral density @xmath14 , @xmath15 , @xmath16 being the average current @xcite . it turns out that the noise is strongly enhanced avove the poisson value in the regimes ( ii ) , ( iii ) , and ( iv ) , and may even become super - poissonian in the regime ( i ) , when the current is not renormalized . in this article , we consider the only regime not addressed so far : weak coupling @xmath13 and high frequency @xmath11 . we show that it shares many features with the low - frequency classical regime described above . even though we have not been able to identify any bistable regimes , we still find the two regimes of zero and finite amplitude , the latter demonstrating strong mechanical feedback . we find that the noise , in contrast to the low - frequency case , is always sub - poissonian . at weak coupling , the motion of the oscillator is classical , and the behavior of the system is characterized by the joint distribution function , @xmath17 . here , @xmath2 is the charge state of the set . we assume that the set is biased close to the edge of one of the coulomb diamonds , so that only two charge states are important for transport , for definiteness @xmath8 and @xmath1 . furthermore , @xmath18 and @xmath19 are the coordinate and the velocity of the oscillator . the starting point of our classical approach is the boltzmann ( master ) equation for the distribution function @xcite , @xmath20 = 0 ; \\ \cal{f}&= & - m { \omega}^2 x - \frac{m { \omega}v}{q}+ f_n \ ; ; \label{force}\\ \mbox{st}\ [ p ] & = & ( 2n-1 ) \left ( \gamma^{+}(x ) p_0 - \gamma^{-}(x ) p_1 \right ) \ , \label{rates2}\end{aligned}\ ] ] which holds for an arbitrary relation between @xmath6 and @xmath9 . here , the total force @xmath21 acting on the oscillator is the sum of the elastic force , friction force , and charge - dependent coupling force , respective to the order of terms in eq . ( [ force ] ) , @xmath22 is the quality factor . we count the position of the oscillator from its equilibrium position in the @xmath8 state . in this case , the `` collision integral '' @xmath24 $ ] in the right - hand side represents single electron tunneling . there are four tunnel rates , @xmath25 , where the subscripts @xmath26 and @xmath27 denote tunneling through the left or right junction , and the superscripts @xmath28 and @xmath29 correspond to the tunneling to and from the island , respectively ; @xmath30 . each rate is a function of the corresponding energy cost @xmath31 associated with the addition / removal of an electron to / from the island in the state @xmath32 via left or right junction ( @xmath33 ) . two independent energy differences are determined by electrostatics and depend linearly on the voltages . there is also a contribution to each energy from the shift of the oscillator , @xmath34 , @xmath35 , where @xmath36 are the corresponding energy differences in the absence of mechanical motion . the condition @xmath37 means that the motion of the oscillator is very slow compared with the typical time an electron spends in the set device . in this situation , the probabilities @xmath38 and @xmath39 average over the fast osicllator motion . in the leading order , if we parameterize @xmath40 , @xmath41 , @xmath42 , these probabilities do not depend on @xmath43 . consequently , we expand the probabilities in the following way , @xmath44 with @xmath45 . here and below we disregard the terms proportional to @xmath46 , @xmath47 , with @xmath48 . this procedure is similar to the transformation of boltzmann equation into the diffusion equation in the semi - classical theory of electron transport in metals . we can obtain a closed set of equations for @xmath49 by multiplying eq . ( [ mastereq ] ) with @xmath50 , @xmath51 and @xmath52 and subsequently averaging over the phase , throwing out @xmath53 and @xmath54 terms . it is important that the tunnel rates only depend on the coordinate and not of velocity of the oscillator , and thus are functions of @xmath55 and not @xmath56 . after some algebra , we obtain @xmath57 , @xmath58 where the angluar brackets denote averaging over the phase @xmath43 , and the function @xmath59 obeys the equation @xmath60 and we have disregared the mechanical damping @xmath61 . the stationary solution of eq . ( [ mastereq1 ] ) is easily found as @xmath62 note that , similarly to the low - frequency case @xmath63 , the distribution ( [ stationary ] ) is very sharp . indeed , the typical energy @xmath64 is of the order of the applied voltage @xmath65 , and all energies which occur in eq . ( [ stationary ] ) are in our classical consideration much bigger that the quantum energy @xmath66 of the oscillator . the function @xmath67 can have positive as well as negative sign . if it becomes negative at some values of energy ( amplification instead of the dissipation ) , there is a possibility that the strong feedback regime emerges . the stability regions in the gate - bias voltage plane . bold solid lines indicate the edge of the coulomb diamonds . insets show the sketch of @xmath59 in each region . the horizontal lines indicate bias voltages used for current and noise scans in figs . 2 and 3 . ] to illustrate the energy dependence of the probability , we have chosen exponential energy dependence used previously for low frequencies in ref . @xcite ," +"during the last years , ample evidence for the presence of intruder excitations , in particular at and near closed - shell regions @xcite has been accumulated throughout the nuclear mass table . such intruder excitations , which give rise to shape coexistence and collective band structures , are particularly well documented in the @xmath2 ( sn ) and @xmath1 ( pb ) mass regions . they can be associated with many - particle many - hole proton excitations across the closed shells @xcite but can also be studied , in an equivalent way , using potential energy surface calculations @xcite . after the discovery of @xmath0 intruder excitations in the even - even pb nuclei , down to mass @xmath3 @xcite , the development of recoil and recoil - decay - tagging ( rdt ) techniques and of heavy - ion induced fusion - evaporation reactions @xcite have led to a wealth of new data on collective bands in the pb isotopes that have neutron number near @xmath4 . the large number of experiments carried out over the last few years are described in a review paper by julin _ et al . _ study of the fine - structure of alpha decay of the very neutron - deficient nuclei has also proven to be an excellent tool @xcite to identify excited @xmath0 states and was used for the first observation of a set of three low - lying @xmath0 excitations in @xmath5pb @xcite . the above two major experimental techniques have been instrumental in exploring unexpected new phenomena concerning intruder states and shape coexistence . with these methods , data have become available on @xmath6pb @xcite , @xmath5pb @xcite , @xmath7pb @xcite and @xmath8pb @xcite . the experimental evidence for close - lying @xmath0 excitations and for associated collective band structures ( see fig . [ pbrudi ] ) has brought about the need to explore and study the effects of mixing among these structures . a first attempt using two - level mixing for the low - lying @xmath0 and @xmath9 excitations in @xmath10pb was carried out by van duppen _ et al . _ the importance of mixing between bands was put in a broader context by dracoulis @xcite in the os - pt - hg - pb region . more recently , detailed two - band mixing calculations @xcite and an attempt to perform a three - band mixing study in @xmath5pb @xcite have been reported , albeit all starting from phenomenological band - mixing assumptions . so , there is a clear need to perform a detailed study of these nuclei . we also mention that intruder @xmath0 states and associated bands have been studied in the neutron - deficient pt nuclei @xcite down to mass @xmath11 and in the po nuclei @xcite in an effort to distinguish collective vibrational excitations from intruder states . deformed mean - field calculations @xcite have indicated the possibility of obtaining oblate and prolate minima close to the spherical ground - state configuration in the total energy surface for the pb nuclei for neutron numbers close to @xmath4 . in the hg nuclei with a ground state corresponding to a slightly deformed oblate configuration , a second , prolate configuration is predicted with minimal energy near mid - shell ( @xmath4 ) , while in the pt nuclei a crossing of both minima is found and the prolate deformed minimum becomes the lowest configuration at mid - shell . in the po nuclei the situation is more complicated @xcite with an oblate minimum which approaches the spherical ground - state configuration near @xmath12 , and a prolate minimum which becomes dominant in the ground state for even lower neutron numbers . the above studies have the drawback that only the static potential energy surface properties are studied . many - particle many - hole ( @xmath13p-@xmath14h ) excitations can not be incorporated easily in full large - scale shell - model studies because of the extremely large dimensions of the model spaces involved . these @xmath13p-@xmath14h excitations , however , can be handled within an algebraic framework of the interacting boson model ( ibm ) @xcite . the inclusion in ibm of the simplest 2p-2h intruder excitations in the form of two extra nucleon pairs ( two bosons ) and the study of the mixing with the regular configurations was suggested by duval and barrett @xcite and applied in the pb region to the hg nuclei @xcite , the pt nuclei @xcite and the po nuclei @xcite . these ibm - mixing calculations , however , generally implied the introduction of many parameters . calculations including up to 6p-6h excitations have been carried out , using a simplified hamiltonian , with the aim of studying high - spin properties and backbending within the ibm configuration mixing picture by j. jolie et al @xcite . in an effort to remove the obstacle of introducing many parameters when carrying out such ibm configuration mixing calculations with various mp - nh excitations , the symmetries connecting particle and hole bosons have been put forward in an algebraic framework and led to the introduction of a new label , called _ intruder spin _ or @xmath15 spin @xcite and to applications in the pb region @xcite . in this approach , explored in detail in a series of papers @xcite , both the particle and hole shell - model configurations are handled as interacting particle- and hole - like @xmath16 and @xmath17 bosons . the method also allows , in principle , the mixing of two dynamical symmetries . the experimental need to explore three families each with a different intrinsic structure ( spherical , oblate and prolate or , in a spherical shell - model language , the 2p-2h and 4p-4h intruder excitations next to the regular ones of 0p-0h type ) forms the starting point of the present study . an exploratory calculation of this kind within an algebraic framework has already been reported @xcite but was confined to the @xmath0 band heads . in this paper an ibm - mixing calculation that describes the three different intrinsic ` shape ' configurations is performed , and applied to the very neutron - deficient pb nuclei . the regular ( reg ) 0p-0h states are described in terms of @xmath18 bosons while the intruder 2p-2h and 4p-4h states require @xmath19 and @xmath20 bosons , respectively . the model space thus consists of the sum of three symmetric u(6 ) representations @xmath21\oplus[n+2]\oplus[n+4]$ ] . the model hamiltonian has the form @xmath22 the different parts are @xmath23 with the @xmath17-boson number operator @xmath24 and the quadrupole operator @xmath25 where @xmath26 stands for a regular , 2p-2h or 4p-4h configuration . the parameter @xmath27 corresponds to the single - particle energy needed to create a 2p-2h excitation , corrected for the gain in binding energy due to pairing . likewise , @xmath28 corresponds to the single - particle energy needed to create a 4p-4h excitation ( corrected for pairing ) , with @xmath29 . eigensolutions depend primarily on the ratio @xmath30 . for @xmath31 the solution is vibrational while for @xmath32 it is rotational . in addition , the parameter @xmath33 in the quadrupole operator ( [ q ] ) determines whether the solution is su(3 ) ( axially deformed , @xmath34 ) or so(6 ) ( triaxially unstable , @xmath35 ) . the hamiltonians used in ( [ hamiltonian ] ) represent the simplest parametrisation of the ibm which encompasses its different limits , u(5 ) vibrational , su(3 ) rotational and so(6 ) @xmath36 soft . often a rotational term @xmath37 is added but this is not needed here . the mixing of the different configurations is induced by @xmath38 , which is assumed to be of lowest possible order in the @xmath16 and @xmath17 bosons , @xmath39 with @xmath40 where @xmath41 and @xmath42 mixes the regular ( 0p-0h ) and 2p-2h configurations while @xmath43 mixes the 2p-2h and 4p-4h configurations . note that care is taken to introduce different ( 0p-0h)-(2p-2h ) and ( 2p-2h)-(4p-4h ) mixing parameters , @xmath44 and @xmath45 , respectively , and that there is no direct mixing between the 0p-0h and 4p-4h configurations . the latter statement is suggested by the observation that the matrix element of a two - body interaction between 0p-0h and 4p-4h states is zero . to obtain an estimate of the relation between @xmath44 and @xmath45 , assume in first approximation that the dominant component of the 2p-2h and 4p-4h configurations involves pairs of particles ( holes ) in a single @xmath46 ( @xmath47 ) shell coupled to zero angular momentum . for a pairing force the following ratio of mixing matrix elements is obtained : @xmath48 in the limit of large shells , the mixing between the 2p-2h and 4p-4h @xmath0 states is thus twice as strong as that between the ground state and the 2p-2h states . in contrast , the corresponding ratio , obtained with the mixing hamiltonian ( [ mix ] ) and a u(5 ) vibrational classification of states , equals @xmath49 in the limit of large boson number , @xmath50 should thus be twice as big as @xmath51 to recover the ratio in eq . ( [ ratio ] ) . in the present application to the pb isotopes , the boson number @xmath18 is such that the square root in eq . ( [ u5 ] ) equals about 0.8 , by which factor @xmath50 should be reduced to account for the finite boson number . another and perhaps more important fact is that both eqs . ( [ ratio ] ) and ( [ u5 ] ) are derived for a spherical configuration . it is clear that deformation may drastically change the ratio of mixing matrix elements and , specifically , it may reduce both matrix elements because of the smaller overlap between states with different deformation . thus the microscopic estimate @xmath52 can not be adhered to rigidly and several calculations corresponding to different combinations of mixing matrix elements must be explored . in the even - even pb nuclei , @xmath53 valence neutrons form a ground state which is predominantly of seniority zero , @xmath54 . this can be viewed as a condensate of neutron pairs coupled to @xmath0 . excited states are first built from one broken pair ( @xmath55 ) with @xmath56 , next two broken pairs ( @xmath57 ) @xmath58 and so on . to describe these spherical states in an ibm context , we consider the hamiltonian ( [ reg ] ) with a spherical structure [ symmetry limit u(5 ) ] and which has @xmath59 as the only parameter . we fix this parameter to the @xmath60 state of the heavier pb isotopes @xmath61 to 204 , where the @xmath13p-@xmath14h intruder states are high in energy and have little effect on the low - excited spherical states ( see fig . [ pbrudi ] ) . we do not consider the one broken pair @xmath62 ( @xmath63 boson ) or @xmath64 ( @xmath26 boson), states , which can only be described within extended boson models . a constant hamiltonian for this regular configuration , @xmath65 , yields a constant excitation energy for the @xmath60 state , independent of the number of bosons . the excitation energy of the observed states , however , changes slightly with mass number @xmath66 ( because of shell effects ) . we choose @xmath67 mev ; this value is a compromise between a @xmath60 state which is somewhat too low and other states that increase too rapidly in energy with angular momentum . a better fixing of @xmath59 could have been obtained by a variation of @xmath59 linear with the number of bosons . for the sake of simplicity this is not done here . the spectroscopic information on the neutron - deficient pb isotopes is limited . we use" +"inflation @xcite postulates that the very early universe underwent a period of accelerated expansion . it is typically described via the dynamics of the inflaton , a scalar effective degree of freedom coupled to gravity . quantum fluctuations of the inflaton and other light fields constitute the most widely studied mechanism for producing primordial density perturbations ( for reviews see refs . these perturbations induce temperature fluctuations in the cosmic microwave background radiation ( cmb ) and , as a consequence of their gravitational growth , lead to the formation of the large scale structure of the universe ( lss ) . a key corollary of the inflationary hypothesis is that precise measurements of the cmb and the distribution of galaxies in the sky constrain the physical mechanism that drives the accelerated expansion , opening a remarkable window into the physics of the very early universe . in recent years , high - quality observations of the cmb have been provided by the wmap satellite @xcite , acbar @xcite , the south pole telescope ( spt ) @xcite and the atacama cosmology telescope ( act ) @xcite , while the sloan digital sky survey ( sdss ) @xcite has probed the density perturbations at low redshifts . further , data from the planck satellite @xcite will soon be available to the cosmological community , and several major lss surveys are now underway or are being planned . inflation can be realized in a vast number of ways , and these scenarios are typically distinguishable via their predictions for the statistical properties of the primordial perturbations . some models are purely _ ad hoc _ , while others satisfy naturalness constraints , or can be derived from candidate theories of fundamental physics . given the plethora of models that exist , it is fruitful to consider the corresponding inverse problem : given cosmological data , can we deduce the mechanism underlying inflation ? this problem is often referred to as _ reconstruction _ ideally , reconstruction would recover the effective action of the `` inflationary sector '' of high energy physics , but carrying out this program for a fully general scenario is not likely to be feasible , even with data from the next generation of astrophysical experiments . consequently , present - day implementations of reconstruction incorporate a ( sometimes implicit ) prior restricting attention to a specific category of models usually a single inflaton with a canonical kinetic term , minimally coupled to einstein gravity . this paper builds on the slow roll reconstruction algorithm , proposed by easther and peiris @xcite . slow roll reconstruction does not require the slow roll _ approximation _ , but rather relies on the truncated hamilton - jacobi slow roll _ expansion _ this is a phenomenological description of inflation , obtained by expanding the hubble parameter as a power series , with the inflaton field as the independent variable or `` clock '' . we focus on scales which are directly probed by observations , making minimal assumptions regarding the reheating mechanism and the expansion history of the universe during the `` primordial dark age '' @xcite . given the long history of the inflationary inverse problem , slow roll reconstruction has a number of antecedents . in particular , other approaches to the inverse problem based on the hamilton - jacobi equations include ref . @xcite and `` monte carlo reconstruction '' @xcite , which was further developed in refs @xcite . separately , @xcite constrained the slow roll parameters by requiring that the duration of inflation was sufficient to solve the classic cosmological problems , while cline and hoi reconstructed inflationary models that allow for a significant running of the scalar spectral index within the hamilton - jacobi formalism @xcite . leach and collaborators constrained inflation by writing the spectral indices in terms of the slow roll parameters @xcite . a similar scheme to slow roll reconstruction was discussed in refs . likewise , ref . @xcite used the wmap5 dataset and sdss data release 7 lrg data to constrain the hubble slow roll parameters , while ref . @xcite obtained constraints on the power spectra of curvature and tensor perturbations using priors based on single field slow roll inflationary models . we implement slow roll reconstruction within modecodehiranya / modecode ] , a publicly available solver for the inflationary background and perturbations @xcite . as shown by liddle @xcite the background dynamics corresponding to the truncated slow roll hierarchy can be solved analytically , yielding the corresponding inflationary potential @xmath3 . adding this potential to the menu of models supported within modecode yields a simple and robust implementation of slow roll reconstruction . further , modecode performs a full numerical computation of the inflationary perturbation spectrum , making no use of the slow roll approximation when computing the power spectrum . we then estimate the slow roll parameters using the wmap7 data , and the recent spt and sdss dr7 data releases . the principal advantage of implementing slow roll reconstruction within modecode is that , by using the nested sampler multinest @xcite with cosmomc @xcite , we compute bayesian evidence at each order in the truncated slow roll hierarchy . this information determines the number of slow roll parameters that are required to account for the data , and thus the optimal order at which to truncate the hierarchy . in addition , we carefully construct the priors for the slow roll parameters to ensure that the computed evidence values are realistic @xcite . finally , we compute two heuristic model selection statistics the profile likelihood ratio and the akaike information criterion for the truncated slow roll hierarchy , and compare these to the bayesian inferences . this is the third in a sequence of papers on bayesian analysis of inflation , and optimal approaches to constraining inflationary models with astrophysical data . the first @xcite focussed on estimating the free parameters in specific inflationary models , while the second @xcite addressed the model selection problem in inflation and the computation of bayesian evidence . the paper is organized as follows : in section [ sec : srr ] we describe slow roll reconstruction and summarize its strengths . section [ sec : method ] contains a detailed description of our analysis , and summarizes the data used to generate the constraints . we present our results in section [ sec : results ] , and summarize the implications of our findings in section [ sec : conclusions ] . during inflation the background metric is well - described by the flat friedmann robertson walker metric @xmath4 where @xmath5 is the scale factor and , as usual , the hubble parameter @xmath6 where dots denote derivatives with respect to time , @xmath7 . inflation is , by definition , a period of accelerated expansion during which @xmath8 . slow roll reconstruction @xcite is based on the inflationary flow hierarchy . this is obtained by rewriting the second friedmann equation , @xmath9 , as @xmath10 where @xmath11 is the reduced planck mass and primes denote derivatives with respect to @xmath12 . we define the slow roll parameters , @xmath13 : @xmath14 ^ 2 \equiv \epsilon\ ] ] for @xmath15 , and @xmath16 for @xmath17 . these are related to the hubble slow roll parameters by noting that @xmath18 and @xmath19 @xcite . we obtain the hamilton - jacobi equations @xcite by differentiating @xmath20 with respect to @xmath12 , yielding an infinite hierarchy of differential equations where @xmath21 is determined by the two previous terms in the expansion . if @xmath22 for all @xmath23 at a specific value of @xmath12 , the hierarchy truncates , and these terms must be zero for all values of @xmath12 . as pointed out by liddle @xcite , this ensures that the higher - order derivatives of @xmath24 vanish for all @xmath12 , which is equivalent to requiring that @xmath24 is a polynomial of finite order , @xmath25 where a subscript @xmath26 denotes a quantity evaluated at @xmath27 . multiplying @xmath28 by a constant leaves the @xmath20 unchanged ; as we will see below , @xmath29 corresponds to the overall energy scale of the inflationary era . the coefficients @xmath30 , @xmath31 , @xmath32 in equation ( [ eq : srrdef ] ) are then related to the hubble slow roll parameters by @xmath33 the system is not modified by the shift @xmath34 , but this rescaling does implicitly redefine the @xmath35 . we remove this ambiguity without loss of generality by assuming that the slow roll parameters are measured at the instant at which @xmath36 . further , the slow roll hierarchy simplifies when @xmath37 , leading to a distinct class of solutions , and we test both n - parameter "" and low-@xmath0 n - parameter "" models @xcite in what follows . given an expression for @xmath24 we can always obtain the corresponding potential @xmath3 @xcite by recalling that @xmath38 and replacing @xmath39 with @xmath40 , @xmath41\,.\label{eq : v}\end{gathered}\ ] ] this expression is a function of the @xmath35 and thus the slow roll parameters , so slow roll reconstruction can be implemented by adding equation ( [ eq : v ] ) to the `` menu '' of inflationary models supported by modecode @xcite . the fourier components of the scalar and tensor modes @xmath42 and @xmath43 are obtained by solving @xmath44 where @xmath45 and the subscript @xmath46 denotes a derivative with respect to conformal time @xmath47 . initial conditions for these modes are set by the bunch - davies vacuum when the mode @xmath48 is well within the horizon , and the amplitude of the power spectrum , defined by @xmath49 is computed from the solution when the mode is much larger than the horizon and frozen in : @xmath50 as usual , @xmath51 denotes the curvature perturbations in comoving gauge , and sometimes the notation @xmath52 is used . the amplitude of the power spectrum can also be computed in the slow roll approximation . evaluated at @xmath53 ( the scale which exits the horizon as @xmath27 ) , the amplitude is given in terms @xmath29 and the slow roll parameters by : @xmath54 ^ 2}{\pi\epsilon_\ast } \frac{h_\ast^2}{8\pi}\ , , \label{eq : asr}\ ] ] where @xmath55 denotes @xmath56 to second order in the slow - roll expansion . here , @xmath57 , and @xmath58 is the euler - mascheroni constant @xcite . slow roll reconstruction treats the individual terms in the slow roll hierarchy as free parameters . by implementing the potential , equation ( [ eq : v ] ) , within modecode @xcite we obtain posterior distributions for @xmath59 ( or subsets of these variables ) and compute bayesian evidence to determine the optimal truncation - order for this expansion . modecode modifies cosmomc @xcite , which is used in conjunction with the multinest sampler @xcite . consider the probability distribution for a set of parameters @xmath60 , given a model @xmath61 and the data @xmath62 , denoted by @xmath63 @xcite . bayes theorem yields the _ posterior _ @xmath64 where @xmath65 is the likelihood , @xmath66 is the prior , and @xmath67 is the bayesian evidence . since the probability is normalized to unity we can compute the evidence directly , via @xmath68 which is an @xmath69-dimensional integral over a volume defined by the parameter ranges permitted by the prior . using bayes theorem again , we have @xmath70 given the _ a priori _ probability ratio @xmath71 , @xmath72 yields the ratio of probabilities for the two models , in the light of the data . any _ a priori _ preference for @xmath73 over @xmath74 is quantified by @xmath71 ; this ratio is always set to unity in our analysis . consequently , the evidence ratio @xmath72 expresses the relative betting odds "" for two models . the evidence , equation ( [ eq : evidence ] ) , depends" +"seyfert galaxies , quasars , and other active galactic nuclei ( agn ) often show radial velocity offsets between their broad emission lines , narrow emission lines , and host galaxy lines ( stellar absorption and/or h i 21-cm emission ) , and there is a long history of investigations into the nature of these offsets , beginning with penston ( 1977 ) , netzer ( 1977 ) , osterbrock & cohen ( 1979 ) , and gaskell ( 1982 ) . in addition , many studies have concentrated on differences in line profile , asymmetry , width ( e.g. , full - width at half maximum [ @xmath1 ) , peak , and/or velocity centroid as a function of ionization potential or critical density for lines from the same region , such as the narrow - line region ( nlr ; osterbrock 1981 ; pelat , alloin , & fosbury 1981 ; de robertis & osterbrock 1986 ; de robertis & shaw 1990 ; busco & steiner 1992 ; moore , cohen , & marcy 1996 ; komossa et al . 2008a ) or broad - line region ( blr ; wilkes 1984 ; crenshaw 1986 ; osterbrock & mathews 1986 ; corbin 1990 ; tytler & fan 1992 ; sulentic , marziani , & dultzin - hacyan 2000 ; richards , et al . 2002 ; snedden & gaskell 2007 ) . even for the same emission line from a low - redshift agn , such as the commonly used [ o iii ] @xmath25007 line , a perusal of the nasa extragalactic database ( ned ) demonstrates that the heliocentric redshift in terms of radial velocity ( cz ) can differ substantially in excess of the quoted errors from one study to the next , due to wavelength calibration uncertainties , different measurement techniques , or aperture effects , for example . thus , some care must be taken when determining velocity offsets between different lines , but there is no doubt from the above references that the offsets in many sources are real and significant . recent investigations have sparked renewed interest in the study of velocity offsets , because they have been used to indicate the possible existence of multiple agn in a galaxy , or an agn that is displaced with respect to the gravitational center of a galaxy . the most convincing evidence comes from galaxies that show active nuclei that are spatially offset from their optical centers , as well as emission lines that are offset in radial velocity from the systemic velocities of the host galaxies . for example , the evidence for multiple agn in ngc 3341 ( @xmath3 0.027 ) appears to be incontrovertible ( barth et al . three separate nuclei can be identified in a sloan digital sky survey ( sdss ) image of this galaxy . the central nucleus has a liner / h ii composite spectrum , an offset nucleus at a distance of 5.1 kpc from the center has a seyfert 2 spectrum at a velocity offset of @xmath4200 km s@xmath0 , and another offset nucleus at a distance of 8.4 kpc has a possible liner spectrum with a similar velocity offset . barth et al . suggest that the offset nuclei are due to the fueling of the supermassive black holes ( smbhs ) in two dwarf galaxies that are merging with the primary disk galaxy . another agn that has generated a lot of interest and speculation is the quasar sdss j092712.65 + 294344.0 ( @xmath3 0.71 ) , which shows two sets of emission lines ( one set of narrow lines and one set of broad plus narrow lines ) separated by 2650 km s@xmath0 ( komossa , zhou , & lu 2008b ) . in this case , the sdss image shows only an unresolved quasar multiple nuclei have not been detected in groundbased images . most of the suggested explanations for the double set of emission lines are based on mergers or interactions of galaxies and , possibly , their smbhs . komossa et al . ( 2008b ) suggest that the system with broad lines is a recoiling smbh carrying its blr and high - ionization nlr with it and leaving behind the bulk of the ( lower - ionization ) nlr . the recoil is due to coalescence of two black holes which , under the right conditions , can result in anisotropic gravitational radiation that carries away linear momentum , ejecting the merged smbh at velocities up to @xmath54000 km s@xmath0 in the opposite direction ( campanelli et al . 2007 ; baker et al . 2008 ) . another possible explanation is that this sdss quasar contains a binary smbh , in which the blr and high - ionization nlr are due to accretion onto the smaller smbh , and the low - ionization nlr is an envelope surrounding the pair of smbhs ( dotti et al . 2008 ; bogdanovi , eracleous , & sigurdsson 2009 ) . heckman et al . ( 2009 ) suggest a third possibility , which has been used to explain the properties of the nearby agn ngc 1275 : the narrow redshifted lines are associated with a small galaxy falling into the center of a rich cluster of galaxies where it encounters a large galaxy with an agn that shows both broad and narrow lines . finally , shields , bonning , and salviander ( 2009 ) suggest that the double set of emission lines in sdss j092712.65 + 294344.0 may be due to a chance alignment of two agn , possibly within a massive cluster . although two sets of emission lines that are offset in radial velocity are rare , many agn show velocity offsets between the emission lines from their nlrs and the stellar absorption lines or h i 21-cm emission from their host galaxies . comerford et al . ( 2009 ) present a study in which 32 of 91 seyfert 2 galaxies with red host galaxies at 0.34 @xmath6 0.92 show velocity offsets between their [ o iii ] emission lines and stellar absorption lines that lie in the range @xmath550 km s@xmath0 to @xmath5300 km s@xmath0 ( two of these agn show double peaked emission lines as well ) . comerford et al . suggest that the velocity offsets are likely due to displaced agn that are moving with respect to their host galaxies . the same explanations for the double set of emission lines in sdss j092712.65 + 294344.0 can then be invoked to explain the velocity offsets between the nlr and host galaxy , if one of the agn in these scenarios is dispensed with or replaced by an inactive smbh . however , comerford et al . ( 2009 ) suggest that the most plausible explanation is inspiralling smbhs after a galaxy merger , which move to the gravitational center of the merger remnant via dynamical friction . they leave open the possibility , however , that the velocity centroids of the emission lines are offset from the systemic velocity of the host galaxy due to a combination of outflows and dust extinction in the nlr , although they say this is an unlikely explanation for their sample . in this paper , we show that in low - redshift seyferts , velocity offsets of the narrow emission lines with respect to the host galaxies are indeed due to mass outflows in the nlr and partial extinction of the outflows by circumnuclear dust . this is not a new idea , as a number of previous studies suggested that the combination of dust , either inside or between the nlr clouds , and radial motion , in the form of inflows or outflows , could be the cause of asymmetries and velocity shifts in the narrow lines ( capriotti , foltz , & byard 1979 ; heckman et al . 1981 ; whittle 1985 ; dahari & de robertis 1988 ; de robertis & shaw 1990 ; veilleux 1991a ) . subsequently , a number of studies based on long - slit observations with ground - based telescopes suggested that outflows and dust obscurations could produce the observed profile asymmetries ( storchi - bergmann , wilson , & baldwin 1992 ; arribas , mediavilla , & garca - lorenzo 1996 ; christopoulou et al . 1997 ; rodrguez - ardila et al . we can now investigate this issue in more detail using spatially - resolved optical spectra of the nlr ( @xmath501 resolution ) from the space telescope imaging spectrograph ( stis ) on board the _ hubble space telescope _ ( _ hst _ ) . first , we provide a new characterization of the velocity offsets of the narrow lines in seyfert galaxies , this time separated by seyfert type . the best sample to use is that of nelson & whittle ( 1995 ) , which is based on measurements of moderate - resolution ( 80 230 km s@xmath0 ) ground - based spectra of a large collection of agn ( mostly seyfert galaxies ) with @xmath7 0.043 . the advantage of this dataset , in addition to its size and spectral resolution , is that the observations cover regions in which both strong emission lines and stellar absorption lines are present , reducing possible systematic effects . the blue spectra cover h@xmath8 and [ o iii ] @xmath94959 , 5007 emission and mg i @xmath105167 , 5173 , 5184 stellar absorption , and the red spectra cover [ s iii ] @xmath29069 emission and ca ii @xmath108498 , 8542 , 8662 stellar absorption . nelson & whittle show that their stellar velocities , combined from the mg i and ca ii triplets , are in agreement with the published h i 21-cm velocities to within the published uncertainties . from table 4 in nelson & whittle ( 1995 ) , we adopted the stellar absorption velocity ( @xmath11 ) and used the [ o iii ] emission velocity centroid ( @xmath12 ) for each agn to determine the velocity offset : @xmath13 . in the few cases where [ o iii ] velocities were not listed , we used [ s iii ] velocities instead . the mean uncertainties of the sample are 15 km s@xmath0 in @xmath11 and 7 km s@xmath0 in @xmath12 , which added in quadrature yield an uncertainty in @xmath14 of 17 km s@xmath0 . to be conservative , we consider an offset @xmath15 3@xmath16 , i.e. @xmath17 @xmath18 50 km s@xmath0 , to be significant . we identified the agn in this dataset that are seyfert galaxies and determined their types using information in ned ( placing seyfert 1.8s and 1.9s into the type 2 category ) . this yielded a total of 65 seyfert 1 or 2 galaxies with velocity offsets determined in a uniform manner . in figure 1 , we plot histograms of the velocity offsets in 50 km s@xmath0 bins . the distributions of both seyfert types peak near zero km s@xmath0 , but both show an extended tail on the blueshifted side that goes up to @xmath4200 to @xmath4250 km s@xmath0 . combining the two histograms , 23/65 ( 35% ) of the seyferts show blueshifted emission lines with @xmath19 @xmath450 km s@xmath0 , whereas 4/65 ( 6% ) of the seyferts show redshifted lines with @xmath20 @xmath2150 km s@xmath0 . these results are in agreement with many other studies , which find that the [ o iii ] lines in low - redshift agn often have blue asymmetries ( more flux in the blue side of the profile ) and/or blueshifted peaks or centroids with respect to their systemic velocities , whereas few show red asymmetries or redshifted velocity offsets ( heckman et al . 1981 ; whittle 1985 ; de robertis & shaw 1990 ; veilleux 1991b ; bian , yuan ," +"one of the most important properties of complex systems is community structure . real - world complex systems are organized in a modular way , with clusters of units sharing similar dynamics or functionality . however , while the clusters are internally cohesive , they can maintain contrasting dynamics . the problem of resolving and identifying these mesoscopic structures , without any prior information , is extremely challenging . in financial markets , the mesoscopic scale corresponds to sets of stocks that share similar price dynamics . the knowledge of the market structure is highly valuable , and can assist in hedging risks and for better understanding of the market . consequently , over the past years , scientists have deployed and developed many time series techniques to retrieve qualitative information regarding the hierarchy and structure of financial markets @xcite . + a promising approach is that of employing community detection techniques , developed in network theory @xcite , on empirical correlation matrices ( resulted from multiple time series ) . however , the methods are originally constructed to detect dense clusters of nodes within graphs ( networks ) , and are not adapted to deal with correlation matrices . recently , a novel method was proposed , which has been specifically designed to detect communities from correlation matrices of multiple time series @xcite . when applied to financial time series , the method was able to capture the dynamical modularity of real markets . remarkably , the method identified clusters of stocks which are correlated internally , but are anti - correlated with each other . + traditionally , the main object of time series analysis is the characterization of patterns in the amplitude of the increments of the quantities of interest ( stock price in our case ) . the analysis requires a weighted description of the system , i.e. both the amplitude and the sign of the activity . indeed , a time series of increments enclose complete information about the amplitude of the fluctuations of the original signal . however , a significant part of this information is encoded in the purely ` binary ' projection of the time series , i.e. its sign . recent studies have shown various forms of statistical dependency between the sign and the absolute value of fluctuations @xcite . recently , a study has shown a robust empirical relationship between binary and non - binary properties of real financial time series @xcite . the research shows that binary signatures , which retain only the sign of fluctuations , encode significant information regarding the full behaviour of the stock ( both amplitude and direction ) . motivated by these recent results , here we further explore the higher - order relations between financial time series and their corresponding binary signatures , in a more complex setting . here we study whether the binary signatures of assets can reproduce the same complex community organization of financial markets , as the weighted information . + to this end , we use the daily closing prices of the stocks of three indexes ( s@xmath0p500 , ftse100 and nikkei225 ) over the period 2001 - 2011 . for each index , we restrict our sample to the maximal group of stocks that are traded continuously throughout the selected period . this results in 445 stocks for the s@xmath0p500 , 78 stocks for the ftse100 and 193 stocks for the nikkei225 . given a stock price @xmath1 where @xmath2 denotes one of the @xmath3 stocks in the index , and @xmath4 denotes one of the @xmath5 observed temporal snapshots ( days ) , the log - return is defined as @xmath6.\ ] ] for each stock in the system we use the time series of it s log - returns for our analysis . this is the construct we refer to as the `` weighted time series '' throughout the rest of the paper . in contrast , the `` binary signatures '' only reveal the direction of the fluctuation ( sign ) in the price and are defined as @xmath7= \left\{\begin{array}{rr } + 1&r_i(t)>0\\ 0&r_i(t)=0\\ -1&r_i(t)<0 \end{array}\right .. \label{eq : sign}\ ] ] in fig . [ fig : binarize ] we show a simple example of a weighted time series , along with the corresponding binary projection . + the two types of information are in fact different descriptions of the same system , and are used to construct cross - correlation matrices . in turn , we deploy three popular community - detection algorithms @xcite specifically adapted , where necessary , for the correct use of cross - correlation matrices @xcite . we examine and quantify similarities and variations in the organization of the markets for these two representations . this approach reveals some interesting results . first , we can quantify the level of information encoded within the binary signatures , with respect to the full weighted time series . secondly , we observe that both the binary and weighted representations yield very similar structures , which indicates that most of the information regarding the structure of financial communities is already encoded within the sign of a stock . + is not shown in the plots , but the its value is reported in each panel . ] in this section we analyse the eigenvalue density distribution of the cross - correlation matrices for the two representations of the data ( binary and weighted ) . when plotting the density distribution one can identify specific spectral properties that have structural implications . in other words , it is possible to identify distinct eigenvalues in the spectrum , which correspond to correlated clusters of stocks , and typically indicate a non - trivial structure . + to begin , we first need to discuss a filtering technique , based on random matrix theory ( rmt ) @xcite , which is used to identify non - random properties of empirical correlation matrices . the majority of the eigenvalues present in the spectrum of an empirical correlation matrix result from randomly induced correlations between the time series . in the generic case , where one measures the correlation between @xmath3 independent random time series for @xmath5 time steps ( the observed period ) , then the resulting correlation matrix would be an @xmath3 by @xmath3 wishart matrix , whose statistical properties are well known @xcite . in the limits where @xmath8 and @xmath9 the eigenvalues of the wishart matrix are distributed according to a marchenko - pastur distribution @xmath10 and @xmath11 otherwise . the boundaries @xmath12 and @xmath13 are dependent on the data size and given by @xmath14 ^ 2.\ ] ] this analytic curve represents the boundaries of the bulk eigenvalues , which predominantly represent noise , and so have little meaning assigned to them . the eigenvalues outside this range however have structural implications , and correspond to groups of correlated stocks @xcite . as a result , any empirical correlation matrix @xmath15 can be identified as a sum of of two matrices : + @xmath16 where @xmath17 is the random part aggregated from the eigenvalues in the random spectrum ( @xmath18 ) @xmath19 we refer to @xmath20 as the `` structured '' component , which is composed from those eigenvalues above the boundary of the bulk eigenvalues . @xmath21 . + moving forward , in financial markets it well established that stocks typically move up or down together , an effect known as the market mode . this effect is indicated by the presence of a very large eigenvalue @xmath22 , orders of magnitude larger than the rest . since this eigenvalue represents a common factor influencing all the stocks in a given market , from a structural perspective , the market mode eigenvalue signifies the presence of one single super - community , containing all the stocks in the market . + thus , the other eigenvalues ( not including the market mode ) , which deviate from the bulk , @xmath23 are the ones corresponding to mesoscopic clusters , i.e. groups of stocks with similar dynamics . this observation results in a further decomposition of the empirical correlation matrix @xmath24 where @xmath25 represents the market mode , and @xmath26 represents the remaining correlated groups . these sub - groups of correlated stocks comprise the mesoscopic structure of the market . they are also referred as `` group modes '' in some of the literature @xcite . + our focus here is to detect these eigenvalues in the spectrum of both the binary and weighted data . moreover , we want to explore the similarities and differences between the two spectra to inform us about the corresponding structures yielded by each type of data . + in figure [ dist1 ] we plot the eigenvalue density distribution for the three different indices . the top row corresponds to the weighted representation ( log - returns ) , and the bottom row corresponds to the binary representation ( binary signatures ) . we can observe the known structure of the financial markets in the weighted data , however this complex structure also exists in the binary data . this result is non trivial . we can observe a market mode , and several deviating eigenvalues also in the `` simpler '' binary data ( with the same order of magnitude ) . + we also want to inspect whether both descriptions of the system function the same under randomization . the returns of each stock were separately permuted randomly , therefore preserving the total return of the stocks and destroying the daily correlation between the returns . once the time series entries are shuffled , both binary and weighted correlation matrices end up as elementary random matrices . as discussed before , the eigenvalues of such matrices will be distributed with a marchenko - pastur distribution . in figure [ dist2 ] we plot the density distribution of the shuffled data for the three different indices . the top row corresponds to the weighted representation ( log - returns ) , and the bottom row corresponds to the binary representation ( binary signatures ) . as expected , in both cases we observed the known characteristics of a random matrix . the spectra of both representations collapsed to the known analytic curve . + to sum up this section , we identified a sub - group structure both in the weighted and the binary representation of the three indices . each of the binary spectra we studied retain all the known properties of a `` regular '' ( weighted ) spectrum ( random bulk , market mode and group modes ) . this result propels us to do a more refined analysis , and to further explore ( and compare ) the sub - group structure of the different indices . in the next section we will apply community detection algorithms to extract a more detailed structure for both representations , so that we can better quantify the similarities and the variations . .the 10 industry sectors in the global industry classification standard ( gics ) , with the color representation used to highlight the sectors in the following figures . [ cols=""<,^,<,^ "" , ] once we obtain the community structure using the different algorithms , our goal is to quantify the dissimilarities ( or similarities ) between the different partitions ( binary and weighted ) . for this task we apply the variation of information ( vi ) measurement @xcite . the variation of information is an information - theoretic measure of the distance between two partitions . the different partitions @xmath27 and @xmath28 represent @xmath3-dimensional vectors where the @xmath2-th component @xmath29 denotes the set in which node @xmath2 is placed by that particular partition . the variation of information involves the mutual information @xmath30 which is defined as @xmath31 where @xmath32 is the joint probability distribution , and @xmath33" +"quasars , and agn in general , are often supposed to be powered by accretion of gas into supermassive black holes ( bhs ) . in this case , large dormant bhs are expected in the nuclei of nearby galaxies ( soltan 1982 ; rees 1984 ; cavaliere & padovani 1986 ) . assuming accretion at a known fraction of the eddington rate and efficiency of radiation of 10% in units of @xmath0 , it is possible to estimate the expected mass function of dormant bhs . this mass function implies a number density of large bhs ( @xmath1 m@xmath2 ) compatible with the hypothesis that a bh is present in each bright bulge . recent detailed observations of the cores of nearby galaxies have lead to the discovery of massive dark objects in most cases ( magorrian et al . 1998 ; van der marel 1999 ) . even though many details are still uncertain , many authors agree in claiming a correlation between the mass of the massive dark object and the host bulge . interpreting these dark objects as the expected dormant bhs , the bh bulge correlation strongly suggests a connection between quasar activity and the formation of galactic bulges . it is assumed that the accretion of matter onto a bh of mass @xmath3 is a fixed fraction @xmath4 of the eddington rate , so that the quasar luminosity is @xmath5 , where @xmath6 . the efficiency of accretion @xmath4 is assumed to increase from 0.1 for the smallest bhs ( @xmath7 m@xmath2 ) to 1 for the largest ones ( @xmath8 m@xmath2 ) . then , the mass function of dormant bhs is calculated by integrating the luminosity function of quasars ( see salucci et al . 1999a for details ) . we assume that a significant fraction of agns are heavily obscured , and give the dominant contribution to the hard x - ray cosmological background ( see , e.g. , celotti et al . 1995 ; comastri et al . 1995 ; fiore et al . we include such objects using the model of comastri et al . ( 1995 ) . the resulting expected mass function of dormant bhs is shown in fig . 1 ( dashed line ) , for @xmath9 km / s / mpc and @xmath10 . the mass function of dormant bhs residing in nearby galaxies is estimated with two independent methods ( see salucci et al . 1999a for details ) . firstly , the mass function of galactic bulges is convolved with a fiducial bh bulge relation ( a lognormal , with width 0.3 dex and average @xmath11 ) . 1 shows the resulting mass function ( continuous line ) . secondly , exploiting the correlation between radio power from the core of elliptical galaxies and bh mass ( @xmath12 , where @xmath13 , see also franceschini et al . 1998 ) , the radio luminosity function of elliptical cores is convolved with a bh radio power relation to obtain another estimate of the mass function of the dormant objects . the result is again shown in fig . 1 ( points with errorbars ) . the three determinations of the mass function of dormant bhs agree for reasonable values of the parameters involved . this highlights a dichotomy ( in a statistical sense ) in the behaviour of bhs . larger objects ( @xmath14 m@xmath2 ) are hosted in ellipticals , shine as bright quasars at high redshift , almost at the eddington luminosity , are hardly reactivated and hardly obscured , while smaller bhs ( @xmath15 m@xmath2 ) are hosted in the bulges of spiral galaxies , shine also at low redshift with a lower luminosity ( in eddington units ) , and may be reactivated and obscured . the abundance of bhs in the bulges of spiral galaxies is more difficult to estimate . upper limits have been determined by salucci et al . ( 1999b ) by analyzing nearly a thousand rotation curves for spirals . we have constructed an analytical model for the joint formation of ellipticals and quasars in the framework of hierarchical cdm models . the details are given in monaco , salucci & danese ( 1999 ) . in a bulge , quasar activity and the main burst of star formation , which mark the main `` shining phase '' of a galactic dark matter halo , are likely to be close in time ( see , e.g. , hamann & ferland 1993 ; see also best , these proceedings ) . it is supposed that the shining phase of a galactic halo is delayed with respect to its dynamical formation . this delay is assumed to be small for the halos corresponding to large ellipticals , and increasingly larger for smaller halos . in this way the hierarchical order is inverted for halo shining . this is done to reproduce the apparent anti - hierarchical evolution of quasars while preserving a correlation between bulge and bh mass . the mass of the bh formed during the shining phase is assumed to depend on the halo mass , and to be modulated by the same variable which determines the morphological type , so as to obtain a bh - bulge relation . this variable is assumed to be either the spin of the dark matter halo or the fraction of the merging masses at the formation time . the model reproduces successfully the main observable quantities relative both to elliptical galaxies and quasars ; see monaco et al . ( 1999 ) for details . the results shown in this paper are for a flat cdm model with @xmath16 , cosmological constant and @xmath9 km / s / mpc . 2 shows the predicted mass function for the dark matter halos of ellipticals , compared with that inferred from the luminosity function and reasonable hypotheses on the mass - to - light ratios of ellipticals . 3 shows the comparison between the predicted and observed quasar luminosity functions at different redshifts . the data are taken from pei ( 1995 ) , boyle et al . ( 1993 ) ( @xmath17 to 3 ) and kennefick , djorgovski and meylan ( 1996 ) ( @xmath18 ) . boyle b. j. , griffiths r. e. , shanks t. , stewart g. c. , georgantopulos i. , 1993 , mnras , 260 , 49 cavaliere a. , padovani p. , 1988 , apj , 333 , l33 celotti a. , fabian a. c. , ghisellini g. , madau p. , 1995 , mnras , 277 , 1169 comastri a. , setti g. , zamorani g. , hasinger g. , 1995 , a&a , 296 , 1 fiore et al . 1998 , nature , in press franceschini a. , vercellone s. , fabian a. , 1998 , mnras , 297 , 817 hamann f. , ferland g. , 1993 , apj , 418 , 11 kennefick j.d . , djorgowski s.g . , meylan g. , 1996 , aj , 11 , 1816 magorrian j. , tremaine s. , richstone d. , bender r. , bower g. , dressler a. , faber s.m . , gebhardt k. , green r. , grillmair c. , kormendy j. , lauer t. , 1998 , aj , 115 , 2285 monaco p. , salucci p. , danese l. , 1999 , mnras , in press ( astro - ph/9907095 ) pei y.c . , 1995 , apj , 438 , 623 rees , m. j. , 1984 , ara&a , 22 , 471 salucci p. , szuszkiewicz e. , monaco p. , danese l. , 1999a , mnras , 307 , 637 salucci p. , ratnam c. , monaco p. , danese l. , 1999b , mnras , submitted ( astro - ph/9812485 ) soltan a. , 1982 , mnras , 200 , 115 van der marel r.p . , 1999 , aj , 117 , 744" +"the cosmic x ray background ( xrb ) is the combined x ray emission from all extragalactic x ray source populations , integrated over cosmic time . surveys made using _ rosat _ resolved 7080 percent of the xrb into discrete sources @xcite at soft energies ( 0.52.0 kev ) . the majority of these sources are qsos and seyfert 1 galaxies : unobscured active galactic nuclei ( agn ) with broad emission lines @xcite . however , the xrb can not be explained solely by extrapolating these sources to fainter fluxes as their spectra are softer than that of the xrb . to reproduce the xrb spectrum , an additional population of faint hard sources is required . leading x ray background synthesis models identify the faint hard sources with intrinsically absorbed agn @xcite . the absorbed agn are expected to constitute 80 to 90 percent of the total agn population @xcite . the anticipated population of faint , hard sources has now been detected in _ chandra _ and _ xmm newton _ surveys @xcite . however , even before the launch of _ xmm newton _ and _ chandra _ , a number of x ray surveys were carried out using _ rosat _ , _ asca _ , and _ beppo_sax to investigate the absorbed agn population @xcite . these surveys covered large areas of sky and so were particularly useful for finding relatively bright , and thus easily studied , examples of the absorbed agn population . the sources detected in these surveys exhibit interesting , and somewhat surprising properties . for example , @xcite found that agn from the _ beppo_sax high energy large area survey ( hellas ) could be divided into two groups according to their optical and near ir properties . one group of sources have point - like optical / near ir counterparts with colours typical of optically selected qsos . the other group of sources are extended in the optical / near ir and have colours dominated by the host galaxy stellar population . despite having a wide range of x ray absorbing column densities up to @xmath4 , none of the sources studied by @xcite appeared to have colours dominated by a reddened agn . comparison of _ rosat _ and _ beppo_sax data on hellas sources yielded another unexpected result : @xcite found that a significant fraction of the absorbed objects in hellas have an additional soft component in their x ray spectra . this could be due to scattered x rays which do not pass through the absorber , alternatively it might indicate a hot gas component as observed in starburst galaxies . perhaps one of the most puzzling results is that in many agn whose x ray spectra indicate a substantial absorbing column ( @xmath5 @xmath6 ) , the corresponding optical spectrum shows little or no evidence for dust reddening @xcite . this suggests that the absorbing media of agn typically have much lower dust - gas ratios than the interstellar medium of our galaxy @xcite . observations of hard x ray selected , absorbed agn have the potential to reveal much about the dominant , absorbed xrb - producing population of agn . here we report new x ray and optical observations of the hellas source , an absorbed x ray source , optically classified as a seyfert 1.9 galaxy @xcite . it has a broad component to its h@xmath7 emission line ( hence the seyfert 1.9 classification ) but its optical / near ir colours appeared to be completely dominated by its host galaxy @xcite . it was proposed to have a _ _ counterpart , ( and thus a significant soft x ray excess ) by @xcite . throughout this paper we assume a flat @xmath8 cosmology with @xmath9 and a hubble constant of 70 @xmath10 . is a serendipitous source in two _ xmm newton _ observations of markarian 766 . the first observation was performed on 20th may 2000 and had an exposure time of 28 ks in epic mos ( an intermediate resolution x ray imaging spectrometer , * ? ? ? the second observation took place exactly one year later , with a mos exposure time of 127 ks . in both observations the epic pn camera was operated in small window mode , and hence did not record any data for . the data were processed using the _ xmm newton _ science analysis system ( sas ) v5.3 . periods of high background in the 2001 observation were excised from the event lists , to leave 95 ks of useful exposure time . there were no periods of high background during the may 2000 observation , so the total useful exposure time of the two observations is 123 ks . at an off axis angle of 8.6 arc minutes , this corresponds to an effective exposure time of 82 ks at 2 kev . for the purpose of obtaining an accurate source position , images and exposure maps were constructed in the energy band 110 kev . these images were source searched using the sas routines eboxdetect and emldetect . a linear shift of @xmath11 2 arc seconds , based on the relative position of markarian 766 in the epic images and the 2mass catalogue , was applied to the x ray position of to match the optical / ir astrometric reference frame . we extracted x ray spectra in the energy range 0.212 kev for the source and background from each exposure , including all valid single , double and triple x ray event patterns . we have used the latest epic mos redistribution matrix files and generated appropriate ancillary response files for our spectra using the sas task arfgen . the source has a similar countrate and similar x ray spectrum in both observations . therefore the spectra from both observations and both mos cameras were co - added to maximise signal to noise . finally , the resulting spectrum was grouped to a minimum of 50 counts per channel . the online apmmike / apmcat/ ] and 2mass databases were used to find the optical / ir counterpart for . in addition , an i band image was obtained in january 2002 during photometric conditions using the andalucia faint object spectrograph and camera ( alfosc ) on the nordic optical telescope ( not ) . an optical spectrum of was also obtained using alfosc in january 2002 . a ten minute integration was taken using grism 4 ( 32009100 ) with a slit 1.8 arc sec wide providing a resolution of 23 . relative flux calibration was determined from an observation of the standard star feige 66 . the _ xmm newton _ derived position for is given in table [ tab : positions ] . the statistical uncertainty on this position is sub - arc second , and the systematic uncertainty is @xmath13 arc sec @xcite , a significant improvement upon the @xmath13 arc minute uncertainty of the hellas position @xcite . at the x ray position we find unambiguous counterparts in the apm and 2mass catalogues , and their positions are given in table [ tab : positions ] . there is no corresponding _ rosat _ counterpart . we provide a summary of the optical / ir counterpart s photometric properties in table 2 . the spectrum of the optical counterpart is shown in figure [ fig : optspec ] . it is a seyfert 1.9 galaxy at a redshift @xmath14 . the position of the optical counterpart reported by the hellas team @xcite is incorrect . however , the spectrum of the optical counterpart shown in @xcite has exactly the same emission line ratios as seen in our not spectrum . subsequently we have learned that the spectrum and redshift given by @xcite are in fact for the correct optical counterpart , but the reported co - ordinates were mistakenly given for a second object observed simultaneously through the same slit ( a. comastri , private communication ) . .x ray , optical and ir positions of @xmath12 [ cols=""<,^,^ "" , ] [ tab : opt_mags ] we have used xspec v11.2 to analyze the x ray spectrum . the results described in this section are given in table [ tab : results ] and all errors on the fit parameters are quoted at 90 per cent confidence for one interesting parameter ( @xmath15 ) . ( 2.9,2.5 ) ( 0.0,3.0 ) the spectrum is shown in figure [ fig : xmmspec ] ; the low count rate below 1 kev implies that the spectrum is heavily absorbed . we therefore fitted an absorbed power - law model . a galactic component to the absorption model was included , with @xmath16 , @xcite . this simple model is a good fit to the data and is overplotted in figure [ fig : xmmspec ] . the best fit power - law photon index is @xmath0 , and the best fit column density intrinsic to is @xmath17 . the observed 210 kev flux is @xmath18 , with a corresponding unobscured rest frame 210 kev luminosity of @xmath19 . reprocessing of the primary power - law radiation by cold material will result in a fe @xmath20 emission line at 6.4 kev and a reflected component , which has an fe k edge at 7.1 kev @xcite . addition of a narrow line at a rest frame energy of 6.4 kev does not produce a significant improvement to the fit . adding a cold reflection component also results in an insignificant improvement in fit . the reflection component is poorly constrained and the 90 percent upper limit to the equivalent width of the fe @xmath21 line ( 111 ev ) is compatible with the typical level of reflection seen in seyfert 1 galaxies @xcite and with the reprocessing expected in the absorbing medium @xcite . some seyfert 2 galaxies show broad optical emission lines in polarised light ( e.g. * ? ? ? * ) , implying that some of the nuclear radiation is scattered into our line of sight without passing through the absorbing medium . we have therefore added a second intrinsically unabsorbed power - law component to our model . this does not significantly improve the fit , and the normalisation of the scattered power - law component is @xmath22 of the primary , absorbed , power - law component . in several heavily absorbed seyfert galaxies the spectrum below 1 kev is dominated by emission from photo - ionised gas @xcite . the strongest soft x ray emission feature in these objects is the ovii triplet of emission lines at rest frame energy of 0.57 kev which is unresolved at the epic spectral resolution . addition of a narrow rest frame 0.57 kev emission line does not significantly improve the fit . lccccccc model & @xmath23 & intrinsic @xmath24 & ew & line flux & scattered & r & @xmath25 + & & ( @xmath26 ) & ( ev ) & ( @xmath27 ) & fraction ( % ) + absorbed power - law & @xmath28 & @xmath29 & & & & & 69/73 + + absorbed power - law & @xmath30 & @xmath31 & @xmath32 & @xmath33 & & & 66/72 + + iron @xmath20 line + absorbed power - law & @xmath34 & @xmath35 & @xmath36 & @xmath37 & & @xmath38 & 66/71 + + reflection + iron @xmath20 line + absorbed power law & @xmath28 & @xmath39 & & & @xmath40 & & 68/72 + + scattered component + absorbed power - law & @xmath41 & @xmath42 & - & @xmath43 & & & 66/72 + + ovii line + ( 2.9,2.5 ) ( 0.0,-2.2 ) the observed ir colours of r k=5.0 , j h=1.5 and h k=1.4 are all too red for a spiral or elliptical galaxy at @xmath14 , where one" +"the dmrg algorithm was introduced by steven white @xcite , as an algorithm for calculating ground state properties of principally one - dimensional strongly correlated systems in condensed matter physics . the connection between dmrg and matrix product states @xcite ( also known as finitely correlated states ) was first made by rommer and stlund @xcite , who identified the thermodynamic limit of dmrg with a position - independent matrix product wavefunction . although dmrg had already proven itself to be useful empirically , this was an important step in rigorously establishing the physical basis of the algorithm due to the concrete and easy to manipulate form of matrix product states . work on the spectra of density matrices @xcite , later formulated as scaling of the von neumann entropy @xcite has placed the algorithm on a firm footing , showing that the required computational effort ( realized via the basis dimension @xmath0 ) is essentially a function of the entanglement of the wavefunction @xcite , which for one - dimensional ground - states scales at worst logarithmically with the system size @xcite . computationally , mps algorithms came to the fore with the assistance of a quantum information perspective , leading to algorithms for periodic boundary conditions @xcite , and finite temperature algorithms based on density operators @xcite . at around the same time , methods for simulation of real time evolution were developed in dmrg @xcite , which can also benefit from mps formulations @xcite . the common theme of mps approaches is to allow algorithms that operate on multiple , distinct wavefunctions at the same time . this is possible in the original formulation of dmrg only by constructing a mixed effective hilbert space that is weighted appropriately to represent all of the relevant states simultaneously . this is inefficient , as the algorithms typically scale as @xmath1 ( or up to @xmath2 for periodic boundary conditions @xcite ) in the number of basis states @xmath0 , so increasing @xmath0 so as to represent multiple states in the same basis is typically much slower than performing separate operations on each basis . in addition , the mixed basis approach lacks flexibility . while traditional dmrg programs calculate the wavefunction and a few ( often predetermined ) expectation values or correlation functions , if instead the wavefunction is calculated in the mps representation of eq . ( [ eq : mpwavefunction ] ) it can be saved for later use as an _ input _ for many purposes . perhaps the simplest such operation beyond the scope of traditional dmrg is to calculate the _ fidelity _ , or _ overlap _ between the wavefunctions obtained from separate calculations . in the mps formulation , this calculation is straightforward . nevertheless the determination of the scaling function for the fidelity of finite - size wavefunctions for different interaction strengths , provides a new tool for investigating phase transitions and crossover phenomena @xcite . indeed , due to the simplicity of the calculation the fidelity is likely in the coming years to be the first choice for quantitatively determining critical points . similar measures of entanglement , such as the concurrence and single- and two - site entropy @xcite , are also straightforward to calculate , hence the mps formalism allows us to apply directly the emerging tools of quantum information to the study of realistic systems in condensed matter physics . an alternative measure , the loschmidt echo @xcite is important because , unlike many of the quantum information theoretic measures , this is directly accessible in experiments while showing the rich behavior of the simpler measures . the loschmidt echo is more time - consuming to measure numerically as it requires a full time evolution simulation rather than a direct measurement , nevertheless it is well within the current state of the art @xcite . in this paper , we focus on the case of open boundary condition matrix product states . this does not preclude calculation of periodic systems , however the entanglement of such periodic states is increased such that in the large @xmath3 limit ( where @xmath3 is the lattice size ) , the number of states kept tends to the square of that required for open boundary conditions @xcite . algorithms exist for periodic boundary conditions @xcite and infinite systems @xcite ( not to be confused with the ` infinite - size ' dmrg algorithm ) , and the basic formulas introduced here carry over to these cases , but we do not describe the specific algorithms here . in sec . [ sec : mps ] , we introduce the basic formulation of matrix product states , and formulas for the fidelity . [ sec : operators ] is devoted to a new approach , whereby we construct the hamiltonian operator itself as an mps , with many advantages . we cover some remaining details of the dmrg algorithm in sec . [ sec : dmrg ] , before discussing in detail the use of abelian and non - abelian quantum numbers in sec . [ sec : quantumnumbers ] . we finish with a few concluding remarks in sec . [ sec : conclusions ] , including some observations on finite temperature states . we denote an mps on an @xmath3-site lattice by the form @xmath4 the local index @xmath5 represents an element of a local hilbert space at site @xmath6 . the two important cases we cover here are when @xmath5 runs over a @xmath7-dimensional local basis for a wavefunction @xmath8 , in which case we refer to this as a matrix product wavefunction ( mpw ) , or @xmath5 is a @xmath9-dimensional local basis for all operators acting on a local site , which we refer to as a matrix product operator ( mpo ) . in this paper , we use mps for a generic state irrespective of the form of the local space , and use mpw or mpo as necessary when the distinction between wavefunctions and operators is important . in general , the matrix product form can also represent periodic @xcite and infinite ( non - periodic ) states @xcite , but here we use only the open - boundary form equivalent to the wavefunction obtained by dmrg @xcite . to enforce this boundary condition , we require the left - most matrix @xmath10 to be @xmath11 dimensional , and the right - most matrix @xmath12 to be @xmath13 . here we have introduced @xmath0 as the basis size , or dimension of the _ matrix basis _ of the @xmath14-matrices . this quantity is often denoted @xmath15 , or sometimes @xmath16 , in the quantum information literature , but we emphasize it is exactly the same quantity in all cases . in general @xmath0 is position dependent , as we do not require the @xmath14-matrices to be square even away from the boundary . because of the 1-dimensional basis at the boundaries we can regard the mps wavefunction to be a sequence of operators attached to left and right ( or outgoing and incoming ) vacuum states . this makes the operator product in eq . ( [ eq : mpwavefunction ] ) an ordinary number , so the trace operation can be dropped . in practice , a mps state with no particular constraints on the form of the @xmath14-matrices is numerically difficult to handle . we are always free to insert some product of a non - singular @xmath17 operator @xmath18 and its inverse @xmath19 in the middle of our mps , thus we can apply an arbitrary transformation to the matrix basis of an @xmath14-matrix , as long as we make the corresponding transformation to its neighbor . using this freedom , we can transform the @xmath14-matrices into a form where they are orthonormalized , that is , we prefer that they satisfy one of two possible constraints , @xmath20 states satisfying these conditions are orthonormalized in the sense that if all @xmath14-matrices to the left of some matrix @xmath21 are orthogonalized in the left - handed sense , then the basis on the left - hand side of @xmath21 is orthonormal ( _ ie _ the identity operator in the effective hilbert space is trivial ) . conversely , if all @xmath14-matrices to the right of @xmath21 are orthogonalized in the right - hand sense , then the basis on the right - hand side of @xmath21 is orthogonal . usually , we want both these conditions to be true simultaneously . note that it is not , in general , possible for _ all _ of the @xmath14-matrices ( including @xmath21 itself ) to be in orthonormal form at the same time . there are several ways of transforming an arbitrary mps into this normalized form . two ways that we consider here are the singular value decomposition ( svd ) , and the related reduced density matrix , as used in dmrg @xcite . the simplest , and in principle the fastest , is the svd , well - known from linear algebra @xcite . for example , for the left - handed orthogonality constraint on @xmath22 , where we have re - inserted the matrix indices @xmath23 , we consider @xmath24 to be a single index of dimension @xmath25 , giving an ordinary @xmath26 dimensional matrix , and carry out the singular value decomposition , @xmath27 where @xmath28 is column - orthogonal , @xmath29 , and @xmath30 is row - orthogonal , @xmath31 . @xmath15 is a non - negative diagonal matrix containing the singular values . this form coincides with the schmidt decomposition , where @xmath15 gives the coefficients of the wavefunction in the schmidt basis @xcite . the matrix @xmath28 therefore satisfies the left - handed orthogonality constraint , so we use this as the updated @xmath14-matrix , and multiply the @xmath14-matrix on the right by @xmath32 . this implies that the @xmath14-matrix on the right is no longer orthonormalized ( even if it was originally ) , but we can apply this procedure iteratively , to shift the non - orthogonal @xmath14-matrix to the boundary or even beyond it at which point the @xmath33 @xmath14-matrix coincides with the norm of the wavefunction . an important point here is that we can choose to discard some of the states , typically those that have the smallest singular value . this reduces the matrix dimension @xmath0 , at the expense of introducing an approximation to our wavefunction , such that the squared norm of the difference of our approximate and exact wavefunctions is equal to the sum of the squares of the discarded singular values . note however that the singular values only correspond to the coefficients of the schmidt decomposition if all of the remaining @xmath14-matrices are orthogonalized according to eq . ( [ eq : normalizationconstraint ] ) . if this is not the case , the singular values are not useful for determining which states can be safely discarded . alternatively , we can construct the reduced density matrix , obtained by tracing over half of the system . this is achieved by @xmath34 which is a @xmath35 matrix , with @xmath0 eigenvalues coinciding with the values on the diagonal of @xmath36 , and the remaining eigenvalues are zero . again , the eigenvalues are only meaningful if the remaining @xmath14-matrices are appropriately orthogonalized . the utility of the density matrix approach over the svd , is that we can introduce mixing terms into the density matrix which can have the effect of stabilizing the algorithm and accelerating the convergence , which is further discussed in sec . [ sec : dmrg ] . the overlap of two mps is an operation that appears in many contexts . for wavefunctions this gives the fidelity of the two states , and for operators this is equivalent to the operator inner product @xmath37 which induces" +"with the rapid growth in demand for higher data rates , wireless technology is shifting towards the systems with multiple antennas . multiple - input multiple - output ( mimo ) systems in wireless communications provide significant improvements in wireless link reliability and the achievable capacity @xcite . recently , the systems with large number of antennas ( tens to hundreds of antennas ) called as _ large - mimo _ systems are getting increased attention @xcite because they provide additional multiplexing and diversity gains . using spatial multiplexing in mimo systems , multiple data streams can be transmitted simultaneously from different transmit antennas . however , the detection of these data streams at the receiver end is challenging . to achieve minimum bit error rate ( ber ) performance in mimo systems , an exhaustive search over all the possible transmit vectors is required . this is called as the maximum likelihood ( ml ) search for symbol vector detection in mimo systems . however , as the number of antennas grow , the number of possible transmit vectors also increases exponentially and thus the ml search becomes computationally impractical . sphere decoder , a well known mimo detector achieves near ml performance but is practical only up to limited number of dimensions @xcite . + the traditional mimo detection techniques involve linear detection such as zero forcing ( zf ) detector and minimum mean squared error ( mmse ) detector . these detectors use linear transformation of the received vector in order to estimate the transmitted symbol vector . comparatively the mmse detector is superior over zf detector in terms of ber performance , but still their performance is far inferior compared to the ml performance . another type of detection involve non - linear detectors such as vertical bell labs layered space time architecture ( v - blast ) @xcite which utilizes ordered sic for symbol vector detection . some of the other mimo detection technique involve ant colony optimization based mimo detection @xcite , message passing based algorithm @xcite , channel hardening based algorithm @xcite , and lattice reduction aided mimo detection @xcite . as an alternative , in this study we employ sic based detection technique for mimo detection problem . + sic based mimo detection is a well known detection technique where symbols are detected sequentially @xcite . in sic , after detecting each symbol , its interference is canceled from the received vector in order to improve the instantaneous signal to interference plus noise ratio ( sinr ) for the remaining symbols . it is also known as layered detection where in each layer , one symbol is detected . however , it suffers from error propagation which occur due to wrong decisions in early stages of the algorithm @xcite . for improving the performance of sic , a well known technique known as v - blast @xcite technique is used which performs the following steps : ( 1 ) snr based ordering in the detection sequence , ( 2 ) using zf or mmse for nulling the interference among the data streams and ( 3 ) detecting a symbol and canceling its interference i.e. sic . further , to mitigate the effect of error propagation , one of the available algorithms in the literature include multi - branch sic ( mb - sic ) algorithm @xcite where the concept of multiple branch ( mb ) processing is utilized . each branch of mb - sic differs in ordering of the detection sequence thus resulting in a higher detection diversity over the conventional sic . recently , a multiple feedback ( mf ) strategy is proposed in @xcite for sic based mimo detection . multiple feedback sic ( mf - sic ) algorithm proposed in @xcite is based on the concept of shadow are constraint ( sac ) where if the decision fall in the shadow region ( unreliability region ) then multiple constellation points are used in the decision feedback loop . the best symbol from the multiple symbols used in the decision feedback is selected using the ml criteria . + in this article , we propose an improved multiple feedback successive interference cancellation ( imf - sic ) for symbol vector detection in mimo spatial multiplexing systems . in mf - sic , once a decision falls into the shadow region , conventional sic is used to find the best one symbol for the corresponding layer . however , it may happen that while computing the best symbol for a given layer , multiple decisions from the subsequent layers fall into the shadow region . this condition is not checked in mf - sic which sometimes results in error propagation and limits the ber performance . in improved mf - sic ( imf - sic ) , we overcome this limitation by checking the shadow region criteria recursively rather than using the conventional sic for searching the best candidate symbol . this results in significant reduction in error propagation and thus the ber performance can be improved . also , we propose an ordered imf - sic ( oimf - sic ) algorithm where we employ the log likelihood ratio ( llr ) based dynamic ordering in the detection sequence @xcite . by the term dynamic ordering we mean that after every successful decision about a symbol , the ordering of the detection sequence is updated based on new llr values . in oimf - sic , same ordering pattern is followed even for searching the best symbol when a decision is found unreliable . simulation results show that the proposed algorithms significantly outperform the conventional sic and the mf - sic based detection methods , and that they achieve a near ml performance . + rest of the article is organized as follows . in sect . [ sec2 ] , we present mathematical model of mimo system . an overview of some of the traditional mimo detection methods is given in sect . the proposed algorithms for symbol vector detection in mimo spatial multiplexing systems is discussed in sect . [ sec4 ] . in sect . [ sec5 ] , we show the simulation results on comparison of ber performance . finally , in sect . [ sec6 ] we conclude the article . in this section , we discuss the mathematical model of mimo system as shown in fig.[figs1 ] . we consider a point to point spatially multiplexed mimo link with @xmath0 transmit antennas and @xmath1 receive antennas . in spatial multiplexing , each antenna transmits a different information symbol @xmath2 for @xmath3 . let @xmath4^t$ ] be the @xmath5 dimensional transmit vector , @xmath6^t$ ] denote the transpose of a matrix . each entry @xmath2 of the transmit vector @xmath7 is taken from a signal constellation @xmath8 , for example @xmath9 for 4-qam signaling . the channel over which the symbol vector @xmath7 is transmitted is assumed to be a rayleigh distributed flat fading channel . let us consider an @xmath10 complex channel matrix @xmath11 with its elements @xmath12 for @xmath13 and @xmath14 assumed to be independent and identically distributed ( i.i.d . ) as complex normal with mean 0 and variance 1 i.e. @xmath15 . the received symbol vector @xmath16 , after demodulation and matched filtering can be written as @xmath17 where @xmath18 is the additive white gaussian noise ( awgn ) with its element @xmath19 for @xmath13 as i.i.d . the signal to noise ratio ( snr ) is defined as @xmath21 , where @xmath22 is the average energy per symbol defined as @xmath23)$ ] and @xmath24 is the element - wise noise variance . tr(@xmath25 ) denote the trace of a matrix , @xmath26 $ ] denote the expectation operation and @xmath27 denote the hermitian of a matrix . the channel state information ( csi ) is assumed to be perfectly known at the receiver but is unknown at the transmitter . the ml solution for a given received vector @xmath16 and a known channel matrix @xmath11 can be found as @xmath28 ml detection ( mld ) requires an exhaustive search over @xmath29 possible transmit symbol vectors where @xmath30 is cardinality of the constellation set @xmath8 . this search grows exponentially with increase in the modulation order ( @xmath30 ) or increase in the number of transmit antennas ( @xmath0 ) or both . in this section , we discuss some of the traditional mimo detection techniques such as linear detection techniques which involve zero forcing ( zf ) based mimo detection and minimum mean squared error ( mmse ) based mimo detection , and nonlinear detection techniques such as sic based mimo detection . in zf based mimo detection , a linear transformation matrix @xmath31 is used in such a way that it removes the effect due to the channel impairments on the received vector @xmath16 i.e. @xmath32 which is the pseudo inverse of channel matrix @xmath11 . the linear transformation of the received vector using @xmath31 can be written as @xmath33 thus the zf estimate of the transmitted symbol can be found as @xmath34,\ ] ] where @xmath35 $ ] is the quantization operation which maps the soft values on to the nearest constellation point . the computational complexity of zf receiver is very less , however the ber performance is far inferior to the ml performance . the main drawback of zf based mimo detection is the problem of noise enhancement which degrades its performance . mmse based mimo detection is based on finding a suitable linear transformation matrix which minimizes the mean squared error between the transmit vector @xmath36 and the transformed received vector as @xmath37.\ ] ] the solution to eq . [ eq5 ] can be written as @xmath38 using the transformation matrix @xmath39 , the mmse solution can then be computed as @xmath40.\ ] ] mmse based mimo detection overcomes the problem of noise enhancement in zf detectors . thus it achieves better ber performance over zf but still the performance of mmse receiver is inferior as compared to the ml performance . one more drawback is that the mmse solution needs knowledge of the noise variance @xmath24 . in sic based mimo detection , the symbols transmitted from different transmit antennas are detected in a sequential manner . after detecting a symbol for a particular transmit antenna , its interference is canceled from the received vector in order to reduce the interference between different data streams at the receiver . the received vector in eq . [ eq1 ] can be rewritten as @xmath41 using the knowledge of channel matrix @xmath11 a filter @xmath42 is defined as @xmath43 where @xmath44 is the matrix with its column taken from the @xmath45 to @xmath0 columns of the channel matrix @xmath11 . we use vector @xmath46 as the vector left after removing the interference due to @xmath47 as @xmath48 using @xmath42 , the first symbol @xmath2 is estimated as @xmath49=\mathcal{q}[\mathbf{w}_i^h\mathbf{y}_i],\ ] ] where @xmath50 is estimate of the transmitted symbol @xmath2 . @xmath42 , @xmath51 and @xmath46 are updated after every successful decision about a symbol . sic is an iterative detection technique , where in every iteration one symbol is detected . thus a total of @xmath0 iterations are performed to detect the complete symbol vector . a pseudo code of sic based mimo detection is given in algorithm [ algo1 ] . ; ; compute @xmath52 @xmath53 @xmath54 $ ] update @xmath55 update @xmath56 $ ] however , sic suffers from the problem of error propagation which occurs due to the wrong decisions in early stage of the algorithm . once an error occurs , it propagates to the later stages and thus increases the number of errors . this degrades the ber performance of sic based mimo detection . in this section , first we discuss the mf - sic based algorithm for symbol vector detection in mimo systems . we will then" +"beryllium has one single stable isotope , @xmath0be . spectral lines of be have been identified in the sun , in the near uv region that is observable from the ground , quite some time ago by @xcite . the lines tentatively identified included the be i lines at @xmath1 3321.011 , 3321.079 and 3321.340 , and the be ii resonance lines at @xmath1 3130.422 and 3131.067 ( wavelengths from * ? ? ? * ; * ? ? ? however , it has been shown that the identification of the be i lines was erroneous @xcite . only the be ii @xmath2s@xmath2p@xmath3 resonance lines at @xmath4 3130 are now used to determine be abundances in late - type stars . other be lines can be found in the uv below 3000 , but are only observable from space and seem to be of limited use . isotopic shifted lines of unstable @xmath5be and @xmath6be have been searched for , but were never detected . high signal - to - noise ( s / n ) spectra in the near uv is hard to obtain because of atmospheric extinction . in addition , the spectral region of the be lines is crowded with other atomic and molecular lines ( see the solar spectrum in fig . [ fig : sun ] ) . some of these blending lines are still unidentified , as for example the one contaminating the blue wing of the 3131.067 line . early analyses of be abundances were reviewed by and @xcite . the solar be abundance seems to have been first determined by @xcite . the approximation of local thermodynamic equilibrium ( lte ) has been shown to result in correct abundances for the sun . the solar be abundance also seems to be largely insensitive to 3d hydrodynamical effects . the current value of the solar meteoritic abundance of be is a(be)(x ) = @xmath7 [ n(x)/n(h ) ] + 12 , i.e. an abundance by number in a scale where the number of hydrogen atoms is 10@xmath8 . ] = 1.32 @xcite while the photospheric abundance is a(be ) = 1.38 . nevertheless , most 1d lte model atmosphere analyses of be in the sun tend to find values between a(be ) = 1.10 and 1.15 . the difference is ascribed to near - uv continuum opacity missing in the computations @xcite . beryllium is not produced in significant amounts by the primordial nucleosynthesis , because there are no stable elements with mass number 5 or 8 to act as an intermediate step in synthesising @xmath0be @xcite . in addition , be is rapidly destroyed by proton capture reactions when in regions inside a star with a temperature above @xmath4 3.5 @xmath9 k @xcite . therefore , stars do not produce be . in stars like the sun , for example , be is only present in the external regions of lower temperature ( see fig . 1 of * ? ? ? * ) . in evolved stars , where the convective envelope has increased in size and mixed the surface material with the interior , be , unlike li , is usually not detected . beryllium has never been detected in li - rich giants . long ago , it was understood that be can only be produced by the spallation of heavier nuclei , mostly from carbon , nitrogen , and oxygen @xcite . the only known way to produce significant amounts of be is by cosmic - ray induced spallation in the interstellar medium ( ism ) , as first shown by @xcite and . two channels of cosmic - ray spallation might work to produce be . in the so - called _ direct process _ , be is produced by accelerated protons and @xmath10-particles that collide with cno nuclei of the ism . in the _ inverse process _ , accelerated cno nuclei collide with protons and @xmath10-particles of the ism . if the first channel dominates in the early galaxy , be should behave as a secondary element , as its production rate would be proportional to the metallicity of the ism . if the second channel dominates , be should instead behave as a primary element . the two behaviors can be distinguished by the analysis of be abundances in metal - poor stars . for primary elements , one should observe a linear correlation between @xmath7(be / h ) and the metallicity [ fe / h ] = log [ n(a)/n(b)]@xmath11 @xmath12 log [ n(a)/n(b)]@xmath13 with a slope close to one . for secondary elements , the slope should be around two . linear relations with the two slopes are compared in fig . [ fig : slopes ] . also shown are the be abundances of metal - poor stars determined by . it is clear then that be behaves as a primary element , meaning that the inverse process dominates ( as first suggested by * ? ? ? the determination of abundances of be in metal - poor stars were first attempted by and . but it was with the works of @xcite and @xcite that the linear correlation with slope of one became well established . beryllium abundances in metal - poor stars have been further investigated in several works since then . with the inverse process dominating , and considering that cosmic - rays are globally transported across the galaxy , then the be production in the early galaxy should be a widespread process . it follows that , at a given time , the abundance of be across the galaxy should have a smaller scatter than the products of stellar nucleosynthesis ( such as fe and o ) , as suggested by @xcite and @xcite . in this case , be abundances could be used as a time scale for the early galaxy . this is an interesting application that still needs to be further constrained . cubes ( cassegrain u - band brazil - eso spectrograph ) is a new medium - resolution ground based near uv spectrograph for use at the vlt ( very large telescope ) . cubes is being constructed by brazilian institutions together with eso ( see barbuy et al . this volume , for more details ) . the properties of cubes are still not finalized , but it will have a resolution of at least r = 20000 and should provide access to the wavelength range between 30004000 . cubes will be more efficient than uves @xcite in the near uv . uves ( ultraviolet and visual echelle spectrograph ) is the current spectrograph at the vlt that is able to obtain high - resolution spectra in this region . there is an expected gain of about three magnitudes at 3200 . this gain in sensitivity will expand the number of targets that can be observed . among the main science cases for cubes are the study of abundances of be , c , n , o , and of heavy neutron - capture elements in metal - poor stars ( see also siqueira - mello , this volume and bonifacio , this volume ) . most of the future new instruments and facilities ( such as the e - elt , european extremely large telescope ) are now being optimized for the red and near - infrared spectral regions . thus , cubes has the potential of being an unique instrument in terms of sensitivity , spectral range , and resolution . with respect to current eso instruments , cubes will outperform both uves and x - shooter . cubes should also be more efficient than other ground - based near - uv capable spectrographs , such as hires ( high resolution echelle spectrometer ) at the keck observatory and hds ( high dispersion spectrograph ) at the subaru telescope . regarding space - based telescopes , the hst ( hubble space telescope ) has two uv spectrographs , the space telescope imaging spectrograph ( stis ) and the cosmic origins spectrograph ( cos ) . nevertheless , the hst will likely not be operational when cubes comes online ( @xmath4 2017/2018 ) . the wso - uv ( world space observatory - ultraviolet ) , a 170 cm space based telescope , that should be launched in 2016 will provide access to the uv region ( see shustov , this volume ) . the wso - uv is however optimized for the region between 1150 - 3200 . it is thus not a competitor but complementary to cubes . = @xmath122.85 ) , bd@xmath1213 3442 ( [ fe / h ] = @xmath122.80 ) , g64 - 12 ( [ fe / h ] = @xmath123.20 ) , g64 - 37 ( [ fe / h ] = @xmath123.15 ) , and lp 815 - 43 ( [ fe / h ] = @xmath122.75 ) as open circles . also shown is the upper limit for star bd+44 493 ( [ fe / h ] = @xmath123.80 ) , as an open triangle , width=264 ] the linear relation with slope close to one between log(be / h ) and [ fe / h ] is well established down to [ fe / h ] = @xmath122.5/@xmath123.0 ( but see also * ? ? ? * for a slightly different view ) . going to the extremely metal - poor regime ( [ fe / h ] @xmath14 @xmath123.00 ) , however , the situation is less clear . the detection of be in two stars ( lp 815 - 43 and g64 - 12 ) with [ fe / h ] @xmath4 @xmath123.00 by seems to suggest some deviation from the linear trend , with a possible flattening of the relation between log(be / h ) and [ fe / h ] . the be abundance of a third star ( g64 - 37 ) , analyzed by @xcite , seems to be consistent with this flattening , although these authors argue that there is only evidence for a dispersion of the be abundances . the be abundances of these three stars , together with the stars from , and of stars bd+03 740 and bd@xmath1213 3442 ( [ fe / h ] = @xmath122.85 and @xmath122.80 , respectively ) are shown in fig . [ fig : poor ] . the be abundances and metallicities of these extremely metal - poor stars were redetermined by @xcite . a be upper limit of log(be / h ) @xmath15 @xmath1213.80 was determined for the carbon - enhanced metal - poor star bd+44@xmath16 493 with [ fe / h ] = @xmath123.80 by @xcite . this limit is in principle consistent with an extension of the linear trend between be and metallicity to lower values of fe ( see fig . [ fig : poor ] ) . care in the interpretation is needed because the origin of the carbon enhancement in this type of stars is also not well established . if any kind of transfer of material from evolved stars ( which are depleted in be ) is involved , the surface abundance of be would be diluted . whether the flattening exists or not is thus still not clear , because be abundances have been determined in only a few stars with metallicity around or below [ fe / h ] = @xmath123.00 ( see * ? ? * ; * ? ? ? a number of different scenarios could cause such flattening , each one with its own astrophysical implication . @xcite , for example , suggest that a be plateau , although an order of magnitude below of the current detections , could be the result of an inhomogeneous primordial nucleosynthesis . the identification of such a primordial plateau of be , similar to the one observed for li , might be an important test" +"it is generally believed that galaxies are formed within the deep potential wells of the virialized dark matter ( dm ) halos and that clusters of galaxies are recently collapsed objects . the study of the physical properties of the dm halos in cosmological models therefore provides important clues to our understanding of the universe . in this letter , we report a fitting formula for the two - point correlation function @xmath11 of the dm halos in hierarchical clustering models . the accuracy of the fit is about @xmath12 in @xmath13 for a wide range of halo masses . the two - point correlation function of dm halos has been the subject of many recent attempts at analytical modelling ( e.g. cole & kaiser @xcite ; mann , heavens , & peacock @xcite ; mo & white @xcite , hereafter mw96 ; catelan et al . @xcite ; porciani et al . @xcite ) as well as of n - body simulation studies ( e.g. white et al . @xcite ; efstathiou et al . @xcite ; bahcall & cen @xcite ; jing et al . @xcite ; watanabe , matsubara , & suto @xcite ; gelb & bertschinger @xcite ; jing , brner , & valdarnini @xcite ; mw96 ; mo , jing , & white @xcite ) . in particular , using the extended press - schechter formalism to calculate the correlation function of dm halos in lagrangian space ( cf . cole & kaiser @xcite ) and mapping from lagrangian space to eulerian space within the context of the spherical collapse model , mw96 have derived an analytical expression for @xmath13 : [ linear ] _ hh(r;m)=b^2(m)_mm(r ) . this should hold in the linearly clustering regime where the mass two - point correlation function @xmath14 is less than unity . the bias parameter @xmath15 is [ bias ] b(m ) = 1+^2 - 1_c=1+_c ^2(m)-1_c , where @xmath16 is the linearly evolved rms density fluctuation of top - hat spheres containing on average a mass @xmath17 , @xmath18 , and @xmath19 ( see mw96 and references therein for more details about these quantities ) . the parameter @xmath20 will be called the peak height for convenience . equations ( 1 ) and ( 2 ) were found in good agreement with their n - body results by mw96 and by mo et al . ( @xcite ) , but their tests were limited to high mass halos with @xmath21 due to limited mass and force resolutions . the formula has been widely used : from modeling the correlation function of different types of galaxies ( e.g. , kauffmann et al . @xcite ; baugh et al . @xcite ) to interpreting the observed clustering of various extragalactic objects ( e.g. , mo et al . @xcite ; mo & fukugita @xcite ; matarrese et al . @xcite ; steidel et al . @xcite ; coles et al . @xcite ; fang & jing @xcite ) . we have measured the two - point correlation functions for the dm halos in a large set of high - resolution n - body simulations . each simulation uses @xmath4 particles , and a wide range of hierarchical models are covered : four scale - free models and three representative cdm models . moreover , each model is simulated with three to four different realizations , and two different box sizes are used for each cdm model . with these simulations of very high accuracy , we can determine @xmath22 for a wide range of the halo mass @xmath17 . as a result , we find that the linear bias ( eq . [ linear ] ) is a good approximation in the linearly clustering regime , but the bias parameter given by eq.([bias ] ) agrees with the n - body results only for massive halos with mass @xmath23 , where @xmath3 is a characteristic non - linear mass scale defined by @xmath24 . for the less massive halos , the n - body results imply significantly higher bias than the analytical prediction eq . ( 2 ) and the difference in the correlation amplitude amounts to a factor @xmath8 for @xmath25 . fortunately , the difference between the n - body results and the mw96 formula can be modeled by a simple fitting formula ( 3 ) . this formula can fit the simulation bias parameter for halo mass @xmath26 with an accuracy of about 5% . the new findings have profound implications for the formation of the large scale structures . one of the most interesting applications of the fitting formula would be the clustering of galaxies , since the local late type and dwarf galaxies are believed to have mass @xmath27 and to form recently ( redshift @xmath28 ; mo et al.@xcite ) while @xmath29 is expected for the present universe ( cf . the simulations will be described in section 2 , with emphasis on the aspects relevant to this letter . in section 3 , we will present the correlation function of the halos and the fitting formula . the implications for theories and observations are discussed in section 4 . the two - point correlation functions of halos are studied both for scale - free models and for representative cdm models of hierarchical clustering . in the scale - free models , a power - law power spectrum @xmath30 is used for the initial density fluctuation and the universe is assumed to be einstein de sitter , @xmath31 . four models with @xmath32 , @xmath33 , @xmath34 , and @xmath35 are studied . because these models are conceptually simple and exhibit interesting scaling properties , it is relatively easy to understand how physical properties depend on the shape of the power spectrum and , perhaps more importantly , to distinguish the physical effects from numerical artifacts , since the latter should not in general obey the scaling relations . for this reason , we will extensively use the scaling property that the bias parameter @xmath36 depends only on the halo mass @xmath17 scaled by @xmath3 , i.e. @xmath37 for each @xmath5 . this scaling property manifests itself when the bias parameter for @xmath37 is plotted for different evolution times . each of our simulations for @xmath38 is evolved for 1000 time steps with a total of seven outputs , and that for @xmath39 is evolved for 1362 steps with eight outputs . the output time interval is chosen so that @xmath3 at each successive output is increased by a factor 2.5 , and the @xmath3 values ( in units of the particle mass ) at the first output are 74 , 59 , 35 , and 13 for @xmath32 , @xmath33 , @xmath34 , and @xmath35 respectively . note that fixing the @xmath3 values is equivalent to fixing the normalization for the power spectra . the time step and the integration variables are taken similarly to efstathiou et al . ( @xcite ) . in this letter we will rely on these scale - free models to understand how the halo - halo correlation depends on the shape of the power spectrum . then we will examine whether the result obtained from the scale - free models can be applied to cdm models , since cdm models , at least variants thereof , are believed to be close to reality . three cdm models are very typical : one is the ( ever ) standard cdm model ( scdm ) , one is an open model with @xmath40 and with a vanishing cosmological constant @xmath41 ( ocdm ) , and the other is a flat lower density model with @xmath40 and @xmath42 ( lcdm ) . these cdm models are completely fixed with regard to the dm clustering if the initial density power spectrum is fixed . for our simulations , the linear cdm power spectrum of bardeen et al . ( @xcite ) for the primordial harrison - zeldovich spectrum is used for the initial condition , which is fixed by the shape parameter @xmath43 and the amplitude @xmath44 ( the rms top - hat density fluctuation on radius @xmath45 ) . the values of ( @xmath46 , @xmath44 ) are ( 0.5 , 0.62 ) for scdm , ( 0.25 , 1 ) for ocdm , and ( 0.20 , 1 ) for lcdm . each model is simulated with our vectorized @xmath47 code on the fujitsu vpp300/16r supercomputer at the national astronomical observatory of japan . each simulation is performed with @xmath4 ( @xmath48 million ) particles and with good force resolution @xmath49 ( where @xmath50 is the simulation box size ) . to properly understand the effect of the cosmic variance , three to four independent realizations are generated for each simulation of one model . furthermore , two different box sizes , @xmath51 and @xmath52 , are adopted for each cdm model . further details about the code and the simulations will be given in a forthcoming paper ( jing , in preparation ) , where many clustering statistics of the dark matter will also be presented . the cdm simulations with box size @xmath51 were used by jing & suto ( @xcite ) to study the constraints on cosmological models of the high concentration of the lyman break galaxies at redshift @xmath53 discovered by steidel et al . the dm halos are identified with the friends - of - friends ( fof ) algorithm with a linking parameter @xmath54 times the mean particle separation . the halos with at least 20 members are used for the clustering analysis . it is known that the mass defined by the members of such fof groups is very close to that defined by the spherical overdensity ( so ) virialization ( cole & lacey @xcite ) and that the mass function of such fof groups follows the predictions of the ps formalism ( e.g. lacey & cole @xcite ; mo et al . more importantly , the correlation function of dm halos is quite robust to reasonable halo identification methods , since , for example , the correlation function of the fof groups is statistically indistinguishable from that of the so groups ( mo et al . @xcite ) . therefore , it would suffice to use the fof groups for the present purpose . the first concern of this work is whether the bias of the halos is linear ( eq . [ linear ] ) in the linearly clustering regime . we have calculated the ratio of @xmath11 to @xmath55 for every simulation output . some examples which are also typical are shown in figure [ fig1 ] , which show the ratio at two different outputs of the @xmath56 simulation for three different halo masses . the results are plotted only for the linear clustering regime i.e. @xmath57 , as only this regime is considered here . error bars are calculated by averaging over the different realizations . it is remarkable that the ratio is a constant within the @xmath58 error bars , i.e. the bias is linear and the bias parameter @xmath36 is a function of @xmath17 only . this statement is consistent with many previous studies , but is shown here with higher accuracy . since @xmath15 depends only on @xmath17 , we predict that for a scale - free model , if the mass @xmath17 is scaled by the characteristic mass @xmath3 , the bias parameter @xmath36 depends only on the scaled mass @xmath37 . interestingly , by definitions of @xmath20 and @xmath3 , the scaled mass obeys a simple relation to the peak height @xmath20 , i.e. @xmath59 . thus it is also very convenient to compare the simulation data of @xmath60 with the formula of mw96 ( cf . . [ bias ] ) . in figure [ fig2 ] , we plot the square of the bias parameter @xmath61 as" +"jastrow wavefunction @xcite is a pair - product ansatz for a strongly correlated many - body bosonic ground state . exactly optimized form of the pair function can be found with the correlated basis functions ( cbf ) theory and the diagrammatic theory @xcite . however , such solutions are often either unknown or unavailable from open sources . meanwhile , the jastrow wavefunction is widely used as an approximation to the ground state in first - principles quantum many - body methods , both for bosons @xcite and as a part of a fermionic wavefunction @xcite . in particular , diffusion monte carlo ( dmc ) requires such an approximation as its guiding ( importance - sampling ) function ; the path - integral ground state monte carlo ( pigs ) @xcite does not require importance sampling yet benefits greatly when a high - quality approximate ground state is used as its boundary condition @xcite . in such cases , the numerical efficiency and convenience of obtaining the trial functions is often important to practitioners . the pair factors of the jastrow ansatz , when used in the dmc , are often extracted by solving the pair scattering equation for small inter - particle separation , and only to the leading order . such a solution usually needs to be additionally parametrized with one or several variationally - optimized variables . in this work , we revisit this standard procedure . instead of parametrizing the leading - order solution to the pair equation , we parametrize the scattering equation itself . the trial functions are optimized in the space of solutions of such parametrized equations . we find that this results in a robust and straight - forward methodology which provides an excellent description of the ground state . we are considering a system of identical bosons with pairwise interaction potential . the hamiltonian can be written as @xmath1 we assume the bijl - jastrow ansatz for the many - body ground state of this system , @xmath2 the kinetic energy of this function can be written as @xmath3 in a homogeneous system , the last term vanishes if one assumes that the three - body correlations are sufficiently weak , and the eigenvalue equation of hamiltonian ( [ eq : full - hamiltonian ] ) is fulfilled so long as factors @xmath4 satisfy the pair equation @xmath5 the energy @xmath6 is equal to @xmath7 , @xmath8 being the eigenenergy of the many - body ground state , and must in fact vanish for an infinite system . we retain this term as our calculations use finite periodic systems and @xmath6 can be used to satisfy corresponding boundary requirements . direct solutions of the pair scattering equation similar to ( [ eq : pair - equation - f ] ) were used by pahnparipande @xcite as part of a variational ansatz for nuclear matter . however , as we will see below , direct solutions of this equation are far from optimal for our systems of interest . it was realized early on that the dominant contribution to the quality of the pair factor comes from its behavior at small distances , where the potential energy diverges for a hard - core interaction . indeed , to this day solving eq . ( [ eq : pair - equation - f ] ) to the first leading order at short distances remains the standard prescription when a simple , few - parameter function is desired . this is often understood as solving the kato cusp condition @xcite for the divergence in @xmath9 , similar to the way one handles interactions such as _ e.g. _ electronic states in the coulomb potential or states in a finite - strength contact potential . such terminology is not strictly correct for the potentials with analytical hard - core part . in fact , at short distances , the optimal pair factors for hard - core interactions vanish exponentially faster than the divergence of corresponding potential or kinetic energy contributions . the expectation values for both the potential and kinetic energies exist and carry no irregularities . likewise , the wavefunction has well - defined derivatives everywhere where it does not vanish . this is the reason why the leading - order solution of eq . ( [ eq : pair - equation - f ] ) can be additionally parametrized without forfeiting the variational principle . on the contrary , systems with true cusp condition must satisfy their cusp condition exactly in order to cancel non - analytic terms that arise in the schrdinger equationl ; such pair factors can not be meaningfully parametrized in the vicinity of the divergence . we write the pair factors in the positive - defined form as @xmath10 which is the conventional pseudopotential form but with the prefactor @xmath11 omitted for the sake of simplicity . the pair equation ( [ eq : pair - equation - f ] ) reads @xmath12 ^ 2 \right ) + v(r ) = \varepsilon , \label{eq : pair - equation - u - start}\ ] ] where @xmath13 is the physical dimensionality of the system . if the pair potential energy diverges at small distances as @xmath14 with @xmath15 , the other leading term in eq . ( [ eq : pair - equation - u - start ] ) is in fact @xmath16 and one has wkb - like solution @xmath17 and @xmath18 in practice , this solution does not yield an optimal energy but is in fact significantly improved by additional parametrization , @xmath19 where the constant @xmath20 can be determined by minimizing the variational energy . as mentioned above , such a parametrization is possible because every term of the pair equation ( [ eq : pair - equation - f ] ) remains analytical , and in fact even infinitely differentiable . indeed , @xmath21 moreover , the power of the divergence in @xmath22 can also be treated variationally for the same reason . the above approach alone allows to account for most of the correlation energy of the dense strongly correlated bosonic systems . numerous works have been devoted to improving the pair ansatz beyond the form of eq . ( [ eq : leading - term - u2 ] ) . one of the most studied systems in this regard is liquid helium-4 . this system has been the subject of about every quantum monte carlo method that is applicable , which included a large amount of work with explicit variational monte carlo with the jastrow ansatz . the simplest variational ansatz for helium consists of the parametrized leading - term solution proposed by mcmillan and by schiff and verlet @xcite , or similar solutions @xcite . the improvements beyond the leading order for helium can be seen as falling into the following categories : ( a ) addition to the leading term ( [ eq : leading - term - u2 ] ) of various explicit short- and long - range corrections derived from known general properties of the system @xcite , ( b ) parametrization of the mid - range behavior of @xmath22 focused primarily on improving the variational energy or structural properties @xcite , and ( c ) extracting the solution to the pair equation ( [ eq : pair - equation - u - start ] ) beyond the leading order , or using such solutions as a basis set @xcite . these approaches are considered in some detail below . additionally , one can use the pair functions obtained with paired phonon analysis ( ppa ) method @xcite . for instance , ppa optimization of campbell and pinski was used as a guiding function in ref . . this method requires the hnc approximation and is out of our scope . the best forms of the jastrow function miss the ground state of liquid helium by about one degree kelvin per particle . a large part of this energy can be accounted for by including three - body correlations into the wavefunction @xcite . partially , the three - body correlations can be captured by the shadow wavefunction ( swf ) method @xcite which has since taken over explicit wavefunctions for the variational description of liquid helium . however , our interest is limited to the explicit jastrow pair terms . \(a ) this approach relies on knowing the general properties of the static structure function of the system . it allows to recreate the physically important features that otherwise are missed by the leading - order solution . most remarkable of these corrections is the infinite - range tail in @xmath22 which must arise in the presence of zero - point phonons in the system @xcite . other corrections to @xmath22 were initially tied to the mid - range excitation structure of helium , that is , to the presence of the roton minimum @xcite . as the mid - range behavior is critical for achieving good varitational energy , parametrising @xmath22 in this region has a significant impact on the variational energy , disregarding the origin of such correction . overall , this approach leads to a rapid escalation of the parametrization of the pair factor . the leading order term must still be present , contributing one or two parameters . the phonon tail adds between one and two parameters ( speed of sound , and a distance cutoff @xmath23 ) , and at least three parameters are required for a simple gaussian mid - range correction ( its location , width and strength ) . \(b ) if one is solely interested in minimizing the variational energy , or in replicating a known observable such as the pair distribution function , it is possible to this end to employ heavy parametrization of the pair function @xcite . such attempts have been quite successful , but in all cases relied on on using six and more parameters . here we are seeking approaches that are much straight - forward methodologically . \(c ) trying to directly solve the pair scattering equations leads to the pair functions that are extremely poor in accounting for the correlation energy . moreover , as will be shown below , such energies depend very strongly on the size of the simulation cell . pandharipande and schmidt used the solutions of the pair equation as a variational anzatz for helium @xcite . a sharp cutoff allowed to limit the energy divergence , and the offset @xmath24 in ref . , used to satisfy boundary condition for @xmath4 at the cutoff , is equivalent to @xmath6 in ( [ eq : pair - equation - u - start ] ) . unfortunately , the energy in ref . was extracted in an approximate way . a more productive approach , with excellent variational results , was reported by vitiello and schmidt in . it was shown that when the pair equation is treated as an eignevalue problem , the set of lowest eigenfunctions can be used as a basis for expressing the pair function . that is , their approach uses the pair equation as a _ source _ of good variational functions . on the other hand , the need to combine multiple eigenstates means one has once again to deal with as many as ten variational parameters . this work can be seen as extending the approach of pandharipande and schmidt . however , instead of parametrizing a linear combination of functions arising from the pair equation , we choose to parametrize the equation itself . the pair function is selected from the space of solutions of a modified and parametrized version of the differential eq . ( [ eq : pair - equation - u - start ] ) . straight - out solution of the pair eq . ( [ eq : pair - equation - u -" +"the twirl operation was introduced by bennett _ @xcite in the context of entanglement purification of mixed states . the first step in many of these protocols is the twirl operation which converts an arbitrary mixed state of a two qubit system , @xmath0 , into a werner singlet state @xmath1 @xcite , an incoherent mixture of @xmath2 parts of a maximally entangled singlet state , @xmath3 , and @xmath4 parts of the maximally mixed state , @xmath5 the key idea behind the twirl is that the singlet state is invariant under any bilateral unitary transformation of the two qubits ( that is , any operation where identical local unitaries are applied to the two qubits ) , whereas any other state will be affected . a randomly chosen bilateral rotation should serve to average any other state , converting an arbitrary mixed state to a werner singlet . ( note that the twirl sequence does not _ create _ new singlet , rather it _ preserves _ the singlet , while averaging out all other terms . ) this provides a good `` in principle '' definition of the twirl operation , but in practice it is important to consider what a random bilateral rotation really is , and how it can actually be implemented . early work in this field concentrated on reducing the infinite set of randomly chosen rotations down to a small finite set . originally it was suggested @xcite that the twirl could be achieved using a set of four bilateral rotations , although it was later shown that a set of twelve bilateral rotations are both necessary and sufficient @xcite . this approach is sensible for conventional quantum information processors , but with ensemble devices , such as nuclear magnetic resonance ( nmr ) quantum computers , it is useful to use a different approach . in such devices it is in fact easier to perform rotations by angles that vary continuously over the ensemble than by angles from some small carefully chosen set . in nmr devices , for example , the application of a strong magnetic field gradient @xcite performs a rotation around the @xmath6 axis with a rotation angle that depends strongly on the position of a given molecule within the spatial ensemble ; integrating over the position within the sample is then equivalent to applying a random rotation . in the language of nmr this is often referred to as a _ crush gradient _ pulse . for simplicity we will sometimes describe a crush gradient as a random rotation around the @xmath6-axis , as the effect on the averaged density matrix is the same , but when considering experimental implementations it is necessary to be more precise . the use of field gradients forms the basis of spatial averaging methods , used in nmr quantum computing to prepare pseudo - pure states @xcite . field gradients have also been used to average out error terms @xcite , to project qubits into the zeeman basis @xcite , and to simplify density matrices prior to partial state tomography @xcite . the alternative procedure , in which one rotation chosen from a small set is applied , requires several experiments to be performed , and in the context of nmr quantum computing is usually known as temporal averaging . in subsequent sections we explore different methods for implementing the twirl , concentrating on those which are best suited to ensemble techniques . we begin by noting that any set of bilateral rotations which performs a twirl must correspond to a set of single qubit rotations which , when considered from the viewpoint of a single qubit subsystem , averages any state of a single qubit to the maximally mixed state . as we shall see , however , averaging a single qubit is a necessary but not a sufficient condition for a set of rotations to act as a twirl . averaging a single qubit gives some useful insight into the problem of twirling a two qubit state . a single qubit state can be represented by a ray on the bloch sphere and an arbitrary rotation will move this ray over the surface of the sphere . each rotation @xmath7 is defined by a rotation angle @xmath8 about an axis @xmath9 parameterized by a tilt angle @xmath10 and an azimuthal angle @xmath11 . an arbitrary single qubit state is completely defined by three real parameters , which are conventionally taken as the expectation values of the single spin pauli operators @xmath12 @xcite . for scrambling an arbitrary state to the maximally mixed state , we must choose a convenient set of operations , which scrambles each of these pauli operators individually . a tempting , but incorrect , approach is to apply random rotations about random axes , that is to take @xmath8 as being uniformly distributed between @xmath13 and @xmath14 , while the rotation axes defined by @xmath10 and @xmath11 are uniformly distributed over the sphere ; we call this set of rotations @xmath15 . brute force integration shows that the continuous set of random rotations around random axes , @xmath15 , does not completely randomize the state of a single qubit , and so _ can not _ constitute the basis for a twirl operation ; instead it reduces the bloch vector to one third of its original length . in retrospect the reason for this behaviour is clear : random rotations around axes perpendicular to the original state will completely average it , while rotations around axes parallel or anti - parallel to the state will leave it unaffected . thus the overall effect of @xmath15 must be to scale down the state , rather than to average it completely . the significance of the scaling by one third is discussed below . a better definition of a random rotation is provided by considering the description of a rotation by means of its euler angles . while many different conventions for describing euler angles exist , the essential feature is that any rotation can be decomposed as a sequence of three rotations around two axes . for example any rotation can be achieved by the sequence of rotations @xmath16 where rotations are applied from left to right . a random distribution of euler rotations can be achieved by taking @xmath8 as uniformly distributed between @xmath13 and @xmath14 , with the rotation axes defined by @xmath10 and @xmath11 uniformly distributed over the sphere ; we call this set of rotations @xmath17 . it might seem that @xmath17 is the same as @xmath15 , but they are in fact quite different : in particular @xmath17 completely averages a single qubit , while @xmath15 does not . this is easily seen by noting that the first rotation will average @xmath18 and @xmath19 , while the second and third will average @xmath20 . as any state of a single qubit can be written as a linear combination of these basic matrices and the maximally mixed state , the first two operations will average _ any _ state . it is clear from the above that a random euler rotation will average any single qubit , but this process is perhaps excessive , as two rotations suffice . ( we will see below that this is not true when considering a true twirl applied to two qubits . ) the sequence of rotations @xmath21 where both @xmath10 and @xmath11 are now taken as uniformly distributed between @xmath13 and @xmath14 , will average any single qubit ; as before this is most simply seen by considering the result for @xmath18 , @xmath19 and @xmath20 . indeed this process can be simplified still further : as described by bennett _ @xcite is is possible to average a single qubit by randomly selecting from the four operations @xmath22 . since @xmath23 is equivalent to a @xmath24 rotation , and ( neglecting global phases ) @xmath25 it is clear that this operation is equivalent to applying either @xmath13 or @xmath26 at random , and then applying @xmath13 or @xmath27 at random ; a similar result has been described by hayden et al @xcite . thus instead of choosing the two angles in equation [ rotzy ] at random from uniform distributions , we can choose at random from two particular values . this process of replacing a continuous rotation by a small number of discrete values is an example of a quite general procedure . for rank @xmath28 and rank @xmath29 tensors , continuous rotations about a fixed axis , can in fact , always be replaced by discrete rotations : we can `` hop '' between the angles @xmath30 , with @xmath31 and @xmath32 , and the overall effect is the same as rotating continuously about the same axis @xcite . it is _ sometimes _ possible to use @xmath33 , but this can not be relied on in general . the rotation through @xmath30 is the member @xmath34 of the cyclic group @xmath35 @xcite ; in this way , the continuous rotations can be replaced by discrete group operations and the continuous integrals over the rotation angle @xmath8 , can be substituted by _ group theoretical averages _ , such as @xmath36 the simplest discrete group that can generally be used for averaging is the cyclic @xmath37 group , which is employed by nmr spectroscopists in the form of magic angle hopping @xcite , a discrete version of its continuous counterpart , magic angle spinning @xcite . the group theoretical framework has also been used in the context of bang - bang decoupling protocols @xcite , which seek to average out system - environment interactions by applying fast , discrete and periodic control impulses to _ only _ the system , with the control propagators faithfully representing the members of a discrete cyclic group @xmath38 . this approach hints at another method for performing complete averaging of a single qubit . we have already noted that random rotations around a random axis do not completely average a single qubit , but simply rescale its length by one third . this process is , as usual , equivalent to applying a rotation through an angle of @xmath39 , @xmath40 or @xmath41 around a random axis . clearly a @xmath39 rotation can have no effect , while the effect of the @xmath40 and @xmath41 rotations must be the same . from this it can be deduced that a @xmath40 rotation around a random axis will completely average a single qubit , and this is indeed the case . finally we turn to the issue of practical experimental implementations . for a conventional quantum information processor the obvious approach is to use the smallest discrete set of operations ; for the case of averaging a single qubit this is the set of four rotations described by bennett _ et al . _ with an ensemble processor , such as an nmr quantum computer , it is better to use a procedure based on continuous rotations , corresponding to spatial averaging . clearly the best approach is to apply random rotations around two orthogonal axes , such as @xmath6 and @xmath42 . a strong magnetic field gradient , denoted * g * , will effect a random rotation around the @xmath6 axis , and rotations around other axes can be achieved by combining gradients with single qubit gates ( radiofrequency pulses ) which can be treated as rotating the axis system . thus the sequence @xmath43 will completely average a single spin . note that this procedure is not completely equivalent to equation [ rotzy ] , as it should strictly speaking be followed by a @xmath44 pulse to rotate the axes back to their original positions , but as the maximally mixed state will not be affected by the rotation this final stage may be safely omitted . the discussion above assumes that the gradient pulses are instantaneous" +"quenched disorder induces an extrinsic inhomogeneity in otherwise translationally invariant pure systems . as a result , the equilibrium and out - of - equilibrium physics of disordered systems may be influenced by rare collective events , such as `` avalanches '' , statistically unlikely regions , such as `` droplets '' or `` griffiths regions '' , and by the proliferation of `` metastable states '' . our objective is to develop a theory describing the long - distance physics of such systems through a nonperturbative functional renormalization group ( np - frg ) method and our first focus is the equilibrium behavior of the random - field model . we showed in previous papers , which we refer to as i@xcite and ii@xcite , that the effect of avalanches and droplets can be captured by an approach based on the rg flow of the cumulants of the renormalized disorder , provided that the full functional dependence of the latter is accounted for.@xcite a functional rg is therefore required to let the singular behavior due to rare events or regions emerge along the flow , as also shown in the case of the equilibrium and forced behavior of manifolds in a random environment.@xcite the issue of metastable states , which , at zero temperature where the concept is well defined , refers to the presence of many minima of the microscopic hamiltonian ( bare action ) not simply related by symmetry transformations , is a recurring conundrum in theories of disordered systems . in the case of the random - field ising model ( rfim ) under study , it has a clear manifestation . the critical behavior of the model being controlled by a zero - temperature fixed point,@xcite the long - distance physics can be described through the properties of the ground state which , due to the presence of the random field , is obtained as the solution of a stochastic field equation . by standard field - theoretic manipulations , this leads to a theory expressed in terms of superfields . parisi and sourlas@xcite showed that a supersymmetry of the theory , more specifically the invariance under rotations of the underlying superspace , implies the property of dimensional reduction , according to which the critical behavior of the rfim in @xmath4 dimensions is identical to that of the pure ising model in @xmath5 dimensions . the property however has been proven to be wrong in low enough dimension.@xcite at the same time , it has been understood that the superfield construction breaks down because of the presence of many solutions of the stochastic field equation.@xcite however , in the parisi - sourlas formalism , it is not possible to disentangle breaking of superrotational invariance and collapse of the formalism due to the appearance of multiple solutions . in the companion paper , henceforth referred to as paper iii,@xcite we have shown how to resolve the above conundrum and to combine an extended superfield approach with the np - frg formalism . in particular , ground - state selection can be achieved by adding a weighting factor involving an auxiliary temperature and letting at the end of the manipulations the auxiliary temperature go to zero in the exact np - frg equations for the cumulants of the renormalized disorder . the resulting property of `` grassmannian ultralocality '' then allows one to specifically investigate supersymmetry ( superrotational invariance ) and its spontaneous breaking along the rg flow . such an investigation is the purpose of the present paper . the outline of the article is as follows . in sec . [ sec : model ] , we briefly summarize the main steps of the np - frg in a superfield formalism that we have developed in paper iii . this allows us to recall definitions , notations , and rg equations that will be used in the present article . in particular , we stress two important , and distinct , formal properties of the superfield theory : grassmannian ultralocality "" and superrotational invariance "" . we also consider the rg flow of the ward - takahashi identities associated with the latter and the consequences for the choice of the infrared regulator . in sec . [ sec : surot invariance ] , we show through our np - frg formalism that the superrotational invariance nonperturbatively leads to dimensional reduction . we conclude the section by building a scenario for a spontaneous breaking of the superrotational invariance along the rg flow that is based on our previous results on the appearance of a cusp "" in the functional dependence of the cumulants of the renormalized random field,@xcite and we propose a continuation of the np - frg flow equations when spontaneous breaking has taken place . [ sec : approximation scheme ] is devoted to the development of a supersymmetry - compatible nonperturbative approximation scheme for the exact np - frg equations . it relies on combined truncations of the cumulant expansion and the expansion in spatial derivatives of the field . we also provide details on the numerical resolution . in sec . [ sec : results ] we present the results . we show in particular that breakdown of the dimensional reduction predictions for the critical exponents of the rfim occurs below a critical dimension @xmath0 . we compute the critical exponents as a function of dimension down to @xmath2 and we find good agreement with the best available estimates in @xmath2 and @xmath3 . finally , we show that scaling is described by three independent exponents , contrary to a proposed conjecture.@xcite a short account of this work has appeared in ref . we start by briefly recalling the main features of the formalism presented in the preceding article , with the associated definitions and notations . in paper iii,@xcite we have developed a np - frg theory for describing the equilibrium long - distance physics of the rfim that is based on an extension of the parisi - sourlas@xcite supersymmetric formalism . the latter relies on the fact that the critical behavior of the model is dominated by disorder - induced fluctuations , thermal fluctuations being subdominant , and can therefore be studied by looking directly at zero temperature . the equilibrium properties are then described by the ground state which is solution of the following stochastic field equation @xmath6}{\delta \varphi(x ) } = j(x),\ ] ] where we have added an external source ( a magnetic field ) @xmath7 conjugate to the @xmath8 field and the action @xmath9 $ ] is given by @xmath10 where @xmath11 , @xmath12 , with @xmath13 a random ( magnetic ) field sampled from a gaussian distribution of zero mean and variance @xmath14 . two key ingredients of our extension of the parisi - sourlas formalism are : \(1 ) the need to consider multiple copies ( or replicas ) of the original system with the same disorder , each copy being coupled to a different applied source , in order to generate cumulants of the renormalized disorder with their full functional dependence , thereby allowing for the emergence of a nonanalytic behavior in the field arguments , \(2 ) the introduction of a weighting factor involving an auxiliary temperature @xmath15 to the solutions of the stochastic field equation , so that when @xmath15 appraches 0 only the ground state contributes to the generating functional . by using standard field - theoretical techniques,@xcite one then ends up with a superfield theory for multiple copies in a curved superspace , with @xmath16=\exp ( \mathcal w^{(\beta)}[\{\mathcal j_a\}])=\overline{\exp(\sum_{a=1}^n\mathcal w_h^{(\beta ) } [ \mathcal j_a ] ) } \\&= \int \prod_{a=1}^{n}\mathcal q\phi_a \exp \bigg(-s^{(\beta)}[\{\phi_a\ } ] + \sum_{a=1}^{n } \int_{\underline x } \mathcal j_a(\underline x ) \phi_a(\underline x)\bigg ) , \end{aligned}\ ] ] where the multicopy action is given by @xmath17 = \sum_{a=1}^{n } \int_{\underline{x } } \left [ \frac 12 ( \partial_{\mu}\phi_a(\underline{x}))^2+u_{b}(\phi_a(\underline{x}))\right ] \\&- \frac{\delta_b}{2}\sum_{a_1=1}^{n}\sum_{a_2=1}^{n } \int_{x}\int_{\underline{\theta}_1\underline{\theta}_2 } \phi_{a_1}(x,\underline{\theta}_1)\phi_{a_2}(x,\underline{\theta}_2 ) . \end{aligned}\ ] ] in the above equations , we have introduced a superspace ( coordinates @xmath18 ) comprising the @xmath4-dimensional euclidean space ( coordinates @xmath19 ) and a @xmath20-dimensional grassmannian space ( anticommuting coordinates @xmath21 ) ; the metric is flat in the euclidean sector and curved in the grassmannian one with the curvature proportional to @xmath22 . ( for instance , the integral over superspace is defined as @xmath23 . ) we have also defined superfields @xmath24 , with one auxiliary bosonic ( response "" ) field @xmath25 and two auxiliary fermionic ( ghost "" ) fields @xmath26 and @xmath27 , and associated supersources @xmath28 . the action in eq . ( [ eq_superaction_multicopy ] ) is invariant under a large group of ( bosonic and fermionic ) symmetries . when expanded in increasing number of sums over copies , the generating functional of the connected green s functions , @xmath29 $ ] , gives access to the cumulants of the random generating functional @xmath30 $ ] . we have next applied the np - frg formalism to this superfield theory . this proceeds by first adding an infrared ( ir ) regulator that enforces a progressive account of the fluctuations to the bare action , @xmath31 where the two cutoff functions @xmath32 and @xmath33 are related through @xmath34 with @xmath35 the euclidean momentum , @xmath36 the strength of the renormalized random field , and @xmath37 the field renormalization constant . this ensures that all symmetries of the theory are satisfied . this includes the superrotational invariance found when the theory is restricted to a single copy and to @xmath38 : it then corresponds to @xmath39 , a property that is valid at the microscopic ( uv ) scale @xmath40 ( see also below ) . one next introduces the effective average action@xcite @xmath41=-\mathcal w_k^{(\beta)}[\{\mathcal j_a\}]+\sum_a\int_{\underline x } \phi_a(\underline x ) \mathcal j_a(\underline x ) -\delta s_k^{(\beta)}[\{\phi_a\}]$ ] , whose dependence on the ir cutoff @xmath42 is governed by an exact renormalization - group equation ( erge ) . the effective average action can also be expanded in increasing number of sums over copies , each term of the expansion being then related through the legendre transform to the cumulants of @xmath30 $ ] . we refer to the @xmath43th order term of the expansion of @xmath41 $ ] as the @xmath43th `` cumulant of the renormalized disorder '' . these expansions in increasing number of sums over copies lead to systematic algebraic manipulations that allow one to derive from the erge for @xmath41 $ ] a hierarchy of coupled erge s for the cumulants of the renormalized disorder . we have unveiled an important property of the random generating functional @xmath30 $ ] : the latter satisfies a specific dependence on the grassmann coordinates , which we have called grassmannian ultralocality "" , if and only if a unique solution of the stochastic field equation is included in its computation . this translates into an ultralocal "" property of the cumulants of the renormalized disorder . grassmannian ultralocality `` becomes a property of the superfield theory when @xmath44 ; it is also asymptotically found for finite @xmath22 when @xmath45 ( after going to dimensionless quantities ) . it then reflects the desired ground - state dominance . when this property is satisfied ( _ e.g. _ by setting @xmath46 ) , the erge s for the cumulants simplify and only involve ultralocal '' quantities that can be evaluated for physical fields @xmath47 , _ i.e. _ for superfields that are uniform in the grassmann subspace . for illustration , we give below the erge s for the first two cumulants under the property of grassmannian ultralocality "" , which will be needed in the following : @xmath48= \\&- \dfrac{1}{2 } \tilde{\partial}_t \int_{x_2x_3}\widehat{p}_{k;x_2x_3}[\phi_1 ] \big(\gamma_{k2;x_2,x_3}^{(11)}\left[\phi_1,\phi_1\right ] - \widetilde{r}_{k;x_2x_3}\big ) \end{split}\ ] ] and @xmath49=\\ & \dfrac{1}{2 } \tilde{\partial}_t \int_{x_3x_4}\big \{- \widehat{p}_{k;x_3x_4}\left[\phi_1\right ] \gamma_{k3;x_3,.,x_4}^{(101)}\left[\phi_1,\phi_2,\phi_1\right ] + \\ & \widetilde{p}_{k;x_3x_4}\left[\phi_1,\phi_1\right ] \gamma_{k2;x_3x_4,.}^{(20)}\left[\phi_1,\phi_2\right ] + \frac{1}{2}\widetilde{p}_{k;x_3x_4}\left[\phi_1,\phi_2\right ] \\ &" +"the large magellanic cloud ( lmc ) has revealed a very complex structure both in the stellar and in the gaseous component . the elongation of the stellar disk in the direction of the galactic center , its substantial vertical thickness , the warp and the strong asymmetric bar are naturally predicted by numerical simulations as a result of the gravitational interaction between the lmc and the galaxy ( bekki & chiba 2005 , mastropietro et al . 2005 , hereafter m05 ) . the old stellar distribution appears to be quite smooth in the outer parts of the disk , with no signs of spiral structures out to a radius of 10 kpc @xcite . within the same radius the hi large scale structure reveals the presence of several asymmetric features that have no equivalent in the old stellar disk . the gaseous disk is characterized by the presence of an elongated region located at the south - east of the galaxy and aligned with the border of the optical disk , where the column density distribution shows a steep increase @xcite . since the lmc proper motion vector is directed to the east , it appears natural to associate this high density region with ram - pressure acting on the leading edge of the disk due to the orbital motion of the lmc and its consequent interaction with the diffuse hot gas in the halo of the milky way ( mw ) . the presence of an extended hot halo surrounding galaxies and in hydrostatic equilibrium within the dark matter potential is expected by current models of hierarchical structure formation . in the mw , x - ray absorption lines produced by hot ( @xmath1 k ) gas are detected in the spectra of several bright agn @xcite . some ionization features discovered in the magellanic stream and high velocity clouds indicate that this distribution of hot gas extends well beyond the galactic disk ( @xmath2 kpc ) . constraints from dynamical and thermal arguments fix its density in a range between @xmath3 and @xmath4 cm @xmath5 at the lmc distance from the galactic center ( but kaufmann et al . 2009 suggest a value ten times higher ) . @xcite have performed a detailed analysis of the lmc global star formation rate using asymptotic giant branch stars . they find an irregular and patchy distribution in age , with the youngest carbon - rich systems located at the south - east of the disk . the present star formation activity is rather clumpy and concentrated in stellar complexes characterized by intense hii emission and associated with bright h@xmath0 filamentary bubbles . most of these very young structures lie on the south - east of the disk , in the proximity of 30 doradus , the largest star forming region of the lmc , some are located in the bar and the remainder form an asymmetric pattern that covers the entire disk with no apparent relation to the global geometry of the satellite . it is not clear which is the overall physical mechanism responsible for triggering star formation with the observed asymmetric pattern and different models have been proposed in the past . the stochastic self - propagating star formation ( sspsf ) model predicts a clear age gradient in the lmc s stellar complexes , with the edges being younger with respect to the center , in contradiction with observations @xcite . @xcite proposed a scenario where the bow shock originated by the motion of the lmc through the hot galactic halo compresses the leading edge of the disk and induces star formation . the pressure at the south - eastern edge of the lmc is indeed 10 times higher than the average in the rest of the lmc @xcite . this model , which assumes the orbital motion vector lying in the plane of the disk , predicts increasing ages of the stellar complexes in the direction of the rotation , due to the fact that the material compressed at the front side of the disk moves , in time , away to the side . the youngest systems would indeed lie at the south - east border of the disk , where the relative velocity between the corotating interstellar medium and the external diffuse gas is maximum . several giant structures along the outer east and north edge of the lmc actually show a progression in age in a clockwise direction : moving from south - east to the north lmc 2 , 30 doradus and lmc 3 , lmc 4 , ngc1818 . in particular the difference in age between 30 doradus and lmc4 is exactly their distance along the border of the disk divided by the satellite s rotational velocity ( harris , private communication ) . studied the recent star formation history of the lmc using cepheids and other supergiant stars and found that although the majority of the star formation events in the last 30 myr are concentrated on the east border , others are distributed across the entire disk in partial contrast with the bow shock induced star formation model , that can not explain them . in this work we use high resolution sph simulations to study the effects of the interaction between the lmc interstellar medium and the diffuse hot halo of the mw . we want to investigate whether the ram - pressure acting on the leading edge of the lmc disk is responsible for the increase in density observed in the south - east and for triggering star formation . the analytic model of @xcite assumes a pure edge - on model , but according to @xcite the present angle between the lmc disk and the orbital motion is nearly @xmath6 . even in the absence of precession and nutation , this angle is subjected to large variations during the orbital period in such a way that compression produced by the external hot gas can affect in time both edge - on and face - on . moreover , the ram - pressure felt by the lmc is not constant and has a maximum when the satellite approaches the perigalacticon . the motion of the lmc through the hot halo of the mw during the last 1 gyr is modeled using `` test wind tunnel '' simulations with increasing ram - pressure values . the paper is structured as follows . section 2 describes the models and the star formation criteria adopted , section 3 illustrates the results of simulations without star formation , focussed on the investigation of pure effects of compression on the lmc interstellar medium while section 4 describes the runs where star formation is activated . several simulations have been performed , assuming different star formation models , disk inclinations and hot halo densities . the initial conditions of the simulations are constructed using the technique described by @xcite . our disk galaxy model is a multi - component system with a stellar and gaseous disk embedded in a spherical nfw @xcite dark matter halo . the density profile of the dark matter halo is adiabatically contracted in response to baryonic infall @xcite . the stellar disk follows an exponential surface density profile of the form : @xmath7 where @xmath8 and @xmath9 are the disk mass and radial scale length ( in cylindrical coordinates ) , respectively , while the thin vertical structure has a scale length @xmath10 : @xmath11 the gaseous disk is characterized by an exponential profile with the same radial and vertical scale length as the stellar component and by a constant density layer which extends up to 8@xmath9 . the structural parameters of the disk and the halo are chosen so that the resulting rotation curve resembles that of a typical bulgeless late - type ( sc / sd ) disk galaxy . they are similar to those adopted in m05 for the initial lmc model and reproduce quite well the peak of the rotation curve inferred by @xcite ( fig . as seen in m05 , the interaction with the mw does not affect significantly the stellar and dark matter mass in the inner @xmath12 kpc of the lmc and consequently the global rotation curve within this radial range . the choice of an extended gaseous component for the initial lmc model is motivated by the fact that spiral galaxies in the local universe are commonly observed to be embedded in extended disks of neutral hydrogen significantly larger than their stellar component . as seen in m05 , the combined effect of tidal interactions and ram - pressure stripping can remove a significant fraction of gas from a lmc disk orbiting within the hot halo of the mw , with a ram - pressure stripping radius which is a factor of three smaller than the initial radius of the gaseous disk . also in the case of a lmc with orbital velocities significantly higher @xcite hydrodynamic and gravitational forces together are effective in resizing and reshaping the extended gaseous disk of the satellite beyond 8 kpc . in the present work we neglect the presence of gravitational forces focusing on the effects of pure ram - pressure . therefore we do not expect to see a significant decrease in the radius of the gas distribution . however , in order to take in account the loss of cold gas from the disk of the satellite and the star formation events , we assumed an initial amount of gas in the disk which is about @xmath13 times larger than the hi mass in the lmc ( @xmath14 @xmath15 according to putman et al . 2003 ) . the mass within the virial radius is set equal to @xmath16 m@xmath17 and the fraction of mass in the disk is @xmath18 , equally distributed between the gaseous and stellar component . the contribution of the different components to the global rotation curve , assuming a disk scale length @xmath19 kpc and a dark halo concentration @xmath20 ( where @xmath21 is defined as @xmath22 , with @xmath23 and @xmath24 virial and scale radius of the nfw halo , respectively ) is plotted in fig . [ rotcurve ] . the halo spin parameter , which sets the disk scale length in our modeling , is @xmath25 , where @xmath26 relates the angular momentum @xmath27 and the total energy @xmath28 of a system with virial mass @xmath29 through the relation @xmath30 the initial stellar disk of the satellite galaxy has , within its scale radius @xmath9 , a central mass surface density of @xmath31 ( fig . [ diskprofile ] ) , that corresponds to a b - band surface brightness of @xmath32 , assuming a mass to light ratio @xmath33 . the central gas surface density is only @xmath34 since a significant fraction of gas is distributed in the external disk . assuming @xmath35 hi abundance this value corresponds to an hydrogen column density of @xmath36 within @xmath9 , comparable with the values observed by @xcite with the lmc parkes multibeam hi survey . in order to obtain a strongly stable disk against bar formation even in the presence of significant gas stripping and consequent perturbation of the satellite potential , the thickness of the stellar component is set such that the toomre s @xcite stability criterion is largely satisfied . in particular the toomre s parameter for the stellar disk : @xmath37 where @xmath38 is the radial velocity dispersion , @xmath39 is the local epicyclic frequency and @xmath40 the unperturbed stellar surface density , has a minimum at the disk scale length with @xmath41 . for a gaseous disk the stability of the disk is expressed in terms of the gas sound speed @xmath42 and surface density @xmath43 through the relation : @xmath44 the gaseous disk has initially a constant temperature of 10000 k , which implies @xmath45 and @xmath46 . according to and @xcite , the stability of" +"discrete breathers ( db ) have the defining properties of being spatially localized and having time - periodic dynamics . they are also called _ intrinsically localized _ , in distinction to anderson localization triggered by disorder . a necessary condition for their existence is the nonlinearity of the equations of motion of the system , and the existence of discrete breathers has been proved rigorously for some classes of systems @xcite . in contrast to their analogs in continuous systems , the existence of discrete breathers is a generic phenomenon , which accounts for considerable interest in these objects from a physical point of view in the last decade . in fact , recent experiments could demonstrate the existence of discrete breathers in various real systems such as low - dimensional crystals @xcite , antiferromagnetic materials @xcite , josephson junction arrays @xcite , molecular crystals @xcite , coupled optical waveguides @xcite , and micromechanical cantilever arrays @xcite . for a review on the topic see @xcite . more than a decade ago , discrete breathers have been observed in numerical simulations of , among others , the fermi - pasta - ulam ( fpu ) system @xcite , a chain of nonlinearly coupled masses . although existence of db as exact periodic solutions was proved already some years ago for a large class of oscillator networks @xcite ( not containing the fpu system ) , a proof of their existence in the fpu system has been obtained only recently @xcite . a generalization of the concept of db are so - called traveling db , spatially localized solutions which travel along the chain . at least as approximate solutions they have been observed numerically in the fpu system . a proof of their existence , however , has not been achieved so far , and in fact it is doubted that traveling db exist as exact solutions in this system . the theoretical analysis of approximate traveling db is still an open problem which will be tackled in this article . we consider traveling db as long - living transient structures which can be described by an effective hamiltonian as presented in @xcite . we distinguish three types of localized structures , characterized by their degree of localization , which can be found in the fpu dynamics . examples of these different types are plotted in figure 1 , where from type i to type iii the degree of spatial localization is increasing . type i is similar to a standing wave . it is not a proper db , as its localization depends on the system size , but its energy envelope is sort of localized in a finite system . type ii is exponentially localized , but , as the width of the structure is not that small with respect to the intersite distance , it is called a weakly localized db . type iii depicts a strongly localized db , similar to those first discovered numerically @xcite . all three of these structures are observable in fpu systems as ( transient ) traveling localized objects , called traveling discrete breathers , and we will distinguish in the following between these three types when deriving their effective dynamics . three types of traveling db in fpu . type i : weakly localized standing wave . type ii : weakly localized db . type iii : strongly localized db . the red line in the upper plot represents the local energy . , width=453 ] the outline of this article is as follows : section [ sec : fpu ] provides some basic definitions regarding the fpu model . in section [ sec : proc ] , the method of the effective hamiltonian is briefly recalled , providing the necessary ingredients for its application . section [ sec : waves ] succinctly recalls some results from @xcite , describing the motion of db of type i. in section [ sec : weak ] , an effective hamiltonian is constructed for a family of db of type ii , providing a good framework to understand the traveling motion of weakly localized db in fpu chains . finally , in section [ sec : strong ] , the case of strongly localized db is treated . here , instead of calculating the effective hamiltonian explicitly , the so - called peierls - nabarro barrier is computed , which provides already useful information about the moving properties of db of type iii . let us consider a chain of oscillators whose dynamics is determined by the hamiltonian @xmath0,\ ] ] with momenta @xmath1 and positions @xmath2 . @xmath3 and @xmath4 characterize , respectively , the on - site potential and the ( nearest - neighbor ) interaction potential . the fpu model is defined by the choices @xmath5 where @xmath6 . note , however , that the theory of the next section applies to a more general class of models . the method of the effective hamiltonian has been exposed in @xcite in a general framework . it is briefly recalled here before applying it to the fpu model in the subsequent section . let us define a traveling db of ( [ eq : chaingen ] ) as a function of the form @xmath7 where the function @xmath8 is increasing in @xmath9 , and such that @xmath10 . it is localized in @xmath11 ( e.g. , @xmath12 for some @xmath13 ) and periodic in @xmath14 , @xmath15 . to be slightly more general , one may think of @xmath16 being replaced by a function @xmath17 monotonic in @xmath18 , where @xmath19 and @xmath20 is a function of small amplitude , periodic with a frequency which is small compared to @xmath21 . the point is that , in a moving frame with velocity @xmath22 , one sees a discrete breather at rest with frequency @xmath21 . it is generally believed that solutions of the form ( [ eq : tdb ] ) do not exist as exact solutions in generic systems , although a proof of this conjecture has been accomplished only for a certain class of systems @xcite . however , it may be possible to get _ approximate _ traveling db of the form ( [ eq : tdb ] ) when the following conditions can be met : 1 . find a two - parameter family of approximate ( non - traveling ) discrete breathers of ( [ eq : chaingen ] ) of the form @xmath23 where @xmath9 characterizes the amplitude of the db and @xmath24 its position "" . typically , for a chain having some translation symmetry , and for fixed @xmath9 , there are two such positions where there is an exact db : a site - centered "" db with integer @xmath24 , and a bond - centered "" db with half - integer @xmath24 . by interpolating between these exact solutions , approximate db can be constructed for any real @xmath24 . + next , consider the family of functions @xmath25 the idea is that there may be a `` doppler effect '' of the traveling db , @xmath26 , which can be described by adding a phase shift @xmath27 to @xmath28 , where @xmath29 is called the _ momentum _ of the db . the point is that ( [ eq : fammdb ] ) still describes approximate db for small enough @xmath29 . 2 . compute , for each member of the family @xmath30 , the symplectic area @xmath31 with period @xmath32 . in the case where @xmath33 , like for the hamiltonian ( [ eq : chaingen ] ) , one can write @xmath34 where @xmath35 denotes the mean value over one period and @xmath36 is the kinetic energy . this calculation should result in a symplectic area @xmath37 proportional to @xmath9 , or related to @xmath9 by a simple functional relation . if this is not the case , the parametrization in ( [ eq : fammdb ] ) should be changed , indexing the family in terms of @xmath38 . the fact that @xmath37 is a proper choice as a parameter is explained in @xcite . in short , this can be justified by stating that @xmath37 is an adiabatic invariant of the dynamics @xcite . 3 . compute the symplectic form @xmath39 restricted to the coordinates @xmath40 . this is achieved by evaluating @xmath41 which should be non - zero for any @xmath42 , and the restricted symplectic form reads @xmath43 . then , an effective hamiltonian is computed as the mean ( over one period ) of the original hamiltonian along the family of db , @xmath44 and , finally , the dynamics of @xmath42 is given by @xmath45 for small enough @xmath29 , and assuming @xmath46 for @xmath47 ( otherwise shift @xmath48 to have this ) one may expand the effective hamiltonian so that it takes on the form @xmath49 providing that @xmath50 be non - zero and finite . the latter defines an effective inertia , although @xmath50 may be negative . in fact , as discussed in @xcite ( especially in examples of section 6 therein ) , the sign of @xmath50 can be interpreted as the sign of an effective anharmonicity of the breather solutions . the second term in ( [ eq : heffdb2 ] ) is a periodic function ( of period @xmath51 ) which defines a _ peierls - nabarro potential _ for discrete breathers , as introduced and discussed in @xcite . in these papers it is shown that the critical points of @xmath52 correspond to exact discrete breathers of the full model . in the simplest situation there are two types of critical points associated , respectively , with the stable discrete breathers and the unstable ones . the difference of @xmath53 at these points , say @xmath54 and @xmath55 , is called the _ peierls - nabarro barrier _ @xmath56 the absolute value in this equation is necessary in case of negative @xmath50 . for @xmath50 positive , the minima are associated with stable db , and the maxima with unstable db , otherwise the stability is just reversed . in any case , the smaller this barrier is , the higher is the mobility of a traveling discrete breather , and the better it is in general described by the effective hamiltonian . in the next sections we apply this scheme to the analysis of the mobility of various types of localized solutions in the fpu model . in this section , a particular type of localized solutions is considered , termed type i in the introduction , which have the shape of a standing wave . they do not constitute proper db , as the localization depends on the system size . the method of the effective hamiltonian was applied to this type of solutions in @xcite . here , we summarize these results in order to compare them to those for the proper db solutions obtained in the following sections . consider an fpu chain with , say , an odd number @xmath57 , @xmath58 , of masses and periodic boundary conditions . there exists , in the linear regime ( @xmath59 ) , a family of standing waves @xmath60 whose envelope is localized in space , as it is a sine function with wavelength equal to twice the chain length ( see figure [ f1 ] , type i ) . moreover , it is observed numerically that the localization strength is enforced when the nonlinearity is turned on , @xmath61 . this family ( [ eq : standingw ] ) complies with ( [ eq : famdb ] ) , as it is parametrized by @xmath9 and @xmath24 , while @xmath62 is fixed . such a wave can be put into slow motion when @xmath63 and @xmath64 are non - zero . to `` add momentum '' to this standing" +"many processes in physics involve boundary surfaces which requires the solution of boundary and initial value problems . the introduction of a moving boundary into the physics usually precludes the achievement of an exact analytic solution of the problem and recourse to approximation methods is required @xcite ( see also references therein ) . in the case of a moving plane boundary a time - dependent translation of the embedding space immobilizes the boundary at the expense of the increased complexity of the differential equation . it is the aim of this work to present an example of a soluble moving boundary and initial value problem in cylindrical geometry . the problems with moving boundary arise in many area of physics . one important example is sudden expansion of hot plasma with a sharp boundary in an external magnetic field which is particularly of interest for many astrophysical and laboratory applications ( see , e.g. , @xcite and references therein ) . such kind of processes arise during the dynamics of solar flares and flow of the solar wind around the earth s magnetosphere , in active experiments with plasma clouds in space , and in the course of interpreting a number of astrophysical observations @xcite . to study the radial dynamics and evolution of the initially spherical or cylindrical plasma cloud both analytical and numerical approaches were developed ( see , e.g. , refs . @xcite and references therein ) . the plasma cloud is shielded from the penetration of the external magnetic field by means of surface currents circulating inside the thin layer on the plasma boundary . ponderomotive forces resulting from interaction of these currents with the magnetic field would act on the plasma surface as if there were magnetic pressure applied from outside . after some period of accelerated motion , plasma gets decelerated as a result of this external magnetic pressure acting inward . the plasma has been considered as a highly conducting media with zero magnetic field inside . from the point of view of electrodynamics it is similar to the expansion of a superconductor in a magnetic field . an exact analytic solution for a uniformly expanding , highly conducting plasma sphere in an external uniform and constant magnetic field has been obtained in @xcite . the non - relativistic limit of this theory has been used by raizer @xcite to analyse the energy balance ( energy emission and transformation ) during the plasma expansion . the similar problem has been considered in ref . @xcite within one - dimensional geometry for a plasma layer . in our previous paper @xcite we obtained an exact analytic solution for the uniform relativistic expansion of the highly conducting plasma sphere in the presence of a dipole magnetic field . in the present paper we study the uniform expansion of the highly conducting plasma cylinder in the presence of a constant magnetic field . for this geometry we found again an exact analytical solution which can be used in analysing the recent experimental and simulation data ( see , e.g. , refs . @xcite and references therein ) . we consider the moving boundary problem of the highly conducting plasma cylinder expansion in the vacuum . consider a cylindrical region of space with radius @xmath0 at the time @xmath1 containing a neutral infinitely conducting plasma which has expanded at @xmath2 ( with @xmath3 ) to its present state from a linear source located at @xmath4 . we assume that at any time @xmath1 the plasma cylinder is unbounded in @xmath5 direction ( i.e. the cylinder is located at @xmath6 ) . to solve the boundary problem we introduce the cylindrical coordinate system @xmath7 with the @xmath5-axis along the plasma cylinder symmetry axis and the azimuthal angle @xmath8 is counted from the plane ( @xmath9-plane ) containing the vector of the constant and homogeneous magnetic field @xmath10 . the angle @xmath11 between the vector @xmath10 and the @xmath5-axis is arbitrary . the unperturbed magnetic field is expressed by the vector potential , @xmath12 , where this potential is @xmath13 $ ] with the cylindrical components @xmath14 the components of the vector @xmath10 are @xmath15 , @xmath16 , and @xmath17 . here @xmath18 and @xmath19 are the components of the magnetic field transverse and parallel to the @xmath5-axis , respectively . as the cylindrical plasma cloud expands it both perturbs the external magnetic field and generates an electric field . within the cylindrical plasma region there is neither an electric field nor a magnetic field . we shall obtain an analytic solution of the electromagnetic field configuration . we consider the case of the uniform expansion of the plasma cylinder @xmath20 with a constant expansion velocity @xmath21 . this special case of the uniform expansion falls within the conical flow techniques which has been applied previously in ref . @xcite . from symmetry considerations one seeks a solution for the total ( i.e. , the unperturbed potential @xmath22 plus the induced one ) vector potential of the form @xmath23 with @xmath24 , where @xmath25 is the velocity of light . since the external region of the conducting cylinder is devoid of free charge density , a suitable gauge allows the electric and magnetic fields to be derived from the vector potential @xmath26 . having in mind the symmetry of the unperturbed magnetic field and the fact that the electromagnetic fields do not depend on the coordinate @xmath5 it is sufficient to choose the vector potential in the form @xmath27 , @xmath28where @xmath29 is some unknown function . the components of the electromagnetic field are expressed by this function as @xmath30^{\prime } , \label{23a } \\ & & h_{z } = h_{0\parallel}\left[\frac{\zeta } { 2}\chi ^{\prime } \left ( \zeta \right ) + \chi \left ( \zeta \right ) \right ] , \nonumber \\ & & e_{\varphi } = \frac{h_{0\parallel}}{2}\zeta ^{2}\chi ^{\prime } \left ( \zeta \right ) , \,\ , e_{z}=h_{0\bot } \zeta ^{2}\chi^{\prime } \left ( \zeta \right ) \sin \varphi , \label{23}\end{aligned}\]]@xmath31 , where the prime indicates the derivative with respect to the argument . the equation for the vector potential @xmath32 is obtained from the maxwell s equations which for the unknown function @xmath29 yields an ordinary differential equation @xmath33 this equation is to be solved in the external region @xmath34 subject to the boundary and initial conditions . here @xmath35 is the plasma cylinder radius at the time @xmath1 . the initial conditions are at @xmath2 @xmath36the first initial condition states that the initial value of @xmath37 is that of a homogeneous unperturbed magnetic field . the second initial condition states that there is no initial electric field . boundary conditions should be imposed at the cylindrical surface @xmath0 and at infinity . because of the finite propagation velocity of the perturbed electromagnetic field the magnetic field at infinity will remain undisturbed for all finite times . further , no incoming wave - type solutions are permitted . thus , for all finite times @xmath38 at @xmath39 . the boundary condition at the expanding cylindrical surface is @xmath40 which is equivalent to the relation @xmath41 ( see eq . ) with @xmath42 . in addition imposing that @xmath43 at @xmath44 we obtain another boundary condition @xmath45 . the solution of eq subject to the initial and boundary conditions may be written as @xmath46where @xmath47 the complete solution may finally be written in the form at @xmath48 ( or @xmath49 ) @xmath50 , \nonumber \\ h_{\varphi } = -h_{0\perp}\sin \varphi \left[1+\frac{\mathcal{u}\left(\zeta\right)}{\mathcal{f}\left(\beta \right)}\right ] , \label{34a } \\ h_{z } = h_{0\parallel}\left[1+\frac{1}{\mathcal{f}\left ( \beta \right ) } \ln \frac{1+\sqrt{1-\zeta ^{2}}}{\zeta } \right ] , \nonumber \\ e_{\rho}=0 , \quad e_{\varphi } = \frac{h_{0\parallel}}{\mathcal{f}\left(\beta \right)}\frac{\sqrt{1-\zeta ^{2}}}{\zeta } , \label{34 } \\ e_{z } = h_{0\perp}\sin \varphi \frac{2\sqrt{1-\zeta ^{2}}}{\mathcal{f}\left(\beta\right ) \zeta } , \nonumber\end{aligned}\]]@xmath51 , @xmath52 at @xmath53 ( or @xmath54 ) and @xmath55 at @xmath56 ( or @xmath57 ) . from eqs . , , and it can be easily checked that the boundary condition on the moving surface , @xmath58 $ ] ( or @xmath59 , @xmath60 ) , is satisfied automatically . it is also imperative to determine the surface current density induced due to the moving boundary . this can be done employing the maxwell s equation @xmath61 . it is clear that the surface current has only two components and @xmath62 with @xmath63 , where @xmath64 is the linear surface current . using eqs . and as well as the maxwell s equation we obtain @xmath65 = \frac{c}{4\pi \gamma ^{2}}h_{\varphi}\left ( r\right ) \nonumber \\ & & = -i_{0\perp } \sin \varphi \frac{2}{\gamma ^{3}\beta ^{2}\mathcal{f}\left ( \beta \right ) } , \label{eq : curr } \\ & & i_{\varphi } = -\frac{c}{4\pi } \left [ h_{z}\left ( r\right ) -\beta e_{\varphi } \left ( r\right ) \right ] = -\frac{c}{4\pi \gamma ^{2 } } h_{z}\left ( r\right ) \nonumber \\ & & = -i_{0\parallel } \frac{1}{\gamma ^{3}\beta ^{2}\mathcal{f}\left ( \beta \right ) } . \label{eq : curr1}\end{aligned}\ ] ] here @xmath66 is the relativistic factor of the expanding boundary and @xmath67 . note that the moving boundary modifies the surface current which now contains an extra factor @xmath68 @xcite . consider now briefly the non - relativistic limit of eqs . and . this limit can be obtained using at @xmath69 and @xmath70 the asymptotic expression @xmath71 which yields @xmath72 , and @xmath73 in the lowest order with respect to the factor @xmath74 the components of the electric field are given by @xmath75 , @xmath76 . it is seen that the parallel component @xmath77 of the magnetic field remains unchanged in the case of non - relativistic expansion . previously significant attention has been paid @xcite to the question of what fraction of energy is emitted and lost in the form of electromagnetic pulse propagating outward of the expanding plasma . in this section we consider the energy balance during the plasma cylinder expansion in the presence of the homogeneous magnetic field . when the plasma cylinder of the zero initial radius is created at @xmath2 and starts expanding , external magnetic field @xmath10 is perturbed by the electromagnetic pulse , @xmath78 , @xmath79 , propagating outward with the speed of light . the tail of this pulse coincides with the moving plasma boundary @xmath0 while the leading edge is at @xmath80 . ahead of the leading edge , the magnetic field is not perturbed and equals @xmath10 while the electric field is zero . our starting point is the energy balance equation ( poynting equation ) @xmath81where @xmath82 $ ] is the poynting vector and @xmath83 ( with @xmath84 ) is the surface current density . the energy emitted to infinity is measured as a poynting vector integrated over time and over the lateral surface @xmath85 of the cylinder with radius @xmath86 , length @xmath87 and the volume @xmath88 ( control cylinder ) enclosing the plasma cylinder ( @xmath89 or @xmath90 ) . integrating over time and over the volume @xmath88 eq . can be represented as @xmath91where @xmath92here @xmath93 is the radial component of the poynting vector . note that the total flux of the energy over the bases of the control cylinder determined by the poynting s vector component @xmath94 vanishes due to the symmetry reason . @xmath95 and @xmath96 are the total electromagnetic energy and its change ( with minus sign ) in a volume @xmath97 , respectively . @xmath98 is the energy transferred from plasma cylinder to electromagnetic field and is the mechanical work with minus sign performed by the plasma on the external electromagnetic pressure . at @xmath2 the electromagnetic fields are given by @xmath51 and @xmath99 . hence @xmath100 is the total energy of the magnetic field in a volume @xmath97 and is given by @xmath101 . then the change of the electromagnetic energy @xmath102 in a volume @xmath97 can be evaluated as @xmath103 in eq . @xmath104 is the volume of the control cylinder excluding" +"corot is a space experiment devoted to asteroseismology and extrasolar planet search through the observations of planetary transits . it has recently discovered a hot jupiter , corot - exo-2b , orbiting with a period of 1.743 days around a main - sequence g7 star which displays a remarkable photospheric activity @xcite . given the late spectral type and short rotation period ( about 4.5 days ) of the star , its activity is regarded as the manifestation of magnetic fields in the atmosphere , amplified and modulated by a hydromagnetic dynamo . in this paper , we present some preliminary results about the spot modelling of such a star , indicated as corot - exo-2a , which is a good proxy for the young sun , probably at an age of approximately 0.5 gyr @xcite . a detailed account of the results obtained from the spot modelling of the light curve of corot - exo-2a will be provided in @xcite . corot - exo-2a was observed from may 16 to october 5 , 2007 . we extracted from the data archive the n2 chromatic light curves having a sampling of 512 s during the first week and 32 s thereinafter . the red , green and blue fluxes were summed up to get the white light flux and transits were removed by means of the ephemeris and parameters of @xcite . we initially disregarded all data points at a distance from the mean greater than 4.2 standard deviations of the whole data set ; then , we subtracted a moving - median filtered version of the light curve ( box - car extension : 1 orbital period of the satellite , i.e. , 6184 s ) and discarded the points at a distance greater than 3 standard deviations of the residuals . finally , we computed normal points by binning the data on a time interval of one orbital period of the satellite . we apply the maximum entropy ( hereinafter me ) spot modelling method of @xcite , to whom we refer the reader for more details . the model assumes that the photosphere of the star is subdivided into 200 surface elements of size @xmath1 which are covered by cool spots , solar - like faculae and unperturbed photosphere . following @xcite and @xcite , who suggested that faculae have a secondary role in the light variations of late - type stars significantly more active than the sun , we neglect solar - like faculae in this preliminary study and defer their consideration to @xcite . the fraction of the area of each surface element covered by cool spots is given by the filling factor @xmath2 , so @xmath3 is the fraction occupied by the unperturbed photosphere . a stable and unique map , specified by the vector of the filling factor values @xmath4 , is derived by minimizing a linear combination of the chi square @xmath5 and the entropy functional @xmath6 , i.e. : @xmath7 where the lagrangian multiplier @xmath8 rules the trade - off between light curve fitting , as measured by the @xmath5 , and the regularization , as measured by the entropy functional @xmath6 . the optimal lagrangian multiplier is determined iteratively by making the mean of the residuals deviate by one standard error of the normal points from the value obtained without regularization ( see * ? ? ? the stellar parameters are taken from @xcite and @xcite . the stellar rotation axis is assumed to be perpendicular to the orbital plane of the planet . the spot temperature is assumed @xmath9 k below that of the unperturbed photosphere . the light curve is divided into 45 subsets of duration 3.15611 days because the rapid change of the spot pattern does not allow us to obtain a good fit with longer time intervals ( cf . * ; * ? ? ? * for the case of the sun ) . the lomb - scargle periodogram gives a period of the rotational modulation of @xmath10 days . the sequence of best fits obtained with our me model is shown in fig . [ lanzaf1 ] together with the residuals versus time . the best fit is always very good , with an average standard deviation of @xmath11 in relative units . since the inclination of the stellar rotation axis is very close to @xmath12 , only the distribution of the spotted area vs. longitude can be derived through the spot modelling . we plot the normalized spot filling factor versus longitude and time in fig . [ lanzaf2 ] . the longitude increases in the same direction of the stellar rotation and the orbital motion of the planet . the adopted rotation period for the model star is 4.5221 days . the star shows two active longitudes one of which does not migrate appreciably in the adopted reference frame , i.e. , has a rotation period of 4.5221 days , while the other shows a slow migration indicating a rotation period of 4.5543 days . interpreted in terms of surface differential rotation , this indicates a significantly smaller relative amplitude than in the sun , i.e. , about 1 percent . individual spots show an angular velocity about 1.3 percent smaller than that of the active longitudes . the total spotted area is plotted vs. time in fig . [ lanzaf3 ] and shows a cyclic oscillation with a period of @xmath13 days , as derived from lomb - scargle periodogram . it is interesting to note that such a period is close to 10 times the synodic period of the planet as seen by the active longitude pattern rotating in 4.5221 days . this may suggest a possible star - planet magnetic interaction ( see @xcite and @xcite for a possible interpretation ) . it is important to notice that a different spot temperature gives different absolute values of the spotted area , but does not affect the cyclic variation we have found . such a variation is not readily apparent from the light modulation because two spots on opposite hemispheres are usually responsible for the flux variations observed in corot - exo-2a , thus the light curve amplitude is not a good indicator of the total spotted area in this star . , where @xmath2 is the spot covering factor and @xmath14 its maximum value , versus time and longitude for our me spot models . the two dashed vertical lines mark longitudes @xmath15 and 360@xmath16 beyond which the distributions are repeated to easily identify spot migration . the contour levels are separated by 10 percent of the maximum filling factor , with light yellow indicating the maximum covering factor and dark blue the minimum . ] the present study is based on observations obtained with corot , a space project developed and operated by the french space agency , cnes , with partecipation of the science program of esa , estec / rssd , austria , belgium , brazil , germany and spain . afl , ip , gl and sm have been partially supported by the italian space agency ( asi ) under contract asi / inaf i/015/07/0 , work package 3170 . 9 alonso , r. , auvergne , m. , baglin , a. , ollivier , m. , moutou , c. , et al . 2008 , a&a , 482 , l21 bouchy , f. , queloz , d. , deleuil , m. , loeillet , b. , hatzes , a. p. , et al . 2008 , a&a , 482 , l25 gondoin , p. 2008 , a&a , 478 , 883 lanza , a. f. 2008 , a&a , 487 , 1163 lanza , a. f. , rodon , m. , pagano , i. , barge , p. , llebaria , a. 2003 , a&a , 403 , 1135 lanza , a. f. , rodon , m. , pagano , i. 2004 , a&a , 425 , 707 lanza , a. f. , bonomo , a. s. , rodon , m. 2007 , a&a , 464 , 741 lanza , a. f. , pagano , i. , leto , g. , messina , s. , aigrain , s. , et al . 2008 , a&a , submitted lockwood , g. w. , skiff , b. a. , henry , g. w. , henry , s. , radick , r. r. , baliunas , s. l. , donahue , r. a. , soon , w. 2007 , apjs , 171 , 260" +"a key component to understanding star formation lies in determining the dynamical nature of globules and cores of molecular clouds from which stars form . this is typically done using molecular lines , and observations of asymmetry or self - reversal in the line profiles of optically thick species portray the motion of the outer layers of material within a cloud . many of the spectra measured from starless cores and globules have blue asymmetirc profiles , such that the blue side of the profile is stronger than the red side , suggestive of red - shifted self - absorption and infall motion . for example , in their survey of starless cores , @xcite found that approximately one third of the cores they observed displayed bona fide infall motions in the outer layers and therefore were consistent with expectations of collapse . in this survey and in a number of others , however , there were a number of cores that displayed evidence for blue - shifted self - absorption in their spectra , e.g. , cb246 , l1521f and l429 - 1 . this is an indication of expansion but with no protostar in the core , what mechanism drives the expanding motions ? there are also cores and globules which show both redshifted and blueshifted self - absorption simultaneously in a single map of one molecular transition , for example , l1512 , l1689b , l1544 @xcite , and b68 @xcite . other cores and globules have spectra that shift from redshifted to blueshifted self - absorption depending on which molecular transition is observed . for example , self -absorption in the source l1157 is redshifted in the hco@xmath0(@xmath4 ) line profile but blueshifted in the hco@xmath0(@xmath5 ) line profile @xcite . clearly complex motions are occurring in the various layers of the cores but it is not clear what causes them . @xcite concluded that the pattern of redshifted and blueshifted self - absorption observed across the source in l1689 is caused by rotational motion in the globule . in b68 , where the spatial pattern switches from blueshifted to redshifted profiles both east and west of the center of the globule , the observed line profiles can not be explained by rotation . @xcite proposed that b68 could be in a quasi - stable state near hydrostatic equilibrium , and the systematic velocity field observed is likely to be caused by oscillatory motions within the outer layers of the globule . for stable and quasi - stable clouds , such motions are predicted by theory , e.g. , @xcite showed that small amounts of rotation can cause an initially gravitationally unstable cloud to stabilize and oscillate ; @xcite in considering the thermal and dynamical balance in low mass dense cores find that a quasi - equilibrium state can be established , which is not static but is pulsationally stable , and in their hydrodynamic study of starless cores , @xcite found that cores could oscillate with periods of about one million years ( or the sound crossing time ) if perturbed by a modest external force . such oscillatory behavior is a signature of dynamical equilibrium , and therefore , the presence of such complex patterns in their spectral line maps could indicate pulsationally stable initial states for the star - forming cores and globules . in this study , we have obtained high angular resolution spectra of the source listed in the catalogue of @xcite as . it is a small , round , dark globule situated in the pipe nebula with no associated iras , msx or spitzer space telescope point sources , and is therefore almost certainly starless . its distance has not been directly determined but it is associated with the pipe nebula , for which some distance estimates have been made . the most reliable estimate to date is 130 pc determined by using infrared extinction measurements for hipparcos stars , @xcite . in their bonnor - ebert sphere fitting analysis , however , @xcite report a distance of 70 pc , which compares to the value of 90 pc derived in a similar fashion for b68 , also , incidently , part of the pipe nebula complex . in this paper , we adopt the @xcite distance of 130 pc . the angular diameter of , as apparent in optical images , is @xmath2 4.5@xmath6 , which is @xmath2 35,000 au ( 0.17 pc ) at 130 pc . section [ sec : obs ] describes our observations of , and [ sec : results ] , is a description of the results . we detected expanding motions in hco@xmath0and cs line profiles across the surface of but since no protostar has been detected , the source of this expansion is a mystery . in [ sec : disc ] , we show that the core is bound and self - gravitating and we propose that pulsation or oscillatory motion within the cloud layers may account for the observed expanding motions . finally , we present evidence for molecular depletion in the central regions of the core . the observations reported here were made in july 2003 using the 30-m iram millimeter - wave telescope at pico veleta in spain . the dual mixer , dual - channel receiver was tuned to observe the molecules listed with their respective frequencies , beamwidths and velocity resolutions in table [ tb : linpars ] . the frequency - switching mode was used to obtain the observations , and system temperatures were 150 - 200 k. the chopper wheel method was used for calibration . the spectrometer is an autocorrelator configured to give the velocity resolutions listed in table [ tb : linpars ] . beam efficiencies were @xmath2 0.75 for the lower frequency 80 - 115 ghz range , and @xmath2 0.6 for the higher frequency 197 - 266 ghz range . observations were made in a grid with a reference position at , . hco@xmath0 , and were uniformly sampled such that a region centered on the reference position was observed every 24@xmath7 out to a maximum distance of 96 @xmath7 in right ascension and 120@xmath7 in declination , a total of 9 @xmath8 11 or 99 spectra for each species . this grid spacing is approximately one beamwidth , slightly over for hco@xmath0 and under for c@xmath1o . the n@xmath9h@xmath0 and cs emission was much weaker and less extended so the grid size was reduced to 5 @xmath8 5 around the reference point with an additional two measurements directly north , east , south and west of the center , resulting in a total of 33 spectra for these species . the spacing between measurements was also 24@xmath7 , approximately one beamwidth for each of the molecules . data reduction was done using the standard iram package class and idl ( interactive data language by research systems , inc . ) . figure [ spec ] shows the , and spectra at the reference position . the cs and hco@xmath0 profiles display a split asymmetric , double - peaked shape while the c@xmath1o line is single - peaked , though slightly asymmetric . the c@xmath1o line appears to bisect the cs and hco@xmath0 profiles in velocity indicating that the two latter lines are likely optically thick and self - reversed . the blue - shifted sense of the self - absorption in the self - reversals is indicative of expansion motions in the outer cloud layers . individual spectra of the hco@xmath0 and emission from across are simultaneously displayed in figure [ c18ohcomap ] for comparison . examination of the figure shows similar double - peaked , self - reversed hco@xmath0 emission profiles at several positions around the center of the globule . in all cases the sense of the asymmetry is the same suggesting expansion of the outer cloud layers . in most other positions the hco@xmath0 lines display blue - shifted self - absorption relative to c@xmath1o , also consistent with expansion motions . as can be seen in figure [ c18ocsmap ] cs spectra are also clearly self - reversed with blue - shifted self - absorption similar to the hco@xmath0 lines in positions where the hco@xmath0 was also self - reversed , but the signals have lower intensity . similar to hco@xmath0 , the other cs spectra appear to exhibit asymmetric profiles relative to c@xmath1o with a sense indicative of expansion motions . the critical density ( @xmath10 @xmath11 ) at which cs emission occurs is the same as that for hco@xmath0 emission ( ungerechts et al . 1997 ) so it is reasonable to assume that the two emission lines probe the same layer of material in the cloud . a rough estimate of the expansion speed of material was determined by comparing the velocity of the stronger hco@xmath0 peak to the peak velocity of a c@xmath1o spectrum at the same position . the peak velocities were obtained by fitting gaussian line profiles to the spectral lines . this resulted in velocity differences which are all negative confirming that the blueshifted profiles are characteristic of expansion , and indicating that material is expanding in the cloud over the whole layer under observation with a mean expansion velocity of -0.09 @xmath12 0.04 km s@xmath13 . the same process was applied to the cs spectra and the velocity differences were also found to be negative everywhere with a mean difference ( expansion velocity ) of -0.12 @xmath12 0.02 km s@xmath13 . this is similar to the range of @xmath14 for hco@xmath0 . this expanding motion is therefore also evident in the cs line emission profiles . another estimate of the expansion speed of material within the cloud was obtained using the model of @xcite . this model can only be applied to positions ( 10 positions ) where there is a clear double peak . in this model , the expansion velocity , @xmath15 is given by , @xmath16 where @xmath17 is the brightness temperature of the dip , @xmath18 is the height of the blue peak above the dip with its corresponding velocity , @xmath19 , @xmath20 is the height of the red peak above the dip with its corresponding velocity , @xmath21 , @xmath22 is the velocity dispersion of an optically thin line ( c@xmath1o here ) . for the hco@xmath0 lines , the mean expansion speed was calculated to be -0.07 @xmath12 0.02 and and for the cs lines , -0.07 @xmath12 0.02 km s@xmath13 ; both these estimates are somewhat lower than those derived from the peak velocity difference method in the previous paragraph . nonetheless , though somewhat uncertain , the overall expansion speeds we estimate are formally less than the one dimensional sound speed of @xmath23 0.19 km s@xmath13 in a 10 k gas . figure [ c18opkv ] shows maps of the variation of the velocity of the peak in the c@xmath1o spectra . the peak velocities were determined from gaussian fits to the line profiles . we note that a few of the and lines are flat - topped , broadened or slightly asymmetric , indicating that the lines are slightly optically thick . the two maps , however , do reveal a systematic velocity gradient increasing from upper left to lower right of the map . to estimate the magnitude and direction of this gradient , the method of @xcite was used as adapted by @xcite . the velocity gradient is assumed to be linear when projected against the plane of the sky so the observed velocity @xmath24 can be related to the velocity gradient @xmath25 using @xmath26 @xmath27 and @xmath28 are right ascension and declination offsets in arcseconds . @xmath29 is the systemic velocity of the cloud and @xmath30 is the angle between north and the direction of the velocity gradient of magnitude @xmath25 . a least - squares fit of a two - dimensional plane" +"code coverage is a common metric in software and hardware testing that measures the degree to which an implementation has been tested with respect to some criterion . in its simplest form , one starts with a model of the program , and a partition of the behaviors of the model into _ coverage goals _ test _ is a sequence of inputs that determines a behavior of the program . the aim of testing is to explore as many coverage goals as possible , ideally as quickly as possible . in this paper , we give complexity results for several coverage problems . the problems are very basic in nature : they consist in deciding whether a certain level of coverage can be attained in a given system . it is thus somewhat surprising that the problems have not been considered previously in the literature . finite - state directed graphs have been used as program models for test generation of reactive systems for a long time ( see @xcite for surveys ) . a coverage goal is a partition of the states of the graph , and a test is a sequence of labels that determine a path in the graph . the maximal coverage test generation problem is to hit as many partitions as possible using a minimum number of tests . in the special case the partitions coincide with the states , the maximal coverage problem reduces to the chinese postman problem for which there are efficient ( polynomial time ) algorithms @xcite . in this paper , we show that the maximal coverage problem becomes np - complete for graphs with general partitions . we also distinguish between _ system complexity _ ( the complexity of the problem in terms of the size of the graph ) and the _ coverage complexity _ ( the complexity of the problem in terms of the number of coverage goals ) . then , the problem is nlogspace in the size of the graph ( but that algorithm uses space polynomial in the number of propositions ) . we consider the special case where the graph has a special `` reset '' action that takes it back to the initial state . this corresponds in a testing setting to the case where the system can be re - initialized before running a test . in this case , the maximal coverage problem remains polynomial , even with general partitions . directed graphs form a convenient representation for deterministic systems , in which all the choices are under the control of the tester . testing of non - deterministic systems in which certain actions are controllable ( under the control of the tester ) and other actions are uncontrollable lead to _ game graphs _ @xcite . a game graph is a directed labeled graph where the nodes are partitioned into tester - nodes and system - nodes , and while the tester can choose the next input at a tester node , the system non - deterministically chooses the next state at a system node . then , the test generation problem is to generate a test set that achieves maximal coverage no matter how the system moves . for general game graphs , we show the complexity of the maximal coverage problem is pspace - complete . however , there is an algorithm that runs in time linear in the size of the game graph but exponential in the number of coverage goals . again , the re - initializability assumption reduces the complexity of coverage : in case there is a re - initialization strategy of the tester from any system state , the maximal coverage problem for games is co - np - complete . dually , we show that the problem of whether it is possible to win a safety game while visiting fewer than a specified number of partitions is np - complete . finally , we consider the coverage problem in bounded time , consisting in checking whether a specified number of partitions can be visited in a pre - established number of steps . we show that the problem is np - complete for graphs , and is pspace - complete for game graphs . optimization problems arising out of test generation have been studied before in the context of both graphs and games @xcite . however , to the best of our knowledge , the complexities of the coverage problems studied here have escaped attention so far . while we develop our theory for the finite - state , discrete case , we can derive similar results for more general models , such as those incorporating incomplete information ( the tester can only observe part of the system state ) or timing . for timed systems modeled as timed automata , the maximal coverage problem is pspace - complete . for timed games as well as for ( finite state ) game graphs with incomplete information , the maximal coverage problem becomes exptime - complete . in this section we define _ labeled graphs _ and _ labeled games _ , and then define the two decision problems of coverage , namely , _ maximal coverage _ problem and _ coverage with bounded time _ problem . we start with definition of graphs and games . a _ labeled graph _ @xmath0 consists of the following component : 1 . a finite directed graph with vertex set @xmath1 and edge set @xmath2 ; 2 . the initial vertex @xmath3 a finite set of atomic propositions @xmath4 ; 4 . a labeling function @xmath5 that assigns to each vertex @xmath6 the set @xmath7 of atomic propositions true at @xmath8 . for technical convenience we will assume that for all vertices @xmath9 , there exists @xmath10 such that @xmath11 , i.e. , each vertex has at least one out - going edge . * paths in graphs and reachability . * given a labeled graph @xmath12 , a _ path _ @xmath13 in @xmath12 is a infinite sequence of vertices @xmath14 starting from the initial vertex @xmath3 ( i.e. , @xmath15 ) such that for all @xmath16 we have @xmath17 . a vertex @xmath18 is reachable from @xmath3 if there is a path @xmath19 in @xmath12 and @xmath20 such that the vertex @xmath21 in @xmath13 is the vertex @xmath18 . a _ labeled game graph _ @xmath22 consists of the components of a labeled graph along with a partition of the finite vertex set @xmath1 into @xmath23 . the vertices in @xmath24 are player 1 vertices where player 1 chooses outgoing edges , and analogously , the vertices in @xmath25 are player 2 vertices where player 2 chooses outgoing edges . again for technical convenience we will assume that for all vertices @xmath9 , there exists @xmath10 such that @xmath11 , i.e. , each vertex has at least one out - going edge . * plays and strategies in games . * a _ play _ in a game graph is a path in the underlying graph of the game . a strategy for a player in a game is a recipe to specify how to extend the prefix of a play . formally , a strategy @xmath26 for player 1 is a function @xmath27 that takes a finite sequence of vertices @xmath28 ending in a player 1 vertex @xmath6 , where @xmath29 and @xmath30 , representing the history of the play so far , and specifies the next vertex @xmath31 choosing an out - going edge ( i.e. , @xmath32 . a strategy @xmath33 is defined analogously . we denote by @xmath34 and @xmath35 the set of all strategies for player 1 and player 2 , respectively . given strategies @xmath36 and @xmath37 for player 1 and player 2 , there is a unique play ( or a path ) @xmath38 such that ( a ) @xmath15 ; ( b ) for all @xmath39 , if @xmath40 , then @xmath41 ; and if @xmath42 , then @xmath43 . * controllably recurrent graphs and games . * along with general labeled graphs and games , we will also consider graphs and games that are _ controllably recurrent_. a labeled graph @xmath12 is _ controllably recurrent _ if for every vertex @xmath18 that is reachable from @xmath3 , there is a path starting from @xmath18 that reaches @xmath3 . a labeled game graph @xmath12 is _ controllably recurrent _ if for every vertex @xmath18 that is reachable from @xmath3 in the underlying graph , there is a strategy @xmath26 for player 1 such that against all player 2 strategies @xmath37 , the path starting from @xmath18 given the strategies @xmath26 and @xmath37 reaches @xmath3 . controllable recurrence models the natural requirement that systems under test are _ re - initializable _ , that is , from any reachable state of the system , there is always a way to bring the system back to its initial state no matter how the system behaves . * the maximal coverage problem . * the _ maximal coverage problem _ asks whether at least @xmath44 different propositions can be visited . we now define the problem formally for graphs and games . given a path @xmath45 , let @xmath46 be the set of propositions that appear in @xmath13 . given a labeled graph @xmath12 and @xmath47 , the maximal coverage problem asks whether there is path @xmath13 such that @xmath48 . given a labeled game graph @xmath12 and @xmath47 , the maximal coverage problem asks whether player 1 can ensure that at least @xmath44 propositions are visited , i.e. , whether @xmath49 such that for all player 2 strategies @xmath50 we have @xmath51 . the maximal _ state coverage _ problem is the special case of the maximal coverage problem where @xmath52 and for each @xmath53 we have @xmath54 . that is , each state has its own label , and there are @xmath55 singleton partitions . * the coverage with bounded time problem . * the _ coverage with bounded time problem _ asks whether at least @xmath44 different propositions can be visited within @xmath56-steps . we now define the problem formally for graphs and games . given a path @xmath57 and @xmath58 , we denote by @xmath59 the prefix of the path of length @xmath60 , i.e. , @xmath61 . given a path @xmath57 and @xmath58 , we denote by @xmath62 . given a labeled graph @xmath12 and @xmath47 and @xmath63 , the coverage with bounded time problem asks whether there is path @xmath13 such that @xmath64 . given a labeled game graph @xmath12 and @xmath47 , the maximal coverage problem asks whether player 1 can ensure that at least @xmath44 propositions are visited within @xmath56-steps , i.e. , whether @xmath49 such that for all player 2 strategies @xmath50 we have @xmath65 . * system - tester game . * a _ system _ @xmath66 consists of the following components : * a finite set @xmath67 of states with the starting state @xmath68 . * a finite alphabet @xmath69 of input letters . * a transition relation @xmath70 . * a finite set of atomic propositions @xmath4 and a labeling function @xmath5 that assigns to each state @xmath71 the set of atomic propositions true at @xmath71 . we consider _ total _ systems such that for all @xmath72 and @xmath73 , there exists @xmath74 such that @xmath75 . a system is _ deterministic _ if for all @xmath72 and @xmath76 , there exists exactly one @xmath77 such that @xmath75 . the tester selects an input letter at every stage and the system resolves the non - determinism in transition to choose the successor state . the goal of the tester is to visit as many different propositions as possible . the interaction between the system and the tester can be reduced to a labeled game graph @xmath78 as follows : * _ vertices and" +"ever since the discovery of graphene@xcite there has been interest in merging the unique two dimensional massless relativistic dirac fermion spectrum of graphene with superconductivity . a few years ago , graphene superconductor - normal metal - superconductor ( sns ) josephson junctions were successfully fabricated.@xcite here superconductivity is induced in the s regions of the graphene through proximity to superconducting contacts deposited on top of these regions , and , through the josephson effect , a finite supercurrent can exist even in the n region of the graphene . one of the key properties of a sns junction is the current - phase relation ( cpr ) , and , very recently , the first direct measurement of the cpr in graphene sns junctions appeared.@xcite theoretically , ballistic graphene sns junctions were studied even before the first experimental results . several novel features were discovered , such as specular andreev reflection,@xcite and a finite supercurrent in undoped graphene at zero temperature , despite the point - like fermi surface.@xcite these results , along with most theoretical results on the josephson effect in graphene sns junctions,@xcite have employed the dirac - bogoliubov - de gennes ( dbdg ) formalism , where the standard bdg formulation is applied to the dirac spectrum.@xcite to solve the resulting equations , rigid boundary conditions are assumed for the superconducting order parameter @xmath3 , such that @xmath3 takes on a fixed , non - zero value in s , whereas it is zero in n. however , such an approach explicitly ignores any processes in which @xmath3 is reduced in the s regions , such as proximity effect or depairing by current ( see e.g. ref . [ ] for a review ) . moreover , with the josephson current in the dbdg approach usually calculated as the current carried by sub - gap andreev bound states , this method is limited to junction lengths @xmath1 , where @xmath4 is the superconducting coherence length . other , related methods have been employed to relax some of the constraints in the original works , but they still apply rigid boundary conditions for @xmath3.@xcite in fact , in order to not apply any boundary conditions on @xmath3 at the s@xmath0n interface , a self - consistent treatment is needed . one such method is the self - consistent tight - binding ( tb ) bdg formalism , where one only assumes that the superconducting contacts induces a pairing potential into the graphene and then solve self - consistently for @xmath3 in the whole sns structure.@xcite not only does this approach give an explicit calculation of the full proximity effect , including current depairing , but it also results in a josephson current appropriately calculated from this proximity effect . previous works by the authors@xcite employing this formalism at zero temperature showed on some corrections to the cpr compared to the dbdg results , as well as deviations for the critical current as function of junction length . now , with experimental data on the cpr in graphene at hand , it is of large interest to theoretically map out the temperature dependence of the cpr in graphene . very recently , some theoretical temperature dependent cpr results appeared using the dbdg approach,@xcite but otherwise all theoretical work have been at zero temperature . the goals of this work are thus twofold : ( 1 ) : establish the correct cpr in ballistic graphene sns josephson junctions as function of temperature using the self - consistent tb bdg formalism . ( 2 ) : determine how well the dbdg approach captures the cpr , and , if applicable , determine the source(s ) of discrepancy . we will here show that both the proximity effect depletion of superconductivity in the s regions and depairing by current are large in short junctions ( @xmath1 ) . in fact , these effects lead to a cpr where the critical current is reached for a phase @xmath2 . this is true over a large temperature range and even more prominent for high doping levels in the graphene . in order to capture these effects a self - consistent solution of @xmath3 is crucial since rigid boundary conditions explicitly ignores any such processes in the s regions . for longer junctions ( @xmath5 ) the proximity effect depletion is unchanged but depairing by current is now not a big issue , and here @xmath6 . in this junction length regime the dbdg approach using andreev bound states is not formally justified , and due to a large proximity effect , a self - consistent approach is still needed . the rest of the article is organized as follows . in the next section we briefly introduce the methods used , both the self - consistent approach and the dbdg equation using rigid boundary conditions . then in section iii we report our results , including the temperature dependent cpr for different junctions as well as an analysis of the influence of proximity effect and current depairing on the cpr . finally , we summarize our key findings and comment on the applicability of our results to current and future experiments . our starting point is the nearest neighbor tight - binding hamiltonian on the graphene lattice together with an on - site @xmath7-wave superconducting order parameter @xmath8 , which is induced by the proximity to external superconducting contacts : @xmath9 here @xmath10 ( @xmath11 ) creates an electron with spin @xmath12 on the a ( b ) sublattice in unit cell @xmath13 . @xmath14 ev is the nearest neighbor hopping amplitude , whereas @xmath15 is the chemical potential . we will assume that , due to the external contacts , the chemical potential is rather large and constant in the s regions whereas it can be tuned ( to a constant value ) with a back gate voltage in the n region . for an analytical treatment within the dbdg framework we set @xmath16 , whereas @xmath17 with @xmath18 . here @xmath19 is set to the standard bcs temperature dependence . this amounts to applying rigid boundary conditions on @xmath8 at the s@xmath0n interface . by treating the s and n regions separately , the above hamiltonian can be fourier transformed and the kinetic energy linearized around the dirac points to produce the standard dbdg equation:@xcite @xmath20 where @xmath3 and @xmath21 take on different , but constant , values in the s and n regions , as described above . moreover , @xmath22 , where @xmath23 with @xmath24 being the lattice constant of graphene . the strategy for calculating the josephson current in the junction is to first obtain the energy spectrum for the andreev - bound states in the n region . this is done by matching the wave functions given by eq . ( [ eq : dbdg ] ) at the two s@xmath0n interfaces and then solve for the allowed energy eigenstates , @xmath25 . the general expression for the josephson current can then be written as:@xcite @xmath26 where the summation over @xmath27 denotes all andreev levels and the summation over @xmath28 denotes the transverse momentum index . here , @xmath29 is the phase drop across the junction,@xmath30 is the fermi - dirac distribution function , and the prefactor of 4 is due to the spin- and valley - degeneracy . let us first consider the case of @xmath31 , i.e. no fermi level mismatch ( flm ) in the junction . in the wide junction limit where the junction width @xmath32 satisfies @xmath33 , we may replace the summation over discrete transverse momentum indices with an integral as follows : @xmath34 where the integration over the angle @xmath35 takes into account all possible trajectories . the andreev levels in a sns junction with no flm have the form:@xcite @xmath36 where for graphene @xmath37 has the specific form : @xmath38}.\end{aligned}\ ] ] inserting the above equations in to eq . ( [ eq : jos ] ) and introducing the normalization constant @xmath39 , where @xmath40 is the superconducting coherence length , we arrive at the expression : @xmath41 ^ 2}{\delta_0\varepsilon_+ } \frac{\tau\sin\phi\cos\theta}{\tanh^{-1}(\beta\varepsilon_+/2)},\end{aligned}\ ] ] where @xmath42 is the inverse temperature . finally turning our attention to the flm case , a similar procedure@xcite leads to the expression : @xmath43 where @xmath44 is given by eq . ( 17 ) in ref . [ ] . in the self - consistent numerical treatment we do not predetermine the value of @xmath8 nor apply rigid boundary conditions at the s@xmath0n interface . instead we assume that the influence of the superconducting contacts on the underlying graphene is only through an induced attractive pairing potential . for @xmath7-wave pairing the simplest potential is a constant , non - zero , attractive hubbard-@xmath45 term in the s regions . by applying the mean - field approximation to the attractive hubbard model we reproduce eq . ( [ eq : h ] ) but with an added self - consistency condition @xmath46 where @xmath47 in s but zero in n. we can now solve self - consistently for @xmath8 by first guessing a profile for @xmath8 throughout the sns junction , solving eq . ( [ eq : h ] ) with this guess , recalculating @xmath8 using eq . ( [ eq : selfcons ] ) , and then reiterate this process until two subsequent @xmath8 profiles are within a predetermined error margin . in order to study the proximity effect between the s and n regions in the graphene we focus on the pairing amplitude @xmath48 . while @xmath8 will only be non - zero in the s regions , @xmath49 can , due to proximity effect leakage from s to n , be non - zero even in n. alongside this leakage also comes a depletion of @xmath50 in s such that @xmath51 close to the interface . it is this latter process that , as we will show below , significantly changes the cpr . the other important property is the josephson current @xmath52 that flows through the junction if there exists a phase difference @xmath29 in @xmath8 across n. from the continuity equation for the charge current we can , using the self - consistent solution for @xmath8 , calculate @xmath52 . for additional details on this self - consistent method see ref . we will assume clean , smooth interfaces such that a fourier transform along the direction parallel to the interface is applicable . in the self - consistent treatment , the type of interface can be varied but with an on - site pairing the direction of the interface will not matter . we will here use the zigzag interface , such that one unit cell is @xmath53 long . moreover , we will only consider the wide junction regime , @xmath54 . in the self - consistent treatment the junctions are naturally infinitely wide , due to fourier transforming along the interface , whereas in the dbdg approach @xmath55 is used . for a direct comparison between the two methods the current will be given in units of @xmath56 . in this article we will focus on a few representative values for the various physical input parameters . in the superconducting s regions we use @xmath57 and @xmath58 . these values give @xmath59 , and a superconducting coherence length @xmath60 unit cells . this satisfies @xmath61 in both s and n , a requirement for the dbdg solution , and will also allow us to self - consistently investigate both the @xmath1 and @xmath5 regimes , where @xmath62 is the length of the n region . moreover , with these values we get s regions as small as 50 unit cells displaying clear bulk behavior , which is advantageous due to the the computational demands of the self - consistent method . note though that for a direct comparison with an experimental setup @xmath63" +"towards observing gravitational waves , several gravitational wave interferometers on earth are steadily developing today , such as the laser interferometric gravitational wave observatory ( ligo ) @xcite , tama300 @xcite , geo600 @xcite , and virgo @xcite . thus it will be possible for us to detect gravitational waves directly in the near future . it is believed that mergers of binary neutron - star - neutron - star ( ns - ns ) , neutron - star - black - hole ( ns - bh ) , and bh - bh , or supernovae , and so on , can become strong sources of gravitational waves . after these violent events occur , compact objects may be left and may be turbulent . then gravitational waves are emitted from them . at this time , these gravitational waves convey information on the source object . if these gravitational waves are directly detected on earth , it is possible to obtain some information about the sources . this research field is called `` gravitational wave astronomy . '' in this field , there is an attempt to obtain information about properties of the equation of state ( eos ) of high density matter . this is one of the most important purposes of gravitational wave astronomy . gravitational waves are emitted by the nonspherical oscillation of compact objects . the oscillations are damped out as gravitational waves carry away the oscillational energy . such oscillations are called quasinormal modes ( qnms ) . the qnms have complex frequencies whose real and imaginary parts correspond to the oscillational frequency and damping rate , respectively . the qnms fall into two types from their nature . one involves fluid modes which are connected with the stellar matter . the other involves spacetime modes which are the oscillations of spacetime metric . moreover , the fluid modes are classified into various types . the well - known modes are the @xmath0 , @xmath4 , and @xmath5 modes @xcite . the fluid modes have a characteristic that the damping rate im(@xmath6 ) is much smaller than the oscillational frequency re(@xmath6 ) . the @xmath0 mode is the fundamental mode . there exists only one @xmath0 mode for each index @xmath7 of spherical harmonics @xmath8 . the @xmath4 mode is the pressure or acoustic mode , whose restoring force is caused by the pressure gradient inside the star . the @xmath5 mode is the gravity mode , which arises from buoyancy in a gravity field . the @xmath9 and @xmath10 modes are spacetime modes @xcite . unlike the fluid modes , the damping rate of the @xmath9 and @xmath1 modes is comparable to or larger than the oscillational frequency . for the qnms of neutron stars , so far many authors have argued the possibilities for determining the eos in the high density region and/or for restricting the properties of neutron stars , such as the radius @xmath11 or mass @xmath12 , by employing the observed gravitational wave of several nonradial modes @xcite . as a candidate for a star which is smaller than neutron stars , the possibility of a quark star or a compact star , which is supported by degenerate pressure of quark matter , has been pointed out . such a quark star has been investigated by many authors ( see , e.g. , refs . @xcite and references therein ) . in their view , it is commonly assumed that such quark stars contain quark matter in the core region and are surrounded by hadronic matter , although they are in the branch of neutron stars @xcite . witten @xcite suggested another type of quark star . if the true ground state of hadrons is bulk quark matter , which consists of approximately equal numbers of @xmath13 , @xmath14 , and @xmath3 quarks ( `` strange matter '' ) , there exist self - bound quark stars . they are called `` strange stars . '' in this case , their mass and radius are smaller than those of typical neutron stars , which are @xmath15 10 km and @xmath16 , respectively . because we do not have reliable information about the equilibrium properties of hadronic and quark matters at high densities , it is not clear what kinds of quark stars are realized . recently , drake @xmath17 @xmath18 . reported that the deep chandra letg+hrc - s observations of the soft x - ray source rx j1856.53754 reveal an x - ray spectrum quite close to that of a blackbody of temperature @xmath19 ev @xcite . the data contain evidence for the lack of spectral features or pulsation @xcite . drake @xmath17 @xmath18 . also reported that the interstellar medium neutral hydrogen column density is @xmath20@xmath21 @xmath22 . with the results of recent hst parallax analyses , that yields an estimate of 111170 pc for distance @xmath23 to rx j1856.5 - 3754 . combining this range of @xmath23 with the blackbody fit leads to a radiation radius of @xmath248.2 km . that is smaller than typical neutron star radii @xcite . thus they suggested that the x - ray source may be a quark star . in the meanwhile , in ref . @xcite , walter and lattimer claimed that the blackbody model adopted in ref . @xcite could not explain the observed uv - optical spectrum . they undertook to fit the two - temperature blackbody and heavy - element atmosphere models which were discussed in ref . @xcite in x - ray and uv - optical wavelengths . from their analyses they found that the radiation radius was 1226 km and was consistent with that of a neutron star . however , this model can not explain the lack of spectral features . in addition , recently braje and romani also suggested a two - temperature blackbody model , which can reproduce both the x - ray and optical - uv spectral @xcite . although their model is inconsistent with the fact that pulsation is not detected , this might be explained by the object being a young normal pulsar and its nonthermal radio beam missing the earth s line of sight . however , they can not also answer why there are no features in the observed x - ray spectrum . in ref . @xcite , burwitz @xmath17 @xmath18 . discussed the possibility of a condensate surface which is made of unknown material to explain both the uv - optical and x - ray spectra in a neutron star . more recently , some groups discussed the possibility that the effects of a strong magnetic field ( @xmath25 ) @xcite or rapid rotation ( @xmath26 ) @xcite may smear out any spectral features . in these situations , however , it seems that there are no reliable models that account for all the observational facts . it is still controversial whether rxj1856.5 - 3754 is a normal neutron star or some other compact star like a quark star . here we adopt the simplest picture , which is used by drake @xmath17 @xmath18 . @xcite : the uniform temperature blackbody model . as for gravitational waves emitted from quark stars , yip , chu , and leung studied nonradial stellar oscillation for stars whose radius is around 10 km @xcite . kojima and sakata demonstrated the possibility of distinguishing quark stars from neutron stars by using both the oscillational frequency and the damping rate of the @xmath0 mode @xcite . sotani and harada showed that the @xmath0 and lowest @xmath1 modes depend strongly on the eos of quark matter and the properties of quark stars , where the lowest @xmath1 mode is the one which has the largest frequency among all @xmath1 modes @xcite . then they pointed out the possibility of determining the eos and/or the stellar properties . furthermore , they also studied @xmath9 modes in detail . however , they clearly showed that @xmath9 modes do not depend much on the eos of quark matter and are not important for constraining the model parameters from observations . in their work , however , they assumed that the star is a pure quark star and that the eos is described by a simple bag model which has only one parameter : i.e. , the bag constant @xmath2 . in general , there are a variety of parameters even within bag models : e.g. , the bag constant @xmath2 , the strange quark mass @xmath27 , the fine structure constant in qcd @xmath28 , and so on . in particular , if the effects of nonvanishing strange quark mass @xmath29 are taken into account , the structure of quark stars can be affected considerably ( for recent analyses , see ref . @xcite and references therein ) . in this situation , we compute the qnms in the bag model used in ref . citekohri:2002hf and investigate the possibility of restricting the model parameters by the observations of qnms . in this study , we deal with only @xmath0 and the lowest @xmath1 modes in response to the results in ref . @xcite . effective theories of quantum chromodynamics ( qcd ) , such as bag models , perturbation theories , or finite - temperature lattice data , are difficult to test by experiments , especially in a low temperature and high density regime . to further study them and fit their model parameters , we should compare the theoretical predictions in such models with experimental data e.g . , data in relativistic heavy ion collision experiments and so on . thus , in this situation information about compact objects obtained by astrophysical observations is indispensably valuable , being independent of the above - mentioned ground - based experiments in nuclear physics or particle physics . among the astrophysical observations , the observation of gravitational waves emitted from oscillating compact objects is quite unique because gravitational waves directly convey information on the internal structure of compact objects , where the density would reach the nuclear density . the plan of this paper is as follows . in sec . [ sec : quarkstar ] we introduce the basic equation including the eos to construct quark stars as the source of gravitational waves and to give the properties of quark star structure . we present a method of determining the qnms for the case of spherically symmetric stars in sec . [ sec : method ] . in sec . [ sec : result ] we show the numerical results for the qnms for the quark star constructed in sec . [ sec : quarkstar ] . in this section we present the dependence of the qnms on the parameters of the eos and stellar properties , and discuss the possibility of determining the eos of quark matter . we conclude this paper in sec . [ sec : conclusion ] . we adopt units of @xmath30 , where @xmath31 , @xmath32 , and @xmath33 denote the speed of light , reduced planck s constant , and gravitational constant , respectively , and the metric signature of @xmath34 throughout this paper . we assume that the quark star is static and spherically symmetric . in this case the metric is described by @xmath35 where @xmath36 and @xmath37 are metric functions of @xmath38 and @xmath37 is related to the mass function @xmath39 as @xmath40 the mass function @xmath39 is the gravitational mass inside a surface of radius @xmath38 and satisfies @xmath41 where @xmath42 is the energy density . the equilibrium stellar model is constructed by solving the equations @xmath43 equation ( [ dpdr ] ) is the tolman - oppenheimer - volkoff ( tov ) equation @xcite . in addition to the above equations we need an eos to compute the star configuration . the stellar surface @xmath44 is the position where the pressure vanishes , and the stellar mass @xmath12 is defined as" +"the shapes of pne are well known to demonstrate an amazing variety shapes ( e.g. sahai et al . 2011 ) . balick & frank ( 2002 ) reviewed many possible shaping mechanisms and in the case of binarity remarked : _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ the bottom line is that although binarity is a popular mechanism for forming axisymmetric structures on pne , * direct evidence * to support the efficacy of the process is not strong . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ at the time only @xmath012 close binary central stars were known ( bond 2000 ) and no strong trends in nebula morphology were apparent ( bond & livio 1990 ) . since then dramatic progress has been made with more than 40 close binaries now known ( e.g. miszalski et al . this improvement was largely driven by the improved multiplex advantage offered by the ogle microlensing survey ( udalski 2009 ) which allowed for many discoveries to be made by miszalski et al . ( 2008 , 2009a ) . substantial progress has also been helped by improved observing strategies including targeting pne with suspected post - ce morphologies ( miszalski et al . 2011a ) and the use of less nebula - contaminated filters to obtain lightcurves ( miszalski et al . in addition to the ogle discoveries more close binaries were found by hillwig et al . ( 2010 ) , hajduk et al . ( 2010 ) , corradi et al . ( 2011 ) , santander - garca et al . ( 2011 ) and miszalski et al . ( 2011a , 2011c , 2011d ) . fewer wide binary systems are known and they mostly have chemically peculiar giants or sub - giants ( e.g. bond et al . 2003 ; frew et al . 2011 ; miszalski et al . figure [ fig : fig1 ] shows a selection of these new binaries . the majority of binary central stars discovered have orbital periods less than 1 day ( miszalski et al . 2009a , 2011a ) . this is firm evidence that these systems passed through the poorly understood ce phase ( iben & livio 1993 ) . post - ce pne offer one of the best opportunities to measure the orbital period distribution directly after the ce phase since the nebula guarantees the period is ` fresh ' and has not yet been altered by further angular momentum loss . this is a crucial ingredient for improving ce population synthesis models that currently rely upon a parametric formalism ( see boffin & miszalski 2011 for further discussion ) . with the excellent sensitivity of the ogle survey miszalski et al . ( 2009a ) determined the close binary fraction in pne to be at least @xmath1% and ruled out the presence of a significant population of binaries with periods greater than @xmath01 day . the most promising aspect of the new discoveries will be the ability to obtain accurate keplerian masses once radial velocity orbits are measured . this will greatly improve our understanding of pn evolution that is currently heavily dependent on models for central star masses . miszalski et al . ( 2009b ) analysed images of an enlarged sample of 30 post - ce pne to find at least 1/3 had canonical bipolar morphologies . the actual bipolar fraction may be as high as 6070% because of inclination effects , but this remains to be proven via kinematic modelling . a large proportion of the sample also showed low - ionisation structures ( lis , gonalves et al . 2001 ) and collimated polar outflows or jets . the lis occur in small knots ( e.g. ds 1 ) , rings of knots ( e.g. the necklace ) or in more extreme configurations ( e.g. ngc 6326 ) and may be produced by a photoionising wind interacting with dust and gas placed in the orbital plane during the ce phase . if this scenario is correct , then the uncanny resemblance between sn1987a and the necklace may imply a binary progenitor was responsible for the bipolar nebula and ring of knots seen in sn1987a ( see e.g. boffin & miszalski 2011 ) . the extreme set of knots in ngc 6326 also suggest a binary origin for morphologically similar features in a 30 ( miszalski et al . 2011d ) . jets are prominent in a 63 , the necklace and ethos 1 providing the first clear evidence for a binary origin of these features ( soker & livio 1994 ) . kinematics of these nebulae show the jets are older than the main nebula , suggesting that they were launched by a temporary accretion disk around the companion established during or prior to the ce phase . such a configuration also explains why the jets in post - ce pne are not highly collimated due to orbital motion and precession ( see e.g. raga et al . some of these systems were successfully discovered by pre - selecting for these nebula trends ( miszalski et al . 2011a ) , however a much larger campaign is needed to verify these initial results . it has long been known that close binary central stars , consisting of a white dwarf primary and a main sequence secondary , display narrow emission lines of c iii , n iii and c iv originating near an irradiated zone on the secondary ( e.g. pollacco & bell 1994 ) . miszalski et al . ( 2011c , 2011d ) emphasised the real overlap between the orbit - dependent irradiated emission and the so - called `` weak emission line '' central stars ( _ wels _ , tylenda et al . wels _ could therefore turn out to be close binary stars if high quality time - series spectroscopy were to reveal radial velocity shifts in these lines and confirmed by periodic lightcurves . this would go a large way towards explaining the _ wels _ which do not fit any central star classification schemes ( mndez 1991 ; crowther et al . those which are not found to be close binaries might be classified as [ wn / wc ] ( todt et al . 2010 ) or [ wc]-pg1159 ( parthasarathy et al . 1998 ) . in summary , the _ wels _ are a description of spectroscopic features and not a stellar classification to be used in central star catalogues . in close binaries the weak emission lines do not originate from the primary , as proven by ngc 6326 ( miszalski et al . 2011d ) , and therefore can not be considered for the basis for any classification . if not a close binary , then the object should be left as unclassified or assigned into the [ wn / wc ] or [ wc]-pg1159 class if there is sufficient supporting information . analysis of new examples befitting these latter classes will be presented elsewhere . in the sample of known close binaries only ngc 6778 ( miszalski et al . 2011d ) shows type - i chemical abundances ( perinotto et al . the high he / h and n / o ratios seen have long been considered to be only produced by progenitors massive enough to experience hot bottom burning ( @xmath2 @xmath3 ) , however in this case we may be seeing an alternative close binary channel to produce type - i pne ( karakas et al . 2009 ; karakas & lugaro 2010 ) . keplerian masses of ngc 6778 and future expected discoveries will shed much greater insight into the origin of type - i pne than hitherto possible . the level of s - process enrichment in nebulae ( sterling & dinerstein 2008 ) and barium central stars ( e.g. bond et al . 2003 ; miszalski et al . 2011e ) is also a valuable tool to further understand type - i pne ( see also karakas & lugaro , these proceedings ) . work so far suggests that binarity or some other process may be reducing the s - process enrichment in type - i pne , although the binary fraction of the sterling & dinerstein ( 2008 ) sample is yet to be determined . abell 70 is a particularly interesting case since it is a s - process enhanced g8iv - v companion and shows type - i abundances at @xmath02 kpc below the galactic plane , far away from where massive progenitors are expected ( miszalski et al . the central stars of three peculiar pne are known to show r coronae borealis - like dust obscuration events : ngc 2346 ( mndez et al . 1982 ) , hen 3 - 1333 ( cohen et al . 2002 ) and m 2 - 29 ( hajduk et al . 2008 ) . miszalski et al . ( 2011b ) showed that the quasi - periodic events are not triggered by a binary companion interacting at periastron , but rather occur at the inner edge of a dust disk at @xmath0100 au ( e.g. chesneau et al . such dust disks are however thought to depend upon binaries for their formation ( van winckel et al . 2009 ; chesneau 2011 ) . so far only ngc 2346 has been proven to be a binary . miszalski et al . ( 2011b ) proved that the galactic bulge pn m 2 - 29 does not have a close binary central star as previously claimed and suggested instead that an unobserved yellow subgiant may be present to account for the d-type symbiotic star features . balick , b. , & frank , a. 2002 , ara&a , 40 , 439 boffin , h. m. j. ," +"continuous measurement of quantum systems @xcite , the study of quantum systems states under the influence of observation prolonged in time , has been a topic of considerable activity in recent years . particularly , for the measurement of an individual microscopic system that is weakly coupled to measurement apparatus , the system s state and its conditioned evolution in time , the so - called diffusive - type quantum state trajectory @xcite , have been intensively explored for applications in quantum information and quantum control . some of the active fields are quantum state estimation ( i.e. , estimating the pre - measurement state of an ensemble of identically prepared systems @xcite ) , conditional reversal of measurement @xcite , and the preparation of entangled states @xcite . the ability to continuously measure quantum systems also opens the possibility of feedback control @xcite , which has also been investigated for topics such as the stabilization of coherent oscillations @xcite and rapid state purification @xcite . this growing interest in the quantum systems under weak continuous measurement has motivated a thorough analysis of quantum trajectory statistics . of notable importance are advances in experiments , such as the measurement of superconducting qubits @xcite , which has allowed the tracking of the trajectories of the quantum state with high fidelity in a single measurement run , allowing the statistics of selected subensembles of trajectories to be explored . the authors recently developed an action principle @xcite over a doubled quantum state space , based on a path integral representation of probability distributions of quantum trajectories . the action principle , implemented by extremizing of the stochastic path integral s action , was used to investigate the optimal behaviour of the trajectories with arbitrary constraints , such as fixing the final boundary condition @xcite . the stochastic path integral and the optimum likelihood approach provide a convenient way to investigate statistical distributions and globally optimal dynamics of quantum state evolution , in addition to the stochastic master equations describing the quantum trajectories and the lindblad master equations describing their average evolution @xcite . in this paper , we continue the development of the stochastic path integral formalism @xcite , to further explore advantages of having the full joint probability distribution of quantum trajectories . this includes computing statistical averages or expectation values with the ability to condition on definite quantum states at particular times . we present several examples of the formalism including a qubit system under the influence of measurement alone , measurement with concurrent unitary dynamics , and qubit measurement with feedback control . in these examples , the statistics of qubit trajectories are computed using developed techniques for the path integral , such as multi - dimensional gaussian integrals and diagrammatic expansion theory . moreover , in an example of qubit measurement with linear feedback , we utilize a phase portrait analysis to investigate the most likely behaviour of the system dynamics , revealing a simple and practical approach for qubit state stabilization . there have been past works on continuous quantum measurements with path integrals , so we wish to discuss how our approach bears both similarities and differences to them . an early approach suggested by feynman @xcite and later independently developed by mensky @xcite is a restricted path integral : a modified version of the feynman path integral to only sum over paths that contribute to a measurement record . caves , and also barchielli @xcite , constructed similar path integrals by adding coarse - graining ( resolution ) functions describing the effect of the measurement . in these path integral approaches , one considers the distribution of the measurement records ( it can be derived from the probability amplitude , see appendix [ app - otherpathint ] ) , whereas in our approach , we formulate a path integral in quantum state space to represent a joint probability distribution of the measurement readouts as well as quantum state trajectories . wei and nazarov discussed a different approach to continuous measurements using the keldysh path integral technique @xcite . in breuer and petruccione s path integral @xcite , the notion of the sum over pure state paths in hilbert space is applied , resulting in a different type of doubled state space that does not yield an action functional . the stochastic path integral formalism and the analysis of its action are also applied in classical stochastic processes . for instance , the formalism is used in studying the dynamics and distribution of transmitted electronic charge @xcite , the neural network @xcite , and the large deviations from typical behaviours ( rare events ) @xcite . our approach is similar to the martin - siggia - rose formalism @xcite , which involves adding conjugate fields through the fourier integral form of delta functionals enforcing diffusive dynamics . notably , one can think of the quantum trajectories on a finite dimensional state space as analogous to classical random processes in configuration space of that dimension . this paper is organized as follows . in section [ sec - mainspi ] , we review the stochastic path integral formalism and its extremized action equations , for a general finite - dimensional system with a markovian setup for weak continuous measurement . in section [ sec - qubit ] , a specific measurement setup for a qubit is presented , which is used throughout this paper . in section [ sec - qnd ] , we show that , in the case without qubit hamiltonian , we can perform the full path integration directly to get the multi - time correlation functions for the preselected and postselected qubit state . in section [ sec - purbexpand ] , the diagrammatic expansion theory is presented as an alternative approximation method for computing multi - time correlation functions , with examples for qubit measurement with rabi oscillation . in section [ sec - feedback ] , qubit measurement with feedback control and its optimal dynamics are investigated using the path integral and the action principle approaches . the conclusion can be found in section [ sec - conclusion ] . a series of supplementary discussions and some detailed calculations that are not included in the main text are presented in the appendixes . we consider the distribution of quantum state trajectories for continuous quantum measurement . a quantum state trajectory , or simply a quantum trajectory , is an evolution of a quantum state in time , conditioned on a detector readout realization . this conditional state trajectory is also known as a solution of stochastic master equations , unravelling master equations in lindblad form . let us discretize the measurement readout into @xmath0 time points and denote @xmath1 as a measurement realization . each @xmath2 is a readout obtained between time @xmath3 and @xmath4 , and is assumed dependent only on a quantum state right before its measurement ( markov assumption ) . we define a series of quantum states @xmath5 , written as a @xmath6-dimensional parametrized vector @xmath7 , where the components are the expansion coefficients of the density operator @xmath8 written in some orthogonal operator basis , such as the @xmath9 generalized gell - mann matrices @xmath10 of a @xmath11-state system @xcite . for a two - state system , the matrices @xmath10 for @xmath12 are the pauli matrices , and @xmath13 is a vector in bloch sphere coordinates . the quantum state trajectory can be computed with an update equation of the form , @xmath14 $ ] , taking into account the measurement back - action from the measurement readout @xmath2 , and also considering the unitary evolution from the measured system s hamiltonian . since the distribution of the measurement readout only depends on the quantum state right before the measurement in this markovian approach , we can then write the joint probability density function ( pdf ) of all measurement outcomes and state trajectories @xmath15 given an initial state @xmath16 and a set of other constraints @xmath17 as , @xmath18 this is a time step product of @xmath19 , the conditional probability distribution for the measurement outcome @xmath2 given the system state before the measurement @xmath20 , and @xmath21)$ ] , the ( deterministic ) conditional probability distribution for the quantum state after the measurement , given the state at the previous time step and the measurement readout . the prefactor @xmath22 $ ] in eq . is a function of quantum states and readouts at any times , accounting for constraints used in selecting a sub - ensemble of the quantum trajectories , such as initial - state and final - state conditions . the benefit of having the joint pdf eq . is that it contains all the statistical information about the system s evolution under measurement , and it allows us to selectively work with sub - ensembles of quantum trajectories simply by adding constraints ( or conditions ) to the joint distribution . statistical moments can be computed from this joint pdf by integrating over its variables . for example , an expected value of an arbitrary functional @xmath23 $ ] is given by @xmath24_1^n { \mathrm{d}}[r_k]_0^{n-1 } { \cal p}_{\zeta } { \cal a}$ ] , where we define a notation for the multiple integral , @xmath25_{1}^{n } \equiv \int\!\ ! { \mathrm{d}}{{\bm q}}_{1 } \cdots { \mathrm{d}}{{\bm q}}_{n}$ ] . direct integration of these quantities using the joint pdf as in eq . , however , can be a challenging task even for a simple qubit measurement problem . as such , we are motivated to write the joint pdf in a path integral form with an action ( or exponent ) , so we can perform the integration using techniques developed in quantum theory such as a diagrammatic perturbation theory . the path integral representation of the joint pdf in eq . can be attained by writing the delta functions for the state update @xmath26)$ ] for @xmath27 to @xmath28 in the fourier integral form , i.e. , @xmath29 for each @xmath30 and each component of the vector @xmath7 , and then rewrite other terms in exponential forms . the conjugate variables for those delta functions are denoted by @xmath31 for @xmath27 to @xmath28 . we refer to ref . @xcite and its appendixes for a thorough discussion about this transformation and the construction of the path integral . as a result , the joint pdf is then given in a path integral form , @xmath32_{0}^{n-1 } \exp({\cal s}),\end{aligned}\ ] ] where the integrals are over all possible paths of @xmath33 and the action @xmath34 is defined as , @xmath35 ) + \ln p(r_k | \bm{q}_k ) \bigg\}.\end{aligned}\ ] ] we note that @xmath36 is an additional term determined by the formation of @xmath37 in eq . , and @xmath38 is a prefactor absorbing normalization constants . for an example , we consider a sub - ensemble of trajectories that obey conditions on the initial and final states . the theoretical analysis of this kind of constraint is presented in ref . the initial state is fixed at @xmath39 and the final state is at @xmath40 . this leads to the constraint term @xmath41 in eq . and the preselected and postselected joint pdf , @xmath42 , which is written in a path integral form as , @xmath43_{-1}^{n } \exp({\cal s}_{{{\bm q}}_i , { { \bm q}}_f}),\end{aligned}\ ] ] where the path integral s action is , @xmath44 ) + \ln p(r_k | \bm{q}_k ) \bigg\}.\end{aligned}\ ] ] we note that , in eq . and , two additional conjugate variables , @xmath45 and @xmath46 , are introduced , because we have written the delta functions in @xmath47 , one for the initial state and another for the final state , in the fourier integral form . we can investigate the path integral s largest contribution by solving for its action s extrema . taking the variation of" +"over the past few years , cellular and wireless networks have been challenged by the increasing number of mobile internet services and the constant growth of mobile data traffic . future radio access networks should provide reduced latency , improved energy efficiency , and high user data rates in dense and high mobility network environments . the architecture of future communication networks will be heterogeneous in nature , i.e. macrocell with many small cells . the great challenge will be the employment of novel interference management strategies that will manage interference , without increasing the system s overhead , and provide high data rates and reliable transmissions . interference alignment ( ia ) was introduced by maddah - ali et al . in @xcite , and jafar and shamai in @xcite for the mimo x channels , and by cadambe and jafar in @xcite for the @xmath0-user interference channel , where @xmath1 degrees of freedom ( dof ) can be achieved . ia aligns the interfering signals present at each receiver into a low dimensional subspace , by linearly encoding signals in multiple dimensions , resulting in the desired signal being in a dimension unoccupied by interference links . initially , ia required global channel state information ( csi ) and was computationally complex . further work on ia led to the scheme of blind ia , presented by wang , gou and jafar in @xcite and jafar in @xcite , for certain network scenarios , which can achieve full dof in the absence of csi at the transmitters ( csit ) , thus reducing the system overhead . furthermore , blind ia was introduced , by jafar in @xcite , for cellular and heterogeneous networks , by `` seeing '' frequency reuse ( i.e. orthogonal allocation of signaling dimensions ) as a simple form of interference alignment . blind ia in heterogeneous networks was generalized in @xcite for the case of @xmath0 users in the macrocell and @xmath0 femtocells with one user each , introducing kronecker ( tensor ) product representation and a variation of model parameters to optimize the sum rate performance . a special case of blind ia , known as topological interference management ( tim ) , was introduced by jafar in @xcite . tim takes into consideration the position of every user in the cell(s ) , and based on their channel strength , weak interference links are ignored , resulting in @xmath2 dof achieved for every user in the siso broadcast channel ( bc ) . in @xcite , sun and jafar research the scheme of tim for the case of multiple receive and transmit antennas , concluding that only the former can provide more dof in the network . unlike orthogonal frequency division multiple access ( ofdma ) and single - carrier frequency division multiple access ( sc - fdma ) currently employed in 4 g mobile networks , the scheme of non - orthogonal multiple access ( noma ) , proposed in @xcite by saito et al . , is based on a non - orthogonal approach to future radio access . according to noma , multiple users are superimposed in the power domain at the transmitters , and successive interference cancellation ( sic ) is performed at the receivers , improving capacity and throughput performance . power allocation and quality - of - service ( qos ) for edge - cell users , has been a major issue to tackle in systems employing noma . it has been shown , in @xcite , that for the bc , if noma is employed with the aid of coordinated multiple point ( comp ) and _ _ alamouti code , satisfactory rates for edge - cell users can be achieved without degrading the performance of users closer to the base station . moreover , with an adaptive power and frequency resource allocation algorithm , as proposed in @xcite , targeting inter - cell interference , in order to boost the total throughput , reliable transmissions to edge - cell users can be obtained . furthermore , in @xcite , authors study two different power allocation schemes , a fixed one and a cognitive radio inspired one , in a mimo - noma model by using signal alignment and stochastic geometry . recently , research on noma has been focusing on user pairing to reduce complexity and improve efficiency . cooperative noma schemes , where users with higher channel gains have prior information about other users messages , have been developed @xcite . user pairing has been introduced in two noma schemes , discussed in @xcite , with one scheme employing fixed power allocation ( f - noma ) and another one inspired by cognitive radio ( cr - noma ) , with users grouped differently in each one of the two noma schemes . in addition , user pairing has been studied in conjunction with the problem of power allocation , in @xcite , based on a new design of precoding and detection matrices . user pairing and the performance of noma have been also studied from an information theory perspective , as discussed in @xcite , researching the relationship between the rate region achieved by noma and the capacity region of the bc , observing that different power allocation to users corresponds to different points on the rate region graph , and showing that noma can outperform tdma not only in terms of the sum rate , but for every users s rate as well . from the schemes of tim and noma , a hybrid tim - noma scheme emerged , introduced in @xcite for the siso bc and in @xcite for the mimo bc . the hybrid tim - noma scheme divides users into groups , and manages `` inter - group '' interference based on the principles of tim , and `` intra - group '' interference based on noma . the hybrid scheme can achieve double the sum rate of tdma for high snr values . in this paper , based on @xcite , we introduce two interference management schemes employed in heterogeneous networks . for both schemes , we consider a @xmath0-user macrocell and @xmath3 femtocells with one user each , taking into consideration the position of every user in the cell . the first scheme is a hybrid tim - noma scheme based on @xcite . the novelty of this scheme is the fact that it changes the way user - grouping is performed compared to @xcite . users in the macrocell belong to one group and then there exist @xmath4 groups of femtocells . inter - cell interference is managed based on tim and intra - cell interference based on noma . the second scheme is blind ia in heterogeneous networks , which constitutes further work on @xcite . our contribution is the additional consideration of interference caused to femtocells by transmissions in the macrocell , and the existence of more than one femtocells around a macrocell user . the algorithms of both schemes are described by using kronecker ( tensor ) product representation . based on our results , the hybrid scheme can achieve more total dof compared to tdma , whereas blind ia outperforms tdma in terms of dof in most cases . we show that both schemes achieve higher sum rates than tdma , as depicted in figure [ fig : journal1 - 1 - 1 - 2 - 1 - 1 - 1 - 1 - 1 - 1 ] . finally , comparing the two schemes , blind ia provides better sum - rate and ber performance to macrocell users , whereas the hybrid scheme results in better performance for the users in the femtocells , and based on its power allocation scheme provides qos to edge cell users . the rest of the paper is organized as follows . section 2 describes the general network architecture , and the example - model which is used to describe the two schemes . sections 3 and 4 present the model description and achievable sum rate of the hybrid and blind ia schemes respectively . section 5 describes the special case of blind ia when @xmath5 , i.e. only one femtocell interferes with every user in the macrocell . section 6 discusses our results and the performance of the two schemes in terms of dof , ber and sum rate . finally , section 7 summarizes the main findings of our work and discusses further developments . , width=226,height=188 ] , width=226,height=188 ] consider the broadcast channel of a heterogeneous network , as shown in figure [ fig : heterogeneous - network:- ] , with 1 macrocell and @xmath3 femtocells . at the _ @xmath6 _ mimo bc of the _ macrocell _ , there is one transmitter _ @xmath7 _ with _ @xmath8 _ antennas , and _ @xmath0 _ users equipped with _ @xmath8 _ antennas each . transmitter _ @xmath7 _ has @xmath8 messages to send to every user , and when it transmits to user _ @xmath9 _ , where @xmath10 , it causes interference to the other @xmath11 users in the macrocell and all the femtocell users @xmath12 . @xmath4 femtocells are considered to interfere with every macrocell user . at the _ @xmath6 _ mimo bc of each _ femtocell _ , there is one transmitter _ @xmath13 _ with @xmath8 antennas , and one user @xmath12 equipped with @xmath8 antennas . when transmitter _ @xmath13 _ transmits to user @xmath12 , it causes interference to the macrocell user _ @xmath9 _ and to all or some ( depending on the scheme we use ) of the remaining @xmath14 neighbouring femtocell users @xmath12 . we consider that all channels remain constant over @xmath15 time slots ( i.e. supersymbol ) and we take into consideration the position of users in the cells , as summarized in table [ tab : ch7-distance - metrics - in ] . in the hybrid tim - noma scheme , users are divided into @xmath16 groups . in the macrocell , all users belong to the same group @xmath17 . in addition , there are @xmath4 different groups of femtocell users , with @xmath18 for @xmath19 . moreover , @xmath8 messages are transmitted to every user in the femtocells . in the blind ia scheme , the number of neighbouring femtocells can not be greater than 3 , i.e. @xmath20 , with @xmath21 . there is no grouping in the macrocell . every macrocell user receives interference from @xmath4 femtocells . thus , for all @xmath22 , with @xmath10 , femtocell users are divided into two groups : group @xmath23 consists of @xmath24 femtocell users @xmath12 , i.e. @xmath25 , where @xmath26 and @xmath27 . group @xmath28 consists of femtocell users @xmath12 , i.e. @xmath29 , where @xmath30 . femtocells in @xmath23 do not interfere with each other . femtocells in @xmath28 interfere with all femtocells in @xmath23 . in addition , @xmath31 messages are sent to users in @xmath23 , and @xmath32 messages are sent to users in @xmath28 . users in macrocell and @xmath33 femtocell ( @xmath5 ) with 1 user each ( @xmath34 transmit and receive antennas).[fig : heterogeneous - network:- ] ] in this paper , we consider the following example model : in the macrocell , there are @xmath35 users , @xmath34 messages intended for every user , and _ @xmath34 _ transmit and receive antennas . additionally there are @xmath33 femtocells ( note that @xmath5 ) , with _ @xmath34 _ transmit and receive antennas _ _ each . for the hybrid scheme , we consider @xmath34 messages sent to every femtocell user , @xmath36 time slots and @xmath37 groups ( @xmath38 ) , and for the blind ia scheme , @xmath39 messages sent to users in @xmath23 , @xmath40 time slots and @xmath41 groups ( @xmath42 ) . .distance metrics for the example model heterogeneous" +"type ii spicules @xcite observed in the chromosphere are thought to be , at least in part , responsible for the transfer of mass from the dense chromosphere into the corona and are suggested to play an important role in coronal heating and solar wind acceleration processes ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? data further indicate that the type ii spicules have a disk counterpart , so - called rapid blue - shifted excursions ( rbes ) , associated with the network fields @xcite . rbes are continuation of ca ii 854.2 nm rbes , which tend to be located closer to the network fields @xcite . type ii spicules ( hereafter spicules ii ) appear to possess physical properties different from classical spicules : a shorter lifetime ( between 10 s and 100 s ) , smaller width ( 150 700 km ) as well as much higher line - of - sight ( 50 150 km s@xmath2 ) and transverse ( 10 km s@xmath2 ) velocities @xcite . spectroscopic studies also indicate that the plasma in these events is heated throughout their lifetime and the related upflows exhibit jet - like properties @xcite . spicules ii are also known to exhibit rotational as well as transverse / swaying , volume filling motions ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) with amplitudes of 10 - 30 km s@xmath2 and periods of 100 - 500 s ( see review by @xcite ) . the displacements are perpendicular to spicules axis and are interpreted as upward or downward propagating alfvn - like motions @xcite , or mhd kink mode waves ( e.g. , * ? ? ? * ; * ? ? ? there is little consensus among researchers on the origin of type ii spicules . while some works suggest that reconnection process @xcite , and oscillatory reconnection @xcite in particular , may account for their origin , others propose that strong lorentz force @xcite or propagation of the p - modes @xcite may be the origin . moreover , @xcite argues that spicules ii could be warps in 2d sheet - like structures , while @xcite questions the existence of spicules ii as a distinct class altogether . the related difficulties in the interpretation of solar data mainly arise from the limited spatial resolution and complexity of the chromosphere ( e.g. , * ? ? ? * ; * ? ? ? in this study we focus on the relationship between the occurrence of rbes and the changes in the underlying dynamics of photospheric magnetic fields . we use h@xmath0 - 0.1 nm and magnetic field data obtained with the new solar telescope ( nst , * ? ? ? * ; * ? ? ? * ) installed at the big bear solar observatory ( bbso ) . on september 8 , 2011 and august 14 , 2011 the nst acquired quiet sun data near the north pole and in a coronal hole ( ch ) located near the solar equator at heliocentric - cartesian position ( 460``45 '' ) . in both cases the acquired data included blue wing h@xmath0 - 0.1 nm images taken with a zeiss lyot filter with a 0.025 nm bandpass . the august 14 , 2012 coronal hole data set spans nearly 100 min time interval with two 8 min data gaps ( see figs . 2 and 3 ) and it was complemented by magnetic field measurements performed with the infrared imaging magnetograph ( irim , * ? ? h@xmath0 data were speckle reconstructed @xcite , aligned and de - stretched to remove residual image distortion due to seeing and telescope jitter . the intensity of each image was adjusted to the average level of the set and the final image pixel size was 0.052 arcsec . irim is an imaging solar spectro - polarimeter that uses a pair of zeeman sensitive fe i lines present in the near infrared at 1564.85 nm and 1565.29 nm . the system is based on a 2.5 nm interference filter , a unique 0.025 nm birefringent lyot filter , and a fabry - prot etalon and it is capable of providing a bandpass as low as 0.01 nm over a field of view ( fov ) of 50 @xmath3 25 . with the aid of adaptive optics , we obtained circular and linear polarization images with spatial and temporal resolution of 0"".25 and 43 s , respectively . in this study we focus on the morphology of the magnetic field with only stokes v data being used . polarization calibration , based on muller matrix , was employed for irim data to minimize the cross - talk @xcite . the current calibration successfully corrects the cross - talk from m3 to the focal plane , and the matrix elements for correction of q or u into v are of order of 10@xmath4 . the correction of cross - talk introduced by the primary and secondary mirrors causes only a small error ( @xmath56 - 8% of the analysed signal ) and was not attempted . to convert irim data numbers into physical units ( gauss ) we used co - temporal and co - spatial hinode sot / nfi measurements . the two data sets were carefully co - aligned and the best fit to the corresponding regression plot produced the coefficient of conversion . the august 14 , 2011 data set is of undisturbed photosphere inside a ch . two small clusters of bps , marked as n and p ( figure [ ha_irim ] , top panel ) , were associated with opposite polarity fields and connected by a system of dynamic loops that were intermittently filled with jet - like plasma flows . the locations of the most persistent rbe activity ( darker areas ) , were not evenly distributed over the fov : rbes most frequently stemmed from two distinct areas enclosed by boxes . the exception is the rbe activity associated with closed field lines connecting two n and p clusters , which will not be considered here . the potential field model showed that the right side of p ( i.e. , the area enclosed by boxes ) was dominated by small - scale ( @xmath5 3 mm ) loops , while large - scale loop system was present on the left side of p. this asymmetry may lead to the formation of an extended magnetic canopy above the small - scale emerging dynamic fields on the right side of cluster p. in figures [ cuta ] and [ cutb ] , we show x - t plots made along the cuts a and b ( figure [ ha_irim ] , dotted lines ) . in each figure , the top panel is an h@xmath0 - 0.1 nm x - t plot , while the bottom panel is an x - t plot of irim stokes v data . a total of 364 h@xmath0 - 0.1 nm images were used to produce the top panel with the slit width of 6 pixels ( 0.23 mm ) . the bottom panel was produced from 94 irim magnetograms and a 2.9 mm slit was used . in both top panels , the darkest h@xmath0 - 0.1 nm x - t features were outlined by a yellow contour at an arbitrary intensity level . the dashed line segments highlight several steep x - t tracks representing an upward motion of rbes . the lower end of the line segments ( or dark tracks ) marks the occurrence time and the initial position of the event along the slit . similarly , the lower part of the areas , enclosed by the contours , represent roots of rbes , while the upper part are rbe tips . we would like to stress that the level of rbe activity at these cuts is intermittent rather than constant : periods of enhanced rbe production are separated by long intervals of relative quietude ( figure [ cuta ] and [ cutb ] ) . a new period of rbe activity usually begins with the development of a dark jet - like feature , followed by series of increasingly thinner and fainter rbes ( see the h@xmath0 - 0.1 nm x - t intervals between t=39 min and t=45 min , t=64 min and t=70 min in figure [ cuta ] and t=38 44 min and t=94 99 min in figure [ cutb ] ) . we overplotted the contours and tracks on the irim x - t plots shown in the lower panels of figures [ cuta ] and [ cutb ] . there appears to be a tendency for the groups of rbes ( and not necessary individual tracks ) to occur when a new magnetic flux appears in the photosphere . by using a parabola , we outlined the several most prominent episodes of enhanced rbe activity associated with underlying dynamical changes in the magnetic field such as the appearance of mixed and/or unipolar fields . the first parabola in figure [ cuta ] has its apex set at x=0.7 mm and t=38 min , when clear and persisting magnetic field changes began to occur at a location x. in this particular case , the magnetic field at x=0.7 mm was mostly weak ( grey ) before positive ( white ) polarity patch appeared at approx t=38 min . as the patch grew ( t=40 - 44 min ) , some negative polarity fields appeared within the slice as well . at the same time , series of rbes occurred with their long and dark , possibly highly inclined h@xmath0 - 0.1 nm tracks stopping approx . 0.7 mm short of the center of the positive polarity patch . note that data , presented in @xcite , suggests that roots of ca ii 824.5 nm rbes tend to be located lower in the chromosphere and closer to magnetic field concentrations , as compared to the roots of h@xmath0 rbes . the difference can be as large as 1.5 mm so that the real plasma outflows in the above example may originated much closer to the network flux concentrations . the apex of the second parabola marks emergence of a negative polarity ( black ) fields . it is not clear whether two sets of rbes that occurred between t=64 and t=67 min are related to this emergence episode since the t=66 min track could have originated at x=3.2 mm as the dashed line suggests ( top panel ) . however , the third group of rbes that began at t=68 min seems to be temporally and spatially correlated with the new negative flux . note that an emerging bipole may not always have its poles of equal intensity , or its axis parallel to the cut lines shown in fig . 1 . in this case only one polarity will appear in the slice , while the other polarity could be either outside the slice , masked by the surrounding the same polarity fields , or be much weaker and less pronounced . however , the most important observation is that the appearance of a new ( bi- or mono - polar ) flux at a given location , which suggests ongoing restructuring of the surrounding chromospheric fields as the new flux makes its way into the solar atmosphere . the first parabola in figure [ cutb ] has its apex at t=36 min , when we assume the new bipole was beginning to emerge . the bipole showed signs of development ( flux increase , some pole separation ) and a prolonged series of rbes appeared in association with the emergence . the second parabola in figure [ cutb ] at t=67 min and x=1" +"phase dislocations carried by the wavefront of a light beam are associated with the zero - intensity points where the light intensity vanishes . the phase of the wave is twisted around such points creating a structure associated with _ an optical vortex_. optical beams with phase dislocations play an important role in linear singular optics @xcite . in self - focusing nonlinear media , an intense finite - extent laser beam becomes localized due to the self - trapping mechanism which can compensate for the beam diffraction . the nonlinear self - action of light may result in the formation of stationary structures with both intensity and phase remaining unchanged along the propagation direction . such self - trapped stationary structures of light beams are termed _ spatial optical solitons _ when such solitons have phase singularities , they determine the internal structure of the beam ; they can be stabilized by the light self - action generating nonlinear self - trapped optical beams carrying phase dislocations . examples of such beams include _ vortex solitons _ @xcite with point screw dislocations , _ multipole vector solitons _ @xcite with @xmath0-edge dislocations , and more complicated _ ` necklace'_-type beams @xcite and _ soliton clusters _ @xcite with a combination of a screw dislocation at the beam center and , generally , @xmath1-edge dislocations , where @xmath1 is the phase jump between neighboring peaks in the intensity distribution @xcite . the fundamental optical solitons show a fascinating combination of the properties of classical wave - packets together with a number of particle - like properties demonstrated in their elastic and inelastic interactions and mutual scattering , when each of the solitons preserves its identity . moreover , the coherent interaction between the solitons depends strongly on a relative phase what provides an additional degree of freedom to control the interaction . we may draw an analogy between spatial soliton and the ` atom of light ' , and then the soliton collision and interaction can be treated in terms of the effective forces acting between these effective ` atoms ' . following this concept , the higher - order multi - hump optical beams can be regarded as bound states of ` atoms ' trapped by a common potential induced in a nonlinear medium . a balance of the interaction forces acting between the solitons is the necessary condition for the formation of the soliton ` clusters ' or ` molecules of light ' . in this paper we investigate the excitation of higher - order beams , including optical vortices and soliton clusters , through the inelastic soliton scattering and mutual trapping of initially well - separated fundamental solitons , the effect resembling a synthesis of ` soliton molecules ' . in addition , we propose the application of this effect in the context of ` soliton algebra ' @xcite regarding the fundamental spatial solitons as the information carriers , and the transformation of an optical pattern induced by the soliton interaction as all - optical soliton switching . optical vortices were introduced as the first example of a stationary light beam with the phase twisted around its core ; the twist is proportional to @xmath2 with integer @xmath3 , the so - called topological charge of the phase dislocation @xcite . the physical model analyzing the evolution of the slowly varying field envelope @xmath4 is described by the nonlinear schrdinger equation , @xmath5 where @xmath6 is the transverse laplacian , and @xmath7 is the propagation distance measured in the units of the diffraction length . function @xmath8 describes the nonlinear properties of an optical medium , and it is assumed to depend on the total beam intensity , @xmath9 . the simplest spatially localized solution of equation carrying a phase dislocation , i.e. the vortex soliton , can be written in the form : @xmath10 , where @xmath11 and @xmath12 are the beam amplitude and propagation constant , respectively , while @xmath13 and @xmath14 are the polar coordinates in the transverse plane . in self - focusing nonlinear media , such vortex beams are the subject of the azimuthal modulational instability which result in splitting of the doughnut ring - like structure into a certain number of the fundamental solitons . the number of splitters and their dynamics are determined by the topological charge of the phase dislocation corresponding to the beam angular momentum ( see , e.g. , @xcite and references therein ) . the simplest higher - order scalar stationary solutions found for the model are a family of the radially symmetric solitons which includes radial modes with nodes in form of concentric rings . the important characteristic of these states is the _ soliton spin _ determined as a ratio of two conserved quantities , the beam angular momentum and the beam power . for the vortex soliton , the spin coincides with the topological charge @xmath3 of the phase dislocation carried by the vortex . because of the condition of the field univocally , the topological charge @xmath3 is quantized and has integer value . the fundamental spatial solitons and their higher - order radial states have zero spin . novel types of the higher - order self - trapped optical beams can be introduced as _ azimuthally modulated _ self - trapped structures in the form of the so - called ` necklace ' beams @xcite . however , it was found that a combination of the edge - phase dislocation with @xmath0-out - of - phase neighbor peaks can not produce a stationary state , and the structure becomes slowly expanding @xcite . such a stabilization is indeed possible for a more complicated system including the attraction between several incoherent beams @xcite . another approach to this problem is to combine the screw dislocation in the origin of a ring - shaped beam with the edge dislocation within the necklace @xcite . the screw dislocation introduces a centrifugal force to the ring , being also responsible for spiralling and mutual repulsion of the solitons in the case of vortex break - up @xcite , and the edge dislocations prevents noise - induced instability break - up of the ring . because of a nonzero angular momentum , the whole structure rotates with its propagation . as a result , the stabilization of the ring - shaped multihump beams requires complex phase distribution characterized by _ fractional _ value of the soliton spin @xcite . a phase distribution required for the formation of quasi - stationary higher - order self - trapped optical beams was found in references @xcite where the concept of _ soliton cluster _ was introduced . in this approach , the azimuthally modulated beam is regarded as a bound state of the interacting fundamental solitons . because of phase - sensitive interaction , the requirement of the balance of the interaction forces between the solitons determines the beam phase in the form of a _ staircase - like _ screw dislocation . compares the vortex phase dislocation ( left column ) with the phase of a four - soliton cluster , having well defined @xmath15 steps between the soliton positions ( right column ) . it was found @xcite that a _ radially stable _ dynamical bound state is formed if these phase - jumps satisfy the condition @xmath16 , with @xmath17 being the number of solitons in the ring . stability of the soliton clusters has been tested numerically for different nonlinear media , including cubic saturating , competing cubic self - focusing and quintic self - defocusing , and competing quadratic and cubic self - defocusing nonlinearities @xcite . the idea has been also extended to higher dimensions , covering the case of the spatio - temporal vortex solitons and light bullets . the common outcome of these studies is the confirmed robustness of the soliton clusters to random noise and strong radial perturbations . in the latter case , the pulsating states viewed as the radial excitations of ` soliton molecule ' have been observed . nevertheless , soliton clusters are the subject of modulational instability , and they are unstable with respect to azimuthal perturbations . the remarkable feature of this instability is that the number of the fundamental solitons flying off the main ring after the splitting is determined mainly by the topological charge @xmath3 instead of the initial number @xmath18 of solitons , similar to the vortex solitons . for what follows , we stress the fact that the conservation of the angular momentum of an optical beam in an isotropic medium determines the dynamics of splitters after break - up , so that the initial ` spin ' angular momentum of vortex or cluster can be viewed as being _ transformed _ into the orbital momentum of the spiralling splitters @xcite . recent progress in both theoretical and experimental studies of the higher - order optical spatial solitons brought the soliton community to the gates of the direct search for all - optical soliton - based switching schemes , when the initial data carried by the light distribution on the front - face of the nonlinear medium can be processed , in a predictable and controllable way , by employing the light self - action effects . one of the examples of such an approach is the recently proposed concept of the ` soliton algebra ' @xcite , based on the instability - induced break - up of optical vortices to the controllable number of the fundamental solitons . this idea also represents the example of a nontrivial approach to the soliton instability , when the symmetry - breaking instability , usually regarded as a serious disadvantage in using spatial solitons , is employed as _ a key physical mechanism _ for all - optical soliton switching from a given initial state ( optical vortex ) to the known final state defined by a certain number of fundamental solitons . this approach can be generalized to a broad variety of scalar and vector higher - order _ metastable _ solitons . the symmetry - breaking soliton instability may serve as a physical mechanism for all - optical switching with only one disadvantage it is a one - way process describing the transition from an initial higher - order state ( a soliton molecule or cluster ) to a number of simple stable states ( dipole - mode and fundamental solitons ) . below , we propose the opposite process , viewed as the excitation or ` synthesis ' of higher - order states from predefined number of initially separated solitons , or ` atoms of light ' , in a nonlinear bulk medium . indeed , introducing molecules of light would not be self - consistent without the possibility of mutual trapping of the free atoms or molecule synthesis . to demonstrate this phenomenon , we propagate numerically the ring - shaped arrays of initially well separated coherently interacting fundamental solitons in a saturable nonlinear medium . shows a characteristic example of a set of six solitons which have their relative phases growing in steps of @xmath19 along the ring , being initially directed to collide with each other . this initial condition corresponds to the inversion of the instability - induced ring break - up , so that the solitons move towards the ring instead of flying away . we observe highly inelastic collision of the solitons when they strongly interact overlapping and loosing their identity . nevertheless , the initial phases of the solitons are tilted in such a way that the total phase of the beams forms a screw dislocation in the ring origin which prevents a simple fusion of all solitons . instead , the ring - shaped structure is formed . similar situation is observed in with an array of eight solitons and the formation of a metastable vortex ring . due to large amplitude modulations" +"our understanding of the qcd matter at low temperatures ( @xmath0 ) and high baryon number densities ( @xmath1 ) has developed rapidly over the past few years ; for recent reviews , see @xcite . a likely scenario is that in this region , quarks form cooper pairs and new condensates develop . one of the most interesting questions today concerns the detailed mapping of the qcd phase diagram , especially in the above region where qcd may exhibit a colour superconducting phase . in this context , the light quark masses ( @xmath3 ) are expected to play an important role . figure 1 shows two likely scenarios corresponding to @xmath4 and @xmath5 . the transition between the quark - gluon plasma ( qgp ) phase and the colour superconducting phase is expected to be first order , in qcd @xcite . in this paper , we study the first - order phase transition between the qgp phase and the colour superconducting phase ( fig . our approach is phenomenological and is similar in spirit to that adopted by ct and kharchenko @xcite . they , however , studied the bose - einstein condensation in a gas of trapped atomic hydrogen at temperatures @xmath6 and densities @xmath7 @xmath8 . temperatures and densities that we shall consider here are , of course , vastly different , and qgp has very little in common with the atomic hydrogen gas . _ interestingly , however , as we shall see , the same physics of activation energy barrier governs the formation of droplets in both cases . _ it is important to get a handle on the cold and dense quark matter because of its possible relevance to the neutron - star core . while the region of _ asymptotic _ densities is amenable to rigorous calculations , the same can not be said about the region of _ intermediate _ densities studied here . both numerical ( lattice ) and direct experimental studies of this region of the qcd phase diagram are out of reach at the moment . hence a phenomenological study such as the present one is appropriate and worthwhile . it has allowed us to make quantitative statements about the schematic phase diagram in fig . 1 . alford et al . @xcite have discussed droplet formation in the transition between the hadronic matter phase and the 2sc phase ( fig . 1 ) , at @xmath9 , as a function of density . the chiral symmetry is restored inside their droplets ( which they call nucleons ) but is broken outside . neergaard and madsen @xcite also have studied the droplet formation but in the qgp to hadronic matter transition occurring at low baryon number densities . in this paper , we have considered the qgp to colour - superconducting phase transition occurring at high @xmath1 . _ to our knowledge , droplet formation in this transition has not been discussed previously in the literature . _ our droplets are the opposite of those in @xcite in the sense that the chiral symmetry is broken inside our droplet , but is restored outside . consider a gas of weakly interacting quarks , antiquarks and gluons in a volume @xmath10 . we take @xmath11 and @xmath12 to be the massless current quarks ( fig . 1 ) . we are interested in low temperatures ( @xmath0 ) and high number densities ( @xmath13 ) such that @xmath14 where @xmath15 is the thermal wave length ( see appendix ) . we also need the baryon number density @xmath16 to be large compared to that for the normal nuclear matter , namely 0.17 @xmath17 . if the interactions among the particles are treated to the lowest order in @xmath18 , the strong coupling constant ( fig . 2 ) , the baryon number density is given by ( @xmath19 ) @xmath20,\ ] ] where @xmath21 2 ( spin ) @xmath22 3 ( colour ) @xmath22 3 ( flavour ) = 18 is the quark degeneracy factor , @xmath23 is the boltzmann constant and @xmath24 is the quark chemical potential @xcite . for a given baryon number density @xmath1 and temperature @xmath0 , eq . ( 1 ) uniquely fixes @xmath24 . this in turn determines the total energy and pressure of the gas as @xmath25,\\ p_{gas } & = & e_{gas}/3v.\end{aligned}\ ] ] here @xmath26 2 ( spin ) @xmath22 8 ( colour ) = 16 is the gluon degeneracy factor . it was possible to obtain the above analytic expressions because we have considered the gas of quarks as well as antiquarks , rather than a gas of quarks alone @xcite . at low @xmath0 and high @xmath1 , the @xmath24 terms in the pressure dominate and the gluonic pressure arising from the first term in eq . ( 2 ) , is quite negligible . we now consider the first - order phase transition from qgp to the superconducting phase as the temperature is lowered ( fig . 1 ) . in the latter phase , as a result of the attractive one - gluon - exchange interaction between quarks in the colour @xmath27 channel , quarks near the fermi surface tend to pair up as bosons . these are the cooper pairs which we assume to be massless . density fluctuations in the metastable qgp gas may provide suitable conditions for nucleation and growth of a droplet of the superconducting phase . the high - temperature phase ( qgp ) is present around the droplet and the low - temperature superconducting phase exists inside the droplet . we will presently explore the energetics for the formation of such a droplet by calculating the energy barrier between the two phases . we have given above the expressions for number density , energy and pressure of the qgp ; see eqs . ( 1)-(3 ) . we now derive corresponding expressions for the superconducting phase inside the droplet . before we begin , it is necessary to recall important differences between the bcs superconductor and the colour superconductor . ( a ) in the bcs theory of superconductivity the ratio of the energy gap ( @xmath28 ) to the fermi kinetic energy for a typical metal is of the order of @xmath29 . in contrast , in the problem under consideration , the gap @xmath28 is estimated to vary between several tens of mev to about 100 mev @xcite , and the quark chemical potential @xmath24 appearing in eq . ( 1 ) takes values between @xmath30 and @xmath31 mev for the @xmath1 and @xmath0 considered here . ( b ) in the bcs superconductor , the debye energy @xmath32 is much smaller than the chemical potential @xmath33 , while in the colour superconductor , the two may be of the same order of magnitude . ( c ) finally , if @xmath13 is the density of electrons and @xmath34 the pippard coherence length which measures the spatial extension of the cooper pair wave function , then in the bcs theory , @xmath35 . in the present case , on the other hand , @xmath36 fm for @xmath37 mev , and @xmath38 for the densities considered in this paper . this suggests that the @xmath39 pairs are rather compact objects unlike cooper pairs of electrons in a metal . for a good discussion of these and related issues , see a review article by kerbikov @xcite . we shall make use of the above points while deriving expressions for thermodynamics quantities of the droplet . for the sake of simplicity , we shall assume that all quarks in the energy interval @xmath40 form cooper pairs and all other quarks remain unpaired , and shall ignore other interactions . consider a spherical region of radius @xmath41 , volume @xmath42 , containing @xmath43 quarks out of which @xmath44 remain unpaired and @xmath45 undergo cooper pairing , when the pairing interaction is `` switched on '' . we have @xmath46 where @xmath47^{-1}$ ] with @xmath48 . the corresponding energies @xmath49 are @xmath50 in the last equation @xmath51 is the number of cooper pairs ( bosons ) in the droplet and @xmath52 is the energy of the ground state of the single - particle spectrum of a spherical cavity of radius @xmath41 . due to the small size of the droplet , even the lowest excited state has energy which is very large compared to the temperature . therefore all the @xmath39 pairs tend to occupy the ground state @xcite . next , entropies @xmath53 are given by @xmath54,\\ s_2 & = & s_1 + \frac{d_q v_d}{(2 \pi)^3 } \int^{\mu_q}_{\mu_q-\delta } 4 \pi p^2 dp \left [ f \ln f + ( 1-f ) \ln ( 1-f ) \right],\\ s_3 & = & 0.\end{aligned}\ ] ] @xmath55 can be taken to be zero for the reasons given above . finally , the pressures @xmath56 are calculated as follows : @xmath57 the thermodynamic potential @xmath58 for massless quarks is given by @xmath59.\ ] ] hence @xmath60 \nonumber \\ & = & \frac{e_1}{3v_d}-\frac{ktd_q}{2 \pi^2}\int_{\mu_q-\delta } ^{\mu_q } p^2 dp \ln\left[1 + \exp \beta ( \mu_q - p ) \right ] . \nonumber\end{aligned}\ ] ] performing the last integration by parts and rearranging the terms , one finally gets @xmath61 \}.\ ] ] the quantal pressure @xmath62 is given by @xmath63 it is easy to verify that if @xmath28 is set equal to zero , i.e. if no pairing is allowed to take place , @xmath45 , @xmath64 , @xmath62 vanish and @xmath44 , @xmath65 , @xmath66 , @xmath67 become equal to @xmath43 , @xmath68 , @xmath69 , @xmath70 , respectively . contribution of antiquarks to the above thermodynamic quantities is smaller by many orders of magnitude . although we have included it in our calculations its effect is negligible . the droplet pressure @xmath71 is given by @xmath72 where @xmath67 and @xmath62 are as in eqs . ( 14)-(15 ) , @xmath73 and @xmath74 are the corresponding pressures due to antiquarks and @xmath75 is the pressure due to gluons in the droplet . consider once again the spherical region of radius @xmath41 . initially , i.e. before the pairing interaction is switched on , there are @xmath43 quarks , @xmath76 antiquarks and a certain number of gluons in it . in the final state , i.e. when the pairing interaction is on , there are @xmath44 quarks , @xmath51 quark pairs , @xmath77 antiquarks , @xmath78 antiquark pairs and the same number of gluons as before . the activation energy ( @xmath79 ) is defined as the difference between the helmholtz free energies ( @xmath80 ) in the final and initial states . since the gluonic contribution cancels out , one gets @xmath81 in the limit @xmath82 , this @xmath79 vanishes . the reader may wonder why surface tension of the droplet makes no appearance in our formalism . in the classical theory of nucleation , there are two competing contributions to the energy of a droplet : droplet formation reduces bulk free energy but only at the cost of surface energy . the former contribution wins if the droplet radius exceeds a certain critical value , while the surface tension ensures that a droplet with a smaller radius shrinks and disappears . in the formalism presented here , energy of the droplet is calculated quantum mechanically . it is clear from eq . ( 9 ) that small droplets have large quantal energy and tend to dissolve back into the qgp gas . this is similar to the effect of the surface tension in the classical theory . moreover , the thermal wavelength ( @xmath15 ) of the quarks is so large that a classification of particles as those localized on the surface and those in the interior breaks down . in short , we did not neglect the surface energy ; it is included in the total free energy of the quantal" +"it appears quite common that observed flux ratios between gravitationally lensed quasar images are difficult to match while image positions can be fitted easily with simple smooth mass models . @xcite argued these anomalous flux ratios as evidence for substructures in lens galaxies . if this is true , it serves as a powerful probe of substructures in galactic halos which may not be luminous enough @xcite . for instance , @xcite concluded that substructures should comprise @xmath1 ( 90% confidence ) of the mass of typical lens galaxies in order to explain flux ratios in several lens systems . since the cold dark matter ( cdm ) model predicts @xmath2 of mass in substructures ( e.g. , * ? ? ? * ; * ? ? ? * ) , they argued that the result strongly supports for the cdm model . not all anomalous flux ratios can be ascribed to the simpleness of the smooth part of lens potentials @xcite or any propagation effects because the degree of the ( de-)magnification in observations depends on image parities ( e.g. , * ? ? ? * ) . however , a caveat is that the fraction of substructures is in practice a very sensitive function of distances from the halo center : both numerical simulations ( e.g. , * ? ? ? * ) and analytic models ( e.g. , * ? ? ? * ) clearly demonstrate that substructures preferentially lie in outer parts of dark halos . this means that very little substructure is projected within the einstein radius , since the einstein radius is usually much smaller than the virial radius of halos . thus the fraction of substructures in the cdm model appears to be _ smaller _ than that required to explain anomalous flux ratios in gravitational lenses if we take the spatial distribution of substructures into account @xcite . * see also @xcite ) claimed that the discrepancy may be resolved by considering extragalactic halos along line of sight . another possible explanation is some contributions from stellar microlensing . for instance , @xcite took mid - infrared images of b1422 + 231 and pg1115 + 080 , and concluded that the anomalous flux ratio of pg1115 + 080 is likely to be caused by stellar microlensing . in this _ letter _ , we present a possible alternative route to anomalous flux ratios . specifically , we consider the compound lens system such that a lens galaxy lies in a group or cluster , and discuss to what extent substructures in the group / cluster could contribute to cause anomalous flux ratios . although the situation is not universal , recent studies indicate that such compound systems ( including incidence of foreground groups ) appear to be quite common @xcite . observations imply that many of them lie in groups , and lens systems in clusters are less common . the effect of correlated matter outside the lens halo was studied by @xcite , however they considered typical field galaxies as lens objects , thus the situation is somewhat different from ours . throughout the letter we assume a lambda - dominated cosmology with the mass density parameter @xmath3 , the vacuum energy density parameter @xmath4 , the dimensionless hubble constant of @xmath5 , and the rms fluctuation normalization @xmath6 . the results presented here will be , however , depend little on the specific choice of cosmological parameters . following @xcite , we compute the fraction of the projected surface density , @xmath7 , to discuss the efficiency of flux anomalies . to do so , we use an analytic model of substructures developed by @xcite . the model takes account of two dominant dynamical processes that drive dominantly subhalo evolution : one is mass - loss caused by tidal interaction with the host halo , and the other is the orbital decay caused by dynamical friction which drives massive subhalos to the inner part of the host halo . the model also considers the formation epoch variation of the host halo , and the orbital decay of satellite halos outside the host halo virial radius . it was shown that the derived analytic distributions agree well with the results of recent high - resolution n - body simulation @xcite . although the model may be less realistic than semi - analytic approaches @xcite , it has the advantage of being able to compute spatial and mass distributions very easily . the fraction of the projected surface density @xmath7 is defined by the projected mass in substructures within an annulus with radii @xmath8 and @xmath9 divided by the projected total mass within the annulus . we choose @xmath8 and @xmath9 so that the annuli are equally spaced in @xmath10 with a step size 0.2 , where @xmath11 is a virial radius of a halo that corresponds to a lens galaxy . first , we compute @xmath7 in an isolated halo with mass @xmath12 . the mass inside a cylinder with radius @xmath13 are computed as @xmath14 @xmath15 where @xmath16 is the average density within a sphere of radius @xmath17 , and @xmath18 is an angle with respect to the projection direction . we can calculate the density profile of substructures @xmath19 and corresponding mass @xmath20 by integrating the distributions of substructures @xcite over the mass of substructures . then the mass fraction of substructures is @xmath21 where the mass within annuli is denoted as @xmath22 . for a compound lens . the projected masses @xmath23 , @xmath24 , and @xmath25 are given by equations ( [ eq : mass ] ) , ( [ eq : mh ] ) , and ( [ eq : mhs ] ) , respectively . [ fig : conf ] ] next we consider the situation that a lens galaxy lies in a group or cluster . in this case , the lens galaxy should correspond to a substructure ( hereafter referred as primary substructure ) in a host halo with mass @xmath26 . then to compute the lens potential we have to consider the mass associated the host halo ( group or cluster ) as well as the mass of the substructure . here we consider the situation that another substructure in the host halo causes anomalous flux ratios in gravitational lenses ( hereafter referred as secondary substructure ) . to quantify this contribution , we compute @xmath7 in this compound lens system . when @xmath13 is much smaller than the virial radius of the host halo , the mass of dark matter and substructures associated with the host halo can be approximated as @xmath27 with @xmath28 being the virial radius of the host halo with mass @xmath26 and @xmath29 being the impact parameter of the primary substructure ( see figure [ fig : conf ] ) . then the mass fraction from substructures in the host halo is @xmath30 where @xmath31 is the mass associated with the primary substructure calculated from equation ( [ eq : mass ] ) . although the primary substructure suffers from tidal stripping which makes the size of the substructure smaller , we neglect this because the contribution of the outer part to the mass estimate is quite small . as a function of projected radius @xmath13 . the fractions of an isolated lens ( eq . [ [ eq : fsub1 ] ] ) and compound lens ( eq . [ [ eq : fsub2 ] ] ) are plotted by solid and dashed lines , respectively . we assume the lens ( sub-)halo with @xmath32 , the host halo with @xmath33 , the impact parameter of the lens subhalo in the host halo @xmath34 . they are placed at @xmath35 . the vertical dotted lines indicate the position of typical lensed images , @xmath36 @xcite . [ fig : fsub ] ] we calculate @xmath7 in the following setup : the mass of the isolated halo or the primary substructure , which corresponds to the lens object , is @xmath37 . as a redshift , we choose a typical lens redshift of @xmath35 . for the compound system , we set the mass of the host halo @xmath38 ( i.e. , @xmath39 ) . the virial radii of the lens and host halos are @xmath40 and @xmath41 , respectively . the primary substructure is placed so that the impact parameter becomes @xmath34 . the value of the impact parameter is slightly smaller than the average impact parameter calculated from the radial distribution of substructures assuming the ratio of substructure to host halo masses to be @xmath42 ( see figure 3 of @xcite ) , @xmath43 , but is a reasonable value if we take account of the bias due to the convergence of the host halo ( see [ sec : sum ] ) . we integrate the mass of substructures in the range @xmath44 ( @xmath45 ) to compare our results with those of @xcite . however , almost universal form of the mass function of substructures @xcite assures that relative amount of @xmath7 between isolated and compound lens systems does not change very much even if we shift the range to lower masses . figure [ fig : fsub ] shows @xmath7 as a function of the projected radius @xmath13 . we plot @xmath7 for both isolated compound systems . we note that for the compound system we show @xmath7 from host group / cluster only : the lens galaxy in group / cluster itself should also have substructures that will increase @xmath7 of the compound lens system further . for the isolated halo , we reproduce the result of @xcite . we find that @xmath7 for the compound lens is comparable to , or even higher than , that for the isolated lens at the position of typical lensed images , @xmath36 . to examine how the result is dependent on our specific setup describe above , in figure [ fig : fsub_par ] we show the dependence of @xmath7 for the compound lens on several parameters . we find that @xmath7 is quite sensitive to the impact parameter @xmath29 but rather insensitive to other parameters including the mass of the host halo . therefore we conclude that substructures in the host halo of the compound lens could be a dominant source of anomalous flux ratios when the impact parameter is @xmath46 . the predicted values , however , are still @xmath47 ( without baryons ) and thus they do not completely eliminate , though do reduce , the discrepancy between predicted and observed fraction of substructures . for the compound lens on several parameters : the impact parameter @xmath29 ( _ upper left _ ) , the redshift @xmath48 ( _ lower left _ ) , and the mass of the host halo @xmath49 ( _ lower right _ ) . we change each parameter by fixing the other parameters to the fiducial values . [ fig : fsub_par ] ] the expected level of the contribution from substructures in a group / cluster can also be estimated by a simple argument . in our fiducial parameter set , the convergence at image position ( @xmath50 ) is @xmath51 ( assuming a source redshift @xmath52 ) , and the external convergence is @xmath53 . on the other hand , at @xmath54 of a virial radius the fraction of substructures is @xmath55 ( see figure [ fig : fsub ] ) . from these numbers , @xmath7 is estimated as @xmath56 the estimated number is roughly consistent with the result presented in figure [ fig : fsub ] . the external convergence @xmath57 is a strong function of the impact parameter , thus the reason that @xmath58 is sensitive to the impact parameter @xmath29 can be also understood from this expression . we have examined the impact of lens galaxy environments on substructure lensing . using an analytic model of substructures constructed by" +"from cosmic ray studies , there is a clear evidence that energies of primary cosmic rays extend up to enormous energies of more than @xmath0ev with highest energy cosmic rays detected by fly s eye ( hires ) collaboration @xcite , yakutsk air shower array @xcite and the agasa experiment @xcite . at the same time , the highest energy cosmic rays represent still a _ terra incognita _ with respect to the processes powering them . the key question of modern astrophysics - namely , _ what is the nature of the cosmic high energy world ? _ - has to be considered as unsolved . there is no probe except for neutrino which could help us to answer this question . electrically charged protons and heavier nuclei , whose arrival direction is scrambled by galactic and intergalactic magnetic fields , are able to point back to the sources of their acceleration only above approximately 110eev ev , 1tev@xmath1ev , 1pev@xmath2ev , 1eev@xmath3ev , 1zev@xmath4ev , correspondingly . ] . @xmath5-rays keep the initial direction but the universe is not transparent for them at energies above tev range since they annihilate into electron - positron pairs in an encounter with a 2.7k cosmic microwave background photons or with infra - red radiation . for example , @xmath5-quantum of 1pev energy can not reach us even from the galaxy center ( 10 kpc ) . neutrons are too short - live particles and they are not in time to cross even our galaxy before decaying if their energy is below several eev . thus , neutrino remains the only _ i ) _ weak interacting ; _ ii ) _ stable ; and _ iii ) _ neutral probe which can reach the earth ( where we are able to observe it ) from the cosmological distances keeping original direction and pointing back to the source of its origin , meeting thus the basic requirements of _ astronomy_. mev - range neutrino astronomy have been existing for forty years with two neutrino sources identified so far , namely the sun and supernova sn-1987a , which at the moment remain the only two experimentally proved extraterrestrial neutrino sources . development of ultra- and extremely high energy 30tev30pev ; extremely high energy range ( ehe ) is @xmath630pev , respectively . ] neutrino astronomy is under way , being still in its infancy . it started in 1960 with academician markov s suggestion to use a natural basins ( lakes or seas ) to deploy there a large volume neutrino telescopes @xcite . the large instrumented volume is needed due to the two basic reasons : firstly , expected fluxes of uhe / ehe neutrinos are very low and , secondly , cross section of neutral current ( nc ) and charged current ( cc ) neutrino interactions @xmath7 ( by which neutrinos are supposed to be detected ) is small despite its increase with the neutrino energy . to detect neutrinos associated with highest energy cosmic rays one needs a kilometer scale detectors . after the first experimental steps at the middle of the 1970th ( the dumand project @xcite ) and detection of the first underwater atmospheric neutrino at the middle of the 1990th ( the baikal experiment @xcite ) experimental groups and collaborations moved to the next stage : creation of detectors with effective areas of 0.1 km@xmath8 and higher with an ultimate goal to build neutrino telescopes with effective volumes of one cubic kilometer . this talk reviews the physical goals and experimental status for ultra- and extremely high energy neutrino astronomy focusing , first of all , on operating and planned deep underwater / ice cherenkov neutrino telescopes . underwater / ice neutrino telescopes ( unts ) represent a 3-d arrays of photomultipliers deployed deep in the lake , ocean or in the polar ice at the depth of 1 to 4 kilometers to provide with a shield against the sun and moon light background and background of atmospheric muons . detection principle is based on registration of the cherenkov photons emitted by charged leptons ( including those emitted by secondaries produced along their way in the water or ice and by their decay products ) which are generated in cc neutrino interactions @xmath9 ( see fig . [ fig : principle ] ) . also hadronic showers produced in nc neutrino interactions @xmath10 inside unt sensitive volume can be detected by radiated cherenkov photons . pmt hit times and positions provide with a possibility to reconstruct the track or shower vertex while a charge collected on pmt anodes allows to reconstruct the energy . thus , there can be two main event topologies in unts ( fig . [ fig : topo ] ) : * * track event * in case of muon of any energy or tau - lepton with energy @xmath112pev ( approximately above this energy tau - lepton is able to propagate remarkable distance before decay thanks to the lorentz factor ) ; * * shower event * in case of electron , tau - lepton with energy @xmath122pev and nc interactions of all flavor neutrinos . however , real events may contain both topologies . track of uhe / ehe muon or tau - lepton is complemented by showers produced by secondaries which are generated in the muon interactions : bremsstrahlung , direct @xmath13-pair production , photonuclear interactions and knock - on electron production . with some probability these showers can take the major fraction of @xmath14/@xmath15 energy and even all the energy ( first of all due to bremsstrahlung ) . thus , a combined topology * track@xmath16shower * takes place . as well as , a tau - lepton track with a subsequent decay create such combined topology . cc muon neutrino ( or tau neutrino if @xmath17 is in multi - pev range or higher ) interaction within unt sensitive volume with an hadronic shower in the neutrino interaction vertex and subsequent charged lepton track also produces a combined topology which is even more complex in case of tau - lepton if it decays inside sensitive volume providing thus with at least two showers : in neutrino interaction point and at the decay point ( so called double bang @xcite ) . on the other hand , at energies below pev range two showers at the tau neutrino interaction vertex and at the tau - lepton decay point are so close to each other that can not be separated at reconstruction ( also tau - lepton track can not be distinguished ) and thus , such an event can be considered as a pure shower one . the main goal of uhe / ehe neutrino astronomy is to determine the origin of high energy cosmic rays . for this it is needed to detect natural flux of the high energy neutrinos measuring neutrino energy , directional information and intensity . expected sources of uhe / ehe neutrinos are as follows ( more detailed review can be found , e.g. , in @xcite ) : * steady sources like , e.g. , active galactic nuclei ( agn ) , supernova remnants ( snr ) or microquasars ; * transient sources like gamma ray bursts ( gbr ) ; * decay of superheavy particles or topological defects . detection of uhe / ehe neutrinos and identification of their sources would allow to clarify the origination of uhe / ehe cosmic rays and to understand the processes by which the nature fills the universe with the highest energy particles . accuracy of energy measurements in unts is not too high . energy reconstruction is based on the increase of emitted cherenkov light due to muon ( @xmath15 ) catastrophic energy losses above @xmath181tev . also , amount of cherenkov photons produced by both hadronic and electromagnetic shower is more or less proportional to the shower energy . but due to stochastic nature of energy losses and due to the fact that an unt represent a non - dense detector with pmts spaced by typically 10 - 100 m , unts can not be a good calorimeter : for instance , dispersion of the @xmath19 distribution ( where @xmath20 is the true muon energy and @xmath21 is the reconstructed energy , respectively ) is around @xmath220.5 at @xmath235tev and @xmath220.3 for @xmath24100tev which means that the muon energy resolution is at the level of 2 - 3 only ( see fig . [ fig : enerres ] ) . besides , an additional un - avoided error at neutrino energy measurement comes from the fact that fraction of energy that is taken by charged lepton at neutrino cc interaction has a distribution and if neutrino interaction occurs far apart unt sensitive volume and , hence , shower energy can not be reconstructed , reconstructed charged lepton energy is not a good estimator for the neutrino energy . angular resolution for track events at uhe / ehe range is , typically , at @xmath250.1@xmath261.0@xmath26 level ( fig . [ fig : angres ] ) and it is sufficient for search of point - like neutrino sources . the first main background for neutrino events comes from down - going atmospheric muons and it is suppressed by putting unt as deeper as possible to provide with a shield of water or ice ( each 1 km of water suppress the atmospheric muon background by approximately one order of magnitude ) and by selecting of up - going events as neutrino candidates . the second background is due to atmospheric neutrinos . the flux of astrophysical neutrinos is expected to behave like @xmath27 whereas the atmospheric neutrino spectrum falls like @xmath28 , yielding a better signal - to - background ratio at higher energies . thus , atmospheric neutrino background can be suppressed by setting the off - line energy threshold at the level @xmath2910 - 100tev . except for deep underwater or ice neutrino detection other techniques are also discussed and used ( for more detailed review see @xcite ) : * detection of coherent cherenkov radio waves emitted by electromagnetic showers @xcite ; * acoustic pulses generated in matter heated by uhe / ehe cascades due to ionization energy losses @xcite ; * detection of neutrino interactions by horizontal air showers ( both with traditional earth - based large extensive air shower arrays @xcite and with satellite space - based detectors @xcite ) . such kind of experiments have a high energy thresholds ( at eev energy range ) and are aimed to detection of highest energy neutrinos . target masses for neutrino interaction are at the level of giga - tons and higher providing with opportunity to detect weak neutrino fluxes . all the models for generation of uhe / ehe particles can be divided roughly by two main classes . _ bottom - up _ models consider initially low energy particles which are accelerated up to uhe / ehe , typically , by shock waves propagating in accretion disks around black holes or along the extended jets emitted perpendicularly to the disk . neutrino are supposed to be produced in decays of mesons which are generated by interaction of accelerated particles with surrounding matter or photon fields . such models predict @xmath27 behavior of neutrino spectrum . by normalization of the neutrino flux to the known cosmic ray flux one can obtain an upper bound of @xmath30 gev@xmath31 @xmath32 s@xmath31 sr@xmath31 ( waxman - bahcall limit @xcite ) to the neutrino flux integrated over all possible sources or _ diffuse _ neutrino flux ( fig . [ fig : limit ] ) . more detailed consideration which involves , in particular , the source transparency , leads to bounds at the level between the waxman - bahcall limit and @xmath33 gev@xmath31 @xmath32 s@xmath31 sr@xmath31 ( @xcite , mpr obscured and mpr transparent in fig . [ fig : limit ] )" +"one - dimensional ( 1d ) atomic chains created on semiconductor templates have recently attracted much attention due to new phenomena characteristic for a reduced dimensionality @xcite . the most spectacular examples include a breakdown of fermi liquid theory @xcite and peierls metal - insulator transition @xcite . a specially attractive route to create such 1d structures is a process of self - organization of atoms into very regular arrays of parallel metallic chains on stepped semiconducting or insulating substrates @xcite . in this case electrons near the fermi energy are completely decoupled from the substrate due to band gap in electronic spectrum of the substrate . the chain atoms are bounded to the surface by low energy states which do not contribute to electronic properties of the system . the si(335)-au surface is one of the simplest examples of high - index surfaces which stabilize the one - dimensional structures , and has been studied by number of techniques , including : reflection high energy electron diffraction ( rheed ) @xcite , scanning tunneling microscopy ( stm ) @xcite , angle - resolved photoemission spectroscopy ( arpes ) @xcite and first principles density functional theory ( dft ) @xcite . in particular , the stm topography data show regular arrays of monoatomic chains separated by width of si(335 ) terrace and a few nanometers long @xcite . the arpes spectra taken in the direction parallel to the steps show two highly dispersive bands crossing the fermi energy ( @xmath0 ) , thus indicating one - dimensional metallic nature of the system @xcite . the structural model of the si(335)-au surface has also been proposed @xcite and confirmed later by the dft calculations @xcite , which well describes all the available experimental data . recently , other materials ( na , pb , in ) deposited on au decorated si(335 ) surface have also been studied @xcite . perhaps lead is the most intensively studied among them . unlike si(335)-au surface , in which gold substitutes si atoms in the surface layer , the si(335)-au / pb is a representative of new class of systems in which the deposited material forms one - dimensional structures adsorbed on - top of the surface . the lead deposited on flat si(111)-au(6@xmath16 ) surface forms well ordered monoatomic layers @xcite , and is known to weakly interact with the si substrate @xcite . thus , in the case of si(335)-au / pb structure , one can expect a more pronounced one - dimensional character of chains as compared to clean si(335)-au reconstruction . indeed , the deposition of 0.28 ml of pb on reconstructed si(335 ) surface ( 0.28 ml gives exactly 1 pb atom per si(335 ) unit cell ) also leads to one - dimensional objects on the surface . the stm topography shows a few nanometers long chains placed in between si chains of original si(335)-au surface @xcite . the photoemission spectra taken in the @xmath2 $ ] direction ( i.e. parallel to the steps ) , show a highly dispersive band crossing the fermi energy and quite flat bands in the @xmath3 $ ] direction ( perpendicular to the steps ) , thus indicating clear one - dimensional character of the reconstruction . a more detailed analysis of morphology of the surface and of the arpes data is difficult or even impossible without appealing to dft calculations . it is the purpose of the present work to propose a structural model of the si(335)-au / pb surface and calculate corresponding band structure . here i present a structural model of the pb chains on si(335)-au surface , derived from total energy dft calculations . it features single pb atom per si(335 ) unit cell placed near the au chain . the pb atoms are bonded to neighboring si and au atoms , forming monoatomic chain located @xmath4 nm above the surface . this picture is consistent with the stm topography data of ref . @xcite , and also confirmed by simulated stm topography images . on the other hand , the calculated band structure for the present model clearly shows one - dimensional character , i.e. a strong dispersion in the direction parallel to the steps and their lack in the direction perpendicular to them , and remains in good agreement with the arpes spectra of ref . the rest of the paper is organized as follows . in sec . [ details ] the details of calculations are presented . the structural and electronic properties of the clean si(335)-au surface are briefly discussed in sec . [ clean ] . the structural model of pb chains , simulated stm topography images and the band structure are presented and discussed in sec . [ model ] , [ stm ] , [ band ] , respectively . the influence of step - edge buckling on electronic properties is discussed in sec . [ buckling ] . finally , sec . [ conclusions ] contains some conclusions . the calculations have been performed using standard pseudopotential density functional theory and linear combination of numerical atomic orbitals as a basis set , as implemented in the siesta code @xcite . the local density approximation ( lda ) to dft @xcite , and troullier - martins norm - conserving pseudopotentials @xcite have been used . in the case of pb and au pseudopotentials , the semicore @xmath5 states were included . a double-@xmath6 polarized ( dzp ) basis set was used for all the atomic species @xcite . the dzp utilizes two radial functions for each angular momentum and additional polarization shell . the radii of the orbitals for different species were following ( in bohrs ) : si - 5.13 ( @xmath7 ) , 6.59 ( @xmath8 ) and 5.96 ( @xmath9 ) , au - 4.39 ( @xmath5 ) , 6.24 ( @xmath10 ) and 5.79 ( @xmath11 ) , pb - 3.56 ( @xmath5 ) , 4.68 ( @xmath12 ) , 5.30 ( @xmath10 ) and 6.48 ( @xmath11 ) , and h - 5.08 ( @xmath13 ) and 4.48 ( @xmath14 ) . a brillouin zone sampling of 24 nonequivalent @xmath15 points , and a real - space grid equivalent to a plane - wave cutoff 100 ry ( up to 82 @xmath15 points and 300 ry in the convergence tests ) have been employed . this guarantees the convergence of the total energy within @xmath16 mev per atom in the supercell . the si(335)-au / pb system has been modeled by four silicon double layers and a vacuum region of 18 . all the atomic positions were relaxed except the bottom layer . the si atoms in the bottom layer were fixed at their bulk ideal positions and saturated with hydrogen . to avoid artificial stresses , the lattice constant of si was fixed at the calculated value , 5.41 . the atomic positions were relaxed until the maximum force in any direction was less than 0.01 ev / . the deposition of 0.28 ml of gold on si(335 ) surface forms well ordered arrays of chain structure . the surface consists of ( 111 ) terraces which have a width @xmath17}$ ] ( 1.26 nm ) @xcite . each terrace contains a single row of gold atoms running parallel to the step edge , i.e. in the @xmath2 $ ] direction . the gold chain is formed by substitution of si atoms in the middle of terrace . the step edge si atoms form a honeycomb substructure @xcite , which is a common feature of all the au - induced vicinal si surfaces @xcite . the structural model of the si(335)-au surface is shown in fig . [ fig1 ] , where the si surface atoms ( si@xmath18-si@xmath19 ) are labeled by numbers 1 - 6 , and the gold atom by au . + originally this model has been proposed as a simple truncation of si(557)-au reconstruction @xcite , and later confirmed by dft calculations @xcite . the stm topography data @xcite show a single chain per terrace , which is associated with the step edge si atoms rather than with the au chain . the gold substitutes some of top layer si atoms in the middle of terrace , and is not visible to stm . this has also been confirmed by dft calculations @xcite . see also simulated stm topography images presented in fig . the arpes spectra show two highly dispersive bands crossing the fermi energy in the direction parallel to the steps , and quite flat bands in the direction perpendicular to them @xcite , clearly indicating one - dimensional metallic nature of the system . the dft calculations indicate that one of the bands crossing @xmath0 is associated with the step edge si atoms , having unsaturated dangling bonds , while the other one originates from hybridization of the au and neighboring si atoms in the middle of terrace in the surface layer @xcite . one - dimensional structures of pb on si(335)-au reconstruction one obtains assuming single pb atom per si(335)-au unit cell , which corresponds to the experimental pb coverage - 0.28 ml @xcite . the total energy calculations show that pb atoms prefer to adsorb on the surface . the substitution of pb atoms into top si layer is energetically less favorable , as the surface energy is by 0.3 - 0.6 ev ( per unit cell ) higher in comparison to clean si(335)-au surface and pb atom in the bulk fcc structure . similarly , the substitution into the second si layer is not preferred . in this case the energy cost is 1 ev . the exception is the substitution of pb at the step edge , where the energy gain is 0.31 ev . more than 40 structural models have been investigated , and only five of them lead to stable structures . corresponding surface energies , with respect to clean si(335)-au surface and bulk pb atom , are shown in table [ tab1 ] . .[tab1 ] the relative surface energies of most stable structural models of si(335)-au / pb structure . the energies are referred to clean si(335)-au surface and pb atom in the bulk fcc structure . [ cols=""^,^,^,^,^ "" , ] the differences in energy are rather small , however , as it will be argued later , the model with the lowest energy , i.e. si@xmath20-au - au model , is the best candidate for a true model of pb chains on si(335)-au surface . note the nomenclature used here reflects the bonding of lead with corresponding surface atoms . for labeling see fig . [ fig2 ] . the structural model with the lowest surface energy features pb atoms located 2 @xmath21 above the surface near the gold chain , and is shown in fig . [ fig2 ] . + as one can read off from the figure , lead is bounded to two au atoms and one si@xmath20 atom , but not to si@xmath22 atom ( fig . [ fig2 ] ) . the pb - si@xmath20 bond length is equal 2.75 , and pb - au - 2.92 . both bonds are shorter than the pb bonds in the bulk fcc structure ( 3.46 ) . the presence of pb atoms on - top of the surface also modifies positions of underneath au and si atoms , leading to change in their bond lengths . thus the au - si@xmath22 bond is equal 2.52 , and au - si@xmath23 - 2.47 , to compare with 2.43 @xmath21 and 2.38 , respectively , in the clean si(335)-au surface . what is more important , presence of pb atoms also leads to a strong rebonding at the step edge . in the clean si(335)-au surface , the si atoms near the step edge form a sort of honeycomb chain ( see fig . [ fig1 ] )" +"the issue of whether increasing the complexity of a network contributes to its dynamical instability has long been debated . this ` complexity vs stability ' debate is especially acute in the field of ecology @xcite , as it relates to the importance of diversity for the long - term survival of ecosystems . however , understanding the relation between the network structure and its stability ( with respect to dynamical perturbations ) is crucial , as it is related to the robustness of systems as ubiquitous as power grids , financial markets , and even complex societies and civilizations@xcite . pioneering studies on the stability of networks , both theoretical@xcite and numerical@xcite , suggested that increasing the network complexity , as measured by its size ( @xmath0 ) , density of connections ( @xmath1 ) and the strength of interactions between coupled elements ( @xmath2 ) , almost inevitably leads to the destabilization of any arbitrary equilibrium state of the system . this result , known as the may - wigner stability theorem , seemed to fly in the face of conventional wisdom that higher diversity makes a system more capable of surviving perturbations and has since led to much research on the connection between network complexity and stability@xcite . the may - wigner argument @xcite confines itself to analyzing the local stability of an arbitrarily chosen equilibrium point of the network dynamics . under such constraints , the explicit dynamics at the nodes can be ignored and the stability is governed by the leading eigenvalue of the linear stability matrix @xmath3 . as a first approximation , one can consider the network elements to be coupled randomly with each other . if the connection weights between linked nodes follow a gaussian distribution ( with mean 0 and variance @xmath4 ) , then it follows that @xmath3 is a random matrix . therefore , existing rigorous results on the eigenvalue distribution of random matrices can be applied , which allows one to make the assertion that the network is almost certainly stable if @xmath5 , and almost certainly unstable otherwise . objections to the may - wigner argument have often revolved around the assumption of a randomly connected network . as pointed out by many ecologists , most networks occurring in nature are not random , and seem to have structures such as trophic levels in the predator - prey relations between different species . some early studies seemed to suggest that introducing a hierarchical organization ( e.g. , by partitioning the adjacency matrix of the network into blocks @xcite or by having tree structures @xcite ) can increase the stability of a network under certain conditions . however , no general consensus on this issue has yet been achieved . the introduction of small - world "" connection topology@xcite has allowed the possibility of having different kinds of structures in a network , other than a straightforward hierarchy of levels . small - world networks have the global properties of a random network ( short average path length between the elements ) while at the local level they resemble regular networks with a high degree of clustering among neighbors . in fact , several empirically obtained food web networks have been analyzed by different research groups looking for evidence of small - world structure . initial reports of small - world ecological networks based on the analysis of 4 food webs @xcite have been challenged by a study based on 7 food webs @xcite , and , more recently , by a comprehensive analysis of 16 food webs covering a wide variety of habitats@xcite . the latter studies did not see significantly high clustering in most of these systems , compared to a random network . in light of this , it is inevitable to ask oneself whether the introduction of small world connectivity confer any advantage to the network . if the occurrence of higher than average clustering has no functional significance , then the occurrence of small - world structures in a few networks are probably due to chance alone . in particular , we can ask whether introducing such structures in a network can make it more stable , and therefore , able to survive perturbations compared to its random counterpart . in this paper we strive to answer the above question . although there have been previous studies on the eigenvalue distribution of small - world networks@xcite , the issue of stability has not been looked at in any depth . in the next section , we have described the basic model used to study the stability of the network as its structure is changed from regular through small - world to random . the results of extensive numerical studies is reported in section 3 , which suggests that the stability - instability transition occurs at the same critical value independent of the network structure ; but the nature of this transition ( as measured by the finite - size scaling exponent ) changes with the topology . finally , we conclude with a brief discussion of the implications of our results . to observe the stability of networks at the small - world regime we follow the basic watts - strogatz construction @xcite . a ring consisting of @xmath0 nodes , with each node connected to @xmath6 neighbors ( i.e. , neighborhood size is @xmath7 ) , is rewired with probability @xmath8 . in other words , a fraction @xmath8 of the links among the nodes in the lattice are broken and then randomly reconnected , subject to the condition that the total number of links does not change and that two nodes are not connected by more than one directed link . as outlined in ref.@xcite , increasing @xmath8 decreases both the average path length and the clustering between nodes . in addition , we introduce randomly distributed weights to each of the links . following may @xcite , we generate the corresponding linear stability matrix @xmath3 , such that , the non - zero entries are chosen from a gaussian distribution with mean 0 and variance @xmath4 . in addition , to ensure that the nodes are individually stable in the absence of connections , the diagonal elements of @xmath3 are chosen to be @xmath9 . for a given @xmath8 , the stability of the resulting network is then examined by observing the sign of the leading eigenvalue @xmath10 of @xmath3 as a function of size ( @xmath0 ) , connectance ( @xmath11 ) and strength of connectivity ( @xmath2 ) . if @xmath12 , the network is considered unstable . the corresponding probability of stability @xmath13 is calculated by carrying out a large number of network realizations . while this analysis does not explicitly consider dynamics , recent studies@xcite indicate that including the dynamics of the nodes does not qualitatively change the results obtained using the above technique . it is possible that a sparsely connected network can be broken up into disconnected clusters by the rewiring procedure . for this reason , in the simulations reported here we have used @xmath14 , which ensures that the entire network remains connected . note that , unlike another study on the stability of small - world networks @xcite , we are analyzing the stability of an asymmetric sparse matrix whose non - zero entries are normally distributed . as mentioned in the previous section , we observe the order parameter @xmath13 against the different network complexity parameters . for instance , keeping @xmath0 and @xmath1 fixed , as we increase @xmath2 , @xmath13 decreases from 1 to 0 , i.e. , the network shows a stability - instability transition . the critical parameter value , @xmath15 , at which the transition occurs remains unchanged as we vary the connection topology from regular ( @xmath16 ) through small - world to random ( @xmath17 ) . this implies that changing the connection topology does not affect the stability of a network . however , the transition appears to get sharper as the network becomes more random . = 5.5 in to quantitatively measure the increase in steepness with randomness we used finite - size scaling analysis . the sharpness of the stability - instability transition increases with @xmath0 for all topologies ; finite - size scaling allows us to measure how the relative width of the transition region decreases with increasing @xmath0 . it was noted by may@xcite that for random networks , this scales as @xmath18 . we have carried out this analysis for networks with different values of @xmath8 , where the width of the transition region scales as @xmath19 , and we observe the variation of @xmath20 with @xmath8 . as shown in fig . 1 , @xmath21 for regular networks , and gradually decreases with @xmath8 , ultimately becoming @xmath22 for @xmath17 ( as expected at the random network limit ) . = 5.5 in = 5.5 in to understand why the nature of the stability - instability transition is affected by the network topology , we look at the eigenvalue plain of the regular and random networks ( fig . the eigenvalues of the latter are bounded by a circle centered at @xmath9 and having a radius of @xmath23 . however , for regular networks , there are extensions from this circle along the real axis . the largest eigenvalues are located on this ` tail ' . the extended tails of the eigenvalue distribution for @xmath24 are shown in greater detail in fig . 3 . for @xmath17 , the distribution is bounded , as predicted by wigner s semicircle theorem . however , in the presence of clustering ( i.e. , as @xmath25 ) , the distribution extends out of the limits predicted by the semicircle distribution . the stability of the network is governed by the maximal eigenvalue . for the regular network , this is found at the tail of the eigenvalue distribution where the relative variance of @xmath10 is much larger than if it was located in the bulk ( as is the case for @xmath17 ) . this results in a smoother transition from stability to instability for regular networks . = 5.5 in it has been pointed out in ref . @xcite that in real - world networks , links are ` expensive ' . therefore , we also looked at the case where @xmath7 is fixed as the system size increases ( so that @xmath1 decreases with @xmath0 ) . for low values of @xmath7 ( relative to fixed @xmath0 ) we observe that the eigenvalue distribution shows a peak at the center , presumably due to contributions from small isolated clusters as mentioned in ref . @xcite . at higher values of @xmath7 , we observe distributions similar to the ones obtained for the constant @xmath1 case reported before . however , a major difference was the relation between system size ( @xmath0 ) and the largest eigenvalue , @xmath10 , as well as the fraction of real eigenvalues , @xmath26 ( fig . 4 ) . for random networks , @xmath10 attains a constant value for large values of @xmath0 . further , as pointed out in ref . @xcite , the excess density of real eigenvalues decreases with @xmath0 roughly as @xmath27 . however , for regular networks , @xmath10 grows with @xmath0 as @xmath28 ( in fig . 4 , @xmath29 ) and the excess density of real eigenvalues becomes constant for large @xmath0 . this implies that as the regular network increases in size , the tail of the eigenvalue distribution gets longer ( while the bulk remains fixed in size , similar to random networks ) . also , more and more eigenvalues migrate from the complex plane to the real axis , keeping its density constant even though the system size ( and hence , the total number of eigenvalues ) is" +"this paper presents a formal statement and an assisted proof of a jordan curve theorem ( jct ) discrete version . in its common form , the theorem says that the complement of a continuous simple closed curve ( a jordan curve ) @xmath0 in an affine real plane is made of two connected components whose border is @xmath0 , one being bounded and the other not . the discrete form of jct we deal with states that in a finite subdivision of the plane , breaking a ring @xmath1 of faces increases by @xmath2 the connectivity of the subdivision . it is a weakened version of the original theorem where the question of bound is missing . however , it is widely used in computational geometry and discrete geometry for imaging , where connection is the essential information @xcite . in fact , we only are in a combinatoric framework , where any embedding is excluded , and where bounding does not make sense . in computational topology , subdivisions are best described by map models , the most general being _ hypermaps _ we propose a purely combinatorial proof of jct based on this structure . the hypermap framework is entirely formalized and the proofs are developed interactively and verified by the coq proof assistant @xcite . using an original way to model , build and destruct hypermaps , the present work brings new simple constructive planarity and connectivity criteria . it proposes a new direct expression of jct and a simple constructive proof with algorithmic extensions . it is also a large benchmark for the software specification framework we have been developing in the last fifteen years for map models used in geometric modeling and computer imagery @xcite . the useful coq features are reminded and the whole process is described , but the full details of the proofs are omitted . section [ rw ] summarizes related work . section [ ma ] recalls some mathematical materials . section [ fh ] proposes basic hypermap specifications . section [ pc ] proves constructive criteria of hypermap planarity and connectivity . section [ fr ] inductively specifies the rings and their properties . section [ jct ] proves the discrete jct . section [ cl ] concludes . the jct is a result of classical plane topology , first stated by c. jordan in 1887 , but of which o. veblen gives the first correct proof in 1905 . in 1979 , tutte proposes operations and properties of combinatorial maps , _ e.g. _ planarity and euler s formula , defines rings and proves a discrete jct @xcite . our theorem statement is comparable , but our framework is modeled differently and all our proofs are formalized and computer - assisted . in 2003 , g. bauer and t. nipkow specify planar graphs and triangulations in isabelle / isar to carry out interactive proofs of euler s formula and of the five colour theorem @xcite . however , they do not approach the jct . in 2005 , a. kornilowicz designs for the mizar project a semi - automated classical proof of a continuous form of jct in an euclidean space @xcite . in 2005 also , on his way towards the proof of the kepler conjecture in the flyspeck projet , t. hales proves the jct for planar rectangular grids with the hol light system , following the kuratowski characterization of planarity @xcite . in 2005 always , g. gonthier _ _ prove the four colour theorem using coq . plane subdivisions are described by hypermaps , and euler s formula is used as a global planarity criterion @xcite . a local criterion , called _ hypermap jordan property _ , is proven equivalent . the main part of this work is the gigantic proof of the four colour theorem with hypermaps and sophisticated proof techniques . the hypermap formalization is very different from ours and it seems that jct is not explicitly proven there . finally , since 1999 , we carry out experiments with coq for combinatorial map models of space subdivisions @xcite . [ hd ] a _ hypermap _ is an algebraic structure @xmath3 , where @xmath4 is a finite set whose elements are called _ darts _ , and @xmath5 , @xmath6 are permutations on @xmath4 . if @xmath7 , @xmath8 is the @xmath9-_successor _ of @xmath10 , @xmath10 is the @xmath9-_predecessor _ of @xmath8 , and @xmath10 and @xmath8 are said to be @xmath9-_linked_. in fig . [ fig : uhmap1 ] , as functions @xmath5 and @xmath6 on @xmath11 are permutations , @xmath12 is a hypermap . it is drawn on the plane by associating to each dart a curved arc oriented from a bullet to a small stroke : @xmath13-linked ( resp . @xmath2-linked ) darts share the same small stroke ( resp . bullet ) . by convention , in the drawings of hypermaps on surfaces , @xmath9-successors turn counterclockwise around strokes and bullets . let @xmath12 be a hypermap . ( orbits and hypermap cells)[oc ] + ( 1 ) let @xmath14 be @xmath15 functions in @xmath4 . the _ orbit _ of @xmath16 for @xmath14 is the subset of @xmath4 denoted by @xmath17 , the elements of which are accessible from @xmath10 by any composition of @xmath14 . + ( 2 ) in @xmath18 , @xmath19 is the @xmath13-orbit or _ edge _ of dart @xmath10 , @xmath20 its @xmath2-orbit or _ vertex _ , @xmath21 its _ face _ for @xmath22 , and @xmath23 its _ ( connected ) component_. in fig . [ fig : uhmap1 ] the hypermap contains @xmath24 edges ( strokes ) , @xmath25 vertices ( bullets ) , @xmath25 faces and @xmath26 components . for instance , @xmath27 is the edge of dart @xmath26 , @xmath28 its vertex . faces are defined , through @xmath29 , for a dart traversal in counterclockwise order , when the hypermap is drawn on a surface . then , every face which encloses a bounded ( resp . unbounded ) region on its left is called _ internal _ ( resp . _ external _ ) . in fig . [ fig : uhmap1 ] , the ( internal ) face of @xmath30 is @xmath31 and the ( external ) face of @xmath32 is @xmath33 . let @xmath34 and @xmath35 be the numbers of darts , edges , vertices , faces and components of @xmath18 . ( euler characteristic , genus , planarity ) + ( 1 ) the _ euler characteristic _ of @xmath18 is @xmath36 . + ( 2 ) the _ genus _ of @xmath18 is @xmath37 . + ( 3 ) when @xmath38 , @xmath18 is said to be _ planar_. for instance , in fig . [ fig : uhmap1 ] , @xmath39 and @xmath40 . consequently , the hypermap is non planar . these values satisfy the following results : @xmath41 is an even integer and @xmath42 is a natural number . a non empty connected @xmath43 i.e. with @xmath44 @xmath43 planar hypermap satisfies @xmath45 . when @xmath46 , the _ representation _ of @xmath18 on an _ orientable closed _ surface is a mapping of edges and vertices onto points , darts onto open oriented jordan arcs , and faces onto open connected regions . it is an _ embedding _ when every component of @xmath18 realizes a partition of the surface . then , the genus of @xmath18 is the minimum number of _ holes _ in an orientable closed surface where such an embedding is possible , thus drawing a subdivision , or a polyhedron , by hypermap component @xcite . for instance , all the components of the hypermap in fig . [ fig : uhmap1 ] can be embedded on a torus ( @xmath2 hole ) but not on a sphere or on a plane ( @xmath13 hole ) . when a ( planar ) hypermap component is embedded on a plane , the corresponding subdivision has exactly one unbounded ( external ) face . but a non planar hypermap can never be embedded on a plane : in a drawing on a plane , some of its faces are neither internal nor external , _ e.g. _ @xmath47 in fig . [ fig : uhmap1 ] . conversely , any subdivision of an _ orientable closed _ surface can be modeled by a hypermap . in fact , the formal presentation which follows is _ purely combinatorial _ , _ i.e _ without any topological or geometrical consideration . -.3 cm to state the version of jct we will prove , we need the concepts of _ double - link _ , _ adjacent faces _ and _ ring of faces _ in a hypermap @xmath48 . ( double - link and adjacent faces ) + ( 1 ) a _ double - link _ is a pair of darts @xmath49 where @xmath8 and @xmath50 belong to the same edge . + ( 2 ) the faces @xmath51 and @xmath52 of @xmath18 are said to be _ adjacent by the double - link _ @xmath49 if @xmath8 is a dart of @xmath51 and @xmath50 a dart of @xmath52 . we choose a face adjacency _ by an edge _ rather than _ by a vertex _ as does w.t . tutte @xcite . in fact , due to the homogeneity of dimensions @xmath13 and @xmath2 in a hypermap , both are equivalent . ( ring of faces ) [ rof ] + a _ ring of faces _ @xmath1 of length @xmath15 in @xmath18 is a non empty sequence of double - links @xmath53 , for @xmath54 , with the following properties , where @xmath55 and @xmath56 are the edge and face of @xmath57 : + ( 0 ) _ unicity : _ @xmath55 and @xmath58 are distinct , for @xmath59 and @xmath60 ; + ( 1 ) _ continuity : _ @xmath56 and @xmath61 are adjacent by the double - link @xmath53 , for @xmath62 ; + ( 2 ) _ circularity _ , or _ closure : _ @xmath63 and @xmath64 are adjacent by the double - link @xmath65 ; + ( 3 ) _ simplicity : _ @xmath56 and @xmath66 are distinct , for @xmath59 and @xmath60 . this notion simulates a jordan curve represented in dotted lines in fig . [ fig : uring4bis ] on the left for @xmath67 . then , we define the _ break along a ring _ , illustrated in fig . [ fig : uring4bis ] on the right . ( break along a ring ) [ bar ] + let @xmath1 be a ring of faces of length @xmath15 in @xmath18 . let @xmath68 , for @xmath69 , be a hypermap sequence , where the @xmath70 are recursively defined by : + ( 1 ) @xmath71 : @xmath72 = @xmath5 ; + ( 2 ) @xmath73 : for each dart @xmath74 of @xmath4 : @xmath75 = if @xmath76 then @xmath77 else if @xmath78 then @xmath57 else @xmath79 + then , @xmath80 is said to be obtained from @xmath18 by a _ break along _ @xmath1 . finally , the theorem we will prove in coq mimics the behaviour of a cut along a simple jordan curve of the plane ( or of the sphere ) into two components : let @xmath18 be a planar hypermap with @xmath35 components , @xmath1 be a ring of faces in @xmath18 , and @xmath81 be the break of @xmath18 along @xmath1 . the number @xmath82 of components of @xmath81 is such that @xmath83 . -.3 cm in coq , we first define an inductive type dim for the two dimensions at stake : inductive dim : set:= zero : dim | one : dim . all objects being typed in coq , dim has the type set of all concrete types . its _" +"massive stars dominate the feedback to the local interstellar medium ( ism ) in star - forming galaxies via their stellar winds and ultimate death as core - collapse supernovae . in particular , wolf - rayet ( wr ) stars typically have wind densities an order of magnitude higher than massive o stars . they contribute to the chemical enrichment of galaxies , they are the prime candidates for the immediate progenitors of long , soft gamma ray bursts ( grbs , woosley & bloom 2006 ) , and they provide a signature of high - mass star formation in galaxies ( schaerer & vacca 1998 ) . spectroscopically , wr stars are spectacular in appearance , with strong , broad emission lines instead of the narrow absorption lines which are typical of normal stellar populations ( e.g. beals 1940 ) . the class are named after wolf & rayet ( 1867 ) who identified three stars in cygnus with such broad emission lines . it was immediately apparent that their spectra came in two flavours , subsequently identified as those with strong lines of helium and nitrogen ( wn subtypes ) and those with strong helium , carbon , and oxygen ( wc and wo subtypes ) . gamov ( 1943 ) first suggested that the anomalous composition of wr stars was the result of nuclear processed material being visible on their surfaces , although this was not universally established until the final decade of the 20th century ( lamers et al . 1991 ) . specifically , wn and wc stars show the products of the cno cycle ( h - burning ) and the triple-@xmath2 ( he - burning ) , respectively . in reality , there is a continuity of physical and chemical properties between o supergiants and wn subtypes . typically , wr stars have masses of 1025 @xmath1 , and are descended from o - type stars . they spend @xmath010% of their @xmath05myr lifetime as wr stars ( meynet & maeder 2005 ) . at solar metallicity the minimum initial mass for a star to become a wr star is @xmath025 @xmath1 . this corresponds closely to the humphreys & davidson ( 1979 ) limit for red supergiants ( rsg ) , according to a comparison between the current temperature calibration of rsg and stellar models that allow for mass - loss and rotation ( e.g. levesque et al . 2005 ) . consequently , some single wr stars are post - red supergiants within a fairly limited mass range of probably 2530@xmath1 . evolution proceeds via an intermediate luminous blue variable ( lbv ) phase above 30@xmath1 . for close binaries , the critical mass for production of a wr star has no such robust lower limit , since roche lobe overflow or common envelope evolution could produce a wr star instead of an extended rsg phase . the strong , broad emission lines seen in spectra of wr stars are due to their powerful stellar winds . the wind is sufficiently dense that an optical depth of unity in the continuum arises in the outflowing material . the spectral features are formed far out in the wind and are seen primarily in emission . the line and continuum formation regions are geometrically extended compared to the stellar radii and their physical depths are highly wavelength dependent . the unique spectroscopic signature of wr stars has permitted their detection individually in local group galaxies ( e.g. massey & johnson 1998 ; massey 2003 ) , collectively within knots of local star forming galaxies ( e.g. hadfield & crowther 2006 ) , and as significant contributors to the average rest - frame uv spectrum of lyman break galaxies ( shapley et al . 2003 ) . the present review focuses on observational properties of classical wolf - rayet stars in the milky way and beyond , plus physical and chemical properties determined from spectroscopic analysis , plus comparisons with interior evolutionary models , and provides revisions to the topic with respect to the excellent abbott & conti ( 1987 ) review . low mass ( @xmath3 ) central stars of planetary nebulae displaying a wolf - rayet spectroscopic appearance ( denoted [ wr ] ) are not considered . nevertheless , analysis tools discussed here are common to both types of star ( e.g. crowther et al . visual spectral classification of wr stars is based on emission line strengths and line ratios following smith ( 1968a ) . wn spectral subtypes follow a scheme involving line ratios of niii - v and hei - ii , ranging from wn2 to wn5 for ` early wn ' ( wne ) stars , and wn7 to wn9 for ` late wn ' ( wnl ) stars , with wn6 stars either early or late - type . a h suffix may be used to indicate the presence of emission lines due to hydrogen ( smith , shara & moffat 1996 ) . complications arise for wn stars with intrinsically weak emission lines . for example , wr24 ( wn6 ha ) has a heii @xmath44686 emission equivalent width that is an order of magnitude smaller than those in some other wn6 stars ; the ` ha ' nomenclature indicates that hydrogen is seen both in absorption and emission . from a standard spectroscopic viewpoint , such stars possess mid to late wn spectral classifications . however , their appearance is rather more reminiscent of of stars than classic wn stars , since there exists a continuity of properties between normal o stars and late - type wn stars . these stars are widely believed to be massive o stars with relatively strong stellar winds at a rather early evolutionary stage . they are believed not to represent the more mature , classic he - burning wn stars . smith , crowther & prinja ( 1994 ) extended the wn sequence to very late wn1011 subtypes in order to include a group of emission line stars originally classified as ofpe / wn9 ( bohannan & walborn 1989 ) . wn11 subtypes closely resemble extreme early - type b supergiants except for the presence of heii @xmath44686 emission . a quantitative comparison of optical line strengths in of and wnl stars is presented in figure 8 of bohannan & crowther ( 1999 ) . r127 ( wn11 ) in the large magellanic cloud ( lmc ) was later identified as a lbv ( stahl et al . 1983 ) , whilst a famous galactic lbv , ag car exhibited a wn11-type spectrum at visual minimum ( walborn 1990 ; smith et al . 1994 ) . various multi - dimensional classification systems have been proposed for wn stars ; they generally involve line strengths or widths , such that strong / broad lined stars have been labelled wn - b ( hiltner & schild 1966 ) , wn - s ( hamann , koesterke & wessolowski 1993 ) or wnb ( smith , shara & moffat 1996 ) . of these , none have generally been adopted . from a physical perspective , strong- and weak - lined wn stars do form useful sub - divisions . therefore we shall define weak ( -w ) and strong ( -s ) wn stars as those with heii @xmath45412 equivalent widths smaller than or larger than 40 . an obvious limitation of such an approach is that intrinsically strong - lined wn stars would be diluted by binary companions or nearby stars in spatially crowded regions and so might not be identified as such . wne - w stars tend to exhibit triangular line profiles rather than the more typical gaussian lines of wne - s stars ( marchenko et al . 2004 ) , since one observes material much closer to the stellar core that is being strongly accelerated . wc spectral subtypes depend on the line ratios of ciii and civ lines along with the appearance of o iii - v , spanning wc4 to wc9 subtypes , for which wc46 stars are ` early ' ( wce ) and wc79 are ` late ' ( wcl ) . rare , oxygen - rich wo stars form an extension of the wce sequence , exhibiting strong ovi @xmath53811 - 34 emission ( kingsburgh , barlow & storey 1995 ) . the most recent scheme involves wo1 to wo4 subtypes depending on the relative strength of ov - vi and c iv emission lines ( crowther , de marco & barlow 1998 ) . finally , civ @xmath45801 - 12 appears unusually strong in an otherwise normal wn star in a few cases , leading to an intermediate wn / c classification ( conti & massey 1989 ) . wn / c stars are indeed considered to be at an intermediate evolutionary phase between the wn and wc stages . representative examples of wn and wc stars are presented in figure [ wnc - montage ] . various x - ray to mid - ir spectroscopic datasets of galactic wolf - rayet stars are presented in table [ atlas ] , including extreme ultraviolet synthetic spectra from model atmospheres ( smith , norris & crowther 2002 ; hamann & grfener 2004 ) . wr stars can not be distinguished from normal hot stars using ubv photometry . broad - band visual measurements overestimate the true continuum level in extreme cases by up to 1 magnitude , or more typically 0.5 mag for single early - type wr stars due to their strong emission - line spectra . consequently , westerlund ( 1966 ) introduced narrow - band @xmath6 filters that were specifically designed to minimize the effect of wr emission lines ( although their effect can not be entirely eliminated ) . these passbands were later refined by smith ( 1968b ) and by massey ( 1984 ) , such that most photometry of wr stars has used the @xmath7 filter system , which is compared to johnson ubv filters in fig . [ wnc - montage ] . as with normal stars , @xmath8 photometry permits a determination of the interstellar extinction , @xmath9 . let us adopt a typical ratio of total , @xmath10 to selective , @xmath11 extinction , @xmath12 . following turner ( 1982 ) , the broad - band and narrow - band optical indices for wr stars are then related by : @xmath13 a direct determination of wr distances via stellar parallax is only possible for @xmath14 vel ( wc8+o ) using _ hipparcos _ , and even that remains controversial ( millour et al . otherwise , cluster or association membership is used to provide an approximate absolute magnitude - spectral type calibration for milky way wr stars . the situation is much better for wr stars in the magellanic clouds , although not all subtypes are represented . typical absolute magnitudes range from @xmath15 = 3 mag at earlier subtypes to 6 mag for late subtypes , or exceptionally 7 mag for hydrogen - rich wn stars . the typical spread is @xmath160.5 mag at individual subtypes . conti ( 1976 ) first proposed that a massive o star may lose a significant amount of mass via stellar winds , revealing first the h - burning products at its surface , and subsequently the he - burning products . these evolutionary stages are spectroscopically identified with the wn and wc types . this general picture has since become known as the ` conti scenario ' . such stars should be over - luminous for their mass , in accord with observations of wr stars in binary systems . massey ( 2003 ) provides a more general overview of massive stars within local group galaxies . wolf - rayet stars are located in or close to massive star forming regions within the galactic disk . a catalogue is provided" +"at the next generation of linear @xmath3 colliders the experimental precision of @xmath4 will exceed current standards by one order of magnitude . to ensure the success and strengthen the physics case of such a machine , a precise understanding of the theoretical predictions is of paramount importance . in particular bhabha scattering is important for luminosity monitoring , and hence a vital ingredient of almost every measurement . recent studies @xcite have focused on the calculation of the two - loop qed matrix element to massless bhabha scattering , i.e. the photon and the electron are treated as massless particles . to further increase the theoretical understanding of the bhabha cross section and to control collinear singularities we consider the electron to be a massive particle . at the energy scale foreseen for the next generation of @xmath3 colliders , electroweak corrections can not be ignored . while it is certainly a good approximation to consider small angle bhabha scattering to be highly dominated by pure qed corrections , this does not apply to the whole phase space . taking the electron mass into account in the genuine qed calculation will open the door to more involved multi - scale electroweak higher order calculations . here we are presenting the first progress made towards a complete two - loop calculation . at the born level the bhabha scattering process @xmath5 is characterized through an @xmath6- and a @xmath7-channel photon exchange diagram . one - loop radiative corrections constitute the two - loop calculation in the form of @xmath8 contributions to the cross section . to generate the diagrams in the form of a postscript file , as well as in symbolic notation for further algebraic manipulation , we use diana , the diagram analyser by tentyukov and fleischer @xcite . we choose to work in the feynman gauge gauge . ] . this has the advantage that tadpole contributions are energy independent and hence do not contribute to the physical cross section . self - energy , vertex and box diagrams make their appearance in equal parts as @xmath6- and @xmath7-channel diagrams . the following ten diagrams have been calculated . + we decompose the full one - loop matrix element into 12 amplitudes , that is in fact into 24 amplitudes , counting the @xmath6- and @xmath7-channel contributions separately . for compactness we omit the spinors . the richness in structure is indeed only required for the box contributions . the self - energies and vertices contribute to only two of the structures below . we would like to remark at this point that the products of dirac @xmath9 matrices @xmath10 to @xmath11 can in principle be simplified at the cost of artificially introducing @xmath12 , which we decided to avoid altogether . @xmath13 \ , f_1 \nonumber \\ { \cal m}_2 & = \left [ \ , \ps_4 \ , \times \ , 1 \ , \right ] \ , f_2 \nonumber \\ { \cal m}_3 & = \left [ \ , 1 \ , \times \ , \ps_2 \ , \right ] \ , f_3 \nonumber \\ { \cal m}_4 & = \left [ \ , \ps_4 \ , \times \ , \ps_2 \ , \right ] \ , f_4 \nonumber \\ { \cal m}_5 & = \left [ \ , \gamma_{\mu } \ , \times \ , \gamma_{\mu } \ , \right ] \ , f_5 \nonumber \\ { \cal m}_6 & = \left [ \ , \gamma_{\mu } \ , \ps_4 \ , \times \ , \gamma_{\mu } \ , \right ] \ , f_6 \nonumber \\ { \cal m}_7 & = \left [ \ , \gamma_{\mu } \ , \times \ , \gamma_{\mu } \ , \ps_2 \ , \right ] \ , f_7 \nonumber \\ { \cal m}_8 & = \left [ \ , \gamma_{\mu } \ , \gamma_{\nu } \ , \times \ , \gamma_{\nu}\ , \gamma_{\mu } \ , \right ] \ , f_8 \nonumber \\ { \cal m}_9 & = \left [ \ , \gamma_{\mu } \ , \gamma_{\nu } \ , \ps_4 \ , \times \ , \gamma_{\nu } \ , \gamma_{\mu } \ , \right ] \ , f_9 \nonumber \\ { \cal m}_{10 } & = \left [ \ , \gamma_{\mu } \ , \gamma_{\nu } \ , \times \ , \gamma_{\nu } \ , \gamma_{\mu } \ , \ps_2 \ , \right ] \ , f_{10 } \nonumber \\ { \cal m}_{11 } & = \left [ \ , \gamma_{\mu } \ , \gamma_{\nu } \ , \ps_4 \ , \times \ , \gamma_{\nu } \ , \gamma_{\mu } \ , \ps_2 \ , \right ] \ , f_{11 } \nonumber \\ { \cal m}_{12 } & = \left [ \ , \gamma_{\mu } \ , \gamma_{\nu } \ , \gamma_{\rho } \ , \times \ , \gamma_{\rho } \ , \gamma_{\nu } \ , \gamma_{\mu } \ , \right ] \ , f_{12 } \end{aligned}\ ] ] the entire calculation is parametrized through the corresponding 12 form factors for every diagram . symmetries allow to further compress the calculation . this is in particular valuable for the box contributions , which are the most complex part of the calculation . first of all we found internal symmetries relating various form factors of one given box diagram to other form factors of the same diagram : @xmath14 the contribution in brackets is only present for so - called dotted - box diagrams , which will be presented in the next section . + actually this symmetry somehow reflects the non - minimal choice of amplitude - basis we made . further conventional crossing symmetry can be applied to relate @xmath6- and @xmath7- channel diagrams . moreover we found one additional symmetry relating crossed box ( cb ) diagrams to direct box ( db ) diagrams in the same channel : @xmath15 and interchanging @xmath16 successively . the space - time dimension @xmath17 reflects our choice of dimensional regularization . it is sufficient to calculate one box diagram and obtain the form factors of the remaining three box diagrams via those symmetry relations . to reduce the various one - loop integrals we rely upon two different techniques . first we follow the prescription of passarino and veltman @xcite with the subtle difference from the original work that the tensor decomposition is performed with respect to inner momenta . favourably we use the method first proposed by davydychev @xcite to reduce one - loop tensor integrals into scalar integrals and changing the space - time dimension _ d _ , and later extended to multi - loop tensor integrals by tarasov @xcite . let @xmath18 be a one - loop @xmath19-point vector ( tensor ) integral , @xmath20 the loop - momentum , @xmath21 the propagator corresponding to the @xmath22-th line of the diagram appearing in the @xmath23-th power , with the special case @xmath24 . those integrals can be written as @xmath25 } \\ i_{n}^{\mu\ , \nu } & = & \int ^{d } k_{\mu } \ , k_{\nu } \ , \prod_{r=1}^{n } \ , \frac{1}{c_r^{\nu_r } } \\ \nonumber & & \hspace{-1 cm } = - \sum_{i , j=1}^{n-1 } \ , p_i^{\mu}\ , p_j^{\nu } \ , ( 1 + \delta_{i\ , j } ) \ , \ , i_{n , ij}^{[d+]^2 } -\frac{1}{2 } \ , g^{\mu \nu } \ , i_{n}^{[d+ ] } \ , , \end{aligned}\ ] ] where @xmath26 $ ] is an operator shifting the space - time dimension by two units and @xmath27 is the original scalar integral with one additional power in the @xmath28-th and @xmath29-th propagators . having reduced the tensor integrals to scalar integrals the generic space - time dimension @xmath30 needs to be re - established . for this we use the recurrence relations first proposed in @xcite , which are complementary to those obtained via integration by parts @xcite , and later simplified and extended to zero gram determinants in @xcite . let @xmath31 and the cayley determinant @xmath32 then the so - called signed minors @xmath33 are defined as the rows @xmath34 and columns @xmath35 erased from the cayley determinant @xmath36 .. ] making successive use of the following three recurrence relations leads to scalar master integrals @xmath37 and @xmath38 in @xmath39 dimensions : @xmath40 i^{(d)}_n \nonumber \\[2 mm ] { 0\choose 0}_n \nu_j { \bf j^+ } i_n^{(d)}&\ ! = & \!\ ! - \sum_{i , k \ , i\neq k}^n { 0j\choose 0k}_n \,\ , \nu_i \ , { \bf k^- } { \bf i^+}\ , i_n^{(d ) } + \nonumber \\ & & \hspace{-3 cm } \left [ \left ( 1 + \sum_{i=1}^n \nu_i - d \right ) { 0\choose j}_n \ ! - \sum_{k=1}^n { 0j\choose 0k}_n \ ! ( \nu_k-1 ) \right ] \ , i_n^{(d ) } \nonumber \\[2 mm ] & & \hspace{-2.5 cm } ( d-\sum_{i=1}^{n}\nu_i+1 ) \left ( \right)_n i^{(d+2)}_n = \nonumber \\ & & \hspace{-1 cm } \left [ { 0 \choose 0}_n - \sum_{k=1}^n { 0 \choose k}_n { \bf k^- } \right]i^{(d)}_n \ , , \end{aligned}\ ] ] the operators @xmath41 raising the power of the corresponding propagator by one unit , while @xmath42 reduces the power of the @xmath43-th propagator by one unit . for zero gram determinants @xmath44 , similar recurrence relations are needed and are available in @xcite . effectively a zero gram determinant reflects the kinematical boundaries of phase space where a given @xmath19-point function can be expressed through scalar integrals of lower rank . typical examples of such simplifications are @xmath45 & & \hspace{-4 cm } b_0(m_e^2;m_e^2,0 ) = \frac{1}{2 } \ , \frac { ( d-2)}{(d-3 ) } \frac{a_0(m_e^2)}{m_e^2 } \ , .\end{aligned}\ ] ] two - loop contributions to the bhabha matrix element can be classified according to the topological properties of the corresponding diagrams . in this section we focus on the contributions originating from the renormalization of the electron mass . to accommodate the renormalization contributions , every internal electron propagator in fig . [ fig:1loop ] has to be replaced by @xmath46 with @xmath47 the electron mass counter - term . from eq . ( [ eqn : massren ] ) we understand that we have to calculate all possible permutations of the diagrams in fig . [ fig:1loop ] with one of the loop - internal electron propagators squared . now , since the mass renormalization term @xmath48 contains 1/@xmath49 uv poles , the one - loop master integrals @xmath37 and @xmath38 are needed in @xmath50 to ensure that all finite terms are taken into account properly . the @xmath51-expansion of @xmath52 is pretty straightforward . the hypergeometric presentation of 1-loop scalar master integrals in arbitrary dimensions @xmath39 was given in @xcite . from these results the @xmath51-expansion can be obtained and will be presented in @xcite . the electron propagator appearing squared does not really impose further complications in the recurrence relations approach . for this part of the calculation we refrain from further pursuing the independent calculation based upon the passarino veltman reduction method . given the scope of this article we can not present the full analytical result here . to give an idea of the structure we present exclusively the form factors @xmath53 for the various @xmath6-channel topologies in the appendix . we use the following abbreviations @xmath54 in this article we have presented the complete one - loop originating contribution to the two - loop bhabha cross section . we decomposed the matrix element into 12 amplitudes and presented the result in the form of the corresponding form factors . mass renormalization lead to dotted diagrams , which we reduced to scalar integrals by making use of recurrence relations . two - loop factorizable form factors were presented . a.w . thanks the organizers for a very stimulating conference . 10 m. tentyukov and j. fleischer , comput . * 132 *" +"the study of simple lattice models has emerged as an effective way to understand nonequilibrium steady states and phase transitions @xcite . in particular , the simple exclusion process @xcite and the zero range process @xcite , owing to their simplicity and richness , have emerged as paradigms for nonequilibrium systems . when such processes are considered with periodic boundary conditions , a phase transition can occur either due to dynamical features such as particle jump rates @xcite , chipping and aggregation @xcite , or due to the presence of disorder on the lattice @xcite . on the other hand , the presence of open boundaries , where particles can be inserted and removed , is significant enough to lead to boundary - induced phase transitions @xcite . the phase diagram is well understood for the basic version of the asymmetric simple exclusion process with open boundaries . besides its analytic solutions @xcite , the underlying physical mechanism is also well understood in terms of the group velocity @xcite as well as the domain wall velocity and collective velocity @xcite . recently it was reported that some additional dynamical features such as evaporation and deposition @xcite or nonlocal hopping @xcite lead to new kinds of phases and phase transitions . in this paper , we study the phase transition in a generalized version of the one - dimensional symmetric simple exclusion process ( ssep ) with open boundaries where the additional feature of nonlocal hopping is included . by increasing the nonlocal hopping rate ( or equivalently decreasing the input rate of particles at the boundaries ) , the system undergoes a first order phase transition from a finite density ( fd ) phase into an empty road ( er ) phase with zero density via a clustered state at the transition . this is quite different from the dynamic instability transitions found in the totally asymmetric simple exclusion process ( tasep ) with nonlocal hopping studied previously @xcite . in the tasep variant , the particle clusters are stable and moving with a drift velocity depending on the nonlocal hopping rate in the most part of the fd phase . in our case , the clusters are stationary on average and stable only at the transition . they expand until they fill up the whole system in the fd phase and shrink away in the er phase where the whole system is empty except for finite - size clusters clinging to the boundaries . at the transition , the particle clusters are distributed over the system with a power - law gap ( intercluster distance ) distribution . the periodic - boundary ( pb ) version of our model was already investigated @xcite in terms of a mass transport process . there are similarities and also differences , compared to the open - boundary case . in the pb setup , the number of particles is conserved and plays the role of the external parameter . as the particle density decreases , one finds a continuous condensation ( phase separation ) transition from a homogeneous density state to a state with an infinite stretch of empty sites ( macroscopic mass at a site in the language of the mass transport model ) . the homogeneous density state is basically the same as the fd state in our open - boundary setup except near the boundaries . the same applies to the critical state . however , the condensed state includes the background particle clusters with the critical gap distribution over a finite fraction of the system besides the macroscopic gap , while the exponential gap distribution only near the boundaries ( vanishing fraction of the system ) is found in the er phase . based on the cluster dynamics analysis , we show that the particle density controls the stability of a cluster . clusters are stable only at a specific density against nonlocal hopping events , which determines the transition point . high - density clusters expand mainly by local hopping events , while low - density clusters shrink easily by nonlocal hopping events . we claim that two seemingly different transitions in both boundary setups are caused by the same mechanism based on the cluster stability . we will also argue that the difference in the nature of the condensed and er phase is simply due to the presence of possible exits for particles through the open boundaries . the conventional ssep has been well studied with both periodic and open boundary conditions @xcite . with periodic or symmetric open boundary setups , the ssep is an equilibrium system with no phase transitions . although our dynamical rule in the bulk and at the boundaries does not break the left - right symmetry present in the ssep , the extra feature of nonlocal hopping drives the system out of equilibrium and leads to a significant change in the steady - state nature for both boundary setups . as a result , contrary to the conventional ssep with open boundaries , our modified version exhibits an abrupt nonequilibrium transition on varying the input rates at boundaries and the nonlocal hopping rate . this paper is organized as follows : in sec . [ phase diagram ] , we describe our model and present the numerical results for the phase diagram , clustering , gap distributions , density profile , and finite - size properties . in sec . [ cluster analysis ] , we develop a cluster dynamics analysis at the mean - field level . the cluster stability determines the transition line , which is compared with numerical results . finally , we discuss the physical origin of this abrupt transition as well as the difference in the periodic version . we conclude the paper in sec . [ conclusion ] with a brief summary . phase diagram . the symbols with error bars are obtained from our numerical data and the dashed line is estimated by the cluster mean - field prediction . to guide the eyes , a solid line is drawn through the data points . ] at the transition @xmath0 . the solid line is drawn with @xmath1 . ] consider a chain of length @xmath2 with sites , @xmath3 , that can either be empty or occupied by a particle with hard core repulsion , thus the occupancy @xmath4 . the chain is open and in contact with two reservoirs at @xmath5 and @xmath6 , respectively . the evolution rule for our process is as follows : select a site randomly including two reservoirs ( @xmath7 ) . if the site @xmath8 is occupied by a particle ( or one of the reservoirs ) , we attempt to move the particle . the move is successful only if the target site is unoccupied . the particle either tries to move to the nearest - neighboring site to the left(right ) with probability @xmath9 ( local hopping ) , or it tries to jump to the unoccupied site directly behind the nearest occupied site in the left(right ) direction with probability @xmath10 respectively ( nonlocal hopping ) ; see fig . [ dynamics ] . in case the chain is completely empty in the chosen direction , the particle jumps all the way into the reservoir . if one of the reservoir sites , @xmath11 , is selected , a particle tries to jump on the nearest - neighboring site ( @xmath12 ) with probability @xmath13 . nonlocal hopping events from the reservoirs are not allowed in our setup . the particles at the left and right edge of the chain leave the system with probability @xmath14 . figure [ phase ] shows the phase diagram obtained from our monte carlo simulations with road lengths up to @xmath15 as well as the cluster mean - field ( mf ) prediction which will be discussed in sec . [ cluster analysis ] . at @xmath16 , the process reduces to the conventional ssep where the stationary state is well known to be the reservoir - controlled uniform phase which we shall call the finite density ( fd ) phase . here , the bulk ( road ) density @xmath17 is known exactly as @xmath18 . the fd phase extends into @xmath19 for all @xmath20 with @xmath17 decreasing slowly with @xmath21 . for strong nonlocal hopping ( large @xmath21 ) , the stationary state changes into the empty road ( er ) phase with @xmath22 with finite - size _ mother _ clusters clinging to reservoirs . the phase transition from the fd phase into the er phase turns out to be always discontinuous with a jump of @xmath23 at the transition @xmath0 ( fig . [ jump ] ) . this implies that this instability transition is caused by competition of the bulk density against the nonlocal hopping rate . the boundary parameters such as the input rate @xmath20 only play an implicit role in this transition via determining the bulk density . this suggests that our open - boundary version should be very similar , if not identical , to the periodic - boundary version which is controlled directly by the bulk density and the nonlocal hopping rate . in fact , the phase boundary is known exactly for the periodic - boundary version as @xmath24 @xcite , which is also likely to determine the phase boundary in our open - boundary setup . our numerical results strongly support this . however , it is not trivial to find the bulk density @xmath17 as a function of @xmath20 and @xmath21 . we estimate this at the mean - field level in sec . [ cluster analysis ] and the corresponding phase boundary is shown in fig . [ phase ] , which agrees reasonably well with numerical results . versus @xmath21 at @xmath25 for various system sizes up to @xmath15 . ] for finding @xmath26 particles on the road at @xmath25 for various @xmath27 ( from right to left ) at @xmath28 . the fd - er transition occurs at @xmath29 . ] at @xmath25 for various system sizes up to @xmath15 . the crossing points converge to the point at @xmath30 and @xmath31 . ] to establish the phase diagram accurately , we measure various quantities in the steady state such as the particle density @xmath32 with @xmath33 , the density fluctuations @xmath34 , and the binder cumulant @xmath35 . in fig . [ density ] , the bulk density @xmath17 is plotted against @xmath21 at @xmath25 . the systematic shift in the data with increasing size clearly indicates that , in the infinite - size limit , there will be a discontinuous jump in @xmath17 at @xmath0 . figure [ probden ] shows the evolution of the probability distribution @xmath36 for finding @xmath37 particles on the road across the transition . at the transition estimated as @xmath29 , we see an abrupt change into a broad distribution , which is again a signature of a discontinuous transition . the instability threshold @xmath38 can be accurately estimated by the crossing points of the binder cumulant @xmath39 . [ binder ] shows a nice convergence of the crossing points to the transition point @xmath30 . the binder cumulant @xmath39 takes a value of @xmath40 in the fd phase and @xmath41 in the er phase . at the transition , @xmath31 . note that the distributions in the er phase and at the transition are slightly different from those for the tasep variant studied in @xcite . we also observe that the density fluctuation @xmath42 becomes maximum at the transition as expected ( not shown here ) . all other data for various values of @xmath20 show a similar behavior to the @xmath25 case . numerical data for the phase boundary and the density jump are shown in figs . [ phase ] and [ jump ] . for the gap size @xmath43 on" +"quantum key distribution ( qkd ) protocols @xcite allow two distant parties , traditionally called alice and bob , to produce a shared random bit string consisting of 0 s and 1 s known only to them , which can be used as a key to encrypt and decrypt messages . based on fundamental principles such as the quantum no - cloning principle @xcite , qkd provides an unconditionally secure way to distribute random keys through insecure channels . while the first qkd scheme to be proposed , the bennett brassard ( bb84 ) protocol @xcite was a prepare - and - measure protocol , which used separable states , a connection between nonlocality @xcite and security was first suggested by the ekert protocol @xcite . the basic intuition here is that eve s attack causes a reduction in the correlation between legitimate parties , which is now understood as due to the monogamy of nonlocality in non - signaling theories @xcite . it is also known that nonlocality helps security not only in the traditional qkd scenario ( where eve attacks the channel ) but even in the more stringent device - independent ( di ) scenario , where neither the prepared initial states nor the devices are trusted . security here must be guaranteed simply via certain statistical checks typically sufficiently high violation of a bell inequality and without requiring a detailed characterization of devices @xcite . the nonlocality , and hence entanglement , considered above is _ inter_-particle entanglement , and the bell - inequality violating property ( i.e. , nonlocality ) pertains to the correlations obtained by spatially separated measurements by a sender ( alice ) and receiver ( bob ) . a different kind of entanglement is that between two degrees of freedom of the _ same _ particle , i.e. , intra - particle entanglement . this has been discussed by basu et al . @xcite in the context of a mach zehnder type interferometric set - up for demonstrating the violation of non - contextuality . an experiment using single neutrons was performed by hasegawa et al . @xcite . here , for the first time , we propose the use of the resource of intra - particle entanglement for qkd . by its nature , bell tests with intra - particle entanglement must be local . interestingly , such local bell tests have also been proposed in the case of bipartite systems for self - testing schemes employed to certify the state preparation process or the source of quantum states @xcite . our method also evokes a comparison with one - sided diqkd , in which the alice s devices are untrusted , but bob s are trusted @xcite , and where the statistical check is based on steering inequalities @xcite . an interesting counterpoint here is provided by the scenario of measurement di , in which , the devices for measurement , rather than that of the sender , is untrusted @xcite . relative to inter - particle entanglement , intra - particle entanglement is easy to generate . in the optical case , considered here , linear optics suffices . however , the local nature of intra - particle entanglement means that it is unsuitable for many quantum information processing tasks , like quantum teleportation or dense coding . it is an interesting question whether it is useful for cryptography , which we answer here in the affirmative . experimental demonstrations of various qkd protocols were discussed in @xcite . the practical violation of the bell s inequality in the cryptographic context was first considered in an experiment by jennewein et . @xcite , but no quantitative measure of security was derived from the observed violation . later , ling et . al . @xcite performed an experiment on entanglement - based qkd , in which the violation of bell - chsh inequality is used to also quantify the degree of security according to the criterion of refs . @xcite . in this work , our accent is mainly on introducing intra - particle entanglement between position ( path ) and polarization of photons , as a useful and easy - to - prepare resource for qkd , which presents novel elements when state preparation devices , in addition to the channel , are allowed to be insecure . we do so by showing that this qkd is secure against certain `` side channels '' that leak secret data ( such as alice s or bob s settings and outcome information ) , whereas the corresponding version of bb84 is not secure . clearly , there is no protection against an unrestrictedly powerful side channel . hence , we must assume that it can not be `` obvious '' . examples of typical side channels are timing information on the devices used , observations of power consumption or electromagnetic leaks bearing some heat signature of devices , or even a click sound produced by an optical element . we quantitatively find that the bell - inequality violating ( biv ) property of the path - polarization correlations can be used to guarantee security against an individual side - channel attack , which would render insecure qkd in the standard scenario . here an incoherent attack is one where eve attacks alice s particles along the transmission channel individually and measures them independently , without the involvement of any joint measurement . further details , such as coherent attacks , optical losses in the channel and universal composability are important future directions of this work , not considered here . an important aspect of using intra - particle - based entanglement , which we consider in more detail elsewhere @xcite , is to generalize the goldenberg vaidman protocol for orthogonal state- based cryptography @xcite , as a method to thwart general individual and coherent attacks @xcite on intra - particle entanglement - based qudits . this article is divided as follows : in sect . [ sec : ipe ] , we introduce the notion of intra - particle entanglement and present simple generation schemes for path - polarization intra - particle entanglement . in sect . [ sec : scha ] , we introduce an augmented key distribution protocol , suitable for a side - channel attack scenario , in which the sender alice must verify the quality of intra - particle entanglement just before transmitting the particle to the receiver bob , and after all optical elements used for the encoding process have been applied . in sect . [ sec : cheq ] , an individual attack scheme by eve is considered . her action is to depolarize the initial maximally entangled state into an intra - particle werner state , for which the entanglement and biv properties are readily known . the condition for secure extraction of secret bits is studied in comparison with the availability of these properties in the noisy state received by bob . in sect . [ sec : sidecha ] , we demonstrate the usefulness of intra - particle entanglement in protecting against a class of side - channel attacks that rely on flaws in certain optical elements such as quarter - wave plates ( qwps ) . finally , we present our conclusions in sect . [ sec : conclu ] . let us consider a photon that is initially polarized along the vertical direction ( its state denoted by @xmath0 ) . taking into consideration its path ( or position ) variables , the joint path - polarization state can be written as @xmath1 where the subscripts @xmath2 and @xmath3 refer to the path and the spin ( i.e. , polarization ) variables , respectively . a photon in the state @xmath4 with alice is incident on a beam splitter ( bs1 ) , whose transmission and reflection probabilities are @xmath5 and @xmath6 respectively , where @xmath7 ( cf . [ fig : bb84 ] ) . the reflected and transmitted states from bs1 are designated by @xmath8 and @xmath9 , respectively . here we recall that for any given lossless beam splitter , arguments using the unitarity condition show that for the particles incident on the beam splitter , the phase between the transmitted and the reflected states of the particle is @xmath10 . note that the beam splitter acts only on the path states without affecting the polarization state of the particles . the state of a particle emergent from bs1 can then be written as @xmath11 where @xmath12 our simplest basis , called @xmath13 , can be generated without using the beam splitter : @xmath14 a basis consisting of path - polarization entangled elements and which is mutually unbiased with @xmath13 , is @xmath15 , given below in eq . ( [ fourstate ] ) . it is produced by a linear optical set - up consisting of a beam splitter , a half - wave plate ( hwp ) , qwp and a phase shifter ( ps ) . for example , @xmath16 is produced from @xmath17 , by passing the particle through a bs1 , applying hwp on the transmitted wave packet @xmath18 , followed by the application of qwp on both arms . the hwp has the action @xmath19 which form the basis @xmath15 . the bases @xmath13 and @xmath15 are mutually unbiased in the sense that any element in either basis is an equal weight superposition ( apart from phase factors ) of elements of the other basis . to measure the state in an arbitrary separable basis @xmath20 , where @xmath21 and @xmath22 denote direction vectors of unit magnitude , one passes the particle through a beam splitter of suitable bias that de - rotates the position to the computational basis , and then uses two detectors , both set alike to measure the polarization along @xmath21 . for example , if @xmath23 , the beam splitter is chosen with coefficients of transmission and reflection being @xmath24 and @xmath25 , respectively . these coefficients can be set at the time of manufacture by the reflection coating applied to a beam splitter , and their ratio determines whether the element functions as a balanced ( 50:50 ) or unbalanced ( say 90:10 ) beam splitter . the particular measurements basis settings @xmath26 we require in order to evaluate the bell observable , are given in eq . ( [ eq : settings ] ) . in dimension @xmath27 , there are @xmath28 mutually unbiased bases ( mubs ) . another mutually unbiased entangled basis , denoted @xmath29 , in addition to sets @xmath13 and @xmath15 , is : @xmath30 two others ( separable state ) mubs , which may be denoted @xmath31 and @xmath32 , can be produced by applying @xmath33 and @xmath34 to the elements of basis @xmath13 ( [ fourstate0 ] ) , where @xmath35 , while @xmath36 . all these states are easy to prepare , requiring only linear optical elements . by suitably applying the linear optical elements of beam splitters , hwp , qwp and ps . bob may recombine the reflected and the transmitted channels at bs2 . finally , bob performs path and polarization measurements using the polarizing beam splitters pbs1 and pbs2.,width=377 ] alice s states are analyzed in bob s system , consisting of a beam splitter ( bs2 ) , followed by polarization analyzer in each output arm . for example , if she sends the state @xmath16 or @xmath37 , then after emerging from bs2 ( cf . [ fig : bb84 ] ) , the corresponding resulting states at bob s site are given by @xmath38 where @xmath39 , @xmath40 , @xmath41 and @xmath42 . in each of the five mubs , given by states ( [ fourstate0 ] ) , ( [ fourstate ] ) , ( [ fourstate1 ] ) , etc . , alice and bob designate basis" +"a fundamental result arising from cold dark matter ( cdm ) numerical simulations is that the density profiles of dm halos are universal in form across a wide range of mass scales from dwarf galaxies to clusters of galaxies ( navarro , frenk & white 1997 , hereafter nfw ) . internal to some scale radius @xmath6 , the dark matter profile assumes a power law form , @xmath7 . whilst there is some dispute amongst the simulators about the precise value of @xmath8 with values ranging from 1.0 to 1.5 , ( moore et al . 1998 , hereafter m98 ; ghigna et al . 2000 , power et al . 2002 ) , a clear measurement of @xmath8 in a range of objects would offer a powerful test of the cdm paradigm . the largest observational effort in this respect to date has been via dynamical studies of low surface brightness ( lsb ) and dwarf galaxies , suggesting softer ( @xmath9 ) dm cores than expected on the basis of the numerical simulations ( e.g. de blok & bosma 2002 , salucci & burkert 2000 ) , although the issue remains somewhat controversial ( e.g. van den bosch & swaters 2001 ) . similar tests have recently been extended to regular spiral ( jimenez , verde & oh 2002 ) and elliptical galaxies ( treu & koopmans 2002 ) . some observational constraints are available at the scale of massive clusters , from lensing ( e.g. tyson , kochanski & dellantonio 1998 ; williams et al . 1999 ; smith et al.2001 ) , x - ray analysis ( mahdavi & geller 2001 ) and dynamics of cd galaxies ( kelson et al . 2002 ) . since massive clusters probe a totally different scale and physical conditions than galaxies , it is crucial to understand their mass distribution to test the universality of the dm profiles . in this paper we present the first application of a new method to determine the luminous and dark mass distribution in the inner regions of massive clusters with giant arcs around a central bcg . the method combines lensing analysis with stellar kinematical measurements of the bcg . the two ingredients provide complementary information on the relevant scales ( @xmath10 kpc ) , allowing us to disentangle the luminous and dark components of the total mass distribution . we have chosen the cluster ms2137 - 23 as a first application of our method since it is an approximately round system , has an isolated bcg and a very well - studied arc system . fort et al . ( 1992 ) first pointed out the potential significance of the radial and tangential gravitational arcs as a means of constraining the mass distribution on @xmath11100 kpc scales , and mass models have been developed subsequently ( mellier et al . 1993 , hammer et al . 1997 ; hereafter m93 , h97 ) . the redshifts of the radial and tangential arcs were predicted to lie in the range 1@xmath122 ( m93 ) . a key issue in the earlier work is whether the radial arc is , in fact , a lensed feature . m93 and miralde - escud ( 1995 ; hereafter me95 ) also point out the importance of determining the stellar velocity dispersion profile of the bcg to weigh the stellar contribution to the mass . following the earlier suggestions , we present new observations of the cluster ms2137 - 23 with the keck ii telescope . we provide spectroscopic confirmation of the arcs and measure a velocity dispersion profile for the central bcg . the spectroscopic data are used together with archival hst images to constrain the luminous and dm distribution of the cluster . in the following , @xmath13 is the radial coordinate in 3-d space , while @xmath14 is the radial coordinate in 2-d projected space . we adopt h@xmath15=65 km s@xmath16,mpc@xmath16 , @xmath17 and @xmath18 for the cosmological parameters . we observed ms2137 - 23 using the echelle spectrograph and imager ( esi ; sheinis et al . 2002 ) on the w. m. keck - ii telescope for a total integration time of 4900s ( 2@xmath191800s + 1300s ) on 21 july , 2001 . the seeing was @xmath20 and the @xmath21 slit was oriented north - south to include the bcg , radial arc , and tangential arc ( figure 1 ) . the spectroscopic goals were two - fold : a determination of the redshift of the arcs and a measurement of the internal kinematics of the central galaxy . an iraf package was developed for the specific task of removing echelle distortions while preserving the 2-d shape of the spectrum essential for the latter goal ( easi2d , sand et al . 2002 , in preparation ) . the instrumental resolution of esi was measured from unblended sky lines to be 30@xmath227 km s@xmath16 . the velocity dispersion profile of the bcg ( figure 2 ) was measured using spectral templates based on several g - k giants observed with a @xmath23 slit . these were smoothed to match the instrumental resolution of the @xmath24 slit and redshifted to that of the bcg ( @xmath25=0.313 ) . analysis was restricted to a region around the g band by virtue of the high signal / noise and minimal effect of sky line residuals , using the gauss - hermite pixel - fitting software ( van der marel 1994 ) . the error bars shown in fig . 2 represent a combination of uncertainties arising from poisson noise and systematics , the latter determined from the scatter observed using different templates and continuum fits . the high spectral resolution of esi proved crucial in clinching the redshifts of the arcs as the emission lines are located in a crowded region of oh sky background . the two top panels in fig . [ fig : vdprof ] show the relevant portion of the esi spectra for the tangential and radial arcs , with the observed emission lines identified as the [ oii ] doublet at @xmath26 and @xmath27 respectively . the [ oii ] doublet is clearly resolved for the tangential arc and it is reasonable to suppose that the missing component for the radial arc is obscured by sky emission . no other lines are detected on either spectra , down to the blue cutoff of esi at @xmath28 . this makes it unlikely that the single line observed for the radial arc is any of the common lines such as h@xmath29 , h@xmath8 , [ oiii]4959 , 5007 , civ1549 , heii1640 , c[iii]1909 because bluer lines would be detected assuming typical flux ratios . the identification of the line with ly@xmath29 at @xmath30 is also unlikely given that the arc is detected in the hst f702w image ( see below ) . detailed modeling of ms2137 - 23 based on the image configurations predicted that the sources for the arcs would be at nearly the same redshift ( m93 , h97 ) . hst wfpc2 images of ms2137 - 23 ( go 5402 , pi : gioia ) , comprising 10 f702w exposures with a total integration time of 22.2ks , were used to measure the surface photometry of the bcg and to locate arc positions . the exposures were reduced in a standard way , using the iraf package drizzle ( fruchter & hook 2002 ) . the circularized surface brightness profile ( in agreement with h97 ) was obtained using the iraf task ellipse and a fit performed as described in treu et al . ( 1998 , 2001a ) taking into account the hst point - spread function . the best fitting @xmath31 parameters are summarized in table 1 . to convert from f702w magnitudes to v magnitudes a k - color correction was calculated using the same method as treu et al . rest frame photometric quantities were corrected for galactic extinction using @xmath32 = 2.435e(b - v)=0.122 ( schlegel et al . 1998 ) . [ cols= "" < , > "" , ] table 1 : relevant spectro - photometric quantities we now combine the observed spectroscopic and photometric data to constrain the matter distribution in the central region of ms2137 - 23 . first we introduce a simple two - component spherical mass model comprising the stellar mass of the bcg and a dm halo ( sec . 3.1 ) . we then constrain the free parameters of the model using the position of the critical lines ( 3.2 ) and the velocity dispersion profile ( 3.3 ) . for the luminous component we used a jaffe ( 1983 ) @xmath33 mass density profile of total mass m@xmath34 , which reproduces well ( see below ) are virtually unchanged , while slightly larger values of m / l for the stellar component are obtained . ] the observed surface brightness profile ( with @xmath35 = 0.76@xmath36 ) . the dm halo is modeled as , @xmath37 representing a generalization of the cdm - motivated halos , with an inner slope @xmath8 ( nfw and m98 correspond to @xmath38 respectively ; @xmath39 is the critical density ) . we assume that the bcg lies at the center of the overall potential . for a given stellar mass - to - light ratio @xmath40/@xmath41 both @xmath42 and @xmath36 can be deduced from the surface photometry leaving 4 free parameters in our mass model : 1 ) @xmath40/@xmath41 ; 2 ) the inner slope of the dm profile @xmath8 ; 3 ) the dm density scale @xmath43 ; and 4 ) the dm scale radius @xmath6 . given our two - component spherical model , we adopted a simple lensing analysis using only the positions and redshifts of the radial and tangential arcs ( see bartelmann 1996 ) . the locations of the radial and tangential arcs can be estimated by calculating the position of the corresponding radial and tangential critical curves of the projected mass distribution . the jacobian matrix of the lens mapping has two eigenvalues , @xmath44 and @xmath45 , where @xmath46 and @xmath47 is a dimensionless function proportional to the mass inside projected dimensionless radius @xmath48 ( see , e. g. , bartelmann 1996 , schneider , ehlers , falco 1992 ) . tangential and radial critical curves occur when @xmath49 and @xmath50 , respectively . in practice , the position of the tangential arc constrains the _ total enclosed mass _ , while the position of the radial arc constrains its _ derivative_. a proper account of ellipticity is essential for detailed lens modeling where the shape , magnification , and morphology of multiple lensed images is being reproduced . me95 , however , considered several different simple mass models where only the position of the radial and tangential critical lines were being measured and found that the position of the two was affected very little by the introduction of ellipticity . therefore , we conclude that a spherical model is appropriate for our analysis . for every set of free parameters \{@xmath51 , @xmath8 , @xmath52 , @xmath6 } , we can compute the predicted position of the arcs , find the likelihood assuming gaussian distributions , and constrain the acceptable mass models . the largest radius at which the mass is probed is that corresponding to the location of the tangential arc ( 75.8 kpc ) . now @xmath6 is expected to be much greater than 100 kpc in cdm clusters ( bullock et al . 2001 ; see also wu 2000 ) . in this case , the location of the critical lines depends only marginally on @xmath6 and the combined luminous and dark density profile has only 3 free parameters ( we fix @xmath53 kpc in the following ) . fig . 3 shows the likelihood contours ( 68% , 95% and 99% )" +"the phases of quantum chromodynamics ( qcd ) at nonzero temperature and density are a subject of continuing interest . while numerical simulations on the lattice can be of use at nonzero temperature when the quark density is small , standard monte carlo techniques are not of use in cold , dense quark matter . one expansion which is of utility is to expand in the limit of a large number of colors @xcite . for cold , dense quark matter quarks in the fundamental representation , coupled to an @xmath12 gauge theory this gives a `` quarkyonic '' phase @xcite . keeping the quark chemical potential , @xmath2 , of order one as the number of color @xmath13 , the free energy for this phase is dominated by that of quarks . nonetheless , excitations near the fermi surface are confined , perhaps baryonic , whence the name . in this paper , we consider chiral symmetry breaking in quarkyonic matter . we consider a phenomenological model for confinement , taking the timelike component of the gluon propagator to be @xmath14 . this is valid in coulomb gauge , for a spatial momentum @xmath15 , and corresponds to a potential which rises linearly in coordinate space . such a propagator was originally suggested by gribov @xcite and zwanziger @xcite . to use such a propagator in cold , dense , quark matter , it is necessary to assume that gluons are insensitive to screening by quarks . for this to be true , the number of flavors , @xmath6 , must be @xmath16 , and the chemical potential must satisfy @xmath17 , where @xmath3 is the renormalization mass scale of qcd @xcite . chiral symmetry breaking in such a model has been studied by glozman and wagenbrunn @xcite and by guo and szczepaniak @xcite , for values of @xmath18 . we work in the extreme quarkyonic limit , @xmath19 , so that the effects of chiral symmetry breaking in vacuum can be ignored . it is possible for chiral symmetry breaking to occur at large @xmath2 , since we are , by assumption , in a confined regime . of course there is no guarantee that our results apply to qcd , where @xmath20 ; nevertheless , there is certainly some range of @xmath1 , @xmath6 , and @xmath2 , where it does . if applicable to qcd , our results are of interest to intermediate densities , where both conventional nuclear physics and perturbative treatments fail . notably , this may include the astrophysics of neutron stars . in vacuum , chiral symmetry breaking occurs through the pairing of a left handed quark with a right handed anti - quark , @xmath21 , and vice versa . this condensate is , of course , spatially uniform , so that the spontaneous breaking of chiral symmetry does not disturb the lorentz invariance of the vacuum . now consider the effects of a fermi sea , where there is a net excess of quarks over anti - quarks . the analogy of the usual condensate is illustrated in fig . [ qqbar ] . energetically , it costs essentially zero energy to excite a quark right at the edge of the fermi sea . on the other hand , it costs at least @xmath22 to pull an anti - quark out from deep in the dirac sea . ( remember that we assume that @xmath2 is very large . ) thus the usual condensate can not be formed spontaneously , and anti - quarks will not enter into our analysis henceforth . there are numerous features which are not captured by the illustration in fig . [ qqbar ] . we really should draw not one , but two fermi seas : one for left handed quarks , and one for right handed quarks . to avoid unnecessary duplication , instead we assume that the quark , denoted by a filled circle , is always left handed , and that the anti - quark , denoted by an open circle , is right handed . the quark and anti - quark are also assumed to have the same color , so that any condensate is @xmath23 , and survives in the limit of large @xmath1 . if the quark has momentum @xmath15 , then the anti - quark , formed by removing a quark with momentum @xmath15 from the dirac sea , has momentum @xmath24 . thus the quark anti - quark pair has no net momentum , and this condensate is spatially uniform , as in vacuum . [ 1.0 ] , while its momentum is @xmath25.,title=""fig : "" ] in the presence of a fermi sea , though , it is also possible for chiral symmetry to be broken by pairing , say , a ( left - handed ) quark and a ( right - handed ) quark hole . if both the quark and the quark hole are near the edge of the fermi surface , then it costs little energy to excite them , and the energetic penalty paid to excite an antiquark can be avoided . the natural analogy to the condensate in vacuum is illustrated in fig . [ exciton ] , pairing a quark with momentum @xmath15 , and a hole , formed by removing a quark with momentum @xmath15 from the fermi surface . the momentum of the hole is then @xmath24 , so the quark - hole pair has no net momentum , and is spatially constant . in condensed matter physics , an excitation as in fig . [ exciton ] is known as an exciton . naively , we might expect that excitons are suppressed , since the relative momentum between the particle and the hole , @xmath26 , is large . [ 1.0 ] .,title=""fig : "" ] however , this is not the only way for quarks and their holes to break the chiral symmetry . consider pairing a ( left handed ) quark , with momentum @xmath15 , and the hole formed by removing a ( right handed ) quark with the _ opposite _ momentum , @xmath24 , from the fermi sea . the quark hole then has the same momentum as the quark , @xmath27 , so that the resulting condensate is _ not _ uniform , and has a net momentum @xmath28 ; this is , it varies as @xmath29 , where @xmath30 is the direction along which the pair moves , @xmath31 . such condensates do not occur in vacuum , where they would imply the spontaneous breaking of rotational symmetry . in condensed matter physics , though , such non - uniform condensates are common , and known as density waves @xcite ; this is then a chiral density wave . note that the relative momentum between the quark and its hole is small , so such a condensate may be favored . [ 1.0 ] , @xmath32.,title=""fig : "" ] in this paper we show that in the gribov - zwanziger model , that the exciton pairing of fig . [ exciton ] is not generated , but that the chiral density wave of fig . [ cdw ] is . again , this is familiar from systems in condensed matter : typically excitons are only created dynamically as resonances , such as by the absorption of light , and usually do not condense . density waves are common , especially for systems in @xmath8 dimensions @xcite . we will investigate all dirac and flavor structures , and show which types are preferred . for completeness , we illustrate the pairing between two quarks which leads to color superconductivity in fig . [ clr_super ] . this is pairing between a quark at one edge of the fermi surface , with momentum @xmath27 , and another quark at the other edge , with momentum @xmath24 . since pairing is between two quarks , the condensate has no net momentum and is spatially uniform . for this reason , pairing can occur over the entire fermi surface , in a spatially symmetric state . so far , we have not emphasized the @xmath1 and @xmath6 dependence of pairing , which is not captured by the illustrations in figs . [ qqbar ] - [ clr_super ] . the pairing in figs . [ exciton ] and [ cdw ] is between a quark and a quark hole of the same color , so the condensate is @xmath23 . further , to the extent that @xmath33 , the condensate is rather insensitive to @xmath6 . in contrast , the diquark pairing of color superconductivity depends upon @xmath1 and @xmath6 in an essential way . fermi statistics greatly constrains the pairing between two quarks ( or two quark holes ) : it is always anti - symmetric in color , so there are strong relations between the spatial wavefunction , flavor , and chirality . for instance , in case of @xmath34 and @xmath35 , spatially symmetric condensates form by anti - symmetrizing in flavor ; this condensate pairs quarks of the same chirality together , and so does not break the chiral symmetry . on the other hand , for @xmath36 and @xmath35 , the preferred condensate does break the chiral symmetry , through color - flavor locking @xcite . for more than three colors , the gaps for color superconductivity depend sensitively upon which representation one assumes the quarks to lie in . if the quarks are in the fundamental representation , then since the pairing for color superconductivity is anti - symmetric in the colors of the two quarks , the gap is not a color singlet , and is suppressed at large @xmath1 . it is also possible , however , to generalize qcd by letting the quarks lie in the two - index , anti - symmetric representation of color @xcite . this limit is rather different from that which we consider in this paper . there are @xmath37 quarks in this limit , so that gluons are affected the quarks , and there is no quarkyonic phase . this is like taking the number of flavors , @xmath6 , to grow with @xmath1 . in such a limit color superconductivity is not suppressed at large @xmath1 . it is not clear which of these two limits is most like qcd , with three colors and three light flavors . we suggest that it is useful to consider all possible limits , and to see what qualitative conclusions might be tested in qcd . [ 1.0 ] .,title=""fig : "" ] if a channel for color superconductivity exists , then cooper pairs will form for arbitrarily weak coupling . thus color superconductivity is always the dominant pairing mechanism at asymptotically large chemical potential . the essential question is then , how large does the chemical potential have to be for color superconductivity to win out over other pairing mechanisms , such as chiral density waves ? that chiral density waves @xcite dominate at large @xmath1 was first demonstrated by deryagin , grigoriev , and rubakov @xcite . using a perturbative gluon propagator , @xmath38 in momentum space , they find that chiral density waves form , with a condensate @xmath39 in magnitude , where @xmath40 is the qcd fine structure constant , measured at a scale @xmath41 . implicitly , the computation assumes that dense quarks form a fermi liquid , so that pairing is from quarks ( and holes ) within @xmath42 of the edge of the fermi sea . in contrast , quarkyonic matter is not a fermi liquid because of confinement of quarks . low energy excitations , within @xmath43 of the edge of the fermi sea , interact not through the perturbative gluon propagator , but through the gribov - zwanziger form , @xmath0 . a chiral density wave forms , with the" +"quantum electrodynamics ( qed ) is the only quantum field theory which can be successfully applied to a broad range of effects ( bound states , scattering , decay ) and energies from microwave radiation to high energies in the gev range and deliver us various accurate predictions for measurable quantities with an uncertainty reaching the ppt level . qed of photons and leptons is an absolutely correct theory in a sense that its lagrangian is well defined and in principle there is no problem for performing any calculations . however , that is not sufficient since exact calculations are strongly limited by increasing difficulties in the calculation of higher - order effects and we always have to deal with a finite number of terms in the perturbative expansion . a question therefore arises how to estimate terms , which are too complicated to be calculated and sometimes that is in part art . however , qed is in some way incomplete since electromagnetic interactions may involve hadrons and strong interactions which can not be calculated _ ab initio_. the weak interactions may also be involved , but usually it is not a problem to find related contributions . however , there is a basic theoretical problem while performing comparison to experiment . theory is not in position to predict any numbers . what theory can only do is to express some measurable quantity in terms of others . in particular , to produce any quantitative prediction within bound state qed , we need to be first able to determine with a proper accuracy values of basic fundamental constants ( the rydberg constant @xmath0 , the fine structure constant @xmath1 as well as different masses and magnetic moments ) and auxiliary parameters ( such as the proton charge radius ) due to the hadronic sector , which are necessary input data for bound state qed calculations . however , there is no way to solve the bound state problem in general . the application of qed to the bound state forms a field called _ bound state qed _ , which experiences its own difficulties , additionally to qed problems for free particles . bound state qed is quite attractive as a training field to solve the bound state problem in quantum theory . it may be helpful for few - nucleon nuclei and for hadronic particles . in particular , there is a similarity in physics of positronium and quark - antiquark systems ( mesons ) . the difficulties of precision qed calculations for free particles are mainly due to an increasing number ( up to one thousand ) of complicated diagrams ( the four - loop level ) . the bound state qed theory deals with much simpler diagrams , however , the charged particles are bound there rather than free , and thus the coulomb exchange may be not a small effect . a detailed review on qed calculations for light atoms can be found in @xcite . the free qed involves only one small parameter @xmath1 , while the bound state qed theory needs at least three and all three expansions are not quite good@xcite . indeed , we still have to deal with @xmath1 , the power of which indicates the number of qed loops involved . the expansion is asymptotical but that is not important since the bound state calculations mainly need one - loop and two - loop contributions , with three - loop effects being important rather seldom . the coulomb strength @xmath2 appears because of binding effects and the parameters @xmath1 and @xmath2 behave in a quite different way . there is a number of contributions where we need to sum over an infinite number of coulomb exchanges ( e.g. the bethe logarithm ) . importance of all the exchanges assumes their essentially non - relativistic behaviour and still allows a @xmath2 expansion , which can not be avoided since calculations exact in @xmath2 are possible for a few contributions only . however , that is not a well behaving expansion , because the limit @xmath3 is related to an unbound two - body system and thus leads to a non - analytic behaviour of perturbative expressions . the non - analyticity in coulomb systems is usually accompanied with numerous logarithmic factors . for @xmath4 ( hydrogen , muonium , positronium ) one can find : the corrections known up to now may include up to cube of this logarithm , @xmath6 ( for the lamb shift ) , and up to logarithm squared for hyperfine structure and positronium physics@xcite . for several reasons the non - logarithmic contributions also involve big coefficients@xcite . a bound state problem supposes that we deal with an atom consisting of an orbiting particle(s ) and an attractor ( nucleus ) and that involves one more parameter , a ratio @xmath7 of masses of the orbiting particle ( mainly an electron ) and the nucleus which for conventional atoms is @xmath8 , for muonium is @xmath9 and for positronium is @xmath10 . the behaviour of the expansion in @xmath7 is not good since the limit @xmath11 is related to a kind of bound neutrino "" . the non - analytic behaviour shows itself in logarithmic terms and , e.g. , for muonium @xmath12 . some more parameters are involved due to nuclear effects , such as , e.g. , a ratio of the bohr radius to the nuclear radius . thus , the bound state qed theory involves a rather rich spectrum of problems and it deserves to be tested , particularly in spite of the lack of well established universal prescriptions appropriate for the two - body bound state problem in general . there are two basic problems of the precision bound state qed theory : lamb shift and hyperfine structure . the lamb shift calculations mainly need an external field approximation , while recoil corrections are less important and only the simplest of them are involved . in contrast , calculations of the hyperfine interval are crucially affected by the recoil effects , while some external field effects ( e.g. , the higher - order two - loop corrections ) are relatively less important . most of interest to positronium properties is due to recoil effects which are crucial since @xmath10 . for this reason we consider here in more detail studies of the hyperfine structure in light atoms . magnetic effects are relativistic effects and thus , in contrast to the coulomb interaction responsible for the lamb shift , the higher momentum transfers and shorter distances are more important . at shorter distances the recoil and nuclear - structure effects are enhanced . the nuclear effects in hydrogen and other light atoms dominate over the bound state qed@xcite . still there are three possible qed tests with the hyperfine structure in which the problem of nuclear effects can be avoided . a comparison of the @xmath13 and @xmath14 hyperfine intervals that offers a specific difference@xcite @xmath15 which is immune to leading effects of the nuclear structure . a comparison of conventional and muonic atoms for the same nucleus . a study of a pure leptonic atomic system such as muonium and positronium determination of the @xmath14 hyperfine interval in muonic hydrogen is in part the goal of an psi experiment@xcite which is now in progress . the hfs interval in the @xmath13 and @xmath14 states was successfully studied for several light atoms . the more complicated measurement is related to the metastable @xmath14 state@xcite . @xmath16 theory is compared to experiment in fig . [ f : d21 ] . the theory of @xmath16 for several atoms is summarized in table [ t : d21 ] . the dominant uncertainty of qed theory is due to higher - order one - loop and two - loop corrections in order @xmath17 and @xmath18 and recoil corrections in order @xmath19 ( in units of the @xmath13 hfs splitting ) . the higher - order nuclear effects also substantially contribute to the uncertainty . the muonium theory of the @xmath13 hyperfine interval is summarized in table [ t : mu ] . the dominant uncertainty of qed theory@xcite is due to higher - order recoil corrections in order @xmath19 and @xmath20 which are also in part responsible for the uncertainty of @xmath16 ( see above ) . the other important part of the uncertainty is related to the determination of the leading term ( so - called fermi energy ) @xmath21 in terms of fundamental constants @xmath22 and @xmath1 and inaccuracy in their determination . as mentioned before , the recoil effects are better seen in positronium . below we consider the positronium spectrum and a comparison of theory to experiment . we find that the uncertainty in calculating all experimentally studied transitions is related to the same recoil contributions as for the muonium hfs interval . the recoil effects play a crucial role in a two - body bound problem showing how closely the bound system is to a real two - body system . however , the significance of positronium is not limited by the possibility to verify the theory of recoil corrections . since the corrections of interest are enhanced ( @xmath7 is not a suppressing factor any longer ) , the fractional accuracy for successful high - precision tests is now relatively low . as a result , in contrast to hydrogen , the interpretation of the measurements of the @xmath23 interval does not crucially involve knowledge of the rydberg constant with high accuracy . a study of the hyperfine interval does not require a value of the fine structure constant with high accuracy as it is in muonium . since @xmath10 , it is not necessary to determine either @xmath7 or @xmath24 in an additional experiment . in other words , positronium offers several high precision tests of bound state qed without determinations of fundamental constants with high accuracy . the hyperfine and recoil effects are enhanced and thus can be seen not only in a direct study of the hyperfine structure but also in the investigation of the gross or fine structure in contrast to hydrogen and muonium . thus , positronium offers a few transitions which can be studied with high accuracy ( see table [ t : pos ] ) . adding to that an opportunity of different experiments on positronium annihilation , we find a big variety of properties to be studied . it is not even necessary to mention that as a light pure leptonic atomic system , the positronium atom is free of hadronic effects . it is important that positronium is light because hadronic effects in leptonic systems involve a high momentum transfer . they can be seen in muonium and in the muon anomalous magnetic moment they are responsible for a dominant part of the theoretical uncertainty , while they are strongly suppressed for positronium and the anomalous magnetic moment of electron . since positronium is a very specific atom , the notation for positronium is slightly different from other two - body atoms . first , in two - body atoms , even in hydrogen and muonium , it is customary to keep the value of the nuclear charge @xmath25 in order to recognize exchange photons and photons of qed radiative effects and thus to trace the origin of different corrections . in positronium there is an interference between both kinds of photons because of annihilation diagrams and thus it is meaningless to keep @xmath25 . hydrogen and other two - body atoms are one - electron systems and one can use for them both small ( e.g. , @xmath13 ) and capital ( e.g. , @xmath26 ) letters to denote levels . the former are used for an electron , while the latter are for all electrons in an atom and that is indeed the same for single - electron" +"in recent years isospin dependent phenomena received much consideration because of their ability to reveal information on the asymmetry term of the nuclear equation of state ( eos ) . relying on the fact that in heavy systems in which the neutron density exceeds the proton density the asymmetry term is repulsive for neutrons and attractive for protons , theoretical models of heavy ion reactions predicted different neutron composition of the liquid and vapor phases @xcite . more important for studies on eos , the difference in chemical composition of the gas and liquid phases during a liquid - gas phase transition reflects the magnitude of the asymmetry term and its density dependence . thus , the seminal work of mueller and serot @xcite based on a relativistic mean - field model of nuclear matter with arbitrary proton fraction anticipated that is energetically more favorable for an unstable asymmetric nuclear matter to separate into a neutron rich low density phase and a neutron poor high density one . later on , the isospin dependent boltzmann - uehling - uhlenbeck transport model @xcite , different mean field approaches @xcite , the antisymmetrized molecular dynamics model @xcite , the stochastic mean field model @xcite , etc . reconfirm this isospin fractionation phenomenon in both infinite and finite systems . moreover , in order to offer a more realistic description of the dynamics of charged asymmetric nuclear matter ref . @xcite analyzes the effect of the long - range coulomb interaction reaching the conclusion that its effect is to diminish the isospin fractionation . trying to identify this process in experimental multifragmentation data , isoscaling techniques based on grandcanonical assumptions have been applied . the results obtained from reactions involving different combinations of @xmath2sn and @xmath3sn at 50 mev / nucleon bombarding energy @xcite , @xmath4sn+@xmath5ni central collisions at 35 mev / nucleon @xcite , multifragmentation reactions induced by high energy protons @xcite and @xmath6ni,@xmath6fe + @xmath6ni,@xmath6fe at 30 , 40 and 47 mev / nucleon @xcite proved the expected increase of neutron concentration in the gas phase with respect to the liquid phase . the aim of the present work is to investigate fragment average isospin distributions within a microcanonical multifragmentation model which includes in a realistic way the most important ingredients of the nuclear multifragmentation phenomenon and whose phase diagram was studied previously . the advantages of such a study are obvious . firstly , taking into account that decaying nuclei are small isolated systems , a rigorous statistical treatment requires a microcanonical framework and not an analytically tractable grandcanonical approach . secondly , with respect to dynamical models , statistical models have the advantage of dealing with precisely defined fragments . thus , this study is expected to offer a complementary understanding of the problem . the paper is organized as follows . section ii presents the results obtained within the microcanonical multifragmentation model ( mmm ) @xcite in three distinct cases : ( 200 , 82 ) with and without coulomb interaction and ( 50 , 23 ) with coulomb interaction . fragments average isospin distributions are investigated as a function of fragment charge in each situation . characteristic shapes of @xmath0 versus @xmath1 distributions are found in each zone of the phase diagram . interesting finite size effects are identified for low multiplicities . section iii investigates the dependence of the above distributions as a function of source isospin . to verify whether the observed signals survive the sequential evaporation stage , effects of the secondary decays are discussed in section iv . in order to establish a link with dynamical models predictions , interpretation of the gas and liquid phases with respect to the cluster size is performed in section v. conclusions are drawn in section vi . while methods to identify phase transitions in small non - extensive systems accumulate , more importance is given to the fact that by principle the most correct statistical approach to be used for exploding nuclei is the microcanonical one @xcite . in the present paper the mmm version @xcite of the microcanonical multifragmentation model @xcite is used . in this model fragments are placed in a spherical container defining the freeze - out volume . all configurations allowed by mass , charge , total energy , total momentum and total angular momentum conservation laws and not forbidden by geometrical constraints ( overlapping between fragments or with container s walls ) are spanned by a metropolis monte carlo trajectory in the configuration space . the key quantity of the model is the weight of each configuration which has a non - analytically tractable form and enters the expression of any physical observable . the break - up fragments relevant for thermodynamics may be excited highly enough to de - excite by sequential particle emission . if not explicitly mentioned otherwise , the present study focuses on the break - up stage of the reaction but for the sake of completeness a brief discussion of effects of secondary decays will be included . depending on whether fragments are assimilated with hard non - overlapping spheres ( i ) or normal nuclear density malleable objects ( ii ) , one may distinguish two freeze - out scenarios . even if for a given state of the statistically equilibrated source characterized by the mass , charge , excitation energy and freeze - out volume the two scenarios may lead to different results , the thermodynamics associated to the model is qualitatively the same . the ( ii ) freeze - out scenario has the important advantage of allowing the system to reach high densities being thus preferable when one aims to investigate the phase diagram . while realistic by their microcanonical foundation , statistical multifragmentation models may be criticized because of the too simplistic treatment of the freeze - out volume . indeed , it is hard to imagine that fragment production into vacuum takes place in a fixed size spherical box , but rather in a volume fluctuating from event to event and characterized by it average value . statistical models used the fixed volume hypotheses in order to diminish , presumably without significant consequences , the dimension of the configuration space . more recent works @xcite suggest to treat the multifragmenting nucleus in a modified microcanonical ensemble in which the volume is allowed to fluctuate and the microcanonical weight of a configuration @xmath7 is multiplied by @xmath8 ( where @xmath9 is the inverse temperature and @xmath10 is a pressure ) , the average value of the volume being determined by its lagrange multiplier @xmath11 . the fact that in the case of time dependent open systems the thermodynamical definition of volume is still an open problem is illustrated by the different concepts presently employed . thus , dynamical models define the freeze - out volume by the spatial extension of the system when fragments cease to interact with each other otherwise than by coulomb field , implying thus a minimum distance of 2 - 3 fm between them . a somehow similar image in the sense that volume does not act as an external constraint corresponds to the dynamical models which define the freeze - out volume with respect to the freeze - out time , a notion which assumes chemical equilibrium : fragments can still exchange nucleons but their multiplicity has to be time independent . maybe one of the most illustrative examples on what freeze - out volume may mean within dynamical models in contrast to the statistical ones , is given by the recent study of ref . @xcite . here authors show that freeze - out volume depends dramatically on freeze - out instant and fragment multiplicity . as the message of the present work relies on the thermodynamical characterization of the nuclear system , we stress that in the case of mmm the volume is even more than an un - physical fictitious container which obliges the _ pre - formed _ fragments not to separate , but dictates also their partition as volume enters the statistical weight of a configuration . apart the obvious explicit dependence , volume acts via the thermal kinetic energy defined as the difference between the total available energy ( input quantity ) and all other partial energies ( internal excitation , coulomb interaction and fragment formation @xmath12 ) . the phase diagram associated with mmm was studied in ref . @xcite and the conclusions must be underlined . for small systems , like ( 50 , 23 ) , irrespectively whether the coulomb interaction is present or not , the system evolves from the liquid phase present at low excitation energies to the gas phase corresponding to vaporized matter by crossing the coexistence zone . for large systems , like ( 200 , 82 ) , which experience stronger coulomb fields , the situation becomes more interesting . when one turns the coulomb interaction off , the system exhibits the same behavior as a small system . when the coulomb field is activated the critical temperature and pressure decrease such that , for freeze - out volumes up to about @xmath13 , the system may evolve from the liquid phase to gas or supercritical fluid without crossing the phase coexistence zone @xcite . in the following we shall present the mmm predictions on fragment average isospin distributions in different points of the nuclear phase diagram and stress the fact that @xmath0 versus @xmath1 manifests different behavior in the liquid , phase coexistence and gas regions . as a general comment , we mention that the investigation of the phase space along constant @xmath11 paths was arbitrary and the description of the system within a modified microcanonical ensemble with fluctuating volume @xcite is not essential for the conclusions of the present study . thus , the same behavior of @xmath0 vs. @xmath1 distributions determined by the event localization inside the phase diagram was obtained for constant volume approximation ( standard microcanonical approach ) . the phase diagram of the nuclear system ( 200 , 82 ) without coulomb and hard - core interactions ( ( ii ) freeze - out scenario ) is represented in fig . [ fig:200_-c_phd ] in the temperature - excitation energy , pressure - excitation energy and pressure - temperature planes . the solid lines represent iso-@xmath11 trajectories for different values of @xmath11 ranging from @xmath14 @xmath15 to @xmath16 @xmath15 , as indicated on the figure . the borders of the phase coexistence region were evaluated using maxwell construction on the iso-@xmath11 caloric curves and are plotted with dashed lines . the borders of the spinodal region are defined as the locus of the inflexion points of @xmath17 curves and are plotted with dotted lines . the critical point is characterized by the following set of values : @xmath18=9.1 mev , @xmath19 mev/@xmath20 , @xmath21=6.75 mev / nucleon and @xmath22=1.33 . the shapes of @xmath0 versus @xmath1 distributions have been investigated along all iso-@xmath11 paths represented in fig . [ fig:200_-c_phd ] . to illustrate the conclusions , we scan the phase space along the trajectory characterized by @xmath23 @xmath15 . the states accessed in this way are similar to the ones obtained in nuclear multifragmentation reactions . thus , as the excitation energy increases from 2 to 12 mev / nucleon , the temperature ranges around 6 mev and the average freeze - out volume increases linearly from 2@xmath24 to 16@xmath24 . once clarified the thermodynamical behavior of the system and before investigating the fragment average isospin distributions as a function of fragment size , it is useful to have a clear picture on the fragment size distributions produced in the considered multifragmentation events . [ fig:200_-c_z ] depicts the fragment charge distributions ( upper panel ) and charge distributions of the largest fragment in each event ( lower panel ) . even if , our main purpose for plotting @xmath25 is only to illustrate" +"understanding and controlling entanglement in many - body systems is one of the most important challenges in quantum mechanics today . the rewards are significant and are expected to not only lead to new insights into the properties of solid state systems and phase transitions @xcite , but also to new designs for highly efficient quantum information devices . ultra - cold bosonic gases offer an ideal arena to explore many - body entanglement , as experimentalists have at their disposal _ designer _ condensed matter systems whose parameters can be controlled with unprecedented precision @xcite . entanglement often exists naturally in the ground state of a many - body system @xcite , where it resides between the degrees of freedom of the particles and is a property of the first quantised many - body wavefunction . however , in ultra - cold gases the particles are inherently indistinguishable , which requires the symmetization of their many - body wavefunction and means that the hilbert space no longer has the tensor product structure required to define entanglement . the first quantised many - body wavefunction of indistinguishable particles may therefore contain quantum correlations @xcite , but such correlations are usually considered unable to violate a bell inequality or process quantum information @xcite . ultra - cold gases are also well described within the framework of second quantisation , where instead of working directly with the many - body wavefunction , one defines a complete set of field modes that are occupied by particles . second quantisation therefore offers the possibility of entanglement between modes . entanglement is dependent on the choice of modes , but provided the correct choice is made , investigating entanglement between _ distinguishable _ modes @xcite circumvents the difficulties of defining entanglement between indistinguishable particles @xcite . to illustrate the differences between particle and mode entanglement , let us consider two non - interacting bosons in a trap at zero temperature . in first quantisation , the wavefunction is the symmetrized product , @xmath0 , where @xmath1 is the ground state of the confining potential . no entanglement exists between the particles , since indistinguishability forbids us from assigning to any particle a specific set of degrees of freedom . conversely , in second quantisation one can define a pair of spatial modes , @xmath2 and @xmath3 , where each mode occupies half the confining geometry . since both the particles are coherently distributed over these modes , the system is described by the entangled state , @xmath4 , where @xmath5 denotes @xmath6 particles in mode @xmath2 and @xmath7 particles in mode @xmath3 ( with @xmath8 ) . in this paper we outline a scheme for the detection of bi - mode and multi - mode spatial entanglement for a finite temperature , interacting bose gas of any ( including unknown ) particle number . we show that entanglement is detected via the single - particle reduced density matrix ( sprdm ) . we apply our scheme to the example of a harmonically trapped , interacting boson pair @xcite , where the sprdm also acts as a quantifier of entanglement . we find that for all interaction strengths , entanglement between pairs of modes rapidly decreases with temperature . while at zero temperature a significant amount of entanglement remains even in the limit of infinite interaction . moreover , we note that our detection scheme is also relevant to recent proposals to observe non - locality of single particle between spatial modes @xcite . and @xmath9 . the modes are combined at a @xmath10 beamsplitter and the particles in the output modes @xmath11 and @xmath12 are counted . ] the correlations of entanglement are locally basis independent , so that one needs to measure each mode in at least two bases in order to differentiate them from classical correlations . while a superselection rule that forbids coherent superpositions of eigenstates of different mass @xcite seems to rule such measurements out for any atomic system , recent work has shown that such measurements are theoretically possible @xcite . moreover , it has recently been predicted that this natural mode entanglement of massive particles can be used as a resource for quantum communication @xcite . however , in practice it will be difficult to locally manipulate , i.e. rotate , the spatial modes . in the following we will show that spatial entanglement can also be detected and quantified by making _ operations on the modes . let us consider a gas in a confining geometry ( see fig . [ fig : schematic ] ) which is mathematically , but not necessarily physically , divided into two , non - overlapping spatial modes , @xmath13 and @xmath9 . the field operators , @xmath14 and @xmath15 , create and destroy particles in mode @xmath16 , where @xmath17 ensures that the commutation relations , @xmath18=\delta_{ij}$ ] , are satisfied . the quantity , @xmath19 , specifies how the set of points in a spatial mode are averaged over . to generate interference , the particles in the two spatial modes , @xmath13 and @xmath9 , are mixed at a 50:50 beamsplitter , which transforms the input modes as @xmath20 and @xmath21 . after the beamsplitting operation , the number of particles in the output modes , @xmath11 and @xmath12 , are counted and compared to the fully separable case . if the number of coincidences is different to the separable case , we can conclude that there must have been entanglement between the spatial modes . a bosonic gas of fixed particle number , @xmath22 which is in a fully separable state w.r.t . the spatial modes @xmath13 and @xmath9 can be written as @xmath23 where @xmath24 . the beamsplitter transforms this state such that if the total number of particles is even , one detects the same number of particles in each of the output modes , i.e. @xmath25 . for an odd number of particles an ensemble average leads to the same result @xcite . conversely , if the initial state of fixed particle number is of an arbitrary form , @xmath26 , the difference in particle numbers detected in the modes @xmath11 and @xmath12 may be non - zero due to entanglement between the modes . @xmath27 -{\textrm{tr}}\left[\hat\psi_d^{\dag}\hat\psi_d\hat\rho\right]\right| = 2|\epsilon_{ab}|,\ ] ] where @xmath28 = \int_{a}d\vec{x}\int_{b}d\vec{x}'g(\vec{x})g^*(\vec{x } ' ) \rho^{(1)}(\vec{x},\vec{x}').\ ] ] we have derived the above result using the fourier decomposion of the field operators , @xmath29 and @xmath30 in terms of the momentum modes , @xmath31 , as @xmath32 and likewise for @xmath33 . when @xmath34 is non - zero , the state @xmath26 is different to the separable case and is therefore necessarily entangled w.r.t . the bi - modal split into @xmath13 and @xmath9 . the quantity @xmath34 is given by the off - diagonal elements of the sprdm which is defined as @xmath35 . here @xmath36 is the number of bosons that occupy the @xmath37-th momentum mode . the sprdm is a one - body correlation function , which characterises important coherence properties of a many - body system @xcite and its off - diagonal elements are related to the visibility of interference fringes in a two slit experiment @xcite . our scheme therefore applies to systems whose correlations from a basic group of one particle @xcite . states of the form , @xmath38 , whose correlations are second order are not detected by the sprdm . such states require careful engineering of bosonic systems @xcite , although they may form naturally in fermionic systems , i.e. cooper pairs in superconductors . our scheme is applicable to all bosonic gases trapped in orthodox geometries . next , let us show that @xmath34 can also be used to _ quantify _ mode entanglement for certain systems , one of which is the boson pair model discussed below . for this @xmath34 must fulfil three basic criteria @xcite : ( i ) @xmath34 is zero when the state is separable , ( ii ) @xmath34 is invariant under local unitary operations and ( iii ) @xmath34 does not increase under local general measurements and classical communication ( lgm+cc ) . the validity of ( i ) is shown above and ( ii ) is guaranteed since the trace is basis independent . one can prove ( iii ) as follows . to implement lgm+cc , the two spatial modes , @xmath13 and @xmath9 , are each coupled to a local environment by a general completely positive map . the environments are allowed to communicate classically ad infinitum and the total number of particles in the gas and environment is fixed . one can then show that @xmath34 does not increase under lgm+cc . the above scheme can also analyse multi - mode entanglement , i.e. the simultaneous entanglement of more than two modes . in the following we use the different notions of separability discussed in @xcite . a general @xmath39-mode state is fully separable and contains no entanglement if it is a convex combination of states for each mode , @xmath40 . here each composite state , @xmath41 corresponds to a single spatial mode with a fixed number of particles . on the other hand , entanglement may be present between certain subsets of spatial modes , for which one can define a @xmath42-separable state , @xmath43 , where @xmath44 with equality when the state is fully separable as above . when the composite state , @xmath41 describes more than one spatial mode , the spatial modes contained within @xmath45 are necessarily entangled otherwise @xmath45 would be written as a product of states for the individual modes , @xmath46 , and the overall state of the system would be @xmath47-separable , where @xmath48 @xcite . to determine whether a given @xmath39-mode state contains multi - mode entanglement , one can check a bi - partite entanglement criterion between all @xmath49 unique divisions of the system into two _ blocks _ , @xmath2 and @xmath3 . depending on which pairs of blocks are found to be separable one can conclude that the state has entanglement between different subsets of spatial modes . here the bipartite entanglement criterion is @xmath50 $ ] of eq . , i.e. the sprdm between two blocks of spatial modes , @xmath51 and @xmath52 . the field operators , @xmath53 and @xmath54 , for blocks of spatial modes are defined as @xmath55 and @xmath56 , where @xmath57 and @xmath58 ensures that the commutation relations , @xmath59=\delta _ { { x } , { y}}$ ] , are satisfied . we now describe how entanglement changes for the ( i ) fully separable ( ii ) the @xmath42-separable and ( iii ) the fully entangled states : ( i ) the fully separable state , @xmath60 , admits no interference between all @xmath49 partitions into blocks , i.e. @xmath61 for all @xmath51 and @xmath52 . ( ii ) a @xmath42-separable state , @xmath62 where @xmath63 , admits no interference for @xmath64 partitions into blocks from the total of @xmath49 partitions , i.e. @xmath65 for @xmath64 choices of @xmath2 and @xmath3 . ( iii ) a fully entangled state , @xmath66 , admits interference for all @xmath49 choices of blocks , i.e. @xmath67 for all @xmath68 and @xmath69 . the fully entangled state , @xmath70 , necessarily contains some form of multi - mode entanglement , since otherwise there would exist a decomposition such that @xmath26 is @xmath42-separable . . temperature is scaled in units of @xmath71 . ] in the following we will apply our scheme to the physically realistic model of a harmonically trapped pair of ultracold , interacting , bosonic atoms in effectively one dimension . the hamiltonian of such a system is given by @xmath72 where all lengths are scaled in units of the ground state size and all energies in units of the harmonic frequency . the one dimensional coupling constant , @xmath73 , is related" +"formulating strong - field transport in electron lattice has always been one of the most challenging theoretical goals in condensed matter physics @xcite . this is more true with today s advanced nano - lithography techniques where we can now realize electron lattice driven far from equilibrium . even though this is an old problem , we are still in search of a firm theoretical paradigm to approach the problem in general . one of the central puzzles is dissipation . in equilibrium , the presence of an open environment in contact with a system introduces thermalization , and once the temperature is defined , we often use canonical or grand canonical ensemble , and do not consider the coupling to the environment as an explicit parameter . we naturally ask whether such simplifying ansatz may be possible in nonequilibrium , at least for steady - state description . in nonequilibrium , we do not know such tremendously simplifying paradigms to take the role of the environment as an implicit parameter which can be hidden in thermalization process . on the contrary , the dissipation is considered as an integral part of the nonequilibrium process , and we need to include the dissipation mechanism explicitly for sound theoretical description . in some systems , however , the dissipation process can be simplified . in quantum dots ( qds ) under a finite dc bias , electron reservoirs coupled to the qd also act as energy source / drain and the energy relaxation is assumed to happen far away from qd and inside a battery . the electrical leads are then modeled as non - interacting reservoirs , and the electron transport is viewed as a transmission problem @xcite . by taking the open limit , the excess energy can be taken infinitely far away from the qd , and the problem supports steady - state @xcite . various quantum simulation methods have been proposed to study the transient behaviors of interacting models @xcite . in the limit where a steady - state exists , the nonequilibrium state can also be described within the time - independent statistical mechanics framework @xcite , from which hershfield @xcite proposed the nonequilibrium density matrix @xmath6,\ ] ] with the reservoir energy @xmath7 for the source ( @xmath8 ) and drain ( @xmath9 ) with the continuum index @xmath10 . @xmath11 is the creation operator of the full scattering state as the solution of the _ whole _ system of quantum dot and the leads . @xmath12 is the chemical potential of the respective reservoirs . the scattering state formulation , although conceptually appealing , has initially been applied only to limited models @xcite due to the difficulty of finding the scattering states . in recent years , several steady - state methods @xcite have been developed and have been extended to general models . recently , the attention of the field has turned to lattice nonequilbrium problems . even at a very stage of the field , there have been important findings in the nonequilbrium processes , most notably that electrons under a dc electric field seem to build up internal energy quite quickly , reaching a quite different steady - state from equilibrium strongly correlated states @xcite . one of the most popular technique of solving lattice many - body models has been the dynamical mean - field theory ( dmft ) @xcite . its success has been well documented in the description of the mott transition and strong - correlation physics in equilibrium . while there have been a fair amount of dmft works to electric - field driven lattice systems , the validity of the local approximation is still unconfirmed and subject to intense debate . there have been numerous attempts to simulate nonequilibrium physics in lattice models , often through isolated hamiltonians @xcite suited for quench dynamics of cold atom systems in optical lattice , periodically driven systems @xcite , and some basic dissipation models @xcite . however , in part due to the numerical difficulties in simulating long time - evolution , most of the efforts have focused on high - field phenomena such as the dielectric breakdown in mott insulators @xcite . the main emerging picture of the calculations is that the external field drives the electronic lattice systems into hot temperature , generally regardless of the nature of many - body interaction . even though the picture is in agreement between many groups , the detailed understanding of the nature of the hot electron state and its eventual fate in more realistic setting is not available . to gain systematic understanding of such nonequilibrium state , the dissipation should be included in explicit models and their analytic behavior has to be studied with the damping as a controlled parameter . one of the goals of this paper is to introduce steady - state formulation via scattering state method for lattice with fermion baths and comprehensively analyze the model to show that the system possesses many properties which are expected of physical systems , for instance , consistent picture as the boltzmann transport theory . in the process , an argument will be made that the fermion bath model and the steady - state methods are a good minimal system to study nonequilibrium strong correlation physics . in the previous paper @xcite by one of authors , the fermion bath model under a dc electric field has been shown to reproduce the key ingredients as predicted by the classical boltzmann transport theory , and to have a stead - state solution . the occupation number as a function of mechanical momentum has been shown to have the fermi sea shift by the drift velocity proportional to the scattering time and the electric field . furthermore , the dc current has been derived to be consistent with the boltzmann transport result applied to nanostructures @xcite . in this work , we further develop the solution to show that the scattering state formulation is applicable , and therefore a wide range of new techniques can be developed to solve the interacting lattice nonequilibrium phenomena . explicit calculations from temporal gauge and the coulomb gauge with scattering state formulation show that they are completely consistent with each other . the coulomb gauge enables the time - independent formalism , making physical interpretations more transparent . we calculate explicitly the local distribution function , from which we derive that the effective temperature scales as @xmath13 with a numerical constant @xmath1 , tight - binding parameter @xmath2 , the bloch oscillation frequency @xmath3 and the damping parameter @xmath4 . the effective temperature exhibits a singular limit of @xmath14 for @xmath5 . this proves that one should not take the damping as an implicit process , as treated in equilibrium theory . finally we derive , via the energy flux conservation with the joule heating , a general dc current relation as a functional of local green s functions as an extension of the meir - wingreen formula @xcite to lattice models , and confirm the linear response theory . the main text of the paper is organized as follows . in section ii , the method introduced in ref . is further developed for green s functions in the temporal gauge . in section iii , we introduce the coulomb gauge and show that the green s functions in both gauges become identical in the long - time limit . in section iii we further discuss several important nonequilibrium quantities : the local distribution function and the effective temperature in a , time - evolution of wave - packet in b , dissipation and energy flux in c , and finally the derivation of the dc current in interacting models in d. appendices provide detailed analytic calculations . to demonstrate the equivalence of the time - dependent temporal gauge to the scattering - state formalism with time - independent coulomb gauge , we start with the one - dimensional non - interacting model considered earlier @xcite . we study a quadratic model of a one - dimensional @xmath15-orbital tight - binding model connected to fermionic reservoirs ( see fig . [ fig1 ] ) under a uniform electric field @xmath16 . the effect of the electric field for time @xmath17 is absorbed in the temporal gauge as the peierls phase @xmath18 in the hopping integral @xcite @xmath2 . here @xmath19 is the bloch oscillation frequency and @xmath20 is the step function . the time - dependent hamiltonian then reads @xmath21 with @xmath22 as the ( spinless ) electron operator on the tight - binding chain on site @xmath23 , @xmath24 with the reservoir fermion states connected to the site @xmath23 with the continuum index @xmath25 along each reservoir chain of length @xmath26 . the length @xmath26 is taken to infinity , and the time scale @xmath27 ( with fermi velocity of the chain @xmath28 ) for the wave to reach the end of the reservoir chain is considered larger than any other time scales in the problem . as discussed in ref . , the hamiltonian can be diagonalized in each @xmath10-sector as @xmath29 with @xmath30d^\dagger_kd_k+\sum_{\alpha}\epsilon_\alpha c^\dagger_{k\alpha}c_{k\alpha}\nonumber \\ & & -\frac{g}{\sqrt{l } } \sum_{\alpha}(c^\dagger_{k\alpha}d_k+{\rm h.c.}),\end{aligned}\ ] ] with the fermion operators fourier transformed to the wave - vector basis . here @xmath31 is the tight - binding dispersion at zero @xmath16-field . the reservoir states formed by @xmath32 acts as an open particle source with its chemical potential set at zero energy . the problem can be solved with @xmath33 as the unperturbed hamiltonian and @xmath34 as the time - dependent perturbation , @xmath35-\cos(k)\right\}d^\dagger_k d_k \equiv v(t)d^\dagger_k d_k.\label{eq : pert}\ ] ] this block - diagonal hamiltonian is nothing but a resonant level model coupled to a reservoir , with the level s energy oscillating in time @xcite . with the perturbation of one - body terms of a finite degrees of freedom , one can write the dyson s equation for the retarded and lesser green s functions as @xcite @xmath36{\bf g}_{k,0}^<[i+{\bf v}{\bf g}_k^a],\label{eq : glss}\end{aligned}\ ] ] where @xmath37 and @xmath38 are the lesser and retarded green s function matrices , respectively . @xmath39 and @xmath40 are for the non - interacting limit . the multiplication of green s function matrices denotes time integration . following ref . , the retarded green s function is @xmath41 with the damping parameter @xmath42 for reservoirs of flat density of states of infinite bandwidth . the local retarded green s function @xmath43 becomes @xmath44 with the zero - th bessel function @xmath45 . here , the gauge - invariant local function becomes a function of only the relative time , @xmath46 . fourier transformation with respect to the relative time gives @xmath47 by using the bessel function relation @xcite @xmath48 ^ 2e^{im\alpha}$ ] . the lesser green s function can be simplified in a straightforward calculation from eq . ( [ eq : glss ] ) following the similar procedures as in ref . in the long - time limit ( @xmath49 ) as @xmath50 where @xmath51 with the self - energy @xmath52 from the damping taken as the perturbation . although the above equation has been derived with the time - dependent peierls term eq . ( [ eq : pert ] ) as the perturbation , the same result can be obtained when the damping is considered as perturbation in the limit that transient terms die out . the local lesser green s function can be computed as @xmath53 , which again renders the green s function only dependent on the relative time . after changing the dummy variables @xmath54 and @xmath55 , we have @xmath56 with @xmath57\nonumber \\ & & \times \sin\frac{\omega s}{2}\sin\frac{\omega s'}{2}.\nonumber\end{aligned}\ ] ] again by utilizing the bessel function relation @xcite @xmath58 @xmath59 with @xmath60 , the fermi - dirac function at zero temperature . from the identity @xcite , @xmath61 , @xmath62 although the two green s" +"in 1988 , a new approach to the relativistic dynamics appeared . by an appropriate conformal ( 3 + 1 ) splitting of the schwarzschild spacetime , the so - called optical reference geometry was defined @xcite . it was demonstrated that this geometry enables us to define the inertial forces in the framework of general relativity , providing a description of test particle motion in accordance with our newtonian intuition @xcite , @xcite . later , the definition of the optical reference geometry and related inertial forces was generalized , extending its applicability to any spacetime @xcite , @xcite , @xcite , @xcite . the optical reference geometry was also thoroughly studied in particular spacetimes , such as schwarzschild - de sitter @xcite , @xcite , reissner - nordstrm @xcite , reissner - nordstrm - de sitter @xcite , kerr @xcite , @xcite or kerr - newman @xcite , illustrated by embedding diagrams @xcite , @xcite , @xcite , and the inertial forces formalism was applied for solving specific problems in relativistic dynamics @xcite , @xcite . behaviour of the centrifugal force is closely related to the shape of embedding diagrams of the optical geometry , therefore many properties of the relativistic dynamics in the spacetimes were effectively illustrated and directly visualized . in the present work we extend our previous studies @xcite , @xcite to the case of the stationary and axially symmetric kerr - de sitter ( kds ) spacetimes , reflecting thus their basic properties incorporating a combined influence of the rotation of source and the cosmic repulsion , recently indicated by wide range of cosmological tests . it is worth to stress that the kds black - hole spacetimes could be important in understanding astrophysical phenomena exposed around supermassive black holes in giant active galactic nuclei as demonstrated in @xcite , @xcite . we show that the application of the inertial forces concept proves to be very effective and provides simpler and intuitive approach to some relativistic problems , as compared to the standard general relativistic methods . the standard methods based on the covariant formulation of physical laws in a given background ( geodesic equation , energy momentum conservation , etc . ) can be then replaced by the well developed methods familiar from newtonian physics when inertial forces related to the optical geometry are used , making a significant technical simplification in treating physical processes in curved backgrounds and enabling their interpretation in the newtonian way . thus the present paper could be also considered to be an introduction in developing a new approach to study astrophysical phenomena . we give some explicit examples how the analysis of the inertial forces could immediately and in a very simple way make an enlightenment of the properties of the circular motion of test particles and perfect fluid . the structure of the paper is similar to the previous study of the optical geometry of the kerr - newman spacetimes @xcite , whereas the content is more extensive , mainly in the parts concerning the inertial forces application in the relativistic dynamics . , we briefly present basic general definitions of the optical geometry and inertial forces , focusing on the stationary and axially symmetric spacetimes and circular motion . , kds geometry is introduced . although the properties of the kds spacetimes are well known , we briefly discuss them here again , in order to simply demonstrate the so - called chinese boxes method , used later in much more complicated cases for discussions of the properties of the inertial forces and embedding diagrams . , the inertial forces in the kds spacetimes are determined for general circular motion , and their properties are briefly discussed and thoroughly represented for the equatorial circular motion . , some examples of the relativistic dynamics are shown from the point of view of the inertial forces formalism . there are many interesting relativistic problems , which can be simply investigated by using the inertial forces formalism . we present such problems that have been studied by the standard general relativistic methods as well , in order to show immediately the effectiveness and simplicity of the inertial forces approach . namely the equatorial circular motion is studied , simply providing important findings for the test particle and photon circular motion @xcite , equatorial static radius and static equilibrium positions of test particles on the axis of symmetry @xcite . another astrophysically relevant application of the inertial forces formalism is demonstrated in deducing projection of the relativistic euler equation that allows determination of the perfect fluid equilibrium toroidal configurations @xcite . , the embedding diagrams of the equatorial plane of the optical reference geometry of kds spacetimes are discussed and constructed . the whole optical geometry can not be embeddable , therefore we discuss limits of embeddability . we establish relations between the shape of the embedding diagrams and the behaviour of the centrifugal force , investigating turning points of the diagrams . finally , the embeddability of photon circular orbits is discussed and typical embedding diagrams are constructed . , we summarize results of our investigation of the optical reference geometry formalism in the kds spacetimes , and compare them with results obtained for previously studied backgrounds . in stationary spacetimes described by a metric @xmath0 ( with signature + 2 ) , the definition of the optical reference geometry requires an introduction of family of special observers with a timelike , unit , and hypersurface orthogonal field @xmath1 and with its field equal to the gradient of a scalar function , i.e. , @xcite @xmath2}=0.\end{aligned}\ ] ] such a vector field can be chosen in the form @xmath3 whereas it corresponds to the unit field of stationary observers parallel to a timelike vector field @xmath4 . then the local instantaneous space of the observers is described by the metric @xmath5 the so - called _ directly projected geometry_. its conformally adjusted metric @xmath6 is the so - called _ optical reference geometry_. the @xmath7 of a test particle with a rest mass @xmath8 can be decomposed in the reference frame of the special observers with the @xmath1 by using the relation @xmath9 where @xmath10 is the unit spacelike vector parallel to the @xmath11 of the particle in the space and @xmath12 is the lorentz factor ( the speed of light @xmath13 ) . moreover , there is @xmath14 , @xmath15 , where @xmath16 is a projection tensor . note that the vector @xmath10 is defined only along the world line of the particle . but in our construction , it is necessary to know how @xmath10 changes along @xmath1 . this can be done in several different ways ( different gauges ) . the gauge used by m. abramowicz and his co - workers assures that the lie derivation of @xmath10 with respect to @xmath17 vanishes , i.e. , @xmath18 , which causes that the coriolis force defined below vanishes in static spacetimes @xcite . the @xmath19 of the particle can be written in the form @xmath20 where @xmath21 . by using the spacelike unit vector parallel to @xmath10 in the optical reference geometry , i.e. , the vector @xmath22 , its covariant form @xmath23 , the scalar @xmath24 , identity @xmath25 and condition of hypersurface orthogonality , the projection of the into the space can be written as @xmath26 where @xmath27 and @xmath28 . now , the inertial force in the space @xmath29 , related to the real force by the equation @xmath30 , can be decomposed into the sum of the gravitational @xmath31 , centrifugal @xmath32 , coriolis @xmath33 and euler @xmath34 forces familiar from the newtonian physics , i.e. , @xmath35 where @xmath36 note that in the context of the optical reference geometry approach , the gravitational force ranks among the inertial forces . in static and spherically symmetric spacetimes , the field ( [ 3 ] ) can be chosen with the vector being the timelike killing vector field @xmath37 , which is orthogonal to the spacelike azimuthal killing vector field @xmath38 . however , in stationary and axially symmetric spacetimes , the killing vector fields @xmath39 and @xmath40 are not orthogonal in general . thus the vector has to be chosen in order to satisfy the hypersurface orthogonality condition . it is easy to check that the vector field @xmath41 , where @xmath42 is hypersurface orthogonal and thus the field @xmath43,\end{aligned}\ ] ] which corresponds to the field of the locally non - rotating frames moving along circular orbits with the angular velocity @xmath44 , defines the special observers @xcite . since the vector field @xmath1 is hypersurface orthogonal , the unit vector @xmath10 , used in the decomposition ( [ 8 ] ) , must be located in the hypersurface . on the other hand , the @xmath45,\end{aligned}\ ] ] corresponding to the general circular motion of a test particle with an angular velocity @xmath46 , is not hypersurface orthogonal . moreover , the circular motion is directed along the killing vector @xmath40 , i.e. , @xmath47 then , by using expressions ( [ 8 ] ) and ( [ 31 ] ) , the lorentz factor and velocity are given by the relations @xmath48 and components of the inertial forces ( [ 13])-([16 ] ) are given by the relations @xmath49,\\ \label{37 } c_k = m\gamma^2v\,(\xi^i\xi_i)^{-3/2}e^{-\phi}[\xi^i\xi_i\nabla_{k}{(\eta^i\xi_i)}-\eta^i\xi_i\nabla_k{(\xi^i\xi_i)}],\\ \label{38 } e_k = m\,e^{\phi}\gamma^3 u^i\nabla_i(v ) \tilde{\tau}_k.\end{aligned}\ ] ] the newtonian character of the inertial forces formalism appears after introducing the quantities @xmath50 where @xmath51 is angular velocity relative to the lnrf . then we can write @xmath52 and the inertial forces ( [ 35])-([38 ] ) can be rewritten to the form @xmath53 the quantity @xmath54 corresponds to the so - called radius of gyration , defined by the relation @xmath55 generalizing in a special way its definition introduced and discussed for the static schwarzschild spacetimes in @xcite , @xcite . the quantity @xmath56 is the conserved specific angular momentum and @xmath57 is a scalar called pseudo - energy of the particle . since the vector field @xmath4 is not a killing vector field , such pseudo - energy is not conserved in general stationary and axially symmetric spacetimes . of course , in the static spacetimes , @xmath58 is conserved , being defined in the standard way as @xmath59 . the radius of gyration plays an important role in the theory of rotational effects in strong gravitational fields . the direction of increasing radius of gyration gives a preferred determination of the local outward direction relevant for the dynamical effects of rotation , whereas the direction becomes misaligned with the global outward direction in strong fields @xcite . in the standard boyer - lindquist coordinates @xmath60 and geometric units @xmath61 , the line element of the kds geometry is given by the relation @xmath62 ^ 2+\nonumber\\ \frac{\rho^2}{\delta_r}dr^2+\frac{\rho^2}{\delta_{\theta}}d\theta^2,\end{aligned}\ ] ] where @xmath63 the mass @xmath64 , specific angular momentum @xmath65 , and cosmological constant @xmath66 are parameters of the spacetime . it is convenient to introduce a dimensionless cosmological parameter @xmath67 for simplicity , we put @xmath68 hereafter . equivalently , also the coordinates @xmath69 , @xmath70 , the line element @xmath71 , and the parameter @xmath65 are expressed in units of @xmath64 and become dimensionless . the kds spacetimes , being stationary and axially symmetric , admit both the killing vector fields @xmath39 and @xmath40 , whereas @xmath72 , @xmath73 and @xmath74 . the only intrinsic singularity of the kds solution is the ring singularity in the equatorial plane and it is given by the relation @xmath75 . stationary regions of the spacetimes are determined by the relation @xmath76 and limited by the inner and outer black - hole horizons at @xmath77 and @xmath78 and by the cosmological horizon at @xmath79 , which are real roots of the equation @xmath80 . then spacetimes containing three horizons are black - hole spacetimes , while spacetimes containing one horizon ( the cosmological horizon" +"new near - ir luminescence , quite different from much - studied bi@xmath2-related luminescence @xcite , was discovered in 2001 in bismuth - doped aluminosilicate glass @xcite . then optical amplification at 1.3 m was demonstrated @xcite . ever since bismuth - doped glasses and optical fibers based on such glasses attract a considerable interest due to a broadband ir luminescence in the range of 1.0 1.7 m employed successfully in fiber lasers and amplifiers ( see e.g. the review @xcite ) . although the origin of the ir luminescence is still not clear , recently a belief has been strengthened that subvalent bismuth centers are responsible for the luminescence @xcite . in our opinion , monovalent bismuth centers are of a particular interest . glasses as disordered systems are very complicated to study impurity centers structure . in this regard , crystals may be of interest as model hosts containing bismuth - related centers . in particular , crystalline halides of monovalent metals are convenient hosts for monovalent bismuth centers . these crystals have a simple structure ( primitive , , or face - centered , , cubic lattice ) . bismuth can easily form monovalent substitutional centers in such lattice . similar subvalent thallium and lead centers in crystals were studied extensively ( e.g. thallium in @xcite and lead in , m@xmath3ca , sr , ba @xcite ) . by analogy , the models of bismuth - related centers in oxide glasses for fiber optics were suggested @xcite . bismuth - related ir luminescence in cubic halide crystals was studied for the first time in @xcite , then in ( ) @xcite and recently in ( ) @xcite . two models of the centers in were suggested in @xcite , namely , a monovalent bismuth substitutional center , @xmath0 , and a dimer center , @xmath1 , formed by two @xmath0 substitutional centers in the nearest cation sites with an extra electron . in what follows we report the results of computer modeling of bismuth - related centers in and crystals . to study the origin of the ir luminescence in and , we performed a computer simulation of the structure and absorption spectra of three bismuth - related centers possibly occurring in both crystals . basing on the assumptions made in @xcite and on analogy with centers in alkaline halide crystals ( see e.g. @xcite ) , we studied the @xmath0 substitutional center as the main form of bismuth embedding in and , the @xmath1 dimer center , and and complexes formed by the bismuth substitutional center and anion vacancy in its first coordination shell . the modeling was performed in a supercell approach . @xmath4 or supercells ( 54 atoms ) was chosen to model @xmath0 and or centers , and @xmath5 supercell ( 72 atoms ) was used for @xmath1 . in the central region of the supercell certain cations were substituted by bismuth atoms and an anion vacancy was formed by a removal of one chlorine or iodine atom . charged centers were simulated changing the total number of electrons in the supercell . equilibrium configurations of bismuth centers were found by a complete optimization of the supercell parameters and atomic positions with the gradient method . all such calculations were performed using package @xcite in the plane wave basis in the generalized gradient approximation of density functional theory with ultra - soft pseudopotentials built with pbe functional @xcite . the pseudopotential sources were taken from the pslibrary v. 0.3.0 pseudopotential library @xcite . + to test the approach , and lattice parameters were calculated for the unit cell and supercells with both atomic positions and cell parameters completely optimized . the results convergence was tested with respect to the plane wave cutoff energy and to the @xmath6 points grid . the energy cutoff @xmath7 ev and the number of @xmath6 points @xmath8 in the irreducible part of the unit cell brillouin zone were found to be enough to converge the total energy within @xmath9 ev per atom and to reproduce the experimental lattice parameters with a relative accuracy of @xmath10% . the geometry of each supercell was reproduced with a relative accuracy better than 2% with only @xmath11 point of the supercell taken into account and better than 1% using 8 @xmath6 points in the supercell in the irreducible part of the supercell brillouin zone . the total energy convergence was not worse than that in the case of the unit cell . configurations of bismuth - related centers obtained by this means were used to calculate the electron localization functions using the programs from package , the electron density distribution and effective charges of atoms by bader s method using bader v.0.28 code @xcite , and the absorption spectra of the centers by bethe - salpeter equation method based on all - electron full - potential linearized augmented - plane wave approach @xcite . the absorption spectra calculations were performed using code @xcite in the local spin density approximation with pw - ca functional @xcite . spin - orbit interaction essential for bismuth - containing systems was taken into account . scissor correction was applied to transition energies calculation with the scissor value found using modified becke - johnson exchange - correlation potential known to yield accurate band gaps in many solids @xcite . the non - overlapping muffin - tin ( mt ) spheres of maximal possible radii @xmath12 were used . convergence of the results was tested with respect to plane - wave cutoff energy , to the angular momentum cutoff for the mt density and potential , and to the @xmath6 points grid choice . the plane - wave cutoff , @xmath13 , was determined by the @xmath14 relation with @xmath15 being the smallest mt radius . the angular momentum cut - off was taken to be @xmath16 . the self - consistent calculations were performed on the @xmath17 grid of @xmath6 points uniformly distributed in the irreducible part of the supercell brillouin zone . further increasing the cutoff and @xmath6 points density did not lead to significant changes in the results . the total energy self - consistence tolerance was taken to be @xmath9 ev per atom . more dense @xmath18 @xmath6 points grid was applied to calculate dipole matrix elements in optical spectra calculations . simplified configurational coordinate diagrams of bismuth - related centers were calculated in a model restricted to the lowest excited states with a displacement of bismuth atom(s ) along @xmath19 $ ] axis for @xmath0 and centers and along @xmath20 $ ] axis for @xmath1 center . in spite of the fact that the model is inherently rough , it shows that in all the centers studied the stokes shift corresponding to a transition from the first excited state to the ground one do not exceed the accuracy of the excited state energy calculation . hence it seems reasonable enough to estimate the ir luminescence wavelengths by taking this stokes shift to be zero . calculation of @xmath0 substitutional center shows that both in and in the crystal lattice is distorted rather slightly around it : bismuth atom lies in the cation site , the nearest chlorine or iodine atoms are displaced by almost @xmath22 towards the bismuth cite , @xmath23 being the crystal lattice constant ( @xmath24 nm in and @xmath25 nm in ) , and the nearest thallium or cesium atoms are displaced apart from the bismuth cite . so bi@xmath26cl and bi@xmath26tl distances are 0.3120 and 0.3889 nm , respectively ( 0.3320 and 0.3834 nm in perfect crystal ) and bi@xmath26i and bi@xmath26cs distances are 0.3641 and 0.4624 nm , respectively ( 0.3955 and 0.4567 nm in perfect crystal ) . bader analysis of the electron density around @xmath0 center in showed the atomic effective charges to be @xmath27 , @xmath28 , and @xmath29 in -bismuth atom , in each of the nearest chlorine atoms , and in each of the nearest thallium atoms , respectively . the same analysis in yielded @xmath30 , @xmath31 , and @xmath32 atomic effective charges in bismuth atom , in each of the nearest iodine atoms , and in each of the nearest cesium atoms , respectively . the effective atomic charges in perfect and crystal lattices calculated by the same approach were found to be @xmath33 and @xmath29 in chlorine and thallium atoms , respectively , and @xmath34 and @xmath32 in iodine and cesium atoms , respectively . in the total charge localized in cation cite and the neighboring anion sites was changed from @xmath35 in perfect lattice to @xmath36 in the lattice with bismuth substitutional center . in csi this total charge was changed from @xmath37 in perfect lattice to @xmath38 in the lattice with bismuth substitutional center . this shows that the electron density was displaced into the space between bismuth atom and the nearest anions and may be considered as slight covalent contribution to bi@xmath26cl and bi@xmath26i interaction . in such displacement is more noticeable ( fig . [ fig : bi+_elfs ] ) . the calculated energy levels of the @xmath0 center in and are shown in figs . [ fig : bi+_tlcl_levels ] and [ fig : bi+_csi_levels ] , respectively , together with the corresponding transitions . it should be noticed that splitting of the @xmath0 ion states in bismuth substitutional centers in and is not described by crystal field theory due to total cubic symmetry of bismuth ion environment , unlike to the case of center @xcite . in this case the splitting is caused by electron density redistribution with a covalent contribution formed . absorption near 1.0 , 0.8 , 0.7 , and @xmath39 m is found in the @xmath0 center in . the above - mentioned excited states evaluative calculation allows one to expect a luminescence in near 1.0 m excited in this absorption bands . in the ir luminescence in the 1.21.3 m range may be expected to be excited in absorption bands near 1.2 , 0.7 , 0.5 , and @xmath40 m. besides , in another one luminescence transition , with much a lower lifetime , may occur near 0.8 m. the modeling shows that the @xmath1 dimer centers can actually occur both in and crystals . in @xmath1 centers the bismuth atoms are found to be displaced from the adjacent cation sites by @xmath42 and @xmath43 towards each other , so that the bi@xmath26bi distance is reduced to 0.2903 and 0.2961 nm in and , respectively . the nearest chlorine or iodine atoms are displaced towards the dimer , and the nearest thallium or cesium atoms are displaced apart from the dimer . as a result , the bi@xmath26cl and bi@xmath26tl distances are 0.3060 and 0.3960 nm , respectively ( 0.3320 and 0.3834 nm , respectively , in perfect crystal ) , and the bi@xmath26i , and bi@xmath26cs distances become -0.3314 and 0.4743 nm , respectively , as compared to 0.3955 and 0.4567 nm , respectively , in perfect lattice . bader s method analysis of electron density around the center shows that the excess electron charge , @xmath44 , is localized almost completely in the first coordination shell of two bismuth sites , mainly in bismuth atoms and partially in the nearest chlorine or iodine atoms ( fig . [ fig : bi2+_elfs ] ) . in the effective charge in each of the bismuth atoms is found to be @xmath45 , and the effective charge in each of the nearest chlorine and thallium atoms is @xmath33 and @xmath46 , respectively . so , as compared to @xmath0 center , positive charge in each of the bismuth atoms is decreased by @xmath47 , negative charge in each of the neighboring chlorine atoms is increased by @xmath48 , and positive charge in each of the nearest thallium atoms is decreased by @xmath49 . hence the excess total charge localized in two bismuth atoms and their nearest neighbors turns out to be" +"thermochemical models have been used to describe alkali @xcite , titanium and vanadium @xcite , carbon , nitrogen , and oxygen @xcite , sulfur and phosphorus @xcite , condensate ( e.g. , * ? ? ? * ; * ? ? ? * ) chemistry in the atmospheres of gas giant planets , brown dwarfs , and low - mass dwarf stars . here we continue and extend these previous studies by using thermochemical equilibrium calculations to model the chemical behavior of fe , mg , and si in substellar objects . iron , magnesium , and silicon are the most abundant rock - forming elements in a solar composition gas , and condensed as iron metal ( fe ) , and forsterite ( mg@xmath0sio@xmath1 ) and enstatite ( mgsio@xmath2 ) will produce the most massive cloud layers in substellar atmospheres . cloud formation strongly affects the optical and infrared spectra of substellar objects by removing gases from the overlying atmosphere and by introducing solid or liquid cloud particles ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? the large and growing number of discovered brown dwarfs ( @xmath3750 ) and extrasolar planets ( @xmath3400 ) makes it impractical to model the thermochemistry of all objects individually @xcite , as was done for jupiter and saturn @xcite and gliese 229b @xcite . instead , we adopt an approach similar to that of our previous papers @xcite and determine the abundance of each chemical species as a function of pressure , temperature , and metallicity , plotted in abundance contour diagrams . our results are thus independent of any particular pressure - temperature profile , and in principle , the atmospheric profile for any object may be superimposed on the abundance diagrams to determine its equilibrium atmospheric chemistry . in some instances , the behavior of key gases may be diagnostic of atmospheric temperature and/or tracers of weather in substellar objects . we begin with a brief description of our computational method ( @xmath4[s computational method ] ) , and then present our results for iron chemistry in substellar atmospheres in @xmath4[s iron chemistry ] . we first give an overview of iron chemistry in a solar composition gas and identify important gases and condensates ( @xmath4[ss overview of iron chemistry ] ) . this is followed by more detailed discussion of the chemical behavior individual fe - bearing gases as a function of temperature , pressure , and metallicity ( @xmath4[ss chemical behavior of iron - bearing gases ] ) . wherever possible , we note relevant spectroscopic observations of fe - bearing gases in substellar objects . our results for iron are then summarized by illustrating fe gas chemistry along the atmospheric profiles of representative substellar objects ( @xmath4[ss iron chemistry in substellar objects ] ) . a similar approach to magnesium and silicon chemistry follows in @xmath4[s magnesium chemistry ] and @xmath4[s silicon chemistry ] , respectively . we conclude with a brief summary in @xmath4[s summary ] . thermochemical equilibrium calculations were performed using a gibbs free energy minimization code , previously used for modeling the atmospheric chemistry of saturn @xcite and sulfur and phosphorus chemistry in substellar objects @xcite . thermodynamic data for the equilibrium calculations were taken from the compilations of @xcite , @xcite , the fourth edition of the janaf tables @xcite , and the thermodynamic database maintained in the planetary chemistry laboratory @xcite . this database includes additional thermodynamic data from the literature for compounds absent from the other compilations . all calculations were conducted using elemental abundances from @xcite for a solar system ( i.e. , protosolar ) composition gas . the effect of metallicity on sulfur and phosphorus chemistry was examined by running computations at [ fe / h ] = -0.5 dex ( subsolar ) , [ fe / h ] = 0 dex ( solar ) , and [ fe / h ] = + 0.5 dex ( enhanced ) metallicities . the metallicity factor , @xmath5 , is defined as @xmath6 $ ] . we assume that the elemental abundance ratios for mg , si , and other elements of interest vary similarly with [ fe / h ] ( e.g. , [ mg / h ] @xmath7 [ si / h ] @xmath7 [ fe / h ] ) over the range of metallicities considered here ( see * ? ? ? * ; * ? ? ? * ; * ? ? ? when considering the chemical behavior of individual gases , we focus on higher temperatures ( 800 k and higher ) , where thermochemical processes are expected to dominate over disequilibrium processes such as photochemistry or atmospheric mixing ( e.g. , see * ? ? ? we assume that condensates settle gravitationally into a cloud layer and are removed from the cooler , overlying atmosphere . this equilibrium cloud condensate scenario for the deep atmospheres of giant planets and brown dwarfs is supported by several lines of evidence ( e.g. , see * ? ? ? * and references therein ) . first , the presence of germane ( geh@xmath1 ) and the absence of silane ( sih@xmath1 ) in the upper atmospheres of jupiter and saturn ( even though si is expected to be much more abundant than ge ) can be explained by the removal of si from the gas into silicate clouds deeper in the atmosphere , whereas ge remains in the gas phase @xcite . secondly , the detection of h@xmath0s in jupiter s troposphere by the _ galileo _ entry probe indicates that fe must be sequestered into a cloud layer at deep atmospheric levels , because the formation of fes would otherwise remove h@xmath0s from the gas above the @xmath8 k level @xcite . third , absorption from monatomic k gas in the spectra of t dwarfs @xcite requires the removal of al and si at deeper atmospheric levels , because k would otherwise be removed from the observable atmosphere by the condensation of orthoclase ( kalsi@xmath2o@xmath9 ) @xcite . the presence of monatomic na gas in brown dwarfs @xcite also suggests al and si removal , because albite ( naalsi@xmath2o@xmath9 ) condensation would otherwise effectively remove na from the observable atmosphere . furthermore , the removal of na by na@xmath0s cloud formation is consistent with the observed weakening of na atomic lines throughout the l dwarf spectral sequence and their disappearance in early t dwarfs ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? finally , as we note below , the disappearance of iron , magnesium , and silicon spectral features in later spectral types is consistent with removal of these elements into cloud layers . in our thermochemical model , the abundances of fe- , mg- , and si - bearing gases above the clouds are computed assuming saturation ( equilibrium ) vapor pressure . if supersaturation occurs , a condensate will form and settle toward the cloud layer to restore equilibrium . figure [ figure iron chemistry overview ] illustrates model atmospheric profiles for an m dwarf ( @xmath10 = 2600 k , @xmath11 ; * ? ? ? * ) , an l dwarf ( @xmath10 = 1800 k , @xmath11 ; * ? ? ? * ) , the hot , close - in ( pegasi ) planet hd209458b ( @xmath10 = 1350 k ; * ? ? ? * ) , the t dwarf gliese 229b ( @xmath10 = 960 k ; * ? ? ? * ) , and jupiter ( @xmath10 = 124 k ) , indicated by dashed lines . we note that jovian atmospheric chemistry differs slightly than that for a solar - metallicity gas because jupiter has a heavy element enrichment comparable to [ fe / h ] @xmath7 + 0.5 dex @xcite . also shown in figure [ figure iron chemistry overview ] are lines indicating where a(ch@xmath1 ) = a(co ) and a(h@xmath0 ) = a(h ) . these boundaries are important because carbon and oxygen affect the chemical behavior of many fe , mg , and si - bearing gases . methane is the dominant carbon - bearing gas in jupiter and t dwarfs ( such as gliese 229b ) whereas co is the dominant carbon - bearing gas in l dwarfs and pegasi planets ( such as hd209458b ) . molecular hydrogen dissociates into monatomic h at high temperatures and low pressures ( lower right corner of figure [ figure iron chemistry overview ] ) . however , h@xmath0 is the dominant form of hydrogen in substellar objects , and we therefore take @xmath12 throughout the following . this approximation holds for metallicities up to [ fe / h ] @xmath7 + 0.5 dex ; at higher metallicities the h@xmath0 mole fraction abundance decreases as the relative abundance of heavy elements increases ( e.g. , @xmath13 at [ fe / h ] @xmath7 + 1.0 dex ) . the dotted line in figure [ figure iron chemistry overview ] shows the condensation curve for fe metal , with an open circle denoting its normal melting point ( 1809 k ) . iron condensation occurs via @xmath14 the equilibrium condensation temperature ( @xmath15 ) of fe is approximated by @xmath16,\ ] ] where higher pressures and/or metallicities lead to higher fe condensation temperatures . iron cloud formation effectively removes nearly all iron from the atmosphere , and the abundances of fe - bearing gases above the clouds rapidly decrease with altitude . monatomic fe gas is the dominant fe - bearing gas in a protosolar composition gas until it is replaced by fe(oh)@xmath0 at low temperatures and high pressures . the conversion between fe and fe(oh)@xmath0 is represented by the net thermochemical reaction @xmath17 and the solid line dividing the fe and fe(oh)@xmath0 fields in figure [ figure iron chemistry overview ] indicates where these gases have equal abundances a(fe ) = a(fe(oh)@xmath0 ) @xmath18fe@xmath19 , where @xmath20fe@xmath19 is the total amount of iron in the gas . the position of this line is given by @xmath21,\ ] ] showing that an increase in metallicity will shift the fe - fe(oh)@xmath0 boundary to higher temperatures and lower pressures . in other words , an increase in metallicity increases the stability field of fe(oh)@xmath0 for otherwise constant conditions . the mole fraction abundance of monatomic fe as a function of pressure and temperature is shown in figure [ figure iron gas 1]a . as mentioned above , monatomic fe is the dominant fe - bearing gas over a wide range of pressures and temperatures in a solar system composition gas . below the fe clouds , the abundance of fe gas is representative of the total iron content of the atmosphere ( @xmath22 ) , and its abundance is given by @xmath23.\ ] ] upon fe metal condensation , the amount of iron in the gas rapidly decreases and the equilibrium fe gas abundance is governed by its vapor pressure over solid or liquid iron , represented in reaction ( [ reaction fe condensation ] ) . the mole fraction abundance of monatomic fe above the clouds is given by @xmath24 inversely proportional to @xmath25 . the fe gas abundance is independent of metallicity in this region because it depends solely on the temperature - dependent vapor pressure of iron . as described below ( see @xmath4[sss iron hydride , feh ] and @xmath4[sss iron monohydroxide , feoh ] ) , this expression can be used with chemical equilibria to determine the abundances of other iron gases in substellar atmospheres . equations giving the abundance of fe ( and other fe - bearing gases ) as a function of temperature , pressure , and metallicity below" +"recently , there is growing interest in spontaneous pattern forming processes that can yield regular microscopic textures . a widely studied example is phase separation , shown by various chemical and physical processes . most of the experiments are concerned with initially homogeneous systems , where pattern formation starts after a temperature quench shifts the system into an unstable state . however , a new stream of research is being defined by studies on those processes where phase separation takes place in the wake of moving fronts . two mechanisms are known to yield spinodal phase separation behind traveling fronts . in the first , the concentration of the phase - separating compound lies between the spinodal points , but the temperature only drops below the critical value , required for the instability to occur , behind a quenching front . alternatively , when the concentration is initially in the stable regime , a source front shifting it in between the spinodal points can switch the system into the unstable , pattern - forming range . some important aspects on these mechanisms are listed as follows . computational studies on phase separation under directional quenching are presented in @xcite and @xcite . the phase separation was studied is the framework of the cahn - hilliard equation . at high velocities of the cooling front , irregular morphology ( i m ) emerged . at decreasing front velocities , stripes parallel to the quenching front , termed lamellar morphology ( lm ) , and stripes perpendicular to the front , termed columnar morphology ( cm ) were found . although little attention has been paid to the systematic investigation of the textures when the stripes were oblique to the front , we will consider these kind of patterns , and refer to them as oblique morphology ( om ) . the examination of phase separation in the wake of source fronts has been motivated by the desire to set up a minimal model of the liesegang phenomenon , in which a series of precipitate stripes emerge in the wake of the diffusion front of a reagent , referred to as the `` outer electrolyte '' , that penetrates into a hydrogel containing an `` inner electrolyte '' . modeling the formation of the one - dimensional liesegang patterns has been achieved by assuming that the reaction of the electrolytes yields an intermediary compound first , that separates into high and low density regions according to the cahn - hilliard equation . several experimental results have been reported on two - dimensional striped structures formed in the wake of filiform source fronts . besides the classical liesegang experiments @xcite , a great variety of such patterns have been found in the @xmath0 reaction in polyvinyl - alcohol ( pva ) hydrogel medium @xcite . parallel and oblique morphologies have also been observed in this reaction . however , up to this time , no mathematical models have been elaborated for describing these formations . in this paper we investigate the formation of the microscopic , striped ( `` secondary '' ) patterns emerging in the @xmath0 reaction running in pva hydrogel sheets . the main characteristics of the parallel and oblique morphologies observed in the experiments have been reproduced by computer simulations based on phase separation described by the cahn - hilliard equation . the @xmath0 reaction has been studied in a `` liesegang - like '' setup , with @xmath1 as the outer electrolyte , and @xmath2 as the inner electrolyte homogenized in pva hydrogel . details of the sample preparation are described in . the @xmath1 penetrates into the gel by diffusion , and its reaction with the inner electrolyte leads to a great variety of precipitate structures . these have been classified into `` primary '' and `` secondary '' patterns @xcite . in the following , the formation of the secondary , striped microscopic patterns is examined . first , the reaction - diffusion front of the @xmath1 sweeps through the gel , which is assumed be the source of a compound that phase separates into high - density ( @xmath3 precipitate ) and low - density ( free of precipitate ) stripes . the @xmath3 precipitate stripes are mostly parallel to the reaction - diffusion front , and in some cases oblique morphology has also been found . although the source front can not be observed by the naked eye , the oblique morphology can be identified by an intrinsic characteristic : in the case of the lamellar morphology , the stripes appear one by one along the source front , that is , their growth does not proceed via the elongation of their end points . in contrast , in the case of the oblique morphology , the stripes have growing endpoints in the wake of the source front , and they form an angle with the envelope of their terminal points . the character of the striped microscopic patterns is correlated with the speed of the source front . although the source front is not visible , it is followed by a sharp precipitation front , where a blue - green compound is formed that shows no structure when investigated with an optical microscope @xcite . this is referred to as the active border of the blue - green precipitate , it can easily be observed even by the naked eye , and is likely to follow the shape and the speed of the source front . if the front velocity is between @xmath4 , uniformly distributed colloidal precipitate forms ahead of the active border , but behind the source front . when the velocity is even smaller , the precipitate starts to show a pattern : a regular structure of parallel stripes of colloidal precipitate appears . smaller front velocities lead to longer stripe wavelengths @xcite . note that in contrast to the hypotheses presented in @xcite , it is not believed any more that the active border is the source of the stripes precursor . the first emerging stripes will be parallel to the active border . when the source front does not change its shape and orientation , the subsequent stripes will form parallel to the previous stripes and the front as well , giving rise to a lamellar morphology . according to video microscope observations , a possible scenario for the formation of the oblique stripes is the following : when the source front suddenly changes its shape or orientation , _ e.g. _ as a result of an influx of the outer electrolyte from a novel direction , the newly formed stripes can not follow the front s altered orientation , but form more or less parallel to the previous ones . the newly formed stripes elongate only up to the limit of the region already visited by the source front , with the envelope of their growing endpoints being parallel to the actual position of the front ( fig . the process of phase separation , occurring in the wake of the @xmath0 reaction - diffusion front , has been modeled by the cahn - hilliard equation with a ginzburg - landau free energy @xcite . although one of the equilibrium densities of this free energy is negative , and therefore , in our case unphysical , the equation can easily be rescaled to a form where both equilibrium densities are positive . however , for the sake of simplicity and without offending the physical content , we have used the free energy with minima at @xmath5 and @xmath6 . in order to focus our attention to the pattern formation , the reaction - diffusion system that produces the phase separating chemical has not been included in our model . in order to describe the source front , a gaussian - type source term @xmath7 has been added to the cahn - hilliard equation : @xmath8+s(x , y , t;v ) \label{ch}\ ] ] where @xmath9 ; \label{gauss}\ ] ] initially , the concentration of the compound @xmath10 is set to the stable magnitude @xmath11 in the whole rectangular simulation area , where @xmath12 is a random uniform deviate distributed between @xmath13 @xcite . this deviate has been added to the model in order to make it more realistic . the value @xmath14 is increased by the source , moving with constant speed @xmath15 , to the constant value @xmath16 @xcite . the speed @xmath15 of the source , as well as the concentration @xmath16 next to the source front , are considered as independent simulation parameters . having the speed @xmath15 fixed , the value of @xmath16 is determined by the amplitude @xmath17 and the width @xmath18 of the gaussian source . if @xmath16 lies in between the spinodal points , that is , @xmath19 , the system will be unstable against linear perturbations , and phase separation will take place in the wake of the front . as time goes on , the concentration profile @xmath20 tends to reach the equilibrium values , and a `` ripening '' of the regions with the stable concentrations will take place as well . however , the initial conditions , as well as the movement of the gaussian - type source `` front '' will strongly affect the emerging patterns . these features will be our primary concern . the equation ( [ ch ] ) was solved on a rectangular grid using the finite difference method.$ ] and the fourth order term was approximated by @xmath21 -8 [ c(x_{i-1},y_j)+c(x_{i+1},y_j)+c(x_i , y_{j+1})+c(x_i , y_{j-1 } ) ] + 20c(x_i , y_j ) $ ] ] periodic boundary conditions have been used in both directions . the time evolution of the system was computed by explicit simple time marching on a rectangular grid . the mesh size was @xmath22 , while the time step was @xmath23 . a negligible change in some selected simulation results was only observed when the mesh size was halved and the time step was diminished @xmath24 times . it is also important to mention that the effect of the grid anisotropy on the simulation results was also of minor importance . this has been checked by comparing pattern formation in the wake of source fronts with different orientations . the speed of the source front , as well as the initial conditions , play a decisive role in determining the character of the pattern formation . in this section , our concern will be to investigate their influence . initially , the concentration was set to @xmath11 in the simulation area . this was increased by the front to @xmath16 , a value being in between the spinodal points . in the following , the results for the case @xmath25 will be presented , and major differences for @xmath26 will be mentioned . in our investigations , the source fronts were traveling with different constant speed values . although in the experiments the front speed varies in time , this change is usually not significant for @xmath27 stripe wavelength , and the front speed can be considered locally constant . different pre - patterns with @xmath28 introduced in the @xmath29 space units region of the simulation area highly affected the character of the patterns emerging even after the front sweeps through this region . note that the source was started at @xmath30 space units from the @xmath31axis of the simulation area . in the following , patterning at three different initial conditions are presented . the effects of the front speeds are also discussed within these cases . a. ) in the simplest scenario , the front is started parallel to the @xmath31axis of the rectangular grid , and sweeps with constant speed and orientation toward the opposite edge . the concentration is @xmath11 all over the simulation area , that is , no initial patterning is introduced in the system . depending on the front" +"recent successful observation of degenerate boson - fermion mixture ( dbfm ) of trapped alkali - metal atoms by different experimental groups @xcite initiated intensive experimental studies of different novel phenomena @xcite . among these experiments , apart from the study of dbfm @xmath1li @xcite , @xmath2na-@xmath3li @xcite and @xmath4rb-@xmath5k @xcite , there have been studies of degenerate fermion - fermion mixtures ( dffm ) of two components of @xmath5k @xcite and @xmath3li @xcite . the collapse in a dbfm of @xmath4rb-@xmath5k atoms has been observed @xcite and studied @xcite by modugno _ et al . _ and by the present author @xcite and more recently by ospelkaus _ there have also been investigations on the formation of bright @xcite and dark @xcite solitons in a dbfm . several theoretical investigations @xcite of a trapped dbfm studied the phenomenon of mixing - demixing when the boson - fermion repulsion is increased . for a weak boson - fermion repulsion at 0 k both the bose - einstein condensate ( bec ) and the degenerate fermi gas ( dfg ) have maxima of probability density at the center of the harmonic trap . however , with the increase of boson - fermion repulsion , the maximum of the probability density of the dfg could be slowly expelled from the central region . with further increase of boson - fermion repulsion , the dfg could be completely expelled from the central region which will house only the bec . this phenomenon has been termed mixing - demixing in a dbfm . the phenomenon of demixing has drawn some attention lately as in a demixed state an exotic configuration of the mixture is formed , where there is practically no overlap between the two components and one can be observed and studied independent of the other . it has been argued @xcite that such a demixed state in dbfm should be possible experimentally by increasing the interspecies scattering length near a feshbach resonance . in view of this it is of interest to see if , in addition to a dbfm , such a demixed state appears in a dffm . the purpose of this paper is to study and illustrate this mixing - demixing phenomenon in a trapped dffm using a coupled time - dependent mean - field - hydrodynamic model inspired by the success of a similar model in the investigation of fermionic collapse @xcite and bright @xcite and dark @xcite solitons in a dbfm . the conclusions of the study on bright soliton @xcite are in agreement with a microscopic study @xcite , and those on collapse @xcite are in agreement with experiments @xcite . there have been prior suggestions of mixing - demixing in a trapped dffm upon an increase of interspecies repulsion . roth and feldmeier @xcite discuss the possibility of demixing mathematically using a energy density functional approach . _ @xcite demonstrate demixing numerically using model hydrodynamic flow equations . in contrast to these previous time - independent studies for stationary states , the present study relies on a time - dependent formulation and demonstrates demixing also for an increase of the trapping frequencies and should be considered complimentary to these previous investigations . the present suggestion of demixing with an increase of trapping frequency is easier to implement experimentally than increasing the interspecies scattering length using a feshbach resonance . we look for mixing - demixing in a trapped dffm in the spherically - symmetric as well as quasi - one - dimensional configurations . for a weak fermion - fermion repulsion , we find the formation of a fully mixed state with both the fermion clouds occupying the central region of the trap . if the fermion numbers of the two types of fermions are largely different , a fully demixed state of dffm appears with the increase of fermion - fermion repulsion , when the component with smaller number of fermions is completely expelled from the central region of the trap which is occupied only by the component with the larger number of fermions . this demixing also appears for increasing trap frequencies which increases the fermion density and hence fermion - fermion repulsion thus resulting in a demixing . to the best of our knowledge this is the first study of mixing - demixing in a dffm using a time - dependent formulation capable of investigating nonequilibrium states . previous studies of demixing @xcite employed time - independent formulations appropriate for stationary states only . in sec . ii we present the mean - field - hydrodynamic model we use in our investigation in the spherically - symmetric as well as quasi - one - dimensional configuration . the numerical results are presented in sec . iii where we illustrate demixing with the increase of interspecies repulsion and of the harmonic trapping potential . finally , in sec . iii a brief summary of our findings are given . a proper description of a dffm should employ @xcite a fully antisymmetrized microscopic slater determinant wave function for each component . however , a simplified mean - field - hydrodynamic lagrangian for a dfg has been used successfully to study a dbfm @xcite , which we shall use in the present investigation . the virtue of the mean - field model over a microscopic description is its simplicity and good predictive power . to develop a set of practical time - dependent mean - field - hydrodynamic equations for a dffm , we consider the following lagrangian density @xcite @xmath6 where @xmath7 is the mass of component @xmath8 , @xmath9 a complex probability amplitude , @xmath10 the real probability density , @xmath11 the number , @xmath12 @xmath13 , and @xmath14 is the confining trap . here the interspecies coupling is @xmath15 with the reduced mass @xmath16 and @xmath17 is the interspecies scattering length . the interaction between intra - species fermions in spin - polarized state is highly suppressed due to pauli blocking term @xmath18 and has been neglected in eq . ( [ yy ] ) and will be neglected throughout . the kinetic energy terms in this equation @xmath19 are derived from a hydrodynamic equation for the fermions @xcite and contribute little to this problem compared to the dominating pauli blocking term in eq . ( [ yy ] ) . however , the inclusion of the kinetic energy terms in eq . ( [ yy ] ) leads to a smooth solution for the probability density everywhere @xcite . to keep the algebra simple and without losing generality in our calculation we shall take equal fermion masses : @xmath20 this simulates well the fermion mixtures of ground and excited states of @xmath3li @xcite and @xmath5k @xcite atoms observed experimentally . the lagrangian density of each fermion component in eq . ( [ yy ] ) is identical to that used in refs . @xcite . the mean - field dynamical equations for the system are just the usual euler - lagrange ( el ) equations @xmath21 where @xmath22 are the three space components , and @xmath23 refer to the fermion components . with lagrangian density ( [ yy ] ) the following el equations of motion are derived in a straight - forward fashion @xcite : @xmath24\psi_j=0 , \nonumber \\ j \ne k=1,2 . \end{aligned}\ ] ] this is essentially a time - dependent version of a similar time - independent model used recently for fermions @xcite . for a stationary state eqs . ( [ e ] ) yield the same result as the formulation of ref . for a system with large number of fermions both reduce to @xcite the well - known thomas - fermi approximation @xcite : @xmath25^{3/2}$ ] , with @xmath26 the chemical potential . in the spherically - symmetric case we take @xmath27 and @xmath28 now transforming to dimensionless variables defined by @xmath29 , @xmath30 @xmath31 and @xmath32 we get @xcite @xmath33\phi_j ( { x};\tau)=0 , \end{aligned}\ ] ] where @xmath34 and @xmath35 , @xmath36 the normalization of the wave - function components is given by @xmath37 we next reduce eq . ( [ e ] ) to a minimal quasi - one - dimensional form in a cigar - shaped geometry where the confining trap of anisotropy @xmath38 has the form @xmath39 with @xmath40 the radial vector and @xmath41 the axial vector . for a cigar - shaped geometry @xmath42 , we consider solutions of eq . ( [ e ] ) of the type @xmath43 where @xmath44 corresponds to the respective circularly symmetric ground - state wave function in the absence of nonlinear interactions and satisfies @xmath45 with normalization @xmath46 now the dynamics is carried by @xmath47 and the radial dependence is frozen in the ground state @xmath48 . the separation of the variables is suggested by the structure of eq . ( [ e ] ) . averaging over the radial mode @xmath49 , i.e. , multiplying eq . ( [ e ] ) by @xmath50 and integrating over @xmath40 , we obtain the following one - dimensional dynamical equations @xcite : @xmath51 \varphi_{{j}}(z , t)=0,\end{aligned}\ ] ] where @xmath52 and @xmath53 @xmath54^{2/3},\end{aligned}\ ] ] where @xmath55 in eq . ( [ j ] ) the normalization is @xmath56 . in eq . ( [ j ] ) , we introduce the dimensionless variables @xmath57 , @xmath58 , @xmath59 , with @xmath60 , so that @xmath61{\phi}_{{j}}(x,\tau)=0,\quad j\ne k = 1,2 , \end{aligned}\ ] ] where @xmath62 @xmath63 and @xmath64 however , by taking @xmath65 we can modify the harmonic trap . in eq . ( [ n ] ) , the normalization condition is given by @xmath66 . of eq . ( [ j ] ) vs @xmath41 for @xmath67 and @xmath68 in the quasi - one - dimensional case ( @xmath69 ) for @xmath70 ( a ) 50 nm , ( b ) 100 nm , ( c ) 150 nm , and ( d ) 400 nm . , title=""fig : "" ] of eq . ( [ j ] ) vs @xmath41 for @xmath67 and @xmath68 in the quasi - one - dimensional case ( @xmath69 ) for @xmath70 ( a ) 50 nm , ( b ) 100 nm , ( c ) 150 nm , and ( d ) 400 nm . , title=""fig : "" ] of eq . ( [ j ] ) vs @xmath41 for @xmath67 and @xmath68 in the quasi - one - dimensional case ( @xmath69 ) for @xmath70 ( a ) 50 nm , ( b ) 100 nm , ( c ) 150 nm , and ( d ) 400 nm . , title=""fig : "" ] of eq . ( [ j ] ) vs @xmath41 for @xmath67 and @xmath68 in the quasi - one - dimensional case ( @xmath69 ) for @xmath70 ( a ) 50 nm , ( b ) 100 nm , ( c ) 150 nm , and ( d ) 400 nm . , title=""fig : "" ] we solve the coupled mean - field - hydrodynamic equations ( [ d1 ] ) and ( [ n ] ) numerically using a time - iteration method based on the crank - nicholson discretization scheme elaborated in @xcite . we discretize the mean - field equations using time step @xmath71 and space step @xmath72 . in the quasi - one - dimensional case we span @xmath73 from @xmath74 to @xmath75 , and in the three - dimensional case we span @xmath73 from 0 to 30 . in both cases we start with the gaussian ground - state solution of the linear harmonic oscillator problem as input at @xmath76 while we set the nonlinearities @xmath77 . in the three - dimensional case governed by eq . ( [ d1 ] ) we take @xmath78 and in the one - dimensional case governed by eq . ( [ n ] ) we take @xmath79 . with these" +"the antarctic neutrino telescope amanda @xcite and the future km@xmath0 icecube @xcite are designed to observe high - energy neutrinos from astrophysical sources . the ice is instrumented with photomultipliers to pick up the cherenkov light from secondary charged particles . in order to reach the large volume needed to detect the expected small fluxes at high energies , the density of optical modules is far too sparse to measure , for example , solar neutrinos . however , it has been recognized for a long time that these instruments can detect a supernova ( sn ) neutrino burst because the cherenkov glow of the ice can be identified as time - correlated noise among all phototubes @xcite . this approach has been used by amanda to exclude the occurrence of a galactic sn over a recent observation period @xcite . for amanda the physics potential of a possible sn observation is essentially limited to its detection , notably in the context of the supernova early warning system ( snews ) that would alert the astronomical community several hours before the optical explosion @xcite . for the future icecube with 4800 optical modules , however , the number of detected cherenkov photons would be of order @xmath2 and thus so large that several interesting physics questions could be addressed in earnest . the observed quantity is the number of cherenkov photons caused by the sn neutrinos as a function of time , i.e. a measure of the energy deposited by the neutrinos in the ice . therefore , the information about the sn signal is far more limited than what can be extracted from a high - statistics observation in super - kamiokande or other low - energy experiments that detect individual events . however , galactic sne are so rare , perhaps a few per century , that the chances of observing one depend crucially on the long - term stability of the neutrino observatories . once icecube has been built it may well operate for several decades , backing up the low - energy experiments . besides the detection and associated early warning one could measure important details of the neutrino light - curve , for example the existence and duration of the initial sn accretion phase , the overall duration of the cooling phase , and so forth . such an observation would provide a plethora of astrophysically valuable information . however , from the perspective of neutrino physics a _ simultaneous _ observation in both icecube and another large detector such as super - kamiokande or hyper - kamiokande would be especially useful . assuming that the neutrinos have traversed significantly different paths through the earth , the two signals could well show measurable differences caused by neutrino oscillations in matter . as this earth effect shows up only for certain combinations of neutrino mixing parameters , a dual observation may well distinguish , for example , between the normal and inverted neutrino mass hierarchy . it is well known that observing sn neutrinos with two or more detectors with different earth - crossing lengths is extremely useful , but icecube s potential has not been explored in this context . with all the low - energy observatories being in the northern hemisphere , icecube s location in antarctica is uniquely complementary for this purpose . any oscillation signature depends on the small flavor - dependent differences between the fluxes and spectra at the source . if these differences were as large as had been assumed until recently there would be little question about icecube s usefulness for co - detecting the earth effect . however , a more systematic study of the flavor - dependence of the sn neutrino fluxes and spectra reveals that these differences are more subtle , although by no means negligible @xcite . we evaluate icecube s potential as a co - detector from the perspective of these `` pessimistic '' assumptions about the primary fluxes and spectra . this paper is organized as follows . in sec . [ at - icecube ] , we show that the neutrino signal from a galactic supernova can be measured at icecube with a sub - percent statistical precision . in sec . [ earth - effects ] , we calculate the earth matter effects on this signal and illustrate that it is possible to detect them in conjunction with another high statistics experiment . sec . [ concl ] concludes . the sn neutrinos streaming through the antarctic ice interact according to @xmath3 and some other less important reactions . the positrons , in turn , emit cherenkov light that is picked up by the optical modules ( oms ) frozen into the ice . while the expected number of detected photons per om was calculated in refs . @xcite , we revisit their estimate for two reasons . first , the sn signal was directly scaled to the historical sn 1987a observation in kamiokande ii so that the exact assumptions about the neutrino flux are not directly apparent . second , the expected number of cherenkov photons detected by one om was based on estimating an effective ice volume seen by one om . however , it is much simpler to work in the opposite direction and start with the homogeneous and isotropic cherenkov glow of the ice caused by the sn neutrinos . the om is immersed in this diffuse bath of photons and picks up a number corresponding to its angular acceptance and quantum efficiency . as a first simplification we limit ourselves to the signal caused by the inverse @xmath4 reaction @xmath3 . the @xmath5 fluence ( time - integrated flux ) at earth is @xmath6 we define the `` sn fudge factor '' as @xmath7 where @xmath8 is the total energy leaving the sn in the form of @xmath5 after flavor oscillations have been included , @xmath9 is the average @xmath5 energy , and @xmath10 the distance . the energy deposited in the ice per target proton is @xmath11 . for the inverse @xmath4 cross section we ignore weak - magnetism and recoil corrections and also the difference between @xmath5 and positron energy so that @xcite @xmath12 for the neutrino flux of each neutrino and anti - neutrino species we assume a distribution of the form @xcite @xmath13\,,\ ] ] where @xmath14 is the average energy , @xmath15 a parameter that typically takes on values 2.55 depending on the flavor and the phase of neutrino emission , and @xmath16 the overall flux at the detector in units of @xmath17 . this distribution implies @xmath18 altogether we thus find @xmath19 with @xmath20 this fudge factor can also be taken to include deviations from the simplified energy dependence of the cross section and deviations from the assumed spectral shape . the cherenkov angle for photon emission by a charged particle is @xmath21 where @xmath22 is the medium s refractive index and @xmath4 the particle s velocity . with @xmath23 for ice , neglecting the @xmath24-dependence , and @xmath25 we have @xmath26 . a particle with unit charge produces cherenkov photons per unit path length and per unit wavelength band according to @xmath27 where @xmath28 is the fine - structure constant . assuming that @xmath22 and thus @xmath29 are independent of wavelength we integrate over @xmath24 and find @xmath30 taking the useful wavelength range to be 300600 nm this translates into 319 photons per cm pathlength . taking the positron mean free path to be 12 cm for an energy of 20 mev , and taking it to be proportional to its energy , the number of useful cherenkov photons per deposited neutrino energy is @xmath31 with yet another fudge factor @xmath32 . the density of ice is @xmath33 , corresponding to about @xmath34 proton targets . therefore , the sn neutrinos produce @xmath35 useful cherenkov photons per unit volume of ice . multiplying this number with the speed of light and dividing by @xmath36 gives us the resulting diffuse photon flux in units of @xmath37 . however , the average lifetime of these photons is @xmath38 with @xmath39 the absorption length . therefore , the neutrino - induced photon fluence is found by multiplying the flux with @xmath38 , @xmath40 where @xmath41 . the number of events produced by this fluence in a given om depends on the average quantum efficiency taken to be @xmath42 . in addition , it depends on the angular acceptance , i.e. the effective photo cathode detection area @xmath43 times the angular acceptance range @xmath44 . therefore , in one om we expect @xmath45 with @xmath46 this result is independent of the presence of bubbles in the ice that scatter the photons . the cherenkov glow of the ice represents an isotropic and homogeneous distribution that is not changed by elastic scattering . in order to compare our result with the one derived in ref . @xcite we need to translate their assumptions into our fudge factors . the @xmath5 distribution was taken to follow a fermi - dirac spectrum with @xmath47 mev , implying @xmath48 mev . the distance of the sn was taken to be 10 kpc , and the total energy release was scaled to the kamiokande ii signal for sn 1987a . with our choice of the @xmath4 cross section these assumptions correspond to @xmath49 erg , i.e. to @xmath50 . these authors also used a quadratic energy dependence of the cross section . integrating over their fermi - dirac spectrum they effectively used @xmath51 . further , they assumed 3000 useful cherenkov photons for 20 mev deposited energy , i.e. effectively @xmath52 . for the absorption length they used 300 m , i.e. @xmath53 . finally , they assumed a quantum efficiency of 25% , a cathode area of 280 @xmath54 , and an acceptance range of @xmath55 , i.e.@xmath56 . altogether , we find for these assumptions @xmath57 per om . this compares with 273 in ref . @xcite , i.e. our result is larger by a factor 1.5 . the result in ref . @xcite was backed up by a detailed monte carlo treatment of the production and propagation of cherenkov photons in the amanda detector . therefore , the difference may well relate to details of the om acceptance and wavelength - dependent quantum efficiency and photon propagation . many of these details will be different in icecube where 10 inch photomultiplier tubes and different regions of ice will be used . detailed values for the detector - dependent fudge factors must be determined specifically for icecube once it has been built . the main difference between the assumptions in ref . @xcite and our estimate is the absorption length . when using amanda as a sn observatory a realistic value was taken to be around 100 m @xcite . the vast difference between these estimates is that the former was based on the measured absorption length in a dust - free region of the ice . for our further estimates we stick to 100 m as a conservative assumption . in our derivation we have used the time - integrated neutrino flux , amounting to the assumption of a stationary situation . the absorption time for photons is very small , @xmath58 . the sn signal will vary on time scales exceeding 10 ms . therefore , the cherenkov glow of the ice follows the time - variation of the sn signal without discernible inertia . hence one may replace the neutrino fluence with a time - dependent flux and @xmath59 with an event rate @xmath60 . moreover , for our further discussion it will be useful to consolidate our fudge - factors into one describing the detector response , and others characterizing the neutrino flux . therefore , we summarize our prediction for the event rate per om in the form @xmath61 where @xmath62 is the @xmath5 luminosity after flavor oscillations and @xmath63 here" +"the oort cloud @xcite remains the most mysterious part of our solar system , primarily because it can not be directly observed . our only observational clues to the size , shape , mass and composition of the oort cloud come from observations of long - period comets . the demographics of observed long - period comets have been the starting point of almost all attempts to model the oort cloud ( eg . * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . until the last ten or so years , the vast majority of comets were discovered by systematic eyeball searches , using small telescopes @xcite . these surveys have been highly effective at identifying large samples of comets , and in deriving their orbital parameters . they do , however , have three major drawbacks : * unknown selection function : it is very unclear how often different parts of the sky are surveyed , and to what depth . surveys are clearly more sensitive to comets with bright absolute magnitudes and perihelia close to the earth , but the strength of this effect is very hard to estimate @xcite . * limited range of comets observed : eyeball surveys find few comets fainter than an absolute magnitude of 10 and with perihelia beyond 3au . * poorly defined photometry : these surveys quote the `` total brightness '' of a comet . total cometary magnitudes are notoriously unreliable . they are typically measured by defocussing a standard star to the same apparent size as the comet , but this apparent size is heavily dependent on observing conditions and observational set - up . despite these drawbacks , many attempts have been made to derive the basic parameters of the long period comet population from eyeball - selected historic samples . the most heroic and influential attempt was that of @xcite . everhart carried out an exhaustive analysis of the historical circumstances in which comets were discovered , over a 127 year period . he developed a model for the sensitivity of the human eye , and used it to calculate the period over which a given historical comet could have been seen . this was then used to estimate the completeness of the comet sample : if a given type of comet was typically seen early in its visibility window , surveys should be complete for this type of comet . if the mean time to find a given type of comet is , however , comparable to the length of the estimated visibility window , the completeness is probably low . using this method , everhart estimated that for every comet seen , another 31 were missed . a more modest and recent attempt was that of @xcite . he restricted himself to the brightest and nearest comets , for which he claimed ( on the basis of discovery trends ) historical surveys were highly complete . the statistics of these comets were simply extrapolated to larger perihelia and fainter absolute magnitudes , with no correction for observational incompleteness . as one would expect , the flux of long - period comets through the inner solar system estimated by @xcite is much lower that that estimated by @xcite . despite these attempts , several basic questions about the demographics of long - period comets remain unresolved . one question concerns small comets @xcite : those with nuclear radii less than @xmath0 km ( absolute magnitudes @xmath1 ) . extrapolating the everhart data implies that there should be a large population of such comets . @xcite was unable to tell whether his model predicted a large population of such comets or not . a second question concerns the number of comets per unit perihelion . @xcite found that this number rises from the sun out to 1au , but was unable to determine whether it keeps rising at larger perihelia . @xcite found no significant rise , but had large enough error bars to bracket both of everhart s possibilities . the observational situation has changed radically in the last few years . the advent of large format sensitive ccds has allowed automated surveys to supplant eyeball searches as the main mechanism for finding new long - period comets . most long period comets are now being found as by - products of various automated searches for near - earth objects , such as the lincoln near - earth asteroid research ( linear ) project @xcite , the catalina sky survey , loneos and neat @xcite . many are also found by space - based coronagraphs as they approach very close to the sun @xcite , though these are mostly fragments of recently disintegrated larger comets @xcite . in this paper , i attempt to deduce the statistical properties of the long - period comet population from one of these ccd surveys : the linear survey . this has a far better defined selection criterion than any historical eyeball survey , and extends to much larger perihelia and fainter absolute magnitudes . it thus allows both an independent check and an extension of previous estimates of the long - period comet population . near earth asteroid ( neo ) surveys are not optimized for comet detection . while they find many long - period comets , they do not publish their raw data , nor all the details one would like of their exact detection algorithms and sky coverage . in particular , they do not publish on - going photometry of the comets they discover . nonetheless , enough information is available to make a first pass at estimating the true population of long - period comets from their data . there have been previous attempts to use these surveys to detemine the true populations of neos ( eg . * ? ? ? * ) and dormant comets @xcite , but this paper is the first attempt of which i am aware to do this for active comets . in the next few years , the situation should further improve , with the advent of a new generation of wide - field survey telescopes , such as skymapper , pan - starrs @xcite and gaia @xcite . these surveys will predominantly find comets much fainter and more distant than historical surveys . the analysis in this paper allows a first estimate of just how many long - period comets these surveys can find , and how best to identify them . i start off by defining a sample of comets drawn from the linear sample , and examining its properties , which are very different from those of eyeball samples ( [ sample ] ) . a model of the long - period comet population is then generated ( [ model ] ) based on and extrapolating the historical eyeball - selected surveys . a monte - carlo simulation of this comet population as it would be observed by linear is then developed ( [ montecarlo ] ) . the results are compared to the observed sample in [ compmodels ] : i find that the hughes model is quite a good fit to the data , but that the everhart model is not . i derive my own best - fit model of long - period comet demographics . the consequences of this new model are many : i examine them in [ discussion ] before drawing conclusions in [ conc ] . of the several near - earth asteroid surveys now under - way , the lincoln near - earth asteroid research ( linear ) project @xcite was most suitable for constraining the long - period comet population . this is because : * they discover more comets than any other single survey . * they publish sky charts on their web page showing the area of the sky observed during each lunation , with the point - source magnitude limit reached at each location . * their sky coverage and magnitude limit is relatively simple and uniform across this period . the comet sample was defined as follows : 1 . the comet has an orbital period longer than 200 years . 2 . the comet reached perihelion between 2000 jan 1 and 2002 dec 31 . the comet was either discovered by linear between these dates , or could have been discovered by linear between these dates had it not already been discovered by someone else , or discovered prior to 2000 jan 1 . the 2000 - 2002 date range was chosen because comet details ( from the catalog of cometary orbits , * ? ? ? * ) and sky - maps ( including limiting magnitudes ) are available . @xcite listed 25 comets as having been discovered or co - discovered by linear which met our criteria . i needed , however , to add two additional sub - samples : * comets discovered prior to 2000 , but which reach perihelion in the period 2000 - 2002 , and which could have been first discovered by linear within this period , had they not already been found . * comets discovered in 2000 - 2002 inclusive by other surveys , but which would subsequently have been seen by linear during this period . potential members of the two additional sub - samples were selected from @xcite . each candidate was checked for its detectability by linear , using the ephemerides and predicted magnitudes generated by the minor planet center . the predicted positions and brightnesses were compared to the maps of linear sky coverage . these maps show only the integrated coverage per lunation , not the night - by - night or hour - by - hour coverage , but most of these comets move slowly enough that this should nt much matter . this process added another 27 comets to our sample . 8 had been detected by linear during 1999 , but reached perihelion in 2000 or 2001 . most of the remainder were first identified by other near - earth asteroid surveys , particularly the catalina sky survey , loneos and neat . for every comet in our final sample , the original discovery details ( as distributed by the central bureau of astronomical telegrams ) were checked . from these , the discovery date , discovery magnitude @xmath2 and discovery circumstances were noted . the discovery magnitudes are total magnitudes ( m1 ) . it is not clear how reliable and homogeneous these magnitudes are , but no better source of ccd photometry is available . they are based on ccd observations by professional astronomers of typically barely resolved objects , and so should be good to @xmath3mag . absolute magnitudes @xmath4 were computed from these discovery magnitudes @xmath2 . the standard equation was used : @xmath5 ( eg . * ? ? ? * ) , where @xmath2 is the observed total magnitude at discovery and @xmath6 a power - law parameterization of the dependence on heliocentric distance . as is conventional for solar system work , the absolute magnitude is defined as the observed magnitude if the object were at a distance of 1 au from both the earth and the sun . following @xcite , the dynamically new and old comets were treated differently ( the new ones are much brighter at large heliocentric radii , at least on their way in ) . a comet is classed as dynamically new if its original semi - major axis @xmath7 is @xmath8 10,000 au , old if @xmath9 10,000 au , and undetermined if the orbit class in @xcite is ii or worse . for new comets , @xmath10 was used if they are seen pre - perihelion and @xmath11 if seen afterward . for old comets , the values are 5.0 and 3.5" +"graph modification problems lie in the intersection of algorithmics , graph theory , and network analysis . formally , a graph modification problem is given as follows . herein , graph modification operations include edge deletions , insertions , and contractions , and vertex deletions . classic examples for @xmath1 are `` being edgeless '' ( this is known as vertex cover when the allowed modification operation is vertex deletion ) and `` being a disjoint union of cliques '' ( this is known as cluster editing when the allowed modification operations are edge deletion and insertion ) . we will deal with simple and natural graph modification problems that are motivated by real - world applications . in these applications , the common way of solving these problems is via heuristics . we present four main themes on how the interaction between parameterized algorithmics and heuristics can take place , each time illustrated by some `` key '' graph modification problems . in section [ sec : hcd ] , we consider a graph - based clustering problem that has been defined only implicitly by means of a greedy heuristic @xcite . we describe how a natural np - hard parameterized problem ( referred to as highly connected deletion ) can be derived from this , and how this leads to further insight into the corresponding clustering approach @xcite . in section [ sec : deganon ] , starting with a practically successful heuristic for anonymizing social networks @xcite ( the corresponding np - hard problem is known as degree anonymity ) , we describe how a closer inspection yields that either the corresponding approach provides optimal solutions in polynomial time or one can derive a polynomial - size problem kernel with respect to the parameter maximum vertex degree of the underlying graph @xcite . moreover , we briefly indicate how this led in a feedback loop , so to speak to improvements also for the heuristic approach @xcite . in section [ sec : fast ] , we study parameterized local search the parameter is the degree of locality @xcite . local search is a key technique in combinatorial optimization and the design of `` improvement heuristics '' . we address both limitations and prospects of this approach . we discuss , among others , the np - hard example problems vertex cover and feedback arc set in tournaments . in section [ sec : pbo ] , we finally discuss how one may speed up parameterized algorithms by a clever use of heuristics . in particular , we discuss parameterization above lower bounds derived from linear programming relaxations @xcite ( here the key example is the np - hard vertex cover problem ) , and the idea of programming by optimization @xcite ( here the key example is the np - hard cluster editing problem ) . we draw some final conclusions in section [ sec : concl ] . [ [ preliminaries . ] ] preliminaries . + + + + + + + + + + + + + + we assume familiarity with fundamental concepts of graph theory , algorithms , and complexity . a _ parameterized problem _ is a set of instances of the form @xmath2 , where @xmath3 for a finite alphabet @xmath4 , and @xmath5 is the _ parameter_. a parameterized problem @xmath6 is _ fixed - parameter tractable _ , shortly , if there exists an algorithm that on input @xmath2 decides whether @xmath2 is a yes - instance of @xmath6 in time @xmath7 , where @xmath8 is a computable function independent of @xmath9 . a parameterized problem @xmath6 is _ kernelizable _ if there exists a polynomial - time algorithm that maps an instance @xmath10 of @xmath6 to an instance @xmath11 of @xmath6 such that @xmath12 for some computable function @xmath13 , @xmath14 , and @xmath10 is a yes - instance of @xmath6 if and only if @xmath11 is a yes - instance of @xmath6 . the instance @xmath11 is called a _ kernel _ of @xmath2 . a problem that is w[1]-hard does not admit a fixed - parameter algorithm , unless the widely believed conjecture fpt@xmath15w[1 ] fails . in the following , we illustrate how the consideration of heuristic algorithms may lead to the definition of new interesting graph modification problems . our example concerns the interplay between two standard approaches for graph - based data clustering . one approach is to formalize desired properties of clusters and then to find a clustering of the graph such that the output clusters fulfill these properties . this clustering can be obtained by modifying the input graph for example by deleting edges so that all remaining edges are only inside clusters . starting with cluster editing @xcite , there are by now numerous parameterized algorithmics studies on graph modification problems related to clustering , varying on the cluster graph definition @xcite , the modification operation @xcite , or both @xcite . most of the examples of variants of cluster editing evolved primarily from a graph - theoretic interest . another approach is to define the clustering algorithmically , that is , to describe an algorithm that outputs a clustering and to analyze the properties of the clusters that are produced by the algorithm . in this section , we discuss how the consideration of a popular and natural clustering algorithm due to @xcite leads to the definition of the graph modification problem highly connected deletion . this is our key example for how to obtain practically motivated parameterized graph modification problems by a closer inspection of known heuristics . the study of this new problem then may yield new challenges for parameterized algorithmics and , furthermore , provide a better understanding of the strengths and weaknesses of the original heuristic algorithms . we will first discuss the original algorithm and then how we obtain the definition of highly connected deletion from this algorithm . posed the following connectivity demands on each cluster : the _ edge connectivity _ @xmath16 of a graph @xmath0 is the minimum number of edges whose deletion results in a disconnected graph , and a graph @xmath0 with @xmath17 vertices is called _ highly connected _ if @xmath18 . @xcite . ] the algorithm by @xcite partitions the vertex set of the given graph such that each partition set is highly connected by iteratively deleting the edges of a minimum cut in a connected component that is not yet highly connected . the output clusters of the algorithm are the connected components of the remaining graph which are then highly connected . the definition of being highly connected ensures several useful cluster properties , for example that at least half of the possible edges are present within each cluster and that each cluster has diameter at most two @xcite . while hartuv and shamir s algorithm guarantees to output a partitioning into _ highly connected _ subgraphs , it iteratively uses a greedy step to find small edge sets to delete . as a consequence , it is not ensured that the partitioning comes along with a _ minimum number of edge deletions _ making the resulting graphs consist of highly connected components . this naturally leads to the edge deletion problem highly connected deletion where the goal is to minimize the number of edge deletions ; this optimization goal is addressed only implicitly by hartuv and shamir s algorithm . = 10000 ( input ) at ( -3.75 + 0.05,+ 0.75 - 0.05 ) * input : * ; ( input.north west)+(-0.05,+0.05 ) rectangle ( 1.75,-- 0.25 ) ; = [ circle , draw = black!80,minimum size=12pt , inner sep=0pt ] at ( 0,+ 0.7 ) @xmath19 ; = [ circle , draw , fill = black!20,minimum size=5pt , inner sep=2pt ] iin 1, ... ,3 ( t - i ) at ( 0.7 cos(360 * i/ 3 - 3*(180 / 3))-2.5,0.7 sin(360 * i/ 3 - 3*(180 / 3 ) ) ) ; ( t-1 ) edge[- ] ( t-2 ) ; ( t-2 ) edge[- ] ( t-3 ) ; ( t-3 ) edge[- ] ( t-1 ) ; iin 1 , ... , ( k - i ) at ( cos(360 * i/ - 3*(180 / ) ) , sin(360 * i/ - 3*(180 / ) ) ) ; iin 2 , ... , ; ( k - i ) edge[- ] ( k- ) ; i/ in 1/4,1/5,2/5,3/5 ( k - i ) edge[- ] ( k- ) ; ( t-1 ) edge[- ] ( k-5 ) ; ( t-2 ) edge[- ] ( k-3 ) ; ( t-1 ) edge[- ] ( k-4 ) ; ; ( solution ) at ( -3.75 + 0.05,+ 0.75 - 0.05 ) * solution : * ; ( solution.north west)+(-0.05,+0.05 ) rectangle ( 1.75,-- 0.25 ) ; iin 1, ... ,3 ( t - i ) at ( 0.7 cos(360 * i/ 3 - 3*(180 / 3))-2.5,0.7 sin(360 * i/ 3 - 3*(180 / 3 ) ) ) ; ( t-1 ) edge[- ] ( t-2 ) ; ( t-2 ) edge[- ] ( t-3 ) ; ( t-3 ) edge[- ] ( t-1 ) ; iin 1 , ... , ( k - i ) at ( cos(360 * i/ - 3*(180 / ) ) , sin(360 * i/ - 3*(180 / ) ) ) ; iin 2 , ... , ; ( k - i ) edge[- ] ( k- ) ; i/ in 1/4,1/5,2/5,3/5 ( k - i ) edge[- ] ( k- ) ; ( t-1 ) edge[dashed ] ( k-5 ) ; ( t-2 ) edge[dashed ] ( k-3 ) ; ( t-1 ) edge[dashed ] ( k-4 ) ; interestingly , in the worst case the algorithm by @xcite does not give a good approximation for the optimization version of highly connected deletion . consider two cliques with vertex sets @xmath20 and @xmath21 , respectively , and the additional edges @xmath22 for @xmath23 . then these additional edges form a solution set of size @xmath24 ; however , hartuv and shamir s algorithm will ( with unlucky choices of minimum cuts ) transform one of the two cliques into an independent set by repeatedly cutting off one vertex , thereby deleting @xmath25 edges . the following theoretical results are known for highly connected deletion @xcite . it is np - hard even on 4-regular graphs and , provided the exponential time hypothesis ( eth ) @xcite is correct , can not be solved in subexponential time . on the positive side , there is a kernelization that can in polynomial time reduce an instance to one containing at most @xmath26 vertices , and an fpt algorithm that solves highly connected deletion in @xmath27 time . as to the relevance of parameterized algorithmics for highly connected deletion , one has to note that the mentioned fpt algorithm is impractical . in terms of exact solutions , an integer linear programming formulation combined with data reduction rules ( partially coming from the kernelization results ) , however , performs reasonably well @xcite . even when relaxing the goal to find exact solutions for highly connected deletion , data reduction turned out to be beneficial in combination with heuristics ( improving running time and solution quality ) @xcite . in a nutshell , the most practical contribution of parameterized algorithmics in this example is the development of efficient and effective data reduction rules , also helping to improve inexact solutions based on heuristics . a further benefit of considering a formally defined edge modification problem highly connected deletion is that the objective is now independent of a heuristic method used to find it . thus , it becomes possible to evaluate the biological quality of the objective @xcite . as to potential for future research with respect to highly connected deletion , so far other modification operations combined" +"neutral pion photoproduction on the proton at low energies is specially sensitive to chiral dynamics . considering the range of energies from threshold to 500 mev , the total cross section appears to be clearly dominated by the magnetic dipole excitation of the @xmath1 . its role is more important here than for the charged pions photoproduction , because of the smallness of the electric dipole contribution for the neutral pion channels . of course , approaching low energies , the relevance of the @xmath0 resonance decreases fast and may become negligible as we get far from its mass and because of the @xmath2-wave nature of its contribution . close to threshold , charged pion photoproduction has a relatively large cross section that can be well described by just tree - level diagrams which lead to a substantial electric dipole moment . however , the situation is quite different for the neutral pion channels which present a much smaller cross section . qualitatively , this is also well understood as the theoretical models produce a tiny @xmath3-wave amplitude , which actually vanishes in the chiral limit @xmath4 . the smallness of the lowest order tree - level contributions offers a good opportunity for the study of higher order terms of the chiral lagrangian and of loop effects . in fact , one of the important successes of chiral perturbation theory ( chpt ) was the discovery in refs . @xcite of the importance of the loop contributions for the @xmath5 channels . this allowed to solve the serious discrepancies between data @xcite and the low energy theorems ( let ) obtained by previous theoretical models @xcite based on current algebra and the partial conservation of the axial current @xcite . the model of refs . @xcite was further improved in refs . @xcite using a more systematic approach , heavy - baryon chpt ( hbchpt ) , which allows for a proper power counting scheme . the neutral pion photoproduction off protons was analyzed to fourth order in hbchpt in @xcite finding a good agreement with the data that were available at the time . however , the new and very precise data for the @xmath6 reaction obtained at the mainz microtron ( mami ) @xcite have clearly shown the limits of this approach . in ref . @xcite , it has been shown that fourth order hbchpt agrees well with data only up to around 20 mev above threshold . an alternative relativistic renormalization scheme of the baryons chpt , the extended on mass shell ( eoms ) chpt @xcite has been successfully applied to the study of several physical observables such as pion scattering , baryon magnetic moments and axial form factors , baryon masses among others @xcite . the eoms approach is covariant , satisfies analyticity constraints lost in the hb formulation and usually converges relatively faster . surprisingly , a fourth order eoms calculation of the @xmath6 process described the experimental data even slightly worse than the hb one @xcite . a possible reason for the poor agreement could be due to the importance of the @xmath0 resonance , not included in the aforementioned calculations as an explicit degree of freedom . here , it could be more visible than for other channels due to the smallness of the nucleonic contributions of the lowest orders . this was already pointed out by hemmert et al . in ref . actually , they obtained a moderate effect for the electric dipole amplitude at threshold in their hb approach . this result was further explored in ref . @xcite , also in a hbchpt static calculation , finding a sizable cancellation of the @xmath0 contributions by fourth order loop effects . however , it could be expected that , in a dynamical calculation ( with the full @xmath0 propagator ) , the effects could grow very fast as a function of the photon energy as the invariant mass of the system at threshold is close to the resonance mass ( @xmath7 ) . of course , the @xmath0 effects could be accounted for by a change in the low energy constants ( lecs ) and by higher order terms . however , if the @xmath0 resonance plays an important role , its inclusion could lead to a faster convergence and more natural values of the lecs . the possible relevance of the @xmath0 mechanisms for this process was also signaled in refs . @xcite . our purpose in this work is to explore the influence of the @xmath0 mediated mechanisms in the photoproduction of @xmath5 off protons . we will calculate the process in the purely nucleonic eoms chpt scheme up to order @xmath8 and will add the @xmath0 resonance contribution at tree level . we will compare our results with the precise data on the near threshold angular cross sections and photon asymmetries from ref . @xcite and study the range of validity of our expansion . for an @xmath9 calculation , the relevant terms of the chiral lagrangian , including only pions , nucleons and photons as degrees of freedom are shown below with the superscript indicating the chiral order . we follow the naming conventions for the lecs from @xcite . at first order we have @xmath10 where @xmath11 is the nucleon doublet with mass @xmath12 and @xmath13 is the covariant derivative given by @xmath14.\ ] ] the meson fields appear through @xmath15 with @xmath16 the pion decay constant , and also in @xmath17 . $ ] the photon field @xmath18 couples through @xmath19 where @xmath20 is the pauli matrix and @xmath21 is the ( negative ) electron charge . at second order , there are only two relevant terms @xmath22 \right)\sigma^{\mu\nu}\psi+\dots,\ ] ] where @xmath23 and for our case @xmath24 . $ ] finally , at third order we have @xmath25 \mathrm{d}_\beta\psi \right\}+\text{h.c.}\\ + & d_9\frac{\mathrm{i}}{2m}\left\ { \bar\psi\varepsilon^{\mu\nu\alpha\beta}\text{tr}\left[f_{\mu\nu}^+ \right]u_\alpha \mathrm{d}_\beta\psi \right\}+\text{h.c.}\nonumber\\ + & d_{16}\frac{1}{2}\left\ { \bar\psi\gamma^{\mu}\gamma_5\text{tr}\left[\chi_+\right]u_\mu\psi \right\}\nonumber\\ + & d_{18}\frac{\mathrm{i}}{2}\left\ { \bar\psi\gamma^{\mu}\gamma_5[\mathrm{d}_\mu,\chi_-]\psi \right\}+\dots,\nonumber\end{aligned}\ ] ] where @xmath26,$ ] @xmath27 . we will work in the isospin limit as it was done in ref . @xcite , hence @xmath28 , the pion mass squared . we also need the purely mesonic term @xmath29},\end{aligned}\ ] ] where @xmath30 and whose covariant derivative acts as @xmath31 at @xmath9 , there is a large number of contributions to the pion photoproduction process , including both tree - level diagrams and loops . a full set of the loop diagrams can be found , e.g. , in ref . @xcite . in the next figures , we show the relevant diagrams for our specific channel ( real photons , neutral pions ) . we also omit the crossed ones . in fig . [ fig:1 ] , we show the tree - level diagrams . both , the @xmath32 and the @xmath33 vertices contain pieces of chiral order running from one to three . however , the contact @xmath34 term starts at third order . the loop terms , contributing up to @xmath9 , are depicted in figs . [ fig:2 ] , [ fig:3 ] , [ fig:4 ] and [ fig:5 ] . the loop diagrams have been evaluated applying the eoms renormalization scheme . first , we have removed the infinities using the modified minimal subtraction @xmath35 scheme @xcite . then , after making an expansion of the amplitudes , @xmath36 with @xmath3 and @xmath37 the mandelstam variables of order one and the mandelstam variable @xmath38 of order 2 as in ref.@xcite . ] we have removed the power counting breaking terms ( those with a chiral order lower than the nominal order of the loop ) . obviously , the diagrams from fig . [ fig:2 ] , which contain exclusively mesonic loops , do not break the power counting . + + furthermore , we have to consider the wave function renormalization of the external legs . in our calculation we only include it at @xmath39 on the external proton legs of the tree diagrams of @xmath40 as all other corrections are at least @xmath41 . this amounts to multiplying the amplitude obtained for those terms by a factor @xmath42 finally , we should mention that , apart from @xmath43 , at @xmath9 , the @xmath44 scattering amplitude depends only on some specific combinations of the lecs : @xmath45 , @xmath46 and @xmath47 . the electromagnetic excitation of the @xmath1 has been much investigated since the late fifties @xcite . most of the work has dealt with energies around the resonance region , where the @xmath0 usually plays a dominant role . in the last years , we could mention the review of ref . @xcite and , e.g. , some works on pion electro- and photoproduction @xcite , or compton scattering evaluated in covariant chpt @xcite . there are also some recent advances incorporating the @xmath0 as a dynamic degree of freedom in the analysis of @xmath48 scattering @xcite in the same eoms approach that we use here . for the neutral pion photoproduction close to threshold , the @xmath0 isobar effects have been calculated in hbchpt @xcite , in a static approach , obtaining only moderate effects . here , we will consider the tree - level @xmath0 resonance diagrams , which include the direct one from fig . [ fig:6 ] and the crossed one , in a dynamic fashion maintaining the energy dependence of the resonance propagator . to describe the @xmath0 interactions we use consistent lagrangians which ensure the decoupling of the spurious spin-1/2 components of the rarita - schwinger field . the relevant pieces are @xmath49 where @xmath50 and @xmath51 are the electromagnetic field and its dual . there are two couplings for the pion ( @xmath52 , @xmath53 ) and two for the photon , the magnetic piece ( @xmath54 ) of chiral order two and the electric piece ( @xmath55 ) of order three . at third order , the lagrangian contains an additional @xmath56 coulomb coupling which vanishes for real photons . the conventions and definitions for the isospin operators @xmath57 can be found in ref . actually , we neglect the @xmath53 piece in our calculation for simplicity and because its value has been found to be consistent with zero @xcite . for the other constants , we take @xmath58 , @xmath59 and @xmath60 @xcite . the value for @xmath52 can be directly obtained from the @xmath0 width , and @xmath54 and @xmath55 were obtained fitting pion electromagnetic production at energies around the resonance peak . [ fdd ] tree diagram for @xmath5 photoproduction off protons.,title=""fig:"",scaledwidth=45.0% ] in the standard chiral counting scheme for diagrams without @xmath0 resonances , the order @xmath61 of a diagram with @xmath62 loops , @xmath63 vertices from @xmath64 , @xmath65 pionic propagators and @xmath66 nucleonic propagators is given by @xmath67 another small parameter , @xmath68 , appears when we introduce the @xmath0 resonance and several prescriptions have been used in the literature to establish an appropriate power counting scheme for this case @xcite . here , we follow the `` @xmath69 counting '' scheme . in our low - energy range , very close to the pion production threshold , we count @xmath70 as being of @xmath71 , following ref . hence , one obtains the rule @xmath72 where now @xmath73 is the number of @xmath0 propagators . thus , we have taken into account all the amplitudes up to order @xmath74 according to this counting rule , as well as the @xmath0 tree - level contribution proportional to @xmath55 of order @xmath75 . the effect of this latter piece is negligible . the mechanisms including @xmath0 loops would start contributing at @xmath75 . we compare our model with the full set of data of refs . @xcite on the angular cross section and @xmath76 , the linearly polarized photon asymmetry @xmath77 with @xmath78 and @xmath79 the angular cross sections for photon polarization perpendicular and parallel to the reaction" +"turbulent aerosols are of interest in a variety of natural and technological systems . two very important examples are water droplets in turbulent rain clouds @xcite and dust grains in turbulent accretion disks around growing stars @xcite . in both of these systems the aerosol is unstable because the suspended particles collide ( leading to aggregation or possibly fragmentation of the aerosol particles ) . the collision processes therefore have significant consequences : the formation of rain in one case , and the widely hypothesised mechanism for the formation of planets in the other . collisions always occur due to molecular diffusion , but ( as pointed out by smoluchowski @xcite ) , macroscopic fluid motion can considerably increase the collision rate . if the suspended particles are sufficiently heavy ( so that their inertia becomes relevant ) , they can move relative to the fluid . in this case the occurrence of caustics will typically increase the collision rate by several orders of magnitude @xcite . if the aerosol particles are sufficiently light , their molecular diffusion can make a significant contribution to the collision rate , which can be estimated by standard kinetic theory . in this paper we are concerned with the effect of macroscopic motion of a fluid on small particles which have insignificant inertia , so that they follow the flow ( advective motion ) . the seminal papers in this area were due to smoluchowski @xcite , who first considered the effect of shear of the fluid flow on collisions , and saffman & turner @xcite , who gave a formula for the collision rate which has formed the basis for most subsequent work on this problem . their paper was motivated by a problem in meteorology argued that small - scale turbulence in convecting clouds can accelerate collisions between microscopic water droplets , thus initiating rain formation : in this case the particles are brought into contact by hyperbolic or shearing motions of the turbulent flow . the formula for the collision rate by saffman & turner @xcite has been used frequently in the past five decades in cloud physics and in chemical engineering problems . it appears to be widely accepted that their expression is an exact relation for the collision rate in a dilute suspension . in the following we show that the saffman - turner estimate describes an initial transient of the problem only . for particles suspended in incompressible flows , the collision rate falls below the initial transient ( which thus constitutes an upper bound ) . for particles advected in a compressible flows , however , homogeneously distributed particles will cluster in a compressible fluid ( see for example @xcite ) . the clustering may increase the collision rate beyond its initial transient . the saffman - turner approximation treats the flow surrounding a test particle as if it were a steady hyperbolic flow , while in reality the flow fluctuates as a function of time . in section [ sec : 3.2 ] below we give an extension of the saffman - turner formula which does give the collision rate exactly . unfortunately the formula contains information about the time - dependence of the flow , and it is impossible to evaluate it in the general case . because of the importance of understanding collision rates for aerosol particles , it is desirable to find exactly solvable cases which can be used as a benchmark for numerical studies . the collision rate must depend on a dimensionless parameter describing how quickly the fluid velocity fluctuates , the kubo number @xcite . we are able to obtain precise asymptotic results on the collision rate in the limit where the kubo number approaches zero . in this case , particle separations undergo a diffusion process . by solving the corresponding fokker - planck equation we can determine the collision rate exactly . the remainder of this paper is organised as follows . in section [ sec : 2 ] we introduce the equations of motion and the dimensionless parameters of the problem . section [ sec : 3 ] discusses the saffman - turner theory and our extension of it . section [ sec : 3.1 ] describes the expression for the collision rate given in @xcite which is the starting point of our discussions . ( some new results on the evaluation of the saffman - turner expression are described in the appendix ) . in section [ sec : 3.2 ] we discuss our exact formula for the collision rate , and explain why the saffman - turner approximation describes an initial transient only . in sections [ sec : 4]-[sec : 6 ] we discuss how exact asymptotic results may be found for the limit of small kubo number . a fokker - planck equation for the probability density of the separation of particles is described in section [ sec : 4 ] . in section [ sec : 5 ] this is used to obtain the steady - state collision rate and section [ sec : 6 ] gives the full time dependence of the collision rate . these results are compared to numerical simulations in section [ sec : 7 ] , which also contains some concluding remarks , discussing scope for further work in this area . finally , we remark that a brief summary of some of the results of this paper has already been published @xcite . here we discuss the problem in greater depth and generality , and derive expressions for the time - dependent collision rate which were not discussed in @xcite . we consider spherical particles of radius @xmath0 in a fluid with velocity field @xmath1 which has an apparently random motion , usually as a result of turbulence . we assume that the suspended particles do not modify the surrounding flow . when the inertia of the particles is negligible , they are advected by the flow : @xmath2 it is assumed that direct interactions between the particles can be neglected until they collide . in other words , the particles follow equation ( [ eq : 2.1 ] ) until their separation falls below @xmath3 . we model the complex flow of a turbulent fluid by a random velocity field @xmath4 . we consider flows in both two and three spatial dimensions and for convenience we use a gaussian distributed field when we carry through concrete computations . in most cases we are concerned with incompressible flow , satisfying @xmath5 . particles floating on the surface of a fluid may experience a partly compressible flow @xcite , as may particles in gases moving with speeds comparable to the speed of sound . for these reasons we also consider partially compressible flows . it is convenient to construct the random velocity field @xmath1 from scalar stream functions or potentials @xcite . in two spatial dimensions we write @xmath6 where @xmath7 is a normalisation factor and @xmath8 and @xmath9 are independent gaussian random functions . we shall use angle brackets to denote averaging throughout . the fields @xmath10 and @xmath11 have zero averages , @xmath12 , @xmath13 and they both have same correlation function , @xmath14 : @xmath15 where @xmath16 and @xmath17 . this two - point correlation function @xmath14 is a smooth function decaying ( sufficiently rapidly ) to zero for large values of @xmath18 and @xmath19 . for @xmath20 , the flow ( [ eq : 2.2 ] ) is incompressible . for finite values of @xmath21 it acquires a compressible component . in the limit of @xmath22 the flow is purely potential . in some cases the physics of a problem dictates that @xmath8 and @xmath9 should have different correlation functions ; many of our results can be generalised in this way . in three spatial dimensions we write @xmath23 where @xmath24 and @xmath9 are four independent scalar fields with zero mean and with the same correlation function @xmath14 ; and @xmath25 is a normalisation factor . in the remainder of this paper we choose the normalisation factors to be of the form @xmath26 where @xmath27 is the standard deviation of the magnitude of the velocity and @xmath28 denotes the second derivative of the correlation function ( [ eq : 2.3 ] ) with respect to its first argument . fully - developed turbulent flows have a power - law spectrum in the inertial range , covering a wide band of wavenumbers @xcite . this feature can be incorporated by giving @xmath14 a suitable algebraic behaviour over a range of values of @xmath18 , as explained in @xcite . the long - ranged behaviour of the velocity field is not , however , relevant to the advective collision mechanism . it therefore suffices to consider a model with a short - ranged velocity correlation : for the numerical work reported in this paper we used following form of the correlation function @xmath29 where @xmath30 is a constant . in our numerical simulations we represent the flow field by its fourier components which are subject to an ornstein - uhlenbeck process as suggested by sigurgeirson & stuart @xcite . lc + & + particle size & @xmath0 + typical velocity fluctuation & @xmath27 + correlation length of the flow & @xmath31 + correlation time of the flow & @xmath32 + number density of particles & @xmath33 + compressibility & @xmath21 + spatial dimension & @xmath34 + + our problem is characterised by the six parameters listed in table [ tab:1 ] . from the parameters in table [ tab:1 ] , three independent dimensionless combinations can be formed : @xmath35 the first parameter characterises the dimensionless speed of the flow and is called kubo number , discussed in @xcite . note that @xmath36 is not possible , because the motion of the fluid places an upper limit on the correlation time . steady , fully developed turbulence corresponds to @xmath37 . the kubo number can be small for randomly stirred fluids . it is only in the limit @xmath38 that we are able to obtain precise and explicit estimates for the collision rate : this case is considered in sections [ sec : 4]-[sec : 6 ] . the second parameter in ( [ eq : 2.7 ] ) is the packing fraction of particles . throughout we assume that this parameter is small . similarly , the third parameter in ( [ eq : 2.7 ] ) is usually taken to be small . we note that kalda @xcite has considered the collision rate for particles in a non - smooth velocity field : this could be relevant to the case where @xmath39 . throughout this paper we consider the rate of collision of a given particle with any other particle , denoting this by @xmath40 . some papers consider the total rate of collision per unit volume . if the spatial density of particles is @xmath33 , the total rate of collision per unit volume is @xmath41 ( the factor of @xmath42 avoids double - counting ) . we will not be concerned with what happens after particles undergo their first collision : in different physical circumstances they may coalesce , scatter , or fragment , but in this paper we are concerned only with their first contact . we assume that the particles are spherical ( or circular , in two - dimensional calculations ) and that they all have the same radius , @xmath0 . we regard the particles as having collided when their separation reaches @xmath3 , and we neglect effects due to the interaction of the particles and the fluid . in practice the fluid trapped between approaching particles may slightly reduce the collision rate @xcite , but this effect can be accounted for by replacing the radius by an effective radius . the problem of calculating the rate of collision therefore reduces to the following problem . we" +"one of the main aims of researches in nuclear physics is to describe the ground - state properties of all nuclei in the periodic table with one method . unfortunately , due to lack of understanding in strong interaction and numerical difficulties in handling nuclear many - body problems , so far all microscopic descriptions are only possible on a phenomenological ground . the most successful theories of this type are the conventional hartree - fock method with effective density - dependent interactions @xcite and its relativistic analog , the relativistic mean field ( rmf ) theory @xcite . the hartree - fock method is based on the non - relativistic kinematics , in which the spin - orbit interaction and the density dependent interaction are important ingredients . while the rfm theory is based on the relativistic kinematics , in which the nucleons , the mesons and their interactions are the ingredients . therefore , the spin appears automatically and the interplay of the scalar and the vector potentials leads naturally to a proper spin - orbit interaction and appropriate shell structure . such a property is very important for the extrapolation of a phenomenological model to study exotic nuclei , which have become accessible in recent years due to developments in accelerator technology and detection techniques @xcite . the rmf theory has been very successful for the description of many nuclear properties including binding energies , nuclear radii and deformations from the proton drip line to the neutron drip line @xcite . however , the number of nuclear properties investigated by the rmf model is still considerably less than those done by its non - relativistic counterpart . to describe nuclear ground - state properties over a wide mass region properly , we must take into account both deformation effects and pairing correlations simultaneously . it has been known for a long time that most nuclei except for a few with and near magic numbers are deformed and most of them can be described by axial deformations . in the present work , we adopt the expansion method in the harmonic - oscillator basis to describe the single - particle wave functions in the deformed mean field potential @xcite . in the original work of gambhir . @xcite , the pairing correlations are treated in the bcs framework using a constant pairing interaction with a pairing window . this method has been found to be incapable of describing exotic nuclei where the continuum effects become important near the drip lines . on the other hand , recently it was demonstrated that the use of a zero - range @xmath3-force in the particle - particle channel was able to take into account the couplings to the continuum nicely in the non - relativistic mean filed models @xcite . this bcs framework with the zero - range @xmath3-force has been introduced into the relativistic mean filed models with the spherical shape @xcite . the zero - range @xmath3-force acting on the paired nucleons in the bcs framework is able to pick up the states ( resonant states ) having a large overlap with the occupied states below the fermi surface @xcite . we , therefore , have introduced the zero - range @xmath3-force in the bcs framework into the expansion method @xcite in the deformed rmf model and demonstrated its applicability in ref . this method has been applied to study the properties of light nuclei @xcite , particularly the proton - skins in the ar isotopic chain and the neutron - skins in the na isotopic chain , and the alpha - decay properties of the lately synthesized superheavy elements 115 and 113 @xcite . when applying this method to the neutron - rich nuclei , due to their large spacial extension , we do not expect the description of the sudden increase of neutron radii in halo nuclei , which were found if we had solved the rmf equations in coordinate space @xcite . however , except for the neutron radii of the halo nuclei , other properties could be reproduced with satisfactory accuracy by this method @xcite . one way out of this deficiency for the description of halo nuclei is to use the expansion method in the woods - saxon basis @xcite , which unfortunately is only possible for spherical nuclei at present . the zr and sn isotopic chains have received lots of attention for a long time . the zr isotope has a semi - magic proton number 40 , and its neutron number can be ( semi- ) magic numbers 40 , 50 and 82 . most recently , several rmf calculations show that the so - called giant halos may occur in the zr isotopic chain where neutron number goes beyond 82 @xcite . the evolution of deformation , the potential energy surfaces , the microscopic structure of coexisting configurations , and shape transitions in heavy zr isotopes have been discussed extensively since a long time ago ( see refs . @xcite ) , where sophisticated models have been employed and detailed analysises have been made . in the present work , our discussions of the evolution of the deformation in the zr isotopic chain ( including that of the sn isotopic chain ) are restricted to the mean field level . we would like to also compare our predictions with those of two of the most successful non - relativistic mean field models , the finite - range droplet model ( frdm ) @xcite and the hartree fock + bcs method ( hf+bcs ) @xcite . we notice that the effect of the proton - neutron pairing for @xmath4zr is also revisited lately @xcite . the sn isotope has long been of special interest for nuclear physicists not only because it has a magic proton number 50 , but also due to its extremely long isotopic chain . experimentally both the double magic nuclei , the neutron - deficient @xmath0sn and the neutron - rich @xmath2sn , have been produced . we expect that its isotopes will even extend to the next neutron magic number , @xmath5 , which will be one of the objects of the present study . most sn isotopes have been found to be spherical both experimentally and theoretically , particularly those nuclei with @xmath6 , but whether or not such a trend can continue to the next neutron - magic number , @xmath5 , remains to be an interesting and yet open question . recently , samanta et al . suggested that the pb isotope ( @xmath7 ) loses its magicity around @xmath8 based on the extended bethe - weizscker mass formula @xcite . this motivates us to study also the magicity of @xmath9 by the rmf method . the rmf model is particularly suitable for such a purpose because of its natural description of spin - orbit interaction . just like zr isotopes , sn isotopes have also been investigated quite a lot both in relativistic @xcite and non - relativistic mean field @xcite models . however , most of them are limited to either spherical assumptions , or even - even nuclei , or just part of the isotopic chain . the same limitations are also true for zr isotopes . in the present work , we apply the recently formulated deformed rmf+bcs method with a zero - range @xmath3-force in the pairing channel @xcite to the analysis of the ground - state properties of zr and sn isotopes from the proton drip line to the neutron drip line . in particular , we would like to study the neutron - rich nuclei in both isotopic chains and the magicity of @xmath9 in the neutron - rich region . we use the tma @xcite and nl3 @xcite parameter sets for the rmf lagrangian density , which are two of the most successful parameter sets in the relativistic mean field model . in sec . 2 , we briefly present the rmf model with deformation effects and pairing correlations . the numerical details and discussions will be presented in sec . 3 and a summary of the present study is given in sec . we briefly present here the formulation of the rmf model with deformation effects and pairing correlations . we employ the model lagrangian density with nonlinear terms for both @xmath10 and @xmath11 mesons , as described in detail in ref . @xcite , which is given by @xmath12 where the field tensors of the vector mesons and of the electromagnetic field take the following forms : @xmath13 and other symbols have their usual meanings . based on the single - particle spectra calculated by the rmf method , we perform a state - dependent bcs calculation @xcite . the gap equation has a standard form for all the single particle states . i.e. @xmath14 where @xmath15 is the single particle energy and @xmath16 is the fermi energy . the particle number condition is given by @xmath17 . as have been done in the recent works @xcite , a zero - range @xmath3-force @xmath18 is used in the particle - particle channel in order to take into account the continuum effects properly . for nuclei with odd number of nucleons , a simple blocking method without breaking the time - reversal symmetry is adopted . the ground state of an odd system is described by the wave function , @xmath19 here , @xmath20 denotes the vacuum state . the unpaired particle sits in the level @xmath21 and blocks this level . the pauli principle prevents this level from participating in the scattering process of nucleons caused by the pairing correlations . as described in ref . @xcite , the gap equation with one level @xmath21blocked "" has the form : @xmath22 with the corresponding chemical potential determined by @xmath23 . this blocking procedure is performed at each step of the self - consistent iteration and more numerical details will be discussed below . for heavy nuclei more harmonic - oscillator shells in the expansion of fermion and boson fields have to be used in order to achieve reliable convergence . however , computation time increases dramatically with the increase of the number of shells . the common procedure to tackle this problem is to limit the number of shells by studying the convergence behavior in the region of interest . for this reason , we investigate in detail three nuclei @xmath2sn , @xmath24sn and @xmath25zr , which are chosen to represent spherical neutron - rich nuclei , spherical drip - line nuclei and deformed halo nuclei . for the case of @xmath2sn , with the basis parameter @xmath26 , it is found that for @xmath27 , where @xmath28 and @xmath29 are the numbers of shells used in the expansion of fermion and boson fields , the desirable convergence is obtained properly . the increase of @xmath30 from 14 to 20 changes the total binding energy @xmath31 and the binding energy per particle @xmath32 by about @xmath33 , while the rms charge radii @xmath34 is changed by @xmath35 and the rms neutron radii @xmath36 is changed by @xmath37 . for @xmath2sn , even 12 shells can obtain the satisfactory convergence as shown in table i. similar conclusion can be made for @xmath24sn ( table ii ) except that now a minimum of 14 shells is needed . things are a little bit different for @xmath25zr ( table iii ) , which has been predicted to be a halo nucleus @xcite . with @xmath30 increasing from 14 to 20 , @xmath31 and @xmath32 change by about @xmath38 , while @xmath34 is changed by @xmath35 , and @xmath36 is changed by @xmath39 . in our calculations the ground state of @xmath25zr has a deformation of @xmath40 . setting @xmath41 equal to @xmath42 , we find that @xmath43 is changed by about @xmath44 when @xmath30 increases from 14 to 20 . in conclusion , we find that" +"let us start by defining intrinsic "" absorption in terms of gas that is ( or was ) part of the overall agn / host galaxy environment . this definition excludes only very distant , cosmologically intervening material , such as intergalactic clouds or unrelated galaxies . it reminds us that , especially in quasar studies , absorption can occur in a wide range of environments . the rich variety of intrinsic absorbers yields numerous diagnostics of both the agn phenomenon and the agn host galaxy connection . a short list of reasons for studying intrinsic absorption might include the following . @xmath0 intrinsic absorbers are a fundamental component of agn environments . they are common in type i ( broad emission line ) agns ( see below ) , and might be ubiquitous if the absorbing gas fills only part of the sky as seen from the central continuum source . in addition , the amounts of absorbing gas might be enormous rivalling or exceeding the mass in the broad emission line region . @xmath0 many intrinsic absorbers are involved in agn outflows . the flows are driven by the same accretion processes that feed the central super - massive black hole ( smbh ) and fuel other agn energetics . the need for accreting matter to expel angular momentum probably means that the wind mass loss rates , @xmath1 , are directly proportional to the mass accretion rate , @xmath2 . @xmath0 the relationship between outflow and accretion also implies that intrinsic absorbers are connected to the basic physics of smbh growth and agn evolution . @xmath0 intrinsic absorption that occurs far from the agn might uniquely measure a variety of regions in the host galaxies , such as the interstellar medium , gas streams in galactic halos , or galactic super - winds driven by starburst activity . @xmath0 the metal abundances in high - redshift intrinsic absorbers can provide unique constraints on the amount of star formation and the overall maturity of young galactic or proto - galactic nuclei . @xmath0 the metal - rich gas expelled by high - redshift agns might be a significant source of metal pollution "" to the intergalactic medium at early cosmic times . in this brief review , we focus on a few issues regarding absorption line classification , the relationships between classes , and the implications of partial coverage of the background light source(s ) . see also the reviews by crenshaw , kraemer , & george ( 2003 ) , hamann ( 2000 ) , hamann & ferland ( 1999 ) , and the asp conference series volumes ( 128 and 255 ) devoted to agn mass loss . agn absorption lines are classified empirically by the full width at half minimum ( fwhm ) of their profiles . the class definitions necessarily evolve as we encounter new phenomena and assimilate different measurement schemes . nonetheless , standardized classes are essential . the main classes are the narrow "" absorption lines ( nals ) , the broad "" absorption lines ( bals ) , and a catch - all intermediate class called the mini - bals . bals are blueshifted from the systemic ( emission line ) redshift by as much as @xmath30.2@xmath4 , and clearly form in winds form the central engine . weymann et al . ( 1991 ) introduced a bal - nicity "" index to define this class . hall et al . ( 2002 ) proposed a less restrictive index to include a wider range of line widths . we strongly advocate the use of quantitative indices , but a reasonable starting point for casual conversation is that bals have continuous absorption over @xmath5 km / s , with at least some portion of the profile having a velocity shift @xmath6 km / s compared to systemic . bals are further divided into subclasses according to the degree of ionization apparent in the lines . hibals "" have nominally siiv @xmath71394,1403 and civ @xmath71548,1551 ( or perhaps ciii @xmath8977 ) as their lowest ionization lines . lobals "" include lower ionization stages , such as mgii @xmath72796,2804 . felobals "" have more extreme low - ionzation regions that produce excited - state absorption in feii ( requiring densities @xmath9 @xmath10 ) . a useful ( but physically arbitrary ) definition of nals is that they are narrow enough _ not _ to blend important uv doublets , e.g. , the civ pair with separation @xmath3500 km / s . thus we require fwhm @xmath11 to 300 km / s . nals with velocity shifts @xmath12 km / s from systemic are also call associated "" absorption lines ( aals ) because of their plausible physical relationship to the agn . no one has yet sub - divided aals into hiaals and loaals analogous to the bals , but it would be interesting to compare sub - classes based on these properties . mini - bals have fwhms intermediate between the nals and bals . they appear at the same range of blueshifted velocities as the bals , and they also clearly form in agn outflows . examples of high - velocity mini - bals can be found in jannuzi et al . ( 1996 ) and hamann et al . ( 1997a ) . for the bals , see weymann et al . ( 1991 ) , reichard et al . ( 2003 ) , and hall et al . ( 2002 ) . for the aals , see foltz et al . ( 1986 ) and ganguly et al . see also the reviews cited above . figure 1 lists the major absorption line classes along with some properties and speculation that we will describe below . the detection frequencies given in the figure are our own educated guesses , except for the quasar aals ( g. richards , priv . comm . ) , seyfert 1 aals ( crenshaw et al . 1999 ) , and the hibals and lobals ( weymann et al . 1991 , reichard et al . 2003 ) . note that we list all seyfert 1 absorbers as nals , even though some may be considered mini - bals . quasar nals are known to form in a wide range of environments , from outflows like the bals to unrelated gas or galaxies at large ( cosmologically significant ) distances from the agn ( weymann et al . nals in low - redshift seyfert 1 galaxies might be almost exclusively intrinsic , but there is still a range of possible locations within the global agn / host galaxy environment . an important goal , therefore , is to identify the intrinsic nals and locate the absorbing regions with respect to the agns / host galaxies . one strategy is to examine the probabilities . for example , quasars have an over - density of nals near the emission redshift , i.e. , more than expected for a random distribution of cosmologically intervening material ( weymann et al . 1979 , foltz et al . others have noted that the presence and/or strengths of nals correlate with agn properties such as luminosity , radio - loudness , and radio lobe orientation ( wills et al . 1995 , richards et al . 1999 , richards 2001 ) . these relationships imply that a substantial fraction of quasar aals ( @xmath1350% ) , and probably some of the highly blueshifted ( @xmath14 km / s ) nals , are intrinsic to quasars . we can also examine individual absorbers to look for i ) absorption line variability , ii ) profiles that are broad and smooth compared to thermal speeds , iii ) partial line - of - sight coverage of the background light source , and iv ) high gas densities based on excited - state absorption lines ( see below , also tripp , lu , & savage 1996 , hamann et al . 1997b , 2001 , barlow & sargent 1997 , ganguly et al . 1999 , narayanan & hamann 2003 ) . these characteristics often appear together and suggest an intrinsic origin because they are most easily understood in terms of the dense and dynamic environments near agns . brandt , laor , & wills ( 2000 ) showed that the strengths of intrinsic absorption lines ( e.g. , @xmath15(civ ) ) correlate roughly with the amount of x - ray absorption . moreover , the column densities derived for the x - ray absorbers are much larger than earlier estimates from the uv lines , to the point where some bal quasars have thompson thick x - ray absorbers with @xmath16 @xmath17 ( hamann 1998 , gallagher et al . 1999 , mathur et al . 2000 , arav et al . 2002 ) . in some seyfert 1 galaxies ( e.g. , kaspi et al . 2002 ) we know that the x - ray absorbing gas is outflowing at modest speeds with the uv line absorbers . it would be more problematic for models invoking radiative acceleration if the large x - ray columns in bal quasars turn out to be outflowing at bal speeds ( hamann 1998 ) . in any case , we have an expectation that mass loss rates increase generally with line strength , as shown in figure 1 . other studies suggest that , in very rough terms , the amount of reddening , the percent polarization , and perhaps the ir luminosities are all nominally higher in bal quasars and may increase toward lower ionizations through the bal class ( weymann et al . 1991 , schmidt & hines 1999 , brotherton et al . 2002 , hall et al . 2002 , richards et al . 2003 , reichard et al . 2003 , and refs . therein ) . it is not known if these tendencies extend to the mini - bals or aals . agn evolution is something of a holy grail because we know almost nothing about it . unlike stars and galaxies , we have yet to identify young "" or old "" agns . it has been suggested that the felobal and lobal quasars represent a young phase because their enormous column densities , low ionizations , and reddening might be signatures of an energetic agn that is still partially enshrouded in its dusty parental environment ( voit , weymann , & korista 1993 , gregg et al . 2000 , brotherton et al . 2002 , and refs . therein ) . perhaps this evolutionary path continues through the bals to the mini - bal and aal stages as the outflows gradually weaken ( figure 1 ) . however , orientation probably also plays an important role . most models have bal winds rising up out of the accretion disk and flowing close the the disk plane ( murray et al . 1995 , proga , stone , & kallman 2000 ) . viewing angles close to the disk plane should plausibly lead to larger absorption column densities , detections of lower ionization stages , and perhaps increased reddening and polarization ( schmidt & hines 1999 , elvis 2000 ) . similar arguments may apply to the aals ( wills et al . it seems likely that orientation and evolution both contribute to differences between the absorber classes . one observational difficulty is that agn lifetimes are short compared to their host galaxies , so we can not argue that young / old agns reside in young / old galaxies . in particular , agn luminosities , @xmath18 , are related to the mass accretion rate onto the central smbh , @xmath2 , by an efficiency factor , @xmath19 . the luminosities are also some fraction , @xmath20 , of the theoretical eddingtion limit , @xmath21 , such that @xmath22 where @xmath23 is the smbh mass" +"a central issue in the field of spintronics is the design of spin - based electronic devices.@xcite they may involve ferromagnets or external magnetic fields to control the spin degree of freedom.@xcite but recently , all - electric spintronic devices also have gained interest.@xcite they rely on spin - orbit ( so ) interaction , the strength of which is tunable via external gates in semiconductor heterostructures,@xcite a basic requirement for the realization of a spin field - effect transistor . a spin - polarized current in a semiconductor can be generated by spin injection . here we focus on an alternative route that relies on pumping . by varying the parameters of a mesoscopic system periodically in time , a finite charge or spin current can be sustained . experimental studies have investigated charge pumping in several mesoscopic devices.@xcite spin pumping has been experimentally realized in the presence of an external magnetic field.@xcite theoretical studies of spin pumping involve external magnetic fields,@xcite ferromagnetic leads,@xcite and also so coupling.@xcite in the present paper , we consider the minimal model that contains so interaction : a quantum dot with two spin - degenerate orbital levels . such a two - level quantum dot with more than two leads has been suggested as a spin filter.@xcite we focus on the _ adiabatic _ limit of pumping , i.e. , the parameters are varied slowly in time compared to the dwell time of the mesoscopic system.@xcite adiabatic pumping of charge and spin through such a two - level dot has been considered in the limit of vanishing charging energy.@xcite it was found that this system can act as an _ all - electric spin battery _ , i.e. , a finite spin current can be achieved without ferromagnets by electrically controlling the dot parameters . for specific symmetries in the tunnel coupling of the dot to the leads even pure spin currents have been suggested . from the analysis of ref . , which was based on a scattering - matrix approach,@xcite it is not clear whether and how the conclusions can be transferred to quantum dots with non vanishing coulomb interaction . to answer this question is the main goal of the present paper . in order to take the coulomb interaction into account , we use a diagrammatic real - time approach@xcite that allows for arbitrary strengths of the coulomb interaction . we focus on the limit of weak tunnel coupling , for which we perform a systematic perturbation expansion to lowest order . to emphasize the role of coulomb interaction , we compare the limit of vanishing coulomb interaction with the limit of an infinitely large charging energy . the paper is organized as follows . in sec . [ model ] we introduce the model that describes the so interaction in a two - level quantum dot with coulomb interaction . section [ method ] deals with the technique to calculate the pumped charge and pumped spin during one pumping cycle . to study the dependence of the pumped charge ( spin ) on the four tunnel - matrix elements in a transparent way , we introduce in sec . [ isospin ] an isospin representation of the orbital degree of freedom . finally , in sec . [ res ] we present the results for the pumped charge and pumped spin . ( color online ) energy scheme of the two - level quantum dot . the two orbital , spin - degenerate levels can be varied in time . they are tunnel coupled to the left ( l ) and the right ( r ) lead , with tunnel - matrix elements @xmath0 . the leads have the same chemical potential @xmath1 . ] we consider a quantum dot with two spin - degenerate orbital levels @xmath2 ( with labels @xmath3 for the orbital and @xmath4 for the spin ) , tunnel coupled to the left ( l ) and the right ( r ) lead ( see fig . [ fig : model ] ) . the system is described by the hamiltonian @xmath5 here , @xmath6 is the hamiltonian of the isolated dot , @xmath7 of the leads , and @xmath8 of the tunneling between dot and leads . the hamiltonian for the isolated quantum dot contains two parts . the single - particle contribution for the two orbitals @xmath9 with energy @xmath10 , which are coupled by so interaction , can be cast in the @xmath11 matrix @xmath12 for the basis @xmath13 , where the spin quantization axis is chosen arbitrarily . here , @xmath14 denotes the vector of pauli matrices , @xmath15 is the identity matrix , and @xmath16 is a real vector describing the so coupling . the matrix in eq . has the most general form that allows time - reversal symmetry . it has been used in the context of pumping@xcite and was also recently applied to electron - transport in the presence of a magnetic field@xcite and to study the josephson current through a double - dot structure.@xcite in the following , we choose the spin quantization axis parallel to @xmath16 so the matrix becomes diagonal in spin space . the second part of the dot hamiltonian accounts for the charging energy @xmath17 , where @xmath18 is the total number of dot electrons and @xmath19 an external gate charge . without loss of generality , we can choose @xmath20 ( any other value can be achieved by a constant shift of the energies @xmath10 ) . this leads ( up to an additive constant ) to the dot hamiltonian @xmath21 where the operator @xmath22 creates an electron in state @xmath2 and the corresponding number operator is @xmath23 . we used the notation @xmath24 for spin parallel ( antiparallel ) to @xmath16 , @xmath25 , and @xmath26 . the leads are modeled as reservoirs of noninteracting electrons , @xmath27 where @xmath28 is the creation operator for an electron with spin @xmath29 and momentum @xmath30 in lead @xmath31 . tunneling between dot and leads is described by the hamiltonian @xmath32 with ( spin - independent ) tunnel - matrix elements @xmath0 for tunneling between lead @xmath31 and orbital @xmath9 . pumping is achieved by varying system parameters periodically in time . in this paper , we assume that the energy levels @xmath33 can be changed in time via external gates capacitively coupled to the system . in principle , the external gates also may affect the so coupling , the tunnel couplings , and the electro chemical potential of the leads ( via parasitic capacitances ) . to simplify the discussion , however , we assume for the following these parameters to be constant in time . we focus on the regime of adiabatic pumping , which is achieved for pumping frequencies @xmath34 smaller than the inverse of the dwell time . this is valid for @xmath35 , where @xmath36 is the tunnel - coupling strength , @xmath37 , with @xmath38 . the density of states @xmath39 is assumed to be flat and equal for the left and right leads . we choose a gauge where all four tunnel - matrix elements are real . to study the effect of coulomb interaction , we compare results for the limit of noninteracting ( @xmath40 ) and infinitely strong interacting ( @xmath41 ) electrons on the dot . in the latter case , the total number of electrons in the quantum dot can only be zero or 1 . to calculate the pumped charge and pumped spin , we use a diagrammatic real - time approach to adiabatic pumping through quantum - dot systems . @xcite for the present context , we extend the analysis of ref . to allow for a time - dependent transformation of the basis states . this is necessary since the so coupling couples time - dependent orbital levels , which , in turn , makes the dot eigenstates time dependent . we start in sec . [ density ] with the kinetic equation for the reduced density matrix in its general form , which describes the time evolution of the dot s degrees of freedom . subsequently , we perform both an adiabatic expansion , i.e. , a perturbation expansion in the pumping frequency ( sec . [ adiabatic ] ) and a perturbation expansion in the tunnel - coupling strength ( sec . [ tunnel ] ) to describe the limit of weak tunnel coupling . the pumped charge and pumped spin currents to lowest order in @xmath36 and @xmath34 are derived in sec . [ pumped ] . finally , in sec . [ weak ] , we perform the limit of weak pumping which assumes small amplitudes of the pumping parameters . the main idea of the diagrammatic real - time technique is based on the fact that the leads are described as large reservoirs of noninteracting electrons which can be integrated out in order to arrive at a reduced density matrix @xmath42 for the dot degrees of freedom only . for a matrix representation with matrix elements @xmath43 ( for the diagonal elements we introduce the notation @xmath44 ) , it is convenient to use the eigenstates @xmath45 with corresponding eigenenergies @xmath46 as a basis . for this , we employ a time - dependent unitary transformation @xmath47 acting on the dot hamiltonian @xmath6 , such that @xmath48 is diagonal . the time evolution of the reduced density matrix is given by the kinetic equation @xmath49\nonumber\\&+ \int^{t}_{-\infty}{\ : \mathrm{d}t^\prime \ : } { \bm{\mathcal{w}}}(t , t^\prime)\ \bm{p}(t^\prime)\ , . \label{master}\end{aligned}\ ] ] the bold face indicates tensor notation . the reduced density matrix @xmath42 and @xmath50 are tensors of rank 2 , while @xmath51 and @xmath52 are tensors of rank 4 , i.e. , @xmath53 the kernel element @xmath54 describes the transition from @xmath55 at time @xmath56 to @xmath57 at time @xmath58 . it is given by the sum over all irreducible blocks on the keldysh contour which correspond to the described transition . the elements of @xmath51 are differences of the eigenenergies defined as @xmath59 . the second term @xmath60 $ ] originates from the time dependence of the transformation @xmath61 , and @xmath62 denotes the time - derivative of @xmath61 . in the following adiabatic expansion and the expansion in the tunnel - coupling strength , we follow the lines of ref . . in the limit of slow variation of the system parameters , such that the duration of one pumping cycle , @xmath63 , is much larger than the dwell time of an electron in the quantum dot , we can perform an adiabatic expansion of eq . , which is equivalent to an expansion of all time dependencies around the final time @xmath58 and to systematically keep all contributions that contain one time derivative . for this , we first do a taylor expansion of the reduced density matrix around the finite time @xmath58 , i.e. , @xmath64 . we then expand the kernel and the density matrix in the pumping frequency , i.e. , @xmath65 and @xmath66 . the instantaneous order , indicated by the index @xmath67 , describes the limit where all system parameters are frozen at time @xmath58 . the adiabatic correction , labeled by @xmath68 , contains one time derivative , i.e. , it collects all contributions to first order in the pumping frequency @xmath34 . the difference in the eigenenergies of the isolated dot , @xmath69 , is of instantaneous order , while @xmath70 belongs to the adiabatic correction . since both @xmath71 and @xmath72 depend only on the difference @xmath73 , it is convenient to perform the laplace transform @xmath74 . using the short notations @xmath75 and @xmath76 , the kinetic equation reads @xmath77 in instantaneous order , and @xmath78\nonumber\\&+{\bm{\mathcal{w}}}^{(a)}_t \bm{p}^{(i)}_t+\partial{\bm{\mathcal{w}}}^{(i)}_t{\ : \frac{\mathrm{d}}{\mathrm{d}t}}\bm{p}^{(i)}_t \label{meqa}\end{aligned}\ ] ] for the adiabatic correction . the normalization condition for the density matrix is expressed as @xmath79" +"during cell life , membranes are submitted to an inhomogeneous and variable environment . local inhomogeneities can be strongly related to biological processes , which has led to experiments investigating the effect of local modifications on biomimetic membranes @xcite . for instance , in the inner membrane of mitochondria , the enzymes that use the local ph difference across the membrane to synthesize adenosine triphosphate , the cell s fuel , are located in membrane invaginations called cristae @xcite . experiments on model lipid membranes have shown that a local ph change can induce a local dynamical membrane deformation @xcite , and in particular the formation of cristae - like invaginations @xcite : membrane shape is tightly coupled to local ph inhomogeneities . other concentration inhomogeneities in the environment of a cell have a crucial biological role , for instance in chemotaxis or in paracrine signaling . it is therefore of great interest to study the response of a biological membrane to a local modification of its environment . motivated by experiments conducted on biomimetic membranes , we have developed a theoretical description of the dynamics of a lipid bilayer membrane submitted to a local concentration increase of a substance that reacts reversibly and instantaneously with the membrane lipid headgroups . we focus on the regime of small deformations , and we treat linear membrane dynamics in the spirit of ref . @xcite . while our first works focused on the simple case of a constant modification of the membrane involving only one wavelength @xcite , we have recently extended our theoretical description in order to take into account the spatiotemporal profile of the fraction of chemically modified lipids resulting from the local reagent concentration increase @xcite . this profile is determined by the diffusion of the reagent in the solution that surrounds the membrane . in ref . @xcite , we compared the predictions of this theoretical description to experimental measurements of the deformation of the membrane of giant unilamellar vesicles caused by local microinjection of a basic solution , and we obtained good agreement between theory and experiment . in the present article , we pursue the theoretical investigation of the effect of a local chemical modification on a lipid membrane . in general , the dynamics that results from a local reagent concentration increase is quite complex , as it involves the evolution of the reagent concentration profile simultaneously as the response of the membrane . this is the case in the experimental data analyzed in ref . @xcite , which corresponds to microinjection steps lasting a few seconds . here , we show that the effect of the evolution of the reagent concentration profile on the membrane dynamics becomes negligible some time after the beginning of the reagent concentration increase , after what the dynamics corresponds to the response of the membrane to a chemical modification imposed instantaneously . we find that studying this regime enables to extract interesting properties of the membrane response . the article is organized as follows . first , in sec . [ mbr_dyn ] , we review the linear dynamics of a membrane submitted to a local chemical modification . then , in sec . [ res ] , we study separately the dynamics associated with each of the two effects that can arise from a chemical modification , namely a spontaneous curvature change and an equilibrium density change of the external monolayer . we find that a local asymmetric density perturbation between the two monolayers of the membrane relaxes by spreading diffusively in the whole membrane . intermonolayer friction plays a crucial part in this behavior . subsequently , in sec . [ res_b ] , we treat the general case where both effects are present , and we show how the ratio of the spontaneous curvature change to the equilibrium density change induced by the local chemical modification can be extracted from the dynamics . this ratio can not be deduced from the study of global modifications of vesicle equilibrium shapes in light of the area - difference elasticity model @xcite . finally , sec . [ ccl ] is a conclusion . for the article to be self - contained , the present section reviews the linear dynamics of a membrane submitted to a local chemical modification , starting from first principles . the main points of this description were presented in ref . @xcite . in that article , we compared theoretical predictions to experimental measurements of the deformation of a membrane submitted to a local and brief ph increase . here , our aim will be to go further in the analysis of our theoretical description in order to understand the fundamental properties of the response of a membrane to a local chemical modification . our description of the bilayer membrane is based on a local version of the area - difference elasticity membrane model @xcite . we focus on small deformations of an infinite flat membrane , and we denote the upper monolayer by @xmath0 and the lower one by @xmath1 . in the absence of a chemical modification , the local state of each monolayer is described by two variables : the local total curvature @xmath2 defined on the membrane midlayer , which is common to both monolayers , and the local scaled density @xmath3 , defined on the midlayer of the membrane , @xmath4 being a reference density . the sign convention for the curvature is chosen in such a way that a spherical vesicle has @xmath5 . the free energy @xmath6 per unit area in monolayer @xmath7 reads @xcite : @xmath8 where @xmath9 represents the tension of the bilayer and @xmath10 its bending modulus , while @xmath11 is the stretching modulus of a monolayer , and @xmath12 denotes the distance between the neutral surface @xcite of a monolayer and the midsurface of the bilayer . as we assume that the two monolayers of the membrane are identical before the chemical modification , these constants are the same for both monolayers . the spontaneous curvatures of the two monolayers have the same absolute value @xmath13 and opposite signs , since their lipids are oriented in opposite directions . the expression for @xmath6 in eq . ( [ fpm0 ] ) corresponds to a general second - order expansion in the small dimensionless local variables @xmath14 and @xmath15 , around the reference state which corresponds to a flat membrane with uniform density @xmath16 . it is valid for small deformations around this reference state : @xmath17 and @xmath18 , where @xmath19 is a small dimensionless parameter used for bookkeeping purposes , which characterizes the amplitude of the small deformations of the membrane around the reference state . mathematically , @xmath19 is considered infinitesimal . note that in general , both @xmath2 and @xmath14 , which describe local small deformations around the reference state , are functions of time and of position on the membrane . let us now focus on the way the membrane free energy is affected by the local chemical modification . we consider that the reagent source , which corresponds to the micropipette tip in an experiment , is localized in the water above the membrane . besides , membrane permeation and flip - flop are neglected given their long timescales . hence , the chemical modification only affects the upper monolayer , i.e. , monolayer @xmath0 , and not the lower one . let us denote by @xmath20 the local mass fraction of the lipids of the upper monolayer that are chemically modified : @xmath20 depends on time and position since it arises from the local chemical modification . we assume that the reagent concentration is small enough for @xmath20 to remain small at every time and position on the membrane , and we characterize this smallness through @xmath21 . in order to describe the chemically modified membrane , we have to include the third small variable @xmath20 in our second - order expansion of @xmath22 . we obtain @xcite : @xmath23 where the constants @xmath24 , @xmath25 , and @xmath26 describe the response of the membrane to the chemical modification . these constants depend on the reagent that is injected . their physical meaning will be explained in the next paragraph . besides , the non - analytical mixing entropy term @xmath27 has been added to our second - order expansion @xcite . note that we assume that the three small dimensionless local variables @xmath20 , @xmath14 and @xmath28 are of the same order . in fact , in the present work , the deformation of the membrane and the density variation are caused by the local chemical modification , i.e. , they are a response to @xmath20 , which justifies that @xmath28 and @xmath14 are of the same order as @xmath20 . we refer the reader to ref . @xcite for more details on the derivation of eqs . ( [ fpm0 ] ) and ( [ fmod ] ) . the effect of the chemical modification ( i.e. , of @xmath20 ) on the upper monolayer is twofold . first , the scaled equilibrium density on the neutral surface of the upper monolayer is changed by the amount @xmath29 to first order . second , the spontaneous curvature of the upper monolayer is changed by the amount @xmath30 to first order , with @xmath31 . these results are obtained by minimization of the free energy of a homogeneous monolayer with constant mass ( see [ ap_sc_dens ] ) . hence , the constants @xmath24 and @xmath32 describe the linear response of the monolayer equilibrium density and of its spontaneous curvature , respectively , to the chemical modification . this explains the physical meaning of the constants @xmath24 and @xmath26 in eq . ( [ fmod ] ) . note that @xmath25 corresponds to the quadratic response of the membrane to the chemical modification , but it will not have any relevant effect in the following . the elastic force densities in a monolayer described by the free - energy densities in eqs . ( [ fpm0][fmod ] ) have been derived in ref . @xcite to first order in @xmath19 , using the principle of virtual work . as we focus on small deformations of an infinite flat membrane , it is convenient to describe it in the monge gauge by the height @xmath33 , @xmath34 , of its midlayer with respect to the reference plane @xmath35 . then , @xmath36 to second order . such a description is adapted to practical cases where the distance between the reagent source and the membrane is much smaller than the vesicle radius . the force per unit area of the reference plane , which we call `` force density '' , then reads to first order in @xmath19 @xmath37 where @xmath38 is the tangential component of the force density in monolayer @xmath7 "" , while @xmath39 is the total normal force density in the membrane . in these formulas , we have introduced the antisymmetric scaled density @xmath40 , and the constant @xmath41 . these expressions show that both the equilibrium density change and the spontaneous curvature change ( i.e. , both @xmath24 and @xmath32 ) can yield a normal force density , and thus a deformation of the membrane , while only the equilibrium density change can yield a tangential force density and induce tangential lipid flow . an illustration of the role of these force densities in the membrane response to a local chemical modification is provided in fig . [ mem_fig ] . ) . ( a ) : membrane at equilibrium in the reference state ( flat shape , uniform lipid densities in both monolayers ) . ( b ) : membrane just after the instantaneous local chemical modification : the membrane has not deformed yet at this stage , and the densities are still uniform . some lipids of monolayer @xmath0 are modified" +"in time - reversal experiments a signal emitted by a localized source is recorded at an array of transducers . it is then re - emitted into the medium reversed in time , that is , the part of the signal that is recorded first is sent back last . because of the time - reversibility of the wave equation the back - propagated signal refocuses approximately at the location of the original source because the array is limited in size . a striking experimental observation is that the presence of inhomogeneities in the medium improves the refocusing resolution . the explanation for this super - resolution is multipathing : waves in complex media that are captured by the recording array have undergone multiple scattering making it effectively larger than its physical size . another important feature of super - resolution in time reversal is that the refocused signal does not depend on the realization of the random medium . that is , the refocused signal is deterministic . super - resolution and self - averaging of refocused signals in complicated media has been observed both in laboratory experiments ( see reviews @xcite and references therein ) and in underwater acoustic wave propagation over long distances ( tens of kilometers ) @xcite . time - reversal techniques have numerous applications ranging from medicine to communications and , more recently , imaging in random media @xcite . the first mathematical analysis of time - reversal in random media was given by clouet and fouque @xcite , who analyzed refocusing and self - averaging of time - reversed pulses in a one - dimensional layered random medium . their result was extended to a three - dimensional layered medium in @xcite . super - resolution in spatial refocusing and its statistical stability for multi - dimensional waves in random media was analyzed in @xcite , in a remote - sensing regime where the paraxial or parabolic wave equation can be used . the refocusing of the average signal in a full three - dimensional medium , in the regimes of random geometrical optics and radiative transfer ( transport ) , was studied in @xcite . we also mention that another source of multipathing is the mixing of waves by the boundaries in an ergodic cavity . this has been studied experimentally in @xcite and mathematically in @xcite . the purpose of this paper is to analyze time reversal in the radiative transfer regime using the parabolic wave equation , when the waves interact fully with the random inhomogeneities . we prove mathematically that the refocused signal is self - averaging , which means that it does not depend on the realization of the random medium . the mathematical quantitiy that we analyze is the wigner measure of a pair of oscillatory solutions of the random schrdinger equation . in the present setting , the random potential depends in a markovian way on the variable @xmath1 , the main direction of propagation of the waves . this allowed us to use in @xcite a martingale method to prove that the average of the wigner distribution converges to a solution of the radiative transfer equation . in this paper we use additional regularity of the wigner measure , available in time - reversal when there is some blurring at the recording array , to show that the whole wigner distribution , and not only its average , converges weakly , as a schwartz distribution and in probability , to the deterministic solution of the transport equation . the blurring at the recording array provides a priori bounds for the wigner transform in @xmath0 . these bounds and the markovianity of the random potential in the direction of propagation make the time - reversal problem more tractable mathematically and allow us to prove in a fairly simple and straightforward manner self - averaging of the time - reversed signal . we recall that the wigner transform is a convenient tool to analyze high frequency wave propagation in deterministic @xcite and random media @xcite . introduced by wigner in 1932 @xcite , it has been used extensively in the mathematical literature recently . convergence of the average wigner distribution to the solution of the radiative transfer equation was first proved by h. spohn in @xcite for time - independent potentials on small time intervals . this result was extended to global in time convergence by l. erds and h .- yau @xcite . these proofs involve infinite neumann ( diagrammatic ) expansions for the solution of the schrdinger equation and are quite involved technically . the corresponding problem with time - dependent potentials is much simpler mathematically . it was treated by us in @xcite in the markovian case , and by f. poupaud and a. vasseur @xcite in the case of finite - range time correlations . in this paper we use the fact that the wigner family arising in time - reversal problems is more regular than the usual one because blurring is added at the recording array . this provides some additional regularity usually obtained by considering mixtures of states as , for instance , in @xcite . the paper is organized as follows : we describe the scaling and obtain an expression for the back - propagated signal in terms of the wigner transform in section [ sec : signal ] . the main result and assumptions on the random medium are formulated in section [ sec : mainresult ] . the proofs are presented in section [ sec : wigner ] . this work was partially supported by onr grants n00014 - 02 - 1 - 0088 and n00014 - 02 - 1 - 0089 . g. bal was supported in part by nsf grant dms-0072008 , g. papanicolaou by grants afosr f49620 - 01 - 1 - 0465 and nsf dms-9971972 , and l. ryzhik in part by nsf grant dms-9971742 and the alfred p. sloan foundation . the pressure field @xmath2 satisfies the scalar wave equation @xmath3 here @xmath4 is the local wave speed that we will assume to be random , and the laplacian operator includes both direction of propagation , @xmath1 , and the transverse variable @xmath5 . in the physical setting , we have @xmath6 . we consider dimensions @xmath7 to stress that our analysis is independent of the dimension . if we assume that at time @xmath8 , the wave field has a `` beam - like '' structure in the @xmath1 direction , and if back - scattering may be neglected , we can replace the wave equation by its parabolic approximation @xcite . more precisely , the pressure @xmath9 may be approximated as @xmath10 where @xmath11 satisfies the schrdinger equation @xmath12 with @xmath13 the transverse laplacian in the variable @xmath14 . the refraction index @xmath15 , and @xmath16 in ( [ eq : ansatz ] ) is a reference speed . the rigorous passage to the parabolic approximation from the wave equation has been analyzed in @xcite in the deterministic case , and @xcite in a one dimensional random medium . a formal derivation of the paraxial approximation that leads to the radiative transfer regime is given below in section [ sec : scaling ] . we assume that the original source is located in the plane @xmath17 , and the time - reversal mirror is located in the plane @xmath18 as depicted in figure [ fig1 ] . during the first stage of a time reversal experiment the signal propagates for a time @xmath19 , or equivalently , over a distance @xmath20 , so that the signal arriving at the time - reversal mirror is given by @xmath21 where the green s function solves @xmath22 then the signal is time reversed . for three - dimensional acoustic pulses , this means that the pressure field is kept unchanged and that the sign of its time derivative is reversed . in the parabolic approximation , this is equivalent to phase conjugation , where @xmath11 is replaced by its complex conjugate @xmath23 . we assume that the recording array occupies a compact subset of the plane @xmath18 , and introduce a real - valued aperture function @xmath24 . it represents the restriction of the signal onto the array , and possible amplification by the array that may vary from one receiver to another . in the absence of amplification it is given by the characteristic function of an array set @xmath25 . we also allow for some blurring of the recorded signal , modeled by a convolution with kernel @xmath26 . the signal at @xmath27 after time reversal takes then the form @xmath28 the last step consists in letting the signal propagate back to the origin @xmath17 and time reversing it one more time @xmath29 the last step , phase - conjugating at the source , is not performed in real physical experiments but is convenient if we need to compare the back - propagated signal to the original signal . it affects neither the degree of refocusing nor the self - averaging effect . the back - propagated signal in time is given at the plane @xmath17 by @xmath30 we will be interested in the sequel in the refocusing and self - averaging properties of the back - propagated signal @xmath31 for each fixed frequency . self - averaging of the time signal @xmath32 then follows from ( [ eq : psib - time ] ) when @xmath33 has compact support in @xmath34 . an interesting conclusion of this paper is that the additional blurring by convolution with the kernel @xmath35 makes the signal @xmath31 self - averaging for every frequency @xmath34 . this should be contrasted with the situation studied in @xcite , where no blurring was introduced and self - averaging was observed only for the full time signal . we recall the formal passage from the reduced wave equation to the parabolic equation ( [ eq : sch ] ) described in the appendix to @xcite and explain how the radiative transfer scaling arises in this context . we start with the reduced wave equation @xmath36 and look for solutions of ( [ red - wave ] ) in the form @xmath37 then we obtain @xmath38 the refraction index @xmath39 is weakly fluctuating so that it has the form @xmath40 where @xmath41 models random fluctuations that will be described in detail in section [ sec : random - refr - ind ] . here , @xmath42 and @xmath43 are the correlation lengths of @xmath41 in the transverse and longitudinal directions , respectively , and the small parameter @xmath44 measures the strength of the fluctuation . the waves propagate over a distance @xmath45 in the @xmath14-plane and @xmath46 in the @xmath1-direction , and we rescale @xmath14 and @xmath1 accordingly . we also introduce a carrier wave number @xmath47 and replace @xmath48 , @xmath49 being the non - dimensional wave number ( we drop the prime below ) . the physical parameters determined by the medium are the length scales @xmath42 , @xmath43 and the non - dimensional parameter @xmath50 . we now explain the scaling of the parameters @xmath45 , @xmath46 and @xmath47 in the radiative transfer regime . equation ( [ red - unscaled ] ) in the non - dimensional variables @xmath51 , @xmath52 becomes after we drop the primes @xmath53 we introduce the following small parameters : @xmath54 and rewrite ( [ red - scaled ] ) as @xmath55 let us assume now that @xmath56 and denote @xmath57 . then ( [ red - param ] ) becomes after multiplication by @xmath58 @xmath59 observe that when @xmath60 and @xmath61 , the first term in ( [ red - param1 ] ) is small and may be neglected in the leading order since @xmath62 . then ( [ red - param1 ] ) becomes @xmath63 which is the parabolic wave equation ( [ eq : sch ] ) in" +"diluted magnetic semiconductors ( dms ) based on iii - v semiconductors doped with mn have attracted a lot of interest recently , after critical temperatures for the onset of ferromagnetism of the order of 110 k have been found in ga@xmath0mn@xmath1as , for @xmath2.@xcite more recently , critical temperatures larger than room temperatures have been reported in mn - doped gan , enhancing the hope for extensive technological applications of these materials.@xcite while there is general agreement that the magnetism is due to charge - carrier mediated , effectively ferromagnetic interactions between the mn spins , there are various theoretical models attempting to understand their detailed behavior . the dms are alloy systems , with inherent positional disorder of the mn atoms ; further , spin - orbit coupling may play a significant role for hole doping . a theoretical treatment which takes into account all these factors , and their effects on the magnetic and transport properties of dms , is not yet available . instead , theoretical models have tended to concentrate on different aspects of the problem . one class of models , where much work has been done , neglects both the disorder and spin - orbit coupling effects . at large carrier densities , where coulomb potentials of the impurity ( mn ) atoms are effectively screened out , and other disorder effects ( such as those coming from as antisite defects which are believed to be the cause of the large compensation observed experimentally ) can be neglected , the former at least can be justified . in such a case , holes occupy a fermi sea at the top of the valence band.@xcite studies of the spin - wave spectra@xcite , monte - carlo studies@xcite as well as dynamical mean - field theory studies@xcite have been performed . overall , their results are rather similar to the physics one would expect to hold in a conventional ferromagnet . more recently , it has been proposed that spin - orbit coupling of the valence band , in the high carrier density ( strongly metallic ) regime leads to an rkky coupling between mn moments that is _ anisotropic _ in spin space , and where the positional disorder effectively leads to random anisotropy.@xcite this would lead to frustration effects on the magnetic ordering , and therefore unusual ferromagnetism . a number of very useful ab - initio studies have also been published.@xcite in parallel , we have studied effects of positional disorder on the magnetic ordering ( in the absence of spin - orbit coupling ) of an impurity band model,@xcite developed from previous work done in the context of insulating ii - vi dms compounds.@xcite such an approach should be of relevance at low doping concentrations x , at and below the metal - insulator transition , and possibly even above . evidence for the existence of impurity - like states is provided by ab - initio studies,@xcite which found that occupied hole states near the fermi level have wave - functions mostly concentrated on and near the mn impurity . more recently , angle resolved photoemission spectroscopy has revealed the existence of the impurity band in ga@xmath0mn@xmath1as with @xmath3 ( very close to the metal - insulator transition).@xcite a scanning tunneling microscope study @xcite demonstrates the existence of an impurity band in ( ga , mn)as samples with x=0.005 - 0.06 . optical spectroscopy@xcite also identifies the impurity band for x=0.0001 and x=0.05 samples . electron densities in localized states , as well as states close to the mobility edge , can be far from homogeneous , unlike bloch waves . at low mn concentrations and high degree of compensation ( which comes from charged centers ) seen in dms , short length - scale density fluctuations could be significant . this can lead to inhomogeneities in the local charge densities at different mn sites , which in turn leads to ( microscopically ) inhomogeneous magnetizations of the magnetic ions in the ordered phase . such inhomogeneity would be expected to alter the nature of the collective magnetic excitations ( spin waves ) of the magnetically ordered system , which in turn would affect charge transport through the magnetic excitation processes which give rise to spin - flip scattering . in this paper , we develop a numerical scheme to calculate the spin wave spectrum for a finite but large size model of coupled fermions and spins , in the presence of quenched disorder . we show that the method accurately reproduces the results for a lattice model of small size obtained from a standard treatment of spin waves via the random phase approximation.@xcite we then apply the method to the model of ref . , and study in detail its collective magnetic excitations . the plan of the paper is as follows . the model hamiltonian for dms is described in section ii . section iii is devoted to developing the numerical scheme . the accuracy of the scheme is tested by comparing it with the standard rpa method in section iv . in particular , we demonstrate that we can use our scheme to study large size systems , beyond the capability of the standard rpa approach . section v presents the results obtained by applying the scheme to the model of section ii , including the density of states and nature of the eigenvectors of the magnetic excitations of the coupled fermion - spin system . we summarize our conclusions in section vi . in the following we develop the formalism for an impurity band hamiltonian that we believe to be appropriate for describing ( at least qualitatively ) the diluted magnetic semiconductor ga@xmath0mn@xmath4as for low doping @xmath5 ( in the insulating phase , or not too far from the metal - insulator transition ) . however , generalizations of this method for other types of hamiltonians , crystal structures , parameters etc . can be done in a straightforward manner . the iii - v host semiconductor is assumed to have the zinc - blende structure appropriate for gaas . experimental measurements@xcite suggest that valence - ii mn substitutes for valence - iii ga . as a result , the @xmath6 mn dopants are randomly distributed at positions @xmath7 , @xmath8 on the @xmath9 fcc ga sublattice , corresponding to @xmath10 . all throughout this paper , we assume periodic boundary conditions . due to the valence mismatch , each mn introduces a charge carrier ( hole ) in the system . however , experimentally it is found that the hole concentration is considerably suppressed through compensation processes . as a result , the number of holes is only a fraction @xmath11 of the number of mn atoms @xmath12 . each mn atom also has a @xmath13spin @xmath14 from its half - filled @xmath15 level . the magnetic properties of the doped semiconductor are related to the exchange interaction between the mn spins and the charge carrier spins . this interaction is known to be antiferromagnetic ( afm ) , and proportional to the probability of finding the charge carrier at the corresponding mn site . recently , we proposed a simple impurity - band model to describe the behavior of the charge carriers for the low - doping regime.@xcite the main justification is that near and below the metal - insulator transition ( @xmath16 ) the density of charge carriers is not large enough to effectively screen the attractive coulomb potential of the mn dopants . as a result , bound , hydrogen - like impurity states are created about each mn site , at an energy @xmath17 ry above the top of the valence band . due to interactions , these impurity states lead to the appearance of an impurity band , and the holes first occupy states in this band . only if the concentration of holes ( or the temperature ) is large enough , are states in the valence band itself occupied by holes . thus , it is reasonable to attempt a description of the charge carriers behavior only in terms of this impurity band . as in previous work,@xcite in the following we will use the electron formalism to treat the problem . this is equivalent to performing a particle - hole transformation which leads to an inversion @xmath18 of the charge carrier spectrum . thus , instead of emptying the top of a valence - like impurity band ( i.e. , introducing holes in the system ) we instead occupy the bottom of a conduction - like impurity band . we also make the simplifying assumption that the isolated impurity wave - function for a charge carrier trapped near the mn at site @xmath7 is the @xmath19 hydrogen orbital @xmath20 , where @xmath21 is the appropriate bohr radius related to the effective mass of the heavy hole ( @xmath22 for gaas ) and the binding energy ( @xmath23 mev for mn in gaas).@xcite our approach neglects both the complicated orbital form of the acceptor wave - function ( ref . ) and spin - orbit coupling . the former is not expected to lead to any qualitative changes . it has recently been proposed that spin - orbit coupling leads to frustration in the magnetic ordering.@xcite these effects are left out in the present study , which concentrates on the effect of disorder . a study combining both effects is indicated for future work . we consider the hamiltonian @xmath24 here , @xmath25 creates a charge carrier with spin @xmath26 in the impurity state centered at site @xmath7 . the first term describes the hopping of charge carriers between impurity states . we use the parameterization @xmath27 ry , where @xmath28 , of magnitude and form appropriate for hopping between two isolated 1@xmath29 impurities which are not too close to one another . @xcite this hopping term has been shown to lead to the appearance of an impurity band which has a mobility edge , as well as a characteristic energy for the occupied states in agreement with physical expectation.@xcite the second term of the hamiltonian ( [ 1.1 ] ) describes the afm exchange between the mn spin @xmath30 and the charge carrier spin @xmath31 [ @xmath32 are the pauli spin matrices ] . this afm exchange is proportional to the probability of finding the charge carrier trapped at @xmath33 near the mn spin at @xmath34 , and therefore @xmath35 . based on calculations of the isolated mn impurity in gaas , we estimate the exchange coupling between a hole and the trapping mn ( @xmath36 ) to be @xmath37 mev.@xcite as already stated , the number of mn atoms is @xmath6 , and therefore there are a total of @xmath38 states in the impurity band . the number of charge carriers is fixed to @xmath39 , where we take @xmath40 . in ref . we studied the relevance of various other terms , such as an on - site potential ( associated with the coulomb potential of the compensation centers ) , hubbard - like on - site repulsion ( describing interactions between charge - carriers ) , external magnetic field etc . while they lead to various _ quantitative _ changes , we believe that the _ qualitative _ picture we present in the following sections is not changed by their absence . the random phase approximation ( rpa ) describes the collective excitations of a system about its self - consistent @xmath41 mean - field ground state . in order to clarify the notation used , we begin this section with a very short review of the derivation of the relevant equations for the mean - field ground state . we use the equation - of - motion approach of ref . . at the mean - field level , we are trying to find non - interacting fermionic quasiparticles through a unitary transformation of" +"in a couple of experiments , the measurement of the frequencies of collective modes in trapped fermi gases revealed a lot of interesting information on the equation of state , the validity of superfluid hydrodynamics , and the superfluid - normal phase transition @xcite . more recently , the transition from the hydrodynamic to the collisionless regime in the normal phase was also studied @xcite . however , since the frequencies of the collective modes depend on the trap frequencies , a precise knowledge of the latter is required for a meaningful interpretation of the collective - mode data . a possibility to determine the trap frequency with high precision is the measurement of the frequency of the sloshing mode @xcite , which is an oscillation of the center of mass of the trapped atom cloud . in a harmonic trap , this oscillation ( also called kohn mode ) is undamped and its frequency coincides exactly with the trap frequency in the corresponding direction , independently of the number of atoms @xmath0 , or their interaction , their temperature @xmath1 etc . this is a consequence of the kohn theorem @xcite and follows from the fact that the center - of - mass oscillation decouples completely from the internal dynamics of the gas if the interaction is translationally invariant and the external potential is harmonic @xcite . however , in practice the trap potential is never exactly harmonic . in optical dipole traps @xcite , the potential is typically gaussian ( corresponding to the intensity profile of the laser beam ) . because of this anharmonicity , the frequency of the sloshing mode is shifted , and the shift depends on the system parameters such as @xmath0 , @xmath1 , the scattering length @xmath2 characterizing the interaction strength , etc . furthermore , the sloshing mode is no longer undamped . the anharmonicity of the trap complicates considerably the analysis of collective - mode experiments . in ref . @xcite the measured frequencies were corrected for the anharmonicity effects by giving them in units of the measured frequency of the sloshing mode . however , it is clear that the damping rates of the modes can not be corrected in this way . in ref . @xcite , the damping rate of the sloshing mode was used to estimate the increase of the damping rate of other modes due to the anharmonicity . both corrections are ad - hoc prescriptions without rigorous justification . it is therefore strongly desirable to get a better understanding of the anharmonicity effects on the sloshing mode . the aim of the present paper is to describe theoretically the frequency shift and the damping rate of the sloshing mode in an anharmonic trap . we will compare our results with the experimental data available from the innsbruck group @xcite and with the numerical results by wu and zhang @xcite . we will also discuss in detail the damping mechanism of the sloshing mode . in an anharmonic potential , the center - of - mass motion is no longer decoupled from the internal degrees of freedom of the cloud . we will see that the damping of the transverse sloshing mode is a consequence of its coupling to other damped collective modes , in particular to the radial dipole mode and the bending mode . the framework of our study is the boltzmann equation , including mean field @xcite and in - medium cross - section @xcite . especially the mean field is expected to be important in the present context , because it can have a sizable effect on the density profile , i.e. , on how far the cloud extends into the anharmonic region of the trap potential . the boltzmann equation is solved approximately with the help of the phase - space moments method . this method , when extended beyond the lowest order , has proven to be in very good quantitative agreement with the results of a full numerical simulation @xcite . it has also been quite successful for the description of the experimental results for the frequency and damping rate of the radial quadrupole mode @xcite . in the present case of the sloshing mode , we include phase - space moments of first and third order . the paper is organized as follows . the general formalism is briefly presented in sec . [ sec : formalism ] . then we specify our model for the experimental trap potential in sec . [ sec : potential ] . in sec . [ sec : firstorder ] , we give a formula for the frequency shift of the sloshing mode within the first - order moments method . then we extend the ansatz to third order in sec . [ sec : thirdorder ] . the physical contents of the extended ansatz and the numerical results are discussed . in sec . [ sec : cubic ] the third - order ansatz is used to describe also the radial dipole , radial octupole , and bending modes . finally , in sec . [ sec : cl ] , we will conclude . throughout the paper , we use units with @xmath3 . in this section , we give a short summary of the formalisms of refs . more details can be found there . we consider a balanced two - component ( @xmath4 ) fermi gas of atoms with mass @xmath5 and interspecies attractive interaction ( scattering length @xmath6 ) , trapped in a potential @xmath7 . the framework we use to describe the collective dynamics of the system in the normal - fluid phase is the boltzmann equation . we assume that the two components move in phase , so that only one distribution function @xmath8 is needed . it is normalized to @xmath9 , and expectation values of one - body operators are given by @xmath10 as in ref . @xcite , we include in - medium effects in both the transport and the collision parts of the boltzmann equation : a mean field like potential @xmath11 and the in - medium modified cross - section @xmath12 , respectively . within the thomas - fermi or local - density approximation ( lda ) , the equilibrium distribution function reads @xmath13 } + 1},\ ] ] where @xmath14 is the mean field in equilibrium , @xmath15 is the chemical potential , and @xmath16 is the inverse temperature . as in ref . @xcite , we obtain @xmath14 from the single - particle self - energy in ladder approximation , evaluated at the fermi level . in the weak coupling limit , this reduces to the hartree term @xmath17 , where @xmath18 is the density per spin state , and it remains finite for all interaction strengths up to the unitary limit , @xmath19 . in equilibrium , the main effect of the mean field is to enhance the density in the center of the trap , as shown in fig . 3 of ref . @xcite . for the study of collective oscillations , it is sufficient to consider small deviations from equilibrium and to linearize the boltzmann equation with respect to @xmath20 . if we write the variation of the distribution function in the form @xcite @xmath21 with @xmath22 , the linearized boltzmann equation can be written as @xmath23\ , , \label{eq : boltzlin}\end{gathered}\ ] ] where @xmath24 denotes the poisson bracket , @xmath25 is the perturbation of the trap potential that is used to excite the collective mode , @xmath26 is the variation of the mean field due to the variation of the density , and @xmath27 $ ] is the linearized collision term . since we want to calculate the so - called response function , we take the perturbation to be a pulse , @xmath28 as in ref . @xcite , we approximate the variation of the mean field by @xmath29 the linearized collision integral reads @xmath30 = \int \frac{d^3p_1}{(2\pi)^3 } \int d \omega\ , \frac{d\sigma}{d\omega } \frac{|{{\bm{\mathrm{p}}}}-{{\bm{\mathrm{p}}}}_1|}{m } { f_{\mathit{eq}}}f_{{\mathit{eq}}1 } { \bar{f}_{\mathit{eq}}}^\prime \bar{f}_{{\mathit{eq}}1}^\prime\\ \times ( \phi+\phi_1-\phi^\prime-\phi_1^\prime)\,,\end{gathered}\ ] ] where an obvious notation for the different @xmath31 and @xmath32 at the momenta before ( @xmath33 , @xmath34 ) and after the collision ( @xmath35 , @xmath36 ) has been used . note that , especially near the critical temperature , the in - medium cross - section @xmath12 can differ strongly from the free one @xcite . as in ref . @xcite , we are looking for a semi - analytical solution of the boltzmann equation ( [ eq : boltzlin ] ) by using the method of phase - space moments . in this section , we will generalize the formalism of that paper to the case of an arbitrary trap potential @xmath37 and with mean field @xmath11 . the basic idea is to approximate the function @xmath32 by a polynomial in the components of @xmath38 and @xmath33 with time - dependent coefficients @xmath39 , @xmath40 where the @xmath41 are suitable basis functions , e.g. , monomials in the components of @xmath38 and @xmath33 . multiplying the linearized boltzmann equation ( [ eq : boltzlin ] ) by @xmath42 and integrating over phase space , one obtains , after a fourier transform with respect to @xmath43 , a set of @xmath44 coupled linear algebraic equations for the @xmath44 coefficients @xmath45 . in matrix form , they read @xmath46 where @xmath47\ , , \label{eq : acollij}\end{gathered}\ ] ] and @xmath48 the variation of the mean field in eq . ( [ eq : adeltauij ] ) is defined as @xmath49 equations ( [ eq : atransij ] ) and ( [ eq : ai ] ) correspond to eqs . ( 14 ) and ( 16 ) in ref . @xcite which have been simplified by integration by parts . comparing eqs . ( [ eq : ac = a])-([eq : ai ] ) with the analogous ones of ref . @xcite , eqs . ( 11)-(16 ) , one sees that the mean field gives rise to a new term , @xmath50 . however , one should keep in mind that implicitly all terms depend on the mean field since it modifies the equilibrium distribution @xmath51 . one can see that the matrices @xmath52 and @xmath53 are symmetric , @xmath54 is antisymmetric , whereas @xmath50 has no defined symmetry . in practice , the calculation of the matrices is straight - forward , but tedious , and we made use of the mathematica software to express the numerous matrix elements in terms of a smaller number of integrals over equilibrium quantities . without an external perturbation @xmath55 , i.e. , for @xmath56 , eq . ( [ eq : ac = a ] ) has a solution with non - vanishing coefficients @xmath39 only if @xmath57 . the frequencies @xmath58 for which this happens are obviously given by the eigenvalues of the matrix @xmath59 . if they are well separated , it is possible to interpret them as the frequencies of the eigenmodes of the system . in general , they are complex , and their imaginary part describes the damping rate of the corresponding mode @xcite . however , as discussed in ref . @xcite , when the moments method is extended to higher order , there can be many eigenvalues belonging to a single collective mode . in this case , the scattering of the eigenvalues , which goes over into a continuous spectrum in the limit of an infinite number of moments @xcite , corresponds to a new contribution to the damping ( landau damping ) in addition to the imaginary parts coming from the collision term . in order to obtain the mode frequency and damping rate in this case , it is useful to look at the response function which contains the contributions of all eigenvalues . we denote by @xmath60 the fourier transform of" +"there is a strong observational evidence that active galactic nuclei ( agn ) , x - ray transients and gamma - ray bursts ( grbs ) are associated with black holes that accrete matter via a surrounding accretion disk . the exact mechanism by which these phenomena are produced involves the interaction between a rotating black hole , the accretion disk and the electromagnetic field @xcite . however , magnetic fields play a key role in understanding of these process . the enormous observed energy in agn is related with the presence of magnetic field in these nuclei @xcite . the existence of radio jets is also attributed to the presence of strong magnetic fields in centers of agn and quasars @xcite . a general exact relativistic model that describes such astrophysical objects require an exact solution of coupled einstein - maxwell field equations that represent the superposition of a kerr black hole with a stationary disk and electromagnetic fields . as a first approximation one could consider a static system composite by a schwarzschild black hole and a thin disk immersed in a magnetic field . exact solutions of the einstein equations representing the field of a static thin disks without radial pressure were first studied by bonnor and sackfield @xcite , and morgan and morgan @xcite , and with radial pressure by morgan and morgan @xcite . several classes of exact solutions of the einstein field equations corresponding to static thin disks with or without radial pressure have been obtained by different authors @xcite . rotating thin disks that can be considered as a source of a kerr metric were presented by bick and ledvinka @xcite , while rotating disks with heat flow were were studied by gonzlez and letelier @xcite . the static superposition of a disk and a black hole was first considered by lemos and letelier @xcite . thin disks in presence of electromagnetic field have been discussed as sources for kerr - newman fields @xcite , conformastationary metrics @xcite and for magnetostatic axisymmetric fields in @xcite . monopole and dipole layers in curved spacetimes were analyzed in @xcite , and electromagnetic sources distributed on shells in a schwarzschild background in @xcite . also , conformastatic disk - haloes in einstein - maxwell gravity were considered in @xcite , variational thermodynamics of relativistic thin disks in @xcite , and models of perfect fluid disks in a magnetic field for conformastatic spacetimes in @xcite . in this work we consider the exact static superposition of a schwarzschild black hole and a thin disk in presence of a magnetic field . the method used to include the magnetic field is the well - known complex potential formalism proposed by ernst @xcite , using as seed solutions simple vacuum spacetimes representing the field of a thin disk and a black hole . the paper is organized as follows . in sec . ii we discuss the einstein - maxwell equations in the case of magnetostatic fields and we present a summary of the procedure to obtain models of thin disks with a purely azimuthal pressure and current . in order to have a stable configuration in absence of radial pressure , the matter in the disks also in interpreted as made of two pressureless ( dust ) streams of counterrotating charged particles ( counterrotating model ) moving along electrogeodesic . using the rayleigh criterion we derivate for circular orbits the stability conditions of the particles of both streams . in sec . iii the formalism for superposing the field of a disk and a static black hole in the vacuum @xcite is extended to the case of magnetized weyl fields . in sec . iv we consider two models of disks , one of infinite extension based on a kuzmin - chazy - curzon metric and other finite based on the first morgan - morgan disk . also a simple model of active galactic nuclei is studied based on the superposition of a black hole , a kuzmin - chazy - curzon disk and two rods representing jets @xcite , in presence of magnetic field . finally , in sec . v we summarize and discuss the results obtained . the line element for a static axially symmetric spacetime in weyl s canonical coordinates @xmath0 is given by @xcite @xmath1 , \label{eq : met}\ ] ] where @xmath2 and @xmath3 are functions of the coordinates @xmath4 and @xmath5 only . the vacuum einstein - maxwell equations , in geometrized units such that @xmath6 , are given by @xmath7 where @xmath8 \label{eq : tab}\ ] ] is the electromagnetic energy - momentum tensor , @xmath9 the electromagnetic field tensor , and @xmath10 the electromagnetic four potential . for magnetostatic axially symmetric fields @xmath11 , where @xmath12 is the magnetic potential which also is function of @xmath13 and @xmath5 only . the other symbols have the usual meaning , i.e. , @xmath14 , @xmath15 covariant derivate , etc . for the metric ( [ eq : met ] ) , magnetostatic einstein - maxwell equations give @xmath16&=&0 , \label{eq : e - m1 } \\ f\nabla^{2}f&=&\nabla f\cdot\nabla f + 2\rho^{-2}f^{3}\nabla a\cdot\nabla a , \label{eq : e - m2 } \\ \lambda,_\rho&=&\rho\left(\psi^{2},_{\rho}-\psi^{2},_{z}\right)+\frac{1}{\rho } \left(a^{2},_{\rho}-a^{2},_z\right)f , \label{eq : e - m3 } \\ \lambda,_z&=&2\rho\psi,_{\rho } \psi,_{z}+\frac{2}{\rho}a,_{\rho}a,_{z}f , \label{eq : e - m4}\end{aligned}\ ] ] where @xmath17 is the standard differential operator in cylindrical coordinates and @xmath18 . in vacuum , the solutions of the above system of equations correspond to the well - known weyl solutions ( @xmath19 , @xmath20 ) and the equation ( [ eq : e - m2 ] ) is the laplace s equation . solutions of the einstein - maxwell equations ( [ eq : einmax1 ] ) - ( [ eq : einmax2 ] ) representing the field of a thin disk at @xmath21 with electric current can be constructed assuming the components of the metric tensor and the electromagnetic potential continuous across the disk , and its first derivatives discontinuous in the direction normal to the disk . this can be written as @xmath22 = g_{ab , z}|_{_{z = 0^+ } } \ - \ g_{ab , z}|_{_{z = 0 ^ - } } \ = \ 2 \ g_{ab , z}|_{_{z = 0^+ } } , \label{eq : b } \\ a_{b } \ & = & [ a_{b , z } ] = a_{b , z}|_{_{z = 0^+ } } \ - \ a_{b , z}|_{_{z = 0 ^ - } } \ = \ 2 \ a_{b , z}|_{_{z = 0^+}}. \label{eq : a } \end{aligned}\ ] ] the application of the formalism of distributions in curved spacetimes to the einstein - maxwell equations @xcite give us @xmath23 where @xmath24 is the usual dirac function with support on the disk , @xmath25 is the electromagnetic tensor ( [ eq : tab ] ) , @xmath26 is the energy - momentum tensor on plane @xmath21 , and @xmath27 \delta^z_b , \label{eq : ja}\ ] ] is the electric current density on the disk . @xmath28 $ ] means the jump of maxwell tensor across the disk . the `` true '' surface energy - momentum tensor of the disk @xmath29 and the `` true '' surface current density @xmath30 are given by @xmath31 where @xmath32 is the `` physical measure '' of length in the direction normal to the disk . for the metric ( [ eq : met ] ) , the nonzero components of @xmath33 are @xmath34 [ eq : emt ] and in the magnetostatic case the only nonzero component of the current density is @xmath35 where all the quantities are evaluated at @xmath36 . in terms of the orthonormal tetrad @xmath37 , where @xmath38 the surface energy density @xmath39 and the azimuthal pressure @xmath40 on the disk are given by @xmath41 and the azimuthal current density by @xmath42 thus we have a disk only with pressure and electric current in azimuthal direction . because there is no radial pressure or tension to support the gravitational attraction , the matter distribution is unstable . in addition , since the spacetime is static we have no rotation . in order to have a stable configuration in absence of radial pressure , we need assume the counterrotating hypothesis , that is the matter in the disk is considered made of two pressureless streams of counterrotating charged particles , i.e. , that circulate in opposite directions . even though this interpretation can be seen as merely theoretical , there are observational evidence of counterrotating matter components in certain types of galaxies @xcite . we assume @xmath43 where @xmath44 @xmath45 are the matter densities of each stream , @xmath46 the electric charge densities , and @xmath47 the normalized four - velocities ( @xmath48 ) , which for circular orbit are @xmath49 , where @xmath50 are the angular velocities of each stream . now , using the continuity equation ( the bianchi identity ) @xmath51 and eq . ( [ eq : tabdisk ] ) @xmath52 , we obtain @xmath53 . but from maxwell equations @xmath54 , then @xmath55 . in the disk this gives @xmath56 and using ( [ eq : sabsum ] ) and ( [ eq : jsum ] ) we have @xmath57 . thus using ( [ eq : sabcon ] ) and ( [ eq : jacon ] ) we obtain @xmath58 i. e. , each stream follow a electrogeodesic motion . for circular orbits reads @xmath59 and in the case magnetostatic @xmath60 where @xmath61 obtains normalizing @xmath62 , that is @xmath63 using ( [ eq : sabsum ] ) - ( [ eq : jacon ] ) and ( [ eq : motion ] ) one finds -@xcite @xmath64 with respect to the orthonormal tetrad ( [ eq : tetrad1 ] ) - ( [ eq : tetrad2 ] ) the 3-velocity has components @xmath65 and for equatorial circular orbits the only nonvanishing velocity components is given by @xmath66 which represents the circular speed of the particles as seen by an observer at infinity . in vacuum the speed @xmath67 of counterrotation ( rotation curves or rotation profile ) of the particles in the disk is given by @xmath68 to analyze the stability of the particles of the two streams in the case of circular orbits in the equatorial plane we use an extension of rayleigh criteria of stability of a fluid at rest in a gravitational field @xcite . the method works as follows . any small element of the matter distribution analyzed ( in our case a test particle of the streams ) is displaced slightly from its path . as a result of this displacement , forces appear which act on the displaced matter element . if the matter distribution is stable , these forces must tend to return the element to its original position . the relativistic lagrangian for a test particle of the streams in presence of a gravitational and magnetic field is given by @xmath69 where @xmath70 is the specific electric charge . for magnetostatic axially symmetric fields there are two constants of motion @xmath71 where @xmath72 is the relativistic specific energy and @xmath73 the specific angular momentum . the motion equation ( [ eq : motion ] ) can be cast as a balance equation @xmath74 where the term first on the left - hand side represents the gravitational force @xmath75 , the term second the the lorentz force @xmath76 , and the term on the right - hand side the centrifugal force @xmath77 acting on the test particle . so we have a balance between the total force @xmath78 and the centrifugal force . we now consider the particle to be initially in a circular orbit with radius @xmath79 and we slightly displace it to a higher orbit @xmath80 . the angular momentum of particle remains equal to its initial value @xmath81 which implies that the centrifugal force in its new" +"the thermodynamic analogue of the casimir effect originating from the confinement of vacuum fluctuations @xcite is the critical casimir effect due to the presence of long - ranged thermal fluctuations in a fluid close to its critical point at @xmath0 . the corresponding critical casimir forces have been predicted theoretically by fisher and de gennes in 1978 @xcite . experimentally , critical casimir forces have been studied only during the last decade when first measurements were performed indirectly via monitoring the thickness of wetting films upon approaching a critical end point @xcite . later on , the critical casimir force has been measured directly by using colloidal particles suspended in a binary liquid mixture @xcite . generically , the surfaces , which confine a binary liquid mixture , preferentially attract one of its two components leading to either positive [ @xmath1 or negative [ @xmath2 values of the scalar order parameter @xmath3 which describes the difference between the local concentration of one of the two components and its critical value . this generic preference of the surfaces confining the liquid can be described by effective surface fields . upon approaching @xmath4 , the critical adsorption profiles , which describe the concentration enhancement near the surface , become long ranged due to the concomitant divergence of the bulk correlation length @xcite . in semi - infinite systems , the transition from the phase in which only the region near the single surface is ordered to the one in which also the bulk is ordered is known as the extraordinary or normal transition @xcite . for two surfaces opposing each other , depending on the mutual combinations of boundary conditions ( bcs ) critical casimir forces are either attractive or repulsive . their range is set by the bulk correlation length @xmath5 . whereas in fluids @xmath5 is typically of molecular size , it attains values of the order of micrometers upon approaching the critical point @xcite . thus , critical fluctuations may induce effective interaction potentials with a strength of several @xmath6 at the nanometer and micrometer scale . moreover , critical casimir forces are universal in character : due to the divergence of the correlation length molecular details of the confined binary liquid mixture become irrelevant and only a few gross features of the system determine the main characteristics of the critical casimir forces @xcite . from a lower , parallel , crenellated wall which exhibits a periodic pattern with period @xmath7 consisting of rectangular crenels of width @xmath8 and depth @xmath9 and merlons of width @xmath10 and height @xmath9 . the system is spatially invariant in the @xmath11-direction . for later reference , the box at the bottom summarizes the definitions of the various scaling variables which the scaling function of the critical casimir force depends on ; @xmath12 is the reduced temperature @xmath13 and @xmath14 is the nonuniversal amplitude of the bulk correlation length @xmath15 in the disordered phase , which defines the universal critical exponent @xmath16 . , title=""fig:"",width=302 ] from a lower , parallel , crenellated wall which exhibits a periodic pattern with period @xmath7 consisting of rectangular crenels of width @xmath8 and depth @xmath9 and merlons of width @xmath10 and height @xmath9 . the system is spatially invariant in the @xmath11-direction . for later reference , the box at the bottom summarizes the definitions of the various scaling variables which the scaling function of the critical casimir force depends on ; @xmath12 is the reduced temperature @xmath13 and @xmath14 is the nonuniversal amplitude of the bulk correlation length @xmath15 in the disordered phase , which defines the universal critical exponent @xmath16 . , title=""fig:"",width=321 ] [ fig : sketch ] in view of nano- and micro - electromechanical devices , nowadays various experimental techniques are available to endow solid surfaces with precisely defined geometrical or chemical structures ( see , e.g. , refs . critical casimir forces for _ chemically _ structured confinements have been studied theoretically @xcite as well as in experiments with colloidal particles @xcite . it has been demonstrated that such patterns induce _ lateral _ critical casimir forces which can be used to trap particles reversibly along the lateral direction in a designated way @xcite . moreover , a suitable combination of attractive and repulsive critical casimir forces may even lead to stable levitation @xcite . here , we study critical casimir forces for _ geometrically _ structured confinements . the quantum - electrodynamic casimir effect in the presence of geometrically structured surfaces has been studied theoretically and experimentally for various surface topographies @xcite . two opposing surface gratings are subject to lateral quantum electrodynamic casimir forces @xcite . in this context , experimental studies focus on spherical particles near crenellated surfaces , i.e. , forming grooves with rectangular cross - sections @xcite . typically , the radius of the spherical particles is much larger than the period of the pattern of the crenellated surface such that , effectively , in the region of closest approach the system mimics the geometrical setup of a planar wall near a parallel , crenellated surface . critical adsorption and critical casimir forces for geometrically structured confinements have been studied for structures shaped as wedges and ridges with triangular cross - section @xcite , as well as for truncated wedges @xcite . it was found that , for large distances between a sawtooth - shaped wall and a planar wall , the critical casimir force effectively corresponds to the one between two planar walls ; on the other hand , for short distances between the two surfaces , the tips of the ridges dominate the order parameter profile and the characteristic power law behavior of the critical casimir force differs from that for planar surfaces @xcite . the present study extends these previous investigations @xcite into various directions . we consider a crenellated substrate close to a planar substrate at minimal surface - to - surface distance @xmath17 , as shown in fig . [ fig : sketch ] . the details of the geometry as well as the finite - size scaling of the critical casimir phenomena are described in section [ sec : theory ] . we calculate universal scaling functions for the critical casimir forces and for the order parameter profiles within mean - field theory and for identical chemical bcs at both walls ( @xmath18 configuration ) . in section [ sec : profiles ] we first study the universal features of the order parameter profiles close to @xmath4 for the geometry under consideration . second , in section [ sec : force ] we study the critical casimir forces acting on such geometrically structured substrates . finally , in section [ sec : summary ] we summarize our main findings . according to the theory of finite - size scaling , the singular contribution to the critical casimir force is described by a universal scaling function , which is independent of the molecular details of the binary liquid mixture and depends only on the bulk universality class of the associated critical point @xcite . here , we focus on the ising universality class characterized by a scalar order parameter @xmath3 , which encompasses the experimentally relevant binary liquid mixtures and simple fluids . upon approaching the critical point of the fluid , the bulk correlation length diverges as @xmath19 , where @xmath20 in spatial dimension @xmath21 and @xmath22 in spatial dimension @xmath23 @xcite ; @xmath24 are nonuniversal amplitudes characterized by the universal ratio @xmath25 in @xmath21 and @xmath26 in @xmath23 . the sign of the reduced temperature @xmath27 is chosen such that @xmath28 corresponds to the mixed ( disordered ) phase of the fluid , whereas @xmath29 corresponds to the ordered phase , corresponding to spontaneous phase separation . for an upper critical point the homogeneous phase is found at high temperatures , and one has @xmath13 . however , many experimentally relevant binary liquid mixtures exhibit a lower critical point ; in this case @xmath30 . in general , the sign and the amplitude of the critical casimir force depend on the types of effective chemical bcs at the walls and on the geometry of the confining surfaces . here we focus on the case of equal , symmetry - breaking @xmath31 bcs , which corresponds to the generic case of preferential adsorption of one of the two species of a binary liquid mixture . this leads to an attractive critical casimir force @xcite . inspired by experiments encompassing binary liquid mixtures of water and lutidine ( with a lower critical point at @xmath32 ) @xcite , here a binary liquid mixture with a lower critical point is considered at fixed pressure and at its critical composition . first , we briefly review the film geometry . in this case the liquid is confined between two parallel , macroscopically extended walls at a distance @xmath33 . according to renormalization group theory the critical casimir force @xmath34 per area of one wall , which is acting on the parallel walls ( @xmath35 ) , scales as @xcite @xmath36 the scaling function @xmath37 depends only on a single scaling variable given by the film thickness @xmath33 in units of @xmath38 , raised to the power @xmath39 . for equal chemical bcs , as discussed here , @xmath40 is negative , so that the critical casimir force is attractive . for @xmath41 the scaling function of the critical casimir force reduces to a universal constant value , the so - called critical casimir amplitude @xcite : @xmath42 accordingly , at @xmath4 the critical casimir force decays algebraicly @xmath43 . away from criticality , the critical casimir force decays exponentially as a function of @xmath44 . the scaling function @xmath37 has been calculated exactly in @xmath45 @xcite , for @xmath46 using a perturbative field - theoretical method @xcite or a local - functional method @xcite , and in @xmath21 numerically via monte carlo simulations @xcite . in the following we consider a crenellated wall located at a minimal surface - to - surface distance @xmath17 from a planar wall as sketched in fig . [ fig : sketch ] . the width and depth of the crenels are given by @xmath8 and @xmath9 , respectively , and the structure is periodic along the lateral @xmath47-direction with period @xmath7 , so that the width of the merlons , i.e. , the surface - to - surface separation between two neighboring crenels , is given by @xmath10 . accordingly , the corresponding universal contribution to the critical casimir force @xmath48 per area of the planar wall scales as @xmath49 where the geometrical parameters form the following scaling variables : @xmath50 the critical casimir force between a crenellated and a planar wall attains the value of the corresponding force between two planar walls in various limits . for very shallow crenels , i.e. , in the limit @xmath51 or @xmath52 , the following relation holds : @xmath53 as will be discussed in more detail below , we find that for narrow crenels with @xmath54 , the order parameter profile attains the form of the planar wall geometry , _ independent _ of the value of @xmath55 : @xmath56 similarly , for @xmath57 , one has @xmath58 for very broad crenels compared with the film thickness , i.e. , @xmath59 , the limiting behavior of the scaling function of the critical casimir force is given by the average of the scaling functions for two planar walls at distances @xmath17 and @xmath60 , respectively . this corresponds to the so - called proximity force approximation ( pfa ) , which we discuss in the following . within the pfa the surfaces are subdivided into infinitely small elements parallel to each other , and the resulting force is obtained by pairwise adding the individual contributions to the force . the derjaguin approximation is a special case of the pfa for smoothly curved surfaces . detailed comparisons of the derjaguin" +"mathematical biology is a fast growing , well recognised area of research . although not clearly defined yet , is consider one of the most exciting modern applications of mathematics . the increasing use of mathematics in biology is inevitable as biology becomes more quantitative . the complexity of the biological sciences makes interdisciplinary approach essential . in particular , mathematical modelling of the dynamics of populations interactions is a very challenging and important task . in building a mathematical description of interacting populations , the main goal is to capture the essential features of a complex trophic web with a mathematically tractable model . the result is , usually , a non - linear dynamical system , which may be expressed as a set of either differential or difference equations . classical examples are the pioneering works of lotka ( 1932 ) and volterra ( 1931 ) . such models may be understood as describing the time evolution of population averages in a closed ecosystem . in this context , one can devise two broad categories of models : _ ad hoc _ models , intended to give a phenomenological mathematical description of the dynamics , and _ ab initio _ models , which try to stablish sets of dynamical rules based on or inspired by the biology of the populations . the majority of classical population models are deterministic . recently , due to the growing availability of affordable computer power , _ individual - based models _ have been becoming popular . instead of describing only population sizes , they treat them as collections of individuals with distinctive characteristics . some of those models have been successfull in tackling important biological problems , such as ageing and the evolution of sex ( penna , 1995 ) and ( oliveira , 1999 ) . the possibility of combining elements of population dynamics and genetics into mathematical models is indeed exciting and promising . individual - based models are , in general , stochastic models , known to have a rich variety of behaviors , and sometimes differing markedly from their deterministic counterparts . classical models for competition between two species usually predict exclusion or divergent evolution of resource exploitation . these predictions are massively corroborated by experience and observation . such results are commonly summarized in gause s competitive exclusion principle : to coexist , species must differ in their resource use ; otherwise one of them ends up extinct ( gause , 1935 ) . however , recent experimental data show that coexistence is possible for very similar species competing for the same resources _ without _ niche partition ( louzada , 1996 ) . motivated by this experimental challenge to classical competition theory , we propose an individual - based stochastic competition model , which is essentially a modification of a deterministic lotka - volterra type model . we introduce , as the individual characteristic , a rudimentary `` genotype '' , which determines the individual s adaptation to the environment , as well as its interaction with the other species . in section ii we describe the model and its implementation . in section iii we present the results of computer simulations of the model proposed in section ii , and discuss their implications to coexistence in real ecosystems . we present our final remark and summarize the conclusions in section iv . the continuous - time , deterministic lotka - volterra model for competition between two species is given by the equations @xmath0 where @xmath1 , @xmath2 are the populations sizes at time @xmath3 , @xmath4 , @xmath2 are the intrinsic growth rates ; @xmath5 , @xmath6 , are the competition strengths . it is well known that equations [ classical_lv ] have critical points @xmath7 and that @xmath8 corresponds to exclusion of one species , while @xmath9 corresponds to coexistence . when @xmath10 the coexistence critical point is globally stable , whereas for @xmath11 the exclusion points are the globally stable ones , and coexistence becomes a saddle point . put in biological terms , whenever intra - specific competition is stronger than inter - specific competition there can be coexistence ; otherwise one species always exclude the other . we are interested in building a `` microscopic '' model for competition which is able to mimic the most common biological observations , namely competitive exclusion and coexistence by character displacement . the model should also be able , given some specific conditions , to reproduce the less commonly observed coexistence by _ converging _ evolution . we start by converting equations [ classical_lv ] into probabilistic rules for individual reproduction / death as follows ( may , 2001 ) . the intra - specific competition term , @xmath12 is interpreted as a death process , giving a death probability @xmath13 . the probability that each individual of population @xmath14 reproduces succesfully is given by @xmath15 , @xmath16 . this simple set of stochastic rules is more easily related to the discretized version of equations [ classical_lv ] , @xmath17 now time is a discrete variable , labeling generations , and the parameters should be interpreted as being the ones in equations [ classical_lv ] multiplied by the time interval between generations . it is worth mentioning that the discretized version [ discrete_lv ] is identical to the continuous version ( equations [ classical_lv ] ) in the limit of very large populations . thus , it shares with the continuous model the critical points and their stability properties , as can be easily seen by direct iteration of equation [ discrete_lv ] . up to now the `` microscopic '' character of the model , meaning its description using rules for _ individual _ birth / death processess , can be considered merely formal . it differs from equation [ discrete_lv ] only in a well - known demographic stochasticity @xcite , that is relevant just in the limit of small populations . our next step is to make the model really `` microscopic '' , by endowing each individual with a property ( which we call a genotype ) , that will modify competition and intrinsic growth . the phenotype will then be a measure of how close an individual s genotype is to the optimal genotype for a particular environment . the individual s genotype is also compared to the genotypes of individuals of the competing species . the closer they are , the stronger the competition is . genotypes @xmath18 $ ] are 32-bit strings , associated with individual @xmath19 in population @xmath20 . from each @xmath18 $ ] two phenotypic traits are derived : its normalized hamming distance to the environmentally determined optimal genotype @xmath21 , @xmath22=\frac{\langle g_i[l],g_{opt}\rangle}{32}\ , , \ ] ] and its average normalized hamming distance to the individuals of the opposing population , @xmath23 = \frac{1}{n_j}\sum_{m=1}^{n_j}\frac{\langle g_i[l],g_j[m]\rangle}{32},\,\ , j\neq i.\ ] ] in order to simulate a harsh environment , we impose severe penalties to individuals that depart from @xmath21 : their intrinsic reproduction probability is assumed to decrease exponentially with @xmath24 $ ] as @xmath25)\ , , \ ] ] where @xmath26 is a parameter regulating the environment `` harshness '' . the competition will be modified according to @xmath27n_j),\,\ , j\neq i\ , .\ ] ] which is a much milder dependence on the phenotype than that imposed by the environment . in order to allow the species to `` evolve '' , at every birth event the newborn inherits a copy of its mother s genotype with a possible `` mutation '' , represented by a flip of a random bit . the possibility of mutation introduces `` real '' ( as opposed to the formal demographic ) stochasticity into the model , and should alter its dynamical behaviour . to investigate the dynamics we simulate the model in a computer our interest is to study the emergence of coexistence other than the `` trivial '' coexistence of the classical lotka - volterra model of equations [ classical_lv ] . thus we start with a situation where intra - specific competition is weaker than inter - specific competition . we also assume , for the time being , symmetric competition ( @xmath28 ) , and identical initial intrinsic reproduction rates ( @xmath29 ) . the genotypes of both populations are randomly distributed with uniform probability over the space of 32-bit sequences . no special meaning is attributed to any particular sequence other than the optimal genotype @xmath21 . for the situation just described , the only critical points of the cassical model are @xmath30 . simulations of the proposed model show evolution towards coexistence , as can be seen in figure [ fig1 ] . there , initial populations are the same , @xmath31 , but the asymptotic steady state is not symmetric . due to random fluctuations , one of the species is forced to move away from @xmath21 , as can be seen in the inset , while the other approaches it as much as possible . this makes the average distance between the two populations genotypes very large , which minimizes the effects of competition . we may interpret this result as the system spontaneously attainning some kind of niche partition . , @xmath32 , @xmath33 . the black and red curves are populations 1 and 2 , respectively , with @xmath31 . b ) average distance between populations genotypes and @xmath21 , @xmath34 , showing evolution towards niche partition . c ) first and final distribution of genotypes showing divergent evolution . ( the simulation was run for a much longer time than shown to guarantee that the asymptotic regime had been reached ) . ] for @xmath35 one of the species is excluded . this means that the coexistence state ( or states ) , contrary to the situation in the classical lotka - volterra model , has limited basins of attraction , and it is interesting to estimate the sizes of those basins . starting with @xmath36 , for example , the system reaches a steady state with average populations different from the case of figure [ fig1 ] . this is an indication of existence of mutliple coexistence critical points in this model . nevertheless , all these coexistence states correspond to niche partition . in figure [ basin ] we plotted the initial points from which a coexistence state is reached for fixed values of the parameters . as can be seen , the basin of attraction of the stability region is rather limited , in contrast with the classical lotka - volterra coexistence point being globally stable . the simulations also showed cases of coexistence with converging evolution to a single phenotype , corresponding to a distance between individual s genotypes and @xmath21 , that allows for near - maximum variability inside populations . in these cases , exemplified by the results of figure [ coex_conv ] , asymptotic inter - specific competition is weaker than the asymptotic intra - specific competition . once again , evolution leads to a situation compatible with the classical lotka - volterra dynamics . . c ) first and final distribution of genotypes showing convergent evolution . ( the simulation was run for a much longer time than shown to guarantee that the asymptotic regime had been reached ) . ] another interesting case of coexistence has very similar steady - state population sizes and also similar values of @xmath37 , as seen in figure [ coex_aleat ] . however , the average genotypic distance between populations may be high . this is indeed what happens in this particular case , as can be seen in fig . [ coex_aleat]b . once again , the system found its way through evolving towards minimal competition , and coexistence is thus possible . , are both large . this is compatible with large initial variability inside each population" +"the atmospheric helium abundances of sdbs are poorly understood . from the typical abundance patterns of these stars , which show a depletion of light elements as well as an enrichment of heavy metals , it has been concluded that diffusion play an important role in their atmospheres . however , diffusion models predict an almost total depletion of helium in contrast to what is observed . the helium abundances of sdbs range from slightly above solar down to @xmath3 . mass loss caused by stellar winds as well as extra mixing in the atmosphere have been invoked to counteract gravitational settling and explain the observed helium abundances ( see * ? ? ? * and references therein ) . @xcite found a correlation of helium abundance with temperature . the hotter the sdb , the more helium is present in its atmosphere . similar correlations have been found by other groups ( see e.g. vennes et al . these proceedings ) . however , @xcite also reported the discovery of two distinct sequences showing a similar correlation with temperature , the lower sequence being offset by about @xmath4 from the upper sequence . the majority of stars lie on the upper sequence . those sequences could not be clearly identified in other datasets so far ( e.g. * ? ? ? * ; * ? ? ? @xcite combined the then published data sets and found the stars of the upper sequence to lie near the extreme horizontal branch ( ehb ) band in the @xmath5-plane , as expected , whereas the lower - sequence stars lie in a much more dispersed area ( see figs . 2,3 in * ? ? ? gravitational settling can also lead to isotopic anomalies in stellar atmospheres . in the case of helium the light isotope @xmath0he can be enriched with respect to the usually much more abundant @xmath6he . such an enrichment has initially been found in main sequence b stars with subsolar helium abundance @xcite . however , @xcite detected strong line shifts in the sdb star sb290 and the blue horizontal branch star phl25 indicating that basically the whole helium content of the atmosphere consists of @xmath0he . later on @xcite and @xcite found another three sdbs , where @xmath0he is enriched in the atmosphere . here we present the results of a quantitative spectral analysis of a sample of 46 sdb stars from high resolution spectra . plotted against effective temperature . the filled symbols mark the results from our study . filled red diamonds mark objects where isotopic shifts due to an enrichment of @xmath0he were detected , filled circles objects with atmospheres dominated by @xmath6he . upper limits are marked with triangles . the solid horizontal line is drawn at solar helium abundance . the two dotted lines are regression lines for the two distinct helium sequences taken from @xcite . results taken from the literature are plotted as grey symbols @xcite.,width=377 ] 46 bright subdwarf b stars were observed with the feros spectrograph ( @xmath7 , @xmath8 ) mounted at the eso / mpg 2.2 m telescope in la silla . five stars were observed with the foces spectrograph ( @xmath9 , @xmath10 ) mounted at the caha 2.2 m telescope . the data were reduced with the midas package . medium resolution spectra of 13 stars were obtained with the isis spectrograph ( @xmath11 ) mounted at the wht . 13 sdbs discovered in the course of the edinburgh - cape blue object survey @xcite have been observed with the grating spectrograph and intensified reticon photon counting system on the 1.9 m telescope of the saao ( @xmath12 ) . spectra of five sdbs have been taken with the cafos spectrograph mounted at the caha 2.2 m telescope ( @xmath13 ) . atmospheric parameters and helium abundances have been determined by fitting model spectra to the hydrogen balmer and helium lines @xcite of the high - resolution spectra using the spas routine developed by h. hirsch . the parameter determination from the high - resolution spectra needs to be checked and systematic effects have to be quantified properly . in order to do this we analysed medium - resolution spectra in the same way as the high - resolution data and derived systematic uncertainties by comparing the results . he ( solid ) and @xmath0he lines ( dotted ) are plotted as vertical lines.,title=""fig:"",width=377 ] he ( solid ) and @xmath0he lines ( dotted ) are plotted as vertical lines.,title=""fig:"",width=377 ] [ fig : abun ] shows the helium abundances of our sample plotted against the effective temperature . all but two of our programme stars have subsolar helium abundances typical for sdb stars . the correlation of helium abundance with temperature discovered by @xcite can be clearly seen as well as the two distinct sequences showing a similar correlation with temperature . combining these data with the results of other studies the underlying pattern becomes apparent . in fig . 1 our results are overplotted with the two regression lines calculated by @xcite and based on their results . the two lines match very well with the sequences seen in our sample . we define a dividing line between the two helium sequences at @xmath14 accordingly , 36 stars ( @xmath15 ) are associated with the upper sequence while 15 ( @xmath16 ) belong to the lower one . the respective fractions of the full sample of 349 sdbs are @xmath17 and @xmath18 . -diagram for the entire sample under study . the helium main sequence ( hems ) and the ehb band ( limited by the zero - age ehb , zaehb , and the terminal - age ehb , taehb ) are superimposed with ehb evolutionary tracks for solar metallicity taken from @xcite labelled with their masses . red open symbols mark objects where isotopic shifts due to an enrichment of @xmath0he were detected , filled symbols objects with atmospheres dominated by @xmath6he . the diamonds mark stars belonging to the upper helium sequence , the circles stars belonging to the lower sequence . the triangles mark the three sdbs with enriched @xmath0he from the literature.,width=377 ] searches for the @xmath0he isotope in stellar atmospheres have so far been restricted to a few stars only . the high resolution spectra are perfectly suited to search for small shifts in the rest wavelengths of the helium lines due to the enrichment of @xmath0he . those shifts can be modelled quite accurately and show a typical pattern . while some lines like hei5876 are only shifted by @xmath19 towards redder wavelengths , the shifts of hei4922 and hei6678 are significant ( @xmath20 and @xmath21 respectively , * ? ? ? displacements of this order can be easily detected in the high resolution spectra . the spy sample @xcite has not been studied , because the uves spectra did not cover the sensitive hei6678 line . all stars of our sample have been examined . in 8 cases isotopic shifts due to the presence of @xmath0he are clearly visible ( see fig . [ fig : isotop ] ) . hence @xmath22 of our programme stars show the @xmath0he anomaly . as can be seen in fig . [ fig : abun ] seven belong to the upper helium sequence , while only one star belongs to the lower sequence . this may be a selection effect , because sdbs with low helium abundance show only weak lines , which are less suited to detect isotopic shifts . the distribution of these stars in the @xmath23-@xmath24-diagram is shown in fig . [ fig : tefflogg ] including the three sdbs with isotopic shifts taken from literature . it can be clearly seen that they cluster in a narrow temperature range between @xmath1 and @xmath2 with bd+482721 ( @xmath25 ) being the only exception . given the uncertainties , this @xmath0he - strip may be pure . most stars show clear shifts of the hei line at @xmath26 indicating that almost all helium in the atmosphere is @xmath0he . bd+482721 , ec12234@xmath272607 and pg1519 + 640 show strong lines of @xmath0he blended with weak components of @xmath6he . these three stars cover the whole @xmath0he temperature strip . the isotope ratio is therefore not correlated to the effective temperature . an @xmath0he isotope anomaly has first been found for chemically peculiar main sequence stars of spectral type b. the @xmath0he - stars were found at effective temperatures between @xmath28 and @xmath29 separating helium - poor stars at lower @xmath23 from helium - rich stars at higher @xmath23 @xcite . in fig . [ fig : tefflogg ] a similar pattern can be seen for the sdbs . the stars enriched in @xmath0he occupy a small strip in @xmath23 , while the helium abundance decreases towards lower temperatures and rises towards higher temperatures . @xcite carried out diffusion calculations and predict a mild enrichment of @xmath0he , but due to gravitational settling of the heavier isotope this should be the case in all sdbs . hence , the @xmath0he strip stars lacks an explanation . @xcite argued that diffusion is responsible for this effect . at low temperatures the radiation pressure is not strong enough to support helium in the atmosphere . as soon as the temperature reaches a certain threshold value , the less massive @xmath0he can be supported , but not the more abundant @xmath6he . this leads to an enrichment of @xmath0he in the atmosphere . at even higher temperatures both isotopes are enriched and the isotopic anomaly vanishes as the helium abundance rises . dorman , b. , rood , r. t. , & oconnell , r. w. 1993 , apj , 419 , 596 edelmann , h. , heber , u. , hagen , h .- j . 2003 , a&a , 400 , 939 edelmann , h. , heber , u. , & napiwotzki , r. 2001 , an , 322 , 401 fred , m. , tomkins , f. s. , brody , j. k. , & hamermesh , m. 1951 , phys . rev . , 82 , 406 geier , s. , hirsch , h. , tillich , a. , et al . 2011b , a&a , 530 , 28 hartoog , m. r. , & cowley , a. p. 1979 , apj , 228 , 229 heber , u. 1991 , iaus , 145 , 363 heber , u. , & edelmann , h. 2004 , ap&ss , 291 , 341 heber , u. , reid , i. n. , & werner , k. 2000 , a&a , 363 , 198 hu , h. , tout , c. a. , glebbeek , e. , & dupret , m .- a . 2011 , mnras , in press lisker , t. , heber , u. , napiwotzki , r. , christlieb , n. , han , z. , et al . 2005 , a&a , 430 , 223 maxted , p. f. l. , heber , u. , marsh , t. r. , north , r. c. , 2001 , mnras , 326 , 139 michaud , g. , richer , j. , & richard , o. 2011 , a&a , 529 , 60 morales - rueda , l. , maxted , p. f. l. , marsh , t. r. , north , r. c. , & heber , u. 2003 , mnras , 338 , 752 stensen , r. h. , silvotti , r. , charpinet , s. , et al . 2010 , mnras , 409 , 1470 otoole , s. j. 2008 , asp conf . ser . , 392 , 67 saffer , r. a. , bergeron , p. , koester , d. , liebert , j. 1994 , apj , 432 , 351 stobie , r. s. , kilkenny , d. , odonoghue , d. , et al . 1997 , mnras" +"it is well recognized that the photoemission process involves an interplay between the bulk and surface phenomena as the excited electron must be ejected from the surface in order to reach the detector . the intensity measured in an arpes ( angle - resolved photoemission spectroscopy ) experiment , therefore , fundamentally involves the properties of the relevant initial and final states in the presence of the surface . as a result , the arpes intensity can differ greatly from the spectral density of the initial state involved in the excitation . an understanding of this difference @xmath3 the so - called matrix element effect , is essential for a satisfactory interpretation of the arpes spectra , and this is particularly so in complex materials such as the high - tcs@xcite . bearing these considerations in mind , we have carried out extensive simulations of the arpes spectra in @xmath4 ( bi2212 , bisco ) within the first - principles band theory framework . the pristine phase with the body centered tetragonal lattice structure is assumed ; the computationally more demanding case of the orthorhombic and modulated lattices is hoped to be taken up in the future . we focus on the excitation of states in the vicinity of the fermi energy ( @xmath5 ) around the @xmath1 symmetry point which have been the subject of intense scrutiny and controversy in the high - tc literature . for example , the issue of bilayer splitting@xmath3 expected to be relatively large within the conventional lda - based band theory picture at @xmath6 in bisco , has been debated for some time , even though a consensus in favor of the existence of a bilayer splitting appears to be emerging in the recent months@xcite . the fundamental question has been whether or not strong correlations localize electrons in the @xmath0 layers , yielding a 2d electron gas and a zero bilayer splitting with significant implications for the mechanism of superconductivity in the cuprates.@xcite this study gives insight into these and related aspects of the ground state electronic structure by delineating the connection between the arpes spectra and the character of the underlying initial and final states . for this purpose , we have developed the one - step methodology @xcite for modeling the photoemission process so that arbitrarily complex systems with many basis atoms can be treated @xcite . the previous one - step work has been limited to a maximum of two atoms per unit cell @xcite which is not adequate for the cuprates ; bisco , for example , involves 30 atoms per conventional unit cell even for the pristine lattice . in the one - step approach , the interaction of light with the solid is treated as a single quantum mechanical event and the artifical distinctions between the processes of excitation , transport and ejection of the photoelectron invoked in the earlier three - step models @xcite are not made . the one - step scheme is thus inherently more satisfactory than the three - step model since the surface is incorporated in the latter in an _ ad hoc _ manner . on the other hand , it often tends to be difficult to identify the behavior of individual transitions within the one - step methodology where the initial and final states must be damped , causing these states to broaden and overlap , blurring distinctions between various transitions . for this reason , we have also developed the three - step model for complex lattices@xcite . useful insight is adduced here into different contributions to the arpes spectrum of bisco by examining the momentum matrix element for bulk transitions in the solid in the spirit of the three - step approach . the specifics of some of the main issues addressed in this article and highlights of the new results presented are as follows . the dependencies of the arpes intensity on the energy and polarization of the incident light are clarified for the excitation of states near the @xmath6 point . the response of the antibonding and bonding combinations of states from the @xmath0 bilayers is found to display a strong energy and polarization dependence . moreover , the behavior of the antibonding and bonding states differs significantly so that by a judicious choice of these experimental parameters even closely placed bilayer bands could be distinguished . also , photon energies where the intrinsic cross - section for exciting certain states of the pristine lattice is large will be best suited for studying these states ; in contrast , when this cross - section is relatively small , the effects of deviations from the tetragonal symmetry of the system via various distortions and modulations will become more prominent . further , we show how some systematics of the polarization dependencies can be understood in the cuprates via straightforward arguments involving the symmetries of the initial and final states . turning to questions related to individual transitions , we discuss the nature of the momentum matrix element for bulk excitations within a three - step type model in terms of contributions from various basis atoms and different angular momentum channels . the character of the bonding and antibonding initial states as well as that of the relevant final states at @xmath6 is clarified . an analysis of these results reveals dramatically how different contributions to the momentum matrix element can interfere constructively or destructively to enhance or supress the weights of photoelectrons excited from particular atomic sites and/or specific angular momentum channels . this remarkable result which , to our knowledge , has not been recognized previously in the literature , hints that the arpes matrix element may allow us to zoom in on the properties of very specific transitions even in complex unit cell materials . concerning relevant literature , refs . discuss some of our earlier work on bisco , @xmath7 ( ncco ) , @xmath8 ( ybco ) and @xmath9(y124 ) . in particular , ref . emphasizes the importance of matrix element effects in arpes spectra , while ref . undertakes an extensive comparison between the one - step predictions over a wide region in the momentum space when the initial state energy is held fixed at the @xmath5 with the corresponding experimental arpes results giving the fermi surface map in bisco . there is of course a large body of available work on the photoemission theory and refs . would provide a brief selection . on the experimental side as well the arpes studies of bisco are far too numerous to be cited with any completeness , and we refer only to a few representative papers . an outline of this article as is follows . the introductory remarks are followed in section ii by a consideration of formal matters ; a few equations for the one - step model are presented ( subsection iia ) , and the problem of computing the momentum matrix element in a general lattice is formulated ( subsection iib ) . section iii delineates the relevant features of the lattice geometry ( subsection iiia ) and the band structure of bisco ( subsection iiib ) . the results of sections ii and iii serve as a source of frequent reference in the subsequent discussion . section iv is divided into several subsections to go over various salient features of the arpes spectra from @xmath6 . the aspects addressed concern : photon energy dependence ( subsection iva ) ; effect of final state width ( subsection ivb ) ; polarization dependence ( subsection ivc ) ; and , the final state band structure and momentum matrix element ( subsection ivd ) . section v takes up the question of the nature of the transition matrix element and the origin of specific spectral features in terms of the characters of the initial and final states and is divided into three parts dealing with : contributions of different atomic sites ( subsection va ) ; contributions of various angular momentum channels ( subsection vb ) ; and , comments on the @xmath2 dependence of the spectral intensities ( subsection vc ) . finally , section vi summarizes our results and makes a few concluding remarks . we begin by recalling that the arpes intensity in the one - step model can be expressed as@xcite @xmath10 where the ket @xmath11 denotes a free electron state with momentum , @xmath12 , parallel to the crystal surface , @xmath13 ( @xmath14 ) is the retarded ( + ) or advanced ( - ) one - electron green function for the final ( initial ) state and @xmath15 is the interaction hamiltonian in terms of the vector potential @xmath16 of the incident photon field and the electron momentum operator @xmath17 . for our purposes , we rewrite eq . [ y1 ] by using the representation @xmath18 of the green function @xmath14 as a sum over the spectral functions @xmath19 for various initial states @xmath20 which yields @xmath21 here we have replaced @xmath22 by the final state wavefunction @xmath23 . substituting form for @xmath24 in eq . [ y2 ] , and neglecting the term proportional to @xmath25 by assuming that the vector potential a varies smoothly , i.e. wavelength of light is much larger than the unit cell dimensions@xcite , we obtain @xmath26 notably , the summation over @xmath20 not only encompasses different initial state bands , but also involves an integration over @xmath27 . a computationally practical formula follows by invoking the identity @xmath28 which is valid when the potential term is @xmath17 independent . the matrix element in eq . [ y5 ] is easily recast using eq . [ y6 ] as @xmath29 where @xmath30 and @xmath31 are the initial and final state energies , respectively . the nature of the photointensity based on the one - step eq . [ y1 ] can be delineated in terms of the momentum matrix element @xmath32 of eq . [ y5 ] . however , the wavefunctions @xmath33 and @xmath23 occuring in eqs . [ y3 ] - [ y7 ] are complicated quantities which include multiple scattering effects in the presence of the surface and damped initial and final state propagators . although the full one - step calculation should always be kept in mind , insight into the results may be obtained by simplifying the situation and replacing @xmath33 and @xmath23 by the corresponding bloch wavefunctions @xmath34 in the _ bulk _ crystal and the resulting matrix element @xmath35 for optical transitions . it should be emphasized that the optical matrix element must in general be supplemented with other information specific to the photoemission experiment ( e.g. symmetry of the final state ) before connection with a particular measurement can be made . this issue will be addressed as needed in the remainder of this article . the formalism for evaluating the optical matrix element for a general lattice within the kkr scheme is given in refs . ; an outline of aspects relevant for the purposes of this article is as follows . the starting point is the kkr wavefunction for a general lattice which can be expressed within the unit cell as @xcite @xmath36 where @xmath37 is a composite angular momentum index and @xmath38 denotes different basis sites . @xmath39 are expansion coefficients and @xmath40 is the radial part of the bloch wavefunction on site @xmath38 in angular momentum channel @xmath41 . @xmath42 are real spherical harmonics . using expressions of eq . [ y8 ] for the initial and final states yields @xmath43 where the primed indices refer to the final state and @xmath44 is a unit vector along the direction @xmath45 . @xmath46 involves an integral over the radial part of the initial and final state wavefunction and their derivatives and is given by @xmath47 \right . \\ \hspace*{1 cm } + \displaystyle { l + 1 \over r } \left [ { p_{l" +"a theory of quantum gravity is necessary to describe the quantum behavior of space and time and to understand what happens in strong gravitational fields , when curvature reaches the planckian regime . finding this missing theory of quantum gravity is one of the big open problems in theoretical physics today , and it concerns the most fundamental ingredients of our existing theories : space - time and its curvature , the arena in which physics happens . but general relativity still stands apart from the quantum field theories of the standard model as a classical theory . there exists to date no known way to consistently couple a classical theory to a quantum theory , and neither do we know how to quantize gravity . while several theoretical approaches are being pursued with success , this success has so far been exclusively on the side of mathematical consistency , and the connection of these approaches to reality is still unclear . the problem how to resolve the tension between quantum field theory and general relativity is more than an aesthetic unease . this tension signals that our understanding of nature is incomplete , but it also offers an opportunity to improve our theories . the missing theory of quantum gravity has the potential to revolutionize our understanding of space , time and matter . progress on the theory of quantum gravity however has been slow . the problem has been known since more than 80 years now . since then we gained a great many insights about the nature of the problem but the big breakthrough has left us waiting . next to the technical difficulties , the reason for the slow progress is lack of experimental guidance . the possibility that quantum gravitational phenomena might be observable has not been paid much attention to till the late 90s , and even now the awareness that this possibility exists is slow to sink into the minds of the community . however , without making contact to observation , no theory of quantum gravity can ever be accepted as a valid description of nature . in the absence of a fully - fledged theory , this search for observable consequences proceeds by the development of phenomenological models . such models parameterize properties that the theory of quantum gravity could have with the purpose of allowing to experimentally test or at least constrain the presence of these properties . this in turn guides the development of the theory . general reviews of phenomenological models for quantum gravity can be found in @xcite . in this contribution to the ahep special issue on ` experimental tests of quantum gravity and exotic quantum field theory effects ' we will discuss a possible phenomenological consequence of quantum gravity that has so far received very little attention the existence of space - time defects . in many approaches to quantum gravity such as causal sets , spinfoams , causal dynamical triangulation , loop quantum gravity , and emergent and induced gravity scenarios based on condensed matter analogies space - time is fundamentally discrete and the smooth background geometry that we see only emerges as an approximation at low energies and large distances @xcite . in this case , one expects that the apparently smooth background geometry is imperfect and has defects , just because perfection would require additional explanation . in the following , we will review the recently proposed model for space - time defects @xcite and summarize the constraints on the prevalence of these defects that can be derived from observation . we will then discuss which steps can be taken to improve the model so that the constraints touch on the interesting parameter range . whether or not space - time is fundamentally discrete is a question of central importance for the development of the theory . but this discreteness typically makes itself noticeable at the planck length , which is hard if not impossible to access experimentally . thus , instead of searching for direct evidence for the planck scale discreteness , we here propose to look for imperfections in this discreteness . such imperfections in space - time will cause deviations from general relativity , since general relativity rests on the assumption that space - time is a manifold and locally smooth and differentiable . because general relativity is an extremely well - tested theory even smallest deviations can become noticeable , making space - time defects a promising phenomenological consequence to search for . looking for space - time defects as evidence for the presence of a discrete geometry is akin to looking for specks of dirt as evidence for the presence of a window . that such defects should exist is a model - independent expectation for all approaches to quantum gravity in which geometry has a fundamentally discrete structure . but the prevalence , distribution , and properties of the defects will depend on the details of the underlying fundamental theory . this way , the phenomenological model can bridge the gap between theory and experiment . in the following we will aim to parameterize the consequences of space - time defects so that contact can be made to the underlying theory if the relevant parameters can be extracted . in contrast to defects in condensed matter systems , space - time defects are not only localized in space but also in time . they do not have worldlines but are space - time events . space - time defects can come in two different versions , local defects and nonlocal defects . the general case would be a hybrid of both , but treating these two types separately is helpful to develop the theory . we will first discuss the nonlocal defects . one of the reasons it is expected that quantum gravity necessitates nonlocality is that the notion of the planck length as a minimal length implies that it is meaningless to distinguish points below this distance these points are not local ( or not points , depending on your perspective ) . but besides this , during the last decades it has also become increasingly clear that a resolution of the black hole information loss problem requires some type of nonlocality @xcite . meanwhile , a completely different line of investigation has led to the conclusion that requiring the planck energy to be an observer - independent component of a four - momentum , necessitates to give up absolute locality . instead one might have to settle on a weaker locality requirement , which has been called ` relative locality ' @xcite . while planck - scale nonlocality has received quite some attention , for example in the well - studied models for quantum field theory with a minimal length @xcite , here , we will focus on a feature whose phenomenology has so far received very little attention : macroscopic nonlocality , where macroscopic means much larger than the planck length . macroscopic nonlocality can be expected to arise in approaches towards quantum gravity in which space - time is only to good approximation a smooth manifold but fundamentally a network ( graph ) consisting of nodes and links which can carry additional charges or degrees of freedom . the reason is that the emergence of a manifold from the network will not be perfect , but it will have defects . and since our macroscopic notion of distance only emerges with the space - time and the metric that we define on it , there is no reason why these defects should respect the emergent macroscopic locality . this has been demonstrated explicitly by markopoulou and smolin in @xcite for the case of spin networks . their argument can be briefly summarized as follows . states of the spin - network describe spatial slices of space - time and they change in time by a set of allowed evolution moves , which are local according to the locality of the network . certain spin network states , called ` weave states ' , match to good precision ( up to planck scale corrections ) , slowly varying classical spatial metrics . the structure of nodes and links of the network carries information about area and volumes and thus the geometry that the network fundamentally describes . it can then be shown that it is possible to act with a large number of local evolution moves on a state without nonlocal links and by this create a state that contains macroscopically nonlocal links . this is possible without changing the classical state that it approximates , thus the existence of the classical approximation alone can not be used to rule out these nonlocal links . a nonlocal link is , intuitively , a link in the network that does not respect the emergent macroscopic locality . more strictly it can be identified by the number of nodes on the shortest closed loop that it is part of . for the nonlocal link this will be a large number of nodes , while all the local links have a small number of nodes ( depending on the valence of the network ) . see figure [ fig1 ] for illustration . , width=377 ] in the example by markopoulou and smolin , the states with nonlocal links are still allowed solutions and thus valid semi - classical space - times , but do not respect the macroscopic locality . because of simple combinatorics , one finds that there are in fact many more nonlocal states than local states . this means the locality of the state that we live in today is not perfect ; nonlocal links should be all around us . this situation was aptly dubbed ` disordered locality ' in @xcite . the argument by markopoulou and smolin is an explicit example one can have in mind . but the expectation for the existence of nonlocal defects is more general than that , it arises because perfection requires additional explanations or selection criteria that we do not have . now such macroscopic locality might strike one as something to be avoided , since we do not seem to experience it , but this is a question of experimental constraints . to really understand the implications of such nonlocality one first needs to develop a phenomenological model that parameterizes the effects , and then contrast them with data . such a model was developed in @xcite . this model does not start with an underlying discrete structure , but instead deals with the defects in the local structure as deviations from the smooth background geometry of general relativity . the central assumption for the model @xcite is that lorentz - invariance is preserved on the average since violations of lorentz - invariance are strongly disfavored by the data . lorentz - invariance , maybe not so surprisingly , proves to be very restrictive on the type of nonlocality that is allowed . the distribution of nonlocal defects in this model is assumed to be given by the only presently known lorentz - invariant discrete distribution on minkowski space , which is defined by the poisson - process described in @xcite . with this distribution , the probability of finding n points in a space - time volume @xmath0 is p_n(v ) = , [ pois ] where @xmath1 is a constant space - time density and @xmath2 a parameter of dimension length . a particle that encounters a nonlocal defect will experience a translation in space - time . the translation vector is parameterized in a probability distribution which besides @xmath2 introduces a parameter of dimension mass , @xmath3 , and a parameter of dimension length @xmath4 . @xmath3 and @xmath4 ( both real - valued and positive ) quantify the translation , @xmath5 that the particle experiences at the non - local defect p_y^= , y_y^= ^2 , [ sign ]" +"recently a progress has been brought about to understand the confinement mechanism in qcd - like theories by compactifying the theories in one spatial dimension with the period @xmath5 . because of the asymptotic freedom , the small @xmath5 theory is in the weak - coupling regime ( @xmath6 ) in qcd(adj . ) on @xmath7 . instanton is a particle - like soliton of codimension @xmath8 in @xmath8-dimensional spacetime . if @xmath2 twisted boundary conditions are imposed , we can obtain fractional instantons which have fractional amount of instanton number . a molecule of fractional instantons and anti - instantons are generally called bions . for compactified space with small @xmath5 , the perturbative analysis is reliable and shows that the wilson holonomy stabilizes the @xmath2 twisted boundary condition . in this case , one can demonstrate the condensation of classical field configurations composed of fractional instantons and anti - instantons with magnetic charge , which are called magnetic bions . condensation of magnetic bions implies the confinement in the compactified theory . it is anticipated that this phenomenon continues to hold for large @xmath5 , suggesting the confinement even for uncompactified theory . it has also been pointed out that neutral bions play an important role in explaining the resurgence phenomenon @xcite . neutral bions are composite of fractional instantons and anti - instantons with vanishing topological charge ( instanton number ) and zero magnetic charge . although perturbation series in field theories are divergent , the borel transformation is useful to obtain the re - summation of such divergent series . the borel transform often exhibits singularities on the positive real axis producing an imaginary ambiguities in the borel - resummed results . it has been found that these ambiguities in quantum mechanics are cancelled by contributions from molecule of instanton and anti - instantons @xcite . however , asymptotically free field theories like qcd and the @xmath0 nonlinear sigma models exhibits similar but more serious singularities near the origin , which are called infrared renormalons @xcite . recently it has been found that the nonperturbative contributions around the neutral saddle points also have imaginary ambiguities . these imaginary ambiguities of bion amplitudes are found to cancel @xcite precisely the imaginary ambiguities associated with the infrared renormalons , resulting in a more rigorous foundation of field theory . this phenomenon is called the resurgence . it is expected that full semi - classical expansion including perturbative and non - perturbative sectors , which is called resurgent expansion @xcite , leads to unambiguous and self - consistent definition of field theories in the spirit of quantum mechanical examples @xcite . however , it is not straightforward to verify these arguments in gauge theories directly , since it is difficult to find an explicit ansatz of bion configurations . at this stage , it is quite interesting and useful to study simpler models in lower dimensions @xcite instead of gauge theories in four spacetime dimensions . in particular , models in two spacetime dimensions are more tractable compared to gauge theories in four dimensions , but have many features which are common to gauge theories in four dimensions . among them , the @xmath0 model in two spacetime dimensions has been studied as a toy model @xcite of the yang - mills theory in four spacetime dimensions , because of their interesting features such as the dynamical mass gap , the asymptotic freedom and the existence of instantons as bogomolnyi - prasad - sommerfield ( bps ) solutions @xcite . the @xmath0 model on @xmath9 with twisted boundary conditions admits bps fractional instantons as configurations with the minimal topological charge @xcite ( see also refs . @xcite ) . in ref . @xcite , generic arguments on bion configurations were given in the @xmath0 model on @xmath9 with @xmath2 twisted boundary conditions , based on the independent instanton description taking account of interactions between far - separated fractional instantons and anti - instantons . more recently , exact non - bps solutions were found in the @xmath0 model on @xmath9 with the @xmath2 twisted boundary condition @xcite . the simplest non - bps solution that they found is a four - instanton configuration composed of two fractional instantons ( instanton charge @xmath3 ) and two fractional anti - instantons ( @xmath4 ) for @xmath10 placed at particular relative positions . their study suggests that it is likely that bion configurations needed to understand the resurgence phenomenon may not be solutions of field equations . it has been known that field configurations other than the solution of the equations of motion may give significant contributions in the functional integral . recently we constructed ansatz of bion configurations that are guaranteed to become solutions of the field equations asymptotically as separations between constituent fractional instantons get larger , and studied interactions of constituent fractional instantons in bion configuration @xcite . more recently , we have also studied bions in the grassmann sigma models which include the @xmath0 model as a subclass @xcite . since bions in nonlinear sigma models in two spacetime dimensions are interesting and more tractable , let us consider the @xmath0 model . to describe the target space @xmath11 , we denote an @xmath12-component vector of complex scalar fields as @xmath13 , and a normalized complex @xmath12-component vector composed from @xmath14 as @xmath15 latexmath:[\[n(x ) \equiv \omega(x)/|\omega(x)| , \quad two dimensions for the nonlinear sigma model with @xmath0 as the target space is given by @xmath17 and the topological charge representing @xmath18 is defined by @xmath19 where @xmath20 and @xmath21 . our convention of the covariant derivative is @xmath22 with a composite gauge field @xmath23 we consider @xmath1 as the geometry of base manifold , and configurations on it satisfying periodicity in the @xmath24 direction with the period @xmath5 . the lagrangian @xmath25 and topological charge @xmath26 can be expressed in terms of the projection operator @xmath27 and using the complex coordinate @xmath28 , @xmath29\,,\\ q&=&2\int d^2 x { \rm tr } \left[{\bf p } ( \partial_{\bar z}{\bf p } \partial_{z } { \bf p}-\partial_{z}{\bf p}\partial_{\bar z } { \bf p } ) \right]\,.\end{aligned}\ ] ] we define the euclidean energy density ( lagrangian ) @xmath30 , and the topological charge density @xmath31 as functions of @xmath32 after the integration over @xmath24 : @xmath33\ , , \\ % q&={1\over{\pi}}\int dx_{1 } q(x_{1 } ) q(x_{1})&=&{1\over{\pi}}\int dx_{2 } { \rm tr } \left[{\bf p } ( \partial_{\bar z}{\bf p}\partial_{z } { \bf p}-\partial_{z } { \bf p}\partial_{\bar z } { \bf p } ) \right]\,.\end{aligned}\ ] ] we can perform the bogomolnyi completion to obtain the bogomolnyi bound @xcite for the total energy @xmath34 @xmath35 the bogomolnyi bound with the upper sign is saturated when the following bps equation is satisfied @xmath36 the solution of the bps equation is precisely holomorphic @xmath37 . the bogomolnyi bound with the lower sign is saturated when the following anti - bps equation is satisfied @xmath38 the solution of the anti - bps equation is anti - holomorphic @xmath39 . in the following we omit the coupling @xmath40 for simplicity unless stated otherwise . let us give a brief review of resurgence and the importance of bion contributions . it has been known that the number of feynman diagrams in quantum field theory grows factorially . this factorially divergent perturbation series of quantum field theory is usually discussed by means of the borel transform . the borel transform method is applicable to the following class of divergent series ( called gevrey-1 ) @xmath41 where @xmath42 are constants . the borel transform @xmath43 is defined as @xmath44 and the borel resummation @xmath45 is defined as @xmath46 one can easily see that the borel resummation @xmath45 reproduces the original sum @xmath47 correctly whenever one can exchange the integral and the sum . otherwise , we need to define the sum in terms of the borel resummation . as a simplified toy model , let us consider a factorially divergent series of the following one with alternating signs @xmath48 then the borel transform becomes an analytic function without singularities on the positive real axis @xmath49 therefore the borel resummation is well - defined as an integral along the positive real axis @xmath50 this alternating factorially divergent series is a typical example of borel summable divergent series . on the other hand , if perturbation series is not alternating , the factorially divergent series gives the borel transform with singularities on positive real axis and the borel resummation has imaginary ambiguities . for instance , suppose that the perturbation series @xmath51 gives non - alternating factorially divergent series like @xmath52 the borel transform has a singularity on positive real axis @xmath53 @xmath54 therefore the borel resummation has imaginary ambiguities depending on the choice of integration contours to avoid the singularity ( equivalently the analytic continuation from negative real axis ) @xmath55 this ambiguous imaginary part has to be cancelled by contributions from other saddle points in the path - integral . in quantum mechanics or scalar field theories , the position of the singularity in the borel plane has been found to correspond to molecules of instanton and anti - instanton @xcite . however , the asymptotically free theories like qcd and the @xmath0 model give additional singularities due to ir renormalons which are much closer to the origin and hence give much larger contributions . recent study @xcite showed that the bion amplitudes give the nonperturbative contribution needed to cancel the imaginary ambiguity due to the ir renormalons . when one space direction is compactified to @xmath56 with the circumference @xmath5 , there is a possibility to impose non - periodic boundary condition . moreover , asymptotic free theory becomes weakly coupled , and the stable configurations of wilson holonomies of @xmath57 subgroup of @xmath58 can be analyzed perturbatively @xcite . it turns out that the following @xmath59 twisted boundary condition is most favorable under certain conditions @xmath60\ , . \label{znc}\ ] ] this @xmath2 twisted boundary condition corresponds to the vacuum with the symmetry breaking @xmath61 . the wilson - loop holonomy in the compactified direction is given by @xmath62 where the gauge fields @xmath63 is the composite gauge field defined in eq . ( [ eq : composite_gauge_field ] ) of the @xmath0 model . the simplest solution of the bps equation ( [ eq : bpseq ] ) satisfying the @xmath59 twisted boundary condition in eq . ( [ znc ] ) is given by @xmath64 one can easily see that these bps solutions give the total action @xmath34 and the topological charge @xmath26 as @xmath65 therefore we call this bps solution as a fractional instanton . the fractional instanton is located at @xmath66 . a neutral bion is a molecule of fractional instantons and anti - instatons and is unstable under the annihilation process . then we anticipate that generic neutral bion configuration is not a solution of field equations . therefore we wish to construct a field configuration that reduces to a solution at least for far - separated fractional instantons and anti - instantons asymptotically . from the bps solution in eq.([eq : fractional_instanton ] ) and their complex conjugates , we are naturally led to consider the following ansatz for the @xmath67 model satisfying the @xmath2 twisted boundary condition in eq . ( [ znc ] ) @xmath68 a fractional instanton is located at @xmath69 , and a fractional anti - instanton is at @xmath70 , respectively . this configuration becomes a solution of field equations asymptotically as the separation @xmath71 goes to infinity . for @xmath72 , this configuration corresponds to a @xmath73 instanton ( @xmath74 , @xmath75 ) and a @xmath73 anti - instanton ( @xmath74 , @xmath76 ) at large separations . the total action and the net topological charge in the large - separation limit are given by @xmath77 the topological charge is unchanged as the separation between the fractional instanton and the anti -" +"the visible matter distribution of the universe forms a complex web - like network composed of filaments and sheets separated by voids ( bond et al . 1996 ; aragn - calvo et al . galaxies are continuously funneled into higher density cluster environments through these structures . in the hierarchical structure formation scenario , z @xmath2 0 filaments are the current end point of large - scale structure evolution . investigating filamentary structures around dynamically young clusters should thus yield valuable information on their assembly histories . studying the large - scale galaxy distribution around the virgo cluster , the nearest rich , young cluster ( aguerri et al . 2005 ) , should therefore provide constraints on its formation and evolution at the current epoch . from three - dimensional mapping of nearby galaxies , tully ( 1982 , hereafter t82 ) identified prolate and oblate over - densities of galaxies around the virgo cluster . these were however not clearly revealed as conventional narrow filaments , but were rather sparse , mainly due to the limited sample size . a better characterization of these structures requires improved statistics from larger galaxy samples , particularly those with fainter galaxies . recent spectroscopic surveys of galaxies such as the sloan digital sky survey ( sdss ; e.g. , sdss data release 7 , abazajian et al . 2009 ) do enable the exploration of possible filamentary structures within an extensive volume around the virgo cluster . moreover , radial velocity information on numerous galaxies combined with distance data allows to investigate potential dynamical relationships between the filaments and the virgo cluster . the primary goal of our study is thus to revisit the large - scale structures in the vicinity of the virgo cluster using an up - to - date statistically robust dataset , to test whether the t82 structures can be better characterized and identified as filaments . we also search for previously unknown structures that may now be apparent . finally , we investigate whether the structures are physically connected to the virgo cluster using hubble diagrams . throughout this paper , we assume a hubble constant of @xmath3 = 100 @xmath4 km s@xmath5 mpc@xmath5 , where @xmath4 = 0.74 ( tully et al . 2008 , hereafter t08 ) . while the sdss is large and homogeneous , it does not cover most of the southern hemisphere and the spectroscopy is incomplete for both bright ( @xmath6 @xmath7 16 ) and faint ( @xmath6 @xmath8 20 ) objects ( e.g. , kim et al . 2014 ) . we therefore adopt here the hyperleda database ( paturel et al . 2003 ) , which while heterogeneous and necessarily incomplete does contain multiple other surveys in addition to the sdss data release 7 ( abazajian et al . 2009 ) . for our analysis , we extracted all galaxies with available radial velocities less than 6000 km s@xmath5 in the region 115 deg @xmath1 r.a.(j2000 ) @xmath1 240 deg and @xmath935 deg @xmath1 decl.(j2000 ) @xmath1 60 deg ( see figure 1 ) . this ensures the inclusion of all structures potentially associated with the virgo cluster ( with a mean radial velocity of @xmath21000 km s@xmath5 and a velocity dispersion of @xmath2800 km s@xmath5 ; binggeli et al . however , as no distinct structure in the vicinity of the virgo cluster is identified beyond a velocity of 3300 km s@xmath5 , we henceforth only discuss the 9168 galaxies within that range . we examined the radial velocities of 755 sdss filament galaxies , finding a mean difference of 6 km s@xmath5 and a dispersion of 63 km s@xmath5 with respect to hyperleda velocities ( the latter typically averaging multiple surveys ) . we therefore conclude that the radial velocity information of our sample is not significantly affected by the compilation of different sources in hyperleda . to construct an accurate spatial distribution of the galaxies , we first converted the observed heliocentric radial velocities to velocities relative to the centroid of the local group , and then applied a correction for infall into the virgo cluster ( mould et al.2000 ) . based on the assumption of a linear relationship between redshift and distance , all galaxies were then mapped in the three dimensions of the cartesian supergalactic coordinate system : sgx , sgy , sgz ( t08 ) . our search for filamentary structures was conducted within the cuboid enclosed by the following limits : -25 @xmath0 mpc @xmath1 sgx @xmath1 25 @xmath0 mpc , + 4 @xmath0 mpc @xmath1 sgy @xmath1 27 @xmath0 mpc , + -25 @xmath0 mpc @xmath1 sgz @xmath1 25 @xmath0 mpc . + the use of this extended region enables a more accurate characterization of large - scale filamentary structures than the study of t82 . we rejected galaxies within a radius of 3.6 mpc from the virgo cluster center ( at least two times the virial radius ; mclaughlin 1999 ) , to avoid contamination from cluster galaxies with large infall velocities that are gravitationally bound to the cluster inside the infalling region ( mamon et al . 2004 ; falco et al . this leaves 8401 galaxies with which to search for large - scale structures . the sgx - sgz plane is best to look for large - scale structures , as positional errors are small in this plane ( roughly in the plane of the sky ) but substantial along the sgy axis ( roughly along the line of sight and thus affected by deviations from the hubble flow ) . the detection of filaments was thus performed by applying the following steps : 1 . we constructed a series of different sgx - sgy - sgz volume slices with an arbitrary depth of 2 @xmath0 mpc along the sgy axis . candidate structures were then selected by visual inspection of the sgx - sgz projection of each slice , looking for overdense and long ( i.e. , filamentary ) galaxy distributions . if a candidate structure was continuously present in consecutive slices , we accordingly estimated its full range in three dimensions . 2 . we performed three - dimensional third - order polynomial fitting with weighting by the local galaxy density to the visually selected candidate structures . if the standard deviation of the fit to a candidate structure was less than 1.5 @xmath0 mpc ( comparable to or less than the typical thickness of filaments in simulations and observations ; e.g. colberg et al . 2005 ; akahori & ryu 2010 ; choi et al . 2010 ; vazza et al . 2014 ) , the structure was retained and classified as a filament . if not , the candidate structure was rejected . we further applied a two - sigma clip to the galaxies around the fitted lines ( i.e. , the filament spines ) , to extract the galaxies that belong to each filament . the authenticity of each candidate structure was verified by looking at a multitude of sgx - sgy - sgz projections , and the more diffuse ( i.e. , non - filamentary ) nature of the rejected structures was assessed ( chance projections , sheets , etc ) . with the search strategy above , we identified seven filaments and one sheet in the volume surrounding the virgo cluster , divided into two subsamples with distinct sgy ranges ( see sec . figure 1 shows the spatial distribution of the 1013 galaxies belonging to these structures in the equatorial coordinate system . the properties of these structures are summarized in table 1 . we note that all structures mostly consist of faint galaxies ( m@xmath1019 ; @xmath288@xmath11 of the total sample ) . finally , we collected redshift - independent distances of sample galaxies from the nasa / ipac extragalactic database ( ned ) , with 229 matches . we calculated the distances ( @xmath12 ) and radial velocities ( @xmath13 ) of these galaxies relative to the virgo cluster center ( karachentsev & nasonova 2010 ) , adopting a distance of the virgo cluster from us of 16.5 mpc ( mei et al . 2007 ) . in this instance , for the calculation of @xmath13 ( t08 ) , the heliocentric radial velocities were corrected for the motion of the local sheet and local void only ( and _ not _ for virgo - centric infall ) . finally , peculiar velocities ( @xmath14 ) were derived using the following equation : @xmath15 figure 2 presents the distribution of six filaments with 4 @xmath0 mpc @xmath1 sgy @xmath1 16 @xmath0 mpc in the sgx - sgz projected plane ( fig . 2a ) and the sgx - sgy - sgz three - dimensional space ( fig . we named these filaments after the structures designated as clouds or spurs by t82 ( fig . 2c ) . by construction , all the filaments are narrower and longer than the broader and more diffuse t82 structures . all are also elongated toward the virgo cluster , suggesting they are related to it . it is interesting to note that when we apply our search strategy to the t82 sample , the t82 structures are _ not _ identified as filaments . this is most likely due to the small t82 sample size , as the number of galaxies in each filament is two or three times larger in our sample . in addition , while the majority of galaxies in t82 are bright ( m@xmath2019 ) , our structures are mainly composed of less luminous galaxies ( m@xmath2119 ) . bright galaxies ( large open circles in figs . 14 ) exhibit an uneven distribution with numerous gaps along the filaments . conversely , the large number of low - luminosity galaxies available here ( small filled circles in figs . 14 ) helps to better delineate continuous filaments by filling in the gaps . the leo ii cloud appears to be a multi - stem clump rather than a single prolate one ( fig . 2c ) . indeed , in a more extensive area around the leo ii cloud , we identified two filaments , leo ii a and b. the leo ii b filament traces a sparse region of the cloud , whereas the leo ii a filament includes the main clump of the leo ii cloud and is one of the largest structures we detect ( 16 @xmath0 mpc long in the sgx - sgz plane ) , with a curved shape . it is known that warped or irregular filaments are more common and are on average longer than straight filaments ( colberg et al . 2005 ) . over 150 galaxies in the six filaments identified in figs . 2a and 2b have a redshift - independent distance . their hubble diagram in the virgo - centric reference frame is presented in figure 2d . most galaxies in all these filaments exhibit a distinct deviation of their radial velocities from an unperturbed hubble flow ( red line ; see also the median values in the inset ) , suggesting appreciable infall toward the virgo cluster . we also plot a model of the radial infall velocity profile of the virgo cluster ( blue line ) , adopting the model of falco et al . ( 2014 ; eq . 6 , representing the mean velocity of infalling galaxies in the outer regions of the cluster ) with a virial radius of 1.55 mpc ( mclaughlin 1999 ) and a virial velocity of 800 km s@xmath5 ( binggeli et al . the observed distribution of radial velocities of the filament galaxies is entirely consistent with the expected infall profile , confirming that all these filaments are dynamically connected to the virgo cluster ( see also karachentsev et al . 2014 ) . figures 3a and 3b are analogous to" +"perturbative methods are indispensable in order to establish consistent theories of particle interactions , and to predict quantitatively their experimental manifestations . the anticipation of new phenomena in modern experiments and theoretical extensions of the standard model , requires cross - sections for complicated processes . this has driven a remarkable progress in the development of new computational methods . at the one - loop level , the calculation of cross - sections with five external legs is gradually becoming a routine activity ( e.g. @xcite ) . at two - loops , there have been recent successful computations of amplitudes with four external legs and up to three kinematic scales ( e.g. @xcite ) . at three - loops and beyond , amplitudes with up to one parametric variable have also been computed ( e.g. @xcite ) . many new processes with higher final - state multiplicity , number of loops , and kinematic scales , have been identified to be important at the tev energy frontier . the aim of our paper is to provide a new method which can be used to compute loop amplitudes for such , more complicated , processes . loop integrations are cumbersome due to the presence of infrared singularities . loop integrals with many kinematic scales have , in addition , a complicated analytic structure with respect to their kinematic parameters . the tensor structure in gauge theories is also an issue , since it proliferates the number of terms . a general method for computing arbitrary loop integrals should extract their infrared and ultraviolet singularities , and treat simply kinematic discontinuities and threshold singularities . for practical applications , it should also be able to handle tensor integrals efficiently . there is no method which addresses satisfactorily all these issues ; known techniques can compute a limited number of amplitudes where some simplifications occur in special cases . following a traditional approach to calculate loop amplitudes , one reduces the number of terms to a few master integrals and computes the latter analytically . one - loop integrals can be reduced using the classical method of passarino and veltman @xcite . for generic multi - loop computations one can derive reduction identities from integration by parts @xcite and the invariance of scalar integrals under lorentz transformations @xcite . there is a large variety of approaches for evaluating the master integrals analytically . for example , one can compute integrals with a simple singularity structure and a small number of kinematic scales by integrating directly their feynman parameter representation . for more complicated cases one can use advanced techniques , such as the method of differential equations @xcite . this approach can fail , however , if we apply it to complicated processes . the reduction algebra is hard , and the expressions of amplitudes in terms of master integrals may have spurious singularities which hamper their numerical evaluation . the extraction of @xmath1 poles in the master integrals , the evaluation of the coefficients of the @xmath1-expansion in terms of known analytic functions , and the analytic continuation of the latter to physically interesting kinematic regions are also involved . it is , thus , very well motivated to improve or replace the `` traditional scheme '' and to develop new automated methods . one - loop amplitudes can be entirely determined in four dimensions in terms of basic functions such as logarithms and polylogarithms that appear in the one - loop scalar box . new methods introduce sophisticated algorithms for the reduction to the basic functions ; by either numerical or analytical techniques , they control the appearance of spurious singular terms and minimize the size of the intermediate expressions @xcite . recently , cross - sections for @xmath2 processes at nlo were computed @xcite using such techniques . a method , which is inspired by techniques for real radiation at nlo , renders one - loop graphs numerically integrable @xcite with the introduction of universal subtraction terms . a different approach uses unitarity , dualities , and analyticity properties for the determination of one - loop amplitudes @xcite . beyond one - loop , there has been a significant progress in the automation of the reduction methods to master integrals @xcite . the infrared structure of multi - loop integrals is substantially more complex than at one - loop ; the development of methods for their numerical evaluation is more difficult . nevertheless , there is significant progress in this direction @xcite . a powerful numerical method for multi - loop calculations is the method of sector decomposition @xcite ; it simplifies recursively the singularities of feynman parameterizations and allows a straightforward expansion in @xmath1 . the method of sector decomposition has been very succesfully employed in the computation of several multi - leg integrals at one , two and three loops @xcite . this method has been introduced , recently , for the purely numerical evaluation of multi - loop amplitudes @xcite . however , it is perplexing how to apply it for loop - integrals in non - euclidean regions . in 1999 , smirnov @xcite and , soon later , tausk @xcite , introduced a new method for the evaluation of loop integrals . in their pioneering papers , smirnov and tausk @xcite computed analytically the first infrared divergent double box integrals . in @xcite new two - loop integrals for @xmath3 massless processes were computed . in @xcite the method was applied to double - box integrals with one additional mass - scale . the method was spectacularly applied in the computation of three - loop amplitudes @xcite in @xmath4 supersymmetric yang - mills theory , shedding light to novel cross - order perturbative relations of the theory @xcite . the smirnov - tausk method is based on a few simple ideas . starting from the feynman parameterization of a loop integral we can derive a new representation in terms of a multiple complex contour integral . such , mellin - barnes ( mb ) , parameterizations have enabled compicated loop calculations by using powerful methods for complex integration @xcite . smirnov and tausk exploited a novel property of these representations . infrared divergences localize on simple poles inside the complex integration volume . we can isolate the divergent pieces of the integral at @xmath5 , by using the cauchy theorem . after subtracting the divergent residues , we can perform a taylor expansion in @xmath1 , and sum up the remaining infinite series of residues . finally , we can work to derive analytic expressions for the infinite sums in the coefficients of the expansion in terms of logarithms , generalized polylogarithms @xcite , and more complicated functions . the smirnov - tausk method is very powerful ; however , it is laborious and intricate . the isolation of the divergent residues in multiple mellin - barnes integrals is convoluted . in addition , it is difficult to identify infinite sums in terms of polylogarithm functions with known analyticity properties . as a consequence , the analytic continuation in physical kinematic regions is also involved . due to these complications , the method has been applied to a few master integrals with a small number of kinematic scales . in this paper , we generalize the method to a broader spectrum of applications . as a first task , we automate the procedure for the isolation of the divergent residues at @xmath0 . smirnov @xcite and tausk @xcite use different techniques for finding these residues . the approach of smirnov is very intuitive , but daedal . we have found that the technique described by tausk in ref . @xcite resembles closely to a programmable algorithm . we have used it as a guide and we have written computer programs which subtract the @xmath6 poles in arbitrary mellin - barnes integrals . in our method , we avoid entirely the painstaking tasks of finding analytic expressions for infinite sums in terms of polylogarithms , and performing the analytic continuation in the arguments of polylogarithms . mellin - barnes representations are valid in kinematic regions where loop integrals may be complex - valued . we have found that , in a broad spectrum of applications , it is simple to calculate the representations numerically . the only analytic continuation that is ever required is that of logarithms with a single kinematic scale as an argument . an important goal of our method is to calculate loop amplitudes in realistic gauge theories . we have found that tensor integrals and , furthermore , diagrams which belong to the same topology can be calculated collectively . as we will show , the integrand of a representation for a scalar integral will be a product of gamma functions and powers of kinematic invariants , while that of a generic tensor will be the same integrand as in the scalar integral multiplied by a polynomial in the integration variables . the evaluation of polynomials is fast in a numerical program ; the computational cost for evaluating tensor integrals or loop diagrams is not significantly larger than evaluating scalar integrals . the only practical issue that we need to address , is the book - keeping of the various terms that contribute to the polynomial ; we present an efficient solution of this problem here . in this paper , we apply our method to a number of examples . we , first , test our method in scalar and tensor integrals of the one - loop massless hexagon topology . the purpose of this computation is to introduce our method for tensor integrals and to demonstrate that we can tackle problems which are relevant in computations of physical amplitudes . we present here results for tensors through rank six , in both the euclidean and the physical region for @xmath7 processes . the numerical programs that we have constructed are suitable for the evaluation of the qcd amplitudes in four - jet production at hadron colliders . in the second set of examples , we compute scalar two and three - loop integrals which are known analytically in all kinematic regions : the massless planar @xcite and cross @xcite double - box , the massless double - box with one off - shell leg @xcite , and the massless planar triple - box @xcite . they serve to cross - check our algorithms and to demonstrate that we can easily reproduce state - of - the - art computations . our numerical results are in excellent agreement with the analytic expressions . we also present a number of new results that would require significant efforts for their computation with traditional approaches . we present , for the first time , double - box integrals with up to four kinematic parameters , and triple - box integrals with up to three kinematic parameters computed in all physical regions . in section [ sec : mbrepresentations ] , we explain our technique for deriving mellin - barnes representations for loop integrals . in section [ sec : analytic ] , we describe our routines for performing an @xmath1-expansion of mellin - barnes representations for scalar integrals . we extend these results to loop integrals with tensor numerators in section [ sec : tensors ] and , in section [ sec : numerical ] , we present our methods for the numerical integration . section [ sec : results ] is devoted to present our results for several integrals at the one , two and three loop level . finally we present our conclusions . we start with a brief discussion on the derivation of mellin - barnes representations for loop integrals from their feynman parameterization . the construction of parameterizations is not unique , and various representations of the same integral may have quite different features . for example , they could have a different integral dimensionality , or they could" +"the taurus tunable filter ( ttf ) instruments @xcite@xcite at the anglo - australian ( aat ) and william herschel telescopes ( wht ) have seen use in many key areas of astrophysics . low - redshift science has included studies of brown dwarf atmospheric variability and the identification of optical counterparts to galactic x - ray sources . at high - redshifts , science has been driven by measurement of the cosmic star - formation history , identification of galaxy clustering around high - redshift qsos , deep imaging of jet - cloud interactions in powerful radio galaxies , and the detection of a large ionized nebula around a nearby qso . this paper describes the characteristics of these instruments and the future role they could play at the vlt . a tunable filter @xcite is a special type of fabry - perot interferometer incorporating three features that traditional astronomical fabry - perot instruments lack . a tunable filter : ( 1 ) can move its parallel glass plates over a large range , ( 2 ) has anti - reflection coatings optimised over a broad range of wavelengths , and , ( 3 ) operates at much narrower plate spacings than traditional devices . these characteristics mean that tunable filters operate at lower resolving powers ( @xmath0 to 1000 ) than traditional instruments . the first taurus tunable filter ( ttf ; @xcite@xcite ) was introduced at the anglo - australian observatory ( aao ) in early 1996 by j. bland - hawthorn . this red device operates in the range 6500 9500 at the aforementioned resolving powers , thereby giving an adjustable passband width of 6 to 65 . two years later a second fabry - perot coated for 3700 6500 gave the potential for tunable imaging across the full optical range . since the fabry - perot is an interference device , many orders of interference are present simultaneously . therefore , one needs to use a blocking filter to remove light from all but the one order of interest . there are a dozen different @xmath1 300 - wide blocking filters used with ttf . more details on the ttf instruments can be found at the aao s ttf home page ( http://www.aao.gov.au/ttf/ ) . ttf is used in a cassegrain - mounted focal reducer ( taurus-2 ) , which consists of a simple camera - collimator arrangement with a straight - through optical path . the optical train of taurus-2 has aperture and focal plane filter wheels at the telescope focus , then the collimator , two further wheels in the parallel beam for the fabry - perot and pupil plane masks , the camera and finally the detector . the design of taurus-2 is very similar to that of the fors instruments on the vlt . there are identical copies of taurus-2 at both the aat and wht , although taurus-2 is no longer offered at the wht . taurus-2 at the aat has been scheduled with tunable filters in continuous semesters since 1996 . tuning is achieved through controlled changes to the separation between the glass plates : initial wavelength and bandpass selection is made by making a large adjustment ; subsequent scanning is done through much smaller changes ( fig . [ tuning ] ) . the plates are moved and stabilised by electronics attached to the outside of the focal reducer . a further development at the aao was the synchrony of filter tuning with the shuffling of charge on the ccd . the basis of the technique is the use of two or more _ different _ regions of the _ one _ ccd frame to image the sky at different wavelengths . exposure of a particular ccd region / wavelength combination can be made many times before the ccd frame is finally read - out . figure [ chargeshuff ] illustrates the technique . by splicing the multiple exposures of each band , variable conditions during the total imaging time are effectively averaged out . hence , precise differential photometry is possible in conditions when it otherwise would not . of course , a portion of the ccd frame must be sacrificed to allow extra room for the shuffle . however , the coincidental introduction of over - sized @xmath2 k ccds at the aat circumvented this problem . many areas of astrophysics have utilised the tunable filter to undertake a diverse range of science . these projects point the way toward the science possible with a tunable filter on an 8 m - class telescope . the following is a representative ( rather than comprehensive ) list of recent results with the taurus tunable filter ( ttf ) on the two 4-m telescopes . * * extended nebula around a nearby qso . * shopbell , veilleux and bland - hawthorn @xcite obtained deep h@xmath3 imaging of the @xmath4 quasar mr 2251@xmath5178 . this revealed ionised gas over a 200 kpc region around the quasar , suggesting its photoionisation of a surrounding hi gas envelope as the cause of the emission , rather than a merger event or interaction . * * field populations of star - forming galaxies . * the scanning ability of ttf was used by jones and bland - hawthorn @xcite to search for the emission - line signatures of star - forming galaxies at @xmath6 . this narrowband selection found excess numbers of line - emitters over those from traditional broadband - selected redshift surveys , implying higher star - formation densities over these redshifts . figure [ examplegalaxies ] shows two ttf - selected galaxies from this survey . * * searching for weather in brown dwarfs . * tinney and tolley @xcite used charge - shuffled time - series imaging of brown dwarfs in two passbands sensitive to variations in effective temperature . variability was found in one of the two stars surveyed , over observations spanning one - third of its rotation period , indicative of surface features . * * high - redshift gravitationally lensed galaxies . * hewett and collaborators @xcite have used the tunable filter to search for gravitationally lensed galaxies at @xmath7 . giant , bulge - dominated @xmath8 ellipticals are identified as potential lenses through anomalous emission - lines in 2df galaxy redshift survey spectra . ttf is tuned to the line to see if a @xmath7 galaxy ( being lensed by the elliptical ) is responsible for the emission . * * time series photometry of a stellar x - ray source . * time - series photometry of the x - ray star v2116 ophiuchi was undertaken by deutsch , margon and bland - hawthorn @xcite . the tunable filter was tuned to the prominent oi @xmath9 line in this object , thought to pulse in - phase with the x - ray source . these observations ruled - out any such variability . * * galaxy clustering around high - redshift qsos . * baker and collaborators @xcite tuned ttf to the @xmath10 quasar mrc b0450@xmath5221 to search for nearby clustering galaxies . nine galaxies were found with emission - lines matching [ oii ] at the redshift of the qso . of the five accessible for spectroscopic follow - up , three were positively identified with [ oii ] and another with a possible line detection . * * warm ionised gas around nearby radio galaxies . * ttf was used on the wht by tadhunter and collaborators @xcite for h@xmath3 imaging of two radio - galaxies at @xmath11 and 0.09 . faint emission - line structures were found beyond the radio axes , in addition to the usual bright structures along the radio jets . other tunable filter projects currently in progress include imaging of filamentary structures in edge - on spiral galaxies , star - formation regions in nearby elliptical galaxies , h@xmath12 imaging in face - on spirals and h@xmath3 imaging of nearby galaxy cluster cooling flows . it is likely that such scientific diversity would continue for a tunable filter at the vlt . there is currently no tunable filter capability on vlt nor on any 8 10 m - class telescopes elsewhere . however , the osiris instrument @xcite planned for the 10 m grantecan telescope will have tunable imaging , as will the soar telescope currently under construction in chile @xcite . tunable filters are commercially available from queensgate instruments in several sizes , along with the associated control electronics . while a detailed technical assessment is yet to be done , an informal study has shown that a 116 mm tunable filter can be accommodated in fors-2 if the upper of the two grism wheels were removed @xcite . the full spectroscopic capability of fors-2 is preserved , although more frequent grism changes are required . in such a case , the echelle mode would be lost from fors-2 but could be incorporated into fors-1 instead . most importantly , no major hardware modifications are required and the control electronics come from queensgate . software would need to be upgraded to include control of the instrument , to maximise observing and calibration efficiency . more discussion of the various options available can be found in @xcite . a tunable filter on the vlt would have the ability to tune _ between _ the brightest oh night - sky lines . moreover , the narrow bandpass would increase the usefulness of fors during bright - time . as a 3-d survey instrument , a tunable filter would complement the multi - object spectroscopic capabilities of the fors instruments well . tunable filters avoid the problems of sky subtraction experienced with other 3-d devices such as ifus . furthermore , none of the special reduction techniques used for kinematic fabry - perot data are required for tunable filter data because of the much lower spectral resolutions utilised . tunable filters have been used for many extragalactic and galactic stellar programmes at the aat and wht over recent years . the ability to synchronise charge - shuffling with tuning of the filter has allowed precise differential imaging to be undertaken by some of these programmes , even in variable conditions . implementing a tunable filter at the vlt in fors appears technically feasible . the primary operational change would be more frequent grism installations to maintain all the spectroscopic modes currently available . j. cepa , m. aguiar , v.g . escalera , i. gonzalez - serrano , e. joven , l. peraza , j.l . rasilla , l.f . rodriguez , j.j . gonzalez , f.j . cobos , b. sanchez , c. tejada , j. bland - hawthorn , c. militello , f. rosa . in : _ optical and ir telescope instrumentation and detectors , proc spie 4008 _ , ed . by m. iye and a.f.m . moorwood , ( spie : washington , 2000 ) , pp . 623 p.c . hewett , s.j . warren , j.p . willis , j. bland - hawthorn , g.f . lewis . in : _ imaging the universe in three dimensions , asp conference series 195 _ , ed . by w. van breugel and j. bland - hawthorn , ( asp : san francisco , 2000 ) , pp ." +"recently it has been proposed by several authors that objects other than black holes could be formed by gravitational collapse of a massive star . black hole horizons introduce number of theoretical problems and a consensus of solutions of those problems has not yet been reached @xcite , @xcite . one proposal , which was initiated recently by mazur and mottola ( m - m ) @xcite-@xcite is the so called gravastar "" . in this scenario , quantum vacuum fluctuations are expected to play a non - trivial role in the collapse dynamics . a phase transition is believed to occur yielding a repulsive de sitter core which helps balance the collapsing object thus preventing horizon ( and singularity ) formation @xcite , @xcite . it is expected that this transition occurs very close to the limit @xmath2 so that , to an outside observer , it would be very difficult to distinguish the gravastar from a true black hole . since this proposal , different versions of the original gravastar model have appeared with all variety of ingredients . for example , it has been shown how a gravastar structure can form from a born - infeld scalar field such as that predicted by low energy string theory @xcite or supported from non - linear electrodynamics @xcite . in the multi - layer structure of the m - m model with de sitter core and asymptotical schwarzschild outside region , additional features have been added . in @xcite gravastar solutions have been studied in a generalized ( reissner - nordstrm ) exterior and solutions of the model stemming from the original mazur - mottola model have been analyzed . gravastar type solutions in the context of solutions to einstein s equations with tube - like cores have also been recently considred @xcite . pioneering in - depth studies of spherically symmetric systems with desitter asymptotics may be found in @xcite - @xcite . more recently several papers have appeared discussing limits on gravastars and how to distinguish them from black holes @xcite , @xcite . it has recently been shown @xcite that the gravastar configuration ( see the next section for the elaborated physical model of it ) has to have anisotropic pressures which in addition should obey some of the energy conditions of general relativity . in this context one would ideally construct such a spherically symmetric model of an anisotropic fluid with a corresponding equation of state . the model , by the definition of the gravastar , should not possess a horizon , it should to be stable and its ( anisotropic ) pressures and density ideally would not violate energy conditions . certainly this last requirement is somewhat relaxed in the sense that configurations constructed in this way will violate some of the ( usual ) energy conditions from its very initial definition . full reviews of gravastar models may be found in @xcite and @xcite . in this paper we present solutions for the gravastar as proposed by cattoen , faber and visser ( cfv ) @xcite . in their paper an attractive sketch ( see fig.[fig:1 ] drawn here for the convenience of the reader ) is given as a guide to all the future gravastar model builders . in the next section a general description of gravastars as anisotropic fluid spheres is presented . in section 3 we describe the evolution of the anisotropic gravastar model and one of the solutions ( model 1 ) which reproduces the cfv sketch of the anisotropic gravastar . the value of the surface redshift is calculated while a more elaborate analysis of this important quantity is relegated to a future work . section 4 is devoted to the solution ( model 2 ) which starts from the construction of an equation of state and consistently solving the remaining generalized tolman - oppenheimer - volkoff equation . stability of this solution with respect to axial perturbations is calculated . finally , we conclude with comments and possible extensions of the anisotropic gravastar solutions . einstein s field equations , being exceedingly complicated because of their nonlinear character , have one most important closed form solution outside a spherical star of total mass @xmath3 , namely the schwarzschild metric . its line element in curvature coordinates is @xmath4 where @xmath5 . for the interior of the star one has to choose a physically reasonable "" stress - energy tensor . one attractive possibility is to use the perfect fluid model of matter where @xmath6 with @xmath7 and @xmath8 the energy density and pressure respectively in the co - moving frame of the fluid , and @xmath9 being the fluid four - velocity . in the static case , which is studied here , the interior metric may be written as @xmath10 the einstein equations , @xmath11 , give a system of equations : @xmath12 these are supplemented with the conservation law @xmath13 , which in this case yields only one non - trivial equation : @xmath14 t^{1}_{\;1 } -\frac{1}{2 } \lambda^{\prime } t^{0}_{\;0 } -\frac{2}{r}t^{2}_{\;2}=0\;. \label{eq : conslaw}\ ] ] elimination of the function @xmath15 from the above under - determined system leads to a convenient form of the conservation equation i.e. the tolman - oppenheimer - volkov ( tov ) @xcite , @xcite equation : @xmath16[m(r)+4\pi p(r)r^3]}{r^2[1 - 2m(r)/r]}\ ; , \label{eq : tov}\ ] ] with @xmath17 one may also specify an equation of state which relates pressure and density . if , for simplicity , we adopt at this stage a constant density profile function ( with built - in boundary conditions ) @xmath18 then it turns out to be an oversimplification which leads to analytic integration of ( [ eq : tov ] ) and the corresponding field equations but pressure and density do not obey the energy conditions which are analogous to the requirement of mass positivity in the newtonian mechanics . with the isotropic fluid and the above homogeneous energy density static solutions are allowed for objects with a restricted total mass @xmath3 to radius @xmath19 ratio i.e. @xmath20 @xcite . the idea of anisotropy in the spherically symmetric geometry was perhaps first introduced by g. lematre @xcite and suggested by einstein ( as quoted in ref . the limiting case of @xmath21 is mentioned there and the remaining transversal pressure was said to be enough to support a ( stable ) sphere ( see also @xcite ) . further development has brought different refinements of the original anisotropy notion ( see the papers @xcite - @xcite for studies and further references ) . the perfect fluid requires that the pressure in the interior of a star be isotropic , leading to calculations of isotropic polytropes for descriptions of objects like white dwarfs or neutron stars . another option giving more freedom to the equation of state within the spherical symmetry is the introduction of the stress - energy tensor which is anisotropic in its principal pressures . the anisotropy is sometimes ( spontaneously ) produced by extending the notion of a ( perfect ) fluid to phenomenological models including eg . scalar fields , or strongly interacting matter , although it is not known how large this anisotropy may be in realistic models . the stress - energy tensor for an anisotropic matter / fluid distribution is given by @xmath22 where @xmath0 is the radial pressure in the co - moving frame and ( again ) due to the spherical symmetry , the angular components are identified and are denoted as transversal pressures , @xmath1 . the vector @xmath23 is orthogonal to the fluid four - velocity ( @xmath24 ) . in the gravastar model , the core interior is assumed to be given by a de sitter solution so the appropriate pressure / density ratio value equal to minus one should be implemented as an initial condition for the density profile function , as well as a corrector to an equation of state connecting the pressure and density . for the moment we assume constant energy density @xmath25 . in addition to the ( energy ) density in a prescribed form , a relation between the radial @xmath0 and the tangential @xmath1 pressures should be given . an ansatz for the anisotropy measure , @xmath26 will be used following the hints given in @xcite . bounds on the anisotropy measure are calculated and are expressed in terms of the compactness "" @xmath27 , so our ansatz has the following form : @xmath28 the constant @xmath29 will simplify the ( numerical ) calculation and it is a measure of anisotropy for this version of the gravastar model . the tov equation now assumes the following form : @xmath30[\rho_0 + 3p_r(r ) ] } { 1 - 8r^2\pi\rho_0 /3}\right].\ ] ] with the initial condition @xmath31 , requiring also that @xmath32 . the radial pressure @xmath33 is given by @xmath34 } \right)\right].\ ] ] where the compactness "" is @xmath35 , while the transversal pressure can be obtained through ( [ eq : mod1delta ] ) , and is given by @xmath36 } \right)\right]+\mu\alpha^2\right\}.\end{aligned}\ ] ] for all @xmath37 , both pressures start at @xmath38 in the centre of the gravastar . at @xmath39 ( if one would allow such a density profile ) the values are @xmath40 , @xmath41 . only for values @xmath42 , does the radial pressure reach positive values before returning back into the negative pressure region . it is also worth noting that this simple model does not lead to an equation of state , since the energy density does not change within the star . as previously mentioned , this oversimplified model with the constant ( energy ) density function as given above can not reproduce the sketched figure [ fig:1 ] . i.e. it can not provide a gravastar in the proposed model without the surface layer structure as required by junction conditions . the most obvious extension is to use perhaps the same ansatz for the equation of state connecting the behaviour of radial and tangential pressures as given in ( [ eq : mod1delta ] ) . for the density one takes some non - homogeneous distribution which will give a more complex dependence of @xmath33 and lead to a possible solution ( see the model 1 below ) . certainly the ansatz could be replaced by a calculated equation of state and introduce again an inhomogeneous density distribution ( see the model 2 below ) . on these two possibilities the new results of this paper are based . in order to have a reasonably realistic radial pressure component we demand the ( most natural ) weak energy condition ( wec ) be satisfied everywhere : @xmath43 also , we require @xmath44 and , since stability of the fluid / gravastar requires that @xmath45 must not increase outwards , @xmath46 the above wec obviously implies : @xmath47 the so called null energy condition ( nec ) . there is also a dominant energy condition ( dec ) which requires that @xmath48 \quad\text{and}\quad p_t(r)\in [ -\rho(r),+\rho(r ) ] , \label{eq : dec}\ ] ] and which implies the other two energy conditions . another commonly studied energy condition is the strong energy condition ( sec ) which states that , for our static system , @xmath49 since gravastars possess a desitter core , it is not possible to satisfy this energy condition . within the normal range of the gravastar it could be reasonable to propose that the speed of sound shall not exceed 1 ( speed of light ) . this requirement is reasonable to apply in the region where one could expect that the unusual physics govern most of the physical processes ( i.e. where the matter possesses the least exotic behaviour ) . from the sketch in figure [ fig:1 ] this is expected to be in the gravastar atmosphere , so @xmath50 in this region one should" +"the multiplicity of red giant period - luminosity ( p l ) relations has been a major discovery on the road to interpreting complex light variations of these stars . following the two seminal papers by @xcite and @xcite , a picture has emerged that can be summarized as follows : large - amplitude mira stars pulsate in the fundamental mode , whereas smaller - amplitude semiregulars are often multimode pulsators , in which various overtone modes can be excited ( see also * ? ? ? besides the pulsating p l sequences ( seq . a , b and c , as labeled by @xcite ) , two other sequences were suggested : seq . e with red giants in eclipsing binaries and seq . d with stars that have long secondary periods ( lsps ) . the latter pose a great mystery and the nature of their slow variations is still not understood , with several different mechanisms proposed @xcite . the basic picture of multiple p l relations has been confirmed by many independent studies , mostly based on @xmath0-band magnitudes . it has emerged that the original five sequences have further details , including a break at the tip of the red giant branch ( rgb ) , which is due to the existence of distinct rgb pulsators that are mixed with the more evolved agb variables ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? almost all authors have accepted the existence of the distinct sequences of red giant binaries ( seq . e ) and lsp stars ( seq . d ) . the only exception was @xcite , who showed that seqs . e and d seem to merge at a specific luminosity ( as measured by the wesenheit index ) and suggested that this may imply the binary origin of lsps . here we report on a combined analysis of macho observations of eclipsing binaries and red giants in the large magellanic cloud , which shed new light on these stars and on the lsp phenomenon . our results are based on two sets of publicly available almost eight - year long macho light curves . a detailed description of the macho project can be found in @xcite . some of the data are offered for download through the macho website ( http://wwwmacho.mcmaster.ca ) , where one can choose specific samples based on an automated classification of variability type . using the web interface , we individually downloaded all light curves classified as eclipsing binaries ( 6833 stars ) and as red giant variables ( classified as wood a , b , c and d classes ; 2868 stars ) . in the case of the eclipsing binaries , it became obvious very quickly that the classification was not perfect , and a large fraction of stars turned out to be cepheids , rr lyrae stars or long - period variables . we also found that the catalogued periods were incorrect for a significant number of stars . we therefore reclassified all 6833 stars and re - determined their periods , using the following procedure ( more details will be given elsewhere ) . periods were first estimated using the phase dispersion minimization method @xcite . we then checked all the folded light curves by eye and refined the periods with the string length method @xcite , which is more reliable than pdm when the light curve contains long flat sections and very narrow minima , as is the case for many eclipsing binaries . also , in many cases pdm gave harmonics or subharmonics of the true period , which was only recognized through the visual inspection of every phase diagram . we also examined the color variations to identify and exclude pulsating stars with sinusoidal light curves . after this analysis , 3031 stars remained as genuine eclipsing or ellipsoidal variables . next , we classified the binary sample using fourier decomposition of their phase diagrams . @xcite showed that light curves of w uma systems ( contact binaries ) can be quantitatively described using only two coefficients , @xmath1 and @xmath2 , of the cosine decomposition @xmath3 . @xcite tested the behavior of semi - detached and detached systems in the @xmath4 plane by decomposing theoretical light curves into fourier coefficients . we found that only stars with `` w uma - like '' light curve shape composed the sequence ( which is plotted in fig.[pl ] ) , while detached and semi - detached systems are spread everywhere in the p l plane . our second set of light curves were those of the 2868 publicly available macho red giant variables . since they often show multiply periodic light variations , we determined periods with iterative sine wave fitting . as a measure of significance , we also estimated the @xmath5 ratio of the peaks in the fourier spectra . since the noise in the fourier spectrum increased toward lower frequencies , different values of the @xmath5 were used when determining whether a peak was real for different period - luminosity relations ( @xmath5 cutoff was set to 3 for seq . a@xmath6 , 4 for seq . a , 6 for seqs . b , c and 10 for seq . we omitted periods close to 1 yr , because many light curves show variations with this period that are not real . as a result , a total of 4315 significant frequencies were identified for the 2868 stars . we studied these two samples in the p l plane . in order to reduce the effects of interstellar extinction and allow a direct comparison with previous results in the literature , we plotted the period@xmath0 magnitude relation . we obtained near infrared magnitudes by cross - correlation with the 2mass all - sky point source catalog ( http://irsa.ipac.caltech.edu ) , with a search radius of 3@xmath7 . the resulting p l diagram is shown in the left panel of fig . [ pl ] . to our surprise , l relation of the binary sample did not follow seq . e , as we had expected . instead , they overlapped with seq . d , which at first sight appears to give strong evidence for the binary origin of seq . d and prompted us to investigate the issue in more detail . the combined p l plot in fig . [ pl ] shows the well - known complex structure of distinct sequences . besides sequences a , b , c , d and e , we also detect the existence of the faintly visible new short - period p l sequence ( seq . a@xmath6 ) on the left - hand side boundary of the diagram ( labeled as a@xmath8 and b@xmath8 in @xcite and @xmath9 in @xcite ) . the eclipsing stars ( pluses ) seem to merge with seq . d rather than forming seq . e as adopted in the literature @xcite . to clarify this issue , we re - checked periods for : ( i ) stars on seq . e in fig . 1 of @xcite , for which the identifiers and basic data were kindly provided by peter wood ; ( ii ) stars on seq . e in our fig . [ pl ] ( black dots ) . in both cases , it turned out that for most of the objects , the given periods were half of the true ones , as one might expect from a fourier analysis of eclipsing binary light curves . we have carefully double - checked all individual light curves on seq . e and d and corrected the periods ( see fig . [ example ] ) . the final p l plot is shown in the right panel of fig . [ pl ] . as a result of the period correction , the sequence between c and d , which is known as seq . e in the literature , has completely disappeared . a few stars remain in the gap but practically none of them are eclipsing binaries . the majority turn out to be mira stars that are very red ( @xmath10 mag ) and are presumably carbon - rich miras that are dimmed by circumstellar dust clouds ( bottom panel of fig . [ example ] ) . we propose to retain the label e for the sequence of ellipsoidal variables in its corrected position ( right panel of fig . [ pl ] ) . in the literature , only @xcite plotted the eclipsing binary sequence at the correct ( doubled ) period . however , they did not discuss this issue and one can still find more recent studies where seq . e was shown at the wrong period . @xcite have , however , shown that roche geometry gives a good fit to the ogle ellipsoidal variables . we have also checked this on the macho sample . we calculated the theoretical orbital periods of systems at mass ratios of 1 , where the components fill their roche lobes . for this , we used evolutionary models of @xcite and applied equations of section 4 in @xcite . ( note , however , that the definition of @xmath11 in their eq . 1 actually gave @xmath12 as the filling factor . ) for the calculations we took the evolutionary tracks of the 0.85 @xmath13 and 2.5 @xmath13 models , since theses masses represent the mass limits of stars that evolve through the rgb and agb . the @xmath0 magnitudes of the models were determined from @xmath14 vs. @xmath15 calibrations , combined from @xcite and @xcite . in the right panel of fig . [ pl ] we show these two limits ( the shorter period line belongs to the higher mass ) . for any other mass ratios , the orbital periods shift towards smaller values . this simple approach with roche geometry describes remarkably well the observed period - luminosity relation of ellipsoidal variables in the macho sample , in agreement with the study of @xcite . however , the ogle sample contains a larger fraction of ellipsoidals and most of them have longer periods than are predicted by the models . those stars do not entirely fill the roche lobe @xcite . it is also worth mentioning that the low fraction of ellipsoidal / eclipsing rgb stars in the macho data ( 1.5% ) was used by @xcite as an argument against the binary origin of lsps . however , the ogle statistics clearly showed that there are at least 10 times more such rgb stars , and so that argument is no longer valid . since the lower mass model fits seq . d quite well , the question arises : how similar are the ellipsoidal and lsp variables ? to assess this , we examined the amplitudes of these stars . @xcite mentioned that amplitudes of lsps are positively correlated with the brightness of the star . compared to ogle data , the macho observations have the advantage of giving information on the color variations . we examined the amplitudes in the macho blue and red bands of the binary and lsp stars , and also included seq . c stars , which allow a comparison with stars that we know to be pulsating . the amplitudes were measured by fitting smooth spline functions to the phased light curves . the resulting blue peak - to - peak amplitudes are shown as a function of @xmath0 magnitude in fig . [ amlu ] , where several features are apparent . firstly , the amplitudes of ellipsoidal variables ( circles in the upper" +"real quantum systems are always coupled to environments . research in the last two or three decades has shown that system environment interactions greatly affect quantal coherences in the system . open - system dynamics can often be described by a master equation for the reduced density matrix of the system . the full hamiltonian is written as the sum of system - only , environment - only and system environment interaction terms . the master equation for the system then depends on the system - only hamiltonian plus other terms derived from the fundamental system environment couplings . these additional pieces induce an effective non - unitary evolution for the system that can , for example , lead to an apparent loss of quantal coherence . in many studies , the system - only hamiltonian is taken to be the sum of one - body terms . an example of relevance to this paper arises for a system of @xmath0 particles , each in a one - dimensional symmetric double well . the system hamiltonian @xmath1 describes particle @xmath2 oscillating with frequency @xmath3 between the left and right sides of its well independently of the other particles in the system . when system environment coupling is added , this behaviour can be drastically modified , with the quantum zeno @xcite or freezing phenomenon being the most extreme example . the purpose of this paper is to contribute to a study of closed and open quantum system evolution that goes beyond one - body system hamiltonians by including interaction terms between the system particles . this is a vast and extremely rich field of enquiry , with many possible lines of development . for reasons to be explained below we will focus on two topics . the first is entanglement creation through adiabatic evolution and its degradation due to environmental influences . the second is quantum information error protection through adiabatic evolution . common to both topics is the use of adiabatic avoided level crossing dynamics . this special case of quantum mechanical time evolution has applications in diverse areas of physics , from the mikheyev - smirnov - wolfenstein effect for neutrino oscillations @xcite to quantum computation @xcite . we use it here because it allows non - trivial dynamics to occur while retaining both an element of theoretical simplicity plus visualisability with the aid of level crossing diagrams . whenever one has more than a single particle in one s quantum system , entanglement adds spice to the analysis . entangled states are a unique feature of quantum mechanics , first studied in connection with the issue of non - locality @xcite . they are also of critical importance in discussions of decoherence , measurement and the quantum - to - classical transition @xcite . more recently , entanglement has emerged as a useful resource in the field of quantum information theory , enabling processes such as quantum cryptography @xcite and teleportation @xcite . the production and manipulation of entangled states is a key element in any realisation of a quantum computer @xcite . as our first topic , we describe an efficient method for the preparation of entangled states which utilises the level crossing structure of the system s energy eigenstates . specifically , we discuss the bell states in the case of a bipartite system , @xmath4 states in a tripartite system and generalised @xmath5 states in multi - partite systems . we then subject the evolving systems to environmental interactions that affect the entanglement production process . we show that the outcome depends on the form of system - environment coupling : entanglement degradation is the generic effect , but the special case of `` motional narrowing '' noise actually leads to zero degradation . calculations presented in ref.@xcite simply took initial bell states and computed the evolution of entanglement in the presence of environmental noise . the present work is a natural extension of this . as a separate but related topic , we show that a method of error protection using entangled states emerges from a variation of the above procedure . we devise a scheme to protect the information encoded in a single qubit from bitflip and phaseflip errors . our goal is to construct a master equation which seamlessly joins the dynamics of qubit encoding , error protection and decoding to the environment - coupling influences responsible for error generation . while the outcome of the open system evolution can be dissected into these quantum information theoretic subprocesses , the actual dynamics is simply what you get when you solve a certain master equation . the building block for our multi - partite systems is the two - state system of a particle in a one - dimensional double well , chosen for its generic properties and broad interest ( see ref.@xcite ) . the well is taken to be partitioned by a barrier of height @xmath6 that is large compared to the ground state energy @xmath7 . ( the two lowest energy levels will be collectively called the `` ground state '' . for a symmetric well with @xmath8 they are nearly degenerate . ) adopting quantum information theoretic parlance , we denote by `` qubits '' the states occupying the two - dimensional hilbert space spanned by the left and right sides of the well ( in the ground state ) . the left and right eigenstates , denoted @xmath9 and @xmath10 , correspond to the @xmath11 and @xmath12 eigenvalues of @xmath13 , respectively . for an isolated well , the hamiltonian has the form @xmath14 where the energy splitting @xmath15 is essentially a tunneling rate between the two sides of the well , and the parameter @xmath16 is the well bias . we begin with a bipartite two - state system , the simplest system in which one may discuss entanglement . our aim here is to produce one of the bell states , @xmath17 dynamically from certain initially factorisable states . let us denote the two - particle ( reduced ) density matrix of qubits 1 and 2 as @xmath18 and consider a hamiltonian of the form presented in eq . ( [ 1ham ] ) for each of the two qubits , together with a third term which couples them : @xmath19 \otimes { \:\mbox{\sf 1 } \hspace{-0.37em } \mbox{\sf 1}\,}+ { \:\mbox{\sf 1 } \hspace{-0.37em } \mbox{\sf 1}\,}\otimes \left [ \omega \sigma_{x2 } + f(t ) \sigma_{z2 } \right ] + \lambda \sigma_{z1 } \otimes \sigma_{z2}. \label{2ham}\ ] ] observe that the hamiltonian is invariant under the interchange of the two qubits . for simplicity , only the well biases @xmath16 are allowed to vary with time , and we demand that @xmath20 . this last condition is necessary in order for the desired level crossing structure to arise . ( it is implicitly assumed that only the lowest states in each well are populated . we will need to relax this condition later on when we couple the system to a hot bath . ) the four eigenstates separate into an antisymmetric singlet state @xmath21 for all values of @xmath15 , @xmath16 and @xmath22 , and a symmetric triplet composed of linear superpositions of the set @xmath23 , which asymptotes to @xmath24 for large @xmath25 s . note that the permutation symmetry of the hamiltonian ensures that the evolution of the singlet state is disconnected from that of the triplet states at all times so we are dealing with an effectively three - state system . in fig . [ 2qubit ] , we plot the energy level diagram as a function of @xmath16 . the states @xmath26 and @xmath27 experience avoided level crossings with @xmath28 at @xmath29 and @xmath30 respectively , labelled points @xmath31 and @xmath32 in fig . [ 2qubit ] . hence , an initial state @xmath33 created at @xmath34 will continue to reside in the lowest energy eigenstate provided that @xmath16 varies sufficiently slowly with time , and be adiabatically transformed , across point @xmath31 , to the entangled state @xmath35 where @xmath36 corresponds to any point in the period of time during which @xmath16 lies in the range @xmath37 . further adiabatic evolution beyond point @xmath32 will turn @xmath38 once more into a factorisable state @xmath39 . note in eq.([marshmallow ] ) that the entangled state @xmath40 inevitably contains some order @xmath41 $ ] `` contamination '' from the states @xmath42 and @xmath39 , which can not be arbitrarily minimised without jeopardising the adiabaticity of the transitions at points @xmath31 and @xmath32 ( see later ) . figure [ ent ] illustrates the evolution of the entanglement for @xmath38 , and we remind the reader again that the bell state @xmath21 can not be generated in this manner because of symmetry requirements . in this figure , the degree of entanglement is defined to be the _ entropy of entanglement _ @xmath43 which is the von neumann entropy of the reduced density matrix obtained by tracing out either of the two qubits @xcite , @xmath44 where @xmath45 is the density matrix obtained after tracing out particle 2 ( 1 ) . the related concept , _ entanglement of formation _ @xmath46 , to be used below , is a generalisation of the entropy of entanglement for a _ mixed _ state of two qubits @xcite . the entanglement will stay approximately constant at @xmath47 when @xmath16 is in the range @xmath37 . note that if the two qubits had different oscillations frequences , @xmath48 , mixing between the almost degenerate states @xmath49 is not prohibited by permutation symmetry ( or the lack thereof ) . in this case , the degree of entanglement will vary significantly in the period @xmath37 , attaining the maximal value of @xmath47 only at the point @xmath50 . observe that if we had started instead in the state @xmath27 which is approximately the highest energy eigenstate , we could in principle obtain the entangled state @xmath51 at the point @xmath50 . however , an inspection of the hamiltonian @xmath52 rewritten in the symmetrised basis @xmath53 , shows that the splitting between the relevant energy eigenstates for the @xmath54 transition at @xmath50 is of order @xmath55 , as opposed to @xmath56 for the @xmath57 transition considered earlier . it follows that the resonance width at point @xmath58 is necessarily some @xmath59 times narrower than those at points @xmath31 and @xmath32 . their respective adiabaticity parameters , defined as @xmath60 where @xmath61 is the splitting between the energy eigenstates , `` res '' denotes evaluated at resonance , and @xmath62 indicates an adiabatic process , must also differ correspondingly by some factor of @xmath63 . explicitly , @xmath64 characterise the three resonances . hence , in order to manufacture the state @xmath51 , a slowly varying @xmath16 together with control over its accuracy to within @xmath65 are necessary . navely , the severity of the precision requirement seems easily alleviated by enlarging @xmath15 . the benefit of a wider resonance width , however , is compensated for by a concomitant increase in the contamination from the @xmath28 state which contributes at order @xmath59 . by comparison , the production of @xmath28 from @xmath42 requires only that we stop the evolution somewhere between @xmath66 , and is therefore a much simpler task . in the presence of environmentally - induced noise , we must solve a master equation for the reduced density matrix of the system . the form of the master equation depends on whether or not the environment is hot enough to induce transitions to excited states of the double wells . we first consider coupling to a cold environment , so that each particle remains in the ground state of its double well . the evolution of @xmath67 is governed by @xmath68 -\gamma_{\text{relax}}[\zeta , [ \zeta , \rho ] ] -\gamma_{\text{relax}}[\zeta ' , [ \zeta ' , \rho]],\ ] ] where @xmath69 and @xmath70" +"currently , experiment suggests that there are more scalar mesons than can be accommodated in a single quark - model nonet . many qcd motivated models predict the existence of non-@xmath8 mesons such as glueballs @xcite , hybrids @xcite , @xmath9 @xcite and @xmath10 @xcite states . it is tempting to say that these ` spare ' experimental states are the unconventional mesons allowed by qcd but , with scalar glueball and multiquark states expected to have masses comparable to the conventional @xmath11 states , which _ are _ the extra states ? in the work that follows we hope to shed some light on this question by attempting to determine which of the 5 scalar - isoscalar mesons currently listed in the particle data group tables @xcite is the lightest @xmath12 meson in this channel . to address this question we will use the qcd sum rule technique . the answer has importance for chiral symmetry breaking in qcd , see for instance @xcite . qcd sum rules are integral expressions that relate the hadronic and partonic regimes , _ i.e. _ the low energy world of resonances with the high energy world of ( tractable ) qcd . since their conception over twenty years ago @xcite , qcd sum rules have become an established technique both for calculating hadronic properties in channels , where the qcd expressions are under control , and , conversely , estimating qcd parameters ( such as the masses of the quarks ) in channels where there is good experimental information . using qcd sum rules in the scalar channel is not a new idea . they were first applied to the scalar mesons in @xcite where laplace sum rules were used ( for a recent review of laplace sum rules see @xcite ) . here the phenomenological side was represented using the , now standard , resonance + continuum ansatz , with resonances being represented as @xmath13-functions and the continuum being calculated entirely within perturbative qcd . as only the operator product expansion ( ope ) terms , discussed in sect . [ sec : ope ] , were taken into account on the theory side , _ exact _ mass degeneracy between the lightest isoscalar and isovector was found , with . the @xmath14 state was predicted to have a mass of around 1.35 gev . these findings were supported by bramon and narison @xcite , who used qcd sum rules to calculate the couplings of the @xmath4 and @xmath15 to two photons . again modelling the resonances with @xmath13-functions the authors concluded that a @xmath11 interpretation of these two mesons could not be ruled out with the data then available . the effects of going beyond the ope were studied in @xcite , where instantons ( see sect . [ sec : instantons ] ) were included on the theoretical side , but not in the qcd continuum on the phenomenological side . once again the resonances were treated as @xmath13-functions and only the isospin-1 channel was considered . it was concluded that the lightest @xmath11 state in this channel had a mass @xmath16 1 gev . for the light scalar mesons the zero - width approximation is not a good one and the first attempt to go beyond it in a sum rule investigation was by elias _ _ @xcite . here resonances were represented by breit - wigner formulae , which , whilst better than a @xmath13-function , still do not adequately describe the complex structure in the scalar sector . a further abstraction was introduced by replacing these breit - wigner shapes with a riemann sum of rectangular pulses . laplace sum rules were used , but in an integral form which requires the calculation of perturbative expressions at rather low energy scales . again instantons were included , but not in the continuum . in the isovector channel , the @xmath15 was found to decouple from the sum rule and the mass of the lightest quarkonium isovector was consistent with the @xmath17 . in the isoscalar channel the conclusions were not so clear cut , it was predicted that the lightest quarkonium here should have a width less than half of its mass , and although the @xmath4 could not be ruled out as the main contributor a lighter state was preferred . similar conclusions were reached in @xcite . this study used both laplace and finite energy sum rules , again requiring perturbative expressions to be evaluated at low energies . the authors noted , that for a consistent treatment of the borel sum rules , the instanton effects should also be included in the qcd continuum contribution . the sum rules were dominated by an isoscalar with mass around 1 gev and an isovector with mass around 1.5 gev , thus suggesting the @xmath4 and @xmath17 as the lightest @xmath11 states in their respective channels . however , in the same work , a comparison to a more realistic resonance shape predicted resonance parameters for the lightest quarkonium of @xmath18 mev and @xmath19 mev . these parameters are not consistent with the @xmath4 , but could describe a breit - wigner fit to the @xmath3 . in @xcite , maltman used pinched weight finite energy sum rules to calculate the decay constants of the @xmath15 and @xmath17 , which were then compared with the decay constant of the , presumably @xmath11 , @xmath20 . instantons were included and all qcd integrals were carried out in the complex plane , which improves the convergence of perturbative expressions . the isovector decay constants were found to be of comparable size , suggesting a similar structure for both . the author concluded that this favoured a unitarised quark model @xcite scenario , where two physical hadrons can arise from one ` seed ' state . in the work that follows we will apply qcd finite energy sum rules introduced in sect . 2 to the scalar - isoscalar channel . on the theoretical side we will include in sects . 3 and 4 instanton effects as well as the ope terms up to dimension six and use the contour improvement prescription to increase the convergence of perturbative expressions . on the the phenomenological side in sect . 5 we will incorporate experimental data directly by relating the hadronic vacuum polarisation to the @xmath21 scattering amplitude via the pion s scalar form - factor . the sum rules are evaluated in sect . 6 and we present our conclusions in sect . 7 . the connection between quarks and hadrons is through the vacuum polarisation , @xmath22 . this is defined by the correlation function of two currents , _ i.e. _ @xmath23 where @xmath24 and the currents are chosen so as to select the desired channel . in this work we are considering the scalar - isoscalar mesons and so we choose the renormalisation group invariant current @xmath25 where @xmath26 and we use the symbol @xmath27 to denote an effective light - quark . the second equality follows because we ignore the two - gluon intermediate state , whose contribution is @xmath28 and so can be safely neglected . -plane showing the so called ` pacman ' contour which is used to derive the fesrs . [ fig : pacman ] ] ' '' '' @xmath22 is analytic everywhere in the complex @xmath29plane except along the time - like axis , so for any weight function , @xmath30 , which is real for all real @xmath31 and analytic within the ` pacman ' contour shown in fig . [ fig : pacman ] we can write @xmath32 on the left - hand side of eq . ( [ eq : fesr ] ) we have an integral in the physical region , and here we choose to describe the integrand using hadronic physics ( either with experimental data or a phenomenological parameterisation ) . on the right - hand side we have an integral in the non - physical region ( complex @xmath31 ) , and here we use field theory ( _ i.e_. qcd ) to calculate the integrand . the assumption that eq . ( [ eq : fesr ] ) holds for a range of values of @xmath1 is a statement of global quark - hadron duality , _ i.e. _ the integral of an hadronic expression is equal to the integral of an expression written in terms of partonic degrees of freedom . early sum rule work used positive integer powers of @xmath31 as weight functions . in this work we wish to investigate the lightest meson in the channel , and so we choose a decaying exponential , . on the phenomenological side , this weight function will suppress the region of the integral @xmath33 , and so by varying @xmath34 we can control which regions of the integrand contribute most significantly to the sum rule . if we also include integer powers of @xmath31 in the weight function then we can build up a family of sum rules . almost by definition , at energies where resonances dominate the spectral density , the implications of qcd are not straightforwardly calculable . if qcd _ were _ tractable then the technology of qcd sum rules would be redundant . this means that , for moderate values of @xmath1 , our straightforward qcd description of @xmath22 must fail , at the very least , in the region of the positive real axis ( see fig . [ fig : pacman ] ) . however , it is believed @xcite that it is _ only _ in the region of the positive , real axis that the straightforward qcd description is particularly unreliable and that in the rest of the @xmath31-plane calculable qcd provides a good description of the correlator . consequently we introduce a zero into the weight function at the point where the circle joins the real axis , _ i.e. _ @xmath1 . thus our sum rules have the weight function and we denote them by the symbol @xmath35 . elsewhere in the literature they are often referred to as pinched weight sum rules . then the left hand side of eq . ( 3 ) becomes @xmath36 introducing this zero into the weight function has a number of advantages . firstly , on the theoretical side we avoid the problem , just described , of the failure of qcd on the part of the circle near the positive real axis . secondly , on the phenomenological side , we have introduced a second factor with a tendency to suppress the higher energy portion of the integral and consequently reduce the dependence on the exact value of @xmath1 @xcite . the parameter @xmath1 is not entirely free : it must be large enough that the qcd expressions we are able to calculate are expected to be a good approximation to the full correlator , yet @xmath1 should be small enough that we have experimental information . the art of sum - ruling is to find ( sensible ) values of @xmath1 for which over a wide range of the unphysical parameter @xmath34 . when this occurs we say that the sum rules are _ although the current eq . ( [ eq : current ] ) is rg - invariant , the correlator it gives rise to is not . as well as making the calculation of the correlator within qcd more difficult , this would also lead to an unwanted scale dependence in our final results . the second derivative of this correlator , @xmath37 , _ is _ rg - invariant . as @xmath37 is also analytic within the contour shown in fig . [ fig : pacman ] , we could choose to write the sum rules completely in terms of this quantity , but @xmath38 is not directly related to any physical quantity and so we would lose" +"low frequency quasi - periodic oscillations or lfqpos are common features observed in x - rays emitted from stellar mass black holes . x - ray transient sources in our galaxy exhibit various types of qpos with frequencies ranging from mhz to a few hundreds of hz ( morgan , remillard & greiner 1997 ; paul et al . 1998 ) . since a black hole does not have hard surface , emission of oscillating hard x - rays is very puzzling . several models are present in the literature to explain the origin of the quasi - periodic oscillations ( qpos ) . kato & fukue ( 1980 ) suggested trapped oscillations in gaseous disks around supermassive black holes and tried to explain 100d time variabilities in these objects . carroll et al . ( 1985 ) found oscillations of the disk using purely newtonian potential in their 3d numerical simulation . ` diskoseismology ' model by nowak & wagoner ( 1991 ) , uses acoustic oscillations of the disk arising out of dispersion relation . molteni , sponholz and chakrabarti ( 1996 ) , in the context of super massive black holes , mentioned that resonance caused by agreement of bremsstrahlung type cooling and infall time scale in the post - shock region of an advection flow is the cause of oscillation of the emitted radiation . titarchuk et al . ( 1998 ) , identifies low frequency qpos associated with the viscous magneto - acoustic resonance oscillation of the transition layer surrounding the compton cloud . stella and vietri ( 1999 ) explains qpos in terms of orbital precession and show that nearly correct frequencies can be generated by this way . trudolyubov et al . ( 1999 ) explains lfqpo using perturbation inside a keplerian disk while titarchuk & osherovich ( 2000 ) and shirakawa & lai ( 2002 ) use global disk oscillation and oscillation of warped disk for the purpose . rodriguez et al . ( 2002 ) and tagger et al . ( 2004 ) propose that lfqpos could be due to magnetohydrodynamic ( mhd ) instability of magnetized accretion disks known as the accretion - ejection instability ( aei ; also see , tagger & pellat 1999 ) which combines spiral and rossby waves propagating in the disk . recently , propagating mass accretion rate fluctuations in hotter inner disk flow ( ingram & done , 2011 ) , and oscillations from a transition layer in between the disk and hot comptonized flow ( stiele et al . , 2013 ) were used to explain the origin of qpos . while these models can explain the frequency , explanation of the strong q - factor ( ratio of frequency and the full width at half maximum ) , or coherency observed in some systems is more difficult . since black holes do not have hard surfaces , the so - called ` beat - frequency ' type models ( lamb et al . 1985 ) as is used for neutron stars can not be used . furthermore , none of these models attempt to explain long duration continuous observations and the evolutions of qpos during the outburst phases of transient bhcs . meanwhile , chakrabarti ( 1989 , 1990 ) showed that black holes can have boundary layers in that unique standing shocks can form due to strong centrifugal barrier ( which act as hard surfaces ) in the vicinity of the horizon where infalling energy may be dissipated and jets / outflows may be formed . this post - shock region could oscillate if its cooling time scale roughly agrees with the infall time in this region ( molteni , sponholz & chakrabarti , 1996 ; chakrabarti & manickam , 2000 ) . the shock oscillation model ( som ) by chakrabarti and his collaborators naturally explains lfqpos . the post - shock region is known as the centrifugal pressure dominated bondary layer or cenbol . chakrabarti & titarchuk ( 1995 , hereafter ct95 ) , based on the viscous transonic flow solution ( chakrabarti , 1990 ) postulated that higher - viscosity flow in equatorial region will be keplerian and it is immersed inside a lower - viscosity flow which also has much lower angular momentum . this so - called two component advective flow solution ( tcaf ) not only can explain the spectral properties of a black hole , the lfqpos can also be explained just by making an extra assumption that they occur only when the cooling time scale due to comptonization in cenbol roughly matches with the infall - time scale in the post - shock flow . thus the same shock - wave , used for spectral formation , can also be used for lfqpos . garain et al . ( 2014 , hereafter ggc14 ) , using monte carlo simulations coupled with hydrodynamic simulations clearly demonstrated that observed lfqpos could indeed be the results of resonance phenomenon . the frequencies and q - values are found to be in acceptable ranges . the hypothesis that lfqpos are due to resonance could be tested easily in outbursting sources , as the accretion rates of the keplerian and low - angular momentum components evolve continuously and fulfillment of resonance condition may be easier . in fact , as we show below , in these sources , resonance condition may remain satisfied in several successive days and the qpos evolve accordingly . movement of the shock is also driven primarily by compton cooling ( mondal , chakrabarti & debnath , 2015 , hereafter mcd15 ) . this so - called propagating oscillatory shock ( pos ) model ( chakrabarti et al . , 2008 ; debnath et al . , 2010 , 2013 ; nandi et al . 2012 ) also explains the evolution of the qpos in both the rising and declining phases of outbursts in several black hole candidates . generally speaking , as the day progresses in the rising phase , the rate of cooling goes up with more supply of soft photons from the keplerian component of flow , shifting the shock closer to the black hole resulting in a reduction of cenbol size and increasing the qpo frequency in the process ( msc96 ; das et al . 2010 ; mondal & chakrabarti , 2013 ) . the reverse is true in the declining phase . in the literature , there are mentions of three types ( a , b and c ) of lfqpos ( casella et al . , 2005 ) . type c lfqpos are characterized in the power spectrum by a strong ( up to @xmath1% rms ) , narrow ( @xmath2 ) , and variable peak ( centroid frequency ) and intensity varying by several percent in a few days at frequencies @xmath3 hz , superposed on a flat - top noise ( ftn ) that steepens above a frequency comparable to the qpo frequency . type b lfqpos are characterized by a relatively strong ( @xmath4rms ) and a narrow peak ( @xmath5 ) . there is no evidence of ftn , although a weak red noise is detected at very low frequencies . type a lfqpos are characterized by a relatively weak ( few percent rms ) and a broad peak ( @xmath6 ) around 8 hz . a very low amplitude red noise is observed . so far , no study has been made to quantify the cooling and infall time scales inside the cenbol , and explicitly compute them for any outbursting source on a daily basis to check if they are close to each other . in this paper , we do this study for c type lfqpos mentioned above , which increases monotonically during the rising ( hard and hard - intermediate spectral states ) phase of the outburst . it is possible that less sharper qpos ( types b and a ) are also due to resonance phenomenon , either weakly resonating cenbol ( type b ) or the shockless centrifugal barrier ( type a ) . this aspect would be treated elsewhere . in the next section , we derive estimates of the time scales and argue why resonance could be quite normal inside the post - shock region where comptonization is the strongest cooling process stellar black holes . for super massive black holes , other cooling processes could be important and the results would change accordingly . in 3 , we discuss the methodology . in 4 , we compute different time scales from observations and compare them on days when qpos occur . finally , in 5 , we make concluding remarks . we start with ct95 configuration of tcaf solution where a high viscosity keplerian disk of accretion rate @xmath7 is immersed in a low - keplerian halo of accretion rate @xmath8 which undergoes an axisymmetric shock transition at @xmath9 around a black hole of mass @xmath10 , where @xmath11 is the mass of the sun . let the shock of height @xmath12 be of compression ratio ( i.e. , ratio of pre - shock to post - shock velocities @xmath13 and @xmath14 respectively ) @xmath15 . we consider stellar mass black holes so that comptonization is the dominating cooling process . for supermassive black holes , where the tcaf solution applies equally well ( chakrabarti , 1995 ) , bremsstrahlung and synchrotron processes may also be important . this will be dealt with elsewhere . the average number density of electrons inside the post - shock region ( cenbol ) is : @xmath16 where , @xmath17 is mass of a proton . total thermal energy inside the cenbol ( assuming geometrical shape of a cylinder ) of electron temperature @xmath18 which can be radiated by inverse comptonization is , @xmath19 where each particle is assumed to have a thermal energy of @xmath20 . for a two temperature flow , electrons cool faster than protons . hence the proton temperature @xmath21 is higher by a factor of @xmath22 . @xmath21 is obtained from energy conservation ( chakrabarti , 1989 ) at the shock location : @xmath23 where , @xmath24 is the polytropic constant for a relativistic flow of polytropic index @xmath25 , @xmath26 and @xmath27 are the adiabatic sound speeds in the pre- and post - shock flow respectively . assuming totally ionized hydrogen gas , @xmath28 at cooler pre - shock flow , @xmath29 , we get , @xmath30 the cooling rate of the intercepted seed photons by cenbol electrons is calculated as follows : if @xmath31 be the flux of radiation at @xmath32 on the standard disk ( shakura & sunyaev , 1973 ) , the integrated flux from @xmath33 outwards is given by , @xmath34 where , @xmath35 . if a fraction @xmath36 is intercepted by the cenbol and their net energy is enhanced by a factor of @xmath37 by inverse comptonization , we have the cooling rate @xmath38 . accordingly , the cooling time scale is given by , @xmath39 the infall time scale @xmath40 inside cenbol comes from the infall time of matter slowed down by shock compression and turbulence in the post - shock region . @xmath41 the ratio of @xmath42 and @xmath40 after some simplification is given by , @xmath43 where , @xmath44 is the ratio of halo rate and the disk rate . note that terms inside @xmath45 are essential to incorporate physics of comptonization : @xmath46 measures relative abundance of electrons vis - a - vis seed photons , @xmath36 measures the degree of intercepted photons which are comptonized , @xmath37 measures an average factor by which each intercepted seed photon energy is enhanced and finally @xmath15 is the factor by which bulk velocity of the electron cloud ( cenbol ) is slowed down by centrifugal pressure supported shocks and turbulence . most importantly , eq . ( 8) does not explicitly depend on the mass" +"the transport of energy or heat has been intensively studied since fourier introduced his famous law of heat conduction in 1807 . surprisingly , still 200 years later , some fundamental problems remain unsolved@xcite . contrary to our everyday experience , the appearance of diffusive behavior according to fourier s famous law is difficult to obtain from the direction of any underlying microscopic theory . a question of central relevance concerns the classification of the transport properties of a system into _ normal diffusive _ or _ ballistic _ behavior . in the classical domain , it seems to be largely accepted that normal energy transport , i.e. , spatial diffusion instead of ballistic transport or localization , requires the chaotic dynamics of a nonintegrable system @xcite . in the quantum regime , however , the question whether diffusive behavior follows from the underlying theory turns out to be a controversial issue @xcite . this is mostly due to the nontrivial character of the question , how energy is transported on the microscopic scale . amongst the many different techniques of investigating transport in quantum mechanics , let us consider two approaches in more detail here . the first one is the prominent green - kubo formula . derived on the basis of linear response theory it has originally been formulated for electrical transport@xcite . therein , the system is perturbed by an external force , first the electric field , applied to the system . the resulting current of charge is viewed as the response to this external perturbation . finally , the transport coefficient ( conductivity ) follows from a current - current autocorrelation . the same approach is also used in the different case of density driven transport , e.g. , the transport of energy or heat . in such a situation , the current is driven by a much more complicated mechanism ( the coupling of reservoirs to the system ) than simply an external force , which can be nicely written as a term within the hamiltonian of the system . nevertheless , the correlation function is ad hoc transferred to the density driven scenario by replacing the electrical current by the energy or heat current@xcite . however , the justification of this replacement remains a conceptual problem here . one big advantage of this widely used approach is certainly its computability after having diagonalized the system s hamiltonian . a nice overview of results from the kubo formula for spin models can be found , e.g. , in the work by heidrich - meisner@xcite ( for further reading we suggest the comprehensive literature cited therein ) . however , in most cases , a direct analytical solution for an infinite system is not feasible and the interpretation of the results for finite systems seems to be not straight forward . for a finite system , the frequency dependent transport coefficient consists of numerous delta peaks with different weights at frequencies @xmath0 and is zero elsewhere . how to extract the dc - conductivity ( interesting especially for the energy transport ) of the finite system from this result or extrapolate the conductivity for the infinite one is a difficult question@xcite . a different approach to investigate the transport behavior of a system is more connected to the experimental measurement of heat conductivities : the system is directly coupled to heat baths of different temperatures within the theory of open quantum systems@xcite . that means that the liouville von neumann equation , describing the time evolution of the density operator of the system , is extended by incoherent damping terms simulating the influence of the heat baths . how to set up the correct dynamical equation here is highly nontrivial and involves the combination of many subtle approximation schemes . in the case of an improper approach , the derivation can lead to mathematically correct , but physically irrelevant dynamical equations as discussed recently@xcite . having derived a proper quantum master equation ( qme ) , the interpretation of the results for finite systems is relatively easy : after finding the stationary state of the dissipative dynamics , all interesting quantities as currents and energy profiles are simply accessible by computing the expectation value of the respective operator . however , also this approach is restricted to finite systems since a complete analytical solution for larger systems is not available . thus , the extrapolation to infinite systems needs a careful discussion to exclude errors due to the finite size of the investigated models as well . in the present paper , we will consider several model systems according to their transport properties . this is mainly done by the bath coupling method as discussed above , and by comparing with results from the kubo formula . let us start in sect . [ sec:2 ] with an introduction to the qme , the necessary observables and the monte carlo wave - function technique@xcite which is used to integrate the qme . afterwards , we will present the results for several model systems : for chainlike systems in sect . [ sec:3 ] and more complex ones in sect . [ sec:4 ] , followed by our summary and conclusion . the considered system consists of @xmath1 weakly coupled subunits described by the hamiltonian @xmath2 the first part @xmath3 of the hamiltonian contains the local spectra of the subunits . the second part @xmath4 describes the interaction between adjacent sites with the coupling strength @xmath5 . here , we require that the interaction is weak in the sense that the energy contained in the local part is much larger than the energy contained in the interaction part , @xmath6 . more concretely , we will investigate one - dimensional ( 1d ) or quasi-1d chains of two - level atoms or spin-1/2 particles . both , two - level atoms and spins , are described by the same algebra , and thus , it is convenient to use the pauli operators @xmath7 as a suitable operator basis here . the above mentioned weak coupling claim is fullfilled by introducing a local zeeman splitting @xmath8 , where we require that @xmath9 is much larger than the coupling constant @xmath5 . note that this _ weak internal coupling _ constraint is a necessary precondition for the validity of the master equation introduced below , i.e. , we are not able to consider systems with @xmath9 approaching the same magnitude as @xmath5 here . hence , the models described by the hamiltonian given in eq . ( [ eq:1 ] ) are not to be confused with spin chains in cuprates , e.g. , where the local field is always close to zero , and thus , small compared to the coupling strength . however , the discussed models can be seen as spin chains in strong external fields , or simply as weakly coupled chains of two - level atoms as frequently considered in quantum optics and quantum information theory . to investigate the transport properties of these systems , they will be explicitly coupled to independent environments of different temperatures . let us discuss the appropriate ( qme)@xcite to describe this situation in the following section . in general , the derivation of the qme from a microscopic model@xcite ( a system coupled to an infinitely large environment ) relies on some well known approximation schemes the markov@xcite assumption , the born approximation and the secular approximation@xcite . recently , there was a discussion on how to derive a suitable lindblad@xcite qme in a nonequilibrium scenario@xcite , i.e. , an equation to investigate transport in weakly coupled quantum systems . the lindblad form of a qme defines a trace and hermiticity preserving , completely positive dynamical map@xcite , which thus retains all properties of the density operator at all times . in order to approach this dynamical equation the approximations are carefully carried out in a minimally invasive manner , to retain the central nonequilibrium properties of the model . it was shown that this _ nonequilibrium _ lindblad qme is in very good accord with the results of the redfield master@xcite equation ( non - lindbladian ) , contrary to the standard lindblad qme in the weak coupling limit@xcite . in a nonequilibrium investigation , one needs two heat baths at different temperatures _ locally _ coupled to the system , i.e. , the heat baths couple only to a subunit at the edge of the system . the qme of such a situation yields @xmath10 _ { } } + { \mathcal{d}}_{l}({\hat{\rho } } ) + { \mathcal{d}}_{r}({\hat{\rho}})\,,\ ] ] where the dissipator @xmath11 refers to the left heat bath and @xmath12 to the right one , depending on the full density operator @xmath13 of the system , i.e. , the state of the chain described by the hamiltonian ( [ eq:1 ] ) . both dissipators depend on the coupling strength @xmath14 between system and bath as well as the temperature of the bath , respectively . besides those incoherent damping terms , eq . ( [ eq:2 ] ) contains a coherent part containing the hamiltonian ( [ eq:1 ] ) of the system . the dissipator describing the heat bath coupled to a subunit at the edge of the system yields @xmath15_{+}}\big)\ ] ] with @xmath16 for the left and @xmath17 for the right heat bath . the lindblad operators @xmath18 are given by @xmath19 with the creation and annihilation operators @xmath20 . here , the operators given in eqs . ( [ eq:4a ] ) and ( [ eq:4b ] ) belong to the left bath and those in eqs . ( [ eq:4c ] ) and ( [ eq:4d ] ) to the right one . the coefficient matrices depend on the respective bath temperature @xmath21 and are defined as @xmath22 according to the rates @xmath23 with the bath coupling strength @xmath14 . this concrete form of the @xmath24-matrices follows from a phenomenological ansatz for the spectral density of the environment , here chosen to be of ohmic@xcite kind . a remarkable property of eq . ( [ eq:3 ] ) is that it can be brought into lindblad form by diagonalizing the coefficient matrices @xmath24 . the complete dissipative part of eq . ( [ eq:2 ] ) then reads @xmath25_{+}}\big)\ ] ] with @xmath26 being linear combinations of the operators @xmath18 defined in eqs . ( [ eq:4a])-([eq:4d ] ) and @xmath27 being non - negative numbers . that it is indeed possible to derive a lindbladian qme is very important here , since a standard stochastic unravelling of this special type of equation is feasible . although extended stochastic schemes exist for the solution of general qmes such as , e.g. , the redfield equation @xcite , these methods have turned out to be less efficient , in general , than the standard approach . the most interesting state of a nonequilibrium scenario is the local equilibrium state , i.e. , the stationary state of the qme ( [ eq:2 ] ) . this state can be characterized by two central observables the energy gradient and the energy current . let us use @xmath28 as a local energy density at site @xmath29 with @xmath30 being the state of the system at time @xmath31 . since we are investigating internally weakly coupled subunits in the limit @xmath32 the local energy density is approximated by the local hamiltonian here . therefore , we neglect completely the contributions to the local energy by the interaction . however , due to the smallness of @xmath5 , these parts would be very small contributions to the above given energy density , and thus , would not dramatically change the results . in order to obtain a current operator between two adjacent sites in the system , we consider the time evolution of the local energy operator given by the heisenberg equation" +"the discovery of very bright quasars , with luminosities @xmath10 , at redshift @xmath11 in the sloan digital sky survey ( sdss ) suggests that some smbhs as massive as a few@xmath12 already existed when the universe was less than 1 gyr old ( see , e.g. , fan 2006 for a review ) . the presence of these smbhs presents a puzzle . metal free stars , with masses @xmath13 , are expected to form at redshifts as high as @xmath14 ( abel et al . 2002 ; bromm et al . 2002 ; yoshida et al . 2008 ) , and leave behind remnant bhs with similar masses ( heger et al . however , the natural time - scale , i.e. the eddington time , for growing these seed bhs by @xmath15 orders of magnitude in mass is comparable to the age of the universe ( e.g. haiman & loeb 2001 ) . this makes it difficult to reach @xmath16 without a phase of rapid ( super eddington ) accretion , unless a list of optimistic assumptions are made in hierarchical merger models , in which multiple seed bhs are allowed to grow without interruption , and to combine into a single smbh ( haiman 2004 ; yoo & miralda - escud 2004 ; bromley et al . 2004 ; shapiro 2005 , volonteri & rees 2006 ; li et al . 2007 ; tanaka & haiman 2009 ) . an alternative class of explanations involves rapid gas accretion or collapse . in this family of models , primordial gas collapses rapidly into a smbh as massive as @xmath17 ( oh & haiman 2002 ; bromm & loeb 2003 ; koushiappas et al . 2004 ; lodato & natarajan 2006 ; spaans & silk 2006 ; begelman et al . 2006 ; volonteri et al . 2008 ; wise & abel 2008 ; regan & haehnelt 2009 ; shang et al . 2010 ) , possibly by accreting onto a pre existing smaller seed bh ( volonteri & rees 2005 ) , or going through the intermediate state of a very massive star ( bromm & loeb 2003 ) , a dense stellar cluster ( omukai et al . 2008 ) , or a `` quasistar '' ( begelman et al . 2008 ) . these so called `` direct collapse '' models involve metal free gas in relatively massive ( @xmath18 ) dark matter halos at redshift @xmath19 , with virial temperatures @xmath0k . the gas that cools and collapses in these halos must avoid fragmentation , shed angular momentum efficiently , and collapse rapidly . these conditions are unlikely to be met , unless the gas remains `` warm '' , i.e. at temperatures @xmath20k . in particular , in recent numerical simulations , shang et al . ( 2010 ) found that the gas in such halos , when collapsing in isolation , forms @xmath4 efficiently , and cools to temperatures of @xmath21 k. although no fragmentation was seen , the gas could ultimately fragment on smaller scales that have not yet been resolved ( e.g. turk et al . 2009 ) . more importantly , even if fragmentation was avoided , the cold gas flows inward at low velocities , near the sound speed of @xmath22 , with a correspondingly low accretion rate of @xmath23 . this results in conditions nearly identical to those in the cores of lower - mass minihalos ; extensive ultra high resolution simulations have concluded that the gas then forms a single @xmath24 star ( abel et al . 2002 ; bromm et al . 2002 ; yoshida et al . 2008 ) or perhaps a massive binary ( turk et al . 2009 ) , rather than a supermassive star or bh . @xmath4cooling in early galaxies may be avoided when the gas is exposed to an intense uv flux @xmath25 , either directly photo dissociating @xmath4 ( in the lyman werner bands near a photon energy of @xmath26ev ) or photo dissociating the intermediary @xmath27 ( at photon energies @xmath28ev ) . requiring the photo - dissociation timescale , @xmath29 , to be shorter than the @xmath30formation timescale , @xmath31 , generically yields a critical flux that increases linearly with density , @xmath32 . since the gas in halos with @xmath0k can cool via atomic lyman @xmath33 radiation and loose pressure support , it inevitably collapses further . as a result , in these halos , the critical flux is high , @xmath34 ( depending on the assumed spectral shape ; shang et al . 2010 ; see also omukai 2001 and bromm & loeb 2003 who found similar , but somewhat higher values ) , which exceeds the expected level of the cosmic uv background at high redshifts . only a small subset of all @xmath0k halos , which have unusually close and bright neighbors , may see a sufficiently high flux ( dijkstra et al . 2008 ) . in order to avoid fragmentation , the gas in these halos must also remain essentially free of any metals and dust ( omukai et al . 2008 ) , which may be incompatible with the presence of such nearby luminous galaxies . in this paper , we consider a different possibility to keep the gas warm , relying on heating by a primordial magnetic field . several mechanisms have been proposed to produce a global primordial magnetic field ( pmf ) , with a field strength of order 1 ( comoving ) ng , during inflation and/or during various phase transitions in the early universe ( see , e.g. widrow 2002 and references therein ) . if present , the pmf can be strongly amplified by flux freezing inside a collapsing primordial gas , affecting @xmath4formation and cooling . sethi et al . ( 2008 ; hereafter s08 ) have shown that 0.2 - 2 ng fields can significantly enhance the @xmath4 fraction during the early stages of collapse . schleicher et al . ( 2009 ) found similar results , and emphasized that at the high densities ( @xmath35 ) corresponding to later stages of the collapse , magnetic heating from 0.1 - 1ng fields results in significantly elevated temperatures . in this paper , we consider field strengths higher than those in the two previous studies by s08 and schleicher et al . our main result is that , in analogy with the uv irradiation , there exists a critical magnetic field , which leads to a bifurcation of behaviors . if the pmf has a strength above @xmath36 ng , then the collapsing gas is kept warm ( @xmath1 k ) until it reaches the critical density @xmath3 at which the roto vibrational states of @xmath4 approach local thermodynamic equilibrium . @xmath4cooling then remains inefficient , and the temperature stays near @xmath5k , even as the gas collapses further . on the other hand if @xmath37 , @xmath4cooling is delayed , but the gas eventually cools down below @xmath38k . the critical magnetic field strength we find is a factor of @xmath39two higher than the existing upper limit from the cmb anisotropies ( yamazaki 2010 ; see more discussion in 5 below ) . however , it can be realized in the rare @xmath7 regions of the spatially fluctuating @xmath8field . as we argue , the abundance of halos located in these high field regions is sufficient to explain the number of the @xmath9 quasars observed in the sdss . the thermal and ionization history of gas collapsing into a high redshift halo , in the presence of a primordial magnetic field , is described in detail in s08 . the dissipation of the magnetic field owing to ambipolar diffusion and to decaying turbulence in the post recombination era can substantially alter the ionization fraction and temperature of the gas , even beginning before the halo collapse ( sethi & subramanian 2005 [ hereafter ss05 ] ; yamazaki et al . 2006 ; s08 ; schleicher et al . 2009 ) . here we extend the analysis of s08 up to a higher particle density in the collapsing halo , and explore higher magnetic field strengths . in addition , we made the following changes : ( a ) we track the density evolution of gas in a collapsing halo with the model of dekel and birnboim ( 2006 ; this affects the compressional heating rate ) , ( b ) we updated the @xmath40 chemistry network ; specifically , we use the recent compilation in shang et al . ( 2010 ; the most significant change is an increase in the collisional @xmath4dissociation rate ) . the evolution of the ionization fraction ( @xmath41 ) , magnetic field energy density ( @xmath42 ) , temperature ( @xmath43 ) , and @xmath4 molecule fraction ( @xmath44 ) are described by the equations @xmath45 c + \nonumber \\ & & + \ , \gamma_e n_b ( 1-x_e)x_e \\ { de_b \over dt } & = & { 4 \over 3 } { \dot \rho \over \rho } - \left({de_b \over dt}\right)_{\rm turb } - \left({de_b \over dt}\right)_{\rm ambi } \\ { dt \over dt}&=&{2 \over 3 } { \dot{n_b } \over n_b } t+k_{ic } x_e ( t_{\rm cbr } -t ) + { 2 \over 3 n_b k_b } ( l_{\rm heat } -l_{\rm cool } ) \ , , \\ { d x_{\rm \scriptscriptstyle h_2 } \over dt}&=&k_m n_b x_e ( 1-x_e-2 x_{\rm \scriptscriptstyle h_2 } ) - k_{\rm des } n_b x_{\rm \scriptscriptstyle h_2 } \,.\end{aligned}\ ] ] the symbols here have their usual meaning ; further details and relevant processes are discussed in s08 . we list here only the processes that have been added or updated . most of these processes relate to the formation and destruction of @xmath40 . the net rate of formation of @xmath40 through the @xmath46 channel is given by : @xmath47 the notation of the reaction rates follows the appendix of shang et al . ( 2010 ) , except that @xmath48 is the rate of destruction of @xmath49 by cmb photons , which , in our case , is important before the collapse regime ( eq . 8 in s08 ) . the net destruction rate of @xmath50 , @xmath51 , is : @xmath52 the dominant reaction rates for the range of ionization fractions , densities , and temperatures we obtain in the entire range of our models are : @xmath53 , @xmath54 , @xmath55 , @xmath56 , and @xmath57 , assumed to be zero here , and @xmath56 could become more important if we used the rates as given by schleicher et al . ( 2009 ) and capitelli et al . if these rates are used , then the critical value of @xmath58 needed to destroy @xmath40 in the collapsing halos decreases to @xmath59 ( cf . figure 1 below ) . ] the cooling processes that dominate @xmath60 in primordial gas in the density and temperature range we consider are : ( a ) compton cooling @xmath61 ( eq . 15 in s08 ) , ( b ) atomic h cooling ( eq . 16 in s08 ) , and ( c ) @xmath4 molecular cooling ( galli & palla 1998 ) . the heating rate @xmath62 is given by the magnetic field decay owing to decaying turbulence @xmath63 and ambipolar diffusion @xmath64 . in practice , we find that ambipolar diffusion always dominates in our case ; the dissipation rate is given for this process by ( cowling 1956 ; shu 1992 ; ss05 ) : @xmath65 all quantities in eq . ( [ eq : amdif ] ) are expressed at redshift @xmath66 . the time dependence of the decay rate is given by @xmath67 during the pre - collapse stage , and @xmath68 during the collapse phase . here @xmath69 is the power spectrum of the" +"liquid state theory experienced remarkable successes in the understanding of the properties of dense , simple fluids @xcite and more recently , of complex liquids , like colloidal suspensions or globular polymers @xcite . however a fully quantitative description of phase transitions can not be obtained by standard integral equations or diagrammatic expansions and requires specially devised approaches . the freezing transition , often dominated by geometrical constraints , is usually understood on the basis of density functional theory @xcite , while fluctuation induced phenomena , like the liquid - vapour transition , need the completely different theoretical framework provided by the renormalization group method @xcite . the hierarchical reference theory of fluids ( hrt ) was formulated more than 25 years ago as an attempt to reconcile the renormalization group ( rg ) approach , an extremely general and successful theory of second order phase transitions formulated in field - theoretical language , and the microscopic point of view adopted within liquid state theory @xcite . the main goal of hrt was to develop a unified theory able to reproduce the universal properties at the critical point , as obtained by rg techniques , together with the non universal features of realistic models of fluids , present both in the critical region ( e.g. critical density and temperature , short range correlations ) as well as far from the critical point . a comprehensive presentation of the hrt formalism , including a detailed derivation of the basic equations and an extensive discussion of its critical properties , can be found in ref . the earliest applications of hrt to simple fluids and to the ising model are briefly discussed in the same reference . however , most of the more interesting results and extensions were developed later . by now it is therefore appropriate to summarize the advances in hrt which took place in the last decade , providing a guidance to the most significant recent applications . such a critical discussion of the hrt formalism also gives the opportunity to emphasize its relationship with other theoretical tools which have been independently developed in different frameworks . since the early nineties , sophisticated functional , non perturbative rg techniques ( nprg ) were devised within field theory , leading to a boost of applications to many and diverse physical situations : from particle physics , to quantum many body theory , to classical statistical mechanics @xcite . only recently it was recognized that , despite the different language and physical context , a deep relation ties hrt and nprg @xcite , whose developments have proceeded quite independently for 20 years in distinct scientific communities . to introduce the hierarchical reference theory of fluids it is convenient to refer to a system of @xmath0 classical particles confined in a volume @xmath1 , in spatial dimension @xmath2 , interacting via a pairwise potential @xmath3 . generalizations to classical spin systems , quantum fluids and magnets do not present additional difficulties and will be examined in the next sections . the grand canonical partition function @xmath4 of the model is written as : @xmath5= \sum_n \frac{z^{n}}{n!}\int { \rm d } { \bf r_1} ... {\rm d } { \bf r_n } \ , e^ { -\beta\sum_{i < j } v({\bf r}_i - { \bf r}_j)-\beta\sum_i u({\bf r}_i ) } \label{gran}\ ] ] where the fugacity @xmath6 is related to the chemical potential @xmath7 and to the thermal wavelength @xmath8 by @xmath9 with @xmath10 . an external field @xmath11 is also included for convenience and @xmath4 is considered as a functional of @xmath11 . a detailed derivation of the hrt equations and a thorough discussion of their properties can be found in ref . @xcite via diagrammatic methods @xcite . here we provide a brief introduction of the physical content of the method together with a simpler , less technical derivation . since the pioneering works by van der waals , a large part of liquid state theory is based on the idea that the strongly repulsive short range interaction , distinctive of the interatomic potentials , provides a constraint to the available phase space , determining an important contribution to the entropy of the fluid , while the mainly attractive , regular part of @xmath3 dominates the internal energy . this is certainly true for the special , although prototypical , case in which @xmath3 has hard core at short distances , but holds also in the general case of soft core potentials . the different role played by the singular and regular contributions to the interparticle potential is manifest in lattice gas models , where particles live on the sites of a lattice : hard core repulsion between particles gives rise to the single occupancy constraint , which allows to map the lattice gas onto an ising model with a spin - spin interaction proportional to the regular part of the interparticle potential . mean field approaches developed for specific models , like van der waals equation in simple fluids or weiss theory in magnets , suggest that only the latter interaction triggers the order parameter fluctuations , responsible for the order - disorder transitions . in fluid models , both the singular and the regular part contributions are included in the interaction @xmath3 which should then be split in a reference , singular , part @xmath12 and in the regular remainder @xmath13 . the partition function ( [ gran ] ) can be written in a suggestive form by introducing the configurational density "" @xmath14 whose thermal average is just the density profile @xmath15 , which reduces to the ordinary average density @xmath16 for @xmath17 . in the following , the properties of the reference system will be considered as known . the fluctuating order parameter of the liquid - vapour phase transition in fluids is then identified as the configurational density and @xmath4 is written as @xmath5 = \sum_n\frac{(z\,e^{-\frac{1}{2}\phi(0)})^{n}}{n!}\ , \int { \rm d } { \bf r_1} ... {\rm d } { \bf r_n } \ , e^{-\beta h_r}\ , e^{\frac{1}{2}\int { \rm d}{{\bf x}}_1 \,{\rm d}{{\bf x}}_2 \phi({{\bf x}}_1-{{\bf x}}_2 ) \ , \hat\rho({{\bf x}}_1 ) \,\hat\rho({{\bf x}}_2 ) } \label{xi1}\ ] ] where the regular dimensionless interaction has been defined as @xmath18 and the reference hamiltonian is @xmath19 according to the previous remarks , @xmath20 defines a non - trivial integration measure , limiting the phase space available to the particles . by factorizing the reference @xmath0-particle canonical partition function @xmath21 , ( [ xi1 ] ) can be also expressed as : @xmath5 = \sum_n\frac{(z\,e^{-\frac{1}{2}\phi(0)})^{n}}{n!}\,e^{-\beta\,a_r(n ) } \,\left \langle \exp\left ( \frac{1}{2}\int \frac{{\rm d}{{\bf q}}}{(2\pi)^d } \,\tilde\phi({{\bf q}})\ , \hat\rho({{\bf q}})\,\hat\rho(-{{\bf q}})\right ) \right \rangle_r \label{xi2}\ ] ] where the average @xmath22 refers to the gibbs measure of the reference fluid , and the fourier transforms of the potential @xmath23 and of the density fluctuations @xmath24 have been defined . such a form is particularly suitable as a starting point for a reformulation of wilson s renormalization group picture in hamiltonian systems . in the momentum space rg formulation @xcite , a sequence of systems , labeled by a wave - vector @xmath25 , is defined by allowing density fluctuations only at wave - vectors @xmath26 larger than the cut - off @xmath25 . the evolution of the physical properties of the model is then followed starting from the limit @xmath27 , where the system reduces to the reference one with a shift @xmath28 in the chemical potential , to the final value @xmath29 , where the cut - off is removed and the original partition function @xmath4 is retrieved . expression ( [ xi2 ] ) can easily accommodate the presence of a cut - off @xmath25 : @xmath30 = \sum_n\frac{(z\,e^{-\frac{1}{2}\phi(0)})^{n}}{n!}\,e^{-\beta\,a_r(n ) } \,\left \langle \exp\left ( \frac{1}{2}\int \frac{{\rm d}{{\bf q}}}{(2\pi)^d } \,\tilde\phi({{\bf q}})\,\theta ( q - q)\ , \hat\rho({{\bf q}})\,\hat\rho(-{{\bf q}})\right ) \right \rangle_r \label{xiq}\ ] ] where @xmath31 is the heaviside step function . this definition embodies basic principle of hrt : a cut - off in density fluctuations is equivalent to a cut - off in the regular part of the two body interaction for the evaluation of the fluctuation corrections to the free energy , leading to the definition of a cut - off dependent potential @xmath32 . it is customary to perform a legendre transform defining a cut - off dependent helmholtz free energy @xmath33 as a functional of the density profile @xmath15 : @xmath34 = -kt\,\log \xi_q[u({{\bf r } } ) ] - \int { \rm d}{{\bf r}}\ , \left ( u({{\bf r}})-kt\,\log z\right ) \,\rho({{\bf r } } ) \label{leg0}\ ] ] finally , it is also convenient to include in the definition of the free energy functional the mean field contribution due to the residual interaction @xmath35 : @xmath36 = a_q[\rho({{\bf r } } ) ] + \frac{1}{2}\int { \rm d}{{\bf r}}\,{\rm d}{{\bf r}}^\prime \left [ w({{\bf r}}-{{\bf r}}^\prime ) - w_q({{\bf r}}-{{\bf r}}^\prime)\right ] \ , \rho({{\bf r } } ) \,\rho({{\bf r}}^\prime ) \label{leg}\ ] ] in this way , for @xmath37 , @xmath38 reduces to the mean field approximation of the full free energy , which is recovered as @xmath39 . this way to artificially eliminate the long wave - length fluctuations from the thermodynamics is referred to as sharp cut - off "" . however it is often more convenient to deal with a smooth cut - off "" procedure , where the @xmath40-function in the definition of @xmath41 is substituted by a smoothed step function , denoted in the following as @xmath42 which is continuous and differentiable for every @xmath43 and tends to the step function in the @xmath44 limit : @xmath45 after having defined the cut - off dependent free energy , @xmath38 via eq . ( [ leg ] ) , the next step is to write the exact evolution ( or flow ) equation governing the change in the physical properties of the model when the cut - off @xmath25 is varied . this goal is most easily achieved in the smooth cut - off formulation , where an infinitesimal increase of the cut - off @xmath25 leads to an infinitesimal change in the potential @xmath41 . according to standard first order perturbation theory @xcite we get , in a uniform fluid , @xmath46 where @xmath47 is the total correlation function of a fluid interacting through a potential @xmath48 and @xmath49 . this smooth cut - off hrt equation has been obtained for the first time in ref . @xcite as an attempt to apply the renormalization group ideas to microscopic models . note that the total correlation function @xmath50 rather than the radial distribution function @xmath51 appears in the evolution equation ( [ evol1 ] ) because the mean field contribution has been subtracted in the definition of the @xmath25-dependent free energy ( [ leg ] ) . the total correlation function can be conveniently expressed in terms of the direct correlation function @xmath52 by use of the ornstein - zernike relation : @xmath53 the limit @xmath54 in eq . ( [ wqsmooth ] ) requires some care , as already recognized in the description of the sharp cut - off hrt equation and also discussed in field theoretical approaches @xcite , because of the emergence of a discontinuity in @xmath55 precisely on the same surface @xmath56 where the @xmath57-function singularity develops in @xmath58 . such a discontinuity originates from the random phase contribution to the exact direct correlation function , being the single term where the regular part of the potential appears outside any integration . if @xmath59 denotes the direct correlation function of the reference fluid , the first terms of the perturbative expansion read @xmath60 all the remaining contributions , being integrated , do not display discontinuities in the whole @xmath26-space . this suggests to introduce a modified correlation function @xmath61 which remains continuous also in the sharp cut - off limit @xmath54 :" +"the linear failure rate distribution with parameters @xmath1 and @xmath2 , ( @xmath3 ) which is denoted by @xmath4 , has the cumulative distribution function ( cdf ) @xmath5 and probability density function @xmath6 note that if @xmath7 and @xmath8 , then the lfr distribution is reduced to exponential distribution with parameter @xmath9 ( @xmath10 ) , and if @xmath11 and @xmath12 then we can obtain the rayleigh distribution with parameter @xmath13 ( @xmath14 ) . a basic structural properties of @xmath15 is that it is the distribution of minimum of two independent random variables @xmath16 and @xmath17 having @xmath18 and @xmath14 distributions , respectively ( sen and bhattachrayya , 1995 ) . if @xmath19 denotes the cdf of a random variable then a generalized class of distributions can be defined by @xmath20 for @xmath21 and @xmath22 , where @xmath23 is the incomplete beta function ratio and @xmath24 is the incomplete beta function . many authors considered various forms of @xmath19 and studied their properties : eugene et al . ( 2002 ) ( beta normal distribution ) , nadarajah and kotz ( 2004 ) ( beta gumbel distribution ) , nadarajah and gupta ( 2004 ) and barreto - souza et al . ( 2011 ) ( beta fr@xmath25chet distribution ) , famoye et al . ( 2005 ) , lee et al . ( 2007 ) and cordeiro et al . ( 2008 ) ( beta weibull distribution ) , nadarajah and kotz ( 2006 ) ( beta exponential distribution ) , akinsete et al . ( 2008 ) ( beta pareto distribution ) , silva et al . ( 2010 ) ( beta modified weibull distribution ) , mahmoudi ( 2011 ) ( beta generalized pareto distribution ) , cordeiro et al . ( 2011 ) ( beta - exponentiated weibull distribution ) , cordeiro et al . ( 2011 ) ( beta - weibull geometric distribution ) , singla et al . ( 2012 ) ( beta generalized weibull distribution ) , cordeiro et al . ( 2012 ) ( beta generalized gamma distribution ) and cordeiro et al . ( 2012 ) ( beta generalized normal distribution ) . in this article , we propose a new four parameters distribution , referred to as the blfr distribution , which contains as special sub - models : the beta exponential ( be ) , beta rayleigh ( br ) , generalized linear failure rate ( glfr ) and linear failure rate ( lfr ) distributions , among others . the main reasons for introducing blfr distribution are : ( i ) the additional parameters introduced by the beta generalization is sought as a means to furnish a more flexible distribution . ( ii ) some modeling phenomenon with non - monotone failure rates such as the bathtub - shaped and unimodal failure rates , which are common in reliability and biological studies , take a reasonable parametric fit with this distribution . ( iii ) the blfr distribution is expected to have immediate application in reliability and survival studies . ( iv ) blfr distribution shows better fitting , more flexible in shape and easier to perform and formula for modeling lifetime data . the reminder of the paper is organized as follows : in section 2 , we define the blfr distribution and outline some special cases of the distribution . we investigate some properties of the distribution in this section . some of these properties are the limit behavior and shapes of the pdf and hazard rate function of the blfr distribution . section 3 provides a general expansion for the moments of the blfr distribution . in section 4 , we discuss maximum likelihood estimation and calculate the elements of the observed information matrix . application of the blfr distribution is given in the section 5 . a simulation study is performed in section 6 . finally , section 7 concludes the paper . consider that @xmath26 is the density of the baseline distribution . then the probability density function corresponding to ( [ eq.fb ] ) can be written in the form @xmath27 we now introduce the blfr distribution by taking @xmath28 in ( [ eq.fb ] ) to be the cdf ( [ eq.flfr ] ) of the lfr distribution . hence , the blfr density function can be written as @xmath29 and we use the notation @xmath30 . the hazard rate function of blfr distribution is given by @xmath31 plots of pdf and hazard rate function of the blfr distribution for different values of it s parameters are given in fig . [ fig.den ] and fig . [ fig.hz ] , respectively . 1 . if @xmath32 , then we get the generalized linear failure rate distribution ( @xmath33 ) which is introduced by sarhan and kundu ( 2009 ) . 2 . if @xmath32 and @xmath7 , then we get the generalized exponential distribution ( ge ) ( gupta and kundu , 1999 ) . 3 . if @xmath32 and @xmath11 , then we get two - parameter burr x distribution which is introduced by surles and padgett ( 2005 ) and also is known as generalized rayleigh distribution ( gr ) ( kundu and raqab , 2005 ) . if @xmath34 , then ( 2.2 ) reduces to the linear failure rate distribution ( @xmath35 ) distribution . if @xmath7 , then we get the beta exponential distribution ( @xmath36 ) which is introduced by nadarajah and kotz ( 2006 ) . if @xmath11 , then we get the beta rayleigh distribution ( @xmath37 ) which is defined by akinsete and lowe ( 2009 ) and is a special case of beta weibull distribution ( famoye et al . , 2005 ) . if the random variable @xmath38 _ _ has blfr distribution , then the random variable @xmath39 satisfies the beta distribution with parameters @xmath40 and @xmath41 . therefore , @xmath42 satisfies the beta exponential distribution with parameters 1 , @xmath40 and @xmath41 ( @xmath43 ) . 8 . if @xmath44 and @xmath45 , where @xmath46 and @xmath47 are positive integer values , then the @xmath48 is the density function of @xmath46th order statistic of lfr distribution . the following result helps in simulating data from the blfr distribution : if @xmath49 follows beta distribution with parameters @xmath40 and @xmath41 , then @xmath50 follows blfr distribution with parameters @xmath51 , and @xmath41 . for checking the consistency of the simulating data set form blfr distribution , the histogram for a generated data set with size 100 and the exact blfr density with parameters @xmath52 , @xmath53 , @xmath54 , and @xmath55 , are displayed in fig [ fig.gd ] ( left ) . also , the empirical distribution function and the exact distribution function is given in fig [ fig.gd ] ( right ) . in this section , limiting behavior of pff and hazard rate function of the blfr distribution and their shapes are studied . * theorem 1 . * let @xmath48 be the pdf of the blfr distribution . the limiting behaviour of @xmath56 for different values of its parameters is given bellow : i. : : if @xmath57 then @xmath58 . ii . : : if @xmath59 then @xmath60 . iii . : : if @xmath61 then @xmath62 . : : @xmath63 . * proof : * the proof of parts ( i)-(iii ) are obvious . for part ( iv ) , we have @xmath64 it can be easily shown that @xmath65 and the proof is completed . * theorem 2 . * let @xmath48 be the density function of the blfr distribution . the mode of @xmath56 is given in the following cases : i. : : if @xmath57 and @xmath67 then @xmath48 has a unique mode in @xmath68 i. : : if @xmath57 and @xmath69 then @xmath48 has a unique mode in @xmath70 . ii . : : if @xmath59 then @xmath48 has at least one mode . * proof : * the proof is obvious and is omitted . * theorem 3 . * let @xmath71 be the hazard rate function of the blfr distribution . consider the following cases : i. : : if @xmath57 and @xmath72 then blfr distribution has an increasing hazard rate function . ii . : : if @xmath73 and @xmath72 then the hazard rate function of the blfr distribution is an increasing . : : if @xmath74 blfr distribution has a decreasing hazard rate function for @xmath75 , and @xmath71 is constant for @xmath76 . : : if @xmath77 and @xmath72 then @xmath71 is a bathtub - shaped . * proof : * \i . if @xmath57 then @xmath78 . therefore @xmath79 which is an increasing and linear function with respect to @xmath80 \ii . consider @xmath81 it implies that @xmath82 for @xmath83 and also , it is increasing with respect to @xmath84 . we have @xmath85 . now , rewriting the blfr density as function of @xmath86 , @xmath87 say , we obtain @xmath88 therefore , we have @xmath89 and we conclude that the hazard function of blfr distribution is increasing . \iii . if @xmath7 then @xmath90 and @xmath91 thus we have @xmath92 where @xmath93 , which implies the decreasing ( increasing ) hazard rate functions in this cases . \iv . it is difficult to determine analytically the regions corresponding to the upside - down bathtub shaped ( unimodal ) and bathtub - shaped hazard rate functions for the blfr distribution . however , by some graphical analysis we can shows : bathtub - shaped hazard rate function correspond to @xmath77 and @xmath72 . the proof is completed . here , we present some representations of cdf , pdf , and the survival function of blfr distribution . the mathematical relation given below will be useful in this section . if @xmath41 is a positive real non - integer and @xmath94 , then @xmath95 and if @xmath41 is a positive real integer , then the upper of the this summation stops at @xmath96 , where @xmath97 \1 . we can express ( [ eq.fb ] ) as a mixture of distribution function of generalized lfr distributions as follows : @xmath98 where @xmath99 and @xmath100 is distribution function of a random variable which has a generalized lfr distribution with parameters @xmath9 , @xmath13 , and @xmath101 . we can express ( [ eq.fblfr ] ) as a mixture of density function of generalized lfr distributions as follows : @xmath102 where @xmath103 is density function of a random variable which has a generalized lfr distribution with parameters @xmath9 , @xmath13 , and @xmath101 . the cdf can be expressed in terms of the hypergeometric function and the incomplete beta function ratio ( see , cordeiro and nadarajah , 2011 ) in the following way : @xmath104 where @xmath105 . the @xmath106th moment of blfr distribution can be expressed as a mixture of the @xmath106th moment of generalized lfr distributions as follows : @xmath107 where @xmath108 is density function of a random variable @xmath109 which has a generalized lfr distribution with parameters @xmath9 , @xmath13 , and @xmath101 . consider @xmath110 is a random sample from blfr distribution . the log - likelihood function for the vector of parameters @xmath111 can be written as @xmath112 where @xmath113 . the log - likelihood can be maximized either directly or by solving the nonlinear likelihood equations obtained by differentiating ( [ eq.like ] ) . the components of the score vector @xmath114 _ _ are given by @xmath115 where @xmath116 is the digamma function . for interval estimation and hypothesis tests on the model parameters , we require the observed information matrix . the @xmath117 unit observed information matrix @xmath118 is obtained as @xmath119.\ ] ] where the expressions for the elements of @xmath120 are @xmath121 @xmath122 where @xmath123 is the trigamma function . under conditions that are fulfilled for parameters in the interior" +"the classical cosmology based on the equations of general relativity involving the principles of thermodynamics , hydrodynamics , the plasma theory and the field theory comes across a number of conceptual difficulties known as the problems of standard big - bang cosmology @xcite . these are the problems of singularity , size , age , flatness , total entropy and total mass of the universe , large - scale structure , dark matter , isotropy of the cosmic background radiation and others . the various models were proposed for the solution of these problems . the inflationary model @xcite is the most popular one . there are alternative approaches which use the idea that in the early universe the fundamental constants ( velocity of light , gravitational constant , fine - structure constant ) had the values different from the modern @xcite . the observations of type ia supernovae ( sne ia ) indicate that our universe is accelerating @xcite . this conclusion which appeared as partly unexpected for the cosmologists a few years ago nowadays practically does not called in question @xcite . the concept of a dark energy was proposed for the explanation of this phenomenon @xcite and the modern investigations in this field are directed toward filling of this idea with concrete contents @xcite . the presence of the cosmological problems points to incompleteness of our knowledge about the universe . it is generally accepted that the conclusions of classical theory of gravity can not be extrapolated to the very early epoch . at the planck scales one must take into account the quantum effects of both matter and gravitational fields . there can not be any doubt that our universe today contains the structural elements which bear the traces of comprehensive quantum processes in preceding epochs . the small cosmic microwave background anisotropy and observed large - scale structure of the universe @xcite can be given as necessary examples ( see below ) . the application of basic ideas underlying quantum theory to a system of gravitational and matter fields runs into difficulties of a fundamental character which do not depend on the choice of a specific model . the problem of separation of true degrees of freedom under the construction of quantum gravity becomes of fundamental importance @xcite . it is commonly thought that the main reason behind such difficulties is that there is no natural way to define a spacetime event in general covariant theories @xcite . at the present time these difficulties are not overcome in the most advanced versions of quantum gravity . also the quantum gravity can not rely on experimental data @xcite . therefore it is appropriate to construct the consistent quantum theory within the framework of the simple ( toy ) exactly soluble cosmological model . as it is well known the model of a homogeneous , isotropic universe ( friedmann - robertson - walker model ) describes good enough the general properties of our universe . in this paper we study the model of quantum universe proposed in @xcite . it does not meet with the problems mentioned above and comes to the frw model with positive spatial curvature within the limits of large quantum numbers . in section 2 we propose the method of removing ambiguities in specifying the time variable in the frw model by means of modification of the action functional and find the solutions of obtained classical field equations . the section 3 is devoted to the quantum theory for a system of gravitational and matter fields . here we formulate the equation which is an analog of the schrdinger equation and turns into the wheeler - dewitt one for the minisuperspace model in special case . we concentrate our attention on study of the quantum universe which can be found in a region that is accessible to a classical motion inside the effective barrier formed by the interaction of the fields . we discuss the properties of the wave function of the universe and study the universe in low - lying and highly exited quasistationary states on the basis of exact solution of proposed quantum equation . in this section we calculate the proper dimension of the nonhomogeneities of matter density and the amplitude of the fluctuations of the cosmic background radiation temperature in highly exited state of the universe and propose a new possible quantum mechanism of their origin . the results are compared with the observed parameters of our universe . the flatness of the universe and the large value of the entropy today receive their natural explanation . the observed accelerated expansion emerges as a macroscopic manifestation of the quantum nature of the universe . throughout the paper the notation _ universe _ ( with capital letter u ) relates to our universe , while _ universe _ ( with small letter u ) corresponds to arbitrary cosmological system of considered type . for simplicity we restrict our study to the case of minimal coupling between geometry and the matter . considering that scalar fields play a fundamental role both in quantum field theory and in the cosmology of the early universe we assume that , originally , the universe was filled with matter in the form of a scalar field @xmath0 with some potential @xmath1 . as we shall see the replacement of the entire set of actually existing massive fields by some averaged massive scalar field seems physically justified . assuming that the field @xmath0 is uniform and the geometry is defined by the robertson - walker metric , we represent the action functional in the conventional form @xmath2 . \label{1}\end{aligned}\ ] ] here @xmath3 is the time parameter that is related to the synchronous proper time @xmath4 by the differential equation @xmath5 , where @xmath6 is a function that specifies the time - reference scale , @xmath7 is a scale factor ; @xmath8 and @xmath9 are the momenta canonically conjugate with the variables @xmath10 and @xmath0 , respectively . the hamiltonian @xmath11 is given by @xmath12 \equiv n\ , { \cal r } , \label{2}\ ] ] where the @xmath10 is taken in units of the length @xmath13 , @xmath14 is the planck length , and @xmath0 in units of @xmath15 . the energy density will be measured in units @xmath16 . the function @xmath17 plays the role of a lagrange multiplier , and the variation @xmath18 leads to the constraint equation @xmath19 . the structure of the constraint is such that true dynamical degrees of freedom can not be singled out explicitly . in the model being considered , this difficulty is reflected in that the choice of the time variable is ambiguous ( the problem of time ) . for the choice of the time coordinate to be unambiguous , the model must be supplemented with a coordinate condition . when the coordinate condition is added to the field equations , their solution can be found for chosen time variable . however , this method of removing ambiguities in specifying the time variable does not solve the problem of a quantum description . therefore we shall use another approach and remove the above ambiguity with the aid of a coordinate condition imposed prior to varying the action functional . we will choose the coordinate condition in the form @xmath20 where @xmath21 is the privileged time coordinate , and include it in the action functional with the aid of a lagrange multiplier @xmath22 @xmath23 , \label{4}\ ] ] where @xmath24 \label{5}\ ] ] is the new hamiltonian . the constraint equation reduces to the form @xmath25 parameter @xmath21 can be used as an independent variable for the description of the evolution of the universe . corresponding canonical equations reduce to the form @xmath26 integrating the equation for @xmath22 , we obtain @xmath27 , where @xmath28 is a constant and the multiplier @xmath29 is introduced for further convenience . the full set of equations for the model in question becomes @xcite @xmath30 @xmath31 where @xmath32 . equation ( [ 6 ] ) represents the einstein equation for the @xmath33 component , while equation ( [ 7 ] ) is the equation of motion @xmath34 for the field @xmath35 . ( @xmath36 is the energy - momentum tensor of the scalar field . ) from the analysis of the einstein equations for this model it follows that inclusion of the coordinate condition ( [ 3 ] ) in the action functional leads to the origin of the additional energy - momentum tensor in these equations @xmath37 that can be interpreted as the energy - momentum tensor of radiation . in the ordinary units @xmath28 is measured in @xmath38 . the choice of radiation as the matter reference frame is natural for the case in which relativistic matter ( electromagnetic radiation , neutrino radiation , etc . ) is dominant at the early stage of universe evolution . if our universe were described by the model specified by action functional ( [ 4 ] ) , it would be possible to relate the above radiation at the present era to cosmic microwave background . a feature peculiar to the model in question is that it involves a barrier in the variable @xmath10 described by the function @xmath39 . this barrier is formed by the interaction of the scalar and gravitational fields . it exists for any form of the positive definite scalar - field potential @xmath40 and becomes impenetrable on the side of small @xmath10 in the limit @xmath41 . in general case ( @xmath42 ) there are two regions accessible to a classical motion : inside the barrier ( @xmath43 ) and outside the barrier ( @xmath44 ) , where @xmath45 and @xmath46 are the turning points ( @xmath47 ) specified by the condition @xmath48 . the set of equations ( [ 6 ] ) and ( [ 7 ] ) determines the @xmath10 and @xmath0 as the functions of time @xmath21 at given @xmath1 . when the rate at which scalar field changes is much smaller than the rate of universe evolution , i.e. @xmath49 , where @xmath50 is the hubble constant , and @xmath51 , the equations ( [ 6 ] ) and ( [ 7 ] ) become @xmath52 @xmath53 where @xmath54 and @xmath39 depend parametrically on @xmath0 . in the zero - order approximation @xmath55 . the solution to equation ( [ 6 ] ) can be refined by taking into account a slow variation of the field @xmath35 with the aid of the equation @xmath56 where @xmath54 stands for a potential term . the solutions of the equation ( [ 91 ] ) which determine the scalar field dynamics were studied in the inflationary models @xcite . the solution of the equation ( [ 9 ] ) at fixed value of @xmath0 can be represented in the form @xmath57^{1/2 } , \label{92}\ ] ] where we denote @xmath58 here @xmath59 gives the initial condition for some instant of time @xmath60 . at @xmath61 and @xmath62 the corresponding scale factors are given in @xcite . the solution ( [ 92 ] ) shows that in the region @xmath63 the universe expands in the de sitter mode from the point @xmath64 , but in the region @xmath65 it evolves as @xmath66^{1/2}$ ] for @xmath67 that describes the evolution of the universe which density was dominated by radiation and as @xmath68 with @xmath69 near the point of maximal expansion @xmath70 . the estimations for @xmath45 demonstrate that at small enough @xmath71 the value @xmath72 can reach the modern values of the scale factor in our universe . so , for the state of the universe with @xmath73 and @xmath74 gev/@xmath75 ( the mean matter - energy density in our universe at the present era ) we have @xmath76 cm . in the extreme case of @xmath77 , where there is no radiation , the region @xmath43 contracts to the point @xmath78 , and the expansion can" +"ngc 1232 is a nearly face on , gas rich , sc galaxy . face on galaxies provide excellent targets for studies of radial properties , such as the chemical enrichment of the interstellar medium ( e.g. , mccall , rybski , & shields 1985 ; vila costas & edmunds 1992 ; zaritsky , kennicutt , & huchra 1994 ; ferguson , gallagher , & wyse 1998 ) or the velocity dispersion of the neutral gas ( e.g. , van der kruit & shostak 1982 , 1984 ; shostak & van der kruit 1984 ; dickey , hanson , & helou 1990 ; boulanger & viallefond 1992 ; kamphuis & briggs 1992 ; rownd , dickey , & helou 1994 ) . ngc 1232 first came to our attention as part of a study of radial trends in elemental abundances ( van zee , salzer , & haynes 1998a ; van zee 1998b ) . the outermost region observed by van zee ( 1998a , b ) has an abnormally low oxygen abundance and a higher n / o ratio than expected at that radius . such features may arise from asymmetries in the disk , or from perturbations induced by tidal interactions . we thus decided to investigate the neutral gas distribution and kinematics of ngc 1232 to determine if there were kinematic peculiarities associated with this particular region , or more generally in the outer gas disk . with a relatively low inclination angle , approximately 30 , ngc 1232 is also a prime candidate for studies of the neutral gas velocity dispersion as a function of radius . since the hi distribution typically extends a factor of 1.3 to 2 times the size of the optical disk in sc galaxies ( e.g. , broeils & rhee 1997 ) , one might naively expect a decrease in the observed velocity dispersion beyond the radius of active star formation [ star formation activity may not be truncated in spiral galaxies , however ( ferguson 1998b ) ] . previous studies of the neutral gas velocity dispersion in face on spiral galaxies have been inconclusive . while some observations indicate that the velocity dispersion may decrease with radius ( e.g. , ngc 6946 , boulanger & viallefond 1992 ) , others indicate that the velocity dispersion is constant in the outer gas disk ( e.g. , ngc 1058 , dickey 1990 ) . such studies are hampered by two main problems : ( 1 ) rotational broadening and ( 2 ) insufficient spectral resolution . the observations of ngc 1232 presented in this paper have adequate spectral resolution , but suffer from significant rotational broadening , in part due to a severe warp in the gas disk . nonetheless , these observations do provide additional insight on radial trends of the neutral gas velocity dispersion in spiral galaxies . the physical parameters of ngc 1232 are summarized in table [ tab : global ] . throughout this paper , we adopt a distance of 21.5 mpc ( van zee 1998b ) , based on an assumed h@xmath1 of 75 mpc@xmath2 and a virgocentric infall model . optically , ngc 1232 is a rather nondescript sc galaxy with well defined spiral arms and optical colors ( de vaucouleurs 1991 ) that are typical for late type spiral galaxies . its total hi mass and m@xmath3/l@xmath4 ratio are also quite typical of the class . on the other hand , it s far infrared luminosity ( soifer 1989 ) is significantly lower than typical for sc galaxies ( see , e.g. , roberts & haynes 1994 for trends as a function of hubble type ) . this paper is organized as follows . the hi synthesis observations and data reduction are presented in section [ sec : obs ] . the neutral gas distribution and kinematics of ngc 1232 are discussed in section [ sec : ana ] . a brief discussion and summary are presented in sections [ sec : disc ] and [ sec : conc ] . finally , the results of optical spectroscopy of the spatially nearby system ngc 1232a are summarized in an appendix . hi synthesis imaging observations of ngc 1232 were conducted by the nrao summer students with the dnc configuration of the very large array ( vla ) on 1992 july 4 . the observations spanned 5 hours , with a total on source integration time of 227 minutes . the correlator was used in 2ad mode with the right and left circular polarizations tuned to 1684 . the total band width was 1.56 mhz . the on line hanning smoothing option was selected , producing final spectral data cubes of 127 channels , each 2.6 wide . standard tasks in aips ( napier 1983 ) were employed for calibration and preliminary data reduction . calibration of this data set was complicated by the fact that the west arm of the array was shadowed during the observations of the primary flux density calibrator , 3c 286 . however , the observations of 3c 286 were sufficient to set the flux density scale ; phase and bandpass calibration was derived from observations of a nearby continuum source , b0237233 . with an observed flux density of 6.21 jy at 1412.5 mhz , the observations of b0237233 had adequate signal to noise for calibration of both the phase and the bandpass . after calibration , the line data was transformed to the _ x y _ plane . a robust weighting technique was employed by the aips task imagr to optimize the beam shape and noise levels of the final data cubes ( briggs 1995 ) . the `` robustness parameter '' in imagr controls the weighting of the _ u v _ data , permitting a fine tuning between sensitivity and resolution . as currently implemented , a robustness of 5 corresponds to natural weighting of the _ u v _ data ( maximizing sensitivity ) while a robustness of 5 corresponds to uniform weighting ( lower sensitivity , but better spatial resolution ) . the relevant imagr parameters for three data cubes are listed in table [ tab : maps ] . throughout this paper we will refer to the robustness of 1.0 cube as the `` low resolution cube , '' to the robustness of 0.5 cube as the `` intermediate weight cube , '' and to the robustness of 0.5 cube as the `` high resolution cube . '' all subsequent analysis of the data cubes was performed within the gipsy package ( van der hulst 1992 ) . line emission from ngc 1232 filled most of the bandpass ( channels 7 to 121 ) . since the few line free channels were at the extreme edge of the bandpass , they had poor noise characteristics and thus were insufficient to create an accurate model of the continuum emission in either the _ u v _ or _ x y _ planes . continuum subtraction was a necessary step in the data reduction process , however , since ngc 1232 has 58.5 mjy of continuum emission at l band ( condon 1987 ) . continuum subtraction was conducted in the _ x y _ plane , with a continuum image created separately for each data cube . to create the continuum image , the mean of the inner 100 channels ( 1553.8 @xmath5 1814.3 ) was computed . this image was severely contaminated by the line emission of the galaxy ; the region of galaxy emission was blotted from the image and replaced with the value 0 . next , the mean was computed for channels with velocities between 1538.2 and 1561.6 ( line emission from only the eastern half of the galaxy ) and for channels with velocities between 1811.7 and 1835.2 ( line emission from only the western half of the galaxy ) . the continuum sources coincident with the galaxy emission were recovered from these two maps . the final continuum image for each resolution was inspected to verify that all of the continuum sources were recovered ; an example of one of these continuum images ( from the intermediate weight data cube ) is shown in figure [ fig : cont ] . the continuum image for each resolution was subtracted from every channel of the data cube to produce the final continuum free data cubes . selected channels from the continuum subtracted intermediate weight data cube are presented in figure [ fig : chans ] . the continuum subtraction appears to have been successful ( see , for instance , the baseline of the integrated flux density profile , figure [ fig : flux ] ) . note , however , that even if the continuum subtraction had not been as successful , the subsequent analysis of the gas kinematics and dynamics would still be valid . in particular , the velocity field and velocity dispersion measurements are fairly robust , even in the presence of continuum emission ; only the total gas distribution would have been significantly effected by poor continuum subtraction . to determine if the total hi flux density was recovered in the hi synthesis observations , the flux density was measured in each channel of the continuum subtracted data cubes . the flux density profile , corrected for primary beam attenuation , is shown in figure [ fig : flux ] . qualitatively , the flux density profile is similar to those obtained from single dish observations ( fisher & tully 1981 ; reif 1982 ; staveley smith & davies 1988 ) . the total flux density recovered from the low resolution data cube was 122.4 @xmath0 12.2 jy , in good agreement with previous single dish measurements ( e.g. , 115.5 @xmath0 7.2 jy , green bank 43 m [ fisher & tully 1981 ] ; 127.9 @xmath0 13.8 jy , jodrell bank [ staveley smith & davies 1988 ] ) . thus , despite the calibration problems and missing short spacings , the flux density scale appears to be correct , and the total hi flux density has been recovered . the slight asymmetry between the two horns of the integrated hi profile has been ascribed to emission from the spatially nearby galaxy ngc 1232a ( eso 547g016 ) ( e.g. , reif 1982 ; becker 1988 ) . however , there is no apparent gas density enhancement or perturbation in the velocity field near this object ( see figure [ fig : mom ] ) . furthermore , a heliocentric optical velocity of @xmath6 was measured from several emission lines with the palomar 5 m telescope ; further details of the emission lines observed in this galaxy are presented in the appendix . this newly derived redshift is in basic agreement with the velocity listed in ned ; thus , this object does not appear to be physically associated with ngc 1232 . both moment analysis and gaussian fitting were used to characterize the gas distribution , velocity field , and velocity dispersion of ngc 1232 . moment maps of each data cube were computed in the following manner . first , the low resolution cube was smoothed to a resolution of twice the beam ; second , the smoothed cube was clipped at the 2@xmath7 level ; the resultant clipped cube was then interactively blanked to remove spurious noise spikes . signal was identified based on spatial continuity between channels . a conditional transfer was used to blank the corresponding locations in the low , intermediate , and high resolution data cubes ( corrected for primary beam attenuation ) based on the blanked , smoothed cube . moment maps of the blanked data cubes were created with the gipsy task moments . in addition , gaussian fits to the observed line profiles at each position in the unclipped data cubes were obtained with the gipsy task gaufit . in" +"wireless powered communication network has arisen as a new system with stable and self - sustainable power supplies in shaping future - generation wireless communications @xcite . the enabling technology , known as simultaneous wireless information and power transfer ( swipt ) , has particularly drawn an upsurge of interests owing to the far - field electromagnetic power carried by radio - frequency ( rf ) signals that affluently exist in wireless communications . with the transmit power , waveforms , and dimensions of resources , etc . , being all fully controllable , swipt promises to prolong the lifetime of wireless devices while delivering the essential communication functionality , as will be important for low - power applications such as rf identification ( rfid ) and wireless sensor networks ( wsns ) ( see @xcite and the references therein ) . on the other hand , privacy and authentication have increasingly become major concerns for wireless communications and physical ( phy)-layer security has emerged as a new layer of defence to realize perfect secrecy transmission in addition to the costly upper - layer techniques such as cryptography . in this regard , relay - assisted secure transmission was proposed @xcite and phy - layer security enhancements by means of cooperative communications have since attracted much attention @xcite . in particular , cooperative schemes can be mainly classified into three categories : _ decode - and - forward ( df ) _ , _ amplify - and - forward ( af ) _ , and _ cooperative jamming ( cj ) _ @xcite with cj being most relevant to phy - layer security . specifically , coordinated cj refers to the scheme of generating a common jamming signal across all single - antenna relay helpers against eavesdropping @xcite , while uncoordinated cj considers that each relay helper emits independent artificial noise ( an ) to confound the eavesdroppers @xcite . it is expected that in the scenarios where the direct link is broken between the transmitter ( tx ) and the legitimate receiver ( rx ) , some of the relays have to take on their conventional role of forwarding the information while others will perform cj @xcite . a recent paradigm that generalizes all the above - mentioned cooperation strategies is _ cooperative beamforming ( cb ) mixed with cj _ @xcite , where the available power at each relay is split into two parts : one for forwarding the confidential message and the other for cj . however , mixed cb - cj approaches may be prohibitive in applications with low power devices because idle relays with limited battery supplies would likely prefer saving power for their own traffic to assisting others communication . in light of this , swipt provides the incentive for potential helpers to perform dedicated cb mixed with cj at no expense of its own power , but opportunistically earn harvested energy . motivated by this , our work considers secrecy transmission from a tx to a legitimate rx with the aid of a set of single - antenna wireless energy harvesting ( weh)-enabled af - operated relays in the presence of multiple single - antenna eavesdroppers . as a matter of fact , cooperative schemes that involve weh - enabled relays was recently investigated in @xcite . we consider the use of the _ dynamic power splitting ( dps ) _ receiver architecture , initially proposed for swipt in @xcite , which divides the received power with an adjustable ratio for energy harvesting ( eh ) and information receiving ( ir ) . weh - enabled relays using dps receivers have also been considered in @xcite and @xcite , without ( w / o ) and with secrecy consideration , respectively . note that there is also interest in addressing the threat that weh receivers may attempt to intercept the confidential messages in swipt - enabled networks @xcite . nevertheless , we will focus on exploiting the benefits of weh - enabled relays when they are trustful . in particular , motivated by the strong interest in swipt and the vast degree - of - freedom ( dof ) achievable by cooperative relays , this paper aims to maximize the secrecy rate with the aid of weh - enabled af - operated relays , subject to the eh power constraints of individual relays by jointly optimizing the cb of the relays and the cj covariance matrix . in this paper , we assume that there is no direct link between the source and destination nodes , and perfect global channel state information ( csi ) is available for the case of centralized optimization . it is worth pointing out that although our setting may look similar to @xcite , their optimal cb - cj design is not applicable to ours due to the multiplicative nature in beamforming weights incurred by the power splitting ( ps ) ratios that intrinsically poses more intractability to our optimization problem . further , our work also differs from @xcite where an efficient algorithm was proposed to maximize the secrecy rate for the optimization of the ps ratios and af relay beamforming . the difference is twofold . first , an was not considered in the second transmission phase in @xcite and in addition , their algorithm only converged to a local optimum , as opposed to our work that gives the global optimal solutions for cb . the rest of the paper is organized as follows . section [ sec : system model ] describes two types of weh - enabled rx architecture for the af relays and defines the secrecy rate region of the relay wiretap channel . section [ sec : problem formulation ] then formulates the secrecy rate maximization problems that jointly optimize the an ( or cj ) and the af - relay cb for the weh - enabled relays operating with the two types of rx . the problems are respectively solved by centralized schemes in section [ sec : centralized ] and distributed approaches in section [ sec : distributed ] . section [ sec : numerical results ] provides simulation results to evaluate the performance of the proposed schemes . finally , section [ sec : conclusion ] concludes the paper . _ notations_we use the uppercase boldface letters for matrices and lowercase boldface letters for vectors . the superscripts @xmath0 , @xmath1 , @xmath2 and @xmath3 represent , respectively , the transpose , conjugate , conjugate transpose operations on vectors or matrices , and the optimum . in addition , @xmath4 stands for the trace of a square matrix . moreover , @xmath5_{i , j}$ ] denotes the @xmath6th entry of a matrix , while @xmath7 and @xmath8 represent the euclidean norm and the entry - wise absolute value square of a vector , respectively . also , @xmath9 denotes a diagonal matrix with its diagonal specified by the given vector and @xmath5_{i=1}^n$ ] represents an @xmath10 vector with each element indexed by @xmath11 . furthermore , @xmath12 and @xmath13 stand for product and hadamard product , respectively . @xmath14 denotes the field of complex ( real ) matrices with dimension @xmath15 and @xmath16}$ ] indicates the expectation operation . finally , @xmath17 is short for @xmath18 . in this paper , we consider secrecy transmission in a swipt - enabled wsn , where a tx ( alice ) wants to establish confidential communication with the legitimate rx ( bob ) with no direct link but with the aid of @xmath19 weh - enabled sensors operating as af relays , denoted by @xmath20 , in the presence of multiple eavesdroppers ( eves ) , denoted by @xmath21 , all equipped with single antenna . we assume that there is no direct link from the tx to any of the eves , due to , for instance , severe path loss or shadowing , as illustrated in fig . [ fig : system model ] . we consider a two - hop relaying protocol based on two equal time slots and the duration of one transmit - slot is normalized to be one unit so that the terms `` energy '' and `` power '' are interchangeable with respect to ( w.r.t . ) one transmit - slot . at the receiver of each af relay , we introduce two types of weh - enabled receiver architecture , namely , _ static power splitting ( sps ) _ ( fig . [ fig : subfig : sps rx ] ) and _ dps _ ( fig . [ fig : subfig : dps rx ] ) , both of which allow the relay to harvest energy and receive information from the same received signal . specifically , the receiver first splits a portion of @xmath22 , of the received power for eh and the rest @xmath23 for ir , @xmath24 . the @xmath22 portion of harvested power is further divided into two streams with @xmath25 used for generating the an to confound eves and @xmath26 used for amplifying the received signal , where @xmath27 is the @xmath11th element of the received signal @xmath28 , and @xmath29 denotes the eh efficiency . note that dps with adjustable @xmath22 s is presently the most general receiver operation because practical circuits can not directly decode the information from the stream used for eh @xcite and sps is just a special case of dps with @xmath30 , @xmath24 , fixed for the whole transmission duration . however , sps , advocated for its ease of implementation , is introduced separately in the sequel for its simplified relay beamforming design . in the first transmit - slot , the received signal at each individual relay can be expressed as @xmath31 where the transmit signal @xmath32 is a circularly symmetric complex gaussian ( cscg ) random variable with zero mean and unit variance , denoted by @xmath33 , @xmath34 denotes the complex channel from the tx to the @xmath11th relay , @xmath35 is the transmit power at the tx , and @xmath36 is the additive white gaussian noise ( awgn ) introduced by the receiving antenna of the @xmath11th relay , denoted by @xmath37 . as such , the linearly amplified baseband equivalent signal at the output of the @xmath11th relay is given by @xmath38 where @xmath39 denotes the complex af coefficient , and @xmath40 denotes the noise due to signal conversion from the rf band to baseband , denoted by @xmath41 . since @xmath42 is constrained by the portion of the harvested power for forwarding , i.e. , @xmath26 , @xmath39 is accordingly given by @xmath43 where @xmath44 denotes the phase of the af coefficient for the @xmath11th relay . next , we introduce the cj scheme . denote the cj signal generated from @xmath19 relays by @xmath45^t$ ] and define its covariance matrix as @xmath46 $ ] . then the coordinated cj transmission can be uniquely determined by the truncated eigenvalue decomposition ( evd ) of @xmath47 given by @xmath48 , where @xmath49)$ ] is a diagonal matrix with @xmath50 s denoting all the positive eigenvalues of @xmath47 and @xmath51 is the precoding matrix satisfying @xmath52 . note that @xmath53 denotes the rank of @xmath54 which will be designed later . as a result , the cj signal can be expressed as @xmath55 where @xmath56 s are drawn from the columns of @xmath57 , and @xmath58 s are independent and identically distributed ( i.i.d . ) complex gaussian variables denoted by @xmath59 , which is known as the optimal distribution for an @xcite . on the other hand , @xmath60 , @xmath24 , denotes the power constraint for jamming at the @xmath11th relay , which implies that @xmath61 where @xmath62 is a diagonal matrix with its diagonal @xmath63 ( a unit vector with the @xmath11th entry equal to @xmath64 and the rest equal to @xmath65 ) . note that the cj scheme proposed above" +"radio tomographic imaging ( rti ) systems @xcite localize and track people in indoor areas using the received signal strength ( rss ) measurements made by a network of multiple static wireless devices . these devices are called `` rf sensors '' because their rf interface is their mode of sensing . instead of requiring people to carry an electronic device ( _ e.g. _ , rfid tag , mobile phone , etc . ) , an rti system uses the changes in rss on the network s links to estimate the attenuation field caused by the presence and movements of people found in it . rti systems can be used to enable context awareness @xcite , in ambient - assisted living ( aal ) applications @xcite , and in tactical operations or crisis situations @xcite . an effect we have observed over many deployments is that the performance of an rti system can be dramatically altered ( improved or degraded ) by small ( sub - wavelength ) position changes of the deployed rf sensors . two rti deployments in the same area , with rf sensors deployed in ostensibly the same positions , may have significantly different tracking performance . we show an example of how rti performance is improved by moving one sensor in section [ sec : fade_level_effect ] . one may systematically improve rf sensor locations , and thus rti system performance , by a long and tedius procedure we call `` guess - and - retest '' . first , rf sensors are deployed , and a experiment is conducted with the deployer moving in a known path , by which the tracking error of the rti system is calculated . next , the deployer : 1 . picks a sensor to be the _ sensor - under - test _ and moves it a few cm in one direction or another . re - performs the known - path experiment and re - calculates the error . if the tracking error increases , the deployer moves the sensor - under - test back to its original position . repeat from step 1 . while `` guess - and - retest '' is possible and will ultimately reduce localization error , it is extraordinarily time - consuming and as such is unsuitable for a real - world deployment of a commercial rti system . in this paper , we introduce an rti system composed of a network of the autonomously rotating rf sensors , which we call _ servo - nodes _ , shown in figure [ fig : servo_node ] . each servo - node is equipped with a servo motor and is capable of performing small - scale , _ i.e. _ , on the order of a wavelength , adjustments of the position of the rf sensor . further , we suggest and justify a simple network - wide quality metric which is based solely on link channel measurements when no person is in the area , and thus does not require the deployer to conduct any known - path experiment . together , the quality metric and the servo - nodes allow each sensor to quickly , _ i.e. _ , within seconds , `` dial it in '' , _ i.e. _ , rotate to optimize its own position . we show via three deployments that this procedure , which we refer to as _ calibration _ , reduces localization error by 30% to 37% . the key to the improvement is in the optimization of link _ fade level _ , the degree to which rss is changed by constructive or destructive multipath fading . if multipath components arrive at the receiver antenna with nearly the same phase , the link is said to be in _ anti - fade _ , and its rss is relatively high . alternatively , if components have nearly opposite phase , a link is said to be in _ deep fade _ , and its rss is relatively low @xcite . since the phases of each component changes at a different rate as the antenna is moved , we observe the effect of small - scale fading @xcite . previous works @xcite have demonstrated that the change in rss induced by a person obstructing the link line , _ i.e. _ , the straight line connecting transmitter and receiver , strongly depends on the fade level of the link . anti - fade links measure a consistent attenuation only when the person is located in the proximities of the link line . in contrast , deep fade links measure a variation in rss ( either increase or decrease ) also when the person is located at unpredictable positions far away from the link line . anti - fade links thus provide generally more informative and reliable information about a person s position . we propose that maximizing the sum of rss on all links measured during empty - room conditions will increase , on average , link fade levels , and thus improve rti tracking accuracy . servo - nodes do nt move the sensors far enough to alter large scale path loss on links , thus any increase in rss can be attributed to a change in small - scale fading that makes the multipath phasor sum more constructive . with the link multipath arranged to be more constructive , there is a higher probability that the link will exhibit a more reliable and predictable attenuation behavior when obstructed by a person . the predictable behavior of the link thus improves rti localization accuracy . instead of `` guess - and - retest '' , the deployer simply turn on and deploys servo - nodes and leaves the room . the sensors self - calibrate and rotate to a ( local ) optimum position . even better , the servo - nodes could periodically recalibrate to adjust to changing environmental conditions over months and years . we present results from three deployments , _ i.e. _ , a typical one bedroom apartment , a highly cluttered university laboratory , and a large office space . preliminary experiments are conducted in the apartment with a multi - node platform ( see figure [ fig : cardboard_nodes ] and section [ sec : multi_node_platform ] ) that simulates the functioning of a servo - node . the servo - nodes ( see figure [ fig : servo_node ] and section [ sec : servo_nodes ] ) are used in the subsequent ( lab and office ) deployments . we also describe two different calibration procedures that iteratively adjust position and orientation of the nodes composing the rotating rti system . both procedures aim at increasing the overall rss of the links of the network in static conditions , so as to create more anti - fade links and consequently improve the localization accuracy . the results of the deployments show that a system composed of rotating rf sensors in random positions , _ i.e. _ , with random orientation , achieves a localization accuracy similar to the one of a _ standard _ rti system composed of static nodes all with the same orientation . however , when the servo - nodes are calibrated , rti localization error is reduced on average by 30% compared to a standard rti system with the same number of sensors . alternatively , the calibrated servo - node system can achieve the same accuracy as a system of standard sensors , but with 37% fewer sensors . in this section , we describe the multi - node platform and the rotating servo - nodes used in the deployments , the procedures applied to calibrate the position and orientation of the rf sensors , and the rti method used to process the rss measurements collected in the experiments . to conduct preliminary experiments , we created a multi - node platform ( see figure [ fig : cardboard_nodes ] ) with eight battery - powered rf sensors attached to a rigid cardboard tile and positioned clockwise along the perimeter of a circle having a @xmath0 cm radius . each sensor of the platform has different orientation . the platform was designed to simulate the functioning of the rotating servo - nodes ( see section [ sec : servo_nodes ] ) , having an rf sensor in each of the eight positions where the servo motor can position its own sensor . the servo - nodes are composed of two parts : the rf sensor , _ i.e. _ , a ti cc2531 usb dongle @xcite , and the servo motor , _ i.e. _ , a gws digital sail winch servo @xcite . the rf sensor operates in the @xmath1 ghz ism band . it has a maximum nominal transmit power of @xmath2 dbm and can transmit on one of @xmath3 selectable frequency channels , which are @xmath4 mhz apart , as specified by the ieee 802.15.4 standard . the servo motor can rotate one full turn ( @xmath5 degrees ) through the standard @xmath6-@xmath7 ms pulse width modulation ( pwm ) . a rigid cardboard circle , having a @xmath0 cm radius , is glued to the winch of the servo motor . the rf sensor is in turn attached to the cardboard circle so that its antenna is perpendicular to the surface of the circle . the cc2531 platform controls the position of the servo motor through one of its i / o ports . we programmed the nodes so to be able to rotate them to eight different positions ( @xmath8 ) , @xmath9 degrees apart . the rf sensors collect rss measurements on the selected frequency channels by running the _ multi - spin _ communication protocol @xcite . the packets broadcasted by the servo - nodes and received at the central sink node include the rss measurements of the links of the network and indicate the current position of the servo - nodes . multi - spin reserves one slot at the end of each tdma communication cycle in order for the sink node to communicate a new position to one of the servo - nodes . we now introduce two different procedures to calibrate the small - scale position and orientation of the rf sensors . the first , which we refer to as _ incremental _ calibration , was used with the multi - node platform for preliminary experiments carried out in the one bedroom apartment . the second , which we refer to as _ network _ calibration , was used with the servo - nodes in experiments carried out in the laboratory and office space . after positioning the first sensor ( _ i.e. _ , # 1 in figure [ fig : apartment_nodes ] ) , the other sensors are deployed and calibrated by applying the following iterative procedure : 1 . pick a spot to temporarily deploy the multi - node platform . the spot is chosen so as to maximize the length of the calibrated links and cover the whole deployment area uniformly ( _ e.g. _ , one can iteratively use the four cardinal points as a reference ) ; 2 . in static conditions , _ i.e. _ , with no people in the deployment area , measure for a short period of time ( _ e.g. _ , 10 s ) the rss of all the links among the eight sensors on the multi - node platform and the sensors already calibrated and deployed . 3 . for sensor @xmath10 on the multi - node platform , calculate @xmath11 , _ i.e. _ , the mean of the time - averaged rss in static conditions of all the links between @xmath12 and the other sensors @xmath13 already calibrated and deployed , as : @xmath14 where @xmath15 is the set of measured frequency" +"capella ( @xmath2 aur ; g1iii / g8iii ) is the strongest non - solar coronal source accessible to high - sensitivity high - energy telescopes , and has been a common calibration target for x - ray and euv instruments such as _ euve _ , , xmm-_newton _ , etc . it is a remarkably stable source , with no discernible flaring activity . even though the emission structure has shown changes , especially in the high - temperature regime ( see e.g. , dupree et al . 1996 , young et al . 2001 ) , and there is considerable evidence for the dominant emission to change between the g1iii primary and the g8iii secondary ( e.g. , linsky et al . 1998 , johnson et al . 2002 , ishibashi et al . 2006 ) , the overall luminosity has remained steady over many years . for instance , argiroffi et al . ( 2003 ) detected a change of 3% in hrc - s / letgs data over the span of a year , and found no variability at timescales of @xmath3 ks . recently , analysis of acis - s / hetgs data ( raasen et al . 2007 , westbrook et al . 2007 ) found variations over long timescales , such as an @xmath4 intensity enhancement in early 2006 , but no evidence for any variability at timescales @xmath5 ks . variability in stellar coronae is ubiquitous , and has been detected in all types of coronally active stars ( stassun et al . 2006 , caramazza et al . 2007 , westbrook et al . 2007 , gdel 2004 , and references therein ) and over a wide range of timescales ( kashyap & drake 1999 , favata et al . 2005 , stassun et al . 2006 , pease et al . 2006 , colombo et al . this variability can occur due to many causes , ranging from cyclical dynamo variations ( timescales of decades to years ) , to rotational modulation ( months to hours ) , to active region evolution ( hours to days ) , to flaring ( hours to minutes ) . generally , active stars are characterized by recurrent flares ( see e.g. , gdel 2004 ) that are recognized in x - ray and euv light curves as sudden increases in the luminosity followed by a slower decay . however , as activity increases , the flares start to occur closer in time to each other , and it becomes increasingly difficult to resolve them in the light curve ( cf . kashyap et al . 2001 ) . prominent flares are nevertheless detected in numerous active binaries ( see e.g. , osten & brown 1999 , osten et al . 2004 ) . despite being one of the more coronally active stars , with a strong high temeperature emission component ( brickhouse et al . 2000 ) , flares have never been observed on capella ( table [ t : capella ] ) . it is unknown whether this is due to a lack of flaring activity to contribute to the heating , or due to a preponderance of flares such that individual events can not be distinguished ( cf . kashyap et al . 2001 ) . here we consider recent observations of capella made with the / ( [ s : data ] ) . we analyze these data and find that variability indeed can be detected at short timescales ( [ s : analysis ] ) , suggesting that the latter explanation is more plausible . rl + ( r.a . , dec)@xmath6 & ( 05:16:41.3591 , + 45:59:52.768 ) + distance & 13.4 pc + orbital period & 104 days + components & g1iii / g8iii + separation & 109 r@xmath7 + mass & 2.56 / 2.69 [ m@xmath8 + radius & 9.2 / 12.2 [ r@xmath8 + m@xmath9 & 0.14 / 0.25 + @xmath10 & 0.74 / 0.87 + rotational velocity & 36 / 3 [ km s@xmath11 + s , dashed otherwise ) . the data comprise 40 obsids ( noted at the top of each segment , along with the day since 2005-dec-01 that the observation started ) . the sim offset at which each observation is carried out is indicated at the bottom of each segment . [ f : ctrt],width=528 ] capella was observed as a calibration target with the / over two cycles from december 2005 to january 2007 ( see figure [ f : ctrt ] ) . all the observations were carried out at the telescope aimpoint , but at different locations on the detector corresponding to different offset values of the science instrument module ( sim ) . the count rates shown in figure [ f : ctrt ] have been corrected for the qe ( quantum efficiency ) values at the observation location and thus represent flat - fielded light curves matched to the qe at the nominal aimpoint . the qe corrections are made separately for each bin of the light curves as the source dithers across the detector . note however that this detailed correction is ignorable ; it causes changes of @xmath12 when compared with count rates corrected with a qe averaged over the entire dither pattern ( see also [ s : hz43 ] ) . we have reduced the data using the software for the interactive analysis of observations ( ciao v3.4 ) and using the most recent calibration products ( caldb v3.2 ) . the high count rates observed ( @xmath13 ) , coupled with the sharp point spread function ( psf ; it falls to 1% of the maximum at @xmath14 away from the peak ) , provides an unprecedented opportunity to study small changes in the x - ray brightness of capella . the source counts are extracted from a circle with radius 8x the size of the psf ( @xmath15 ) , and the background is locally estimated from a surrounding annulus of radii ( @xmath16 ) . assuming a raymond - smith thermal emission model with a dominant temperature component at 6 mk and a h column n@xmath17 @xmath18 , we find with webpimms that the counts - to - energy conversion factor is @xmath19 ergs @xmath18 ct@xmath20 for different metallicities . this suggests x - ray luminosities of capella in the 0.15 - 4.5 kev passband of @xmath21 ergs s@xmath20 ( cf . l@xmath22 ergs s@xmath20 based on _ einstein_/ipc observations ; strassmeier et al . it is clear from the light curve ( figure [ f : ctrt ] ) that capella undergoes slow changes in its luminosity over timescales of weeks and months , with count rates ranging from @xmath23 . for instance , note the drop in intensity between obsids 6552 and 6555 , which are separated by 16 days , to @xmath24 mm between these two observations , and it could be argued that uncalibrated differences in the qe uniformity may account for the drop in intensity . however , the similarity of count rates between observations 6558 and 6559 , both of which were carried out on the same day , but at sim offsets of @xmath25 and @xmath26 mm respectively , indicates that the drop in intensity is real . ] and the difference between obsids 6559 and 8360 , which are done @xmath27 yr apart , but are both carried out at the same detector location ( thus precluding calibration differences as a factor ; see [ s : hz43 ] below ) . this impression is confirmed by an autocorrelation analysis ; we construct count rate light curves @xmath28 at various binning sizes @xmath29 and compute the autocorrelation @xmath30 where @xmath31 is the average count rate in the @xmath32 bins in the light curve . the autocorrelation for @xmath33 s is shown in figure [ f : autocorr ] as the dark blue curve ( curves for other bin sizes are similar ) , along with estimates of the 95% and 99% uncertainties for each lag time @xmath34 . these uncertainties are computed via monte carlo simulations , by constructing 1000 light curves with the same number of bins as in @xmath28 , as poisson deviates for an unvarying source intensity of @xmath35 . the autocorrelation drops linearly until it becomes indistinguishable from statistical noise at a lag time of @xmath36 ks ; this is the typical signature of variability which occurs at timescales @xmath1 ks , such that count rates that are separated by longer timescales are essentially uncorrelated . at larger lag times , @xmath37 ks , the autocorrelation appears to rise again , but this is not distinguishable from statistical noise . ks , the autocorrelation drops further and becomes significantly @xmath38 , suggesting that the count rates are anticorrelated at large timescales , i.e. , the intensity tends to fluctuate over long temporal separations . however , these values are not physically meaningful , since the data gaps between observations are large and the lag time ceases to be a useful construct . note that typical observation times are 5 ks , and the observation times for contiguous obsids ranges from 12 to 62 ks , with a median of 19 ks ( see figure [ f : ctrt ] ) . ] this is consistent with the results found by raasen et al . ( 2007 ) and westbrook et al . ( 2007 ) , who found similar variations over similar timescales . however , at a counts intensity level of @xmath39 ( obtained from acis - s / hetg dispersed counts ) they were unable to detect any variability at timescales @xmath40 ks corresponding to the durations of the observations , even using sophisticated algorithms such as the one described by gregory & loredo ( 1992 ) . here , we observe the source with a counts intensity an order of magnitude higher , and are thus able to investigate the variability at shorter timescales . note that argiroffi et al . ( 2003 ) also find no variability at timescales @xmath41 ks , but again , the hrc - s / letgs data they rely on has count rates of @xmath42 , which is too small to detect the existence of variability on capella . because the observations are done in short segments , it is useful to consider the effect of removing large timescale effects on the autocorrelation . we thus reconstruct the light curve by offsetting that computed in each obsid by the average intensity of the source during that obsid ( i.e. , for each segment the average count rate is set to @xmath26 ) , and recompute the autocorrelation . this has the effect of completely removing variations at timescales greater than @xmath43 of the typical exposure time , and will reveal any variability that may exist at very small timescales . the result of this is shown as the pale blue curve in figure [ f : autocorr ] . this is everywhere consistent with no variability . because the typical observation time is 5 ks , this suggests that there is no variability variability on capella at timescales @xmath42 ks . note that offsetting the light curves by different amounts at different times , as we have done in this exercise , introduces additional statistical uncertainty into the results because of a non - stationary bias , and therefore the power of the test to detect a variability signal is decreased . in order to determine whether there does exist variability over timescales of @xmath44 ks , we test the dispersion of the fluctuations ( see [ s : overdisp ] ) . the large count rates of capella seen with the afford us the capability to analyze the light curve at short timescales . in order to test the constancy of the intensity within" +"the external shock model predicts afterglows characterized by a power - law decay in time , with the possible presence of breaks connecting branches of different slope ( & rees 1997 ) . such changes are due to either geometrical properties of the fireball ( geometrical beaming , rhoads 1999 ) or to spectral transitions ( e.g. from a cooling to a non - cooling electron population , sari , piran & narayan 1998 ) . in the pre-_swift _ era , most afterglows were consistent with the simplest version of this model . there were , however , notable exceptions , such as grb 000301c ( masetti et al . 2000 ) , grb 021004 ( lazzati et al . 2002 ) , and grb 030329 ( matheson et al . all these bursts displayed optical variability in the form of bumps or wiggles superimposed on the smooth power - law decay . a number of explanations have been discussed in the literature to account for the variations in the optical afterglow brightness . these include inhomogeneities in the external density ( wang & loeb 2000 ; lazzati et al . 2002 ; heyl & perna 2003 ) , refreshed shocks due to the collision of a late shell of plasma with the external shock material ( rees & 1998 ) , angular inhomogeneities in the fireball energy distribution ( nakar , piran & granot 2002 ) and gravitational lensing ( loeb & perna 1998 ; garnavich , loeb & stanek 2000 ) . different mechanisms to produce variability in afterglows can in principle be distinguished through their temporal and spectral properties . in practice , however , a consensus has not been yet reached due to the lack of unambiguous observations . more recently , _ swift _ observations have revealed that flaring activity is relatively common in the early phases of grb afterglows , sometimes extending for over a day ( e.g. , chincarini 2006 ; obrien et al . the temporal properties of the flares , their intensity , and their spectra suggest an origin that is unrelated to the external shock ( chincarini 2006 ; falcone et al . 2006 ) , at least for a fraction of the bumps . late episodes of `` prompt emission '' can have two different origin . one possibility is that the inner engine itself is active for a time as long as the detection time of the x - ray flare . alternatively , the engine can be short - lived but produce , together with the fast ejecta , a tail of slower material . such slower material can produce internal dissipation ( and therefore prompt emission ) at late time . slow shells ejected immediately after the fast ejecta will not produce an external shock at the canonical external shock radius since the ambient medium has been swept by the external shock produced by the fast ejecta , which develops earlier . distinguishing between these two scenarios bears important implications for the physics of the grb engine . in this paper we discuss the timescales of flares in the different scenarios . we show that at least a large fraction of x - ray flares are due to a long lasting activity of the grb engine , rather than to external shock activity or to the emission of slow shells immediately after the prompt emission ends . this paper is organized as follows : in sect . 2 we compute external shock timescales while in sect . 3 we consider prompt emission flares and in sect . 4 we discuss our results and compare them to _ swift _ data . we summarize our findings in sect . 5 . consider flaring activity produced by a sudden brightening of the external shock . we consider now a brightening that involves the whole surface of the external shock . even if the duration of the activity in the comoving frame is negligible , the observer at infinity still detects photons over a finite amount of time , due to the `` curvature effect '' ( see fig . [ fig : curva ] ) . the shape of the observed pulse is therefore the narrowest possible in time . a longer activity in the comoving frame will produce a longer pulse , obtained by convolution of the two functional shapes . let us define the quantity @xmath0 to be the energy released by the unit area of the fireball as a result of the flaring activity , in the comoving frame . the flux received at infinity is given by ( see also kumar & panaitescu 2000 ) : @xmath1 where @xmath2 is the distance to the source , @xmath3^{-1}$ ] is the doppler factor , @xmath4 is the fireball surface and @xmath5 the time in the observer frame . this is given by : @xmath6\ , . \label{eq : tobs}\ ] ] equation ( [ eq : tobs ] ) holds for any self - similar dynamical evolution where @xmath7 , as long as @xmath8 . note that we indicate with the subscript @xmath9 quantities ( such as lorentz factor and speed ) of the external shock , and without subscript the same quantities for the material just behind the shock . it can be shown that @xmath10 ( e.g. , sari 1997 ) . easy considerations show that the only non constant quantity in eq . ( [ eq : fnu ] ) is the doppler factor , since @xmath11 , and all the radiation is emitted at constant radius @xmath12 . if we assume that we are far from a break in the afterglow spectrum , @xmath13 and the functional shape of @xmath14 can be rewritten as : @xmath15 solving eq . ( [ eq : tobs ] ) for @xmath16 , and expressing time in unit of the start time of the flare @xmath17 $ ] , the flare profile can be written as : @xmath18 where @xmath19 . equation [ eq : fnu2 ] can be used to provide a lower limit to an observationally sound definition of the flare duration . defining the duration as the full width at half maximum ( fwhm ) of the pulse , and the reference time as the time t@xmath20 of the flare maximum , we obtain : @xmath21 equation ( [ eq : dtt ] ) depends on both the dynamics and spectrum of the external shock . a steeper spectrum and/or a more slowly evolving fireball will cause a narrower flare . note that in this case ( i.e. impulsive rebrightening of the shock ) , the maximum coincides with the start time . should the activity in the comoving frame last for a finite amount of time , a rising phase would be observed . a more detailed treatment , including the width of the shell of shocked material would also provide a profile with a finite rising time . figure [ fig : dtt ] shows the time scale ratio for four typical values of @xmath22 as a function of the spectral index . the most relevant case for x - ray flares is the adiabatic ism case , with a spectral slope @xmath23 . we find for that specific case : @xmath24 . in an analogous context , zhang et al . ( 2006 ) discussed the possible production of flares by various mechanisms such as density bumps , post - energy injection in the blast wave , and two - components or patchy jets . in all cases , they concluded that the characteristics of the flares were not generally consistent with what predicted by these models ( i.e. @xmath25 and a slower - than observed flux decline ) . here , we have derived detailed , quantitative , upper limits on the value of @xmath26 . our constraints are somewhat tighter than what previously derived by different authors in the context of the external model for flares ( e.g. , ioka , kobayashi & zhang 2005 ) but comparable to more recent results ( wu et al . 2006 ) . our method differs in two important ways from what done in previous work . first , we have computed the actual functional shape of the flare , and defined rigorously the time reference we adopt ( the peak ) and the time width ( the fwhm ) . in previous works , these quantities were usually poorly defined , and the results could only be approximate . secondly , we considered the difference between the lorentz factor of the shock and that of the shocked material . this factor by itself leads to flares which are broader by a factor of two . chincarini ( 2006 ) presents a distribution of @xmath27 for a sample of _ swift _ x - ray flares that is defined as the ratio of the gaussian @xmath28 over the peak time . the distribution is shown in their fig . 8 and shaded in fig . [ fig : dtt ] . since for a gaussian the @xmath29 is equal to @xmath30 , we can easily convert their definition of @xmath31 into our definition . we conclude that the distribution of @xmath27 of _ swift _ x - ray flares is characterized by @xmath32 and has average @xmath33 . considering fig . [ fig : dtt ] , we conclude that most , if not all , the detected rebrightenings are not related to events taking place on the external shock , unless only a small portion of the shock is involved in the rebrightening . flares caused by a small portion of the shock are possible , but are unlikely to be very strong . nakar & granot ( 2006 ) studied the effect of a blob of high density interacting with the shock . they find that the rebrightening is minor , and characterized by a very slow rise . alternatively , a large rebrightening on a small timescale can be observed if a narrow opening angle shell refreshes a small part of the external shock ( granot , nakar & piran 2003 ) . this is not likely to be the case for the _ swift _ x - ray flares , since most of them are observed before the jet break time ( chincarini 2006 , obrien 2006 ) and the opening angle of the jet grows with time ( lazzati & begelman 2005 ; morsony , lazzati & begelman 2006 ) rather than decrease . since the largest majority of flares is unlikely to be produced within the external shock , it must be produced during the initial phase of internal dissipation . in the following we therefore discuss flaring activity in the context of the prompt emission . in this case one can envisage two possible scenarios for their production : _ ( a ) _ shells that are produced during the grb phase but that dissipate at much later times ; _ ( b ) _ shells produced at late times by a long - lived engine and dissipating on a timescale comparable to that of the engine duration . zhang et al . ( 2006 ) also concluded that the flares have an internal origin , but directly assumed that the engine must have been long - lived . in this section we try to discriminate between the scenarios _ ( a ) _ and _ ( b)_. being able to discriminate between these two scenarios bears important implications for our understanding of the physics of the inner grb engine ( see more discussion on this in 4 ) . in the following , we discuss the two scenarios above , provide diagnostics for each of them , and show that the current _ swift _ data is already able to discriminate between the two flare - production mechanisms . _ (" +"we are interested in predicting the hadronic cross section , which is known to factorize into parton distribution functions and the partonic cross section _ h_1h_2(p_1 , p_2 ) = _ ab _ 0 ^ 1 x_1 x_2 f_a / h_1(x_1 , ) f_b / h_2(x_2 , ) _ ab(x_1p_1 , x_2p_2 ; ( ) , , ) . the summation runs over initial state partons @xmath0 , i.e. massless quarks and gluons . the parton distribution function @xmath1 can be understood as the probability density for finding parton @xmath2 inside hadron @xmath3 carrying the momentum @xmath4 . parton distribution functions are non - perturbative objects and have to be determined experimentally . + in contrast , the partonic cross section @xmath5 can be calculated using perturbative qcd . including terms up to next - to - next - to - leading order , its expansion in the strong coupling @xmath6 reads _ ab = ^(0)_ab + ^(1)_ab + ^(2)_ab . the leading order contribution is known as the born approximation and reads ^(0)_ab = ^_ab = _ n _ n^(0 ) | _ n^(0 ) _ n , where @xmath7 is the number of final state particles and @xmath8 the phase space measure . the measurement functions @xmath9 defines the infrared safe observable and prevents @xmath7 massless partons from becoming soft or collinear . the @xmath10-loop matrix element is denoted by @xmath11 . for details of the notation we refer to @xcite . + beyond leading order , we decompose the cross section according to the number of particles in the final state . at next - to - leading order ( nlo ) we have [ eq : nlo ] ^(1)_ab = ^_ab + ^_ab + ^_ab , with ^_ab = _ n+1 _ n+1^(0 ) | _ n+1^(0 ) _ n+1 , ^_ab = _ n 2 _ n^(0 ) | _ n^(1 ) _ n . starting at this order , separate contributions suffer from soft and collinear ( infrared ) divergences . they appear as poles in the regulator @xmath12 after setting the space - time dimension to @xmath13 . we distinguish between explicit virtual poles , that emerge in the one - loop matrix element @xmath14 of the virtual contribution @xmath15 , and real poles , that appear after integrating the phase space of the additional parton of the real contribution @xmath16 . all poles cancel in the sum . + at next - to - next - to leading order ( nnlo ) we get [ eq : nnlo ] ^(2)_ab = ^_ab + ^_ab + ^_ab + ^_ab + ^_ab , where [ eq : nnloexp ] ^_ab = _ n+2 _ n+2^(0 ) | _ n+2^(0 ) _ n+2 , + ^_ab = _ n+1 2 _ n+1^(0 ) | _ n+1^(1 ) _ n+1 , + ^_ab = _ n ( 2 _ n^(0 ) | _ n^(2 ) + _ n^(1 ) | _ n^(1 ) ) _ n . the double - real contribution @xmath17 contains two additional massless partons in the final state that can become unresolved and lead to poles in @xmath12 after the phase space integration is performed . the real - virtual contribution @xmath18 consists of the one - loop amplitude integrated over the @xmath19 particle phase space . in addition to virtual poles of the one - loop matrix element , it develops real poles by integrating the phase space of one unresolved particle . the double - virtual contribution @xmath20 contains only explicit virtual poles in the two - loop amplitude and the squared one - loop amplitude . the sum of all contributions in is finite . , @xmath21 and @xmath22 are not mentioned in this discussion . for details see @xcite . ] + in general it is not possible to perform phase space integrations analytically . furthermore , to be able to compare a predicition with experimental data the phase space integration should be implemented in a flexible monte - carlo software to adapt the observable to the experimental setup easily . + subtraction methods at nlo have been established to handle infrared singularities before numerical integrations are performed . catani - seymour subtraction @xcite and fks subtraction @xcite are commonly used schemes . + at nnlo , subtraction schemes become more involved . antenna subtraction @xcite and @xmath23 - subtraction @xcite are the most advanced proposals and have already been applied to @xmath24 @xcite , @xmath25 @xcite , higgs production @xcite and vector boson pair production @xcite and other non - trivial examples @xcite . + in these schemes poles cancel analytically . we illustrate this by taking the real and virtual contribution of a nlo cross section in . the real - radiation cross section is made integrable in four dimensions by a suitable subtraction term that mimics the behaviour of the squared matrix element in the singular limits . adding the subtracted term back and integrating it analytically over the unresolved one - particle phase space provides poles that cancel the poles of the virtual contribution . finally , both phase space integrals are numerically integrable in four dimensions . + at nnlo the procedure is similar : subtraction terms for real unresolved particles are introduced to render the phase space integrable . analytically integrated subtraction terms cancel the explicit poles of virtual contributions . + here we present stripper ( sector improved phase space for real radiation ) , a nnlo subtraction scheme that is completely numerical and avoids cumbersome analytic integrations . the scheme was introduced in @xcite and generalized to arbitrary final states in @xcite . it has been first applied to top - quark pair production @xcite , and subsequently to other processes of low multiplicity : higgs @xmath26 jet @xcite , charmless bottom quark decay @xcite , top quark decay @xcite , single top quark production @xcite , muon decay @xcite and z decay @xcite . + the scheme was initially formulated using conventional dimensional regularization ( cdr ) , where momenta and spin degrees of freedom of resolved and unresolved particles are treated in @xmath13 dimensions . unresolved particles are either virtual particles of loop contributions or real - radiated particles that can become soft or collinear . in contrast to analytic subtraction schemes , momenta of resolved particles are explicitly parameterized in @xmath27 dimensions . the explicit dimension increases as the multiplicity of the final state rises , e.g. for top - quark pair production already five dimensions have been parameterized explicitly . it turns out that stripper in cdr is not applicable for high multiplicities . in addition , tree - level matrix elements , that appear in subtraction terms , have to be provided to several powers in @xmath12 . available software only provides them up to @xmath28 . + thus , it has been necessary to reformulate the scheme in t hooft - veltman regularization ( hv ) , where momenta and spin degrees of freedom of resolved particles are four - dimensional . + in this proceeding , we explain the general idea of stripper in order to obtain a laurent series in @xmath12 for @xmath17 , where each coefficient can be calculated numerically . afterwards , we shortly point out how it can be reformulated in hv to provide a self - contained subtraction scheme for nnlo calculations . the detailed description is to be found in @xcite . the subtraction scheme stripper is an algorithmic method to extract real singularities of different contributions in . each part will be given as a laurent series in @xmath12 , where each coefficient has been calculated numerically . the final result , after summing the different parts , is finite . + we outline the method for @xmath17 as given in . since it contains two additional , potentially unresolved , partons , the phase space integral has the most complicated infrared structure . + first , we split the phase space into double - collinear and triple - collinear sectors . in a triple - collinear sector singularities are generated as three specific partons become collinear to each other and/or two of them soft . in a double - collinear sector singularities emerge as two specific pairs of partons become collinear and/or two of them soft . + in a next step , we parameterize the collinear particles in each sector separately using energies and angles . we illustrate the parametrization on the basis of a triple - collinear sector , where the three particles are in the final state : the reference momentum indicating the triple - collinear direction is denoted by @xmath29 . the momenta of the unresolved partons are named @xmath30 and @xmath31 . each momentum is parameterized by its energy and a @xmath32-dimensional unit vector in spherical coordinates r^r^0 1 + , u_1^u_1 ^ 0 1 + , u_2^u_2 ^ 0 1 + . the unresolved particles energies are rescaled by their maximal value @xmath33 , @xmath34 , for @xmath35 . the soft limit is approached as @xmath36 and/or @xmath37 . using rotations in @xmath32-dimensions , the scalar products between the three given momenta take the following form = _ 1 = 1 - 2_1 , = _ 2 = 1 - 2_2 , = _ 1 _ 2 + _ 2 _ 1_2 . parametrization of a triple - collinear sector , where the three partons are in the final state . the reference momentum is @xmath38 , the unresolved momenta are denoted by @xmath39 and @xmath40 . the sum of momenta of remaining resolved particles is @xmath41 . ] this parametrization is shown in figure [ fig : parametrization ] . the limit of @xmath42 at zero indicates the collinear limit of one of the unresolved partons and the reference parton . @xmath43 is collinear to @xmath44 when @xmath45 and @xmath46 . a non - linear transformation of @xmath47 to @xmath48 , _ 2 _ 2(_1,_2 , ) , then ensures that @xmath47 always vanishes as @xmath49 . accordingly , all possible collinear limits are indicated only by two variables : @xmath50 and @xmath51 . furthermore , if we find a formulation in hv , meaning that all other momenta and the reference momentum are four - dimensional , at most six dimensions are needed to parameterize all possible scalar products consistently . + at this point , four physical variables @xmath52 parameterize all possible soft and collinear limits in a given sector . additional sector decompositions @xcite in those variables factorize all possible overlapping singularities that appear at nnlo . in practice this amounts to split each sector again . for example double - soft overlapping singularities are disentangled using [ eq : decomp ] 1=(_1-_2)+ ( _ 2-_1 ) . the decomposition of the phase space due to soft overlapping singularities is sufficient to factorize all possible limits in a double - collinear sector . in a triple - collinear sector the phase space is split into five additional sectors to factorize collinear and soft - collinear overlapping singularities . this splitting is accompanied by a transition from physical variables @xmath53 to corresponding sector variables @xmath54 . + finally , the full double - real radiation cross section can be written as a sum over different decomposed triple- and double - collinear sectors ^_ab=_s ^,s_ab . each contribution has the following form ^,s_ab=_0 ^ 1 _ 1_2_1_2 . the function @xmath55 is finite in the limit of vanishing arguments . all appearing singularities are factorized in the sector variables . poles are extracted by an iterative usage of the plus distribution in each variable [ eq : plus ] _ 0 ^ 1x=+_0 ^ 1x . we obtain a laurent series in @xmath12 and all coefficients are calculated numerically . the described procedure is process independent , since it is possible to use the known universal infrared - limits of qcd amplitudes for the subtraction terms in" +"early spectroscopic observations of cool giant stars revealed violet - displaced absorption in the optical line profiles of strong electronic transitions of singly - ionized and neutral atoms , and mass - loss rates of @xmath0 to @xmath1 m@xmath2 yr@xmath3 were inferred @xcite . more evidence of such winds came in the form of radio emission lines from abundant molecules , in particular the amplified stimulated emission from hydroxyl at @xmath4 cm @xcite . thermal line emission from carbon monoxide at mm wavelengths enabled measurements of the wind speed and mass - loss rate for carbon stars as well as stars with oxygen - rich envelopes @xcite . methods for determining the mass - loss rate using radio techniques are described by fredrik schier elsewhere in these proceedings . infrared surveys revealed stars which are heavily reddened by circumstellar dust . the association between these dust - enshrouded stars and masers was quickly made , and the accompanying dust emission became a very useful tracer of mass loss @xcite . it also explained the pumping of the masers through infrared emission , but most importantly it provided a mechanism for driving the wind . strong pulsation of the cool photospheres of these stars acts as a piston to increase the scaleheight of the molecular atmosphere , facilitating the condensation of grains @xcite . the continuum opacity of the grains allows for efficient transfer of momentum from the stellar radiation field onto the dust grains . if the density is high enough then the dust and gas are coupled , mostly via grain - h@xmath5 collisions . high mass - loss rates were estimated for these stars , @xmath6 to @xmath7 m@xmath2 yr@xmath3 @xcite . the _ spitzer space telescope _ has made it possible to detect the infrared emission from circumstellar dust around red giants and red supergiants ( rsgs ) in many local group galaxies for the first time . this enables the study of mass loss and dust production in a rich variety of environments inaccessible before , for example in the wolf - lundmark - melotte dwarf galaxy @xcite but also galactic globular clusters such as the extremely metal - poor messier 15 @xcite , whilst more thorough and detailed studies are possible in the magellanic clouds . as technological progress inflates the observable universe , much of the groundbraking work is done in uncharted territory and at the limit of sensitivity , running into many of the types of problems that were faced in the 1970s in studies of nearby stars . it is thus essential to understand the methods that are applied to measure mass - loss rates from these infrared data , and in particular to be aware of their assumptions and limitations . circumstellar dust grains absorb stellar light mainly at optical ( and ultraviolet ) wavelengths , and re - emit it mainly at infrared wavelengths . the shape of the observed spectral energy distribution ( sed ) depends on the optical properties of the grains and on the optical depth of the envelope . for a spherically symmetric geometry the integral under the sed yields the bolometric luminosity , provided that the distance is known . the sed does _ not _ allow a direct measurement to be made of the mass - loss rate . under the assumption of radiative equilibrium between the capture of photons and isotropic emission by the heated grain , and applying the continuity equation , one obtains a crude relationship that summarises the problem quite well @xcite : @xmath8 where we notice that although the optical depth , @xmath9 , is proportional to the ( gas+dust ) mass - loss rate , @xmath10 , it also depends on the dust : gas mass ratio , @xmath11 , the expansion velocity of the wind , @xmath12 , as well as the luminosity , @xmath13 . simple radiation - driven dust wind theory predicts how the wind speed should depend on the luminosity and dust : gas ratio . this can be used to compute the expected wind speed for stars for which we have no direct measurement of it . the momentum equation relates the motion of the matter and photon fluids : @xmath14 where the optical depth properly accounts for the scattering of photons off the circumstellar grains . hence , combination with eq . ( 1 ) yields : @xmath15{l}.\ ] ] it seems deceptively reasonable that the dust : gas ratio depends on metallicity . unfortunately , this is a difficult parameter to measure directly . first evidence for the metallicity dependence of the wind speed of red giants was presented by @xcite who detected six oh / ir stars in the lmc . @xcite enlarged this sample , and from a comparison with the wind speeds and luminosities of oh / ir stars in the galactic centre they could confirm eq . ( 3 ) and indicate that the dust : gas ratio is linearly proportional to metallicity : @xmath16 in the absence of direct measurements of wind speed and dust : gas ratio , it is therefore recommended to abide by the following scaling relation : @xmath17 the metallicity dependence of dust - driven winds is reviewed in @xcite . the optical depth of the dust envelope can be derived from the observed sed by comparison with synthetic seds . the latter are produced by computing simultaneously the radiation transfer through the dust envelope , and the thermal balance between the grain heating through irradiation and cooling through reradiation . the principles underlying these computations were first outlined for the non - grey case by @xcite , @xcite and @xcite . three commonly used codes that solve the equations of radiation transfer and thermal equilibrium were developed independently in the 1990s : the code of @xcite , the dusty code @xcite , and the modust code @xcite . of these , only dusty is publicly available fortunately it is also well documented and relatively easy to use . the latest generation of codes are based on monte carlo techniques for tracing the energy packets on their journey through the dust envelope @xcite , culminating in the publicly available photo - ionization / dust radiation transfer code mocassin @xcite . as an illustration , the dusty code is used to generate a series of model seds with a visual optical depth between @xmath18 and 100 , for an oxygen - rich red giant and a carbon star ( fig . 1 ) . corresponding mass - loss rates are @xmath19 to @xmath20 m@xmath2 yr@xmath3 for a typical asymptotic giant branch ( agb ) star at solar metallicity , but note that the difference in luminosity between massive rsgs and the tip of the red giant branch corresponds to a two orders of magnitude difference in the mass - loss rate inferred from the shape of the sed alone . differences in optical depth manifest themselves most through extinction of stellar light at @xmath21 @xmath22 m , the strength of discrete features associated with certain minerals mainly in the @xmath23 to 30 @xmath22 m region , and a general elevation of the spectrum over that of a naked star at @xmath24 @xmath22 m . the extinction only becomes noticeable when @xmath25 approaches unity , as it is difficult to isolate its effect from the depression of the stellar continuum due to blanketing by molecular bands in cool giants , and from the interstellar contribution to the extinction . because the absorbed photons are more energetic than the reradiated photons , small optical depths readily give rise to detectable amounts of excess emission at longer wavelengths . in particular , silicates shine efficiently around @xmath23 @xmath22 m , and the resulting emission feature can be used to detect mass - loss rates as low as a few @xmath26 m@xmath2 yr@xmath3 in low - luminosity or metal - rich red giants but here , too , the sensitivity is limited by molecular absorption bands and uncertainty in the stellar continuum ( stars are not blackbodies ) as well as the detailed mineralogy . for the examples shown in fig . 1 , the mass - loss rate turns out to be related to the visual extinction , @xmath27 ( @xmath28 ) , as @xmath29 . incidentally , replacing @xmath9 by @xmath30 in eq . ( 5 ) and calibrating against the computed models yields a practically identical constant of proportionality for both silicates and amorphous carbon grains . hence : @xmath31 = 1.5\times10^{-9}\ , z[{\rm z}_\odot]^{-0.5 } l[{\rm l}_\odot]^{0.75 } a_{\rm v}^{0.75}.\ ] ] this provides a new , simple and versatile recipe for estimating mass - loss rates . as a shortcut to comprehensive modeling of the sed , various relationships have been suggested between the optical depth and a monochromatic infrared flux or a single infrared colour . the main reason why this is interesting , is because it may not be possible or economic to sample all of the sed . the _ infrared astronomical satellite _ ( _ iras _ ) made it possible to measure the long - wavelength tail of the dust emission from galactic red giants . this was first quantified by @xcite , who proposed a formula for the mass - loss rate as a function of the flux density at 60 @xmath22 m it depends also on the wind speed , distance , luminosity , dust : gas ratio , and the `` mean wavelength of the light emerging from the star and its circumstellar dust shell '' ( which requires measurement of a significant portion of the sed ) . the formula was adapted to be used at 25 @xmath22 m by @xcite and @xcite . both formulae compare favourably with measurements of the mass - loss rate from the co(j=1@xmath320 ) rotational transition at @xmath33 mm . relationships between mass - loss rate and colours are appealing as they are distance invariant , but in the light of the previous discussion this seems a rather deceptive advantage as they must depend on the star s luminosity . such ( and other unaccounted for ) dependencies are not fully appreciated when they are derived for relatively uniform samples of stars , for instance carbon stars or nearby low - mass red giants in a narrow range of metallicity . formulae are considered successful if they yield mass - loss rates to an intrinsic accuracy of a factor two or so , but the same accuracy can not be guaranteed if applied outside its validity domain ( not limited by just colour range ) . i nonetheless summarise in table 1 several formulae for the mass - loss rate as a function of infrared colour . where a second reference is given the data presented by the former were first parameterised by the latter . linear , square - root or asymptotic functions have been suggested . they share many of the basic assumptions , and notably they are all evaluated for stars of a ( near ) solar metallicity even the mass - loss rates for the presumably metal - poor magellanic stars were derived adopting values for the dust : gas ratio and wind speed typical for red giants encountered in the solar neighbourhood . the approaches of @xcite , @xcite , @xcite , and of @xcite ( parameterised by * ? * ) and @xcite ( parameterised in this review ) are based on modeling of the seds to derive mass - loss rates and then correlating with the near - infrared colours of the same stars . the approach of @xcite ( parameterised by * ? ? ? * ) is similar as they use the @xcite formalism to derive the mass - loss rate , which is a crude way of modeling the sed . they found that the correlation between the mass - loss rate and 25:60 @xmath22 m flux" +"currently accepted theories and many experimental results suggest that hadronic matter changes to quark matter in high - density and/or high - temperature regimes by way of the deconfinement transition . the properties of quark matter have been actively studied theoretically in terms of the quark gluon plasma , color superconductivity @xcite , magnetism @xcite , and experimentally in terms of relativistic heavy - ion collisions @xcite , and early - universe studies and compact stars @xcite . such studies are continuing to provide exciting results @xcite . presently , we consider that compact stars consist of not only nuclear matter but also other matter such as hyperons and quarks . we call such stars _ hybrid stars_. because many theoretical calculations have suggested that the deconfinement transition is of the first order at low temperature and high density @xcite , we assume that it is a first - order phase transition here . the gibbs condition @xcite then gives rise to various structured mixed phases ( smps ) . the smps proposed by heiselberg et al . @xcite and glenndening and pei @xcite suggest a crystalline structure for the mixed phase in the cores of hybrid stars . such structures are called `` droplets '' , `` rods '' , `` slabs '' , `` tubes '' , and `` bubbles '' . we present the equation of state ( eos ) for the mixed phase taking into account the charge screening effect @xcite without relying on any approximations . we investigate the inner structures of these stars @xcite . in this paper , we review the inner structures of hybrid stars and apply our eos to a stationary rotating star . we use the eos given in our paper @xcite , which is presented in our framework . therefore , our approach is only briefly explained here . thermal equilibrium is implicitly achieved at @xmath0 . we consider that the hadronic and quark matter and the mixed phase are @xmath1 stable . we employ density functional theory ( dft ) under the local density approximation @xcite . to account for the confinement , we introduce a sharp boundary between the two phases employing the bag model @xcite with a surface tension parameter @xmath2 . the determination of the surface tension between hadronic and quark matter is a difficult problem . thus , many authors have treated the surface tension as a free parameter and have observed its effect @xcite ; we take the same approach in this study . to determine the charge screening effect , we also conduct the calculations without the screening effect . we then apply the eos derived in our paper @xcite to the tolman oppenheimer volkoff ( tov ) equation @xcite . after that , we apply our eos to a stationary rotating star . [ cols=""^,^ "" , ] we see an important relation between radius and rotation . ordinarily , the `` radius '' of the star is single - valued because we consider that the star is spherical . however , if the star is rapidly rotating , we have to pay attention to the different `` radii '' . because of the effect of the rotation , a star deforms from a sphere to an ellipse . therefore , we introduce two values , @xmath3 and @xmath4 , which are the equatorial radius "" and the polar radius "" , respectively . figure [ r - f_sc ] shows @xmath3 and @xmath4 with respect to rotation . if the rotation rate is 400 hz or faster , the two radii are different . therefore , we have to note the effects of rotation on rapidly rotating stars . in this study , we demonstrated how charge screening affects the hadron quark mixed phase in the cores of hybrid stars , taking into account rotation effects . we found that the inner structures are strongly affected . in particular , a core consisting of quark matter could appear due to the charge screening effect . another case , kaon condensation , has been studied @xcite and the results are similar to those of our papers @xcite . we used a simple model for quark matter and nuclear matter . to obtain a more realistic picture of the hadron quark phase transition , we need to take into account color superconductivity @xcite and the relativistic mean field theory @xcite . we will then be able to provide more realistic results . neutron stars have other important physics magnetic fields . however , the origin of these magnetic fields is still unknown . there are ways to explain magnetic fields based on the spin - polarization of the quark matter @xcite . however , whether the quark matter exists or not strongly depends on the eos . in this calculation , we did not take into account magnetic fields . if we include a magnetic field , the resluts are very interesting with respect to the rotation of the star . this work was supported in part by the principal grant of the kagawa national college of technology ." +"quantum control over atom - light interaction is at the core of many recent developments that have greatly extended the horizon of cold - atom physics . a prominent example is the experimental realisation of synthetic spin - orbit coupling ( soc ) in ultracold atomic gases @xcite . by coupling atomic states with raman lasers , the internal and the external degrees of freedom of the atoms are also coupled . this effective soc interaction modifies the single - particle dispersion spectra , and can lead to novel quantum states in both the few - body @xcite and the many - body settings @xcite . of particular interest is the possibility of preparing and probing topological states in cold atomic gases under synthetic soc . while solid - state materials with topologically non - trivial properties have been extensively studied in recent years @xcite , ultracold atomic gases may serve as ideal platforms for the quantum simulation of exotic topological matter @xcite . for instance , the highly tunable parameters of cold atoms should offer unprecedented control over interatomic interactions in a topological material , and thus would provide the intriguing opportunity of simulating topological states in a strongly interacting system . another exciting example in the quantum control over atom - light interaction is the combination of ultracold atoms and cavity quantum electrodynamics in the strong - coupling regime , where quantum effects of both the atoms and the cavity photons become dominant @xcite . in these atom - cavity hybrid systems , an outstanding feature is the interplay between the atoms and the cavity field : while the cavity field couples the internal states of atoms and affects the collective properties of the ensemble , the ensuing dynamics of the atomic gas feeds back on the cavity photons . hence , the cavity field not only serves as a dynamical variable for the many - body system , it also provides a means to detect , non - destructively , key properties of the hybrid system . a seminal experimental achievement in these systems is the recent observation of the dicke superradiance in a bose - einstein condensate ( bec ) coupled to cavity light fields @xcite . in the experiment , as the system becomes superradiant , the back action of the cavity photons on the the atoms leads to a self organisation of the bec . furthermore , it has been demonstrated later that the dynamical structure factor of the bec can also be probed by monitoring photons leaking out of the cavity @xcite . when the bec is replaced by a spinless degenerate fermi gas , it has been shown theoretically that the superradiant cavity field opens a bulk gap at the fermi surface , whereas the back action of the fermi gas gives rise to an enhancement of superradiance due to the nesting effect @xcite . in this work , we study a special atom - cavity hybrid system , where the cavity field participates in raman processes generating a synthetic soc . thus , this scenario combines the two interesting developments mentioned above . similar schemes have attracted much research interest recently @xcite . for a two - component bec in a cavity , it has been shown that the cavity - assisted soc can lead to a rich phase diagram @xcite ; whereas for a two - component degenerate fermi gas , an exotic topological superradiant ( tsr ) state can be stabilised @xcite . in the tsr state , the bulk gap opened by the superradiant cavity photons also protects topologically non - trivial properties of the fermi gas . as a result , local order parameters coexist with global topological invariants in the tsr state . here , we extend the studies in ref . @xcite , and characterise in detail various properties of the tsr state . at the core of our discussion is the interplay of atoms and the cavity field . we first demonstrate that the cavity - induced inter - band couplings play a crucial role in inducing the topological phase transition between the conventional and the tsr state . for this purpose , we compare the phase diagrams of relevant tight - binding models involving different number of bands , and show explicitly that only by taking the lowest several bands into consideration would one recover , qualitatively , the phase diagram from a full - band calculation . this enables us to derive a minimum tight - binding hamiltonian for our system , which is helpful for generalising the steady - state phase diagram of the current system to other related systems . importantly , we notice that , in general , the multi - band effect is crucial in studying raman - induced synthetic soc in lattice systems . this conclusion is consistent with a recent study on laser - induced soc in lattice models @xcite . we then investigate the back action of the topological phase transition of the fermi gas on the cavity photon . across the topological phase boundary between the trivial superradiant state and the tsr state , the bulk gap closes and opens again . we show that at this phase boundary , the fermi surface at half filling lies exactly at the gap closing point . as a result , a spin - down state on the fermi surface would be scattered by a raman process to the spin - up state , which is also on the fermi surface . this is essentially the nesting effect discussed in refs . @xcite , for a spinless fermi gas in a cavity . we show that the nesting effect here leads to a peak structure in the variation of the cavity photon occupation at the topological boundary . which can be used as a clear signature for the topological phase transition . in the remainder of the work , we discuss the robustness of the tsr state by investigating the steady - state phase diagram under various circumstances . we find that the tsr state as well as the general outlook of the phase diagram are robust against finite - temperature effects , and that the tsr state should persist even in the absence of a background lattice potential . we also show that with a larger number of atoms in the cavity , which is most likely the case in experiments , the tsr state is actually more stable . hence , our study should be helpful for future experimental preparation and detection of the tsr state . the paper is organised as follows : in sec . [ sec : model ] , we outline the system configurations and our derivation of the model hamiltonian of the quasi - one dimensional fermi gas . then , in sec . [ sec : phasediag ] , we briefly review general properties of the tsr state and present the typical steady - state phase diagram . as the focus of the current work , sec . [ sec : feedback ] is devoted to the discussion on the mutual feedback interactions between atoms and the cavity field . in sec . [ sec : robust ] , we examine the robustness of the tsr state and discuss effects of finite temperature , background lattice potential and atom number . we also discuss issues related to the experimental implementation of our system . finally , we summarise in sec . [ sec : summary ] . we consider a quasi - one - dimensional , two - component fermi gas strongly coupled to an optical cavity . while the cavity is transversely pumped by a laser field , the pumping laser and the cavity field couple two hyperfine states in the ground - state manifold of each atom in two - photon raman processes ( see fig . [ fig : config ] ) . while fermions in the cavity are non - interacting , they are subject to a background lattice potential , whose parameters can be controlled independently . this can be achieved , for example , by using a two - mode cavity @xcite . while the atoms are coupled to one of the modes ( pumped by a in fig . [ fig : config ] ) , the other mode is longitudinally pumped and provides the background potential ( pumped by b in fig . [ fig : config ] ) . the effective hamiltonian for a single atom in the fermi gas can be written as @xcite @xmath0\hat{\psi}_{\sigma } \nonumber\\ & -&\delta_{a}\hat{a}^{\dagger}\hat{a } + \eta\left[\int d\boldsymbol{r}\hat{\psi}_{\uparrow}^{\dagger}\left(\hat{a}e^{ik_{0}z}+\hat{a}^{\dagger}e^{-ik_{0}z}\right)\cos\left(k_{0}x\right)\hat{\psi}_{\downarrow}+\rm{h.c.}\right],\end{aligned}\ ] ] where @xmath1 ( @xmath2 ) are the fermionic field operators for different hyperfine states , @xmath3 is the annihilation operator for the cavity field , @xmath4 , @xmath5 is the atomic mass , and @xmath6 represents hermitian conjugate . here , @xmath7 is the three dimensional kinetic energy , @xmath8 is the radial trapping potential , where we consider the tight radial confinement to be in the @xmath9@xmath10 plane . while an effective zeeman field @xmath11 is applied along the @xmath10 axis , the background lattice potential is given as @xmath12 . @xmath13 is the wave vector of the cavity modes , which are approximately the same . the cavity detuning @xmath14 , where @xmath15 is the resonant frequency of the cavity mode a , and @xmath16 is the frequency of the transverse pumping laser . we may then define @xmath17 , and the effective rabi frequency of the cavity - assisted raman processes @xmath18 , where @xmath19 is the single - photon detuning of the raman processes . under tight radial confinement , we assume that only the ground state of the radial degrees of freedom is occupied . the fermionic field operator can be written as @xmath20 where @xmath21 is the characteristic width of the radial harmonic confinement , with the transverse trapping frequency @xmath22 . @xmath23 is the field operator in the transverse directions . integrating out the transverse degrees of freedom , the effective one - dimensional hamiltonian is @xmath24\hat{\psi}_{\sigma}-\delta_a\hat{a}^{\dagger}\hat{a}\nonumber\\ & + & \eta_{a}\left(\hat{a}+\hat{a}^{\dag}\right)\left[\int dx\hat{\psi}_{\uparrow}^{\dagger}\cos\left(k_{0}x\right)\hat{\psi}_{\downarrow}+\rm{h.c.}\right],\end{aligned}\ ] ] where @xmath25 with @xmath26 . considering the cavity decay rate @xmath27 , we can write down the equation of motion for the cavity field @xmath28\nonumber\\ & + & \eta_{a}\left[\int dx\hat{\psi}_{\downarrow}^{\dagger}\cos\left(k_{0}x\right)\hat{\psi}_{\uparrow}+\rm{h.c.}\right].\end{aligned}\ ] ] we consider the steady - state solution of the system under the stationary condition @xmath29 , where @xmath30 is the cavity mean field . from the stationary condition , we have @xmath31}{\delta_{a}+i\kappa-\xi_{a}\sum_{\sigma}\int dx\langle\hat{\psi}_{\sigma}^{\dagger}\hat{\psi}_{\sigma}\rangle\cos^{2}\left(k_{0}x\right)}.\ ] ] apparently , when the system is in the steady state , the cavity mean field @xmath32 depends on the spin - spin correlation @xmath33 of the fermi gas , while the latter is in turn affected by the cavity mean field through the effective hamiltonian ( [ eqn : effh ] ) . these observations clearly demonstrate the feedback interactions between the cavity field and the fermi gas . the steady state of the system can be solved self - consistently from eqs . ( [ eqn : effh ] ) and ( [ eqn : alpha ] ) . starting from an appropriate initial cavity field @xmath34 , we diagonalise the effective hamiltonian eq . ( [ eqn : effh ] ) for the energy spectrum . we then solve for the chemical potential from the number equation @xmath35 . the cavity mean field @xmath32 is then updated via eq . ( [ eqn : alpha ] ) . we repeat the process until @xmath32 converges . note that we only consider the interesting case when the fermions in the background lattice potential are at half filling . as the transverse pumping strength @xmath36 increases past a critical value , the cavity - atom hybrid system undergoes a superradiant phase transition . upon the onset of superradiance , the relevant cavity mode ( mode a ) becomes macroscopically occupied , and the spin - spin" +"the specific features of the nica ( nuclotron based ion collider facility ) research programme @xcite , and in particular ( a ) the broad range of reactions planned to be studied , ( b ) the relatively modest collision energy @xmath0 , placing the whole programme close to that of the cern sps , ( c ) the possibility to measure reactions at different energies , and ( d ) the elasticity of taking measurements both in fixed target and collider modes , make it well suitable for studying the interplay of strong and electromagnetic interactions in nuclear collisions . what we specifically address in the present proposal is the _ electromagnetic interaction between charged particles produced in the collision and the nuclear remnant that does not participate directly in the reaction _ ( the spectator system ) . this latter phenomenon is of particular interest because , as discussed in our earlier works @xcite , _ it provides independent information on the space time - evolution of the reaction _ : the space - time evolution of the particle production process , the fragmentation ( break - up ) of the spectator system , and the interplay between the two . it is to be noted that with the well - known exception of hbt measurements @xcite , the experimental programmes at the sps , rhic and lhc provide direct information essentially only on the final ( or near - to - final ) state particles in _ momentum space _ ( @xmath1 , @xmath2 , @xmath3 ) . much less is possible as far as providing information on the evolution of the reaction in _ position space _ ( @xmath4,@xmath5,@xmath6 ) , which on the other hand is extremely important in view of our understanding of the heavy ion reaction . here nica could strongly contribute to the overall knowledge in the whole heavy ion field , with very little competition from existing experiments . the corresponding measurements would in particular include _ particle spectra , charged particle ratios _ ( @xmath7 , @xmath8 , etc . ) and _ directed flow_. this paper is organized as follows . in section [ sectwo ] , we discuss the principal features of the spectator - induced electromagnetic effect , with particular emphasis on its importance as a new source of information on the mechanism of the nuclear reaction . in section [ secthree ] , we define the possible future contribution of nica . in section [ secfour ] , we shortly address the subject of competition from other experiments . we present our conclusions in section [ secfive ] . it is not surprising that various kinds of electromagnetic interactions in nucleus - nucleus collisions were studied in the past ( a partial overview can be found in @xcite ) . the problem of coulomb corrections to hbt measurements belongs in fact to the `` standard '' in the analysis of heavy ion experimental data . numerous works exist also on the influence of the electromagnetic field on the spectra of particles produced at _ mid - rapidity _ ( that is , in the vicinity of @xmath9 ) in central heavy ion reactions and rapidity @xmath10 in the nucleon - nucleon c.m.s . ] however , these concentrate on the electromagnetic field induced by the presence of initial charge in the `` participant zone '' , that is , the charge of the _ participating nucleons _ in central nucleus - nucleus collisions , see above , while the spectator charge will produce the largest effect at higher values of @xmath11 and in peripheral collisions . ] . on the other hand , it seems that the theoretical and experimental analyses of the electromagnetic interactions between _ nuclear remnants _ and produced particles were performed mostly at lower energies . very sizeable electromagnetically - induced distortions were observed there @xcite . an important , much more recent result , was reported in nuclear collisions at several gev / nucleon , where the non - relativistic approach to the coulomb field brought information on the space - time evolution of the process of nuclear fragmentation @xcite . in the energy regime of the cern sps and above , up to now our main range of interest , we were aware of only one earlier experimental measurement @xcite . the latter was unfortunately restricted to a very narrow acceptance range ( forward angles i.e. @xmath12 ) , and to an extremely small number of data points ( between two and four , depending on collision centrality ) which limited its scientific usefulness . ratios measured by the na49 experiment at the cern sps , drawn as a function of @xmath11 at fixed values of @xmath13 ( listed from top to bottom curve ) ; ( b ) result of the monte carlo simulation described in the text . the figure comes from @xcite.,scaledwidth=85.0% ] for this reason , we performed a series of experimental and theoretical studies of the influence which the spectator charge exerts on charged pion and charged kaon spectra @xcite . out of these , a consistent picture emerges which can be summarized as follows : 1 . the presence of the spectator - induced electromagnetic field brings a very sizeable distortion to @xmath7 ratios observed in the final state of `` peripheral '' ( large impact parameter ) pb+pb reactions measured at a beam energy of 158 gev / nucleon ( @xmath14 gev ) . this is shown in fig . [ fig : figone](a ) , where the @xmath11-dependence of @xmath7 ratios is drawn in the projectile hemisphere of the reaction , for fixed values of pion transverse momentum @xmath13 . this effect is so strong that the @xmath7 ratio goes close to zero in the vicinity of @xmath15 , violating isospin symmetry and thus unequivocally confirming the electromagnetic origin of the whole phenomenon . note that the latter value of @xmath16 corresponds , at low transverse momenta , to pions moving at the same velocity as the spectator system , thus confirming that electromagnetic repulsion ( attraction ) of positive ( negative ) pions from positively charged spectator protons is indeed at the cause of this behaviour . + ( left ) and @xmath8 ( right ) ratios , for particles produced in peripheral pb+pb collisions . the different panels correspond to different pion and kaon emission times @xmath17 . the figure comes from @xcite.,scaledwidth=75.0% ] 2 . our simple monte carlo model of the electromagnetic interaction @xcite brings a very reasonable description of the main features of this effect as shown in fig . [ fig : figone](b ) . the unique region where a more significant disagreement between data and model can be seen ( @xmath18 , low @xmath13 ) has been identified as due to the process of _ nuclear fragmentation ( break - up ) of the spectator system _ ; a discussion of this subject can be found in @xcite . 3 . a very similar electromagnetic effect is also present in high energy collisions of lead ions with lighter nuclei which we recently investigated @xcite . 4 . the electromagnetic distortion observed in fig . [ fig : figone](a ) _ depends on the specific space - time scenario imposed on pion emission_. this is illustrated in fig . [ fig : figtwo ] ( left ) where the results of our model calculations are drawn in the full range of @xmath11 , @xmath19 , for different values assumed for the time of pion emission @xmath17 . the characteristic distortion pattern imposed by the two spectator systems at positive and negative @xmath11 appears clearly sensitive to @xmath17 ( with typically lower @xmath7 ratios obtained for larger @xmath17 at higher values of @xmath11 ) . _ this implies that the electromagnetic effect provides independent information on the evolution of the non - perturbative process of pion production in space and time _ the electromagnetic distortion of charged kaon ( @xmath8 ) ratios , fig . [ fig : figtwo ] ( right ) , exhibits basic qualitative similarities to the effect seen for pions , however , with pronounced differences on the quantitative level . the position of the deep `` valley '' in the ratio is displaced towards higher values of @xmath11 , and the region of highest sensitivity to the kaon emission time is moved towards very high @xmath11 ( @xmath20 ) . 6 . finally , as apparent in fig . [ fig : figthree ] , the spectator - induced electromagnetic force exerts also _ a noticeable influence on pion directed flow , @xmath21_. our very recent monte carlo calculation ( not yet published ) predicts a well - defined pattern in the rapidity dependence of the _ electromagnetically - induced _ directed flow of positive pions , with a large peak in the vicinity of projectile and target rapidities . as such , directed flow of charged pions ( @xmath22 , @xmath23 ) appears as another observable where , also through electromagnetic effects , new information on the space - time evolution of the reaction can become available . . the simulation assumes the pion emission time @xmath17 equal to zero . directed flow is integrated over @xmath13 from 0 to 1 gev / c.,scaledwidth=75.0% ] the above description is , of course , highly simplified ( the interested reader is invited to visit the enclosed bibliography for a more detailed account ) , but nevertheless constitutes a good starting point for the present proposal . as it comes from the considerations above , and as has also been suggested to us in numerous discussions with experts , the spectator - induced electromagnetic effects discussed here have very specific characteristics which make them attractive for numerous future studies : 1 . they can be large in specific regions of phase space ; 2 . they can bring large distortions to various collision characteristics observed in the final state ( like charged particle ratios or directed flow ) and at the same time , they can provide information about the intrinsic space - time scenario of particle emission ( formation times , parton fragmentation , resonance decays , hydrodynamics , etc ) . as such , in principle they should be studied in any possible reaction at any possible energy , whenever this is possible . this is particularly important in the present situation where the available experimental information remains very limited . in the high energy regime ( sps energies and above ) , no experimental data set other than what was discussed above is known to us . no possibility of obtaining such information at rhic or lhc is apparent to us due to strict experimental limitations . for this reason , we see here a good scientific prospect for nica . the principal detector requirements needed in order to perform measurements of the spectator - induced electromagnetic effect are particle momentum vector reconstruction and particle identification capabilities ( including in particular charge differentiation ) , as well as a relatively wide acceptance coverage defined in terms of longitudinal and transverse momenta . once these conditions are fulfilled , measurements of particle spectra ( preferably double differential spectra of the type @xmath24 ) become accessible . measurements of directed flow ( as well as possibly higher harmonics ) are characterized by additional requirements well known to the community . in the range of collision energies specified in @xcite , the nica / mpd apparatus looks promising in view of the requirements specified above . with the extremely broad spectrum of reactions planned to be analysed , including in particular proton - nucleus and nucleus - nucleus collisions with an impressive versatility of projectiles and targets , we propose a _ detailed , systematic experimental study of charged particle spectra and directed flow with a special emphasis on charge asymmetries induced by" +"in the field of coding theory , calculations of good upper and lower bounds on the size of a code serves as a benchmark for code design . techniques of constructing subspace codes for error correction in random network coding ( also called ` projective space codes ' ) are similar to the techniques used to construct binary codes . a projective space code is defined as a subset of subspaces of a vector space . the viewpoint of lattice theory for projective space codes has already been suggested @xcite . a lattice is a partially ordered set in which any two elements have a least upper bound and a greatest lower bound . the set of all subspaces of a vector space is called a projective space and the set of all subsets of a set is called a power set . both the power set and the projective space form lattices under inclusion order . a ` lattice scheme ' is defined as a subset of a lattice . it has already been observed in @xcite that binary codes and projective space codes are lattice schemes . binary codes are power set schemes and projective space codes are projective space schemes . the lattice framework common to projective space codes and binary codes have also been observed in @xcite and @xcite . the authors of @xcite establish that the projective space codes are analogs of classical binary codes . they also investigate the notions of linearity and complements of a code . in @xcite , the relationship between binary codes and projective space codes is investigated thoroughly using the framework of lattices and a generalized notion of orthogonal complement is introduced for lattices . one of the ways to generate a bound on the code size is to capture a bare minimum structure for the bound through an appropriate mathematical abstraction and generalize the approach . for example , the introduction of ` association schemes ' captured the notion of sphere packing and sphere covering arguments in traditional coding theory @xcite and strengthened the bounds by a linear programming approach . in our paper , the notion of singleton bound is generalized using the framework of lattices . since error correcting codes for random network coding was proposed in @xcite , there has been a lot of activity in the theory of projective space codes . the authors of @xcite consider projective space codes in which all the subspaces are of the same dimension . such codes are called constant dimension codes . the koetter - kschischang singleton bound ( kks bound ) for constant dimension codes was derived and achieved asymptotically in @xcite . in the case of binary codes , hamming distance between two binary vectors is a metric on the binary coding space . similarly the subspace distance , introduced in @xcite , between two subspaces of a vector space is a metric on the projective space . in a projective space , the number of elements in a sphere of a particular radius depends on the center of that sphere @xcite . however , in the case of binary codes , the number of elements in a sphere depends only on the radius of the sphere and not on the center of the sphere . so the subspace distance on the projective space behaves differently from the hamming distance on the usual binary vectors . as noted in @xcite , the anticode bound introduced in @xcite gives a setting in which one can get tighter sphere packing bounds for constant dimension codes . a close look at the bounds for subspace distance and non - existence of nontrivial perfect codes has been given in @xcite . an appropriate generalization for singleton bounds ( analogous to association scheme for sphere packing / covering bounds ) is not known yet . in this paper , we propose that the lattice framework is appropriate for generalizing singleton bounds . we derive an upper bound on the size of a lattice scheme , which will be called lattice singleton bound ( lsb ) for the remainder of the paper . we get the kks bound and the classical singleton bound as special cases of the lsb . while most results in projective space codes assume that the dimensions of the subspaces in the code are constant , a few papers in literature have considered codes with non - constant dimension . in particular , the authors of @xcite derive a gilbert - varshamov type bound , which we will term as ` etzion vardy- gilbert varshamov bound ' ( ev - gvb ) , for non - constant dimension codes . we derive a _ new _ upper bound on the code size for non - constant dimension codes by applying the lsb to the projective lattice . to the best of our knowledge , our singleton bound is the first upper bound for non - constant dimension codes . the construction of constant dimension codes have been the main focus in the field of code constructions for projective spaces . the first constant dimension subspace codes introduced in @xcite achieve the kks bound asymptotically . and there is no known code constructions that exactly achieve the singleton bound proposed in @xcite . the question of achieving that singleton bound is an open question . a large class of constant and non - constant dimension codes using ferrer s diagrams and lifted rank metric codes are constructed in @xcite . the authors of @xcite report marginal improvements over the size of the code compared to the codes of @xcite . a plot of code sizes of the codes reported in @xcite compared to a plot of our upper bound shows that both the reported codes have code sizes that are close to optimal . this also establishes that our upper bound is tight for atleast certain coding parameters . the contributions of this paper are as follows : 1 . we derive a singleton bound in the framework of lattices . we recover the singleton bound for binary codes and the singleton bound for constant dimension subspace codes ( kks bound ) as special cases of our lsb . we obtain a new singleton bound for non - constant dimension subspace codes . we compare our bound on the code size with the code sizes of non - constant dimension codes found in the literature . we also compare our upper bound with a gilbert - varshamov type lower bound . the plots reveal that our bound is tight for certain parameters of the code . the paper is organized as follows : we introduce the preliminaries of lattices in section [ sec_lat_prelims ] . section [ sec_lat_sch ] introduces the idea of lattice schemes where it is shown that classical codes and subspace codes are both lattice schemes . section [ sec_main_res ] introduces the singleton bound in the framework of lattice schemes and contains the main theorem of this paper . section [ sec_main_res ] contains the main distinguishing feature of projective space codes which we believe make singleton type bounds weak in projective spaces . in section [ sec_upp_bou ] , we obtain a new upper bound for non - constant dimension codes and plot our upper bound with ev - gvb along with different codes constructed in the literature . finally , in section [ sec_conc ] , we conclude by summarizing our contributions and discussing the scope for future work . _ notations : _ a set is denoted by a capital letter and its elements will be denoted by small letters ( for example , @xmath0 ) . the set @xmath1 is defined as @xmath2 . all the sets considered in this paper will be finite . given a set @xmath3 , @xmath4 denotes the number of elements in the set and for a subset @xmath5 of @xmath3 , @xmath6 denotes the complement of the set @xmath5 in @xmath3 . for two sets @xmath5 and @xmath7 , @xmath8 denotes the cartesian product of the two sets , i.e. @xmath9 . @xmath10 represents the symmetric difference of sets , i.e. @xmath11 . a lattice will be denoted by @xmath12 and sometimes we will drop the join and the meet notation , simply calling it @xmath13 . @xmath14 denotes the finite field with @xmath15 elements where @xmath15 is a power of a prime number . @xmath16 denotes all the non zero elements of @xmath14 . the symbol @xmath17 denotes a vector space ( generally over @xmath14 ) . for a subset @xmath18 of @xmath17 , @xmath19 denotes the linear span of all the elements in @xmath18 . given two subspaces @xmath5 and @xmath7 , @xmath20 denotes the smallest subspace containing both @xmath5 and @xmath7 . let @xmath17 be a @xmath21 dimensional space over @xmath14 . then the symbol @xmath22 denotes the grassmanian , i.e. the set of all @xmath23 dimensional subspaces of @xmath17 . the number of elements in @xmath22 is denoted as @xmath24 . @xmath25 denotes the @xmath21 dimensional vector space of @xmath21-tuples over @xmath14 . given a vector @xmath26 , @xmath27 denotes the @xmath28-th co - ordinate of @xmath29 . the support of @xmath26 ( denoted by @xmath30 ) is defined as the set of indices where the vector is non - zero . @xmath31 denotes the vector space @xmath25 with the hamming metric , i.e. @xmath32 . this section serves as a quick introduction to lattice theory . all the lattice theory definitions and theorems required for the rest of the paper are given in this section . we follow notations and definitions from @xcite . [ def_poset_order ] a _ poset _ is a pair @xmath33 , where @xmath34 is a set and @xmath35 is a binary relation ( called the _ order relation _ ) on the set @xmath34 satisfying : 1 . ( reflexivity ) for all @xmath36 2 . ( antisymmetry ) if @xmath37 , then @xmath38 3 . ( transitivity ) if @xmath39 , then @xmath40 for the remainder of the paper , @xmath34 denotes a poset with @xmath35 as the order relation . if @xmath41 and @xmath42 , then we use the shorthand @xmath43 . @xmath41 is read as `` x is less than y '' or `` x is contained in y '' . an _ upper bound _ ( _ lower bound _ ) of a subset @xmath3 of @xmath34 is an element @xmath44 containing ( contained in ) every @xmath45 . the _ least upper bound _ ( _ greatest lower bound _ ) of @xmath3 is the element of @xmath34 contained in ( containing ) every upper bound ( lower bound ) of @xmath3 . if a least upper bound , or a greatest lower bound of a set exists , it is unique due to the antisymmetry property of the order relation ( definition [ def_poset_order ] ) . the least upper bound of a set @xmath3 is denoted by sup @xmath3 and the greatest lower bound is denoted by inf @xmath3 . a _ lattice _ @xmath13 is a poset which has the property that @xmath46 , the sup@xmath47 exists and inf@xmath47 exists . the sup@xmath47 is denoted by @xmath48 ( read as `` a _ join _ b '' ) and the inf@xmath47 is denoted by @xmath49 ( read as `` a _ meet _ b '' ) . the lattice itself is denoted by @xmath12 . we will assume , for the purposes of the paper , that all the lattices are finite and have a unique greatest element denoted by @xmath50 , and a unique least element denoted by @xmath51 . a _ sublattice _ of a lattice @xmath13 is a subset @xmath52 of @xmath13 that satisfies the following condition : @xmath53 a map @xmath54 from @xmath13 to @xmath52 is said to be a _ lattice homomorphism _ if it satisfies the following conditions : 1" +"since the observation and explanation of the gunn - effect in the early 60 s it has been known that traveling field inhomogeneities are generated by negative differential velocity ( ndv).@xcite the properties of these traveling gunn - domains have been studied extensively theoretically and experimentally @xcite leading to several proposals for applications . the most important application is probably the frequency generator . although oscillator devices based on the gunn - effect operating in the range of 100 ghz have been reported,@xcite gunn - oscillators have not led to the expected breakthrough in technology . this is largely due to the difficulties in tuning the oscillation frequency . furthermore , it is impossible to vary the drift velocity vs field characteristics ( @xmath0 curve ) except by using different bulk materials ( e.g. , gaas , ingaas or inp ) . these problems may be overcome by using an entirely different class of ndv exhibiting materials formed by semiconductor superlattices . in an applied electric field perpendicular to the two - dimensional layers , several different transport mechanisms such as miniband transport , resonant tunneling , and real - space transfer from well to barriers ( @xmath1 transport ) give rise to complex @xmath0 curves with several regions of ndv as shown in fig . [ slwfield ] . in contrast to the above mentioned materials , the tunability of the barrier and well thickness as well as the control over the barrier height in the superlattice can be used to tailor the drift velocity vs field @xmath0 characteristics . by proper engineering , samples with several ndv regions can be manufactured with control over previously inaccessible features such as the actual shape of the ndv ( cf . [ slwfield ] ) . the frequency of the oscillations also depends on the number of moving charges in the superlattice , which may be controlled by varying the doping in the quantum wells . currently , three different types of superlattice oscillations due to ndv have to be distinguished : * the most prominent type of oscillations is found , when carriers within the miniband are accelerated beyond the brillouin zone boundary , where their drift velocity becomes negative . in the absence of scattering , the electron wave packet then oscillates with the bloch frequency @xmath2 , where @xmath3 and @xmath4 denote the superlattice period and planck s constant , respectively.@xcite these so - called bloch oscillations were predicted for superlattices by esaki and tsu in 1970.@xcite inspired by the prospect of thz frequency generators based on superlattice bloch oscillators , a long series of investigations targeting the miniband regime followed leading to the observation of damped bloch oscillations in experiments with pulsed optical excitation a few years ago.@xcite * a different type of oscillations occurs in the miniband regime , when the scattering times are shorter than the tunneling times . in this case transient charge accumulations traveling through the superlattice may lead to oscillations in the current . experiments using pulsed optical excitation of carriers in superlattices with wide minibands showed damped oscillations with frequencies up to 20 ghz.@xcite more recently , reflection gain up to 60 ghz in doped superlattices with miniband widths of up to 80 mev was demonstrated.@xcite * very recently a third type of oscillations has been shown to exist in weakly coupled superlattices in field regions where tunneling into higher subbands takes place.@xcite as a consequence of domain formation , this type of oscillations may also be observed in field regions where the electrons tunnel between the lowest subbands . while the first two oscillation types have never been observed under constant bias conditions , this new type is shown to operate over a broad frequency range practically independent of the external circuit and without any external triggering . in this paper we investigate experimentally and theoretically the third type of oscillations in lightly and moderately doped superlattices ( sl ) . this type of oscillations may be generally observable in the ndv regime of the @xmath0 characteristics of such superlattices . in a companion paper , @xcite we have shown that self - sustained oscillations may exist if the dimensionless doping parameter , @xmath5 ( @xmath6 is the 3d sl doping , and @xmath7 is the field at the resonance we consider ) lies between two values @xmath8 which can be calculated numerically from the local @xmath0 characteristics ( @xmath9 is the number of sl periods ) . if several tunneling resonances exist ( cf . fig . [ slwfield](a ) and ( b ) ) the frequency of the oscillations increases with increasing index of the subband involved in the tunneling resonance . this observation is attributed to the larger drift velocities associated with the resonances involving higher subbands . furthermore , several new oscillatory modes without the typically well - defined domains are shown to exist . these oscillatory modes can be tuned in frequency simply by changing the applied voltage . because the oscillations are observable even at room temperature , we suggest to use superlattice oscillators based on resonant tunneling into higher subbands as a tunable source for high frequencies . four gaas / alas superlattice structures , grown by molecular beam epitaxy , are discussed in this paper . the samples are hereafter referred to as 9.0/4.0 ( doped and undoped ) , 9.0/1.5 , and 13.3/2.7 , where the first number refers to the gaas well width and the second to the alas barrier thickness in nm ( cf . table [ samples ] ) . the superlattices are embedded between two highly doped al@xmath10ga@xmath10as contact layers with a doping density n@xmath11=2@xmath12 @xmath13 ( si for @xmath14- and be for @xmath15-type doping ) forming @xmath14-@xmath16-@xmath14 and @xmath15-@xmath17-@xmath14diodes . after evaporating auge / ni contacts onto the top and substrate side and alloying them for ohmic connections , the samples are wet - etched into mesas of 120 @xmath18 m diameter . the circular top contacts of 70 @xmath18 m diameter leave a large part of the mesas uncovered to allow for optical access . all experiments are performed at 5 k in a he - flow cryostat using high - frequency coaxial cables with a bandwidth of 20 ghz . the time - averaged current - voltage data are recorded with a keithley smu236 . the time - resolved current is detected with a tektronix sampling oscilloscope csa 803 using the ghz sampling head sd-32 . [ iv6750 ] shows the current - voltage ( i - v ) characteristics of the doped 9.0/4.0 sample in forward bias . clearly visible are two plateau regions with almost constant current between 0.5 and 4 v and 6.5 and 8.5 v. to prove that these plateaus are related to the subband resonances , time - of - flight ( tof ) measurements were performed on an undoped 9.0/4.0 reference sample ( @xmath15-@xmath17-@xmath14 diode).@xcite the peak photocurrent is thereby taken as a measure for the inverse transport time , which at low excitation densities is directly proportional to the drift velocity for homogeneous fields . note that for the presentation in fig . [ iv6750 ] the built - in voltage ( @xmath19 v ) of the @xmath15-@xmath17-@xmath14 diode has been subtracted from the reverse bias voltage applied to the @xmath15-@xmath17-@xmath14 diode and the sign has been inverted . the resonances for tunneling from the first into the second ( @xmath20 ) as well as into the third ( @xmath21 ) conduction subband are clearly observed at 6 and 15 v , respectively . the low - field transmission maximum ( @xmath22 ) , which in the case of a strongly coupled superlattice corresponds to miniband conduction , is not resolved in this sample , because the transport time is too long in this field range to be resolved with this method . however , it has been shown previously that even weakly coupled superlattices exhibit a negative differential drift velocity in this regime.@xcite in addition to the @xmath23 resonances due to @xmath24-subbands in the gaas wells and the exponential nonresonant background , a pronounced step - like increase of the peak photocurrent is observed at about 10 v , which is assigned to enhanced transport through the lowest @xmath25-level in the alas barriers . the lowest @xmath25-states of the alas barriers are energetically located in such a way that transport through these @xmath25 states becomes possible at voltages between the @xmath20 and @xmath21 resonances . in the drift velocity vs field characteristics , this @xmath1 resonance leads to a step - like increase of the drift velocity as indicated by the dotted line in fig . [ slwfield](b ) . the voltages of the observed resonances can be compared to the calculated energy levels listed in table [ samples ] . for example , the bias voltages @xmath26 for @xmath27 resonances are calculated using @xmath28 where @xmath29 denotes the energy of the injecting conduction subband and @xmath30 the energy of the conduction subband , in which the carriers are tunneling into . @xmath9 refers to the number of periods and @xmath31 to the electron charge . in the case of @xmath1 resonances , however , the distance between the levels is reduced to half the superlattice period . therefore , an additional factor of 2 has to be included , i.e. , @xmath32 where @xmath33 denotes the energy of the receiving state in the barrier . the voltages for the @xmath24 resonances @xmath20 and @xmath21 are calculated using eq . ( [ resonances1 ] ) resulting in 5.4 and 14.6 v for the 9.0/4.0 sample , respectively . using eq . ( [ resonances2 ] ) , we obtain a resonance voltage of 8.2 v for the @xmath34 resonance in this sample . all values agree well with the observed values . note that all observed resonances appear at slightly higher voltages due to field inhomogeneities and screening effects . to investigate the electric field inside the superlattice , photoluminescence ( pl ) measurements have been performed.@xcite due to the quantum - confined stark effect ( qcse ) , the pl from regions with strong electric fields is red - shifted with respect to the pl from low - field regions . the experiments reveal that in both plateau regions of this sample the pl consists of two peaks with their respective intensity depending on the applied bias voltage . this stark - splitting of the pl signal is taken as direct evidence for the existence of two distinct electric - field domains , which are formed because of ndv and current conservation . for the first plateau the consequence of this conservation law is depicted by the dashed line in fig . [ slwfield](b ) . clearly , the electric field of the low - field domain ( @xmath35 ) corresponds to the @xmath22 resonance peak , while the field strength of the high field domain ( @xmath36 ) lies on the next rising branch of the @xmath0 characteristics slightly below the @xmath20 resonance.@xcite applied to the second plateau , the current conservation law ( dashed lines in fig . [ iv6750 ] ) shows that the high field domain in this voltage region forms as a consequence of resonant transport through the @xmath37 level in the barriers ( @xmath34 transport ) . in contrast to previous work,@xcite where this new formation mechanism was considered for the first time , this measurements provide the first direct evidence relating @xmath25-levels in the barriers to domain formation . however , it should be mentioned that it is not very surprising to observe domain formation due to transport through the @xmath37 level . for domain formation to occur , only a _ minimum of the @xmath0 curve _ is required in conjunction with a sufficiently high carrier density.@xcite in that sense the subject of domain formation and conditions for oscillations can be discussed simply by looking at the" +"lyman alpha ( ly@xmath4 ) emitting galaxies ( laes ) have been used for years as probes of the high - redshift universe ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? these studies have shown that laes are fairly common from 2 @xmath2 z @xmath2 7 , and more interestingly , their properties do not evolve strongly with time , with stellar populations and observed ly@xmath4 luminosity functions which are roughly constant over this redshift range . @xcite discovered @xmath0 100 low - redshift laes from 0.2 @xmath2 z @xmath2 0.45 with the galaxy evolution explorer ( galex ) . they ruled out objects with ly@xmath4 line widths @xmath5 1200 km s@xmath6 as broad - lined active galactic nuclei ( agn ) , although they typically could not rule out narrow - lined agn , as the ciii ] or civ diagnostic lines were either too faint , or located in a noisy part of the spectrum . they found that the ly@xmath4 luminosity function of these objects was substantially different than at high - redshift , with low - redshift laes having a lower surface density and being typically less luminous in the ly@xmath4 line . in @xcite , we studied the physical properties of 30 of these laes which had optical counterparts in the extended chandra deep field south ( cdf s ) and extended groth strip ( egs ) , and found them to be significantly older and more massive than their high - redshift counterparts , with typical ages of a few gyr , and stellar masses of @xmath0 10@xmath7 m@xmath8 . a few of these objects were poorly fit , which could imply agn contamination , but with only one object detected in x - rays , we could not discern agns from star - forming galaxies . in this letter , we present an optical spectroscopic study of 23 of these low - redshift laes in order to determine the agn fraction in laes at low redshift . while deharveng et al . have already ruled out most broad - lined agn , optical spectroscopy will enable us to search for narrow - lined agn . where applicable , we assume h@xmath9 = 70 km s@xmath6 mpc@xmath6 , @xmath10 = 0.3 and @xmath11 = 0.7 ( c.f . * ? ? ? * ) . we observed 23 low - redshift laes in the egs using hectospec at the 6.5 m mmt , which has a 1@xmath12 diameter field - of - view @xcite . we obtained 2 hours of spectroscopy on 19 march 2009 , with spectral coverage from @xmath0 3650 - 9200 , and spectral resolution of @xmath0 5 . we used the external specroad pipeline for data reduction ( developed by juan cabanela ; private communication ) . this pipeline performs standard spectroscopic reductions , including bias , dark and flat correction , and wavelength calibration ( rms residuals @xmath13 0.1 ) . we flux - calibrated the spectra using observations of sloan digital sky survey ( sdss ) f - type stars . further details on the observations and data reduction , as well as tabulated line fluxes , will be presented in a future paper ( finkelstein et al . 2009 , in prep ) . the 23 laes varied in redshift from 0.2 @xmath1 z @xmath1 0.45 , thus we found 31 possible spectral lines which we could detect , from mgii @xmath14 2796 , 2803 to [ sii ] @xmath156733 . we examined the expected position ( using the redshift from @xcite as a first estimate ) of each of the expected lines in each spectrum , and noted whether it was detected . we fit a gaussian curve to each detected line , using the mpfit idl software package , obtaining the continuum flux , central wavelength , gaussian @xmath16 and line flux . errors on each of these parameters were estimated via monte carlo simulations by varying each spectral data point within its photometric uncertainty . table 1 lists the object redshifts as determined from this spectroscopy , which are consistent with ( and refine ) those published in @xcite . figure [ fig : fullspec ] shows spectra of two of the observed laes , one which we classify as an agn , and one which is dominated by star formation . while some features are obviously different in the agn , many still appear the same , thus one requires numerous diagnostics to investigate the presence of an agn . combining our spectra with the public data from the all wavelength extended groth strip international survey ( aegis ; @xcite ) , we perform five tests to search for agn . we first search for broad - lined agn by examining the widths of permitted lines . we then search our dataset for emission lines from ions which require high energies to ionize their current state , such as [ nev ] ( 126.2 ev ) . next , we use ratios of emission lines to classify them using diagnostic plots from ( * ? ? ? * hereafter bpt ) . we then use infrared data from the _ spitzer space telescope _ to probe for warm dust re - emission from absorbed high - energy photons . finally , we use archival _ chandra x - ray observatory _ data to search for x - ray emission , which could be indicative of an accretion disk around a central black hole . in the following section , the object ids refer to those defined in @xcite . in table 1 we list these ids along with the ids from @xcite . lines from the broad - line region of agns have velocities @xmath17 1000 km s@xmath6 , while narrow - line region lines have widths @xmath1 500 km s@xmath6 . depending on the orientation , one may only see one of these regions , leading to two separate classification of agns : broad - lined agn ( blagn , also called type 1 or seyfert 1 ) , and narrow - lined agn ( nlagn ; type 2 ; seyfert 2 ) . for each object , we measured the characteristic line velocity widths for all detectable , permitted transitions of hi , hei and heii . only egs24 has a velocity width @xmath5 1000 km s@xmath6 , with v = 1064 @xmath18 17 km s@xmath6 , and thus likely contains a blagn . the remaining objects have v @xmath19 300 km s@xmath6 , implying that if an agn is present in the rest of the sample , it is narrow - lined . [ nev ] and heii are two of the strongest indicators of agn activity to which our data are sensitive . we detect [ nev ] @xmath153347 or [ nev ] @xmath153427 in egs16 , egs17 , egs18 and egs24 at @xmath5 3 @xmath16 significance , and in egs14 and egs20 , at 2.9 and 2.0 @xmath16 , respectively . the heii @xmath154686 line is also an agn indicator , and this line is observed at @xmath20 3 @xmath16 significance in egs2 , and at 2.6 @xmath16 in egs24 . we note that although heii emission can also come from the winds of wolf - rayet stars , these lines are typically broad ( e.g. , * ? ? ? * ) , and thus that is likely not the case here . in addition , while the [ nev ] emission is most likely due to an agn , there is the possibility that it arises due to shocks , although none of our objects solely identified by this line inhabit the bpt plane ( see 3.3 ) near the shock models of @xcite ( c.f . [ neiii ] @xmath153869 is detected in numerous objects . however , this line may not conclusively point to an agn , as its ionization potential is not much greater than [ oiii ] . as a control sample , we examined sdss spectroscopic data , to see where objects with detected [ neiii ] emission inhabit the bpt diagram . we found that at all fluxes , objects with [ neiii ] emission populate both the star - forming and agn sequences , implying that [ neiii ] emission is not conclusive evidence of an agn . in figure 2 we plot ratios of h@xmath4/[nii ] versus [ oiii]/h@xmath21 to diagnose the ionizing source within a galaxy @xcite . in this plane galaxies segregate nicely , with separate star - forming and agn sequences . the contours represent the two sequences as defined using @xmath0 10@xmath22 sdss galaxies , with the lighter contours representing the star - forming sequence , and the darker contours representing the agn sequence . we plot each of our objects on this plane using the various colored symbols . we also plot the theoretical maximum starburst line from @xcite and the star formation / agn demarcation line from @xcite . we estimated flux limits for undetected lines by placing mock emission lines in the spectrum , and decreasing the line strength until the detection significance dropped below 3 @xmath16 , finding that 1 @xmath16 line flux limits were typically @xmath13 1.0 @xmath23 10@xmath24 erg s@xmath6 @xmath25 . in objects where any of these lines was undetected , we plot their 3 @xmath16 upper - limits . egs1 , egs3 , egs14 , egs15 and egs24 appear to unambiguously lie on the agn sequence , and we henceforth classify them as agn . egs24 has already been noted for its broad emission lines , as well as its [ nev ] and heii emission , and egs14 also has a 2.9 @xmath16 [ nev ] detection . although egs1 , egs3 and egs15 were not indicated by either of our previous classification methods , they are located very far from the star - forming sequence , and significantly higher than the maximum starburst curve . however , egs1 appears to be in the liner regime , and thus if an agn is present , it may not be dominating the observed continuum and line fluxes . egs16 , egs17 and egs21 lie in regions which could correspond to either agn or star - forming galaxies , as well as near the kauffmann et al . demarcation line . egs16 and egs17 have detected [ nev ] emission . as egs21 was not indicated by any of our previous methods , thus we also only consider it a possible agn . @xcite also derived classifications using lines of oi and [ oii ] , and their fig . 4 , which plots oi @xmath156300/h@xmath4 versus [ oii]/[oiii ] , shows a clear separation in oi @xmath156300/h@xmath4 , with nearly all power - law ionization objects ( i.e. agn ) having log(oi / h@xmath4 ) @xmath17 -1 , and all star - forming objects having log(oi / h@xmath4 ) @xmath1 -1.5 . we find that out of the five objects which have @xmath20 3 @xmath16 detections of oi @xmath156300 , egs10 and egs24 exhibit log(oi / h@xmath4 ) indicative of agn activity , of -0.74 and -1.05 , respectively . egs10 was not indicated by any of our previous classification methods , thus we now regard it as a possible agn . @xcite defined a color - color region using colors from the _ spitzer _ infrared array camera ( irac ) which preferentially selects agn in the redshift range of our sample ( 20%" +"hierarchical semi - markov models such as hhmm @xcite and hscrf @xcite are deep generalisations of the hmm @xcite and the linear - chain crf @xcite , respectively . these models are suitable for data that follows nested markovian processes , in that a state in a sub - markov chain is also a markov chain at the child level . thus , in theory , we can model arbitrary depth of semantics for sequential data . the models are essentially members of the probabilistic context - free grammar family with bounded depth . however , the main drawback of these formulations is that the inference complexity , as inherited from the inside - outside algorithm of the context - free grammars , is cubic in sequence length . as a result , this technique is only appropriate for short data sequences , e.g. in nlp we often need to limit the sentence length to , says , @xmath0 . there exists a linearisation technique proposed in @xcite , in that the hhmm is represented as a dynamic bayesian network ( dbn ) . by collapsing all states within each time slice of the dbn , we are able achieve linear complexity in sequence length , but exponential complexity in depth . thus , this technique can not handle deep architectures . in this contribution , we introduce an approximation technique using gibbs samplers that have a potential of achieving sub - cubic time complexity in sequence length and linear time in model depth . the idea is that , although the models are complex , the nested property allows only one state transition at a time across all levels . secondly , if all the state transitions are known , then the model can be collapsed into a markov tree , which is efficient to evaluate . thus the trick is to sample only the markov transition at each time step and integrating over the state variables . this trick is known as rao - blackwellisation , which has previously been applied for dbns @xcite . thus , we call this method rao - blackwellisation gibbs sampling ( rbgs ) . of course , as a mcmc method , the price we have to pay is some degradation in inference quality . recall that in the linear - chain crfs @xcite , we are given a sequence of observations @xmath1 and a corresponding sequence of state variables @xmath2 . the model distribution is then defined as @xmath3 where @xmath4 are potential functions that capture the association between @xmath5 and @xmath6 as well as the _ transition _ between state @xmath7 to state @xmath8 , and @xmath9 is the normalisation constant . thus , given the observation @xmath5 , the model admits the markovian property in that @xmath10 , where @xmath11 is a shorthand for @xmath12 . this is clearly a simplified assumption but it allows fast inference in @xmath13 time , and more importantly , it has been widely proved useful in practice . on the other hand , in some applications where the state transitions are not strictly markovian , i.e. the states tend to be persistent for an extended time . a better way is to assume only the transition between _ parent - states _ @xmath14 , whose elements are not necessarily markovian . this is the idea behind the semi - markov model , which has been introduced in @xcite in the context of crfs . the inference complexity of the semi - markov models is generally @xmath15 since we have to account for all possible segment lengths . the hierarchical semi - markov conditional random field ( hscrf ) is the generalisation of the semi - markov model in the way that the parent - state is also an element of the grandparent - state at the higher level . in effect , we have a _ fractal _ sequential architecture , in that there are multiple levels of detail , and if we examine one level , it looks exactly like a markov chain , but each state in the chain is a sub - markov chain at the lower level . this may capture some real - world phenomena , for example , in nlp we have multiple levels such as character , unigram , word , phrase , clause , sentence , paragraph , section , chapter and book . the price we pay for these expressiveness is the increase in inference complexity to @xmath16 . one of the most important properties that we will exploit in this contribution is the _ nestedness _ , in that a parent can only transits to a new parent if its child chain has terminated . conversely , when a child chain is still active , the parent state must stay the same . for example , in text when a noun - phrase is said to transit to a verb - phrase , the subsequence of words within the noun - phase must terminate , and at the same time , the noun - phrase and the verb - phrase must belong to the same clause . the parent - child relations in the hscrf can be described using a state hierarchical topology . figure [ fig : topo - model ] depicts a three - level topology , where the top , middle and bottom levels have two , four , and three states respectively . each child has multiple parents and each parent may share the same subset of children . note that , this is already a generalisation over the topology proposed in the original hhmm @xcite , where each child has exactly one parent . [ cols=""^ "" , ] deep neural architectures ( dna ) such as deep belief networks @xcite and deep boltzmann machines @xcite have recently re - emerged as a powerful modelling framework which can potentially discover high - level semantics of the data . the hscrf shares some similarity with the dna in the way that they both use stacking of simpler building blocks . the purpose is to capture _ long - range _ dependencies or _ higher - order _ correlations which are not directly evident in the raw data . the building blocks in the hscrf are the chain - like conditional random fields , while they are the restricted boltzmann machines in the dna . these building blocks are different , and as a result , the hscrf is inherently sequential and localised in state representation , while the dna was initially defined for non - sequential data and distributed representation . in general , the distributed representation is richer as it carries more bits of information given a number of hidden units . the drawback is that probabilistic inference of rbm and its stacking is intractable , and thus approximation techniques such as mcmc and mean - field are often used . inference in the hscrf , on the other hand , is polynomial . for approximation , the mcmc technique proposed for the hscrf in this paper exploits the efficiency in localised state representation so that the rao - blackwellisation can be used . perhaps the biggest difference between the hscrf and dna is the modelling purpose . more specifically , the hscrf is mainly designed for discriminative mapping between the sequential input and the nested states , usually in a fully supervised fashion . the states often have specific meaning ( e.g. noun - phrase , verb - phrase in sentence modelling ) . on the other hand , dna is for discovering hidden features , whose meanings are often unknown in advance . thus , it is generative and unsupervised in nature . finally , despite this initial difference , the hscrf can be readily modified to become a generative and unsupervised version , such as the one described in ( * ? ? ? training in hscrfs can be done simultaneously across all levels , while for the dna it is usually carried out in a layer - wise fashion . the drawback of the layer - wise training is that errors made by the lower layers often propagate to the higher . consequently , an extra global fine tuning step is often employed to correct them . there have been extensions of the deep networks to sequential patterns such as temporal restricted boltzmann machines ( trbm ) @xcite and some other variants . the trbm is built by stacking rbms both in depth and time . another way to build deep sequential model is to feed the top layer of the deep networks into the chain - like crf , as in @xcite . we have introduced a novel technique known as rao - blackwellised gibbs sampling ( rbgs ) for approximate inference in the hierarchical semi - markov conditional random fields . the goal is to avoid both the cubic - time complexity in the standard inside - outside algorithms and the exponential states in the dbn representation of the hscrfs . we provide some simulation - based evaluation of the quality of the rgbs with respect to run time and sequence length . this work , however , is still at an early stage and there are promising directions to follow . first , there are techniques to speed up the mixing rate of the mcmc sampler . second , the rbgs can be equipped with the contrastive divergence @xcite for stochastic gradient learning . and finally , the ideas need to be tested on real , large - scale applications with arbitrary length and depth . h. h. bui , d. q. phung , and s. venkatesh . hierarchical hidden markov models with general state hierarchy . in d. l. mcguinness and g. ferguson , editors , _ proceedings of the 19th national conference on artificial intelligence ( aaai ) _ , pages 324329 , san jose , ca , jul 2004 . j. lafferty , a. mccallum , and f. pereira . conditional random fields : probabilistic models for segmenting and labeling sequence data . in _ proceedings of the international conference on machine learning ( icml ) _ , pages 282289 , 2001 . sunita sarawagi and william w. cohen . semi - markov conditional random fields for information extraction . in bottou l saul lk , weiss y , editor , _ advances in neural information processing systems 17 _ , pages 11851192 . mit press , cambridge , massachusetts , 2004 ." +"magnetic reconnection@xcite frequently occurs at and around magnetic null points : locations where the magnetic field strength equals zero.@xcite magnetospheric null points have been identified using multipoint _ in situ _ measurements as the nulls pass through the spacecraft constellation.@xcite null points in the solar atmosphere have been identified through extrapolation of the photospheric magnetic field and morphology in coronal emission.@xcite numerical simulations of magnetic reconnection and plasma turbulence at low guide fields frequently show the formation and evolution of null points,@xcite as do numerical experiments of typical solar events such as flux emergence.@xcite two - dimensional , non - degenerate magnetic null points are classified as x - type or o - type depending on the local magnetic field structure . if we define @xmath0 as the jacobian matrix of the magnetic field at the null point , then a null point will be x - type if @xmath1 , o - type if @xmath2 , and degenerate if @xmath3 . magnetic reconnection in two dimensions can only occur at null points.(e.g . * ; * ? ? ? * ) in three dimensions , the structure of non - degenerate magnetic null points is significantly more complex.@xcite null lines and null planes are structurally unstable and unlikely to exist in real systems.(e.g . * ; * ? ? ? * ) the magnetic field structure around a linear three - dimensional null point includes separatrix surfaces ( or fans ) of infinitely many field lines that originate ( or terminate ) at the null , and two spine field lines that end ( or begin ) at the null . a negative ( or type a ) null point has separatrix surface field lines heading inward toward the null point with spine field lines heading outward from the null point . in contrast , a positive ( or type b ) null point has separatrix surface field lines heading outward away from the null point and spine field lines heading inward toward the null point . separators ( also known as x - lines by some in the magnetospheric community ) are magnetic field lines that connect two nulls . separators that include a spine field line are not structurally stable , so separators in real systems will almost always be given by the intersection of two separatrix surfaces . null points , separatrix surfaces , spines , and separators are the topological boundaries that divide the magnetic field into distinct domains and are therefore preferred locations for magnetic reconnection.@xcite three - dimensional magnetic reconnection can also occur without nulls,@xcite especially in regions such as quasi - separatrix layers where the magnetic connectivity changes quickly . motion of magnetic null points and reconnection regions occurs during any realistic occurrence of magnetic reconnection . in earth s magnetosphere , x - line retreat has been observed in the magnetotail@xcite and poleward of the cusp.@xcite at the dayside magnetopause @xcite and in tokamaks,@xcite the combination of a plasma - pressure gradient and a guide field leads to diamagnetic drifting of the reconnection site that can suppress reconnection . laboratory experiments frequently show reconnection site motion and asymmetry , often due to geometry or the hall effect.@xcite during solar flares , the reconnection site often rises with time as the flare loops grow and can also show transverse motions.(e.g . * ; * ? ? ? * ) theoretical models of magnetic reconnection often assume symmetry such that each magnetic null coincides with a flow stagnation point in the reference frame of the system . when asymmetry is introduced , there is in general a separation between these two points,@xcite and in some cases a stagnation point might not even exist near a null point.@xcite in all of these situations , there will generally be plasma flow across the magnetic null and the null will change position . interestingly , the velocity of a null point will generally not equal the plasma flow velocity at the null point.@xcite this effect is similar to the flow - through mode of reconnection.@xcite during asymmetric magnetic reconnection in partially ionized plasmas , there may exist neutral flow through the current sheet from the weak magnetic field ( high neutral pressure ) side to the strong magnetic field ( low neutral pressure ) side due to the neutral pressure gradient.@xcite in previous work,@xcite we derived an exact expression for the motion of an x - line when its location is constrained to one dimension by symmetry . in resistive magnetohydrodynamics ( mhd ) , x - line motion results from a combination of advection by the bulk plasma flow and resistive diffusion of the normal component of the magnetic field . in this work , we present exact expressions for the motion of linear null points in three dimensions and discuss the typical properties of the bifurcations of degenerate magnetic null points . section [ linear ] contains a derivation of the motion of linear null points in a vector field . section [ magnetic ] uses the results from section [ linear ] to describe the motion of magnetic null points . section [ bifurcation ] considers the local bifurcation properties of magnetic null points and provides three examples . section [ discussion ] contains a summary and discussion of this work . we define @xmath4 as the time - dependent position of an isolated null point in a vector field @xmath5 . we define @xmath6 as the value of the vector field at the null ; while @xmath7 for all time , @xmath8 when the null point is moving . we define @xmath9 to be the velocity of this null , @xmath10 the local structure of a non - degenerate null point can be found by taking a taylor expansion and keeping the linear terms.@xcite the linear structure is then given by @xmath11 where @xmath12 . the elements of the jacobian matrix @xmath0 evaluated at the null are given by @xmath13 where @xmath14 is the row index and @xmath15 is the column index . the trace of @xmath0 equals zero when @xmath16 , and @xmath17 . next we take the derivative following the motion of the null , @xmath18 this expression gives the total derivative of the magnetic field at the null point using the null s velocity in an arbitrary reference frame . this derivative equals zero because the magnetic field at the null by definition does not deviate from zero as we are following it . by solving for @xmath9 in eq . [ convectiveder ] , we arrive at the most general expression for the velocity of the null point @xmath19 which is valid for vector fields of arbitrary dimension . this derivation provides an exact result as long as @xmath0 is non - singular . an alternate derivation for eq . [ ubasic ] starts from the first order taylor series expansion of @xmath20 with respect to time and space about a magnetic null point , @xmath21 this first order expansion is valid in the limit of small @xmath22 and @xmath23 . we define @xmath24 as the position of the null point at @xmath22 . setting @xmath25 provides a unique solution for @xmath26 , and we again arrive at eq . [ ubasic ] . unlike the previous paragraph , this derivation uses the linearization approximation . [ ubasic ] may also be derived from the implicit function theorem . equation [ ubasic ] shows that a null point will move along the path for which @xmath20 and @xmath27 are oppositely directed . the null point will move faster if the vector field is changing quickly in time or varying slowly in space along this path . this exact result for @xmath9 can be applied to find the velocity of linear null points in any time - varying vector field with continuous first derivatives in time and space about the null point . a unique velocity @xmath9 exists as long as @xmath0 is non - singular . if @xmath0 is non - singular , then there exists exactly one radial path away from the null for which the vector field is pointed in a particular direction . we next consider the case where @xmath20 is a magnetic field rather than just any vector field . the derivation of eq . [ ubasic ] does not invoke any of maxwell s equations . we now introduce faraday s law , @xmath28 where @xmath29 is the electric field . by combining eqs . [ ubasic ] and [ faraday ] , we arrive at the relation @xmath30 which additionally requires continuous first derivatives of the electric field in space about the null point . this expression does not depend on any particular ohm s law , and indeed can be applied in situations where there is no ohm s law . next we consider the resistive mhd ohm s law , @xmath31 where @xmath32 is the plasma flow velocity and @xmath33 is the current density . the resistivity @xmath34 is assumed to be uniform for simplicity . [ ufaraday ] then becomes @xmath35 where all quantities on the right hand side are evaluated at the magnetic null . this expression requires that @xmath20 has continuous first derivatives in time and continuous second derivatives in space about the null point . null point motion in resistive mhd results from a combination of advection by the bulk plasma flow and resistive diffusion of the magnetic field . even in the absence of flow , null points may still move in resistive situations . the plasma flow velocity _ at _ the null point does not equal the velocity of the null point itself.@xcite a schematic showing null point motion due to resistive diffusion is presented in fig . [ mechanism ] . along the @xmath36 direction . above and below the null , @xmath37 . the negative @xmath38 diffuses along the @xmath36 direction into the immediate vicinity of the null point . at a slightly later time , the magnetic field at the current position of the null point will have @xmath37 . the negative @xmath38 diffusion cancels out positive @xmath38 to the right of the null point , so the resulting null point motion is to the right . reproduced with permission from ref . . copyright 2010 american institute of physics.,width=321 ] equation [ ufaraday ] can also be evaluated using an ohm s law containing additional terms . for example , we can choose our ohm s law to be @xmath39 where @xmath40 is the bulk ion velocity , @xmath41 is the electron density , @xmath42 is the elementary charge , and @xmath43 is a scalar electron pressure . for @xmath44 , eq . [ ufaraday ] becomes @xmath45 where quantities are again evaluated at the null point . the first term on the right hand side corresponds to the magnetic field being carried with the electron flow velocity , @xmath46 , rather than the bulk plasma flow , the second term corresponds to the resistive diffusion of the magnetic field at the null , and the third term corresponds to the biermann battery . we next consider the emergence and disappearance of magnetic null points , with an emphasis on the instantaneous velocity of separation or convergence of the bifurcating null - null pair . the local approach taken here complements global bifurcation studies.@xcite thus far we have only considered non - degenerate null points for which the local magnetic field can be described by eq . [ bmr ] using only the linear terms in the taylor series expansion . as long as @xmath0 is non - singular at the null , then there exists a unique velocity corresponding to the motion of that null point . non - degenerate null points are therefore structurally stable and can not disappear unless @xmath0 becomes singular.@xcite in contrast , degenerate null points are structurally unstable and generally exist instantaneously as" +"the minimal dilatonic gravity ( mdg ) model is a proper generalization of the einstein general relativity ( gr ) . its purpose is to solve some of the problems , which appear when one tries to describe the nature using gr as a theory of gravity and the standard model of particle physics , and could be a part of a more general theory . it was introduced for the first time by ohanlon ( ohanlon,1972 ) without relation with cosmology and astrophysics . his point was to give some field - theoretical basis for the fujii s `` fifth force '' . an additional field @xmath0 was introduced there and the term `` dilaton '' was used for the field @xmath0 . the idea of a possible relation of the ohanlon model with astrophysics and cosmology was introduced and developed in the articles ( fiziev , 2000 ) , ( fiziev , 2002 ) , ( fiziev , 2003 ) , ( fiziev , 2013 ) , ( fiziev , 2014a ) , ( fiziev , 2014b),where the cosmological constant @xmath1 was bring into use in mdg . this model is based on the following action for the gravi - dilaton sector @xmath2 where @xmath3 is the einstein constant , @xmath4 is the newton gravitational constant , and @xmath5 is the dilaton field . the values of @xmath0 must be positive since the change of the sign would lead to the change of the sign of the gravitational factor @xmath6 , which leads to antigravity . the value @xmath7 must be excluded , because the gravity is turned off . @xmath8 is also unacceptable since it leads to an infinite gravitational factor , and the cauchy problem is not well posed . the function @xmath9 defines the cosmological potential . it must be a positive single value function of the dilaton field by astrophysical reasons . all the physical requirements for the cosmological potential @xmath9 , necessary for a sound mdg model , can be found in ( fiziev , 2013 ) . a class of withholding potentials is introduced there . these confine dynamically the values of the dilaton @xmath0 in the physical domain . the introduced scalar field @xmath0 leads to a variable gravitational factor @xmath10 instead of the gravitational constant @xmath4 . the cosmological potential @xmath9 is introduced to consider a variable cosmological factor instead of the cosmological constant @xmath1 . in gr , with the cosmological constant @xmath1 we have @xmath11 and @xmath12 . due to its specific physical meaning , the field @xmath0 has unusual properties . the mdg without a cosmological term corresponds to the brans - dicke theory with an identically vanishing parameter @xmath13 . the mdg is only locally equivalent to the f(r ) theories and , in general , yields different physical consequences ( fiziev , 2013 ) . more information about the f(r ) theories can be found in the following publications ( clifton , 2012 ) , ( de felice , 2010 ) , ( faraoni , 2006 ) , ( frolov , 2008 ) , ( nojiri s. , 2007 ) , ( nojiri s. , 2011 ) , ( sotiriou , 2010 ) , ( starobinsky , 1980 ) , ( starobinsky , 2007 ) . some physical and astrophysical consequences of mdg are described in ( fiziev , 2000),(fiziev , 2002 ) , ( fiziev , 2003 ) , ( fiziev , 2014a ) , ( fiziev , 2014b ) . in particular , in ( fiziev , 2000 ) mdg - modifications of the classical gr effects in the solar system : the nordtvedt effect , the time delay of electromagnetic waves ( the shapiro effect ) , and the perihelion shift were considered . in the weak field approximation it was shown that mdg is compatible with all known observational data if the mass @xmath14 of dilaton is large enough . the strongest estimate @xmath15 can be derived from modern data of cavendish type experiments at short distances . in terms of the compton length @xmath16 this gives exponential decrease of the dilaton field at distances longer than @xmath17 . at present , the experimental fixing of the mass @xmath14 , or the compton length @xmath16 is the most important open physical problem in both mdg and f(r ) theories of gravity . for now , the only estimate is the one from cosmology : @xmath18 see ( starobinsky , 2007 ) . it corresponds to the compton length @xmath19 which is far below that available for current and future experiments . this value makes hopeless finding some difference between mdg and gr outside the real bodies of star scales or of smaller dimension . the problem with different masses of dilaton @xmath0 may be solved in the framework of mdg using more complicated cosmological potentials with several minima ( fiziev , 2013 ) . depending on the surrounding environment . we prefer to investigate for the beginning only the simplest mdg model as defined by eq . . ] around each minimum we may have very different masses of the scalar field @xmath0 , or more precisely , of its small deviation @xmath20 . this means that we may have very different coefficients of the quadratic terms in the taylor series expansion of the dilatonic potential ( see below ) in the vicinity of the corresponding minimum . these different masses may be seen at different scales , and may differ essentially from the one derived from cmb cosmological data , which corresponds to the huge scale of the visible universe . hence , we need to study effects of mdg at different scales ( fiziev 2014b ) , ( capozziello , 2014 ) . thus , we arrive at the idea of studying stars , and especially neutron stars , in the framework of mdg . the neutron stars are very interesting objects for our purposes , since in them the strong gravitational fields are known to exist . hence , the effects of mdg on the neutron stars structure may be significant . however , in addition there exists a specific numerical problem . it turns out that the available at present computer programs are able to work only for ( maybe ) unrealistic large values of the compton length @xmath21 . on the other hand , these scales correspond to the scales of a typical neutron star , and it is interesting to study the effects of mdg on them for corresponding small masses @xmath14 , at least as a preliminary study of this issue . the first such investigation was carried out in ( fiziev , 2014a , b ) . there the most idealized equation of state ( eos ) of the neutron matter was used , namely eos of ideal fermi gas at zero temperature . the idea was to compare the mdg and gr results exploring the simplest textbook example with a clear physical ground and well known physical approximations . the present paper , being a proper extension of the ms thesis of kalin marinov ( sofia university , october 2014 ) , considers a more realistic but also idealized example of a polytropic equation of eos following ( damour , 1993 ) . in the literature , one can find several dozens of `` realistic '' eos , based on different physical models of matter in neutron stars . unfortunately , at present we are not able to make a decision what is the right eos for neutron stars , from both the observational and theoretical point of view . the two constructed groups of eos : the soft and the stiff ones , give still hardly distinguishable results from the observational point of view in the framework of each group . in this situation it seems reasonable to study the effects of the change of the very theory of gravity using the simplest known eos with a clear physical ground . the next step : a study of more realistic models for comparison with nature will make sense only after revealing the basic new effects of mdg in stars , and after overcoming the numerical problems with ( maybe ) more realistic masses @xmath14 . thus , the present paper is just the next step towards realistic models of neutron stars in the mdg . the field equations of mdg with a matter field can be written in the form @xmath22 @xmath23 here @xmath24 is the standard energy - momentum tensor of the matter , and @xmath25 is the trace of the same tensor . the dilatonic potential is introduced through the relation @xmath26 , more precisely , it is its first derivative with respect to the variable @xmath0 . by standard notation @xmath27 is the einstein tensor . the static stars are spherically - symmetrical objects with great precision , so we use a space - time interval in the spherical coordinates ( landau , 1975 ) @xmath28 where r is the radial variable . after some more algebra , the equations describing ssss in mdg are obtained . for the inner domain @xmath29 $ ] , where @xmath30 is the radius of the star the structure is determined by the following system : @xmath31 @xmath32 @xmath33 @xmath34 here the four unknown functions are @xmath35 and @xmath36 , respectively , the mass , the pressure , the dilaton , and the dilaton pressure . the following indications are used in the system : @xmath37 in the above equations @xmath38 denote the effective values of the energy density and pressure , and they combine in them the matter energy density and pressure , the cosmological energy density and pressure , the dilatonic energy density and pressure . the numerical values in the parameters @xmath39 and @xmath40 are selected in such a way that the radius @xmath41 is in kilometers and the mass @xmath42 is in solar masses . the boundary conditions in the center of the star are @xmath43 the boundary conditions on the edge of the star are determined by the condition @xmath44 ( and @xmath45 ) . then @xmath46 the radius of a neutron star for physically sound equations of state varies : @xmath47 km . outside of the star , where @xmath48 and @xmath49 we have a dilaton sphere , or a dilasphere . the structure is determined by a shortened system @xmath50 . equation is omitted . in the exterior domain we use as left boundary conditions . the right boundary conditions are defined by the cosmological horizon @xmath51 @xmath52 where the de sitter vacuum is reached : @xmath53 . the polytropic equation of state we used to solve the equations - for neutron ssss in mdg has the following form @xmath54 , @xmath55 . we choose @xmath56 x @xmath57 g and @xmath58 @xmath59 . the value for the parameters @xmath60 and @xmath61 are chosen , so that the solutions are close to the results from the realistic equation of state ( diaz alonso , 1985 ) . the values @xmath62 and @xmath63 are used to fit equation ii from ( diaz alonso , 1985 ) , as done in ( damour , 1993).the chosen equation of state is suitable , because the maximum mass of a neutron star calculated with it in gr is close to the maximum observed mass of a neutron star ( demorest , 2010 ) , ( antoniadis , 2013 ) cc cc cc cc figures 1 and 2 describe the internal structure of the neutron star . the results for the mass and pressure are not essentially different from the results in gr . the behaviour of the new , for the model , variable , the dilaton @xmath0 , must be carefully examined on fig . the dilaton is decreasing near the edge of the star , as expected , but in the core of the star there is an" +"at the present time the most popular version of multidimensional ( md ) gravity is a kaluza - klein gravity ( for review see ref . @xcite ) in which all space - like directions are equivalent , i.e. extra coordinates are the same as the space coordinates . such approach is very natural but it has a great problem with the sharing of extra dimensions ( ed ) . in other words we should have some natural mechanism for the sharing the ed and space coordinates . it is well known that it is very difficult to realize such mechanism in the empty spacetime . it is necessary to introduce some external matter field for such sharing of ed . of course such way kills the einstein s idea that the matter can be effectively constructed from the pure geometry . there is another possibility for the renewal of the above - mentioned einstein s idea . we would like to return to the initial interpretation of kaluza - klein theory in which that all physical quantities should not depend on the ed . how it can be done ? we offer to take the ed as a gauge group ( for example , u(1 ) , su(2 ) or su(3 ) and so on ) . the advantages of such an approach are obvious : ( a ) we will have the matter as the gauge fields ; ( b ) the ed make up a symmetric space and therefore the physical fields will not depend on the extra coordinates . the first item ( a ) follows from the following theorem @xcite , @xcite : _ let @xmath0 be the group fibre of the principal bundle . then there is a one - to - one correspondence between the @xmath0-invariant metrics @xmath1 ( @xmath2 are the multidimensional indices ) on the total space @xmath3 and the triples @xmath4 . _ @xmath5 ^ 2 + g_{\mu\nu}(x^\alpha ) dx ^\mu dx^\nu \label{intr-1}\ ] ] _ here @xmath6 is einstein s pseudo - riemannian metric on the base ; @xmath7 is the gauge field of the group @xmath0 ( the off - diagonal components of the multidimensional metric ) ; @xmath8 is the symmetric metric on the fibre . _ this theorem tells us that the inclusion the off - diagonal components of the md metric is equivalent to the inclusion gauge fields ( u(1 ) , su(2 ) or su(3 ) ) and a scalar field @xmath9 which is connected with the linear size of the extra dimensions . these geometrical fields can act as the source of the exotic matter necessary for the formation of the wormhole s ( wh ) mouth . such solutions were obtained in ref s . @xcite @xcite @xcite @xcite . these solutions are spherically symmetric wh - like metrics ] with finite longitudinal size . the throat of these wh - like solutions is located between two invariant surfaces on which @xmath10 . these results indicate that the exotic matter necessary for the formation of the wh mouth can appear in * _ vacuum multidimensional gravity _ * from the off - diagonal elements of the metric ( the gauge fields ) and from the metric on the fibre ( the scalar field ) , rather than coming from some externally given exotic matter . the second item ( b ) leads to the fact that all physical fields ( scalar field @xmath11 , gauge fields @xmath12 and 4d metrical tensor @xmath13 ) do not depend on the extra coordinates . moreover the ed have an additional structure : every point is an element of a group ( gauge group u(1 ) , su(2 ) or su(3 ) ) , and _ * such structure can not be destroyed by any perturbations . * _ this means that not any physical particle can penetrate to the ed . otherwise it will destroy the symmetry of the ed and consequently an algebraic structure of the gauge group . in fact the gravity on the principal bundle give us the natural way for the compactification and sharing of the ed . in this case the multidimensional ( md ) spacetime is a total space of the principal bundle with su(2 ) structural group . the fibre of this principal bundle ( the ed ) is su(2 ) gauge group and the base is the 4d spacetime . the langrangian is @xmath14 where @xmath0 is the determinant and @xmath15 is the ricci scalar of the md metric . according to above - mentioned theorem the md metric on the total space is @xmath16 where @xmath17 here @xmath18 are the coordinates on the total space ; @xmath19 is the md index ; @xmath20 ; @xmath21 is the coordinates on the group @xmath22 ( @xmath23 ) ; @xmath24 are the coordinates on the base of the bundle ; @xmath25 ; @xmath26 is the sieben - bein index ; @xmath27 is the @xmath28-bein ; @xmath29 are the 1-forms on the group @xmath22 satisfying @xmath30 ; ( @xmath31 ) are the structural constants for the gauge group @xmath22 ; the signature of the md metric is @xmath32 . we must note that the functions @xmath33 can depend only on the @xmath34 points on the base as the fibres of our bundle are homogeneous spaces . varying with respect to our physical degrees of freedom @xcite leads to the following equations system @xmath35 according to above - mentioned theorem the following dimensional reduction of the ricci scalar @xmath36 on the total space of the principal bundle ( @xcite ) @xmath37 \label{sec2 - 90}\end{aligned}\ ] ] here @xmath38 are the ricci scalars of the base and structural group of the principal bundle respectively ; @xmath39 is the volume of the group @xmath22 . the independent degrees of freedom in the gravity on the principal bundle are : scalar field @xmath40 , gauge potential @xmath41 and 4d metric tensor @xmath42 . the most important difference of this theory from the modern variants of the kaluza - klein gravity is that here we should vary on the @xmath11 but not with the every component of the metric on the ed ( @xmath43 and so on ) . this leads to essential decreasing of the number of gravitational equations and to appearing of wh - like vacuum solutions which are necessary for the einstein / wheeler idea `` mass without mass '' and `` charge without charge '' . for the ordinary 7d kaluza - klein theory with the einstein equations @xmath44 we have @xmath45 equations . in our case the number of eq s , are @xmath46 . such essential simplification of the theory structure leads to the fact that in our case vacuum solutions ( wormhole - like ) appear which can not exist in the ordinary kaluza - klein gravity ( where we must destroy the primary einstein idea about a geometrization of physics and insert a multidimensional matter ) . another remarkable peculiarity of such kind of gravitational theories is that the linear sizes of the ed can essentially differ from the planck scale . it follows from the above - mentioned fact that not any physical test particle ( and consequently not any physical body ) can penetrate into the ed as far as it would destroy the algebraic ( consequently symmetric ) structure of the ed . therefore the essential property of the gravity on the principal bundle is that _ the linear size of the ed can be distinguished from the planck scale . _ and finally in these gravitational theory does not appear the compactification problem because the ed are the compact gauge group : u(1 ) , su(2 ) , su(3 ) or another compact lie group . this means that in our approach the compactification problem is not dynamical one and the compactness of the ed is inserted initially in such kind of the md theory . we will search a solution for the following 7d metric ( here we follow to ref . @xcite ) @xmath47 here @xmath48 is some constant , @xmath49 ( @xmath50 ) are the maurer - cartan form with relation @xmath51 @xmath52 where @xmath53 are the euler angles on the fibre . we choose the potential @xmath54 in the ordinary monopole - like form @xmath55 let us introduce the color electric @xmath56 and magnetic @xmath57 fields @xmath58 here the field strength components are defined via @xmath59 , @xmath60 is the determinant of the 3d space matrix , ( @xmath61 ) are the space index . in our case we have @xmath62 the substitution to the 7d gravitational equations leads to the following system of equations @xmath63 the equations and correspond to the ordinary yang - mills "" equations after the dimensional reduction . in the consequence of the wh symmetry the functions @xmath64 and @xmath65 are symmetric and the functions @xmath66 and @xmath67 can be either symmetric or antisymmetric . consequently we would like to consider the following different cases 1 . the function @xmath66 is symmetric and the function @xmath67 is antisymmetric ; 2 . the function @xmath66 is antisymmetric and the function @xmath67 is symmetric ; 3 . both functions @xmath66 and @xmath67 is antisymmetric ; 4 . both functions @xmath66 and @xmath67 is symmetric . the first case was considered in the ref . the result is that there are three type of solutions : wormhole - like , infinite and finite flux tubes solutions . now we will write the initial conditions for the 4d metric functions . at the center of symmetry of the wh ( @xmath68 ) we can expand functions @xmath69 and @xmath65 by this manner @xmath70 here we introduce the dimensionless coordinate @xmath71 ( @xmath72 ) and redefine @xmath73 , @xmath74 , @xmath75 . then we can rescale time and the constant @xmath76 so that @xmath77 . thus we have the following initial conditions for the functions @xmath69 and @xmath65 for the numerical calculations @xmath78 in this case we have the following expansion of functions @xmath79 and @xmath80 at the origin @xmath81 this equation is written in dimensionless variables . the constrained equation for the initial data give us @xmath82 as @xmath83 we have the following constraint for @xmath84 : @xmath85 . the numerical calculations are presented on the fig s , , , , . in this case the numerical calculations show us that the @xmath86 function is monotonically decreasing one and consequently its behaviour is defined with the value of @xmath87 . give us the following expression @xmath88 on the fig . this curve is shown . as a result we see that @xmath89 for all @xmath84 and consequently it confirms our numerical investigation that @xmath86 is monotonically decreasing function . in this case we have the following expansion of functions @xmath79 and @xmath80 at the origin @xmath90 this equation is written in dimensionless variables . the constrained equation ( [ sec3 - 130 ] ) for the initial data give us @xmath91 the positivity condition of @xmath92 give us @xmath93 in the chosen range of the parameters @xmath94 the numerical calculations lead to the fact that on the @xmath95 plane there are two regions with the different solutions type . on fig . these regions with the different type of solutions are shown . the numerical calculations are presented on the fig s , , , , . we see that there is two type of solutions . the first type with decreasing @xmath96 we can name as a wh - like solutions . for this type of solutions we have the following condition @xmath97 . with an accuracy of the numerical calculations we can say that there is a point @xmath98 for which @xmath99 . probably in these points @xmath10 that is similar to the 5d case investigated in ref.@xcite . we intend to investigate in more details the behavior of the metric close to such points" +"be / x - ray binaries are x - ray sources composed of a be star and a neutron star . most of these systems are transient x - ray pulsars displaying strong outbursts in which their x - ray luminosity increases by a factor @xmath1 ( see negueruela 1998 ) . in addition , those systems in which the neutron star does not rotate fast enough for centrifugal inhibition of accretion to be effective ( see stella et al . 1986 ) display persistent x - ray luminosity at a level @xmath2 erg s@xmath3 . the high - energy radiation is believed to arise due to accretion of material associated with the be star by the compact object . it has long been known that accretion from the fast polar wind that is detected in the uv resonance lines of the be primaries can not provide the observed luminosities , even for detections at the weakest level ( see waters et al . 1988 and references therein ; see also the calculations made for x persei by telting et al . therefore it is believed that the material accreted comes from the dense equatorial disc that surrounds the be star . waters et al . ( 1989 ) modelled the radial outflow as a relatively slow ( @xmath4 km s@xmath3 ) dense wind . however most modern models for be stars consider much slower outflows , due to strong evidence for rotationally dominated motion ( quasi - keplerian discs ) . this is due not only to the line shapes ( see hanuschik et al . 1996 ) , which set an upper limit on the bulk motion at @xmath5 ( hanuschik 2000 ) , but also to the success of the global one - armed oscillation model ( which can only work in quasi - keplerian discs ) at explaining v / r variability in be stars ( hummel & hanuschik 1997 ; okazaki 1997ab ) . the viscous decretion disc model ( okazaki 1997b ; porter 1999 ; negueruela & okazaki 2000 ) considers material in quasi - keplerian orbit with an initially very subsonic outflow velocity that is gradually accelerated by gas pressure and becomes supersonic at distances @xmath6 , i.e. , much further than the orbits of neutron stars in be / x - ray transients . the transient a0535 + 26 is one of the best studied be / x - ray binaries ( clark et al . 1998 and references therein ) . it contains a slowly rotating ( @xmath7 ) neutron star in a relatively wide ( @xmath8 ) and eccentric ( @xmath9 ) orbit around the b0iiie star v725 tau ( see finger et al . 1996 ; steele et al . 1998 ) . after its last giant outburst in february 1994 ( clark et al . 1998 ; negueruela et al . 1998 ) , the strength of the emission lines in the optical spectrum of v725 tau has declined steadily . the last normal ( periodic ) outburst took place in september 1994 and the source has since not been detected by the batse experiment on board _ v725 tau , the optical counterpart to a0535 + 26 , was observed on november 7th 1998 , using the 4.2-m william herschel telescope , located at the observatorio del roque de los muchachos , la palma , spain . the telescope was equipped with the utrecht echelle spectrograph using the 31.6 lines / mm echelle centred at h@xmath0 and the site1 ccd camera . this configuration gives a resolution @xmath10 over the range @xmath11 . the data have been reduced using the _ starlink _ packages ccdpack ( draper 1998 ) , echomop ( mills et al . 1997 ) and dipso ( howarth et al . 1997 ) . a detailed analysis of the whole spectrum is left for a forthcoming paper . in figure [ fig : opt ] , we show the shape of h@xmath0 , h@xmath12 and @xmath136678 . when in emission , these three lines sample most of the radial extent of the circumstellar envelope . however , it is apparent that the lines seen in fig . [ fig : opt ] correspond to photospheric absorption from the underlying star . the emission contribution from circumstellar material , if any , is certainly very small . the asymmetry in the shape of h@xmath0 and @xmath136678suggests that some fast - moving material is present close to the stellar surface ( see hanuschik et al . 1993 ; rivinius et al . 1998 for the discussion of low - level activity in disc - less be stars ) , but the circumstellar disc is basically absent . h@xmath12 , which , when in emission , is typically produced at distances of a few @xmath14 , looks completely photospheric . in be stars h@xmath0 probes a region extending to @xmath15 , as measured from line - peak separation ( hummel & vrancken 1995 ) and direct imaging ( quirrenbach et al . 1997 ) . again , circumstellar material seems to be almost absent from this region . there is weak emission emission in - filling at the line centre transient emission components have been seen in this star during the disc - less state ( haigh et al . 2000 ) , a behaviour typical of disc - less be stars ( rivinius et al . 1998 and references therein ) . ( 250,250 ) ( 0,0 ) observations of the source were taken using the proportional counter array ( pca ) on board _ rossixte _ on 1998 august 21 and 1998 november 12 for a total on - source time of 4170 s and 2250 s , respectively . in both observations there is an excess of @xmath16 counts / s/(5 pcu ) in the 2.515 kev range of the standard2 data compared to the faint source background model . fits to power - law models with interstellar absorption result in flux estimates of @xmath17 and @xmath18 ( 210 kev ) for the two observations respectively . these can only be considered as upper limits on the flux , due to the uncertain contribution of diffuse galactic disc emission to the count rates ( valinia & marshall 1998 ) . the issue of whether the source of high energy radiation was active or not during the low activity optical phase can be solved by searching for the previously reported x - ray pulsations at @xmath19103.5-s spin period ( e.g. , finger et al . 1996 ) . in order to improve the signal - to - noise , we accumulated events from the top anode layer of the detectors . we also used the latest version of the faint background model . for the power spectral analysis we selected a stretch of continuous data and divided it into intervals of 309 s. a power spectrum was obtained for each interval and the results averaged together . given that the pulse frequency ( @xmath20 hz ) lies on a region dominated by red noise , we have to correct for such noise if the statistical significance of the pulsations are to be established . first , we fitted the poisson level by restricting ourselves to the frequency range 0.20.4 hz , that is far away from the region where the red noise component may contribute appreciably . the strongest peak in the power spectrum corresponds to @xmath21 . we also searched for periodicities in the light curves by folding the data over a period range and determining the @xmath22 of the folded light - curve ( epoch - folding technique ) . in this case we used 20 phase bins ( 19 degrees of freedom ) and a range of 100 periods , around the expected period . this method has the advantage that the result is not affected by the presence of gaps in the data , hence a longer baseline can be considered than with fourier analysis . times in the background subtracted light - curve were converted into times at the solar - system barycentre . the result for the 1998 november observation is shown in fig [ fig : epoch ] . we found that the peak at @xmath23 is significant at @xmath24 , confirming that the source was active during the observations . ( 250,280 ) ( 0,0 ) it is worth mentioning that the detection levels shown in fig . [ fig : epoch ] were obtained without _ a priori _ knowledge of the frequency of pulsations . in other words , we searched for pulsations in the frequency / period range shown in the figure . if we take into account the fact that we are interested in the pulse period _ at _ @xmath25 , the peak becomes still more significant . the analysis of the 1998 august observation provides a much less significant detection . a peak at the expected frequency ( @xmath26 hz ) is seen in the power spectrum . however , epoch - folding analysis gave a significance of @xmath27 only when we considered one single period , that is , the number of trials is one . a search for pulsations in a period range did not yield any maximum above the 3-@xmath28 detection level although a peak at the 103-s period is present ( see fig . [ fig : epoch2 ] ) ( 250,280 ) ( 0,0 ) the pulse shape ( see figure [ fig : pulse ] ) is nearly sinusoidal , as expected from the absence of second or higher harmonics in the power density spectra . the amplitude of the modulation is @xmath29 count s@xmath3 in the 320 kev energy range , which implies a pulse fraction of @xmath30% . given the unknown contribution from galactic disc diffuse emission , this represents only a lower limit to the pulsed fraction in the signal from the source . we have divided the november 1998 observation into two sections , corresponding to the peak of the pulse ( phase bins 0.6 to 1.0 ) and the interpulse minimum ( phase bin 0.10.5 ) . an absorbed power - law fit in the energy range 2.710 kev to the two spectra gave @xmath31 , @xmath32 , @xmath33 ( 18 dof ) for pulse maximum and @xmath34 , @xmath35 , @xmath36 ( 18 dof ) for pulse minimum . the two values are consistent with each other within the error margins . the lack of spectral changes with phase requires any significant component of the detected flux due to diffuse emission to have a spectrum similar to that of the pulsar . ( 250,280 ) ( 0,0 ) formally the x - ray spectra are equally well represented by an absorbed power - law , blackbody and bremsstrahlung models . table [ tab : models ] shows the spectral fit results . all these models gave fits of comparable quality , which means that we are unable to distinguish meaningfully between the different spectral models of table [ tab : models ] , even though the blackbody fit is unlikely to have any physical meaning , because of very small emitting area and the fact that it does not require any absorption ( introducing @xmath37 does not improve the fit ) see rutledge et al . ( 1999 ) for a discussion of the physical inadequacy of this model for neutron stars . the value of the hydrogen column density ( @xmath37 ) , which is consistent for the power - law and bremsstrahlung fits , is too high to be purely interstellar . the interstellar reddening to the source must be smaller than the measured @xmath38 ( steele et al . 1998 ) , which is the sum of interstellar and circumstellar contribution from the disc surrounding the be star . according to the relation by bohlin" +"although , the cosmic dust grains are in general not homogeneous spheres , usually the observed absorption , scattering and extinction data are interpreted using calculations based on mie theory , which is strictly valid for homogeneous spherical particles . dust grains ejected from stars are more likely to be non - spherical and inhomogeneous , viz . porous , fluffy and composites of many small grains glued together , due to grain - grain collisions , dust - gas interactions and various other processes . since there is no exact theory to study the scattering properties of these inhomogeneous grains , there is a need for formulating models of electromagnetic scattering by these grains . mathis & whiffen ( 1989 ) , mathis ( 1996 ) , dwek ( 1997 ) and li & greenberg ( 1998 ) have proposed composite grain models consisting of silicate and amorphous carbon as constituent materials . they have used effective medium approximation ( emt ) to calculate the optical constants for composite grains and then used the mie theory to calculate extinction cross sections for spheres . in emt the inhomogeneous particle is replaced by a homogeneous one with some average effective dielectric function. the effects related to the fluctuations of the dielectric function within the inhomogeneous structures can not be treated by this approach of the emt . iati etal ( 2004 ) have studied optical properties of composite grains as grain aggregates of amorphous carbon and astronomical silicates , using the transition matrix approach . recently voshchinnikov etal ( 2006 ) and voshchinnikov & henning ( 2008 ) have studied the effect of grain porosity on interstellar extinction , dust temperature , infrared bands and millimeter opacity . they have used both , the emt - mie based calculations and layered sphere model . earlier , we have used discrete dipole approximation ( dda ) to study the extinction properties of the composite grains ( vaidya etal 2007 ) . for the description on the dda see draine ( 1988 ) . the dda allows the consideration of irregular shape effects , surface roughness and internal structure within the grain ( wolff et al . 1994 , 1998 and voshchinnikov et al . 2005 ) . for discussion and comparison of dda and emt methods , including the limits of the effective medium theory , see bazell and dwek ( 1990 ) , perrin and lamy ( 1990 ) , perrin and sivan ( 1990 ) , ossenkopf ( 1991 ) and wolff et al ( 1994 ) . the paper has the following sections : in section 2 we give the validity criteria for the dda and the composite grain models . in section 3 we present and discuss the results of our computations and compare the model curves with the observed ir fluxes obtained by iras satellite . the main conclusions of our study are given in section 4 . we use the computer code developed by dobbie ( 1999 ) to generate the composite grain models used in the present study . we have studied composite grain models with a host silicate spheroid containing n= 9640 , 25896 and 14440 dipoles , each carved out from @xmath4 , @xmath5 and @xmath6 dipole sites , respectively ; sites outside the spheroid are set to be vacuum ( void ) and sites inside are assigned to be the host material . it is to be noted that the composite spheroidal grain with n=9640 has an axial ratio of 1.33 , whereas n=25896 has the axial ratio 1.5 and n=14440 has the axial ratio 2.0 . the volume fractions of the graphite inclusions used are 10% , 20% and 30% ( denoted as f=0.1 , 0.2 and 0.3 ) details on the computer code and the corresponding modification to the ddscat code ( draine & flatau 2003 ) are given in dobbie ( 1999 ) , vaidya et al . ( 2001 , 2007 ) and gupta et al . the modified code outputs a three - dimensional matrix specifying the material type at each dipole site ; the sites are either silicate , graphite or vacuum ( void ) . for an illustrative example of a composite spheroidal grain with n=9640 dipoles , please see figure 1 ( also vaidya et al , 2007 ) . there are two validity criteria for dda ( see e.g. wolff et al . 1994 ) ; viz . ( i ) @xmath7 , where m is the complex refractive index of the material , k=@xmath8 is the wavenumber and d is the lattice dispersion spacing and ( ii ) d should be small enough ( n should be sufficiently large ) to describe the shape of the particle satisfactorily . the complex refractive indices for silicates and graphite are obtained from draine ( 1985 , 1987 ) and that for ice is from ( irvine & pollack 1968 ) . for any grain model , the number of dipoles required to obtain a reliable computational result can be estimated using the ddscat code ( see vaidya and gupta 1997 and 1999 , vaidya etal 2001 ) . for the composite grain model , if the host grain has n dipoles , its volume is n(d)@xmath9 and if a is the radius of the host grain , n(d)@xmath9 = 4/3@xmath10 , hence , n = 4@xmath11 , and if @xmath12=1 and k=2@xmath13 the number of dipoles n can be estimated at a given wavelength and the radius of the host grain . it must be noted here that the composite spheroidal grain models with n=9640 , 25896 and 14440 have the axial ratio 1.33 , 1.5 and 2.0 respectively and if the semi - major axis and semi - minor axis are denoted by x/2 and y/2 respectively , then @xmath14 , where a is the radius of the sphere whose volume is the same as that of a spheroid . in order to study randomly oriented spheroidal grains , it is necessary to get the scattering properties of the composite grains averaged over all of the possible orientations ; in the present study we use three values for each of the orientation parameters ( @xmath15),i.e . averaging over 27 orientations , which we find quite adequate ( see e.g. wolff etal 1998 ) . earlier , we had studied the extinction properties of composite spheroidal grains in the spectral region 3.4 - 0.10@xmath16 m ( vaidya etal 2007 ) . in the present paper , we study the absorption properties of the composite spheroidal grains with three axial ratios , viz . 1.33 , 1.5 and 2.0 , corresponding to the grain models with n=9640 , 25896 and 14440 respectively , in the wavelength region 7.0 - 14.0@xmath16 m . the inclusions selected are graphites / ices / or voids . figure 2 ( a - c ) shows the absorption efficiencies ( @xmath17 ) for the composite grains with the host silicate spheroids containing 9640 , 25896 and 14440 dipoles , corresponding to axial ratio 1.33 , 1.5 and 2.0 respectively with a power law size distribution of a range of grain sizes from 0.005 - 0250@xmath16 m in steps of 0.005@xmath16 m . the three volume fractions , viz . 10% , 20% and 30% , of ice inclusions are also listed in the top ( a ) panel . the effect of the variation of volume fraction of inclusions is clearly seen for all the models . it is to be noted that the wavelength of the peak absorption shifts with the variation in the volume fraction of inclusions . these absorption curves also show the variation in the width of the absorption feature with the volume fraction of inclusions . all these results indicate that the inhomogeneities within the grains play an important role in modifying the 10@xmath16 m feature . it is also seen in fig . 2 that the shape of the q@xmath18 curve also varies with the axial ratio , ar of the composite grain , and the absorption peak shifts towards shorter wavelength as the ar incereases . odonnell ( 1994 ) has investigated the variation of the 10@xmath16 m feature with the grain composition using spheroidal composite grains containing inclusions of either amorphous carbon , tholins or vacuum . he found that the inclusion of tholins or carbon increases the absorption on the short wavelength side of the 10@xmath16 m feature . further , the inclusion of tholin also broadens the 10@xmath16 m feature . figure 3 shows the absorption efficiency for the composite grains ( n=9640 , ar=1.33 , a=0.10@xmath16 m ) with host silicate and graphite inclusions ( thick lines ) . it is seen that the q@xmath18 decreases as the the volume fraction of inclusions f increases and the absorption peak shifts towards shorter wavelength and broadens with the volume fraction of inclusions . we have compared our results on the absorption efficiencies of the composite grains obtained using the dda with the results obtained using the emt - t matrix based calculations . these results are also displayed in figure 3 ( in thin lines ) . for these calculations , the optical constants were obtained using the maxwell - garnet mixing rule ( bohren and huffman 1983 ) . description of the t - matrix method / and code is given by mishchenko ( 2002 ) . since maxwell - garnett rule provides the extreme cases of the possible values of the effective dielectric constants of the two - component mixture ( see chylek et al , 2000 ) , we have used this rule . on the other hand , bruggeman mixing rule applies to a two - component mixture with no distinguishable inclusions embedded in a definite matrix ; i.e. it applies to a completely randomly inhomogeneous medium ( bohren & hoffman , 1983 ) . in the figure 3 we have also shown the absorption efficiency for the composite grain with f=0.2 using bruggeman rule . it is seen that the absorption curves obtained using emts ( maxwell - garnett and bruggeman mixing rules ) deviate considerably from the curves obtained using dda . the dda allows consideration of irregular shape effects , surface roughness and internal structure within the grain ( wolff et al 1994 , 1998 ) . in emt the inhomogeneous grain is replaced by a homogeneous one with some average effective dielectric function , the effects related to the fluctuations of the dielectric function within the inhomogeneous structures can not be treated by the emts and material interfaces and shapes are smeared out into a homogeneous average mixture saija etal 2001 ) . perrin and lamy ( 1990 ) have calculated extinction cross sections for the composite grains , using both the emts , as well as the dda . they found that for small porous grains the results given by maxwell - garnett are much better than the results given by the bruggeman theory . the criteria of validity of the respective effective theories are not clear ( perrin and lamy , 1990 ) . we have used more accurate dda method to calculate the absorption cross sections for the composite grains . however , it would still be very useful and desirable to compare the dda results for the composite grains with those computed by other emt / mie type / t matrix techniques in order to examine the applicability of several mixing rules . ( see wolff etal 1998 , voshchinnikov and mathis 1999 , chylek et al . 2000 , voshchinnikov etal 2005 , 2006 ) . the application of dda , poses a computational challenge , particularly for the large values of the size parameter @xmath19 and the complex refractive index m of of the grain material would require large number of dipoles and that in turn would require considerable computer memory and cpu time (" +"electromagnetic waves in the microwave regime play an indispensable role in present plasma experiments . they are used for diagnostic and heating purposes in low- and high - temperature plasmas , see e.g. refs . @xcite . in tokamak plasmas , for example , microwaves with a power in the mw regime are injected to stabilize so - called neoclassical tearing modes ( ntms ) . this instability modifies the plasma current profile by the generation of small scale magnetic islands and can ultimately lead to a disruption @xcite . to suppress the growth of this instability , a localized current is driven by injected microwaves , in order to restore the original current profile @xcite . microwaves emitted by the plasma , on the other hand , can be used to obtain , for example , the spatial distribution of the electron temperature or to investigate its dynamical behavior @xcite . in all these cases , the microwaves have to traverse the plasma boundary , a region in which substantial density fluctuation levels as high as 100% are observed in fusion plasmas @xcite . these fluctuations can disturb the microwaves injected into the plasma or emitted by it and thereby lead to reduced coupling efficiencies to the plasma or to ambiguous emission measurements , respectively . this paper seeks to allow an estimation of the perturbing effect of density fluctuations on a traversing microwave beam . the investigations of microwaves propagating through a plasma dates back to the beginning of ionospheric research , when microwaves emitted by strong astronomical radio sources were detected and studied on earth after they had passed through the ionosphere @xcite or when radio waves were emitted from ground and their reflection from the ionosphere was studied @xcite . microwave sources started to become available for substantial plasma heating and first numerical studies based on geometrical optics assumptions were performed in order to estimate the deteriorating effect of a turbulent plasma edge layer on an injected microwave beam @xcite . recently , this topic has gained new momentum due to the importance of effective non - inductive current drive schemes in fusion relevant plasmas @xcite . the work presented here investigates the perturbing effect of a turbulent plasma density layer on a traversing microwave beam by means of full - wave simulations . no restricting assumptions about the size or amplitude of the turbulent structures therefore need to be made . the full - wave treatment is required due to the large fluctuation levels that occur in fusion edge plasmas and due to the size of the density structures which can be on the order of the wavelength of the microwave . the properties of the turbulence are varied in a series of parameter scans in order to identify the most perturbing case . although full - wave simulations can be quite resource - demanding in terms of computational power and memory , their application has been increased recently to cases in magnetized plasmas where geometrical optics assumptions generally fail @xcite . this has been made possible due to the continuously increasing computational power @xcite and the creation of large scientifically focused computational cluster facilities . understanding and ensuring numerical stability of full - wave codes for cases with strong density gradients in magnetized plasmas is a topic of ongoing research @xcite . a significant amount of that research deals with reflectometry , where an injected low - power microwave beam is _ reflected _ by the turbulent density layer ( instead of being _ transmitted _ like in the cases mentioned in the beginning ) and used to probe the turbulence layer itself @xcite . for the scenarios considered here ( density below cut - off and moderate density gradients ) , stability of the simulations is not an issue . this work is the continuation of a preceding study which dealt with the influence of single blob - like structures on a traversing microwave beam @xcite . the paper is organized as follows : details about the simulation technique and the density fluctuations used in the simulations are described in sec . [ s.numerics ] . the data analysis methods are presented in sec . [ s.analysis ] . in sec . [ s.results ] , the simulation results are discussed and in sec . [ s.consequences ] , their consequences for two experimental cases are outlined . the summary given in sec . [ s.summary ] concludes the paper . this section briefly describes the codes that have been used to simulate the plasma microwave interaction and how the turbulent density profiles were generated . ipf - fdmc is a full - wave code based on the finite - difference time - domain scheme @xcite . it solves maxwell s equations ( [ e.maxwell1 ] ) , ( [ e.maxwell2 ] ) and the fluid equation of motion for the electrons , eq . ( [ e.ipffdmc_j ] ) , on a 2d cartesian grid . hence , it is based on a cold plasma description . the code has been used previously to study the o - sx mode conversion process and to investigate microwave heating in general ( see refs . @xmath0 with @xmath1 the electron plasma frequency , the electron cyclotron frequency and the background magnetic field . an electron collision frequency @xmath2 is included in eq . ( [ e.ipffdmc_j ] ) to resolve the energy accumulation which occurs if an x - mode encounters the upper - hybrid resonance . the emit-3d code @xcite is also based on the finite - difference time - domain scheme . like ipf - fdmc , it is capable of simulating microwaves propagating through a cold magnetized plasma . it solves the equations , however , in a 3d geometry . due to the increased computational resources when going to a 3d treatment , extensive parameter scans are performed with the 2d code ipf - fdmc only . this is a valid simplification for the case of perpendicular injection ( with respect to the background magnetic field ) since the turbulence is essentially 2d in nature ( see sec . [ s.density ] for details ) . for a number of cases , the results from both codes are compared . dedicated scenarios which require a 3d treatment are also presented and discussed . the injected microwave is modelled as a gaussian beam with the beam waist located in the antenna plane . neglecting the phase terms , the electric field distribution in the antenna plane reads @xmath3 , with @xmath4 the coordinate across the antenna and @xmath5 the spot size of the beam , i.e. the radius at the beam waist . the default value for the simulations is @xmath6 with @xmath7 the vacuum wavelength of the injected microwave . despite the relatively small beam waist , the divergence of the beam is negligible for the default size of the computational grid , which is @xmath8 . the interaction with the density turbulence occurs thus when the wave fronts of the microwave are still parallel , like in fusion plasmas , where the beam waists are usually larger by an order of magnitude . this grid has been chosen in order to be able to perform the required ensemble averaging ( as discussed in the following section ) within a reasonable computational time . an o - mode is injected at the bottom of the 2d grid and the background magnetic field @xmath9 is directed perpendicular to it . the normalized magnetic field is set to a constant value of @xmath10 , where @xmath11 is the angular frequency of the injected microwave . the boundaries of the simulation grid were set to be non - radiating . on the time scale of the microwave , the fluctuations appear to be frozen : the typical frequency scales are in the khz range @xcite , whereas the microwave frequency lies in the ghz range . the important parameter is the group velocity of the injected o - mode which can be expressed as , with @xmath12 . if the turbulent structures are interpreted as drift - wave structures , their phase velocity can be estimated by the electron diamagnetic drift velocity , yielding values which are typically @xmath13 @xcite . hence , even if the density reaches values of 99.9% of the cut - off density , the resulting group velocity of the wave is still a factor of 1000 larger than the velocity of the density structures and the assumption of a frozen plasma in the frame of the microwave is therefore justified . to properly study the influence of density fluctuations on traversing microwaves , it is necessary to have a sufficiently large number of turbulent density profiles , since only averaging over an ensemble of profiles makes the results statistically relevant . a hasegawa - wakatani drift - wave turbulence model within the bout++ framework @xcite is used to generate such a set of profiles which can be accessed at @xcite . drift - wave turbulence is thought to be the dominant mechanism responsible for the anomalous transport observed in the tokamak plasma edge @xcite . hasegawa and wakatani derived a simple model to describe this turbulence in a 2d unsheared magnetic field @xcite , and it has been used both to simulate edge turbulence as well as to benchmark more complex models @xcite . the geometry in the full - wave simulations is such that a homogeneous background density @xmath14 is chosen onto which a layer of turbulent density is superimposed . figure [ f.fullwave_grid ] shows an example , where the turbulence layer has a depth of @xmath15 in the @xmath16-direction . the spatial extension into the @xmath4-direction is @xmath17 and will not be varied . a smooth transition is employed over a few grid points between the homogeneous background plasma and the turbulence layer . the emitting antenna injecting a gaussian beam is placed at the lower boundary of the grid and a receiving antenna at the upper boundary of the grid . both antennas extend along the whole @xmath4-direction . the distance between the antennas and the boundary of the turbulence layer is set to one vacuum wavelength @xmath7 , i.e. in fig . [ f.fullwave_grid ] , the emitting antenna is defined at @xmath18 and the receiving antenna at @xmath19 . since the simulations are based on a time - dependent scheme , they start with the injection of the microwave beam and are stopped when a steady state solution has been achieved . over the receiving antenna , the time - averaged wave electric field , reminiscent of an rms - value , is continuously recorded as a function of the coordinate @xmath4 : @xmath20 where @xmath21 is the time coordinate , @xmath22 and the superscript @xmath23 denotes the perturbation due to the . such an antenna signal is acquired for each turbulence slice considered . figure [ f.detant_signal ] shows this signal for a few turbulence slices together with the signal for the homogeneous , i.e. the unperturbed case . the effect of the turbulence on the microwave can be clearly seen . to quantify the scattering of the microwave beam , two different methods are used . the first method consists of calculating a scattering parameter @xmath24 as the sum of the squared deviations of the @xmath25 signal between the turbulence case and the homogeneous case : @xmath26 this compresses the result from one turbulence slice into a single value . ensemble averaging is then performed over many turbulence samples in order to become statistically relevant . the number of samples @xmath27 in one ensemble depends on the average spatial size of the density structures : if are very small compared to the vacuum wavelength , many of them exist in one turbulence slice resulting already in a good average . when , in contrast , the spatial dimensions of the" +"if sufficient power is supplied to a granular system contained in a cylindrical container by a vertically vibrating wall , fluidization occurs . once a steady state is obtained , the energy input to the system by the wall is , on average , balanced by the energy dissipated in inelastic grain - grain and grain - wall collisions . this energy flux is responsible for various effects including non - linear temperature profiles , heap formation@xcite and convection @xcite . recent experiments using positron emission particle tracking ( pept)@xcite have observed buoyancy - driven convection in a highly fluidized granular system for a range of grain numbers and shaker amplitudes . while convection effects have been observed in a two - dimensional model system @xcite , no simulation studies of a three dimensional system corresponding to the pept experiments have yet been reported . we study the behavior of a model system in which the grains are modeled as inelastic hard spheres . most of the previous studies of this model focused on the homogeneous cooling state , clustering , and kinetic and hydrodynamic theory for particles with small inelasticity@xcite . unlike many other many - body systems , the model studied here closely matches the experimental system . in particular , the number of particles is identical and we use values of particle - particle and particle - wall restitution coefficients that were determined by independent experimental measurements . we show that the model reproduces accurately the experimentally observed density and granular temperature profiles@xcite . moreover , for a range of conditions , a velocity field exists for which there is a net circulation . interestingly , the direction and intensity of the circulation are strong functions of the particle - wall restitution coefficient . in addition , we suggest a modification to the experiment that may generate new convection patterns . the system consists of a number @xmath0 of hard spheres contained in a cylinder of radius @xmath1 . the spheres collide inelastically with each other and with the side walls with coefficients of restitution @xmath2 and @xmath3 , respectively . between collisions , the spheres are subject to a downward constant acceleration due to the ( vertical ) gravitational field . energy is injected into the system by the bottom wall which vibrates with a symmetric saw - tooth profile characterized by an amplitude @xmath4 and a period @xmath5 . we do not expect the behavior of the system to be strongly dependent on the form of the profile@xcite . the equations describing the dynamics , which follow from conservation of momentum , for the particle side - wall , particle bottom - wall and particle particle collisions are : @xmath6 @xmath7 @xmath8\hat{{\bf n}}\ ] ] respectively where @xmath9 is the velocity of particle @xmath10 in the @xmath11 plane , @xmath12 is the velocity of the bottom wall , @xmath13 is the @xmath14 vertical component of the velocity of particle @xmath10 , @xmath15 is the unit position vector of particle @xmath10 and @xmath16 is the unit center - to - center vector between the colliding pair @xmath10 and @xmath17 . note that we have taken the tangential restitution coefficient for sphere - sphere , and sphere - wall , collisions equal to one . the normal restitution coefficient for sphere - bottom wall collisions was also taken as unity . one problem with the event - driven simulation is that a sphere may collide more and more frequently with the side wall as the radial component of its momentum is dissipated . to avoid the inelastic collapse@xcite , which has been observed in simulations of bulk granular systems , we simply inject a small amount of energy in the radial direction when the radial velocity falls below a cut - off value . this condition arises infrequently and its handling in this way has no discernible effect on the results . to reproduce the experimental conditions of wildman et al @xcite we used parameter values @xmath18 , @xmath19 , @xmath20 . taking the unit of length as the sphere diameter , @xmath21 , the cylinder radius is @xmath22 . since the base - wall particle coefficient is not given , we assume a value of one . the shaker amplitude is thus left as the only adjustable parameter for the comparison of the simulation with the experiments . we performed different runs with a dimensionless shaking amplitude varying between @xmath23 and @xmath24 . to generate the initial configuration , spheres were inserted sequentially and randomly in the cylinder without overlap . a preliminary simulation was then performed , typically for @xmath25 collisions per particle , in order to allow the system to reach the stationary non - equilibrium state . figure [ fig:1 ] displays the mean velocity field for the system of inelastic spheres in the @xmath26 plane ( @xmath27 denotes the radial distance from the axis of the cylinder ) when the reduced shaker amplitude is @xmath28 . the field is averaged over the azimuthal angle and approximately @xmath29 collisions ) . a torroidal convection roll is clearly present in which the particles flow , on average , up from the center and down the side wall . note that , unlike the related rayleigh - bnard phenomenon , the roll is asymmetric . the velocity field is in near quantitative agreement with that observed experimentally by wildman et al . @xcite . in particular , the center of the vortex roll is at @xmath30 in reduced units which corresponds to @xmath31 in experiments@xcite . the shape of the roll , as well the location of its center , do not change appreciably as the shaker amplitude is varied between @xmath32 . to highlight the role played by the wall , we performed additional simulations in which the wall - sphere collision is taken as elastic ( a perfect wall for which the wall - particle restitution coefficient is equal to 1 ) with the other parameters unchanged . the mean velocity field of this simulation is quite different from the inelastic case . although some convection is apparent in figure [ fig:2 ] , ( particles on average flow up the wall and down to the center ) . it is weaker by about an order of magnitude in intensity ( compare the velocity units at the top of figs . [ fig:1 ] and . [ fig:2 ] ) and the roll direction is _ opposite_. to quantify the bulk convection , we have calculated the total velocity correlation , @xmath33@xcite where @xmath34 label the cells in the hydrodynamic region , @xmath35 their total number and @xmath36 where the sum @xmath37 is over the @xmath38 neighboring cells of @xmath34 . see figure [ fig:6 ] . bulk convection is present when @xmath39 is different from zero . for @xmath20 , as the shaker amplitude is increased the total velocity correlation @xmath40 becomes different from zero when @xmath41 , increases until @xmath42 and stays roughly constant for larger amplitudes . a similar behavior was observed in the experiments of wildman et al . for @xmath43 , @xmath40 is almost equal to zero for all amplitudes ( figure [ fig:6 ] ) . a close examination of the corresponding flow velocity fields show that the amplitude of the circulation of particles up the wall and down to the center exists for @xmath41 , a feature which is not well handled by the calculation of the order parameter . figure [ fig:3 ] shows the granular temperature as a function of the altitude , @xmath14 , for different values the radial position . these results agree well with the experiments ( fig.1 of ref@xcite ) except for an underestimated maximum close to the basewall . these differences could result from the base - particle collisions which are assumed elastic in simulations . a minimum in the granular temperature profile is observed in the current simulations ( and also in experiments ) in the neighborhood of the center of the cylinder , but becomes weaker close to the wall cylinder . fig [ fig:4 ] displays the same profiles for the system with @xmath43 : the temperature minimum in the vertical direction is more pronounced , but the temperature varies little in the radial direction . the existence of a minimum in the granular temperature along the @xmath14-direction is a phenomenon which is also present in the absence of convection@xcite and results from the fact that at high altitudes the density and collision frequency are small , leading to a small number of hot particles . figure [ fig:5 ] displays a packing fraction plot which agrees qualitatively with the experimental results , except in the bottom region of the side wall where the density is higher than in experiments . nevertheless , there is a maximum in the density profile in the vertical direction , whatever the radial distance . moreover , there is also a maximum along the radial direction which is a consequence both of the compressible nature of the inelastic hard sphere system and of the small wall - particle restitution coefficient . when @xmath43 , the radial density gradient almost vanishes . although a complete theoretical treatment of the convection is beyond the scope of this letter , we present some simple arguments that may help to rationalize the observed behavior . the rayleigh - bnard convection which is the paradigm for pattern formation in classical fluid mechanics , has been extensively studied over the past three decades@xcite . a temperature gradient applied to a fluid leads to a competition between buoyancy and disspation , which leads to the occurence of rolls above a threshold characterized by the non dimensional rayleigh number @xmath44 , which characterizes the ratio of the two forces . for larger temperature gradients , on observes a cascade of bifurcations ending in a chaotic regime . for classical fluids , hydrodynamic equations reproduce the observed patterns remarkably well . the range of validity of continuum equations applied to granular materials , which contain a sink term in the energy equation to account for the dissipation of energy during collisions , is more restricted . hydrodynamic equations can provide a good description of inelastic spheres @xcite , provided that the particles packing fraction remains @xmath45 ( below which the mean free path becomes comparable to the diameter of the cylinder ) . similarly , if the packing fraction is too large ( @xmath46 ) the dissipation becomes too strong and the description breaks down . using such an approach , brey et al.@xcite obtained temperature profiles for an open granular system , _ without convection _ and predicted the presence of a minimum as a function of @xmath14 , coinciding with the limit of validity of the hydrodynamic equations . when @xmath20 , the hydrodynamic description breaks down close to the wall ( high density and temperature gradient , strong dissipation ) . the onset of the bulk convective regime with a `` real '' wall is lowered because of the existence of the radial temperature gradient in addition to the vertical one . this can explain both the direction of circulation and the lowering of the threshold of convection compared to the case when the wall is perfect and no bulk convection is present . the circulation of particles is restricted close to the sidewall where strong dissipation is not well described by hydrodynamic equations . a kinetic approach is required close to the cylinder . our simulations clearly demonstrate the relevance of the inelastic hard sphere model for describing the experimental study of wildman et al@xcite and underline the key influence of the cylinder wall on the convection . experimentally , unlike in the simulations , the wall - particle restitution coefficient is not an easily tunable parameter . we therefore propose a modification to the experiment that may lead to the observation of new phenomena" +"understanding the formation of massive stars is crucial to an understanding of the formation of stars in general and of galaxies . many , perhaps most , stars form in clustered environments where massive stars are present ( lada 1992 , williams & mckee 1997 ) . only massive star formation is readily studied at the distances of other galaxies . in particular , the discovery that star formation at substantial redshifts is often heavily obscured by dust ( e.g. , frayer et al . 2000 ; chapman et al . 2001 ) indicates that study of the history of star formation in galaxies , hence the major part of galaxy formation , can be related to what we learn about massive star formation in our own and nearby galaxies . here we consider a number of issues surrounding the formation of massive stars , beginning with a comparison to what we know about the formation of low mass stars , proceeding through some systematic studies of early stages of massive star formation , and ending with some speculations about the initial conditions for massive star formation . in the case of low mass stars , a well - established evolutionary paradigm prevails , and a standard model of star formation ( shu et al . 1987 ) provides a detailed target for observational tests . various alternative models have also been proposed and observers are beginning to compare these models to observations . the evolutionary paradigm is based on the class system ( lada & wilking 1984 , lada 1987 ) , originally proceeding from class i ( deeply embedded ) to iii ( revealed star , weak - line t tauri star ) via class ii ( roughly the same as classical t tauri stars ) . the recent advances in submillimeter capability have revealed a self - luminous phase that is still more embedded than class i , and andr , ward - thompson , & barsony ( 1993 ) called this phase class 0 . the initial conditions for low mass star formation appear to be amenable to study in dense regions without any evidence for internal luminosity . variously called pre - protostellar cores ( ppcs ) , pre - stellar cores , or class @xmath0 sources , these objects first became obvious as peaks of submillimeter emission . while they roughly coincide with molecular emission regions , the molecular line emission did not directly reveal the high densities , apparently because of substantial molecular depletion ( e.g. , caselli et al . 2001 ) , caused by the high densities and low temperatures in the cores of these regions . the temperatures are low enough ( @xmath1 k ) that even the submillimeter emission is decreased toward the centers ( evans et al . 2001 ) , but the dust continuum emission is much more revealing than the molecular line emission that has usually been used to trace dense regions . the extended class system relies on a mixture of slopes ( lada & wilking 1984 , lada 1987 ) , peaks , and ratios ( andr et al . 1993 ) in the spectral energy distribution ( sed ) of dust emission . an alternative that unifies these methods and provides a continuous variable is the bolometric temperature ( ) introduced by myers & ladd ( 1993 ) . chen et al . ( 1995 ) showed that the class boundaries corresponded well to certain values of . however , , being defined by the spectrally averaged mean frequency , can be heavily affected by emission at relatively short wavelengths , where geometrical effects are conflated with evolutionary effects . for the early stages , there are two important boundaries : class @xmath0 to class 0 ; and class 0 to class i. there are usually insufficient measurements to define for class @xmath0 sources ; the test for class @xmath0 status is that there is no evidence for internal luminosity . for the class 0/i boundary , one can use either @xmath2k ( chen et al . 1995 ) or the ratio of emission beyond 350 to total luminosity , @xmath3 ( andr et al . 1993 ) . to what extent can we carry the observational paradigm and theoretical models for low - mass star formation over to the case of massive star formation ? working with a modest sample size ( 14 ) , van der tak et al ( 2000 ) found rather poor correlations between different potential tracers of age . it is not very surprising that the sed may not correlate with evolution in the same way as for low mass stars ; for massive stars forming in clusters , the sed will be dominated by the most luminous object that is still embedded and the evolution of the various objects is unlikely to be highly synchronized . the class ii phase in particular may have little meaning : for low mass stars , this is the phase when the sed is dominated by a disk ; the presence of disks around massive stars is less firmly established . finally , the evolution of massive stars is so much faster that we can not expect the gentle unfolding of the sed as the dust moves from envelope to disk to star in the low mass case . instead , massive stars reach the main sequence , form hii regions , blow ionized winds , etc . before much of the material in the envelope has fallen in . what other evolutionary tracers might prove useful ? clearly , the emergence of an hii region , first as an ultra - compact hii region , marks an important evolutionary boundary . if we are looking for the earliest stages , we want to study sources before uc hii regions form . there are two general ideas for evolutionary tracers at earlier times : masers and chemical signatures . while oh masers appear to be associated with hii regions , h@xmath4o and possibly ch@xmath5oh ( e.g. , minier , conway , & booth 2001 ) masers appear to be associated with early stages , when molecular outflows produce shocks . hot cores ( warm , dense , chemically - rich regions ) also appear to precede uc hii regions ( see van der tak 2002 for a discussion of this approach ) . the hot cores could in principal be heated internally ( and hence analogous to class 0 sources ) or externally ( hence analogous to class @xmath0 sources ) . there have been many detailed studies of individual regions of massive star formation , but systematic studies of large samples of regions using uniform analytical methods are just becoming available ( e.g. , plume et al . 1992 , 1997 , bronfman et al . 1996 , sridharan et al . 2001 ) . in the next section , we report on recent work on the sample identified by plume et al . water masers provide a large sample of objects with accurate positions for further study ( e.g. , cesaroni et al . many masers are _ near _ uc hii regions , but their positions do not coincide , consistent with the masers revealing an earlier stage . in addition , the presence of a h@xmath4omaser ensures the existence of some very dense gas . the models of these masers also require shocks , suggesting that some star formation and associated outflow has begun . consequently , we have pursued a series of studies of the gas and dust in the directions of water masers , beginning with a survey for emission in the 76 transition of cs ( plume , jaffe , & evans 1992 ) . a large fraction of the maser sources were detected in the cs 76 survey , leading to a follow - up study using cs 21 , 32 , 54 , and in a few cases , @xmath6 transitions to constrain the density via lvg calculations of the molecular excitation ( plume et al . 1997 ) . for many sources , c@xmath7s data provided a check on optical depth effects in cs . that study found high densities in many sources , with a mean in the log of density , @xmath8 , of @xmath9 , with the average taken over 71 sources . plume et al . ( 1997 ) also mapped a few sources crudely ( cross - scans ) to estimate sizes and masses . to obtain better data on sizes , masses of dense gas , density distributions , etc . , we have made fully sampled maps of a large fraction of the plume et al we mapped 63 regions in cs 54 ( shirley et al . 2002 ) and 24 regions in cs 76 ( knez et al . in addition , we have mapped the 350 continuum emission from dust toward 51 of these regions ( mueller et al . details of the observations and analysis can be found in those papers , and a more complete study of one of the objects can be found in lee et al . ( 2002 ) . here we focus on the overall results , summarizing and comparing the results from the different tracers , while accounting for differences among the samples in the different studies . for all the samples , the fwhm size of each core was determined by deconvolving the telescope main beam fwhm from the observed fwhm of the core . in most cases , the deconvolved angular sizes determined in this way were slightly larger than the beam size , characteristic of a power - law emission distribution ( terebey et al . 1993 ) . also , the cs 76 sizes were smaller than the cs 54 sizes , as expected for a centrally peaked density distribution because the critical density for the 76 line is 3 times greater than that for the 54 line ( cf . evans 1999 ) . for power law distributions , the size defined in this way should not be considered a physical boundary . instead , we use it , along with the distance , to calculate a fiducial radius for convenient comparisons . similarly , the mass in a power law distribution can only be specified for a given radius ; when comparing masses from various techniques , it is important to compare for the same fiducial radius . because the cs 54maps have the largest extents , thus tracing the core farther down the density distribution , we compare all masses calculated to be inside the radius of the cs emission : @xmath10 , where @xmath11 is the fwhm angular extent of the map of cs 54 emission and @xmath12 is the distance . the modeling follows the scheme represented by figure 1 , though at present some of the processes are incompletely implemented . the modeling of the dust emission is described by mueller et al . a density power law ( @xmath13 ) is assumed , a radiative transport code is used to compute a self - consistent , and the resulting and @xmath14 are used to compute the dust emission over the full sed . for comparison with maps of submillimeter continuum emission , the emission is convolved with the measured beam response and chopping is simulated . comparison of the predicted intensity profile to that obtained in the observations allows one to choose the best fitting power law index for the density . comparison to the observed integral of the sed constrains the internal luminosity of the forming stars , while comparison to the emission at submillimeter wavelengths constrains @xmath15 and hence the mass . the mass also depends on the assumed opacity at 350 ( @xmath16 ) , and the overall shape of the sed depends on the full behavior of the" +"quantum fluctuations give rise to numerous fascinating physical effects , especially on sub - micrometer scales . some of these phenomena have been extensively studied and carefully measured , thus demonstrating their relevance for both fundamental physics and future technologies @xcite . recently , there has been a renewed interest in fluctuation - induced interactions in nonequilibrium systems . a prominent example is quantum friction @xcite , the quantum drag force between two uncharged , polarizable objects in relative motion . a large part of the existing literature on quantum friction considers an atom ( or some other microscopic object ) moving in front of a flat surface , where the corresponding material is modeled using local optics , i.e. assuming a spatially local material whose electric permittivity only depends on frequency @xcite . within the assumption of local optics , several conceptual questions have been addressed in the literature , including the functional dependence of the frictional force on the atom s velocity @xcite , the impact of non - markovian effects @xcite , and even the relevance of nonequilibrium correlations @xcite . at short distances from the surface , however , a local description of the material becomes inadequate . earlier works @xcite have already shown that spatial dispersion can lead to corrections to equilibrium dispersion forces . also , in the case of surface - surface quantum friction , different material models that include spatial dispersion have been used to describe the drag force @xcite . the authors of these works have demonstrated that for short distances spatial nonlocality can lead to an enhancement of the force relative to the case of a local material model @xcite . these works , however , have resorted to the so - called local thermal equilibrium ( lte ) approximation , where it is assumed that the subsystems in relative motion are at equilibrium with their immediate surroundings . such a procedure allows to utilize results of equilibrium thermodynamics , like the fluctuation - dissipation theorem @xcite , but neglects the contribution due to nonequilibrium correlations @xcite . in fact , recent work has shown that the lte approximation is not well justified for atom - surface quantum friction and underestimates the magnitude of the drag force @xcite . since the lte approximation relies on a short correlation length of the fluctuations that mediate the interaction , one can expect that , when spatial dispersion is taken into account , the deviation from the lte result is even larger than in the local optics treatment . in this work , we study effects of spatial dispersion in atom - surface quantum friction and compare the results obtained using the lte approximation with those obtained using a full nonequilibrium approach . we show that spatial dispersion enhances the failure of the lte approximation , resulting in a 95% deviation from the full nonequilibrium result compared to the 80% deviation previously reported within local optics @xcite . in addition , we show that the inclusion of spatial nonlocality strongly affects the functional distance dependence of the frictional force in the low - velocity limit . in contrast to the local optics case , where both the lte and the full nonequilibrium approach predict the same distance scaling law for the quantum frictional force , their distance behaviors are different in the presence of spatial dispersion . consider an atom driven by an external force and moving with non - relativistic velocity ( @xmath0 ) at constant height @xmath1 parallel to a conducting isotropic half - space . the atom is modeled as an electric dipole , described by the quantum operator @xmath2 . due to the interaction of the atom with the surrounding quantum electromagnetic field a drag force will progressively balance the external drive until the system reaches a nonequilibrium steady state , where the motion continues with constant velocity . dissipation in the material gives rise to a nonzero memory time , such that in the nonequilibrium steady state we can ignore the transient acceleration process and assume that the atom has reached the trajectory @xmath3 @xcite ( we assume that the motion is along the @xmath4-direction ) . in earlier work @xcite , we have shown that the zero - temperature drag force felt by the atom in such a situation can be written as @xmath5,\end{aligned}\ ] ] where @xmath6 is the parallel component of the three - dimensional electromagnetic wave vector @xmath7 @xcite . for symmetry reasons , the frictional force is only along the direction of the motion , i.e. @xmath8 . quantum friction is determined by the velocity - dependent nonequilibrium power spectrum tensor of the dipole fluctuations , @xmath9 , and by the fourier transform ( in time and @xmath10-direction ) of the electromagnetic surface green tensor , @xmath11 . in eq . and in the remainder of the paper the subscript @xmath12 ( @xmath13 ) denotes the real ( imaginary ) part of an expression and the superscript @xmath14 gives the symmetric part of a tensor @xcite . the green tensor is given by the sum of a vacuum contribution @xmath15 and a scattering contribution @xmath16 . because of lorentz invariance , only the latter contributes to the final result @xcite . in all this work we focus on atom - surface distances within the surface s near - field region . in this case the part of the scattered green tensor relevant to quantum friction @xcite is @xmath17~,\end{aligned}\ ] ] where @xmath18 is the vacuum permittivity . the description of the material properties enters via the transverse magnetic reflection coefficient , @xmath19 , which in general depends on both the frequency and , for symmetry reasons , the modulus of the wavevector @xmath20 . in a spatially local description of the material and in the near - field limit , the dependence on the wave vector disappears and the reflection coefficient is only a function of frequency @xcite . in order to calculate the nonequilibrium power spectrum , we model the dipole s internal dynamics as a harmonic oscillator @xcite @xmath21 where @xmath22 is the oscillator s frequency , @xmath23 is the electric field , and @xmath24 is the static polarizability tensor , assumed to be symmetric for simplicity ( it is proportional to a projector parallel to the direction of the dipole moment ) . we suppose that the oscillator has no intrinsic dissipation and that all the dissipative dynamics arises from the coupling to the electromagnetic field . the harmonic oscillator model allows for an analytical expression of @xmath9 given by @xcite @xmath25,\end{aligned}\ ] ] where , in contrast to the lte approach which relies on the equilibrium fdt , this nonequilibrium fdt contains the extra term @xmath26\\ \times&\underline{\alpha}(\omega , v_x)\cdot\underline{g}_i(\mathbf{p},z_{a},\omega+p_xv_x)\cdot\underline{\alpha}^*(\omega , v_x ) . \end{split}\end{aligned}\ ] ] in the previous equations @xmath27 is the velocity - dependent atomic polarizability . in this expression , @xmath28 and @xmath29 denote , respectively , the velocity - dependent radiative damping and frequency shift @xcite @xmath30&,\\ \label{gammarate } \frac{\omega\gamma(\omega , v_{x})}{\omega_{a}^{2}}=\int \frac{d^{2}\mathbf{p}}{(2\pi)^{2}}\mathrm{tr}\left[\underline{\alpha}_{0}\cdot\underline{g}_{i}(\mathbf{p},z_{a},\omega+p_xv_x)\right ] & .\end{aligned}\ ] ] according to eq . , the frictional force in eq . decomposes in two contributions , @xmath31 the first , @xmath32 , is what one would have obtained by applying the lte approximation , while the second , @xmath33 , is the correction entirely due to the nonequilibrium dynamics of the system . previous works @xcite have shown that the quantum frictional process is characterized by a non - resonant and a resonant contribution , both being a function of the atomic velocity and the atom s separation from the surface . the resonant part occurs for sufficiently high velocities which bring the atomic transition frequency within the range of the surface plasmon - polariton resonances that exist at the vacuum / material interface . here , we consider only the non - resonant part of the frictional force which takes place at lower velocities and is more likely to play a central role in typical experimental setups . in appendix [ low - velocity ] we show that the main contribution to the force comes from the frequency range @xmath34 ( see also refs . @xcite ) . therefore , at sufficiently low velocities @xcite the drag force is determined by the low - frequency behavior of the material s electromagnetic response . under the assumption that the material is ohmic for these low frequencies ( we will see below that this applies to our nonlocal model ) , the low - velocity approximation of the lte and the nonequilibrium contributions to the friction can be written as ( see appendix [ low - velocity ] ) @xmath35^{2 } } , \label{generalasymplte}\\ f^{j}&\approx- 2\hbar\frac{v_{x}^{3}}{\pi}\phi_{1}^{2}\frac{\mathcal{d}^{2}_{1}(z_{a})}{\left[1-\delta(0,0)/\omega_{a}^{2}\right]^{2}}.\end{aligned}\ ] ] [ generalasymp ] this shows that at low velocities the zero - temperature frictional force grows as the third power of the atom s velocity @xcite . in the above expressions , we have introduced the abbreviations @xmath36 associated with the dipole s direction in space , and @xmath37 which depends on the properties of the surface ( the prime indicates the first derivative with respect to the frequency ) . the functions @xmath38 are the [ @xmath39-th derivative with respect to @xmath40 of the low - frequency behavior of the electromagnetic density of states near the vacuum / material interface . in particular , @xmath41 is related to the atomic decay rate induced by the interaction with the radiation ( radiative damping ) . show that , under the assumption of ohmic dissipation , the lte and the nonequilibrium correction have the same functional dependency on the velocity , while their behavior as a function of the distance can be distinct . in the local optics approximation , however , we have that @xmath42 , @xmath43 , and @xmath44 ( see eq . in appendix [ nonlocalimpedance ] ) . in this case @xmath32 and @xmath33 have the same @xmath45 distance dependency , as was already shown in @xcite . the previous results allow for a quantitative evaluation of the impact of spatial dispersion on quantum friction . we describe the properties of a metallic surface using the so - called semi - classical infinite barrier ( scib ) model @xcite . in this model , electrons are treated as a fermi fluid whose dynamics is governed by the boltzmann equation . at interfaces , electrons are assumed to be specularly reflected by an infinite potential barrier @xcite . although more sophisticated models are available ( see , for example , refs . @xcite ) , the scib model takes into account important phenomena , such as landau damping @xcite , which are absent in simpler nonlocal models ( e.g. the hydrodynamic model ) @xcite . landau damping occurs when the frequency and the wavevector of the radiation fulfill the condition @xmath46 , i.e. , when the quasi - particle s velocity @xmath47 becomes comparable to the phase velocity @xmath48 of the radiation , @xmath49 ( @xmath50 ) . since quantum friction is very sensitive to any form of dissipation present in the system @xcite , this intrinsic damping due to the exchange of energy between the electronic wave function and the radiation @xcite will play an important role in our analysis . within the scib model , the reflection coefficient takes the form @xcite @xmath51 where @xmath52 is the transverse magnetic surface impedance and @xmath53 is the corresponding vacuum value . in the non - retarded limit ( formally equivalent to the limit for @xmath54 ) we have @xcite @xmath55 such that the reflection coefficient only depends on the longitudinal part of the bulk dielectric function @xmath56 where @xmath57 is the metal s dissipation rate , @xmath58 is the plasma frequency , @xmath59 , \label{fl}\end{aligned}\ ] ] and @xmath60 with @xmath61 the fermi velocity . equation is the semi - classical limit of lindhard s quantum dielectric function @xcite , valid for wavavectors much smaller than the fermi" +"given the diversity of mass and length scales , redshifts , initial conditions and physical processes that take part in the hierarchical formation of galaxies , the fact that most galaxies exhibit some common key properties , such as an exponential disk profile e.g. @xcite , and follow common scaling relations such as star formation rate - stellar mass relation ( e.g. @xcite ) is remarkable . such simple relations may imply that despite the diversity of initial and end states , there is a subset "" of universal processes that effectively dominate these relations . even though many constituents are necessary to model correctly galaxy formation to its last detail , a toy model that involves as few parameters and processes as possible , and can nevertheless yield those key properties , is powerful in its ability to offer intuition towards their understanding . this approach has motivated the _ ` equilibrium - model ' _ ( or ` bathtub - model ' ) @xcite that has been used to investigate the content of galaxies , both gaseous and stellar , the associated star formation rate ( sfr ) , metallicities , and the relations between them , especially for the ( blue ) main sequence "" of galaxies . these models typically assume an equilibrium relation ( see for example @xcite ) , @xmath9 , where @xmath10 is the sfr , @xmath11 is the gas mass of the disk and @xmath12 is the gas - to - star depletion time ( or turn - over "" time , @xcite ) . in addition , the outflowing baryonic mass out of the galaxy , back to the circum- or intergalactic medium ( cgm / igm ) in these models is proportional to the sfr , @xmath13 , where @xmath14 is the mass - loading factor , set by energy and momentum injection back into the interstellar medium ( ism ) . to date , all of the equilibrium models have been applied to galaxies as a whole , ignoring the internal disk structures . in contrast , in this paper we formulate a radially resolved model , in which the equilibrium relations are local "" and functions of ( planar ) distance from the disk centres , and assuming that the gas dynamics is set by the mass - continuity equation and global angular momentum conservation . our model is self - consistent , as star formation , disk rotation , outflows and the disk size are all set dynamically with the disk evolution . we study in detail how systems that follow these simple assumptions evolve , reach a ( quasi-)steady state , accumulate stellar mass , and analyze dynamically their surface density and toomre-@xmath15 profiles . in our presentation , we show that many of our numerical results can be derived analytically , by solving simplified cases of the full ( partial differential ) equations , for our single phase ism . the paper is organised as follows . in [ sec : setup ] we write the evolution equations and the assumptions of our model , and discuss a dimensionless representation for it . in [ sec : cossnap ] we consider a cosmological snapshot in which we hold the cosmological conditions constant , and analyze the consequent steady state and the convergence to it . next , in [ sec : cosevol ] we generalise the cosmological snapshot , by accounting for the evolution of the halos , and varying baryon accretion rates . in [ sec : results ] we analyze the results of our model for the cosmologically evolving system , and present a parameter study . we summarise in [ sec : discussion ] . we consider an evolving , rotationally supported , star forming disk , within a cosmologically growing dm halo . the halo accretes baryonic matter from its cosmological neighbourhood , at some given rate @xmath16 , forms stars continuously , and expels matter back to the cgm / igm at a rate proportional to the star formation rate . our radially resolved equilibrium model is based on the dynamics set by mass - continuity and angular momentum conservation , together with local equilibrium relations . the mass continuity equation in cylindrical coordinates ( assuming cylindrical symmetry ) includes cosmological accretion , and star formation and outflows as source and sink terms , and follows the gas surface density in the disk , @xmath17 . it can therefore be written as @xmath18 where @xmath19 and @xmath20 are the local "" sfr and outflow rates respectively , @xmath21 is the radial gas velocity within the disk ( inflow velocity is @xmath22 ) , and where for the second equality we have assumed ` local ' equilibrium relations , @xmath23 to solve the mass - continuity equation , we will have to specify the boundary condition at some outer radius @xmath24 , and the gas radial inflow velocity @xmath25 at each radius . we do that as follows : * we assume that the entire ( thin ) baryonic disk , gas+stars , is confined to a radius @xmath26 , so that @xmath27 . we determine @xmath26 by setting the specific angular momentum of the accreted gas onto the disk , at any time @xmath28 , equal to that of the parent halo with a given ( cosmological ) spin parameter @xmath29 where @xmath30 and @xmath31 are the angular momentum , energy and the virial mass of the halo , respectively , and @xmath32 is newton s gravitational constant . observations and simulations suggest that the specific angular momentum of the baryonic disks indeed remain globally equal to the parent halos as the disks evolve despite the complex inflow and outflow patterns ( e.g. @xcite ) . we therefore do not impose cosmological initial conditions for the cumulative mass distribution of specific angular momentum found in dark matter only simulations ( e.g. * ? ? ? * in realistic disks , the radial gas inflows depend in a complex way on local conditions and global tidal torques and bar instabilities . in our model we assume an azimuthally averaged gas inflow velocity , @xmath25 , at each radius @xmath33 , and we consider three cases . the first two are ( _ a _ ) constant radial inflow velocity , @xmath34 , and ( _ b _ ) radial inflow velocity that satisfies @xmath35 , where @xmath36 is the inflow velocity at the outer disk radius @xmath26 . the third case is motivated by a viscous disk in which the dissipated energy in one rotational timescale , which is of order @xmath37 , where @xmath38 and @xmath39 is the rotational velocity at each radius , is compensated by the gain in potential energy , @xmath40 @xcite , leading to ( _ c _ ) @xmath41 . our case ( _ c _ ) in combination with our mass conservation eqn . ( [ eq : dimen ] ) is similar to the viscous evolution models presented by @xcite and @xcite but with the inclusion of inflow and outflows , and self consistent star formation . with the gas surface density @xmath42 we can keep track of the gas mass in the disk out to distance @xmath43 as a function of time @xmath44 the total gas mass in the disk is @xmath45 . to obtain the accumulated stellar mass @xmath46 one has to integrate the sfr over time , and assume some stellar migration profile . we will assume in this paper that once formed , stars do not migrate radially , but rotate around the disk center together with the inflowing gas , so that @xmath47 where @xmath48 denotes a time before star formation has begun . solving for @xmath42 will also enable us to examine the local toomre-@xmath15 parameter @xcite , that quantifies the stability of the gas in the disk with respect to star formation , as a function of the galactocentric distance . by definition , @xmath49 where @xmath50 is the gas sound speed ( thermal plus turbulent ) and @xmath51 is the epicyclic frequency @xmath52 we approximate @xmath39 by the keplerian rotational velocity for a spherical mass distribution @xmath53 , that is composed of the gaseous and stellar disk components , plus the extended dark matter distribution @xmath54 we assume that the rotation curves for our two - dimensional disks differ only slightly than for spherical mass distributions ( see @xcite ) . we ignore pressure support along the disk plane ( c.f . @xcite ) . it is useful to rescale to dimensionless form . we define dimensionless time and distance coordinates , @xmath55 where @xmath56 is the crossing time , @xmath57 the normalised inflow velocity is @xmath58 we then define the dimensionless accumulation "" parameter @xmath59 and the normalised surface density @xmath60 thus in dimensionless form the mass - continuity equation is @xmath61 this dimensionless representation is valid only if @xmath16 and @xmath36 are constant , which is a reasonable assumption only if the disk reaches a steady - state faster than the time it takes @xmath16 to change significantly . we assume this in [ sec : cossnap ] , but relax this assumption in [ sec : cosevol ] , which will force us back to eqn . ( [ eq : dimen ] ) . in terms of this dimensionless notation , the fixed constant inflow velocity is written as @xmath62 , the @xmath63 case is written as @xmath64 and the @xmath65 case can be written as @xmath66 , where @xmath67 is a dimensionless mass "" , and the coefficient @xmath68 is set by the input parameters . we start by solving the disk evolution equation for a cosmological snapshot "" , for which the halo mass and cosmological inflow rates are constant , and the dimensionless version of our model is valid . we focus first on steady state solutions with ( [ sec : ysf ] ) and without ( [ sec : nsf ] ) star formation . we demonstrate that simple mass conservation naturally leads to disks with exponential profiles over many length scales . finally , in [ sec : cca ] we examine the timescale for the convergence to steady - state . quantitatively , the case of no star formation ( i.e. infinite depletion time ) , is considered simply by setting @xmath69 in eqn . ( [ eq : cont ] ) . in steady state , the inflow velocity is independent of time , and the continuity equation can be easily solved , yielding @xmath70 this solution is valid for @xmath71 or @xmath72 ( cases ( _ a _ ) and ( _ b _ ) ) discussed above . for @xmath66 ( case ( _ c _ ) ) eqn . ( [ eq : yqss ] ) is also satisfied but depends on @xmath73 , so this is actually a differential equation on its own , rather than a solution for the surface density . ignoring the dm halo , i.e. , assuming that the entire rotation curve , and hence the inflow velocity are determined solely by the baryonic matter in the disk , this differential equation can also be solved analytically . using eqn . ( [ eq : m ] ) the differential equation for the surface density can be written as @xmath74 solving this differential equation , setting the constant of integration so that @xmath75 , and writing the solution in terms of @xmath76 , we get @xmath77 comparing this solution to eqn . ( [ eq : yqss ] ) shows that in the no - star formation no - dm case , the constant inflow velocity is a better fit to the physically motivated case ( _ c _ ) , in which the inflow velocity changes by @xmath78 per cent across the entire disk . the dimensionless gas profiles , for all three inflow" +"interaction of electromagnetic radiation with atoms has led to interesting quantum features such as antibunching and squeezing . in particular , interaction of two - level atoms with squeezed light has extensively been studied by many authors @xcite . these studies show that the squeezed light modifies the width of the spectrum of the incoherent light emitted by the atom . on the other hand , cavity qed in semiconductor systems has been the subject of interest in connection with its potential application in optoelectronic devices @xcite . for example , such optical systems hold potential in realization of optical devices that exhibits exceptional properties such as monomode luminescence with high gain allowing the realization of thresholdless laser . the quantum properties of the light emitted by a quantum well embedded in a microcavity has been studied by several authors @xcite . unlike antibunching observed in atomic cavity qed , the fluorescent light emitted by the quantum well exhibits bunching @xcite . in the strong coupling regime when the coupling frequency between the exciton and photon is larger than the relaxation frequencies of the medium and the cavity the intensity spectrum of the exciton - cavity system has two well - resolved peaks representing two plaritons resonance @xcite . in the experimental setting , et al_. @xcite demonstrated exciton - photon mode splitting in a semiconductor microcavity when the quantum well and the optical cavity are in resonance . subsequent experiments on exciton - photon coupling confirmed normal mode splitting and oscillatory emission from exciton microcavities @xcite . in this work , we study the effect of the squeezed light generated by a subthreshold degenerate parametric oscillator ( opo ) on the squeezing and statistical properties of the fluorescent light emitted by a quantum well in a cavity . the system is outlined in fig . degenerate opo operating below threshold is a well - known source of squeezed light @xcite . we explore the interaction between this light and a quantum well with a single exciton mode placed in the opo cavity . our analysis is restricted to the weak excitation regime where the density of excitons is small so that the interactions between an exciton and its neighbors can be neglected . further , to gain insight into the physics we investigate the dynamics of the fluorescent light emitted by the quantum well in the strong coupling regime , which amounts to keeping the leading terms in the photon - exciton coupling constant @xmath0 . we show that the fluorescent light exhibits bunching and quadrature squeezing . the former is due to the fact that two or more excitons in the quantum well can be excited by absorbing cavity photons . this implies there is a finite probability that two photons can be emitted simultaneously . we also show that the squeezed light leads to narrowing of the width of the spectrum of the fluorescent light . we obtain the solution of the quantum langevin equation for a cavity coupled to vacuum reservoir . the resulting solution , in the strong coupling limit , is used to calculate the intensity , spectrum , second order correlation function and quadrature squeezing of the fluorescent light . we consider a system composed of a semiconductor quantum well and a degenerate parametric oscillator operating below threshold . in a degenerate parametric oscillator , a pump photon of frequency @xmath1 is downconverted into a pair of identical sinal photons of frequency @xmath2 . the signal photons are highly correlated and this correlation is responsible to the reduction of noise below the vacuum level . such a system produces a maximum intracavity squeezing of 50@xmath3 . in a quantum well , the electromagnetic field can excite an electron from the filled valance band to the conduction band thereby creating a hole in the valance band . the electron - hole system possesses bound states which is also called exciton states analogous to the hydrogenic states or more precisely to the positronium bound states . we assume that the density of the excitons is small so that exciton - exciton interaction is negligible . the hamiltonian describing the parametric process and interaction between exciton and cavity mode in the rotating wave approximation and at resonance is given by @xmath4 here @xmath5 and @xmath6 , considered as boson operators , are the annihilation operators for the cavity and exciton modes , respectively ; @xmath0 is the exciton cavity mode coupling ; @xmath7 is the hamiltonian associated with the dissipation of the cavity and exciton modes by vacuum reservoir modes . we assume here that the amplitude of the field @xmath8 that drives the cavity is real and constant . the quantum langevin equations of the system taking into account the cavity dissipation @xmath9 and the exciton spontaneous emission @xmath10 can be written as @xmath11 @xmath12 where @xmath13 and @xmath14 are the langevin noise operators for the cavity and exciton modes , respectively . both noise operators have zero mean , i.e. , @xmath15 . for a cavity mode damped by a vacuum reservoir , the noise operator satisfy the following correlations : @xmath16 @xmath17 the exciton noise operators satisfy the following correlations : @xmath18 @xmath19 in this section we analyze the photon statistics of he fluorescent light by calculating intensity , intensity spectrum and second order correlation function in the strong coupling regime . the solution of eqs . and is rigorously derived in the appendix . in the paper paper is devoted to the dynamics of the system in the strong coupling regime . to this end , imposing the strong coupling limit ( @xmath20 ) , which amounts to keeping only the leading terms in @xmath0 , one obtains from eqs . and that @xmath21 . as a result , the solution given by eqs . and reduce to @xmath22\notag\\ & + \int_{0}^{t}dt^{\prime } ~~\big[\lambda_{3}(t - t^{\prime})f_{e}(t^{\prime})+\lambda_{4}(t - t^{\prime})f_{e}^{\dagger}(t^{\prime})\big],\end{aligned}\ ] ] @xmath23\notag\\ & + \int_{0}^{t}dt^{\prime } ~~\big[\lambda_{1}^{(-)}(t - t^{\prime})f_{e}(t^{\prime})+\lambda_{2}^{(-)}(t - t^{\prime})f_{e}^{\dagger}(t^{\prime})\big],\end{aligned}\ ] ] where @xmath24 e^{-(\kappa+\gamma)t/4},\end{aligned}\ ] ] @xmath25e^{-(\kappa+\gamma)t/4},\end{aligned}\ ] ] @xmath26 @xmath27 all quantities of interest which describe the dynamics of the system can fully be analyzed using these solutions . the dynamical behavior of the intensity of light emitted by a single quantum well in gaas microcavity has been measured experimentally @xcite . we here seek to study the dynamical behavior of the light emitted by a single quantum well interacting with squeezed light . the intensity of the fluorescent light is proportional to the mean number of excitons in the system . using eq . and the properties of the noise forces , we readily obtain @xmath28\sinh(\varepsilon t)\notag\\ & -(\kappa+\gamma)\frac{2\varepsilon \sinh ( \varepsilon t)+(\kappa+\gamma)\cosh(\varepsilon t)}{(\kappa+\gamma)^2 - 4\varepsilon^2}\notag\\ & + \frac{\gamma-\kappa } { 2 g } \text{sinh}^2 ( \varepsilon t/2)\text{sin}(2 g t)\bigg]e^{-(\kappa+\gamma)t/2},\end{aligned}\ ] ] where @xmath29 is the mean exciton number in the cavity at initial time . we assumed that the cavity mode is initially in vacuum state . it is easy to see that in the steady state the mean exciton number reduces to @xmath30 which is a contribution to intensity of the fluorescent light due to the optical parametric oscillator . vs scaled time @xmath31 for @xmath32 , @xmath33 , @xmath34 and for different values of @xmath35 . ] near threshold vs scaled time @xmath31 for @xmath36 , @xmath33 , @xmath37 and for different values of @xmath35 . ] in fig . 2 , we plot the intensity as a function of scaled time @xmath31 for different values of the scaled pump field amplitude @xmath35 . in this figure we have assumed that the cavity in initially prepared in such a way that it contains one exciton(@xmath37 ) but no photon . for simplicity we have taken the cavity and exciton decay rate to be the same , i.e. , @xmath38 . this figure shows the effect of the parametric oscillator on the intensity fluorescent light . it is not hard to see that the intensity oscillates with frequency equal to the coupling constant @xmath0 , which is a signature of exchange of energy between the cavity and exciton modes . moreover , the amplitude of the oscillations depends on the amplitude of the pump field , @xmath39 , which represents the optical parametric oscillator in our system . the stronger the pump field and the higher the amplitude of oscillation and the longer it takes to reach the steady state value of the intensity . it worth emphasizing that since optical parametric oscillator is operating below threshold , the parameter @xmath39 is constrained by the inequality @xmath40 . we thus interpret @xmath41 as threshold condition for the parametric process . in the vicinity of the threshold the mean exciton number increases rapidly and exceeds unity as illustrated in fig . this shows that even though there is one exciton in the cavity initially , there is a finite probability for the squeezed light in the cavity to excite two or more excitons in the quantum well . this has an interesting effect on the photon statistics of the fluorescent light as discussed in section c. we next proceed to calculate the power spectrum of the fluorescent light . the power spectrum of the fluorescent light can be expressed in terms of the bosonic operator as @xmath42 in the strong coupling regime the correlation function that appears in the integrand of the power spectrum in the steady state has the form @xmath43 e^{-(\kappa+\gamma)\tau/4}.\end{aligned}\ ] ] substituting this result in eq . and keeping the leading order in @xmath0 , we obtain the power spectrum of the fluorescent light to be @xmath44,\end{aligned}\ ] ] where @xmath45 are the half widths of the lorentzians centered at @xmath46 . we immediately see that the width of the power spectrum depends on the amplitude of the pump field . ] vs scaled frequency @xmath47 for @xmath36 , @xmath33 , @xmath34 , and for different values of @xmath35 . ] we observe that the maximum of the power spectrum occurs when the frequency equal to the coupling constant ( @xmath0 ) . in order of explore the effect of the squeezed light on the width of the spectrum it is convenient to plot the the power spectrum normalized by its maximum value , i.e. , @xmath48 . in fig . [ fig4 ] , we plot the normalized spectrum as a function of @xmath49 for different values of the pump amplitude ( @xmath39 ) . as clearly indicated in the figure , the the higher the amplitude of the pump field ( the degree of squeezing ) , the narrower the width has become . it is also worth noting that the narrowing of the width is more pronounced close to the threshold , i.e. , when the squeezing approaches to its maximum value . this is in contrary to the result obtained when the quantum well is coupled to a squeezed vacuum reservoir , where the spectrum is independent of the squeeze parameter @xcite . we further note that the spectrum has two peaks symmetrically located at @xmath50 . this is the result of the strong coupling approximation ( @xmath51 ) . both peaks have the same width which depends on the exciton and cavity modes decay rates and the amplitude of the pump field . [ g2 ] we now turn our attention to the calculation of autocorrelation function , which is proportional to the probability of detecting one photon at @xmath52 given that another photon was detected at earlier time t. quantum mechanically autocorrelation is defined by @xmath53 using the gaussian properties of the noise forces @xcite , the autocorrelation function in the steady state can be put in a simpler form @xmath54 in order to find a closed form analytical expression for the autocorrelation function , one has to determine the two time correlation functions that appear in eq . . this can be done using the solution along with the correlation properties of the noise forces . after" +"the monte carlo method is a fundamental computational tool in science . its goal is to sample configurations @xmath0 in a given state space from a probability distribution @xmath1 . this can usually not be achieved directly for multi - dimensional distributions . markov - chain monte carlo methods @xcite overcome this problem by generating configurations @xmath2 starting from an initial configuration @xmath3 which belongs to a simpler distribution @xmath4 ( often a fixed initial condition , or some ad - hoc random choice ) . configurations @xmath5 are then generated from @xmath6 according to a stochastic algorithm which guarantees , as time moves on , that @xmath7 departs from the initial condition and converges for @xmath8 towards the equilibrium distribution @xmath9 . the markov - chain approach can be implemented for arbitrary distributions @xmath10 , using for example the metropolis and the heat - bath algorithms . for many applications , enormous effort has gone into designing fast algorithms for which one reaches @xmath11 for reasonable running times @xmath12 . in this paper , we are concerned with a related problem : rather than to find the fastest algorithm for a given problem , we are interested in quantifying the speed of a given markov - chain algorithm . this is , we want to prove after which time @xmath12 the sample @xmath5 is equilibrated . it then reflects the equilibrium distribution and no longer the initial configurations . in many practical applications , it is extremely difficult to decide from within the simulation whether it has indeed equilibrated @xcite . instead , one must validate the simulation results with other approaches , from exact solutions to experimental data . the correct characterization of the convergence towards equilibrium from within the simulation has remained a serious conceptual and practical problem of the monte carlo method . from a fundamental viewpoint , the problem of rigorously proving convergence of a simulation was solved , at least in principle , through a paradigm called `` exact sampling '' , which allows to generate , with markov chains , samples @xmath0 directly from the equilibrium distribution @xmath10 without any influence of the initial configuration@xcite . in practice , however , it has not been possible to implement exact sampling for many complicated problems , as for example disordered systems , for which standard methods of evaluating equilibration times fail . the reason for this difficulty is as follows : exact sampling proves for a given markov - chain simulation that the correlation of the initial configuration with the configuration at time @xmath12 strictly vanishes . this is done by showing explicitly that all possible initial configurations @xmath13 yield the same output under coupled monte carlo dynamics . in many simple models , one can prove this coupling property indirectly . in general , however , one must indeed survey the entire configuration space . this is usually too complicated to be achieved . we recently developed a local - patch algorithm@xcite which indeed monitors the entire configuration space of complicated systems , even for very large sizes . the approach uses local information , concentrated on so - called `` patches '' . the scale of these patches increases during the simulation . information on patches can then be combined for the entire system to provide a crucial upper bound for the ( global ) coupling time , and to generate an exact sample . the algorithm was demonstrated to work for spin glasses at lower temperatures than previous methods @xcite , even though the physically interesting regime has still not been reached yet . the local - patch algorithm is quite general : in addition to spin glasses , we implement it in this paper for hard disks and improve on previous results @xcite . the successful application of exact sampling to hard - sphere systems is remarquable because the configuration space is continuous so that , naively , its complete survey appears out of reach . a markov chain is fully characterized by the so - called `` transfer matrix '' of transition probabilities between any two configurations @xmath14 and @xmath15 . as will be illustrated shortly ( section [ s : coupling_one_d ] ) in a specific example , the largest eigenvalue of the transfer matrix is @xmath16 and the corresponding eigenvector @xmath17 describes the equilibrium state . the convergence towards equilibrium is governed by the spectrum of the transfer matrix and by the overlap of the eigenvectors @xmath18 with the initial configuration : @xmath19 in the limit of infinite simulation time , the second - largest eigenvalue determines the exponential convergence of the probability distribution towards equilibrium . this eigenvalue sets a time scale @xmath20 and the convergence is as @xmath21 the rigorous determination of convergence properties of markov chains has been undertaken in many cases , from urn models to card - shuffling ( see @xcite ) , diffusion processes , and many more ( see @xcite ) . efficient algorithms , as for example the bunching method @xcite are commonly used to perform an empirical error analysis of monte carlo data in more complicated cases , where rigorous calculations are out of the question . however , these methods are not failsafe . in practice , it is often difficult to extract @xmath22 from the large number of physically relevant time scales . in disordered systems , for example , there is often no reliable way to ascertain that the simulation has run long enough , and @xmath22 may be much larger than assumed ( see e.g. @xcite , sect . 1.5 ) . in the limit of infinite times @xmath23 , the markov chain converges towards the equilibrium distribution , and the positions @xmath5 become independent of the initial condition . the loss of correlation with the initial condition is evident for markov chains that couple , that is , which for each possible initial condition @xmath3 produce the same output @xmath5 . in many cases of interest this happens after a finite global `` coupling time '' @xmath24 , which depends on the realization of the markov chain . propp and wilson @xcite realized that this coupling property allows one to draw `` exact '' samples from the distribution @xmath10 . this approach , called `` coupling from the past '' , eliminates the problem of analyzing the convergence properties . however , to establish that a markov chain has coupled , the entire state space of the system must be supervised . this was believed infeasible except for special problems where the dynamics conserves a certain ( partial ) ordering relation on configurations . a partial order is conserved in heat - bath dynamics of the ferromagnetic ising model , whereas the frustration in the spin - glass model foils this simplification . [ s : coupling_one_d ] we first discuss convergence and coupling for a markov chain describing the hopping of a single particle on a simple @xmath25-site lattice with periodic boundary conditions ( see fig . [ f : one_d_single ] ) . in one time step , the particle hops with probability @xmath26 from one site to its two neighbors : @xmath27 in addition , we have @xmath28 . the equal hopping probabilities imply via the detailed balance condition @xmath29 that the stationary probability distribution @xmath30 of this problem is independent of @xmath14 . this system s monte carlo algorithm is encoded in the @xmath31 transfer matrix @xmath32 : @xmath33 the eigenvalues of @xmath32 are @xmath34 + 1 $ ] ( with multiplicities ) that is , for @xmath35 , @xmath36 . the largest eigenvalue , @xmath37 corresponds to the conservation of probabilities . by construction , it is associated with the equilibrium solution @xmath38 . the second - largest eigenvalue is @xmath39 . for @xmath35 we have @xmath40 . this eigenvalue controls the long - time corrections to the stationary solution , which vanish as @xmath41^{t } = { \exp { \left[}- t/{\tau_{\text{corr}}}{\right]}}$ ] , with @xmath42 we note that the time scale @xmath22 only describes the asymptotic behavior of the correlation . the calculation of the time @xmath12 at which the probability distribution @xmath7 itself is within a suitably chosen @xmath43 of a the equilibrium distribution @xmath10 is more involved ( see , for example , @xcite ) . [ s : coupling ] as illustrated in fig . [ f : one_d_diffusion ] , the monte carlo algorithm can be formulated in terms of random maps . in our example , this means that instead of prescribing one move per time step , as in fig . [ f : one_d_single ] , we now sample moves for all times @xmath12 and all sites @xmath14 , in such a way that the dynamics of a single particle again satisfies the detailed balance condition of eq . ( [ e : detailed_balance ] ) . the most natural implementation of this approach is illustrated in fig . [ f : one_d_diffusion ] : arrows are chosen independently for all times @xmath12 and all sites @xmath14 . at time @xmath44 , for example , the particle should move down from sites @xmath45 , @xmath46 , @xmath47 and @xmath48 and straight from site @xmath49 . we can now check the outcome of the monte carlo calculation . in the example of fig . [ f : one_d_diffusion ] , from time @xmath50 on , all initial configurations of the single particle yield the same output . this is remarkable because , evidently , at this time the initial conditions are completely forgotten . the coupling time @xmath51 is a random variable ( @xmath52 in fig . [ f : one_d_diffusion ] ) which depends on the realization of the full monte carlo simulation from time @xmath44 onwards ( until coupling has been reached ) . the independence of random maps on different time steps implies that the probability for not coupling vanishes at least exponentially fast in the limit @xmath8 . under the random - map dynamics , an initial state with @xmath25 particles eventually evolves into a state with one particle ( in later sections , spin - glass configurations will take the place of the single - particle positions ) . more generally , a state with @xmath14 configurations can evolve at each time step into a state with @xmath53 configurations . figure [ f : one_d_diffusion ] displays a sequence of random maps and illustrates the associated time - forward search of the coupling time . this extended monte carlo dynamics on @xmath14-configuration states can again be described by a transfer matrix : @xmath54 where the block @xmath55 ( of sizes @xmath56 ) concerns all the processes which lead from a state at time @xmath12 with @xmath14 configurations to a state with @xmath57 configurations at time @xmath58 . the upper left block of this matrix , @xmath59 , is the original matrix from eq . ( [ e : one_particle_mc ] ) . as an example , we find from eq . ( [ e : algo_probabilities ] ) the following elements of this transfer matrix : @xmath60 etc . the matrix @xmath61 describes a physical system with variable particle number ( from @xmath45 to @xmath25 ) and a space comprising @xmath62 states , the number of non - empty states in this new simulation ( for a problem of @xmath25 spins , the number of configurations is @xmath63 and the total number of @xmath14-configuration states ( states with @xmath14 configurations ) is @xmath64 ) . the `` forward '' transfer matrix @xmath65 allows us to compute the coupling probabilities as a function of time in fig . [ f : coup_proba ] . the matrix @xmath61 is block - triangular in the number of particles @xmath66 , with the @xmath67 block given by @xmath59 . therefore , all the eigenvalues of @xmath59 are also eigenvalues of @xmath61 . in particular , the largest eigenvalue of @xmath61" +"research on quantum statistical properties of light has been a subject of intense investigations and discussions . in view of the very wide - spread potential applications , the influence of material bodies on the quantum features of light must be thoroughly investigated . typical quantum effects that are closely related to the change of the quantum vacuum due to the presence of material bodies are the casimir effect @xcite ( for a review , see @xcite ) and the purcell effect @xcite ( see also @xcite ) . though there has been a large body of work on the problem of quantization of the electromagnetic field in dielectric media ( for a review , see @xcite ) , most work has been concentrated on nonabsorbing media . roughly speaking , there have been two routes to treat radiation in absorbing media . in the first , attention has been restricted to equilibrium field correlation functions that are calculated by employing the dissipation - fluctuation theorem @xcite . in the second , explicit field quantization has been performed ( for a review , see @xcite ) . a consistent quantization scheme for the electromagnetic field in bulk material has been given by huttner and barnett @xcite . using the mesoscopic hopfield model @xcite for a dielectric , they have diagonalized the bilinear hamiltonian of the system that consists of the electromagnetic field , a harmonic - oscillator polarization field , and an infinite set of harmonic - oscillator reservoir fields responsible for absorption . by starting directly with the phenomenological maxwell equations for the macroscopic electromagnetic field , the scheme can naturally be extended to arbitrary inhomogeneous media @xcite characterized by a space- and frequency - dependent complex permittivity that satisfies the kramers - kronig relations . the theory is based on a source - quantity representation of the electromagnetic field , where the field operators are expressed in terms of a continuous set of fundamental bose fields via the green tensor of the classical problem ( for details , see also @xcite ) . the green - tensor formalism is well suited to study the behavior of the quantized electromagnetic field in the presence of dispersing and absorbing bodies . in particular , it has successfully been applied to the study of input - output relations @xcite , the spontaneous emission @xcite , the resonant energy exchange @xcite , the resonant dipole - dipole interaction @xcite , and the casimir effect @xcite , and also various geometries ( including multilayer structures ) have been considered . it is worth noting that the theory not only takes into account material absorption in a consistent way but it also includes automatically evanescent - field contributions generated , e.g. , by radiating atoms that are very close to the bodies under consideration . for the particular case of a dispersing and absorbing dielectric structure in vacuum , without active light sources at any finite distance from the structure ( and without active light sources inside the structure ) , a ratherinvolved hybrid quantization scheme has been proposed @xcite and used to study the problem of three - dimensional input - output relations @xcite . in the scheme , the whole space is divided into two regions , namely a dielectric scattering region and a vacuum region that surrounds the scattering region . the quantization in the vacuum region is performed on the basis of a mode decomposition of the electromagnetic - field operators in a similar way as in vacuum quantum electrodynamics , whereas the contribution of the dielectric scattering region is taken into account by applying the green tensor formalism @xcite . the argument is @xcite that the green tensor formalism alone is not complete , because it does not explicitly treat the boundary of the medium with free space and thus does not describe explicitly the scattering and emission processes which are usually experimentally investigated . this is of course not the case as the above mentioned applications @xcite and the following study of the three - dimensional input - output relations at multilayer plates clearly show . moreover , when there are active light sources at _ finite distances _ from the scattering region , then the incoming field contains both propagating and evanescent components . the latter ones , which are typically observed for small distances , are not included in the hybrid quantization scheme @xcite and the input - output relations derived from it @xcite . however , they are automatically included in the green tensor formalism @xcite . in the following we consider the problem of the three - dimensional input - output relations for the electromagnetic - field operators at the boundaries of a dielectric planar multilayer structure in more detail , by applying the green tensor formalism and extending our previous one - dimensional analysis @xcite to three dimensions . to be quite general , we allow ( i ) for the presence of active light sources at arbitrary positions inside and/or outside the multilayer plate and thus ( ii ) for both propagating - field components and evanescent - field components . in particular , in cavity qed the active sources are typically inside the plate , and the outgoing fields are not only determined with the incoming fields and the noise fields ( unavoidably associated with material absorption ) but also with the fields generated by the sources inside the plate . on the contrary , in optical near - field microscopy the active ( probe ) sources are typically outside the plate , but near its surface . employing the well - known three - dimensional green tensor for a multilayer plate @xcite , we introduce amplitude operators for the input and output fields as well as for the fields inside the plate and derive input - output relations both in the two - dimensional fourier space and in the coordinate space . finally , the problem of introduction of bosonic input and output operators in the two - dimensional fourier space is considered in detail . the paper is organized as follows . in sec . [ sec : ba ] the quantization scheme is briefly summarized and the green tensor for a multilayer plate is introduced . in sec . [ sec : gr ] the generally valid input - output relations are derived , and the problem of formulating input - output relations for bosonic field operators is studied . a summary and some concluding remarks are given in sec . [ sec : co ] followed by an appendix , in which relevant commutation relations are derived . to study optical fields interacting with active sources in the presence of dispersing and absorbing ( linear ) dielectric bodies , we first note that on a length scale that is large compared with interatomic distances in the bodies , the effect of the bodies can be described within the frame of macroscopic maxwell equations in terms of a spatially varying permittivity which is a complex function of frequency . this concept , which is widely used in classical optics also applies in quantum optics . let us assume that the active light sources are neutral atoms and consider an arbitrarily inhomogeneous medium characterized by a permittivity @xmath1 where the real part @xmath2 and the imaginary part @xmath3 are necessarily related to each other through the kramers - kronig relations , due to the causality principle . the motion of the atoms and the medium - assisted electromagnetic field is then governed by the multipolar - coupling hamiltonian @xcite @xmath4 \!\!\bigg\}^2 \nonumber \\[1ex ] & & + \,\frac{1}{2\epsilon_0 } \sum_{a , a ' } \int { \mbox{\rm d}}^3{r } \ , \hat{\bf p}_{a}({\bf r})\cdot \hat{\bf p}_{a'}({\bf r } ) -\sum_a \int { \mbox{\rm d}}^3{r}\ , \hat{{\bf p}}_{a}({\bf r})\cdot \hat{\bf e}({\bf r } ) , \end{aligned}\ ] ] where @xmath5 numbers the atoms , and @xmath6 numbers the charged particles inside the @xmath5-th atom . further , @xmath7 and @xmath8 are respectively the operators of coordinates and canonical momenta of the particles , and @xmath9\ ] ] is the operator of the polarization of the @xmath5-th atom at position @xmath10 . the @xmath11 [ and @xmath12 are bosonic field operators that play the role of fundamental variables of the electromagnetic field and the medium , including a reservoir necessarily associated with material absorption . the commutation relations for the operators @xmath13 and @xmath14 are @xmath15 = \delta _ { \mu \mu'}\delta ( \omega - \omega ' ) \delta ^{(3)}({\bf r } - { \bf r } ' ) , \ ] ] @xmath16 = 0,\ ] ] where the greek letters label the cartesian coordinates @xmath17 . in eq . ( [ 2 ] ) , the operators @xmath18 and @xmath19 of the medium - assisted electromagnetic field are expressed in terms of the fundamental variables as follows : @xmath20 @xmath21 @xmath22 @xmath23 where the integration should be performed over all space , and @xmath24 is the classical green tensor , which can be found from the equation @xmath25 together with appropriate boundary conditions at infinity . equations ( [ 6 ] - [ 9 ] ) can be considered as generalization of the familiar mode decomposition that would apply if dispersion and absorption could be disregarded . instead of dealing with equations of motion for mode operators , equations of motion for the fields @xmath11 must be treated . it should be pointed out that since the real part @xmath2 and the imaginary part @xmath3 of the permittivity are related to each other through the kramers - kronig relations , @xmath3 can not vanish identically for really existing media . clearly , @xmath26 can be very small , so that @xmath27 in eq . ( [ 9 ] ) is very small in certain areas of space ( @xmath28 ) . however , this statement says nothing about the magnitude of the total integral over the coordinate @xmath28 , because of the following integral relation for the classical green tensor @xmath29 , \end{aligned}\ ] ] where we have adopted the convention of summation over repeated vector - component indices . in particular , this relation enables one to include also vacuum - like areas in the consideration . thus , all the calculations are to be performed by assuming a permittivity close to unity with a small but finite imaginary part in those areas , and at the end the permittivity may be set equal to unity . in practice , experimental realization of ( macroscopic ) vacuum areas is of course fictional . scheme of the multilayer dielectric plate . the hatched regions indicate the presence of active light sources . , width=326 ] as mentioned , the quantization scheme is valid for an arbitrary space dependence of the permittivity . here , we consider a multilayered planar structure ( fig . [ fig ] ) , whose permittivity is defined in a stepwise fashion ( the @xmath30-direction is chosen to be perpendicular to the layers ) : @xmath31 where @xmath32 0 , \ , & \mbox{otherwise } , \end{array } \right.\ ] ] and @xmath33 is the ( complex ) permittivity of the @xmath34-th layer . in the above , the index @xmath34 labels the region on the left of the plate , the region on the right of the plate , and the layers of the plate . for simplicity , we express the @xmath30-coordinate dependence in shifted coordinate systems , introduced in each layer separately , so that the range of the @xmath30-coordinate is taken to be for the region on the left of the plate , for the region on the right of the plate , and for the @xmath34-th layer of the plate with thickness @xmath35 . exploiting the translational symmetry in the lane , we may represent the green tensor as a two - dimensional fourier integral @xmath36 where , and is" +"neutrinos are produced in states of given flavors electron , muon or tau that are mixtures of mass eigenstates . as different masses propagate with different phases , the mixture at some distance from a neutrino source may be different from the initial one , resulting in a disappearance of the initial flavor and an appearance of other flavors in the neutrino beam . quantitatively , the phase of the state of mass @xmath0 and momentum @xmath1 at the time @xmath2 from the production is @xmath3 at the distance @xmath4 from the source and , therefore , the disappearance and appearance probabilities depend on the squared mass differences , @xmath5 , ratio @xmath6 , @xmath7 being the neutrino energy , and mixing angles , @xmath8 , describing how mass eigenstates mix to form states of definite flavor . this phenomenon , called the neutrino oscillations , has been well established in the past two decades and is now considered one of the major discoveries in particle physics , celebrated by two recent nobel prizes @xcite . the values of the oscillation parameters two squared mass differences and three mixing angles are being measured with an increasing precision , thanks to a global effort that produced a number of experiments currently taking data or planned in the near future . within the next two decades , the precision is expected to be sufficient to begin testing the unitarity of the mixing matrix @xcite , discover the neutrino - mass hierarchy @xcite and unambiguously determine the value of the dirac phase , @xmath9 , violating the charge - parity ( cp ) symmetry of neutrino mixing @xcite . these results are going to have profound consequences for possible extensions of the standard model , building models of the neutrino masses and our understanding of the matter - antimatter asymmetry in the universe . in this topical review , we discuss systematic uncertainties in ongoing and future long - baseline ( @xmath103001300 km ) neutrino - oscillation experiments using conventional beams @xcite . such neutrino beams are tertiary products , originating from the decay of mesons predominantly pions produced in interactions of the primary proton beam with a target . as the resulting neutrinos are not monoenergetic , to extract the oscillation parameters from the collected event distribution , their energies have to be reconstructed on an event - by - event basis from the measured kinematics of particles in the final state . depending on the beamline , the relevant neutrino energies extend from a few hundred mev to a few gev , at which the dominant interaction mechanisms change from quasielastic to resonant and nonresonant meson production @xcite . because the oscillation parameters are extracted from the energy dependence of event distributions , their accurate determination requires an accurate reconstruction of neutrino energy . while the reconstruction would involve smallest uncertainties for scattering off free protons and deuteron @xcite , owing to the low cross sections involved , it is necessary to employ nuclear targets as detector materials to ensure high statistics of collected events . as a consequence , however , description of nuclear effects turns out to be one of the largest sources of systematic uncertainties in the oscillation analysis of modern long - baseline experiments . additionally , when energy reconstruction requires the kinematics of produced hadrons to be measured , detector effects may play an important role and uncertainties of the detector response contribute to the systematic uncertainties of the extracted oscillation parameters @xcite . over the past decade , the extensive neutrino - scattering program has yielded a wealth of experimental cross sections for carbon or hydrocarbon , ch @xcite , and much fewer results for other targets , such as water@xcite , argon @xcite , iron @xcite and lead @xcite . it is important to note that there seem to remain puzzling tensions between different measurements such as @xcite or @xcite which have attracted a sizable attention of the theoretical community . a number of approaches developed to describe nuclear response to other probes has been extended to neutrino interactions , and the understanding of nuclear effects relevant to neutrino - oscillation experiments has clearly improved @xcite ; see also recent reviews @xcite . however , many problems still await a quantitative explanation . while for detector targets containing hydrogen the pion - production events on free protons can be separated out @xcite , current and future neutrino - oscillation experiments are going to collect data predominantly for interactions with the targets of atomic numbers @xmath11 ranging from 12 to 40 , for which accurate and complete nuclear models permitting fully trustable data analysis are not available yet . the main difficulty of developing theoretical models useful to oscillation experiments stems from the flux average over polychromatic beams @xcite . as any data bin may receive contributions from a range of neutrino energies and different interaction mechanisms , understanding the source of discrepancies between theoretical results and experimental data is a formidable task . for example , resonant pion production followed by pion absorption in medium leads to the same final state as single - nucleon knockout . at the kinematics of the long - baseline oscillation experiments , nuclear models must be able to describe relativistic products of interaction . additionally , experiments employing tracking detectors require predictions of exclusive cross sections for different hadronic final states . this topical review is organized as follows . after general remarks regarding systematic uncertainties of measurements of cp violation in , we present our procedure of the oscillation analysis in . in sections [ sec : nucleareffects ] and [ sec : detectoreffects ] we illustrate the importance of nuclear and detector effects for an accurate reconstruction of neutrino energy and an unbiased extraction of oscillation parameters , discussing selected results from our previous publications @xcite . finally in we summarize this review . in recent and ongoing oscillation experiments , it has been a common practice to use the spread between different theoretical descriptions of nuclear effects , implementations of the same model in monte carlo generators , detector response parametrizations etc . as an estimate of the associated systematic uncertainties . while this method seems very effective , a word of caution is in order . non - negligible correlations between the ingredients used to find the uncertainties such as common assumptions of nuclear models or fine - tuning of event generators to the same data may lead to sizable underestimates , making this procedure insufficient and unreliable . for the next 20 years , the long - baseline neutrino - oscillation program is most likely going to employ conventional beams @xcite . this technique of producing neutrino beams has been used for a few decades : an intense proton beam is impinged on a target typically made of beryllium or graphite in order to produce mesons , mainly pions . the target is embedded within a horn an electromagnet producing a toroidal magnetic field that focuses secondary particles of a selected charge and defocuses those of the opposite charge . the horn polarization determines whether the resulting beam will be made of neutrinos or antineutrinos . it is important to point out that the beams and their contaminations by wrong - sign mesons in the neutrino and antineutrino modes are not related in a meaningful way . therefore , while using the same beamline , target and horn , the neutrino or antineutrino runs of an experiment could be considered two separate experiments . an accurate determination of the neutrino flux its flavor composition and energy spectrum exclusively from the proton - beam parameters , meson - production data for thick targets and horn configuration is a challenging task . state - of - the - art methods of controlling systematic uncertainties of a neutrino beam have been developed for the minos @xcite and minerva @xcite experiments , largely thanks to using two horns of adjustable positions at the numi beamline @xcite . it is not clear whether such a feature difficult to realize for off - axis beams is going to be available for future oscillation experiments . therefore , the beam normalization uncertainty of about 5% achieved in the minos and minerva experiment , can be expected also in future oscillation experiments employing conventional beams . note , however , that recently proposed new concepts of neutrino beams , such as @xmath12storm @xcite , would allow the neutrino flux to be determined with an accuracy of the order of 1% . to extract the probability of oscillation between the neutrino flavors @xmath13 and @xmath14 , experiments collect event distributions @xmath15 with respect to a set of observables @xmath16 , such as the charged lepton s energy and cosine of its production angle , @xmath17 in the above equation , the normalization factor @xmath18 depends on the beam power , data collecting time , fiducial mass etc . the flux expected in the detector , @xmath19 , and the oscillation probability @xmath20 are both functions of the true neutrino energy @xmath7 . the differential cross section @xmath21 describes likelihood for a neutrino of the flavor @xmath14 and energy @xmath7 to produce an event of kinematics @xmath16 . the detection efficiency is denoted as @xmath22 . systematic uncertainties in neutrino - oscillation experiments can be effectively reduced by using an unoscillated event distribution measured in the near detector system to predict the distribution expected in the far detector . this method of exploiting the cancelation of correlated uncertainties giving the best results when the near and far detectors are functionally identical has been used with great success in the reactor experiments daya bay @xcite , reno @xcite and double chooz @xcite to measure the mixing angle @xmath23 with remarkably high precision . barring the differences in the backgrounds and in the geometric acceptances of the beam , the ratio of the energy - unfolded event distributions in a disappearance experiment , @xmath24 , has in this case the simple interpretation @xmath25 where the far - to - near flux ratio , @xmath26 , reduces to the ratio of the squared distances from the neutrino source , @xmath27 and the oscillation probability in the near detector is @xmath28 . unlike in the reactor experiments , in long - baseline studies , the relevant cross sections are currently known with an accuracy of 1020% and the procedure of energy unfolding in much more involved . additionally , in the near and far sites , different detectors are usually employed and the differences in backgrounds and beam acceptances are non - negligible . for a disappearance measurement , minos can serve as a benchmark of how well the near - to - far comparison does reduce systematic uncertainties @xcite . in @xmath29 appearance measurements , the situation is even more involved . the final and initial flavors of neutrino are different , which leads to a dependence of the near - to - far event distributions ratio on the cross sections ratio @xmath30 . as the beams are designed to minimize the @xmath31 contamination in order to reduce the background in the far detector , direct measurements of the @xmath31 cross sections suffer from the statistics lower typically by 23 orders of magnitude than in the @xmath32 case and from larger uncertainties coming from both the flux and detector response @xcite . for example , in the recent t2k analysis @xcite , the total systematic uncertainty is estimated to be 16.6% , with the flux and detector - response contributions of 12.9 and 8.4% , respectively . there are no obvious methods to reduce those uncertainties and measurements for electron antineutrinos are going to be even more challenging . however , it is important to note that all available data are consistent with lepton universality . to emphasize the importance of reduction of systematic uncertainties in appearance measurements , let us make a simple estimate of" +"the @xmath3 symmetry of the order parameter ( op ) in high temperature ( high-@xmath4 ) superconductors is nowadays well established by various phase - sensitive experiments , the most striking being the observation of a half flux quantum in a tricrystal geometry by tsui _ et al . _ also the zero - bias conductance peak ( zbcp ) found in different tunnel experiments @xcite on @xmath5$]-oriented boundaries of yba@xmath6cu@xmath7o@xmath8 gave a strong hint for @xmath0-wave symmetry as was first pointed out by hu @xcite . however , in more recent experiments , several puzzling questions arose . for example a splitting of the zbcp was observed @xcite and zbcp s were reported even for @xmath9$]-oriented junctions @xcite . disorder effects were examined as well in experiment where the disorder of the junctions was increased by ion irradiation @xcite . a decreasing height of the zbcp was observed whereas the width stayed constant . the most successful approach to treat such inhomogeneous problems is the theory of quasiclassical green s functions @xcite . the properties of surfaces or interfaces are included by effective boundary condition . for a specular surface the green s function has to be continuous on a classical trajectory ( see fig . [ spec ] ) . in this most simple model the pair - breaking effect of surfaces as well as the existence of a zbcp can be explained : if quasiparticles are scattered to branches with a different op ( @xmath10 ) the pairing is suppressed and bound states can occur due to andreev scattering . if a quasiparticle is scattered with a sign change of the op the zbcp exists , too . in this framework it was also shown @xcite that the splitting of the zbcp is in agreement with the existence of a subdominant order parameter ( @xmath11 ) in the vicinity of the surface . the generalization of the boundary conditions to a specular interface was carried out by zaitsev @xcite . in this situation the green s function on four trajectories must match at the interface , which leads to quite complicated non - linear boundary conditions . as surface roughness is present in experiments , models were developed to include disorder in the theory . one possibility , first suggested by ovchinnikov @xcite , is to use the boundary conditions for the specular situation and cover the surface with a thin dirty layer where equations for the dirty case must be applied . in numerical studies of boundary problems similar techniques were used @xcite . also a scattering matrix approach , which is related to the randomly rippled wall model @xcite , was applied to disordered surfaces @xcite ; the solution was given in a born - like approximation . except for models with unitary scatterers @xcite , all calculations show a broadening of the zbcp due to disorder . often the surface roughness is only present on scales much smaller than the coherence length . in this case , the boundary conditions for the quasiclassical green s function can be formulated in terms of the scattering matrix ( @xmath12-matrix ) , as it has been recently suggested in @xcite . a rough interface does not conserve the momentum parallel to the surface , and , therefore , it couples waves ( _ i.e. _ quasiclassical trajectories ) with different propagation direction . the microscopic structure of the interface enters the theory via the @xmath12-matrix . in the absence of detailed knowledge about the microscopic structure of the surface , the @xmath12-matrix has to be taken as a phenomenological input . due to the very short in - plane coherence length in high-@xmath4 superconductors ( @xmath13 ) structures on larger scales occur as well . then the translational invariance parallel to the surface is lost on this length scale and a full 2d treatment of the problem is necessary , in which the trajectories are considered individually ( see fig . [ coh - inc ] ) . for example , in cuprates facets with typical dimensions of @xmath14 are present at interfaces @xcite . this leads to the existence of a zbcp even for [ 100 ] tunnel junctions as was pointed out by fogelstrm _ et al . _ @xcite . in our study we use the scattering matrix approach presented in @xcite to describe surfaces with microscopic roughness . we will discuss two kinds of surfaces : first , we study a microscopically disordered surface , which is described by random matrices . in contrast to earlier calculations we are able to consider individual realizations of the disorder ; we examine averaged quantities as well as fluctuations . afterwards we focus on an @xmath12-matrix that describes a surface with tilted mirrors , where few trajectories are connected at the surface . in the following section we will briefly introduce the quasiclassical theory for superconductors . subsequently we will present the boundary conditions in the form most suitable for our purpose and discuss the general properties . in section [ ressurf ] we derive the s - matrices for different situations and present the related results . we conclude with a discussion of our results and compare them to other approaches . in our studies of boundary effects of unconventional superconductors we use the theory of quasiclassical green s functions introduced by eilenberger @xcite . this approximation of gorkov s theory is valid in the quasiclassical limit ( @xmath15 ) . several review articles have been written on this subject , e.g. by schmid @xcite or larkin and ovchinnikov @xcite . the quasiclassical propagator in nambu space @xmath16 is determined by the eilenberger equation @xmath17 + i\hbar({\bf v_{\rm f}}\cdot{\boldsymbol\nabla } ) \hat g(\omega,{\bf r},{\bf k}_{\rm f})=0\ ] ] where @xmath18 represent the pauli matrices and @xmath19 additionally a normalization condition is needed to obtain the physical solution of the equation @xmath20 the op must obey the self - consistency equation @xmath21 here @xmath22 indicates the average over the fermi surface . in thermal equilibrium the keldysh propagator @xmath23 is given by the the advanced and retarded propagator @xmath24 @xmath25 for simplicity we make some further assumptions concerning the microscopic properties : for the interaction we choose @xmath26\cos[2(\varphi'-\alpha)]$ ] @xcite which generates a @xmath0-wave op with orientation @xmath27 ( see fig . [ spec ] ) @xmath28.\ ] ] in addition we assume an isotropic two - dimensional model with a spherical fermi surface . + after the determination of the op all physical properties can be calculated from the quasiclassical green s function . for example , the angle - resolved local density of states ( dos ) reads @xmath29,\ ] ] where @xmath30 is the normal state dos . in many cases the knowledge of the angle - averaged dos is sufficient @xmath31 the dos at the surface can directly be measured via the differential conductance @xmath32 for normal - metal - insulator - superconductor tunnel - junctions . for @xmath33 it is given by @xcite @xmath34 where the transmission probability is chosen as @xmath35 and @xmath36 is the area of the contact . the current - density can be calculated from the keldysh green s function via @xmath37 \right\rangle_{{\bf k}_{\rm f}}.\ ] ] it has been shown that the decomposition introduced by maki and schopohl @xcite is suitable for the numerical integration of the eilenberger equation as well as for analytical considerations ( see [ sbcs ] ) @xmath38 considering the physical meaning , the functions @xmath39 and @xmath40 are closely related to the particle and hole amplitudes in the andreev equation as was discussed in detail in @xcite . with this construction the normalization condition is obeyed automatically . by putting in this decomposition in eq . ( [ eile ] ) it can be seen that the functions @xmath41 and @xmath42 are given by the equations @xmath43 these equations can be solved on classical trajectories labeled by the fermi wave vector @xmath44 . for each direction @xmath45 one has to integrate two ordinary differential equations in order to construct the full propagator . + the matsubara technique can be used as well to calculate the op @xmath46 and the current - density @xmath47 \right\rangle_{{\bf k}_{\rm f}}.\ ] ] the energy integrals turn to sums over discrete matsubara frequencies @xmath48 and the matsubara propagator @xmath49 is determined by the relation @xmath50 one crucial point for investigating the effects of boundaries is still missing . as the quasiclassical condition does not apply in the vicinity of surfaces and interfaces we have to treat the scattering of quasiparticles by effective boundary conditions . the properties of the boundary enter the calculations only at this point . in our work we use the general theory recently derived in @xcite . the starting point is the andreev - like equation for the particle- and hole - like amplitudes which factorize the eilenberger green s function in eq . [ gmat ] ( see @xcite for details ) . in this approach , it is possible to consider roughness that occurs on length scales much smaller than the coherence length . all information on the microscopic shape of the boundary is provided by the scattering amplitudes from the in - trajectories ( @xmath51 ) to the out - trajectories ( @xmath52 ) ; they are gathered in the scattering matrix @xmath53 . for simplicity we consider only a finite number @xmath54 of discrete in- and out - trajectories @xmath55 , @xmath56 with equidistant angles . following @xcite the boundary conditions are determined using the functions @xmath57,\\ \label{bc - startb } b_l(\alpha)&=\det[{\bf 1}-{\bf s}\hat a_l^\alpha{\bf s}^{\dagger}\hat b]\end{aligned}\ ] ] with the diagonal @xmath58-matrices @xmath59 the solutions of @xmath60 and @xmath61 provide the boundary conditions @xmath62 as the determinant is a linear function of each of the matrix elements the functions @xmath63 and @xmath64 are linear in @xmath65 and @xmath27 . we can solve the boundary condition by calculating @xmath63 and @xmath64 for two arbitrary values of @xmath65 and @xmath27 ; for @xmath66 and @xmath67 we obtain @xmath68 with the boundary condition the green s function can be calculated : at first the integration of eq . ( [ ria ] ) on the in- and of eq . ( [ rib ] ) on the out - trajectories is performed starting from the known bulk values @xcite @xmath69 towards the boundary ( @xmath70 : bulk op ) . then the boundary conditions must be applied to get the @xmath41 s on the out- and the @xmath42 s on the in - trajectories at the boundary and the succeeding integration on these trajectories provides the missing @xmath41 s and @xmath42 s . the properties of the boundaries enter only via the @xmath12-matrix . the value @xmath71 is the probability of scattering from @xmath72 to @xmath73 . we choose the numbering of the trajectories so that @xmath74 reproduces the specular case . due to current conservation @xmath53 must be unitary @xmath75 with a suitable choice of @xmath53 arbitrary physical situations can be treated by this technique . some examples are presented in chapter [ ressurf ] . we are also able to connect basic symmetries of the physical situation with transformation properties of the scattering matrix . the symmetry operations for the mirror and the time - reversal symmetry are illustrated in fig . [ symms ] . the mirror symmetry of the surface ( @xmath76 ) is given by the transformation @xmath77 the time - reversal symmetry operation is represented by @xmath78 since we are discussing different types of roughness which occur in experiments we have to find adequate scattering matrices for each situation . as the unitarity condition ( [ unitarity ] ) must be obeyed we represent @xmath53 by the relation @xmath79 in the subsequent sections [ ransurf ] and [ facsurf ] we present s - matrices for random surfaces as well as for surfaces with small tilted mirrors and physical properties such as the op" +"the rapid time variabilities and the compactness problem ( see , e.g. , a review by piran @xcite ) suggest that gamma - ray bursts ( grbs ) should arise from internal shocks within relativistic flows . in the standard model , a strong magnetic field is generated , and electrons are fermi - accelerated in shocked regions . the physical conditions in the shocked region imply @xcite that protons may be also fermi - accelerated to energies @xmath0 ev . high - energy protons in the grb photon field can create high - energy neutrinos via photopion production @xcite . future observations of neutrinos will be important to prove the standard model of grbs and the particle acceleration theory . the highest energy of neutrinos brings us information on physical conditions of grbs . recently , @xcite have shown that the kaon contribution becomes important for neutrino production from jets in supernovae . they considered mildly relativistic jets that are much more baryon - rich than a fireball of grbs where collisions among accelerated protons ( @xmath1 ) occur efficiently @xcite , making pions and kaons that decay into neutrinos . since high - energy charged mesons will cool down before they decay into neutrinos , the highest energy of neutrinos is determined by the equilibrium of the cooling timescale and the decay timescale of mesons . considering synchrotron cooling , the highest energy of mesons that decay into neutrinos is proportional to @xmath2 , where @xmath3 and @xmath4 are the mass and the lifetime of mesons at rest , respectively . so , @xcite pointed out that the heavier mass of kaons than pions leads to dominance of neutrinos from kaon decay in the highest energy region . we note that the contribution of kaons for neutrino production may also be important even in internal shocks of grbs . in this study , we calculate the spectrum of neutrinos from grbs , taking account of decaying modes of charged kaons into neutrinos . also , we consider the contribution of long - lived neutral kaons , @xmath5 , for neutrino production , which was not taken into account in the previous work . it is noted that @xmath5 does not cool at all before decay into neutrinos and has some decaying modes into charged pions and neutrinos . so , it is expected that the highest energy of neutrinos comes from the decay of long - lived neutral kaons . in this letter , using the monte carlo method , we show that the highest energy neutrinos mainly come from kaons even in internal shocks of grbs . in 2 , we explain our model and method . the numerical results are in 3 . 4 is devoted to discussion . our method of simulation is essentially the same as in @xcite but quantitatively improved . in this study , we adopt experimental results for the cross sections of @xmath6 , @xmath7 , @xmath8 , and @xmath9 @xcite for @xmath10 gev , where @xmath11 is the photon energy in the proton rest frame . we neglect the reaction @xmath12 , because the cross section is too small and the neutrino production rate is independent of this reaction . since we do not have experimental data of multi - pion production for @xmath13 gev , we extrapolate the cross section by a constant value . however , our total photoabsorption cross section agrees well with the experimental value for @xmath14 gev @xcite . for the pion production by @xmath15 , we adopt the same cross sections as @xmath16 . kaons are produced via @xmath17 , @xmath18 , and @xmath19 , or @xmath20 , @xmath21 , and @xmath22 . since there are no detailed and precise data of kaon production experiments , we adopt values theoretically obtained for the cross sections of kaon production from @xmath16 and @xmath15 @xcite . as shown in figure 1 , the contribution of kaon production seems negligible . however , the importance of kaon production will be shown later . of course , @xmath1 collisions may also create mesons . since the number of target photons is much larger than the proton number density in our case , we neglect the effects of @xmath1 collisions . the inelasticity is approximated by a conventional method as @xmath23/2 $ ] , where @xmath24 is the invariance of the square of the total four - momentum of the @xmath16 ( @xmath15 ) system , and @xmath25 is the proton mass . for the double - pion production , we approximate the inelasticity by replacing @xmath3 with @xmath26 . our parameter set is similar to that in @xcite : the total photon energy in a burst @xmath27 , the number of light - curve pulses ( or spikes ) @xmath28 , the lorentz factor of the shells @xmath29 , and shell - collide distances from the central engine @xmath30 . the number @xmath28 corresponds to the number of shells that emit gamma rays . the photon energy deposited into each shell is therefore @xmath31 . in the standard model , shells can collide and emit gamma rays at distances @xmath30 larger than @xmath32 cm from the central sources , where @xmath33 is the time between shell ejection events . for simplification , @xmath30 and @xmath29 are common for all @xmath28 shells in this simulation . the photon number spectrum in the energy range @xmath34 in the shell rest frame is set at @xmath35 for 1 ev @xmath36 1 kev and @xmath37 for 1 kev @xmath38 mev . the break energy 1 kev corresponds to @xmath39 kev in the observer frame . for @xmath40 ev , the synchrotron self - absorption may be crucial @xcite , while the pair absorption may be crucial for @xmath41 mev ( e.g. , see asano & takahara 2003 , peer & waxman 2004 ) . although the upper bound of the photon energy depends on the model parameter because of pair production , we fix the value as 10 mev ( @xmath42gev in the observer frame ) . since higher energy protons mainly interact with lower energy photons , the production rate of very high energy neutrinos is not sensitive to this upper bound . the shell width in the comoving frame is assumed to be @xmath43 , as conventionally assumed , although there is the possibility of thinner shells @xcite . we express the energy density of the magnetic field as @xmath44 times the photon energy density . in this letter , we adopt @xmath45 . we inject protons with a number spectrum proportional to @xmath46 above 10 gev in the shell rest frame . the maximum proton energy is determined by the condition that the larmor radius is smaller than both the size scale of the emitting region and the energy - loss length . we estimate the energy - loss length using synchrotron , inverse compton , and photomeson cooling processes . the total energy of the accelerated protons in a shell is assumed to be the same as @xmath47 . our method pursues energy loss processes of each baryon via synchrotron , inverse compton , and photomeson cooling processes during the dynamical timescale @xmath48 in the shell rest frame . we have simulated for a wide range of parameters as @xmath49-@xmath50 ergs , @xmath51-@xmath52 , @xmath53-@xmath52 , and @xmath54-@xmath55 cm . of course , larger @xmath27 and smaller @xmath30 are favorable for neutrino production , and as @xcite showed , very luminous bursts are required to detect neutrinos on the earth . therefore , we show only one representative example in this letter . the parameter values are @xmath56 ergs , @xmath57 ( @xmath58 ergs ) , @xmath53 , and @xmath54 cm . the corresponding variability timescale @xmath59 ms , which is not so far from the typical observed timescale @xmath60 s. since the allowed region of the grb parameters is wide , there may be both optically thin and thick sources to thomson scattering @xcite . our example would imply that @xmath30 is close to the photosphere . when it is assumed that the energy density of protons is the same as the photon energy density and the average proton energy is mildly relativistic ( @xmath61 ) , the proton number density in the comoving frame is obtained as @xmath62 . this means that the optical depth for the thomson scattering is @xmath42 for our parameter set . photon scatterings do not sufficiently affect the gamma - ray spectrum for this marginal optical depth . from our simulation , we obtain spectra of created mesons as is shown in figure 2 . one - half of neutral kaons are @xmath5 , while the rest are @xmath63 . since the cross sections of kaon production are smaller than those of pion production , the number of kaons is much less than pions . however , the highest energy charged mesons will cool down before they decay into neutrinos . our results for other parameter sets agree with the condition of ultra high energy cosmic - ray production obtained by @xcite : @xmath64 cm . in the case of figure 2 , also protons above @xmath55 ev cool down before they escape from the shell . we follow the behavior of pions and kaons until they decay into positrons ( electrons ) and neutrinos using the same method as in @xcite . synchrotron and inverse compton emissions are taken into account . charged kaons have six decay modes ; @xmath65 ( 63% ) , @xmath66 ( 21% ) , @xmath67 ( 6% ) , @xmath68 ( 5% ) , @xmath69 ( 3% ) , and @xmath70 ( 2% ) , while @xmath5 will decay into @xmath71 ( 39% ) , @xmath72 ( 27% ) , @xmath73 ( 21% ) , and @xmath74 ( 13% ) . in figure 3 , total neutrino spectra emitted from this example are shown . although there are fewer kaons than pions , the highest energy neutrinos originate from kaons around @xmath75 ev . since very high flux is required to detect neutrinos from grbs by a @xmath76 neutrino detector such as icecube @xcite , we consider an optimistic case : a grb occurs at 30 mpc , and the detection efficiency of upward - going neutrinos with energy @xmath77 is assumed to be @xmath78 for @xmath79 ev , although it may be difficult to measure energies of neutrinos above @xmath80 ev by icecube . figure 4 shows the detectable number of spectra of neutrinos in this case . the vertical axis @xmath81 roughly corresponds to the detectable number in each energy range . in this case , the expectation value of neutrinos from kaons is 0.1 - 1 by a @xmath76 detector . however , for very high energy neutrinos , it may be possible to build detectors with effective volume orders of magnitude larger than @xmath76 , such as the extreme universe space observatory ( @xmath82 detector ) , because the earth is thick for such neutrinos . from the step - function - like features in the spectra , we can easily distinguish origins of neutrinos . as shown in figures 3 and 4 , @xmath5-decay neutrinos are dominant above @xmath83 ev , although the flux is too dim to detect on the earth . on the other hand , the contribution of @xmath5-decay in the energy band below @xmath83 ev is not so prominent . since we have considered many decaying modes , the production ratio of high - energy muon and electron neutrinos is not 2:1 exactly . however , the neutrinos will be almost equally distributed between flavors as a result of vacuum neutrino oscillations @xcite . so , there may be a possibility that tau neutrinos are detected through double - bang events @xcite . as we have shown in this letter , the highest energy neutrinos may originate from kaons in grb internal shocks . the detection" +"the resonant excitation by coherent optical radiation of an electronic transition in a semiconductor , e.g. a valence- to conduction - band excitation , creates a quantum - mechanical coherent superposition of the initial and final states of the transition , called optical polarization . the non - linear optical properties of this coherent superposition , together with its time evolution , can be used to provide a sensitive measurement of many fundamental parameters of the semiconductor material @xcite including elastic and inelastic scattering , energy level splittings between nearly degenerate states , energy relaxation , as well as associated information such as land g - factors and band - mixing . in general , non - linear laser spectroscopy is a very established and well understood means to probe these phenomena @xcite . however , the description of the non - linear optical response of a semiconductor crystal can be considerably more complex than for simple isolated and non - interacting atoms @xcite . this is particularly true for the case of the ultrafast optical spectroscopy used for the study of the sub - picosecond dynamics of photoexcited carriers in bulk systems as well as in semiconductor heterostructures @xcite . the life - time of the coherent quantum - mechanical superposition generated by an ultrafast laser excitation , called `` dephasing time '' , determines the typical time - scale on which coherent phenomena can be observed . such dephasing time reflects the role played by the various `` incoherent '' , i.e. phase - breaking , mechanisms in destroying the phase coherence induced by the laser photoexcitation . since semiconductors are characterized by very short electron - hole dephasing times , of the order of few hundreds of femtoseconds @xcite , coherent phenomena manifest themselves only through ultrafast optical experiments with sub - picosecond time resolutions @xcite . on this time - scale , the ultrafast evolution of photoexcited electron - hole pairs will reflect the strong coupling between coherent and incoherent dynamics , thus providing invaluable information on the non - equilibrium relaxation processes occurring in the semiconductor , e.g. carrier - carrier and carrier - phonon scattering . the aim of this paper is to review the basic aspects related to coherent phenomena in semiconductors . in particular , we will focus on the ultrafast coherent vs. incoherent carrier dynamics as well as on coulomb - correlation effects in photoexcited semiconductors . the paper is organized as follows . in the remainder of this section , after a brief historical account of coherent experiments in solids , we will try to gain more insight into the concept of coherence by introducing a simplified description of the light - matter interaction in terms of a two - level model . in section [ s.tb ] we will discuss the theoretical approach commonly used for a realistic description of both coherent and incoherent phenomena in various semiconductor structures , e.g. bulk systems , semiconductor superlattices , quantum wells and wires . section [ s.bulk ] deals with ultrafast carrier photoexcitation and relaxation in bulk semiconductors ; in particular , we will discuss the dominant role played by coherence on the carrier photogeneration process . in section [ s.sl ] we will review and discuss typical field - induced phenomena in superlattices , namely bloch oscillations and wannier - stark localization , as well as their dephasing dynamics . section [ s.qwr ] is devoted to the analysis of the coherent optical response of quasi - one - dimensional systems ; more specifically , we will discuss the strong modifications induced by coulomb correlation on the linear and non - linear optical spectra of realistic quantum - wire structures . finally , in section [ s.suco ] we will summarize and draw some conclusions . coherent phenomena in atomic and molecular systems have been investigated for a long time @xcite . the first spin echo experiment @xcite was performed in 1950 on protons in a water solution of fe@xmath0 ions . pulses in the radio frequency range were generated by means of a gated oscillator with pulse widths between 20 @xmath1s and a few milliseconds . with these pulses dephasing times of the order of 10 ms have been measured . in the 1960s echo experiments were brought into the visible range @xcite . a q - switched ruby laser produced pulses of approximately 10 ns duration which were used to observe photon echoes from ruby . in this case the dephasing times were of the order of 100 ns . as already pointed out , for the observation of any coherent dynamics the pulse width has to be shorter than the typical dephasing time . since in semiconductors electron - hole dephasing times are much shorter they are in the range of a few picoseconds down to some femtoseconds , coherent experiments in semiconductors had to wait until the development of suitable lasers able to generate sub - picosecond pulses . the physical phenomena governing the ultrafast carrier dynamics in photoexcited semiconductors can be divided into two classes : _ coherent phenomena _ , i.e. phenomena related to the quantum - mechanical phase coherence induced by the laser photoexcitation , and _ incoherent phenomena _ , i.e. phenomena induced by the various phase - breaking scattering mechanisms . the above classification in terms of coherent and incoherent phenomena is not purely academic ; it corresponds to rather different experimental techniques for the investigation of these two different regimes . from an historical point of view , the optical spectroscopy in semiconductors started with the analysis of relatively slow incoherent phenomena ( compared to the electron - hole dephasing time - scale ) . the investigation of nonequilibrium carriers started with the analysis of the incoherent energy - relaxation processes in the late 1960s using cw - lasers @xcite . in the 1970s pulse sources for the study of photoexcited carriers became available @xcite and this initiated time - resolved studies of the energy - relaxation process . many experiments based on different techniques have been performed @xcite : band - to - band luminescence @xcite which monitors the product of electron and hole distribution functions , band - to - acceptor luminescence @xcite which provides information on the electron distribution functions only , and pump - and - probe measurements @xcite where the measured differential transmission is proportional to the sum of electron and hole distribution functions . the theoretical analysis of these relaxation phenomena is commonly based on the semiclassical boltzmann theory . the boltzmann equations for both electron and hole distribution functions are commonly solved by means of semiclassical monte carlo simulations @xcite . in addition to the analysis of incoherent energy - relaxation processes , the ultrafast optical spectroscopy has allowed the investigation of coherent phenomena . as already pointed out , a coherent laser field creates , in addition to a non - equilibrium carrier distribution , a coherent polarization . the investigation of the coherent dynamics in semiconductors started in the 1980s . different aspects have been investigated @xcite : the optical stark effect @xcite , the dephasing of free carriers @xcite and excitons @xcite , quantum beats related to various types of level splittings @xcite , charge oscillations in double - quantum - well systems @xcite and superlattices @xcite , many - particle effects @xcite , and the emission of coherent thz radiation @xcite . these experiments can not be analyzed within the framework of the boltzmann equation . the reason is that this coherent polarization reflects a well - defined phase relation between electrons and holes , which is neglected within the semiclassical boltzmann theory . any proper description requires a quantum - mechanical treatment where , in addition to the distribution functions of electrons and holes , also the interband polarization is taken into account as an independent variable . several approaches have been used in the literature @xcite : bogoliubov transformations @xcite , nonequilibrium green s functions @xcite , band - edge equations based on the real - space density matrix @xcite , and the density matrix formalism in momentum space @xcite . during the last decade the time resolution has been further improved down to few tens of femtoseconds @xcite . on such extremely short time - scale coherent effects can no longer be neglected and are found to play a dominant role also for the case of typical incoherent measurements such as time - resolved and time - integrated luminescence . in such conditions , the carrier dynamics is the result of a strong interplay between coherent and incoherent phenomena . therefore , the traditional separation between coherent and incoherent approaches for the theoretical investigation of photoexcited semiconductors is no longer valid . what is needed is a comprehensive theoretical framework able to describe on the same kinetic level both classes of phenomena as well as their mutual coupling . to this purpose , a generalized monte carlo method for the analysis of both coherent and incoherent phenomena has been recently proposed @xcite . the spirit of the method is to combine the advantages of the conventional monte carlo approach @xcite in treating the incoherent , i.e. phase - breaking , dynamics with the strength of a quantum - kinetic approach in describing coherent phenomena @xcite . in particular , the coherent contributions are evaluated by means of a direct numerical integration while the incoherent ones are `` sampled '' by means of a conventional monte carlo simulation in the three - dimensional @xmath2-space . this theoretical approach has ben applied successfully to the analysis of various ultrafast optical experiments , e.g. four - wave - mixing studies of many - body effects in bulk gaas @xcite and luminescence studies of the hot - carrier photogeneration process @xcite . in order to clarify the concept of phase coherence , let us consider the simplest physical model for the description of light - matter interaction , i.e. an optically driven two - level system @xcite . within a two - level picture , a ground state @xmath3 with energy @xmath4 and an excited state @xmath5 with energy @xmath6 are mutually coupled by a driving force , e.g. an external field , and/or by their mutual interaction , e.g. coulomb correlation . the two - level - system hamiltonian @xmath7 is the sum of a free - level contribution @xmath8 and of a coupling term @xmath9 here , the usual second - quantization picture in terms of creation ( @xmath10 ) and destruction ( @xmath11 ) operators has been introduced @xcite . the two terms forming the coupling hamiltonian @xmath12 will induce transitions from state @xmath3 to @xmath5 and vice versa according to the coupling constant @xmath13 . as a starting point , let us consider a single - electron system . in the absence of interlevel coupling ( @xmath14 ) , we have two stationary states , @xmath15 ( @xmath16 being the vacuum state ) , corresponding to a single electron in level @xmath3 or @xmath5 , respectively . on the contrary , in the presence of interlevel coupling , the state of the system is , in general , a linear superposition of the non - interacting states in equation ( [ eq1.4 ] ) : @xmath17 whose coefficients obey the following equations of motion : @xmath18 again , we see that in the absence of interlevel coupling ( @xmath19 ) there is no time variation of the coefficients , i.e. if the system is prepared in state @xmath20 or @xmath21 it will remain in such eigenstate . on the contrary , the interlevel coupling induces a time variation of the coefficients . the above two - level model provides the simplest description of light - matter interaction in atomic and molecular systems @xcite as well as in solids @xcite . the coupling term in equation ( [ eq1.3 ] ) has the same structure of a" +"it is generally expected that in a full description of quantum gravity the geometry of space - time at small scales will not resemble that of a manifold . the nature of this `` quantum geometry '' is one of the fundamental issues in the search for a quantum theory of gravity . one argument for quantum geometry is that quantum field theories give our best descriptions of microscopic physics , yet they must be regularized in order to yield meaningful predictions . the trouble being that quantum field theory suffers from ultra - violet divergences due to physical processes occurring at arbitrarily large momenta , or equivalently , arbitrarily small distances . some fundamental regularization that fixes these divergences can probably be interpreted as a modification of geometry at extremely short distances , perhaps even such that the concept of arbitrarily small distances is meaningless . another argument extends heisenberg s classic _ gedankenexperiment _ in support of the uncertainty relations . the observation of structures at very small distances requires radiation of very short wavelength and correspondingly large energy . attempting to observe a sufficiently small structure would thus require such a high concentration of energy that a black hole would be formed and no observation could be made . if this is so , then distances below about the plank scale are unobservable and thus operationally meaningless . if short distances are meaningless , then perhaps precise locations are as well . this suggests the possibility of uncertainty relations between position and position , analogous to the standard ones between position and momentum ; this has been argued on physical grounds ( see @xcite , or @xcite for a review ) and from string theory ( see @xcite ) . an uncertainty relation between , say , @xmath4-position and @xmath5-position , would mean that the @xmath4 and @xmath5 coordinates do not commute . since coordinates are just functions on space(-time ) this suggests that the algebra of functions on space might not be commutative ( see @xcite ) . that is the fundamental idea of noncommutative geometry . in noncommutative geometry ( see @xcite ) , familiar geometric concepts ( metric , measure , bundle , etc . ) are reformulated in an entirely algebraic way . this allows the generalization of geometry by replacing the algebra of functions on space with a noncommutative algebra . it may be that such a noncommutative generalization of ordinary geometry can describe the true quantum geometry of space - time . as i will explain , noncommutativity is no guarantor of regularization ( see also @xcite ) . in this paper , i will discuss a specific class of noncommutative geometries which do have the requisite regularization property . these models are not physically realistic ; they generalize euclidean ( space ) rather than lorentzian ( space - time ) geometry ( a sin shared by lattice models ) and they are not gauge theories . however , it is plausible that more realistic models may share some of the characteristics of these ones . although regularization in these geometries is quite manifest , a toolkit for coaxing actual predictions from field theory there has been lacking . my aim here is to present an approximation technique for field theory calculations in this regularization . this will show the leading order effects of noncommutativity on quantum field theory . the existing theory of noncommutative geometry ( see @xcite ) is largely inspired by the so - called gelfand theorem . according to this theorem , there is an exact correspondence between commutative c@xmath6-algebras and locally compact topological spaces . for any locally compact topological space , the algebra of continuous functions vanishing at @xmath7 is a commutative c@xmath6-algebra , and any commutative c@xmath6-algebra can be realized in this way . this suggests that c@xmath6-algebras in general should be considered as noncommutative algebras of `` continuous functions '' , and thus that the category of c@xmath6-algebras is the category of noncommutative topologies . the next step is to go from noncommutative topology to noncommutative geometry ; the most versatile noncommutative version of a riemannian metric is given by a dirac operator . on an ordinary manifold , taking the commutator of the dirac operator , @xmath8 , with a differentiable function gives @xmath9_- = i\gamma^jf_j \mbox.\ ] ] taking the norm of this gives @xmath10_-\rvert } = { \lvert\nabla f\rvert}$ ] ; thus , the dirac operator can detect the maximum slope of a function . from this , a construction for the distance between two points can be obtained ( see @xcite ) . this shows that the dirac operator contains all information of the riemannian metric . it also knows which functions are differentiable , smooth , lipschitz , etc . a c@xmath6-algebra with a dirac operator thus constitutes a noncommutative riemannian geometry . using a couple of additional structures , it is possible to characterize noncommutative riemannian manifolds axiomatically ( see @xcite ) . unfortunately , it is only known how to do this for what amounts to metrics of _ positive definite _ signature . this does not allow for the noncommutative generalization of space - time . another problem with these noncommutative manifolds is that they _ do not _ tend to regularize quantum field theory . a variation of noncommutative geometry that does have this property is matrix geometry ( see @xcite ) . in matrix geometry , every structure has only finite degrees of freedom . unfortunately , there is no axiomatic characterization of matrix geometries , as for noncommutative manifolds . the problem of characterizing noncommutative space - time is daunting ( see @xcite ) . the trouble is that the analytic properties of the dirac operator which are essential in the positive - definite case are not there in space - time . with everything finite , all analytic considerations evaporate in the case of matrix geometry , suggesting that the problem of noncommutative space - time might be solvable once matrix geometry is better understood . most existing applications of noncommutative geometry to physics have concerned connes - lott models . in these ( with the question of space - time deferred ) a simple type of noncommutative manifold provides an interesting interpretation of the standard model of particle physics . in particular , the higgs field and gauge bosons are unified . here , i am pursuing a different way of applying noncommutative geometry to physics . i am following @xcite and exploring the regularization effects of matrix geometry . i will begin in sec . [ regularization ] by discussing what it takes to regularize quantum field theory and describing the geometric quantization construction that is the basis of my approach . in sec . [ regularized.action ] , i discuss how to construct the action functional in this regularization , in slightly greater generality than has previously been discussed explicitly . this is followed by a brief speculation on convergence when the regularization is removed . perturbation theory in this regularization has not been described in detail before ; i present this in sec . [ feynman ] . in sec . [ scales ] , i explain ( heuristically ) how the infra - red and ultra - violet cutoff scales are balanced around the noncommutativity scale . in particular , the ultra - violet cutoff only exists when there is an infra - red cutoff . in sec . [ flat ] , i describe the weyl quantization of flat space and the effect of this on quantum field theory , giving a geometric algorithm for the modification . this is a prelude to the main result of this paper . i present , in sec . [ deformation ] , an approximation technique for perturbative calculations in this regularization . i illustrate exact and approximate calculations with a few examples in sec . [ examples ] , and in sec . [ divergences ] , i discuss the effect on noncommutativity on degrees of divergence . a euclidean quantum field theory can be defined by a path integral over the space of classical field configurations . given an action functional @xmath11 $ ] , the vacuum expectation value of some functional , @xmath12 $ ] , of the quantum fields is defined by z0f [ ] 0:= _ f [ ] e^-s [ ] , [ pathint]where the partition function , @xmath13 , is a normalizing factor such that @xmath14 . the celebrated divergences which plague quantum field theory are primarily due to the fact that the space of classical field configurations , @xmath15 , is infinite - dimensional ; this leaves the functional integral measure @xmath16 formal and awkwardly ill - defined . in the usual treatment of quantum field theory , perturbative feynman rules are derived from the formal path integral . unfortunately , these feynman rules typically lead to infinite results . in order to get meaningful results from computations , the feynman rules are usually regularized _ ad hoc_. this is quite effective for perturbative calculations since the details are independent of the choice of regularization . however , reality is not a perturbation . physical phenomena such as quark confinement are not reflected in strictly perturbative theories . a complete description of reality will presumably involve a nonperturbative regularization . in a euclidean quantum field theory , a nonperturbative regularization is implemented at the level of the path - integral rather than perturbation theory . one approach to regularization is to replace the original space of field configurations with some finite - dimensional approximation ; this essentially guarantees a finite theory . if @xmath17 is a single scalar field on a compact manifold , @xmath18 , then the space of field configurations is the algebra of smooth functions , @xmath19 . where algebra goes , other structures will surely follow ; for this reason , and simplicity , i shall largely restrict attention to a scalar field . to regularize , we would like to approximate @xmath20 by a finite dimensional algebra . the standard approach is to use the algebra of functions on some finite set of points a lattice which approximates @xmath18 . unfortunately , a lattice is symmetry s mortal enemy . if the space @xmath18 possesses a nontrivial group of isometries , it would be desirable to preserve these as symmetries in the regularized theory ; but for instance , in a lattice approximation to @xmath1 , the best possible approximation to the @xmath21-symmetry is the 60-element icosahedral group . we can maintain much greater symmetry with noncommutative approximating algebras . geometric quantization provides a method of constructing noncommutative approximations . as the name suggests , geometric quantization was originally intended as a systematic mathematical procedure for constructing quantum mechanics from classical mechanics . geometric quantization applies to a symplectic manifold ( originally , phase space ) with some additional structure ( a `` polarization '' ) . the terminology of quantization is unfortunate here , since i am concerned with quantum field theory . insofar as geometric quantization goes here , the manifold is not to be interpreted as phase space , the hilbert spaces are not to be interpreted as spaces of quantum - mechanical states , and the algebras do not consist of observables . in this paper , `` quantization '' and `` quantum '' have nothing to do with each other . here i shall use geometric quantization with a `` complex polarization '' . for a compact khler manifold , @xmath18 , this generates a sequence of finite - dimensional matrix algebras @xmath22 which approximate the algebra @xmath20 in a sense that i shall explain below . a khler manifold is simultaneously a riemannian , symplectic , and complex manifold . these structures are compatible with each other , such that raising one index of the symplectic 2-form , @xmath23" +"in this note , we review the connection between ads / cft duality and quark - gluon plasma ( qgp ) experiments at rhic ( see ref . @xcite for a review of qgp physics ) . rhic stands for relativistic heavy ion collider at brookhaven national laboratory . heavy ion "" comes from the fact that it collides heavy ions such as gold nuclei @xmath1au instead of usual @xmath2 , @xmath3 or @xmath4 . the goal of the experiment is to realize the deconfinement transition and form the quark - gluon plasma . in principle , it should be possible to form qgp if one has high enough temperature or high enough density . however , it is not an easy job to confirm qgp formation because of the following problems : first , what one observes is not qgp itself but only the by - products after hadoronization , and one has to infer what had happened from the by - products . second , those secondary particles are mostly strongly - interacting , and the perturbative qcd is not very reliable for the current and near - future experimental temperatures . to resolve these problems , many attempts are made to identify the generic signatures of qgp . some of the generic signatures discussed to date are as follows : 1 . the elliptic flow which may be the consequence of very low viscosity of qgp 2 . the jet quenching 3 . @xmath5-suppression all of these signatures have been discussed in the ads / cft duality , so i review recent developments focusing on these phenomena . d - branes represent a @xmath6 gauge theory . ] since this review is aimed at non - experts , i first give a short course on string theory , in particular emphasizing on how gauge theories and black holes are described in string theory . figure [ fig : string ] shows main ingredients of string theory . there are two kinds of string : open strings with endpoints and closed strings with no endpoints . as i will show you shortly , an open string represents a gauge theory . a closed string represents a graviton . an open string propagates through spacetime just like a closed string , but an open string can also have its endpoints on an object , the so - called d - brane . the open string i consider in this lecture is always of this type . the easiest way to see that an open string represents a gauge theory is look at how the string oscillates . figure [ fig : level1 ] shows the simplest open string oscillation ( in 4 dimensions ) . as you can see , the string can oscillate in two directions . so , the open string has two degrees of freedom at this level . these degrees of freedom represent the two polarizations of the photon . in this sense , the open string represents a gauge theory . of course , our interest here is not qed , but rather qcd , so how can one describe a yang - mills theory ? an open string has endpoints on a d - brane , but if there are @xmath7 coincident d - branes , open strings can have endpoints in various ways ( fig . [ fig : sym ] ) . these new degrees of freedom precisely correspond to @xmath6 degrees of freedom . since these open strings are constrained to have their endpoints on the d - brane , the gauge theory described by the d - brane is localized on the d - brane . the d - branes arise with various dimensionalities . a d - brane with a @xmath8-dimensional spatial extension is called the d@xmath8-brane . namely , the d0-brane is point - like , the d1-brane is string - like , the d2-brane is membrane - like , and so on . thus , the d@xmath8-brane describes a @xmath9-dimensional yang - mills theory . we are interested in 4-dimensional gauge theories , so consider the d3-brane in order to mimic qcd . on the other hand , a closed string represents a graviton . again , the easiest way to see this is to look at how the string oscillates ( fig . [ fig : closed ] ) . in general , the oscillations on a string have two modes : the left - moving modes and right - moving modes . for an open string , these modes mix each other at endpoints , but these modes become independent for a closed string . so , one can oscillate the right - moving mode in one direction and the left - moving mode in the other direction . in a sense , a closed string oscillates in two directions simultaneously . this property explains the spin-2 nature of the graviton . in fact , a graviton also oscillates in two directions simultaneously . strictly speaking , a closed string represents a graviton and two undiscovered scalar particles , the dilaton and the axion . since each mode has two degrees of freedom , a closed string has 4 degrees of freedom at this level ( in 4 dimensions ) . the graviton has only 2 degrees of freedom , and two scalar fields cover the remaining degrees of freedom . we have seen that we can get a gauge theory from the d - brane , but it is not clear if the d - brane is simply described by a gauge theory . this is because string theory is more than a gauge theory , namely it has gravitons . at this point , it is not clear if the effect of gravity can be neglected . according to general relativity , any energy - momentum tensor curves spacetime . the d - brane of course has some energy , so how the d - branes curve spacetime ? since gravity is described by the newton potential _ newton ~ , one can measure the effect of curvature by @xmath10 . according to string theory , the newton constant @xmath11 and the mass @xmath12 of the d - brane are given by g & ~ & g_s^2 , + m & ~ & n / g_s , where @xmath13 is the string coupling constant which governs the strength of the interactions between strings . , which is consistent with the hypersurface picture of the d - brane , and the open strings attached represent the fluctuations of the d - brane . ] so , one gets @xmath14 . this means that as long as @xmath15 , one can neglect the effects of gravity and spacetime remains flat . in this case , the d - brane is simply described by a gauge theory . on the other hand , when @xmath16 , the d - brane starts to curve spacetime , and eventually it should become a black hole . so , in this case , the d - brane can be described by a black hole . the black hole here is not the usual schwarzschild - like black hole . we consider a d - brane , an object with infinite spatial extension . thus , the black hole formed from the d - brane has an horizon which extends indefinitely and is called the black brane . "" to summarize , one can describe the d - brane both by a gauge theory and by a black hole ; which description is better depends on the value of @xmath17 . the string coupling and the yang - mills coupling @xmath18 are related by @xmath19 ( see sec . [ sec : details ] ) , so @xmath17 is nothing but the standard t hooft coupling , @xmath20 . this suggests that the black hole is the large t hooft coupling limit of a gauge theory . since t hooft coupling is the effective coupling of a gauge theory , the black hole is the strong coupling limit of the gauge theory ( fig . [ fig : largen ] ) . thus , the strategy here is to use black holes in order to compute gauge theory observables in the strong coupling regime . our argument here is very rough , but more refined version of the argument is known as the ads / cft duality @xcite ( see ref . @xcite for a review ) . the precise correspondence is as follows : + & & _ 5 s^5 . [ eq : dual ] here , @xmath21 means that the theory has 4 supercharges which are the maximum number of supercharges for a 4-dimensional theory . also , @xmath22 stands for the five - dimensional anti - desitter space . desitter was a dutch astronomer who found a solution of einstein equation with a constant positive curvature in 1917 . the space @xmath22 instead has a constant negative curvature ; this explains the prefix anti . "" one can reach this correspondence by studying the d3-brane more carefully , but i will skip the argument . instead , i explain the correspondence from the symmetry point of view in appendix . we will use the finite temperature version of the duality and its cousins ; in this case , one needs to replace @xmath22 by a black hole in @xmath22 , which is known as the schwarzschild-@xmath22 black hole : + & & + & & _ 5 ) s^5 . according to the rhic experiment , qgp behaves like a liquid . the ads / cft then implies that a black hole also behaves like a liquid . then , plasma quantities should be calculable from black holes . in fact , black holes and hydrodynamic systems behave similarly . consider adding a perturbation to a black hole , _ e.g. _ , drop some object ( fig . [ fig : hydro ] ) . then , the shape of the black hole horizon becomes irregular , but such a perturbation decays quickly , and the black hole returns to the original symmetric shape . the no - hair theorem is one way to see this . according to the theorem , the stationary black hole is unique and symmetric . thus , the perturbed black hole can not be stable . if you regard this as a diffusion , the diffusion occurs since the perturbation is absorbed by the black hole . this behavior is very similar to a liquid . suppose that one drops a ball in a water pond . then , you generate surface waves , but they decay quickly , and the water pond returns to a state of stable equilibrium . in hydrodynamics , this is a consequence of viscosity . thus , one can consider the notion of viscosity for black holes as well . and the viscosity "" for black holes should be calculable by considering the above process . let me remind you of freshman physics of viscosity . as a simple example , consider a fluid between two plates and move the upper plate with velocity @xmath23 ( fig . [ fig : viscosity ] ) . as the fluid is dragged , the lower plate experiences a force . this force is the manifestation of the viscosity . in this case , the force @xmath24 the lower plate experiences per unit area is given by = . the proportionality constant @xmath25 is called the ( shear ) viscosity . microscopically , the viscosity arises due to the momentum transfer between molecules . figure [ fig : viscosity ] shows a close - up view of the fluid and i put an artificial boundary to divide the fluid into two parts . the molecules collide with each other and are exchanged randomly through the" +"colloidal gels are components of everyday products such as foodstuffs , fabric conditioners , cosmetics , shampoos , and even toothpaste , yet despite their practical importance they present many challenges to our understanding of disordered materials . a gel is a solid containing a network of particles which is formed when a colloidal dispersion with attractive interactions @xmath0 is quenched deep into a two - phase region of phase space @xcite . driven far out - of - equilibrium , the kinetics of phase separation are dramatically slowed down or , in the limit of strong short - range attractions ( @xmath1 with @xmath2 the range of the attractive interactions and @xmath3 the particle radius ) , totally arrested . partial phase separation generates a disordered network , whose initial structure is controlled by the strength of interaction @xmath0 , the range @xmath4 of the potential , as well as the volume fraction @xmath5 of colloids . the long - time structural integrity of this network is , in the majority of cases , constrained by the gravitational stress exerted by its own weight . given sufficient time , a gel settles under gravity , if it is not density - matched . we distinguish two limiting cases : in strong gels , where the attractive interactions are large in magnitude ( @xmath6 and narrow in range @xmath1 ) , compaction occurs smoothly at a rate which decreases progressively with time . the time dependence of the height of the gel in this case is well described by a poroelastic settling model @xcite ; by contrast , in weak gels where attractions are comparable to @xmath7 and wide in range @xmath8 so that thermal fluctuations are significant , an anomalous behaviour called _ delayed collapse _ is observed . a weak gel , instead of instantaneously settling , hesitates for a well defined delay period @xmath9 without any sign of macroscopic settling , before suddenly undergoing a rapid and catastrophic collapse . delayed collapse has been observed in a wide variety of systems @xcite so the response appears to be a universal feature of weak gels yet to - date no theoretical framework has emerged to account for this process . the existence of a measurable delay in the collapse of a weak colloidal gel looks , at first sight , rather surprising . in a crystalline solid yield usually happens spontaneously at a well defined stress and there is no latency before the material flows . similarly , if a constant gravitational stress is applied to a free - flowing colloidal suspension sedimentation occurs essentially instantaneously . the anomalous response evident in a weak gel has been interpreted as the signature of a non - equilibrium solid - to - fluid transition , triggered by erosion of the gel network by internal flows @xcite , progressive fracture by an applied gravitation stress @xcite , or as a consequence of thermal restructuring of the network @xcite . the origins of delayed collapse are both scientifically fascinating as well as being technologically relevant because colloidal gels are often used to stabilize complex product formulations against macroscopic phase separation . the network of particles supports the gravitational stress exerted by the formulation and suppresses unwanted sedimentation of the product . this trick , widely used by formulators , works only for @xmath10 ( where @xmath11 is the age of the gel ) as the gel instability at @xmath9 eventually restores equilibrium and phase separation starts again . in such cases , @xmath9 fixes the ultimate physical self - life of the product . a demand for robust long - life formulations has heightened the need for a better microscopic understanding of the process of delayed collapse so that gel instability may be predicted and controlled . much of the work to date on gel collapse has focused on macroscopic features , typically by measuring the time evolution of the height @xmath12 of a gel , rather than on the internal structure and dynamics of a gel . however in the last few years new techniques , such as confocal scanning microscopy @xcite and photon correlation imaging @xcite has revealed that colloidal gels have a complex hierarchical structure , with different structural features at different length scales . so while at the individual particle level , a gel consists of dense aggregated colloids , the aggregates are organized on the micro - scale into relatively thick strands of particles , which at the mesoscale are assembled into a percolating network able to transmit a stress . in a weak gel , the stress bearing network has a number of distinctive characteristics . first , it is mechanically heterogeneous with a complex structure consisting of weakly connected soft regions of low particle density coexisting with stiff dense strands of spheres . the strands of the gel may be several radii thick , depending on the strength and range of the attractive interactions . second , the network is dynamic and restructures with time , as inter - particle bonds break and reform via thermal fluctuations . a microscopic understanding of just how such a spatially and temporally disordered network evolves in time and how it transmits stress is still elusive yet just such an insight is essential for the prediction and control of delayed collapse . the goal of this paper is to summarize the key features of delayed collapse in weak depletion gels , to speculate on their origins , and to identify the key issues that still remain to be resolved . we briefly review the features of delayed collapse seen in the gravitational settling of weak gels . with a few recent exceptions , the majority of the previous work reported to date has focused on macroscopic features such as the time evolution of the height of a gel . we discuss the microscopic changes in the gel as it restructures by the breaking and reforming of inter - particle bonds . using this experimental insight , we propose a new model for delayed collapse which emphasises the connectivity of the stress - transmitting network . finally , we explore the role of an external applied force on the delay time of a gel and interpret the results in light of the new model . of a depletion gel ( @xmath13 , @xmath14 nm ) with @xmath15 , and different polymer concentration @xmath16 . ( b ) probability distribution @xmath17 for the delay time of a gel with @xmath18 , @xmath19 nm at @xmath20 , @xmath21 . the solid line shows a fit to a gaussian . ( c ) dependence of the mean delay time @xmath22 on the polymer concentrations for a gel with @xmath13 , @xmath23 nm , @xmath15 . the solid line depicts the estimated single bond lifetime @xmath24 . , scaledwidth=90.0% ] in this section , we recall the principle _ macroscopic _ features of delayed collapse in weak gels . we focus on the time - dependent evolution of the total height @xmath12 of a gel in a gravitational field , as a function of its age @xmath11 . typically a suspension is randomized by shaking or mixing at time @xmath25 and then left undisturbed during the sedimentation process . the height @xmath12 usually displays three regimes @xcite : an initial lag period of width @xmath9 where the height falls slowly but continuously with age , a non - linear regime of rapid collapse where the interface velocity @xmath26 speeds up with @xmath11 , and finally a region of compaction where the height relaxes asymptotically towards an equilibrium value . the three - stage nature of delayed collapse is exemplified by the data reproduced in fig . [ fig : mockup](a ) on the settling of depletion gels @xcite with @xmath15 for polymer concentrations @xmath27 $ ] . we use two sizes of low polydispersity surfactant - stabilized poly(dimethyl siloxane ) ( pdms ) emulsion droplets suspended in a refractive - index and near - density matched mixture of 1,2-ethane diol and water . the suspension of large droplets had a hydrodynamic radius of @xmath28 nm and a polydispersity of 0.17 while the small droplets had a radius of @xmath29 nm and a polydispersity of 0.18 . a depletion attraction was induced by the addition of either the anionic polyelectrolyte xanthan ( @xmath30 = 4.66 x 10@xmath31 g mol@xmath32 , radius of gyration @xmath33 nm ) or neutral hydroxyethylcellulose ( @xmath30 = 1.3 x 10@xmath31 g mol@xmath32 , radius of gyration @xmath34 nm ) depending on the range of attractions required . the majority of experiments were conducted using a combination of large emulsion droplets and xanthan to give a colloid - polymer mixture with an attractive range of @xmath35 @xcite . a small number of results were obtained using a colloid - polymer mixture with an attractive range of @xmath36 @xcite , obtained by combining small emulsion droplets with hydroxyethylcellulose . the magnitude of the attractions between droplets was adjusted by varying the concentration @xmath16 of added polymer , which is expressed in units of the overlap concentration @xmath37 . the relative buoyancy of the emulsion droplets is @xmath38 kg m@xmath39 , with @xmath40 and @xmath41 the densities of the droplet and solvent mixture respectively . this relatively small density difference explains the absence , evident in fig . [ fig : mockup](a ) , of any discernible settling during the lag phase . this is in contrast to many of the earlier studies where the initial stages of gel settling were often characterized by a relatively broad change in the height around @xmath42 as the gel was already settling slowly before the regime of rapid collapse started . this makes it more difficult to identify precisely the point where rapid collapse starts . in the pdms system it is straight - forward to determine the characteristic delay time @xmath9 , which is taken as the time at which the height @xmath12 of the gel first begins to noticeably drop from its initial value @xmath43 . in this paper we concentrate on the physical and chemical factors that determine the duration @xmath9 of this initial lag period . experiments reveal @xcite that the characteristic delay time @xmath9 has a number of distinctive characteristics : first , measurements of @xmath9 from samples of identical materials display a significant statistical variance @xcite ; and second , the average delay time @xmath22 is very sensitive to the magnitude of the attractive interactions _ i.e. _ doubling the polymer concentration in a depletion system may increase the delay time by 12 orders of magnitude @xcite . figures [ fig : mockup](b ) and ( c ) confirms the generality of these conclusions in the pdms system . to establish the extent of statistical variations in the delay time , we performed 116 repeat measurements of the delay time on a depletion gel @xcite with @xmath18 ( @xmath19 nm ) in a temperature controlled environment with @xmath44 . each of the runs was made on a freshly - prepared gel sample under identical conditions to ensure that individual runs were uncorrelated . the resulting values of @xmath9 were used to construct the probability distribution @xmath17 of delay times shown in fig . [ fig : mockup](b ) . an appreciable variation in the measured delay times is seen with a scatter of about 14 % . the distribution @xmath17 is symmetric and well fitted by a gaussian distribution ( solid line in fig . [ fig : mockup](b ) ) which suggests that delayed collapse is a consequence of a large number of independent uncorrelated stochastic events . a clue to the nature of the stochastic events responsible for delayed collapse is revealed by the strong correlation evident in fig . [ fig : mockup](c ) between the mean delay time @xmath22 and the lifetime @xmath24 of an individual colloid - colloid bond . to estimate the bond lifetime" +"inflation offers a simple solution to the shortcomings of the standard hot big bang model . in addition , its predictions about the initial density perturbations , leading to the observed structure formation , are in a remarkable agreement with measurements of the cosmic microwave background ( cmb ) temperature anisotropies . among the various inflationary models , one should select the ones which lead to a better agreement with data , with the additional requirement that such models should be naturally built within a fundamental theoretical framework . in spite of its enormous success , inflation remains still a paradigm in search of a model . despite the elegance of chaotic inflation @xcite , this simple model faces a fine tuning problem . consistency , between predictions for the amplitude of cmb temperature anisotropies and measurements , requires a tiny coupling constant . to avoid this problem , linde @xcite has proposed hybrid inflation , a model of inflation based on einstein gravity , but driven by a false vacuum . in this model , the inflaton field rolls while another scalar field remains trapped in a false vacuum state . the false vacuum becomes unstable when the magnitude of the inflaton field falls below some critical value , leading to a phase transition to the true vacuum . the energy density is dominated by the false vacuum energy density so that the phase transition signals the end of hybrid inflation . the phase transition at the end of inflation leads to topological defect formation @xcite . theoretically motivated inflationary models can be built in a context of supersymmetry ( susy ) and supergravity ( sugra ) theories . @xmath1 supersymmetric models contain complex scalar fields , which often have flat directions in their potential , thus offering natural candidates for inflationary models . in this framework , hybrid inflation ( driven by the f - terms or the d - terms ) are the most standard models . such inflationary models lead generically to cosmic string formation at the end of the inflationary era . cosmic strings in supersymmetric theories may have new properties , as compared to their non - supersymmetric counterparts ; we do not address this issue here . a gauge symmetry can be broken spontaneously in @xmath1 globally supersymmetric theories , either by adding f - terms to the superpotential or , in the abelian case , by introducing fayet - iliopoulos ( fi ) d - terms . the higgs mechanism leads generically @xcite to abrikosov - nielsen - olesen ( ano ) strings . depending whether they were formed at the end of f- or d - term inflation they are called f - term or d - term strings , respectively . f - term inflation is potentially plagued with the @xmath0-problem , while d - term inflation avoids it . this problem arises from the presence of large corrections ( of the order of the hubble parameter during inflation ) to the inflaton mass , which spoil the required flatness of the inflaton potential . d - term inflation can be successfully implemented in the framework of sugra , while in addition , it can be easily accommodated within string theory models . in the simplest models of d - term inflation within sugra , in which the constant fi term gets compensated by a single complex scalar field at the end of the inflationary era , the d - term strings formed at the end of inflation are topologically stable , since @xmath2 , with @xmath3 the vacuum manifold of the broken u(1 ) symmetry . our study concerns such models . however , they have been proposed @xcite models where d - term strings can become unstable . for example , one can introduce additional matter multiplets so as to obtain a non - trivial global symmetry such as su(2 ) , leading to a simply connected vacuum manifold and the production of semi - local strings . alternatively , it has been suggested @xcite that the waterfall higgs fields are non - trivially charged under some other gauge symmetries @xmath4 , such that the vacuum manifold , @xmath5/ u(1)$ ] , is simply connected , leading to the formation of semi - local strings . d - term inflation requires the existence of a non - zero constant fi term , which can be added to the lagrangian only in the presence of a u(1 ) gauge symmetry . this extra u(1 ) symmetry can be of a different origin . some models have been suggested for field - dependent fi terms , arising in the presence of a chiral superfield @xmath6 shifting under u(1 ) . the imaginary part of the scalar part of the chiral superfield plays the rle of an axion , and cancels the chiral anomaly by shifting under the u(1 ) symmetry . such a u(1 ) symmetry is called _ anomalous _ , or _ pseudo - anomalous _ since the total anomaly vanishes . here the fi term depends on the real part of the chiral superfield . in supersymmetry , models with anomalous fi terms have been developed @xcite within heterotic string theory . in a cosmological setup one has first to assume the stabilisation of the chiral superfield @xmath6 ; the rle of @xmath6 may be played by any modulus ( a dilaton or any volume modulus ) . only if this assumption holds the dilaton - dependent d - term can be considered as a constant fi term . however , the issue of dilaton and moduli stabilisation in the heterotic string theory is far from being resolved . it is still not clear how to derive constant fi terms from string or m - theory and only field - dependent d - terms have been identified . as we will discuss , in absence of constant fi terms , local supersymmetry requires the superpotential to be invariant under the u(1)-gauged symmetry . in the context of theories with large extra dimensions , brane inflation occurs in a similar way as hybrid inflation within supergravity , leading to cosmic string - like objects . in string theories , d - brane @xmath7-anti - brane annihilation leads generically to the production of lower dimensional d - branes , with d3- and d1-branes , which are d - strings , being predominant @xcite in iib string theories . to illustrate brane inflation let us consider @xcite a d@xmath8-@xmath9 system in iib string theory . six of the spatial dimensions are compactified on a torus , while the branes move relatively to each other in some directions . as the two branes approach , the open string modes between the branes develop a tachyon , thus an instability . brane inflation @xcite ends by a phase transition mediated by open string tachyons . since the tachyonic vacuum has a non - trivial @xmath10 homotopy group , one concludes that there must exist stable tachyonic string solutions with @xmath11 co - dimensions ; they are stable bps ( bogomolnyi - prasad - sommerfield ) d@xmath12-branes . since all dimensions are compact these daughter branes are seen as one - dimensional objects for a four - dimensional observer ; they are the d - strings . the d - strings ( d1-branes ) have been identified @xcite in the low - energy supergravity with the d - term strings . the justification for this conjecture is that only d - term strings remain bps states in @xmath13 supergravity . in supergravity , f - term strings break all the supersymmetries , whereas the d - term strings preserve half of it . an interesting and successful brane inflationary model is the d3/d7 one @xcite , which has also an effective description as a d - term inflationary model . the flat direction of the inflaton potential is associated with the shift symmetry , which protects the inflaton field from acquiring a large mass that would spoil the required flatness of the potential . in its original version this model leads to the formation of topologically stable ano bps strings . in a later developed version @xcite of the d3/d7 model , where in terms of an effective gauge theory the model has a local u(1 ) gauge symmetry and a global su(2 ) symmetry , semi - local strings are formed . such strings can unwind without any cost of potential energy . in what follows we concentrate on inflationary models leading to the formation of topologically stable strings . strings formed at the end of an inflationary era , contribute @xcite in the spectrum of temperature anisotropies ; their contribution is heavily constrained from cmb data . compatibility between cmb measurements and theoretical predictions constrain @xcite the parameters space ( mass scales and couplings ) of the inflationary models . these constraints have been obtained @xcite for d - term inflation within minimal sugra . here , we would like to investigate whether the constraints on the parameters space are a result of our choice of minimal supergravity , or whether they are a generic outcome of d - term hybrid inflation . we will therefore examine d - term inflation originated by different choices of the khler potential . the main motivation being that a minimal khler potential can be considered as a peculiar and unmotivated choice @xcite . we base our study in a formulation of supergravity constructed from superconformal theory , since the standard formulation may be insufficient in the presence of constant fayet - iliopoulos terms @xcite . to be able to constrain the parameters space of the models we should know the power spectrum of a cosmic strings network and the allowed upper limit on the cosmic string contribution to the measured temperature anisotropy spectrum . the upper limit imposed on the cosmic string contribution to the cmb data depends on the numerical simulation employed in order to calculate the cosmic string power spectrum . the upper limit found in the literature @xcite is @xmath14 or @xmath15 , depending on the simulation , with @xmath16 confidence level . there are some uncertainties in these results due to the cosmic string evolution codes they are based on was found using the results of ref . @xcite , based on the velocity - dependent one - scale model for the string evolution . this approach is certainly not the best . the upper limit of @xmath15 was found using the results of ref . @xcite ; however recently the authors have corrected @xcite a mistake in their code , which has not been taken into account in ref . note however that the corrected version of the code @xcite seems to give similar results . we believe that the recent publication given in ref . @xcite is the best , at present , approach . ] and therefore in our calculations we use an average value for the upper bound equal to @xmath17 . note that none of the existing simulations take into account a non trivial microstructure of the cosmic strings formed : however they have been shown to be superconducting in supersymmetric abelian symmetry breaking through f- or d - terms @xcite . we plan the rest of the paper as follows : in section ii we address hybrid d - term inflation , first within the standard formulation of supergravity , and subsequently within the effective supergravity theory built upon superconformal field theory . in the rest of the paper we focus on the second approach . we briefly review the effective supergravity formulation because of its consequences for d - term inflation , often not taken into consideration . in section iii we review d - term inflation in minimal supergravity . in section iv we discuss inflation in a supergravity theory with shift symmetry . in section v we consider d - term" +"in a previous paper @xcite in reactions of @xmath0c and @xmath1li projectiles on a @xmath0c target , it has been shown that the total reaction cross section , inclusive fragment cross sections and fragment momentum distributions are sensitive to the assumed proton and neutron radial density distributions of the projectile . these results stimulated us to further investigate effects of nuclear shape of neutron rich isotopes in the heavy ions reactions . a special attention in our investigations will be given to the neutron halo nuclei for the following reason . recent developments of radioactive nuclear beams enabled one to study a detailed structure of nuclei far from the stability line @xcite . the neutron halos have been observed in nuclei near the neutron drip line by reaction measurements with intermediate and high energy radioactive nuclear beams . these nuclei are of a special interest in relation to shell structures near the drip line and to new excitation modes associated with the excess neutron on the nuclear surface . in this paper we use the method of hyperspherical functions ( hsf ) @xcite to construct the densities of the light drip line nuclei . such nuclei typically have small binding energies and extended radial densities , and for them a suitable treatment of the tails of nuclear radial wave functions is essential . physically such wave functions should have exponential tails . a main advantage of the hsf is that it provides a realistic radial wave functions at large distances . in addition , the spurious center - of - mass motion is removed from the onset and the symmetries are properly taken into account . in @xcite , an attempt was made to provide a unified description of @xmath2li rather than just a single isotope . instead of trying to parameterize the effective interaction for each isotope , a simple parametrization for all the isotopes is used . furthermore , there is no inert core and all the nucleons are properly antisymmetrized . finally , because jacobian coordinates are used , no problems are encountered with the treatment of the center of mass . the binding energy of a nucleus serves as a natural scale in this approach and is related to all other observables . in order to account for the clusterization effect more precisely in our calculations , we expand the hsf in the translationally invariant many body harmonic oscillator ( ho ) functions @xcite and implement the nuclear structure straight in the densities . we use a few one - body oscillator parameters in order to better reproduce the experimentally observed mean - square radii ( rms ) and density distributions . these densities are then used in monte carlo simulations of nucleon - nucleon collisions , in which the total and inclusive cross sections and transverse momentum distributions of fragments are calculated . thoroughly tested , this approach gives a clear picture of nuclear shape . the paper is organized as follows . in section ii , the hsf method is described . next we elaborate on the details of the expansion with respect to the radial wave functions of a ( 3a-3)-dimensional harmonic oscillator . in section iii , we give a brief summary of the light isotopes and construct their young diagrams . knowing the underlying symmetries , we first build the `` normal '' @xmath0c density and compare it with other approximations . we calculate the elastic form - factor and run a @xmath0c + @xmath0c simulation to see how it works in a standard case . armed with the results , we proceed to the neutron rich @xmath1li and also @xmath1be , @xmath1c for comparison . in order to make the paper more coherent , we include all the densities in section iii and analyze the reactions in section iv . the results are in reasonable agreement with experiment and other theoretical approaches . our conclusions are summarized in section v. the hsf method involves a collective variable ( hyperradius @xmath3 ) which is related to the mean - square radius of the nucleus @xmath4 , i.e. , to the mean nuclear density . the excitations of this degree of freedom correspond to the monopole oscillation of the nucleus as a whole and thus the density can be treated as dynamic variable . the wave function @xmath5 of a nucleus with @xmath6 nucleons is translationally invariant and depends on the @xmath7 jacobi coordinates , defined as @xmath8 \\ & \vdots & \nonumber \\ x_{a-1 } & = & \sqrt{\frac{a-1}{a}}\bigg [ \frac1{a-1 } \sum_{i=1}^{a-1 } { \bf r}_i - { \bf r}_a \bigg ] \nonumber \end{aligned}\ ] ] here @xmath9 is the coordinate of the @xmath10th nucleon . each coordinate is a distance between the @xmath11-th nucleon and and the center of mass of the groups of nucleons @xmath12 . the hyperspherical coordinates ( hyperradius @xmath3 and @xmath13 hyperspherical angles ) are chosen as @xmath14 for @xmath15-dimensional space of the jacobi coordinates . for this set of coordinates , the volume element @xmath16 reads @xmath17 where the solid angle element @xmath18 is @xmath19 the laplacian is given by @xmath20 the hyperspherical functions , or @xmath21harmonics , are the eigenfunctions of the angular part of the laplacian @xmath22 the value of @xmath23 is the analog of the angular momentum at @xmath24 and is called the global momentum . the subscript @xmath25 denotes all the quantum numbers necessary to enumerate the various degenerate states of eq . ( [ ang ] ) . for @xmath25 it is expedient to use the young diagram @xmath26 $ ] and the yamanouchi symbol @xmath27 , characterizing the @xmath21harmonics properties relative to the @xmath28nucleon permutations , and @xmath29 to designate the orbital momentum , spin and isospin of this state . the wave function of a nucleus is then expressed in the form of an expansion in the @xmath21harmonic polynomials @xcite @xmath30 r lst \label{expan}\end{aligned}\ ] ] the hamiltonian reads @xmath31 here @xmath32 is the mass of a nucleon . the schroedinger equation for the radial function @xmath33 can be written as @xmath34 \right \ } \ , \chi_{k\gamma}(\rho ) = \frac { 2m}{\hbar^2 } \sum_{k^\prime\gamma^\prime \neq k\gamma } w^{k^\prime\gamma^\prime}_{k\gamma}(\rho ) \chi_{k^\prime\gamma^\prime}(\rho ) \label{schrod}\end{aligned}\ ] ] where @xmath35 , and @xmath36 are the matrix elements of the nucleon - nucleon interaction @xmath37 which may be expressed through the two - body fractional parentage coefficients in the form @xmath38 r lst m_l m_s m_t | \hat v | ak^\prime [ f ] r^\prime l^\prime s^\prime t^\prime m_{l^\prime } m_{s^\prime } m_{t^\prime } > \nonumber \\ & = & \frac{a(a-1)}{2 } \sum_{k_2 , \gamma_2 } < ak[f ] r lst | ( a-2 ) k_2 [ f ] r_2 l_2 s_2 t_2 \lambda(l^{\prime \prime } k^{\prime \prime } ) ; l_0 s_0 t_0 > \nonumber \\ & \times & < s_0 t_0 | w_{\sigma\tau}|s_0 t_0 > \ , r^{k k^\prime}_{k^{\prime \prime } l_0 } ( \rho ) \nonumber \\ & \times & < ( a-2 ) k_2 [ f ] r_2 l_2 s_2 t_2 \lambda(l^{\prime \prime } k^{\prime \prime } ) ; l_0 s_0 t_0 | ak^\prime [ f ] r^\prime l^\prime s^\prime t^\prime > \end{aligned}\ ] ] here @xmath39 @xmath40 is the spin - isospin part of the interaction matrix element . the collective potential @xmath36 is given by integrals containing two - body matrix elements together with the @xmath21harmonics fractional parentage coefficients . in the previous investigations @xcite it was shown that with the hsf one may use the same formulas for the fractional parentage coefficients which were obtained earlier with the translationally invariant shell model . in this case the talmi - moshinsky coefficients must be replaced by the raynal - revai coefficients , 6j - symbols must be added for the over - binding of the global momentum @xmath23 , and additional phase multipliers are inserted . their use has led to a significant improvement of the computations @xcite . the calculation is simplified if only the first few terms in the expansion ( [ expan ] ) , i.e. , @xmath41 and @xmath42 are taken into account . usually one adopts the @xmath43 approximation in which all values of k greater than @xmath44 ( @xmath45 ) are neglected . the success of this approximation lies in the fact that the centrifugal barrier reduces the contributions of configurations with @xmath23 greater than @xmath43 in the equations determining the hyperspherical wave functions . the system ( [ schrod ] ) has an analytical solution for the harmonic oscillator potential @xmath46 @xcite . the energy eigenvalues are given by @xmath47 with the eigenfunctions @xmath48 where we have introduced a dimensionless parameter @xmath49 with @xmath50 and the associated laguerre polynomials are defined as @xmath51 let us briefly examine critical regimes for the schroedinger equation ( [ schrod ] ) . as @xmath52 , it is reduced to @xmath53 with the trivial eigenfunction @xmath54 on the other hand , as @xmath55 , the eq . ( [ schrod ] ) reads @xmath56 and the eigenfunction has the following asymptotical behavior @xmath57 as was mentioned in the introduction . we will return to this important point in next the section . now we can express radial functions @xmath58 in terms of the @xmath59-dimensional harmonic oscillator , as shown on figure 1 for the @xmath60c nucleus , @xmath61 and the expansion coefficients are given by @xmath62 with the oscillator frequency @xmath63 determined so that the maximum of the lowest oscillator function @xmath64 coincides with the maximum of the lowest hyperspherical function @xmath65 . we will deal only with the ground state wave function and use @xmath66 for short . it is striking that the overlap integral of the ground state radial function @xmath67 with the lowest oscillator function @xmath64 is @xmath68 . at the same time , the contribution to @xmath67 of the two - quantum oscillator excitation is exceptionally small . a very small value of the coefficient @xmath69 is not fortuitous but conforms to the theorem @xcite , which states that if the oscillator frequency @xmath63 is chosen to make the overlap integral of @xmath64 and @xmath67 maximal , then the overlap integral of @xmath67 with @xmath70 is strictly zero . as we have already noted , in choosing @xmath63 we did not achieve a maximum value of the @xmath67 , @xmath64 overlap , but assured only a coincidence of the maxima of these functions . however , if such a condition is satisfied , the overlap integral of the functions is fairly near the maximum , and the coefficient @xmath69 is very small , although nonvanishing . this circumstance casts light on the origin of close agreement between the results of the translationally invariant shell model and the hsf method for the ground state . since the function @xmath70 can not be mixed with @xmath64 , the shell function in the hsf method is improved by admixture of states with oscillator energy @xmath71 and higher . because of the large difference between the energies of these states and the ground state , this admixture is small . then one can derive the binding energy as a function of the interaction matrix elements @xmath72 \nonumber \\ & + & \sum_{\mu } \frac { c_\mu}{c_\nu } \ , \int r_{\nu k } ( \rho ) w^{k \mu}_{k\nu } ( \rho ) r_{\mu k } ( \rho ) \rho^{3a-4 } d\rho \label{bind}\end{aligned}\ ] ] the rms of a nucleus is given by @xmath73 \label{rmso}\end{aligned}\ ] ] using the young - yamanouchi classification scheme @xcite , which stems from the orthogonal representation of a given permutation group , and with the knowledge of the total spin and isospin of the nucleus , we determine the symmetry with a corresponding young diagram @xmath26 $ ] of each isotope . in table i results of the classification of @xmath74li , @xmath75be , @xmath76b ( for completeness ) , and @xmath77c nuclei are collected . the lithium sequence , illustrated in figure 2 , reflects the" +"an open universe , with @xmath0 , seems to fit most astronomical observations . in connection with cdm , it gives the best fit to the observed clustering ( see e.g. ref . @xcite ) ; a similar value is requested for explaining the dynamics of bound objects on relatively small scales ( see e.g. ref . @xcite ) ; it also increases the age of the universe , alleviating the conflict with the age of the globular clusters . further , @xmath0 is in better agreement with direct geometrical estimates from number counts ( see e.g. ref . @xcite @xcite ) . however , as it is well known , inflation predicts @xmath1 . this contradiction is one of the most interesting problems in modern cosmology . it is certainly possible that the observations in favour of an open universe are too limited to be representative of the whole universe , and that higher values of @xmath2 will be found at larger scales . on the other hand , it is also possible to choose the initial conditions in inflation so as to give @xmath3 today , either by starting with an extremely small density parameter at the beginning of inflation , or by assuming that inflation lasted less than 60 @xmath4-foldings or so . both possibilities , however , introduce that fine - tuning of the initial conditions that inflation itself tried to overcome ; moreover , there would be also a conflict with the microwave background isotropy @xcite . two ways out of the enigma have been proposed so far . the first , the single- bubble scenario @xcite @xcite @xcite , assumes that a single giant bubble nucleated from a false vacuum ( fv ) state , when the universe was already flat because of previous inflationary expansion , and inflated for about 60 @xmath4-foldings afterward : our horizon is contained inside the bubble , and appears to be locally open . the weak point of this model is the old graceful exit problem : inflation never ends outside the bubble , and there is no reason why we should live inside that infinitesimal fraction of space which nucleated out of the false vacuum , unless one invokes anthropic arguments . other problems of the single - bubble model have been discussed in ref . @xcite . in the second proposal , the many - bubbles scenario @xcite , one has a two - field potential : while a field drives the inflationary slow - rolling , the second one performs a phase transition , generating bubble - like open universes , with all possible density parameters , from zero to unity , and all possible sizes . here the phase transition completes , all the universe eventually nucleates out of the fv state , but again there is no reason to expect nor a preferential value of @xmath2 , nor a bubble size big enough to contain our horizon . actually , it is difficult to avoid the conclusion that most of the volume is inside bubbles nucleated at the end of inflation , thus exponentially smaller than our observed universe . linde @xcite argues that eventually quantum cosmology will explain why we live in a open universe ( if we really do ) . the model we propose in this work implements a many - bubble scenario in which the nucleation rate varies in such a way to give a @xmath3 universe with maximal probability . in our model , the peak of the bubble nucleation can be chosen to occur early enough to have super - horizon - sized bubbles , approximating a @xmath3 universe by today , and narrow enough to consider our universe as typical . in other words , a flat , huge ( or infinite ) universe appears to be composed of locally open super - horizon - sized bubbles . it is remarkable that local observations , @xmath2 and the amplitude of perturbations , and the `` natural '' assumption that our universe is typical , put strong constraints on the theory parameters , i.e. the fundamental scales of the inflation and of the primordial phase transition . our model , outlined in the next section , has been already introduced in ref . @xcite to produce large scale power out of the remnants of the primordial phase transition . all what we have to do here is to determine the parameters so to tune the nucleation peak at super - horizon scales . to realize our scenario we need two pre - requisites . first , we need two channels , a false vacuum channel , to drive the inflation in the parent universe , and a true vacuum channel , to drive the shorter inflation inside the bubbles . second , we need a tunneling rate tunable in time , so as to produce a nucleation peak at the right time . it is remarkable that the same model that we introduced in ref . @xcite has just these features . this is certainly not the unique possibility , but we will show that it is a rather simple one . the model works in fourth order gravity @xcite , and exploits two fields : one , the scalaron @xmath5 ( i.e. the ricci scalar ) drives the slow - rolling inflation ; the second , @xmath6 , performs the first - order phase transition . the phase transition dynamics is governed both by the potential of @xmath7 and by its coupling to @xmath5 ; the dynamics of the slow - roll is `` built - in '' in the fourth order lagrangian . we already presented our model in detail in ref . @xcite ; here we sketch its main features . our starting point is the lagrangian density @xmath8 , where ( @xmath9 ) @xmath10 and @xmath11 the coupling of the scalaron with @xmath6 can be thought of as a field - dependent effective mass @xmath12 just like in brans - dicke gravity the coupling is a field - dependent planck mass . putting @xmath13 , one finds in the slow - rolling regime @xmath14 which is essentially the only dynamical equation we need . in the following , the instant labelled _ in _ will correspond to the beginning of the last @xmath15 @xmath4-foldings of inflation . the theory ( [ lagra ] ) can be conformally transformed @xcite into canonical gravity with the new metric @xmath16 once written in the conformal frame , our model becomes indistinguishable from a ordinary gravity theory with two fields governed by a specific potential . in the slow - rolling approximation useful relations link @xmath17 and the number @xmath18 of @xmath4-foldings to the end of inflation : @xmath19 correspondingly , @xmath20 . the value @xmath21 is fixed by the request that the largest observable scale , @xmath22 , was crossing out the horizon @xmath21 @xmath4-foldings before the end of inflation , and it is close to 60 for standard cosmological values @xcite . from ( [ lagra ] ) and ( [ conformal ] ) we obtain then einstein gravity with two scalar fields @xmath6 and @xmath23 , coupled by a potential given by @xmath24\,.\ ] ] the choice of a quartic for @xmath25 and a mass term for @xmath26 realizes the two conditions discussed above : @xmath27 this carves in fact in ( [ conpot ] ) two parallel channels of different height , separated by a peak at @xmath28 . the degeneracy of @xmath29 in @xmath30 and @xmath31 is indeed removed by @xmath32 ; the true vacuum ( tv ) channel remains at @xmath33 , while the false vacuum ( fv ) channel is slightly displaced from @xmath34 . in ref . @xcite we evaluated the tunneling rate @xmath35 for our model , defined as @xmath36 where @xmath37 is of the order of the energy of the false vacuum , and @xmath38 is the minimal euclidean action , i.e. the action for the so - called bounce solution of the euclidean equation of motion . the calculation of @xmath38 is simplified in the limit @xmath39 , i.e. for @xmath40 . in this case in fact @xmath41 and we can directly use coleman s formulas @xcite to evaluate @xmath38 , provided we are in the thin wall limit ( twl ) . if @xmath42 ( @xmath43 ) is the potential energy of the false vacuum ( true vacuum ) state , and @xmath44 is the energy at the top of the barrier , the twl is guaranteed if @xmath45 , i.e. if @xmath46 the result is ( ref . @xcite ) @xmath47 the eulidean action decreases as @xmath48 decreases ; the bubble nucleation is then more likely to occur during the last stages of inflation than at earlier times . finally , we can write the relevant parameter @xmath49 , i.e. the number of bubbles per horizon volume per hubble time ( quadrihorizon , for short ) , as @xmath50 where we have introduced a new parameter @xmath51 to mark the time at which there is on average one bubble per quadrihorizon , roughly corresponding to the end of the phase transition . it is useful to keep in mind that , as we will show later , @xmath52 . @xmath51 , or @xmath37 , in principle , can be derived in terms of the potential parameters @xcite ; the derivation is , however , very difficult : as customarily done in extended inflation ( see e.g. @xcite ) , we will determine @xmath51 by requesting that the transition eventually ends . to summarize , our model has four characteristic quantities : the slow - rolling inflationary rate , set by @xmath53 ; the difference in energy between vacua states , set by @xmath54 ; the barrier height , set by @xmath55 ; and finally the separation between the vacua states , set by @xmath34 . these constants completely define the slow - rolling and the phase transition dynamics . in the next section we proceed to the evaluation of the tunneling probability , and show that we can tune the parameters to give @xmath3 today with maximal probability . let the number of bubbles per horizon nucleated in the time interval @xmath56 be @xmath57 , where @xcite @xmath58 \ , , \label{ourspe}\ ] ] where @xmath59 is the nucleation rate , and where @xmath60 is the horizon volume at @xmath21 . the quantity @xmath61 is proportional to the tunneling rate per volume , @xmath35 , and to the fv volume left at the time @xmath62 ( the volume not already occupied by bubbles ) . if after a certain time the exponential term in ( [ ourspe ] ) decreases faster than @xmath63 increases , the fv volume fraction decreases ; if this decrease is faster than @xmath35 increases , then @xmath61 will have a turnaround somewhere , indicating that the transition is being completed . the rest of this paper is essentially devoted to find the condition for this maximum to occur at the right time . the @xmath4-folding time @xmath48 is defined as @xmath18 , where @xmath64 , so that we can put @xmath65 since in all what follows we have @xmath66 ( i.e. , the nucleation occurs around @xmath21 ) , we can write @xmath67\,,\ ] ] where @xmath68 we will neglect the mild dependence of @xmath69 on @xmath48 compared to the exponential dependence of @xmath35 . during inflation , @xmath70 , so that we can integrate easily the argument of the exponential in eq . ( [ ourspe ] ) , and obtain finally @xmath71 \,,\ ] ] where @xmath72 and @xmath73 and where @xmath74 expanding the argument of the exponential to the second order , we can approximate ( [ dndt ] ) as a gaussian curve . the second order term in ( [ qq ] ) should be included as well ; however , for the values" +"soft gamma - ray repeaters ( sgrs , for a recent review see @xcite ) are a small group ( 47 ) of peculiar high - energy sources generally interpreted as `` magnetars '' , i.e. strongly magnetised ( @xmath110@xmath2 g ) , slowly rotating ( @xmath3 5 - 8 s ) neutron stars powered by the decay of the magnetic field energy , rather than by rotation @xcite . they were discovered through the detection of recurrent short ( @xmath40.1 s ) bursts of high - energy radiation in the tens to @xmath4hundred kev energy range , with peak luminosity up to 10@xmath5 - 10@xmath6 erg s@xmath7 , above the eddington limit for neutron stars . the rate of burst emission in sgrs is highly variable . bursts are generally emitted during sporadic periods of activity , lasting days to months , followed by long `` quiescent '' time intervals ( up to years or decades ) during which no bursts are emitted . occasionally sgrs emit `` giant flares '' , that last up to a few hundred seconds and have peak luminosity up to 10@xmath8 - 10@xmath9 erg s@xmath7 . only three giant flares have been observed to date , each one from a different source ( see , e.g. , @xcite for 052666 , @xcite for 1900 + 14 , @xcite for 180620 ) . persistent ( i.e. non - bursting ) emission is also observed from sgrs in the soft x ray range ( @xmath1010 kev ) , with a typical luminosity of @xmath410@xmath11 erg s@xmath7 , and , in three cases , periodic pulsations with periods of 5 8 seconds have been detected . such pulsations proved the neutron star nature of sgrs and allowed the derivation of spin - down at rates of @xmath410@xmath12 s s@xmath7 , consistent with dipole radiation losses for magnetic fields of the order of b@xmath410@xmath13 - 10@xmath2 g. the x ray spectra are generally described with absorbed power laws , but in some cases strong evidence has been found for the presence of an additional blackbody - like component with a typical temperature of @xmath40.5 kev @xcite . over the last few years the satellite @xcite , launched in 2002 and operating in the 15 kev-10 mev energy range , has provided a wealth of new results concerning the two brightest sgrs , 180620 and 1900 + 14 . most aspects concerning the sgrs , short bursts , giant flares , and persistent emission , have been investigated , and new results have been found for each of them . we will review them here . [ [ sec : zerosei ] ] was discovered by the interplanetary network ( ipn ) in 1979 @xcite . it lies in a crowded region close to the galactic centre . @xcite discovered a quiescent x - ray pulsating ( @xmath14=7.48 s ) counterpart , which was spinning down rapidly ( @xmath15=2.8@xmath1610@xmath17 s s@xmath7 ) . if this spindown is interpreted as braking by a magnetic dipole field , its strength is @xmath110@xmath2 g. the source activity is variable , alternating between quiet periods and very active ones . after a period of quiescence , became active in the summer of 2003 @xcite . its activity then increased in 2004 ( see e.g. @xcite ) . a strong outburst during which about one hundred short bursts were emitted in a few minutes occurred on october 5 2004 @xcite . finally a giant flare , whose energy ( a few 10@xmath8 erg ) was two orders of magnitude larger than those of the previously recorded flares from sgr 0526 - 66 and sgr 1900 + 14 , was emitted on december 27@xmath18 2004 ( see e.g. @xcite ) . the results presented in this section are based on observations obtained with the ibis coded mask telescope @xcite , and in particular with its low - energy ( 15 kev-1 mev ) detector isgri @xcite . more than 400 short bursts have been detected with ibis / isgri . they have been identified either using the triggers provided by the burst alert system ( ibas , @xcite ) , or by computing light curves with 10 ms time resolution and looking for significant excesses corresponding to the direction of . [ [ spectral - evolution ] ] spectral evolution + + + + + + + + + + + + + + + + + + all the bursts detected by ibis are typical in terms of duration and spectra . the new result provided by the analysis of the sample is the spectral evolution within the bursts . by computing time resolved hardness ratios , @xcite showed that some bursts evolve significantly with time , especially the ones with a fast rise exponential decay ( fred ) profile . the hardness ratios have been computed using the background subtracted light curves in two energy bands ( 20 - 40 ( @xmath19 ) and 40 - 100 ( @xmath20 ) kev ) and were defined as @xmath21=(@xmath20@xmath19)/(@xmath20+@xmath19 ) . it turns out that the bursts peaks tend to be spectrally softer than the bursts tails . this behaviour had been reported earlier only for two peculiar bursts originating from . these two bursts were quite different from usual bursts , lasting about 1 s and having a very hard spectrum ( @xmath22 100 kev , @xcite ) . one example of this kind of evolution detected in regular bursts for is shown in fig . [ fig : evol ] . the spectral behaviour described above gives rise to a global hardness - intensity anti - correlation . in fact , by considering all the individual time bins of all the bursts this anti - correlation within the bursts has been discovered ( see fig . [ fig : hi ] ) . to investigate the statistical robustness of the correlation found , the spearman rank - order correlation coefficient of the 217 data points , @xmath23 , has been computed , which is 0.49 . this corresponds to a chance probability of 4@xmath1610@xmath24 ( 7.4 @xmath25 ) that the distribution is due to uncorrelated data . according to an f - test the data are significantly ( 8@xmath25 ) better described by a linear fit ( @xmath26 ) than by a constant . this correlation still lacks of a solid theoretical interpretation since the current magnetar scenario does not provide a clear prediction of the burst spectral evolution with time . [ [ number - intensity - distribution ] ] number - intensity distribution + + + + + + + + + + + + + + + + + + + + + + + + + + + + + we derived the fluences of 224 bursts using the vignetting and dead - time corrected light curves . we applied a conversion factor between counts and physical units derived by the spectral analysis of the brightest bursts and assuming that the averaged burst spectra do not change much between bright and faint bursts ; for details see @xcite . these fluences have been used to compute the number - intensity distribution ( log n - log s ) of the bursts . the experimental distribution deviates significantly from a single power - law ( fig . [ fig : logn ] ) . this is first of all due to the fact that the source has been observed at different off - axis angles . the faintest bursts are missed when the source is observed at large off - axis angles . in order to correct for this effect we have computed the effective exposure of the source , taking into account the variation of sensitivity at various off - axis angles . this yields the exposure - corrected cumulative distribution shown by the dashed line in fig . [ fig : logn ] . since the numbers at each flux level are not statistically independent , one can not use a simple @xmath27 minimisation approach to fit the cumulative number - intensity distribution . so we have used the unbinned detections and applied the maximum likelihood method @xcite , assuming a single power - law distribution for the number - flux relation ( @xmath28 ) . we have used only the part of the distribution where completeness was achieved ( i.e. @xmath293@xmath1610@xmath30 erg @xmath31 ) . in this case the expression to be maximised is @xmath32 where @xmath33 are the unbinned fluxes , @xmath34 is the ratio between the maximum and minimum values of the fluxes , and @xmath35 is the total number of bursts . this method yields @xmath36=0.91@xmath370.09 . if a single power - law model is an adequate representation of data , the distribution of the quantities @xmath38 should be uniform over the range ( 0,1 ) . in our case , a kolmogorov - smirnov ( k - s ) test shows that a power law is an appropriate model , yielding a probability of 98.8% that the data are well described by our model . we then divided the bursts into two samples comprising 51 and 173 bursts respectively . the division is based on the periods of different activity of the source : the 51 bursts were detected in 1 year and the 173 in 2.5 months . the two slopes derived with the maximum likelihood method are @xmath36=0.9@xmath370.2 for the low level activity period and @xmath36=0.88@xmath370.11 for the high level one . the two slopes are statistically consistent with each other and a k - s test shows that the probability that the two distributions are drawn from the same parent distribution is 93% . thus we conclude that the the relative fraction of bright and faint bursts is not influenced by the level of activity of the source . [ [ the - large - outburst - of - october-5 - 2004 ] ] the large outburst of october 5 2004 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + on october 5 2004 ibas triggered at 13:56:49 ut on a series of bursts originating from . detailed analysis of this event showed the presence of more than 100 bursts ; the activity ended at 14:08:03 ut . some bursts were so bright that they saturated the available telemetry share for ibis , generating some data gaps lasting up to 10 - 20 s. the initial part of the outburst is shown in fig . [ fig : biglc ] the fluence of the entire outburst as measured by isgri is 1.5@xmath1610@xmath39 erg @xmath31 , with a spectrum which is considerably harder than that of the usual short bursts : @xmath40=58@xmath372 kev , using a thermal bremsstrahlung model . this fluence value is however heavily affected by the saturation of the brightest bursts and represents only a lower limit to the real fluence . in order to recover the complete fluence of the event we used the data from the anticoincidence shield ( acs ) of the spectrometer spi @xcite . as can be seen in fig . [ fig : biglc ] ( upper panel ) , only the brightest bursts are visible in these data and hence they represent complementary information to the isgri data . we used the monte carlo package mggpod @xcite and a detailed mass modelling of spi and the whole satellite ( see @xcite and references therein ) to derive the effective area of the acs for the direction of . we computed the acs light curve with a binsize of 0.5 s and estimated the background by fitting a constant value to all the data of the same pointing excluding the bursts . we used the background subtracted light curve to compute the fluence of" +"the study of galaxy formation and evolution requires detailed information about statistically significant samples of dim objects . this , in turn , requires deep imaging and spectroscopy over wide areas of the sky . in pursuit of these data , several wide - deep surveys are now underway . those covering several square degrees or more either lack spectroscopic follow - up ( e.g. noao dwfs , @xcite , and odts , @xcite ) or are restricted to the study of objects at @xmath9 ( except for quasars ) by their imaging depth e.g. the sloan digital sky survey ( @xcite and @xcite ) , the virmos - vlt deep survey ( @xcite , @xcite ) and deep2 @xcite . other surveys target the high - redshift universe with deep hst imaging over fractions of a square degree i.e. the hubble deep fields @xcite , the hubble ultra deep field ( hudf ) , goods @xcite , and gems @xcite . spectroscopic coverage is feasible over these areas but is presently unable to probe deeper than @xmath10 , making the added imaging depth useful only for morphological studies and photometric redshifts . the multiwavelength survey by yale - chile ( musyc ) probes the intermediate regime of a square degree of sky to the spectroscopic limit of @xmath10 . section 2 describes the design of our survey . 3 reports our imaging observations for the extended hubble deep field south . 4 describes our imaging reduction , and 5 covers our photometric calibration and photometry . 6 gives our results for @xmath4-band number counts and the sky density and angular clustering of @xmath6-selected lyman break galaxies . 7 concludes . our analyses assume a standard @xmath11cdm cosmology with @xmath12=0.27,@xmath13 , and @xmath14=70km / s / mpc . the multiwavelength survey by yale - chile ( see http://www.astro.yale.edu/musyc ) is designed to provide a fair sample of the universe for the study of the formation and evolution of galaxies and their central black holes . the core of the survey is a deep imaging campaign in optical and near - infrared passbands of four carefully selected @xmath15 fields . musyc is unique for its combination of depth and total area , for additional coverage at x - ray , uv , mid- and far - infrared wavelengths and for providing the @xmath16 photometry needed for high - quality photometric redshifts over a square - degree of sky . the primary goal is to study the properties and interrelations of galaxies at a single epoch corresponding to redshift @xmath17 , using a range of selection techniques . we chose to use the @xmath0 filter set in the optical in order to obtain six nearly - independent flux measurements with the broadest possible wavelength coverage . lyman break galaxies at @xmath5 are selected through their dropout in @xmath18-band images combined with blue continuua in @xmath19 ( @xmath20 in the rest - frame ) typical of recent star formation @xcite . imaging depths of @xmath18,@xmath21,@xmath22,@xmath23 were chosen to detect the lbgs , whose luminosity function has a characteristic magnitude of @xmath24 in @xmath25 , and to find their lyman break decrement in the @xmath18 filter via colors @xmath26 . lyman @xmath27 emitters at @xmath5 are selected through additional deep narrow - band imaging using a 50 fwhm filter centered at 5000 . these objects can be detected in narrow - band imaging and spectroscopy by their emission lines , allowing us to probe to much dimmer continuum magnitudes than possible for lyman break galaxies . it has recently become clear that optical selection methods do not provide a full census of the galaxy population at @xmath28 , as they miss objects which are faint in the rest - frame ultraviolet @xcite . with this in mind , musyc has a comprehensive near - infrared imaging campaign . the nir imaging comprises two components : a wide survey covering the full square degree and a deep survey of the central @xmath29 of each field . this division between deep and wide was chosen because of the @xmath30 field - of - view of the ispi near - infrared camera on the ctio 4 m telescope . the @xmath31 point source sensitivities of the wide and deep components are @xmath32 and @xmath33 respectively . nir imaging over the full survey area provides a critical complement to optical imaging for breaking degeneracies in photometric redshifts and modeling star formation histories . deeper @xmath34 imaging over @xmath29 subfields opens up an additional window into the @xmath35 universe as the @xmath36 selection technique @xcite will be used to find evolved optically - red galaxies at @xmath37 through their rest - frame balmer/4000 break . extensive follow - up spectroscopy is being conducted over the square degree . a subset of the color - selected lyman break galaxy candidates will turn out to be agn based on broad- or narrow - line emission features seen in follow - up spectroscopy @xcite . damped lyman @xmath27 absorption systems @xcite at @xmath38 , which comprise the neutral gas reservoir needed to form most of the stars in the universe @xcite , will be searched for in the spectra of the brightest color - selected lbg / agn candidates ( typically quasars at @xmath28 ) . in addition to the optical and near - infrared , imaging campaigns at other wavelengths and follow - up spectroscopy are integral parts of musyc . x - ray selection will be used to study agn demographics over the full range of accessible redshifts , @xmath39 , ( see * ? ? ? * ) with spitzer imaging used to detect optically- and x - ray - obscured agn @xcite . this also allows a census of accreting black holes at @xmath5 in the same fields to study correlations between black hole accretion and galaxy properties at this epoch . future epochs of optical imaging will be used to conduct a proper motion survey to find white dwarfs and brown dwarfs in order to study galactic structure and the local initial mass function ( see * ? ? ? * ) ; the additional epochs will also enable a variability study of agn . the four survey fields ( see table [ tab : fields ] ) were chosen to have extremely low reddening , hi column density @xcite , and 100@xmath40 m dust emission @xcite in order to facilitate satellite coverage with spitzer , hst , chandra , and xmm , to take advantage of existing multiwavelength data and to enable flexible scheduling of observing time during the year . additionally , each field satisfies all of the following criteria : minimal bright foreground sources in the optical and radio , high galactic latitude ( @xmath41 ) to reduce stellar density , and accessibility from observatories located in chile . the survey fields will be a natural choice for future observations with alma . the remainder of this paper describes our optical images and catalog of e - hdfs . the techniques used for data reduction and photometry are the same as those used for the analysis of the other three fields . optical imaging from the full survey will be reported in e. gawiser et al . ( 2005 , in preparation ) . the near - infrared data will be discussed in r. quadri et al . ( 2005 , in preparation ) . the e - hdfs has deep public space - based observations at uv , optical , near - infrared , and far - infrared wavelengths . the hdfs itself covers a small @xmath42 central region with wfpc2 plus stis and nicmos regions , with deep ground - based jhk coverage of the wfpc2 region available from the fires survey @xcite . spitzer irac and mips coverage of the central @xmath43 is being performed in gto time . the extended area around hdfs has previously been imaged by @xcite and @xcite to a depth sufficient for the study of galaxies at @xmath44 . these images were made public and combined with deep h - band images by the las campanas infrared survey ( lcirs , @xcite ) to study red galaxies out to @xmath45 . our survey goes about one magnitude deeper in ubvri@xmath46 to probe the @xmath2 universe . our extended hubble deep field south ( e - hdfs ) field center ( see table [ tab : fields ] ) was chosen to keep a bright star ( m=6.8 ) which lies just north of the wfpc2 field off of the ctio+mosaic detectors . lcirs covered an h - shape centered on wfpc2 and thereby provides public @xmath47-band coverage of roughly half of our e - hdfs field . optical images of e - hdfs were taken on the nights of 2002 october 6,8,10,12 and 2003 may 26,27,28 using the 8192@xmath488192 pixel mosaic ii camera consisting of 8 2048@xmath484096 ccds , each with 2 amplifiers , on the blanco 4 m telescope at ctio . afternoon calibrations were obtained , including zero - second exposures to trace the readout bias pattern , and domeflats in each filter to be observed except for @xmath18 for which the counts from the dome lamps were insufficient . twilight flats were therefore obtained for the @xmath18 filter . dark exposures of comparable length to the imaging observations were obtained , but due to the negligible dark current they were not used for data reduction . a standard dither pattern was used to fill in gaps between the 8 ccds . the pixel scale is 0.267@xmath49/pixel , leading to coverage spanning @xmath50 of sky with each pointing . figure [ fig : filters ] shows the filter response curves and their multiplication with the ccd quantum efficiency and atmospheric transmission at one airmass . table [ tab : obs ] gives details of the exposure times in each filter for each run along with the approximate average seeing measured in the raw images during observations . the seven nights were mostly cloudless , but moderate clouds affected some of the @xmath22 imaging of e - hdfs on 2002 october 10,12 and some of the @xmath4 imaging on 2003 may 28 ; our reduction methods described below allow these images to be used without biasing the photometry . photometric standard fields from @xcite large enough to cover the full mosaic ii field of view were observed each night , and the nights of 2002 october 6 and 2003 may 26 proved photometric . @xmath0 images from ctio4m+mosaic ii were reduced using the mscred and mscdb packages in iraf v.2.12 following the noao deep wide field survey cookbook v.7.02 . we used custom software to work around a few difficulties in these packages , as described below . a composite zero image is subtracted from each raw image to remove the amplifier bias level and pattern . the resulting image is then `` flat - fielded '' by dividing by a composite domeflat , or a composite twilight flat in the case of @xmath18-band . superskyflat _ for each filter is made by combining all of the flat - fielded , unregistered images taken in each filter each night with rejection used to remove sources . our 2@xmath51 amplitude dither pattern was designed to eliminate the wings of bright sources from the _ superskyflat_. each flat - fielded image is then divided by the appropriate _ superskyflat _ , which offers an estimate of the pixel - by - pixel response to the spectrum of the night sky with sufficient counts to achieve 1% precision per pixel . because the _ superskyflat _ was produced using flat - fielded images , dividing by it serves to remove the original domeflat ( twilight flat ) from the reduction process . the real influence of the original flat - fielding is to remove the illumination pattern and gross pixel - to - pixel variations before looking for" +"the standard model ( sm ) works remarkably well , yet leaves many questions unanswered . among these open issues are the solution to the hierarchy problem , the smallness of the cosmological constant , the origin of the baryon - antibaryon asymmetry of the universe , the identity of dark matter ( dm ) , and the origin of fermion flavor and masses . in formulating models of physics beyond the sm , it is not unreasonable to consider that the addition of new physics may simultaneously address more than one of these questions . for example , supersymmetry famously solves the hierarchy problem@xcite and , as long as r - parity is conserved or nearly conserved , provides a plausible dm candidate@xcite . similarly , models of asymmetric dm@xcite have tried to link the observed value of the dm relic density to the baryon asymmetry . such strategies often lead to novel and interesting avenues of inquiry . here , we review some studies which have attempted to extend the idea of sm flavor to the dark sector . there are numerous recent examples@xcite of works investigating scenarios where dm is composed of multiple species , while many past studies have taken dm to be the lightest of a complicated dark sector . additionally , there are models@xcite wherein unflavored dm is stabilized or rendered long - lived by requiring dm interactions with the sm fields to obey flavor conservation . however , in this review , we will focus on scenarios in which dm and the sm fermions both transform under the same flavor group . historically , studies of dm have usually assumed it to consist of a single , weakly - interacting particle . given the multitude of long - lived species in the visible sector , however , the assumption of a single particle to explain the entirety of dm may be naive . at the same time , the existence of three generations of fermions has led to many models of high - scale flavor interactions . as we do not know how dm interacts with itself or with the sm fields , it is reasonable to suppose that perhaps the dark sector contains multiple species and that flavor interactions could be a link between the dark and visible sectors . another motivation for flavored dm is the current possible tension between the dm relic density and constraints from direct detection . as is well - known , the wimp miracle is the surprisingly good agreement between the weak scale and the scale of dm interactions which would yield the observed dm relic density . however , the results of direct detection experiments such as xenon100@xcite place limits of order @xmath0 ( for a coupling constant of order unity ) on the scale of vector effective four - fermion interactions@xcite between dm and @xmath1 and @xmath2 quarks for dm masses between @xmath3 gev and @xmath4 tev ; scalar interactions between dm and @xmath1 and @xmath2 quarks are even more strongly constrained . interactions between the dark sector and leptons or the heavier quarks may help mitigate this tension . it should be noted that flavored dark matter is a potentially immensely rich subject . the relatively weak constraints on interactions of dm with leptons@xcite and non - first - generation quarks allow possible implications for collider studies , direct detection , indirect detection , and low - energy flavor observables . additionally , there are numerous models of flavor into which dm could be incorporated . in this review , we attempt to give a rough survey of some possible lines of inquiry and review those results which exist in the literature . the remainder of this review is organized as follows . in sec . [ sec : const ] , we list some of the most important observables for constraining models of flavored dark matter . we then give an overview of basic model - building considerations in sec . [ sec : modbuild ] . [ sec : flavmod ] discusses the application of existing flavor concepts to dm , with an emphasis on minimal flavor violation . we then discuss flavored dm collider phenomenology in sec . [ sec : pheno ] , and , finally , in sec . [ sec : conc ] , we conclude . here , we briefly summarize some observables which are likely to be relevant for placing constraints on models of flavored dm . the observables we discuss here roughly fall into two categories : constraints from dm properties and constraints from flavor observables . we will save a discussion of collider phenomenology until sec . [ sec : pheno ] . a basic requirement that any model of dm must fulfill is that it must allow for a relic density in agreement with that observed , @xmath5@xcite . if dm is composed of a single thermal relic , this implies a thermally - averaged annihilation cross - section of @xmath6 . however , flavored dm can introduce a few slight complications into the relic density calculation by virtue of having multiple dark sector states or by having strongly flavor - dependent couplings to sm fields . the existence of multiple dark sector states can affect the dm relic density via multiple routes . for example , it may occur that multiple flavors of dm are stable or sufficiently long - lived to comprise today s relic density . alternatively , if the mass splitting between dm species is sufficiently small such that multiple dm species are present at freezeout , coannihilations can be relevant for calculations of the relic density . such a case was achieved@xcite using an analysis based on minimal flavor violation@xcite ; the role of minimal flavor violation in flavored dm models will be expanded on in sec . [ sec : flavmod ] . additionally , the interactions between the sm and dm which determine the relic density may be strongly flavor - dependent and vary greatly from model to model . these interactions may be loop - suppressed@xcite or controlled by small yukawa couplings@xcite . lastly , we point out that the possibility of achieving the observed relic density via asymmetric dm has briefly been considered@xcite . a second basic requirement of dm candidates is that they evade current constraints from direct detection . current results from xenon100@xcite place upper bounds on the spin - independent dm - nucleon cross - section as low as @xmath7 . like the relic density , direct detection cross - sections in flavored dm models can have some interesting features . among these features is that the interactions of flavored dm with quarks can have important dependence on yukawa couplings and ckm angles ; for example , in some scenarios@xcite , the dm direct - detection cross - section can be dominated by interactions via the @xmath8 quark . alternatively , the dm - nucleon cross - section may be loop - suppressed , such as in the case of dm that interacts preferentially with leptons or third - generation quarks@xcite . however , more exotic direct detection signatures are also possible . if splittings between dm flavors are sufficiently small that multiple species comprise dm today , exothermic down - scattering in direct detection experiments is possible@xcite ; in such a scenario , an incoming dm particle @xmath9 scatters into a lighter flavor @xmath10 , giving a final state with more kinetic energy than what would occur in elastic scattering . conversely , up - scattering can occur , rendering flavored dm an example of inelastic dark matter@xcite ; larger mass splittings may effectively eliminate the spin - independent dm - nucleon cross - section ; this can be achieved for flavored dm by , for example , using small majorana mass terms@xcite . we now discuss the relevance of flavor observables . if the dm interacts with quarks , significant constraints may be obtained from meson mixing . lower bounds on the new physics scale for tree - level contributions to @xmath11 mixing are @xmath12 for cp - conserving interactions ; constraints are tighter in the case of cp violation@xcite . dark sector fields can contribute to @xmath11 mixing via loop diagrams which may be additionally suppressed by small yukawas or ckm angles@xcite ; in specific flavor models , new physics contributions of loops of visible - sector particles may also have to be taken into account@xcite . constraints can similarly be obtained from @xmath13 and @xmath14 mixing . in addition to meson mixing , rare decays could also be enhanced via contributions from loops of dark sector particles . for quark - flavored dm , the decay @xmath15 may be relevant ; similarly , @xmath16 may give useful constraints on leptonically - interacting flavored dm . if flavored dm is sufficiently light , it can also show up as missing energy in particle decays . constraints on effective operators coupling light dm to sm fields can be derived from the flavor - changing decays @xmath17 , @xmath18 , and @xmath19 , where @xmath20 is an invisible ( possibly multiparticle ) state ; such constraints are strongly dependent on the interaction considered@xcite . additionally , decays of the top quark , @xmath21 , can be relevant for models of flavored dm@xcite ; @xmath22 evidence for such a decay is expected at the 14 tev lhc for branching fractions greater than @xmath23 , assuming @xmath24 of integrated luminosity@xcite . these observables will play a part in specific constructions of flavored dm , to which we now turn . as the intersection of dm and flavor can yield a potentially immense space of ideas to explore , here we schematically outline some of the choices one may make when building a model of flavored dm . in doing so , we will point out avenues which may be investigated and discuss those scenarios which currently exist in the literature . in addition to basic dm properties such as its mass and spin , flavored dm carries flavor quantum numbers which must be specified . this requires , however , also specifying the flavor quantum numbers of the sm fermions . for example , one could devise models where all of the sm fermions carry flavor quantum numbers . alternatively , one may speculate that the top quark , having a mass very close to the electroweak scale , may have interactions not shared with the leptons or other quarks . additionally , one may consider flavor models where the only sm fields that participate are the charged leptons or the neutrinos . finally , for each one of these options , we can also choose to have the flavor symmetry act on just the left - handed fields , just the right - handed fields , or both . related questions concern the symmetry group itself . is the symmetry global or local ? is the dm in the same representation of the symmetry group as some subset of the sm fermions ? if the symmetry is global , what mediates interactions between the dark sector and the sm ? are the interactions between the sm and the dark sector renormalizeable or represented by higher - dimension operators ? some possible answers to each of these questions will be explored as we discuss specific models below . we now review some models currently in the literature . we will group these models into four categories by the type of flavor they carry . the first of these categories , quark - flavored dm , is the most extensively studied ; we will initially focus on interactions which involve the light ( i.e. , non - top ) quarks . next , we look at an example of top - flavored dm , with its clear relevance to collider phenomenology . then , we consider charged - lepton - flavored dm" +"future @xmath8 colliders will likely have the option of operating in @xmath9 or @xmath10 collision modes @xcite . these modes are reached by compton scattering laser light off one or more of the incoming fermion beams , and then colliding the resulting high energy photons with the remaining fermion beam or with each other . there is a large potential for @xmath11 and @xmath12 collisions to elucidate possible physics beyond the standard model ; previous investigations have focused on anomalous couplings @xcite , searches for extra dimensions @xcite , properties of supersymmetry @xcite , and a broad host of other topics . one subject that deserves further study is @xmath3-violating gauge boson self - couplings . @xmath3 violation is one of the most poorly understood aspects of the standard model ( sm ) . present data merely fixes the value of the @xmath3 violating phase in the ckm matrix , and can not test if this phase constitutes the only source for @xmath3 violation . in fact , studies of baryogenesis within the sm suggest that additional @xmath3 violating terms are required in order to generate the observed baryon asymmetry in the universe @xcite . most discussions of @xmath3 violation at photon colliders work within the context of models such as supersymmetry , and focus upon either higgs or top quark production @xcite . however , since almost every extension of the sm contains new @xmath3 violating phases , it is desirable to eliminate any possible theoretical bias by studying @xmath3 violation within the generic context of an effective lagrangian approach , without assuming any underlying mechanisms . a handful of such works have been performed in the past @xcite , concentrating on @xmath13 , @xmath14 , or top quark production . here , we extend these studies by examining possible @xmath3 violating quartic gauge boson couplings . @xmath12 colliders are particularly suited to studying such couplings ; they can be probed in @xmath5 scattering processes , unlike at @xmath8 colliders . the sm contributions to the processes @xmath0 , @xmath15 , and @xmath16 , including electroweak contributions , were first computed in @xcite . recently , they have been reexamined @xcite , and shown to exhibit several interesting features that motivate our analysis . the sm amplitudes vanish at tree level , and may therefore be quite sensitive to the effects of new physics . at one loop they acquire large imaginary parts , completely dominated at high energies by the helicity amplitudes @xmath17 , @xmath18 , and @xmath19 , where @xmath20 denotes the direction of transverse polarization relative to the beam direction . such amplitudes can interfere strongly with @xmath3 violating contributions from new sources , yielding greatly enhanced sensitivity to these new effects . in addition , the ability to polarize both the initial laser light and fermion beams allows the construction of observables which are sensitive only to these interference effects . these properties , together with the experimental cleanliness of @xmath0 , @xmath1 , and @xmath2 scattering , suggest that these processes might provide powerful tools in searches for new physics . in this paper we will show that @xmath0 , @xmath1 , and @xmath2 at a photon collider can provide sensitive tests of @xmath3 violation in the gauge boson sector . we limit our study to genuinely quartic gauge boson operators , as contributions to the two point functions are strongly excluded by current data and the three point functions are likely better tested elsewhere . we consider manifestly su(2 ) @xmath4 u(1 ) invariant operators constructed from the appropriate field strength tensors , making no assumptions as to the origin of electroweak symmetry breaking . as a result , our operators are of dimension eight . throughout the paper we will identify features of our analysis that might be useful for other new physics searches using these processes . the paper is organized as follows . we first present the density matrix formalism for photon - photon collisions in some detail , both for completeness and to motivate the expression for the ensemble average of the scattering amplitude , which will be used throughout our analysis . we then briefly discuss the construction of the anomalous @xmath3 violating operators we have studied . our results for the three processes considered are presented next , including discussions of the various initial laser and fermion beam polarizations . finally , we present our conclusions , including a comparison of our resulting sensitivity to these effects with others in the literature . in this section we present the density matrix formalism for photon - photon collisions . our discussion is similar to that found in the literature ( see , for example , @xcite ) , but is included here to provide motivation for eq . ( 9 ) , which is used throughout our analysis . consider a photon moving along the @xmath22 axis ; its polarization vectors for positive and negative helicities are given by @xmath23 we will denote the photons corresponding to states with these polarizations by @xmath24 . the most general photon state can be written in this basis as @xmath25 where @xmath26 and @xmath27 . writing this state in 4-vector form demonstrates that the choices @xmath28 and @xmath29 lead to circularly polarized states , while @xmath30 leads to a linearly polarized state . the angle @xmath31 describes the direction of linear polarization in the @xmath32 plane . the experimental setup in @xmath9 colliders has been described in detail elsewhere @xcite ; briefly , one compton scatters laser photons off fermion beams , and then collides the backscattered photons . when observing the scattering process @xmath33 , the energies or helicities of the incoming photons are not known ; they will be statistically distributed , with the specific distribution being determined by the details of the compton scattering process . when measuring the differential cross section , one no longer determines @xmath34 , but rather the ensemble average of @xmath35 : @xmath36 where the sum over @xmath37 sums over all possible initial states weighted by @xmath38 , the probability of their occurrence . we can write this in the form @xmath39 where we have introduced the density matrix for the incoming photons in the basis defined by @xmath40 : @xmath41 let us compute the density matrix for the laser photon of eq . ( 2 ) ; introducing the notation @xmath42 and @xmath43 , we have @xmath44 @xmath45 and @xmath46 measure the amounts of circular and linear polarization , respectively . this is consistent with the polarizations for the values @xmath47 and @xmath30 noted before . after the compton scattering process , the degrees of linear and circular polarization are described by distributions which are dependent upon the fraction of the fermion beam energy the laser photons acquire . denoting this fraction by @xmath48 , and the helicity distribution functions by @xmath49 , the density matrix becomes @xmath50 the eigenvalues of this matrix are @xmath51 we no longer have a pure state unless @xmath52 . as the processes considered in this paper involve two compton scattered photons , the complete density matrix will be the tensor product of the density matrix for each photon . also , since one of the initial laser photons will be moving along the @xmath53 axis , we must take @xmath54 in its density matrix . referring back to eqs . ( 4 ) and ( 7 ) , we can write the ensemble average for the process @xmath33 as @xmath55 \nonumber \\ & & + \xi_c ( x_2 ) \left [ \mid { \cal m}_{++ } \mid^2 - \mid { \cal m}_{-- } \mid^2 - \mid { \cal m}_{+- } \mid^2 + \mid { \cal m}_{-+ } \mid^2 \right ] \nonumber \\ & & + \xi_c ( x_1 ) \xi_c ( x_2 ) \left [ \mid { \cal m}_{++ } \mid^2 + \mid { \cal m}_{-- } \mid^2 - \mid { \cal m}_{+- } \mid^2 - \mid { \cal m}_{-+ } \mid^2 \right ] \nonumber \\ & & + 2 \xi_{t } ( x_1 ) \xi_{t } ( x_2 ) \ , { \rm re } \left [ { \cal m}_{+- } { \cal m}^{*}_{-+ } e^{2i ( \phi_1 + \phi_2 ) } + { \cal m}_{++ } { \cal m}^{*}_{-- } e^{2i ( \phi_1 - \phi_2 ) } \right ] \nonumber \\ & & -2 \xi_{t } ( x_1 ) \ , { \rm re } \left [ { \cal m}_{++ } { \cal m}^{*}_{-+ } e^{2i \phi_1 } + { \cal m}_{+- } { \cal m}^{*}_{-- } e^{2i \phi_1 } \right ] \nonumber \\ & & -2 \xi_{t } ( x_2 ) \ , { \rm re } \left [ { \cal m}_{+- } { \cal m}^{*}_{++ } e^{2i \phi_2 } + { \cal m}_{-- } { \cal m}^{*}_{-+ } e^{2i \phi_2 } \right ] \nonumber \\ & & + 2 \xi_{t } ( x_1 ) \xi_c ( x_2 ) \ , { \rm re } \left [ { \cal m}_{+- } { \cal m}^{*}_{-- } e^{2i \phi_1 } - { \cal m}_{++ } { \cal m}^{*}_{-+ } e^{2i \phi_1 } \right ] \nonumber \\ & & + 2 \xi_{c } ( x_1 ) \xi_t ( x_2 ) \ , { \rm re } \left [ { \cal m}_{-- } { \cal m}^{*}_{-+ } e^{2i \phi_2 } - { \cal m}_{+- } { \cal m}^{*}_{++ } e^{2i \phi_2 } \right ] \bigg\ } \,\ , , \end{aligned}\ ] ] where , for example , @xmath56 denotes the helicity amplitude for incoming photons with helicities @xmath57 and @xmath58 . we have suppressed the final state @xmath59 ; depending upon the process considered the observable final state might require a sum over various helicities . this expression will be used to construct observables for all the processes considered in this paper . the physical cross section involves a convolution of this scattering amplitude with the photon number density function of each photon . the explicit form of this function , as well as the forms for the linear and circular helicity distribution functions , can be found in the appendix . here we construct the most general set of operators that contribute to neutral gauge boson self - interactions , subject to the following constraints . we consider only su(2 ) @xmath4 u(1 ) invariant operators , and further restrict these to @xmath3-odd terms . as the effects of @xmath3-odd trilinear operators have been extensivley studied @xcite , we consider only those terms that lead to quartic or higher gauge boson interactions . we also make no assumption as to the mechanism of electroweak symmetry breaking . these restrictions lead us to the following set of seven dimension eight operators constructed from the @xmath7 and @xmath60 field strength tensors : @xmath61 here @xmath62 is the su(2 ) field strength tensor and @xmath63 the u(1 ) field strength tensor . we have introduced the notation @xmath64 and our convention for the @xmath65 tensor is @xmath66 . a brief comment on the completeness of these operators is in order . @xmath3 violating operators containing three @xmath67 tensors are reducible to those containing only one such tensor , as the product of two @xmath67 tensors can be written as a determinant of metric tensors . operators such as @xmath68 , where the @xmath67 tensor contracts an index on each field strength tensor , are reducible to those where the @xmath67 tensor fully contracts one of the field strength tensors through use of the schouten identity ( see the first reference in @xcite , @xcite ) , @xmath69 which states that no tensor antisymmetric in five indices exists in four dimensions . similarly , the operators @xmath70 can be reduced to those listed in eq . ( 10 ) through use of the identity @xmath71 this is true for @xmath72 antisymmetric in four - dimensional spaces ( an analog holds in arbitrary dimensions @xcite ) . finally , since the" +"there is presently a strong interest in computation and information processing based on fundamental principles of quantum mechanics @xcite . quantum information technology has the potential both to address problems that can not be solved by standard , classical information technology as well as to radically improve the performance of existing classical schemes . the prospect of scalability and integrability with conventional electronics makes solid state systems a likely future arena for quantum information processing . of particular interest is the entanglement between the elementary charge carriers , quasiparticles , in meso- or nanoscopic solid state conductors . entanglement , or quantum mechanical correlations , constitutes a resource for any quantum information process . moreover , due to controllable system properties and coherent transport conditions , conductors on the meso and nano scale constitute ideal systems for the generation and detection of quasiparticle entanglement . this opens up for quantum bits based on the spin or orbital quantum states of individual electrons , the ultimate building blocks for solid state quantum information processing . to date quasiparticle entanglement has however remained experimentally elusive . in particular , there is no unambiguous experimental demonstration of entanglement between two spatially separated quasiparticles . a class of mesoscopic systems that appear promising for a successful entanglement experiment are conductors without direct interactions between the quasiparticles . it was shown by beenakker _ et al _ @xcite that fermions emitted from a thermal source can , in contrast to bosons , be entangled by scattering at a beam - splitter . this was originally discussed for electron - hole pairs @xcite and shortly afterward for pairs of electrons @xcite . since then there has been a large number of works on entanglement of non - interacting particles , see e.g. @xcite for a number of representative papers and also @xcite for a review . several of the entanglement proposals have been based on electrical analogs of optical interferometers and beam - splitter geometries . such electronic systems are conveniently implemented in conductors in the quantum hall regime , where electrons propagate along chiral edge states @xcite and quantum point contacts constitute reflectionless beam - splitters @xcite with controllable transparency , see e.g. @xcite . recent experimental progress on electronic mach - zehnder @xcite and hanbury brown twiss @xcite interferometers has provided further motivation for a theoretical investigation of entanglement in such systems . in addition , the experimental realization @xcite of time - controlled single - electron emitters @xcite in quantum hall systems has opened up the possibility for a dynamical generation of entangled quasiparticles , entanglement on demand @xcite . in this work we will focus on the electronic two - particle , or hanbury brown twiss , interferometer . a theoretical proposal for an implementation of this two - particle interferometer ( 2pi ) in a conductor in the quantum hall regime was proposed by two of us , p.s and m.b . , together with e. v. sukhorukov in ref . recently , the heiblum group , including one of us , i.n . , was able to realize the 2pi in a versatile system which could be electrically tuned between with two independent mach - zehnder interferometers and a 2pi . in perfect agreement with the theoretical predictions @xcite , the two - particle interference pattern was visible in the current correlations but not in the average current . as discussed in ref . @xcite , there is an intimate relation between two - particle interference and entanglement in the fermionic 2pi . under ideal conditions , i.e. zero temperature and perfect coherence , two - particle interference implies that the two particle wave function is on the form @xmath0 . \label{introsing}\ ] ] here @xmath1 denote the sources and @xmath2 the sites of detection , as shown in fig . [ system ] . the wavefunction @xmath3 is maximally entangled , it is a singlet in the orbital , or pseudo spin , space @xmath4 . however , in the experiment @xcite , @xmath5 visibility of the current correlation oscillations was observed . this indicates that both decoherence and finite temperature is important . dephasing can qualitatively be accounted for @xcite by a suppression of the off - diagonal components of the density matrix @xmath6 . it was shown that at zero temperature the entanglement survives for arbitrary strong dephasing . the effect of finite temperature was not investigated at the time of the experiment . the experimental findings thus raised two important questions : are the electrons reaching the detectors at a and b entangled and if so , can this two - particle entanglement be unambiguously detected by measurements of currents and current correlators , the standard quantities accessible in electronic transport measurements ? in our recent work @xcite we provided a positive answer to both these questions . we first calculated the entanglement of the emitted two - particle state and found that the state was clearly entangled . thereafter we showed that under very general conditions the entanglement of the reduced two - particle density matrix provides a lower bound for the entanglement of the emitted two - particle state . since the reduced density matrix is possible to reconstruct tomographically by current and current correlation measurements @xcite , this provides an unambiguous way to detect the entanglement of the emitted state . in the present paper we discuss these findings in more detail . interference is most often investigated in structures that lead to a superposition of amplitudes of a single particle . however , in 1956 , hanbury brown and twiss ( hbt ) invented an optical interferometer based on correlations of light intensities @xcite , an optical 2pi , see fig . [ system ] . the intensity interferometer allowed hbt to determine the angular diameter of a number of visual stars , not possible with available single particle , or michelson , interferometers . the hbt intensity interferometer displays two distinct but fundamentally interrelated features : + @xmath7 first , there is a direct statistical effect since photons from a thermal light source tend to bunch , whereas fermions would anti - bunch . this effect has been used in a large number of experiments in different fields of physics such as elementary particles @xcite , solid state @xcite and free @xcite electrons and recently cold atoms @xcite . + @xmath7 second , light from two different , completely uncorrelated sources gives rise to an interference effect in intensity correlations but not in the intensities themselves . this is the two - particle interference effect . in optics , various aspects of two - particle interference have been investigated extensively since the hbt - experiment , see e.g. @xcite for a short review , and is still a subject of interest @xcite . in electronics , only very recently was a fermionic two - particle interferometer realized @xcite , the subject of this work . + fundamentally both of these effects are related to the symmetry of the multiparticle wave function under exchange of two particles . we note that albeit the hbt - experiment could be explained by a classical electro - magnetic theory , a compelling quantum mechanical picture based on individual photons was put forth soon after the experiment @xcite . importantly , for fermions no classical theory exists . to obtain a qualitative understanding of the physics of two - particle interferometers it is rewarding to compare the properties of optical , bosonic interferometers and electronic , fermionic interferometers . in fig . [ system ] a schematic of a two - particle interferometer , topologically equivalent to the hbt - interferometer , is shown . a natural measure of the correlations between the particles at @xmath8 and @xmath9 is the probability to jointly detect one particle at @xmath8 and one at @xmath9 . an expression for this joint detection probability for photons was derived by glauber @xcite . in ref . @xcite this was adapted to detection of electrons . here we consider the probability to detect one photon / electron in detector @xmath10 , @xmath11 , at time @xmath12 and one in detector @xmath13 , @xmath14 at a time @xmath15 , given by @xmath16 the photon / electron creation operators at a are @xmath17 , with @xmath18 creating a particle in @xmath10 at energy @xmath19 and similarly at b. for photons we consider thermal sources in @xmath20 and @xmath21 while @xmath22 and @xmath23 are left empty . a detector frequency window of size @xmath24 is assumed , over which the distribution functions of the sources are constant , i.e. @xmath25 . for electrons we assume zero temperature and the sources @xmath20 and @xmath21 biased at @xmath26 while sources @xmath22 and @xmath23 are grounded . only quasiparticle excitations , @xmath27 are considered . the probabilities are normalized such that @xmath28 . following the scattering theory for intensity / current correlations for bosons / fermions emitted from thermal sources @xcite , we get @xmath29+|s_{a\alpha 2}|^2|s_{b\beta 2}|^2\left[1\pm g(\tau)\right ] \nonumber \\ & + & |s_{a\alpha 1}|^2|s_{b\beta 2}|^2+|s_{a\alpha 2}|^2|s_{b\beta 1}|^2 \nonumber \\ & \pm & g(\tau)\left[s_{a\alpha 1}^*s_{b\beta 2}^*s_{b\beta 1}s_{a\alpha 2}+s_{a\alpha 1}s_{b\beta 2}s_{b\beta 1}^ * s_{a\alpha 2}^*\right ] \label{jdpt}\end{aligned}\ ] ] where @xmath30 contains the time dependence , with @xmath31 the coherence time for electrons and @xmath32 for photons . here @xmath33 is the amplitude to scatter from source 2 to detector @xmath10 etc . the upper / lower signs @xmath34 correspond to electrons / photons . several interesting conclusions can be drawn directly from eq . ( [ jdpt ] ) : \1 ) for @xmath35 , @xmath36 approaches zero and @xmath37 is just proportional to the product of the two mean currents / intensities . the fermionic versus bosonic statistics of the particle plays no role . \2 ) for shorter times , @xmath38 , @xmath36 is finite and the statistics is important . note that , as pointed out above , that the statistics of the particles enter in two different ways . + i ) the first two terms in eq . ( [ jdpt ] ) describe a direct bunching ( + ) or anti - bunching ( - ) effect for two particles emitted from the same reservoir within a time @xmath38 . this effect would still be present if one of the sources @xmath20 or @xmath21 is removed . + ii ) the last two terms describe the two - particle , or exchange @xcite , interference , where the @xmath34 sign explicitly follows from the interchange of the two detected particles . this two particle interference is only present when both sources are active . for semitransparent beam - splitters @xmath39 and @xmath40 and coincident detection @xmath41 we have @xmath42 & \mbox{fermions } \\ \frac{1}{4}\left[1+\frac{\alpha\beta}{2}\cos \phi\right ] & \mbox{bosons } \end{array}\right . \label{jdpt2}\end{aligned}\ ] ] where @xmath43 is a scattering phase . from this expression a very important difference between bosonic and fermionic thermal sources is apparent : the visibility @xmath44 of the oscillations is @xmath20 for fermions but only @xmath45 for bosons . this is directly related to the fact that while the emitted fermionic two - particle state is maximally entangled , the bosonic state is unentangled @xcite . in ref . @xcite we proposed an implementation of an electronic 2pi in a conductor in the quantum hall regime , with electrons propagating along single , spin polarized edge states ( see fig . [ hbtferm ] ) . two electronic reservoirs @xmath1 biased at @xmath26 act as sources for electrons while the reservoirs @xmath46 as well as the detector reservoirs are grounded . all reservoirs are kept at the same temperature @xmath47 . moreover , we consider here only the linear regime in voltage where electron - electron interactions can be neglected . this regime is relevant for the experiment @xcite . the qpc s at @xmath39 and @xmath40 act as beamsplitters with transparencies @xmath48 and @xmath49 respectively ." +"the direct kinetic effect of a considerable lepton asymmetry @xmath1 ( either initially present or dynamically generated ) on cosmological nucleosynthesis ( cn ) has been investigated in @xcite , and cosmological constraints on its value have been obtained . the effect of neutrino oscillations on cn was also studied and stringent bounds on oscillation parameters were obtained @xcite . neutrino oscillations , proceeding in the primordial plasma during cn epoch , can effect @xmath2 yield by ( a ) bringing additional degrees of freedom into the primordial heat bath@xcite , ( b ) depleting the neutrino and antineutrino number densities thus slowing the weak interactions @xmath3 , ( c ) distorting the neutrino and antineutrino spectrum @xcite , ( d ) producing neutrino - antineutrino asymmetry ev@xmath4 @xcite , however for @xmath5 , a considerable asymmetry growth was registered in precise numerical studies @xcite . ] @xcite , which on its turn influences the evolution of the neutrino and antineutrino ensembles and the oscillation pattern @xcite . in this work we discuss the simultaneous effect of a lepton asymmetry and neutrino oscillations on cn . two different cases of lepton asymmetry are analyzed : an initially present and generated in oscillations asymmetry . we have studied the role of a lepton asymmetry on cn with oscillations , effective after electron neutrino decoupling . we have shown by a numerical analyses of the kinetics of nucleons and the oscillating neutrinos and antineutrinos in cn epoch , that much smaller asymmetries @xmath6 exert considerable _ indirect effects _ on cn through oscillations , due to the fact that even very small asymmetries change the medium induced neutrino potential energy and influence the evolution of the oscillating neutrinos . the prejudice that in order to influence nucleosynthesis the neutrino asymmetry first must grow to a considerable value @xmath1 , is not applicable for the case of nucleosynthesis _ with oscillations_. and changing primordial helium-4 yield @xmath7 @xcite . ] lepton asymmetry influences cn with oscillations in several ways : the neutrino and antineutrino ensembles evolve differently in comparison with the case without asymmetry , i.e neutrino number densities , their depletion and spectrum distortion are changed . also due to asymmetry term neutrino and antineutrino become strongly coupled and evolve differently . lepton asymmetry changes as well the oscillation pattern , i.e. leads to an enhancement or suppression of oscillations . all these resultt into changed light elements yields , compared with the oscillatory case without asymmetry . this indirect asymmetry influence on cn is considerable @xcite . however , inorder to reveal it asymmetry should be considered selfconsistently with the neutrinos and nucleons evolution . the results obtained without the account of the indirect effects differ by many orders of magnitude from the real picture @xcite . numerical analysis , accounting for the asymmetry effect selfconsistently with neutrino and nucleons evolution , was provided in refs . see also ref . @xcite , where an precise analytical study of the asymmetry evolution , accounting for its back effect on oscillating neutrinos , was proposed . in the nonresonant case the oscillations produced asymmetry was shown to have a negligible role in cn @xcite . however , in the resonant oscillation case the asymmetry effect on cn is considerable @xcite . in general , dynamically produced asymmetry suppresses oscillations @xcite , which leads to less overproduction of helium-4 in comparison with cn with oscillations but without an asymmetry account . hence , the bounds on oscillation parameters are alleviated at small mixing angles @xcite . we present in sec . [ s3 ] the updated cosmological constraints for electron - sterile oscillation case , accounting precisely for the oscillations generated asymmetry . the effect of small initial lepton asymmetries ( @xmath8 ) on cn with nonresonant active - sterile oscillations was precisely studied in @xcite . it was found that asymmetry is able to enhance oscillations , besides its well known ability to suppress them @xcite , thus leading correspondingly to an over- or under - production of helium . our analysis has shown ( see sec . [ s4 ] . ) that the initially present asymmetry is able to alleviate cn bounds at large mixings and to tighten the bounds at small mixings ( see also refs . @xcite ) . in the next section we present the precise kinetic approach for the description of lepton asymmetry effects on cn in the presence of oscillations . we have used for the precise analysis the synthesis of helium-4 . according to the standard cn the primordial helium yield depends on two compelling processes , determinning the nucleons freezing : universe s cooling , @xmath9 and weak processes , @xmath10 . three neutrino flavours , zero lepton asymmetry and equilibrium neutrino number densities and spectrum are assumed . in the case of cn with oscillations and with lepton asymmetry , all these assumptions do not work . according to ( a)-(d ) : neutrino oscillations change the number of neutrino flavours ; they may produce nonequilibrium neutrino number densities ( particularly the electron neutrino density may be considerably reduced in favour of the sterile neutrino density ) ; the neutrino spectrum may be distorted in active - sterile oscillations ; besides , even if initially the lepton asymmetry is assumed zero resonant oscillations may lead to a considerable growth of the asymmetry , which on its turn effects neutrinos and nucleons evolution via oscillations . this nonequilibrium picture is hard to describe analytically . kinetic effect on cn . therefore , its role in nucleosynthesis was accounted for after it has grown `` enough''and hence , the indirect effect of asymmetry during its growth has been neglected . the asymmetry back effect on oscillations , in case considered at all , was assumed to be only towards suppressing oscillations . ] inorder to account for the different effects of oscillations and asymmetry on cn a selfconsistent numerical analysis of the kinetics of the oscillating neutrinos , the nucleons freeze - out and the asymmetry evolution is necessary . in our analysis the set of the following coupled integro - differential equations describing the evolution of the neutrino @xmath11 and neutron number densities @xmath12 was solved simultaneously and selfconsistently : @xmath13 + i \sqrt{2 } g_f \left({\cal l } - q / m_w^2 \right)n_\gamma \left [ \alpha , \rho(t ) \right ] + { \rm o}\left(g_f^2 \right ) , \nonumber\\ \nonumber\\ { \partial\bar\rho(t ) \over \partial t } & = & h p_\nu~ { \partial \bar\rho(t ) \over \partial p_\nu } + \nonumber\\ & + & i \left [ { \cal h}_o,\bar\rho(t ) \right ] + i \sqrt{2 } g_f \left(-{\cal l } - q / m_w^2 \right)n_\gamma \left [ \alpha , \bar\rho(t ) \right ] + { \rm o}\left(g_f^2 \right ) , \label{kin}\end{aligned}\ ] ] @xmath14 \nonumber\\ & & - \int { \rm d}\omega(e^+,p,\tilde{\nu } ) |{\cal a}(e^+n\to p\tilde{\nu})|^2 \left[n_{e^+ } n_n ( 1-\bar{\rho}_{ll } ) - n_p \bar{\rho}_{ll } ( 1-n_{e^+})\right].\end{aligned}\ ] ] where @xmath15 , mixing just in the electron sector was assumed @xmath16 . @xmath17 is the momentum of electron neutrino , @xmath18 stands for the number density of the interacting particles , @xmath19 is a phase space factor and @xmath20 is the amplitude of the corresponding process . these equations provide simultaneous account of the different competing processes , namely : neutrino oscillations , hubble expansion and weak interaction processes . @xmath21 is the free neutrino hamiltonian . the ` nonlocal ' term @xmath22 arises as an @xmath23 propagator effect , @xmath24 . @xmath25 is proportional to the fermion asymmetry of the plasma and is essentially expressed through the neutrino asymmetries @xmath26 , where @xmath27 and @xmath28 . the neutron and proton number densities , used in the kinetic equations for neutrinos , are substituted from the numerical calculations of eq . ( 2 ) . on the other hand , @xmath29 and @xmath30 at each integration step of eq . ( 2 ) are taken from the simultaneously performed integration of the set of equations ( 1 ) . the equations are for the neutrino and neutron number densities in momentum space . this allows to account precisely for the spectrum distortion effect and neutrino depletion effects of oscillations , as well as to follow the evolution of the neutrino asymmetry and its back effect at each neutrino momentum . in our numerical analysis the spectrum distortion was described by 1000 bins for the nonresonant case and by 5000 bins for the resonant case . in case the spectrum was described by @xmath31 bins , a system of @xmath32 coupled integro - differential equations following from ( 1 ) and ( 2 ) , was numerically solved . the numerical analysis was provided for the characteristic temperature interval @xmath33 $ ] and the full set of oscillation parameters of the active - sterile oscillation model @xcite . we calculated precisely the @xmath34-freezing , essential for the production of helium , till temperature @xmath35 mev , and accounted adiabatically for the following decays of neutrons till the start of nuclear reactions at about @xmath36 mev . our numerical analysis showed that in the resonant oscillation case the dynamical neutrino - antineutrino asymmetry grows up to 4 orders of magnitude . i.e. starting with asymmetries of the order of the baryon one it reaches maximum a value @xmath37 . hence , having in mind this small value the registered asymmetry effect is totally due to its _ indirect _ influence on cn via oscillations . dynamically produced asymmetry at small mixing angles suppresses oscillations , which leads to less overproduction of @xmath2 in comparison with cn with oscillations but without an asymmetry account . hence , the cosmological constraints on oscillation parameters are alleviated at small mixing angles . = 1.5 mm [ cols= "" < , < , < "" , ] the updated constraints on active - sterile neutrino oscillations , precisely accounting for the asymmetry generation , spectrum distortion and the depletion of the neutrinos , are presented in fig . 1 . the plots correspond to @xmath38 . the net _ indirect _ asymmetry effect on cn is given for the resonant case by the difference between the dashed curve ( without asymmetry account ) and the solid one . due to asymmetry growth account , and the corresponding suppression of oscillations , @xmath7 overproduction is not so strongly expressed at small mixing angles , hence cn constraints are alleviated at small mixing angles for @xmath39 . in the resonant case the cosmological constraints at large mixings are @xmath40 ev@xmath4 . in the nonresonant case @xmath41 an analytical fit to the exact constraints is : @xmath42 ev@xmath4 . the constraints in both cases are strengthened compared to the previous ones @xcite due to the precise account of the spectrum distortion and to the exact kinetic approach to the neutrinos and nucleons evolution . according to these constraints the low active - sterile solution to the solar neutrino problem , which is favoured by the analysis of the recent experimental data of total measured rates and day and night spectrum measured by superkamiokande @xcite is almost completely excluded @xcite . the role of initially present relic asymmetries on cn with nonresonant active - sterile oscillations was precisely studied , following the lines of work described in sec . [ s2 ] . a wide range of @xmath43 values @xmath44 $ ] was analyzed . such small asymmetries have only indirect effects on cn . on fig.2 the dependence of the produced helium , in a cn model with oscillations on the initial asymmetry is plotted . it was found that the asymmetry is able also to _ enhance _ oscillations , besides its well known ability to suppress them . the enhancement is a synthetic effect of a resonant wave passing through neutrino spectrum till lepton asymmetry changes sign and followed by a similar ` spectrum" +"the subject of superfluidity in ultracold trapped fermionic gases is an exciting field @xcite , not only for its implications in atomic physics , but also because there are important implications for condensed matter systems , including perhaps high temperature superconductors @xcite . there are two important aspects which are particularly notable about these systems , from the perspective of the present paper . they can be tuned in various ways which are not available to nature - made superconductors . thus , one can study the entire regime from bcs to bose - einstein condensation ( bec ) , simply by the application of a magnetic field in concert with a feshbach resonance . moreover , one can vary the concentrations of the two spin species arbitrarily @xcite ; in a fashion , this simulates the application of a magnetic zeeman field . this latter tuneability has important implications for other sub - disciplines in physics such as dense qcd and ( isospin asymmetric ) nuclear matter @xcite . equally important is the fact that there is a rich collection of experimental data from two different atomic physics groups @xcite on @xmath2li gases near unitarity , with which one can compare various theoretical results . the goal of this paper is to present an overarching theoretical framework for dealing with fermionic gases over the entire range of bcs to bec crossover and the entire range of temperature , as well as the entire range of population imbalance . the foundations of this theory lie with the initial observation of eagles @xcite and of leggett @xcite that the bcs - like wavefunction has a much greater generality than was originally recognized at the time of its proposal . it is capabable of describing both bcs and bec like systems , providing the pairing attraction is tuneable from arbitrarily weak ( bcs ) to arbitrarily strong ( bec ) and one self consistently solves for the fermionic chemical potential . this mean field - like ground state wave function is also readily generalized to include population balance . indeed , there are at least three well studied phases @xcite which have been proposed to accomodate a difference in the population of the two spin species . what we want to stress is that these same mean field theories have a natural extension to finite temperature @xcite . this extension will be a focus of the present paper . at strictly zero temperature , there is a rather extensive literature @xcite on these population - imbalanced superfluids and superconductors , including recently the effects of the crossover from bcs to bec . there have also been some studies at finite @xmath0 , which are at the mean field level and do not include the effect of the non - condensed pairs @xcite we consider here . the three most studied phases are the sarma ""- like @xcite or breached pair states in which ( as in bcs theory ) the condensed pairs have zero net momentum , but polarization can , nevertheless , be introduced . at @xmath3 this state appears to be stable in the deep bec regime . additionally , two different phases @xcite have been proposed by larkin and ovchinnikov and by fulde and ferrell ( loff ) in which the condensate has a net momentum of a pre - determined @xmath4 or of @xmath5 . even more elaborate crystalline lattices of various @xmath6 have also been contemplated @xcite . it is believed that these states are more appropriate closer to the bcs side of resonance , although rather little has been determined about the two - plane wave "" loff state near @xmath3 or in the presence of crossover effects . added to this complexity is the possiblity of heterogeneous or phase separated states @xcite . in this paper we will present the theoretical formalism for the sarma and one and two - plane wave loff states at zero and finite @xmath0 as one varies from bcs to bec . we note that because theories of population imbalanced superfluids are ( currently , without exception ) based on bcs - leggett - type @xcite ground states , it is important to determine their finite temperature implications within this broad class of ground states , as we do here . our premise is that the effects of finite @xmath0 , which necessarily must be accomodated in any comparison with experiment , must be compatible with the @xmath3 formalism . indeed , one of the most important effects of temperature is to stabilize the sarma - like phase . in this way one finds an intermediate temperature superfluid @xcite , one that exists at @xmath7 , but not at @xmath3 . our studies of the two - plane wave loff state present new results by extending the current literature away from the landau - ginzburg regime ( near @xmath1 ) . with this class of generalized mean field theories we will show that the effects of temperature enter in a fashion which is strongly reminiscent of bose gas condensation . except in the bcs limit , pairs form at higher temperatures , than the ( transition ) temperature @xmath1 at which they condense . thus we have to distinguish the excitation gap [ called @xmath8 from the order parameter [ called @xmath9 . alternatively , this means that there is an excitation gap ( or pseudogap @xmath10 ) for fermionic excitations even in the normal phase . it also implies that below @xmath1 there will be additional modes of exciting the condensate via pair excitations . these latter are non - condensed or incoherent pairs with finite center of mass momentum . we have found @xcite that in a trapped geometry they are particularly important for providing a mechanism of getting polarization into the gas . & & @xmath11 , @xmath12 + & & + & & + these effects of finite @xmath0 can be compared with an alternative class of theories in the literature based on work by nozieres and schmitt - rink ( nsr ) @xcite . this approach is known to lack self - consistency @xcite . we stress that the finite temperature nsr approach was not designed to be consistent with the standard ground state equations . this observation has also been made in ref . indeed , these latter authors have presented in considerable detail @xcite a more complete finite @xmath0 approach based on the @xmath1 calculations of ref . @xcite . a major concern about this class of theories remains to be addressed . because the gap and the number equations are not treated on an equivalent basis , it is possible that the superfluid density will not consistently vanish at @xmath1 . at this temperature there has to be a precise , but delicate cancellation of paramagnetic and diamagnetic current contributions , as found in the present theory @xcite . in a related fashion , pseudogap effects ( associated with the presence of non - condensed pairs ) appear , within an nsr - based approach , in the number equation but not in the gap equation . we begin at the more physical level by stressing the analogy between condensation in this composite boson or fermionic superfluid and condensation in a gas of ideal point bosons . our theory treats self - consistently two - particle and one - particle green s functions on an equal footing . because the physics is so simple and clear , we can fairly readily anticipate the form of the central equations of this bcs - bec generalization of bcs theory . it is important to stress , however , that these equations can be derived more rigorously from a truncated series of equations of motion for the appropriate green s functions @xcite . there are three principle equations which govern bose condensation : the vanishing of the bosonic chemical potential at all @xmath13 is the first . throughout this paper we will refer to this condition as the bec condition "" . it is related to the usual thouless criterion , but the latter is generally associated only with the temperature @xmath1 . the second equation is the boson number equation . all bosons "" must be accounted for as either condensed or non - condensed . the third equation is the number of non - condensed bosons "" , which are created by thermal excitations . this is determined simply by inserting the known excitation spectrum of the excited pairs or bosons , into the bose distribution function . with this equation , and the first equation , one can then deduce the number of condensed bosons . these three central equations for bosons are indicated in table i , on the far right , for true point bosons , and in the second column for the composite bosons which appear in fermionic superfluids . for these composite bosons the quantity which provides a measure of the number "" of bosons ( @xmath14 ) is given by @xmath15 ( up to a constant coefficient , @xmath16 ) . this is reasonably easy to see . in the fermionic regime , when the fermionic chemical potential is positive , @xmath15 represents the square of the excitation gap . this is the energy which must be supplied to break apart the pairs . thus , @xmath15 , in some sense then , reflects the number of pairs . how does one quantitatively establish the appropriate boson number "" for the fermionic case ? this is determined via the self consistent gap equation for @xmath17 , which , in turn , is determined using the first condition : that the pair chemical potential is zero at and below @xmath1 . how does one compute the number of excited pairs ? once the gap equation is interpreted in terms of the appropriate non - condensed pair propagator , then one knows the related excitation spectrum @xmath18 of this propagator . the quantity @xmath16 which appears in the last equation of the table ( for the composite bosons ) gives the relation between the gap associated with non condensed pairs ( @xmath10 ) and the number of pairs ( @xmath19 ) . it can be readily calculated in this theory ; once one has the non - condensed pair propagator , @xmath16 appears as the inverse residue . ( deep in the bec regime , @xmath16 is relatively simple to compute , for here the boson number density approaches the asymptote @xmath20 , where @xmath21 is the fermion density ) . more precisely , the total number of bosons in the present case has to be determined self - consistently through the gap equation . it also involves the fermion number equation through the related fermionic chemical potential . in this last context , it should be stressed that there is one important aspect of the fermionic superfluids , which is not apparent in table i. for bcs - bec crossover , it is essential to derive the self consistent equation for the fermionic chemical potential ; in this problem the fermions are the fundamental statistical entity . this can be readily accomplished within the same framework used to arrive at the gap equation . the vanishing of the pair chemical potential is associated with a particular choice for the pair propagator involving dressed green s functions . these , in turn , determine the fermionic chemical potential through the fermion number equation . in the next two sections we turn to the gap and number equations , and show through a green s function formulation , how strongly these two equations are inter - connected . the rest of the paper is organized as follows . we conclude this section with a summary of the central equations associated with our @xmath0-matrix scheme . in sec . [ sec : ii ] , we present a mean - field" +"the slow relaxation of density in granular materials under tapping has attracted much theoretical interest recently @xcite since knight @xmath0 @xmath1 @xcite carried out systematical experimental measurements of density as a function of time for a vibrated granular material . the experimental data of knight @xmath0 @xmath1 @xcite can be most satisfactorily fitted using a functional form : @xmath2}\ ] ] where @xmath3 is the average density in the system at time instant @xmath4 . here @xmath5 , @xmath6 , @xmath7 and @xmath8 are constant parameters . this four parameter fit was obtained from experimental data without theoretical motivation . previous theoretical models predicted different functional forms . in the model of barker and mehta @xcite , particles can relax both independently , as individual particles , and collectively , as clusters . their model leads to a sum of two exponential terms , which is not in accord with the logarithmic form of eq.(1 ) . the model proposed by hong @xmath0 @xmath1 @xcite is based on a diffusing void picture . it predicts a power law dependence of height reduction as a function of time , @xmath9 with @xmath10 , which means that the density increases linearly until saturation . using frustrated ising models , herrmann and his collaborators @xcite gave a numerical confirmation of the logarithmic density relaxation as eq . ( [ log ] ) in their monte carlo simulations . in their models , frustration plays a crucial role . they claim that frustration is generated in granular materials by the steric constraints imposed by the hard core repulsion of neighboring grains and the subsequent interlocking . the link of the frustrated lattice gas models to real granular packing is explained in refs . @xcite . in this paper , we propose a one dimensional discrete lattice model for granular compaction under tapping based on a simple physical picture . numerical solutions to the model equation indicate that the density relaxes in a logarithmic manner , precisely as eq . we also solve the continuum version of the model analytically in the asympototic limit ( @xmath11 ) to confirm eq . this paper is organized as follows . section ii presents the model equation . numerical and analytical solutions to the equation are given in sections iii and iv respectively . section v is devoted to discussion . the density of particles @xmath12 should satisfy the continuity equation : @xmath13 where @xmath14 is the current density . we may rule out any simple density gradient term in the current density which leads to isotropic diffusion , since the thermal energy is too small to triger the motion of grains . the current density may be written as a product of density and velocity : @xmath15 to specify the the functional form of velocity , let us consider a one dimensional lattice model along z direction . gravity is along the negative z axis . in the absence of tapping , motion of grains under the action of gravity is possible only when the geometric constraint is satisfied , i.e. , enough void space below the grain . if @xmath16 is the particle density , the void density at the site just below is @xmath17 . therefore , the velocity is nonzero only when the ratio @xmath18 less than @xmath19 . this means a step function for the velocity @xmath20 : @xmath21 in the absence of tapping . the effect of tapping in granular compaction is to overcome the bottleneck effect , i.e. , to make the geometric constraints not as strict as the above . motion of grains is also possible when @xmath22 with the help of tapping . we may therefore replace the above step function with a peak function of an exponential form : @xmath23 where @xmath24 and @xmath25 are constants dependent of the vibrational intensity @xmath26 with the amplitude @xmath27 and the frequency @xmath28 of oscillation and @xmath29 the gravitational constant . the precise @xmath30dependences of @xmath25 and @xmath24 are beyond the scope of the present theory . substituting eq . ( [ vel ] ) and eq . ( [ flux ] ) into eq . ( [ con ] ) , we obtain our model equation for density relaxation : @xmath31 with @xmath32 where @xmath33 is infinitesimal in the continuum limit . this model is defined more definitely on a lattice : @xmath34 where @xmath35 is given by eq . ( [ current ] ) putting @xmath36 . in order to solve numerically eq . ( [ model ] ) , we supply two fixed boundary conditions , @xmath37 at the bottom and @xmath38 at the top of the system . the following discrete version of eq . ( [ latticemodel ] ) ensures no flux at the boundaries , i.e. , conservation of particle density as a whole is ensured at each time step @xmath39 with @xmath35 given by eq . ( @xmath40 ) with @xmath36 . we update \{@xmath41 } according to eq . ( [ rule ] ) from random initial conditions with \{@xmath42 } equal to random numbers distributed uniformly from @xmath43 to @xmath44 . 1 shows snapshots of density profiles at three different time steps . we see that as particles move downward voids move upward and pile at the top . as soon as we start updating from a random initial configuration , a sharp interface between a particle phase and a void phase begins to emerge . its position can be easily identified as the location where density changes sharply from non zero value to zero . since the position of the interface takes only integer values on the lattice and information extracted from it is therefore limited , we resort to calculate the position of center of mass @xmath45 & = & \sum_{z=1}^{l } z \rho(z , t).\end{aligned}\ ] ] we take it for granted that the average density measured in experiments is proportional to the inverse of @xmath46 . we determine the proportional prefactor as follows . the minimum value of h can be obtained from a density distribution of a step function , i.e. , @xmath47 which is actually a static solution to the model equation eq . ( [ rule ] ) . here @xmath48 is determined by the density conservation and is a time independent quantity : @xmath49 . the value of @xmath50 corresponding to eq . ( [ step ] ) is @xmath51 . we therefore use the following expression for the average density @xmath52 starting from random initial configurations , we discard the data for initial transient time period and do not make computation of @xmath3 until at the interface between the particle phase and the void phase the density jumps from zero to some reasonably finite value . our density of unity corresponds to the densest close packing and it sets the scale for density . for the case of sphearical particles in reality , the densest close packing has a density of about 0.64 while the mechanically least stable configurations have the most loose value of about 0.55 @xcite ( in our scale 0.859 ) . 2 shows one typical plot of @xmath3 calculated from the lattice model . the time step when we start calculating @xmath3 in fig . 2 is set to be the time origin . it is the instant when the density gap at the interface is about @xmath53 in our density scale . the numerical data in fig . 2 can be very well fitted by the logarithmic form of eq . ( [ log ] ) , which is also shown in the figure . 3 displays two density profiles at different time steps for the particle phase while zero density in the void phase is not plotted . we find that the density profile can be fitted by the following expression @xmath54^{\beta(t)}.\ ] ] where @xmath55 , @xmath56 and @xmath57 are time dependent parameters . the fit to the numerical data is also plotted in fig . 3 . in the whole range the density is step - function - like @xmath58 where @xmath59 is the location of the interface . ( [ z - step ] ) is different from the generalized fermi dirac distribution proposed by hayakawa and hong @xcite and found by herrmann and his collaborators in simulations of frustrated ising models @xcite . the generalized fermi dirac distribution does not have a singularity in the density profile but changes continuously from larger values to zero rapidly within a boundary layer whose width is determined by one of the parameters in the distribution . on the other hand , our model gives a sharp interface between the particle phase and the void phase and therefore the model does not permit any density value smaller than the most loose density for granular compaction . in this sense , we may say that in addition to the granular solid phase and the void phase the generalized fermi dirac distribution allows a granular @xmath60 phase where density changes drastically @xcite . our model describes only the granular compaction under tapping where the grains do not fly as in a gas ( and therefore no inertia terms appear in the velocity expression eq . ( [ vel ] ) ) . as we observed in the simulations , there is always a sharp interface between the particle phase and the void phase . we may therefore generally postulate the solution to eq . ( [ model ] ) as @xmath61 where @xmath62 is the step function such that @xmath63 for @xmath64 and @xmath65 for @xmath66 . we now determine the time dependence of the location of the interface @xmath59 by solving the equation in its continuum version , eq . ( [ model ] ) . substituting eq . ( [ 0 ] ) into the left hand side of eq . ( [ model ] ) , we obtain @xmath67 where dot stands for time deriative . the @xmath68 function in eq . ( [ 0 ] ) gives us the following @xmath69 in eq . ( [ current ] ) @xmath70 & = & f(a(z , t ) , a_{-}(z , t ) ) \theta(b(t ) - z)\end{aligned}\ ] ] where @xmath71 stands for the value of @xmath72 just below @xmath73 , i.e. @xmath74 with infinitesimal @xmath33 . here @xmath75 thus , the right hand side of eq . ( [ model ] ) reads @xmath76 integrating the right hand sides of eq . ( [ 1 ] ) and of eq . ( [ 2 ] ) from @xmath77 to @xmath78 and taking the limit of @xmath79 , we obtain @xmath80 now we make an approximation . from the simulations we know that @xmath81 depends on @xmath73 very weakly . the parameter @xmath57 in eq . ( [ z - dep ] ) decreases as time increases . when @xmath11 , @xmath82 . we therefore make the following aussmption in the asymptotic limit of @xmath11 @xmath83 the conservation of total density is then expressed as @xmath84 with the same @xmath48 as in eq . ( [ step ] ) . using eq . ( [ atinterface ] ) , eq . ( [ ass1 ] ) and eq . ( [ ass2 ] ) we have @xmath85 letting @xmath86 leads in the asymptotoc limit ( @xmath87 ) @xmath88 where @xmath89 is constant . putting @xmath90 , we have @xmath91 now we integrate eq . ( [ x ] ) for @xmath4 from @xmath92 to @xmath4 and for @xmath93 from @xmath94 to @xmath95 where @xmath96 and @xmath97 are the average density ( i.e. , a(t ) ) of the particle phase at time @xmath92 and @xmath4 respectively @xmath98 the asymptotic solution of eq . ( [ int_1 ] ) is readily obtained by using the formular @xmath99 and the expansion for @xmath100 @xmath101.\ ] ] the final form for eq . ( [ int_1 ] )" +"in this paper , we describe a new methodology for studying persistence of topological features across a family of spaces or point - cloud data sets . this theory of _ zigzag persistence _ generalises the successful and widely used theory of persistence and persistent homology @xcite . moreover , zigzag persistence can handle several important situations that are not currently addressed by standard persistence . the zigzag persistence framework is activated whenever one constructs a _ zigzag diagram _ of topological spaces or vector spaces : a sequence of spaces @xmath0 where each adjacent pair is connected by a map @xmath1 or @xmath2 . the novelty of our approach is that the direction of each linking map is arbitrary , in contrast to the usual theory of persistence where all maps point in the same direction . this paper has three principal objectives : * to describe several scenarios in applied topology where it is natural to consider zigzag diagrams ( section [ sec : intro ] ) . * to develop a mathematical theory of persistence for zigzag diagrams ( sections [ sec : zigzags ] and [ sec : zigzag2filt ] ) . * to develop algorithms for computing zigzag persistence ( section [ sec : algorithms ] ) . there is one subsidiary objective : * to introduce the _ diamond principle _ , a calculational tool analogous in power and effect to the mayer vietoris theorem in classical algebraic topology ( section [ sec : further ] ) . this is a theoretical paper rather than an experimental paper , and we devote most of our effort to covering the mathematical foundations adequately . the technical basis for zigzag persistence comes from the theory of graph representations , also known as quiver theory . we are deeply indebted to the practitioners of that theory ; what is new here is the emphasis on algorithmics and on applications to topology ( particularly sections [ sec : intro ] , [ sec : algorithms ] and [ sec : further ] ) . one of the principal challenges when attempting to apply algebraic topology to statistical data is the fact that traditional invariants such as the betti numbers or the fundamental group are extremely non - robust when it comes to discontinuous changes in the space under consideration . persistent homology @xcite is the single most powerful existing tool for addressing this problem . a typical workflow runs as follows @xcite . the input is a _ point cloud _ , that is , a finite subset of some euclidean space or more generally a finite metric space . after an initial filtering step ( to remove undesirable points or to focus on high - density regions of the data , say ) , a set of vertices is selected from the data , and a simplicial complex @xmath3 is built on that vertex set , according to some prearranged rule . in practice , the simplicial complex depends on a coarseness parameter @xmath4 , and what we have is a nested family @xmath5}$ ] , which typically ranges from a discrete set of vertices at @xmath6 to a complete simplex at @xmath7 . persistent homology takes the entire nested family @xmath8 and produces a _ barcode _ or _ persistence diagram _ as output . a barcode is a collection of half - open subintervals @xmath9 , which describes the homology of the family as it varies over @xmath4 . an interval @xmath10 represents a homological feature which is born at time @xmath11 and dies at time @xmath12 . this construction has several excellent properties : * there is no need to select a particular value of @xmath4 . * features can be evaluated by interval length . long intervals are expected to indicate essential features of the data , whereas short intervals are likely to be artefacts of noise . * there exists a fast algorithm to compute the barcode @xcite . * the barcode is a complete invariant of the homology of the family of complexes @xcite . * the barcode is provably stable with respect to changes in the input @xcite . in contrast , any individual homology group @xmath13 is highly unstable . the major limitation of persistence is that it depends crucially on the family @xmath8 being nested , in the sense that @xmath14 whenever @xmath15 . this applies to the current theoretical understanding as well as the algorithms . zigzag persistence addresses this limitation . if we discretise the variable @xmath4 to a finite set of values , the family of simplicial complexes can be thought of as a diagram of spaces @xmath16 where the arrows represent the inclusion maps . if we apply the @xmath17-dimensional homology functor @xmath18 with coefficients in a field @xmath19 , this becomes a diagram of vector spaces @xmath20 and linear maps , where @xmath21 . such a diagram is called a _ persistence module_. what makes persistence work is that there is a simple algebraic classification of persistence modules up to isomorphism ; each possible barcode corresponds to an isomorphism type . our goal is to achieve a similar classification for diagrams in which the arrows may point in either direction this is zigzag persistence , in a nutshell . we consider some problems which arise quite naturally in the computational topology of data . [ densityprofile ] some of the most interesting properties of a point cloud are contained in the estimates of the probability density from which the data are sampled . deep structure is sometimes revealed after thresholding according to a density estimate ( see @xcite for an example drawn from visual image analysis ) . however , the construction of a density estimation function @xmath22 invariably depends on choosing a smoothing parameter : for instance @xmath23 might be defined to be the number of data points within distance @xmath24 of @xmath25 ; here @xmath24 is the smoothing parameter . it happens that different choices of smoothing parameter may well reveal different structures in the data ; a particularly striking example of this occurs in @xcite . statisticians have invented useful criteria for determining what the ` appropriate ' value of such a parameter might be for a particular data set ; but another point of view would be to analyse all values of the parameter simultaneously , and to study how the topology changes as the parameter varies . the problem with doing this is that there is no natural relationship between , say , the @xmath26 densest points as measured using two different parameter values . this means that one can not build an increasing family of spaces using the change in parameters , and so one can not use persistence to analyze the evolution of the topology . on the other hand , there are natural zigzag sequences which can be used to study this problem . select a sequence of parameter values @xmath27 and a percentage @xmath28 , and let @xmath29 denote the densest @xmath30 of the point cloud when measured according to parameter value @xmath24 . we can then consider the union sequence @xmath31 or the intersection sequence @xmath32 as we see in section [ subsec : strongdiamond ] , there is essentially no difference between the zigzag persistent homology of the union and intersection sequences of a sequence of spaces . here that assertion needs to be filtered through the process of representing the data subsets @xmath29 as simplicial complexes . [ sampling ] suppose we are given a very large point cloud @xmath33 . if it is too large to process directly , we may take a sequence of small samples @xmath34 and estimate their topology individually , perhaps obtaining a persistence barcode for each one . how does this reflect the topology of the original sample @xmath33 ? on one hand , if most of the barcodes have similar appearance , then one might suppose that @xmath33 itself will have the same barcode . on the other hand , one needs to be able to distinguish between a single feature detected repeatedly , and multiple features detected randomly but one at a time . if we detect @xmath35 features in @xmath36 on average , are we detecting @xmath35 features of @xmath33 with detection probability 1 , or @xmath37 features with detection probability @xmath38 ? once again , there is a need to correlate features across different instances of the construction . the union sequence comes to the rescue : @xmath39 in this case , the intersection sequence is not useful at the level of samples , because two sparse samples are unlikely to intersect very much . the approach in this example is analogous to bootstrapping in statistics , where measurements on a large data set are estimated by making repeated measurements on a set of samples . [ landmarking ] in computational topology , there exist several techniques for modelling a point cloud data set @xmath33 by a simplicial complex @xmath3 : the cech complex , the vietoris rips complex , the alpha complex @xcite , the witness complex @xcite , and so on . the witness complex @xmath40 , in particular , depends on the choice of a small subset of ` landmark ' points @xmath41 which will serve as the vertex set of @xmath3 . roughly speaking , a simplex @xmath42 with vertices in @xmath43 is included in @xmath44 if there is some @xmath45 which witnesses it , by being close to all the vertices . how does the witness complex @xmath40 depend on the choice of landmark set ? there is no direct way to compare @xmath40 with @xmath46 for two different choices of landmark sets @xmath47 . however , it turns out that one can define a witness _ bicomplex _ @xmath48 which maps onto each witness complex . the cells are cartesian products @xmath49 , where @xmath50 have vertices in @xmath47 respectively . a cell @xmath49 is included provided that there exists @xmath45 which simultaneously witnesses @xmath42 for @xmath44 and @xmath51 for @xmath52 . given a sequence @xmath53 of landmark subsets , one can then construct the biwitness zigzag : @xmath54 long intervals in the zigzag barcode will then indicate features that persist across the corresponding range of choices of landmark set . the fundamental requirement is then for a way of assessing , in a zigzag diagram of vector spaces , the degree to which consistent families of elements exist . the point of this paper is that there is such methodology . we will interpret the isomorphism classes of zig - zag diagrams as a special case of the classification problem for quiver representations ( see @xcite for background on this theory ) . there turns out to be a theorem of gabriel @xcite which classifies arbitrary diagrams based on dynkin diagrams , and which shows in particular that the set of isomorphism classes of zigzag diagrams of a given length is parametrised by barcodes just as persistence modules are . long intervals in the classification define large families of consistent elements , hence indicate the presence of features stable across samples , landmark sets , or parameter values for a density estimator . in section [ sec : zigzags ] we describe the theory of decompositions of zigzag modules . these decompositions produce zigzag persistence barcodes analogous to the barcodes of persistent homology . the foundational theorem of gabriel is stated without proof . in section [ sec : zigzag2filt ] we develop the machinery of right - filtrations , which turn out to be the right tool for accessing the decomposition structure of a zigzag module . this is an important section for the reader who wishes to make serious use of zigzag persistence . in section [ sec : algorithms ] , we present a general - purpose algorithmic framework for calculating zigzag persistence , and we show how this operates in" +"the theory of inflation provides an explanation for many observed properties of our visible universe , in particular its homogeneity and isotropy ( see e.g. @xcite and @xcite for reviews ) . it also gives an explanation for the origin of small density perturbations which eventually gave rise to the structures in our universe . these aspects are well understood . however , from the particle physics point of view , a suitable candidate for the inflaton field has yet to be found @xcite . among the many candidates , hybrid inflation @xcite is a particularly well motivated one , especially in supersymmetric models @xcite@xcite . there has been a lot of recent work investigating the possibility of realising inflation within string theory ( see e.g. @xcite@xcite for reviews ) . the most natural framework for brane inflation is the brane - antibrane system where an attractive force leads to a potential for the interbrane distance @xcite@xcite . inflation ends with an open string tachyonic instability similar to hybrid inflation . this scenario has been extensively studied and leads to interesting phenomena such as @xmath4-string formation at the end of inflation . one particular issue in these models comes from the need for moduli stabilisation during inflation . if this is not achieved , the potential for the moduli is of runaway type destroying the existence of slow roll inflation . this problem can be circumvented using the kklt scenario whereby the kahler moduli are stabilised once the complex moduli have been stabilised and non - perturbative gaugino condensation has occurred on d7 branes @xcite . the coupling to inflation has been studied in kklmmt where a fine - tuning of the inflaton superpotential has been advocated @xcite . one can also use a shift symmetry to alleviate the @xmath2 problem @xcite@xcite . another way of realising hybrid inflation in string models can be obtained using the d3/d7 system , see e.g. @xcite@xcite . in this case the end of inflation happens at a lower scale than the planck scale , when the charged open string fields between the branes condense . the d3/d7 system can be modelled using an @xmath5 supersymmetric @xmath4-term inflation model @xcite . the interbrane distance plays the role of the inflaton and the charged open strings between the branes are the waterfall fields . when the supergravity corrections are neglected , i.e. in global supersymmetry , and assuming that the kahler moduli have been stabilised , the inflaton direction is flat . slow roll inflation is driven by the one loop logarithmic corrections as the one loop quadratic divergences are inflaton - independent . in this paper , we are investigating @xmath0-term hybrid inflation with the inflationary superpotential @xmath6 where @xmath7 is the @xmath8 gauge coupling , in the presence of additional moduli fields . it would be very interesting to derive the origin of @xmath9 from fundamental string theory @xcite . we treat the supergravity case going beyond the global supersymmetry analysis . we show that the treatment of fayet - iliopoulos @xmath4-terms ( i.e. when @xmath10 ) needs extra care in supergravity . to include such a term would require additional fields and the study of their stabilisation . for simplicity we therefore do not include inflationary @xmath4-terms in our models . inflation is then driven by the presence of the non - vanishing @xmath9 . we show that supergravity corrections , and supergravity - induced interactions with a moduli sector induce a tree level slope and mass for the inflaton @xcite . moreover there are additional contributions from the quadratic divergence part of the one - loop corrections , since they are inflaton - dependent in supergravity , as opposed to inflaton - independent in global supersymmetry . in general these effects spoil the flatness of the inflationary potential . we show that most of the tree - level problems can be removed by including shift symmetries in the inflaton sector , and taking the moduli sector to be no - scale . it then appears that a viable slow - roll inflation model can be found with limited fine - tuning of the moduli sector . however we also find that the coupling between the inflaton and the moduli has the effect of inducing a small variation of the moduli during inflation . despite the small size of this variation , it gives a significant contribution to the inflaton slope and violates slow - roll inflation . the paper is arranged as follows . in section [ sec : v ] , we construct the full potential for our combined model of inflation and moduli stabilisation . we calculate tree and one loop level parts of the potential , and describe symmetries which help maintain the flatness of the inflaton potential . in section [ sec : mod ] we determine the role of moduli fields during inflation , and show their effect is significant . we find the constraints corresponding to the cobe normalisation and the wmap3 spectral index constraint in section [ sec : con ] . our arguments and analysis apply to a general moduli sector , although as a specific example , we also give explicit results for the kklt model , which has just one moduli field @xmath11 . in section [ sec : kklt ] we study particular choices of racetrack superpotentials for the kklt scenario , and find that the running of the moduli field during inflation typically leads to a large value of @xmath2 . a small value of @xmath2 could only be achieved if the moduli superpotential is heavily fine - tuned . finally in section [ sec : nogo ] we consider models where a minkowski vacuum after inflation is obtained without the need for a lifting term . a model with this property is also interesting as it may give a small gravitino mass , as is required to have an low energy sparticle spectrum . we derive a no - go theorem which states that , for no - scale models with no lifting term , no such stable supersymmetry breaking minkowski vacua can be found . we conclude in section [ sec : conc ] . as already discussed , many string theory inflation scenarios can be modelled at low energy with a supergravity description of hybrid inflation . the system uses three fields , the inflaton @xmath12 measuring the inter - brane distance and two charged fields @xmath13 ( which in the d3/d7 system would represent the open strings between the two types of branes ) . the fields interact according to the superpotential ( [ inflasec ] ) with @xmath10 , which has been studied extensively in the literature . in @xcite it was shown how the fayet - iliopoulos @xmath4-term arose from fluxes on the d7 brane , allowing @xmath4-term inflation in this system . here we will focus almost exclusively on hybrid inflation which is driven only by @xmath0-terms ( so @xmath14 ) , although exactly how such terms are embedded in string theory remains to be found . including inflationary @xmath4-terms in a supergravity theory creates extra complications , as we will discuss in the following subsection . using ( [ inflasec ] ) and taking to @xmath15 we obtain @xmath16 this potential has an @xmath17 origin which was derived in @xcite . during inflation , when the waterfall fields @xmath18 , the potential is @xmath19 which gives a positive contribution to the inflation energy . extending this model to a supergravity theory , and working in units with @xmath20 , we replace the above @xmath0-term by @xmath21 where @xmath22 , and @xmath23 is the kahler potential for @xmath12 and @xmath13 . the simplest possibility would be @xmath24 . it was originally thought that extending the @xmath4-term in the above model to sugra would be straightforward . however it was later discovered that in order to have a fayet - iliopoulos term @xmath25 appearing in a supergravity theory , the superpotential must have charge @xmath26 @xcite . thus the extension of ( [ susyinf ] ) to sugra described in the earlier paper @xcite requires reconsideration . to preserve the properties of @xmath12 and its role as the inflaton , it should be uncharged @xcite . this is only possible when @xmath10 and the charges of @xmath13 are shifted to @xmath27 , where @xmath28 . now all the contributions to @xmath29 from any other sectors of the theory would also have to be charged . this would be for instance the case with the mssm superpotential . since they are , _ a priori _ , unrelated to inflation , this seems unnatural . hence we have an incompatibility between a non - vanishing @xmath9 and a fayet - iliopoulos term @xmath25 . in the usual inflationary scenario , inflation is driven by the fayet - iliopoulos term . one possibility is to introduce a fayet - iliopoulos term with a gauge invariant superpotential . this can be achieved in supergravity with a @xmath4-term by making the @xmath30 pseudo - anomalous . we extend the model to include one modulus @xmath31 and matter fields @xmath32 , all of which are charged under the pseudo - anomalous @xmath30 gauge group . the relevant part of the kahler potential for these fields is @xmath33 where the gauge field , @xmath34 has been included ( the usual kahler potential appearing in the scalar potential expression is obtained by putting @xmath35 formally ) . the potential arising from the @xmath4-term is then @xmath36 where we have taken the gauge coupling function to be @xmath37 in order to cancel the @xmath30 anomaly . we see that a fayet - iliopoulos term can give rise to inflation when @xmath10 , assuming that @xmath31 and @xmath32 can be stabilised by a suitable superpotential . during inflation , the waterfall fields @xmath13 vanish . this implies that the @xmath30 @xmath4-term and the @xmath9 dependent part of the @xmath0-term potential give rise to the inflation energy @xmath38 when @xmath10 and the extra fields are stable , this resembles the usual inflation energy in hybrid inflation . if on the other hand we just use the @xmath0-term to give inflation , there is no need to introduce the additional fields @xmath32 and @xmath31 . the fayet - iliopoulos @xmath4-term must then be zero , due to the gauge invariance of @xmath29 , so @xmath39 . we will take @xmath40 and assume this is the case for the rest of the paper . the string theory origin for @xmath9 has yet to be found @xcite . we are interested in the hybrid inflation scenario based on the superpotential above ( [ inflasec ] ) . we are also taking into account the effects of a separate sector , so the total superpotential is @xmath41 the @xmath42 are moduli and matter fields , which are usually assumed to be stable during inflation . with one modulus in @xmath0-theory no stabilisation was obtained @xcite . here we consider the most general case in supergravity with more than one moduli field and generic superpotential @xmath43 . the moduli dependent part of the superpotential @xmath43 is then responsible for stabilising the moduli fields . the total kahler potential has the form @xmath44 with @xmath45 we have imposed two shift symmetries in the @xmath46 sector to alleviate the @xmath2 problem of supergravity inflation . this is an extension to the usual @xmath12 shift symmetry @xcite@xcite . in string theory , this corresponds to the translational invariance of the brane system . for the full superpotential ( [ wfull ] ) , the @xmath0-term part of the potential can be expanded as @xmath47 \ , , \end{aligned}\ ] ] where @xmath48 denotes the real part of @xmath49 , and we have defined @xmath50 there is also a contribution to @xmath51 from the @xmath4-term @xmath52}\left(|\phi^+|^2 - |\phi^-|^2\right)^2 \ , .\ ] ] in this paper we will be particularly interested in" +"the equilibrium statistical mechanics successfully describes various types of phase transitions including ferromagnetic - paramagnetic transitions , gas - liquid transitions , and liquid - solid transitions . for structural glass transitions , whose precise definition is not obvious , the understanding has been accumulated from several viewpoints @xcite . in particular , in addition to an insightful phenomenological argument @xcite , which is often referred to as _ a random first - order transition scenario _ ( rfot ) , the analysis within the equilibrium statistical mechanics has provided quantitative results for structural glass transitions @xcite . at present , it has become widely conjectured that a thermodynamic glass transition , if it exists , is described as a one - step replica symmetry breaking ( 1rsb ) in the spin glass terminology . despite such successes , a theory of glass transition in finite - dimensional , short - range interaction systems is still one of challenging problems in physics , because the theory on the basis of equilibrium statistical mechanics has been established only for models with infinite - range interaction or on a random graph . here , let us recall a history of studies on critical phenomena . the van der waals theory is the first breakthrough of theory for critical phenomena , which might correspond to rfot for glass transitions . it should be noted that the statistical mechanics of a model with an infinite - range interaction exactly predicts critical phenomena in accordance with the van der waals theory @xcite . this reminds us a relation between 1rsb in mean - field type models and rfot in phenomenology . then , the existence of a critical point within the equilibrium statistical mechanics of short - range interaction hamiltonians was shown by peierls @xcite , kramers - wannier @xcite , and onsager @xcite . in particular , onsager solved the two - dimension ising model exactly and proved that critical phenomena in finite dimensions are qualitatively different from the van der waals theory ( or the curie - weiss theory in ferromagnetic - paramagnetic transitions ) . since then , the significance of critical phenomena in finite dimensions has been recognized and much effort has been done in order to connect between onsager s result and the van der waals theory . we now understand a great picture of critical phenomena . however , with regard to glass transitions , there is no exactly solved example in finite dimensions ; rather , there is no finite - dimensional , short - range interaction model for which the existence of a glass transition is understood theoretically . thus far , toward establishment of statistical mechanics of glass transition in finite dimensions , several lattice models have been proposed . one example is a class of models proposed by biroli and mzard @xcite , in which at most @xmath0 neighboring particles are allowed to contact with each particle . although this simple model exhibits a glass transition when it is defined on a random graph , crystallization occurs in finite - dimensional lattices except for subtle cases @xcite . in the other model proposed by ref . @xcite , crystallization might be prohibited , and the numerical experiment has been performed in order to explore the nature of thermodynamic glass transitions @xcite . however , it seems difficult to develop a theoretical argument for this model in finite dimensions . furthermore , finite - dimensional quenched - disordered spin models that exhibit 1rsb under the mean - field approximation have been studied numerically @xcite . however , the numerical computation is much harder than standard spin glass models , and a precise theory for the model might be quite challenging . ( see ref . @xcite as such a theoretical attempt . ) in contrast to previous studies , we first propose finite - dimensional hard - constraint models for which ground states can be constructed theoretically . here , the ground states are obtained by taking the limit of the chemical potential to be infinitely large , because the chemical potential is the only thermodynamic intensive variable in such models . indeed , we can show that our model possesses uncountably infinite number of ground states in the infinite size lattice , and typical ground states are irregular in the sense that they do not exhibit any long - range positional order characterized by the existence of bragg peaks . note that quasi - periodic ground states are classified as regular ground states . let us denote a set of all ground - state configurations by @xmath1 , which we can specify theoretically for our models . now , we introduce an overlap with a ground state configuration @xmath2 , which is denoted by @xmath3 . since @xmath3 is defined for each ground state @xmath4 , we have an infinite - dimensional vector @xmath5 . we refer this vector to as _ the order parameter _ , because this corresponds to the magnetization in the ising model . we explain the correspondence by reviewing the phase transition in the two - dimensional ising model . when the temperature is higher than the critical temperature , in the thermodynamic limit , there exists a unique expectation value of observables with being independent of boundary conditions . however , the independence of boundary conditions is broken below the critical temperature . in general , a state of the system without the uniqueness is referred to as _ the ordered phase_. the dependence on boundary conditions is most easily observed when the expectation of the magnetization is considered under the spin - up boundary condition or the spin - down boundary condition . we here notice that the magnetization is equivalent to the overlap with one ground state . we thus consider the overlap with each ground state as the generalization of the magnetization . we also generalize spin - up and spin - down boundary conditions to special boundary conditions that uniquely determine a ground - state configuration for a series of system sizes going to the infinity . we call such a boundary condition a _ gs - boundary condition_. since we have the glass order parameter @xmath6 in our models , we can investigate whether or not the expectation value of @xmath6 takes a different value under every gs - boundary condition . if the dependence is shown , the existence of an ordered phase characterized by the parameter @xmath6 is claimed . from a fact that a typical ground state does not exhibit a long - range positional order , we identify the ordered phase as _ the glass phase_. as far as we know , such an approach to glass problems has never been attempted . this paper is organized as follows . in section [ model - wang ] , we start with a definition of lattice molecule models we study . the molecules in the models are represented by hard wang tiles @xcite and the molecule density obeys a grand canonical ensemble . in section [ model-4 ] , we consider a simple model in this class . we show that the model possesses an infinite series of irregular ground - states , while no thermodynamic transition occur . in section [ 3dmodel ] , as an extension of the model , we propose a three - dimensional model in which a thermodynamic glass transition is observed . we present theoretical arguments and numerical evidences for the thermodynamic glass transition . section [ remarks ] is devoted to concluding remarks . let @xmath7 be a square lattice . we formulate a statistical mechanical model in the lattice @xmath8 . each site can be occupied by at most one molecule . a molecule is characterized by its shape , represented by @xmath9-colors given on edges of a unit square . since tiles with colored edges are called _ wang tiles _ , the molecules in our model may be interpreted as wang tiles . when left , right , bottom and top edges of a wang tile are colored by @xmath10 , @xmath11 , @xmath12 and @xmath13 , respectively , we denote the quartet of colors by @xmath14 . below , the colors will be identified with integers if the correspondence is explicitly given . ( see figure [ tile ] . ) among @xmath15 different wang tiles , we select @xmath16 different tiles . these are called _ prototiles _ and the set of prototiles is denoted by @xmath17 . each prototile is represented by an integer @xmath18 , @xmath19 . at each site @xmath20 , we define @xmath21 if there is a molecule congruent to a prototile @xmath22 and as @xmath23 if the site is empty . we call an empty site a _ hole_. the set of tile configurations @xmath24 is denoted by @xmath25 . we study statistical mechanics of the molecules under a boundary condition imposed at sites in @xmath26 and @xmath27 , where @xmath28 and @xmath29 . the bulk region @xmath30 is denoted by @xmath31 , and the number of sites in the bulk region is @xmath32 . specifically , we consider the case that the interaction between molecules is described by a hard constraint that molecules are allowed to contact each other only when contiguous edges of tiles have the same color . we then assume a grand canonical ensemble @xmath33 where @xmath34 for configurations that satisfy the constraint that contiguous edges have the same color , otherwise @xmath35 ; @xmath36 is the chemical potential of molecules taking a value in @xmath37 $ ] , and @xmath38 is the density of molecules defined by @xmath39 . \label{density}\ ] ] here , the temperature is set to be unity and its value is irrelevant for the problem . the normalization constant @xmath40 in ( [ gc ] ) is the partition function , which is explicitly given by @xmath41 configurations realized in the limit @xmath42 are ground - states in statistical mechanics . a tile configuration without holes , which is referred to as a _ complete tiling _ in this paper , provides a ground state . thermodynamic properties associated with the density are determined by the pressure function @xmath43 defined by @xmath44 the expectation value of the density @xmath45 is given by @xmath46 furthermore , the entropy density @xmath47 is related to the pressure in term of the legendre transformation @xmath48 . \label{entoropy}\ ] ] statistical behavior of the model depends on the choice of a set of @xmath16-types of molecules @xmath17 . as the simplest example , let us consider the set @xmath17 with @xmath49 , in which all the edges of one type are red and all the edges of the other type are green . in this model , ground states are understood as the complete tilings occupied by one color when the open boundary condition @xmath23 for @xmath50 is assumed . when @xmath36 is sufficiently large , the number density of red tiles depends on boundary condition even in the limit @xmath51 . on the other hand , when @xmath36 is sufficiently small ( negatively large ) , tile configurations are disordered and all statistical quantities are independent of boundary conditions in the limit @xmath51 . the @xmath52 symmetry breaking occurs at some @xmath36 beyond which there exists an ordered phase . the universality class near the transition is identical to that of the two - dimensional ising model . a unique feature of wang - tiles is that the operation of any turing machine is simulated by a complete tiling for an appropriate set @xmath17 . ( see ref . @xcite for the research history . see also ref . @xcite as an instructive paper for this issue . ) according to computation theory , this means that there is no algorithm that determines whether or not a complete tiling is possible for a given set @xmath17 @xcite . in" +"even though the aim of mathematical modelling in epidemiology has always been to help predicting the patterns of spread of infectious diseases , the complexity of real populations has always constrained modellers to use strong assumptions . even though these do not always guarantee the existence of analytic solutions , at least the models become _ tractable_. on the other hand , the search for analitical simplicity , or beauty , has sometimes taken over more practical considerations . one of the strongest assumptions used in most epidemiological models is the law of mass action @xcite . first proposed by chemists , it postulates that in dynamical equilibrium the rate of a chemical reaction is proportional to the concentrations of the reactants , and can be derived from the probability of collision between reacting molecules . the analogy between the movements of molecules and living beings , drawn almost a century ago @xcite , leads to the epidemiological version of this postulate : the ` force of infection ' is proportional to the densities of infected and uninfected individuals ( called ` susceptibles ' in the epidemiological literature ) . it implies assuming that the population has no structure , i.e. that every person can be in contact with every other ( ` random mixing ' ) . in general , however , members of a population interact only with a very small subset of it . thus , one way to go beyond the random mixing assumption is to consider that the members of the population form a social network . its definition depends strongly on the type of interaction necessary to transmit the disease whose spread is being modelled . the advantage of this over the random mixing approach is that models can be better adapted to specific populations . needless to say , this implies having more data about the social structure , as well as new concepts and tools to analyse them . fortunately , these are provided by social network analysis , a field that has developed rapidly in recent years @xcite . the mathematics are not as straightforward as in the analysis of mass - action models , but for some cases some interesting results can be obtained by using approximations ( some of them derived from statistical physics ) . one example is the simple relationship that exists for a disease with infectivity @xmath0 and an infectious period @xmath1 , between the relative epidemic threshold @xmath2 , and the topological properties of the network @xcite : @xmath3 where @xmath4 is the mean of the degree distribution of the social network , and @xmath5 is its variance . network epidemiology seems particularly well suited for the analysis of the spread of sexually transmitted diseases , as the definition of the network in this case is more straightforward ( although not free of problems , see @xcite ) . the large number of surveys of sexual behaviour carried out in the last three decades has provided an invaluable resource for modellers . interestingly , one common feature of many sexual networks built from survey data is that their degree distribution has a very long tail : there exist a small number of individuals who have a very large number of sexual contacts . mathematically , this means that , even though @xmath4 is rather small ( typically less than 3 ) , @xmath5 can be very large . applying eq . ( [ statthres ] ) to such networks ( what , as explained below , is not altogether correct ) would lead to the conclusion that , for those populations , even diseases with very low infectivity can trigger an epidemic . it has even been argued that some sexual networks have power law degree distributions with infinite variance @xcite , which would imply a vanishing epidemic threshold , but there is some controversy about this @xcite . one aspect that is usually disregarded in the network approach is the dynamic nature of social interactions . it is reasonable to assume that this dynamics produces a steady - state , in which the distribution of contacts does not change , even though at all times individuals are free to end their existing relationships and create new ones . ( [ statthres ] ) is derived for a static network , and is sometimes used to estimate the epidemic threshold of populations whose structure is deduced from sexual behaviour surveys . respondents to these surveys , however , are usually asked about number of partners over a certain time period , and the distribution thus obtained is often used as a proxy for the steady state , or _ instantaneous _ distribution . but it is difficult to ascertain how close distributions of accumulated contacts can be to the instantaneous distribution @xcite . it is often suggested that if the time period asked about in the survey is similar to the infectivity period of the disease analysed , epidemic thresholds can be calculated by using the proxy network ( see for example @xcite ) . but in general this argument remains at a qualitative level . in principle , it should be possible to see whether the dynamics affects the spread of the disease only by generating a steady state distribution or there are other effects independent of this . models that take into account the dynamic nature of social network usually consider that the formation and dissolution of links between individuals are stochastic processes @xcite . more recently , such models have also been used to understand the spread of infectious diseases @xcite . but , in general , the additional complication of dealing with network dynamics has led either to models that have analytical solutions but that are too simple to be applied in a realistic setting , or to models that rely exclusively on numerical simulations , from which it is difficult to draw general conclusions . the model of network dynamics presented in the next section is an attempt at overcoming these limitations . it can be tailored to give similar accumulated degree distributions to those obtained in real surveys , as shown in the third section , but it also allows us to obtain some very general analytical results for the influence of network dynamics on the propagation of infectious diseases , using mean field techniques . we consider a population of @xmath6 individuals epidemiologically identical . as in this case it has been shown that static models with individuals placed on a bipartite network give identical predictions to models where the population is not divided into two groups @xcite , we have assumed that partnerships can be established between any two individuals . thus , even though our model applies strictly only to homosexual populations , its predictions should be qualitatively correct for heterosexual populations with similar epidemiological variables for both sexes . partnerhips can be established and dissolved with a rate that depends on features of the two individuals . as the only dynamic attribute we consider is the number of partners , we first assume that rates depend only on it . thus , the rate of partnership creation between individuals @xmath7 and @xmath8 is @xmath9 and the rate of partnership dissolution is @xmath10 , where @xmath11 and @xmath12 are the number of current sexual partners of @xmath7 and @xmath8 at time @xmath13 . as we only deal with steady states , hereafter the @xmath13 dependence is dropped from all quantities . in equilibrium , the master equation for the steady state degree distribution @xmath14 becomes : @xmath15 where @xmath16 is the average probability that an individual with @xmath17 partners gets a new partner and @xmath18 is the average probability that an individual breaks one of his existing relationships . in principle , the link creation probability should be averaged only over those individuals that are not current partners of the individual . however , as in real populations @xmath17 is much smaller than @xmath6 , this quantity is very well approximated by the average over the entire population : @xmath19 for the link dissolution probability , the distribution that should be used to calculate the average is @xmath20 , the degree distribution of the individuals that are connected to an individual having @xmath17 partners . however , if we assume that the dynamics does not generate a significant assortative mixing by degree , @xmath20 can be written as @xmath21 . this is not a too stringent assumption , since there seems to be no definite tendency in mixing with respect to sexual activity : some sexual networks have been found to be weakly assortative @xcite , some neutral @xcite and some disassortative @xcite . the resulting average link dissolution is , then , @xmath22 solving eq . ( [ equil ] ) gives the steady state degree distribution : @xmath23 for @xmath24 . @xmath25 is obtained by normalizing the distribution . @xmath14 can also be written as @xmath26 where the @xmath6 parameters @xmath27 ( @xmath28 ) are obtained by solving the @xmath6 self - consistency equations @xmath29 if a model is to be used for understanding the spread of a disease in a real population , its parameters should be adjusted by comparing with the available population data . for simpler models , it has been suggested that this could be done by using an empirical instantaneous distribution @xcite . in our model , however eqs . ( [ steady ] ) and ( [ selfconsi ] ) show that rescaling the link creation and dissolution functions does not change the equilibrium distribution . this was to be expected , because changing the time scale can not change the nature of the steady state reached . thus , time scales should be obtained from other population measurements . an important problem of this approach is that , unfortunately , information about instantaneous degree distributions is usually _ not _ available . instead , almost all surveys ask respondents about the number of sexual contacts accumulated over a certain time period . thus , what we need to know from the model is the distribution of accumulated contacts ( i.e. the probability of having had @xmath17 contacts during a given time period ) , @xmath30 , which can be written as @xmath31 where @xmath32 is the probability of having @xmath33 _ new _ contacts over a time period of length @xmath34 , conditional on having @xmath35 partners at the beginning of that period . the equations that these conditional probabilities satisfy are @xmath36 + \nonumber \\ & & n \sigma_n \ , [ p_t(m|n-1)-p_t(m|n ) ] \label{cumu}\end{aligned}\ ] ] for @xmath37 , with @xmath38 and @xmath39 . with the aid of some mathematical software , such as mathematica or matlab , this recursion can be solved exactly , for any desired value of @xmath34 ( see appendix ) . using this , the parameters @xmath40 and @xmath41 can be adjusted to fit the distributions obtained in any given survey . an example of this is given in the next section . the number of self consistency equations to be solved ( eqs . [ selfconsi ] ) imposes a practical constraint on the models that can be effectively analized . one of the simplest ways to reduce the number of equations to only one is to consider functions of the form @xmath42 and @xmath43 . this choice has the added advantage of ensuring that there is no assortative mixing by degree . note that if @xmath44 is an increasing function of @xmath17 , individuals with many partners are more likely to attract new ones . this is usually known as preferential attachment in the network literature @xcite . interestingly it has been shown that this is likely to play a role in the formation of sexual networks @xcite . first we analyze two different models , called a and b , that generate almost the same instantaneous" +"interstellar medium is turbulent with magnetic fields playing a critical role in the key processes , including star formation , propagation and acceleration of cosmic rays as well as regulating heat and mass transfer between different phases . therefore it is essential to have a reliable way of studying magnetic fields . unfortunately , there only a few ways of tracing magnetic fields and their applicability is limited . for instance , tracing magnetic fields with aligned grains ( see @xcite ) requires either the availability of the background stars , if the polarization via extinction is employed , or sensitive far infrared measurements , which frequently imply the use of the space - based instruments . another major technique that employs synchrotron polarization mostly traces magnetic fields in the warm and hot phases of the interstellar medium ( ism ) ( see @xcite for the list of the idealised ism phases ) . using spectroscopic data for tracing magnetic fields was first suggested and demonstrated in @xcite using the anisotropy of correlation functions of the velocity channel maps . the new approach was motivated by the theoretical advancements establishing that the mhd turbulence is anisotropic ( @xcite , herafter gs95 , @xcite , see @xcite for a review ) and should translate into the anisotropy of the observed correlation fluctuations . later this approach was employed with the use of velocity centroids @xcite and @xcite and the principal component analysis ( pca ) @xcite of the spectroscopic data . in its pca incarnation the idea of tracing magnetic field anisotropies was applied to the observational data in @xcite with the results of anisotropies shown to be consistent with the starlight polarization measurements . further development of the technique resulted in the development of techniques using the anisotropies for obtaining the media magnetization , as it parameterized by the alfven mach number @xcite and the separation of compressible and incompressible turbulence components of observational data as discussed in @xcite . on the basis of the aforementioned improved understanding of the nature of mhd cascade a new technique employing velocity centroid gradients ( vcgs ) was introduced in @xcite ( @xcite , henceforth gl17 ) . instead of appealing to anisotropic velocity correlations as in @xcite the new technique made use of velocity gradients that , according to the mhd turbulence theory tend to be perpendicular to the _ local _ direction of the magnetic field . this idea was further extended in @xcite ( @xcite , henceforth yl17 ) where a robust practical procedure for vcg calculations was suggested . in the latter paper we also applied the new technique to the galfa 21 cm data and demonstrated a good correspondence between the magnetic field tracing with the vcgs and the planck polarization arising from aligned grains . this result motivates the further study of vcgs properties that we undertake in this paper . we note parenthetically that vcgs are not the only way to trace magnetic field using velocity gradients . intensity gradients within the position - position- velocity ( ppv ) channel maps have been recently suggested as an alternative way of exploring the magnetic field topology @xcite . on the basis of the earlier studies of the statistics of channel maps versus the statistics obtained with velocity centroids ( see @xcite and ref . therein ) one can expect that the velocity channel gradients in @xcite ( @xcite , henceforth ly17 ) may have advantages for studying supersonic turbulence as well as tracing the 3d distribution of turbulence . at the same time , the vcgs may have advantages for studying subsonic turbulence . the comparison of the two technique will be done elsewhere . another way of exploring the gradients was introduced in @xcite ( @xcite , henceforth lylc17 ) . this approach employs synchrotron intensity gradients ( sigs ) and provides a way of tracing magnetic field in turbulent environments the synergy of which to the vcg technique we explore in this paper . the theoretical basis for the sigs is the same as for the vcgs however , in the presence of gravity , the response of the sigs and the vcgs is different which provides a way to identify the regions where the matter is subject to the gravitational collapse , as we discuss in the paper . the density statistics is also affected by mhd turbulence . mhd turbulence can imprint some of its properties to density , making its statistics at low sonic mach numbers anisotropic ( see @xcite ) . while both from theory and simulations we expect the density to be a worse tracer of magnetic fields , especially at high sonic mach numbers , the very differences between the velocity and anisotropies can be informative of the properties of the turbulent media . this is the synergy that we also explore in this paper . we note that the first report of the correlation of the magnetic fields and density gradients was done within the numerical study by @xcite reported the alignment of density gradients and magnetic fields with simulation as well as the change of the alignment that occurs after the effects of self - gravity get important starting with a particular density threshold . in our study we make a step further and explore the point - wise tracing of magnetic fields by the intensity gradients ( igs ) as well as the nature of the deviations of the igs directions from those of magnetic field . we show a significant synergy of using the igs , the vcgs and the dust polarimetry data . in addition , we provide a detailed study on how self - gravity lead to the rotation of both vcg and ig vectors and the physics behind it . we also explore the ways of improving the ig tracing of magnetic field by suggesting the procedure filtering for the shocked gas regions . as a separate but related development it is important to mention the study in @xcite . there a good correlation of directions of the filaments observed in the ppv galfa channel maps and the magnetic field direction as revealed by planck polarimetry was reported . as a result the filaments were identified as a tracer of magnetic field direction in hi high latitude gas . while in the original study the filaments were identified with the actual spacial density enhancements , we believe that the interpretation depends on the thickness of the velocity channel used . indeed , according to @xcite within the sufficiently thin velocity channels the intensity fluctuations are caustics mostly induced by velocity fluctuations . therefore , depending on the velocity channel thickness , the filament tracing is related either to revealing of velocity statistics or density statistics or both . the comparison of the empirical techniques is an interesting problem that we will discuss in another paper . self - gravity is expected to modify the properties of the flow in the vicinity centers of the gravitational collapse . the change of the properties of mhd turbulence within such regions is expected to be the result of vcgs changing their properties , in particular their alignment with the magnetic fields . the density distribution is even more affected by self - gravity . indeed , a recent study by @xcite , reported that the igs rotate with respect to magnetic fields when arriving some density threshold in super - alfvenic high density self - gravitating simulation . while the work from @xcite does not address how self - gravity dynamically change the alignment of igs and vcgs , that encourages a detailed study on how self - gravity can possibly lead to the rotation of gradient vectors and the physics behind it . in this paper , we address the issue of how vcgs and igs behave in the regions of self - dominant gravity for the case of sub- and trans - alfvenic clouds , how does the stage of collapse correlated to the alignment of gradients , and how can the aforementioned phenomenon can be used on tracking self - gravitating regions in observation . in what follows we briefly summarize the theoretical arguments that justify the use of the vcgs in [ sec:1 ] , explain our simulation setting in [ sec:1.5 ] and numerical approach for gradient calculation in [ sec:2 ] . we provide a comparison of the alignment of vcgs and igs with magnetic fields in different physical conditions in [ sec:3 ] , and providing methods on improving the alignment . we explore the properties of the vcgs in sub - alfvenic self - gravitating clouds in [ sec:4 ] and explore their synergistic use with the igs . we illustrate our method in [ sec:5 ] using observational data in [ sec:5 ] . we compare our methods to the method of anisotropy of correlation in [ sec:6 ] . we compare our method to others and discuss our results in [ sec:7 ] . we summarize our results in [ sec:8 ] . the theoretical motivation for studying magnetic fields using vcgs are discussed in our earlier papers ( gl17 , yl17 , ly17 ) as well as in the paper on the sigs ( lylc17 ) . in short , in the presence of fast turbulent reconnection @xcite the motions that do not induce magnetic field bending are preferentially excited . these are the motions perpendicular to the local direction of magnetic field . this fact is numerically confirmed in @xcite and is the corner stone of the modern theory of mhd turbulence ( see @xcite ) . due to this alignment of velocity motions , the gradient of velocities are largest perpendicular to the _ local _ direction of magnetic field . it is important that the gradient amplitude for the gs95 turbulence is increasing with the decrease of the eddy scale . therefore the smallest eddies that are most aligned with the local direction of the magnetic field contribute most to the gradients . as a result , by tracing the velocity gradients one can trace the magnetic field direction . the motions at the turbulence injection scale can be super - alfvenic , i.e. faster than the alfven velocity @xmath0 . the gs95 theory is not applicable to such motions . however , as the turbulent velocity decrease with the scale , e.g. for kolmogorov turbulence @xmath1 , for a realistically extended turbulence inertial range at small scales the motions gets subalfvenic and obey the gs95 theory . therefore , by filtering the contributions from larger scales we may still trace the magnetic fields using velocity gradients . in the presence of gravity , the velocity field is modified . in particular , for subcritical collapse when magnetic field dominate the dynamics , the motions are expected along the stiff magnetic field lines , making velocity gradients aligned with magnetic field . similarly , for supercritical collapse , the collapsing material is expected to drag relatively weak magnetic fields . this should also make magnetic fields and velocity gradients aligned . in other words , for the regions with significant self - gravity effects we expect the change of the direction of magnetic field and velocity gradient alignment from being perpendicular to magnetic field to becoming parallel to magnetic field . ( see section [ subsec:4.1 ] for a detailed discussion ) in gl17 and yl17 the velocity centroids were used as a measure of velocity that is available from observations . the velocity centroids were shown to reflect the statistics of underlying velocity field well , at least for subsonic mhd turbulence @xcite . in the present paper we explore numerically the utility for the vcgs to trace magnetic fields in mhd turbulence for various turbulent driving environments , e.g. different combination of sonic and alfvenic mach number , different compression of fluids in non self - gravitating as well" +"most of the energy released in the nuclear fission process appears in the kinetic energy of the fission fragments . a first order estimate of the magnitude of the total kinetic energy release is that of the coulomb energy of the fragments at scission , i.e. , @xmath3 where z@xmath1 , r@xmath1 are the atomic numbers and radii of fragments 1 and 2 . recognizing that the fragments are deformed at scission , one can re - write equation 1 as @xmath4 where the coefficient 1.9 ( instead of the usual 1.2 - 1.3 ) represents the fragment deformation . for symmetric fission , z@xmath5=z@xmath6=z/2 and a@xmath5 = a@xmath6=a/2 , then we have @xmath7 trajectory calculations @xcite for alpha particle emission in fission have shown that the fission fragments are in motion at scission with a pre - scission kinetic energy of 7.3 mev and an additive term representing this motion is needed . thus we have the viola systematics "" @xcite that say @xmath8 the deformed scission point fragments will contract to their equilibrium deformations and the energy stored in deformation will be converted into internal excitation energy . thus we can define a related quantity , the total excitation energy , txe , in fission as @xmath9where q is the mass - energy release . one quickly realizes that these quantities depend on the mass split in fission which in turn , at low excitation energies , may reflect the fragment nuclear structure . the txe is the starting point for calculations of the prompt neutron and gamma emission in fission , the yields of beta emitting fission fragments , reactor anti - neutrino spectra , etc . as such , it is a fundamental property of all fissioning systems and sadly not very well known . as a practical matter , one needs to know the dependence of the tke and txe on neutron energy for the neutron induced fission of technologically important actinide fissioning systems like @xmath10u(n , f),@xmath0u(n , f ) , and @xmath11pu(n , f ) . the first question we might pose is whether the tke should depend on the excitation energy of the fissioning system . does the energy brought in by an incident neutron in neutron induced fission appear in the fragment excitation energy or does it appear in the total kinetic energy ? in a variety of experiments , one finds that increasing the excitation energy of the fissioning system does not lead to significant increases in the tke of the fission fragments or changes in the fragment separation at scission . however , there may be more subtle effects that render this statement false in some circumstances . for example , we expect , on the basis of the coulomb energy systematics given above , that the tke will be proportional to changes in the fission mass splits which in turn can depend on the excitation energy . for the technologically important reaction @xmath0u(n , f ) , madland @xcite summarizes the known data @xcitewith the following equations @xmath12 @xmath13 where e@xmath1 is the energy of the incident neutron and t@xmath14and t@xmath15 are the average total fission fragment kinetic energy ( before neutron emission ) and the average fission product kinetic energy after neutron emission , respectively . these quantities are related by the relation @xmath16\ ] ] these data show a modest decrease in tke with increasing excitation energy for the neutron energy interval e@xmath1 = 1 - 9 mev . there is no clearly identified changes in the tke values near the second chance fission threshold , a feature that is important in semi - empirical models of fission such as represented by the gef code.@xcite in this paper , we report the results of measuring the total kinetic energy release in the neutron induced fission of @xmath0u for neutron energies e@xmath1 = 3.2 -50 mev . the method used for the measurement is the 2e method , i.e. , measurement of the kinetic energies of the two coincident fission products using semiconductor detectors . the time of flight of the neutrons inducing fission was measured , allowing deduction of their energy . the details of the experiment are discussed in section ii while the experimental results and a comparison of the results with various models and theories is made in section iii with conclusions being summarized in section iv . this experiment was carried out at the weapons neutron research facility ( wnr ) at the los alamos neutron science center ( lansce ) at the los alamos national laboratory @xcite . white spectrum "" neutron beams were generated from an unmoderated tungsten spallation source using the 800 mev proton beam from the lansce linac . the experiment was located on the 15r beam line ( 15@xmath17-right with respect to the proton beam ) . the calculated ( mcnpx ) white spectrum "" at the target position is shown in figure 1 . @xcite the proton beam is pulsed allowing one to measure the time of flight ( energy ) of the neutrons arriving at the experimental area . a schematic diagram of the experimental apparatus is shown in figure 2 . the neutron beam was collimated to a 1 cm diameter at the entrance to the experimental area . at the entrance to the scattering chamber , the beam diameter was measured to be 1.3 cm . a fission ionization chamber @xcite was used to continuously monitor the absolute neutron beam intensities . the @xmath0u target and the si pin diode fission detectors were housed in an evacuated , thin - walled aluminum scattering chamber . the scattering chamber was located @xmath18 3.1 m from the collimator , and @xmath18 11 m from the neutron beam dump . the center of the scattering chamber was located 16.46 m from the production target . the @xmath0u target consisted of a deposit of @xmath0uf@xmath19 on a thin c backing . the thickness of the @xmath0u was 175.5 @xmath20 g @xmath0u/@xmath21 while the backing thickness was 100 @xmath20g/@xmath21 . the isotopic purity of the @xmath0u was 99.91 @xmath22 . the target was tilted at 50 @xmath17 with respect to the incident beam . fission fragments were detected by two arrays of si pin photodiodes ( hamamatsu s3590 - 09 ) arranged on opposite sides of the beam . the area of the individual pin diodes was 1 @xmath21 . the distance of the detectors from the target varied with angle from 2.60 cm to 4.12 cm . the coincident detector pairs were at approximately 45 , 60 , 90 , 115 , and 135 @xmath17 . the alpha particle energy resolution of the diodes was 18 kev for the 5475 kev line of @xmath23am . the time of flight of each interacting neutron was measured using a timing pulse from a si pin diode and the accelerator rf signal . absolute calibrations of this time scale were obtained from the photofission peak in the fission spectra and the known flight path geometry . the energy calibration of the fission detectors was done with a @xmath24cf source . we have used the traditional schmitt method @xcite . some have criticized this method especially for pin diodes . however with our limited selection of detectors , we were unable to apply the methods of @xcite to achieve a robust substitute for the schmitt method . the measured fragment energies have be to be corrected for energy loss in the @xmath0uf@xmath25 deposit and the c backing foil . this correction was done by scaling the energy loss correction given by the northcliffe - schilling energy loss tables @xcite to a measured mean energy loss of collimated beams of light and heavy @xmath24cf fission fragments in 100 @xmath20 g/@xmath21 c foils . the scaling factor that was used was a linear function of mass using the average loss of the heavy and light fission fragments as anchor points . the correction factors at the anchor points were 1.24 and 1.45 for the heavy and light fragments , respectively . similar factors were obtained if the srim code @xcite was used to calculate de / dx . these large deviation factors from measured to calculated fission fragment stopping powers have been observed in the past @xcite , and represent the largest systematical uncertainty in the determination of the kinetic energies . the measured average post - neutron emission fission product total kinetic energy release for the @xmath0u(n , f ) reaction(table 1 ) is shown in figure 3 along with other data and predictions @xcite . the evaluated post - neutron emission data from madlund @xcite are shown as a dashed line while the individual pre - neutron emission measurements of @xcite are shown as points . the point at e@xmath1 = 14 mev is the average of @xcite and @xcite . the slope of the measured tke release ( this work ) is in rough agreement with the previous measurements @xcite at lower energies . also shown are the predictions of the gef model @xcite . gef is a semi - empirical model of fission that provides a good description of fission observables using a modest number of adjustable parameters . the dashed line in figure 1 is a semi - empirical equation ( tke = 171.5 -0.1e * for e * @xmath26 9 mev ) suggested by tudora et al . @xcite qualitatively the decrease in tke with increasing neutron energy reflects the increase in symmetric fission ( with its lower associated tke release ) with increasing excitation energy . this general dependence is reflected in the gef code predictions with the slope of our data set being similar to the predictions of the gef model but with the absolute values of the tke release being substantially less . in figure 4 , we show some typical tke distributions along with gaussian representations of the data . in general , the tke distributions appear to be gaussian in shape . this is in contrast to previous studies @xcite which showed a sizable skewness in the distributions . in figure 5 , we show the dependence of the measured values of the variance of the tke distributions as a function of neutron energy along with the predictions of the gef model of the same quantity . the measured variances are larger than expected . at low energies ( near the second chance fission threshold ) the observed variances show a dependence on neutron energy similar to that predicted by the gef model , presumably reflecting the changes in variance with decreasing mass asymmetry . at higher energies ( 11 - 50 mev ) the variances are roughly constant with changes in neutron energy . models @xcite would suggest that most of the variance of the tke distribution is due to fluctuations in the nascent fragment separation at scission . the constancy of the variances is puzzling . using the q values predicted by the gef code , one can make a related plot ( fig . 6 ) of the txe values in the @xmath0u(n , f ) reaction . the bump "" in the txe at lower neutron energies is pronounced and the dependence of the txe upon neutron energy agrees with the gef predictions although the absolute values are larger . we conclude that : ( a ) for the first time , we have measured the tke release and its variance for the technologically important @xmath0u(n , f ) reaction over a large range of neutron energies ( 3.2 - 50 mev ) . ( b ) the dependence of the tke upon e@xmath1 seems to agree with semi - empirical models although the absolute value does not . ( c ) understanding the variance and its energy dependence for the tke distribution remains a challenge . this work was supported in part by the director , office of energy research , division of nuclear physics of the office" +"the gas and dust that is ejected by dying stars and from which new stars will form , is constantly being processed chemically as well as physically ( _ e.g. _ , * ? ? ? * ) . a particularly rich and diverse route is followed by carbon . in the cool surroundings of carbon stars evolved stars that have dredged up large amounts of carbon to the stellar surface more than 60 individual molecular species have been identified , including benzene , polyynes and cyanopolyynes @xcite . in addition , the spectra reveal diverse dusty materials such as hydrogenated amorphous carbon ( hac or a - c : h ) and silicon carbide ( sic ) . as the mass - loss process strips the outer layers of the star , a hot ( @xmath0 k ) central white dwarf becomes exposed , whose strong uv irradiation further processes the ejecta and makes them visible as a planetary nebula ( pn ) . a key component of the carbon dust inventory in pne are polycyclic aromatic hydrocarbons ( pahs ) and pah - like species , a class of large and hardy carbonaceous species whose formation mechanisms are unclear @xcite . although not a single pah member has been identified in space , their characteristic spectral features at infrared wavelengths are observed throughout the universe , from which it is inferred that they reside ubiquitously in space and could lock up as much as 15% of the cosmic carbon ( _ e.g. _ , * ? ? ? two other large aromatic species have been recently identified in space : c@xmath1 and c@xmath2 . these are the best - known members of the family of fullerenes , a class of molecules made of hexagonal and pentagonal aromatic carbon rings , fused in the shape of a hollow sphere or ellipsoid . the most abundant of these molecules , the buckminsterfullerene c@xmath3 , has the structure of an old - fashioned black and white soccer ball . the near - spherical carbon configuration of these two molecules , which have a closed surface , a closed - shell electron distribution and an almost unstrained network , results in a very high stability against dissociation and prolonged exposure to high temperature . fullerenes , in particular c@xmath3 , have peculiar and appealing photochemical , electrochemical and physical properties , which can be exploited in various fields , from nanotechnology to medicine , to space science . c@xmath3 and c@xmath4 were discovered during laser ablation experiments on graphite targets , aiming to study long carbon chains in interstellar clouds @xcite . because of their remarkable stability , fullerenes appeared particularly suited to survive the harsh conditions of the interstellar medium . their unique properties indicate that they may play an important role in organic astrochemistry and astrobiology . cosmic fullerenes remained elusive until the recent discovery of c@xmath3 and c@xmath4 in the planetary nebula tc 1 by @xcite . fullerenes have since been confirmed in many more evolved star environments @xcite , as well as in young stellar objects @xcite , reflection nebulae ( rne ) @xcite and photodissociation regions @xcite . fullerenes can be efficiently synthesized in the laboratory by the vaporization of carbon rods in an electric arc @xcite and from hydrocarbon combustion under optimised conditions @xcite . however , the formation routes of fullerenes in space are still unknown . we review the currently known formation mechanisms of fullerenes in the laboratory ( [ earth_sec ] ) , showing why these methods would not work in space ( [ not_working_sec ] ) . we propose an alternative pathway , consistent with astrophysical conditions , based on the photo - processing of a family of carbonaceous species which we name `` arophatics '' ( [ our_mechanism_sec ] ) . we discuss the observations of fullerenes in pne ( [ observations_sec ] ) and finally we summarize our conclusions ( [ conclusions_sec ] ) . the original discovery of c@xmath3 and c@xmath4 dates back to 1985 with the experiment of @xcite . in this experiment , carbon species were vaporized from a graphite target into a he flow with tunable pressure / density . the vaporization was done by a pulsed laser , the resulting carbon clusters were expanded in a supersonic molecular beam , photoionized and their masses measured by a time - of - flight mass spectrometer . vaporization at low he pressure ( less than 10 torr ) leads to a broad distribution of clusters , with 38 to 120 carbon atoms ( always even numbers ) , with c@xmath3 and c@xmath4 present but not the dominant species . at a pressure of 760 torr the c@xmath3 and c@xmath4 peaks clearly dominated . when the expansion of the he+carbon cluster mixture was delayed , the resulting mass distribution was completely dominated by c@xmath3 - 50% of total large cluster abundance , and c@xmath5 , with 5 % of total large cluster abundance . these distributions have been interpreted as due to the increasing number of he - cluster and cluster - cluster collisions , resulting in the `` survival of the fittest '' , i.e. the more stable clusters . the famous icosahedral soccer ball structure was proposed for the first time for c@xmath6 , and later confirmed by spectroscopic studies @xcite . however , the elementary reaction mechanisms occurring during the `` thermalization '' process remained unknown . @xcite experimentally studied the gas - phase formation of carbonaceous compounds . their first experiment was essentially a replication of the kroto experiment , i.e. laser vaporization of a graphite target in a quenching atmosphere of he or he / h@xmath7 with pressures between 3.3 and 26.7 mbar . the vibrational temperature of the laser - induced plasma was estimated to be between 4000 and 6000 k for the laser power densities used . in a second set of experiments , the laser - induced pyrolysis of c@xmath7h@xmath7 and c@xmath8h@xmath8 using a pulsed laser with high power densities was studied . the resulting condensation temperatures were above 3500 k , comparable with the vaporization experiment . in a third set of experiments , laser - induced pyrolysis of the same hydrocarbon precursors was carried out , but this time at a much lower temperature ( max 1700 k ) . the analysis of the condensation products showed a striking effect of the temperature . during the high temperature experiments , only fullerene - like soot and fullerenes were produced . during the low temperature experiments , only soot and pahs were formed ( 100 % pahs at @xmath9 1000 k ) . the results clearly tell that the temperature determines which kind of condensates will be formed . moreover , the two pathways seem to be mutually exclusive , at least under these experimental conditions : fullerenes and pahs can not be formed together . it is important to note that high pressure has been used during the experiments to concentrate the condensation within a small volume , i.e. to mantain a high density of the condensing species . the laboratory experiments described in the previous sections do not tell us how fullerene is formed from graphite and hydrocarbons , but only under which conditions this happens . the elementary reaction mechanisms involved in the formation of fullerenes can be investigated performing quantum chemical molecular dynamics simulations @xcite . in one set of simulations a hot carbon vapor was reproduced by putting 40 randomly oriented c@xmath7 molecules in a tiny 20 cubic box @xcite . the system was let to evolve , and extra c@xmath7 molecules were added at fixed times in order to simulate an open environment . during the first stage , the system was kept at a constant temperature of 2000 k and giant carbon cages self - assembled . during the second stage of the simulation the temperature was raised to 3000 k , and the shrinking of these hot giant fullerenes down to c@xmath10 was observed @xcite . the formation of the giant cages starts with nucleation of polycyclic structures ( hexagons and pentagons ) from entangled polyyne chains . this is followed by growth of the structure and finally cage closure similar to the self - capping of open - ended single - walled nanotubes . because of the rapid gain of energy due to cage closure , the giant fullerenic cages are produced in a vibrationally highly excited state . the excess energy has to be dissipated , either by unimolecular dissociation or collision with other carbon clusters or carrier gas atoms . the simulations show that the newly produced giant fullerenes inevitably shrink to smaller sizes . all the road maps to fullerene formation proposed by previous models were associated with intermediate structures that are in thermodynamic equilibrium , while a hot carbon vapor is indeed a system far from thermodynamic equilibrium . in the model developed by irle , morokuma and collaborators , for the first time the dynamic self - assembly of fullerene molecules occurs as an irreversible process emerging naturally under the nonequilibrium conditions typical of a hot carbon vapor . the experimental results of @xcite have presented evidence of the spontaneous tendency of electron - irradiated graphite to include pentagons in its hexagonal network , hence form curved structures . this has been further confirmed by @xcite , who have shown that fullerenes can form directly from graphene in a similar fashion . in the experiment of chuvilin and co - workers , a sheet of graphene was exposed to a beam of energetic 80 kev electrons . the energy transferred to the graphene results in the loss of carbon atoms from the edges of the sheet . if the size of the graphene flake is not too big ( less than a few hundreds of carbon atoms ) , the loss of carbon atoms at the edge will lead to the formation of pentagons , which triggers the curving of graphene into a bowl - shaped structure . further carbon removal from the edges using the electron beam will reduce the size of the curved structure until it is sufficiently small to zip up its open edges and isomerize into a closed fullerene structure . @xcite claim having identified the fundamental processes leading to the formation of fullerenes in a recent experimental work , based on laser vaporization of pure c@xmath3 in the presence of carbon vapor . according to this study , fullerenes would self - assemble bottom - up through a closed network growth ( cng ) mechanism based on the ingestion of atomic carbon and c@xmath7 clusters . it should be noted that the work from @xcite provides experimental evidence of the growth of larger fullerenes from pre - existing c@xmath3 only . because the experiments show that the cng of larger fullerenes does not result in the production of c@xmath6 , it is deduced that c@xmath3 formation must be a result of cng from smaller fullerenes . however , the initial formation mechanism of such smaller fullerenes is still under debate . although all the chemical ingredients and the required temperatures for graphite vaporization and hydrocarbon combustion can be found in astrophysical environments , the densities are far too low to proceed to fullerene formation on reasonable timescales . in space , the most favourable conditions for fullerene formation via vaporization / combustion are found in a post - shock gas . in such environments the fullerene building blocks , i.e. c@xmath11 groups and polycyclic species coming from the fragmentation of pahs @xcite , ought to exist in the required vibrationally excited states . however , the post - shock carbon densities are low and represent a serious obstacle to fullerene formation . we have derived the scaling rule ( eq . [ scaling_eq ] ) relating the time @xmath12 , required for fullerene condensation , with the initial density @xmath13" +"the heavy mass expansion for inclusive decays of heavy hadrons has become a generally accepted tool . although there are hints that there could be problems in the calculation of lifetimes ( the @xmath1lifetime ) within this framework , the @xmath2 expansion seems to be an appropriate method to access semileptonic processes@xcite . however , if one is aiming at a complete description of the spectra ( i.e. energy of the charged lepton @xmath3 or the hadronic invariant mass @xmath4 ) in general problems are encountered in the endpoint region , where @xmath5 becomes small . typically this invariant mass is of the order @xmath6 , the mass of the decaying hadron . this is true in almost all phase space ; however , getting closer to the endpoint it has become popular to distinguish two regions . the first region is the one with very small @xmath7 and also very small hadronic energy @xmath8 ( here @xmath9 is the velocity of the decaying hadron ) ; here the proper description is a summation over the very few exclusive channels contributing in this region . however , in the second region where the hadronic energy is still large @xmath10 but the invariant mass @xmath5 becomes small , namely @xmath11 , there is still the possibility to obtain a proper qcd description of the decay . in this case it has been shown @xcite that one may resum the leading twist terms into a universal light - cone distribution function ( or shape function ) for the heavy quark . this function is entirely non - perturbative and may be written formally as a forward matrix element of a non - local operator . this nonlocal operator corresponds to the fourier transform of the wilson line @xcite . on the other hand , there are computable perturbative corrections which exhibit logarithmic singularities close to the endpoint region . to first order in @xmath12 the leading contribution to the spectrum close to the endpoint is of the form @xmath13 , where @xmath14 is now the partonic analogue of the hadronic invariant mass of the final state . upon integration this yields the usual sudakov logarithms . several methods have been proposed to combine both perturbative and non - perturbative contributions . at least for the doubly logarithmic terms this should be possible since they are process independent and hence could be assigned to the universal shape function . in addition , close to the endpoint , a resummation of the double logarithms becomes necessary , since these terms become large . such a resummation may be achieved by setting up an evolution equation for the shape function as it has been proposed in @xcite . in the present note we use such an evolution equation and solve it analytically by putting in the one loop result for the anomalous dimensions . in the next section we express the hadronic invariant mass spectra in terms of the shape function , thereby defining a limit in which the leading twist dominates . in section 3 we consider the renormalization of the shape function and set up an evolution equation and derive the anomalous dimension in section 4 . finally we solve the evolution equation analytically and discuss the implications for the evolution of the moments of the shape function . in inclusive decays such as @xmath15 and @xmath16 the effective hamiltonian takes the general form @xmath17 where @xmath18 is a hadronic current and @xmath19 is either leptonic or photonic . we shall in the following consider the invariant mass spectrum of the final state hadrons . we denote with @xmath5 the square of this invariant mass . the spectrum may be written as @xmath20 where phase space integration over the leptonic and hadronic total momentum @xmath21 , @xmath22 is denoted by @xmath23 , respectively . the leptonic ( or photonic ) and hadronic tensors are defined as @xmath24 the non - hadronic part can be calculated perturbatively and is treated in the following as a known function of @xmath21 . the object of our interest is the hadronic part , @xmath25 which in general can not be determined perturbatively . proceeding along standard lines we have @xmath26 the hadronic current is usually a bilinear function of two quark operators one of which is a heavy @xmath27 quark . using the fact that the heavy mass @xmath28 sets a large scale compared to @xmath29 we may set up an operator product expansion in the usual way . we write @xmath30 where @xmath31 represents a massless quark and the large part of the @xmath27quark momentum has been explicitely removed from the field by a phase redefinition . this leaves us with @xmath32 in the following we are interested in the endpoint region , which is defined by a specific kinematical limit denoted large energy limit . we shall define this limit first in terms of the partonic total momentum of the final state @xmath33 corresponding to the partonic invariant mass @xmath14 and the partonic energy @xmath34 . in the endpoint region the total energy @xmath34 of the final state scales with the heavy quark mass @xmath28 while the invariant mass @xmath14 is of @xmath35 such that the light cone component @xmath36 of the total final state momentum remains finite of @xmath37 : @xmath38 we shall relate the partonic variables to the hadronic ones at the end of the section . it has been shown @xcite that in the limit ( [ limit ] ) the leading contribution may be obtained by contracting the light quark @xmath39 b_v ( x ) | b(p ) \rangle .\end{aligned}\ ] ] this expression may be taylor - expanded around @xmath40 and the expansion resummed to yield formally @xmath41 in the following , @xmath42functions as in the preceding expression are defined by their fourier transform , which involves a path - ordered exponential as in ( [ wilson ] ) . performing the @xmath43integration we get @xmath44 in the endpoint region ( [ limit ] ) @xmath45 is almost light like and can be decomposed as @xmath46 thus in ( [ eq : qcontr ] ) we can approximate ( @xmath47 ) @xmath48 neglecting terms of @xmath49 : @xmath50 for the perturbative calculation in the next section it is useful to rewrite @xmath51 in terms of the imaginary part @xmath52 where @xmath53 using heavy quark symmetry to disentangle the dirac structure of this expression we finally arrive at @xmath54 where @xmath55 . here we have introduced the shape function or light cone distribution function for the heavy quark @xmath56 the light cone structure function @xmath57 measures the probability of finding a heavy quark with light cone component @xmath58 inside the b meson and is a universal function . up to now we have worked in terms of partonic variables , while experimentally only hadronic variables are of interest . introducing the hadronic light cone variable in terms of the hadronic invariant mass squared @xmath5 and the hadronic energy @xmath59 we have @xmath60 we find that the support of @xmath57 is the interval @xmath61 such that @xmath62 . in reality , the spectrum is peaked near @xmath63 . the shape function may directly be measured in a inclusive semileptonic or radiative decay by measuring the spectrum of the hadronic light cone variable @xmath64 . in the last section we have shown , that in the large energy limit the integrated hadronic tensor @xmath65 can be approximated by the quantity @xmath51 defined in the large energy limit of qcd . up to now only non perturbative corrections resummed in the structure function are included . to really establish the approximation we have to check that this also works perturbatively , since it is well known that in the kinematical region of small invariant mass @xmath66 the perturbative spectrum is plagued by large logarithmic corrections . therefore we should require that order by order in perturbation theory the leading ir singularities of @xmath65 arising in the large energy limit should be reproduced by @xmath51 . the leading logarithms are universal and hence we may assign them to be perturbative corrections to the structure function . in order to identify the relevant ir singularities which have to be reproduced by perturbative corrections to the structure function we shall first consider the hadronic invariant mass spectrum calculated in full qcd in the large energy limit . the relevant terms of the one loop contribution can be generically written as @xmath67\ ] ] where the real functions @xmath68 are regular in the limit @xmath69 with @xmath36 fixed . from this we easily identify the ir singularity as the @xmath70term since @xmath36 is held fixed in the large energy limit . if the large energy limit makes sense in perturbation theory , we have to require that exactly this term is reproduced by the @xmath71corrections to the light cone distribution function . the origin of this logarithmic divergence in the spectrum can be traced back to double logarithms of the correlator @xmath72 . thus to one - loop order the double logarithmic terms in @xmath72 and @xmath73 have to match in the large energy limit . it therefore suffices to look for the most singular feynman integrals contributing to the correlators at @xmath71 . the one - loop corrections to the shape function consist of vertex diagrams , self - energy contributions and a box - type diagram . however , in full qcd the uv divergencies of the self - energy diagrams cancel with the uv divergency of the vertex diagram because of current conservation . for the shape function divergent pieces appear in the self energy of the heavy quark which will be taken into account below . the self - energy insertion into the light - cone propagator does not contribute . thus , we can restrict ourselves to the vertex diagrams shown in figure [ fig : fig1 ] . = 12.6 cm the part of the vertex correction in full qcd ( first term in fig.[fig : fig1 ] ) responsible for double logarithms reads @xmath74 } \nonumber \,,\end{aligned}\ ] ] where @xmath75 is the residual momentum of the heavy quark and the integration measure indicates dimensional regularization with @xmath76 . on the other hand , we can directly compute the corrections to the shape function either by reading off the propagator from ( [ eq : corrleeft ] ) or by the usual way of calculating corrections to wilson lines @xcite . the corresponding expression is @xmath77 in which the leading logarithms have to match the full qcd result ( [ eq : threeqcd ] ) . evaluating the corresponding integrals @xmath78 and @xmath79 to double logarithmic accuracy and supressing constant terms we get @xmath80 \nonumber\,,\end{aligned}\ ] ] where @xmath81 note that ( [ eq : dbllogqcd ] ) is valid up to single logarithmic corrections . due to the presence of both uv and collinear divergencies , a @xmath82 pole appears . however , both singularities are of uv nature in the sense that the integral converges for @xmath83 and can therefore be removed by renormalization , as will be explained below . in the difference of both integrals @xmath84 \nonumber\end{aligned}\ ] ] the double logarithms do not cancel . the operator to be renormalized [ i.e. , the operator defining the light - cone distribution function ( [ eq : strufu ] ) ] is of nonlocal nature . hence , we can introduce an integration over @xmath85 , which plays the role of a summation over a continuous operator basis labeled by @xmath85 , to absorb the local as well as the nonlocal uv divergencies in ( [ eq : diffint ] ) into a renormalized distribution function . furthermore , the difference of integrals ( [ eq : diffint ] ) has a finite part . in order to reproduce the amplitudes ( defined in a definite scheme , e.g. @xmath86 ) of full qcd in the effective" +"* * * * quantum teleportation has found important applications for realization of various quantum technologies @xcite . teleportation of quantum states has been demonstrated between light beams @xcite , trapped atoms @xcite , superconducting qubits @xcite , defect spins in solids @xcite , and from light beams to atoms @xcite or solid state spin qubits @xcite . it is of both fundamental interest and practical importance to push quantum teleportation towards more macroscopic objects . * * * * observing quantum phenomenon in macroscopic objects is a big challenge as their strong coupling to the environment causes fast decoherence which quickly pushes them to the classical world . for example , quantum coherence is hard to survive in mechanical vibration of macroscopic solids , which involves collective motion of a large number of strongly interacting atoms . despite this challenge , achieving quantum control for the optomechanical systems becomes a recent focus of interest with remarkable progress * * @xcite**. this is driven in part by the fundamental interest and in part by the potential applications of these systems for quantum signal transduction * * @xcite * * , sensing * * @xcite * * , and quantum information processing * * @xcite**. there are typically two routes to achieve quantum control for the optomechanical systems : one needs to either identify some isolated degrees of freedom in mechanical vibrations and cool them to very low temperature to minimize their environmental coupling * * @xcite * * , or use the ultrafast laser technology to fast process and detect quantum coherence in such systems * * @xcite**. a remarkable example for the latter approach is provided by the optomechanical control in macroscopic diamond samples * * @xcite * * , where the motions of two separated diamonds have been cast into a quantum entangled state * * @xcite**. in this paper , we report an experimental demonstration of quantum teleportation from light beams to the vibrational states of a macroscopic diamond sample of @xmath2 mm@xmath3 in size under ambient conditions . the vibration states are carried by two optical phonon modes , representing collective oscillation of over @xmath4 carbon atoms . to facilitate convenient qubit operations , we use the dual - rail representation of qubits instead of the single - rail encoding used in previous experiments * * @xcite * * and generate entanglement between the paths of a photon and different oscillation patterns of the diamond represented by two phononic modes . using quantum state tomography , we demonstrate entanglement fidelity of @xmath5 with the raw data and of @xmath6 after the background noise subtraction . using this entanglement , we prepare arbitrary polarization states for the photon and teleport these polarization states to the phonon modes with the bell measurements on the polarization and the path qubits carried by the same photon . the teleportation is verified by quantum process tomography , and we achieve a high average teleportation fidelity , about @xmath7 ( or @xmath8 ) after ( or before ) subtraction of the background noise . to verify the phonon s state before its fast decay , our implementation of teleportation adopted the technique of reversed time ordering introduced in ref . * * @xcite * * where the phonon s state is read out before the teleportation is completed . similar to the pioneering teleportation experiment of photons @xcite , our implementation of teleportation is conditional as the bell measurements are not deterministic and require postselecting of successful measurement outcomes . and generates a stokes photon in the forward direction and an excitation in the optical phonon mode of the diamond ( denoted by the state @xmath9 ) . the optical phonon mode corresponds to relative oscillation of the atoms in each unit cell of the diamond lattice , as illustrated by the figure on the right side . a read beam after a controllable delay converts the phonon excitation to an anti - stokes photon which can be used for state readout . the corresponding wavelengths and frequencies are shown in the figure . the state @xmath10 denotes the electron conduction band which is far detuned from the optical excitation . * b * , a scheme for generation of entanglement between a phonon in the diamond and a propagating photon . the phonon state is represented by a superposition of different oscillation modes of the diamond , while the photon state is represented by its spatial modes . * c * , readout of the phonon state with the read beams by coherently converting the phonon modes into the corresponding anti - stoke photon modes . * d * , a teleportation scheme using the photon - phonon entanglement . an input state is prepared by the message sender , alice , on the photon s polarization degree of freedom . the photon thus carries two qubits , one by its polarization and one by its spatial modes . alice performs bell measurements on these two qubits . conditional on certain measurement outcomes , the phonon state is projected to the same state input on alice s side , which is read out and verified by bob , the message receiver . , width=321,height=264 ] we illustrate our entanglement generation and quantum teleportation scheme in fig . 1 , using a type iia single - crystal synthetic diamond sample cut along the @xmath11 face from the element six company . due to the strong interaction of atoms in the diamond , the optical phonon mode , which represents relative oscillation of the two sublattices in the stiff diamond lattice ( see fig . 1a ) , has a very high excitation frequency about @xmath12 @xmath13 near the momentum zero point in the brillouin zone . the corresponding energy scale for this excitation is significantly higher than the room temperature thermal energy ( about @xmath14 @xmath13 ) , and thus the optical phonon mode naturally stays at the vacuum state under ambient conditions , which simplifies its quantum control * * @xcite**. the coherence life time of the optical phonon mode is about @xmath15 ps at room temperature , which is short but accessible with the ultrafast laser technology for which the operational speed can be up to about @xmath16 thz * * @xcite**. we excite the optical phonon modes through ultrafast laser pulses of duration around @xmath17 fs from the ti - sapphire laser , with the carrier wavelength at @xmath18 nm . the diamond has a large bandgap of @xmath19 ev , so the laser pulses are far detuned from the conduction band with a large gap about @xmath20 thz . each laser pulse generates , with a small probability @xmath21 , an excitation in the optical phonon mode and a stokes photon of wavelength @xmath22 nm in the forward direction ( see fig . 1a ) . the relevant output state has the form @xmath23 |\text{vac}\rangle , \ ] ] where @xmath24 and @xmath25 represent , respectively , the creation operators for an optical phonon and a stokes photon , and @xmath26vac@xmath27 denotes the common vacuum state for both the photon and the phonon modes . to generate entanglement , we split the laser pulse into two coherent paths as shown in fig . 1b , and the pulse in each path generates the corresponding phonon - photon correlated state described by eq . when there is an output photon , in one of the two paths , it is in the following maximally entangled state with the phonon excitation@xmath28here , @xmath29 or @xmath30 represents an excitation in the upper or lower path , and its subscript denotes the nature of the excitation , `` n '' for a phonon and `` t '' for a photon . we drop the vacuum term in eq . ( 1 ) as it is eliminated if we detect a photon emerging from one of the two paths . after entanglement generation , the photon state can be directly measured through single - photon detectors . to read out the phonon state , we apply another ultrafast laser pulse after a controllable delay within the coherence time of the optical phonon mode and convert the phononic state to the same photonic state in the forward anti - stokes mode at the wavelength of @xmath31 nm ( see fig . the state of the anti - stokes photon is then measured through single - photon detectors together with linear optics devices . note that the retrieval laser pulse could have a carrier frequency @xmath32 different from that of the pump laser . for instance , with @xmath32 near the telecom band , our teleportation protocol would naturally realize a quantum frequency transducer that transfers the photon s frequency to a desired band without changing its quantum state . a quantum frequency transducer is widely recognized as an important component for realization of long - distance quantum networks * * @xcite**. to realize teleportation , we need to prepare another qubit , whose state will be teleported to the phonon modes in the diamond . similar to the teleportation experiments in refs . * * @xcite * * , we use the polarization state of the photon to represent the input qubit , which can be independently prepared into an arbitrary state @xmath33 , where @xmath34 and @xmath35 denote the horizontal and the vertical polarization states and @xmath36 are arbitrary coefficients . the bell measurements on the polarization and the path qubits carried by the same photon can be implemented through linear optics devices together with single - photon detection ( see fig . 1d ) , and the teleported state to the phononic modes is retrieved and detected through its conversion to the anti - stokes photon . same as ref . * * @xcite * * , the short life time of the diamond s vibration modes requires us to retrieve and detect the phonon s state before applying detection on the stokes photon , thus the phonon s state is measured before the teleportation protocol is completed . the reversed time ordering in this demonstration of quantum teleportation makes it unsuitable for application in quantum repeaters which requires a much longer memory time , however , it does not affect application of our teleportation experiment for realization of a quantum frequency transducer or a new source of entangled photons as discussed above . mhz , a carrier wavelength of @xmath18 nm , and a polarization along the @xmath37 direction , are split by a birefringent calcite into two coherent paths with equal amplitudes . after rotation of the pulse polarization to equal superposition of @xmath38 and @xmath39 again with a half wave plate ( hwp1 ) set at @xmath40 , we introduce a time delay of @xmath41 fs to the two polarization components @xmath42 and @xmath43 with a birefringent bbocrystal . we use the lead pulse of @xmath42 polarization as the write beam and the lagged pulse of @xmath43 polarization as the read beam . after semicircle hwps set at @xmath44 and @xmath45 , respectively , at the upper and lower paths , the polarization states of the pump beams are shown in the figure before the diamond sample . the write beam is focused by the lens l1 on the diamond sample and generates a stokes photon in one of the paths and an excitation in the corresponding optical phonon modes of the diamond . the stokes photon , at the wavelength of @xmath22 nm , is transmitted by the dichromatic mirror dm1 after the collection lens l2 , with its two paths recombined by the calcite c2 . to verify entanglement , we do not need hwp3 and the optical elements in the state preparation box . the lens l3 and l4 are used to adjust the distance between the two optical paths so that they can be combined at the calcite c2 . the single - photon detector" +"the solar p - mode parameters have been demonstrated to vary with time and to be closely correlated with the solar activity proxies ( chaplin et al . [ 1 ] ; salabert et al . [ 2 , 3 ] ; komm et al . these temporal variations provide insights to infer the interior of the sun and its structural and dynamical changes throughout the solar cycle . however , clear differences between p - mode frequencies and solar activity during the unusually minimum of cycle 23 have been reported ( broomhall et al . [ 5 ] ; salabert et al . the origin of the p - mode variability is thus far from being properly understood and a better comprehension of its relationship with solar ( and stellar , garca et al . [ 7 ] ) activity cycles will help us in our understanding of the dynamo processes . we analyzed observations collected by the space - based , sun - as - a - star instruments global oscillations at low frequency ( golf , gabriel et al . [ 8 ] ) and variability of solar irradiance and gravity oscillations ( virgo , frhlich et al . [ 9 ] ) onboard the _ solar and heliospheric observatory _ ( soho ) spacecraft . golf measures the doppler velocity in the d1 and d2 sodium lines ( garca et al . virgo is composed of three sun photometers ( spm ) at 402 nm ( blue ) , 500 nm ( green ) , and 862 nm ( red ) . a total of 5202 and 5154 days of golf and virgo observations respectively covering more than 14 years between 1996 and 2010 were analyzed , with respective duty cycles of 95.4% and 95.2% . these datasets were split into contiguous 365-day subseries , with a four - time overlap . the power spectrum of each subseries was fitted to extract the mode parameters ( salabert et al . [ 11 ] ) using a standard likelihood maximization function . subseries with duty cycles less than 90% ( basically around the soho vacation , 19981999 ) were removed . each mode component was parameterized using an asymmetric lorentzian profile , including the @xmath0 and 5 modes when visible . the temporal variations of the mode parameters were defined as the difference between reference values ( taken as the average over 19961997 ) and the parameters of the corresponding modes observed at different dates . their weighted averages over the central part of the 5-minute oscillation power ( @xmath12200 3400 @xmath2hz ) were then calculated . mean values of daily measurements of the 10.7-cm radio flux were used as a proxy of the solar surface activity . linear regressions were performed between the temporal variations of the mode parameters and the radio flux using independent points only . the color code in the following figures corresponds to the virgo blue , green , and red channels respectively . llll @xmath3 & @xmath4 & @xmath5 & @xmath6 + @xmath7 & @xmath8 & @xmath9 & @xmath10 + lll instrument & @xmath11 & correlation + golf blue period & @xmath12 & @xmath13 + golf red period & @xmath14 & @xmath15 + virgo blue & @xmath16 & @xmath17 + virgo green & @xmath18 & @xmath19 + virgo red & @xmath20 & @xmath21 + the temporal variations of the mode excitation and damping parameters from virgo were averaged over the @xmath22 , 1 and 2 modes . the changes in mode amplitudes @xmath3 and linewidths @xmath4 are shown on fig . [ fig : virgo_amp ] . note that due to absolute calibration problems and the changes of the observing wings , the golf amplitudes and linewidths are not exploitable for the moment . a proper calibration is currently underway . in order to compare with virgo , we performed , as described in sec . [ sec : anal ] , a preliminary analysis of the global oscillation network group ( gong , harvey et al . [ 12 ] ) @xmath22 data ( gong.nso.edu/data/ ) . similar fluctuations from the year 2006 in mode amplitudes ( open circles on fig . [ fig : virgo_amp ] ) and linewidths are observed as in virgo . the changes from maximum - to - minimum of the solar cycle are given in table [ tab : paramchanges ] and are consistent with previous work ( e.g. , jimnez - reyes et al . [ 13 ] ; salabert and jimnez - reyes [ 14 ] ) . + ( top row ) temporal variations ( @xmath23 ) in mode asymmetry @xmath11 ( a , b ) and in rotational splitting ( nhz ) ( e , f ) measured from golf data as a function of time and radio flux . the vertical dashed lines separate the blue- , red- , and blue - wing golf periods . ( bottom row ) temporal variations ( @xmath23 ) in mode asymmetry @xmath11 ( c , d ) and in rotational splitting ( nhz ) ( g , h ) measured from virgo data as a function of time and radio flux . the solid lines in panels b , d , f , and h represent the best fits from weighted linear regressions.,title=""fig : "" ] ( top row ) temporal variations ( @xmath23 ) in mode asymmetry @xmath11 ( a , b ) and in rotational splitting ( nhz ) ( e , f ) measured from golf data as a function of time and radio flux . the vertical dashed lines separate the blue- , red- , and blue - wing golf periods . ( bottom row ) temporal variations ( @xmath23 ) in mode asymmetry @xmath11 ( c , d ) and in rotational splitting ( nhz ) ( g , h ) measured from virgo data as a function of time and radio flux . the solid lines in panels b , d , f , and h represent the best fits from weighted linear regressions.,title=""fig : "" ] ( top row ) temporal variations ( @xmath23 ) in mode asymmetry @xmath11 ( a , b ) and in rotational splitting ( nhz ) ( e , f ) measured from golf data as a function of time and radio flux . the vertical dashed lines separate the blue- , red- , and blue - wing golf periods . ( bottom row ) temporal variations ( @xmath23 ) in mode asymmetry @xmath11 ( c , d ) and in rotational splitting ( nhz ) ( g , h ) measured from virgo data as a function of time and radio flux . the solid lines in panels b , d , f , and h represent the best fits from weighted linear regressions.,title=""fig : "" ] ( top row ) temporal variations ( @xmath23 ) in mode asymmetry @xmath11 ( a , b ) and in rotational splitting ( nhz ) ( e , f ) measured from golf data as a function of time and radio flux . the vertical dashed lines separate the blue- , red- , and blue - wing golf periods . ( bottom row ) temporal variations ( @xmath23 ) in mode asymmetry @xmath11 ( c , d ) and in rotational splitting ( nhz ) ( g , h ) measured from virgo data as a function of time and radio flux . the solid lines in panels b , d , f , and h represent the best fits from weighted linear regressions.,title=""fig : "" ] different temporal variations of the sun - as - a - star p - mode frequencies are observed between individual angular degrees @xmath22 , 1 , and 2 ( salabert et al . [ 6 ] ) and are consistent between the observations from golf and the 3 virgo / spms ( fig . [ fig : golf_freq ] ) . they might be interpreted as different geometrical responses to the spatial distribution of the solar magnetic field beneath the surface of the sun . moreover , the peculiar behavior of the individual modes around the long and deep activity minimum of cycle 23 is of particular interest . the peak asymmetry @xmath11 of the pairs @xmath24 = 0 - 2 and @xmath24 = 1 - 3 modes shows significant temporal variations with solar activity ( fig . [ fig : golf_asym ] and table [ tab : changeasym ] ) . similar changes are obtained between velocity ( golf ) and intensity ( virgo ) measurements , while jimnez - reyes et al . [ 15 ] found opposite variations . no significant correlation between asymmetry and signal - to - noise ratio is observed . no correlation is observed between the temporal variations of the mean @xmath25 and 2 rotational splittings and the 11-year solar cycle ( fig . [ fig : golf_asym ] ) . however , some similar fluctuations between golf and virgo are present . note also that the golf splittings show a jump between the red - wing period and the second blue - wing period starting end of 2002 . we analyzed more than 14 years of radial velocity and intensity helioseismic sun - as - a - star data collected by the space - based golf and virgo instruments respectively to study the temporal variations of the low - degree p - mode parameters ( excitation , damping , frequency , peak asymmetry , and rotational splitting ) with solar activity . the observed changes in excitation and damping parameters confirm previous results . the frequency shifts present differences between individual @xmath24 modes , for instance showing different minima for cycle 23 . the peak asymmetry shows significant and similar variations between radial velocity and intensity measurements . the rotational splittings do not show correlations with the 11-year solar magnetic cycle . the golf and virgo instruments onboard soho are a cooperative effort of many individuals , to whom we are indebted . soho is a project of international collaboration between esa and nasa . the 10.7-cm radio flux was obtained from the national geophysical data center . ds acknowledges the support of the grant pnaya2007 - 62650 from the spanish national research plan . this work has been supported by the cnes / golf grant at the sap cea - saclay" +"the interface between the a- and b - phase of he is the only known boundary between two superfluid systems . the interface motion that accompanies the first order phase transition from the undercooled a- into the b - phase is subject to extended experimental and theoretical investigation . within the hydrodynamic regime , the structure of the interface dynamics can be rigorously determined by connecting the hydrodynamic modes on both sides of the interface with the appropriate connecting conditions ( cocos ) . this has already been done @xcite for the planar interface . in the present work , we generalize the hydrodynamic description to interfaces of finite curvature , taking as an example spherical b - phase bubbles growing in a bath of undercooled a - phase . to gain a qualitative understanding , consider first planar growth . for small growth velocities , the released latent heat serves as the source for two second sound step functions , emitted in opposite directions @xcite . the steps move with @xmath0 and @xmath1 if the a - phase is located on the right and @xmath2 denotes the second sound velocity . if the interface velocity @xmath3 becomes larger than @xmath2 , both steps are left behind in the b - phase . the same is true for spin waves if an external magnetic field produces excess magnetization at the interface @xcite . the reference velocity is now of course the spin wave velocity @xmath4 , rather than @xmath2 . qualitatively , bubble growth is not much different , except that the surface tension delivers an extra push towards the energetically more favorable b - phase : neglecting the anisotropy , radial step functions of second sound are emitted out- and inward for @xmath5 . the inward moving step functions quickly equalize the temperature distribution within the b - phase bubble . for @xmath6 , both radial waves of second sound remain inside the bubble while the temperature remains homogeneous in the a - phase . the spin wave and the magnetization behave accordingly . ( though spin waves are emitted only for higher interface velocities @xmath7 @xcite ) the case @xmath8 may seem academic but one really can not discount the possibility that it was indeed already observed @xcite . then , even both spin waves remain inside the bubble where neither the temperature nor the magnetization is homogeneous . causality sees to it that the a - phase is completely unperturbed . the complication of bubble growth is in its time dependence . while planar growth keeps both @xmath3 and the amplitudes of the emitted waves constant , neither are in bubble growth . the growth velocity is not constant because the pushing surface tension , proportional to the inverse of the bubble radius @xmath9 , is not . the amplitudes are not constant , because first of all , they vary as @xmath10 when moving away from the interface ; second , the amplitudes in addition are functions of @xmath11 . ( in fact , there is a retardation effect , the amplitudes are functions of @xmath12 , where @xmath13 is the time of flight @xmath14 or @xmath15 . ) the anisotropy of @xmath2 and @xmath4 will distort the radial wave into an elliptical shape , with the principal axes being parallel and perpendicular to @xmath16 , the orbital preferred direction . ( we presume @xmath16 to be uniform . ) in addition , the growth and kapitza coefficients are also @xmath16-dependent , and this directly distorts the bubble . ( given enough time , of course , the surface tension will drive the bubble into the shape that minimizes the surface energy ; generally , it is somewhere inbetween , reflecting some stationary balance between the surface tension and the uneven growth . ) assuming the same eccentricity for both ellipses , we can rescale to obtain isotropic growth and radial waves to perform the calculations . afterwards , the distortion into elliptical waves is achieved by taking the correct value of the anisotropic velocity for the two principle axes . if there are many bubbles present , their growth can be considered completely independent for @xmath17 , because the magnetic signals barely feed back to the growth @xcite , while the second sound waves , which do feed back , are confined to the interior of the bubbles . for @xmath18 however , the many emitted second sound waves heat up the surrounding a - phase . since the latent heat is not completely evacuated , the growth velocity slows down accordingly . a b - phase bubble is thermodynamically stable only if its radius exceeds the critical value @xmath19 ) @xcite , where @xmath20 denotes the interface tension and @xmath21 is the difference in the chemical potential across the interface ( for every quantity @xmath22 , we define : @xmath23 and @xmath24 ) . since @xmath25 vanishes at the coexistence point , @xmath26 diverges if @xmath27 approaches @xmath28 . at lower temperatures , , where @xmath29 is the mean free path of the quasi particles , the hydrodynamic description becomes valid only after the bubble has nucleated and reached an appropriate size by ballistic processes . 1 shows the respective length scales as a function of temperature . as pointed out by leggett and yip @xcite the nucleation process itself is likely to be of exotic nature . the cocos @xcite , we shall employ fall into three categories , those for the conserved quantities , those for the symmetry variables and the parameterization of the surface entropy production . for the locally conserved quantities , the cocos state the continuity of the respective currents , expressing the fact that conserved quantities can not accumulate within , or be depleted from , a region of microscopic width . this is not true , however , if the momentum current traverses a curved interface , where the radial bulk momentum current differs by the interfacial momentum current @xcite @xmath30 . ( note that @xmath31 : in equilibrium the pressure is larger on the a - phase side . ) with prime denoting the rest frame of the interface , the cocos are : @xmath32 the notations : mass current @xmath33 , pressure @xmath34 , nonlinear part of the momentum current @xmath35 , energy current @xmath36 and spin current @xmath37 . the behavior of the symmetry variables in the interface region is related to the elasticity of the order parameter within the interface . since the elastic coefficients are of comparable order of magnitude in the interface as in the bulk liquid , we have coherence of the symmetry variables across the interface . more specifically , we have for the phase angle @xmath38 and the rotation angle @xmath39 in spin space @xmath40 it is by means of eq . ( [ rbphi ] ) that the interface tension acts in accelerating the growth process . since ( [ rbphi ] ) implies @xmath41 , the interface tension couples to the dynamics through the pressure dependency of the chemical potential and coco ( [ rbmomentum ] ) is implicitly incorporated . when the growth starts at @xmath42 we find the initial interface velocity to be twice as fast as in the planar case . this effect should be accessible to experimental probe . the irreversibility of the phase transition is accounted for by the growth coefficient @xmath43 for @xmath6 , and by the kapitza resistance @xmath44 for @xmath5 , respectively . both @xmath43 and @xmath44 are effective , integrated quantities and functions of various surface onsager coefficients , thermodynamic susceptibilities and bulk transport coefficients @xcite . the rate of interface entropy production @xmath45 is then respectively given as @xmath46 where @xmath47 is the entropy current . so except eq . ( [ rbmomentum ] ) , all cocos retain their form of planar growth . the solution of these cocos in sec . [ sec : dyn ] shows the following result : the growth velocity decreases with @xmath48 towards the limiting value @xmath49 ( of the planar growth ) ; while the amplitudes of second sound generated during the growth show some intricate time dependency . in sec . [ sec : spin ] , we discuss the magnetic signals emitted by the growing bubble . these are more accessible to experimental probe . the general case of @xmath50 interacting bubbles @xmath51 is discussed in sec.[sec : nbub ] . we consider the magnetic signals emitted during bubble growth for @xmath52 . as discussed in ref . @xcite , the magnetization is for @xmath53 essentially given by its equilibrium values @xmath54 . the small deviations from the equilibrium values do not change much , going from planar to bubble growth . for higher velocities , @xmath55 , the dipole - interaction is negligible , the magnetic signals turn into spin waves and become delocalized . here , the circumstances of bubble growth are more complicated and are what we shall consider . the feed - back of the spin - dynamics to the growth velocity @xmath56 is negligible if @xmath56 is not too close to @xmath57 @xcite . hence , we may take @xmath56 , as calculated in sec . [ sec : dyn ] without the inclusion of the magnetic fields , as an input : @xmath58 where @xmath49 denotes the limiting value of the interface velocity for large @xmath59 , i.e. @xmath60 of planar growth . the explicit values for @xmath49 are given in eqs . ( [ rpinfslow ] ) and ( [ rpinffast ] ) for weak and strong undercooling , respectively . the solution of the differential equation ( [ rpvt ] ) subject to the initial condition @xmath61 then reads @xmath62 the inverse of ( [ tauvx ] ) can also be written in a closed form , see app . [ app : xvtau ] . we shall work with the longitudinal model @xcite , which contains only two dynamical variables : the magnetization and the dipole angle @xmath63 ( where @xmath64 is that between @xmath65 and @xmath16 , and @xmath66 is the angle around @xmath67 ) . the initial scenario contains a b - phase bubble of radius @xmath68 , exposed to a homogeneous magnetic field @xmath69 . within the bubble , we assume a uniform @xmath67-texture , parallel to @xmath69 ; in the surrounding a - phase we have @xmath70 , @xmath71 . although the uniformity of the @xmath67-texture contradicts the equilibrium a - b interface @xcite , we shall neglect this complication as in ref.@xcite . the coordinates are chosen such that @xmath69 points in the z - direction , while the x - axis coincides with @xmath16 . the spin - hydrodynamics in the a - phase is then given by the wave equation @xmath72 where @xmath73 and @xmath74 denote the spin wave velocities parallel and perpendicular to the preferred direction @xmath16 . the consequences of neglecting spin diffusion will be discussed at the end of this section . [ sebwgl ] shows that the outgoing wave fronts will be of ellipsoidal shape with a rotational symmetry around @xmath16 . assuming a growing bubble with the same eccentricity , as discussed in the introduction , we may distort the coordinates to render both ellipsoids ( interface and wave front ) spherical : @xmath75 ( @xmath76 is the spin - superfluid velocity . ) the b - phase spindynamics need not be considered explicitly . after the initial time lag of @xmath77 , the imploding wave front meets at the center . there , the excess magnetization ( always parallel to the external field @xmath69 ) from opposite directions add up , while the spin superfluid velocities @xmath78 ( all having the same sign along the radial direction ) from opposite directions cancel . so homogeneous magnetization and vanishing @xmath78 is a good approximation . with @xmath79 , we can safely neglect terms of order" +"the celebrated kortweg - de vries ( kdv ) equation is a well - studied non - linear dynamical system , first evoked for the description of _ solitary waves _ @xcite in shallow water @xcite . it has , since then , found much applications @xcite . an integrable model @xcite , it arises from the compatibility condition of two linear equations , the well - known lax - pair @xcite . the fact that one of them is the linear schrdinger operator , connects this non - linear equation to quantum mechanical eigenvalue problem of the reflectionless potential @xcite . it has both localized and periodic cnoidal wave solutions , which appear in the lax equation as potentials , giving rise to bound states @xcite and band structure @xcite , respectively . a number of methods , viz . , inverse scattering @xcite , hirota bilinear @xcite etc . , have been developed to find the general multi - soliton solutions of the kdv hierarchy . the kdv solutions are connected by the miura transformation @xcite to the modified kdv ( mkdv ) equation @xcite , which also has found diverse physical applications . it appears in the description of van alfvn waves in collisionless plasma @xcite , phonons in anharmonic lattice @xcite , interfacial waves in two - layer liquid with gradually varying depth @xcite , transmission lines in schottky barrier @xcite and ion acoustic solitons @xcite , to mention a few . [ [ section ] ] in addition to the fundamental localized soliton solution : @xmath4 $ ] and its periodic counterpart , @xmath5 $ ] , recently real superposed solutions have been found to satisfy the kdv equation @xcite . here , we show that kdv equation possesses @xmath2-symmetric , localized and cnoidal wave solutions , which appear in complex conjugate pairs . interestingly , the sum of the paired solution is also a solution of the kdv equation , whereas the difference is not . the existence of these solutions can be traced to the fact that , there are two distinct mkdv equations , @xmath6 whose solutions are related through @xmath7 . the miura transformation for the solution of kdv , @xmath8 , then implies that , @xmath9 , is also a solution . we find complex @xmath2-odd solutions for the mkdv equation , where the sum and the differences of the pair are also solutions . this , in turn , generates more general complex superposed solutions for the kdv equation . the complex soliton solutions are analogs of bloch solitons in magnetic systems @xcite . the @xmath2-symmetric soliton solution is shown to be isospectrally related to the fundamental solution @xmath10 , in the lax equation . we start here with the kdv equation , @xmath11 where , @xmath12 , @xmath13 , @xmath14 and @xmath15 . it is straightforward to check that , the following pair of complex periodic solutions satisfy the kdv equation : @xmath17 , where @xmath18 , provided @xmath19 , @xmath20 and @xmath21 , @xmath22 being the modulus parameter . evidently , velocity c exhibits two disjoint domains : for @xmath23 , the solution is right moving , while for the remaining half , @xmath24 , it is left moving . it is interesting to note that , the sum of the complex pair is the well - known cnoidal wave solution , with @xmath25 and @xmath26 , whereas the difference of the pair is no longer a solution . the real ( @xmath27 ) and imaginary parts ( @xmath28 ) of the solutions are plotted in fig . 1 , which are even and odd functions of the argument , respectively . the fundamental soliton has higher intensity in comparison to the superposed solution . + fig . 1 : plots of real ( solid ) and imaginary ( dashed ) parts of @xmath29 , for @xmath30 ( purple ) and @xmath31 ( green ) . the inset shows intensities of superposed ( red ) and fundamental ( blue ) soliton solutions , with the latter being larger . for all the cases , @xmath32 . the following factorizable , superposed solution also satisfies kdv equation : @xmath34 , provided @xmath35 , @xmath36 and @xmath37 . as in the previous case , here also , oppositely propagating modes occupy two different domains of @xmath22 . the real and imaginary parts of the solutions are plotted in fig . also , addition of the paired localized solutions ( @xmath30 ) yields the fundamental soliton with higher intensity . 2 : plots of real ( solid ) and imaginary ( dashed ) parts of @xmath38 , for @xmath30 ( purple ) and @xmath31 ( green ) . the real parts are symmetric , whereas the imaginary ones are antisymmetric about @xmath39 . for @xmath32 , the inset shows intensities of superposed ( red ) and fundamental ( blue ) soliton solutions , with the latter being larger . for @xmath22 = 1 , superposed pairs reduce to @xmath2-symmetric complex form : @xmath40 . use of the cole - hopf transformation : @xmath41 , in one of the miura route : @xmath42 , yields @xmath43 . the galilean invariance of the kdv equation @xcite allows a constant shift in @xmath44 , leading to @xmath45\psi=0 $ ] , the one dimensional schrdinger equation with a scarf - type @xmath2-symmetric potential @xcite . soliton solutions can be generated through iso - spectral deformation of the potential @xcite , wherein both the wave function and the potential can change , leaving the spectrum invariant . depending on the number of bound states , this iso - spectral flow introduces parameters , suitably interpretable as time variables @xcite . the complex scarf potential is known to be iso - spectral to the real @xmath46 potential @xcite , explaining the common real eigenvalues for both these potentials . + + kdv also posseses real superposed singular @xcite solution : @xmath47 , with @xmath48 , @xmath49 and @xmath50 . for the mkdv equation , @xmath51 , there exist solutions in the form of complex superposition . the following parity odd superposition solution solves mkdv equation : @xmath53 , provided @xmath54 and @xmath55 . unlike kdv , the sum of the pair , as well as their difference , simultaneously satisfy the mkdv dynamics . in case of the sum , @xmath56 is an exact solution , when @xmath57 and @xmath58 , while for the difference , @xmath59 is also an exact solution , provided @xmath60 and @xmath61 . these form of solutions generate more general superposed solutions for kdv equation . the real and imaginary parts of the paired solutions are plotted in fig . 3 , which are odd and even functions of the argument , respectively . the corresponding intensity is constant , @xmath62 . 3 : plots of real ( solid ) and imaginary ( dashed ) parts of @xmath63 , for @xmath30 ( purple ) and @xmath31 ( green ) . the real parts are antisymmetric , whereas the imaginary ones are symmetric about @xmath39 . the inset shows intensities of individual ( black ) , added ( red ) and subtracted ( blue ) fundamental soliton solutions , with @xmath32 . another form of complex periodic pair will satisfy the mkdv equation : @xmath65 , provided @xmath66 , @xmath67 and @xmath68 . in case of @xmath30 , one obtains @xmath69 , which is odd under @xmath2 operation . it is interesting to note that , the velocity of the pair , @xmath70 is @xmath71 times the velocity of @xmath72 solution and the velocity of the pair , @xmath73 is @xmath71 times the velocity of @xmath74 solution . 4 plots the real and imaginary parts of the paired solutions , which again are odd and even functions , respectively . intensity associated with the excitation is constant , @xmath75 and is independent of the modulus parameter . real , singular superposition solutions of the form @xmath76 , also satisfy mkdv dynamics , with @xmath77 and @xmath78 . + fig . 4 : plots of real ( solid ) and imaginary ( dashed ) parts of @xmath79 , for @xmath30 ( purple ) and @xmath31 ( green ) . the real parts are antisymmetric , whereas the imaginary ones are symmetric about @xmath39 . the inset shows intensities of individual ( black ) , added ( red ) and subtracted ( blue ) fundamental soliton solutions , with @xmath32 . in conclusion , trivially @xmath2-symmetric kdv equation is shown to posses @xmath2-symmetric complex solutions , with asymptotically vanishing intensity for the solitons . in the corresponding lax equation , the @xmath2-symmetric potential supports real eigenvalues and is iso - spectrally connected to the real potential @xmath10 , the fundamental soliton solution . iso - spectral deformation @xcite has been useful in generating the multi - soliton solution for the kdv equation . the realization of the same in the case of complex @xmath2-symmetric potentials needs careful investigation . the fact that in the @xmath2-symmetric phase , an inner product @xcite is defined , may facilitate in obtaining these multi - soliton solutions through iso - spectral deformation . for the mkdv equation , @xmath2-odd solutions have been found to be exact solutions , which generate general @xmath2-symmetric potentials for the kdv equation , through miura transformation . the kdv and other integrable systems , like boussinesq hierarchy , manifest in two - dimensional induced gravity @xcite and conformal field theory @xcite . the implication of the complex @xmath2-symmetric solutions in the context of two - dimensional gravity is worth exploring ." +"some twenty years ago alexander and mctague applied the formalism of landau theory to the freezing transition of atomic materials @xcite . using symmetry arguments they suggested that a bcc crystal should be the universally favored crystal structure , independent of interaction details . this theory attempts to describe the solid as a small , spatially periodic perturbation of a liquid . in a recent paper @xcite we argued that such an approach should only be valid near the liquid - solid spinodal , at which the liquid state becomes locally unstable . the position of the spinodal is determined by the fourier transform of the liquid direct correlation function @xmath2 , and is given by the smallest density @xmath3 for which the equation @xmath4 has a solution . moreover , the perturbative approach does not apply to the local minima of the free energy in order - parameter space , which correspond to metastable or stable crystals , but rather to its saddle points . for the latter we confirmed universal behavior near the spinodal , which may have implications for nucleation @xcite . the hard - sphere fluid has become the canonical model for freezing , since it captures in the most simple form the dominant packing effects while attractive interactions are believed to play only a secondary role . the best current theories for hard - sphere freezing are various versions of density - functional theory ( dft ) @xcite . usually they are explicitely constructed to reproduce the percus - yevick approximation @xmath5 for the hard - sphere direct correlation function . in fig . [ fig : cpspin ] we show the values of @xmath6 evaluated at the wave number @xmath7 corresponding to the maximum at a given density @xmath3 . one finds that there is no solution to eq . ( [ spindef ] ) at physical densities @xmath3 below the space filling density @xmath8 where @xmath9 is the particle diameter ( at and beyond this limit @xmath5 is not defined ) . this implies that those dfts do not exhibit a liquid - solid spinodal at all . therefore the saddle point solution branch of the stationarity equation derived from the density functional can not connect to the liquid branch when the bulk density is increased . on the other hand , hard - core systems are characterized by a close - packing density as the maximum possible density of a given crystal structure . upon approaching this limit a suitably defined crystalline order parameter , e.g. , the inverse width of the density peaks , will diverge along the stable ( minimum ) branch . one may surmise that that is also true along the saddle point branch . thus an alternative scenario to the bifurcation of a crystalline solution from the liquid at a spinodal point as discussed in [ bif ] , are two solid solution branches smoothly connected to each other at low densities which diverge at close packing and are completely isolated from the liquid . in order to test this hypothesis in the present work we examine the close - packing limit in detail using dfts that have previously been applied to the low - density solid near the phase transition . clearly , the strong localization of the particles in this limit provides an extreme case for such liquid - state based theories . hence it is a good testing ground for assessing the qualities of different approximations . in contrast to most dft studies of the hard - sphere solid we do not restrict the shape of the density peaks to gaussians , but allow for general spherically symmetric peaks . this is especially interesting for the completely anharmonic hard - sphere crystal for which there is no a priori argument to justify gaussians , even for small amplitude particle oscillations . the starting point of density - functional theory is the free energy functional of the inhomogeneous particle density @xmath10 with the general form @xmath11=f_{id}[\rho({{\bf r}})]+f_{ex}[\rho({{\bf r}})].\ ] ] the ideal gas contribution is given by [ @xmath12 @xmath13=\int d^3r \rho({{\bf r}})[\ln\rho({{\bf r}})\lambda^3 - 1]\ ] ] with the thermal de broglie wavelength @xmath14 . while the excess part @xmath15 is not known exactly , a large number of approximate forms have been suggested and applied to various problems in the last decades @xcite . as we do not strive for completeness we will consider only two representative variants in this paper : the ramakrishnan - yussouff functional @xcite which is one of the first and simplest approximations that have been studied , and the fundamental measure functional developed by rosenfeld and coworkers @xcite which at the present is believed to provide the best theoretical description of the hard - sphere fluid . from a given functional the equilibrium density distribution at a given bulk density @xmath16 is obtained by minimization under the constraint @xmath17 . the value of the functional at its minimum is the actual free energy of the system . for both functionals we performed numerical calculations at a series of bulk densities as well as an analytical analysis of the close - packing limit which enables us to determine the asymptotic density profile and free energy . the ramakrishnan - yussouff functional follows from a density expansion of @xmath15 around the homogeneous state truncated at the quadratic term : @xmath18 here @xmath19 is the free energy density and @xmath20 the direct correlation function ( dcf ) of the hard - sphere liquid at an effective density @xmath21 , both of which are commonly approximated by the analytically known solutions of the percus - yevick integral equation . in a solid the density consists of a sum of identical peaks centered at the lattice sites @xmath22 : @xmath23 throughout this paper it is assumed that the peaks are normalized @xmath24 and that the nearest - neighbour distance @xmath25 in the lattice is determined by the bulk density , @xmath26 where @xmath9 is the particle diameter and @xmath27 is the maximum possible density . in order to reduce the dimensionality of the integrations we moreover assume that @xmath28 is spherically symmetric . deviations from this symmetry exist @xcite , but are small especially near close packing @xcite . however , in contrast to most solid phase calculations which assume @xmath28 to be gaussian here we do not restrict its shape . by insertion of eq . ( [ rhogen ] ) in eq . ( [ fry ] ) one obtains @xmath29 where @xmath2 is the fourier transformed dcf and the integral kernel is given by @xmath30 the angles @xmath31 , @xmath32 , and @xmath33 are those between @xmath34 and @xmath22 , @xmath35 and @xmath22 , and @xmath34 and @xmath35 , respectively , and @xmath36 . the contribution from @xmath37 simplifies to @xmath38 without loss of generality one may restrict the domain of @xmath28 to the wigner - seitz cell , so that the ideal contribution to the functional can be written as @xmath39.\ ] ] by minimizing and taking into account the normalization eq . ( [ rhonorm ] ) one finds the stationarity equation @xmath40}{4 \pi \int dr r^2 \exp[\frac{1}{4\pi } \sum_{{\bf r}}\int dr ' { r'}^2 \rho_\delta(r ' ) w(r , r',r)]}.\ ] ] the percus - yevick approximation for the hard - sphere dcf has the simple form @xmath41 the density - dependence of the coefficients @xmath42 can for example be found in [ hansen:86 ] . in the present context its most important feature is the cutoff at the particle diameter which leads to @xmath43 for @xmath44 . hence for the strongly peaked profiles in high density solids only the first shell of lattice vectors ( @xmath45 ) and the term with @xmath37 must be taken into account . we have calculated @xmath46 by numerical integration using the trapezoidal rule with @xmath47 mesh points , while an analytical expression for @xmath48 was derived from eq . ( [ wr0 ] ) . the stationarity equation is then discretized in @xmath49 and solved by iteration . an underrelaxation scheme @xmath50 proved helpful to ensure convergence . here @xmath51 is the profile after the @xmath52-th iteration and @xmath53 is the right hand side of eq . ( [ elggen ] ) calculated from @xmath51 . a typical value of the constant @xmath54 was 0.2 . the resulting profiles are shown in fig . [ fig : rhory ] . their width scales with the free distance @xmath55 that a sphere can move into the direction to its neighbour if the latter is kept fixed . the profile shapes approach a limiting form discussed below . their most striking property is the occurrence of a maximum at intermediate distances @xmath49 . this unphysical behavior vanishes in the close - packing limit . the dcf has been evaluated at the bulk density , @xmath56 . this most obvious choice has the disadvantage that the solid has a higher free energy than the liquid at all densities , as already pointed out in [ baus:85 ] . in the earliest dft work the density of the coexisting liquid has been used instead , but that is not very reasonable when high density solids are considered . other schemes to select a density @xmath21 of an `` effective liquid '' have been proposed [ baus:85,baus:89,evansrev:92 ] , which always imply @xmath57 . figure [ fig : rhoryliq ] shows density profiles obtained with an arbitrarily chosen value @xmath58 which is close to the freezing density . now the maximum does not occur and the convergence to the limiting shape is faster . the profiles are considerably flatter at small @xmath49 than a gaussian of the same width . the results shown in figs . [ fig : rhory ] and [ fig : rhoryliq ] clearly demonstrate that , in spite of contrary claims @xcite , simple density - functional theories based on the percus - yevick dcf do exhibit a well - defined close - packing limit at which the peak width goes to zero . we will analyze this limit in more detail in the following . let us assume that for small @xmath59 the profile behaves as @xmath60 with a width @xmath61 where @xmath62 with @xmath63 fixed . we shall show that the stationarity equation has a solution consistent with these assumptions . the ideal free energy in this limit becomes ( with @xmath64 and @xmath65 ) @xmath66.\ ] ] the relevant contributions to @xmath15 are @xmath67 and @xmath68 ) { \nonumber}\\ & = & 4\pi^2 c(\bar\rho,\sigma ) \tilde w(s , s',\alpha)+o(\delta)\end{aligned}\ ] ] where @xmath69 thus we finally have in leading order in @xmath70 @xmath71 where @xmath72 denotes the number of nearest neighbours . the total free energy can now be minimized in two different ways . first , one can restrict to profiles of a fixed shape @xmath73 , e.g. , gaussians , and differentiate only with respect to the scaled width @xmath63 for fixed @xmath0 which gives @xmath74 due to the form of @xmath75 for @xmath76 one has @xmath77 and thus the right hand side of eq . ( [ elgal ] ) also decays . on the other hand , for @xmath78 @xmath79 tends to a positive constant ( since @xmath80 is negative ) , thus its derivative will be negative for sufficiently well behaved @xmath73 . therefore the right hand side of eq . ( [ elgal ] ) is zero both at @xmath81 and @xmath82 and positive in between which implies a maximum at a finite value of @xmath63 . this can be explicitely checked for gaussians ( @xmath83 ) and step functions ( @xmath84 ) for which the integrals in eq . ( [ fexasy ] ) yield @xmath85 and @xmath86 . depending on the height of this maximum eq . ( [ elgal ] ) has zero or two solutions . in the first case there are no stationary points with vanishing" +"quantum mechanics ( qm ) , particularly featured by @xmath0 and @xmath1 , has been always facing the fundamental critics since its establishment @xcite . the exact physical meaning of `` quantum '' is unclear , which leads to the well - known `` weirdness '' . the development of quantum field theory ( qft ) , which is often viewed as an improved form of qm , does not resolve the seminal problems in qm , such as the direct physical meaning of wave function and phase , the role of quantization and measurement , etc . the problem of the foundation of qm has been widely concerned again due to the progress of quantum information and quantum computing ( qiqc ) @xcite . the concepts of nonlocality and entanglement have proven their importance , yet , there exist confusions between them @xcite . for the research of foundation of qm , we can briefly clarify two sub - fields , one is the interpretation of qm @xcite , the other is the post - qm @xcite . the problems and confusions on basic concepts even philosophy , such as the classical @xcite , hidden variable @xcite , collapse @xcite , etc are mostly addressed in the interpretations . post - qm also devotes to the complete mathematical form of qm , such as the information - theoretic approach @xcite , the khler structure approach @xcite , etc . the standard qm bases on several assumptions , and the physical explanations of the copenhagen ( orthodox ) interpretation are not satisfying . uncertainty and complementarity are emphasized ; however , for uncertainty , there are different explanations , either based on measurement , knowledge , propensity , or reality @xcite . for the statistical meaning of the wave function and measurement , the disagreement is more notable . born viewed statistics as inherent , while einstein , by epr - argument @xcite , viewed statistics as a result of incompleteness of qm . the notable `` jump '' and `` collapse '' do not have clear physical pictures . the most primary problem is that the copenhagen interpretation did not give an exact and direct meaning to the wave function , e.g. , why @xmath1 is complex ? indeed , there are direct efforts to explain the physical meaning of wave function , which led to the hidden variable method and bohm mechanics @xcite . every particle is endowed with definite coordinate and trajectory under the restraint of guiding wave . also , there exists the physical collapse theory aimed to explain collapse @xcite . however , it modifies the schrdinger equation and the linearity , which is shown to be the analogy of the approaches based on decoherence @xcite . coherence and decoherence , which were not demonstrated in the standard qm , have gained lots of attentions these years . for instance , the many - world interpretation @xcite views the universe as a coherent entity , and there exist the inner observer and relative state . the consistent ( decohered ) history approaches @xcite take the time evolution and measurement into account , and demonstrate the structure of quantum logic . in zurek s exsistential interpretation @xcite , the uncertainty principle is re - explained from the view of information , and the born s rule is deduced via the symmetry of envariance . recently , kinds of information - theoretic theories @xcite are developed , where qm is viewed as a kind of information processing theory . with all these progresses , however , the exact essence of quantum has not been drawn . at the same time , the continuous argument on foundation of qm also arose the reflection of the primary philosophical conception , which can not be avoided in the quantum physics . the problem that why we can not easily understand qm just brings the problem that why we think the classical mechanics ( cm ) is normal . in this paper , our standing point is to view qm as a special kind of `` description '' of motion , from which , there is no good or bad of qm and cm @xcite . the theories , with equations and models , deal with the same nature only revealing different aspects and properties . the state vector in hilbert space can capture the properties of coherence , e.g. , interference , which is exotic for cm . on the contrary , trajectory is the basic idea in cm and the macroscopic world , yet , not in qm , due to the uncertainty . we note the trajectory in the path - integral method , which borrows ideas from cm , only has mathematical meaning . in practice ( reality ) , to employ which description depends on its efficiency . in this work , we start from one new concept , `` scope '' , to check the foundation of qm . we focus on the basic concepts and ideas in qm , mostly relating to superposition . we do not intend to construct a broader theory with the standard qm as the special case , the methods based on scope mainly belong to the interpretation of qm . scope describes the `` structure of motion '' , i.e. , the logic and systematic potential action region of the movement of a certain object ( system ) . that is , from scope we can get the ability and the whole structure of the motion of the matter . the merits of the concept of scope are multi - folds . firstly , the direct one , the weirdness of qm can be resolved based on scope , the wave function and superposition can get their physical meaning . secondly , the abstract qm can gain solid natural foundation and physical essence , i.e. , qm is a totally new kind of description different with cm ( including statistical mechanics ) and also relativity . thirdly , scope can bring new ideas . for instance , the wave function and superposition principle can also be used in the mesoscopic and macroscopic scales , that is , the concept of scope is universal , can not be restricted by the scale . also , qm may not rely on the hilbert space , since scope itself can form a kind of space , also there can be other kinds of space , e.g. , tangnet @xcite , relating to quantum information and entanglement . forth , another point , the concept of scope may have new indication of the basic ideas of nature and philosophy , e.g. , it means every object has finite ability of motion . this work is divided into four parts . in sec . [ sec : open ] , we start from the concept of openness , which is central for qm , to clarify several basic physical ideas . in sec . [ sec : scope ] , we introduce the new concept of `` scope '' , from which we discuss the physical meaning of superposition and entanglement , and to address the foundation of qm . in sec . [ sec : entanglement ] , we study several kinds of quantum states , and we analyze the degree of entanglement and information . several topics are discussed in the appendix . one is the differences between scope and other existed methods , where we state that the concept of scope has never been proposed before . another one is the model for the reduced entanglement , by comparison with the two - body problem in cm . last , we study the physical meaning of entanglement measures at present , like negativity , relative entropy of entanglement . in sec . [ sec : conclusion ] , we conclude and discuss briefly the physical roles of scope in the foundation of qm . in this section , before the study on the concept of scope and entanglement , we show that the concept of openness is fundamental in qm . openness means that the quantum object can not be separated from the outside world , and the basic subject in qm is the open system , just the opposite of cm @xcite . the physical reason for openness is the existence of quantum coherence . we show that all the basic equations in qm demonstrate the openness and coherence . the quantum coherence leads to many crucial facts , such as the double - slit interference , coherent and squeezed state of light , also the heisenberg s uncertainty principle , etc . relating to measurement , the uncertainty principle states that any measurement disturbs the state of the quantum system , since the coherence is disturbed . on the contrary , the nature light from sun is not coherent as it is a kind of mixture . in cm , there is no coherence , which is the main distinction between quantum and classical dynamics @xcite . usually , in qm the method of density matrix @xcite is employed to capture coherence , which is represented by the non - diagonal elements . a diagonal density matrix is said to be classical as the coherence vanishes . in qft , there exists coherence since the quantum field itself is the coherent entity , such as vacuum , electromagnetical field etc , although the density matrix is not often used . `` coherent '' means that the field as a whole has fixed amplitude and phase . the micro - particles , as the excited state of field , have coherence since interactions between them are due to the field . the facts of particle creation , classicality , and decoherence lead to the degeneracy of coherence , yet , particle can go back to its ground state via the annihilation operator , thus , re - excite the coherence @xcite . in addition , we note that the standard qm does not focus on the properties of field , e.g. , the creation and vanish of particles , also the origin of ensemble , which we will discuss below . in qm , there was the argument that whether quantum theory describes the dynamics of the single system or the ensemble @xcite . according to the standard qm , the existence of ensemble is _ a priori _ fact . for instance , in the double - slit interference experiment , the ensemble of electrons is used , the electrons are viewed as identical , and the state of electrons are the superposition of two modes corresponding to the two slits . here , qm can not explain the origin of the ensemble ; in contrast , qft can give the creation - annihilation picture of the ensemble of electrons . the quantum states of each electron before entering the slit are not necessarily orthogonal , and there exists field among the electrons , that is , the existence of ensemble does not mean there is no coherence . yet , the methods of qm are believed as universal @xcite , thus , it should provide the physical picture for ensemble . recently , there are efforts to indicate the quantum origin of ensemble via entanglement @xcite . it is shown that the system within the coherent universe behaves as the canonical ensemble , as if the universe were in the mixed state , in which each pure state has the equal probability . physically , there can be kinds of coherence and decoherence processes in qm , which relates to the distinction between the fine - grained and coarse - grained description of states of the system @xcite . we will further analyze this in the study of density matrix below . in addition , we note that the concept of ensemble is similar to `` mixture ''" +"the heterogeneous network ( hetnet ) , where low - power low - complexity base - stations ( bss ) are overlaid with conventional macro bss , is being considered as a promising paradigm for increasing system capacity and coverage in a cost - effective way . due to orthogonal frequency division multiple access ( ofdma ) mechanism adopted in these networks , intra - cell interference is nearly null . however , the inter - cell interference ( ici ) potentially introduced by hierarchical layering of cells becomes a fundamental limiting factor to the hetnet performance . to cope with ici , fractional frequency reuse ( ffr ) , which was originally proposed in conventional macro - only networks @xcite , is considered to be an efficient technique for ofdma - based hetnets @xcite . compared to other ici coordination schemes , the ffr method requires minimal cooperation among bss and has a less complex operational mechanism , attracting the increasing research efforts @xcite . in a regular macro - only network as shown in fig . [ fig_macroffr ] , the design of ffr is relatively a simple task . the basic mechanism is to share the available frequency band among a reuse-1 pattern and three reuse-3 patterns . the _ reuse pattern _ ( or simply _ pattern _ ) is defined as a combination of on / off activities of bss . for example , the reuse-1 pattern simply activates all the bss , and a reuse-3 pattern activates only one bs among neighboring three bss . to allocate the frequency band to different cells can be viewed equivalently as allocating frequency resources among different patterns . as a simple approach suitable in this homogeneous network , we can optimize a single parameter @xmath0 to control the bandwidth allocated to universally reused subbands , and then divided the rest of bandwidth evenly among three reuse-3 modes . as a result , each cell can schedule less vulnerable users ( e.g. , at cell - center ) to the universal subbands and cell - edge users to the subbands with lower number of active bss . however , in a network consisting of macro and densely deployed small cells , the frequency reuse planning is no longer a simple task , due to the irregular cell location and overlaid cell deployment . the important challenges are : \1 . how can we select the most important patterns ? . how can we allocate the frequency resources among the selected patterns ? obviously , the above questions are highly coupled with the user traffic distribution and user association policy . a cell with less number of associated users will likely be allocated less frequency resources . in this paper , we target at jointly optimizing the user association and multi - cell frequency allocation , and shed light on the above questions . ffr has attracted lots of research efforts from both academia @xcite and industrial standardizations @xcite . the joint power and frequency allocation for ofdma ffr has also been studied , for example in @xcite and references cited therein . however , despite their coupled nature , the joint user association and frequency allocation for ffr has rarely been investigated . in @xcite , the authors studied a dynamic user association problem in a ffr network . however , the frequency partitioning is assumed given beforehand and fixed . in @xcite , the authors jointly optimized the user association , power and frequency allocation . however , the formulation and methodology only apply to the uplink sum rate maximization . in this paper , we formulate the joint user association and multi - cell frequency allocation problem by treating the frequency allocation as frequency partitioning among multiple patterns . to solve the obtained mixed - integer nonconvex problem , we develop a tabu search algorithm . tabu search is regarded as a metaheuristic that guides a local search procedure to explore the solution space beyond local optimality @xcite . our development is based on the effective exploitation of problem structure , hence results in a efficient algorithm . the proposed scheme significantly improves cell - edge and median user throughput compared to no frequency allocation , without sacrificing the overall network throughput . we also provide practical criterion to narrow down the number of candidate patterns to reduce the complexity . note that reuse pattern selection has been studied in a _ time division multiple access ( tdma ) _ macro - only network in @xcite , which is different from our formulation . besides , the hetnet deployment requires new criterion to select essential patterns . we consider a downlink ofdma hetnet , where a number of small cells are embedded in the conventional macro cellular network . the set of all cells is denoted as @xmath1 , and the cardinality @xmath2 . a set of users @xmath3 , with @xmath4 , are distributed in the network and we assume that each user is associated with only one serving cell . denote by @xmath5 the association indicator matrix , i.e. , @xmath6 if user @xmath7 is associated with cell @xmath8 , and @xmath9 otherwise . since each user is served by only one cell , we should have @xmath10 . we use @xmath11 to denote the channel gain between bs @xmath8 and user @xmath7 at subcarrier @xmath12 , where @xmath13 is the large - scale channel gain including path loss and shadowing , @xmath14 accounts for the small - scale fading . we assume @xmath15 are independent and identically distributed ( i.i.d . ) . following the shannon s formula , the ergodic rate of user @xmath7 served by @xmath8-th bs under pattern @xmath16 , in bit / s / hz , can be written as @xmath17\ ] ] where @xmath18 with @xmath19 denoting the fast fading coefficient between bs @xmath8 and user @xmath7 over an arbitrary frequency subcarrier , @xmath20 and @xmath21 are the transmit power of bs @xmath8 per hz and the received noise power per hz , respectively . we assume if bs @xmath8 is active transmit power is evenly distribute across all frequencies , i.e. , @xmath22 where @xmath23 is the total transmit power of bs @xmath8 and @xmath24 is the system bandwidth ; otherwise @xmath25 if bs @xmath8 is muted under pattern @xmath16 . we further assume uniformly distributed noise effect over frequencies . hence the ergodic rate of ( [ ratepercarrier ] ) is uniform across the whole bandwidth for any pattern . assuming that the set of users associated with the same bs share all the frequency resources according to a chosen scheduler , e.g. , round - robin scheduler ) . please see eq.(8 ) in @xcite ] , we can denote the average rate of user @xmath7 under pattern @xmath16 as @xmath26}\ ] ] where @xmath24 is the total bandwidth , @xmath27 represents the number of users associated with bs @xmath8 . given the set of all possible reuse patterns @xmath28 , @xmath29 , @xmath30 can can be pre - calculated using ( [ ratepercarrier ] ) and treated as constants . the resource allocation strategy is to distribute total @xmath24 bandwidth among different patterns . let @xmath31 be the allocation profile , where @xmath32 represents the fraction allocated to pattern @xmath16 and @xmath33 . then we can express the average user rate after frequency allocation as @xmath34 our objective is to maximize the long - term network utility by optimizing the joint pattern selection and user association , as rcl[problem1 ] _ , & & u ( , ) = _ k _ k ( |r_k ) [ obj ] + & & _ kb \{0,1 } [ integer constraint ] + & & _ b _ kb = 1 , k + & & _ i 0 , i + & & _ i _ i = 1 where @xmath35 is expressed in ( [ ratecombined ] ) , and @xmath36 provide a means for service differentiation . note that our developed algorithm can also work for any other concave utility functions . the formulation of ( [ problem1 ] ) is a mixed - integer nonconvex problem . even we relax the integer constraint of ( [ integer constraint ] ) to allow any continuous value between 0 and 1 for @xmath37 , the resulting problem is still nonconvex because the objective function is not jointly concave in @xmath38 and @xmath39 . thus , the globally optimal solution is prohibitive for reasonably sized network . our contribution is to develop efficient algorithms to find out good solutions . the approach we adopted is based on the tabu search . tabu search has obtained optimal and near optimal solutions to a wide variety of combinatorial problems @xcite . in the following , we describe the details of the tabu search procedure to solve problem ( [ problem1 ] ) . generally speaking , tabu search starts from an initial solution and moves at each iteration from the current solution to the best one in its neighborhood , even if this leads to a deterioration of the objective function value , so as to allow escaping from local optimum . the search is guided by two types of memory : short - term and long - term memory . at each iteration , the move being performed is recorded in the short - term memory and the reverse move is forbidden ( i.e. , _ tabu _ ) for a certain number of iterations ( _ tabu tenure _ ) , to avoid cycling . the tabu status of a move can be revoked through an _ aspiration _ criterion if this move improves the best solution found so far . the long - term memory is used to force the search into previously unexplored areas of the search space by a _ diversification strategy_. the key elements of our tabu search is the follows . the definition of the search space is simply the space of all possible solutions that can be visited during the search . for the problem of ( [ problem1 ] ) , the search space could naturally be the set of all feasible @xmath38 and @xmath39 . the basic iterative step of any tabu search procedure involves moving from a current solution in the search space to one of its `` neighbors '' according to suitably defined neighborhood structure . in accordance with our definition of the search space , we define the neighborhood structure by considering moves in which a single strategy is modified , i.e. , the association of a single user , or the pattern profile @xmath39 is changed . hence , the number of neighbors in our definition is @xmath40 . one advantage of our definition of the neighborhood is that it allows efficient evaluation of the objective function for _ all _ possible neighbors of the current solution . note that if the integer variable @xmath38 is given the problem of ( [ problem1 ] ) becomes a convex problem in @xmath39 , which can be easily solved by some off - the - shelf approaches @xcite . on the other hand , for fixed @xmath39 the evaluation of the objective function by allowing only a single user to change its association can be directly calculated by simple arithmetic operations . at current iteration , if user @xmath7 changes its association from bs @xmath41 to @xmath42 , we declare tabu moving user @xmath7 back to bs @xmath41 no matter from which bs , and record this in the tabu list as @xmath43 . on the other hand , if pattern profile @xmath39 is modified at current iteration , we record @xmath44 in the tabu list ( by treating the profile parameter @xmath39 as the @xmath45-th user ) . a new move is forbidden as long as it remains on the tabu list . the" +"the rs cvn binary system class is loosely defined as consisting of a chromospherically active evolved star orbiting within a few days around a main - sequence or subgiant companion ( hall 1976 ) . their short rotation period implies high levels of activity ( e.g. , noyes et al . 1984 ) , observed as strong emission of chromospheric lines and saturated x - ray emission ( dempsey et al . 1993 ) . the high - resolution x - ray spectra of the brightest and nearby rs cvn binary systems obtained by _ xmm - newton _ are well - exposed and provide a high signal - to - noise ratio . abundant coronal elements ( c , n , o , ne , mg , si , s , ar , ca , fe , and ni ) produce a rich spectrum of electronic transitions in the euv and x - rays , allowing us to perform benchmark studies of atomic databases . recent results with _ chandra _ and _ xmm - newton _ show that models reproduce the observed spectra fairly well ( e.g. , audard et al . 2001a , behar , cottam , & kahn 2001 ) , although a significant number of lines , mainly from si , s , ar , and ca l - shell lines , are either absent in the atomic databases or are not properly reproduced ( audard et al . in this study , we have therefore discarded wavelength ranges where such lines dominate in order not to bias the convergence of the spectral fits , and especially to get more accurate elemental abundances . past stellar coronal abundance determinations have been done with ccd spectra of moderate spectral resolution ( e.g. , drake 1996 , gdel et al . 1999 ) or with low sensitivity spectrometers ( e.g. , drake , laming , & widing 1995 , laming , drake , & widing 1996 , schmitt et al . 1996 , drake , laming , & widing 1997 ) . abundance studies of stellar coronae are a powerful means to better understand the well - studied , but still puzzling , abundance pattern in the sun : in brief , the solar corona and the solar wind display a so - called `` first ionization potential '' ( fip ) effect , for which the current consensus is that the abundances of low - fip ( @xmath0 ev ) elements are _ enhanced _ relative to their respective photospheric abundance , while the abundances of high - fip ( @xmath1 ev ) elements are photospheric ( e.g. , haisch , saba , & meyer 1996 ) . stellar coronal spectra often showed a metal abundance deficiency relative to the _ solar _ photospheric abundances ( schmitt et al . 1996 ) , with fe / fe@xmath2 in active rs cvn binary systems . more detailed studies with _ euve _ showed either the absence of any fip - related bias ( drake et al . 1995 ) , or the presence of a fip effect in inactive stellar coronae ( drake et al . 1997 ) . the current generation of x - ray observatories , _ xmm - newton _ and _ chandra _ , combine high spectral resolution with moderate effective areas to routinely obtain excellent data to measure abundances in stellar coronae . an analysis of a deep exposure of the _ xmm - newton _ rgs spectrum ( brinkman et al . 2001 ) of the rs cvn binary system hr 1099 showed a trend towards enhanced high - fip elemental abundances ( normalized to o and relative to the solar photospheric abundances , anders & grevesse 1989 ) , while low - fip elemental abundances were depleted ; this effect was dubbed the `` inverse fip '' effect . different active stars also show such a trend ( gdel et al . 2001ab ) , while the intermediately active binary capella displays neither a fip nor an ifip effect ( audard et al . it is practice to normalize stellar coronal abundances to the _ solar _ photospheric abundances , while they should better be normalized to the _ stellar _ photospheric abundances . the latter are , however , hard to measure due to enhanced chromospheric activity , high rotation rate and the presence of spots in active stars , particularly in rs cvn binaries . nevertheless , for some stars , photospheric abundances are known . gdel et al . ( 2002 ; also in these proceedings ) discuss the transition from an inverse fip effect to a `` normal '' fip effect in the long - term coronal evolution from active to inactive solar analogs ; all targets have photospheric abundances indistinguishable from those of the sun , which suggests that the observed transition is real . while low - fip elements appear underabundant in the quiescent state , a notable increase of the abundances of `` metals '' during flares is often observed ( e.g. , ottmann & schmitt 1996 , favata et al . 2000 ) . more precisely , time - dependent spectroscopy of a large flare in ux ari ( gdel et al . 1999 ) showed that low - fip elements increased more significantly than the high - fip elements . a recent high - resolution x - ray spectroscopic study of a flare in hr 1099 with _ xmm - newton _ showed a similar behavior ( audard , gdel , & mewe 2001b ) . in this `` electronic '' paper , we present a study of abundances in rs cvn binary systems observed by _ xmm - newton_. in brief , it shows i ) a transition from an inverse fip effect to an absence of a fip bias with decreasing activity , compatible with a similar transition observed in solar analogs ( gdel et al . 2002 ; also in these proceedings ) , ii ) a depletion of low - fip elemental coronal abundances with increasing average coronal temperature , while high - fip elemental abundances stay constant , iii ) an enhancement of low - fip elemental abundances during flares , while high - fip elemental abundances again stay constant . and , and capella binned at 500 s. epic mos2 light curves are shown , except for capella where the sum of the rgs1 first and second order light curves is given , due to substantial pile - up and optical contamination of the epic data . note that the epic count rate for hr 1099 is smaller as we had to use an annulus extraction region to account for pile - up in the central part of the psf . also , note that only the quiescent part of hr 1099 has been included in the analysis ; see fig . 6 for the flare analysis ( also audard et al . 2001b ) . ] _ xmm - newton _ observed a number of rs cvn binary systems as part of the rgs stellar guaranteed time program ( see gdel et al . in these proceedings ) . here , we present an analysis of the quiescent observations of hr 1099 , ux ari , @xmath3 and , and capella . their light curves are shown in figure 1 and their high - resolution rgs spectra in figure 2 . the rgs1 , rgs2 , and epic mos2 spectra ( except for capella where no epic data are available ) were fitted simultaneously in xspec 11.0.1aj ( arnaud 1996 ) with the ` vapec ` model . we have removed significant parts of the rgs spectra above 20 to take into account the incompleteness and inaccuracy of the atomic database for non - fe l - shell transitions . additionally , some fe l - shell lines with inaccurate atomic data were not fitted . a free multiplicative constant model has been introduced for cross - calibration uncertainties , finite extraction region and , in the case of hr 1099 , an annulus - shaped extraction region . notice that rgs1 and rgs2 each suffer from the loss of one ccd , but the combined spectra cover the whole rgs wavelength range ( den herder et al . 2001 ) . here we present results from fits on a grid of 10 components with fixed t , but free em and abundances ( the latter linked between the components ) . figure 3 shows the coronal abundances normalized to the o abundance in order to ease comparison between the different stars . we used the solar photospheric abundances from anders & grevesse ( 1989 ) , except for the fe abundance which was taken from grevesse & sauval ( 1999 ) . the panels are ordered in decreasing activity from top to bottom . clearly , ratios for high - fip elements exceed the ratios for low - fip elements in very active stars ( hr 1099 , ux ari ) , while for the less active , not tidally locked @xmath3 and , a poor correlation is observed . in the intermediately active capella , no fip bias is present although a possible weak fip effect could be suggested . however , any bias is definitive only if coronal abundances of stars are compared to their respective photospheric abundances rather than to the solar values . unfortunately , few photospheric abundances are known for rs cvn binaries . @xmath3 and is an exception : we have used the abundances derived by donati , henry , & hall ( 1995 ) to normalize our coronal abundances ( fig . 4 ) . again , no clear correlation can be observed . such a procedure needs to be applied to stars that do show a clear ifip bias when normalized to solar photospheric values . new accurate measurements of photospheric abundances in these objects are timely . the `` average '' temperature of a stellar corona is an indicator of activity that is defined here as @xmath4 , where @xmath5 and @xmath6 are the 10-t model temperatures and emission measures , respectively . we present samples of the abundance ratios relative to o ( for the low - fip fe and the high - fip ne ) as a function of @xmath7 ( fig . data points from solar analogs ( gdel et al . 2002 ; in these proceedings ) have been added ; the panels show a very different behavior : while the fe / o ratios exponentially decrease with increasing temperature , the ne / o ratios show no correlation with the average coronal temperature . similar behavior is observed in other low - fip and high - fip elements , respectively . and relative to _ stellar _ photospheric abundances ( donati et al . 1995 ) as a function of fip . ] while the preceding results are valid fo a quiescent state , previous data showed that the average metallicity z or the fe abundance can increase during large flares . medium spectral resolution observations with _ asca _ allowed gdel et al . ( 1999 ) to obtain time - dependent measurements of several elemental abundances during a large flare in ux ari . they found that low - fip elements increased more significantly than the high - fip elements , although the latter could not be well - constrained due to blending ( ne ) or low signal ( ar ) . a similar behavior was observed with recent _ xmm - newton _ data of a flare in hr 1099 ( audard et al . 2001b ) . here we present results of a reanalysis of this flare applying a more recent calibration . figure 6 shows the fe / o and ne / o ratios as a function of the average temperature during quiescence" +"modified gravity ( for a review , see e.g. @xcite ) constitutes an interesting dynamical alternative to @xmath0cdm cosmology in that it is also able to describe with success the current acceleration in the expansion of our universe , the present dark energy epoch . the specific class of modified @xmath1 gravities ( for a review , see e.g. @xcite ) has undergone many studies which suggest that this family of gravitational alternatives for dark energy is able to pass the constringent solar system tests . the investigation of cosmic acceleration as well as the study of the cosmological properties of @xmath1 models has been done in refs . the possibility of a natural unification of early - time inflation with late - time acceleration becomes a realistic and quite natural possibility in such models , as is demonstrated e.g. in ref . @xcite . recently , the importance of modified gravity models of this kind has been reassessed with the appearance of the so - called ` viable ' @xmath1 models @xcite . those are theories which satisfy both the cosmological as well as the local gravity constraints , which had caused in the past a number of serious problems to some of the first - generation theories , that had to be considered now as only approximate descriptions from more realistic theories . the final aim of all those phenomenological models is to describe a segment as large as possible of the entire history of our universe , as well as to recover all local predictions of einstein s gravity that have been already verified experimentally , with very good accuracy , at the solar system scale . it is remarkable that , as was demonstrated in refs . @xcite , some of these realistic models lead to a natural unification of the early - time inflation epoch with the late - time acceleration stage . let us recall that , in general ( see e.g. @xcite , for a review ) , the total action for the modified @xmath1 gravitational models can be written as [ xxx7 ] s = d^4 x + s_(m ) . here @xmath2 is a suitable function of the scalar curvature @xmath3 , which defines the modified gravitational part of the model . the general equation of motion in @xmath4 gravity with matter is given by [ xxx22 ] g _ f(r ) - r _ f(r ) - g _ f(r ) + _ _ f(r ) = - t_(m ) , where @xmath5 is the matter energy - momentum tensor and @xmath6 is the derivative of @xmath1 with respect to its argument @xmath3 . for a generic @xmath1 model is not easy to find exact static solutions . however , if one impose some restrictions , one can proceed along the following lines . first , we may require the existence of solutions with _ constant _ scalar curvature @xmath7 , and we arrive at f(r_0)r_=g_. [ geneqrc ] taking the trace , we have the condition 2f(r_0)=r_0f(r_0 ) [ b ] and this means that the solutions are einstein s spaces , namely they have to satisfy the equation r_=g_= g _ , [ e ] @xmath8 being a solution of eq . ( [ b ] ) . this gives rise to an effective cosmological constant , namely _ eff==. [ l ] the purpose of our work will be to study the appearance of multiply de sitter space solutions in several realistic models of modified gravity . the occurrence of multiply de sitter solutions plays a fundamental role in modified gravity because it permits to describe the inflation stage as well as current @xmath0cdm cosmology in terms of this theory alone without any need for either fine - tuning of a cosmological constant nor of introducing extra scalar fields . in summary , this is a minimal and at the same time very powerful approach which circumvents some of the hardest problems of present day physics . one may argue that these theories are equivalent to introducing extra scalar fields , but this equivalence has been proven to hold at the classical level only , not at the quantum one . in addition , the cosmological interpretation of modified gravity solutions is different from that of scalar field cosmology . the paper is organized as follows . in the next section we discuss a viable modified gravity model @xcite in an attempt to study de sitter solutions there . it is shown that , for some values of the parameters , it is possible to find several de sitter spaces ( as a rule , numerically , for small values of the curvature exponent ) ; one of them may serve for the inflationary stage , while the other one can be used for the description of the dark energy stage . the evolution of the effective equation of state parameter is investigated numerically . 3 is devoted to the analysis of the same question in a slightly generalized model which is known to describe the unification of the early - time inflation with the late - time acceleration epochs @xcite . the same numerical investigation is carried out , and a multiply de sitter universe solution is constructed . in section 4 , the corresponding problem is investigated for a viable model of tangential modified gravity , proposed in ref . @xcite . having in mind the possibility to use a sds universe for the description of cosmic acceleration , those solutions for modified gravity are investigated in sect . comparison of the free energies of the de sitter and the sds solutions , for the viable model of the second section , is then made . finally , some outlook is given , together with the conclusions , at the end of the paper . in this section we will study de sitter solutions in realistic modified gravity models using a dynamical system approach . we shall start from the following form for the initial action @xmath9 , \label{1.1}\ ] ] where @xmath10 is some function of the geometrical invariants . in order to make use of the method of dynamical systems , we work in the metric corresponding to a spatially - flat frw universe , namely @xmath11 from here , the frw equation can be written in the following way ( for more details see ref . @xcite ) @xmath12 where @xmath13 the `` dot '' over the symbol means derivative with respect to time @xmath14 , while @xmath15 and @xmath16 represent the derivative of @xmath10 with respect to @xmath17 and @xmath18 respectively . in what follows we will mainly concentrate on the simplest case @xmath19 . let us consider the following choice for the function @xmath20 @xcite , which represents a very interesting subclass of viable modified gravitational models @xmath21 where the constant @xmath22 has dimension of mass , while @xmath23 , @xmath24 , @xmath25 are some positive dimensionless constants . note that here @xmath26 $ ] , @xmath27 , @xmath28 . after making variation , it is chosen @xmath29 . introducing a nonzero constant @xmath25 is here equivalent to introducing a shift in the effective cosmological constant , and for this reason we will assume @xmath30 in our further computations . finally , we can write eq . ( [ 1.3 ] ) for the function in ( [ 1.5 ] ) as @xmath31 , \end{array } \label{1.6}\ ] ] where @xmath32 . this equation can be rewritten as a dynamical system , namely @xmath33 it is easy to see that the critical points of this system are the de sitter points ( @xmath34 ) . to investigate the nature of these points we need to determine them explicitly , a non - trivial problem in the general case . it is however easy to obtain from ( [ 1.6 ] ) the equation satisfied by the critical points @xmath35 : @xmath36 the same result can be obtained directly starting from equation ( [ b ] ) of the previous section . it is convenient to introduce the notation @xmath37 , for further investigation of this equation . so , finally , we have @xmath38 first of all we find one ( trivial ) root of this equation @xmath39 ( it corresponds to @xmath40 ) , what allows us to reduce the order of the equation . ( note also that , if @xmath41 , eq . ( [ 1.9 ] ) takes a more complicate form and then it does not have the trivial root @xmath39 . ) but nevertheless the equation still is of @xmath42-order and in the interesting case ( @xmath43 ) ; this is too high and the roots can not be found algebraically . we need a specific discussion of this problem . it is clear that if there are too many ( say 10 or 20 ) de sitter points in the theory , it looks like a classical analogue ( at a reduced scale , of course ) @xcite of the string landscape vacuum structure in which case it will be far from trivial to obtain the standard cosmology . nevertheless , something can be done even in this case , by comparing the energies of the corresponding de sitter solutions , which should in fact differ , as is discussed in sect . v. using descartes rule of signs , we find that eq . ( [ 1.9 ] ) can have 2 or 0 positive roots . more detailed information can be obtained by using sturm s theorem . unfortunately it is not possible to apply it in the general case ( for arbitrary @xmath44 ) , so we need to investigate separately each of the different cases , @xmath45 , and see which one is more interesting from a cosmological viewpoint . we have therefore undertaken here a systematic analysis of all possible cases in this region of values of @xmath44 . computations are rather involved ( specially for larger @xmath44 ) , but the final results are not so difficult to describe analytically . we have found , for any of the values of @xmath44 considered , in the range above , that the number of roots depends on the parameter @xmath46 only , and that there is an @xmath47 such that , for @xmath48 , eq . ( [ 1.9 ] ) has no positive roots , while for @xmath49 , eq . ( [ 1.9 ] ) has two positive roots . we here now enumerate our results systematically : @xmath50 ; @xmath51 ; @xmath52 ; @xmath53 ; @xmath54 ; @xmath55 ; @xmath56 ; @xmath57 . note also that , near the critical point @xmath47 , both solution are very close to each other when they exist ( a real value of @xmath49 ) , and they are complex conjugate to each other for @xmath48 . this means that , in a situation where these two roots differ substantially , it must necessarily be @xmath58 . the ds - points described above can be used for the construction of inflationary or late - time acceleration behavior ( depending on the value of the scale factor @xmath59 ) . to this aim , the corresponding ds point must be unstable in the inflationary stage but can be either unstable or stable for the late - time acceleration one . however , this is in fact not a strictly necessary condition , since even for stable ds inflation , the exit from it can be achieved by a coupling with matter , through the effect of small non - local term or by some other mechanism . unfortunately , an all - round investigation of stability of the ds point turns out to be very difficult in the general case . for the recent analysis of critical points in more general modified gravity theories depending on all geometrical invariant see" +"physics of graphene perception begins when one compares landau levels in two dimensional schrdinger and dirac theories . such spectacular phenomenon as unconventional quantum hall effect @xcite is caused by the anomaly of the lowest landau level ( lll ) @xcite which for dirac fermions in graphene is field independent and can accommodate only half the usual number of the states from the conduction band and takes the other half from the valence band . the easiest way to accomplish this peculiar feature of the lll is to solve a pair of the dirac equations that describe excitations near two inequivalent @xmath0 points of graphene s brillouin zone . normally this is done in a constant homogeneous magnetic field , although this property of the lll for dirac fermions is topologically protected for inhomogeneous field configurations and in the presence of ripples @xcite . the simplest inhomogeneous field configuration which contains nontrivial aharonov - bohm physics can be created by an infinitesimally thin solenoid . in practice such magnetic field configuration may be obtained when a type - ii superconductor is placed on top of graphene or semicondunducting heterojunction hosting a 2d electron gas ( 2deg ) with quadratic dispersion . while graphene devices still have to be fabricated , devices like this with a superconducting film grown on top of a semiconducting heterojunction ( such as gaas / algaas ) hosting a 2deg have in fact been fabricated twenty years ago @xcite and theoretically well studied ( see e.g. refs . ) . theoretically a problem of the dirac fermions in the field of aharonov - bohm flux was encountered in the context of cosmic strings by gerbert and jackiw @xcite . while for the solutions of the dirac equation with nonzero angular momentum the square integrability requirement specifies which of the two independent solutions should be taken , they noticed this is not the case for the zero angular momentum . for the zero momentum there is an ambiguity as both solutions are square integrable , but divergent as @xmath1 at the origin , where @xmath2 is the space coordinate . the ambiguity of the solution selection is caused by the singular nature of the infinitesimally thin solenoid vector potential at the origin . this problem has initiated a vast theoretical literature which addresses interesting aspects related to the rigorous treatment of the solutions of the dirac equation with the aharonov - bohm potential ( see e.g. refs . for a review ) . in the condensed matter context the dirac fermions in the field of solenoid emerged during the study of the dirac - bogolyubov - de gennes quasiparticles in the vortex state of @xmath3-wave superconductors @xcite ( see also @xcite for a review ) . due to the divergence of the zero mode solutions theory predicts a formation of nonzero local density of states ( ldos ) near the vortex center . however , this theoretical prediction based on the dirac nature of quasiparticles in @xmath3-wave superconductors does not agree with the results of scanning tunneling spectroscopy ( sts ) measurements @xcite in high - temperature superconductors . finally we mention a related problem of the description of topological defects in graphene based on the dirac equation with a pointlike pseudomagnetic vortex which has also been studied intensively , see e.g. refs . . the purpose of the present paper is to study the electronic excitations in graphene in the field of the aharonov - bohm flux and compare them with the corresponding results for 2deg with a quadratic dispersion . we rely on the existing studies of the dirac fermions in the aharonov - bohm potential , but focus on the specific features of graphene such as the presence of two inequivalent @xmath0 points which implies that one should consider the solutions for both inequivalent irreducible representations of the dirac @xmath4 matrices . also to avoid unnecessary formal complications we consider the physical regularization of the problem modeling a finite radius flux tube created by the abrikosov vortex . we utilize the simplest case of magnetic field concentrated in a thin cylindrical shell of small but finite radius @xmath5 when @xmath6 @xcite . in contrast to high - temperature superconductors dirac description of the quasiparticles in graphene is proven valid under the different conditions . in particular , sts measurements of graphene flakes on graphite @xcite exhibit the structural and electronic properties expected of pristine graphene such as the development of a single sequence of pronounced landau level peaks corresponding to massless dirac fermions in a homogeneous magnetic field . we propose to perform sts measurements for graphene penetrated by vortices from a type - ii superconductor , because the dirac theory predicts rather peculiar behavior of ldos not expected for the 2deg with a quadratic dispersion of carriers . the paper is organized as follows . in sec . [ sec : model ] we introduce the model hamiltonians and discuss the regularization of the aharonov - bohm potential used in this work . [ sec : schrodinger ] is devoted to the nonrelativistic case , and the relativistic case is discussed in detail in sec . [ sec : dirac ] . the structure of both sections is the same : we consider the solution of the corresponding schrdinger or dirac equation , construct the green s function ( gf ) with coinciding arguments , obtain the dos and study the behavior of the ldos . in sec . [ sec : concl ] our final results are summarized . we consider nonrelativistic and relativistic hamiltonians . the 2d nonrelativistic ( schrdinger ) hamiltonian has the standard form @xmath7 where @xmath8 , @xmath9 with the vector potential @xmath10 , planck s constant @xmath11 and the velocity of light @xmath12 describes a spinless particle with a mass @xmath13 and charge @xmath14 . the dirac quasiparticle in graphene is described by the hamiltonian @xmath15 where the matrices @xmath16 and @xmath17 are defined in terms of the pauli matrices as @xmath18 here @xmath19 labels two unitary inequivalent representations of @xmath4 gamma matrices , so that one considers a pair of dirac equations corresponding to two inequivalent @xmath20 points of graphene s brillouin zone . in eq . ( [ hamilton - rel ] ) @xmath21 is the fermi velocity and @xmath22 is the dirac mass ( gap ) , which is introduced in the hamiltonian for generality . note that we consider the simplest case when the gap has the same sign for @xmath19 [ see ref . for a discussion of more general cases ] . while tight binding calculations show that the quasiparticle excitations in graphene have a linear dispersion at low energies @xcite and are described by the massless dirac equation with @xmath23 @xcite , recent sts measurements revealed a mass gap near the dirac point in a single layer graphene sample suspended above a graphite substrate @xcite . since this gap and its origin are intensively studied both theoretically and experimentally in the last few years , here we consider a generic case with a finite value of @xmath22 . the vector potential of a vortex at the origin directed in the @xmath24 direction is @xmath25 where @xmath26 is the flux of the vortex expressed via magnetic flux quantum of the electron @xmath27 with @xmath28 , . ] where the value @xmath29 corresponds to the flux created by the abrikosov vortex . the magnetic field is then @xmath30 the essential difference between the schrdinger @xmath31 and dirac @xmath32 equations in this case can be seen if one squares the latter : @xmath33 \right ) \psi = ( e^2 - \delta^2 ) \psi,\ ] ] where the commutator @xmath34 = -\frac{e}{\hbar c } b_z(\mathbf{r})\ ] ] which introduces pseudo - zeeman term which is related to the sublattice rather than the spin degree of freedom . it should be mentioned that in the case of graphene the components of the spinor @xmath35 are associated with a sublattice rather than a spin degree of freedom . since the hamiltonian ( [ hamilton - rel ] ) originates from a nonrelativistic many - body theory , the zeeman interaction term has to be explicitly added to this hamiltonian . this resembles the case of the nonrelativistic hamiltonian ( [ hamilton - nonrel ] ) which becomes pauli one when the interaction between the magnetic moment of the spin and an external magnetic field is added . in the present paper we do not include the spin degree of freedom neither in ( [ hamilton - nonrel ] ) nor in ( [ hamilton - rel ] ) . ( [ dirac - squared ] ) and ( [ commutator ] ) identify the origin of complications @xcite in the problem with a singular vortex ( [ a - singular ] ) when a singularity in @xmath36 occurs at a singular point of the differential equation ( [ dirac - squared ] ) . to avoid these complications one can consider a vortex with a finite radius flux tube @xcite , i.e. with the magnetic field and vector potential written in cylindric coordinates @xmath37 : @xmath38 where @xmath39 is a profile function with a compact support satisfying the normalization @xmath40 and connected to the profile function @xmath41 by the relation @xmath42 . the simplest choice of the field distribution @xmath39 which regularizes the problem with the solutions solely expressed in terms of bessel functions is a magnetic field concentrated on the surface of the cylinder of radius @xmath5 , @xmath43 . then , the corresponding profile function @xmath44 in the limit @xmath45 we recover the aharonov - bohm potential ( [ a - singular ] ) but avoiding formal complications . as shown in ref . @xcite , there is no dependence on the detailed form of @xmath39 in the limit @xmath6 provided that @xmath46 . in the present paper we restrict ourselves by considering the profile function ( [ step - profile ] ) . in this section we recapitulate the results of refs . for nonrelativistic case . they are important not only for comparison with relativistic case , but also because the relativistic result is constructed using the nonrelativistic one . in the limit @xmath47 the admissible solution of the schrdinger equation is always a regular solution which in polar coordinates @xmath48 takes the form @xmath49 where @xmath50 is the bessel function with the wave vector @xmath51 which is related to the quasiparticle energy @xmath52 via @xmath53 . the eigenfunction expansion for the retarded schrdinger gf reads @xmath54 or after substituting the wave function ( [ solution - nonrel ] ) it becomes @xmath55 where @xmath56 . since an analytic continuation of the gf ( [ nonrel - gf ] ) on the imaginary axis in the complex momentum plane , @xmath57 is free of singularities , it is convenient to work with the corresponding gf @xmath58 where @xmath59 in eq . ( [ nonrel - gf - continued ] ) we already set two arguments coinciding , @xmath60 , because in the present work we consider the dos only . as we will see below , the function @xmath61 is also used in the representation of the dos for the dirac fermions . after the calculation of the gf ( [ g - continued ] ) is done , the ldos per spin projection can be found by returning back to the real momentum axis @xmath62 the gf @xmath63 was calculated in ref . using the contour integration technique . a weak point of this calculation was discussed in @xcite , where the same method was applied to obtain the @xmath64-dependent contribution to the gf , @xmath65 with coinciding arguments when the approach of @xcite is valid . referring to the derivation of @xcite , here we simply start from the corresponding expression for @xmath66 obtained in ref . @xmath67 notice that eq . ( [ delta - g - marino ]" +"the investigation of stellar populations within the nearest 50 pc of the sun arouses great interest in the astronomical community . this is largely because a detailed study of the kinematics and statistical properties of a stellar ensemble in this region of the galaxy makes it possible to gain an insight into the genesis of the circumsolar region and to test the models of galactic structure and evolution . this is reflected in a whole series of papers ( see , e.g. , @xcite ; @xcite ) . dwarf stars ( predominantly m dwarfs , subdwarfs , white and brown dwarfs ) , which constitute the main population of the solar neighborhood , are noticeably brighter than more distant objects of this type , which makes them the most convenient and often the only accessible targets for studies . such empirical relations as mass luminosity and mass radius are important tests of the models for the structure of stars and their atmospheres . whereas theoretical models for comparatively massive stars ( 13 @xmath3 ) show good agreement with observations , there are difficulties for low - mass stars ( see , e.g. , @xcite ) . they can be overcome in part by improving the mentioned relations . this requires revealing a large number of binary systems and determining their orbits . the parameters of the mass function and the fraction of binary system in a given stellar population can be estimated on the basis of cosmogonic models . comparison of such estimates with observations enables a justified choice of the most probable scenario for the formation and evolution of stellar populations to be made ( @xcite ) . therefore , revealing binary systems among low - luminosity objects is an important research direction . the topicality of the problems under consideration contributed to the implementation of several projects in the 20th century aimed at detecting fast stars ( @xcite ; @xcite ) and determining their proper motions and trigonometric parallaxes ( @xcite ) . as a rule , the stars in the solar neighborhood are distinguished by large proper motions ( @xmath4 0.1 arcsec@xmath5yr@xmath6 ) . this has allowed a sample of low - luminosity objects to be produced by detecting such relatively fast objects on the basis of astrometric observations . not by chance , the lspm catalog of fast stars ( @xcite ) is invoked for the selection of low - luminosity objects more often than others . the passage to ccd detectors has rekindled interest in this subject matter . at present , several research groups in the world are actively working in this direction . for example , the recons group ( riedel et al . 2014 ) or the mearth project ( @xcite ) . a project to investigate stars with large proper motions was also implemented at the pulkovo observatory ( @xcite ) . the gaia space observatory has been operating at the lagrange point l2 already for more than a year . the main product of this space mission is an astrometric catalog ( coordinates , velocities , distances , photometric data ) of a billion stars down to 20@xmath7 . the final accuracy of the astrometric parameters will be unprecedentedly high ( for single 16 m stars , @xmath830 @xmath9as for the positions and 25 @xmath9as@xmath5yr@xmath6 for the proper motions ) . this will allow an enormous number of binary systems containing low - mass components to be detected and investigated ( @xcite ) . in many cases , reliable orbits will be constructed and the masses will be determined . note that the revolution periods for a large number of binary systems are considerably longer than the operation time of the gaia space telescope . therefore , a combination of ground - based and space observations performed at different epochs and gaia data seems promising for a global search of astrometric binaries among low - luminosity stars ( @xcite ) . such a combination of data from the fk5 and hipparcos catalogs has already shown the efficiency of this approach for analyzing the motions of the brightest stars in the sky ( @xcite ) . traditionally , to investigate the motions of the components of visual double stars , their observations are regularly carried out over decades ( @xcite ) . a careful analysis of the data series often leads to the detection of stars with invisible companions , also known as , astrometric binaries ( @xcite ) . for most nearby low - luminosity stars , we have no such dense , long , and homogeneous series of observations . we are dealing with occasional observations from different projects ( which makes them inhomogeneous from the standpoint of the accuracy and systematic errors of the stellar coordinates ) . the idea of searching for astrometric binaries under such conditions was implemented by @xcite as applied to the brightest stars in the sky ( stars from the fk6 catalog ) . it consists in the fact that the stellar proper motion determined at a large epoch difference ( 50100 yr ) reflects the mean motion of the photocenter of an unresolved stellar pair ( quasi - mean proper motion ) , while the proper motion determined in a time interval of @xmath810 yr corresponds to the instantaneous motion with some probability ( quasi - instantaneous proper motion ) . a statistically significant difference between these proper motions may suggest that we are dealing with a binary system . such stars are called @xmath2-binary candidates in wielen s terminology . physically , assigning a star to the category of @xmath2 binaries implies the detection of evidence for nonlinearity of its motion over the celestial sphere . several factors can be responsible for this effect . a classic example is an optically unresolvable binary system . in this case , we are dealing with a nonlinear motion of the binary s photocenter relative to its center of mass . a situation where the star being investigated is a component of a wide pair and the second star is too faint to be detectable in the images is possible . within the framework of the pulkovo program of research on stars with large proper motions , we have made an attempt to extend wielen s idea to fast stars . to improve the quasi - instantaneous proper motions , we performed astrometric observations of 1123 selected stars from the lspm catalog . the quasi - mean proper motions were taken from the lspm catalog . as a result , 70 @xmath2 binaries were revealed ( @xcite ) . a significant shortcoming of the previous study is that the original stellar coordinates from the catalogs and surveys ( m2000 , cmc14 , 2mass , sdss dr7 ) and the lspm proper motions represent the hcrf / tycho-2 system only formally . it is natural to expect more reliable results if the proper motions are determined just as was done in photographic astrometry or in the problem of determining the trigonometric parallaxes of stars . in this paper , we attempted to implement precisely this approach , i.e. , the ccd frames from different surveys were considered as a set of images entering into a single parallactic series . the parameters of the transition to the reference frame were calculated . the systematic errors of the stellar coordinates were taken into account . based on the derived set of coordinates for a program star in the system of the reference frame , we calculated the proper motions and quantities that allowed us to reach a conclusion about whether the star belongs to the category of @xmath2 binaries . our detailed technique and results are presented in the succeeding sections of this paper . as previously ( @xcite ) , stars from the lspm catalog were included in our program of observations . the main list contains 1972 stars down to 17@xmath7 in the declination zone from 30@xmath10 to 70@xmath10 . these are mostly stars with @xmath4 300 mas@xmath5yr@xmath6 ( 1507 stars ) . for various reasons , we added 465 stars . some of them have large photometric parallaxes ; a number of stars were added to analyze the possibility of investigating comparatively slowly moving objects ( @xmath4 100 mas@xmath5yr@xmath6 ) . the distribution of observational program stars over the celestial sphere is shown in fig . figure [ fig2 ] demonstrates how the program objects are distributed in total proper motion , magnitude , mass , and heliocentric distance . on the whole , this is an almost complete sample . the lspm catalog contains almost all existing fast stars down to @xmath11 ( @xcite ) . therefore , it can be said that the pulkovo observational program includes all of the stars that can be effectively observed in pulkovo in the corresponding ranges of magnitudes and proper motions . our ccd observations were carried out with the pulkovo normal astrograph ( d = 330 mm , f = 3500 mm ) from 2008 to 2015 . they were necessary to increase the accuracy of the quasi - instantaneous stellar proper motions . an s2c camera ( with a working field of @xmath12 arcmin at a scale of 900 mas / pix ) was used before 2014 . a sbig st - l-11k camera ( with a working field of @xmath13 arcmin at a scale of 530 mas / pix ) was installed in 2014 and 2015 . the imaging was performed at hour angles @xmath14 h by series from 5 to 10 frames with exposure times of 60 or 120 s , depending on the magnitude of the program star . in several cases , for faint stars the number of frames in a series was increased to 40 to achieve the required signal - to - noise ratio by the summation of individual frames . the concept of a virtual observatory , when the results of observations ( including the images of sky fields ) are accessible via the internet , has long been used in astronomical practice . the sky surveys containing ccd frames or scans of photographic plates of the entire sky or much of it are of interest to us . in this paper , we used data from sdss dr12 ( @xcite ) , 2mass ( @xcite ) , wise ( @xcite ) , and stsci dss ( @xcite)(scans of possi - o and possii - j plates ) . for all of the listed surveys , there is a convenient interface to request the fits files . the necessary data were downloaded automatically with a specially developed application , and it took several days to do so due to the large volume of wise data ( the fields in this survey were imaged with numerous overlaps ) . for wise , we used the frames of only the `` cold '' part of the mission in the w1 and w2 bands to ensure an acceptable signal - to - noise ratio for the images of faint stars . we analyzed all ccd frames and scans of poss1 and poss2 plates according to a unified scheme . a shapelet decomposition ( @xcite ) was used to fit the stellar images on each frame . the pixel coordinates of the stellar image photocenter were varied according to the scheme from the paper cited above to ensure the minimum of the sum of the residuals squared . the same principle was applied to automatically select the decomposition order . typical examples of the fits to the images of a comparatively bright star on the frames from different surveys are shown in fig . [ fig3 ] . on the whole , the image measurement technique works reliably . some problems were observed with the choice of a decomposition order for the sdss frames . based on the structure of the distribution of residuals , we can assume that the order" +"owing to proximity , the sun influences the earth s climate and environment . overwhelming evidence is building up that the solar cycle and related activity phenomena are correlated with the earth s global climate and temperature , the sea surface temperatures of the three ( atlantic , pacific and indian ) main ocean basins , the earth s albedo , the galactic cosmic ray flux that in turn is correlated with the earth s cloud cover and , indian monsoon rainfall ( hiremath and mandi 2004 and references there in ; georgieva _ et . _ 2005 ; hiremath 2006b ) . the transient parts of the solar activity such as the flares and the coronal mass ejections that are directed towards the earth create havoc in the earth s atmosphere by disrupting the global communication , reducing life time of the earth bound satellites and , keep in dark places of the earth that are at higher latitudes by breaking the electric power grids . owing to sun s immense influence of space weather effects on the earth s environment and climate , it is necessary to predict and know in advance different physical parameters such as amplitude and period of the future solar cycles . there are many predictions in the literature ( ohl 1966 ; feynman 1982 ; feynman and gu 1986 ; kane 1999 ; hathaway , wilson and reichmann 1999 ; badalyan , obrido and sykora 2001 ; duhau 2003 sello 2003 ; maris , poepscu and besliu 2003 ; euler and smith 2004 ; maris , poepscu and besliu 2004 ; kaftan 2004 ; echer _ et . _ 2004 ; gholipour _ et . al . , _ 2005 ; schatten 2005 ; li , gao and su 2005 ; svaalgaard , cliver and kamide 2005 ; chopra and dabas 2006 ; dikpati , toma and gilman 2006 ; du 2006 ; hathaway and wilson 2006 ; clilverd _ et . al . , _ 2006 ; tritakis and vasilis 2006 ; lantos 2006 ; lundstedt 2006 ; wang and sheeley 2006 ; choudhuri , chatterjee and jiang 2007 ; javaraiah 2007 ) on the previous and future 24th solar cycles and beyond . most of these studies mainly concentrate on prediction of the amplitude ( maximum sunspot number during a cycle ) . however , prediction of period ( length ) of a solar cycle is also very important parameter and the present study fills that gap . recently we modeled the solar activity cycle as a forced and damped harmonic oscillator that consists of both the sinusoidal and transient parts ( eqn 1 of hiremath 2006a ) . from the 22 cycles ( 1755 - 1996 ) sunspot data , the physical parameters ( amplitudes , frequencies , phases and decay factors ) of such a harmonic oscillator are determined . the constancy of the amplitudes and the frequencies of the sinusoidal part and a very small decay factor from the transient part suggests that the solar activity cycle mainly consists of persistent oscillatory part that might be compatible with long - period ( @xmath2 ) alfven oscillations . in the present study , with an _ autoregressive _ model and by using the physical parameters of 22 cycles , we predict the amplitudes and periods of future 16 solar cycles . thus prediction from this study can be considered as a _ physical and precursor _ method . a pth order _ autoregressive _ model relates a forecasted value @xmath3 of the time series @xmath4 $ ] , as a linear combination of @xmath5 past values @xmath6 , where the coefficients @xmath7 are calculated such that they minimize the uncorrelated random error terms , @xmath8 . the routine is available in idl software . important condition for using an _ autoregressive model _ is that the series must be _ stationary _ such that it s mean and standard deviation do not vary much with time . hence , one can not apply _ autoregressive model _ directly to the observed sunspot series as it consists of near sinusoidal trends whose amplitudes and the standard deviations entirely different for different solar cycles . on the other hand , the derived physical parameters of the forced and damped harmonic oscillator ( hiremath 2006a ) for all the 22 solar cycles are stationary and , hence in the following , we use an _ autoregressive _ model to predict the future 15 solar cycles . the solution of the forced and damped harmonic oscillator ( see the equation 1 of hirmath 2006a ) of the solar cycle consists of two parts : ( i ) the _ sinusoidal _ part that determines the amplitude and period of the solar cycle and , ( ii ) the _ transient _ part that dictates decay of the solar cycle from the maximum year and also determines bimodal structure of the sunspot cycle around the maximum years for some cycles . in the present study , we use physical parameters of the sinusoidal part only to predict amplitude and period of future cycles . using past 22 cycles physical parameters , we construct the next ( 23rd ) solar cycle and presented in fig 1 . except decaying part of the solar cycle , one can notice that the predicted curve exactly matches with the observed curve . with this encouragement and from an _ autoregressive _ model , the physical parameters of future 16 solar cycles are computed and reconstructed solar cycles are presented in fig 2 . for the coming cycles 24 - 38 , the results are summarized in table 1 . in table 1 , the first column represents the cycle number , the second column represents the year from minimum - minimum , the third column represents the period ( length ) of the solar cycle and , the last column represents the maximum sunspot number during a cycle . it is interesting to note that the amplitude of the cycle 24 is low compared to the amplitude of cycle 23 and is almost similar to average value computed from all of the predicted models ( @xmath9 ) . other interesting predictions are : ( i ) during the cycles 26 , 27 , 34 . 37 and 38 , the sun will experiences a very high solar activity , ( ii ) during cycle 31 ( 2087 - 2099 ad ) the sun will experiences a very low sunspot activity and , ( iii ) length of the solar cycles vary from 8.65 yrs for the cycle 33 to maximum of 13.07 yrs for cycle 25 . to conclude , the solar cycle is modeled as a forced and damped harmonic oscillator . from the previous 22 cycles sunspot data , the physical parameters such as the amplitudes , the frequencies and phases of such a harmonic oscillator are determined . the sinusoidal part of the forced and damped harmonic oscillator of previous solar cycles is considered for the prediction of future 16 cycles . with an _ autoregressive _ model and using previous 22 cycles parameters , coming 16 solar cycles are reconstructed from the predicted parameters . important results of this prediction are : the amplitude of coming solar cycle 24 will be smaller than the present cycle 23 and around 2087 - 2099 ad , the sun will experiences a very low sunspot activity . badalyan , o. g. , obrido , v. n & sykora , j. 2001 , solar physics , 199 , 421 chopra , p & dabas , r. s. 2006 , in the cospar proceedings , beijing choudhuri , a. r. , chatterjee , p & jiang , j. 2007 , astro - ph/0701527 clilverd , m. a. , clarke , e. , ulich , t. , rishberth , h & jarvis , m. j. , 2006 . space weather , vol 4 , s09005 dikpati , m. , toma , g. d & gilman , p. 2006 , geophys . lett . , 33 , l05102 du , z. l. 2006 , a&a , 457 , 309 duhau , s. 2003 , sol . phys . , 213 , 203 echer , e. , rigozo , n. r. , nordemann , d. j. r & vieira , i. e. a. 2004 , annales geophysicae , 22 , 2239 feynman , j. 1982 , jgr , 87 , 6153 feynman , j & gu , x. y. 1986 , rev . geophys . , 24 , 650 georgieva , k. , kiro , b. , javaraiah , j & krasteva , r. 2005 , planet . , 53 , 197 gholipour , a. , lucas , c. , arabi , b. n & shafiee , m. 2005 , solar . phys , 67 , 595 javaraiah , j. 2007 , mnras letters , doi : 10.1111/j.1745 - 3933.2007.00298.x hathaway , d. , wilson , r. m & reichmann , j. 1999 , jgr , 104 , 375 hathaway , d & wilson , r. m. 2006 , geophys . lett . , 33 , l18101 hiremath , k , m & mandi , p. i. 2004 , new astronomy , 9 , 651 hiremath , k. m. 2006a , a&a , 452 , 591 hiremath , k. m. 2006b , ilws workshop , goa , india , edts : gopalswamy , n and bhattacharya , a. , p. 178 kaftan , v. 2004 , in the proceedings of iau symp 223 , p. 111 kane , r. p. 1999 phys . , 189 , 217 lantos , s. 2006 , sol . , 236 , 399 lundstedt , h. 2006 , advance . res . , 38 , 862 mari , s. g. , popescu , m. d. , & besliu , d. 2003 , romanian . , 13 , 139 mari , s. g. , popescu , m. d. , & besliu , d. 2004 , in the proceedings of iau symp 233 li , k.j . , gao , p. x & su , t.w . 2005 , chin . j. astron . astrophys . , vol 5 , no 5 , 539 ohl , a. i. 1966 , sol . dannye , no . 12 , 84 sello , s. 2003 , a & a , 410 , 691 schatten , k. 2005 , geophys . res . let , 32 , l21106 svalgaard , l. , cliver , e. w & kamide , y. 2005 , geophysical . let , 32 , l001104 vasilis , t. , helen , m & george , g. 2006 , in the proceedings of aip conference , 848 , 154 wang , y. m & sheeley , jr , n. r. 2006 , nature phys , vol 2 , issue 6 , 367 rrrrrrrr 23 & 1996.00 - 2007.73 & 11.73 & 136@xmath114 + 24 & 2007.73 - 2017.07 & 9.34 & 110@xmath111 + 25 & 2017.07 - 2029.56 & 12.49 & 110@xmath111 + 26 & 2029.56 - 2041.50 & 11.94 & 157@xmath116 + 27 & 2041.50 - 2053.51 & 12.00 & 180@xmath118 + 28 & 2053.51 - 2064.30 & 10.80 & 140@xmath114 + 29 & 2064.30 - 2075.01 & 10.71 & 149@xmath115 + 30 & 2075.01 - 2086.79 & 11.78 & 118@xmath112 + 31 & 2086.79 - 2097.95 & 11.16 & 63@xmath16 + 32 & 2097.95 - 2108.84 & 10.89 & 108@xmath111 + 33 & 2108.84 - 2117.49 & 8.65 & 128@xmath113 + 34 & 2117.49 - 2126.92 & 9.43 & 170@xmath117 + 35 & 2126.92 - 2139.99 & 13.07 & 139@xmath114 + 36 & 2139.99 - 2151.74 & 11.75 & 159@xmath116 + 37 & 2151.74 - 2163.19 & 11.45 & 187@xmath119 + 38 & 2163.19 - 2175.48 & 12.29 & 187@xmath119 +" +"it is known that the distributions of income and wealth possess some robust and stable features which are independent of the economy - specific conditions @xcite . but the exact form of the distribution is still debated @xcite . it has been a tradition in the economics literature to model the left tail and the mode of the distributions of the incomes with a log - normal @xcite distribution and the right tail with a pareto distribution i.e. , a power law @xcite . however , a number of recent studies in econophysics literature argue that the left tail and the mode of the distribution is best described by the exponential or gamma distribution and the right tail of the distribution follows a power law ( see ref . also , a significant number of attempts have been devoted to explain the emergence of a consensus in a society and the possibility of a non - trivial phase - transition in the average opinion of the society ( see ref . @xcite ) . here , we propose a stochastic map which attempts to produce all of the aforementioned features at different limits and in addition , it shows some new features as well . below , we propose the model and discuss its relative merits and demerits with respect to the kinetic exchange models which also generates similar results . for related literature , see ref . @xcite for theoretical and numerical results on the kinetic exchange models of markets . @xcite for detailed analysis of the limit distributions of the solution of random difference equations ( of the form @xmath0 ; we will use only a few very particular instances of it ) . @xcite characterizes gamma distribution which arises from a random difference equation . @xcite was the first paper that suggested that multi - agent interactions in the kinetic wealth exchange models can be simplified and and viewed from from the point of view of a single agent . @xcite was possibly the first paper that connected the stochastic maps and the kinetic exchange models . the kolkata kinetic wealth exchange models have been successful to generate a realistic description of the income / wealth distributions ( see ref . many - body interactions are the key ingredients of this class of ( kinetic ) exchange models . in this paper , we mainly use a single agent framework to discuss the distributional issues . there is no agent - agent interaction in this model . in this regard , our treatment is closer to the _ representative _ agent paradigm of the modern economics . the specific structure of the market is also not discussed here . we represent the interaction of the agent with the market with a map of the following form , @xmath1 where @xmath2 , @xmath3 and @xmath4 are linear functions of a single parameter @xmath5 with @xmath6 such that @xmath7 for @xmath8=1 , 2 and 3 . we assume that @xmath9 , @xmath10 takes value either a positive , finite value ( we assume @xmath10 = 1 , for convinience ) or @xmath11 ( or a sufficiently large value ) and @xmath12 $ ] and independent , unless specified . in all the simulations , we have assumed @xmath13 = 1 . we denote the time index by subscripts for exogenous random variables ( @xmath14 and @xmath15 ) which we shall drop when no confusion arises . while the parameter space is seemingly too large to be considered in details , we shall restrict it considerably by assuming very simple forms of @xmath16 for all @xmath8 . we can interpret it in the following way . an agent has @xmath17 amount of wealth ( or money ) at time @xmath18 of which he saves a random fraction and invests the rest . his return from investment is represented by the additive term @xmath19 . however , there is an upper limit of @xmath17 represented by @xmath10 . since we interpret the random multiplicative term as the savings propensity , we assume that @xmath20 for all @xmath18 i.e. , savings propensity is never greater than 1 . our interest lies in finding the pdf ( probability density function @xmath21 ) in the steady state . it may be noted that the above map ( ignoring @xmath10 ) has the general form @xmath22 which has been studied in great details by ref . @xcite . in this paper , we have focused on a few particular instances of it for our purpose . ref . @xcite mapped the asset exchange models into ` random iterated function systems ' . but it was concerned with the ` yard - sale ' model and the ` theft - and - fraud ' model ( see ref . @xcite ) whereas we focus on the cc and ccm models ( the models that introduced fixed and distributed savings propensities in the kinetic exchange models ; see ref . @xcite ) and that is why we have borrowed the basic structure ( a fraction of the total wealth is saved and the rest is invested ) from the kolkata wealth exchange models ( i.e. , the cc and ccm models ) . we assume @xmath23 , @xmath24 , @xmath25 and @xmath26 . the equation becomes @xmath27 see fig . [ almostgamma ] for steady state distributions corresponding to different values of @xmath5 . we restrict our attention to the case @xmath28 as opposed to other positive numbers , for two reasons . one , this choice of @xmath29 makes the average a constant , independent of @xmath29 ( as the cc and ccm models ; see ref . @xcite ) and secondly , to simplify the calculations . we will relax this assumption in section [ subsec : case 2 ] where we will assume @xmath29 is negative and we will see that the exponents of the power law distributions differ for different values of @xmath29 . though we do not know the exact algebraic form of the steady state distributions produced by eqn . [ gamma1 ] , we can find out its moments in order to describe them qualitatively . we can ignore the time index in the steady state . taking expectations over both sides of eqn . [ gamma1 ] , we get @xmath30 also , we have the variance of @xmath31 as @xmath32 where @xmath33 . now , we make a few almost trivial observations . note the fact that @xmath34 . hence , @xmath35 can be written as @xmath36 ( by defn . of @xmath37 ) i.e. , @xmath38 . also , @xmath14 and @xmath15 are uniformly distributed . therefore , @xmath39 = 1/2 = @xmath40 and @xmath41 = 1/3 = @xmath42 ( recall that @xmath43 = 1/12 = @xmath44 ) . using all of these and by expanding eqn . [ variance ] we get @xmath45 \left(v(m)+1\right ) \nonumber\\ & & + \frac{1}{3}(1-\lambda)^2+\frac{1}{2}(1-\lambda^2)-1 . \nonumber\end{aligned}\ ] ] simplifying the above expression we get the result for @xmath46 , @xmath47 which clearly shows that the distribution tends to a delta function as @xmath48 . with @xmath5 = 0 , eqn . [ gamma1 ] produces a distribution with a sharp peak at @xmath31 very close to 1 . however , for @xmath49 this sharpness goes away . one can consider an even simpler case with @xmath50 = @xmath51 for all @xmath18 so that the map becomes @xmath52 which is almost the same as the usual kinetic exchange model with a constant savings factor i.e. , the cc model ( see ref . @xcite ; see also ref . @xcite ) , @xmath53 the variance of the distribution generated by eqn.[gamma3 ] is given by @xmath54 for the sake of completeness , we mention that the variance of the distribution generated by eqn . [ gamma4 ] is given by ( see ref . @xcite ) @xmath55 it is noteworthy that for @xmath56 , the distribution generated by eqn . [ gamma3 ] has a peculiar form which is known as dickman distiburtion ( see ref . @xcite ) . for @xmath57 , @xmath21 is flat and for @xmath58 , the distribution has a downward slope ( see fig . [ almostgamma1 ] ) . see ref . @xcite , for this type of maps which has been used in number theory , in biology ( see ref . @xcite ) and in many other areas ( see ref . @xcite ) . see ref . @xcite for simulations on the pdf generated by eqn . [ gamma3 ] with @xmath59 . it is to be noted that we can not generate an exponential distribution from eqn . [ gamma3 ] since its maximum variance is 1/2 ( for @xmath59 ) whereas the variance of the exponential distribution generated by the following eqn . ( see ref . @xcite ) @xmath60 is unity . hence this model can not generate purely exponential distribution which is a drawback since recent studies argue that the income / wealth distributions in the real world fits very well with exponential pdfs @xcite . it is trivial to note that in the usual kinetic exchange models , it is the presence of the trading partner s wealth @xmath61 ( in the @xmath8-th agent s wealth evolution equation ; eqn . [ exp ] ) that contributes to the higher variance . we assume @xmath23 , @xmath62 , @xmath63 and @xmath26 . the relevant equation is @xmath64 ref . @xcite studied this type of discrete stochastic equations ( see eqn . [ kesteneqn ] ) as a generic model for generating power law pdf . but a necessary condition for the mechanism to generate a power law pdf is that the random multiplicative term @xmath65 ( @xmath66 in eqn . [ power2 ] ) must be greater than 1 sometimes . in the current context , this condition is not satisfied ( according to our interpretation , @xmath67 is the savings propensity and hence it is always less than unity ) . to avoid this problem , we assume a population of agents each of which interacts with the market according to eqn . [ power2 ] . note that the agents do not interact among themselves . in the spirit of the kinetic exchange models , we show that if there is a population of @xmath68 agents with different @xmath5 but each of the income evolution process is modelled by eqn . [ power2 ] , then a power law in the income distribution will be observed . however , there is an important difference with the usual kinetic exchange models which are completely conservative . any trading activity in such markets would be a @xmath69 game i.e. , if somebody wins then his / her trading partner has to lose . we relax that assumption here . for simulations , we assume that there are 200 agents each endowed with an initial wealth equals to 1 . each of the agent s wealth evolution is governed by eqn . [ power2 ] . clearly , there is no interactions between the agents . however , the agents are assigned different @xmath5s which are fixed over time for any given agent ( see ref . @xcite ) . in particular , we assume that @xmath5 is uniformly distributed among the agents . for each agent , simulations are done for @xmath70 time - steps and the corresponding pdfs are averaged for @xmath71 time - steps . resulting distributions are averaged over all agents . following ref . @xcite , a very simple proof is considered below . note that ( in the steady state ) by taking expectations on both sides of eqn . [ power2 ] , we can rewrite it as @xmath72 by taking total differentiation and rearrenging terms , we get @xmath73 where @xmath31 represents @xmath74 . hence , the average amount of" +"in general relativity , the vaidya solution @xcite is a nonstatic generalization of the schwarzschild geometry and has some unique features . it describes the geometry of unpolarized radiation , represented by a null fluid emerging from a spherically symmetric source @xcite . therefore , the vaidya metric may model back - reaction effects for evaporating black holes ( bhs ) . glass and krisch @xcite extended the vaidya geometry to include both a radiation fluid and a string fluid ( see also @xcite by same authors ) by allowing the mass to be a function of both retarded time and distance along the outgoing null geodesics . the collapse of the null fluid described by the vaidya solution in the flat minkowski space has been studied by dadhich and ghosh @xcite . they first obtained the analogue of the vaidya line - element on the brane for studying the collapse of the null fluid in a flat minkowski cavity on the brane , the back reaction of the bulk on the brane , favouring formation of a bh against naked singularity ( see also @xcite ) . the end state of collapse of the null radiation with a string fluid was considered by govinder and govender @xcite . they also investigated the collapse of ricci - flat metrics and showed that the presence of a string fluid could lead to the appearance of locally naked singularity for null fluids . mcclure et al . @xcite analyzed cosmological versions of vaidya s radiating stellar exterior . they found a two - fluid solution that consists of a null fluid and an imperfect fluid which contains an inhomogeneous dark energy ( de ) component with negative energy density for the spacetimes of an accelerating cosmological reference frame . baccetti et al . @xcite assumed an early onset of bh evaporation and investigated its consequences for the simple system of a collapsing uniform thin shell , with an outgoing vaidya metric outside @xcite and minkowski metric inside . they obtained the equation of motion of the collapsing shell by means of the junction conditions on metric and the extrinsic curvature . the bh evaporation in conformal gravity was studied by bambi et al . @xcite . since massless particles are naturally conformally invariant , the simplest model of gravitational collapse in conformal gravity is given by the collapse of a thin shell of radiation with vaidya s space outside the shell and conformally - flat inside . they chose the radiation stress tensor to be that of a null dust ( see @xcite , where the authors generalized the vaidya solution in de rham - gabadadze - tolley massive gravity . our motivation in this paper is too look for a null fluid with nonzero radial pressure as the source of the vaidya geometry . sec.2 introduces the imperfect fluid stress tensor and studies its structure and the kinematical properties of a timelike congruence of observers . in sec.3 one calculates the total energy flow through a @xmath6 surface and its relation with the brown - york energy @xmath7 . a modified regular form of the vaidya metric is introduced in sec.4 and its properties are investigated . the modified quasilocal energy @xmath7 is analyzed in sec.5 , both as a function of @xmath4 and as a function of mass @xmath8 of the object , a celestial body or a bh . we conclude with some general remarks in sec.6 . throughout the paper we use geometrical units @xmath9 , unless otherwise specified . vaidya @xcite solved einstein s equations for a spherically - symmetric radiative body with the stress tensor of radiation @xmath10 , where @xmath11 is a null vector directed radially and @xmath2 is defined as the energy density of radiation measured locally by an observer with 4-velocity field @xmath12 , so that @xmath13 @xcite . the line - element can be written as @xmath14 where @xmath15 , @xmath16 is schwarzschild time coordinate , @xmath17 is the tortoise coordinate and @xmath18 is the advanced ingoing time coordinate . the parameter @xmath5 is the mass of the radiating spherically - symmetric object and @xmath19 stands for the metric of the unit two - sphere . we consider only the region @xmath20 for ( 2.1 ) , to avoid the signature flip at the horizon . it is valid for both ordinary celestial objects and for bhs . the geometry ( 2.1 ) is generated by the energy - momentum tensor given above , with only one nonzero component @xmath21 and zero trace , where @xmath22 . in other words , it corresponds to a null fluid with no pressures , i.e. , a null dust . that interpretation originates from the fact that the tensor @xmath23 resembles the stress tensor for a perfect fluid @xmath24 when @xmath25 . we remind that li et al . @xcite have not specified what is the 4-velocity @xmath12 , namely , what are its components . we consider now a different interpretation of the source of the vaidya metric and take the energy - momentum tensor corresponding to an imperfect fluid with energy flux @xcite @xmath26 where @xmath27 is the radial pressure , @xmath28 are the transversal ( tangential ) pressures , @xmath29 is the energy flux 4-vector and @xmath30 is a unit spacelike vector orthogonal to @xmath12 . we have @xmath31 and @xmath32 . we look now for the expression of the quantities @xmath33 for ( 2.2 ) and ( 2.3 ) to represent the same stress tensor . let us take a velocity vector field of the form ( for simplicity we replaced @xmath5 with @xmath8 ) @xmath34 i.e. an observer sitting at @xmath6 from ( 2.5 ) and the properties of @xmath30 , we find that @xmath35 as we previously specified , the mixed stress tensor which generates ( 2.1 ) has only one nonzero component : @xmath21 . defining , as obvious , the energy density of the null fluid as @xmath36 , it is an easy task to obtain @xmath37 where @xmath38 has been used . keeping in mind that @xmath39 , the expression for @xmath28 results immediately from ( 2.4 ) : @xmath40 , so that the fluid has no tangential pressures . the trace of ( 2.4 ) yields @xmath41 whence @xmath42 . hence , the null fluid has a nonzero radial pressure . from here we find that the isotropic pressure is @xmath43 , as for incoherent radiation . the current is obtained from ( 2.4 ) as @xmath44 which gives us @xmath45 and @xmath46 , as it should be for a null fluid . having now the physical parameters entering ( 2.4 ) , we may compare @xmath47 from ( 2.4 ) with that from ( 2.2 ) , to obtain @xmath48 whence @xmath49 with the help of @xmath50 from ( 2.5 ) , we get the components of the acceleration 4-vector of the congruence @xmath51 the proper acceleration reads @xmath52 and the scalar expansion is given by @xmath53 let us discuss briefly the energy conditions fulfilled by the stress tensor ( 2.4 ) . we consider our source of the vaidya solution is better than the standard one , where the radial pressure does not appear . it is hidden by the null vector @xmath54 which in our interpretation is a difference between a timelike vector @xmath12 and a spacelike vector @xmath30 , orthogonal to @xmath12 . the standard interpretation as a null dust is introduced by a formal analogy with a perfect fluid with no pressures . we conjectured a general expression ( 2.4 ) of the source and imposed it to be traceless and to have one nonzero component only , i.e. @xmath55 , for to be in accordance with the standard solution . we have used the choice @xmath20 , otherwise @xmath18 becomes a spacelike coordinate . with @xmath3 ( we are working with ingoing radiation ) , @xmath56 ( @xmath57 is obtained when @xmath58 , namely in the static situation ) . in other words , the wec is obeyed . same is valid for the other energy conditions : nec , sec and dec . being null , the fluid observes the condition @xmath59 . it is worth noting that @xmath2 is divergent at the origin and at the evolutionary hypersurface @xmath60 ( the apparent horizon ) , because of the nonstatic character of the spacetime . , where @xmath61 is the areal radius . one obtains @xmath62 , or @xmath60 we could have also used the method from @xcite ( the vanishing of the scalar expansion on the null vector field along null geodesics ) . ] we shall see later how the divergence at @xmath63 could be removed . the currents @xmath64 and @xmath65 from ( 2.10 ) are inward directed because @xmath3 and are also divergent on the horizon . as far as the acceleration of the congruence is concerned , we notice that the invariant acceleration from ( 2.14 ) becomes the standard schwarzschild counterpart when @xmath58 . having now the components of the stress tensor and the basic physical quantities associated to it , our next task is to compute the total energy flow measured by an observer laying at @xmath6 @xcite @xmath66 where @xmath67 and @xmath68 are given by ( 2.5 ) and ( 2.6 ) , respectively . to find @xmath69 we remove the @xmath4-line and @xmath4- column in @xmath70 and obtain @xmath71 . with @xmath21 , eq . ( 3.1 ) yields @xmath72 where @xmath4 is fixed and @xmath8 is the variable of integration . one obtains @xmath73 with @xmath74 a constant of integration ( w.r.t . @xmath8 ) . it may be determined by imposing that @xmath75 when @xmath8 vanishes , so that @xmath76 . hence @xmath77 a plot of @xmath78 versus @xmath8 , at constant @xmath4 , is depicted in fig.1 . one notes that the derivative @xmath79 diverges at @xmath80 . ( 3.4 ) , taken as a function of @xmath4 , resembles the quasilocal energy ( qle ) for a schwarzschild bh @xcite . an observation is in order here : lundgren et al . plotted @xmath81 even for @xmath82 . however , we have to keep in mind that @xmath4 becomes timelike in that region and to cover both regions ( @xmath82 and @xmath83 ) in the same plot seems to be inappropriate . due to the square root from ( 3.4 ) , the derivative @xmath79 is infinite at the horizon , which is like the infinite value of @xmath84 from the lundgren et al . we also observe that the derivation of the qle @xmath85 by the authors of @xcite remains valid even when the mass of the object is time - dependent , as in our situation , because the expressions of the connection coefficients that we need are @xcite @xmath86 as in the static case . therefore , the extrinsic curvature of the two - boundary preserves its value . it is clear from ( 2.1 ) that we must impose @xmath87 since at @xmath60 a signature flip takes place and @xmath18 becomes a spacelike coordinate . in addition , being nonstatic , the metric ( 2.1 ) has no a timelike killing vector and so an event horizon can not be obtained . in that case an apparent horizon is more appropriate . to extend the metric ( 2.1 ) beyond the evolutionary surface @xmath60 we introduce an exponential factor in the metric , rendering the stress tensor regular at the origin therefore , we propose the geometry @xmath88 with @xmath89 . the above line - element may be obtained by a similar manner as that for ( 2.1 ) . we begin with the regularized schwarzschild spacetime @xcite @xmath90 and move to the eddington - finkelstein coordinates with @xmath91 that will give @xmath92 the above recipe works also when @xmath93 , even though @xmath94 can not be obtained explicitely as a" +"a bipolar hyper - shell model has been proposed for the north polar spur ( nps ) ( sofue 1977 ) , in which the nps and its western and southern counter - spurs are interpreted as due to a dumbbell - shaped shock front induced by a giant explosive event at the galactic center . such an impulsive energy input may have been originated by a starburst 15 million years ago ( sofue 1984 , 1994 ) . an alternative mechanism to cause such giant shells in the halo would be a single energetic explosion at the galactic nucleus ( oort 1977 ) . giant shell structures could also be produced by a stellar - wind driven coherent galactic wind ( e.g. , heckman et al 1990 ) . since the cooling time in the halo is much longer than the shell s life time , any of these mechanisms will , however , result in a similar shocked shells in the halo , given the same amount of total energy . another alternative , traditional idea to explain the nps is the local - shell hypothesis , in which the nps is interpreted as due to a very unique supernovae remnant of the largest diameter in the galaxy ( berkhuijsen et al . 1971 ; egger 1993 ; egger and aschenbach 1995 ; and the literature cited therein ) . the propagation of a shock front in the galactic halo can be simulated by applying a shock - tracing method developed by sakashita ( 1971 ) and mllenhoff ( 1976 ) to a case of point explosion at a center of a disk surrounded by a halo and intergalactic uniform gas ( sofue 1984 ) . the galactic - center explosion hypothesis tries to explain the nps as well as the other spurs surrounding the galactic center region by a single galactic event , based not only on the morphology but also on a distance estimate of nps from soft - x ray extinction ( sofue 1994 ) . in the present paper , we revisit the galactic - center explosion hypothesis . we will extend the arguments given in sofue ( 1994 ) , which were based on the winsconsin x - ray experiments data ( mccammon et al 1983 ; mccammon and sanders 1990 ) . we will discuss the origin of the nps and related galactic spurs using the 408-mhz all - sky radio data ( haslam et al 1982 ) and the rosat x - ray images ( snowden et al 1997 ) . we simulate x - ray all - sky views based on the bhs ( bipolar hyper - shell ) model in order to morphologically reproduce the rosat all - sky views at various energy bands . we also discuss the implication of the bipolar hyper shell in dating and measuring the recent galactic starburst . we further propose to use the rosat all - sky data to probe the physics of gas in the galactic halo and intergalactic space of the local group . 1 we compare the radio and x - ray views of the whole sky in the @xmath2 coordinates in aitoff diagrams . 1a shows an enhanced view of galactic radio spurs obtained by applying a relieving technique ( sofue 1993 ) to the 408 mhz all - sky map ( haslam et al . 1b is the rosat all - sky map in the r45 ( @xmath30.75 kev ) band as reproduced from snowden et al ( 1997 ) . these figures demonstrates that the major galactic spurs both in radio and x - rays are found in the central @xmath4 region around the galactic center . the north polar spur ( nps ) and its western and southern counterparts compose giant @xmath5 shapes , drawing a dumbbell shape centered on the galactic center and necked at the galactic plane . fig . 2 shows a radio view in a 100 squared region around the galactic center . here , a relieving method to enhance the spurs has been applied in the direction of longitude ( left panel ) and in the radial direction ( right panel ) . the nps comprises a well - defined radio arc anchored to the galactic plane at @xmath6 , and draws a giant arc toward the north galactic pole . the radio brightness along the nps increases toward the galactic plane , attaining a maximum at @xmath7 . the width of the spur ( half - intensity length across ) decreases toward the galactic plane , and therefore , the nps ridge becomes sharper toward the galactic plane ( sofue and reich 1979 ) . 2 the nps draws a giant loop toward high latitudes , and returns to the galactic plane where it merges with a spur emerging from the galactic plane at @xmath8 . we call this western spur nps - west . a western half of loop iv , which is highly asymmetric and lacks the eastern half , makes a part of nps - west . the nps and nps - west , thus , compose a giant @xmath5 shape in the halo above the galactic center , with its axis roughly coinciding with the galactic rotation axis at @xmath9 . a southern counterpart of the nps is visible at @xmath10 , extending from @xmath11 toward @xmath12 , which we call the south polar spur ( sps ) . also , a western counterpart of sps is found at @xmath13 to @xmath14 , which we call sps - west . these four spurs , nps , nps - west , sps , and sps - west , are the most prominent features among the numerous galactic radio spurs . these four spurs compose a huge dumbbell - shape necked at the galactic plane and are about symmetric with respect to the galactic center . we comment that loop i , which has been defined as a complete loop of diameter 120centered on @xmath15 , is hard to trace in the present enhanced images ( fig . 1 , 2 ) . as shown in fig . 1b , the r45-band ( 0.75 kev ) x - ray intensity at @xmath16 has a global enhancement around the galactic center , which is due to the high - temperature gas in the galactic bulge ( mccammon et al 1983 ) . snowden et al ( 1997 ) have further noticed cylindrical features in the r45 and r67 ( 1.5 kev ) band maps , which emerge from the central galactic disk toward the halo . they also attribute these features to high - temperature gas around the galactic center . this fact indicates that the local hi disk is transparent at @xmath17 for x - rays at @xmath18 kev . a giant shell structure of the nps is clearly visible in the r45 and r67 bands . in fig . 3 we compare the radio and r45-band images of the nps . the western end of the x - ray nps also returns to the galactic plane at @xmath19 ( nps - west ) , and draws a giant @xmath5 together with the nps . southern counterparts to these features are also visible . particularly , the sps - west is clearly recognized in x - rays : an r45-band spur emerges from @xmath20 toward the southern galactic pole , which is symmetric to the nps about the galactic center . the sps is also visible at @xmath21 , though fainter in r45-band , while it is more clearly visible in an r45/r67-ratio map . these northern and southern x - ray spurs are associated with the radio spurs ( nps , nps - west , sps , and sps - west ) , and draw a dumbbell - shape necked at the galactic plane . we may , hence , interpret that snowden et al.s `` cylinder '' would comprise the nps , nps - west , sps and sps - west . the r12-band ( 0.25 kev ) x - ray emission from the nps is strongly absorbed below @xmath22 , and is hardly visible below 30 ( snowden et al 1997 ) . the nps shows up most clearly in the r45-band ( 0.75 kev ) , while the emission is significantly absorbed in the galactic disk at @xmath23 . r67-band ( 1.5 kev ) x - rays are also strongly absorbed near the galactic plane , indicating that the x - rays from the nps originates in the space further than the hi disk ( sofue 1994 ) . moreover , the x - rays become harder toward the galactic plane , as indicated by the clear decrease in the r45 to r67 intensity ratio toward the galactic plane . by comparing the r45 and r12-band intensities , we have shown that the hi mass toward @xmath24 to be @xmath25 h @xmath26 , which is greater than the observed value ( @xmath27 h @xmath28 ) . sofue ( 1994 ) has thus shown that the x - rays at @xmath29 originate _ beyond _ the hydrogen layer , and the distance is greater than 0.6 kpc . namely , the nps is an object which is located in the galactic halo . the distance to the nps has been subject to debates . we now know that it is beyond 0.6 kpc , which would allow us two possible interpretations : one possibility is that the nps is a local object at @xmath30 kpc , originating from supernova explosions at high altitude out of the galactic plane . another possibility is that it is a galactic - scale object related to the galactic center activity . we interpret the observed radio and x - ray features in terms of the galactic - center explosion hypothesis . our idea is based on the symmetric appearance of the radio and x - ray shells with respect to the galactic plane and the galactic center , which compose a huge dumbbell shape apparently centered on the galactic center ( gc ) . we , here , assume that the center of the dumbbell coincides with the gc , and take the distance to the gc to be 8 kpc . then , the radius of each shell is several kpc . our idea is also based on the fact that many spiral galaxies exhibit galactic - scale outflows in the forms of dumbbell - shaped shocks , bipolar cylinders , and galactic - scale jets , and we consider that the milky way galaxy would have experienced similar phenomena . ngc 253 exhibits a dumbbell - shaped shells in x - rays above and below the galactic plane , each about 5 kpc diameter ( vogler and pietsch 1999a ; pietsch et al 1999 ) , which would be a result of a starburst and related outflow ( heckmann et al . ngc 3079 exhibits a pair of radio continuum shells in the halo in both sides of the nucleus , each about 3 kpc diameter , which is considered to be an ejection from the central activity ( duric et al 1983 ) . it also exhibits an h@xmath31 cone - shaped shell of radius about 1 kpc , coaxial to the radio shells , most likely induced by an outburst from the nuclear region ( cecil 1999 ) . m82 is a starburst galaxy , which ejects a galactic - scale flow through bipolar cylindrical jets ( nakai et al 1987 ) . we emphasize that all these out - of - plane features , including the hyper shell in the milky way , require a similar amount of total energy input in the central regions of the galaxies , which is of the order of @xmath32 to @xmath33 ergs ( e.g. pietsch et al 1999 ) , or equivalent to @xmath34 to @xmath1" +"multilayers built from ferromagnetic layers with various spacer layers include a wide variety of magnetic film systems that have been intensively studied during last years . due to remarkable phenomena as giant magnetoresistance , exchange - spring behaviour and/or exchange bias , and surface enhanced magnetic anisotropy , such nanostructures have already found a number of applications and are considered as promising candidates for nonvolatile magnetic recording media.@xcite on the other hand , nanoscale superlattices and similar structures provide convenient model systems to study different aspects of surface magnetism and magnetic ordering in confining geometry . in particular , much attention has been given to multilayers composed of antiferromagnetically coupled ferromagnetic nanolayers . @xcite such layered synthetic antiferromagnets can be separated into two classes according to the symmetries ruling their magnetic properties : superlattices with relatively strong uniaxial anisotropies include low - symmetry multilayers with effective uniaxial magnetic anisotropy in the layer planes , e.g. epitaxial systems deposited on ( 110 ) , ( 211 ) faces of cubic substrates.@xcite also multilayer systems with perpendicular anisotropy belong to this class.@xcite magnetization processes in these nanostructures are strongly influenced by the uniaxial anisotropy which is responsible for specific phenomena such as `` surface spin - flop '' @xcite or field - induced metamagnetic jumps.@xcite on the other hand , the uniaxial anisotropy may be absent in layered systems with higher symmetry . these represent another large and intensively investigated class of synthetic antiferromagnetic nanostructures . superlattices with planar magnetization grown on ( 001 ) faces of cubic substrates , e.g. multilayers from materials combinations as co / cu @xcite , fe / si @xcite co / cr , @xcite or fe / cr , @xcite belong to this class . in the case of weak four - fold anisotropy , their magnetic properties are mostly determined by the interlayer exchange interactions which may include an important _ biquadratic _ contribution . @xcite evidence of strong biquadratic exchange interaction has been given in a number of experimental papers for fe / cr two - layers and multilayers @xcite , for fe / si(001 ) multilayers @xcite ) . strong effective four - fold anisotropies have been found in systems such as co / cr(001 ) or fe / cr(001 ) . @xcite the competition between magnetic anisotropy , applied fields and exchange energies may cause complicated magnetic effects and processes . in fact , a great number of novel magnetic configurations and remarkable reorientational effects in external fields have been found in such superlattices . @xcite in particular , recent experimental results using modern depth - resolving techniques reveal spatially inhomogeneous magnetic structures , e.g. in fe / cr(001 ) superlattices,@xcite and specific reorientation effects imposed by four - fold planar ( tetragonal ) anisotropy.@xcite the understanding and interpretation of the complex magnetization processes found in such systems @xcite requires a theoretical underpinning . theoretical activity in this field is largely based on analytical and numerical calculations mostly within phenomenological approaches . @xcite these studies have demonstrated the general validity of the phenomenological models to describe the magnetization processes in antiferromagnetic nanostructures . @xcite for the system under discussion the phenomenological theory has been developed to describe effects of 90 degree couplings and a concomitant complex evolution of domain structures in fe / cr / fe layers.@xcite four - fold anisotropy effects have been theoretically investigated in ref . for sandwich structures with @xmath2=2 ferromagnetic layers coupled through a spacer . multilayer systems provide also experimental models to study effects of the confining surfaces on antiferromagnetic structures.@xcite in this context , specific inhomogeneous magnetic states described for theoretical models in ref . , have recently been observed in fe / cr superlattices.@xcite the existing theoretical results , however , are restricted to special cases and are not sufficient for an exhaustive description of the magnetic states and field - induced reorientional effects observed in recent experiment . @xcite in this paper we provide a theoretical analysis of magnetic states and magnetization processes in planar antiferromagnetic superlattices with and without four - fold anisotropy in magnetic fields applied within the multilayer plane . in such magnetic superlattices the exchange interlayer coupling is an oscillatory function of the spacer thickness.@xcite depending on the spacer thickness an alternating sequence of ferromagnetic and antiferromagnetic interlayer couplings is realized , and , by adjusting the spacer thicknesses , very different strengths of antiferromagnetic coupling can be realized . on the other hand , the four - fold anisotropy includes interface - induced contributions which implies a strong dependency of the effective average anisotropy of each ferromagnetic layer on the layer thickness.@xcite thus , the effective magnetic interactions can vary in extremely broad ranges for such multilayers in dependence on the chosen materials combinations and thicknesses , see e.g. ref . , where for a co / cu(001 ) two - layer system with a wedged spacer layer the ratio between four - fold anisotropy energy and the exchange coupling is changed by orders of magnitude . in contrast to bulk planar antiferromagnets , where an essentially fixed hierarchy for the strengths of the magnetic interactions holds,@xcite in these artificial antiferromagnetic systems the ratios between different magnetic energies , respectively the phenomenological parameters in the magnetic free - energy , may assume practically arbitrary values . moreover , as the interlayer exchange is weak compared to direct exchange interactions , the fields to induce spin - reorientation phenomena are similarly weak and experimentally accessible . the rich phase diagrams for these systems precludes an analysis in all details . the phase space in terms of the phenomenological parameters includes a large variety of different magnetic states with a corresponding multitude of spontaneous and field - induced phase - transformations . in a first step to such an analysis , all laterally homogeneous states in such multilayers must be found . they are the building blocks for a domain theory.@xcite for the case of laterally homogeneous states of each ferromagnetic sublayer one has a system that behaves like an antiferromagnetically coupled chain of stoner - wohlfarth particles . this simplified one - dimensional model for the behaviour across the multilayer stack also yields the limiting case for the magnetization processes with maximum hystereses . again , a direct analysis of all magnetic states even for these one - dimensional models yields an intricate succession of phase diagrams and magnetization curves.@xcite in this paper , we avoid the cumbersome task of listing and classifying _ all _ solutions and transitions . instead , we provide a broad physically intuitive picture of the physical effects due to the different exchange or anisotropic forces , and those imposed by the confining geometry of the system . to this end , we study limiting cases of the model . this includes the case of strictly zero anisotropy with and without biquadratic exchange , and the case of infinite anisotropy with fixed four - fold orientation of the magnetizations in each layer . for the antiferromagnetic two - layer systems ( @xmath2=2 ) , i.e. the sandwich structures ( experimentally realized as ferromagnetic / spacer / ferromagnetic trilayers ) , we provide a detailed investigation of the magnetic phase - diagram for arbitrary orientation of fields in the layer planes . based on this , we can understand the _ basic _ magnetic configurations in the multilayers , and we can give a map of the _ topologically different types _ of magnetic phase diagrams . we use standard methods to analyse magnetic phases and transitions within the phenomenological approach and the theory of phase transitions.@xcite the one - dimensional chain models are considered as composite order - parameters with many components ( @xmath2 components in a multilayer stack composed of @xmath2 ferromagnetic / spacer bilayers ) and a characteristic structure of couplings between the components defined by interlayer exchange and the surfaces . from this point of view , the very rich phase - diagrams and correspondingly complex sequences of magnetic configurations can be understood . for the general cases of the model , the equations for equilibrium and phase stability can be solved only by numerical methods . with the methods and results expounded below , one can extend the analysis to specific experimental cases in all detail . the solutions for the one - dimensional chain models include various field - induced canted and inhomogeneous states with a net magnetization . based on the phase diagrams of these models , the evolution of laterally inhomogeneous ( domain ) states and magnetization processes can be discussed.@xcite in this connection , the coexistence regions of different phases in the vicinity of discontinuous ( first - order ) magnetic phase transitions are important . in external fields , thermodynamically stable domain - configuration from these competing phases can be established in extended multilayers this is crucial for an understanding of the hysteretic magnetization processes under coercivity mechanisms . the paper is organized as follows . after introducing the model and mathematical tools ( sec . ii ) we consider the effects of the bilinear and biquadratic exchange interactions in the next section ( sec . iii ) . in sec . iv we investigate in detail four - fold anisotropy effects in antiferromagnetically coupled two - layers and then discuss the generalization of these finding to the case of multilayers . in sec . iv we discuss domain states and magnetization processes by using qualitative arguments . in the concluding part we discuss possible extensions of the theory , and we suggest some useful experiments to enhance our understanding of magnetization processes in antiferromagnetic superlattices . let us consider a stack of @xmath2 ferromagnetic plates infinite in @xmath3- and @xmath4-directions and with finite thickness along @xmath5-axis . the magnetization of the layers is @xmath6 , and there are indirect interlayer - exchange couplings through spaces between them . the phenomenological energy of the system can be written in the following form @xmath7 -\mathbf{h}\cdot \sum_{i=1}^{n}\zeta_i \mathbf{m}_i - \frac{1}{2}\sum_{i=1}^{n } k_i\left ( \mathbf{m}_x^4 + \mathbf{m}_y^4 \right ) \label{energy1}\end{aligned}\ ] ] where @xmath8 ( @xmath9 ) are unity vectors along the @xmath10-th layer magnetization . @xmath11 designate deviations of the magnetization in the @xmath10-th layer from the averaged value @xmath12 . we assume that @xmath13=0 , i.e. the layer magnetizations are restricted to the layer plane . @xmath14 and @xmath15 are constants of bilinear and biquadratic exchange interactions , respectively ; @xmath16 are constants of the in - plane four - fold anisotropy . the functional ( [ energy1 ] ) generalizes similar models considered earlier in a number of studies on exchange @xcite and anisotropy @xcite effects in planar antiferromagnetic systems . within this approach the ferromagnetic layers are considered as homogeneously magnetized blocks with constant values of the magnetic interactions . this assumption deserves some comment . it is well - established that in magnetic nanostructures surface / interface exchange and relativistic interactions strongly modify electronic and magnetic properties within all volume of the magnetic constituents @xcite . this means that the values of the exchange or anisotropy parameters , and the magnetizations include large interface / surface - induced components which may strongly vary across the thickness of the individual layers.@xcite however , the hypothesis of magnetic homogeneity in the ferromagnetic nanolayers in the models of type ( [ energy1 ] ) has a solid physical basis and is justified by successful applications of these models to describe magnetization processes in layered ferro- and antiferromagnetic nanostructures.@xcite this relies on the fact that in ferromagnetic nanolayers the intrinsic ( direct ) exchange coupling are usually very strong and overcome surface / interface induced interactions . thus , they play the dominating role to determine the magnetic order _ within _ the layers , which reacts also very stiffly on all external and induced magnetic forces . furthermore , in these planar systems the stray field forces confine the magnetization of the layers into their plane" +"rapid stellar evolution is generally accompanied by intense mass loss phenomena . during both the pre - main - sequence ( richer et al . 2000 ) and the post - main - sequence evolution ( sahai 2002 ) , there are phases during which the mass loss has a distinctly non - spherically symmetric distribution . the overall geometry is often best described as hourglass - shaped or wide - bipolar , although in several cases the flows can take the form of narrow jets . actually , the observation of bipolar jets is not limited to stellar outflows but these are also commonly observed in active galactic nuclei ( agn ) . in fact , pictorial models of protostars and agn are indistiguishable , where the salient features include a central object , surrounded by an active accretion disk and a perpendicularly directed bipolar jet ( blandford & payne 1982 ) . these morphological similarities could suggest the same physics ( momentum re - distribution ) to operate , over a wide range of physical scales , and could provide a connection between stellar and extragalactic astrophysics . this familarity is further illustrated by the fact that chandra and xmm - newton recently have detected the flows from pre - main - sequence objects in ( likely thermal ) x - rays ( pravdo et al . 2001 , favata et al . 2002 ) . this carries the study of these flow phenomena also into the traditionally home domain of agn , i.e. that of high energy astrophysics . although many of the details remain uncertain , there is little doubt that the energy is ultimately extracted from the gravitational and magnetic fields of the source . the understanding of outflow phenomena is thus intimately related to the understanding of the overall energy and momentum budget of the star / galaxy formation process and implies , as such , more general ramifications . extragalactic and post - main - sequence stellar outflows , as well as circumstellar disks and high - mass star forming regions , are addressed elsewhere in these proceedings . here , we shall focus on outflows from low - mass objects in their early stages of pre - main - sequence evolution . although stellar rotation is most likely controlled by local processes , as observationally indicated by the randomly oriented rotation axes , even galactic differential rotation alone would suffice to result in break - up of the contracting protostars , unless their angular momentum would be redistributed with high efficiency . viscous disk accretion is commonly invoked to accomplish this , through disk locking or a stellar wind ( rebull , wolff & strom 2004 ; matt & pudritz 2004 ) . however , the observational evidence appears only partially supportive for this widely accepted scenario and a convincingly strong relationship between stellar rotation and the presence of protostellar disks in young low - mass pre - main - sequence stars has yet to be established ( mathieu 2003 ) . the presence of accretion disks is generally also required as a pre - requisite for theoretical models of outflows . recently , models have been developed which simultaneoulsly address the physics of both gravitational collapse and the origin of outflows ( see , e.g. , tomisaka 2002 and references therein ) . these models take also rotation and magnetic fields explicitly into account , needed for the angular momemtum transport in the viscous accretion disks ( balbus & hawley 1991 , stone et al . 2000 ) or off the disks ( knigl & pudritz 2000 , shu et al . 2000 ) . according to contopoulos & sauty ( 2001 ) , the removal of angular momentum could in certain circumstances become extremely efficient , viz . expressable in terms of the ratio of the mass loss to the mass accretion rate , _ m_@xmath1/_m_@xmath2 . recent reviews on this and related topics are by reipurth & bally ( 2001 ) and those collected in the volume of protostars & planets iv , including those by eislffel et al . ( 2000 ) , hartigan et al . ( 2000 ) , knigl & pudritz ( 2000 ) , richer et al . ( 2000 ) and by shu et al . ( 2000 ) . to summarise shortly , a generalised theory of hh / jet and molecular flows has to account for at least the following observed properties : _ length scales _ of @xmath3pc to a few parsec , _ opening angles _ of @xmath4 to @xmath5 , _ space velocities _ of some kms@xmath6 to several @xmath7kms@xmath6 , _ gas kinetic temperatures _ of @xmath8k to a @xmath9k . further , based on the assumption of momentum conservation , derived mass loss rates scale with the radiative luminosity of the central source(s ) , i.e. _ m_@xmath10 , where @xmath11 to 1 . in regions of low mass star formation , observed ( line of sight ) magnetic field strengths are generally less than @xmath12 g on the arcminute scale ( crutcher et al . 1993 ; crutcher & troland 2000 ) . it should be realised that only a few of the above parameters have been determined with sufficiently high accuracy . in addition , time dependent effects can not be ignored as several flows show evidence for time variablity . observed outflows display a wide range of effective collimation and a dichotomy of theoretical models for the driving of outflows has emerged , which differentiates between wide - angle winds ( shu et al . 1991 , 2000 ) and collimated jets ( stahler 1994 ) . in the former case , a stellar wind or a wind from the disk surface is transferring momentum to the surrounding molecular material , whereas in the latter case , molecular outflows are thought to be molecular material entrained through a turbulent layer of a stellar jet / herbig - haro flow . hh - flows are often observed to be spatially associated with molecular outflows . observations with the iso - lws have provided convincing evidence that hh - flows and molecular outflows have a common physical cause ( liseau et al . 1997 ; saraceno et al . 1998 ) . all model families tend to reproduce observed outflow properties , such as the mass - velocity relation , @xmath13 with @xmath14 , and the ` hubble law ' , @xmath15 with @xmath16 . recent supporting arguments for the wide - angle wind hypothesis have been provided by matzner & mckee ( 1999 ) and by gardiner , frank & hartmann ( 2003 ) . however , questions regarding the launching and collimation are left open . downes & cabrit ( 2003 ) argue in favour of the jet - driving hypothesis , but their main results seem not very different from those of the wind - driven models by lee et al . ( 2000 ) . as discussed by ray ( 2000 ; see also : cabrit , raga & gueth 1997 ) , both model categories have their strengths - but also their weaknesses . the respective shortcomings might be overcome , if the possibility of temporal evolution of the outflows is considered , where initially highly collimated molecular ` jet - flows ' evolve into increasingly less collimated outflows as they age . the , by far , most outstanding problem concerns the origin of the outflows . to gain further insight , direct observation of the regions of acceleration would most likely be required . mhd models make detailed predictions of where this should happen and what the angular velocity of the rotating flow should be ( bacciotti et al . 2002 ; presenti et al . the relevant scale is set by the alfvn radius , the physical size of which depends on the details of the favoured model . but somewhat losely , one may distinguish x - winds , which are generated within only a few @xmath17 ( @xmath18au ) of the central source , and disk winds , which are launched within a fraction of an au to some au . at the typical distance of outflows in low mass star formation regions of some @xmath19pc , acceleration regions are thus expected to subtend angles of less than a milliarcsec to a few tens of milliarcsec . a related issue is that of the mechanism of initial flow collimation , occuring over similarly small spatial scales , whether mhd or not . of great relevance to the physics of star formation is of course the evolutionary status of the central driving source , be it single be it binary / multiple , the latter seemingly more likely ( m.barsony , private communication ) . age estimates of outflow engines range from only a few thousand to about a million years . one of the key questions is to what extent the properties of observed flows , showing great diversity , can be directly linked to the pre - main - sequence age of their driving sources . in particular , one would wish to establish the value and the time dependence of the ` @xmath20-factor ' on an observationally firm basis . this factor , defined as _ m_@xmath1=@xmath21_m_@xmath22 , is a measure of the relative importance of mass inflow and mass outflow for an individual source . mhd models concur with a value of @xmath23 . in order to understand the underlying physics of the outflows at their root , it is thus important to learn , whether time evolution alters this ` constant ' in a systematic way . an item of great importance regards the understanding of the stability of interstellar clouds against their self - gravity , i.e. cloud lifetimes are many times longer than their free - fall time scales . observed cloud ` turbulence ' is generally believed to accomplish this , although the energy source , injecting and maintaining the turbulent motions , has yet to be uniquely identified . outflows from young stellar objects represent one of the known prime candidates . outflows also offer the opportunity to study the physics of a particular class of interstellar shock waves . these tend generally to be radiative and reasonably thermally stable . specific problems include upstream - downstream communication , particle acceleration , shock cooling and grain destruction processes . specifically for the jet - driven outflow models , the problem exists how to account for the wide angles of observed molecular outflows . these flows are more often the rule than the exception . in other words , the mechanism for the momentum transfer in the transverse direction has yet to be uniquely identified . in relation to this , it is important to provide firm observational data for the internal ( jet ) and external ( surrounding medium ) densities , as the driving of the molecular flows could be accomplished only by underdense jets . the development of instabilities in the molecular flow ( high velocity knots or ` bullets ' , see bachiller 1996 ) , possibly related to this issue , is not well understood either . as mentioned in the previuos paragraph , outflows affect their environment physically , but their molecular clouds may also transform chemically . on a global scale , the effects of outflows on the chemical evolution of their host cloud have been addressed by bergin , melnick & neufeld ( 1998 ) . these models focus on the relative abundance , as a function of the time , of primarily a few key species ( chemistry and cooling ) such as o@xmath0 and h@xmath0o . at the time , these models appeared elegant and highly attractive . unfortunately , and unexpectedly , _ nature _ did not agree , as observations with swas ( snell et al" +"the detailed study of electroweak symmetry breaking and of the properties of a hypothetical sm higgs boson are some of the physics goals motivating the construction of a linear electron collider . the centre - of - mass energy of the collider would be 500gev ( ilc ) or 3tev ( clic ) , which will be decided upon analysis of the lhc data @xcite . in both cases , however , several interesting physics channels will appear in multi - jet final states , often accompanied by charged leptons and missing transverse energy . the di - jet energy resolution should be such that _ z _ and _ w _ masses can be determined with an accuracy comparable to the natural decay width of these bosons . this translates into a jet energy resolution of 34% over the whole energy range . two kind of calorimeters are under study to meet this requirement @xcite . one proposes to measure and correct for the fluctuations of the electromagnetic and hadronic components on a shower by shower basis . the second is based on the _ particle flow _ ( _ pf _ ) approach : the momentum of jet charged particles are measured with the tracking system , tracks and showers being matched thanks to a high segmentation of the calorimeters . several technological options are studied by the calice collaboration : silicon or scintillator for a sampling ecal with tungsten absorbers , scintillator or gaseous chambers for the fe or w hcal . in the gaseous detector case , r&d on rpc , gem and micromegas are actively pursued . they are an attractive option with respect to the large area to be instrumented : 3000m@xmath1 in the sid detector concept @xcite . in addition , because there is only one sensor per layer ( a gas layer ) , higher cell segmentation can be achieved than with scintillators ( 1 versus 9@xmath0 ) with plausibly better _ pf _ performance . on the other hand , due to the large signal fluctuations in gaseous detectors , the charge information is of limited use . this may limit the single particle energy resolution necessary for measuring the neutral content of jets . as a result , gaseous hadronic calorimeters are essentially digital ( 12bits per channel ) . in the last ten years , the so - called bulk fabrication process has widened the field of application of micromegas detectors @xcite . it consists in the lamination of a stainless steel mesh ( 20@xmath2 m diameter wires woven to a square pattern ) and photosensitive insulating films onto a pcb . after patterning of the films to pillars , the mesh is strongly encapsulated in between the pillars at a constant distance from the anode pcb plane . it is therefore well suited for manufacturing large area micromegas detectors . furthermore , the final assembly is robust , the mesh resistant to sparks and the gain uniformity relatively good , about @xmath310% @xcite . attractive features of micromegas for a hadron calorimeter are excellent performance to mip , high rate capability and , in suitable gas mixtures , no sentivity to neutrons and negligible aging . as mentioned already , the energy measurement is relevant for neutrals but also for very high energy charged particles against which the tracker resolution worsen . there , the energy is measured by calorimetry only and it is desirable to minimize both stochastic and constant terms ( _ a_/@xmath4@xmath5_b _ ) that govern the resolution . in order to improve _ a _ and linearity , it has been proposed to digitize signals with 2bit resolution . this semi - digital readout scheme has been adopted by micromegas and rpc hcal projects ( sdhcal ) . lamination of the mesh and the pcb between rolls imply that the bulk process is applied to flat pcb . hermeticity requirements and huge number of channels of an ilc / clic hcal , however , make it unavoidable to integrate front - end asic on detectors . therefore , lapp group and cern workshop made the bulk process compatible with asic equipped pcb . the final assembly , called an active sensor unit or asu , consists of a pcb with 1@xmath0 pads plus mesh on one side and asics on the other side ( fig.[m2_pics ] ( left ) ) . prototype during assembly.,title=""fig:"",scaledwidth=38.0% ] prototype during assembly.,title=""fig:"",scaledwidth=38.0% ] the first asu was constructed in 2008 . it consisted of a matrix of 8@xmath68 pads read out by one dirac chip and was successfully tested in cern / ps particle beams @xcite . subsequently , asus of larger area were fabricated and equipped with hardroc2 chips @xcite . the size adopted for the construction of a 1m@xmath1 detectors is 32@xmath648@xmath0 . optimized for the efficient detection of micromegas signals , a new asic called microroc was developed by the lal / omega group and the lapp electronics department . the one square meter prototype features 9216 readout channels ( 96@xmath696 pads ) . it is assembled from six asu glued on a stainless steel supporting plate and surrounded by a plastic frame ( figure [ m2_pics ] ( right ) ) . another stainless steel plate holds a copper drift electrode . the 3 mm drift gap is defined by the frame height and is kept constant over all chamber area by tiny spacers placed between the asu . each asu consists of woven mesh and a pcb with 48@xmath632 readout pads of 1@xmath61@xmath7 and 24 microroc chips . the readout of two asu is chained serially and connected to the data acquisition system by three detector interface boards ( dif ) . the dif is a mezzanine board , it allows to load the asic configuration , readout the data from the asic memory and also to provide system clock and power . another board , called inter - dif , is placed between the dif and the asu to provide voltage to drift and mesh electrodes ( @xmath8500v ) . the gas is distributed by one inlet and outlet traversing the frame of the chamber whose total thickness is about 1 cm . the prototype is equipped with a newly developed 64-channel asic called microroc . each asic channel features a diode network embedded inside the silicon to protect against discharges , a charge preamplifier followed by 2 shapers of different gain and shaping time tunable between 75 and 200ns , 3 discriminators allowing setting of 3 readout thresholds with 10-bit dacs and a 127 event depth memory with 200ns time - stamping of hits ( fig.[mr_circuitry ] ) . the dynamic range of the low and high gain shaper are 200 and 400fc respectively . the output of the high gain shaper is connected to 2 discriminators which are used to define the low and medium channel threshold while a third discriminator , linked to the low gain shaper , is available to set the high threshold . the 3 thresholds are common to the 64 chip channels . a 4-bit offset , however , can be used to vary the individual pedestal positions . it virtually provides a channel to channel control of the 3 thresholds . a detailed characterization of 341 asics was carried out to verify their overall functionality and determine their settings ( offsets and thresholds ) . the procedure and the results can be found in @xcite . a telescope and the 1m@xmath1 prototype were installed in sps / h4 for 18 days during august 2011 . at an average trigger rate of 100hz in spill , 6 millions muons and pions in the ratio 85/15 were recorded . muons were used to assess the prototype performance to mips under various detector settings . shower signals were measured with a pion beam focused at a small iron block placed 0.5 m upstream of the prototype . installed in the sps / h4 beam line , the set - up consisted of a telescope and the prototype each placed on a movable table , a gas distribution panel , two racks with trigger electronics and power supplies and a fast acquisition pc ( figure [ setup_noise ] left ) . the telescope is a mechanical structure holding small micromegas tracking chambers equipped with pads or strips for tracking and three scintillators plus pmt for triggering . all the detectors were flushed with a non flammable gas mixture of ar / cf@xmath9/__i__c@xmath9h@xmath10 95/3/2 at a total flow of 4l / h . the iterative procedure to align the pedestals described in @xcite was run at the beginning of the test ( fig.[setup_noise ] ( right ) ) . later , noise conditions were monitored with daily short dedicated runs . the target noise rate was 10mhz / channel . compared to a particle rate of 10hz per channel in the center of the muon beam , it yields a high signal to noise ratio of about 10@xmath11 . [ [ mesh - voltage - scan ] ] mesh voltage scan + + + + + + + + + + + + + + + + + the efficiency is measured by finding a muon track in the telescope , extrapolating its impact point at the prototype and searching for hits inside a 3@xmath63 pad area at the time of the trigger ( window of 600ns ) . the multiplicity is calculated as the average number of hits whenever at least one hit is present . both quantities were measured at various mesh voltages and shaping times with the beam spreading over roughly hundred pads . a preliminary analysis leads to the trends showed in figure [ eff_mult_vmesh_scan ] where a high efficiency is reached at all shaping settings . at 390v mesh voltage ( gas gain around 3000 ) , 1fc hit threshold and 200ns shaping , one records an efficiency of 98% and a multiplicity of 1.12 . both are very well compatible with small prototype performance previously measured in similar conditions @xcite . [ [ threshold - and - angular - scan ] ] threshold and angular scan + + + + + + + + + + + + + + + + + + + + + + + + + + thanks to a careful calibration of the electronics before the test beam , a threshold scan could be performed ( figure [ eff_thr ] ( left ) ) . the slight inflexion point at half of the range follows from the landau distribution turnover . the lowest running threshold is about 1fc . further increase to 2fc leads to a dramatic drop of the noise rate by 3 orders of magnitude while leaving the efficiency almost unchanged . pad multiplicity is directly impacted by the angle of incidence of traversing muons . its dependence to the angle was studied by rotating the prototype with respect to the beam direction . as is seen in figure [ eff_thr ] ( right ) , it remains below 1.5 at angles as large as 60@xmath12 . directed at a 20 cm thick block of iron downstream of the telescope , a 150gev / c pion beam was used to produce hadron showers which would propagate to the prototype placed half a meter downstream . this set - up allows to get a first idea of the response of the prototype in high multiplicity showers . in addition , the possibility to distinguish by use of the three thresholds multi - particles and single particle within 1@xmath0 cells can be examined . finally thanks to the possibly large spatial extend of some showers , a uniformity measurement can be carried out quickly . [ [ uniformity ] ] uniformity + + + + + + + + + + the superimposition of 10@xmath13 pion events measured at a mesh voltage of 350v ( mip efficiency" +"the seyfert 1 galaxy mcg6 - 30 - 15 at @xmath0 has been the centre of much interest since a broad iron line was discovered in its x - ray spectrum with the _ asca _ satellite ( tanaka et al 1995 ) . iron line emission is part of the reflection spectrum produced by the hard x - ray power - law continuum in the source irradiating the accretion disc ( guilbert & rees 1988 ; lightman & white 1988 ; ross & fabian 1993 ) and is broadened and skewed by doppler , gravitational redshift effects , and light aberration and bending ( fabian et al 1989 ) . the low energy extent of the line can reveal the inner radius of the accretion disc and thus the black hole spin ( for reviews see fabian et al 2000 ; reynolds & nowak 2003 and fabian & miniutti 2006 ) . the iron abundance in mcg6 - 30 - 15 appears to be about 23 times the solar value ( fabian et al 2002 ) , making the iron line particularly strong . mcg6 - 30 - 15 was observed several more times with _ asca _ ( iwasawa et al 1996 , 1999 ; matsumoto et al 2003 ; shih et al 2002 ) , by _ bepposax _ ( guainazzi et al 1999 ) , _ rxte _ ( lee et al 1999 ; vaughan & edelson 2001 ) and by _ xmm newton _ ( wilms et al 2001 ; fabian et al 2002 , 2003 ; vaughan & fabian 2004 ) . all of these observations confirmed the presence and general broad shape of the iron line . evidence that the black hole in mcg6 - 30 - 15 is rapidly spinning has been obtained from the extreme breadth of the line by iwasawa et al ( 1996 ) , dabrowski et al ( 1997 ) , wilms et al ( 2001 ) , fabian et al ( 2002 ) and most recently reynolds et al ( 2005 ) , who determine a spin parameter @xmath1 . the _ xmm newton _ work emphasizes that much of the emission arise from smaller radii , between @xmath2 @xmath3 ( where @xmath4 ) . this may help to explain the otherwise puzzling spectral variations shown by the source . shih et al ( 2002 ) , fabian et al ( 2002 ) , fabian & vaughan ( 2003 ) and taylor , uttley & mchardy ( 2003 ) found that the spectral variability can be explained by a simple two component model consisting of a highly variable power - law continuum ( of almost fixed spectral slope ) and a much less variable reflection spectrum , which of course includes the iron line . the reflection ( and iron line ) strength do not follow the power - law continuum intensity , as expected in a simple reflection picture . the small radius of much of the emission can however explain this behaviour when it is recalled that as well as strong gravitational red - shifting occurring in this region , there is also strong gravitational light bending . this can disconnect variations in the continuum from those of the reflection and has led to the development of the light - bending model ( fabian & vaughan 2003 ; miniutti et al 2003 , 2004 ) , which is a generalization of earlier work on the strong field regime ( martocchia & matt 1996 ; reynolds & begelman 1997 ) . if the source of the continuum emission ( assumed to be an isotropic emitter ) changes location close to the black hole , then , even if the continuum has a constant intrinsic luminosity , it appears to the outside observer to change in brightness . this is just due to gravity bending the light rays out of the line of sight by different amounts depending upon the precise location of the source . much of the radiation is bent down onto the disc , so the observed reflection intensity changes little . the two component variability pattern and its light bending interpretation have recently found application in many other accreting black hole sources ( fabian et al 2004 , 2005 ; miniutti , fabian & miller 2004 ; ponti et al 2006 ) . one striking feature of the model reflection spectrum is a large reflection hump peaking at 2040 kev . this is where the disc albedo is highest ; at lower energies the albedo is reduced by photoelectric absorption and at higher energies it is reduced ( at a given energy ) by compton down - scattering of the photons ( see e.g. george & fabian 1991 ) . the presence of the compton hump has been confirmed in the spectrum of mcg6 - 30 - 15 by _ bepposax _ and rxte observations ( guainazzi et al 1999 ; lee et al 2000 ; fabian et al 2002 ) . what those observations have not done is to determine the variability of the compton hump and show that it varies in the same way as the rest of the reflection spectrum . here we carry out this important step with the hard x - ray detector ( hxd ) on _ suzaku_. we concentrate on the _ suzaku _ data above 3 kev since there is a complex warm absorber in mcg6 - 30 - 15 ( otani et al 1996 ; lee et al 2001 ; turner et al 2003,2004 ) . the difference spectrum between low and high states of the source shows that absorption is minimal above 3 kev ( fabian et al 2002 ; turner et al 2004 ) and high energy transmission grating ( hetg ) spectra from _ chandra _ show no absorption feature around 6.5 kev which would indicate absorption by species of intermediate ionization which could affect our fits ( young et al 2005 ) . mcg6 - 30 - 15 was observed four times by _ suzaku _ ( mitsuda et al 2006 ) , once between august 1719 in 2005 for about 45 ks and three times in january 2006 with longer exposures . here we focus on the three 2006 observations performed between 914 ( 150 ks ) , 2326 ( 99 ks)and 2730 ( 97 ks ) january 2006 . we use event files from revision 0.7 of the _ suzaku _ pipeline . version 0.7 processing is an internal processing applied to the _ suzaku _ data obtained during the suzaku working group phase , for the purpose of establishing the detector calibration as quickly as possible . some processes that are not critical for most of the initial calibration and scientific studies , e.g. , aspect correction , fine tuning of the event time tagging of the xis data , are skipped in version 0 processing , making the quality of the products limited in these directions compared with the official data supplied to guest observers . the xis data were screened with xselect as standard ( see e.g. koyama et al 2006 ) . the xis products were extracted from circular regions of 4.3 radius centred on the source , while background products were extracted from two smaller circular regions offset from the source ( and avoiding the chip corners with calibration sources ) with a total area equal to that of the source region . the latest response and ancillary response files provided by the instrument teams were used . for the hxd / pin ( takahashi et al 2006 ) , instrumental background spectra were extracted from time dependent models provided by the hxd instrument team , based upon a database of non x - ray background observations made by the pin diode to date . since the background modeling is the key issue for the hard x - ray measurement with the hxd , the hxd team has provided two independent background models , model a and b , which use different algorithms ( kokubun et al . spectral analysis of the source spectrum using the two models was found to give statistically indistinguishable results for the three 2006 january mcg6 - 30 - 15 observations over the whole 1445 kev band used here , and we use the background model a in our analysis . the response files appropriate for the xis nominal position observation were chosen dated as of 2006/08/07 . we have extracted products for the three front illuminated ccd xis detectors ( xis0 , xis2 , and xis3 ) and for the back illuminated ccd ( xis1 ) . the xis2 and xis3 detectors are found to produce remarkably similar spectra in the whole band used here . the xis0 spectrum is slightly flatter than that from the xis2 and xis3 detectors so we proceed by co adding just the xis2 and xis3 products in our analysis ( see yaqoob et al 2006 for mention of structures in the xis0 and xis1 spectra ) . in fig . [ totallc ] , we show the broad - band 0.512 kev background subtracted light curve from the xis2 and xis3 detectors during the three pointed observations in 2006 . we also show , as a reference , the count rate levels selected to define the high flux ( hf ) and low flux ( lf ) states which will be used to study the spectral variability of mcg6 - 30 - 15 . as normal for this source ( thought to harbour a black hole with a mass of @xmath5 , mchardy et al 2005 ) the light curve exhibits large amplitude and relatively short timescale variability with variations up to factors 23 in a few ks . we start our analysis of the _ suzaku _ data by considering the 312 kev time averaged co added spectrum from the xis2 and xis3 front illuminated ccd detectors . ( xis response and ancillary files 20060213.rmf and 20060415.arf , with a 6 mm extract radius , were used . ) the most important feature in this energy band is the strong , skewed , relativistic fe k@xmath6 line which characterizes the x ray spectrum of mcg6 - 30 - 15 enabling us to explore the nature and geometry of the accretion flow close to the central black hole with much higher accuracy than in any other object so far . in fig . [ feprofiles ] we show the ratio of the data to a simple power law model fitted in the 34 kev and 7.512 kev band and absorbed by the galactic column density ( @xmath7 @xmath8 ) . the residuals clearly show the asymmetric and broad fe k@xmath6 line profile ( top panel ) . in the bottom panel , we superimpose the fe k@xmath6 profile as observed with the _ xmm newton _ epic pn camera in 2001 . the agreement between the two instruments is remarkable and demonstrates the excellent level of the _ suzaku _ xis calibration even in the early stages of the mission . the 210 kev flux is @xmath9 erg @xmath8 s@xmath10 in the _ xmm newton _ observation and @xmath11 erg @xmath8 s@xmath10 in the _ suzaku _ one . notice the absorption / emission structures in the blue wing of the relativistic line which are clearly detected by both the epic pn and the xis detectors with excellent agreement . as a first attempt to fit the fe k@xmath6 line profile we consider the simplest possible spectral model comprising a power law continuum absorbed by a column of neutral matter ( fixed at the galactic value @xmath12 @xmath8 ) and a set of gaussian emission lines . we consider first three gaussian emission lines : a narrow unresolved @xmath136.4 kev emission line ( the narrow component of the fe line from distant matter ) , two narrow unresolved @xmath136.7 kev and" +"flow rate measurements of liquid metals are required in various technological processes ranging from the cooling of nuclear reactors to the dosing and casting of molten metals.@xcite electromagnetic flowmeters are essential in the diagnostics and automatic control of such processes . a variety of electromagnetic flowmeters have been developed starting from the late 1940s and described by shercliff.@xcite the standard approach is to determine the flow rate by measuring the potential difference induced between a pair of electrodes by a flow of conducting liquid in the magnetic field.@xcite this approach is now well developed and works reliably for common liquids like water,@xcite but not so for liquid metals . major problem in molten metals , especially at elevated temperatures , is the electrode corrosion and other interfacial effects , which can cause a spurious potential difference between the electrodes . the electrode problem is avoided by contactless eddy - current flowmeters , which determine the flow rate by sensing the flow - induced perturbation in an applied magnetic field.@xcite the main problem with this type of flowmeters is the weak field perturbation which may be caused not only by the flow . we showed recently that the flow - induced phase shift of ac magnetic field is more reliable for flow rate measurements than the amplitude perturbation.@xcite another contactless techniques for flow rate measurements in liquid metals is the so - called magnetic flywheel invented by shercliff,@xcite who prescribes _ a `` plurality '' _ of permanent magnets distributed equidistantly along the circumference of a disk , which is mounted on an axle and placed close to a tube carrying the liquid metal flow . the eddy currents induced by the flow across the magnetic field interact with the magnets by entraining them , which makes the disk rotate with a rate proportional to that of the flow . this type of flowmeter , described also in the textbook by shercliff@xcite and extensively used by bucenieks,@xcite was recently successfully reembodied under the name of the lorentz force velocimetry ( lfv).@xcite recently , we suggested an alternative and much more compact design of such a flowmeter , which conversely to shercliff s flywheel uses just a single magnet mounted on the axle it can freely rotate around and magnetized perpendicularly to it.@xcite we also introduced a basic mathematical model and presented first experimental implementation of this type of flowmeter.@xcite when such a magnet is placed properly at a tube with the liquid metal flow , it starts to revolve similarly to shercliff s flywheel . but in contrast to the latter , which is driven by the electromagnetic force acting on separate magnets , the single magnet is set into rotation only by the torque . this driving torque is due to the eddy currents induced by the flow across the magnetic field . as the magnet starts to rotate , additional eddy currents are induced , which brake the rotation . an equilibrium rotation rate is attained when the braking torque balances the driving one , and this rate depends only on the flow velocity and the flowmeter arrangement , whereas it is independent of the electromagnetic torque itself . thus , the equilibrium rotation rate is affected neither by the magnet strength nor by the electrical conductivity of the liquid metal provided that the friction on the magnet is negligible . this a major advantage of the single - magnet rotary flowmeter over the lfv approach , which relies on direct force measurements.@xcite in this paper , we present an extended theory of the single - magnet rotary flowmeter and compare it with experimental results . two limiting cases of long and short magnets are analyzed using linear - dipole and single - dipole approximations . we obtain simple analytic solutions for the force and torque on slowly moving and rotating magnets due to eddy currents in the layers of infinite horizontal extent and arbitrary depth . this allows us to find the equilibrium rotation rate of the magnet at which the torques due to the translation and rotation balance each other . we also consider an active approach , where the force on the magnet is used to control its rotation rate so that the resulting force vanishes . this rotation rate , similarly to the equilibrium one , is proportional to the layer velocity and independent of its conductivity and the magnet strength . the torque on a magnetic dipole rotating about an axis normal to a thin sheet has been calculated by smythe using an original receding image method.@xcite reitz uses this method to calculate the lift and drag forces on the coils of various geometries moving with constant velocity above a conducting thin plate.@xcite the lift force , which at high speeds approaches the force between the coil and its image located directly below it , varies as the velocity squared in the low - speed limit considered in this paper . the drag force is found to vary inversely and directly with the velocity at low and high speeds , respectively . palmer finds analytical expressions for the eddy current forces on a circular current loop moving with a constant velocity parallel to a thin conducting sheet.@xcite the force on a rectangular coil moving above a conducting slab has been calculated numerically by reitz and davis using the fourier transform method.@xcite the same problem for the magnetic dipole of arbitrary orientation placed next to a thin slowly moving slab is addressed by kirpo _ @xcite the force and torque on a transversely oriented dipole above a slowly moving plane layer of arbitrary thickness has been found analytically in the context of the lfv.@xcite fast computation of forces on moving magnets are of interested also for the eddy current force testing techniques.@xcite this paper is organized as follows . the following section presents two simple mathematical models of the single - magnet rotary flowmeter , which are used to calculate analytically the force and torque on the magnets moving and rotating slowly above a layer of infinite lateral extent . the limits of long and short magnets , which are approximated by linear and point dipoles , are considered in secs . [ sub:2d ] and [ sub:3d ] , respectively . section [ sec : exp ] presents the flowmeter implementation details and test results . the paper is concluded by a summary in sec . [ sec : con ] . schematic view of the single - magnet rotary flowmeter with the @xmath0-axis directed out of the plane of figure . ] consider a horizontally unbounded planar layer of electrical conductivity @xmath1 occupying the lower half - space and moving as a solid body with a constant velocity @xmath2 parallel to a permanent magnet placed at a distance @xmath3 above its surface and rotating with a constant angular velocity @xmath4 around an axis parallel to the surface and perpendicular to @xmath5 velocities are assumed sufficiently low for the magnetic field of induced currents to be negligible compared to the field of the magnet . the origin of cartesian coordinates is set at the center of the magnet with the @xmath6 @xmath0 and @xmath7 axis directed along @xmath8 @xmath9 and downward normally to the surface , respectively , as shown in fig . [ cap : sketch ] . in the following , two limiting cases will be considered in which the magnet will be assumed either much longer or much shorter than @xmath10 we start with a long cylinder magnetized perpendicularly to its axis about which it can freely rotate.@xcite in this case , the magnetic field is approximated by that of a two - dimensional ( linear ) dipole with the vector potential @xmath11 which has only the @xmath0-component @xmath12 where @xmath13 is the vacuum permeability and @xmath14 is the linear dipole moment , which is perpendicular to @xmath15 and directed at the angle @xmath16 from the positive @xmath17 axis ; @xmath18 is the radius vector from the magnet axis , and @xmath19 and @xmath20 are the cylindrical radius and the polar angle in the cylindrical coordinates around the @xmath0-axis . the magnetic field of linear dipole is @xmath21 eddy currents are induced by two effects : the translation of the layer and the temporal variation of the magnetic field due to its rotation . the latter vanishes in the co - rotating frame of reference , where the magnetic field is stationary , while the layer appears to move with the resulting velocity @xmath22 which contains also an apparent rotational motion of the layer @xmath23 opposite to that of the magnet . the density of eddy currents is given by ohm s law for a moving medium @xmath24 where @xmath25 is the electric potential . in this case , no electric potential is induced because the e.m.f . , @xmath26 is both solenoidal and tangential to the surface . if the induced magnetic field is negligible as originally assumed , eddy currents can be represented as the superposition @xmath27 where @xmath28 and @xmath29 are the currents induced by the translation and rotation , respectively . it is important to note that in the approximation under consideration with a fixed magnetic field distribution , eddy currents are determined only by the instantaneous velocities . besides that eddy currents are coplanar to the surface and , thus , mutually independent over the depth of the layer consequently , a layer of finite thickness may be represented as a semi - infinite one with zero velocity at @xmath30 where @xmath31 is the distance of the lower boundary of finite - thickness layer from the magnet . this , in turn , is equivalent to the superposition of two semi - infinite layers with the second layer at @xmath32 moving oppositely to the first one at @xmath33 so that the resulting velocity vanishes at @xmath34 in the following , this approach allows us to construct the solution for a finite - thickness layer by taking the difference of two half - space solutions , which is subsequently denoted by @xmath35_{h_{1}}^{h_{2}},$ ] where @xmath36 stands either for the force or the torque due to the eddy currents in a half - space . moreover , by the same arguments , this approach can easily be extended to @xmath7-dependent velocity distributions @xmath37 , for which general solution can be constructed as a superposition of solutions for thin layers moving with various velocities given by @xmath38 where @xmath39_{h_{1}}^{h_{2}}/\left[z\right]_{h_{1}}^{h_{2}}$ ] for @xmath40 and @xmath41 the linear force density experienced by an infinitely long magnet due to the layer translation , which according to the momentum conservation law is opposite to that acting upon the layer itself , can be written as @xmath42 where the integral is taken over the @xmath43-cross - section of the layer . the @xmath0-component of force is absent due to the @xmath44 reflection symmetry . in the low - speed limit under consideration , when force varies linearly with the velocity , there is also no @xmath7-component of force . this is the case because according to the linearity @xmath45 when @xmath46 while the latter transformation is equivalent to the rotation of the coordinate system by @xmath47 around the @xmath7-axis , which leaves the @xmath7-components invariant . in polar coordinates with the surface defined by @xmath48 we obtain @xmath49 the linear torque density , which because of the aforementioned symmetries has only the @xmath0-component , can be found as @xmath50 where @xmath51 the linear force density due to the rotation , defined by @xmath52 is found as @xmath53 the linear torque density due to the rotation , as that due to the translation above , has only the @xmath0-component @xmath54 which is not defined for a semi - infinite layer because the last integral diverges . nevertheless , expression ( [ eq : m1-gen ] ) can still be evaluated for the layer of finite depth by substituting the infinite limit in the last integral" +"transverse collective oscillations have been recently excited in the radial plane of an elongated cylindrically symmetric condensate @xcite . they are quasi-2d excitations and indeed , at very low temperatures , the measured frequencies of the transverse monopole and quadrupole modes are found to be in very good agreement with the theoretical predictions obtained by linearizing the gross - pitaevskii equation for a trapped two - dimensional ( 2d ) system . moreover , it has been experimentally found that the transverse breathing mode of an elongated condensate exhibits unique features . first , the excitation frequency is close to twice the radial trapping frequency , it is almost independent of the strength of the two - body interaction and the number of particles , and it is nearly independent of temperature . and second , the transverse breathing mode has a very small damping rate compared to other modes . the measured damping rate of the transverse quadrupole mode is approximately one order of magnitude larger than the one of the transverse breathing mode . this is in contrast to the 3d case , where both monopole and quadrupole modes have similar decay rates . these striking properties experimentally found for the transverse breathing mode are in agreement with the unique features predicted for the breathing mode in 2d isotropic condensates @xcite : its frequency is a universal quantity and it is an undamped mode . one can conclude that these features are characteristic of the reduced dimensionality thus , providing a demonstration of the two - dimensional nature of the transverse oscillations of an elongated condensate . therefore , a highly anisotropic cigar - shaped trap can be considered as a first approximation as an infinite cylinder along the @xmath0-direction . in the present paper we consider a cylindrical condensate and calculate at zero temperature the transverse spectrum of excitations , by solving the linearized gross - pitaevskii equation in 2d , and the modes with non - zero momentum @xmath1 along the longitudinal axis , as well . the main purpose is to investigate the coupling between quasi-2d ( transverse ) collective oscillations and thermal excitations in the collisionless regime . we study the landau damping as a decay mechanism of transverse collective modes as a function of temperature , in which a transverse collective oscillation is annihilated in a collision with a thermal excitation to give rise to another excitation . this paper is organized as follows . in sec . ii we calculate the transverse spectrum of excitations of a cylindrical condensate by solving the linearized gross - pitaevskii equation in 2d within the bogoliubov theory . we obtain also the modes with non - zero @xmath1 . in sec . iii we briefly recall the perturbation theory for the interaction between collective modes of a condensate and thermal excitations ( developed in ref . we apply this theory to calculate the decay rate due to landau damping of a transverse oscillation . in sec . iv we discuss the main results for the transverse quadrupole mode . the situation with the singular transverse breathing mode is also discussed . at low temperature , the elementary excitations of a trapped weakly interacting degenerate bose gas are described by the time - dependent gross - pitaevskii ( gp ) equation for the order parameter : @xmath2 where @xmath3 is the interaction coupling constant , fixed by the @xmath4-wave scattering length @xmath5 , @xmath6 is the atomic mass and the order parameter is normalized to the number of atoms in the condensate @xmath7 . the confining potential is usually cylindrically symmetric and it is given by @xmath8 , with @xmath9 . the ratio between axial ( @xmath10 ) and radial ( @xmath11 ) trapping frequencies defines the anisotropy parameter of the trap @xmath12 . experimentally , in ref . @xcite , the transverse modes have been excited in the radial plane of a highly anisotropic cigar - shaped trap , with @xmath13 . thus , as a reasonable approximation , we consider an idealized cylindrical trap that is uniform in the @xmath0-direction ( @xmath14 ) and has isotropic trapping potential in the radial plane @xmath15 the harmonic trap frequency @xmath16 provides a typical length scale for the system , @xmath17 . we assume a cylindrical condensate with large longitudinal size @xmath18 compared to the radial size @xmath19 , and with a number of atoms per unit length @xmath20 . at low temperatures , the dynamics of the condensate is described by the linearized time - dependent gp equation . assuming small oscillations of the order parameter around the ground - state value @xmath21 \ , , \label{fluctuation}\ ] ] where @xmath22 is the chemical potential , the normal modes of the condensate can be found by seeking fluctuations such as @xmath23 the functions @xmath24 and @xmath25 are the particle "" and hole "" components characterizing the bogoliubov transformations , and @xmath26 is the frequency of the corresponding excited state . the transverse excitations of a highly elongated condensate can be obtained by neglecting oscillations along the longitudinal direction and thus , looking for fluctuations in the transverse plane of the form @xcite @xmath27 where we have used cylindrical coordinates ( @xmath28 ) . transverse excitations are quasi-2d modes . to calculate landau damping we must also consider thermal excitations having a quasi - continuous spectrum at @xmath29 with the finite longitudinal wave vector @xmath1 along @xmath0 direction . to study these modes we look for solutions that correspond to propagating waves of the form @xcite @xmath30 inserting ( [ fluctuation ] ) , ( [ deltapsi ] ) and ( [ deltapsilong ] ) in eq . ( [ tdgp ] ) and retaining terms up to first order in @xmath24 and @xmath25 , it follows three equations . the first one is the nonlinear equation for the order parameter of the ground state , @xmath31 \psi _ { 0}(r_{\perp } ) = \mu \psi _ { 0}(r_{\perp } ) \ , , \label{groundstate}\ ] ] where @xmath32 , and @xmath33 ; while @xmath34 and @xmath35 obey the following coupled equations @xcite : @xmath36 u_{k}(r_{\perp } ) \nonumber \\ & & + g\psi _ { 0}^{2}v_{k}(r_{\perp } ) \label{coupled1 } \\ -\hbar \omega v_{k}(r_{\perp } ) & = & \left [ h_{0}+\frac{\hbar ^{2}}{2m}\left ( \frac{m^{2}}{r_{\perp } ^{2}}+k^{2}\right ) -\mu + 2g\psi _ { 0}^{2}\right ] v_{k}(r_{\perp } ) \nonumber \\ & & + g\psi _ { 0}^{2}u_{k}(r_{\perp } ) \;. \label{coupled2}\end{aligned}\ ] ] we solve the linearized gp equations eqs . ( [ groundstate]-[coupled2 ] ) at zero temperature , to obtain the ground state wave function @xmath37 , the eigenfrequencies @xmath38 and hence the energies @xmath39 of the excitations , as well as the corresponding functions ( @xmath40 ) . in a cylindrical trap the modes of the condensate are labeled by @xmath41 , where @xmath42 is the number of nodes in the radial solution , @xmath43 is the @xmath0-projection of the orbital angular momentum , and @xmath1 is the longitudinal wave vector . the quantum numbers @xmath42 and @xmath43 are discrete ( @xmath44 , and @xmath45 ) whereas @xmath1 for highly elongated condensates ( @xmath46 ) is a real number , and thus , it is a continuous index . moreover , it can be seen from eqs . ( [ coupled1 ] ) and ( [ coupled2 ] ) , that levels with @xmath47 or @xmath48 are exactly degenerated . the excitation spectrum of a cylindrical condensate presents different branches labeled by ( @xmath49 ) that are continuous and increasing functions of @xmath50 @xcite . for a given mode , i.e. , fixed @xmath42 and @xmath43 , the frequency of excitation is @xmath38 . we have numerically checked from eqs . ( [ coupled1 ] ) and ( [ coupled2 ] ) that the state with ( @xmath51 ) and @xmath52 corresponds to the transverse breathing mode with excitation frequency equal to @xmath53 , and that it is independent of the strength of the two - body interaction potential and the number of particles . of course , according to the universal nature of this mode noted above , this general result is also valid in the thomas - fermi ( tf ) limit , where the dispersion relation can be found analytically@xcite . however , the functions @xmath24 and @xmath25 for this mode do not coincide in general with their thomas - fermi limit . the state with ( @xmath54 ) and @xmath52 is a transverse quadrupole mode whose frequency depends on the two - body interaction , ranging from the tf value @xmath55 , valid for large condensates ( @xmath56 or equivalently @xmath57 ) , to the noninteracting value @xmath53 . therefore , the transverse quadrupole has to be obtained numerically by solving eqs . ( [ coupled1 ] ) and ( [ coupled2 ] ) in each particular value of the dimensionless parameter @xmath58 . in the present work , we use the numerical solutions to calculate the landau damping of collective modes . it is well known that the dipole mode ( @xmath59 ) is unaffected by two - body interactions due to the translational invariance of the interatomic force which can not affect the motion of the center of mass @xcite and its excitation frequency is @xmath60 . it is worth stressing that the independence of the interaction of the transverse monopole mode , is a unique property of 2d systems , related to the presence of a hidden symmetry of the problem described by the two - dimensional lorentz group so(2,1 ) @xcite . let us consider a collective mode with frequency @xmath61 , and the excited states @xmath62 available by thermal activation , with energies @xmath63 and @xmath64 , respectively . suppose that this collective mode has been excited and , therefore , the condensate oscillates with the corresponding frequency @xmath61 . due to interaction effects , the thermal cloud of excitations can either absorb or emit quanta of this mode producing a damping of the collective oscillation . we want to study the decay process in which a quantum of oscillation @xmath65 is annihilated ( created ) and the @xmath66-th excitation is transformed into the @xmath67-th one ( or viceversa ) . the energy is conserved during the transition process , therefore @xmath68 where we assume that @xmath69 . this mechanism is known as landau damping . another possible decay mechanism , also due to the coupling between collective and thermal excitations , is the beliaev damping @xcite , which is based on the decay of an elementary excitation into a pair of excitations . let us define the dissipation rate @xmath70 through the following relation between the energy of the system @xmath71 and its dissipation @xmath72 : @xmath73 assuming that the damping is small , one can use perturbation theory to calculate the probabilities for the transition between the @xmath66-th excitation and the @xmath74-th one , both available by thermal activation , yielding the following expression for the landau damping rate @xcite : @xmath75 where the transition frequencies @xmath76 are positive , and the delta function ensures the energy conservation during the transition process . we have assumed that the thermal cloud is at thermodynamic equilibrium and the states @xmath62 are thermally occupied with the usual bose factor @xmath77^{-1}$ ] . the `` damping strength '' has the dimensions of a frequency and is given by @xmath78 the matrix element that couples the low - energy collective mode ( @xmath79 ) with the higher energy single - particle excitations ( for which we use the indices @xmath62 ) is @xcite @xmath80 . \label{matrixel}\end{aligned}\ ] ] in this work we calculate the quantities @xmath81 by using the numerical solutions @xmath24 and @xmath25 of eqs . ( [ groundstate]-[coupled2 ] ) into the integrals ( [ matrixel ] ) , avoiding the use of further approximations in the spectrum of excitations . in cylindrically symmetric traps ," +"the approximate bcs solution of the pairing hamiltonian has been extensively used in condensed matter to study pairing correlations in ultra - small metallic grains @xcite . a much better approximation is given by the density matrix renormalization group @xcite . but , the pairing hamiltonian admits an exact solution worked out by richardson at the beginning of the sixties @xcite . a more recent derivation of the exact solution can be found in ref . the first application of the richardson exact solution was done in ultra - small grains system @xcite . references @xcite and @xcite marks the resurgence of the richardson s exact solution of the pairing hamiltonian . the acknowledge to richardson in refs . @xcite constitutes a recognition to him after forty years in the oblivion . the richardson exact solution has been used to study the effect of the resonant single - particle states on the pairing hamiltonian @xcite . in ref . @xcite the authors gave an interpretation of the pair energies from the richardson solution . they relate the pairing correlations with the pair energies distribution in the complex plane . the pairing hamiltonian is not only exactly soluble but also quantum integrable @xcite . besides the constant pairing , a very special kind of separable pairing interaction also admits an exact solution @xcite . a review on exact solutions of the pairing hamiltonian can be found in the ref . @xcite . the pairing hamiltonian approximates the influence of the residual interaction acting among the valence states lying close to the fermi level . however , it is an open question how one must treat pairing in the continuum . previous studies on the contribution from the continuum to pairing have been reported in refs . @xcite . in this paper we reformulate the problem of determining the exact eigenenergies of the pairing hamiltonian when the continuum is included . real and complex energy representations of the continuum are used . the bcs approximation is not a convenient tool to treat many - body pairing close to the drip line @xcite . it is the intention of this paper to give an exact treatment of the many - body pairing which overcomes the drawbacks of the bcs treatment . the paper is organized as follows . section [ sec.method ] briefly reviews the derivation of the richardson equations with the continuum represented on the real energy axis or in the complex energy plane . in sec . [ sec.result ] the low lying states of even carbon isotopes are evaluated and a comparison of the solutions using the real energy representation are compared with the ones obtained in the complex energy representation . the trajectory of the pair energies are analyzed as a function of the pairing strength . the continuum pair energies are introduced in this section . finally , sec . [ sec.discussion ] summarizes the main results of the paper . in this section the richardson equations for a continuum basis is given . first the continuum is included by enclosing the system in a large spherical box . after the final equations have been obtained , we take the limit of the box to infinity and introduce the single particle level density . in order to avoid the fermi gas we take the derivative of the phase shift for the continuum part of the single particle level density @xcite . finally , we parametrized the cspld for the resonant partial waves and make the analytic continuation to the complex energy plane . in this sub - section we follow the derivation of the exact solution as it was given by jan von delft and fabian braun in ref . the inclusion of the system in a large spherical box provides a finite discrete set of negative ( bound ) energies and an infinite discrete set of positive ( continuum ) energies . let us called @xmath2 the discrete energy with degeneracy @xmath3 , with @xmath4 . the pairing hamiltonian is given by , @xmath5 with @xmath6 . we introduce the pair creation operator @xmath7 which creates a pair of time reversal states with quantum number @xmath8 . following von delft and braun @xcite , who were inspired by a suggestion by richardson , we propose the @xmath9-body ( @xmath10 ) eigenfunction as the antisymmetrised product of @xmath11 wave functions as , @xmath12 where the energies @xmath13 are related to the eigenvalues @xmath14 of the hamiltonian @xmath15 by @xmath16 in order to meet the eigenvalue equation @xmath17 , the parameters @xmath13 , called pair energies , must verify the following set of @xmath11 couple system of equations @xcite @xmath18 where the first summation contains negative and positive energies . the interpretation of this set of equations , called richardson equations , is that the many - body fermions with pairing force behave like the many - boson system with one - body force . both systems are described by the same wave function with the difference that the fermions have to satisfy the richardson equations ( [ eq.rich ] ) in order to fulfill the pauli principle @xcite . in making the limit of the box to infinity the single particle states becomes more and more dense . in that limit the sum becomes an integral , i. e. , @xmath19 the single particle density @xmath20 is the sum of the bound ( negative energy ) states plus the continuum ( positive energy ) states . we make the anzatz that the single particle density in the continuum is given by the derivative of the phase shift @xcite , @xmath21 the index @xmath22 refers to bound states and @xmath23 to continuum states . the first summation is over the valence bound states while the second one is over the continuum partial waves . in practical applications an upper limit @xmath24 is set for the number of partial waves . the richardson equations in a representation which includes the continuum becomes , @xmath25 where the factor @xmath26 takes into account the blocking effect of the @xmath27 unpaired states @xcite . the cspld becomes , @xmath28 the presence of the single particle resonances appear in the cspld , as well as in the cross sections , as bumps . they correspond to states in the continuum ( positive energy states ) which are well localized inside the nuclear surface for a time greater than the characteristic nuclear time @xcite . one can thus split the summation in resonant ( @xmath29 ) and non - resonant ( @xmath30 ) ( background ) contributions as , @xmath31 the single particle density for the resonant states at energies @xmath32 and widths @xmath33 can be written as @xcite . @xmath34 the resonant parameters can be represented by a single complex number @xmath35 which corresponds to the eigenvalue of the mean - field hamiltonian with pure outgoing boundary condition @xcite . by rotating the integration contour of the resonant part of the cspld to the negative imaginary axis , and applying the cauchy theorem , one gets the richardson equations in terms of the complex energy states , @xmath36 where @xmath37 in an overstatement ( the `` density '' @xmath38 can not be defined outside the integral ) one could say that the background contribution to the richardson equation has a real part coming from the non - resonant scattering partial wave states @xmath39 and a complex contribution @xmath38 which is a remnant of the complex analytic extension from @xmath40 . because the presence of the complex energy gamow states in the second summation in eq . ( [ eq.rich2 ] ) , the complex contribution of @xmath38 is necessary to make @xmath41 real . in eq . ( [ eq.rich2 ] ) we have assumed that there is not blocking effect due to continuum states . for the seniority zero case and neglecting the background , eq . ( [ eq.rich2 ] ) reduces to the richardson equations in the gamow basis introduced in ref . @xcite . in this case the complex pairing energies are not complex conjugate to each other , i.e. @xmath41 may be complex . the solution of the richardson equations ( [ eq.rich_cont ] ) with the `` boundary condition '' , @xmath42 and the blocking effect , determine the ground state and the excited state energies of the pairing hamiltonian . the @xmath43c nucleus has three bound configurations ( sec . [ sec.sp ] ) . the first @xmath44 and second @xmath45 configurations can accommodate a single pair , while the third configuration @xmath46 can accommodate three pairs . the configurations @xmath44 , @xmath45 , and @xmath46 are related to the single particle states @xmath47 , @xmath48 , and @xmath49 , respectively . then @xmath50 , @xmath51 , and @xmath52 . from the bound configurations we can accommodate up to five pairs ( @xmath53c ) . because the inclusion of the continuum we will be able to go beyond the nucleus @xmath53c . the ground state ( g.s . ) configuration for a system with @xmath11 corresponds to fill the lowest @xmath11 configurations by solving the richardson eq . ( [ eq.rich_cont ] ) with the blocking coefficient @xmath54 because the g.s . has seniority zero and there are no unpaired states ( all @xmath55 ) . for example , the g.s . of the isotope @xmath56c corresponds to solving one single richardson equation ( [ eq.rich_cont ] ) with the boundary condition @xmath57 . let us called this configuration @xmath58 . the g.s . of the isotope @xmath59c corresponds to solving two richardson equations ( [ eq.rich_cont ] ) with the boundary conditions @xmath60 and @xmath61 . this is the configuration @xmath62 , and so on . the ground state energy @xmath14 is given by eq . ( [ eq.e ] ) with @xmath63 and so on . we have to distinguish between excited states with seniority zero and seniority two . + _ seniority zero ( @xmath64 ) : _ the seniority zero excited states are found by solving as many equations ( [ eq.rich_cont ] ) as pairs , like for the g.s . , but with a boundary condition other than the ground state . for example , the first and second @xmath65 excited states of @xmath56c are found as the solution of a single equation with the boundary conditions @xmath61 , and @xmath66 , respectively . we called such configurations @xmath67 and @xmath68 . as a second example let us consider the first @xmath65 excited state of @xmath69c . it is found by solving three equations ( [ eq.rich_cont ] ) with the boundary conditions @xmath57 , @xmath70 , and @xmath66 . we called this configuration @xmath71 . the energy @xmath14 of the @xmath64 excited state is like eq . ( [ eq.e ] ) but using the excited pair energies . _ seniority two ( @xmath72 ) : _ the seniority two states are found by solving @xmath73 equations ( [ eq.rich_cont ] ) , where @xmath74 is the mass number of the isotope . this is one equation less than the number of pairs in the ground state . the factor @xmath75 in eq . ( [ eq.rich_cont ] ) is given by @xmath26 , where @xmath76 labels the blocking configuration . for example , to find the @xmath72 states in @xmath56c one does not need to solve any equation since @xmath77 . the @xmath72 state energy is just the sum of the single particle energies @xmath78 of the unpaired levels @xmath79 and @xmath80 . let us assumed that the blocking states for the isotope @xmath59c are the configurations @xmath45 and @xmath46 , i. e. @xmath81 , and @xmath82 . then , we have to solve a single equation with @xmath83 , @xmath84 and @xmath85 and the boundary condition @xmath60 . let us call this configuration @xmath86 which gives the degenerate levels @xmath87 . the energy of such a state is" +"cyg x-1 is a persistent x - ray source believed to be powered by accretion onto a black hole from a massive companion . most of the time cyg x-1 spends in the hard state and sometimes it switches to the soft state ( see , e.g. , liang & nolan 1984 ; zhang et al . 1997 ; poutanen 1998 ; gierliski et al . the x - ray luminosity above @xmath2 is estimated to be about @xmath3 ( gierliski et al . 1997 ) , assuming the distance to the source , @xmath4 ( massey , johnson , & degioia - eastwood 1995 ; malysheva 1997 ) . variability of cyg x-1 was extensively studied with various instruments ( see , e.g. , ling et al . 1987 ; gilfanov et al . 1995 ; phlips et al . 1996 ; kuznetsov et al . 1997 ; paciesas et al . 1997 ; wen et al . 1999 ; brocksopp et al . 1999 ; bauciska - church et al . 2000 ) . these studies show the stability of the hard state of cyg x-1 . the photon flux above 50 kev is normally @xmath5 with variations by a factor 2 . in this letter , we analyze the period of the unusually strong hard x - ray activity of cyg x-1 on 1999 april 21 . two strong outbursts activated the batse/_cgro _ ( fishman et al . 1989 ) onboard trigger . we analyze the temporal structure of the outbursts in the four lad energy channels 14 , estimate the peak luminosity of cyg x-1 , and discuss possible implications for theoretical models of accretion in this object . the unusual activity of cyg x-1 can be traced back to 1999 april 19 ( tjd 11287 ) . two events recorded on april 19 were found in the batse data during search for non - triggered gamma - ray bursts ( grbs ) ( stern et al . 1999 , 2000a ) . the best fit locations were within @xmath6 from cyg x-1 ( @xmath7 errors exceeded @xmath8 for those events ) . we use the location procedure described in stern et al . ( 2000b ) which is similar to that used for grb location by pendleton et al . the estimated peak fluxes above 50 kev were about 0.3 and @xmath9 which is high as compared with the normal flux from cyg x-1 . on april 20 , batse detectors were triggered by another event with right ascension , @xmath10 , and declination , @xmath11 ( batse estimate , note also that this event is identified as a grb in the batse data base ) . again , the location was close to cyg x-1 ( slightly beyond 1@xmath12 error circle ) . and @xmath13 . ] the peak flux of this event was about @xmath14 . on april 21 , the two brightest outbursts occurred , with the interval @xmath15 hours . between and after the two outbursts , cyg x-1 demonstrated nothing unusual , being in the hard state with normal luminosity . the summary of all the five events is given in table 1 . we will concentrate on the two brightest events on april 21 ( two last lines in table 1 ) . the locations of both events coincide with the location of cyg x-1 with 2@xmath16 accuracy . in principle , it might be accidental projections of grbs on cyg x-1 . the probability that one of @xmath17 detected grbs with comparable brightness will appear within 2@xmath16 from cyg x-1 is about 0.3 . however , the probability of appearance of two such grbs from the same location within 2.5 hours is low , @xmath18 . besides , the long duration of the events , @xmath19 s , is very unusual for grbs . one concludes that the events are outbursts of cyg x-1 . table 1 + summary of outbursts on 1999 april 19 - 21 [ cols=""^,^,^,^,^,>"",options=""header "" , ] we then compute the cross - correlation coefficient between channels 2 and 3 , @xmath20 ) ( see table 4 ) . the cross - correlation decreases during the outbursts and becomes very low in interval e. it confirms that the soft component gets so soft that it practically does not contribute to the signal in channel 3 . in interval f , the cross - correlation is high , confirming that the soft component has disappeared and we see only the second ( hard ) component in all the three channels . the luminosities of the soft and hard components can be roughly estimated from the step - like cut offs at 64.05 ks and 64.1 ks , respectively . the average luminosity of cyg x-1 in time interval e above 50 kev ( 30 kev ) is @xmath21 ( @xmath22 ) in the soft component and @xmath23 ( @xmath24 ) in the hard component . the normal hard state of cyg x-1 was studied using the earth occultations which occur on each orbit of the _ cgro_. the step in the light curve at the moment of occultation shows the amplitude of the signal from cyg x-1 in each energy channel . the study of cyg x-1 with this method was done by ling et al . ( 1997 ) and paciesas et al . we performed a similar analysis for @xmath25 occultations and evaluated the flux from cyg x-1 and the hardness ratio @xmath26 ( ratio of the signal count rates in channels 3 and 2 ) for each occultation . the results are shown in figure 2 . the observed large dispersion in the hardness ratio may be caused by the measurement errors rather than intrinsic variability of cyg x-1 . to estimate the errors we did a similar analysis of 80 occultations of the crab nebula which is known to be a steady source . we found @xmath27 and the count rate @xmath28 , where the errors represent the standard deviations . the major cause of the errors is the uncertainty in the changing background ( to have good statistics one has to fit the signal on a relatively long period @xmath29 s before and after the occultation , and the background curvature plays a role ) . one should note that the error in the hardness ratio of cyg x-1 is likely to be smaller than that for the crab since its flux is larger . in the outbursts , these errors are even smaller . = 7.5 cm for comparison we also show the estimates of the flux and hardness ratio for the two april 21 outbursts . note that outburst 11289c and interval f of outburst 11289e have hardness ratios similar to the normal hard state . interval e of outburst 11289e is significantly softer . the presence of two emission components ( soft , highly variable , and hard , with lower variability ) in outburst 11289e is intriguing . are they present in the normal state of cyg x-1 ? in the sample of 63 occultations we found that the fractional rms of the count rate ( i.e. the ratio of the rms to the mean count rate ) in channel 2 was higher than that in channel 3 in 47 cases . this indicates higher variability in channel 2 ( the probability of such an accidental excess is @xmath30 ) . the decreasing of the variability with energy was also observed in the 240 kev band ( nowak et al . 1999 ; revnivtsev et al . these facts are consistent with the presence of a hard component with a low variability though this interpretation is not unique . note also that gierliski et al . ( 1997 ) got the best fit to the broad - band x - ray spectrum of cyg x-1 with two thermal comptonization components of different temperatures . the hard state of cyg x-1 has been a puzzle since its discovery . the standard accretion disk model ( shakura & sunyaev 1973 ) was not able to explain the x - ray spectrum , and two modifications of the model were suggested : a two - temperature hot disk and an active corona atop the standard disk ( see beloborodov 1999a for a recent review ) . the advective hot - disk models ( e.g. esin et al . 1998 ) are consistent with the observed spectrum and luminosity of cyg x-1 if the accretion rate has a specific value @xmath31 @xmath32 and the viscosity parameter @xmath33 . here @xmath36 @xmath37 is the eddington luminosity . small variations in the accretion rate , @xmath38 , were predicted to destroy the hard state ( esin et al . 1998 ; but see also zdziarski 1998 ) . by contrast , the luminosity of cyg x-1 is known to vary by a factor of two without substantial changes in the spectral shape ( e.g. , paciesas et al . 1997 ; gierliski et al . such fluctuations already challenged the model , and the hard outbursts analyzed in this letter are even more difficult to explain . the model would work only assuming a specific dependence @xmath39 that keeps @xmath40 ; @xmath41 then should be about unity at the peak of the outburst . in the context of the disk - corona model , the outbursts can be interperted as an enhanced coronal activity of the accretion disk . in this model , the x - ray spectral slope is controlled by one parameter , the feedback factor due to x - ray reprocessing by the disk . the hard - state spectrum of cyg x-1 is well explained if the coronal plasma is ejected away from the disk with a mildly relativistic velocity @xmath42 ( beloborodov 1999b ; malzac , beloborodov , & poutanen 2001 ) . alternatively , the observed emission may be produced by a static corona atop a strongly ionized disk ( e.g. , ross , fabian , & young 1999 ; nayakshin 1999 ) . the corona becomes @xmath43dominated at high luminosities and its temperature decreases ( e.g. , svensson 1984 ; stern et al . 1995 ; poutanen & svensson 1996 ) . pair creation may cause the shift of the spectral break in outburst 11289e to smaller energies . cyg x-1 is a massive x - ray binary and it may be fed mainly by the donor wind . then the pattern of accretion can change completely compared to the standard viscous @xmath44disk or its modifications . the captured wind matter has a low angular momentum , just about critical for disk formation ( illarionov & sunyaev 1975 ) . under such conditions , a small - scale inviscid disk forms , which accretes super - sonically ( beloborodov & illarionov 2001 ) . the disk forms in the ring - like caustic of the accretion flow where energy is liberated in inelastic collision of gas streams . a comptonized power - law spectrum is then emitted with a standard break at @xmath29 kev , and it has appearance of a normal hard state of cyg x-1 . the two - component emission in outburst 11289e probably requires a two - zone emission model . for instance , the soft component may be associated with a variable coronal emission atop the disk , and the hard component with an inner relativistic jet . a corona - jet model was recently proposed by brocksopp et al . ( 1999 ) based on correlations between the x - rays and the radio emission observed in cyg x-1 . the april 1999 outbursts were , however , too short to have a significant impact on the flux in radio and no substantial changes were detected ( r. fender and g. pooley , private communication ) . in the context of the wind - fed accretion model" +"in this contribution we present our results @xcite for @xmath0-induced one pion production cross sections in mineral oil ( @xmath1 ) for neutrino energies below 2gev . these results are compared to the experimental data obtained by the miniboone collaboration @xcite . our calculational starting point is the pion production model at the nucleon level of refs . @xcite , that we have extended from the @xmath2 region up to 2gev neutrino energies by the inclusion of the @xmath3 resonance . apart from the @xmath2 already present in the model , the @xmath3 resonance gives the most important contribution in that extended energy region @xcite . in - medium corrections in the production process include pauli - blocking , fermi motion , and the modification of the @xmath4 resonance properties inside the nuclear medium . not only the @xmath4 propagator is modified , but there is also a new pion production contribution ( referred to as @xmath5 in the following ) that comes from the changes in the @xmath4 width in the nuclear environment . for pion final state interaction ( fsi ) we use a cascade program that follows ref . @xcite where a general simulation code for inclusive pion nucleus reactions was developed . when coherent pion production is possible we evaluate its contribution using the model in refs . @xcite . due to lack of space , here we shall just show the results . for details we refer the reader to ref @xcite . our results are qualitatively similar to those obtained by other groups @xcite . we start by showing total cross sections for a given neutrino energy . in the left panel of fig . [ fig : totalccpip ] we compare with miniboone data our results for @xmath6 production in a charged current ( @xmath7 ) process . our cross sections are below data for neutrino energies above @xmath8gev . the contribution from the @xmath9 resonance only plays a role above @xmath10gev , making some 8% of the total at the highest neutrino energy . the @xmath5 term contributes for all energies , being around 8% of the total . similar results are obtained for a final @xmath11 ( right panel ) . ( left ) and @xmath12 ( right ) total production cross section for @xmath13 @xmath7 interaction in mineral oil . dashed line : @xmath14 contribution . dotted line : @xmath15 contribution . double - dashed dotted line : coherent contribution . solid line : total contribution . broken line : same as solid line but without the @xmath5 contribution . dashed - dotted line : same as solid line but without the contribution from the @xmath9 . experimental data taken from refs . @xcite and @xcite.,title=""fig : "" ] ( left ) and @xmath12 ( right ) total production cross section for @xmath13 @xmath7 interaction in mineral oil . dashed line : @xmath14 contribution . dotted line : @xmath15 contribution . double - dashed dotted line : coherent contribution . solid line : total contribution . broken line : same as solid line but without the @xmath5 contribution . dashed - dotted line : same as solid line but without the contribution from the @xmath9 . experimental data taken from refs . @xcite and @xcite.,title=""fig:"",height=183 ] total production cross section for cc interaction in mineral oil . solid line : our full model with @xmath16 . dashed line : full model with @xmath17 . dashed - dotted line : full model with @xmath18 . experimental data taken from ref . @xcite.,height=170 ] in fig . [ fig : totalccpipca5 ] we show the effects in our results of changing the value of the dominant axial nucleon - to - delta form factor within the uncertainties in its determination in ref . a larger value than the central one we use ( @xmath16 ) seems to be preferable in the high energy region . cross section for charged current @xmath19 production by @xmath13 in mineral oil . captions as in fig . [ fig : totalccpip ] . we also show in the right panel results without fsi of the final pion ( double - dotted dashed line ) . data from ref . @xcite . , title=""fig:"",height=170 ] cross section for charged current @xmath19 production by @xmath13 in mineral oil . captions as in fig . [ fig : totalccpip ] . we also show in the right panel results without fsi of the final pion ( double - dotted dashed line ) . data from ref . title=""fig:"",height=170 ] ( left panel ) and @xmath20 ( right panel ) cross section for @xmath7 @xmath12 production by @xmath13 in mineral oil . captions as in figs . [ fig : totalccpip ] and [ fig : cctpi ] . data from ref . @xcite . , title=""fig:"",height=170 ] ( left panel ) and @xmath20 ( right panel ) cross section for @xmath7 @xmath12 production by @xmath13 in mineral oil . captions as in figs . [ fig : totalccpip ] and [ fig : cctpi ] . data from ref . @xcite . , title=""fig:"",height=170 ] in fig . [ fig : cctpi ] we compare results , convoluted with the neutrino flux in ref . @xcite , for the differential @xmath21 cross section for @xmath7 @xmath19 production by @xmath13 . we disagree with data for @xmath22 above 0.15gev . the agreement improves if we artificially remove fsi ( see right panel ) . also in the right panel we show the effects of not including the @xmath5 or @xmath9 contributions . by neglecting the @xmath5 contribution the cross section decreases by some 10% around the peak at @xmath23gev . the @xmath9 plays a very minor role since the neutrino flux peaks at around 600mev . differential @xmath24 and @xmath20 cross sections for @xmath7 @xmath12 production by @xmath13 are shown in fig.[fig : ccpi0 ] . for their evaluation we take the neutrino flux from ref . our model agrees with data for pion momentum below 0.2gev / c but it produces too few pions in the momentum region from 0.22 to 0.55gev / c . as seen from the angular distribution those missing pions mainly go in the forward direction . the effects of ignoring fsi are also shown in both panels . cross section per nucleon for @xmath25 @xmath12 production by @xmath13 ( left panel ) and @xmath26 ( right panel ) in mineral oil . captions as in figs . [ fig : totalccpip ] and [ fig : cctpi ] . data from ref . @xcite . , title=""fig:"",height=173 ] cross section per nucleon for @xmath25 @xmath12 production by @xmath13 ( left panel ) and @xmath26 ( right panel ) in mineral oil . captions as in figs . [ fig : totalccpip ] and [ fig : cctpi ] . data from ref . title=""fig:"",height=173 ] cross section per nucleon for @xmath25 @xmath12 production . captions as in figs . [ fig : totalccpip ] and [ fig : cctpi ] . data from ref . @xcite.,title=""fig:"",height=173 ] cross section per nucleon for @xmath25 @xmath12 production . captions as in figs . [ fig : totalccpip ] and [ fig : cctpi ] . data from ref . @xcite.,title=""fig:"",height=173 ] in figs . [ fig : ncmom ] and [ fig : nccos ] we present the results for neutral current ( @xmath25 ) production that we compare with data by the miniboone collaboration @xcite . in each case we use the @xmath0 fluxes reported in ref . [ fig : ncmom ] shows the different contributions to the @xmath24 differential cross section . our results show a depletion in the @xmath27gev / c momentum region though the agreement is better than in the @xmath7 case . the results agree with data if one neglects fsi . looking now at the differential @xmath20 cross sections shown in fig . [ fig : nccos ] , one can see that our results agree better with data in the antineutrino case where we are within error bars except in the very forward direction . a clear deficit in the forward direction is seen for the reaction with neutrinos but the agreement is better than in the corresponding @xmath7 reaction . in both cases , the coherent contribution is shown to be very relevant in the forward direction . once more , if one artificially switches off fsi effects we get a good agreement with data . this research was supported by the spanish ministerio de economa y competitividad and european feder funds under contracts nos . fpa2010- 21750-c02 - 02 , fis2011 - 28853-c02 - 01 , fis2011 - 28853-c02 - 02 and csd2007 - 00042 , by generalitat valenciana under contract no . prometeo/20090090 and by the eu hadronphysics3 project , grant agreement no . 283286 . 9 hernndez e , nieves j and vicente vacas m j 2013 _ phys . _ d * 87 * 113009 aguilar - arevalo a a _ et al . _ [ miniboone collaboration ] 2011 _ phys _ d * 83 * 052007 aguilar - arevalo a a _ et al . _ [ miniboone collaboration ] 2011 _ phys _ d * 83 * 052009 aguilar - arevalo a a _ et al . _ [ miniboone collaboration ] 2009 _ phys . rev . _ d * 81 * 013005 salcedo l l , oset e , vicente - vacas m j and garcia - recio c 1988 _ nucl . _ a * 484 * 557 amaro j e , hernndez e , nieves j and valverde m 2009 _ phys . rev . _ d * 79 * 013002 hernndez e , nieves j and valverde m 2010 , _ phys . _ d * 82 * 077303 lalakulich o and mosel u 2013 _ phys . _ c * 87 * 014602 sobczyk j t and zmuda j 2013 _ phys . rev . _ c * 87 * 065503" +"the polcor instrument is a combined imager , coronograph and polarimeter built for the nordic optical telescope ( not ) . polcor provides sharp images ( resolution down to 02 ) , has a well - defined psf ( resulting in a higher image contrast ) and a high - quality polarimeter . + we observed three sources using polcor / not : the binary s - type agb star w aql , and the two detached shell carbon stars u cam and dr ser . observations of the polarized light around the stars trace the circumstellar dust distribution and thus enables the search for structures and asymmetries in the circumstellar envelope . though this study the geometry of the mass loss can be investigated which will give important clues not only to the processes at play , but also to the transition from the agb phase to the planetary nebula phase . the circumstellar dust distribution around the binary star w aql is mapped and found to be asymmetric , both on large ( 10 ) and on smaller ( 1 ) scales ( fig . 1 ) . the large - scale images show what appears to be a dust - density enhancement on the south - west side of the star and the inner region appears bi - polar through the coronographic mask . these structures are in agreement with what could be expected from binary interaction ." +"rotational brownian motion of colloidal particles is a classical subject in statistical physics @xcite . contrary to its translational cousin , _ i.e. _ `` usual '' brownian motion , it does not result in changes of the particle location and is hence not as easily demonstrated in experiments . if , however , the suspended particles carry an electric or magnetic moment their orientation couples to external fields and the electric or magnetic relaxation properties of the suspension are direct consequences of the rotational diffusion of the constituting particles . in particular , in the well developed theory of ferrofluids the importance of rotational brownian motion for the theoretical description of the often complex and surprising hydrodynamic and magnetic properties was recognized already a long time ago @xcite . ferrofluids are suspensions of nano - size ferromagnetic grains in carrier liquids like water or oil . they combine the hydrodynamic properties of newtonian fluids with the magnetic behaviour of superparamagnets @xcite . due to the viscosity of the carrier liquid there is a coupling between the rotation of the magnetic grains and the local vorticity of the hydrodynamic flow . this coupling can , _ e.g. _ , be used to spin up ferromagnetic drops floating in a non - magnetic fluid of the same density with the help of a _ rotating magnetic field _ @xcite . complementary , a rotational ferrofluid flow exposed to a static magnetic field exhibits an enhanced shear viscosity @xcite . various related effects such as `` negative '' rotational viscosity @xcite , magneto - vortical resonance @xcite , and anomalously enhanced ac - response due to coherent particle rotation @xcite have been investigated . they rely on the exchange of angular momentum between rotating particles and an oscillating magnetic field . in these cases , the imposed non - zero _ flow vorticity _ of the ferrofluid is crucial for breaking the symmetry between clockwise and counter - clockwise particle rotation . in the present paper we investigate a much more indirect and subtle aspect of the interplay between rotational brownian motion of ferrofluid particles and their relaxation dynamics in an external magnetic field . we will show that a suitably designed time dependent external magnetic field _ without net rotating component _ may rectify the fluctuations of the particle orientation and set up a _ noise - induced _ rotation of the ferromagnetic grains . we will hence investigate how angular momentum can be transferred from an _ oscillating _ magnetic field to a ferrofluid _ at rest_. the effect was predicted theoretically and demonstrated experimentally in a previous short communication @xcite . in the present paper we provide much more details on the theoretical description and add several new results . the extraction of directed motion from random fluctuations is an old and controversial problem in statistical mechanics with a long and interesting history @xcite . although excluded by the second law of thermodynamics for equilibrium systems , rectification of fluctuations _ is _ possible in systems driven sufficiently far away from thermal equilibrium @xcite . the problem has gained renewed attention under the trademarks of `` thermal ratchets '' and `` brownian motors '' due to its possible relevance for biological transport @xcite and the prospects of nano - technology @xcite . ferrofluids are ideal systems to investigate such fluctuation driven transport phenomena and also to demonstrate them experimentally @xcite : as already discussed above , the rotational dynamics of the ferromagnetic grains is strongly influenced by thermal fluctuations . appropriate time - dependent potentials can be easily designed with the help of external magnetic fields . finally , directed rotational transport in ferrofluids should manifest itself as systematic rotation of the ferromagnetic nano - particles . this in turn can be easily detected from the resulting _ macroscopic _ torque on the carrier liquid . various somewhat related but still quite different phenomena in rotational dynamical systems are treated in @xcite . throughout the paper we will use two basic approximations which simplify the analysis considerably and which are rather common for ferrofluids @xcite . the first is to neglect neel - relaxation of the magnetization , _ i.e. _ the rotation of the magnetization vector with respect to the ferromagnetic particle . this is justified for particle sizes that are not too small and amounts to assuming that the magnetic moments are firmly attached to the geometry of the particles . any reorientation of the magnetic moment hence requires a rotation of the particle as a whole . the second approximation is to neglect dipole - dipole interactions between the particles . although these interactions may be important in concentrated ferrofluids , they are negligible in sufficiently diluted ones . the ratchet mechanism of central interest in the present investigation can operate without any particle - particle interaction . we will hence assume that our ferrofluids are sufficiently diluted and use a _ single particle _ model . for a more quantitative assessment of the role of the dipole - dipole interactions see _ e.g. _ @xcite and references therein . the paper is organized as follows . in section [ sec : model ] we introduce the general framework for describing the rotational brownian motion of a single suspended ferromagnetic particle in an external magnetic field . section [ sec : symm ] gives a detailed account of the symmetries characteristic of our system and discusses how these symmetries influence the possibility for a ratchet mechanism to operate . in section [ sec : fpe ] the central fokker - planck equation describing our system is analyzed . besides an investigation of the weak noise limit we describe the numerical solution of the fokker - planck equation and compare the results with two different approximate treatments yielding analytical expressions for the transferred angular momentum . finally , section [ sec : conc ] contains some conclusions . we consider the rotational motion of a spherical particle of volume @xmath0 and magnetic moment @xmath1 immersed in a liquid with dynamic viscosity @xmath2 and subject to a horizontal , time dependent , spatially homogeneous magnetic field @xmath3 . the field is composed of a constant part @xmath4 parallel to the @xmath5-axis and an oscillatory part @xmath6 with period @xmath7 along the @xmath8-direction @xmath9 different choices for the time dependence of @xmath10 are of interest . in the present paper we will mainly discuss two cases which are each representative for a whole class . our first standard choice is @xmath11 where the amplitudes @xmath12 , and the phase @xmath13 are control parameters . the main features of this time dependence are a zero average over one period and the presence of a higher harmonic of the basic frequency . as a second example , we will also discuss the form @xmath14 for which the average over one period is different from zero . it arises naturally if the constant field component is not perpendicular to the time dependent one . in any case , the magnetic field is of a pure oscillatory character , _ i.e. _ it _ does not contain a net rotating component_. the orientation of the particle at time @xmath15 is described by the unit vector @xmath16 where @xmath17 denotes the modulus of the magnetic moment . the time evolution of @xmath18 is given by @xmath19 where @xmath20 denotes the instantaneous angular velocity of the particle . changes of @xmath21 are due to torques on the particle . denoting by @xmath22 the angular part of the three dimensional nabla operator , the magnetic torque @xmath23 derives from the potential energy @xmath24 of a magnetic dipole in an external field @xcite . further , the viscosity @xmath2 of the carrier liquid gives rise to a viscous torque @xcite @xmath25 additionally , the interaction between the rotating particle and the surrounding liquid also causes thermal fluctuations which generate a stochastic torque @xcite @xmath26 here , @xmath27 is a vector of independent , @xmath13-correlated gaussian noise sources of zero mean , the noise intensity is related to the temperature @xmath28 and the dissipation ( [ defvisctor ] ) of the carrier liquid by the fluctuation - dissipation relation , and @xmath29 stands for boltzmann s constant . denoting the moment of inertia of the particle by @xmath30 , the equation of motion for @xmath21 acquires the form @xmath31 eqs.([evol1 ] ) and ( [ evol2 ] ) form a closed set of equations for the description of the rotational motion of the particle . using experimentally relevant parameter values ( density of the particle @xmath32 kg / m@xmath33 , particle radius @xmath34 nm , viscosity @xmath35 pas , time scale @xmath36 s ) we find that the first term on the l.h.s . ( [ evol2 ] ) is five to seven orders of magnitude smaller than the second one . we may hence safely neglect inertial effects @xcite and find for @xmath21 in the overdamped limit @xmath37 where we have introduced @xmath38 . using this result in ( [ evol1 ] ) yields a closed equation for the time evolution of @xmath18 @xmath39 it is convenient to introduce dimensionless units . to this end we measure time in units of the inverse of the external driving frequency , @xmath40 , use @xmath41 as unit for the magnetic field strength , @xmath42 , and rescale the noise intensity according to @xmath43 . the evolution equation for the orientation @xmath18 then reads @xmath44 introducing the brownian relaxation time @xmath45 we note that the rescaled , dimensionless noise intensity @xmath46 occurring in ( [ evol4 ] ) just gives the ratio between the relevant deterministic and stochastic time scales in the system : @xmath47 to proceed , we parametrize the orientation @xmath18 of the magnetic particle by two angles @xmath48 and @xmath49 according to @xmath50 from ( [ evol4 ] ) we then find the following langevin equations for the time evolution of these angles @xcite @xmath51 in the dimensionless units adopted , the noise intensity @xmath46 is given by ( [ defd ] ) and the potential ( [ defu ] ) takes the form @xmath52 the thermal fluctuations @xmath53 and @xmath54 are given by two independent , @xmath13-correlated gaussian noise sources of zero mean . note that in ( [ lan2 ] ) we are dealing with multiplicative white noise but since the multiplicative function is independent of @xmath55 , no ambiguity ( ito- vs. stratonovich - interpretation @xcite ) arises . it is instructive also to consider the simplified situation of a one - dimensional dynamics in which the vector @xmath18 is assumed to be constrained to the horizontal @xmath5-@xmath8-plane . accordingly , ( [ lan1 ] ) is replaced by @xmath56 and ( [ lan2 ] ) simplifies to @xmath57 where @xmath58 the observable of foremost interest in the present investigation is the time and ensemble averaged torque ( [ defmagtor ] ) exerted by the magnetic field upon the magnetic particle in the long time limit , _ i.e. _ after initial transient have died out . since the magnetic field ( [ deffield ] ) is constrained to the @xmath5-@xmath8 plane , only the @xmath59-component of this magnetic torque can be different from zero . suppressing the subscript @xmath60 in ( [ defmagtor ] ) from now on , we denote the averaged @xmath59-component of the magnetic torque by @xmath61 , where @xmath62 stands for the ensemble average over the different realizations of the noise terms in ( [ lan1 ] ) , ( [ lan2 ] ) and the overbar represents the time average over one period of the magnetic field . using ( [ deffield ] ) and ( [ defmagtor ] ) we get @xmath63 exploiting ( [ defpot ] ) and ( [ lan2 ] ) one readily finds the equivalent expressions @xmath64 for reasons of ergodicity , the ensemble average in ( [ torav ] ) is equivalent" +"gaining control over the external and the internal degrees of freedom of molecules is of great interest for a range of areas in molecular science . one approach , dating as far back as the 1920s @xcite , relies on the application of inhomogenous ( static or low frequency ) magnetic and electric fields . this has proven most useful for controlling the full three - dimensional motion of molecules , including control of the velocity distribution , bringing molecules to a stand still , storing them for extended periods of times and trapping them in a confined volume ( for a recent review see @xcite ) . an alternative and complementary approach relies on the use of non - resonant non - ionizing laser fields typically supplied by pulsed lasers . many studies during the last decade have shown that strong non - resonant laser fields can effectively manipulate the external degrees of freedom of isolated gas phase molecules . the manipulation results from laser - induced forces and torques due to the interaction between the induced dipole moment and the laser field itself . examples of manipulation include deflection @xcite , focusing @xcite and slowing @xcite of molecules through the dependence of the non - resonant polarizability interaction on the intensity distribution in a laser focus . likewise , the dependence of the induced dipole interaction on molecular orientation has proven highly useful for controlling the rotation of a variety of molecules @xcite . in particular , the spatial orientation of molecules can be sharply confined with respect to axes that are fixed in the laboratory . molecular manipulation by induced dipole forces extends beyond the external degrees of freedom and has also been demonstrated for the internal degrees of freedom such as vibrational motion @xcite in molecular hydrogen . notably , the electrical field from laser pulses can modify energy potential barriers such that photoinduced bond breakage of a small linear molecule is guided to yield a desired final product @xcite . in the case of larger molecules control of the lowest frequency vibrational modes attracts special interest since some of these modes correspond to motion along well - defined reaction coordinates separating two conformational minima ( conformers ) . although many molecules contain large number of conformers it is often just two conformers that dominate important chemical properties , for instance chirality . a particularly important example is found in axially chiral molecules @xcite such as biaryl systems . in these molecules rotation about a single stereogenic carbon - carbon ( c - c ) bond axis changes the molecule from one enantiomer into the opposite enantiomer ( mirror image ) . recently , we demonstrated that the laser - induced nonresonant polarizability interaction can also be used to influence the internal rotation of an axially chiral molecule around the stereogenic c - c bond axis @xcite . in particular , we showed that by fixing the c - c bond axis of a substituted biphenyl molecule in space , using laser induced alignment by a long laser pulse , it was possible to initiate torsional motion of the two phenyl rings by a short laser pulse polarized perpendicular to the fixed axis . the purpose of the present work is to extend our recent paper @xcite . in particular , we discuss our theoretical modelling in detail . a ns laser pulse aligns @xcite the stereogenic axis of 3,5-diflouro-3,5-dibromo - biphenyl ( dfdbrbph ) along its polarization . this enables a much shorter fs pulse , which we will refer to as the kick pulse , to both initiate torsional motion and set the molecule into rotation around the fixed axis . the internal as well as external rotational motion is monitored by fs time - resolved coulomb explosion imaging . the inset of fig . [ fig1 ] shows a model of the dfdbrbph molecule with the stereogenic axis marked by red . according to our quantum chemical calculations , the laser - free torsional potential , illustrated by the red dotted curve in fig . [ fig1 ] , has minima at dihedral angles of @xmath0 corresponding to the r@xmath1 and s@xmath1 enantiomeric forms , and where the dihedral angle is the angle between the two phenyl rings . the twisted equilibrium shape is characteristic of biphenyl compounds . the traditional view is that this non - planarity results from competition between stabilization via conjugation of the @xmath2-orbital systems and steric repulsion between the ortho - positioned atoms @xcite . we might mention that alternative explanations have recently been discussed @xcite . our strategy for controlling @xmath3 relies on a transient modification of the field - free potential curve by a fs kick pulse ( fig . [ fig1 ] ) . the modification , caused by the nonresonant polarizability interaction @xcite converts the initial stationary quantum states , localized near the minima of the torsional potential , into vibrational wave packets , i.e. , coherent superpositions of several quantum states . the temporal evolution of these wave packets gives rise to time - dependent torsional motion , and the grey and the black curves in fig . [ fig1 ] show the calculated expectation values of @xmath3 for a particular set of laser parameters . the stereogenic c - c bond axis is fixed in the laboratory frame by adiabatic alignment utilizing a moderately intense , linearly polarized ns laser pulse @xcite . the ns pulse is intense enough to keep the c - c axis tightly confined , yet weak enough to modify the torsional potential only slightly . the fs kick pulse is applied with its polarization perpendicular to the aligned c - c bond axis to ensure primarily influence on torsion while avoiding other possible vibrational motion . the dfdbrbph compound is prepared as a racemate and the experiment is carried out on isolated molecules at rotational temperatures of a few kelvin . under these conditions we have equal numbers of molecules initially localized in the @xmath4 or 39@xmath5 conformation ( see fig . [ fig1 ] ) and no thermally induced transitions between the two conformations occur . the intense probe pulse , sent at time @xmath6 with respect to the kick pulse , removes several electrons from the molecules , thereby triggering coulomb explosion into ionic fragments . in particular , the br@xmath7 and f@xmath7 fragment ions recoil in the planes defined by the br- and f - phenyl rings . by recording the velocities of both ion species with two - dimensional ion imaging @xcite , we determine the instantaneous orientation of each of the two phenyl planes at the time of the probe pulse . between the br- and f - phenyl planes . the asymmetry in the potential is obtained by orienting the molecules ( here with the br - phenyl plane out of the paper ) , 3d aligning them , and by polarizing the kick pulse at an angle of 13@xmath5 with respect to the second most polarizable axis ( smpa ) ( see fig . [ fig2 ] ) . the red dotted curve at large times illustrates the laser - free time - independent torsional potential . for the s@xmath1 enantiomer , starting out with @xmath8 , the time varying potential induces an oscillatory motion ( grey curve ) corresponding to torsion confined within the initial well . by contrast , due to the induced asymmetry between the two wells , the initial r@xmath1 enantiomer is traversing the central torsional barrier , and ends up as an s@xmath1 enantiomer undergoing internal rotation ( black curve ) . the kick pulse has an intensity of @xmath9 w@xmath10@xmath11 and a duration of 1.0 ps ( fwhm ) . the torsional motion may be monitored by fs time - resolved coulomb explosion imaging . the inset shows a model of the dfdbrbph molecule with the sterogenic axis marked by red ( grey ) . ] to account for the motion of the nuclei of the dfdbrbph molecule we make use of two sets of coordinate systems ( see fig . [ fig2 ] ) : a molecular fixed ( mf ) frame attached to the molecule and a laboratory fixed ( lf ) frame specified by the lasers . the mf coordinates are chosen with the @xmath12 axis along the stereogenic axis pointing from the phenyl ring with the bromines towards the phenyl ring with the flourines , and the @xmath13 axis is chosen along the phenyl ring with the bromines . the lf coordinates are chosen with the @xmath14 axis along the polarization direction of the ns pulse and the @xmath15 axis along the kick pulse polarization direction . in agreement with the experimental observations ( cf . [ sec : results ] ) , we assume that the stereogenic axis of the dfdbrbph molecule is aligned along the @xmath14 axis . and the laboratory fixed @xmath16 coordinate axes . the dotted line indicates the second most polarizable axis ( smpa ) , which is located 11@xmath5 from the br - phenyl ring and 28@xmath5 from the f - phenyl ring . ] also , we neglect all normal modes , except the lowest one , which corresponds to torsion ( see sec . [ subsec : qmcalc ] for details on quantum chemical calculations , justifying , e.g. , this assumption ) . in this simplified situation and in the absence of the kick pulse the task is reduced to describing the coupled rotations of the two ( rigid ) phenyl rings of the molecule as given in the lf frame by the hamiltonian [ atomic units , @xmath17 , are used throughout unless indicated otherwise ] @xmath18 where @xmath19 , is the angle of the @xmath20 phenyl ring with respect to the kick pulse polarization axis , @xmath21 the moment of inertia for rotation of the @xmath20 phenyl ring around the stereogenic axis ( @xmath22 , @xmath23 ) and @xmath24 is the laser - free torsional potential as obtained from quantum chemical calculations ( fig . 3 ) . by changing the coordinates to the dihedral angle @xmath25 between the two phenyl rings and the weighted azimuthal angle @xmath26 , characterizing the rotation of the molecule , with @xmath27 , we obtain @xmath28 here @xmath29 is the total moment of inertia of the molecule for rotation around the stereogenic axis and @xmath30 is a relative moment of inertia for the two phenyl rings around the axis . a full rotation of either phenyl ring leaves us with the same molecule implying @xmath31-periodic boundary conditions of the eigenfunctions of @xmath32 from eq . , i.e. , @xmath33 , with @xmath34 and @xmath35 integers . we shall assume that this property also applies to @xmath36 and @xmath3 , so that we simply need to consider eigenfunctions @xmath37 of eq . that separates into rotation of the molecule as described by the @xmath31-periodic function @xmath38 and torsion accounted for by the @xmath31-periodic function @xmath39 . [ rigorously , the bounds for @xmath36 depend on @xmath3 @xcite . at the time scales of interest , however , a molecule generally only makes a small fraction of a full rotation so that the effect of @xmath36-@xmath3 coupling is negligible . ] the separation is physically motivated by considering the energy scales related to rotation and torsion . the energy scale of the prior is given by @xmath40ev . for torsion , on the other hand , the relevant energy is determined by the torsional potential , and a harmonic approximation of the potential near the minimum at @xmath41 yields a frequency corresponding to the energy @xmath42 mev . using that the period of motion is of the order planck s constant divided by the energy , we therefore see that the molecule rotates ( @xmath36 change ) on a nanosecond time scale , whereas the torsion ( @xmath3 change ) is of picosecond duration ." +"scale relativity allows one to give foundations to the postulates @xcite and motion equations @xcite of quantum mechanics , and to gauge theories of particle physics @xcite , in particular to electromagnetism @xcite , by providing them with a geometric interpretation in the framework of a fractal space - time . successive velocity doublings proceeding from the giving up of the differentiability assumption allows one to obtain the motion equations as geodesic equations of this fractal space - time , thus implementing quantum covariance . we have therefore been able to derive successively : the schrdinger equation @xcite , which applies to non - relativistic particles , the free klein - gordon @xcite and dirac @xcite equations and finally the pauli equation @xcite , which is the non - relativistic limit of the dirac equation and which applies to the behavior of a non - relativistic spin 1/2 particle , e.g. a non - relativistic electron . we will come back in more details in the following to the two equations of interest here , klein - gordon and dirac . moreover , the relativity principle applied to scales implies that the scale of an internal structure on a fractal geodesic is modified by a displacement in space - time and reciprocally . this property allows one to construct the electromagnetic field and the electric charge while giving them a physical meaning , thus implementing scale covariance . recall that in scale relativity quantum covariance is implemented by the use of a covariant velocity operator , @xmath0 . owing to a first symmetry breaking , that of @xmath1 , this operator becomes complex . when one adds the breakings of @xmath2 and of @xmath3 , one gets a bi - quaternionic operator . being complex or bi - quaternionic , these operators are used to write the motion equations of free particles under the form of geodesic equations @xmath4 a complex velocity operator inserted in the above equation allows one to recover the usual free klein - gordon equation @xcite . recall this applies to the motion of a relativistic spinless particle non - submitted to an external field . with a bi - quaternionic velocity operator , one obtains a bi - quaternionic klein - gordon - like equation . the free dirac equation follows as its square root @xcite . it applies to a relativistic spin 1/2 particle , such as the electron and its anti - particle , the positron , non - submitted to an external field . these two particles are represented , in standard quantum mechanics , by only one object , the bi - spinor , which has all the mathematical properties of a bi - quaternion . this shows that the scale relativity formalism is perfectly appropriate to reproduce phenomena observed in microphysics . in the framework of electromagnetism , scale relativity identifies gauge transformations , whose nature was previously unknown , with global scale transformations , @xmath5 , in `` scale space '' . it allows also to recover , while giving it a geometric interpretation as a scale covariant derivative , the usual form of the covariant derivative of quantum electrodynamics , i.e. @xmath6 eventually , charges emerge naturally as conserved quantities in scale transformations . up to there , everything is perfect as regards scale relativity . our aim is now to recover , from the first principles of scale relativity , both equations klein - gordon and dirac , but for particles submitted to an external electromagnetic filed . the first idea which crosses our mind is to combine both tools , scale covariant derivative ( qed ) and quantum covariant velocity operator , by writing the strongly covariant geodesic equation : @xmath7 we obtain actually , when integrating this equation , the usual klein - gordon equation for a relativistic spinless particle in an external electromagnetic filed . proud of this success , we hoped then to be able to recover the electromagnetic dirac equation by applying exactly the same method which was so successful in the case of free particles , i.e. extracting the square root of the bi - quaternionic electromagnetic klein - gordon - like equation . more exactly , we had shown in @xcite that a bi - quaternionic free klein - gordon - like equation amounts to applying twice to the wave function the time part of the dirac equation and then to equal it to its squared spatial part . now , this is no more the case when an electromagnetic field comes into play . an additional term appears and we have shown it corresponds to the coupling between the intrinsic magnetic moment , or spin , of the electron and the magnetic field . this term is the relativistic analogue of that implying the electron magnetic moment in the pauli equation . the conclusion is this method is not well - adapted and we must use another one . instead of implementing a strong covariance , as in the former method , we are going to use both tools , quantum covariance and scale covariance , as in standard quantum mechanics . first , we apply the quantum covariance and we obtain the free klein - gordon and dirac equations as before . then , we replace in these equations the ordinary derivative , @xmath8 , by its `` inertial '' scale covariant part , @xmath9 . we obtain thus the electromagnetic dirac equation under its usual form , where the spin - magnetic field coupling does not appear explicitly . we have seen that the only quantum covariant geodesic equation yields the free dirac equation . when we add the scale covariance directly at the level of the geodesic equation , we obtain an additional term representing the spin - magnetic field coupling . the explanation is as follows . in scale relativity , spin proceeds directly from the fractality of space - time , while charges , which stem from transformations in scale space , are only indirect consequences of this fractality . hence , the influence of fractality through spin is more fundamental and must be applied first , independently from that of the field . spin is an intrinsic quantum property of the particles , component of the total angular momentum which is itself a constant of motion . it takes only integer or half - integer values of @xmath10 . in scale relativity , the spin 1/2 can have two different interpretations . in the first , one considers it as a quantum charge of the electron / positron . in this case , a term representing the coupling of this charge to the external field appears explicitly in the equations . this interpretation corresponds to the way spin stems when the first strongly covariant method is used to obtain the motion equations . it can also be considered as directly linked to the fractal geometry of space - time . in this case , its coupling to the magnetic field is implicit and there is no additional term in the dirac equation which recovers its usual form , as when the second method is used . this interpretation has been illustrated with numerical simulations aiming at visualizing the typically spinorial form of some geodesics in a fractal space - time ( see fig . [ fig1 ] ) @xcite . ) in a fractal space . realization chosen between an infinity of possible realizations . ] owing to the principle of relativity of scales , scale variables are explicit functions of the space - time coordinates . this implies , for every displacement in such a space - time , the appearance of a change in scale interval due to the fractal geometry , which reads @xmath11 where @xmath12 is the ( active ) electric charge and @xmath13 defines the electromagnetic field . it can be shown that the passive electric charge @xmath14 is equal to the active electric charge @xmath12 @xcite . the electric charge , a mere property of the electron stemming from scale transformations , must be considered therefore of a less fundamental nature than the spin , itself a component of a first integral of motion . we have seen that the internal nature of spin , intrinsically linked to the fractal geometry of space - time is more fundamental than that of the charges , which also stem from this fractality , but less directly . therefore , strong covariance , which can be properly applied to recover the electromagnetic klein - gordon equation , since this equation does not imply spin , must be replaced by a weaker covariance in the case of the dirac equation where spin is involved ." +"a central factor in the application of machine learning to a given task is the _ inductive bias _ , _ i.e. _ the choice of hypotheses space from which learned functions are taken . the restriction posed by the inductive bias is necessary for practical learning , and reflects prior knowledge regarding the task at hand . perhaps the most successful exemplar of inductive bias to date manifests itself in the use of convolutional networks ( @xcite ) for computer vision tasks . these hypotheses spaces are delivering unprecedented visual recognition results ( _ e.g. _ @xcite ) , largely responsible for the resurgence of deep learning ( @xcite ) . unfortunately , our formal understanding of the inductive bias behind convolutional networks is limited the assumptions encoded into these models , which seem to form an excellent prior knowledge for imagery data , are for the most part a mystery . existing works studying the inductive bias of deep networks ( not necessarily convolutional ) do so in the context of _ depth efficiency _ , essentially arguing that for a given amount of resources , more layers result in higher expressiveness . more precisely , depth efficiency refers to a situation where a function realized by a deep network of polynomial size , requires super - polynomial size in order to be realized ( or approximated ) by a shallower network . in recent years , a large body of research was devoted to proving existence of depth efficiency under different types of architectures ( see for example @xcite ) . nonetheless , despite the wide attention it is receiving , depth efficiency does not convey the complete story behind the inductive bias of deep networks . while it does suggest that depth brings forth functions that are otherwise unattainable , it does not explain why these functions are useful . loosely speaking , the hypotheses space of a polynomially sized deep network covers a small fraction of the space of all functions . we would like to understand why this small fraction is so successful in practice . a specific family of convolutional networks gaining increased attention is that of _ convolutional arithmetic circuits_. these models follow the standard paradigm of locality , weight sharing and pooling , yet differ from the most conventional convolutional networks in that their point - wise activations are linear , with non - linearity originating from product pooling . recently , analyzed the depth efficiency of convolutional arithmetic circuits , showing that besides a negligible ( zero measure ) set , all functions realizable by a deep network require exponential size in order to be realized ( or approximated ) by a shallow one . this result , termed _ complete depth efficiency _ , stands in contrast to previous depth efficiency results , which merely showed _ existence _ of functions efficiently realizable by deep networks but not by shallow ones . besides their analytic advantage , convolutional arithmetic circuits are also showing promising empirical performance . in particular , they are equivalent to simnets a deep learning architecture that excels in computationally constrained settings ( ) , and in addition , have recently been utilized for classification with missing data ( ) . motivated by these theoretical and practical merits , we focus our analysis in this paper on convolutional arithmetic circuits , viewing them as representative of the class of convolutional networks . we empirically validate our conclusions with both convolutional arithmetic circuits and _ convolutional rectifier networks _ convolutional networks with rectified linear ( relu , @xcite ) activation and max or average pooling . adaptation of the formal analysis to networks of the latter type , similarly to the adaptation of the analysis in carried out by , is left for future work . our analysis approaches the study of inductive bias from the direction of function inputs . specifically , we study the ability of convolutional arithmetic circuits to model correlation between regions of their input . to analyze the correlations of a function , we consider different partitions of input regions into disjoint sets , and ask how far the function is from being separable w.r.t . these partitions . distance from separability is measured through the notion of _ separation rank _ ( @xcite ) , which can be viewed as a surrogate of the @xmath0 distance from the closest separable function . for a given function and partition of its input , high separation rank implies that the function induces strong correlation between sides of the partition , and vice versa . we show that a deep network supports exponentially high separation ranks for certain input partitions , while being limited to polynomial or linear ( in network size ) separation ranks for others . the network s pooling geometry effectively determines which input partitions are favored in terms of separation rank , _ i.e. _ which partitions enjoy the possibility of exponentially high separation rank with polynomial network size , and which require network to be exponentially large . the standard choice of square contiguous pooling windows favors interleaved ( entangled ) partitions over coarse ones that divide the input into large distinct areas . other choices lead to different preferences , for example pooling windows that join together nodes with their spatial reflections lead to favoring partitions that split the input symmetrically . we conclude that in terms of modeled correlations , pooling geometry controls the inductive bias , and the particular design commonly employed in practice orients it towards the statistics of natural images ( nearby pixels more correlated than ones that are far apart ) . moreover , when processing data that departs from the usual domain of natural imagery , prior knowledge regarding its statistics can be used to derive respective pooling schemes , and accordingly tailor the inductive bias . with regards to depth efficiency , we show that separation ranks under favored input partitions are exponentially high for all but a negligible set of the functions realizable by a deep network . shallow networks on the other hand , treat all partitions equally , and support only linear ( in network size ) separation ranks . therefore , almost all functions that may be realized by a deep network require a replicating shallow network to have exponential size . by this we return to the complete depth efficiency result of , but with an added important insight into the benefit of functions brought forth by depth they are able to efficiently model strong correlation under favored partitions of the input . the remainder of the paper is organized as follows . [ sec : prelim ] provides a brief presentation of necessary background material from the field of tensor analysis . [ sec : cac ] describes the convolutional arithmetic circuits we analyze , and their relation to tensor decompositions . in sec . [ sec : sep_rank ] we convey the concept of separation rank , on which we base our analyses in sec . [ sec : analysis ] and [ sec : inductive_bias ] . the conclusions from our analyses are empirically validated in sec . [ sec : exp ] . finally , sec . [ sec : discussion ] concludes . the analyses carried out in this paper rely on concepts and results from the field of tensor analysis . in this section we establish the minimal background required in order to follow our arguments , referring the interested reader to @xcite for a broad and comprehensive introduction to the field . the core concept in tensor analysis is a _ tensor _ , which for our purposes may simply be thought of as a multi - dimensional array . the _ order _ of a tensor is defined to be the number of indexing entries in the array , which are referred to as _ modes_. the _ dimension _ of a tensor in a particular mode is defined as the number of values that may be taken by the index in that mode . for example , a @xmath1-by-@xmath2 matrix is a tensor of order @xmath3 , _ i.e. _ it has two modes , with dimension @xmath1 in mode @xmath4 and dimension @xmath2 in mode @xmath3 . if @xmath5 is a tensor of order @xmath6 and dimension @xmath7 in each mode @xmath8:=\{1,\ldots , n\}$ ] , the space of all configurations it can take is denoted , quite naturally , by @xmath9 . a fundamental operator in tensor analysis is the _ tensor product _ , which we denote by @xmath10 . it is an operator that intakes two tensors @xmath11 and @xmath12 ( orders @xmath13 and @xmath14 respectively ) , and returns a tensor @xmath15 ( order @xmath16 ) defined by : @xmath17 . notice that in the case @xmath18 , the tensor product reduces to the standard outer product between vectors , _ i.e. _ if @xmath19 and @xmath20 , then @xmath21 is no other than the rank-1 matrix @xmath22 . we now introduce the important concept of matricization , which is essentially the rearrangement of a tensor as a matrix . suppose @xmath5 is a tensor of order @xmath6 and dimension @xmath7 in each mode @xmath8 $ ] , and let @xmath23 be a partition of @xmath24 $ ] , _ i.e. _ @xmath25 and @xmath26 are disjoint subsets of @xmath24 $ ] whose union gives @xmath24 $ ] . we may write @xmath27 where @xmath28 , and similarly @xmath29 where @xmath30 . the _ matricization of @xmath5 w.r.t . the partition @xmath23 _ , denoted @xmath31 , is the @xmath32-by-@xmath33 matrix holding the entries of @xmath5 such that @xmath34 is placed in row index @xmath35 and column index @xmath36 . if @xmath37 or @xmath38 , then by definition @xmath31 is a row or column ( respectively ) vector of dimension @xmath39 holding @xmath34 in entry @xmath40 . a well known matrix operator is the _ kronecker product _ , which we denote by @xmath41 . for two matrices @xmath42 and @xmath43 , @xmath44 is the matrix in @xmath45 holding @xmath46 in row index @xmath47 and column index @xmath48 . let @xmath5 and @xmath49 be tensors of orders @xmath13 and @xmath14 respectively , and let @xmath23 be a partition of @xmath50 $ ] . the basic relation that binds together the tensor product , the matricization operator , and the kronecker product , is : _ i , j=_i , j_(i - p),(j - p ) [ eq : mat_tensor_prod ] where @xmath51 and @xmath52 are simply the sets obtained by subtracting @xmath13 from each of the elements in @xmath25 and @xmath26 respectively . in words , eq . [ eq : mat_tensor_prod ] implies that the matricization of the tensor product between @xmath5 and @xmath49 w.r.t . the partition @xmath23 of @xmath50 $ ] , is equal to the kronecker product between two matricizations : that of @xmath5 w.r.t . the partition of @xmath53 $ ] induced by the lower values of @xmath23 , and that of @xmath49 w.r.t . the partition of @xmath54 $ ] induced by the higher values of @xmath23 . the convolutional arithmetic circuit architecture on which we focus in this paper is the one considered in , portrayed in fig . [ fig : nets_patterns](a ) . instances processed by a network are represented as @xmath6-tuples of @xmath55-dimensional vectors . they are generally thought of as images , with the @xmath55-dimensional vectors corresponding to local patches . for example , instances could be @xmath56-by-@xmath56 rgb images , with local patches being @xmath57 regions crossing the three color bands . in this case , assuming a patch is taken around every pixel in an image ( boundaries padded ) , we have @xmath58 and @xmath59 . throughout the paper , we denote a general instance by @xmath60 , with @xmath61 standing for its patches . the first layer" +"it has long been recognized that when an atom is situated in a material medium , the local electromagnetic field acting on it differs from the macroscopic one due to the gaps between the atom and the surrounding medium atoms , which are ignored on a coarse - grained macroscopic scale @xcite . accounting for the difference between the two fields hence requires a correction the local - field correction . classical calculations of local - field effects , which typically have their origin in near dipole - dipole interactions , can be found in textbooks ( see , e.g. , ref . @xcite ) . in quantum theory , investigations of local - field effects are often related to the problem of the spontaneous decay of an excited guest atom embedded in a ( dielectric ) host . local - field effects in spontaneous decay have been studied , e.g. , for crystals @xcite and disordered dielectrics @xcite on the basis on microscopic models for coupled atomic dipoles . in macroscopic descriptions , local - field effects are frequently taken into account by regarding the guest atom as being enclosed in a virtual @xcite or real ( spherical ) cavity @xcite surrounded by the medium , with the cavity size being small compared to the relevant transition wavelength . the cavity in the former model is virtual in the sense that it does not perturb the macroscopic field . it is filled by the atoms comprising the medium , which produce no net effect at the central position in important special cases such as cubic or random structures . in the latter model , the field is modified by the presence of the cavity , which is an empty region containing only the guest atom . microscopic models often tend to agree with the virtual - cavity results @xcite , while many recent experiments on spontaneous emission in dielectrics support the real - cavity model @xcite . it has been presumed that while the virtual - cavity model applies to interstitial atoms , the real - cavity model is specific to substitutional atoms , and that the case of substitutional atoms occurs prevalently for impurity atoms in disordered dielectrics @xcite . since in the approaches to the local - field effects , the host medium has typically been assumed to be a bulk medium that extends homogeneously to infinity , the question of the effect of the size and shape of the host medium on the local field has arisen . in a macroscopic approach , the spontaneous - decay rate of an excited atom in some free - space region can be given in terms of the imaginary part of the green tensor of the macroscopic maxwell equations , which characterizes the ( macroscopic ) environment of the atom . this relation in principle allows for including local - field corrections for atoms embedded in arbitrary material configurations by assuming a real ( spherical ) cavity surrounding the atom and calculating the corresponding green tensor . using the real - cavity model , toma @xcite studied the local - field correction to the spontaneous - decay rate of an excited atom , which is located at the center of a dispersing and absorbing dielectric sphere . reformulating the result by representing it in a form , which does not explicitly refer to the highly symmetric system considered , he made the conjecture that it may also remain valid beyond the specific example and hence also apply to other locations of the atom and other shapes of the host body . based on a numerical computation of the respective green tensors , rahmani and bryant @xcite considered the case of an atom at an arbitrary location within a dielectric sphere or a dielectric cube . comparing their results for the dielectric sphere including the local - field correction with earlier results disregarding the local - field correction @xcite , they suggested a rate formula , which in the case of weakly absorbing material corresponds to toma s formula . however , since their approach relies heavily on numerical calculations , it can not produce explicit expressions for the quantities that are related to the local - field correction . the exact analytical evaluations of the green tensors of realistic systems which have finite sizes and include a cavity can be very cumbersome . in this paper , we present an attempt to overcome this difficulty by writing the green tensor as a born series in terms of the susceptibility , where in many situations one can restrict oneself to several leading - order terms . in particular , we show that to linear order the spontaneous - decay rate of a guest atom in a dielectric host body can be separated into a term representing the local - field correction to the decay rate in free space and a term related to the scattering green tensor of the body without the atom a result which exactly corresponds to toma s conjecture mentioned above . furthermore , we show that for atoms which are situated at the interior of a macroscopic body toma s conjecture remains valid beyond the linear order . we illustrate the theory by discussing in detail the case of an atom embedded in a spherical dielectric body . the paper is organized as follows . the basic equations for the spontaneous - decay rate and the born expansion of the green tensor determining the rate are given in sec . [ sec_be ] . they are used in sec . [ subsec_rc ] to study the problem of the local - field corrected decay rate within the frame of the real - cavity model , and a proof of toma s formula is given . the examples of an atom embedded in a bulk dielectric medium or in a dielectric sphere are examined in sec . [ sec_ex ] , followed by a summary ( sec . [ sum ] ) . consider an excited two - level electric - dipole emitter , henceforth referred to as an atom , which is positioned at @xmath0 and surrounded by dispersing and absorbing dielectric bodies . the spontaneous - decay rate can be given in the form of @xcite @xmath1 where @xmath2 and @xmath3 are the ( real ) dipole matrix element and ( shifted ) frequency of the relevant atomic transition , respectively , and @xmath4 @xmath5 @xmath6 . the green tensor of the bodies , @xmath7 , satisfies the equation @xmath8 ( @xmath9 , unit tensor ) together with the boundary condition @xmath10 where @xmath11 is the frequency- and space - dependent complex permittivity which satisfies the kramers kronig relations . note that satisfaction of the boundary condition ( [ e4b ] ) is ensured by assuming @xmath12 @xmath13 @xmath14 . equation ( [ e3 ] ) always applies when the atom is placed in some free - space region . separating the green tensor into bulk and scattering parts @xmath15 and @xmath16 , respectively , @xmath17 and taking into account that in the case where the bulk part refers to free space , the relation @xmath18 holds ( see , e.g. , ref . @xcite ) , we may rewrite eq . ( [ e3 ] ) as @xmath19 where @xmath20 is the spontaneous - decay rate in free space . if the atom is embedded in a body , application of eq . ( [ e3 ] ) requires special care in two respects . firstly , the coincidence limit of the bulk part of the green tensor diverges when the permittivity of the body is complex , as is the case in general . only if material absorption can be neglected so that the permittivity can be regarded as being real , @xmath21 @xmath22 @xmath23 , this limit exists , @xmath24 ( see , e.g. , ref . @xcite ) , leading to @xmath25 secondly , the green tensor of the macroscopic maxwell equations does not account for the fact that the local field felt by the atom is different from the macroscopic one in general . that is , even if absorption is neglected , the rate formula ( [ eq.10 ] ) is not complete because it lacks the local - field corrections . to calculate the ( scattering part of the ) green tensor for an arbitrary arrangement of dielectric bodies , it may be helpful to use an appropriate born expansion . decomposing the permittivity as @xmath26 and assuming that the solution @xmath27 to the equation @xmath28 is known [ where @xmath29 is defined as in eq . ( [ e5 ] ) with @xmath30 instead of @xmath31 , the green tensor can be written in the form of a born series , @xmath32\nonumber\\ & \quad\times \overline{\bm{g}}(\mathbf{r},\mathbf{s}_1,\omega)\!\cdot\ ! \overline{\bm{g}}(\mathbf{s}_1,\mathbf{s}_2,\omega)\!\cdots\ ! \overline{\bm{g}}(\mathbf{s}_k,\mathbf{r}',\omega),\end{aligned}\ ] ] as can be verified using the relationships @xmath33,\\ \label{e11 } \hat{h}\,\delta_k\bm{g}(\mathbf{r},\mathbf{r}',\omega ) = & \;\frac{\omega^2}{c^2}\chi(\mathbf{r},\omega ) \bigl[\delta_{k-1}{\bm{g}}(\mathbf{r},\mathbf{r}',\omega ) \nonumber\\ & \ ; -\delta_k\bm{g}(\mathbf{r},\mathbf{r}',\omega)\bigr ] \qquad\mbox{for } k>1.\end{aligned}\ ] ] the expansion ( [ e8 ] ) of the green tensor is valid for arbitrarily spatially varying @xmath34 and @xmath35 . obviously , it may be very useful when @xmath36 can be regarded as being a ( small ) perturbation to @xmath30 such that one makes only a small error by disregarding the higher - order terms . in particular , this is the case if the bodies are weakly polarizable , as we shall assume in the following . for weakly polarizable bodies , it is natural to regard the susceptibilities of the bodies as a small perturbation to the free - space permittivity @xmath34 @xmath5 @xmath37 @xmath38 @xmath39 , i.e. , @xmath40 @xmath41 @xmath42 . this means that we focus on frequencies that are sufficiently far from a resonance frequency of the dielectric material . note that the small ( positive ) imaginary part of @xmath30 ensures that @xmath43 fulfills the boundary condition according to eq . ( [ e4b ] ) so that the spatial integrals in eq . ( [ e9 ] ) converge . we have ( see , e.g. , ref . @xcite ) @xmath44 where @xmath45 @xmath46 @xmath5 @xmath47 @xmath48 @xmath49 , @xmath50 @xmath5 @xmath51 , @xmath52 @xmath5 @xmath53 , @xmath54 @xmath5 @xmath55 . separating the green tensor into bulk and scattering parts in accordance with eq . ( [ e14.2 ] ) , assuming the atom to be located in a free - space region such that @xmath56 [ cf . ( [ eq.6 ] ) ] , and applying eq . ( [ e8 ] ) , we may represent the scattering part of the green tensor in the rate formula ( [ e14.4 ] ) as @xmath57 for @xmath58 and @xmath59 belonging to a free - space region , substitution of eq . ( [ e13 ] ) into eq . ( [ e9 ] ) yields the first- and second - order terms in the born expansion , @xmath60 and @xmath61 , respectively , as follows : @xmath62 e^{i\sqrt{1+i\eta}\,(q+q')}\end{aligned}\ ] ] [ @xmath46 @xmath5 @xmath47 @xmath48 @xmath63 , @xmath54 @xmath5 @xmath55 , @xmath64 @xmath5 @xmath65 , @xmath66 @xmath5 @xmath67 ; @xmath68 @xmath5 @xmath63 @xmath48 @xmath49 , @xmath69 @xmath5 @xmath70 , @xmath71 @xmath5 @xmath72 , @xmath73 @xmath5 @xmath74 , @xmath75 e^{i\sqrt{1+i\eta}\,(q+q')}\nonumber\\ & + \frac{k^7}{64\pi^3}\!\int\!\mathrm{d}^3s_1\ , \chi(\mathbf{s}_1,\omega)\ ! \int\!\mathrm{d}^3s_2\,\chi(\mathbf{s}_2,\omega ) e^{i\sqrt{1+i\eta}\,(q_1+q_{12}+q_2 ) } \nonumber\\ & \quad\times\bigl[a_1a_{12}a_2\bm{i } -a_1a_{12}b_2\tilde{\mathbf{u}}_2\tilde{\mathbf{u}}_2 -a_1b_{12}a_2\tilde{\mathbf{u}}_{12}\tilde{\mathbf{u}}_{12 } \nonumber\\ & \qquad -b_1a_{12}a_2\tilde{\mathbf{u}}_1\tilde{\bm{u}}_1 + a_1b_{12}b_2(\tilde{\mathbf{u}}_{12 } \!\cdot\!\tilde{\mathbf{u}}_2 ) \tilde{\mathbf{u}}_{12}\tilde{\mathbf{u}}_2\nonumber\\ & \qquad + b_1a_{12}b_2(\tilde{\mathbf{u}}_1 \!\cdot\!\tilde{\mathbf{u}}_2 ) \tilde{\mathbf{u}}_1\tilde{\mathbf{u}}_2 + b_1b_{12}a_2(\tilde{\mathbf{u}}_1 \!\cdot\!\tilde{\mathbf{u}}_{12 } ) \tilde{\mathbf{u}}_1\tilde{\mathbf{u}}_{12 } \nonumber\\ & \qquad -b_1b_{12}b_2(\tilde{\mathbf{u}}_1 \!\cdot\!\tilde{\mathbf{u}}_{12 } ) ( \tilde{\mathbf{u}}_{12 } \!\cdot\!\tilde{\mathbf{u}}_2 ) \tilde{\mathbf{u}}_1\tilde{\mathbf{u}}_2\bigr]\end{aligned}\ ] ] [ @xmath76 @xmath5 @xmath47 @xmath48 @xmath77 , @xmath78 @xmath5 @xmath77 @xmath48 @xmath79 , @xmath80 @xmath5 @xmath79 @xmath48 @xmath49 ; @xmath81 @xmath5 @xmath82 , @xmath83 @xmath5 @xmath84 , @xmath85 @xmath5 @xmath86 for @xmath87 @xmath88 @xmath89 . consider an excited two - level atom embedded in an arbitrary dispersing and absorbing" +"two - level emitters interacting with a cavity photon mode are widely studied in quantum optics with respect to spontaneous emission and superradiance @xcite , cooperativity and lasing @xcite , as well as the emission of nonclassical light @xcite . for sufficiently weak light - matter coupling , when the photon - dressing of emitter states is negligibly small , the emitter - cavity system can be studied with the quantum optical master equation , usually in combination with the rotating - wave approximation @xcite . the quantum optical master equation fails at strong light - matter coupling , to the extent that it predicts unphysical emission at zero temperature if the number of photons in the ground state is finite @xcite . the correct theoretical description of systems with ( ultra-)strong light - matter coupling @xcite has attracted increasing interest recently @xcite . essentially , the quantum optical master equation has to be replaced by a master equation expressed in the photon - dressed emitter eigenstates @xcite . while the master equation remains markovian , which is justified because of the weak emitter - environment and cavity - environment couplings @xcite , it now requires full diagonalization of the interacting emitter - cavity hamiltonian . such an equation was used in recent studies of photon blockade effects @xcite , spontaneous conversion of virtual to real photons @xcite , and the emission of nonclassical light from a single emitter @xcite . in this paper we study the emission of few emitters in a cavity , with particular focus on the photon statistics of the emitted light . our goal is the characterization of temperature and coupling regimes where nonclassical light @xcite is generated . a major result will be the identification of two clearly distinguished neighboring regimes with pronounced sub - poissonian and super - poissonian photon statistics at strong coupling . our results are obtained with the full input - output formalism @xcite and master equation @xcite without further approximations . to understand the relevance of the different approximations involved in traditional quantum optics treatments we make two comparisons . first , we compare the results that are obtained when the counter - rotating light - matter interaction terms are included in the hamiltonian to those when they are dropped . second , we contrast the results obtained with the full master equation with results from the quantum optical master equation . the latter comparison will clearly show the necessity of using the correct master equation already at weak coupling if the photon statistics is of interest . this issue has been studied conclusively for a single emitter in ref . @xcite , which also contains glauber function plots for few emitters in the supplemental material but omits the further analysis of the situation that we give here . the paper is organized as follows . in sec . [ sec : model ] we introduce the physical situation under study together with the master equation used for its analysis . in sec . [ sec : spectra ] we discuss the emission spectra in relation to the energy spectra of the emitter - cavity hamiltonian , while the statistics of the emitted photons is studied in sec . [ sec : statistics ] . we conclude in sec . [ sec : concl ] . the appendices collect further information on the theoretical approach . [ app : inout ] gives details of the input - output formalism . in app . [ app : me ] we derive the master equation , and give a few analytical results for the photon statistics in app . [ app : analyt ] . the interaction of @xmath1 two - level emitters with a single cavity photon mode is described by the dicke model @xcite @xmath2 where the operator @xmath3 annihilates ( creates ) a cavity photon with frequency @xmath4 and @xmath5 ( @xmath6 ) is the corresponding lowering ( raising ) operator for the @xmath7th emitter with transition energy @xmath8 . throughout this work , we consider the resonant case @xmath9 . we allow for different emitter - photon coupling strengths for the co - rotating ( @xmath10 ) and counter - rotating ( @xmath11 ) interaction terms . changing @xmath11 relative to @xmath10 interpolates between the tavis - cummings ( tc ) limit ( @xmath12 ) without and the dicke limit ( @xmath13 ) with counter - rotating terms . both situations can be realized experimentally @xcite . the rotating - wave approximation consists in replacing the dicke by the tc limit . dissipation arises from the coupling of the emitters and the cavity to the environment . for a bosonic environment the coupling terms are of the form @xmath14 where @xmath15 is a ( hermitian ) emitter or cavity operator and the @xmath16 are bosonic operators for the environment photons ( at frequencies @xmath17 with coupling constants @xmath18 ) . as the operator @xmath15 we choose the field operator @xmath19 for the coupling of the cavity and the transition operator @xmath20 for the coupling of the @xmath7th emitter to the environment . at sufficiently weak coupling to the environment , the emitter - cavity system density matrix @xmath21 obeys a markovian master equation @xcite @xmath22 - { \mathrm i}\frac{1}{2 } \sum_\omega \xi(\omega ) \big [ s_\omega^\dagger s_\omega , \rho(t ) \big ] \nonumber\\ & & + \frac{1}{2 } \sum_\omega \chi(\omega ) \big ( \big [ s_\omega \rho(t ) , s_\omega^\dagger \big ] + \big [ s_\omega , \rho(t ) s_\omega^\dagger \big ] \big ) \ , , \nonumber\\\end{aligned}\ ] ] where @xmath23 is the projection of @xmath15 onto transitions between eigenstates @xmath24 , @xmath25 of @xmath26 with energy difference @xmath27 ( see app . [ app : me ] for a derivation ) . for the sake of notational simplicity we state the master equation for a single coupling term . multiple coupling terms lead to additional contributions of the same form . the functions @xmath28 and @xmath29 in eq . follow from the environment spectral function @xmath30 and its analytical continuation @xmath31 into the upper half plane , with @xmath32 . for a thermal environment with inverse temperature @xmath33 we get @xmath34 \quad & \text { if } \omega > 0 \ ; , \\[0.25ex ] \gamma(-\omega ) n(-\omega , t ) & \text { if } \omega < 0 \end{cases}\ ] ] and @xmath35 \quad & \text { if } \omega > 0 \ ; , \\[0.25ex ] - { \mathop{{\rm re}}}\gamma(-\omega + { \mathrm i}0^+ ) n(-\omega , t ) & \text { if } \omega < 0 \ ; , \end{cases}\ ] ] with the bose - einstein distribution function @xmath36 note that in the zero temperature limit @xmath37 such that the master equation contains only dissipative terms for transitions @xmath38 with positive energy @xmath39 , i.e. , dissipation correctly leads to energy decrease . in particular , the problem of unphysical emission from the ground state encountered for the quantum optical master equations is resolved . in the present work we assume an ohmic spectral function @xmath40 for the cavity - environment coupling , and use @xmath41 in all numerical computations . to reduce the number of free parameters we assume the same spectral function @xmath42 for the emitter - environment couplings . the respective environment temperatures are also identical . as we show in app . [ app : me ] , the master equation splits into two equations of motion @xmath43 for the matrix elements @xmath44 of the density operator . in these equations , @xmath45 and @xmath46 s_{k , n } + { \mathrm i}e_n \,.\ ] ] the general solution of eq . is @xmath47 because @xmath48 for all @xmath49 , the off - diagonal elements of @xmath50 decay exponentially . hence , the stationary state fulfills @xmath51 the diagonal elements @xmath52 are determined by the stationary solution of the pauli master equation . if the system is coupled to a thermal environment as in eqs . and , the stationary solution of eq . is the thermal state @xmath53 of the system corresponding to the temperature @xmath54 of the environment . the emission spectrum and photon statistics can now be computed through a standard input - output formalism ( see app . [ app : inout ] ) , which leads to the projected cavity - environment coupling operator @xmath55 describing the emission . the correlation functions of @xmath56 and @xmath57 characterize the properties of the emitted light . the emission spectrum of the cavity is @xmath58 and the second - order glauber function @xcite reads @xmath59 note that evaluation of eqs . , requires diagonalization of the hamiltonian @xmath26 . because the stationary state @xmath60 from eq . is diagonal in the eigenbasis @xmath25 of @xmath26 , we can evaluate the @xmath61-integration in eq . analytically as @xmath62 ^ 2 + [ { \mathop{{\rm re}}}(z_m+z_n)]^2 } \ , . \nonumber\end{aligned}\ ] ] the emission spectrum @xmath63 is the sum of lorentz peaks with width @xmath64 at the respective transition energies @xmath65 , which according to eq . are shifted relative to the transition energies @xmath66 of the closed system by a lamb shift that results from coupling to the environment . it is instructive to compare the master equation to the quantum optical master equation @xcite @xmath67 - { \mathrm i}\sum_\pm \frac{\xi_\pm}{2 } [ s_\pm^\dagger s_\pm , \rho(t ) ] \\ & & + \sum_\pm \frac{\chi_\pm}{2 } \big ( \big [ s_\pm \rho(t ) , s_\pm^\dagger \big ] + \big [ s_\pm , \rho(t ) s_\pm^\dagger \big ] \big ) \ ; , \nonumber\end{aligned}\ ] ] which is obtained by replacing the projected operators @xmath68 with the ` bare ' operators @xmath69 , and by assuming @xmath70 , @xmath71 in the vicinity of a typical transition energy @xmath72 . note that @xmath73 for the cavity - environment coupling and @xmath74 for the emitter - environment coupling . evidently this approximation can be valid only for weak light - matter coupling @xmath75 , when the dressing of emitter states by cavity photons can be neglected . because the quantum optical master equation does not distinguish between energy - increasing and energy - decreasing transitions , which are equally contained in the unprojected operator @xmath15 because of hermiticity , it can lead to unphysical predictions such as emission out of the ground state . furthermore , because failure to observe the above distinction is tantamount to a high - temperature approximation , one will expect that the quantum optical master equation fails at the prediction of non - thermal photon statistics at low temperatures . therefore , we use the more general master equation . the first characterization of the light generated in the cavity is provided by the emission spectrum . because the emission spectrum depends on the ( lamb - shifted ) energy spectrum of the dicke hamiltonian we start with a discussion of the eigenvalues of @xmath26 for few emitters , before we turn to the actual function @xmath63 obtained from numerical solution of the master equation . to construct the energy spectrum of @xmath26 we notice first that the eigenstates of @xmath1 uncoupled two - level emitters can be classified as angular momentum eigenstates with total angular momentum @xmath76 . since @xmath26 commutes with the total angular momentum operator , states with different @xmath77 do not mix even at finite coupling @xmath78 . for fixed @xmath77 , the @xmath79 quantum number @xmath80 can assume the values @xmath81 , and a corresponding emitter eigenstate has energy @xmath82 . note that for @xmath83 the classification in terms of @xmath77 , @xmath80 is not exhaustive , since different emitter states can have identical values . however , these states give the same contribution to the emission spectrum . the cavity photon eigenstates are fock states @xmath25 with energies @xmath84 . schematic energy level pattern for the construction of the spectrum of the dicke model . horizontal arrows" +"ionizing radiation is both hazardous and beneficial to living organisms , and is extensively used for cancer treatment in radiation therapy @xcite . a major problem in the application of ionizing radiation to cancer treatment is the protection of normal cells and tissues against unavoidable exposure to radiation during radiation treatment . it is now well understood that the ionization or excitation of the dna molecules , either directly or indirectly , can lead to dna single or double strand breaks . as a result , misrepaired dna molecules can lead to specific genetic aberrations and/or mutations which could cause carcinogenesis in normal cells or lead to fatal damage in normal or cancer cells @xcite . it has been shown that low linear - energy - transfer ( let ) ionizing radiation creates approximately 1,000 single strand breaks ( ssbs ) and 40 double strand breaks ( dsbs ) per gray ( 1gy=1j / kg ) in typical mammalian cells @xcite . the level of dna molecular base damage is around 2,500 to 25,000 per gy in a cell , which is about 2.5 to 25 times the yield of sugar - phosphate induced damage in the dna backbone @xcite . in indirect mechanisms , the water molecules surrounding the dna molecule which compose 80% of a cell , may be excited by ionizing radiation in form of free radicals , e.g. , a charged neutral hydroxyl ( oh ) . the motion of oh - radicals which are randomly produced throughout the cell is governed by diffusion processes . massive dna damage can result from a large number of dna dehydrogenations caused by free radicals . for example , a free radical can diffuse to reach a dna molecule and remove a hydrogen ion from it to form a water molecule . detailed studies at the molecular level is necessary to bring the radiation - induced dna damage under control . in this work , we apply a quantum physical description of molecular interactions to propose a mechanism that could allow the manipulation of dna radio - sensitivity . in particular the pauli exclusion principle @xcite which prevents two electrons with parallel spin form occupying a single spatial orbital , plays a major role and is used to magnetically manipulate the diffusion of hydroxyl radicals and the oh - dna relative motion . it has been shown in studies in semiconductor physics and quantum optics that the pauli exclusion principle can be used to rectify electrical currents passing through weakly coupled quantum dots @xcite and to induce ferromagnetic ordering by photo - generated carriers in magnetic semiconductor hetero - structures @xcite . a free radical carries an odd number of electrons with an unpaired spin in the outermost open shell . due to the reduction of the exchange interaction , the pairing of opposite spin electrons in the open orbital of the free radical with an electron in a dna molecule makes free radicals highly reactive . in the process of dehydrogenation of a dna molecule by free radicals an unpaired hole ( a half - empty orbital ) is transferred to the dna . in the absence of spin - orbit coupling and hyperfine interaction the spin of transfered electron is conserved . the electronic ground state of dna - molecule is @xmath0 spin - singlet ( in the absence of an external magnetic field ) . the oh - radical which contains nine electrons is a doubly degenerate ground state with @xmath1 , where we have conveniently taken the quantization axis along the @xmath2-axis . the degeneracy of the ground state can be lifted by applying a weak magnetic field which couples to the electron spin through the zeeman interaction @xcite , @xmath3 . here @xmath4 is the zeeman energy , @xmath5 is the electron @xmath5-factor ( @xmath6 ) , @xmath7 is the bohr magneton ( @xmath8 ev / tesla ) , and @xmath9 is the strength of external magnetic field . in a random interaction of radiation with a biological system the initial direction of oh - radical magnetic moment immediately after its generation is also random . however , by applying a weak external magnetic field ( @xmath10 ) ( which defines the quantization axis ) and using a circularly polarized light field parallel to the direction of the light propagation , as shown in fig.[fig0]a , a molecular transition corresponding to @xmath11 can be induced by means of optical pumping @xcite of the oh - radicals @xcite . here @xmath12 denotes the total angular momentum of diatomic oh - radical @xcite . alternatively , tchniques such as electron spin resonance ( esr ) can be used to achieve strong polarization of free radicals , as recent advances in esr have demonstrated the capability of detecting the transfer of electron spin polarization between radicals @xcite . in this case microwaves can be used for the optical transitions . in a similar fashion , by applying a second circularly polarized light field one may excite an electron - hole pair ( exciton ) in the dna molecule . because the circularly polarized light carries angular momentum @xmath13 , the exciton has a particular spin polarization . here the spin of exciton is @xmath14 with polarization along the light propagation direction ( because of angular momentum selection rules ) . [ fig0 ] schematically shows the generation of the optically pumped exciton by circularly polarized light . the injection of photo - electrons with the spin out of equilibrium may lead to a dramatic effect in the collective dynamical behavior of dna - molecules and the interaction with oh - radicals . for example the oh - dna repulsive magnetic force provides a potential barrier which blocks the diffusion pathway ( see fig . [ fig0]b ) of oh - radicals toward the dna - molecules . this is expected to hinder the dna dehydrogenation and consequently increase the cell radio - resistivity . to verify this hypothesis , an _ ab_-initio molecular dynamical model , which is the mathematical formulation that governs the appropriate dynamics of the molecular system @xcite is deployed . we have used the car - parrinello molecular dynamics ( cpmd ) @xcite model , in which the potential energy of the system can be calculated on - the - fly , as needed for the conformations of the dynamical trajectory to simulate the chemical reaction pathways . because the absorption of a circularly polarized photon alters the local electronic state of a dna - molecule , we confine our simulation to a particular segment , e.g. , only a part of the dna where the injected exciton is localized and the optical transition takes place . to illustrate this , let us consider a system of interest consisting of a dna nucleotide base , ( e.g. , guanine ) in the presence of the oh - radical . we assume that a photon with circular polarization interacting with guanine can induce an optical transition in the form of an @xmath14 exciton . here we investigate the effect of an exciton produced in this way on the guanine - dehydrogenation pathway , assuming that another photon generated through interactions with ionizing radiation ( such as radiotherapy x - rays or cosmic rays ) creates a free radical in the vicinity of guanine . because the local density of free radicals and excitons are large and are comparable , the events described in our calculation can be observed with reasonable probability . we adopt computational parameters and variables needed for the cpmd calculation of the dynamical trajectory of the gas phase nucleotide bases in the presence of oh - radicals following refs . @xcite , where the consistency of cpmd results for guanine with other quantum chemistry approaches has been investigated . we identify the dehydrogenation of the nucleotide bases as a function of their spin multiplicity . the ground and excited states of the nucleotide correspond to spin singlet ( @xmath0 ) , and spin triplet ( @xmath14 ) states . the latter can be realized through the application of circularly polarized light as discussed above ( see fig . [ fig0 ] ) . our cpmd is implemented in a plane - wave basis within local spin density approximation ( lsda ) with an energy cutoff of 70 rydberg ( ry ) , and with becke @xcite exchange and lee - yang - parr ( blyp ) gradient - corrected functional @xcite . norm conserving ultrasoft vanderbilt pseudo - potentials were used for oxygen , hydrogen , nitrogen and carbon . the cpmd micro - canonical dynamics ( constant energy ensemble ) were performed after wave - function optimization following dynamical equilibration at t=300k and re - quenching of the wave - function . an isolated cubic cell of length 13.229 @xmath15 with poisson solver of martyna and tuckerman @xcite was used . our cpmd studies consist of two classes of spin - restricted calculations , as the total spin along the quantum axis is subjected to the constraints @xmath16 , and @xmath17 , corresponding to doublet and quartet spin configurations . in both calculations the initial distance between oh - radical and nucleotide is considered to be about 1.5 @xmath15 . we selectively choose an initial coordinate for oh - radical in the neighborhood of the nucleotide where the hydrogen transfer shows a reactive path in normal state of dna ( the doublet spin configuration in the absence of circularly polarized light and magnetic field ) . the polarization state of the system is spin doublet ( @xmath18 ) . ] the polarization state of the system is spin quartet ( @xmath19 ) induced by circularly polarized light in the presence of weak magnetic field . due to injected polarized photo - electrons localized in guanine , the dehydrogenated guanine does not form . ] the initial and final states of the molecules are shown in figs . [ fig1a]-[fig1c ] . the final configurations of the molecules have been obtained after 0.6 ps where the rearrangement of the atomic coordinates have been deduced from a dynamical trajectory calculated by cpmd . according to our results , a rapid dehydrogenation of the nucleotides takes place for a system with @xmath16 ( total spin - doublet ) as shown in fig . [ fig1b ] . this process leads to the formation of a water molecule . in contrast , as shown in fig . [ fig1c ] , in the quartet spin configuration the repulsive exchange interaction , analogous to heisenberg anti - ferromagnetic coupling which originates from the pauli exclusion principle , blocks the exchange of hydrogen and hence the chemical reaction . in fig . [ fig5 ] the evolution of the n@xmath20 hydrogen in the guanine and free radical oxygen distance is shown . as it is seen the abstraction of hydrogen occurs around @xmath21fs in the spin singlet state of guanine , and the injection of @xmath14 exciton in guanine blocks the hydrogen abstraction . [ fig6 ] shows the kohn - sham energies ( equivalent to potential energy in classical molecular dynamics ) of the spin singlet and spin triplet of the guanine in the presence of the oh free radical as a function of time , calculated by the cpmd at t=300k corresponding to a canonical dynamics ( constant temperature ensemble ) . a drop in kohn - sham energy in spin singlet multiplicity is indication of dehydrogenation of h@xmath22 in the guanine by oh free radical . to systematically check the convergence of the results , we increased the size of the molecule by adding sugar - phosphate rings to guanine and found that this has no influence on the spin - blocking effect . to estimate the energy needed for the polarization of the nucleotide in the absence of oh - radicals , we calculated the energy of the ground and excited states" +"the lognormal distribution appears in a wide range of natural and social phenomena ( see , e.g. , @xcite ) . in fluid turbulence , it is well - known that the distribution is an important consequence of the kolmogorov s 1962 theory for modeling fluctuations of the energy cascade rate across scales @xcite . in this 1962 theory , we have a very clear picture why the lognormal distribution was the first candidate of the cascade fluctuations in his refined phenomenology . namely , the energy cascade at high reynolds number can be modeled as a multiplicative process consisting of a large number of independently and identically distributed random variables . this large number is important for the central limit theorem to be applicable to the logarithm of the multiplicand . there is a different example of lognormally distributed variables in turbulence . laboratory experiments of turbulent boundary layers in 1980 s suggest that spanwise separations between the low - speed streaks follow the lognormal distribution @xcite . in this case , the underlying mechanism of the lognormally distributed streaks is not as clear as in the kolmogorov 1962 phenomenology because a multiplicative structure for the streaks is not found immediately . in this paper we consider yet another lognormal example in turbulence , which was recently found experimentally @xcite . in ref.@xcite , it is observed that the coarse - grained squared velocity and squared velocity increments over distance @xmath0 @xmath1 ^ 2 d x \label{du2}\end{aligned}\ ] ] are lognormally distributed when the averaging scale @xmath2 is set to @xmath3 . here @xmath4 is the correlation length defined as the integral scale of the velocity correlation function @xmath5 and the velocity @xmath6 can be either longitudinal or transverse velocity component . since the lognormal property holds when @xmath2 is comparable to the large scale @xmath4 , this property is called `` large - scale lognormality '' . for the asymptotic regime @xmath7 , as a usual result of the central limit theorem , the distribution of the coarse - grained quantities become closer and closer to normal ( gaussian ) distribution . notice that the large - scale lognormality , which we consider here , concerns the range of the coarse - graining scale @xmath3 , which is different from the final gaussian state in @xmath7 . the large - scale lognormality was observed in the experiments of grid turbulence , turbulent boundary layers , and turbulent jets , suggesting its universality @xcite . but again as in the case of the streaks in the boundary layer turbulence , why the coarse - grained turbulence data are lognormally distributed is not clear . our final goal is to understand its mechanism why they are so . as a first step to this goal , we address the following question : is the large - scale lognormality a general property of correlated random variables , not restricted to large - scale fluctuations of turbulence ? the previous results @xcite lead us to recognize that this balance between @xmath2 and @xmath8 is most important for the lognormality . in order to answer the question , we use the ornstein - uhlenbeck process ( ou process ) as a simplest way to generate correlated random variables with the correlation length @xmath8 and check whether or not the coarse - grained quantities like eqs.([u2 ] ) and ( [ du2 ] ) follow lognormal distributions in the range @xmath9 . our numerical results suggest that the answer to the question is yes . then we study , by analytical calculations of moments , further details on how the ou data become close to the lognormal variables . we believe that this simple approach using the stochastic process has some value since reproducing the large - scale lognormality by direct numerical simulations of the navier - stokes equations can be computationally quite expensive . it requires a very large domain size as compared with the correlation length . in statistics , taking logarithm of a positive random variable is known as a common way of symmetrizing transformation , which makes the skewness of the transformed variable closer to zero @xcite . in this language , the large - scale lognormality suggests that , even with correlation , the log transformation can produce near gaussian behaviour successfully already when the averaging scale @xmath2 is of the order of the correlation scale @xmath8 . the present study can be interpreted as a model study how the log transformation begins to work for the correlated random variable by changing the coarse - graining scale . this paper s organization is the following . in sec . [ s : num ] , we present numerical data of the ou process reproducing the large - scale lognormality . we then in sec . [ s : analy ] provide analytical calculations of moments of the ou process to study how they are close to those of the lognormal distribution . we provide summary and discussion in sec . [ s : dcr ] . we begin here by listing basic properties of the ou process ( see , e.g. , @xcite and also @xcite in the context of turbulence modeling ) . the process is described by the langevin equation @xmath10 where the langevin noise @xmath11 is a gaussian white noise having the ensemble - averaged mean and variance @xmath12 the linear addition of the gaussian uncorrelated noise @xmath11 makes the solution @xmath13 to eq.([ou ] ) to be a gaussian random variable . however the first term of the right hand side brings temporal correlation . namely , by writing the initial position as @xmath14 , @xmath13 is characterized as a correlated - in - time gaussian random variable with the mean and variance @xmath15 ^ 2 \rangle & = & \kappa t_l ( 1 - { { \rm e}}^{-2t / t_l}).\end{aligned}\ ] ] the correlation function can be calculated analytically as @xmath16 [ x(t + s ) - \langle x(t + s ) \rangle ] \big\rangle & = & \nonumber \\ \langle [ x(t ) - \langle x(t ) \rangle ] ^2 \rangle { { \rm e}}^{-|s| / t_l}.\end{aligned}\ ] ] therefore the integral scale of the ou process is given as @xmath17 [ x(t + s ) - \langle x(t + s ) \rangle ] \rangle } { \langle [ x(t ) - \langle x(t ) \rangle ] ^2 \rangle } d s = t_l.\end{aligned}\ ] ] if the large - scale lognormality observed in turbulence @xcite is a property of correlated random variables , it is then likely that the following coarse - grained data of the ou process @xmath18 ^ 2 d t , \label{dx2 } \end{aligned}\ ] ] are lognormally distributed when the averaging scale @xmath2 is in the similar range , such as @xmath19 . equations ( [ x2 ] ) and ( [ dx2 ] ) correspond to the turbulence quantities eqs.([u2 ] ) and ( [ du2 ] ) , respectively . ( color online ) probability density functions ( pdf ) of ( a ) @xmath20 ( eq.([x2 ] ) ) and ( b ) its logarithm @xmath21 . the random variables are normalized to have zero mean and unit standard deviation . the averaging scales here are @xmath22 , which correspond to the curves from top to bottom . the pdfs are shifted vertically by being multiplied by factor @xmath23 for clarity . the solid curve denotes the gaussian distribution.,title=""fig : "" ] ( color online ) probability density functions ( pdf ) of ( a ) @xmath20 ( eq.([x2 ] ) ) and ( b ) its logarithm @xmath21 . the random variables are normalized to have zero mean and unit standard deviation . the averaging scales here are @xmath22 , which correspond to the curves from top to bottom . the pdfs are shifted vertically by being multiplied by factor @xmath23 for clarity . the solid curve denotes the gaussian distribution.,title=""fig : "" ] ( color online ) same as fig . [ pdf ] but for the squared increment ( a ) @xmath24 ( eq.([dx2 ] ) ) and ( b ) its logarithm @xmath25 . here the averaging scales are @xmath22 , which correspond to the curves from top to bottom.,title=""fig : "" ] ( color online ) same as fig . [ pdf ] but for the squared increment ( a ) @xmath24 ( eq.([dx2 ] ) ) and ( b ) its logarithm @xmath25 . here the averaging scales are @xmath22 , which correspond to the curves from top to bottom.,title=""fig : "" ] we now check whether or not the random variables ( [ x2 ] ) and ( [ dx2 ] ) follow lognormal distributions by doing numerical simulation of the ou process ( [ ou ] ) . we use the numerical method called exact updating formula of the ou process proposed in ref.@xcite with the parameters @xmath27 . the integrals in eqs . ( [ x2 ] ) and ( [ dx2 ] ) are numerically calculated as @xmath28 ^ 2,\nonumber \\\end{aligned}\ ] ] where @xmath29 and @xmath30 . figures [ pdf ] and [ pdfd ] show probability density functions ( pdf ) of @xmath20 and @xmath24 with or without taking logarithm for various averaging scales @xmath2 . the number of samples for the @xmath31 case is @xmath32 ( for smaller @xmath2 cases , the number is much larger ) . for the largest values of @xmath33 shown here , the pdfs are close to gaussian distributions as a consequence of the central limit theorem . as we decrease the averaging scale @xmath2 to the correlation scale @xmath34 , the distributions of @xmath20 and @xmath24 deviate from the gaussian distribution . in contrast , the log variables @xmath35 and @xmath36 remain to be nearly gaussian as shown in figs.[pdf](b ) and [ pdfd](b ) . hence @xmath20 and @xmath24 are lognormally distributed in this range of @xmath2 . this behavior is similar to the turbulence data analyzed in ref.@xcite . in addition , for the squared increments @xmath24 with various @xmath37 , qualitatively same results are obtained . the approach to the lognormal distribution can be observed more quantitatively by looking at how the skewnesses and flatnesses of the log variables @xmath38 change as functions of @xmath2 ( the skewness @xmath39 and flatness @xmath40 of a random variable @xmath41 are defined as @xmath42^{3/2 } , f(z ) = \langle ( z - \langle z \rangle)^4 \rangle / [ v(z)]^{2}$ ] , where @xmath43 is the variance @xmath44 ) . in fig . [ moments ] , it is seen that the moments of the variables with logarithm @xmath45 approach already around @xmath46 to the values of the gaussian distributions @xmath47 whereas the moments of the variables without logarithm are still different from them . this is consistent with the behavior observed in figs.[pdf ] and [ pdfd ] . for the increments @xmath24 , the skewness and the flatness can depend on the difference @xmath0 . indeed a clear @xmath0-dependence is seen in fig.[varir ] . however , the fast convergence to the gaussian of the @xmath36 around @xmath48 is not affected by this dependence . in fact , these graphs of the different @xmath0s can be collapsed to one curve by normalizing @xmath2 with a different correlation scale from @xmath34 as we will show at the end of the next section . in summary , we observe that the large - scale lognormality holds also for the ou process as in the turbulence case @xcite . further details on the behavior of the skewness and flatness of the ou process are studied analytically in the next section . ( color online ) the skewness of @xmath20 ( a ) and of @xmath24 ( @xmath49 ) ( b ) ; the flatness of @xmath20 ( c ) and of @xmath24 ( d ) with or" +"in a previous work @xcite we have investigated the sensitivity of the @xmath4 reactions to short range correlations ( src ) , meson - exchange currents ( mec ) and final state interactions ( fsi ) . the src are related to the short - distance repulsion of the nucleon - nucleon potential @xcite . the search for src effects in nuclear systems is done by studying deviations from mean field results @xcite . the exchange of mesons between interacting nucleons produces electromagnetic currents called mec . effects related to the mec have been clearly identified in few - body systems @xcite . in heavier nuclei , however , a clean identification of mec effects is hidden , to a large extent , by the uncertainties of the nuclear wave function @xcite . the fsi account for the re - interaction of the emitted nucleon with the remaining nucleus . a successful approach to describe nucleon emission data induced by both electrons and photons @xcite , treats the fsi with an optical potential whose parameters are fixed to reproduce elastic nucleon - nucleus scattering data . almost all the experimental work relative to the photo - emission of a single proton in medium - heavy nuclei , has been done with unpolarized photons @xcite . we are aware of only two experiments of @xmath5 type . in the first one , wienhard _ et al . _ @xcite studied the @xmath1o(@xmath6)@xmath7n reactions in the giant resonance region by using photons with energies between 15 and 25 mev . in the other experiment , yokokawa _ et al . _ @xcite used as a target the @xmath0c nucleus and the photon energies varied between 40 and 70 mev . the recent development of tagged photon facilities opens new perspectives for this type of experiments . for example the mainz microtron ( mami ) @xcite and the new tagged photon beam line at max - laboratory , in lund @xcite , can make experiments with polarized photons and produce data with a high energy resolution . this allows a clear separation of the different states of the residual nucleus @xcite . at mami , polarized photon beams have been already used to study @xmath0c(@xmath8 ) , @xmath0c(@xmath9 ) and @xmath0c(@xmath10 ) reactions @xcite . at max - laboratory two experiments with polarized photons have been proposed . in the first one , linearly polarized bremsstrahlung photons will be used to make compton scattering on @xmath11he and @xmath0c nuclei . in the second experiment cross sections and asymmetries of the two - particle photodisintegration of @xmath12li and @xmath13li nuclei will be measured . another experimental facility which produces polarized gamma - ray beams is higs , at the duke university in durham @xcite , where the first measurements of the @xmath14h(@xmath15,n)p analyzing power near threshold have been done @xcite . the experimental situation is rapidly evolving and the possibility of using polarized photons to study the structure of medium - heavy nuclei is a solid perspective . in this work we study this possibility from the theoretical point of view , by using a nuclear model recently developed to investigate electromagnetic excitations of the nucleus in inclusive @xcite , single @xcite and double coincidence @xcite experiments . the starting point of our approach is the continuum shell model implemented with the optical potential to take into account the fsi . by using this model to describe nuclear excited states we treat the mec by considering one - pion exchange diagrams @xcite . we improve this picture by implementing the src acting on one - body electromagnetic currents . the src are considered by calculating all the diagrams containing a single correlation line . the validity of this approach has been verified in ref . @xcite by comparing nuclear matter charge responses obtained with our model and with a full correlated basis function calculation . in our previous investigation @xcite we found that photoemission cross sections have a greater sensitivity to src than electron scattering cross sections . the src effects are relevant at photon energies above 100 mev and for proton emission angles above 80 degrees . unfortunately , in these kinematics , also the mec play an important role , and their effects hide those of the src . for these reasons we find interesting to investigate the possibility of disentangling mec and src with polarization observables . the paper is organized as follows . in sect . [ sec : model ] we briefly define the observables we want to study , and present the basic ideas of our model . in sect . [ sec : results ] we show our results and discuss separately the effects of the fsi , of the src and of the mec . finally , in sect . [ sec : conclusion ] we summarize our findings and draw our conclusions . we describe a process where a proton of momentum @xmath16 is emitted from a nucleus after the absorption of a linearly polarized photon of momentum @xmath17 and energy @xmath18 . the geometry of the process is presented in fig . [ fig : axis ] . we indicate with @xmath19 the angle between the spin and the momentum of the photon and with @xmath20 the angle between the @xmath17 and @xmath16 vectors . the cross section for this process can be written as @xcite : @xmath21 \ , , \label{eq : xsect}\ ] ] where @xmath22 is the proton mass and the nuclear responses @xmath23 and @xmath24 are defined as : @xmath25 in the above equations @xmath26 and @xmath27 indicate the initial and final states of the nuclear system , with energies @xmath28 and @xmath29 respectively . since we deal with real photons we have that , in natural units , @xmath30 , and only the transverse components of the nuclear current @xmath31 are active : @xmath32 in electron scattering there is an additional contribution to the electromagnetic current , a longitudinal term , related to the nuclear charge distribution . in our calculations we have considered only the situations where the spin of the photon is parallel or orthogonal to @xmath17 . we call respectively @xmath33 and @xmath34 the cross sections of these two cases . we have studied the photon asymmetry defined as @xcite : @xmath35 a linearly polarized photon gives information on the structure function w@xmath36 , which does not contribute to the unpolarized cross section . the asymmetry @xmath37 can be thought as the correction factor needed to obtain the polarized cross section ( @xmath38 ) from the unpolarized one ( @xmath39 ) , i.e , @xmath40 since @xmath23 is always positive , the sign of the asymmetry is the sign of the structure function @xmath24 . we have restricted our calculations to doubly closed shell nuclei ; then , the nuclear ground state has zero angular momentum and positive parity , i.e , @xmath41 . we describe the ground state as a slater determinant of single - particle wave functions produced by a mean - field potential of woods - saxon type with the parameters given in ref . @xcite for @xmath0c and ref . @xcite for @xmath1o and @xmath2ca . we write the nuclear final state as @xcite : @xmath42 in the above equation , @xmath43 describes the excited state of the @xmath44 nucleons system with total angular momentum @xmath45 , @xmath46axis projection @xmath47 , and parity @xmath48 . this state is composed by a particle in a continuum wave , with orbital and total angular momenta @xmath49 and @xmath50 respectively , projection @xmath22 , energy @xmath51 and momentum @xmath52 , and a residual nucleus with hole quantum numbers @xmath53 , @xmath54 , @xmath55 and @xmath56 . we have indicated with @xmath57 the spherical harmonics and with @xmath58 the clebsch - gordan coefficients @xcite . in our calculations the @xmath59 state is a slater determinant constructed on the ground state slater determinant by substituting the hole wave function @xmath60 with the continuum wave function @xmath61 . this continuum single particle wave function is calculated by using a complex optical potential which is supposed to take into account the fsi . with this procedure , particle and hole wave functions are not any more orthogonal . the effects of this inconsistency have been found to be negligible in the kinematics under investigation @xcite . the continuum shell model above presented has been modified to take into account the src in both initial and final state . we have considered only the case of scalar correlation functions acting on one - body ( ob ) currents . following the basic steps of the correlated basis function theory , we made a cluster expansion of the transition matrix elements of eqs . ( [ eq : wt ] ) and ( [ eq : wtt ] ) to eliminate the unlinked diagrams @xcite . at this point we restrict our calculations by considering all , and only , the terms linear in the correlation function . this implies the evaluation of four two - body diagrams and six three - body diagrams , for each ob operator considered . this procedure is necessary to guarantee the correct normalization of the many - body wave functions @xcite . a detailed description of the src model can be found in @xcite . in our calculations we have considered only the mec terms presented in fig . [ fig : diamec ] generated by the exchange of a single pion . following the model developed in refs . @xcite we have calculated the seagull diagram ( a in fig . [ fig : diamec ] ) , the pionic diagram ( b in fig . [ fig : diamec ] ) and the other two @xmath3 currents diagrams . the expressions of the seagull and pionic terms are given in ref . for the @xmath3 currents terms we use the following expression , more general than that used in @xcite : @xmath62_3 \ , { \mbox{\boldmath $ \sigma$}}(k ) \times \nabla_k \ , { \mbox{\boldmath $ \sigma$}}(l ) \cdot \nabla_k \ , h(\varepsilon_{kl},{\bf r}_k-{\bf r}_l ) \right . \\ & & \nonumber \left . - \ , 4 \tau^3 ( l ) \ , \nabla_k \ , { \mbox{\boldmath $ \sigma$}}(l ) \cdot \nabla_k \ , h(\varepsilon_{kl},{\bf r}_k-{\bf r}_l ) \right\ } + ( k \leftrightarrow l ) \ , . \label{eq : isobar}\end{aligned}\ ] ] where @xmath63 is the effective pion - nucleon coupling constant , @xmath64 is the pion mass and @xmath65 is the fourier transform of the dynamical pion propagator @xcite @xmath66 we have indicated with @xmath67 the pion - nucleon form factor and with @xmath68 the energy of the exchanged pion . as it is clear from fig . [ fig : diamec ] mec are two - body operators , then they could lead also to excited state with two particle in the continuum . we neglect their contribution which we found to be extremely small in inclusive processes @xcite , and we expect to be negligible also in the case under investigation . in our calculations the four single particle states involved in the mec calculations are , the continuum state of the emitted particle , the hole state characterizing the residual nucleus , and other two states below the fermi level . in this situation the @xmath68 energies of eq . ( [ eq : isobar ] ) are uniquely defined . as stated above , in our model the src act only on the ob currents , therefore mec and correlations interplay only trough the interference between the transition amplitudes . we present in this section the results of the @xmath5 reaction on @xmath0c , @xmath1o and @xmath2ca target nuclei . we are interested in the excitation energy region above the giant resonance and below the pion production threshold . in this region , the collective phenomena characterizing the giant resonances are not any" +"mass determinations of neutron stars ( ns ) can provide essential constraints on the equation of state of nuclear matter ( van kerkwijk , van paradijs & zuiderwijk 1995 ) . compact object masses are now known accurately for radio pulsars , all of which are consistent with @xmath13 0.07 m@xmath8 ( thorsett et al . 1993 ) , but have been very difficult to obtain in low mass x - ray binaries ( lmxbs ) both because their ns do not pulse and because the optical flux from the companion is usually overwhelmed by reprocessed x - ray emission from the accretion disk ( van paradijs & mcclintock 1995 ) . only in the quiescent state of soft x - ray transients ( sxts ) can the faint companion be detected and dynamical information extracted . an accurate constraint on the ns mass , however , requires knowledge of both the system inclination @xmath14 and the mass ratio @xmath15 in addition to the amplitude of the radial velocity curve of the companion @xmath16 . + the transient xte j2123 - 058 , discovered in june 1998 , offers an excellent opportunity to achieve this . the presence of a ns is confirmed by type - i bursts ( tomsick et al . 1999 ; homan et al . 1999 , gneiding , steiner & cieslinski 1999 ) which makes it one of only 4 ns sxts known . the optical counterpart showed clear triangular - shaped minima repeating on the orbital period of 6 hrs which consequently evolved to an ellipsoidal modulation before the system entered quiescence at @xmath17 ( tomsick et al . 1999 ; soria , wu & galloway 1999 ; zurita et al . 2000 ; hynes et al . the modulation yielded @xmath18 ( zurita et al . 2000 ) but it should be noted that systematic effects related to the assumed outburst irradiation model might have some importance . + the secondary star is suspected to be of late k - type in order to transfer matter within the constraints of a 6 hr orbit . photometric colours obtained during quiescence also suggest the presence of a late - k companion ( see zurita et al 2000 , shahbaz et al . 2001 ) . in this paper we report the first spectroscopic detection of the companion star in j2123 - 058 and its radial velocity curve using the _ kueyen _ vlt ( sections 3 and 4 ) . sections 5 and 6 deal with the analysis of the @xmath3 emission . in section 7 we present the spectroscopic constraints on the components masses , together with implications for the disc instability model and discuss constraints on the formation scenario implied by the observed systemic velocity . we obtained a total of 20 spectra of j2123 - 058 during observations with the fors-2 spectrometer of the _ kueyen _ vlt on august 23 and 24 , 2000 ( ut ) . we used grism 600r ( with the order - sorting filter gg435 + 31 ) , centered at 6300 with a 0.7 `` slit on the first night . on the second night , the seeing deteriorated ( up to 1.2 '' ) and so we decided to use a 1 arcsec slit . the spectral resolution , as measured from the fwhm of the arclines , was 2.7 and 4.0 for the two nights , respectively . exposure times of 2200 s were employed . + the data were de - biased and flat - fielded in the usual way . the spectra for j2123 - 058 were then extracted using standard optimal extraction techniques which optimize the signal - to - noise ratio of the final spectra ( horne 1986 ) . calibration henear arc images were obtained in daytime with the telescope parked at the zenith . the @xmath0-pixel scale was derived through fourth - order polynomial fits to 40 lines resulting in an rms scatter better than 0.3 . internal flexure was measured by cross - correlation of the sky spectra and was found to be @xmath19 20 km s@xmath2 ( @xmath19 0.4 pixel ) throughout the night . relative shifts of every target spectrum to the first one were applied and the zero point ( -18 @xmath20 2 km s@xmath2 ) obtained through a gaussian fit to the strong @xmath06300.3 oi line on the first sky spectrum . the spectra were subsequently rebinned into a constant velocity scale of 52 km s@xmath2 pixel@xmath2 . + spectra of several k and m - type giants ( table 1 ) were obtained with the same set - up ( slit width=0.7 "" ) for the cross - correlation analysis . a database of k - type main sequence stars ( table 2 ) , observed with the ids on the int with similar wavelength coverage and resolution ( see casares et al . 1996 ) were also used for the spectral type classification . prior to the cross - correlation the spectra were rectified to the continuum ( which was subtracted afterwards ) by masking the emission lines ( h@xmath21 , hei @xmath05875 , @xmath06678 ) and fitting a low - order spline to the remainder . then , individual radial velocities were extracted by cross - correlation with each template star in the range @xmath225600 - 6520 , after masking out the atmospheric and interstellar band at @xmath226270 - 6320 . note that the nad feature at @xmath225890 - 96 was included in the cross - correlation because is a strong feature in late - type stars and , given the high galactic latitude of j2123 - 058 , this is only marginally affected by interstellar absorption ; the ew of the interstellar nad measured by hynes et al . ( 2001 ) is less than 15 % of our observed value of 4.2 ( see fig . 2 ) . its effect is less than 1 km@xmath2 on the radial velocity curve . a few spectra from the first night have very poor statistics and consequently yield unreliable radial velocities . this was improved by co - adding the individual spectra into 16 phase bins , using the established orbital period of @xmath23 days ( zurita _ et al . the new radial velocities were fitted with a sine - wave at this period , the resulting parameters being displayed in table 1 . lccccc _ template_&_spectral type_&_@xmath24 _ & _ @xmath25 _ & _ @xmath26 _ & _ @xmath27 _ + _ star _ & & _ ( km s@xmath2 ) _ & _ ( + 2451779.0 ) _ & _ ( km s@xmath2 ) _ & + + hr 5265 & k3 iii & -112@xmath2010&0.6515 @xmath20 0.0015 & 285 @xmath20 9 & 1.8 + hr 5178 & k5 iii & -109@xmath2011&0.6520 @xmath20 0.0012 & 289 @xmath20 9 & 1.8 + hr 6159 & k7 iii & -111@xmath2011&0.6520 @xmath20 0.0017 & 287 @xmath20 12 & 1.3 + hr 5496 & m1 iii & -108@xmath2013&0.6515 @xmath20 0.0015 & 290 @xmath20 10 & 1.7 + hr 5603 & m3 iii & -111@xmath2015&0.6517 @xmath20 0.0017 & 287 @xmath20 11 & 1.6 + + column 3 lists the systemic velocities after correcting for the template radial velocities ( as given by simbad ) and instrumental flexure on template spectra . this latter correction could not be accounted for in the same way as in the target spectra because of the faintness of the sky spectra . instead , this was estimated by simply measuring the central wavelength of the h@xmath11 line , by fitting gaussians to the line core . notice the small scatter in the distribution of @xmath28-velocities which render confidence in the technique applied to compensate for differential flexure corrections . the statistical mean is -110 @xmath20 1 km s@xmath2 but the real error is probably underestimated . as a better representation of the uncertainty in the true systemic velocity we prefer to quote the mean of 1-@xmath29 uncertainties of the fits to the radial velocity curves . therefore , our favoured determination of the systemic velocity in j2123 - 058 is @xmath30 km s@xmath2 . + note the consistent values of the other parameters in table 1 which suggest @xmath31 and @xmath32 km s@xmath2 ( all quoted errors are @xmath33 ) . the combination of our @xmath34 determination with that of zurita et al . ( 2000 ) enables us to refine the orbital period to @xmath35 d. we note that hr6159 yields a significantly lower @xmath36 than the rest and , therefore , we adopt the orbital parameters derived using this template . adopting @xmath37 km s@xmath2 , the implied mass function is @xmath38 m@xmath8 . the phase - folded radial velocity curve , for the case of the k7 iii template , is shown in the top panel of fig . 1 . figure 2 presents the doppler - corrected average spectrum of j2123 - 058 in the rest frame of the secondary , together with some spectral - type standards . different weights were assigned to different spectra in order to maximize the signal - to - noise ratio . photospheric absorption features from the companion are clearly visible , such as the metallic blends at @xmath06165 and @xmath06495 and the nai doublet at @xmath05890 - 6 . these are clearly broader in j2123 - 058 than in the luminosity class iii templates but this is purely an instrumental effect since the averaged spectrum is dominated by the higher quality spectra from the second night , obtained through a 1 "" slit . several molecular tio bands ( e.g. @xmath226150 - 6250 , @xmath226960 - 90 and @xmath227020 - 50 ) are also evident and these can be used to rule out spectral types k3 ( and earlier ) and m1 ( and later ) . the spectral type of the companion is most probably in the range k5 - 7 . + both the spectral type and luminosity class of the secondary can be efficiently determined by subtracting different broadened versions of the templates ( to compensate for the instrumental resolution mismatch ) from the doppler - corrected sum of the target until the lowest residual is obtained ( as performed in e.g. marsh , robinson & wood 1994 ) . the broadened templates are multiplied by a factor @xmath39 to account for the shallowness of the absorption features in j2123 - 058 , which are diluted by the continuum excess of the accretion disc . the results of the optimal subtraction analysis are presented in table 2 . as expected , main sequence templates yield systematically lower @xmath40 , with a minimum for spectral types k7 - 8 v. the relative contribution of the companion star to the total flux in the r - band is constrained to the range @xmath41 . lcccc _ template _ & _ spectral _ & _ broadening _ & _ @xmath42 _ & _ @xmath36 _ + & _ type _ & _ ( km s@xmath2 ) _ & & ( d.o.f.=632 ) + + hr 5265 & k3 iii & 230 & 1.00 @xmath20 0.14 & 0.300 + hr 5178 & k5 iii & 210 & 0.85 @xmath20 0.11 & 0.293 + hr 6159 & k7 iii & 200 & 0.84 @xmath20 0.11 & 0.300 + hr 5496 & m1 iii & 155 & 0.68 @xmath20 0.10 & 0.312 + hr 5603 & m3 iii & 120 & 0.52 @xmath20 0.08 & 0.324 + + hd 184467 & k2 v & 190 & 1.43 @xmath20 0.17 & 0.267 + hd 154712 a & k4 v & 170 & 0.90 @xmath20 0.10 & 0.263 + hd 296974 & k5 v & 185 & 0.83 @xmath20 0.09 & 0.257 + 61 cyg a & k5 v & 220 & 0.83 @xmath20 0.09 & 0.258 + 61 cyg b & k7 v & 185 & 0.77 @xmath20 0.08" +"in recent years a considerable improvement in the study of large - scale structure has been obtained with the development of three - dimensional codes able to follow simultaneously the evolution of dark and baryonic matter . it is important to include the gas in n - body simulations for at least two reasons : first we must estimate the large amount of gas that is observed in clusters of galaxies through x - ray emission ; second , we must remove any ambiguity in the identification of galaxies . in the numerical simulations , the hydrodynamical equations have been solved either using mesh based methods @xcite or particle methods like the smoothed particle hydrodynamics @xcite . the latter , being lagrangian methods , have the advantage of covering a larger range of clustering scales , but they are not very reliable in low density regions for the calculation of thermodynamical quantities . eulerian methods , on the contrary , give a better estimate of thermodynamical quantities , but are constrained by the limited grid resolution in their capability of following the collapse of high density regions . a large dynamical range can be attained only by increasing the number of grid - points , but this is obviously limited by the available computer memory . at present the largest mesh used in eulerian calculations has @xmath4 grid - points . the analysis of the evolution at different cosmological scales is obtained by changing the physical normalization of the box size , and sometimes the results obtained at a given scale are used for setting up initial and boundary conditions at another scale ( e.g. cen & ostriker 1992 ) . since three - dimensional calculations pose severe limits on the number of grid - points used in eulerian methods , there has been in recent years an attempt to make up for the lack of resolution with the use of more accurate algorithms . one is looking for numerical methods able to well describe both low density regions and strong gradients in the fluid flow . very interesting is , for example , the possibility of introducing mesh refinement schemes in grid - based codes which , associated with shock capturing methods , would considerably improve the resolution in high density regions @xcite . the limited resolution reachable in three - dimensional codes makes sometimes difficult to separate , in the discussion of results , those effects which are only numerical from those which contains real physical information . analysis like the one of kang et al . ( 1994 ) are very useful for discriminating between different methods in three dimensions , but , because of the limitation in computer memory affecting all of the methods , a simultaneous one - dimensional analysis of the same phenomena appears quite convenient . working only in a single dimension makes possible to span a large dynamical range and to follow structure formation at different scales . approximate analytic solutions and their behaviour in highly non - linear regimes can also be better tested in one - dimensional calculations ( e.g. williams et al . recently , quilis , ibnez & saez ( 1994 ) have studied the applicability of modern high - resolution shock - capturing methods to the study of cosmological structures in presence of pressure forces . however , they do not follow at the same time the dynamics of the dark matter and so they are not able to compare the clustering properties of the two different components . in our work , instead , we study the evolution of cosmological one - dimensional perturbations when both baryonic and dark matter are considered . a detailed study of the evolution of gas and collisionless matter in a single pancake was presented by bond et al . ( 1984 ) and shapiro & struck - marcell ( 1985 ) . in both of these works one - dimensional calculations of the coupled evolution of baryonic and dark component were performed including the effects of radiative and compton cooling terms and thermal conductivity of the gas . the main difference between these two analyses is in the choice of the numerical algorithm used for solving the hydrodynamical equations which was lagrangian in one case @xcite and eulerian in the other one @xcite . a similar analysis has been recently done by thoul & weinberg ( 1994 ) , for a spherical configuration . they also have used a lagrangian approach which has the advantage of giving a higher resolution where needed without having , in one - dimension , the same problems of grid distortion present in more dimensions . all of the previous one - dimensional works following the coupled evolution of dark and baryonic matter consider isolated perturbations in the expanding universe and start their simulations when hydrodynamical effects begin to become important in the evolution . the information concerning the formation epoch and mass of these isolated structures is derived from n - body calculations assuming some model of large - scale structure formation . in this work we do not limit our attention to isolated perturbations but we want to explore the differences in the statistical properties of the one - dimensional clustering of baryonic and dark matter ( hereafter bm and dm , respectively ) components in an expanding background . we analyse the effect of pressure forces and adiabatic heating in the dynamics of the gas and we do not include , at this stage , cooling terms in our computations . our aim is to understand first the evolution of one - dimensional structures only in the presence of `` compressible '' effects . in addition , the inclusion of cooling processes requires the specification of characteristic time and length scales in the problem and in one - dimensional cosmological calculations it is not obvious how one can choose these quantities in connection with theory and observations . therefore , we have preferred to make simulations which are scale - free ; the absence of features in the primordial power - spectrum together with the higher spatial resolution implied by the use of one - dimensional simulations would permit to better discriminate between numerical artifacts and physical effects in the results . at the end , physical information on the computed quantities can easily be extracted by fixing the normalization quantities , like the box size and the final time . the plan of the paper is as follows . in section 2 we introduce the dynamical equations both for the hydrodynamical variables and for collisionless matter . the numerical methods used for the solution of these equations are also presented together with some numerical tests . the results obtained in numerical simulations of cosmological one - dimensional structures are shown in section 3 . discussion and conclusions are drawn in section 4 . in this section we present the dynamical equations that we use for evolving the bm and dm components in the case of one - dimensional perturbations . we assume a flat universe ( @xmath5 ) in which the bm component accounts for @xmath6 of the total mass ( @xmath7 ) and the rest is in the form of dm ( @xmath8 ) . in the present analysis we neglect the effects of radiative and compton coolings and any possible external heating . the dm component is approximated as a pressureless fluid and the bm component as a perfect fluid . we introduce the following set of dimensionless variables : @xmath9 where @xmath10 is the comoving coordinate , @xmath11 is the time , @xmath12 is the cosmological expansion factor , @xmath13 is the peculiar gravitational potential , @xmath14 and @xmath15 are the matter and internal energy densities , respectively . we have three basic units of normalization : the final time @xmath16 , the comoving cell size @xmath17 and the mean baryon density @xmath18 at time @xmath16 . for a cosmological application we can take @xmath16 and @xmath18 equal to the present age and density of the universe , respectively . the evolution of the collisional component is described by the following set of hydrodynamical equations : @xmath19 = 0\ , \ ] ] @xmath20 = -{\dot a\over a}\tilde \varrho \tilde v-{1\over a}\tilde \varrho{\partial\tilde \phi\over\partial\tilde x}\ , \ ] ] @xmath21 = -2{\dot a\over a}\tilde \epsilon-{1\over a } \tilde p{\partial \tilde v \over\partial \tilde x}\ , \ ] ] where @xmath22 is the comoving pressure . we use the equation of state of an ideal gas with adiabatic index @xmath23 , so that @xmath24 the physical temperature @xmath25 is related to the previous normalized quantities by @xmath26 where @xmath27 is boltzman s constant and @xmath28 the mass of the proton . in the dynamical equations for the collisionless particles we use as time integration variable the scale factor @xmath29 : @xmath30 @xmath31 the peculiar gravitational potential due to both the bm and dm component is computed by solving the poisson equation : @xmath32 where @xmath33 and @xmath34 is the newton s constant . the hydrodynamical equations have been integrated using the flux corrected transport ( fct ) method @xcite , a hybrid shock capturing method . in this method two difference schemes are blended together : a second order lax - wendroff scheme is used in regions of smooth flow , while a first order lax scheme is used near discontinuities . then second order accuracy is ensured everywhere except near flow jumps where the dissipation introduced by the low order scheme guarantees monotonicity in the behaviour of flow variables . the blending between the two schemes is controlled by a monotonicity constraint that leads to the sharpest possible discontinuity profiles . however , if the grid is not sufficiently fine , very strong gradients can be represented as a sequence of discontinuous jumps . this effect usually does not hinder the convergence of the method and can be reduced or completely avoided refining the grid @xcite . for the integration of the collisionless matter we have used a particle - mesh code @xcite . we use the same mesh as in the hydrodynamical part of the code , while the number of particles is a multiple of the number of mesh points in order to have a good resolution also in low density regions . the interpolation used for computing the mass density and the forces acting on each particle is obtained by a tsc scheme ( e.g. hockney & eastwood 1981 ) , which ensures a good accuracy in the estimates of previous quantities without leading to an excessive slowing down of the computation . for the time integration we use a second order leap - frog method so that the accuracy in the n - body is comparable to that attained in the hydrodynamical part of the code . the peculiar gravitational potential is computed using the standard fast fourier transform technique . the accuracy of the code has been tested against known analytical solutions . for the hydrodynamical part we performed the shock tube test comparing the analytical and numerical solutions . we found a very good agreement in smooth regions , while the shock is numerically diffused over about five grid - points . the evolution of an initial sinusoidal perturbation has been instead used for testing the performance of the n - body code : in this case the numerical solution has been compared with the results obtained using the zeldovich approximation @xcite which provides the exact one - dimensional solution up to shell crossing . in figure 1 we compare , just before shell crossing , the resulting dm distributions for the zeldovich and n - body solutions for two different choices of the number of grid - points @xmath35 ( @xmath36 and @xmath37 ) . the number of particles is instead kept fixed and set equal to @xmath38 . we notice that already with the smallest number of grid - points" +"the number of astrophysical sources thought to possess surface magnetic fields above the quantum critical field strength of g has been steadily growing in recent years . the five presently known soft gamma - ray repeaters ( sgrs ) and six or seven anomalous x - ray pulsars ( axps ) are believed to be magnetars , neutron stars having surface fields in the range @xmath0 g ( duncan & thompson 1992 ) . in addition , the parkes multibeam survey ( manchester et al . 2001 ) has discovered at least six new radio pulsars that have surface fields near or above critical , and several with fields comparable to those of some of the magnetars . the radiation processes that determine the observed x - ray and gamma - ray spectra in these sources are operating in the extreme relativistic and quantum regimes and thus require treatment that is accurate in such environments . one process that is particularly important in the source emission models is resonant compton scattering , in which electrons scatter photons at the cyclotron resonance with a cross section much larger than at continuum energies . relativistic electrons can blue - shift low energy photons into the resonance , upscattering the photons into a high - energy continuum ( daugherty & harding 1989 , dermer 1990 ) . the quantum electrodynamical ( qed ) cross section for compton scattering at the cyclotron fundamental ( herold 1979 ) and higher harmonics ( daugherty & harding 1986 , bussard , alexander & mszros 1986 ) , accurate in arbitrarily high magnetic fields , has been known for some time . however , these derivations do not treat the natural line widths that render the cross section finite at the cyclotron resonances . in order to use such rates in spectral calculations in astrophysical models , the line widths that originate from the lifetimes of the excited landau states must be included in the cross section ( wasserman & salpeter 1980 ) . the width of the @xmath1th resonance is equal to the cyclotron decay rate from that state ( pavlov et al . 1991 ) , and the prescription for incorporating the widths in the qed cross section in the high - field regime has been discussed by harding & daugherty ( 1991 ) and graziani ( 1993 ) . including resonant line widths in the scattering cross section necessarily requires spin - dependent decay rates , which appear in an infinite sum over landau state @xmath1 and spin of the intermediate virtual states , even in the case of ground state - to - ground state scattering in the fundamental . different spin states have different decay rates , and thus different resonant energy denominators . since the electrons and positrons in intermediate states have non - zero momentum parallel to the magnetic field , it is important to use basis states that yield a spin dependence that is lorentz invariant , i.e. boosts along the magnetic field do not lead to a mixing between the spin states . as is true for all quantum processes , the spin - dependent rates and cross sections depend on the choice of electron wavefunctions in a uniform magnetic field . historically , several choices of wavefunctions have been used in calculations of the scattering cross section and cyclotron decay rates . the two most widely used wavefunctions are those of johnson & lippman ( 1949 ) and sokolov & ternov ( 1968 ) . the johnson & lippman ( jl ) wavefunctions are derived in cartesian coordinates and are eigenstates of the kinetic momentum operator . the sokolov & ternov ( st ) wavefunctions , specifically their `` transverse polarization '' states , are derived in cylindrical coordinates and are eigenfunctons of the magnetic moment operator . given the different spin dependence of the st and jl eigenstates , one must use caution in making the appropriate choice when treating spin - dependent processes . herold , ruder & wunner ( 1982 ) and melrose and parle ( 1983 ) have noted that the st eigenstates have desirable properties that the jl states do not possess , such as being eigenfunctions of the hamiltonian including radiation corrections , having symmetry between positron and electron states , and diagonalization of the self - energy shift operator . as found by graziani ( 1993 ) , the st wavefunctions also diagonalize the landau - dirac operator , and are the physically correct choices for spin - dependent treatments and for incorporating widths in the scattering cross section . although the spin - averaged st and jl cyclotron decay rates are equal , the spin - dependent decay rates are not , except in the special case in which the initial momentum of the electron parallel to the field vanishes . perhaps the most fundamental argument against use of the jl wavefunctions is that radiative corrections cause excited jl landau levels to become unstable to spin - flip transition within landau states on timescales comparable to the timescale for decay to a lower landau state . these radiative corrections to the magnetic moment break the spin degeneracy of both the st and jl excited landau states ( herold , ruder & wunner 1982 ) , causing spin - dependent energy level shifts , and implying a dependence of the rates for spin - flip transitions within a landau state on the choice of wavefunctions . the rates of such spin - flip transitions within split st landau states have been evaluated ( geprgs et al . 1994 ; see also parle 1987 ) , and are found to be of order of for , which is negligible compared to decay rates between landau states . the existence of such relatively long - lived states is a premise of the s - matrix formalism and is also essential to any astrophysical calculations involving spin - dependent transitions between landau states . in contrast , it is anticipated that since the jl eigenstates do not diagonalize the self - interaction hamiltonian including radiation corrections ( i.e. the mass operator ) , the associated mixing incurred in s - matrix evaluations will render spin - flip transition rates with fixed comparable to ordinary cyclotronic rates with changes in , a situation that is unphysical . in this paper we discuss the lorentz tranformation characteristics of cyclotron decay rates for both st and jl formulations , and derive simplified expressions for the decay rates from an arbritrary excited landau state to the ground state . we show that the st eigenstates preserve separability of the spin dependence under lorentz boosts along the local magnetic field , a desirable property that does not extend to the jl formalism , for which such lorentz boosts mix the corresponding spin states . in the st formulation , by taking advantage of its spin - state preserving characteristics , our analytic simplifications can be elegantly applied to the spin - dependent decay rates ; in the jl formalism the simplifications can be compactly applied only to the spin - averaged rates . the resulting expressions replace integrals over emergent photon angle with series of legendre functions of the second kind , which correspond to sums of elementary functions , easily yielding simple asymptotic forms . the expressions derived here should have wide applicability to modeling cyclotron emission , compton scattering and other qed processes in super - critical fields . for such magnetar - type fields , resonant scattering takes place primarily at the fundamental , since the cyclotron energy exceeds 1 mev . although the resonant scattering line widths formally involve infinite sums over landau states , in the case of the fundamental resonance the sum is dominated by the @xmath2 state , whose width is equal to the @xmath3 cyclotron decay rate . for cyclotron scattering in higher harmonics @xmath4 , the intermediate sums in the vertex functions have the largest contributions from the @xmath5 state . however , for , cyclotron transitions to the ground landau state dominate ( sokolov , zhukovskii & nikitina 1973 , white 1974 , harding & preece 1987 ) , so that cyclotron decay rates for @xmath3 transitions treated in this paper should be good approximations to the widths of excited states , a circumstance pertinent to astrophysical models of magnetars . this presentation of spin - dependent cyclotron rates appropriately focuses first on the formulation generated using the _ transverse polarization _ eigenstates of the dirac equation derived by sokolov & ternov ( 1968 ) for electrons in a uniform magnetic field * b*. explicit forms for them can also be found in herold , ruder & wunner ( 1982 ) and harding & preece ( 1987 ) , whose exposition on cyclotron emission essentially forms the basis of results developed here . herold et al . observed that these states diagonalize the operator that describes the electronic self - energy shift in an external magnetic field . another attractive feature of the sokolov & ternov eigenstates is that they possess charge conjugation symmetries , i.e. between electron ( positive energy ) and positron ( negative energy ) : see eq . ( 12 ) of herold , ruder & wunner ( 1982 ) . an additional asset of these wavefunctions that is enunciated here is that they yield cyclotron rates whose spin dependence is effectively separable from lorentz transformations along the field : i.e. such boosts do not mix spin states . this is a very useful characteristic that is not present in the johnson & lippmann formalism addressed in section [ sec : jlformalism ] below . herold , ruder & wunner ( 1982 ) obtained general expressions in their eq . ( 17 ) for the spin - dependent cyclotron rate for transitions between arbitrary landau levels , but for the case of zero initial momentum parallel to the field . latal ( 1986 ) independently obtained similar results for cyclotron transitions to the ground state , but retained arbitrary initial momenta along * b * ; his eq . ( 22 ) forms the starting point for the exposition here . denoting as the spin quantum number of the initial electron , ground state transitions are characterized by a single final spin . the energy level quantum numbers are initially , and after the transition . latal s spin - dependent _ total _ rates can be written in the form @xmath6 where is the magnetic field strength , expressed dimensionlessly hereafter in units of the quantum critical field gauss , and the _ spin - averaged _ , total cyclotron transition rate for is given by @xmath7 \label{eq : gammave_st}\\[-5.5pt ] & \times & \ ; \dover{(1-\xi)^{n-1}}{(1+\xi)^{n+1}}\biggl ( 1 + 2nb - \dover{1}{\xi } \biggr ) \ ; \exp \biggl ( - n\ , \dover{1-\xi}{1+\xi } \biggr ) \ ; .\nonumber\end{aligned}\ ] ] here is the compton wavelength of the electron over , and other quantities in this equation are defined as follows . for initial and final dimensionless momenta ( i.e. , in units of ) , and respectively , parallel to the field , the electron s initial energy and final energy , both dimensionless ( i.e. , in units of ) , are @xmath8 this convention of using dimensionless energies and momenta will be adopted throughout the paper . the integration variable is the angle cosine of the emitted photon with respect the magnetic field direction , i.e. for photon wavenumber vector . no integration by parts has been performed when obtaining eq . ( [ eq : gammave_st ] ) , so that the cyclotron rate , differential in photon angles , , again averaged over initial electron spins , corresponds directly to the integrand of eq . ( [ eq : gammave_st ] ) : @xmath9 corresponding spin - dependent differential cyclotron rates can be deduced from eq ." +"the unprecedented development of laser technologies in recent two decades , mainly due to chirped pulse amplification technique @xcite , has allowed increase of intensity of laser sources in the first stage a six orders of magnitude @xcite reaching the relativistic intensities @xmath0@xmath1 in the infrared and optical domains , respectively , then exceeding these values up to @xmath2 for current superpower laser beams of ultrarelativistic intensities @xcite . in many laboratories @xcite compact lasers can deliver @xmath3 petawatt short pulses , with focused intensities as high as @xmath4 . next generation multipetawatt and exawatt optical laser systems @xcite will be capable to deliver ultrahigh intensities exceeding @xmath5 , which are well above the ultrarelativistic regime of electron - laser interaction . at such intensities the radiation - matter interaction enters the phase of ultrafast dynamics in supershort time scales , with formation of such important fields in condensed - matter - physics that the attoscience at1,at2,atto1,atto2,atto3,atto4 , and relativistic optics mourou , rel - rep2,br .- kr.,rel - rep1,pukh are . the appearance of laser sources with ultrarelativistic intensities has opened real possibilities for revelation of many nonlinear electrodynamic phenomena at the interaction of superpower radiation fields with high brightness accelerator beams @xcite , relativistic plasma targets of solid densities @xcite , and qed vacuum @xcite.laser sources of such enormous intensities predetermine , in particular , the future of laser accelerators @xcite of superperhigh energies , including laser - plasma accelerators @xcite . thus , currently available optical lasers provide @xmath6 up to @xmath7 , meanwhile with the next generation of laser systems one can manipulate with beams at @xmath8 @xmath9 . in such ultrastrong laser fields , electrons can reach to ultrarelativistic energies . however to obtain ultrarelativistic net energies for field - free electrons we need the third body for satisfaction of conservation laws for energy - momentum of a free electron ( after the interaction ) with absorption / radiation of photons in the field of a plane monochromatic wave @xcite , or take advantage of nonplane character of tightly focused supershort laser pulses @xcite . nevertheless , the actual way to get net energy exchange of relativistic electrons is using of coherent processes of laser - particle interaction with the additional resonances . among those the induced cherenkov , compton , and undulator processes are especially of interest @xcite . these are coherent induced processes where a critical intensity of stimulated wave exists ( because of coherent character of corresponding spontaneous process ) above which the induced process proceeds only in one direction - coherent radiation ( wave amplification ) , or absorption ( particle acceleration ) depending on the particle initial velocity with respect to resonance value ( satisfying the condition of coherency ) of each process . the latter is the most important feature of nonlinear resonance inherent in these processes to get high net energy change of particles , specifically for laser acceleration @xcite , or free electron laser ( fel ) @xcite , as well as to generate relativistic electron beams of low energy spreads and emittances due to the threshold nature of nonlinear resonance in these induced coherent processes . in principle , the realization of acceleration or inverse problem of fel in any laser - induced process requires the possible largest coherent length of particle - laser stimulated interaction at which the accumulation of particle energy in the acceleration regime , or coherent radiation -in the wave amplification regime take place on the whole coherent length of certain process . in other cases , the existence of an additional resonance ( e.g. , in a static magnetic field @xcite ) is necessary where the particle - wave interaction cross section enhances by many orders in magnitude . these are the linear resonances well enough investigated during the past decades . here we will consider laser - induced processes on free electrons with the large effective gain of interaction due to nonlinear resonance achieved in the given field of a strong laser radiation . in the induced cherenkov , compton , and undulator processes such resonance is adequate to fulfilment of condition of coherency between the particle and wave achieved in the field at the aforementioned critical intensity of the total wave - field . in the result of such interaction , at the laser intensities larger than critical value a nonlinear threshold phenomenon of particles reflection or capture take place -accelerating or decelerating electrons on the shortest interaction lengths , even shorter than a laser wavelength @xcite . in contrast to induced cherenkov process @xcite where the intensities of applied laser fields are confined by ionization threshold of dielectric media @xcite in vacuum processes in the induced compton @xcite and undulator @xcite ones there is no restriction on the electromagnetic ( em ) field strengths that allows to apply current superpower laser beams of ultrarelativistic intensities mourou for acceleration of particles up to superhigh energies . the other practical difference between these induced processes is in the relativistic character of initial resonance width of particles to reach the threshold value of corresponding nonlinear resonance in the field for reflection / capture phenomenon . thus , in contrast to cherenkov and undulator processes where practically initial relativistic / ultrarelativistic particles are needed for realization of nonlinear cherenkov resonance in gaseous media @xcite , or nonlinear resonance in a magnetic undulator with the step of the order of a few @xmath10 @xcite , induced compton mechanism for particles reflection / capture and , consequently , acceleration regime practically may be realized for arbitrary initial energies of the particles @xcite . in particular , using laser pulses of near frequencies one can accelerate initially nonrelativistic beams , or even particles in rest . second , at the same frequencies of counterpropagating laser pulses in the induced compton process one can achieve the cancellation of particles transverse momenta acquired in the field to obtain quasi - colinear particles bunches from the emerging relativistic electron targets ( elimination of a bunch angular divergence ) , as it has been proposed in the paper @xcite for generation of uniform relativistic electron layers at the coherent compton backscattering on the ultra - thin solid foils ( see , also , @xcite ) . a promising way for achieving of laser - driven electron acceleration is the use of a plasma medium @xcite . however , the laser - plasma accelerator schemes face problems connected with the inherent instabilities in laser - plasma interaction processes . on the other hand , the spectrum of direct acceleration mechanisms of charged particles by a single laser pulse is very restricted , since one should use the laser beams focused to subwavelength waist radii , or use subcycle laser pulses , or use radially polarized lasers , violating the plane character of a coherent laser pulse for particles acceleration by a single wave - pulse in vacuum without the third body . all these scenarios with different field configurations have been investigated both theoretically and experimentally in the works 22_exp , a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15,a16,a17 . note that beside the focusing of a laser pulse to subwavelength waist radii we can get nonplane laser beam by terminating the field , either by reflection , absorption , or diffraction @xcite . the proof of principle experiment of this type has been reported in ref . @xcite . here it is used initially relativistic electron beam and a moderately strong laser pulse . to obtain dense enough electron bunches it is reasonable to consider electrons acceleration from nanoscale - solid plasma - targets meyer - ter - vehn , mirror1,mirror2,mirror3 at intensities high enough to separate all electrons from ions @xcite . thus , combining these two schemes one can obtain ultrarelativistic solid density electron bunches 11b,12b,13b,14b,15b,16b,17b,18b . such bunches can be used to obtain high - flux of positrons , @xmath11-quanta @xcite with possible applications in material science , medicine , and nuclear physics . the recent achievements in the laser technology related to implementation of supershort femtosecond laser sources and subsycle pulses of relativistic intensities exceeding the intra - atomic fields open real opportunities for realization of laser - plasma accelerators of ultrahigh energies mey .- ter,1p,2p,3p,4p,5p,6p,7p,8p . these schemes are based on the laser - plasma - wake - field and laser - beat - wave mechanisms of laser - assisted acceleration in plasma . the interaction of such powerful radiation fields with the plasma has led to generation of quasi - monoenergetic relativistic electron beams in laser - driven plasma accelerators a9,a10,a11,a12,a13,a14,a15,a16,a17 . concerning the interaction of ultrashort laser pulses of relativistic intensities with the free electrons in vacuum , i.e. the implementation of laser accelerators , one should note that experiments in this area are gathering power at present . one of the first laser accelerator concepts is the inverse cherenkov accelerator ( ica ) . the ica scheme has been investigated since the advent of lasers [ see , for example , @xcite ] . the appearance of powerful laser sources already in the next decade after the first lasers has stimulated comprehensive theoretical @xcite and experimental p1,p2,p3,p4,p5,kim1,kim2,kim3,kim4 investigations towards the implementation of both induced cherenkov problems ica and cherenkov laser realization in diverse schemes of multiphoton interaction that makes a phase velocity matching of em wave with a particle by controlling the refraction index of gaseous medium so as to be a wave phase velocity in a dielectric medium less than light speed in vacuum . various interaction schemes of electrons with stimulating radiation have been considered as with ultrarelativistic electron beams in a gaseous medium for the optical region @xcite , as well as with mildly relativistic beams in dielectric waveguides for the microwave region w1,w2,w3,w4,w5,w6,w7,w8,w9,unmag . in the latter case , the electron beam passes over the dielectric in the vacuum surface cherenkov process that enables one to avoid the impeding factors of the medium ( the multiple scattering of electrons on atoms , the ionization losses in the medium etc . ) . besides , the usage of solid - state dielectric as a slow - wave structure ( with rather high dielectric constant @xmath12 , @xmath13 ) enables the achievement of electron - wave synchronism by mildly or moderately relativistic electron beams . it is important to note that the effect of critical field exists even in a very week wave field if the interaction occurs in the region close to the initial cherenkov resonance . therefore one can not escape these peculiarities restricting only the intensity of the external wave field and solve the problem in the scope of the linear theory even for very week wave fields @xcite . note that regarding the induced cherenkov process a series of systematical wrong works have been made during the last two decades of past century , which were discussed in special review @xcite devoted to consideration of those results . in the mentioned review the all principal mistakes have been shown in detail , therefore in the current review article we will not repeat the analysis of those papers which reader can get in the review @xcite . the particle reflection phenomenon from a slowed plane wave pulse has been applied also for cases where the group velocity of a wave pulse due to the dispersion can be less than light speed in vacuum @xcite : in ref . @xcite for the case of a plasma , in ref . @xcite at the focusing of an ultrashort laser pulse in vacuum , in the so - called by authors dispersion - dominated propagation regime . nonlinear resonance of threshold nature requiring shortest acceleration length also takes place at the charged particle interaction with strong laser radiation _ _ _ _ and static magnetic field along the wave propagation direction _ _ _ _ ( when the resonant effect of the wave on the particle rotational motion in the uniform magnetic field is possible )" +"quantum computers offer the promise of fundamentally faster processing based upon quantum mechanical properties . although a physical device of a useful size is still to be built , many quantum algorithms have already been discovered . the most important of these are the algorithms introduced by @xcite and @xcite , which can factor integers and search an unsorted database respectively , significantly faster than the best known classical algorithms @xcite . quantum walks were initially introduced in both continuous @xcite and discrete @xcite time , in direct analogy with their classical counterparts , and have since been studied extensively @xcite . in the same way that classical random walks are used in computer science for algorithm design , many quantum algorithms have been developed based upon quantum walks , with varying speed ups over the best known classical algorithms for the same problem , @xcite . these solve the problems using two different approaches : hitting times and searching . in hitting time problems we start from a specific vertex and want to get to another as quickly as possible . these problems have yielded the largest speed up , including exponential speed ups over the classical case , @xcite . searching for an entry in an unsorted database is a classically time - consuming problem taking on average a time of @xmath0 to search a set of @xmath1 entries . grover s algorithm , @xcite , improves on this to @xmath2 by using a technique known as amplitude amplification . the same speed up can be obtained using a quantum walk method on various structures @xcite . in @xcite , @xcite extends the original results of @xcite @xcite to show a continuous time quantum walk , on an unweighted graph of bounded degree , is universal for quantum computation . @xcite gives an explicit construction that converts a standard gate model computation into a graph , on which a continuous time quantum walk executes an algorithm by traversing the graph . in this paper , we show the equivalent construction of a universal gate set using the discrete time quantum walk in place of the continuous . this confirms that both the continuous and the discrete time quantum walks can be regarded as computational primitives . the construction requires an exponentially large graph for the size of the input as we require @xmath3 wires for an @xmath4 qubit input . the quantum walk takes place on this @xmath1-vertex graph just as the continuous time walk does in the construction by childs @xcite . it is already known that a quantum walk on an @xmath1-vertex graph can be simulated efficiently by a universal quantum computer using @xmath5 gates , provided there is a simple rule to compute the neighbours of any vertex @xcite . thus , by performing the quantum walk on a quantum computer , the binary encoding brings the resources required back to the expected level . our construction for the universal gate set in discrete time is similar to @xcite but has maximum degree , @xmath6 , of eight at any vertex as opposed to three in the continuous case . the continuous time walk can easily be propagated in one direction with no reflection at the vertices . the discrete time walk is not so straightforward , it can only be propagated in one direction by using a specific coin corresponding to the @xmath7 operation . using this coin restricts the graph to vertices of degree two , providing no way to construct higher degree structures . thus we must use a double - edged wire to accomplish directional propagation . this solution has its roots in the connection between the continuous and discrete time walks . @xcite @xcite has shown that , as we take the continuous limit of the discrete time walk on the line , we actually get two copies of the continuous time walk propagating in opposite directions . @xcite @xcite later showed a direct correspondence between the discrete and continuous time quantum walks on arbitrary graphs . in the same work , @xcite shows how a discrete time walk can be used , at its limit of small eigenvalues , to approximate the continuous time walk . he uses this ` lazy ' quantum walk approach to allow the discrete time walk to propagate in the same way as the continuous . this same approach could be used in this case to allow the computation to be performed on the same structures defined in @xcite . however , this would require the discrete time walk to approach the limit at which it is doing very little at each timestep . this would then increase the overhead required to allow completely deterministic computation . we begin by describing the discrete time quantum walk briefly in section [ sec : discrete ] , then move on to show structures on which the discrete time quantum walk will allow perfect state transfer in section [ sec : char ] . these structures allow us to construct the elements we need to perform computation . section [ sec : gate ] shows the universal gate set we choose and how we implement these using the discrete time walk . section [ sec : circuits ] describes how we can link these gates and structures together to form any quantum circuit , and elaborates on how this is efficient , despite the size of the graph being exponential in the number of gates required . finally , in section [ sec : conc ] we discuss our findings and the differences with the continuous time construction of @xcite . consider a classical random walk on a line in which a walker starts at a specific position and , depending on the outcome of a coin toss , moves either left or right . the outcome after many runs is a binomial distribution about the starting position with a spread ( quantified by the standard deviation ) of @xmath8 where @xmath9 is the number of timesteps . a discrete time quantum walk is the direct analog of the classical walk with the walker replaced by a quantum particle carrying a two state quantum system for the coin . the coin toss is effected by a unitary operator . although this is now deterministic , if we were to measure the coin we would get a random output as in the classical case . we start the quantum walker at the origin and act upon it with a unitary operator for the coin toss , followed by a conditional shift operation ( to obtain the movement of the walker ) at each timestep . we write the basis states of the walker as an ordered pair , @xmath10 , denoting the position of the walker , @xmath11 , and the state of the coin , i.e. , heads ( @xmath12 ) or tails ( @xmath13 ) . the simplest unitary operator is the hadamard operator , h , which acts on the state as @xmath14 the shift operation , s , acts thus @xmath15 the first three timesteps starting at the origin are as follows @xmath16 as the walk progresses , quantum interference occurs whenever there is more than one possible path of @xmath9 steps to the position . this can be both constructive and destructive , as shown in eq . ( [ 3steps ] ) , which causes some probabilities to be amplified or decreased at each timestep . the walk on the line has been solved analytically @xcite where it was first remarked that the quantum walk spreads quadratically faster than the classical one . the choice of operator at each vertex can greatly affect the dynamics of the walk and its propagation across the structure . a bias can be introduced @xcite , for @xmath17 , this is done using a generalisation of the hadamard operator , @xmath18 where @xmath19 is the bias in the coin . setting this to @xmath20 returns the standard hadamard operator , eq . ( [ hadamard ] ) . similarly , the choice of the walker s initial state is also important , unlike in the classical random walk . a good review of these effects can be found in @xcite . for universal computation we need a quantum walk on a more complex graph . in graph theory , a general graph , g , is an ordered pair consisting of a set of vertices , v , and a set of edges , e , which link the vertices . the number of edges incident on a vertex is the degree of the vertex , fig . [ graph ] shows a small general graph which has vertices of varying degree . it is also undirected , meaning that the edges allow movement in both directions . a different operator ( coin ) is needed at vertices with @xmath21 in order to act on the entire state space @xcite . the grover coin can be extended to any degree at a vertex , @xmath22 - i_{d } , \label{grover}\ ] ] where @xmath6 is the degree of the vertex and @xmath23 is the identity matrix of the same dimension . coins of degree four will be needed at most of the vertices in our computational graphs . the grover coin in four dimensions , eq . ( [ grover ] ) , reduces to @xmath24 . \label{grover4}\ ] ] ) , operating on the incoming amplitude @xmath25 . ] + using these higher dimensional coins can cause the walker to be reflected back upon itself with some probability . figure [ reflection ] shows this reflection for a vertex of degree @xmath26 . in quantum walk search and other quantum walk algorithms this can be useful to provide interference . however , here we need to ensure the walker moves in one direction only , from left to right , so it most resembles the circuit model of quantum computation . we show how we accomplish this forward only propagation in section [ sec : gate ] . as a preliminary to our quantum computation scheme , we discuss structures on which perfect state transfer can be achieved using the discrete time quantum walk . perfect state transfer has been investigated in the context of spin chains by @xcite @xcite . the propagation of the state through spin systems follows the same dynamics as a continuous time quantum walk . perfect state transfer can occur on chains of length 2 or 3 , hypercubes of any size , and chains with different coupling strengths engineered to optimise state transfer . the closely related properties of instantaneous mixing and periodic cycles have been studied in detail for quantum walks . for the continuous time quantum walk , instantaneous mixing has been investigated by @xcite @xcite . they showed @xcite this is achieved on cycles of 2 , 3 and 4 vertices only . for the discrete time walk , slightly larger cycles show exact periodic behaviour . @xcite @xcite showed that a cycle of 4 vertices has a periodicity of 8 timesteps after which the entire state returns to the starting position . @xcite @xcite showed more periodic cycles exist , cycles of 2 , 3 , 4 , 5 , 6 , 8 and 10 were shown numerically to be periodic by varying both the bias and phase in the coin . perfect state transfer occurs at half the periodic cycle for even cycles , where we obtain the entire state at the opposite point of the cycle as shown in fig . [ transfer ] . for our case of using the walk for computation , we require the walk to travel perfectly in a single direction . on the structures mentioned , the quantum walk travels around the cycle in both directions and interferes to produce perfect state transfer . using a completely" +"plankton patchiness has many causes , with origins both in biological and physical factors . over small scales ( @xmath0 mm to @xmath1 m ) , biological factors on the individual scale such as mating , predator avoidance , finding food and the diel vertical migration ( upward and downward swimming at certain times during the @xmath2h day ) are crucial factors for the emergence of plankton patchiness @xcite . on larger length scales ( @xmath1 m to @xmath3 km ) , physical processes such as turbulence , currents and eddies are the principal causes of patterns . it has been shown that the relative intensity of zooplankton patchiness is greater than that of phytoplankton at all spatial scales @xcite . mackas and boyd @xcite developed a method to count individual particles in a continuous stream of seawater . this permitted them to use shipborne sampling to find transects of zooplankton abundance and chlorophyll fluorescence , which provides an appropriate method for estimating phytoplankton concentration , and to make a spectral analysis of the spatial heterogeneity . they found that small spatial scale contribution to the total patchiness is much greater for zooplankton , which is reflected in the fact that power spectra are less steeply sloped for zooplankton than for phytoplankton . moreover , they found that the spatial patterns of phytoplankton and zooplankton are negatively correlated . satellite imagery allows the obtention of greater spatial coverage and a better time resolution than shipborne sampling . the analysis of changes in the spectrum of visible light due to absorption and fluorescence of chlorophyll pigments allow the estimation of phytoplankton biomass . et al . _ @xcite performed a spectral analysis of satellite images , the results of which lead them to believe that phytoplankton patchiness is controlled by mesoscale ( @xmath4-@xmath3 km ) water motions . phytoplankton have small mobility , consisting of vertical migration limited to over a few meters per day and may therefore be considered almost as a passive scalar advected by the ocean currents . many model systems have been put forward to explain pattern formation in such planktonic systems . to cite a few , abraham @xcite has considered the role of non - diffusive advection in plankton pattern formation and lpez _ _ e__t al . @xcite and hernndez - garcia _ _ e__t al . @xcite offer a comprehensive overview of modeling of plankton dynamics as chaotic advection . however , the important effects of noise have usually been neglected . this work is organized as follows : in the next section , we briefly discuss models of population growth used in ecology ; in sect . [ sec : noise ] we describe the effects of noise in such models ; in sect . [ sec : space ] we analyze how the inclusion of diffusion and advection can generate patterns in population dynamics ; in sect . [ sec : spectral ] , we discuss spectral analysis , one of the main tools used in studying plankton patterns ; we give final remarks in sect . [ sec : conclusion ] . in ecology , continuous growth population dynamics is usually modelled by a system of differential equations which correspond to the conservation equations for each population , in which the rate of change of the different species is related to birth , death and migration processes . predator - prey models are usually defined through @xmath5 where @xmath6 represents the prey population , @xmath7 the predator population and the functions @xmath8 and @xmath9 account for the usually nonlinear interactions between the species . a general starting point is the lotka - volterra model , in which @xmath10 , and @xmath11 , with @xmath12 , @xmath13 , @xmath14 and @xmath15 positive constants . however , this model has some drawbacks , since its solutions are not structurally stable @xcite , meaning that small perturbations can exert large effects on the amplitude of oscillation , for example . an improvement is given by a logistic growth of the prey , which limits the prey population even in the absence of predators . this feature is taken into account by the function @xmath16 , where @xmath17 is a linear birth rate , @xmath18 is the carrying capacity of the environment , and @xmath14 a parameter related to the predation rate . the response function @xmath19 , to be more realistic , should saturate to account for satiation . a possible choice is the holling type iii functional response @xmath20 @xcite . an equation with these terms and considering a constant number of predators @xmath21 was used to model the outbreak of the spruce budworm @xcite . in that case , the carrying capacity is related to the foliage ( food ) available in the trees , and the functional response models a switching on of the predation rate by birds at a given threshold population of the prey . in other words , if the prey population is low , the predator ( birds ) will find a different source of food and if the prey population is high enough , it will become a source of food . moreover , the saturation in the functional response represents the fact that there is a maximum uptake of food by the birds . a model similar to the one for the spruce budworm was used together with a time - dependent growth rate @xmath22 , and @xmath23 , with @xmath24 and @xmath25 positive constants , to model the interaction of phytoplankton and zooplankton with different timescales that lead to rapid increases of phytoplankton population known as `` spring blooms '' and `` red tides '' @xcite . deterministic population models rarely capture all of the features of dynamical systems , since real systems are influenced by changes in the environment which are in essence random . this inherent unpredictability of the environment may manifest itself in fluctuating birth rates , carrying capacities and other parameters which characterize biological systems . a deterministic treatment is more adequate for very large populations . however , the population of zooplankton is considerably smaller than that of phytoplankton and a stochastic approach is more realistic . the reason for the inclusion of noise is the fact that zooplankton interact with fish and whales which are present in even smaller numbers and are far from being evenly distributed . nevertheless , in many cases , the inclusion of noise may destabilize a system and lead to the extinction of a given species . the linear stability of a system of @xmath26 species @xmath27 depends on the eigenvalues of the matrix with components @xmath28 which governs the dynamics near equilibrium in the linear approximation . for a system without noise to be stable , it is necessary that all eigenvalues have negative real parts . if we define @xmath29 as minus the largest real part of the eigenvalues , then the stability criterion becomes @xmath30 . in the presence of fluctuations characterized by variance @xmath31 , the stability criterion should be changed to @xmath32 @xcite . the noise will generally tend to decrease the average population number by increasing the severity of the population fluctuations . to see the effects of noise , we will consider the model @xmath33 where @xmath34 is a random term , and @xmath35 and @xmath36 are the phytoplankton and zooplankton populations , respectively . as pointed out in @xcite , the intrinsic rate of zooplankton growth is lower than that of phytoplankton , what should lead to the formation and maintenance of only very large scale features . they concluded that a mechanism ( maybe behavioral in origin ) with shorter time scale should be at play to account for the small - scale patchiness observed . this is the motivation for the inclusion of a multiplicative noise term , since fluctuations originate from processes which depend on the local concentration , such as the reproduction process and the consumption by larger animals . therefore , we take @xmath37 ^ 2 \delta ( t - t')$ ] , where @xmath38 is a fluctuating growth rate . an _ a posteriori _ reason for not considering additive noise is that it may allow the concentration of zooplankton to reach negative values , which is unreasonable . in the study of stochastic population dynamics in the poisson approximation , an expression for the fluctuations around the deterministic limit in which the noise amplitude is state dependent is also arrived at @xcite . the inclusion of noise of this type may easily destabilize the system , since unrealistically large fluctuations may arise even for very small values of @xmath39 . in the absence of noise , the populations will converge to the stable equilibrium given by @xmath40 . \label{zoo_eq}\end{aligned}\ ] ] figure [ fig : noise ] shows how the populations fluctuate around their average stable values @xmath41 and @xmath42 , but the fluctuations can eventually take the system to the unstable equilibrium @xmath43 and @xmath44 . this negative effect of noise can be attenuated by the inclusion of space variables and diffusion or advection , as will be seen in the next section . the inclusion of noise does not always have a negative impact on dynamics ; in some systems , its effects can be particularly important and can lead to unexpected results such as stochastic resonance @xcite , a phenomenon characterized by the enhancement of the response of a system to a periodic driving force in the presence of noise . stochastic resonance has been studied in many systems , including spatially extended systems and pattern - forming systems , such as the swift - hohenberg equation @xcite . another interesting possibility is the suppression of internal noise by the application of an external noise source @xcite . the models considered up to now are in a sense incomplete , since they provide a mean - field description of the variations of the population in which only global changes are considered . even though average population densities and even some naturally occurring phenomena such as outbreaks can be predicted , many other features of the systems are left out , pattern formation being one of these . turing @xcite studied how diffusion together with nonlinear local interactions could lead to the emergence of heterogeneities even when starting from homogeneous conditions in a homogeneous environment . reaction - diffusion equations of the form @xmath45 have been used since then to model pattern formation in system on a wide range , from chemical reactions to bacterial chemotaxis and animal coat patterns @xcite . initially , models of plankton spatial heterogeneity and patchiness were based on these types of equations , in which the populations are investigated theoretically by some variation on the predator - prey models derived from on the lotka - volterra model with an added diffusive term . a study of the plankton population stability with this model was performed by steele @xcite . levin and segel @xcite introduced an autocatalytic effect in phytoplankton density and differential dispersal rates which favor higher herbivore motility to account for the origin of planktonic patchiness . with their hypothesis , they found a transition from a uniform stable state to a new steady state in which plant and herbivore are more concentrated in certain regions , depending on the model parameters . however , in the case of planktonic populations , diffusion is only important for the movement of plankton on small scales ( centimeter scales ) , in which many biological factors are also important . moreover , the experimental results from @xcite show that zooplankton is more patchily distributed and indicate that analytical models used for describing phytoplankton which are based on a perturbative analysis of the scale - dependent balance between turbulent diffusive flux and exponential reproductive growth are inapplicable for explaining the zooplankton heterogeneity over these scales . in simulations with models based" +"many important problems in the theory of integrable systems and approximation theory can be recast as riemann - hilbert problems for a matrix - valued unknown . via the connection with approximation theory , and specifically the theory of orthogonal polynomials , one can also study problems from the theory of random matrix ensembles and combinatorics . roughly speaking , solving a riemann - hilbert problem amounts to reconstructing a sectionally meromorphic matrix from given homogeneous multiplicative `` jump conditions '' at the boundary contours of the domains of meromorphy , from `` principal part data '' given at the prescribed singularities , and from a normalization condition . so , many asymptotic questions in integrable systems ( _ e.g. _ long time behavior and singular perturbation theory ) and approximation theory ( _ e.g. _ behavior of orthogonal polynomials in the limit of large degree ) amount to determining asymptotic properties of the solution matrix of a riemann - hilbert problem from given asymptotics of the jump conditions and principal part data . in recent years a collection of techniques has emerged for studying certain asymptotic problems of this sort . these techniques are analogous to familiar asymptotic methods for expanding oscillatory integrals , and we often refer to them as `` steepest - descent '' methods . the basic method first appeared in the work of deift and zhou @xcite . the first applications were to riemann - hilbert problems without poles , in which the solution matrix is sectionally holomorphic . later , some problems were studied in which there were a number of poles a number held fixed in the limit of interest in the solution matrix ( see , for example , the paper @xcite on the long - time behavior of the toda lattice with rarefaction initial data ) . the previous methods were extended to these more complicated problems through the device of making a local change of variable near each pole in some small domain containing the pole . the change of variable is chosen so that it has the effect of removing the pole at the cost of introducing an explicit jump on the boundary of the domain around the pole in which the transformation is made . the result is a riemann - hilbert problem for a sectionally holomorphic matrix , which can be solved asymptotically by pre - existing `` steepest - descent '' methods . recovery of an approximation for the original sectionally meromorphic matrix unknown involves putting back the poles by reversing the explicit change of variables that was designed to get rid of them to begin with . yet another category of riemann - hilbert problems consists of those problems where the number of poles is not fixed , but becomes large in the limit of interest , with the poles accumulating on some closed set @xmath0 in the finite complex plane . a problem of this sort has been addressed @xcite by making an explicit transformation of the type described above in a single fixed domain @xmath1 that contains the locus of accumulation @xmath0 of all the poles . the transformation is chosen to get rid of all the poles at once . in order to specify it , discrete data related to the residues of the poles must be interpolated at the corresponding poles by a function that is analytic and nonvanishing in all of @xmath1 . once the poles have been removed in this way , the riemann - hilbert problem becomes one for a sectionally holomorphic matrix , with a jump at the boundary of @xmath1 given in terms of the explicit change of variables . in this way , the poles are `` swept out '' from @xmath0 to the boundary of @xmath1 resulting in an analytic jump . there is a strong analogy in this procedure with the concept of balayage ( meaning `` sweeping out '' ) from potential theory . in establishing asymptotic formulae for such riemann - hilbert problems , it is essential that one make judicious use of the freedom to place the boundary of the domain in which one removes the poles from the problem . placing this boundary contour in the correct position in the complex plane allows one to convert oscillations into exponential decay in such a way that the errors in the asymptotics can be rigorously controlled . if the poles accumulate with some smooth density on @xmath2 , the characterization of the correct location of the boundary of @xmath1 can be determined by first passing to a continuum limit of the pole distribution in the resulting jump matrix on the boundary of @xmath1 , and then applying analytic techniques or variational methods . the continuum limit is justified as long as the boundary of @xmath1 remains separated from @xmath0 . this idea leads to an interesting question . what happens if the boundary of @xmath1 as determined from passing to the continuum limit turns out to intersect @xmath0 ? far from being a hypothetical possibility , this situation is known to occur in at least three different problems : 1 . * the semiclassical limit of the focusing nonlinear schrdinger hierarchy with decaying initial data . * see @xcite . this is an inverse - scattering problem for the nonselfadjoint zakharov - shabat operator . on an _ ad hoc _ basis , one replaces the true spectral data for the given initial condition with a formal wkb approximation . there is no jump in the riemann - hilbert problem associated with inverse - scattering for the modified spectral data , but there are poles accumulating asymptotically with the wkb density of states on an interval @xmath0 of the imaginary axis in the complex plane of the eigenvalue . the methods described above turn out to yield rigorous asymptotics for this modified inverse - scattering problem as long as the independent time variable in the equation is not zero . for @xmath3 , the argument of passing to the continuum limit in the pole density leads one to choose the boundary of @xmath1 to _ coincide _ in part with the interval @xmath0 . strangely , if one sets @xmath3 in the problem from the beginning , an alternative method due to lax and levermore @xcite and extended to the nonselfadjoint zakharov - shabat operator with real potentials by ercolani , jin , levermore , and macevoy @xcite can be used to carry out the asymptotic analysis in this special case ; this alternative method is not based on matrix riemann - hilbert problems , and therefore when taken together with the methods described in @xcite does not result in a uniform treatment of the semiclassical limit for all @xmath4 and @xmath5 . at the same time , the lax - levermore method that applies when @xmath3 fails in this problem when @xmath6 . 2 . * the zero - dispersion limit of the korteweg - de vries equation with potential well initial data . * as pointed out above , the original treatment of this problem by lax and levermore @xcite was not based on asymptotic analysis for a matrix - valued riemann - hilbert problem . but it is possible to pose the inverse - scattering problem with modified ( wkb ) spectral data as a matrix - valued riemann - hilbert problem and ask whether the `` steepest descent '' techniques for such problems could be used to reproduce and/or strengthen the original asymptotic results of lax and levermore . in particular , we might point out that the lax - levermore method only gives weak limits of the conserved densities , and that a modification due to venakides @xcite is required to extract any pointwise asymptotics ( _ i.e. _ to reconstruct the microstruture of the modulated and rapidly oscillatory wavetrains giving rise to the leading - order weak asymptotics ) . on the other hand , `` steepest descent '' techniques for matrix - valued riemann - hilbert problems typically give pointwise asymptotics automatically . it would therefore be most useful if these techniques could be applied to provide a new and unified approach to this problem . + if one tries to enclose the locus of accumulation of poles ( wkb eigenvalues for the schrdinger operator with a potential well ) with a contour and determine the optimal location of this contour for zero - dispersion asymptotics , it turns out that the contour must contain the support of a certain weighted logarithmic equilibrium measure . it is a well - known consequence of the lax - levermore theory that the support of this measure is a subset of the interval of accumulation of wkb eigenvalues . consequently , the enclosing contour `` wants '' to lie right on top of the poles in this problem , and the approach fails . in a sense this failure of the `` steepest descent '' method is more serious than in the analogous problem for the focusing nonlinear schrdinger equation because the contour is in the wrong place for all values of @xmath4 and @xmath5 ( the independent variables of the problem ) , whereas in the focusing nonlinear schrdinger problem the method fails generically only for @xmath3 . * the large degree limit of certain systems of discrete orthogonal polynomials . * fokas , its , and kitaev @xcite have shown that the problem of reconstructing the orthogonal polynomials associated with a given continuous weight function can be expressed as a matrix - valued riemann - hilbert problem . it is not difficult to modify their construction to the case when the weight function is a sum of dirac masses . the corresponding matrix - valued riemann - hilbert problem has no jump , but has poles at the support nodes of the weight . the solution of this riemann - hilbert problem gives in this case the associated family of discrete orthogonal polynomials . if one takes the nodes of support of the discrete weight to be distributed asymptotically in some systematic way , then it is natural to ask whether `` steepest descent '' methods applied to the corresponding riemann - hilbert problem with poles could yield accurate asymptotic formulae for the discrete orthogonal polynomials in the limit of large degree . indeed , similar asymptotics were obtained in the continuous weight case @xcite using precisely these methods . + unfortunately , when the poles are encircled and the optimal contour is sought , it turns out again to be necessary that the contour contain the support of a certain weighted logarithmic equilibrium measure ( see @xcite for a description of this measure ) which is supported on a subset of the interval of accumulation of the nodes of orthogonalization ( _ i.e. _ , the poles ) . for this reason , the method based on matrix - valued riemann - hilbert problems would appear to fail . in this paper , we present a new technique in the theory of `` steepest descent '' asymptotic analysis for matrix riemann - hilbert problems that solves all three problems mentioned above in a general framework . we illustrate the method in detail for the first case described above : the inverse - scattering problem for the nonselfadjoint zakharov - shabat operator with modified ( wkb ) spectral data , which amounts to a treatment of the semiclassical limit for the focusing nonlinear schrdinger equation at the initial instant @xmath3 . this work thus fills in a gap in the arguments in @xcite connecting the rigorous asymptotic analysis carried out there with the initial - value problem for the focusing nonlinear schrdinger equation . application of the same techniques to the zero dispersion limit of the korteweg - de vries equation will be the topic of a future paper , and a study of asymptotics for discrete orthogonal polynomials using these methods is already in" +"massive quiescent galaxies often have dense cores @xcite while the morphology of star - forming galaxies is typically dominated by exponential disks rather than central bulges ( e.g. , * ? ? ? massive star - forming galaxies are expected to transform their morphology from disk - dominated to bulge - dominated . understanding the formation history of the bulge component is a critical step toward revealing the origin of the hubble sequence . at the peak epoch of galaxy formation ( @xmath16 ) , the most massive , @xmath17 , star - forming galaxies still have extended disks , but are rapidly building up their central cores through dusty , compact starbursts @xcite . bulge formation in a short period of @xmath181 gyr at @xmath16 is also corroborated by observations of old stellar populations and enhanced [ @xmath19/fe ] ratios in massive quiescent galaxies at @xmath20 ( e.g. , * ? ? ? * ; * ? ? ? all these findings suggest that central cores of massive galaxies have a different formation history than outer disks . the next step is to characterize the kinematics of these dense cores in the process of formation , which will shed light on their formation mechanisms and subsequent evolution . at high - redshift , the kinematics of dusty star - forming cores in massive galaxies are difficult to study . while h@xmath19 studies with near - infrared spectrographs have made significant progress in understanding the kinematics of core formation ( e.g. , @xcite ; e. wisnioski et al . 2017 , in preparation ) , the h@xmath19 line is not an ideal tool for investigating the kinematics of forming cores because of dust attenuation . multi - wavelength high - resolution imaging and emission line maps reveal that the central regions in massive high - redshift galaxies are often strongly attenuated by dust @xcite . co line observations provide a more robust means of obtaining kinematic information for dusty objects , as well as the molecular gas properties ( e.g. , * ? ? ? * ; * ? ? ? * ) . in local ultraluminous infrared galaxies ( ulirgs ) , molecular gas is concentrated into rotating nuclear disks or rings ( e.g. , * ? ? ? * ) . moreover , the physical condition of the gas is totally different from that in normal star - forming galaxies . in normal star - forming regions , co emission mainly comes from an ensemble of self - gravitating molecular clouds . although the co line is typically optically thick in each virialized molecular cloud , it is possible to count the number of clouds and estimate the total molecular gas mass . we use the co - to - h@xmath13 conversion factor of @xmath21 ( k km s@xmath9pc@xmath15)@xmath9 including a correction for helium since it is calibrated by virial mass measurements , optically thin dust emission and @xmath22-ray observations in the milky - way disk ( see review in ) . a co - based gas mass with the galactic conversion factor , however , often equals or exceeds a dynamical mass in local ulirgs and smgs , which could imply a smaller conversion factor ( e.g. , * ? ? ? * ; * ? ? ? this variation of @xmath23 could be caused by a high star formation rate ( sfr ) surface density in extreme environments . the intense uv radiation heats the nearby dust and the gas temperature increases through efficient energy exchange with hot dust @xcite . then , the co surface brightness increases more rapidly than the gas mass surface density . in this letter , we report results from co @xmath24 observations of two massive galaxies at @xmath1 using atacama large millimeter / submillimeter array ( alma ) to study the spatial distribution and the kinematics of molecular gas in the starburst cores . we assume a chabrier initial mass function ( imf ; @xcite ) and adopt cosmological parameters of @xmath25 = 70 km s@xmath9 mpc@xmath9 , @xmath26=0.3 , and @xmath27 = 0.7 . we focus on the most massive star - forming galaxies with @xmath17 since this mass range is important for formation of dense cores ( e.g. , * ? ? ? we select two galaxies at @xmath28 ( u4 - 16795 and u4 - 16504 ) from subaru narrow - band imaging in the sxdf field @xcite . the narrow - band based redshift has uncertainties of @xmath29 . the two galaxies are located within the primary beam of alma band-3 receivers ( a beam width at half power of @xmath30 ) as the projected separation is 97 . both galaxies have a compact dusty star - forming core , which is probed by 870 @xmath4 m dust continuum emission @xcite . we compute the stellar mass using the fast spectral energy distribution fitting code @xcite and the 3d - hst multi - wavelength photometric catalog @xcite using the stellar population synthesis models of @xcite , exponentially declining star formation histories , and dust attenuation law of @xcite . the total stellar mass is @xmath31 for u4 - 16795 and @xmath32 for u4 - 16504 . in deep hawk - i/@xmath33-band maps , 81% and 71% of the total fluxes come from the central 15 aperture region for u4 - 16795 and u4 - 16504 , respectively . we take into account these factors when comparing the stellar mass with other masses ( section [ sec;gasmass ] ) . u4 - 16795 is detected in a deep @xmath34-pacs 160 @xmath4 m map from archival data ( see for the methodology ) and u4 - 16504 is detected in a deep @xmath35-mips 24 @xmath4 m map ( pi : j. dunlop ) . following the recipes of @xcite , we derive sfrs of @xmath36(sfr/@xmath37yr@xmath38 for u4 - 16795 and @xmath36(sfr/@xmath37yr@xmath39 for u4 - 16504 from a combination of the rest - frame 2800 and infrared luminosities . the targets are located on the massive end of the star - forming main sequence at @xmath16 ( e.g. , * ? ? ? we observe the co @xmath0 emission line ( @xmath40 ghz ) of the two massive galaxies with alma band-3 receivers covering the frequency range of 9599 and 107111 ghz . the calibration is processed through the common astronomy software application package ( casa ; @xcite ) . we use the tclean task with natural weighting to make a channel map with a velocity width of 50 km s@xmath9 and dirty continuum maps excluding the frequency range of the co line . the synthesized beamsize is 066@xmath41055 . the rms levels are 147 @xmath4jy beam@xmath9 in the channel map and 8.1 @xmath4jy beam@xmath9 in the continuum map . [ cols=""<,^,^,^,^,^,^,^,^,^ "" , ] velocity - integrated co fluxes within the 15 aperture . the uncertainties are estimated from the standard deviation of 200 random aperture photometry measurements . stellar mass and co - based gas mass within the 15 aperture . the 5@xmath42 limit of 3 mm continuum - based gas mass within the 15 aperture through the gas - to - dust ratio of 120 . the range corresponds to the dust emissivity of @xmath43=0.4 - 1.5 g@xmath9@xmath44 . we robustly detect co @xmath0 emission in both galaxies as seen in the spatially - averaged spectra within a 15 aperture ( figure [ fig;spectra ] ) . we measure total fluxes within a 15 aperture in the velocity - integrated maps to derive the co line luminosities ( table [ tab;mass ] ) . both galaxies show a spatial offset between the blue- and red - shifted co components with a velocity width of 150 km s@xmath9 ( figure [ fig;spectra ] ) . the two central positions determine the kinematic major axis of the molecular gas disks . we also derive line - of - sight velocities by fitting a gaussian function to the co line spectrum in each spatial pixel . the velocity field maps show a monotonic gradient along the kinematic major axis ( figure[fig;spectra ] ) , suggesting rotation of the molecular gas . in this section , we construct the dynamical model of the dusty star - forming cores through the following three steps : ( 1 ) determining a minor - to - major axis ratio ( @xmath45 ) of the 870 @xmath4 m continuum emission , ( 2 ) measuring an effective radius ( @xmath46 ) of the co line emission , and ( 3 ) exploring the best - fit dynamical model . error , respectively . the red dashed line presents the best - fitting model of the 870 @xmath4 m dust emission . the x - axis gives the circularized uv distance . ] 02-resolution 870 @xmath4 m continuum maps are available for both galaxies @xcite . in smgs at high - redshift , the dust emission is well described by an elliptical exponential disk @xcite . we derive effective radii , @xmath46 , along the major axis of the 870 @xmath4 m continuum emission assuming an inclined disk with an exponential profile while @xcite have adopted circular disk models ( @xmath47 ) . we use the uvmultifit tool to fit the visibility amplitudes to models in the @xmath48 plane . for u4 - 16795 , the best - fit values and fitting errors are @xmath2 kpc , @xmath49 and position angle of pa@xmath50=35@xmath51 . note that the morphological major axis of the 870 @xmath4 m continuum emission is well aligned with the kinematics major axis of the co line emission ( @xmath52pa@xmath50-pa@xmath53 ) , supporting ordered rotation @xcite . we also perform the visibility fitting for u4 - 16504 with an elliptical disk , but could not obtain meaningful constraints on the axis ratio . circular disk models give an effective radius of @xmath3 kpc . next , we derive effective radii of the co line emission using the axis ratio of the dust emission . we fix to @xmath54 and pa@xmath55 for u4 - 16795 , and @xmath47 for u4 - 16504 . figure [ fig;visibility ] shows the observed visibility amplitudes and the best - fit models . the effective radii are @xmath5 kpc for u4 - 16795 and @xmath6 kpc for u4 - 16504 , which are larger than those of the 870 @xmath4 m continuum emission . this result naively suggests that the dust is more concentrated than the molecular gas , which is consistent with negative radial gradients in dust - to - gas mass ratio seen in nearby star - forming galaxies . on the other hand , galaxy centers tend to have higher dust temperatures compared to the outer region @xcite , making the dust mass size larger than the 870 @xmath4 m size . high - resolution alma observations at high - frequency band ( e.g. , 450 @xmath4 m ) will allow us to determine the radial gradient in dust temperature ( section [ sec;dust ] ) and identify if the apparent size difference originates in the dust properties or the intrinsic gradients of dust - to - gas mass ratio . we find that both massive galaxies observed here exhibit signatures of disk - like rotation in their co velocity fields ( figure [ fig;spectra ] ) . assuming that the molecular gas is in rotating disks , we investigate the kinematic properties by fitting dynamical models to the data in the position - velocity ( pv ) diagram along the kinematic major axis ( figure [ fig;residual ] ) . we use the dysmal code @xcite to generate pv diagrams for an exponential disk , spatially convolved with a 066@xmath41055 gaussian beam . we take into account the effect of pressure support , reducing the observed rotation velocity ( e.g. , * ? ? ? * ; * ? ? ? the effective radii of the gas disks are fixed to those measured in" +"the discovery of a bright gamma - ray burst ( grb ) , 080916c , by the recently launched fermi satellite is an important advance toward our understanding of these spectacular explosions . the large area telescope ( lat ) onboard the fermi satellite can detect photons in the energy range from 20mev to @xmath0300gev ( hereafter we will call it the lat band ) . lat observed photons of energy up to 13 gev from grb 080916c where the flux was close to the threshold of its sensitivity ( abdo et al . 2009 ) , and this detection suggests that the lorentz factor of the outflow in this explosion was @xmath2 ( greiner et al . 2009 ) . a number of different proposals have been put forward for the generation of high energy photons in grbs . for instance , one possible mechanism is the synchrotron process either electron or proton synchrotron e.g. meszaros & rees ( 1994 ) , totani ( 1998 ) , zhang & meszaros ( 2001 ) . another possibility is inverse - compton scattering of lower energy photons produced in the same region ( such as the synchrotron - self - compton process ) or of an external origin e.g. meszaros & rees ( 1994 ) , pilla & loeb ( 1998 ) , dermer et al . ( 2000 ) , sari & esin ( 2001 ) , wang et al . ( 2001a , 2001b ) , zhang & meszaros ( 2001 ) , granot & guetta ( 2003 ) , guetta & granot ( 2003 ) , piran et al . ( 2004 ) , beloborodov ( 2005 ) , fan et al . ( 2005 & 2008 ) , fan & piran ( 2006 ) , wang et al . ( 2006 ) , galli & guetta ( 2008 ) , zou et al . yet another class of high energy photon generation mechanism is hadronic collisions and photo - pion production e.g. katz ( 1994 ) , derishev et al . ( 1999 ) , bahcall & meszaros ( 2000 ) , dermer & atoyan ( 2004 ) , razzaque & meszaros ( 2006 ) , gupta & zhang ( 2007 ) , fan & piran ( 2008 ) . please see fan & piran ( 2008 ) for a review of the extensive literature on high energy photon generation processes . in this _ letter _ we provide multiple lines of evidence that show that high energy photons and late time x - ray and optical afterglow emissions from grb 080916c were produced via the electron synchrotron process in the external shock ; lower energy photons ( @xmath3mev ) had a different origin . in the next section we provide a summary of the observed data for grb 080916c . in 3 we describe the expected high energy emission from the external shock and compare that with the data for grb 080916c , and in 4 we show that the entire optical and x - ray afterglow data for this burst is consistent with the external shock model . moreover , using the external shock parameters determined from the late afterglow data alone ( @xmath4day ) we show that the expected emission at @xmath5mev during the prompt phase is entirely in agreement with the observed fermi / lat data ( 4 ) . the main conclusions are summarized in 5 . grb 080916c was detected by fermi ( abdo et al . 2009 ) in the energy band @xmath68kev13gev . the spectrum of grb 080916c peaked at @xmath7 kev ; the flux was independent of frequency below the peak , i.e. @xmath8 , whereas above the peak a single power - law function , @xmath9 , extending from @xmath7 kev to 13 gev provided a good fit to the data ( time dependences of these quantities can be found in fig . 3 of abdo et al . the electron energy distribution index ( @xmath10 ) corresponding to this spectrum was 2.4 . the lat band photon flux rose as @xmath11 during the first 4s of observations ( the time is measured starting from the first detection of photons in the 8kev10mev band ) , and declined as @xmath12 from 4s to 1400s . the light curve for lower energy photons on the other hand declined as @xmath13 for the initial 55s , and subsequently it underwent a steep decline of @xmath14 which is often seen in the sub - mev band of grbs ( tagliaferri et al . 2005 , nousek et al . 2006 ) and marks the end of the emission activity of the source . thus , photons of energy @xmath5mev lagged lower energy photons by 4s , and that is an important discovery by fermi . the other puzzling discovery is that radiation in the lat band lasts for a much longer duration of time than lower energy emission . x - ray and optical observations began about 1 day after the trigger time . optical observations allowed to determine a photometric redshift for this burst , @xmath15 ( greiner et al . 2009 ) . using the usual convention , @xmath16 , the x - ray data decayed as @xmath17 with @xmath18 , both values completely consistent with the shape of the optical light curve and its spectral energy distribution : @xmath19 and @xmath20 ( see fig . 2 of greiner et al . 2009 ) . since the spectrum from 8 kev to 13 gev had the shape of a band function ( two power - law components smoothly joined ) it has been suggested that the observed radiation over the entire 6-decades interval in frequency was produced by the same source ( abdo et al . 2009 , wang et al . 2009 , zhang & peer 2009 ) . however , a closer analysis of the fermi data shows that this possibility can be ruled out . the first evidence for two different sources of radiation one dominating in the sub - mev band and the other at @xmath1mev comes from the fact that the flux in the 50300 kev band declined weakly with time ( @xmath21 ) during the initial 55s and then underwent a steep decline ( @xmath14 ) with a distinct signature of a short lived source of lifetime 55s when the source is suddenly turned off ( kumar & panaitescu 2000 ) ; where @xmath22 is the spectral index which for grb 080916c was @xmath61 in the 50300 kev energy band for @xmath23s . ] . this rapid decay in flux in the x - ray band has been observed in @xmath660% of all bursts detected by the swift satellite ( evans et al . in contrast , the source for high energy photons declining as @xmath24 was active for at least 1400s , when the flux fell below the fermi / lat sensitivity ( see fig . 4 of abdo et al . 2009 ) . further evidence for two distinct sources is provided by the detection of several other bursts by the fermi satellite for which the same behavior is seen : a longer lasting source for high energy photons relative to sub - mev photons ( see , e.g. ohno et al . 2009 , cutini et al . 2009 ) . it is striking that the decay of the lat light curve ( @xmath25 ) is exactly what one expects for synchrotron radiation from the shock heated circum - stellar medium ( csm ) by the relativistic jet of a grb such that @xmath26 . as a result of radiative losses the maximum electron energy is such that the synchrotron frequency in the shocked fluid rest frame is @xmath27mev or @xmath28gev in the lab frame ( see e.g. cheng & wei 1996 , fan & piran 2008 ) . however , this limiting synchrotron frequency depends on the details of the electron scattering process , and it is likely to be higher for highly relativistic shocks . ] ; from here on we will refer to this as external shock or es . we show that it is not only the time dependence of the es emission but also its magnitude that are the same as fermi / lat observations ( with no dependence of the flux in the lat band on unknown , and therefore adjustable , parameters ) . a number of uncertainties plague the emission calculation from a shock - heated gas . the largest of these are the unknown strength of the magnetic field , and the density of the circum - stellar medium . fortunately , it turns out that the observed flux at a frequency @xmath29 that is larger than all characteristic frequencies for the shocked gas , namely the synchrotron peak and cooling frequencies , is independent of these two highly uncertain parameters ( kumar 2000 , panaitescu & kumar 2000 ) . photons of energy @xmath010@xmath30mev safely satisfy this frequency criterion . the flux in this case can be shown to be equal to @xmath31 where @xmath32 and @xmath33 are the fractions of energy of the shocked gas in electrons and magnetic fields respectively , @xmath34s is the time since the beginning of the explosion in the observer frame ( in units of 10s ) , @xmath35 is photon energy in units of 100mev , @xmath36erg is the scaled isotropic kinetic energy in the es , @xmath37 is the compton-@xmath37 parameter , @xmath38 is the redshift and @xmath39 is the luminosity distance to the burst . the second equality in equation ( 1 ) was obtained by taking @xmath40 , @xmath41s , @xmath42 and @xmath43 ; @xmath44 because of klein - nishina effects even though @xmath45 , and furthermore , cooling o es electrons by inverse compton scattering of prompt @xmath46-ray photons can be shown to be weaker than synchrotron cooling . note that the flux at 100mev is approximately proportional to @xmath47 , the energy in electrons ; it is independent of the density of the circum - stellar medium ( @xmath48 ) , and has an extremely weak dependence on @xmath33 which for all practical purposes can be ignored . according to equation ( 1 ) the time dependence of the flux should be @xmath49 ( @xmath40 for grb 080916c ) which is in excellent agreement with the observed flux decay of @xmath12 in the lat band . we note that a good fraction of the energy of the explosion was released during the initial 8s of the burst , and for the next 47s the energy deposited in the external medium increased as @xmath50 , and thereafter no additional energy was added to the es . therefore , for @xmath51s @xmath52s the light curve decay should have been @xmath53 due to energy injection in es ( a slightly steeper decay @xmath54 will in fact occur during this time interval due to radiative loss of es energy ) , and for @xmath55s the decay attains the asymptotic slope of @xmath49 . before the deceleration time , i.e. @xmath56s , the es light curve is expected to rise as @xmath57 which is significantly shallower than the observed rise of @xmath58 . this is a very puzzling feature that could probably shed light on the onset of the es and the particle acceleration mechanism . the observed 4s lag for the high energy photons at the beginning of the burst is due to the time it takes for energy transfer from grb jet to the external shock i.e. , the deceleration time ( sari & piran 1999 ) . for a sample of 10 well observed and studied grb afterglows it is found that @xmath59 ( panaitescu & kumar 2001 ) , and for grb 080916c , @xmath60 at @xmath41s . therefore , from equation ( 1 ) we find that the flux at 100 mev from shock heated external medium" +"when studying mechanical systems , a hamiltonian formulation of problems is often advantageous , since equations of motion can be easily obtained from a scalar function @xmath0 representing the total energy of the system . the resulting set of first - order differential equations describes the time evolution of the dependent variables on a differentiable manifold . in what follows next we deal with the case where the phase space is an euclidean space @xmath1 with the coordinates being the generalized positions @xmath2 and momenta @xmath3 with @xmath4 and @xmath5 being the number of the system s degrees of freedom . except for a few special cases , where the solution of the equations of motion can be written in a closed analytic form , the system s trajectories in phase space must be approximated by numerical means . due to their excellent performance , especially over long integration times , the so - called symplectic integration techniques are of particular interest for the numerical integration of hamiltonian systems . numerical integration algorithms showing symplectic properties can be traced back to isaac newton s ` principia mathematica ' ( 1687 ) @xcite . the main reason why symplectic integrators ( sis ) have become so popular over the past decades lies in the fact that they offer remarkable long - term energy conservation . in fact , the local error in the system s total energy does not grow with time as is the case for most non - symplectic methods ( see e.g. * ? ? ? * ) . the underlying reasons for the excellent performance of symplectic integrators in this respect were understood only in the late @xmath6 century ( see e.g. * ? ? ? * ; * ? ? ? * and references therein ) . recently , it was shown that sis are also highly efficient in the integration of the variational equations needed for the computation of chaos indicators like the maximum lyapunov characteristic exponent ( mlce ) ( see e.g. * ? ? ? * ) , the smaller ( sali ) @xcite and generalized alignment index ( gali ) @xcite when using the so - called ` tangent map ' method @xcite . due to these benefits , sis have become a standard technique in hamiltonian dynamics with particular importance in long - term integrations of multidimensional systems . in cases where the hamiltonian @xmath0 can be separated in two parts @xmath7 , which offer individually integrable state transition maps , various symplectic integrators have been developed over the past years . for an overview see @xcite and references therein . however , in many physical problems the hamiltonian can not be split in merely two separable parts . in this paper we focus on general hamiltonian systems that can be split in exactly three integrable parts . we will show how high order symplectic integration methods for these kinds of systems can be constructed . using two different hamiltonians as examples , we will compare triple split methods with respect to their computational efficiency and energy conservation . this paper is structured as follows : in section [ sec : si ] we give a brief introduction to the theory of sis . in section [ sec:3part ] we present a systematic way to construct high order sis for three part hamiltonian systems . we apply these methods and compare their efficiency using a toy model ( section [ sec : toy ] ) as well as the disordered discrete nonlinear schrdinger equation ( section [ sec : dnls ] ) as showcases . in section [ sec : conclusion ] we summarize our results . finding and solving the equations of motion for dynamical systems can be greatly simplified , when a description in a hamiltonian framework is possible . given a twice continuously differentiable function @xmath8 which represents the total mechanical energy of a system , the equations of motion simply derive from @xmath9 and @xmath10 represents the vector of generalized coordinates and momenta . furthermore , @xmath11 is the @xmath5-dimensional identity matrix , and @xmath12 the @xmath13 matrix with all its elements equal to zero , with @xmath5 being the number of degrees of freedom of the dynamical system . differential equations derived from hamiltonian systems possess a special geometric quality related to the matrix @xmath14 - they are ` symplectic ' . to be more precise , the continuous flow of the system , i.e. the continuous function @xmath15 , which maps initial conditions into system states at time @xmath16 , keeps the symplectic geometric structure @xmath14 intact ( for a proof see e.g. * ? ? ? * ) . in analogy , discrete integration algorithms that conserve @xmath14 are called ` symplectic ' as well . let us consider the example of the so - called ` symplectic euler ' integration method applied to the well known harmonic oscillator problem . here , @xmath17 , @xmath18 and the flow map @xmath19 , which is the action of the lie group @xmath20 on the plane @xmath21 , is approximated by the symplectic euler scheme @xmath22 where @xmath23 is the integration time step . the numerical integration method is explicit and it is defined by the state transition matrix @xmath24 @xmath25 a straightforward calculation shows that @xmath26 which means that @xmath24 preserves @xmath14 . therefore , the integration method presented in equations ( [ eq : syeul ] ) is indeed symplectic . there are many possible ways of constructing symplectic integrators , but operator splitting is one of the most transparent concepts . we slightly reformulate hamilton s equations of motion ( [ eq : ham ] ) @xmath27 where @xmath28 is a differential operator and @xmath29 is the poisson bracket . ] . note that the symplectic structure is now contained implicitly in the poisson bracket . the formal solution of differential equations ( [ eq : lie ] ) reads @xmath30 if the hamiltonian can be written as a sum of functions , e.g. @xmath31 , the bilinearity of the poisson bracket allows us to rewrite equation ( [ eq : exp ] ) @xmath32 the combined map @xmath33 , @xmath34 usually does not permit an analytic solution , but the individual exponential maps @xmath35 might . in the case of @xmath36 the operator splitting is then executed as follows @xmath37 in our example , analytic solutions can indeed be found for the individual maps , since @xmath38 depends only on the generalized momenta @xmath39 , representing e.g. the total kinetic energy of the system . similarly , @xmath40 is a pure function of the generalized coordinates , e.g. the potential energy . such an approach is suitable for creating explicit integration algorithms of first order in @xmath23 . for higher order integrators that permit larger time steps we will have to take a more careful look at the approximation in equation ( [ eq : split ] ) . in fact , one can show that the operator splitting produces error terms of higher order in @xmath23 due to the baker - campbell - hausdorff ( bch ) relation @xcite @xmath41+\frac{\tau^3}{12}([l_a,[l_a , l_b]]-[l_b,[l_a , l_b]])+\hdots},\label{eq : bch } \end{tiny}\ ] ] where @xmath42 $ ] denote commutators for the operators @xmath43 and @xmath44 , i.e. @xmath45=l_al_b - l_bl_a$ ] . this representation has lead @xcite to the conclusion that , in fact , not the intended system , but a dynamical system close to the original one is solved exactly by the split maps . for example it is easy to see that for the harmonic oscillator , the corresponding symplectic euler map @xmath46{c } q_{\tau } \\ p_{\tau } \end{array } \right)=\left ( \begin{array}[h]{cc } 1 & \tau \\ -\tau & 1-\tau^2 \end{array } \right)\left ( \begin{array}[h]{c } q_0\\ p_0 \end{array } \right)\ ] ] leaves the ellipse @xmath47 invariant and thus it preserves exactly a perturbed energy . as can be seen from equation ( [ eq : bch ] ) , the difference between the original and the nearby system is a polynomial in @xmath23 with the commutators of the split operators as coefficients . while the exact solution of a nearby dynamical system explains the bounded local error in energy , equation ( [ eq : bch ] ) also contains the reason why variable time stepping destroys the favorable energy conservation properties of symplectic algorithms . changing the time step means changing the analytically solved nearby hamiltonian continuously . consequently , the advantage of solving a system which stays in the vicinity of the original one is lost . the standard procedure of constructing methods of higher order @xmath48 usually consists of trying to find numerical coefficients @xmath49 and @xmath50 , so that a sequence of split maps eliminates consecutive terms of the bch expansion @xmath51 see for instance @xcite . the well - known leap - frog ( aka strmer / verlet ) method of order two is obtained in this way by setting @xmath52 and @xmath53 . it can be shown @xcite that it is not possible to construct integrators of order @xmath54 having only positive steps . since negative steps limit the stability of the algorithm , it is tempting to circumvent this problem . for the special case of nearly integrable systems of the form @xmath55 with @xmath56 very efficient symplectic integrators with only positive steps can be constructed , as is shown in @xcite . let us now consider general hamiltonians that can be split in three parts @xmath57 , where each of the maps @xmath58 , @xmath59 and @xmath60 has an analytic solution . then the construction of a symplectic integration method can be achieved as follows @xmath61 the simplest integration scheme is of first order and is just the concatenation @xmath62 . in composition with its adjoint method ( which is also symplectic ) this yields already a time - reversible scheme of order two , which we will call @xmath63 , i.e. @xmath64 this integrator has already been applied for the numerical study of astronomical problems @xcite . some sporadic attempts to construct higher order three part split sis for specific dynamical systems have also been performed . advanced methods , for instance , especially designed for molecular dynamics are given in @xcite , while optimized algorithms for highly accurate long - term integration of astronomical problems are presented in @xcite . recently , an attempt to systematically construct high order three part sis was carried out in @xcite . in that paper , several sis were presented for the integration of a hamiltonian system that splits in three integrable parts . in addition , the performance of these numerical schemes for the integration of a multidimensional hamiltonian system of particular physical interest was studied . in the following subsections we will discuss various approaches to integrate a general three part hamiltonian problem following the ideas presented in @xcite . in @xcite it was shown that the concatenation of time symmetric splittings can produce higher order methods using analytically derived coefficients only . with this approach one can construct a si : @xmath65 of order @xmath66 starting from a si : @xmath67 of even order @xmath48 by @xmath68 with @xmath69 applying this procedure to the second order @xmath63 method ( [ eq : abc2 ] ) for @xmath70 , one obtains a si of order 4 with 13 steps , which will be called @xmath71 @xmath72 starting from @xmath71 and using equation ( [ eq : yoshida ] ) again , one could continue and build a method of order 6 . although this procedure is straightforward , it is not optimal with respect to the number of required steps , i.e. force evaluations per time step . as was already pointed out in @xcite , alternative methods can be applied to obtain more economical integrators of high order , although the new coefficients can not be given in" +"in the last years a strong effort has been devoted to understand both the equilibrium and out - of equilibrium properties of ultrathin magnetic films @xcite . these materials have attracted much attention mainly due to their potential applications , such as information storage @xcite . ultra - thin films find also many important applications both in biotechnology and pharmacology . it is today a well established experimental fact that the magnetization processes in ultra - thin magnetic films are ruled by the microscopic competition between short range ferromagnetic couplings and long - range frustrated antiferromagnetic dipolar interactions , which give place to very novel dynamical and static behaviors @xcite . it is worth mentioning that both the theoretical and the experimental interest in studying systems with competition between short - range ordering interactions and long range frustrating interactions widely exceeds the field of ultra thin films . actually , many different experimental systems can be modeled by this kind of microscopic interactions , which give place to very rich dynamical and static properties . in soft matter physics for instance , we can mention diblock copolymer melt and cross linked polymer mixtures , among others . type i superconductors and rare earth layers that occur in the perovskite structure of reba@xmath9cu@xmath10o@xmath11 ( where re represents a rare earth from the lanthanide series ) can be very well modeled with these interactions @xcite . it has also been frequently suggested that competing interactions can explain many of the phenomenological features observed in the glass formation process and in supercooled liquids @xcite . summarizing , many of the conclusions drawn from this work can be surely be applied to a large variety of physical systems . for sufficiently thin films the magnetic moments align perpendicular to the plane of the film , indicating that the surface anisotropy is sufficient to overcome the anisotropy of the dipolar interaction which favors in - plane ordering . works in two dimensional uniaxial spin systems , where the spins are oriented perpendicular to the lattice and coupled with these kind of interactions , have shown a very rich phenomenological scenario concerning both its equilibrium statistical mechanics @xcite and non - equilibrium dynamical properties @xcite . in particular , some of these results @xcite showed the existence of different types of slow relaxation dynamics when the system is quenched from a disordered high temperature configuration to a subcritical temperature , depending on the relative strengths of the dipolar and exchange interactions . under these circumstance one can use a uniaxial ising representation for describing the magnetic moments @xcite . the ultra thin film is then described by the hamiltonian @xmath12 where the spin variable @xmath13 is located at site @xmath14 of a square lattice , the sum @xmath15 runs over all pairs of nearest neighbor sites and @xmath16 runs over all distinct pair of sites of the lattice ; @xmath17 is the distance ( in crystal units ) between sites @xmath14 and @xmath18 , @xmath4 represents the quotient between the exchange @xmath0 and dipolar @xmath1 coupling parameters ( @xmath19 ) . the energy is measured in units of @xmath1 , which is always assumed to be antiferromagnetic @xmath20 . hence @xmath21 means ferromagnetic exchange coupling . we have recently studied in detail @xcite the low temperature phase diagram of this system in the region where the change in the relaxation properties has been observed . we showed that for very low temperatures metastable states appear . in this work we investigate the effects of the presence of these metastable states on the far - from equilibrium dynamical properties of the system . in section [ meta ] we present a review of the equilibrium phase diagram and metastability properties in the region of interest . in section [ slow ] we analyze the magnetic domain growth or coarsening dynamics of the system when it is quenched from a disordered state ( which corresponds to infinite temperature ) to a temperature below the ordering transition for different values of @xmath4 . using monte carlo simulations we study the statistics of domains of the striped phases h1 and h2 . we then analyze the temporal behavior of the average linear size of the domains @xmath22 . we show that the coarsening dynamics is strongly affected by the presence of metastable states , which generate blocking clusters of the metastable phase where the domain walls of the stable phase become pinned . such blocking clusters generate free energy barriers to the domain growth dynamics that are independent of the linear domain size . some conclusions and remarks are summarized in section [ conclu ] . the overall features of the finite temperature phase diagram associated with hamiltonian ( [ hamilton1 ] ) were described by macisaac and coauthors @xcite by means of monte carlo simulations on @xmath23 lattices and analytic calculations of the ground state @xcite . they found that the ground state of hamiltonian ( [ hamilton1 ] ) is the antiferromagnetic state for @xmath24 @xcite . for @xmath25 the antiferromagnetic state becomes unstable with respect to the formation of striped domains structures , that is , to state configurations with spins aligned along a particular axis forming ferromagnetic stripes of constant width @xmath26 , so that spins in adjacent stripes are anti - aligned , forming a super lattice in the direction perpendicular to the stripes . at high temperatures , of course , the system always becomes paramagnetic . specific heat calculations showed that the transition between the paramagnetic and the striped phases is a second order one @xcite . we have recently @xcite performed monte carlo simulations of hamiltonian ( [ hamilton1 ] ) on square lattices up to @xmath27 sites using periodic boundary conditions and heat bath dynamics . our calculations focused on the low temperature region of the @xmath2 phase diagram for values of @xmath4 between @xmath28 and @xmath29 , which includes the transition line between the @xmath30 and the striped phase with width @xmath5 ( @xmath6 ) and also the transition line between the @xmath6 phase and the striped phase with width @xmath7 ( @xmath8 ) . first we calculated , through the energy fluctuations , the specific heat @xmath31 as a function of temperature for different values of @xmath4 and different system sizes up to @xmath27 sites . by considering the peaks in the specific heat we obtained the second order critical line between the paramagnetic and the low temperature ordered phases @xmath6 and @xmath8 . these results ( see fig . [ diagrama_fases ] ) slightly improved those obtained by macisaac and coauthors @xcite for @xmath23 lattices , thus showing a fast convergence of the critical temperature for increasing system sizes , at least for small values of @xmath4 . phase diagram @xmath2 in the region of parameters under study . filled triangles correspond to the critical temperatures @xmath32 obtained by specific heat calculations for the phase transition between the ordered antiferromagnetic ( af ) and striped phases @xmath6 and @xmath8 and the paramagnetic ( * para * ) one . filled circles ( open squares ) correspond to the stability line of the @xmath6 ( @xmath8 ) phase , obtained by analyzing the staggered magnetization @xmath33 ( @xmath34 ) . filled diamonds correspond to the first order transition lines between the @xmath6 and @xmath8 phases and also between the @xmath6 and @xmath30 phases , obtained by the free energy numerical calculations . the shaded region indicates the presence of metastable states . ] [ fig1 ] next , through a numerical study of the free energy , we analyzed the transition between the @xmath6 and @xmath8 phases . the free energy of the phase @xmath6 ( @xmath8 ) was calculated for increasing ( decreasing ) values of @xmath4 . we observed a continuous change of the minimal free energy from one phase to the other , with a discontinuous change in the slope for @xmath35 indicating the presence of a first order phase transition @xcite . this transition is indicated by means of diamonds in fig . [ diagrama_fases ] . we have also repeated these calculations for the transition line between the @xmath6 and @xmath30 phase , finding similar results . close to @xmath35 the free energy displays a multivalued behavior characteristic of a first order phase transition . this behavior signals the metastable nature of these phases in some parts of the phase diagram . to characterize the presence of metastable states observed in the transition between the @xmath6 and @xmath8 phases we introduced the staggered magnetizations @xmath33 and @xmath34 , and also their associated susceptibilities @xmath36 and @xmath37 for the @xmath6 and @xmath8 phases these quantities permitted us to analyze the stability of both phases in the different parts of the phase diagram . in fig . [ diagrama_fases ] the shaded region indicates the presence of metastable states . it is important to stress that in the shaded region inside phase @xmath6 the only phase observed to be metastable was @xmath8 . for @xmath38 metastables states of phases of higher width were observed , leading to a much more complicated metastable region . in this work we will focus only on the dynamical behavior of the system in the @xmath6 region . as we will show in the next section , for a fixed value of @xmath4 inside this region different dynamical regimes are observed as the temperature is lowered and one enters the region of metastability . when a system is quenched from a high temperature disordered phase into a low temperature ordered phase domains form and grow , a process that is known as coarsening . the coarsening process has been extensively studied both experimentally and theoretically over the past decade @xcite . perhaps the most thoroughly studied system , and also the most common example is the ising model . when this system is quenched from a high temperature to one below its critical temperature ( @xmath39 ) ferromagnetic domains of up and down spins form and coarsen . the system presents curvature driven growth and the characteristic domain size @xmath22 grows with time as @xmath40 . if the system is cooled to zero temperature the domain walls can be easily determined as bonds between oppositely oriented spins , but if the system is cooled to a temperature different from zero it becomes difficult to define domains and domain walls since small islands generated by thermal fluctuations arise . to overcome this problem , derrida @xcite proposed a new method to measure properties related to coarsening in the presence of thermal fluctuations . this method was extended by hinrichsen and antoni @xcite to determine domain walls for nonzero temperatures . the method compares the state of a system with replicas in the different ground state configurations when they are all submitted to the same thermal noise , that is , when the same sequence of random numbers is used to update all systems . in this way , if one starts from a replica in the ordered state a spin flip will be a consequence of the thermal noise . when a spin flip occurs simultaneously in all the replicas it can be considered as a thermal fluctuation , otherwise the fluctuation will be due to the coarsening process . we used this technique to study the dynamics of domain walls , and characterize the coarsening process , when the system described by hamiltonian ( [ hamilton1 ] ) is quenched from a high temperature disordered state into the region where it orders . in particular we focus our interest on the growth of domains of the striped phase @xmath6 when the metastability line is crossed for values of @xmath41 ( see fig.[diagrama_fases ] ) . to characterize the growth of the domains we determined first the domain areas @xmath42 , by counting the number of spins inside each domain . the characteristic ( linear ) domain size was calculated as @xmath43" +"providing an unambiguous proof of the cosmic - ray origin until now has been elusive , despite many decades of attempts and controversial claims ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? cosmic - rays are mainly protons and heavy ions ( hadrons ) and , in a few percent , electrons and positrons . supernova remnants ( snrs ) are ideal candidates for the cosmic - ray production up to energies near @xmath1 = @xmath2 ev . the snr energy output in the galaxy can indeed supply the energy budget necessary to maintain the present population of cosmic - rays . furthermore the observations of ultra - relativistic electrons support the hypothesis that also protons are accelerated in these objects ( for a recent review see * ? ? ? * and references therein ) . proving the fact that the snr origin of hadronic cosmic - rays is difficult because of the complexity of the snr - environment interaction . from an observational point of view , a direct proof can be given by an unambiguous detection of the gamma - ray emission expected from neutral pion decay in hadronic interactions . however radiation from co - spatially accelerated electrons can mask and sometimes overcome the expected neutral pion decay signature of proton / ion emission in the 100 mev - a few tev energy range . recent analysis suggests that several gamma - ray observations of snrs can be understood in terms of accelerated hadrons @xcite . however it is currently not possible to exclude that the observed @xmath3-ray emission is produced by leptons alone . the discrepancies between leptonic and hadronic models are expected to be more evident at low energies ( 50 - 100 mev ) . gamma - ray astronomy in this energy band is very challenging because of high background - noise flux and of the strong multiple scattering suffered by electrons originating from @xmath3-ray events . the agile / grid instrument ( calibrated in the 50 mev - 10 gev band ) , however , has already shown its ability to provide an energy spectrum starting at 50 mev for bright objects @xcite . in this paper we report on a low - energy @xmath3-ray and multiwavelength spectrum for the snr w44 in order to constraint the emitting particle spectrum and discriminate between leptonic and hadronic models . snr w44 is a well studied middle - aged snr located in the galactic disk at a distance of @xmath4 kpc from earth @xcite . w44 is an ideal system to test the presence of accelerated hadrons and the interplay between hadronic and leptonic models . radio ( * ? ? ? * and references therein ) and x - ray @xcite mapping of the snr show a roughly elliptical shocked shell and a centrally peaked emission respectively . in the ir band @xcite it is evident that the shell is expanding into a dense surrounding medium ( @xmath5 @xmath6 ) . @xcite discovered the radio pulsar psr b1853 + 01 with distance and age compatible with the snr . @xcite and then @xcite found a massive molecular cloud interacting with the south - eastern side of the remnant . evidence for a more complex system of massive mcs and for their interactions with the remnant , shown by some features typical of a strong shock , was given by @xcite and then by @xcite . the mc - snr interactions were confirmed by the maser oh ( 1720 mhz ) emission reported by @xcite and then by @xcite . + the first estimation of the spectral radio index variations as a function of position over the remnant was done by @xcite : the eastern limb spectrum was consistent with a diffusive shock acceleration model and the spectrum flattening in the westernmost arc confirmed the mc - snr interaction observed in ir and optical band . + gamma - ray emission from this snr has been detected by the fermi / lat instrument at energy e@xmath7200 mev @xcite , suggesting the presence of accelerated protons interacting with the surrounding medium . agile - grid data were analyzed using the agile standard analysis pipeline . we used @xmath3-ray events filtered by means of the @xmath8 agile filter pipeline ( as described in * ? ? ? * ) . in order to discriminate between background events and gamma rays , the grid and anticoincidence system ( acs ) signals are processed , reconstructed and selected by a dedicated software @xcite . we used the most recent versions of the diffusion model @xcite and of the calibration files , available at the asdc site ( www.asdc.asi.it ) . we created counts , exposure and galactic background gamma - ray maps with a bin - size of @xmath9 x @xmath9 . in order to derive the source average flux and spectrum we ran the agile point source analysis software alike ( * ? ? ? * based on the maximum likelihood technique described in @xcite ) over the whole observing period 2007 july - 2011 april . both statistic and systematic uncertainties are taken into account . the spectrum was obtained by computing the @xmath3-ray flux in six energy bins selected with the aim to have a significance @xmath10 . in order to study the source morphology , we obtained an intensity map integrated over the energy range where the grid angular resolution is optimal ( e@xmath7400 mev ) . agile detects snr w44 with a significance of 15.8 @xmath11 as an extended source . figure [ w44]a shows agile gamma - ray intensity map above 400 mev of the w44 region with the 324 mhz vla radio contours . the gamma - ray morphology remarkably resembles the quasi - elliptical pattern of the interior of the radio shell , especially coinciding with the radio brightness enhancements toward the north - west and south - east regions . both the radio pulsar psr b1803 + 01 position @xcite and its ( small ) pulsar wind nebula ( * ? ? ? * and references therein ) are inconsistent with the gamma - ray morphology detected by agile . moreover , @xcite excluded the presence of a pulsation in the @xmath3-ray signal . figure [ w44]b shows the co emission at a kinematic velocity compatible with the distance of w44 , tracing the presence of mcs in the w44 surroundings , together with the gamma - ray contour levels . it can be inferred that the south - eastern side of the @xmath3-ray source overlaps with the mc - snr interaction region . in the northern part of the shell , the @xmath3-ray and co emissions are not correlated , however many studies of the surrounding interstellar medium showed the presence of dense gas not traced by co @xcite . figure [ w44]c displays an sii map overlaid with x - ray and gamma - ray contours . the strong sulfur [ sii ] emission , along with h@xmath12 emission , indicates the presence of shocked gas @xcite . figure [ w44_spec ] shows the agile w44 photon energy spectrum for the whole range 50 mev- 10 gev . the measured flux above 400 mev is @xmath13 photons @xmath14 s@xmath15 . in this figure are also shown fermi / lat spectral points @xcite over an energy range 0.2 - 30 gev . in the band where the spectra overlap , the sets of data are compatible at 1@xmath11 . in this regard it is important to stress how agile is able to detect the emission from w44 in the energy range 50 mev-300 mev extending the spectrum to energies substantially lower than those previously obtained . this spectrum shows a clear decrement at photon energies lower than 400 mev , confirming the expectations based on neutral pion emission from accelerated protons / ions : a peak energy near 1 gev for hadron energy spectra flatter than @xmath16 ( e.g. , * ? ? ? the gamma - ray spectrum becomes steep at higher energies with a photon power - law index @xmath170.1 , in agreement with previous measurements @xcite . leptonic - only models of gamma - ray production have to satisfy the very well determined spatial and spectral constraints provided by the radio , optical , and gamma - ray emissions . for both the bremsstrahlung and inverse compton cases we tested the class of leptonic - only models attempting to reproduce the observed gamma - ray spectrum for different input leptonic spectra ( see table 1 ) . we used a phenomenological approach based on two evidences : a ) the synchrotron spectrum implies that the radio electron distribution is well described by a power - law over a wide range of energies , b ) the discontinuity in the slope of the gamma - rays spectrum implies a discontinuity in the emitting particle spectrum . we assumed three electron distributions that can , in principle , describe this behavior : 1 ) a power - law with a high energy cut - off , @xmath18 , ( as in * ? ? ? * ) , 2 ) a power - law with a low energy cut - off , @xmath19 , ( as in * ? ? ? * ) , 3 ) a broken power - law , @xmath20 , ( as in * ? ? ? * ) , where @xmath21 is the cut - off energy and @xmath22 is the normalization constant . + since the distributions with a cut - off ( 1 and 2 ) fail to reproduce simultaneously both the radio and @xmath3-ray spectrum , we refer to the distribution ( 3 ) . the best fit to the gamma - ray data is obtained with @xmath23 gev , and indices @xmath24 and @xmath25 above and below @xmath26 , respectively . synchrotron emission originating from this distribution can be evaluated for different values of the average magnetic field . figure [ spec3 ] shows the case of the most `` favorable '' leptonic - only model characterized by @xmath27 @xmath28 g ( other cases turn out to be even less favorable ) . we find that , at high frequencies , the calculated synchrotron spectrum is in strong disagreement ( factor larger than 4 ) with the radio emission produced co - spatially to the gamma - ray one ( * ? ? ? * and figure [ w44 ] ) . furthermore , the inferred average density , _ _ n__= 300 @xmath6 , is too large ( by a factor of three ) compared with the circumstellar medium constraints @xcite ; a lower value for @xmath29 would be incompatible with the gamma - ray spectrum fitting . similar or even stronger contradictions with the multiwavelength data apply to other leptonic - only models that we systematically explored for a large variety of parameters . + in the case of inverse compton dominated models , two sources of soft photons are available : the cosmic background radiation ( cbr ) and the interstellar radiation field ( isrf ) . in the first case , a second peak in the gamma - ray spectrum is unavoidably expected with a peak energy @xmath30 1 tev , in contradiction with the upper - limits obtained from tev cherenkov telescopes . in the case of interaction with isrf , instead , the calculated synchrotron peak is not compatible with the radio continuum data for any reasonable value of the magnetic field in the snr shell . we can then reliably exclude leptonic - only models of emission for snr w44 . it is interesting to determine the main physical parameters of an emission model dominated by hadrons in the gamma - ray" +"dust plays important roles in cosmic star formation and evolution of the galaxies . the basic ingredients of dust grains are metals produced through past stellar activity , and thus the main reservoir of dust is conventionally thought to be mainly confined in interstellar space within galaxies . @xcite , however , suggested the existence of dust filling the intracluster space within the coma cluster . this motivated the investigation of the abundance and spatial distribution of dust in different environments , including the color - excess of background objects due to dust optical - uv reddening @xcite , and the fir dust emission from individual objects @xcite , and from stacking analysis @xcite . recently , mnard et al . ( 2010a : hereafter msfr ) investigated the distribution of dust around galaxies by measuring the angular correlation between sdss galaxy distribution and distant quasar colors . they found that the mean @xmath1-@xmath2 reddening profile around sdss galaxies is well approximated by a single power - law : @xmath3 where @xmath4 is the angular separation between foreground galaxies and background quasars . furthermore they discovered that the above power - law extends even for @xmath5 . the angular scale corresponds to several mpc at the mean redshift @xmath6 of their sdss galaxy sample . this is far beyond the typical scale of galactic disks , and even larger than the virial radius of typical galaxy clusters . msfr appear to interpret their result as an evidence for an extended dust surrounding an individual galaxy beyond a few mpc , which we refer to as _ the circum - galactic dust model _ ( cgd model ) . their interpretation , however , is rather subtle . the mean reddening profile from their measurement @xmath7 is close to that of the angular correlation function of galaxies . thus the detected dust reddening may be equally explained by the summation of the dust component associated with the central part of galaxies according to the spatial clustering of those galaxies , which will be referred to as _ the inter - stellar dust model _ ( isd model ) . in practice , it is difficult to distinguish between the cgd and isd models on the basis of the statistical correlation analysis alone as performed by msfr . therefore a complementary and independent method to constrain the nature of the dust is needed . this is exactly what we attempt to propose in this paper . for that purpose , we measure the dust far - infrared ( fir ) emission of the sdss galaxies by image stacking analysis . similar analysis on the sfd galactic extinction map ( * ? ? ? * sfd ) has detected the fir emission of sdss galaxies ( * ? ? ? * kys13 ) . we return to the @xmath0 intensity map by sfd , instead of their extinction map , and perform the stacking analysis of the same galaxy sample used by msfr . if the detected fir emission originates from the same dust component as the msfr reddening measurement , the emission to absorption ratio puts a constraint on dust temperature , which would in turn offer complementary information to distinguish between the cgd and isd models mentioned above . the present paper is organized as follows . the data used in the current analysis are described in section 2 . in section 3 , we perform the stacking analysis of the msfr galaxy sample on iras / sfd @xmath0 map . we show the constraint on the dust temperature from the detected fir emission combined with the msfr reddening measurement . we present summary and conclusions of the paper , and discuss future outlook in section 4 . throughout the analysis , we assume the standard @xmath8cdm cosmology with @xmath9 , @xmath10 , and @xmath11 . we select our galaxy sample from the sdss dr7 photometric galaxies with 5 passbands , @xmath12 , @xmath1 , @xmath13 , @xmath2 , and @xmath14 , in northern galactic cap , which covers @xmath157600 @xmath16 . for details of the photometric data , see @xcite . we conservatively masked @xmath17 of the total area following the sdss mask definition . we also removed the objects with bad photometry or fast - moving flag according to the photometry flags , which are suspicious to be correlated with the galactic foreground . see @xcite for more details of our data selection . for the current analysis , we impose the same @xmath2-band magnitude cut , @xmath18 , as the msfr sample for a direct comparison with their results , where the magnitudes of the galaxies are correct for galactic extinction using the sfd map @xcite . our final sample collects @xmath19 galaxies . for far - infrared data , we use the all - sky diffuse 100@xmath20 map provided by sfd ; they have carefully processed the original iras / issa 100@xmath20 sky map , removing the scan pattern of _ iras _ , correcting calibration errors based on cobe / dirbe data , and subtracting zodiacal dust emission and bright point sources with @xmath21 . hereafter , we adopt a gaussian with @xmath22 for the point spread function ( psf ) of sfd / iras map , as measured by similar stacking analysis by kys13 . following the procedures of kys13 , we stack the sfd / iras 100@xmath20 map over @xmath23 squares centered on each sdss galaxy . each image is randomly rotated around the center . the resulting stacked image shows clear circular signature of dust emission associated with those galaxies ( kys13 ) . the radial profile of the raw stacked image is shown in figure [ fig : profile]a . the quoted error bars reflect the _ rms _ in each radial bin ( @xmath24 ) . the radial profile is reasonably well fitted by gaussian corresponding to the psf around the central region , but exhibits an extended tail beyond the psf width , @xmath22 , which corresponds to roughly @xmath25 for the mean redshift @xmath26 of the sdss galaxies . at sufficiently large @xmath4 , the stacked flux should be dominated by the galactic foreground , which is uncorrelated with the sdss galaxies and expected to be constant . the stacked flux , however , increases beyond @xmath27 . while we do not completely understand the behavior ( see also discussion in kys13 ) , it may be partly due to the fact that the sdss survey region is designed to be located at the low - extinction region , therefore towards high galactic latitudes . thus the outskirt of the sdss region is surrounded by low galactic latitudes with relatively higher values of the 100@xmath20 intensity , and the stacked flux centered at the sdss region tends to be systematically larger at larger @xmath4 . nevertheless the profile for @xmath28 matches nicely that expected from angular correlation functions of sdss galaxies ( okabe et al . in preparation ) . this is why we adopt the profile modeling discussed below . ( before subtracting the offset level due to the galactic dust ) . shaded region indicates the data with @xmath29 that are not used in the current analysis . ( _ b _ ) ; radial profile of the stacked image after subtracting the offset level of @xmath30}$ ] , which is computed assuming @xmath31 and shown as the dashed line in panel a. the lines indicate the best - fits for @xmath32 ( black dotted ) , @xmath33 ( red solid ) , and @xmath34 ( blue dot - dashed ) ; see equation ( [ eq : model ] ) . just for reference , we plot the power - laws of @xmath35 , 0.86 and 1.05 in dashed lines , which covers the ranges of the msfr result in equation ( [ eq : egimsfr ] ) . ] ( before subtracting the offset level due to the galactic dust ) . shaded region indicates the data with @xmath29 that are not used in the current analysis . ( _ b _ ) ; radial profile of the stacked image after subtracting the offset level of @xmath30}$ ] , which is computed assuming @xmath31 and shown as the dashed line in panel a. the lines indicate the best - fits for @xmath32 ( black dotted ) , @xmath33 ( red solid ) , and @xmath34 ( blue dot - dashed ) ; see equation ( [ eq : model ] ) . just for reference , we plot the power - laws of @xmath35 , 0.86 and 1.05 in dashed lines , which covers the ranges of the msfr result in equation ( [ eq : egimsfr ] ) . ] we adopt the following radial density profile of dust : @xmath36 where @xmath32 and @xmath33 represent the contributions from the central single galaxy ( single term ) and from the clustered neighbor galaxies ( clustering term ) , respectively , and @xmath37 is the background level of the foreground galactic dust emission . , @xmath32 , and @xmath33 are equivalent to @xmath38 , @xmath39 , and @xmath40 used in kys13 , respectively , except that @xmath41 denotes the sfd map extinction in units of [ mag ] , whereas @xmath42 in this paper denotes the intensity in units of [ mjr / sr ] . ] we assume that the galactic foreground , @xmath37 , should be uncorrelated with the sdss galaxies , and thus is assumed to be constant at @xmath28 . since the psf of sfd / iras map is well approximated by gaussian , @xmath43 is written as @xmath44 where @xmath22 is the gaussian width of psf . the clustering term @xmath33 is written in terms of @xmath32 and angular two - point correlation function ( 2pcf ) of galaxy , @xmath45 , as @xmath46 where @xmath47 is the differential number count of galaxies ( whether or not detected by sdss ) as a function of @xmath48 . we assume that the single term is written as a function of @xmath49 alone , therefore the dependence on other physical quantities is neglected . we approximate the angular 2pcf is described as a single power - law in this angular scale @xcite ; @xmath50 where the amplitude @xmath51 is a function of @xmath49 , but the index @xmath52 is assumed to be a constant and independent of @xmath49 . in this case , equation ( [ eq : cterm ] ) reduces to @xmath53 where @xmath54 denotes the confluent hypergeometric function , and @xmath55 we fit the radial profile of the stacked image using equations ( [ eq : model ] ) , ( [ eq : istheta ] ) , and ( [ eq : ictheta ] ) . in doing so , we do not use equation ( [ eq : ic0 ] ) , but treat @xmath56 simply as one of the fitting parameters empirically determined from the observed profile . consistency of the resulting @xmath56 with equations ( [ eq : wtheta ] ) and ( [ eq : ic0 ] ) independently measured for sdss galaxies is an interesting topic ( kys13 ) , which will be discussed in detail elsewhere ( okabe et al . in preparation ) . we estimate the statistical errors using the jackknife resampling method by dividing the entire sdss sky area into 400 patches of equal area . the detected emission profile at small @xmath4 is affected due to the iras psf , and should not be directly compared with the msfr measurement . therefore , we use the clustering term , which is relevant for @xmath57 , for the dust temperature constraint in the following section . in fact , the psf effect on the clustering term vanishes at large @xmath4 and equation ( [ eq : ictheta ] ) reduces to the power - law as @xmath58 since we" +"supergiant high mass x - ray binaries ( hmxbs ) account for one third of the galactic hmxb population . the compact object has an early type supergiant star as a companion and the accretion unto the compact object occurs via stellar wind or roche lobe overflow . they are subdivided into roche lobe filling supergiants with short spin periods and underfilled roche lobe supergiants with longer spin periods @xcite . a majority of supergiant hmxbs are persistent sources . some of the supergiant hmxbs , called the highly absorbed supergiant hmxbs , have very strong absorption with column density of absorbing matter n@xmath6 @xmath4 . igr j16393 - 4643 belongs to this increasing class of heavily absorbed hmxbs detected by the _ integral _ survey of the galactic plane , that are mainly concentrated in the spiral arms . it was first discovered with the _ asca _ observatory during survey of the galactic plane @xcite and was named as ax j1639.0 - 4642 . it has a spin period of @xmath7 910 s and a 4.2 days orbital period @xcite and occupies a unique position near the top edge of underfilled roche lobe supergiant systems in the corbet diagram @xcite . due to the lack of detailed studies of such systems , igr j16393 - 4643 makes an interesting candidate to study the timing and spectral properties of the short orbital period and long spin period supergiant systems . the x - ray spectrum of the pulsar is characterised by a highly absorbed power - law with an exponential cut - off along with fe fluorescence lines @xcite . the strong absorption of the order @xmath8 @xmath4 is an evidence of a dense circumstellar environment surrounding the pulsar . previous observations with _ xmm - newton _ indicates the presence of a soft excess in the spectrum which could be due to x - rays scattering by the stellar wind @xcite . here we present the simultaneous broad - band pulse profiles and spectral characteristics of the pulsar igr j16393 - 4643 obtained from a _ suzaku _ observation . we also present results from the orbital intensity profile analysis of igr j16393 - 4643 using _ swift - bat _ light - curves . the energy resolved pulse profiles are created for the first time for this source . the broad - band spectral characteristics are studied both for the phase averaged as well as resolving the pulse phase into peak phase and trough phase . these results provide valuable insights into the nature of the such underfilled roche lobe supergiant systems . _ suzaku _ is the fifth japanese x - ray astronomy satellite launched in july 2005 . it consists of two sets of co - aligned scientific instruments , the x - ray imaging spectrometer ( xis ) , operating in the energy range 0.2 - 12 kev and hard x - ray detector ( hxd ) , operating in the energy range 10 - 600 kev . the xis consists of three front illuminated ccd detectors and one back illuminated ccd detector @xcite , out of which three ccds xis0 , xis1 and xis3 are currently operational . the hxd consists of silicon pin diodes operating in energy range 10 - 70 kev and gso crystal scintillators extending the energy range till 600 kev @xcite . igr j16393 - 4643 was observed with _ suzaku _ during 12 march 2010 ( obsid : 404056010 ) with an useful exposure time of @xmath7 44 kilosecs over a span of about 120 kilosecs . the observations were carried out at the ` xis nominal ' pointing position and the xis were operated in ` standard ' data mode in the ` normal window ' option , having a time resolution of 8 secs . for both the xis and hxd data , we have used the filtered cleaned event files which are obtained using the pre - determined screening criteria described in the suzaku abc guide . the xis light - curves and spectra were extracted from the cleaned event files by selecting circular regions of 3 around the source centroid . the background light - curves and spectra were extracted by selecting circular regions of same size away from the source centroid . for hxd / pin background , simulated ` tuned ' non x - ray background event files ( nxb ) corresponding to the month and year of the observation was used to estimate the non x - ray background . the cosmic x - ray background was simulated as suggested by the instrument team with appropriate normalisations and response files . the response files for xis were created using caldb ` 20140211 ' and for hxd / pin , response files were obtained from the _ suzaku _ guest observer facility . for the timing analysis of the source , we have applied barycentric corrections to the event data files using the ftools task ` aebarycen ' . light - curves with time resolution of 1 s and 8 s were extracted from hxd / pin ( 12 - 50 kev ) and xis ( 0.3 - 12 kev ) respectively . figure . [ lightcurves ] shows the light - curves binned with a time bin of 908 secs _ i.e _ at the pulsar spin period , in xis and pin along with the hardness ratio . the count - rate in xis and pin increases gradually from the start of the observation upto 100 kilosecs by a factor of @xmath7 2 and then decreases by a similar factor till the end of the observation ( also see second and third panel in figure [ orbital ] ) . the hardness ratio remained constant throughout the observation . we have used long term light - curve of igr j16393 - 4643 in 15 - 50 kev _ swift - bat _ energy band to estimate the orbital period of the system ( p@xmath9 = 366150 secs ; consistent with @xcite ) . we then folded the xis and pin light - curves with the _ swift - bat _ light - curves , to investigate the orbital phase of the _ suzaku _ observation . the minimum of the orbital intensity profile is taken as orbital phase zero , corresponding to epoch mjd : 53417.955 . figure [ orbital ] shows an indication that the system is an eclipsing binary , which was also reported previously by @xcite . the eclipse duration is short with the eclipse semi - angle @xmath0 17@xmath1 . the _ suzaku _ observations were carried out roughly from orbital phase 0.55 - 0.9 _ i.e _ prior to going into the eclipse . as seen in figure [ orbital ] , the count - rate in xis and pin increases by a factor of @xmath7 2 during orbital phase @xmath7 0.65 - 0.8 and then again decreases till the end of the observation . the orbital intensity profile created with _ swift - bat _ is averaged over many orbital cycles , whereas the orbital intensity profile created with xis and pin show variability on sub - orbital timescales , similar to that seen in oao 1657 - 415 @xcite . we have searched for pulsations in the light - curves by applying pulse folding and @xmath10 maximization technique and the pulse period was found to be 908.79 @xmath11 0.01 secs . we then created the energy resolved pulse profiles by folding light - curves extracted in different energy bands with the pulse period . light - curves from xis0 , xis1 and xis3 were added together to create the pulse profiles in xis energy band 0.3 - 12 kev and sub bands within . from figure [ pulseprofiles ] , we see that the pulse profiles have a complex morphology with some energy dependance , which was also seen with _ xmm - newton _ @xcite and _ rxte pca _ @xcite , but the broad - band nature of the pulse profiles are brought out from this _ suzaku _ observation . due to the presence of high column density of absorbing matter , very few photons are detected below 4 kev . the epoch for creation of the pulse profiles is adjusted to make the minima appear at phase zero in the pin 12 - 50 kev energy band . the pulse minima is seen to become deeper at higher energies . a phase lag is seen in the energy resolved pulse profiles in the two xis energy bands compared to the pin energy bands , which is shown in figure [ xis_pin ] for pulse profiles created in xis energy band 0.3 - 6.0 kev and 6 - 12 and in pin energy band 12 - 50 kev . we have performed the pulse phase averaged spectral analysis of igr j16393 - 4643 using spectra from three xis and pin . the energy range chosen for spectral fitting was 3.0 kev to 10.0 kev for xis , since there were hardly any photons below 3.0 kev . for pin , the energy range was chosen from 15 kev to 50 kev . the xis spectra were rebinned by a factor of 12 upto 5 kev , by a factor of 6 from 5 - 7 kev and again by a factor of 12 from 7 - 10 kev . the pin spectra was rebinned by a factor of 2 till 22 kev , by 8 from 22 - 45 kev and by a factor of 12 for the rest . the spectral fitting was done with xspec 12.8.1 . to fit the continuum spectra , we have tried several standard continuum models used for hmxb pulsars like cut - off power - law ( cutoffpl ) , power - law with high energy cut - off ( highecut , @xcite ) , power - law with a fermi - dirac cut - off ( fdcut , @xcite ) , and negative and positive power - law exponential ( npex , @xcite ) . the power - law with highecut and power - law with fdcut spectral models provided the best fits to the phase averaged spectrum with physically acceptable parameter values and henceforth , we report results from these two spectral models . we fitted the spectra simultaneously with all the parameters tied , except the relative normalisations of the instruments which were kept free . a 6.4 kev fe k@xmath12 line was also found in the spectra , which was modelled by a gaussian emission line . the 7.1 kev k@xmath13 line detected in the spectra with the _ xmm - newton _ observation @xcite was marginally detected here with the 90 @xmath14 upper limit on the line flux as @xmath15 photons @xmath4 s@xmath16 and equivalent width of 33 ev , consistent with the upper limits quoted for _ xmm - newton _ observation ( @xmath17 photons @xmath4 s@xmath16 and 120 ev respectively ; @xcite ) . the best fit parameter values of phase averaged spectrum for 90@xmath14 confidence limits ( except for @xmath18 and equivalent width of the fe line which are given for 1@xmath19 confidence limits ) for the two spectral models power - law with highecut and power - law with fdcut are given in table 1 . figure [ spectra ] shows the best fit phase averaged spectrum using power - law with highecut and power - law with fdcut models , along with the residuals . [ table ] [ cols=""^,^,^,^,^,^,^"",options=""header "" , ] the energy dependence of the pulse fraction as seen in the xis and pin energy bands ( figure [ pulseprofiles ] and figure [ xis_pin ] ) indicates a significant change in the spectrum with the pulse phase and we investigate the same with pulse phase resolved spectroscopy at the peak and trough of the pulse profile . the xis" +"recently , the problem of the electromagnetic gauge invariance in the deeply virtual compton scattering ( dvcs ) and similar exclusive processes has intensively been discussed in the literature , see for example @xcite . this development explored the similarity with the earlier studied inclusive spin - dependent processes @xcite , and the transverse component of momentum transfer in dvcs corresponds to the transverse spin in dis . the gauge invariance of relevant amplitudes is ensured by means of twist three contributions and the use of the equations of motion providing a possibility to exclude the three - particle ( quark - gluon ) correlators from the amplitude . after combining with the two - particle correlator contributions , one get the gauge invariant expression for the physical amplitude or , in the case of lepton - hadron processes , for the corresponding hadron tensor @xcite . this method was originally developed in the case of the particular inclusive processes with transverse polarized hadrons , like structure function @xmath1 in dis @xcite and single spin asymmetry ( ssa ) @xcite due to soft quark ( fermionic poles @xcite ) . at the same time , the colour gauge invariance of the so - called gluonic poles contributions @xcite was previously explored @xcite by other methods relying on the wilson exponentials @xcite . here we combine the approaches described above and apply them in the relevant case of the drell - yan ( dy ) process where one of hadrons is the transversally polarized nucleon . the ssa in the dy process was first considered in qcd in the case @xcite of the longitudinally polarized hadron . this observable is especially interesting if the second hadron is a pion , because of the sensitivity @xcite to the shape of pion distribution amplitude , being currently the object of major interest @xcite ( see also @xcite and ref . therein ) . the imaginary phases in the ssa with longitudinally polarized nucleon are due to the hard perturbative gluon loops @xcite or twist @xmath2 contribution of the pion distribution amplitude @xcite . at the same time , the source of the imaginary part , when one calculates the single spin asymmetry associated with @xmath3 process , is the quark propagator in the diagrams with quark - gluon ( twist three ) correlators . this leads @xcite to the gluonic pole contribution to ssa . it has been reproduced ( up to the derivative term , corresponding to the case of single inclusive drell - yan process , when only one of the leptons is observed ) in the case of the non - zero boundary condition imposed on gluon fields , and the asymmetric boundary conditions have been considered as a privileged ones @xcite . the reason is that these boundary conditions provide the purely real quark - gluon function @xmath4 which parameterizes @xmath5 matrix element . by this fact the diagrams with two - particle correlators do not contribute to the imaginary part of the hadron tensor related to the ssa . this property seems quite natural , as the corresponding diagram does not have a cut capable of producing the imaginary phase @xcite . in our paper , we perform a thorough analysis of the transverse polarized dy hadron tensor in the light of the qed gauge invariance , the causality and gluonic pole contributions . we show that to restore the electromagnetic gauge invariance of the transverse polarized dy hadron tensor , it is mandatory to add the extra diagram contribution ( cf . @xcite ) , also at the twist three level . in contrast to the naive assumption , we demonstrate that this new additional contribution is directly related to the certain complex prescription in the gluonic pole @xmath6 of the quark - gluon function @xmath4 . it is essential that this prescription is process - dependent , supporting the idea of effective process - dependent sivers function ( see e.g.@xcite and refs . therein ) related to this correlator . in more detail , we show that the causal pole prescription in the quark propagator , involved in the hard part of the standard diagram , supports the choice of a contour gauge and , in turn , the representation of the quark - gluon function @xmath4 in the form of the gluonic pole with the mentioned complex prescription . this representation must be extended on the diagram , which naively does not contribute to the imaginary part . they ensure a new contribution to the imaginary part which is necessary to maintain the electromagnetic gauge invariance . finally , the account for this new contributions corrects the ssa formula for the transverse polarized drell - yan process by the factor of @xmath7 . we study the contribution to the hadron tensor which is related to the single spin ( left - right ) asymmetry measured in the drell - yan process with the transversely polarized nucleon : @xmath8 , where the virtual photon producing the lepton pair ( @xmath9 ) has a large mass squared ( @xmath10 ) while the transverse momenta are small and integrated out . the left - right asymmetry means that the transverse momenta of the leptons are correlated with the direction @xmath11 where @xmath12 implies the transverse polarization vector of the nucleon while @xmath13 is a beam direction @xcite . the dy process with the transversely polarized target manifests @xcite the gluonic pole contributions . since we perform our calculations within a _ collinear _ factorization , it is convenient ( see , e.g . , @xcite ) to fix the dominant light - cone directions for the dy process shown at fig . [ fig - dy ] @xmath14 so that the hadron momenta @xmath15 and @xmath16 have the plus and minus dominant light - cone components , respectively . accordingly , the quark and gluon momenta @xmath17 and @xmath18 lie along the plus direction while the antiquark momentum @xmath19 along the minus direction . focusing on the dirac vector projection , containing the gluonic pole , let us start with the standard hadron tensor generated by the diagram depicted on fig . [ fig - dy](a ) : @xmath20}_\alpha ( k_1,\ell ) \ , \bar\phi^{[\gamma^- ] } ( k_2)\times \nonumber\\ & & \text{tr}\biggl [ \gamma_\mu \gamma^- \gamma_\nu \gamma^+ \gamma_\alpha \frac{\ell^+\gamma^- - k_2 ^ -\gamma^+ } { -2\ell^+ k_2 ^ - + i\epsilon } \biggr ] \ , , \end{aligned}\ ] ] where @xmath21}_\alpha ( k_1,\ell ) \stackrel{{\cal f}_2}{= } \langle p_1 , s^t | \bar\psi(\eta_1)\gamma^+ ga_{\alpha}(z ) \psi(0 ) | s^t , p_1\rangle , \quad \bar\phi^{[\gamma^-]}(k_2)\stackrel{{\cal f}_1}{= } \langle p_2 | \bar\psi(\eta_2)\gamma^- \psi(0)| p_2\rangle .\end{aligned}\ ] ] throughout this paper , @xmath22 and @xmath23 denote the fourier transformation with the measures @xmath24 respectively , while @xmath25 and @xmath26 mark the inverse fourier transformation with the measures @xmath27 analyzing the @xmath28-structure of ( [ hadten1 - 2 ] ) , we may conclude that the first term in the quark propagator singles out the combination : @xmath29 with @xmath30 which will lead to the matrix element of the twist three operator , @xmath31 with the transverse gluon field . after factorization , this matrix element will be parametrized via the function @xmath4 . the second term in the numerator of the quark propagator separates out the combination @xmath32 with @xmath33 . therefore , this term will give @xmath34 which , as we will see now , will be exponentiated in the wilson line @xmath35 $ ] . indeed , this part of the standard hadron tensor is given by @xmath36}_{\mu\nu}&= & \int d\mu ( k_i;x_1,y ) \ , \text{tr}\biggl [ \gamma_\mu \gamma^- \gamma_\nu \gamma^+ \gamma^- \gamma^+ \biggr ] \ , \bar\phi^{[\gamma^- ] } ( k_2 ) \times \\ & & \frac{1}{2 } \int dz^- \int d\ell^+\ , \frac{e^ { - i\ell^+ z^-}}{\ell^+ - i\epsilon } \int d^4\eta_1 \ , e^{-ik_1\cdot\eta_1 } \langle p_1 , s^t | \bar\psi(\eta_1)\ , \gamma^+ \ , ga^+(0,z^-,\vec{{\bf 0}}_t ) \ , \psi(0 ) \nonumber\end{aligned}\ ] ] where @xmath37 \ , .\end{aligned}\ ] ] note that the prescription @xmath38 in the denominator of this expression directly follows from the standard ( see , e.g. @xcite ) causal prescription for the massless quark propagator in ( [ hadten1 - 2 ] ) . integrating over @xmath39 , one can immediately obtain the corresponding @xmath40-function in ( [ hadten1 - 3 ] ) : @xmath41}_{\mu\nu}&= & \int d\mu ( k_i;x_1,y ) \ , \text{tr}\biggl [ \gamma_\mu \gamma^- \gamma_\nu \gamma^+ \biggr ] \ , \bar\phi^{[\gamma^- ] } ( k_2 ) \times \nonumber\\ & & \int d^4\eta_1 \ , e^{-ik_1\cdot\eta_1 } \langle p_1 , s^t | \bar\psi(\eta_1)\ , \gamma^+ \ , ig \int\limits_{-\infty}^{+\infty } dz^- \ , \theta(-z^- ) a^+(0,z^-,\vec{{\bf 0}}_t ) \ , \psi(0 ) |s^t , p_1\rangle \ , .\end{aligned}\ ] ] including all gluon emissions from the antiquark going from the upper blob on fig . [ fig - dy](a ) ( the so - called initial state interactions ) , we get the corresponding @xmath42-exponential in @xmath43}_\alpha ( k_1,\ell)$ ] . the latter is now represented by the following matrix element : @xmath44 \ , \psi(0 ) |s^t , p_1\rangle \ , , \end{aligned}\ ] ] where @xmath45 = pexp\biggl\ { - i g \int\limits_{-\infty}^{0 } dz^- \ , a^+(0,z^-,\vec{{\bf 0}}_t ) \biggr\}\ , .\end{aligned}\ ] ] if we include in the consideration the gluon emission from the incoming antiquark ( the mirror contributions ) , we will obtain the wilson line @xmath46 $ ] which will ultimately give us , together with ( [ pexp-1 ] ) , the wilson line connecting the points @xmath47 and @xmath48 in ( [ me - pexp ] ) . this is exactly what happens , say , in the spin - averaged dy process @xcite . however , for the ssa , these two diagrams should be considered individually . indeed , their contributions to ssas , contrary to spin - averaged case , differ in sign and the dependence on the boundary point at @xmath49 does not cancel . to eliminate the unphysical gluons from our consideration and use the factorization scheme @xcite , we may choose a _ contour _ gauge @xcite @xmath50=1 \,\end{aligned}\ ] ] which actually implies also the axial gauge @xmath51 used in @xcite . let us discuss the problem of gauge choice in more detail . in ( [ cg2 ] ) , the so - called starting point @xmath52 ( see , @xcite ) is fixed to be at @xmath49 owing to the certain complex prescription @xmath53 in the quark propagator in ( [ hadten1 - 2 ] ) . if we would change the starting point @xmath52 on @xmath54 , this would correspond to the choice of the anticausal "" complex prescription @xmath38 . on the other hand , the axial gauge @xmath51 is independent on the choice of @xmath52 and we are able to eliminate the wilson line by choosing simply @xmath51 without referring to the starting point @xmath52 . nevertheless , since our prescription @xmath53 in the quark propagator uniquely fixes the starting point @xmath52 at @xmath55 , the expression for the wilson line ( [ pexp-1 ] ) hints the choice of gauge ( [ cg2 ] ) . imposing this gauge one arrives @xcite at the following representation of the gluon field in terms of the strength tensor : @xmath56 moreover , as we will demonstrate below , if we choose instead an alternative representation for the gluon in the form : @xmath57 ( which corresponds to the gauge condition @xmath58=1 $ ] and also results in @xmath51 ) keeping the causal prescription @xmath53 in ( [ hadten1 - 2 ] ) , the cost of this will be the breaking of the electromagnetic gauge invariance for the dy tensor . we are now ready to pass to the term with @xmath59 in ( [ hadten1 - 2 ] ) which gives us finally the" +"the idea that chaotic scattering @xcite may play an important role in various problems in celestial mechanics became widely accepted after the pioneering work of petit and hnon @xcite . in their study of satellite encounters ( also known as hill s problem ) , they provided evidence for the presence of chaotic scattering by analyzing the dependence of a suitable parameter characterizing the outgoing asymptotic motion on the same parameter in the incoming asymptotics . they pointed out that the irregular behaviour of this scattering function , showing singularities on a fractal set , reflects the existence of scattering trajectories that are asymptotic to bounded orbits of the system . the bounded orbits form a fractal set called the chaotic set or nonattracting invariant set @xcite in phase space with stable manifolds extending smoothly into the region of asymptotic motion . whenever the initial condition of a scattering trajectory is placed on a stable manifold , it gets trapped in the corresponding bounded orbit , so the structure of the singularities in the scattering function reflects the fractal structure of the chaotic set . by presenting trajectory plots of various types , petit and hnon underlined this structure but attempted no detailed characterization of it . in this paper , we provide a hierarchic analysis of chaotic scattering in hill s problem by studying a slightly different scattering function , giving the dependence of the dwell time on the initial conditions , combined with a careful examination of scattering orbits . this method has recently been applied to a simple model of chemical reactions @xcite making properties of the hierarchic organization clear in that problem . at first , we give a brief introduction in sec . [ sec - hill ] to hill s problem based on ref . @xcite , then we present the dwell time function and the basic ideas of its hierarchic analysis in sec . [ sec - dwtime ] . in sec . [ sec - orbits ] , a selection of scattering orbits is used to point out the presence of a ternary organization in the scattering data and , correspondingly , in the structure of the chaotic set . finally , in sec . [ sec - discuss ] , we discuss the consequences of our findings including the possible use of the hierarchic information in the calculation of average quatities in hill s problem or other models exhibiting chaotic scattering . the behaviour of two small bodies ( satellites ) moving along coplanar circular orbits around a large central object ( the planet ) in the same ( counterclockwise ) direction can approximately be described , in each other s vicinity , by hill s equations @xcite : @xmath0 with @xmath1 . the coordinates @xmath2 and @xmath3 describe the positions of the satellites relative to each other , after an appropriate change of scales , in a comoving reference frame rotating around the planet . ( in particular , if one of the satellites is much smaller than the other , then these coordinates simply give the position of the small satellite while the big one rests in the origin . ) these equations contain no free parameter . they can be derived as the hamiltonian equations of motion from a suitable function @xmath4 , and , as a consequence , they give rise to a conserved quantity @xmath5 playing the role of energy in the problem . hill s equations allow general coplanar motions of the satellites , not just circular orbits . neglecting the interaction between the satellites , the `` free '' orbits can be parametrized by the difference @xmath6 of the two semimajor axes and a parameter @xmath7 called the reduced eccentricity ; for circular obits @xmath8 and @xmath6 is just the difference of the two orbit radii . therefore , the family of circular initial orbits can be parametrized by a single parameter @xmath6 ( apart from a trivial constant that can be transformed out by a suitable choice of the origin of time ) , and the constant of motion @xmath9 can be expressed through @xmath6 : @xmath10 . the symmetries of the equations also allow us to assume @xmath11 . we will concentrate on this situation in the following and leave the case of more general initial conditions to the discussion . if @xmath12 , the satellites slowly approach and get close to each other ( i.e. , they have an encounter ) due to the difference in their periods . during the encounter , their interaction must be taken into account ; as a result , they may perform complicated motion in the proximity of each other for a while , but then separate again and move away from each other asymptotically along generic elliptic orbits characterized by parameters @xmath13 and @xmath14 . bearing in mind the hamiltonian character of the problem , this process can be thought of as a scattering event from an incoming asymptotics with a given value of @xmath6 and @xmath8 into an outgoing asymptotics characterized by @xmath13 and @xmath14 . the complicated motion during the encounter , which gives the chaotic features to the scattering , is a manifestation of transient chaos @xcite , i.e. , chaotic motion on a finite time scale . in ref . @xcite , the function @xmath15 was used to point out the presence of chaotic scattering ; in the next section , we use a nowadays standard approach based on the dwell time ( or time delay ) function . in chaotic scattering processes , the dwell time function @xcite , measuring the time spent by a particle in the region of strong interaction with the scatterer , shows irregular behaviour similar to that of other scattering data . we can construct it by choosing a one - parameter family of initial conditions and recording the dwell times for the trajectories . in our case of satellite encounters , the family of initial circular orbits parametrized by @xmath16 is a natural choice . to give the initial conditions uniquely , we choose the origin of time so that at @xmath17 the initial @xmath3 coordinate is a fixed value @xmath18 , while ( as a consequence of @xmath19 and @xmath8 ) @xmath20 and @xmath21 is obtained from @xmath9 . the incoming asymptotics then corresponds to moving downward along a vertical straight line with @xmath22 and @xmath23 . we choose a circle with radius @xmath24 around the origin as the interaction zone and define the dwell time @xmath25 as the time spent by the orbit inside this circle . the plot of the function @xmath26 is shown in fig . [ fig - dwtime]a . the irregular structure of @xmath26 appears as a set of singularities crowding in four narrow regions separated by smooth behaviour . these regions themselves , called the transition zones in ref . @xcite , have a similar structure as shown by the blowup in fig . [ fig - dwtime]b . since the singularities correspond to trajectories asymptotically trapped by the confined orbits of the chaotic set , the self - similar pattern of singularities reflects the fractal structure of that set ; thus , an analysis of the set of singularities will provide important information on the organization of the chaotic set @xcite . the fractal pattern of singularities suggests that we consider the function @xmath26 as built of a few basic blocks containing the singularities and separated by smooth regions ( valleys ) . in turn , these basic blocks are considered again as containing smaller blocks separated by smaller regions of smooth behaviour . this approach yields a whole hierarchy of blocks sitting on top of the set of singularities : the basic blocks are on the first level of the hierarchy , the subblocks contained in them go to the second level , etc . the blocks on a given level of the hierarchy provide a coverage of the set of singularities : the higher we look into the hierarchy , the higher resolution we obtain in the coverage . to carry out this hierarchic decomposition of the time delay function , we need rules telling us how to break the continuous picture based on the variable @xmath25 into the obvious discreteness introduced by the hierarchy . these rules determining which of the singularities belong together in one block at a certain level of the hierarchy should reflect the intrinsic organization of the chaotic set . as was shown in ref . @xcite for a smooth potential model , this can be achieved by linking the rules of block construction to the topological complexity of scattering trajectories so that the orbits of the valleys separating the blocks at a given level have the same degree of complexity in their structures . + + + one measure of the orbit complexity can be the number of crossings the orbits produce with a suitably chosen poincar section . the function @xmath27 giving the number of crossing of a trajectory from our family of initial conditions with the surface @xmath28 can be considered as a _ discretized _ dwell time function : it can be shown that all the periodic orbits of the system cut this surface , so the longer a scattering trajectory follows a particular periodic orbit , the larger the number of crossings @xmath29 become . the discretized time delay function is plotted in fig . [ fig - ncross ] ; its similarity to fig.[fig - dwtime ] is obvious . the discreteness introduced in the picture will make the decomposition process easier to implement , since the smooth changes in @xmath25 are now replaced by plateaus of fixed heights that can be compared to one another . in the next section , we will obtain the rules of block construction for @xmath27 [ and thus for @xmath26 ] by looking at the topological properties of scattering orbits in hill s problem . the scattering orbits approach , along their incoming asymptotics , the interacting region around the origin where they perform their central parts consisting of localized and usually complicated motion ( for shorter or longer times , depending on the initial conditions ) , and finally escape downward or upward . since it is the central part that can get close to the bounded orbits of the chaotic set , we will concentrate on the central parts of scattering orbits , ignoring differences in their escapes . in the hierarchic decomposition of @xmath27 or any other scattering function , we would like to set apart orbits from one another according to the complexity of their central parts . for this purpose , the value @xmath29 is a good indicator but we also need a visual evaluation of the graph of the orbit to make necessary distinctions between different orbit types . our main goal is to represent the valleys of the dwell time function with scattering orbits , so that the comparison of these orbits can tell us whether two given valleys belong to the same level in the hierarchy or not ( we will say that a valley is of the @xmath31th level if the shortest block containing it belongs to level @xmath32 ) . for the comparison , we will identify some key elements in the orbit plots so that the number of these elements in the orbit will give the level number of the corresponding valley in the hierarchy . + + as can be seen from figs . [ fig - dwtime ] and [ fig - ncross ] , all the singularities of the dwell time function are contained in the domain between @xmath33 and @xmath34 @xcite . above @xmath35 , all the trajectories escape downwards , the simplest ones making only one crossing with the @xmath2 axis , on the positive @xmath2 side ( fig . [ fig - traj1]h ) . approaching @xmath35 from" +"in ( * ? ? ? * hereafter mas11 ) we presented thermal model fits for @xmath6 main belt asteroids that were observed during the fully cryogenic portion of the wide - field infrared survey explorer ( wise , * ? ? ? * ) mission , which ran from 7 january 2010 to 6 august 2010 . sensitivity to solar system objects was enabled by the neowise augmentation to the wise mission @xcite which provided capability for processing and archiving of single - frame exposures and detection of previously known and new asteroids and comets . on 6 august 2010 the hydrogen ice in the outer cryogen tank was exhausted and the telescope began to warm up , resulting in an almost immediate loss of the w4 ( @xmath7 m ) channel and a decreasing sensitivity in w3 ( @xmath8 m ) beginning the 3-band cryo portion of the mission . on 29 september 2010 the hydrogen ice in the inner cryogen reservoir , used to cool the detectors , was exhausted and the w3 channel was lost . from 29 september 2010 to 1 february 2011 , wise continued to survey the sky in the neowise post - cryo survey phase @xcite , searching for new near - earth objects ( neos ) and completing the survey of the largest main belt asteroids ( mbas ) using the two shortest bandpasses : w1 ( @xmath9 m ) and w2 ( @xmath3 m ) . mbas have temperatures of @xmath10k , depending on their distance from the sun and surface properties . this places the peak of their blackbody flux near @xmath11 m . during the fully cryogenic portion of the wise mission the w3 bandpass straddled this peak and was the primary source of data used for identification and analysis of the thermal emission from mbas . for objects detected during the 3-band cryo portion of the mission we used the w3 data to constrain the thermal emission , and thus the diameter , of the objects as the telescope warmed up , the integration times in w3 were shortened to prevent saturation of the detectors from the increasing thermal emission of the telescope @xcite , resulting in a decrease in sensitivity to sources in the bandpass . during the post - cryo survey only w1 and w2 were operational : for mbas w1 was sensitive solely to reflected light , while w2 was a blend of reflected and emitted flux dictated by the object s physical and orbital parameters ( e.g. distance to sun at the time of observation , surface temperature , albedo , etc . ) . in this work , we present preliminary thermal model fits for 13511 main belt asteroids observed during the 3-band cryo phase of the wise survey and the neowise post - cryo survey . during the fully cryogenic portion of the survey , detectability of most minor planets was dominated by their thermal emission and so was essentially independent of their albedo @xcite . however , the post - cryo survey data at @xmath9 m and @xmath3 m are a mix of reflected and emitted light . thus detectability is strongly coupled to albedo . additionally , objects with lower temperatures will have a smaller thermal emission component to their flux in the w2 band , resulting in a less accurate estimate of diameter . in general , diameter fits using either the 3-band cryo or the post - cryo survey data will typically have larger errors and lower precision than fits from the fully cryogenic survey given in mas11 , though they still provide useful information about the observed population of mbas . one of the drivers for completing the neowise survey of the inner main belt after the cryogen was exhausted was to have a complete census of the largest asteroids , particularly those that may be members of asteroid families . having this list allows us to constrain the mass of the pre - breakup body and more precisely model the age of the family @xcite . we present in this work preliminary albedos and diameters for objects observed during the 3-band cryo and post - cryo survey and discuss the accuracy of these values because these fits use data processed with the preliminary survey calibration values . future work by the neowise team will include second - pass processing of the raw data with finalized calibration values as well as extraction of sources at lower signal - to - noise that will precede a final release of albedos and diameters . in mas11 we focused our analysis on data taken during the fully cryogenic portion of the wise mission . for this work , we analyze the 3-band cryo and post - cryo survey observations taken by wise as part of the neowise survey . observations obtained between modified julian dates ( mjds ) of 55414 and 55468 are available in the 3-band cryo single - exposure database , served by the infrared science archive ( irsa ) . post - cryo data , spanning a mjd range of 55468 to 55593 , are archived in the neowise preliminary post - cryo database and also served by irsa . data from the 3-band cryo survey were released to the public on 29 june 2012 and preliminary data from the neowise post - cryo survey were released to the public on 31 july 2012 . we note that the post - cryo survey data have only undergone first - pass processing , and users are strongly encouraged to consult the explanatory supplement @xcite associated with the database . we follow the same method as described in mas11 to acquire detections of mbas that have been vetted both by our internal wise moving object processing system ( wmops ; * ? ? ? * ) and by the minor planet center ( mpc ) . this includes the use of the same quality flag settings from the pipeline extraction for cleaning of detections before thermal fitting as discussed in mas11 . of the 14638 objects observed by wise between mjds 55414 and 55593 , 13511 mbas had data of sufficient quality to perform thermal model fits . due to the nature of wise s orbit and the synodic period of mbas , approximately half of the objects observed during the 3-band cryo and post - cryo survey had also been observed earlier during the fully cryogenic survey . we use these overlap objects as standards to evaluate the accuracy of the thermal model fits using these data ( see section [ sec.overlap ] ) . while in some cases extremely irregularly shaped slow - rotating objects may show significant changes in projected area between epochs and thus large variations in both emitted and reflected flux , this is expected to be a small fraction of all objects observed and only to add a small component of random error to the comparison @xcite . following the procedure discussed in mas11 , we use a faceted neatm thermal model to determine the diameter and albedo of the mbas observed after the outer cryogen tank was exhausted . in most cases we only have thermal emission data in a single band , and so we are forced to assume a beaming parameter for the models . we use a beaming parameter of @xmath12 , based on the peak of the distribution for mbas given in mas11 . our measured flux in w2 is typically dominated by thermal emission , however the reflected component of the w2 flux will influence our models . in order to remove the reflected component from the measured w2 flux , we need to determine the optical geometric albedo ( @xmath13 ) and assume a ratio between the near - ir ( nir ) and optical albedos . in mas11 we were able to fit this ratio for objects with with observations in @xmath14 and/or @xmath15 as well as @xmath16 and @xmath17 , however we can not do this for the post - cryo survey data . following the best - fit value from mas11 , for those objects we assume a nir / optical reflectance ratio of @xmath18 . in all cases , we also assume that the reflectivity in w1 is identical to that in w2 ( @xmath19 ) . for objects with very red spectral slopes this may not necessarily be a good assumption ( cf . * ; * ? ? ? * ) however without additional data ( e.g. spectral taxonomy ) it is impossible to disentangle these two values for this dataset . to determine optical albedo we used the @xmath4 absolute magnitude and @xmath20 slope parameter given in the minor planet center s mpcorb file , and updated using other databases following mas11 . we note that recent work has shown that these @xmath4 values may be systematically offset in some magnitude ranges by up to @xmath21mags when comparing predicted and observed apparent magnitudes @xcite . this will affect the albedos that we calculate for the asteroids presented here , which in turn will change the relative contribution of emitted and reflected light in w2 . unlike the results presented in mas11 , where the diameter determination is independent of the optical @xmath4 measurement , any future revision to the measured @xmath4 values will require a refitting of the thermal models and will likely result in an change in modeled diameter . @xcite showed a comparison between the thermal fits performed with the post - cryo survey data and non - radiometrically determined diameters for a range of neos and mbas to derive a relative accuracy of @xmath0 on diameter and @xmath1 on albedo . as a parallel check we have taken objects that were observed both before and after the exhaustion of the outer cryogen reservoir and compared the diameters and albedos found here to those values given in mas11 . of the fits presented here , 7222 unique objects also appeared in the fully cryogenic observations that were presented in mas11 . of these , 2844 were observed during the 3-band cryo phase of the survey and 4403 were observed during the post - cryo survey ( note that 25 objects appeared in all three phases of the survey ) . for all objects seen in both the post - cryo survey and in the fully cryogenic 4-band survey , we have refit the 4-band cryo data using only the w1 and w2 measurements as a way of differentiating changes in the quality of fit due to the loss of w3 and w4 sensitivity from changes due to the different observing circumstances . the results of this test are shown in figure [ fig.refit ] . we include a running box average of the data in order to assess the population trends , which bins by 100 objects , in steps of 20 . in general these tests follow the expected one - to - one relationship , with the exception of the comparison of the 2-band and 4-band fits of the fully cryogenic data ( figure [ fig.refit]b ) , which deviates at both high and low albedos , and effect that was also observed for the neos in the post - cryo survey data by @xcite . @xcite have shown that high albedo objects tend to have optical / nir reflectance ratios of @xmath22 , while objects with low albedos tend to have reflectance ratios of @xmath23 ( though d - type objects deviate from this trend and have very large reflectance ratios ) . as we use a fixed reflectance ratio of @xmath24 , low albedo objects with w1 measurements will have a final fitted @xmath13 below the true value , while high albedo objects will have a @xmath13 slightly above , which corresponds to the twist observed in figure [ fig.refit]b . ) while the right column shows the comparison of the visual" +"broadband molecular line surveys are an effective tool for investigating the rich molecular inventory of star - forming regions@xcite . from detailed analyses of the spectral signatures of molecular clouds , their chemical abundances and physical properties ( e.g. temperature and density ) can be determined . the derived parameters can then be used to test and guide models of the source and develop our understanding of the physics and chemistry of the interstellar medium . these surveys are often made available to the public , which allow for other researchers to pursue more detailed investigations or to search for new molecular species in the data . a number of new radio astronomical observatories , both single - dish telescopes and interferometeric arrays , have recently begun operations that offer significant advances in bandwidth and sensitivity over older facilities . these new observatories will lead to a dramatic increase in the number of publicly available spectral surveys in the coming years . developing strategies to aid in the analysis and interpretation of these spectra , therefore , is an important goal in the field of astrochemistry . the large number of data channels associated with these surveys necessitates efficient methods for modeling and visualization of the data and results , as the spectrum should be fit globally characterizing all molecules simultaneously , rather than one at a time , and across the full survey bandwidth . millimeter and submillimeter spectra of chemically rich regions are characterized by a dense line forest at lower signal levels , made up largely of features from complex organics , which emit at many frequencies due to their large partition functions . many features therefore consist of blends that contain contributions from several molecules . once the spectral signatures of known molecules are characterized down to the noise limit , new species , which can be hidden in the spectrum by the features of molecules that emit more strongly , can be identified . this manuscript presents early results from a spectral survey toward sagittarius b2(n ) acquired using the heterodyne instrument for the far infrared ( hifi)@xcite aboard the herschel space observatory@xcite . sgr b2(n ) has the greatest observed chemical complexity of any molecular cloud in our galaxy , and a large fraction of the @xmath0170 molecules detected thus far in the interstellar medium@xcite were first detected in this source . this region has been the target of a number of broadband spectral surveys using ground - based observatories in the centimeter and millimeter wavelength regions@xcite . hifi is a high - resolution spectrometer with continuous coverage from 4801250 ghz and 14101910 ghz . most of this frequency range is inaccessible from the ground due to atmospheric absorption , so hifi offers a new look into a well - studied molecular source . additionally , by providing a census of which molecules are emitting in each frequency range , this survey can be used to aid in characterizing the submillimeter spectra of other molecular clouds . we present an analysis of the emission spectrum of methanol in this spectrum , which is detected through a large number of transitions ranging widely in frequency and excitation energy . this data set serves as an example of the herschel legacy spectral surveys that we expect will be highly useful to the astronomical community in the coming years . the observations reported here were acquired as part of the herschel observations of extra - ordinary sources ( hexos ) guaranteed time key program@xcite . the hexos program consists primarily of complete hifi surveys of five sources within the sagittarius b2 and orion star - forming regions : sgr b2(n ) , sgr b2(m ) , orion kl , orion s , and the orion bar . the sgr b2(n ) observations presented in this manuscript ( hifi bands 2b , 3a , and 3b ) were acquired on 1617 september 2010 using the wide band spectrometer ( wbs ) with a spectral resolution of 1.1 mhz , pointed towards the sgr b2(n ) hot core with coordinates @xmath1 and @xmath2 . hifi is a double sideband ( dsb ) spectrometer , and each frequency was observed with a redundancy of 8 ( i.e. , with eight different local oscillator settings ) in order to eliminate ghost transitions in the spectrum . data reduction was performed using version 8.0 of the herschel interactive processing environment ( hipe)@xcite . after standard pipeline processing and spur removal , the continuum was fit and removed . strong lines ( with line minus continum antenna temperature greater than 10 k ) were removed and flagged , and the _ dodeconvolution _ task in hipe was performed on the data sets both with and without the strong lines included . the strong lines were then added back into the deconvolved single - sideband ( ssb ) spectra , along with the fit continuum . spectra were obtained in both instrumental polarizations , which in the figures presented here were averaged together to improve the signal - to - noise ratio . no channel weighting or gain correction were included in the data reduction . all of the figures presented here are of deconvolved ssb spectra , smoothed to a velocity resolution of @xmath00.7 km / s . the deconvolved spectra were modeled using xclass@xcite , which accesses the cdms@xcite and jpl@xcite spectral databases . this software makes the local thermodynamic equilibrium ( lte ) approximation , which assumes that all of the energy level populations for a given spatial component can be described by a boltzmann distribution . this approach is a necessary first step for large - bandwidth spectral analyses such as these ; a wide variety of programs that go beyond the lte approximation are available , but are significantly more computationally intensive to implement . additionally , for many of the molecules observed in this spectrum , especially the more complex molecules ( with complex "" here being defined as having six or more atoms@xcite ) that make up a large fraction of the line density , rates for collisional excitation by h@xmath3 , necessary to solve for statistical equilibrium between radiative and collisional processes , either have not been calculated , or the rates available in the literature do not cover the energy or temperature range observed in surveys ( especially for sub - mm / far - ir surveys such as with hifi ) . the lte approximation is a good one in the limit of dense gas , as is seen in the sgr b2(n ) hot core ( @xmath4h@xmath5 @xmath6)@xcite . in figure 1 we show a portion of the hifi spectrum toward sgr b2(n ) , demonstrating the molecular diversity seen in this source . panel ( a ) shows the spectrum from 714801 ghz ( band 2b of hifi ) , which represents 7% of the total spectral coverage . earth s atmosphere is opaque in most of this band due to the water transition at 752 ghz . a large number of features are observed , both in emission and in absorption against the source continuum , which in this frequency region arises from thermal emission from dust . the molecular carriers of the strongest features are identified . methanol is the only complex organic to have strong features ( @xmath7 k ) in this band ; this molecule is observed to have high line density in many surveys of dense molecular clouds due to its high abundance and complex asymmetric top spectrum , which make it a common tool with which to constrain the physical structure of dense molecular clouds@xcite . panel b shows a 3 ghz subset of this spectrum ( the region indicated with a dashed box in panel a ) , with molecule assignments based on our preliminary modeling labeled . it can be seen that , in addition to methanol , seven other molecules ( including complex species like dimethyl ether , ethanol , and ethyl cyanide ) have features detected in this frequency range . where more than one molecule has been listed in the assignment for a particular feature , our model calculates that both ( or all ) molecules have features that contribute substantially to the flux of the observed feature . each of the species identified in this figure has been detected through a large number of transitions in this survey . to date we have identified approximately 40 molecules , which range in size from light hydrides ( e.g. water , ammonia ) to complex molecules such as methanol , dimethyl ether ( ch@xmath8och@xmath8 ) , and methyl formate ( hcooch@xmath8 ) . most molecular features are attributed to the sgr b2(n ) core ; the observed central velocities and linewidths vary from molecule to molecule due to different spatial distributions and excitation , but for most molecules the dominant component has a central velocity of + 64 km / s and a linewidth of @xmath07 - 10 km / s , as in previous analyses of this source@xcite . additionally , some simpler molecules are found to have features arising from line - of - sight clouds with different velocity shifts , as have been previously measured toward this source@xcite . the full analysis of this spectrum is currently in progress , and will be presented in a future publication . while most of the strongest features in this survey are readily identified , making confident line identifications of weaker transitions is challenging due to the combination of baseline excursions ( which are common at the @xmath00.1 k level ) and line blending . many of the unidentified lines are likely due to transitions of molecules that are included in the full - band model , but are currently not in the spectral catalogs . laboratory work to identify these transitions , which are due to vibrationally excited states , isotopologues , or other weak features , is needed , and is being undertaken for some abundant complex species@xcite . nevertheless , particularly for complex species with high line densities , it is possible to make confident identifications of catalogued transitions down to the noise floor , if a large number of transitions from each molecule are observed with consistent kinematic parameters and intensities based on modeling , and no lines predicted by the model to be present are missing . in recent years several new weakly emitting complex molecules have been identified in sgr b2(n ) at millimeter wavelengths with this approach@xcite . figure 2 shows an example of the lte modeling procedure and weak line identification using the spectrum of methanol . panel a shows a strong q - branch which has been used to fit the parameters of the lte model , particularly rotational temperature and column density . a key advantage to bands like this one is that a large number of lines are found in a small frequency range , so that frequency - dependent effects such as beam dilution and dust absorption do not affect the relative intensities between transitions . as the transitions span a wide range in lower - state energy , from 90.9 @xmath9 for the @xmath10 transition at highest frequency in the plot ( 835003.87 mhz ) to 511.5 @xmath9 for the @xmath11 transition at lowest frequency ( 830720.59 mhz ) , this band allows for the rotational temperature to be well constrained . the best - fit lte model , which was refined using the full hifi spectrum of methanol , is overplotted . this model predicts that @xmath02000 lines of methanol present in the spectral catalogs have intensities greater than 0.2 k ( including transitions from @xmath12ch@xmath8oh , @xmath13 and @xmath14ch@xmath8oh , @xmath15 ) . two components are required to achieve a satisfactory fit to the methanol emission spectrum , the parameters of which are presented in table 1 ; we note that while this model is fairly successful" +"the standard thin accretion disk model @xcite has been widely applied to x - ray binaries and active galactic nuclei . due to the basic assumption of the energy balance between the viscous heating and the radiative cooling , such a model was known to be invalid for super - eddington accretion case , where the advective cooling is probably significant . instead , the slim disk model @xcite was introduced to describe super - eddington accretion disks . however , there exists some conflict between the theory and the observation . the theory predicts that the advection is negligible for @xmath1 ( e.g. , * ? ? ? * ; * ? ? ? * ) , where @xmath2 is the eddington luminosity , which indicates that the standard disk model should be valid up to @xmath2 . on the contrary , some works on the black hole spin measurement showed that the standard disk model is likely to be inaccurate for @xmath3 ( e.g. , * ? ? ? * ) . moreover , even the recent general model for optically thick disks ( e.g. , * ? ? ? * ; * ? ? ? * ) , which unifies the standard thin disk and the slim disk , could not help to obtain a self - consistent spin parameter for @xmath3 ( e.g. , * ? ? ? * ) . in our opinion , the above conflict may be resolved if the vertical structure is well incorporated . most previous works on accretion disks focused on the radial structure in cylindrical coordinates ( @xmath4 , @xmath5 , @xmath6 ) . for the vertical structure , however , a simple well - known relationship @xmath7 "" or @xmath8 "" was widely adopted , where @xmath9 is the half - height of the disk , @xmath10 is the sound speed , and @xmath11 is the keplerian angular velocity . such a relationship comes from the vertical hydrostatic equilibrium with two additional assumptions . one is the approximation of gravitational potential : @xmath12 , and the other is a one - zone approximation or a polytropic relation @xmath13 in the vertical direction ( e.g. , * ? ? ? * ) , where @xmath14 is the total ( gas plus radiation ) pressure and @xmath15 is the density . obviously , the above assumptions work well for geometrically thin disks , but may be inaccurate for the mass accretion rate @xmath16 approaching the eddington one @xmath17 , for which the disk is probably not thin . consequently , the relationship @xmath8 "" may be invalid for @xmath18 . without the potential approximation , our two previous works investigated the geometrical thickness of accretion disks and the validity of the relationship @xmath8 "" . @xcite adopted the explicit gravitational potential in cylindrical coordinates and found that the above relationship is inaccurate for @xmath18 , and therefore the disk can be geometrically thick . @xcite took spherical coordinates to avoid the approximation of gravitational potential , and found that an advection - dominated accretion disk is likely to be quite thick . in these two works , however , the polytropic relation is still adopted in the vertical direction , which takes the place of the energy balance per unit volume between the viscous heating and the advective cooling plus the radiative cooling . the validity of such a polytropic relation , however , remains questionable , in particular for large @xmath16 due to dominant radiation pressure . the purpose of this paper is to revisit the vertical structure of radiation pressure - supported disks by taking into account the local energy balance and to study the variation of energy advection with mass accretion rates . the paper is organized as follows . equations and boundary conditions are derived in section 2 . a global view of the solutions in the @xmath19-@xmath20 diagram is presented in section 3 . for a typical radius @xmath21 , the vertical structure and the energy advection are investigated in section 4 . the two - dimensional solutions and the convective stability are studied in section 5 . summary and discussion are made in section 6 . we consider a steady state axisymmetric accretion disk in spherical coordinates ( @xmath20 , @xmath22 , @xmath5 ) and use the newtonian potential , @xmath23 , where @xmath24 is the black hole mass . following @xcite , we assume @xmath25 for simplicity , which means a hydrostatic equilibrium in the @xmath22 direction . simulations , ( e.g. , * ? ? ? * figure 3 ) , however , revealed that @xmath26 will be significant for extremely high accretion rates such as @xmath27 . as shown in the following sections , our solutions mainly correspond to @xmath16 around @xmath17 . for such accretion rates , the validity of @xmath25 remains a question . the basic equations of continuity and momentum take the forms ( e.g. , * ? ? ? * ) : @xmath28 @xmath29 @xmath30 @xmath31 where @xmath32 and @xmath33 are respectively the radial and azimuthal velocity , @xmath34 and @xmath35 are respectively the radial and vertical radiation flux , @xmath36 is the gas pressure , @xmath37 is the opacity of electron scattering , and @xmath38 is the @xmath39 component of the viscous stress tensor , @xmath40 . following the spirit of @xmath41 stress prescription , we assume the kinematic viscosity coefficient @xmath42 , where @xmath10 is the sound speed defined below ( equation ( 7 ) ) , and @xmath43 is the keplerian velocity . we would stress that , even though the @xmath41 stress prescription has been widely adopted for theoretical studies , simulations of magnetorotational turbulence have shown that the stress does not well scale locally with the pressure . for instance , the simulations on thin disks by a shearing box showed that , the time and box - averaged results are likely to support that the stress is proportional to the thermal ( gas plus radiation ) pressure ( e.g. , * ? ? ? * figure 3 ) . however , figure 16 of @xcite shows that the maximal thermal pressure is located on the equatorial plane , whereas figure 11 shows that the maximal stress is obviously not at the same place . these two figures reveal that the stress is not proportional to the pressure locally . in the present study , for simplicity , we will keep the local @xmath41 stress prescription for numerical calculation , which is a weak point of this work . the energy equation including gas and radiation is written as ( e.g. , * ? ? ? * ) @xmath44 = -p { { \mbox{\boldmath $ \nabla$ } } } \cdot { { \mbox{\boldmath $ v$ } } } - { { \mbox{\boldmath $ \nabla$ } } } { { \mbox{\boldmath $ v$ } } } { { \mbox{\boldmath $ : $ } } } { { \mbox{\boldmath $ p$ } } } - { { \mbox{\boldmath $ \nabla$ } } } \cdot { { \mbox{\boldmath $ f$ } } } + \phi_{\rm vis } \ , \ ] ] where @xmath45 and @xmath46 are the internal energy density of the gas and the radiation , respectively . @xmath47 is the radiation pressure tensor , @xmath48 is the viscous dissipative function , and the radiation flux @xmath49 is expressed as @xmath50 in this work , we focus on the region inside the photosphere , so we can take the well - known eddington approximation , i.e. , @xmath51 and the eddington tensor @xmath52 . since we only study the radiation pressure - supported disks , the gas pressure @xmath36 and the gas internal energy density @xmath45 will be dropped in our calculation . in order to avoid directly solving the partial differential equations , some assumptions on the radial derivatives ( @xmath53 ) are required . following the spirit of self - similar assumptions ( e.g. , * ? ? ? * ; * ? ? ? * ) , we adopt the following radial derivatives for @xmath10 and @xmath46 : @xmath54 where the sound speed @xmath10 is defined as @xmath55 based on the above two radial derivatives , the following four derivatives can be inferred from equations ( 1)-(7 ) : @xmath56 with all the above derivatives , we can remove the @xmath53 "" terms in equations ( 2 ) and ( 4)-(6 ) , and the following equations are then obtained from equations ( 2)-(6 ) : @xmath57 @xmath58 @xmath59 @xmath60 @xmath61 @xmath62 the seven equations , equations ( 7)-(13 ) , enable us to solve for the seven variables : @xmath32 , @xmath33 , @xmath10 , @xmath15 , @xmath46 , @xmath34 , and @xmath35 . there are two differential equations in this system . in addition , the position of the surface is unknown . thus , totally three boundary conditions are required to determine a unique solution . an obvious boundary condition on the equatorial plane is @xmath63 . however , this condition is not applicable for numerical calculation since it is automatically matched as indicated by equation ( 9 ) . combining equations ( 9 ) and ( 11 ) we can derive the following equation : @xmath64 an alternative boundary condition on the equatorial plane is then obtained from the above equation ( the left - hand side is zero thus the right - hand side should also be zero ) : @xmath65 the second boundary condition is a definition of the surface . we define the photosphere as the position above which the optical depth is around unity . the condition can be written as @xmath66 where @xmath67 ( @xmath68 ) is the polar angle of the photosphere . the third condition is related to the mass accretion rate : @xmath69 in our calculation we set @xmath70 , @xmath71 @xmath72g@xmath73 , and @xmath74 , where the value of @xmath41 is taken from recent simulations @xcite . the eddington accretion rate is expressed as @xmath75 , where @xmath76 is a radiative efficiency of the flow . we choose @xmath77 since it is comparable to the schwarzschild black hole efficiency of 0.057 . the dimensionless accretion rate is defined as @xmath78 . with the equations and boundary conditions in section 2 , we can numerically derive the @xmath22-direction distribution of physical quantities for a given @xmath19 at a certain radius @xmath20 . the radiation pressure - supported disk solutions in the @xmath19-@xmath20 diagram are shown in figure 1 , where @xmath79 is the schwarzschild radius . the parameter space is divided into three regions by two parallel solid lines , roughly with @xmath80 . the region above the upper solid line is denoted by outflow "" , where we can not find solutions . no solution exists probably due to the assumption of @xmath81 in advance . in our view , a real flow located in this region may have @xmath82 and the inflow accretion rate may decrease inward . the physical understanding could be that , for high accretion rates and particularly for the inner radii , the viscous dissipation may be sufficiently large such that the radiation pressure is too strong to be balanced by the gravitational force . thus , outflows may be driven by the radiation pressure and the inflow @xmath19 drops inward . on the other hand , simulations of supercritical accretion flows ( e.g. , * ? ? ? * figure 6 ) showed that the inflow accretion rate roughly follows the @xmath80 relationship for @xmath83 at @xmath84 ( corresponding to @xmath85 due to the definition of @xmath17 with @xmath77 ) . the slope of the upper solid line in figure 1 , which may be regarded as maximal accretion rates due to our calculation , agrees well with the slope in the above simulations . the region under the lower solid line is denoted by gas pressure "" , where no" +"the field of photonic crystals , driven by its importance for applications in various areas of photonics , has attracted considerable attention during last the ten years @xcite-@xcite . the one - dimensional _ resonant bragg grating _ @xcite-@xcite or _ resonantly absorbing bragg reflector _ @xcite-@xcite has been of particular interest . an idealized model of a resonant bragg grating often considers a linear homogeneous dielectric host medium containing an array of thin films with resonant atoms or molecules . the thickness of each film is much less than the wavelength of the electromagnetic wave propagating through such a structure . the dynamics of ultrashort light pulses in the gratings containing films embedded with two - level atoms of the grating has been studied in @xcite-@xcite . the transition frequencies of atoms are assumed to be near the bragg frequency . light interaction with such gratings was described by equations of reduced maxwell - bloch type . this work demonstrated self - induced transparency in these gratings and the existence of the solitary waves in such structures @xcite . it was also shown @xcite that bright as well as dark solitons can exist in the spectral gap . progress in nanofabrication of novel optical materials has allowed the design of metal - dielectric nanocomposite materials , which have the ability to sustain nonlinear plasmonic oscillations . an example of such a material is a dielectric with embedded metallic nanoparticles @xcite-@xcite . in this paper we consider ultrashort pulse interaction with bragg structures containing thin films with metallic nanoparticles . the bragg resonance frequency and carrier wave frequency in our considerations are assumed to be close to the plasmonic resonance frequency of the nanoparticles . losses in realistic plasmonic oscillations are of considerable importance . here we consider an idealized case , wherein pulse duration is much shorter than the characteristic time of losses , so that the effects of losses can be neglected . in the limit of the slowly - varying envelope approximation we derive governing equations for two counter - propagating electromagnetic waves interacting with plasmonic oscillation - induced medium polarization . this system of equations represents the two - wave maxwell - duffing type model . we find exact solitary wave solutions of this system and , via computer simulations , analyze stability of these solutions . we consider a grating consisting of an array of thin films which are embedded in a linear dielectric medium . in our derivation of the governing equations we follow @xcite-@xcite , wherein bragg resonance arises if the distance between successive films is @xmath0 , @xmath1 . it was shown in @xcite that counter - propagating electric field waves @xmath2 and @xmath3 in the slowly - varying envelope approximation satisfy the following system of equations : @xmath4 where @xmath5 is the mismatch between the carrier wavenumber and the bragg resonant wavenumber . the description of the evolution of material polarization in the slowly - varying amplitude approximation requires modeling of the thin films response to an external light field . the dielectric properties can be attributed to plasmonic oscillations , which are modeled by lorentz oscillators . the simplest generalizations of this model include anharmonicity of plasmonic oscillations @xcite . in this paper we consider an array of thin films containing metallic nanoparticles which have cubic nonlinear response to external fields @xcite . the macroscopic polarization @xmath6 is governed by the equation @xmath7 where @xmath8 is plasma frequency and @xmath9 is the transition frequency between energy levels resulting from the dimensional quantization . losses of the plasmonic oscillations are taken into account by the parameter @xmath10 . it is assumed that the duration of the electromagnetic pulse is small enough that dissipation effects can be neglected . starting from the slowly - varying envelope approximation , standard manipulation leads to @xmath11 terms varying rapidly in time , which are proportional to @xmath12 , are neglected . in this equation @xmath13 is the electric field interacting with metallic nanoparticles . in the problem under consideration we have @xmath14 . due to the limitations of nanofabrication , the sizes and shapes of nanoparticles are not uniform . in practice , deviation from a perfectly spherical shape has a much larger impact on a nanoparticle s resonance frequency than does variation in diameter . this shape variation causes a broadening of the resonance line . the broadened spectrum is characterized by a probability density function @xmath15 of deviations @xmath16 from some mean value @xmath17 . when computing the total polarization , all resonance frequencies must be taken into account . the contributions of the various resonance frequencies are weighted according to the probability density function @xmath15 ; the weighted average is denoted by @xmath18 in equations ( [ 21.1]),([21.2 ] ) . in what follows , @xmath19 denotes the refractive index of the medium containing the array of thin films , and @xmath20 is the effective density of the resonant nanoparticles in films . the effective density is equal to @xmath21 , where @xmath22 is the bulk density of nanoparticles , @xmath23 is the width of a film , and @xmath24 is the lattice spacing . we study a medium - light interaction in which resonance is the dominant phenomenon . as such , the length of the sample is smaller than the characteristic dispersion length . in this case the temporal second derivative terms in equations ( [ 21.1],[21.2 ] ) can be omitted . the resulting equations are the two - wave maxwell - duffing equations . they can be rewritten in dimensionless form using the following rescaling : @xmath25)\mathcal{p},\ ; \zeta = ( \omega _ { p}/2c)x,\ ; \tau = t / t_{0}.\ ] ] here @xmath26 , while @xmath27 is a characteristic amplitude of counter - propagating fields . in dimensionless form , the two - wave maxwell - duffing equations read @xmath28 where @xmath29 is a dimensionless coefficient of anharmonicity , @xmath30 is the dimensionless mismatch coefficient , @xmath31 is the dimensionless detuning of a nanoparticle s resonance frequency from the field s carrier frequency . in a coordinate system rotating with angular frequency @xmath32 , @xmath33 equations ( [ svepequations ] ) become @xmath34 further simplification of the system ( [ rotatingframe ] ) can be achieved by introducing new variables @xmath35 which allow decoupling of one equation from the system of three equations . in these new variables the polarization @xmath36 is coupled with only one field variable . simple transformations give @xmath37 as one can see , we have a coupled system of equations for @xmath38 and @xmath36 . we consider localized solitary wave solutions of ( [ 26.3])-([26.3.2 ] ) in the limit of narrow spectral line @xmath39 , where @xmath40 and @xmath41 are spectral widths of a signal and spectral line @xmath42 . in this case the spectral line can be represented as a dirac @xmath32-function : @xmath43 . equations ( [ 26.3.1 ] ) , ( [ 26.3.2 ] ) can then be re - written as follows : @xmath44 scaling analysis of this system shows that solitary wave solutions can be represented as @xmath45 here @xmath46 is velocity of the solitary wave , @xmath47 is a scale - invariant parameter in a coordinate system moving with the solitary wave , and functions @xmath48 , @xmath49 satisfy the following system of equations : @xmath50 the only dimensionless parameter which remains in the system is @xmath51 which characterizes the deviation of carrier frequency from the plasmonic frequency @xmath52 and the bragg resonance frequency @xmath53 . the system of ordinary differential equations ( [ ode ] ) has integral of motion for pulse - like solutions decaying as @xmath54 @xmath55 this allows the following parametrization of solutions : @xmath56 where @xmath57 , @xmath58 , and @xmath59 are real - valued functions satisfying @xmath60 if we set @xmath61 , then we have @xmath62 taking into account equations ( [ amplitudephasecompact ] ) we have the conservation law @xmath63 substituting ( [ secondconsevationlaw ] ) into the second equation of ( [ amplitudephasecompact ] ) and subsequent integration gives the following expression for @xmath57 : @xmath64 where @xmath65 . the right - hand side is positive real - valued for all @xmath66 if @xmath67 . using the conservation law ( [ secondconsevationlaw ] ) we obtain an expression for @xmath68 : @xmath69 now we integrate @xmath70 and find @xmath71 finally , we determine @xmath59 : @xmath72 this pulse exists only if value of the parameter @xmath73 is inside the interval @xmath67 . the maximal value of the amplitude of this solitary solution is @xmath74 the phases @xmath58 and @xmath59 are nonlinear . their behavior is asymptotically linear as @xmath75 . if @xmath76 , then the limiting values of the phases satisfy @xmath77 ) , ( [ 26.3.1 ] ) and conditions as @xmath78 , one can show that @xmath79 we are interested in the energies of the dimensionless fields @xmath80 , @xmath81 , and of the polarization @xmath36 . @xmath82 finally , for electric fields @xmath83 and for polarization @xmath84 we have @xmath85 the energy of a solitary wave is @xmath86 finally we have the energies of electric fields and polarization @xmath87 ratios of energies in different fields as well as polarization have the following form @xmath88 therefore , energy partitioning is determined solely by the parameter @xmath46 , which is a dimensionless combination of main system parameters . the shape and phase of the incident optical pulse are controllable in a real experimental situation . to model pulse dynamics in the bragg grating it is natural to consider asymptotic mixed initial - boundary value problem for equations ( [ svepequations ] ) . we define initial conditions as @xmath89 with no incident field at the right edge of the sample , and with incident field at the left edge defined as follows : @xmath90 , \;\ ; \theta = \arctan\left(\tanh\left[1.5\left(\tau - 3.0\right)\right ] \right).\end{aligned}\ ] ] in our case the spatial simulation domain was chosen as @xmath91 $ ] . parameters @xmath92 and @xmath93 were given values @xmath94 as one can see , we gave the initial pulse the same configuration of phase in a topological sense as would be found in a solitary wave solution . this point is important , because otherwise the phase difference can not relax to the symmetry of the stationary wave which is revealed in ( [ phi_expression ] ) . as a result , in numerical simulations it is difficult to achieve solitary wave type dynamics of the pulse without the proper phase configuration of the incident pulse . the second field boundary condition was set to be @xmath95 in the first experiment we injected a pulse , which is relatively close to the solitary wave solution . the results are shown in figs . [ f1.1.map]-[q.1.map ] , which clearly represent two stages of the pulse evolution . surface.,width=384 ] surface.,width=384 ] surface.,width=384 ] in the first stage ( @xmath96 ) of evolution we observed fast excess energy damping in radiation of quasi - linear waves in both directions and relaxation to a solution roughly similar to the stationary solution . then we observed a stage of pulse shape refinement ( @xmath97 ) with consequent propagation of the solution very close to ( [ r_solution ] ) . the lower part of the figure [ q.1.map ] shows the creation of multiple spatially frozen `` hot spots '' of the medium polarization . in these hot spots the energy of oscillations is arrested in the grating . this `` stopping light '' phenomenon is due to self - modulation of the medium polarization caused by nonlinear effects which we shall discuss in more detail elsewhere . during the second experiment we used a pulse of lower amplitude : @xmath98 , \nonumber \\ \theta & = & \arctan\left(\tanh\left[1.5\left(\tau - 3.0\right)\right ] \right).\end{aligned}\ ] ] results are represented in figs . [ f1.2.map]-[q.2.map ] . surface.,width=384 ] surface.,width=384 ]" +"the study of collective flow in nuclear collisions at high energies has been attracting increasing attention from experimentalists @xcite . this is partly because recent progress has been made in the development of new techniques suitable for flow studies at high energies @xcite . instead of studying @xmath0 , in these new methods a fourier expansion of the azimuthal distribution of particles is used in which the first harmonic coefficient , @xmath1 , quantifies the directed flow and the second harmonic coefficient , @xmath2 , quantifies the elliptic flow . in some cases @xmath3 and @xmath4 were reported , which in modern terminology , are twice the square of the sub - event resolution . using these new techniques anisotropic flow has now been observed for heavy symmetric systems at both the ags and sps . at the ags the e877 collaboration pioneered the use of the fourier expansion method to measure @xmath1 and @xmath2 . they studied these quantities ( as well as @xmath5 ) from a calorimeter as a function of centrality in different pseudorapidity windows @xcite . then they studied nucleons as well as pions as a function of pseudorapidity for different centralities @xcite . using their spectrometer to identify particles while still obtaining the event plane from the calorimeter , they measured @xmath1 and @xmath2 as a function of @xmath6 for different rapidities and centralities @xcite . they also reported @xmath0 as a function of rapidity @xcite . in their latest papers they extended this study to light nuclei @xcite . the e802 collaboration studied @xmath0 for light nuclei in the target rapidity region using a forward hodoscope to determine the event plane @xcite . at the sps na49 first observed elliptic flow in a calorimeter study which reported @xmath4 as a function of centrality @xcite . wa98 reported @xmath3 as a function of centrality for protons and @xmath7 in the target rapidity region @xcite . they also studied @xmath0 in the target rapidity region @xcite . na45 used silicon drift detectors to study @xmath1 and @xmath2 as a function of pseudorapidity @xcite . na49 has presented a differential study of @xmath1 and @xmath2 as a function of @xmath6 and @xmath8 @xcite and has also started to study the centrality dependence @xcite . also , the importance of flow for other measurements has just begun to be studied . for two particle correlations relative to the event plane the mathematical scheme has been worked out @xcite . some first results have been given by wa98 @xcite . also , for non - identical particles the correlation relative to the event plane has been discussed @xcite . anisotropic flow , in particular elliptic flow , in spite of the relatively small absolute value of the effect , contains very rich physics . in general words , it is very sensitive to the equation of state which governs the evolution of the system created in the nuclear collision . being such , anisotropic flow provides important information on the state of matter under the extreme conditions of the nuclear collision . the anticipated phase transition to qgp should have a dramatic effect on elliptic flow due to the softening of the equation of state . first it was pointed out in the pioneering work of ollitrault@xcite , who suggested elliptic anisotropy as a possible signature of transverse collective flow . within the hydro - dynamical model ollitrault analyzed the role of different equations of state and phase transitions on the final anisotropy . hung and shuryak @xcite suggested scanning with beam energy in order to look for the qcd phase transition . using their idea of the softest point in the equation of state combined with hydro - dynamical calculations , rischke @xcite predicted a dramatic drop in the elliptic flow signal at the corresponding beam energies ( in the original calculations this was at ags energies ) . sorge has shown@xcite that the elliptic flow is very sensitive to the pressure at maximum compression , which is the most interesting time in the system evolution . recent studies @xcite within the parton cascade model yield similar conclusions providing also the relation between the strength of the elliptic flow and parton - parton cross sections . recently , sorge also tried @xcite to combine the early system evolution in accordance to a qgp equation of state with a later hadron cascade . he looked at the centrality dependence of the elliptic flow in order to detect qgp production . summarizing this part , we would conclude that the effect of qgp should be seen in the anisotropic flow dependence on the energy of the colliding nuclei , or in the dependence on the centrality of the collision . if the situation would be such that a qgp is produced only in a small fraction of the collisions than fluctuations in flow would be one of the best observables for this effect . the formation of dcc in nuclear collisions could also result in an event anisotropy . it could be due to the anisotropic shape of the dcc domains @xcite or just to local fluctuations in the charged multiplicity , which should result in `` orthogonal '' flow in charged and neutral sectors @xcite . the very magnitude of anisotropic flow is sensitive to the degree of equilibration in the system . note that at present there is no calculation based on the hydro - dynamical picture which accounts for the experimentally observed values of the effect . this could have its origin in the obvious difficulties of hydrodynamic model calculations , but it could also indicate a non - applicability of the picture to nuclear collisions . the cascade models such as rqmd describe the data much better . from this point of view the analysis of elliptic flow in the collision - less and hydrodynamic limits performed in @xcite is very interesting . the hbt interferometry performed relative to the event plane @xcite becomes also extremely important at this point . does the system really expand in the reaction plane as prescribed by hydrodynamics ? simultaneous measurements of the anisotropic flow and the two - particle , identical as well as non identical @xcite , correlations in principle should answer this question . we must also mention the importance of anisotropic flow measurements to the vast variety of other measurements , which from first look have nothing to do with anisotropic flow . let us consider high @xmath6 particle production . it could be that the production mechanism ( hard parton scattering ) is very insensitive to the in - plane expansion , but that the rescattering of high @xmath6 partons is different in the different directions of particle emission due to the anisotropic geometry of the collision zone . this would lead to anisotropy in high @xmath6 particle production and gives another opportunity to study how it develops @xcite . another example is hbt measurements averaged over all orientations of particle emission . one would think that this does not require reaction plane measurements , but this is not really true . the mixed pair distribution usually used in the correlation function calculation can strongly depend on the relative orientation of the reaction plane of the events used to create the mixed pair . therefore one should have this information even in the case where the dependence of the hbt parameters on the reaction plane is not studied . the study of azimuthal anisotropy of unidentified charged hadrons needs the momenta of the particles but does not have any unusual requirements for calibrations , momentum resolution , acceptance , efficiency , two - track resolution , or two - track efficiency . however , for future analyses it would be good to have particle identification . the anisotropy in the azimuthal distribution of particles is often characterized by @xmath1 , @xmath2 and called directed and elliptic flow respectively . this anisotropy , especially @xmath2 , plays an important role in high energy nuclear collisions and is expected to be even more important at rhic energies @xcite . the azimuthal distribution of particles is described by a fourier expansion @xcite @xmath9\right),\ ] ] where @xmath10 is the true reaction plane angle . the reaction plane is defined by the beam direction and the impact parameter vector @xmath11 . in a given rapidity ( @xmath8 ) and @xmath6 interval the coefficients are determined by @xmath12 \rangle.\ ] ] similarly this fourier expansion can be done in coordinate space , where for a given rapidity and @xmath6 interval the coefficients are determined by @xmath13 \rangle\ ] ] where @xmath14 are the particle space coordinates at freeze - out . of course , these equations only apply to simulations where one knows @xmath10 . comparing the anisotropy coefficients in momentum space ( @xmath15 ) with the anisotropy coefficients in coordinate space ( @xmath16 ) as a function of @xmath6 helps us to understand the space - time evolution of nucleus - nucleus collisions @xcite . to study this space - time evolution at rhic , @xmath17 au+au collisions at @xmath18 = 200 @xmath19gev have been analyzed using the rqmd v2.4 model . [ vxrx_rqmd]a - d show the first harmonic both in momentum and coordinate space for nucleons and pions . for nucleons at mid - rapidity note the similarity in shape of @xmath1 versus @xmath8 and r@xmath20 versus @xmath8 . here 1a ) both the slopes of @xmath1 versus @xmath8 and r@xmath20 versus @xmath8 show a reversal of sign . this finds an explanation in a picture with strong ( positive ) space - momentum correlations , taking into account the correlation between nucleon stopping and the original position of the nucleons in the transverse plane @xcite . for pions , the rapidity dependence of @xmath1 is predominantly governed by rescattering on comoving nucleons [ vxrx_rqmd]e - h show @xmath2 for nucleons and pions . for both nucleons and pions @xmath2 is positive and is larger for particles with @xmath21 gev . particles acquire a large @xmath6 when they are produced by a hard collision ( which should not produce an event anisotropy ) or when they have a large number of soft collisions ( rescattering ) . the latter would explain the increase in @xmath2 and it explains why r@xmath22 goes from negative for nucleons integrated over all @xmath6 to positive for nucleons with large @xmath6 . collective flow and the coefficients @xmath1 and @xmath2 are usually associated with soft processes . however , the coefficients describe the event anisotropy and are not limited to only soft physics . at rhic energies hard processes become important . they happen early in the reaction and thus can be used to probe the early stage of the evolution of a dense system . during this time a quark - gluon plasma ( qgp ) could exist . associated with hard processes are jets . however , when the transverse energy of the jets becomes smaller it becomes increasingly difficult to resolve them from the `` soft '' particles . these jets with @xmath23 5 gev are usually refered to as mini - jets . at rhic energies it has been estimated that 50% of the transverse energy is produced by mini - jets @xcite . medium induced radiative energy loss of high @xmath6 partons ( jet quenching ) could be very different in a hadronic medium and a partonic medium . recently it was shown that this energy loss per unit distance , @xmath24 , grows linearly with the total length of the medium @xcite . for non central collisions the hot and dense overlap region has an almond shape . this implies different path lengths and therefore different energy loss for particles moving in the in - plane versus the out - plane direction . to study this anisotropy with respect to the reaction plane @xcite , @xmath25 au+au collisions at @xmath26 = 200 @xmath19gev have been generated" +"the understanding of confinement and , more generally , of the principles that govern the low energy dynamics in qcd is , perhaps , the most interesting unanswered question in the theory of strong interactions . the strongly coupled dynamics of the four dimensional non abelian gauge theories has so far proven to be forbiddingly complicated . a fruitful approach to cope with such situation can be to turn to simpler , more tractable models , that nevertheless capture at least some of the important features of the real theory . from this point of view , three dimensional non abelian gauge theories are of particular interest since they are , indeed , confining , and have a strong coupling dynamics . on the other hand they can be continuously deformed into the weak coupling region without encountering any phase transition . the prototypical case is the @xmath1 gauge theory with an adjoint higgs field - the georgi - glashow model . these weakly coupled theories are confining , just like their strongly coupled counterparts . here , however , confinement can be studied using semiclassical methods , as first done by polyakov for the @xmath1 case @xcite , and later on generalized to @xmath2 theories @xcite . a related feature of these models is that their spectra has a large gap between the light ( light ` photons ' ) and heavy ( heavy massive gauge bosons ) states . this makes the identification of the relevant low energy degrees of freedom relatively easy , and also allows one to construct the low energy effective lagrangian explicitly . it turns out that this effective lagrangian exhibits the confinement phenomenon in a very simple and straightforward way _ on the classical level_. in a nutshell , the natural degrees of freedom turn out to be magnetic vortex fields first introduced by thooft @xcite , and the confinement mechanism is realized as confinement of topological solitons for those vortex fields . the structure of the effective lagrangian is robustly determined by the spontaneously broken magnetic @xmath0 symmetry @xcite . this approach has been motivated by earlier work @xcite , it was advanced and formulated in @xcite , and further clarified in @xcite . it has also been argued in @xcite , that the same type of effective lagrangian remains valid in the strongly coupled limit of pure gluodynamics . in this situation , the components of the vortex field are naturally identified with the scalar and pseudoscalar glueballs , which according to lattice results are indeed the two lowest states in the spectrum of @xmath3 dimensional gluodynamics @xcite . the confinement mechanism for the strongly coupled regime remains , in this picture , essentially the same as for the weakly coupled phase . all previous work dealt exclusively with theories having no matter fields in fundamental representation . the purpose of this note is to address the question of what effect dynamical fundamental ` quarks ' have on this low energy structure . that that effect exists and must be nontrivial can be seen from one basic observation : in the presence of fundamental charges , the vortex field ( which is the effective low energy degree of freedom ) is no longer a local field . the effective lagrangian can not , therefore , be a simple local scalar theory as in @xcite . we will show below that , in the presence of fundamental matter , the magnetic @xmath0 in the effective lagrangian is _ gauged _ , the value of the gauge coupling being inversely proportional to the mass of the ( lightest ) dynamical quark . we will construct such an effective lagrangian , which moreover in the limit of the infinitely heavy quarks reduces to the effective theory of @xcite . the presence of fundamental quarks implies the existence of a conserved baryon number charge . we will see how this charge is represented in the low energy theory , and will study the structure of finite energy baryon states . quite surprisingly , we find that these states naturally have a bag - like structure . the value of the vortex field in the region of space which contains the quarks , is much lower than its value in the vacuum . the potential energy associated with this difference in the expectation values can also be naturally identified with the bag constant . the plan of this paper is the following . in section [ glue ] , we give a lightning review of the results of @xcite . we discuss the magnetic @xmath0 symmetry , its order parameter ( the vortex operator ) , and the structure of the effective lagrangian in pure gluodynamics . in section [ fund ] we explain the basic physics of the changes in this structure in the presence of the fundamental charges . in section [ low ] we show how to define the relevant low energy degrees of freedom , and how to construct the effective lagrangian in this case . in section [ baryon ] , we study the structure of the baryon states . finally we conclude in section [ discus ] with a short discussion . consider the pure su(n ) gauge theory in @xmath3 dimensions @xmath4 as was argued by thooft in @xcite , this theory possesses a global @xmath0 symmetry which is spontaneously broken in the vacuum . the explicit realization of this symmetry was found in @xcite . the generator of the @xmath0 group is ( up to a multiplicative constant factor ) the fundamental wilson loop along the spatial boundary of the system @xmath5 in @xcite , the conservation of @xmath6 was proved taking the pure gluodynamics limit of the georgi - glashow model . this , however , can also be shown directly by calculating the commutator of @xmath6 with the yang - mills hamiltonian @xmath7 : @xmath8=\lim_{c\to\infty}\oint_c dx_i { \rm tr } \left [ p e_i(x)\exp\{i\oint_{c(x , x ) } dy_ia^i(y)\ } \right ] \to_{c\to\infty}0 \;. \label{commutator}\ ] ] here , the integral in the exponential on the right hand side starts and ends at the point of insertion of the electric field . the vanishing of the commutator follows from the fact that it only involves electric fields at spatial infinity , and in a theory with a finite mass gap those fields should vanish at infinity . to dispel any doubt about the vanishing of this commutator we note that the situation is completely analogous to the commutator of any ` conserved charge ' which is defined as an integral of a local charge density @xmath9 the commutator of such a charge with a hamiltonian contains also a surface term , since the charge density @xmath10 never commutes with the hamiltonian density but rather gives a total derivative in the commutator . for a conserved charge , due to the continuity equation , this surface term is equal to the circulation of the spatial component of the current @xmath11=i\oint_c dx^ij_i\;.\ ] ] the vanishing of this term again is the consequence of the vanishing of the physical fields at infinity in a theory with a mass gap . when the charge is not conserved , the commutator contains also a bulk term in addition to the surface contribution . it is the absence of the bulk terms that is the distinctive property of a conserved charge . the same conclusion is reached if , rather than considering the generator of the algebra , one considers the commutator of the group element for either continuous or discreet symmetry groups . we see , therefore , that the commutator in ( [ commutator ] ) indeed tells us that @xmath6 is a conserved operator . next , a simple argument establishes that the magnetic @xmath0 symmetry is spontaneously broken in the vacuum if the wilson loop @xmath12 has an area law behaviour @xcite . the argument goes like this . the vev of @xmath12 is the overlap of the vacuum state @xmath13 with the state @xmath14 which is obtained from the vacuum by acting on it with @xmath12 . when acting on the vacuum state , @xmath12 performs the @xmath0 transformation at all points within the area @xmath15 bounded by the loop . if the vacuum wavefunction depends on the configuration of the @xmath0 non invariant degrees of freedom ( the state in question is not @xmath0 invariant ) the action of @xmath12 affects the state everywhere inside the loop . in the local theory with finite correlation length the overlap between the two states approximately factorizes into the product of the overlaps taken over the region of space of linear dimension of order of the correlation length @xmath16 @xmath17 where the label @xmath18 is the coordinate of the point in the center of a given small region of space . for @xmath18 outside the area @xmath15 the two states @xmath19 and @xmath20 are identical and therefore the overlap is unity . however for @xmath18 inside @xmath15 the states are different and the overlap is therefore some number @xmath21 smaller than unity . the number of such regions inside the area is obviously of order @xmath22 and thus @xmath23 the vev of @xmath12 then falls off as an area . conversely , if the vacuum is @xmath0 invariant , the wavefunction does not depend on the configuration of the non invariant degrees of freedom . the action of @xmath12 then alters the state only along the perimeter and @xmath12 has the perimeter law behaviour in the unbroken phase . thus the area law behaviour of the fundamental wilson loop is tantamount to the breaking of the magnetic @xmath0 symmetry in the vacuum of pure gluodynamics . the only requirement that this argument presupposes is the existence of * local * degrees of freedom which are non invariant under @xmath0 , or in other words the existence of a * local * order parameter . such an operator can indeed be constructed explicitly . this is the magnetic vortex creation operator @xmath24 @xcite,@xcite,@xcite . the defining property of @xmath24 is that it satisfies the following commutation relation with the spatial fundamental wilson loop @xmath25 @xmath26 where @xmath27 is the linking number of the curve @xmath28 and the point @xmath18 , or in other words , @xmath29 if @xmath30 , and @xmath31 if @xmath32 , where @xmath15 is the region of the plane bounded by @xmath28 . an explicit representation for @xmath33 is given by writing it as the operator that performs a ` singular gauge transformation ' @xmath34 here , the hypercharge generator @xmath35 is defined as @xmath36 the electric field is written in the matrix notation @xmath37 , with @xmath38 denoting the @xmath2 generator matrices in the fundamental representation , and @xmath39 is the hypercharge density due to gluons @xmath40 $ ] . the function @xmath41 is the planar angle of the vector @xmath18 . using gauss law @xmath42 this operator ( on the states that satisfy gauss law ) may be written in an alternative representation @xmath43 the integration here is along the branch cut in the definition of the planar angle @xmath44 , which is an infinite line that starts at the point @xmath18 and goes to infinity . there are two crucial properties of the definition eq.([v2 ] ) that insure that the operator @xmath24 is a local physical field : 1 . gauge invariance . the definition is not explicitly gauge invariant . nevertheless , one can show @xcite,@xcite that @xmath24 transforms a physical state into another physical state . that is to say that the matrix elements of @xmath24 between a physical and an unphysical state vanish . by physical state we mean a state which satisfies the non abelian gauss law . by virtue of this property the definition eq.([v2 ] ) can be used as long as the matrix elements of @xmath24 ( or any power of @xmath24 with insertions of" +"air bubbles can be entrapped in a wide variety of flows with a free surface @xcite . such entrapped bubbles can have large effects on phenomena such as bulk gas concentrations and sound emission @xcite . in addition , bubbles can be a nuisance for industrial processes , where they cause defects , obstructions or noise @xcite . various different mechanisms for air entrapment have been proposed in the literature . for example , it is well known that the impact of a drop on a free surface ( e.g. rain ) can induce an inertial cavity collapse that results in an oscillating bubble @xcite . at lower impact speeds , air films can be trapped between a liquid drop and a liquid or a solid wall , by lubricating effects of the medium . such a lubricating film can delay or completely avoid coalescence . in the extreme case such an air film can even cause a droplet to float on the liquid surface @xcite . depending on whether this film simply drains or becomes unstable , air entrainment might occur @xcite . however , it has been predicted that bubbles can also be entrapped during a coalescence with zero impact velocity , for which no lubricating film develops . in this case the bubbles form by reconnecting capillary waves that result in toroidal bubble rings as described theoretically @xcite . in this paper we focus on entrapment of air bubbles that form when a sessile drop impacts with a moving meniscus . this is relevant for applications such as dip - coating and immersion lithography ( fig . [ fig : chap4_problemsketch ] ) . dip - coating is a very common setup both for applications and fundamental studies , where a solid plate is plunged into or withdrawn from a liquid reservoir . a very similar geometry is present in immersion lithography , a technology used in semi - conductor industry : replacing the air in between a lens and the silicon wafer by a liquid leads to an increase in the numerical aperture of the system , allowing for the projection of smaller structures . a simplified version of the flow geometry for immersion lithography is sketched in figure [ fig : chap4_problemsketch ] c - d ) . the `` meniscus '' consists of a liquid bridge held between the hydrophilic glass plate and a wafer which is usually made partially wetting by a coating . the water will preferably remain in the gap , due to the contact with the hydrophilic glass plate , even when the substrate is in motion . a first mechanism for bubble entrapment is that at high velocities , the contact line can become unstable resulting in entrainment of a thin air film @xcite or bubbles @xcite . a second mechanism that leads to bubbles in these applications is due to residual drops , which are left on the substrate . these drops move along with the substrate and collide with the reservoir ( dip - coating ) or liquid bridge ( immersion lithography ) . air bubbles are generically entrapped during a collision of such a sessile drop with the meniscus . we present an experimental study on the formation of bubbles resulting from the impact of a sessile drop with a meniscus close to a moving contact line . the sessile drop always coalesces with the meniscus . as summarized in fig . [ fig : chap4_overview ] , however , we identified two scenarios for bubble entrapment . first , when the contact takes place at or very close to the moving contact line ( i.e. at @xmath0 , with @xmath1 the impact height with respect to the moving substrate ) we observe `` floating bubbles '' . these bubbles are spherical and float in the bulk of the liquid bridge . second , when the first contact between the sessile drop and the meniscus takes place above the moving contact line ( @xmath2 ) also a `` sticking bubble '' can be formed . this bubble is attached to the substrate and moves with the wafer . it should be noted that apart from these two cases , the coalescence can also result into no bubble formation , or a combination of floating bubbles and sticking bubbles . as summarized in fig . [ fig : chap4_overview ] , this depends on whether or not the airsheet breaks up during the coalescence . the paper is organized as follows . we first introduce the experimental setup ( sec . [ sec : chap4_setup ] ) . then we will discuss the formation mechanism of the two possible types of bubbles appearing during the drop - meniscus collision ( sec [ sec : chap4observations ] ) , and quantify the size of the entrapped bubbles , as a function of the impact velocity and the size of the sessile drop ( sec . [ sec : chap4bubblesizes ] ) . the latter section also includes explanations for the size of the two types of bubbles . the paper ends with a discussion ( section [ sec : chap4_discussion ] ) . the experimental setup consists of a coated glass wafer ( @xmath3 mm ) clamped to a turntable that is rotated with controlled angular velocity @xmath4 @xmath5 . the rotational motion of the wafer approximates a linear motion in the camera reference frame , due to the small droplet size compared to the radial position on the wafer ( @xmath6 mm ) . a detailed description of a similar setup is given in winkels et al . @xcite . the geometry in which the collision between a sessile drop and a meniscus is realized is sketched in fig . [ fig : chap4_setup ] . a small glass plate ( @xmath7 mm ) is fixed in the camera reference frame at a height @xmath8 mm above the substrate and close ( @xmath9 mm ) to the edge of the wafer . the gap between the wafer and the glass plate is filled with water ( millipore , milli - q , advantage a10 ) resulting in a liquid bridge with a pinned contact line at the hydrophilic glass plate and a mobile contact line at the coated wafer ( @xmath10 ) . with this construction , the liquid is held fixed in the camera reference frame also when the wafer is rotated . the liquid bridge then slides over the wafer , such that at the front and at the rear of the bridge there is a moving contact line . within the experimental range of velocities , we observe no air entrainment unless there is a collision with an incoming sessile drop . the two main control parameters in the experiment are the size and velocity of the impacting drop . before each measurement a sessile droplet is created on the wafer with multiple drops from a micro - drop generator ( microdrop technologies , md - e-3000 in combination with a md - k-130 dispenser head , single drop diameter @xmath11 @xmath12 ) . we achieve drop sizes in the range @xmath13 mm . the sizes are determined from side view recordings . the wafer velocity , and hence the impact velocity of the sessile drop , is varied over the range @xmath14 m / s . the process of impact and the subsequent bubble formation is recorded simultaneously with two high speed cameras . for the top view a shimadzu hpv1 or photron sa1.1 ( framerates @xmath15 kfps ) is used , connected to a long distance microscope ( navitar 12x zoom with 1.5x front lens ) obtaining a maximum resolving power of 2 @xmath16 . the side view is captured simultaneously with a pco1200s camera ( used at @xmath17 kfps ) attached to a lens ( jenoptik , jenmetar 1x/12 ld ) . to image the formation of the bubbles , the meniscus is viewed from above through the top glass plate , as shown in fig . [ fig : chap4_setup]a . in combination with backlit illumination the meniscus turns black , while the wetted area inside the liquid bridge turns bright . typical image recordings are shown in fig . [ fig : chap4_setup]b . the contact line of the sessile drop is marked with the yellow line : prior to impact , the drop is hidden behind the meniscus in the top view recordings . during the coalescence , the region where the drop and meniscus have merged will actually turn bright and can thus be monitored very accurately . note that the white ring that appears in the bright part of the image is an optical artefact without fluid mechanical meaning ( see fig . [ fig : chap4_floating]a ) . finally , we note that the liquid bridge can exhibit a rather complex geometry . the meniscus can be convex or concave depending on the gap height , volume of liquid and the dynamic contact angle . throughout our experiments we have tuned these parameters in order to keep the impacting meniscus as `` flat '' as possible in the side view . by avoiding strongly concave or convex menisci , we have been able to obtain conditions where the bubble formation is highly reproducible . namely , the geometry of impact is then a spherical cap with angle @xmath18 , colliding with a meniscus that can be approximated by a `` plane '' with dynamic contact angle @xmath19 . then a simple geometrical argument suggests that if @xmath20 , @xmath21 , while if @xmath22 , @xmath23 . the combination with for example the dynamic contact angle as a function of velocity , would give a possible predictive tool for the impact height @xmath1 as a function of velocity provided that meniscus profile can be kept perfectly flat . in our experiments we observe the impact height from the top view measurements and investigate the resulting coalescence dynamics and possible bubble formation process . we first consider the case where the coalescence is initiated at the contact line , with impact height @xmath0 within experimental accuracy . the subsequent coalescence is directed upwards , away from the substrate . the outcome of the experiment is that either a floating bubble is formed inside the liquid , or no bubble is formed . figure [ fig : chap4_floating ] shows a typical image sequence in the case a floating bubble is entrapped . below the experimental stills we provide sketches of the side view , to clarify the various stages of the bubble formation . these sketches serve as illustration and do not provide a fully accurate description of the deformation . a sessile droplet with size @xmath24 , moves from left to right with velocity @xmath25 ( fig.[fig : chap4_floating]i ) . the yellow solid line indicates the contact line of the sessile drop which is hidden behind the black meniscus prior to impact . the white dashed line denotes the moving contact line of the meniscus . interestingly , a small deformation of the contact line can be observed at time @xmath26 @xmath27 before impact ( white arrow , fig . [ fig : chap4_floating ] , @xmath28 @xmath27 ) . this deformation is due to the lubrication pressure building up in the air between the drop and the meniscus . subsequently , the coalescence process starts at , or at least very close to , the contact line ( fig . [ fig : chap4_floating]ii ) . during the upward motion of the coalescing bridge a pocket of air is enclosed , resulting into a floating bubble ( fig . [ fig : chap4_floating]iii ) . the coalescence continues while the spherical bubble floats inside the liquid bridge ( @xmath29 @xmath27 , fig.[fig : chap4_floating ] ) . the floating bubble is stable and remains inside the liquid bridge also after drop collision ( fig" +"the minimum - cost flow ( mcf ) problem is a well - studied problem with many applications , for example , modeling transportation and communication networks @xcite . over the last half century many algorithms have been developed to solve it . the first algorithms proposed in the 1960s were all pseudo - polynomial . these include the out - of - kilter algorithm by minty @xcite and by fulkerson @xcite , the cycle canceling algorithm by klein @xcite , the network simplex ( ns ) algorithm by dantzig @xcite , and the successive shortest path ( ssp ) algorithm by jewell @xcite , iri @xcite , and busacker and gowen @xcite . in 1972 edmonds and karp @xcite proposed the capacity scaling algorithm , which was the first polynomial mcf algorithm . in the 1980s the first strongly polynomial algorithms were developed by tardos @xcite and by orlin @xcite . later , several more strongly polynomial algorithms were proposed such as the minimum - mean cycle canceling ( mmcc ) algorithm by goldberg and tarjan @xcite and the enhanced capacity scaling algorithm by orlin @xcite , which currently has the best worst - case running time . for a more complete overview of the history of mcf algorithms we refer to ahuja et al . @xcite . when we compare the performance of several mcf algorithms in theory and in practice , we see that the algorithms that have good worst - case bounds on their running time are not always the ones that perform best in practice . zadeh @xcite showed that there exist instances for which the network simplex ( ns ) algorithm has exponential running time , while the minimum - mean cycle canceling ( mmcc ) algorithm runs in strongly polynomial time , as shown by goldberg and tarjan @xcite . in practice however , the relative performance of these algorithms is completely different . kovcs @xcite showed in an experimental study that the ns algorithm is much faster than the mmcc algorithm on practical instances . in fact , the ns algorithm is even the fastest mcf algorithm of all . an explanation for the fact that the ns algorithm performs much better in practice than indicated by its worst - case running time is that the instances for which it needs exponential time are very contrived and unlikely to occur in practice . to better understand the differences between worst - case and practical performance for the ns algorithm and the mmcc algorithm , we analyze these algorithms in the framework of smoothed analysis . smoothed analysis was introduced by spielman and teng @xcite to explain why the simplex algorithm usually needs only a polynomial number of iterations in practice , while in the worst case it needs an exponential number of iterations . in the framework of smoothed analysis , an adversary can specify any instance and this instance is then slightly perturbed before it is used as input for the algorithm . this perturbation can model , for example , measurement errors or numerical imprecision . in addition , it can model noise on the input that can not be quantified exactly , but for which there is no reason to assume that it is adversarial . algorithms that have a good smoothed running time often perform well in practice . we refer to two surveys @xcite for a summary of results that have been obtained using smoothed analysis . we consider a slightly more general model of smoothed analysis , introduced by beier and vcking @xcite . in this model the adversary can not only specify the mean of the noisy parameter , but also the type of noise . we use the following smoothed input model for the mcf problem . an adversary can specify the structure of the flow network including all nodes and edges , and also the exact edge capacities and budgets of the nodes . however , the adversary can not specify the edge costs exactly . for each edge @xmath8 the adversary can specify a probability density @xmath9\rightarrow [ 0,\phi]$ ] according to which the cost of @xmath8 is drawn at random . the parameter @xmath3 determines the maximum density of the density function and can therefore be interpreted as the power of the adversary . if @xmath3 is large , the adversary can very accurately specify each edge cost and we approach worst - case analysis . if @xmath10 , the adversary has no choice but to specify the uniform density on the interval @xmath11 $ ] and we have average - case analysis . brunsch et al . @xcite were the first to show smoothed bounds on the running time of an mcf algorithm . they showed that the ssp algorithm needs @xmath12 iterations in expectation and has smoothed running time @xmath13 , since each iteration consists of finding a shortest path . they also provide a lower bound of @xmath14 for the number of iterations that the ssp algorithm needs , which is tight for @xmath15 . these bounds show that the ssp algorithm needs only a polynomial number of iterations in the smoothed setting , in contrast to the exponential number it needs in the worst case , and explains why the ssp algorithm performs quite well in practice . in order to fairly compare the ssp algorithm with other mcf algorithms in the smoothed setting , we need smoothed bounds on the running times of these other algorithms . brunsch et al . @xcite asked particularly for smoothed running time bounds for the mmcc algorithm , since the mmcc algorithm has a much better worst - case running time than the ssp algorithm , but performs worse in practice . it is also interesting to have smoothed bounds for the ns algorithm , since the ns algorithm is the fastest mcf algorithm in practice . however , until now no smoothed bounds were known for other mcf algorithms . in this paper we provide smoothed lower and upper bounds for the mmcc algorithm , and a smoothed lower bound for the ns algorithm . for the mmcc algorithm we provide an upper bound ( section [ ubmmcc ] ) for the expected number of iterations that the mmcc algorithm needs of @xmath0 . for dense graphs , this is an improvement over the @xmath16 iterations that the mmcc algorithm needs in the worst case , if we consider @xmath3 a constant ( which is reasonable if it models , for example , numerical imprecision or measurement errors ) . we also provide a lower bound ( section [ lbconstantphi ] ) on the number of iterations that the mmcc algorithm needs . for every @xmath1 , every @xmath17 , and every @xmath18 , we provide an instance with @xmath19 nodes and @xmath20 edges for which the mmcc algorithm requires @xmath4 iterations . for @xmath21 we can improve our lower bound ( section [ lbbigphi ] ) . we show that for every @xmath22 and every @xmath17 , there exists an instance with @xmath19 nodes and @xmath20 edges , and @xmath6 , for which the mmcc algorithm requires @xmath5 iterations . this is indeed a stronger lower bound than the bound for general @xmath3 , since we have @xmath23 for @xmath6 . for the ns algorithm we provide a lower bound ( section [ lbns ] ) on the number of non - degenerate iterations that it requires . in particular , we show that for every @xmath1 , every @xmath24 , and every @xmath25 there exists a flow network with @xmath19 nodes and @xmath20 edges , and an initial spanning tree structure for which the ns algorithm needs @xmath26 non - degenerate iterations with probability @xmath27 . the existence of an upper bound is our main open problem . note that our bound is the same as the lower bound that brunsch et al . @xcite found for the smoothed number of iterations of the ssp algorithm . this is no coincidence , since we use essentially the same instance ( with some minor changes ) to show our lower bound . we show that with the proper choice of the initial spanning tree structure for the ns algorithm , we can ensure that the ns algorithm performs the same flow augmentations as the ssp algorithm and therefore needs the same number of iterations ( plus some degenerate ones ) . in the rest of our introduction we introduce the mcf problem , the mmcc algorithm and the ns algorithm in more detail . in the rest of our paper , all logarithms are base @xmath28 . a _ flow network _ is a simple directed graph @xmath29 together with a nonnegative capacity function @xmath30 defined on the edges . for convenience , we assume that @xmath31 is connected and that @xmath32 does not contain a pair @xmath33 and @xmath34 of reverse edges . for the mcf problem , we also have a cost function @xmath35 $ ] on the edges and a budget function @xmath36 on the nodes . nodes with negative budget require a resource , while nodes with positive budget offer it . @xmath37 is a nonnegative function on the edges that satisfies the capacity constraints , @xmath38 ( for all @xmath39 ) , and flow conservation constraints @xmath40 ( for all @xmath41 ) . the cost @xmath42 of a flow @xmath43 is defined as the sum of the flow on each edge times the cost of that edge , that is , @xmath44 . the objective of the minimum - cost flow problem is to find a flow of minimum cost or conclude that no feasible flow exists . in our analysis we often use the concept of a _ residual network _ , which we define here . for an edge @xmath45 we denote the reverse edge @xmath34 by @xmath46 . for flow network @xmath31 and flow @xmath43 , the residual network @xmath47 is defined as the graph @xmath48 . here @xmath49 is the set of _ forward edges _ with capacity @xmath50 and cost @xmath51 . @xmath52 is the set of _ backward edges _ with capacity @xmath53 and cost @xmath54 . here @xmath55 is also called the _ residual capacity _ of edge @xmath8 for flow @xmath43 . the mmcc algorithm works as follows : * first we find a feasible flow using any maximum - flow algorithm . * next , as long as the residual network contains cycles of negative total cost , we find a cycle of minimum - mean cost and maximally augment flow along this cycle . * we stop when the residual network does not contain any cycles of negative total cost . for a more elaborate description of the mmcc algorithm , we refer to korte and vygen @xcite . in the following , we denote the mean cost of a cycle @xmath56 by @xmath57 . also , for any flow @xmath43 , we denote the mean cost of the cycle of minimum - mean cost in the residual network @xmath47 by @xmath58 . goldberg and tarjan @xcite proved in 1989 that the minimum - mean - cycle canceling algorithm runs in strongly polynomial time . five years later radzik and goldberg @xcite slightly improved this bound on the running time and showed that it is tight . in the following we will focus on the number of iterations the mmcc algorithm needs , that is , the number of cycles that have to be canceled . a bound on the number of iterations can easily be extended to a bound on the running time , by noting that a minimum - mean cycle can be found in @xmath59 time , as shown by karp @xcite . the tight bound on the number of iterations that the mmcc algorithm needs is as follows . [ strponbound ] the number of iterations needed by the" +"many nonequilibrium systems typically exhibit currents of different observables ( e.g. , mass , energy , spin , etc . ) which characterize their macroscopic behavior . these currents fluctuate , and the ( large deviation ) functional which determines the probability of these fluctuations is a natural candidate to generalize the concept of _ free energy _ to nonequilibrium systems . in this way , understanding how microscopic dynamics determine the long - time averages of these currents and their fluctuations is one of the main objectives of nonequilibrium statistical physics @xcite . an important step in this direction has been the development of fluctuation theorems @xcite , which relate the probability of forward and backward currents reflecting the time - reversal symmetry of microscopic dynamics . these are relations of the form @xmath0 where @xmath1 is the probability of observing a time - integrated current @xmath2 after a long time @xmath3 , and @xmath4 is some constant such that @xmath5 corresponds to the rate of entropy production @xcite . despite this progress , we still lack a general approach based on few simple principles to understand current statistics in nonequilibrium systems . this has triggered an intense research effort in recent years . for instance , bertini , de sole , gabrielli , jona - lasinio and landim @xcite have recently introduced a hydrodynamic fluctuation theory ( hft ) to study both current and profile large dynamic fluctuations in nonequilibrium steady states , providing a variational principle which describes the most probable ( possibly time - dependent ) profile responsible of a given current fluctuation . simultaneously , bodineau and derrida @xcite have conjectured an additivity principle for current fluctuations which enables one to explicitely calculate the current distribution for 1d diffusive systems in contact with two boundary baths . this principle , which is equivalent within hft to the hypothesis that the optimal profile is time - independent @xcite , has been recently confirmed in a model of heat conduction @xcite . the predictions derived from the additivity principle and the hydrodynamic fluctuation theory have been tested in few models for which the exact current distribution can be calculated . for more general cases in which no exact solutions are available , new algorithms that allow the direct evaluation of large deviation functions in computer simulations have been recently proposed @xcite . these methods are based on a modification of the microscopic dynamics , so that the rare events responsible of the current large deviation are no longer rare . though successful , the new algorithms seem to suffer from finite - size effects when measuring the probability of extreme current deviations @xcite . here again the existence of simplified models for which exact solutions can be obtained is essential to elucidate the origin and importance of these finite - size corrections in simulations . the aim of this paper is to present one of these simplified models , i.e. a toy model of heat transport between two thermal baths at different temperatures . the simplicity of this model allows us to gain a better understanding of : ( i ) system statistics during a large deviation event and how it reflects the time reversibility of microscopic dynamics , and ( ii ) finite - size corrections to the direct evaluation of large deviation functions . the model and the calculation of its current large deviation function are presented is section ii . the probabilities of having certain configuration at the end of a large deviation event and for intermediate times are calculated in section iii , while section iv is devoted to analyze their relation in terms of the reversibility of microscopic dynamics . simulation results are described in section v , together with an analysis of finite - size corrections affecting the direct evaluation of large deviation functions . this analysis provides a deep understanding of the range of validity of this simulation method , which otherwise can be determined using the gallavotti - cohen fluctuation theorem . finally , section vi contains our conclusions . our toy model consists in a single lattice site characterized by an energy @xmath6 . this site is coupled to two thermal baths at different temperatures , @xmath7 ( left ) and @xmath8 ( right ) , and we assume @xmath9 without loss of generality . dynamics is stochastic and proceeds as follows : ( i ) with equal probability , we randomly choose the system to interact with one of the heat baths , @xmath7 or @xmath8 ; ( ii ) a new energy @xmath10 is drawn from the distribution @xmath11 corresponding to the ( inverse ) temperature of the selected heat bath , @xmath12 , with @xmath13 . the presence of a temperature gradient then forces the system out of equilibrium . the transition rate @xmath14 from configuration @xmath15 to @xmath10 interacting with bath @xmath13 can be written as @xmath16 and @xmath17 . the transition rate is normalized , @xmath18 , thus guaranteeing the conservation of probability during the stochastic evolution . this model can be regarded as the single - site version of the one - dimensional kipnis - marchioro - presutti ( kmp ) model of heat conduction @xcite . having a single site then implies that no energy diffusion takes place , but only energy exchange with the thermal reservoirs . associated to the interaction with the baths there is an energy current through the system , @xmath19 . we may define this current at the microscopic level in different ways . for the time being , let us define @xmath19 in a symmetric way @xmath20 in this way , positive currents correspond to the transport of energy from the left to the right reservoir . in the steady state , the probability density for having an energy @xmath15 can be trivially calculated @xmath21 and hence local equilibrium does not hold for this toy model . notice that @xmath22 , despite being non - gibbsian , can be related to the transition rate @xmath23 via detailed balance . the mean energy is @xmath24 , while the average current is @xmath25 . therefore fourier s law trivially holds in this system for arbitrarily large temperature gradients , @xmath26 , with a thermal conductivity @xmath27 . moreover , in equilibrium ( @xmath28 ) , current fluctuations have a variance @xmath29 . these values of @xmath30 and @xmath31 agree with the thermal conductivity and current variance of the spatially - extended kmp model @xcite , reinforcing the view that this model is just the single site version of the kmp process . let now @xmath32 be the probability of having the system in configuration @xmath15 with a total _ time - integrated _ current @xmath33 after a long time @xmath3 , starting from a configuration @xmath34 . this probability depends also on the temperatures of the boundary thermal baths , but we drop this dependence here for notation convenience . @xmath32 obeys the following master equation in a general context , meaning `` sum over configurations '' , independently of whether configuration space is discrete or continuous . in fact , for the model studied here configuration space is continuous , and sums become integrals over the system energy . ] @xmath35 iterating in time , we can write the above probability as @xmath36 \ , . \nonumber\ ] ] this is nothing but the weighted sum over all possible phase - space paths @xmath37 starting at @xmath34 and ending at @xmath15 , with duration @xmath3 , such that the total time - integrated current is @xmath33 . one may then write the probability of observing a total current @xmath33 as @xmath38 . for long times @xmath39 obeys a large deviation principle @xcite @xmath40 where @xmath41 is the current large - deviation function ( ldf ) , which does not depend on the initial state @xmath34 . the function @xmath41 is typically everywhere negative except for @xmath42 , for which it is zero , meaning that current fluctuations away from the average are exponentially unlikely in time . in most cases it is convenient to work with the moment - generating functions of the above distributions @xmath43 and @xmath44 . for long @xmath3 , one can show that @xmath45 , where @xmath46 $ ] is the legendre transform of the current ldf . we can now define a modified dynamics , @xmath47 , so @xmath48 this dynamics is however not normalized . for our particular model @xmath49 the simplicity of this single - site model allows the direct calculation of the _ sum _ ( [ pi2 ] ) . let us start by defining the following recurrence @xmath50 with @xmath51 . in this way , eq . ( [ pi2 ] ) can be written as @xmath52 a simple induction argument shows that @xmath53 where @xmath54 are some coefficients , and @xmath55 for the integrals to converge . plugging this into into eq . ( [ pi3 ] ) we arrive at @xmath56 the coefficients @xmath57 obey the following recurrence ( in matrix form ) @xmath58 with @xmath59 and @xmath60 . the recurrence matrix @xmath61 has eigenvalues @xmath62/2 $ ] , @xmath63 , and associated eigenvectors @xmath64 $ ] , with @xmath65 using these eigenvectors as a basis , we write @xmath66 , so @xmath67 . for long times the largest eigenvalue ( @xmath68 ) dominates , so @xmath69 and @xmath70 in this limit . using these long time asymptotics in eq . ( [ pi4 ] ) , and recalling that @xmath71 $ ] for long times , we find @xmath72 \right\ } \ , . \label{muss}\ ] ] fig . [ mussth ] shows @xmath73 versus @xmath74 for different values of the ratio @xmath75 . for all pairs @xmath76 , we have @xmath77 due to the normalization of @xmath39 , see the definition of @xmath78 in eq . ( [ pi1 ] ) and discussion below . one can also check that the first derivative of @xmath73 evaluated at @xmath79 yields the average current @xcite , i.e. @xmath80 . in addition , as a result of the time reversibility of microscopic dynamics , the gallavotti - cohen fluctuation relation @xcite holds for this system , @xmath81 with @xmath82 . this relation for @xmath73 is equivalent to the usual fluctuation relation @xmath83 for the current ldf @xcite . we now study the system energy distribution in a large deviation event of ( long ) duration @xmath3 and time - integrated current @xmath33 . one may measure this distribution at a time @xmath84 such that : ( i ) @xmath85 , i.e. for intermediate times , or ( ii ) for @xmath86 , i.e. at the end of the large deviation event . we first focus on endtime statistics . consider then the probability @xmath87 of having a configuration @xmath15 _ at the end _ of a large deviation event associated to a current @xmath88 . one can easily show in the long time limit that @xmath89 $ ] , where @xmath90 is the current conjugate to parameter @xmath91 , such that @xmath92 , with @xmath78 defined in eq . ( [ pi4 ] ) and @xmath93 . for long times @xmath94 converges to the following distribution , independent of both @xmath3 and the initial state @xmath34 , @xmath95 \ , , \label{pendss}\ ] ] where @xmath96 is a normalization constant , and we have used that @xmath97 for @xmath98 . to compute the energy distribution for intermediate times , @xmath99 , let @xmath100 be the probability that the system was in configuration @xmath15 at time @xmath84 when at time @xmath3 the total current is @xmath33 , starting from configuration @xmath34 . this probability can be written as @xmath101 \ , , \nonumber\ ] ] where we do not sum over @xmath15 . defining the moment - generating function of the above distribution , @xmath102 , we can again check that the probability weight of configuration" +"most models of dark energy in the present universe predict that its effective equation of state satisfies the null energy condition ( nec ) @xmath1 , where @xmath2 and @xmath3 are the effective dark energy density and pressure , respectively . however , the observations do not rule out that dark energy is phantom , i.e. , it violates nec . as an example , the 7-year wmap+bao+sn data @xcite give the following bound on the equation of state with time - dependent @xmath4 at @xmath5 : @xmath6 which is not entirely inconsistent with @xmath7 . even though phantom dark energy can be accomodated within general relativity @xcite , it is legitimate to ask whether effective phantom behavior can be obtained in modified gravity theories , such as @xmath8 or scalar - tensor gravity . this question can be addressed , in particular , within a popular approach @xcite employing the reconstruction of model parameters from the redshift expansion of observables , combined with the experimental constraints on non - gr gravity . the main conclusion is that with current observational data , the reconstructed de behaves more or less like the cosmological constant , but it is still possible to have phantom stage today . in this paper we follow a somewhat different route and ask what sort of the scalar - tensor lagrangian can lead to effective phantom de at the present epoch without violating constraints from solar system and local gravity experiments , time-(in)dependence of the gravity constant , etc . we also ask whether fine - tuning of initial data is necessary and how long the duration of the phantom stage can be in the past . our results are somewhat disappoining . we find that models with the present phantom de can be made consistent with all constraints , but one of the functions entering the scalar - tensor lagrangian must have rather specific shape , and the initial data must be strongly fine - tuned . also , the phantom stage must have begun fairly recently , at @xmath0 . before that the scalar field was undistinguishable from quintessence . all this disfavors the effective phantom behaviour in the scalar - tensor gravity . in fact , as we point out towards the end of this paper , some of the unpleasant properties we discuss must be present in scalar - tensor models for effective dark energy irrespectively of whether it is phantom or not . this paper is organized as follows . in section ii we present the equations governing the homogeneous cosmological evolution in the scalar - tensor gravity . we recall in section iii the experimental constraints on the non - gr gravity , that place bounds on the parameters of the theory . in section iv we define the expansion coefficients of the functions entering the lagrangian and reformulate the bounds of section iii in terms of these coefficients . in section v we put together all consistency requirements for the effective phantom dark energy today and arrive at qualitative understanding of the properties of the functions defining the theory . also , the maximum redshift at which the phantom phase could begin is estimated . section vi contains a numerical example . we conclude in section vii . by definition , the effective dark energy density and pressure @xmath9 and @xmath10 are the quantities entering the gr - looking evolution equations for the homogeneous and isotropic universe , @xmath11 where @xmath12 and @xmath13 are matter energy density and pressure , and we set @xmath14 . using ( [ e : fri1 ] ) and ( [ e : fri2 ] ) , one writes @xmath15 where @xmath16 . we are going to make use of this relation in the context of the scalar - tensor gravity . the action of this theory is @xmath17 ( mostly positive signature ) , where the action for the usual matter @xmath18 does not depend on @xmath19 . one can always redefine the field to have a convenient form of either @xmath20 or @xmath21 . we will use the general form of @xmath20 and set @xmath22 from the action ( [ e : action ] ) one obtains the gravitational equations , @xmath23 and equation of motion for the field @xmath19 , @xmath24 let us specify to the homogeneous , isotropic and spatially flat universe with metric @xmath25 since matter does not interact with @xmath19 , the scale factor @xmath26 has the same meaning as in gr . using eqs . ( [ e : ein ] ) and ( [ e : phi ] ) one gets the following set of equations : @xmath27 the equation for the matter density has the usual form , @xmath28 it is convenient for futher analysis to switch from the evolution in time to the evolution in redshift . this can be done by using the relation @xmath29 in this way one obtains from ( [ e : fr1j ] ) , ( [ e : fr2j ] ) and ( [ e : phj ] ) the evolution equations in terms of redshift : @xmath30f ' \label{e : fr2z}\\ h^{2}(1+z)^{2}\phi''&+[hh'(1+z)^{2}-2h^{2}(1+z)]\phi'=3[2h^{2}-hh'(1+z)]\frac{f'}{\phi'}-\frac{u'}{\phi ' } , \label{e : phz}\end{aligned}\ ] ] where prime denotes @xmath31 . the properties of functions defining the theory are strongly constrained by local and solar system experiments . this is a major problem for the effective nec - violating behavior in the scalar - tensor gravity . one important parameter is the brans dicke `` constant '' @xmath32 . it is straightforward to obtain the expression for @xmath33 in our parametrization by redifining the scalar field . one finds @xmath34 the lower bound on the present value of @xmath33 is obtained from the kassini experiment @xcite . it reads ( the subscript @xmath35 denotes the quantities at the present epoch ) @xmath36 a bound of another sort follows from the experiments on the time dependence of the gravity constant . in our case the local gravity constant @xmath37 is given by @xcite @xmath38 the experimental constraint on the time evolution of @xmath37 can be found in refs . for @xmath5 it reads @xmath39 we also know that the gravitational constant relevant for cosmology should not change significantly since big bang nucleosynthesis @xcite , @xmath40 it is the latter constraint that plays a significant role in our analysis , see section v. a convenient way to analyze the evolution at small redshifts is to expand all functions in the taylor series in redshift @xmath41 . on the other hand , we are mainly interested in the dependence on @xmath19 , so we will use the mixed expansion . at @xmath5 , without loss of generality we choose @xmath42 and by definition of the newton gravity constant we have @xmath43 here is our definition of the expansion coefficients : @xmath44 without loss of generality we take @xmath45 . from eq . ( [ e : fr1z ] ) it is straightforward to obtain the relation between the derivatives at the present time , @xmath46 we will also need @xmath47 and @xmath48 to obtain the expression for @xmath4 . from eqs . ( [ e : fr1z ] ) , ( [ e : fr2z ] ) we get @xmath49.\label{e : h22}\end{aligned}\ ] ] our main purpose is to understand the behavior of @xmath50 and @xmath51 as functions of the scalar field , so we expand them in @xmath19 : @xmath52 the relationship between the expansion coefficients entering ( [ e : ff ] ) and ( [ e : f ] ) is @xmath53 we now recall the constraint on @xmath54 , eq . ( [ wbd ] ) , and make use of eq . ( [ wf ] ) . with our normalization @xmath55 , we get very strong upper bound on @xmath56 : @xmath57 this means that the field @xmath19 is presently near the extremum of the funcion @xmath20 . such a conclusion appears inevitable in modified gravity , see , e.g. , ref . @xcite . it follows from eq . ( [ phsh ] ) that @xmath58 , so eq . ( [ e : f1 ] ) implies that @xmath59 is also small , latexmath:[\[\label{f1r } the first derivative of @xmath50 in the analysis of the present epoch . we note in passing that a small value of @xmath61 could have been anticipated , since the gr tests are very precise , and only a slight deviation from gr can be tolerated today . using ( [ phsh ] ) and neglecting the term with @xmath59 , we obtain for the present value of the field derivative with respect to redshift @xmath62 this simple relation will be instrumental in what follows . now we use the expression ( [ e : omega ] ) for @xmath63 to find out which parametrs can be responsible for the effective phantom behavior . making use of eqs . ( [ e : f1]),([e : f2 ] ) and ( [ f1r ] ) we get @xmath64 by extracting the second derivative of the field from eq . ( [ e : phz ] ) , we find @xmath65 so , there are essentially two parameters that could yield @xmath66 , namely , @xmath67 and @xmath68 . we begin our discussion with the latter . the possible contribution of the potential to the phantom effective equation of state comes from the third term in ( [ ww0 ] ) ( the second term in the numerator is positive in virtue of eq . ( [ ph2 ] ) ) and is given by @xmath69 it is strongly supressed by small @xmath56 , so this contribution can be sizeable only if the potential @xmath70 is very steep today . however , steep potential would lead to the rapid acceleration of the scalar field , so the phantom phase would be very short in the past . furthermore , the fast evolution of the scalar field together with large @xmath71 would imply rapid change in time of the effective dark energy density . to elaborate on the latter point , let us consider the parameter @xmath72 observationally , @xmath73 is not large : the wmap analysis @xcite gives @xmath74 . on the other hand , making use of eq . ( [ e : omega ] ) and neglecting the terms with @xmath75 we obtain @xmath76 where @xmath77 and @xmath78 are : @xmath79+\nonumber\\ & + \frac{1}{3(1-\omega_{m,0})}\left[12f_{2}+\frac{3f_{2}^{2}}{2}+9f_{2}\omega_{u,0}-\frac{9}{2}f_{2}\omega_{m,0 } -30\omega_{u,0}\right.\nonumber\\ & \left.+24(1-\omega_{m,0})+6\phantom{\frac{1}{1}}\right]-\frac{1}{3(1-\omega_{m,0})^{2}}\left(-f_{2}+6\omega_{u,0}+3\omega_{m,0}-6\right)^{2}. \label{ww12}\end{aligned}\ ] ] the parameter @xmath80 can not be very large , see below , so for large @xmath81 the value of @xmath82 is controlled by @xmath77 term in the expression ( [ ww1 ] ) . to have sizeable contribution ( [ mar10 - 1 ] ) and at the same time satisfy the observational constraint on @xmath82 , one would need the cancellation between @xmath83 and @xmath84 , which in turn would require strong fine - tuning . barring this possibility , we arrive at the conclusion that @xmath85 , so the contribution ( [ mar10 - 1 ] ) is very small . from now on we neglect it . the remaining terms in eq . ( [ ww0 ] ) can be simplified by using ( [ ph2 ] ) : @xmath86 thus , the phantom behaviour today is controlled entirely by @xmath87 . to have @xmath88 at the present time , one requires that @xmath89 together with the bound ( [ mar11 - 1 ] ) , this implies that today the field @xmath19 must be close to a relatively sharp maximum of the function @xmath20 . clearly , such a special state requires fine - tuning of both the function @xmath20 and initial conditions in the theory . we continue the discussion of the shape of @xmath20 and recall the constraints on the time - dependence of the gravity constant . given the small value of @xmath75 and large" +"classification is an important task in many fields including biomedical research , engineering , sociology and many others . how to construct a classification rule based on a labeled data set is a classical statistical problem . in machine learning literature , there are several types of learning problems discussed , and depending on how labeled subjects are included into a learning process , they are usually termed as supervised , unsupervised or semi - supervised learning @xcite . recently , due to technical innovation , `` big data '' becomes a buzz phrase in many fields , and we now often encounter with data sets that have huge amount of unlabeled data . hence , how to utilize these unlabeled data efficiently to construct a classification rule becomes an important problem . because to label each unlabeled subject is usually costly and inefficient , a common approach is active learning ( see , for example , * ? ? ? * ; * ? ? ? . this type of a leaning process will only inquire the label information for the `` selected '' subjects , which are usually chosen based on the information learned in the previous learning stages , and then include the newly labeled subjects into its training stage . a learning process will usually go on until a prefixed criterion is reached , such as a prefixed total number of labeled subjects to be used in the training stage . moreover , because in an active learning process , subjects are dynamically and sequentially selected , labeled and then added to the training set , this process is naturally related to sequential experimental designs in statistics , where a new observation / experiment is conducted at some particular design points selected according to the information obtained using the data gathered up to current stage . since data are observed adaptively , this type of methods are also related to the stochastic approximation process , which was first discussed in @xcite . their original procedure is called robbins - monro ( rm ) procedure and can be viewed as a stochastic version of newton - raphson method for nonlinear root - finding problems . following @xcite , sequential design methods have been intensively studied , and there are even more papers discussed different modifications of rm procedure and their corresponding convergence rates . recently , @xcite further modified rm procedure to improve on its efficiency . this type of procedures is nonparametric in the sense that no parametric model assumption is presumed . however , rm procedure can also be derived from a parametric form . for example , using the maximum likelihood estimate ( mle ) of a logistic model , @xcite proposed a logit - mle method for binary data that uses the currently available labeled data to fit a logistic model , and then select the next input with the desired probability based on the fitted logistic model . because a classification rule construction under active learning framework can be formulated as a problem of estimating the threshold boundary between two groups , which can usually be defined using a probability quantile , it can also be viewed as a stochastic root - finding procedure described above . moreover , logistic models are commonly used models in binary classification problems , and the properties of sequential estimation for generalized linear model ( glm ) under general adaptive designs are well studied @xcite . hence , it is natural to construct a binary classification rule , sequentially and adaptively , by putting all these ingredients together . an active learning algorithm developed in @xcite , which combines the logic - mle of @xcite and d - optimal design is a successful example . although , the existence and uniqueness of mle can be achieved after quite a few initial observations @xcite , it may still suffer from severe bias , when sample size is small , which usually results in an inefficient learning process . in modern literature , @xcite developed a bayesian extension of wu s approach , where they used the maximum a posterior ( map ) estimates of the parameters of a logistic model rather than mles . @xcite suggested a new sequential experimental design for glm , where observations are selected sequentially based on a bayesian d - optimality criterion and bayesian estimates of model parameters . these methods motivate us to study a novel modification of @xcite . as in conventional regression analysis , it is well - known that when the number of dimensionality of the unknown vector of parameters becomes large , the estimated information of it will be very unstable . because active learning processes usually rely such kind of information , the unstable estimates of parameters will also affect the learning process . in the real example studied in @xcite , those two variables are selected based on experts opinions . however , this situation is rare and there are usually more variables considered for a real example . thus , how to stabilize a learning process in high dimensional case is difficult and important . in this paper , we focus on the higher dimensional data sets . a bayesian sequential design is used and the related computational issues are discussed . in addition , for practical usages , we also study the effects of using different sizes of labeled data sets as an initial training set of an active learning process . as to the subject selection during a process , the major difference between a sequential design and an active learning process is that with sequential design , an experiment will be conducted at the selected points , while in active learning processes with existent unlabeled data , we can only select points near the theoretical ones from an existent data set . hence , how to select the next point based on the available information plays a key role in an active learning process . @xcite aimed at shortening the distance between the estimated boundary and the true one , such that their subject selection scheme heavily depends on the initial model assumption . in practice , the form of true model is usually unknown . hence , in order to diminish the effect of model assumptions , we adopt a different design point selection scheme . the advantage of the proposed method will be discussed from both theoretical and practical aspects . the rest of this paper is organized as follows . in section [ sec : method ] , we first review the active learning algorithm @xcite , and then discuss the proposed algorithm and some modifications . simulation results and numerical studies with real data sets are presented in sections [ sec : sim ] and [ sec : real ] , respectively . section [ sec : discu ] is a summarization . technical details are given in appendix . let @xmath0 be the explanatory vector of subjects and variable @xmath1 or @xmath2 denotes the category a subject belonging to . suppose that @xmath3 be the probability model of @xmath1 given @xmath4 . assume further that each variable has a positive relationship with the response ; that is , for larger value of @xmath5 , the higher the probability of @xmath6 . then @xcite assumed that @xmath7 had a parametric form @xmath8 where @xmath9 , @xmath10 for each @xmath11 , and @xmath12 . let @xmath13 be a vector of @xmath14 parameters . then following ( [ model-1 ] ) , for a given @xmath15 , @xmath16 is a bernoulli random variable with mean @xmath17 . model ( [ model-1 ] ) can be re - written as a conventional logistic regression model : @xmath18 where @xmath19 and @xmath20 . the fisher information matrix of @xmath21 with a set of design points @xmath22 is @xmath23 where @xmath24 is the regression matrix with @xmath11th row , @xmath25 equal to @xmath26 and @xmath27 is a diagonal matrix with @xmath28 $ ] , @xmath29 . it is clear that this information matrix is non - linear in @xmath21 and depends on the unknown @xmath21 only through @xmath27 . suppose that @xmath30 are observed labeled data of size @xmath31 . using this training set , we obtain an using the current estimates of parameters , the classification rule based on the estimate of @xmath32 becomes @xmath33 with an estimated boundary @xmath34 where @xmath35 when there is no extra information , such as @xmath36 available . ( in general , the cutting point for a logistic classification function is 0.5 . however , when there is a prior information about the event , such as prevalence rate in epidemiology study , the cutting point will usually be adjusted accordingly . this will be discussed later . ) therefore , the active learning problem under this set up becomes how to recruit a set of training subjects efficiently such that when a learning process is stopped , the final classification function @xmath37 will have good prediction power . intuitively , in order to have an efficient learning process , we should learn the most uncertain subjects first , because to do it this way may most improve a classifier . thus , when using a probabilistic learning model in an active learning framework , the most commonly used query for getting new data is the uncertainty sampling @xcite , where an active learner will query the label information of instance whose class membership is least certain . for a binary classification problem , this simply means to query the instance whose membership probability is closest to @xmath38 @xcite . thus , in a binary classification case the uncertainty is usually measured by @xmath39 where @xmath40 . ( note that in @xcite , they used only one parameter for measuring the uncertainty and adjusting the cutting point , and said that this parameter can be data dependent . however , our numerical studies show that for our method , using two different parameters for measuring uncertainty and adjusting cutting point , separately , will usually perform better . regarding this phenomenon , more discussions , based on statistical decision theory viewpoints , are given in section [ sec : uneven ] . ) let @xmath41 be the unlabeled data set . then rank points in @xmath41 in ascending order based on ( [ model-6 ] ) , and an active learning procedure will choose the top ranked point as follows : @xmath42 that is , to choose the one with an estimated probability closest to 0.5 as the next point to be labeled . because in high dimensional cases , there may be a lot of points that have the same or similar @xmath43 , we choose top @xmath44 points as candidates first , where @xmath44 , in our method , is decided by a local d - efficiency method using a locally optimal design discussed in @xcite and @xcite . ( for the details of this method , please refer to their original papers . ) as mentioned in @xcite , to use ( [ model-7 ] ) as the only criterion can not provide good estimates of model parameters , and the method of optimal design can be a good supplement to this disadvantage . thus , let @xmath45 be the set of candidate points that are screen out using ( [ model-7 ] ) . we then access these candidates further with some optimal experimental design criterions . one of the major differences between our method and the one in @xcite is that we use an uncertainty sampling method instead of distance based scheme to select the candidate set . the effect of uncertainty sampling becomes obvious when the difference between the sample sizes of two groups is large . this situation happens very often in those problems that aim for detecting a set of rare subjects within a large data set" +"pulsars were discovered in 1967 when bell and hewish were observing the interplanetary scintillations ( ips ) of compact radio sources , using a fixed dipole array at 81.5mhz ( @xcite ) . chart recordings were examined by eye for evidence of intrinsically pulsed signals , which looked somewhat different from the scintillating quasars being studied . within a few months , the first cambridge pulsar search discovered a total of six pulsars : psrs b0329 + 54 , b0809 + 74 , b0834 + 06 , b0950 + 08 , b1133 + 16 , and b1919 + 21 ( @xcite ) . soon afterward the dipole array returned to nearly full - time studies of ips , compact radio sources , and the interplanetary medium the purposes for which it had been designed . most pulsar searching since 1968 has been done at radio frequencies around 400mhz and higher , where the sky background is lower , interstellar dispersion and scattering are less of an impediment , and much larger bandwidths can be gainfully used . nevertheless , in 1993 it seemed to us for a number of reasons that a second cambridge pulsar search at 81.5mhz would be a worthwhile undertaking . the ips dipole array has been doubled in size since 1968 , and now has a geometric collecting area of 36,055m@xmath4 or 3.6 hectares approximately half that of the 305 m telescope in arecibo , puerto rico . the discovery of psr j0437@xmath14715 by johnston _ et al . _ ( 1993 ) demonstrated the existence of at least one very strong , nearby , millisecond pulsar . we reasoned that if similar pulsars exist in the northern sky , the 3.6-hectare array should be capable of detecting them , especially if their low - frequency radio spectra are steeper than those of most slowly rotating pulsars , as suggested by foster _ et al . _ ( 1991 ) . fortunately , the nature of the cambridge array is such that co - opting any one of its 16 simultaneous beams for pulsar searching can be done with only minimal disruption to its continuing ips studies . the 3.6 hectare array is a meridian - transit instrument consisting of 4096 full - wave dipoles operating at a wavelength @xmath5 m . the dipoles are arranged in 32 east - west rows of 128 dipoles each , with a spacing between rows of @xmath6 wavelengths . a branched feeder network combines the signals within each row , properly phasing them for a celestial source on the meridian . summed signals from the 16 northern - most and 16 southern - most rows are then combined in a matched pair of `` butler matrices '' to form simultaneous beams at 16 declinations in the range @xmath7 . for ips studies the two half - arrays are used as a north - south phase - switching interferometer ( @xcite ) ; however , for our pulsar observations we connected the two halves as a total - power phased array . a modified set of 16 beams can be generated by inserting an extra phase gradient in the north - south direction across the entire array , thereby shifting each beam north by half a beamwidth , or about @xmath8 . the declination of the peak response for each of the 32 possible beams is given by @xmath9 \,,\ ] ] where the beam number , @xmath10 , is an integer in the range 116 for the unshifted beams , and a half - integral value between 1.5 and 16.5 for the shifted beams ( @xcite ) . the beams have half - power widths of @xmath11}$ ] in declination . a reflecting screen lies @xmath12 beneath each row , and is inclined towards the south at 50 degrees to the vertical in order to increase the sensitivity of the array at lower declinations . however , tappin ( 1984 ) has shown that the declination power response , @xmath13 , of the antenna follows that expected for an array of dipoles @xmath12 above a flat , horizontal reflecting screen ; he finds no evidence for increased sensitivity at lower declinations . let @xmath14 represent the angle of the reflecting screen to the horizontal , and define the following three additional angles : @xmath15{0mm}{12.5 mm } \psi & \equiv & \left(\frac{\pi d}{\lambda}\right)\sin{\phi } + \left(\frac{n-10}{16}\right)\pi , \\ * \alpha & \equiv & \left(\frac{32\pi d}{\lambda}\right)\sin{\phi}.\end{aligned}\ ] ] the normalized declination power response can then be expressed as @xmath16\ , \frac{\sin^2{16\psi}}{{16 ^ 2}\sin^2{\psi}},\ ] ] where the three factors on the right - hand side arise from the interference between the two array halves , the reflecting screen , and the 16 phased rows in each half , respectively . following tappin , we take @xmath17 . inserting the peak - response declinations of equation ( [ eqn : camb_d0 ] ) into equation ( [ eqn : camb_d ] ) then shows that @xmath13 is maximized by phasing the array so as to use the plus sign in the first factor for integral beam numbers , and the minus sign for half - integral beam numbers . the top panel of figure [ fig : camb_beams ] shows the combined declination response afforded by the antenna for the whole survey , obtained by summing the calculated power responses of all 32 beams . the peak gain of each beam is proportional to the effective collecting area of the array , which falls off as the cosine of zenith angle . because of this foreshortening , several of the beams have secondary responses comparable to or even greater than their primary responses . as examples , the bottom panel of figure [ fig : camb_beams ] shows the individual power responses of beams 1 ( solid curve ) and 10 ( dashed curve ) . the true declinations of sources detected in the beams with large secondary responses can be determined from their transit times through the east - west beam : a source at declination @xmath18 has a half - power transit time of @xmath19 seconds ( @xcite ) . for the secondary responses at @xmath20 , transit times are shifted by 12 hours . our observations were carried out between november 1993 and june 1994 . we phased the array for a given beam number , @xmath21 , 1.5 , 2 , 2.5 , , 16.5 , and recorded data continuously for 24 hours as the sky drifted overhead . observations were repeated as demanded by interference , equipment malfunction or mis - adjustment , etc . , until each of the 32 beams had been observed and produced high - quality data at least twice . figure [ fig : camb_skymap ] illustrates the full sky coverage of the survey . we analyzed beams 16 and 16.5 for signals entering via their secondary responses , rather than the primary ones . consequently the survey provided useful sensitivity between declinations of @xmath0 and @xmath22 , with a few small areas missing because of interference . note , however , that because of array foreshortening at low declinations and the `` scalloped '' overall response as a function of @xmath18 , as well as the large variation in background temperature over the sky , our sensitivity even to low - dispersion , long period pulsars varied by more than an order of magnitude over the surveyed area . as described in more detail below , the median sensitivity for low - dispersion pulsars with periods @xmath23s was about 200mjy . when the 3.6-hectare array is being used solely for ips observations , the southernmost 14 beams are observed simultaneously . we diverted a single beam on a given day for pulsar observations , thereby causing only minimal disruption to the ips work . signals from the two halves of the array , properly phased for the desired beam , were extracted from the two butler matrices and added . the resulting signal was mixed to intermediate frequency of 10.7mhz and then to baseband , using quadrature local oscillators . an automatic gain control served to keep the post - detection noise level constant . the in - phase ( `` real '' ) and quadrature ( `` imaginary '' ) baseband signals were low - pass filtered at 0.47mhz ( the filters are 60db down at 0.5mhz ) , sampled at a 1mhz rate , and digitized in a 12-bit analog - to - digital converter controlled by a programmable digital signal processor ( dsp ; analog devices adsp-21020 ) on a vme board made by the ixthos corporation . the incoming data were double - buffered in fast memory on the dsp board . at intervals of 256@xmath24s the adsp-21020 performed a 256-point complex fourier transform on the incoming data and squared the resulting magnitudes . three consecutive power spectra were summed , and every 768@xmath24s the difference between the 256-channel power spectrum and an exponentially - weighted mean of spectra over the past 1.5s was one - bit sampled . the resulting bits were packed into 32-bit words and passed to a controlling workstation , which wrote them onto magnetic tape along with the running averages and root - mean - square deviations of the summed power spectra and the date , time , and beam number . a full day s observing session generated about 3.5 gb of data , which fit comfortably on a single 8 mm tape cassette . searching for pulsar signals was accomplished by reading the recorded data from tape into another workstation . the one - bit data were unpacked and divided into consecutive blocks with length comparable to the beam transit time at the relevant declination . block lengths of @xmath25 samples were used for beams 110 , 16 , and 16.5 ; @xmath26 samples for beams 10.513 ; and @xmath27 samples for beams 13.515.5 . these numbers correspond to transit times of 101 , 201 , and 403s . beams 16 and 16.5 were processed using the short block length so as to remain sensitive to pulsars in their secondary responses at declinations near @xmath0 and @xmath28 , respectively . the total amount of computing was substantial : with the dec axp3000/400 workstation used to do most of it , about 3.6 days of computing was required for each day of observations nearly eight months of continuous computing , in all . the search program analyzed each beam area independently . progressive delays were introduced between the 256 spectral channels in a manner that optimally produces time series at different dispersion measures ( @xcite ) . curvature in the delay - versus - frequency relation was compensated by shifting the middle two - thirds of the spectral channels by one channel . for each data block , the one - bit samples were optimally de - dispersed at 256 dispersion measures evenly spaced between 0 and 12.78@xmath2pc . additional dispersion ranges were generated by first adding successive pairs of time samples in each spectral channel , and then reapplying the de - dispersion algorithm . the de - dispersed time series in each new range thus had half the length of those in the previous range , and the upper half of each group of dispersions extended the ranges of those already computed . in this manner , each data block was also de - dispersed by 128 dispersion measures evenly spaced across each of the following ranges : 12.8325.60 , 25.6551.25 , and 51.30102.55@xmath2pc . for each data block a total of 640 de - dispersed time series were fourier transformed and analyzed for harmonic content . after removing known sources of periodic interference ( in particular , the 274hz phase - switching frequency used for ips studies ) , the search program identified the strongest periodicities by interpolating between the complex fourier coefficients and finding the peak amplitudes" +"quantum dots @xcite are artificial electron systems ( es ) realizable in modern semiconductor structures . in these systems two - dimensional ( 2d ) electrons move in the plane @xmath0 in a lateral confinement potential @xmath1 . the typical length scale @xmath2 of the lateral confinement is usually larger than or comparable with the effective bohr radius @xmath3 of the host semiconductor . the relative strength of the electron - electron and electron - confinement interaction , given by the ratio @xmath4 , can be varied , even experimentally , in a wide range , so that the dots are used to be treated as artificial atoms with tunable physical properties . experimentally , quantum dots were intensively studied in recent years , using a variety of different techniques , including capacitance @xcite , transport @xcite , far - infrared @xcite and raman spectroscopy @xcite . from the theoretical point of view , quantum dots are ideal physical objects for studying effects of electron - electron correlations . different theoretical approaches , including analytical calculations @xcite , exact diagonalization @xcite , quantum monte carlo ( qmc ) @xcite , density functional theory @xcite and other methods @xcite , were applied to study their properties , for a recent review see ref . @xcite . until recently most theoretical work was performed in the regime of strong magnetic fields , when all electron spins are fully polarized . in the past three years a growing interest is observed in studying the quantum dot properties in zero magnetic field @xmath5 @xcite . the aim of these studies is to investigate the fermi liquid wigner solid crossover in the dots , at a varying strength of coulomb interaction . detailed knowledge of the physics of such a crossover in microscopic dots could be compared with that obtained for macroscopic 2des @xcite and might shed light on the nature of the metal - insulator transition in two dimensions @xcite . so far , full energy spectra of an @xmath6-electron parabolic quantum dot in zero magnetic field , as a function of the interaction parameter @xmath7 , were published only for @xmath8 ( quantum - dot helium @xcite ) . for larger @xmath6 a number of results for the ground state energy of the dots were reported at separate points of the @xmath7 axis . sometimes , however , results obtained by different methods contradict to each other , and full understanding of physical properties of @xmath6-electron dots at @xmath5 has not yet been achieved . even for three electrons in a parabolic confining potential ( quantum - dot lithium ) available in the literature results are somewhat confusing and do not give a clear and exact picture of the ground state of the dot . egger et al . reported in @xcite on a transition from a partly to a fully spin - polarized ground state at @xmath9 caused by the intra - dot coulomb interaction ( @xmath10-component of the total spin @xmath11 changes from @xmath12 to @xmath13 ) . this conclusion was based on results of qmc calculations ( multilevel blocking algorithm ) . for the @xmath12 state calculations gave at @xmath14 _ slightly lower _ energy , than for the @xmath13 state , and higher energies at @xmath15 , 8 and 10 . in a subsequent ( erratum ) publication @xcite other ( corrected ) values for the energy of these states were reported . at @xmath14 they gave _ the same _ energies of the 1/2 and 3/2 states . the conclusion from these two publications in the part concerning the three - electron quantum dot is thus not clear . husler @xcite , calculating the energy spectrum of a three - electron dot using the so - called pocket state method , gave a more definite indication on the existence of such a transition . he presented his results , however , in some specific for the method and not - directly related to @xmath7 units , which does not allow one to quantitatively characterize the transition ( e.g. to get the value of the interaction parameter @xmath7 at the transition point ) . husler also pointed out that some indications on such a transition can be also seen in earlier studies of a three - electron dot : in ref . @xcite ( @xmath16 ) the ground state of the dot at @xmath5 was found to be partly spin - polarized , while in ref . @xcite with a substantially larger value of @xmath7 the fully spin - polarized state turned out to have the lower energy . as seen from this brief outline , available data indicate that this transition seems to exist but it is not yet quantitatively understood , and its physical origin is not completely clear . it is also not clear whether and how this transition in the spin state of the system is related to the fermi - liquid wigner - molecule transition in the dot . in this paper i present results of a complete theoretical study of a three - electron parabolic quantum dot . using exact diagonalization technique , i calculate full energy spectrum of the dot , as a function of the interaction parameter in the range @xmath17 . at @xmath18 i find a transition in the ground state of the dot , accompanied by the change of the total spin quantum number . i study the densities and the pair - correlation functions in the ground and the first excited states of the system at a number of @xmath7-points , including the vicinity of the transition . these results show that physical properties of the dot dramatically change at the transition point , corresponding to properties of fermi liquid at @xmath19 , and of a wigner molecule at @xmath20 . i also calculate some thermodynamic properties of the dot : the heat capacity and the volume - pressure diagram . the temperature dependence of the heat capacity clearly exhibits characteristic features , related to the transition , in the temperature range corresponding to a few k for typical parameters of gaas dots . other experimental consequences from predictions of this paper are also discussed . in section [ mmm ] i briefly describe the model and the method used in calculations . results of the work are presented in section [ results ] . concluding remarks can be found in section [ concl ] . i consider three 2d electrons moving in the plane @xmath0 in a parabolic confining potential @xmath21 , @xmath22 . the hamiltonian of the system @xmath23 ( @xmath24 ) commutes with operators of the total angular momentum @xmath25 , ( squared ) total spin @xmath26 and projection of the total spin @xmath27 on some ( @xmath28- ) axis ( not necessarily coinciding with the @xmath10-axis ) . this gives three conserving quantum numbers @xmath29 , @xmath30 and @xmath31 . no magnetic field is assumed to be applied to the system . a complete set of single - particle solutions of the problem @xmath32 is the product of the fock - darwin orbitals @xcite @xmath33 and the spin functions @xmath34 . here @xmath35 is the oscillator length , and @xmath36 are the radial , asimutal ( angular momentum ) and spin quantum numbers of the single - particle problem ( @xmath37 and @xmath38 are integer , @xmath39 ) . all the single - particle states ( [ set ] ) can be ordered and enumerated , e.g. @xmath40 , @xmath41 , @xmath42 , etc . the energy of the states ( [ set ] ) does not depend on spins , @xmath43 a complete set of many - particle states @xmath44 , @xmath45 is formed by placing particles in different single - particle states , e.g. @xmath46 , @xmath47 , @xmath48 , where @xmath49 are slater determinants @xmath50 and @xmath51 . all the many - particle states @xmath44 can be also arranged , e.g. in order of increasing of their total single - particle energy @xmath52 and enumerated . expanding the many - body wave function in a complete set of many - particle states , @xmath53 i get the schrdinger equation in the matrix form , @xmath54 the conservation of the total angular momentum @xmath55 and the projection of the total spin @xmath31 allows one to chose the many - body states for the expansion ( [ mbwf ] ) under additional constraints @xmath56 this reduces the size of the matrix in ( [ evprob ] ) and facilitates calculations . numerically diagonalizing the eigenvalue problem ( [ evprob ] ) i get a set of energy levels @xmath57 and corresponding eigenfunctions @xmath58 as a function of the interaction parameter @xmath59 . the number @xmath60 enumerates the energy levels of the system in the subspace of levels with given @xmath55 and @xmath31 . after the diagonalization problem is solved , the eigenvalues of the total spin are calculated for each level @xmath61 from @xmath62 all the matrix elements of the hamiltonian @xmath63 and of the operator @xmath64 are calculated analytically . all the energy levels with non - zero @xmath55 and @xmath31 are degenerate , @xmath65 presenting below results for the energy of the states @xmath66 , i omit the corresponding signs [ for instance , @xmath67 stands for @xmath68 with all possible combinations of signs ] . degeneracy of levels are calculated accounting for ( [ degeneracy ] ) . after the schrdinger problem is solved and all the energy levels and the eigenfunctions are found , i calculate the density of spin - up and spin - down polarized electrons in the states @xmath69 , and the corresponding pair - correlation functions . these quantities are calculated as averages of the operators @xmath70 and @xmath71 with the eigenfunctions @xmath72 . all the matrix elements of the operators ( [ dens ] ) and ( [ pcf ] ) are calculated analytically . as the method offers an opportunity to find all the energy levels of the system , one can also calculate thermodynamic properties of the dots . i calculate the heat capacity as @xmath73 , where @xmath74 @xmath75 is the temperature , and the sum is taken over all ( low - lying ) energy levels accounting for their degeneracies . the number of all many - particle states in the problem is infinite , and the size of the matrix @xmath63 in eq . ( [ evprob ] ) is infinite too . to perform practical calculations i restrict the number of many - particle states in the expansion ( [ mbwf ] ) so that the total single - particle energy ( [ totspenergy ] ) of the involved many - body states is smaller than some threshold value @xmath76 , @xmath77 . the larger the threshold energy @xmath76 , the broader the range of @xmath7 in which results are convergent and reliable . typically , less than 1000 many - particle states were sufficient for all the calculations presented below . convergency of the method is illustrated on figure [ convergency ] , where the energy @xmath78 of the lowest state ( @xmath79 ) with @xmath80 is shown as a function of @xmath59 for increasing threshold energy @xmath76 . the curves are labeled by @xmath76 and the number of many - body quantum states @xmath81 involved in the expansion ( [ mbwf ] ) . one sees that including about 1000 many - body states leads to very accurate results for the energy at @xmath82 . notice that below i present results for the energy in the interval @xmath83 , where the method is practically exact : at @xmath84 i found that @xmath85 at @xmath86 , and @xmath87 at @xmath88 . the difference comprises @xmath89 % . all the lengths in this section are measured in units @xmath2 , all the energies in units @xmath90 , the densities and the pair - correlation functions in units @xmath91" +"as molecular dynamics ( md ) is limited to microscopic systems and time scales , most chemical or biological reactions can not be simulated using straightforward md . one can literally wait ages before detecting a single event in a typical computer simulation . in the early 1930s , wigner and eyring made the first attempts to overcome this problem by introducing the concept of the transition state ( ts ) and the so - called ts theory ( tst ) approximation @xcite . later on , keck @xcite demonstrated how to calculate the dynamical correction , the transmission coefficient . this work has later been extended by bennett @xcite , chandler @xcite and others @xcite , resulting in a two - step approach . first the free energy as function of a reaction coordinate ( rc ) is determined . this can be done by e.g. umbrella sampling ( us ) @xcite or thermodynamic integration ( ti ) @xcite . then , the maximum of this free energy profile defines the approximate ts dividing surface and the transmission coefficient can be calculated by releasing dynamical trajectories from the top . this approach is , in principle , exact and independent of the choice of rc . however , the method becomes inefficient when the transmission coefficient is small . a proper choice of the rc can maximize the transmission coefficient and is hence crucial for the efficiency of the method . there exist different formalisms for the transmission coefficient formula which differ in the way trajectories are counted . we discuss the standard bennett - chandler ( bc ) @xcite , the history dependent bc ( bc2 ) @xcite , and the effective positive flux ( epf ) @xcite formalism . we show that the latter should always be preferred due to a lower average pathlength and a faster convergence . however , whenever a lot of correlated recrossings occur , the transmission coefficient will be very low and all these methods become inefficient . in high dimensional complex systems it can be a very difficult task to find a proper rc . moreover , whenever the dynamics is diffusive , even an optimal rc can result in a very low transmission and hence a poor efficiency . a new approach came with transition path sampling ( tps ) @xcite that is not based on the free energy barrier as starting point . tps is rather an importance sampling of dynamical trajectories . hence , it is a monte carlo ( mc ) sampling in path space rather than phase space . the tps method has been advocated as a method that does not need a rc and is akin to throwing ropes in the dark @xcite . this might be true if one wants to sample a set of reactive trajectories , but it is not for the calculation of reaction rates . in fact , the original approach to calculate reaction rates within the framework of tps required the definition of an order parameter and the calculation of the reversible work when the endpoint of the path is dragged along this parameter . for the sampling of reactive pathways , the order parameter needs only to distinguish between the two stable states . however , in the algorithmic procedure to calculate reaction rates with tps , the order parameter becomes very similar to a rc . still , it has been speculated that this approach is less sensitive to the problems related to an improper rc ( or order parameter ) . indeed , in this article we prove for the first time that this is true using the approach of transition interface sampling ( tis ) @xcite . tis increases the efficiency of the original tps rate calculation considerably by allowing the pathlength to vary and by counting only positive effective crossings . the overall reaction rate in tis is obtained from an importance sampling technique that uses a discrete set of interfaces between the stable states . hence , tis could be considered a dynamical analogue of us in path space . for diffusive systems the partial path tis ( pptis ) was invented that uses the assumption of memory loss @xcite . in this article we discuss the case of sharp barriers . here recrossings occur mainly due to the wrong choice of rc . in a follow - up article we will treat the diffusive case . up to now , it is not clear how these methods compare in efficiency and the need for benchmark systems has been put forward several times . it is not always easy to perform comparative calculations since it is not simple to know if each method is equally optimized for a specific system . therefore , in this paper we analyze a system for which the efficiency of the methods can be calculated analytically with only a few approximations . this does not only give a transparent comparison of the efficiency of the different methods , but also allows to obtain scaling laws for how this efficiency changes as function of the barrier height and width . moreover , we give some rules for how the methods can be optimized , for instance , by choosing the proper width of the us windows and the position of interfaces in tis . these rules are important for the simulation community , as they can be used as a rule of thumb in daily practice , when any method needs to be optimized . the principal component to measure the efficiency of the methods will be the _ cpu efficiency time _ @xmath0 which is the lowest computational cost needed to obtain an overall statistical error equal to one . we give a detailed analysis of how @xmath0 can be calculated for some very general cases in the appendix sections [ sgn ] and [ secect ] . it also gives the important result of how one should divide a total fixed simulation time over a set of different simulations to obtain the best overall efficiency . in sec . [ secmet1 ] , we outline the first class of methods , the reactive flux ( rf ) methods , and present their principal formulas . in sec . [ secmet2 ] , we do the same for the second class of methods , the path sampling methods . [ secsys ] introduces the 2d benchmark system where the angle @xmath1 indicates how far the chosen rc is deviated from the optimal one . [ secres ] is the main section of our paper in which we apply the different methods of sec . [ secmet1 ] and [ secmet2 ] to the analytical benchmark system of sec . [ secsys ] . finally , we discuss the important point of hysteresis for the two types of methods and show that this is less likely to occur for the path sampling methods . we summarize the results in sec . [ seccon ] . moreover , to support the readability of this paper we have added a list of symbols and abbreviations in app . [ alos ] and [ aloa ] . in all combined free energy and transmission coefficient based methods , the rate equation follows from @xmath2 where the reaction rate @xmath3 is expressed as a quasi - plateau value at a time @xmath4 of a time dependent reaction rate function @xmath5 . this function is given by the corrected flux through an hypersurface @xmath6 , that is is a collection of phase points @xmath7 , defined by the reaction coordinate @xmath8 and transition state ( ts ) value @xmath9 . the ts value @xmath9 is standardly taken as the maximum in the free energy profile along @xmath10 . both tst , bc , bc2 and epf can be expressed as @xmath11 { \rangle}}{{\langle}\theta(\lambda^*-\lambda(x_0 ) ) { \rangle } } , \label{kgen}\end{aligned}\ ] ] where @xmath12 is the dirac delta function , @xmath13 the heaviside step function , @xmath14 is the phase point at a time @xmath15 , and @xmath16 is a trajectory that includes @xmath17 . ensemble averages @xmath18 in phase and path space are defined in app . [ subsensem ] . ( [ kgen ] ) measures the flux contributed by pathways leaving the surface @xmath9 at @xmath19 under the influence of a correction functional @xmath20 $ ] . the functional @xmath21 has different forms for tst , bc , bc2 , and epf . the rate equation ( [ kgen ] ) can be rewritten as a product of two factors : the probability to be on top of the barrier times the transmission function @xmath22 : @xmath23 with @xmath24 and @xmath25 { \rangle}_{\delta(\lambda(x_0)-\lambda^*)}. \label{defr}\end{aligned}\ ] ] here , @xmath26 implies that the ensemble @xmath27 is constrained at the surface @xmath28 . substitution of eqs . ( [ defr],[defrp ] ) in eq . ( [ kpk ] ) using eq . ( [ wens ] ) gives back eq . ( [ kgen ] ) . eqs . ( [ kpk]-[defrp ] ) show the two - step procedure . the probability @xmath29 and the time dependent transmission function @xmath22 are calculated in two separate simulations . as for the rate @xmath3 , the unnormalized transmission coefficient @xmath30 follows from a plateau in this time dependent function : @xmath31 . this factor corrects for the correlated recrossings . in [ subsfe ] , we discuss the methods to compute @xmath29 or , equivalently , the free energy barrier @xmath32 . then , in [ sectrans ] we discuss the methods to determine the transmission coefficient @xmath30 . define the following @xmath33 box functions : @xmath34 \theta[\lambda_r+i\gamma+\gamma-\lambda(x ) ] , \nonumber \\ w_m(x)&=\theta[\lambda(x)+d\lambda-\lambda^ * ] \theta[\lambda^*-\lambda(x ) ] , \nonumber \\ w_0(x)&=\theta[\lambda^*-\lambda(x ) ] , \label{windows1 } \\ w_j(x)&= \theta[\lambda(x)-\lambda_r-(j-1 ) \gamma ] \theta[\lambda_r+j \gamma+\gamma - \lambda(x ) ] , \nonumber \end{aligned}\ ] ] with @xmath35 and @xmath36 . here @xmath9 is the ts , @xmath37 is a value in the reactant well and @xmath38 is a small length scale . @xmath39 and @xmath40 represent the dimensions of the us windows ; @xmath41 is the width of the window and @xmath39 is the overlap such that @xmath42 ( see fig . [ umbrel ] ) . neglecting higher orders terms in @xmath38 , we can write @xmath43 to calculate eq . ( [ freeensam ] ) , we can simply run an md simulation and count the number of times that the transition state region interval is visited . the weight function @xmath44 in the ensemble acts like an infinite wall at @xmath45 and prevents the unnecessary exploration of the product region . however , as @xmath46 is vanishingly small for high barriers , this straight - forward method will usually fail . using eq . ( [ wens ] ) and the relations @xmath47 , @xmath48 for all @xmath49 we can rewrite eq . ( [ freeensam ] ) as @xmath50 the final property is now calculated from a series of simulations in which each pair @xmath51 so that they can be determined accurately . the implementation of us using rectangular windows via mc is straightforward . the standard mc sampling is performed starting from a point inside the window . as soon as the mc procedure generates a point outside this window , this point is automatically rejected and the old point is kept . if the procedure is performed by means of md , the window boundaries simply act as infinitely hard walls . however , due to practical problems related to a discontinuous force profile , md simulations are usually performed with parabolic windows instead of rectangular ones . instead of performing several simulations using rectangular windows , one can also use a single biasing function @xmath52 : @xmath53 again , the equivalence between eq . ( [ freeensam ] ) and eq . ( [ ussb" +"one of the purposes of investigating the nucleon resonances(@xmath7 ) is to understand the non - perturbative dynamics of quantum chromodynamics(qcd ) . one possible approach to realize this is to compare the predictions of qcd - inspired models with the resonance parameters which can be extracted from the data of pion photoproduction and electroproduction reactions . in recent years , precise data including polarization observables have been obtained in the @xmath8 region for pion photoproduction at legs@xcite and mainz@xcite , and for pion electroproduction at thomas jefferson national accelerator facility(jlab)@xcite , mit - bates@xcite and nikhef@xcite . these data now allow us to investigate more precisely the electromagnetic excitation of the @xmath8 resonance . in ref.@xcite we have developed a dynamical model(henceforth called the sl model ) to extract the magnetic dipole(m1 ) and electric quadrapole(e2 ) strengths of the @xmath1 transition from the pion photoproduction data . the precise polarization data from legs and mainz were essential in our analysis . in this paper , we report on the progress we have made in extending the sl model to investigate the pion electroproduction reactions in the @xmath8 excitation region . we will make use of the recent data from jlab and mit - bates to explore the q@xmath2-dependence of the @xmath9 transition and make predictions for future experimental tests . the dynamical content of the sl model has been given in detail in ref.@xcite . the essential feature of the model is to have a consistent description of both the @xmath10 scattering and the electromagnetic production of pions . this is achieved by using a unitary transformation method to derive an effective hamiltonian defined in the subspace @xmath11 from the interaction lagrangians for @xmath12 and photon fields . the resulting model has given a fairly successful description of the very extensive data for pion photoproduction . the extension of the sl model to investigate pion electroproduction is straightforward . the formulae needed for calculating the current matrix elements of pion electroproductions are identical to that given in ref.@xcite except that a form factor must be included at each photon vertex . therefore no detailed presentation of our model will be repeated here . similarly , we will not give detailed formulae for calculating the electroproduction cross sections since they are well documented@xcite . the sl model is one of the dynamical models developed @xcite in recent years . compared with other approaches based on the tree - diagrams of effective lagrangians@xcite or dispersion - relations@xcite , the main objective of a dynamical approach is to separate the reaction mechanisms from the excitation of the internal structure of the hadrons involved . within the sl model , this has been achieved by applying the well - established reaction theory within the hamiltonian formulation(see , for example , ref.@xcite ) . in particular , the off - shell non - resonant contributions to the @xmath1 form factors can be calculated explicitly in a dynamical approach . only when such non - resonant contributions are separated , the determined `` bare '' @xmath1 form factors can be compared with the predictions from hadron models . within the sl model , this was explored in detail and provided a dynamical interpretation of the long - standing discrepancy between the empirically determined magnetic m1 strength of the @xmath1 transition and the predictions from constituent quark models . in this work , we further explore this problem utilizing the @xmath6-dependence accessible to electroproduction reactions . furthermore , the coulomb(scalar ) component @xmath13(@xmath14 ) of the @xmath1 form factor will be determined . in section ii , we briefly review the essential ingredients of the sl model and define various form factors which are needed to describe pion electroproduction reactions . with the mainz data@xcite , we have slightly refined our model at the @xmath5 photon point . this will be reported in section iii . the electroproduction results are presented and compared with the data in section iv . in section v , we give a summary and discuss possible future developments . within the sl model , the pion photoproduction and electroproduction reactions are described in terms of photon and hadron degrees of freedom . the starting hamiltonian is @xmath15 with @xmath16 where @xmath17 is the free hamiltonian and @xmath18 describes the absorption and emission of a meson(@xmath19 ) by a baryon(@xmath20 ) . in the sl model , such a hamiltonian is obtained from phenomenological lagrangians for @xmath21 and photon fields . in a more microscopic approach , this hamiltonian can be defined in terms of a hadron model , as attempted , for example , in ref . @xcite . it is a non - trivial many body problem to calculate @xmath10 scattering and @xmath22 reaction amplitudes from the hamiltonian eq . ( [ hamilt ] ) . to obtain a manageable reaction model , a unitary transformation method@xcite is used up to second order in @xmath23 to derive an effective hamiltonian . the essential idea of the employed unitary transformation method is to eliminate the unphysical vertex interactions @xmath24 with @xmath25 from the hamiltonian and absorb their effects into @xmath26 two - body interactions . in the sl model , the resulting effective hamiltonian is defined in a subspace spanned by the @xmath10 , @xmath27 and @xmath8 states and has the following form @xmath28 where @xmath29 is a non - resonant @xmath10 potential , and @xmath30 describes the non - resonant @xmath31 transition . the @xmath8 excitation is described by the vertex interactions @xmath32 for the @xmath33 transition and @xmath34 for the @xmath35 transition . the vertex interaction @xmath36 is illustrated in fig . the non - resonant @xmath30 consists of the usual pseudo - vector born terms , @xmath37 and @xmath38 exchanges , and the crossed @xmath8 term , as illustrated in fig . 2(the non - resonant term due to an intermediate anti-@xmath8 state was found to be very weak and can be neglected ) . most of the dynamical models have the above form of the hamiltonian . however , the sl model has an important feature that the deduced effective hamiltonian @xmath39 is energy independent and hermitian . hence , the unitarity of the resulting reaction amplitudes is trivially satisfied . furthermore , the non - resonant interactions @xmath30 and @xmath29 are derived from the same @xmath23 of eq . ( [ hamilt ] ) , and hence the @xmath10 and @xmath27 reactions can be described consistently . such a consistency is lost if @xmath29 is either constructed purely phenomenologically as done in refs.@xcite or taken from a different theoretical construction as done in refs.@xcite . this consistency is essential in interpreting the extracted @xmath1 form factors since the non - resonant interactions @xmath29 and @xmath30 can dress the @xmath1 vertex . as discussed in refs.@xcite , only the dressed @xmath1 transition can be identified with the data . the importance of the non - resonant effects on the @xmath40 transition is also stressed recently in ref.@xcite . from the effective hamiltonian eq . ( [ hamile ] ) , it is straightforward to derive a set of coupled equations for @xmath10 and @xmath27 reactions . the resulting pion photoproduction amplitude can be written as @xmath41 where @xmath42 is the current operator and @xmath43 is the photon polarization vector . it can be decomposed into two parts @xmath44 the non - resonant amplitude @xmath45 is calculated from @xmath30 by @xmath46 where the @xmath10 free propagator is defined by @xmath47 the amplitude @xmath48 in eq . ( [ tmatg ] ) is calculated from the non - resonant @xmath10 interaction @xmath29 by solving the following equation @xmath49 the dressed vertices in eq . ( [ tmatt ] ) are defined by @xmath50\gamma_{\delta\rightarrow\pi n}. \label{vertp}\end{aligned}\ ] ] in eq.([vertg ] ) , we also have defined @xmath51 . \nonumber\end{aligned}\ ] ] the @xmath8 self - energy in eq . ( [ tmatt ] ) is then calculated from @xmath52 as seen in the above equations , an important consequence of the dynamical model is that the influence of the non - resonant mechanisms on the resonance properties can be identified and calculated explicitly . the resonance position of the amplitude defined by eq . ( [ tmatt ] ) is shifted from the bare mass @xmath53 by the self - energy @xmath54 . the bare vertex @xmath55 is modified by the non - resonant interaction @xmath30 to give the dressed vertex @xmath56 , as defined by eq . ( [ vertg ] ) . in the sl model , it was found that the extracted m1 strength of the bare vertex @xmath57 is very close to the values predicted by the constituent quark models@xcite , while the empirical values given by the particle data group(pdg)@xcite can only be identified with the dressed vertex @xmath58 . the above equations can be solved for arbitrary photon four - momentum @xmath59 . for investigating the electroproduction reactions , we only need to define a form factor at each photon vertex in figs . 1 - 2 . for the non - resonant interactions(fig . 2 ) , we follow the previous work@xcite . the usual electromagnetic nucleon form factors(given explicitly in the appendix a of ref.@xcite ) are used in evaluating the direct and crossed nucleon terms . to make sure that the non - resonant term @xmath30 is gauge invariant , we set @xmath60 where @xmath61 is the form factor for the contact term , @xmath62 is the pion form factor for the pion - exchange term , and @xmath63 is the nucleon isovector form factor(also given explicitly in the appendix a of ref.@xcite ) . the form factors for the vector meson - exchange terms are chosen to be @xmath64 where @xmath65 is the vector meson mass and the coupling constants @xmath66 for @xmath67 are deduced from the @xmath68 decay widths and are given in ref.@xcite . the prescriptions eqs . ( [ formv])-([coupv ] ) have been commonly used in most of the previous investigations such as that in refs.@xcite . undoubtly , this is an unsatisfactory aspect of this work . on the other hand , `` dynamically '' sound progress in solving the gauge invariance problem can not be made unless a microscopic theory of hadron structure is implemented consistently into our model . this is beyond the scope of this work . for the @xmath1 form factors , we extend eq . ( 4.15 ) of ref.@xcite to write in the rest frame of the @xmath8 @xmath69 , \label{vertgd}\end{aligned}\ ] ] where @xmath70 , @xmath71 is the photon four - momentum , and @xmath72 is the photon polarization vector . the transition operators @xmath73 and @xmath74 are defined by the reduced matrix element @xmath75 in edmonds convention@xcite . the parameterizations of the form factors @xmath76 , @xmath77 and @xmath78 will be specified in section iv . with the form factors defined in eqs.(12)-(14 ) , both the non - resonant term @xmath30 and the bare vertex @xmath57 are gauge invariant . however the full amplitude defined by eq . ( [ tmatt ] ) involves off - shell @xmath10 scattering , as defined by eqs . ( [ tmatg])-([self ] ) , is not gauge invariant . there exists a simple prescription to eliminate this problem phenomenologically . this amounts to defining the conserved currents for eq.([tj ] ) as @xmath79 where @xmath80 is calculated from our model defined above , and @xmath81 is an arbitrary four vector . it is obvious that the currents @xmath82 defined by eq . ( [ gauj ] ) satisfies the gauge invariance condition @xmath83 . if we use the standard choice of the photon momentum @xmath84 and choose @xmath85 , we then have @xmath86 and @xmath87 the above equations mean that within our approach any @xmath88 observable depending on the z - component of the current is determined by eq . ( [ gau00 ] ) using the" +"in a remarkable series of experiments in the nineties , sophisticated cooling techniques were used to expose the quantum nature of ultracold dilute gases . for bosons , the realization of bose - einstein condensation ( bec ) in 1995 @xcite revealed the importance of the underlying aggregating statistics for the existence of a broken symmetry phase in weakly interacting systems . for fermions , the statistics has just the opposite effect . due to the pauli exclusion principle , low energy collisions of fermionic particles are strongly suppressed , worsening the thermalization between the atoms and , therefore , making the cooling techniques more involved . nevertheless , a few years later another milestone experiment was realized in which a quantum degenerate fermi gas was observed @xcite . since then , research with both types of degenerate quantum gases has experienced a strong growth , and different trends have been pursued , each showing interesting and relevant connections to other fields of physics such as atomic , molecular and condensed matter physics . rotating quantum gases constitute one of these fast growing areas . in the case of bosons in a harmonic trap , intensive investigations have been carried out , both theoretically @xcite and experimentally @xcite . if the rotation frequency @xmath1 is of the order of ( but smaller than ) the radial trapping frequency @xmath2 , i.e. @xmath3 , the rotation is called slow . in this regime , intrinsic properties of rotating systems like the temperature dependence of the moment of inertia @xcite , rotation induced excitations @xcite , and the formation of vortices @xcite have been considered . if one rotates faster , vortex arrays are created @xcite where small - amplitude oscillations , so called tkachenko modes , have been observed @xcite and theoretically investigated @xcite . in addition , fast rotating ( @xmath4 ) becs have been linked to fascinating many - body phenomena such as the integer quantum hall effect @xcite or its fractional version @xcite , and are suspected to display quantum phase transitions to non superfluid strongly correlated states @xcite . in the fast rotation regime , experiments in harmonic traps are limited by the loss of confinement due to centrifugal forces when the rotation frequency approaches the axial harmonic trapping frequency . to overcome this problem , a. l. fetter suggested adding a quartic term to the trap potential @xcite . the successful experimental implementation of such a quartic term was carried out in the group of j. dalibard in paris @xcite . in their set - up a laser is used to stir the quartically trapped condensates , making possible the exploration of many properties of the system such as , for instance , the vortex distribution , the optical density @xcite , and the shape oscillations @xcite . the experimental realization triggered further theoretical research focusing on bose - einstein condensates ( bec ) . for instance , their collective oscillations @xcite , thermodynamical @xcite and dynamical @xcite properties have been considered in the presence of the quartic term . thus , the question arises , what new features come about through the interplay between rotation and fermionic statistics . in a harmonic trap , some properties have already been investigated . for instance , the moment of inertia and its relation to quadrupole oscillations , in a framework valid for bosons and fermions @xcite , and the collective excitations @xcite have been studied . in the superfluid phase , formation of vortices @xcite has been observed and a rotation - induced phase separation has been proposed @xcite . in addition , the influence of the landau levels on the density profiles of two - dimensional polarized fermions in the context of the integer quantum hall effect @xcite and the experimental feasibility of fractional quantum hall states @xcite have also been theoretically considered . in the case of an anharmonic trap , apart from studying the breathing mode in the bardeen - cooper - schrieffer ( bcs)-bec crossover regime @xcite , fermions have not been considered and most of the interesting aspects of the physics of rotating systems remain restricted to pure harmonic confinement . at low temperatures , polarized atomic fermi gases are essentially non - interacting due to pauli blocking and the fact that p - wave interactions are negligible in such systems . however , due to the fermi pressure , particles tend to avoid the center of the trap , so that , effectively , a statistical interaction arises even in the case of an ideal gas , which bears some analogies with repulsively interacting bosons @xcite . in this work we are concerned with rotating ideal fermi gases of spin polarized particles rotating with frequency @xmath1 . we consider the same trap configuration as in the paris experiment , which will be described in detail in section [ sec:2 ] . in section [ sec:3 ] we outline a general approach to formally justify the semiclassical approximation for calculating the density of states in anharmonic traps . furthermore , we apply this technique to the paris trap and see that a treatment within the semiclassical approximation is justified . in section [ sec:4 ] we consider ground - state properties of such a system in a similar semiclassical approach . we start by evaluating the fermi energy for arbitrary rotation , then we obtain the particle density , the momentum distribution , and free expansion time - of - flight absorption pictures . in section [ sec:5 ] temperature effects are considered and we derive expressions for the grand - canonical thermodynamic properties in terms of incomplete fermi functions . in addition we analyze analytic low- and high - temperature expansions . for the latter , a virial theorem approach is also presented . section [ sec:6 ] discusses the main results of this work emphasizing the effects of rotation and anharmonicity in comparison to a non - rotating harmonic trap and presents an outlook for the field . in the following we consider a trap potential which is anharmonic and consists of harmonic axially symmetric magnetic trapping supplemented by an additional gaussian trapping term in the @xmath5-plane . the gaussian laser beam is approximated by its fourth order taylor series @xmath6 where @xmath7 and @xmath8 are the laser intensity and width , respectively . the radial distance to the origin is denoted by @xmath9 . the first term in is just a shift in the energy scale and will be neglected in the following . the second order term will be absorbed into the harmonic trapping term . the last term is the one responsible for the quartic confinement and is characterized by the anharmonicity constant @xmath10 . it is important to notice that the harmonic trapping in the @xmath11-direction is not affected by the gaussian laser potential and is characterized by its harmonic oscillator frequency @xmath12 . an issue in the field of rotating quantum gases is that the rotation frequency , with which the condensate effectively rotates , might be different from the one of the stirring laser , due to changes in the shape dependent rotation properties of the gas such as the moment of inertia @xcite . we neglect these effects and assume that a stirring laser can adiabatically add angular momentum to the particles , so that the gas rotates with frequency @xmath1 , yielding an additional centrifugal harmonic term to the trap potential in the co - rotating frame @xcite . under these considerations , the rotating anharmonic potential takes the form @xcite @xmath13 where @xmath14 and @xmath15 are the axial harmonic energy and length scales , respectively , @xmath16 denotes the anisotropy of the trap , @xmath17 represents the anharmonicity of the trap , and @xmath18 is the mass of the atomic species under consideration . the rotation is taken into account with the parameter @xmath19 . adopting the values given for the paris experiment @xcite , the resulting rotating trap is then described by the radial harmonic trapping frequency @xmath20 , the axial harmonic trapping frequency @xmath21 , the force constant @xmath22 of the quartic trapping term , the anisotropy @xmath23 , and a tunable rotation frequency @xmath1 induced by the stirring laser . in the paris experiment , a bec was obtained with the bosonic isotope @xmath24 , for which the dimensionless anharmonicity takes the value @xmath25 . since fermionic species like @xmath26 and @xmath27 have been sympathetic cooled by using the bosonic atoms @xmath24 @xcite and @xmath28 @xcite , respectively , we consider them likely candidates for experiments with ultracold degenerate fermi gases in the paris trap . for definiteness , we evaluate all results of this paper for the parameters of the trap of the paris experiment and the @xmath26 species , for which we have @xmath29 ( see table [ tab:1 ] ) . let us discuss the trap potential and some of its peculiarities concerning rotation . for the moment , we restrict ourselves to the @xmath5-plane . as depicted in fig . [ fig:1 ] , for slow rotations , i.e. @xmath30 , the minimum of the potential is located at the origin . rotating faster one eventually reaches the point where the harmonic confinement vanishes ( @xmath31 ) and the trap is purely quartic . hereafter this will be called critical rotation . if the rotation is made even faster , one achieves the supercritical regime , where the harmonic confinement becomes centrifugal and the trap minimum is moved to @xmath32 and , with respect to the origin , has a depth given by @xmath33 which naturally characterizes the anharmonic trap . the lowest available potential energy is , thus , @xmath34 , in the supercritical case . , for the parameters given at table [ tab:1 ] at both sub- and supercritical rotations . for the latter , a minimum at @xmath35 appears due to the centrifugal nature of the harmonic term.[fig:1],width=288 ] llllll @xmath36 ( hz ) & @xmath37 ( hz ) & @xmath38 & @xmath39 ( jm@xmath40 ) & @xmath41 & @xmath42 + @xmath43 & @xmath44 & @xmath45 & @xmath46 & @xmath47 & @xmath48 + in this section we briefly discuss the meaning and the implementation of the semiclassical approximation for a system of particles possessing one - body hamiltonian @xmath49 with the eigenvalue equation @xmath50 where @xmath51 and @xmath52 denote the @xmath53-th single - particle eigenstate and eigenvalue , respectively . in view of studying the various thermodynamic properties of the system , one is usually interested in evaluating sums of the form @xmath54 where @xmath55 is some function of the single - particle energy levels . the semiclassical approximation consists in considering the energy levels so close to one another that the sum over them can be taken as an integral over a phase space density : @xmath56 to this end we define the density of states @xmath57 where @xmath58 is the dirac delta distribution . in the following we investigate for the parameters of the table [ tab:1 ] whether it is justified to approximate the density of states semiclassically according to @xmath59,\label{eq : g-1b}\ ] ] where @xmath60 denotes the single - particle classical hamiltonian . in systems where the exact energy spectrum is known , e.g. a harmonic trap , the validity of this approximation can be determined by comparing and . however , in the case that the energy spectrum is unknown , as for the present anharmonic potential , we must take a different approach to justify the semiclassical approximation . to this end , we determine not only the leading semiclassical approximation @xmath61 , but also its subleading correction @xmath62 . after setting the relevant energy scale of the system , the validity of the semiclassical approximation can be determined by the _ relative _ magnitude of the correction . we first treat the general case and , then , specialize to the anharmonic" +"the phase transition in the early universe could produce different kinds of topological defects which have some important implications in cosmology@xcite . domain walls are two - dimensional defects , and strings are one - dimensional defects . point - like defects also arise in same theories which undergo the spontaneous symmetry breaking , and they appears as monopoles . the global monopole , which has divergent mass in flat spacetime , is one of the most interesting defects . the idea that monopoles ought to exist has been proved to be remarkably durable . barriola and vilenkin @xcite firstly researched the characteristic of global monopole in curved spacetime , or equivalently , its gravitational effects . when one considers the gravity , the linearly divergent mass of global monopole has an effect analogous to that of a deficit solid angle plus that of a tiny mass at the origin . harari and loust @xcite , and shi and li @xcite have shown that this small gravitational potential is actually repulsive . furthermore , li _ et al _ @xcite have proposed a new class of cold stars which are called d - stars ( defect stars ) . one of the most important features of such stars , comparing to q - stars , is that the theory has monopole solutions when the matter field is absent , which makes the d - stars behave very differently from the q - stars . the topological defects are also investigated in the friedmann - robertson - walker spacetime @xcite . it is shown that the properties of global monopoles in asymptotically ds / ads spacetime @xcite and the brans - dicke theory @xcite are very different from those of ordinary ones . the similar issue for the gravitational mass of composite monopole , i.e. , global and local monopole has also been discussed @xcite . the huge attractive force between global monopole @xmath0 and antimonopole @xmath1 proposes that the monopole over - production problem does not exist , because the pair annihilation is very efficient . barriola and vilenkin have shown that the radiative lifetime of the pair is very short as they lose energy by goldstone boson radiation @xcite . no serious attempt has made to develop an analytical model of the cosmological evolution of a global monopole , so we are limited to the numerical simulations of evolution by bennett and rhie @xcite . in the @xmath2-model approximation , the average number of monopoles per horizon is @xmath3 . the gravitational field of global monopoles can lead to clustering in matter , and later evolve into galaxies and clusters . the scale - invariant spectrum of fluctuations has been given @xcite . furthermore , one can numerically obtain the microwave background anisotropy @xmath4 patterns @xcite . comparing theoretical value to the observed rms fluctuation , one can find the constraint of parameters in global monopole . on the other hand , non - canonical kinetic terms are rather ordinary for effective field theories . the k - field theory , in which the non - canonical kinetic terms are introduced in the lagrangian , have been recently investigated to serve as the inflaton in the inflation scenario , which is so - called k - inflation @xcite , and to explain the current acceleration of the universe and the cosmic coincidence problem , k - essence @xcite . armendariz - picon _ et al _ @xcite have discussed gravitationally bound static and spherically symmetric configurations of k - essence fields . another interesting application of k - fields is topological defects , dubbed by k - defects @xcite . monopole @xcite and vortex @xcite of tachyon field , which as an example of k - field comes from string / m theory , have also been investigated . the mass of global k - monopole diverges in flat spacetime , just as that of standard global monopole , therefore , it is of more physical significance to consider the gravitational effects of global k - monopole . in this paper , we study the gravitational field of global k - monopole and derive the solutions numerically and asymptotically . we find that the topological condition of vacuum manifold for the formation of a k - monopole is identical to that of an ordinary monopole , but their physical properties are disparate . especially , we show that the mass of k - monopole can be positive in some form of the non - canonical kinetic terms . in other words , the gravitational field can be attractive or repulsive depending on the non - canonical kinetic term . we shall work within a particular model in units @xmath5 , where a global @xmath6 symmetry is broken down to @xmath7 in the k - field theory . its action is given by @xmath8,\ ] ] where @xmath9 and @xmath10 is a dimensionless constant . in action ( [ s0 ] ) , @xmath11 , where @xmath12 is the @xmath13 triplet of goldstone field and @xmath14 is the symmetry breaking scale with a dimension of mass . after setting the dimensionless quantities : @xmath15 , @xmath16 and @xmath17 , action ( [ s0 ] ) becomes @xmath18,\ ] ] where @xmath19 . the hedgedog configuration describing a global k - monopole is @xmath20 where @xmath21 and @xmath22 , so that we shall actually have a global k - monopole solution if @xmath23 at spatial infinity and @xmath24 near the origin . the static spherically symmetric metric can be written as @xmath25 with the usual relation between the spherical coordinates @xmath26 , @xmath27 , @xmath28 and the `` cartesian '' coordinate @xmath29 . introducing a dimensionless parameter @xmath30 , from ( [ s ] ) and ( [ config ] ) , we obtain the equations of motion for @xmath31 as @xmath32f'-\frac{2}{r^2}f\right\}+ \ddot{k}\frac{x'f'}{a } - \lambda^2f(f^2 - 1)=0,\end{aligned}\ ] ] where the prime denotes the derivative with respect to @xmath33 , the dot denotes the derivative with respect to @xmath34 and @xmath35 . since we only consider the static solution , positive @xmath34 and negative @xmath34 are irrelevant each other . in this paper , we will assume @xmath36 to be valid for negative @xmath34 . the einstein equation for k - monopole is @xmath37 where @xmath38 is the energy - momentum tensor for the action ( [ s ] ) . the tt and rr components of the einstein equations now could be written as @xmath39 where @xmath40 and @xmath41 is a dimensionless parameter . although the existence of global k - monopole , as well as the standard one , is guaranteed by the symmetry - breaking potential , there exist the non - canonical kinetic term in k - monopole which certainly leads to the appearance of a new scale in the action and the mass parameter in the potential term . however , the non - canonical kinetic term is non - trivial . at small gradients , it can be chosen to have a same asymptotical behavior with that of the standard one , so that it ensures the standard manner of a small perturbations . while at large gradient we choose it to have a different form from the standard one . in the small @xmath34 case , we assume that the kinetic term has the asymptotically canonical behavior , which can avoid `` zero - kinetic problem '' . if @xmath42 , we have @xmath43 , and @xmath44 then there is a singularity at @xmath45 ; and @xmath46 then the system becomes non - dynamical at @xmath45 . for the monopole solution , it is easily found that @xmath47 at @xmath48 . on the other hand , we assume that the modificatory kinetic term @xmath49 and @xmath50 at @xmath51 . one can easily obtain the equation of motion inside the core of a global monopole after assuming that @xmath51 in the core of the global monopole . the equations of motion are highly non - linear and can not be solved analytically . next , we investigate the asymptotic behaviors of global monopole with non - linear in @xmath34 kinetic term . to be specific , we consider the following type of kinetic term @xmath52 where @xmath53 is a parameter of global k - monopole . it is easy to find that global k - monopole will reduce to be the standard one when @xmath54 . it is easy to check whether the kinetic term ( [ kx ] ) satisfy the condition for the hyperbolicity @xcite @xmath55 which leads to a positive definite speed of sound for the small perturbations of the field . the stability of solutions shows that for the case @xmath56 , the range @xmath57 must be excluded . however , this will not destroy the results which are carried out from the case @xmath58 . we here only consider the cases for @xmath58 . using eqs.([gold])-([t11 ] ) , we get the asymptotic expression for @xmath59 , @xmath60 , and @xmath61 which is valid near @xmath62 , @xmath63}{60\,\left ( 1 + 5\beta\,{{f_0}}^2 \right)}{r}^3 \\\nonumber & + & \frac{f_0\left[\left ( 9 + 7\beta\,\lambda^2 \right ) \,\epsilon^2 \,{{f_0}}^2 + 36\beta^2\,\epsilon^2 \,{{f_0}}^6 \right ] } { 60\,\left ( 1 + 5\beta\,{{f_0}}^2 \right ) } { r}^3+o(r^4)\end{aligned}\ ] ] @xmath64 @xmath65 where the undetermined coefficient @xmath66 is characterized as the mass of k - monopole , which can be determined in the numerical calculation . in the region of @xmath48 , similarly we can expand @xmath61 , @xmath59 and @xmath60 as @xmath67 \left(\frac{1}{r}\right)^2\\\nonumber & + & o(r^{-3 } ) \\\label{br } b(r)&=&(1-\epsilon^2)+m_{\infty}\frac{1}{r } - \frac{\epsilon^2 \,\left ( 1 -\beta \lambda^2 \right ) } { \lambda^2 } \left(\frac{1}{r}\right)^2+o(r^{-3}),\end{aligned}\ ] ] where the constant @xmath68 will be discussed in the following . using shooting method for boundary value problems , we get the numerical results of the function @xmath61 which describes the configuration of global k - monopole . in fig.[f ] we show the function @xmath61 for @xmath54 , @xmath69 , @xmath70 and @xmath71 respectively and for given values of @xmath10 and @xmath72 . obviously , the configuration of field @xmath31 is not impressible to the choice of the parameter @xmath53 . as a function of @xmath33 . here we choose @xmath73 , @xmath74 and @xmath75 . the four curved lines are plotted when @xmath54 , @xmath69 , @xmath70 and @xmath71 respectively . , width=288 ] from eqs.([fs ] ) and ( [ fb ] ) , it is easy to construct global k - monopole which has the same asymptotic condition with standard global monopole , _ i.e. _ , @xmath31 will approach to zero when @xmath76 and approach to unity when @xmath77 . actually there is a general solution to einstein equation with energy - momentum tensor @xmath38 which takes the form as ( [ t00 ] ) and ( [ t11 ] ) for spherically symmetric metric ( [ metric ] ) @xmath78r^2dr\ ] ] @xmath79.\ ] ] in terms of the dimensionless quantity @xmath72 , the metric coefficient @xmath59 and @xmath60 can be formally integrated and read as @xmath80 @xmath81 the small dimensionless parameter @xmath72 arise naturally from einstein equations and clearly @xmath82 describes a solid angular deficit of space - time . a global k - monopole solution @xmath31 should approach unity when @xmath83 . if this convergence is fast enough , then @xmath84 and @xmath85 will also rapidly converge to finite values . therefore , from eqs.([fb])-([br ] ) we have the asymptotic expansions : @xmath86 where @xmath87 . one can easily find that the dependence on @xmath72 of the asymptotic expansion for @xmath61 is very weak , in other words , the asymptotic behavior is quite independent of the scale of symmetry breakdown @xmath88 up to value as large as the planck scale . on the contrary , @xmath84 depends obviously on @xmath88 . as a function of @xmath33 . here we choose @xmath73 , @xmath74 and" +"it is observationally well established that the velocity dispersion of main sequence stars increases with advancing spectral type . this fact has been recognised ever since velocity dispersions were first measured in the solar neighbourhood ( e.g. king 1990 ) . initially these observations were explained as the result of equipartition of energy because the mass of the stars decreases along the main sequence . however the two - body relaxation time scale is much too long to have any effect on the stellar velocity ellipsoid , prompting explanations relying on collective effects instead . some of the different functional forms that have been suggested for the velocity dispersion - age relation are reviewed by lacey ( 1991 ) . this increase in velocity dispersion , or heating , depends on the roughness of the gravitational potential in the disk , so knowledge about the shape of the velocity ellipsoid will tell us a great deal about the dynamical history of a disk . until recently direct measurements of the three - dimensional shape of the velocity ellipsoid have been restricted to the solar neighbourhood . observations of the stellar velocities in external spiral galaxies have concentrated on systems that are either close to edge - on or face - on ( van der kruit and freeman 1986 ; bottema 1995 ) and will therefore only provide information about a single component of the velocity dispersion . from these measurements only indirect inferences can be drawn about the shape of velocity ellipsoids in galaxies because the results of a small sample of _ different _ galaxies are being compared in a statistical way . moreover , this shape will be subject to rather large uncertainties because the errors of the face - on and edge - on galaxies are compounded , and because relating face - on and edge - on galaxies is rather delicate . in this pilot study we show that it is possible to derive the shape of the velocity ellipsoid within a _ single _ galaxy . we use the fact that an intermediate - inclination galaxy shows different projections of the velocity dispersion at different galactocentric azimuths . in section 2 the method by which we extract the velocity dispersions information is described . in section 3 we apply this analysis to the large early type spiral ngc 488 and in section 4 we discuss the results obtained for ngc 488 and compare them to the velocity ellipsoid in the solar neighbourhood . in cylindrical polar coordinates @xmath0 the line - of - sight velocity dispersion as a function of ( intrinsic ) position angle @xmath1 in a thin axisymmetric disk is @xmath2 \sin^2 i + \sigma_z^2 \cos^2 i , \ ] ] which can be written as @xmath3.\ ] ] thus , it consists of an element with a @xmath4 variation that depends only on the components of the dispersion in the plane of the galaxy , and an element with no dependence on @xmath1 that depends on all three components of the velocity dispersion . observations along at least two axes ( preferably the major and minor axes , which provide maximum leverage ) , are therefore required to extract both coefficients . furthermore , in disk galaxies , in which most orbits are well - described by the epicycle approximation the radial and azimuthal dispersions obey the relation @xmath5 where @xmath6 is the circular speed in the galaxy . ( in the solar neighbourhood , this expression reduces to @xmath7 , where @xmath8 and @xmath9 are the oort constants . ) within the epicycle approximation the stellar rotation speed @xmath10 equals the circular speed @xmath11 , so the righthandside of eq . [ eq : ax ] can be derived from the same spectral observations that are used to measure the velocity dispersions . the effect of higher - order approximations on this formula are discussed by kuijken & tremaine 1991 , who showed that the strongest deviations from eq . [ eq : ax ] are to be found at radii of several disk scale lengths ( see also cuddeford & binney 1994 ) . where the circular speed @xmath6 can be measured separately ( e.g. , from an emission - line rotation curve ) , a further constraint on the dispersions and velocities is the asymmetric drift equation , @xmath12 -r\frac{\partial \sigma^2_{r z}}{\partial z}\ ] ] the last term of equation 4 describes the tilting of the velocity ellipsoid . the two limiting cases of this tilting term are zero and ( @xmath13 ) . orbit integration by binney & spergel ( 1983 ) and by kuijken & gilmore ( 1989 ) suggest that in the solar neighbourhood the truth lies close to midway between the two extremes . as will be seen below , the uncertainty in this term is not a concern in the present analysis . in summary , the three components of the stellar velocity ellipsoid can be deduced from measurements of the line - of - sight dispersions along two position angles in a galaxy disk . the two sets of measurements , together with the ratio of tangential and radial velocity dispersions appropriate for nearly circular orbits , provide the three equations necessary to deproject the ellipsoid . if the asymmetric drift can also be measured , e.g. when a rotation curve for cold interstellar gas is available , the system is overdetermined , allowing a consistency check on the result . we choose the large early type spiral ngc 488 for this analysis because of its regular optical appearance and its intermediate inclination . table 1 lists some properties of this galaxy . note the very high rotational velocity ( peterson 1980 ) . .parameters of ngc 488 [ cols=""<,^ "" , ] we have tested this procedure on a large ( @xmath14 ) set of artificial major and minor axis spectra , created from the template star to resemble the observed galactic spectra as closely as possible , with a different poisson noise realisation for each spectrum . the best - fit parameters obtained from these spectra scatter with the same dispersion as the errors obtained from any individual fit to a spectrum . therefore , we conclude that the parameters returned by the fit programme are reliable . an obvious extension to our fitting procedure would be to use different scale lengths for the @xmath15 and @xmath16 dispersion components . unfortunately the data are not of sufficient quality to allow for a six parameter fit . one of the six eigenvalues that we obtained from diagonalising the correlation matrix was much larger than the other five , a clear indication that a six parameter fit is stretching the data a bit too much . interestingly , the kinematic scale length of the disk appears to be comparable to the photometric one . this is not the expectation from local isothermal approximation for disks , which predicts a scale length double the photometric one . the most likely explanation is probably the fact that we measure the scale length in the b band while the stellar mass distribution is best traced in the k band , the near infra - red . empirically it is found that scale lengths in the k band are shorter than the b band up to a factor of about 2 ( de jong 1995 , figure 4 and peletier et al . 1996 ) . alternatively the approximation of a local isothermal distribution breaks down . the fits described above are to the stellar data only . the lowest panel in fig . 2 shows the emission line data of peterson and the predictions from our two fits . both our fits are fully consistent with these data , and provide extra confirmation of the validity of our analysis . ( a simple power - law fit to the emission - line data plotted in fig . 2 gives a power index of 0.18 @xmath17 0.13 . ) unfortunately there are no measured emission line velocities in the inner part of the disk . peterson gives velocities around 195 km / s near a radius of 10 arcsec which are a little higher than our fits would predict . however there is no reason why a power - law rotation curve should persist into those central , bulge dominated regions . this is the first direct measurement of the vertical - to - radial velocity dispersion ratio anywhere outside the solar neighbourhood . previous determinations have all been indirect , and hence suffer from large uncertainities . the method we have described here is quite straightforward , and could be applied to many systems . the derived value of @xmath18 , which is effectively the average ratio near one photometric scale length , is somewhat higher than the solar neighbourhood value of 0.52 @xmath17 0.03 that wielen ( 1977 ) derived from the mccormick sample of k and m dwarfs . however , the error of 0.03 is the purely statistical error , but the scatter between the published observational estimates of this ratio suggests that the true error may be larger ( see lacey 1991 ) . any difference between the two ratios is consistent with the findings about the relative effects of the two dominant heating mechanisms , molecular clouds and spiral structure , as we now show . heating by molecular clouds was originally proposed by spitzer and schwarzschild ( 1951 ) . they proposed that stars in star - cloud encounters gain kinetic energy at the expense of the clouds because of the huge masses of the latter . subsequent analysis by lacey ( 1984 ) and @xmath19-body simulations by villumsen ( 1985 ) showed however that this mechanism saturates rather quickly ( once the stars have sufficient energy that they spend most of their time outside the cloud layer the heating rate drops ) and could not fully explain the observed heating . an alternative proposal to heat the disk , due to barbanis and woltjer ( 1967 ) , explains the heating as the result of stars scattering from spiral irregularities in the galactic potential . carlberg and sellwood ( 1985 ) have extended this work and showed that this can indeed heat up the disk . however this process can not heat the stars efficiently in the vertical direction because the vertical oscillation frequency of stars is much larger than the frequency at which a spiral wave sweeps past the stars orbiting the disk . hence the stars respond almost adiabatically to this force . giant molecular clouds create large spiral wakes , often much larger than a cloud itself ( julian and toomre 1966 ) . this interplay between clouds and spiral irregularities is not yet completely understood but it is clear that they are not independent . jenkins and binney ( 1990 ) examined the combined effects of both processes based on monte carlo simulations of the fokker - planck equation describing these processes . they expressed the relative importance of heating by spiral structure to heating by clouds by a parameter denoted @xmath20 and calculated the corresponding ratio of @xmath21 ( see their figure 2 ) . from the observed shape of the velocity ellipsoid and velocity dispersion - age relations they concluded that in the solar neighbourhood the heating of the disk is dominated by spiral structure ( @xmath22 ) . the mean surface density of the cloud layer near the sun is 1.8 @xmath23 pc@xmath24 ( clemens , sanders and scoville 1988 ) . from the fcrao extragalactic co survey ( young et al . 1995 ) a mean surface density for ngc 488 is derived of 3.5 @xmath23 pc@xmath24 . ( young et al . find that the co layer in ngc 488 is best described by a uniform distribution with a radius of 1.65 arcmin and a co flux of @xmath25 jy" +"a _ unit disk graph _ @xmath7 is a graph whose @xmath0 vertices can be mapped to points in the plane and whose @xmath8 edges are defined by pairs of points within euclidean distance at most @xmath9 from one another . alternatively , one can regard the vertices of @xmath7 as mapped to coplanar disks of unit diameter , so that two vertices are adjacent whenever the corresponding disks intersect . a _ dominating set _ @xmath10 is a subset of the vertices of a graph such that every vertex not in @xmath10 is adjacent to some vertex in @xmath10 independent set _ is a subset of mutually non - adjacent vertices . an _ independent dominating set _ is a dominating set which is also an independent set . note that any maximal independent set is an independent dominating set . dominating sets in unit disk graphs are widely studied due to their application in wireless ad - hoc networks @xcite . since it is * np*-hard to compute a minimum dominating set of a unit disk graph @xcite , several approximation algorithms have been proposed @xcite . such algorithms are of two main types . _ graph - based algorithms _ receive as input the adjacency representation of the graph and assume no knowledge of the point coordinates , whereas _ geometric algorithms _ work in the real ram model of computation and receive solely the vertex coordinates as input . if the coordinates of the @xmath0 disk centers are known , the @xmath8 edges of the corresponding graph @xmath7 can be figured out easily . it can be done in @xmath2 time under the real ram model with floor function and constant - time hashing , and in @xmath11 time without those operations @xcite . thus , for the price of a conversion step , graph - based algorithms can be used when the input is a unit disk realization of @xmath7 . however , unless * * p**=*np * , no efficient algorithm exists to decide whether a given graph admits a unit disk realization @xcite , let alone exhibit one . as a consequence , geometric algorithms can not be efficiently transformed into graph - based algorithms . in this paper , we introduce approximation algorithms of both types , benefiting from the same approximation factor analysis . the proposed graph - based algorithm runs in @xmath2 time , and the geometric algorithm runs in @xmath4 time regardless of @xmath8 . [ [ previous - algorithms ] ] previous algorithms + + + + + + + + + + + + + + + + + + + a graph - based @xmath1-approximation algorithm that runs in @xmath2 time was presented in @xcite . the algorithm computes a maximal independent set , which turns out to be a @xmath1-approximation because unit disk graphs contain no @xmath12 as induced subgraphs , as shown in that same paper . consists of a vertex with @xmath13 pendant neighbors . ] polynomial - time approximation schemes ( ptas ) were first presented as geometric algorithms @xcite and later as graph - based algorithms @xcite . also , a graph - based ptas for the more general disk graphs was proposed in @xcite . unfortunately , the complexities of the existing ptass are high - degree polynomials . for example , the ptas presented in @xcite takes @xmath14 time to obtain a @xmath1-approximation ( the analysis from @xcite ) . although its analysis is not tight , the running time is too high even for moderately large graphs . the reason is that these ptass invoke a subroutine that verifies by brute force whether a graph admits a dominating set with @xmath15 vertices . the verification takes @xmath16 time , and it is unlikely that this can be improved ( unless * * fpt**=*w[1 ] * , as proved in @xcite ) . such a subroutine is applied to several subgraphs , and the value of @xmath15 grows as the approximation error decreases . a similar strategy was used in @xcite to obtain a ptas for the minimum independent dominating set . the lack of fast algorithms with approximation factor less than @xmath1 was recently noticed in @xcite , where geometric algorithms with approximation factors of @xmath17 and @xmath18 and running times respectively @xmath19 and @xmath20 were presented . while a significant step towards approximating large instances , those algorithms require the geometric representation of the graph , and their running times are still polynomials of rather high degrees . linear and near - linear - time approximation algorithms constitute an active topic of research , even for problems that can be solved exactly in polynomial time , such as maximum flow and maximum matching @xcite . it is useful to contrast the minimum dominating set problem with the maximum independent set problem . while a maximal independent set is a @xmath1-approximation to both problems , it is easy to obtain a geometric @xmath18-approximation to the maximum independent set problem in @xmath4 time @xcite . in the graph - based version , a related strategy takes roughly @xmath21 time , though . no similar results are known for the minimum dominating set problem . the existing ptass for the minimum dominating set problem in unit disk graphs are based on some packing constraints that apply to unit disk graphs . one of these constraints is the _ bounded growth property _ : the size of an independent set formed by vertices within distance @xmath22 of a given vertex , in a unit disk graph , is at most @xmath23 . note , however , that the bounded growth property is not tight . for example , for @xmath24 , it gives an upper bound of @xmath25 vertices where the actual maximum size is @xmath1 . since the bounded growth property is strongly connected to the problem of packing circles in a circle , obtaining exact values for all @xmath22 seems unlikely @xcite . [ [ our - contribution ] ] our contribution + + + + + + + + + + + + + + + + our main result consists of the two approximation algorithms given in section [ s : algorithm ] : a graph - based algorithm , which runs in linear @xmath2 time , and its geometric counterpart , which runs in @xmath26 time in the real ram model , regardless of the number of edges . the approximation factor of both algorithms is @xmath3 . the strategy in both cases is to construct a @xmath1-approximate solution using the algorithm from @xcite , and then perform local improvements to that initial dominating set . our main lemma ( lemma [ l : irreducible ] ) uses forbidden subgraphs to show that a solution that admits no local improvement is a @xmath3-approximation . since the dominating sets produced by our algorithms are independent sets , the same approximation factor holds for the independent dominating set problem . proving that a certain graph is _ not _ a unit disk graph ( and is therefore a forbidden induced subgraph ) is no easy feat . we make use of an assortment of results from discrete geometry in order to prove properties of unit disk graphs that are interesting _ per se_. for example , we use universal covers and disk packings to show that the neighborhood of a clique in a unit disk graph contains at most @xmath27 independent vertices . these properties , along with a tighter version of the bounded growth property , are collected in section [ s : forbidden ] , and allow us to show that certain graphs are not unit disk graphs . consequently , the analyses of our algorithms employ a broader set of forbidden subgraphs which include , but are not limited to , the @xmath12 . additionally , in section [ s : partial ] , we show that a possible , somewhat natural refinement to our graph - based algorithm leads to a tighter @xmath5-approximation , albeit for the price of an extra @xmath28 multiplying factor in the time complexity of the algorithm . in this section , we introduce some lemmas about the structure of unit disk graphs . these lemmas will be applied to prove our approximation factors in sections [ s : algorithm ] and [ s : partial ] . we start by stating three previous results from the area of discrete geometry . the first lemma comes from the study of universal covers ( for a recent survey see @xcite ) . [ l : universal_cover ] if a set of points @xmath29 has diameter @xmath9 , then @xmath29 can be enclosed by a circle of radius @xmath30 . packing congruent disks in a circle is a well - studied problem . exact bounds on the radius of the smallest circle packing @xmath15 unitary disks are known for some small values of @xmath15 , namely @xmath31 and @xmath32 @xcite . the bound for @xmath33 will be useful to us . [ l : pack13 ] the radius of the smallest circle enclosing @xmath34 points with mutual distances at least @xmath9 is @xmath35 . the _ density _ of a packing is the ratio between the covered area and the total area . the following general upper bound is useful when no exact bound is known . [ l : density ] every packing of two or more congruent disks in a convex region has density at most @xmath36 . given a graph @xmath37 and a vertex @xmath38 , let @xmath39 denote the _ open neighborhood _ of @xmath40 and let @xmath41 = n(v ) \cup \{v\}$ ] denote the _ closed neighborhood _ of @xmath40 . more generally , the _ open @xmath22-neighborhood _ of a vertex @xmath40 is the set of vertices @xmath42 such that the distance between @xmath40 and @xmath42 in @xmath7 is exactly @xmath22 , while the _ closed @xmath22-neighborhood _ of a vertex @xmath40 is the set of vertices @xmath42 such that the distance between @xmath40 and @xmath42 in @xmath7 is at most @xmath22 . for a set @xmath43 , we let @xmath44 and @xmath45 = n[v ] \cap s$ ] . finally , given a subgraph @xmath46 of @xmath7 , the closed neighborhood of @xmath46 , denoted @xmath47 $ ] , is the set of vertices that belong to the closed neighborhood of some vertex of @xmath46 . the following two lemmas concern neighborhoods in unit disk graphs . [ l : clique ] the closed neighborhood of a clique in a unit disk graph contains at most @xmath27 independent vertices . by lemma [ l : universal_cover ] , the points which define a clique in a unit disk graph can be enclosed by a circle of radius @xmath30 . therefore , the points corresponding to the closed neighborhood of such a clique are enclosed by a circle of radius @xmath48 . by lemma [ l : pack13 ] , a circle enclosing @xmath34 points with mutual distances at least @xmath9 has radius at least @xmath35 . since @xmath49 , the lemma follows . [ l:2neighborhood ] given an integer @xmath50 , the closed @xmath22-neighborhood of a vertex in a unit disk graph contains at most @xmath51 independent vertices . all @xmath0 disks of diameter @xmath9 corresponding to the closed @xmath22-neighborhood of a vertex @xmath40 must be enclosed by a circle @xmath52 of radius @xmath53 centered on @xmath40 . each disk of diameter @xmath9 has area @xmath54 and @xmath52 has area @xmath55 . using lemma [ l : density ] , we have @xmath56 , and the lemma follows . we say that a graph @xmath7 is _ @xmath57-pendant _ if there is a vertex @xmath40 in @xmath7 with @xmath15 vertices of degree @xmath9 in the open neighborhood of @xmath40 and @xmath58 vertices of degree @xmath9 in the open @xmath59-neighborhood of @xmath40 . we refer" +"in the field of optomechanics , one is always designing mechanical systems with lowest possible friction @xcite and highest possible optomechanical coupling constant @xcite . this is because one would like to produce and use coherent phonons with long coherence time . one prominent application of coherent phonons is in storage and retrieval of light using optomechanical systems @xcite . an attractive system which has received considerable attention is the levitated microsphere trapped in an optical cavity . both trapping and levitation can be produced by optical fields @xcite . another very attractive system is superfluid he , which has zero viscosity . it is known to have acoustic phonons with almost zero friction at low temperatures , a finite value arising only from thermal three - phonon scattering processes @xcite . de lorenzo and schwab @xcite have performed initial optomechanical experiments on superfluid he by coupling it to a superconducting resonator . flowers - jacobs _ et al . _ @xcite have reported progress in doing optomechanics with superfluid he using optical cavities . in view of the current interest @xcite in the optomechanics with superfluid he , we present in this paper theoretical foundations of optomechanics in such systems . the organization of this paper is as follows . in sec . ii , we derive the basic semiclassical equations for the optomechanical interactions in superfluid he . in sec . iii , we present a hamiltonian formulation of the problem in terms of the canonical variables , so that this can be adopted for quantized phonon and photon fields . the theory is formulated in terms of the fields , both electromagnetic and fluid density , so that situations involving many phonons and photons of different frequencies can be handled . in sec . iv , we present a quantized description of the optomechanical interactions . we present estimates for the strength of the optomechanical interactions . the linear optomechanical interaction shift of the cavity resonance per photon is quite significant in cavities like a fiber cavity @xcite . we derive the canonical form @xcite of the hamiltonian for linear optomechanical interactions in superfluid he . having obtained the canonical form , we can study all the physical processes that have been studied with other optomechanical systems . an estimate of the single step two - phonon antistokes process due to acoustic nonlinearity is also given in this section . in sec . v , we discuss two - step two - phonon processes , which are shown to be significant in superfluid he . it may be noted that the knowledge of the linear interaction hamiltonian ( [ 04.19 ] ) with the strength of @xmath1 estimated after eq ( [ 04.15 ] ) is sufficient to understand the processes in sec . v. when the electromagnetic cavity is designed in such a way that allowed optical modes are such that no anti - stokes upconversion is possible via the absorption of any single phonon in the medium , one must consider absorption of two phonons for possible upconversion . such a process can be controlled well when these phonons are external phonons injected in the medium . because of the intrinsic nonlinearity of the superfluid he , we have the new possibilities arising from the combination of the superfluid nonlinearity and the optomechanical interactions . in this section , we start with the fundamental equations @xcite for the superfluid density @xmath2 and the velocity @xmath3 and we obtain modifications of these due to interaction with the electromagnetic fields . the basic equations for @xmath2 and @xmath3 in the absence of the electromagnetic fields are given by @xmath4 @xmath5 where the stress tensor @xmath6 is given by @xmath7 here @xmath8 is the pressure in the superfluid . we have set the viscosity term zero . we note that we have a set of nonlinear equations as pressure is generally expanded @xcite in terms of the normalized deviation @xmath9 from the equilibrium value @xmath10 : @xmath11 we now discuss the modification of eqs . ( [ 2.1 ] ) and ( [ 2.2 ] ) due to the interaction with the electromagnetic fields . clearly eq . ( [ 2.1 ] ) remains unchanged . we need to modify eq . ( [ 2.2 ] ) by the addition of the maxwell stress contribution @xmath12 to eq . ( [ 2.2 ] ) _ i.e. _ @xmath13 the form of the maxwell stress tensor depends on the nature of the medium . it is derived from the considerations of the electromagnetic force on the medium . on dropping the magnetic polarization contribution , the force on a linear medium can be written as @xmath14 here @xmath15 is the electromagnetic field and @xmath16 is the optical dielectric function of the isotropic superfluid . the electromagnetic force can also be written in an alternate form @xcite @xmath17 the dielectric function of the medium depends on @xmath18 through the density _ i.e. _ @xmath19 $ ] and hence @xmath20}{\partial\rho } \vec\nabla\rho,\ ] ] and hence eq . ( [ 2.7 ] ) reduces to @xmath21.\end{aligned}\ ] ] using eq . ( [ 2.9 ] ) , eq.([2.5 ] ) becomes @xmath22 = 0.\ ] ] the equations eqs . ( [ 2.1 ] ) and ( [ 2.10 ] ) are the basic equations for the optomechanical interactions in superfluid he . the only assumption that we made in deriving eq . ( [ 2.10 ] ) is the linear electromagnetic response @xmath23 $ ] of superfluid he . the equations ( [ 2.1 ] ) and ( [ 2.10 ] ) are to be supplemented by the expansion ( [ 2.4 ] ) . the electric field obeys the equation @xmath24\vec{e}\right ) = 0,\ ] ] which is obtained from the maxwell equations . in the hamiltonian description , one introduces the conjugate variables @xmath25 and @xmath26 and the classical velocity is related to @xmath27 via @xmath28 the hamiltonian description of the superfluid equations ( [ 2.1 ] ) and ( [ 2.2 ] ) is well - known and for completeness , we recall the main aspects . the unperturbed hamiltonian density is @xmath29 and the interaction term is @xmath30 the function @xmath31 is related to the pressure via the thermodynamic relation @xcite @xmath32 using the total hamiltonian @xmath33 , we can see how eqs.([3.2])-([3.4 ] ) lead to eqs.([2.1 ] ) and ( [ 2.2 ] ) . for this purpose , we use the hamiltonian formulation for fields @xcite @xmath34 = -\sum_j\frac{\partial}{\partial r_j } [ \rho v_j ] \nonumber\\ & = -\vec{\nabla}\cdot(\rho\vec{v } ) , \label{3.5 } \\ \dot{\phi } & = \frac{\delta h}{\delta\rho } = \frac12(\nabla\phi)^2 + \frac{\partial}{\partial\rho } [ \rho w(\rho ) ] \nonumber\\ & = \frac12v^2 + \left(w + \frac{p(\rho)}{\rho } \right ) . \label{3.6}\end{aligned}\ ] ] we can convert eq.([3.6 ] ) into an equation for @xmath35 as follows @xmath36\vec{v } - \rho\vec{\nabla}\left[\frac12v^2 + w + \frac{p(\rho)}{\rho}\right ] \nonumber \\ & = -\rho(\vec{\nabla}\rho)\frac{\partial}{\partial\rho } \left[w+\frac{p(\rho)}{\rho}\right ] - \vec{\nabla}\cdot[\rho\vec{v}\vec{v } ] \nonumber \\ & = - \vec{\nabla}\cdot[\rho\vec{v}\vec{v } ] - \vec{\nabla}\cdot(p{\overleftrightarrow}{i}),\end{aligned}\ ] ] where @xmath37 is the unit tensor . the eqs.([3.5 ] ) and ( [ 3.7 ] ) are identical to eqs.([2.1 ] ) and ( [ 2.2 ] ) respectively . the hamiltonian for optomechanical interactions in superfluid he will then be @xmath38-\epsilon_0}{2})e^2 , \label{3.11}\end{aligned}\ ] ] where @xmath39 is the polarization in superfluid medium . using eq . ( [ 3.8 ] ) , the equations for the canonical conjugate variables @xmath2 and @xmath27 are @xmath40 a simple exercise shows that eq.([3.13 ] ) is equivalent to the eq.([2.10 ] ) for @xmath41 . the hamiltonian ( [ 3.8 ] ) depends on the density @xmath2 to all orders . in order to bring out some of the important physical process , we consider an expansion of @xmath42 in powers of the deviation @xmath43 , @xmath44 from the equilibrium value @xmath10 . we will examine terms up to second order in @xmath43 . the expansion of the optomechanical interaction term is straight forward : @xmath45 = \epsilon[\rho_0 ] + \rho_0\left(\frac{\partial\epsilon}{\partial\rho}\right)_0\tilde\rho + \frac12 \rho_0 ^ 2\left(\frac{\partial^2\epsilon}{\partial\rho^2}\right)_0\tilde{\rho}^2 + \dots , \label{3.14}\\ \mathcal{h}^{\text{(em)}}_1 = - \frac{\epsilon(\rho_0)-\epsilon_0}{2}e^2 - \frac12 g_1\epsilon_0 \tilde\rho e^2 - \frac12 g_2\epsilon_0 \tilde\rho^2 e^2 + \dots , \label{3.15 } \\ g_1 = \frac{\rho_0}{\epsilon_0}\left(\frac{\partial\epsilon}{\partial\rho}\right)_0 , \qquad g_2 = \frac{\rho_0 ^ 2}{2\epsilon_0}\left(\frac{\partial^2\epsilon}{\partial\rho^2}\right)_0 . \nonumber\end{gathered}\ ] ] here @xmath46 and @xmath47 are the coupling constants for the linear and quadratic optomechanical interactions . a rough estimate of @xmath46 and @xmath47 can be obtained from the experimental data @xcite on liquid he : @xmath48 where the molecular polarizability @xmath49 is @xmath50m@xmath51mole , @xmath52kg / mole , equilibrium density @xmath53kg / m@xmath54 , and hence @xmath55 further , @xmath56 and therefore the term @xmath57 contributes to small frequency shifts of the electromagnetic fields . we will ignore such frequency shifts . the term @xmath58 gives the nonlinearities of the superfluid in the absence of any applied electromagnetic fields . we write @xmath59 as @xmath60 and use @xmath61 , to obtain @xmath62 the parameter @xmath63 is called the gruneisen constant @xcite and has the value @xmath64 . in eq.([3.18 ] ) , @xmath65m / sec ) is the velocity of sound . the nonlinear conversion of phonons , as determined by the @xmath66 term in eq . ( [ 3.19 ] ) , has been discussed by wright _ et al . _ @xcite . in order to simplify @xmath67 in powers of @xmath43 , we need to find the expansion of @xmath68 , which can be obtained from eq.([3.12 ] ) , which to lowest order in density yields @xmath69 in order to do the quantization , we invoke the space - time structure of the electromagnetic and density ( acoustic ) fields . we would be studying optomechanical interactions in a cavity which could be an optical one like a fiber cavity @xcite or a superconducting one @xcite . the electromagnetic field can be written as a superposition of orthogonal and orthonormal transverse modes @xmath70 _ i.e. _ @xmath71 where the mode function @xmath70 has frequency @xmath72 and is a solution of @xmath73 . the hamiltonian ( [ 3.10 ] ) for the electromagnetic field leads to @xmath74 where we used the orthogonality of the mode functions @xmath75{\mathrm{d}}^3r = \delta_{ij}$ ] . in order to do the quantization , we identify @xmath76 with @xmath77 . thus the amplitude @xmath78 is to be replaced by the annihilation operator @xmath79 via @xmath80 therefore , the quantized form of the electric field is @xmath81 and the unperturbed hamiltonian is @xmath82 we expand the phonon field in terms of the normalized mode functions @xmath83 with frequency @xmath84 , @xmath85 note that @xmath83 has the dimension @xmath86 and hence @xmath87 has the dimension @xmath88 . the quantization of the free phonon field is more complicated due to the nonlinear nature of the interaction term ( [ 3.3 ] ) . in order to do the quantization , we look at the harmonic version of ( [ 3.3 ] ) , _ i.e. _ we use eq.([3.19 ] ) up to order @xmath89 . we next find @xmath90 ( eq.([3.2 ] ) ) to lowest order _ i.e. _ up to second order in density . from eqs.([3.20 ] ) , ( [ 04.6 ] ) and ( [ 04.7 ] ) , we can easily obtain @xmath91 and hence for a given mode @xmath92 we thus quantize the phonon field via @xmath93 where @xmath94 is the bosonic annihilation operator for the phonon with frequency @xmath84 . the unperturbed hamiltonian for the phonon field @xmath95 is @xmath96 the terms of the order @xmath97 can be obtained by using the expansion ( [ 3.19 ] ) . these correspond to three phonon scattering processes . the quantized form of the interaction hamiltonian ( [ 3.15 ] ) can now be obtained by using eqs.([04.4 ] ) and ( [ 04.11 ]" +"spontaneous emission by an excited atom is one of the most studied examples of a quantum process and may be attributed , at least in part , to fluctuations in the electromagnetic vacuum @xcite . the vacuum field is modified by the local environment and this , in turn , leads to a modification of the spontaneous emission rate . in this way the spontaneous emission rate can be changed by embedding the radiating atom inside a dielectric host @xcite , or by changing the boundary conditions either by a cavity @xcite or a suitable surface @xcite . recent experiments have examined the emission by atoms embedded in dielectric hosts @xcite and have encouraged us to re - examine the problem of local - field corrections to the bulk modification of the spontaneous decay rate . the total decay rate @xmath0 can be split into two parts , @xmath1 in which we associate the transverse decay rate @xmath2 and the longitudinal decay rate @xmath3 with the contributions of the transverse and longitudinal fields respectively . the dielectric - induced modification of the spontaneous emission rate in free space can be ascribed to two effects associated with the bulk ( macroscopic ) field in the medium and the other arising from the local ( microscopic ) field . the bulk field correction multiplies the rate by the refractive index at the transition frequency @xcite . local - field corrections present more of a problem and have a form that is strongly model - dependent . for the clausius - mosotti model , which introduces a virtual cavity surrounding the atom , a classical treatment of the local - field corrections leads to the form @xcite @xmath4 for the transverse decay rate of an atom in a bulk dielectric of refractive index @xmath5 @xmath6 @xmath7 @xmath8 @xmath9 @xmath10 . in eq . ( [ 1 ] ) , @xmath11 @xmath7 @xmath12 is the free - space spontaneous emission rate , where @xmath13 and @xmath14 are , respectively , the atomic transition frequency and the dipole transition matrix element . the local field correction in eq . ( [ 1 ] ) arises from writing the local electric field in terms of the macroscopic electric field and the commonly used induced polarization field . it does not , however , take account of the fluctuating component of polarization associated with absorption losses . in this paper we investigate the changes that arise within the clausius - mosotti model when this fluctuating component is included . recently , a scheme for quantizing the electromagnetic field in an arbitrary linear dielectric medium has been proven to be consistent with qed @xcite . it relies on the introduction of an appropriately chosen infinite set of basic - field operators @xcite and their connection to the electromagnetic field operators via the classical green function . this scheme is a generalization of the approach introduced by huttner and barnett @xcite based on a hopfield model @xcite of a homogeneous dielectric using fano diagonalization @xcite to obtain collective ( polariton ) excitations of the electromagnetic field , the polarization and the reservoir . as we will show below , the scheme can also be applied to local - field quantization that is consistent with qed and used for calculating the modified spontaneous decay rate including the local quantum effects of the fluctuating medium polarization . the paper is organized as follows . after a short review of the quantization scheme in sect . [ quantization ] we introduce the quantum local - field correction in sect . [ localfield ] . we then apply the scheme to the calculation of the spontaneous decay rates in sect . [ emission ] followed by some concluding remarks in sect . [ conclusions ] . details of the calculation will be given in the appendix . we begin with a brief review of the quantization scheme used throughout the paper . further details can be found in @xcite . the spectral decomposition of the electric and magnetic field operators is given by @xmath15 where @xmath16 and @xmath17 satisfy maxwell s equations @xmath18 & = & \underline{\hat{\rho}}({\bf r},\omega ) , \end{aligned}\ ] ] @xmath19 [ @xmath20 @xmath7 @xmath21 @xmath9 @xmath22 is the permittivity ] . the operator noise current density @xmath23 and the operator noise charge density @xmath24 , which had to be introduced in order to be consistent with the dissipation - fluctuation theorem , are related to the noise polarization @xmath25 as @xmath26 and satisfy the equation of continuity @xmath27 the operator noise current density @xmath28 is obtained from a bosonic vector field @xmath29 , @xmath30 & = & \delta_{ij } \delta({\bf r - r ' } ) \delta(\omega-\omega ' ) , \\ \left [ \hat{f}_i({\bf r},\omega ) , \hat{f}_j({\bf r'},\omega ' ) \right ] & = & \left [ \hat{f}_i^\dagger({\bf r},\omega ) , \hat{f}_j^\dagger({\bf r'},\omega ' ) \right ] = 0.\end{aligned}\ ] ] the quantization scheme implies that all electromagnetic field operators can be expressed in terms of the basic fields @xmath29 , which may be regarded as being the collective excitations of the electromagnetic field , the medium polarization , and the reservoir . for example , the electric - field operator @xmath31 satisfies the partial differential equation @xmath32 such that @xmath33 where @xmath34 is the tensor - valued green function of the classical problem . it can then be proven @xcite that this quantization scheme is fully consistent with qed for arbitrary linear dielectrics . if we think of an atom located at some space point @xmath35 inside the dielectric , then the macroscopic field of sect . [ quantization ] will not , in fact , be the field felt by the atom . from classical electrodynamics we know that we should introduce what is called the local field at the location of the atom @xcite . there are essentially two ways of introducing the local field . first , one could cut out a _ real _ cavity @xcite ( most commonly a sphere ) around the atom and calculate , in our scheme , the electric field inside the cavity according to eq . ( [ 15 ] ) . this would lead us to introduce the electric field operator @xmath36 by the relation @xmath37 where @xmath38 is the green function of the classical problem of an inhomogeneous medium that consists of the real cavity surrounded by the dielectric in which the atom is embedded . to avoid the solution of the inhomogeneous problem , commonly a simpler _ virtual_-cavity model of clausius - mosotti - type is used . in this model the local field is ( approximately ) related to the macroscopic field , which in our scheme can be obtained according eq . ( [ 15 ] ) , with the green function for the bulk - medium problem . in classical optics the electric field is usually corrected by adding a term proportional to the polarization , @xmath39 where @xmath40 \underline{\bf e}({\bf r},\omega ) , \ ] ] from which it follows that @xmath41 \underline{\bf e}({\bf r},\omega ) .\ ] ] this classically corrected local field is just the field used for the derivation of the rate formula ( [ 1 ] ) . in classical optics ( [ 18 ] ) corresponds to the zero - temperature limit . it does not , however , hold in operator form in quantum optics . regarding eq . ( [ 18 ] ) as an operator equation would strongly contradict the qed equal - time commutation relations in general , so that the operator counterpart of eq . ( [ 18a ] ) will not be a true electric field . in order to obtain a canonical operator equation , we have to complement eq . ( [ 18 ] ) by a noise polarization @xmath42 : @xmath43 \underline{\hat{\bf e}}({\bf r},\omega ) + \underline{\hat{\bf p}}{^n}({\bf r},\omega ) .\ ] ] using the quantization scheme in sec . [ quantization ] , from eq . ( [ 8 ] ) the noise polarization @xmath42 is given by @xmath44 combining eqs . ( [ 17 ] ) and ( [ 20 ] ) , a local electric - field operator @xmath45 \underline{\hat{\bf e}}({\bf r},\omega ) + \frac{1}{3\epsilon_0 } \,\underline{\hat{\bf p}}{^n}({\bf r},\omega)\end{aligned}\ ] ] can be introduced , with @xmath42 being given in eq . ( [ 21 ] ) . in order to prove the consistency of the quantized local field with qed , we compute the ( equal - time ) commutation relation between the fundamental local fields @xmath46 and @xmath47 . for this purpose we note that the local magnetic - field operator is given by , on using eqs . ( [ 6 ] ) , @xmath48 where the symbol @xmath49 stands for the principal part . recalling eqs . ( [ 2 ] ) and ( [ 3 ] ) , the local - field operators in real space are @xmath50 and @xmath51 expressing the local electric and magnetic fields in terms of the basic fields @xmath29 , from the calculation given in app . [ appendix ] it is found that @xmath52 } \nonumber\\&&\hspace{2ex } = \ , - \frac{i\hbar}{\epsilon_0 } \epsilon_{ikl } \partial_l^{r } \delta({\bf r}-{\bf r ' } ) \left\{1+{\textstyle\frac{1}{9}}\big[\epsilon({\bf r},0)-1\big]\right\ } , \end{aligned}\ ] ] and it is easily seen that @xmath53 = \left [ \hat{b}_i{^{\!\!\rm loc}}({\bf r } ) , \hat{b}_k{^{\!\!\rm loc}}({\bf r'})\right ] = 0 .\ ] ] the result reveals that the local - electric field operator ( [ 22 ] ) and the associated magnetic field operator ( [ 24 ] ) can be regarded as being consistent with quantum theory , provided that the ( real ) static permittivity @xmath54 @xmath7 @xmath55 satisfies the condition @xmath56 equivalently , the static refractive index @xmath57 @xmath7 @xmath58 must be small compared with @xmath59 @xmath60 @xmath61 . it should be noted that a term proportional to the @xmath62 function @xmath63 can be added to the right - hand side of eq . ( [ 24 ] ) in order to recover ampere s law when the equation is multiplied by @xmath64 . obviously , this ambiguity reflects the fact that the static magnetic field can not be inferred from the static electric field . from a simple calculation it can be shown that such a term does not change the commutation relation ( [ 27 ] ) . since it is only relevant at zero frequency , it does not play any role in the calculation of the decay at transition frequency @xmath13 . in order to take into account a possible deviation of the symmetry of the material from cubic symmetry , a structure constant @xmath65 can be included in eq . ( [ 17 ] ) such that @xcite @xmath66 \ , \underline{\bf p}({\bf r},\omega).\ ] ] regarding this equation as an operator equation with @xmath67 from eq . ( [ 20 ] ) and following the line in appendix [ appendix ] , it can be seen that eq . ( [ 27 ] ) changes to @xmath68 } \nonumber\\&&\hspace{2ex } = \ , - \frac{i\hbar}{\epsilon_0 } \epsilon_{ikl } \partial_l^{r } \delta({\bf r}-{\bf r ' } ) \left\{1+\frac{\alpha^2}{9}\big[\epsilon({\bf r},0)-1\big]\right\ } , \end{aligned}\ ] ] where the parameter @xmath69 in related to @xmath65 by @xmath70 thus , consistency with quantum theory is achieved , if the condition @xmath71 is fulfilled . the spontaneous decay rate of a ( two - level ) atom at transition frequency @xmath13 placed at point @xmath35 is given by @xmath72 ( @xmath73 @xmath74 @xmath75 ) . in what follows we consider a homogeneous bulk material , i.e. , @xmath20 @xmath76 @xmath77 , and assume that the inequality ( [ 27a ] ) is fulfilled . using eq . ( [ 22 ] ) , the vacuum expectation value of the local electric - field operators in the limit can be written as the sum @xmath78 where @xmath16" +"it is widely accepted that infrared singularities are generally stronger in thermal field theories with bosons , compared to their counterparts at zero temperature . this is due to the singular behavior of the bose - einstein statistical weight at zero energy , which affects massless bosonic fields , the statistical weight ( to be evaluated on - shell in the real - time formalism ) is bounded by @xmath0 . ] . as a consequence of these stronger singularities , only partial results exist concerning their cancellation in the calculation of observable quantities in thermal massless theories ( see @xcite for instance ) . so far , there is no general translation in the language of thermal field theory of the arguments given for this cancellation at @xmath1 by kinoshita @xcite , and lee and nauenberg @xcite . the resummation of hard thermal loops ( htl in the following ) @xcite cures partly this problem by giving a thermal mass to otherwise massless fields , like gauge bosons . nevertheless , the static magnetic ( transverse ) modes remain massless in this framework and may still generate infrared singularities , as exemplified by the calculation of the fermion damping rate @xcite . in qcd , it is believed that a thermal mass for the static transverse modes is generated non perturbatively at the scale @xmath2 , but this mass may be too small to be an efficient regulator . , arising from the htl resummation in the hard limit . _ ] a particular area where this infrared problem becomes relevant is the thermal production of particles . in this paper , we focus mainly on the production of photons by a quark gluon plasma . the production rates are calculated as the imaginary part of a self - energy diagram evaluated at finite temperature @xcite , and are expected to be observable quantities that should come out finite in a consistent calculation . in a recent study @xcite , it has been shown that 2-loop contributions involving the bremsstrahlung mechanism overwhelms 1-loop contributions for the production of a soft real photon . the insertion of an exchanged gluon in the hard quark loop ( see fig . [ fig:2-loop ] ) generates collinear singularities which are power like in 2-loop diagrams while they are only logarithmic in the 1-loop contributions : as a consequence , when these singularities are regularized by the resummation of the thermal mass @xmath3 on the quark propagators , the two - loop diagrams get an enhancement by powers of @xmath4 , where @xmath5 is the strong coupling constant . the contribution of the diagram of fig . [ fig:2-loop ] , although dominated by a soft gluon , is infrared finite . in fact , even the contribution of the transverse gluon is finite in this particular calculation , due to kinematical constraints . indeed , it is trivial to see that the two delta functions corresponding to the cut quarks @xmath6 become @xmath7 in the limit of vanishing @xmath8 , and that the latter pair of delta functions do not have a common support if @xmath9 : for the bremsstrahlung process we are considering here the energies @xmath10 and @xmath11 have the same sign and hence @xmath12 and @xmath13 can not vanish simultaneously , whatever the value of @xmath14 . it is therefore kinematics , via the _ fermion _ thermal mass , that prevents infrared singularities in this particular topology by providing a natural cutoff of order @xmath15 on the gluon momentum @xmath8 . this statement was tested in @xcite by studying the limit @xmath16 . a stronger divergence was found in the transverse gluon contribution , indicating that @xmath17 played a role in the regularization of this potentially dangerous contribution . but this kinematical cut - off does not apply to additional soft gluons one may insert in the quark loop , like in the diagram of fig . [ fig:3-loop ] for instance . indeed , in topologies involving more than one exchanged gluon , the kinematical argument given above constrains only the _ sum _ of the momenta of the cut gluons . therefore , we know that @xmath18 can not vanish , which tells us that ( for instance ) @xmath8 has a lower bound at the scale @xmath15 , but @xmath19 can still become arbitrary small is of order @xmath15 and @xmath8 can become arbitrary small . ] and this leads to an infrared divergence for the cut depicted on fig . [ fig:3-loop ] when the ultra - soft gluon is transverse . indeed when compared to the 2-loop diagram , the additional gluon provides ( i ) two coupling constants , ( ii ) two quark propagators , ( iii ) a set of gluon spectral density and statistical weight and ( iv ) the phase - space of the additional gluon . collecting everything , we can estimate by a crude power counting : @xmath20 where @xmath21 is the spectral function of the additional gluon , where @xmath22 is introduced as a regulator on the integral over @xmath23 . we used the fact that the quarks are hard , and mostly on - shell because of the cut crossing the quark loop . it is important to stress here that each fermion propagator brings an extra factor @xmath23 in the denominator thus contributing to the infrared sensitivity of the above expression . the conclusions of this naive power counting are the following : * if the additional gluon is longitudinal , its cutoff is a thermal mass of order @xmath15 , and the corresponding contribution is suppressed by one power of @xmath5 compared to the 2-loop one . * if the additional gluon is transverse it is natural to assume the regulator to be the magnetic mass @xmath24 , and we have @xmath25 . therefore , it seems that if we keep adding transverse gluons in the quark loop , we generate contributions that are all of the same order of magnitude . this fact is very similar to the argument given by linde for the breakdown of perturbation theory in thermal qcd , although in the different context of the calculation of the free energy @xcite . there is nevertheless one reason why this power counting may be too naive . one should indeed keep in mind that this estimate is valid only for a given cut through the 3-loop diagram . it does not take into account potential compensations that may occur when one is summing all the possible cuts . in this paper , we are going to study in more detail this possibility , and its interplay with a magnetic mass at the scale @xmath2 . an important feature of the above example is the fact that the _ quark propagators _ participate in the overall infrared divergence of the diagram . in fact , if some quark propagators were not becoming singular in the ir limit , the diagram would have been finite by power counting . this can be generalized to a topology with an arbitrary number of exchanged gluons ( but without 3- and 4-gluon vertices ) . indeed , for these topologies , the number of loops @xmath8 is related to the number of gluons @xmath26 by : @xmath27 one of the @xmath8 loop integrals is an integration @xmath28 over the quark momentum which is hard , and is not concerned by the ir problem . the remaining @xmath29 integrals are over the momenta of the @xmath26 soft gluons . the fact that @xmath30 tells that even if each gluon comes with the singular factor @xmath31 , it is accompanied by a phase space @xmath32 which is enough to make the integral finite . for these topologies , it is the quark propagators which are ultimately responsible for the ir divergences . indeed , it is trivial to see that if one quark propagator is cut , then some other quark propagators become infinite when the gluon momenta go to zero . this is the reason why we are going to focus on the quarks , and do not care about the gluon propagators . it is rather easy to show that there are cancellations at the level of the quark propagators occuring in the calculation of the imaginary part of @xmath33 . let us illustrate that in the reasonably general situation where we have a single quark loop to which are connected the two external photons , and an arbitrary number of internal gluons ( but without non - abelian couplings , see fig . [ fig : kln - generic ] ) . to simplify , we detail only the lower fermion line , and hide the details of the upper line in a complicated function we do not need to specify . , running from @xmath34 to @xmath35 , indicates which quark propagator is cut on the lower fermion line . _ ] since we are going to demonstrate cancellations among the various contributions to the dispersive part of the photon polarization tensor , it is convenient to work in the r / a formalism @xcite , in which cutting rules exist that are both very simple and very close to the @xmath1 ones @xcite . therefore , all the contributions to the imaginary part of @xmath36 can be obtained by cuts dividing the diagram into two connected pieces , each of these parts containing at least one external leg . by summing over the index of the cut quark on the lower fermion line , the contribution of the diagram of fig . [ fig : kln - generic ] can be written as . failing to do this , we would get a contribution suppressed compared to the 2-loop result . ] @xmath37 f(p^0,p,\{l_i\})\nonumber\\ & & \!\!\!\!\!\!\!\times\sum_{i=0}^{n } \delta((p+k_i)^2-m^2_\infty)\prod_{j\not = i}{1\over{(p+k_j)^2-m^2_\infty}}\end{aligned}\ ] ] where the function @xmath38 hides all the details about the denominators on the upper quark line ( as well as the fermionic statistical factors , which do not play any role in the following ) , and where we have defined @xmath39 we can now use the @xmath40 functions to perform explicitly the integral over @xmath41 , which gives after splitting the propagators into positive and negative energy terms @xmath42\prod_{j=0}^n{1\over{2\omega_j } } \nonumber\\ & & \!\!\!\!\!\!\times \sum_{\build{i=0}\over{\epsilon=\pm 1}}^{n } \!f(\alpha_i^\epsilon , p,\{l_i\ } ) \prod_{j\not = i}\!\big[{1\over{\alpha_i^\epsilon-\alpha_j^+ } } -{1\over{\alpha_i^\epsilon-\alpha_j^-}}\big ] \label{eq : kln-1}\end{aligned}\ ] ] where we denote @xmath43 and @xmath44 . according to this definition , all the @xmath45 become equal to @xmath46 when the gluon momenta go to zero . we see that denominators where both @xmath47 s carry the same sign vanish in this limit . the ir singularities therefore show up in the vanishing denominators @xmath48 . only the second line in eq . ( [ eq : kln-1 ] ) is relevant in the following discussion , and it can be compactly rewritten as @xmath49 one can simply observe that for every denominator @xmath48 with numerator @xmath50 appears a denominator @xmath51 with a numerator @xmath52 ( all the other denominators being the same ) . the simple poles therefore cancel trivially . this can be extended to the more complicated situation where more than two @xmath47s tend to a common value , which amounts to prove that these denominators appear in a combination that remains finite for any configuration of the @xmath47s . for that purpose , let us consider an expression like since the compensations occur in fact for each given set of @xmath53s . ] @xmath54 and show that such a quantity is always finite provided some regularity property of the function @xmath38 . the shortest way to see that is to notice that @xmath55 is the leading coefficient of the lagrange polynomial of degree @xmath35 that interpolates between the points @xmath56 : @xmath57 as such , @xmath55 is finite for every values of the @xmath47 s if the" +"evolutionary game theory ( egt ) is becoming a general theoretical framework to analysis strategies behaviors @xcite . egt is rooted in the classical game theory ( cgt ) @xcite and the theory of evolution @xcite . different from cgt , egt predicts there could exist persistent cycles in the evolutionary trajectories in the strategy space @xcite . as an example let us consider the standard rock - paper - scissors ( rps ) game . this is a prototype game in textbooks @xcite . in this game , dynamics equations ( e.g. , the standard replicator dynamics equations ) in egt predict that the evolutionary trajectory will cycle around the nash equilibrium persistently . however , the cgt predicts full random behavior : the system is in a mixed - strategy equilibrium with each cyclic motion being balanced completely by its reverse cyclic motion . according to the cgt theory , cycles ( also referred to as excess loops ) can not be observed in the evolutionary trajectories in the long run @xcite . empirical examples of the rps cycles are constantly being discovered in nature , e.g. , three morphs male lizard @xcite and others @xcite . the environment for animal contests is decentralized , in which the encounter is pairwise , but population strategy shows cyclic behaviors @xcite . in general , human economic behaviors ( e.g. , exchanges ) are also pairwise and not centralized @xcite . to test egt in human game experiments @xcite , the traditional setting is decentralized ( see review @xcite ) , in which a subject in each round competes with one random - pairwise opponent within a finite population @xcite . in such traditional setting experiment , whether the trajectories are persistent cycles instead of convergence to a nash equilibrium remains an open question @xcite . till now , no persistent cycle has been confirmed in the rps experiment under such a traditional setting @xcite , and furthermore no dynamics observation has been reported quantitatively . in this paper we study the evolutionary trajectories of the rock - paper - scissors game from the perspective of non - equilibrium statistical physics . in non - equilibrium statistical physics studies , formulating a physically meaningful measure of the distance from equilibrium is an area of active research @xcite . an equilibrium system satisfies the detailed balance condition , which ensures the time reversal symmetry . however , detailed balance is broken in a non - equilibrium system even in its stationary state , therefore various dynamical patterns may show up in the evolutionary trajectory . several non - equilibrium order parameters , such as entropy production @xcite and velocity @xcite , have been constructed to characterize the distance from equilibrium . in this work we carry out laboratory experiments on the rps game , and we detect the possible existence of persistent cyclic flows using an angular frequency as the non - equilibrium order parameter . a non - zero angular frequency serves as a quantitative measure of the distance from equilibrium for the evolutionary trajectories . we also compare our experimental observations with the predictions of a simple non - equilibrium model , the discrete - time logit dynamical process with a noise parameter @xmath2 . our experiments are the standard rps games with the experimental setting of discrete time , random pairwise matching and local information . this setting has its reality in biology and economics @xcite . we collect a total number of twelve experimental trajectories from our experiments ( each trajectory is the result of @xmath3 rounds of the game ) and then analyze these trajectories . like other previous experiments @xcite and theories @xcite , the evolutionary trajectories are highly stochastic , but using our non - equilibrium order parameter we are able to confirm that cycles exist and do not dissipate . the mean frequency of cycles is about @xmath1 period per experimental round . this mean value is used to evaluate the noise parameter @xmath2 of the logit dynamics model , and a value of @xmath4 is obtained . this paper is organized as following . in the next section we introduce the standard rps game in the traditional setting and describe our data analysis protocol . in section [ sec : results ] we describe our main experimental results . the experimental results are compared with the predictions of the discrete - time logit dynamics model in section [ sec : model ] . we conclude this work in the last section . there are three different pure strategies in the rock - paper - scissors game , namely rock ( @xmath5 ) , paper ( @xmath5 ) and scissors ( @xmath6 ) . these three strategies form a directed circle @xmath7 , namely @xmath5 beats @xmath6 , @xmath6 beats @xmath8 , and @xmath8 in turn beats @xmath5 . in our experiments we use the simple payoff matrix shown in table [ rpspaoffmatrix ] to make the rps game a constant - sum game : in each play between two players , the winning player gets a payoff @xmath9 ( i.e. , two experimental points ) while the losing player gets a payoff @xmath10 ; if there is a tie then each player gets an equal payoff @xmath11 . .[rpspaoffmatrix ] payoff matrix of the rock - paper - scissors game . the value of each matrix element is the payoff of the row player s strategy given the strategy of the column player . [ cols=""^,^,^,^ "" , ] the last four rows are the statistical results of the @xmath12 experimental groups above . the row titled as @xmath13-value is @xmath14-test result by setting the null hypothesis @xmath15 for the @xmath12 samples . 95%u(l ) means the upper ( lower ) bound of @xmath16 confidence interval over the @xmath12 samples . to theoretically understand the experimental observations , we now study a noisy best - response process as a simple model for the rps game , namely the discrete - time logit dynamics @xcite . multiple equilibria and limit cycles in the logit dynamics has also been studied in a very recent paper by hommes and ochea @xcite in the continuous - time limit . suppose the population of @xmath17 players is in the social state @xmath18 after the @xmath14-th round of the game . let us denote by @xmath19 the mean payoff of the strategy @xmath20 for this social state . from the payoff matrix of table [ rpspaoffmatrix ] we can easily obtain that @xmath21 we assume that at the @xmath22-round of the game , each player of the population will choose a strategy from @xmath23 independently of all the other players . and we further assume that the time - dependent probability @xmath24 for a player to choose strategy @xmath25 is @xmath26 the parameter @xmath2 is referred to as the inverse temperature "" of the logit dynamics , its value quantifies the rationality degree of human agents in strategy interaction @xcite . in the limiting case of @xmath27 each strategy will be chosen with the uniform probability @xmath28 . for this simple markovian process , the transition probability @xmath29 from a social state @xmath18 at time @xmath14 to another social state @xmath30 at time @xmath22 is expressed as ( noticing that @xmath31 ) @xmath32 } } { ( e^ { \beta ( x + 2 z ) } + e^{\beta ( y + 2 x)}+ e^{\beta ( z + 2 y ) } ) ^n } \ ; . \label{eq : transition}\end{aligned}\ ] ] the steady - state probability @xmath33 that the system is in the social state @xmath18 at @xmath34 can be obtained by solving the following fixed - point equation @xmath35 because the transition probability from any social state @xmath18 to any another social state @xmath30 is positive , eq . ( [ eq : fixedpoint ] ) has a unique solution with the normalization property @xmath36 @xcite . it is not difficult to prove that the steady - state probability distribution has the following rotational symmetry @xmath37 this rotational symmetry ensures that @xmath38 namely the logit dynamics will reach the nash equilibrium @xmath39 at @xmath40 . it can be checked numerically and analytically that , for any @xmath41 , the detailed balance condition is violated at the steady - state of the logit dynamics . for two different social states @xmath42 and @xmath30 , in general we will find that @xmath43 because of the violation of detailed balance , directional flows may persist in the system even at @xmath40 . the steady - state mean cycling frequency @xmath44 of the discrete - time logit dynamical process with population size @xmath0 . the solid line is theoretical result obtained with eq . ( [ def : freq - theta ] ) ; the cross ( @xmath45 ) symbols with error bars are obtained by averaging over many simulated evolutionary trajectories of length @xmath3 . the mean experimental frequency of @xmath46 and its @xmath16 confidence upper and lower bound are marked by the dashed lines . ] we are especially interested in the directional flow around the nash equilibrium point . consider two social states @xmath18 and @xmath30 on the evolutionary trajectory at two consecutive time points @xmath14 and @xmath47 . if either @xmath18 or @xmath30 is identical to the nash equilibrium point , the transition @xmath48 is _ not _ a rotational motion around the nash equilibrium , and we set the corresponding rotational angle @xmath49 to be zero . the nash equilibrium point may be sitting on the rectilinear line that passing through the social states @xmath18 and @xmath50 . if this is the case , the transition @xmath51 is also _ not _ a rotational motion around the nash equilibrium , and its rotational angle @xmath49 is again set to be zero . in all the remaining cases , the social states @xmath18 , @xmath30 and the nash equilibrium point form a triangle in the social state plane of fig . [ fig:28state ] . the magnitude of the rotational angle @xmath49 is just the angle of this triangle at vertex point @xmath52 , it must be less than @xmath53 . the rotational angle @xmath49 is defined as positive if the rotation from @xmath18 to @xmath54 with respect to the nash equilibrium point is counter - clockwise , otherwise it is defined as negative . at the steady - state of the discrete - time logit dynamics , the mean frequency @xmath44 that the evolution trajectory rotates around the nash equilibrium point can then be computed by the following formula @xmath55 probability of staying in the social state @xmath42 for a population of size @xmath0 . the horizontal axis is the predicted probability by the discrete - time logit dynamics model with inverse temperature @xmath56 , while the vertical axis is the empirical probability measured from the @xmath12 experimental trajectories . because of the rotational symmetry ( [ eq : rotation ] ) , the @xmath57 social states can be coarse - grained into ten groups : ( 1 ) , @xmath58 ; ( 2 ) , @xmath59 ; ( 3 ) , @xmath60 ; ( 4 ) , @xmath61 ; ( 5 ) , @xmath62 ; ( 6 ) , @xmath63 ; ( 7 ) , @xmath64 ; ( 8) , @xmath65 ; ( 9 ) , @xmath66 ; ( 10 ) , @xmath67 . all the social states of a given group have the same stationary probability ( the same horizontal - axis value ) according to the theoretical model , but their measured probabilities might be different ( the mean vertical - axis value and the standard error ) . ] for the population size @xmath0 , we show in fig . [ fig : anglen6 ] the steady - state mean frequency @xmath44 as a function of the inverse temperature @xmath2 . to check the correctness of the theoretical calculations ," +"the celebrated saffman - taylor instability @xcite arises when a less viscous fluid pushes a more viscous one in the thin gap of a hele - shaw cell . the less viscous fluid can be either injected at an end of a channel - shaped cell ( rectangular geometry ) @xcite , or from the center of the cell ( radial geometry ) @xcite . in both geometries the interface separating the fluids may deform , leading to the formation of fingerlike patterns , commonly known as viscous fingers . during the last four decades , the viscous fingering instability has been extensively studied , both theoretically @xcite and experimentally @xcite . much of the research in this area has examined the case in which the fluids involved are newtonian . for newtonian fluids , it is observed that the fingers grow and compete dynamically , resulting in a single stable finger in the rectangular geometry , and in patterned structures markedly characterized by the spreading , and subsequent splitting of the finger tips in the radial setup . a whole different class of interfacial patterns arise when the saffman - taylor instability is studied by taking the displaced fluid as non - newtonian @xcite . in contrast to most newtonian fluids , non - newtonian fluids differ widely in their hydrodynamic properties , with different fluids exhibiting a range of effects from elasticity and plasticity to shear thinning and shear thickening . experiments using non - newtonian fluids in radial and rectangular hele - shaw cells have revealed a wide variety of new patterns , showing snowflake - like shapes @xcite and fracturelike structures @xcite . instead of the traditional , tip - splitting - dominated newtonian patterns , these experiments @xcite exhibit dendritic fingers and side branching . this morphological diversity and rich dynamical behavior motivated a number of theoretical studies of the problem @xcite . one major difficulty faced by researchers is that , as opposed to the newtonian case , the pressure field is no longer laplacian . this implies a serious theoretical challenge , since _ a priori _ one would not be allowed to directly apply a darcy s law approach to attack the problem . the instability of radial hele - shaw flows involving non - newtonian fluids has been studied theoretically by sader _ et al . _ they considered power law fluids , and performed a linear stability analysis without making use of darcy s law . essentially , they showed that decreasing the power law index dramatically increases the growth rates leading to a more rapid development of the fingering patterns . a darcy s law - type approach has been proposed by bonn and collaborators @xcite . suggested a modified darcy s law including a shear rate dependent viscosity , and showed that , within their approach , the pressure field remains laplacian . in a series of interesting papers kondic _ et al . _ @xcite , and subsequently fast _ et al . _ @xcite extended reference @xcite ideas and derived a generalized darcy s law from first principles , where viscosity depends upon the squared pressure gradient . it turns out that the darcy s law formula proposed by bonn _ et al . _ @xcite follows from the more basic version rigorously derived by kondic _ et al . _ efficient numerical simulations performed in references @xcite have shown that shear thinning can suppress tip - splitting and leads to the formation of dendritic structures , presenting a clear side branching behavior . theoretical studies of the fully nonlinear stages of hele - shaw flow with non - newtonian fluids rely heavily on intensive numerical simulations @xcite . on the analytical side , the structure of the fingering dynamics in such complex fluids is largely restricted to linear stability investigations @xcite . much less attention has been paid to the analytical investigation of the dynamics that bridges the _ initial _ ( purely linear ) and _ final _ ( fully nonlinear ) time regimes . in addition , theoretical as well as experimental analyses of flow of shear thickening fluids in hele - shaw cells still need to be addressed . in this paper we carry out the analytical weakly nonlinear analysis for the _ intermediate _ stages of evolution , and examine _ both _ shear - thinning and shear thickening cases . we adapt a weakly nonlinear approach originally developed to study newtonian hele - shaw flows @xcite , to the non - newtonian situation . we focus on the onset of the nonlinear effects , and try to understand how mode - coupling dynamics leads to basic morphological features and behaviors observed in non - newtonian hele - shaw flows . the article is organized as follows : section [ derivation ] formulates our theoretical approach . we perform a fourier decomposition of the interface shape , and from an alternative form of darcy s law study the influence of weak shear effects on the development of interfacial patterns . in contrast to the analysis for newtonian fluids , conventionally based on a scalar velocity potential , we employ a vector velocity potential capable of describing vorticity arising from the non - newtonian fluid flow . coupled , nonlinear , ordinary differential equations governing the time evolution of fourier amplitudes are derived in detail . section [ discussion ] discusses both linear and weakly nonlinear dynamics . it concentrates on the effect of shear thinning and shear thickening on finger tip - splitting and side branching . section [ 1 ] briefly discusses our linear stability results . linear results are useful and instructive , but do not allow accurate predictions of important interfacial features . in section [ 2nd ] we show that some of such features can indeed be predicted and more quantitatively explained by our analytical mode - coupling approach . at second order we find a mechanism for finger tip - splitting in non - newtonian hele - shaw flow : it is suppressed ( favored ) for shear thinning ( thickening ) fluids . our results indicate absence of side branching in the weak shear limit and early flow stages , but suggest that it could be enhanced ( inhibited ) for shear thinning ( thickening ) fluids . section [ rectangular ] discusses mode - coupling in rectangular flow geometry . our chief conclusions are summarized in sec . [ conclude ] . the hele - shaw cell ( fig.1 ) consists of two parallel plates separated by a small distance . the cell thickness @xmath0 is considered to be much smaller that any other length scale in the problem , so that the system is essentially two - dimensional . consider the displacement of a viscous , non - newtonian fluid by a newtonian fluid of negligible viscosity in such confined geometry . the surface tension between the fluids is denoted by @xmath1 . the newtonian fluid is injected at a constant areal flow rate @xmath2 at the center of the cell . the initial circular fluid - fluid interface is slightly perturbed , @xmath3 ( @xmath4 ) , where the time dependent unperturbed radius is given by @xmath5 @xmath6 being the unperturbed radius at @xmath7 . the interface perturbation is written in the form of a fourier expansion @xmath8 where @xmath9 denotes the complex fourier mode amplitudes and @xmath10=0 , @xmath11 , @xmath12 , @xmath13 is the discrete polar wave number . in our fourier expansion ( [ z ] ) we include the @xmath14 mode to keep the area of the perturbed shape independent of the perturbation @xmath15 . mass conservation imposes that the zeroth mode is written in terms of the other modes as @xmath16 . the relevant hydrodynamic equation for newtonian hele - shaw flows , darcy s law @xcite , states that the gradient of the pressure is proportional to the fluid velocity , and oriented in the opposite direction with respect to the fluid flow @xmath17 where @xmath18 and @xmath19 are , respectively , the gap - averaged velocity and pressure in the fluid . the viscosity of the fluid is represented by @xmath20 . to model non - newtonian hele - shaw flows , we use a suitable form of the darcy s law in the weak shear thinning or thickening limit . we follow bonn _ et al . _ @xcite and consider their shear rate dependent viscosity in the weak non - newtonian limit @xmath21 @xmath22},\ ] ] where @xmath23 is the shear rate , @xmath24 , @xmath25 denotes the characteristic relaxation time of the fluid , and @xmath26 is a constant , zero - shear viscosity . the parameter @xmath27 measures the shear dependence : @xmath28 corresponds to the newtonian fluids , and @xmath29 ( @xmath30 ) gives the shear thinning ( thickening ) case . by substituing eq . ( [ approx_visc ] ) into eq . ( [ darcy ] ) we obtain an alternative form of darcy s law ideally suited to describe weak non - newtonian effects @xmath31 here @xmath32 ~p$ ] represents a generalized pressure field , and @xmath33 is a small parameter that expresses the non - newtonian nature of the displaced fluid : @xmath34 corresponds to the newtonian case , while @xmath35 ( @xmath36 ) describes the shear thinning ( thickening ) case . taking the divergence of eq . ( [ new_darcy ] ) and using incompressibility ( @xmath37 ) the pressure is seen to be anharmonic ( nonvanishing laplacian ) . our subsequent analysis incorporates this effect , in contrast to the treatment in ref . @xcite . indeed , an alternate route to our eq . ( [ new_darcy ] ) is to start with viscosity depending on the square of the pressure gradient ( as in kondic , _ et al . _ @xcite ) , then approximate the pressure gradient with the velocity for small @xmath38 . our pertubative approach keeps terms up to the second order in @xmath15 and up to first order in @xmath38 . considering the fact that the viscosity of the newtonian fluid is negligible , the generalized pressure jump condition at the interface can be written as @xcite @xmath39 where @xmath40 and @xmath41 is the curvature in the direction parallel to the plates . the weakly nonlinear approach to radial , newtonian hele - shaw flow developed in reference @xcite , related the fluid velocity to a _ scalar _ velocity potential @xmath42 , this replacement made possible by the irrotational nature of the flow for newtonian fluids . for non - newtonian fluids , in contrast , flows governed by the modified darcy s law ( [ new_darcy ] ) exhibit vorticity . hence we perform our calculations using a _ vector _ potential @xmath43 . the most general form of the vector potential can be written as @xmath44 \hat { \bf z},\ ] ] where @xmath45 are the fourier coefficients of the velocity vector potential and @xmath46 is the outward unit - normal to the upper cell plate . the radial and polar components of the fluids velocities are @xmath47 and @xmath48 note that the vector potential reduces to the unperturbed steady flow with a circular interface ( @xmath49 , @xmath50 ) when @xmath51 and also when @xmath52 . we exploit the fact that @xmath53 must be curl free , and impose the so - called solvability condition @xmath54 . it simplifies the general form of the vector potential expansion given in eq . ( [ gen_vec_pot ] ) . the solvability condition reveals that , without loss of generality , one can rewrite the vector potential as @xmath55 \right \}~\hat { \bf z},\ ] ] replacing the array of coefficients @xmath45 with the simpler set of @xmath56 and @xmath57 . observe that the vector potential ( [ vec_pot ] ) is simply a superposition" +"the minimal supersymmetric standard model ( mssm ) is one of the most important candidates for the physics beyond the standard model . the strongly interacting superpartners , gluinos and squarks with mass lighter than 2.5 tev can be discovered at the large hadron collider at cern ( lhc ) @xcite . the physics run of lhc will start in 2008 . among the supersymmetric ( susy ) particles , the lightest susy particle ( lsp ) plays a key role . in cosmology , it is a candidate for the cold dark matter in the universe . at the lhc , the signals of the supersymmetric particles depends on the nature of the lsp . it may be the lightest neutralino @xmath4 , which escapes from detection and leads to missing @xmath5 in the event . another possibility for the lsp is the gravitino @xmath1 , the superpartner of the graviton . the gravitino coupling to other particles in the mssm sector is extremely small , namely proportional to @xmath6 . the next lightest susy particle ( nlsp ) , whose decay products necessarily include the gravitino , is therefore long - lived . we discuss the scenario where the lsp is the gravitino and the long - lived nlsp carries charge . a natural candidate for a charged nlsp ( cnlsp ) is the lightest scalar tau , @xmath7 , which can be significantly lighter than the other sleptons due to the left - right mixing induced by the off diagonal matrix element @xmath8 . the charged particle leaves tracks in the central detectors ( atlas and cms ) , giving additional information for the susy particle reconstructions . if the nlsp decays in the main detectors , a displaced vertex may be observed as well . the expected lifetime of the cnlsp @xmath9 is unconstrained , because it is proportional to @xmath10 the yet unknown gravitino mass squared . on the other hand , the gravitino mass is proportional to the total susy breaking scale in the hidden sector , therefore the determination of the lifetime is an important physics goal . the lifetime measurement gives direct information on the hidden sector . a particle decays efficiently in the main detectors ( cms and atlas ) if the decay length is sufficiently short , @xmath11 ( 10m)@xmath12 , where @xmath13 is the number of produced susy particles . on the other hand , for typical susy production cross sections , a direct observation of the decay is very difficult for @xmath14 sec . however , it has been pointed out that the cnlsp stopped by the ionization loss in the material may be studied in detail @xcite . an idea for a stopper based on a water tank is presented in ref.@xcite , where the water can be transported away from the detector site , for concentration and further study . in ref . @xcite , a detector consisting of a tracker and heavy stopping material is proposed , which can measure the arrival time and the location where the cnlsps are stopped , in addition to the energy of the decay products . another possibility , which requires minimal experimental modification , is to study the cnlsp which are stopped in the main detector or surrounding rock @xcite . as pointed out in ref . @xcite , the study of the cnlsp decays can probe the underlying supergravity in nature . with the gravitino mass inferred from the kinematics , the additional cnlsp lifetime measurement will test an unequivocal prediction of supergravity . moreover , the study of a rare 3body decay @xmath15 can reveal the peculiar couplings of the gravitino and the gravitino spin @xmath16 . in this paper , we consider the physics of the cnlsp @xmath9 decays that can be done with the heavy material stopper detector @xcite , because only a detector of this type can cover a wide range of lifetime @xmath17 @xmath18 years ) . we find that the mass of the gravitino can be measured if it is sufficiently heavy ( roughly @xmath19 ) . in that case , one can check if the lifetime is consistent with the supergravity interpretation . as we shall see , the lsp mass resolution is however poor if @xmath20 . in that case , it is very hard to prove that the decay @xmath21 plus an invisible particle @xmath22 is indeed caused by the supergravity interaction involving @xmath23 . we should note that , because of the extremely weak coupling of the gravitino , if there is any unknown supersymmetric particle @xmath22 which couples rather weakly to the mssm particles , the lightest mssm particle may decay into @xmath22 instead of @xmath1 even if the @xmath1 is the lsp . for example , the superpartner of the axion , the axino @xmath2 , can be such a particle . however , we found that it may be possible to discriminate the case of @xmath24 and the case of @xmath25 , by investigating the three body decay @xmath26 as suggested in @xcite , with enough statistics . this paper is organized as follows . in section [ sec : detector ] , we discuss a possible detector setup . we found an @xmath27 kton detector ( up to 8 kton ) may be placed next to the cms detector without serious modification of the cms experiment itself , but with non - negligible modifications to the cms cavern side walls . in section [ sec : modelpoints ] , we select several model points and estimate the expected number of the stopped particles for @xmath28 fb@xmath29 and 3000 fb@xmath29 . in section [ sec : twobody ] , we discuss the measurement of the two body decay @xmath30 . the three body decay of the cnlsp is studied in section [ sec : three - body ] . section [ sec : discussion ] contains the discussion and comments . 44mcms & 15 m & 12.5kt & 21 m [ atlascms ] in this section , we discuss the possibility to install massive stoppers next to the lhc detectors , cms and atlas . it turns out that the cms cavern may allow for an easier installation and more room for a massive stopper , compared to the atlas cavern . the parameters of the two detectors are listed in table . [ atlascms ] . the diameter of the cms detector is smaller , therefore the massive stopper can be placed closer to the interaction point at cms . the weight of the cms detector is about twice as large as that of atlas . because of the large weight , the cavern of cms is designed so that it can sustain a massive object safely , which includes a reinforced floor to spread the detector pressure more equally . a potential massive stopper with a weight of around a few kton can be placed on both sides of the cms detector , but it will need a reorganization of the scaffolding and gallery paths on the cavern walls , to make room for such an additional detector . the assembly and construction of the two detectors is also very different . most of the cms detector components are assembled on the ground , and about 15 large detector units will be lowered in the cavern for final assembly works . hence the installation is less integrated with the cavern , leaving relatively more freedom and thus changes needed in the cavern to install massive stoppers are somewhat simpler @xcite . on the other hand atlas detector is assembled mostly in its cavern . the huge magnets toroids and outside muon system fill up the cavern . the cryogenic system in the atlas cavern is also taking space outside the detector @xcite . is the collision point . right : two stopper detectors and a circle about the size of cms detector are superimposed on the cross section of cms cavern uxc 55 , drawing taken from ref . @xcite . , title=""fig:"",width=264 ] is the collision point . right : two stopper detectors and a circle about the size of cms detector are superimposed on the cross section of cms cavern uxc 55 , drawing taken from ref . , title=""fig:"",width=264 ] we assume two stoppers with the size 3.5 m @xmath31 15 m @xmath31 15 m and the average density @xmath32g/@xmath33 , hence , the total weight of the detector is 8 kton . this is maximum possible rectangular parallelepiped volume that can be placed in the cavern , with the given space to the cavern wall and with its long edge being the same as that of the cms barrel part ( see fig . [ fig : stopper ] ) . the stoppers are thus placed 8.5 m away from the interaction point . we also assume that stopping power of the cms detector is equivalent to @xmath34 g/@xmath35 iron , where @xmath36 is angle between the cnlsp direction and the beam direction . the number comes from the average density of cms detector , 3.37g/@xmath33 , which leads to the weight per @xmath35 for the radial direction of @xmath37 . as discussed in the previous paper @xcite , the stopper can be a hadronic and electromagnetic calorimeter simultaneously , if the detector consists of layers of dense stopper and tracking devices . the measurement of the energy of the decay product of the cnlsp is the key ingredient to explore the cnlsp interactions to the @xmath22 particle . in this paper we assume that the cnlsp is the scalar tau lepton @xmath0 , which decays mostly as @xmath38 where @xmath39 or @xmath2 . the @xmath40 decays into @xmath41 , or into @xmath42 and @xmath43 s . we do not consider the decays into @xmath44 , because the muon energy can not be measured unless the stopper contains a magnetic field . the energy of the leptons are much softer than the parent @xmath40 energy anyway , so that they are less useful for the study of the decay kinematics . a large volume detector is advantageous to measure the energy of the @xmath40 decay products , because the detector must contain most of the energy of the showers from the @xmath40 decay products . to fully absorb the hadronic cascade one needs sufficient thickness of the calorimeter . the required thickness for an iron calorimeter ( density is 7.87g/@xmath33 ) is listed in ref . @xcite , and is about 170 ( 120 ) cm for 100 gev single hadron energy for 99% ( 95% ) containment respectively , equivalent to 1337.9g/@xmath35 ( 944.4g/@xmath35 ) . to measure the energy with sufficient accuracy by a stopper with @xmath45 5g/@xmath33 , the distance between the decay position and the end of the detector along the shower path must be at least 190 cm . a simplified monte carlo simulation shows that 63% of the @xmath9 decays satisfy this condition . high energy photons and electrons initiate electromagnetic cascades , which are much easier to contain in a detector . the energy deposition along the axis of the cascade is well described by a gamma distribution , where the maximum occurs at @xmath46 , where @xmath47 is the radiation length . the energy deposition terminates around @xmath48 . ( see fig.27.17 of @xcite . ) for the case of iron ( @xmath49 ) , 200g/@xmath35 thickness of the material is needed to stop the electromagnetic cascade . the difference in the absorption length is used to discriminate isolated photons from hadron , which would be useful to study @xmath50 decay . in a previous paper @xcite , we discussed the possibility to re - use of the existing 1 kton detector , such as soudan ii @xcite as the cnlsp stopper . the soudan ii consists of the layers of @xmath51(m ) long drift tubes and thin iron plates" +"it is well - established that the best solution of the solar neutrino oscillation is msw - lma ; this is strongly supported by many experiments results@xcite@xcite@xcite@xcite@xcite . for this solution it is expected that the @xmath0 survival probability in the low energy region ( @xmath11 mev ) is higher than in the high energy region ( @xmath210 mev ) , because for low energies vacuum oscillation is dominant while for high energies matter oscillation is dominant . so a transition from vacuum to matter oscillation should exist , roughly between 1.0 and 10.0 mev , in the energy range in which solar neutrinos predominate . the recoil electron energy threshold of super - kamioakande is around 5 mev , so super - kamiokande has a chance to discover the low - energy upturn in the spectrum . to realize this goal , reducing background and systematic uncertainty below 5.5 mev and lowering the recoil electron energy threshold are important @xcite . if we can take 5 years of 4 mev threshold data with 70% reduced background below 5.5 mev and half the energy - correlated systematic uncertainty compared to sk - i , we should observe a spectrum as shown in fig . [ fig4 ] and might discover this energy spectrum distortion . so , starting with the data of sk - iii , making these detector and analysis improvements has been high priority work . since the end of sk - i , we have worked hard to reduce background and systematic uncertainties , improving several key items . the following sections will introduce some of them . a major background for the solar neutrino observation at sk is the radioactivity from radon ( rn ) in our otherwise extremely pure water . this ultra - pure water which fills the detector is made from natural mine water using a very high efficiency water purification system . the rn background events are very similar to solar events , so it is very difficult to remove them using only analysis tools . as a result , many rn events could be included in the final data set . to reduce this background , the improvement of the rn reduction efficiency of the sk water purification system is the most effective approach . so , since the end of sk - i we have upgraded the system several times , including the addition of a new heat exchanger and two reverse osmosis units for sk - iii . in addition , we investigated the water flow in the tank by purposefully injecting radon - enriched water . tracing the resulting background events in time from this injected rn , we found stagnation of water in the top and bottom of the detector volume which increased the background . to counter this effect we installed new pipes and changed the water flow . previously , the water was supplied from the bottom of the inner detector ( i d ) and drained from the top of both the i d and outer detector ( od ) . now , it is supplied from the i d bottom and drained from the top and bottom in the i d and od , with a total flow two times faster than before . as a result we have a central region with half the background ( yellow box in fig . [ figver ] ) as compared with sk - i , making lowering of the energy threshold a possibility . note that the excessive background near the wall and bottom of sk - iii also existed in sk - ii . this background is from the fiber reinforced plastic ( frp ) pmt covers which were added at the start of sk - ii in order to protect against propagating shock waves from pmt implosions , and so could not be reduced by improving the water system . it posed a significant obstacle to enlarging the fiducial volume below 6.5 mev . the vertex shift , defined as a vector from an averaged position of the reconstructed vertices of the data to that of corresponding monte carlo ( mc ) data , has been one of the main systematic uncertainties for the solar neutrino flux measurement since the beginning of sk - i@xcite . because it could make events move in or out of the fiducial volume , it is a non - negligible systematic uncertainty . vertex shift is measured by placing a ni - cf gamma ray source at several positions of the tank . the reconstructed data vertices were shifted more than 10 cm from the real source position inward toward the tank center , in contrast those of mc which were shifted less than 10 cm . the origin of the excessive shift of the data was a mystery since sk - i . in sk - iii , we investigated this mystery , resolving it just ten days before the end of sk - iii . it turned out that relative hit timing within a wide range ( @xmath3100 nsec ) was not perfect due to characteristics of our electronics . we measured the timing linearity by artificially shifting the external trigger timing , a common stop signal of individual tdcs for each hit channel . we found that hit timing should be corrected -0.7@xmath4 to restore linearity . after the correction was applied the vertex shift shortened significantly ( see fig . [ figversh ] ) . as a result , the background events around the wall ( inside brown ellipse ) were reduced and the fiducial volume between 5.0 and 6.5 mev could be enlarged up to 13.3 kton ( fig . [ figver_vs ] ) . in addition , we can apply the same correction for sk - i / ii and expect to reduce the systematic uncertainty of the sk - i / ii data , because the sk - iii daq is the same as that of sk - i / ii . time variation of data ( black ) and mc ( red ) over the full sk - iii period with fixed water transparency.,width=302 ] of several positions before and after the position dependent mc installation , width=302 ] that the water quality in sk changes as a function of time was known ; the sk - i mc took it into account @xcite . in sk - iii we also measured the time variation of the water transparency using @xmath5-@xmath6 decay data , as well as the wavelength dependence of various scattering and absorption water coefficients using a nitrogen / dye laser system @xcite . using the full period of sk - iii , we investigated possible relationships among the water transparency and water coefficients and found , similar to sk - i , the only apparent connection was between water transparency and the absorption coefficients . so we installed the absorption coefficients as a function of the water transparency measured by @xmath5-@xmath6 decay data and the scattering coefficients as a constant for the water transparency . as a result we had a time dependent mc . we tested this mc with muon decay data . figure [ figtimdecaye ] shows the @xmath7 time variation of data and mc in sk - iii assuming a fixed water transparency . @xmath7 is the effective number of hits to yield the same value at any position in the sk tank by applying several corrections to the number of hits @xcite . one such correction takes into account the water transparency . to observe the effect of the time variation of water transparency directly , we did nt apply this correction , and confirmed that mc tracks the data properly . we also found a position dependence in the water quality . the existence of position dependence due to the water flow has been debated since sk - i . we installed light injectors on the barrel of the detector and tried to find it , but this method could nt resolve the question . finally , in sk - iii , using several calibration sources we concluded that position dependence not only exists but also changes as a function of time . so we made a position dependent mc by installing a z - dependence in the water coefficients varied by the so - called top - bottom asymmetry as measured using calibration data over the full sk - iii data - taking period . we tested this mc with calibration data @xcite . we took the data at several positions(fig . [ figdtp ] ) . before correction the difference between data and mc was @xmath33% at the top of the detector , @xmath32% in the center , and @xmath31% at the bottom , but after correction was less than 1% at the top and in the center . however , the difference at the bottom became larger ; it still needs improvement . another large source of systematic uncertainty in sk - i is the angular resolution @xcite . because this uncertainty comes essentially from the hit pattern difference between data and mc , we must tune the mc to reduce the uncertainty . the mc was tuned several times . daq - related items like single photoelectron response , timing resolution , etc . , and optical properties like scattering and absorption coefficients , the reflectance of pmts , etc . , were tuned using several calibration sources , as was done for sk - i @xcite . when we calculated the difference of the angular resolution of data and mc , their agreement was not improved compared with sk - i . so we explored several optical properties using mc , finally finding that halving the original value for the reflectivity of a black sheet which covers the i d wall gave better agreement . until that time we used the sk - ii value for black sheet reflectivity , even though the materials of sk - ii / iii black sheet are different . to confirm this finding , we put a light injector with a black sheet reflector into the sk tank and measured the amount of direct light and reflected light for specific incident angles . figure [ example_black ] shows the ratio of the amount of charge due to reflected light versus direct light of data ( black ) and half reflectivity mc ( red ) . this shows reasonable agreement , even if the 337 nm result ( upper figure ) still needs tuning . next , we improved the direction fitter itself . in essence , the likelihood function that represents the distribution of the opening angle between the particle direction and the vector from the reconstructed vetex to the hit pmt position was improved . in sk - i it was made for 10 mev mc electrons @xcite , while for sk - iii several energy bins were considered . as a result , we achieved about 10% better angular resolution around 5 mev than in sk - i ( fig . [ example_veres ] ) . in addition to the above efforts , we retuned most of the reconstruction tools and reduction criteria to reduce their systematic uncertainties . we are continuing to tune those items whose tuning results were nt sufficiently good , as mentioned in the previous sections . as the determination of our systematic errors is still under way , we ca nt show the exact numbers of the systematic uncertainties yet . as a result of the above efforts , we took good solar neutrino data during the full super - kamiokande - iii data - taking period , which ran from august of 2006 through august of 2008 . currently 298 live days of data with a lower total energy threshold of 4.5 mev is finished being analyzed . this section shows the" +"in this paper , we study online learning problems within a drifting - games framework , with the aim of developing a general methodology for designing learning algorithms based on a minimax analysis . to solve an online learning problem , it is natural to consider game - theoretically optimal algorithms which find the best solution even in worst - case scenarios . this is possible for some special cases ( @xcite ) but difficult in general . on the other hand , many other efficient algorithms with optimal regret rate ( but not exactly minimax optimal ) have been proposed for different learning settings ( such as the exponential weights algorithm @xcite , and follow the perturbed leader @xcite ) . however , it is not always clear how to come up with these algorithms . recent work by rakhlin et al . @xcite built a bridge between these two classes of methods by showing that many existing algorithms can indeed be derived from a minimax analysis followed by a series of relaxations . in this paper , we provide a parallel way to design learning algorithms by first converting online learning problems into variants of drifting games , and then applying a minimax analysis and relaxations . _ drifting games _ @xcite ( reviewed in section [ sec : drifting ] ) generalize freund s `` majority - vote game '' @xcite and subsume some well - studied boosting and online learning settings . a nearly minimax optimal algorithm is proposed in @xcite . it turns out the connections between drifting games and online learning go far beyond what has been discussed previously . to show that , we consider variants of drifting games that capture different popular online learning problems . we then generalize the minimax analysis in @xcite based on one key idea : _ relax a 0 - 1 loss function by a convex surrogate_. although this idea has been applied widely elsewhere in machine learning , we use it here in a new way to obtain a very general methodology for designing and analyzing online learning algorithms . using this general idea , we not only recover existing algorithms , but also design new ones with special useful properties . a somewhat surprising result is that our new algorithms are totally _ parameter - free _ , which is usually not the case for algorithms derived from a minimax analysis . moreover , a generalized notion of regret ( @xmath0-regret , defined in section [ sec : hedge ] ) that measures how good the algorithm is compared to all but the top @xmath0 fraction of candidates arises naturally in our drifting - games framework . below we summarize our results for a range of learning settings . * hedge settings : * ( section [ sec : hedge ] ) the hedge problem @xcite investigates how to cleverly bet across a set of actions . we show an algorithmic equivalence between this problem and a simple drifting game ( dgv1 ) . we then show how to relax the original minimax analysis step by step to reach a general recipe for designing hedge algorithms ( algorithm [ alg : hedge_recipe ] ) . three examples of appropriate convex surrogates of the 0 - 1 loss function are then discussed , leading to the well - known exponential weights algorithm and two other new ones , one of which ( normalhedge.dt in section [ sec:3algs ] ) bears some similarities with the normalhedge algorithm @xcite and enjoys a similar @xmath0-regret bound _ simultaneously _ for all @xmath0 and horizons . however , our regret bounds do not depend on the number of actions , and thus can be applied even when there are infinitely many actions . our analysis is also arguably simpler and more intuitive than the one in @xcite and easy to be generalized to more general settings . moreover , our algorithm is more computationally efficient since it does not require a numerical searching step as in normalhedge . finally , we also derive high probability bounds for the randomized hedge setting as a simple side product of our framework _ without _ using any concentration results . * multi - armed bandit problems : * ( section [ sec : gen ] ) the multi - armed bandit problem @xcite is a classic example for learning with incomplete information where the learner can only obtain feedback for the actions taken . to capture this problem , we study a quite different drifting game ( dgv2 ) where randomness and variance constraints are taken into account . again the minimax analysis is generalized and the exp3 algorithm @xcite is recovered . our results could be seen as a preliminary step to answer the open question @xcite on exact minimax optimal algorithms for the multi - armed bandit problem . * online convex optimization : * ( section [ sec : gen ] ) based the theory of convex optimization , online convex optimization @xcite has been the foundation of modern online learning theory . the corresponding drifting game formulation is a continuous space variant ( dgv3 ) . fortunately , it turns out that all results from the hedge setting are ready to be used here , recovering the continuous exp algorithm @xcite and also generalizing our new algorithms to this general setting . besides the usual regret bounds , we also generalize the @xmath0-regret , which , as far as we know , is the first time it has been explicitly studied . again , we emphasize that our new algorithms are adaptive in @xmath0 and the horizon . * boosting : * ( section [ sec : gen ] ) realizing that every hedge algorithm can be converted into a boosting algorithm ( @xcite ) , we propose a new boosting algorithm ( nh-boost.dt ) by converting normalhedge.dt . the adaptivity of normalhedge.dt is then translated into training error and margin distribution bounds that previous analysis in @xcite using nonadaptive algorithms does not show . moreover , our new boosting algorithm ignores a great many examples on each round , which is an appealing property useful to speeding up the weak learning algorithm . this is confirmed by our experiments . * related work * : our analysis makes use of potential functions . similar concepts have widely appeared in the literature @xcite , but unlike our work , they are not related to any minimax analysis and might be hard to interpret . the existence of parameter free hedge algorithms for unknown number of actions was shown in @xcite , but no concrete algorithms were given there . boosting algorithms that ignore some examples on each round were studied in @xcite , where a heuristic was used to ignore examples with small weights and no theoretical guarantee is provided . we consider a simplified version of drifting games similar to the one described in @xcite ( also called chip games ) . this game proceeds through @xmath1 rounds , and is played between a player and an adversary who controls @xmath2 chips on the real line . the positions of these chips at the end of round @xmath3 are denoted by @xmath4 , with each coordinate @xmath5 corresponding to the position of chip @xmath6 . initially , all chips are at position @xmath7 so that @xmath8 . on every round @xmath9 : the player first chooses a distribution @xmath10 over the chips , then the adversary decides the movements of the chips @xmath11 so that the new positions are updated as @xmath12 . here , each @xmath13 has to be picked from a prespecified set @xmath14 , and more importantly , satisfy the constraint @xmath15 for some fixed constant @xmath16 . at the end of the game , each chip is associated with a nonnegative loss defined by @xmath17 for some nonincreasing function @xmath18 mapping from the final position of the chip to @xmath19 . the goal of the player is to minimize the chips average loss @xmath20 after @xmath1 rounds . so intuitively , the player aims to `` push '' the chips to the right by assigning appropriate weights on them so that the adversary has to move them to the right by @xmath16 in a weighted average sense on each round . this game captures many learning problems . for instance , binary classification via boosting can be translated into a drifting game by treating each training example as a chip ( see @xcite for details ) . we regard a player s strategy @xmath21 as a function mapping from the history of the adversary s decisions to a distribution that the player is going to play with , that is , @xmath22 where @xmath23 stands for @xmath24 . the player s worst case loss using this algorithm is then denoted by @xmath25 . the minimax optimal loss of the game is computed by the following expression : @xmath26 where @xmath27 is the @xmath2 dimensional simplex and @xmath28 is assumed to be compact . a strategy @xmath29 that realizes the minimum in @xmath30 is called a minimax optimal strategy . a nearly optimal strategy and its analysis is originally given in @xcite , and a derivation by directly tackling the above minimax expression can be found in @xcite . specifically , a sequence of potential functions of a chip s position is defined recursively as follows : @xmath31 let @xmath32 be the weight that realizes the minimum in the definition of @xmath33 , that is , @xmath34 . then the player s strategy is to set @xmath35 . the key property of this strategy is that it assures that the sum of the potentials over all the chips never increases , connecting the player s final loss with the potential at time @xmath7 as follows : @xmath36 it has been shown in @xcite that this upper bound on the loss is optimal in a very strong sense . moreover , in some cases the potential functions have nice closed forms and thus the algorithm can be efficiently implemented . for example , in the boosting setting , @xmath37 is simply @xmath38 , and one can verify @xmath39 and @xmath40 . with the loss function @xmath41 being @xmath42 , these can be further simplified and eventually give exactly the boost - by - majority algorithm @xcite . the connection between drifting games and some specific settings of online learning has been noticed before ( @xcite ) . we aim to find deeper connections or even an equivalence between variants of drifting games and more general settings of online learning , and provide insights on designing learning algorithms through a minimax analysis . we start with a simple yet classic hedge setting . in the hedge setting @xcite , a player tries to earn as much as possible ( or lose as little as possible ) by cleverly spreading a fixed amount of money to bet on a set of actions on each day . formally , the game proceeds for @xmath1 rounds , and on each round @xmath9 : the player chooses a distribution @xmath10 over @xmath2 actions , then the adversary decides the actions losses @xmath43 ( i.e. action @xmath6 incurs loss @xmath44 $ ] ) which are revealed to the player . the player suffers a weighted average loss @xmath45 at the end of this round . the goal of the player is to minimize his `` regret '' , which is usually defined as the difference between his total loss and the loss of the best action . here , we consider an even more general notion of regret studied in @xcite , which we call _ @xmath0-regret_. suppose the actions are ordered according to their total losses after @xmath1 rounds ( i.e. @xmath46 ) from smallest to largest , and let @xmath47 be the index of the action that is the @xmath48-th" +"in different contexts like biological systems or chemical reactions , many out of equilibrium dynamics combine diffusive and dissipative features which can be described macroscopically by reaction - diffusion equations . in order to analyze these systems from a microscopic point of view , a lattice gas model with fast stirring and a local creation - annihilation mechanism has been introduced in @xcite by combining a symmetric simple exclusion process ( ssep ) and a glauber dynamics . another example of driven dissipative system is a granular gas where the energy is dissipated through inelastic collisions . direct analytic approaches of the granular gases are notoriously difficult , but stochastic toy models have been proposed in order to capture some aspects of the physics @xcite or for simulation purposes @xcite . the particle system introduced in @xcite in contact with two heat bath shares also similar features . in non - equilibrium statistical mechanics , there is no analogous to the gibbs formalism and the large deviation functional can be viewed as a substitute for the free energy . in particular , the large deviations of the current received a lot of attention over the last few years ( see @xcite for reviews ) . exact expressions of the large deviation functional have been obtained for conservative diffusive stochastic dynamics in contact with reservoirs @xcite@xcite . in this paper , we generalize these results to the non - conservative stochastic dynamics which combine a fast stirring and a glauber dynamics as in @xcite . the relevant macroscopic parameters to describe these stochastic systems are the density , the conservative current ( from the stirring dynamics ) and the non - conservative current ( from the glauber dynamics ) . the large deviation functional gives the exponential cost of observing a deviation of these three parameters simultanously . the large deviations for the density have been already studied in @xcite and the long - range correlations of the steady state in @xcite . the large deviations of the injected power were computed for a different non - conservative stochastic dynamics in @xcite . the large deviation functional derived in measures the cost of observing a joint deviation of the density and the currents . thus the density large deviations obtained in @xcite can be recovered from the functional by optimizing the deviations on the currents . in the same way , observing an atypical conservative current imposes a non trivial constraint on the density and the non - conservative current . as a consequence , we argue in section [ sec : variance ] that the local conservative current fluctuations are produced by a different mechanism than in the case of conservative dynamics . for some choice of the glauber rates , the steady state may exhibit a phase transition . this instability of the steady state leads to a new kind of dynamical phase transition for the current which is presented in section [ sec : phase transition ] . the fluctuation relation for the entropy production has been investigated in the framework of dissipative systems in @xcite . using the exact expression of the large deviation functional , we discuss its symmetry properties with respect to time reversal and recover the fluctuation relation for the entropy production . contrary to the conservative dynamics , the entropy production is no longer proportional to the current injected in the system , but depends in a complex way on the currents and the density . to fix the idea , we first recall in section [ subsec : microscopic ] the microscopic model introduced in @xcite . as it will be clear from section [ sec : hydrodynamic limit ] , the details of the microscopic evolution will not be important to study the macroscopic limit and one can consider more general dynamics than the one introduced in section [ subsec : microscopic ] . the relevant macroscopic parameters are defined in section [ sec : hydrodynamic limit ] and some concrete examples are then discussed in section [ sec : some concrete examples ] . we consider a particle system on a one dimensional chain with @xmath0 sites @xmath1 . the state of each site @xmath2 can be occupied or empty and is encoded by @xmath3 . during the infinitesimal time interval @xmath4 , each particle has a probability @xmath5 of jumping to the left if the left neighboring site is empty , @xmath5 of jumping to the right if the right neighboring site is empty . furthermore at each site @xmath2 , a creation or an annihilation can occur with probability @xmath6 , where the rate @xmath7 can depend on the local configuration around the site @xmath2 . the simplest rates are constant creation and annihilation rates @xmath8 in which case @xmath9 . we will also consider more complicated rates leading to dynamical phase transitions . finally , to model the effect of reservoirs of particles at the boundaries another creation / annihilation mechanism is acting on the boundary sites : during each time interval @xmath4 a particle is created at site 1 ( if it is empty ) with probability @xmath10 and removed with probability @xmath11 ( if it is occupied ) . similarly at site @xmath0 , particles are created or removed at rate @xmath12 . we stress the fact that the stirring of the particles and the action of the reservoirs is much faster ( by a factor @xmath13 ) than the creation / annihilation mechanism in the bulk . the particles perform random walks thanks to the stirring mechanism . thus in the large @xmath0 limit , a particle created at the boundary has a positive probability to go through the system without being annihilated . this is the correct scaling to ensure a competition between the two mechanisms of the dynamics and therefore a non trivial thermodynamic limit ( @xmath14 ) . rephrased in mathematical terms , the previous dynamics is a markov chain with generator given by @xmath15 + \sum_{i\in \{1,n\ } } c(i , \eta ) \big ( f(\eta^i ) - f ( \eta ) \big)\\ & & \qquad \qquad + n^2 \sum_{i = 1 \ { \rm or } \ n } ( { \alpha}_i^+ ( 1 -\eta_i ) + { \alpha}_i^- \eta_i ) \big ( f(\eta^i ) - f ( \eta ) \big ) \ , , \end{aligned}\ ] ] where the configuration @xmath16 is obtained from @xmath17 by swapping the occupation numbers of the sites @xmath18 and the configuration @xmath19 is obtained from @xmath17 by changing the occupation number at site @xmath2 from @xmath20 to @xmath21 . the microscopic currents associated to the previous dynamics are defined as : _ the conservative current . _ for a given edge @xmath22 , let @xmath23 be the number of jumps from site @xmath2 to site @xmath24 minus the number of jumps from site @xmath24 to site @xmath2 during the time interval @xmath25 $ ] . _ the non - conservative current . _ we denote by @xmath26 the number of particles created at site @xmath2 during the time interval @xmath25 $ ] . in the same way , @xmath27 denotes the number of particles annihilated at @xmath2 . microscopically this leads to the following conservation law at each site @xmath2 and any time @xmath28 @xmath29 one can also consider more general stirring processes than the ssep of section [ subsec : microscopic ] ( e.g. the zero range process or a kawasaki dynamics @xcite ) . in the macroscopic limit ( @xmath14 ) this will lead to a non - trivial hydrodynamic limit provided that the diffusive dynamics is speeded up by a factor @xmath13 compared to the glauber part . the details of the microscopic evolution will be averaged out in the thermodynamic limit and the macroscopic equations will depend only on a few relevant macroscopic parameters which we describe below . we first consider the _ purely diffusive _ evolution in contact with the reservoirs at the boundary ( i.e. when @xmath30 ) . according to the hydrodynamic formalism @xcite , a given diffusive lattice gas can be characterized by the diffusion coefficient @xmath31 and the conductivity @xmath32 both depending on the density @xmath33 . following @xcite , one way to define these coefficients is to consider a one dimensional system of length @xmath0 connected to reservoirs at its two ends . since the number of particles is preserved by the dynamics , it is equivalent to measure the current @xmath23 through any bond @xmath22 . when both reservoirs are at the same density @xmath33 , the variance of the current @xmath23 transfered during a long time @xmath34 from one reservoir to the other is given for large @xmath0 by @xmath35 where @xmath36 denotes the expectation of the dynamics starting from the invariant measure . the conductivity @xmath32 is defined by . note that the scaling wrt @xmath0 comes from the fact that the diffusive dynamics has been speeded up with a rate @xmath13 . on the other hand if the left reservoir is at density @xmath37 and the right reservoir at density @xmath33 , the average current is given , for small @xmath38 and large @xmath0 , by @xmath39 which is simply fick s law and defines the function @xmath31 . for the ssep , @xmath40 and @xmath41 @xcite . at time @xmath28 and for @xmath42 in @xmath43 $ ] , the macroscopic density is denoted by @xmath44 when @xmath14 @xmath45 we stress the fact that the microscopic diffusion has been speeded up by a factor @xmath13 thus @xmath28 stands already for a macroscopic time . at the boundary , the density is imposed by the reservoirs at any time @xmath28 @xmath46 where the reservoir densities are those of the dynamics defined in section [ subsec : microscopic ] . finally we define the macroscopic conservative current at @xmath47 $ ] up to time @xmath28 @xmath48 where @xmath49 vanishes in the thermodynamic limit ( @xmath14 ) . its time derivative @xmath50 stands for the local current at @xmath42 and according to , its typical value is given by @xmath51 thus the hydrodynamic limit is given by @xcite @xmath52 with the boundary conditions . we investigate now the hydrodynamic behavior of the _ full dynamics_. let @xmath53 be the invariant measure of the stirring dynamics at the uniform density @xmath54 . ( for the ssep then @xmath53 is simply the bernoulli product measure at density @xmath54 ) . at time @xmath55 , the system starts at constant density @xmath54 from the measure @xmath53 , then for any site @xmath56 $ ] in the bulk @xmath57 where the macroscopic annihilation rate @xmath58 and the macroscopic creation rate @xmath59 are obtained by averaging the microscopic rates over the measure @xmath53 @xmath60 the measure @xmath53 is in general no longer invariant for the full dynamics , however the fast stirring ( with an @xmath13 rescaling ) dominates locally and maintains the system in a local equilibrium . even though , the density @xmath61 evolves under the action of the dynamics , the local statistics remain given by @xmath62 up to some small corrections which are vanishing for large @xmath0 . thus when @xmath14 , can be generalized to later times by adding the diffusion term and the density relaxes by following the hydrodynamic equation @xmath63 where the potential is given by @xmath64 and the boundary conditions are imposed by the left and right reservoirs @xmath65 and @xmath66 . in particular , the steady state density @xmath67 satisfies @xmath68 these heuristic ideas have been rigorously justified in @xcite for the microscopic model of section [ subsec : microscopic ] ( in this case @xmath69 ) . the macroscopic non - conservative current at @xmath47 $ ] up to time @xmath28 is defined by @xmath70 its time derivative @xmath71 stands for the local current at @xmath42 and is typically given by @xmath72 after rescaling , the microscopic conservation law reads @xmath73 the previous models can" +"optical ring potentials ( orps ) with axial symmetry are considered as basic building blocks and the simplest nontrivial closed - loop circuits in atomtronics @xcite and atom interferometry @xcite . atoms can be trapped by means of the optical dipolar force in high or low intensity regions with red - detuned @xcite or blue - detuned @xcite light , in what follows called bright and dark potentials , respectively . on the one hand , bright orps have been proposed and demonstrated with high - azimuthal - order laguerre gaussian ( lg ) beams @xcite and also with annular microlenses @xcite . azimuthal lattices within orps have been demonstrated with time orbiting of light beams @xcite and by interference of lg beams of different azimuthal orders @xcite . a one - dimensional stack of orps in a line has been proposed in an optical cavity @xcite and demonstrated with axicon beams @xcite . experimental storage and propagation of ultra - cold atoms and bose - einstein condensates ( becs ) in bright orps have been reported recently @xcite . dark orps on the other hand are optical fields with an annular region of minimum intensity @xcite , such as closed - loop optical singularities @xcite , for which the region of minimum intensity is exactly zero . for ultra - cold atoms , dark orps have the advantage of substantially reducing atom heating and decoherence rates @xcite because of the low rate of spontaneous photon scattering as well as producing intrinsically flat potential minima . blue - detuned orps have been experimentally reported by means of lg beams generated with spatial light modulators ( slms ) @xcite and by amplitude masks @xcite . these two techniques might experience the following limitations : ( i ) a significant fraction of the input power is lost and , therefore , it does not contribute to create the optical trap , ( ii ) the smoothness and , therefore , the quality of the trapping potential is limited by the size and number of pixels for the slms and the resolution of the printing system for the amplitude masks , and ( iii ) an accurate control on the position and alignment of the optical elements being used is required . as a consequence , these two techniques yield typically not null intensity minima . producing orps with zero - intensity annular regions both along the radial and axial directions is a challenging task . in this case , the dark potential forms toroidal dark focus , i.e. , a region of minimum intensity confined by higher intensities ( light walls ) both in the axial and radial directions . a toroidal dark focus has only been demonstrated using a superposition of two lg beams @xcite . in this article , we present a new method to generate a dark orp by means of the phenomenon of conical refraction ( cr ) @xcite , occurring in biaxial crystals . cr leads to a set of two concentric bright rings enclosing a dark ring of null intensity , known as poggendorff dark ring ( pdr ) . we theoretically investigate the three - dimensional ( 3d ) field distribution around the cr pdr and show both theoretically and experimentally that it is a toroidal dark focus . we also discuss the use of the pdr as a blue - detuned orp for ultra - cold atoms and demonstrate this with a @xmath0rb bec . this technique has the advantage of the easy generation of the toroidal dark trap , which only needs a focused gaussian beam and a biaxial crystal . in addition , cr provides the full conversion of the input power into the toroidal dark trap , in contrast to the previously reported methods which introduce losses due to diffraction in the generation of lg beams . these features make the cr toroidal dark - focus beam very attractive for particle @xcite and atom @xcite trapping , in particular with blue - detuned light beams @xcite . the article is organized as follows : in section [ seccr ] we give an introduction to the cr phenomenon , presenting its main fundamental characteristics : section [ secpcr ] presents the exact paraxial solution of the light pattern after propagation along one of the optic axes of a biaxial crystal , while its asymptotic approximation is presented in section [ secacr ] . in section [ secatomscr ] , we investigate the use of the toroidal dark trap provided by cr for the trapping of ultra - cold atoms with blue - detuned light . in section [ harmonic_approach ] we apply the harmonic approximation around the pdr and present expressions for the trapping frequencies and height of the potential barriers as a function of the physical parameters of the trapping system . then , both numerical simulations and experimental data for a @xmath0rb bec trapped in the pdr are shown in section [ secnum ] . finally , the main conclusions are summarized in section [ seccon ] . conical refraction @xcite is observed when a focused light beam passing along an optic axis of a biaxial crystal ( bc ) is transformed into a light ring at the focal plane . each pair of diagonally opposite points of the cr ring are orthogonally linearly polarized , as shown by double arrows in fig . [ figcr_cone_ring ] . therefore , a complete ring with uniform azimuthal intensity distribution is observed only for randomly ( rp ) or circularly ( cp ) polarized input beams ( fig . [ figcr_cone_ring](a ) ) , while for linearly polarized ( lp ) input beams the intensity pattern is azimuthally crescent with a zero - intensity point , where the polarization is orthogonal to the one of the input beam . this polarization distribution , which constitutes an essential signature of the cr phenomenon , significantly differs from the usually known radial and azimuthal polarization modes and only depends on the orientation of the plane of the crystal optic axes @xcite . the cr geometric optical approximation of the ring radius , @xmath1 , is the product of the crystal length , @xmath2 , and the cr semi - angle @xmath3 , i.e. , @xmath4 @xcite . the cr semi - angle @xmath3 depends on the principal refractive indices of the crystal as @xmath5 , where we have assumed @xmath6 . moreover , under conditions of @xmath7 the cr pattern at the focal plane is formed by a pair of concentric bright rings separated by the poggendorff dark ring ( fig . [ figcr_cone_ring ] ) . here , @xmath8 is the waist of the focused input beam , defined as the radius of the @xmath9 relative intensity , i.e. @xmath10 . finally , as far as cr beam evolution is concerned , the focal plane is a symmetry plane along the beam propagation direction @xcite . the cr rings are observed at the focal plane , and more involved structures including secondary rings are found as one moves along the beam propagation direction . at points given by @xmath11 from the focal plane a bright spot known as the raman spot @xcite appears on the beam axis , where @xmath12 denotes the rayleigh range of the focused input beam . in this section we describe the properties of the optical field at and close to the dark region of the poggendorff ring . the paraxial solution describing cr was derived by belsky and khapalyuk @xcite and later reformulated by berry @xcite . for a uniformly polarized and cylindrically symmetric input beam it gives an electric field vector : @xmath13 where @xmath14 and @xmath15 . @xmath16 is the azimuthal component in cylindrical coordinates and @xmath17 is the orientation of the plane of the optic axes of the crystal . @xmath18 and @xmath19 are the amplitude and unit vector of the electric field @xmath20 of a focused input beam with waist @xmath21 and rayleigh range @xmath22 . @xmath23 and @xmath24 with @xmath25 define , respectively , normalized axial and radial components in cylindrical coordinates with origin at the ring center ( @xmath26 ) at the focal plane ( @xmath27 ) . @xmath28 and @xmath29 are the main integrals of the belsky khapalyuk berry ( bkb ) solution , which describes the general properties of the cr beam . these integrals read : @xmath30 where @xmath31 , @xmath32 being the spatial wave - vector and @xmath33 is the @xmath34-order bessel function of the first type and @xmath35 is the radial part of the 2d transverse fourier transform of the input beam . for cp and lp inputs the intensity distribution behind the crystal becomes , respectively @xmath36 \cos \left ( 2 \phi - \left ( \varphi + \varphi_0 \right ) \right),~ \label{eqs_output_beam_intensity_lp}\end{aligned}\ ] ] where @xmath37 is the polarization azimuth of the linearly polarized input light with @xmath38 . the asymptotic solution for the poggendorff dark ring , i.e. , for @xmath39 , is obtained by using the asymptotic expansion of bessel functions @xmath40 . here we have centered the normalized radial component in cylindrical coordinates at @xmath41 by using @xmath42 . in this case @xmath43 and the electric field can be written as @xcite : @xmath44 where @xmath45 and @xmath46 therefore , the asymptotic intensity distributions @xmath47 and @xmath48 for cp and lp input beams are , respectively , @xmath49 for lp input beams ( see eq . ( [ eqs_cr_ring_intensity_lp ] ) ) , the output intensity distribution lacks azimuthal symmetry . in this case the cr ring has a maximum and a zero intensity at azimuthal angles @xmath50 and @xmath51 , respectively . these points possess , correspondingly , the same and the orthogonal polarization relative to that of the input beam , respectively ( fig . [ figcr_cone_ring](b ) ) . in the following we will analyze the case of a cp input beam , for which the cr output intensity is azimuthally symmetric and its spatial distribution is described by eq . ( [ eqs_cr_ring_intensity_cp ] ) . for a gaussian input beam with normalized transverse profile of the electric field amplitude @xmath52 , its fourier transform is @xmath53 . @xmath54 is the power of the input beam . for this case , eq . ( [ eqs_cr_ring_polarization ] ) can be analytically evaluated through the kummer confluent hyper - geometric function @xmath55 @xcite : @xmath56 , ~ \label{eqs_fxi_gauss_general_bks_weberfns}\end{aligned}\ ] ] where @xmath57 . the solid line in fig . [ figpoggendorfdark_1d_x_z](a ) shows the square modulus of eq . ( [ eqs_fxi_gauss_general_bks_weberfns ] ) at the focal plane ( @xmath27 ) . @xmath58 , gives the radial position of the poggendorff dark ring at the focal plane , being @xmath59 . in other words , the radius of the pdr is smaller than the geometric approximation of the cr ring , @xmath60 , by approximately half the waist of the input beam . note that @xmath61 , with @xmath62 . in the radial direction the pdr is confined by two maxima at @xmath63 and @xmath64 , respectively ( see table [ table1 ] ) . along the z direction , the lowest intensity barrier is observed also at the radial position of the pdr , i.e. , at @xmath65 as shown in fig . [ figpoggendorfdark_1d_x_z](b ) . at this radial point the positions of the intensity maxima along @xmath66 obtained from eq . ( [ eqs_cr_ring_intensity_cp ] ) and ( [ eqs_fxi_gauss_general_bks_weberfns ] ) are @xmath67 . therefore , the pdr is confined by walls of light in all directions and forms a toroidal dark - focus . table [ table1 ] presents the positions of the pdr and of the maxima in the radial ( @xmath68 ) and axial ( @xmath69 ) directions . .positions of the poggendorff dark ring and of the maxima in the radial ( @xmath70 ) and axial ( @xmath71 ) directions . [" +"@xcite discovered an excitation mechanism of stellar oscillations that is related to the opacity behaviour in ionisation zones : the @xmath0-mechanism , where @xmath0 denotes the opacity . this mechanism occurs when the opacity varies during compression phases so as to block the emerging radiative flux @xcite . ionisation regions correspond to a strong increase in opacity that leads to the _ opacity bumps _ responsible for the local excitation of modes . these driving zones should nevertheless be located at a precise radius inside the star , neither too close to the surface nor to deep , in order to balance the damping that mainly occurs at the surface . it defines the so - called _ transition region _ that shapes the limit between the quasi - adiabatic interior and the strongly non - adiabatic surface . for classical cepheids that pulsate in the fundamental acoustic mode , this transition region is located at a temperature @xmath1 k corresponding to the second helium ionisation @xcite . however , the bump location is not solely responsible for the acoustic instability . a careful treatment of the @xmath0-mechanism would involve dynamical couplings with convection , metallicity effects and both realistic equations of state and opacity tables @xcite . the purpose of our model is to simplify the hydrodynamic approach while retaining the _ leading - order _ phenomenon e.g . the location of the opacity bump or its amplitude such that feasible direct numerical simulations of the @xmath0-mechanism with convection can be achieved . we first focus on radial modes propagating in a purely - radiative and partially - ionised layer and then restrict our study to the 1-d case . our model consists of a _ local zoom _ about an ionisation region and is composed by a monatomic and perfect gas ( with @xmath2 ) under both a constant gravity @xmath3 and kinematic viscosity @xmath4 . all quantities in our model are dimensionless , e.g. temperature is given in unit of the surface temperature of the star , length in unit of a fraction of the star radius and velocity in unit of the sound speed at the surface . in order to easily investigate the influence of the opacity bump on the stability , we adopt the following conductivity hollow to mimic this bump ( as @xmath5 , see * ? ? ? * hereafter paper i ) : @xmath6,\ ] ] with @xmath7 and @xmath8 . here @xmath9 is the equilibrium temperature profile , @xmath10 is the hollow central temperature , and @xmath11 and @xmath12 denote its slope , width and relative amplitude , respectively . examples of common values of these parameters are provided in fig . [ fig : profile - rad ] . and @xmath13.,width=302 ] using the well - known work integral formalism ( e.g. * ? ? ? * ) , it is easy to show that the following condition is necessary to get unstable modes by @xmath0-mechanism in variable stars : @xmath14 however , this condition is not sufficient as the ionisation region should also be located at a given location in the star , neither too deep nor too close to its surface . this area is the so - called _ transition region _ that separates the quasi - adiabatic interior from the strongly non - adiabatic surface and is defined by ( e.g. * ? ? ? * ) @xmath15 where @xmath16 is the integrated mass between the considered point and the surface , @xmath17 the mode period and @xmath18 the luminosity . @xmath19 is the ratio between the thermal energy embedded between the given radius and the surface and the energy radiated during an oscillation period . coefficient ( eq . [ eq : psi ] ) . the superimposed green zone represents the location where @xmath20 . * b * ) the real part of the work integral plotted for the three different equilibrium models . the dot - dashed black line is for the constant radiative conductivity case . * c * ) corresponding radiative conductivity profiles . * d * ) corresponding equilibrium fields @xmath21 ( eq . [ eq : kt]).,width=302 ] in order to check these two conditions , we perform a linear stability analysis by using the linear solver builder code @xcite . by starting with the conductivity profiles shown in fig . [ fig : profile - rad ] , we first compute the equilibrium setup that is solution of both the hydrostatic and radiative equilibria given by @xmath22 = 0 , \label{eq : equil}\ ] ] where @xmath23 and @xmath24 denote the equilibrium pressure and density . then , we solve the linear oscillation equations for the perturbations by seeking normal modes of the form @xmath25 with @xmath26 , where @xmath27 is the mode frequency and @xmath28 its growth or damping rate ( unstable modes corresponding to @xmath29 ) . by varying the hollow parameters , we then determine the physical conditions that lead to unstable modes excited by the @xmath0-mechanism in our layer ( cf . paper i ) . the two criteria ( [ eq : kt ] ) and ( [ eq : psi ] ) predict that modes are unstable for a `` sufficient '' hollow ( adequate amplitude and width ) that is located in the transition region . using the work integral computed from the obtained eigenvectors , we indeed recover instability strips for the @xmath0-mechanism by considering the three different equilibrium setups ( fig . [ fig : wi ] ) : * the first case ( dotted blue line , @xmath30 ) corresponds to a hot star with an ionisation region close to the surface . as the surrounding density is small , @xmath31 and the conductivity hollow hardly influences the work integral : driving is unable to prevail over damping , leading to @xmath32 or _ stable _ modes . * in the second case ( solid green line , @xmath33 ) , the radiative conductivity begins to decrease significantly at the location of the transition region where @xmath34 . as a consequence , driving becomes important . furthermore , the radiative conductivity increase occurs where non - adiabatic effects are already significant , i.e. @xmath35 there . it means that no damping occurs between the hollow position and the surface as the radiative flux perturbations are frozen - in . driving is overcoming damping in this case , therefore @xmath36 and modes are _ unstable_. * the third case ( dashed red line , @xmath37 ) corresponds to a cold star of which ionisation region is located deeper in the stellar atmosphere where @xmath38 . ionisation then occurs in a quasi - adiabatic location . as a consequence , the excitation provided by the conductivity hollow can not balance the damping arising at the top of the layer , thus @xmath39 and modes are _ stable_. in conclusion , our first radiative model of the @xmath0-mechanism is well able to reproduce the main physics involved in the oscillations of cepheid stars : _ one should have @xmath40 to drive the oscillations ; _ ( ii ) _ the thermal engine underlying the conductivity hollow should also be located in the transition region where @xmath41 ( fig . [ fig : wi ] ) . to confirm both the results obtained previously in the linear stability analysis and to investigate the resulting nonlinear saturation , we perform direct numerical simulations of our problem . the idea is to start from the most favourable initial conditions found in the stability analysis and then advance the general hydrodynamic equations in time . we use a modified version of the public - domain finite - difference pencil code that includes an implicit solver of our own for the radiative diffusion term in the temperature equation ( * ? ? ? * hereafter paper ii ) . * b ) * the resulting spectrum after integrating over depth . * c ) * comparison between normalised momentum profiles for @xmath42 modes according to the dns power spectrum ( solid black line ) and to the linear stability analysis ( dotted blue line).,width=302 ] to determine which modes are present in the dns in the nonlinear - saturation regime , we first perform a temporal fourier transform of the momentum field @xmath43 and plot the resulting power spectrum in the @xmath44-plane ( fig . [ fig : fourier]a ) . the mean spectrum follows by integrating @xmath45 over depth ( fig . [ fig : fourier]b ) . with this method , acoustic modes are extracted because they emerge as `` shark - fin profiles '' about definite eigenfrequencies @xcite . several discrete peaks corresponding to normal modes well appear but the fundamental mode close to @xmath46 clearly dominates . moreover , the linear eigenfunctions are compared to the mean profiles computed from a zoom taken in the dns power spectrum about eigenfrequencies @xmath46 and @xmath47 ( fig . [ fig : fourier]c ) . the agreement between the linear eigenfunctions ( dotted blue lines ) and the dns profiles ( solid black lines ) is remarkable . in summary , [ fig : fourier ] shows that several overtones are present in the dns , even for long times . these overtones are however _ linearly stable _ suggesting that some underlying energy transfers occur between modes through nonlinear couplings . these nonlinear interactions are investigated thanks to a tool that measures the sound generation by turbulent flows ( e.g. * ? ? ? it involves projections of the dns physical fields onto the regular and adjoint eigenvectors that are solutions to the linear oscillation equations . the projection coefficients then give the time evolution of each acoustic mode that is present in the dns _ separately_. furthermore , as the evolution of the kinetic energy of each mode is also accessible with this method , one can follow the energy transfer between modes . and @xmath48 acoustic modes.,width=302 ] figure [ fig : nrj ] shows an example of the time evolution of the kinetic energy ratio @xmath49 for the two modes @xmath50 ( i.e. the fundamental one ) and @xmath48 ( i.e. the second overtone ) . here @xmath51 denotes the kinetic energy embedded in the acoustic mode of order @xmath52 , while @xmath53 is the total kinetic energy in the simulation . after its linear transient growth , a given fraction of the fundamental mode energy is progressively transferred to the second overtone until the nonlinear saturation is achieved above time @xmath54 , with finally @xmath55 of the total kinetic energy in the @xmath56 mode and the remaining @xmath57 in the @xmath48 one . we recall that it is at a first glance surprising to detect this second overtone at long times because it is linearly stable and should normally be damped by diffusive effects . the reason for its presence lies in a favored coupling in the period ratio between these two modes . indeed , the fundamental period is @xmath58 in this simulation while the @xmath48 one is @xmath59 . as a consequence , the corresponding period ratio is close to one half ( @xmath60 ) such that the second overtone is involved in the nonlinear saturation through a 2:1 resonance with the fundamental mode . the linear growth of the fundamental mode is then balanced by the pumping of energy to the stable second overtone that behaves as an energy sink , leading to the full limit - cycle stability . after the previous results obtained on purely radiative models in 1-d , we next address the convection - pulsation coupling that is suspected to quench the radial oscillations of cepheids close to the red edge . the idea is to slightly modify the unstable radiative setup to obtain a convective zone superimposed to the ionisation region in 2-d simulations . the convective instability obeys schwarzschild s" +"an open quantum system has been extensively studied for potential applications to quantum computation and quantum information processing @xcite . through the interaction with a reservoir a quantum system loses its coherent information . this is a so - called _ decoherence process _ decoherence has been regarded as a critical obstacle against quantum information processing . however , as the notion of `` reservoir engineering '' has been suggested for laser cooled trapped ions @xcite , the studies on the decoherence have moved to control it in laboratories instead of suffering from it @xcite . many of these studies have been based on markovian reservoirs @xcite . a markovian reservoir is characterized by two essential properties : a ) _ weak _ coupling with a system by which born approximation is validated and b ) _ rapid _ relaxation time such that the information of the system is diffused over the reservoir in a rather short time compared to the time scale in which the system changes . in the perspective of engineering a reservoir , it is desirable to study the decoherence caused through a non - markovian reservoir . it is strongly believed that a solid - state realization of quantum information processing may be extremely useful @xcite . the decoherence phenomena for solid state systems including a photonic band gap material and a quantum dot can not always be understood under the markovian assumption @xcite . the evolution of a single - mode atomic cavity in a non - markovian reservoir has been studied for an atom laser @xcite . a non - markovian reservoir has `` memory effects '' such that it preserves the coherent information of the system within its relaxation time . in order to analyze how many operations can be performed by preserving the coherent information of the system , one may consider three types of characteristic times : operation time @xmath0 for a single quantum operation on the system , decoherence time @xmath1 due to the interaction between the system and the reservoir , and the relaxation time @xmath2 within the reservoir . when a quantum system decoheres in a markovian reservoir with @xmath3 , the time correlation of fluctuations in the reservoir is neglected . however , in a non - markovian reservoir with @xmath2 comparable to @xmath1 , it is expected that the time correlation between fluctuations during the time interval @xmath4 raises a correlated influence on the system . once perturbed by the system , the reservoir may memorize a part of the system s information during @xmath2 @xcite . this memorized information will be fed back to the system at another perturbation within @xmath2 . it is expected that the correlated influence significantly suppresses the decoherence of the system @xcite . an extremal example for the memory effects by a non - markovian reservoir is that two atoms , which are prepared initially in a product states , come to be in an entangled state through the interaction with a common thermal reservoir @xcite . in ref . @xcite , the reservoir consists of a single - mode field with no relaxation , @xmath5 . it is desirable to study decoherence processes by bridging the gap between the two limiting cases of @xmath6 and @xmath7 . dynamics of an open system may be obtained from a quantum liouville equation of the total system that consists of the system and the reservoir @xcite . the reduced density operator of the system needs to be positive at all times . the positivity does not need to be altered by the presence of any other system , in other words , the reduced density operator of the system needs to be completely positive if the system and the reservoir are initially uncorrelated @xcite . the complete positivity was intensively discussed for a markovian reservoir @xcite . for a non - markovian reservoir , it was discussed for a master equation derived by using an operator sum representation with coarse - graining approximation @xcite . a random telegraph signal model was studied for a system in a non - markovian reservoir @xcite . however the complete positivity of the system density operator in a non - markovian reservoir is still an important problem to be unraveled . in this paper , we propose an effective hamiltonian approach to investigate the decoherence of a quantum system in a non - markovian reservoir . instead of deriving a non - markovian master equation , the formalism is based on the notion of an effective reservoir , _ i.e. _ , certain collective degrees of freedom in the reservoir that is responsible for the decoherence . we show that _ the reduced dynamics of the open system is completely positive _ and the complete positivity is naturally imposed from the effective hamiltonian approach . as examples for completely positive decoherence , we present three typical decoherence processes for a qubit such as dephasing , depolarizing , and amplitude - damping . the effects of the non - markovian decoherence are compared to the markovian decoherence . dynamics of an open quantum system has commonly been investigated by a master equation for the density operator or a fokker - planck equation for the quasi - probability function such as a wigner function @xcite . it is however difficult to derive a completely positive master equation for a system interacting with a general non - markovian reservoir . we suggest an effective hamiltonian approach by introducing the notion of `` effective variables '' in the environment . it will be shown that the large ( normally infinite ) number of environmental degrees of freedom , which we call `` environmental variables '' , is reductive into a small number of _ effective environmental variables _ in the sense that both cases result in the same master ( or fokker - planck ) equation for the system . for instance , a markovian thermal environment is reductive into a collective single - mode boson field in a thermal state @xcite . the property of being reductive into the small effective environmental variables , that leads to the correct and equivalent description of the reduced dynamics for a system , is predicted by two observations . first , at a given time @xmath8 , the density operator @xmath9 of the system @xmath10 can always be purified to a pure state @xmath11 of a larger composite system consisting of the system @xmath10 and an ancillary system @xmath12 , such that @xmath9 is obtained by tracing the pure state over the ancillary system , _ i.e. _ , @xmath13 provides all physical descriptions relating to the system and the ancillary system is called effective variable(s ) , which is in effect certain collective degrees of freedom , of the environment at the given time @xmath8 . secondly , the effective variables may be dynamic over the whole environmental variables as the interaction time @xmath8 passes . on the other hand , the dynamics of the effective variables can be absorbed by time - dependent coupling constants while keeping the effective variables stationary . the set of the time - dependent coupling constants and the effective variables contains all the information of the environment that governs the decoherence of the system . we call this set an effective environment . suppose @xmath14 is an interaction hamiltonian between a system @xmath10 and an effective environment @xmath12 . we write the interaction hamiltonian @xmath14 , in the interaction picture , in the form of @xmath15 where @xmath16 is a hermitian operator for the system @xmath10 and @xmath17 with hermitian operator @xmath18 is for the effective environment @xmath12 . the unit of @xmath19 is used throughout the paper . here , the time - dependent coupling constant @xmath20 is a hermitian matrix . the composite system @xmath21 is assumed initially in a product state , @xmath22 the effective environment @xmath12 consists of collective degrees of freedom in the environment @xmath23 @xcite . its initial state @xmath24 is not necessarily an thermal state even when the real environment is thermal . the hilbert space of the effective environment and the time - dependent interaction hamiltonian @xmath14 are determined such that they result in the correct reduced dynamics of the system . they may be determined from first principle calculation such as the time - convolutionless projection - operator method @xcite . the use of the time - convolutionless projection - operator method is presented in sec . once the effective environment is determined , one may consider and solve the quantum liouville equation for the composite system , @xmath25.\end{aligned}\ ] ] the evolution operator is now given as @xmath26 where @xmath27 is the time - ordering operator . in most cases , it is convenient to let @xmath28 or @xmath29 so that @xmath30 $ ] where @xmath31 . this simpler form of @xmath32 has advantages for later discussions from the calculational point of view . the total system is described by the density operator @xmath33 and the reduced density operator of @xmath10 is given by partially tracing the total density operator over @xmath12 , @xmath34 letting @xmath35 be the orthonormal basis set of @xmath12 that diagonalizes @xmath36 , the reduced dynamics of the system is described by a kraus representation ( or operator sum representation ) @xcite : @xmath37 where @xmath38 . note that the superoperator @xmath39 is a linear operator in the hilbert - schmidt space of density operators . calligraphic letters are used for superoperators on the hilbert - schmidt space throughout the paper . it is remarkable that the existence of the kraus representation @xmath40 directly implies the complete positivity of the evolution superoperator @xmath41 @xcite . this fact was already guaranteed since the hamiltonian formalism was adopted in the present approach of effective environment . this approach is applicable to the system decohering in a non - markovian as well as a markovian environment . the present approach of effective environment has several advantages in describing the reduced dynamics of a system . firstly , it provides the correct and equivalent description , similar to the master equation . secondly and most importantly , it guarantees the complete positivity in a general environment like a non - markovian environment . thirdly , it enables the analysis of the structure for effective variables , in a given environment , that are directly responsible for the decoherence . this analysis will be given in sec . [ sec : qubit ] . lastly , one may simulate the decoherence in an experiment by introducing such an effective environment and controlling the coupling to the given system . in the previous section we showed that the the effective environment approach provides the description of the reduced dynamics of a quantum system , which decoheres through an environment , provided the hilbert space of the effective environment , its initial state @xmath24 and the time - dependent interaction hamiltonian @xmath14 are determined . in this section we suggest a scheme which determines them by a first principle theory , in particular , the time - convolutionless projection - operator method @xcite which has been employed to study non - markovian environments for quantum information processing @xcite . consider the total system of a quantum system and an environment . the total system is assumed to have the hamiltonian , @xmath42 where @xmath43 , @xmath44 , and @xmath45 are the hamiltonians for the system , the environment , and their interaction respectively . it is straightforward to generalize that @xmath43 may contain time - dependent external fields to control a quantum operation on the system . for a typical form of the interaction hamiltonian , we consider a caldeira - leggett - type model @xcite given by @xmath46 where @xmath47 is a hermitian operator acting on the system and @xmath48 is a fluctuating boson field due to perturbation arising from the system . here , @xmath49" +"the existence of extreme - energy cosmic rays ( eecr ) with energies above the greisen - zatsepin - kuzmin ( gzk ) cutoff @xcite of about @xmath2 ev , presents an outstanding problem @xcite . nucleons and photons with those energies have short attenuation lengths and could only come from distances of 100 mpc or less @xcite , while plausible astrophysical sources for those energetic particles are much farther away . data from the hires experiment @xcite brought the violation of the gzk cutoff into question . yet the ee events in even the hires data set remain unexplained since the local universe ( @xmath3 mpc ) is devoid of strong candidate sources . this controversy will be solved conclusively by the pierre auger hybrid observatory @xcite , perhaps as soon as summer of 2005 . here we assume that the published agasa spectrum is correct . interestingly , it is the absence of events above @xmath4 ev in these data , rather than the presence of events above @xmath5 ev , that motivates this work . among the solutions proposed for the origin of the highest energy events observed by agasa , an elegant and economical solution to this problem is the `` z - burst '' mechanism : annihilation at the @xmath6-resonance of extreme - energy neutrinos ( @xmath7 ) coming from remote sources , and relic background neutrinos within @xmath8 mpc of earth , produces the nucleon and photon eecrs @xcite . the observed eecrs from the z - bursts are the emission analogues of the absorption features ( z - dips ) predicted long ago @xcite . one of the most appealing features of the @xmath6-burst mechanism is that the energy scale of @xmath9 ev at which the unexpected events have been detected , is generated naturally . the @xmath6-resonance occurs when the energy of the incoming @xmath7 is @xmath10 where @xmath11 is any of the three masses of the relic neutrinos . given the lower limit @xmath12 ev deduced from atmospheric oscillations for the heaviest neutrino mass , at least one @xmath13 is below @xmath14 ev . since the individual energies of the nucleons and photons emerging from the z - burst can not exceed the total energy of the burst , @xmath13 is the new end - point of the eecr energy - spectrum in this mechanism . partitioning this burst energy among the @xmath15 final state particles , one arrives at precisely the primary energies needed to produce events observed above the gzk energy . combining their recent measurements of the anisotropies of the cosmic microwave background ( cmb ) radiation with data on the large scale structure of the universe , wmap @xcite produced a strong limit on neutrino masses , @xmath16 ev . since a single neutrino mass above @xmath12 ev implies near mass - degeneracy for all three active neutrinos ( given the mass - squared splittings from neutrino oscillation data , described below ) one has @xmath17 ev at the 95% cl . however , objections @xcite to the priors assumed , or to the data sets included , have led to a relaxed bound @xmath18 ev , or @xmath19 ev . a subsequent analysis @xcite which includes wmap , 2df , and sdss data , and another which includes these and galaxy cluster data @xcite , have arrived at the bound , @xmath20 ev . still another analysis @xcite with cmb and lss data finds @xmath21 ev , but finds @xmath22 ev when priors from supernova data and the hubble key project are included . these newer bounds are very similar to the original wmap bound . in this work we focus on a particular feature of the agasa spectrum , namely the end - point energy . requiring that the z - burst mechanism not overproduce events beyond this agasa end - point , we derive a lower bound on the neutrino mass . the significance of an end - point energy for constraining model fluxes has been noted much earlier in the context of topological defect decay @xcite . a more ambitious project would be to actually fit the neutrino mass to the full agasa spectrum . this has been done , by fodor , katz and ringwald ( fkr ) @xcite . however , the allowed range of the neutrino mass that results is not tight . rather , it depends sensitively on how one parameterizes the transition from non - burst spectrum to burst spectrum near and above the ankle . fkr find @xmath23 fitted mass ranges of 0.1 to 1.3 ev if all ee events are assumed to originate with z - bursts , 0.02 to 0.8 ev if an additional extra - galactic source of ee protons is allowed , and 1 to 7 ev if an additional galactic - halo source of ee protons is allowed . super - kamiokande has provided a strong evidence for the oscillation in atmospheric showers of two neutrino species with mass - squared splitting @xmath24 = @xmath25 = @xmath26 ev , consisting of nearly equal amounts of @xmath27 and @xmath28 , and little or no @xmath29 @xcite . if neutrino masses are hierarchical , like the other leptons and quarks , then @xmath30 the mass of the heavier of the two oscillating neutrinos ( call it @xmath31 ) . some previous works @xcite on z - burst production of the eecrs have made this assumption . however we will show in this work that @xmath32 ev is not compatible with the agasa end - point spectrum if z - bursts produce the eecr . the reason is that with @xmath33 ev , the new eecr cutoff @xmath34 ev predicts too many super gzk eecr events beyond the agasa end - point . as the relic neutrino mass increases , @xmath35 decreases , and the features in the ee spectrum move progressively to lower energies . in particular , the number of events predicted at high energy decreases , and the number beyond the agasa end - point becomes compatible with zero for @xmath36 ev . note that our result is much sharper than , but compatible with , the allowed mass ranges of the fkr models with no additional ee proton source , or with an additional extra - galactic source of ee protons . in the next section we present our simulations and the resulting spectrum of eecr in detail . we have performed simulations of the photon , nucleon and neutrino fluxes coming from a uniform distribution of z - bursts "" , namely @xmath37 annihilations at the z pole ( @xmath38 ) . the burst energy is given in eq . 1 . our simulations cover the range @xmath39 ev for relic neutrino mass . the z - bursts were simulated using pythia 6.125 @xcite , and the absorption of photons and nucleons was modeled using energy - attenuation lengths provided by bhattacharjee and sigl @xcite , supplemented by radio - background models by protheroe and biermann @xcite . we simulated a uniform distribution of about @xmath40 z particles up to a maximum @xmath41 . if other z - burst spatial distributions are used , the main features of the spectrum of the ultra - high energy nucleons , photons and neutrinos remain the same as given below . the decay of the z bosons through all possible channels was done automatically by the pythia routines @xcite , using the default options of this program . for comparison with our later figures , we show in fig . 1 the spectra given by pythia , normalized per z boson , for @xmath42 ev ; redshifts and energy absorption are not included in pythia . the multiplicities that pythia gives per z - decay are 1.6 nucleons , 17 photons , 15 @xmath29 , 30 @xmath43 and 0.23 @xmath44 ( in each case counting particles and antiparticles ) . in our simulation , each z boson generated by pythia was placed on the `` event list '' of the cascade generator at a randomly selected distance . the cascade of decay products was then boosted . the @xmath45 factor corresponding to an energy @xmath46 in eq . ( 1 ) is @xmath47 we then followed the propagation of the nucleons , photons and neutrinos resulting from the boosted z - decays . the gamma factor of the secondary particles was corrected to include their red - shifting subsequent to the z - decay . each neutrino , nucleon or photon was created by pythia in the initial cascade at a fixed position , with fixed energy and direction of motion with respect to the earth frame of reference . the distance each particle had to travel before reaching earth was compared with the appropriate attenuation length in space for the particle energy . if the distance was smaller than the attenuation length , the particle was assumed to reach earth unchanged . in the opposite case , the energy and momentum of the particle were degraded by a factor @xmath48 after traveling a distance equal to the attenuation length ( and the particle was placed again in the list constituting the cascade at the new position , with the degraded energy and momentum ) . neutrinos do not interact in their propagation . thus , the energy spectra of the three kinds of neutrinos were simply generated by summing the number of particles over energy bins and normalizing to neutrino multiplicities per z times the total number of z particles used . on the other hand , nucleons and photons do suffer energy - absorption interactions , and here we included energy absorption . the propagation process for nucleons and photons was continued until particles reached earth and were counted in the final spectra , or until particle energies became too small to be significant . in the latter case , the particles were simply discarded from the cascade . at this point , the final nucleon and photon spectra were appropriately normalized to the total number of z - particles used , as was done with the neutrinos . the results are given in fig . 2 for @xmath49 , with a fit to the six most energetic occupied bins in the agasa data @xcite . these bins consist of 24 events spanning the energy range from @xmath50 ev to @xmath51 ev . the energy - attenuation of the nucleons and especially photons requires more discussion . for nucleon attenuation , uncertainties are small , and so the predicted gzk suppression is highly credible . for the nucleon energy attenuation , we used the length given by bhattacharjee and sigl in the fig . 9 of ref . , based on results from ref . @xcite and @xcite . however , for photon energy - attenuation , the length is quite uncertain , due to the uncertain spectrum of the absorbing radio background . the photon flux shown in fig . 2 as curve ( 1 ) results from using the attenuation length shown in fig . 11 of ref . @xcite , based on observations of clark et al . protheroe and biermann @xcite produced two models for the radio background which lead to shorter interaction lengths ( and therefore more absorption ) than those based on clark et al . from the interaction lengths they provided , we constructed approximate attenuation lengths for the models of protheroe and biermann . we did so by reducing the attenuation length based on clark et al . by the ratio of the respective interaction lengths , and obtained the curves ( 2 ) and ( 3 ) in fig . 2 . since mean interaction lengths and mean energy - attenuation lengths do not have exactly the same energy dependence , our construction is an approximation . however , we believe the three curves which we display give a good representation of" +"quantum computation requires the mitigation of errors that occur due to faulty controls and unwanted interactions with the environment @xcite . fault - tolerant quantum error correction is one method for mitigating these errors with the advantage that provable arbitrary quantum computation is possible given constraints on the error rates and the error locality @xcite . there are many possible error correcting codes @xcite and the mapping of abstract models involving qubits on a completely connected graph to a more realistic local architecture leads to a number of choices that makes analytical comparison of codes difficult . in these systems it is typical to use simulation to determine the error correcting properties @xcite . although simulation of quantum systems is difficult @xcite , simulation of error correction can be done efficiently for stabilizer codes where the process of error correction only includes gates in the clifford group @xcite . a standard error model is a depolarizing channel where a pauli operator from a chosen probability distribution is applied at every possible error position @xcite . the depolarizing channel efficiently simulates common laboratory processes such as dephasing . it also serves as a good approximation for most error process that lead to a steady - state in which the system becomes maximally mixed . these are unital channels that map completely mixed states to completely mixed states . in nature it is also common to encounter interactions with the environment that lead to non - unital error channels in which the maximally mixed states are not a fixed point of the error process . one example is amplitude damping where , given enough time , all density matrices map to a single pure state . if an error channel is far from unital , then simulating it with pauli errors gives large approximation errors making it hard to extract useful results . in this paper , we go beyond simulating errors with the conventional pauli depolarizing channel ( pc ) . instead of only restricting to pauli errors , we allow any subset of efficiently simulable gate errors to occur . in particular , we look at subsets generated by including all clifford group operators and/or pauli measurements to the pc channel . we show that adding clifford errors and/or measurement errors always results in more accurate approximations and results in significant improvements for most error channels . we consider an approximating error channel to be valid if it has a smaller fidelity than the target error channel and choose the best valid approximation by minimizing the hilbert - schmidt metric . the paper is organized as follows . in section [ sec : realchannels ] we first describe the simulable error processes and introduce our expansions to the pc . we then mention two important error channels that can not be simulated in the stabilizer formalism and finally we describe our method for approximating a general error channel with our new models . in section [ sec : results ] we compare how well these models approximate the two error channels mentioned in section [ sec : realchannels ] and also a collection of random error channels . in section [ sec : conclusions ] , we conclude and describe future research directions . throughout the paper we use @xmath0 , @xmath1 , and @xmath2 to represent the pauli matrices with associated eigenvectors @xmath3 , @xmath4 , and @xmath5 respectively . it is convenient to consider the interaction of the environment with the system for a fixed time . then the system dynamics can be represented by a set of time - independent kraus operators that form an error channel . we begin by considering all error channels that can be simulated efficiently within the stabilizer formalism . next we examine two specific error channels that are outside of the stabilizer formalism . finally , we discuss a method by which we create an error channel that approximates a target channel . the stabilizer formalism allows for efficient simulation on a classical computer of operators from the clifford group operating on states stabilized by pauli operators @xcite . the clifford group for @xmath6-qubits can be generated from cnots and the 1-qubit clifford gates . as error channels , the probabilistic application of 1-qubit clifford operators can be represented by the following kraus operators : @xmath7 identity + @xmath8 pauli operators + @xmath9 = @xmath10 s - like operators + @xmath11 hadamard - like operators + @xmath12 for @xmath13 rotations about the face centers + @xmath14 , where @xmath15 and @xmath16 is the unit vector from the origin to one of the eight faces of the 1-qubit clifford octahedron @xcite . the stabilizer formalism also includes non - unital operators . the simplest are measurement operations in the pauli basis . more intricate non - unital kraus operations can be represented as measurements followed by gates conditioned on the measurement outcomes . we limit ourselves to non - unital operators that result in translations along the pauli axes . for each eigenstate , @xmath17 , of a pauli operator , we define the following two kraus operators with the same classical probability : @xmath7 measurement - induced translations + @xmath18 notice that the effect of these two operators is to discard the state with a probability of @xmath19 and replace it by @xmath20 . the effect on a state , when represented on the bloch sphere , is to translate it toward @xmath20 . to ensure trace preservation , we set @xmath21 where @xmath22 sums over all other operators . throughout the paper we will refer to four sets of these error process : pc , cc , pmc , and cmc . the pauli channel ( pc ) , introduced above , is limited to pauli errors . the clifford channel ( cc ) includes all efficiently simulable unitary gates . the pauli and measurement channel ( pmc ) includes all pauli errors and all measurement - induced translation errors . finally , the clifford and measurement channel ( cmc ) includes all clifford errors and all measurement - induced translation errors . we use these as approximation channels to the error channels presented below . .kraus operators corresponding to the 4 efficiently simulable error channels . [ cols=""^ , < "" , ] [ table : summary ] figure [ fig : rand ] illustrates the distance between each random error channel and the best approximation as a function of the distance between the error channel and the identity channel . the fidelity constraint guarantees that the approximation will always be more distant from the identity than the error is . notice that as the amount of operators in the error models increases , both the mean and the median distance between each model and the random error decreases and the distributions become more compact , as summarized in table [ table : summary ] . although the approximations with the cc had a smaller mean distance and a more compact distribution than the ones with the pmc , it is not clear that this difference is significant . the most important improvement occurs when we add both the unital clifford gates and the non - unital measurement - induced translations . for the cmc , for 48@xmath23 of the generated random process matrices the distance of the best approximation was less than 0.001 , while for the other error channels the fraction of approximations with a distance in this interval was not greater than 6@xmath23 . we have presented an extension to the random pauli error model which is still compatible with efficient simulation using the gottesman - knill theorem and leads to a computationally tractable description of realistic error models like amplitude damping . for ease of calculation , we have used the average distance as the measure to be optimized under two different fidelity constraints of the error channels relative to an error free channel . we have also only focused on single qubit errors in the absence of quantum operations . once we consider simulating operations over many qubits , we will need a distance measure that is composable over tensors . a more natural distance measure in this regard is the diamond norm @xcite . our method can be extended to multi - qubit channels but the optimization becomes more difficult as the number of clifford operators grows quickly with @xmath6 . in many cases , symmetries of the underlying error channels will minimize the number of clifford operators that must be considered . in future work , we will compare for a specific error correction circuit how the logical error rate compares for the models . we expect in the case of multiple rounds of error correction a substantial difference between error models with distinct fixed points . the authors thank aram harrow for valuable comments . av and krb acknowledge support from the national science foundation through the quantum information for quantum chemistry center for chemical innovation ( che-1037992 ) . mg , ls , and krb were also supported by the office of the director of national intelligence - intelligence advanced research projects activity through army research office contract w911nf-10 - 1 - 0231 and department of interior contract d11pc20167 . disclaimer : the views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements , either expressed or implied , of iarpa , doi / nbc , or the u.s ." +"since the mode - coupling theory ( mct ) of the liquid - glass transition has been proposed in the mid - eighties @xcite , considerable work has been done in order to compare its predictions with experimental data and computer simulation results @xcite . most of these tests of the mct are based on the use as fitting functions of the quasi - universal laws that are obtained from an asymptotic analysis of the family of non - linear equations to which the mode - coupling equations belong and that are valid only in the vicinity of the predicted so - called ideal glass transition singularity . for experimental data , this is essentially the only practicable approach , since typical glass - formers are molecular liquids for which a first - principle study is out of reach and since most experiments , like dynamic light - scattering spectroscopy @xcite , probe complex mechanisms in which various types of dynamical processes are entangled . in the case of computer simulations , the situation appears more comfortable , since simple systems can be considered for which all the data needed for an extensive comparison with the theory can be directly obtained with high precision . however , it turns out that one still has to rely on asymptotic results of the theory at some point . indeed , one finds that the mct is not able to predict accurately the location of the putative ideal glass transition : it has thus to be determined from the simulation results , usually with a fit to an asymptotic law , in order to calibrate the comparison between theory and simulation @xcite . such a use of the asymptotic laws does not go without difficulties , originating in the fact that the ideal glass transition is never observed as such : it is usually argued to be avoided because of the existence of so - called `` activated processes '' not taken into account by the theory , whose effect is to restore the ergodicity of the system in the predicted ideal glassy state . thus the transition is expected to be replaced by a smooth crossover between two dynamical regimes , one dominated by the mode - coupling mechanism and the other dominated by activated processes . a first problem with the occurrence of these additional processes is that it hinders a clear separation of time scales between the fast transient dynamics and the structural relaxation , with which mct exclusively deals , and thus makes the domain where the asymptotic regime of mct is expected more difficult to resolve . in addition , the study of the corrections to the asymptotic laws shows that these laws are valid only in a very small domain around the ideal glass transition @xcite : it can thus be expected that the dynamics in this domain will be markedly affected by crossover effects . finally , from a more pragmatic point of view , since the asymptotic laws of the theory apply to rather specific aspects of the dynamics ( for instance , in the @xmath0 relaxation regime , since the shape of the relaxation itself is non - universal , the main quantitative asymptotic prediction deals with the variation of the relaxation time with temperature ) , only selected parts of the available experimental information are usually involved in most experimental tests of the mct on molecular glassformers , a situation which can be considered quite unsatisfactory . for these reasons , it appears desirable to have a means to test the mct on experimental data which is not limited to the use of the critical predictions of the theory and which is able to give an overall account of the dynamics . this can precisely be achieved within the so - called schematic approach to experimental data . schematic mode - coupling models are simple sets of mode - coupling equations retaining the essential non - linear structure of the equations of the mct in one or two equations and with only a few parameters . they played a major role in the development of the theory to investigate the universal properties of the general mode - coupling equations and to demonstrate the potentialities of the theory @xcite . recently , they have been found useful as quantitative models for numerical fits of experimental data covering a wide time or frequency range . the basic idea behind this schematic approach to experimental data is that , since all equations of the mode - coupling type share distinctive universal properties , meaningful informations are likely to be obtained if a suitable minimal set of equations of this family is used as an effective mode - coupling model to describe experimental data . one interest of the method is then that the universal properties of the mode - coupling equations are used in a milder sense than in their usual direct applications : it is thus possible to numerically take into account corrections to the asymptotic laws that can be important if the system is too far from its putative ideal glass transition . in addition , one can tentatively describe the full dynamics , including the non - universal @xmath0 relaxation and the fast transient dynamics ( although through rather crude approximations ) , and thus possibly overcome the problem of insufficient separation of time scales . for these reasons , the schematic approach appears as a method of choice to critically investigate the validity of the previous tests of the theory based on the asymptotic laws . of course , the power of the method comes at a price : even a minimal schematic model ( in a sense to be defined latter ) will have numerous adjustable parameters . this makes the approach numerically extremely flexible , and one finds for instance that it is possible to give an account of the experimental dynamics with an ideal mct schematic model even at low temperatures where ideal mct is known inadequate . thus one should not overestimate the physical meaning of the fitted parameters . however , as was found in previous works , by critically looking at the results of a schematic analysis , one can address from a renewed point of view the problem of testing the predictions of the mct on experimental data . in the present paper , the third of a series devoted to the schematic approach to experimental data @xcite , we aim to address various issues that have been overlooked in previous works , in order to better settle and understand the principles and results of this approach . in the next section , we give an overview of the schematic studies proposed so far and of the models on which they were based . in sec . [ sec3 ] , a set of simple requirements that need to be fulfilled in order to define a suitable minimal schematic model is proposed . in sec . [ sec4 ] , we examine the influence of the choice of the schematic model on the results of the analysis of a given set of experimental data , and sec . [ sec5 ] is devoted to a tentative validation of the method , by analyzing model spectra with well defined properties within the schematic approach . we finally present our conclusions and draw perspectives for the approach . in this section , we give an overview of the schematic studies proposed so far . this gives us the opportunity to settle a few definitions and notations to be used latter . the first schematic study has been proposed by alba - simionesco and krauzman @xcite , where they analyzed low - frequency raman scattering spectra of the fragile glassformer metatoluidine with various two - correlator schematic models . one of them , based on the so - called f@xmath1 model @xcite , is defined by the equations [ f12model ] @xmath2 with initial conditions @xmath3 , @xmath4 , @xmath5 , and has subsequently been used in studies of raman spectra of other glassformers @xcite and , more importantly , of depolarized light - scattering spectra of salol and ckn [ @xmath6 covering a wide frequency range ( more than four decades ) @xcite . in all these works , where other choices for the memory - function @xmath7 have occasionally been considered @xcite , the fitting function was defined , up to an amplitude factor , as the susceptibility associated with the effective correlator @xmath8 another widely used model differs only from the preceding one through the choice @xmath9 an expression first proposed by sjgren @xcite , and the use as the fitting function of the susceptibility associated to @xmath10 , with an adjustable amplitude factor . it has been used to study depolarized light - scattering spectra of glycerol @xcite and orthoterphenyle ( otp ) @xcite , as well as coherent neutron - scattering and brillouin spectra of @xmath11 @xcite . an extended mct version of this model has also been used recently to study depolarized light - scattering , dielectric - loss and incoherent neutron - scattering spectra of propylene carbonate @xcite . finally , self - intermediate scattering functions obtained by molecular dynamics simulations of a nickel - zirconium model have been analyzed by teichler @xcite with a single - correlator model with @xmath7 defined as @xmath12 at variance with the works mentioned above , a retarded damping term involving four adjustable parameters has been used in the present case instead of the simple markovian approximation made in eq . involving the single parameter @xmath13 . looking at the equations , one sees that these models involve _ a priori _ a large number of fitting parameters . to reduce this number , simplifying assumptions are usually made : in refs . , , , and , the only temperature - dependent parameters are chosen to be @xmath14 and @xmath15 , whereas in ref . , these are @xmath15 and @xmath16 , and in ref . , @xmath14 , @xmath15 and @xmath16 change with temperature , the latter depending also on the wave vector modulus in all schematic studies proposed so far , a certain degree of arbitrariness has often been involved in the choice of the details of the model to be used . the most serious case relates perhaps to the use of the memory function in our preceding works @xcite , which , at variance with sjgren s model@xcite , can not be given any precise theoretical foundations . but other minor choices can also be questioned . there is indeed no physical reason to prefer using a simple correlator as the fitting function instead of a composite one like in eq . , the apparent advantage of the former choice , which seems to make the relation between the fitting function and the dynamical variable probed by the experiment transparent , relying on a mere tautology . one can also wonder why , for similar experimental data and schematic equations , the effective vertex entering the second memory function ( @xmath17 or @xmath16 ) has been held constant with temperature in refs . and and not in ref . for instance , where it is @xmath14 which has been kept fixed . in most cases , these various choices have been only validated _ a posteriori _ by the success of the model to fit the data under study and/or the obtention of parameters whose variations match the expectations from the microscopic theory @xcite . there are nevertheless a few difficulties that could be expected , related to the possible existence of non - generic features of the chosen model . indeed , as stated in the introduction , generic mode - coupling equations display remarkable universal properties @xcite , but , when a schematic model is considered , because it is very simple , one can experience severe limitations" +"if quantum gravity lies fundamentally in ten spatial dimensions , then the seven `` extra '' dimensions must somehow be hidden . the traditional approach , going back to kaluza and klein , is to make extra dimensions very small , close the planck scale . recently there has been a resurgence of interest in another approach where many of the extra dimensions are of much larger size@xcite . the standard model fields are confined to a three - dimensional wall or `` brane '' , a 3-d defect in the higher - dimensional space ; only gravity can propagate in the other dimensions or `` bulk '' . these ideas are observationally constrained from the particle - physics side and from the gravity side . roughly speaking , the success of the standard model limits the unification energy scale to energies well above 1 tev , although some of the most interesting brane+bulk scenarios are those where the unification scale is not many orders of magnitude more than a tev , providing a solution to to the `` hierarchy problem . '' laboratory measurements of gravity limit the size ( or radius of curvature ) of the extra dimensions to be smaller than about 0.3 mm@xcite . constraints of a model - dependent nature , including astrophysical ones , extend these limits , since the models generally add new particles and interactions to the standard model ( e.g.,@xcite ) . a broad range of unification scales and brane configurations is consistent with current constraints ; the unification scale and extra dimension size can be anywhere between the tev / mm limits and the planck scale . this broad range of possibilities of course just reflects the relative lack of data in the physics / cosmology `` desert '' . standard unification ideas often show running couplings extrapolated from actual experiments at 100 gev by 14 orders of magnitude to the unification scale at @xmath5 gev , but there are few direct particle data beyond the tev scale . a similar lacuna appears in the cosmological data ; we can cite direct information from cosmic abundances about microphysical processes as early as 1 mev , which can be affected by inhomogeneities originating as early as 100 gev ( e.g. @xcite ) and about earlier inflationary effects on very large scales ( such the microwave background anisotropy , e.g. @xcite ) , but we have almost no direct data about early `` mesoscopic '' structure on comoving scales smaller than a few centimeters at 100 gev ( a quantity of energy about equal to the mass of the earth ) at times earlier than @xmath6 second ( except possibly for the mean baryon - to - photon ratio and the mean density of some forms of dark matter . ) scalar metric perturbations are very effectively erased on these small scales by neutrino diffusion long before they can have any effect on observables such as element abundances@xcite . small - scale perturbations in baryon / photon ratio @xmath7 on small scales , even of large amplitude , are erased by nucleon diffusion before nucleosynthesis@xcite . from most of cosmic history ( in log space ) since the planck time , and on most scales of structure , only the tensor modes gravitational waves survive to the present . new gravitational wave observatories now under development will soon achieve a critical level of sensitivity at frequencies where they can plausibly detect the relic stochastic background of gravitational waves from cosmological events far into the early , previously unobservable `` mesoscopic '' era . one of the most interesting possible sources of radiation , from the point of view of both physics and cosmology , is the formation of our 3-brane . this paper surveys broadly the circumstances and the values of parameters the number and the size of large extra dimensions , and the scale of unification for which the background might be detected with current technology . to create a detectable background , the metric during the unification era must be far from equilibrium it must be close ( within a few orders of magnitude ) to chaotic on the mesoscopic scale of the horizon at unification . such circumstances can indeed be more generic than the usual assumption of a uniform equlibrium system . the brane+bulk configurations being contemplated are classical setups : the vacua of the fundamental theory have effective potentials that tend to drive them to forming classical three - dimensional defects . the details of the stabilization of the setup are not known but the cosmological formation of such defects is in general not an equilibrium achieved by a microscopic quantum process it involves macroscopic ( or at least mesoscopic ) collective dynamics , in the same way that spontaneous symmetry breaking occurs in the standard higgs mechanism . in the cosmological context , symmetry breaking during the setting up of the brane is likely to create gravitational waves via mechanisms analogous to such intense classical sources as cosmic strings or first - order phase transitions . the properties of the waves can be informative about both the physics of the brane and its early cosmological history . the formation and stabilization of the brane are associated with two new geometrical degrees of freedom , radion modes governing the size or curvature of the extra dimensions and nambu - goldstone modes corresponding to spatial variations in brane displacement@xcite . the characteristic scales of the resulting broadband background spectra can be estimated from general scaling considerations . the characteristic amplitude of the metric perturbations induced by brane condensation is of the the order of unity and the characteristic frequency is the horizon scale . we will use the `` maximal amplitude '' and `` hubble frequency '' to estimate the extra - dimensional scales accessible to gravitational wave detectors . the characteristic scale for setting up our 3 + 1 world is the gravitational timescale @xmath8 in standard 3 + 1 general relativity . this is cleanly determined by general relativity and thermodynamics except for a weak dependence on the particle - physics uncertainties encapsulated in the number of effective relativistic degrees of freedom @xmath9 ( e.g.@xcite ) . the characteristic frequency of observed gravitational waves is thus@xcite the hubbble frequency redshifted to the present day , @xmath10 : @xmath11 the estimate is valid back to the threshold of the extradimensional dynamics : @xmath12 , ( where @xmath13 is the size or curvature radius of the largest extra dimension ) , or @xmath14 , whichever comes first . the fiducial `` maximal '' energy density is set@xcite by the mean energy density in all relativistic species ( photons and three massless neutrinos ) , @xmath15 , where @xmath16 refers to the hubble constant . the energy density of relativistic matter redshifts in the same way as gravitational waves so they have the same ratio of energy densities today as when the waves were generated . ( constraints from nucleosynthesis limit the gravitational waves to about 10% or less of the relativistic matter density , or rms strain about three times smaller than the maximal value . ) at the low frequencies observed by spacecraft interferometers ( such as lisa ) there are many astrophysical foregrounds , including known sources such as galactic binaries . a stochastic background can however be distinguished from other sources of noise and astrophysical wave sources by resolving the background in frequency . for the projected sensitivity of lisa , a maximal background is detectable above the instrument noise or the other likely astrophysical foregrounds@xcite over a frequency range from about @xmath17 to @xmath18hz . in the center of this range , @xmath19hz , backgrounds are detectable with @xmath20 at the higher frequencies observed by ground - based observatories ( e.g. , ligo , virgo , tama300 , geo600 ) it could well be that other stochastic astrophysical backgrounds are relatively weak , and that the observable sources are so limited in time duration and frequency that the main contribution to the rms noise comes from the instrument itself . in this case we can use the entire bandwidth to measure the background and reach a level which places meaningful constraints on backgrounds@xcite . the most promising technique is to correlate the signals from two interferometers within a wavelength of each other . combining two early ligo or virgo systems will likely achieve a sensitivity@xcite @xmath21 and ligo ii may reach another two orders of magnitude below this@xcite close to the level where other stochastic astrophysical backgrounds ( such as neutron star emission ) may be expected . sufficient sensitivity to constrain primordial stochastic backgrounds may be expected for early ground - based interferometers roughly from 50 to 500 hz . there are many possible `` brane worlds '' with various configurations of large extra dimensions . to simplify the discussion we will assume that there are @xmath22 equal - size largest extra dimensions of size @xmath13 and all the others are much smaller , of size @xmath23 where @xmath24 is the true fundamental unification scale . the apparent ( usual ) planck mass in 3 + 1-d , @xmath25 , is approximately given by @xmath26 where @xmath27 is the volume of the extra dimensions . in our situation , @xmath28 where @xmath29 is the volume of @xmath22 extra large dimensions . thus each choice of @xmath22 defines a relation between @xmath24 and @xmath13 , shown in figure [ fig : variousn ] . the various relations intersect at @xmath30 : @xmath31 gravity is `` normal '' law for @xmath32 , and @xmath33 for @xmath34 . ] on scales larger than @xmath13 ; standard field theory holds on the brane at energies below @xmath24 . the cosmological formation of the brane setup is regulated on the gravitational timescale . in the 3 + 1-d era , this is just given by the hubble scale discussed above , @xmath35 which defines the usual gravitational relationship between length and energy . if we follow 3 + 1-d cosmology back using this equation , we come first to either ( 1 ) the time when @xmath36 and extra - dimensional effects come into play on a small scale , possibly associated with a first - order phase transition ; or ( 2 ) the time when @xmath37 , and the geometrical degrees of freedom of the extra dimensions are important even on large scales . in general the excitation of the extra - dimensional modes has a different character depending on whether @xmath38 lies above or below the hubble relation @xmath39 . the former case produces displacement modes at with a scale determined by @xmath13 ; the latter case produces radion modes with a scale determined by @xmath24 . the hubble relation @xmath40 is degenerate with the @xmath41 relation between @xmath13 and @xmath24 , meaning that in this case macroscopic and microscopic departures from the standard picture happen at about the same time . the transition to new microscopic unification physics and to 5-dimensional cosmological expansion would both happen at the same point on these lines , also corresponding to the condensation of the brane and the creation of the gravitational waves . in the @xmath42 case where @xmath43 , the condensation of the brane ( at @xmath36 ) takes place while the hubble length is still much smaller than @xmath13 . in this case a long evolution takes place after the brane forms ( and non - gravitational fields are confined to 3d as today ) , during which the cosmological evolution involves one classically large extra dimension and the usual relativistic cosmology does not apply . in particular there is not time for signals to propagate as far as @xmath13 in an expansion time . if the formation of the brane spontaneously breaks poincar invariance of the whole spacetime , the position of the brane when it condenses is therefore uncorrelated on scales larger than" +"the experimental realization of bose - einstein condensates of quasiparticles in solid - state systems has provided a new example of macroscopically coherent quantum states of matter . solid - state condensates exhibit striking fundamental differences from traditional quantum fluids such as atomic bose gases and superfluid liquid helium . much recent interest@xcite has been devoted to exciton - polaritons , which exist as normal modes of strongly coupled excitons and photons in semiconductor microcavities . due to the short lifetime of the quasiparticles , these condensates exist in a dynamic balance between pumping and decay rather than in true thermal equilibrium . as such , these systems are capable of spatial and temporal pattern formation similar to that exhibited by lasers.@xcite hallmark features of superfluidity such as quantized vortices@xcite and persistent currents@xcite have been observed in polariton condensates . spatial patterns and soliton dynamics have been seen to arise spontaneously in both one@xcite and two@xcite dimensions . intrinsic disorder in the material@xcite or deliberately designed potentials@xcite induce currents that may further facilitate symmetry breaking in the polariton system leading to novel patterns . in particular , vortices have been seen to nucleate and get trapped because of the nonuniformities of the potential landscape.@xcite most of the models that have been successfully and extensively used to describe pattern formation in polariton condensates are based on the complex ginzburg - landau equation ( cgle ) , which is also used in the theory of lasers and thus illustrates the similarities between the two systems . such models have been applied to vortex nucleation and motion,@xcite spatial density modulations,@xcite solitons@xcite and vortex lattices.@xcite various different modifications of this model have been considered , such as including separate dynamics of the reservoir , or modeling processes of thermal relaxation . under the assumption of fast relaxation of the reservoir and small condensate densities these modifications all simplify and the model can be written as : @xmath0 \psi \end{split}\ ] ] where @xmath1 describes a trapping potential , @xmath2 is a ( spatially varying ) pump rate , and @xmath3 is a nonlinearity which causes pumping to reduce as density increases some such nonlinear process is clearly necessary for the system to be stable , and the form included is the simplest such nonlinearity . linear losses are included in @xmath4 . anticipating that we will consider a harmonically confined system , eq . ( [ eq : cgpe ] ) is stated in oscillator units , measuring energy in units of @xmath5 , length in units of the oscillator length @xmath6 , and time in units of @xmath7 , where @xmath8 is the oscillator frequency of the trapping potential , and @xmath9 is the effective mass of the polariton . the values assumed in the numerical simulations are discussed at the start of sec . [ sec : prop - rotat - state ] . the polarization degree of freedom of the polaritons provides additional possibilities in pattern and defect formation , such as allowing for spatially separate vortices of left and right polarization.@xcite further possibilities for pattern formation arise in the presence of a magnetic field that favors circular polarization and therefore competes with the interactions , which favor equal densities of the polarization components , and also with any anisotropy resulting from strain fields induced by mechanical stress . the cgle can be modified to include these effects,@xcite but in this paper we will consider linear polarization only . in the absence of pumping and decay terms , the steady states of the cgle are often well approximated by the stationary thomas - fermi solution . one rather surprising feature of the cgle is that there exist many cases where the presence of pumping and decay significantly modifies the stable density profile . a particularly surprising case is that in a harmonic trap , the stationary state is unstable , and a rotating lattice is formed as the result of this instability.@xcite spontaneously formed vortices have been observed in polariton condensates,@xcite but these have been isolated , stationary vortices , pinned by the disorder potential in the sample . the spontaneous formation of a regular , rotating vortex lattice@xcite has not been seen experimentally . the aim of this paper is therefore to study the robustness of such lattices , and to discuss how one may overcome the difficulties that might arise in detecting a rotating vortex lattice . we consider the robustness of vortex lattices with respect both to deformations of the circular harmonic trapping potential considered previously , @xcite and also to modifications of the cgle , such as energy relaxation . we find that there is definite sensitivity to the trapping potential both elliptical distortion as well as background disorder can destroy the regular vortex lattice and replace it with a chaotic regime , and we present numerical results for the critical distortion and disorder that destroy the lattice . this fragility with respect to the geometry of the trapping potential contrasts with the relative robustness of the vortex lattice to other terms that might be present in the cgle , such as phenomenological approaches to the inclusion of relaxation processes . detection of moving vortices in a polariton condensate is non - trivial . polariton condensates can be imaged directly using the photons escaping from the semiconductor microcavity . each image requires that light be gathered over a non - negligible period of time , and therefore any moving feature will tend to smear out . hence rotating configurations would not be directly visible in time integrated images . we show that these problems can be overcome by using a defocused homodyne imaging scheme , allowing stationary repeatable images to be observed , which fully characterize the vortex lattice . the remainder of this paper is organized as follows . section [ sec : inst - non - rotat ] discusses the instability of the stationary state , showing how this instability can be found analytically for weak pumping and decay . section [ sec : prop - rotat - state ] then considers the vortex lattices that result from this linear instability , presenting results for elliptical trapping potentials , and traps with additional disorder present . section [ sec : detect - rotat - vort ] presents schemes for detecting rotating vortex lattices , and section [ sec : conclusions ] summarizes these results . as commented above , the presence of pumping and decay destabilizes the stationary thomas - fermi potential in a circular trap , which in turn leads to the appearance of the vortex lattice.@xcite in this section we discuss how , for weak pumping and decay , this instability can be found analytically , providing some insight into how and why the stationary state becomes unstable . this section provides an outline and the main results of the analytical stability calculation ; further technical details are given in appendix [ sec : line - stab - analys ] . in order to find the leading order effects of pumping and decay , one may linearize both in fluctuations and in the effects of pumping and decay , i.e. , one considers first the density profile and fluctuations about this in the absence of pumping and decay , and then determines how these are modified by non - zero @xmath4 and @xmath3 . using @xmath10 and @xmath11 , one may rewrite eq . ( [ eq : cgpe ] ) as a pair of real equations : @xmath12 where @xmath13 . in these equations , an approximation has already been made in neglecting the quantum pressure terms ; this approximation is appropriate for sufficiently smooth density profiles ( i.e. , for clouds much larger than the healing length @xmath14 ) . by substituting @xmath15 into eqs . ( [ eq : madellung ] ) , and linearizing in @xmath16 , the fluctuations obey @xmath17 in the absence of pumping and decay , the steady state is given by @xmath18 , where @xmath19 is the unit step function and @xmath20 , so the terms in eq . ( [ eq : linearised ] ) involving @xmath21 vanish . in this case ( [ eq : linearised ] ) can be reduced to the single equation @xmath22 which has eigenfunctions @xmath23 labeled by angular momentum @xmath24 , where @xmath25 are hypergeometric functions of the radial variable @xmath26 ( see appendix [ sec : exact - zeroth - order ] ) . these eigenfunctions have frequencies @xmath27 we may now use the solutions ( [ eq : hypgeom ] ) and ( [ eq : eigenfrequencies ] ) as a basis on which to consider perturbatively the effects of pumping and decay . we will work here to first order in @xmath4 and @xmath3 , in order to see the qualitative change introduced by pumping . this first - order treatment will predict an instability that already explains the behavior seen when all orders are considered in the numerical results presented in ref . and in sec . [ sec : prop - rotat - state ] . at first order,@xcite the steady state of eq . ( [ eq : madellung ] ) is given by @xmath28 and @xmath29 . integrating the first of eq . ( [ eq : madellung ] ) over the entire space gives @xmath30 . to find the change to the frequencies of the fluctuations , it is helpful to consider eq . ( [ eq : linearised ] ) in the form @xmath31 where @xmath32 represent the right eigenfunctions of the matrix of differential operators @xmath33 . note that in this identification , the terms involving @xmath21 in eq . ( [ eq : linearised ] ) should be considered part of @xmath34 . the change to the eigenfrequency induced by pumping and decay is thus @xmath35 \middle/ \left [ \int d^2r \psi^l_{0i } \psi^r_{0i } \right ] , \right.\ ] ] where @xmath36 indicate left eigenfunctions . finding left and right eigenfunctions separately is necessary as the operator @xmath37 is not self - adjoint ; further details are given in appendix [ sec : pert - theory - non ] . using the hypergeometric solutions described above , and following the outlined procedure ( see appendix [ sec : eval - overl - hyperg ] for details ) , one finds the shift @xmath38.\ ] ] the crucial feature of this result is that for any @xmath39 there is always @xmath40 ( for instance @xmath41 ) , such that this expression is positive . this implies that the eigenfrequencies acquire a positive imaginary part and the corresponding eigenmodes , which are those with large angular momentum , will therefore grow , leading to vortex nucleation ( cf . atomic bose - einstein condensates where vortices are nucleated when external stirring causes unstable eigenmodes to arise@xcite ) . the same procedure may be repeated includinging various modifications to the cgle . one such modification that may be easily incorporated is an energy - relaxation term , causing time evolution toward lower energy states , i.e. , @xmath42 . the introduction of this term is common in literature on atomic bose - einstein condensates , where it models the atomic transfer between the condensate and the thermal cloud . these effects can be accurately modeled by a quantum - boltzmann equation describing the population dynamics of the quantum states . at lowest order of approximation this leads to the same ansatz.@xcite such terms have also been used in modeling polariton condensates.@xcite as described in appendix [ sec : line - stab - gener ] , including such an effect at linear order changes the steady state chemical potential to @xmath43 , and the frequency shift becomes @xmath44.\ ] ] thus such relaxation , although driving the cgle toward its low - energy states , is not sufficient to kill the instability for any @xmath39 and any finite @xmath45 ," +"electron scattering is one of the most important processes in determining the emergent thermal spectrum from models of optically thick accretion discs around black holes and neutron stars . electron scattering opacity generally dominates absorption opacity in the atmospheres of the innermost regions of such discs @xcite . in the case where coherent ( thomson ) scattering is a good approximation , the resulting local thermal spectrum of some annulus in the disc is generally harder than a blackbody with the same effective temperature , due to incomplete thermalization at the scattering photosphere . however , incoherent ( compton ) scattering in the disc surface layers by thermal electrons can reduce this spectral hardening by increasing the energy exchange between the photons and the plasma @xcite . in addition to the disc atmosphere itself , many models invoke a powerful corona above the disc consisting of high temperature or nonthermal electrons that compton upscatter disc photons to produce the energetically significant hard x - rays that exist in certain classes of active galactic nuclei and in certain black hole x - ray binary accretion states ( e.g. @xcite ) . these hard x - rays in turn interact with the relatively cool disc atmosphere to produce reflection spectra that are widely observed in many black hole sources ( e.g. @xcite ) . in this work we explore turbulent comptonization , which is the effect of comptonization by bulk , turbulent electron motions on photon spectra @xcite . in sources with radiation pressure dominated accretion flows , bulk velocities may exceed thermal electron velocities , a phenomenon first pointed out in @xcite . the turbulent speeds @xmath0 on the outer scale of an mhd turbulent cascade will be of order the alfvn speed , and the ratio of this to the root mean square electron thermal velocity is therefore @xmath1 here @xmath2 , @xmath3 , and @xmath4 are the gas , radiation , and magnetic pressures , respectively , and @xmath5 is the ratio of the proton to electron mass . stratified shearing box simulations of magnetorotational turbulence generally have disc atmospheres that are supported by magnetic fields rather than thermal pressure @xcite . hence the first factor generally exceeds unity in an otherwise radiation pressure dominated disc . bulk speeds on the outer scale of the turbulence will therefore exceed the electron thermal speeds whenever the radiation pressure to gas pressure ratio exceeds the ratio of the proton to electron mass ratio , and even smaller depending on how magnetically supported is the disc atmosphere . in this regime , bulk comptonization by the turbulence may dominate thermal comptonization in determining the shape of the spectrum emitted by a local patch of the disc . this regime is commonly reached for near eddington accretion on black holes of all mass scales . indeed , the inner disc solution of the standard geometrically thin model of @xcite gives vertically averaged radiation to gas pressure ratios of approximately @xmath6 where @xmath7 is the ratio of turbulent stress to thermal pressure , @xmath8 is the black hole mass , @xmath9 is the radiative efficiency of the disc as a whole , @xmath10 is the luminosity in eddington units , and @xmath11 is the radius in the disc in units of the gravitational radius @xmath12 . hence the radiation to gas pressure ratio of the innermost disc will generally exceed the proton to electron mass ratio for near - eddington accretion even for stellar mass black holes , and certainly for supermassive black holes . on the other hand , energy exchange between the photons and the plasma is generally dominated by true absorption opacity in standard disc models for the most supermassive black holes @xcite , which may reduce bulk comptonization by turbulence in these sources . we are also motivated by observational evidence in many sources for a cooler , more optically thick medium that also compton upscatters disc photons in high luminosity sources , but not to the high energies usually associated with the more traditional external corona . the soft x - ray excess of the type 1 seyfert ngc 5548 was fit by @xcite with a warm ( @xmath13 kev ) optically thick ( @xmath14 ) comptonizing medium . similar parameters were obtained for the soft x - ray excess of the type 1 seyfert mrk 509 by @xcite : @xmath15 kev and scattering optical depth @xmath16 to @xmath17 . @xcite fit the soft x - ray excess of the extreme narrow line seyfert 1 re j0134 + 396 assuming extra comptonization within the disc atmosphere itself with @xmath18 kev and @xmath19 . such a spectral decomposition is consistent with the lack of short time scale variability in the soft x - ray excess compared to the hard x - rays in this source @xcite . @xcite fit the soft x - ray excesses of eleven bright quasars with comptonization in a medium with @xmath20 kev and @xmath21 . @xcite fit soft intermediate state spectra of the black hole x - ray binary gx 339 - 4 with a comptonizing medium with @xmath22 kev and @xmath23 . thermal comptonization fits to the soft x - ray spectra of a number of ultraluminous x - ray sources have @xmath24 kev and @xmath25 @xcite . such fits have been nicely confirmed with _ nustar _ and _ xmm - newton _ spectra of the ultraluminous x - ray sources ngc 1313 x-1 and x-2 , which require warm @xmath26 kev , optically thick @xmath27 comptonizing media @xcite . @xcite and @xcite suggest that one way of forming these optically thick cool coronae is by a radiation pressure driven outflow . the alternative we consider here is bulk comptonization by turbulence in the disc atmosphere itself . comptonization by bulk motions in the accretion flow has also been considered by others . @xcite considered bulk comptonization in converging flows and shocks . starting from this seminal work , bulk comptonization by radial flows has been calculated in detail by numerous authors @xcite . @xcite included bulk comptonization in their monte carlo calculations of photon spectra from radiation mhd simulations of super - eddington accretion flows , and found that it produced significant spectral hardening which resembled spectra of ultra - luminous x - ray sources . here we focus on smaller scale bulk comptonization by turbulence within the disc atmosphere itself . turbulent comptonization has also been invoked in other areas of astrophysics . @xcite and @xcite used then current limits on cosmic microwave background temperature anisotropies to constrain possible turbulent energy on cosmological scales prior to recombination . @xcite considered comptonization by alfvnic turbulence in a relativistic outflow as a model for the spectrum of gamma - ray bursts . the purpose of this paper is to determine how photon spectra produced by turbulent comptonization depend on properties of the turbulence itself , and how to resolve and interpret this effect in radiation mhd simulations . the structure of this paper is as follows . in section [ sec_general ] we show that the macroscopic physical origins of turbulent comptonization energy exchange are work due to radiation pressure and viscous dissipation due to the radiation viscous stress tensor , and we discuss why this requires us to treat divergenceless turbulence separately from turbulence with non - zero divergence . in section [ sec_energy_exchange ] we discuss the consequences of this for correctly implementing radiative transport in simulations , and derive the appropriate radiation energy equation in both lab and fluid frame variables . in section [ sec_incompressible ] we address the conjecture of @xcite that turbulent comptonization can be treated as thermal comptonization by solving the kompaneets equation with an equivalent wave "" temperature critically dependent on the photon mean free path . we show this is true only for divergenceless turbulence , derive the exact wave temperature with an analytic solution of the radiative transfer equation , and use this result to discuss how the wave temperature depends on the power spectrum of the turbulence . to provide physical insight , we also perform an intuitive , heuristic calculation of the wave temperature which well approximates the analytic solution . in section [ sec_compressible ] we consider bulk comptonization by turbulence with non - zero divergence . we show that comptonization by turbulence whose wavelengths are short relative to the photon mean free path can be treated as thermal comptonization with an equivalent temperature given by the full turbulent power . in the limit of extremely optically thick turbulence , we show how the evolution of local photon spectra can be understood in terms of compression and expansion of the strongly coupled photon and gas fluids . in section [ sec_discussion ] we discuss our results , and we summarize our findings in section [ sec_conclusion ] . in order to determine how photon spectra produced by turbulent comptonization depend on properties of the turbulence itself , it is useful to understand the distinct macroscopic physical origins of net energy exchange due to this effect . we show that these are simply the work done by radiation pressure and radiation viscous dissipation , and discuss the major consequences of this . we limit our consideration in this paper to non - relativistic velocities . before proceeding , we define terms and quantities that will be used repeatedly . by bulk comptonization we mean comptonization by bulk motions in general , and by turbulent comptonization we mean bulk comptonization specifically due to turbulence . we denote the characteristic photon mean free path @xmath28 , where @xmath29 is the electron density and @xmath30 is the thompson cross section . we denote the typical length scale for bulk velocity variations @xmath31 , such as the wavelength if there is a well - defined spatial period . unless otherwise stated , by the terms optically thin and thick we mean @xmath32 and @xmath33 , where @xmath34 and @xmath35 are the minimum and maximum length scales in the turbulent cascade , respectively , not referring to the optical depth that a photon would need to travel to escape the medium . net energy exchange due to bulk comptonization is simply the net energy exchange between gas mechanical energy and radiation . inside the photosphere , the mechanical energy loss rate per unit volume to radiation is @xmath36 where @xmath37 is the lab frame radiation pressure tensor . this can also be written as @xmath38 where @xmath39 is the trace of the radiation pressure tensor , @xmath40 is the radiation viscous shear stress tensor , and @xmath41 is the velocity shear tensor . we see that the energy exchange is separated into two pieces , one due to only a diverging velocity field and another due to a shearing velocity field in the presence of a radiation viscous shear stress tensor . the first piece has contributions from two effects , ordinary work done by radiation pressure , and radiation viscous dissipation . the former effect is first order in velocity since it is due to the contribution to @xmath42 that is zeroth order in velocity . energy exchange due to viscous effects , on the other hand , is second order in the velocity , as @xmath43 and the relevant contribution to @xmath42 must themselves be at least first order in velocity since they are a consequence of the velocity field . @xcite conjectured that turbulent comptonization can be treated as thermal comptonization by solving the kompaneets equation with an equivalent wave "" temperature critically dependent on the photon mean free path . this is physically intuitive for divergenceless turbulence since in this case energy exchange is entirely due to radiation viscous dissipation and is therefore second order in velocity . in section [ sec_incompressible ] we prove this conjecture for an arbitrary , divergenceless velocity field of uniform density , derive the exact expression for the wave temperature , and show how it is" +"[ cols=""<,^,^,^,^,^,^,^,^,^,^"",options=""header "" , ] recent afterglow observations of short gamma - ray bursts ( sgrbs ) have provided various information about their environments which can be interpreted as circumstantial evidence linking sgrbs with mergers of compact binaries such as double neutron stars ( ns - ns ) @xcite and black hole - neutron star ( bh - ns ) ( see @xcite for a latest review ) . on the other hand , the compact binary merger scenario is challenged by the detection of jet breaks in the afterglow of some sgrbs and the deduced small jet opening angle of @xmath0 . the formation of such a collimated jet in compact binary merger has not been clarified yet ( see e.g. , ) . one of the most interesting features in the latest numerical - relativity simulations @xcite is that ns - ns mergers in general are accompanied by a substantial amount of dynamical mass ejection . interestingly , the excess in near - ir band observed by _ hubble space telescope _ in _ swift _ sgrb 130603b ( @xcite ) is explained by the kilonova / macronova model @xcite provided that a large amount of mass @xmath2 is ejected in the ns - ns merger and it is powered by the radioactivity of r - process nuclei @xcite . such massive ejecta will have a large impact on the dynamics of the jet and the observed collimation could be naturally explained by their interactions . in this _ letter _ , we numerically investigate the jet propagation in the material ejected by double neutron star mergers based on a scenario indicated both by our latest numerical - relativity simulations and the observations of sgrb 130603b . the scenario is summarized as follows ( see fig.[f1 ] ) . * according to latest numerical relativity simulations adopting equations of state ( eoss ) which are compatible with the recent discovery of massive neutron stars with @xmath3 @xcite , a hypermassive neutron star ( hmns ) is the canonical outcome formed after the ns - ns merger for the typical binary mass ( @xmath4@xmath5 ) @xcite . * during and after the merger a large amount of mass @xmath6 is ejected ( phase ( ii ) ) . this size of ejecta is required to explain the kilonova candidate associated with sgrb 130603b . according to our numerical - relativity simulations @xcite , the morphology of the ejecta is quasi spherical for the case of the hmns formation . in particular , the regions along the rotational axis is contaminated significantly by the mass ejection . * such a large amount of mass can be ejected only if the eos of neutron - star matter is relatively soft @xcite . in this case , the massive ns formed after the merger is expected to collapse to a bh _ within several tens of milli seconds _ ( phase ( iii ) ) , forming a massive torus around it . * after the formation of the bh - torus system , a jet would be launched and it propagates through the expanding merger ejecta ( phase ( iv ) ) . a sgrb will be produced only if the jet successfully breaks out of the ejecta . note that our scenario is different from that explored by previous studies based on the newtonian studies , in which the mass ejection is not isotropic but is concentrated along the orbital plane . in this case , there will be little interaction with the jet and ejecta , and no collimation by the ejecta is expected . indeed , found no strong collimation by the disk wind ( see also @xcite ) , since their simulations were carried out in rather dilute ejecta ( @xmath7 ) . after studying the dynamics of the jet in the presence of the expanding ejecta , we discuss the canonical model for explaining a particular event , sgrb 130603b . with the observationally consistent parameter set , we show that relativistic jets successfully break out of the dynamical ejecta and travel with the required collimation angle . for constructing ejecta profile models , the results from numerical relativity are employed as the reference . we first analyze results in @xcite , and then fit the ejecta profile along the pole by the following formulae as @xmath8 in the above expressions , @xmath9 , @xmath10 , @xmath11 , and @xmath12 denote the onset time of jet injection ( measured from the merger time ) , radius , rest - mass density , and velocity of ejecta , respectively . other variables , @xmath13 , @xmath14 , @xmath15 , and @xmath16 are fitting parameters . the power - law index of density distribution ( @xmath13 ) has more or less dependence on the dynamics of merger , which is in the range @xmath17 . we choose the middle of this value @xmath18 in this study . @xmath14 denotes the velocity at the dynamical ejecta front ( we set @xmath19 ) . @xmath16 denotes the snapshot time at which we refer to the result of numerical relativity merger simulations . we set @xmath20ms , since the morphology of ejecta has been determined by that time and the outer ejecta continues to be in the homologous expansion phase @xcite . the location of forward shock wave at @xmath16 is denoted as @xmath21 , which is set as @xmath22 cm . the rest - mass density @xmath23 can be expressed as a function of ejecta mass ( @xmath24 ) as ; @xmath25 where @xmath26 @xmath27 denotes the central remnant mass , which is chosen as @xmath28 , and @xmath29 denotes the escape radius , which is defined as @xmath30 . the pressure of ejecta is set as @xmath31 with @xmath32 , which is cold enough not to affect the jet and ejecta dynamics . according to these formulae , we determine the ejecta profile as a function of @xmath9 and @xmath24 . we first examine the case of @xmath33 ( see table [ tab : model ] ) , which is the approximate value of the required mass for explaining the kilonova associated with sgrb 130603b @xcite , and then we study the dependece on @xmath24 ( _ m - m3 , m - m2 - 2 , m - m1 _ ) . @xmath9 corresponds to the time of jet injection , which is supposed to be the operation timing of the central engine . for this there are no observational constraints . we set @xmath34ms as the reference value , since our numerical - relativity simulations predict that the life time of hmns is likely to be several tens of milli seconds to explain the large mass of ejecta @xmath35 as well as the large mass of torus surrounding a black hole . for comparison , we study @xmath36ms case for one model ( _ m - ti500 _ , see table [ tab : model ] ) . using the ejecta profile obtained above as initial conditions , we perform axisymmetric simulations of jet propagation by employing a relativistic hydrodynamical code @xcite . we assume that the central engine successfully operates in the vicinity of the compact remnant , and the jet is injected with constant power from the innermost computational boundary . in these simulations , we focus only on exploring the interaction between the jet and ejecta . therefore , the computational domain covers from @xmath29 to @xmath37 cm . the canonical jet power is set to be @xmath38erg / s for all models , which is comparable with the average jet power of sgrb 130603b ( see @xcite for the collimation - correlated jet energy and also duration of prompt emission ) . we also prepare the model _ m - l4 _ for which @xmath39erg / s to study the dependece of the jet luminosity . throughout our simulations , we use the gamma - law eos with @xmath40 . the initial lorentz factor ( @xmath41 ) and specific enthalpy ( @xmath42 ) are set to @xmath43 and @xmath44 , which result in the terminal lorentz factor as @xmath45 . the initial jet opening angle ( @xmath46 ) is also not well constrained by observations , and hence we set @xmath47 as the reference value with @xmath48 for the study of dependence on @xmath46 ( _ m - th30 , m - th45 _ ) . note that @xmath47 is larger than the opening angle of @xmath49 , so that the initial thermal expansion of the jet would not be significant ( see e.g. , @xcite ) . simulations are carried out until the shock reaches the outer boundary or time becomes @xmath50 s after the jet injection . our models are summarized in table [ tab : model ] . starting from the initial moment of jet injection at the chosen post - merger time , the jet begins to burrow through the homologously expanding ejecta with mildly relativistic velocity . in the left two panels of fig . [ f2 ] , we display the density contour maps for _ m - ref _ at the time of jet breakout and the end of our simulation . at a short distance from the inner boundary , the jet structure changes from conical to cylindrical one due to the confinement by the dense ejecta . the small cross section of the jet head allows the shocked jet matter to escape sideways and generates hot cocoon around the jet . even though the density gradually decreases with the radius , the surrounding cocoon keeps confining the jet near the pole , and eventually the jet head successfully breaks out of the edge of the ejecta . the overall properties of the interaction between ejecta and jet are very similar to those in the context of the collapsar model @xcite . a remarkable difference between the jet propagation in the ns - ns ejecta and the stellar mantle is that the background fluid is no longer stationary and expands with time . the jet head chases the ejecta edge from behind , and needs to catch up with it for the relativistic breakout ; otherwise it would become non - relativistic ejecta and will never produce sgrbs ( see below ) . for less massive ejecta case ( _ m - m3 _ ) , the jet experiences less confinement and propagates faster than _ m - ref _ ( see right panels in fig . even so , the hot cocoon is formed by the jet - ejecta interaction and works to weakly confine the jet . in order to analyze the cocoon confinement and its degree , we use the dimensionless jet luminosity parameter ( @xmath51 , where @xmath52 denotes the ambient density above the jet head ) following the study by @xcite . by employing equations ( [ eq : rho])([eq : resc ] ) and imposing the condition @xmath53 , @xmath54 can be roughly estimated as ; @xmath55 where @xmath56 and @xmath57 and @xmath58 denote the radius of the jet head and the time after the merger , respectively . according to @xcite , ) , but we employ it for a qualitative argument . more detailed analytical criterion is currently under study @xcite . ] the condition of cocoon confinement is @xmath59 . in the vicinity of @xmath29 ( @xmath60 ) , all models ( including _ m - m3 _ ) satisfy the confinement condition , which indicates that the jet undergoes a collimation once at least . the cocoon pressure decreases with time because the density of ejecta has steep radial gradient ( @xmath61 ) . despite the weakening cocoon pressure , the opening angle of the jet becomes smaller than the initial one . in order to analyze the degree of the collimation more precisely , we define the average jet opening angle as @xmath62 where" +"complex networks @xcite have been conjectured to be embedded in hidden metric spaces , in which distances among nodes encode their similarity and , thus , their likelihood of being connected @xcite . this hypothesis , combined with a suitable underlying space , has offered a geometric interpretation of the complex topologies observed in real networks , including scale - free degree distributions , the small - world effect , strong clustering as a reflection of the triangle inequality , and self - similarity . it has also explained their efficient inter - node communication without a knowledge of the complete structure @xcite . moreover , it has been shown that for networks whose degree distribution is scale - free , the natural geometry of their underlying metric space is hyperbolic @xcite . all these results have then been used to propose geometric models for real growing networks that reproduce their evolution and in which preferential attachment emerges from local optimization principles @xcite . finally , mapping real complex networks into a hidden metric space has yielded a sustainable solution to the scaling limitations of the internet @xcite , and has shed light on the hierarchical organization of biochemical pathways in cells @xcite . these achievements have been accomplished while considering a _ binary _ network representation in which links either exist or are absent . there exists , however , a class of complex networks for which the magnitude of the interactions between nodes ( i.e. , the weights ) plays a central role in their structural organization and dynamics @xcite . for instance , the quantification of the rich - club effect in real weighted networks , in sharp contrast to results in unweighted representations , unveils the formation of alliances in multipolarized environments or the lack of cohesion even in the presence of rich - club ordering @xcite . similarly , the propagation of emergent diseases in the international airports network is intimately linked to the number of passengers flying from one airport to the other @xcite . a shift towards a paradigm of weighted networks is therefore in order to fully understand the interplay between their structural organization and their function . while several models have been proposed to address this matter @xcite , none of them , except to some extent the maximum - entropy class of models @xcite , is general enough to reproduce the topology and weighted structure of real weighted complex networks . in this paper , we present a general and versatile class of weighted networks embedded in hidden metric spaces . built upon the so - called _ newtonian _ class of binary networks in hidden metric spaces @xcite , our framework preserves all the qualities of complex topologies embedded in underlying metric spaces and , in addition , it allows to enforce explicitly the strength ( sum of weights of a node ) distribution and the correlation between the strength and the degree of nodes . moreover , the level of coupling between the weights and the underlying metric space enables to control the local disparity of the weights associated to the nodes @xcite as well as the shape of the weight distribution . our model lends itself to analytical treatment and includes an approach to estimate whether an underlying metric space is needed to explain the weighted features of real networks . one of the most remarkable aspects of the proposed class of models is the fact that the degree and strength distributions can be adjusted independently of the coupling with the underlying metric space . this critical property opens the path towards the uncovering of the natural geometry or real weighted complex networks . indeed , using our model , we find strong empirical evidence of metric properties in real networks , not only at the level of their topology but also in their weighted structure . our model is a nontrivial generalization to weighted networks of a class of random networks with hidden variables embedded in a metric space @xcite . in this model , @xmath0 nodes are uniformly distributed with density @xmath1 in a @xmath2-dimensional homogeneous and isotropic metric space -dimensional spheres of radius @xmath3 . however , the constraint of having constant density implies that the radius diverges in the thermodynamic limit and , thus , the metric space is equivalent to a @xmath2-dimensional euclidean space . ] , and are assigned a hidden variable @xmath4 according to the probability density function ( pdf ) @xmath5 . two nodes with hidden variables @xmath4 and @xmath6 separated by a metric distance @xmath7 are connected with a probability @xmath8 where @xmath9 is a free parameter and @xmath10 is an arbitrary positive function taking values within the interval @xmath11 . whenever the integral @xmath12 is bounded , the free parameter @xmath13 can be chosen such that @xmath14 . hence , @xmath4 corresponds to the expected degree of nodes , so the degree distribution can be specified through the pdf @xmath5 @xmath15 regardless of the specific form of @xmath10 ( see apps . [ sec : app_average_degree_of_nodes ] and [ sec : app_degree_distribution ] for details ) . the freedom in the choice of @xmath16 allows us to tune the level of coupling between the topology of the networks and the metric space , which in turn allows us to control many properties such as the clustering coefficient and the navigability @xcite . moreover , the form of the connection probability in eq . implies that networks generated with this model are small worlds for any heterogeneous pdf @xmath5 since high degree nodes are then likely to be connected regardless of the metric distance between them @xcite . to generalize this model to weighted networks , a second hidden variable @xmath17 is associated to each node . this new hidden variable can be correlated with @xmath4 so , hereafter , we assume that the pair of hidden variables @xmath18 associated with the same node are drawn from the joint pdf @xmath19 . the weight of an _ existing _ link between two nodes with hidden variables @xmath4 , @xmath17 , @xmath6 and @xmath20 , respectively , and at a metric distance @xmath7 is distributed according to the pdf @xmath21 where @xmath22 is any probability density function in the domain @xmath23 with @xmath24 , and where @xmath25 with @xmath26 and @xmath27 . the particular form of the distribution of weights eq . implies that the weight between nodes @xmath28 and @xmath29 can be written as @xmath30 where @xmath31 is a random variable drawn from the pdf function @xmath32 . equations and constitute the keystone of our model . indeed , as shown in app . [ sec : app_average_strength_of_nodes ] , the form of eq . is the only ensuring that @xmath33 , provided that the integral @xmath34 converges . the new hidden variable @xmath17 can therefore be interpreted as the expected strength of a node , and the joint pdf @xmath35 controls the correlation between degrees and strengths in the network . indeed , as shown in app . [ sec : app_average_strength_of_nodes_given_degree ] , the average strength of nodes with a given degree , @xmath36 , relates to the first moment of the conditional pdf @xmath37 , @xmath38 , through the relation @xmath39 therefore , when @xmath40 then @xmath41 . this limit stands as a good approximation for the behaviour of high degree nodes in real weighted networks . remarkably , these relations hold independently of the specific form of the connection probability @xmath10 and of the distribution of weights @xmath22 , thus conferring great versatility to our model . even more remarkable , the shape of the connection probability @xmath10 and the value of the parameter @xmath42coupling topology and weights to the metric space do not affect the relations @xmath43 and @xmath44 and , therefore , the join degree - strength distribution @xmath45 . this property conveys a degree of control over the weight distribution as well as over the disparity of nodes which is independent of the specification of degrees and strengths and , more importantly , opens the possibility to measure the metric properties of complex weighted networks . all results presented in the previous section hold in arbitrary dimension and for any form of the connection probability @xmath10 and weight probability density @xmath22 in eqs . and . to apply the formalism to real weighted networks , we particularize to the @xmath46 model as generator of the topology @xcite . in that model , we choose the circle @xmath46 of radius @xmath48 to be the underlying geometry over which nodes are uniformly distributed with density @xmath49 . distances among nodes are measured in terms of arc lengths , that is , two nodes with angular positions @xmath50 and @xmath51 are therefore at a distance @xmath52 where @xmath53 . the connection probability is set to @xmath54 where @xmath55 is a free parameter that can be used to tune the clustering . equation casts the ensemble of networks generated by the model into exponential random networks @xcite , i.e. , networks that are maximally random given the constraints imposed by the free parameters ( that is , @xmath5 and @xmath56 ) . to obtain a scale - free degree distribution , hidden variables @xmath4 are distributed according to @xmath57 with @xmath58 and @xmath59 . notice that by keeping the explicit dependence in the upper cutoff it is possible to model networks with @xmath60 and a hard cutoff , as found for instance in airport networks @xcite . moreover , since it is generally more convenient to fix the average degree @xmath61 explicitly , we choose @xmath62 such that @xmath63 and fix the remaining free parameters @xmath64 and @xmath65 externally . , i.e. , the _ natural _ cut - off of a scale - free distribution @xcite . however , in general @xmath64 can take any value in response to particular mechanisms at play , like the limited capacity to handle more than a given number of connections in the airport network . ] from eq . , we expect @xmath66 where @xmath67 is the generalized incomplete gamma function . ( the regular complete and incomplete gamma functions can be retrieved by setting the bounds @xmath68 and @xmath69 to the appropriate values ) . whenever @xmath70 , a condition holding for most realistic degree distributions , the double incomplete gamma function scales as @xmath71 with @xmath72 and @xmath73 @xcite . ] to assign weights on top of the topology generated by the model , the noise distribution in eq . is chosen to be a gamma distribution of average @xmath24 , that is , @xmath74 this particular choice allows us to interpolate with a single parameter between a zero noise limit when @xmath75 , exponential noise when @xmath76 , and strongly heterogeneous noise when @xmath77 . finally , to control the correlation between strength and degree and , therefore , to tune the strength distribution , we assume a deterministic relation between hidden variables @xmath17 and @xmath4 of the form @xmath78 , as observed in real complex networks @xcite . from eq . , we thus expect @xmath79 notice that the relation between average strength and degree in the previous expression is totally independent of the underlying metric space . it implies that the strength distribution scales as @xmath80 for @xmath81 with @xmath82 . figure [ fig : illustration ] shows the basic topological and weighted properties of a network generated using eqs . and compares them to the theoretical predictions presented in this section . apart from some expected fluctuations due to finite size , the agreement between the two is excellent . geometry has a strong effect on the strength and weight distributions , which depend on the coupling parameter @xmath42 . in fact , as shown in appendix [ sec : app_theoretical_calculations ] , the second moment of the strength distribution @xmath83 is proportional to the integral @xmath84 , which diverges whenever" +"physics in warped higher dimensional spacetimes may play an important role in nature , as illustrated by the rs1 model @xcite . however , effective field theory calculations are particularly complicated in such contexts . when warp factors vary greatly in the extra dimension(s ) it becomes difficult to power - count the size of feynman diagrams . for examples of such calculations see refs . @xcite . in this paper , we begin a program of honing `` holographic renormalization group '' ideas @xcite , applied to the rs scenario in @xcite , into a tool for simplifying and gaining insight into warped effective field theory . in particular we will apply this tool to understand the robustness of the goldberger - wise stabilization mechanism @xcite within effective field theory , although the methods are clearly very general . we use the ads / cft conjecture to inspire the form of a concrete and explicit renormalization group procedure , but do not rely on any unproven aspects of the conjecture . the form our rg will take is as a flow of effective field theories in rs1-type geometries of varying radius , @xmath0 , theories with smaller @xmath0 having lower warped down effective energy cutoffs . two effective theories lying on the same flow are matched to describe the same physics at energies below the lower of the two associated cutoffs . in particular this means that matched theories with different radii have the same `` ir '' or `` visible '' brane positions , but different `` uv '' or `` hidden '' brane positions . the matching is accomplished by tuning the hidden brane localized lagrangian as a function of @xmath0 . this 4d lagrangian depends on the values of bulk fields induced on the hidden brane . we will show that formally the flow of hidden brane lagrangians looks like a wilsonian rg flow of purely 4d effective field theories . a crucial feature of the associated 4d effective lagrangians is that they are local which greatly simplifies power - counting . we identify a conformal fixed point in the rg as the concrete realization of the ads / cft connection within our formalism . refs . @xcite have developed a related rg formalism focusing on renormalization of boundary divergences and properties of the holographic stress tensor . rg flows associated to branes in codimension two were studied in refs . while this paper was being completed , refs . @xcite appeared , which also discusses similar rg ideas . the utility of our rg formalism is this ; one can integrate the flow to take low - energy calculations in a highly warped compactification where they are difficult , to simpler calculations in a much smaller compactification ( smaller @xmath0 ) where the effect of warping is much less significant . of course this requires computing the effective couplings on the hidden brane in the new compactification , but this is facilitated by perturbing about the conformal fixed point and by working systematically in the small couplings of the theory . in this paper , we deal only with classical and tree - level quantum effective field theory involving a bulk scalar field , deferring a treatment of full effective quantum field theory with varying spins . already at this level , many of the non - trivial features of the rg procedure come into play . the paper is organized as follows . in section ii , we discuss free field theory and point out the basic rg structure and fixed point . in section iii , we apply our results to rederive in a simple way the goldberger - wise stabilization mechanism when the bulk scalar is identified with the one introduced by goldberger and wise . ( since we do not make gravity dynamical , our analysis is necessarily restricted to neglect the backreaction of the scalar on the geometry , the same approximation made in the original analysis . ) in section iv , we generalize our rg procedure to include a large class of interactions , in the bulk and on branes . we then use this in section v to demonstrate the robustness of the goldberger - wise mechanism within classical effective field theory in a manner that lends itself to generalization to the quantum case . in section vi , we switch from the language of classical field theory to consider tree - level feynman diagrams , setting the stage for the case of quantum loops , and showing how one deals with general effective interactions . section vii contains some concluding remarks . we consider a bulk 5d scalar field , @xmath1 , propagating on a fixed rs1 background with metric , @xmath2 the @xmath3 coordinate parametrizes the direction in a compact orbifolded space . this is a slice of ads space bounded by the hidden brane at @xmath4 and the visible brane at @xmath5 . we take @xmath6 . in this section we begin by studying a simple action which is exactly quadratic in @xmath1 , @xmath7 where @xmath8 the brane actions are written in terms of the induced brane metrics , @xmath9 and the dimensionless @xmath10-derivative expansions ( the 4d dalembertian is @xmath11 for the metric defined in ( [ metric1 ] ) and ( [ gident ] ) ) . @xmath12 and similarly for @xmath13 . the subscript `` @xmath14 '' denotes that the brane terms are quadratic in fields , which we generalize later . we denote the dimensions explicitly in units of the warping constant , @xmath15 . note that 4d general covariance ensures that in the space of 4-momenta , @xmath16 , the operator @xmath17 . the equation of motion is @xmath18 in 4-momentum space this is @xmath19 strictly in the bulk , @xmath20 satisfies the @xmath21 independent differential equation @xmath22 with boundary conditions @xmath23 we now define an `` effective '' hidden brane whose location is a variable , @xmath24 . we seek a new set of `` effective couplings '' on this brane replacing @xmath25 on the original hidden brane , @xmath26 where @xmath27 is the induced metric on the brane , which imply a new set of boundary conditions at @xmath28 , @xmath29 we require : 1 . the matching condition that @xmath30 which are solutions to the original equations of motion ( inluding boundary conditions ) , ( [ bulkeom ] ) , are also solutions to the effective equations of motion when confined to the effective domain @xmath31 . the boundary condition that @xmath32 for @xmath33 . this is obviously consistent with the previous requirement . + we interpret @xmath34 as a set of running couplings , @xmath35 , and associated 4d generally - covariant derivative operators , @xmath36 , just as in ( [ lambdadefn ] ) . we would like to find the `` renormalization group '' flow , @xmath37 , of this set . we proceed by taking the logarithmic derivative of the boundary condition ( [ bca ] ) , use the bulk equation of motion ( [ zhindpeom ] ) as @xmath38 to eliminate second @xmath3-derivatives of @xmath1 at @xmath28 , and ( [ bca ] ) again to eliminate any first @xmath3-derivatives of @xmath1 at @xmath28 , thereby obtaining + [ lambda2running ] _ 2 ( q^2a^2 , a ) = 4 _ 2 - + 2 - 2(qa)^2 . clearly , the @xmath28 dependence in the first variable of @xmath39 is entirely fixed by 4d general covariance . we will focus on the non - trivial dependence in the second variable , getting a set of @xmath40 functions , @xmath41 since @xmath16 varies freely , this represents a set of coupled differential equations for the @xmath42 . this flow has a set of fixed points . in the vicinity of such fixed points , the rg flow simplifies . when @xmath43 for all @xmath44 we solve the differential equation @xmath45 to find the fixed point @xmath46 this can be expanded in powers of @xmath47 and therefore corresponds to a local fixed - point effective brane lagrangian when written in position space . there is another solution , involving @xmath48 s , which is non - analytic in @xmath16 and therefore can not be interpreted as a local lagrangian on the effective brane . it is therefore rejected . for small momentum ( @xmath49 ) @xmath50 . as @xmath51 ( [ closedfixpt ] ) tells us @xmath52 . the same result is also obvious from the @xmath40 function equation ( [ lambda2running ] ) by first setting @xmath51 . in fact one can solve ( [ lambda2running ] ) for the fixed point by working order by order in powers of @xmath53 . this will generate ( [ closedfixpt ] ) as a series in @xmath53 . at leading order ( [ lambda2running ] ) implies ( _ 2^*(0 ) ) ^2 - 4 _ 2^*(0 ) - 2=0 . taking the positive root to match ( [ closedfixpt ] ) as @xmath54 , we again find @xmath55 at higher order in @xmath53 we find @xmath56 . this method of working out the @xmath40 functions in powers of @xmath53 will be more useful when we add interactions and the coupled rg equations are not soluable in closed form . notice that nowhere did the matching procedure specifically require that the bulk metric be ads space . for example , expressions equivalent to ( [ lambda2running ] ) and ( [ lambda20fixpt ] ) can be obtained for a 5d flat spacetime with the extra dimension taken as an orbifolded circle . since there is no curvature @xmath15 , we measure the coupling @xmath34 with an arbitrary mass scale @xmath57 . we use the metric @xmath58 so that the @xmath40 function has no explicit @xmath28 dependence . we find @xmath59 there is no fixed point for @xmath60 . for @xmath61 the fixed point is @xmath62 thus for massless or sufficiently light bulk fields there is no fixed point about which the rg flow simplifies . in particular there is no guarantee that one can match the original theory to an effective one in which the extra dimension is much smaller , with only small perturbations to the effective hidden brane action . that is a special property of having ( nearly ) ads bulk geometry . carefully taking the flat space limit of rs1 , one can check that ( [ lambda2running ] ) makes a smooth transition to ( [ minkrunning ] ) . adding a tadpole term to both branes will allow us to reproduce the goldberger - wise stabilization mechanism @xcite using the rg analysis . since in this paper we are keeping a fixed background geometry for simplicity , we will necessarily be making the same approximation as goldberger and wise , of neglecting the back - reaction of the scalar profile on the geometry . however , we expect that the generalization to dynamical gravity is straightforward . exact solutions that exhibit stability have been examined in @xcite . a perturbative approach to stability treating the back reaction in a systematic way was discussed in @xcite . consider now the theory @xmath63 where we now use @xmath64 units . note that @xmath65 are constants , not functions of @xmath16 like @xmath66 . the field @xmath1 must satisfy the boundary condition @xmath67 as before we attempt to match onto a theory with the new hidden boundary , @xmath68 as in the previous section , we take the logarithmic derivative of this boundary condition , ( [ gwbc ] ) , and use the bulk equation of motion as well as ( [ gwbc ] ) to eliminate any @xmath3-derivatives of @xmath1 . we arrive at the equation @xmath69 we will formally treat the hidden boundary value of the field , @xmath70 , as allowed to take arbitrary values , leading to rg equations @xmath71 where the partial" +"although heavy quark spectroscopy is now a rather mature subject , a number of interesting issues remain . in particular , the detailed properties of the excitation spectrum of heavy - light mesons ( @xmath6 ) and their light hadronic transitions are yet to be fully understood . experimentally , much of this excitation spectrum remains to be observed . only the ground state s - waves and a few of the @xmath7 p - waves are presently well established . however , many of these states will be accessible in the present and future b factories : cleo , babar , belle , cdf , d0 , btev and lhc b. besides furthering our understanding of qcd dynamics , the detailed study of these excited states may have practical benefits . for example , triggering on excited states may provide an efficient method of same side b tagging in hadron colliders . tagging is essential to the study of cp violation in the b system . the theoretical tools available to determine the properties of excited states in heavy - light systems include heavy quark effective theory ( hqet ) and low energy chiral effective theory @xcite . unfortunately , these tools are not sufficient to determine the detailed properties of these states . lattice gauge theory is the only existing technique which allows the systematic study of all the aspects of qcd in heavy - light systems . detailed studies of the p - wave excited heavy - light states within the quenched approximation already exist @xcite . future lattice studies will provide more insight into the nature of qcd dynamics as well as the masses and static properties of heavy - light hadrons . it is clear that a model to estimate the hadronic transitions from excited state to ground states would also be very useful . such a formalism has been developed and applied extensively to transitions in heavy - heavy @xmath8 systems @xcite . however , heavy - light mesons are more difficult because the light quark is subject to the full nonperturbative qcd dynamics . one possible approach to providing a framework for these hadronic transitions is to use the chiral quark model @xcite . this has been suggested by goity and roberts @xcite . in this paper we closely follow the work done in refs . @xcite . to compute the masses and wavefunctions of the excited states we use a dirac equation for the light quark in the potential generated by the heavy quark ( including first order corrections in the heavy quark expansion and mixing effects ) . we then use these masses and wavefunctions to compute the hadronic decay amplitudes of excited heavy mesons in the context of a chiral quark model @xcite . the main differences between the present and preceding works are in the choice for the parameters of the chromoelectric potential and in the inclusion of mixing effects both in the spectrum and in the decay amplitudes . moreover we use our results for the radial wavefunctions of the excited mesons to make a comparison with recent lattice results . from the comparison we extract an estimation for @xmath9 , the effective coupling of the quark to the pseudoscalar mesons . we find @xmath10 we present numerical results for the low - lying spectrum ( excited states up to the 3s states ) . we also compute the pseudoscalar meson hadronic transitions for these states as a function of the chiral quark model effective coupling constant . comparing our results with recent experimental width measurements we estimate this effective coupling @xmath5 . in section 2 , we discuss our determination of the spectrum of excited states . our notation , the choice of the potential , inclusion of mixing and other order @xmath11 corrections are explained . details of the masses and wavefunctions are presented for the low - lying excitation spectrum . comparison is made with present experimental data . our treatment of hadronic decays is described in section 3 . the analytic results are summarized in eqs . ( [ amplitude]-[use_amplitude ] ) . explicit expressions for the coupling coefficients appearing in these equations are given in appendix a. also in section 3 , details of the partial rates for the 1s and 1p states in the @xmath0 and @xmath1 systems are presented . again comparison is made with present experimental data . a complete list of remaining results for masses and partial decay widths is reported in appendix b. the general hamiltonian of the heavy - light system can be expanded in powers of ( @xmath11 ) @xmath12 however , even within the heavy quark limit , the general form of the zeroth order hamiltonian , @xmath13 , still involves the full nonperturbative qcd dynamics for the remaining degrees of freedom ( including light quark pair creation and gluonic degrees of freedom ) . at present it can not be solved analytically . we are forced to resort to use a relativistic potential model for @xmath13 . we model the most general heavy - light meson ( in the @xmath14 family ) , h , as a bound state of a light quark ( @xmath15 ) and a heavy quark ( @xmath16 ) . the heavy quark is treated as a static source of chromoelectric field and the only quantum number associated with it is its spin . the light quark is treated relativistically and its state is described by the wavefunction @xmath17 . in analogy with the hydrogen atom , we introduce the following quantum numbers : * @xmath18 , the number associated with the radial excitations ; * @xmath19 , the orbital angular momentum ; * @xmath20 , the total angular momentum of the light quark ; * @xmath21 , the component of @xmath20 along the @xmath22 axis ; * @xmath23 , the total angular momentum of the system ; * @xmath24 , the component of @xmath23 along the @xmath22 axis ; * @xmath25 , the spin of the heavy quark along the @xmath22 axis ; the parameters of our model are the masses of the light quarks ( @xmath26 for @xmath27 ) , the masses of the heavy quarks ( @xmath28 for @xmath29 ) and the chromoelectric potential of the heavy quark ( @xmath30 ) . the total wavefunction of the system can be decomposed as follows @xmath31 where @xmath32 are the usual clebsh - gordan coefficients and @xmath33 is a two component spinor representing the heavy quark . ( [ notation0 ] ) is a solution of the following eigenvalue problem @xmath34 where @xmath35 is the hamiltonian of the system . the energy levels in eq . ( [ dirac ] ) do not depend on @xmath24 because of rotational invariance . we rewrite eq . ( [ notation0 ] ) introducing the most general parameterization for the four spin components of the light quark wavefunction @xmath36 here @xmath37 are spherical harmonics that encode the angular dependence while @xmath38 , @xmath39 are real functions that encode that radial dependence . @xmath40 and @xmath41 are fixed , up to an overall phase , by imposing a normalization condition . our choice of the phase is such that @xmath42 within our basic framework , @xmath43 is given by the relativistic dirac hamiltonian @xmath44 and the rotational - invariant potential is the sum of a constant factor ( @xmath45 ) , a scalar part ( @xmath46 ) and ( the zeroth component of ) a vector part ( @xmath47 ) @xmath48 the constant @xmath45 is a an overall energy shift that depends on the heavy quark flavor and , in general , it is not equal to @xmath28 , as often assumed in the literature . for this reason we consider @xmath28 and @xmath49 two independent parameters of the model . asymptotic freedom suggests that at short distances the potential is dominated by a vector part that asymptotically approaches a coulomb potential , @xmath50 . on the other hand lattice simulations indicate that at large distances the potential is confining , scalar and asymptotically linear , @xmath51 . the naive assumption about a short distance coulomb - like divergent behavior of the potential is doomed because it gives rise to ultraviolet divergences ( as discussed in ref . @xcite and ref . @xcite ) . it this context the divergence arises in the @xmath11 correction to the energy and it is due to the inconsistency of a static point - like source ( the heavy quark ) within a relativistic framework . one solution is assuming that the heavy quark is static but not point - like , therefore the potential that it generates is a convolution of the coulomb - like potential and the square of the heavy quark wavefunction ( peaked around the center of mass of the system and smeared within some small length scale @xmath52 ) . more generally , one is allowed to cure this divergence by regulating the potential close to the origin ( on a length scale of the order @xmath52 ) . different choices for the regulator are allowed and they do not affect the physics we want to describe , providing that @xmath52 is small enough . the values of the parameters that appear in the hamiltonian , on the contrary , depend on this choice since they run with @xmath53 . in fact , to obtain the same spectrum , different choices for the regulator imply different fitting parameters . we chose to regulate the vector potential by assuming a gaussian shape for the wavefunction of the heavy quark , @xmath54 , and with this choice @xmath55 for the scalar potential we assume a simple linear form @xmath56 we observe that @xmath57 is not a physical parameter since it can be absorbed into the definition of @xmath26 . for this reason @xmath57 will be omitted from now on . summarizing , the nine parameters of our model are @xmath58 where @xmath59 and @xmath60 are mass parameters for the light @xmath61 and @xmath62 quarks respectively , equivalent to constituent quark masses shifted by the constant amount @xmath57 of eq . ( [ potential2 ] ) , which is undetermined in our model . @xmath63 is the mass of the @xmath57 quark with @xmath64 the corresponding energy shift . analogously for the @xmath65 quark . for any given set of input parameters we solve the eigenvalue problem , eq . ( [ dirac ] ) , using the hamiltonian of eq . ( [ dirac2 ] ) and the potential specified by eqs . ( [ potential ] ) , ( [ potential1 ] ) and ( [ potential2 ] ) . in this way we determine the radial wavefunctions @xmath67 and @xmath68 associated to the energy levels @xmath69 . we then compute @xmath11 corrections to the energy levels in first order perturbation theory @xmath70 where , ignoring for the moment the mixing of the states , @xmath71 the analytical expression for @xmath72 has been derived in ref . @xcite using the bethe - salpeter formalism . in terms of the radial wavefunctions ( after the analytical integration of the angular part ) , we rewrite @xmath73 as a sum of three contributions @xmath74 these terms are respectively : * the kinetic energy @xmath75 r^2 \text{d}r \label{i1}\end{aligned}\ ] ] with @xmath76 . * a shift due to spin - orbit interaction @xmath77 \ ! r^2\text{d}r \label{i2}\ ] ] for @xmath78 , or @xmath79 \ ! r^2\text{d}r \label{i3}\ ] ] + for @xmath80 . * the hyperfine splitting @xmath81 in eqs.([e1 ] ) and ( [ e2 ] ) we assumed that the hamiltonian was diagonal . this is not the case because the @xmath82 interaction term in the hamiltonian mixes states . in general correction terms can mix any states with the same total angular momentum , @xmath23 , and parity , @xmath83 , however , there are only two types of sizable mixings ." +"galaxy mergers and interactions play a key role in cosmological evolution , affecting galaxy morphology , the star - formation history by triggering intense bursts of star formation @xcite , and active galactic nuclei ( agn ) via the growth of central supermassive black holes @xcite . besides spectacular episodes of star formation , . interacting galaxies , in relatively isolated pairs or galaxy groups containing at least one gas rich member , are ideally suited where such interactions take place in a group , the stripped gas evolves under the influence of the intra - group medium ( igm ) while at the same time contributing to it . studying the stripped gas can reveal information about gas dynamics , star formation , igm enrichment and the formation of tidal dwarf galaxies ( tdgs ) . star formation beyond the galaxy disks and the principles governing it have attracted a lot of recent attention @xcite and the advent of ultraviolet ( uv ) and mid - infrared ( mir ) telescopes like galex and spitzer have enabled major advances in such studies . star formation from tidally stripped gas . atomic and molecular gas observations of such systems provide the conditions under which star formation is triggered in these regions . these entities known as tidal dwarf galaxies ( tdgs ) @xcite . due to active ongoing star formation they normally have characteristic blue colours and high velocity dispersions . typical hi masses of tdgs few times 10@xmath2 m@xmath3 and stellar masses are few times 10@xmath4 m@xmath3 @xcite . besides contributing to the dwarf galaxy population , tdgs provide us with further insights towards understanding galaxy evolution @xcite . in addition to tidally stripped gas and galactic winds @xcite , in situ star formation in tidal debris can be an important source of igm enrichment . @xcite estimate that star - formation rate ( sfr ) as low as 1.5@xmath510@xmath6 m@xmath3 yr@xmath7 maintained for 1 gyr , can raise the igm metallicity by @xmath01@xmath510@xmath6 solar . this value compares well with the metallicity floor "" @xmath01.4@xmath510@xmath6 solar in the damped lyman alpha ( dla ) gas , observed over a redshift range of 0.5 to 5 @xcite . in this letter we present one of the most spectacular cases of the impact on hi of a tidal interaction between a pair of spirals , ngc 3212 and ngc 3215 , which make up the arp 181 system and possibly a third small galaxy . ngc 3212 has been classified as an ` s ? ' galaxy at a redshift of 0.0324 , while ngc 3215 has been classified as an ` sb ? ' galaxy at a redshift of 0.0316 @xcite . we adopt a distance of 130 mpc ( assuming h@xmath8=75 ) for the system and at this distance 1 arcmin translates to @xmath0 39.4 kpc . hi in arp 181 was observed with the giant metrewave radio telescope _ ( gmrt ) _ on december 31st , 2008 . details of the observations given in table [ table1 ] . the baseband bandwidth used was 8 mhz for the hi 21-cm line observations giving a velocity resolution of @xmath013 km s@xmath7 . to signal to noise ratio the velocity resolution was smoothed to @xmath026 km s@xmath7 . the gmrt data were reduced using astronomical image processing system ( aips ) software package . bad malfunctioning antennas , antennas with abnormally low gain and/or radio frequency interference ( rfi ) were flagged . the flux densities are on the scale of @xcite , with flux density uncertainties of cubes were produced following continuum subtraction in the uv domain using the aips tasks ` uvsub ' and ` uvlin ' . the task ` imagr ' was used to obtain the final cleaned image cubes . from these cubes the integrated and velocity field maps were extracted using the aips task ` momnt ' ( using a 3@xmath9 cut - off ) . to analyse the structures , we produced image cubes of different resolutions by tapering the data with different uv limits and using uniform weights for the high resolution maps . .gmrt observation details [ cols= "" < , < "" , ] the lower left panel of figure [ fig1 ] shows the velocity field of the western mass . the lower right panel of shows the high - resolution hi image ( contours ) of a zoom in to the region where most of the hi mass in the system detected . figure [ fig1 ] ( upper panel ) , shows that almost the entire hi mass of the system is detected well beyond the optical disks of ngc3212 and ngc3215 and is connected to ngc3212 by a low density hi bridge . the hi not coincident with the optical tidal tail but runs parallel . the western mass has two distinct intensity maxima at positions 10@xmath10 27@xmath11 37.@xmath121 , 79@xmath13 49@xmath14 36.7@xmath15 and 10@xmath1027@xmath11 25.@xmath121 , 79@xmath13 49@xmath14 16.62@xmath15 , hereafter referred to as hp(n ) and hp(s ) respectively . hp(s ) approximately coincides with a small blue spiral sdss j102726.32 + 794911.9 no published redshift . however information in @xmath16 confirms this galaxy is at similar redshift to the arp 181 system . hp(n ) from ngc 3212 ( figure [ fig1 ] ) . the total hi flux density recovered from this system from the gmrt observations is 3.3 @xmath17 0.2 jy to the single dish value of 2.3 @xmath17 1.5 jy @xcite . using hi map , the hi content of individual galaxies and the western mass was estimated . the two galaxies , ngc3212 and ngc3215 contain 2.7@xmath5 10@xmath4 m@xmath3 and 7.9@xmath5 10@xmath2 m@xmath3 respectively the western hi mass along with the tidal bridge the uncertainty on estimates are @xmath010% . the velocity field of the western hi mass shows no signs of regular rotation at this velocity resolution . however there is a gradient from both east and west , converging near the positions of the intensity maxima , especially hp(n ) . within the limits of current spectroscopic data arp 181 appears to be a fairly isolated system . the nearest similar size neighbour is cgcg 350 - 053 projected at an angular distance of @xmath030.4@xmath18 ( 1.4 mpc ) with a velocity separation of @xmath0 2000 . there are several small galaxies projected close to arp 181 , but they lack spectroscopic data to confirm their distances . thus it is possible arp 181 is a galaxy group dominated by ngc3212 and ngc3215 . the system has been previously observed with spitzer @xcite , galex @xcite and in h@xmath1 ( @xmath16 ) . based on their galex and optical observations , @xcite conclude this system potentially hosts one or more tdgs . they suggested the two objects at positions 10@xmath10 27@xmath11 26.@xmath122 , 79@xmath13 49@xmath14 12.3@xmath15 and 10@xmath10 27@xmath11 40.@xmath121 , 79@xmath13 49@xmath14 45.3@xmath15 their optical spectroscopic observations confirmed the galaxy at position 10@xmath10 27@xmath11 26.@xmath122 , 79@xmath13 49@xmath14 12.3@xmath15 system . this galaxy appears to have spiral features in the sdss images , and extremely blue in nuv g. according to @xcite , this may be a dwarf galaxy which a part of the group or a recently detached tdg . the object at position 10@xmath10 27@xmath11 40.@xmath121 , 79@xmath13 49@xmath14 45.3@xmath15,is their second tdg candidate , although its association with the arp 181 system remains to be confirmed spectroscopically @xcite . the our observations reveal tidal interaction between ngc 3212 , ngc 3215 and sdss j102726.32 + 794911.9 seems to be a likely as there is no nearby neighbour of similar size in similar redshift range within @xmath0 3mpc radius . also both the arp 181 severely hi deficient indicating from the galaxies . to determine gas loss from a spiral is to compare its hi surface density deficiency is log@xmath19 @xcite , where where @xmath20 is the total hi mass of a galaxy and @xmath21 is the optical major isophotal diameter ( in kpc ) measured at or reduced to a surface brightness level m@xmath22 = 25.0 mag / arcsec@xmath23 . while @xcite used the ugc major diameters , we have used the rc3 diameters and used the modified values from @xcite . the expected value of this parameter for an early type spiral ( sb ) is 6.91 @xmath17 0.26 . since morphological sub - classifications are not available for ngc 3212 and ngc 3215 , we compared these galaxies against sb type spirals . the hi surface density values for ngc 3212 and ngc 3215 are hi deficient by a factor of 10 . the tidal bridge connecting ngc3212 to the also supports that this hi mass is a tidal debris from the arp 181 interaction . the small dwarf system , sdss j102726.32 + 794911.9 , may also be participating in the interaction . the high - resolution hi image ( lower right of figure [ fig1 ] ) shows the hp(s ) to be offset by @xmath0 5@xmath15 ( a beam ) from the optical centre of sdss j102726.32 + 794911.9 and its hi extends in the direction of the candidate tdg . however , given its size , the hi mass contributed by this system another scenario . under this scenario hp(s ) is lsb . the sdss images show distinct spiral pattern in sdss j102726.32 + 794911.9 and thus it is possible that only the central bright part of this galaxy is visible . however , two significant this scenario . the hi column density peak value for the high - resolution map reaches a higher value than the low - resolution map , indicating the to be compact and clumpy . the peak values and dimensions of the hi clumps in the high - resolution hi map are similar for hp(n ) and hp(s ) , consistent with both being . also contrary to what is expected of a big lsb spiral , we find no signs of regular rotation in this mass . instead the velocity field of the western mass is chaotic and ( lower panel figure [ fig1 ] ) shows an interesting gradient suggesting infall of gas from the eastern and the western sides towards the central region . thus we find this more like tidal debris than an interacting massive lsb disk . as explained in section 3 , the debris has two peaks , hp(n ) and hp(s ) , and we confirm these peaks coincide , with small offsets ( @xmath0 5@xmath24 , with the two dwarf galaxies described in @xcite , the tdg and sdss j102726.32 + 794911.9 respectively . from the channel images and the gmrt spectrum , we find this is the tdg candidate suggested by @xcite . the in the low - resolution ( @xmath0 30@xmath15 ) map for this object is 6.6@xmath510@xmath25@xmath26 . at a distance of 130 mpc , a 30@xmath15 beam samples @xmath018 kpc . the mass of the debris and the hi column density values are a good match with those found in tdgs @xcite . the high - resolution ( @xmath0 10@xmath15 ) hi map further confirms the hi peak to be associated with the tdg as well as hi extension to the east towards the tidal tail of ngc3212 . hp(s ) on the other hand , coincides with the small , very blue galaxy either a dwarf galaxy or a recently detached tdg . our high - resolution hi image ( lower right of figure [ fig1 ] ) shows an offset ( @xmath0 5@xmath15 ) between the galaxy and the hi peak . from the gmrt spectrum , we find the hi either interacting with the tidal debris the latter option is unlikely as the galaxy is bright in sdss z band suggesting presence of an old stellar population a recently formed tdg . unlike the diffuse structure associated with hp(n ) , bright in the" +"quantum phase transition has been studied for a long time . in quantum magnetism , the magnetic field is the most familiar parameter to cause quantum phase transitions . an @xmath0 heisenberg antiferromagnetic ( haf ) chain and an @xmath1 two - leg haf ladder are typical examples of one - dimensional quantum spin systems which show quantum phase transitions induced by the magnetic field . these systems have the unique ground state separated from excited states by a finite excitation gap , at zero field . as the magnetic field is gradually applied , the excitation gap is going to vanish . @xcite after the collapse of the excitation gap , the system enters into a field - induced critical phase . the field - induced critical phase lies in a range @xmath2 . here @xmath3 and @xmath4 are called as a lower and an upper critical field . for @xmath5 , the system is in the gapped phase . and for @xmath6 , the system is in another gapped phase where the spins are fully polarized . @xmath4 is also called as a saturation field . the quantum phase transitions at @xmath7 and @xmath8 bring about reconstructions of the excitation spectrum . especially , dynamical properties of low - energy excitations are dramatically changed . recently , dynamics of electron spins in the field - induced critical phases are actively investigated by various experimental techniques . @xcite among these experimental techniques , electron spin resonance ( esr ) occupies a unique position in its sensitivity to interactions between electron spins . in fact , thanks to this advantage of esr , many interesting esr experiments have been performed in one - dimensional quantum spin systems under high magnetic field . @xcite these recent precise esr experiments highlights necessity of reliable quantitative theory of esr in the field - induced critical phase . despite the theoretical and experimental importance of the field - induced critical phase , esr in the field - induced critical phase is less studied by theorists . this situation is in contrast to the fact that @xmath1 haf critical chain whose low - temperature esr is well understood . @xcite although esr of the @xmath0 haf chain has been studied in several works , they were mostly concerned with esr in gapped phases . @xcite it is the objective of the present paper to fill this gap by developing a theory of esr in the field - induced critical phase , especially around quantum critical points , of one - dimensional quantum spin systems in an organized manner . in this paper , we consider an @xmath0 haf chain with a general form of a single - ion anisotropy @xmath9 \label{eq : h}\end{aligned}\ ] ] in the whole range of the magnetic field , from zero field @xmath10 to the saturation field @xmath8 . @xmath11 and @xmath12 refer to the principal axes of the single - ion anisotropy . @xmath13 and @xmath14 are land @xmath15 factor of electron spin and @xmath14 is bohr magneton . we put @xmath16 unless otherwise stated . in particular , we focus on a shift of the resonance frequency ( esr shift ) caused by weakly anisotropic spin - spin interactions . we reported , in our preceding rapid communication , @xcite that the esr shift in the range @xmath17 is well explained by , the so - called form factor perturbation theory @xcite ( ffpt ) around an integrable field theory . in the case of @xmath0 haf chain , the o(3 ) nonlinear sigma model ( nlsm ) plays the role of the unperturbed integrable field theory in ffpt . in the rapid communication , @xcite we applied the ffpt to the analysis of the esr shift in @xmath18 and @xmath19 , where we utilized a close relation of effective field theories in two different regions , @xmath18 and @xmath20 . this paper is also intended to take a closer look at this remarkable feature . in the next section , we will briefly review a general framework of perturbative treatments for the esr shift . we consider esr shifts in three regions : the low - field gapped region ( sec . [ sec : gapped ] ) ; the region near the lower critical field ( sec . [ sec : hc1 ] ) ; and the region near the upper critical field ( sec . [ sec : hc2 ] ) . in each region , we introduce an effective field theory and apply it to the analysis of the esr shift at low temperature . [ sec : ndmap ] is devoted to a comparison of our theory with recent esr experiments @xcite of the @xmath0 haf compound ndmap . in appendix [ app : exchange ] , we discuss a qualitative difference of the single - ion anisotropy and an exchange anisotropy from the viewpoint of esr shifts . here we briefly review the perturbation theory of the esr shift . esr experiments measure an absorption of an electromagnetic wave by electron spins , where a microwave is typically applied . from the absorption spectrum , we are able to extract information on dynamics of electron spins . within the linear response theory , the esr spectrum @xmath21 is written in terms of the retarded green s function , @xmath22 \rangle\biggr ] . \label{eq : chi}\ ] ] here @xmath23 denote transverse components of the total spin @xmath24 , which is the generator of the global su(2 ) symmetry . thus , if the whole hamiltonian preserves the su(2 ) symmetry in the spin space , is trivially constant . in the presence of the magnetic field , the symmetry of the hamiltonian is lowered to u(1 ) at most . if spin - spin interactions preserve the su(2 ) symmetry , eq . is still simple despite the presence of interactions . @xmath25 the resonance frequency @xmath26 equals to the paramagnetic one @xmath27 at any temperature . if spin - spin interactions do not preserve the su(2 ) symmetry , the above discussion breaks down and the resonance frequency is shifted from the paramagnetic one . let us assume that the hamiltonian is composed of the three terms : @xmath28 where @xmath29 represents su(2 ) symmetric interactions , @xmath30 is the zeeman term , and @xmath31 represents anisotropic interactions . the model falls into the form of eq . . if the anisotropic interaction is weak , we are able to consider a perturbative expansion of the resonance frequency in the anisotropy @xmath32 . the first order perturbative expansion of the resonance frequency was proposed first by kanamori and tachiki @xcite and later applied to quantum spin systems by nagata and tazuke . @xcite ref . derived the esr shift @xmath33 from equal - time correlations at the lowest order in a general formalism , @xmath34 , s^- ] \rangle_0}{2\langle s^z \rangle_0 } + \cdots . \label{eq : nt}\ ] ] the average @xmath35 is taken with respect to the unperturbed hamiltonian @xmath36 , @xmath37 while we thus far treated the esr spectrum as a function of the frequency @xmath38 with a fixed @xmath39 in above discussions , this is often not the case in actual esr experiments . the esr spectrum is usually obtained as a function of @xmath39 with a fixed @xmath38 . in this case , the esr shift is defined as @xmath40 @xmath41 is the resonance field . note that the @xmath15 factor used in is determined at the high temperature limit . by definition , approaches zero as @xmath42 . at a low temperature @xmath43 , it generaly holds that @xmath44 . according to refs . , within the first order accuracy , the esr shift satisfies @xmath45 , s^- ] \rangle_0}{2\langle s^z \rangle_0}. \label{eq : nt_h}\ ] ] we should emphasize that eq . is equivalent to . therefore , as long as we are concerned with the first order perturbation theory around , it does not matter whether we change @xmath38 or @xmath39 . we apply the formula to our model , namely , @xmath46 . \label{eq : sia}\end{aligned}\ ] ] the esr shift is , in this case , given by @xmath47 \label{eq : yd}\end{aligned}\ ] ] the unit vector @xmath48 is parallel to the magnetic field . @xmath49 is represented as @xmath50 in the principal @xmath51 coordinate in . @xmath52 is a constant ( independent of @xmath53 and @xmath39 ) if the orientation of the magnetic field is fixed . for simplicity , we hereafter set @xmath54 where @xmath55 is the unit vector along the @xmath56 axis , that is @xmath57 in the principal axis coordinate . we call @xmath58 as a normalized esr shift . the normalized esr shift is useful for our purpose because it can be applied to systems with any value of @xmath59 and @xmath60 . @xmath61 . the system size is @xmath62 sites . the lower critical field @xmath63 and the upper critical field @xmath64 are guided by the dotted and the dashed lines respectively . there is an extremum around @xmath65 . this non - monotonic behavior of the esr shift is understood by the finite temperature crossover . ] we numerically evaluate the normalized esr shift from quantum monte carlo ( qmc ) calculations . the qmc results of the @xmath39 dependence of @xmath58 is shown in fig . [ fig : qmc ] . we find several characteristics from fig . [ fig : qmc ] . ( i ) the normalized shift is approximately proportional to @xmath39 in the ranges @xmath66 and @xmath2 . the slope @xmath67 is negative in the former and positive in the latter range . ( ii ) the normalized shift has a minimum around @xmath7 . the field which gives the minimum increases as the temperature increases . ( iii ) the normalized shift becomes zero at a certain value of @xmath39 because @xmath68 and @xmath69 hold at @xmath10 and the saturating value @xmath70 is positive . note that the field dependence in fig . [ fig : qmc ] is qualitatively different from that of @xmath1 haf two - leg ladder systems . @xcite in @xmath1 haf two - leg ladder systems , we fail to find the change of the sign of the esr shift . namely , the normalized shift is non - zero from the infinitely weak field to the saturation field ( see fig.1 in ref . ) . the above three features suggest that the magnetic field dependence of the normalized esr shift reflects the finite - temperature crossover . in the following , we analyze the normalized shift in the gapped , lower critical , and upper critical regions . first we review the zero - field case , then we will extend the argument to the low - field case . the unperturbed model in the absence of the magnetic field , @xmath71 has an excitation gap @xmath72 , @xcite which is called as the haldane gap . haldane proposed that haf chains with an integer quantum spin number @xmath73 have an excitation gap @xmath74 based on a semiclassical field theory , the o(3 ) nonlinear sigma model ( nlsm ) . @xcite the o(3 ) nlsm has a lagrangian , @xmath75 the contraction @xmath76 was taken . for simplicity we put the spin - wave velocity to unity . the field @xmath77 represents an antiferromagnetic order : @xmath78 the uniform component @xmath79 is quadratic in @xmath80 . the coupling constant @xmath81 is equal to @xmath82 or @xmath83 mod @xmath84 . the o(3 ) nlsm is integrable when @xmath85 ( mod @xmath84 ) . in the case @xmath86 , the o(3 ) nlsm is critical . @xcite on the other hand , in the case @xmath87 of our interest , the o(3 ) nlsm has massive triplet particles , which is called magnons , as the lowest excitations . the triplet" +"in petroleum reservoirs in order to find the lithology , the well - logging technique has proved adequate for oil exploration and production . parallel to the research of oil and gas fields , some features of petrophysical quantities obtained by well - logging could be analyzed and described in terms of the kind and content of the fluids within the pores . the quantities investigated in this research includes gamma emission ( gr ) , which is a measure of the natural radiation of the formation ; sonic transient time ( dt ) , which is a recording of the time required for a sound wave to travel through a formation ; neutron porosity ( nphi ) , which uses high - energy neutrons that collide with various atoms of both the formation material and fluids , reporting the existence of hydrogen in the pore space @xcite . these help us insight into the spatial heterogeneity of the properties of the large scale porous media , such as porosity , density , and the lithology at distinct length scales @xcite . in geological systems external forces besides internal instabilities cause the system to become a complex system . in order to analyze geological systems the theory of complex systems needs to be implemented . in this theory the probability density function ( pdf ) , entropy , and the degree of non - gaussianity is used . however the working parameter in this study is the entropy which is an important bases in thermodynamics . entropy was introduced in @xmath2 by rudolf julius emmanuel clausius @xcite . later boltzmann showed that entropy could be expressed in terms of the probabilities related to the microscopic structures of the system @xcite . when a system is in contact with a large reservoir , the boltzmann - gibbs entropy is obtained as : @xmath3 where @xmath4 is the probability of the microscopic configuration @xmath5 @xcite , and @xmath6 is the boltzmann constant . so one can conclude that entropy is subject to the probabilities of possibilities in system , reflecting the information upon the physical system @xcite . it is well - known in the classical boltzmann - gibbs ( bg ) statistical mechanics that the gaussian pdf under appropriate constraints , maximizes the bg entropy . bg statistics has been successful in explaining the behavior of systems in which short spatial / temporal interactions are significant @xcite . tsallis in @xmath7 proposed an entropy for systems that may have a multifractal , scale - free or hierarchical structure in the occupancy of their phase space as in the form @xcite @xmath8 which generalizes @xmath9 @xcite . where @xmath10 is nonnegative , concave , experimentally robust ( or lesche - stable @xcite ) and yield a finite entropy production per unit time @xcite . note that the applicability of tsalis entropy becomes important for systems with long - ranged correlations which involve strong interactions , glassy systems , fractal processes , some types of dissipative dynamics and other systems that in some way violate ergodicity . the entropy of expression @xmath11 has been applied to a wide range of science such as physics , biology , chemistry , economics , geophysics @xcite and medicines @xcite and references therein . at depth @xmath12 to @xmath13 of a gas well in southwest of iran.,width=377,height=207 ] we use well log data from a gas well in southwest of iran . these data are gamma ray radioactivity ( gr ) , sonic transient time ( dt ) and neutron porosity ( nphi ) taken every @xmath14 at the depth interval of @xmath15 meters . the logged interval includes asmari formation which is one of the main oil producer formations in iran reservoirs and consists mainly of fractured carbonate , sand stone , shaly sand and a trace of anhydrate . @xmath16 shows gr , dt and nphi data sets from the depth , @xmath17 , of @xmath12 to @xmath18 . our analysis is based on the increment of the petrophysical quantities shown by @xmath19 in various scales , @xmath20 , which @xmath21 . in this article we describe the petrophysical quantities using the pdf and non - gaussian degree , @xmath0 , based on tsallis entropy in section @xmath22 . we explain the connection between entropy ( less of information ) and the non - gaussian factor @xmath23 ( intermittency ) for these data sets in section @xmath24 and the conclusions are stated in section @xmath25 . . these estimations are fulfilled on petrophysical quantities such as gamma emission ( gr ) , sonic transient time ( dt ) and neutron porosity ( nphi ) that measured in space interval @xmath14 from a gas well in southwest of iran . solid lines are theoretical estimation achieved by fitting data sets to eq . since the shannon entropy is the logarithm of the probability , the entropy is extensive . as known the shannon entropy is considering all phenomenon based on the boltzmanian probability distribution function ( pdf ) . while , in general the experimental systems have no reason to obey the boltzmanian distribution . tsallis added a power of @xmath0 to the probability to be able to generalize the shannon entropy to all phenomenon , this causes the entropy not to be extensive . as the value of @xmath0 increases , the effects of the tails become more pronounced . hence , in systems where @xmath0 is greater than unity the minority is more pronounced compared a gaussian ( @xmath28 ) system . in other words having the value of @xmath0 greater than unity , non - gaussianity appears . in order to determine the non - gaussian degree of the system , @xmath0 , it is essential to determine the probability distribution function analytically . following the formalism of @xcite , we obtain the probability distribution function . since the most probable distribution corresponds to the maximum entropy , the variational principle is applied to @xmath27 . the continuous version of @xmath27 is stated as : @xmath29^{q } dx } } { q-1},\ ] ] where @xmath30 is the natural constraint corresponding to the normalization of eq . @xmath31 and @xmath32^{q } } { \int{[p(x)]^{q } dx } } dx}\equiv \langle x \rangle_{q } = \overline{\mu}_{q } , \,\,\,\,\ \int{(x-\overline{\mu}_{q})^{2 } \frac { [ p(x)]^{q } } { \int{[p(x)]^{q } dx } } dx}\equiv \langle ( x-\overline{\mu}_{q})^{2 } \rangle_{q } = \overline{\sigma}_{q},\ ] ] are the natural constraints corresponding to the generalized and mean variance of @xmath33 respectively , see @xcite . , for the @xmath24 data sets . this estimation has been made by determining the pdf based on tsallis entropy then exert @xmath34 test method . right panel : representation of entropy vs. the scales by employing the definition of tsallis entropy eq . @xmath31 for gr ( square ) , dt ( delta ) and nphi ( right triangle).,width=491,height=207 ] implementing the lagrange method in order to find the optimizing distribution under the constraints , we obtain @xcite @xmath35^{\frac { 1 } { 1-q } } \ , \ ( q<3),\ ] ] where @xmath36^{-1}.\ ] ] in order to characterize the non - gaussian degree of the system , @xmath0 , the @xmath34 test method is employed . if @xmath0 is close to @xmath16 , the pdf tends to be gaussian , hence , an uncorrelated series is expected . on the other hand , the large value of the non - gaussian factor @xmath0 , illustrates strong correlations and similarity of neighbors in data sets which affects the behavior of the system . therefore it can be concluded that high @xmath0 is a hallmark of having information about the system . for any @xmath0 a pdf could be plotted as shown in fig . @xmath22 . in fig . @xmath22 the pdf is plotted using eq . @xmath26 ( solid curves ) and the data sets ( symbols ) , showing a satisfactory consistency . to state more specifically , in order to estimate @xmath0 , we use the likelihood method which works by minimizing the parameter @xmath37 which defined as : @xmath38^{2}}{\sigma^{2}_{emperical}(x)+\sigma^{2}_{q}(x)},\ ] ] where @xmath39 is computed directly from the empirical series and @xmath40 is given by eq . @xmath41 is the mean standard deviation of @xmath39 and @xmath42 is associated with the probability density function derived by eq . the global minimum value of @xmath37 corresponds to the best value of @xmath0 . the best estimation of @xmath0 , corresponding to eq . ( 5 ) , yields the pdf which fits well to the empirical pdf . the entropy index @xmath0 versus the scales is shown in fig . @xmath24 ( left panel ) for any specific petrophysical series . note that the system is described by a specific @xmath0 for any scale . taking a close look at fig . @xmath22 and fig . @xmath24 we deduce that the non - gaussian pdf corresponds to large @xmath0 , specially at small scales . this means that @xmath0 is showing the efficiency of non - guassianity . as seen in the three panels of fig . @xmath22 , non - gaussianity of gr is more pronounced in comparison to dt and nphi . hence , powerful correlations and large fluctuations in the series are observed which influence the other quantities and gives an insight to the formation of the system . however , it could be seen in the third panel which is for nphi , that the pdf is non - gaussian at small scales but tends to be gaussian at large scales which corresponds to large and small values of @xmath0 respectively . as the values of @xmath0 in nphi tends to @xmath16 , no correlation exists , hence no information about the porosity would be available @xcite . in the right panel of fig . @xmath24 , the entropy of the data sets are plotted vs. the scales . it is shown that the entropy of gr has its least value at all scales , meaning that we have fine information about the existence of shaly layers detected by gamma ray . hence , the entropy decreases as the scale increases . also it is shown that the entropy of nphi is small at small scales which proves the existence of local correlation , but increases for large scales . this expresses the separated and uncorrelated porosity . comparing fig.@xmath22 and fig . @xmath24 we deduce that small entropy corresponds to non - gaussian pdf . note that this result is always true specially when the scale is small . . solid lines display linear fitting corresponding to the mentioned quantities.,width=340,height=264 ] in order to show the multifractal characteristic of the data sets the tsalis difference information needs to be calculated @xcite @xmath43,\ ] ] where transition is performed between states @xmath44 and @xmath45 . since the generalized entropy @xmath10 ( eq . @xmath11 ) has been introduced based on the concept of multifractals , so the degree of multifractality corresponds to the information evolution . actually , because the phase space of a multifractal geometry is occupied heterogeneously , we expect high information rate in this system . in fig.@xmath25 , it is shown that the difference information received from gr is high and increasing when the scale becomes greater , that is a hallmark of strong multifractality across the scales . on the other hand , the difference information for nphi is rapidly descending , meaning that the information at large scales is lost . note that weak difference information for dt suggests that dt may be nearly monofractal @xcite . to describe the pdf of the velocity difference between two points in fully developed turbulent flows , castaing et al . @xcite introduced the following equation based on a log - normal cascade model @xcite : @xmath46 where @xmath47 , @xmath48 are positive parameters . by taking the limit" +"low mass x - ray binary ( lmxb ) systems consist of a compact object accreting from a low mass companion star . the orbit of the lmxbs is expected to evolve due to mass transfer and redistribution of the angular momentum arising from the interaction of the binary components . the orbital evolution of x - ray binaries can be measured by four different ways . when the compact object is a pulsating neutron star , the pulse arrival time delay over the binary period is used to determine the orbital parameters of the system and multiple measurements of the orbital epoch over a long period are used to determine the orbital evolution @xcite . orbital evolution in some black hole x - ray binaries ( bhxbs ) , has been measured by constructing the radial velocity curve of the companion star from the doppler shifts of the spectral lines @xcite . in the eclipsing binaries , connecting the mid eclipse time can give information on the long term evolution of the orbital period and an accurate determination of orbital period derivatives @xcite . the orbital evolution can also be measured from the stable orbital modulation of light curves @xcite . the orbital period of x - ray binaries can increase ( for example , x 2127 + 119 : @xcite ; sax j1808.43658 : @xcite ; 4u 182237 : @xcite 4u 1916053 : @xcite ) or decrease ( for example , 4u 1820 - 30 : @xcite ; her x-1 : @xcite , @xcite ; a 0620 - 00 & xte j1118 + 480 : @xcite ; ax j1745.6 - 2901 : @xcite ; nova muscae 1991 @xcite ) smoothly over several years of measurements . the orbital period can also undergo distinct epochs of sudden change , as observed in exo 0748 - 676 @xcite and xte j1710281 @xcite . is one of the rare lmxbs , that show x - ray eclipses in their light curves @xcite . it is a transient x - ray source which was discovered in 1976 @xcite from observations made with the sas-3 x - ray observatory . through several follow - up observations , an orbital period of @xmath47.1 hr and an eclipse duration of @xmath415 min were determined @xcite . about 2 years after its discovery , the x - ray intensity declined and the source was not detectable for the subsequent more than 20 years @xcite . during another outburst and a renewed activity in 1999 , burst oscillations with a period of @xmath41.8 ms were reported @xcite , which could be the spin period of the neutron star . after being x - ray bright for about 2.5 years , the source went into quiescence near the beginning of 2001 . comparing the orbital period of measured from two eclipses during the first outburst and from four eclipses during the early part of the second outburst , @xcite reported an orbital period decay and determined an average decay timescale of 10@xmath3 yr . but since this source was not detectable for a long time in between the two outbursts , there is no detailed record of the orbital period changes . later , @xcite determined two more mid - eclipse times of , using the _ beppo_-sax data during the second outburst . these measurements , along with the previous values , however , were not compatible with a simple orbital decay as was suggested earlier by @xcite . all the available eclipse measurements at this stage ( eight ) , indicated some complexity in the orbital solution of this source . recently , went into another outburst @xcite , thus enabling a definitive study of its orbital evolution . in this work , we have determined mid - eclipse times using newer _ rxte_-pca and _ xmm - newton _ observations of this source , made during the second and the current outburst . the _ rxte_-pca consists of an array of five collimated proportional counter units with a total photon collection area of 6500 @xmath5 @xcite . we have analyzed 24 archived observations of made with the _ rxte _ observatory . the observation log is given in table 1 . the pca data collected in the event mode was used to generate the light curves , using the ftool - seextrct from the astronomy software package heasoft - ver 6.10 . the analysis was done in the energy band 2@xmath620 kev . the background was estimated using the ftool - pcabackest . faint source model was taken from the _ rxte _ website . thereafter , barycentric corrections were applied to all x - ray timings . xmm_-newton observatory @xcite carries three x - ray mirrors and three focal plane instruments , each with a field of view of about 30@xmath2 30 . complete x - ray eclipses of have been observed during two _ xmm_-newton observations . we have analyzed both of these archived observations . the first of these observations was made during the second outburst . it lasted for @xmath431.5 ks and covered two complete eclipses . another @xmath442.9 ks long observation during the current outburst covered one complete eclipse . observation details are summarized in table 1 . we have analyzed the 0.2 - 10 kev epic - pn data , using the xmm science analysis system ( sas version 8.0.0 ) . source counts were extracted from a circular region of radius 40centered on the position of the target . background events were extracted from a similar source - free circular region . background subtracted light curves were barycenter corrected using the sas tool barycen . spectroscopic results from the february 2001 observation have been reported earlier by @xcite . they have reported the presence of two eclipses . however , they did not report the mid - eclipse times for the purpose of orbital evolution measurement . figure [ fig : sample ] shows two sample background subtracted light curves of , binned with 3 seconds and including an eclipse lasting for @xmath4900 s. the mid eclipse times were determined by modeling each ingress and egress transition with a @xmath7step and ramp "" model , which has been successfully employed in case of other eclipsing binaries @xcite . the variable parameters of the model are , the pre - ingress , eclipse , and post - egress count rates ; the ingress and egress duration , the eclipse duration and the mid - eclipse time . considering all the components to be freely variable , we first fitted the seven - parameter model to the light curves covering the eclipse and @xmath4150 s before and after the eclipse ( similar to @xcite ) . for _ rxte_-pca , it was found that the value of pre - ingress and the post egress count rates were similar and the eclipse ingress and egress duration were also similar within errors . the parameter space for _ rxte_-pca , was thus reduced to five . from all the observations of _ rxte _ and _ xmm_-newton , we have determined 27 mid - eclipse time measurements . the mid - eclipse times and the corresponding 1@xmath8 statistical errors are given in table 1 . the durations of ingress and egress have been mentioned separately for the _ xmm_-newton observations . the orbit numbers are in accordance with the eclipse time measurements given in @xcite . as compared to other observations , the mid eclipse times determined from the _ rxte _ observations have smaller error , except in two observations where count rate was relatively low . short timescale intrinsic variability in the intensity of the lmxb can modify the ingress / egress and thus effect the mid - eclipse time measurements . therefore , in order to estimate the additional random error in the mid - eclipse time measurements due to variability in the source , we simulated eclipses ( with similar parameters as given in table 1 ) at several positions in an _ rxte_-pca light curve . differences of the values of the mid - eclipse time that were used for simulation and those measured from the simulated data , were found to be about 1.3 seconds . therefore , for further analysis , we have considered this value as an additional random error due to the intrinsic intensity variation of the lmxb , and have quadratically added it to the statistical error of each mid - eclipse time measurement . [ cols=""<,^,<,^,<,^,^ "" , ] @xmath9 the numbers in bracket indicate the 1@xmath8 errors we have determined 27 new mid - eclipse times of the x - ray binary using data from _ rxte _ and _ xmm_-newton observatories . these measurements have been used to determine the orbital evolution in this system . orbital evolution of lmxbs is complex and is known to display different trends . the orbital separation is known to increase in most of the lmxbs , at timescales which are shorter than that predicted by a conservative mass transfer or by gravitational wave radiation @xcite . a decreasing orbital period has been observed in a few lmxbs and some short period bhxbs . but the orbital decay in these systems is also unusual and is much faster than that predicted by conventional methods of gravitational wave radiation , magnetic braking and mass loss from the system @xcite . interaction with a third body could be responsible for a large orbital decay observed in two lmxbs @xcite . orbital period glitches have been observed in a couple of lmxbs , and are attributed to be due to magnetic cycling of the secondary star @xcite . even though most of the lmxbs show a reasonably good quadratic fit to the mid - eclipse time records , there are signatures of deviation from a constant orbital period derivative present on longer timescales @xcite . the mid - eclipse time history of seems to be quite unusual . the combined data spanning three outbursts and covering @xmath440 years of timeline , indicates an orbital decay . in addition , a large number of measurements in a two year period during the second outburst show sinusoidal variation in the eclipse timing residual , perhaps indicating the presence of a third body around this source . we can consider the x - ray binary ( the inner binary ) to be a point mass in an approximate binary motion with this third body . in that case , the sinusoidal residual is due to orbital motion of the inner binary around the center of mass of the whole system . this is similar to the pulse arrival time delay of a binary x - ray pulsar , except that instead of a periodic pulse , we have a periodic eclipse . for a 1.4 @xmath10 neutron star , the mass of the companion star lies between 0.250.9 @xmath10 @xcite . assuming the radius of the orbit of the x - ray binary ( having an estimated total mass in the range 1.652.3 @xmath10 ) around the center of mass of the system to be same as amplitude of the sinusoidal residual , the third body ( assumed to be co - planar with the inner binary ) should have a mass range of 0.01950.0257 @xmath10 ( i.e. , 20.526.9 jupiter mass ) and an estimated range for orbital radius between 750860 lt - sec . the two extremes of this estimation are graphically shown in figure [ fig : simulation ] . taking m@xmath11 and r@xmath11 as the mass and radius of orbit of the binary ; and m@xmath12 and r@xmath12 as the mass and orbital radius of the third object , we have drawn curves for the expressions below for two extremes of the mass of the inner binary , i.e. , 1.65 @xmath10 ( dashed line ) and 2.3 @xmath10 ( solid line ) , respectively" +"it is sometimes believed , that all interesting phenomena in the universe happen at interfaces @xcite . following this line of thought , we believe that the study of the dynamics of interfaces provides a key for understanding generic features of non - equilibrium phenomena . the electrochemical deposition of metals from aqueous solutions in quasi - two - dimensional geometries is an easily accessible growth phenomenon of such an interface . the emerging structures show a broad variety of growth patterns including fractals , seaweed or dendrites . for a recent review see @xcite and references therein . the focus of this paper is on the electrodeposition of finger deposits @xcite : after the addition of a small amount of an inert electrolyte like sodium sulphate to a copper sulphate solution , the morphology of copper deposits changes from a typical fractal or dense - branched red copper structure to some fine - meshed texture with a fingerlike envelope . figure [ fig : finger ] gives an example of the early stage of a deposit formed under these circumstances . the underlying mechanism is believed to be qualitatively understood . the increase of the electric conductivity enables alternative reaction paths like the reduction of @xmath0 . the resulting increase of the @xmath1h value triggers the formation of a copper hydroxide gel ( @xmath2 ) in front of the advancing deposit @xcite . when considering , that the fluid between the copper filaments contains no gel , the ensuing situation resembles the saffman - taylor instability , where a more viscous fluid is pushed by a less viscous one and their interface develops the same type of fingering ( see ref . @xcite for a recent survey ) . the saffman - taylor instability is strongly influenced by the surface tension of the interface . in this paper we use that idea to measure the strength of an effective surface tension associated to the hydrogel - water interface by analyzing the dispersion relation . it should be remarked , that the nature of surface tension between miscible fluids is still an active area of research @xcite . another necessary ingredient for the occurrence of fingers are density - driven convective currents in front of the growing deposit : if convection is suppressed by turning the electrodeposition cell in a vertical configuration , fingers are not longer formed @xcite . for that reason it appears to be essential to understand the nature of the convection field in our experiment , which we examine using particle image velocimetry ( piv ) . the organization of the paper is the following : in section [ ch : setup ] we introduce the experimental setups . section [ ch : disp ] is devoted to the dispersion relations , with [ ch : disp_img ] covering some technical aspects and [ ch : disp_results ] presenting the measured dispersion relations and analyzing the results for a textured electrode . in section [ ch : piv ] we discuss the piv measurements : [ ch : piv_result_anode ] is devoted to the anode while [ ch : piv_result_cat ] summarizes our results for the cathode . finally , section [ ch : conclusion ] contains our conclusions . the electrodeposition is performed in a cell with two glass plates of 8 x 8 @xmath3 area as side - walls . two parallel copper wires ( 99.9 % , goodfellow ) separated by a distance of 4 cm serve as electrodes and spacers . their diameter @xmath4 ranges between 125 @xmath5 m and 300 @xmath5 m . figure [ fig : setup ] a ) shows a sketch of this setup . we use a coordinate system where the x axis is parallel to the electrode , the y axis points from the cathode to the anode and the z axis is perpendicular to the glass plates . the space between the electrodes is filled with an aqueous solution of 50 mm @xmath6 and 4 mm @xmath7 for the measurements of the dispersion relations and 50 mm @xmath6 and 7 mm @xmath7 for the piv experiments . all solutions are prepared from merck p.a . chemicals in non deaerated ultrapure @xmath8 . all measurements are performed with constant ( within 0.4 % ) potential between the electrodes ranging between 12 v and 19 v. the average current density is below 35 @xmath9 . was taken that way . ( c ) side view of the dark field microscopy used for the piv . image [ fig : dark_field ] gives an example of this illumination technique . the ovals inside the cell indicate the convection rolls . , width=325 ] .image acquisition systems used in the experimental setups . [ cols= "" < , < , < , < , < , < "" , ] the two targets of our investigation require two different ways of illumination ( sketched in fig . [ fig : setup ] ( b ) and ( c ) ) and image acquisition ( summarized in table [ tab : setup ] ) . since the measurements of the dispersion relation demand a high spatial resolution we used a kodak megaplus 6.3i ccd - camera with 3070 x 2048 pixel mounted on a nikkor slr macro lens with 105 mm focal length and a spacer ring . to take full advantage of the spatial resolution of 7.9 @xmath5 m per pixel it was necessary to employ a khler illumination @xcite using filtered light with a wave length of 405 nm from a tungsten lamp . images are taken in intervals @xmath10 of 5 s and are directly transferred with a frame - grabber card to the hard disk of a pc . to visualize the velocity field inside the cell , we added latex tracer particles to the electrolyte . we used particles with 0.3 @xmath5 m diameter , which stay suspended due to brownian motion . since we can not resolve these particles with our optical system , we used dark - field microscopy : only light scattered from objects inside the cell falls into the lens . image [ fig : dark_field ] gives an example , the white area at the bottom represents the growing deposit , the points above correspond to tracer particles . we did not observe electro - osmosis as reported in @xcite , but the particles show some tendency to coagulate and settle to the bottom plate . this problem is handled in later stages of the image processing . images were acquired using an olympus szh stereo microscope and a sony xc 77rr ce ccd - camera with 512 x 512 pixels which resulted in a spatial resolution of 17 @xmath5 m per pixel . @xmath10 was 2 s and images were also directly transferred to a pc . to characterize the instability of a pattern forming systems there is a quite common method : starting with the uniform system , one adds a small sinusoidal perturbation of wavenumber @xmath11 and amplitude @xmath12 and investigates its temporal evolution . as long as the system is in the linear regime the perturbation will grow or shrink exponentially : @xmath13 the dependency of the growth rate @xmath14 on the wavenumber @xmath11 is called dispersion relation . in the context of electrodeposition dispersion relations have been measured for the initial phase of compact @xcite and ramified @xcite growth and calculated to explain the stability of the dense radial morphology @xcite . in order to measure the dispersion relation the first step is to track down the temporal evolution of the front : in the image taken at time @xmath15 we identify for each column @xmath16 the height @xmath17 of the deposit . this is done in two steps : first we search for the pair of pixels with the highest gray value gradient in each column . second we perform a sub - pixel interpolation by calculating the point of inflexion between these two pixels . by evaluating a stationary edge , we could demonstrate that the error of this algorithm is smaller than 0.1 pixel . however the random fine structure of the deposit acts like the addition of shot noise to @xmath17 . we try to mitigate this effect by applying a median filter with 7 pixel width @xcite . figure [ fig : front_dev ] shows @xmath17 for 4 various times of an experiment . of the front tracking . the curve at the bottom corresponds to the initial position of the cathode . above the front at 156 s , 259 s , 362 s and 466 s after the beginning of the experiment . the experiment is the same as the one presented in fig . [ fig : finger ] . the part of length @xmath18 between the dashed lines was chosen by the cut - out algorithm for further processing.,width=325 ] our next aim is to do a fourier decomposition of @xmath17 to examine the dynamics of the amplitudes @xmath19 of the individual modes @xmath20 . because our initial conditions are random noise , which can be understood as a superposition of various modes with different wavelengths @xmath21 , we encounter a leakage problem : we observe our system in a window of width @xmath22 . the ratio @xmath23 of the dominant modes is almost always fractional . this has a very unpleasant consequence for the fourier transformation , which computes the amplitudes for integer mode numbers : power of the dominant modes is transfered to other less excited modes and spoils the measurement of the growth rates there . a common answer to this issue is the usage of a windowing function @xcite , which does not eliminate leakage , but restricts it to neighboring mode numbers . the price to be paid is , that this leakage will now occur even if @xmath22 is a common multiple of all wavelengths contained in the initial signal . in this paper we use a different approach , which is illustrated in fig . [ fig : front_dev ] : we cut out a part of @xmath17 of width @xmath18 and offset @xmath24 and use only this part for the subsequent analysis . @xmath24 and @xmath18 , which are constant for the whole run of the experiment , are chosen such that the left and the right end of the cut - out have the same height : @xmath25 and the same slope : @xmath26 fulfilling eq . [ eq : rwod_1 ] and eq . [ eq : rwod_2 ] for all times is for all practical purposes identical to the statement that @xmath18 is a common multiple of all wavelengths contained in @xmath17 , that is the condition under which no leakage occurs . in practice , [ eq : rwod_1 ] and eq . [ eq : rwod_2 ] can be satisfied only approximately . the algorithm followed to select @xmath24 and @xmath18 minimizes the sum over the height differences according to eq . [ eq : rwod_1 ] while it assures , that the sum over the slope differences according to eq . [ eq : rwod_2 ] does not exceed a threshold . the average height difference obtained in that way is @xmath27 3 pixels while the slope difference threshold was 1 pixel / pixel , both values correspond to the noise level of @xmath17 . the final step is a standard fourier decomposition of the cut - out parts of @xmath17 . for each fourier amplitude we tried to fit the temporal evolution with the exponential growth law given by eq . [ eq : exp_growth ] . [ fig : wachstum ] gives an example for two modes , corresponding to the experiment displayed in fig . [ fig : front_dev ] . the time interval for the exponential fits is indicated by the solid symbols . the start time is" +"the mid infrared emission bands at 3.3 , 6.2 , 7.7 , 8.6 , 11.3 and 12.7 are ubiquitous in the interstellar medium ( ism ) . the coincidence of these bands with characteristic wavelengths of aromatic molecules and attached functional groups ( see e.g. allamandola et al . @xcite ) is sufficiently convincing to call them aromatic infrared bands ( aibs ) . other , more neutral designations are unidentified infrared bands ( uibs ) or infrared emission features ( iefs ) . the designation should stabilize in the future . their carriers are very small grains ( or big molecules ) heated transiently by the absorption of a single uv ( sellgren et al . @xcite ) or visible ( uchida et al . @xcite ; pagani et al . @xcite ) photon . they are often identified with polycyclic aromatic hydrocarbons ( pahs ) ( lger & puget @xcite , allamandola et al . duley & williams ( @xcite ) and duley et al . ( @xcite ) have proposed an alternative interpretation in which the carriers of the aibs are not free particles but `` graphitic islands '' ( i.e. akin to pahs ) loosely attached to each other so that the heat conductivity is small . then their thermal behaviour is comparable to that of free particles . similar models have been also proposed by others . the carriers could also be very small particles . in this letter , we will not enter into this debate and will simply call them the _ aib carriers_. the origin of the aib carriers is still unclear . the idea that they are formed in the envelopes of carbon stars is not supported by observation and meets with theoretical difficulties ( e.g. cherchneff et al . they might be formed outside carbon star envelopes from carbonaceous particles condensed previously in these envelopes . schnaiter et al . ( @xcite ) and others have proposed such an evolutionary scheme from carbon stars to planetary nebulae . however the aib carriers formed in this way might not survive the strong uv field of planetary nebulae . for example , cox et al . ( @xcite ) find no aib in the helix nebula , an old carbon rich planetary nebula . another possibility is that they are formed in the ism from carbonaceous grains or carbonaceous mantles covering silicate nuclei . boulanger et al . ( @xcite ) and gry et al . ( @xcite ) have suggested that the strong variations in the iras 12/100 interstellar flux ratio are due to the release of transiently heated particles ( emitting at 12 ) by bigger particles , respectively due to uv irradiation or to shattering by shocks . thanks to the infrared space observatory ( iso ) , we know now that in the general ism the emission in the iras 12 band is dominated by aibs . variations in the ratio of aib carriers to big grains are thus confirmed . laboratory experiments shed some light on this process . scott et al . ( @xcite ) have observed the release of aromatic carbon clusters containing in excess of 30 carbon atoms by solid hydrogenated amorphous carbon ( hac ) irradiated by a strong uv laser pulse . the energy deposited by the laser pulse per unit target area is similar to the energy of a central collision between two grains of 10 nm radius at a velocity of 10 km s@xmath0 . this is an indication for a possible release of aib carriers in interstellar shocks . iso has also shown the existence of variations of aib spectra that may be related to a transformation of carbonaceous grains . recently , uchida et al . ( @xcite ) have observed a broadening of the 6.2 , 7.7 and 8.6 aibs when going from strong to weak radiation field in the reflection nebula vdb17 = ngc1333 . they also notice an increase of the flux ratio @xmath1(5.509.75)/@xmath1(10.2514.0 ) with increasing radiation field in several reflection nebulae . we present mid ir spectrophotometric and co(21 ) line observations of another reflection nebula , ced201 , that shed light into this transformation . section 2 describes briefly the observations and reductions . 3 describes the results , and sect . 4 contains a discussion and the conclusions . the observations have been made with the 32@xmath232 element mid - infrared camera ( isocam ) on board of iso , with the circular variable filters ( cvfs ) ( see cesarsky et al . @xcite for a complete description ) . the observations employed a 6/pixel magnification , yielding a field of view of about 3@xmath23 . full scans of the two cvfs in the long - wave channel of the camera have been performed , covering a wavelength range from 5.15 to 17 . 10 exposures of 2.1s each were added for each step of the cvf , and 20 extra exposures were added at the beginning of each scan in order to limit the effect of the transient response of the detectors . the total observing time was about 1 hour . the raw data were processed as described in cesarsky et al . ( @xcite ) using the cia software ( starck et al . however , the new transient correction described by coulais & abergel ( @xcite ) has been applied , yielding considerable improvements with respect to previous methods . the reflection nebula ced201 is a rather compact object at a distance of 420 pc ( casey @xcite ) , on the edge of a molecular cloud . it is excited by the b9.5v star bd + 69@xmath31231 . witt et al . ( @xcite ) notice that the radial velocity of this star differs from that of the molecular cloud by 11.7 @xmath4 3.0 km s@xmath0 so that ced201 is probably the result of an accidental encounter of the star with the molecular cloud , while for most other reflection nebulae the exciting star was born _ in situ_. an arc - like structure located between the star and the denser parts of the cloud to the north and the north - east at about 18 from the star might represent a shock due to the supersonic motion of the star . it is not very clearly visible on fig . 1 but is well visible on the red poss1 image delivered by aladin ( http://aladin.u-strasbg.fr ) . our cvf observation shows a small source surrounded by a faint extended emission ( fig . the absolute positioning of the isocam images is uncertain due to the lens wheel not always returning to its nominal position ( the maximum error is 2 times the pixel field of view , viz . 12 arcsec here ) and the images have to be recentered on known objects when possible . since we see on the spectra of the pixels corresponding to the strong source a continuum between 5.15 and 5.5 that we attribute to the photospheric emission of the exciting star ( see fig . 3 ) , we have recentered the cvf image at these wavelengths on the nominal simbad position of bd + 69@xmath31231 ( @xmath5(j2000 ) = 22h 13 m 27s , @xmath6(j2000 ) = 70@xmath3 15 18 ) . this resulted in fig . unfortunately the astrometry of bd + 69@xmath31231 is itself somewhat problematic due to the surrounding bright nebulosity and the location of the cvf image on the optical image is correspondingly uncertain . also , the proper motion of the star from the original bd position is unknown . 2 presents a set of co(21 ) spectra of the molecular cloud obtained by us at the caltech submillimeter observatory with 30 hpbw and 30 sampling . these observations are better sampled than the co(21 ) map of kemper et al . ( @xcite ; 21 hpbw , 60 sampling ) but are in good agreement . the line intensity peaks in the direction of the star , probably due to local excitation of co. the higher resolution @xmath7co(21 ) map of kemper et al . ( @xcite ; 21 hpbw , 20 sampling ) shows that this is not the position of maximum column density which peaks well to the ne of the star , confirming this conclusion . the @xmath8co profiles are double peaked in this area , in particular towards the arc , and this makes difficult the search for line wings which would be a signature of a shock . there is however some suggestion of a negative velocity wing near the star , in the same sense as the radial velocity of this star . 3 displays a set of 7@xmath27 cvf spectra on a grid with 6@xmath26 spacing centered on the exciting star . one sees typical aib spectra near the emission peak evolving towards fainter , different spectra 1218 arcseconds away . the spectra near the peak show not only the classical aibs , but also the s(3 ) rotation line of h@xmath9 at 9.6 and the s(5 ) line at 6.91 or the line of [ ] at 6.98 , which can not be separated at our resolution . the 12.7 aib might be contaminated by the [ ] 12.8 line . these spectra are typical for a low excitation photodissociation region ( pdr ) . the aibs are superimposed on a continuum rising towards long wavelengths . this could be the continuum emission of very small grains ( vsgs ) . the aibs are broader and much fainter relative to the continuum . the 11.3 aib is now the strongest one at this location . the 7.7 and 8.6 aibs are merged into a single broad band . the most striking feature is the strong emission plateau extending from 11 to 14 . these spectra resemble class b spectra ( tokunaga @xcite ) ( class a spectra are the usual aib spectra ) . 3 shows a behaviour of the spectrum with radiation field similar to that observed by uchida et al . ( @xcite ) in some other reflection nebulae . we find a trend for the 7.7 aibs to become broader at _ fainter _ radiation fields away from the exciting star , fig . the trend is not clear for the other bands , but we should not forget that there is contamination by the aibs from foreground and background material . we suggests that some carbonaceous material that emits the continuum and broad bands far from the star is processed through the effect of the star that moves through the molecular cloud , producing aib carriers : the continuum is only 2 times fainter 12 from the star than close to the star , demonstrating the partial disappearance of its carriers near the star while the aibs become very strong . the very appearance at relatively large distances from the star ( at least 18 ) of a continuum rising towards long wavelengths is surprising . this continuum must be emitted by vsgs heated by single ( visible ) photons . these grains must be quite smaller than the `` classical '' vsgs which require a strong radiation field to emit in the wavelength range of isocam ( contursi et al . the spectra seen far from the star remind strongly of class b spectra seen in carbon rich proto planetary nebulae ( guillois et al . @xcite ) . in the laboratory , such spectra are produced ( in absorption ) by natural coals rich in aromatic cycles ( guillois et al . @xcite ) or by a - c : h materials produced by laser pyrolysis of hydrocarbons ( herlin et al . @xcite ; schnaiter et al . @xcite ) . in ced201 , these carbonaceous grains must be very small ( radius of the order of 1 nm ) since they are heated transiently by" +"a quantum game @xcite describes the strategic interaction among a set of players sharing quantum state(s ) . players strategic choices , or strategies @xcite , are local unitary transformations on the quantum state . the state evolves unitarily and finally the players payoffs , or utilities , are obtained by measuring the entangled state . it turns out that under certain situations sharing of an entangled quantum state can put the players in an advantageous position and more efficient outcome(s ) of the game can then emerge . for readers not familiar with the formalism of quantum theory @xcite , sharing an entangled state can be considered equivalent to the situation in which the players have ( shared ) access to a ` quantum system ' having some intrinsically non - classical aspects . a quantum game would then involve a strategic manoeuvring of the shared quantum system in which different and perhaps more efficient outcome(s ) of the game can emerge due to non - classical aspect(s ) of the shared system . now , it is well known that non - classical , and thus apparently strange , aspects of a shared quantum system can be expressed as constraints on probabilities relevant to the shared system . usually expressed as constraints in correlations , the famous bell s inequality bell1,bell2,bell3,aspect , chsh , peres can be re - expressed as constraints on the relevant joint probability and its marginals fine1,fine2,halliwell1,halliwell2 . essentially , bell s inequality emerges as being the necessary and sufficient condition requiring a joint probability distribution to exist given a set of marginals . it is well known that bell s inequality can be violated by a set of quantum mechanical probabilities the probabilities that are obtained by the quantum probability rule . this turns out to be the case even though the quantum probabilities are normalized as the classical probabilities are . this is because for a set of marginal ( quantum ) probabilities that are obtained via the quantum probability rule , the corresponding joint probability distribution may not exist . the possibility to express truly non - classical aspects of a quantum system in only probabilistic terms @xcite has led to suggestions for schemes of quantum games iqbalweigert , iqbal , iqbal1,iqbal2,chappell , iqbal3 that do not refer to quantum states , unitary transformations , and/or the quantum measurement . in a classical game allowing mixed strategies , the players strategies are convex linear combinations , with real coefficients , of their pure strategies @xcite . players strategies in a quantum game @xcite , however , are unitary transformations and thus belong to much larger strategy spaces . in order to obtain an improved comparison between classical and quantum games , it was suggested that the players strategy sets need to be identical . this has motivated proposals @xcite of quantum games in which players strategies are classical , as being convex linear combinations ( with real coefficients ) of the classical strategies , and the quantum game emerges from the non - classical aspects of a shared probabilistic physical system as expressed by the constraints on relevant probabilities and their marginals @xcite . in the usual approach in the area of quantum games @xcite , a classical game is defined , or given , at the start and its quantum version is developed afterwards . the usual reasonable requirement being that the classical mixed - strategy game can be recovered from the quantum game . one then studies whether the quantum game offers any non - classical outcome(s ) . in this paper , the players strategies in the quantum game remain classical whereas the new quantum , or non - classical , outcome(s ) of the game emerge from the peculiar quantum probabilities relevant to the quantum system that two players share to play the game . in contrast to the usual approach in quantum games , in which the players strategies are unitary transformations , here we consider a particular classical strategy pair and then enquire about the set of games for which that strategy pair can exist as a nash equilibrium ( ne ) @xcite . in particular , for a given strategy pair , we investigate whether there are such games for which that strategy pair can exist as a ne only when the corresponding bell s inequality is violated by the quantum probabilities relevant to the shared quantum system . we consider two - player games that can be played using the setting of generalized einstein - podolsky - rosen ( epr ) experiments peres , chsh , cereceda . as is known , in this setting a probabilistic version of bell s inequality can be obtained fine1,fine2,cereceda , halliwell1,halliwell2 . we consider particular strategies and find the sets of games for which the strategies can exist as a ne only when bell s inequality is violated . by identifying such games , we show that there exist strategic outcomes that can only be realized when the game is played quantum mechanically and also only when the corresponding bell s inequality is violated . a number of papers @xcite discuss using the setting of generalized einstein - podolsky - rosen ( epr ) experiments cereceda for playing quantum games . essentially , this is because this setting permits consideration of probabilistic version of the corresponding bell s inequality , which allows constructing quantum games without referring to the mathematical formalism of quantum mechanics including hilbert space , unitary transformations , entangling operations , and quantum measurements @xcite . in the setting of the generalized epr experiment , alice and bob are spatially separated and are unable to communicate with each other . in an individual run , both receive one half of a pair of particles originating from a common source . in the same run of the experiment , both choose one from two given ( pure ) strategies . these strategies are the two directions in space along which spin or polarization measurements can be made . as is the case for notation for coins , we denote these directions to be @xmath0 , @xmath1 for alice and @xmath2 , @xmath3 for bob . each measurement generates @xmath4 or @xmath5 as the outcome . experimental results are recorded for a large number of individual runs of the experiment . payoffs are then awarded that depend on the directions the players choose over many runs ( defining the players strategies ) , the matrix of the game they play , and the statistics of the measurement outcomes . for instance , we denote @xmath6 as the probability of both alice and bob obtaining @xmath4 when alice selects the direction @xmath0 whereas bob selects the direction @xmath2 . we write @xmath7 for the probability @xmath6 and @xmath8 for the probability @xmath9 and likewise one can then write down the relevant probabilities as @xmath10 being normalized , epr probabilities @xmath11 satisfy the relations @xmath12 consider ( [ epr probabilities ] ) where , for instance , when it is the interaction between alice s type @xmath13 and bob of type @xmath14 , and the stern - gerlach detectors are rotated along these directions , the probability that both experimental outcomes are @xmath5 is @xmath15 and the probability that the observer @xmath14 s experimental outcome is @xmath4 and observer @xmath13 s experimental outcome is @xmath5 is given by @xmath16 . the other entries in ( [ epr probabilities ] ) can similarly be explained . we now consider a game between two players alice and bob , which is defined by the real numbers @xmath17 and @xmath18 for @xmath19 , and is given by @xmath20 for this game , we now define the players payoff relations as @xmath21 where @xmath22 , for example , is alice s payoff when she plays @xmath0 and bob plays @xmath3 . it can be seen that in the way it is defined , the game is inherently probabilistic . that is , in ( [ gamedef ] ) the players payoffs even for their pure strategies assume an underlying probability distribution as given by ( [ epr probabilities ] ) . now , we can also define a mixed - strategy version of this game inherently probabilistic game as follows . consider alice playing the strategy @xmath0 with probability @xmath23 and the strategy @xmath24 with probability @xmath25 whereas bob playing the strategy @xmath26 with probability @xmath27 and the strategy @xmath3 with probability @xmath28 . using ( [ gamedef],[payoffparts ] ) the players mixed strategy payoff relations can then be obtained as @xmath29 assuming that the strategy pair @xmath30 is a nash equilibrium , we then require @xmath31 that takes the form @xmath32 although this game is played using the setting of generalized epr experiments , in which the players strategies consist of choosing between two directions , one can notice that under appropriate conditions , the game can be reduced to the usual mixed - strategy version of the standard two - player two - strategy noncooperative game . non - cooperative games were investigated in the early work in the area of quantum games . to see this , we consider the case when @xmath33 and then from eqs . ( [ payoffparts ] ) and ( [ normalization ] ) we obtain @xmath34 nash inequalities for the strategy pair @xmath35 then take the form @xmath36 which give us nash inequalities for the mixed strategy @xmath37 for the following symmetric game @xmath38 when @xmath39 this game results in the well known game of prisoners dilemma . as is well known , for this game @xmath40 comes out as the unique ne . we note that , in a particular run of the epr experiment , the outcome of @xmath4 or @xmath5 ( obtained along the direction @xmath0 or direction @xmath41 ) is independent of whether the direction @xmath2 or the direction @xmath42 is chosen in that run . similarly , the outcome of @xmath4 or @xmath43 ( obtained along @xmath2 or @xmath3 ) is independent of whether the direction @xmath0 or the direction @xmath41 is chosen in that run . these requirements , when translated in terms of the probability set @xmath44 are expressed as @xmath45 a convenient solution of the system ( [ normalization],localityconstraint ) , as reported in @xcite is the one for which the set of probabilities @xmath46 is expressed in terms of the remaining set of probabilities @xmath47 that is given as @xmath48 this allows us to consider the elements of the set @xmath49 as independent variables . relevant to the epr setting is the chsh ( clauser - horne - shimony - holt ) form of bell s inequality that is usually expressed in terms of the correlations @xmath50 , @xmath51 , @xmath52 , @xmath53 . using ( [ epr probabilities ] ) the correlation @xmath54 , for instance , can be obtained as @xmath55 expressions for the correlations @xmath56 , @xmath57 , and @xmath58 can similarly be obtained . the chsh sum of correlations is given as @xmath59 and the chsh inequality stating that @xmath60 holds for any theory of local hidden variables . the set of constraints on probabilities @xmath11 that are imposed by the tsirelson s bound _ _ _ _ @xcite _ _ _ _ state that the quantum prediction of the chsh sum of correlations @xmath61 , defined in ( [ chsh(a ) ] ) , is bounded in absolute value by @xmath62 i.e. @xmath63 . taking into account @xcite the normalization condition ( [ normalization ] ) , the quantity @xmath61 can equivalently be expressed as @xmath64 bell s inequality can thus be written as @xmath65 and is violated when the discriminant @xmath66 . bell s inequality is violated when the discriminant attains a negative value . we note from ( [ nashinequalities ] ) that the nash inequalities for the strategy pair @xmath67 take the form @xmath68 \geq" +"_ program title : _ lambertw + _ catalogue identifier : _ aenc_v1_0 + _ program summary url : _ http://cpc.cs.qub.ac.uk/summaries/aenc_v1_0.html + _ program obtainable from : _ cpc program library , queen s university , belfast , n. ireland + _ licensing provisions : _ gnu general public license version 3 + _ no . of lines in distributed program , including test data , etc . : _ 1335 + _ no . of bytes in distributed program , including test data , etc . : _ 25283 + _ distribution format : _ ` tar.gz ` + _ programming language : _ c++ ( with suitable wrappers it can be called from c , fortran etc . ) , the supplied command - line + utility is suitable for other scripting languages like sh , csh , awk , perl etc . + _ computer : _ all systems with a c++ compiler . + _ operating system : _ all unix flavors , windows . it might work with others . + _ ram : _ small memory footprint , less than 1 mb + _ classification : _ 1.1 , 4.7 , 11.3 , 11.9 . + _ nature of problem : _ find fast and accurate numerical implementation for the lambert w function . + _ solution method : _ halley s and fritsch s iterations with initial approximations based on branch - point expansion , + asymptotic series , rational fits , and continued logarithm recursion . + _ additional comments : _ distribution file contains the command - line utility ` lambert - w ` . doxygen comments , included in + the source files . makefile . + _ running time : _ the tests provided take only a few seconds to run . the lambert w function is defined as the inverse function of the mapping and thus solves the equation . this solution is given in the form of the lambert w function , and according to eq . it satisfies the following relation , since the mapping in eq . is not injective , no unique inverse of the @xmath2 function exists ( except at the minimum ) . as can be seen in fig . [ f : lambertw ] , the lambert w function has two real branches with a branching point located at @xmath3 . the bottom branch , @xmath4 , is defined in the interval @xmath5 $ ] and has a negative singularity for @xmath6 . the upper branch @xmath7 is defined for @xmath8 $ ] . the earliest mention of the problem of eq . is attributed to euler @xcite . however , euler himself credited lambert for his previous work in this subject , lambert s transcendental equation @xcite . the @xmath0 function started to be named after lambert only recently , in the last 20 years or so ; nevertheless , the first usage of the letter @xmath9 appeared much earlier @xcite . recently , the @xmath0 function amassed quite a following in the mathematical community @xcite . its most faithful proponents are suggesting elevating it among the present set of elementary functions , such as @xmath10 , @xmath11 , @xmath12 , @xmath13 , etc . the main argument for doing so is the fact that w is the root of the simplest exponential polynomial function given in eq . . we will acknowledge these efforts by strict usage of a _ roman _ symbol w as its name . in blue and @xmath7 in red . the branching point at @xmath3 is indicated with a green dash . ] while the lambert w function is called ` lambertw ` in the mathematics software tool _ @xcite and ` lambertw ` in the matlab programming environment @xcite , in the _ mathematica _ computer algebra framework this function @xcite is implemented under the name ` productlog ` ( in the recent versions an alias ` lambertw ` is also supported ) . in open source format the lambert w function is available in the special - functions part of the gnu scientific library ( gsl ) @xcite , unfortunately implemented using only the slower halley s iteration ( see discussion in section [ s : timing ] ) . there are numerous , well documented applications of @xmath0 , certainly abundant in mathematics ( like linear delay - differential equations @xcite ) , numerics @xcite , computer science @xcite and engineering @xcite , but surprisingly many also in physics , just to mention a few ( without preference ) : quantum mechanics ( solutions for double - well dirac - delta potentials @xcite ) , quantum statistics @xcite , general relativity ( solutions to ( 1 + 1)-gravity problem @xcite , inverse of eddington - finkelstein ( tortoise ) coordinates @xcite ) , statistical mechanics @xcite , fluid dynamics @xcite , optics @xcite etc . the main motivation for the implementation in this work comes from the research in cosmic ray physics where it has been in use already for several years @xcite and new interesting applications are appearing frequently @xcite . in the next sections let us describe two new examples that arise from this field of astrophysics . . _ bottom : _ a family of one - parametric gaisser - hillas functions @xmath14 for @xmath15 in the range from 1 to 10 with step 1.,title=""fig : "" ] + . _ bottom : _ a family of one - parametric gaisser - hillas functions @xmath14 for @xmath15 in the range from 1 to 10 with step 1.,title=""fig : "" ] the moyal function and the related distribution was proposed as a good approximation for the more complicated landau distribution @xcite used in descriptions of energy loss of charged particles passing through matter @xcite . the un - normalized moyal function is defined as and can be seen in fig . [ f : moyal - gh ] ( top ) . its inverse can be written in terms of the two branches of the lambert w function , in experimental astrophysics the moyal function is used for phenomenological recovery of the saturated signals from photomultipliers @xcite , where the largest parts of the saturated signals are obscured by the limited range of the analog - to - digital converters . in astrophysics the gaisser - hillas function is used to model the longitudinal particle density in a cosmic - ray air shower @xcite . we can show that the inverse of the three - parametric gaisser - hillas function , is intimately related to the lambert w function . using rescale substitutions , the gaisser - hillas function is modified into a function of one parameter only , the family of one - parametric gaisser - hillas functions is shown in fig . [ f : moyal - gh ] ( bottom ) . the problem of finding an inverse , for @xmath16 , can be rewritten into according to the definition , the two ( real ) solutions for @xmath17 are obtained from the two branches of the lambert w function , note that the branch @xmath18 or @xmath19 simply chooses the right or left side relative to the maximum , respectively . the gaisser - hillas function is intimately related to the gamma distribution which was successfully used somewhat earlier @xcite in an approximate description of the mean longitudinal profile of the energy deposition in electromagnetic cascades . it is trivial to show that the inverses of the gamma and inverse - gamma distributions @xcite are expressible in terms of the lambert w function as well . before describing the actual implementation let us review some of the possible numerical and analytical approaches to find @xmath0 . for @xmath20 and @xmath21 we can take the natural logarithm of eq . and rearrange it into from here it is clear that an analytical expression for @xmath0 will exhibit a certain degree of self similarity . the @xmath0 function has multiple branches in the complex domain . due to the @xmath20 and @xmath21 conditions , eq . represents the positive part of the @xmath7 principal branch and in this form it is suitable for evaluation when @xmath22 , i.e. when @xmath23 . unrolling the self - similarity in eq . as a recursive relation , the following curious expression for @xmath7 is obtained , or in the shorthand of a continued logarithm , the above expression clearly has the form of successive approximations , the final result given by the limit , if it exists . for @xmath24 and @xmath25 we can multiply both sides of eq . with @xmath18 , take logarithm , and rewrite it into a similar expansion for the @xmath4 branch , again , this leads to the similar recursion , or as a continued logarithm , for this continued logarithm we will use the symbol @xmath26}(x)$ ] where @xmath27 denotes the depth of the recursion in eq . . starting from yet another rearrangement of eq . , we can obtain a recursion relation for the @xmath28 part of the principal branch @xmath29 , we can apply halley s root - finding method @xcite to derive an iteration scheme for @xmath30 by writing the second - order taylor series since root @xmath31 of @xmath32 satisfies @xmath33 we can approximate the left - hand side of eq . with 0 and replace @xmath31 with @xmath34 . rewriting the obtained result into and using newton s method @xmath35 on the last bracket , we arrive at the expression for halley s iteration for the lambert w function where this method is of the third order , i.e. having @xmath36 will produce @xmath37 . supplying this iteration with a sufficiently accurate first approximation of the order of @xmath38 will thus give a machine - size floating point precision @xmath39 in at least two iterations . for both branches of the lambert w function a more efficient iteration scheme exists @xcite , where @xmath40 is the relative difference of successive approximations at iteration @xmath27 , the relative difference can be expressed as where the error term in this iteration is of a fourth order , i.e. with @xmath41 we obtain @xmath42 . supplying this iteration with a sufficiently reasonable first guess , accurate to the order of @xmath38 , will therefore deliver machine - size floating point precision @xmath39 in only one iteration and excessive @xmath43 in two ! the main goal now is to find reliable first order approximations that can be fed into fritsch s iteration . due to the lively landscape of the lambert w function properties , the approximations will have to be found in all the particular ranges of the function s behavior . the following section deals with finding the appropriate initial approximations in the whole definition range of the two branches of the lambert w function . on the top and @xmath7 on the bottom.,title=""fig : "" ] + on the top and @xmath7 on the bottom.,title=""fig : "" ] the inverse of the lambert w function , @xmath44 , has two extrema located at @xmath45 and @xmath46 . expanding @xmath47 to the second order around the minimum at @xmath48 we obtain the inverse @xmath47 is thus approximated in the lowest order by a parabolic term implying that the lambert w function will have square - root behavior in the vicinity of the branch point @xmath49 , to obtain the additional terms in eq . we proceed by defining an inverse function , centered and rescaled around the minimum , i.e. @xmath50 . due to this centering and rescaling , the taylor series around @xmath51 becomes particularly neat , using this expansion we can derive coefficients @xcite of the corresponding inverse function from eq . we see that @xmath52 . using @xmath53 as an independent variable we can write this series expansion as where the lowest few coefficients @xmath54 are" +"this paper continues our effort to use the subaru telescope to search for proper motions among very faint stars . our first paper ( @xcite ) examined a series of images of the subaru deep field ( sdf ) ( @xcite ) , located close to the northern galactic pole ( @xmath1 , @xmath2 ) . we report here on a similar analysis of images of the subaru / xmm - newton deep survey ( sxds ) field ( @xcite , @xcite , @xcite ) , which lies at high galactic latitude in the southern galactic hemisphere ( @xmath3 , @xmath4 ) . as in our earlier work , we are taking advantage of a dataset compiled for the study of very distant extragalactic objects ; the long time coverage necessary to detect supernovae and agn provides us with the baseline needed to measure proper motions for a significant number of stars in our own milky way . we pay special attention to members of the faintest stellar populations , white dwarfs . since we will follow very closely the methods used in our analysis of the sdf , we urge the reader to consult @xcite for a detailed description of some procedures we may mention only briefly here . however , the sxds dataset differs from the sdf dataset in one very important way : it consists of a mixture of images taken through two passbands , the suprime - cam @xmath5 and @xmath6 ( @xcite ) , while the sdf data was all taken through @xmath6 . this inhomogeneity complicates efforts to determine the selection effects which define our sample of moving objects ; therefore , we discuss in depth our tests of the magnitudes and motions to which our analysis of the sxds is reasonably complete . one of our goals in this project is to compare observed sets of moving stars to those predicted by various models of stellar populations in the milky way . we will need a good understanding of the selection effects on the observations in order to compare them fairly to models in a future paper . section 2 describes the observations and the steps we took to convert the raw images into clean , seamless mosaic images . we list in section 3 our procedures for finding and measuring the properties of stars in the images , yielding a list of formal motions for tens of thousands of stars . most of these motions , of course , were not significantly different from zero , and so we discuss in section 4 our techniques for selecting a small subset of stars with significant proper motions . we used artificial stars inserted into our images to estimate the completeness of our sample as a function of magnitude and motion , and , to a limited degree , color . in section 5 , we briefly compare our sample of moving stars with those found in the sdf and predicted in the the besanon model ( @xcite ) . we also highlight one very interesting star , which combines a large proper motion with a very faint apparent magnitude . the subaru / xmm - newton deep survey ( sxds ) involves sensitive measurements across a wide range of wavelengths over a region of about 1.3 square degrees ( @xcite , @xcite ) . since the main goal of the project is to study extragalactic objects , the field is located at relatively high galactic latitude ( @xmath7 ) . we analyze a subset of the optical images taken with the subaru 8.2-meter telescope and suprime - cam camera ( @xcite ) . the regions in the southern ( sxds - s ) and eastern ( sxds - e ) sections of the survey ( see figure [ fig : sxdsregions ] and table [ table : regions ] ) were observed at least 11 times over the period september , 2002 , to january , 2008 . we provide a list of the observations in table [ table : journal ] . note that data taken on september 29 and september 30 , 2002 , were combined to form a single composite image . l c c c c name & min ra & max ra & min dec & max dec + sxds - e & 02:18:55 & 02:20:34 & -05:17:24 & -04:43:12 + sxds - s & 02:16:37 & 02:18:54 & -05:32:22 & -05:06:50 + ( 80mm,80mm)figure1.eps l c c r ut date & julian date - 2,450,000 & filter & exptime ( seconds ) + & sxds - e & & + 2002 sep 29 , 30 & 2548.5 & @xmath6 & 3000 + 2002 nov 1 & 2579.9 & @xmath6 & 3000 + 2002 nov 1 & 2580.0 & @xmath5 & 1500 + 2002 nov 2 & 2580.8 & @xmath6 & 1800 + 2002 nov 9 & 2587.8 & @xmath6 & 2820 + 2002 nov 9 & 2588.0 & @xmath5 & 210 + 2002 nov 29 & 2608.0 & @xmath6 & 1800 + 2003 sep 22 & 2905.0 & @xmath6 & 6000 + 2003 oct 2 & 2915.1 & @xmath6 & 1271 + 2003 oct 21 & 2934.1 & @xmath6 & 1400 + 2005 sep 28 & 3642.0 & @xmath6 & 3600 + 2008 jan 9 & 4474.8 & @xmath5 & 2400 + + & sxds - s & & + 2002 sep 29 , 30 & 2548.4 & @xmath6 & 3000 + 2002 nov 1 & 2579.9 & @xmath6 & 3600 + 2002 nov 1 & 2580.0 & @xmath5 & 2400 + 2002 nov 2 & 2580.8 & @xmath6 & 1800 + 2002 nov 9 & 2587.8 & @xmath6 & 2580 + 2002 nov 9 & 2588.0 & @xmath5 & 2400 + 2002 nov 29 & 2608.0 & @xmath6 & 1500 + 2003 sep 22 & 2905.0 & @xmath6 & 4500 + 2003 oct 2 & 2915.1 & @xmath6 & 2040 + 2005 sep 28 & 3642.0 & @xmath6 & 2040 + 2008 jan 9 & 4474.7 & @xmath5 & 2400 + we followed the procedure described in @xcite to reduce the raw images and combine them to form a single seamless mosaic for each night . the fwhm of the mosaics varied from @xmath8 on the best night to @xmath9 on the worst , but since the plate scale was @xmath10 per pixel , all images were adequately sampled . the limiting magnitude varied slightly , but on average was about @xmath11 ( see section 3 ) . these measurements reach about @xmath12 magnitudes deeper than those reported in @xcite ; combined with the larger sky coverage , this study encompasses a larger volume . we estimate the effective volume for stars of absolute magnitude @xmath13 to be 130000 cubic parsecs , about four times as large as that of @xcite ( the value of 14000 cubic parsecs shown in table 1 of that paper was an error ; the proper value is 28000 cubic parsecs ) . we now describe briefly the steps we took to reduce the clean mosaic images into a list of starlike objects , and then to find objects with significant motions . the reader can find a detailed description of our methods in @xcite . our first step was to identify and measure the properties of starlike objects . we used the `` stars '' program in the _ xvista _ package ( @xcite ) to find objects with @xmath14 . the images taken on september 22 , 2003 , contained the largest number of objects : 79000 in sxds - e and 86000 in sxds - s . we therefore made this the fiducial epoch for matching and astrometry . we broke each image into overlapping subsections roughly @xmath15 on a side and used the _ match _ package ( @xcite ) to transform the subsections in each image to the fiducial s coordinate system . we looked for matches between epochs using a maximum separation of @xmath16 from the fiducial position of each star . this places an upper limit of about @xmath17 per year on the proper motions we could detect , but , as we will show later , this does not have a strong effect on the results . in order to test the completeness of our object detection , we used a set of artificial stars inserted into the images of sxds - s . because this field was observed one fewer time than sxds - e , the limits we derive from it will likely be conservative estimates for sxds - e . the tests are complicated by the mixture of passbands in the dataset : eight in @xmath6 and three in @xmath5 , including the critical final image taken in 2008 . we therefore ran three sets of tests , using artificial stars with colors @xmath18 of @xmath19 , @xmath20 and @xmath21 magnitudes . for each color , we created 1000 artificial stars and inserted them at locations known to be free of real stars in each image . we then executed our procedures to find and match stars . we required stars to appear in at least five epochs to qualify for further study . figure [ fig : completenesspqr ] indicates that the fraction of artificial stars entering our proper motion study dropped to 50% at @xmath22 regardless of color . ( 80mm,80mm)figure2.eps a large number of objects qualified for the next step by appearing in at least five images : 47589 in sxds - s and 45500 in sxds - e . we considered the row and column positions of each object separately , making a linear fit to each as a function of time . as described in @xcite , we derived the one - dimensional motion in rows and columns , as well as the uncertainty in each motion . figure [ fig : movingresiduals ] indicates that the precision of our measurements of position in the sxds is roughly the same as that of our measurements in the sdf . the median deviation in each direction from the fitted motion ranged from @xmath23 for bright unsaturated stars to @xmath24 for the faintest objects in our sample . we defined statistics @xmath25 and @xmath26 as the ratios of motion to uncertainty in each direction , and computed the overall significance of each object s motion as @xmath27 . we chose a conservative threshold , @xmath28 , to create samples of `` candidates for stars with proper motions . '' only a small number of objects entered these samples : 40 in the sxds - s and 33 in the sxds - e . the fraction of all objects having significant motions was only about @xmath29 , smaller than the @xmath30 found in the sdf . since the uncertainties in individual measurements were roughly the same in both areas , but stars were measured almost twice as frequently in the sdf , a fixed value of @xmath31 corresponds to a smaller absolute motion in the sdf than in the sxds fields . the time sampling of our survey was far from uniform , and there was a three - year gap between the penultimate and final measurement . moreover , that final measurement was made through the @xmath5 filter , rather than the @xmath6 filter used for most of the images . since that final image influences the proper motions strongly , it is possible that there might be some color dependency in our proper motion sample . therefore , we ran a set of tests using three sets of artificial stars : one group had colors @xmath32 , one ( @xmath33 , and one @xmath34 . we generated 1000 stars in each group with @xmath6-band magnitudes @xmath35 and proper motions @xmath36 per year in random directions . we inserted these artificial stars into our images , analyzed them as described above , and counted the number which" +"the crab pulsar ( psr b0531 + 21 ) is a young radio pulsar with a spin frequency @xmath2 and frequency derivative @xmath3 ( lyne et al . its characteristic magnetic field is about @xmath4 at the magnetic poles ] . the crab pulsar has been monitored continuously for decades years by various telescopes since it was discovered in 1968 ( lyne et al . 1993 ; lyne et al . 2015 ; wang et al . its braking index is @xmath5 ( lyne et al . different braking index values @xmath6 , @xmath7 and @xmath8 are also reported between glitches ( wang et al . 2012 ; lyne et al . observational details are given in table [ parameters ] . long - term observations have found that almost all pulsars ( except accreting x - ray pulsars in binary systems ) are spinning down . the spin - down behavior can be described by a power law ( lyne et al . 1993 ) : @xmath9 here , @xmath10 is usually taken as a constant and @xmath11 is the braking index . the braking index and second braking index are defined respectively ( livingstone et al . 2005 ) : @xmath12 @xmath13 where @xmath14 is the pulsar spin frequency , @xmath15 , @xmath16 and @xmath17 are the first , second and third frequency derivative , respectively . the spinning down of pulsars is usually assumed to be braked by the magnetic dipole radiation ( shapiro & teukolsky 1983 ) . in the magnetic dipole radiation model , a neutron star rotates uniformly in vacuo at a frequency @xmath14 and possesses a magnetic moment @xmath18 . the corresponding slowdown rate is : @xmath19 where @xmath20 is the magnetic dipole moment ( @xmath21 is the polar magnetic field and @xmath22 is the radius of neutron star ) , @xmath23 is the moment of inertia , @xmath24 is the speed of light , and @xmath25 is the angle between the rotational axis and the magnetic axis ( i.e. , the inclination angle ) . the spin down behavior of pulsar in this model can be described as @xmath26 . the braking index is exactly three if @xmath27 , and @xmath25 are constant . to date , only eight pulsars , including the crab pulsar , have measured the meaningful braking indices for they are young and own relatively larger @xmath15 ( espinoza et al . 2011 ; lyne et al . their braking indices are all smaller than three . it means that there are other physical processes needed to slow down the pulsar . many mechanisms have been proposed in order to explain the braking index observations , e.g. , the pulsar wind model ( xu & qiao 2001 ; wu et al . 2003 ; contopoulos & spitkovsky 2006 ; yue et al . 2007 ) , a changing magnetic field strength ( lin et al . 2004 ; chen & li 2006 ; espinoza et al . 2011 ) , a changing inclination angle ( lyne et al . 2013 ) , and additional torques due to accretion ( liu et al . 2014 ) . however , these models are more or less not consistent with observations or can not simulate the long - term evolution of pulsars . and these models can not explain the different braking indices detected between glitches ( wang et al . 2012 ; lyne et al . furthermore , the effect of pulsar death ( death line , ruderman & sutherland 1975 ; or death valley , chen & ruderman 1993 ; zhang et al . 2000 ) should be considered in modeling the long term rotational evolution of the pulsar ( contopoulos & spitkovsky 2006 ) . the pulsar wind model considers both the pulsar spin - down and the particle acceleration in the magnetosphere ( xu & qiao 2001 ; wu et al . 2003 ) . in this paper , an updated pulsar wind model is built based on previous researches ( xu & qiao 2001 ; yue et al . 2007 ; contopoulos & spitkovsky 2006 ; li et al . it includes : ( 1 ) both magnetic dipole radiation and particle outflow , and their dependence on the inclination angle ; ( 2 ) the particle outflow depends on the specific acceleration model ; ( 3 ) the primary particle density may be much larger than the goldreich - julian charge density ; ( 4 ) the effect of pulsar death is considered in modeling the rotational evolution of the pulsar . this model can calculate both the short term and long term evolution of pulsars . it is applied to the crab pulsar which has the most detailed timing observations . possible applications to other sources are also illustrated . the pulsar wind model and model calculations of the crab pulsar are presented in section 2 . discussions and conclusions are given in section 3 and section 4 , respectively . [ parameters ] .observations of the crab pulsar . [ cols=""<,<"",options=""header "" , ] notes : ( a ) : @xmath28 is the coefficient of primary particle density @xmath29 . ( b):@xmath25 and @xmath30 are respectively the inclination angle and the magnetic field . ( c ) : @xmath31 is the initial period . ( d):@xmath32 and @xmath33 are the transition period and corresponding age . at this transition point the braking index is @xmath34 . because the minimum braking index of model sclf(ics ) is @xmath35 , there is no such a transition point , which can be seen in the evolution in @xmath1 diagram ( see figure [ figevo&models ] ) . ( e ) : @xmath36 and @xmath37 are the period and age when pulsar stops radio emission . the death period is calculated by equation ( [ pdeath ] ) . a braking index @xmath8 has been monitored after the removal of the effects of glitches during an epoch when there are many glitches occured ( lyne et al . 2015 ) . it is different from the long term underlying braking index @xmath38 of the crab pulsar . previously , wang et al . ( 2012 ) have measured two different values of braking index @xmath39 and @xmath40 between glitches . they attribute it to the effect of varying particle wind strength ( wang et al . it is generally accepted that glitch is caused by the inner effect but may lead to some effect in the outer magnetosphere , for example : the changing of primary particle density during this epoch . in the pulsar wind model , it can be denoted by the changing coefficient of particle density @xmath41 . then equation ( [ nwind ] ) should be modified : @xmath42 equation ( [ nkappa ] ) can be rewritten as : @xmath43 where @xmath44 is the characteristic age , @xmath45 can be viewed as the typical time scale of the changing particle density . when the magnetosphere is in equilibrium ( i.e. , when the glitch activities of the pulsar is not very active ) , the time scale of particle density variation ( @xmath46 ) may be very large ( i.e. , larger than the characteristic age @xmath47 ) . the third term in equation ( [ ntauk ] ) does not contribute . but , if they are comparable with each other , the braking index changes substantially . in other words , when the outflow particle density increases and the effect of particle wind becomes stronger , means @xmath48 or @xmath49 , the braking index will be smaller than @xmath38 . but when the outflow particle density decreases ( @xmath50 or @xmath51 ) , the braking index will be larger than @xmath38 . as the out - flow particle density tending to a certain value ( larger or smaller than previous value ) , the braking index tends to its underlying value ( @xmath38 ) . generally , the increased ( or decreased ) component of the outflow particle density ( may be @xmath52 ) is so much small that it can be ignored . figure [ fignk ] shows the braking index as function of @xmath46 for the crab pulsar in the vg(cr ) model . in order to better understand the observations of @xmath53 ( lyne et al . 2015 ) , we consider the @xmath48 only . as we can see in this figure , the braking index is insensitive to @xmath46 when it is larger than @xmath54 . but , when it is comparable with the characteristic age ( about @xmath0 yr ) , the braking index decreases sharply . when braking index is @xmath8 , the changing rate of the particle density is @xmath55 . in this interval ( from mjd 51000 to mjd 53000 , about @xmath56 years ) , the particle density has changed by @xmath57 . the change of particle density will result in changes of radiation energy loss rate and period derivative . their changes respectively are : @xmath58 and @xmath59 . the pulsar wind model can be tested with observations ( jodrell bank monthly ephemeris of the crab pulsar ) . the effect of glitches is not taken into consideration in the pulsar wind model . the changes of period and period derivative caused by glitches should be added ( lyne et al . 2015 ) . figure [ figob&model ] is the model calculation compared with observations ( without modelling the transient variation caused by glitches ) . when the amplitude of glitches is relatively small , the change of particle density is not obvious , then the model calculations ( the blue points ) fit well with observations ( the black points ) . however , when the amplitude of glitches is large , the effect of glitches must be added ( the red points ) . moreover , the effect of particle density change should be taken into consideration . a factor @xmath60 ( which is calculated above ) is added to the red points ( from mjd 51804.75 afterwards ) , shown as the green points . the green points can match the general trend of the observations . in the vg(cr ) model . the dashed line is the underlying braking index @xmath38 . the dotted line is the smaller braking index @xmath8 measured during glitch activities ( lyne et al . 2015 , figure 7 there).,scaledwidth=45.0% ] the pulsar period and its fist derivative evolution with time in the vg(cr ) model are shown in the first and second panel of figure [ figparameters ] . the curves evolve slowly in its early age and then rise sharply , indicating that the crab pulsar is mainly braked by magnetic dipole radiation firstly and then mainly by particle wind . the transition period is @xmath61 and age of the crab pulsar will be @xmath62 calculated in the vg(cr ) model ( see table [ tab_calculations ] ) . the braking index evolution with time in the vg(cr ) model is shown in the third panel of figure [ figparameters ] . braking index decreases from @xmath63 to @xmath64 different minimum braking indices for different acceleration models . the bottom panel of figure [ figparameters ] shows the second braking index evolution with time . the curve gradually decreases from @xmath65 to 30/49 . figure [ figevo&short ] shows the evolution of the crab pulsar in @xmath1 diagram from birth to its @xmath66 years old . these points are respectively taken when the crab pulsar is : @xmath67 , @xmath68 , @xmath62 , @xmath69 and @xmath66 years old . period derivative evolves with period by a function of @xmath70 ( espinoza et al . 2011 ) . in the log - log plot , the evolution curve evolves with a slop ( @xmath71 ) . as the braking index falling from @xmath63 to @xmath67 , the pulsar" +"emission at 511 kev , the characteristic signature of positron annihilation , has been observed in the direction of the galactic centre ( gc ) , since the 1970s . apparently diffuse gamma - ray emission at approximately this energy was first detected in 1970 by the balloon - borne experiments of the rice group ( johnson , harnden , & haymes 1972 ; johnson & haymes 1973 ; haymes et al . 1975 ; preliminary indications were also reported in haymes et al . 1969 ) and was confirmed as positron annihilation emission in 1978 by the balloon - borne experiments of the bell - sandia group ( leventhal , maccallum , & stang 1978 ; leventhal et al . high - energy balloon experiments and space observatories through the early 1990s continued to detect the 511 kev emission ; however the relatively low spatial resolution of these detectors prevented determination of the true location and distribution of the emission ( see purcell et al . 1997 , jean et al . 2003 , or teegarden et al . 2005 for a summary of these early observations ) . specifically , from these data it is unclear whether the emission is truly diffuse , or if it originates either from a single discrete source ( _ e.g . _ sgr a * or 1e1740.7 - 2942,``the great annihilator '' ) or from a small number of discrete but unresolved sources . some early detections suggested time variability in the signal , indicating a small number of discrete sources , but these variations were not confirmed in subsequent observations ( _ e.g . _ purcell et al . 1997 ; teegarden et al . 2005 ) . with the advent of space observatories of increasing sensitivity , spectral coverage , and spatial resolution , the resultant improvement in data quality now provides much stronger constraints on the origin of the emission . in particular , observations of the gc by the spi spectrometre on the satellite integral ( the international gamma - ray astrophysicsl laboratory ) have recently produced the most detailed map of the anomalous 511 kev emission to date ( kndlseder et al . 2005 ; weidenspointner et al . 2006 , 2007 ) . the spi / integral map clearly shows this emission arising from the central @xmath01.5 kpc ( @xmath2@xmath3 ) of the galaxy , with a fainter component of 511 kev flux detected from the remainder of the galactic disk . the smoothness of the emission constrains the number of discrete sources responsible to be in excess of @xmath0 8 ( kndlseder et al . 2005 ) , as do point source limits of @xmath4 ph @xmath5 s@xmath6 from searches with the ibis imager on integral ( de cesare et al . most recently , weidenspointner et al . ( 2008 ) have detected a longitudinal asymmetry in the disk component of the emission , which matches the asymmetry in the distribution of the brightest low - mass x - ray binaries ( lmxbs ) detected by the ibis instrument on integral , suggesting that these @xmath7 objects may account for much of the disk component of the 511 kev emission . diffuse emission from the galactic centre , unaccounted for by known sources , has also been observed at several other wavelengths , notably high - frequency radio ( 2163 ghz ) with wmap ( finkbeiner 2004a ) and soft x - rays ( 110 kev ) with _ e.g. _ heao and chandra ( worrall et al . 1982 , muno et al . the origin and nature of the diffuse emission is puzzling in each case . in the case of the diffuse x - ray component , a population of discrete but unresolved point sources was originally postulated as a possible source of the emission ( see _ e.g. _ skibo et al . 1997 , valinia & marshall 1998 ) . with the advent of high - resolution x - ray imaging using chandra , a large new population of low x - ray luminosity sources has indeed been identified in the central 2@xmath3@xmath80.8@xmath3of the gc ( 300@xmath8120 pc at a gc distance of 8.5 kpc ; wang et al . 2002 , muno et al . 2003 , muno et al . 2006 ) . many of these @xmath04200 discrete x - ray sources are likely to be accreting binaries , including high and low mass x - ray binaries and cataclysmic variables . however , it is worth noting that these detected sources only account for 10% of the previously observed diffuse 2 - 10 kev emission ( ebisawa et al . 2001 , muno et al . 2003 ) , so an even larger population of still fainter sources ( with @xmath9@xmath10erg@xmath10s@xmath6 ) could exist at the gc ( but see muno et al . 2004 who argue that the spectral characteristics of the remaining diffuse x - ray emission are inconsistent with a stellar x - ray source origin ) . in any case , it is not clear how much these new populations might contribute to the diffuse flux at lower ( _ e.g . _ wmap ) or higher ( _ e.g . _ integral ) energies . in this paper , we consider the hypothesis that jet outflows from x - ray binary systems ( xrb ) , which are accretion - powered mass - transferring binaries containing a black hole ( bh ) or neutron star ( ns ) , are the main source of the 511 kev emission in the gc . this idea has been explored previously by various authors , notably ramaty & lingenfelter ( 1979 ) , prantzos ( 2004 ) , kndlseder et al . ( 2005 ) , and guessoum et al . these previous studies generally focused on the large - scale discrete jet ejections produced by the class of luminous black hole xrbs known as `` microquasars '' . however , it is now thought that luminous black hole xrbs much more commonly produce lower - luminosity `` steady '' jets , and that these outflows are `` on '' for a substantially greater fraction of the xrb duty cycle than the large - scale ejection events ( gallo et al . we note that neutron star x - ray binaries are , in principle , also possible sources of jet positrons . the fraction of low magnetic field ns xrbs with outflows could be as high as @xmath0 100% ( fender 2006 ; migliari & fender 2006 ) . however , they show a different scaling than black hole xrbs between x - ray luminosity and radio luminosity ( i.e. @xmath11 in bh systems and @xmath12 in ns systems ; miglari & fender 2006 ) . as a result of this scaling , the jets from quiescent neutron star x - ray binaries are likely to be several orders of magnitude weaker than those from quiescent bh x - ray binaries , if one assumes the same scaling relations continue into quiescence . more likely , though , is that the scaling relation becomes even steeper for neutron stars as they fade more deeply into quiescence than the current radio flux limits allow us to probe ; the emission from the faintest neutron star xrbs is generally dominated by thermal crustal emission from cooling neutron stars , rather than by accretion power ( _ e.g . _ rutledge et al . 2001 ) . also , while some luminous high - mass x - ray binaries ( hmxbs ) have been observed to emit jets ( e.g. cyg x-1 , cyg x-3 ) , these systems are predominantly located in the galactic disk ( grimm et al . thus these canonical bh hmxbs of which there are only a few known in the entire milky way are not a class of objects which can cause an excess of high - energy flux in the bulge relative to the galactic disk . recent integral observations have detected a population of lower - luminosity , x - ray hard , high - mass xrbs including highly - obscured hmxbs and `` supergiant fast x - ray transients '' , a number of which are located in the bulge ( chaty et al . however , there is as yet no evidence for jet outflows in these hmxbs . furthermore , the nature of the compact objects in these systems is currently not known ; but we note that of those canonical hmxbs for which the nature of the compact object has been identified , the majority contain neutron stars rather than black holes . finally , in a detailed study of the spatial distribution of integral - detected xrbs ( including the new highly - obscured systems ) , lutovinov et al . ( 2005 ) find that the angular distribution of hmxbs in the inner galaxy is significantly different from that of lmxbs specifically , lmxbs are clearly the dominant population within the bulge , significantly overabundant as compared with the hmxbs in this region . thus while we can not rule out a high - energy flux contribution in the bulge from these newly discovered low - luminosity hmxbs , we will not consider them further here . therefore in this paper we primarily consider jets from low - mass black hole binaries . it seems plausible that steady , low - luminosity outflows from galactic bh xrbs contribute substantially to the annihilation line emission , and possible also to the diffuse emission observed at other wavelengths . the outline of the paper is as follows . in section 2 , we first review the 511 kev observations of the gc and discuss possible sources for the positrons . in section 3 , we outline a simple model for positron production in ( quiescent ) lmxb jets . in section 4 , we briefly examine the unexplained diffuse gc emission observed at microwave and x - ray wavelengths , and consider whether this emission could also originate in outflows from low - luminosity lmxbs . in section 5 , we discuss the recent association of the disk component of the 511 kev emission with bright lmxbs detected by ibis , pointing out some unresolved problems with this association . we conclude by proposing several observational tests that may help elucidate the nature of the population responsible for the 511 kev emission . since its initial discovery almost 40 years ago , our picture of the annihilation emission from the gc has gradually become clearer . the emission amounts to @xmath13 photons @xmath14 s@xmath6 , coming from a region roughly @xmath15 in radius around the gc . assuming the mean distance to the positron sources is the distance to the gc , 8.5 kpc , this flux corresponds to an integrated luminosity of @xmath16 photons / s emitted within a region 1.5 kpc in radius . after initial suggestions of temporal variability in the flux , extensive observations over the 1990s have ruled this out at any substantial level ( see purcell et al . 1997 for a summary of this evidence ) . the detailed spatial distribution of the emission has become much clearer since observations first by osse on cgro , and then more recently by spi on integral . the most recent analyses of 4 years of spi / integral data ( weidenspointner et al . 2008 ) suggest two main components : a central bulge and an asymmetric disk . the bulge component is reasonably well described by a single gaussian with a fwhm of 6@xmath17 , but even better described by a superposition of two gaussians of fwhm of 3@xmath17 and 12@xmath17 , or alternately a compact , symmetric bulge component from @xmath180.5 kpc , and an extended shell of emission from @xmath191.5 kpc . the disk component is" +"the burrows - wheeler transform ( bwt ) is a widely used preprocessing technique in lossless data compression @xcite . it brings every word into a form which is likely to be easier to compress @xcite . its compression performance is almost as good as ppm ( prediction by partial matching ) schemes @xcite while its speed is comparable to that of lempel - ziv algorithms @xcite . therefore , bwt based compression schemes are a very reasonable trade - off between running time and compression ratio . in the classic setting , the bwt maps a word of length @xmath0 to a word of length @xmath0 and an index ( comprising @xmath3 bits ) . thus , the bwt is not bijective and hence , it is introducing new redundancies to the data , which is cumbersome and undesired in applications of data compression or cryptography . instead of using an index , a very common technique is to assume that the input has a unique end - of - string symbol @xcite . even though this often simplifies proofs or allows speeding up the algorithms , the use of an end - of - string symbol introduces new redundancies ( again @xmath3 bits are required for coding the end - of - string symbol ) . we discuss bijective versions of the bwt which are one - to - one correspondences between words of length @xmath0 . in particular , no index and no end - of - string symbol is needed . not only does bijectivity save a few bits , for example , it also increases data security when cryptographic procedures are involved ; it is more natural and it can help us to understand the bwt even better . moreover , the bijective variants give us new possibilities for enhancements ; for example , in the bijective bwt different orders on the letters can be used for the two main stages . several variants of the bwt have been introduced @xcite . an overview can be found in the textbook by adjeroh , bell , and mukherjee @xcite . one particularly important variant for this paper is the sort transform ( st ) , which is also known under the name schindler transform @xcite . in the original paper , the inverse of the st is described only very briefly . more precise descriptions and improved algorithms for the inverse of the st have been proposed recently @xcite . as for the bwt , the st also involves an index or an end - of - string symbol . in particular , the st is not onto and it introduces new redundancies . the bijective bwt was discovered and first described by scott ( 2007 ) , but his exposition of the algorithm was somewhat cryptic , and was not appreciated as such . in particular , the fact that this transform is based on the lyndon factorization went unnoticed by scott . gil and scott @xcite provided an accessible description of the algorithm . here , we give an alternative description , a proof of its correctness , and more importantly , draw connections between scott s algorithm and other results in combinatorics on words . further , this variation of the bwt is used to introduce techniques which are employed at the bijective sort transform , which makes the main contribution of this paper . the forward transform of the bijective st is rather easy , but we have to be very careful with some details . compared with the inverse of the bijective bwt , the inverse of the bijective st is more involved . * outline . * the paper is organized as follows . in section [ sec : prelim ] we fix some notation and repeat basic facts about combinatorics on words . on our way to the bijective sort transform ( section [ sec : lst ] ) we investigate the bwt ( section [ sec : bwt ] ) , the bijective bwt ( section [ sec : lbwt ] ) , and the sort transform ( section [ sec : st ] ) . we give full constructive proofs for the injectivity of the respective transforms . each section ends with a running example which illustrates the respective concepts . apart from basic combinatorics on words , the paper is completely self - contained . throughout this paper we fix the finite non - empty alphabet @xmath4 and assume that @xmath4 is equipped with a linear order @xmath5 . a _ word _ is a sequence @xmath6 of letters @xmath7 , @xmath8 . the set of all such sequences is denoted by @xmath9 ; it is the free monoid over @xmath4 with concatenation as composition and with the empty word @xmath10 as neutral element . the set @xmath11 consists of all non - empty words . for words @xmath12 we write @xmath13 if @xmath14 or if @xmath15 is lexicographically smaller than @xmath16 with respect to the order @xmath5 on the letters . let @xmath17 be a non - empty word with letters @xmath18 . the _ length _ of @xmath19 , denoted by @xmath20 , is @xmath0 . the empty word is the unique word of length @xmath21 . we can think of @xmath19 as a labeled linear order : position @xmath22 of @xmath19 is labeled by @xmath18 and in this case we write @xmath23 , so each word @xmath19 induces a labeling function @xmath24 . the first letter @xmath25 of @xmath19 is denoted by @xmath26 while the last letter @xmath27 is denoted by @xmath28 . the _ reversal _ of a word @xmath19 is @xmath29 . we say that two words @xmath12 are _ conjugate _ if @xmath30 and @xmath31 for some words @xmath32 , i.e. , @xmath15 and @xmath16 are cyclic shifts of one another . the @xmath33-fold concatenation of @xmath19 with itself is denoted by @xmath34 . a word @xmath15 is a _ root _ of @xmath19 if @xmath35 for some @xmath36 . a word @xmath19 is _ primitive _ if @xmath35 implies @xmath37 and hence @xmath38 , i.e. , @xmath19 has only the trivial root @xmath19 . the _ right - shift _ of @xmath39 is @xmath40 and the @xmath22-fold right shift @xmath41 is defined inductively by @xmath42 and @xmath43 . we have @xmath44 for @xmath45 . the word @xmath41 is also well - defined for @xmath46 and then @xmath47 where @xmath48 . we define the _ ordered conjugacy class _ of a word @xmath49 as @xmath50 = ( w_1 , \ldots , w_n)$ ] where @xmath51 . it is convenient to think of @xmath50 $ ] as a cycle of length @xmath0 with a pointer to a distinguished starting position . every position @xmath22 , @xmath8 , on this cycle is labeled by @xmath52 . in particular , @xmath25 is a successor of @xmath27 on this cycle since the position @xmath1 is a successor of the position @xmath0 . the mapping @xmath53 moves the pointer to its predecessor . the ( unordered ) conjugacy class of @xmath19 is the multiset @xmath54 . whenever there is no confusion , then by abuse of notation we also write @xmath50 $ ] to denote the ( unordered ) conjugacy class of @xmath19 . for instance , this is the case if @xmath19 is in some way distinguished within its conjugacy class , which is true if @xmath19 is a lyndon word . a _ lyndon word _ is a non - empty word which is the unique lexicographic minimal element within its conjugacy class . more formally , let @xmath50 = ( w , w_2 , \ldots , w_n)$ ] , then @xmath55 is a lyndon word if @xmath56 for all @xmath57 . lyndon words have a lot of nice properties @xcite . for instance , lyndon words are primitive . another interesting fact is the following . [ thm : lyndon ] every word @xmath58 has a unique factorization @xmath59 such that @xmath60 is a non - decreasing sequence of lyndon words . an alternative formulation of the above fact is that every word @xmath19 has a unique factorization @xmath61 where @xmath62 for all @xmath22 and where @xmath63 is a strictly increasing sequence of lyndon words . the factorization of @xmath19 as in fact [ thm : lyndon ] is called the _ lyndon factorization _ of @xmath19 . it can be computed in linear time using duval s algorithm @xcite . suppose we are given a multiset @xmath64 of lyndon words enumerated in non - decreasing order @xmath65 . now , @xmath66 uniquely determines the word @xmath67 . therefore , the lyndon factorization induces a one - to - one correspondence between arbitrary words of length @xmath0 and multisets of lyndon words of total length @xmath0 . of course , by definition of lyndon words , the multiset @xmath68 of lyndon words and the multiset @xmath69 , \ldots , [ v_s]}\right\}}$ ] of conjugacy classes of lyndon words are also in one - to - one correspondence . we extend the order @xmath5 on @xmath4 as follows to non - empty words . let @xmath70 be the infinite sequences obtained as the infinite power of @xmath19 . for @xmath71 we write @xmath72 if either @xmath73 or @xmath74 and @xmath75 for @xmath76 , @xmath77 with @xmath78 , and infinite sequences @xmath79 ; phrased differently , @xmath72 means that the infinite sequences @xmath80 and @xmath81 satisfy @xmath82 . if @xmath15 and @xmath16 have the same length , then @xmath83 coincides with the lexicographic order induced by the order on the letters . for arbitrary words , @xmath83 is only a preorder since for example @xmath84 and @xmath85 . on the other hand , if @xmath86 and @xmath87 then @xmath88 . hence , by the periodicity lemma @xcite , there exists a common root @xmath89 and @xmath90 such that @xmath91 and @xmath92 . also note that @xmath93 whereas @xmath94 for @xmath78 . intuitively , the _ context of order @xmath2 _ of @xmath19 is the sequence of the first @xmath2 letters of @xmath19 . we want this notion to be well - defined even if @xmath95 . to this end let @xmath96 be the prefix of length @xmath2 of @xmath97 , i.e. , @xmath96 consists of the first @xmath2 letters on the cycle @xmath50 $ ] . note that our definition of a context of order @xmath2 is left - right symmetric to the corresponding notion used in data compression . this is due to the fact that typical compression schemes are applying the bwt or the st to the reversal of the input . an important construction in this paper is the _ standard permutation _ @xmath98 on the set of positions @xmath99 induced by a word @xmath100 @xcite . the first step is to introduce a new order @xmath101 on the positions of @xmath19 by sorting the letters within @xmath19 such that identical letters preserve their order . more formally , the linear order @xmath101 on @xmath102 is defined as follows : @xmath103 if @xmath104 let @xmath105 be the linearization of @xmath106 according to this new order . now , the standard permutation @xmath98 is defined by @xmath107 . [ exa : start ] consider the word @xmath108 over the ordered alphabet @xmath109 . we have @xmath110 . therefore , the positions in @xmath19 are @xmath111 . for instance , the label of position @xmath112 is @xmath113 . its lyndon factorization is @xmath114 . the context of order @xmath115 of the prefix @xmath116 of length @xmath117 is @xmath118 and the context of order @xmath115 of the factor @xmath119 is @xmath120 . for computing the standard permutation we write @xmath19 column - wise , add positions , and then sort the pairs lexicographically : [ cols=""^,^,^"",options=""header "" , ] this yields the standard permutation @xmath121 the conjugacy class @xmath50 $ ] of @xmath19 is depicted in figure [ sfg : w ] ; the" +"consumer reviews are invaluable as a source of data to help people form opinions on a wide range of products . beyond telling us whether a product is ` good ' or ` bad ' , reviews tell us about a wide range of _ personal experiences _ ; these include objective descriptions of the products properties , subjective qualitative assessments , as well as unique use- ( or failure- ) cases . the value and diversity of these opinions raises two questions of interest to us : ( 1 ) how can we help users navigate massive volumes of consumer opinions in order to find those that are _ relevant _ to their decision ? and ( 2 ) how can we address specific _ queries _ that a user wishes to answer in order to evaluate a product ? to help users answer specific queries , review websites like _ amazon _ offer community - q / a systems that allow users to pose product - specific questions to other consumers . our goal here is to respond to such queries automatically and on - demand . to achieve this we make the basic insight that our two goals above naturally complement each other : given a large volume of community - q / a data ( i.e. , questions and answers ) , and a large volume of reviews , we can automatically _ learn _ what makes a review relevant to a query . we see several reasons why reviews might be a useful source of information to address product - related queries , especially compared to existing work that aims to solve q / a - like tasks by building knowledge bases of facts about the entities in question : * general question - answering is a challenging open problem . it is certainly hard to imagine that a query such as `` will this baby seat fit in the overhead compartment of a 747 ? '' could be answered by building a knowledge - base using current techniques . however it is more plausible that some review of that product will contain information that is relevant to this query . by casting the problem as one of surfacing relevant opinions ( rather than necessarily generating a conclusive answer ) , we can circumvent this difficulty , allowing us to handle complex and arbitrary queries . * fundamentally , many of the questions users ask on review websites will be those that _ ca nt _ be answered using knowledge bases derived from product specifications , but rather their questions will be concerned with subjective personal experiences . reviews are a natural and rich source of data to address such queries . * finally , the massive volume and range of opinions makes review systems difficult to navigate , especially if a user is interested in some niche aspect of a product . thus a system that identifies opinions relevant to a specific query is of fundamental value in helping users to navigate such large corpora of reviews . to make our objectives more concrete , we aim to formalize the problem in terms of the following goal : _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ goal : _ given a query about a particular product , we want to determine how relevant each review of that product is to the query , where ` relevance ' is measured in terms of how helpful the review will be in terms of identifying the correct response . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ the type of system we produce to address this goal is demonstrated in figure [ fig : examp ] . here we surface opinions that are identified as being ` relevant ' to the query , which can collectively vote ( along with all other opinions , in proportion to their relevance ) to determine the response to the query . * product : * braven brv-1 wireless bluetooth speaker , title=""fig : "" ] + * query : * `` i want to use this with my ipad air while taking a jacuzzi bath . will the volume be loud enough over the bath jets ? '' + + m0.78>m0.07 & vote : + `` the sound quality is great , especially for the size , and if you place the speaker on a hard surface it acts as a sound board , and the bass really kicks up . '' & yes + + `` if you are looking for a water resistant blue tooth speaker you will be very pleased with this product . '' & yes + + `` however if you are looking for something to throw a small party this just does nt have the sound output . '' & no + + etc . . + + * response : * yes this simple example demonstrates exactly the features that make our problem interesting and difficult : first , the query ( ` is this loud enough ? ' ) is inherently subjective , and depends on personal experience ; it is hard to imagine that any fact - based knowledge repository could provide a satisfactory answer . secondly , it is certainly a ` long - tail ' query it would be hard to find relevant opinions among the ( 300 + ) reviews for this product , so a system to automatically retrieve them is valuable . third , it is linguistically complex few of the important words in the query appear among the most relevant reviews ( e.g. ` jacuzzi bath'/`loud enough')this means that existing solutions based on word - level similarity are unlikely to be effective . this reveals the need to learn a complex definition of ` relevance ' that is capable of accounting for subtle linguistic differences such as synonyms . finally , in the case of figure [ fig : examp ] , our model is able to respond to the query ( in this instance correctly ) with a binary answer . more importantly though , the opinions surfaced allow the user to determine the answer themselves in this way we can extend our model to handle general open - ended queries , where the goal is not to answer the question _ per se _ , but rather to surface relevant opinions that will help the questioner form their own conclusion . it seems then that to address our goal we ll need a system with two components : ( 1 ) a _ relevance _ function , to determine which reviews contain information relevant to a query , and ( 2 ) a prediction function , allowing relevant reviews to ` vote ' on the correct answer . however as we stated , our main goal is _ not _ to answer questions directly but rather to surface relevant opinions that will help the user answer the question themselves ; thus it may seem as though this ` voting ' function is not required . indeed , at _ test _ time , only the relevance function is required this is exactly the feature that shall allow our model to handle arbitrary , open - ended , and subjective queries . however the voting function is critical at _ training _ time , so that with a large corpus of already - answered questions , we can simultaneously learn relevance and voting functions such that ` relevant ' reviews are those that vote for the correct answer . the properties that we want above are captured by a classical machine learning framework known as _ mixtures of experts _ @xcite . mixtures of experts are traditionally used when one wishes to combine a series of ` weak learners'there the goal is to simultaneously estimate ( a ) how ` expert ' each predictor is with respect to a particular input and ( b ) the parameters of the predictors themselves . this is an elegant framework as it allows learners to ` focus ' on inputs that they are good at classifying it does nt matter if they sometimes make incorrect predictions , so long as they correctly classify those instances where they are predicted to be experts . in our setting , individual reviews or opinions are treated as experts that get to vote on the answer to each query ; naturally some opinions will be unrelated to some queries , so we must also learn how relevant ( i.e. , expert ) each opinion is with respect to each query . our prediction ( i.e. , voting ) function and relevance function are then learned simultaneously such that ` relevant ' opinions are precisely those that are likely to vote correctly . at test time , the relevance function can be used directly to surface relevant opinions . we evaluate our model using a novel corpus of questions and answers from _ we consider both binary questions ( such as the example in figure [ fig : examp ] ) , and" +"our compilation of measured redshifts for clusters from the catalogue of abell , corwin , & olowin ( 1989 , aco ) has been maintained since 1989 ( andernach 1991 ; andernach , tago , & stengler - larrea 1995 ( ats95 ) ; andernach & tago 1998 ( at98 ) ) and is the only such compilation including both a- and s - clusters . different from previous compilations ( e.g. struble & rood 1999 , sr99 , who include a - clusters only ) , we systematically scan the literature for galaxy redshifts . surveys like the lcrs ( shectman et al . 1996 ) , 2df , 6df ( jones et al . 2004 ) , and sdss ( abazajian et al . 2004 ) prove to be rich in aco cluster redshifts . our selection criteria for galaxy redshifts , and the cluster parameters we include in our compilation can be found in ats95 and at98 . the number of references contributing cluster redshifts has increased so much that one of us ( ha ) now compiles all individual galaxy positions and redshifts , so as to ease the merging of different data sources . for clusters with large @xmath4 and _ several _ papers to merge , this work is in progress . our current compilation is based on 685 references , growing by @xmath540 per year . sixty percent of the 3715 mean redshifts , and 86% of the 1875 velocity dispersions are based on our own calculations , using individual galaxy data . over 330 redshifts are based on the merging of galaxy data from four or more references . we do not include any photometric redshifts nor any galaxy velocities with errors @xmath6600kms@xmath2 . in order to merge galaxy data from different sources for the same cluster , we need individual galaxy positions , velocities , and errors . lack of these data prevents the merging of many data sources or calculation of @xmath1 ( e.g. , we list over a dozen clusters with @xmath7 but no @xmath1 reported ) . often publications do not state whether redshifts are geo- , helio- or galactocentric . the fact that the data releases of large projects like 2df , 6df , sdss , etc . , tend to be _ cumulative _ ( i.e. each release contains previous ones , often with reprocessed data ) rather than _ incremental _ , makes the updating of our compilation very tedious . to calculate @xmath8 and @xmath1 for a cluster , we first search for any relative maxima in the redshift distribution of galaxies within the cluster area . around each relative maximum we include into a single cluster component all galaxies within @xmath9kms@xmath2 from that maximum . we use this value also as a minimum velocity gap for subclusters closely spaced along the line of sight . only if subclusters were published with a smaller separation in velocity ( mostly due to components separated in the plane of the sky ) , we adopt them from the literature _ as is_. apart from three known pairs of duplicate clusters in aco , and six further pairs reported by at98 , we propose a3742=s924 as an additional identity . redshifts ( based on at least one galaxy measured ) are now available for 59% of all 4076 a - clusters and for 54% of all 1174 supplementary southern s - clusters , which is an almost 4-fold increase over abell et al . only 2.7% of the redshifts are beyond a factor two from their photometric estimates ( see sect.3 ) . a significant improvement over previous compilations is that 67% ( compared to 43% in sr99 ) of the redshifts are based on @xmath0 measured galaxies , and can thus be considered `` reliable '' . this , as well as the almost 3-fold increase in the number of known velocity dispersions over sr99 , is due to our efforts to merge all available data sources , especially in the regime of low @xmath4 . there are 1245 ( sub)clusters with @xmath1010 , of which 276 have @xmath1050 ( the typical minimum for dynamical studies ) , and 95 ( sub)clusters have @xmath11 . the total number of galaxies involved for all our listed ( sub)clusters is @xmath556,800 ( 9500 of which in s - clusters ) , including some overhead for overlapping clusters for which it is not possible to assign galaxies uniquely to one cluster . we quote @xmath1 for 1353 different abell clusters ( 1080 a- and 273 s - clusters , for a total of 1875 subclusters ) . the median @xmath1 for all 1875 ( sub)clusters is 636kms@xmath2 , and their distribution shows an almost gaussian main peak at @xmath5630kms@xmath2 with a dispersion of @xmath5275kms@xmath2 , followed by a weak tail out to 2000kms@xmath2 ( probably containing some line - of - sight superpositions or mergers ) . for the rich aco clusters ( a - names ) we use the redshift estimate by peacock & west ( 1992 , kindly provided by m.west ) , while for the s - clusters we use a function originally proposed by abell et al.(1989 ) for southern a - clusters , but scaled down by 30% on the basis of 196 s - cluster redshifts ( andernach 1991 ) . now , with three times the number of s - cluster redshifts in hand , we confirm s - clusters to have on average 30% lower @xmath12 than the aco estimate . it is not clear whether this is due to an excess foreground contamination of redshifts , or due to a systematic overestimate of @xmath13 of the clusters caused by background contamination . we do * not * confirm the claim by at98 that s - clusters suffer more from line - of - sight superposition than a - clusters : currently 16% of both a- and s - clusters appear with more than one redshift entry , and it rather seems that deeper and deeper surveys ( like 2df or sdss ) tend to find more clusters along the line of sight . redshifts are now available for all except 60 ( 1.5% ) rich ( a- ) clusters with estimated redshift z@xmath140.1 , while 17 s - clusters ( 7% ) with @xmath150.05 ( and 240 , or 32% , with @xmath150.1 ) still lack a measured redshift . there is still plenty of high - galactic - latitude sky with galaxies brighter than @xmath16 unexplored in redshift . however , these gaps are getting smaller : e.g. , we found that only the increment of 6df - fdr ( jones et al . 2004 ) over 6df - edr yields new redshifts for @xmath5250 clusters with no previous @xmath12 , about half of these with @xmath17 . based on now 15 years of compilation experience we anticipate that only in @xmath510 years from now the redshift completeness of the aco catalogue may get close to 100% . the distribution of @xmath1 for the 1875 ( sub)clusters depends strongly on @xmath3 . we find median values of @xmath1 of 556kms@xmath2 for 651 ( sub)clusters with @xmath18 , 616kms@xmath2 for 564 ( sub)clusters with @xmath19 , and 703kms@xmath2 for 597 ( sub)clusters with @xmath20 . these medians are slightly lower than those reported in at98 due to a more careful clipping of outliers . as shown by plionis et al . ( 2004 ) @xmath1 increases with both @xmath3 and with abell count @xmath21 . this correlation may be partly due to an observer s tendency to measure more redshifts in richer clusters and thus the @xmath22 correlation may be a reflection of the known richness dependence of @xmath1 . the morphological classification available for most aco clusters is the `` bautz - morgan '' ( bm ) type . using only subclusters with the highest @xmath3 , we find that the mean and median @xmath1 for 664 ( sub)clusters of `` early '' bmtype ( @xmath23ii ) are _ lower _ by @xmath545kms@xmath2 than for 614 ( sub)clusters of `` late '' bmtype ( @xmath24ii ) . a kolmogorov - smirnov test gives only a 1.8% chance for these samples to be drawn from the same population . the direction of this trend is surprising , as earlier bm types are expected to be more evolved and to have higher x - ray luminosity , and thus to show a higher @xmath1 ( david , forman , & jones 1999 ) . these authors found that x - ray luminosity is correlated with both abell richness class @xmath25 and bm type , but also that @xmath25 may be overestimated in the southern aco . using updated x - ray samples and more cluster parameters , like @xmath26 , we plan to shed more light on the relation between cluster dynamics and bm type . we used our compilation in the past to establish the presently most complete catalogues of superclusters ( scl ) of abell- and x - ray clusters ( e.g. einasto et al . 2001 ) , and showed that x - ray clusters are more strongly clustered into superclusters than are optical clusters . we used the scl catalogue to confirm that the richest superclusters occupy a more or less regular lattice of 120@xmath27mpc grid size ( einasto , et al . 1994 , saar et al . based on the _ current _ compilation we extended our scl catalogue out to @xmath28 . in particular , several very interesting scls were revealed . the most prominent abell supercluster crossed by the northern lcrs slices is scl126 ( @xmath12=0.084 ) in the direction of virgo . four out of a total of seven aco member clusters of this scl lie within a sphere of diameter @xmath29mpc . three clusters in this scl are strong x - ray sources , and four contain radio sources . this makes scl126 one of the most unusual superclusters currently known . the shape ellipsoids , based on abell clusters , on lcrs loose groups ( lclg , tucker et al . 2000 ) , and on lcrs galaxies in scl126 , all have axis ratios of @xmath51:4 , and are located perpendicular to the line of sight ( einasto , m. et al . this may be evidence for a `` squashing effect '' of galaxies falling into scls ( kaiser 1987 ) , accompanied by merging and other processes causing x - ray and radio emission from the clusters . the core of scl126 may have started to collapse ( gramann & suhhonenko 2002 ) . another prominent scl is `` horologium reticulum '' ( scl48 at @xmath300.064 ) , crossed by all southern lcrs slices . this supercluster consists of several concentrations of abell clusters and lclgs which are connected by filaments of galaxies , groups and clusters that surround underdense regions ( einasto , m. et al . 2003b ; einasto , j. et al . 2003b ) . galaxy groups from the lcrs and sdss in high - density environments ( superclusters of abell clusters ) are also richer and more massive than groups in low - density environments ( einasto , m. et al . 2003a , b ; einasto , j. et al . 2003 ) . abazajian , k. , adelman - mccarthy , j. k. , ageros , m. a. , et al . 2004 , aj , 128 , 502 abell g. o. , corwin h. g. jr . , & olowin r. 1989 , , 70 , 1 andernach , h. 1991 , in _ large - scale structures and peculiar motions _ , eds . d. w. latham & l. n. dacosta ) , asp conf . 15 , 279 andernach , h. , tago , e. , & stengler - larrea , e. 1995 , ap.lett . &" +"the problem of a single particle interacting with its environment is encountered frequently in condensed matter physics , and in many variations . such scenarios appear in the form of genuine defects in materials , like magnetic impurities in metals and the associated ubiquitous kondo problem.@xcite impurity problems are also often used as a stepping stone to gain insight into the behavior of strongly correlated systems , such as studying a single hole doped into a mott insulator helps understanding some properties of high - temperature superconductors.@xcite in recent years , impurity problems have also started to gain some attention in the context of ultracold atomic gases . amongst others , the fermionic polaron problem has been studied thoroughly in connection with strongly imbalanced fermi gases close to a feshbach resonance,@xcite where a single `` spin - down '' atom interacting with a fermi sea of `` spin - up '' atoms appears as a polaronic quasiparticle and eventually forms a two - particle bound - state with one of the majority atoms if the interactions are strong enough.@xcite more generally , such polaronic problems appear when we consider the nature of the threshold of spectral functions of gapped excitations above many - body ground states.@xcite here we are interested in a seemingly similar problem , where a mobile impurity is coupled to a continuum of gapless excitations at a quantum critical point , instead of gapless particle - hole excitations at a fermi surface . in particular , we want to study the situation where bosons in an optical lattice are tuned to the superfluid - mott insulator transition,@xcite and a single atom of a different species is coupled to the bosons via a density - density interaction . this scenario is especially interesting due to the recent experimental implementation of quantum - gas microscopes,@xcite which allow tracking the motion of the impurity through the bosonic bath . indeed , a recent combined experimental and theoretical work has addressed a very similar situation in an effectively one - dimensional system.@xcite we are going to focus on the other experimentally relevant , two dimensional situation instead . from our perspective , this case also happens to be the most interesting scenario , because in @xmath0 spatial dimensions the critical behavior at the sf - mi transition is described by a non - trivial fixed point without well - defined quasiparticle excitations.@xcite recently there has been a renewed interest in this particular transition as experiments succeeded in observing the so - called higgs amplitude mode.@xcite the main motivation for our work is the prospect of studying aspects of quantum critical transport in a clean , well - defined experimental setting . calculating transport coefficients of systems close to a quantum phase transition remains a challenging problem in theoretical condensed matter physics . the main reason is that all traditional methods for calculating transport properties rely on a quasiparticle picture of the low - energy excitations above the ground - state , which breaks down at a quantum critical point . indeed , strongly coupled conformal field theories ( cft ) that describe physical properties of physical systems close to quantum critical points typically have no well defined quasiparticle excitations . some progress has been made recently using the so called ads / cft correspondence , which circumvents this problem by mapping the strongly coupled cft to a dual , weakly coupled gravitational theory , where transport coefficients can be computed reliably.@xcite in this paper our main interest is to calculate the diffusion constant @xmath1 of the impurity as a function of temperature in the quantum critical regime , shown in fig . [ fig : phase ] . this diffusion constant can be measured directly in experiments with quantum - gas microscopes by evaluating the mean square displacement @xmath2 of the impurity atom from its initial position after a time @xmath3 @xmath4 where the brackets denote an average over many experimental realizations and the time @xmath5 has to be larger than the typical collision time @xmath6 , below which the impurity propagates ballistically . several theoretical works have addressed similar questions using the holographic correspondence in the context of a heavy quark moving through a quark gluon plasma.@xcite here we will use a conventional method based on the boltzmann equation , however , which turns out to provide an adequate description at low temperatures . the quantum criticality of the bulk critical point has a single characteristic time which controls transport and relaxational processes close to equilibrium @xmath7.@xcite we will show here that the situation with impurity motion is not as universal , and the impurity time scale is determined by an interplay between several couplings which are formally irrelevant at the critical point . one of the these couplings is the inverse effective mass , @xmath8 , of the mobile impurity ; there is the associated energy scale @xmath9 , where @xmath10 the velocity of the bulk bosonic excitations at the critical point . the value of @xmath11 controls the quantum wave packet spread of the impurity at short times . the other `` irrelevant '' parameters couple the impurity to the bulk excitations , and associated energy scales determine the diffusion of the impurity at long times even at the lowest temperatures . one of our interesting results is that the diffusion constant of the impurity does _ not _ depend on @xmath11 at low temperatures , however . the rest of the paper is organized as follows . in section [ sec : ft ] we derive an effective low energy theory for a mobile impurity coupled to bosons at the superfluid mott - insulator ( sf - mi ) transition and we show that the presence of three - body interactions changes the theory significantly at the particle - hole symmetric point . in section [ sec:2p ] we study perturbative self - energy corrections to the impurity propagator and calculate its diffusion constant as a function of temperature , neglecting three - body interactions . we repeat these calculations including three - body interactions in section [ sec:3p ] and show that this changes the results qualitatively at low temperatures . finally we perform a renormalization group analysis of the effective field theory in sec . [ sec : rg ] . we start by deriving the effective low - energy theory for a bose - hubbard model at the sf - mi critical point in @xmath0 spatial dimensions , following ref . . a convenient starting point is to consider particle- and hole- excitations on top of a mott insulating state , which are described by the lagrangian @xmath12 here the fields @xmath13 and @xmath14 represent particle- and hole excitations on top of a state with an integer filling of bosons . the respective energy gaps for these excitations are denoted by @xmath15 and @xmath16 , their effective masses by @xmath17 and @xmath18 . the last term in eq . creates or annihilates particles and holes in pairs , as required by the conservation of the total number of bosons , and we do not explicitly show higher order terms in the fields @xmath19 and @xmath20 that are allowed by symmetry . ultimately we are interested in the experimentally relevant situation where the transition happens at a constant density , i.e. at the tip of the mott - lobe . this happens only if the gaps @xmath15 and @xmath16 are equal , such that particles and holes condense at the same time when the gap closes . for the moment we will consider the general case , however , and parametrize the gaps as @xmath21 now we add a single , mobile impurity atom to the bosons , the dynamics of which is described by the free particle lagrangian @xmath22 where the field @xmath23 represents the impurity and the chemical potential @xmath24 has to be adjusted such that the density of impurities is zero . this is important only at finite temperatures , however , where we need to ensure that no artificial , thermally excited impurities exist . at zero temperature we can safely set @xmath25 . within a microscopic bose - hubbard like model the coupling between the impurity and the bosons is an onsite density - density interaction , which is a pure two - body interaction in the simplest case . since the local boson density is given by the difference between particle- and hole- densities ( up to the constant average number of bosons that we neglect in the following , as it only renormalizes the impurity s chemical potential ) , the interaction term in our effective field theory takes the form @xmath26 where the subscript @xmath27 of the coupling constant @xmath28 indicates that this term derives from a two - body interaction . furthermore we include a term that descends from a three - body interaction @xmath29 because in the case of particle - hole symmetry ( @xmath30 ) this interaction generates couplings that are _ more _ relevant in an rg sense than those deriving from two - body interactions only , as will be shown below . to avoid confusion we note that a three - body interaction in the bose - hubbard model of the form @xmath31 , where @xmath32 denotes the number of bosons on site @xmath33 and @xmath34 is the impurity creation operator , also generates a term of the form in addition to . for brevity we will always refer to the term in as the three - body interaction , however . eventually our system is described by the total lagrangian @xmath35 in order to arrive at the more familiar low energy theory for the sf - mi critical point we define the fields @xmath36 and integrate out the field @xmath37 . after a rescaling of @xmath38 and defining @xmath39 as well as @xmath40 we arrive at our final result @xmath41 the terms shown are the leading order terms within a gradient expansion . for the case of particle - hole symmetry ( @xmath42 , i.e. @xmath43 ) the dynamical critical exponent of the bosons is @xmath44 and the critical point is described by the well known @xmath45 cft in @xmath46 dimensions . even more interesting , the direct interaction term between the bosons and the impurity @xmath47 vanishes if only two - body interactions are present . this somewhat counterintuitive result ( in the sense that the particle - hole symmetric interaction term vanishes if the @xmath48-theory is particle - hole symmetric ) can be understood from the fact that the two - body interaction term @xmath49 is invariant under a particle - hole transformation ( @xmath50 ) _ only _ in combination with @xmath51 . this is not true for the three - body interaction term @xmath52 , however , and that is why the parametrically smaller @xmath53 generates a term that is more relevant than the one generated by two - body interactions at the particle - hole symmetric point . the leading order terms that are consistent with the symmetry @xmath54 = \mathcal{l}[\psi^ * ; -\delta ,- u_2,u_3 ] \label{syms}\ ] ] are the ones shown in eq . . also note that the two - body interaction @xmath28 couples the impurity density @xmath55 to the time - like component of the bosonic current - density @xmath56 . we stress again that we focus solely on the particle - hole symmetric case ( @xmath30 ) in the rest of the paper . a tree - level scaling analysis of the lagrangian using the exact critical exponents of the bosonic cft shows that both interactions @xmath28 and @xmath53 are irrelevant in @xmath0 spatial dimensions at the p / h - symmetric point . indeed , performing a scaling with @xmath44 gives the scaling dimensions @xmath57 = ( d-1+\eta)/2 $ ] and @xmath58 = d/2 $ ] for the fields , as well as @xmath59 = d+1 - 1/\nu$" +"the famous debate between einstein , podolsky , rosen ( epr ) and bohr @xcite , about the nature of quantum correlations of a bi - partite state has played a key role in the investigation of entanglement properties of light in modern quantum optics , and has initiated a new branch of physics called quantum information . epr used in their arguments a wave function that exhibits a perfect correlations between positions and momenta of two massive particles ( labeled @xmath0 and @xmath1 ) . in the position and momentum representations the epr state takes the following forms @xmath2 quantum correlations of the entangled epr state have been implemented experimentally for massless particles : photons . in the case of light , the quantum mechanical position and momentum observables are played by the electric field : phase and amplitude quadratures . the well known two - mode gaussian squeezed states of light are physical realization of the epr state . those states lie at the heart of quantum cryptography @xcite , quantum information @xcite and quantum teleportation @xcite . there are few efficient ways of producing gaussian epr correlated states . one of them uses a kerr nonlinear medium in optical fibers to entangle phase and amplitude quadratures @xcite . however , the nonlinearity has to be relatively small to achieve a gaussian state . the other method uses a beam splitter as a nonlocal operation that creates entanglement . a typical setup consists of two initially separable amplitude squeezed beams which interfere at the 50/50 beam splitter . recent applications of entangled two - mode squeezed states of light in quantum information processing have generated a lot of interest in mixed gaussian states . although there are mathematical criterions for the entangled properties for mixed two - partite gaussian systems @xcite , they are not easy experimentally realizable . it is the purpose of this paper to show that hanbury - brown and twiss ( hbt ) interference can reveal the quantum nature of entanglement of two - particle mixed gaussian states . we show that it is possible to construct a quantum witness operator , closely related to the hbt interference @xcite , that probe entanglement of a mixed epr gaussian state . using hong , ou and mandel ( hom ) interferometry we discuss the entangled properties of time resolved interference of the epr state . we show that the deep in hom interference can provide a useful tool to study quantum separability of continuous - variable gaussian epr states . a non - degenerated optical parametric amplification , involving two modes of the radiation field , provides a physical realization of the epr state ( [ epr ] ) . the quantum state generated in this process has the following form @xmath3 is a thermal distribution with a mean number @xmath4 of photons in each mode . using field quadratures eigenstates : @xmath5 , we obtain that the wave function of such a system ( [ epr2 ] ) is gaussian and has the form @xmath6 in the limit of @xmath7 , the two - mode squeezed state ( [ nopa ] ) becomes the original epr state ( [ epr ] ) . the state ( [ nopa ] ) is not entangled only if @xmath8 . the simplest mixed generalization of the epr state involves a gaussian density operator @xmath9 , being a gaussian operator of the field modes described by the annihilation and creation operators @xmath10 and @xmath11 . this gaussian density operator of the two modes is fully characterized by its second moment expectation values of the modes . in the case of a mixed epr state the only non - vanishing field correlations are @xmath12 where @xmath4 is a mean number of photons in each mode , and @xmath13 correspond to the amount of correlation between the two modes . for @xmath14 , the epr state reduces to the pure state given by ( [ nopa ] ) . as it has been discussed in several papers ( see the tutorial @xcite and references therein ) , this mixed epr state is separable for @xmath15 and its density operator can be expressed in a sum of product states ( werner separability criterion ) @xmath16 where @xmath17 , @xmath18 are the density operators of the two modes and @xmath19 , with @xmath20 . the mixed epr state is entangled and non - separable if @xmath21 second and higher orders of coherence of a light beam can reveal its quantum nature , which can not be observed in young - type interference experiments . second - order interference involving intensity - intensity correlations have been first applied by hanbury - brown and twiss in stellar interferometry @xcite . in modern quantum optics , second - order interference has been used as powerful tool to study nonclassical properties of light @xcite . hanbury - brown and twiss ( hbt ) interference measures a second - order normally ordered intensity - intensity correlation function . in fig . [ fig:2 ] we have depicted a setup for hbt interference that involves two light beams with annihilation operators @xmath0 and @xmath1 interfering at the beam splitter . a correlation between clicks of two detectors corresponds to a normally ordered intensity - intensity correlation function . the hbt interference exhibits a typical pattern of the form : @xmath22 , where @xmath23 and @xmath24 are phase differences between the beams @xmath0 and @xmath1 in front of the detectors . these phases include geometrical phases and phases due to the possible action of the beam splitter . in this setup the two phases can be controlled experimentally . @xmath25 is a second - order interference visibility . for a classical source of light this visibility is always bounded : @xmath26 . this classical limit is violated for single photons , as it has been shown in the pioneering experiments performed by mandel @xcite . @xmath27 we shall apply the hbt setup to study the mixed gaussian epr state . at the detectors ( @xmath28 ) the positive - frequency part of electric field corresponding to modes @xmath29 and @xmath30 ( normalized to the number of photons ) is as follows @xmath31 the corresponding field intensity operator at the screen is equal to @xmath32 from this expression , we obtain that the normally ordered second - order intensity correlation is @xmath33\,.\end{aligned}\ ] ] for the epr beams in a mixed state , with mean @xmath4 photons and correlation @xmath13 described by the relations from eq.([eprcorr ] ) , the fourth - order field correlations needed in the hbt calculations are equal to @xmath34 as a result the hbt intensity correlation function ( [ eq : hbt_correlation ] ) , for a continuous variable mixed epr state , has the following form @xmath35 with the second - order fringe visibility equal to @xmath36 for a separable ( classical ) output state we have : @xmath37 . in the case of no correlation in the output state @xmath38 , the visibility is @xmath39 , as it should be for a thermal state . for entangled states this visibility is quantum i.e. , it violates the classical inequality : @xmath40 . in fig . [ fig : visibility_1 ] and fig . [ fig : visibility_2 ] we have depicted the visibility ( [ eq : visibility_epr ] ) as a function of the correlation parameter @xmath13 for two different values of @xmath41 . based on the above visibility analysis one can introduce a hbt witness operator @xmath42 the mean value of this operator , @xmath43 is positive for separable mixed epr states and negative for entangled mixed epr states . the analysis of second - order interference , can be extended to the case of photon pulses which duration is long compared to the time resolution of photodetector . such single - photon emitters are already in use @xcite . a source produces single photon pulses with a relative delay which interfere at the beam splitter . simple analysis of beam splitter s action on impinging photons shows , that both photons will leave the same outport of the beam splitter . a relative delay is small enough to keep the pulses partially overlapping . even though the overlapping is not complete , its time duration is longer than the time resolution of the detector . therefore , the temporal effects can not be neglected any more when detecting pulses and the time delay @xmath44 between detected pulses at two separate detectors has to taken into account . experiments investigating interference for such pulses with different frequencies have already been performed @xcite . we restrict our description of the single - photon wave packets in the space - time domain to one - mode fields with electric field operators : @xmath45 and @xmath46 . the phases @xmath23 and @xmath24 are included in the mode functions phases . these mode phases contain an additive stochastic component related to the random arrival time of the correlated photons at the beam splitter or detectors . the time dependent electric fields of the two - mode output state is described by the beam splitter transformation ( see eq . ( [ eq : bs_transformation ] ) ) @xmath47 the joint coincidence of detecting photons from mode @xmath29 and @xmath30 at delayed times @xmath48 and @xmath49 can be obtained directly from the following second - order temporal coherence function @xmath50 using the mode functions , with random phases in the output state , we note that the only contributing terms to the second - order coherence function are the following @xmath51\ , \langle a^{\dagger}b^{\dagger } a\ , b\rangle\big\}.\end{aligned}\ ] ] as an example we shall use in the calculations a special model of phase fluctuations . we will assume that the mode functions have random phases typical for a stationary stochastic phase diffusion model . in this example , the only non - vanishing autocorrelations of the mode functions are @xmath52 in these formulas we have assumed that the statistical correlations are stationary and gaussian with coherence times @xmath53 and @xmath54 . the stationary intensities are : @xmath55 and @xmath56 . applying the above temporal correlations of the mode functions , combined with the epr correlations of a mixed state given by eq . ( [ 4correlations ] ) , we obtain that the second - order coherence function is stationary ( dependents only on time @xmath44 ) and has the form @xmath57 we shall simplify this formula further assuming that the mode intensities are equal : @xmath58 . setting @xmath59 the formula above reduces to @xmath60 with the second - order visibility @xmath25 equal to ( [ eq : visibility_epr ] ) . from this formula we obtain that a joint coincidence probability to detect a photon at time @xmath48 and another photon at time @xmath49 is @xmath61 where @xmath62 is a dimensionless time with @xmath44 expressed in units of @xmath63 . this coincidence probability exhibits a typical hong - ou - mandel deep @xcite . in fig . [ fig : ent_pure_1 ] , we have depicted the joint coincidence probability for a state with @xmath64 . the upper curve ( @xmath64 and @xmath65 ) is a border between separable and nonseparable epr states . the lower curve ( @xmath64 and @xmath66 ) describes hom interference of an entangled pure epr state . the region between the two curves corresponds to nonseparable mixed epr sates . for @xmath64 the minimum value the hom deep for a pure state is achieved at a zero coincident rate and is equal to @xmath67 . for the epr state given by eq . ( [ epr2 ] ) , with a small value of @xmath4 , one can get a significant increase of the the deep . for a weak two - mode pure squeezed state @xmath68 we can approximate the formula ( [ epr2 ] ) by" +"the investigation of strangeness contributions to static properties of the nucleon is particularly interesting as it gives unambiguous access to low - energy manifestations of virtual or sea quark effects . different strangeness currents of the form @xmath1 test the strangeness component of different nucleon observables , such as mass ( @xmath2 ) , spin ( @xmath3 ) , or magnetic moment ( @xmath4 ) . here we are concerned with the magnetic moment only , or , more generally , with the nucleon form factors of the vector current . the standard model provides access to two different flavor combinations of the three light quark contributions to the electric ( @xmath5 ) and magnetic ( @xmath6 ) form factors due to the electromagnetic and the weak vector currents , @xmath7 -1 mm in order to obtain a full flavor decomposition of the vector current , one therefore has to invoke isospin ( or charge ) symmetry in the form @xmath8 and use the neutron electromagnetic form factors as the third input . these relations are at the heart of the extensive experimental program to extract the _ weak _ form factors of the proton @xmath9 from parity - violating electron scattering @xcite . if one relaxes this assumption and allows for charge - symmetry breaking , however , the relation between weak vector form factors , electromagnetic form factors of proton and neutron , and strangeness is complicated by an additional term , @xmath10 where @xmath11 . in other words , the charge - symmetry - violating form factors @xmath12 generate `` pseudo - strangeness '' , and in order to reliably extract strangeness effects , the former have to be calculated from theory . this is becoming a necessity in particular in view of the increasingly tighter bounds on strangeness deduced from experiment @xcite . the isospin - breaking form factors @xmath12 have been addressed in various models of the strong interactions , in particular in constituent quark @xcite or light - cone meson baryon models @xcite ( see also ref . @xcite for a comparative review ) . these are afflicted by several problems : first , as in general with model calculations , it is extremely difficult to quantify the inherent uncertainties ; second , the symmetries of the standard model may be violated . e.g. , quark models @xcite predict @xmath13 for the charge - symmetry breaking magnetic moment , which is only due to a specific symmetry of the quark model wave function employed , not , as we shall see below , due to a symmetry of the standard model , and may consequently lead to an underestimation of isospin - breaking effects in particular at small @xmath14 . chiral perturbation theory ( chpt ) @xcite , on the other hand , is ideally suited for an analysis of isospin violation . it is tailor - made to analyze the dependence of low - energy observables on quark masses , in particular on the light quark mass difference @xmath15 , and the consistent inclusion of electromagnetic effects is also well - understood @xcite . as the isospin - violating form factors can be calculated in su(2 ) chpt , they are not affected by convergence problems to the extent the strangeness form factors are ( see ref . @xcite for a review on the latter ) . particular emphasis will be put on the analysis of the leading moments of the isospin - violating form factors , magnetic moment as well as electric and magnetic radius terms , @xmath16 the two radius terms are unaffected by low - energy constants up to leading ( @xmath17 ) and next - to - leading ( @xmath18 ) order and can be expressed entirely in terms of the neutron - to - proton mass difference @xmath19 @xcite , with the result @xcite @xmath20 note that these expressions for the radii are entirely non - analytic in the quark masses . their simplicity is remarkable : the pion mass difference @xmath21 can not play a role as it only breaks charge _ independence _ , not charge symmetry ; furthermore , up to @xmath22 for @xmath23 and @xmath24 for @xmath25 , no photon loops contribute , nor are there any two - loop effects . in fact , chpt is more predictive here than for the usual electromagnetic form factors of the nucleon ( see e.g. ref . @xcite ) , precisely because polynomial counterterm contributions must be suppressed by isospin - breaking factors @xmath15 or @xmath26 , and hence by two orders in the chiral expansion . in order to complete the chiral representation , we have to estimate the combination of low - energy constants entering @xmath27 . this is done by invoking the principle of resonance saturation : low - energy constants in effective theories incorporate the effects of heavier states not included in the theory as explicit degrees of freedom . in our case , the relevant contributions are provided by vector mesons including @xmath28 mixing @xcite : @xmath29 ~ , \nonumber \\ g_m^{u , d}(t ) \bigr|_{\rm mix } & = & \frac{\theta_{\rho\omega}}{m_v(m_v^2-t)^2 } \bigl [ \bigl(t + \kappa_\omega m_v^2\bigr)g_\omega f_\rho - \bigl(t + \kappa_\rho m_v^2\bigr)g_\rho f_\omega \bigr ] ~. \label{eq : mix}\end{aligned}\ ] ] the necessary couplings can be extracted from experimental data within certain errors . such an inclusion of phenomenological vector - meson contributions has been shown to cure the main deficits of a chiral one - loop representation of the usual nucleon electromagnetic form factors @xcite , and is expected to work even better here due to the stronger suppression of even higher mass states in the mixing amplitudes . still , the uncertainties in particular in the vector - meson nucleon coupling constants @xmath30 , @xmath31 @xcite limit the precision of the prediction for the isospin - violating form factors ; see ref . @xcite for a detailed discussion . although , strictly speaking , the chiral representation of the form factors to @xmath22 ( @xmath23 ) and @xmath24 ( @xmath25 ) only requires an estimate for the low - energy constant entering the isospin - violating magnetic moment , the representation eq . also allows to assess higher - order counterterms contributing to the radii . numerically one finds that , although formally subleading , the large vector - meson couplings tend to overwhelm the loop contributions eq . in the radii , which scale with the ( small ) nucleon mass difference . we therefore include the full mixing amplitudes in the final predictions . the total results for the charge - symmetry - breaking form factors are shown in fig . [ fig : ffresults ] . the error bands combine an estimate of chiral corrections at higher order with the above - mentioned uncertainties in the input coupling constants for the resonance contributions . although these combined uncertainties are sizeable , several conclusions can still be drawn : the effects of isospin breaking remain at the percent level ; the @xmath14-dependence of the form factors is rather moderate in the low - energy region . we note that the symmetries of the standard model do _ not _ dictate @xmath27 to vanish , indeed we find @xmath32 . the validity of these results , and in particular of the prediction for @xmath33 @xcite , has been criticized as an `` extreme estimate '' in ref . @xcite and too large in comparison to ref . @xcite ; in particular the input on @xmath34 , @xmath35 @xcite has been questioned . this criticism is unwarranted for the following reasons . the central value for @xmath27 is due to pion - loop contributions at a scale @xmath36 , where changing the scale by a factor of 2 leads to a shift of @xmath37 only . completely scale - independent is the next - to - leading order correction in @xmath27 ( which is @xmath38 , hence non - analytic in the quark masses ) , which can be read off as the difference between the full and the dashed curve in the magnetic form factor in fig . [ fig : ffresults ] , and which contributes roughly 40% of the central value . the potentially controversial vector meson contributions only lead to the uncertainty range of @xmath39 . furthermore , the large anomalous @xmath40 coupling found in ref . @xcite leads to the _ lower _ edge of the band in @xmath25 , fig . [ fig : ffresults ] , hence to a sizeable cancellation with the pion - loop terms ; reducing these couplings makes the total result larger , not smaller . quite to the contrary , the quark model results for @xmath25 @xcite are too small at low @xmath14 by wrongly enforcing @xmath41 to vanish . cccc experiment & electric / magnetic & @xmath42 & @xmath43 + sample & @xmath6 & @xmath44 & @xmath45 + a4 & @xmath46 & @xmath47 & @xmath48 + happex & @xmath49 & @xmath50 & @xmath51 + table [ tab : results ] compares the specific linear combinations of @xmath23 and @xmath25 at @xmath52 with the experimentally extracted values for strangeness form factors . we find that the charge - symmetry - breaking shifts are still smaller than other experimental uncertainties , but should be kept in mind for precision determinations of strange matrix elements . as another illustration , in the latest combined analysis of forward and backward asymmetries at a4 @xcite , the following values for the strange form factors were extracted at @xmath53 : @xmath54 isospin breaking shifts the central values according to @xmath55 for @xmath56 and @xmath57 for @xmath58 , with negligible additional errors due to the theoretical uncertainties of @xmath59 and @xmath60 , respectively . again , these shifts are within the given error bars , but already of a comparable size . parity - violating electron scattering on @xmath61he gives clean access to the strange _ electric _ form factor @xmath56 , as the @xmath62 target does not allow for magnetic or axial vector transitions . however , in addition to effects of charge - symmetry breaking in the electric form factor as discussed in the previous section , an @xmath63 admixture in the @xmath61he wave function yields a contribution to the measured asymmetry @xmath64 @xcite , @xmath65 where @xmath66 are the nuclear form factors corresponding to isoscalar / isovector charge operators , and @xmath67 is a different isospin - breaking linear combination of single - nucleon form factors . the measured asymmetry @xmath68 \times 10^{-6}$ ] at @xmath69 gev@xmath70 @xcite leads to @xmath71 . single - nucleon isospin violation contributes @xmath72 to @xmath73 , while isospin mixing in the @xmath61he wave function amounts to @xmath74 , leaving a mere strangeness contribution of @xmath75 . we have performed an analysis of the charge - symmetry - breaking nucleon form factors , using a combination of chiral perturbation theory and resonance saturation that relies as far as possible on the symmetries of the standard model and experimental data . although we predict the isospin - breaking magnetic moment @xmath76 to be different from zero ( in contrast to certain model predictions ) , both electric and magnetic form factors are small , and their momentum - transfer dependence moderate . the contributions of isospin violation to parity - violating asymmetries are as yet smaller than some of the experimental uncertainties in extracting strange form factors , but clearly , charge - symmetry - breaking effects become an essential ingredient for precision extractions of strangeness matrix elements . i am grateful to my coworkers randy lewis , michele viviani , and rocco schiavilla for a very fruitful collaboration , and further to randy for useful comments on these proceedings . i thank the organizers of pavi09 for the invitation to this most enjoyable workshop . partial financial support by the project `` study of strongly interacting matter '' ( hadronphysics2 , grant" +"the global financial crisis that started in 2007 has stimulated an extensive literature on numerous credit - related themes such as risk assessment , financial contagion , regulatory indebtedness or liquidity ratios , misuse of derivatives ( see for example @xcite ) . as the crisis unfolded , the understanding of the credit exposure at an individual bank level , as well as at an aggregate systemic standpoint became increasingly important . a given bank was perceived safer or riskier based not only on its balance sheet figures or growth estimates , but also on the financial strength of the insurance companies who would step in in the case of a debtor s default , the financial distress of the peers with whom the bank had more interbank exposure , liquidity dry - ups which could trigger massive asset fire - sales , or even the assigned probability to a lender of last resort type of bailout from the central government @xcite . insurance companies played a key function in the network : they had the commitment to enter the scene if a given asset failed to make promptly payments . however once it became clear that insurance companies would be not be able to compensate for every risky asset they had insured , it also became apparent that a financial distress event could propagate across the entire financial system @xcite . banks would have to start recognizing massive asset losses , and if a bank defaulted , other interconnected institutions could follow , potentially triggering a bankruptcy cascade @xcite . people fearing for its savings could line up and withdraw their deposits causing a so - called bank run , as was for example observed in the united states , united kingdom , iceland , spain , or brazil @xcite . this context is pertinent to the present work , as nowadays much of the discussion continues to be how to define and regulate higher capital requirements , while at the same time weighting the trade - offs involved , namely higher costs , or lending shifting to the shadow banking ( @xcite ) . this paper contributes to this academic discussion by using a network - based framework to examine the structure and inner dynamics behind the links between financial institutions in different countries . the application of network theory to the financial markets @xcite gave place to a new set of methodologies to study interaction in interconnected agents , institutions or financial products ( e.g. portfolios , stock indices , derivatives ) . however its literature is fairly recent , and to our knowledge none has studied the banking system structure using actual ( non - simulated ) data from banks financial statements across several countries . to the extent that actual interbank data ( e.g. loans , repos , swaps ) is not publicly available , we argue that relevant implications can still be derived upon the common behavior of certain key balance sheet items . as we have learned from the crisis , two banks can be exposed to each other s risk , even if there is no financial transaction between them : if a bank fails , market conditions ( liquidity , stock prices , mergers or acquisitions expectations ) are all likely to experience cascade consequences . in general , financial institutions , be them commercial banks , investment banks , development banks , broker - dealers , or credit unions , fall under the supervision of each country s central bank . these institutions , henceforth referred to as banks , must usually submit their quarterly or monthly financial statements to the corresponding central bank regulator . this article takes advantage of that rich , homogeneous and regular available information , and uses balance sheet data from 2005 to 2010 from five emerging countries : argentina , brazil , mexico , south africa , and taiwan . we then construct banking functional networks from the leverage dependence across financial institutions , and analyze the structure of this networks . we find configurations that tend to group into large clusters at relatively low correlation levels . a modular structure characterized by one large bank community , some small ones and isolated banks is also found in all countries . in addition , we propose and simulate a model of corporate and interbank loans that generates rich and diverse balance sheet growth . and when we construct simulated banking functional networks according to their leverage dependence , we find results that are consistent with the empirical networks . despite the absence of actual interbank contracts , these findings translate into relevant policy implications in terms of contagion and concentration , as well as suggest potential avenues for future research . the paper is divided as follows . section ii describes the data and the methodology , section iii describes the main results of the paper , section iv simulates a model of interbank loans and compares with empirical data , and section v concludes . we study the interaction between financial institutions using balance sheet data from 2005 to 2010 from five developing countries : argentina , brazil , mexico , south africa , and taiwan . we retrieve total assets and total liabilities for each financial institution sampled at a monthly or quarterly basis , whichever is more frequent in its reporting . let @xmath0 and @xmath1 be the total assets and liabilities , respectively , for bank @xmath2 at time @xmath3 . for each country , the number of banks @xmath4 , fluctuates in time , and thus @xmath5 is a stochastic birth and death process . throughout the observed period 2005 - 2010 the existing banks at 2005 may fall bankrupt , merge with others , or simply survive until 2010 . on the other side , new banks can appear in between , say in 2006 , thus modifying @xmath5 as well . as the purpose of this work is to study the interaction between banks , we shall remove from the dataset those banks with incomplete observations . for example , if a bank stops or starts reporting data in 2007 , its observations are removed from that country . let @xmath6 be the banks that satisfy the previous condition , i.e. the effective number of banks studied . the following table shows both the number of banks in 2005 and 2011 ( @xmath7 and @xmath8 ) , as well as the number of banks present throughout the time investigated ( @xmath6 ) . table 1 also includes the number of banks births ( deaths ) , @xmath9 ( @xmath10 ) , during the period 2005 - 2011 . . financial system size of the five countries studied in the period 2005 - 2011 . @xmath11one bank from brazil and one from south africa were excluded because of missing data in some time periods . [ cols=""^,^,^,^,^,^ "" , ] for instance in brazil 49 banks were created and 28 disappeared between 2005 and 2011 . only two of these new banks have gone out of the banking system before 2011 . except for brazil , the rest of the countries satisfy the following equation : @xmath12 we divide the countries into two groups according to their size @xmath6 , one composed by argentina and brazil , and the other composed by mexico , south africa and taiwan . the first group represents a large size banking system with @xmath13 and the second a smaller banking system with @xmath14 . also notice the different dynamics between brazil ( also mexico ) and taiwan : whereas in the former country the number of banks increased over time , in the latter decreased . by contrast , argentina and south africa exhibit very small fluctuations in @xmath5 for the period studied . the construction of a network of associations out of balance sheet variables requires selecting an interaction metric that meets two general properties . first , it should be robust to spurious correlations so that we avoid as much as possible to use a non - stationary variable that may increase or decrease simply following a global trend . and second , it should be relevant to describe an economic process . in other words , if two banks are associated with a given variable , it should mean that they are subject to certain equivalent market or economic conditions , and therefore may share the same risk . we argue that balance sheet aggregates such as assets are inappropriate to define a network , and instead propose to use the leverage ratio . consider for instance total assets , which are regarded as a proxy of bank size , and are subject to a large number of global or macroeconomic circumstances . under normal market conditions , the assets of a financial institution are expected to grow with time , as a result of general growth of the economy , inflation , balance sheet effects from expansionary monetary policy , population ( customer base ) growth , increased access to banking services ( banking penetration ) , higher value of the securities held by the bank ( stocks or debt ) . it seems that almost any pair of banks , regardless whether they are contractually linked or not , will yield a positive assets correlation , and thus will incorrectly suggest an overlinked network . we instead propose using the degree of indebtedness , henceforth referred to as the leverage ratio , as the metric on which to base the interactions . we define the leverage as follows @xmath15 where liabilities and equity refer to the balance sheet variables of a given bank which must satisfy the usual accounting identity : @xmath16 , and as measured at book value . therefore , the leverage ratio of bank @xmath2 , @xmath17 , indicates what fraction of equity and debt this bank is using to finance its assets . consider for instance panel ( a ) and panel ( b ) of fig . 1 , which shows an example where the leverage increases and decreases , respectively . the former may happen , for instance , through a credit quality shock , such that the value of the existing claims decreases and the bank increases its loan loss provision . such loan write - offs translate into a reduction in total equity , thus increasing the ratio . the leverage can also rise if , for example , the bank simply issues debt to finance a potential acquisition or expand its credit portfolio . what regards to panel ( b ) , a bank may deleverage by prepaying debt with its own cash , where both total assets and liabilities decrease . it is also possible for the shareholders to conduct a capital increase , with proceeds either paying down debt or cushioning its assets . these examples illustrate only a few of the many different scenarios why a leverage ratio may fluctuate within a given financial institution . finally , to address the stationary concern fig . 2 depicts the median ( results remain unchanged with the average ) leverage ratio for each country as a function of time . contrary to what happens with liabilities and assets ( fig . a.1 ) , the leverage ratio does not exhibit any strong time dependence . each country exhibits its own leverage range , with more or less fluctuations over time . taiwan , for example , is characterized by exhibiting a large median leverage ratio ( @xmath18 ) while argentina and brazil exhibit a lower ratio ( @xmath19 ) . leverage levels across countries are expected to differ due to different bank capital regulation . each country may impose its own restrictions on hedging operations , ability to buy or sell foreign currency , place debt in the national or international markets ( and at which currency" +"gamma - ray bursts ( grbs ) are the most powerful explosions in the universe , and are thus considered to be a possible source of ultra - high energy ( uhe ) cosmic rays . short - duration bursts are believed to be a result of the collision of two compact objects and long - duration bursts are thought to be beamed emission from the collapse of a high - mass star into a black hole . see @xcite for reviews of the basic theories of grbs . in the widely - accepted fireball shock model , relativistic plasma in a jet collides either with the surrounding material or with the outflow itself , producing the observed gamma - ray prompt emission through synchrotron and inverse compton scattering of electrons @xcite . protons are also thought to be accelerated in these shocks via the fermi mechanism @xcite . these uhe protons then interact with the photons , going through a @xmath10 resonance and producing charged pions which decay , yielding uhe neutrinos @xcite . the first calculations of this prompt uhe neutrino emission use an e@xmath11 proton injection spectrum with energies up to e=@xmath12 gev , and predict an e@xmath13 neutrino spectrum in the uhe regime , with the steepening of the spectrum due to synchrotron cooling of the uhe pions @xcite . the detection of uhe neutrinos from grbs would support their identification as the sources of the highest energy cosmic rays , a longstanding mystery in particle astrophysics . previous searches for neutrino production have been perfomed by the icecube @xcite and rice collaborations @xcite , but this is the first search for uhe neutrinos from grbs above 10@xmath9 gev . a full description of the anita - i instrument can be found in @xcite , and a description of instrument modifications for anita - ii is in @xcite and @xcite . briefly , the anita experiment is a nasa long duration balloon experiment that searches for coherent , impulsive , broadband radio emission ( 200 - 1200 mhz ) from electromagnetic showers induced by uhe neutrinos interacting in the antarctic ice sheet @xcite . the second flight of the anita experiment launched on 2008 december 21 , flew for 31 days , 28.5 of which were live days , and recorded over 26 million triggers . forty quad - ridged , dual - polarization horn antennas search for radio impulses which could be caused by neutrino interactions in the ice sheet . the trigger requires coherent power in neighboring antennas , and the threshold is limited by thermal - noise emission from the ice . over 98.5% of recorded events were fluctuations of thermal noise . the trigger is designed to optimize efficiency on neutrino - like signals : vertically - polarized , broadband impulses . signals from each polarization of each antenna are recorded in a 100 ns window for each triggered event , allowing for directional determination on an event - by - event basis using interferometric techniques , also described at length in @xcite . anita is most sensitive to neutrinos which come from between the horizon and a payload elevation angle ( angle above the horizontal ) of @xmath14 . we are able to construct a more sensitive search for uhe neutrinos from grbs compared to the previously reported diffuse uhe neutrino search with anita - ii @xcite because the short time window given by the burst duration dramatically reduces background in the signal region , allowing us to lower our analysis threshold and look for very weak signals which also have a time and direction correlation with the observed grb . there are two sources of background for an anita neutrino search . the first is thermal - noise fluctuations , which are easily removed with a set of cuts on the strength of waveform correlation among neighboring antennas and the signal strength . the second is man - made noise , which can be removed because it tends to cluster with locations of known human activity and with other events . the details of event reconstruction , thermal - noise rejection , and man - made noise rejection are discussed in @xcite and @xcite . compared to the diffuse neutrino search , we loosen numerical values of thermal - noise cuts . the cuts against man - made noise remain the same . 00 abbasi , r. , _ et al . _ 2010 , apj 710 , 346 - 359 abbasi , r. , _ et al . _ 2011 , arxiv:1101.1448 alvarez - muiz , j. & halzen , f. 1999 , apj 521 , 928 askaryan , g. 1962 , jetp 14 , 441 becker , j. 2008 , phys . 458 , 173 - 246 besson , d. , _ et al . _ 2007 , astropart . 26 , 367 - 377 dermer , c. d. & atoyan , a. 2006 , new j. phys . 8 , 122 gcn : the gamma - ray bursts coordinates network , http://gcn.gsfc.nasa.gov/ gorham , p. , _ et al . _ 2009 , astropart . 32 , 10 gorham , p. , _ et al . _ 2010 , phys . rev . d 82 , 022004 ; arxiv:1011.5004 guetta , d. , _ et al . _ 2004 , astropart . 20 , 429 halzen , f. & hooper , d. 2002 , rept . 65 , 1025 meszaros , p. 2001 , science 291 , 79 meszaros , p. 2002 , ann . 40 , 137 meszaros , p. & rees , m. 1993 , apj 405 , 278 razzaque , s. , _ et al . _ 2003 , phys . rev . d 68 , 083001 vieregg , a. g. 2010 , phd dissertation , university of california , los angeles waxman , e. 2003 , nucl . 118 , 353 waxman , e. & bahcall , j. 1997 , phys . 78 , 2292 waxman , e. & bahcall , j. 1999 , phys . d 59 , 023002 waxman , e. & bahcall , j. 2000 , apj 541 , 707 wick , s. d. , dermer , c. d. , & atoyan , a. 2004 , astropart ." +"strongly - correlated electron systems are currently of great interest in the condensed matter physics and quantum chemistry communities . @xcite despite the differences , for example , between frustrated lattices and chemical bond breaking , the strong - correlation phenomenon in these systems has similar roots which are manifested by the breakdown of the mean - field picture . regardless of the details of the problem at hand , strong - correlation has significant impact on many important aspects of the physics of various systems and can not be ignored . @xcite a low computational cost , qualitatively correct description of strongly - correlated materials would have great impact on the quality of theoretical predictions . hence , the quest for developing novel , as well as improving existing approaches for strong - correlation continues unabated . one of the reasons that robust methods for the treatment of strong - correlation are so elusive is related to the size of the systems of current interest . with increasing number of electronic degrees of freedom , the numerical complexity of exactly solving the problem quickly becomes prohibitively large ; approximate methods must be therefore employed . an ideal approximation should provide a systematic and qualitatively correct description that is computationally accessible and does not deteriorate with system size . such an ideal tool would be therefore applicable to a broad range of problems . from a practical point of view , approximate methods should offer a good compromise between accuracy and computational cost . many methods are available to tackle the strong - correlation problem ; they include quantum and variational monte carlo , @xcite dynamical mean - field theory ( dmft ) , @xcite density matrix renormalization group ( dmrg ) @xcite , methods based on symmetry breaking and restoration , @xcite and methods based on a gutzwiller variational approach . @xcite this list is not , by any means , exhaustive . the effort to develop new approximations is continuously undertaken . recently , knizia and chan introduced density matrix embedding theory ( dmet ) , @xcite a novel and promising tool as demonstrated by the high quality results obtained on hubbard lattices . dmet has its roots in the embedding dmft framework , where the complexity of the entire system is reduced by partitioning the problem into a fragment plus an entangled bath . together , they constitute an impurity model . as opposed to dmft , the dmet impurity model is frequency - independent and therefore significantly simpler . @xcite dmet is designed to reproduce the entanglement of the impurity rather than its green s function . moreover , the construction of the effective bath is achieved in an algebraic way . in particular , if the impurity hamiltonian is defined in a basis derived from a product state , the complexity of the impurity basis construction amounts to a rather small matrix diagonalization . @xcite density matrix embedding theory has been benchmarked for model 1d and 2d one - band hubbard lattices , @xcite and in chemical systems . @xcite in the present work , we focus on the former in order to further investigate the properties of this novel methodology . in particular , we analyze the convergence criterion employed in the initial study . @xcite we follow the alternative criterion , introduced in ref . and prove that in periodic systems it allows us to gain full control over the lattice filling . additionally , we investigate the impact of the effective bath basis on the quality of results . the formalism here presented allows for spin symmetry breaking in the underlying lattice mean - field solution that is used to construct the key ingredients of the dmet procedure . the only symmetry constraint retained is lattice translational symmetry , although in the present work we understand it in an extended cell formalism . this means that the adopted translational unit cell is identical to the dmet fragment for which the calculations are performed . we also suggest an approximation that substantially reduces the number of parameters to be optimized . in particular , we show that it is sufficient to limit the density matrix fitting to diagonal elements , i.e. , we propose , what we call _ density _ , as opposed to _ density matrix _ embedding . we provide a detailed numerical analysis of the results obtained with this approach . in particular , we benchmark the aforementioned approximation against high quality reference data and exact solutions for energies , two - body correlation functions , and compressibility . the latter allows us to access the mott gap in the hubbard model . @xcite the present section is organized as follows . first , for clarity and to make this work self - contained , we review the basic principles of dmet . we discuss the properties of the embedding basis and sketch the algorithm . we then proceed to discuss the convergence criterion , which is by no means unique . the suggested route to incorporate broken symmetry embedding is described subsequently . in order to outline the key ideas of dmet , let us assume that we are given the exact ground state @xmath0 for the system of interest . then , it is possible to perform a schmidt decomposition of this wavefunction according to @xcite @xmath1 and @xmath2 can be chosen such that the former represents a particular set of lattice site states , which we call the fragment . the latter must then be the complement that spans all the sites excluded from @xmath3 , and we refer to it as the bath . the summation in the above equation is limited by the dimension of the smaller of these two sets . these bases are then used to project the hamiltonian into the schmidt states of the fragment , @xmath3 , and bath , @xmath2 @xcite @xmath4 details of matrix elements of the projected hamiltonian , usually refer to as impurity hamiltonian , are not relevant here . for a discussion regarding the impurity hamiltonian , the reader is referred to ref . . the key point to notice is that the size of the new basis ( though many - body in principle ) can be chosen much smaller than that of the original problem , if formulated in a single particle basis . as discussed in ref . , the original hamiltonian @xmath5 and the impurity hamiltonian @xmath6 share the same ground state @xmath0 ; information about the expectation values of @xmath5 can be extracted by studying @xmath6 . unfortunately , in practical applications , we do not have access to the exact solution . the embedding states have to be approximated . the fundamental simplification of dmet is to replace the exact solution with a mean - field ( here understood as hartree - fock ) wavefunction , which is a simple product wavefunction ansatz . in this case , the schmidt fragment and bath bases can be represented in terms of single particle states . this greatly simplifies the computational treatment of the impurity problem and , as we show in this section , provides an effective truncation of the dimension of single particle basis for the problem at hand . let us follow the procedure more closely on a specific example , a hubbard hamiltonian . in this case , @xmath7 where @xmath8 connects nearest neighbors , @xmath9 is the on - site repulsion parameter , and @xmath10 is an effective one - body potential that we wish to introduce ; the rationale behind this potential will become apparent in the following . at this point , let us just notice that @xmath10 is contained within the fragment and it is periodically replicated over the lattice . in the limit of vanishing potential @xmath10 , the hamiltonian reduces to the standard hubbard model . the first step in dmet is to solve the above problem at the mean - field level . this procedure yields a single slater determinant @xmath11 , where @xmath12 creates a hole ( occupied ) state @xmath13 and @xmath14 is a bare vacuum . the product runs from 1 to the number of electrons . the hole creation operators are defined by the underlying hartree - fock transformation @xmath15 from physical fermions @xmath16 , @xcite @xmath17 the basis @xmath18 takes into account the position and the spin degrees of freedom . in order to construct the fragment and bath states needed to define the impurity hamiltonian , we introduce the operator @xmath19 that projects the hole levels onto the single particle basis contained within the fragment . additionally , we have the complement @xmath20 such that @xmath21 , where @xmath22 is the identity operator . following ref . , one can define an overlap matrix @xmath23 , @xmath24 where the indices @xmath25 and @xmath26 run over hole states . this hermitian matrix can be brought to diagonal form by a unitary transformation @xmath27 satisfying @xmath28 , where @xmath29 contains at most @xmath30 nonzero eigenvalues ( here @xmath31 is the number of electrons in the lattice whereas @xmath32 is the size of the single particle fragment basis ) . in the following , we will assume that @xmath33 and that all @xmath32 eigenvalues are different from 1 and 0 ( otherwise , special care has to be taken while constructing the fragment and bath states ) . for each of the nonzero eigenvalues , one may construct a fragment state latexmath:[\[\begin{aligned } \label{fstate } and a bath state latexmath:[\[\begin{aligned } \label{bstate } the single particle states that correspond to vanishing eigenvalues of @xmath23 are considered as the inert core states @xmath35 . following ref . , the states corresponding to vanishing eigenvalues of @xmath23 denote orbitals with zero probability of being in the fragment space . similarly , one can think of the inert core states as states with vanishing coupling to the fragment states in the mean - field one - particle density matrix . the reader is referred to appendix [ ap : idem ] for more details . in dmet , the inert core single particle states are eliminated from the impurity problem ( _ i.e. _ they are not included while projecting the hamiltonian onto the impurity hamiltonian ) . therefore , dmet retains only a small portion of the large number of single particle states constituting the original hilbert space of the problem . in fact , the total dimension of the single particle basis is just twice the dimension of the single particle basis spanned by the fragment . this is clear from the particular properties of the spectrum of @xmath23 ( eq . [ mmat ] ) for the mean - field wavefunction . in other words , the hilbert space of the impurity model is significantly smaller than that of the original problem . it is also determined by the size of the fragment . armed with fragment and bath single particle states , which we shall refer to as an embedding basis , one can construct an impurity hamiltonian ( henceforth , for brevity of notation , the indices in the impurity hamiltonian denote spin and space coordinates ) , @xmath36 in the above , @xmath37 denotes bath creation operators whereas @xmath38 denotes either fragment or bath ones . the @xmath39 and @xmath40 denote the one- and ( antisymmetrized ) two - body terms of the hubbard hamiltonian projected onto the embedding basis , respectively . similarly , @xmath41 corresponds to the additional effective potential . at this point , we would like to point out that this potential , introduced in eq . [ eq : hubham ] , does not affect directly the one - body part of the impurity hamiltonian in the fragment space . in other words , the fragment part of the impurity hamiltonian corresponds to the physical hamiltonian . as the" +"superconductivity in cuprate materials still poses many questions that lack a theoretical understanding . one is about the maximum value of the critical temperature for superconductivity ( @xmath0 ) that could be achieved due to the pairing mechanism , which also concerns the effects that limit @xmath0 in practice . traditionally , the answer to this question was refined by synthesizing new materials or by changing control parameters such as external pressure . a new approach is the manipulation of materials properties such as order parameters by driving phonons with light @xcite . in the underdoped regime , @xmath0 is presumably limited by the occurrence of a pseudogap . the nature of this pseudogap state has not yet been clarified , and it is often interpreted as a state with competing orders or preformed pairs . recent experiments in which the properties of underdoped cuprates are manipulated by driving phonons with light are promising to provide further insights about the physics in the underdoped regime . a series of remarkable experiments reported for example evidence for transient superconducting states induced by light in underdoped yttrium @xcite ( ybco ) and lanthanum @xcite ( lco ) based cuprates far above @xmath0 , and even up to room temperature in the former case . in lanthanum - based cuprates , a transient superconducting state can be induced above @xmath0 around 12% hole doping @xcite , where superconductivity competes strongly with stripe order . in equilibrium and above @xmath0 , stripe order frustrates hopping perpendicular to the copper oxygen layers and destroys interlayer coherence . stimulation with light leads to a melting of stripe order , which enhances the interlayer coherence and gives rise to a transient superconducting state @xcite . the situation for yttrium based compounds @xcite is less clear . from an experimental point of view , there is evidence for the melting of a competing order parameter @xcite , redistribution of interlayer coupling @xcite and non - equilibrium lattice distortions @xcite . evidence also exists for a precursor superconducting state in equilibrium @xcite . several theories try to explain the transient superconducting state as a product of a redistribution of spectral weight @xcite or parametric cooling @xcite of phase fluctuations due to periodic driving , exploiting the bilayer structure of ybco . an alternative scenario invokes competition between bond - density wave ( bdw ) order and superconductivity in a three - dimensional model , where light modulates the interlayer hopping and influences the competition of orders @xcite . in the experiments on ybco , the enhancement of superconductivity is observed when mid - infrared light couples resonantly to infrared phonons @xcite , which in turn excite raman phonons via nonlinear couplings @xcite . it thus does not seem to be related to a photo - induced redistribution of quasiparticles @xcite . the phonon frequencies are mismatched with the plasma resonance and a direct coupling to phase fluctuations seems inefficient . all three above - mentioned theories have difficulties in explaining why bdw correlations melt and pairing correlations appear on roughly the same time scales , while the disappearance of pairing correlations and the reappearance of bdw correlations happens on very different scales @xcite . moreover , the proposed mechanisms either make use of the fact that ybco is a bilayer cuprate or the electron hopping perpendicular to the copper oxygen layers plays a prominent role . it is generally believed that the important physics of cuprate superconductors takes place in the copper oxygen planes , with the spacer layers mainly serving as charge reservoirs . it is therefore interesting to ask whether light - induced superconductivity could be achieved in a single copper oxygen plane . this question is intriguing because such a mechanism could also be at work in other cuprate materials that have one or multiple copper oxygen layers per unit cell and where experiments are more difficult . in this paper we propose a mechanism for light - induced superconductivity based on the competition between bdw correlations and superconductivity , which may be applicable slightly above the equilibrium @xmath0 where the system is close to a bdw instability @xcite . we describe the interplay of bdw and pairing fluctuations with a phenomenological non - linear sigma model @xcite , and investigate the external driving of this model by coupling it to phonons via electrons . parameter quenches of the non - linear sigma model have been studied by fu _ et al . _ in ref . . the electrons are described as a fractionalized fermi liquid ( fl@xmath1 ) @xcite , which is a model for the pseudogap state in underdoped cuprates . it shows bdw correlations at an axial wave vector that connects the tips of fermi arcs @xcite , as seen in experiment @xcite . an important ingredient of our theory is the enhanced coupling of electrons and phonons at the bdw wave vector that is observed in experiments . it leads to a strong softening of the phonon dispersion @xcite and a phonon linewidth that increases strongly with decreasing temperature @xcite . our theory traces back the enhanced electron - phonon coupling to vertex corrections due to short - range antiferromagnetic fluctuations and explains the phonon renormalization above @xmath0 as being a consequence of strong bdw fluctuations . however , the enhanced electron - phonon coupling does not directly lead to an enhancement of @xmath0 because it is restricted to a small region in momentum space and certain non - linear couplings between phonons and pairing fluctuations nearly cancel in our model . instead , the combination of strong phonon softening and phonon anharmonicities allows for the efficient driving of phonons near the bdw wavevector by light pulses . these strongly driven phonons suppress bdw fluctuations by enhancing their mass , thereby enlarging the relative size of the phase space for pairing , which enhances superconducting correlations . this paper is organized as follows . in sec . [ sec : model ] , we introduce the effective models for competing bdw and pairing correlations , for electrons in underdoped cuprates ( the fl@xmath1 ) , their mutual coupling as well as the coupling between electrons and phonons . the most important roles in our theory are played by order parameters and phonons , whereas the electrons only act as intermediaries between them . in sec . [ sec : phonon ] , we introduce a model for driven phonons and describe its renormalization by interaction effects as well as its dynamics close to a bdw instability . we find strong phonon softening that can entail momentum - selective driving and large amplitudes at the bdw wave vector . in sec . [ sec : box ] , we derive effective couplings between phonons , bdw and pairing fluctuations and describe how the driving of phonons impacts the interplay between bdw and pairing fluctuations . large phonon amplitudes at the bdw wave vector can lead to a suppression of bdw correlations in favor of superconductivity . this interplay is summarized in fig . [ fig : flowdiagram ] . in sec . [ sec : disc ] we discuss our results and draw conclusions . we are interested in the temperature region above the critical temperature for superconductivity @xmath0 , where ybco shows strong bond - density wave fluctuations @xcite . in this regime , the interplay between superconducting and bond - density wave fluctuations can be described by a landau theory of competing orders . in order to minimize the number of couplings in such a theory we choose to use a classical non - linear sigma model ( nlsm ) that correctly captures various qualitative features of the behavior of competing orders in the pseudogap phase slightly above @xmath0 @xcite , @xmath2 and @xmath3 are complex bosonic fields describing pairing and bdw fluctuations , respectively . they are combined into an @xmath4 order parameter with fixed length in order to focus on angular fluctuations . at the lowest temperatures , superconductivity is favored due to the positive mass term for bdw fluctuations . as @xmath5 is increased , superconducting order is lost , which is aided by the strengthening of bdw fluctuations . as will become clear in the following sections , our mechanism does not specifically require this model and will work for a generic landau theory of competing orders , since it relies only on the discrepancies in mass renormalizations of different order parameters . we derive the coupling of the non - linear sigma model to phonons from a phenomenological model for electrons in underdoped cuprates , which we take as a fractionalized fermi liquid ( fl@xmath1 ) @xcite . in this model , the fermi surface is gapped out in the anti - nodal region of the brillouin zone and reconstructed into hole - like pockets with low spectral weight on their back - sides . it shows incommensurate bdw fluctuations that are peaked at axial wave vectors close to those seen in experiment @xcite . the model is defined by the action @xmath6 where @xmath7 are fermionic grassmann fields , @xmath8 collects matsubara frequencies @xmath9 and momenta @xmath10 , @xmath11 , @xmath12 and @xmath13 is the inverse electron propagator . @xmath14 describes short - range electron - electron interactions . the other terms couple electrons to bdw fluctuations , @xmath15-wave pairing fluctuations and phonons , respectively , and are detailed below . the electron propagator is given by @xmath16 where @xmath17 is the electron dispersion , @xmath18 the self - energy of the fl@xmath1 and @xmath19 . the hopping parameters used in this work are listed in the caption of fig . [ fig : fs ] . the fermi liquid form of the propagator in eq . is manifest if it is rewritten in the following two - band "" form , @xmath20 the gap parameter @xmath21 arises from short - range antiferromagnetic order @xcite and leads to the reconstruction of the fermi surface . the parameters @xmath22 and @xmath23 control the location of the hole pockets . for @xmath24 but @xmath25 , they are centered at @xmath26 . setting these fl@xmath1 parameters to zero , we recover the large fermi surface "" . examples for a large and small fermi surface are shown in fig . [ fig : fs ] . we will also comment on the impact of using a small vs. a large fermi surface on our theory . the parameter @xmath27 measures the weight of the fermionic quasiparticles relative to that of incoherent excitations and is not important for our purposes . we thus set @xmath28 . 3.1 in with color encoding spectral weight . for this figure , and for the rest of this work , we use @xmath29 , @xmath30 , @xmath31 , @xmath32 , @xmath33 , @xmath34 , @xmath35.,title=""fig:"",width=288 ] 3.1 in with color encoding spectral weight . for this figure , and for the rest of this work , we use @xmath29 , @xmath30 , @xmath31 , @xmath32 , @xmath33 , @xmath34 , @xmath35.,title=""fig:"",width=288 ] we take into account nearest - neighbor exchange interactions , @xmath36 where @xmath37 , in order to mimic the strong short - range antiferromagnetic correlations that are found in underdoped cuprates . these can induce bdw instabilities @xcite of the fl@xmath1 . for simplicity we restrict ourselves to nearest - neighbor exchange . further neighbor and density - density interactions could be added , but are not expected to change our results in an essential way . in order to study the interaction between phonons and pairing as well as bdw fluctuations , we introduce fermion - boson couplings . the coupling of electrons to bdw fluctuations and cooper pairs could be derived from hubbard - stratonovich transformations of short - range interactions . for simplicity , we use phenomenological expressions and couple bdw fluctuations and electrons via @xcite @xmath38 where @xmath39 is the coupling strength and @xmath40 sums over" +"in recent years , social media networks , vital platforms for sharing contents with others in the era of web 2.0 , such as youtube , facebook , delicious , amazon , flickr and wikipedia , to name just a few , have experienced explosive growth @xcite . these systems record the fingerprints of every user s activity and every item s popularity , providing a wealth of data "" to study the dynamics of human activity and item popularity at the global system scale . in particular , it is found that the probability distributions of the activity degree of users , e.g. , editing in wikipedia @xcite , voting in news2 @xcite as well as favorite marking in flickr @xcite , and the popularity degree of items , e.g. , the number of fans a photo has in flickr @xcite , follow a power law . the power law distributions are explained by the rich - get - richer mechanism @xcite , which is also called preferential attachment in the field of complex networks @xcite . however , how these two distributions arise simultaneously due to human activity has yet to be determined . the activity dynamics @xcite and popularity dynamics @xcite have been investigated in the literatures , respectively . however , human activity and item popularity , two perspectives of the cross links between users and items , are interdependent ; therefore , we can not study the dynamics of one aspect alone . in addition , individuals are always embedded in a social network . it is widely believed that information can spread quickly along social links using user - to - user exchanges , also known as `` word - of - mouth '' exchanges ; moreover , the users behaviors are strongly influenced by their neighbors @xcite . in particular , the social degree and the activity degree depend on each other @xcite . hence , it is considered worthwhile studying social networks to obtain deeper insights into the dynamics of human activity and item popularity . until now , there has been no clear picture as to how online human activity and item popularity coevolve , so it is crucial to investigate the evolution of empirical human activity and item popularity as well as the theoretical model to obtain a better understanding of the possible generic laws governing the formation of activity distribution and popularity distribution . in this paper , we first characterize the evolution of human activity and item popularity in the amazon , flickr , delicious and wikipedia networks . it is found that in such social media networks , both relative probabilities of users creating cross links and items acquiring cross links are proportional to the degree of activity and degree of popularity , respectively . in particular , the inactive users are more likely to trace popular items than the active users . based on empirical observations , we then propose an evolving model based on two - step random walk . finally , we justify the validity of our model by comparing the results of model with that of empirical networks . this work could shed light on the understanding of evolution of user activity and item popularity in social media networks , and it also could be helpful in certain applications , such as designing efficient strategies for virtual marketing and network marketing , etc . ) , and the activity degree ( @xmath0 ) ; i4 has the popularity degree ( @xmath1 ) . please note that there is no social links in some cases , such as wikipedia.,width=288 ] * data description and notations . * the delicious data set was downloaded from http://data.dai-la bor.de/corpus/delicious/ , and consists of 132,500,391 bookmarks , 50,221,626 urls ( books ) , and 947,835 users between september , 2003 and december 31 , 2007 @xcite . the amazon user - movie rating data set was obtained from stanford large network dataset collection ( http://snap.stanford.edu/data/web-a mazon.html ) @xcite . the data consists of 7,911,684 ratings , 267,320 movies and 759,899 users between august 1997 and october 2012 . the flickr data set was collected by daily crawling flickr over 2.5 million users from nov 2 , 2006 to dec 3 , 2006 , and again daily from february 3 , 2007 to may 18 , 2007 ( http://socialnetworks.mpi-sws.org/datasets.html)@xcite . here , we only considered the users who had at least one favorite photo . with this constraint , there are 497,937 users , 11,232,836 photos and 34,734,221 favorite - markings in the data . the wikipedia ( english ) data set was download from http://konect.uni- koblenz.de/networks/edit-enwiki . the data set consists of 21,416,395 articles written collaboratively by 3,819,691 volunteers around the world before september , 2010 . the four datasets consist of individuals and items , such as movies in amazon , urls ( books ) in delicious , photos in flickr , and articles in wikipedia . moreover , users are able to show interest in these items using the network feature of rating in amazon , bookmarking in delicious , favorite - marking in flickr , and editing in wikipedia . therefore , these systems are topologically equivalent . for analysis purposes , the user - item data can be mapped into a two - layer network , as shown schematically in fig . this network has two types of nodes : @xmath2 users and @xmath3 items totally . in principle , the individuals are embedded in a social network . for example , flickr and delicious allow users to make friends . therefore , there should be two types of links : the cross links between users and items as well as the social links among users . mathematically , the topology shown in fig . [ fig1 ] can be characterized by two matrices . @xmath4 , an @xmath5 adjacency matrix , represents the social links among users , with element @xmath6 if user @xmath7 declares user @xmath8 as his friend , otherwise @xmath9 . similarly , @xmath10 , an @xmath11 adjacency matrix , characterizes the cross links , with element @xmath12 if user @xmath7 is interested in the item @xmath13 , otherwise @xmath14 . to be specific , we defined the following types of degrees to characterize the multi - relational connections . two degrees are related to the cross links : ( 1 ) the activity degree : @xmath15 , i.e. , the number of items interested by user @xmath7 ; ( 2 ) the popularity degree @xmath16 , i.e. , the number of users who are interested in the item @xmath13 , which reasonably represents the popular extent in the network ; and ( 3 ) the social degree @xmath17 , i.e. , the number of friends for a given user . note , @xmath18 and @xmath19 are two different perspectives of the cross links connecting users and items . * measuring preferential attachment . * here , we explain the method for measuring the phenomenon of preferential attachment on temporal data @xcite . the basic idea is to investigate whether new links are likely to attach to nodes with larger degree ( size ) . we calculate the empirical value of the relative probability @xmath20 that a new cross link formed within a short period @xmath21 connects to a user ( item ) , which has a degree of @xmath22 at the time @xmath23 , as follows , @xmath24 here , @xmath22 is the degree at time @xmath23 . @xmath25 is the number of nodes with exact degree @xmath22 at @xmath23 , but creating ( acquiring ) new cross links within next small interval @xmath21 ( e.g. , one day in this article ) . @xmath26 is the number of users ( items ) with degree @xmath22 at @xmath23 . the preferential attachment hypothesis states that the rate @xmath20 with which a node with @xmath22 links acquires new links is a monotonically increasing function of @xmath22 @xcite , namely @xmath27 . to obtain a smooth curve from noisy data , we take the cumulative function form instead of @xmath20 : @xmath28 in our measurement , @xmath22 can be either degree of activity @xmath18 or degree of popularity @xmath19 . this method has been successfully used to verify the preferential attachment mechanism of ba model @xcite in empirical evolving networks @xcite and theoretical models @xcite . .basic statistics of the data sets constructed for our study . showing the number of users @xmath2 , the number of items @xmath3 , the number of cross links @xmath29 , the average degree of activity @xmath30 and the average degree of popularity @xmath31 [ cols=""^,^,^,^,^,^"",options=""header "" , ] [ alpha ] figure [ figure-2 ] shows the cumulative function @xmath32 with respect to the degree of activity and degree of popularity . we see that the relative cumulative probability @xmath33 ( @xmath34 ) for users ( items ) to create ( acquire ) cross links is proportional to the existing degree of activity ( popularity ) . in particular , the cumulative functions @xmath35 approximately follow a straight line on the log - log scale , indicating that the relative cumulative probability of generating new degrees satisfies a power law with respect to the existing degrees , which can be characterized by the positive exponent @xmath36 where @xmath37 with @xmath38 denoting the degree . in table [ alpha ] , we list the characteristic exponents @xmath39 and @xmath40 determined by least - square fitting the @xmath35 functions for small @xmath41 as the curves deviate from the straight line for large @xmath41 due to low statistics . the positive exponents @xmath39 and @xmath40 indicate that the active users ( with a higher degree of activity ) have greater chance to create new cross links than the inactive users ( with a lower degree of activity ) , while the popular items ( with a higher degree of popularity ) have greater chance to attract new cross links . for different groups of users and @xmath33 for different groups of items ( in the insets ) , in amazon(a ) , flickr ( b ) , delicious ( c ) and wikipedia ( d ) . the users and items are classified into different groups according to the degree of activity and the degree of popularity . , width=528 ] as these four systems expand rapidly , we then investigate the formation of cross links between new users ( items ) and existing items ( users ) . in the insets of fig . [ figure-2 ] , @xmath33 characterizes the relative probability that the existing users are interested in new items with respect to the users degree of activity , whereas @xmath42 characterizes the relative probability that the existing items attract the attentions of new users with respect to the items degree of popularity . interestingly , as seen in the insets of fig . [ figure-2 ] , these cumulative functions also follow a power law . the positive exponents @xmath39 and @xmath40 indicate that the newly created items are more likely to attract the attentions of active users , while the new users are more likely to be interested in popular items . the above results suggest that the users are likely to trace popular items overall , and that the active users are more likely to create new cross links than the inactive users . for users with different activity degree . * ( a ) amazon , ( b ) flickr , ( c ) delicious and ( d ) wikipedia . the users are classified into following types according to different degrees of activity , i.e. , @xmath43 , @xmath44 , @xmath45 , @xmath46 and @xmath47 . the values of @xmath48 fluctuate significantly for large @xmath19 due to low statistics.,width=528 ] what is the influence of activity ( popularity ) degree on the intensity of users tracing popular items (" +"cold , dense quark matter is a color superconductor @xcite . for two massless quark flavors ( say , up and down ) , cooper pairs with total spin zero condense in the color - antitriplet , flavor - singlet channel . in this so - called two - flavor color superconductor , the @xmath0 gauge symmetry is spontaneously broken to @xmath1 @xcite . if we choose to orient the ( anti- ) color charge of the cooper pair along the ( anti- ) blue direction in color space , only red and green quarks form cooper pairs , while blue quarks remain unpaired . then , the three generators @xmath2 and @xmath3 of the original @xmath0 gauge group form the generators of the residual @xmath1 symmetry . the remaining five generators @xmath4 are broken . ( more precisely , the last broken generator is a combination of @xmath5 and the generator @xmath6 of the global @xmath7 symmetry of baryon number conservation , for details see ref . @xcite and below ) . according to goldstone s theorem , this pattern of symmetry breaking gives rise to five massless bosons , the so - called nambu - goldstone bosons , corresponding to the five broken generators of @xmath0 . physically , these massless bosons correspond to fluctuations of the order parameter , in our case the diquark condensate , in directions in color - flavor space where the effective potential is flat . for gauge theories ( where the local gauge symmetry can not truly be spontaneously broken ) , these bosons are `` eaten '' by the gauge bosons corresponding to the broken generators of the original gauge group , _ i.e. _ , in our case the gluons with adjoint colors @xmath8 . they give rise to a longitudinal degree of freedom for these gauge bosons . the appearance of a longitudinal degree of freedom is commonly a sign that the gauge boson becomes massive . in a dense ( or hot ) medium , however , even _ without _ spontaneous breaking of the gauge symmetry the gauge bosons already have a longitudinal degree of freedom , the so - called _ plasmon _ mode @xcite . its appearance is related to the presence of gapless charged quasiparticles . both transverse and longitudinal modes exhibit a mass gap , _ i.e. _ , the gluon energy @xmath9 for momenta @xmath10 . in quark matter with @xmath11 massless quark flavors at zero temperature @xmath12 , the gluon mass parameter ( squared ) is @xcite @xmath13 where @xmath14 is the qcd coupling constant and @xmath15 is the quark chemical potential . it is _ a priori _ unclear how the nambu - goldstone bosons interact with these longitudinal gluon modes . in particular , it is of interest to know whether coupling terms between these modes exist and , if yes , whether these terms can be eliminated by a suitable choice of ( t hooft ) gauge . the aim of the present work is to address these questions . we shall show that the answer to both questions is `` yes '' . we shall then demonstrate by focussing on the gluon of adjoint color 8 , how the nambu - goldstone mode affects the spectral density of the longitudinal gluon . our work is partially based on and motivated by previous studies of gluons in a two - flavor color superconductor @xcite . the gluon self - energy and the resulting spectral properties have been discussed in ref . @xcite . in that paper , however , the fluctuations of the diquark condensate have been neglected . consequently , the longitudinal degrees of freedom of the gluons corresponding to the broken generators of @xmath0 have not been treated correctly . the gluon polarization tensor was no longer explicitly transverse ( a transverse polarization tensor @xmath16 obeys @xmath17 ) , and it did not satisfy the slavnov - taylor identity . as a consequence , the plasmon mode exhibited a certain peculiar behavior in the low - momentum limit , which can not be physical ( cf . fig . 5 ( a ) of ref . it was already realized in ref . @xcite that the reason for this unphysical behavior is the fact that the mixing of the gluon with the excitations of the condensate was neglected . it was moreover suggested in ref . @xcite that proper inclusion of this mixing would amend the shortcomings of the previous analysis . the aim of the present work is to follow this suggestion and thus to correct the results of ref . @xcite with respect to the longitudinal gluon . note that in ref . @xcite fluctuations of the color - superconducting condensate were taken into account in the calculation of the gluon polarization tensor . as a consequence , the latter is explicitly transverse . however , the analysis was done in the vacuum , at @xmath18 , not at ( asymptotically ) large chemical potential . the outline of the present work is as follows . in section [ ii ] we derive the transverse and longitudinal gluon propagators including fluctuations of the diquark condensate . in section [ iii ] we use the resulting expressions to compute the spectral density for the gluon of adjoint color 8 . section [ iv ] concludes this work with a summary of our results . our units are @xmath19 . the metric tensor is @xmath20 . we denote 4-vectors in energy - momentum space by capital letters , @xmath21 . absolute magnitudes of 3-vectors are denoted as @xmath22 , and the unit vector in the direction of @xmath23 is @xmath24 . in this section , we derive the gluon propagator taking into account the fluctuations of the diquark condensate . a short version of this derivation can be found in appendix c of ref . @xcite [ see also the original ref . nevertheless , for the sake of clarity and in order to make our presentation self - contained , we decide to present this once more in greater detail and in the notation of ref . @xcite . as this part is rather technical , the reader less interested in the details of the derivation should skip directly to our main result , eqs . ( [ transverse ] ) , ( [ longitudinal ] ) , and ( [ hatpi00aa ] ) . we start with the grand partition function of qcd , [ z ] @xmath25\,\ , , \ ] ] where @xmath26 = \int { \cal d } \bar{\psi } \ , { \cal d } \psi\ , \exp \left [ \int_x \bar{\psi } \left ( i \gamma^\mu \partial_\mu + \mu \gamma_0 + g \gamma^\mu a_\mu^a t_a \right ) \psi \right ] \ , . \label{zquarks}\ ] ] is the grand partition function for massless quarks in the presence of a gluon field @xmath27 . in eq . ( [ z ] ) , the space - time integration is defined as @xmath28 , where @xmath29 is the volume of the system , @xmath30 are the dirac matrices , and @xmath31 are the generators of @xmath32 . for qcd , @xmath33 , and @xmath34 are the gell - mann matrices . the quark fields @xmath35 are @xmath36-component spinors , _ i.e. _ , they carry dirac indices @xmath37 , fundamental color indices @xmath38 , and flavor indices @xmath39 . the action for the gauge fields consists of three parts , @xmath40 where @xmath41 is the gauge field part ; here , @xmath42 is the field strength tensor . the part corresponding to gauge fixing , @xmath43 , and to fadeev - popov ghosts , @xmath44 , will be discussed later . for fermions at finite chemical potential it is advantageous to introduce the charge - conjugate degrees of freedom explicitly . this restores the symmetry of the theory under @xmath45 . therefore , in ref . @xcite , a kind of replica method was applied , in which one first artificially increases the number of quark species , and then replaces half of these species of quark fields by charge - conjugate quark fields . more precisely , first replace the quark partition function @xmath46 $ ] by @xmath47 \equiv \left\ { { \cal z}_q[a ] \right\}^m$ ] , @xmath48 being some large integer number . ( sending @xmath49 at the end of the calculation reproduces the original partition function . ) then , take @xmath48 to be an even integer number , and replace the quark fields by charge - conjugate quark fields in @xmath50 of the factors @xmath46 $ ] in @xmath47 $ ] . this results in @xmath51 = \int \prod_{r=1}^{m/2 } { \cal d } \bar{\psi}_r \ , { \cal d } \psi_r \ ; \exp \left\ { \sum_{r=1}^{m/2 } \left [ \int_{x , y } \bar{\psi}_r(x ) \,{\cal g}_0^{-1 } ( x , y)\ , \psi_r(y ) + \int_x g\ , \bar{\psi}_r(x ) \ , a_\mu^a(x)\,\hat{\gamma}^\mu_a\ , \psi_r(x ) \right ] \right\ } \,\ , . \label{zquarks2}\ ] ] here , @xmath52 labels the quark species and @xmath53 , @xmath54 are @xmath55-component nambu - gorkov spinors , @xmath56 where @xmath57 is the charge conjugate spinor and @xmath58 is the charge conjugation matrix . the inverse of the @xmath59-dimensional nambu - gorkov propagator for non - interacting quarks is defined as @xmath60^{-1 } & 0 \\ 0 & [ g_0 ^ -]^{-1 } \end{array } \right)\,\ , , \ ] ] where @xmath61^{-1}(x , y ) \equiv -i \left ( i \gamma_\mu \partial^\mu_x \pm \mu \gamma_0 \right ) \delta^{(4)}(x - y)\ ] ] is the inverse propagator for non - interacting quarks ( upper sign ) or charge conjugate quarks ( lower sign ) , respectively . the nambu - gorkov matrix vertex describing the interaction between quarks and gauge fields is defined as follows : @xmath62 where @xmath63 and @xmath64 . following ref . @xcite we now add the term @xmath65 and the corresponding charge - conjugate term @xmath66 , where @xmath67 , to the argument of the exponent in eq . ( [ zquarks2 ] ) . this defines the quark ( replica ) partition function in the presence of the gluon field @xmath27 _ and _ the diquark source fields @xmath68 , @xmath69 : @xmath70 \equiv \int \prod_{r=1}^{m/2 } { \cal d } \bar{\psi}_r \ , { \cal d } \psi_r \ ; \exp \left\ { \sum_{r=1}^{m/2 } \left [ \int_{x , y } \bar{\psi}_r(x ) \,{\cal g}^{-1 } ( x , y)\ , \psi_r(y ) + \int_x g\ , \bar{\psi}_r(x ) \ , a_\mu^a(x)\,\hat{\gamma}^\mu_a\ , \psi_r(x ) \right ] \right\ } \,\ , , \label{zquarks3}\ ] ] where @xmath71^{-1 } & \delta^- \\ \delta^+ & [ g^-_0]^{-1 } \end{array } \right)\ ] ] is the inverse quasiparticle propagator . inserting the partition function ( [ zquarks3 ] ) into eq . ( [ zqcd ] ) , the ( replica ) qcd partition function is then computed in the presence of the ( external ) diquark source terms @xmath72 , @xmath73 $ ] . in principle , this is not the physically relevant quantity , from which one derives thermodynamic properties of the color superconductor . the diquark condensate is not an external field , but assumes a nonzero value because of an intrinsic property of the system , namely the attractive gluon interaction in the color - antitriplet channel , which destabilizes the fermi surface . the proper functional from which one derives thermodynamic functions is obtained by a legendre transformation of @xmath74 $ ] , in which the functional dependence on the diquark source term is replaced by that on the corresponding canonically conjugate variable , the diquark condensate . the legendre - transformed functional is the effective action for the diquark condensate . if the latter is _ constant _ , the effective action is , up to a factor" +"the interaction of fluid / fluid interfaces with solid boundaries is of fundamental importance to a variety of wetting and dewetting phenomena . in this paper , we present a computational framework for the inclusion of a general fluid / solid interaction , treated as a temporally and spatially dependent body force , in a direct solver of the navier - stokes equations . this approach allows for computing fluid wetting properties ( such as equilibrium contact angle ) based on first principles , and without restriction to small contact angles . due to the complexities involved in modeling dynamics of fluids on solid substrates , a significant amount of modeling and computational work has been carried out using the long - wave ( lubrication ) approach . still , even within the long - wave approach , a difficulty arises when employing the commonly used no - slip boundary condition at the fluid / solid interface : a non - integrable shear - stress singularity at the moving contact line . simulating dynamic contact lines therefore requires additional ingredients for the model . one option is to include fluid / solid interaction forces with conjoining - disjoining terms which lead to a prewetted ( often called ` precursor ' ) layer in nominally ` dry ' regions . this approach effectively removes the ` true ' contact line , consequently avoiding the associated singularity @xcite . a second approach is to relax the no - slip condition and instead assume the presence of slip at the fluid / solid interface . both slip and disjoining pressure approaches have been extensively used to model a variety of problems including wetting , dewetting , film breakup , and many others ( see e.g. @xcite for reviews ) . while the approach based on the long - wave model has been very successful , it does include limitations inherent in its formulation : in particular , the restriction to small interfacial slopes ( strictly speaking , the slopes much less than unity ) , and therefore small contact angles . we have shown in our earlier work @xcite that , depending on the choice of flow geometry , the comparison between the solutions of the long - wave model and of the navier - stokes equations may be better than expected ; however , still for slopes of @xmath0 , quantitative agreement disappears . therefore , one would like to be able to consider wetting / dewetting problems by working outside of the long - wave limit , while still considering the most important physical effects ; such as fluid / solid interaction forces . these fluid / solid interactions are known to be crucial in determining stability properties of a fluid film ; without their presence , a fluid film on a substrate is stable , since there are no forces in the model to destabilize it . in particular , for thin nanoscale films , fluid / solid interaction forces may be dominant . we note that the approaches based on the derjaguin approximation to include the van der waals or electrostatic interactions into the model in the form of a local pressure contribution ( disjoining pressure ) acting on the fluid / solid interface are derived under the assumption of a flat film @xcite . therefore these approaches can not be trivially extended to the configurations involving large contact angles . in the context of direct simulations of the navier - stokes equations with free interfaces , a large variety of methods are used to track the evolution of the interface . lagrangian methods conform the computational grid to the interface ( e.g. @xcite ) . eulerian methods require a separate mechanism to track the interface location ; these include front tracking methods ( e.g. @xcite ) , and interface capturing methods such as volume of fluid methods and level set methods . the latter two methods easily treat topology changes , and with recent developments have been shown to be effective for simulating surface tension driven flows @xcite . a common feature of volume of fluid methods is that contact angles are imposed geometrically , in that the angle at which the interface intersects the solid substrate is specified as a boundary condition on the interface @xcite . such approaches were used to model the dynamics of non - wetting drops , that could even detach from the substrate @xcite , as well as spreading drops @xcite . the van der waals interaction has been implemented previously in a volume of fluid based solver for the liquid / liquid interaction of colliding droplets @xcite , but to our knowledge has not been considered for flows involving wetting phenomena . a variety of other computational methods have been considered in the context of wetting / dewetting . here we mention phase - field methods that treat two fluids with a diffuse interface by means of a smooth concentration function , which typically satisfies the cahn - hilliard or allen - cahn equations , and is coupled to the navier - stokes equations . jacqmin @xcite describes a phase - field contact angle model that use a wall energy to determine the value of the normal derivative of the concentration on a solid substrate . this model has been used to study contact line dynamics @xcite , and similar models have been considered in the investigation of the sharp interface limit of the diffuse interface model @xcite . lattice - boltzmann methods have also treated the contact angle with a wall energy contribution @xcite . these approaches have explained a variety of phenomena related to spreading of fluids on solid substrates , but do not consider explicitly the stabilizing and destabilizing forces between fluid and solid , as has been done via disjoining pressure within the context of the long - wave model . the liquid / solid interaction is naturally included in molecular dynamics ( md ) simulations @xcite that typically consider lennard jones potential between fluid and solid particles . however , md simulations are , in general , computationally expensive , even when simulating nanoscale systems . one would like to be able to include liquid - solid interaction within the framework of a continuum model . here , we present a novel approach , based on a volume of fluid formulation , which includes the fluid / solid interaction forces into the governing navier - stokes equations , without limitations inherent in the long - wave model . this inclusion allows for arbitrary contact angles to be incorporated based on modeling the underlying physics , in contrast to conventional volume of fluid methods . the presented approach also leads to the regularization of the viscous stress since the fluid film thickness never becomes zero . furthermore , our framework can account for additional physical effects , such as instability and breakup of thin fluid films , that would not be described if fluid / solid interaction forces were not explicitly included . we note here that while film rupture can also occur in phase - field based approaches ( as in @xcite ) , this seems to be due to the presence of a rather thick interface , and not due to the explicit inclusion of destabilizing liquid / solid interaction forces . in the present paper we focus on formulating and discretizing the model , and on discussing issues related to convergence and accuracy . to validate our proposed numerical scheme , we consider two representative examples , involving relaxation and spreading of sessile drops with various contact angles on a substrate . these benchmark cases permit comparison of our results with well established analytical solutions for a particular flow regime . the application of the method to the study of thin film stability including dewetting will be considered in the sequel @xcite . the rest of this paper is organized as follows . we describe the details of the fluid / solid interaction in sec . [ sec : model ] . in sec . [ sec : methods ] , we describe two finite - volume methods for the discretization of the considered fluid / solid interaction forces . the presentation in these two sections applies to any generic fluids . in sec . [ sec : results ] we present a comparison of the two considered discretization methods for equilibrium and spreading drops , for a particular choice of material parameters . in sec . [ sec : conc ] , we give an overview and future outlook . consider a perfectly flat solid substrate covered by two immiscible fluids . for clarity , we will refer to these fluids as the liquid phase ( subscript @xmath1 ) , and the vapor phase ( subscript @xmath2 ) , although the present formulation applies to any two fluids . assume that gravity can be neglected , and also ignore any phase - change effects , such as evaporation and condensation . there are three relevant interfacial energies : the liquid / solid , @xmath3 , the vapor / solid , @xmath4 , and the liquid / vapor , @xmath5 , energies . the contact angle is commonly defined as the angle between the tangent plane of the interface between the liquid and vapor phases and the solid substrate at the point where the interface meets the surface . at equilibrium , the contact angle , @xmath6 , and the surface energies are related by young s equation @xcite : @xmath7 if there is a nonzero contact angle at equilibrium , the liquid partially wets the solid surface ; if the equilibrium configuration is a flat layer covering the whole substrate , then it fully wets the solid surface . it is also possible for the liquid to be non - wetting , where the liquid beads up into a sphere on the surface . the wetting behavior of the system can be characterized by the equilibrium spreading coefficient , defined by : @xmath8 which expresses the difference in energy per unit area between a surface with no liquid , and one with a layer of liquid ( what we call ` dry ' and ` wet ' states , respectively ) . wetting is determined by the sign of @xmath9 ; partial wetting occurs for @xmath10 , and complete wetting for @xmath11 @xcite . the above characterization of the contact angle is straightforward for static configurations and at macroscopic length scales . if these assumptions are not satisfied , definitions of contact angles become more complex . in the literature , a distinction is made between the apparent contact angle , @xmath12 , and the microscopic contact angle , @xmath13 , distinguished by the distance from the contact line at which the measurement is made @xcite . the contact angle resulting from measuring on macroscopic length scales is @xmath12 , while @xmath13 is measured at short length scales which are still long enough so that the continuum limit is appropriate @xcite . the microscopic contact angle , @xmath13 , is often identified with @xmath6 , which is commonly used in the derivation of spreading laws , such as the classical cox - voinov law @xcite . it should be noted that the details of the fluid behavior on nano scales in the vicinity of the fluid fronts and associated contact lines are far from being completely understood @xcite , and the way in which the contact angle arises at small scales is a subject of ongoing research @xcite . the surface energies entering eq . and eq . arise due to the van der waals interaction between the different phases that are relevant on short length scales . three kinds of van der waals interactions are usually considered : interactions between polar molecules , interaction of molecules that have an induced polarization , and the dispersion forces @xcite . the dispersion interaction is" +"complex networks @xcite may be affected by structural perturbations that modify their behavior or even lead to their collapse . of all potential structural perturbations , the removal of individual nodes has received most attention . it has been found that complex networks are robust to accidental failures , yet fragile to targeted attacks knocking down their most connected nodes @xcite . a similar approach has been applied in biology to metabolic networks which , as compared to other large - scale cellular networks , prove to be of particular interest due to the availability of high quality reconstructions based on complementary sources of experimental data , and due to the possibility of experimentally validating computational predictions @xcite . metabolic networks , modeled as complex networks @xcite , have been tested in terms of robustness in a wide variety of in silico experiments . typical _ in silico _ strategies to quantify _ structural robustness _ of metabolic networks against removal of a single reaction consider the downstream effect of the removal and the size of the resulting cascade . properties of the cascade , e.g. , size or length , could then be considered as proxies for the potential damage inflicted by the removal . finally , one would like to obtain estimates for the statistical significance of the obtained observations , which could be empirically carried out with respect to a well - chosen null model . for instance , by applying this strategy in combination with degree preserving randomization ( see sections 2.2 and 2.3 ) , smart and coworkers @xcite have determined that bacterial organisms may have evolved towards reducing the probability of having large cascades , thus , increasing robustness . recently , more complicated perturbations have also been considered , namely , removal of pairs of reactions and sets of genes @xcite , and the topological significance of the results was evaluated with respect to degree preserving randomization . the employed degree preserving null model has its roots in the configuration model @xcite for bipartite networks @xcite , that results in randomized network variants in which node degrees are preserved . however , such a degree preserving randomization does not account for the most basic physico - chemical constraints , and may lead , in the case of metabolic networks , to consideration of a reaction which is not mass ( i.e. , stoichiometrically ) balanced ( a reaction which does not preserve the same type and number of atoms on its substrate and product sides ) . as a result , the randomized networks may not be chemically feasible . as an alternative , a novel null model called mass - balanced randomization has been recently proposed @xcite to account for this issue . mass - balanced randomization results in randomized network variants in which : ( 1 ) every reaction is mass balanced and ( 2 ) degrees of reactions are unaltered . by comparing the differences between the analyzed property in the original network and in its randomized variant , this null model is able to distinguish between properties which result solely from physico - chemical constraints and those selected for by evolutionary pressure @xcite . here we explore the metabolic networks of _ staphylococcus aureus _ @xcite and _ escherichia coli _ @xcite to determine the extent to which the robustness against the failure of individual reactions and pairs of reactions , as quantified by the number of non - viable reactions caused upon the initial removal(s ) of a single reaction or a pair of reactions , is bounded by structural constraints . to this end , we compare cascades in the original networks with those obtained from the two null models referred above : degree preserving ( dp ) and mass - balanced ( mb ) randomization . we find that the two null models give very different results , which is explained in terms of the properties of the networks obtained by both randomization methods . we use kolmogorov - smirnov tests @xcite to statistically assess whether the null models are enough to explain the resulting damage distributions in the original networks . interestingly , we find that the two organisms exhibit cascades whose properties lie between those expected from the two considered null models , which suggest that factors other than node degrees or physical principles affect the considered features . moreover , our findings point out that , in the analyzed metabolic networks , evolutionary pressure may not have lead towards minimized damage spreading , which opposes earlier findings based solely on degree preserving randomization . our results reinforce the importance of choosing an appropriate null model according to the question at hand , since the null model ultimately affects the interpretation of the findings . we have modeled metabolic networks as bipartite graphs @xcite , whereby the set of nodes is portioned into metabolites and reactions , and there are no links between nodes of the same type . metabolites are connected to the reactions by directed links , which allow differentiating between reactants and products . every reversible reaction is split into two irreversible reaction nodes , so that every reaction node included in the representation corresponds to an irreversible reaction . we use two different bacterial organisms in this study . _ e. coli _ is the most studied prokaryotic organism and it is the bacterial model which is most frequently used due to ease of experimental manipulation . to construct the bipartite representation of the metabolic network of _ @xcite , we use data from the bigg database . the resulting network contains @xmath0 reactions and @xmath1 metabolites . _ s. aureus _ is an anaerobic bacterium which is present world - wide . its bipartite directed network reconstruction was obtained from @xcite , and consists of @xmath2 reactions and @xmath3 metabolites . the networks of the two analyzed species show marked similarities with respect to the cumulative degree distributions . for metabolites , the degree distribution shows a typical power - law form , @xmath4 , with an exponent @xmath5 for _ s. aureus _ and @xmath6 for _ e. coli_. on the contrary , reactions show a peaked distribution centered at the average degree corresponding to each network , having a value of @xmath7 for _ s. aureus _ and a value of @xmath8 for _ e. coli_. a cascading failure algorithm @xcite is applied to spread the initial perturbation through the network and to compute the corresponding damage . crucial to the algorithm are the concepts of viable metabolites and reactions . a metabolite is considered viable if it has at least one incoming and one outgoing connection , so as to prevent depletion or accumulation . this structural condition is a prerequisite for the network as a whole to operate at a positive steady state . on the other hand , reactions are viable if and only if all of the participating metabolites are viable . the algorithm then starts with a network from which an initial set of reactions is removed . in the following step , all reactions and metabolites that , as a consequence , become non - viable are removed , which in its turn results in additional changes of the viability status of the nodes . when only viable reactions and metabolites remain in the network , the damage inflicted by the initial perturbation is quantified as the final number of non - viable reactions ( see figure [ fig:1 ] ) . here , we consider perturbations by initially removing every single reaction and each pair of reactions . and 7 and 8 with @xmath9 depending on whether they are reactants or products of the reversible reaction . the cascade starts when reaction @xmath10 fails . b ) therefore , metabolites 3 and 6 become non - viable . because metabolite 6 is connected to reaction @xmath11 , the later becomes non - viable , turning also metabolite 12 non - viable . notice that metabolite 11 loses one _ in _ connection , but it is still viable , meaning that one of the waves of the cascade stops here . however the other wave keeps spreading . c ) metabolite 5 becomes inviable , causing the reversible reaction @xmath12 to remain viable only towards the production of metabolites 7 and 8 . e ) consequently , metabolite 4 becomes non - viable , and so its associated reactions also become non - viable . the cascade spreads until all metabolites and reactions affected by the cascade remain viable . finally , note that metabolites 1 , 2 , 3 , 13 , and 14 , which initially have no incoming or outgoing connections , are not considered inviable by the algorithm.,scaledwidth=57.0% ] benchmark cascades are computed by first randomizing the original network and then performing the cascade algorithm on the randomized version . for each of the two null models , damage distributions are obtained for a hundred realizations , then averaged , and finally compared to the original damage distribution to assess the statistical significance and quantitative behavior of the observation . the degree preserving randomization method approximates the configuration model for bipartite networks @xcite and works as follows . a pair of links of the network is chosen at random and their targets are swapped , unless this would lead to the repeated occurrence of a metabolite in a reaction . the randomization algorithm is summarized as follows : 1 . pick two links at random : @xmath13 and @xmath14 or @xmath15 and @xmath16 . 2 . swap the end of the links avoiding repeated links and self - production : ( @xmath17 and @xmath18 or @xmath19 and @xmath20 ) . 3 . repeat until we perform @xmath21 swappings , where @xmath22 is the total number of links . 4 . make several realizations of the randomized metabolic network following the three previous steps . the links from reversible reactions are rewired independently of those from irreversible reactions , using the same steps previously mentioned , in order to preserve the degrees of metabolites corresponding to reversible and irreversible reactions , respectively . a scheme showing this algorithm is shown in figure [ fig:2 ] . it is easy to show that the networks obtained using this method preserve the degrees of both metabolites and reactions , as illustrated in figure [ fig:1b ] . mass - balanced randomization generates randomized networks by rewiring the links corresponding to substrate - reaction or product - reaction relationships , while preserving atomic mass balance of the reactions @xcite . given a reaction @xmath23 , its atomic mass balance is given by:@xmath24 where @xmath25 is the set of substrates and @xmath26 the set of products in @xmath23 , @xmath27 are the vectors of sum formulas of @xmath28 and @xmath29 , respectively , and @xmath30 , @xmath31 their stoichiometric coefficients . for instance , consider the reaction @xmath32 , with @xmath33 @xmath34 @xmath35 . then , @xmath36 may be substituted by a compound @xmath37 with @xmath38 from within the network , resulting in the randomized reaction 2 @xmath39 , which satisfies equation [ eq : mass_balance ] since @xmath40 ( figure [ fig:2 ] ) . in addition to substituting individual substrates or products , the method also allows more complex substitutions involving pairs of substrates or products , yielding a large number of possible substitutions . the motivation for preserving atomic mass balance of reactions , a fundamental physico - chemical constraint , is that the resulting null model allows estimating the importance of network properties with respect to evolutionary pressure . as biological systems and their properties evolve under physical constraints and evolutionary pressure , a null model which satisfies physical principles but does not account for evolutionary pressure differs from a metabolic network only in the properties which are affected by evolutionary pressure . thus , a property" +"350 has been the subject of many studies in the optical / near infrared and radio regimes and most wavelengths in between . it is highly obscured at short wavelengths and bright at long wavelengths . the object was originally part of the planetary nebulae survey of @xcite , but was later reclassified as an region . @xcite observed 350 at mid infrared wavelengths and showed the optical nebula was offset from the radio source due to a strong gradient in the foreground extinction . @xcite determined precise offsets between the radio , infrared and optical sources which validate the @xcite model . 350 , also known as the galactic radio source g70.31.6 , has been extensively observed at long wavelengths . @xcite provided a high angular resolution map at 2 cm which resolved the ionized gas into a clumpy arc like or shell like structure on scales smaller than 1@xmath1 . @xcite included this object in their catalog of regions , describing it as a core halo type while @xcite observed the larger nebula in the continuum and radio recombination line h76@xmath4 . the radio morphology is extended in two lobes to the nw and se and @xcite found a velocity gradient along the lobes which led them to suggest the structure was an ionized outflow extending 10 s of arcseconds from the center of the region . @xcite presented br@xmath3 and br@xmath4 emission line maps at greater than arcsecond resolution and followed this work @xcite with molecular line maps which they modeled as arising from a large scale molecular torus ( roughly perpendicular to the ionized outflow of * ? ? ? * ) . more recent work has centered on near infrared and mid infrared wavelengths and higher angular resolution data . @xcite observed the nebula in the @xmath0band using speckle techniques to provide an order of magnitude higher angular resolution than previous near infrared work , and @xcite used the subaru 8 m telescpe and mid infrared imager comics to obtain 0.5@xmath1 resolution images and spectra near 10 . in this paper , we present @xmath0band integral field spectroscopy of 350 obtained on the gemini north 8 m telescope with the near infrared integral field spectrograph . these data were taken in conjunction with the facility adaptive optics system and result in the most detailed data cube yet for the core of 350 . in an earlier paper @xcite , we presented similar data for the region g45.45@xmath50.6 . in that case , several massive stars were identified by photospheric lines and other objects showed signatures of buried massive young stellar objects . g45.45@xmath50.6 clearly harbors a rich cluster . @xcite make similar conclusions based on their eso vlt sinfoni integral field spectrograph observations for the region in the cluster [ dbs2003]8 . previous investigators have suggested the same may be true of 350 : @xcite , @xcite , and @xcite . our data identify multiple continuum sources in 350 and support the multiple star model , but we also show that the excitation in the central few arcseconds of 350 is likely dominated by a single object ( the unresolved continuum peak ) . in the following , the distance to the nebula is based on the work of @xcite . the @xcite distance is derived from a compilation of velocities and a rotation model ; harris distance needs to be reduced due to a revised distance to the galactic center ( * ? ? ? * used a distance of 10 kpc ) . adopting a value of 8 kpc gives a reduction by a factor of 0.8 resulting in a distance to the region of about 7 kpc . data were obtained with the near infrared integral field spectrograph ( nifs ) at the cassegrain focus of the gemini north fredrick c. gillett 8m telescope on mauna kea , hawaii on the night of 20 july , 2006 ( hst ) . nifs was used with the facility adaptive optics ( ao ) module altair in natural guide star ( ngs ) mode . nifs is fully described by @xcite ; see also @xcite for a more detailed description of similar observations with nifs as described here . briefly , nifs slices an approximately three arc second by three arc second field into 29 spectral segments of 0.1@xmath1 width ( the `` slit '' width ) and @xmath6 3@xmath1 in length . the scale along the spatial dimension is 0.043@xmath1 pix@xmath7 . the resulting `` spaxels , '' or spatial pixels , are thus 0.043@xmath1 @xmath8 0.1@xmath1 in size , and each contains a full spectrum covering one of the near infrared bands . in the present paper , @xmath0band spectra are presented for the galactic region 350 . the ao guide star used for altair is located 10.2@xmath1 to the south and west of 350 and has an @xmath9 magnitude of 12.7 according to the usno catalog ( source i d : u1200_14213688 ) . there was thin cirrus at the time of the observations , and the seeing ( at 5000 , corrected to zenith ) reported during the observations by altair was approximately 0.45@xmath1 . the observations were obtained at relatively high airmass ( 1.5 ) , and altair was run at 500 hz . the observations consisted of a single coadded frame taken on source and a second frame obtained on a nearby ( @xmath6 50@xmath1 west ) blank field . each frame had a total exposure time of 600 seconds ( 15@xmath840s ) on source and 600 seconds on sky . nifs was oriented with a position ( pa ) of 70 degrees east of north to correspond approximately to the orientation of the large scale ionized flow from 350 @xcite . this pa is aligned with the outflow direction . the spectral resolving power of nifs in the @xmath0band is @xmath10 5160 which results in a linear dispersion of 2.13 / pixel . this dispersion , combined with the large format array gives a full wavelength coverage at @xmath11 of about 4200 accounting for some minor truncation in the final data cube due to the systematic shift of wavelength in each slitlet from the staircase design of the image slicer . the line maps and spectra presented here were obtained using the gemini nifs iraf data reduction package ( version 1.9 ) . the nifs iraf package allows for full reduction to the `` image cube '' stage where a final cube has a roughly 60@xmath862 pixel image plane and a 2040 pixel spectral depth . first , raw images are prepared for reduction by standard gemini procedures that create the fits image variance and data quality extensions . next , the data are sky subtracted , flatfielded , rectified spatially , and wavelength calibrated ( see * ? ? ? * for a full description of these steps ) . the last two steps result in a uniform spatial spectral trace for each image slice row and a linear wavelength scale . it is important to remember that the final iraf data cube resamples each slitlet to two 0.05@xmath1 pixels for convenience ; the angular resolution in this dimension is still 0.1@xmath1 . a lamp image of ar and xe lines was used to determine the dispersion along each slice and as a function of the spatial dimension of each slice . a quadratic polynomial was used in this case which produced typical uncertainties in the position of a spectral line of approximately @xmath2 0.2 ( @xmath6 1/10 pixel ) . final spectra are interpolated to a linear wavelength solution . the spectra were next corrected for telluric absorption by division by the spectrum of an a0 v star ( hip 102568 ) . the spectrum of hip 102568 was corrected for intrinsic br@xmath3 absorption by fitting a voigt profile to the telluric spectrum . particular care was taken in the fit in order to remove this feature from the telluric standard as accurately as possible . the final wavelength calibrated , spatially rectified , and telluric corrected images were transformed into data cubes . the spatial pixel scale was resampled to 0.05@xmath1 in the fine dimension and block replicated to 0.05@xmath1 in the course dimension providing for a uniform scale as described in the previous section . line maps presented below were extracted from these cubes using nfmap . the zero point of the wavelength calibration is confirmed by the positions of oh airglow lines in the sky image . analysis of these lines shows the zero point is accurate to @xmath2 2.5 . the calibration results in an observed blueshift of the nebular lines of approximately 3.8 ( 1.8 pixels or @xmath1253 ) . lines are identified on a spectrum extracted from a 2.5@xmath1 diameter aperture centered on the nifs fov ; see figure [ spec ] . the spectrum is flux calibrated using the results of ( * ? ? ? * see below ) . the line positions and relative strengths compared to br@xmath3 for this integrated spectrum are given in table 1 . an image of the continuum near 21700 is shown in figure [ c217 ] along with the radio continuum image from @xcite . the continuum passband extracted was 9 pixels ( 19.2 ) wide . the appearance of sources in our continuum image is similar to the speckle @xmath0band image presented by @xcite who report an angular resolution of 0.11@xmath1 in their image derived from observations obtaddiained under 1.1@xmath1 seeing . @xcite identify 10 point sources in their image , though some of these appear more extended than others , and this is consistent with the continuum image shown in figure [ c217 ] . the brightest source in figure [ c217 ] is source # 1 of @xcite . the size of the most compact source in our image , source # 8 of @xcite , is about 3.7 pixels in the fine sampling direction suggesting a fwhm of 0.19@xmath1 . source # 1 is more extended than this in the present image ( @xmath6 4.9 pixels ) , but this is due to crowding with nearby blended sources and the intense nebular emission surrounding it . @xcite report source # 1 to be `` point like . '' the 10 sources identified by @xcite are clearly seen in figure [ c217 ] with the possible exception of their source # 2 which is close to source # 1 and not obvious in our image . the @xcite sources are indicated by filled circles in figure [ c217 ] . an additional point source ( named `` 8n '' ) appears near @xmath13 which is indicated by a single contour in figure 2 of @xcite . in addition to these objects , there are other knots or clumps which might contain embedded sources , or may be density enhancements in the region . these clumps appear to match well the morphology in figure 1 of @xcite . an exception is the `` x - like '' structure centered on source # 1 described by @xcite . we see no evidence of this feature in the lower contours of the nebular emission even though similarly bright clumps from the @xcite image do show up in our image . the mid infrared images of @xcite also do not show this feature , though diffraction spikes from the telescope secondary are present in their images . @xcite identified four bright sources in the core region of 350 covered by figure [ c217 ] in 913 images with somewhat lower angular resolution . the three brightest , okym13 , were unresolved as individual point sources . okym3 was associated with source # 1 by @xcite . the source labeled stho1 in figure [ c217 ] is the peak of [ ] emission in the maps of @xcite . these authors suggest stho1 is the location of an embedded massive star ." +"topological transport phenomena have been attracting a great deal of interest , because they exhibit universal properties that are insensitive to perturbations and independent of material details . a classical example of such a transport phenomenon is the integer quantum hall ( iqh ) effect in two - dimensional ( 2d ) electron systems , first discovered in 1980 , @xcite which is characterized by an integer quantization of the hall conductivity in unit of @xmath2 . the iqh effect has been observed in a large variety of materials , ranging from traditional semiconductors , to oxides , @xcite graphene , @xcite and topological insulators ( tis ) . @xcite laughlin @xcite interpreted the iqh effect in terms of an adiabatic charge pump . thouless , kohmoto , nightingale , and nijs @xcite established a relation between the quantized hall conductivity of the iqh system and a topological invariant , the first chern number . thouless and niu @xcite also related the amount of charge pumped in a 1d charge pump to the chern number . a variant of the iqh effect , the quantum spin hall ( qsh ) effect , was proposed recently , @xcite which has been experimentally realized in hgte quantum wells @xcite and inas / gasb bilayers . @xcite extension of the idea of the qsh effect has led to the discovery of 3d tis . @xcite a qsh system , which is also called a 2d ti , has an insulating band gap in the bulk and a pair of gapless helical edge states at the sample boundary . when the electron spin is conserved , a qsh system can be viewed as two independent iqh systems without landau levels . @xcite different from the charge , the spin does not obey a fundamental conservation law . in general , when the spin conservation is absent , unconventional topological invariants , either the @xmath3 index @xcite or the spin chern numbers , @xcite are needed to describe the qsh systems . the time - reversal ( tr ) symmetry is considered to be a prerequisite for the qsh effect , which protects both the @xmath3 index and gapless nature of the edge states . however , based upon the spin chern numbers , it was shown that the bulk topological properties remain intact even when the tr symmetry is broken . @xcite this finding evokes interest to pursue direct investigation and possibly utilization of the robust topological properties of the tis , besides using their symmetry - protected gapless edge states which are more fragile in realistic environments . unlike the first chern number underlying the iqh systems , which is embedded into the hall conductivity , up to now the topological invariants in the tis have not been directly observable . several experimental methods were proposed , but have not been realized . one was to measure the topological magnetoelectric effect , @xcite for which experimental complexities exist . @xcite fu and kane @xcite put forward an abstract 1d model , in which the spin pumping was related to the @xmath4 index in the limit of weak coupling . however , how this fictitious model could be implemented is still unknown . furthermore , from the viewpoint of application , generalization of the idea of the @xmath4 pump to higher dimension is meaningless , because according to the @xmath4 theory , @xcite only the states at the tr - invariant point of the brillouin zone can contribute to the spin pumping , and so the pumping rate can not be enhanced by increment of dimension . in a recent work , @xcite the more general case of finite coupling between the pump and electrode is investigated by using the scattering matrix method . it was found that the spin pumping in the model of fu and kane can survive finite scattering of magnetic impurities , and so may be attributed to the spin chern numbers rather than the @xmath3 index . some other authors @xcite proposed to pump quantized charge through the helical edge states by precessing a magnet covering the edge of a 2d ti , so that the number of gapless edge channels can be counted through electrical measurement . this method is indirect , in the sense that the topological invariants are intrinsic properties of the bulk electron wavefunctions , which do not immediately determine the charge pumping in the edge channels . here we predict an intriguing bulk topological pumping effect , directly driven by nonzero spin chern numbers , in a qsh system electrically modulated in adiabatic cycles . as a consequence of the topological spectral flows of the spin - polarized wannier functions ( spwfs ) in the bulk of the system , spin can be pumped into a nonmagnetic electrode continuously without net charge transfer . the total amount of spin pumped per cycle is proportional to the ( cross - section ) width of the sample , and insensitive to the material parameters and spin - mixing effect due to the rashba spin - orbit coupling . this electrical spin pump establishes a basis , on which spintronic applications taking advantage of the robust topological properties of the tis can be developed . especially , if a half - metallic electrode with spin polarization parallel ( or antiparallel ) to the @xmath5-axis is used , a quantized charge pumping conductivity , @xmath6 ( or @xmath7 ) , can be measured by electrical means , demonstrating a way to observe the spin chern numbers @xmath0 directly . let us consider a 2d model hamiltonian @xmath8 with @xmath9-m(t)\hat{\sigma}_{z}\ . \label{hamil}\ ] ] here @xmath10 is the electron charge , @xmath11 is the 2d momentum , @xmath12 is the vector potential of an @xmath13 electric field @xmath14 applied along the @xmath15 direction with @xmath16 and frequency @xmath17 being designated , and @xmath18 . this model can describe both the qsh materials , the hgte quantum wells , @xcite and inas / gasb bilayers , @xcite in the linear order in momentum . for definity of discussion , we confine ourselves to the hgte quantum wells , for which @xmath19 with @xmath20 are the pauli matrices for spin , and @xmath21 for the electron and hole bands . as will be discussed below , the time - dependent mass term @xmath22 can be induced by varying the voltages of the dual gates . @xmath23 represents the rashba spin - orbit coupling @xcite @xmath24\ . \label{rashba}\ ] ] to the linear order in momentum , the rashba spin - orbit coupling is nonvanishing only in the electron band . @xcite within the adiabatic approximation , for a bulk sample there exists a finite energy gap between the conduction and valence bands for @xmath25 or @xmath26 . at @xmath27 and @xmath26 , the conduction and valence bands touch at @xmath28 and @xmath29 or @xmath30 with @xmath31 . to clarify the topological properties underlying the spin / charge pumping , we consider @xmath32 as a parameter , and calculate the spin chern numbers @xmath0 in the standard way , @xcite on the torus of the two variables @xmath33 and @xmath34 with @xmath35 as the period . the spin chern numbers are obtained as @xmath36 for @xmath37 , and vanish elsewhere . not surprisingly , the band touching points @xmath38 serve as the critical points . ( vertical axis ) . the parameters are taken to be @xmath39 , @xmath40 , @xmath41 , and @xmath42 , with @xmath43 as the lattice constant and @xmath44 ( @xmath45 ) as the hopping integral of the tight - binding hamiltonian . , width=288 ] we now consider a system consisting of a pump for @xmath46 , an electrode for @xmath47 , and a potential barrier in between . the total hamiltonian of the system reads @xmath48 where @xmath49 has been given above , and @xmath50 is the hamiltonian of the electrode . a possible experimental setup for realizing this hamiltonian is explained in appendix a in more details . in the barrier region , the term @xmath51 opens an insulating gap of size @xmath52 , which accounts for contact deficiencies between the pump and electrode . the crucial role of the nonzero spin chern numbers in the spin / charge pumping process can be visualized by using the spwfs , which were first introduced in ref . we construct a tight - binding hamiltonian for the effective 1d system at any given @xmath53 according to eq . ( [ htot ] ) , and diagonalize the total hamiltonian of the pump and electrode numerically . following the same procedure as calculating the spin chern numbers , @xcite the space occupied by electrons is partitioned into two spin sectors after diagonalizing the spin operator @xmath54 in the occupied space . by definition , the states in the two spin sectors are essentially the maximally spin - polarized states . then we construct the wannier functions @xcite for the spin - up and spin - down sectors , respectively , which are called the spwfs . the evolution of the centers of mass of the spwfs for @xmath55 and @xmath56 is shown in fig . [ fig_1 ] . we see that the wannier centers for the spin - up sector move right and those for the spin - down sector move left , each center shifting on average a lattice constant per cycle . within the adiabatic approximation , time @xmath57 plays the same role as the momentum of an additional dimension , @xcite namely , @xmath58 . therefore , when @xmath53 is considered as a parameter , the evolution of the wannier functions of the effectively 1d system related to various @xmath59 with time @xmath60 can be understood from the static properties of a 2d system associated with various @xmath59 and @xmath61 . in the general theory , @xcite the relationship between the chern number and the spectral flows of the wannier functions in a 2d system has been established . according to this theory , the average displacement of each of the centers of the spwfs in the spin - up ( spin - down ) sector with changing @xmath61 ( or @xmath60 ) from @xmath62 to @xmath63 , in units of the lattice constant , must equal to the spin chern number @xmath64 ( @xmath65 ) . therefore , the nontrivial transfer of the spwfs observed in fig . 1 is a direct manifestation of the nonzero spin chern numbers @xmath66 in the pump ( for @xmath67 ) . more interestingly , we see that such spectral flows can go across the finite barrier ( @xmath68 ) , and extend into the electrode , even though the barrier and electrode are topologically trivial . physically , because the system needs to recover its original eigenstates when each cycle ends , the nontrivial spectral flows of the spwfs in the ti need to constitute closed loops through formation of edge states at the boundary , @xcite or extend into the electrode . however , localized edge states can not exist at the finite barrier due to quantum tunneling effect , so the transfer of the spectral flows of the spwfs into the electrode occurs . this result will be further confirmed by direct calculation based upon the scattering matrix theory in the next section . the spwfs are just another equivalent representation of the occupied space , and so the counter spectral flows of the wannier centers in the two spin sectors represent the true movements of the electrons . if the rashba spin - orbit coupling were neglected , the wannier functions would be the eigenstates of @xmath69 . the nontrivial spectral flows indicate that at the given @xmath53 , in each cycle a spin - up electron goes from the pump into the electrode , and a spin - down electron moves oppositely . therefore , no net charge transfer occurs but a" +"galaxy clusters play an important role in precision cosmology that complements other techniques like type ia supernovae luminosity - distance relation measurements @xcite , baryonic acoustic oscillations ( baos ) angular - distance relation measurements @xcite , and observations of the cosmic microwave background radiation ( see @xcite for a review ) . for example , @xcite exploit dark energy s influence on the growth of structure by using 37 moderate - redshift and 49 low - redshift clusters to measure the shape of the galaxy - cluster mass function and its redshift evolution , which constrain the dark - energy density parameter @xmath1 to @xmath2 in a non - flat @xmath3 cosmology and the dark energy equation of state parameter @xmath4 to @xmath5 in a flat cosmology . @xcite have obtained similar results from measurements of the evolving number density of the largest clusters in order to constrain @xmath4 to @xmath6 . strategies like these that compare model predictions to galaxy - cluster sample statistics inevitably confront sample error and sample bias . future surveys expected to gather samples of 1040 thousand galaxy clusters will maximize survey reach while maintaining sufficient observation quality in order to minimize sample error , but they still must grapple with a major source of sample bias , which is scatter in the relationship used to infer cluster mass from an observable mass proxy . an important mass - observable relation for galaxy cluster studies connects dark matter halo mass to the temperature of the intracluster medium ( icm ) inferred from its x - ray spectrum ( its `` x - ray temperature '' @xmath7 ) . in this paper we investigate the possibility of correcting for scatter in this relation using temperature - inhomogeneity in the icm , and discuss challenges that may exist in such a program . a significant amount of uncertainty in the dark - energy constraints obtainable from large cluster surveys derives from uncertainty in scatter about the mean scaling relations obeyed by galaxy clusters bulk properties @xcite . the key galaxy cluster property to measure when trying to constrain dark energy with clusters is the cluster s mass , which can not be directly observed . theoretical considerations predict correlations among halo mass and more readily observed cluster properties , like its galaxy richness , the velocity dispersion of its galaxies , @xmath7 , the sunyaev - zeldovich decrement , the gas mass , and @xmath8 parameter , which is the product of @xmath7 and the gas mass inferred from x - ray observations @xcite . theory also predicts intrinsic scatter in these relations owing to variation in cluster dynamical state ( see , for example * ? ? ? * ; * ? ? ? * ; * ? ? ? one way to deal with intrinsic scatter is to join a cluster model to a cosmological model and simultaneously fit for the parameters of both , leveraging the statistical power of large surveys and `` self - calibrating '' the mass - observable relations . another approach is to combine observables that tend to depart from the expected scaling relations in opposite ways , yielding a new , low - scatter composite observable . an example low - scatter composite observable is @xmath8 , since at a given halo mass , offsets in the measured gas mass at fixed total mass tend to anti - correlate with offsets in the measured temperature @xcite . another family of low - scatter composite observables attempt to measure structural variation directly . mergers , relaxation , and non - adiabatic processes like radiative cooling , star formation , and feedback ought to leave a visible imprint that may allow us to measure and correct for scatter . for example , one might use imaging to quantify resolved morphological substructure . @xcite apply two observationally - motivated structure measures , the power ratios @xcite and the centroid shift @xcite , to a sample of galaxy clusters simulated with @xcite . they find that cluster structure correlates strongly with bias in mass estimates derived from @xmath7 under the assumption of hydrostatic equilibrium and accounting for cluster structure can be used to correct some of the bias . similarly , @xcite apply the power ratios , centroid shift , and axial ratio @xcite substructure measures to the same sample of simulated clusters used in this paper , and find that cluster substructure correlates with departures from the mean relationship in the sense that clusters with more substructure tend to have a lower temperature at a given mass , and can be used to refine mass estimates derived from the icm x - ray temperature . @xcite likewise find that greater substructure , as quantified with power ratios , correlates with lower temperature at a given mass . @xcite find a strong correlation between mass - temperature scatter and halo concentration in their sample of simulated clusters , with cooler clusters appearing more concentrated than warmer clusters at similar mass . @xcite observe , however , that line - of - sight projection effects lead to significant uncertainties in morphologically - derived substructure measures . substructure also becomes more difficult to resolve at high redshift . spectral signatures of dynamical state are therefore attractive because they are aspect - independent and redshift - independent . one such spectral signature of dynamical state is the `` temperature ratio '' @xcite , which divides a `` hardband '' spectral - fit temperature by a `` broadband '' spectral - fit temperature . an energy cut applied to a broadband spectrum produces a hardband spectrum and serves to filter out cooler line - emitting components of the icm . @xcite studied the effects of relaxation on the observable properties of galaxy clusters , using a sample of numerically - simulated galaxy clusters generated by @xcite . they found that hardband ( 2.09.0 kev ) x - ray spectral fit temperatures average @xmath920% higher than broadband ( 0.59.0 kev ) temperatures and suggested that this effect may signal the presence of cool , luminous sub - clusters lowering the broadband temperature . @xcite corroborated these findings in simulations that included radiative cooling . figures [ fig : f01 ] and [ fig : f02 ] illustrate the effect . both show a counts spectrum and single - temperature fit for a typical , unrelaxed cluster in our sample , with an aperture set at @xmath10 and a core region out to @xmath11 excised . figure [ fig : f01 ] is for a single - temperature model fit to the broad band , while figure [ fig : f02 ] is for the hard band . note the excess emission relative to the model above 4.0 kev and the deficit below 2.5 kev that arises because the model can not simultaneously fit both a hot component and a cooler , line - emitting component @xcite . figure [ fig : f02 ] shows the same spectrum , but with the residuals for a model fit just to the hard band . in this case the fit is much better over the range from 2.0 to 7.0 kev but under - predicts the emission below 2.0 kev . @xcite suggested that the temperature skewing they observed might indicate a real temperature skewing detectable in real clusters using . @xcite fit single - temperature emission models to the hard band ( 2.07.0 kev ) and broad band ( 0.77.0 kev ) for a large ( n = 192 ) sample of clusters with observations selected from the data archive . these authors show that for a large , heterogeneous sample of clusters across a broad temperature range , the distribution of has a mean of 1.16 and an rms deviation @xmath12 , with tending to be larger in merging systems . they also report that while this signal is significant in the aggregate , the errors for any single measurement and the scatter across all of the measurements together pose challenges for any effort to use either to select for merging systems or to obtain more accurate mass estimates . in order to meet these challenges it is important also to examine and similar spectral signatures of dynamical state in a simulation context . like the original study of @xcite , this paper examines the temperature ratio for a sample of simulated clusters and simulated observations , and as in the subsequent study by @xcite , the simulated clusters analyzed here were generated using a hydrodynamical code with radiative cooling included . this paper is organized as follows . in @xmath13 , we describe the simulated clusters in our sample along with the 2 code for generating their mock x - ray observations . in @xmath14 , we present our analysis methods and define the spectral signatures of dynamical state we examine . in @xmath15 , we report and discuss our results , and @xmath16 summarizes our work . this study is based on an analysis of 118 clusters simulated using the cosmological hydrodynamics tree+sph code gadget-2 @xcite , which were simulated in a standard @xmath17 cold dark matter ( @xmath17cdm ) universe with matter density @xmath18 = 0.3 , @xmath19 = 0.7 , @xmath20 = 0.04 , and @xmath21 = 0.8 . the simulation includes radiative cooling assuming an optically - thin gas of primordial composition , with a time - dependent uv background from a population of quasars , and handles star formation and supernova feedback using a two - phase fluid model with cold star - forming clouds embedded in a hot medium . all but four of the clusters are from the simulation described in @xcite , who simulated a box @xmath22 on a side , with @xmath23 dark matter particles and an equal number of gas particles . the present analysis considers the 114 most massive clusters within this box at @xmath24 , which all have @xmath25 greater than @xmath26 . these are referred to as the b04 sample in the remainder of this paper . by convention , @xmath27 refers to the mass contained in a sphere which has a mean density of @xmath28 times the critical density @xmath29 , and whose radius is denoted by @xmath30 that cluster set covers the @xmath91.5 - 5 kev temperature range , but the @xmath22 box is too small to contain significantly hotter clusters . we therefore supplemented it with four clusters with masses @xmath31 and temperatures @xmath32 kev drawn from a dark - matter - only simulation in a larger @xmath33 box @xcite , referred to in this paper as the d09 sample . the cosmology for this simulation also was @xmath17cdm , but with @xmath21 = 0.9 . these were then re - simulated including hydrodynamics , radiative cooling , and star formation , again with gadget-2 and using the zoomed - initial - conditions technique of @xcite , with a fourfold increase in resolution . this is comparable to the resolution of the clusters in the smaller box . adding these four massive clusters to our sample gives a total of 118 clusters with @xmath25 in the range @xmath34 to @xmath35 . the mean structural properties of massive clusters drawn from a sample with @xmath21 = 0.9 may differ somewhat from those of similar - mass clusters in a @xmath21 = 0.8 universe because they reflect a more advanced state of cosmic evolution . however , these four additional clusters carry minimal statistical weight in the context of the overall sample . they are included primarily to evaluate whether the mean and dispersion of their @xmath36 values are consistent with those of the lower - mass systems . the simulated galaxy clusters in our sample are processed with the _ x - ray map simulator _ version 2 ( 2 ) @xcite to generate x - ray images suitable for standard reduction techniques . in its first step 2 uses the outputs" +"an important issue for transport in nanosystems concerns the role of electronic interactions . for one dimensional conductors such as carbon nanotubes , electronic correlations are known to lead to dramatic behavior , such as a zero bias anomaly in the tunneling conductance@xcite . recently , the problem of electron injection in the bulk of a nanotube , which extremities are connected to leads , was examined@xcite . for an infinite carbon nanotube length , it was shown that the measurement of both current auto- and cross - correlations in the current could lead to a diagnosis of the anomalous ( non - electron ) charges arising from collective excitations propagating in the nanotube . this work was followed other studies@xcite where the role of fermi liquid leads connected to the nanotube was investigated in view of detecting anomalous charges . for the injection geometry of ref . , the zero - frequency noise cross - correlations vanish as a result of multiple andreev - like reflections at the contacts : only electrons can be accepted by the right and left contacts . to a first approximation , current and auto - correlation noise were shown to follow the schottky relation@xcite with a fano factor corresponding to the electron charge . the purpose of the present work is to focus on the finite size effects which are manifest in this transport geometry , and is two - fold . first , we wish to reexamine whether this schottky relation is indeed followed for all parameters in this finite size geometry . indeed , there are several frequency scales in this geometry . the inverse of the voltage scale @xmath0 corresponds to the time spread of the electron wave packet entering the nanotube . the inverse of the finite length frequency @xmath1 ( @xmath2 is the interaction parameter of the nanotube , @xmath3 is its length ) corresponds to the time of flight of excitations propagating from one contact to the other . we shall show that in the limit where @xmath4 , the schottky behavior with the electron charge as the proportionality factor is violated , leading to a voltage dependent fano factor . the second part of this study concerns photo - assisted noise : an ac bias is superposed to the dc bias imposed between the scanning tunneling microscope ( stm ) tip which injects the electrons , and the nanotube . experimentally , photo - assisted noise has been measured in diffusive wires@xcite , diffusive junctions@xcite and quantum point contacts@xcite . for normal metals , the noise derivative displays steps at integer values of the ratio @xmath5 , where @xmath6 is the ac frequency@xcite . we naturally expect that this behavior is modified by the tunneling density of states exponent of our geometry , leading here to a smoothing of the steps due to electronic correlations . it is the case in the absence of finite size effects . more interestingly , we will show that when finite size effects are present , the noise derivative with respect to voltage has a stepwise behavior , similar to the one obtained for normal metal . indeed , concerning the first part of this study , our previous works on electron injection@xcite did not fully take into account the presence of the leads , in the sense that the tunneling density of states is slightly modified by finite size effects . note that this does not bear any dramatic consequences on our finite frequency noise scheme @xcite which was used to detect anomalous charges in a nanotube connected to fermi liquid leads . in the present zero - frequency noise study , we feel that it is quite interesting to deepen the study of transport because to our knowledge , in most tunneling geometries of mesoscopic physics , the schottky relation is expected to be followed with a voltage independent fano factor . the present numerical study allows to probe to what extends this relation is violated when the voltage is `` low '' , and this violation is rendered more explicit when interactions in the nanotube are strong . the second part of this study deals with photo - assisted noise . photo - assisted transport ( current ) is by no means new : a pioneering work@xcite considered the effect of a microwave fields on the tunnel transfer of electrons between two superconductor films . in mesoscopic devices , photo - assisted noise was first studied theoretically in a normal metal junction , leading , as mentioned above , to a stepwise behavior in the nose derivative@xcite . this latter work was extended to treat normal metal - superconductor junctions@xcite , leading to a diagnosis of the cooper pair charge transferred in an andreev reflection process . it was also applied to the fractional quantum hall effect@xcite where the charge transferred can either be that of a laughlin quasiparticle or that of an electron , depending on whether weak or strong pinching of the point contact placed on a quantum hall bar . so as far as 1d strongly correlated systems are concerned , photo - assisted transport has so far been confined only to chiral luttinger liquids . a further study of photo - assisted transport in non - chiral luttinger liquids is clearly lacking , but most importantly its crucial feature here is to understand how finite size effects of the nanotube modify the `` expected '' behavior . the paper is organized as follows : in sec . ii , we define the geometry which applies to our calculation and we recall the basic assumptions of the model developed in ref . . iii , we concentrate on the calculation of the nanotube current and of the nanotube auto - correlation noise for the numerical study of the voltage dependent fano factor . iv , is devoted to the calculation of photo - assisted transport in a nanotube . we conclude in sec . we consider the following setup : an stm tip close to a carbon nanotube connected to leads at both extremities . a voltage applied between the stm and the nanotube allows electrons to tunnel in the center region of the nanotube . as a result , charge excitations propagate along the nanotube toward the right and left leads . this system is described by the hamiltonian @xmath7 . the nanotube is a non - chiral luttinger liquid@xcite : @xmath8~ , \label{b_ham}\end{aligned}\ ] ] where @xmath9 is the position along the nanotube , @xmath10 and @xmath11 are non - chiral bosonic fields and @xmath12 is the coulomb interactions parameter for each charge / spin , total / relative sectors @xmath13 . we put @xmath14 . because of time reversal symmetry , @xmath15 , and we assume that @xmath2 depends on position@xcite as depicted on fig . [ fig1 ] . the velocities satisfy @xmath16 . 8 cm the electrons in the metallic stm tip are assumed to be non - interacting . for convenience@xcite , the electron field @xmath17 in the stm tip can be described in terms of a semi - infinite luttinger liquid with coulomb interactions parameters all equal to one . the tunnel hamiltonian between the stm tip and the nanotube at position @xmath18 is : @xmath19^{(\epsilon)}~ , \label{ham}\end{aligned}\ ] ] where @xmath20 corresponds to the branch index , @xmath21 to the mode index and @xmath22 to the spin . the superscript @xmath23 leaves either operator unchanged @xmath24 , or transforms it into its hermitian conjugate @xmath25 . the voltage is taken into account via a time dependence of the tunneling amplitude ( peierls substitution ) @xmath26 where @xmath0 is the voltage frequency . the fermionic fields for electrons in the nanotube and in the stm tip are respectively defined by : @xmath27 where @xmath28 is the ultraviolet cutoff of the luttinger liquid model , @xmath29 and @xmath30 are klein factors , @xmath31 is the fermi momentum and @xmath32 is the momentum mismatch associated with the two modes @xmath21 . for further calculation purposes , it is convenient to rewrite the bosonic field @xmath33 in terms of the non - chiral bosonic fields @xmath11 and @xmath10 : @xmath34~,\ ] ] with coefficients @xmath35 , @xmath36 , @xmath37 and @xmath38 , and bosonic fields obeying the equal time commutation relations @xmath39=-(i/2 ) \delta_{jj^\prime}\delta_{\delta\delta^\prime}\,sgn(x - x^\prime)$ ] . @xmath40 is the chiral bosonic field attached to the stm tip , whose keldysh green s function at @xmath18 is given by @xcite : @xmath41,\nonumber\end{aligned}\ ] ] where @xmath42 denotes the upper / lower branch of the keldysh contour . in this section , we present the calculations of current and zero - frequency shot noise . since we have to treat a non - equilibrium situation due to the application of a voltage bias between the stm tip and the nanotube , we define average values of the current and of the unsymetrized noise in the framework of the keldysh formalism@xcite : @xmath43 where @xmath44 denotes time ordering along the keldysh contour and @xmath45 is the total current operator which can be defined through the bosonic field @xmath46 : @xmath47 . it has been shown in ref . that , up to the second order with the tunnel amplitude @xmath48 , the average current and the zero - frequency fourier transform of the noise can be expressed as : @xmath49 where @xmath50 is the keldysh green s function for the stm tip given by eq . ( [ green ] ) , and @xmath51 is the keldysh green s function for the nanotube bosonic field @xmath10 : @xmath52 similar definitions hold for other combinations of bosonic fields : @xmath53 , @xmath54 and @xmath55 . for @xmath56 , we have@xcite : @xmath57\biggr\}~,\end{aligned}\ ] ] where @xmath58 is the reflection coefficient at the lead positions @xmath59 . in addition , @xmath60 , and the green s function @xmath61 can be obtained by the substitution @xmath62 in eq . ( [ green_nano ] ) . the integration over @xmath63 in eq . ( [ courant ] ) and over @xmath64 and @xmath65 in eq . ( [ bruit ] ) can be performed . we obtain : @xmath66 where @xmath67 . from eq . ( [ noise ] ) , we immediately see that the zero - frequency cross - correlations @xmath68 cancel at order @xmath69 , as it is the case for a non - interacting three terminals device@xcite . this is because quasiparticle excitations in the nanotube suffer multiple reflections at the contacts , which lead to a recombination of these in the form of an electron entering the contact on either side , but not both . 8 cm by a careful analysis of eqs . ( [ current ] ) and ( [ noise ] ) , we notice , as announced in the introduction , that three characteristic frequencies are involved : the voltage frequency @xmath0 , the nanotube length frequency @xmath1 , which is related to the time @xmath70 that excitations take to reach the leads from the position @xmath18 , and the cutoff frequency @xmath71 of the luttinger liquid model . taking realistic values : @xmath72 ( carbon nanotube diameter ) , @xmath73 ( carbon nanotube length ) and @xmath74 for the fermi velocity@xcite , we obtain the estimations @xmath75 and @xmath76 . we consider that @xmath77 can vary from 0 to @xmath78 ( i.e. , from 0 to @xmath79 ) . in fig . [ fig2 ] , numerical calculations of the current and the noise of eqs . ( [ current ] ) and ( [ noise ] ) are presented as a function of the ratio @xmath80 . these are plotted in units of @xmath81 where @xmath82 is the gamma function . we observe two different regimes . the first one corresponds to the limit @xmath83 for which the spatial extension of the electron wave packet injected in the nanotube is much smaller than" +"gx1 + 4 is an x - ray binary system harboring a @xmath4130s pulsar ( [ 13 , 10 , 8 ] ) accreting mass from a red giant companion of class m5 iii ( v2116 ophiuchi ; [ 6,2,4,18 ] ) . among the large x - ray binary zoo , we know so far only another system hosting a neutron star ( ns ) with a red giant companion : 4u 1700 + 24 ( [ 16,9 ] ) . gx1 + 4 shows an unpredictably variable x - ray flux on timescales from hours to decades . at the time of its discovery ( [ 13 ] ) it was one of the brightest object in the x - ray sky and it had the largest spin - up rate recorded for any pulsar at that time . the average spin - up trend reversed inexplicably in 1983 switching to spin - down at approximately the same rate . so far a remarkable number of changes in the sign of the torque has been observed for this source ( [ 3 ] ) . this is somehow a peculiar object among the x - ray binaries not only because of its red giant companion , but also because of the high magnetic field that the ns is believed to have ( @xmath5 g ; [ 7,11,5 ] ) . in fact , the presence of a such high magnetic field in a slowly rotating ns with a red giant companion is an intriguing puzzle for the evolutionary scenario of this system . here we report on the timing and spectral x - ray properties of gx 1 + 4 , in particular on a strange drop in the flux occurred in 2000 november 1st during a _ bepposax _ observation . the _ bepposax _ observatory covered more than three decades of energy , from 0.1200kev . the payload was composed by four co - aligned instruments : the narrow field instruments ( [ 1 ] : lecs , 0.110kev ; mecs , 110kev ; hpgspc , 4100kev ; pds , 15200kev ) and the wide field cameras ( [ 12 ] ) . all the four nfi instruments were on during the @xmath43.5days _ bepposax _ observation carried out around 2000 november 1st . the lightcurve of the x - ray source , in the 0.1200kev energy range , showed a large flux variability ( see fig.1 ) . we searched for coherent pulsations performing a power spectrum analysis followed by a phase - fitting analysis , and we found the spin period value of @xmath6s ( phase zero calculated at tjd 11785.000781 ; errors in the text are at 1@xmath7 confidence level ) . in order to study the possible evolution or changes of the timing properties of the source , we divided the observation in 10 time intervals and looked for pulsations all over each interval in different energy bands . making this division we noticed that outside of the low x - ray flux event , all instruments showed pulsations at the same spin period @xmath8s in the whole _ bepposax _ energy range ( see fig.2 ) , while in interval d no pulsed emission was detected below @xmath47kev . as we can see from fig.2 , the pulse shape was highly variable either in time or in energy . comparing the phase at which the minimum of the pulse occurs among the hpgspc profiles , we found shifts in phase between all curves : e.g. the folded lightcurve in the interval l is shifted in phase by 0.22 + -0.05 with respect to that in the interval d. along with the pulse profile changes , the pulsed fraction also varies . during the event the pulsed fraction below 7kev was consistent with zero ( 6% upper limit ) , while it increases until @xmath9% in the 735kev energy range . in order to fit the spectra of the source in all the intervals , we first tried several simple models such as a bremsstrahlung emission , as a blackbody plus a power - law , or as a multicolour blackbody , but all these models gave a bad chi - square value . noticing then that the source spectrum in the low - flux state was exactly what is expected for a compton - reflection dominated spectrum , we tried to fit all the spectra with an absorbed cut - off power law with a reflection component ( pexrav model in _ xspec _ ; [ 15 ] ) . this was actually the best model for all the time resolved spectra ( @xmath10 ) with a very small relative reflection strength ( refl@xmath1100.3 ) outside the event and being @xmath12 during the low - flux event ( see fig.3 ) . the @xmath13 ranged between 748@xmath14@xmath15 , reaching the maximum values just before and after the event , while at higher energies , the spectrum showed a hardening when the compton scattering component started to dominate , soon after the flux dropped . all time - resolved spectra showed at least one emission line . only one broad ( @xmath160.3kev ) fe emission line was present at @xmath176.55kev outside of the low - flux event , while in the intervals d and e , the reduced persistent flux revealed the presence of two narrow lines at @xmath46.45kev and @xmath47.05kev , with very high equivalent widths ( @xmath42.1 and 0.5kev , respectively ) . the interpretation of all these lines is very difficult and uncertain considering the limited energy resolution of the mecs . thus , we can only speculate on the origin of the lines . our idea is that the broad line at 6.55kev might be the blend of the neutral fe @xmath18 around 6.4kev and the ionized fe xxv at 6.7kev , while during the event only the neutral fe components are present , the @xmath18 and the @xmath19 . we report here on the longest uninterrupted observation of the x - ray binary system gx1 + 4 . the most important results of this analysis are : i ) a compton - reflection component dominates the source spectrum during a low - flux emission event , ii ) the discovery of the line at @xmath47.05kev during such low - intensity event , iii ) during the latter , a pulsed x - ray emission was detected only at energies @xmath20 7kev , vi ) the detection of a highly variable pulse profile and v ) the detection of a shift in phase of the minimum of the high - energy pulse profile during the low - flux event . hereafter we consider a few models for this event taking in account the results of our analysis . our first idea was that the x - ray source entered in a different emission status ( as happen for some x - ray binaries ) , where the flux diminishes and the spectrum changes . however , since one spectral model was able to describe all the spectra and that the spectrum during the low - flux event was compton - reflection dominated , we ruled out this first hypothesis . in fact , the reflection component should be produced by a compton thick material that reprocesses the source photons . this reprocessing occurs through the compton - reflection process , where x - rays and @xmath21-rays emitted by a source impinge upon a slab of material ( e.g. accretion disk ) and re - emerge with a spectrum altered by the compton scattering and the bound - free absorption . this process cause a characteristic hardening in the x - ray spectrum which is due to the onset of the reflected component , which appears at energies @xmath2010kev , as a result of the increased importance of the compton scattering in comparison with the bound - free absorption , which instead dominates at low - energies ( [ 21 , 14 ] ) . at this point , we were then interested to figure out the geometry and the nature of the material responsible for the reflection . concerning the geometry , one possibility is that the ns was simply hidden in a partial eclipse caused by the giant companion . the partial covering might be due to part of the giant star ( a spherical cap ) which temporarily occults the ns direct x - ray emission from our line of sight . although this eclipse scenario is consistent with the source variability , however , a wide solid angle of compton thick material around the source is needed in order to produce such highly reflection dominated spectrum , and this large solide angle can not be produced by the stellar companion wind only . moreover , taking into account the large size of the companion star compared with the 10 km radius of the ns , the occurrence of a @xmath490ks eclipse , requires an ad hoc fine tuning of the line of sight inclination with respect to the orbital plane . another possible geometry might be a torus - like accretion disk around the compact source , due to matter coming from the giant companion . the lobes of the torus become thicker and increase in volume with increasing of the accretion rate . the direct emission of the ns would had been hidden by one side of the torus while the other side of the torus reflected it , causing the drop of the flux and the compton reflected spectrum . this model can explain as well the lack of detection of the low - energy pulsations , as they are too weak to keep their coherence through the scattering in the thick torus material . moreover , during the low - emission event the photons make a different path before reaching the observer , compared to the direct emission phases , and this can be the cause of the shift in the spin - phases revealed in the high - energy pulsations ( see fig.2 right panel ) . this scenario requires an highly variable mass accretion rate , possibly due to a variable mass loss from the red giant companion , which is expected from these stars . thus , note that the accretion rate variability of this source , is well supported by the detections of spin - torque variations in the source timing history ( [ 3 ] ) . this latter model we propose in order to explain the low - flux event , is in analogy with what was proposed for some agn sources and for some of the highly absorbed _ integral _ sources ( [ 20,19,17 ] ) . if this scenario is correct we can imagine that the highly absorbed _ integral _ sources are compact binary systems of this type for which our unlucky line of sight , hides the direct emission of the compact object behind the accretion torus lobes . note that the absorption value reached by gx1 + 4 in some part of the observation is similar of the @xmath13 found for some of this highly absorbed _ integral _ sources , although a compton - reflection component was never unambiguously revealed in these sources so far . boella , g. , et al . 1997 , a&as , 122 , 299 chakrabarty d. , et al . 1997a , a&as , 190 , 450 chakrabarty d. et al . 1997b , apj , 481 , l101 chakrabarty d , et al . 1998 , apj , 497 , l39 cui w. et al . 1997 , apj , 482 , l163 davidsen a. , et al . 1977 , apj , 211 , 866 dotani t. , et al . 1989 , pasj , 41 , 427 galloway d.k . , et al . 2001 , mnras , 325 ," +"entanglement plays a central role in quantum information theory . it is considered a resource for quantum communication and teleportation , as well as for various computational tasks @xcite . the importance of understanding entanglement in a relativistic setting has received considerable attention recently @xcite . such an understanding is certainly relevant from a fundamental point of view , since relativity is an indispensable component of any complete theoretical model . however , it is also important in a number of practical situations , for example , when considering the implementation of quantum information processing tasks performed by observers in arbitrary relative motion . entanglement was shown to be an invariant quantity for observers in uniform relative motion in the sense that , although different inertial observers may see these correlations distributed among several degrees of freedom in different ways , the total amount of entanglement is the same in all inertial frames @xcite . in non - inertial frames , entanglement was first studied indirectly by investigating the fidelity of teleportation between two parties in relative uniform acceleration @xcite . more recently , the observer - dependent character of entanglement was explicitly demonstrated by studying the entanglement between two modes of a free scalar field as viewed by two relatively accelerated observers @xcite . a uniformly accelerated observer is unable to access information about the whole of spacetime since , from his perspective , a communication horizon appears . this can result in a loss of information and a corresponding degradation of entanglement . in essence , the acceleration of the observer effects a kind of `` enviromental decoherence '' , limiting the fidelity of certain quantum information - theoretic processes . a quantitative understanding of such degradation in non - inertial frames is therefore required if one wants to discuss the implementation of certain quantum information processing tasks between accelerated partners . in curved spacetime two nearby inertial observers are relatively accelerated due to the geodesic deviation equation . accordingly , the results of @xcite indicate that in curved spacetime even two inertial observers will disagree on the degree of entanglement in a given bipartite quantum state of some quantum field . indeed , a thorough investigation into entanglement in an expanding curved spacetime shows that entanglement can encode information concerning the underlying spacetime structure @xcite . in this paper we analyze the entanglement between two modes of a dirac field described by relatively accelerated parties in a flat spacetime . we are interested in understanding how both the crucial sign change in fermi - dirac versus bose - einstein distributions , and the finite number of allowed states in fermionic systems due to the pauli exclusion principle ( in contrast to the unbounded excitations that can occur in bosonic systems ) , affect the degradation of entanglement produced by the unruh effect . we find that unlike the bosonic case , where the entanglement degrades completely in the infinite acceleration limit , in the fermionic case the entanglement is never completely destroyed . we analyze the degradation of entanglement in the system by applying the constraints of entanglement sharing @xcite and track the information originally encoded in these quantum correlations by employing a set of multi - qubit complementarity relations @xcite . as in @xcite , our results can be applied to the case that alice falls into a black hole whilst rob barely escapes through eternal uniform acceleration . the remainder of this paper is organized as follows . in sec . [ sec : setting ] we consider two modes of a free dirac field that are maximally entangled from an inertial perspective . two parties , an inertial observer named alice and a uniformly accelerating observer named rob , are each assumed to possess a detector sensitive only to one of the two modes . each measures the field with his / her detector and the results are compared in order to estimate the entanglement between the modes . section [ sec : unruh ] discusses the unruh effect for dirac particles as experienced by rob . if a given dirac mode is in the vacuum state from an inertial perspective , then rob s detector perceives a fermi - dirac distribution of particles . this has a strong effect on the entanglement that exists between alice and rob , and therefore plays an important role in any quantum information task they might perform that uses this entanglement as a resource . in sec . [ sec : ent ] we calculate the entanglement between the modes from the perspectives of both alice and rob . due to the presence of a rindler horizon , rob is forced to trace over a causally disconnected region of spacetime that he can not access . accordingly , his description of the system takes the form of a two - qubit mixed state . we calculate the entanglement using mixed state entanglement measures such as the entanglement of formation @xcite and the logarithmic negativity @xcite . we also estimate the total correlations ( classical plus quantum ) via the mutual information @xcite . our results show that the entanglement of formation does not vanish as it does in the bosonic case , but rather reaches a minimum of @xmath0 in the limit that rob moves with infinite acceleration . since the fermionic system we are considering is accurately described by a pure state of three qubits , we study the constraints placed on the system by the phenomenon of entanglement sharing in sec . [ sec : ent_sharing ] . our analysis shows that no inherently three - body correlations are generated in the quantum state . that is , all of the entanglement in the system is in the form of bipartite correlations , regardless of rob s rate of acceleration . using complementarity relations applicable to an overall pure state of three qubits , as well as to the various two - qubit marginals , we identify the different types of information encoded in the quantum state of our system in sec . [ sec : complementarity ] . this enables us to study how specific subsystem properties depend on rob s rate of acceleration and to explain how some of the entanglement from the inertial frame is able to survive in the fermionic system , even at infinite acceleration . finally , we summarize our results and suggest possible directions for further research in sec . [ sec : conclusions ] . consider a free minkowski dirac field in @xmath1 dimensions @xmath2where @xmath3 is the particle mass , @xmath4 the dirac gamma matrices , and @xmath5 is a spinor wavefunction . minkowski coordinates @xmath6 with @xmath7 are the most suitable to describe the field from an inertial perspective . the field can be expanded in terms of the positive ( fermions ) and negative ( antifermions ) energy solutions of the dirac equation @xmath8 and @xmath9 respectively , since they form a complete orthonormal set of modes , @xmath10 in the above , @xmath11 is a notational shorthand for the wavevector @xmath12 which labels the modes . the positive and negative energy minkowski modes have the form @xmath13 where @xmath14 , and @xmath15 is a constant spinor with @xmath16 indicating spin - up or spin - down along the quantization axis , satisfying the normalization relations @xcite @xmath17 , @xmath18 , with the adjoint spinor given by @xmath19 . the above positive and negative energy solutions satisfy the orthogonormality relations @xmath20 where the dirac inner product for two mode functions is given by @xmath21 the modes @xmath22 are classified as positive and negative frequency with respect to ( the future - directed minkowski killing vector ) @xmath23 for @xmath24 , i.e. @xmath25 the operators @xmath26 and @xmath27 are the creation and annihilation operators for the positive and negative energy solutions of momentum @xmath11 which satisfy the anticonmutation relations @xmath28with all other anticommutators vanishing . the minkowski vacuum state is defined by the absence of any mode excitations in an inertial frame , @xmath29where the @xmath30 superscript on the kets is used to indicate the particle and anti - particle vacua , respectively so that @xmath31 . we will use the notation here , and throughout the rest of the work , that the mode index ( @xmath32 ) will be a subscript affixed to the occupation number inside the ket , and that the absence of a subscript on the outside of the ket indicates a minkowski fock state . since @xmath33 , there are only two allowed states for each mode , @xmath34 and @xmath35 for particles , and similarly for anti - particles . consider two maximally entangled fermionic modes in an inertial frame , @xmath36 and @xmath37 indicate the modes associated with the observers alice and rob , respectively . all other modes of the field are in the vacuum state , and therefore the state can be written as @xmath38 . now assume that alice is stationary and has a detector sensitive only to mode @xmath39 . rob moves with uniform acceleration and takes with him a detector that only detects particles corresponding to mode @xmath40 . we ask the question of what is the entanglement between modes @xmath39 and @xmath40 observed by alice and rob , given that rob undergoes uniform acceleration . note that in order to determine the amount of entanglement , alice and rob perform measurements which are then compared by either party in order to estimate the correlations in the results . due to rob s acceleration , at some point alice s signals will no longer reach rob , but rob s signals will always be available to alice , ( see ) . at this point only alice can compare the measurement results and estimate the entanglement of the state . let us now consider the state observed by rob . consider rob to be uniformly accelerated in the @xmath41 plane ( @xmath42 ) . rindler coordinates @xmath43 are appropriate for describing the viewpoint of an observer moving with uniform acceleration . two different sets of rindler coordinates , which differ from each other by an overall change in sign , are necessary for covering minkowski space @xcite . these sets of coordinates define two rindler regions that are causally disconnected from each other . @xmath44 where @xmath45 denotes rob s proper acceleration . the above set of coordinates both give rise to the same metric @xmath46 where @xmath47 are the same in both minkowski and rindler spacetimes . are hyperbolas and lines of constant proper time @xmath48 for the accelerated observer run through the origin . note that while @xmath48 flows in the direction of @xmath49 in region i , it flows in the direction of @xmath50 in region ii , ( i.e the dashed line rotates counter - clockwise for increasing values of @xmath48 ) . a uniformly accelerated observer rob ( @xmath37 ) with acceleration @xmath45 travels on a hyperbola constrained to region i , while a fictitious observer anti - rob @xmath51 travels on a corresponding hyperbola in region ii given by the negative of rob s coordinates . the horizons @xmath52 are lines of @xmath53 which alice ( @xmath54 ) will cross at finite minkowski times.,width=336,height=240 ] a particle undergoing eternal uniform acceleration remains constrained to either rindler region i or ii and has no access to the opposite region , since these two regions are causally disconnected . figure [ fig1 ] serves to illustrate these ideas , as well as to introduce our labeling scheme , where we refer to the accelerated observer in region i as rob ( r ) and to the corresponding fictitious observer confined to region ii ( whose coordinates are the negative of rob s ) as anti - rob @xmath55 . the coordinates @xmath43 have the ranges @xmath56 separately in region i and in region ii . this implies that" +"the triple junction ( tj ) is a line where three grain boundaries ( gbs ) meet together . it is commonly believed that tjs greatly influence properties of nanocrystalline materials and can play a significant role during plastic deformation and diffusional creep . @xcite the tjs are much less studied crystalline defects than gbs or dislocations are . experimental investigations of tjs are complicated by many factors , including their high mobility . @xcite experimental measurements indicate that zinc diffusion along tjs in al is three orders of magnitude faster than along gbs . @xcite tjs can also be the sites of preferred solute segregation . @xcite some theoretical models introduce the assumption of fast tj diffusion to explain the anomalous diffusion and deformation behavior of nanocrystalline materials . @xcite however , no reliable experimental information on self - diffusion along tjs is currently available to verify this assumption . due to the recent progress in the development of interatomic potentials capturing basic properties of materials on the quantitative level , @xcite atomistic simulations offer a means of predicting self - diffusion coefficients that would otherwise be very difficult to measure . for example , the gb self - diffusion coefficients in copper predicted by simulations were found to be in very good agreement with experiment . @xcite to the best of our knowledge , tj diffusion has never been studied by atomistic simulations . as in experiments , the tj motion at finite temperatures poses a major challenge to diffusion simulations . in a few studies published so far , the tj motion was prevented by creating high - symmetry configurations @xcite or restricting the simulations to the 0 k temperature . applying these restrictions , the atomic structure of the tjs at 0 k was carefully examined and their excess energy was estimated ; @xcite however , no diffusion coefficients were computed . tj motion by capillary forces at high temperatures has been studied by two - dimensional lennard - jones simulations . @xcite in this work we apply three - dimensional molecular dynamics ( md ) simulations with an embedded - atom potential to compute self - diffusion coefficients along a representative tj and to compare them with self - diffusion coefficient in the adjoining gbs . since self - diffusion is the only type of diffusion studied here , we will be referring to it for brevity as simply `` diffusion '' . in section [ sec : method ] we show how a tj with controlled grain misorientations can be created in the computer and how its motion can be constrained by boundary conditions . we also introduce our methodology for diffusion calculations . our results are presented in section [ sub : results ] , followed by their discussion and conclusions in section [ sec : discussion ] . we chose copper as the model material , with atomic interactions described by the embedded - atom potential developed in ref . . the same potential was used in the recent study of gb diffusion @xcite . the bulk melting point of cu predicted by this potential is @xmath2 k ( the experimental value is 1356 k ) . our procedure for constructing an equilibrium tj is illustrated in figure [ scem ] . first , a symmetrical tilt @xmath0 boundary was created with the tilt axis parallel to the common @xmath3 $ ] direction of both grains . the grain dimensions are @xmath4 @xmath5 , where the third number @xmath6 . the gb was terminated at a free surface perpendicular to the tilt axis . another @xmath7 @xmath5 grain with the orientation shown in fig . [ scem ] was placed on the surface , forming a non - equilibrium tj . the model was equilibrated by a 2 ns long md run at 1100 k with a periodic boundary condition parallel to the tj and fixed boundary conditions at the bottom and the sides of the block ( the top side is exposed to vacuum ) . the fixed layers , shown in fig . [ scem ] in gray , were 10 @xmath8 thick . further details of the md methodology will be discussed later . during the md anneal , the tj quickly ( within the first 0.1 ns ) moved down , causing migration of the two initially horizontal gbs until an equilibrium configuration was reached . the planes of the moving gbs changed in this process , but the grain misorientation remained the same . the new gb planes were symmetrical with respect to the @xmath1 gb by construction , but they did not align with any particular low - index crystal planes in the grains . these new boundaries will be referred to as general gbs ( ggbs ) . once equilibrated , the tj and the gbs did not move except for small thermal fluctuations . note that the @xmath1 gb is pinned by the fixed region at the bottom while the ggbs are pinned by the surface grooves formed in the corners between the third grain and the two initial grains . finally , a cylindrical region with the axis parallel to the tj was cut out of the tricrystal ( fig . [ scem](c ) ) . the atoms within a 10 @xmath8 thick outer shell of the cylinder were made fixed , whereas all atoms inside the shell were allowed to move during the subsequent md simulations . the fixed shell served to pin the gbs and prevent their migration . note that the cross - section of the shell is not perfectly circular : it contains the previously formed surface grooves and a portion of the bottom fixed layer from the original block . the boundary condition parallel to the tj remained periodic . this cylindrical block contained 81,137 atoms and had the length of 66 @xmath5 . it was used as the initial configurations for the diffusion calculations . the md simulations were performed in the @xmath9 ( canonical ) ensemble using a nose - hoover thermostat . the integration of the equations of motion employed the verlet algorithm with the integration time step of 2 fs . the simulations covered the temperature range from 700 k ( the lowest temperature of reliable diffusion calculations accessible with our computational resources ) to 1315 k ( 12 k below @xmath10 ) . prior to an md run , the block was uniformly expanded / contracted according to the thermal expansion factor at the intended simulation temperature , using the thermal expansion factors computed in ref . . the model was then additionally equilibrated by a 1 ns long md run to approach the equilibrium point defect concentrations at the chosen temperature , followed by a 10 ns long production run for diffusion calculations . as a test of equilibration , the total energy of the simulation block was averaged over several time intervals covering the production stage , and it was checked that these average values followed a normal distribution . similar tests were made for the pressure inside the block . an additional proof of sufficient relaxation comes from the observations that ( i ) during the subsequent diffusion runs ( see below ) , the tj displacements were random and very small ( < 5 @xmath5 ) , and ( ii ) the mean - squared atomic displacements accurately followed the einstein relation . snapshots containing the atomic coordinates were saved every 0.02 ns and later post - processed to compute the diffusion coefficients . the diffusion coefficients @xmath11 were calculated from the linear fits of @xmath12 versus @xmath13 plots using the einstein relation @xmath14 . here , @xmath13 is the diffusion time and @xmath15 is the mean - squared displacement of atoms over the time @xmath13 in the @xmath16 direction parallel to the tj . since the atoms are labeled , @xmath15 was computed by comparing the initial and final coordinates of all atoms initially contained within a selected probe region and averaging their squared displacements in @xmath16 over the time interval between @xmath17 and @xmath18 . this obtained value of @xmath12 was additionally averaged over all choices of the reference time @xmath17 by increasing it from zero to @xmath19 , where @xmath20 is the duration of the entire md run ( 10 ns ) . the maximum diffusion time @xmath13 was chosen to be 1 to 2 ns , depending on the temperature . the probe regions selected for gb diffusion were parallelepipeds aligned with the gb planes ( fig . [ scem_reg ] ) , which had the dimensions @xmath21 , where @xmath22 @xmath8 is the cylinder length . the width @xmath23 @xmath8 parallel to the gb was chosen so that to include as large a gb area as possible but avoid the influence of the tj and the fixed regions . since our goal was to evaluate the diffusivity in the gb core area , the half - thickness of the probe region was @xmath24 @xmath8 , which is close to the typical diffusion width of gbs . @xcite for tj diffusion , the probe region was a cylinder with the radius of @xmath25 placed at the diffusion center of the tj ( fig . [ scem_reg ] ) . special care was taken to keep track of the position of the center . to achieve this , a testing md run was made prior to the production run at each temperature and a group of atoms with the largest magnitude of displacements in @xmath16 was identified . such `` fastest '' atoms were invariably found in the tj region , which was already a qualitative proof of its enhanced diffusivity . the average coordinates of the `` fastest '' atoms were used to select the diffusion center of the tj . furthermore , the position of the center was recomputed for each snapshot during the production simulations and it was found to change only by small amounts that did not exceed @xmath25 . this confirmed the hight stability of our tj geometry . however , the position of the center had to be slightly re - adjusted for each temperature since changes in the contact angles of the gbs could produce tj displacements . diffusion coefficients in liquid copper were computed separately from mean - squared displacements of atoms at several temperatures using a large periodic supercell at zero pressure . the tj and gb structures were examined after `` quenching '' from 700 k to 0 k. although the structures contained a number of quenched - in point defects , the were very coherent and had thicknesses on the order of 2 - 3 interatomic distances . these structures remained quite coherent also at finite , but not too high , temperatures . from the dihedral angle of the gbs , the 0 k energy of the ggb is estimated to be approximately 0.9 of the @xmath1 gb energy . this number is very reasonable , given that the @xmath0 gb has the highest energy among all boundaries studied in refs . and is roughly 10% above the energies of typical high - angle gbs . examination of the md snapshots reveals that the gbs and the tj become increasingly disordered with temperature , as illustrated in fig . [ tj_struct ] . ( the visualization employs the coordination - number mode of the atomeye program , @xcite plotting only atoms whose coordination number is smaller than a certain number . ) near the bulk melting point the gbs become increasingly wider , especially in the tj region , and develop a liquid - like structure . at 1315 k the tj essentially turns into a liquid pipe . typical @xmath15 versus time plots are displayed in fig . ( [ msqd ] ) . their linearity demonstrates that the einstein relation is followed accurately , confirming that we have properly sampled the diffusion" +"the observable baryon asymmetry of the universe ( bau ) and the nonzero neutrino masses @xcite provide strong evidences of physics beyond the standard model ( sm ) . the possibility of unification of the gauge interactions is one of the most intriguing guiding principles for building theories beyond the sm , in this case called the grand unified theories ( gut ) . interestingly , one of the most economical realistic guts may explain both bau and neutrino masses . it is well known that @xmath0 is the minimal group that can provide for grand unification . the first and simplest gut , proposed in @xcite , is based on this group . its scalar sector contains only two representations of @xmath4 and @xmath5 , while each generation of matter fields is embedded in two representations of @xmath6 and * 10*. the @xmath0 symmetry is broken down to the sm one by the vacuum expectation value ( vev ) of the scalar singlet in @xmath5 , and the sm higgs belongs to @xmath4 . in spite of its elegance , this model is ruled out since it can not : * unify the measured sm gauge couplings ; * explain nonzero neutrino masses ; * unify the sm yukawa couplings of charged leptons and down quarks at high scale in the renormalizable level ; * explain present experimental lower bound on the proton lifetime of order @xmath7 years . the first two of these problems were solved by adding a new fermionic * 24 * representation @xcite . however a whole set of high dimensional operators was needed to address the third problem . the renormalizable generalization of the model of @xcite with the minimal number of scalar fields contains only one new scalar @xmath8 representation @xcite , so that the electroweak symmetry is broken by both @xmath9 and @xmath10 vevs , providing for realistic yukawas . ultimately , this nonsupersymmetric renormalizable adjoint @xmath0 theory contains scalars in @xmath4 , @xmath5 and @xmath8 , and matter in @xmath11 , @xmath12 ( @xmath13 ) and @xmath14 . ( see appendix [ app : fields ] for the details . ) it is well known @xcite that the neutrino masses may be generated through type i @xcite and type iii @xcite seesaw mechanisms in the renormalizable adjoint @xmath0 model . in addition , the bau may be explained @xcite by generating the lepton asymmetry in the out - of - equilibrium decays of fermion triplets responsible for the type iii seesaw , and converting it to a baryon asymmetry by sphaleron transitions @xcite in the usual baryogenesis @xcite via leptogenesis ( lg ) scenario @xcite . in this paper we investigate a new range of the parameters where neutrino masses get a sizable contribution from the one - loop coloured seesaw besides the tree level type i and iii seesaw mechanisms . however , since the loop term is proportional to a linear combination of type i and iii seesaw yukawas , the lightest neutrino still remains massless . with the new contribution to neutrino mass , the allowed range in the parameter space for successful lg is enlarged . one of the interesting results of this model of the neutrino masses and lg in the framework of adjoint @xmath0 theory is the upper bound on the proton lifetime of order @xmath15 years @xcite , which can be tested in future . we remark that there is a parameter range in adjoint @xmath0 , which is hard to test at the proton decay experiments @xcite . however within this range the observable neutrino masses and bau can not be generated . in the next section we investigate generation of the neutrino masses together with the unification of the couplings in the considered model . in section [ section : nu_masses_exp ] we discuss parametrization of the yukawa couplings in terms of the neutrino experimental data . in section [ section : lg ] we give formulae for lg . we discuss the numerical results in section [ sec : numerics ] and conclude in section [ sec : summary ] . the interactions relevant for the generation of masses of the adjoint fermions are given by @xmath16 with @xmath17 . the masses of the fermions responsible for the neutrino masses are given by @xcite @xmath18 where the scale of grand unification is @xmath19 . the regime of successful unification determines the approximate mass relations @xmath20 with @xmath21 . for the mass spectrum of adjoint su(5 ) , which is allowed by unification , proton decay and lg , see fig . [ fg : spectrum ] with the description in section [ sec : numerics ] . the yukawa interactions needed to generate the neutrino masses are given by @xmath22 which contains @xmath23 where @xmath24 and the definitions used for the representations and multiplets are given in the appendices [ app : fields ] and [ app : multiplets ] . the scalar doublets @xmath25 and @xmath26 are related to the sm higgs @xmath27 and the heavy scalar @xmath28 by the orthogonal transformation @xmath29 with @xcite @xmath30 the vevs of physical fields are @xmath31 gev and @xmath32 . hence the terms relevant for the neutrino masses generation at tree level , shown in fig . [ fig:1:loop : nu : masses ] @xmath33 and @xmath34 , can be written as @xmath35 and interactions relevant for the one - loop contribution to the neutrino masses , shown in fig . [ fig:1:loop : nu : masses ] @xmath36 , can be written as @xmath37 where in and we have defined @xmath38 notice that in eqs . ( [ h3 ] ) and ( [ h0 ] ) we corrected the result of @xcite . the contribution of @xmath39 to the @xmath40 parameter is zero due to mass degeneracy of @xmath41 and @xmath42 , because the contributions to neutral and charged goldstones @xcite cancel each other . only electrically neutral components of @xmath43 enter the mechanisms illustrated in fig . [ fig:1:loop : nu : masses ] . the quadratic coupling @xmath44 arises from several terms in the adjoint @xmath0 lagrangian . here we take it to be arbitrary , bounded only by perturbativity . the resulting neutrino mass matrix is @xmath45 \label{eq : nu_masses}\end{aligned}\ ] ] with @xmath46 the first term in eq . ( [ eq : nu_masses ] ) is generated in type iii , the second term in i seesaw , as in @xcite . the third term comes from one - loop coloured seesaw @xcite in the limit of small mass splitting @xmath47 , where @xmath48 is the mass of @xmath49 ( @xmath50 ) @xcite . in @xcite the neutrino masses and lg were studied for @xmath51 and hence the one - loop contribution to neutrino masses was neglected . in this paper we are interested in the case of @xmath52 , in which the fermionic octet is relevant to the generation of neutrino masses . show that the number of light massive neutrinos in the considered model is two , which is equal to the maximal number of nonzero independent vectors in the plane defined by the vectors @xmath53 and @xmath54 . and @xmath55 for the couplings are not allowed , because in this case there would be only one massive neutrino . ] however none of @xmath1 , @xmath2 and @xmath3 is decoupled from the generation of the neutrino masses due to its heavy mass or small couplings , as in the two right - handed neutrino models @xcite . on the other hand , some of @xmath43 may not enter particular physical processes , e.g. , @xmath3 decouples from lg , see section [ section : lg ] . such decoupling results in new physics effects , which are dependent on the yukawa couplings @xmath56 , in particular , the allowed parameter range of successful lg is enlarged , see section [ sec : numerics ] . we remark that similar relation among the neutrino masses and lg may be derived in theory with two heavy majorana neutrinos and one light sterile neutrino , which has specific mass and mixing terms with other neutrinos parity and contribute to the neutrino masses due to the interaction with inert scalar doublet , see @xcite . ] @xcite . using the linear relation @xmath57 with @xmath58 eq . ( [ eq : nu_masses ] ) can be rewritten as @xmath59 where @xmath60 and @xmath61 with @xmath62 in the limit @xmath63 matrix @xmath64 goes to @xmath65 with @xmath66 . the neutrino mass matrix in eq . ( [ eq : nu_masses2 ] ) can be rewritten as @xmath67 by using the orthogonal transformation @xmath68 where @xmath69 is a real orthogonal matrix and @xmath70 , where @xmath71 are the eigenvalues of @xmath72 . the three neutrino mass spectra allowed by the oscillation data are * normal hierarchical ( nh ) @xmath73 * inverted hierarchical ( ih ) @xmath74 * degenerate , @xmath75 ev ( @xmath76 ) ; where @xmath77 ev@xmath78 and @xmath79 ev@xmath78 are the mass - squared differences of solar and atmospheric neutrino oscillations @xcite . we use the standard casas - ibarra @xcite parametrization of the yukawa couplings @xmath80 as @xmath81 where @xmath82 ; the pmns lepton mixing matrix @xmath83 can be written as @xmath84 where @xmath85 , @xmath86 , with @xmath87 , @xmath88 and @xmath89 @xcite , while the dirac @xmath90 and majorana @xmath91 @xmath92 violation phases are not fixed by the present experiments . finally , the @xmath93 complex matrix can be written as @xcite @xmath94 in the normal and inverted hierarchy , respectively ; @xmath95 . we define the @xmath92 asymmetry as @xmath96}.\ ] ] in the considered model it is given by @xcite @xmath97\ , f(m_{\rho_0}^2/m_{\rho_3}^2),\end{aligned}\ ] ] where @xmath98 = -\frac{1}{2\sqrt{x } } + \mathcal{o}(x^{-3/2 } ) \quad \text{for } \quad x\gg1\end{aligned}\ ] ] since the only non - vanishing contribution comes from the vertex correction @xcite . we assume that the couplings of @xmath99 and @xmath100 interactions are small comparing to @xmath44 , so that two - loop effects in the @xmath92 asymmetry can be neglected . using the total decay rate @xmath101 where @xmath102 ( signs of the components of @xmath2 ) , the decay parameter @xmath103 , given by the ratio of the decay width of a single @xmath2 component to the expansion rate when @xmath2 starts to become non - relativistic at @xmath104 , can be written as @xmath105 and rewritten as @xmath106 in terms of the rescaled decay rate @xcite @xmath107 and the rescaled hubble expansion rate ( equilibrium @xmath2 mass ) @xmath108 for nh ( ih ) the strong washout regime requires @xmath109 using eqs . , , and , we have the rescaled decay rate @xmath110,\end{aligned}\ ] ] and the total @xmath92 asymmetry @xmath111 \sqrt{m_{1}m_{2}}\ , { \rm im}(s^*c)\right\ } \nonumber\\\end{aligned}\ ] ] with @xmath112 , @xmath113 , and @xmath114 , @xmath115 for nh ( ih ) neutrinos . in the limit @xmath63 we get the standard expressions @xmath116 where in eq . we corrected the result given in @xcite by the factor of 1/2 . boltzmann equations in the unflavoured regime ( @xmath117 gev ) can be written as ( for more details see @xcite and refs . therein ) @xmath118 where @xmath119 , and @xmath120 ( @xmath121 ) is the number density of @xmath122 calculated in a co - moving volume containing one @xmath2 ( all of its three components ) in ultrarelativistic thermal equilibrium : @xmath123 . initially , @xmath124 . the abundance at equilibrium is given by @xmath125 where @xmath126 is a modified bessel function . corresponds to the ` besselk[n , z ] ` function in mathematica . ] the decay factor is @xmath127 where @xmath27 is the hubble rate , and @xmath128 is the thermally averaged dilation factor . the sum @xmath129 , where @xmath130 is the contribution from higgs - mediated scatterings , is given by @xmath131,\ ] ]" +"the observed neutrino fluxes in solar neutrino experiments @xcite and in atmospheric neutrino experiments @xcite lead to a picture of neutrino oscillations with substantial @xmath1 mixing @xcite . for high energies over astronomical distances , astrophysical sources of @xmath2 and @xmath3 can become sources of @xmath4 as well . one method of detecting @xmath4 from astrophysical sources is to look for the charged particles they produced in or near neutrino telescopes . because of the short lifetime of the tau , @xmath5 regeneration can be an important effect as the @xmath4 passes through a significant column depth through the earth @xcite . this is typically relevant for neutrino energies below @xmath6 gev . at higher energies , one can imagine using the earth as a tau neutrino converter @xcite . because of the relatively short interaction length of the neutrino at high energies , column depths on the order of the distance through a mountain or from small skimming angles relative to the horizon are most important . following the tau neutrino conversion , a tau is detected by its decay e.g. , in ice with icecube , rice or the proposed anita detectors , or after it emerges into the air . the possibility of detectable signals depends on the incident fluxes , of which there are a variety of models @xcite , and on the detectors and their sensitivity to various energy regimes . theoretical calculations often rely on approximating the neutrino interaction and tau energy loss in terms of analytic functions of energy and column depth @xcite . these analytic tools are important in exploring the possibility for tau neutrino signals in a variety of detectors , even though ultimately a full simulation of tau production and energy loss is required . in the energy regime where @xmath7 gev huang , tseng and lin have made an evaluation of the smearing of energy due to tau propagation by doing an approximate stochastic evaluation of electromagnetic energy loss of the tau @xcite . looking at fixed incident neutrino energies , they find that the relative energy fluctuation of the tau can become large at high energies , especially for larger column depths . this has the potential to make interpretation of fluxes difficult at high energies . in this paper , we evaluate tau neutrino and tau propagation using a stochastic evaluation of tau electromagnetic energy loss based on the work of ref . @xcite . we find the approximate evaluation of ref . @xcite reliable . in addition to considering mono - energetic incident neutrinos , we also consider incident neutrino fluxes with a power law behavior , @xmath8 . we compare the flux of taus following propagation through 10 km rock and 100 km rock using the stochastic evaluation with estimates of the emerging flux of taus using analytic approximations . we refine some recent parameterizations of the tau energy loss as a function of tau energy@xcite to better approximate the stochastic result for the flux of emerging taus using analytic approximations . the best parameterization of the electromagnetic energy loss parameter @xmath0 is with a logarithmic dependence on tau energy . in the next section , we describe the models for the high energy neutrino nucleon cross section and the tau energy loss used in our monte carlo simulation . results of the simulation and analytic approximations for the tau energy as a function of distance traveled , for monoenergetic neutrinos , appear in section iii . section iv includes results and analytic approximations for power law incident neutrino spectra . a summary of our results and a comparison with a simplified analytic approach are in the final section . our evaluation of neutrino interactions and tau energy loss is performed using a one - dimensional monte carlo computer simulation . the neutrino charged current and neutral current interactions are calculated based on neutrino - isoscalar nucleon cross sections @xcite using the cteq6 parton distribution functions ( pdfs)@xcite . at ultra - high energies , there is a competing effect in the neutrino - nucleon cross section as a function of @xmath9 , the quantity describing the four - momentum squared of the vector boson . pdfs increase as a function of @xmath10 @xcite , however , the vector boson propagator effectively cuts off the growth in @xmath11 at the vector boson mass . for charged current scattering , this means that the value of parton @xmath12 for nucleon four - momentum @xmath13 is approximately @xmath14 in terms of the incident neutrino energy @xmath15 , nucleon mass @xmath16 and @xmath17 boson mass @xmath18 . for @xmath19 gev , one finds that @xmath20 . the cteq6 pdfs are parameterized for @xmath21 , so one must extrapolate for smaller values of @xmath22 . the pdfs at small values of parton @xmath22 ( @xmath23 ) are extrapolated here using a power law @xmath24 matched to dglap evolved pdfs at @xmath25 : @xmath26 this approach is based on the result @xcite that for @xmath27 , the gluon pdf has the approximate form of @xmath28 , and @xmath29 splitting is responsible for the sea quark distributions that dominate the cross section at ultra - high energies . we show in fig . [ fig : lint ] the neutrino interaction length in rock . other approaches to the small @xmath22 extrapolations for ultra - high energy neutrino cross sections yield similar interaction lengths @xcite , to within a factor of approximately @xmath30 at @xmath31 gev . the differential distribution for neutrino nucleon scattering in terms of the lepton inelasticity @xmath32 , @xmath33 is evaluated similarly . we indicate the energy of the tau at the point of its production by @xmath34 . the neutrino interaction probability and resulting tau energy is evaluated using a one - dimensional monte carlo program . in our analytic approximations described below , we use @xmath35 , which is approximately correct at ultra - high energies @xcite . an indication of this is shown by the solid line in fig . [ fig : eavg ] , which shows the ratio of the average tau energy to the initial neutrino energy , as a function of neutrino energy , in the absence of electromagnetic energy loss corrections . our evaluation of the tau electromagnetic energy loss follows the procedure described in ref . @xcite . based on the scheme outlined by lipari and stanev @xcite and others @xcite , we have incorporated the electromagnetic mechanisms of ionization , bremsstrahlung ( brem ) , @xmath36 pair production ( pair ) and photonuclear ( nuc ) scattering . the tau lifetime is taken into account . the average energy lost per unit distance is commonly described by the formula @xmath37 in this expression , @xmath38 is the distance the tau travels . the quantity @xmath39 gev @xmath40/g accounts for ionization energy loss @xcite . here , @xmath0 is @xmath41 for avogadro s number @xmath42 , atomic mass number @xmath43 , tau inelasticity @xmath32 and @xmath44 and nuc . in our treatment here , as in ref . @xcite we separate @xmath0 into continuous and stochastic terms : @xmath45 we treat the tau propagation stochastically , with a series of electromagnetic interactions occurring according to probabilities based on @xmath46 for @xmath47 and the decay probability . for each distance between interactions in the monte carlo program , the tau energy loss calculated from eq . ( 3 ) is supplemented by eq . ( [ eq : dedx ] ) with the substitution of @xmath48 . by doing it this way , we account for the full electromagnetic energy loss , but we limit computer time spent where the cross section is large , but the energy loss is small ( @xmath49 ) . the detailed formulas for the bremsstrahlung @xcite , pair production @xcite and photonuclear @xcite processes are discussed and collected in ref . @xcite . see also ref . @xcite for the muon case . for the muon , @xmath0 is dominated by pair production and bremsstrahlung for @xmath50 gev . at higher energies , @xmath51 grows slowly with energy due to the photonuclear process which contributes a larger fraction for @xmath52 gev . for the tau , the photonuclear process is comparable to pair production , while the bremsstrahlung contribution is suppressed , leading to an increase in @xmath0 with energy for @xmath53 gev . in the analytic approximations discussed below , we will consider several forms of @xmath0 as a function of @xmath54 , and we will treat @xmath55 to guide our discussion , it is useful to compare the relevant constants and distance scales . first , at @xmath56 gev , @xmath57 is much larger than @xmath58 , so we can essentially ignore @xmath58 . the tau range is then characterized roughly by @xmath59 in standard rock ( @xmath60 g/@xmath61 ) . in fact , the range is somewhat larger than this estimate . the decay length of the tau is @xmath62 it is in the energy regime near @xmath56 gev that the transition from the lifetime dominated to the energy loss dominated range for the tau occurs . we begin our discussion by considering single incident neutrino energies to see the effect of energy loss combined with decay probabilities for two different trajectories : through 10 km rock ( 26.5 km.w.e . ) and through 100 km rock . [ fig : eavg ] shows the average tau energy divided by the incident neutrino energy as a function of incident neutrino energy . the average distance that the tau travels after production which survives to emerge from the rock ( 10 , 50 and 100 km ) is shown in fig . [ fig : dleft ] . for 10 km of rock , above @xmath63 gev , the average distance the tau travels is 5 km . the neutrino interaction probability is equal anywhere in the 10 km path , and the energies are large enough that the decay length is long compared to the path . for 50 km and 100 km , fig . [ fig : dleft ] shows that the last @xmath64 km are the most important for the emerging taus . the standard deviation , normalized by the average tau energy , @xmath65 is shown is fig . [ fig : sd ] . higher energies and larger distances lead to larger fluctuations . huang et al.s results in ref . @xcite correspond to our figs . [ fig : eavg ] and [ fig : sd ] and are in good agreement . we comment that by normalizing the standard deviation to the incident neutrino energy rather than average energy of the emerging tau , one finds a more stable result for the ratio . the standard deviation scales approximately as @xmath66 for 10 km rock over the same energy range as the figure , and with a factor of @xmath67 for 100 km rock . a final result for mono - energetic neutrinos is shown in fig . [ fig : evsz ] . each histogram shows the average energy of the emerging tau as a function of the production point @xmath38 for a total depth of 100 km and at fixed initial neutrino energy . the energies of the incident neutrinos are @xmath68 gev for @xmath69 ( lower to upper curves ) . standard approaches to parameterizing the final energy in terms of the initial energy begin with @xmath70 the solution depends on the energy dependence of @xmath0 . several parameterizations have been used , including a linear dependence on energy @xcite and a logarithmic energy dependence @xcite . we consider three cases : @xmath71\ , { e_0}\cr & \cr & \beta = \beta_0+\beta_1\ln(e/{e_0})\ . } \ ] ] the quantity @xmath72 is the distance traveled by the tau after its production . none of the choices for @xmath0 is entirely satisfactory . case ( iii ) is the best approximation to" +"more than a quarter of a century ago , richard feynman @xcite envisioned that a well - controlled quantum mechanical system can be used for the efficient simulation of other quantum systems and thus would be capable of calculating properties that are unfeasible for classical computers . quantum simulation promises potential returns in understanding detailed quantum phenomenon of inaccessible quantum systems , from molecular structure to the behavior of high - temperature superconductors @xcite . moreover , quantum simulations are conjectured to be less demanding than quantum computations by being less stringent on explicit gate operations or error correction @xcite . due to these reasons , quantum simulation has led to many theoretical proposals @xcite . recently , various quantum simulators based on different physical platforms are being constructed , such as atoms in optical lattices @xcite , trapped ions @xcite , nuclear magnetic resonance systems @xcite , superconducting circuits @xcite , as well as single photons @xcite . motivated by the seminal work of knill , laflamme and milburn @xcite photons are proven to be a suitable system for efficient quantum computing and quantum simulation . precise single - photon manipulations and tunable measurement - induced two - photon interactions are the essential ingredients for photonic analog quantum simulation and have been demonstrated . in addition to high - level quantum control , such photonic quantum simulators can produce exotic entangled states which are important for understanding the many - body dynamics in quantum chemistry and solid - state physics @xcite . photons barely interact with the environment , which makes them ideal for exploiting various quantum phenomena . but in contrast to ions or atoms in optical lattices where physical interactions can be easily implemented via coulomb interactions or feshbach resonances , photonic simulations require various preparation steps to achieve controllable effective interactions . first , instead of non - correlated particles , one creates entangled singlet pairs of photons from non - linear crystals and these are used as input states for quantum simulation . in the language of quantum information we would say that each photon brings half an ebit ( one half of the singlet ) of correlation . second , the non - correlated photons are overlapped at a tuneable directional coupler and measured in different output modes to introduce effective non - linearities that create the targeted many - body correlation . this is an effective interaction among the photons ( for detailed calculation see ref . note that the recently proposed universal quantum computation based on coherent photon conversion provides an alternative avenue for achieving photon - photon interaction @xcite . in the case of the simulation of spin-1/2 particles the photon s polarization is ideally suited as horizontally - polarized states @xmath0 and vertically - polarized states @xmath1 representing for example , spin - up and spin - down states . moreover , the ability to prepare symmetric polarization - entangled states @xmath2 , @xmath3 and the anti - symmetric state @xmath4 enables the establishment of states with bosonic and fermionic character @xcite . the latter shares the same quantum correlations as heisenberg - interacting spins or so - called valence bond states @xcite . the theoretical investigation of strongly - correlated spin systems has led to few exact theorems which in some cases are of importance for the quantum simulation of chemical and physical models . in the particular case of a nearest - neighbor antiferromagnetic heisenberg - interacting spin system it was shown by marshall @xcite that the ground state for n spins on a bipartite lattice has total spin zero ( @xmath5 ) . this theorem and its extension @xcite lead to the fact that the ground state must be built as a linear superposition of singlet spin states or valence bonds . this constraint , that forces the ground state s total spin to be zero , gives rise to various valence - bond configurations that are either localized or fluctuating as superposition of different singlet partitionings . localized configurations are typically referred to valence bond solids and delocalized valence - bond states correspond to frustrated quantum spin liquids or resonating valence - bond states @xcite . recently , the photonic quantum simulation of a four spin-1/2 square lattice as an archetype system @xcite showed that quantum monogamy @xcite plays an important role in frustrated heisenberg spin systems . analog quantum simulation uses the advantages of digital and adiabatic quantum simulators by utilizing continuously tunable quantum gates . in ref . @xcite , we reported the analog quantum simulation of the ground state to probe heisenberg - type interactions of a spin-1/2 tetramer . the variable measurement - induced interactions between photons are crucial for our experiments . in conjunction with single - photon manipulation and detection , it allows us to show the dynamics of ground - state energies and pair - wise quantum correlations of this tetramer . here , we present a detailed experimental study of these photon - photon interactions . depending on the interaction strength , frustration within the system emerges such that the ground state evolves from a localized to a delocalized valence - bond state . the quantum monogamy relation is unambiguously demonstrated via entanglement measures @xcite . the experimental setup for studying variable measurement - induced interactions is shown in fig . [ fig : setup ] . our pump source is a mode - locked ti : sapphire femto - second laser with a pulse duration of 140 fs and a repetition rate of 80 mhz . the central wavelength of the pump is at 808 nm . then we use a @xmath6-barium borate crystal ( bbo0 ) to up - convert the pump pulses to ultraviolet ( uv ) pulses via second harmonic generation . the up - converted uv pulses central wavelength is 404 nm with a power of 700 mw . then we clean the uv pulses with several dichroic mirrors ( dm ) . photons 1 and 2 are generated from a bbo crystal ( bbo1 ) via spontaneous parametric down conversion ( spdc ) in a non - collinear type - ii phase matching configuration and in an polarization - entangled state after walk - off compensation @xcite . photons 3 and 4 are generated from bbo2 in a collinear type - ii phase matching configuration and are separated by a polarizing beam splitter ( pbs ) . we guide photons 1 and 3 to a tunable directional coupler ( tdc ) and then detect them by avalanche photodiodes ( apd ) , which together enable the tunable measurement - induced photon - photon interactions to happen . the relative temporal delay between the photons is adjusted with a motorized translating stage mounted on the fiber coupler of photon 1 . fiber polarization controllers ( pc ) are employed to eliminate the polarization distinguishability of the two interfering photons . experimental setup for testing variable measurement - induced interaction between two independent photons . ultraviolet ( uv ) femtosecond laser pulses are up - converted from a mode - locked ti : sapphire laser . the laser pulses are up converted ( bbo0 ) and the obtained temporal duration and repetition rate is 140 fs and 80 mhz , respectively . the uv pulses and the remaining fundamental pulses are separated with several dichroic mirrors ( dm ) . lenses are used to focus and collimate the uv pulses in order to achieve good up and down conversion efficiencies . one pair of the polarization entangled photons ( photons 1 and 2 ) is generated from a @xmath6-barium borate crystal ( bbo1 ) via spontaneous parametric down conversion ( spdc ) in a non - collinear type - ii phase matching configuration . two half - wave plates ( hwp ) and compensating bbo crystals are used to counter walk - off effects in the down - conversion crystal . another pair of correlated photons ( photons 3 and 4 ) is generated from bbo2 in a collinear type - ii phase matching configuration and are separated by a polarizing beam splitter ( pbs ) . single - mode fibers and interference filters ( if ) are used to clean their spatial and spectral modes , respectively . we vary the path length difference between two photons with a motorized translation stage mounted on the fiber coupling stage of photon 1 . fiber polarization controllers ( pc ) are employed to eliminate the polarization distinguishability of the two interfering photons . the tunable measurement - induced interaction among photons is achieved by a tunable directional coupler ( tdc ) , followed by a projective measurement of one photon in each of the four output modes.,scaledwidth=90.0% ] bunching due to the two - photon hong - ou - mandel ( hom ) interference @xcite and the corresponding anti - bunching effect @xcite are crucial for many quantum information processing protocols , especially for photonic quantum computation experiments ( c - phase gate @xcite , entanglement swapping @xcite , etc . ) , as well as for our photonic quantum simulation @xcite . the bosonic nature of the photons shows up when the input states are superimposed at the tdc such that a detection , even in principle , can not distinguish either of them . this leads to a superposition of double occupations on both outgoing modes and thus suppression of the coincidence detections , where one photon is detected in each output mode . the visibility of this hom dip is one when the tdc is set to have equal splitting of transmitted and reflected photons similar to a 50/50 beam splitter . as soon as the two input photons can be partially distinguished by unbalancing the splitting ratio the visibility decreases . the dependence of the ideal visibility ( @xmath7 ) upon the reflectivity of tdc ( @xmath8 ) is the following : @xmath9 in fig . [ fig : tdcresults ] this reflectivity dependent ideal visibility is plotted in the black solid curve . experimental imperfections due to high - order emissions from spdc and group velocity mismatch reduce the visibility . [ fig : tdcresults ] also shows the measured visibilities ( black squares ) and their corresponding fit ( dashed red curve ) . experimental demonstration of variable measurement - induced interaction between two independent photons . ( a ) , ( b ) and ( c ) measured four - fold coincidence counts are plotted versus the relative optical delay between the interfering photons and fitted with a gaussian function , when the reflectivities of the tdc are tuned to be 0.17 , 0.5 and 0.67 , respectively . ( d ) visibility of the hong - ou - mandel ( hom ) dip when measuring four - fold coincidences using a tdc . the black squares are the experimental results . the black solid curve is a theoretical prediction based on eq . [ visibility ] and the red dashed curve is a fit with the only free parameter of @xmath10 , which is about 0.853 . the main reason of this non - ideal value is due to the higher - order emission generated from spdc sources . the error bars are based on a poissonian statistics.,scaledwidth=100.0% ] the main advantage of the precise quantum control of individual particles is that inter - particle entanglement dynamics can be investigated . by using a similar experimental configuration as in ref . @xcite , we study the entanglement distributions among different particles with respect to the effective interaction strength that was tuned by the tdc . for the quantification of the bipartite entanglement in our system , we use the measure of concurrence @xcite , which , for a given state @xmath11 , is @xmath12 , where @xmath13 are the eigenvalues of the matrix @xmath14 in non - increasing order by magnitude with @xmath15 , where @xmath16 ." +"ever since the realization of the atom optics quantum kicked rotor ( aoqkr ) @xcite , it has been one of the workhorses for studies of experimental quantum chaos . it has revealed a wide variety of interesting effects including : dynamical localization @xcite , quantum resonances ( qr ) @xcite , quantum accelerator modes @xcite , and quantum ratchets @xcite . the latter are quantum mechanical systems that display directed motion of particles in the absence of unbalanced forces . they are of considerable interest because classical ratchets are the underlying mechanism for some biological motors and nanoscale devices @xcite . recent theoretical @xcite and experimental @xcite studies have demonstrated that a controllable directed current arises in kicked atom systems at qr . a qr occurs when the kicking period is commensurate with the natural periods of the rotor and is characterized by a quadratic growth of the kinetic energy with time . the question of what happens to a ratchet away from resonance was addressed in a recent theoretical paper @xcite . in that work , the authors developed a classical - like ratchet theory and proposed the existence of a one - parameter scaling law that could be used to predict the ratchet current for a wide variety of parameters . it was also shown that an _ inversion _ of the momentum current is possible for some sets of scaling variables . in this paper , we report the experimental observation of such a ratchet current inversion and the verification of the scaling law for a wide variety of experimental parameters . our experiments were carried out by exposing a bose - einsten condensate ( bec ) to a series of standing wave laser pulses that provided an optical potential periodic in space and time . figure [ rawplot ] shows raw momentum distributions as a function of the pulse period s offset from the first qr and the kick number ( fig . [ rawplot ] ( a ) and ( b ) respectively ) . it can be seen that there are certain values of time offset and kick number where the distribution is weighted more strongly towards negative momentum . this is evidence of a current reversal . furthermore , fig . [ rawplot ] ( a ) and ( b ) contain other similarities . for example , there are parameter regimes where the s ) ( 10 kicks , @xmath0 , @xmath1 ) , and ( b ) kick number ( @xmath2 , @xmath3 and @xmath1 . ) . each momentum distribution was captured in a separate time - of - flight experiment . note that there are features common to both panels , such as a weighting of the distributions towards positive momenta at small values of the independent variable followed by a tendency towards negative momenta at larger values of this parameter . these features are a manifestation of the fact that the mean momentum or ratchet current can be described by a universal scaling law . , width=9,height=10 ] momentum distributions tend strongly towards positive momenta , followed by the current reversal regions where the distributions tend negative . this suggests that it may be possible to use a single - parameter theory to understand the behavior of the system . moreover , since the time offset from qr effectively defines a new planck constant @xcite , we can easily switch from the classical to the quantum regime by a simple change of the pulse period @xcite . the dynamics of the aoqkr system can be described by a hamiltonian which in dimensionless units is @xcite : @xmath4 , where @xmath5 is the momentum ( in units of @xmath6 , two photon recoils ) that an atom of mass @xmath7 acquires from short , periodic pulses of a standing wave with a grating vector @xmath8 ( @xmath9 is the spatial period of the standing wave ) . since momentum in this system is only changed in quanta of @xmath6 , we break down @xmath10 as @xmath11 where @xmath12 and @xmath13 are integer and fractional parts of the momentum respectively and @xmath13 , the quasi - momentum , is conserved . other variables are the position @xmath14 ( in units of @xmath15 ) , the continuous time variable @xmath16 ( integer units ) , and the kick number @xmath17 . the pulse period @xmath18 is scaled by @xmath19 ( the half - talbot time ) to give the scaled pulse period @xmath20 . the strength of the kicks is given by @xmath21 , where @xmath22 is the pulse length , @xmath23 is the rabi frequency , and @xmath24 is the detuning of the kicking laser from the atomic transition . to create a ratchet from this hamiltonian it was shown in @xcite that a superposition of two plane waves should be used for the initial state . a successful approach to treating this system close to resonant values of @xmath25 ( i.e. @xmath26 , with @xmath27 integer ) is the so called @xmath28classical theory . here the scaled pulse period is written as @xmath29 , where @xmath30 , and can be shown to play the role of planck s constant . in this case the dynamics can be understood by the classical mapping @xcite , @xmath31 where @xmath32 is the scaled kicking strength , @xmath33 is the scaled momentum variable and @xmath34/2 $ ] is the scaled position exploiting the spatial periodicity of the kick potential . as mentioned above , for the ratchet we start with a superposition of plane waves @xmath35 $ ] , or equivalently a rotor state @xmath36 $ ] . this leads to the position space probability distribution function @xmath37 $ ] . here @xmath38 is an additional phase used to account for the possibility that the initial spatial atomic distribution is shifted in position relative to the applied periodic potential . although the distribution @xmath39 is quantum in origin , in what follows it will be interpreted as a classical probability . as a function of the scaling variable @xmath40 @xmath17 . in ( a ) @xmath41 was varied by scanning over kick number for different combinations of @xmath42 , @xmath43 and @xmath38 . in panel ( b ) @xmath41 was varied by scanning over @xmath43 with @xmath44 , @xmath45 ( green squares ) , and with @xmath46 , @xmath47 ( red circles ) . also plotted in ( b ) is data from a scan over @xmath42 with @xmath48 , @xmath49 ( blue triangles ) . in both panels , the solid line is the function @xmath50 given by eq . ( [ analytic ] ) . this demonstrates that no matter how @xmath41 is obtained the scaled mean momentum is approximately universal.,width=340,height=359 ] the original application of @xmath28classical theory to the kicked rotor system showed the existence of a one - parameter scaling law for the mean energy @xcite . this was experimentally verified in the vicinity of the first and second quantum resonances ( @xmath51 and @xmath52 ) in ref . it was found that the scaled energy could be written as @xmath53 where @xmath54 @xmath17 is a scaling variable and @xmath55 and @xmath56 are closed form functions of @xmath41 . recently , the existence of a one - parameter scaling law for the ratchet current using the same scaling parameter @xmath41 was proposed @xcite . one of the notable features of this theory is that it predicts that at some values of the scaling variable ( i.e. certain families of real parameters ) an inversion of momentum current can occur . in the pendulum approximation @xcite , the motion of the kicked rotor in continuous time is described by the scaled hamiltonian @xmath57 . here @xmath58 is a scaled momentum variable . near the quantum resonance , using the position space probability distribution function @xmath39 , one can calculate @xmath59 . for @xmath60 , eq . ( [ map ] ) gives a phase space dominated by a pendulum - like resonance island of extension @xmath61 @xcite . hence @xmath62 and @xmath63 essentially contribute in the same way giving @xmath64 so that the map in eq . ( [ map ] ) is @xmath65 . with the scaling variable @xmath41 , the average scaled momentum becomes @xmath66 , where @xmath67 thus the mean momentum ( units of @xmath6 ) expressed in terms of the scaled variables is @xmath68 where @xmath69 can be computed from the above pendulum approximation @xcite . we performed our experiments using a similar set up to that described in @xcite . a bec of about 40000 @xmath70rb atoms was created in the @xmath71 , @xmath72 level using an all - optical trap technique . approximately 5 ms after being released from the trap , the condensate was exposed to a pulsed horizontal standing wave of wavelength @xmath73 . this was formed by two laser beams of wavelength @xmath74 780 nm , detuned @xmath75ghz to the red of the atomic transition . the direction of each beam was aligned at @xmath76 to the vertical to give @xmath77 . with these parameters the primary qr ( half - talbot time @xcite ) occurred at multiples of @xmath78 @xmath79s . each laser beam was passed through an acousto - optic modulator driven by an arbitrary waveform generator . this enabled control of the phase , intensity , and pulse length as well as the relative frequency between the kicking beams . adding two counterpropagating waves differing in frequency by @xmath80 results in a standing wave that moves with a velocity @xmath81 . the initial momentum or quasi - momentum @xmath13 of the bec relative to the standing wave is proportional to @xmath82 , so that by changing @xmath80 the value of @xmath13 could be systematically controlled . the kicking pulse length was fixed at 1.54 @xmath83s , so we varied the intensity rather than the pulse length to change the kicking strength @xmath42 . this was done by adjusting the amplitudes of the rf waveforms driving the kicking pulses , ensuring that the experiments were performed in the raman - nath regime ( the distance an atom travels during the pulse is much smaller than the period of the potential ) . the initial state for the experiment was prepared as a superposition of two momentum states @xmath84 and @xmath85 by applying a long ( @xmath86s ) and very weak standing wave pulse ( bragg pulse ) . by using a pulse of suitable strength , an equal superposition of the two aforementioned atomic states was created ( @xmath87 pulse ) . the bragg pulse was immediately followed by the kicking pulses in which a relative phase of @xmath38 between the beams was applied . this phase was experimentally controlled by adjusting the phase difference between the rf waveforms driving the two aoms . finally the kicked atoms were absorption imaged after @xmath88 ms using a time - of - flight measurement technique to yield momentum distributions like those seen in fig . [ rawplot ] . we now discuss the experiments that were carried out to observe the ratchet effect away from * @xmath51 * resonance . in this case @xmath89 is needed to fulfill the resonance condition @xcite . the measurements involve the determination of the mean momentum of kicked becs for various combinations of the parameters @xmath17 , @xmath42 , @xmath90 and @xmath38 . the measured momentum was then scaled by @xmath91 and is plotted as a function of the scaling variable @xmath41 in fig . [ scaleplot ] . in fig . [ scaleplot](a ) @xmath41 was changed by varying kick number , @xmath17 , while in fig . [ scaleplot](b ) different @xmath41 were obtained by scanning either @xmath43 ( red circles and green squares ) or @xmath42 ( blue triangles ) . the solid line in both panels is a plot of the function @xmath92 given by eq . ( [ analytic" +"after the measurement of the orbital velocities of galaxies within clusters @xcite , many other evidences point to the existence of a form of matter which is not coupled to the electromagnetic or to the strong interactions . among these it is possible to list : the accurate measurements of the cosmic microwave background ( cmbr ) @xcite ; the the galaxies rotation velocities @xcite,@xcite ; the gravitational lensing @xcite ; the abundances of light elements @xcite ; and the large scale structures @xcite . with the measurements of the cmbr @xcite the 23% of the universe is estimated to be cold dark matter ( dm ) , while only 4% _ ordinary _ baryonic matter . dm is coupled with gravitational interaction , and via this force to the ordinary matter . as a matter of fact n - body simulations predict that dm is arranged in large structures called _ halos _ ( @xcite ) . the dm density in a halo is large at the centre , and decreases with the distance . the density profile in the central part of the halo is not experimentally known and is studied by means of fits of n - body simulations or with analytic approaches @xcite . non - gravitational dm couplings are studied with : * the direct search for dm scattering on ordinary matter ; * the indirect study of dm annihilation via the secondary products , both charged and neutral ( e@xmath1 , @xmath2 , @xmath3 , @xmath4 , @xmath0 rays and lower frequency electromagnetic radiation ) . dm particles might produce gamma rays : * if the dm particles self - annihilate in pairs , possibly following the scheme in fig . 1 . this yields a continuum gamma - ray emission , which is produced by hadronization ( or final state radiation ) of the annihilation products and has a cut - off at the dm particle mass . the direct production of two gamma rays as annihilation products is suppressed in many models ( 10@xmath5 - 10@xmath6 of the continuum ) ; * if pseudo - stable dm particles decay in gammas . in this case the gamma - ray flux is proportional to the dm particle density . the dm decay constant is bound to be larger than 10@xmath7 sec and is model dependent @xcite . , @xmath8 , @xmath9 , are favoured as annihilation products . the annihilation into two gamma rays , for some models , is loop - suppressed , with a branching ratio of 10@xmath5 -10@xmath6 . gamma - ray emission is expected after the heavy fermions hadronize . the gamma - ray emission energy spectrum is a continuum with curved shape ( in log - log scale ) and a sharp cut - off at the dm particle mass.,width=313 ] the gamma - ray flux from dm particle annihilation can be decomposed into a particle physics factor and an astrophysical one . the gamma - ray flux from annihilation can be written as : @xmath10 @xmath11 where @xmath12 is the annihilation cross - section , @xmath13 is the relative velocity of the dm particles , @xmath14 is the number of gamma rays emitted per annihilation for each annihilation channel f , b@xmath15 is the branching ratio of the annihilation channel f and m@xmath16 is the mass of the dm particle candidate . @xmath17(l ) is the dm density profile , ie the density of dm as a function of the distance from the halo center . @xmath17(l)@xmath18 is integrated along the observer s line - of - sight ( @xmath19 ) . the gamma - ray flux from decay can be written as : @xmath20 where @xmath21 is the decay constant , @xmath22 is the number of gamma rays emitted for each decay and m@xmath23 is the mass of the dm particle candidate . @xmath24 is the dm density profile . the strong dependence of the emitted @xmath0-ray flux on the dm density profile is evident in the annihilation case , smaller in the decay one . in fact in the decay scenario @xmath17 , not its square , is integrated along the observer s line - of - sight ( @xmath19 , see fig . 2 ) . in order to search for a gamma - ray signal from dm annihilation ( or decay ) , we observe the region from which we expect the largest signals or the best signal - to - noise ratio , where the noise is the gamma - ray background . our galaxy could be embedded in a dm halo with the central density enhancement co - located with the galactic center . as the dm gamma - ray emission is expected to be a function of the dm density profile the galactic center is expected to be the brightest source of gamma rays from dm annihilation ( see fig . 2 and 3 ) . it might be possible to detect the relatively large dm gamma emission ( @xcite , @xcite , @xcite ) , despite the bright gamma - ray emission from astrophysical processes , which is generated both by discrete sources and diffuse backgrounds , in the galactic center region a better ratio between the dark and baryonic matter , and then a weaker gamma - ray background , is foreseen for the dwarf spheroidal galaxies , or in dm sub - structures in the halo @xcite . to the centre of the galaxy for a navarro - frenk - white ( nfw ) halo distribution for decaying dm , solid ( red ) line , compared to the case of self - annihilating dm , dashed ( blue ) line . both signals have been normalised to their values at the galactic poles , @xmath25 = @xmath2690@xmath27 . reproduced from @xcite.,width=332 ] the fermi gamma - ray space telescope is a space observatory for the study of gamma - ray emission from astrophysical sources . it is equipped with two powerful instruments : 1 . the large area telescope ( lat ) , a pair - conversion telescope , composed of a precision silicon - tracker ( 18 double - sided layers ) and a calorimeter ( 8.6 radiation lengths vertical depth ) , each of which consisting of a 4 @xmath28 4 array of 16 modules and surrounded by a segmented anti - coincidence detector ( acd ) . lat is operated as a gamma - ray imager in the energy range between 20 mev to over 300 gev ; 2 . the gamma - ray burst monitor ( gbm ) , a detector covering the 8 kev-40 mev energy range , devoted to the study of the gamma - ray bursts . detailed descriptions of the fermi observatory can be found in @xcite and the lat on - orbit calibration is reported in @xcite . studies of the gamma - ray sources in the energy range between hundreds of mev and tens of gev were performed by means of the sas 2 and cos b satellites in the years 1972 - 1982 and with the energetic gamma - ray experiment telescope ( egret ) onboard of the compton gamma - ray observatory between 1991 and 2000 . egret detected 271 sources @xcite . an half of the egret sources are unidentified , mainly because of the relatively large errors associated with the source locations . the sources detected with egret are mainly members of two classes : active galactic nuclei ( agns ) of fsrq ( flat spectrum radio quasars ) and bl lac types , with powerful relativistic jets of plasma , and pulsars ( spinning neutron stars , with powerful magnetic fields , capable of accelerating particles up to the high energy regime ) . egret was able to detect both discrete sources and diffuse gamma - ray emissions such as the extra - galactic gamma - ray background and the very intense galactic component . the large area telescope has an effective area five times larger , a much better angular resolution , and a sensitivity more than 10 times better than its predecessor egret . the fermi observatory has several scientific objectives , which span many topics of astrophysics and fundamental physics : ( 1 ) the detailed study of pulsars , agns , diffuse emissions and gamma - ray emission from nearby bodies ; ( 2 ) the study of gamma - ray bursts , up to gev energies with the lat and in the better studied kev- mev range by means of the gbm ; ( 3 ) the search for new classes of gamma - ray emitters ; ( 4 ) the possible signals of new physics . the indirect search for dm particles and the investigation of their nature are major research topics for fermi . here we report an update of the indirect search for dm from the galactic center ( gc ) . before the launch of the fermi observatory , the sensitivity of the lat instrument for the indirect search for dm was estimated in @xcite . in this publication many possible targets for the observation of gamma - ray emission from annihilating dm are considered and the possible limits on the velocity - averaged annihilation cross - section ( @xmath29@xmath12v@xmath30 parameter ) are given , as a function of the dm particle mass . for the galactic center , the considered gamma - ray background was the galactic diffuse emission , but not discrete bright gamma - ray sources . the results are obtained by means of @xmath31 analysis . the plot in fig . 4 shows the constraints in @xmath29@xmath12v@xmath30 vs wimp mass for an assumed pure @xmath32 annihilation channel . a likelihood analysis was instead performed in @xcite , on simulations of both annihilating dm gamma - ray emission and gamma - ray background ( both galactic diffuse emission and the known discrete gamma - ray sources ) . with this model it was possible to conclude that the fermi / lat is sensitive to many benchmark realizations of a dm source , under the assumption that the simulation of the gamma - ray background is realistic . for example a dm particle with mass = 50 gev and a @xmath29@xmath12v@xmath30 = 3@xmath2810@xmath33@xmath34s@xmath35 would have provided @xmath36280 events , within a roi of 1.8@xmath27 radius , in 30 ms . in the same time the simulated background would have generated @xmath3620000 events , and a detection at 5@xmath12 would have been possible , with a maximum likelihood analysis , which exploits both the spatial and the spectral information . unfortunately the simulated background did not reproduce the real complexity of the region . @xmath12v@xmath30 parameter between 0.5 and 100@xmath2810@xmath33@xmath34 s@xmath35 . the galactic diffuse emission ( both conventional and optimized galprop models ) was assumed as background , while the sources were not included as background , and a @xmath31 analysis was applied . in fig 3 is reported the region of the @xmath29@xmath12v@xmath30 vs dm mass plane which can be sampled with fermi / lat in 5 years , with the observations of the galactic center . for this plot a pure @xmath32 annihilation channel and a nfw spatial distribution are assumed . , width=302 ] the first release of results on the galactic center region obtained with the fermi / lat instrument , was made with the @xmath37 publication ( @xcite , see table 1 ) . the fermi / lat in 3 months produced a deep and well - resolved map of the @xmath0-ray sky , thus also providing much better localization of the previous known gamma - ray sources . 205 sources were detected during the first 3 months with statistical significance larger than 10 @xmath12 . the minimum flux for detection of this quality changed from the galactic plane regions ( @xmath38(e@xmath30100 mev)=0.4@xmath2810@xmath39@xmath40s@xmath35 ) to the galactic poles ( @xmath38(e@xmath30100 mev)=0.05@xmath2810@xmath39@xmath40s@xmath35 ) , as a" +"the majority of stars will evolve into a white dwarf and a significant fraction of white dwarfs harbours a magnetic field that ranges from a few kg to about 1000 mg @xcite . spectroscopic and spectropolarimetric surveys ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) of white dwarfs have been able to place constraints on the incidence of magnetism among white dwarfs . the incidence of magnetic white dwarfs in the local neighbourhood has been estimated by @xcite to be around 20% . the local sample , as well as various surveys , have shown that the incidence of magnetism as a function of field strength is constant , although @xcite suggested a possible field resurgence at the extremely low - field ( @xmath2 kg ) end of the distribution . a higher incidence of magnetism is also observed in cool polluted white dwarfs . @xcite found an incidence of @xmath3% in cool ( @xmath4 k ) daz white dwarfs . a higher incidence of magnetism was also observed among cool dz white dwarfs @xcite . a recent review on the properties of magnetic white dwarfs can be found in @xcite . the origin of large scale magnetic fields in stars is still one of the main unanswered questions in astrophysics , although recent data , particularly from surveys such as the sloan digital sky survey ( sdss , * ? ? ? * ) , the magnetism in massive stars ( mimes , * ? ? ? * ) and the binarity and magnetic interactions in various classes of stars ( binamics , * ? ? ? * ) may have finally thrown some light into this matter @xcite . magnetism in white dwarfs has been explained with two main evolutionary scenarios . for a long time the leading theory was that the progenitors of magnetic white dwarfs are magnetic ap and bp stars @xcite . under the assumption of magnetic flux conservation , the magnetic field strengths observed in ap stars would correspond to magnetic fields in white dwarfs in excess of 10 mg @xcite . the progenitors of white dwarfs with weaker fields may be other main - sequence stars whose magnetic fields are below our current detection limits or could be dynamo - generated in later stages of stellar evolution . more recently , proposals that strong magnetic fields are created in evolving interacting binaries via a dynamo mechanism during a common envelope ( ce ) phase @xcite have gained momentum as a possible origin for strong magnetic fields in white dwarfs . the main reason for this proposal is that all magnetic white dwarfs appear to be either single or in interacting binaries ( the magnetic cataclysmic variables ) . that is , magnetic white dwarfs are never found paired with a non - interacting , non - degenerate star , which is at odds with the fact that approximately 30% of all non - magnetic white dwarfs are found in non - interacting binaries with a non - degenerate companion ( usually an m - dwarf ) @xcite . this result is hard to explain and leaves the magnetic cataclysmic variables without obvious progenitors . because of this observational peculiarity , the existence of magnetic fields in white dwarfs has been linked to fields generated during ce binary interactions or mergers . the merger scenario during the ce also successfully explains the higher than average mass of isolated magnetic white dwarfs @xcite . the complex magnetic field structure usually observed in rotating high field magnetic white dwarfs would also be in support of a merging hypothesis . however , a few common - proper motion ( cpm ) magnetic plus non - magnetic double degenerate systems are now known @xcite . in some of these cases , the more massive magnetic white dwarf is hotter and hence younger than its non - magnetic companion , which seems to imply that the more massive star evolved later . this apparent paradox can be resolved by postulating that systems of this kind were initially triple systems and that the magnetic white dwarf resulted from the merger of two of the three stars ( e.g. , euvej0317@xmath5855 , * ? ? ? . the study of the magnetic field structure in white dwarfs may also give us important clues on how they formed . normally , a simple dipole is assumed for the field structure , but the study of rotating magnetic white dwarfs have all shown variability , hence revealing much more complex structures . one of the most extreme examples of a rotating magnetic white dwarf is the hot ( @xmath6 k ) and massive ( @xmath7 ) euvej0317 - 855 , which has a rotation period of 12 minutes @xcite . the rotation of the white dwarf reveals a two component magnetic field structure : a high field magnetic spot ( @xmath8 mg ) with an underlying lower field @xcite . another example of a rotating white dwarf with a complex magnetic field structure is wd1953 - 011 @xcite . in this case , the rotation is slower ( @xmath9 days * ? ? ? * ) and the magnetic field strength is much weaker ( 180 kg - 520 kg ) than that of euvej0317 - 855 . nltt12758 was discovered to be a magnetic white dwarf by @xcite . they showed that the circular polarization spectra are variable and that there is also variability in the h@xmath10 core suggesting that nltt12758 is a close double degenerate system . here , we present our analysis of spectroscopic , spectropolarimetric and photometric data of nltt12758 . the observations are presented in section 2 . the orbital and rotation period analyses are described in sections 3.1 and 3.2 , respectively . the stellar and atmospheric parameters are presented in section 3.3 , and we discuss the evolutionary scenarios in section 3.4 . we discuss the case of nltt12758 in comparison to other known double degenerate systems containing a magnetic white dwarf in section 4 and we conclude in section 5 . nltt12758 was first observed with the r .- c . spectrograph attached to the 4 m telescope at cerro tololo inter - american observatory ( ctio ) on ut 2008 february 24 . we used the kpgl2 ( 316 lines per mm ) grating with the slit - width set to 1.5 arcsec providing a resolution of about 8 . we obtained a second set of low - dispersion spectra with the efosc2 spectrograph attached to the new technology telescope ( ntt ) at la silla . two consecutive spectra were obtained on ut 2009 08 27 . we used grism number 11 and set the slit - width to 1.0 arcsec providing a resolution of about 14 . both sets of spectra revealed zeeman splitting in the balmer lines . figure [ fig_efosc2 ] shows the low dispersion spectra . we obtained a first set of spectropolarimetric observations using the focal reducer and low dispersion spectrograph ( fors2 ) attached to the 8 m telescope ( ut1 ) of the european southern observatory ( eso ) in 2009 . we obtained another set of observations using the same set - up in 2013 . we used the 1200 lines mm@xmath11 grism ( 1200r+93 ) centred on h@xmath10 providing a spectral dispersion of 0.73 pixel@xmath11 . we set the slit - width to 1 arcsec providing a spectral resolution of 3.0 . each spectropolarimetric observation consisted of two individual exposures , with the first having the wollaston prism rotated to @xmath12 immediately followed by the second exposure with the wollaston prism rotated to @xmath13 . we also obtained five spectra of nltt12758 with the efosc2 spectrograph in september 2012 . these spectra were obtained with grism number 20 which provides a spectral dispersion of 1.09 per binned pixel . the slit - width was set to 0.7 arcsec providing a resolution of 3.0 . finally we obtained a set of five consecutive spectra of nltt12758 with the x - shooter spectrograph @xcite attached to the vlt at paranal observatory on ut 2014 august 26 . the spectra were obtained with the slit width set to 0.5 , 0.9 and 0.6 arcsec for the uvb , vis and nir arms , respectively . this setup provided a resolution of @xmath14 , 7450 and 7780 for the uvb , vis and nir arms , respectively . the log of the spectroscopic observations is presented in table [ tbl_log ] . ] .spectroscopic observation log [ tbl_log ] [ cols=""<,<,^,^"",options=""header "" , ] + @xmath15 dah+dc + @xmath16 dah+db + @xmath17 dah+dah + @xmath18 masses are calculated using the mass - radius relations of @xcite , the published parameters of the magnetic star and ratio of the stellar radii . + references : ( 1 ) @xcite ; ( 2 ) @xcite ; ( 3 ) @xcite ; ( 4 ) @xcite ; ( 5 ) @xcite ; ( 6 ) @xcite ; ( 7 ) @xcite ; ( 8) @xcite ; ( 9 ) @xcite ; ( 10 ) @xcite ; ( 11 ) @xcite ; ( 12 ) @xcite ; ( 13 ) @xcite ; ( 14 ) @xcite ; ( 15 ) @xcite ; ( 16 ) @xcite ; ( 17 ) @xcite ; ( 18 ) @xcite ; ( 19 ) @xcite in this paper we have reported our studies on the close , super - chandrasekhar double degenerate system nltt12758 consisting of two co wds of similar masses and ages and with one of the two components highly magnetic . the magnetic white dwarf spins around its axis with a period of 23 minutes and they orbit around each other with a period of 1.15 days . although the components of nltt12758 will not merge over a hubble time , systems with very similar initial parameters will come into contact and merge thus undergoing either an accretion induced collapse to become a rapidly spinning neutron star ( an isolated msp ) or a type ia supernova explosion . given the theoretical uncertainties , the jury is still out on the fate of such systems . ak and sv acknowledge support from the grant agency of the czech republic ( p209/12/0217 and 15 - 15943s ) and the ministry of education of the czech republic ( lg14013 ) . this work was also supported by the project rvo:67985815 in the czech republic . sv acknowledges support from the mathematical sciences institute of the australian national university . ep acknowledges support by the ministry of education of the czech republic ( grant lg15010 ) . gpb gratefully acknowledges receipt of an australian postgraduate award . we thank the referee , pier - emmanuel tremblay , for a thorough report and helpful comments on line - broadening theory ." +"accretion provides the energy that powers radiation from the galactic center black hole , sagittarius a * @xcite . the vlt nir discovery of an infalling object onto sgr a * , named g2 , offers an especially exciting possibility for probing the nature of that accretion flow via potential interactions as the object goes through periastron @xcite . if it is a pressure - confined gas cloud , the g2 object is estimated to have a gas mass of @xmath2 , which is comparable to the total accretion flow mass within its closest approach . best estimates indicate a highly eccentric orbit with a periastron to sgr a*of @xmath3 schwarzschild radii ( @xmath4 ) , a mere @xmath5 of the bondi accretion radius , in early 2014 @xcite . the origin , structure , and fate of the object remain uncertain . while the vlt observations of the br-@xmath6 transition indicate that g2 is being disrupted , through tidal processes and possibly through gas dynamical processes , keck nir observations have shown a persistently compact @xmath7 continuum source @xcite . these observational results have led to a range of models , from diffuse clouds to dense , dusty stellar winds surrounding stars @xcite . both the nature of the accretion process and the timescale on which it takes place depend sensitively on the density profile of the accretion region and the initial density structure of the object , among other factors @xcite . proposed models anticipate a steep increase in the accretion rate , potentially by several orders of magnitude , and heightened variability on timescales of months to decades @xcite . the g2 encounter could shed light on the historic and episodic galactic center flares seen through x - ray fluorescence . the processing of g2 s material through the accretion flow around sgr a * presents a unique opportunity to study the radial density and temperature structure of the flow , filling in crucial gaps in our understanding of ultra - low - eddington - luminosity accretion . the long - term monitoring at radio and millimeter wavelengths for sgr a * demonstrates short - term variability and long - term stability , consistent with damped random walk evolution @xcite . since the detection of sgr a * at shorter wavelengths , x - ray and nir light curves have also not shown any secular evolution @xcite . intensive campaigns to monitor sgr a * over a wide range of wavelengths have been launched since the discovery of g2 was announced , none of which have detected significant changes in the flux density or activity of sgr a*@xcite , although those searches did lead to the discovery of the galactic center pulsar psr j1745 - 2900 @xcite . among the predictions for g2 are strong increases in radio through millimeter spectrum driven by two processes . increasing the mass accretion rate at separations of a few schwarzschild radii would be expected to lead to enhanced emission from the accretion flow and/or jet . the timescale for this accretion event may be as short as the free - fall time ( @xmath8 yr ) or as long as the viscous time ( 0.1 100 yr ) . additionally , a strong precursor effect has been predicted for low radio frequencies due to the potential shock forming between the incoming object and the accretion flow @xcite . in this paper , we present karl g. jansky very large array ( vla ) , atacama large millimeter array ( alma ) , and submillimeter array ( sma ) observations that span the time since the discovery of g2 through periastron . in section [ sec : obs ] , we present the observations and analysis techniques . in section [ sec : results ] , we give the results , which show a marked lack of any change in level of activity relative to historical variability . in section [ sec : discussion ] , we discuss and summarize our conclusions . vla observations were carried out as part of a service observing program on the advice of an ad hoc committee ( project code tobs0006 ; * ? ? ? * ) between late 2012 and mid-2014 ( table [ tab : vlaobs ] ) at frequencies between 1 and 41 ghz ( table [ tab : frequencytable ] ) . observations were obtained in 8 separate observing bands , each with a total bandwidth of 2 ghz with the exception of l band observations , which had a total bandwidth of 1 ghz . for each band , the correlator was configured with 16 spectral windows , each with 64 channels , for a total of 1024 channels spanning the bandwidth of 2 ghz ( 1 ghz in the case of l band ) . observations were snapshots of a few minutes duration in each of the eight frequency bands . observations of 3c 286 were obtained for absolute gain calibration . standard pipeline calibration techniques in casa were carried out by nrao staff @xcite . the pipeline produced calibrated visibility files that we then analyzed with our own software . table [ tab : vlaobs ] summarizes beam sizes for sgr a * for l and q band ( 1.5 and 40 ghz , respectively ) from images obtained from all of the data in each epoch . unlike the reduction described below , the images included short baselines as a means of demonstrating the large beams that occurred . the ratio of q to l band beam sizes does not exactly follow the expected frequency scaling ratio , which is indicative of the poorly shaped beams from these snapshot observations and frequency - dependent weighting in the imaging stage . we averaged the data in time into 30s intervals and in frequency for each spectral window . we then exported the data for further analysis with our code . we performed two kinds of analyses . for the first , we extracted flux densities for sgr a * by averaging visibility amplitudes on baselines longer than 50 @xmath9 . past experience has shown that these long baselines are sufficient to exclude the effects of extended structure on the flux density of sgr a * ( e.g. , * ? ? ? * ) . at high frequencies and in extended configurations , we determine flux densities for sgr a * that are consistent with those provided by @xcite . for the second analysis , we used a visibility subtraction method to determine deviations from the average flux density . this method is important for low frequency observations in compact configurations , where the extended flux dominates that of sgr a*. these epochs were reported to have upper limits as high as 15 jy ( e.g. , * ? ? ? * ) . for each epoch , we gridded the visibilities for each spectral window and then found individual grid cells for which there was an overlap between the individual epoch and the remaining ensemble . we differenced each epoch s visibility grid against the grid derived from the ensemble of visibilities ( minus the particular epoch ) . the differential flux density was determined as a weighted sum of the residual visibilities . we applied a weighting scheme that scales as the inverse of the @xmath10 distance . that is , longer baselines have greater weight than shorter baselines in order to bias against contamination from extended structure . different weighting schemes do not qualitatively alter our conclusions . the scatter in the differences determines the error . we then averaged over each observing band and , again , calculated the error based on the scatter in the measurements . this visibility subtraction scheme works well given the large number of data sets and the fine frequency resolution of the observations . the frequency resolution permits us to make comparisons that are not limited by the steep spectral indices of some of the extended structures present in the galactic center . the large number of data sets gives good overlap between extended and compact structures . the method is sensitive to the effect of pairs of observations with significant overlap in @xmath10 coverage , i.e. , those conducted at the same sidereal time and in the same configuration . in this case , the method effectively differences those two epochs and does not provide a difference with respect to the average . this effect can be seen in the epochs 20131129 and 20131229 , in which the flux difference for one mirrors the other . the apparent minimum in rms variability of the flux density excess at 5 ghz is the result of increasing variability toward high frequencies and decreasing accuracy of the method toward low frequencies because of the smaller number of long baselines . we summarize the mean flux densities and differential flux densities in table [ tab : vlaresults ] . we show total intensity and differential spectra for sgr a * in figures [ fig : specvla ] and [ fig : diffspecvla ] . we plot the total intensity spectrum alongside historical average spectra @xcite . ] ] we carried out alma observations between mid-2013 and mid-2014 ( table [ tab : almaobs ] ) , over eight epochs , each with band 6 ( 230 ghz ) and band 7 ( 345 ghz ) receivers . details of the frequency setup are presented in table [ tab : frequencytable ] . one spectral window in each band was configured with higher spectral resolution in order to permit detection of hydrogen recombination lines . we will discuss those results in a separate paper . observations were snapshots with durations of a few minutes . the total flux density , corresponding to stokes i , was produced by summing the response of parallel handed cross - correlations of the orthogonal linearly polarized feeds . we set absolute amplitude calibration with observations of titan and neptune and set bandpass gains with observations of the compact source j1427 - 421 . all calibrator sources and sgr a * were phase - self - calibrated on timescales of a single integration ( 10 sec ) . for sgr a * , phase self - calibration solutions were obtained only for baselines longer than @xmath11 . flux densities for calibrators were determined by bootstrapping amplitude self - calibration solutions to the absolute flux density calibrator . time - dependent amplitude gain solutions were applied to sgr a*. unfortunately , alma observations did not include system temperature measurements on sgr a*itself . the pipeline software applied system temperatures obtained for j1733 - 130 ( nrao 530 ) to sgr a * , which introduces an error because of the different atmospheric optical depth toward these two sources . to correct for this effect , we fitted system temperatures for all sources in each epoch to determine the atmospheric optical depth and then applied the correct system temperature to sgr a*. typical changes to the amplitude gain were a few percent , with a maximum value of 7% . flux densities for sgr a * were obtained through fitting a point - source of unknown flux to visibilities on baselines longer than @xmath11 . we report the results in table [ tab : almaresults ] . we do not report statistical errors on the flux densities because these are typically @xmath12 mjy , much less than the likely uncertainty from gain calibration errors for these bright sources . we show alma spectra for sgr a * and all sources in figure [ fig : specalma ] . ] alma flux densities for the calibrators are consistent with recent sma measurements of flux densities . we plot alma and sma light curves for sgr a * and j1733 - 130 in figures [ fig : almasma ] and [ fig : almasmaj1733 ] . sma data are described" +"the current understanding of the details of quantum hall effect relies crucially on the composite fermion picture @xcite . an important step in the development of this understanding was the introduction of statistical gauge fields and the rle they play in the landau - ginsparg effective action , @xcite . in fact the law of corresponding states of reference @xcite has an interpretation as a beautiful and extremely powerful generalisation of kramers - wannier duality , @xcite @xcite , though references @xcite and @xcite were completely independent of one another and appeared almost simultaneously . kramers - wannier duality is a discrete @xmath0 map of the partition function for the 2-dimensional ising model at one temperature to the same partition function at a different temperature . its power lies in the prediction of the critical temperature without having to solve the model . since its discovery however other techniques have proven more useful not only because the model has since been solved exactly in 2-dimensions but also because , being a discrete symmetry , duality is all or nothing affair . there is no algorithm for finding such symmetries it is hit and miss guesswork . this is one of the reasons why the renormalisation group approach has proven more powerful as a technique for understanding the physics at and near critical points associated with second order phase transitions not only for the 2 and 3-dimensional ising models in the presence of an external magnetic field but also for many other models . the renormalisation group ( rg ) approach can not really be called an algorithm ( it has many different manifestations all of which come under the same general heading of `` rg '' ) but it is nevertheless algorithmic in nature given a field theoretical model one can perturb around free field theory and hope to apply some version of the rg to extract physical information without actually having to solve the model . nevertheless interest in duality has never died perhaps because of the elegance of the idea but also because , if one _ can _ find a duality , one can obtain exact results whereas the perturbative rg is always an approximation . with duality the chances of success are smaller but the payoff is greater . a @xmath0 duality for massive maxwell - chern - simons theory was discovered in @xcite which necessitated the introduction of a complex coupling with positive imaginary part . a generalisation of kramers - wannier duality from @xmath0 to an infinite discrete non - abelian group ( called the modular group , which is defined in the next section ) was discovered for a coupled clock model in @xcite . being a larger group this leads to a much more complicated phase diagram and it has been suggested that a version of this duality applies to potts models with a complex temperature , @xcite . the importance of the modular group , and some of its sub - groups , for the quantum hall effect was realised in @xcite and @xcite and this led to the development of the phase diagram compatible with modular symmetry first presented in @xcite . interest in duality has also seen a major revival recently in the context of super - symmetric gauge theories and string theory ( for a review see @xcite ) . very strong results can be obtained by combining duality symmetry ( when one can be derived ) with rg techniques . this was first done for the quantum hall effect in @xcite . the basic idea is that the duality map should commute with the rg flow which puts very strong constraints on the @xmath1-functions of the theory . for example fixed ( i.e. self - dual ) points of duality symmetry correspond to fixed points of the rg and therefore the @xmath1-functions would be expected to vanish at these points even if they correspond to strongly coupled theories in the field theoretic sense . since @xcite appeared a number of authors has examined the constraints put on the rg flow by modular symmetry under various other assumptions , @xcite,@xcite,@xcite,@xcite,@xcite . indeed one can use this approach , together with particle - hole symmetry , to derive the semi - circle law for transitions for quantum hall transitions very generally without any recourse to a specific microscopic model it follows very generally from the duality symmetry , @xcite . the aim of this paper is to explore further the consequences of this infinite generalisation of kramers - wannier duality for the quantum hall effect . in particular electron spin is incorporated into the duality picture and it is argued that when the splitting of the landau levels due to electron spin is small compared to the cyclotron energy the relevant duality symmetry is smaller than when the landau levels are all well separated . technically speaking the symmetry group is @xmath2 in the former case and @xmath3 in the latter ( these groups are defined in the next section ) . in order to compare this prediction with experiment some extra assumptions about the form of the @xmath1-functions are necessary and here the analysis of @xcite is applied to the case of small spin splitting . this involves a very specific assumption concerning the form of the @xmath1-functions that they are meromorphic in the sense of a natural complex conductivity , @xmath4 ( throughout this paper units are used in which @xmath5 ) . unfortunately this assumption has no microscopic justification to date , rather it is made on the basis of analogy with other models with modular symmetry as a duality , @xcite . however it leads to such specific predictions that is easily falsifiable , though comparisons with experimental data show that its predictions agree very well with the currently available data lending some confidence that a justification may be found in the future . the available data to date , at strong fields and at low enough temperatures for the law of corresponding states to represent a symmetry , seem to be compatible with @xmath3 when the meromorphic ansatz is used , so it is not possible to test the specific predictions made here concerning the @xmath2 case . this must wait for future experiments . an important aspect of the comparison with experimental data made in section six is the normalisation of the longitudinal resistivity , @xmath6 . this is a problem for experiment , which in reality measures the longitudinal resistance @xmath7 , and it is usually assumed these are related by @xmath8 in a rectangular sample of length @xmath9 and width @xmath10 . the assumptions that go into this relation are examined in section five where it is argued that a better formula is @xmath11 where @xmath12 is an undetermined sample dependent function with the universal property that @xmath13 . the duality symmetry of the quantum hall effect however suggests an alternative method for extracting @xmath6 from the experimental @xmath7 , at least for hall - hall transitions . given that the duality group , together with particle - hole symmetry , predicts the semi - circle law one can use this to determine the normalisation of @xmath7 by _ assuming _ the semi - circle law at sufficiently low temperatures . this technique can not determine the normalisation by using a laughlin state - insulator transition because these correspond to vertical lines in the complex @xmath14-plane , which remain vertical under any re - scaling of @xmath6 . however this very fact dictates that laughlin state - insulator crossovers should be semi - circles in the @xmath15-plane for any normalisation of @xmath6 and this gives a quantitative method of determining when the temperature is ` low enough ' for the infinite duality symmetry to be valid the laughlin state - insulator transitions must be semi - circles in the complex @xmath15-plane . when this is the case the normalisation of @xmath6 for a hall - hall transition can be extracted from the experimental data by choosing the normalisation so as to get as close as possible to a semi - circle for the crossover in the complex @xmath14-plane . the layout of the paper is as follows : in section two the definition of the modular group and its various relevant sub - groups is reviewed together with its action in the quantum hall effect ; section three discusses the relation between the modular group and scaling ; section four introduces the specific ansatz of meromorphic @xmath1-functions ; section five is devoted to the relation between the longitudinal resistance and resistivity while section six compares the predictions of section four to existing experimental data . finally section seven contains a summary and conclusions . the law of corresponding states @xcite was originally proposed on the basis of an effective field theory maxwell - chern - simons theory . it provides a powerful method for classifying quantum hall states and transitions between them , both integral and fractional , as well as for hall - insulator transitions . the law is expressed by writing the conductivities ( both longitudinal @xmath16 and transverse @xmath17 ) as functions of the filling factor @xmath18 . then the following transformations were defined in @xcite : * landau level addition transformation ( * l * ) @xmath19 * flux attachment transformation ( * f * ) @xmath20 * particle - hole transformation ( * p * ) @xmath21 as discussed in @xcite under certain circumstances the arrows above can be replaced by equalities and then these transformations become _ symmetries_. this is not expected to be true in general but should hold , for example , as the temperature @xmath22 tends to zero . at almost exactly the same time , but from a completely different perspective , the modular group @xcite or some of its sub - groups @xcite were also implicated as being relevant to these phenomena . in this approach one defines a _ complex _ conductivity , @xmath23 , which by necessity lives on the upper - half complex plane since @xmath24 , and a group action @xmath25 where @xmath26 and @xmath27 are any four integers satisfying @xmath28 . this condition can re - written by defining a @xmath29 matrix @xmath30 and demanding that @xmath31 . it is easy to check from the definition ( [ gammadef ] ) that , for any three such matrices satisfying @xmath32 , we have @xmath33 . thus the group multiplication law is given by matrix multiplication . note that for any given matrix @xmath34 the matrix @xmath35 gives the same transformation since the minus signs cancel above and below in ( [ gammadef ] ) . the resulting group is called the modular group in the mathematical literature , sometimes denoted @xmath36 , and it is related to @xmath37 . matrices of real numbers with unit determinant ( @xmath38 ) obtained by restricting to integral entries . ] they are not quite the same group because @xmath37 distinguishes between @xmath34 and @xmath35 whereas @xmath36 does not , so @xmath36 is obtained from @xmath37 by identifying @xmath34 and @xmath35 as group elements , or in other words projecting out by a @xmath0 factor , so @xmath39 . any element of the modular group can be obtained by taking a string of products of the two generators @xmath40 and @xmath41 . in this matrix notation landau level addition and flux attachment are represented by @xmath42 and @xmath43 and these two transformations generate an infinite discrete group , which is a sub - group of @xmath36 , often denoted by @xmath44 in the mathematical literature ( see @xcite for example , another notation commonly used is @xmath45 , @xcite ) . any element @xmath46 can be represented by some string of products of @xmath47 and @xmath48 . this sub - group is most succinctly described by restricting the integer @xmath49 in the matrix @xmath34 to be even . the" +"electronic bilayer systems have recently drawn increasing attention due to new experimental results on electronic transport @xcite as well as due to the discovery of the novel macroscopic ordering driven by quantum effects.@xcite in a generic situation such systems consist of two spacially separated and mutually insulated semiconducting layers which can be individually gated . on the other hand , the interlayer separation is engineered in such a way that the coulomb interaction between majority carriers in both subsystems is still large . this can be achieved by an appropriate choice for the barrier material . @xcite in such a situation the formation of excitons is possible . even a condensation of such electron - hole pairs was predicted @xcite and subsequently observed in several experiments performed on gaas quantum wells using algaas as the insulating barrier at total filling factor @xmath0 in the quantum hall regime . @xcite while the non - linear transport characteristics of such systems have been investigated before @xcite , their noise properties received only little attention . in we tried to close this gap and have calculated the cumulant generating function ( cgf ) of a bilayer system attached to four different electrodes . some very interesting effects were found , which can only be attributed to the non - trivial interactions between the layers . in order to perform the calculations one had to assume that the transport processes at different junctions occur in an incoherent fashion ( sequential tunneling ) . despite this severe restriction the currents in both layers are correlated due to the locality of the bound electron - hole pairs . here we would like to drop this assumption and consider a fully coherent system . the paper is organized as follows . in the next section we introduce the system and give the details of its mathematical implementation . we briefly review the main results of and adapt them to a recent experimental setup presented in . in section [ s3 ] we present a toy model consisting of two short hubbard chains , which are coupled with each other , so that a formation of an interchain electron - hole pair or exciton is adequately described . in the next step we calculate the full counting statistics , compare the predictions of both models , analyze their similarities and discrepancies . we briefly summarize the results in section [ s4 ] . the basic system we study is depicted in fig . [ fig1 ] : a semiconducting bilayer is contacted by four metallic electrodes via tunnel contacts . the hamiltonian of the system reads @xcite @xmath1 where the term @xmath2 describes the four metallic electrodes which are described as fermionic continua written in terms of electron field operators @xmath3 at chemical potentials @xmath4 . @xmath5 refers to the contacts on the left / right side of the respective layer and @xmath6 labels the top and bottom layer , respectively . we assume the leads to be in the wide flat band limit so that their density of states ( dos ) @xmath7 is constant and denote the fermi distribution functions in the respective electrode by @xmath8 . for the phenomena we would like to consider the spin degree of freedom is irrelevant , therefore we work with a spinless system . @xmath9 is the tunneling hamiltonian describing hopping between each layer of the bilayer and the corresponding metallic electrodes @xmath10 using tunneling amplitudes @xmath11 . finally , @xmath12 describes the bilayer using a simple one - dimensional model as in ( we shall discuss generalizations to higher dimensions later ) @xmath13 where @xmath14 is the longitudinal distance between the right and left side of the semiconductor , @xmath15 is the two - layer spinor and @xmath16 describe the electron / hole single particle hamiltonian of the top and bottom layer . we describe the interlayer coulomb interaction by an exciton order parameter @xmath17 , which in general is a space - dependent quantity . @xcite its absolute value @xmath18 in equilibrium represents the excitonic gap and directly gives the exciton coherence length @xmath19 . it can be determined self - consistently from the interlayer interaction as in bcs theory.@xcite + in order to calculate the cumulant generating function ( cgf ) of charge transfer we use a green s function ( gf ) method developed for quantum impurities in . for every electrode present in the system we have to introduce a fictitious measuring field @xmath20 which counts an electron when it crosses the electrode - semiconductor junction in question . in this manner fluctuations , either caused by the discreteness of charge or thermally induced , can be taken care of . the measuring fields are both contour and time - dependent : they are nonzero only during the measurement time @xmath21 and change sign on the @xmath22 and @xmath23 branch of the keldysh contour . this procedure allows for the calculation of the cgf for arbitrary parameters in eq . ( [ htotal ] ) as discussed in and has already been applied to numerous quantum impurity problems ( see e.g. ) . the cgf can be calculated as a generalized keldysh partition function @xmath24 where @xmath25 is the keldysh contour ordering operator and @xmath26 can be derived from the tunnel hamiltonian in eq . ( [ htunnel ] ) using the substitution @xmath27 . in order to calculate the cgf we then rewrite the expression using the adiabatic potential method in the limit of long measurement times @xmath21 as @xmath28 . the adiabatic potential @xmath29 may in turn be rewritten in terms of the bare and exact - in - tunneling gfs of the system described by eq . ( [ htotal ] ) . the hamiltonian in eq . ( [ hec ] ) is very similar to the bcs hamiltonian . indeed , @xmath30 and @xmath31 can be interpreted as pseudospin indices to map this hamiltonian with the additional exchange of @xmath31 holes to electrons onto bcs theory.@xcite also one has to take into account that electrons and holes each have their own chemical potential @xmath32.@xcite consequently we can also rephrase our problem as the calculation of the spin - dependent cgf for a normal - superconductor - normal ( nsn ) junction with different chemical potentials for the spin species . we want to stress that despite the modelling of the condensate as a perfect homogeneous system in describing the tunneling we assume for the dephasing time @xmath33 : @xmath34 ( incoherent tunneling approximation ) . the cgfs for different normal - superconductor hybrid structures have been considered before . @xcite here the task is to work out the spin - dependent case , to take care of the presence of electrons instead of holes in the lower layer and to address the case of a bilayer contacted from two sides . however , the @xmath17-coupling in eq . is formally a tunneling term . since the layers are supposed to be isolated from each other we have to suppress particle current flowing between the layers . this is very conveniently done by adjusting the chemical potentials in the layers self - consistently . a similar procedure was implemented for a normal - superconductor - normal junction in ref . . under such circumstances it is then unimportant whether we count charges on the left side or the right side of the respective bilayer . this means that we can then calculate the cgf only for the left side and obtain the one for the right side by exchanging @xmath35 . we would like to point out that this self - consistency condition is very different from the conventional one inspired by the bcs theory as it defines the _ relative _ position of the exciton chemical potential with respect to the ones in the external electrodes . using the microscopic hamiltonian approach as outlined in ref . we have obtained the complete expression for the temperature and energy dependent cgf , valid for arbitrary values of the model parameters . @xcite the expression , which has been used for our numerical calculations , is quite lengthy and we do not report it here . nevertheless , all relevant ingredients of the cgf already appear in the limits of small bias ( @xmath36 ) and large bias ( @xmath37 ) , where the expression of the cgf greatly simplifies . indeed in these regimes the non - interacting self - energy due to the ec is either real and purely off - diagonal or imaginary and purely diagonal , like in a superconductor @xcite , while the one due to the normal lead is always diagonal . in these regimes the cgf acquires the following expression @xmath38\right\ } \theta\left(\frac{|\omega_\sigma| - \delta}{\delta}\right ) \nonumber\\ & & + \ln \left\{1 + t_a(\omega ) \left[(e^{i \lambda_{lt } } e^{-i \lambda_{lb } } -1 ) n_{lt } ( 1-n_{lb } ) \right . \nonumber\\ & & \left . + ( e^{i \lambda_{lb } } e^{-i \lambda_{lt } } -1 ) n_{lb } ( 1-n_{lt } ) \right]\right\}\theta\left(\frac{\delta - \max(|\omega_t| , \ ; |\omega_b|)}{\delta}\right)\right ] , \label{cgf}\end{aligned}\ ] ] where @xmath39 and the transmission coefficients are given by @xmath40 the energy - dependent dos of the ec affects the hybridisations @xmath41 where @xmath42 , with the dos of the ec given by @xmath43 . @xmath44 refers to a fermi distribution function at chemical potentials @xmath45 characterising the layer of the semiconductor . we use units such that @xmath46 and @xmath47 . the first line of the cgf describes the supra - gap contribution , which is only due to single electron transport in the simplified form given here and characterised by the normal transmission coefficient @xmath48 . the second line describes the sub - gap contribution due to excitonic andreev reflection @xcite in which an electron and a hole ( in different layers ) enter or leave the ec . @xmath45 now have to be chosen such that @xcite @xmath49 for the sake of simplicity we consider the symmetric case @xmath50 and @xmath51 . then the requirement eq . ( [ self ] ) is always fulfilled for @xmath52 if @xmath53 and @xmath54 . this condition also implies that no current is flowing between the upper and lower layer.@xcite it is interesting to use the above formula to test fluctuation theorems . we have done so for the full result but for the sake of simplicity we illustrate the test for eq . ( [ cgf ] ) . one of the most celebrated examples is the cohen - gallavotti relation , which can be directly related to a symmetry of the cgf.@xcite for a single counting field @xmath55 the cgf is expected to obey in the limit of long measurement time @xcite @xmath56 where @xmath57 is the inverse temperature . however , in our case we encounter several complications compared to this simple case . first , the presence of an interlayer coulomb interaction gives rise to the subgap contribution in eq . ( [ cgf ] ) which couples the top and bottom layer and therefore requires to extend the simple relation in eq . ( [ simplecohen ] ) to both @xmath30 and @xmath31 counting fields . additionally different voltages can be applied on the top and bottom layer . finally , we had to mind self - consistency which we satisfy by setting @xmath58 . still , a relation similar to eq . ( [ simplecohen ] ) holds , namely @xcite @xmath59 even though this is a straightforward generalisation of the cohen - gallavotti relation in eq . ( [ simplecohen ] ) the above relation provides an example how correlations affect the fluctuations in quantum systems . in this way we have supplied an example of a system where a generalized cohen - gallavotti fluctuation theorem holds . from the cgf in ( [ cgf ] ) we can" +"the very high bulk lorentz factor and high magnetic field strengths in outflows of gamma - ray burst ( grb ) make grbs potential sources of ultra - high - energy cosmic rays ( uhecrs ; * ? ? ? * ; * ? ? ? * ; * ? ? ? recent time - resolved detections of gev photons with _ fermi_/lat from grb 080916c and grb 090510 @xcite reveal that the minimum lorentz factor @xmath3 , required to make the sources optically thin for such gev photons , should be @xmath4 . while those high values of @xmath3 are favorable to accelerate protons to very high energies , it makes difficult to produce the photomeson - induced secondary photons and neutrinos frequently discussed by many authors ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? this is because , given the variability timescale @xmath5 , photon luminosity , and spectrum , a higher bulk lorentz factor @xmath6 decreases the photon number density as @xmath7 . the wide - band spectra ( 10 kev - gev ) of grb 080916c are well fitted by a smooth band function @xcite , and in that case the lack of evidence for an extra spectral component is consistent with a low efficiency of photomeson production due to high @xmath6 . however , from 0.5 s to 1.0 s after the trigger time ( @xmath8 ) , the short grb 090510 does exhibit a very significant ( @xmath9 ) spectral deviation to the standard band function . with the parameters of the standard band function at @xmath10 mev , @xmath11 , and @xmath12 , the excess is adequately fit with an additional power law of index @xmath13 . the power law extends from the lowest energy in _ fermi_/gbm ( i.e. , 8 kev ) , to at least 31 gev in _ fermi_/lat . the extra - component counts for about 37% of the total fluence and the powerlaw dominates the standard integrated - band spectrum up to a few tens of kev and above 10 mev . this additional component is the most intense from @xmath14 s to @xmath15 s. there is no clear evidence of existence of an extra component at times after @xmath15 s , however there is not enough statistical significance in the data to fully reject this hypothesis . the onset of the main emission above 100 mev is delayed about 200 ms compared to the main spike from 8 kev up to few mev . no lags have been found below 1 mev with respect to the lowest energy band 8 - 40kev over the whole light curve ( @xmath8 to @xmath16 s ) . above 1 mev , lags increase progressively to reach 248 ms and remaining constant after 40 mev . this extra component could be of leptonic origin , e.g. , external compton emission from internal shocks ( e.g. , * ? ? ? * ) or synchrotron self - compton emission from the reverse shock or forward shock in the early afterglow phase @xcite as discussed for grb 941017 @xcite . in this letter we consider an alternative possibility , namely hadronic models , in particular photomeson cascade and proton synchrotron models @xcite , for representing the extra spectral component of grb 090510 , which is present only in the prompt emission between @xmath8 and @xmath15 s. although the cascade processes initiated by @xmath17/@xmath18/@xmath19 are complicated , the resultant photon signatures of proton cascades mostly appear as synchrotron or inverse compton emission from secondary electron - positron pairs produced via @xmath20 . in such pair cascade processes the effective injection index of secondary pairs tends to be about @xmath21 ( e , g , * ? ? ? * ) so that the synchrotron radiation from secondary pairs yields a flat spectrum in an @xmath22 plot , while the power law index of the extra component in grb 090510 is @xmath23 . however , the inverse compton component from secondary pairs can harden the spectrum as @xcite showed . using the numerical code of monte carlo techniques in @xcite ( see also * ? ? ? * ) , we constrain the hadronic models in this letter . after a short discussion of our methods in [ sec : model ] , we discuss the possibility of photon emission due to accelerated protons for grb 090510 in [ sec : results ] , and summarize the results in [ sec : conc ] . in order to constrain hadronic models for the observed extra spectral component of grb 090510 , we simulate the photon emission with photomeson - induced cascade processes from ultrarelativistic outflows of bulk lorentz factor @xmath6 . the numerical code is the same as that in @xcite , which was matured via a series of grb studies @xcite , so that we omit the detailed explanation for the code . as an optimistic case , which would lead to hadronic cascades , we assume that protons are injected with a power law energy distribution @xmath24 above 10 gev in the outflow rest frame at radii @xmath25 from the central engine . the acceleration timescale of a proton is parameterized as @xmath26 , where @xmath27 is the larmor radius of the proton . the maximum proton energy @xmath28 is determined by equating the acceleration timescale and the expansion timescale of the outflow @xmath29 or the cooling timescale due to proton synchrotron or photomeson production . we assume that the main low - energy component , which is fitted by a band function , is of leptonic origin @xcite , which we do not discuss further . the photon energy distribution in the outflow rest frame is estimated from the time - averaged band parameters from @xmath30 s to @xmath31 s ( @xmath32 mev , @xmath33 , @xmath34 , and the isotropic - equivalent luminosity @xmath35 erg@xmath2s at @xmath36 ) and the numerically obtained extra component originating from protons . the energy distributions of photons and particles are simulated iteratively until they converge to a self - consistent spectrum . on a timescale comparable to @xmath37 , the photon density and the magnetic fields , etc . , can be approximately taken as constant , and we can neglect the emission from particles beyond this timescale after their injection , because the photon density and the magnetic field decline . the physical processes taken into account are 1 ) photon emission processes of synchrotron and klein - nishina regime compton scattering for electrons / positrons , protons , pions , and muons , 2 ) synchrotron self - absorption for electrons / positrons , 3 ) @xmath38 pair production , 4 ) photomeson production from protons and neutrons , 5 ) bethe - heitler pair production ( @xmath39 ) , and 6 ) decays of pions , and muons . the code can also output the spectra of neutrinos from pions and muons . there are five model parameters : the proton acceleration parameter @xmath40 , the proton injection radius @xmath25 , the bulk lorentz factor @xmath6 , the energy density of the magnetic field @xmath41 , and the injection luminosity of accelerated protons @xmath42 . the last two parameters are normalized by the photon energy density of the band component @xmath43 or @xmath44 itself as @xmath45 and @xmath46 . within the time interval between @xmath30 s and @xmath31 s , two high - energy photons of 3.4 gev and 31 gev were detected . these photons belong to the extra component of the prompt emission , whose spectrum is well fitted by a power law of @xmath13 , on which we concentrate here . ( there is in addition a tail extending to @xmath47 s , attributable to an afterglow , which we do not discuss here . ) since the photon statistics above gev are not enough , we do not attempt to carry out a detailed fitting of the spectrum . alternatively , we search for parameter sets that reproduce a comparable fluence of the extra component to that of the band component . first , we consider photomeson cascades , for the most extreme case @xmath48 . [ fig : f1 ] shows two examples of photon spectra , in which the flux of the hadronic component at 3.4 gev is comparable to the band component . the model spectrum with @xmath49 seems consistent with the observed spectrum . the second peak at @xmath50 gev is mainly due to @xmath38 pair absorption . the assumed value of @xmath46 is 200 , which is quite large , so that the proton injection luminosity should be larger than @xmath51 erg@xmath2s in this case . on the other hand , if we adopt a stronger magnetic field such as @xmath52 , the required amount of protons can be suppressed to a lower value of @xmath53 ( @xmath54 erg@xmath2s ) . however , the dominance of synchrotron radiation from secondary pairs makes in this case the spectrum too soft below about 100 kev . such a large deviation from the band function around 10 kev is not seen in grb 090510 . the various timescales for the case of @xmath49 are plotted in fig . [ fig : f2 ] . apparently , the maximum energy of protons @xmath28 is determined by the condition @xmath55 . the low efficiency of hadronic cascade is attributed to the much longer cooling timescale due to photopion production @xmath56 than the expansion timescale of the outflow @xmath37 even at @xmath57 . the target photons for pion production below @xmath58 ev are the band component . above this energy , protons interact with uv - photons below the observed energy range of fermi , where secondary synchrotron photons dominate . in our simulation the synchrotron self - absorption makes a spectral peak of @xmath59 plot at @xmath60 ev , which corresponds to the typical target photon energy for protons of @xmath61 ev , where @xmath56 becomes minimum . in spite of the enhancement of the pion production efficiency due to secondary photons , we still need a large proton luminosity . the curves in fig . [ fig : f2 ] can be shifted by changes of @xmath25 , @xmath6 , and @xmath45 . the increase of @xmath28 due to the decrease of @xmath62 with increasing magnetic fields leads to a higher efficiency of photomeson production . as shown in fig . [ fig : f1 ] , however , we need to decrease the magnetic field to values as low as @xmath49 in order to harden the spectrum , since the klein - nishina effect is crucial . let us consider protons that interact with photons of @xmath63 . the cooling timescale for such protons behaves as @xmath64 , where the photon density @xmath65 . if we adopt a smaller value of @xmath6 , the pion production efficiency would be improved as @xmath66 . however , we should note that there is a lower limit to @xmath6 , which is required to make the source optically thin to gev photons . given the photon luminosity and spectral shape , this minimum lorentz factor can be estimated as shown in the online supporting materials in @xcite . the adopted value @xmath67 in fig . [ fig : f1 ] is close to the lower limit for @xmath68 cm . even if we take a larger @xmath25 , the lower limit of the lorentz factor @xmath69 does not decrease drastically ( since @xmath70 , @xmath71 ) . although a smaller @xmath72 cm and a slightly larger @xmath6 can reduce the required amount of protons , the typical variability timescale @xmath73 in fig . [ fig : f1 ] ( @xmath68 cm and @xmath67 ) is already as small as" +"generalized parton distributions ( gpds ) @xcite parametrize the non - perturbative hadron structure in hard exclusive processes ( for a recent review , see , e.g. , @xcite ) . their measurement would represent a unique way to access several crucial features of the structure of the nucleon , such as the angular momentum sum rule of the proton @xcite , as well as information on the structure of the proton in position space @xcite . therefore , relevant experimental efforts to measure gpds , by means of exclusive electron deep inelastic scattering ( dis ) off the proton , are likely to take place in the next few years @xcite . one of the most promising processes is represented by deeply virtual compton scattering ( dvcs ) @xcite . at twist - two , four helicity - even gpds occur . two of them are usually called unpolarized gpds and labeled @xmath1 and @xmath2 . the first of them gives , in dis kinematics , the usual quark density . the latter turns out to be a spin - flip distribution , in the sense that it implies a change of the spin of the target . the other two are usually called polarized or helicity - dependent gpds . they are labeled @xmath0 and @xmath3 . the first of them yields in dis kinematics the polarized quark density , the second is again a spin - flip distribution . the four of them enter the cross sections for the dvcs process , although the two non - spin - flip ones , @xmath1 and @xmath0 , give the dominant contribution . reasonable estimates are necessary for the planning of experiments . for these quantities , several theoretical predictions have been already produced by using different descriptions of hadron structure : bag models @xcite , soliton models @xcite , light - front @xcite and bethe salpeter approaches @xcite , and phenomenological estimates based on parametrizations of parton distribution functions ( pdfs ) @xcite . besides , an impressive effort has been devoted to study the perturbative qcd evolution @xcite of gpds , and the gpds at twist three accuracy @xcite . chiral - odd gpds deserve a special mention : while they have been shown to be in principle experimentally accessible @xcite , no theoretical estimates are available for them . we are interested in constituent quark model ( cqm ) calculations . in this framework , in order to compare model predictions with data taken in dis experiments , one has to evolve , according to perturbative qcd , the leading twist component of the physical structure functions obtained at the low momentum scale associated with the model , from this so called `` hadronic scale '' , @xmath4 @xcite , to the momentum scale of the data . such a procedure has proven successful in describing the gross features of the standard pdfs by using different cqms ( see , e.g. , @xcite ) . similar expectations motivated the study of gpds in ref . @xcite , where a simple formalism has been proposed to calculate the quark contribution to the gpds from any non relativistic model . as an illustration , results for the gpd @xmath5 , obtained in the non relativistic ( nr ) model of isgur and karl ( ik ) @xcite have been evolved from @xmath6 up to dis scales , to next to leading order ( nlo ) accuracy . in ref . @xcite the same quark contribution has been evaluated , at @xmath6 , using the overlap representation of the gpds @xcite in light - front dynamics , along the lines developed in @xcite . the same approach has been also applied to calculate the valence quark contribution to the helicity - dependent gpds @xcite . in all the papers dealing with cqm listed so far @xcite , only the dokshitzer - gribov - lipatov - altarelli - parisi ( dglap ) region of gpds can be evaluated . to our knowledge , no cqm estimate of the helicity - dependent gpds has been performed in the efremov - radyushkin - brodsky - lepage ( erbl ) region . this is precisely the argument of the present paper , where an approach recently proposed for the unpolarized gpds in a cqm scenario @xcite , providing us with predictions also in the erbl region , will be extended to the helicity - dependent gpds . in ref . @xcite , the procedure of ref . @xcite has been extended and generalized since , as a matter of fact , the latter , when applied to the standard forward case , has been proven to reproduce only the gross features of pdfs @xcite . in order to achieve a better agreement with data , the approach has to be improved . in a series of papers , it has been shown that unpolarized @xcite and polarized @xcite dis data are consistent with a low energy scenario , dominated by complex constituent quarks inside the nucleon , defined through a scheme suggested by altarelli , cabibbo , maiani and petronzio ( acmp ) @xcite , updated with modern phenomenological information . the same idea has been applied to demonstrate the evidence of complex objects inside the nucleon @xcite , analyzing intermediate energy data of electron scattering off the proton . a similar scenario , as old as the cqm itself @xcite , has been extensively used by other groups , starting form the concept of `` valon '' @xcite . in ref . @xcite , the description of the unpolarized forward case of ref . @xcite has been generalized and applied to the calculation scheme of ref . @xcite . as a result , more realistic predictions for the gpds have been obtained and , at the same time , the erbl region , not accessible before , has been explored . in particular , the evaluation of the sea quark contribution has become possible , so that gpds can be calculated , in principle , in their full range of definition . such an achievement will permit to estimate cross - sections that are relevant for actual gpds measurements , providing us with an important tool for planning future experiments . in here , the discussion is extended to helicity - dependent gpds . the description of the polarized forward case of ref . @xcite is generalized to calculate helicity - dependent gpds , following the path that lead to the results of ref . @xcite starting from the calculation of the unpolarized forward structure function in ref . @xcite . as in ref . @xcite , the proposed approach will be applied here in a nr framework , which allows one to evaluate the gpds only for small values of the 4-momentum transfer , @xmath7 ( corresponding to @xmath8 , where @xmath9 is the constituent quark mass ) and small values also for the skewedness parameter , @xmath10 . the full kinematical range of definition of gpds will be studied in a followup , introducing relativity in the scheme . the paper is structured as follows . in the second section , after the definition of the main quantities of interest , a formula for the helicity - dependent current quark gpd @xmath11 , in a cqm with point - like constituents , will be derived . for the same quantity , in the third section , in a scenario dominated by composite constituent quarks , a _ formula in terms of the corresponding quantity of the constituent quark and of a polarized off - diagonal momentum distribution , will be derived in impulse approximation ( ia ) . then , the helicity - dependent constituent quark gpds are built in the fourth section , according to acmp philosophy and using the double distribution ( dd s ) representation @xcite of the gpds . in the fifth section , results obtained by using cqm wave functions of the ik model and our helicity - dependent constituent quark gpds will be shown . conclusions will be drawn in the last section . let us consider a hard exclusive process , where the absorption of a high - energy virtual photon by a quark in a hadron target is followed by the emission of a particle to be later detected ; finally , the interacting quark is reabsorbed back into the recoiling hadron . if the emitted and detected particle is , for example , a real photon , the so called deeply virtual compton scattering process takes place @xcite . we adopt here the formalism used in ref . let us think of a nucleon target , with initial ( final ) momentum and helicity @xmath12 and @xmath13 , respectively . the gpds @xmath14 and @xmath15 are defined through the expression @xmath16 + where @xmath17 is the 4-momentum transfer to the nucleon , @xmath18 is the quark field and m is the nucleon mass . it is convenient to work in a system of coordinates where the photon 4-momentum , @xmath19 , and @xmath20 are collinear along @xmath21 . the @xmath10 variable in the arguments of the gpds is the so called `` skewedness '' , parametrizing the asymmetry of the process . it is defined by the relation @xmath22 , where @xmath23 is a light - like 4-vector satisfying the condition @xmath24 . as explained in @xcite , gpds describe the amplitude for finding a quark with momentum fraction @xmath25 ( in the infinite momentum frame ) in a nucleon with momentum @xmath26 and replacing it back into the nucleon with a momentum transfer @xmath27 . besides , when the quark longitudinal momentum fraction @xmath28 of the average nucleon momentum @xmath29 is less than @xmath30 , gpds describe antiquarks ; when it is larger than @xmath10 , they describe quarks ; when it is between @xmath30 and @xmath10 , they describe @xmath31 pairs . the first and second @xmath28 intervals are commonly referred to as the dglap region and the third as the erbl region @xcite , following the pattern of evolution in the factorization scale . one should keep in mind that , besides the variables @xmath32 and @xmath7 explicitly shown , gpds depend , as the standard pdfs , on the momentum scale @xmath33 at which they are measured or calculated . to make the presentation easier looking , we omit the latter dependence unless when specifically needed . the values of @xmath10 which are possible for a given value of @xmath7 are : 0 / . [ xim ] the known constraints of @xmath34 are : \i ) the so called `` forward '' limit , @xmath35 , i.e. , @xmath36 , yields the usual polarized pdfs h_q(x,0,0)=q(x ) ; [ i ) ] \ii ) the integration over @xmath28 , yields the contribution of the quark of flavor @xmath37 to the axial form factor ( ff ) of the target @xmath38 , called hereafter @xmath39 : dx h_q(x,,^2 ) = g_a^q(^2 ) ; [ ii ) ] \iii ) the polynomiality property @xcite , according to which the @xmath28-integrals of @xmath40 and of @xmath41 are polynomials in @xmath10 of order @xmath42 . in @xcite , the ia expression for the unpolarized @xmath43 , suitable to perform cqm calculations , was obtained . in a similar fashion , we derive next a formula for the helicity - dependent gpd @xmath14 from the definition ( [ eq1 ] ) . using the light - cone spinor definitions as given in the appendix b of @xcite , and defining : @xmath44 , for the light - cone helicity combination @xmath45 one obtains @xmath46 so that , for @xmath47 : @xmath48 i.e. @xmath49 according to this equation , in order to obtain the gpd @xmath34 for @xmath47 one has to evaluate @xmath50 , starting from its definition , eq ( [ eq1 ] ) . using light - cone quantized quark" +"_ antiprotonic helium _ @xmath7he@xmath8 is a metastable three - body system consisting of one electron in the ground state , the helium nucleus and one antiproton @xcite . exotic _ atom can be created whenever an antiproton in the vicinity of a helium atom is slowed down to its ionization energy of @xmath924.6 ev or below . the antiproton can eject one of the two electrons from the ground state and replace it . the antiproton is captured and , due to its high mass , most likely to be in states with high angular momentum and with principal quantum number @xmath10 , @xmath11 being the reduced mass of the system , while the electron remains in the ground state . therefore , these newly - formed atoms occupy circular states with @xmath12 close to @xmath13 , where @xmath12 is the angular momentum quantum number . a majority of 97% of these exotic atoms find themselves in states dominated by auger decay . due to the auger excitation of the electron they ionize within a few nanoseconds after formation . the remaining 3% of antiprotonic helium atoms remain in metastable , radiative decay - dominated states . these states are relatively long lived , having a lifetime of about 1 - 2 @xmath14s a time window that can be used to do laser and microwave spectroscopy measurements @xcite . the interaction of magnetic moments between electron , antiproton and helium nucleus gives rise to a splitting of the @xmath15he@xmath8 energy levels . the coupling of the electron spin @xmath16 and the orbital angular momentum of the antiproton @xmath17 leads to the primary splitting of the state into a doublet structure , referred to as _ hyperfine ( hf ) splitting_. the angular momentum @xmath18 defines the two substates with quantum numbers @xmath19 and @xmath20 . the non - zero spin of the @xmath21he nucleus causes a further , so - called _ super - hyperfine ( shf ) splitting _ , which can be characterized by the angular momentum @xmath22 , where @xmath23 is the spin of the helium nucleus . this results in four shf substates . at last , the spin - orbit interaction of the antiproton orbital angular momentum and antiproton spin @xmath24 in combination with the contact spin - spin and the tensor spin - spin interactions between the particles result in a further splitting of the shf substates into eight substates which we call _ super - super - hyperfine ( sshf ) splitting_. this octuplet structure can be described by the angular momentum @xmath25 . even though the magnetic moment of the antiproton is larger than that of the @xmath21he nucleus , the former has a smaller overlap with the electron cloud . therefore it creates a smaller splitting . the complete hyperfine structure for @xmath15he@xmath8 is illustrated in fig . [ fig : he3_lmwl ] . the interest in @xmath26he@xmath27 arises from an additional contribution to the hyperfine structure caused by the coupling of the nuclear spin to the antiproton orbital momentum with respect to @xmath28he@xmath27 @xcite . such a measurement would allow a more rigorous test of qed theory . the accurate knowledge of the hyperfine structure of antiprotonic helium is essential for the calculation of the laser transition energies at the level of ppb accuracy needed for comparison to laser spectroscopy experiments and the extraction of the antiproton - to - electron mass ratio @xcite . an experimental verification of the hfs splitting in @xmath26he@xmath27 is therefore of great importance . the calculations of the hyperfine structure were developed by two different groups @xcite . this series of experiments , studying the @xmath1 state , was the first attempt to measure the microwave transition frequencies between hyperfine substates of @xmath26he@xmath27 . transitions between the sshf states were induced by a magnetic field oscillating in the microwave frequency range . due to technical limitations of the microwave input power , only the transitions which flip the spin of the electron could be measured . there are four such `` allowed '' sshf transitions for the @xmath1 state of @xmath26he@xmath27 two of which we investigated with the present work : @xmath29 the first observation of a hyperfine structure in antiprotonic helium was achieved in a laser scan of the @xmath30 transitions in @xmath28he@xmath27 @xcite . due to the limited precision achievable in a laser scan , a _ laser - microwave - laser method _ [ fig : he3_lmwl ] ) was introduced in @xcite . it is based on a three - step process involving laser and microwave stimulated resonance transitions . after antiprotonic helium is formed , the atoms in the hyperfine substates are all equally populated . therefore at first a population asymmetry between the sshf substates of the measured radiative decay state @xmath31 needs to be created . this depopulation is induced by a short laser pulse which transfers the majority of antiprotons from one of the hf states of the radiative decay - dominated , metastable parent state to an auger decay - dominated , short - lived daughter state . in this experiment the @xmath32 transition is used . the bandwidth of the laser ( 100 mhz ) and doppler broadening at 6 k ( 300 mhz ) are small enough compared to the difference of @xmath33 ghz so that the @xmath34 transition is not affected and a population asymmetry can be achieved . the antiprotons in the short - lived state annihilate within a few nanoseconds . in the next step , a microwave frequency pulse tuned around the transition frequency between two sshf substates of the metastable state is applied . if the microwave field is on resonance with one of these transitions , it will cause a population transfer and thus partial refilling of one of the previously depopulated states . a second laser pulse will then again cause depopulation of the same hf substate and subsequently auger decay of the transferred atoms and annihilation of the antiprotons in the nucleus will occur . the number of annihilations after the second laser pulse will be the larger the more antiprotons were transferred by the microwave pulse . when the antiprotons first enter the helium gas , a large annihilation peak ( prompt peak ) is caused by the majority of formed @xmath35 atoms which find themselves in auger decay - dominated states and annihilate within picoseconds after formation . at later times , this peak exhibits an exponential tail due to @xmath35 atoms in the metastable states cascading more slowly towards the nucleus . this constitutes the background for the laser - induced annihilation signals . the daughter state has a very short lifetime of @xmath910 ns and thus the population transfer is indicated by a sharp annihilation peak against the background during the two laser pulses . the area under these peaks is proportional to the population transferred to this short - lived state . this spectrum , with the two laser - induced peaks super - imposed on the exponential tail as displayed in fig . [ fig : adats ] is called _ analogue delayed annihilation time spectrum _ or adats . since the intensity of the antiproton pulse fluctuates from shot to shot , the peaks must be normalised by the total intensity of the pulse ( total ) . this ratio is referred to as _ peak - to - total_. the peak - to - total ( ptt ) corresponds to the ratio of the peak area ( @xmath36 or @xmath37 ) to the total area under the full spectrum . if the second laser annihilation peak is further normalised to the first one , the total cancels out . the frequencies of the two sshf transitions can now be obtained as distinct lines by plotting @xmath38 as a function of the microwave frequency . the ratio @xmath38 is largely independent of intensity and position fluctuations of the antiproton beam . the intensity of the transition lines is subject to the time delay between the two laser pulses and thus also to collisional relaxation processes @xcite . this means that , once the first laser has caused depopulation , the system will start to relax through spin exchanging collisions between antiprotonic helium atoms and regular helium atoms . refilling from higher - lying states also contributes to the equalization of the hyperfine substate populations . in general , a short delay @xmath39 is preferable because the signal height will decrease for longer laser delay times as a result of the exponential decay of the metastable state populations . however , the linewidth of the rf transition will increase if the delay is too short . further , far higher rf power will be required to complete one spin - flip . if the delay is too long , the collisional relaxation of the system would already have eliminated any asymmetry between the two states caused by the first laser pulse . the signal would be too low to be observed . the two pulsed lasers were fixed to a wavelength of 723.877 nm , with a pulse length of 8 - 12 ns , to induce the @xmath40 laser transition between the @xmath1 and the @xmath41 state . the pulse length should be comparable to or longer than the auger lifetime of the short - lived state . generally spoken , the longer the laser pulse the larger the achieved depopulation and thus the resulting annihilation signal . the depopulation also depends on the laser pulse energy . it is important to find the appropriate laser fluence where the power is saturated and therefore the laser depletion efficiency is optimized in order to avoid power broadened resonance lines and as a consequence partial depopulation of the other hf transition line f@xmath42 . for this experiment a pulse - amplified continuous - wave laser system with a narrow linewidth of about 100 mhz was used @xcite . the laser fluence was in the range of 20 - 40 mj@xmath43@xmath44 , the laser waist @xmath95 mm , leading to a depletion efficieny of about 90% based on numerical simulations of the laser transition processes @xcite . there are several limitations to the choice of the measured state , such as availability of a laser source in the required frequency range or the splitting of the transitions between the hf states of the daughter and the parent state . the laser transition between the @xmath1 and the @xmath41 state was chosen because it is easily stimulated and the primary population is large , thus leading to a large signal . the captured fraction of antiprotons in the measured metastable state @xmath1 is ( 3 - 4)@xmath45 @xcite . the antiprotons for the experiment are provided by the ad ( antiproton decelerator ) at cern @xcite , with a pulsed beam of ( 1 - 3)@xmath46 antiprotons at an energy of 5.3 mev , a pulse length of 100 - 300 ns , and a repetition interval of about 100 s. the particles are stopped in a helium gas target , with a gas pressure of 250 mbar , cooled down to a temperature of about 6 k. this target is built as a cylindrical chamber whose axis is parallel to the beam direction and which is designed to act also as a microwave cavity resonating in the tm@xmath47 mode . the faces of the cylindrical cavity have a 25 @xmath14 m thick titanium window for the antiproton beam and a 4 mm thick fused silica window for the laser beam to enter @xcite , and are equipped with meshes to contain the microwaves . in order to measure the annihilation decay products two cherenkov counters are mounted around the target volume , connected to photomultipliers ( cf . [ fig : newcryostat ] ) . they are gated off during the initial @xmath7 pulse arrival @xcite in order to count" +"a comprehension of the link between stochastic processes and quantum mechanics can provide a better understanding of the role of space time at a quantum gravity level . indeed , noncommutative geometry , in the way connes , chamseddine and mukhanov provided recently @xcite , seems to fit well the view that a quantized volume yields a link at a deeper level of the connection between stochastic processes and quantum mechanics . this is an important motivation as we could start from a reformulation of quantum mechanics to support or drop proposals to understand quantum gravity and the fabric of space - time . a deep connection exists between brownian motion and binomial coefficients . this can be established by recovering the kernel of the heat equation from the binomial distribution for a random walk ( pascal tartaglia triangle ) and applying the theorem of central limit @xcite . when an even smaller step in the random walk is taken a wiener process is finally approached . so , it is a natural question to ask what would be the analogous of pascal tartaglia triangle in quantum mechanics@xcite . this arises naturally by noting the apparent formal similarity between the heat equation and the schrdinger equation . but this formal analogy is somewhat difficult to understand due to the factor @xmath0 entering into the schrdinger equation . an answer to this question hinges on a deep problem not answered yet : is there a connection between quantum mechanics and stochastic processes ? the formal similarity has prompted attempts to answer as in the pioneering work of edward nelson @xcite and in the subsequent deep analysis by francesco guerra and his group @xcite . they dubbed this reformulation of quantum mechanics as `` stochastic mechanics '' . this approach matches directly a wiener process to the schrdinger equation passing through a bohm - like set of hydrodynamic equations and so , it recovers all the drawbacks of bohm formulation . this view met severe criticisms motivating some researchers to a substantial claim that `` no classical stochastic process underlies quantum mechanics '' @xcite showing contradiction with predictions of quantum mechanics . subsequent attempts to partially or fully recover this view were proposed with non - markovian processes @xcite or repeated measurements @xcite . in this paper we will show that a new set of stochastic processes can be devised that can elucidate such a connection @xcite . we show their existence @xcite and we will determine how spin is needed also in the non - relativistic limit . dirac equation for a free particle is also obtained . these processes are characterized by the presence of a bernoulli process yielding the values @xmath1 and @xmath0 , exactly as expected in the volume quantization in noncommutative geometry . in this latter case , it appears that a stochastic process on a quantized manifold is well represented by a fractional power of an ordinary wiener process when this is properly defined through a technique at discrete time . for our aims we will use the simplest one : the euler maruyama technique . a numerical test will yield the proof of existence for this class of stochastic processes . also , the kernel of the schrdinger equation is numerically obtained through an ordinary brownian motion . the paper is so strctured . in sec . [ sec2_0 ] we discuss noncommutative geometry in informal way , providing a general formula for a stochastic process on a quantized riemannian manifold . in sec . [ sec2 ] , we introduce the fractional powers of a wiener process and we solve the corresponding stochastic equation recovering the wiener process we started from after squaring its square root . in sec . [ sec3 ] , we derive the formula for the square root of a wiener process expressing it through more elementary processes : this shows the need for a clifford algebra and the fokker planck equation is obtained for a free particle . in sec . [ sec4 ] , we show numerically how the kernel of the schrdinger equation is recovered by an ordinary brownian motion just with the extraction of its square root . in sec . [ sec5 ] , we derive the fokker planck equation in presence of a potential and specialize to the case of a harmonic oscillator . in sec . [ sec6 ] , we show how to recover a stochastic process on a noncommutative geometry taking the square root of more wiener processes and using the algebra of the dirac matrices . in sec . [ sec7 ] , we recover the dirac equation as the fokker planck equation for a square root process . finally , in sec . [ sec8 ] conclusions are presented . common wisdom on geometry implies that one has to cope with points and minimum paths between them . indeed , the idea of geometry can be extended without the central concept of points but rather functions and introducing a redefinition of the concept of distance beside the well - known one from a riemannian geometry . this reformulation is due to alain connes @xcite . essentially , one introduces a triple composed by an algebra of functions @xmath2 with an involution operator like complex conjugation , playing the role of coordinates , a hilbert space @xmath3 , that we take the space of the square - summable spinors , and a dirac operator @xmath4 , being @xmath5 a spin connection , representing momenta . the algebra of functions has support on a riemann manifold . when we change the algebra of functions with a noncommutative algebra of operators acting on the given hilbert space , in the same way one quantize a classical theory , one gets a noncommutative geometry . so , a geometry is identified by the triple ( @xmath2,@xmath3,d ) . a function @xmath6 belonging to @xmath2 should satisfy the lipschitz condition on the riemann manifold given by @xmath7 provided the constant @xmath8 exists and @xmath9{\ } { \rm inf}\left(\int_\gamma ds\right)\ ] ] is the usual ( geodesic ) distance on a riemann manifold that coincides with the well - known variational principle of minimum distance between two points . this grants some regularity properties of the functions in @xmath2 and their gradient that is bounded . in this way , we can introduce a new definition of distance dependent just on the algebra of functions @xmath2 and the dirac operator . this is given by @xmath10{\ } { \rm sup}(|f(x)-f(y)| : f\in{\cal a},\lvert df\rvert<1)\ ] ] where the condition on the dirac operator plays a crucial role . in this way , one recovers the ordinary riemann distance between points @xcite . indeed , one has for a spinor @xmath11 @xmath12\psi = i\gamma\cdot\partial f\psi.\ ] ] then we need @xmath13\rvert=\lvert\sqrt{\partial_\mu f\partial^\mu f}\rvert\le 1.\ ] ] this is nothing else than asking the boundedness of the gradient of @xmath6 . we know that @xmath6 is lipshitz on the manifold and so , we can apply the cauchy mean value theorem implying that @xmath14\rvert\le\frac{|f(x)-f(y)|}{d_r(x , y)}\ ] ] because a constant @xmath8 exists that can limit the derivatives on the manifold . now , this implies , due to the condition @xmath15 , that @xmath16 and this means that @xmath17 is the upper extreme as required by our definition of distance . the main conclusion is that the dirac operator plays the role of the inverse of the distance @xmath18 . a noncommutative geometry implies that the volume is quantized with two classes of unity of volume @xmath19 . this has been recently proved by connes , chamseddine and mukhanov@xcite . the two classes of volume arise from the fact that the dirac operator should not be limited to majorana states in the hilbert space and so , we need to associate a charge conjugation operator @xmath20 to our triple @xmath21 . to complete our characterization of our geometry , we recall that the algebra of dirac matrices implies a @xmath22 , the chirality matrix . for an ordinary riemann manifold , the algebra @xmath2 is that of functions and is commuting . remembering that @xmath23=i\gamma\cdot\partial a$ ] , and noting that , in four dimensions , @xmath24 are legal functions of @xmath25 , it is @xmath26[d , x_2][d , x_3][d , x_4]=\gamma^1\gamma^2\gamma^3\gamma^4=-i\gamma^5 $ ] . for generally chosen functions in @xmath25 , @xmath27 , summing over all the possible permutations one has a jacobian , we can define the chirality operator @xmath28\ldots[d , a_d]).\ ] ] so , in four dimension this gives @xmath29 being @xmath20 the jacobian , @xmath30 the vierbein for the riemann manifold and @xmath31 for @xmath32 , a well - known result . we used the fact that @xmath33 , being @xmath34 the metric tensor . so , the definition of the chirality operator is proportional to the factor determining the volume of a riemannian orientable manifold . in order to see if a riemannian manifold can be properly quantized , instead of functions we consider operators @xmath35 belonging to an operator algebra @xmath36 . these operators have the properties @xmath37 this is a set of compact operators playing the role of coordinates as in the heisenberg commutation relations . we have to consider two sets of them @xmath38 and @xmath39 as we expect a conjugation of charge operator @xmath40 to exist such that @xmath41 for a given operator or complex conjugation for a function . this appears naturally out of a dirac algebra of gamma matrices . so , a natural way to write down the operators @xmath35 is by using an algebra of dirac matrices @xmath42 such that @xmath43 with @xmath44 , then @xmath45 we will have two different set of gamma matrices for @xmath38 and @xmath39 that will have independent traces . using the charge conjugation operator @xmath40 , we can define a new coordinate @xmath46 where @xmath47 will project one or the other coordinate . we recognize that the spectrum of @xmath48 is in @xmath19 given eq.([eq : y ] ) . now , we generalize our equation for the chirality operator imposing a trace on @xmath49s both for @xmath38 and @xmath39 , normalized to the number of components , and we will have @xmath50\ldots[d , z]\rangle=\gamma.\ ] ] where we have introduced the average @xmath51 that , in this case , reduces to matrix traces . in order to see the quantization of the volume , let us consider a three dimensional manifold and the sphere @xmath52 . from eq.([eq : z ] ) one has @xmath53\ldots[d , z]\rangle d^3x\ ] ] and doing the traces one has @xmath54 it is easy to see that this will yield@xcite @xmath55 the coordinates @xmath38 and @xmath39 belongs to unitary spheres and the dirac operator has a discrete spectrum , so we are covering all the manifold with a large integer number of these spheres . thus , the volume is quantized as this condition requires . this can be extended to four dimensions with some more work @xcite . differently from an ordinary stochastic process , a wiener process on a quantized manifold will yield the projection of the spectrum @xmath19 of the coordinates on the two kind of spheres @xmath56 . this will depend on the way a particle moves on the manifold taking into account that the distribution of the two kind of unitary volumes is absolutely random . one can construct a process @xmath57 such that , against a toss of a coin , one gets 1 or i as outcome , assuming the distribution of the unitary volumes is uniform . this can be written @xmath58 with @xmath59 a bernoulli process producing the value @xmath60 depending on the unitary volume hit by the particle such that @xmath61 , a deterministic process giving always 1 , and @xmath62 . if we want to consider the brownian motion of the particle on such a manifold we should" +"the crab pulsar wind nebula is powered by its central pulsar born from a supernova explosion in 1054 . it is a very luminous source in almost all wavelengths , from radio to the very high energy ( vhe ) @xmath0-ray bands . the broadband non - thermal emission spectrum is well modeled by a synchrotron - inverse compton ( ic ) scenario with the transition from the synchrotron to ic component occurring at a few hundred mev @xcite . the overall emission seems to be steady , so that the crab nebula has been adopted as a standard candle in high energy astrophysics to calibrate observations from different instruments . however , detailed images of the crab nebula in optical and x - ray bands indicated dynamical structures at small scales . observations by the hubble space telescope revealed wisps and knots in the nebula , and resolved some substructures of the highly variable wisps @xcite . x - ray observations by rosat and chandra uncovered a jet - torus structure of the inner nebula @xcite , and the equatorial ring is found moving outwards with a speed of @xmath3 @xcite . at higher energies in the @xmath0-ray band , detailed structures of the nebula generally can not be resolved . however , comptel and egret observations indicated that the synchrotron radiation in @xmath4 mev is variable on a timescale of @xmath5 yr . in september 2010 , agile collaboration reported a @xmath0-ray flare above @xmath6 mev from the direction of the crab nebula , which lasted for about 3 days ( atel # 2855 ; tavani et al . the flux during the flare period is about @xmath7 times higher than the average one . this flare was soon confirmed by the fermi / lat collaboration ( atel # 2861 ) , and archive search of the fermi / lat data revealed another flare in february 2009 @xcite . there were many other simultaneous or follow - up measurements for the flare in september 2010 in x - ray , optical , infrared and radio bands . however , no significant flux enhancement was discovered . in the vhe @xmath0-ray energies , argo - ybj collaboration claimed the detection of a flux enhancement around tev , with a possibly longer duration ( atel # 2921 ) . however , magic and veritas observed the source with a shorter duration during the flare phase and did not reveal any enhancement in flux ( atel # 2967 , # 2968 ) . it was proposed that the flares was due to synchrotron emission of ultra - relativistic electrons with energies up to @xmath2pev @xcite . considering the fact that the rest frame synchrotron radiation in a magnetic field dominated acceleration regime can not exceed @xmath8 mev due to the fast synchrotron cooling of high energy electrons @xcite , the observed gev emission implies doppler shift of the radiation region or other acceleration mechanisms instead of shock acceleration @xcite . @xcite proposed that the @xmath0-ray variability ( flare ) originated from the `` inner knot '' of the crab nebula ( `` knot 1 '' as defined in @xcite ) , with mildly doppler - boosted emission . the instability of the termination shock may cause the variability as revealed by magnetohydrodynamic ( mhd ) simulations . @xcite suggested that electrons are accelerated in a region behind the shock , and the variability was attributed to changes in the maximum energy of accelerated electrons , electron spectral index or the magnetic field . in this letter we employ a statistical approach to model the @xmath0-ray variability of the nebula . fermi / lat observations have shown that the low - energy synchrotron component is variable on monthly time scale , while the high - energy ic component seems to be stable @xcite . since the synchrotron @xmath0-rays are produced by the highest energy electrons , these observations indicate that fluctuations at the high - energy end of the electron distribution might be responsible for the variability . it is natural to expect that events that can generate the highest energy electrons are rarer , and therefore would lead to the largest fluctuation . therefore the variability and flares in the sub - gev @xmath0-rays can be simply due to the statistical fluctuation of the highest energy electrons achievable in the electron accelerators . lower energy electrons do not suffer from significant fluctuations since many more accelerators can contribute to them simultaneously , which gives rise to a `` steady - state '' emission in both the lower energy synchrotron component and the higher energy ic component . we build a physically possible model to investigate the above picture in more details . we assume that electrons are accelerated in a series of knots with a power - law energy spectrum @xmath9 with the maximum electron energy @xmath10 being proportional to the size of the @xmath11th knotpc , which just corresponds to the size of the emission region as indicated by the day - scale flare . therefore we assume the largest size of the knots is @xmath12 , and for all other knots smaller than @xmath12 the scaling relation between @xmath10 and @xmath13 can well hold . ] . we further assume that the size of knots has a power - law distribution @xmath14 . adding the contribution from all these knots together , noticing that the normalization of the synchrotron spectrum of the knots scales as @xmath15 , we get the total electron spectrum as @xmath16 where @xmath17 is the heaviside step function , @xmath18 is the maximum energy of the largest knot . if @xmath19 , the above integral of the last step is approximately proportinal to @xmath20 given the maximum energy of the largest knot @xmath21 ; if @xmath22 the integral is nearly a constant determined by @xmath18 . therefore the electron spectrum is a power law @xmath23 with power - law index @xmath24 and a cutoff determined by the largest knot . the maximal energy of synchrotron emission in the magnetic field dominated acceleration regime is @xmath8 mev @xcite ( defined by equating the synchrotron cooling time scale to the gyro - period , the minimum of the acceleration time scale ) . for smaller accelerators , the maximum energy is also limited by the size of the accelerator . in order to account for the observations in the @xmath1 mev range , we therefore further employ a mild doppler boost factor . we assume a gaussian distributed lorentz factor of all the knots with a mean value @xmath25 and a standard deviation @xmath26 . such a lorentz factor is consistent with the upper limit of the typical velocity of the jet @xcite . we assume that the angle @xmath27 between the knot motion and the line - of - sight is randomly distributed . the doppler factor @xmath28 ( where @xmath29 is the velocity of the knot in unit of @xmath30 ) therefore is distributed within the range @xmath31 for a @xmath32 distribution of @xmath33 . only knots with large enough size and large enough doppler factor can contribute to high energy synchrotron radiation to account for the flares observed by the fermi / lat . we realize such a picture by a monte - carlo simulation . we directly simulate the synchrotron spectrum in each knot instead of the electron spectrum . the synchrotron spectrum of each knot in its co - moving frame is adopted as @xmath34 , where @xmath35 , @xmath36 is the synchrotron spectral index . where @xmath37 is the power - law index of the overall electron distribution . the magnetic field in each knot is not explicitly used in the calculation . the magnetic field will affect the cooling break of the low energy synchrotron spectrum as well as the high energy cooling time scale . to keep the basic framework of the present study , we may expect the magnetic field not to vary significantly with respect to the knot size . the energy loss of electrons in the knots can be important and needs to be considered . for instantaneous injection of accelerated electrons , the probability of observing electrons at a given energy is proportional to the corresponding synchrotron cooling time @xmath38 . for low energy electrons with cooling time longer than the age of the crab nebula @xmath39 yr , these electrons will survive and accumulate . therefore we can construct a probability function @xmath40 , describing the effect of cooling on the electron spectrum . the cooling time of electrons producing synchrotron photon with energy @xmath41 is @xmath42 yr . for an average magnetic field @xmath43 mg , a mildly doppler factor @xmath44 , electrons producing photons with an energy @xmath45 ev have a cooling time comparable to @xmath46 . the observed spectrum of crab nebula has a break near @xmath47 ev ( see below fig . [ fig : f1 ] ) . in this work we mainly focus on the high energy part of the spectra , e.g. , from x - ray to @xmath0-ray band , then @xmath48 . assuming that the accelerated electrons have a spectrum index @xmath49 , the electron spectrum index in the synchrotron cooling dominated regime is then @xmath50 . here we adopt @xmath51 which corresponds to @xmath52 , as required by fitting the radio - optical data . the maximum value of @xmath53 is taken as @xmath54 mev in the co - moving frame ( corresponding to the largest knot ) . this value is derived according to a fit to the average fermi / lat spectrum of the synchrotron component @xcite , given the lorentz factor distribution . the power - law index of the size distribution is adopted as @xmath55 . adding all the contribution from the knots together we can get a total synchrotron spectrum @xmath56 , which can reproduce the observed optical - mev band data of the crab nebula ( fig . [ fig : f1 ] ) . note that these parameters , i.e. , @xmath33 , @xmath53 , @xmath57 and @xmath58 are not uniquely determined . what we adopt in this work is an illustration of the model . once the data from optical to @xmath0-ray band are reproduced , the discussion below is basically unchanged if a different set of parameters is taken . for each knot we randomly generate an angle @xmath27 and a lorentz factor @xmath33 based on the assumed gaussian distribution , and calculate the doppler factor @xmath59 . then the frequency of synchrotron emission from each knot is shifted from @xmath60 to @xmath61 , and the flux is enhanced to @xmath62 . the contribution from all the knots are summed up to obtain the total emission spectrum . realizations . the thick blue line denote the fit to the multi - wavelength steady state observational data , which can be understood as the average result of many realizations in our model . the black - dashed curve denotes the contribution from a maximum size knot with slightly specific parameters ( see the text ) , which is shown to be able to explain the large flare in september 2010 . the references of the observational data are : radio - optical @xcite , integral @xcite , comptel , fermi / lat @xcite , magic @xcite , hegra @xcite , hess , tibet - as@xmath0 @xcite , and fermi / lat flares @xcite . ] a series of simulated synchrotron spectra are shown in fig . [ fig : f1 ] , which are compared with the observational data of the crab nebula . note that for the integral data we adopt a flux normalization factor @xmath63 in order to be consistent with the extrapolation of comptel data . in a @xmath64 factor was adopted to match the xmm - newton data . the difference of flux normalization may be due to discrepancies in calibration of" +"in a recent paper becker et al . analysed spectra of the four highest redshift quasars discovered by sloan survey . the highest redshift ( @xmath1 ) quasar showed almost no transmitted flux just blueward of the quasar ly - alpha emission line , and on this bases becker et al . concluded that reionization took place at a redshift @xmath2 [ a similar claim was also made by djorgovski et al . based on an extrapolation from a lower redshift observations ] . however , one should be cautious before drawing such a conclusion . indeed , the observed decrease in the mean transmitted flux at @xmath3 might simply indicate a decrease in the mean ionizing intensity rather then a real reionization of the universe . thus , without an understanding of the evolution of the universe around the reionization epoch , the ly - alpha absorption data can not be used to constrain the epoch of reionization [ unless damping wings are observed in the absorption profiles , @xcite ] . fortunately , our theoretical understanding of the process of reionization , in part based on numerical simulations , is solid enough so that the evolution of the ionizing intensity at these redshifts can be predicted with a reasonable confidence level . combining simulations with the observational data indeed allows one to come up with a meaningful value for the redshift of reionization . a set of three simulations have been performed with the slh code and are similar to the simulations reported in @xcite . the main difference with previous simulations is that a newly developed and highly accurate optically thin eddington variable tensor ( otvet ) approximation for modeling radiative transfer @xcite is used instead of a crude local optical depth approximation . the new simulations therefore should be sufficiently accurate ( subject to the usual limitations of numerical convergence and phenomenological description of star formation ) to be used meaningfully in comparing with the observational data . .simulation parameters [ cols=""<,^,^,^,^,^ "" , ] parameters of the three simulations are given in table [ sim ] . all three simulations included @xmath4 dark matter particles , an equal number of baryonic cells on a quasi - lagrangian moving mesh , and about @xmath5 stellar particles that formed continuously during the simulation . the box size was fixed at @xmath6 comoving mpc , and the nominal spatial resolution of the simulation was fixed at @xmath7 comoving kpc , with the real resolution being a factor of two worse . in all cases a flat cosmology was assumed , with @xmath8 , and _ cobe _ normalization was adopted . notice that because of that , a small change in the slope of the primordial power - law spectrum @xmath9 makes a significant effect on the amount of the small - scale power due to a large leverage arm from _ cobe _ scales to the tens - of - kpc scales which are important for reionization . star formation is incorporated in the simulations using a phenomenological schmidt law , which introduces two free parameters : the star formation efficiency @xmath10 [ as defined by eq . ( 6 ) of gnedin ] and the ionizing radiation efficiency @xmath11 ( defined as the energy in ionizing photons per unit of the rest energy of stellar particles ) . these two parameters are listed in the last two columns of table [ sim ] for reference purposes . the star formation efficiency @xmath10 is chosen so as to normalize the global star formation rate in the simulation at @xmath12 to the observed value from steidel et al . , whereas the ultraviolet radiation efficiency @xmath11 is only weakly constrained by the ( highly uncertain ) mean photoionization rate at @xmath13 . the redshift of reionization strongly depends on @xmath11 and is not in fact predicted in a simulation , but can be changed over a reasonable range depending on the assumed value of @xmath11 . i will use this freedom to fit the observational data from becker et al . and instead to constrain the redshift of reionization from the observational data . = 1.0 before one can attempt to measure `` the redshift of reionization '' , we better be sure that such a quantity can be defined . the whole process of reionization is quite extended ( @xmath14 ) , and even the fast process of percolation of ionized bubbles occurs over a sizable redshift interval @xmath15 @xcite . however , one can still define the specific value of the redshift of reionization as the moment which corresponds to the peak rate of increase of the mean free path to ionizing radiation . as can be seen from figure [ figmp ] , the time derivative of the mean free path has a well defined peak , which i use throughout this paper as `` the redshift of reionization '' @xmath16 . = 1.0 figure [ figtz ] shows the mean transmitted flux as a function of redshift for the three simulations described above . in each case the arrow shows the redshift of reionization , and points with error - bars are taken from becker et al . . each point represents an average of up to four quasars , except for the last two points that are derived from a single quasar and thus have no vertical error - bars . it is important to emphasize that the measurement of the mean transmitted flux for each quasar over an interval @xmath17 is quite accurate , with the intrinsic error of only @xmath18 in @xmath19 , but the variation between different lines of sight ( the so - called `` cosmic variance '' ) is much greater , and it is this variation that dominates the vertical error - bar . thus , one ( or better two ) more @xmath20 quasars are required in order to place the vertical error - bars on the open circles . however , because the sharp drop in the mean transmitted flux at @xmath21 is marked by two data points , it is more reliable than simply one point from one quasar . simulations in fig . [ figtz ] differ from the data points in two ways : both the redshift evolution in a simulation and the photoionization rate after reionization ( the amplitude of the curve at low @xmath22 ) are offset relative to the data . as i mentioned above , the free parameter @xmath11 can be used to adjust the simulation to fit the observational data . however , there is no guarantee that with _ one _ parameter i can adjust _ two _ offsets at the same time for a given cosmological model . this fact is extremely important because it allows one to actually put constraints on the cosmological model per se , and i elaborate on this opportunity in the conclusions , but here i am going to ignore this fact and adjust two offsets independently - by sliding the curve both vertically and horizontally - to fit the observational data . because the three curves from three simulations have similar shapes , every simulation can thus be made to fit the data - and , again , in reality , only a narrow range of cosmological models will succeed in doing so . the reason for doing so is to obtain a constraint on the redshift of reionization which does not depend on a ( weakly constrained ) cosmological model . in addition , the simulations presented here are rather small and numerical errors due to incomplete convergence are substantial @xcite . simulations with larger box sizes typically have lower mean transmitted flux after reionization than small box simulation - which implies that amplitudes of three curves are not sufficiently accurate in fig . [ figtz ] . the arbitrary vertical shift of the curves can thus be considered as a `` marginalization '' over the simulation box size . = 1.0 figure [ figta ] shows the fit to the observational data for each of the three simulations . the shaded region also gives an uncertainty of this fit , which can be considered a random uncertainty due to observational errors ( mostly cosmic variance ) . because the last two points have no vertical error - bars , they are only partly used : they only constrain models in the horizontal direction , and their redshift error - bars uncertainty are somewhat arbitrarily increased by a factor of 2 ( to account for the possibility that they can be moved up and down ) . the fact that different cosmological models have slightly different redshifts of reionization when made to fit the observed evolution of the mean transmitted flux illustrates the systematic uncertainty due to unknown cosmological parameters . with these two uncertainties included , i can derive a value for the redshift of reionization in the following form : @xmath23 which is the sole result of this paper . if cosmic variance on the last two points can be estimated , and if it is comparable to the vertical error - bar on the @xmath24 point , then the random error gets reduced from 0.2 to 0.1 . sloan observations of @xmath2 quasars push the frontier of the observable universe right into the epoch of reionization . combined with the most advanced simulations of cosmological reionization to date , the observational data yield a rather precise measurement of the redshift of reionization . this measurement hinges on the assumption that the @xmath1 quasar ( sdssp 1030 + 0524 ) probes an average region of the universe , i.e. that the cosmic variance in the measurement of the mean transmitted flux at @xmath25 is not larger than a factor of 3 - 5 . one or two more @xmath20 quasars are required to confirm or refute this assumption . a strong sensitivity of the redshift of reionization to the amount of small - scale power offers a unique opportunity to place constraints on the slope of the primordial power spectrum - unattainable even with the sloan data on the power spectrum at megaparsec scales . for example , runs b and c in fig . [ figtz ] have similar star formation rates and redshifts of reionization , but differ by a factor of 3 in the mean transmitted flux at @xmath26 only because the slope of the primordial power spectrum @xmath9 differs by mere 0.02 in the two models . sufficiently large simulations that have numerical effects under control are currently feasible and will eventually provide a tight constraint on the amount of small - scale power . becker , r. h. , et al . 2000 , aj , in press ( astro - ph/0108097 ) djorgovski , s. g. , castro , s. m. , stern , d. , mahabal , a. 2001 , apjl , in press ( astro - ph/0108069 ) gnedin , n. y. 2000a , apj , 535 , 530 gnedin , n. y. 2000b , apj , 535 , l75 gnedin , n. y. , abel , t. 2001 , newa , in press ( astro - ph/0106278 ) miralda - escud , j. 1998 , apj , 501 , 15 steidel , c. c. , adelberger , k. l. , ciavalisco , m. , dickinson , m. , pettini , m. 1999 , apj , 519 , 1" +"the casimir force @xcite between uncharged metallic plates attracts considerable attention as a macroscopic manifestation of the quantum vacuum @xcite . with the development of microtechnologies , which routinely control the separation between bodies smaller than 1 @xmath0 , the force became a subject of systematic experimental investigation . modern precision experiments have been performed using different techniques such as torsion pendulum @xcite , atomic force microscope ( afm ) @xcite , microelectromechanical systems ( mems ) @xcite and different geometrical configurations : sphere - plate @xcite , plate - plate @xcite and crossed cylinders @xcite . the relative experimental precision of the most precise of these experiments is estimated to be about 0.5% for the recent mems measurement @xcite and 1% for the afm experiments @xcite . in order to come to a valuable comparison between the experiments and the theoretical predictions , one has to calculate the force with a precision comparable to the experimental accuracy . this is a real challenge to the theory because the force is material , surface , geometry and temperature dependent . here we will only focus on the material dependence , which is easy to treat on a level of some percent precision but which will turn out difficult to tackle on a high level of precision since different uncontrolled factors are involved . in its original form , the casimir force per unit surface @xcite @xmath1 was calculated between ideal metals . it depends only on the fundamental constants and the distance between the plates @xmath2 . the force between real materials differs significantly from ( [ fc ] ) for mirror separations smaller than 1 @xmath3 m . for mirrors of arbitrary material , which can be described by reflection coefficients , the force per unit area can be written as @xcite : @xmath4 ^ 2 e^{-2\kappa l}}{1-r_{\mu } \left [ i\zeta , \mathbf{k } \right]^2 e^{-2\kappa l}}\nonumber \\ & & \kappa=\sqrt{\mathbf{k}^{2}+ \frac{\zeta ^{2}}{c^2 } } \label{force}\end{aligned}\ ] ] where @xmath5 denotes the reflection amplitude for a given polarization @xmath6 @xmath7 the force between dielectric materials had first been derived by lifshitz @xcite . the material properties enter these formulas via the dielectric function @xmath8 at angular imaginary frequencies @xmath9 , which is related to the physical quantity @xmath10 with the help of the dispersion relation @xmath11 for metals @xmath12 is large at low frequencies , thus the main contribution to the integral in eq . ( [ k - k ] ) comes from the low frequencies even if @xmath13 corresponds to the visible frequency range . for this reason the low - frequency behavior of @xmath14 is of primary importance . the casimir force is often calculated using the optical data taken from @xcite , which provides real and imaginary parts of the dielectric function within some frequency range , typically between 0.1 and @xmath15 ev for the most commonly used metals , au , cu and al , corresponding to a frequency interval @xmath16 $ ] rad / s ( 1 ev=@xmath17 rad / s rad / s was used , leading however to a negligible difference in the casimir force ( well below 1% ) . ] ) . when the two plates are separated by a distance @xmath2 , one may introduce a characteristic imaginary frequency @xmath18 of electromagnetic field fluctuations in the gap . fluctuations of frequency @xmath19 give the dominant contribution to the casimir force . for example , for a plate separation of @xmath20 nm the characteristic imaginary frequency is @xmath21 ev . comparison with the frequency interval where optical data is available shows that the high frequency data exceeds the characteristic frequency by 3 orders of magnitude , which is sufficient for the calculation of the casimir force . however , in the low frequency domain , optical data exists only down to frequencies which are one order of magnitude below the characteristic frequency , which is not sufficient to evaluate the casimir force . therefore for frequencies lower than the lowest tabulated frequency , @xmath22 , the data has to be extrapolated . this is typically done by a drude dielectric function @xmath23 which is determined by two parameters , the plasma frequency @xmath24 and the relaxation frequency @xmath25 . different procedures to get the drude parameters have been discussed in the literature . they may be estimated , for example , from information in solid state physics or extracted form the optical data at the lowest accessible frequencies . the exact values of the drude parameters are very important for the precise evaluation of the force . lambrecht and reynaud @xcite fixed the plasma frequency using the relation @xmath26 where @xmath27 is the number of conduction electrons per unit volume , @xmath28 is the charge and @xmath29 is the effective mass of electron . the plasma frequency was evaluated using the bulk density of au , assuming that each atom gives one conduction electron and that the effective mass coincides with the mass of the free electron . the optical data at the lowest frequencies were then used to estimate @xmath30 with the help of eq . ( [ drude ] ) . in this way the plasma frequency @xmath31 ev and the relaxation frequency @xmath32 ev have been found . this procedure was largely adopted in the following @xcite . however , on the example of cu , it was stressed in @xcite that the optical data may vary from one reference to another and a different choice of parameters for the extrapolation procedure to low frequencies can influence the casimir force significantly . bostrm and sernelius @xcite and svetovoy and lokhanin @xcite extracted the low - frequency optical data by fitting them with eq . ( [ drude ] ) . for one set of data from ref . @xcite the result @xcite was close to that found by the first approach , but using different sources for the optical data collected in ref . @xcite an appreciable difference was found @xcite . this difference was attributed to the defects in the metallic films which appear as the result of the deposition process . it was indicated that the density of the deposited films is typically smaller and the resistivity larger than the corresponding values for the bulk material . the dependence of optical properties of au films on the details of the deposition process , annealing , voids in the films , and grain size was already discussed in the literature @xcite . in this paper we analyze the optical data for au from several available sources , where the mid - infrared frequency range was investigated . the purpose is to establish the variation range of the drude parameters and calculate the uncertainty of the casimir force due to the variation of existing optical data . this uncertainty is of great importance in view of the recent precise casimir force measurement @xcite which have been performed with high experimental accuracy . on the other hand , sophisticated theoretical calculations predict the casimir force at the level of 1% or better . these results illustrate the considerable progress achieved in the field in only one decade . in order to assure a comparison between theory and experiment at the same level of precision , one has to make sure that the theoretical calculation considers precisely the same system investigated in the experiment . this is the key point we want to address in our paper . with our current investigation we find an intrinsic force uncertainty of the order of 5% coming from the fact that the drude parameters are not precisely known . these parameters may vary from one sample to another , depending on many details of the preparation conditions . in order to assure a comparison at the level of 1% or better between theoretical predictions and experimental results for the casimir force , the optical properties of the mirrors have to be measured in the experiment . the paper is organized as follows . in sec . [ sec2 ] we explain and discuss the importance of the precise values of the drude parameters . in sec . [ sec3 ] the existing optical data for gold are reviewed and analyzed . the drude parameters are extracted from the data by fitting both real and imaginary parts of the dielectric function at low frequencies in sec . [ sec4 ] . in section [ sec5 ] the drude parameters are estimated by a different method using kramers - kroning analysis . the uncertainty in the casimir force due to the sample dependence is evaluated in sec . [ sec6 ] and we present our conclusions in sec . in figure [ fig1 ] ( left ) we present a typical plot of the imaginary part of the dielectric function , which comprises palik s handbook data for gold @xcite . the solid line shows the actual data taken from two original sources : the points to the right of the arrow are those by thye @xcite and to the left by dold and mecke @xcite . no data is available for frequencies smaller than the cutoff frequency @xmath33 ( @xmath34 ev for this data set ) and @xmath35 has to be extrapolated into the region @xmath36 . the dotted line shows the drude extrapolation with the parameters @xmath31 ev and @xmath32 ev obtained in ref . @xcite . one can separate three frequency regions in fig . [ fig1 ] ( left panel ) . the region marked as 1 corresponds to the frequencies smaller than @xmath33 . the region 2 defining the drude parameters extends from the cutoff frequency to the edge of the interband absorption @xmath37 . the high energy domain @xmath38 is denoted by 3 . we may now deduce the dielectric function at imaginary frequencies ( [ k - k ] ) using the kramers - kronig relation @xmath39 where the indices 1 , 2 , and 3 indicate respectively the integration ranges @xmath40 , @xmath41 , and @xmath42 . @xmath43 can be derived using the drude model ( [ drude ] ) leading to @xmath44 . \label{eps1}\ ] ] the two other functions @xmath45 and @xmath46 have to be calculated numerically . the results for all three functions as well as for @xmath47 are shown in fig . [ fig1 ] ( right ) . one can clearly see that @xmath48 dominates the dielectric function at imaginary frequencies up to @xmath49 ev . @xmath50 gives a perceptible contribution to @xmath51 , while @xmath52 produces minor contribution negligible for @xmath53 ev . as mentioned in the introduction , we may introduce a characteristic imaginary frequency @xmath18 of field fluctuations which give the dominant contribution to the casimir force between two plates at a distance @xmath2 . for a plate separation of @xmath20 nm the characteristic imaginary frequency is @xmath54 ev . at this frequency the contributions of different frequency domains to @xmath55 are @xmath56 , @xmath57 , and @xmath58 . this means that for all experimentally investigated situations , @xmath59 nm , region 1 , corresponding to the extrapolated optical data , gives the main contribution to @xmath51 . it is therefore important to know precisely the drude parameters . the optical properties of gold were extensively investigated in 50 - 70th . in many of those works the importance of sample preparation methods was recognized and carefully discussed . a complete bibliography of the publications up to 1981 can be found in ref . regrettably the contemporary studies of gold nanoclusters produce data inappropriate for our purposes . among recent experiments let us mention the measurement of normal reflectance for evaporated gold films @xcite , which was performed in the wide wavelength range @xmath60 @xmath3 m , but unfortunately does not permit to evaluate independently both real and imaginary parts of the dielectric function . in contrast , the use of new ellipsometric techniques @xcite has" +"blue straggler stars ( bsss ) were first identified in the galactic globular cluster ( ggc ) m3 by @xcite , as a group of stars bluer and brighter than the cluster turn - off stars , thus being more massive than the stars currently evolving at the turn - off ( to ) . since then , bsss have been identified in a variety of stellar systems in very different environmental conditions including : the field @xcite , open clusters @xcite , globular clusters ( e.g. , * ? ? ? * ) , and dwarf galaxies @xcite . their puzzling position in the color - magnitude diagram ( cmd ) suggested that they do not fit in the traditional scheme of stellar evolution for single stars . in fact , in order to populate that region of the cmd , these exotic objects must have experienced a physical process able to allow them to still stay in the core h - burning stage despite of their mass and the cluster age ( for a detailed historical review , see * ? ? ? * ) . presently , two different physical mechanisms are favored for explaining the formation of bsss : _ i ) _ coalescence through direct stellar collisions ( col - bs , * ? ? ? * ) , and _ ii ) _ evolution of primordial binary systems , in which mass transfer between the two components allows the rejuvenation of the secondary component ( mt - bss , * ? ? ? it is also widely accepted that these two scenarios are not in competition , but they could both occur simultaneously in a stellar system . in fact , the coexistence of bsss formed through both the collisional and mass transfer channels is commonly invoked to interpret the radial distribution of bsss in many ggcs . the higher central concentration is explained by an efficient rate of stellar collisions in the densest regions , while the rise at large distance would be due to mt - bsss @xcite surviving in the outskirts . while the scenario for bsss in galactic clusters is well settled , at least from the observational point of view , in contrast , this is not true for dwarf galaxies . in fact , even though the first indication for the presence of bss candidates in the sextans dwarf dates back to @xcite , and , since then , several observational findings suggest the presence of bss candidates in several dsphs ( see , e.g. , * ? ? ? * and references therein ) , we are still faced with the problem of understanding if these candidates are _ genuine _ bsss or _ normal _ core h - burning stars belonging to an , albeit sparse , intermediate - age stellar population . recently , a few studies have focused on the properties of bsss in nearby dsph galaxies in the local group ( lg ) . @xcite presented wide field data for the galaxies draco and ursa minor , concluding that the population of bsss is , in both systems , compatible with the mt - bss scenario . @xcite discussed the properties of bsss in sculptor and fornax . sculptor presents similarities with both draco and ursa minor , as its bss population is also compatible with a mt - bss population . on the contrary , the relatively strong central radial concentration of the bss candidate stars in fornax favors the presence of an intermediate - age stellar population ( in agreement with previous studies of the star formation history ( sfh ) of fornax ) . unraveling the nature of the bss candidates has important implications for our understanding of the sfhs of these galaxies . for example , whenever it is possible to discriminate between a sequence of bsss and a young ms population , it is possible to set a constraint on the age of the last star formation event in a galaxy . therefore , the bss populations in draco , ursa minor , and sculptor suggest that no star formation occurred in the last few gyr in these galaxies . intriguingly , @xcite found a statistically significant anti - correlation between the frequency of bsss and the absolute visual magnitude ( m@xmath0 ) of 8 nearby dsphs . the anti - correlation is valid over a large range of luminosities , and presents a different slope than that of ggcs . in addition , @xcite ruled out the possibility that collisional binaries could have contributed to the observed bss populations and concluded that the bsss in dwarf spheroidal galaxies are mainly formed via mass exchange in primordial binaries . in view of the important implications of the presence of a sizable sample of bsss in a dwarf galaxy , it is worthwhile to apply the approach outlined by @xcite to other dwarfs . the hope is to eventually produce independent constraints useful for addressing the true nature of the bss candidates . l|cc @xmath1 & @xmath2 & @xmath3 + @xmath4 & @xmath5 & @xmath6 + n@xmath7 & @xmath8 & @xmath9 + n@xmath10 & @xmath11 & @xmath12 + f@xmath13 & @xmath14 & @xmath15 + n@xmath16 & @xmath17 & @xmath18 + in this paper , we investigate these issues further by analyzing the properties of candidate bsss in the isolated dsphs cetus and tucana . the data sets are part of the lcid project ( _ local cosmology from isolated dwarfs _ ) , aimed at recovering the full sfhs of six isolated lg galaxies : cetus and tucana ( dsph ) , lgs 3 and phoenix ( dirr / dsph ) , ic 1613 and leo a ( dirr ) . the plan of the paper is as follows : in the next section we briefly describe the photometric data set and outline the criteria for selecting the candidate bsss in the observed cmds . in 3 we investigate the properties of the bss populations . 4 presents the results of dynamical simulations . the discussion and final remarks close the paper . the observations used in this paper have already been presented in ( * ? ? ? * cetus ) and ( * ? ? ? * tucana ) . here we summarize the main points relevant to the following discussion . the images were collected with the acs camera aboard the hst , under the project _ the onset of star formation in the universe : constraints from nearby isolated dwarf galaxies _ ( pid 10505 , pi c. gallart ) . a total of 25 and 32 orbits have been devoted to cetus and tucana , respectively , using the @xmath19 and @xmath20 filter pass bands . the photometric reduction has been performed using the daophot / allframe package @xcite . the final catalog has been calibrated to the vegamag system using the transformations presented in @xcite . the adopted distance modulus and reddening are summarized in table [ tab : tab01 ] , together with other quantities calculated in this work . figure [ fig : samples ] shows the cmds of the two galaxies , with the regions adopted to select the various samples studied superimposed . note that we adopted the same boxes for both galaxies , applying a shift to take into account the differences in distance modulus and reddening . the cmds of both galaxies are @xmath21 mag deeper than the to , reaching @xmath22 mag . the blue plume of candidate bsss emerges clearly in the cmd , for @xmath23 mag , @xmath24 . we defined a box in this region to include the bulk of these stars . note that there are a number of objects between the bsss region and the red giant branch ( rgb ) . we decided not to include these stars for two reasons : _ i ) _ it is possible that blended objects from the most populated to region are polluting this part of the cmd ; _ ii ) _ in this color range , we expect to find stars evolved off the main sequence . also , we did not include the brightest objects ( @xmath25 ) because it is possible that they are extreme horizontal branch ( hb ) stars . also note that we estimated a negligible contamination from both foreground galactic stars ( due both to the small area covered and the high galactic latitude of the two galaxies ) and background galaxies ( thanks to the careful cleaning of the catalogs , see @xcite ) . figure [ fig : samples ] also shows the regions adopted to select stars in the hb , the rgb , and the progeny of bsss during the central helium burning phase . this last box has been placed above the red hb , paying attention not to include the agb clump , which clearly appears in the cmds of both galaxies ( @xmath26 mag ) . 0.8 cm in the box covering the blue plume , we have identified 940 and 1214 objects in cetus and tucana , respectively , which we consider as bss candidates . note that the present data cover a significant fraction of the body of tucana ( tidal radius @xmath27 ) , which was centered in the acs field ( field - of - view @xmath28 ) . however , cetus occupies a larger area in the sky ( @xmath29 , @xcite ) , and the sampled field covers a smaller fraction . moreover , the observed field was offset from the center so that the innermost regions of cetus were not observed @xcite . if we take this into account , following the reasoning of @xcite to estimate the total number of rr lyrae stars , the total number of bss candidates in cetus is estimated to be @xmath30 5,000 stars . the most important question is to assess the nature of these stars . bsss have been found in very different environments , from the field , to low - density stellar systems such as open clusters and dwarf spheroidals , and in most globular clusters . they are therefore common products , and it is reasonable to expect to find them in tucana and cetus as well . therefore , the basic question we are trying to address is : are these candidates genuine bsss , or is there also a significant component of truly young stars ? in the following sections we will try to address this using different observables . 0.4 cm , but we present a zoom of the cmd of cetus ( left panel ) and tucana ( right panel ) , corresponding to the core he - burning stage . in each panel the box represents the region used to select the candidate progeny of the blue plume stars . four tracks are overplotted , for different mass and metallicity assumptions . the filled stars mark the location of the anomalous cepheid variables detected in these galaxies @xcite . , title=""fig:"",width=321 ] the main objective of the lcid project was to derive accurate sfhs for a sample of six isolated galaxies in the local group , in order to understand their evolution in a cosmological context . to do this , we adopted well - established techniques based on the comparison of the observed cmd with a synthetic one . we devoted significant effort to investigating the error budget and also possible systematics affecting our solution , due to the use of different photometric packages , stellar evolutions libraries , sfh codes . the main conclusion ( see * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) of this analysis was that we can rely , within the error bars , on both the uniqueness and stability of the derived solutions . therefore , the most" +"the luminosity function ( lf ) is a very important statistical characteristic of galaxy populations . the lfs provide information about galaxies and their evolution on the cosmological timescale . in this paper we consider the lf of the galaxies with an active star formation in the wave range or emission line in which the lion share of radiation provides by a young stellar population . more exactly we consider the radiation of galaxies shortly after a starburst . these galaxies underwent strong bursts of star formation on a time scale of a few myr . massive young stellar populations , which were formed during the burst , emit plenty of ionising and non - ionising uv radiation . later on , the h@xmath0 and uv luminosities strongly decrease with time after a starburst age @xmath1 myr , when the most massive stars start to fade out . naturally , this is resulted in the changes of the observed lf . this fact affects the lf in the wavelength ranges and emission lines which are good indicators of a star formation , while the lf in the optical range keeps its form . this effect is mostly pronounced for the h@xmath0 , far ultraviolet ( fuv ) , near ultraviolet ( nuv ) and far infrared ( fir ) luminosities . we allow that taking into account the short - term luminosity evolution we can derive a more adequate form of the lf of a sample of star - forming galaxies . the impact of the fading of galaxy luminosities on lf can be quite significant . we describe it for the arbitrary initial luminosity distribution and arbitrary luminosity evolution . to study the impact of the factor under consideration we introduced the initial , the current , the time - averaged , and the sample lfs . in section [ s : lf ] we derive relations between all these lfs in general case of an arbitrary luminosity evolution . as a rule we consider galaxies with a single knot of star formation , but this lf can be applied to galaxies with several knots of star formation , too . in section [ s : lf1 ] we specify these relations for the luminosity evolution of luminous compact galaxies ( lcg ) discussed by @xcite . in the sections [ s : aq ] and [ s : ln ] we use the popular forms of lfs , namely the schechter function and the log - normal one as the initial lfs and derive and analyze the corresponding lfs . our findings are summarised in section [ s : sum ] . the luminosity of the galaxy @xmath2 is maximal one just after a starburst and then decreases due to burning out of short - living massive stellar population : @xmath3 where @xmath4 is time after the starburst and @xmath5 is the luminosity at @xmath6 . the function @xmath7 for the sample of 795 lcgs was derived by @xcite . this sample includes a very extreme population of compact galaxies with very high equivalent widths , representing the high - end tail of the lf of the overall star - forming population . all galaxies in it underwent a burst of star formation less that 6 myr ago . so the radiation caused by the burst - like star formation prevails ( see discussion in * ? ? ? @xcite found that the luminosities in the h@xmath0 emission line , fuv and nuv continuum are described by the relation @xmath8 with @xmath9 myr and different values of the parameter @xmath10 ( see details in * ? ? ? * ) . the same function is valid for the luminosities in the 22 @xmath11 m ir band , calculated using _ wide - field infrared survey explorer _ ( wise ) data and probably for the radio emission at 1.4 ghz @xcite . for generality we start with studying the case of arbitrary @xmath7 . we will specify the relation ( [ e9 ] ) later . we try to determine the effect of the short - term luminosity evolution on the observed lf of some sample of galaxies @xmath12 . in order to do this we need some additional types of lfs . we introduce and consider the initial @xmath13 , the current @xmath14 , the time - averaged @xmath15 , and the sample @xmath12 lfs . we assume that star formation in galaxies from a sample occurs in short bursts separated by large periods without star formation , which are much greater than the lifetimes of stars producing a main part of ionizing uv radiation . then , h@xmath0 , fuv and nuv luminosities greatly decrease before the next consecutive starburst . we also assume for simplicity that all galaxies have only single star - forming region . the initial luminosity distribution @xmath13 describes the distribution of the galaxy luminosities @xmath5 immediately after the termination of the star formation burst . we consider all @xmath5 values for galaxies entering a unit volume and describe their distribution by the function @xmath13 . here @xmath16 is the number of starbursts per unit volume with the initial luminosity in the interval from @xmath5 to @xmath17 . the function @xmath13 would coincide with the luminosity function @xmath15 if there were no temporal luminosity variations . this is a typical situation for the visible wavelength range , in which the radiation from long - lived old stellar populations is dominated . the similar situation occurs in the case of large galaxies with the continuous star formation , when the individual bursts of star formation hardly affect the total luminosity . on the other hand , the h@xmath0 , fuv and nuv luminosities in the lcgs are produced by the radiation of the young stellar population @xcite . therefore they vary on short time scales after the bursts of star formation . after the time interval @xmath4 after the starburst the initial lf @xmath13 turns into the time - dependent current lf @xmath14 because of decrease of galaxy luminosities . roughly speaking , the current lf is what the initial one becomes after time @xmath4 . the lf @xmath18 is the number of galaxies per unit volume in the luminosity interval from @xmath19 to @xmath20 at time @xmath4 after a starburst . the galaxies from the sample are observed at different phases of luminosity evolution , i.e. with different time after the starburst @xmath4 . @xcite have shown that the galaxies from the sample with @xmath21 myr are approximately uniformly distributed over starburst ages @xmath4 . in this case an averaging over the sample corresponds to a time - averaging and therefore the time - averaged current lf @xmath14 coincides with the lf @xmath15 , which we will call the time - averaged lf . here @xmath22 is the number of galaxies per unit volume in the luminosity interval from @xmath19 to @xmath20 . consider the case of monotonous luminosity decrease according to ( [ e1 ] ) with @xmath23 . using the relationship ( [ e1 ] ) we find @xmath24 this current lf should be averaged over the time to find the function @xmath15 : @xmath25 we apply the lf averaging over a time period @xmath26 , which is much larger than the typical starburst age of the lcgs . instead of the time integration we apply an integration over @xmath5 . in the case of constant @xmath19 we obtain the relation @xmath27 from eq . ( [ e1 ] ) , where @xmath28 is the time derivative . thus , @xmath29 where @xmath30 is a time interval during which galaxies with initial luminosities from @xmath5 to @xmath17 have the current luminosity @xmath19 . then @xmath31 here @xmath32 is the maximum initial luminosity of galaxies in the sample . it can be assigned as @xmath33 because @xmath34 is a rapidly decreasing function at large @xmath5 . if a function @xmath7 is constant at @xmath4 @xmath35 @xmath36 and decreases monotonously after @xmath36 , eq . ( [ e5 ] ) is transformed to @xmath37 the number of galaxies from the sample with the luminosity in the interval from @xmath19 to @xmath20 is @xmath38 . here @xmath39 is the number of galaxies entering the sample and @xmath12 is a normalized lf of the sample . to obtain the function @xmath12 we multiply the function @xmath15 by the volume @xmath40 occupied by the sample galaxies with the luminosity @xmath19 the flux - limited sample includes galaxies up to the photometric distance @xmath41 , where @xmath42 is the minimal flux , if extinction is not present . considering flat space and neglecting the differences between the photometric distance and other types of distances in cosmology , we obtain that the volume @xmath40 is proportional to @xmath43 and correspondingly to @xmath44 . thus , we assume @xmath45 for flux - limited samples with small redshifts @xmath46 . for the samples with @xmath47 one ought to use the exact expression for @xmath40 from the relativistic cosmology , e.g. from the @xmath48cdm model . nevertheless , the simplified version with @xmath45 has some advantage . its simple form allows to obtain some useful relations like ( [ eq2 ] ) . for the flux - limited samples with small @xmath46 we obtain the sample lf @xmath49 where the constant is derived from the normalisation condition @xmath50 substituting @xmath7 from eq . ( [ e9 ] ) into eq . ( [ e7 ] ) we obtain @xmath51 where @xmath52 and @xmath53 the parameter @xmath54 has a simple astronomical meaning . h@xmath0 and uv luminosities of a galaxy are constant during the period @xmath36 , which is approximately equal to the lifetime of o stars . after that time luminosities decrease by a factor of @xmath55 during every next time period @xmath36 . there are two marginal cases of eq . ( [ e10 ] ) . the luminosity function is reduced to the standard one ( @xmath56 ) if @xmath57 ( constant luminosities ) or @xmath58 ( step , @xmath59 , where @xmath60 is the heaviside step function ) . the first term in brackets in eq . ( [ e10 ] ) vanishes ( @xmath61 ) if @xmath62 ( monotonous decrease without a plateau ) or @xmath63 ( very slow decrease ) . for the h@xmath0 luminosity function @xmath64 myr@xmath65 @xcite and @xmath66 . for the fuv and the nuv luminosity functions the values of @xmath10 are smaller and the values of @xmath54 are larger therefore , the initial and time - averaged h@xmath0 , fuv and nuv luminosity functions for star - forming galaxies are expected to be different . let us denote lfs for these cases as @xmath67 and @xmath68 . the function @xmath69 is the lf of the sample without the luminosity evolution , i.e. in the case of constant galaxy luminosities . taking into account the luminosity evolution we obtain ( [ e10 ] ) , which can be rewritten in the form @xmath70 there is no point in considering the case @xmath71 as a real lf , but we can do this formally to analyze the properties of sample lf at @xmath72 . let us denote the mean value of some quantity @xmath73 over the sample as @xmath74 the relation @xmath75 is valid for @xmath76 if these integrals are convergent , in particular at @xmath77 . as a result we have the equation @xmath78 connecting the sample averages of @xmath79 for lf @xmath80 taken into account affect of short - term luminosity evolution ( [ e9 ] ) and lf @xmath81 for the sample with invariable luminosities . ( [ eq3 ] ) at @xmath82 connects the sample average luminosities . at @xmath83 it helps in calculation variance , skewness , kurtosis , etc . let us try two popular functions often used as a functional form of lf as a function @xmath69 in ( [ eq1 ] ) . the first" +"the role of inelastic scattering in electron transport through mesoscopic systems is a topic of current theoretical and experimental interest . recent experiments have revealed the importance of the electron - phonon interaction in transport measurements performed on certain mesoscopic systems . in particular inelastic scattering effects have been observed directly in stm measurements of the differential conductance of molecules adsorbed on metallic substrates.@xcite theoretically the effects of inelastic scattering on electron transport through mesoscopic semiconductor devices have been investigated by a variety of methods ranging from green s function techniques@xcite to the fermi golden rule.@xcite some theoretical models have also been proposed to elucidate the effects of molecular vibrations on electron tunneling through molecules contacted by an stm.@xcite recent work has provided a method for calculating the electronic current at finite temperatures for electrons tunneling through a one - dimensional conductor in the presence of phonons.@xcite these approaches have yielded valuable insights into the behavior of specific systems . in the absence of inelastic scattering and electron correlations , landauer theory@xcite provides a general framework for calculations of the electronic current through mesoscopic conductors that are coupled to ideal single- or multi - channel quasi - one - dimensional leads . it relates the electronic current to the transmission probability for an electron incident from the source lead to scatter elastically through the conductor and into the drain . the transmission probability is found by solving the single - electron quantum scattering problem . when inelastic processes such as phonon emission and absorption are considered , electron scattering becomes a many - body phenomenon involving electrons and the various excited phonon states of the system . a non - perturbative approach has been proposed by bon@xmath0a and trugman for treating this scattering problem for a system consisting of a mesoscopic conductor ( which supports the phonon modes ) coupled to two single - channel ideal leads that act as the electron source and drain.@xcite their method approximates the many - body problem by a multi - channel single - electron scattering problem which can be solved exactly . here each channel corresponds to a different vibrational quantum state of the mesoscopic conductor . using their approach it is possible to determine the transmission and reflection probabilities for all inelastic and elastic scattering events that an electron may suffer in the conductor as it goes from the source to the drain . this method has been applied to study the effects of phonons on electron transmission through one - dimensional conductors where the electron - phonon coupling has been modelled using the holstein hamiltonian@xcite and the su - schrieffer - heeger ( ssh ) hamiltonian@xcite . the present article is complementary to the above theoretical work . its purpose is to generalize the landauer theory of electrical conduction to mesoscopic systems with electron - phonon scattering , assuming that the latter is described accurately within the multi - channel single - electron scattering approach of bon@xmath0a and trugman@xcite . i.e. , given the bon@xmath0a - trugman@xcite solution of the inelastic scattering problem , our objective is to calculate the electric current by appropriately generalizing landauer theory . when transport in a many - electron system is described in terms of one - electron scattering processes , the pauli exclusion principle needs to be considered since in general electrons involved in different transitions may compete to occupy the same final state . in treatments of transport based on the boltzmann equation , if the electron scattering is elastic , this competition has no effect because of a mutual cancellation of terms.@xcite however such a cancellation does not occur when scattering is inelastic.@xcite in landauer theory scattering is assumed to be elastic and the electronic current is carried by electrons which occupy single - particle scattering states that extend across the mesoscopic conductor from the source to the drain . these scattering states are orthogonal to each other.@xcite because of this orthogonality , if an electron populates one of these scattering states it does not compete with any of the other filled scattering states . thus in landauer theory ( as in the elastic case of the boltzmann equation ) the pauli exclusion principle for the final states in the scattering processes does not play a role in the determination of the electronic current . in our generalization of landauer theory that includes inelastic scattering , this is no longer true : different scattering processes can send electrons to the same outgoing state and the pauli principle plays an important role in determining the occupations of the outgoing channels . in the boltzman treatment of inelastic scattering the pauli principle is applied to the non - equilibrium one - electron distribution function for the system since transport is an inherently non - equilibrium phenomenon . here we apply an analogous principle : in our extension of landauer theory the pauli exclusion principle is applied to the non - equilibrium electron distributions in the _ outgoing _ channels of the scattering process and these distributions must be determined self - consistently . since some processes may be excluded because of the pauli principle , overall particle conservation is another consideration that must be taken into account when trying to generalize landauer theory to include inelastic scattering . we have developed a practical method for determining these non - equilibrium electron distributions for a class of mesoscopic systems . these systems are similar to those considered by bon@xmath0a and trugman@xcite in that they consists of a mesoscopic conductor which is attached to two single mode ideal leads which act as a source and drain , and phonons are assumed to be present only on the conductor and not on the ideal leads . we consider scattering processes which change the conductor s phonon state or leave it unchanged . each of these processes contributes to the non - equilibrium electron distribution . we determine each contribution self - consistently ( i.e. , in the presence of the other processes that can occur ) in terms of the transmission and reflection probabilities for the given process and the fermi functions that describe the incoming electron distributions in the left and right leads . included in this self - consistent method is the constraint of particle conservation . we do not however include cumulative effects of the current on the phonon distribution in the conductor ; i.e. , we assume that the conductor is in contact with a heat bath . with the non - equilibrium electron distribution determined we then evaluate the current flowing through this system for finite temperatures and bias voltages . as an application of the above theoretical approach we calculate the electronic current as a function of voltage for a two site molecule . the molecule has two single - particle molecular energy levels through which electrons from the leads can resonantly tunnel . it also has two longitudinal phonon modes which can be excited . a ssh hamiltonian is used to represent the electron - phonon coupling . for our model system one of the phonon modes is chosen to have an energy equal to the gap between the two electronic energy levels . because of this , electrons which are resonant with the higher energy level can emit a phonon and be resonant with the lower level . such a process is found to be highly transmitting . when the voltage is high enough that there is a sufficient number of electrons in the left lead that can undergo this process , we find that the current in the right lead due to elastically scattered electrons is reduced significantly due to competition with these inelastically scattered electrons . thus we find that the mutual exclusion between the scattered electrons that make up the non - equilibrium distribution in the drain lead can have important consequences for the electronic current flowing through the molecule . in sec . ii we describe the class of systems that we study and explain how the scattering states are calculated . in sec . iii we present our generalization of the landauer theory and our method for calculating the non - equilibrium the electron distribution and associated electronic currents . we then apply our methodology to a simple model for a two site molecular chain and calculate its current - voltage characteristics in sec . our conclusions are summarized in sec . in the absence of inelastic scattering and electron correlations , electron transport through a mesoscopic conductor can be described in terms of the probability @xmath1 that a single electron with energy @xmath2 scatters through the conductor from the source to the drain at an applied bias voltage @xmath3.@xcite when phonons ( or vibrational modes ) of the conductor are considered , an electron entering from the source can suffer inelastic collisions by absorbing or creating phonons before entering the drain . each of these processes can be described by its own transmission probability . if we assume that the source and drain are single mode leads which are free from phonons , we can characterize the above single electron scattering process by a transmission probability @xmath4 . this describes an electron that enters from the left lead @xmath5 with energy @xmath2 , suffers inelastic collisions on the conductor which change the phonon population on the conductor from @xmath6 to @xmath7 , and then scatters into the right lead @xmath8 with energy @xmath9 . similarly , an electron incident from the left lead can suffer a collision and be reflected back into the left lead . this is characterized by a reflection probability @xmath10 . elastic scattering processes are included with @xmath7 being equal to @xmath6 . for all processes the total energy is conserved , so @xmath9 plus the net energy of all of the created and destroyed phonons is equal to @xmath2 . we now describe a method for calculating these transmission and reflection probabilities for a mesoscopic structure . a schematic of our model for the mesoscopic conductor , which consists of a source ( left ) and a drain ( right ) lead attached to a one - dimensional conductor / wire is depicted in fig . we assume that the leads are ideal and that they only have one electronic channel . phonons are considered to be only on the conductor and not on the ideal leads . an electron flows through the wire under an applied bias @xmath3 . we assume that the voltage drop only occurs at the interface between the wire and the leads with the left lead held at @xmath11 and the right lead held at @xmath12 . we solve the transport problem by solving schrdinger s equation for the many - body wavefunction of the electron - phonon system from which we extract the transmission and reflection coefficients mentioned above . these will be used in the calculation of the non - equilibrium electron distributions and the current which follows in the next section . the hamiltonian @xmath13 of this system can be split up into the hamiltonians for the isolated systems consisting of the left lead @xmath14 , the right lead @xmath15 , and the conductor @xmath16 . it also includes the coupling between the wire and the left and right leads , @xmath17 and @xmath18 respectively . thus we write , @xmath19 we treat each of the above hamiltonians in the tight binding approximation . we model the wire using a set of orthogonal atomic orbitals @xmath20 . each atomic state has an energy @xmath21 with a corresponding creation operator @xmath22 which creates an electron in that state . in our hamiltonian for the wire an electron can hop from orbital @xmath23 to all nearest neighbor orbitals @xmath24 , and this is governed by the hopping parameter @xmath25 for the equilibrium configuration of atoms . the wire also has a discrete set of vibrational modes , each characterized by a frequency" +"with the increasing demand of the astronomical community for statistical work , all the major observatories equipped their telescopes with spectrographs having multiple object capabilities . we can distinguish between small field instruments , less than 10 arcmin , and large field ones , more than one degree instruments , on which we will focus here . the large field ones use essentially fibre fed spectrographs . this is true for small telescopes ( like the uk schmidt ) as well as for the 4 m class ones . the first generation instruments used focal plates with manually inserted optical fibres in plugboards with drilled holes made at the object coordinates . this system is still foreseen for dedicated instruments , as the sloan dss project(limmongkol _ et al . _ 1992 ) , but for general use facilities , automatic fibre handling machines are preferred . two main devices are in operation , robot and arm positioners . the robot positioner plugs the different fibres in sequence whereas the arm positioner moves all the fibres simultaneously . the robot is able to take care of a large number of fibres , but the configuration time is long and the positioning is done in a blind manner although the robot is equipped with a vision system . this does not guarantee the dropping process . arms are fast , but more than 30 are hardly feasible . moreover , they are expensive , except if built in - house . when eso decided to replace its optopus ( lund , 1986 ) starplate system with an automatic one , we opted for the arm approach . in that we were following j. hill and his mx ( hill _ et al . _ 1986 ) and t. ingerson and his argus ( ingerson , 1988 ) , our neighbour instrument at ctio . mx uses 32 arms and argus 24 arms . our fibre positioner mefos , the meudon eso fibre optical system ( gurin _ et al . _ 1993 ) , was built by the observatoire de paris , france , under eso contract . mefos is mounted at the prime focus , providing a large field ( 1 degree ) for the multifibre spectroscopy . the 3.6 m eso telescope has a prime focus triplet corrector delivering a field of one degree , the biggest for a 4 m class telescope until the 2df project will be in full operation at the aat . the focal ratio is f/3.14 , well suited for fibre light input , leading to negligible focal ratio degradation ( gurin _ et al . mefos ( gurin _ et al . _ 1993 ) is put on the red triplet corrector with a trait - point - plan interface , allowing tilt correction , with respect to the optical axis . the telescope z movement of the prime focus is used for focusing . it has 30 arms that can point within the 20 cm , one - degree field . one arm is used for guiding , while the other 29 arms are dedicated to the astronomical objects . figure 1 shows the general arms display . they are distributed around the field as `` fishermen - around - the - pond '' . the arms move radially and in rotation : each arm can cover a 15 degree triangle with its summit at the arm rotation axis and its base in the centre of the field . hence , each arm can access objects at the centre of the field , whereas only one specific arm can reach an object at the field periphery . this situation changes gradually from the centre to the edge of the field . each arm has its individual electronic slave board . the whole instrument is controlled by a pc , independent of the telescope control system ( tcs ) . the arm tips shown on figure 2 are carrying two fibres separated by 1 arcmin . one is used for the object , the other for the sky recording . both are fed to the spectrograph . the object and sky fibre , each 2.5 arcsec in diameter , can be exchanged and the fibre transmission cancelled . + + coupled firmly to the arm tip is an imaging fibre bundle that covers a 35 x 35 arcsec@xmath0 area of the sky . the image bundles are projected on a single thomson 1024 x 1024 thick peltier cooled ccd , and are connected to the pc driving the arms . the image bundle of the arms are moved to the object coordinates and an image of the selected objects can be obtained . figure 3 shows the display of the galaxy field as seen through the 29 windows of the ccd . + + with this procedure , the objects on which the spectral fibre will be positioned can be seen in advance - contrarily to blind positioning . it is to our knowledge the only such instrument . by analysing the position of the object on the image , in combination with the fixed displacement between the image bundle fibre and the spectral fibre within an arm , a precise offset is determined and the arm sent to the optimal object position . this offset takes care of all imprecision due to the telescope , the instrument and inaccurate coordinates . the poor pointing of the telescope , and the fact that the corrector and the instrument are frequently dismounted , would make blind positioning extremely dangerous . the final positioning accuracy , as measured on stellar sources , is 0.2 arcsec rms . to avoid any motion between the telescope and the instrument , the guiding is done in the arm environment . a special arm is dedicated for this task . this arm holds a large image conducting optical fibre with a field of view of 1.8 x 2.5 arcmin . to enlarge the field within which a guide star can be selected , this window can be positioned in 3 different ( adjacent ) positions . the guiding camera is sensitive to v@xmath1 . because of this faint magnitude limit , no guide star has to be defined prior to the observations . the guiding fibre can then remain in the outer position at the edge of the field , leaving more space to the positioning of the arms . in the present stage , the spectral fibres , @xmath2 in diameter and 21 m long , are going from the prime focus down to the cassegrain , where the b&c eso spectrograph is located . this spectrograph is fitted with a f/3 collimator to match the fibre output beam aperture . it has a set of reflection gratings with dispersion range from 2.3 nm / mm to 23.1 nm / mm , and a tek 512 x 512 thin ccd . the first scientific observation was performed in february 1991 with a mefos prototype consisting of nine arms only ( bellenger _ et al . _ 1991 ) . during this period a galaxy of magnitude b=@xmath3 was observed with a resolution of r=370 . the 1@xmath4 exposure resulted in spectrum with a s / n=50 in the red part of the continuum ( 550 nm ) . the first technical run in full configuration at the 3.6 m telescope took place in october 1992 . as only 2 1/2 of the 5 allocated nights were clear , a second run was necessary for the testing and the commissioning . this was carried out in february 1993 during 5 clear nights . some problems with the centering of the image fibres on the object coordinates were noted . it appeared that the optical aberrations correction curve was not accurate enough . we had adopted this curve as it was derived from photography at the prime focus . the mounting of this instrument entails different conditions . by moving an image fibre across the mefos field in real configuration , the correction curve could be adjusted . the objects are now falling within a few arcseconds of the centre of the image fibre helping for their identification . in the 7 nights following this run , mefos was used on two scientific programmes . the instrument worked well and little time was lost due to technical reasons . cuby & mignoli ( 1994 ) studied sky subtraction procedures using mefos with and without beam switching . they were able to measure redshifts for galaxies with magnitudes as faint as b=22@xmath5 from a 90 min exposure ( 2 x 45 min ) . a b=@xmath6 galaxy was observed as well , but the resulting signal to noise ratio of s / n = 7 was too low for a reliable redshift measurement . since then , mefos was used in 84 nights , without a single failure . since april 1994 , mefos has been used without any further support from the building team . in order to compensate the building team of the daec for their efforts , 32 nights of guaranteed time were allocated to scientists of this laboratory . from the submitted scientific proposals , four programmes were selected . each was granted 8 observing nights with mefos . based on the experience gained in one of these programmes , we describe in the following the preparations before an observing run as well as the typical procedures while observing with mefos at the 3.6 m telescope . in the next section we will then discuss a number of specific problems that we encountered while reducing the data , and , at the end , a number of examples and some statistics will allow some insight into results that can be expected from multifibre spectroscopy with mefos . the described procedures as well as the obtained data are , of course , strongly related to the selected project . it is therefore important to know some details about the project when discussing the performance of mefos . the scientific project `` search in the galactic plane toward the great attractor '' aims at mapping the galaxy distribution in velocity space in the zone of avoidance ( zoa ) in the general direction of the cosmic microwave background dipole ( cmb ) and the great attractor . galaxies hidden behind the zoa are important in derivations of the peculiar motion of the local group relative to the cmb , and in explaining the observed streaming ( bulk flow ) motions , as e.g. in the great attractor region . preliminary scientific results have already been presented ( cayatte _ et al . _ 1994 , kraan - korteweg _ et al . _ 1994 , 1996a , b ) . this programme is a continuation of a long - term programme which made use of optopus , the previous multi - fibre spectrograph of eso . a large part of the extragalactic sky is obscured by the milky way . to bridge this gap , we have embarked on a search for galaxies behind the milky way to the low diameter limit of d=@xmath7 and faint magnitude limit using existing sky surveys ( kraan - korteweg & woudt 1994 ) . to date over 10000 previously unknown galaxies were uncovered in the southern milky way ( @xmath8 , with a strong peak @xmath9 ( cf . fig . 1 in kraan - korteweg & woudt , 1994 ) . this range is well suited to the dynamic range of mefos . galaxies in this magnitude interval have an average number density of the order of 100 - 200 galaxies@xmath10 , suggesting a more efficient use of optopus with 50 fibres in a half - degree field . however , the galaxies of this project lie behind the milky way . they are heavily obscured : around one magnitude at" +"conventional communication networks , like the internet , ensure transfer of information generated at some nodes to others . it is known that network coding affords throughput gain over routing in such networks ( see @xcite and references therein ) , and given a network and the demanded source messages at each sink , the network coding problem is to design a network code that maximizes the rate of information transfer from the source nodes to the sinks . but in some networks , like a sensor networks for environmental monitoring , nodes may be interested not in the messages generated by some other nodes but in one or more functions of these messages . designing a network code that maximizes the frequency of target functions computation , called the _ computing capacity _ , per network use at the sinks is known as the _ network computation _ problem @xcite . this subsumes the network coding problem as a special case . environmental monitoring in an industrial unit is an application of network computation where relevant parameter may include temperature and level of exhaust gases which may assist in preventing fire and poisoning due to toxic gases respectively . a simple way to perform network computation is to communicate all the messages relevant to the function required at each sink using either network coding or routing . this is not only highly inefficient in terms of bandwidth usage and power consumption but also undesirable in certain settings . for example , in an election , who voted whom is to be kept confidential but the sum total of votes received by each candidate is to be publicized . an efficient way is that function computation be performed _ in - network _ , i.e. , in a distributed manner . the intermediate nodes on the paths between the sources and the sinks perform network coding and communicate coded messages such that the sinks may compute their desired functions without having to know the value of the arguments . in @xcite , bounds on rate of computing symmetric functions ( invariant to argument permutations ) of data collected by sensors in a wireless sensor network at a sink node were presented . the notion of min - cut bound for the network coding problem @xcite was extended to the function computation problem in a directed acyclic network with multiple sources and one sink in @xcite . the case of directed acyclic network with multiple sources , multiple sinks and each sink demanding the sum of source messages was studied in @xcite ; such a network is called a sum - network . relation between linear solvability of multiple - unicast networks and sum - networks was established . furthermore , insufficiency of scalar and vector linear network codes to achieve computing capacity for sum - networks was shown . coding schemes for computation of arbitrary functions in directed acyclic network with multiple sources , multiple sinks and each sink demanding a function of source messages were presented in @xcite . in @xcite , routing capacity , linear coding capacity and nonlinear coding capacity for function computation in a multiple source single sink directed acyclic network were compared and depending upon the demanded functions and alphabet ( field or ring ) , advantage of linear network coding over routing and nonlinear network coding over linear network coding was shown . connections between matroids and network coding problems were first explored in @xcite wherein matroidal networks were characterized and a construction method to obtain matroidal networks from matroids was given . it was shown in @xcite that if a network admits a scalar linear solution , then the network is matroidal with respect to represenatable matroid . the converse , i.e. , if a network is matroidal with respect to a representable matroid , then it admits a scalar linear solution was given in @xcite . the construction procedure to obtain network from matroids given in @xcite reflects all the independencies but not all the dependencies of the matroids . this problem was addressed in ( * ? ? ? vi ) wherein a method to construct a network from a matroid was given via an index coding problem ; the resultant network reflects all the dependencies and independencies of the matroids and it was shown that a scalar ( vector ) linear solution exists for the network if and only if the matroid has a linear ( multilinear ) representation . also in @xcite and @xcite , relation between network and index coding was studied . similar relation between network computation problems and functional index coding problems ( a generalization of index coding problem proposed in @xcite ) was established in @xcite . in this paper , we explore the relationship of network computation problems and matroid representations . the contributions of this paper are as follows : 1 . in section [ sec_main ] , we give a modified definition of matroidal networks to fit the requirements of network computation problems ; the modified definition subsumes the original definition of @xcite as a special case ( remark [ rem_2 ] ) . 2 . in theorem [ thm1 ] , we show that a scalar linear network code for a given network computation problem with linear functions demanded by sinks exists if and only if the network is matroidal with respect to a representable matroid whose representation satisfies certain constraints imposed by the network computation problem . this generalizes ( * ? ? 12 ) which states that a network coding problem admits a scalar linear solution if and only if it is matroidal with respect to a representable matroid . 3 . in section [ sec_fd ] , we show connection between _ functional dependency relations _ ( fd - relations ) and network computation problems with possibly nonlinear function demands . in proposition [ prop_1 ] , we show that a functional representation of an fd - relation ( determined by the network computation problem ) can be used to obtain nonlinear network codes . this generalizes ( * ? ? ? * proposition 12 ) which states that a network coding problem admits a scalar solution if and only if the corresponding fd - relation has a functional representation . in section [ sec_prelims ] , relevant preliminaries of network computation problem and matroid theory are given . we conclude the paper with a summary of work presented in section [ sec_disc ] . a brief overview of network computation problems and matroids are presented in this section . a @xmath0-ary finite field is denoted by @xmath1 and the set @xmath2 is denoted by @xmath3 $ ] , for some positive integer @xmath4 . the power set of a set @xmath5 is denoted by @xmath6 . the column vector of length @xmath7 whose @xmath4th component is one and all other components are zeros is denoted as @xmath8 . an @xmath9 identity matrix is denoted by @xmath10 and an @xmath11 all zero matrix is denoted by @xmath12 . a network is represented by a finite directed acyclic graph @xmath13 , where @xmath14 is the set of nodes and @xmath15 is the set of directed error - free links ( edges ) , where the edges in @xmath16 correspond to the source messages generated in the network , the edges in @xmath17 correspond to the links between the nodes in the network , and the edges in @xmath18 correspond to the demands of the sink nodes . for a node @xmath19 , @xmath20 is the set of messages generated ( if any ) by node @xmath21 and the incoming links to it from other nodes , and @xmath22 is the set of outgoing links to other nodes and the function demanded ( if any ) by @xmath21 . for an edge @xmath23 from a node @xmath24 to @xmath25 , @xmath24 and @xmath25 are called , respectively , its tail and head and @xmath26 , i.e. , @xmath27 is the set of edges which terminate at the node at which @xmath28 originates . the network may have multiple source nodes and each may generate multiple messages . the source messages are represented by tailless edges @xmath29 that terminate at a source node . the total number of messages generated in the network is @xmath30 and are denoted by random variables @xmath31 , where , for every @xmath32 $ ] , @xmath33 is uniformly distributed over @xmath1 . let @xmath34 be the row vector of source messages and @xmath35 be the set of source messages . each link @xmath36 can carry one @xmath1 element per use , i.e. , capacity of each link is @xmath37 , and @xmath38 is the associated random variable . note that for a source edge @xmath29 , the associated random variable is @xmath39 . the set of sink nodes is denoted by @xmath40 . without loss of generality , we assume that each sink demands only one function of source messages . if a sink demands @xmath41 functions , then such a sink may be replaced by @xmath7 sinks , each demanding one function but receiving the same incoming information . a sink node @xmath42 requests a function @xmath43 , where @xmath44 . the demands @xmath43 of the sink node @xmath42 is denoted by a headless edge @xmath45 originating at @xmath42 . let @xmath46 . a network computation problem @xmath47 is specified by the underlying network , the message set , and the set of sink demands . a network code @xmath48 for a network computation problem @xmath49 is an assignment of a _ global encoding kernel _ @xmath50 to each edge @xmath36 and a decoding function @xmath51 to each sink @xmath52 . for any edge @xmath36 , @xmath53 maps @xmath54 to @xmath38 ( and thus , the distribution of @xmath38 depends upon the network code ) , i.e. , @xmath55 is the data that flows on edge @xmath28 . for any sink @xmath52 , the decoding map @xmath56 takes as input the data on the incoming edges , @xmath57 , and outputs @xmath43 , i.e. , @xmath58 for every tailless edge @xmath59 denoting the source message @xmath33 , @xmath60 is taken to be the global encoding kernel . for every headless edge @xmath45 denoting the demand @xmath43 of sink @xmath61 , @xmath62 is taken to be the global encoding kernel . [ rem_1 ] a. a code is said to be linear if all the global encoding kernels of edges in @xmath17 are linear , i.e. , data on the outgoing edges of each node is a linear combination of data on the incoming edges . also , the global encoding kernels of the outgoing edges of each node is a linear combination of the global encoding kernels of the incoming edges of that node . moreover , the global encoding kernel for an edge @xmath63 can be represented by a length @xmath64 column vector @xmath53 over @xmath1 such that @xmath65 for all @xmath36 , where @xmath53 is called the global encoding vector of @xmath28 . b. similarly , the global encoding kernel of edge @xmath66 , @xmath32 $ ] , can be represented by @xmath67 so that @xmath68 . note that the matrix obtained by juxtaposing global encoding vectors of @xmath69 is the identity matrix @xmath70 . c. if the sink demands are linear then they can be represented by @xmath64 length columns vectors @xmath71 such that @xmath72 . d. if all the sink demands are linear and the network computation problem admits a linear solution , then all the decoding maps will also be linear . for a sink @xmath42 , the decoding map can be represented using a length @xmath73 column vector @xmath56 such that @xmath74 . another way to specify a network code is to list the _ local encoding kernel _ @xmath75 of each edge @xmath36 and the decoding functions of the sinks . that is , a network code" +"in fluid mechanics , the non - slip boundary condition ( nsbc ) states that fluid at the interface between a fluid and a solid surface is stationary with respect to that surface . surface slip arises when there is non - zero relative motion between the interfacial fluid and the solid surface , in which case the nsbc does not apply . in the vast majority of experiments described historically , the nsbc has been an adequate boundary condition @xcite . however , finite surface slip has been the subject of much recent interest and promises to play a significant role in the current and future development of micro- and nanofluidic devices @xcite . navier @xcite first described surface slip as early as the 1820s and his mathematical definition of the slip length has been widely used , for example in recent reviews @xcite and analyses of slip - dependent flow @xcite . slip is a well - studied phenomenon in non - newtonian fluids such as polymer solutions @xcite . for slip of newtonian fluids ( newtonian slip ) , theory is well developed @xcite , but interpretation of experiments has been much more controversial . newtonian slip is important because technologies can usefully be applied to newtonian fluids , but also because understanding of newtonian slip will provide a more profound understanding of fundamental slip mechanics . the physical mechanisms governing slip are affected by variables that include surface chemistry , shear rate , surface structure , newtonian viscosity , non - newtonian behaviour at the molecular scale and combinations of each of these variables @xcite . nanoengineered superhydrophobic surfaces trap gas between the fluid and the surface , producing large slip lengths of the order @xmath410 @xmath5 m @xcite . experimentally , newtonian slip has been investigated using a variety of methods @xcite . the most widely used and precise technique involves measurement of the drainage forces between closely - spaced surfaces in an atomic force microscope ( afm ) or surface force apparatus ( sfa ) and applying an analysis based on reynolds theory of lubrication @xcite . robust , non - zero values of @xmath0 for newtonian fluids at relatively smooth surfaces are typically of the order 10 - 100 nm @xcite . experiments have not established firm quantitative correlations between slip and major experimental variables , such as contact angle @xcite . recently , it has emerged with some clarity that in afm or sfa experiments , the nsbc can be expected to hold on smooth hydrophilic surfaces @xcite , while finite slip lengths of order 10 - 20 nm have been measured on some hydrophobic surfaces @xcite . additionally , the long - held idea that surface roughness should inhibit slip @xcite is now supported by reasonable experimental evidence @xcite . shear - mode oscillations can be used to drive fluid flow , and such systems pose scientific questions that are distinct from those relating to the study of steady fluid flows . oscillating piezoelectric components are likely to prove very useful in future applications . ultrasonic oscillators , well established as important tools for investigating thin films and bulk fluids , can also be used to probe the interfacial forces that are relevant in the study of slip . kanazawa and gordon @xcite analytically coupled a half - space of newtonian fluid to a piezoelectric quartz crystal microbalance ( qcm ) , in which a solid interface oscillates in shear mode , using the nsbc . further reports have presented experiments @xcite and analysis @xcite describing slip of a newtonian fluid adjacent to an oscillating surface . a relatively large set of slip lengths measured using a qcm was obtained by ellis and hayward @xcite . torsional quartz crystal oscillators operating at khz frequencies were initially developed and used for viscoelasticity measurements @xcite and have been used to measure the complex and viscoelastic behaviour of polymer solutions . more recent work has investigated dispersions of colloidal @xcite and micellar @xcite spheres . the shear rates accessible using torsional oscillators are considered advantageously high for such rheological measurements @xcite . a particular configuration , the composite torsional ultrasonic oscillator , was developed and analysed by robinson et al . @xcite and robinson and smedley @xcite , who also derived an equivalent circuit . recently , the first experimental results investigating newtonian slip at a smooth surface using such a device have been reported @xcite , for oscillations at 40 khz . there has been some confusion relating to fundamental aspects of slip , perhaps best characterised by neto et al . @xcite , who noted that dialogue between the qcm community and other researchers interested in slip has been scarce . in order to address this issue , navier s definition of the slip length is used consistently in the current work . an intuitive , consistent and general methodology for slip measurement at an oscillating surface is presented . analytic inconsistencies in the literature are identified and clarified , especially those concerning an oscillating interface . the composite torsional oscillator is introduced along with a full analysis for measurement of newtonian slip using this device . preliminary experiments are presented to demonstrate how this device is used to probe interfacial forces in oscillatory flow . we discuss the interpretation of measurements and the analytical assumptions on which they are based . finally , methods of slip measurement are compared and the advantages of using the composite torsional oscillator are explained . by definition , viscosity @xmath6 is constant and independent of shear rate throughout a newtonian fluid . the velocity field @xmath7 of an incompressible newtonian fluid of density @xmath8 in the presence of pressure gradient @xmath9 and body force @xmath10 can be determined by solving the navier - stokes equation , @xmath11 microfluidic flows have characteristically low reynolds numbers , so the convective derivative @xmath12 is insignificant when compared with the viscous term @xmath13 . solutions to the navier - stokes equation are dependent on flow geometry and boundary conditions . the relevant solution for the current paper concerns a smooth surface oscillating in shear mode in contact with a fluid half - space . in the absence of significant body forces or pressure differentials , the equation of the shear wave induced in the fluid is @xmath14 where @xmath15 is the fluid velocity in the direction of the surface oscillations , @xmath16 is the cartesian direction perpendicular to the solid surface and @xmath17 . the value of @xmath15 at the interface is @xmath18 , which depends on the fluid - surface boundary condition . the time dependence of @xmath15 and @xmath18 is @xmath19 , where the frequency of oscillation is @xmath20 and @xmath21 is time . this solution is relevant for ultrasonic oscillators . boundary slip occurs when the nsbc is contravened , so that there is finite relative motion between a solid surface and an adjacent fluid . navier @xcite characterised the slip boundary condition by defining the slip length @xmath0 . for flow adjacent to a planar , impermeable solid surface , @xmath22 here @xmath23 is the shear velocity relative to and parallel with the surface and @xmath24 is the value of @xmath23 at @xmath25 . navier s definition of slip has been widely used over a long period and has a strong physical basis relating to viscous force at the interface . the fluid shear rate at the interface that appears in eq . [ eq : gen slip length ] also determines the viscous force , @xmath26 slip therefore determines the shear stress at the interface , which is analogous to friction in character . the coefficient @xmath27 , defined as @xmath28 is finite only when there is slip . using eqs . [ eq : gen slip length ] , [ eq : gen viscous stress ] and [ eq : friction define ] , we find @xmath29 it is noted that the nsbc and boundary slip are , respectively , analogous to the regimes of static and sliding solid - solid friction . extending the analogy , we might expect a wide variety of material and interfacial properties to determine the onset and magnitude of solid - liquid friction . if slip length depends on shear rate , eq . [ eq : gen slip length ] becomes non - linear and rate - dependent formulations of slip ( e.g. @xcite ) become relevant . currently , there is conflicting experimental evidence relating to possible shear rate dependence of @xmath0 @xcite . a different physical interpretation of slip length relates @xmath0 to the distance into the solid over which the tangent to the flow profile at the surface must be extrapolated for the velocity to reach zero . in this context , navier s slip length has correctly been described as a fictional distance @xcite and is labelled in fig . [ fig : slip definition ] . the definition of slip length used in some recent slip studies @xcite , and formalised by ellis and hayward @xcite as ( their notation ) @xmath30 , or @xmath31 is distinct from navier s definition in eq . [ eq : gen slip length ] . ellis and hayward s definition corresponds to extrapolation of the flow profile a distance @xmath32 ( fig . [ fig : slip definition ] ) relative to the surface when slip occurs . the value of @xmath32 is equal to @xmath0 only in the case of a linear velocity flow profile . an often - used schematic diagram @xcite , which uses a linear flow profile to depict slip length , appears to have been an important factor in the emergence of eq . [ eq : b_1 ] . we wish to point out that when the flow of a newtonian fluid is driven by an oscillating surface ( as introduced above ) , the shear rate introduces non - zero phase into the value of @xmath0 , which is defined using @xmath23 ( eq . [ eq : gen slip length ] ) . the existence of this phase highlights the limitations of direct quantitative comparison of measurements of @xmath0 using different experimental techniques . when measuring slip at an oscillating surface , it is both intuitive and useful to use the dimensionless complex parameter @xmath33 . this parameter , which simply quantifies the velocity discontinuity between the solid surface and the first liquid layer , simplifies the algebra describing the effect of damping on the equivalent circuit of a piezoelectric oscillator . it is defined by interfacial properties and does not depend on the flow profile , @xmath34 the velocity of the solid surface is @xmath35 and the fluid oscillation is assumed to be dominated by a sinusoidal oscillation of angular frequency equal to that of the solid surface . under this assumption , @xmath36 is equivalent to parameters introduced by ferrante et al . @xcite and used elsewhere @xcite for modelling of slip at an oscillating surface ; to our knowledge , it has not previously been applied to experimental measurements with full consideration of phase dependence . more generally , @xmath36 can be decomposed into fourier components , an approach that has been used when modelling nanobubble - induced slip @xcite . the nsbc is consistent with the values @xmath37 and @xmath38 . for an oscillating surface , flow is relative to surface motion , so @xmath39 the magnitude and phase of @xmath40 relative to @xmath35 are plotted in fig . [ fig : slip phasor ] , for both slip and non - slip cases . figure [ fig : c ] shows that the relative amplitude of oscillation is uniformly non - zero at the surface when slip is present , but varies significantly near the interface ( @xmath41 ) depending on the values of @xmath42 and @xmath43 . further from the surface ( @xmath44 ) , the relative amplitude tends towards" +"in calphad ( calculation of phase diagrams ) modeling@xcite , thermodynamic properties of a solution phase in a ternary or higher - order system are usually obtained through combining those of its constitutive binary systems and occasionally with ternary interaction parameters . since the most dominant interatomic reaction in a multicomponent system is that of the binaries , accurate thermodynamic descriptions which are capable of reproducing the characteristics of binary solution phases are prerequisites to a successful multicomponent thermodynamic modeling . in this regard , considerable efforts have been made to develop models for combining thermodynamic descriptions for binary solution phases to be used in higher - order systems@xcite . in typical thermodynamic modelings , ternary interaction parameters for solid solution phases are not introduced since their thermochemical data , such as mixing enthalpy , which are needed in the parameter evaluation are very difficult to measure . in fact , obtaining accurate thermochemical data for solid solution phases is challenging even for binaries due to sluggish kinetics at low temperatures so that it is hard to reach a complete thermodynamic equilibrium . furthermore , the existence of intermediate phases narrows the experimentally accessible composition range for thermochemical properties of solid solution phases . as the number of elements increases in a multicomponent system , the complexity of acquiring reliable data also increases . consequently , interaction parameters for the excess gibbs energy of binary solid solution phases are usually evaluated only from phase equilibrium data and those of ternary are usually omitted due to the lack of data . fortunately , the dearth of experimental data for solid solution phases can be overcome by atomic level calculations , such as first - principles calculations . specially designed supercells , so - called special quasirandom structures ( sqs ) suggested by @xcite , whose lattice sites are occupied by constituent atoms so as to reproduce the average correlation functions of a completely random solution , are one of the representative methods . sqss can be completely relaxed within density functional theory ( dft ) codes to consider the effect of local relaxation and can also be applied to any other system by changing the atoms because they are structural templates . a limitation is that sqss of a unit cell size that is manageable with present dft codes can only be obtained at certain compositions , e.g. @xmath3=0.25 , 0.5 , and 0.75 in the substitutional @xmath4 binary alloys . nevertheless , first - principles study of sqss at those three compositions permit accurate predictions of various properties of solid solutions . it has already been successfully applied to calculate thermodynamic properties of binary solid solution phases for fcc , bcc and hcp phases@xcite . two ternary fcc sqss in an a - b - c system , which can be applied to four different compositions at @xmath5 ; @xmath6 , @xmath7 ; @xmath8 , @xmath6 , @xmath9 ; and @xmath10 , @xmath11 , are developed to investigate the mixing enthalpies for ternary fcc solid solution phases in the present work . the organization of this paper is as follows : the impact of ternary interaction parameters on a ternary solution phase in the calphad approach is briefly reviewed . then the generated ternary fcc sqss are characterized in terms of their atomic arrangements to reproduce the pair and multi - site correlation functions of completely random fcc solid solutions . finally , the generated sqss are applied to the ca - sr - yb system which presumably has fcc solid solution phases throughout the entire composition range in all three binaries and ternary . the gibbs energy of a ternary solution phase , @xmath12 , is expressed as@xcite @xmath13 where @xmath14 is the mole fraction of element @xmath15 , @xmath16 is the gibbs energy of @xmath12 phase of pure element @xmath15 , @xmath17 and @xmath18 are the excess gibbs energies of the constitutive binary and ternary systems , respectively . the excess gibbs energies for binary and ternary systems can be further described as @xmath19 @xmath20 where @xmath21 is the @xmath22-th order interaction parameter@xcite in a binary and normally described as @xmath23 where @xmath24 and @xmath25 are model parameters evaluated from experimental information . ternary parameter of element @xmath15 , @xmath26 , in eqn . [ eqn : xs2_tern ] also have the form of eqn . [ eqn : xs2_interaction ] . if all three @xmath27-parameters in eqn . [ eqn : xs2_tern ] are identical , as in a ternary regular solution@xcite , @xmath28 then the ternary excess gibbs energy shown in eqn . [ eqn : xs2_tern ] can be further simplified to @xmath29 since @xmath30 in a ternary . thermodynamic properties of solid solution phases can be calculated in several ways ( e.g. , see refs . @xcite ) . a popular approach is to use a database of first - principles calculations to determine the so - called effective cluster interactions ( eci ) that describe the energetics of the alloy system of interest . these interactions are then used as an input for efficient statistical mechanics methods , such as the cluster variation method or monte carlo simulations . while this general approach is able to model ordered phases ( with potential point defects ) and disordered ( with potential short - range order ) within a unified framework , it can be computationally demanding . fortunately , in cases where the sole objective is obtain a reliable thermodynamic model for disordered phases that can be reasonably assumed to lack significant short - range order , the use of sqs provides a considerably more straightforward and computationally efficient approach . as discussed in section [ sec : intro ] , first - principles study of sqs can effectively consider the limitations discussed above , and it has been demonstrated that binary sqss can be applied to calculate thermodynamic properties of binary solid solutions , such as mixing enthalpy , for fcc , bcc , and hcp structures@xcite . it is thus anticipated that first - principles calculations of ternary sqss should be able to reproduce thermodynamic properties of ternary solid solutions if their atomic configurations , which are represented as correlation functions , are very close to those of ternary solid solutions . correlation functions of solid solution phases are well derived in @xcite . in the following section , the correlation functions for binary and ternary systems are briefly summarized . the normalized correlation functions , @xmath31 , in crystalline structures are defined as @xmath32 where the sum is over all the distinctive @xmath33-site clusters , which are geometrically equivalent , in the @xmath34 lattice sites structure . when @xmath33=1 , 2 , 3 , @xmath35 , then @xmath33-site clusters are point , pair , triplets , and so forth . site occupation variables are denoted as @xmath36 , where the subscript @xmath33 indicates that the @xmath33-th constituent located in the corresponding site . the superscript @xmath37 takes values 2 , 3 , @xmath38 , @xmath39 , with @xmath39 as the number of constituents , which represents a constituent @xmath37 at a given lattice site . for binary systems when @xmath40 , conventional values of the site occupation variables @xmath36 are @xmath411 depending on whether a lattice site is occupied by a or b atoms . according to eqn . [ eqn : correlation_function ] , the normalized point correlation function for the second constituent site ( b atom sites ) is given as @xmath42 with @xmath43 = 1 or -1 . it is worth noting that the atom sites do not need to be distinguished in a binary system since they are switchable . with the mole fractions of a and b being @xmath44 and @xmath45 , respectively , ( @xmath46 ) then @xmath47 . for a @xmath33-site cluster , the normalized correlation functions for the binary solid solution is formulated as @xmath48 similarly , for ternary systems when @xmath49 , the values of the site occupation variables @xmath36 conventionally take + 1 , 0 , or -1 if a lattice site is occupied by a , b , or c atoms , respectively . the normalized point correlation function for the second constituent site ( b atom sites ) is given as @xmath42 with @xmath50 + 1 , 0 , or , -1 . for the third constituent site ( c atom sites ) , the correlation function can be given as @xmath51 with @xmath50 + 1 , 0 , or , -1 . with the mole fractions of a , b , and c being @xmath44 , @xmath45 , and @xmath52 , respectively ( @xmath53 ) , then @xmath54 and @xmath55 . the vanishing of @xmath45 is due to its site occupation variable being 0 . for a @xmath33-site cluster with @xmath56 b atom sites and @xmath57 c atom sites ( @xmath58 ) , the normalized correlation functions for the ternary solid solution is denoted as @xmath59 in the present work , two different ternary fcc sqss are generated . the first sqs is at the equimolar composition where @xmath0 and the second is at @xmath1 , @xmath2 . by switching the occupation of the @xmath60 atoms in the second sqs with either @xmath61 or @xmath39 atoms , two other sqss can be obtained where @xmath62 , @xmath63 , @xmath64 and @xmath65 , @xmath66 . therefore , mixing enthalpy at four different compositions in a ternary system can be determined from first - principles total energy calculations of ternary fcc sqss by @xmath67 where @xmath68 represents the total energy of each structure , and the reference states for all pure elements are fcc . when the number of atoms in the ternary sqs is less than 24 , the alloy theoretic automated toolkit ( atat)@xcite has been used to generate ternary fcc sqss . since the atat enumerates all the atomic configurations within each supercell and then checks its correlation functions , the time needed to find sqss increases exponentially as the size of a supercell increases . for the sake of efficiency , to find sqss bigger than 24-lattice sites , a monte - carlo - like scheme@xcite has been used . in each supercell with different lattice vectors , atom positions are randomly exchanged between the atoms and correlation functions of a supercell are calculated after every alternation . if the correlation functions of a new state are getting closer to those of random solutions , then the new configuration is accepted . otherwise the new state is discarded and another configuration will be generated from the previous one . this process continues until the atomic arrangement of a supercell converges to the closest correlation functions of the random solution . in both methods , direct search via atat and monte - carlo - like scheme , a supercell whose correlation functions matches best with that of a completely random structure is chosen as the sqs at a given number of lattice sites . the selected sqss at two different compositions , sqs-24 when @xmath0 and sqs-32 when @xmath1 and @xmath2 , are shown in fig . [ fig : t_sqs ] . these two sqss are selected for later calculations because they are adequate with respect to their size and correlation functions at each concentration @xmath69 . ] . the space groups of both structures are @xmath70 with all the atoms at their ideal fcc sites . the correlation functions of the generated two sqss are given in tables [ tbl : cfternabc ] and [ tbl : cfterna2bc ] , respectively . lcdddddddd & + & random & 3 & 6 & 9 & 15 & 18 & 24 & 36 & 48 + @xmath71[6 ] & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 + @xmath71[12 ] & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0" +"variational methods ( vm ) have long been known as powerful tools in theoretical physics , especially in the context of reduced modeling . as opposed to approximating differential equations , approximating the action functional guarantees that the corresponding model too has a variational structure by definition . this implies that conservation laws are also generally preserved , so a model inherits key features of the original system notwithstanding the reduction @xcite . one of the areas that particularly benefit from this fact is wave theory @xcite , where even crude approximations to an action functional often yield insightful reduced models @xcite . the advantages of vm become especially obvious when one deals with media such as plasmas , which can be nonstationary , inhomogeneous , anisotropic , and exhibit both temporal and spatial dispersion simultaneously @xcite . first - principle differential equations are often unrealistic to handle in this case , whereas vm allow for simple and intuitive modeling . specifically , a wave theory can be constructed as an axiomatic field theory without even specifying the waves nature ( electromagnetic , acoustic , etc . ) . defining the action functional explicitly is needed only to connect the resulting general equations with specific quantities of interest @xcite . for example , this provides a convenient alternative to using maxwell s equations for electromagnetic waves @xcite , which are generally complicated @xcite ( as opposed to the corresponding vm ) even in the geometrical - optics ( go ) limit @xcite . but which exact variational principle does one begin with ? the microscopic least action principle ( lap ) is typically available in the form @xmath0 = 0 $ ] , where @xmath1 describes the wave field , @xmath2 describes the medium , and @xmath3 is a known functional . however , practical applications in the context described above require a different variational principle , where @xmath1 is the _ only _ independent variable , while the medium s degrees of freedom are `` integrated out '' , i.e.,somehow expressed through @xmath1 . if the medium response is adiabatic ( e.g.,if @xmath4 $ ] can be approximated with a local function ) , an effective lap for @xmath1 can be formulated simply as @xmath5 = 0 $ ] , as will also be discussed below . this principle has enjoyed insightful applications , e.g.,in the theory of generalized ponderomotive forces @xcite and nonlinear plasma waves @xcite . however , when the medium response is not adiabatic , the dynamics of @xmath1 becomes dissipative . then , the mentioned effective lap becomes inapplicable , and the problem requires a more subtle approach . this issue has been recently receiving attention in plasma physics @xcite and is also important for advancing variational formulations of plasma and wave kinetics such as in ref . the purpose of the present paper is to find the appropriate modification of the effective lap that would incorporate dissipation under the above assumptions . accommodating dissipative effects within the lap has a long history ( e.g.,cf . @xcite ) both as a formal problem of finding a variational principle for a given equation @xcite and also in modeling physical systems , for example , quantizing radiation in dissipative media @xcite . it is hardly possible to overview the topic here , so the given references are intended as representative but not exhaustive . in any case , the subject of our paper is different from those discussed in literature , particularly , in the following aspects : * we do not address the problem of finding a lap for a system with general dissipation . instead , we consider only emergent dissipation in nonconservative subsystems of systems that are overall conservative . * we avoid the standard approach ( known under many different names @xcite ) where additional independent functions are introduced that serve as lagrange multipliers @xcite . in our formulation , only time - independent lagrange multipliers are used . * we avoid variable transformations that are used ( as in , e.g.,refs . @xcite ) to compensate the loss of the phase space volume caused by dissipation . * in contrast to theories discussed in quantum contexts , our theory is not statistical . instead , we search for a lap that describes deterministic dynamics on a finite time interval for a given initial state of the medium . thus , we can not describe wave fields using the standard fourier representation , and we also have to specify boundary conditions ( bc ) in time , which are often ignored . in fact , it is the attention to these bc that helps accommodate dissipation within a lap . * instead of modeling media as collections of stationary oscillators ( as in , e.g.,refs . @xcite ) , we allow for media that are nonstationary , inhomogeneous , anisotropic , and have both temporal and spatial dispersion simultaneously . moreover , our approach allows treating classical and quantum degrees of freedom on the same footing . * our theory is formulated within the standard calculus of variations . we avoid exotic constructs such as complex actions or fractional derivatives @xcite . feynman integrals , which are used in related quantum theories ( e.g.,see ref . @xcite ) , are also avoided . our main results are as follows . we formulate a variational principle for a dissipative subsystem of an overall - conservative system by introducing constant lagrange multipliers and lagrangians nonlocal in time . we call it the variational principle for projected dynamics ( vppd ) . although the work is originally motivated by needs of the plasma wave theory , our results are applicable to general dynamical systems just as well . in the first part of the paper ( secs . [ sec : notation]-[sec : routh ] ) , we introduce the general approach where @xmath4 $ ] is an arbitrary nonlinear functional and derive an exact effective lap for @xmath1 . in the second part ( sec . [ sec : losc ] ) , we elaborate on applications of this approach to the important special case of linear @xmath4 $ ] , which corresponds to linear media . our formulation is equally applicable to both classical and quantum media . in the third part ( secs . [ sec : asym ] and [ sec : cont ] ) , we discuss various asymptotic approximations of the effective lap for oscillations and waves in linear media , including the quasistatic and go approximation . to our knowledge , this is the _ first variational formulation of dissipative go _ in a general linear medium , which is allowed to be nonstationary , inhomogeneous , nonisotropic , and exhibits both temporal and spatial dispersion simultaneously . also notably , the `` spectral representation '' of the dielectric tensor @xmath6 that enters the go equations is shown to be , strictly speaking , the weyl symbol of the medium dielectric permittivity . ( previously , it has been known that weyl symbols emerge naturally in wave kinetics @xcite . ) this can be considered as an invariant definition of @xmath6 , as opposed to _ definitions used in literature that have been a source of a continuing debate @xcite . our work is also intended as a stepping stone for extending the variational theory of modulational stability in general wave ensembles @xcite to dissipative systems . details will be described in a separate publication . the following notation is used throughout the paper . the symbol @xmath7 denotes definitions , and @xmath8 denotes transposition . for example , for a column vector @xmath1 [ eq . ( [ eq : q ] ) ] , one has @xmath9 , which is a row vector ; i.e.,in this case , @xmath8 merely lowers the index . we assume @xmath10 for any @xmath11 , where @xmath12 is the kronecker delta . ( summation over repeated indices is assumed unless specified otherwise . ) hence , in principle , @xmath13 and @xmath14 could be considered equivalent , but we prefer to retain the distinction because some quantities ( such as coordinates ) are naturally defined with upper indexes , while others ( such as momenta ) are naturally defined with lower indexes . introducing a more fundamental geometrical interpretation will not be needed for our purposes . note also that some indexes will be used _ just _ to introduce new symbols . this applies to all scalars ( e.g.,@xmath15 and @xmath16 ) and to some vectors ( e.g.,@xmath17 , @xmath18 , @xmath19 , @xmath20 ) . we also define @xmath21 . the symbol @xmath22 will denote @xmath23 . the notation `` @xmath24 '' will denote that the equation is obtained by extremizing a corresponding action functional with respect to @xmath11 . the remaining notation is introduced within the main text . finally , the abbreviations used in the text are summarized as follows : + [ cols= "" > , < "" , ] + we start by introducing the general formalism of lagrangian mechanics . although this formalism is commonly found in textbooks ( e.g.,see ref . @xcite ) , it is essential to restate it here , so we can explicitly reference specific definitions and equations later in the text . consider a lagrangian system @xmath25 characterized by some real coordinate vector @xmath26 the dynamics of @xmath25 on a time interval @xmath27 is governed by the lap . we call this interval @xmath28 , and we also use the symbol @xmath28 to denote its duration , @xmath29 . we assume the action functional @xmath30 to have the form @xmath31 = \int^{t_2}_{t_1 } l^{(q)}(t , q , \dot{q})\,dt,\end{gathered}\ ] ] where @xmath32 is called a lagrangian . then , the standard formulation of the lap is as follows : @xmath33 = 0 , \\ \delta q(t_{1,2 } ) = 0.\label{eq : dqzero2}\end{gathered}\ ] ] [ here and further , the notation @xmath34 means `` both @xmath35 and @xmath36 '' ] . note that eq . ( [ eq : dqzero2 ] ) implies bc @xmath37 where @xmath38 and @xmath39 are some given constants . from eq . ( [ eq : aq ] ) , one obtains @xmath40\,\delta q\,dt,\end{gathered}\ ] ] where we introduced the `` canonical momentum '' @xmath41 with @xmath42 , or , more compactly , @xmath43 . the first term on the right in eq . ( [ eq : aux1 ] ) vanishes because @xmath34 are fixed . hence , the lap leads to the following euler - lagrange equations ( ele ) : @xmath44 this is a second - order equation for the @xmath45-dimensional coordinate @xmath1 , so the @xmath46 bc ( [ eq : bcq ] ) ( two per each component of @xmath1 ) provide just the right number of parameters to define a solution of eq . ( [ eq : ele ] ) . alternatively , one can also approach eq . ( [ eq : ele ] ) as an initial - value problem ; then , the condition on on @xmath47 would need to be replaced with a condition on @xmath48 . it is straightforward to extend this formulation to lagrangians that depend also on higher - order derivatives , but we will not consider such extensions for the sake of brevity . now suppose that @xmath25 is coupled to another lagrangian system @xmath49 , which we call the `` medium '' . suppose also that @xmath49 is characterized by some @xmath50-dimensional coordinate @xmath2 . the dynamics of the resulting system @xmath51 is governed by the lap @xmath0 = 0 $ ] , where @xmath3 is the total action . for clarity , we adopt it in the form @xmath52 , where @xmath53 is the lagrangian given by @xmath54 the assumed bc are @xmath55 which introduce @xmath56 bc similar to eq . ( [ eq : bcq ]" +"a phase transition from nuclear to quark matter within a neutron star ( ns ) with millisecond scale rotation period can induce a collapse that releases up to @xmath1erg in energy , which potentially relates this process to violent phenomena such as core collapse supernovae @xcite or @xmath2ray bursts ( grbs ) @xcite . recent numerical simulations suggest that up to a few percent of this energy may be released as gravitational waves ( gws ) @xcite . if a significant fraction of nss undergo such a phase transition induced collapse , the energy released will contribute to cosmological backgrounds in photons , neutrinos , and gws . in the present paper we estimate these backgrounds and point out that the stochastic gw background may be comparable to gw backgrounds from various other astrophysical sources . we specifically compare the power and statistical properties of this potential background with the ones from standard core collapse supernovae @xcite , ns - ns coalescence @xcite , r - mode instabilities in nss with millisecond periods @xcite , and from magnetars @xcite , as well as from various processes in the early universe . we also find a significant constraint on the fraction of the total energy released in such phase transitions in form of mev @xmath2rays . we use natural units with @xmath3 throughout . we first recall that the energy radiated in gws per frequency interval for an individual event at distance @xmath4 , @xmath5 , is related to the fourier transform @xmath6 of the dimensionless strain amplitude @xmath7 by @xmath8 where @xmath9 is newton s constant . we model the strain in the phase transition scenario as @xmath10 which roughly reflects the form found in the simulations in ref . this leads to a fourier transform @xmath11 note that the total energy emitted in gws @xmath12 from eq . ( [ egw ] ) converges for this spectral form . we use @xmath13khz , @xmath14ms for the damping scale which is typical for the most rapidly rotating progenitors in ref . @xcite , and normalize such that @xmath15erg , the more optimistic case from ref . @xcite . most of the energy released in the phase transition is actually carried away in form of photons and neutrinos , whose total energy we will denote by @xmath16erg . this is roughly the energy required to power a @xmath2ray burst . the gravitational wave energy is typically @xmath17 @xcite . the cosmic star - formation rate ( sfr ) and , as a consequence , the formation rate @xmath18 of nss is reasonably well known at redshifts @xmath19 @xcite . especially for @xmath20 it is strongly constrained by the super - kamiokande limit on the electron antineutrino flux from cosmological core collapse supernovae @xcite . in contrast , the sfr is poorly known for @xmath21 . we use the fits shown in fig . [ fig1 ] . we are interested in the number of events per unit mass . this number is given by an expression of the general form @xmath22 where we neglect any redshift dependence . here , @xmath23 is the mass function , usually taken to be of the salpeter form @xmath24 between @xmath25 and @xmath26 , @xmath27 $ ] is the progenitor mass range over which nss form , and the integral in the denominator goes over all stellar masses . further , @xmath28 is the fraction of nss eventually undergoing the phase transition under consideration . the event rate @xmath18 is then given by the product of the sfr and @xmath29 . for nss , @xmath30 , @xmath31 , so that @xmath32 . note that @xmath33 and could be significantly larger if nss are also formed from progenitors with masses @xmath34 . the above value for @xmath29 also roughly corresponds to today s rate of core collapse supernovae which is @xmath35 which is to be expected given that most of the nss are born in type ii supernova events . most of the hot young nss are born with 10 - 20 ms rotation periods due to processes such as magnetic braking . we assume that @xmath36 of the nss undergo a phase transition . this is roughly the estimated fraction of nss which are born with millisecond scale rotation periods @xcite , required to trigger the phase transition . the same sub - population of nss would be relevant for gw emission between @xmath37hz and @xmath38khz from r - mode instabilities in rapidly rotating nss , in contrast to ref . @xcite which assumed @xmath39 . another possible channel for phase transitions to occur in nss is in low - mass x - ray binaries where the ns is spun up by accretion from the low mass companion @xcite . the formation efficiency of such systems is hard to estimate , but typical numbers are @xmath40 @xcite , similar to the estimated fraction of millisecond nss born in core collapse supernovae . even larger values for @xmath29 could be motivated if these phase transitions are connected to short hard @xmath2ray bursts . a best estimate of @xmath41 for the comoving rate of faint short hard @xmath2ray bursts at zero redshift has recently been given @xcite . comparing with fig . [ fig1 ] , this corresponds to @xmath42 , which would correspond to values for @xmath28 comparable to unity . for the ns - ns coalescence and magnetar scenarios , @xmath29 is actually given by the same expression eq . ( [ fraction ] ) , with estimated fractions @xmath43 @xcite and @xmath44 @xcite of all nss contributing , respectively . we will neglect any time delay between star formation and ns formation because the lifetime @xmath45yr of @xmath46 ns progenitors is short compared to the hubble time . for simplicity , we assume that all nss have identical emission characteristics . the energy density in gws at frequency @xmath47 per logarithmic frequency interval in units of the cosmic critical density @xmath48 can be written as @xcite @xmath49 where @xmath18 is the event rate per comoving volume , @xmath50 . the cosmological model enters with @xmath51^{-1}$ ] and , for a flat geometry , @xmath52^{1/2}\,.\ ] ] we will use the parameters @xmath53 , @xmath54 , and @xmath55 with @xmath56 . for a stochastic gw background the dimensionless strain power @xmath57 is related to the dimensionless gw energy density in eq . ( [ los ] ) by @xcite @xmath58 ) assuming about @xmath59 of all nss undergo a phase transition , releasing @xmath60erg in gws . the band represents the uncertainty related to the different sfrs shown in fig . the solid line is the maximal low - frequency tail due to anisotropic neutrino emission . for comparison , the dashed line is the maximal background from conventional type ii supernovae discussed in ref . further , the horizontal dash - dotted lines represent a maximum version of the gw stochastic spectrum produced during slow - roll inflation assuming @xmath61 for the ratio of the tensorial and scalar contributions to the cosmic microwave background radiation anisotropy and @xmath62 for the running of the tensorial power - law index @xcite . the dotted lines show approximate sensitivities of the ground based interferometer ligoiii / euro and ligoiii in correlation mode @xcite , and of possible second generation space - based interferometers such as the big bang observatory ( bbo ) @xcite and the ultimate decigo @xcite , as indicated.,scaledwidth=80.0% ] fig . [ fig2 ] shows the resulting gw background for the ns phase transition scenario , the band representing uncertainties due to the different sfrs from fig . [ fig1 ] , but not due to other quantities such as @xmath12 and @xmath28 which were fixed to fiducial values , as indicated . note that gw densities are proportional to @xmath29 from eq . ( [ fraction ] ) , and thus also to the fraction @xmath28 of nss subject to the phase transition . they are also proportional to the average total gw energy output @xmath12 . as a result , the largest uncertainties come from the parameters @xmath28 and @xmath12 , whereas uncertainties due to the sfr are moderate because the background is dominated by redshifts @xmath63 where the sfr is reasonably well known , see fig . [ fig1 ] . the stochastic gw background from cosmological supernovae was studied recently in ref . @xcite , and its optimistic estimate is reproduced in fig . while the event rate @xmath18 used there is higher than in the present scenario ( since supposedly only a percent fraction of core collapse supernovae likely give rise to nss rotating rapidly enough to undergo phase transitions ) , the individual source signal is very different : in the phase transition scenario , the signal from one event at khz frequencies is much higher than the one due to convection in the simulations in ref . @xcite and , as a consequence , the total energy emitted in gws is much larger , @xmath64 versus @xmath65 . as a result , the background from phase transitions can be comparable or higher ( above @xmath66100 hz ) to the background from conventional type ii supernovae . there could also be an enhanced low frequency tail if the strain @xmath7 converges to a non - vanishing constant for @xmath67 due to anisotropic neutrino emission @xcite . for @xmath68khz , @xmath69 @xcite , where @xmath70 is the total energy emitted in neutrinos , and @xmath71 is the average dimensionless quadrupole . whereas @xmath72 is about an order of magnitude smaller than @xmath73erg in standard type ii supernovae , the anisotropy could be much larger than the order percent anisotropy expected in hot nss without phase transition @xcite . this is because the ns would oscillate strongly and be highly deformed after the phase transition . in one of the simulations in ref . @xcite , for example , the ratio of the polar to equatorial radius is @xmath74 . as in core collapse supernovae , the neutrinos would likely be partially trapped and emitted from a neutrinosphere because the release of @xmath75erg in internal energy would heat up the ns to @xmath76mev . we can parametrize the low - frequency tail as @xmath77 the maximum of this tail , corresponding to the fiducial values in eq . ( [ low - f ] ) is shown in fig . [ fig2 ] and reflects the uncertainty in the low - frequency signal : in the absence of a `` gw memory effect '' , @xmath78const , see eq . ( [ tilde_h ] ) and thus @xmath79 for @xmath80 , see eqs . ( [ egw ] ) and ( [ los ] ) . in contrast , in the presence of burst with memory @xmath81const and @xmath82 for @xmath80 . . the solid line represents that part of the ns - ns coalescence signal from ref . @xcite which has a `` popcorn''-character , similar to the phase transition scenario considered here , see below . the dotted line corresponds to gws from r - mode instabilities emitted by the fastest rotating nss @xcite , assumed to constitute a fraction @xmath83 of all nss . the dashed line shows the magnetar scenario @xcite.,scaledwidth=80.0% ] fig . [ fig3 ] shows various other astrophysical backgrounds for comparison : the solid line shows a possible popcorn like signal from ns - ns coalescence @xcite . we note that other work used a lower maximal frequency which would cut off the signal above @xmath84hz @xcite . the dotted line shows a stochastic background from r - mode instabilities emitting gws between @xmath37hz and @xmath85khz . it has been corrected by the small fraction @xmath86 of all nss nowadays believed to be born with sufficiently small , millisecond scale rotation periods , in contrast to the original refs . @xcite which assumed that a substantial fraction of all nss are born with" +"the aim of ultrarelativistic heavy - ion collision experiments at bnl rhic and at cern lhc is to understand the properties of very hot and dense partonic matter expected to be formed in these collisions . one of the objectives of such experiments is the identification and investigation of a phase transition from hadronic matter to what is known as the quark - gluon plasma ( qgp ) . the hard jets created in hard parton scattering in the initial stages of heavy - ion collision will pass through the hot and dense matter and lose energy by collisional and radiative processes . this phenomenon is known as jet quenching where the high @xmath2 hadrons production has been found to be strongly suppressed @xcite . other very important experimental evidence for the jet energy loss is the dihadron azimuthal correlation . the jet induced hadron pair distribution at rhic shows a double peak structure in the away side @xcite for the intermediate @xmath2 particle . however , it is unclear how the parton - medium interaction affects the distribution . the possible explanation of this observation is that the coupling of jets to a strongly interacting medium may modify the angular distribution @xcite . in this scenario the partonic jets traveling through the qgp leads to formation of mach cones @xcite , cerenkov radiation @xcite and wakes @xcite , which may be observables as collective excitation of the medium . apart from the jet quenching many other signals of this nascent phase of matter have been proposed . these include electromagnetic probes ( photon and dilepton ) @xcite , @xmath3 suppression @xcite , collective flow @xcite and so on . however , the main difficulty in studying these probes lies in the determination of the initial conditions , such as , the isotropization / thermalization time vis - a - vis the initial temperature . in this sense , many properties of the qgp are poorly understood . the most pertinent question is whether the matter produced in relativistic heavy - ion collisions is in thermal equilibrium or not . the collective flow patterns observed at the rhic provide strong evidence for rapid thermalization at less than 1 fm / c after the collision @xcite . on the other hand , using second - order transport coefficients consistent @xcite with conformal symmetry it has been found that the thermalization time has sizable uncertainties due to poor knowledge of the proper initial conditions . plasma instabilities have been suggested to a play a major role in the isotropization process @xcite . shortly after the collision , the rapid expansion of the matter along the beam direction causes faster cooling in the longitudinal direction than the transverse direction , leading to @xmath4 @xcite i.e. , the phase space distributions of plasma particles become anisotropic in momentum space . at some later time , the system returns to an isotropic state due to the effect of the parton interactions which overcomes the plasma expansion rate . therefore , it has been suggested to look for some observables which are sensitive to the early time after the collision . the effect of pre - equilibrium momentum anisotropy on various observables has been studied extensively in the last few years . the collective modes in an aqgp has been investigated in refs . the energy loss of parton in an aqgp has been studied in refs . the effect of anisotropy on the photon and dilepton yield have been investigated rigorously in refs . @xcite . when a high energy jet propagates through plasma , apart from the energy loss , it produces a wake in the plasma . the current and charge density wakes induced by a jet propagating in an isotropic and homogeneous qgp have been investigated by ruppert and muller @xcite . in the high temperature regime , the result shows the wake in both the induced charge and current density due to the screening color charge cloud , but no mach cones appear . on the other hand , in the quantum liquid scenario , if the jet travels supersonically , the wake exhibits an oscillatory behavior and mach cones can appear . however , using the htl approximation , the wake in the induced charge density shows an oscillatory nature in the backward direction at large parton velocity @xcite in case of isotropic plasma . the color response wake in viscous media has been investigated in ref . @xcite . in a previous paper @xcite we studied the wake induced by the jet propagating through the anisotropic plasma . when the parton moves along the anisotropy direction with velocity less than the average plasmon speed ( @xmath5 ) , the anisotropy effect causes a small oscillation of the induced charge density . anisotropy amplifies the oscillatory behavior of the wake potential in the backward space when parton moves along the beam direction with velocity @xmath6 . however , we do not find any oscillatory nature of the wake potential , when the parton moves in the transverse plane with respect to the anisotropy axis . in all the above works the effect of collision has been neglected . the inclusion of collision in the boltzmann equation and its subsequent effect on the wake potential has been investigated in ref . @xcite assuming isotropic plasma . it is found that in case of collisional isotropic plasma , the wake behavior is less pronounced than in isotropic plasma @xcite . now we investigate the wake behavior of the plasma by taking into account collisions in the aqgp . the effect of the collision can easily be taken into account by approximating the collision term in the boltzmann equation with the bgk description @xcite . in this approach , the dielectric function has been calculated in isotropic plasma @xcite and the collective modes of anisotropic collisional plasma @xcite have also been investigated when the wave vector is parallel to the anisotropy direction . by using the bgk collisional kernel , we calculate the dielectric response function of a collisional aqgp for small anisotropy limit . based on this dielectric function , we will investigate the wake potential induced by a fast parton traveling through the collisional anisotropic medium . the organization of the paper is as follows . in sec . ii , we derive the dielectric response function for collisional anisotropic qgp . in sec . iii we use the dielectric function to determine the wake potential in collisional aqgp and discuss the numerical results . finally , we conclude in sec . to obtain the gluon polarization tensor of a collisional qgp , we start from the boltzmann transport equation : v._xf^i_a(p , x)+g^i v_f^_a(x ) _ ^(p)f^i(*p * ) = c^i_a(p , x ) , where @xmath7 , @xmath8 and @xmath9 . @xmath10 $ ] is the gluon field strength tensor with gauge field @xmath11 or @xmath12 , where @xmath13 , @xmath14 with @xmath15 are the @xmath16 group generators in the fundamental and adjoint representations with @xmath17 = \frac{1}{2}\delta^{ab}$ ] , @xmath18 = n_c\delta^{ab}$ ] and @xmath19 is the coupling constant . the scalar functions @xmath20 are found by the projections : @xcite f^q/|q_a(p , x ) & = & 2 tr[_a n^q/|q(p , x ) ] , + f^g_a(p , x ) & = & [ t_a n^g(p , x ) ] , with the colorless background fields @xmath21 and @xmath22 . @xmath23 and @xmath24 are unit matrices in the fundamental and adjoint representation , respectively . the scalar functions @xmath25 are also found by projections : f^q/|q(*p ) & = & [ n^q/|q(p , x ) ] , + f^g(*p ) & = & [ n^g(p , x ) ] . in this paper , we will concentrate on the soft scale , i.e. , @xmath26 . the gauge field fluctuation is @xmath27 and the derivatives are of the order @xmath28 . we can neglect the higher order coupling constant and correspondingly @xmath29 and @xmath30 . the bgk collisional term @xmath31 @xcite can be represented as c^i_a(p , x ) = -with @xmath32 . this bgk collision term corresponds to an improvement of the relaxation time approximation for the collision term of the boltzmann equation @xcite . the collision rate @xmath1 is independent of velocity and particle species . we define the particle number as , n^i_a(x ) = _ * p*f^i_a(p , x ) , n^i_eq = _ * p*f^i_eq(|*p*| ) = _ * p*f^i(*p * ) , with @xmath33 . thus the transport equation reads as : v._xf^i_a(p , x)+g^i v_f^_a(x ) _ ^(p)f^i(*p * ) = -after fourier transformation of @xmath34 and @xmath35 , the above equation can be written as : f^i(p , k ) & = & + & = & f_0^i(p , k)+id^-1(k,*v * , ) _ * p*^f_0^i(p^,k ) + & + & id^-1(k,*v * , ) _ * p*^f^i_eq(*p*^)d^-1(k,*v*^ , ) _ * p*^f^i_0(p^,k ) + ... + & = & f_0^i(p , k)+id^-1(k,*v * , ) ( k ) , where f_0^i(p , k ) = d^-1(k,*v * , ) with @xmath36 , @xmath37 and @xmath38 . * * the induced current for each particle species @xmath39 is j^i_ind a(k ) & = & g_*p*v^f^i_a(p , k ) + & = & g^2_*p*v^^_(p)f^i(*p * ) m_(k , v)d^-1(k,*v*,)a^_a(k ) + g^i(k , ) + & + & g^2_*p*v^f^i_eq(|*p*|)d^-1(k,*v * , ) _ i^-1(k , ) , with @xmath40 , @xmath41d^{-1}(k,{\bf v},\nu)$ ] and + @xmath42 . the total induced current is given by j^_ind a(k ) = 2n_c j^g _ ind a(k ) + n_f[j^q _ ind a(k)+j^|q _ ind a(k ) ] assuming the same distribution functions for the quarks and anti - quarks , the total induced current can be written as j^_ind a(k ) & = & g^2_*p*v^^_(p)f(*p * ) m_(k , v)d^-1(k,*v*,)a^_a(k ) + 2 n_cg ^g(k , ) + & + & g^2(i)v^d^-1(k,*v * , ) _ * p*^^_(p)f(*p*^ ) m_(k , v^)d^-1(k,*v*^,)w^-1(k,)a^_a(k ) + & + & 2in_cg^2 ^ 2v^d^-1(k,*v * , ) s^g(k,)w^-1(k,).[currentdensity ] where @xmath43 . from this expression of the total induced current the self energy can be obtained via ^_ab(k ) = which gives ^_ab(k ) & = & _ abg^2_*p * v^_^(p)f(*p * ) m^(k , v)d^-1(k,*v*,)+_abig^2v^d^-1(k,*v * , ) + & & _ * p*^_^(p)f(*p*^ ) m^(k , v^)d^-1(k,*v*^,)w^-1(k , ) , [ polarization ] which is a symmetric tensor , i.e. , @xmath44 and transverse , i.e. , @xmath45 . since @xmath46 is gauge invariant one can evaluate it in any gauge . in the following we shall evaluate it in the temporal axial gauge where @xmath47 . the anisotropic phase - space distribution function can be obtained from any isotropic distribution function by rescaling only in one direction in momentum space by changing the argument @xcite f(*p * ) = f_(*p * ) = f_iso(*p*^2+(*p.*)^2 ) , where @xmath0 is an adjustable parameter which represents the strength of the anisotropy and the direction of anisotropy is determined by @xmath48 ( assumed to be in the beam direction ) . @xmath49 is an arbitrary isotropic distribution function . using this distribution function , the gluon polarization tensor of a collisional qgp within the bgk approach , is given by @xcite ^ij(k ) & = & m_d^2 v^i d^-1(k,*v * , ) + & + & im_d^2(v^)^id^-1(k,*v*^ , ) d^-1(k,*v*,)w^-1(k , ) where @xmath50 is the isotropic debye mass , represented by m_d^2 = -^_0 dp p^2 . in the limit @xmath51 , the polarization tensor reduces to the self - energy in the anisotropic medium . using the proper tensor basis @xcite , one can decompose the self - energy into four structure functions as ^ij = a^ij + b^ij + c^ij + d^ij where a^ij & = & ^ij - , b^ij = , + c^ij & = & n^in^j , d^ij = k^in^j + kn^ik^j with @xmath52 which obeys @xmath53 and @xmath54 . the" +"the quantum mechanics without probability amplitude was proposed @xcite , leading to the possibility of quantum information processing more directly in terms of probability i.e discrete wigner function @xcite . in the same vein , it is exciting to explore quantum key generation @xcite with polarization correlation function or expectation value of two observers . in general , two observers @xmath0 and @xmath1 will have eigenvalues @xmath2 corresponding to photon detection at the transmitted or reflected port of their analyzers . the correlation function shared by them is @xmath3 , where @xmath4 is the joint probability of detecting a photon in observer @xmath0 and @xmath1 with their analyzers at @xmath5 and @xmath6 , respectively . the maximum / minimum values of @xmath7 are corresponding to correlated / anti - correlated outcomes of @xmath0 and @xmath1 such that the @xmath8 and the @xmath9 . there are totally four correlation functions @xmath10 , where n = 1 , 2 , 3 , 4 , available from intrinsic polarization correlation of weak coherent states @xcite , coherent light mixed with random noise field @xcite and coherent light fields @xcite . these four correlation functions have been demonstrated and used to perform bits correlations between two parties over a distance of 10 km , through a transmission fiber by using weak coherent states in ref.5 . one can predict the outcome of the other by guessing the @xmath11 through their projection angles and photon detection . the secure key bits between two observers @xmath0 and @xmath1 are then generated through sharing four bi - partite correlation functions and photon counting . the essence of the paper is to propose a new scheme for key generation based on single photons bi - partite correlation functions . the proposed experiment setting is similar to simplified epr protocol ( bbm92 ) @xcite , where the epr pairs are replaced with two weak coherent states prepared from a light source in the middle of alice and bob . the light source is two modes ( x , y ) weak coherent states combined through a beam splitter producing two spatially separated quantum channels . we have the product states at the input of the beam splitter such that @xmath12 along the y - direction and @xmath13 . the density matrix of the output state from the beam splitter is dependant on the integration over the phase space of p representation for the input product state . since the @xmath14 and @xmath15 are intrinsically correlated from the same laser , the integration over the phase spaces of @xmath14 and @xmath15 can produce the output state that is intrinsically entangled @xcite . one can see that , the beam splitter transforms the input state @xmath16 into inseparable output state @xmath17 , where @xmath18 is random modulated phase . the inseparable output state can provide four types of bi - partite correlation functions @xmath19 by manipulating the linear phase shifters in box 1 of alice . the security of this scheme is guaranteed by the fact that the nonorthogonality of the product coherent states , which can not be identified by a single measurement . the protocol is strictly depended on equal mean photon number in the mode ( x , y ) i.e. @xmath20 . we will discuss how this condition can restrict more than one photon in a coherent pulse in this protocol and hence to prevent the photon - number splitting attack . the single photons sent to alice and bob are called ancilla photon and signal photon , respectively . the scheme requires coincidence detection of ancilla photon at alice and signal photon at bob . the ancilla photon passes through / reflects from an analyzer at alice is registered as bit 1/0. the signal photon passes through / reflects from an analyzer at bob is denoted as yes/no of his guess on alice s key bit . yes did not mean that bob will have bit 1. it can be bit 0. alice and bob generate key bits through secure communication in the sense that the bit information is encoded on the @xmath21 not the state . we will discuss how the protocol is robust against intercept - resend attack . the security analysis of this scheme may well be different from current weak light protocols @xcite . in this paper , we first outline the sequence of steps for implementing key generation between alice and bob . then , we discuss the physics and experimental detail of each step . finally , we briefly discuss how the protocol can prevent the photon - number splitting and intercept - resend attacks . the proposed experiment setup is shown in fig.1 . the setting is similar to the bbm92 protocol , where the epr pairs are replaced with two mode and phase - modulated weak coherent states , which are intrinsic - correlated from a laser source in the middle of alice and bob . the two weak coherent states are distributed through two pulses within a bit period , which is phase modulated in an asymmetric mach - zehnder interferometer ( mzi ) . four bi - partite correlation functions @xmath22 are assigned into two groups @xmath23 , where @xmath24 and @xmath25 . alice will have the key bit 0 and 1 for the correlation functions @xmath26 and @xmath27 , respectively . alice can randomly choose the correlation function @xmath21 and then her key bits . bob guesses the correlation function based on his polarization angle of his analyzer and records the outcome of his measurement i.e. yes or no of his guess . after the signal transmission , alice then tells bob through classical channel about the sequence of groups @xmath28 that she has randomly chosen . bob can then know alice s key bit by the outcome of his measurement regardless he made a right or wrong guess , so doubling the raw key generation rate . to illustrate the scheme more systematically , we will discuss an example of the key generation as shown in fig.2 . @xmath29 : alice randomly chooses the @xmath30 or @xmath31 by choosing the waveplates combination in box 1 as shown in fig.1 . ( alice randomly chooses the @xmath11 is analog to choosing a random basis in bb84 . ) @xmath32 : alice fixes her polarizer at angle @xmath33 and records the valid detections of the ancilla photon in + spd3 and - spd4 as bit 1 or 0. @xmath34 : bob guesses on the @xmath11 by projecting his polarizer at angles @xmath35 . the @xmath36 means bob s guess on @xmath37 . the @xmath38 means bob s guess on @xmath39 . ( alice only chooses one polarization angle @xmath33 and bob chooses two polarization angles @xmath35 because of the shared @xmath11 . we do not need to perform the violation of bell inequality in ekert s protocol . and also , not like bbm92 , alice and bob do not need to measure the basis @xmath40 , @xmath41 of the incoming photon . ) @xmath42 : the outcomes of bob s guess through the valid detections of signal photon . yes means that the+ spd1 click or his guess is right . no means that the - spd2 click or his guess is wrong . however , bob did not know the alice s key bit yet . ( alternative : alice and bob can detect the presence of eve by broadcasting part of the results obtained by bob in step 3 and 4 . they did not leak any bit information to eve because alice will not announces the group information in step 5 for the exposed data . note that in bb84 , alice and bob announce their choice of bases , and bob never broadcast his result which is the key bit . ) @xmath43 : after the signal transmission , alice announces to bob through classical channel about the group of her choice @xmath44 , not revealing her choice of correlation function . @xmath45 : bob knows alice s key bit after he received the group information and verified with the record of his valid detection . to illustrate this , let s say for the first column , alice announces to bob that the group is @xmath46 . bob s guess on the group @xmath46 is @xmath47 , which is corresponding to bit 1. however , he knows that the guess is wrong through his valid detection in step 4 . from here , he knows alice s key bit is bit 0. ( the random choices of @xmath11 in alice and projection angle @xmath35 in bob did not need to discard half of the raw keys compared to bb84 where alice and bob have the wrong bases . ) we believe that this scheme can provide the raw key generation rate a factor of 2 higher than the bb84 @xcite and b92 @xcite , and double the communication distance as in the simplified epr ( bbm92 ) @xcite and the original ekert s protocol @xcite . we would outline the detail explanation of each step . the light source is located in the middle of alice and bob . a pulsed , @xmath48-polarized laser light with a polarizing beam splitter ( pbs ) is used to provide a weak coherent state @xmath49 with horizontal polarization and another weak coherent state @xmath15 with vertical polarization in an asymmetric mach - zehnder interferometer ( mzi ) . these coherent states are located at two time slots and combined through a perfect 50/50 beam splitter ( bs1 ) , producing two spatially separated beams , i.e. , beam 1 and beam 2 . the input state of the beam splitter is a product state of two mode weak coherent states @xmath50 , which is the prepared state for this protocol . the annihilation operators @xmath51 and @xmath52 are the input field operators for the beam splitter ( bs1 ) and for the coherent states @xmath14 and @xmath15 . the operator @xmath52 is phase - modulated with the phase @xmath53 as @xmath54 , where @xmath55 , and @xmath56 is randomly chosen . the @xmath57 is produced by a phase modulator at the short arm of the mzi . the annihilation operators @xmath58 and @xmath59 are the output field operators for the bs1 , which are sent through beam 2 to bob and beam 1 to alice , respectively . to distribute the operators @xmath60 and @xmath61 to alice and bob , we first place a polarizer at @xmath48 at each output of the bs1 so that two pulses are co - polarized within a bit period . the reason is two orthogonal polarized pulses may be vulnerable to eve attacks . to create single photon quantum channel between the source and bob , the beam 2 is attenuated to single photon level with the mean photon number per pulse @xmath62 . similarly , the beam 1 is further attenuated to single photon level with mean photon number per pulse @xmath62 . the co - polarized two pulses are sent through transmission fibers to alice s and bob s mzi , where the phase demodulators at the short arms induced a phase of @xmath63 . four pulses ( 2 in the x - mode and 2 in the y - mode ) are created within one bit period . the x - y mode ( @xmath64 ) in the middle time slot are used for key generation . the phase ( @xmath65 ) can be accomplished by making use of the phase coding @xmath66 system@xcite , which is proven to be more efficient secure encryption system over long distances . note that we apply phase coding @xmath66 system on a single photon level instead of mesoscopic coherent state . the random phase @xmath18 is unknown to bob and alice . with the assumption of low mean photon numbers for @xmath67 and @xmath68 , the two" +"empirical evidence is mounting that living systems and communities of them might operate at the vicinity of a critical point @xcite . criticality , with its concomitant scale invariance , power laws distributions , and extremely large correlations and response @xcite could be a possible source of functional advantages for biological systems@xcite . in particular , in the brain one of the flagships of the criticality hypothesis it could lead to maximal dynamic ranges , high sensitivity to stimuli , optimal transmission and storage of information , and very diverse dynamical repertoires @xcite . different mechanisms and scenarios have been described in the recent literature to explain how such a critical behavior comes about @xcite . on the other hand , some authors have argued that apparent criticality could be just an artifact of the attempt to fit overly simplified models to complex and highly heterogeneous systems @xcite . in a recent work with a fresh perspective @xcite , criticality has been shown to emerge in communities of individuals / agents trying to communicate with each other and creating a collective entity . this approach considers a community of individuals equipped with a ( genetic , neural , regulation ... ) network representing the internal configuration of each individual agent . the state of each of such networks is controlled by some parameters that completely determine the steady state probability distribution function of internal configurations . it is assumed that the state of each single agent is defined by such a probability distribution . each individual of the community tries to mimic , i.e. to infer or `` understand '' , the state of others within a community . with unexpected generality , under this dynamics , the community experiences a drift toward the critical point of the network dynamics , i.e. at the edge between ordered and disordered states . remarkably , this emerging criticality entails a large variability among individuals ; indeed , in the critical regime , small variations in parameter values are reflected in large state changes . this leads to the somehow surprising conclusion that individuals aiming at understanding each other in the best possible way thus having the possibility to coordinate their behavior and reactions end up exhibiting a large variability . naively , one could have anticipated that such individuals could have converged to an `` ordered phase '' in which a deterministic and fixed output would be easily predictable or , alternatively , to a `` disordered phase '' in which they all would be essentially random and alike . however , as shown in @xcite , such hypothetical solutions turn out to be unstable against fluctuations or noise , and the criticality is the only feasible outcome . in this paper , we present a variant of the model proposed in @xcite , which maintains the same phenomenology , but is formulated in a simpler setting . this allows us to characterize quantitatively the dynamics , being able to describe mathematically both the steady state and the transient under different conditions . using this simpler model , we elucidate how and why criticality comes about and investigate what are the roles of cooperation and competition among agents . the manuscript is structured as follows : in section [ sec : framework ] we outline the framework introduced in @xcite in a simple and concise way . in section [ sec : model ] , we describe a variant of the original model susceptible to mathematical analysis , while in section [ sec : results ] we study the attractors of such dynamics by employing a mathematical formalism which allows to map a community of interacting agents into an effective fokker - planck equation @xcite . finally , in section [ sec : nu ] we study a generalization of the model in which individuals can also cooperate or compete . consider a community of @xmath0 individuals / agents trying to imitate as much as possible the state of each other . each of these individuals is characterized by a set of @xmath1 internal computing units ( i.e. nodes of a network ) that , for simplicity , we assume to take binary values . therefore , the internal state of each single agent is fully characterized by the string @xmath2 . this state changes in time , @xmath3 , obeying some dynamical rules leading to a stationary probability distribution @xmath4 , where the @xmath5-dimensional variable @xmath6 accounts for all the parameters modulating the dynamics ( where @xmath5 is the dimension of the parameter space ) , as for instance the strength of couplings between network nodes . each individual agent ( i.e. its internal state ) is completely determined by the value of @xmath7 and , for simplicity , all individuals are assumed to be identical and to obey the same internal dynamical rules except , possibly , for the specific values of their internal parameters . in other words , each agent is characterized by its coordinates in a common parameter space . let us emphasize that the framework introduced here consists in a rather sketched idealization of specific biological systems , which aims at generality rather than specificity . however , to provide the reader with some intuition , one could think of a community of bacteria in which individuals are sensitive and responsive to others , and they reconfigure their internal state ( as described for instance by their gene regulatory networks , with intricate feedback mechanism between signals and gene state switches ) in order to behave similarly to others . this may be relevant in a variety of processes that require of ( or benefit from ) a collective response at the community level . the main goal of this work is to underline the non - trivial attractors that could emerge out of this type of `` imitation '' game at its relationship with criticality . certainly , our framework should be carefully adapted to describe specific biological problems . before proceeding and for the sake of self - consistency we briefly recall two basic concepts of information theory : the kullback - leibler divergence and the fisher information . readers familiar with these concepts can safely skip the following two paragraphs . * the kullback - leibler ( kl ) divergence * @xcite allows for quantifying the difference between two probability distributions . for instance , given the parameter sets @xmath7 and @xmath8 characterizing two probability distribution functions , the kl divergence from the second distribution to the first is defined as @xcite : @xmath9 where the average @xmath10 is taken over @xmath11 . in short , ( [ eq : kl ] ) measures the deficit of information when @xmath12 is used to approximate @xmath4 @xcite . importantly , the kl divergence constitutes a pseudo - distance , as it does not obey the triangle inequality , and is not symmetric as in general @xmath13 , except in the case in which both distribution are identical ( in which case the divergence vanishes ) . * the fisher information ( fi ) * is a measure of how _ distinguishable _ is a ( finite ) dataset extracted from a probability distribution from another one obtained with slightly different parameter values . for example , there could be a region in @xmath7 space in which @xmath4 are mostly invariant as we change @xmath7 , while in another regions the distribution could be highly sensitive to parameter changes . the fi is defined as @xcite : @xmath14 for @xmath15 . the determinant @xmath16 is a measure of the density of distinguishable distributions in parametric space ( as a function of @xmath7 ) @xcite . in particular , if @xmath16 peaks at @xmath17 , this corresponds to a region in the space of parameters @xmath7 in which distributions are highly sensitive to changes of the parameters . thus , it is not surprising that the fi exhibits a peak at critical points @xcite . to illustrate these concepts , without loss of generality , we can parametrize the internal probability distribution of agents as : @xmath18 where @xmath19 are the so - called `` observable '' functions ( i.e. functions of the internal configuration ) and @xmath20 . if , in particular , @xmath21 , the internal state of each agent corresponds to a mean - field ising model at some temperature @xcite . for such a parametrization , eq . ( [ eq : parametrization ] ) , the fi is @xmath22 , which corresponds to the generalized susceptibility , that is well - known to diverge at critical points . consequently , in terms of information theory , most distinguishable patterns are concentrated around the critical point @xcite . in what follows , we mainly work with two different parametrizations . the simplest one corresponds to the ( zero - field ) ising mean - field model @xcite : @xmath23 which has the advantage of having just only one free parameter @xmath24 ( usually interpreted as the inverse temperature ) and has a fi peaked at @xmath25 , which diverges at @xmath26 in the ( thermodynamic ) limit , @xmath27 . similarly , we also consider the mean - field ising model with an external field ( which has two parameters ) : @xmath28 which has a fi that diverges as @xmath27 at @xmath29 . this corresponds to i ) a line of first order phase transitions for @xmath30 and @xmath31 and ii ) a second order phase transition at @xmath30 and @xmath32 . as it will become clear in what follows , we are more interested in the second case as , for any finite system size @xmath1 , the maximum of the determinant of the fi is closer to @xmath33 ( i.e. the critical point of the second - order phase transition ) than to any other point along the discontinuous phase transition line . we use the notation @xmath34 for the critical point defined in the thermodynamic limit @xmath27 while @xmath35 is used for the maximum of @xmath16 in parameter space for any given size @xmath1 . we introduce a model , which is identical in spirit to the co - evolutionary model in @xcite but which , in contrast , enables for analytical understanding . here we discuss both the original and the modified models , stressing their similitudes and differences . both models consist of a community of @xmath0 individuals aiming at having an internal state / distribution as similar as possible to the others as quantified by their kl divergences to other individuals i.e. aiming at optimizing the information they have from the rest of the community , i.e. at minimizing its information deficit ( see fig . [ fig : model ] ) . in both cases , individual agents are characterized by an internal state ( probability distribution function ) parametrized as described in the previous section . all individuals are identical in principle , but they may differ in their parameter values . in the original model ( see `` coevolutionary model '' in @xcite ) the dynamics proceeded by randomly selecting at each time step a pair of agents ; given that the kl divergence is not symmetric , one of the two agents has a larger `` fitness '' ( i.e. it infers better the state of the other than the other way around ) and thus , as a consequence of this informational advantage , it has a larger probability of generating progeny . reversely , the less fit agent is more likely to die and be removed from the community , while the fittest one generates an offspring that inherits its parameter values with some small variability from it . this dynamical process is iterated in time , defining in this way a genetic algorithm . after sufficiently long time the stable output of this dynamics turned out to be" +"finite - dimensional manifolds , whether smooth , real- or complex - analytic , are commonly defined via charts and atlases . the other standard way of defining them relies on a dual point of view , focussing on the functions rather than on the points themselves , and this is achieved via a sheaf - theoretical approach . more precisely , a smooth @xmath0-dimensional manifold @xmath1 is then defined as a locally ringed space @xmath2 that is locally isomorphic to the locally ringed space @xmath3 . the sheaf - theoretical approach is hardly avoidable when one wants to deal with singular generalizations of manifolds ( varieties or schemes for instance ) , or with non - reduced situations "" , such as supermanifolds , where the rings of functions "" have nilpotents . in this last example , a section of the structural sheaf is not determined by its values on the points of the underlying topological space , which makes the sheaf - theoretical approach particularly relevant in defining supermanifolds . + in finite dimensions , the two definitions of manifolds ( via atlases and as certain locally ringed spaces ) are well - known to be equivalent . in infinite dimensions , the situation is quite different . infinite - dimensional manifolds , whether locally modeled on banach spaces , frchet spaces or general locally convex spaces , have almost always been defined in terms of charts and atlases . one reason for that is the belief , following the thesis of douady @xcite , that the sheaf of scalar - valued functions does not give sufficient information to define the morphisms ( contrary to the finite - dimensional case , where defining the smooth functions valued in @xmath4 suffices to determine the morphisms valued in @xmath5 for every natural number @xmath6 ) . in @xcite , mazet defines a category of infinite - dimensional analytic spaces , precisely in terms of ringed spaces . however , his category leads to pathologies ( such as the sum of two analytic maps not necessarily being analytic ) . douady avoids these pathologies by introducing a third approach for capturing the notion of space , which he uses to define his category of banach analytic spaces . namely , given a category @xmath7 , douady defines a _ @xmath7-functored space _ @xmath8 to be a pair @xmath9 where @xmath10 is a topological space , and @xmath11 is a covariant functor from @xmath7 to the category of sheaves of sets on @xmath10 . in this way , for every object @xmath12 in @xmath7 ( thought of as a possible target ) , one associates a sheaf of sets @xmath13 ( thought of as the sheaf of @xmath12-valued morphisms on @xmath10 ) . compared to a ringed space , a functored space encodes already in its structural functor "" the definition of the morphisms valued in any target space ( from a certain category ) . + the functored space approach obviously adds a supplementary technical layer "" , which can be felt already when defining the local models for banach analytic spaces ( as functored spaces ) . thus , unless the recourse to functored spaces is absolutely necessary , it is preferable to deal with the more traditional setting of ringed spaces , i.e. to associate only a single structure sheaf instead of a sheaf - valued functor to each space . we are thus lead to the question whether the insufficiency of the sheaf of scalar - valued functions pointed out by douady ( and the related pathologies ) appears also in the non - singular setting of infinite - dimensional smooth manifolds . + in this paper , we address this question by observing that the obstruction to define infinite - dimensional manifolds as ringed spaces boils down to the failure of a _ scalarwise smooth _ map between open sets of locally convex spaces to be smooth . more precisely , given two locally convex spaces @xmath14 and @xmath12 , and given an open subset @xmath15 of @xmath14 , we adopt a standard notion of smoothness for maps @xmath16 ( _ cf . _ definition [ bhmn ] ) , following bastiani , hamilton , milnor , neeb , ... then , a map @xmath17 is said to be _ scalarwise smooth _ if the function @xmath18 is smooth for every smooth function @xmath19 . the chain rule implies clearly that smooth maps are scalarwise smooth . the converse is easily seen to be true in finite dimensions ( just take the linear forms @xmath20 dual to a basis @xmath21 ) . in infinite dimensions , the converse is non - trivial . in the first main result of this paper ( theorem [ scalarwise smoothness implies smoothness ] ) , we prove that it is true whenever @xmath12 is mackey - complete and the mackey - closure topology on @xmath14 coincides with the given topology ( the necessary definitions will be recalled throughout the paper , but let us already note that the assumption on @xmath14 corresponds to a large class of locally convex spaces which contains frchet spaces and duals of frchet - schwartz spaces , and that every complete locally convex space is mackey - complete ) . in the second main result of the paper ( theorem [ smooth equals ringed morphism ] and corollary [ manifolds = structure sheaf - smooth manifolds ] ) , we show that for infinite - dimensional manifolds modeled on locally convex spaces @xmath14 satisfying the assumptions of theorem [ scalarwise smoothness implies smoothness ] , the definition via charts and atlases is equivalent to the definition via ringed spaces . finally , we complete our comparison of the various definitions of infinite - dimensional manifolds by showing that the definition via charts and atlases is equivalent to the one based on functored spaces . + our paper is organized as follows . in section 2 , we present a proof of the special case of theorem [ scalarwise smoothness implies smoothness ] , when the domain is @xmath4 . more precisely , we show that for a mackey - complete locally convex space @xmath14 , a curve @xmath22 is smooth if and only if it is scalarwise smooth . while this result and its idea of proof are not new ( compare @xcite ) , they are crucial to our proof of theorem [ scalarwise smoothness implies smoothness ] : we recall them in a concise but self - contained way for the convenience of the reader , which gives us also the opportunity to introduce our notations for the rest of the paper . in section 3 , we recall the definition of smooth maps that we will be using , and prepare and prove theorem [ scalarwise smoothness implies smoothness ] , using as an intermediate step the calculus of _ convenient smoothness _ studied by kriegl and michor . in section 4 , we present in detail the three definitions of infinite - dimensional manifolds under investigation here , and prove the comparison results ( theorem [ smooth equals ringed morphism ] and corollary [ manifolds = structure sheaf - smooth manifolds ] ) mentioned above . + _ acknowledgements . _ we would like to thank alexander alldridge for discussions on douady s espaces foncts "" . the goal of this section is to recall the proof of the following result : if @xmath23 is a map from @xmath4 to a complete real ( hausdorff ) locally convex space @xmath14 , and @xmath24 is the continuous dual of @xmath14 , then smoothness of @xmath25 for every @xmath26 implies the smoothness of @xmath23 ( theorem [ weak smoothness of curves ] ) . while this is obvious if @xmath14 is finite - dimensional ( it is enough to take the projections @xmath27 where @xmath28 is an arbitrary basis of @xmath14 ) , proving that it remains true in the general case requires more work . the strategy ( essentially taken from @xcite ) , is the following . + in any locally convex space , there is a natural notion of bounded set . the collection of these bounded sets ( the von neumann bornology "" ) is not very sensitive to the locally convex topology : a classical theorem of mackey in functional analysis shows that if one varies the topology while keeping the same dual space , the bounded sets remain the same . as a consequence , one can view the bounded sets from the perspective of the weak topology instead of the given topology . in the weak topology , it is natural and immediate that a subset of @xmath14 whose image by every linear functional is bounded must be itself bounded . + on the other hand , for curves , being @xmath29 is ultimately a bornological concept : the @xmath29 curves remain the same if one changes the locally convex topology , while keeping the same underlying bornology . this follows from the fact that a @xmath30 curve is locally lipschitz ( by the mean value theorem ) , and the lipschitz condition ( which is essentially bornological ) , implies continuity . translating smoothness in terms of lipschitz conditions ( involving bounded sets ) , it becomes possible to use the dual characterization of boundedness given by mackey s theorem , to obtain a dual characterization of smoothness . + in what follows , we recall , for the convenience of the reader and for later reference , the details of the above arguments , starting with mackey s theorem , the cornerstone in proving theorem [ weak smoothness of curves ] as well as other results in this paper . for a proof of the former theorem , see , e.g. , theorem 36.2 in @xcite or theorem 8.3.4 in @xcite . + ( mackey s theorem ) let @xmath14 be a locally convex space , and @xmath31 a subset of @xmath14 . if @xmath32 is bounded for every @xmath26 , then @xmath31 is bounded . + let @xmath14 be a locally convex space , and @xmath22 a curve . 1 . if @xmath33 is an open subset of @xmath4 , we say that @xmath23 is * lipschitz * on @xmath33 if the @xmath34 is bounded in @xmath14 . we say that @xmath23 is * locally lipschitz * if every point in @xmath4 has a neighborhood on which @xmath23 is lipschitz . + let @xmath14 be a locally convex space , and @xmath22 a curve . for @xmath35 , we say that @xmath23 is * of class @xmath36 * if all the derivatives of @xmath23 up to order @xmath6 exist , and @xmath37 is locally lipschitz . + if @xmath38 is any subset of @xmath14 , we will denote by @xmath39 the absolute convex hull of the closure of @xmath38 . we will need the following version of the mean value theorem , for curves in a locally convex space . + ( mean value theorem ) let @xmath14 be a locally convex space , and @xmath40\longrightarrow e$ ] a curve which is continuous on @xmath41 $ ] , and differentiable on @xmath42a , b[$ ] . then @xmath43 * proof :* _ cf . _ @xcite , i.1.4 . @xmath44 + let @xmath14 be a locally convex space , and @xmath22 a curve which is differentiable on an open interval @xmath45 . if @xmath46 is bounded on @xmath33 , then @xmath23 is lipschitz on @xmath33 . * proof :* let @xmath47 with @xmath48 . by the mean value theorem , @xmath49 so @xmath50 , and this last set is bounded since the absolute convex hull of any bounded set is bounded . @xmath44 + [ c^k and lip^k ] let @xmath14 be a locally convex space , and @xmath22 a curve . 1 . if @xmath23 is of class @xmath51 , then @xmath23" +"about 80 years of experimental observations and theoretical arguments have pointed out that a large fraction of the universe is composed by dark matter particles . @xmath3 @xmath4 ( mog ) and @xmath5 @xmath6 @xmath7 ( mond ) ; they hypothesize that the theory of gravity is incomplete and that a new gravitational theory might explain the experimental observations . mond modifies the law of motion for very small accelerations , while mog modifies the einstein s theory of gravitation to account for an hypothetical fifth fundamental force in addition to the gravitational , electromagnetic , strong and weak ones . however , e.g. : i ) there is no general underlying principle ; ii ) they are generally unable to account for all small and large scale observations ; iii ) they fail to reproduce accurately the bullet cluster ; iv ) generally they require some amount of dm particles as seeds for the structure formation . ] the presently running dama / libra ( @xmath8 250 kg of full sensitive target - mass ) @xcite experiment , as well as the former dama / nai ( @xmath8 100 kg of full sensitive target - mass ) @xcite , has the main aim to investigate the presence of dm particles in the galactic halo by exploiting the model independent dm annual modulation signature ( originally suggested in ref . @xcite ) . as a consequence of the earth s revolution around the sun , which is moving in the galaxy with respect to the local standard of rest towards the star vega near the constellation of hercules , the earth should be crossed by a larger flux of dm particles around @xmath8 2 june and by a smaller one around @xmath8 2 december . in the former case the earth orbital velocity is summed to the one of the solar system with respect to the galaxy , while in the latter the two velocities are subtracted . this dm annual modulation signature is very distinctive since the effect induced by dm particles must simultaneously satisfy all the following requirements : the rate must contain a component modulated according to a cosine function ( 1 ) with one year period ( 2 ) and a phase that peaks roughly @xmath8 2 june ( 3 ) ; this modulation must only be found in a well - defined low energy range , where dm particle induced events can be present ( 4 ) ; it must apply only to those events in which just one detector of many ( 9 in dama / nai and 25 in dama / libra ) actually `` fires '' ( _ single - hit _ events ) , since the dm particle multi - interaction probability is negligible ( 5 ) ; the modulation amplitude in the region of maximal sensitivity must be @xmath8 7% for usually adopted halo distributions ( 6 ) , but it can be larger ( even up to @xmath8 30% ) in case of some possible scenarios such as e.g. those in ref . thus , this signature is model independent and very effective ; moreover , the developed highly radio - pure nai(tl ) target - detectors @xcite and the adopted procedures assure sensitivity to a wide range of dm candidates ( both inducing nuclear recoils and/or electromagnetic radiation ) , interaction types and astrophysical scenarios . in particular , the experimental observable in dama experiments is the modulated component of the signal in nai(tl ) target and not the constant part of it as in other approaches as those by cdms , xenon , etc . , where in addition e.g. : i ) different target materials are used ; ii ) the sensitivity is mainly restricted to candidates inducing just nuclear recoils ; iii ) many ( by the fact largely uncertain ) selections / subtractions of detectors and of data and ( highly uncertain ) extrapolations of detectors features are applied . the dm annual modulation signature might be mimicked only by systematic effects or side reactions able to account for the whole observed modulation amplitude and to simultaneously satisfy all the requirements given above . no one is available or suggested by anyone over more than a decade @xcite . it is also worth noting that the dm annual modulation signature acts itself as a strong background reduction as pointed out since the early paper by ref . @xcite , and especially when all the above peculiarities can be experimentally verified in suitable dedicated set - ups as it is the case of the dama experiments . the total exposure of dama / libra phase1 is : 1.04 ton @xmath1 yr in seven annual cycles ; when including also that of the first generation dama / nai experiment it is @xmath0 ton @xmath1 yr , corresponding to 14 annual cycles . the variance of the cosine during the dama / libra phase1 data taking is 0.518 , showing that the set - up has been operational evenly throughout the years @xcite . many independent data analyses have been carried out @xcite and all of them confirm the presence of a peculiar annual modulation in the _ single - hit _ scintillation events in the 2 - 6 kev energy interval , which in agreement with the requirements of the dm signature is absent in other parts of the energy spectrum and in the _ multiple - hit _ scintillation events in the same 2 - 6 kev energy interval ( this latter condition correspond to have switched off the beam "" of dm particles ) . all the analyses and details can be found in the literature given above . in particular , fig . [ fg : res ] shows the time behaviour of the experimental residual rates of the _ single - hit _ scintillation events for dama / nai @xcite and dama / libra phase1 @xcite cumulatively in the ( 26 ) kev energy interval . the data points present the experimental errors as vertical bars and the associated time bin width as horizontal bars . the superimposed curve is the cosinusoidal function @xmath9 with a period @xmath10 yr , a phase @xmath11 day ( june 2@xmath12 ) and modulation amplitude , @xmath13 , equal to the central value obtained by best fit on the data points . the dashed vertical lines correspond to the maximum expected for the dm signal , while the dotted vertical lines correspond to the expected minimum . the major upgrades are also pointed out . in order to continuously monitor the running conditions , several pieces of information are acquired with the production data and quantitatively analysed . in particular , all the time behaviours of the running parameters , acquired with the production data , have been investigated : the modulation amplitudes obtained for each annual cycle when fitting the time behaviours of the parameters including a cosine modulation with the same phase and period as for dm particles are well compatible with zero . in particular , no modulation has been found in any possible source of systematics or side reactions ; thus , cautious upper limits ( 90% c.l . ) on possible contributions to the dama / libra measured modulation amplitude have been derived ( see e.g. @xcite ) . it is worth noting that they do not quantitatively account for the measured modulation amplitudes , and are not able to simultaneously satisfy all the many requirements of the signature . similar analyses have also been carried out for the dama / nai data@xcite . no other experimental result has been verified over so long time so accurately and with various significant upgrades of the set - ups . for completeness i mention that sometimes naive statements were put forwards as the fact that in nature several phenomena may show some kind of periodicity . the point is whether they could mimic the annual modulation signature in dama / libra ( and former dama / nai ) , i.e. whether they could quantitatively account for the observed modulation amplitude and also simultaneously satisfy all the requirements of the dm annual modulation signature . the same is also for side reactions . this has already been deeply investigated in ref . @xcite and references therein ; the arguments and the quantitative conclusions , presented there , also apply to the entire dama / libra phase1 data . additional arguments can be found in ref . in particular , ref . @xcite further outlines in a simple and intuitive way why neutrons ( of whatever origin ) , muons and solar neutrinos can not give any significant contribution to the dama annual modulation results and in addition can never mimic the dm annual modulation signature since some of its specific requirements fail . table [ table : tab12 ] summarizes the safety upper limits on the contributions ( if any ) to the observed modulation amplitude due to the total neutron flux at lngs , either from @xmath14,n ) reactions , from fissions and from muons and solar - neutrinos interactions in the rocks and in the lead around the experimental set - up ; the direct contributions of muons and solar neutrinos are also reported there . as seen in table [ table : tab12 ] , they are all negligible and they can not give any significant contribution to the observed modulation amplitude ; in addition , neutrons , muons and solar neutrinos are not a competing background when the dm annual modulation signature is investigated since they can not mimic this signature . for details see ref . @xcite and references therein . in conclusion , dama gives a model - independent evidence at 9.3@xmath2 c.l . over 14 independent annual cycles for the presence of dm particles in the galactic halo . no direct model independent comparison is possible in the field when different target materials and/or approaches are used ; the same is for the strongly model dependent indirect searches 400 ) of the density ; ii ) to boost the annihilation cross section through an assumed new interaction type ; iii ) to adjust the propagation parameters ; iv ) to consider extra - source ( subhalos , imbhs ) ; v ) to consider only a leptophilic candidate to justify the absence of any excess in the antiproton spectrum . finally , other well known sources can account for a similar positron fraction : pulsars , supernova explosions near the earth , snr . ] . in order to perform corollary investigations on the nature of the dm particles , model - dependent analyses are necessary . thus , many theoretical and experimental parameters and models are possible ( see e.g. in @xcite ) and many hypotheses must also be exploited , while specific experimental and theoretical assumptions are generally adopted in the field assuming a single arbitrary scenario without accounting neither for existing uncertainties nor for alternative possible scenarios , interaction types , etc . the obtained dama 9.3 @xmath2 c.l . model independent evidence is compatible with a wide set of scenarios regarding the nature of the dm candidate and related astrophysical , nuclear and particle physics . for examples some scenarios and parameters are discussed e.g. in ref . further large literature is available on the topics ( see for example in the bibliography of ref . @xcite ) . by the fact , both the negative results and all the possible positive hints are largely compatible with the dama model - independent dm annual modulation results in various scenarios considering also the existing experimental and theoretical uncertainties ; the same holds for the strongly model dependent indirect approaches . it is also worthwhile to further recall that these dama experiments are not only sensitive to dm particles with spin - independent coupling inducing just nuclear recoils , but also to other couplings and" +"the stochastic alpha , beta , rho ( sabr ) model introduced by hagan , kumar , lesniewski and woodward in @xcite is now a key ingredient and has become an industry standard on interest rates markets @xcite . it is defined by the pair of coupled stochastic differential equations @xmath0 where @xmath1 , @xmath2 , @xmath3 , and @xmath4 and @xmath5 are two correlated brownian motions on a filtered probability space @xmath6 . its popularity arose from a tractable asymptotic expansion of the implied volatility ( derived in @xcite ) , and from its ability to capture the observed volatility smile ; calibration therefore being made easier using the aforementioned expansion . in today s low interest rate and high volatility environment , the implied volatility obtained by this very expansion can however yield a negative density function for the price process @xmath7 in , therefore exhibiting arbitrage . this problem of negative density in low interest - rate environments has been directly addressed by hagan et . al @xcite , balland and tran @xcite , and andreasen and huge @xcite , who proposed modifications of the original sabr model . there exist several refinements to the asymptotic formula itself : in @xcite obj fine tunes the leading order , and paulot @xcite provides a second - order term . in certain parameter regimes the exact density has been derived for the absolutely continuous part ( on @xmath8 ) of the distribution of @xmath7 : in the uncorrelated case @xmath9 , formulae were obtained in @xcite by applying time - change techniques . the correlated case is much harder , and approximations have been derived using projection methods in @xcite , and using geometric tools in @xcite . barring computational costs , availability of the distribution of the sabr process is equivalent to computing any european prices . this however calls for a computation , not only on the continuous part of the distribution ( on @xmath10 ) , but also of its singular part at the origin . absorbing boundary conditions at the origin ensure ensure that the forward rate process @xmath7 is a true martingale , and the singular part can hence accumulate mass , depending on the starting value of the process , the parameter configuration and the time horizon . the original asymptotic formula typically loses accuracy for long - dated derivatives , when the cev exponent @xmath11 is close to zero , or when the volatility of volatility @xmath12 is large . the parameter @xmath11 governs the dynamics of the smile , and small values thereof are usually chosen when the asymptotic formula fails , namely on markets where the forward rate is close to zero and for long - dated options @xcite . indeed , it comes as no surprise that the orginal formula which is an asymptotic expansion for small values of @xmath13breaks down for large maturities , but it is well known that the reasons for the inconsistencies of the sabr formula are subtler than that . what we highlight here is that the mass at zero can be held accountable for the irregularities in this case as well . while standard numerical methods proved reliable when the process remains strictly positive , computing the probability mass of the sabr model at the origin is a more delicate issue . due to the singularity at the origin , usual regularity assumptions ensuring stability of numerical techniques ( finite differences or monte carlo ) are violated at this point , and a rigorous error analysis for these methods is not ( yet ) available . in addition , producing reference values becomes computationally intensive for short time scales . since much of the popularity of the sabr model is due to the tractability of its asymptotic formula , one should aim at preserving it while taking into account the mass at zero . the parameter sets @xmath9 or @xmath14 are the most tractable , and in fact ( as observed in @xcite ) the only ones where certain advantageous regularity properties of the sabr process can be expected . we therefore concentrate here on the singular part of the distribution for these regimes , that is , we study the probability @xmath15 and provide tractable formulae and asymptotic approximations . the relevance of these parameter configurations is emphasized by recent results @xcite , which suggest a so - called ` mixture ' sabr ( a combination of the @xmath9 and @xmath14 cases ) approach to handle negative interest rates in an arbitrage - free way . from a modelling perspective , one may question the relevance of an absorbing boundary condition at zero in a financial context , where negative rates can actually occur . in fact , from a stochastic analysis perspective , when @xmath14 there is no need to impose such a boundary condition . remarkably however , as pointed out in @xcite , even in market conditions where interest rates become negative , the historical evolution of interest rates suggests that their dynamics follow processes whose probability distribution exhibit a singularity at the origin , which makes the computation of the mass at zero rates relevant for these market scenarios as well . a further application is a direct approximation of the left wing of the implied volatility smile . in order to understand the small - strike behaviour of the sabr smile it is essential to determine the probability mass at the origin : asymptotic approximations of the implied volatility are available , not only for small and large maturities , but also for extreme strikes . roger lee s celebrated moment formula @xcite subsequently refined by benaim and friz @xcite and gulisashvili @xcite relates the behaviour of the implied volatility @xmath16 for small strike @xmath17 and maturity @xmath18 to the behaviour of the price process @xmath7 around the origin . de marco , hillairet and jacquier @xcite , and later gulisashvili @xcite , showed that when the underlying distribution has an atom at zero , the small - strike behaviour of the implied volatility is solely determined by this mass , irrespective of the distribution of the process on @xmath8 . we shall numerically confirm this in the ( uncorrelated ) sabr model , using approximations of the probability mass , in agreement with @xcite . in section [ sec : masszero ] we derive explicit formulae for the mass at zero @xmath15 in the sabr model for finite time as well as for large times in the uncorrelated case . under this assumption , it is possible to decompose the distribution into a cev component and an independent stochastic time change . such time change techniques have been applied to the sabr model in the uncorrelated case in @xcite to determine the exact distribution of the absolutely continuous part of the distribution on @xmath8 . therefore , our formulae complement these by providing the singular part of the distribution ( see @xcite for more details about time change techniques in stochastic volatility models ) . in section [ ss : smalltime ] and section [ section : largetimeuncor ] , we derive asymptotic expansions for the density of time - changed brownian motion inspired by the works of borodin and salminen @xcite , gerhold @xcite and matsumoto and yor @xcite which we use to derive the behaviour of the atom at the origin for short and large times . finally , in section [ sec : impliedvolatility ] , we use these results to determine the left wing ( small strikes ) of the sabr implied volatility . using the formulae provided in @xcite , we highlight the fact that some of the widely used expansions exhibit arbitrage in the left wing , and propose a way to regularise them in this arbitrageable region . the price process @xmath7 in is a martingale ( * ? ? ? * remark 2 ) . if we consider @xmath7 on the state space @xmath19 , the origin , which can be attained , has to be absorbing ( * ? ? ? * chapter iii , lemma 3.6 ) . for two functions @xmath20 and @xmath21 , we shall write @xmath22 as @xmath23 tends to zero whenever @xmath24 . in the case where the correlation coefficient @xmath25 is null , the mass at the origin can be computed semi - explicitly . conditioning on the path of the volatility process @xmath26 , the resulting process @xmath27 satisfies the cev stochastic differential equation @xmath28 starting from @xmath29 , where @xmath30 is a deterministic time - dependent volatility coefficient , and represents , for fixed @xmath31 , a realisation of the paths of @xmath26 . consider now the simple cev equation @xmath32 starting from @xmath33 , and set @xmath34 then @xmath35 , where @xmath5 is a bessel process satisfying the sde ( * ? ? ? * subsection 1.1 ) @xmath36 by it s formula , the process @xmath37 solves the same sde , so that @xmath38 , and therefore @xmath39 . it follows that @xmath7 can be obtained from @xmath40 using the stochastic time change @xmath41 , namely @xmath42 . since this time change is independent of @xmath40 , one can decompose the mass at zero of the sabr model into that of the cev component at zero and the density of the time change : @xmath43 where the mass at zero in the cev model is given by ( see @xcite or ( * ? ? ? * section 6.4.1 ) ) @xmath44 with @xmath45 , the normalised lower incomplete gamma function : @xmath46 . if @xmath47 in , the origin is naturally absorbing , and the mass at zero is given by . when @xmath48 , the solution to is not unique , and a boundary condition at the origin has to be imposed . should one consider the origin to be reflecting , the transition density would then become norm preserving , and no mass at the origin would be present . however , it is easy to see that there is an arbitrage opportunity if the origin is reflecting . formula carries over to the case @xmath48 when the origin is assumed to be absorbing , which we shall always consider from now on . this is of course in line with ( * ? ? ? * chapter iii , lemma 3.6 ) , mentioned above , which states that the origin has to be absorbing for a non - negative supermartingale . since for each @xmath49 , @xmath50 is lognormally distributed , we can write @xmath51 where @xmath52 , @xmath53 ; the density of this functional is given by ( * ? ? ? * formula 1.10.4 ) @xmath54 where the function @xmath55 is defined as @xcite : @xmath56 and where the kummer function @xmath57 reads @xmath58 we now study the behaviour of the mass at zero @xmath59 as time becomes small . the main challenge is to provide a short - time asymptotic formula for the density of the time change process , for which standard expansion techniques are not applicable . the additive functional arising from the density of an integral over the exponential of brownian motion often appears in the pricing of asian options and is of interest on its own . this density is notoriously difficult to evaluate in small time , due to a highly oscillating factor connected to the hartman - watson distribution @xcite and ( * ? ? ? * section 4.6 ) . these numerical issues are discussed in @xcite , and gerhold @xcite used saddlepoint methods to provide short - time estimates . because of the time change and the complexity of the kummer function ( in the integrand ) , small - time asymptotics of the mass at zero can not be estimated directly . instead , we use an inverse laplace transform approach , inspired by @xcite , to provide small -" +"up to now , scanning gate microscopy ( sgm ) has been successfully used to image local electron transport in various mesoscopic systems . in early applications , sgm probed the interference effects produced by microscopic disorder in graphene , @xcite and it was later applied to image electron - hole puddles originating from extrinsic local doping . @xcite in the later experiment , @xcite the tip was coated with a dielectric and placed directly in contact with graphene . the advantage of this approach is that afm topography scans could be performed simultaneously with sgm scans , and the tip could be additionally used to clean the sample . scanning technique was used in ref . to study the spatial inhomogeneity of the local neutrality point , and to measure the efficiency of intentionally embedding ( writing ) charges in graphene . @xcite tip - dependent resistance map of a narrow quantum point contact ( qpc ) , presented in ref . , revealed a significant resistance increase when the tip was placed directly above the sample . the technique is also suitable for the investigation of localization effects . for example , concentric conductance halos were observed in sgm maps scanned around localized states in graphene quantum dots , @xcite narrow constrictions , @xcite and enhanced conductance was reported in narrow nanoribbons . @xcite scanning gate experiments in quantum point contacts were simulated in ref . . in this paper , we investigate the scanning gate experiments of the magnetic focusing devices reported in refs . . before , similar magnetic focusing measurements were performed on semiconductor two - dimensional electron gas ( 2deg ) in parallel with the scanning technique . @xcite we model our device using both quantum and classical transport theory . previously , classical simulation of such a focusing device was done in ref . , and focusing without sgm tip was studied in ref . . a recent paper by kolasiski _ et al . _ @xcite was the first to reproduce some of the experimental findings by applying a full quantum approach . here , we implement the multi - terminal landauer - bttiker formalism to calculate the non - local resistances . we additionally compare the resistance maps of 4-terminal and 6-terminal devices for different combinations of voltage probes . due to the large size of the device , as compared to the electron wavelength , most of the simulated effects can already be captured by the computationally less demanding classical model . in respect to that , we confirm that the classical billiard model can be successfully used to describe transport of relativistic carriers in the presence of inhomogeneous potentials , if the linear graphene spectrum is properly implemented . our analysis of simulated sgm maps confirms and expands on some of the experimental observations reported in refs . . we consider both positively and negatively charged tip , as well as a tip acting in the mixed regime . we show that the main resistance feature ( e.g. the spatial area of reduced resistance ) can be explained by considering geometric relations between the device boundaries , the tip position , and the circular cyclotron orbits . we also found that the finite width of the focusing leads can not be neglected . one of the novel results is that the sgm tip is mainly acting on a set of trajectories that directly connect the injector lead with the tip position . we show that the repelling tip leaves a shadow behind itself , which is mainly situated in areas delimited by two direct cyclotron orbits that connect the tip with the two corners of the injector lead . the specific shape of the tip shadow , which depends on the relative position between the tip and the injector lead , determines the shape of the low resistance region . therefore , at the first focusing peak , the tip is imaging a specific subset of direct trajectories connecting the two focusing leads . this only applies for a repelling tip , or a tip operating in a mixed regime ( repelling and focusing ) . for a tip acting as a focusing lens , the produced sgm maps do not show any significant change in the resistance , therefore they do not provide much useful information in characterization of transport . we additionally compare results between a 4-terminal and a 6-terminal device , and find them to be very similar , although the later induces some asymmetry in the resistance maps . the reason for this similarity is because the resistance is mostly determined by the transmission function between the two focusing leads . in that sense , we confirm the approach taken in ref . , which considered only transmission functions and not resistances . this paper is organized as follows . in sec . [ sec_method ] we describe the focusing system , and indicate how we model the tip potential . next , in sec . [ sec_rmaps ] , we scale the graphene tight - binding hamiltonian and compare relevant quantities , such as the dispersion relation and the current density in a scaled and an unscaled graphene lattice . the resistance of an unperturbed device ( i.e a device without the sgm tip ) is studied in sec . [ sec_sgm ] , while the analysis of sgm scans is done in sec . [ sec_sgm ] . in sec . [ sec_6term ] we present results of a six - terminal device , and discuss the possible causes of spatial asymmetry seen in the experiments . a short summary of our findings is given in sec . [ sec_end ] . the studied system is shown in fig . [ fig : system ] . it is a four - terminal graphene device with the same dimensions as those used in ref . . the only major difference between our system , and that of ref . , is the absence of two upper leads . we implement these two leads in sec . [ sec_6term ] , and discuss the changes they introduce in the sgm maps . magnetic focusing occurs when electron trajectories from the @xmath0 lead ( red curves in fig . [ fig : system ] ) are bent due to an external magnetic field into the @xmath1 lead . depending on the ratio between the width of the @xmath1 lead ( @xmath2 ) and the distance between the leads ( @xmath3 ) , the diverted electron can exit into the @xmath1 or the @xmath4 lead . this switching of the exit lead manifests itself as oscillations in the device resistance . figure [ fig : system ] shows two focusing orbits , where an even number of cyclotron radii matches the separation between the leads , @xmath5 $ ] . focusing occurs as long as @xmath6 . although magnetic focusing is a local phenomena , which depends on specific paths an electron can take in the system , it is usually studied by measuring the resistance of the whole device . a lot of information is lost in such measurements ( e.g. the most probable electron trajectories ) . this spatial information can be retained by scanning - gate measurements , where a sgm tip perturbs the circular electron trajectories , causing the device conductance to become tip - dependent . the conductance maps produced in such measurements reveal how device conductance depends locally on electron passage through that point . graphene magnetic focusing device : the system width is @xmath7 , while the system length is @xmath8 . both horizontal ( armchair ) , and vertical ( zigzag ) leads are metallic . the vertical leads have the same width @xmath9 , and their separation is @xmath10 . the magnetic field is perpendicular to the graphene sheet and points in the negative @xmath11 direction . the potential profile of the afm tip is schematically represented by the white circles.,scaledwidth=48.0% ] according to refs . , a charged stm tip placed above a graphene sheet modifies the local charge density in graphene @xmath12 which depends on the tip relative charge @xmath13 ( here @xmath14 is the actual charge accumulated on the tip , and @xmath15 is the electron charge ) , the distance from the tip to the graphene plane @xmath16 , and the distance from the tip in - plane projection to the current point . a local change in the charge density modifies the local fermi energy @xmath17 which manifests as an additional tip - induced potential . since fermi energy in graphene depends on the charge density through , the induced potential is @xmath18 this potential is a function of the global charge density @xmath19 , and the local charge modification @xmath20 . the global density @xmath19 is set by the back - gate voltage , while the local modification @xmath20 is determined by the tip height and the tip charge . tip - induced potential : ( a)(f ) charge density beneath the tip ( @xmath21 ) . solid black curves show the local charge modification @xmath20 , while dashed black lines mark the global ( unperturbed ) charge density @xmath19 . dotted black curves show the resulting density @xmath22 . colored areas present the absolute density @xmath23 for electrons ( red ) and holes ( blue ) , while induced potential , expressed in charge density units @xmath24 , is shown by the green curves . ( g)(i ) tip - induced potential for three regimes in ( a ) , ( b ) , and ( c ) , respectively . ( j)(l ) directions of the force field acting on the charge carriers : inward ( red ) , and outward ( blue ) , for the corresponding potentials in ( g ) , ( h ) , and ( i ) , respectively.,scaledwidth=48.0% ] an alternative way to look into the perturbation of the tip is through the tip - generated force field . charge carriers that travel through the system experience a force @xmath25 generated by the tip . this force modifies the carrier equation of motion @xcite @xmath26 where @xmath27 is the carrier dynamical mass in graphene ( @xmath28 ) , and is the resulting charge density . [ fig : tip_potential ] shows tip - induced potentials for different combinations of the global charge density and the local charge modification . there are six different regimes in which the tip can operate , but only three of these are unique . the other three regimes can be obtained by exchanging electrons with holes . the first regime is presented in fig . [ fig : tip_potential](a ) . here , a positively charged tip increases the local electron density , which manifests in the negative potential profile shown in fig . [ fig : tip_potential](g ) . the tip - induced force field in fig . [ fig : tip_potential](j ) reveals a focusing nature of the tip . the case of negatively charged tip in fig . [ fig : tip_potential](b ) was previously studied experimentally.@xcite as shown in ref . and in fig . [ fig : tip_potential](h ) , the tip creates a positive potential which then repels the incoming electrons . the force field in this regime , shown in fig . [ fig : tip_potential](k ) , is pointing away from the tip . in both figs . [ fig : tip_potential](a ) and [ fig : tip_potential](b ) , we set to @xmath29 . this density was used in ref . to fit the experimental data , and it corresponds to a tip positioned above the graphene sheet . assuming that the tip charge @xmath30 does not depend on the tip height @xmath16 , in the far - left column of fig . [ fig : tip_potential ] , we" +"the current cosmological model assumes gaussian initial conditions , created by inflation . this assumption regarding the nature of primordial density perturbations can be verified by studying the distribution of temperature fluctuations in the cosmic microwave background ( cmb ) . while the simplest inflationary models predict gaussian primordial perturbations , there are other models of inflation , such as those involving multiple scalar fields , features in the inflaton potential or phase transitions , that could give rise to detectable non - gaussianity . hence studies of gaussianity help distinguish between different early universe scenarios . gaussianity is also a key underlying assumption of cmb data analysis wherein the angular power spectrum fully specifies its statistical properties , and must be tested . non - gaussianity can also be associated with secondary anisotropies in the cmb , or with foreground contamination and systematic effects . prior to the release of wmap data there was no clear evidence of cosmological non - gaussianity . since the release of 1st year wmap data , a number of tests of non - gaussianity have been performed , with somewhat differing results . each statistic is sensitive to a different kind of non - gaussianity , hence there is need for a wide variety of tests . komatsu et al . ( 2003 ) use an optimized test based on the bispectrum , as well as minkowski functionals , while colley & gott ( 2003 ) study the genus , and both groups report consistency with gaussianity . gaztanaga & wagg ( 2003 ) do a 3-pt angular correlation function analysis and find consistency with gaussianity as well . chiang et al . ( 2003 ) perform a study of the phases of spherical harmonics and find some evidence for non - gaussianity at high multipoles . copi et al . ( 2003 ) find some evidence for low @xmath3 correlations and deviation from isotropy . park ( 2003 ) find a large difference between the genus amplitudes of the northern and southern hemispheres and a positive genus asymmetry in the southern hemisphere . eriksen et al . ( 2003a ) compute the 2 and 3-pt correlations and report a significant north - south asymmetry ; eriksen et al . ( 2003b ) use minkowski functionals and find a significant genus in the northern hemisphere and again indications of north - south asymmetry . hansen et al . ( 2004 ) use local curvature and find non - gaussianity / asymmetry in the data on scales of a few degrees . gurzadyan et al . ( 2004 ) find ellipticity in the temperature anisotropy features in the data , consistent with what was found previously in boomerang data . vielva et al . ( 2003 ; hereafter v03 ) report a non - gaussian signal in the southern hemisphere at high significance in the form of kurtosis on @xmath4 scales using the spherical mexican hat wavelet transform on wmap data . some of the detections of non - gaussianity and/or asymmetry thus far reported in the wmap data are at the level of 99% or greater . wavelet transforms are useful tools in non - gaussianity studies because they enable the signal on the sky to be studied on different scales , with simultaneous position localization , so that the obscuring effects of the central limit theorem , that can exist in both real and fourier spaces , are reduced . with wavelets any non - gaussian detection can be localized on the sky in scale and position , so that its nature and source can be better determined . planar wavelets have been used in gaussianity studies of the cmb by pando et al . ( 1998 ) , hobson et al . ( 1999 ) and mukherjee et al . ( 2000 ) , while barreiro et al . ( 2000 ) use the spherical haar wavelet , and cayn et al . ( 2001,2003 ) , martnez - gonzlez et al . ( 2002 ) , and v03 use the spherical mexican hat wavelet ( smhw ) . wavelet methods have been compared with other pixel or fourier based methods in hobson et al . ( 1999 ) , aghanim et al . ( 2003 ) , cabella et al . ( 2004 ) , and the performance of isotropic as well as highly anisotropic multi - scale bases in distinguishing between different sources of non - gaussianity in the cmb has been studied in starck et al . ( 2003 ) . in this paper we use the spherical mexican hat wavelet transform to probe non - gaussianity in the wmap data . we extend the work of v03 by performing new multiple tests of the robustness of the non - gaussian signal . we also look at the non - gaussianity in terms of an excess in the number of cold pixels , and in terms of scale - scale correlations amongst wavelet coefficients . further , we place constraints on a popular form of non - gaussianity ( a quadratic term in the curvature perturbations parametrized by the non - linearity parameter @xmath1 ) . this paper is organized as follows . in 2 , we present results from using the smhw transform on wmap data . whilst confirming the results of v03 , we perform new multiple tests of the robustness of the non - gaussianity signal in the kurtosis spectrum ( a ) through the use of different ( extended ) masks , and ( b ) relaxing the assumption of a simplified noise model . we find that the signal shows up even more significantly in the form of the number of cold pixels ( or coefficients ) . in 3 , we examine scale - scale correlations amongst the wavelet coefficients . we find significant deviations from gaussianity , a corroboration of the signal detected and described in 2 . in 4 we obtain constraints on the non - linearity parameter @xmath1 . we conclude in 5 . a non - gaussianity detection in the 1st year wmap data was reported by v03 . applying the smhw transform to the q - v - w coadded data , and computing the skewness and kurtosis of the wavelet coefficients over scales ranging from about 10 arcmins to 10 degrees , they found that the kurtosis of wavelet coefficients on scales @xmath5 was too high at the 99.9% confidence level . it was found that the excess kurtosis was in the southern hemisphere , while the kurtosis signal in the northern hemisphere was consistent with gaussianity . the signal was shown to be independent of frequency . it is important to determine whether the significance of this non - gaussianity detection is affected by systematic effects , such as the choice of mask , or simplified assumptions about noise . since the spherical mexican hat wavelet transform is a sensitive probe of non - gaussianity , we use it to perform an independent analysis of the 1st year wmap data . the basic steps followed in the analysis are as follows : starting with the foreground cleaned q - v - w coadded data , we bring the map down in resolution to healpix @xmath6 , apply the @xmath7 we mean the @xmath7 mask without sources . ] mask , perform smhw transforms to obtain wavelet coefficients corresponding to the different scales @xmath8 ( also setting the monopole and dipole of the map to zero here ) , apply appropriately extended versions of the mask to the wavelet coefficients of each scale to exclude coefficients contaminated by the mask and known point sources , and compute the skewness and kurtosis of the remaining unmasked coefficients . for our results to be directly comparable we perform the smhw analysis for the same scales used by v03 . for convenience and clarity , the scales @xmath9 ( @xmath10=1,2, ... ,15 ) plotted in the subsequent figures are listed in table 1 . table 1 + [ cols=""<,<,<,<,<,<,<,<,<,<,<,<,<,<,<,<"",options=""header "" , ] we showed in 2 that the skewness signal obtained using a range of masks was consistent with gaussianity . in this section , we use the skewness signal on the 15 scales to compute the limits that can be placed on the amplitude of primordial non - gaussianity , as parametrized by the non - linear coupling parameter , @xmath1 . since the non - linear term ( defined below ) is not dominant and is quadratic , it is the skewness signal in the data , rather than any higher order cumulants , that is expected to be most sensitive to it . the kurtosis signal is not sensitive to this kind of non - gaussianity ( cayon et al . 2003 ) . @xmath1 characterizes the amplitude of a quadratic term added to the curvature perturbations , @xmath11,\ ] ] where @xmath12 are gaussian linear perturbations with zero mean . thus @xmath1 parametrizes the leading order non - linear corrections to the primordial ( curvature ) perturbations . the motivation to use data to place constraints on @xmath1 is to address how gaussian current cmb data are , or how much primordial non - gaussianity , of this particular form , is allowed by the data . such analyses also help compare the sensitivity of different data sets and of different estimators of non - gaussianity to this particular form of non - gaussianity . using an optimal estimator of non - gaussianity based on the bispectrum , namely the cubic statistic , komatsu et al . ( 2003 ) place limits of @xmath13 at 95% confidence using the wmap 1st - year data . they derive 95% confidence limits of @xmath14 based on minkowski functionals . smith et al . 2004 , using vsa data , obtain an upper limit of 3100 at 95% confidence ( their limit being large because their data is sensitive to small scales ) . previously , using cobe dmr data , the bispectrum analysis of komatsu et al . ( 2002 ) placed a limit of @xmath15 , and using the skewness of smhw coefficients cayn et al . ( 2002 ) placed a limit of @xmath16 , both at 68% confidence . using maxima data santos et al . ( 2002 ) placed a 1@xmath17 limit of @xmath18 . we use the non - gaussian simulations of komatsu et al . how these have been produced are described in detail in the appendix of their paper . since producing these maps is a computationally intensive process , we use the 300 available realizations of non - gaussian sky maps at healpix resolution @xmath19=256 to obtain the mean values of skewness at each of the different scales , for different values of @xmath1 . we use gaussian simulations to estimate the covariance matrix of the skewness values for the different scales , and thus in turn to estimate the uncertainty in the measured @xmath1 . since gaussian simulations can be computed several orders of magnitude in time faster , we can estimate the covariance matrix accurately using a larger number of gaussian simulations , and the uncertainty estimated from gaussian simulations is a good approximation to that estimated from non - gaussian simulations for @xmath20 uncertainty indicated by the different curves in figure 8 below are roughly the same indicating that at current sensitivity of the data the uncertainties do not depend on the precise best fit value of @xmath1 . ] . in order to estimate the maximum likelihood @xmath1 , we compare the skewness values of the data at the 15 scales with simulations and use the goodness of fit statistic @xmath21 \sigma_{r_i , r_j}^{-1 } \left [ s(r_j)-\bar{s}_{sim}(r_j)\right],\ ] ] where @xmath22 is the skewness of wmap data on the ith scale @xmath9 , @xmath23 is the mean value from monte carlo simulations , computed" +"to extract reliable continuum results from lattice studies , it is essential to explore a range of @xmath3-values . it is also valuable to employ a fermionic discretisation which has minimal discretisation errors . here we investigate the tadpole improved clover sw action and we present preliminary results for the quenched spectrum at three lattice spacings . we compare our light hadron results at @xmath4 with the conventional sw clover approach and find no statistically significant evidence of further improvement at that @xmath3-value . we use non - local sources to allow a more accurate extraction of ground state masses and couplings . combining our results at all three @xmath3-values , we can extract the continuum limit and assess the size of discretisation effects . we find that dimensionless ratios of observables have small discretisation corrections . we highlight the uncertainties remaining in extracting continuum decay constants because of the reliance on perturbative matching coefficients . the sw fermion action is written in the form @xmath5 with hopping parameter @xmath6 . the quark fields @xmath7 and @xmath8 which appear in any observable must also be transformed ( rotated ) . for an on - shell observable bilinear in the quark fields , the equation of motion can be used to express this as an improved observable given by @xcite @xmath9 where @xmath10 . the size of the clover term in the action is determined by the coefficient @xmath11 . at tree - level , @xmath11 is equal to one . as demonstrated by heatlie _ @xcite , the terms of order @xmath12 are removed for this choice of @xmath11 . a mean field estimate of this coefficient was suggested by lepage and mackenzie @xcite . in this approach , the poor agreement of lattice perturbation theory with monte carlo simulations of short distance observables is explained by the presence of non physical `` tadpole '' diagrams . one expects the power expansion for the gauge link @xmath13 to be valid for sufficiently small @xmath12 . however , tadpole diagrams introduce ultraviolet divergences which can partly cancel the factors of @xmath14 . a solution to this is to rescale the gauge link by a factor @xmath15 , such that @xmath16 . the factor @xmath15 is chosen so that a monte carlo calculation of a short distance observable using the rescaled gauge field agrees with the perturbative calculation . an appropriate choice is @xmath17 inserting this factor into the sw action changes the hopping parameter to @xmath18 and the clover coefficient @xmath11 from 1 to @xmath19 . a perturbative evaluation of @xmath11 by naik @xcite gives a numerically similar value which is some support for the assumption of dominance of the tadpole diagrams . gauge configurations were calculated at @xmath0 , @xmath1 and @xmath2 , using spatial volumes that are approximately the same . at each lattice spacing , propagators at 2 quark masses , straddling the strange quark mass , were calculated for each configuration see table 1 . hadronic correlations were evaluated for each combination of such quarks , yielding three mesonic masses . hence the extrapolation to the chiral limit could be explored using three hadronic masses . the configuration and propagators at @xmath20 and @xmath2 were calculated on a 320 node cray t3d . the gauge configurations and propagators at @xmath0 were calculated respectively on a 16 and 64 node i860 meiko computing surface . for the transformation in eq . [ eq : rotation ] , we take @xmath21 which corresponds to no rotation in the propagators . the propagators were calculated using both non - local and local sources so that ground state and excited state contributions to correlators could be separated effectively . local sinks were employed . at @xmath0 , jacobi smeared sources @xcite were used , and correlations were measured with three combinations ( neither , one , both ) of nonlocal and local quark propagators in a meson . at @xmath20 , local and `` fuzzed '' sources were used @xcite . a fuzzed source can be written in the form @xmath22 where @xmath23 is an su(3 ) matrix representing the average of the fuzzed paths of gauge links from the origin to @xmath24 ( see fig . [ fig : fuzzed ] for a schematic description ) . fuzzing is less computer expensive than jacobi smearing , as the only numerical work involves the averaging of the gauge links . it is gauge invariant and avoids time spent in gauge fixing . we use the fuzzing prescription with 5 iterations as in ref . @xcite and we choose @xmath25 at @xmath20 . an example of the advantage of fuzzing at the source is shown in fig . [ fig : eff - mass - fuzzed ] where an efficient extraction of the ground state vector meson is seen . we focus on the pseudoscalar and vector mesons . in order to evaluate accurately the central value and statistical errors , we fit to as many channels of data as possible . furthermore , to isolate the ground state for a wide range of time slices , we use a two - exponential fit . the two point correlations can be expressed as a sum over transfer matrix eigenstates @xmath26 here @xmath27 where @xmath28 are operators that have overlap with the ground and excited mesonic states @xmath29 and @xmath30 . these operators can be local or nonlocal , or have different gamma matrix structures . for both mesons , we fit simultaneously to all the available local and non - local source correlations of two point functions . in the case of the pseudoscalar , we note that the fields @xmath31 and @xmath32 will create / annihilate the pseudoscalar , hence a simultaneous fit is performed to two point functions with the four combinations pp , ap , pa , aa . these contributions can be described in a factorising fit by the amplitudes @xmath33 and @xmath34 , where @xmath35 is the pseudoscalar state . this provides tight constraints on the fit . we define the lattice decay constant for a pseudoscalar meson , @xmath36 as : @xmath37 where @xmath38 is the _ local _ axial current operator . the lattice @xmath39 will be related to the continuum value @xmath40 by including quark field rotations , setting the scale @xmath12 and including the appropriate matching coefficient @xmath41 . one can determine @xmath36 directly from the factorising fit , without fitting to a ratio of channels as was used previously @xcite . an example of the result of such fits is shown in fig . [ fig : effective_mass_ps ] . likewise , simultaneous fits for the vector meson can be performed using the operators @xmath42 and @xmath43 , and different smearing / fuzzing combinations . the lattice vector decay constant , @xmath44 is defined by @xmath45 where @xmath46 is the local vector current . despite the quite large statistics used in this calculation , the large number of different types of two - point functions requires that a full correlated fit must be carried out carefully . in particular , we employ the methods described by michael and mckerrell@xcite for the inversion of the correlation matrix . at @xmath20 and @xmath2 , we model the correlation matrix with two exponents using the 5-diagonal approximation of ref . @xcite . at @xmath0 , we average all but 20 of the largest eigenvalues of the correlation matrix . we fit to the largest range of @xmath47 consistent with an acceptable @xmath48 . the errors quoted in this preliminary report are statistical only . the ground state pseudoscalar and vector masses are determined by the fits to two - particle correlations as described above . the issue of the rotations of the quark fields is irrelevant to mass determinations and will be discussed later . we define @xmath49 by the requirement @xmath50 for each lattice . at each lattice spacing , a linear extrapolation in the two squared pseudoscalar masses ( where the quark masses are degenerate ) was carried out . the results for @xmath51 are given in table 2 . a full fit using also the meson mass determined from the non degenerate quark mass case is possible , however , the fits gave statistically significant evidence for some curvature in @xmath52 versus @xmath53 . without tadpole improvement , there has been no agreement of non - perturbative lattice determinations of @xmath49 with one loop perturbation theory . for wilson - like fermion actions , it is found that the tadpole improvement factor of @xmath15 makes @xmath54 closer to the tree - level value of 1/8 . for example , a determination of @xmath55 using the @xmath56 clover action @xcite at @xmath4 gave a result of @xmath57 which corresponds to @xmath58 . for the tadpole improved action explored here , we present in table 2 the comparison of the non - perturbative results for @xmath54 with the one loop perturbative calculation . here we have chosen to use a coupling derived from @xmath59 . although the agreement is excellent at @xmath4 , the trend as @xmath3 is decreased is not . this lack of agreement of @xmath55 between non - perturbative determinations and one loop perturbation theory at smaller @xmath3 will cause some uncertainty in normalisation when quark mass factors are included in the determination of the decay constants . the experimental value of the difference @xmath60 remains remarkably constant , at approximately @xmath61 , over a wide range of masses . quenched lattice simulations of relativistic quarks have been in poor agreement with this result , and the discrepancy increases as the quark mass is increased . in the heavy quark regime , such splitting has a leading order dependence on the chromo magnetic coupling of the heavy quark with the gluon field . this is precisely the term which is amplified in the tadpole improved clover action . while one can not make a similar statement in the light quark regime , it is plausible that this modification of the clover term will also have a significant effect there . a comparison at @xmath4 can be made with non tadpole - improved ukqcd data @xcite , based on 60 configurations . these configurations exist as a subset of the @xmath62 configurations available now . a comparison of the results is shown in fig . [ fig : tadpole - comparison ] . unfortunately , there is no significant statistical difference between the two actions . we will soon have results for fuzzed sources in the tadpole - improved mass extraction which should lead to a reduction of errors . the behaviour at all three lattice spacings is shown in fig . [ fig : mvsq - minus - mpssq ] . the scale ( @xmath63 ) is determined from the chirally extrapolated @xmath64 . the fall - off of the splitting with respect to @xmath52 is slightly faster than one would expect by comparison with the physical splittings @xmath65 and @xmath66 . however , until this difference is examined for quark masses around that of the charm quark , the advantage of tadpole improvement in this case remains unproven . the dimensionless ratio of masses is known to have discretisation errors of order @xmath67 for the sw - clover fermionic action . the tadpole - improved variant should preserve this result and is expected to improve on it by reducing the coefficient . we explore this by studying such ratios of observables against an observable proportional ( to leading order ) to @xmath12 . since the wilson gauge action has inherent discretisation errors of order @xmath14 , it is advantageous to use this as a reference . we present ratios of @xmath68 to @xmath69 where @xmath70 is the string tension determined by interpolating all existing data . in fig . [ fig : mrho - on - tension ] , we find that the ratio is constant ( within statistical errors" +"red giant seismology is one of the most beautiful unexpected gift of the space missions corot and . when the corot mission was planned , red giants were seen as unavoidable targets because of their brightness . their observation has however confirmed that they show solar - like oscillations : as in the solar case , turbulent convection in the uppermost atmosphere excite pressure oscillations . pressure oscillation modes detected in low - mass stars at different evolution stages , all along the red giant branch ( rgb ) , allow us to perform ensemble asteroseismology . from such study , expressed by scaling relations , we can derive global stellar properties and get keys for deciphering stellar evolution . mixed modes , absent in the sun , have been discovered in red giants ( beck et al . since they result from the coupling of pressure waves propagating in the envelope with gravity waves propagating in the inner radiative regions , they can be used to directly probe the stellar core , from which they extract unique information on the ongoing nuclear rotation ( bedding et al . 2011 , mosser et al . 2011a ) , or on the inner rotation rate ( beck et al . 2012 , deheuvels et al . 2012 , mosser et al . 2012c ) . a recent review on red giant oscillations can be found in @xcite . results obtained in red giant seismology are discussed in a companion paper ( mosser et al . 2013b ) , with an emphasis on the seismic scaling relations and on red giant interior structure . this proceedings paper deals with tricky points related to the data analysis . in section [ radial ] , we discuss different ways to describe and measure the radial - mode oscillation pattern and explain the conditions providing the most precise measurement of the large separation . in section [ dipole ] , we focus on the dipole mixed - mode pattern and present a toy model used to explain the conditions under which mixed modes are observed . this models helps understand the so - called depressed mixed modes observed in rgb stars , or the large variety of observable gravity - dominated mixed modes . we aim to obtain an efficient description of the radial - mode oscillation pattern , for the most precise measurement of their frequencies . a first step for determining the characteristics of the oscillation pattern consists in the identification of radial modes and in the measurement of the large separation @xmath0 , as it appears as frequency difference between observable modes . the radial oscillation pattern is , at first - order approximation ( e.g. , tassoul 1980 ) , @xmath1 . this form derives from an asymptotic analysis and is therefore valid for large radial orders @xmath2 . in this section , we first discuss different methods for measuring @xmath0 . this large separation is measured around the frequency @xmath3 of maximum oscillation signal , in fact in non - asymptotic conditions . this explains that the measured value @xmath0 must be distinguished from its asymptotic counterpart . then , we investigate the different meanings of the large separation , and also the difference between local and global measurements of @xmath0 . finally , we discuss the meaning of the offset parameter @xmath4 . different methods have been proposed for measuring the large frequency separation of solar - like oscillations . all these methods have been exhaustively compared , in both main - sequence and red giant regimes ( e.g. , verner et al . , hekker et al . 2011 ) . among all methods , the autocorrelation of the time series presents different advantages ( roxburgh & vorontsov 2006 , mosser & appourchaux 2009 ) . computationally , the method is rapid since it is based on fourier transforms . for computing the fourier spectrum of the original time series , a lomb - scargle periodogram is required . then , all following operations are fast fourier transforms of the fourier spectrum . it allows an automated process , efficient for all large separations in the whole range of solar - like oscillations ( from 0.1 to 200@xmath5hz ) . it especially works at very low frequency , where , contrary to other methods , the relative poor frequency resolution is not an issue . dedicated filters can be used to compute the spectrum of the filtered fourier spectrum of the time series . these filters can be adapted to many situations , from the most efficient global measurement of the mean value of the large separation at @xmath3 to its rapid variations with frequency ( mosser 2010 ) . the method can also be used for measuring other frequency separations than the large frequency separation . it has been used successfully to measure the mixed mode spacings ( mosser et al . 2011b ) or the rotational splittings ( mosser et al . + many other methods are used for computing the large separation . since @xmath0 represents the period of the comb - like structure of the oscillation spectrum , its value can be inferred from the autocorrelation of the spectrum . we however note that this autocorrelation , contrary to the autocorrelation of the time series , does not benefit from the rapid calculation provided by the wiener - khinchin theorem . for space - borne observations benefitting from a very high duty cycle , this method appears to be less efficient than the autocorrelation of the times series . the concept of large separation has different meanings , depending on the context . observationally , the large separation @xmath0 is measured from the difference between consecutive radial mode frequencies . the local or global nature of the value is discussed in the next paragraph . mosser et al . ( 2013 ) have shown that @xmath0 is significantly different from the asymptotic value @xmath6 , which is another important acceptation . it corresponds to the value introduced by theoretical asymptotic methods ( tassoul 1980 ) and it scales as the inverse of the acoustic diameter of the star . the large separation intervenes in scaling relations ( belkacem et al . 2013 ) , under the hypothesis that is very close to the dynamical frequency @xmath7 that scales with @xmath8 . + the values @xmath0 , @xmath6 and @xmath7 are close to each other , but different . the measurement of the large separation @xmath0 must try to recover , if possible , @xmath6 and @xmath7 . as shown by , linking @xmath6 to @xmath0 is possible if and only if the second - order asymptotic expansion is considered . then , one has to account for the fact that the large separation is measured in non - asymptotic conditions . the curvature seen in the spectrum is the signature of this second - order term . the relation between @xmath0 and @xmath6 writes @xmath9 the correction term is maximum in the red giant regime ; it corresponds there to a uniform correction , about 3.8% . confusion is often made between @xmath6 and @xmath7 . since scaling relations are extensively used for translating the global seismic parameters into seismic proxies of the mass and radius , it is necessary to avoid this confusion . modeling is therefore useful , as done recently by @xcite who show that , in most cases , the observed large separation is closer to @xmath7 than the asymptotic value @xmath6 . the different methods used for measuring the large separation provide either a local or a global value of the frequency difference between radial modes . for a local measurement , only 2 or 3 radial orders around @xmath3 are considered : @xmath10 , with the radial frequencies @xmath11 and @xmath12 close to @xmath3 . for a global measurement , @xmath0 is a weighted mean value calculated in a broad frequency range around @xmath3 . evil is in the detail : the difference between the local and global measurement is small , but with a systematic component . have shown that this small difference can be used for distinguishing red giants in the red clump or on the rgb . this difference is due to glitches ( miglio et al . 2010 ) that depend on the evolutionary stage . therefore , measuring both the local and global large separations is very useful . this implies that the modulation due to the glitches is not negligible : it perturbs the measurement of the large separation , in a way that is not related to any of the global properties of the asymptotic large separation or dynamical frequencies . therefore , using a global value of @xmath0 is certainly the best way to get rid of the glitches that significantly modulate the large separation . furthermore , the work by mosser et al . ( 2013 ) has shown that the oscillation pattern obeys closely the second - order asymptotic oscillation pattern . this implies that a global large separation will provide a better measurement than a local value , for allowing the translation into the asymptotic value . the last step of the demonstration of the advantages of the global measurement is exposed later ( section [ offset - global ] ) . one needs first to present a method permitting an efficient global measure . for red giants , an efficient measure is made easy by the large homology of the stellar interiors . have shown that interior structure homology of red giants translates into homology of their oscillation spectrum . as a consequence , the large separation is enough to parameterize the low - degree spectrum @xmath13 \ \dnuobs,\ ] ] where the offset @xmath4 , the curvature @xmath14 , and the relative separations @xmath15 are functions of the observed large separation @xmath0 . the curvature term was already suspected in asteroseismology with ground - based observations with a limited frequency resolution , as for instance the procyon observations reported by . this term is necessary to account for the fact that the large separation is measured around @xmath3 , in non - asymptotic conditions ; in fact , it accounts for the gradient in frequency separations ( @xmath16 , according to the derivation of eq . [ univ ] ) . the term @xmath17 is defined by @xmath18 so that @xmath0 is the large separation measured at the frequency @xmath3 . such a formalism ensures the most precise translation from the measurement at @xmath3 to the asymptotic value . the term @xmath17 can be seen as the radial order at @xmath3 . however , contrary to a real radial order , @xmath17 is not an integer . in practice , measuring @xmath0 with the universal pattern is derived from the fit of the observed radial frequencies with a pattern based on eq . quadrupole modes are in fact fitted too , but not dipole modes , since they show a mixed character and have a more complex structure . the use of the universal pattern has proven to be efficient , with the following properties : i ) it accounts for the frequency separation gradient ; ii ) the fitting process helps reduce the realization noise due to the fact that the modes are short lived ; iii ) it also lowers the influence of the modulation due glitches discussed above ; iv ) it provides a measure which is not affected by the mixed - mode pattern . a large part of the accuracy of the universal pattern is due to the introduction of second - order terms . in eq . [ univ ] , the second - order term is expressed by the curvature @xmath14 , which helps for fitting the radial ridge in a large frequency range . if the second - order term were not taken into account , the" +"weak lensing of the large scale structure ( cosmic shear ) is one of the most powerful methods for constraining the cosmological model and is sensitive to both the growth of structure and to the expansion history of the universe ( @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite ) . however , so far weak lensing data has been available for only small regions of the sky ( @xmath3200 deg@xmath4 ) surveys that will produce large weak lensing data sets have begun ( dark energy survey(des ) , hyper suprime - cam(hsc ) , panoramic survey telescope and rapid response system(panstarrs ) , the kilo - degree survey(kids ) ) or are being built ( lsst , euclid , the wide - field infrared survey telescope ( wfirst ) ) . the statistical power of forthcoming weak lensing data sets , which will cover thousands or tens of thousands of square degrees , makes it necessary to consider the effect of systematic errors that could previously be ignored . the cosmic shear analysis relies on the accurate measurement of shapes of as many as tens of billions of background galaxies , to statistically estimate the small distortion ( about @xmath5 ) caused by weak gravitational lensing . to fully benefit from the increased statistical power of the new surveys , systematic errors must not significantly degrade the cosmological parameter errors . some imperfections in ccds become apparent when they record a uniform illumination ( flat fields ) . structure in the images reveals several patterns that are not due exclusively to quantum efficiency variations . concentric arcs , called tree rings ( @xcite , @xcite , @xcite , @xcite , @xcite , @xcite ) are due to impurity gradients in the ccds which cause electric fields transverse to the surface of the ccd . patterns aligned with the rows and columns of the pixels are due to periodic pixel - size variation caused by errors in the masks used in the step - and - repeat process manufacturing ( @xcite ) . both these effects can change the shape of galaxy images . for weak lensing analyses , we quantify the shape changes as spurious shear or spurious convergence . for the tree rings , we show how to calculate the spurious shear and spurious convergence from the flat field images . for the pixel - size variation , we calculate the spurious convergence which is directly related to the size of the pixel . the primary statistics for inferring cosmology from weak lensing surveys is the 2-point correlation function of shear or convergence , and its fourier transform , the power spectrum . the 2-point correlation function of spurious shear must be much smaller than that due to cosmological shear if cosmological parameters are to be accurately inferred . the biases in cosmological parameters are determined by calculating how much the inferred parameters change when the spurious convergence is added to the lensing convergence ( @xcite ) . this paper is organized as follows : in section 2 we give an overview of how we compute the bias in cosmological parameters from the spurious convergence . in section 3 , we describe the measurement of tree rings , the spurious 2-point correlation function it causes , and the parameter bias it induces . in section 4 , we describe the measurement of pixel - size variation , the 2-point correlation function of the spurious convergence and the parameter bias it induces . we summarize our findings and discuss further work in section 5 . weak gravitational lensing causes changes in the apparent position of point sources . for a source at @xmath6 observed at displaced position @xmath7 due to lensing , the shift is described by a 2@xmath82 transformation matrix ( @xcite ) @xmath9 where @xmath10 , the convergence , describes the isotropic distortion ( magnification ) of an extended source , and @xmath11 , @xmath12 , the shears , describe anisotropic distortions of the image . detector imperfections can cause distortions of the images of galaxies resulting in spurious shear and convergence , biasing the cosmological parameter determination . previous work has described biases due to the atmosphere , telescope and detector in terms of spurious shear ( @xcite ) . however the convergence and the shear are alternative descriptions of lensing , the convergence is related to shear ( up to a uniform mass sheet degeneracy ) through a non - local kaiser - squires inversion ( @xcite ) . the power spectrum of convergence is equal to the power spectrum of e - mode shear . we point out here that spurious convergence is in some cases a more convenient description of ccd imperfections than spurious shear . the spurious convergence due to pixel - size variation is easily calculated from the change in the pixel area from its nominal value . since for lensing , convergence is proportional to the mass surface density , it is clear that if we consider an area composed of many pixels , the convergence is just the average of the convergence of the constituent pixels . the bias calculation is performed using a fisher formalism ( see for example @xcite . let @xmath13 be the convergence from weak lensing in a field of view of size @xmath14 , and let @xmath15 be its power spectrum defined as @xmath16 we used the superscript 0 to denote the convergence measured from a pure lensing signal , not including systematic effects . in this equation , and in the remainder of this section , the hat ( @xmath17 ) on a quantity @xmath18 means that the quantity is an estimator and we use the tilde @xmath19 to denote the fourier transform of @xmath18 . the subscripts @xmath20 are shorthands for the multipole moments @xmath21 . we also indicate the dirac delta function and the kronecker delta symbol as @xmath22 respectively . in the limit in which @xmath13 is a gaussian field , the power spectrum estimator @xmath23 has an expectation value @xmath24 and a variance @xmath25 , where the mode number @xmath26 is computed as see @xcite @xmath27 where @xmath28 is the width of the multipole bins used in the analysis . because the convergence field is statistically isotropic , the power spectrum measured at a multipole @xmath29 depends on the magnitude @xmath30 of the two dimensional multipole moment @xmath29 . now let @xmath31 the derivative of @xmath32 with respect to cosmological parameter @xmath33 and @xmath34 the @xmath23 estimator covariance matrix , which we approximate as diagonal @xmath35 defining @xmath36 we can estimate the bias @xmath37 in the cosmological parameters @xmath38 when fitting a field of view with spurious convergence added @xmath39 as @xmath40 where the superscripts @xmath41 , 0 refer to the power spectrum measured from a field of view with and without spurious convergence added ( @xcite ) . the same fisher formalism can be used to estimate the marginalized errors @xmath42 on the parameters when using a single field of view @xmath43 we note that when using the full survey data rather than a single field of view , parameter errors can be much smaller since @xmath44 . for lsst , @xmath45 and @xmath46 . equation ( [ biasexpr ] ) can be further expanded as @xmath47 = m_{\alpha i}\left(p^{sp}_i + \frac{\hat{\tilde{\kappa}}_i^0\tilde{\kappa}_i^{sp,*}+\hat{\tilde{\kappa}}_i^{0,*}\tilde{\kappa}_i^{sp}}{(2\pi)^2}\right)\ ] ] the spurious convergence @xmath48 is calculated from laboratory measurement of the ccds . since the imperfections are fixed on the ccd focal plane , there is only one realization of the spurious convergence and it spans the field of view of the telescope . because of this , the spurious convergence @xmath49 becomes a non stochastic quantity ( and hence written without the hat ) . we can compute the expectation value and standard deviation of the bias estimator ( [ biasestimator ] ) and get @xmath50 @xmath51 since the spurious convergence is non stochastic , the standard deviation of the bias estimator ( [ varbias ] ) is proportional to the standard deviation of @xmath52 , which scales as @xmath53 . these results are correct for a single field of view , when the analysis is scaled to the full survey side the expectation value of the bias does not change , but the standard deviation of @xmath52 gets reduced by a factor of @xmath54 . the same reduction applies to the bias variance in ( [ varbias ] ) . we note that the stochasticity in the bias is due to the cross term in ( [ biasestimator ] ) and is a result of cosmic variance in the lensing convergence field . @xmath55 can be quite large compared to @xmath56 even for @xmath57 . the estimated survey bias is @xmath58 . we will quote the larger of the two values as the estimated survey bias . to compute @xmath59 in the fiducial cosmological model with @xmath60 , as well as the derivatives @xmath31 , we make use of the public code nicaea ( @xcite ) which gives good accuracy for the lensing power spectra in the parameter range we are considering . we assume a redshift distribution of galaxies concentrated in single redshift @xmath61 . in the lensing convergence power spectrum @xmath23 we include the effects of galaxy shape for the assumed @xmath62 galaxies/@xmath63 . an approximate scaling relation of the bias with the galaxy density can be obtained noting that , in the limit in which shape noise dominates , @xmath64 scales as @xmath65 . because the derivatives @xmath66 and the spurious power @xmath67 do not depend on @xmath68 , the bias expectation value does not change with @xmath68 , but its standard deviation roughly scales with @xmath69 . tree rings are due to impurity gradients in the silicon of which ccds are made . the high - purity , high - resistivity silicon used in recent astronomical ccds grows cylindrically from molten state . time variations in temperature , composition , etc . produce radial impurity gradients which result in resistivity gradients . ccds made from slices of the cylindrical boule have electric fields transverse to the main field due to the resistivity gradients leading to the displacement of photo - generated charge . thick ccds used for increased near ir ( @xmath3 1 micron ) sensitivity suffer greater charge displacement due to longer path length . though the tree rings are observed in flat field images , they do not correspond to quantum efficiency variations . instead , they induce a displacement of the collected charge that propagates into astrometric and photometric biases . in this section we describe how to calculate the spurious shear and spurious convergence due to tree rings from the flat - field images and apply the method to the lsst candidate sensors . we then calculate the 2pcf and bias of cosmological parameters . in practice , it is possible to directly measure the astrometric displacement @xmath70 as function of scalar radius @xmath71 , caused by the tree rings by using sets of several dithered exposures of star fields in different photometric bands and constructing star flat "" images ( @xcite , @xcite ) . the displacement is defined from differences between the original position @xmath72 and the displaced position by the tree - ring effect @xmath73 ; it is defined as @xmath74 however , this is not an easy task given that the displacement is small ( of the order of subpixels ) . however , it is easy to measure flux modulation @xmath75 due to tree - ring , defined as @xmath76 where @xmath77 is average flux at radius @xmath71 and @xmath78 is average flux of all pixels . @xcite demonstrated that , to first order , there exists a relationship between the tree - rings flux modulation @xmath75 as measured by the flat fields ( which have higher s / n compared to the one provided by the limited number of stars in the star" +"high mass x ray binaries ( hmxbs ) contain a compact object ( a neutron star or a black hole ) accreting matter from a massive companion star . they can be divided into three different sub - classes , depending on both the donor type ( ob supergiant or be star ) and the x ray activity ( persistent or transient ) : * ( 1)*-supergiant hmxbs with persistent emission ( divided into ( 1a)wind - fed and ( 1b)disk - fed accretors ) , * ( 2)*-be / x ray transients ( although there are also a few be / x ray binaries with persistent low luminosity x ray emission ) and , more recently , the * ( 3)*- supergiant hmxbs with fast transient emission , the so - called supergiant fast x ray transients ( sfxts ) . liu et al . ( 2006 ) list 114 hmxbs located in our galaxy , 66 of which are classified as accreting x ray pulsars . most of them are in binaries with be stars , although the number of hmxbs with supergiant companions is continuously growing thanks to the @xmath0 discoveries in the energy range 17100 kev : indeed , about 70% of the hmxbs discovered with @xmath0host ob supergiants ( bird et al . sfxts are hard x ray transients displaying a high dynamic range of @xmath110@xmath210@xmath3 , with sporadic , recurrent , bright and short ( a few hour long ) flares ( sguera et al . 2005 , 2006 ; negueruela et al . 2006a ) , reaching 10@xmath410@xmath5 erg s@xmath6 . this fast flaring activity is superimposed on outburst phases lasting a few days , shorter than those displayed by be / x ray transients ( romano et al . 2007 ; sidoli et al . 2009 ; rampy et al . their optical association with blue supergiants has led to the identification of ten members ( e.g. halpern et al . 2004 , pellizza et al . 2006 , masetti et al . 2006 , negueruela et al . 2006b , nespoli et al . 2008 ) , together with several candidates with fast hard x ray flaring activity but still unknown optical / ir counterparts . their long term properties ( on timescales of months ) consist of a large flux variability at an average intermediate x ray luminosity of 10@xmath710@xmath8 erg s@xmath6 ( sidoli et al . 2008 ) , between the quiescence and the flare peaks . the lowest luminosity level detected in a few sfxts , 10@xmath9 erg s@xmath6 , sometimes shows a very soft spectrum ( and , likely , no accretion ; e.g. in igr j175442619 , int zand 2005 ) , sometimes a harder x ray emission together with mild flux variability ( indicative of ongoing accretion at a very low level , e.g. igrj084084503 , sidoli et al . a common property of accreting pulsars in hmxbs is the x ray spectral shape , typically characterized by a flat hard power law below 10 kev ( photon index @xmath101 ) , together with a high energy cut - off in the range 1030 kev , sometimes strongly absorbed at soft energies ( walter et al . , 2006 ) . sfxts display a similar spectral shape when they are in outburst , thus it is usually assumed that most of these sources harbour neutron stars , although x ray pulsations have been detected _ only _ in about half of them ( 5 of about 10 members of the class ) with spin periods ranging from 4.7 s ( ax j1841.00536 , bamba et al . 2001 ) to 228 s ( igrj 164654507 , lutovinov et al . 2005 ) and 1246 s ( for the sfxt candidate igrj 164184532 , walter et al . the possibility of the presence of a black hole in non - pulsating sfxts can not be completely ruled out . ( red squares ) , and a few sfxts where both spin and orbital periods are known ( blue circles ) . on the orbital period axis , the position of other four sfxts have been marked , for which the spin periodicities are still unknown . , title=""fig : "" ] + sfxts orbital periods have been determined in 8 sources , spanning a large range as well , between 3.3 days ( igrj 164794514 ; jain et al . 2009 ) and 165 days ( igrj 112155952 ; sidoli et al . 2006 , 2007 ; romano et al . the sfxts for which both the orbital and spin periods are known can be overplotted in the corbet diagram of all known galactic high mass x ray pulsators ( fig . [ fig : corbet ] ) , where three different locii were originally recognized ( corbet 1986 ) : be - star binaries ( where spin periods are correlated with orbital periods ) , supergiant systems with long spin periods ( @xmath1100 - 1000 s ; wind - fed hmxbs ) and narrow orbits ( p@xmath10@xmath110 days ) and supergiant systems with shorter spin periods ( @xmath1110 s ; roche lobe overflow , disk - fed systems ) . one of the puzzling facts about the new supergiant hmxbs discovered with @xmath0is that some sfxts lie in the region typical for be / x ray transients ( like igr j112155952 ) or in an intermediate region of the corbet diagram ( like in the case of igr j184830311 ) , in a sort of _ bridge _ between the two main locii of ob supergiants and be donors . it has been suggested that the sfxts lying in the be / xrbs region of the corbet diagram are indeed the descendant of these binary systems ( liu et al . 2010 , chaty 2010 ) . interestingly , igr j184830311 shows also an x ray flaring activity with a higher duty cycle ( in excess of 3% ) than typically observed from sfxts ( see fig . [ fig : dc ] ) , possibly indicative of an intermediate system between sfxts and persistent hmxbs with supergiant companions , as suggested by rahoui & chaty ( 2008 ) . the other source with a high hard x ray duty cycle is igr j164794514 ( 2.7% ) , with an unknown spin period , while igr j112155952 has a small duty cycle of 0.3 - 0.6% . a sensitive swift / xrt monitoring of igr j184830311 along an entire orbital period caught this sfxt almost always active , except during a specific orbital phase , probably because of an x ray eclipse or a gate mechanism ( romano et al . the source light curve was highly variable , with several flares , with an average x ray luminosity probably modulated by the orbital period , likely because of an eccentric orbit ( e@xmath10.4 , romano et al . thus , it is also possible that a continuum of behavior exists between the persistent supergiant hmxbs and the sfxts with very rare x ray activity . to date the sfxts duty cycles observed at hard x rays ( @xmath11 kev ) are typically small ( fig.[fig : dc ] ) and highly variable from source to source . considering @xmath0 observations of bright flaring activity , the percentage of time spent in flares with respect to the total observing time of the source field can vary between 0.05% and 3 - 4% ( for sfxts in the central region of our galaxy , after 7 years of observations with @xmath0 ; ducci et al . , 2010 ) . ; data from ducci , et al . 2010 ) . , title=""fig : "" ] + despite the huge amount of observational data , several issues are still open : one of the main problems is related with the link between sfxts and hmxbs with supergiant companions and persistent x ray emission . indeed , these two kind of xrbs have both similar compact objects and donor stars , and in a few cases , also very similar short orbital periods ( as in the case of igr j164794514 , jain et al . 2009 , and igr j175442619 , clark et al . so , since in these particular cases , the possibility of different orbital parameters are very likely ruled out as the main mechanism at the origin of the two different classes , other mechanisms should be at work : either a property of the neutron star ( the magnetic field and/or the spin period , as suggested by grebenev & sunyaev 2007 , bozzo et al . 2008 ) or a property of the ob supergiant : a different clumping factor in their strong winds from the supergiant star in persistent hmxbs and in sfxts , or the presence of a preferential plane for the outflowing wind , inclined with respect to the orbital period in sfxts , which is crossed by the neutron star producing the sfxts x ray flaring activity ( sidoli et al . also the ionization effect could play an important role especially in binary systems with narrow orbits ( ducci et al . 2010 ) . to date , none of the different mechanisms proposed for the transient outbursts in sfxts are able to explain all the observational facts ( see sidoli [ 2009 ] for a detailed review ) . the possibility of a different accretion mechanism in persistent hmxbs with supergiant donors and in sfxts is also linked to the open issue of the evolutionary histories of these two subclasses of massive binaries . their census in our galaxy , as well as their proper duty cycles , are also open questions . in conclusion , a more sensitive monitoring campaign of the hard x ray sky is needed , at all timescales , in order to try to answer to all these questions , to discover new periodicities ( both spin and orbital periods ) and know more about their nature , to accurately model their broad band spectra on the shortest timescale possible , to possibly detect cyclotron lines and measure the neutron star magnetic field . this latter is indeed unknown for _ all _ sfxts , except in igr j18483@xmath120311 , where a cyclotron emission line at 3.3 kev has been discovered with @xmath13 indicating a low magnetic field of 3@xmath14 g ( sguera et al . 2010 ) , thus ruling out any magnetar nature for this sfxt . in the following i will report on simulations of sfxts in the framework of two x ray missions perfectly suited to study sfxts and possibly solve most of their open issues : the energetic x - ray imaging survey telescope ( exist , grindlay et al . 2010 ) and the new hard x ray mission ( nhxm , tagliaferri et al . 2010 ) . the high - energy telescope ( het , 5600 kev ) for exist was mainly suited to perform a survey of x ray transients , thanks to its large field of view ( 70 degrees @xmath15 90 degrees ) and an unprecedented sensitivity ( the full sky would have been observed in a two year continuous scanning survey ) , able to detect and quickly localize ( @xmath1620@xmath17 ) x ray sources for rapid follow - up . unfortunately , the decadal survey report on the 13th of august 2010 did not recommend exist . on the other hand , a future mission with the exist concept is certainly needed to investigate the fast x ray transient sky . in fig . [ fig : exist_spec ] i report a spectrum simulated with het , with a spectral shape typical for a sfxt at the peak of its outburst , with a short exposure time of 1 ks . the spectral parameters are the" +"as the nearest large spiral galaxy , m31 is a fundamental benchmark for studies of disk galaxy evolution , and our understanding of the evolution of m31 has changed profoundly during the past decade . there is a large body of evidence ( e.g. ibata et al . 2001 , 2007 ; hammer et al . 2007 ; tanaka et al . 2010 ) that interactions with companion galaxies , some of which may not have survived intact to the present day and remain only as debris trails , have occured throughout the history of m31 . the detection of similar tidal features close to other nearby galaxies ( e.g. martinez - delgado et al . 2010 ) indicates that galaxy - galaxy encounters in the local universe have not been rare , and have played a key role in sculpting the current appearance of many nearby galaxies . the current study focuses on investigating the star - forming history ( sfh ) of m31 during the past few hundred myr , using the brightest resolved stars as tracers . it has been suggested that m31 has interacted with some of its companions during this time , and a key element of our work is to search for observational signatures of this activity . a review that considers the entire history of m31 will guide our understanding of its present - day appearance , and allow a conceptual picture of the key events that shaped its evolution to be developed . to this end , in the remainder of this section we review previous work on the evolution of m31 . while current theories for the buildup of disk galaxies give primacy to the smooth accretion of hot and cold gas , the following focuses on the influence of major and minor mergers , as these imprint observable signatures on the kinematics , spatial distribution , and age distribution of stars . not every interaction can be traced in detail , especially those that happened more than a few dynamical times in the past , and the discussion of the earliest phases of the evolution of m31 are by necessity more speculative than the discussion of the most recent events . the ages listed in what follows should also be viewed as approximations . the initial assembly of m31 likely involved the merger of proto - galactic structures , which contained a mix of gas and stars that had formed _ in situ _ ( e.g. oser et al . 2010 ) . the gas in these structures probably contributed to the assembly of an m31 proto - disk , supplementing material accreted through the large - scale inflow of hot and cold gas . any early disk was likely short - lived due to the high frequency of major mergers . in addition to disrupting the early disk , mergers may also have spurred the formation of a classical metal - poor halo , through the displacement of stars out of the disk plane . stars ejected in such events are expected to dominate the central 20 kpc of halos ( zolotov et al . 2009 ) . at larger radii the majority of halo stars may not have had such a violent origin , and may instead have been accreted from companion galaxies during the first few gyr of galaxy assembly ( font et al . 2008 ; zolotov et al . 2009 ; cooper et al . 2010 ) . a classical metal - poor halo has been detected around m31 ( e.g. kalirai et al . 2006 ; chapman et al 2006 ; ibata et al . 2007 ; koch et al . 2008 ) . there is evidence that m31 accreted a number of satellites early - on . the integrated luminosities , masses ( @xmath6 m@xmath7 ) , and dynamical properties of the m31 and the galactic halos are similar ( chapman et al . 2006 ; ibata et al . 2007 ) , and the properties of galactic globular clusters suggest that 6 8 satellites large enough to form such large star clusters may have been accreted ( e.g. mackey & gilmore 2004 ; forbes & bridges 2010 ) . globular clusters in the m31 halo tend to be associated with tidal debris ( mackey et al . 2010 ) , and the range of ages , chemical mixtures , and overall metallicities amongst m31 clusters ( e.g. beasley et al . 2005 ) hints at diverse progenitors . some objects that were originally identified as globular clusters may not be simple stellar populations ( ssps ) ( e.g. davidge et al . 1990 ; meylan et al . 2001 , fuentes - carrera et al . 2008 ) , but instead may be the remnants of dwarf galaxies that were shredded early in the evolution of m31 ( fuentes - carrera et al . 2008 ) . the properties of classical globular clusters suggest that m31 and the galaxy may have experienced different chemical enrichment histories early - on . when compared with galactic globular clusters , the spectra of many m31 globular clusters have relatively strong cn absorption bands ( e.g. burstein et al . 1984 ; davidge 1990a ) , and this has been attributed to a comparatively large nitrogen abundance in m31 clusters ( burstein et al . such an abundance difference may have its origins in the numbers of present - day stars in globular clusters that formed in the diffuse proto - cluster environments , as opposed to those that formed in the more compact potential wells that existed after cluster formation ( carretta et al . 2010 ) , in the sense that m31 clusters are made up of a smaller fraction of progenitor stars . if correct , then the location of stars in m31 globular clusters on the [ na / fe ] versus [ o / fe ] diagram , which is a diagnostic of the rate of chemical enrichment , should differ from that defined by galactic objects . early merger activity likely also produced a pressure - supported bulge ( e.g. bekki & chiba 2001 ) . aside from the central few arcsec , the integrated spectrum of the m31 bulge at visible wavelengths originates predominantly from old stars ( e.g. davidge 1997 ; puzia et al . 2005 ; saglia et al . the brightest agb stars are well - mixed throughout the central @xmath8 kpc of the m31 bulge , as expected if they formed during a rapid , uniform star - forming episode ( davidge 2001b ) , such as would result from the violent merging of satellites . still , the structural ( e.g. beaton et al . 2007 ) and kinematic ( e.g. morrison et al . 2010 ) properties of the m31 bulge suggest that secular processes may have also contributed to its growth . the material from which stars in the galactic bulge formed may have been chemically enriched by the earliest generation of globular clusters ( davidge 2001a ) . if globular clusters did play a significant role in enriching the early ism of m31 then the chemical properties of stars in the bulge and globular clusters may show similarities . in fact , the strengths of cn absorption bands at visible wavelengths in the integrated spectrum of the inner bulge of m31 are reminiscent of those in m31 globular clusters ( davidge 1997 ) , suggesting a chemical kinship . a thick disk may also have been formed during the early assembly of m31 . using kinematic selection criteria , collins et al . ( 2011 ) detect a thick disk in m31 and find that the component stars are @xmath9 dex more metal - poor than thin disk stars at the same galactic radius . the estimated total mass of the thick disk suggests that it did not form from the destruction of a satellite that follows the trend between [ m / h ] and total mass defined by present - day systems . if the m31 thick disk formed from thin disk stars that were kinematically heated then its ( comparatively ) low metallicity suggests that this happened during early epochs , before the major merger that produced the extended extraplanar component discussed in the next section . the spatial extent of m31 at the end of its initial assembly was significantly smaller than the present - day galaxy . simulations suggest that a galaxy with a present - day mass like that of m31 probably accreted no more than one - half of this mass by moderate redshifts ( stewart et al . 2008 ) , while at @xmath10 the spatial extent of its disk may have been substantially ( by a factor of @xmath11 two - thirds ) smaller than its present - day value ( firmani & avila - reese 2009 ) . the modest size of the m31 progenitor aside , it was this system that served as the seed for the subsequent evolution that lead to the present - day galaxy . mergers were common events during intermediate epochs , and played a key role in sculpting the morphological properties of nearby disk galaxies ( hammer et al . 2007 ; 2009 ; van der kruit & freeman 2011 ) . simulations of a merger between a disk galaxy and a large companion find that the existing disk can be obliterated , with the orbits of disk stars thermalising to form a pressure - supported extraplanar population ( e.g. hopkins et al . a gas disk will re - form if the progenitors have sufficient quanities of gas ( robertson et al . 2006 ; governato et al . 2007 ) . there is evidence that a violent merger occured only a few gyr following the initial assembly of m31 . such an event would have profoundly affected the morphology of m31 , and may have produced features that are usually attributed to more recent interactions ( hammer et al . 2010 ) . the proposed merger heated the disk of m31 and produced a diffuse extraplanar component that is distinct from the classical metal - poor halo . it has long been known that the extraplanar regions of m31 are dominated by stars with metallicities that ( 1 ) are much higher than those in the galactic halo ( e.g. mould & kristian 1986 , pritchet & van den bergh 1988 , durrell et al . 2001 ) and ( 2 ) are consistent with an origin in either a large disk or an smc / lmc - like companion . more recently , a kinematically hot component ( e.g. chapman et al . 2006 ; gilbert et al . 2007 ) has been detected , that has been traced out to extraplanar distances of 60 kpc . this component is distinct from the thick disk , which has a vertical scale height of 3 kpc ( collins et al . the metallicities of stars in this component show little or no trend with distance from the galaxy ( chapman et al . 2006 ; koch et al . 2008 ; richardson et al . 2009 ) . a break in the surface brightness profile occurs near 30 kpc ( ibata et al . 2007 ) , possibly indicating the transition between a violently disturbed inner halo and a more metal - poor classical halo . the lack of sub - structure in the distribution of the moderately metal - rich extraplanar stars suggests that they are not the remnants of a galaxy that was slowly accreted by m31 , but instead are the result of a kinematically violent event . the extraplanar component must have an age of at least a few gyr , as the c / m5 + ratio is @xmath12 throughout the outer regions of m31 ( koch &" +"many theoretical and experimental studies in nuclear structure during the last three decades were devoted to the giant dipole resonance ( gdr ) in highly excited nuclei ( see ref.@xcite for reviews of the subject ) . a recent compilation of the experimental systematics of the gdr built on excited states is given in ref . the most recent experimental measurements are reported in ref . @xcite for gdr in the fusion - evaporation reaction forming the compound nucleus @xmath0mo at high temperature and angular momentum , and in ref . @xcite , where the gdr width in @xmath9tl in the @xmath10 induced fusion reaction was extracted at low temperature . the center of attention has been the evolution of the gdr width as functions of temperature @xmath8 and angular momentum @xmath11 . the gdr line shape and its full - width at half maximum ( fwhm ) @xmath12 are experimentally extracted from the statistical calculations , which use the lorentzian strength function to reproduce the @xmath13-ray spectra detected from the decay of the highly - excited compound nucleus at the excitation energy @xmath14 . they are often compared with the theoretical predictions , which are obtained at a given values of @xmath8 and/or @xmath11 . the extraction of nuclear temperature @xmath8 and angular momentum @xmath11 is crucial for a meaningful comparison between experiment and theory because the initial temperature @xmath15 and/or angular momentum @xmath16 at the first step in the decay of the compound nucleus are significantly higher than the mean values @xmath17 and @xmath18 , obtained by averaging over all daughter nuclei in the decay process . moreover , while the theoretical gdr strength function is calculated at a fixed value of @xmath8 and/or @xmath11 , its experimental counterpart is extracted by fitting the spectrum , which is generated by a multistep cascade decay , where the nucleus undergoes a cooling down from the initial maximal value of @xmath15 ( and/or @xmath16 ) . because of this mechanism , the authors of ref . @xcite have proposed to incorporate the theoretical strength functions into the full statistical decay calculations and compare the results obtained with the experimental data . this method was applied to test the validity of several theoretical models in refs . @xcite , namely the collisional damping model ( cdm ) @xcite , the thermal shape fluctuation model ( tsfm ) @xcite , and the phonon damping model ( pdm ) @xcite . the cdm studies the gdr evolution within the framework of the macroscopic landau - vlasov theory that includes the collision term in the landau integral . the tsfm describes the gdr line shape by calculating the gdr cross section as a thermal average over all shape - dependent cross sections under quadrupole deformations . the pdm describes the broadening of the gdr width at low and medium @xmath8 and @xmath11 as well as its saturation at high @xmath8 and @xmath11 via coupling of the gdr to noncollective particle - hole ( ph ) , particle - particle ( pp ) and hole - hole ( hh ) configurations . the detailed analysis in ref . @xcite shows that neither the tsfm nor cdm could reproduce the gdr data for @xmath19sn , whereas ref . @xcite demonstrates that the pdm describes reasonably well the gdr line shape at @xmath20 2 mev . by including the nonvanishing thermal pairing gap , the pdm is also capable of correctly describing the temperature dependence of the gdr width at low temperature ( @xmath21 2 mev ) @xcite . however , a question still remains open , namely it is not clear if the gdr line shape obtained by averaging the gdr strength functions in the whole interval of @xmath8 and/or @xmath11 , within which the daughter nuclei are populated , is equivalent to the gdr strength function obtained at the mean values @xmath17 of temperature and @xmath18 of angular momentum in these intervals . resolving this issue has a practical importance since if the answer is positive , one can avoid the calculations of many strength functions as the temperature and/or angular momentum decreases starting from @xmath15 and/or @xmath16 to obtain the average line shape , and use the strength function obtained at one given pair of values @xmath17 and @xmath18 instead . the aim of the present paper is to answer this question . the paper is organized as follows . the formalism is presented in sec . [ formalism ] . the results of numerical calculations for gdr strength functions within the pdm , which are averaged by using the empirical probabilities distributions for temperature and angular momentum in @xmath0mo at various excitation energies @xmath4 , are discussed in sec . [ results ] . the paper is summarized in the last section , where conclusions are drawn . [ pdm ] the formalism of the pdm , whose hamiltonian describes a hot spherical system noncollectively rotating about the symmetry @xmath22-axis , has been presented and discussed thoroughly in ref . therefore we summarize here only the final results , which are necessary for the analysis in the present paper . the model hamiltonian is given as @xmath23 where @xmath24 is the pdm hamiltonian of the non - rotating system , described in ref . @xcite , and @xmath25 represents the total angular momentum @xmath26 , which , in the present case , coincides with its @xmath22-projection @xmath25 , that is @xmath27 here the subscripts @xmath28 denote the single - particle states @xmath29 in the deformed basis with the angular momentum @xmath28 and the positive single - particle spin projection @xmath30 , whereas the subscripts @xmath31 denote the time - reversal states @xmath32 ( @xmath33 0 ) . the particle number operator @xmath34 is written as @xmath35 where @xmath36 ( @xmath37 ) is the creation ( annihilation ) operator of a particle with spin @xmath28 , spin projection @xmath38 , and energy @xmath39 . by using eqs . ( [ m ] ) and ( [ n ] ) , the hamiltonian ( [ h0 ] ) transforms into @xmath40 @xmath41 where @xmath42 denotes the chemical potential . the particle ( p ) states correspond to those with @xmath43 , whereas the hole ( h ) states are those with @xmath44 . the operator @xmath45 ( @xmath46 ) is the phonon creation ( annihilation ) operator for a collective vibration with energy @xmath47 . in this way , hamiltonian ( [ h ] ) describes two mean fields , the single - particle mean field ( the first two terms on the right - hand side of eq . ( [ h ] ) ) , and the phonon one associated with the gdr ( the third term ) , as well as the coupling between them ( the last term ) with matrix elements @xmath48 . the gdr acquires a width and the phonon energy @xmath49 undergoes a shift because of this coupling . by including the angular momentum in the first two terms , each of spherical orbital @xmath50 with energy @xmath51 splits into @xmath52 distinctive levels , half of which consists of levels with energies @xmath53 , whereas the other half consists of levels with energies @xmath54 , with @xmath55 , where @xmath56 is the total number of levels . because the effect of thermal pairing on the gdr width is negligible in the region of moderate ( high ) @xmath8 and @xmath11 ( @xmath57 58 mev for @xmath0mo @xcite , we neglect it it in the calculation of the gdr strength functions for simplicity . the chemical potential @xmath42 and the rotation frequency @xmath13 are defined from the equations for conservation of the angular momentum @xmath11 and particle number @xmath58 as @xmath59 where @xmath60 , @xmath61 , @xmath62 with the grand canonical ensemble average @xmath63/{\rm tr}[{\exp}(-\beta h)]$ ] ( @xmath64 ) . the single - particle occupation numbers @xmath65 are approximated with the fermi - dirac distribution : @xmath66 by using the hamiltonian ( [ h ] ) and the method of double - time green s functions , the final equation for the green s function , which describes the phonon propagation , was derived in ref . @xcite as @xmath67^{2}\bigg[\frac{f^{+}_{k'}-f^{+}_{k } } { e - e_k^{-}+e_{k'}^{-}}+\frac{f^{-}_{k'}-f^{-}_{k } } { e - e_k^{+}+e_{k'}^{+ } } \bigg]~. \label{gfinal}\ ] ] the principal value of the polarization operator @xmath68 at a real @xmath69 defines the energy shift from the unperturbed phonon energy @xmath49 to @xmath70 under the effect of particle - phonon coupling , whereas the imaginary part @xmath71 of the analytic continuation of @xmath72 into the complex energy plan @xmath73 defines the phonon damping @xmath74 , whose final explicit expression reads @xmath75^{2 } \bigg[\frac{f_{k'}^{+}-f_{k}^{+ } } { ( \omega - e_k^{- } + e_{k'}^{-})^2+\varepsilon^2}+\frac{f_{k'}^{-}-f_{k}^{-}}{(\omega - e_k^{+ } + e_{k'}^{+})^{2}+\varepsilon^{2}}\bigg]~ , \label{gamma1}\ ] ] where the representation @xmath76 $ ] is used to smooth the @xmath77-functions and to effectively take into account the contribution of the escape width owing to the coupling to continuum . the spectral intensity is found from the analytic properties of green s function ( [ gfinal ] ) as @xmath78/[{\rm e}^{\beta\omega}-1]$ ] , from which one obtains the gdr strength function @xmath79 as @xmath80 $ ] , where @xmath81 denotes @xmath82 calculated at the gdr energy @xmath83 @xcite . the final result is a breit - wigner - like distribution with the energy - dependent half width @xmath74 : @xmath84 ^ 2+\gamma_q^2(\omega)}~. \label{sbw}\ ] ] the fwhm @xmath85 of the gdr is defined as a function of @xmath8 and @xmath11 as @xcite @xmath86~. \label{fwhm}\ ] ] the evaporation width of the compound nuclear states , which comes from the quantum mechanical uncertainty principle @xcite is not included because its effect on the gdr width is expected to be significant only at large values of the average temperature ( @xmath87 3.3 mev ) and average angular momentum ( @xmath87 30@xmath6 ) @xcite . for the comparison with the experimental line shape , which is fitted by using the lorentzian distribution , it is convenient to use the following lorentzian - like strength function @xcite , which is composed of two breit - wigner - like distributions ( [ sbw ] ) ( see , e.g. , eq . ( 16 ) of ref . @xcite ) : @xmath88~. \label{sl}\ ] ] in the fusion - evaporation reactions , where two heavy nuclei coalesce at high energy @xmath4 far above the coulomb barrier , the resulting compound system at high angular momentum decays by evaporating particles in competition with high - energy @xmath13 rays . the gdr is extracted from the high - energy @xmath13 ray spectrum as a lorentzian located at energy of around @xmath89@xcite . during this @xmath13 ray emission the nuclear temperature decreases from its initial value @xmath90 , resulting in a probability distribution @xmath91 of temperature , where @xmath92 is the temperature of the @xmath93-th step in the statistical decay . the same takes place with the angular momentum , which decreases from its initial value @xmath94 , resulting in the probability distribution @xmath95 . given the temperature and angular momentum probabilities distributions @xmath91 and @xmath96 , the average strength function at the excitation energy @xmath4 is calculated as @xmath97 where the strength function @xmath98 can be either @xmath99 ( [ sbw ] ) ( @xmath100 ) or @xmath101 ( [ sl ] ) ( @xmath102 ) obtained at a given pair of values @xmath103 , whereas @xmath104 is the strength function obtained by averaging @xmath98 over the probability distribution of temperature at each value @xmath105 of the angular momentum . the average temperature @xmath17 within the interval @xmath106 , where the probability distribution @xmath91 is determined ( @xmath107 ) , and the average angular momentum @xmath18 within the interval @xmath108 , where the probability distribution @xmath109 is determined ( @xmath110 ) , are calculated as @xmath111 in the present paper the average strength function @xmath112 in eq . ( [ avers ] )" +"the influence of boundaries on the vacuum state of a quantum field leads to interesting physical consequences . well known example is the casimir effect @xcite , when the modification of the zero - point fluctuations spectrum by the presence of boundaries induces vacuum forces acting on the boundaries . it may have important implications on all scales , from cosmological to subnuclear . the particular features of the resulting vacuum forces depend on the nature of the quantum field , the type of spacetime manifold , the boundary geometries and the specific boundary conditions imposed on the field . the casimir effect can be viewed as a polarization of vacuum by boundary conditions . another type of vacuum polarization arises in the case of an external gravitational field . in this paper , we study an exactly solvable problem with both types of sources for the polarization . namely , we consider the vacuum expectation value of the energy - momentum tensor for both scalar and electromagnetic fields induced by a curved boundary in background of robertson - walker ( rw ) spacetime with negative spatial curvature . in order to generate the vacuum densities we use the well known relation between the vacuum expectation values in conformally related problems ( see , for instance , @xcite ) and the corresponding results for an infinite plane boundary moving with uniform acceleration through the fulling rindler vacuum . the latter problem for conformally coupled dirichlet and neumann massless scalar fields and for the electromagnetic field in four dimensional rindler spacetime was considered by candelas and deutsch @xcite . these authors consider the region of the right rindler wedge to the right of the barrier . in @xcite , we have investigated the wightman function and the vacuum expectation values of the energy momentum tensor for a massive scalar field with general curvature coupling parameter , satisfying the robin boundary condition on the infinite plane in an arbitrary number of spacetime dimensions and for the electromagnetic field . we have considered both regions , including the one between the barrier and rindler horizon . the corresponding surface densities induced on the plate have been considered in @xcite . the vacuum expectation values of the energy momentum tensors for scalar and electromagnetic fields for the geometry of two parallel plates moving by uniform acceleration are investigated in avag02 . in particular , the vacuum forces acting on the boundaries are evaluated . in @xcite the casimir energy is evaluated for massless scalar fields under dirichlet or neumann boundary conditions , and for the electromagnetic field with perfect conductor boundary conditions on one and two infinite parallel plates moving by uniform proper acceleration through the fulling rindler vacuum in an arbitrary number of spacetime dimension . a closely related problem for the evaluation of the energy - momentum tensor of a casimir apparatus in a weak gravitational field recently has been considered in @xcite . in particular , it has been shown that the casimir energy for a configuration of parallel plates gravitates according to the equivalence principle . in @xcite the conformal relation between de sitter and rindler spacetimes is used to generate the vacuum expectation values of the energy momentum tensor for a conformally coupled scalar field in de sitter spacetime in the presence of a curved brane on which the field obeys the robin boundary condition with coordinate dependent coefficients . the casimir densities for spherical branes in rindler - like spacetimes have been investigated in @xcite . the organization of the present paper is as follows . in the next section we consider the conformal relation between the problems in the rw spacetime with negative spatial curvature and rindler spacetime . the geometry of the boundary is specified . in section [ sec : scalar ] the vacuum expectation value of the energy - momentum tensor is investigated for a scalar filed with robin boundary condition . the casimir densities in the case of the electromagnetic field with perfect conductor boundary conditions on the plate are discussed in section [ sec : elmag ] . the main results are summarized in section [ sec : conc ] . as a background geometry we shall consider the @xmath0 rw spacetime with the line element@xmath1where @xmath2 and @xmath3 is the line element on the @xmath4-dimensional unit sphere in euclidean space . first of all let us present the rw line element in the form conformally related to the rindler metric . with this aim we make the coordinate transformation@xmath5 with @xmath6 , defined by the relations ( see ref . @xcite for the case @xmath7)@xmath8where @xmath9 is a constant with the dimension of length and we use the notation@xmath10under this transformation the rw line element takes the form@xmath11 in this form the rw metric is manifestly conformally related to the metric in the rindler spacetime with the line element @xmath12:@xmath13 by using the standard transformation formula for the vacuum expectation values of the energy momentum tensor in conformally related problems ( see , for instance , @xcite ) , we can generate the results for the rw spacetime from the corresponding results in the rindler spacetime . first we shall consider the corresponding quantities in the coordinates @xmath14 with the line element ( [ dsrw1 ] ) . these quantities are found by using the transformation formula for conformally related problems : @xmath15 |0_{% \mathrm{rw}}\rangle = [ \xi /a(\eta ) ] ^{d+1}\langle 0_{\mathrm{r}}|t_{i}^{k}% \left [ g_{lm}^{\mathrm{r}},\varphi _ { \mathrm{r}}\right ] |0_{\mathrm{r}% } \rangle + \langle t_{i}^{k}\left [ g_{lm}^{\prime } , \varphi \right ] \rangle ^{% \mathrm{(an ) } } , \label{conftransemt}\]]where the second term on the right is determined by the trace anomaly . in odd spacetime dimensions the conformal anomaly is absent and the corresponding part vanishes : @xmath16 \rangle ^{\mathrm{(an)}}=0 $ ] for even @xmath17 . the vacuum expectation value of the energy - momentum tensor in coordinates ( [ dsrw ] ) is obtained by the standard coordinate transformation formulae . for a second rank tensor @xmath18 , which is diagonal in coordinates @xmath19 , the transformation to coordinates @xmath20 has the form @xmath21 in this paper , as a rindler counterpart we shall take the vacuum energy momentum tensor induced by an infinite plate moving by uniform proper acceleration through the fulling rindler vacuum . we shall assume that the plate is located in the right rindler wedge and has the coordinate @xmath22 . in coordinates @xmath23 the boundary @xmath24 is presented by the hypersurface@xmath25the corresponding normal has the components@xmath26we consider the cases of scalar and electromagnetic fields separately . in this section we consider a conformally coupled massless scalar field @xmath27 on background of spacetime with the line element ( [ dsrw ] ) . the corresponding field equation has the form @xmath28where @xmath29 is the ricci scalar for the rw spacetime . we assume that the field satisfies the robin boundary condition @xmath30on the hypersurface ( [ boundeq ] ) . the expectation value of the energy - momentum tensor induced by the presence of an infinite plane boundary moving with uniform acceleration through the fulling rindler vacuum was investigated in @xcite . for a scalar field @xmath31 it is presented in the decomposed form : @xmath32|0_{\mathrm{r}}\rangle = \langle \tilde{0}_{\mathrm{r}}|t_{i}^{k}[g_{lm}^{% \mathrm{r}},\varphi _ { \mathrm{r}}]|\tilde{0}_{\mathrm{r}}\rangle + \langle t_{% \mathrm{(r)}i}^{k}\rangle ^{\mathrm{(b)}}. \label{tikr}\]]in this formula , @xmath33 are @xmath34 are the vacuum states for the rindler spacetime in presence and absence of the plate respectively and @xmath35 is the part of the vacuum energy - momentum tensor induced by the plate . for the part without boundaries one has @xmath36|\tilde{0}_{\mathrm{r}}\rangle = \frac{a_{d}\xi ^{-d-1}}{% 2^{d-1}\pi ^{d/2}\gamma ( d/2)}\mathrm{diag}\left ( -1,1/d,\ldots , 1/d\right ) , \label{tikr0}\]]with the notation @xmath37 , \label{ad}\]]where @xmath38 for even @xmath39 and @xmath40 for odd @xmath41 , and the value for the product over @xmath42 is equal to 1 for @xmath43 . for a scalar field @xmath31 satisfying the robin boundary condition @xmath44with constant coefficients @xmath45 and @xmath46 , the boundary induced part in the region @xmath47 is given by the formula saha02 @xmath48 . \label{tikrb}\]]here the functions @xmath49 $ ] have the form @xmath50 & = & g^{\prime 2}(z)+\frac{d-1}{z}g(z)g^{\prime } ( z)+\left [ 1-(2d-1)\frac{\omega ^{2}}{z^{2}}\right ] g^{2}(z ) , \notag \\ f^{(1)}[g(z ) ] & = & -dg^{\prime 2}(z)-\frac{d-1}{z}g(z)g^{\prime } ( z)+d\left ( 1+% \frac{\omega ^{2}}{z^{2}}\right ) g^{2}(z ) , \label{figz } \\ f^{(i)}[g(z ) ] & = & g^{\prime 2}(z)+\left ( \frac{\omega ^{2}}{z^{2}}-\frac{d+1}{% d-1}\right ) g^{2}(z),\quad i=2,\ldots , d. \notag\end{aligned}\]]in eq . ( [ tikrb ] ) , @xmath51 and @xmath52 are the modified bessel functions and for a given function @xmath53 we use the notation @xmath54the expression for the boundary part of the vacuum energy - momentum tensor in the region @xmath55 is obtained from formula ( [ tikrb ] ) by the replacements @xmath56 . the formulae given above allow us to present the rw vacuum expectation value in coordinates @xmath57 in the form similar to ( [ tikr ] ) : @xmath15 |0_{% \mathrm{rw}}\rangle = \langle \tilde{0}_{\mathrm{rw}}|t_{i}^{k}\left [ g_{lm}^{\prime } , \varphi \right ] |\tilde{0}_{\mathrm{rw}}\rangle + \langle t_{i}^{k}\left [ g_{lm}^{\prime } , \varphi \right ] \rangle ^{\mathrm{(b ) } } , \label{tikds}\]]where @xmath58 |\tilde{0}_{\mathrm{rw}}\rangle $ ] is the vacuum expectation value in the rw spacetime without boundaries and the part @xmath59 \rangle ^{\mathrm{% ( b)}}$ ] is induced by the boundary ( [ boundeq ] ) . conformally transforming the rindler results one finds @xmath60 |\tilde{0}_{\mathrm{rw}}\rangle & = & [ \xi /a(\eta ) ] ^{d+1}\langle \tilde{0}_{\mathrm{r}}|t_{i}^{k}[g_{lm}^{\mathrm{r}},\varphi _ { \mathrm{r}}]|% \tilde{0}_{\mathrm{r}}\rangle + \langle t_{i}^{k}\left [ g_{lm}^{\prime } , \varphi \right ] \rangle ^{\mathrm{(an ) } } , \label{tikds0 } t_{i}^{k}\left [ g_{lm}^{\prime } , \varphi \right ] \rangle ^{\mathrm{% ( b ) } } & = & [ \xi /a(\eta ) ] ^{d+1}\langle t_{\mathrm{(r)}i}^{k}\rangle ^{\mathrm{% ( b)}}. \label{tikdsb}\end{aligned}\]]under the conformal transformation @xmath61^{2}g_{ik}^{\mathrm{r}}$ ] , the field @xmath62 is changed by the rule @xmath63^{(d-1)/2}\varphi _ { \mathrm{r}% } ( x^{\prime } ) . \label{fieldtrans}\]]now by comparing boundary conditions ( [ bc ] ) , ( [ boundrind ] ) and taking into account eq . ( [ fieldtrans ] ) , one obtains the relation between the coefficients in the boundary conditions : @xmath64as it is seen from this relation , the dirichlet boundary condition in the problem on the rw bulk ( @xmath65 ) corresponds to the dirichlet boundary condition in the conformally related problem for the rindler spacetime . for the case of the neumann boundary condition in the rw bulk ( @xmath66 ) the corresponding problem in the rindler spacetime is of the robin type with @xmath67 . as before , we shall present the corresponding components in coordinates @xmath68 in the form of the sum of purely rw and boundary parts : @xmath69 |0_{\mathrm{rw% } } \rangle = \langle \tilde{0}_{\mathrm{rw}}|t_{i}^{k}\left [ g_{lm},\varphi % \right ] |\tilde{0}_{\mathrm{rw}}\rangle + \langle t_{i}^{k}\rangle ^{\mathrm{% ( b)}}. \label{tikds1}\]]by using the relations ( [ a21 ] ) for the purely rw part one finds ( for the vacuum polarization in rw spacetimes see @xcite and references therein ) @xmath70 |% \tilde{0}_{\mathrm{rw}}\rangle = \frac{2a_{d}[a(\eta ) ] ^{-d-1}}{(4\pi ) ^{d/2}\gamma ( d/2)}\mathrm{diag}\left ( -1,1/d,\ldots , 1/d\right ) + \langle t_{i}^{k}\left [ g_{lm},\varphi \right ] \rangle ^{\mathrm{(an)}}. \label{tik0dsst}\]]in particular , for @xmath7 we have @xcite@xmath71 \rangle ^{\mathrm{(an)}}=% \frac{^{(3)}h_{i}^{k}-^{(1)}h_{i}^{k}/6}{2880\pi ^{2 } } , \label{tikan}\]]where the expressions for the tensors @xmath72 are given in birrell . now it can be easily checked that for the static case , @xmath73 , one has @xmath74 |\tilde{0}_{\mathrm{rw}}\rangle = 0 $ ] . in the special case of the power - law expansion , @xmath75 , with @xmath76 being the synchronous time coordinate , we find@xmath70 |% \tilde{0}_{\mathrm{rw}}\rangle = \frac{c(c^{2}-6c+3)\left ( 3c-4\right ) } { % 2880\pi ^{2}t^{4}}\mathrm{diag}(\frac{3c}{3c-4},1,1,1 ) . \label{tikrwd3}\]]the corresponding energy density is negative for @xmath77 . for the boundary induced energy - momentum tensor in coordinates @xmath57 the spatial part is not isotropic and the corresponding part in coordinates @xmath68 is more complicated ( no summation over @xmath42 ) : @xmath78^{d+1}\langle" +"polarimetry of sn 1987a was obtained from 2262 days after explosion ( jeffery 1991a , and references therein ) . several groups ( jeffery 1991b ; hflich 1991 ) modelled the observations in terms of scattering by the supernova atmosphere ( sutherland & shapiro 1982 ; mccall 1984 ) . the degree of polarization predicted by these models is generally a decreasing function of time after explosion , as can be anticipated from the fact that the atmosphere gets progressively optically thin as the supernova atmosphere expands . eventually electron scattering becomes unimportant and no polarization can be produced . these models are capable of reproducing the observations prior to day 100 after explosion ( hflich 1991 ; jeffery 1991b ) . the observed degree of polarization , however , increased sharply from 0.2% to about 1.6% at around day 100 ( jeffery 1991a ; barret 1988 ) . this behavior is difficult to reconcile in terms of the photospheric scattering model . correction for interstellar polarization ( isp ) is crucial , but is unfortunately quite uncertain . we base our study on the polarimetric data compiled and corrected for isp by jeffery ( 1991a ) , where the isp is estimated from unpublished observations made at la plata observatory at around day 600 . the data show that the degree of polarization increased from about 0.1% at day 2 to about 1% at @xmath0 day 250 . the polarization position angle remains fairly constant during all these observations . the time variability of the polarization indicates that the observed polarization is intrinsically related to the supernova event , regardless of the isp in the direction to the supernova . we show here that dust scattering plays an important role in producing the polarized light of sn 1987a . in 2.1 the survival of dust particles in the vicinity of the supernova is discussed . the dust scattering process and how that leads to the observed polarization is presented in 2.2 . 3 compares the model with various observations . conclusions and a brief discussion are given in 4 . the dust particles in the vicinity of the supernova are destroyed mainly by the intense initial ultraviolet ( uv ) flash of the supernova after the shock breakout . lundqvist & fransson ( 1991 ) , and luo ( 1991 ) inferred that an initial uv flash with net energy @xmath1 ergs and effective temperatures @xmath2k is required to fit the observed light curves of the various nebular emission lines of the circumstellar loops . the luminosities and radiation temperatures they used were taken from models 10h and 10l of woosley ( 1988 ) , and 11e1y6 of shigeyama , nomoto & hashimoto ( 1988 ) . these models and also those by arnett ( 1988 ) give peak luminosities of @xmath3and peak effective temperatures of @xmath4 k. more detailed models by ensman & burrows ( 1992 ) give peak luminosities @xmath5 and @xmath6 k. the distance at which the dust achieves equilibrium temperature @xmath7 is @xmath8 where @xmath9 is the effective temperature of the supernova radiation , @xmath10 is the dust absorption efficiency averaged over wavelength and is a function of the effective temperature @xmath11 of the radiation field , and @xmath12 is the luminosity . evaporation of dust particles occurs when @xmath7 is above the evaporation temperature which is typically around 2000 k. as felten & dwek ( 1989 ) noticed , however , the evaporation / sublimation time scale may be _ longer _ than the duration of the uv flash , and hence , dust can survive at a substantially smaller distance from the progenitor than given in equation ( 1 ) . the time scale for dust evaporation at a temperature @xmath7 , is ( voit 1992 ; guhathakurta & draine , 1989 ) @xmath13 , \eqno(2)\ ] ] where @xmath14 is the binding energy of the dust particles , and @xmath15 is the radius of the dust particle . guhathakurta & drain ( 1989 ) give @xmath16 k for graphite and @xmath17 k for silicate . at @xmath18 k , @xmath19 is @xmath20 s , considerably larger than the duration of the uv flash which is @xmath21 s. only grains heated up to a temperature at which the corresponding evaporation time is shorter than the duration of the uv flash will evaporate . the real temperature above which the dust particles will be destroyed is therefore given by equating @xmath22 and @xmath23 . the radius beyond which the dust particles will survive as a function of the size of the dust particle is plotted in fig . 1 for different models of the supernova explosions . this defines theoretically the minimum distance dust particles can survive the initial uv flash . we define first a polar coordinate system of which the z - axis is along the line of sight and the x - axis is on the plane of sky and defines the zero point of the polarization position angle . the supernova is located at the origin . the number density of csm dust is given by @xmath24 . the scattered light depends sensitively on the shape of the supernova light curve . consider first the case for which the supernova emits natural light at a luminosity per unit frequency @xmath25 over a time @xmath26 . assuming single scattering and @xmath27 , the flux of the scattered light @xmath28 is derived by chevalier ( 1986 ) . the stokes parameters @xmath29 and @xmath30 can be found in a similar and straight forward way . the equations are @xmath31 where the integration is over the plane of the sky , @xmath32 is the grain scattering efficiency , @xmath33 is the geometric cross section of the grain , @xmath34 is the distance to the supernova , and @xmath35 and @xmath36 are elements of the dust scattering matrix ( chandrasekhar 1960 ) as a function of @xmath37 . the scattering phase function @xmath35 can be found in henvey & greenstein ( 1941 ) , and the polarization function @xmath36 approximates the rayleigh function ( white 1979 ) . for the more general case that the supernova light curve is given by @xmath38 , the fluxes and stokes parameters can be obtained by convolving @xmath38 with @xmath39 , @xmath40 and @xmath41 ( cf chevalier , 1986 ) . scattered light contributes also to the observed luminosity , but is only a second order effect in the optically thin case . the net polarization of the supernova is therefore calculated by multiplying the polarization of the scattered light by the ratio of the scattered light to the luminosity of the supernova . our most favored model is achieved by a dust blob of radius 1.2 @xmath42 cm located on the plane of the sky passing through the supernova , at a distance 5.7 @xmath42 cm away from the supernova and a position angle of @xmath43 . the parameters governing dust scattering are : albedo @xmath44 , and peak linear polarization @xmath45 . the optical depth of the blob is 0.36 . in the following this model is compared with observations . we show in fig . 2(a ) the v band polarimetry together with the polarimetry curve calculated using equation ( 3 ) . the v - band light curve is from hamuy & suntzeff ( 1990 ) . the polarimetry data are from jeffery ( 1991a ) . the degree of polarization scales linearly in the adopted optically thin approximation , and satisfactory fits were obtained for @xmath46 , depending sensitively on the distance to the supernova . the dust scattering asymmetry parameter is @xmath47 = 0.3 ( henvey & greenstein 1941 ) . the overall shape of the time evolution of the polarization is well reproduced . the increase of polarization before day 30 is due to the increase of the flux of the highly polarized scattered light as a result of light travel effects . the model predicts an increase at around day 100 when the supernova evolves down from its second optical maximum . this behavior is again due to the fact that the fraction of scattered light increases as the supernova falls below its maximum . the broad spectral features in the polarization spectra which correspond to various absorption and emission lines of the supernova were taken as evidences againest circumstellar scattering . we show here that this is incorrect . the observed polarization depends on both the intrinsic supernova light curve and the scattering process in a complicated way as shown in equations ( 3 ) . because the luminosities at different wavelengths evolve differently , the net polarization at different wavelengths will also be different , especially across strong p - cygni lines . it can be anticipated that broad polarized spectral features can be produced . and indeed , as an example , fig . 2(b ) shows the model polarization spectra on day 100 obtained by using the set of spectroscopic observations of sn 1987a from the ctio archive ( phillips et al . the model polarization spectrum agrees well with the polarization spectra corrected for isp by jeffery ( 1991a ) , considering the fact that the polarization spectra depends sensitively on the corrections for isp . the dust particles responsible for the scattering and polarization emit also in the infrared . the infrared light curve is calculated by assuming @xmath48 for the dust scattering phase function . 3 shows the model results together with the luminosity of the ir component obtained by fitting two black bodies to the early photometric observations ( bouchet et al . although bouchet et al . ( 1989 ) argue that the infrared emissions may come from free free emission of the supernova ejecta , the present model correctly fits the light curve of the infrared emission , in particular the time delay of its maximum compared with the observed light curve . note that the temperature of the dust particles varies with the distance to the supernova , so their emission can not be exactly that of a black body . a self - consistent analysis requires detailed modeling of the dust emission and the early observations which is beyond the scope of this paper . it is encouraging that such a simple analysis already yields surprisingly satisfactory model fits . the polarimetry of sn 1987a can be modeled in terms of scattering by a dusty blob . both the polarimetry curve and the early infrared light curve can be successfully fitted by a csm dust scattering blob . this analysis is , however , far from complete . substantial improvements can be achieved by more detailed modeling . in particular , the polarization position angle also shows clear changes across spectral lines . this suggests that a single scattering blob can not account for all the observed polarization . two or more blobs may improve the model . another possibility is that the observed polarization is a combination of the atmospheric scattering model and the csm dust scattering model presented here . the hypothesized dust blob may be related with the mystery spot discovered in earlier speckle observations ( cropper et al . they are located at almost identical position angles of @xmath49 . further analysis may provide some interesting tests for the authenticity of the speckle sources ( nisenson et al . 1988 ; meikle et al . 1987 ) . our recent observations show that polarization @xmath50 may be a common phenomena in type ii supernovae ( wang et al . a correct picture for the origin of the polarization is therefore critical for the understanding of supernova explosion mechanisms in general , and also in establishing type ii supernovae as extra galactic distance indicators using the expanding photosphere method . if dust scattering is really important in producing polarization , the present study suggests that type ii supernovae are more likely to be associated with" +"the study of topological phases of matter is one of the most vibrant directions of research in contemporary condensed matter physics . one core accomplishment has been the theoretical modeling and experimental discovery of two - dimensional topological insulators . @xcite the integer quantum hall effect ( iqhe ) was an early example of how states could be classified into distinct topological classes using an integer , the chern number , to express the quantized hall conductivity . @xcite in the iqhe , the number of delocalized edge channels is directly tied to the quantized hall conductivity through the chern number . more recently , it has been found that the symmetry under reversal of time acts as a protective symmetry for edge modes in ( bulk ) insulators with strong spin - orbit interactions in two and three dimensions , @xcite and that these systems are characterized by a @xmath0 topological invariant . the discovery of @xmath0 topological insulators has triggered a search for a classification of phases of fermionic matter that are distinct by some topological attribute . for non - interacting electrons , a complete classification , the tenfold way , has been accomplished in arbitrary dimensions . @xcite in this scheme , three discrete symmetries that act locally in position space time - reversal symmetry ( trs ) , particle - hole symmetry ( phs ) , and chiral or sublattice symmetry ( sls ) play a central role when defining the quantum numbers that identify the topological insulating fermionic phases of matter within one of the ten symmetry classes ( see columns 1 - 3 from table [ table : main table ] ) . the tenfold way is believed to be robust to a perturbative treatment of short - ranged electron - electron interactions for the following reasons . first , the unperturbed ground state in the clean limit and in a closed geometry is non - degenerate and given by the filled bands of a band insulator . the band gap provides a small expansion parameter , namely the ratio of the characteristic interacting energy scale to the band gap . second , the quantized topological invariant that characterizes the filled bands , provided its definition and topological character survives the presence of electron - electron interactions as is the case for the symmetry class a in two spatial dimensions , can not change in a perturbative treatment of short - range electron - electron interactions . @xcite on the other hand , the fate of the tenfold way when electron - electron interactions are strong is rather subtle . @xcite for example , short - range interactions can drive the system through a topological phase transition at which the energy gap closes , @xcite or they may spontaneously break a defining symmetry of the topological phase . even when short - range interactions neither spontaneously break the symmetries nor close the gap , it may be that two phases from the non - interacting tenfold way cease to be distinguishable in the presence of interactions . in fact , it was shown for the symmetry class bdi in one dimension by fidkowski and kitaev that the non - interacting @xmath1 classification was too fine in that it must be replaced by a @xmath2 classification when generic short - range interactions are allowed . how to construct a counterpart to the tenfold way for interacting fermion ( and boson ) systems has thus attracted a lot of interest . @xcite the fractional quantum hall effect ( fqhe ) is the paradigm for a situation by which interactions select topologically ordered ground states of a very different kind than the non - degenerate ground states from the tenfold way . on a closed two - dimensional manifold of genus @xmath3 , interactions can stabilize incompressible many - body ground states with a @xmath3-dependent degeneracy . excited states in the bulk must then carry fractional quantum numbers ( see ref . and references therein ) . such phases of matter , that follow the fqhe paradigm , appear in the literature under different names : fractional topological insulators , long - range entangled phases , topologically ordered phases , or symmetry enriched topological phases . in this paper we use the terminology long - range entangled ( lre ) phase for all phases with nontrivial @xmath3-dependent ground state degeneracy . all other phases , i.e. , those that follow the iqhe paradigm , are called short - range entangled ( sre ) phases . ( in doing so , we follow the terminology of ref . , that differs slightly from the one used in ref . the latter counts all chiral phases irrespective of their ground state degeneracy as lre . ) while there are nontrivial sre and lre phases in the absence of any symmetry constraint , many sre and lre phases are defined by some protecting symmetry they obey . if this protecting symmetry is broken , the topological attribute of the phase is not well defined any more . however , there is a sense in which lre phases are more robust than sre phases against a weak breaking of the defining symmetry . the topological attributes of lre phases are not confined to the boundary in space between two distinct topological realizations of these phases , as they are for sre phases . they also characterize intrinsic bulk properties such as the existence of gapped deconfined fractionalized excitations . hence , whereas gapless edge states are gapped by any breaking of the defining symmetry , topological bulk properties are robust to a weak breaking of the defining symmetry as long as the characteristic energy scale for this symmetry breaking is small compared to the bulk gap in the lre phase , for a small breaking of the protecting symmetry does not wipe out the gapped deconfined fractionalized bulk excitations . the purpose of this paper is to implement a classification scheme for interacting electronic systems in two spatial dimensions that treats sre and lre phases on equal footing . to this end , we use a coupled wire construction for each of the symmetry classes from the tenfold way . this approach has been pioneered in refs . and for the iqhe and in refs . and for the fqhe ( see also related work in refs . ) . to begin with , non - chiral luttinger liquids are placed in a periodic array of coupled wires . in doing so , forward - scattering two - body interactions are naturally accounted for within each wire . we then assume that the back - scattering ( i.e. , tunneling ) within a given wire or between neighboring wires are the dominant energy scales . imposing symmetries constrains these allowed tunnelings . whether a given arrangement of tunnelings truly gaps out all bulk modes , except for some ungapped edge states on the first and last wire , is verified with the help of a condition that applies to the limit of strong tunneling . we name this condition the haldane criterion , as it was introduced by haldane in his study of the stability of non - maximally chiral edge states in the quantum hall effect . @xcite we show that , for a proper choice of the tunnelings , all bulk modes are gapped . moreover , in five out of the ten symmetry classes of the tenfold way , there remain gapless edge states in agreement with the tenfold way . it is the character of the tunnelings that determines if this wire construction selects a sre or a lre phase . hence , this construction , predicated as it is on the strong tunneling limit , generalizes the tenfold way for sre phases to lre phases . it thereby delivers lre phases that have not yet appeared in the literature before . evidently , this edge - centered classification scheme does not distinguish between lre phases of matter that do not carry protected gapless edge modes at their interfaces . for example , some fractional , time - reversal - symmetric , incompressible and topological phases of matter can have fractionalized excitations in the bulk , while not supporting protected gapless modes at their boundaries . @xcite stated in a slightly more constructive way , we can think of our approach as ( 1 ) fixing , in a first step , a given desired edge theory at the boundary , and ( 2 ) continue , in a second step , by asking whether such an edge can be consistently defined with a set of symmetry - allowed periodic tunneling terms between wires which manage to gap out all other modes . alluding to a related strategy in philosophy , this is what we call wire deconstructionism of topological phases . the paper is organized as follows . we define the array of luttinger liquids in sec . [ sec : definitions ] . the haldane criterion , which plays an essential role for the stability analysis of the edge theory , is reviewed in sec . [ sec : conditions for a spectral gap ] . all five sre entries of table [ table : main table ] are derived in sec . [ sec : reproducing the tenfold way ] , while all five lre entries of table [ table : main table ] are derived in sec . [ sec : fractionalized phases ] . we conclude with sec . [ sec : discussion ] , where we allude to the generalization of our approach to additional symmetries , bosonic systems , and higher spatial dimensions . and @xmath4 , the scattering between them is forbidden by imposing locality in the limit @xmath5 . ( b ) periodic boundary conditions allow the scattering vector @xmath6 that gaps modes which were protected by locality before . , width=317 ] & @xmath7 & @xmath8&@xmath9 & & short - range entangled ( sre ) topological phase & long - range entangled ( lre ) topological phase + @xmath10 a & @xmath11 & @xmath11&@xmath11&@xmath12 & [ cols=""^ "" , ] + cii & @xmath13 & @xmath13&@xmath14 & & none & + [ table : main table ] we consider an array of @xmath15 parallel wires that stretch along the @xmath16 direction of the two - dimensional embedding euclidean space ( see fig . [ fig : boundaryconditions ] ) . we label a wire by the latin letter @xmath17 . each wire supports fermions that carry an even integer number @xmath18 of internal degrees of freedom that discriminate between left- and right - movers , the projection along the spin-@xmath19 quantization axis , and particle - hole quantum numbers , among others ( e.g. , flavors ) . we label these internal degrees of freedom by the greek letter @xmath20 . we combine those two indices in a collective index @xmath21 . correspondingly , we introduce the @xmath22 pairs of creation @xmath23 and annihilation @xmath24 field operators obeying the fermionic equal - time algebra [ eq : def hat psi s ] @xmath25 with all other anticommutators vanishing and the collective labels @xmath26 . the notation @xmath27 is used for the operator - valued row ( @xmath28 ) and column ( @xmath29 ) vector fields . we assume that the many - body quantum dynamics of the fermions supported by this array of wires is governed by the hamiltonian @xmath30 , whereby interactions within each wire are dominant over interactions between wires so that we may represent @xmath30 as @xmath15 coupled luttinger liquids , each one of which is composed of @xmath18 interacting fermionic channels . by assumption , we may thus bosonize the @xmath22 fermionic channels making up the array . to this end , we follow ref . . within abelian bosonization , this is done by postulating first the @xmath31 matrix [ eq" +"two types of galaxies account for the vast majority of star formation at @xmath2 : the lyman break galaxies ( lbgs ; steidel et al . 1996 , 2003 ) , and the ultra / hyperluminous infrared galaxies detected at submillimeter and millimeter wavelengths ( blain et al . 2002 and references therein ; bertoldi et al . as both selections identify strong star formation , it is tempting to assume they are sampling a common population . however , current observations do not show a large overlap between the two samples . only a small percentage of lbgs are detected with scuba , even though their high star formation rates predict they should be far - infrared ( fir ) luminous ( chapman et al . 2000 ; peacock et al . the reverse is true as well the majority of ultraluminous infrared sources ( ulirgs ; @xmath3 ) are so highly extincted that they would be missed in rest - frame uv - selected surveys for high redshift galaxies like the lbgs ( meurer et al . 1999 ; goldader et al . this difference may imply that the two methods select galaxies at different stages of evolution , or with intrinsically different physical characteristics . the spitzer space telescope gives us the first opportunity to study both populations across a wide range of mid - infrared ( mir ) wavelengths . recently , six extremely bright lbgs were discovered in sloan digital sky survey ( sdss ) spectra ( bentz , osmer , & weinberg 2004 ; hereafter bow ) . the spectra of the six sources are typical of lbgs , with bright rest - frame uv continua and clearly detected stellar and interstellar absorption lines . they appear 2 - 3 magnitudes brighter than the most luminous lbgs in the steidel et al . sample . none of the six show spectral features that would be expected for agn , such as broad or high ionization emission lines . bow find no morphological or environmental indicators which suggest lensing . by contrast , the only comparably bright known lbg is ms1512-cb58 ( yee et al . 1996 ; hereafter cb58 ) ; it is strongly lensed by a dense foreground cluster ( seitz et al . 1998 ) , and has an obvious arclike shape which is discernible from the ground . in this paper , we present the first spitzer detection of an lbg at 16 with the spitzer infrared spectrograph ( irs ; houck et al . 2004 ) `` blue '' peak up filter which is centered at 16 . `` blue '' peak up array . one of the sdss lbgs , j134026.44 + 634433.2 ( hereafter s - lbg-1 ) , was selected as a science verification target for spitzer . the object has a spectroscopic redshift of z=2.79 . throughout the paper , we will adopt a flat , @xmath4-dominated universe ( @xmath5 km s@xmath6 mpc@xmath6 , @xmath7 ) . we obtained 16 imaging of s - lbg-1 on 14 november 2003 with the irs onboard the spitzer space telescope . between exposures , we moved the telescope in a four point dither pattern , with separations of 4 . at each point in the pattern , two nod positions were observed , and two cycles were taken at each nod position . a total of 16 exposures were taken , with integration times of one minute each . the data were reduced using the irs pipeline at the spitzer science center ( see chapter 7 of the spitzer observer s manual ) . individual frames were registered based on the reconstructed pointing ( accurate to better than 1 ) and refined with centroiding of objects . bad pixels were masked before mosaicing . we have not removed the small ( @xmath8% ) geometric distortion in the images . we have several times redundancy for each pixel on the sky , and we remove faint latent images caused by bright sources in pu observations prior to our program . photometric calibration utilized routine observations of a bright standard . we measured the flux in 16 images of hd 46190 to calculate the zeropoint by comparison with template spectra based on normalized kurucz ( 1993 ) models ( cohen et al . a curve of growth was used to estimate total flux for a point source from aperture photometry . we also obtained supporting near - infrared ( nir ) data in the j- and k - bands with the wirc instrument ( wilson et al . 2003 ) on the hale 200-inch telescope . the observations were taken on 27 january 2004 . the field was observed for five dithered exposures in each filter . j - band exposures were two coadds of one minute each , and k - band were two coadds of 30 seconds each . the night was not photometric , but conditions were stable over the few minutes of the observations . the wirc field of view contains @xmath9 2mass stars , which we used to calibrate the photometry and estimate the extinction . the final , registered 16 image ( figure 1 ) has an rms noise of 15 @xmath10jy in an aperture with 5 radius , and 25 @xmath10jy in an aperture of 9 radius . s - lbg-1 is detected , with a flux of @xmath1 mjy . seven other objects are detected ( @xmath11 or more ) in the field , one of which is very bright in the mir and quite faint at optical wavelengths . of these , two have no counterpart in the sdss or wirc imaging . five additional sources are marginally detected ( @xmath12 ) , without optical counterparts . however , given the faintness of these sources it is not surprising that deeper optical / nir data will be needed to identify them . the reddest object , j134025.02 + 634358.3 ( hereafter red-1 ) , is discussed further in section [ sec : ero ] . photometric data from irs and wirc are given in table 1 . the wirc imaging shows no objects in the field that were not detected in sdss . there is no indication that s - lbg-1 is resolved , but it is not expected to be . the 16 imaging is diffraction limited , and the point spread function ( psf ) has a full width at half maximum ( fwhm ) of 4 . s - lbg-1 is compact in both the sdss and wirc imaging , which have fwhm of @xmath13 and @xmath14 , respectively . at the redshift of s - lbg-1 , z=2.79 , one arcsecond corresponds to @xmath15 kpc . the 16 filter extends from 13.3 to 18.6 at fwhm , or 3.5 to 4.9 in the rest frame . this wavelength range encompasses br@xmath16 but does not include the polycyclic aromatic hydrocarbon ( pah ) feature centered at 3.3 ( tokunaga et al . the filter samples the rayleigh - jeans tail of the stellar photospheric continuum emission emission , which can be considerable if the galaxy contains a substantial population of old stars . alternatively , 4 marks the beginning of the rise in emission from warm dust , heated either by very young stars or by an active nucleus . the spectral energy distribution ( sed ) of s - lbg-1 is consistent with a strongly starbursting galaxy ( figure 2 ) . in the figure we show a direct comparison with the spectrum of ngc 5253 ( wu et al . 2002 ) , a `` benchmark starburst '' ( calzetti et al . 1999 ) with regions that have undergone intense star formation in the last 100 myr ( see calzetti et al . 1997 and the reference therein ) , and a substantial older stellar population . it has mir emission from dust heated by massive , young stars ( crowther et al . the sed of s - lbg-1 is redder than ngc 5253 in the uv , but the two match quite well if one magnitude of additional extinction is applied . the rest - frame optical color of s - lbg-1 ( the observed j- and k - band ) is bluer than that of ngc 5253 , perhaps implying a lower fraction of old stars . ellingson et al . ( 1996 ) showed that the optical / nir sed of cb58 could be fit with a recent ( 10 myr ) secondary burst of star - formation added to a large ( 85% by mass ) stellar population with an age of @xmath17 gyr . the young age of the source was later confirmed by uv absorption line studies ( pettini et al . 2002 ) . a marginal detection of cb58 with isocam ( bechtold et al . 1998 ) , at rest - frame 1.8 and 3 , favored a higher percentage of younger stars . taken at face value , the cb58 sed is not consistent with s - lbg-1 unless cb58 rises steeply beyond the rest - frame k - band . the inconsistency could result from a higher dust content in s - lbg-1 and likely a dissimilar spatial distribution of dust , which may not be surprising given the different star formation states of the sources . the intrinsic ( corrected for lensing magnification ) sfr of cb58 is @xmath9 ( teplitz et al . 2000 ) , compared to the @xmath18 in s - lbg-1 ( without correcting for extinction ) . the s - lbg-1 sed is also consistent with a relatively dust - free seyfert galaxy ( figure 2 ) . however , bow see no high excitation lines in the uv . it is also possible that the observed 16 flux of s - lbg-1 indicates a `` buried '' agn that is not seen in the uv . bow discuss the possibility that the s - lbg s are bal qso s , but conclude that they would be unique amongst that class of objects if they were . nonetheless , the luminosity of s - lbg-1 may favor the possibility of agn activity dominating the mir flux . in addition , shorter wavelength spitzer observations of s - lbg-1 are needed to conclusively rule out a very steep mir slope , given the low rest - frame 3 flux of cb58 . laurent et al . ( 2000 ) show that the presence of an agn is revealed in the mir by an excess of emission in the 3 - 6 range . this has been attributed to hot dust emission heated to near sublimation temperatures ( @xmath18 k for silicates and @xmath19 k for graphite ) by the accretion disk . the presence of this continuum has been detected in a number of nearby galaxies hosting an active agn including ngc1068 and ngc4151 ( le floch et al . 2000 , alonso - hererro et al . 2003 ) , as well as centaurus a ( mirabel et al . 1999 ) . however , such excess usually has a positive slope in the 3 - 6 range , making it challenging to identify in distant systems because the old stellar population of the bulge of the galaxy may be missinterpreted as an excess of thermal emission . furthermore , there has been evidence that as the luminosity of dust enshrouded ir galaxies increases beyond @xmath20 , so does the probability that an agn contributes substantially to the heating of the dust ( sanders et al . 1988 ; veilleux , kim , & sanders 1999 ; tran et al . 2001 ) . if the brightest lbgs harbor buried agn , it might indicate that the typical percentage of agn in lbg searches , @xmath21% ( steidel et al . 2002 ) , is underestimated . in" +"in an effort to better constrain the morphology , kinematics , and origin of the warm ionized gas on the outskirts of galaxies we have obtained deep emission - line images of several nearby starburst and active galaxies using the taurus tunable filter ( ttf ) on the 3.9 m anglo - australian and 4.2 m william herschel telescopes ( see veilleux 2001 for more detail ) . in the course of this study , we discovered a remarkable emission - line structure in the early - type spiral galaxy ngc 1482 . this galaxy has so far received relatively little attention in the literature . it is classified as a peculiar sa0/a in the revised 3rd catalogue ( de vaucouleurs et al . 1991 ) based primarily on the presence of a dust lane across the disk of the galaxy . located at a distance of 19.6 mpc ( tully 1988 ) , it is an infrared - bright galaxy with log[l@xmath5/l@xmath6 = 10.5 ( e.g. , soifer et al . 1989 ; sanders , scoville , & soifer 1991 ) , which is rich in molecular gas and dust ( e.g. , sanders et al . 1991 ; young et al . 1995 ; chini et al . 1996 ) and is undergoing vigorous star formation ( e.g. , moshir et al . 1990 ; devereux & hameed 1997 ; thornley et al . 2000 ) . in a recent emission - line imaging survey of early - type spirals , hameed & devereux ( 1999 ) noticed the presence in ngc 1482 of `` filaments and/or chimneys of ionized gas extending perpendicular to the disk . '' the present study expands on the results of hameed & devereux , using deeper emission - line maps at h@xmath1 and [ n ii ] @xmath06583 and complementary long - slit spectra . we find that the [ n ii]/h@xmath1 excitation map of this galaxy is particularly useful at distinguishing between the star - forming disk and the entrained , shock - excited wind material . this excitation signature could be used in the future to more efficiently identify powerful galactic winds in the local and distant universe . ngc 1482 was observed on the night of 2000 december 16 using the `` blue '' taurus tunable filter ( ttf ; bland - hawthorn & jones 1998 ) at the anglo - australian telescope ( aat ) . this instrument was used in the `` charge shuffling / band switching '' mode to maximize sensitivity to faint flux levels . the basic idea is to move charge up and down within the detector at the same time as switching between two discrete wavelengths with the tunable filter . in this way , the on - band image is obtained nearly simultaneously as the off - band ( continuum ) image . for our observations , the charges were moved every minute and the chip was read out after a total integration time of 32 minutes ( i.e. 16 minutes on - band and 16 minutes off - band ) . four sets of observations were obtained of ngc 1482 : two centered on redshifted h@xmath1 for a total on - band integration time of 32 minutes , and two centered on redshifted [ n ii ] @xmath06583 for the same duration . the continuum images for each set of observations were obtained in a straddle mode , where the off - band image is made up of a pair of images that `` straddle '' the on - band image in wavelength ; this greatly improves the accuracy of the continuum removal since it corrects for slopes in the continuum and underlying absorption features ( see also maloney & bland - hawthorn 2001 ) . the wavelength calibration was checked before and after each pair of observations and was found to be stable . the bandpass of the ttf was set to 14.6 throughout the observations . this bandpass was chosen to separate h@xmath1 @xmath06563 emission from [ n ii ] @xmath76548 , 6583 emission , while still producing a monochromatic field of view of several arcminutes , much larger than the total extent of ngc 1482 . phase effects due to the angular fabry - perot interferometer response can therefore be safely ignored in the rest of the discussion . the mitll2a ccd was used for these observations , providing a pixel scale of 0@xmath837 pixel@xmath2 and a field of view of 10@xmath9 @xmath3 10@xmath9 . the observations were obtained under photometric and @xmath10 1@xmath85 seeing conditions . on 2001 september 19 21 , several complementary long - slit spectra were obtained of ngc 1482 . the dual - beam spectrograph ( dbs ) on the mssso 2.3 m telescope was used at the nasmyth f/17.9 focus with the 1200b and 1200r gratings . the ccd was a site 1752 @xmath3 532 @xmath3 15@xmath11 pixel device . at a plate scale 091 pix@xmath2 , a 2 slit gave a resolution of 1.2 fwhm and a wavelength coverage of 4400 5400 and 6100 7050 . on one occasion , the slit was aligned along the minor axis of the galaxy ( p.a . @xmath12 13@xmath13 ; de vaucouleurs et al . 1991 ) passing through the nucleus . in all other cases , the slit was positioned along 103@xmath13 and offset from 0 to @xmath14 16 from the major axis of the galaxy . the exposure times were typically 1200 seconds . figure 1 shows the distribution of the h@xmath1 and [ n ii ] @xmath06583 emission in ngc 1482 . strong h@xmath1 and [ n ii ] emission is detected along the plane of the host galaxy ( p.a . @xmath12 103@xmath15 ) . in addition , an hourglass - shaped structure is seen in both h@xmath1 and [ n ii ] @xmath06583 , extending along the minor axis of the galaxy at least @xmath10 1.5 kpc above and below the galactic plane . this structure is more easily visible in [ n ii ] @xmath06583 than in h@xmath1 . this is particularly apparent in the lower left panel of figure 1 , where we present a [ n ii]/h@xmath1 ratio map of this object . the [ n ii ] @xmath06583/h@xmath1 ratios measured in the disk of the galaxy [ @xmath12 0.3 ( outer disk ) 0.6 ( inner disk ) ] are typical of photoionization by stars in h ii regions , but the ratios in the hourglass structure are 3 7 times larger ( [ n ii ] @xmath06583/h@xmath1 @xmath12 1.0 2.3 ) . this ratio of a collisionally excited line to a recombination line is fundamentally a measure of the relative importance of heating and ionization ( e.g. , osterbrock 1989 ) . [ n ii]/h@xmath1 ratios enhanced relative to h ii regions are often observed in the extraplanar material of normal disk galaxies , including our own ( e.g. , rand , kulkarni , & hester 1990 ; veilleux et al . 1995a ; reynolds , haffner , & tufte 1999 ; hoopes , walterbos , & rand 1999 ; rossa & dettmar 2000 ; collins & rand 2001 ; miller 2002 ) . although photoionization by the hardened and diluted radiation field from ob stars in the disk is partially responsible for these peculiar line ratios ( e.g. , sokolowski 1992 ; bland - hawthorn , freeman , & quinn 1997 ) , a secondary source of ionization or heating is often needed to explain in detail the runs of line ratios in these galaxies ( e.g. , reynolds et al . 1999 ; collins & rand 2001 ; miller 2002 ) . the extreme [ n ii ] @xmath06583/h@xmath1 ratios in the hourglass structure of ngc 1482 also require an additional source of heating . ruling out photoionization by an agn based on the lack of evidence for genuine nuclear activity in ngc 1482 ( e.g. , kewley et al . 2000 ) , the most likely explanation for these unusual line ratios is shock ionization . interaction of an energetic large - scale outflow with the ambient material of a gas - rich host galaxy will cause shock waves with velocities of 100 500 km s@xmath2 . the shocks will produce a strong flux of euv and soft x - ray radiation which may be absorbed in the shock precursor h ii region ( e.g. , dopita & sutherland 1995 ) . arguably one of the best examples known of shock - excited nebulae associated with large - scale galactic winds is the kpc - scale superbubble in the galaxy ngc 3079 ( e.g. , filippenko & sargent 1992 ; veilleux et al . 1994 ; cecil et al . large [ n ii ] @xmath06583/h@xmath1 ratios are observed throughout the bubble , reaching values of @xmath10 3 at the base of the bubble where the widths of the emission lines exceeds 400 km s@xmath2 . h ii region - like line ratios are observed everywhere else in the disk ( veilleux et al . 1995a ) . the kinematics of the line - emitting gas derived from our long - slit spectroscopy of ngc 1482 confirm that the hourglass structure is due to a large - scale galactic wind and that the extreme line ratios are produced through shocks . figure 2 shows the disturbed kinematics in the extraplanar material . line splitting of up to @xmath10 250 km s@xmath2 is detected along the axis of the hourglass structure out to at least 16 ( 1.5 kpc ) above and below the galaxy disk . normal galactic rotation dominates the kinematics of the gas within 5 6 ( @xmath10 500 pc ) from the disk . maximum line splitting often coincides with regions of low emission - line surface brightness . these results can be explained if the extraplanar emission - line material forms a biconical edge - brightened structure which is undergoing outward motion away from the central disk . in this case , the blueshifted ( redshifted ) emission - line component corresponds to the front ( back ) surface of the bicone . the lack of obvious velocity gradient in the centroid of the line emission suggests that the main axis of the bicone lies close to the plane of the sky . the fact that the amplitude of the line splitting does not decrease significantly with distance from the galaxy indicates that the entrained material is not experiencing significant deceleration ( i.e. , it is a blown - out wind ) . the mass involved in this wind can be estimated from the total h@xmath1 emission outside of the disk . defining the wind material as having [ n ii ] @xmath06583/h@xmath1 @xmath16 1 , we get a wind h@xmath1 flux ( luminosity ) of @xmath10 1.7 @xmath3 10@xmath17 erg s@xmath2 @xmath18 ( @xmath10 8.0 @xmath3 10@xmath19 erg s@xmath2 ) with an uncertainty of about @xmath14 25 30% . the [ s ii ] @xmath06731/@xmath06716 line ratios measured from our long - slit spectra indicate that the entrained material has a density @xmath20 @xmath21 . the mass in entrained line - emitting material is therefore @xmath22 3.6 @xmath3 10@xmath23 @xmath24 m@xmath25 where @xmath26 is normalized to 100 @xmath21 ( assuming case b recombination and an effective recombination coefficient for h@xmath1 of 8.6 @xmath3 10@xmath27 @xmath21 s@xmath2 ; osterbrock 1989 ) . a correction for possible dust extinction intrinsic to ngc 1482 will further increase this number ( note that the extinction due to our galaxy , e(b v ) = 0.04 , is negligible ; schlegel et al . a simple kinematic model can be used to estimate a few key wind parameters . the bisymmetric morphology and kinematics of the wind nebula in ngc 1482 suggest that the entrained material lies on the surface of a cylindrically symmetric bicone . if most of the gas" +"the cold dark matter ( cdm ) paradigm and its variations ( e.g. , @xmath7cdm ) have enjoyed remarkable success at explaining the large scale structure of the universe . at the scale of individual galaxies , however , cdm faces several serious challenges ( e.g. , * ? ? ? one of the key predictions of cdm and @xmath7cdm simulations is that all dark matter halos share a universal density profile @xcite . the original calculations predicted a central density profile @xmath8 , where @xmath9 is the galactocentric distance . more recent , higher resolution simulations have found even steeper @xmath10 central cusps ( e.g. , * ? ? ? * ; * ? ? ? * ) . these calculations , however , collide with a number of observational studies of dark - matter density profiles . most of the observations find either central constant density cores ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , or profiles where the density increases more slowly than @xmath11 toward the center ( e.g. , * ? ? ? other authors conclude that the observational evidence available to date is inconclusive , largely due to the lack of high quality high resolution rotation curves @xcite . indeed , using interferometers to obtain rotation curve data with the angular resolution and sensitivity required in order to resolve the central cusps is a daunting task for all but the nearest galaxies . the usual alternative , deriving rotation curves from longslit spectra , provides spatial information only along one dimension . this makes it impossible to separate circular and non circular motions and to check for position angle errors . other potential problems with rotation curves based solely on are the systematic effects introduced by extinction and the local expansion flow of regions , which are especially important close to galaxy centers , precisely where the shape of the rotation curve is most important . a recent study by @xcite , however , shows good agreement between the measured and kinematics in the inner parts of their galaxies , indicating that at least in some galaxies extinction is not a substantial concern . despite the recent body of work on the subject , _ it remains clear that we need more high quality , high resolution rotation curve measurements to advance towards solving the galactic scale dark matter puzzle . _ since both and rotation curve studies are problematic , we have opted for a third , complementary technique : we use co interferometry to measure the inner rotation curves . millimeter wave interferometry avoids the problems inherent to the first two techniques . first , it is much more sensitive to surface brightness than interferometry , allowing us to routinely obtain sensitive data with 5 angular resolution or better while the typical resolution of most studies is @xmath12 . second , not only is co interferometry unaffected by extinction , but it works best near galaxy centers where most molecular clouds are typically found . third , like interferometry but unlike long slit spectroscopy , it provides complete spectral imaging information allowing us to obtain reliable rotation curves . the relative sensitivity advantage of co interferometry stems from the fact that the @xmath13co ( @xmath14 ) rotational transition at 2.6 mm has a wavelength @xmath15 times smaller than the 21 cm spin flip transition . this allows the co antennas to be placed @xmath15 times closer together than the antennas for the same angular resolution . because the sensitivity of aperture synthesis to surface brightness is proportional to the fraction of the filled aperture , compactness confers a considerable sensitivity advantage to millimeter wave interferometers . for example , the ten element berkeley illinois maryland association millimeter array ( bima ; * ? ? ? * ) has a 250 times larger filled aperture fraction than the vla . the difficulty in using co interferometry for dark matter studies , however , is finding suitable target galaxies . late type dwarf galaxies are ideal for such studies , because their density profiles are dominated by dark matter in their inner regions @xcite . although little is known about the molecular gas content of most dwarf galaxies , with a few notable exceptions they are not strong molecular sources . we have obtained co interferometer maps of several nearby dwarf galaxies with single dish detections , a subset of which we selected for rotation curve studies . to further expand the set of suitable sources we are carrying out a systematic survey of nearby dwarf galaxies in co. thus , we expect that the results presented here are only a first glimpse of the final study . we present our observations in [ observations ] , perform a rotation curve study in [ discussion ] , and summarize our results in [ conclusions ] . the source we discuss in this work , ngc 4605 , is an sbc dwarf galaxy . independent photometric estimates place this galaxy @xmath16 mpc @xcite and @xmath17 mpc away ( m. pierce , priv . comm . ) , yielding a physical scale of @xmath18 pc/. the physical resolution of our co observations ( and of our rotation curve ) is therefore @xmath0 pc . the extinction corrected absolute b magnitude of ngc 4605 is @xmath19 and its size is @xmath20 ( @xmath21 kpc ) , very similar to the magnitude and size of the large magellanic cloud ( lmc ) . the line - of - sight inclination of ngc 4605 is @xmath22 , and observations find an inclination corrected linewidth at 20% intensity @xmath23 km s@xmath24@xcite . this indicates a maximum rotational velocity of @xmath0 km s@xmath24 ( again , similar to that of the lmc ) that along with its size and luminosity definitively identifies this galaxy as a dwarf . carbon monoxide millimeter emission was detected in ngc 4605 by @xcite using the fcrao 14 m radio telescope . our first interferometer maps revealed co emission throughout the disk of ngc 4605 , which became the obvious first choice for a rotation curve study . we observed the @xmath13co ( @xmath14 ) rotational transition in ngc 4605 using three configurations of the bima array ( b , c , and d ) between june 2000 and march 2001 . we mapped one bima primary beam , subtending a field with a half power diameter of @xmath25 , sufficient to encompass the co emission . the spectrometer was configured with 2 km s@xmath24 wide channels and a bandpass of 260 km s@xmath24 . the individual tracks were calibrated , combined , imaged , and deconvolved using the clean algorithm within the miriad astronomical package . the resulting naturally weighted map has a beam size of @xmath26 ( @xmath27 pc ) with @xmath28 ( fig . [ intmap ] ) . the individual planes of the datacube have an rms of @xmath29 mjy beam@xmath24 ( @xmath30 mk ) at a velocity resolution of 3 km s@xmath24 . the datacube was used to produce a first moment map of the co emission ( fig . [ velmap ] ) . the map was rotated to align the optical major axis of the galaxy with one of the coordinate axes ( @xmath31 ) , and deprojected using the optical center and inclination angle . the velocity data were corrected by the sine of inclination angle , and sorted in concentric rings of width @xmath32 . to each ring we fit a model @xmath33 , representing the projected effects of translation ( @xmath34 ) , circular ( @xmath35 ) , and radial ( @xmath36 ) velocities . the errors in the velocity map , multiplied by the square root of the beam oversampling factor , are used to weight each point in the fit ( fig . [ annuli ] ) . the error bars for the fits ( which range from 1.4 to 3.6 km s@xmath24 ) are computed using the diagonal of the covariance matrix . we find a small @xmath36 component , increasing outwards to @xmath37 and then leveling off ( fig . [ rotcurve ] ) . this component is never larger than half @xmath35 , and adding it in quadrature to @xmath35 does not significantly change the density profile exponents discussed in this paper . the presence of this component may indicate that the kinematics inside @xmath37 have a position angle slightly different from the optical @xmath38 ( closer to @xmath39 ) . to extend the co rotation curve beyond 50 ( @xmath40 kpc ) , we observed ngc 4605 with the 0.6 m coud auxiliary telescope at lick observatory on the night of 23 april 2001 . we used the hamilton echelle spectrometer with a 75 wide filter centered on ( @xmath41 ) to block adjacent spectral orders . the slit was 640 @xmath42 m ( 6 ) wide and @xmath43 long , oriented along ngc 4605 s major axis at @xmath31 using the facility s focal plane image rotator . our velocity resolution was @xmath44 km s@xmath24 , with a spatial resolution of @xmath45 . this spectral resolution is much higher than that of most published rotation curve studies , and it allows us to very accurately measure the kinematics of the inner disk of ngc 4605 . we integrated for 4.5 hours divided in 30 minute exposures using manual guiding . we reduced the data using iraf . we removed a bias frame from the individual exposures , and combined them using the imcombine routine with its built in cosmic ray rejection algorithm . because no continuum was detected in the individual images , we registered them using offsets obtained by cross correlating the spectra . for wavelength calibration we used exposures of a thar reference lamp , and observations of a radial velocity standard star . to extract the rotation velocities we fit a gaussian to each row of the spectrum . we folded the results into a rotation curve by defining the center of the galaxy to be the point at which the two sides of the rotation curve lined up best . the typical errors in the individual points of the folded rotation curve were less than 2 km s@xmath24 . comparison of the co and rotation data reveals that both tracers are in good agreement over the common region ( fig . [ rotcurve ] ) . thus appears to be a good tracer of the kinematics of the inner disk in ngc 4605 . we developed a simulation to estimate how our finite angular resolution affects both the co and rotation curves ( beam smearing ) . because calculating the effect of the beam smearing requires assuming an underlying velocity field , we performed these computations in an iterative , self consistent manner . the net effect is very small , amounting to a velocity loss of @xmath46 km s@xmath24 for the innermost points and rapidly decreasing outwards . although small , this systematic velocity loss is not entirely negligible in the inner 30 . we removed the effect of beam smearing from the data before performing the fits . we used 2mass @xmath47 data to derive the distribution of mass in the disk of ngc 4605 . the advantage of using @xmath2band observations to model the disk mass over more typical @xmath48 , @xmath49 , or @xmath50 data can not be overemphasized : at @xmath2band the extinction is a factor of @xmath51 down from @xmath49 , and a factor of @xmath52 down from @xmath50 @xcite . we retrieved the archival 2mass atlas image for ngc 4605 and extracted the surface brightness profile using the photometric calibration provided in the fits header . we then fit an exponential disk to the surface brightness profile using data with galactocentric radii @xmath53 $ ] , finding @xmath54 where" +"one of the major recent advances in the understanding of strongly correlated quantum many body systems has been the investigation of quantum entanglement in terms of area laws @xcite , the entanglement spectrum @xcite and the associated entanglement hamiltonian @xcite . the structure of entanglement in gapped quantum systems has resulted in the powerful parameterization of quantum ground states in terms of so - called tensor network states , such as matrix product states ( mps ) @xcite or their higher dimensional analogues , projected entangled pair states ( peps ) @xcite . in a translation invariant tensor network state , the entanglement features can be extracted from the leading eigenvector of the so - called ( quantum ) transfer matrix , which naturally appears whenever the quantum state is mapped to a classical partition function ( using _ e.g. _ a trotter decomposition ) and then sliced along the virtual direction , _ i.e. _ the trotter direction or direction of imaginary time @xcite . in a very recent publication @xcite , we have observed that the other eigenvalues of the transfer matrix also contain useful information , _ i.e. _ they contain crucial information about the elementary excitations and the corresponding dispersion relations of the system . this is in many ways surprising as this information is completely encoded in the ground state description of the system , a priori without any information about the original hamiltonian for which it was the exact or approximate ground state . this relation is extremely useful for the case of two - dimensional systems , where systematic methods to extract the dispersion relation of elementary excitations are virtually non - existent . this was illustrated in ref . by studying the affleck - kennedy - lieb - tasaki model @xcite . however , for the case of two - dimensional quantum spin systems exhibiting topological quantum order , the excitation spectrum can be much richer . in contrast to trivial phases , where the elementary excitations can provably be created as bloch waves of localized perturbations @xcite , elementary excitations in topological phases are typically anyons that come with `` strings attached . '' the peps representation of topologically ordered ground states , either as variational approximation @xcite or as exact description of the levin - wen model wave functions @xcite , has been well established . here we study the full spectrum of the transfer matrix of topologically ordered peps @xcite on the infinite plane or cylinder . much like the prisoners in plato s cave , we observe one - dimensional domain walls in the spectrum of the transfer matrix as shadows of the true anyons in the two - dimensional world . by clarifying how the different anyon sectors are manifested at the virtual level , we can probe the dispersion relation of single anyon states . we discuss how the presence of anyons , and thus of topological order , requires a particular type of symmetry breaking in the fixed point subspace of the transfer matrix and how anyon condensation or confinement @xcite is reflected in these virtual description . we illustrate our results by studying the peps description of the toric code model with string tension and the resonating valence bond state . our results also confirm that we can construct approximate eigenvectors of peps transfer matrices using the matrix product ansatz developed for one - dimensional quantum hamiltonians in @xcite . the convience of the tensor network description of quantum states is that the global , topological properties of the state are reflected in the symmetries of the local tensors . since topological phases are not characterized by local order parameters , these symmetries act purely on the virtual levels of the tensors . in particular , it was recently established that topological order in peps can be characterized by the existence of matrix product operators ( mpo ) which can be pulled through the lattice at the virtual level ( see fig . [ fig : pulling ] ) @xcite . closed mpo loops around a topologically trivial region define the invariant subspace on which the peps tensors are supported and in this way characterizes the topological properties of the state , such as the topological corrections to the entanglement entropy . they act as virtual operators @xmath0 and satisfy a fusion algebra @xmath1 . indeed , as shown in ref . , for the case of the levin - wen string net models , the different mpos @xmath0 can be associated to and labeled by the different string types @xmath2 of the input category that defines the string net model . a peps in a trivial phase is characterized by a single mpo @xmath3 that acts as the identity in the relevant subspace . another interesting case is that of the quantum double models , which can be described using @xmath4-injective peps @xcite . this is a special case of the formalism of ref . where the mpos are labeled by the group elements @xmath5 and correspond to representations @xmath6 of the group action at the virtual level . the pulling through condition is satisfied since the tensors are only supported on the invariant subspace defined by the projector @xmath7 . while the pulling - through conditions ensure that the presence of an mpo string can not be detected locally , noncontractible mpo loops can have global effects , such as adding a nontrivial flux in the system , and can therefore be used to map one ground state to another one . the relevance of these virtual mpos is that also away from the the renormalization group ( rg ) fixed point where the physical string operators are spread out and not exactly known @xcite the mpos at the virtual level remain strictly local and the ` pulling - through ' symmetry of the peps tensor is exactly preserved . the pulling through equation between the peps tensor ( red ) and mpo tensor ( blue ) is characteristic for topological order in peps . ] having a translation invariant peps description of the ground state of a topological phase , one can easily argue that a suitable ansatz to model single anyon excitations is obtained by modifying the ground state tensors in a local region ( e.g. a single site ) and attaching a half infinite string to it , which is exactly given by this mpo at the virtual level . the mpo will give rise to the non - trivial braiding statistics of these excitations , while the pulling - through assures that the bulk of the string is locally unobservable , so that the energy density is left at its ground state value sufficiently far away from the end point . away from the rg fixed point , these excitations will disperse and a proper eigenstate can be obtained by building a momentum superposition with momentum @xmath8 and @xmath9 in the @xmath10 and @xmath11 direction . note that the topological quantum numbers of the anyon excitations are not completely specified by the string type @xmath12 , but are determined by structure of the excitation tensor in the ansatz of fig . [ fig : peps ] . for the case of the quantum doubles , it has been shown that the string type corresponds to the magnetic flux , whereas the charge quantum number is determined by the representation space on which the local tensor is supported @xcite . a complete characterization of the different anyon sectors in the peps formalism would take us to far and is presented elsewhere . a peps ansatz for a topologically non - trivial excitation is constructed from the tensors of the peps ground state ( red ) and a local perturbation ( green ) with an mpo ( blue string ) attached . by building momentum superpositions , the variational excitation energy will depend on the overlap with any difference @xmath13 and @xmath14 between the string end points in ket and bra , as shown here . ] as in ref . , one can now argue that the dominant contribution to the variational dispersion relation is coming from the normalization of these states , which is given by the sum of overlaps of ket and bra with string end points at different positions @xmath15 and @xmath16 , as illustrated in fig . [ fig : peps ] . if we orient the strings along the @xmath10 direction and first contract the tensor network along the @xmath11 direction , the central object will be the transfer matrix @xmath17 in the @xmath10 direction , as defined in fig . [ fig : tm ] . the pulling through condition of fig . [ fig : pulling ] ensures that @xmath17 commutes with infinite mpo strings along the @xmath10 axis in the ket and bra level separately . we thus obtain @xmath18=[\openone\otimes \overline{o}_{i},\mathbb{e}]=0 $ ] , @xmath19 where @xmath0 now denotes an infinite mpo of type @xmath12 along the @xmath10 axis . normalization of the peps ground state requires that the largest eigenvalue of @xmath17 is @xmath20 , and the infinite power of the transfer matrix @xmath17 in the overlap of fig . [ fig : peps ] in the regions @xmath21 and @xmath22 can be replaced by its left and right fixed point @xmath23 and @xmath24 , which we represent as an infinite mps with matrices @xmath25 and @xmath26 ( fig . [ fig : tm ] ) . the ( normal ) transfer matrix @xmath17 and one if its fixed points @xmath24 , which we represent as an infinite matrix product state . excited states @xmath27 of the transfer matrix can be constructed by attaching a half infinite mpo to a local excitation tensor ( green ) , which is equivalent to interpolating between the mps tensors @xmath28 and @xmath29 of two different fixed points . ] the transfer matrix @xmath17 can have a degenerate fixed point structure , since for a given right fixed point @xmath24 , one can build other fixed points @xmath30 for all @xmath31 . one could expect that this generally gives rise to an @xmath32-dimensional fixed point subspace . however , at the rg fixed point of the topological phase , we can easily check that the fixed point subspace of @xmath17 is exactly spanned by @xmath33 for @xmath34 , and is thus only @xmath35-dimensional . the degeneracy and labeling of the fixed point subspace remains intact throughout the topological phase , even though @xmath36 will no longer exactly equal @xmath37 . this implies , in particular , that @xmath38 can be expanded into a linear combination of @xmath39 with @xmath40 , compatible with the fact that fusing @xmath41 will have a fusion channel @xmath42 . we now argue why this property is required in order to support anyonic excitations with a half - infinite virtual string of type @xmath12 . contracting the tensor network in fig . [ fig : peps ] from right to left up to position @xmath43 gives rise to some boundary state @xmath24 in the fixed point subspace , whose precise choice is set by the boundary conditions at @xmath44 . the topological invariance ensures that this choice has no effect on local expectation values . as we now further contract from right to left , we pass the position @xmath43 containing the excitation in the bra level . here , the boundary state is perturbed locally at @xmath45 . in addition , it will be acted upon by a half infinite mpo string of type @xmath12 , which has the effect of changing the mps tensors from @xmath26 to @xmath29 with @xmath46 in the region @xmath47 . at the level of the transfer matrix , the boundary state now takes the form of a domain wall interpolating between the two different fixed points . because of translation invariance , all overlaps corresponding to the momentum superposition in the @xmath10 direction" +"it is now possible to realize ideal quantum measurements on individual quantum objects , for instance atoms , ions and photons . beyond being a tool to monitor the system s evolution , projective quantum measurements can be used to prepare it in specific quantum states . for instance , an ideal quantum non - demolition ( qnd ) measurement of a field s photon number projects it onto a photon - number ( fock ) state @xcite . however , due to the basic quantum indetermination of the measurement outcome , measurement - induced state generation is not deterministic . quantum feedback control techniques @xcite make it possible to overcome this limitation and to produce quantum states on demand . these techniques generally combine weak quantum measurements with a real - time correction of the system s state depending on the classical information extracted from the measurements . beyond preparation of specific states , these feedback schemes can also protect them from decoherence , resulting from the coupling of the system with its environment . in this paper , we propose a quantum feedback scheme for the on - demand preparation of fock states stored in a high - quality superconducting microwave cavity and for their protection against decoherence . this scheme is designed to operate with an existing cavity - qed set - up @xcite . the feedback loop uses three steps . we first extract information on the photon number distribution with a single circular rydberg atom by a qnd process . this atom interacts dispersively with the cavity field and does not exchange energy with it , but experiences a light shift proportional to the photon number . the measurement of this shift , with the help of a ramsey interferometer , provides information on the field intensity . it modifies the field state accordingly through the quantum projection . this information is , in the second step , used to estimate the new cavity field state through a quantum filtering process @xcite . in the third step , we correct the field state , using a coherent field pulse injected in the cavity . the feedback law used to calculate the amplitude of this pulse is chosen by adapting to this discrete situation the lyapunov - based techniques proposed in ref . these three steps represent the three basic components of any feedback loop : a sensor , a controller and an actuator . in contrast to classical closed - loop systems , we use here a quantum sensor . however , both controller and actuator remain classical . by iterating the feedback loop , we steer the cavity towards any target fock state . we also efficiently stabilize it against cavity decay . recently , a similar feedback scheme to generate fock states of light in an optical cavity has been proposed @xcite . it is based on a continuous monitoring of the mean number of photons . instead , we propose here to use a discrete qnd measurement followed by a quantum filtering process providing complete information on the field s density matrix . this precise knowledge of the field s state gives us a much better insight into the feedback action . it could also be an asset in other feedback schemes requiring , for instance , information on the field s phase in addition to its intensity . the paper is organized as follows . in sec . [ sec : setup ] , we describe the elements of the set - up and give realistic experimental parameters . we present the quantum - mechanical operators describing the evolution of the cavity state under measurement , decoherence and pulse injection . section [ sec : ideal ] is devoted to a detailed analysis of the quantum filter and of the feedback law in an ideal situation . we first present the main elements of the feedback loop and describe the tuning of the controller gain . we give qualitative arguments showing that the proposed strategy is stable . the detailed mathematical proof of convergence and stability , relying on stochastic lyapunov techniques will be published elsewhere @xcite . we finally present quantum monte carlo simulations of closed - loop trajectories of the cavity field exhibiting the feedback performances . in section [ sec : real ] , we take into account the known experimental imperfections of the existing set - up . we modify accordingly the feedback algorithm and present extensive simulations of its operation . we conclude in sec . [ sec : conclusion ] . : high-@xmath0 microwave cavity , @xmath1 : box producing rydberg atoms , @xmath2 and @xmath3 : low-@xmath0 ramsey cavities , @xmath4 : atomic field - ionization detector , @xmath5 and @xmath6 : microwave sources coupled to @xmath7 and @xmath8 s , respectively . in a quantum filtering process , a real - time control system analyzes the results of qnd measurements of the cavity field and computes the amplitude of a control injection pulse.,scaledwidth=48.0% ] our quantum feedback algorithm is designed for the ens microwave cavity qed set - up @xcite . its components are depicted in fig . [ fig : setup ] . the microwave field to be controlled is confined in an ultra - high @xmath0 superconducting cavity @xmath7 ( damping time @xmath9 rydberg atoms , flying one by one at 250 m / s across the cavity mode and dispersively interacting with its field , are used as qnd probes of light @xcite . they are prepared in a superposition of two circular rydberg states @xmath10 and @xmath11 ( principal quantum numbers 51 and 50 , respectively ) in the low-@xmath0 cavity @xmath2 , driven by the source @xmath6 , in which they experience a resonant @xmath12-pulse . in the bloch sphere representation , the spin corresponding to the two - level atomic system then points along the @xmath13 direction in the equatorial plane ( states @xmath10 and @xmath11 correspond to north and south poles of the sphere , respectively ; we use a frame rotating at the atomic frequency ) . the light shifts experienced by the non - resonant @xmath14 atomic transition in the cavity field result in a phase shift for the atomic state superposition . at the cavity exit , the atomic spin points along a direction in the equatorial plane at an angle @xmath15 with the @xmath13 axis , correlated to the photon number @xmath16 . the dephasing angle @xmath15 can be controlled by adjusting the atom - cavity detuning @xmath17 and the interaction time . in the large atom - cavity detuning regime , it is a linear function of @xmath16 : @xmath18 , where @xmath19 khz is the vacuum rabi frequency . for the intermediate detuning values used in the experiments , it is a more complex , albeit perfectly known growing function of @xmath16 . a second @xmath12 ramsey pulse in @xmath3 ( phase @xmath20 with respect to that of the pulse in @xmath2 ) followed by the atomic detection ( in the @xmath21 basis ) by the detector @xmath4 amounts to a detection of the atomic spin along an axis at an angle @xmath20 with @xmath13 . it provides information on the cavity field intensity . atoms are sent in the set - up at typical 250 @xmath22s time interval , much shorter than the cavity damping time . note that such a macroscopic time interval is well adapted to elaborate feedback strategies since we have ample time to compute the state estimator and the feedback law between two atomic detections . when no feedback action is performed , the information provided by a few tens of atoms results in a measurement of the dephasing angle @xmath15 and , hence , in a projective qnd measurement of the photon number @xmath16 @xcite . we are interested here instead in the ambiguous information provided by a single atomic detection . detection of the atomic state in @xmath4 projects the field , described initially by the density matrix @xmath23 , onto a new state @xmath24 . depending on the detected atomic state , @xmath25 or @xmath11 , the back - action of the quantum measurement on the field is described by @xmath26 where the operators @xmath27 are given by [ eq : mgme ] @xmath28 @xmath29 here , @xmath30 is the photon number operator with @xmath31 and @xmath32 the photon annihilation and creation operators , respectively . the measurement operators @xmath27 are diagonal in a photon - number basis ( as is @xmath33 ) . they thus preserve fock states , illustrating the qnd nature of the measurement . the projected state is normalized by the probability @xmath34 of detecting the atom in state @xmath35 . the cavity field can also be manipulated by injecting into the mode a coherent field pulse generated by the resonant microwave source @xmath5 . its action is described by the displacement operator @xmath36 , where @xmath37 is the complex amplitude of the injected field . the cavity field after displacement thus reads @xmath38 a proper analysis of the feedback scheme requires to take into account all known imperfections of the experimental set - up . besides projective measurement and coherent evolution , the cavity state also evolves due to decoherence . the field is coupled to a reservoir at non - zero temperature ( @xmath39 k ) , and its dynamics is described by the master equation @xcite @xmath40 where @xmath41 is the cavity decay rate and @xmath42 the equilibrium thermal photon number . moreover , the circular rydberg state preparation is a non - deterministic poisson process . we perform a pulsed excitation from a continuous thermal beam of rubidium atoms , preparing atomic samples at a @xmath43s time interval . the mean number of circular atoms per sample is @xmath44 ( leading to an average time between atoms of 250 @xmath22s ) . the atomic time of flight between @xmath7 and @xmath4 is 350 @xmath22s , corresponding to a delay of @xmath45 atomic samples . the probability for detecting an atom present in a sample is @xmath46 due to finite detection efficiency in @xmath4 . finally , non - ideal atomic state resolution of the field - ionization detector and finite contrast of the ramsey interferometer introduce a probability of erroneous state assignation of @xmath47 . in order to describe the essential elements of the feedback scheme in a simple context , we first consider in this section an idealized experiment with no cavity decay ( @xmath48 ) , a deterministic atomic preparation ( @xmath49 ) , no detection delay ( @xmath50 ) , and a perfect atomic detection ( @xmath51 and @xmath52 ) . the quantum filtering procedure @xcite provides us with an estimate of the field state by using all available information . right after detection of atom number @xmath53 and before injection of the corresponding control , it includes the initial state of the field @xmath54 , information obtained from all @xmath53 atoms detected so far ( labelled @xmath55 ) and all coherent field injections performed in the former feedback loops ( 1 to @xmath56 ) . each of the elementary processes ( atomic detections and displacements ) can be represented by super - operators acting on the field s density matrix . let us note @xmath57 that associated to the detection of atom @xmath58 and @xmath59 that corresponding to the displacement performed in the @xmath60 iteration of the feedback loop . therefore , after detecting atom @xmath53 , the state of the field is @xmath61 here and in the following , all super - operator products are ordered by decreasing indices . note that the expression can be computed iteratively from the recurrence @xmath62 setting @xmath63 . by applying this filter recursively at each cycle , we get a reliable real - time estimate of the field state . based on eqs . and , the super - operators are defined" +"with ages of the order of @xmath2-@xmath3 gyr , globular clusters ( gcs ) are thought to be among the first stellar systems formed at early epochs in the local group . thanks to the general homogeneity in terms of age and chemical composition of their stars , gcs have been used for decades as ideal tracers of the chemistry of their environments , allowing us to reconstruct the chemical enrichment history and the age - metallicity relation of their host galaxies . the current picture of gc formation and evolution moves away from the traditional paradigm of gcs as simple stellar population ( see for instance the seminal paper by * ? ? ? * ) , according to which all the stars in a gc share the same initial chemical abundances for all the chemical elements . in fact , the recent discoveries of multiple sequences in gc colour - magnitude diagrams ( cmds , see e.g. @xcite ) and of star - to - star variations in the chemical abundances of some light elements ( like c , n , na , o , mg , al , see e.g. * ? ? ? * and references therein ) demonstrate that such systems are indeed much more complex . multiple populations ( mps ) are ubiquitous in all gcs studied so far , both in the galactic ( see for example @xcite ) and extra - galactic ( @xcite ) environment . since this chemical pattern has been observed in stars at all the evolutionary stages ( @xcite ) , it can not be explained in terms of internal mixing but it should have been imprinted in stars at formation . several scenarios interpret the photometric and spectroscopic evidence in terms of different generations of stars , with a first generation polluting the gas out of which second generation of stars formed with the products of their internal evolution . a number of candidate polluters have been proposed ( see @xcite for a comprehensive review ) ; namely asymptotic giant branch stars ( @xcite ) , fast - rotating massive stars ( @xcite ) , massive binaries ( @xcite ) and supermassive stars ( @xcite ) . alternative scenarios have been proposed as well , where low - mass stars accrete the polluted material during the pre - main sequence phase to give rise to a chemically peculiar population of stars that is coeval to that with pristine composition ( @xcite ) . the abundance spreads typical of mps involve only a few light elements . for most of the elements ( in particular @xmath1-elements like si , ca and ti , iron - peak and neutron - capture elements ) the stars in a typical gc exhibit a remarkable level of internal homogeneity , thus suggesting that the abundances of these elements in gcs can be used to trace the chemical composition of the gas from which the cluster formed . therefore , the investigation through high - resolution spectroscopy of the chemistry of poorly ( or not yet ) studied clusters is crucial to understand the chemical evolution of the galactic halo ( see e.g. * ? ? ? * ; * ? ? ? * ) and to identify , through the chemical tagging , clusters that likely originated in extragalactic environments @xcite . in this paper , we present the first detailed chemical study of ngc 6362 , an intermediate metallicity clusters which belongs to the low - mass tail of the gc mass distribution , with a mass of only @xmath4 @xcite . we list cluster fundamental properties in tab . [ tab0 ] , along with other useful informations . @xcite firstly measured its iron content ( [ fe / h]= 1.09 @xmath0 0.01 dex ) by analysing 160 giant stars observed with flames at the very large telescope . they also found a bimodal [ na / fe ] distribution , that makes ngc 6362 one of the least massive clusters where mps have been detected . the peculiar radial distribution of its stars , with both first and second populations being completely mixed out to several half light radii , has been interpreted by @xcite as the result of heavy mass - loss due to long - term dynamical evolution . such a claim is also supported by the quite shallow present - day mass function observed for this cluster in @xcite . thus , it would be extremely interesting to investigate whether it also shows other exceptional chemical features or it follows the general trends observed for standard gcs in the milky way with mps . to this end , we here present a detailed chemical analysis of 11 members in ngc 6362 . the paper is organized as follows . the dataset analysed in this work is described in section [ data ] , while the details of the chemical analysis are discussed in section [ analysis ] . we present the results of this study in section [ res ] and we finally discuss them in section [ discuss ] . the dataset analysed in this work was acquired under the programs 093.d-0618(a ) and 097.d-0325(a ) , pi : dalessandro , with the flames spectrograph ( @xcite ) at the eso very large telescope . we used the combined medusa+uves configuration , which allowed the simultaneous allocation of eight uves high - resolution fibres and 132 medusa mid - resolution fibres per exposure . while the stars observed in the medusa mode have been discussed in @xcite , in this work we focus on the eleven stars observed with the uves 580 red arm spectral configuration , with a resolution of r@xmath545000 in the spectral range @xmath6 . targets have been selected from the wide field imager ( wfi ) photometric catalogue presented in @xcite . for this study , only red giant branch ( rgb ) stars brighter than v@xmath7 mag have been targeted ( see figure [ cmd_targ ] ) . also , to avoid contamination from neighbours , only stars with no close ( i.e. within 2 ) sources brighter than v@xmath8 v@xmath9 have been selected . four exposures of 45 min for each target have been secured . two uves fibres have been used to sample the sky background , thus allowing a proper sky subtraction for each individual exposure . cc right ascension ( h : m : s ) & @xmath10:@xmath11:@xmath12 + declination ( @xmath13 : : ) & -@xmath14:@xmath15:@xmath16 + distance ( kpc ) & @xmath17 + r@xmath18 ( ) & @xmath19 + mass ( @xmath20 ) & @xmath21 + @xmath22fe / h@xmath23 $ ] ( dex ) & @xmath24 + [ tab0 ] to reduce the acquired data , we used the last version of the flames - uves common pipeline libraries based eso pipeline , which includes bias - subtraction , flat - field correction , wavelength calibration with a standard th - ar lamp , extraction of one - dimensional spectra and order merging . the accuracy of the dispersion solution has been checked by comparing the observed position of several sky emission lines with their rest - frame position as reported in the sky lines atlas by @xcite . no significant wavelength shifts have been found . once extracted , all the individual ( sky - subtracted ) exposures of each target have been brought to the same reference by correcting for the corresponding heliocentric radial velocity ( see sect.[vrad ] for the details ) , and finally combined together to obtain a median spectrum . the final reduced spectra have signal - to - noise ratio ( snr ) larger than @xmath530 at any wavelength . radial velocities ( v@xmath25 ) have been measured using the wrapper 4dao ( @xcite ) , which allows to run daospec @xcite for large sets of spectra , tuning automatically its main input parameters . for all the eleven targets , we treated the two uves chips of each single exposure independently . for the lower ( l ) chip , v@xmath25 have been computed by using @xmath26 absorption lines , while for the upper ( u ) chip the lines used were @xmath27 . for each target we obtained a remarkably good agreement between the measurements of the two independent chips , finding an average difference of only v@xmath28-v@xmath29 km@xmath30s@xmath31 ( @xmath32 km@xmath30s@xmath31 ) . moreover , we did not find any significant difference among the v@xmath25 measured for the four exposures of each target . this indicates that none of the observed targets are binary systems . we then computed the final values of v@xmath25 as the average value of the eight single exposure measurements ( two chips for each of the four exposures ) and we adopted the dispersion around the mean divided by @xmath33 as uncertainty . heliocentric velocities and related errors are listed in table [ tab1 ] . we measured an average v@xmath25 of v@xmath34 km@xmath30s@xmath31 ( @xmath35 km@xmath30s@xmath31 ) , which is in agreement with the value derived by @xcite ( v@xmath36 km@xmath30s@xmath31 , @xmath37 km@xmath30s@xmath31 ) . according to their v@xmath25 distribution all the targeted stars are members , having v@xmath25 values that lie well within 2@xmath38 from the systemic velocity . effective temperatures ( t@xmath39 ) and surface gravities ( @xmath40 @xmath41 ) for target stars have been derived from their the b and v magnitudes , in the same way as described in in @xcite . we correct magnitudes and colours for differential reddening using the procedure outlined in @xcite ( see also * ? ? ? differential reddening corrections across the whole wfi field of view range from @xmath42=-0.03 $ ] mag to + 0.03 mag around the adopted average colour excess e(b - v)@xmath43 mag ( @xcite ) . errors on the parameters affecting the determination of the absolute colour for the analysed targets , i.e photometric errors or uncertainty on the absolute and differential reddening ( @xmath44}}$ ] and @xmath45}}$ ] , respectively ) could potentially affect our t@xmath39 estimates . thus , to evaluate the uncertainties on @xmath46 we re - determined temperatures assuming typical errors on colors and extinction of @xmath47 mag , @xmath44}}=0.04 $ ] mag and @xmath45}}=0.02 $ ] mag , respectively . we underline that the quoted values are conservative upper limits , since the nominal photometric errors of such bright and well exposed stars are @xmath48 mag , while the errors on the absolute and differential reddening estimates correspond to about the 50% of their value ( see @xcite ) . finally , we measure a typical uncertainty on t@xmath39 of @xmath49 k. stars located in the brightest portion of the rgb , especially those approaching the rgb tip , can be significantly be affected by non - lte effects that spuriously decrease the iron abundances from fei lines leaving those from feii lines unaltered ( see @xcite ) . this causes the spectroscopic derivation of @xmath40 @xmath41 through ionization equilibrium ( i.e. @xmath40 @xmath41 is constrained by imposing that both neutral and ionized iron lines give the same abundance ) to be systematically biased towards lower gravities . thus , we prefer to rely on photometric gravities , derived by using the stefan - boltzmann relation . we adopted an absolute distance modulus of ( m - m)@xmath50 mag ( from @xcite ) , bolometric corrections from @xcite and a mass of @xmath51 . such a mass has been derived from the best fit isochrone taken from the basti dataset ( @xcite ) , with an age of 12 gyr , z=0.004 and @xmath1-enhanced chemical mixture ( corresponding to [ fe / h]@xmath52 dex ) . uncertainties in @xmath40 @xmath41 have been computed by taking into account the errors on t@xmath39 ( as described above ) , bolometric luminosity ( due to all the photometric uncertainties ) and mass ( we assumed @xmath53 , that corresponds to" +"in the scenario of _ secure network coding _ introduced by cai et al . @xcite , a source node transmits @xmath0 packets from @xmath0 outgoing links to sink nodes through a network that implements network coding @xcite , and each sink node receives @xmath0 packets from @xmath0 incoming links . in the network , there is a wiretapper who observes @xmath1 links . the problem is how to encode a secret message into @xmath0 transmitted packets at the source node , in such a way that the wiretapper obtain no information about the message in the sense of information theoretic security . as shown in @xcite , secure network coding can be seen as a generalization of the wiretap channel ii @xcite or secret sharing schemes based on linear codes @xcite for network coding . hence , in secure network coding , the secrecy is realized by introducing the randomness into @xmath0 transmitted packets as follows . suppose the message is represented by @xmath2 packets @xmath3 @xmath4 . then , the source node encodes @xmath5 together with @xmath6 random packets by linear codes , and generates @xmath0 transmitted packets @xcite . silva et al . @xcite proposed the _ universal secure network coding _ that is based on maximum rank distance ( mrd ) codes @xcite . their scheme was universal in the sense that their scheme guarantees that over _ any _ underlying network code , no information about @xmath7 leaks out even if any @xmath6 links are observed by a wiretapper . as shown in @xcite , their scheme with mrd codes is optimal in terms of security and communication rate . however , there exists some restrictions in universal secure network coding with mrd codes . in their scheme , the network must transport packets of size @xmath8 . the mrd code used in the scheme is defined over an @xmath9 , where @xmath10 is an @xmath11-degree field extension of a field @xmath12 with order @xmath13 . thus , the size of the field @xmath10 increases exponentially with @xmath11 , and the restriction of mrd codes with @xmath8 invokes the large computational cost for encoding and decoding of mrd codes if @xmath0 is large . it is undesirable especially in resource constraint environments . considering secure network coding without such a restriction , ngai et al . @xcite , and later zhang et al . @xcite , investigated the security performance of secure network coding based on general linear codes . they introduced a new parameter of linear codes , called the _ relative network generalized hamming weight _ ( rnghw ) , and revealed that the security performance is expressed in terms of the rnghw . the rnghw depends on the set of coding vectors of the underlying network code . hence , the rnghw is not universal . the aim of this paper is to investigate the security performance of universal secure network coding based on general linear codes , which is always guaranteed over _ any _ underlying network code , even over random network code . this paper defines the universal security performance by the following two criteria . one is called the _ universal equivocation _ @xmath14 that is the minimum uncertainty of the message under observation of @xmath1 links , guaranteed independently of the underlying network code . the other is called the _ universal @xmath15-strong security _ , where @xmath15 is a performance measure such that no part of the secret message is deterministically revealed even if at most @xmath15 links are observed . the paper @xcite proposed a specific construction of the secure network coding that attains the universal @xmath16-strong security , and such a scheme is called universal strongly secure network coding @xcite . namely , the definition of universal @xmath15-strong security given in this paper is a generalization of universal strongly secure network coding considered in @xcite for the number of tapped links . in order to express @xmath14 and @xmath15 in terms of code parameters , this paper introduces two parameters of linear codes , called the _ relative dimension / intersection profile _ ( rdip ) and the _ relative generalized rank weight _ ( rgrw ) . the rgrw is a generalization of the minimum rank distance @xcite of a code . we reveal that @xmath14 and @xmath15 can be expressed in terms of the rdip and the rgrw of the codes . duursma et al . @xcite first observed that the _ relative generalized hamming weight _ @xcite exactly expresses the security performance and the error correction capability of secret sharing . our definitions of rgrw and rdip are motivated by their result @xcite . assume that the attacker is able not only to eavesdrop but also to inject erroneous packets anywhere in the network . also assume that the network may suffer from the rank deficiency of the transfer matrix at a sink node . silva et al.s scheme based on mrd codes @xcite enables to correct such errors and rank deficiency at each sink node , where its error correction capability is guaranteed over any underlying network code , universal . this paper also generalizes their result and reveals that the universal error correction capability of secure network coding based on arbitrary linear codes can be expressed in terms of the rgrw of the codes . the remainder of this paper is organized as follows . presents basic notations , and introduces linear network coding . defines the universal security performance and universal error correction capability of secure network coding over wiretap network . defines the rdip and rgrw of linear codes , and introduces their basic properties . in , the universal security performance is expressed in terms of the rdip and rgrw . the security of existing schemes @xcite is also analyzed as applications of the rdip and rgrw in examples [ ex1 ] and [ ex2 ] . gives the expression of the universal error correction capability in terms of the rgrw , and also analyze the error correction of @xcite by the rgrw in example [ ex3 ] . let @xmath17 be the shannon entropy for a random variable @xmath18 , @xmath19 be the conditional entropy of @xmath18 given @xmath20 , and @xmath21 be the mutual information between @xmath18 and @xmath20 @xcite . we write @xmath22 as the cardinality of a set @xmath23 . the entropy and the mutual information are always computed by using @xmath24 . let @xmath12 stand for a finite field containing @xmath13 elements and @xmath10 be an @xmath11-degree field extension of @xmath25 ( @xmath26 ) . let @xmath27 denote an @xmath0-dimensional row vector space over @xmath12 . similarly , @xmath9 stands for an @xmath0-dimensional row vector space over @xmath10 . unless otherwise stated , we consider subspaces , ranks , dimensions , etc , over the field extension @xmath10 instead of the base field @xmath12 . an @xmath28 $ ] linear code @xmath29 over @xmath9 is a @xmath30-dimensional subspace of @xmath9 . let @xmath31 denote a _ dual code _ of a code @xmath29 . a subspace of a code is called a _ subcode _ for @xmath32 , we denote by @xmath33 a _ subfield subcode _ of @xmath29 over @xmath12 @xcite . observe that @xmath34 means the dimension of @xmath29 as a vector space over @xmath10 whereas @xmath35 is the dimension of @xmath36 over @xmath12 . for a vector @xmath37\in\f_{q^m}^n$ ] and a subspace @xmath38 , we denote @xmath39 $ ] and @xmath40 . define a family of subspaces @xmath41 satisfying @xmath42 by @xmath43 . also define @xmath44 . for a subspace @xmath45 , the followings are equivalent : 1 ) @xmath46 ; 2 ) @xmath47 ( * ? ? ? * lemma 1 ) . as in @xcite , we consider a multicast communication network represented by a directed multigraph with unit capacity links , a single source node , and multiple sink nodes . we assume that _ linear network coding _ @xcite is employed over the network . elements of a column vector space @xmath48 are called _ packets_. assume that each link in the network can carry a single @xmath12-symbol per one time slot , and that each link transports a single packet over @xmath11 time slots without delays , erasures , or errors . the source node produces @xmath0 packets @xmath49 , , @xmath50 and transmits @xmath49 , , @xmath51 on @xmath0 outgoing links over @xmath11 consecutive time slots . define the @xmath52 matrix @xmath53 $ ] . the data flow on any link can be represented as an @xmath12-linear combination of packets @xmath54 . namely , the information transmitted on a link @xmath55 can be denoted as @xmath56 , where @xmath57 is called a _ global coding vector _ ( gcv ) of @xmath55 . suppose that a sink node has @xmath58 incoming links . then , the information received at a sink node can be represented as an @xmath59 matrix @xmath60 , where @xmath61 is the transfer matrix constructed by gathering the gcv s of @xmath58 incoming links . the network code is called _ feasible _ if every transfer matrix to a sink node has rank @xmath0 over @xmath12 . the system is called _ coherent _ if @xmath62 is known to each sink node ; otherwise , called _ this section introduces the wiretap network model with packet errors and the nested coset coding scheme in secure network coding @xcite . then , we define the universal security performance in terms of the _ universal equivocation _ and the _ universal @xmath15-strong security _ on the wiretap network model . we also define the universal error correction capability of secure network coding . from now on , only one sink node is assumed without loss of generality . in addition , we focus on the fundamental case of coherent systems in this paper due to the space constraint . but , as in @xcite , all analysis in this paper can be easily adapted to the case of noncoherent systems . following @xcite , assume that in the setup of , there is a wiretapper who has access to packets transmitted on any @xmath63 links . let @xmath64 be the set of @xmath65 links observed by the wiretapper . then the packets observed by the wiretapper are given by @xmath66 , where rows of @xmath67 are the gcv s associated with the links in @xmath64 . in the scenario @xcite , the source node first regards an @xmath11-dimensional column vector space @xmath48 as @xmath10 , and fix @xmath2 for @xmath68 . let @xmath69 \!\in\ ! \f_{q^m}^l$ ] be the secret message , and assume that @xmath3 are uniformly distributed over @xmath70 and mutually independent . under the wiretapper s observation , the source node wants to transmit @xmath7 without information leakage to the wiretapper . to protect @xmath7 from the wiretapper , the source node encodes @xmath7 to a transmitted vector @xmath71\!\in\!\f_{q^m}^n$ ] of @xmath0 packets by applying the _ nested coset coding scheme @xcite on @xmath7 . in @xcite , its special case is called a _ secret sharing scheme based on linear codes_. [ def : nestedcoding ] let @xmath72 be a linear code over @xmath10 ( @xmath26 ) , and @xmath73 be its subcode with dimension @xmath74 over @xmath10 . let @xmath75 be an arbitrary isomorphism . for a secret message @xmath76 , we choose @xmath18 from a coset @xmath77 uniformly at random and independently of @xmath7 . then , the source node finally transmit @xmath18 over the network coded network . includes the ozarow - wyner coset coding scheme @xcite as a special case with @xmath78 . hence , when we set @xmath78 , this is the secure network coding based on ozarow - wyner coset coding scheme @xcite . corresponding to @xmath18 transmitted from the source node , the sink node receives a vector of @xmath58 packets @xmath79 . here we extend the basic network model" +"negatively charged nitrogen - vacancy ( nv@xmath0 ) color centers in diamond are promising candidates for magnetometry with an unprecedented combination of sensitivity and spatial resolution @xcite . in particular , diamonds with high density of nv@xmath0 centers are appealing for ensemble magnetometry @xcite . optically detected magnetic resonance ( odmr ) signals enable probing the energy levels of nv@xmath0 centers , from which the external magnetic field can be inferred . in this work , we analyze lineshapes in odmr signals of nv@xmath0 centers in diamond . specifically , we are able to separate features related to @xmath1c hyperfine interactions from those related to simultaneous spin flips of nv@xmath0 and single substitutional nitrogen atoms ( p1 centers ) . at sufficiently high microwave powers , the weak coupling between the nv@xmath0 and the p1 centers allows both spins to be flipped at the same time , absorbing one microwave photon . in the absence of magnetic fields , the nv@xmath0 center has a magnetic resonance at a frequency of approximately 2870 mhz , which corresponds to a transition between the triplet ground - state magnetic sublevels with electron spin projections @xmath2 and @xmath3 [ see fig . [ fig : nrg ] ] . side resonances around this central resonance have been reported in the literature . these extra resonances are due to coupling between nv@xmath0 centers and other paramagnetic impurities in the diamond lattice . a pair of side resonances asymmetrically offset from the central peak and separated from each other by 130 mhz has been attributed to hyperfine interaction between an nv@xmath0 center and a nearest - neighbor @xmath1c nuclear spin @xcite . hyperfine coupling with @xmath1c spins located in other lattice sites has also been studied in detail @xcite . such interactions have been used to demonstrate quantum information processing using nv@xmath0 centers and @xmath1c nuclear spins @xcite . other side resonances have been observed in nitrogen - rich diamond @xcite . these resonances become particularly pronounced at high microwave powers , where the central resonance saturates , while these side resonances continue to grow with increasing microwave power . understanding this regime is important for understanding light - narrowing effects in odmr and for optimizing the performance of sensors based on ensembles of nv@xmath0 centers in diamond @xcite . at zero magnetic field , et al . _ @xcite report pairs of side resonances separated by 140 and 280 mhz , symmetrically displaced from the central resonance . the resonances separated by 140 mhz are unusually large compared to side resonances at 130 mhz ( see sec . [ randd ] ) , and to our knowledge , they are reported only once in the literature . et al . _ @xcite attribute these resonances to simultaneous spin flips of nv@xmath0 centers and p1 centers . later , resonances separated by approximately 130 mhz , observed by baranov _ et al . _ @xcite and babunts _ et al . _ @xcite in nanodiamonds , were interpreted as being related to coupling between nv@xmath0 centers and substitutional nitrogen atoms . _ and babunts _ et al . _ assumed that these resonances are the same as those of van oort _ et al . _ ; however , they are separated by 130 mhz , asymmetrically located around the central resonance , and are much smaller than those observed by van oort _ et al . _ , so they are more likely to be excellent examples of the side features associated with @xmath1c . the p1 center has electron spin @xmath4 and nuclear spin 1 . at zero field , these spins combine to form states with total angular momenta of @xmath4 and @xmath5 with a small splitting of the latter due to the absence of spherical symmetry in the diamond . as a result , the level separations in the system are grossly unequal \{22 , 127 , and 149 } ( as calculated in sec . [ p1theory ] ) , in contrast to the equal separations incorrectly assumed by van oort _ et al . _ @xcite in this paper we present improved odmr spectra showing the different side resonances in diamonds with both high and low nitrogen concentration . the microwave - power and magnetic - field dependences of these features are studied in detail . we are able to unambiguously ascribe the origins of all the observed side resonances by comparing experimental data with theoretical calculations . furthermore , we show that the side resonances separated by 280 mhz observed in ref . at zero magnetic field are partially unresolved pairs of resonances , one group separated by 260 mhz and another by 300 mhz . we determine the origin of side resonances separated by approximately \{40 , 260 , 300 } mhz to be simultaneous spin flips of the nv@xmath0 centers and p1 centers , and we determine the origin of resonances separated by 130 mhz to be hyperfine coupling to @xmath1c . we note that in measurements of all our samples , including the representative ones we present in this paper , we do not observe the side resonances split by 140 mhz reported by van oort _ et al . _ in our experiment , we used a conventional confocal - microscopy setup shown in fig . [ fig : odmr ] . we focus continuous - wave 532-nm laser light onto the diamond surface and optically pump the nv@xmath0 centers to the @xmath6 ground - state sublevel . the fluorescence ( wavelength @xmath7 638 - 800 nm ) propagates back through the lens , through a dichroic mirror , and onto a detector ( photodiode or photomultiplier tube ) . microwaves are applied with a wire pressed across the diamond surface . the microwave frequency is scanned over the transition between the @xmath6 and the @xmath8 sublevels . on resonance , the nv@xmath0 centers are transferred to the @xmath9 states , which leads to lower red fluorescence intensity than when the centers are in the @xmath6 state ( see the discussion in ref . ) . we also measured rabi oscillations by optically pumping nv@xmath0 centers to the @xmath10 state and applying resonant - microwave frequency lasting a few microseconds while keeping the laser on . this allows us to observe population oscillations between the @xmath6 and @xmath8 states in real time by monitoring fluorescence intensity modulation while microwaves are on . the microwave magnetic field that the nv@xmath0 centers are exposed to depends not only on the microwave power but also on the distance from the transmitting wire . microwave coupling strength is proportional to resonant microwave rabi frequency , which is therefore used as a reference of coupling strength . we used low laser power in order to avoid optical pumping during the duration of oscillation . we tested diamond samples with different amounts of impurities . single - crystal diamonds were obtained from element six with nitrogen concentrations of @xmath11 ppm synthesized by the high - pressure , high - temperature technique ( hpht ) or with nitrogen concentrations of @xmath12 ppm synthesized by chemical - vapor deposition ( cvd ) @xcite . then , the samples were irradiated with relativistic electrons to create vacancies . in the measurements described here , we used the hpht w5 and s8 samples ( s8 was previously studied in ref . ) and the cvd w2 sample , which were subjected to irradiation doses of @xmath13 , @xmath14 , and @xmath15 @xmath16 , respectively . w2 and w5 samples were irradiated at the mainz microtron facility in germany . finally , the diamond samples were annealed in vacuum for 3 h at @xmath17c to combine vacancies with nitrogen atoms to complete the formation of nv@xmath0 centers . based on measurements of the amount of fluorescence emitted from the two samples , we can estimate that the concentration of nv@xmath0 centers is 25 - 100 times larger in the w5 sample compared to the w2 sample . the concentration of nv@xmath0 centers in each sample varies by a factor of 2 - 4 depending on the exact spot on the diamond . figure [ fig : w5 ] shows experimentally obtained odmr spectra at zero magnetic field in the frequency range 2600 to 3150 mhz . at 2870 mhz , we observe the central resonance , which is labeled as resonance a in fig . [ fig : w5 ] . resonance a corresponds to a transition between the @xmath10 and @xmath18 states of the nv@xmath19 center . in measurements taken at small resonant microwave rabi frequencies @xmath20 , which correspond to low microwave powers , the central resonance is split into two resonances because the presence of strain causes mixing between the @xmath18 sublevels and energy splitting between the resulting eigenstates [ see , for example , the measurements taken at @xmath21 mhz and @xmath22 mhz in fig . [ fig : w5 ] ] . contrast , which is defined as the relative change of fluorescence intensity when the microwaves are on and off resonance with a transition , increases with increasing resonant microwave rabi frequency . figure [ fig : contrast ] shows the contrast of each resonance as a function of @xmath20 . the measured contrasts for each resonance were fitted to the function @xcite @xmath23 where @xmath24 is the contrast , @xmath25 is the saturation contrast , and @xmath26 is the saturation rabi frequency . the measured contrasts and the fits are shown in fig . [ fig : contrast ] , and the fitted parameters are shown in table [ fitparameters ] . for resonance a , the saturation rabi frequency was found to be 0.039(7 ) mhz . . fit parameters obtained from a fit of the measured contrast as a function of resonant microwave rabi frequency to eq . ( [ contrast ] ) . data and fits are shown in fig . [ fig : contrast ] . [ cols=""^,^,^"",options=""header "" , ] [ fitparameters ] apart from this central resonance , there are two small resonances in group c , @xmath27 , asymmetrically displaced to the low- and high- frequency sides of the center by around 56 and 70 mhz , respectively . for the lowest microwave power corresponding to @xmath21 mhz , only side - resonance group c and the central resonance are observed [ see fig . [ fig : w5 ] ] . as seen in fig . [ fig : contrast ] and from the fitted parameters in table [ fitparameters ] , the contrasts of resonance groups a and c saturate at similar values of the resonant microwave rabi frequency . this similar growth of contrasts of side - resonance groups a and c is expected , assuming that the c resonances are related to those nv@xmath0 centers which have a nearest - neighbor @xmath1c atom . the nv@xmath0 centers ( electronic spin 1 ) and @xmath1c atoms ( nuclear spin 1/2 ) can interact through the hyperfine interaction , which is strongest when the @xmath1c atom is in a nearest - neighbor position to the vacancy , where the electron density is the highest . the relative sizes of the contrasts can be estimated from the ratio of nv@xmath0 centers with nearest - neighbor @xmath1c atoms to those without nearest - neighbor @xmath1c atoms . since the natural abundance of @xmath1c atoms is 1.1% and there are three nearest - neighbor positions to the vacancy , we expect the ratio of contrasts to be roughly @xmath28 . the factor of 2 appears because the ground state @xmath10 splits into two states : @xmath29 and @xmath30 [ as in fig . [ fig : nv13c ] ] due to the hyperfine interaction ( here @xmath31 is the nv@xmath0 electronic - spin projection and @xmath32 is the @xmath1c nuclear - spin projection ) . in the case that the @xmath1c nuclear spins" +"duality between gravity and gauge theory in spacetime with different dimensionalities has been discovered by maldacena in 1998 @xcite . the type - iib string theory in ads@xmath0 is conjectured to be dual to a gauge theory in four dimensional minkowski spacetime ( @xmath1 ) at the boundary of the ads space . the correspondence can be used as a complementary method to study the strongly coupled gauge theory in four dimensional minkowski spacetime , a cousin of quantum chromodynamics , by avoiding the uncontrollable non - perturbative calculation via the application of weak - strong duality . we can deal with this problem by alternatively performing calculations in the tractable weakly interacting string theory in five ( plus five compact dimensions which provide details that are not relevant here ) dimensional anti de sitter space ( ads@xmath2 ) . the duality is extended to a finite temperature situation by adding a horizon in the radial coordinate @xcite . the string theory in an ads space with black hole horizon in the radial direction is proposed to be dual to a gauge theory at finite temperature . the duality is made quantitative in the sense that the hawking temperature in the bulk theory corresponds to the temperature of the gauge theory on the boundary . the ads / cft correspondence provides the first string - theoretic example of the underlying generic principle of the holographic duality ( i.e. the holographic principle ) . the idea of holographic duality was originally proposed by t hooft @xcite in a generic quantum gravity situation involving a gravitational horizon . the precise string theoretic version was given by susskind @xcite . when an object falls into a black hole , it will be stretched , torn apart into bits and eventually the bits will be smeared out over the horizon . consequently , all of the bulk information is spread over the horizonal surface resulting in an effective boundary description of the bulk theory . the bulk world is holographically encoded on the boundary . connection between ads space and holography was further clarified by witten @xcite after discovery of the ads / cft correspondence . given an ads space , the weakly - coupled bulk gravity theory corresponds to a strongly - coupled boundary gauge theory . adding a black hole to the ads space , the dual gauge theory on the boundary becomes thermal with the temperature equal to the corresponding hawking - page temperature of the background @xcite . it is thus interesting to investigate the intermediate situation where there exists a massive object before gravitational collapse into a black hole in the ads space and search for the dual description in the gauge theory side . it is argued in ref . @xcite that the degenerate fermions in the ads correspond to the composite multitrace operator constructed from product of single trace operators in the large central charge limit on the boundary . it is not unreasonable to think of this free "" fermionic operator as the conformal cousin of a qcd nucleon such as neutron and proton . these free fermions "" , however , still interact with each other by the colour - singlet interaction of order @xmath3 assuming negligible in the large @xmath4 limit . the colour - singlet ( glueball ) exchange on the boundary corresponds holographically to the gravitational interaction in the bulk . while gravity pulls the bulk mass together causing the gravitational collapse , the colour - singlet interaction should be responsible for the deconfinement phase transition of the injected mass in the dual picture . arguably , the gravitational collapse of the star in the ads would correspond to a thermalization process of the dual gauge matter on the boundary @xcite . consideration of the mass limit of the fermionic star in the ads bulk could reveal certain details of the pre - thermalization process in the dual gauge picture . the mass limit of the ads star corresponds to the minimum amount of injected mass required in order for the boundary gauge matter to start the thermalization process ( since the bulk gravitational collapse starts when injected mass exceeds the mass limit ) . specifically , it is also interesting to ask what the dual object of the bulk temperature is on the boundary world before black hole formation ? should it correspond to some parameter characterizing the superheated phase of gauge matter before the start of the thermalization ? moreover , what is the exact nature of the colour - singlet ( glueball exchange ) interaction responsible for the deconfinement of the dual gauge matter into the thermalized deconfined plasma ( which is the dual picture of the gravitational collapse caused by gravity ) ? the heavy - ion collision experiments at rhic and cern s lhc ( large hadron collider ) smash two charged ions at extreme energies , producing dense and hot nuclear matter with properties of the strongly coupled plasma . in the vicinity of the collision point , the induced magnetic field could be enormous @xcite . understanding the physics of dense hot nuclear plasma under such circumstances requires nonperturbative treatments of the strong interaction and the holographic method is one option . one holographic dual of the magnetized nuclear matter at finite temperature is proposed to be a magnetized black brane in the ads space @xcite . it was found that the entropy density of the magnetized brane in the ads obeys the third law of thermodynamics with entropy @xmath5 ( temperature ) for small temperature . in this article , we consider a fermionic star in the holographic ads@xmath2 background in the presence of external magnetic field at finite bulk temperature . the mass limit and other properties of the star is studied with respect to the changes in the magnetic field and bulk temperature . even though there is no complete understanding of the dual description in the gauge theory side of this situation , we argue certain aspects of the duality . in section ii , the tolman - oppenheimer - volkoff ( tov ) equation @xcite in the background ads@xmath2 is calculated starting from the general dimensionality . the energy levels of the bulk charged fermions in the presence of the magnetic field are calculated in the flat space approximation . the pressure and density of the bulk fermions at finite field and temperature are subsequently derived . section iii presents analytic and numerical results for each case of finite temperature and field . the mass limits depend crucially on the field and bulk temperature . the mass - radius relations for each case are discussed in section iv . the bulk adiabatic index and sound speed of the fermions inside the ads star are discussed in section v. the entropy density and total entropy in the bulk are also computed . section vi investigates the dependence of mass limit on the ads radius . section vii contains further discussions and summary of our results the study of the magnetized star in the ads space consists of two main calculations . first , the pressure and energy density need to be calculated for the system of charged fermions in the magnetic field at arbitrary temperature . the star will be assumed electrically neutral and we will focus only on the effect of magnetic field to the charged particles . at zero temperature , the energy states of the charged fermions in the magnetic field are separated naturally into landau levels . the partition function in the macrocanonical ensemble of these energy levels will provide the generic expression for the pressure and energy density of the fermionic system at finite temperature . the pressure and energy density are subsequently used in the equation of state required by the tov equation in the 5-dimensional ads spacetime . even though we will focus on interpreting the results of the bulk ads star in terms of the dual gauge theory , the calculations in the bulk picture are self - consistent and satisfactorily describe a real magnetized fermionic star in the 5-dimensional ads spacetime . in order to study the behaviour of a degenerate star in @xmath6-dimensional ads spacetime , we derive the spherical symmetric tov equation in @xmath6 dimensions as given in appendix [ appa ] . in the presence of external magnetic field , the pressure of the fermionic matter in the star is actually anisotropic due to the quantization of the energy levels . however , in the classical limit where the momentum in the direction of the magnetic field is much larger than the square root of the magnetic field , @xmath7 , the pressure becomes isotropic @xcite and the spherical symmetric tov equation is applicable . the resulting equations of motion describing the ads star in the spherical symmetric approximation are @xmath8 for the temperature @xmath9 , and @xmath10 where @xmath11 is the ads radius , @xmath12 is the area of @xmath13 and @xmath14 . to solve the equations of motion , we need the equation of state or the explicit expression of @xmath15 in terms of the chemical potential @xmath16 . standard evaluation of the partition function requires the layout of energy states of the fermionic system which can be obtained in the following subsection . we now solve the dirac equation to find the relativistic energy level of a charged fermion in the presence of external magnetic field in the 5 dimensional spacetime . as an approximation , we will ignore the effect of curvature on the energy levels of the fermions . the effects of gravity and the ads curvature will be considered only through the einstein equations stated in the previous subsection . starting from the dirac equation in flat space @xmath17 where @xmath18 is the mass of the fermion . the gamma matrices are chosen to be in the dirac representation as the following @xmath19 where @xmath20 and @xmath21 are @xmath22 identity matrix and pauli matrices respectively . we will consider only the positive energy solution since we are interested in the particle not the antiparticle . the positive energy solution @xmath23 satisfies the equation @xmath24 . let @xmath25 and consider a particle in an external magnetic field , the effect of the magnetic field can be taken into account by adding the field momentum , @xmath26 . we will choose the magnetic field to point in the @xmath27 direction and uniformly distributed over the entire @xmath28 space . the equation of motion of the fermion in 5 dimensional space becomes @xmath29 the momentum component in the extra dimension is represented by @xmath30 corresponding to the coordinate @xmath31 . we have assumed the solution in the form @xmath32 and neglect the effect of the ads curvature to the momentum component @xmath30 . this is a good approximation as long as the ads radius of curvature is large compared to the wavelength of the bulk fermions . the energy condition from the equation of motion is given by @xmath33 if we let @xmath34 , then we have @xmath35 from equation ( [ landau energy level 1 ] ) and ( [ landau energy level 2 ] ) , energy is quantized in the @xmath36 plane and contains certain degeneracy of states , _ i.e. _ , there are several states with the same one - particle energy . the number of states @xmath37 of a discrete energy level @xmath38 is @xmath39 where @xmath40(@xmath41 ) is a spin degeneracy independent of @xmath38 . the degeneracy is proportional to the field and vanishes for @xmath42 . the discrete energies from the degrees of freedom of the plane perpendicular to the magnetic field is called the landau levels , characterizing the statistical properties of the fermionic system . extension to finite temperature situation can be done by considering the corresponding partition function . thermodynamical pressure and energy density of the magnetized fermion gas can be calculated from the grand" +"consistent unification of relativity and quantum mechanics remains an unsolved theoretical problem in spite of many efforts applied to its solution in the 20th century . the fundamental difference between relativistic and non - relativistic physics follows from the famous einstein s formula @xmath1 . this formula , in particular , implies that if a system of particles has sufficient energy @xmath2 of their relative motion , then this energy may be converted to the mass @xmath3 of newly created particles . generally , there is no limit on how many particles can be created in collisions , so any realistic quantum mechanical description of high - energy systems should involve states with any number of particles from zero to infinity . the number of particles is not conserved during time evolution . the most familiar example of such a behavior is the emission and absorption of light ( photons ) in electrodynamics . first attempts to describe relativistic quantum systems were undertaken immediately after creation of the formalism of quantum mechanics in 1920 s . a quantum theory of the electromagnetic field was constructed by quantization of the classical maxwell electrodynamics . in lowest perturbation orders , this theory agreed well with experimental results . however , perturbative calculations for the @xmath0-matrix did not work in higher orders , in particular , due to ultraviolet divergences . the way to calculate the @xmath0-matrix in qft accurately in all orders was provided by the renormalized qed formulated by feynman , schwinger , and tomonaga in the late 1940 s . however this approach created a host of other problems . according to the prevailing interpretation , the creation and annihilation operators present in the hamiltonian and lagrangian of qed correspond to _ bare _ particles having infinite masses and charges . however , the bare particles have never been directly observed in experiments . they are believed to be surrounded by clouds of virtual photons and electron - positron pairs , thus forming complex objects called _ dressed _ particles . the dressed particles are supposed to be the eigenstates of the full hamiltonian . they have finite experimentally observable masses and charges . the problem is that the bare particle hamiltonian of qft is formally infinite . although , these infinities cancel out when the @xmath0-matrix is calculated , the hamiltonian is useless if one wants to calculate the time evolution or to find wavefunctions of bound states via diagonalization procedure . two lines of research were initiated to cope with these problems . the _ dressed particle _ approach was suggested by greenberg and schweber @xcite . their goal was to get rid of the bare particles and to express the entire formalism of qft through observable dressed particles only . the operators for dressed particles were sought as unitary transforms of bare particle operators . from another direction , gazek and wilson @xcite introduced the _ similarity renormalization _ formalism . the idea was to apply a unitary transformation to the hamiltonian in order to ensure that interaction potentials rapidly fall off as functions of energy differences , and to guarantee that all loop integrals are convergent . the similarity and dressing transformations are strikingly similar . they can be combined into one unitary _ similarity - dressing _ transformation which achieves two goals at once : the theory can be expressed in terms of real dressed particles and the hamiltonian can be made finite in all perturbation orders . at the same time , the accurate and well - tested @xmath0-matrix of the renormalized theory remains intact . this combined approach was developed in refs . @xcite and dubbed the relativistic quantum dynamics , or rqd . in this paper we will discuss the reasons why the renormalization difficulties ( e.g. , the absence of a well - defined hamiltonian and unsatisfactory treatment of the time evolution ) persist in current relativistic quantum field theories . to avoid unnecessary mathematical complications , we will be working with a simple model theory which , nevertheless , shares some important features with qed . in section 9 we will explain how the similarity - dressing transformation of this model theory leads to a well defined ( perturbatively ) finite hamiltonian that can be used for all kinds of quantum mechanical calculations ( @xmath0-matrix , bound states , time evolution , etc . ) without the need for renormalization . in addition , the rqd formalism does not use the dubious notions of bare and virtual particles . in this paper we will be concerned with three types of phenomena that are normally studied in physical experiments : bound states , time evolution , and scattering . these three areas account for the most of experimental information available about fundamental particles and their interactions . the key theoretical quantity involved in quantum mechanical description of these phenomena is the hamilton operator @xmath4 . the energies @xmath5 and state vectors @xmath6 of bound states can be found as eigenvalues and eigenvectors of the hamiltonian @xmath7 the development of the state vector @xmath8 from time @xmath9 to time @xmath10 is described by the _ time evolution operator _ @xmath11 @xmath12 if the eigenvalues @xmath5 and eigenvectors @xmath13 of the hamiltonian are known and the initial state is represented as a sum ( and/or integral ) over the basis states @xmath14 unfortunately , in most cases , the full spectrum of the hamiltonian is not known , and the time evolution is difficult to predict . this difficulty , however , is not that disappointing , because experimental observations of the time evolution in subatomic world are even more difficult than calculations . most experiments in high energy physics are performed by preparing free particles or their bound states ( like hydrogen atoms or deuterons ) , bringing them into collision , and studying the properties of free particles or bound states leaving the region of collision . in these experiments , it is not possible to observe the time evolution during interaction : particle reactions occur almost instantaneously and one can only register the reactants and products which move freely before and after the collision . this gives a lucky break for theoreticians : in such situations the theory is not required to describe the detailed dynamics of particles during the short interval of collision . it is sufficient to provide a mapping of free states before interaction onto the free states after the interaction . to describe scattering experiments , one needs only the formula for the time evolution from the remote past @xmath15 to the distant future @xmath16 @xmath17 where the @xmath0__-operator _ _ [ s - oper ] is defined by @xmath18 one can read the right hand side of eq . ( [ eq : s - oper ] ) from right to left as a sequence of three steps : ( i ) the non - interaction evolution of the system from time @xmath9 in the past to 0 ; ( ii ) the sudden jump at @xmath19 described by the @xmath0-operator ; ( iii ) the free evolution from @xmath19 to the future time @xmath10 . the most effective technique available for calculations of the @xmath0-operator is the perturbation theory which can be written in many equivalent forms . the dyson time - ordered expansion provides the most economical expressions that can be encoded in familiar feynman diagrams . however , for the discussion in this paper , we found more useful two other perturbative expressions which differ from the dyson s formula only by re - shuffling the terms . the `` old - fashioned '' formula for the @xmath0-operator is @xmath20 where @xmath21 is the interaction part of the total hamiltonian @xmath22 , @xmath23 and the factor latexmath:[$e^{-\epsilon switching the interaction on and off . operators with @xmath10-dependence determined by the free hamiltonian @xmath25 as in eq . ( [ eq:8.67 ] ) will be called _ regular_. using convenient symbols for @xmath10-integrals [ underline ] @xmath26 formula ( [ eq:8.68 ] ) can be written compactly as @xmath27 where @xmath28 another equivalent expression for @xmath0 was suggested by magnus @xcite @xmath29 here the hermitian operator @xmath30 can be represented as a series of multiple commutators with @xmath10-integrations @xmath31 -\frac{1}{6}[\underline{\underline{v(t)},[v(t)},v(t ) ] ] -\frac{1}{6}[\underline{[\underline{v(t)},v(t)]},v(t ) ] \nonumber \\ & \mbox { } & + \frac{i}{12}[\underline{\underline{\underline{v(t)},[[v(t)},v(t)]},v(t ) ] ] \nonumber \\ & + & \frac{i}{12}[\underline{[\underline{\underline{v(t)},[v(t)},v(t)]]},v(t ) ] + \frac{i}{12}[\underline{\underline{[\underline{v(t)},v(t)]},[v(t)},v(t ) ] ] + \ldots \label{eq:8.72}\end{aligned}\ ] ] one important advantage of this representation is that the @xmath0-operator ( [ eq:8.71 ] ) is manifestly unitary . it follows from equations ( [ eq:8.69 ] ) and ( [ eq:8.71 ] ) that operators @xmath32 and @xmath30 are related to each other @xmath33 so finding @xmath30 or @xmath32 are equivalent tasks . the @xmath0-operator and the hamiltonian provide two different ways to describe dynamics . the @xmath0-operator represents only `` integrated '' time evolution from the remote past to the distant future . the knowledge of the @xmath0-operator is sufficient to calculate the scattering cross - sections as well as energies and lifetimes of stable and metastable bound states .- operator on the complex energy plane . ] however , in order to describe the time evolution and the wavefunctions of bound states the full interacting hamiltonian @xmath4 is required . it can be shown @xcite that two hamiltonians @xmath34 and @xmath35 related to each other by a unitary transformation @xmath36 @xmath37 yield the same scattering @xmath38 as long as condition @xmath39 is satisfied . such hamiltonians @xmath4 and @xmath40 are called _ scattering - equivalent_. the energy spectra of two scattering equivalent hamiltonians are identical . however , the eigenvectors are different and , according to eq . ( [ eq:8.61a ] ) , the corresponding descriptions of dynamics are different as well . therefore scattering - equivalent theories may be not _ physically _ equivalent . calculations of bound states , time evolution and scattering is a routine practice in non - relativistic quantum mechanics . however , the situation is less certain in relativistic quantum field theories . as mentioned in introduction , the hamiltonian of renormalized qft is infinite . therefore , it is not immediately clear if the above formulas ( [ eq:1 ] ) - ( [ eq:8.74 ] ) remain valid for the high energy relativistic phenomena , and what modifications , if any , should be introduced in quantum theory to take into account the variable number of particles . in this paper we illustrate the difficulties encountered in quantum field theories by analyzing a simple model theory with variable number of particles . we will demonstrate that the hamiltonian can be redefined so that there is no need for renormalization and usual quantum mechanical techniques remain applicable even in the relativistic case . our model theory describes two kinds of particles . these are massive spinless fermions which will be called _ electrons _ and massless bosons with zero helicity , which will be called _ photons_. here we disregard the spin and polarization degrees of freedom as they are not so important for the discussion of renormalization . to allow for creation and annihilation of particles , the system is described in the fock space which is built as a direct sum of sectors with various numbers of particles . for example , if we denote @xmath41 the no - particle vacuum state , @xmath42 the one - electron hilbert space and @xmath43 the one - photon hilbert space , then the fock space can be written as an infinite direct sum @xmath44 the anticommutation and commutation relations for particle creation and annihilation operators ( @xmath45 , @xmath46 for electrons and @xmath47 , @xmath48 for photons , respectively ) are , as usual , @xmath49 @xmath50 & = & \delta ( \mathbf{p}-\mathbf{p } ' ) \label{eq : cc}\\ \{a_{\mathbf{p}},a_{\mathbf{p}'}\ } & = & \{a^{\dag}_{\mathbf{p}},a^{\dag}_{\mathbf{p}'}\ }" +"the radio frequency dressed potentials ( rf - dressed potentials ) , initially proposed by zobay and garraway @xcite , are considered as convenient tool to trap and manipulate ultra - cold atoms in exotic forms @xcite . non - trivial trapping geometries like ring trap , double well and shell traps have already been demonstrated using potentials generated from various combinations of static magnetic field , radio frequency ( rf ) field and far detuned laser beams @xcite . these trapping geometries provide opportunity to explore basic physics of fermions and bosons in low dimensions , matter wave interferometry @xcite , etc . the ring shaped atom traps , besides being useful for fundamental studies , are also promising for the development of atom gyroscope for precision rotation sensors for navigation @xcite . the rf - dressed potentials , also known as `` adiabatic potentials '' , are energy eigenvalues of an interaction hamiltonian for an atom interacting with an rf - field in presence of a static magnetic field @xcite . dependence of these potentials on the atom - field coupling strength and frequency detuning of the rf - field with the zeeman sub - levels transition frequency , make them inherently position dependent and capable of providing interesting atom - trapping geometries @xcite . the rf - dressed potentials also promise a great flexibility of tailoring them by changing the rf - field strength , polarization , frequency and phase @xcite . by varying the rf - field parameters , the resultant rf - dressed potential can be made time dependent , which may be exploited for multiple purposes , such as initially for evaporative cooling of atom cloud and then for trapping in a designed geometry . such an example of atom trapping in a toroidal geometry has been demonstrated recently by our group by applying an rf - field of varying amplitude and frequency on a cloud of @xmath0 atoms trapped in a quadrupole magnetic trap @xcite . in the earlier work @xcite , it was demonstrated that a quadrupole magnetic trap was converted into a toroidal shaped atom - trap , when the frequency and amplitude of the applied rf - field were ramped ( varied with time ) in the chosen way . in that work , the atom cloud was characterized and studied after the end of the ramp of the rf - field - when rf - field was left on at a fixed final frequency and amplitude . a natural curiosity , however , related to these experiments , remains to understand the various processes involved and their effect on the evolution of the characteristics of the atom cloud during the ramp of the rf - field . in the present work , we have made an attempt to understand the time evolution of the atom cloud , in terms of variation in its shape and number of atoms , during the rf - field ramp ( i.e. during the transformation of the quadrupole trap into an rf - dressed toroidal trap ) . we have performed the simulations considering the atom cloud evolving in a time dependent potential formed due to ramp of rf - field in presence of a static quadrupole magnetic field . the simulations results have been compared with the experimental observations . in the simulations , we have used the direct simulation monte carlo ( dsmc ) technique which is based on an extension of the original proposal of bird @xcite . different variants of dsmc method have already been used to understand the evaporative cooling @xcite and expansion cooling @xcite of atoms . the results of simulations show that , at lower rf - field strength and higher frequency ( at the beginning of ramp of the rf - field ) , the rf - field results in ejection of atoms from the trap , leading to evaporative cooling of the atom cloud . later on , at higher rf - field strength and lower frequency , the atoms can undergo the landau - zener ( lz ) transition which leads to their trapping in an rf - dressed potential of toroidal shape . the results of these simulations explain well our experimental observations related to temporal variation in the number of atoms and shape of the atom cloud in the trap . similar simulations can be performed to predict the dynamics of atom cloud with more sophisticated evolution of the potential which can help in exploring more efficient cooling and trapping schemes . the dsmc method does not require the sufficient ergodicity "" approximation and thus can simulate atomic ensembles far from their equilibrium condition . this makes dsmc technique more suitable to simulate our experimental conditions where a fast ramp of the rf - field parameters ( amplitude and frequency ) is considered . the ergodicity assumption also fails if the mixing time of the atomic samples is longer than the elastic collision time @xcite . for other situations , both classical and quantum kinetic theories of truncated boltzmann distribution of the phase space provide the alternative approaches to the evaporative cooling mechanism @xcite . but these treatments are valid with the assumption of the sufficient ergodicity "" , which means that the phase space density is only a function of energy . the article is organised as follows . the section [ theory and simulations ] of this article presents the theoretical background related to the study along with the method of numerical simulations . the experimental procedure , observations , results of numerical simulations and the comparisons between experiments and simulations have been presented in [ results ] . the conclusion of our work is discussed in section [ conclusion ] . the hyperfine state @xmath1 of @xmath0 is five fold degenerate and splits into zeeman sub - levels in presence of a static magnetic field . we consider the atoms are prepared in the @xmath2 state to trap them in a quadrupole magnetic trap . it is assumed that the trapping magnetic field is not very strong and the energy gap among zeeman sub - levels varies linearly with the field strength . hence , an applied rf - field of appropriate frequency can be simultaneously resonant to all the transitions involving adjacent sub - levels . the rf - field is considered to be ramped to have time varying amplitude and frequency , as discussed specifically later , in a manner as reported in our recent experimental work @xcite . when the rf - field is sufficiently strong ( _ i.e. _ rabi frequency is high ) , the atom - field interaction is described better in the dressed state "" @xcite picture involving the diagonalization of both the static and coupling hamiltonian . in our simulations , we first calculate the rf - dressed potential ( using a formalism based on rotating wave approximation ( rwa ) ) at any instant of time during the ramp of the rf - field . the collision between atoms is formulated in the degenerate internal state ( dis ) approximation which neglects the rabi oscillations during the collisions , as collision between two cold @xmath0 atoms occurs locally in a sub - nanosecond time regime @xcite . this approximation makes it possible to express the scattering amplitudes between pairs of dressed atoms in terms of bare state scattering amplitudes discussed in detail in an earlier work @xcite . the process of rf - evaporation as well as trapping of the atoms in the rf - dressed potential has been studied numerically with the help of a dsmc algorithm , which simulates the motion of an atom in the time varying rf - dressed potential . in the simulations , the landau - zener ( lz ) transition probability is calculated to ascertain if the atom is going to be trapped in the rf - dressed potential or not . depending upon this probability and the coordinates of the atom evolved in the time dependent potential , the final atom cloud trapped in the rf - dressed potential is constructed . we consider the static quadrupole magnetic trap with magnetic field distribution near the trap centre given by @xmath3 , where @xmath4 is the radial field gradient . in this trap , the transition frequency between adjacent zeeman sub - levels is given as , @xmath5 where @xmath6 is the lande s g - factor , @xmath7 is the bohr magneton and @xmath8 is the reduced planck s constant . we consider an atom interacting with a static field @xmath9 and an rf - field of frequency @xmath10 with field vector components @xmath11 , where @xmath12 , @xmath13 and @xmath14 are the perpendicular and parallel components of the rf - field respectively with respect to the local static field vector @xmath9 . the interaction hamiltonian for the atom - field interaction is given as @xcite , @xmath15.\ ] ] where @xmath16 ( @xmath17 ) are the hyperfine operators along the @xmath12 and @xmath13 components and @xmath18 is the hyperfine operator along @xmath14 . if rf - field is taken to be of the form @xmath19 $ ] , then , using a semi classical treatment under rotating wave approximation ( rwa ) , the interaction hamiltonian of eq . ( [ eq : h ] ) can be diagonalised to lead the energy eigen values ( _ i.e. _ rf - dressed potentials ) given as , @xmath20 where @xmath21 @xmath22 -f to f for a given hyperfine state @xmath23 . here @xmath24 is the detuning , @xmath25 is the coupling strength ( _ i.e. _ rabi frequency ) for the adjacent zeeman sub - levels and @xmath26 . knowing @xmath24 and @xmath25 , the potential @xmath27 can be evaluated using eqs.([eq : pot_compact])-([eq : omega ] ) . the eigen states ( _ i.e. _ rf - dressed states ) , corresponding to these eigen values ( _ i.e. _ rf - dressed potentials @xmath27 ) can be written in compact form as , @xmath28 are the bare sates corresponding to zeeman sub - levels of hyperfine level @xmath29 , @xmath30 denotes the dressed states and coefficients @xmath31 are the matrix elements of a unitary rotation matrix which transforms the bare states to the dressed states . the values of few @xmath31 are given in the appendix in terms of the detuning and rabi frequency . a schematic of the variation in rf - dressed potential energy of an atom with position is shown in fig . [ fig : field_line ] for two dressed states @xmath32 and @xmath33 . the region with width @xmath34 represents the interaction region where lz transition probability is high . this region where potential energy curves for two dressed states come close to each other but do not cross each other , unlike the bare state energy curves , is known as the `` avoided crossing '' . ( color online ) schematic of the variation in potential energy of an atom with position in a quadrupole trap in presence of an rf - field . the continuous curves show the adiabatic rf - dressed potentials ( denoted with the subscript a ) including the coupling of rf - field with atom . the dashed lines show the atom - field energy without coupling of rf - field with atom . the red dots correspond to the atoms in @xmath33 state while the blue dots correspond to atoms in @xmath32 state . the width @xmath35 represents the interaction region where lz transition probability is high . for brevity , the potentials for only two states are shown here.,width=309 ] further , eq . ( [ eq : h ] ) can be extended to include the kinetic energy of the atoms . the inclusion of atomic velocity introduces non - adiabaticity in the system which allows the transition between different dressed states near the" +"the 1995 discovery of bose - einstein condensation in dilute ultracold gases @xcite prompted a flurry of activity investigating these fascinating quantum systems . in the experiments , ultracold atoms are confined by magnetic or optical forces , which typically can be represented theoretically by a harmonic potential . lately , however , an increasing amount of interest has focused on bose condensates in more exotic trapping potentials . for example , gupta _ et al . _ @xcite recently produced a condensate in a ring - shaped magnetic waveguide , while experiments at ecole normale suprieure @xcite have been conducted in overlapping magnetic and optical dipole traps , leading to a potential which can be approximated by a function which is quadratic plus quartic in the radial coordinate . this trap potential is especially of interest when the condensate is rotating , since , in contrast to the harmonic case , one can in principle achieve arbitrarily high angular velocities . this leads to interesting new configurations , for example a vortex lattice with a hole at its center , and for even higher angular velocities , annular condensates containing a multiply - quantized `` macrovortex '' . these equilibrium configurations have been studied in a number of papers @xcite , where the angular velocities for transitions between the different states , defining a phase diagram , were calculated in refs . in addition to the static properties , the dynamics have also been addressed , with the collective mode excitations considered in refs . @xcite . alternatively , one could consider the case where , in addition to the quartic term , there is a _ negative _ harmonic term . then the radial trap potential has the form of a `` mexican hat '' , and the condensate can be annular even when there is no rotation . similar trap configurations have been studied elsewhere @xcite . of particular interest , however , is the behavior of the system under rotation , since vortices can enter the condensate and form a stable , multiply - quantized vortex at the center . for example , an important question raised in this configuration concerns the stability of the vortex in the presence of a non - rotating thermal cloud at finite temperatures does the vortex decay by spiraling towards the edge as in a harmonic trap @xcite , or is it metastable ? this is related to the well - known problem of stability of persistent currents in superfluids @xcite , and so is of interest from a fundamental perspective . in order to tackle these types of questions experimentally it is important to possess some way of detecting the presence of a vortex . in a harmonically - trapped condensate this is relatively straightforward , since the fluid circulation around the vortex core creates a hole in the density , which can be detected by standard absorption imaging . since the optical resolution is usually not sufficient to detect vortices _ in situ _ , a period of free expansion following the release of the condensate from the trap is generally required . however , in a trapped annular condensate vortices reside in the center where the density is very low irrespective of the circulation . hence , imaging of a vortex _ in situ _ is precluded , and it is not even obvious _ a priori _ whether it is possible to resolve the vortex after expansion . a more detailed analysis is thus required in order to evaluate the feasibility of this and other possible schemes for vortex detection . in this paper we shall study two - dimensional condensates , where the trap potential has a quartic minus quadratic radial dependence . most of our results for thin annular condensates , however , also apply to more general mexican hat potentials . two dimensions in this context corresponds to either a cylindrical condensate , where the axial length scale greatly exceeds the radial size , or a thin disk - shaped condensate where the system is tightly trapped in the axial direction such that dynamics along this coordinate are `` frozen out '' and can be neglected . both geometries are of experimental interest . we also focus exclusively on condensates in the mean field regime at zero temperature , where the properties can be accurately described by the gross - pitaevskii ( gp ) equation . nevertheless , we should mention that the possibility of obtaining a thin annulus , essentially a one - dimensional system , opens up other interesting regimes beyond mean field , such as a quasi - condensate or tonks - girardeau gas @xcite . we begin by studying the equilibrium states , where both numerical solutions and analytical results are presented . we then characterize the lowest energy excitations , or collective modes , of the condensate . in particular , we use a hydrodynamic model to derive analytical expressions in the limit of thin annuli , as well as to find the mode frequencies numerically . we also compare these results to numerical simulations of the gp equation . this allows us to discuss the use of collective modes to detect vorticity ; namely the splitting between counter - propagating surface and acoustic modes of the condensate . we then consider the expansion of the condensate after switching off the confining potential , finding that the hole due to the vortex is recovered in the expanded density , providing a simple means to detect the presence of the vortex in experiments . finally , we discuss the momentum distribution of an annular condensate , finding that in the limit of thin annuli the function approaches a simple analytical form . for a dilute bose - einstein condensate in the limit of zero temperature , the time - dependent evolution of the condensate wavefunction @xmath0 is described by the gross - pitaevskii ( gp ) equation @xmath1 the interactions between atoms are represented by the parameter @xmath2 , for @xmath3 atoms of mass @xmath4 , with @xmath5-wave scattering length @xmath6 . note that , in addition to the dynamics of the condensate , the time - independent stationary states can be found by substituting @xmath7 into eq . ( [ eq : gp-3d ] ) , whereupon the left - hand side becomes @xmath8 with @xmath9 the chemical potential . the external potential in eq . ( [ eq : gp-3d ] ) is of the form @xmath10 where @xmath11 , with @xmath12 and @xmath13 the radial and axial trap frequencies respectively . in the following we shall mostly use harmonic oscillator units where distance , time and energy are expressed in units of @xmath14 , @xmath15 and @xmath16 respectively . we also take @xmath17 , where the case of @xmath18 has already been extensively studied in a number of papers @xcite . we explicitly consider the gp equation in 2d @xmath19 \psi \ , , \label{eq : gp}\ ] ] where the evolution in the axial coordinate is neglected . physically this can correspond to the case of a cylindrical condensate , where @xmath20 . the interaction parameter then becomes , @xmath21 , in harmonic oscillator units , where @xmath22 represents the number of atoms per unit length along the axial direction . an alternative two - dimensional configuration involves tight axial confinement , such that @xmath23 in physical units . in this geometry , which has been realized experimentally @xcite , the axial dynamics are `` frozen out '' . the axial dependence of the wavefunction is then gaussian , and the 2d gp equation ( [ eq : gp ] ) can be used with @xmath24 @xcite . we first analyze a condensate without a vortex using the thomas - fermi ( tf ) approximation , where the spatial derivative of @xmath25 in eq . ( [ eq : gp ] ) is neglected , so that the density is given by @xmath26 for @xmath27 , and @xmath28 otherwise . the radii of the condensate are evaluated by finding where the density goes to zero . if @xmath29 then there is a single solution of the resulting quadratic equation , @xmath30 , which corresponds to a condensate without a hole . on the other hand , if @xmath31 there are two solutions @xmath32 , and the condensate is annular with a hole in the center . in this case one can write the tf condensate density as @xmath33 for @xmath27 . calculating the radii and chemical potential more explicitly requires the condition that the wavefunction is normalized to unity @xmath34 . the resulting radii can be conveniently expressed as the sum and difference of the squares @xmath35 , yielding @xmath36 @xmath37 where we have defined a new parameter @xmath38 in eq . ( [ eq : rm ] ) . the chemical potential is then @xmath39 this yields the condition @xmath40 for an annular condensate , which we will always assume in the following . the limit @xmath41 corresponds to the case where the width of the annulus becomes much smaller than the radius . the range of validity of the tf approximation for an annular condensate is defined by the condition @xmath42 @xcite , where @xmath43 is the healing length at the density maximum , while @xmath44 is the width of the annulus . using the above expressions yields the explicit relations @xmath45 and @xmath46 . the condensate can also contain a single centered vortex with circulation @xmath47 , where the well - known requirement of quantized circulation in superfluids @xcite constrains the vorticity to integer values @xmath48 . the equilibrium condensate density is represented within the tf approximation as @xmath49 where @xmath9 is the chemical potential in the laboratory ( non - rotating ) frame and the @xmath50 term corresponds to the centrifugal potential barrier resulting from the fluid flow around the vortex . performing an analysis similar to that of the non - rotating condensate gives the following relations @xmath51}{4 } \ , , \label{eq : lambnu - rot}\ ] ] @xmath52 \ , , \label{eq : lambmu - rot}\ ] ] @xmath53 approximate analytical solutions of eqs . ( [ eq : lambnu - rot]-[eq : eta - rot ] ) can be obtained using the expansion @xmath54 , which is most appropriate for @xmath55 . as we shall see this regime is the most interesting for our purposes , since it corresponds to the region where a multiply - quantized vortex is stable . substituting into eqs . ( [ eq : lambnu - rot]-[eq : eta - rot ] ) yields the following results @xmath56 \ , , \label{eq : exp - rp}\ ] ] @xmath57 ( \lambda \nu)^2 \\ \nonumber + \mathcal{o}[(\lambda \nu)^4 ] \ , , \label{eq : exp - rn}\end{aligned}\ ] ] @xmath58 \ , . \label{eq : exp - mu}\ ] ] another important quantity is the energy of the condensate in the presence of a vortex . this is represented in terms of an energy per particle as an integral @xmath59 within the tf approximation the energy becomes @xmath60 eq . ( [ eq : energy - tf ] ) can be approximated analytically using the tf density ( [ eq : density - nu ] ) and the expansions ( [ eq : exp - rp]-[eq : exp - mu ] ) . this eventually yields @xmath61 \ , , \label{eq : energy - ana1}\ ] ] where we have defined the second - order term separately @xmath62 \ , . \label{eq : e_1}\ ] ] interestingly , this term can also be derived by calculating the kinetic energy from the circulation of the vortex @xmath63 , where @xmath64 is approximated by the density without a vortex ( [ eq : density ] ) . the energy in a frame rotating with angular velocity @xmath65 is related to that in the laboratory frame" +"a year ago , there were a number of pieces of evidence that pointed to a connection between grbs ( gamma - ray bursts ) and snae ( supernovae ) ( see @xcite for a review ) . the positions of grbs in galaxies , near star forming regions , were consistent with a massive star origin . in addition to the association of grb 980425 with sn 1998bw , two distant grb afterglows showed evidence for supernovae in their light curves and spectra . in some cases , the afterglow evolution suggested interaction with a freely expanding stellar wind , as expected in the immediate vicinity of a massive star . although the evidence for an association with star forming regions has held up @xcite , the other topics have not provided further support . there have been no further convincing associations of supernovae with grb afterglows . dust echos have been proposed as the mechanism for the two apparent distant supernova cases that have been observed @xcite . the two best observed recent afterglows , grb 991208 and grb 000301c , have been interpreted in terms of expansion in a constant density medium , with jet effects @xcite . all these points weaken the case for a grb sn connection . here , i discuss these recent developments in the context of studies of supernovae and grb afterglows . the shock interactions of supernovae with circumstellar matter can be observed through radio synchrotron emission ( analogous to the synchrotron emission in grb afterglows ) and through x - ray thermal radiation . the radio light curves are characterized by an initial rise followed by a power law decline . a plot of the time of the light curve peak vs. the peak luminosity at that time sorts the observed supernovae into various types @xcite . these properties are related to the density of the gas into which the shock wave is propagating . except for sn 1987a , type ii supernovae are thought to have red supergiant progenitors , which have wind velocities of @xmath1 km s@xmath2 . the inferred mass loss rate from the progenitor of sn 1999em , a recently detected radio supernova @xcite , is @xmath3 . this may be typical of sn ii progenitors ; the well - observed type ii radio supernovae are probably at the upper end of a distribution of circumstellar densities . the most luminous radio supernovae are inferred to have @xmath4 . although some deviation from standard evolution has been found in radio supernovae with red supergiant progenitors @xcite the variations are small compared to those in sn 1987a . the well - known equatorial ring is at a radius of @xmath5 cm , but moderately dense gas probably extends in from this radius because of photoionization by the progenitor star @xcite . the radio luminosity was initially low compared to the red supergiant case because of interaction with the low density progenitor wind , but started to increase in 1990 and rapidly rose to @xmath6 times an extrapolation of the early decline @xcite . during the last few years , the supernova shock wave has started to interact with parts of the equatorial ring that are closest to the supernova @xcite . the changes in radio flux , which are more dramatic than any observed for other type ii supernovae , show what happens when a supernova shock wave runs into dense gas from an earlier evolutionary stage . at the present time , sn 1987a remains unique among the sn iiae and the precise causes for the progenitor evolution to the blue are not clear ; they may have to do with binary evolution . except for sn 1998bw , the sn ib / c that have been observed in the radio have similar properties @xcite . if they are able to efficiently radiate synchrotron emission , the radio flux is approximately in accord with @xmath7 and @xmath8 km s@xmath2 , as expected for a wolf - rayet star @xcite . except for sn 1998bw , the radio light curves show a smooth evolution , although the data are sparse . in the case of sn 1998bw , the observed rise in flux between days 20 and 30 @xcite is more likely to be due to an increase in the energy of the explosion than to an encounter with denser gas @xcite . the evolution is consistent with interaction with a @xmath0 wind extending out to at least @xmath9 cm . if grbs have massive star progenitors , they are likely to be wolf - rayet stars . arguments in favor of this assumption include : ( 1 ) sn 1998bw , the best case of a sn grb association ( grb 980425 ) , was of type ic , with a probable wolf - rayet progenitor . ( 2 ) the high energy of grbs suggest that a moderately massive black hole is involved , which , in turn , requires a massive , @xmath10 , progenitor @xcite . these stars are likely to be wolf - rayet stars at the end of their lives @xcite . ( 3 ) the relativistic flow from a central object may be able to penetrate a relatively compact wolf - rayet star , but probably can not penetrate an extended red supergiant star @xcite . none of these arguments is definitive , but they are suggestive . the grb rate is a small fraction of the sn rate so that a peculiar kind of star with an unusual surroundings could be involved . for example , a binary merger may be needed so that the central black hole has a large rotational energy . the merger process may be associated with a strong equatorial outflow of the stellar envelope . however , the relativistic flow is likely to be along the polar axis , where the mass loss properties may be normal . the best tests for afterglow models are sources with extensive data ; radio data are especially useful because they give information on the absorption frequency and the peak flux and its frequency . the extensive radio data @xcite on grb 970508 can be fitted by a model afterglow interacting with an @xmath11 wind , extending out to @xmath12 cm @xcite . frail et al . @xcite fit the same data by jet expansion in a uniform medium . in their model , jet effects become important at day 25 and there is a transition to spherical nonrelativistic flow at day 100 . the radio data on grbs 991208 and 000301c can also be approximately fitted by a wind model @xcite , but in these cases a broken power law spectrum is needed for the particles in order to fit the higher energy light curves . the jet in a uniform medium models for these objects can assume a single power law spectrum ; however , the evolution of grb 991208 is taken to be in the jet transition phase during the period of observation ( @xmath13 days ) @xcite , whereas grb 000301c is taken to have a sharp transition to asymptotic jet evolution on day 7.3 @xcite . a problem with the jet models is that the evolution is not well defined . the broken power law , wind models can be tested by late observations because different time dependences are expected at radio and optical wavelengths . the wind interaction models @xcite have not included jet effects , although a collimated flow is expected if it must escape from the center of a star . to some extent , this can be justified by the slow apparent evolution of a jet in a wind @xcite . the facts that many afterglows can be fitted by model evolution in a constant density medium and that massive stars are attractive progenitors have led to the suggestion @xcite that the expansion is into the constant density medium that is expected downstream from the termination shock of the massive star wind @xcite . the outer radius of such a region is @xmath14 times the inner radius when the fast wind from a wolf - rayet star runs into a slow wind from a previous evolutionary stage @xcite . models and observations of galactic wolf - rayet stars show that the swept - up shell of red supergiant material at the outer radius is at a distance @xmath15 pc from the star @xcite . this radius is sufficiently large that interaction with the free @xmath0 wind is expected over the typical period of observation of afterglows . the time for the wind to reach the termination shock is relatively short ( @xmath16 years to reach @xmath17 cm ) , so that the assumption of constant wind properties is plausible . in a massive star progenitor model , a high density in the immediate vicinity of the explosion is expected even if the wind passes through a termination shock at a relatively small radius . the prompt optical emission from a grb gives the opportunity to investigate the immediate surroundings ; in the case of grb 990123 , low density ( interstellar medium ) interaction gives a better explanation for the observations @xcite . despite the plausibility of free wind interaction , the uncertainty in the evolution of massive stars leaves open the possibility of interaction with denser material at early times ; ramirez - ruiz et al . @xcite have investigated such a case . the interaction of a grb flow with a dense shell could have different properties compared to a supernova , as exemplified by sn 1987a . in the supernova case , the shock front is continually driven by the lower velocity supernova ejecta with most of the kinetic energy . most grb afterglow models have constant energy , so that although an initial overpressure can be expected upon a collision with a shell , it is not as marked as in the supernova case . in addition , the grb flow is likely to be in a jet , unlike the supernova case . when the beamed flow interacts with a large density jump , it is rapidly decelerated and lateral spreading can occur . the afterglow could make a rapid transition to the asymptotic behavior for a jet flow @xcite . the afterglow of grb 000301c did show a bump followed by a transition to a steeper decline that could be lateral jet expansion , although the bump can be interpreted as a microlensing event @xcite . the possibility of circumstellar dust echos arises naturally for type ii supernovae with red supergiant progenitors because their cool winds are known to contain dust . for the higher estimated mass loss rates , e.g. , @xmath18 for sn 1979c , the progenitor star is expected to be entirely enshrouded in dust . yet when we observe type ii supernovae , there is little evidence for dust absorption in the spectra of the supernovae , including sn 1979c . the probable solution is that the dust near the star is evaporated by the radiation from the supernova and the remaining dust does not have a large optical depth . the radius at which dust becomes so hot that it is evaporated , @xmath19 , occurs at @xmath20 cm for typical supernova and dust parameters @xcite . the circumstellar dust beyond @xmath19 can give rise to infrared and scattered light echos . both sn 1979c and sn 1980k showed evidence for infrared excesses that might be attributable to dust echos @xcite . the late optical light from these supernovae appeared to be dominated by emission from the circumstellar shock wave interactions and did not show dust scattering effects @xcite . roscherr and schaefer @xcite have recently examined the emission from sn iin to search for scattered light echos , but again found that the late emission is dominated by circumstellar shock interactions . circumstellar scattered light echos have" +"cherenkov - drift instability was suggested by kazbegi , machabeli & melikidze @xcite as a possible mechanism for generation of pulsar radio emission and later it was approved in @xcite . in those works the linear theory of cherenkov - drift instability was developed . it was shown , that in the pulsar magnetosphere due to cherenkov - drift instability the orthogonally polarized plasma waves are excited . these waves can escape from the magnetosphere and reach observer as a pulsar radio emission . the necessary condition for the development of cherenkov - drift instability ( as for an usual cherenkov instability ) is a presence of a beam of particles in the relativistic magnetized pair plasma ( consisted of relativistic electrons @xmath0 and positrons @xmath1 ) . generally , cherenkov type instabilities develop due to a resonant interaction between waves and particles of a beam . the resonance occurs , when the electric field vector @xmath2 and the wave vector @xmath3 of generated waves have got components along direction of the beam velocity @xmath4 ( @xmath5 and @xmath6 ) . so , in the magnetized plasma the transverse waves ( @xmath7 ) propagating along the external magnetic field ( @xmath8 ) can not be generated by an usual cherenkov instability ( because it develops on the beam particles moving along the external straight magnetic field lines : @xmath9 and @xmath10 ) . cherenkov - drift instability develops when the beam particles move along slightly curved magnetic field ( scmf ) lines and , hence , drift across the plane where the curved lines lie . the drift motion of beam particles provokes generation of purely transverse as well as longitudinal - transverse waves . generally there are two most important effects caused by the the particle relativistic motion along the scmf line : curvature drift and curvature radiation . the drift velocity is directed across the plane of the scmf lines and is given by the following expression : @xmath11 here @xmath12 denotes the drift velocity of electrons ( positrons drift with the same velocity but in the opposite direction ) ; @xmath13 is the cyclotron frequency of electrons ; @xmath14 is the curvature radius of the magnetic field line ; @xmath15 is lorentz factor of a particle ; @xmath16 is speed of light and @xmath17 is the component of @xmath4 along the magnetic field line . if @xmath18 , the value of drift velocity @xmath12 could be significant . a single particle , moving along the curved field line , radiates so called curvature radiation which can be easily described as a synchrotron radiation in an effective magnetic field ( see e.g. @xcite ) . in 1975 blandford @xcite investigated the curvature radiation of plasma flowing along the scmf lines . the problem was studied in the limit of infinite magnetic field @xmath19 and it was shown that there is no radiation at all : the waves , radiated by each particle , are absorbed by another one . this result was confirmed later in papers @xcite , where spatially unlimited plasma flow was considered . then in the paper by asseo , pellat and sol @xcite the sharp boundary was assumed at the edge of the flow propagating along the curved field line and the possibility of the waves excitation was shown at this boundary . if plasma flow has zero width the instability is reduced to that of goldreich - keeley @xcite . development of cherenkov type instability , taking into account the curvature drift motion , was studied and growth rate was calculated in @xcite for different particular cases . these results were confirmed later after thorough investigation of the problem in @xcite . the instability was called a cherenkov - drift instability . presence of the curved magnetic field lines is the necessary condition for both the cherenkov - drift radiation in plasma and the single particle curvature radiation in vacuum . however , the cherenkov - drift radiation still could not be interpreted as a plasma curvature radiation , analogous to the single particle curvature radiation : as it will be shown below , the cherenkov - drift radiation is not generated in the case of @xmath20 . on the other hand , it is evident that the drift velocity equals to @xmath21 if we assume that @xmath19 . however a single particle radiates even for the infinite intensity of magnetic field . moreover , the single particle radiates the vacuum wave , while the proper waves of the medium ( i.e. relativistic electron - positron plasma ) are generated in the case of cherenkov - drift instability . this particular point was not considered in the works by blandford @xcite and melrose @xcite . polarization of these waves strongly differs from that of vacuum waves . brief examination of the linear theory of cherenkov - drift instability is discussed in section 2 . in section 3 the quasilinear equations for the cherenkov - drift instability are obtained . in section 4 coefficients describing diffusion of particles in momentum space are evaluated . alteration of plasma distribution function is studied . the results are summarized in section 5 . properties of relativistic electron - positron plasma were carefully investigated in series of works @xcite and are still the subject of concern @xcite . the electron - positron plasma of pulsar magnetosphere consists mainly of two components : a bulk of plasma particles with high density and low lorentz factors ( @xmath22 ) and a beam of the primary particles ejected from the stellar surface . density of the beam @xmath23 , where @xmath24 is so called goldreich - julian density . density of secondary plasma @xmath25 , where @xmath26 is the sturrock multiplication factor ( @xmath27 ) @xcite . the electron - positron plasma differs from the electron - ion plasma by lack of gyrotropy . consequently , spectra of waves propagating in the @xmath28 plasma is simpler than that in the electron - ion plasma . it consists of only four types of waves which correspond to four branches on the diagram @xmath29 , where @xmath30 is the wave frequency ( see fig.[spectr ] ) . one of them is high - frequency transverse electromagnetic wave totally located in superluminal area . its phase velocity @xmath31 exceeds speed of light @xmath16 , hence , it is not of interest in our discussion below . the second branch represents the dispersion of purely transverse linearly polarized electromagnetic wave . we call this dispersion curve @xmath32 mode . it is totally located in subluminal area and therefore could be generated by beam particles . its electric field vector @xmath33 is perpendicular to the plane of wave vector and external magnetic field ( @xmath34 ) . the remaining two dispersion curves on the @xmath35 diagram describes the longitudinal - transverse waves propagating in relativistic @xmath36 plasma . one of them is almost superluminal . this wave is purely longitudinal if it propagates strictly along the magnetic field line ( @xmath37 ) , and , in this case called langmuir wave associated with longitudinal oscillations of the charge density . if an angle @xmath38 between @xmath3 and @xmath39 increases , the component of wave electric field @xmath2 starts to grow across @xmath3 : langmuir wave transforms to the longitudinal - transverse wave denoted in fig.[spectr ] as @xmath40 mode . if the angle @xmath38 is small enough ( @xmath41 , where @xmath42 is the langmuir frequency ) , @xmath40 mode is almost longitudinal and crosses @xmath43 line . in this case , @xmath40 mode could be excited , if cherenkov resonance condition @xmath44 is fulfilled . however , for the resonant particles of primary beam , growth rate of the instability is very small @xcite . the wave leaves from the interaction area so quickly that no time is left for significant growth of the wave amplitude . in the case of oblique propagation , @xmath45 , @xmath40 mode is totally superluminal . therefore , @xmath40 mode could not be generated at all by particles of beam . another longitudinal - transverse wave is denoted in fig.[spectr ] as @xmath46 mode . this mode , like @xmath32-wave , is located totally in subluminal area and can easily be generated by plasma particles . its electric field vector @xmath47 is located in ( @xmath34 ) plane . @xmath46 mode is vacuum wave , if it propagates along the magnetic field lines ( @xmath48 ) . its dispersion curve merges with @xmath32 mode ( see fig.[spectr ] ) and can be arbitrarily polarized . in the case of oblique propagation , electric field of @xmath46 wave has the component @xmath49 along the external magnetic field , thereby involving plasma particles in longitudinal oscillations . generation of @xmath46-mode , propagating in perpendicular direction to the plane of scmf lines , is connected with the drift motion of the particles . these waves are also known as _ drift waves _ @xcite . it should be mentioned that , while describing the waves in relativistic @xmath50 plasma , some authors sometimes use terminology which , in our opinion , appears to be misleading . for example , since the work by arons and barnard @xcite , the superluminal longitudinal - transverse wave ( @xmath40 mode ) was called an ordinary ( @xmath51 ) mode , the subluminal transverse wave ( @xmath32 mode ) an extraordinary ( @xmath52 ) mode and the subluminal longitudinal - transverse wave ( @xmath46 mode ) an alfven mode . however ordinary and extraordinary are generally related to the waves propagating across the external magnetic field in usual electron - ion plasma @xcite . moreover , @xmath32 wave ( so called @xmath52 mode ) is the purely transverse wave and its analogue does not exist in the electron - ion plasma . in electron - positron plasma the terminology _ ordinary _ and _ extraordinary _ are used for the waves propagating almost along the magnetic field . as for the alfven mode , in electron - ion plasma such a name is used for an almost linearly polarized , transverse electromagnetic wave with frequency @xmath53 ( where @xmath54 is the cyclotron frequency of ions ) . in the case of @xmath55 and @xmath56 , this wave transforms into right - hand polarized ion - cyclotron mode with frequency @xmath57 and left - hand polarized electron - cyclotron wave with frequencies @xmath58 . the latter case corresponds to the fast magnetosonic wave and is called _ helicon _ for frequencies @xmath59 . therefore , in relativistic @xmath36 plasma , we prefer to call the dispersion curves @xmath32 , @xmath40 and @xmath46 modes respectively , hence avoiding a possible confusion with dispersion curves in electron - ion plasma . to obtain expression for dielectric permittivity tenor components @xmath60 in the case of scmf lines , it is handy to consider the problem in cylindrical coordinates @xmath61 @xcite and direct @xmath62 axis perpendicularly to the plane of the curved magnetic field lines ( see fig.[l2 ] ) . in the papers by kazbegi , machabeli and melikidze @xcite , it was shown that @xmath32 and @xmath63 waves could be generated by particles of the beam when the following resonance condition is satisfied ( for the resonant values of parameters @xmath64 ) : @xmath65 mechanism of wave generation is a modification of the well - known beam - plasma instability . however , this instability differs significantly from the usual beam - plasma instability @xcite . the expressions for the growth rates of the different waves are as follows : @xmath66 for transverse ( @xmath32 ) wave and @xmath67 for longitudinal - transverse ( @xmath63 ) wave ( here @xmath68 is langmuir frequency of resonant particles of the beam ) . these expressions were obtained in papers @xcite . as for growth rate of the drift wave , it was obtained in paper @xcite : @xmath69 the reason for" +"we propose an eulerian approach towards motion representation learning . the main difference between lagrangian and eulerian motion is that lagrangian motion ( optical flow ) focuses on individual points and analyzes their change in location over time . therefore , lagrangian motion performs tracking of points over time and for this it requires a unique matching method between point or patches . on the other hand , eulerian motion considers a set of locations in the image and analyzes the changes at these locations over time . thus , eulerian motion does not estimate where a given point moves to , instead , it measures flux properties . figure [ fig : eulerian ] depicts this difference between eulerian and lagrangian motion . as a specific instance of the eulerian model , we consider phase - based motion . the phase variations over time of the coefficients of the complex - steerable pyramid are indicatives of motion @xcite and form the basis for learning motion representations . the gain of an eulerian motion approach is that it avoids the need for hand - crafted optical flow constructions . phase is an innate property of the image , it does not need to be estimated from explicit patch correspondences . we propose a general - purpose phase - based motion description learning setup that can be used in any task relying on motion . here we explore four use cases : ( i ) action recognition , ( ii ) motion prediction in static images , ( iii ) motion transfer in static images and , ( iv ) motion transfer in video . note that phase - based motion representations are readily applicably to other motion - related task as well , including : human gait analysis , object tracking , action localization , etc . eulerian motion modeling has shown remarkable results for motion magnification @xcite where a phase - based approach significantly improves the quality @xcite and broadens its application @xcite . a phase - based video interpolation is proposed in @xcite and a phase - based optical flow estimation is proposed in @xcite . inspired by the these work , we advocate the use of the eulerian model as exemplified by phase for learning motion representations . optical flow - based motion features have been extensively employed for action recognition in works such as @xcite . these works , use hand crafted features extracted from the optical flow . instead , we propose to input phase - based motion measurements to a cnn to reap the benefits of deep feature representation learning methods . a natural extension of going beyond a single frame in a deep net is by using 3@xmath0 space - time convolutions @xcite . 3@xmath0 convolutions learn appearance and motion jointly . while elegant , it makes it difficult to add the wealth of information that is available for appearance - only datasets through pre - training . in our method , we keep the benefit of pre - training by separating the appearance and the phase - based motion streams . using pre - trained networks is possible in the two - stream network approaches proposed in @xcite . this combines a multi - frame optical flow network stream with an appearance stream and obtains competitive results in practice . the appearance stream can employ a pretrained network . similarly , we also consider the combination of appearance and motion in a two - stream fashion , but with innate phase information rather than using a hand - crafted optical flow . the temporal frame ordering is exploited in @xcite , where the parameters of a ranking machine are used for video description . while in @xcite recurrent neural networks are proposed for improving action recognition . in this paper we also model the temporal aspect , although we add the benefit of a two - stream approach by separating appearance and phase variation over time . in @xcite , optical flow motion is learned from videos and predicted in static images in a structured regression formulation . in @xcite the authors propose predicting optical flow in a cnn from input static images . where these works predict optical flow , we propose to predict the motion through phase changes , which does not depend on pixel tracking . predicting the future rgb frame from the current rgb frame is proposed in @xcite in the context of action prediction . similar to this work , we also start from an input appearance and obtain an output appearance image , however in our case the learning part learns the mapping from input phase information to future phase . animating a static image by transferring the motion from an input video is related to the notion of artistic style transfer @xcite . the style transfer aims at changing an input image or video such that the artistic style matches the one of a provided target image . here , instead , we consider the motion transfer given an input image , transfer the phase - based motion from the video to the image . additionally , we also consider video - to - video transfer where the style of performing a certain action is transferred from a target video to the input video . in @xcite the authors allow the users to change the video by adding plausible object manipulations in the video . similar to this work , we also want to change the video motion after the recording is done , by adjusting the style of the action being performed . the local phase and amplitude of an image are measured by complex oriented filters of the form : @xmath1 , where @xmath2 is the filter orientation and @xmath3 the filter scale @xcite , @xmath4 where @xmath5 is the local phase at scale @xmath3 and orientation @xmath2 , and @xmath6 the amplitude , @xmath7 is the image brightness / input channel , and @xmath8 the convolution operator , and @xmath9 are image coordinates . the filters have multiple scales and orientations , forming a complex steerable pyramid @xcite which captures various levels of image resolution . there is a direct relation between motion and the change measured in phase over time . the fourier shift theorem makes the connection between the variation in phase of the subbands over time and the global image motion . rather than estimating global motion , using a steerable pyramid we can decompose the image into localized subbands and thus , recover the local motion in the phase variations over time . from the above decomposition only the phase , not the amplitude , corresponds to motion . in @xcite the authors show that the temporal gradient of phase computed from a spatially bandpassed video over time , directly relates to the motion field . therefore , here , we focus on local phase at multiple scales and orientations to represent motion . we propose using phase to learn motion representations for solving general motion - related tasks in a deep net . we add phase as an additional motion input channel to a standard appearance ( rgb ) convolutional deep neural network . figure [ fig : idea ] shows our proposed general - purpose phase - based pipeline . the input video frame is decomposed using the complex steerable pyramid into amplitude and phase . both phase and amplitude have multiple corresponding orientations and scales . since the phase is an indicative of motion , we ignore the amplitude and we use the input phase for the motion representation learning . we treat the orientations as input channels while the scales represent different streams of the network , similar to @xcite who use this setup for a different image pyramid . we explore phase - based motion representation learning in four practical use cases . while a thorough in - depth experimental investigation is out of scope , we detail the setup of motion representation learning for each use case . [ cols=""^,^ "" , ] separating appearance and motion in two - streams is effective for action recognition @xcite . for the appearance stream we follow @xcite and use the input rgb frame , which offers the advantage of pre - training features on static images . however , where @xcite uses hand - crafted optical flow features , we propose to use eulerian motion for the second stream with oriented phase over multiple scales , as depicted in figure [ fig : action ] . for evaluating action recognition , a comparison of our two - stream phase - based motion with the two - stream optical - flow approach of @xcite on the two datasets used in their paper hmdb51 and ucf101 is needed . we expect benefits from a phase - based motion representation because it does not depend on a specific hand - crafted optical flow implementation and does not rely on pixel tracking . the benefit of eulerian motion for motion prediction is that the prediction locations are fixed over time . this contrasts sharply with lagrangian motion , as pixels tracked by optical flow may be lost as they move in or out of the frame , or move to the same spatial location . such lost pixels make it hard to recover long - term relations beyond just the next frame . the fixed prediction locations of a eulerian motion representation do not suffer from this and offer long - term relation predictions of several frames . we propose to learn from a given input rgb the output future rgb , by recovering from the rgb the phase scales and orientations , then predicting the multi - scale future phase - orientations and transforming them back into future rgb frames as in figure [ fig : phase_prediction].(a ) . for long - term motion prediction we propose an rnn ( recurrent neural network ) version of this phase - based frame prediction , as depicted in figure [ fig : phase_prediction].(b ) . thus , predicting motion @xmath10 timesteps away from the input . for evaluating motion prediction we use the same datasets as in @xcite hmdb51 and ucf101 , where the authors aim at predicting optical - flow based motion in single images . to evaluate the difference between the predicted motion and the actual video motion , we use pixel accuracy , as in our method we recover the appearance of the future frame . for comparison with @xcite which reports epe ( end point errors ) , we use their chosen optical flow estimation algorithm to recover optical flow from our predicted rgb . similar to @xcite , where the style of a given target painting is transferred to another image , we propose to transfer the short motion of a given video sequence to an input static image . in @xcite a combination of two losses is optimized : content loss which ensures that the objects present in the newly generated image remain recognizable and correspond to the ones in the input image , and a style loss which imposes that the artistic style of the new image is similar to the one of the provided target painting . for motion transfer we have an additional requirement , namely that parts of the image that are similar e.g. horses , people , should move similar . for this we use two pretrained network streams , an rgb stream and a phase stream and consider certain convolutional layers along these streams for estimation rgb / phase responses . therefore , we first estimate an element - wise correlation between the responses at a given convolutional network layer of the input rgb values of the static image and the target video frame : @xmath11 where @xmath12 is the number of channels in the layer @xmath13 , @xmath14 and @xmath15 the responses at layer @xmath13 for" +"understanding the behavior of low - dimensional electronic systems has been one of the main challenges of experimental and theoretical physics in the last years . these systems are important not only as the basic building blocks of nanoelectronic devices , but also for the intricate strongly - correlated phenomena they exhibit . an important subclass is that of metallic ( gapless ) one - dimensional systems , whose low energy dynamics is governed not by fermi liquid theory , but instead by the luttinger liquid ( ll ) paradigm @xcite . this description applies to a wide variety of experimental realizations , including narrow quantum wires in semiconducting heterostructures , metallic nanowires , and carbon nanotubes . closely related are chiral lls , formed at the edges of fractional quantum hall effect ( fqhe ) systems @xcite , and helical lls , the edges of spin quantum hall insulators @xcite . the effect of impurities on these systems is interesting from both the applicative and fundamental points of view . these impurities could also be intentionally introduced , in the form of , e.g. , quantum dots and anti - dots . hence , there is no wonder that such questions have attracted much effort recently . however , most of these studies were restricted to investigation of transport phenomena @xcite , while other effects received much less attention @xcite . in this work we study probably the most basic example of such a system , namely , a single level in the vicinity of a fractional quantum hall edge , or , equivalently @xcite , a level attached to the end of a single ll wire @xcite . we will refer to the two components ( in both systems ) as `` dot '' and `` lead '' respectively . we include in our treatment the effects of short range dot - lead interaction , as well as the influence of an ohmic dissipative bath ( e.g. , electromagnetic fluctuations in gate electrodes ) @xcite . in a recent work @xcite we have studied the thermodynamic properties of the model ( e.g. , the level population , entropy , and specific heat ) , and found that they are _ universal _ , in the sense that they depend on the various interactions in the model ( intra - lead , dot - lead , and dot - bath ) only through a single parameter , the fermi edge singularity exponent . thus , thermodynamics can neither be used to identify non - fermi liquid behavior , nor to extract ll parameters . in this work we proceed to study , both analytically and numerically , the level density of states ( ldos ) , which may be probed by tunneling or absorption spectroscopies . we find that the ldos is sensitive to ll physics , even though its integral ( times the fermi function ) gives the level occupancy , which is universal in the above sense . as we show below , the ldos features power - law behavior near the fermi energy . for not too strong interactions the exponent in this power - law is actually determined by ll physics alone , and is independent of the level - lead and level - bath interactions . this and many other results derived below can not be achieved using perturbative calculations @xcite . the rest of this paper is organized as follows : in sec . [ sec : model_cg ] we present our model , and apply to it the anderson - yuval coulomb - gas ( cg ) expansion @xcite . we then proceed to analytic treatment of the ldos in sec . [ sec : analysis ] , and to numerical calculations in sec . [ sec : numerics ] . finally , we summarize our findings in sec . [ sec : conclude ] . the system is described by the hamiltonian @xmath0 . the first term is the dot hamiltonian @xmath1 , with @xmath2 and @xmath3 the level creation and annihilation operators , respectively , and @xmath4 the level energy . the second term is the lead hamiltonian . it can be written in the form @xmath5 ^ 2 dx,\ ] ] using _ chiral _ bosonic field @xmath6 obeying the commutation relation @xmath7 = i \pi \text{sgn}(x - y)$ ] , where @xmath8 is the velocity of excitations @xcite . the level and the lead are coupled by : @xmath9 the two terms in this equation describe , respectively , dot - lead hopping ( with @xmath10 the tunneling matrix element ) , and local dot - lead interaction whose strength is @xmath11 . the electronic annihilation operator at the end of the lead can be written as @xmath12 , where @xmath13 is a majorana operator , @xmath14 is a short distance cutoff ( e.g. , the lattice spacing ) , and @xmath15 is the ll interaction parameter ( @xmath16 for repulsion , @xmath17 for attraction ) . for a fqhe system with filling @xmath18 , @xmath19 for electron tunneling ( i.e. , a dot outside the fqhe bar ) . finally , the level is coupled to a bath of harmonic oscillators @xcite ( describing , e.g. , electromagnetic fluctuations in control gates ) , governed by @xmath20 . the dot - bath coupling can be written as @xmath21 . we assume ohmic dissipation , i.e. , linear low - frequency behavior of the bath spectral function : @xmath22 . we examine this model employing the anderson - yuval cg expansion @xcite . in this approach , any quantity of interest is expanded to all orders in @xmath10 . this results in a series of correlation functions , which need to be evaluated for vanishing @xmath10.@xcite the level - lead interaction gives rise to a potential at the end of the lead , which alternates between @xmath23 and @xmath24 whenever an electron tunnels in or out of the level . similarly , the @xmath25th bath oscillators experience a shift in its equilibrium position , proportional to @xmath26 . we thus have a sequence of fermi edge singularity events @xcite . the solution of this latter problem enables the calculation of all the terms in the series of correlation functions . recently @xcite we have studied in this way the partition function @xmath27 of the model , whose derivatives with respect to the parameters of the system ( for example , the level energy @xmath4 and the temperature @xmath28 ) give us the thermodynamic properties ( e.g. , the level population , entropy , and specific heat ) . we were able to rewrite the series expansion for @xmath27 in the form of a grand canonical partition function of a classical system of particles . these represent hopping events generated by @xmath10 , and thus reside on the imaginary time axis of the original quantum model , which is a circle with circumference @xmath29 . each particle is assigned a positive ( negative ) charge if it represents tunneling of an electron from the lead to the dot ( from the dot to the lead ) . hence , there must be an even number of charges , which have to appear in alternating order of signs . the position of the @xmath30th particle is @xmath31 , and the sign of the charge of the first particle is denoted by @xmath32 . the partition function then reads : @xmath33 the charges have a fugacity @xmath34 , where @xmath35 is the noninteracting level width [ @xmath36 is the corresponding lead local density of states ] , and @xmath37 is a short - time cutoff . the cg action is given by : @xmath38 } \right\ } v_{c } ( \tau_j-\tau_i ) + \\ \varepsilon_0 \left [ \frac{1-s}{2 t } + s \sum_{i=1}^{2n } ( -1)^i \tau_i \right].\end{gathered}\ ] ] the first term of this classical hamiltonian describes an interaction between the particles , with @xmath39 \}$ ] . this interaction is similar in form to 2d coulomb interaction , and is the origin of the name `` cg expansion '' . the charges are two component vectors , where the two components correspond to the effects of the coupling with the lead and the bath , respectively . they are given by @xmath40 , where the squared - magnitude of the charges , to be denoted by @xmath41 , is the fermi edge singularity exponent of the model . it is defined by behavior of the zero - temperature correlator of @xmath42 with its hermitian conjugate , calculated at @xmath43 . this correlator decays as @xmath44 for long time @xmath45 . in our system we have found that @xmath46 , where @xmath47 is the effective phase shift in the lead due to the dot - lead coupling @xcite . it is equal to @xmath48 in straightforward bosonization , but is more complicated in general . it may be extracted from , e.g. , finite - size energy differences , which could be calculated either numerically or analytically ( via the bethe ansatz ) @xcite . the other part of the cg action accounts for the energetic cost of @xmath4 per unit imaginary time for each interval in which the level is populated . its form is analogous to an electric field applied to the classical system of charges . a typical configuration is depicted in fig . [ fig : cg](a ) . a similar treatment can be given to the ldos , which we shall denote by @xmath49 . it is equal to the imaginary part of the level retarded green function ( multiplied by @xmath50 ) . the retarded green function is in turn the result of analytic continuation of the matsubara green function from the upper half of the complex frequency plane @xcite . the latter green function is defined by @xmath51 , where @xmath52 is the imaginary time ordering operator . following the same methods as above , the numerator of this expression can also be given a cg representation . this cg has the same form as eqs . ( [ eqn : cg_z1])([eqn : cg_z2 ] ) , with two additional charges of sizes @xmath53 , @xmath54 , inserted at @xmath55 and @xmath56 , respectively . these charges correspond to the level creation and annihilation operators appearing in the definition of the green function . in the following we will refer to these as `` d - charges '' , to distinguish them form the other `` @xmath10-charges '' , which originate from the @xmath10 term . the contribution of each such configuration is to be multiplied by @xmath57 to account for the fermi statistics . thus , for @xmath58 the full cg expression for the dot green function is : @xmath59 e^{- s_{cg , d } ( s , \tau , \tau^\prime , \ { \tau_i \ } ) } , \end{gathered}\ ] ] where @xmath60 . the first @xmath61 @xmath10-charges occupy the interval @xmath62 $ ] , the following @xmath63 charges reside in the interval @xmath64 $ ] , and the last @xmath65 @xmath10-charges are in the interval @xmath66 $ ] . the classical action is given by : @xmath67 - |\vec{e}_d|^2 v_c ( \tau-\tau^\prime ) + \\ \varepsilon_0 \left [ \frac{1-s}{2 t } - \sum_{i=1}^{2n } s_i \tau_i + \tau - \tau^\prime \right],\end{gathered}\ ] ] where the sign of the @xmath30th @xmath10-charge is @xmath68 . a typical configuration is shown in fig . [ fig : cg](b ) . similar expressions hold for @xmath69 . comparing the two cg expansions , the following observation emerges : the cg expansion for the partition function contains only three parameters : @xmath70 , @xmath4 , and @xmath71 , while expansion for the green function depends on @xmath15 too ( through @xmath72 ) . hence , the different interaction types ( i.e. , interactions in the wire , the dot - wire interaction , and" +"the search for star clusters in the galaxy is of a great interest for investigators in the recent years . on the one hand , the usage of new methods and instruments in observations allows scientists to involve clusters in solving a larger number of astrophysical problems and raises many new ones , such as : the processes of formation and evolution of young massive clusters , the nature of nuclear star clusters , the presence of multiple populations in globular clusters . on the other hand , the availability of new multiband all - sky surveys stimulates us to search them for new clusters and build a homogeneous catalog of parameters of both newly discovered and already known clusters . in paper i ( koposov et al . 2008 ) , we described the new method of an automated search for star clusters as a density peaks in huge stellar catalogs . it is based on the convolution of density maps with a special 2-d filter , which is the difference between two 2-d gaussian profiles and has zero integral . if convolved with this special filter , the areas of flat or slowly changing background would produce zero signal , whereas the areas of star concentrations would exhibit a high signal . using this method , we analyzed the distribution of stars in two micron all sky survey ( 2mass ) in the field of @xmath3 degrees towards the galactic anticenter and found 15 new open clusters . to verify the reality of detected clusters , we developed a method , which is based on the assumption that probable cluster members lying along the same isochrone on the color - magnitude diagram ( cmd ) should also form the spatial density peak , whereas the background stars should have a flat distribution . the other benefit of this method is that it not only allows to verify a cluster candidate , but at the same time estimates the cluster s main parameters distance , age , and color excess . we employed this method to derive parameters of 12 new and 13 known , but poorly studied clusters , which were also detected in the field of interest , using the technique of @xmath4 and @xmath5 diagrams built with the data from 2mass catalog . later , @xmath6 magnitudes of the stars in three new clusters were measured using ccd images taken at 104-cm telescope of aryabhatta research institute of observational sciences ( aries , india ) . the isochrones fitted to these data using another color - magnitude diagrams , and derived clusters parameters ( glushkova et al . 2009 ) show good agreement with those obtained from @xmath4 and @xmath5 2mass diagrams and therefore independently confirm the reality of clusters found by koposov et al . ( 2008 ) and the correctness of the method of new cluster verification . the aims of this study are : ( 1 ) search for overdensities in the galactic plane in the range of the galactic latitude @xmath7 using 2mass data ; ( 2 ) verification of some of them as a real clusters ; ( 3 ) estimate of their physical parameters using proven technique we have developed earlier . for the new clusters search and verification procedures we made use of http://vo.astronet.ru , the virtual observatory ( vo ) resource of the sternberg astronomical institute ( koposov et al . 2007 ) , which provides fast remote access to 2mass catalog data through the standard vo - compliant interfaces . we detected 11186 overdensities with the significance level of more than @xmath8 in the region of the milky way within the interval of the galactic latitude @xmath1 . since the open clusters subsystem concentrates to the galactic plane where the interstellar extinction reaches maximum and the background changes rapidly , the most from 11186 overdensities should be attributed to the fluctuations of interstellar dust especially towards the galactic center , where the density fluctuations are maximal . we undertook a visual inspection of all detected overdensities by images from digitized sky survey ( dss ) and 2mass catalogs to recognize real density concentrations against these background fluctuations . we selected 962 candidates to clusters and matched them to the online catalogs by dias et al . ( 2002 ) and harris ( 2003 ) . this match demonstrated that 565 candidates are known open clusters , 114 are known globular clusters , whereas 283 overdensities should be examined in detail as a new cluster candidates , some of which may only be attributed to random star concentrations . we ran all these 283 overdensities through our verification procedure , which includes the analysis of their hess - diagrams , color - magnitude diagrams and radial density distributions in accordance with the technique by koposov et al . 149 candidates were decided to be the real star clusters . however , a part of non - selected overdensities may also be real clusters , which we were unable to verify , because they were detected at the sensitivity limit of 2mass catalog . if we extend our data pattern with the data from the sources with a higher limit in @xmath9 magnitudes , then some other overdensities may manifest themselves as real clusters , and their parameters can also be determined . we tested this idea by using galactic plane survey of ukirt infrared deep sky survey , data release 3 ( ukidss gps dr3 , warren et al . 2007 ) as an additional data source . the average 2mass sensitivity in @xmath10 is @xmath11 , whereas in ukidss gps , the magnitude limit for @xmath12-band is as high as @xmath13 . 22 cluster candidates found in 2mass were studied by @xmath4 and @xmath14 diagrams and radial density distributions built using data from ukidss gps . we verified 9 star clusters and determined their distance moduli , ages and color excesses . among these nine objects , four ( sai 50 , sai 131 , sai 133 , and sai 141 in table 1 ) did not reveal themselves as star clusters when only 2mass catalog data were employed , because the upper part of their main sequences and/or red giant branches is only seen on cmd and hess - diagrams . for example , left panel of fig . 1 displays @xmath4 diagram of cluster sai 50 built by data from ukidss gps . one can only see here the red - giant branch limited to the stars fainter than @xmath15 . if we build such a cmd for this cluster with 2mass data only , we would not detect the cluster at all , because the limiting magnitude for @xmath16-band in this catalog is exactly @xmath17 . in fig . 1 , the isochrone is fitted to give the lower estimate of the distance to the cluster . thus , after involving ukidss gps data , the number of confirmed clusters reached 153 . for 130 clusters we automatically obtained main physical parameters : ages , distances and color excesses using the data from 2mass or ukidss gps and isochrones of solar metallicity by girardi et al . @xmath9 magnitudes were taken from the deeper ukidss gps for the nine clusters , whose centers fall into this survey : sai 50 , sai 74 , sai 75 , sai 130 , sai 131 , sai 133 , sai 141 , sai 142 , sai 145 . the center coordinates , diameters , color excesses @xmath2 , distance moduli and ages as @xmath18 are listed in table 1 . we consider the position of the maximum in a density peak as the center of a cluster on the density map . the cluster radius is such a distance from its center , at which the star density becomes flat on the radial density distribution plot . the errors in color excesses , distance moduli and ages were estimated as described by koposov et al . ( 2008 ) : from the differences in the parameters derived by @xmath4 and @xmath5 diagrams . we used the relations @xmath19 , @xmath20 , @xmath21 from the paper by dutra et al . ( 2002 ) to derive the distance modulus and color excess @xmath2 , and the relation @xmath22 from the paper by he et al . ( 1995 ) for @xmath12 magnitudes from ukidss gps . for some clusters , we are able to estimate the upper limit of the age only , in particular , when their color - magnitude diagrams do not contain red - giant stars . besides the cluster name sai ( _ _ s__ternberg _ _ a__stronomical _ _ i__nstitute ) , other names from papers by kronberger et al . ( 2006 ) and by froebrich et al . ( 2007 ) are used in table 1 . as mentioned by koposov et al . ( 2008 ) , the authors of both papers published the list of probable cluster candidates where further investigation is necessary to clarify their nature . some of the overdensities independently found by us coincide with the cluster candidates from papers by kronberger et al . ( 2006 ) and froebrich et al . ( 2007 ) . we performed a thorough analysis of these matching candidates and confirmed some of them as the real clusters . however , remaining candidates turned to be mere random star concentrations or background fluctuations ( we do not publish this list here ) . all clusters from table 1 having the other name according to kronberger et al . ( 2006 ) or froebrich et al . ( 2007 ) , are listed neither in the database of open clusters ( webda ) by paunzen , mermilliod ( 2009 ) , nor in the catalog by dias et al . that is why we consider them as a new clusters . special attention should be given to the cluster sai 92 from table 1 . this cluster is situated @xmath23 to the south - east of ngc 2645 , and both clusters feature approximately the same values of parameters . according to webda , the distance from sun to ngc 2645 equals to 1668 pc ; we estimate the distance to the cluster sai 92 to be @xmath24 pc . color excess @xmath2 in the direction to ngc 2645 is @xmath25 , and to sai 92 , @xmath26 . both clusters are pretty young , but differ in @xmath18 by 0.72 : webda estimates the age of ngc 2645 as 7.283 , whereas the present study gives @xmath27 for sai 92 . however , 0.05 is the formal error , which , as mentioned earlier , should be attributed to the difference in the ages determined by @xmath4 and @xmath5 diagrams . a real error for age estimate by 2mass is not less than 0.3 for clusters which do not contain stars on the red - giant branch . if we build the @xmath28 diagram of ngc 2645 using data from webda and fit them by the isochrone of solar metallicity by girardi et al . ( 2002 ) using the distance and color excess also from webda , then the lower limit for the age is 7.6 in @xmath18 . therefore , the age of both clusters can be considered approximately the same taking into account the real errors of its estimate . apparently , ngc 2645 and sai 92 form a double cluster then . 2 shows the image of @xmath29 x @xmath29 from dss where both clusters fall into . diameters of clusters ( @xmath30 and @xmath31 ) are represented by circles . sai 50 looks like a globular cluster by its age and cmd built using data from ukidss gps , although the errors in parameters are large , because the isochrone was fitted to the red - giant branch only . the left panel of" +"ever since databases have been able to store basket data , many techniques have been proposed to extract useful insights for analysts . one of the first , association rule mining @xcite , also remains one of the most intuitive . association rules are often used to summarize consumer trends in a transaction set or as input to a classifier @xcite . the problem is the very high number of rules , typically in the order of millions . that is exacerbated by the lack of thorough studies of which of the many interestingness measures for ranking rules @xcite is most appropriate for which application domain . we present , a framework to compare the outcome of different interestingness measures applied to association rules generated in the food retail domain . relies on a flexible architecture and on @xcite , our parallel and distributed pattern mining algorithm that runs on mapreduce . the use of real datasets and a close collaboration with experienced domain experts from intermarch , one of the largest retailers in france , has led us to selecting the most relevant measures to rank association rules in the food retail domain . our dataset contains @xmath0 million receipts from stores in all of france , gathered over one year , 2013 . mining this data results in a huge number of rules . for example , using a minimum support of mines frequent rules of the form _ customer segment _ _ product category_. out of these , have a confidence of @xmath2 or higher . table [ tab : eyecatcher ] shows a ranking of the top-10 rules according to 3 different interestingness measures proposed in @xcite . if we denote rules as @xmath3 , _ confidence _ is the probability to observe @xmath4 given that we observed @xmath5 , i.e. , @xmath6 . _ piatetsky - shapiro _ @xcite combines how @xmath5 and @xmath4 occur together with how they would if they were independent , i.e. , @xmath7 . _ pearson s _ @xmath8 , measures how unlikely observations of @xmath5 and @xmath4 are independent . this very small example already shows that these measures result in different rule rankings . [ cols= "" > , < , > , < , > , < "" , ] + we now report the results of a user study with domain experts from intermarch . the goal of this study is to assess the ability of interestingness measures to rank association rules according to the needs of an analyst . as explained in section [ sec : xp : empirical ] , we identified 6 families of measures , and selected a representative of each group for the user study ( table [ tab : groupsummary ] ) . we rely on the expertise of our industrial partner to determine , for each analysis scenario , which family produces the most interesting results . this experiment involved 2 experienced analysts from the marketing department of intermarch . we setup and let analysts select targets multiple times in order to populate the web application s database with association rules ( section [ sec : exploitation ] ) . we let our analysts interact with without any time restriction , and collect their feedback in a free text form . each analyst firstly has to pick a mining scenario among ` demo_assoc ` , ` prod_assoc_t ` , or ` prod_assoc_c ` . then she picks a target category or a target product in the taxonomy . in ` prod_assoc_t ` and ` prod_assoc_c ` , she also has the option to filter out rules whose antecedent products are not from the same category as the target . finally , she chooses one of our 6 ranking measures to sort association rules . neither the name of the measure nor its computed values for association rules are revealed , because we wanted analysts to evaluate rankings without knowing how they were produced . resulting association rules are ranked according to a selected measure . each rule is displayed with its support , confidence and recall , such that analysts can evaluate it at a glance . for each scenario , our analysts are asked which representative measure highlights the most interesting results ( as detailed below , in all cases a few of them were chosen ) . once the analyst selects a target , _ all _ matching rules are returned . the initial motivation of this choice was to determine how many results are worth displaying and are actually examined by the analysts . according to the follow - up interview with the analysts , they carefully considered the first ten results , and screened up to a hundred more . interestingly , analysts mentioned that they also scrolled down to the bottom of the list in order to see which customer segments are not akin to buying the selected category . for example , when browsing demographic association rules , they expected to find \{_50 - 64 _ } @xmath1 _ pet food _ among top results , but also expected \{_<35 , paris _ } @xmath1 _ pet food _ among bottom results . this confirms that all rules should remain accessible . this also indicates that while interestingness measures favor strong associations , it would also be interesting to highlight _ anti_-rules , as those can also convey useful information . we let marketing experts explore all 3 scenarios and express their preference towards groups of measures . in the ` demo_assoc`case , @xmath9 and @xmath10 were both highly appreciated . @xmath9 favors rules such as @xmath11 oise@xmath12 _ flat and carbonated drinks_. these rules are very specific and thus have a very high confidence ( 31,58 % in this particular case ) . however , this comes at the cost of recall ( 0,08 % ) . experts value _ confidence _ much more than _ recall _ , as their priority is finding rules that they consider reliable . a low support is not necessarily an issue , and can lead to the discovery of surprising niche rules that can be exploited nonetheless . as discussed in section [ sec : annotation ] , @xmath10 offers a more balanced trade - off between confidence and recall , and prioritizes rules such as @xmath13 < 35 , * , * @xmath12 _ baby food _ ( confidence 8,57 % , recall 37,61% ) . these rules are interesting because they capture a large fraction of the sales of a given category , but are less reliable and generally less surprising . @xmath14 and @xmath15 were considered as less interesting than @xmath9 and @xmath10 respectively . their results offer similar trade - offs , but with lower confidence each time . @xmath16 and @xmath17 were considered unusable because of their very low confidence . when experimenting with ` prod_assoc ` , we observed a slightly different behavior . by default , the analysts favored @xmath9 and @xmath14 because of the confidence of their results . then , we offered the analysts the possibility of filtering the rules to only keep the ones in which the antecedent contains products from the same category as the target . this led to analysts favoring @xmath10 and @xmath16 . this difference is caused by an important but implicit criterion : the ability of a measure to filter out very popular products . for example , the rule \{_vanilla cream , emmental_}@xmath1 _ chocolate cream _ usually appears just above its shorter version \{_vanilla cream_}@xmath1 _ chocolate cream _ , because the first one has a confidence of @xmath18 and the second @xmath19 . however , experts prefer the second one , because _ emmental _ ( cheese ) is among the heavy hitters in stores . its addition to the rule is hence considered insignificant . this `` noise '' generally increases with _ recall_. hence , when no filtering is available , @xmath9 is selected , but analysts prefer the _ recall _ and _ confidence _ trade - off provided by @xmath10 and @xmath16 . again , @xmath15 suffered from its proximity to @xmath10 with lower confidence , while @xmath17 s confidence was too low . in all cases , analysts mentioned @xmath17 as uninteresting overall because it selects rules of low _ confidence_. in general , sorting by decreasing _ lift _ ( which is close to sorting by decreasing _ confidence _ ) is the preferred choice . combined with the minimum support threshold used in the mining phase , this ranking promotes rules that are considered reliable . however , the preference of the analysts changes when filters are available to narrow down the set of rules to specific product categories . in this case , they favor the compromise between _ confidence _ and _ support _ offered , for instance , by the _ piatetsky - shapiro _ s measure @xcite . to the best of our knowledge , targets datasets which are orders of magnitude bigger ( and sparser ) than those tested in existing work on ranking association rules . this paper is also the first to complement an algorithmic comparative analysis with a user study involving domain experts . the definition of quality of association rules is a well - studied topic in statistics and data mining , summarized in @xcite . in this survey , geng _ et al . _ review as many as 38 measures for association and classification rules . they also discuss 4 sets of properties like symmetry or monotony , and how each of them highlights different meanings of `` rule quality '' , such as novelty and generality . however , we observe no correlation between these properties and the groups of measures discovered using . these 38 measures are compared in @xcite . authors consider the case of extracting and ranking temporal rules ( _ _ event a__@xmath1_event b _ ) from the execution traces of java programs . each measure is evaluated in its ability to rank highly rules known from a ground truth ( java library specification ) . we observe that the measures scoring the highest are all from the groups identified in this work as @xmath9 and @xmath10 , which were also favored by our analysts . there are however some counterexamples , with measures from @xmath9 scoring poorly . the authors then use a statistical approach to build a partial ordering of measures quality . this results in the formation of measure equivalence classes . however , the semantic of these classes is based on the principle of dominance in the evaluation , and not on the comparison of the rankings themselves . hence , the equivalence classes obtained do not match our groups . the main difference between and @xcite is the absence of a ground truth of interesting rules for our dataset . consequently , our evaluation of measures is first comparative , with 4 correlations measures covering both the top of the ranking and the entire ranked list . we then build groups of measures to reduce the number of options presented to expert analysts in the user study . the differences in the results obtained also highlight the importance of performing domain - specific studies , as the properties of data and the expectations of analysts vary significantly . the closest work to ours is herbs @xcite . herbs relies on a different and smaller set of measures to cluster rule rankings . authors perform an analysis of the properties of measures , in addition to an experimental study . the datasets used are from the health and astronomy domains . each of them contains at most transactions and leads to the extraction of 49 to rules . rankings are then compared between all pairs of measures using kendall s @xmath20 correlation measure averaged over all datasets . the largest" +"flat rotation curves of spiral galaxies @xcite can be explained by the presence of a dark matter halo which extends much farther than the luminous disc . while at large distances the gravitational potential is completely dominated by the dark halo , there is still a vivacious debate about whether the dark matter is prevailing in the central parts of bright galaxies , and about whether its radial matter distribution is cuspy , or not @xcite . furthermore , very little is known with certainty about the shape of the halo of disc galaxies and in many cases the halo is simply assumed to be spherical . however , if the disc is indeed an important component in the central parts , it should , due to its gravity , introduce some flattening of the dark matter distribution . furthermore , large scale cosmological @xmath0-body simulations have shown that , at least at large distances from the center , the natural shape of dark halos is triaxial ( see references in @xcite ) with density axial ratios in the range 0.5 0.8 ( @xcite ) . it is thus natural to ask whether the flatness and the various complex structures and substructures of the luminous part of the galaxy will affect the dark matter halo , and to what extent the triaxiality of the halo will change a possible dark matter annihilation signal from the central parts of a galaxy . usually , two types of asphericity are considered : flattening of the halo and departure from axisymmetry . the halo flattening is quantified by the value of @xmath1 , where @xmath2 is the major axis in the galactic plane and @xmath3 is the axis perpendicular to that plane . various observational methods have been used to probe the halo flattening in our own galaxy and in neighboring ones ( e.g. @xcite ) . it was found that the measured flattening can vary over a wide range of values , depending on the galaxy and on the method used . a cross - check of the different methods with their systematic biases on the same galaxy would be welcome but is usually not possible . measurements based on atomic hydrogen favour oblate halos with shortest - to - longest ratios in the very wide range of 0.2 to 0.8 @xcite . for our own galaxy and based on the thickness of the milky way s gas layer , @xcite argue for a rather round halo with flattening @xmath4 , but their result depends heavily on the values of the galactocentric radius @xmath5 and of the galactic rotation speed @xmath6 @xcite . recent studies of the dynamics of the stellar stream coming from the disruption of the sagittarius dwarf galaxy also give a wide range of values , between 0.5 and 1.7 @xcite . the second type of asphericity is a departure from axisymmetry in the galactic plane . this is statistically quite common as a large fraction ( more than 70% ) of present day disc galaxies have bars or ovals @xcite . also , it is now well agreed that our galaxy is barred in its central parts @xcite . bars form naturally also in @xmath0-body simulations , as witnessed already in the early seventies @xcite . more recently , it was realized that the presence of a dark halo can play an active role in the formation of the disc bar , if it is non rigid , _ i.e. _ if it can interact with the disc . indeed , bars evolve and grow stronger by the redistribution of angular momentum within their galaxy . this is emitted by near - resonant material at the inner disc and absorbed by near - resonant material in the outer disc and in the halo @xcite . as a result , the halo also is deformed and acquires a bar structure , which is fatter and shorter than the disc bar , but can concern a considerable amount of mass @xcite . on the observational side , departures from axisymmetry can be checked from the orbits of the baryons , in particular the hi gas that has low velocity dispersion . obtaining a quantitative estimate of such asymmetries is , however , not trivial , since it implies a decoupling of the halo contribution from that of the luminous matter as well as a knowledge of the inclination of the galactic disc @xcite . of course , a direct probe of the halo would enable to see whether the halo deformation follows the barred structure of the disk or not . if the recent egret diffuse gamma ray signal above 1 @xmath7 is interpreted as originating from dark matter , it indeed leads to such a structure with an ellipticity value @xmath8 @xcite . the purpose of this article is to study the impact of an elliptical deformation of the halo on the expected weakly interacting massive particle ( wimp ) dark matter annihilation signal from the galactic center . however , as discussed above , we do not know for certain what the dark matter radial profile is , so that distributions with or without a cusp , and with or without a spike have to be considered . the density enhancement in a cuspy profile follows the deepening of the central gravitational potential due to the baryon cooling through radiative processes @xcite . the presence of a super - massive black hole ( sbh ) at the galactic center can further create a spike , or an enhancement of the cusp , at very short distances from the galactic center @xcite but scatterings on stars and capture of dark matter particles by the sbh could decrease the density in this region @xcite . it is clear that the presence of a spike would boost the annihilation signal by several orders of magnitude . in the sequel , we will see how elliptical distortions interplay with density profiles in the dark matter annihilation signal . since the main observable annihilation signal from the galactic center is with @xmath9-rays @xcite , we will restrict ourselves to this case . the observed gamma - ray flux of energy @xmath10 , from the annihilation of dark matter particles @xmath11 ( with mass @xmath12 and density @xmath13 ) and annihilation cross section @xmath14 ( into final state @xmath15 ) , can be expressed as ( e.g. ref . @xcite ) @xmath16 where @xmath17 is the differential gamma spectrum per annihilation coming from the decay of annihilation products of final state @xmath15 and the integral is taken along the line of sight . it is customary ( see @xcite ) , in order to separate the factors depending on astrophysics from those depending only on particle physics , to introduce the quantity @xmath18 for the line of sight @xmath19 corresponding to the direction @xmath20 , @xmath21 we then define the astrophysical factor @xmath22 as the average of @xmath18 over a spherical region of solid angle @xmath23 , centered on the direction of the galactic center @xmath24 the solid angles @xmath25 and @xmath26 correspond to the angular resolutions in the egret experiment and the hess and glast ones , respectively . the expected gamma - ray flux in an experiment with threshold energy @xmath27 is finally expressed as @xmath28 @xmath29 to compute the quantity @xmath30 , we assume the following effective parameterization for the dark matter halo @xmath31^{(\beta-\gamma)/\alpha } } { [ 1+(r / a)^{\alpha}]^{(\beta-\gamma)/\alpha } } \(\frac{r_0}{r}\)^{\gamma } \;\ ; \(1+\(\frac{r_{sp}}{r}\)^{\gamma _ { sp}-\gamma}\ ) \;\ ; , \label{eq : alphabetagamma}\ ] ] [ t ] .parameters of some widely used non spiky density profiles models and corresponding value of @xmath32 and @xmath33 . [ cols=""^,^,^,^,^,^,^"",options=""header "" , ] in fig . [ fig : a - phi ] , the variations of @xmath34 as a function of @xmath35 for @xmath36 (= 20 deg ; see review @xcite and references therein ) and @xmath37 , and as a function of @xmath38 for @xmath39 and 9 are given for the isothermal , kravtsov , nfw and moore halo profiles . for @xmath40 , @xmath30 increases with @xmath35 , which is expected since the higher density region is stretched along the line of sight in this case . for larger values of @xmath38 , the variation becomes negative , as the stretching in the x axis is misaligned with the line of sight . therefore , @xmath30 is a decreasing function of @xmath38 for a fixed value of @xmath35 . it is important to notice that the impact of the ellipticity is stronger for less cuspy halo profiles ( which are favored by observations ) . indeed , the relative contribution to @xmath30 coming from inner regions inside a small radius @xmath41 increases with @xmath9 . therefore , for higher values of @xmath9 , a larger fraction of the volume integral @xmath42 is not affected by a change in ellipticity , as the observation solid angle is taken constant . to study the influence of the prolate - oblate shape of the halo , we set @xmath43 in eq . ( [ rell ] ) and let @xmath44 vary . the result is given in fig . [ fig : pro - ob ] , for the isothermal , kravtsov , nfw and moore halo profiles . the variation of @xmath30 with the prolate - oblate shape of the halo is again stronger for smaller values of @xmath9 . as we can see on fig . [ fig : pro - ob ] , an oblate deformation induces an enhancement of dark matter density along the line of sight increasing the signal , whereas the prolate shape decreases it and thus could be understood with arguments similar to those above . finally , let s consider the most popular dark matter candidate , _ i.e. _ the neutralino ( @xmath11 ) , which comes from the neutral gauge and higgs boson superpartners in the _ minimal supersymmetric standard model _ ( mssm ) framework . we show in fig . [ fig : flux - exp ] the neutralino dark matter resulting fluxes for a wide sample of supersymmetric models , _ i.e _ we take parameters of the mssm to get bino as well as mixed bino - wino and bino - higgsino neutralino which have higher couplings and cross sections ( see _ e.g. _ @xcite ) . all the points shown satisfy the wmap requirement on relic density and accelerator constraints . as the glast experiment sensitivity will probe a wide range of halo profiles , we clearly see that in addition to the ( essentially inner ) power law behavior of the halo , the geometry also alters the estimation of the fluxes and has to be included in flux calculations . the dark matter annihilation signal from the galactic center has been calculated for different halo characteristics . in particular , we have shown some possible effects of the halo asphericity . the induced corrections are more relevant for flat than for cuspy cores . although a plausible elliptical deformation of the dark matter halo does not change the expected annihilation signal by orders of magnitude , a consistent prediction of the flux from the halo shape or conversely of the halo shape from the signal should take those effects into account . the authors thank albert bosma and jean orloff for interesting and motivating discussions and o. gnedin and h. zhao for useful email exchanges . f .- s . l. and e.n . work is supported by the i.i.s.n . and the belgian federal science policy ( return grant and iap 5/27 ) . c. s. frenk , s. d. m. white , m. davis , g. efstathiou , astrophys . j. * 327 * , 507 ( 1988 ) ; j. dubinski , astrophys . j. * 431 * , 617 ( 1994 ) ; p.a . thomas" +"there are growing evidences from various cosmic observations , including type ia supernova ( snia ) @xcite , cosmic microwave background ( cmb ) @xcite , large scale structures ( lss ) @xcite , and so on , that support for a spatially flat and accelerating universe at the present epoch . in the context of friedmann - robertson - walker cosmology , this acceleration is attributed to the so - called dark energy @xcite . the simplest candidate for the dark energy seems to be a remnant small cosmological constant . however , many physicists are attracted to the idea that the dark energy is due to a dynamical component in the evolution of the universe , such as the quintessence @xcite , the k - essence @xcite , the phantom @xcite , or the quintom @xcite . 1ex recently there have been a lot of works @xcite which study possible connections between neutrinos and the dark energy , generally referred to as the neutrino dark energy . one of the predictions of the class of models of neutrino dark energy is that neutrino masses are not constant , but can vary as a function of space and time . this general prediction can be tested with short gamma ray burst @xcite , cmb and lss @xcite , and much more interestingly and directly in neutrino oscillation experiments @xcite . in this paper we make a concrete study of the possibility of probing the property of dark energy and differentiating its dynamic origin in very long baseline neutrino oscillations . 1ex in general for the models of neutrino dark energy , the lagrangian is given by @xmath0 where @xmath1 is the lagrangian of the standard model describing the physics of the left - handed neutrinos , @xmath2 is for the dynamical dark energy scalar @xmath3 such as quintessence or phantom , and @xmath4 describes the sector that mediates the interaction between the dark energy scalar and neutrinos , and gives rise to variations of the neutrino masses . 1ex at energy much below the electroweak scale , the relevant lagrangian for the neutrino dark energy can be written as @xmath5 where @xmath6 is the kinetic term of neutrinos , @xmath7 is a coefficient which takes the value of @xmath8 for a dirac neutrino and @xmath9 for a majorana neutrino , @xmath10 is the scalar field dependent mass of the @xmath11-th neutrino that characterizes the interaction between the neutrino and the dark energy scalar . 1ex the authors of @xcite have used the recently released snia data to constrain the coupling of the scalar @xmath3 to neutrinos and the property of the dark energy scalar . they found that the model with a phantom scalar is mildly favored . however , the data do not rule out the possibility of the quintessence scalar coupled to neutrinos . in this paper we will show that these two models predict different spatial variation of neutrino masses inside earth and consequently result in different signals in very long baseline neutrino oscillations . 1ex this paper is organized as follows : in section ii we present our mechanism for the neutrino mass variation ; in section iii we study quantitatively the mass - varying effect in the long baseline neutrino oscillations ; section iv is a brief summary . in the standard model of particle physics , a typical term for the neutrino masses can be described by a lepton violating dimension-5 operator @xmath12 where @xmath13 is a scale of new physics beyond the standard model which generates the @xmath14 violations , @xmath15 and @xmath16 are the lepton and higgs doublet , respectively . here we neglect the lepton generation symbol . when the higgs field gets a vacuum expectation value , @xmath17 , the left - handed neutrino receives a majorana mass @xmath18 . in ref . @xcite the authors proposed a model where the dark energy scalar @xmath3 couples to the dim-5 operator . in this model neutrino masses vary along with the evolution of the universe and the neutrino mass limit imposed by baryogenesis is modified . 1ex the dimension-5 operator above is not renormalizable . it can be generated from physics beyond the standard model which involves very heavy particles interacting with standard model particles . at low energies the heavy particles can be integrated out and thus resulting in effective , nonrenormalizable terms . for example , in the model of the minimal see - saw mechanism , we have the neutrino mass term , @xmath19 where @xmath20 are the majorana mass matrix elements of the right - handed neutrinos and @xmath21 the yukawa couplings . the dirac masses of the neutrinos are given by @xmath22 . now integrating out the heavy right - handed neutrinos @xmath23 , one will generate a dim-5 operator as stated above . as pointed out in ref . @xcite , there are various possibilities to have the light neutrino masses varied , such as by coupling the quintessence field to either the dirac masses or the majorana masses of the right - handed neutrinos , or to both . 1ex in this paper we consider the case where the variation of the neutrino masses is caused by a coupling of the dark energy scalar @xmath3 to right - handed neutrinos . with the majorana masses of right - handed neutrinos varying , @xmath20 becomes a function of the dark energy scalar field @xmath3 , @xmath24 . furthermore , we assume a linear relationship between the majorana mass and @xmath3 . then the relevant lagrangian can be written as @xmath25 where @xmath26 are dimensionless constants and @xmath27 is the potential for @xmath3 . the upper minus sign in @xmath28 is for the case of quintessence while the lower plus sign for the phantom . this convention will be used throughout this paper . now the majorana mass matrix elements of the right - handed neutrinos can be written as @xmath29 and consequently via the seesaw mechanism we obtain the masses of the light neutrinos @xmath30 , @xmath31 similar to the study on the mass varying neutrinos in @xcite , here we introduce also a coupling between @xmath3 and the baryon matter with the effective potential for @xmath3 at low energies given by @xcite @xmath32 where @xmath33 is a dimensionless constant @xcite , @xmath34 denotes the energy density of the @xmath35-th matter field , and @xmath36 is the reduced planck mass . the dark energy scalar @xmath3 shall change its value in space @xcite according to the equation of motion @xmath37 in the following we will calculate the evolution of the dark energy field and the corresponding variation of neutrino masses in the earth for both the quintessence and the phantom cases . 1ex the density profile of baryon in the earth is taken as the widely adopted prem model @xcite , in which earth is taken to be spherically symmetric . the atmosphere is treated as a homogenous layer of @xmath38 in thickness with a constant density @xmath39 . defining @xmath40 and @xmath41 with @xmath42 the earth s radius , the baryon density can be expressed as @xmath43 with @xmath44 in units of @xmath45 , and @xmath46 in units of km . we also assume a homogeneous baryon background outside the atmosphere with the density @xmath47 where @xmath48 is the critical energy density of the universe at the present epoch . 1ex with these assumptions , eq . ( [ em ] ) can be simplified as @xmath49 with the boundary conditions @xmath50 @xmath51 here @xmath52 denotes the interface between the static solution and the cosmological one . for @xmath53 , we expect @xmath3 to become a constant : @xmath54 and @xmath55 is the value of the dark energy scalar field on cosmological scales at the present epoch . for simplicity we take @xmath56 which is consistent with the assumption in eq . ( [ bu ] ) that the baryon background becomes very thin and homogeneous for @xmath57 . it should be noted that we require @xmath58 to satisfy the equivalence principle constraints @xcite . 1ex in addition , we take @xmath59 as an example @xcite and then write eq . ( [ em2 ] ) as @xmath60 for this given potential , the value of @xmath55 is @xmath61,\ ] ] with @xmath62 and @xmath63 for the quintessence case , while @xmath64 and @xmath65 for the phantom . here @xmath66 is the equation of the state and @xmath67 is the energy density of the dark energy at the present time ) . ] . 1ex assuming @xmath68 for @xmath69 , which we will show in the later numerical results is reasonable , we can simplify eq . ( [ em3 ] ) as @xmath70 and obtain the solution @xmath71 with @xmath72 and @xmath73 here we have adopted the definition of @xmath74 : @xmath75 . 1ex the evolution of the dark energy field @xmath3 in the baryon matter background with @xmath76 and @xmath77 for the quintessence and the phantom cases , respectively . it is shown that the assumption of @xmath78 can be fulfilled in the whole space . @xmath79 and @xmath80 are for the quintessence and phantom cases , respectively . ] the variation of the neutrino masses in the baryon background with @xmath76 and @xmath77 for the quintessence and the phantom cases , respectively . here @xmath81 is the masses of the left - handed majorana neutrinos and @xmath82 denotes its value on the earth surface . @xmath79 and @xmath80 are for the quintessence and phantom cases , respectively . ] in the numerical calculation , we take @xmath83 and @xmath84 by choosing @xmath85 to satisfy the cosmological observations , @xmath86 and @xmath87 . in fig . [ phi1 ] , we plot @xmath3 as a function of @xmath88 with @xmath76 and @xmath77 for the quintessence and phantom cases , respectively . our results show that in the two cases the variations of the dark energy field can be sizable inside the earth . accordingly , as shown in fig . [ mass1 ] , the neutrino masses could have a significant variation inside the earth . meanwhile we notice that the consequences of the quintessence and the phantom are different due to the opposite behaviors of the dark energy fields . the survival probabilities @xmath100 of @xmath101 in the long baseline @xmath102 and @xmath103 with @xmath76 , @xmath77 and @xmath104 . @xmath79 and @xmath80 are for the quintessence and phantom cases , respectively . note that @xmath105 is identical to the case of decoupling between the neutrino mass and dark energy . in the calculations , we have used @xmath95 , @xmath97 , @xmath96 , @xmath98 , @xmath106 , and a zero cp phase . the left panel if for @xmath107 and the right panel @xmath108,title=""fig : "" ] the survival probabilities @xmath100 of @xmath101 in the long baseline @xmath102 and @xmath103 with @xmath76 , @xmath77 and @xmath104 . @xmath79 and @xmath80 are for the quintessence and phantom cases , respectively . note that @xmath105 is identical to the case of decoupling between the neutrino mass and dark energy . in the calculations , we have used @xmath95 , @xmath97 , @xmath96 , @xmath98 , @xmath106 , and a zero cp phase . the left panel if for @xmath107 and the right panel @xmath108,title=""fig : "" ] the survival probabilities @xmath100 of @xmath101 in the very long baseline @xmath109 and @xmath110 with @xmath76 , @xmath77 , and @xmath104 . @xmath79 and @xmath80 are for the quintessence and phantom cases , respectively . note that @xmath105 is identical to the case of decoupling between the neutrino mass and dark energy . in the calculations , we have used @xmath95 , @xmath97 , @xmath96 , @xmath98 , @xmath106 , and a zero cp phase . the left panel is for @xmath111 and the right panel for @xmath110.,title=""fig : "" ] the survival probabilities @xmath100 of @xmath101 in the very long baseline @xmath109 and" +"establishing the hardware for a quantum network is a challenging task . a source of indistinguishable single photons is required along with a means to store the single photons at each node . single semiconductor quantum dots are excellent sources of single photons : they are bright , robust and fast emitters @xcite . a single quantum dot mimics a two - level atom closely such that single photons can be generated either by spontaneous emission from the upper level @xcite or by coherent scattering of a resonant laser @xcite . subsequently emitted photons are close to indistinguishable @xcite . however , achieving the lifetime - limit has been an elusive goal @xcite , and the wavelength coverage is limited . independently , atomic ensembles have developed into one of the best platforms for optical quantum memories @xcite . the combination of strong absorption and long ground state hyperfine coherence has allowed storage times of miliseconds and efficiencies higher than 75% to be achieved in these systems @xcite . moreover , schemes for broadband operation with single photons at the ghz level have been proposed @xcite and also demonstrated experimentally @xcite ; single photons emitted by a single atom were stored in a bose - einstein condensate of the same species and used to produce entanglement between the two remote systems @xcite . a semiconductor - cold atom quantum hybrid would combine the advantage of the semiconductor ( straightforward single photon generation , large oscillator strength ) with the advantage of the cold atoms ( slow decoherence ) whilst avoiding the disadvantage of the semiconductor ( fast decoherence @xcite ) and the disadvantage of the cold atoms ( complex single photon generation @xcite ) . this would constitute an implementation of a quantum repeater using single photon sources and memories @xcite . unfortunately , the workhorse systems are mismatched in frequency : self - assembled ingaas quantum dots emit typically around 950 nm ; the d1 and d2 transitions of the rb atoms lie at 795 and 780 nm . we note that a frequency match has been achieved with cs @xcite ; a link has also been established with a transition of the yb@xmath0 ion @xcite ; a trapped molecule produces single photons at the na frequency @xcite ; and a new quantum dot growth procedure has led to a first hybrid experiment with rb @xcite . a high quality semiconductor source of single photons frequency - matched to the rb transitions is highly desirable . we present here a close - to - ideal semiconductor source of single photons at the rb d2 wavelength . the emission frequency can be tuned through all the d2-hyperfine lines . we demonstrate lifetime - limited quantum dot linewidths . this points to negligible upper level dephasing and allows us to create photons by coherent rayleigh scattering with weak , resonant excitation . we find that all our experiments ( spectral analysis , intensity autocorrelation , decay dynamics ) can be described in terms of a two - level atom with a common set of parameters . the only significant source of noise is slow relative to radiative emission and results in a telegraph - like blinking behavior . apart from this the system behaves in an ideal way despite the complexity of the solid - state environment . our solid - state source of single photons , fig . [ fig1 ] , consists of a gaas / algaas quantum dot ( qd ) obtained by filling al - droplet - etched nanoholes with gaas @xcite . the holes are formed by depositing 0.5 mono - layer ( ml ) of aluminium at a growth rate of 0.5 ml / s and at a temperature of 600 c on a al@xmath1ga@xmath2as surface . this is followed by a 5 minute annealing step in arsenic ambiance . the holes are then filled with gaas grown at 0.1 ml / s and capped again with al@xmath1ga@xmath2as resulting in strain - free gaas qds . the photoluminescence ( pl ) from the ensemble is adjusted to @xmath3 nm , the wavelength of the rb d2-line , by controlling the exact amount of deposited gaas . [ fig1]b shows a typical pl spectrum from a single qd recorded at @xmath4 k with non - resonant excitation at 633 nm . we observe several lines in the pl spectrum . we identify in particular the neutral exciton ( x ) and a red - detuned charged exciton ( cx ) . the other lines are related to other exciton states , as yet unidentified . to fine tune the qd frequency with respect to the rb transition lines , the sample is glued onto a piezo - electric transducer which induces uniaxial strain in the sample @xcite , fig . [ fig1]a . by scanning the piezo - voltage , reversible tuning over @xmath5 ghz is achieved with very little creep from the piezo - electric elements , see fig . in fact , the emission frequencies of the pl lines are stable over the course of a day such that a stabilization scheme was not necessary in these experiments . w / m@xmath6 ) . we identify the neutral exciton ( x ) and a charged exciton ( cx ) which display narrow linewidths , limited here by the @xmath7 ghz spectrometer resolution . c ) sketch of the qd layer and an afm picture of the nano - holes obtained with in - situ etching @xcite.,width=321 ] we first report resonance fluorescence on a single gaas qd , the artificial rb atom . for this , we use the dark - field microscope sketched in fig . a resonant laser beam is focussed onto the sample with linear polarization ; resonance fluorescence from the qd is detected in the orthogonal polarization @xcite . careful control of the polarization suppresses the back - scattered laser light by 80 db . we find that very weak non - resonant laser light ( @xmath8 nm , @xmath9 nw/@xmath10m@xmath6 ) is a necessary condition to observe resonance fluorescence on cx . this non - resonant excitation quenches the excitation of the neutral x and therefore acts as an optical gate "" @xcite . this result was reproducibly observed on all five qds that we tested . nw/@xmath10m@xmath11 ) . the laser background ( @xmath12 cts / s over the @xmath13 ghz scanning range ) is indicated in green . b ) resonance fluorescence intensity and fwhm as a function of resonant laser power . c ) frequency tuning of cx showing a linear response to the applied voltage with very little creep over the course of several days . the d2 transitions of rb are indicated as dashed lines : ( i ) @xmath14rb @xmath15 , ( ii ) @xmath16rb @xmath17 , ( iii ) @xmath16rb @xmath18 and ( iv ) @xmath14rb @xmath17 . d ) second order correlation of the resonance fluorescence signal . in blue , the detectors response function ( arbitrary units for the y - axis ) measured with ultra - short laser pulses ( @xmath19 ps ) at the qd frequency . the red line results from a fit using eq . [ g2tls ] convoluted with the detectors response function . all data are obtained in the presence of an additional weak , constant non - resonant laser excitation of @xmath20 nw / m@xmath11 . the background associated with the non - resonant excitation is smaller than the detectors dark counts.,width=321 ] to record resonance fluorescence spectra , we monitor the count rate on a ccd camera as we sweep the laser frequency across the qd transition , as illustrated in fig . [ fig2]a for the cx transition of qd1 . the spectrum is fitted with a lorentzian profile , and displays a signal - to - background ratio @xmath21 at the resonance . in the low power regime , the linewidth is @xmath22 ghz , see fig . we confirm the anti - bunched nature of the emitted photons by performing second - order correlation measurements on the resonance fluorescence signal , fig . there is a small bunching on the normalized data ( @xmath23 for @xmath24 ns ) which results from a slow blinking process , discussed below . for @xmath25s , the exact blinking dynamics can be ignored and the data are fitted to the product of a constant pre - factor , which accounts for the qd dead - time ( i.e. the blinking ) , and the second - order correlation function of a resonantly driven two - level system @xcite @xmath26 where @xmath27 is the spontaneous radiative emission rate , @xmath28 corresponds to the pure dephasing rate and @xmath29 , with @xmath30 the rabi frequency of the resonant drive . taking the experimentally measured response of the detectors into account , we find a very nice agreement and thus a coincidence detection probability consistent with zero at zero delay , the signature of pure single photon emission . we now turn to the spectroscopy of the rb atomic ensemble using qd photons . we insert a room temperature @xmath31 mm long rb vapor cell in the detection line . the cell contains both @xmath16rb and @xmath14rb in natural abundance ( @xmath32 and @xmath33 , respectively ) . in a first experiment , qd1 is excited with the non - resonant pump only with @xmath34 w / m@xmath6 , fig . transmission through the atomic cloud is recorded as the piezo - voltage is increased thus tuning the qd emission frequency . as the cx transition is scanned from @xmath35 thz to @xmath36 thz , we observe several dips in the transmission corresponding to the hyperfine structure of the two rubidium isotopes , fig . [ fig2]c . in order to distinguish between the qd and the atomic contributions to the linewidth , we perform a calibration measurement on the vapor cell by measuring the transmission with the laser only ( fwhm @xmath37 mhz @100@xmath10s ) . the result , shown in the appendix ( see fig . [ fig : vaporabsorptionspectrum ] ) , is fitted to the theoretical rb transmission spectrum , where the only unknown is the vapor cell temperature . excellent agreement is found for @xmath38 c , corresponding to a doppler broadening of @xmath39 mhz . to describe the transmission spectrum recorded with qd photons , we then convolve the rb spectrum with a lorentzian profile of width @xmath40 , the qd linewidth under non - resonant excitation . best agreement between the resulting function and the data is obtained for @xmath41 ghz . the modest depth of the transmission peaks reflects the mismatch between the qd linewidth and the atomic spectral width . a lifetime - limited linewidth implies a negligible rate of exciton dephasing in the qd . in turn , this opens the possibility of generating single photons by coherent rayleigh scattering . the resonance fluorescence can be divided into a coherent part , the rayleigh scattering of the incoming laser light , and an incoherent part , resulting from an absorption and re - emission cycle . including pure dephasing , the fraction of coherently scattered photons is given by @xmath42 ( see appendix [ apdx_theory_qdres ] for a complete description of the resonant spectrum . ) the ratio is maximum in the low power regime ( @xmath43 ) , the rayleigh regime , and approaches unity should @xmath44 become negligible compared to @xmath27 . the last point highlights the importance of achieving a small dephasing rate . conversely , the ratio decreases at high power where the strong excitation leads to inelastic scattering ( mollow triplet ) . we explore the possibility of coherent rayleigh scattering in a second experiment where we drive the qd resonantly in the low power limit ( @xmath45 nw/@xmath10m@xmath6 ) . the resulting rb transmission spectrum is shown in fig ." +"the surface - force apparatus developed by tabor and winterton ( 1969 ) and further refined by israelachvili and adams ( 1978 ) , klein ( 1983 ) and parker _ et al . _ ( 1989 , ) has proven useful for the measurement of colloidal forces between atomically smooth transparent surfaces in liquid and gases at molecular scale . in these classical apparatii the distance between the surfaces is measured by the interferometry of white light fringes ( fringes of equal chromatic order , feco ) . this technique allows to measure steady or slowly varying distances , with a resolution of a few @xmath1 . chan ( 1985 ) has employed videocameras to record rapidly changing position of the surfaces with a time resolution about @xmath2 , during the drainage of a fluid out of the contact region . recently , this interferometric method has been improved ( grunewaled ( 1996 ) ) by using expensive high speed video treatments . the first method proposed for doing a dynamical measurement was to use a piezoelectric bimorph ( van alsten ( 1988 ) , israelachvili ( 1989 ) , peachey ( 1991 ) ) , which has also the advantage of allowing opaque surfaces to be used . although parker ( 1992 ) showed that a bimorph can be used to take a measurement from less than a tenth of a second to several minutes , these devices are unsuitable for measurements that take place over many minutes or hours . furthermore , the single - cantilever construction of the bimorph implies that a displacement of his head results also in an angular rotation . the resulting shear motion makes it unsuitable for the measurement of adhesive forces . recently the use of a capacitor dilatometry attachment for the conventional surface - force apparatus has been proposed by stewart ( 1992 ) for statics measurements with a resolution of @xmath3 . ( 1988 , 1989 ) described a surface forces apparatus in which they used capacitors to obtain both the distance and the interaction force between a sphere and a plane . this apparatus is suitable for non tranparent surfaces and dynamical study of confined liquids . in this paper , we propose a new method for measuring displacement at the nanometer scale in surface force apparatus , based on a capacitor included in an oscillator . unlike the capacitive sensor proposed by steward ( 2000 ) or franz et al . ( 1996,1997 ) , our method for the capacitance measurement is a low cost method which does not require the use of a lock - in amplifier , without loss in resolution or dynamic performances . from the point of view of surface forces measurements , the method has the advantages of being linear on a large scale , of allowing mesasurements between non transparent surfaces , and is suitable for dynamical measurements . when used in conjunction with an interferometric technique ( crassous _ in preparation _ ) for the purpose of calibration , this sensor can be used to perform nanorheological measurements or contact forces measurements between the surfaces . a schematic diagram of the surface forces apparatus is given in figure [ fig : sfa_plan ] . this apparatus has several features which distinguish it from the common sfa . first of all , the surfaces are not necessary transparent , since the sfa does not use the feco technique . the surfaces are usually a sphere and a plane . the plane surface is mounted on the left - hand double - cantilever @xmath4 of stiffness @xmath5 . an optical interferometer measures the deflection of @xmath4 to obtain directly the force measurements . the sphere is mounted on the right - hand double - cantilever @xmath6 and can be moved in the direction normal to the plane . the cantilever @xmath6 prevents the rolling of the surfaces . the sphere motion is controlled by three actuactors . the first one is a motorized microscrew driven by a stepping motor . it allows a displacement of @xmath7 nm to @xmath8 cm and is used for a rough positionning of the sphere . the second actuator is a piezoelectric actuator which allows a continuous approach of the two surfaces with a velocity range of @xmath9 to @xmath10 nm.s@xmath11 . the last piezoelectric actuator is designed to add a small sinusoidal motion in to study the dynamic behavior of the sphere - plane interactions . the relative displacement between the sphere and the plane , @xmath12 , is determined by the capacitive sensor described in this article . finally , in order to calibrate the capacitive sensor , a permanent magnet mounted on the cantilever @xmath4 is located in the magnetic field gradient produced by a little coil of copper wire . this setup allows to calibrate the sensor over a large range of displacement ( @xmath13 @xmath14 m ) . all these devices are controlled by a hewlett packard vxi 743 computer equiped with a e1421a 16 channels a / d and d / a converters . a more complete description of this apparatus will be given in a forthcoming publication . the measurement capacitor consists of two duraluminium discs with a radius @xmath15 and a thickness @xmath16 . the typical distance between the plates is typically @xmath17 @xmath18 and the surfaces have been polished to have a roughness smaller than the sistance between the two plates of the capacitor . one plate is fixed on the cantilever supporting the plane @xmath4 , and the other on the cantilever supporting the sphere @xmath6 so that when the surfaces are brought together , the plates of the capacitor do also . parallel alignment of the plates is obtained with a mechanical ball - and - socket joint which is rigidly screwed after the plates have been pushed in contact to obtain the parallelism . the terminals of the capacitor plates are connected to the oscillator with thin copper leads whose compliance is much higher than the one of the cantilever . to decrease the viscous drag induced by the air flow between the plates of the capacitor , some holes are drilled in the moving plate . the weight of the capacitor , which is important for the resonant frequency of our surface force apparatus is roughly @xmath19 . the capacitance @xmath20 of this sensor is typically @xmath21 pf and its serial resistance about @xmath22 . in order to measure the capacitance variations of this sensor , we include it in an oscillator . we use a clapp oscillator containing two fixed capacitor @xmath23 , the variable capacitor @xmath20 , and an inductance @xmath24 ( figure [ fig : oscillateur ] ) . the clapp oscillator is known to have a good stability and to be easy to build ( audouin ( 1991 ) ) . neglecting the leads capacitances and straight capacitances , the frequency of the oscillations of the clapp oscillator is : @xmath25 this formula can be used to have an estimation of the nominal frequency and of the sensitivity of the sensor . using the typical values @xmath26 , @xmath27 pf and @xmath28h , we have a typical frequency of @xmath29 mhz and a typical sensitivity of the order of @xmath13 hz / . this shows that in order to have a precision of @xmath30 nm on the displacement measurement , we have to read frequency variations of @xmath31 hz . for this purpose , we use a hewlett packard hp53132a counter which reaches this precision with an acquisition time of less than @xmath9 s. we emphasize that reading one part in @xmath32 is really easy in a frequency measurement but is difficult and expensive in voltage measurements . the conventional way to make a distance measurement with this device is first to fix the distance between the capacitor s plates at a distance comprised between @xmath33 and @xmath34 and to calibrate the sensitivity for small displacements around this distance . indeed we do not use equation ( [ equ : freq ] ) to determine the sensitivity of the sensor , since this latter depends slightly on the angular parallelism of the capacitors plates . in order to calibrate the sensor , we use an interferometer , which is mounted on our sfa ( schonenberger ( 1989 ) ) and allows to perform easy calibrations . the detailed procedure is as follows : the rhs cantilever @xmath6 is fixed , a force is applied on the cantilever @xmath4 by the mean of the coil / magnet system . the deflection of @xmath4 results in a displacement @xmath35 of the sensor s plate . fixed on @xmath4 , as well as of the mirror . the interferometer gives access to the absolute value of @xmath35 , and the calibration is done by plotting @xmath36 , the frequency of the oscillator as a function of @xmath35 . in order to reduce the noise ( see paragraph [ sec : noise ] ) , we usually integrate the frequency signal over a time of @xmath13 s. fig . [ fig : f_x ] shows the calibration over a displacement range of @xmath37 nm . one can see that the capacitive sensor is very linear . the typical maximum deviation to linearity over this scale is lower than @xmath38 of the total excursion range . the measured sensitivity is : 7.70 hz.@xmath11 . this is closed to the estimated value deduce from equation ( [ equ : freq ] ) but take into account all the straight capacitances . the capacitance measuring circuit is in fact sensitive to stray capacitance between the upper sensing electrode and ground . therefore the value @xmath20 of the capacitance in equation ( 1 ) includes not only the sensor capacitance , but also the value of stray capacitances , the larger of which is the capacitance of the screen cable connecting the sensor to the circuit . the order of magnitude of those stray capacitances can be estimated by increasing the distance between the capacitor electrodes up to the point where it does not affect anymore the frequency of the oscillator . the overall value of the stray capacitance can be as large as @xmath39 . during the typical time of an experiment in a sfa ( typically 30 mn ) and with the environment conditions required by the sfa itself ( the sfa is located in a separated closed room where nobody enters during an experiment ; signal acquisition and experiment control are performed from another room ) , it turns out that the overall stray capacitance does not change significantly except for smooth drifts which can not be distinguished from the thermal drift of the measuring circuit itself ( see hereafter ) . significant change of the stray capacitance occur usually other large period of time ( one day ) or when a change is made on the sensor ( tuning of the distance or orientation of the electrodes , change in the location of the oscillator ) . therefore , the sensitivity of the sensor is periodically calibrated with the interferometer , in order to take in account the changes in sensitivity induced by the modification of the value of the stray capacitance . without any displacement imposed on the cantilevers , we can measure the noise and the thermal drift in a typical situation . those quantities will limit the static performance of our apparatus and the thermal drift must be corrected to obtain an accurate measurement of the relative displacement of the surfaces . figure [ fig : vibration_noise_freq ] shows a typical record of the signal given by the counter converted in displacement . the noise is less @xmath9 nm peak to peak . this is due to the mechanical vibrations on the cantilever @xmath4 . with a simple plexiglass cover over the entire instrument and without any temperature control we find" +"since the first reports on the successful isolation of a stable monolayer of graphene @xcite special efforts have been invested in the exploration of similar materials with novel properties resulting from their ultra - thin two - dimensional nature . those alternative materials have the potential to bypass some of the obstacles existing in the usage of graphene in contemporary electronics i.e. , incompatibility with present day silicon technology and lack of an energy bandgap which is essential for all semiconductor devices . for graphene itself further modification is inevitable in order to tailor its electronic properties . a broad range of chemical decoration @xcite and substitutional doping @xcite have been investigated to open and tune the band gap of graphene . particular attention was given to boron and nitrogen as the first choice elements because of their chemical propinquity to carbon as well as to silicon . @xcite the second row elements have not been omitted , al , si and p doping induce band gap opening in monolayer graphene . @xcite theoretical studies of functionalization of graphene have later been supported by the experimental realization of substitutional doping with b and n atoms via arc discharge using graphite electrodes in the presence of hydrogen and b or n atom incorporating molecules ( pyridine , amonia , @xmath0),@xcite thermal annealing of graphene in the presence of boron oxide @xcite or nitrogen plasma treatment of graphene.@xcite recently , the monolayer honeycomb structure of silicon , silicene , has emerged as a potential few - atom - thick material to replace graphene . as was reported by early theoretical works , silicene is a semimetal with linearly crossing bands and a zero electronic band gap similar to graphene . @xcite furthermore , similar to graphene , electrons propagating through the monolayer crystal structure of silicene are predicted to show massless fermion behavior in the vicinity of the dirac point . additionally , some unique features of monolayer silicene such as quantum spin hall effect,@xcite a large spin - orbit interaction,@xcite a mechanically tunable bandgap@xcite and a valley - polarized metallic phase@xcite have been reported by theoretical studies . moreover , the recent experimental observations and synthesis of silicene @xcite have opened a new path for nanoscale materials which might be easily functionalized chemically or mechanically and incorporated within electronics as we know it today.@xcite very recently we reported the adsorption characteristics of alkali , alkaline earth and transition metal atoms on monolayer silicene.@xcite differing from graphene , one can expect the substitution of b , n , al or p atoms to be more likely on the silicene surface ( fig . [ fig - silicene](a ) ) , as it is more reactive due to its @xmath1-like lattice structure . ( color online ) ( a ) structural parameters for silicene and ( b ) possible adsorption sites on the silicene lattice . ( c ) electronic band dispersion and partial density of states for perfect silicene . the energies are relative to the fermi level ( i.e. , @xmath2 ) . the inset ( d ) displays the calculated spin - orbit gap of 1.47 mev . , width=321 ] in this paper , motivated by the route undertaken with graphene and the recent synthesis of silicene , we investigate the adsorption and absorption of b , n , al and p atoms on the surface of pristine free - standing silicene together with their substitutional doping . our interest is pointed towards the compounds structure , binding energies of the most stable structures and their electronic , magnetic and phonon properties . we find that the adsorbed b , n and p atoms are strongly bonded to the underlying silicene , attached to its surface but also penetrated into the silicon lattice . weaker bonding and immersion is observed for the al atom . these observations differ from the general chemical functionalization of graphene which is highly dependent on the presence of defects and crystal boundaries.@xcite the stability of the ground state structures has also been addressed by using _ ab initio _ molecular dynamics and phonon calculations . our present investigation of the chemical modification of silicene employs density functional theory ( dft ) as implemented in the vasp package.@xcite we have made use of the spin polarized local - density approximation ( lda ) @xcite for the exchange - correlation functional , the projector augmented wave method @xcite and a plane - wave basis set with an energy cutoff of 500 ev . the sampling of the brillouin zone was done for the supercell with the equivalent of a @xmath3 monkhorst - pack @xmath4-point grid for a silicene unit cell ( containing 2 silicon atoms ) . the partial occupancies in the electronic ground state calculation were treated using the tetrahedron methodology with blchl corrections @xcite . for the purpose of the calculation of the density of states a gaussian smearing of the energy levels was applied with standard deviation set to 0.1 ev . to eliminate the interaction emerging from periodic boundary conditions in all three dimensions a @xmath5 supercell was used with the height of 15 to include enough vacuum , and dipole corrections were used . all reported quantitative results of the charge transfer were obtained by usage of the bader charge population analysis @xcite , and the iterative modified hirshfeld charge population analysis . @xcite the relaxation of the atomic positions was performed with forces smaller than 0.01 ev@xmath6 . to reduce the strain induced by the adsorbates / substituents , the lattice parameters were optimized properly . the phonon frequencies for adatom adsorbed / substituted silicene were calculated using the small displacement method.@xcite _ ab initio _ molecular dynamics simulations ( md ) were performed with use of the non - spin polarized local - density approximation ( lda ) @xcite for the exchange - correlation functional , the projector augmented wave method @xcite and a plane - wave basis set with an energy cutoff of 500 ev . the sampling of the brillouin zone was done for the supercell with the equivalent of a @xmath7 monkhorst - pack @xmath4-point grid for a silicene unit cell . the integration of newton s equations of motion was performed using the verlet algorithm where harris corrections were used in order to correct the forces . the simulations were performed within the micro - canonical ( nve ) ensemble with velocities assigned according to the maxwell - boltzmann distribution at the temperature of 500 k during the entire calculation . to avoid large temperature fluctuations velocities were normalized every 40 steps . the total duration of the simulation was 2 ps with the time step equal to 1 fs . first , we consider the adsorption of a single atom on a silicene surface . in contrast to the completely flat one - atom - thick surface of graphene , silicene is buckled as can be seen in fig . [ fig - silicene](a ) and we can expect higher reactivity due to this @xmath1-like lattice structure . similar to graphene , silicene is a semimetal with linearly crossing bands at the fermi level with a zero electronic band gap ( fig . [ fig - silicene](c ) ) . however , effect of spin - orbit coupling , that yields 1.47 mev spin - orbit gap ( fig . [ fig - silicene](d ) ) , is much larger than that of graphenes.@xcite we define the binding energy for adsorption as : @xmath8 . there are three possible adsorption sites on graphene , while as a consequence of the buckled hexagonal lattice structure of silicene has now four different adsorption sites as shown in fig . [ fig - silicene](b ) : above the center of the hexagonal silicon rings ( hollow site ) , on top of the upper silicon atoms ( hill - site ) , on top of the lower silicon atoms ( valley - site ) and on top of the si - si bond ( bridge site ) . ( color online ) diffusion characteristics of b , n , al and p adsorbates . the energies are relative to the binding energy of the most preferable adsorption site . spatial distance is plotted on x axis , the intermediate positions between high symmetry points were obtained by restricting the adatoms movement perpendicular to the silicene surface . the local minima in diffusion energy plots outside of the four high symmetry adsorption sites do not provide stable binding without aforementioned restrictions . , width=321 ] the possible diffusion paths were determined from the energetics of the adatoms on the different lattice points . as shown in fig . [ fig2 ] , each n adsorbate has to overcome an energy barrier of @xmath90.7 ev for diffusion from one bridge site to a neighboring one via a valley site . b adsorbates , because of their stronger binding energy compared to n atoms , see larger migration barriers . diffusion of a b atom from one valley site to another one can occur via a hollow site by overcoming the energy barrier of @xmath92.0 ev . the p adatom has to overcome an energy barrier of @xmath90.9 ev when diffusing between neighboring hill sites via the bridge and valley sites . for the al adatoms the energy barrier is @xmath90.4 ev between two neighboring valley sites . after unconstrained relaxation , the four adsorption sites provide stable or metastable binding , albeit with different binding energy . only the adsorption of an al atom on a bridge site is found to be unstable . for the graphene surface the bridge site was found to be the most favorable adsorption site for both b and n adsorbates.@xcite however , we find that the most favorable adsorption sites on the silicene surface are the valley and bridge sites for b and n adsorbates , respectively . while the adsorption of the b ( n ) atom occurs with a -1.8 ( -4.6 ) ev binding energy on graphene,@xcite for silicene the bonding between b ( n ) and the silicene lattice is stronger with a binding energy of -5.85 ( -5.54 ) ev . the al and p atom preferential adsorption sites were found to be the valley site with a binding energy of -2.87 ev and the hill site with an adsorption energy of -5.28 ev , respectively . we found the adatoms to considerably distort the underlying silicene layer . a b adsorbate is almost completely immersed into the silicene layer and pushes the underling si atom down from its original position . the b adatom average distance from the underlying si layer is only 0.71 as can be seen in table [ table_main ] . n atom adsorption on the bridge site results in si - si bond breakage . a similar effect as with the b adsorption occurs for p and al adatoms , albeit with lower intensity and with up to two times larger average distances from the underlying si layer as can be seen in table [ table_main ] . next we investigate the absorption , i.e. , the substitution of a single si atom with a b , n , al or p atom . the binding energies for substitutional doping are -6.21 , -5.64 , -2.28 and -4.84 ev , for a b , n , al and p atom , respectively . this binding energy for substutution is calculated as follows : @xmath10 . b - si and n - si bonds are shorter than the intrinsic si - si bond lengths , the p - si bond is also slightly shorter but the al - si bond lenght is larger by 0.1 in comparison to the si - si bond length as can be seen in table [ table_main ] ( comparabable to n and b substituted graphene @xcite ) ." +"the possible effect of high energy cosmic ray particles on various atmospheric processes related to atmospheric chemistry and physics is debated over the last years . recent findings suggest an apparent influence of cosmic rays on various atmospheric processes and electric circuit , as well as on minor constituents of the atmosphere @xcite , @xcite . up to present , in most of the proposed and debated models , the induced by cosmic rays , both from galactic and/or solar origin atmospheric ionization plays a key role . our planet earth is constantly bombarded by high , very high and ultra - high energy nuclei , known as cosmic rays , which are the main source of ionization in the troposphere @xcite . the contribution of this particles to the atmospheric ionization is continuous with slight variation in time due to modulation effects in the heliosphere . occasionally solar energetic particles ( seps ) enter the earth atmosphere , penetrate deep into in the atmosphere or even reach the surface , in a such way leading to ground level enhancements ( gles ) . as a result they cause an excess of ionization , specifically over the polar caps @xcite , @xcite . at recent as a result of numerical methods , based on enhanced knowledge of high - energy interactions and nuclear processes several models for estimation of cosmic ray induced ionization in the earth atmosphere have been proposed within good agreement with experimental results @xcite , @xcite , @xcite , @xcite . these models are based on a full monte carlo simulation of the atmospheric cascade . as was recently reviewed they agreed within 1020 @xmath0 @xcite . these full target models allow one to compute the ion production rate , accordingly ionization effect in the atmosphere during major gles as superposition of the contribution of cosmic rays with galactic and solar origin @xcite , @xcite . here we present the results of computation of ion production rate and corresponding ionization effect relative to the average due to galactic cosmic rays during one of the most interesting and major events of the previous 23 solar cycle , namely the gle 59 on bastille day of 14 july 2000 . here we use model similar to @xcite , the full description given elsewhere @xcite . the ion production rate is given by : @xmath1 where @xmath2 is the deposited energy in an atmospheric layer @xmath3 , @xmath4 is the air overburden above a given altitude in the atmosphere expressed in @xmath5 subsequently converted to altitude above the sea level ( a.s.l . ) , @xmath6 is the differential cosmic ray spectrum for a given component @xmath7 : protons p , helium ( @xmath8-particles ) , light nuclei l ( 3 @xmath9 z @xmath9 5 ) , medium nuclei m ( 6 @xmath9 z @xmath9 9 ) , heavy nuclei h ( z @xmath10 10 ) and very heavy nuclei vh ( z @xmath10 20 ) in the composition of primary cr nuclei ( z is the atomic number ) , @xmath11 is the atmospheric density in @xmath12 , @xmath13 is the geomagnetic latitude , @xmath14 is the initial energy of the incoming primary nuclei on the top of the atmosphere , @xmath15 is the geometry factor - a solid angle and @xmath16 = 35 ev is the energy necessary for creation of an ion pair in air @xcite . the integration is over the kinetic energy above @xmath17 , which is defined by the local rigidity cut - off @xmath18 for a nuclei of type @xmath7 at a given geographic location by the expression : @xmath19 where @xmath20 = 0.938 gev / n is the proton s rest mass . accordingly , for seps spectra in equation ( 1 ) , which are considerably varying from event to event , we consider results derived on the basis of ground based measurements with neutron monitors . in this study , the propagation and interaction of high energy protons with the atmosphere are simulated with the planetocosmics code @xcite assuming a realistic atmospheric model nrlmsise2000 considering seasonal influence @xcite @xcite , @xcite . planetocosmics provides detailed simulation of particle interaction with atmosphere in a wide range of energy and altitudes with a very good resolution and allows one to simulate realistically the interactions and , when appropriate , decay of nuclei , hadrons , muons , electrons and photons in the atmosphere . in addition to the detailed detailed information about the flux of secondary particles at a given atmospheric depth it provides the energy loss and deposition , necessary for the computations with eq . ( [ simp_eqn1 ] ) . therefore the model allows one to estimate the ion production rate , accordingly the ionization effect in a whole atmosphere . as mentioned above , the ion production rate during major gles is a superposition of the contribution of galactic cosmic rays ( gcr ) and gle particles , which typically possess an essential anisotropic part . therefore , it is necessary to compute the rigidity cut - off at given geographic position and to apply the described above model using an appropriate model for gcr spectrum as well as to consider explicitly the anisotropy by computation of the asymptotic cones in the region of interest . the mid july 2000 was characterized by intense solar activity , resulting on three x - class solar flares ( including the bastille day flare ) and two halo coronal mass ejections ( cme ) @xcite . the gle 59 event was related to the bastille day x5.8/3b solar flare and the associated full halo cme . the event started at 10:03 ut , reached peak at 10:24 ut and ended at 10:43 ut @xcite . accordingly , the gle onset began between 10:30 and 10:35 ut at several stations with strongest nm increases observed at the south pole ( 58.3 @xmath0 ) and sanae ( 54.4 @xmath0 ) compared to pre - increase levels . in general the event was characterized by a large anisotropy in its initial phase @xcite . with the reconstructed spectra used as input ( see eq . [ simp_eqn1 ] ) the ion production rate during the bastille day event on 14 july 2000 was computed at 1gv and 2 gv rigidity cut - off @xcite . the time evolution of ion production due to cr of galactic and solar origin during the gle 59 is presented in fig . 1 for 1 gv rigidity cut - off , accordingly in fig.2 for 2 gv rigidity cut - off . the computed ion production rate is significant during the main phase of the event at the polar and sub - polar region with rigidity cut - off of about 1 gv . the ion production is significant in the low stratosphere ( fig . 1 ) . during the initial and late phases of the event the ion production is comparable to the average due to gcr , but at altitudes of about 10 km a.s.l . and below the ion production due to gcr is greater than seps , because of the rapidly falling spectra of the solar particles . at high mid latitudes and mid latitudes with rigidity cut - off of about 23 gv , the ion production due to gcr dominates in the whole atmosphere throughout the event ( fig . 2 ) , because the very soft seps spectra . the computed on a step ranging from 5 to 30 min . ion production due to cr of solar and galactic origin allows one to estimate the ionization effect during the gle 59 on 14 july 2000 at several altitudes @xcite . the expected maximal ionization effect relative to the average due to gcrs at 1 gv and 2 gv rigidity cut - offs without considering the anisotropy is shown on fig . 3 . accordingly on fig . 4 is presented the computed total 5 h ionization effect in the earth atmosphere during the gle 59 in the polar and sub - polar region at altitude of about 12 km a.s.l .. the corresponding 24h ionization effect is presented on fig . the event averaged ionization effect at this altitude ( 12 km a.s.l . ) is maximal ( nearly 80 @xmath0 ) in the regions 0@xmath21 30@xmath21 e and 300@xmath21 360@xmath21 e , particularly in the northern hemisphere . accordingly the minimal ionization effect at altitude of 12 km a.s.l , is about 50@xmath0 , and it is observed in anti - sunward direction , namely in the region 120225@xmath21 e. the computed total 24 h ionization effect as shown in fig . 5 is not significant and it is in the order of 5@xmath0 . in the low troposphere is drops to about a 1@xmath0 . the relative to the average due to gcr ionization effect in the polar and sub - polar regions of the earth ( with geomagnetic cut - off rigidities between 0 gv in the cusp , and 1 gv ) is significant during the whole event , specifically in the region of the pfotzer maximum , thus in the lower stratosphere , the tropopause and in the upper troposphere . in the region of high - middle latitudes , as well as in low- middle latitudes the ionization effect is weak during the initial and main phases of the event and negligible during the late phases of the event . the ionization effect rapidly diminishes in the middle and lower troposphere , where the ion production is comparable to the average due to gcr or even smaller , i.e. gcrs produce greater quantity of ions than seps below some 8 km a.s.l . , because the rapidly falling spectra of the latter . this work was supported by the center of excellence resolve ( project no . 272157 ) of the academy of finland . 9 g. a.bazilevskaya et al . , `` cosmic ray induced ion production in the atmosphere '' , space science reviews , _ 137 _ , 149173 , 2008 . a. mishev et al . , `` ionization effect of nuclei with solar and galactic origin in the earth atmosphere during gle 69 on 20 january 2005 '' , journal of atmospheric and solar - terrestrial physics , _ 89 _ , 17 , 2013 . j.m . wissing and m .- b . kallenrode , `` atmospheric ionization module osnabrck ( aimos ) : a 3-d model to determine atmospheric ionization by energetic charged particles from different populations '' , journal of geophysical research , _ 114 _ , a06 , 2009 . a. mishev and p.i.y . velinov , `` a maverick gle 70 in solar minimum . calculations of enhanced ionization in the atmosphere due to relativistic solar energetic particles '' , comptes rendus de lacadmie bulgare des sciences , _ 66 _ , 14571462 , 2013 . a. mishev and p.i.y . velinov , `` time evolution of ionization effect due to cosmic rays in terrestrial atmosphere during gle 70 '' , journal of atmospheric and solar - terrestrial physics , _ 129 _ , 7886 , 2015 . a. mishev and p.i.y . velinov , `` influence of hadron and atmospheric models on computation of cosmic ray ionization in the atmosphere - extension to heavy nuclei '' , journal of atmospheric and solar - terrestrial physics , _ 120 _ , 111120 , 2014 . a. mishev and p.i.y . velinov , `` ionization rate profiles due to solar and galactic cosmic rays during gle 59 on bastille day 14 july 2000 '' , comptes rendus de lacadmie bulgare des sciences , _ 68 _ , 359366 , 2015 . a. mishev and p.i.y . velinov , `` ionization effect due to cosmic rays during bastille day event gle 59 on short and mid time scales '' , comptes rendus de lacadmie bulgare" +"area - minimizing interfaces , such as soap films and elastic membranes without bending and torsional stiffness , are found in a wide variety of man - made and biological structures , and in processes such as liquid confinement in microgravity and enhanced oil recovery . the ability to predict their shape , strength and/or integrity is therefore important . that soap films are not indefinitely stable is clear from the well - known case of the catenoidal film formed between two closely - spaced parallel rings of radius @xmath0 @xcite . as the two rings are pulled apart , the neck gradually thins . this does not continue indefinitely , and at a critical ring separation @xmath1 the surface becomes unstable and jumps to two discoidal films , one in each ring . a related instability is the stretching of a cylindrical bubble between parallel walls @xcite . above a certain wall separation , @xmath2 , the bubble undergoes a `` wine - bottle '' @xcite , or rayleigh - plateau , instability , bulging at one end and thinning at the other . as the stretching continues , the bubble detaches from one wall , and takes a hemispherical shape @xcite . other soap - bubble instabilities are reviewed by @xcite ( @xcite ) . they make the implicit assumption , as we shall do throughout the following , that the amount of surfactant present is sufficiently great that a film does not collapse because its tension becomes too high and that instabilities are not driven by gradients in surface tension . this assumption is certainly valid in our experiments , described below . we first consider the stability of a single planar film . a single rectangular soap film confined between parallel walls , with its ends held by two wires perpendicular to the walls , can be stretched indefinitely by pulling the anchoring wires apart . however , if the film is confined in a cylinder , oriented parallel to the axis and such that the anchoring wires are parallel diameters of the cylinder , we find that this cylindrical constraint induces a surface - tension - driven instability in sufficiently long films . once this instability is triggered , at some critical aspect ratio , the film rapidly deforms and collapses . if the film is twisted , taking the shape of a helicoid , then the instability occurs when the aspect ratio is lower . -shaped wires at each end , meet each other at @xmath3 , and are again free to move on the cylinder wall . the upper y - shaped arrangement of anchoring wires is rotated at fixed aspect ratio , or pulled upwards at fixed @xmath4 ( not shown ) . ( c ) arrangement of four elastic membranes in a cylinder ( simulation only ) . ] most physical systems , however , consist of more than one soap film . in more complex arrangements of multiple soap films , a consequence of area minimization is that these films meet in threes at equal angles of @xmath3 @xcite in what are known as plateau borders . thus , it is important in predicting the stability of foams , which are used in many processes including froth flotation and ore separation @xcite , to determine the degree to which this three - fold arrangement of soap films is susceptible to the same surface - tension - driven instability . we therefore add more soap films parallel to the axis of the cylinder , in both simulation and experiment , and show that these configurations confer no greater stability on the system . the three systems investigated here are shown in figure [ fig : one ] . we used a 10% solution of the commercial detergent fairy liquid to create a single soap film between two parallel pieces of pipe - cleaner ( referred to here as wires ) placed perpendicular to the axis of a perspex cylinder of fixed radius @xmath5 mm and length 300 mm ( as in figure [ fig : one](a ) ) . the upper wire is held in place with a thin perspex ring attached to a handle that allows its position to be controlled . note that there is no volume constraint on the gas neighbouring the film . the film was then slowly stretched by increasing the distance @xmath6 between the wires in small steps from zero ( the point at which the film is formed ) . we define the aspect ratio of the film to be @xmath7 ( rather than the more conventional definition , which is half this ) for consistency with the experiments described below with multiple films . the critical aspect ratio at which the film becomes unstable was found to be @xmath8 . the instability becomes apparent when the film starts to bow outwards while remaining attached to the wires at top and bottom , as shown in figure [ fig : expt ] . the midpoints of the vertical sides of the film move around the cylinder wall until they meet . the film then pinches off into two parts , each of which retract towards the ends of the cylinder . the final state consists of two semicircular films between a wire and the cylinder wall , one at each end of the cylinder . this whole process , from initial bowing of the film to the final collapsed state , can take several tens of seconds due to friction at the wall . we next formed a film and stretched it to a small value of @xmath6 , then twisted it into a helicoid by slowly moving the upper constraint clockwise up to an angle @xmath4 . we then again stretched the film by increasing @xmath6 and recorded the value of @xmath9 at which the film became unstable and collapsed . the critical aspect ratio _ decreased _ with increasing @xmath4 in the manner shown in figure [ fig : plot ] . equivalently , at given aspect ratio @xmath10 , the film can only be twisted up to a certain angle until it becomes unstable and then collapses as before . for aspect ratio , @xmath11 for angle ; simulation @xmath12 for aspect ratio , @xmath13 for angle . the theoretical prediction at @xmath14 , @xmath15 is shown as an asterisk on the horizontal axis.,scaledwidth=90.0% ] both stretching and twisting experiments were repeated with a y - shaped frame , again made from pipe - cleaners ( see figure [ fig : one](b ) ) , to generate data for the collapse of the three - fold film arrangement . each film is a helicoid , and the instability is first apparent when the triple line along the axis of the cylinder ( i.e. the plateau border ) deforms . the critical values of the aspect ratio and twist angle are also shown in figure [ fig : plot ] : they are close to those for the single film case , suggesting that the same mechanism for instability is involved , but are at slightly lower aspect ratio for given twist angle . we used the surface evolver @xcite to determine the shape of a single film at a minimum of surface area . we set @xmath16 and then tessellated the film with about 2000 triangles ( three levels of refinement ) . the edges that lie along the diameters at the end of the cylinder were fixed , and the sides of the film were constrained to move on the curved walls of the cylinder . on stretching the film , in steps of @xmath17 , we found that an eigenvalue of the hessian of energy @xcite first become negative at @xmath18 , close to the value found in the experiments . starting from a small value of @xmath6 , we then twisted the film in increments of one - tenth of a radian before stretching , as in the experiments . in other words , we searched for the instability by increasing @xmath10 at fixed @xmath4 ; this turns out to be equivalent to fixing @xmath10 and increasing @xmath4 . we again recorded the value of @xmath10 at which an eigenvalue of the hessian became negative , as a measure of the triggering of the instability . the critical value of @xmath10 decreased with increasing twist angle , as shown in figure [ fig : plot ] and in broad agreement with the experiments . continuing the simulation after the instability occurs allowed us to produce illustrative snapshots of the collapse of the film ( figure [ fig : two ] ) , although these should be viewed with caution because we have not attempted to model the dynamics of the film . three - fold films were examined in the same way as in the experiments : we placed a y - shaped constraint at each end of the cylinder , with three films between them , and slowly pulled and/or rotated the constraint at one end of the film . each film is again tessellated with about 2000 triangles . the bowing of the central plateau border observed in the experiments during the collapse of the films is repeated in the simulations . figure [ fig : three ] shows how this happens : under stretching two of the three films distort in the same way that the single film does ( figure [ fig : two](a ) ) while under twisting all films respond in the same way and the central plateau border becomes distorted and no longer follows the axis of the cylinder . the critical aspect ratios and twist angles , shown in figure [ fig : plot ] , are almost indistinguishable from the simulations of the single film , indicating that the number of films present does not affect the triggering of the instability . the discrepancy between the experimental and simulation results may be due to the finite size of the wires and the ring supporting the upper wires , which cause deviations in the shape of the films particularly close to the cylinder , and the effects of gravity - driven liquid drainage , which causes the films to be thicker towards their base . both effects are more significant at the highest twist angles . ) . ( b ) mode of instability under twisting for @xmath19.,title=""fig:"",scaledwidth=35.0% ] ) . ( b ) mode of instability under twisting for @xmath19.,title=""fig:"",scaledwidth=35.0% ] twisting any of the simulated soap film configurations up to an angle of @xmath20 leads to instability at a very small height , but note that @xmath20 is not an upper limit to the possible twist angle . we are able to twist the three - fold film up to @xmath21 . plateau s rules preclude the possibility of more than three films meeting along a line . four films , for example , would undergo an immediate topological transition , introducing a new rectangular film between two parallel triple lines . in the case of elastic membranes , there is no such restriction , and to illustrate that this instability is not limited to soap films , we simulated an arrangement of four `` fins '' ( figure [ fig : one](c ) ) . this gives the same critical values for aspect ratio and twist angle ( figure [ fig : plot ] ) . we explain this effect by examining the way in which the single rectangular film collapses . it could be expected that perturbing the film would induce an increase in area , but the presence of the cylinder walls allows the film to reduce its area due to this perturbation . beyond a critical aspect ratio , the increase in film area due to the perturbation is more than compensated for by the reduction in area as the film slides round the" +"if it was not for its binary companion ( the secondary @xmath6car b star ) , the primary massive star ( @xmath0 car a ) would be a ` boring ' star . it is the binary companion that most likely shaped the homunculus ( soker 2003 ; 2007b)@xmath7the bipolar nebula around @xmath0 car that was ejected during the twenty years long great eruption ( davidson & humphreys 1997 ) . the orbital motion is also behind the @xmath8 year periodic variation in the light curve of @xmath0 car , from the radio ( duncan & white 2003 ) to the x - ray band ( corcoran 2005 ) , and in all wavelengths in between ( e.g. , damineli 1996 ; damineli et al . 1998 , 2000 ; whitelock et al . 2004 ; smith et al . 2004 ; abraham et al . 2005 ; hillier et al . 2006 ; nielsen et al . 2007 ) . for some emission bands , and emission and absorption lines , there is a consensus as to their origin , for other there is a dispute . it is agreed that the hard x - ray emission results from the hot postshock secondary stellar wind ( corcoran et al . 2001 ; pittard & corcoran 2002 ; akashi et al . 2006 ; hamaguchi et al . 2007 ) , that most of the radio emission comes from extended ( @xmath9 ) circumbinary ionized gas ( cox et al . 1995 ; duncan & white 2003 ; kashi & soker 2007 ) , and the source of the hard uv radiation is @xmath6car b ( verner et al . 2005 ; duncan & white 2003 ; soker 2007a ) . the location of the plasma emitting the he ii @xmath10 line is in dispute . steiner & damineli ( 2004 ) and martin et al . ( 2006 ) assumed that the he ii emission originates from photoionized regions near the x - ray shock fronts of the two winds . soker & behar ( 2006 ) , on the other hand , postulate that this line originates in the acceleration zone of the secondary wind . in the present paper we dispute the recent suggestion made by nielsen et al . ( 2007 ) that the hei lines originate in the primary wind . this is described in section 2 . in section 3 we describe the blueshift resulting from the orbital motion . in section 4 we analyze the velocity of the lines and try to constrain the orientation angle of the semimajor axis and the inclination of the orbital plane . the orientation angle of the semi - major axis of @xmath0 car is another point of dispute . we summarize in section 5 . the he i lines ( @xmath115877 , 6680 , 7067 , 7283 ) are formed by transitions between excited levels in neutral helium . the main properties of these lines in @xmath0 car are as follows ( nielsen et al . the lines are observed both in absorption and emission , and have p - cygni type profiles at many orbital phases of @xmath0 car . the velocity measured at the minimum of the line profile ( maximum absorption ) relative to the system velocity along the line of sight is blueshifted at all phases . after periastron passage the velocity is @xmath12 . the magnitude of the velocity then increases , reaching @xmath13 at phase @xmath14 ( @xmath15 days before periastron ) . very close to periastron passage there is a sharp rise in the magnitude of the velocity , probably due to a second wind component ( nielsen et al . 2007 ) , to @xmath16 . during the spectroscopic event the absorption line velocity rapidly shifts from @xmath16 to @xmath12 . the equivalent widths of the lines in emission are more or less constant along most of the orbit ( beside some fluctuations ) . at phase @xmath17 they start to drop , reaching a minimum at phase @xmath18 , where they stay for the spectroscopic event of @xmath19weeks . the equivalent widths in absorption are low during most of the orbit . at phase @xmath17 they start to rise reaching a maximum just before phase zero . during the spectroscopic event they sharply drop , partially recovering after the event ( for more detail see nielsen et al . the general behavior of the hei lines in absorption as reported by nielsen et al . ( 2007 ) is qualitatively similar , in both velocity and equivalent width , to the behavior of the he ii @xmath114686 emission line as reported by steiner & damineli ( 2004 ; see also martin et al . 2006 ) . nielsen et al . ( 2007 ) proposed that the hei emission and absorption originate in the primary wind , where the helium is ionized ( or excited ) by the secondary stellar radiation . luminous blue variable stars similar in properties to @xmath0 car a are known to have hei lines with p - cygni type profiles , e.g. , p - cygni itself ( stahl et al . 1993 ; najarro et al . 1997 ) , without any external ionizing source . therefore , it is possible in principle that the source of the hei lines is indeed the primary wind . however , there are some difficulties with this possibility : ( 1 ) what cause the monotonic variation in the blueshift along the orbit ? ( 2 ) why do the equivalent widths of absorption and emission drop for several weeks near periastron passage ? ( 3 ) the most severe problem is the behavior of the he i emission . not only the absorption , put the entire emission part changes its doppler shift with phase . the width of the emission peak does not change much . this is expected if the line is formed by the orbiting secondary star , as we propose . to the contrary , if the line originates in the primary wind , then as regions further out become the source of the line , with their higher velocity , so is the emission peak suppose to be wider . this is not observed ( fig . 2 of nielsen et al . 2007 ) . considering these difficulties , we follow soker & behar ( 2006 ) who attributed the he ii @xmath114686 line to the wind from the @xmath0 car b , and propose the same for the hei lines . namely , we argue that the he i lines originate in the acceleration zone of the secondary wind . wr and o stars are known to have heii and hei lines ( e.g. , crowther & bohannan 1997 ) . the three stars studied by crowther & bohannan ( 1997 ) are somewhat cooler than @xmath0 car b , but the main factor is the mass loss rate ( crowther & bohannan 1997 ) , which is similar to that of @xmath0 car b. these three stars all show the he ii @xmath114686 line in emission , and the he i @xmath115876 line in emission and absorption with equivalent widths of @xmath20 . these stars have he i @xmath116678 emission , and one has this line in absorption as well ( crowther & bohannan 1997 ) . the minimum ( maximum absorption ) in the p - cygni line profiles of the hei lines of o stars occurs typically at a velocity of @xmath17 to @xmath21 times the wind s terminal speed ( prinja et al . 1996 , 2001 , 2006 ) . for the @xmath0 car b this range is @xmath22 , in accord with the observations of nielsen et al . we conclude that the hei line profiles of o stars are similar enough to the line profiles observed from @xmath0 car that we may attribute these lines to the wind from the secondary star . the fast temporal variability in the intensity and speed of these lines from o - stars ( e.g. prinja et al . 2006 ) is evidence of their sensitivity to the wind properties . therefore , small changes in the wind properties might result in large changes in the observed lines profiles . soker & behar ( 2006 ) attributed the large changes in the properties of the he ii @xmath114686 emission line to slight changes in the density of the secondary stellar wind in its acceleration zone . the increase in density might result from the influence of the enhanced x - ray emission arising from the shocked secondary wind further downstream , and/or from accreting mass from the primary stellar wind . a monotonic change after periastron passage might result from the accretion event . although not much mass is accreted during the @xmath19week long accretion phase , it is enough to change the structure of the outer envelope of the secondary star . the secondary itself is still recovering from the 19th century great eruption , when it accreted more than @xmath23 ( soker 2007b ) . therefore , it is possible that the secondary requires several years to reestablish its structure , and before it managed to do so it encounters the next accretion phase . soker & behar ( 2006 ) speculated that the high velocity component appearing very close to periastron passage results from accreted primary wind material by the secondary star . at the beginning of the accretion phase the accreted gas has a relatively high specific angular momentum , and might collimate fast segments of the secondary wind . this might explain the new wind component mentioned by nielsen et al . ( 2007 ) to appear near periastron . despite the above description , it will be much easier to account for the velocity change along the orbit if we observe @xmath0 car such that the secondary is closer to us near periastron , namely , @xmath24 ( see figure [ orbitf ] ) . this implies that the secondary moves away from us after periastron and toward us before periastron . this is opposite to the orbit orientation suggested by nielsen et al . ( 2007 ) . in both cases the orbital plane is tilted by @xmath25 to the line of sight , e.g. , davidson et al . ( 2001 ) give the value @xmath26 , where @xmath5 is the angle between a line perpendicular to the orbital plane and the line of sight . we therefore turn to study the blueshift expected from lines emitted or absorbed in the acceleration zone of the secondary wind . the @xmath0 car binary parameters used by us are as in the previous papers in this series ( soker 2005 ; akashi et al . 2006 ; soker & behar 2006 ; soker 2007a ) , and are compiled by using results from several different papers ( e.g. , ishibashi et al . 1999 ; damineli et al . 2000 ; corcoran et al . 2001 , 2004 ; hillier et al . 2001 ; pittard & corcoran 2002 ; smith et al . 2004 ; verner et al . the assumed stellar masses are @xmath27 , @xmath28 , and orbital period 2024 days , hence the semi - major axis is @xmath29 . the winds properties are not directly relevant to us , but the secondary wind mass loss rate and velocity are similar to other stars having the heii and hei lines ( see section 2 ) ; these are @xmath30 and @xmath31 , respectively . the binary system configuration is presented in figure [ orbitf ] , while in figure [ binary ] we present the variation of the relative speed between the two stars @xmath32 , of the orbital separation @xmath33 , and of the orbital angle @xmath34 , with phase ( equals" +"the response of vacuum to classical external fields or constraints has been studied since more than fifty years . the manifestation of this response are macroscopic forces exerted on boundaries or surfaces where the potential is concentrated . the most famous example is the casimir effect @xcite , which has been recently measured in laboratory with a precision of nearly @xmath0 @xcite . notwithstanding the large size of theoretical work and the experimental efforts many question remain still open . we have in fact by this far no exact knowledge of the law governing the sign of the casimir energy , how exactly the features of the boundary and its geometry influence the response of vacuum . an investigation on the cylindrical geometry has begun in @xcite after the suggestion that a cylinder , as a kind of intermediate shape between the parallel plates and the sphere , could possess a zero casimir stress @xcite . however paper @xcite showed that a perfectly conducting cylinder in the electromagnetic vacuum has a negative casimir energy . a study of the dielectric cylinder has been recently carried out in @xcite and in @xcite , with the interesting result of a vanishing vacuum energy in the dilute case . some light could be further shed into the problem with the study of other quantum fields and other types of background potentials . in this paper we investigate a cylindrical shell with radius @xmath1 , having a delta function @xmath2 as a potential profile . a delta function is an idealization of a strongly concentrated potential . unlike the case of dirichlet boundary conditions the field is continuous on the surface of the shell , therefore the delta function represents a model for a boundary which is not completely hard , but which becomes transparent at high frequencies . this model can be considered as the `` scalar '' version of the dielectric background . a non singular potential would be , of course , more realistic under the physical point of view , but the calculations would be considerably more complicated . a calculation with the delta function has been already carried out for a spherical shell @xcite and for a magnetic flux tube in the vacuum of spinor and scalar fields @xcite . we hope that our work can contribute in the understanding of vacuum as a fundamental aspect of quantum field theory . the cylindrical shell could , besides , find physical applications in the calculation of the quantum corrections to vortices in qcd or in the electroweak theory . another interesting perspective is in the recent discovery of the so called nanotubes @xcite , @xcite , which are large carbon molecules generated in laboratory offering the intriguing possibility of measuring quantum effects on small cylindrical objects . it is also of interest the comparison of the problem of the cylindrical shell with the analogous problem of the magnetic flux tube @xcite . the organization of this paper is as follow : in the next section we collect the basic formulas necessary for the calculation and we present the renormalization procedure , in section 3 and 4 the major part of the analytical calculation is performed . in section 5 the numerical results are given and in section 6 these results are briefly discussed . let us work with a real massive scalar field @xmath3 with mass @xmath4 and let us quantize it in the background of a cylindrical potential . the field equation in cylindrical coordinates @xmath5 , after separation of the variables , reads @xmath6 where @xmath7 is the momentum four vector being @xmath8 its component along the longitudinal axis of the cylinder and @xmath9 is the angular momentum quantum number . @xmath10 is the background potential given by @xmath11 it represents an infinitely thin cylindrical shell whose profile is a delta function . the shell has a circular section of radius @xmath1 and it extends from @xmath12 to @xmath13 in the @xmath14 direction . @xmath15 is a dimensionless parameter giving the strength of the potential . considering eq.(1 ) as a scattering problem , we choose the `` regular solution '' which is given by @xmath16 where @xmath17 , @xmath18 is a bessel function of the first kind , @xmath19 and @xmath20 are the hankel functions of the first and of the second kind and the coefficients @xmath21 and @xmath22 are a jost function and its complex conjugate respectively . @xmath23 is a theta function . the field is therefore free in the regions @xmath24 and @xmath25 . at @xmath26 the field is continuous and we have the following matching conditions @xmath27 where the prime indicates derivative with respect to @xmath28 . + the quantum field is in its vacuum state , its energy is given by half of the sum over all possible eigenvalues @xmath29 of the hamilton operator related with the wave equation ( 1 ) . we define a regularized vacuum energy @xmath30 where @xmath31 is the regularization parameter which we will put to zero after the renormalization , @xmath32 is a mass parameter introduced for dimensional reasons and @xmath33 includes all possible quantum numbers . we will calculate the energy density per unit length of the cylinder given by @xmath34 where @xmath35 are the eigenvalues of the operator contained in ( 1 ) without @xmath8 and with @xmath36 . we carry out the integration over @xmath8 and we arrive at @xmath37 following a well known procedure we transform the sum in ( 7 ) into a contour integral and , dropping the minkowski space contribution , we find @xmath38 where @xmath39 and @xmath40 is the jost function defined in ( 3 ) on the imaginary axis . it contains all the information about the background potential under examination . we will find @xmath41 explicitly in the following section . the energy defined in ( 8) is renormalized by direct subtraction of its divergent part @xmath42 with the normalization condition demanding that the vacuum fluctuations vanish for a field of infinite mass @xmath43 this normalization condition fixes the arbitrariness of the mass parameter @xmath32 ( for more details see @xcite . the condition does not apply to massless fields ) . the isolation of @xmath44 is done with the use the heat - kernel expansion of the ground state energy @xmath45 where the @xmath46 are the heat kernel coefficients related to the background . then we define @xmath47 which includes all the pole terms and all the terms proportional to non - negative powers of the mass . in order to perform the analytical continuation @xmath48 we split the renormalized vacuum energy ( 9 ) into two parts @xmath49 with @xmath50^{1-s } \frac{\partial}{\partial k } [ \ln f_l(ik)- \ln f^{as}_l(ik)]\ ] ] and @xmath51^{1 -s } \frac{\partial}{\partial k } \ln f^{as}_l(ik)-{\cal e}_{div } .\ ] ] here @xmath52 is a portion of the uniform asymptotic expansion of the jost function which must include as many orders in @xmath9 as it is necessary to have @xmath53 in the limit @xmath54 , @xmath55 with fixed @xmath56 , which is sufficient to let the sum and the integral in ( 14 ) converge at @xmath57 . the splitting proposed in ( 13 ) leaves the quantity @xmath58 unchanged , while it permits the substitution @xmath57 in the finite part @xmath59 . we insert solution ( 3 ) into ( 4 ) and we find @xmath60 \nonumber \\ \left(\frac 12 \partial_r \left[f_l(k ) h^{(2)}_l(kr)+f^{\star}_l(k ) h^{(1)}_l(kr)\right ] \right)|_{r = r } = \frac{\alpha}{r } j_{l}(kr ) + \left ( \partial_r j_{l}(kr)\right)|_{r = r}\ . \end{array } \right.\ ] ] the system can be solved for @xmath21 , with the help of the wronskian determinant of the hankel functions @xcite , the result is @xmath61 the corresponding jost function on the imaginary axis can be written in terms of the modified bessel i and k functions , again with the help of @xcite @xmath62 from the jost function ( 19 ) one arrives at the uniform asymptotic expansions @xmath63 for positive @xmath9 and @xmath64 for negative @xmath9 and at the asymptotic expansion @xmath65 for @xmath66 , with the help of the asymptotics of the bessel i and k functions for large indices and large arguments available on @xcite . since the asymptotic jost function consists of three different contributions , the sum over @xmath9 appearing in ( 14 ) and ( 15 ) must also be distinguished in three contributions : a sum over negative @xmath9 , a sum over positive @xmath9 and a contribution coming from @xmath66 . the first two contributions can be summed up analytically in the following way @xmath67 where the dots represent , for simplicity , the rest of the functions in ( 14 ) and ( 15 ) . then , eq.(14 ) and ( 15 ) are rewritten in the form @xmath68^{1 -s } \frac{\partial}{\partial k } \ln f^{as\pm}_l(ik ) \nonumber \\ & & -\frac 14 c_s \int^\infty_m dk [ k^2 -m^2]^{1 -s } \frac{\partial}{\partial k } \ln f^{as}_0(ik ) -{\cal e}_{div } \end{aligned}\ ] ] and @xmath69 \frac{\partial}{\partial k } \left(2\ln f_l(ik)-\ \ln f^{as\pm}_l(ik)\right ) \nonumber\\ & & -\frac{1}{8\pi } \int^\infty_m dk [ k^2 -m^2 ] \frac{\partial}{\partial k } \left(\ln f_0 ( ik)-\ln f^{as}_0(ik)\right)\ , \end{aligned}\ ] ] where @xmath70 and we have used the property @xmath71 of eq.(19 ) . taking the logarithm of the uniform asymptotics of the modified bessel functions and re - expanding in negative powers of the variable @xmath9 ( see @xcite for details on this procedure , see also appendix a ) we find @xmath72 @xmath73 where @xmath74 and the non - vanishing coefficients are @xmath75 in this definition we have included 3 orders in @xmath9 which are sufficient to satisfy condition ( 16 ) . substituting ( 23 ) and ( 24 ) in ( 21 ) and ( 22 ) we find @xmath68^{1 -s } \frac{\partial}{\partial k } \left(\sum_{n=1}^3\sum_jx_{n , j}\frac{t^j}{l^n}\right ) \nonumber \\ & & -\frac 14 c_s \int^\infty_m dk [ k^2 -m^2]^{1 -s } \frac{\partial}{\partial k } \left(\frac{\alpha}{2kr}\ -\ \frac{\alpha^2}{8k^2r^2}\right ) -{\cal e}_{div } \end{aligned}\ ] ] and @xmath69 \frac{\partial}{\partial k } \left(2\ln f_l(ik)-\sum_{n=1}^3\sum_jx_{n , j}\frac{t^j}{l^n } \right ) \nonumber\\ & & -\frac{1}{8\pi } \int^\infty_m dk [ k^2 -m^2 ] \frac{\partial}{\partial k } \left(\ln f_0 ( ik)-\frac{\alpha}{2kr}\ -\ \frac{\alpha^2}{8k^2r^2 } \right)\ .\end{aligned}\ ] ] we call the first addend in ( 27 ) @xmath76 and the second @xmath77 , that is @xmath78 . we go forward with an analytical simplification of ( 26 ) . we call the second addend in ( 26 ) @xmath79 , it can be immediately calculated , giving @xmath80 a simplification of the first addend in ( 26 ) can be achieved with the abel - plana formula ( appendix b ) which transforms the sum over @xmath9 into an integral . then , the first addend in ( 26 ) turns out to be the sum of three contributions @xmath81 @xmath82 @xmath83 where the functions @xmath84 are convergent integrals over @xmath9 given explicitly in appendix b. in appendix b the reader can also find more details about the derivation of the three contributions ( 29 ) , ( 30 ) and ( 31 ) . @xmath85 and @xmath86 contain all the pole terms ( all the divergences of the vacuum energy ) plus the terms proportional to non - negative powers of the mass ( which do not satisfy the normalization condition ) . all these terms are subtracted and are used to calculate the heat - kernel coefficients by means of definition ( 12 ) for @xmath44 . below we give the heat kernel coefficients which we calculated up to the coefficient @xmath87 ( adding four more orders in @xmath88 ) , in the hope that they will be of use for future investigations on the same background @xmath89 one can note how all the integer heat - kernel coefficients depend on odd powers of the coupling constant , while the half - integer coefficients" +"discretized models of @xmath2dimensional euclidean quantum gravity , known as simplicial gravity or dynamical triangulations , have been extensively studied in the past decade . the two dimensional model was proposed quite some time ago in ref . @xcite , and generalized to three and four dimensions in ref . the model is defined by the grand - canonical partition function @xmath4 where @xmath5 and @xmath6 are the discrete cosmological and inverse newton s constants , @xmath7 is the number of @xmath2dimensional simplices , and @xmath8 is the canonical partition function @xmath9 the micro - canonical partition function , @xmath10 , is defined as @xmath11 where the sum is over an ensemble of combinatorial triangulations @xmath12 with a spherical topology and with @xmath13 vertices and @xmath7 @xmath2simplices . for @xmath14 these two numbers are independent . the symmetry factor @xmath15 of a triangulation @xmath16 is given by the number of equivalent labeling of the vertices . including this factor is equivalent to summing over all _ labeled _ triangulations @xmath17 . as a statistical system simplicial gravity displays a wealth of intriguing features . in @xmath14 it exhibits a geometric phase transition separating a strong - coupling _ crumpled _ phase , where the internal geometry of the triangulations collapses , from a weak - coupling _ elongated _ phase characterized by triangulations consisting of `` bubbles '' glued together into a tree - like structure or branched polymers @xcite . both in three @xcite and four dimensions @xcite this transition is discontinuous . in the absence of a continuous phase transition with a divergent correlation length any sensible continuum limit where a theory of gravity might be defined appears to be ruled out this has led to the studies of modified models of simplicial gravity , e.g. by changing the relative weight of the triangulations with a modified measure @xcite , or by coupling matter fields to the theory @xcite . suitable modified the phase structure of the model changes ; the polymerization of the geometry in the weak - coupling limit the elongated phase is suppressed and a new _ crinkled _ phase appears @xcite . the crinkled phase is separated from the other two phases by lines of either a soft continuous phase transitions , or possible a cross - over ( a divergent specific heat is not observed ) . qualitatively the same phase structure , shown schematically in figure 1 , is observed both in three and four dimensions . both in the elongated and in the crinkled phase the canonical partition function is seen to have the asymptotic behavior @xmath18 which defines the string susceptibility exponent @xmath19 . in the crumpled phase , on the other hand , the sub - leading behavior is exponential , corresponding to @xmath20 . many of the properties of the model eq . ( [ part.grand ] ) , in the weak - coupling regime @xmath21 , are reflected by triangulations close to the upper kinematic bound @xmath22 . this is evident both from monte carlo ( mc ) simulations and from the analysis of a strong - coupling expansion ( sce ) of the partition function . for combinatorial triangulations , where each simplex is uniquely defined by a set of @xmath23 distinct vertices , the upper kinematic bound is @xmath24 . although this bound is only saturated in the thermodynamic limit , @xmath25 , for each finite volume there exist triangulations with a well - defined maximal number of vertexes @xmath26 . the ensemble of these triangulations , the _ maximal _ ensemble @xmath27 , defines the micro - canonical partition function @xmath28 in this paper we investigate the properties of the maximal ensemble , mostly restricted to three dimensions , using both mc simulations and a sce , i.e. a direct enumeration of the micro - canonical partition function eq . ( [ part.max ] ) . this investigation is separated into two parts . in the first part we study the pure ( un - modified ) ensemble and show that @xmath29 effectively separates into _ three _ distinct series ( or two series in @xmath30 ) as in general there are several different volumes @xmath7 corresponding to a given @xmath31 . one of those series is an ensemble of _ stacked spheres _ , a particular simple class of triangulations which can be enumerated exactly . this we do in section 3 . the other two series can be considered as `` almost '' stacked spheres , i.e. with one , or two , _ defects _ respectively . heuristic arguments , supported by numerical evidence , show that although the leading asymptotic behavior of the three series is identical , the effect of inserting a defect increases the exponent @xmath19 by @xmath32 ( or @xmath33 ) compared to stacked spheres . this is discussed in section 4 . in the second part of the paper , section 5 , we study the model eq . ( [ part.max ] ) with a modified measure , @xmath34 here @xmath35 is the _ order _ of a vertex @xmath36 , i.e. the number of simplices incident to that vertex . as the measure is modified , varying @xmath37 , we observe a soft geometric phase transition from the elongated phase to a crinkled phase for @xmath38 , in agreement with the phase diagram figure 1 . moreover , a scaling analysis of the transition is consistent with a third order transition ( @xmath39 ) . in the crinkled phase the fractal structure is dominated by a gas of sub - singular vertices , i.e. vertices whose order grows sub - linearly with the volume . the intrinsic fractal structure is characterized by a set of critical exponents : ( i ) a negative string susceptibility exponent @xmath19 , which decreases with @xmath37 . ( ii ) a hausdorff dimension which is either @xmath40 , or @xmath41 ( as @xmath42 ) , depending on whether it is measured on the triangulation itself or its dual graph . ( iii ) a spectral dimension , measured on the dual graph , which increases smoothly from a branched polymer value @xmath43 , at @xmath44 , to @xmath45 at @xmath46 . we have collected some of the more technical issues in two appendixes : in appendix a we list the sce of the three different series , and in appendix b we describe some complications in extracting @xmath19 from measurements of minbu distributions on maximal triangulations . a maximal triangulation is a triangulation which for given volume @xmath7 has the maximal allowed number of vertices @xmath13 . for a combinatorial triangulation this implies : @xmath47 here @xmath48 denotes the floor function , i.e. the biggest integer not greater than @xmath49 . from this definition it follows that in general more then one volume will correspond to a given maximal vertex number . in @xmath50 this defines three different _ series _ , labeled by the @xmath51pairs : @xmath52 the first series @xmath53 has the smallest volume for a given number of vertices and we will call it the _ minimal _ series . likewise , in @xmath30 there are in principle four different series . however , as only combinatorial four - triangulations of _ even _ volume are allowed this reduces to only two : @xmath54 in the space of all triangulations , the different series are related through a set of ( topology preserving ) geometric changes , the @xmath55moves . in a @xmath55move , where @xmath56 , a ( @xmath57)sub - simplex is replaced by its dual ( @xmath58)sub - simplex , provided no manifold constraint is violated . these moves are used in the mc simulations and are ergodic for @xmath59 , i.e. any two triangulations are related through a finite sequence of moves @xcite . = 5.0 in in three dimensions there are two sets of moves : move @xmath60 inserts a vertex into a tetrahedra and its inverse , move @xmath61 , deletes a vertex of order four . in move @xmath62 a triangle separating two adjacent tetrahedra is replaced by a link connecting the opposite vertices . this is shown in figure [ fig.move3d ] . these moves change the number of different @xmath2simplices in the following way : @xmath63 note that only the first set of moves changes both the volume and the number of vertices , and when applied to a maximal triangulation we stay within the particular series , i.e. the different series are internally connected _ via _ this move . the different series are connected , for fixed @xmath13 , by the @xmath62 and the @xmath64moves . however , as it is not possible to apply move @xmath64 to the series @xmath53 ( as triangulations in this series have the minimal volume for a given @xmath13 ) , the only connection which the maximal ensemble has with the rest of the triangulation space is _ via _ move @xmath62 applied to the series @xmath65 . the relations between the different series , _ via _ the @xmath55moves , are shown in figure 3 . [ r][r]@xmath66 [ c][c]@xmath66 maximal ensemble , @xmath53 , @xmath67 and @xmath65 , _ via _ the @xmath55moves.,title=""fig:"",width=377 ] [ moves ] a @xmath2dimensional _ stacked sphere_. however , in @xmath68 this does not define a maximal ensemble as @xmath69 for every ( spherical ) triangulation . ] is a triangulation constructed by successivelly gluing together smallest @xmath2spheres made out of @xmath70 , @xmath2dimensional regular simplexes@xcite . gluing is defined as cutting away one @xmath2simplex in each triangulation and joining the two triangulations by the resulting boundary . gluing a @xmath2sphere corresponds to applying the ( @xmath71)move . from the definitions of stacked spheres and the maximal ensemble it follows that stacked spheres belong to the minimal series @xmath53 . the inverse statement , although less trivial , is also true . this was proven , in three and four dimensions , in two theorems due to walkup @xcite : for any combinatorial triangulation of a 3sphere the inequality @xmath72 holds with equality if and only if it is a stacked sphere . for any combinatorial triangulation of a 4sphere the inequality @xmath73 holds with equality if and only if it is a stacked sphere . from those theorems follows a non - trivial statement : the move @xmath74 , and it inverse @xmath75 , is ergodic when applied to the ensemble of stacked spheres . in contrast , for the non - minimal series this statement is not true . there exist triangulations , @xmath76 , @xmath77 , that can not be reduced to the minimal configuration of the corresponding series by a repeated application of the move @xmath78 . this we have verified numerically . as stacked spheres have a simple tree - like structure , it is possible to calculate the partition function restricted to this ensemble explicitly . in this section we present algorithms for doing so , both for _ labeled _ triangulations ( which enter the mc simulations ) and for the number of _ distinct _ or _ unlabeled _ triangulations . we also show how to generalize the algorithm for counting labeled triangulations to include a modified measure eq . ( [ part.measure ] ) . all the results in this section are based on ref . @xcite which deals with the enumeration of _ simplicial clusters_. a ( @xmath70)dimensional simplicial cluster is a simplicial complex obtained by gluing together @xmath79dimensional regular simplices along their @xmath2dimensional faces . comparing this to the definition of stacked spheres one sees that a @xmath2dimensional stacked sphere is the boundary of a @xmath79dimensional simplicial cluster where the outer faces of the simplicial cluster correspond to the simplices of the stacked sphere . so number of @xmath80dimensional clusters with @xmath81 @xmath79simplices corresponds to the number of stacked spheres with @xmath82 vertices , i.e. @xmath83 simplices . the basic ``" +"the optical properties of the semiconductor structures have been the subject of intensive experimental and theoretical investigation during recent years . technical progress in the semiconductor crystal growth has made it possible to control semiconductor structures in all three spatial dimensions . experimentally , physicists can fabricate the quantum wells , in which a thin semiconductor film is sandwiched between different materials via heterojunctions so that the motion of carriers is confined in the two dimensional thin - film plane . this confinement of carriers to two dimensions gives rise to new quantum effect not observed in bulk materials , for example , an electric field - induced energy shift of the resonance which is called the quantum confined stark effect @xcite . multi - dimensional quantum confined structure , such as quantum wires and quantum dots , are expected to further improve the quantum effect of the optical devices . experiments have shown that the confinement of carriers in these low dimensional semiconductor structures ( ldss s ) can result in novel optical - electronic effects which may lead to fabrication of new optical components . some new fascinating achievements in the areas , such as semiconductor microcavity ( smc ) quantum electrodynamics ( qed ) , quantum dot microlaser and turnstile device @xcite , quantum computer with quantum dot @xcite , and semiconductor random laser @xcite etc . , encourage the study of optical - electronic properties of these micro - structures . the present trend toward smaller - scale nanostructures and the continuous development of new and improved materials have started a steady progress towards fabrication of more ideal optical microcavities . if an ldss is placed in an smc , the optical mode structure of the smc will change around the ldss . using this effect many interesting phenomena , such as tailoring the spontaneous radiation pattern and rate @xcite , the coupled exciton - photon mode splitting in a semiconductor quantum microcavity @xcite , have been demonstrated . therefore the investigation of optical properties of an ldss placed into a semiconductor cavity is very important and necessary for theoretical and experimental physicists . it is known that the interaction between the light and these micro - systems occurs via exciton @xcite which is an electron - hole pair bound by the coulomb attraction . the radiation of exciton exhibits the superradiant character . the initial theoretical @xcite and experimental @xcite studies were focused on the superradiance of the wannier excitons in semiconductor micro - crystallites . then , the superradiance of the frenkel excitons was observed in j aggregates at low temperature @xcite . in 1995 , the superradiance of high density frenkel excitons in a r - phycoerythrin(r - pe ) single crystal was observed at room temperature for the first time @xcite . we have studied the spontaneous radiation of the frenkel excitons in a crystal slab under the condition of low excitation with an exactly solvable model and shown its superradiance nature @xcite . we have also discussed the quantum statistical properties of the output field and the semiconductor qed for the high density excitons in a semiconductor microcavity @xcite . in the former works , our main interest was the resonant interaction between the excitons and the cavity field . but we know that the detuning between the cavity field and exciton always affects the radiation properties of the exciton in the quantum well @xcite . so in this paper we will discuss a general model of the interaction between the high density excitons in a quantum well and a single - mode cavity field . in section ii , we give a general theoretical model of the non - resonant interaction between a single - mode cavity field and the exctions . by virtue of the schwinger s representation of the angular momentum using two boson modes , we approximately obtain the analytical solution of the system . in section iii , the stationary physical spectrum of the excitons , which are initially in the number state or the superposed state of two different number states is presented . a comparison of these results with those of the resonant cases will be also given . finally , a brief summary and conclusion are presented in section iv . in this section , we present a theoretical model to study the interaction between a quantum well and a single - mode cavity field . we assume that the cavity and the quantum well are ideal , and they are in an extremely low temperature circumstance . the quantum well interacts with cavity field via exciton , which is an electron - hole pair bound by the coulomb attraction . at extremely low temperatures , the thermal momentum of the excitons is so small that the thermalized excitons can be neglected . then there are only excitons with zero in - plane momentum . it is well known that when the density of the excitons becomes high , the ideal bosonic model of the excitons is no longer adequate ( in the case of a gaas quantum well , the ideal bosonic model becomes inadequate when the density of the excitons exceeds @xmath0 @xmath1 @xcite ) for a theoretical study . however , we can describe exciton operators as hypothetical bosonic operators . in order to deal with the deviation of the exciton operators from the ideal bosonic operators , we introduce an effective non - linear interaction between these hypothetical ideal bosons to correct the high excitons density effect @xcite . these considerations lead to the following hamiltonian after the rotating - wave approximation is made @xcite : @xmath2 with @xmath3 where @xmath4 are creation ( annihilation ) operators of the excitons with frequency @xmath5 , and @xmath6 are the creation ( annihilation ) operators of the cavity field with frequency @xmath7 . we assume that both of them obey the bosonic commutation relation @xmath8=[a , a^{\dagger}]=1 $ ] . @xmath9 stands for the interaction strength between the cavity field and the excitons . @xmath10 represents an effective interaction constant between the excitons . @xmath10 is assumed as a positive real number , which means that the bi - excitons are not stable in this system of the quantum well . so , it is reasonable to consider that only excitons are present in the quantum well . @xmath11 is a positive real number which describes the phase space filling factor . the ratio of the phase space filling factor to the interaction constant of the excitons is about @xmath12 @xcite . for the sake of simplicity , we assume that the parameters @xmath10 and @xmath11 are of the same order , or @xmath13 . in that case , it is convenient to give the solution of eq.([eq : h0 ] ) using the schwinger s representation of the angular momentum for two - mode bosonic operators @xcite . angular momentum operators can be constructed as @xmath14 and total number operator as @xmath15 using the ladder operators @xmath16 of the cavity field and the exciton operators @xmath17 . it is obvious that @xmath18 is the constant of motion with respect to the hamiltonian ( [ eq : h ] ) . then the total angular momentum operator can be expressed as @xmath19 for any fixed total particle number @xmath20 , the common eigen - states of @xmath21 and @xmath22 are @xmath23 , where @xmath24 are the fock states with @xmath25 photons in the cavity and @xmath26 excitons in the quantum well , respectively . although @xmath27 must be integers , @xmath28 and @xmath29 can both be integers or both be half - odd integers . if we define @xmath30 then eq.([eq : h0 ] ) can be simplified into @xmath31 in terms of an @xmath32 rotation @xmath33 of @xmath34 with @xmath35 and @xmath36 . the eigenfunctions and eigenvalues of hamiltonian ( [ eq : sh ] ) are , respectively , @xmath37 it is clear that eigenfunction @xmath38 represents a dressed exciton state or a polariton state . based on eq.([eq : pp ] ) , using perturbation theory and keeping @xmath10 and @xmath11 parameters up to their first - order , we obtain the eigenvalues of the hamiltonian ( [ eq : h ] ) as : @xmath39 and @xmath40 in order to obtain @xmath41 and @xmath42 , we first calculate the matrix elements of the perturbation term as follows @xmath43 ( j - m-1)(j - m)\delta_{n , m}+\hbar[a(\sin\theta)^{2}-\nu \sin 2\theta ] ( j^{2}-m^{2})\delta_{n , m } \nonumber \\ & & + \hbar[a(\cos\frac{\theta}{2})^{2}\sin \theta -\nu \cos\theta ( \cos\frac{\theta}{2})^2+\frac{\nu}{2}(\sin\theta)^2 ] ( j - m)\sqrt{(j+m)(j - m+1)}\delta_{n , m-1 } \nonumber\\ & & + \hbar[\frac{a}{4}(\sin\theta)^{2 } -\frac{\nu}{4}\sin 2\theta ] \sqrt{(j+m)(j+m-1)}\sqrt{(j - m+1)(j - m+2)}\delta_{n , m-2 } \nonumber \\ & & + \hbar[a\sin\theta ( \cos\frac{\theta}{2})^{2}-\nu \cos\theta ( \cos\frac{\theta}{2})^2+\frac{\nu}{2 } ( \sin \theta)^2 ] \sqrt{(j - m)(j+m+1)}(j - m-1)\delta_{n , m+1 } \nonumber \\ & & + \hbar[a\sin\theta(\sin\frac{\theta}{2})^{2}-\nu \cos\theta ( \sin\frac{\theta}{2})^2-\frac{\nu}{2}(\sin\theta)^2 ] \sqrt{(j+m)(j - m+1)}(j+m-1)\delta_{n , m-1 } \nonumber \\ & & + \hbar[a\sin\theta(\sin\frac{\theta}{2})^{2}-\nu \cos\theta ( \sin\frac{\theta}{2})^2-\frac{\nu}{2}(\sin\theta)^2 ] \sqrt{(j - m)(j+m+1)}(j+m)\delta_{n , m+1}\nonumber \\ & & + \hbar[\frac{a}{4}(\sin\theta)^{2}-\frac{\nu}{4}\sin 2\theta ] \sqrt{(j+m+1)(j+m+2)}\sqrt{(j - m)(j - m-1)}\delta_{n , m+2}\nonumber \\ & & + \hbar[a(\sin\frac{\theta}{2})^{4}-\nu \sin\theta(\sin\frac{\theta}{2})^2](j+m)(j+m-1)\delta_{n , m } , \label{eq : pp1}\end{aligned}\ ] ] 2and then write the eigenvalues of the hamiltonian ( [ eq : h])as : @xmath44 ( j^{2}-m^{2 } ) \nonumber \\ & & + \hbar[a(\cos\frac{\theta}{2})^{4}+\nu \sin\theta ( \cos\frac{\theta}{2})^2 ] ( j - m-1)(j - m ) \nonumber \\ & & + \hbar[a(\sin\frac{\theta}{2})^{4}-\nu \sin\theta(\sin\frac{\theta}{2})^2](j+m)(j+m-1).\end{aligned}\ ] ] all the eigenfunctions of the hamiltonian ( [ eq : h ] ) can be easily obtained using eq.([eq : ee ] ) and eqs.([eq : pp],[eq : pp1 ] ) . then the time evolution operators of the system can be written as @xmath45 consequently , for any initial state @xmath46 , the time - dependent wave function can be obtained as @xmath47 . under the condition of ideal cavity , ideal quantum well , and extremely low temperature , both the excitons and the cavity field have zero linewidth . assumption of ideal quantum well is important to eliminate the linewidth of excitons which may be caused by the fluctuations of the quantum well . so the only broadening mechanism comes from the detecting spectrometer for which the physical spectrum can be defined as @xcite @xmath48 where @xmath49 is the half - bandwidth of the spectrometer , and @xmath50 is the time length of the excitation in the cavity . @xmath51 represents the dipole correlation function of the excitons and is defined as @xmath52 with the initial state @xmath46 of the system , and @xmath53 @xmath54 where the second term comes from the correction of the phase space filling effect @xcite . taking into account the fact that @xmath55 , we can obtain the correlation @xmath51 as @xmath56 with @xmath57 and @xmath58 . it is evident that @xmath28 is determined only by the initial state @xmath46 . then the stationary physical spectrum can be written as @xmath59 , both @xmath60 and @xmath61 must be satistied . according to the above selection rule , eq.([eq : s ] ) can be rewritten as @xmath62 the eigenvalues determine the position of the spectral component and @xmath63 determine the intensity of the spectral lines . the above spectral formula is similar to that of reference @xcite . in the following , we will consider that the system is initially prepared in the bare exciton state using the resonant femtosecond pulse pumping method @xcite . for simplicity , we assume that @xmath64 , so that all frequency quantities have a unit of energy . moreover , we impose that initially there are no photons in the cavity . then for a system , which is initially prepared in the single exciton state , the physical spectrum from @xmath65 to @xmath66 can be simplified into @xmath67 which has double peaks located at @xmath68 and @xmath69 . it is clear" +"the inverse ising problem is intensively studied in statistical physics , computational biology and computer science in the few past years @xcite . the biological experiments or numerical simulations usually generate a large amount of experimental data , e.g. , @xmath2 independent samples @xmath5 in which @xmath6 is an @xmath7-dimensional vector with binary components ( @xmath8 ) and @xmath7 is the system size . the least structured model to match the statistics of the experimental data is the ising model @xcite : @xmath9\ ] ] where the partition function @xmath10 depends on the @xmath7-dimensional fields and @xmath11-dimensional couplings . these fields and couplings are chosen to yield the same first and second moments ( magnetizations and pairwise correlations respectively ) as those obtained from the experimental data . the inverse temperature @xmath12 has been absorbed into the strength of fields and couplings . previous studies of the inverse ising problem on hopfield model @xcite lack a systematic analysis for treating sparse networks . inference of the sparse network also have important and wide applications in modeling vast amounts of biological data . actually , the real biological network is not densely connected . to reconstruct the sparse network from the experimental data , an additional penalty term is necessary to be added into the cost function , as studied in recovering sparse signals in the context of compressed sensing @xcite or in ising model selection @xcite . this strategy is known as @xmath0-regularization which introduces an @xmath0-norm penalty to the cost function ( e.g. , the log - likelihood of the ising model ) . the regularization is able to minimize the impact of finite sampling noise , thus avoid the overfitting of data . the @xmath0-regularization has been studied in the pseudo - likelihood approximation to the network inference problem@xcite and in the setting of sparse continuous perceptron memorization and generalization @xcite . this technique has also been thoroughly discussed in real neural data analysis using selective cluster expansion method @xcite . the cluster expansion method involves repeated solution of the inverse ising problem and the computation of the cluster entropy included in the expansion ( cluster means a small subset of spins ) . to truncate the expansion , clusters with small entropy in absolute value are discarded and the optimal threshold needs to be determined . additionally , the cluster size should be small to reduce the computational cost while at each step a convex optimization of the cost function ( see eq . ( [ cost ] ) ) for the cluster should be solved . this may be complicated in some cases . the pseudo - likelihood maximization @xcite method relies on the complete knowledge of the sampled configurations , and involves a careful design of the numerical minimization procedure for the pseudo - likelihood ( e.g. , newton descent method , or interior point method ) at a large computational cost ( especially for large sample size ) . in this paper , we provide an alternative way to reconstruct the sparse network by combining the bethe approximation and the @xmath0-regularization , which is much simpler in practical implementation . we expect that the @xmath0-regularization will improve the prediction of the bethe approximation . to show the efficiency , we apply this method to the sparse hopfield network reconstruction . our contributions in this work are two - fold . ( 1 ) we provide a regularized quadratic approximation to the negative log - likelihood function for the sparse network construction by neglecting higher order correlations , which yields a new inference equation reducing further the inference error . furthermore , the implementation is much simple by saving the computational time . ( 2 ) another significant contribution is a scaling form for the optimal regularization parameter is found , and this scaling form is useful for choosing the suitable regularization . most importantly , the method is not limited to the tested model ( sparse hopfield model ) , and is generally applicable to other diluted mean field models and even real data analysis ( e.g. , neural data ) . the outline of the paper is as follows . the sparse hopfield network is defined in sec . [ sec_shopf ] . in sec . [ sec_method ] , we present the hybrid inference method by using the bethe approximation and @xmath0-regularization . we test our algorithm on single instances in sec . [ sec_result ] . concluding remarks are given in sec . [ sec_sum ] . the hopfield network has been proposed in ref . @xcite as an abstraction of biological memory storage and was found to be able to store an extensive number of random unbiased patterns @xcite . if the stored patterns are dynamically stable , then the network is able to provide associative memory and its equilibrium behavior is described by the following hamiltonian : @xmath13 where the ising variable @xmath14 indicates the active state of the neuron ( @xmath15 ) or the silent state ( @xmath16 ) . for the sparse network storing @xmath17 random unbiased binary patterns , the symmetric coupling is constructed @xcite as @xmath18 where @xmath19 is the average connectivity of the neuron . @xmath20 independent of the network size @xmath7 . note that in this case , the number of stored patterns can only be finite . in the thermodynamic limit , @xmath17 scales as @xmath21 where @xmath22 is the memory load . no self - interactions are assumed and the connectivity @xmath23 obeys the distribution : @xmath24 mean field properties of the sparse hopfield network have been discussed within replica symmetric approximation in refs . three phases ( paramagnetic , retrieval and spin glass phases ) have been observed in this sparsely connected hopfield network with arbitrary finite @xmath19 . for large @xmath19 ( e.g. , @xmath25 ) , the phase diagram resembles closely that of extremely diluted ( @xmath26 , such as @xmath27 ) case @xcite where the transition line between paramagnetic and retrieval phase is @xmath28 for @xmath29 and that between paramagnetic and spin glass phase @xmath30 for @xmath31 . the spin glass / retrieval transition occurs at @xmath32 . to sample the state of the original model eq . ( [ hami ] ) , we apply the glauber dynamics rule : @xmath33\ ] ] where @xmath34 is the local field neuron @xmath35 feels . in practice , we first randomly generate a configuration which is then updated by the local dynamics rule eq . ( [ gdrule ] ) in a randomly asynchronous fashion . in this setting , we define a glauber dynamics step as @xmath7 proposed flips . the glauber dynamics is run totally @xmath36 steps , among which the first @xmath37 steps are run for thermal equilibration and the other @xmath38 steps for computing magnetizations and correlations , i.e. , @xmath39 where @xmath40 denotes the average over the collected data . the state of the network is sampled every @xmath41 steps after thermal equilibration ( doubled sampling frequency yields the similar inference result ) , which produces totally @xmath42 independent samples . the magnetizations and correlations serve as inputs to our following hybrid inference algorithm . the bethe approximation assumes that the joint probability ( boltzmann distribution , see eq . ( [ ising ] ) ) of the neuron activity can be written in terms of single - neuron marginal for each single neuron and two - neuron marginal for each pair of adjacent neurons as @xmath43 where @xmath44 runs over all distinct pairs of neurons . this approximation is exact on tree graphs and asymptotically correct for sparse networks or networks with sufficiently weak interactions @xcite . under this approximation , the free energy ( @xmath45 ) can be expressed as a function of connected correlations @xmath46 ( between neighboring neurons ) and magnetizations @xmath47 . the stationary point of the free energy with respect to the magnetizations yields the following self - consistent equations : @xmath48 where @xmath49 denotes neighbors of @xmath35 , @xmath50 and @xmath51 . using the linear response relation to calculate the connected correlations for any pairs of neurons , we obtain the bethe approximation ( ba ) to the inverse ising problem @xcite : @xmath52 % \end{split } j_{ij}=-\tanh^{-1}\biggl[\frac{1}{2(\mathbf{c}^{-1})_{ij}}(a_{ij}-b_{ij } ) -m_{i}m_{j}\biggr],\ ] ] where @xmath53 is the inverse of the connected correlation matrix , @xmath54 , @xmath55 and @xmath56 . the couplings have been scaled by the inverse temperature @xmath57 . note that fields can be predicted using eq . ( [ m ] ) after we get the set of couplings . hereafter we consider only the reconstruction of the coupling vector . in fact , the ba solution of the couplings corresponds to the fixed point of the susceptibility propagation @xcite , yet it avoids the iteration steps in susceptibility propagation and the possible non - convergence of the iterations . it was also found that the ba yields a good estimate to the underlying couplings of the hopfield network @xcite . in the following analysis , we try to improve the prediction of ba with @xmath0-regularization . the cost function to be minimized in the inverse ising problem can be written as the following rescaled negative log - likelihood function @xcite : @xmath58\\ & = \ln z(\mathbf{h},\mathbf{j})-\mathbf{h}^{t}\mathbf{m}-\frac{1}{2}{\rm tr}(\mathbf{j}\mathbf{\tilde{c } } ) \end{split}\ ] ] where @xmath59 and @xmath60 . @xmath61 denotes the transpose of the field vector while @xmath62 denotes the trace of matrix @xmath63 . the minimization of @xmath64 in the @xmath65-dimensional space of fields and couplings yields the following equations : [ mj ] @xmath66 where the average is taken with respect to the boltzmann distribution eq . ( [ ising ] ) with the optimal fields and couplings ( corresponding to the minimum of @xmath67 ) . actually , one can use bethe approximation to compute the connected correlation in the right - hand side of eq . ( [ mj2 ] ) , which leads to the result of eq . ( [ ba ] ) . to proceed , we expand the cost function around its minimum with respect to the fluctuation of the coupling vector up to the second order as @xmath68 where @xmath69 defines the fluctuation @xmath70 where @xmath71 is the ( near ) optimal coupling vector . @xmath72 is the gradient of @xmath67 evaluated at @xmath71 , and @xmath73 is the hessian matrix . the quadratic approximation to the log - likelihood has also been used to develop fast algorithms for estimation of generalized linear models with convex penalties @xcite . we have only made explicit the dependence of @xmath67 on the coupling vector . the first order coefficient vanishes due to eq . ( [ mj ] ) . note that the hessian matrix is an @xmath74 symmetric matrix whose dimension is much higher than that of the connected correlation matrix . however , to construct the couplings around neuron @xmath35 , we consider only the neuron @xmath35-dependent part , i.e. , we set @xmath75 in the hessian matrix @xmath76 where @xmath77 and @xmath78 run over distinct pairs of neurons . this simplification reduces the computation cost but still keeps the significant contribution as proved later in our simulations . finally we obtain @xmath79 where an @xmath0-norm penalty has been added to promote the selection of sparse network structure @xcite . @xmath80 is a positive regularization parameter to be optimized to make the inference error ( see eq . ( [ error ] ) ) as low as possible . the @xmath0-norm penalizes small but non - zero couplings and increasing the value of the regularization parameter @xmath80 makes the inferred network sparser . in the following analysis , we assume @xmath71 is provided by the ba solution ( a good approximation to reconstruct the sparse hopfield network @xcite , yielding a low inference error ) , then we search for the new solution to minimize the regularized cost function eq . ( [" +"the discovery of the planet around 51 pegasi ( mayor & queloz 1995 ) has spurred an avalanche of observations over the last 15 years , leading to a census of almost 700 confirmed planets to date . within this data we can find a variety of exotic and unexpected systems , such as planets with short orbital periods , extreme orbital eccentricities , or systems with strong resonant interactions . these observations have also inspired a wealth of theoretical work , on both the origin and structure of such planets . furthermore , planet searches have continued to push the observational thresholds towards lower masses , with current observations now probing below @xmath5 ( mayor et al . 2009a , b ; leger et al . 2009 ; howard et al . 2011 ; batalha et al . 2011 ) , with the hope of eventually finding planets that may convincingly be argued to be hospitable to life . despite the wealth of data and interpretation now available , it is still difficult to draw together the different elements into an overall synthesis , in large part because of the heterogeneous nature of the observations . however , in the next few years a variety of observations offer the possibility to provide new constraints , which may allow us to frame a rigorous context for planet formation and evolution . recently , howard et al . ( 2010 ) and mayor et al . ( 2011 ) published the results of volume limited radial velocity surveys of nearby sun - like stars . the importance of these studies is that one can now begin to compare the relative frequencies of different types of planets , illuminating which are the generic product of the planet formation process , and which are the exotica . the results suggest that lower mass planets ( @xmath6 ) are even more common than gas giants at short periods , and that they appear to form a distinct population for orbital periods @xmath7 days . particularly striking is the fact that the low - mass planet distribution appears to show an upper edge in a plot of mass versus orbital period ; planets are found with masses between the completeness limit of the survey and an upper limit ranging between @xmath8 at @xmath9 day and @xmath10 at @xmath11 days . this is in contrast to the results of the predominant planet population synthesis models ( e.g. ida & lin 2008 ; mordasini , alibert & benz 2009 ) , which predict that this mass range ( @xmath12 ) should be liberally populated with partially - accreted giant planet cores ( `` hot neptunes '' ) that have migrated in from larger radii . in addition to the radial velocity surveys , the kepler satellite has begun to release the contents of its large - scale transit catalogue ( borucki et al . 2011 , lissauer et al . the majority of the present sample are still unconfirmed ` candidates ' , but a variety of tests suggest that the true planetary yield from this sample is expected to be high ( borucki et al . 2011 ) . the kepler sample once again has the advantage of being drawn from a relatively homogeneous program , and the distribution of planetary radii supports the aforementioned claim that the dominant species of short period planets corresponds to radii and masses below that expected from gas giant planets ( howard et al . 2011 ; wolfgang & laughlin 2011 ; youdin 2011 ) . these new surveys highlight the importance of short - period low - mass planets , as the low - mass planets now appear to outnumber their more massive brethren . the origins of such hot neptunes and ` super - earths ' is still poorly understood . most models of their formation ( alibert et al . 2006 ; terquem & papaloizou 2007 ; raymond , barnes & mandell 2008 ; mordasini et al . 2009 ; ida & lin 2010 ; mcneil & nelson 2010 ) adopt the position that they form at larger radii , in a manner related ( if not similar ) to the planets uranus and neptune in our own solar system , and then migrate inwards , to be trapped closer to the star . however , quantitative comparisons with the properties of observed systems remain unsatisfactory ( mcneil & nelson 2010 ) . ultimately , many of the problems with these calculations stem from the properties of the migration models assumed . although the notion of gaseous disk migration has a long , physically motivated provenance ( e.g. goldreich & tremaine 1980 ; ward 1997 ) , the nature of the migration and when it occurs is still a subject of significant uncertainty ( see kley & nelson 2012 for a recent review ) . the principal reason for the revival of interest in migration models was the notion that hot jupiters were emplaced in this fashion ( e.g. lin , bodenheimer & richardson 1996 ) . however , it is becoming clear that these systems represent a small minority of all planetary systems ( e.g. howard et al . 2010 ; mayor et al . 2011 ) and may therefore reflect rather special circumstances . indeed , there is a growing accumulation of recent results demonstrating the misalignment of stellar spin and planetary orbits in many hot jupiter systems ( e.g. winn et al . 2011a and references therein ) . the simplest interpretation is that at least some hot jupiters did not migrate through a gas disk . furthermore , it is no longer clear that migration implies a monotonic inward motion ( e.g. paardekooper & mellema 2006 ; oishi , mac low & menou 2007 ; adams & bloch 2009 ) . with the large numbers of @xmath13 planets now seen at short periods , where the simplest migration models suggest they should not be , indicates that large radial movement need not be ubiquitous in planetary systems . motivated by this renewed skepticism , we have chosen to revisit the question of in situ accumulation of rocky planets on small scales , and to explore the consequences of planet assembly without significant late - time gaseous migration . however , we will consider the possibility that significant radial migration is possible for smaller bodies , before they accumulate into planets , and so we will allow for disks with a wide variety of masses , discussed in [ inventory ] . in [ accum ] we then present the results of a series of traditional in situ planetary accumulation models on scales of 0.051 au , from the resulting disks . in [ accretion ] we investigate the consequences of gas accretion onto the massive rocky cores that form . we address the role of jupiter mass planets in [ hotties ] and evaluate the possible role of photoevaporation in [ evap ] . the prototypical initial condition for assembly of a planetary system is the ` minimum - mass solar nebula ' ( weidenschilling 1977a ; hayashi 1981 ) , based on an estimate of the material required to form our own planetary system . the required surface density of solids ( based here on the hayashi estimate ) is @xmath14 with the gas surface density @xmath15 times larger . this applies interior to the ` snow line ' ( taken to be at @xmath16 au ) . exterior to the snow line the available material in solids is a factor of four higher , reflecting the fact that more volatile elements are able to condense and form solids as the nebular temperature drops . this enhancement brings the solid / gas ratio closer to the estimated metallicity of the sun , which presumably reflects the original composition of the nebular gas . if we integrate this surface density we infer a mass in solids of 3.3@xmath17 interior to 1 au , @xmath18 inside the snow line , and 25.5 @xmath17 within 10 au . this inventory is the minimum amount of mass required to match the solar system planets , but factors of two or three more are not unreasonable , if we assume a certain inefficiency in the process of converting nebular material into planets . in addition , many planet hosting stars are known to show super - solar atmospheric abundances ( gonzalez 1998 ; santos , israelian & mayor 2001 ; fischer & valenti 2005 ; udry & santos 2007 ) , often up to a factor of two . as such , we can reasonably argue for an increase in the above inventory of solids by a factor of five . thus , the simplest extension of the mmsn mass accounting could plausibly provide 17@xmath17 inside 1 au , 29@xmath17 inside the snow line , and 128@xmath17 inside 10 au . the above estimates are still very much in the spirit of the original mmsn model , in which solid material condenses out of a gaseous nebula and accumulates in situ to form planets from the local reservoir of material . however , the modern view of nebular and planetary evolution is considerably more dynamic . recent models have focused largely on the migration of planet - sized bodies , but it has been known for a long time that the dust and small rocks from which planets form are also potentially subject to significant radial migration ( weidenschilling 1977b ; nakagawa , sekiya & hayashi 1986 ; youdin & shu 2002 ; bai & stone 2010 ) . if a significant fraction of the solid material can migrate interior to 1 au while it is still in the form of small bodies , then the potential reservoir of material for the accumulation of terrestrial - class planets could be considerably larger . we will consider mass reservoirs up to 100 @xmath17 , corresponding to a radial concentration of mass by factors of at least 10 . the nature of the processes that produce such radial concentrations is still a subject of active research , and it is not guaranteed that the solids will preserve the same radial profile as the original gas disk . thus we will consider solid surface density profiles with a range of slopes . there is a long history of studies of terrestrial planet accumulation in our own solar system . we adopt the oligarchic model of kokubo & ida ( 1998 ) as our starting point , which provides an analytic prescription for a protoplanetary system consisting of a sequence of annuli , each dominated by a single planetary embryo . simulations of the last stages of gravitational interaction and accumulation of embryos into planets in this model , using n - body techniques ( chambers & wetherill 1998 , agnor , canup & levison 1999 ; chambers 2001 ; raymond , quinn & lunine 2006 ) , shows that configurations of three or four planets emerge naturally from a minimum mass solar nebula disk , although the low masses of mercury and mars in the solar system may require a more localised initial distribution of mass ( hansen 2009 ) . the production of multi - planet systems is fairly robust with respect to varying the amount of mass and the disk density profile ( raymond , quinn & lunine 2005 ; kokubo , kominami & ida 2006 ) , although the masses of the planets tend to scale with the reservoir mass . prior simulations of this process have generally restricted themselves to distances @xmath19 au because of the lack of any closer planet in the solar system ( and shorter timesteps add unecessarily to the computational burden ) . this is also often motivated on the basis of arguments regarding the chemistry of volatiles and a presumed reduction in the mass fraction that condenses out of the nebula" +"kohn - sham ( ks ) density functional theory ( dft ) @xcite is a computational quantum mechanical modeling method used to investigate the electronic structure of many - body systems ( atoms , molecules , and solids ) . in this theory , the ground - state energy of a many - electron system is determined by minimizing a functional of the spatially - dependent electron density rather than searching for the many - body wavefunction . although the exact energy functional has not been determined , approximate models for the functional have yielded accurate predictions for many classes of materials . dft has thus become one of the most widely used methods in electronic structure calculations @xcite . the minimization problem of dft can be recast into the solution of an effective one - electron - type schrdinger equation , the so - called kohn - sham equation , by introducing an effective potential . the ks equation is a nonlinear eigenvalue problem since the effective potential is a functional of the density . it is usually dealt with using a self - consistent field ( scf ) approach @xcite . in practical implementations , the single - electron wavefunctions need to be expanded in terms of some set of mathematical basis functions . the coefficients of the functions in this basis set are the primary values used to build a computational representation . for periodic solids , several different basis sets have been developed among which plane waves , the focus of the present paper . though it has a few drawbacks , this approach has many advantages which make it very popular in materials science and physics . various electronic structure calculation packages ( such as vasp @xcite , quantum espresso @xcite , abinit @xcite , ... ) rely on it . in general , a very large number of plane waves are needed to approximate the wave functions . so a large scale linear eigenvalue problem needs to be solved repeatedly after linearization by the scf method . due to the use fast fourier transform ( which has contributed to the success of this approach ) , large scale parallelization is hard to achieve for the plane - wave method . besides , the solution for the large scale eigenvalue problems requires large scale orthogonal operation and orthogonality needs global operations , which is also the bottleneck of the large scale parallelization . various methods have been proposed for solving the associated eigenvalue problems . the davidson iterative diagonalization @xcite , which reduces to a dense matrix diagonalization , is also hard to parallelize efficiently . the conjugate - gradient - like band - by - band diagonalization @xcite , which uses less memory and is more robust , is inherently sequential . it is actually quite challenging to improve parallel efficiency of plane - wave dft codes on today s supercomputer platforms . in this paper , following ref . @xcite , we propose some parallel orbital - updating based plane - wave basis methods for solving the kohn - sham equation , which improve the scalability of parallelization . in our approach , the solution of the eigenvalue problem is replaced by the solution of a series of independent source problems and some small scale eigenvalue problems . because of the independence of the source problems , these source problems can be solved in parallel essentially . for each source problem , the traditional parallel strategies ( for example , domain decomposition or parallelization in matrix - vector multiplication ) can be used to deal with it in parallel . therefore , our new methods allow for a two - level parallelization : one level of parallelization is obtained by partitioning these source problems into different groups of processors , another level of parallelization is obtained by assigning each source problem to several processors contained in each group . this two - level parallelization makes our new methods more competitive for the large scale calculations . the rest of this paper is organized as follows . first , we provide some preliminaries for the kohn - sham equation , the plane - wave discretization , and scf iteration . then , we propose our new parallel orbital - updating based plane - wave basis methods . next , we implement our algorithms in the software package quantum espresso , and use some numerical experiments to show the efficiency of our new methods . finally , we give some concluding remarks . according to the basic principles of quantum mechanics , the physical properties of a system of @xmath0 interacting electrons in an external potential @xmath1 can be obtained by solving the time - independent schrdinger equation : @xmath2 \psi(\mathbf{r}_1 , \ldots , \mathbf{r}_n ) = e^\mathrm{el}_n \psi(\mathbf{r}_1 , \ldots , \mathbf{r}_n),\ ] ] where @xmath3 are the coordinates of the electrons @xmath4 , @xmath5 is the total electronic energy of the eigenstate @xmath6 and @xmath7 is the electronic wave function . atomic units are used throughout this work @xmath8 . typically , the external potential can be the one due to @xmath9 nuclei in which case : @xmath10 where @xmath11 and @xmath12 are the charges and the positions of the nuclei @xmath13 . dft provides a way to systematically map the many - body ( interacting electrons ) problem onto a single - body problem ( fictiously non - interacting electrons ) in an effective potential @xmath14 in order to determine the ground - state energy @xmath15 by expressing it as a functional of the electronic density : @xmath16 basically , one needs to solve the so - called kohn - sham equation . the kohn - sham equation of a system consisting of @xmath9 nuclei of charges and @xmath0 electrons is the following nonlinear eigenvalue problem @xmath17 @xmath18 where @xmath0 is the number of electrons , @xmath19 is the electron density , @xmath20 is the hartree potential , @xmath21 is the exchange - correlation potential and @xmath22 , defined by , is the external potential due to the nuclei . the ground - state energy of the system of @xmath0 electrons is given by : @xmath23+\int v_\mathrm{ext}(\mathbf{r } ) \rho(\mathbf{r})\;d\mathbf{r } + e_\mathrm{h}[\rho ] + e_\mathrm{xc}[\rho].\ ] ] the kinetic energy @xmath24 $ ] is defined by @xmath25= \sum_{i=1}^{n } -\frac{1}{2 } \int \psi^*_i(\mathbf{r})\delta \psi_i(\mathbf{r})\;d\mathbf{r},\ ] ] which is not the true kinetic energy of the system of interacting electrons . the hartree energy @xmath26 $ ] is given by : @xmath27 = \frac{1}{2 } \int \int \frac{\rho(\mathbf{r})\rho(\mathbf{r}')}{|\mathbf{r}'-\mathbf{r}|}\;d\mathbf{r}d\mathbf{r}'.\ ] ] dft is exact in principle , however , the exchange - correlation functional @xmath28 $ ] as well as @xmath29(\mathbf{r})$ ] are not known and must be approximated . we implement the variational method in to get the weak formulation of kohn - sham equation : find @xmath30 , @xmath31 , such that @xmath32 where @xmath33 from the density functional theory , we know that the ground state of the system can be obtained by solving the lowest @xmath0 pairs of eigenvalues and eigenvectors of the kohn - sham equation . we now consider the periodic boundary conditions in a large volume @xmath34 that is allowed to go to infinity . in periodic solids , there is an infinite number of non - interacting electrons moving in an infinite external potential ( such as the one generated by an infinite number of nuclei ) . however , bloch s theorem @xcite can be invoked to express the wavefunction as the product of a cell - periodic part and wavelike part , whose wavevector is drawn from the first brillouin zone ( bz ) of the reciprocal lattice : @xmath35,\ ] ] with @xmath36 where @xmath37 are the lattice vectors . the infinite number of electrons in the solid is thus accounted for by an infinite number of @xmath38 points in the bz , and only a finite number of electronic states are occupied at each @xmath38 point . for instance , the electronic density is given by : @xmath39 where @xmath40 is the number of occupied states . furthermore , the electronic wavefunctions at @xmath38 points that are very close will be very similar . hence , it is possible to represent the electronic wavefunctions over a region of the bz by the wavefunctions at a single @xmath38 point . this can be exploited for replacing integrals over the bz by a weighted sum on a discrete mesh of well - chosen @xmath38 points . for instance , the one for the electronic density becomes : @xmath41 where @xmath42 are the weights associated to the special @xmath38-points @xmath43 with @xmath44 . in the case of an homogeneous mesh , all the weights are equal and given by @xmath45 . the accuracy of the calculations can always be increased by using a denser set of special @xmath38-points . in semiconductors , a modest number is sufficient to achieve a well - converged sampling density because of the smoothly varying nature of ks states in @xmath38-space . in metals , however , much denser grids are required due to the abrupt change in the occupancy of each state with the wavevector @xmath38 . the cell - periodic part of the wavefunctions can conveniently be represented as an expansion in terms of some set of mathematical basis functions . the coefficients of the functions in this basis set are then the primary values used to build a computational representation . many different basis sets have been developed for use in periodic solid - state calculations ( see ref . @xcite for a detailed description ) . the most natural ( due to the periodicity ) and popular ( due to its ease of use ) is the plane - wave basis set . each function @xmath46 is expressed as a fourier series whose basis states are plane waves whose wavevector is a reciprocal lattice vector @xmath47 ( which are defined by @xmath48 ) : @xmath49.\ ] ] so a wave function can be written as @xmath50,\ ] ] where @xmath51 are the expansion coefficients of the wave function . due to the fact that the coefficients @xmath51 for the plane waves with small kinetic energy @xmath52 are typically more important than those with large kinetic energy @xcite , the plane - wave basis set can be truncated to include only plane waves that have kinetic energies less than some particular cutoff energy @xmath53 , i.e. @xmath54 the plane waves form an orthonormal basis set and do not depend on the location of the nuclei which simplifies the form of the equations and their implementation . furthermore , the size of the basis set ( and therefore the accuracy of the calculations ) can be systematically increased and easily controlled by a single parameter , the cut - off energy @xmath53 @xcite , retaining only those @xmath47-vectors such that @xmath55 . there are however two important disadvantages over other basis sets . first , the number of basis functions required is quite large , which increases computational cost . second , it is quite difficult to represent sharp peaks in the ks states , such as those occurring in the core regions near nuclei due to the singularity of the electron - nuclear coulomb attraction . the states in the core region have however a negligible contribution to the electronic properties of a material . therefore , it is not necessary to represent them or the coulomb potential exactly . first , the states localized entirely within a core region , called core states , may be precomputed ( the frozen core approximation ) , avoiding the need to include them explicitly in the calculation . second , the coulomb potential in the core regions can be replaced with a pseudopotential which is constructed to reproduce the atomic scattering properties and coulombic form outside the core region , but which is weaker and smoother inside ." +"the nature of active galactic nuclei ( agns ) is still an open problem . photometric observations of agns are important for constructing their light curves and to study their variation behavior on different time scales . blazars are an extreme subclass of agns and often show large and violent variations . the variability on very short time scales from minutes to hours is a common property of blazars , and is observed in many objects ( rieke et al . 1976 ; smith et al . 1987 ; sillanpaa et al . 1991 ; carini et al . 1992 ; romero et al . 1994 , 1995a , b , 1997 , 2000 ; heidt & wagner 1995 ; miller & noble 1996 ; villata et al . 1997 , 1999 ; terasranta et al . 1998 ; takalo 1994 ; bai et al . 1999 ; kraus et al . 1999 ; raiteri et al . 1999 ) . bl lacertae ( pks 2200 + 420 ) , the archetype of its class , lies in a giant elliptical galaxy at a redshift of @xmath0 ( miller et al . it is one of the best - studied objects . superluminal components have been observed from the source ( mutel & phillips 1987 ; vermeulen & cohen 1994 ; fan et al . 1996 ; xie et al . , 1992 , 1994 ; webb et al . 1988 ; 1998 ; catanese et al . 1997 ; qin & xie 1997 ; fan et al . 1998a , b ; fan & lin 1999 , 2000 and reference therein ) . its spectrum is usually featureless , but weak emission lines are indeed identified when the source is in the fainter state ( corbett et al . the optical variability is extremely irregular over periods of hundreds of days of continuous observation but a possible @xmath1 14-year period was found in the b light curve ( see fan et al . in addition , some rapid variability over short time scales has been reported : for example , a variation of 1.5 magnitude over a time scale of 20 hours ( weistrop , 1973 ) , daily variation as great as 0.3 magnitude ( carswell et al . 1974 ) , and variation of 0.1 magnitude over 30 minutes in the v band ( corbett et al . 1996 ) . during the 1997 outburst period , it was widely observed in optical bands by many groups ( nesci et al . 1998 ; bai et al . 1999 ; kovael et al . 1999 ; massaro et al . 1999 ; matsumoto et al . 1999 ; miller et al . 1999 ; nikolashvili et al . 1999a , b ; sobrito et al . 1999 ; tosti et al . 1999a , b ; qian et al . 2000 ; ghosh et al . 2000a , b and reference therein ) . bl lacertae is also one of the sources in our observing program . to investigate their short time - scale variability , we have made optical observations of blazars with the 1-m telescope at yunnan astronomical observatory ( yao ) , the 1.56-m telescope at shanghai observatory ( shao ) , and the 2.16-m telescope at beijing observatory ( bao ) ( fan et al . 1997 , 1998a ; qian et al . 2000 ; xie et al . 1992 , 1994 ) . in this paper , we present the bl lacertae optical photometry observed with the 1.56-m telescope at shao during the period 1997 to 1999 . in section 2 , we present the data and analysis ; in section 3 , a brief conclusion . bl lac is one of the regularly monitored objects at shao using the @xmath2 cassegrain focus of the 1.56 m telescope with a liquid nitrogen cooled photometric 200 series ccd camera having @xmath3 pixels . the filters are standard johnson and cousins bvri filters . the field of view is 417 `` , with 1 pixel=0.25 '' . the exposure times are typically set according to the sky conditions . the seeing at the sheshan station of shao usually varies from 1.2 `` to 1.5 '' . the obtained frames were processed with the photometric task apphot of the iraf software package after bias , dark and flat - field corrections . the bias frames were taken at the beginning and the end of the night observation . in addition , some were taken in the middle of the observations . sky flat - field images were taken at dusk and dawn where possible . otherwise , a dome flat was used . the dark and the flat - field corrections are 0.01 to 0.02 mag , mainly contributed by the flat - field . we used stars b and c ( smith et al . , 1985 ) as photometric comparison stars . their colors are @xmath4 , @xmath5 for b and @xmath6 , @xmath7 for c while their magnitudes are @xmath8 , @xmath9 , @xmath10 for b and @xmath11 , @xmath12 , @xmath13 for c. based on the long - term data , the colors of bl lacertae are @xmath14 and @xmath15 on average , while the magnitudes are in the ranges : v = 10.52 to 15.25 , r = 11.78 to 14.91 , and i = 10.74 to 14.19 ( fan et al . because the colors of the comparison stars are similar to those of bl lacertae while the magnitudes of the comparison stars are in the magnitude range of bl lacertae , the reduction of the photometry is simplified , with no needed corrections for color or non - linearity . we determined differential magnitudes of bl - b and b - c from the instrumental magnitudes of bl lacertae ( bl ) , the star b ( b ) , and star c ( c ) . the curves b - c indicate observational uncertainties and the intrinsic variability of the stars . the variability of the target object bl lacertae is investigated by means of the variability parameter , @xmath16 , introduced by romero et al . ( 1999 , see also cellone et al . 2000 ) . to do so , we determine the scatter of the differential magnitudes bl - b and b - c , @xmath17 and @xmath18 , the variability parameter @xmath16 is expressed as @xmath19 . if @xmath20 , then the target is variable . the rms errors are calculated from the two stars using the formula : @xmath21 where @xmath22 is the differential magnitude of stars b and c while @xmath23 is the differential magnitude averaged over the entire dataset , and @xmath24 is the number of the observations on a given night . the results are given in table 1 for filters v , r and i. column ( 1 ) is the julian date , column ( 2 ) the v magnitude , column ( 3 ) the uncertainty in v , column ( 4 ) the r magnitude , column ( 5 ) the uncertainty in r , column ( 6 ) the i magnitude , and column ( 7 ) the uncertainty in i. the light curves are shown in figure 1 for the bands r , v and i. during the 1997 outburst , rapid variations of @xmath25 over 90 minutes by sobrito et al . ( 1999 ) and @xmath26 over 40 minutes by matsumoto et al . ( 1999 ) were found ( see also nesci et al . our observations show that in the period jd 2450692 to jd 2450702 , a variation of about 1 mag over a week is found in the three bands . in the period jd 2450701 to jd 2450701.5 , variations of 0.40mag , 0.27mag , and 0.21mag over a time scale of 100 minutes were found in the v , r , and i wavebands ( see fig . 2 ) suggesting that the variations decrease with increasing wavelength , consistent with the findings of nikolashvili et al . ( 1999a ) . no similar rapid variation was found in our other observations of the source during our monitoring period 1997 to 1999 , which suggests that this does not happen often . the corresponding variability parameters @xmath27 are greater than 10.0 . after the 1997 outburst , it dimmed to a very low state ( fig . 1 ) , with r = 14.76 on jd 2450738 , and then brightened again . the brightening tendency is consistent with the later observation of a high state of r = 12.44 on jd 2451514.32 ( massaro & nesci 1999 ) . on jd 2451328.5 r = 13.10 was observed by tosti & nucciarelli ( 1999 ) . on those days , we have no observations , but our data ( r = 13.24 on jd 2451104 and r = 13.18 on jd 2451379 ) combined with those by tosti & nucciarelli ( 1999 ) , and massaro & nesci ( 1999 ) suggest a brightening tendency . bl lacertae was observed in v , r , and i bands from 1997 through 1999 , which makes it possible for us to discuss the correlated variability among the colors . we analyzed our time - series data to search for time lag using the method of discrete correlation function ( dcf ) ( edelson & krolik 1988 ; also see fan et al . 1998c , and tornikoski et al . 1994 ) . first , we calculated the set of unbinned correlation coeffieient ( udcf ) between data points in the two data streams @xmath28 and @xmath29 , i.e. @xmath30 where @xmath31 and @xmath32 are points in the data sets , @xmath33 and @xmath34 are the average values of the data sets , and @xmath35 and @xmath36 are the corresponding standard deviations . secondly , we averaged the points sharing the same time lag by binning the @xmath37 in suitably sized time - bins in order to get the @xmath38 for each time lag @xmath39 : @xmath40 where @xmath41 is the total number of pairs . the standard error for each bin is @xmath42^{2}\}^{0.5}.\ ] ] the results for time bins of 0.2 days are shown in fig . 2 for v vs. r , r vs. i , and v vs. i respectively . no time delay longer than 0.2 day is found between any two bands . bl lacertae is a variable source through the whole magnetic waveband , and has been observed intensively . in this paper , we presented our measurements of v , r , and i bands for the period of 1997 to 1999 . short time scale variability over @xmath1 100 minutes was found in the three bands , with the variation amplitude found to decrease with wavelength . this variation property was also noted by other authors . the optical variations are found to be correlated with no time delay exceeding 0.2 days . the authors thank dr . wills for the comments and suggestions that improve the paper . jhf thanks dr . g.e . romero for his comments . this work is supported by the national scientific foundation of china ( 19973001 ) and the national 973 project of china ( nkbraf g19990754 ) . bai , j.m . , xie , g.z . , & li , k.h . et al . 1999 , a&as , 136 , 455 carini m. t. , miller h. r. , noble j. c. , goodrich b. d. 1992 , aj 104 , 15 catanese , m. , akerlof , c.w . biller , et al . 1997 , apj , 480 , 562 corbett , e. robinson , axon , d.j . hough , j. et al . 1996 , mnras , 281 , 737 edelson" +"loss of fidelity and decoherence are the twin obstacles to successful applications of quantum information devices . theoreticians like to consider the two separately , while in practical situations both will have destructive effects on quantum information flow . in this spirit it is important to propose a functional definition for the fidelity or better the fidelity amplitude of an open system . to achieve this we shall build on previous work . almost 20 years ago a measurement of the fidelity amplitude in a quantum system was proposed @xcite , though the word itself was not mentioned . a more detailed presentation for a kicked rotor followed years later @xcite , simultaneously with an extensive discussion of the theoretical framework @xcite . the experiment for the kicked rotor was performed successfully in ref . the basic idea is that pure dephasing between a qubit and some system will cause the off diagonal elements or coherences of the density matrix of a pure superposition state of the qubit decay like the fidelity amplitude of the remaining system . our proposition is to follow exactly the same reasoning in the case where the remaining system is open , and thus interpret the decaying coherences as a generalized fidelity amplitude of the intermediate system . for this purpose we have to consider a situation discussed in a previous paper @xcite , where a central system coupled to two nested environments is analyzed to determine the effect of a far environment on the coherence of a central system not interacting directly with the far environment . the intermediate system or `` near environment '' would then be the open system we are analyzing using the qubit as a probe and as the source of the perturbation causing the fidelity decay in the absence of the far environment . our paper will thus fulfill a double purpose : on the one hand we shall introduce a generalized fidelity amplitude and study its behaviour in a `` quantum chaotic '' setting . on the other we shall deepen the understanding of the stabilizing effect on the central system of the coupling of the near environment to a far environment . note that in a previous paper @xcite we introduced pure dephasing between the central system and the near environment , as a simplifying approximation to facilitate calculations , but for the present context this is an essential feature needed in order to establish the relation to fidelity decay of a closed system . considering near and far environment as one closed system , the fidelity amplitude may be expressed as the expectation value of an echo operator @xcite , which describes the forward and backward evolution of an initial state with somewhat different hamiltonians . in the present paper we shall derive a master equation which describes this echo dynamics reduced to the near environment alone . this master equation has the typical structure of master equations of kosakowski - sudarshan - lindblad form @xcite ( henceforth referred to as lindblad equation ) and reduce to lindblad form when the coupling to the central system becomes zero . we then consider the random matrix model already used in ref . @xcite . in that case , the master equation becomes very simple , and allows to obtain a closed integral equation for the generalized fidelity amplitude . we compare the solution of the integral equation with the generalized fidelity amplitude obtained from numerical simulations , and thereby show that the new integral equation applies for a very broad range of coupling strengths between near and far environment . while the random matrix model used here , is much simpler than the one used in ref . @xcite , its effect on the fidelity amplitude is typically indistinguishable . in the next section we shall fix notations and obtain the general master equation for describing the reduced echo dynamics in the near environment . at the end of this section , we derive the master equation for the random matrix model , which is largely equivalent to the model considered in @xcite . in sec . [ n ] we compare the generalized fidelity amplitude obtained from the new integral equation with numerical simulations , and in the last section we draw conclusions . in this section we describe the model in general . the full system consists of three parts , the central system , the near environment and a far environment . in the following section ( sec . [ mh ] ) we start from a hamiltonian formulation , and perform partial traces in order to obtain the reduced dynamics either in the central system or in the near environment . assuming a dephasing coupling between central system and near environment , we can obtain the temporal evolution of the reduced density matrix in the central system , in terms of an asymmetric unitary evolution ( perturbed echo dynamics ) in the composite environment . in sec . [ mm ] we then use the standard born - markov approximation to trace out the far environment , and thereby arrive at a master equation for the reduced echo dynamics in the near environment alone . for the coupling between central system and near environment , we assume that it is of the dephasing type , i.e. that it is given by a single product term , where the factor acting in the central system commutes with the hamiltonian describing the dynamics in the central system . thus , the hamiltonian for this part is given as @xmath0= 0 \ ; . \label{mh : hlambda}\ ] ] this leads to the following expression for the time evolution of the reduced density matrix in the central system @xcite @xmath1 \ ; , \ ] ] which yields for its individual matrix elements ( coherences ) @xmath2 \ ; . \label{mh : fidamp0}\ ] ] here , we use the common eigenbasis of @xmath3 and @xmath4 to express @xmath5 , and therefore the energies @xmath6 and @xmath7 are simply the corresponding eigenvalues of @xmath3 . in what follows we will focus on only one such matrix element , and therefore suppress the indices @xmath8 from now on . we thus set @xmath9 which implies that @xmath10 . this shows that under dephasing coupling , the decoherence in the central system is given by the decay of the fidelity or lohschmidt echo in the near environment . turning the argument the other way around , this shows that it is possible to measure fidelity amplitudes , by coupling the system of interest ( i.e. the near environment ) to a probe system , which at the same time provides the perturbation . such experiments have been proposed and recently realized in different settings using atom interferometry @xcite . [ [ including - the - far - environment ] ] including the far environment + + + + + + + + + + + + + + + + + + + + + + + + + + + + + we now extend the model to include a far environment . we assume the far environment to be as simple as possible and that it allows to be taken into account implicitly in the form of a quantum master equation . hence , we write for the hamiltonian of the full tripartite system : @xmath11 where @xmath12 . here , @xmath13 and @xmath14 are normalized in such a way that @xmath15 gives the magnitude squared of a typical matrix element of the coupling term between near and far environment . with @xmath16 being the average level spacing ( i.e. the inverse level density ) in the spectrum of @xmath17 , we see that @xmath18 is just @xmath19 times the corresponding fermi golden rule transition rate @xcite . finally , @xmath18 itself is related to the decoherence rate for a superposition of @xmath19 states in the near environment . in the simplest case ( see sec . [ n ] ) , @xmath20 is precisely the decay rate of the purity in the intermediate system , in the case where the coupling to the central system is set to zero . within the hamiltonian model described by @xmath21 , the coupling to the far environment requires the following modification to the expression for the fidelity amplitude given in eq . ( [ mh : fidamp0 ] ) : @xmath22 \ ; . \label{mh : fidampgen}\ ] ] differing from the standard formalism , the unitary operators on the left and on the right hand side of the initial state are different . this is why the trace may decrease in time , leading to the loss of coherence for superposition states in the central system @xcite . we follow the standard derivation of the born - markov approximation , e.g. sec . 3.3 of ref . however , due to the asymmetric unitary transformation implied in eq . ( [ mh : fidampgen ] ) , the following derivation requires some care . let us denote the solution in the hilbert space of near and far environment as @xmath23 and thereby introduce @xmath24 as the solution in the interaction picture with respect to the coupling between near and far environment . from the von neumann equation for @xmath25 , @xmath26 we obtain@xmath27 \ ; , \qquad \tilde v_\lambda(t)= { { \rm e}}^{{{\rm i}}h_{\lambda,0}\ , t/\hbar}\ ; v_{{\rm e}}'\otimes v_{\rm f}\ ; { { \rm e}}^{{{\rm i}}h_{0,0}\ , t/\hbar } \ ; . \label{mm : xevolve}\ ] ] the aim of the born - markov approximation ( to be worked out next ) consists in obtaining a master equation for the reduced dynamics in the near environment alone . that is , an evolution equation for @xmath28 $ ] which may not be considered a real quantum state , since for the reasons discussed above , @xmath29 is neither hermitian nor trace - preserving . this quasi - density operator is related to @xmath24 as follows : @xmath30 = { \rm tr}_{\rm f}\big [ u_\lambda(t)\otimes u_{\rm f}(t)\ ; x(t)\ ; u_0(t)^\dagger\otimes u_{\rm f}(t)^\dagger\ , \big ] \ ; , \end{aligned}\ ] ] where @xmath31 and @xmath32 , since @xmath33 and @xmath34 are both separable operators . using the identities @xmath35 = a\ ; { \rm tr}_{\rm f } [ x\ , ] \ ; , \quad { \rm tr}_{\rm f}\big [ x\ ; b\otimes\one\ , \big ] = { \rm tr}_{\rm f } [ x\ , ] \ ; b \notag\\ & { \rm tr}_{\rm f}\big [ \one\otimes a\ ; x\ , \big ] = { \rm tr}_{\rm f}\big [ x\ ; \one\otimes a\ , \big ] \ ; , \end{aligned}\ ] ] we find @xmath36\ ; . \label{mm : rhoetilde}\ ] ] [ [ born - markov - approximation ] ] born - markov approximation + + + + + + + + + + + + + + + + + + + + + + + + + now , we will formally integrate the differential equation for @xmath24 , eq . ( [ mm : xevolve ] ) , and plug the result back into its right hand side : @xmath37 \notag\\ & \qquad - \gamma\ ; \big [ \ , \varrho_{\rm e , f}(0 ) - \frac{{{\rm i}}\gamma}{\hbar}\int_0^t{{\rm d}}\tau\ ; \big ( \ , \tilde v_\lambda(\tau)\ , x(\tau ) - x(\tau)\ , \tilde v_0(\tau)\ , \big ) \ , \big ] \ ; \tilde v_0(t ) \notag\\ & = \gamma\ ; \big [ \ , \tilde v_\lambda(t)\ ; \varrho_{\rm e , f}(0 ) - \varrho_{\rm e , f}(0)\ ; \tilde v_0(t)\ , \big ] - \frac{{{\rm i}}\gamma^2}{\hbar}\int_0^t{{\rm d}}\tau\ ; \big [ \ , \tilde v_\lambda(t)\ ; \big ( \ , \tilde v_\lambda(\tau)\ , x(\tau ) - x(\tau)\ , \tilde v_0(\tau ) \ , \big ) \notag\\ & \qquad\qquad\qquad - \big ( \ , \tilde v_\lambda(\tau)\ , x(\tau ) - x(\tau)\ , \tilde" +"materials with correlated electrons exhibit some of the most intriguing quantum states in condensed matter physics @xcite . since the number of electric charge carriers essentially determines such states , external electric or light field can be applied for controllable manipulations . stability of electric field or light induced states has been demonstrated in some novel systems , where switching occurs between neighboring equilibrium thermodynamic states @xcite . this powerful characteristic can be applied in electric devices such as transistors and memories , which are of great importance to not only the fundamental physics research but also the information processing technology @xcite . correlated materials with a rich set of quantum states delicately balanced on a similar energy scale will be promising platforms to realize such devices . ( a ) crystal structure of @xmath0-tas@xmath1 . ( b ) top view of ta - ta plane of @xmath0-tas@xmath1 . the unit cells of conventional @xmath0 structure and low temperature ccdw structure are denoted with green solid and dashed lines , respectively . the black hexagrams are the so - called `` david star '' pattern in ccdw phase . ( c ) schematic diagrams of `` david star '' ( left ) , ccdw ( middle ) , and nccdw ( right ) in @xmath0-tas@xmath1 . ] the transition metal dichalcogenide ( tmd ) @xmath0-tas@xmath1 is one of the promising candidate due to the multiple competing ground states in it @xcite . as shown in fig . [ fig_1_structure ] ( a ) , @xmath0-tas@xmath1 shows a cdi@xmath1-type layered crystal structure with ta atoms octahedrally coordinated by s atoms . a unit layer consists of one ta layer sandwiched between two s layers . at low temperatures , strong @xmath4-dependent electron - phonon coupling induced periodic lattice distortion makes a @xmath5 superlattice @xcite , in which ta atoms displace to make `` david star '' clusters ( fig . [ fig_1_structure ] ( b ) ) . the outer twelve atoms within each star move slightly towards the atom at the center , leading to the commensurate charge - density - wave ( ccdw ) ground state . in particular , in ccdw state , the correlation effect of @xmath6 electrons of ta atoms turns the system into mott insulating state @xcite . upon heating to 225 k , it undergoes a sequence of first order phase transition to a nearly commensurate ( nc ) cdw . the nccdw phase is composed of metallic incommensurate ( ic ) network and mott insulating ccdw domains . the ccdw domains shrink upon heating and finally disappear at 355 k , while the system transforms to iccdw state . the standard metallic @xmath0 structure appears above 535 k. moreover , when ccdw state is suppressed , superconductivity emerges in this system @xcite . one can expect that the controllable switching between those states will be helpful for figuring out the mechanism of cdw and superconductivity , and realizing the high performance memory and transistor in future technology . to meet this goal , many groups performed investigations on this novel material . yu et al . reported a gate - controlled li ion intercalation can suppress ccdw and introduce superconducivity @xcite . tsen et al . @xcite , hollander et al . @xcite , yoshida et al . @xcite , and mihailovic et al . @xcite reported the in - plane electric field induced transition from ccdw state to nccdw or some metastable hidden state . cho et al . applied perpendicular electric pulse on @xmath0-tas@xmath1 and found positive electric pulse can introduce ic network to suppress mott state at low temperature @xcite . moreover , zhang et al . @xcite , mihailovic et al . @xcite , and han et al . @xcite suggested that light can introduce a transition from ccdw state to nccdw or hidden state as well . in all those manipulations , the transitions are considered to be determined by the charge carrier doping . however , the mechanisms of such transitions are not fully clear yet . in this work , we simulated by first - principles calculations the charge carrier doping effect on cdw in @xmath0-tas@xmath1 . we found that ccdw is stable upon electron doping , while hole doping significantly suppresses ccdw instability , implying different mechanisms of recently reported electric and photoelectric manipulations of cdw in @xmath0-tas@xmath1 . we figured out such mechanism by analysis of carrier doping effects . furthermore , we show that superconductivity with @xmath2 about @xmath3 k can be introduced by hole doping in the system . the density functional theory ( dft ) calculations were carried out using quantum espresso package @xcite with ultrasoft pseudopotentials . the exchange - correlation interaction was treated with the generalized gradient approximation ( gga ) with pw91 parametrization @xcite . the energy cutoff for the plane - wave basis set was 35 ry . the marzari - vanderbilt fermi smearing method @xcite with a smearing parameter of @xmath7 ry was used for the calculations of the total energy and electron charge density . to simulate the monolayer , a vacuum layer more than 15 @xmath8 was introduced . for the bulk sample , brillouin zone sampling is performed on the monkhorst - pack ( mp ) mesh @xcite of @xmath9 , while a denser @xmath10 grid was used in the electron phonon coupling calculations . phonon dispersions were calculated using density functional perturbation theory ( dfpt ) @xcite with an @xmath11 mesh of @xmath12-points . for the monolayer sample , @xmath13-points grids of @xmath14 and @xmath15 and @xmath12-points grids of @xmath16 are used . since the frequency and stability of soft phonon modes were found to be very sensitive to the plane - wave cutoff for the charge density , a large cutoff of 1500 ry was used for the charge density in the phonon calculations @xcite . all the calculation parameters were well tested . in the investigation of carrier doping effects , the electron / hole doping was simulated by increasing / decreasing the total electron numbers of the system , together with a compensating uniform positive / negative background to maintain the charge neutrality . the crystal structure of each doped sample was optimized with respect to lattice parameters and atomic positions . for comparisons , we also calculated some doped samples by using the lattice parameters of pristine tas@xmath1 and relaxing the atomic positions , as described later . the low symmetry cdw structure is usually considered as the high symmetry phase with distortion introduced by some instability . therefore , we firstly investigated carrier doping effects in the bulk @xmath0-tas@xmath1 . the electronic structures and phonon properties for the samples with different doping level were calculated . as examples , figure [ fig_2_bulk ] shows the calculated band structures and fermi surfaces of the pristine bulk @xmath0-tas@xmath1 , the doped bulk @xmath0-tas@xmath1 with the doping level of @xmath17 electrons / f.u . , and the doped bulk @xmath0-tas@xmath1 with @xmath17 holes / f.u . as expected , electron doping increases the lattice parameters and hole doping shrinks the lattice ( figs . [ fig_2_bulk ] ( j ) and ( k ) ) . for the pristine tas@xmath1 , our results are of good agreement with the previous calculations @xcite . there is a gap of @xmath18 ev below fermi energy ( @xmath19 ) ( fig . [ fig_2_bulk ] ( b ) ) . in the @xmath20-@xmath21 direction , the two bands around the gap are nearly flat due to the quasi-2d nature of the layered structure . the band above the gap crosses fermi energy ( @xmath19 ) , forming a 2d electron pocket around @xmath22 point ( figs . [ fig_2_bulk ] ( b ) and ( e ) ) . such gap increases upon electron doping and decreases upon hole doping ( figs . [ fig_2_bulk ] ( a ) and ( c ) ) . electron doping increases @xmath19 . as shown in figs . [ fig_2_bulk ] ( a ) and ( d ) , for the doped bulk @xmath0-tas@xmath1 with @xmath17 electrons / f.u . the rise of @xmath19 expands and opens up the original electron pockets around @xmath22 , leaving hole pockets centered at @xmath23 point . besides the original band crossing @xmath19 , a band with higher energy starts to cross @xmath19 , forming a 2d cylinder - like electron pocket around the zone center . on the contrary , the hole doping enhances the dispersion in the @xmath20-@xmath21 direction and weakens the quasi-2d nature by shrinking the lattice and decreasing the interlayer distance . as shown in figs . [ fig_2_bulk ] ( c ) and ( f ) , for the doped bulk @xmath0-tas@xmath1 with @xmath17 holes / f.u . , the bands close to @xmath19 are not flat anymore . hole doping reduces @xmath19 . the decrease of @xmath19 shrinks the original electron pockets around m point . moreover , a lower energy band starts to cross @xmath19 , forming a 3d hole pocket around @xmath20 point . the phonon instability of the high symmetry structure is considered to be directly related to the cdw distortion : at high temperatures , the phonon of the high symmetry structure softens at cdw vector ( @xmath24 ) . above the transition temperature the phonon frequency near @xmath24 drops but does not go to zero . just below the transition temperature the phonon frequency near @xmath24 is imaginary , meaning there is a restructuring of lattice with a superlattice vector of @xmath24 @xcite . therefore , phonon dispersion without imaginary frequency implies that the structure is stable compared to cdw structure . the phonon calculation is proved to be an effective method to simulate the cdw instability : the calculated phonon dispersions show instability just locating at @xmath24 of some tmds @xcite . more specially , for the present @xmath0-tas@xmath1 , experimental report showed cdw can be suppressed by pressure @xcite , which is correctly simulated by liu s phonon calculation @xcite . in this work we also performed the phonon calculations on each sample . for the pristine @xmath0-tas@xmath1 , our calculation is of good agreement with liu s calculation ( fig . [ fig_2_bulk ] ( h ) ) . the phonon dispersion show instability very close to the ccdw vector @xmath25 . this instability persists at all values of @xmath26 , as shown in inset of fig . [ fig_2_bulk ] ( h ) . for the electron doped sample , the acoustic branches become more unstable . as shown in fig . [ fig_2_bulk ] ( g ) , the unstable modes in the doped bulk @xmath0-tas@xmath1 with with @xmath17 electrons / f.u . appear in @xmath23-@xmath22 and @xmath23-@xmath20 directions , indicating the area of instability are largely expanded . on the contrary , the hole doping significantly stabilizes lattice . as shown in fig . [ fig_2_bulk ] ( i ) , no unstable mode can be found in the phonon dispersion of the doped bulk @xmath0-tas@xmath1 with @xmath17 holes / f.u . since the lowest mode in the pristine tas@xmath1 locates near @xmath27 , we used such mode as an indicator of doping effect on ccdw in tas@xmath1 . the frequency variation of such mode under doping is shown in fig . [ fig_2_bulk ] ( l ) . one can note that upon electron doping the mode is always unstable in bulk @xmath0-tas@xmath1 , while hole doping significantly suppresses the instability . according to our calculation , the lattice becomes completely stable when the doping level is higher than @xmath28 electrons / f.u . since hole doping shrinks the lattice as the high pressure does , we should figure out the suppression of ccdw under hole doping is majorly attributed to whether the lattice compression or to the pure doping effect . we calculated a hypothetic doped @xmath0-tas@xmath1 with n=0.3 holes /" +"the in - medium properties of the vector mesons ( @xmath1 and @xmath0 ) in hot and dense matter have an important role to play in the low mass dilepton production resulting from heavy ion collision experiments . this has , hence , been a topic of great interest in the recent past , both experimentally @xcite and theoretically @xcite . the experimental observation of enhanced dilepton production @xcite in the low invariant mass regime could be due to a reduction in the vector meson masses in the medium . brown and rho suggested the hypothesis that the vector meson masses drop in the medium according to a simple ( br ) scaling law @xcite , given as @xmath2 , where @xmath3 is the pion decay constant and asterisk refers to in - medium quantities . in the framework of quantum hadrodynamics ( qhd ) as a description of the hot hadronic matter , it is seen that the dropping of the vector meson masses has its dominant contribution arising from the vacuum polarisation effects from the baryon sector @xcite , which is not observed in the mean field approximation . this means that the quantum effects do play an important role in the medium modification of vector meson properties . there have also been approaches based on qcd sum rules @xcite which confirm a scaling hypothesis @xcite as suggested by brown and rho , with a saturation scheme that leads to a delta function at the vector meson pole and a continuum for higher energies for the hadronic spectral function . it is , however , seen that such a simple saturation scheme for finite densities does not work and a more realistic description for the hadronic spectral function is called for @xcite . using an effective lagrangian model to calculate the hadronic spectral function , it is seen that such a universal scaling law is not suggested for in - medium vector meson masses @xcite . the medium modifications of the vector mesons have been thus a subject of several investigations . it has been emphasized in the literature @xcite that the properties of the hadrons are modified due to their interactions with the thermal bath , and such modifications are reflected in the dilepton and photon spectra emitted from a hot and dense matter @xcite . dileptons are interesting probes for the study of evolving matter arising from relativistic heavy ion collisions since they do not interact strongly and escape unthermalized from the hot and dense matter at all stages of the evolution . the temperature @xcite and density @xcite modifications of the dileptons from hot hadronic matter as well as from a quark gluon plasma ( qgp ) resulting from heavy ion collisions have been a subject of extensive investigations in the recent past . broadly , two types of modifications for the hadrons in the medium are expected : shift in the pole position for the hadron propagator , giving rise to a modification of the mass , and broadening of the spectral function . in the present work , we shall attempt to study the medium modification of vector meson masses and decay widths in the hot hadronic matter within the framework of quantum hadrodynamics ( qhd ) taking the vacuum polarisation effects into account , and their subsequent effect on the dilepton spectra . in the conventional hadronic models @xcite , the masses of the vector mesons stay constant or increase slightly , in the mean field approximation , i.e. , when the polarization from the dirac sea is neglected @xcite . with the inclusion of quantum corrections from the baryonic sector , however , in the walecka model one observes a drop in the vector meson masses in the medium @xcite . this medium modification of the vector meson masses plays an important role in the enhanced dilepton yield @xcite for masses below the @xmath1 resonance in the heavy ion collision experiments @xcite . it has been emphasized recently that the dirac sea contribution ( taken into account through summing over baryonic tadpole diagrams in the relativistic hartree approximation ( rha ) ) dominates over the fermi sea contribution and @xmath4 is caused by a large dressing of @xmath5 cloud in the medium @xcite . further quantum effects arising from the scalar mesons have been considered @xcite along with the rha for the baryon sector in the context of vector meson mass modifications in strange hadronic matter @xcite . the present method is a step in that direction of studying medium modifications of the vector meson properties including such quantum effects from the scalar mesons in a self consistent manner , along with those arising from the baryon sector . it was earlier demonstrated in a nonperturbative formalism that a realignment of the ground state with baryon - antibaryon condensates is equivalent to the relativistic hartree approximation @xcite . the ground state for the nuclear matter was extended to include sigma condensates to take into account the quantum correction effects from the scalar meson sector @xcite . such a formalism includes multiloop effects and is self consistent @xcite . the methodology was then generalized to consider hot nuclear matter @xcite as well as to the situation of hyperon - rich dense matter @xcite relevant for neutron stars . the effect of vacuum polarisations on the vector meson masses has also been recently studied @xcite . in the present work , we study the effect of such quantum corrections on the in - medium vector meson properties . this apart , for studying @xmath1 meson properties , we take into account the @xmath1-@xmath6-@xmath6 interactions , and their effects on the dilepton production in the low invariant mass regime . the pionic interactions are seen to modify the @xmath1 meson mass only marginally , as already stated in the literature @xcite . due to scalar meson contributions , there is broadening in the @xmath0 and @xmath1 peaks , as compared to rha . this is seen to be quite pronounced for the @xmath0 meson , which leads to smearing and ultimate disappearance of the @xmath0 peak at finite densities @xcite . we organize the paper as follows . we first briefly recapitulate the nonperturbative framework used for studying the quantum correction effects in hot nuclear matter in section ii . the medium modification of the @xmath0 and @xmath1 meson masses and decay widths are considered in section iii . we discuss the effect of these medium modifications on the low mass dilepton spectra in section iv . in section v , we summarize the results of the present work and give an outlook . we briefly recapitulate here the vacuum polarisation effects arising from the nucleon and scalar meson fields in hot nuclear matter in a nonperturbative variational framework @xcite . the method of thermofield dynamics ( tfd ) @xcite is used here to study the ground state "" ( the state with minimum thermodynamic potential ) at finite temperature and density within the walecka model with a quartic scalar self interaction . the temperature and density dependent baryon and sigma masses are also calculated in a self - consistent manner in the formalism . the ansatz functions involved in such an approach are determined through functional minimisation of the thermodynamic potential . the lagrangian density in the walecka model is given as @xmath7 in the above , @xmath8 , @xmath9 , and @xmath10 are the fields for the nucleon , @xmath9 , and @xmath0 mesons with masses @xmath11 , @xmath12 , and @xmath13 respectively . since we are interested in symmetric nuclear matter , the isovector rho meson does not contribute . the quartic coupling term in @xmath9 is necessary for the sigma condensates to exist , through a vacuum realignment @xcite . our calculations thus include the quantum effects arising from the sigma meson in addition to the mean field contribution from the the quartic self interaction of the scalar meson . we retain the quantum nature of both the nucleon and the scalar meson fields , whereas the vector @xmath0 meson is treated as a classical field , using the mean field approximation for the @xmath0 meson , given as @xmath14 . the reason is that without higher order term for the @xmath0 meson , the quantum effects generated due to the @xmath0 meson through the present variational ansatz turn out to be zero . we then write down the expressions for the thermodynamic quantities including the quantum effects . the details regarding the formalism can be found in earlier references @xcite . the energy density , after carrying out the renormalisation procedures for the baryonic and scalar meson sectors @xcite , is obtained as @xmath15 with @xmath16 @xmath17 @xmath18 @xmath19 as the mean field result , contribution from the dirac sea , and contributions from the @xmath0 and @xmath9 mesons , respectively . we might note here that the quantum effects arising here from the scalar meson sector through @xmath9 meson condensates amounts to a sum over a class of multiloop diagrams and , does not correspond to the one meson loop approximation for scalar meson quantum effects considered earlier @xcite . in the above , @xmath20 and @xmath21 are the thermal distribution functions for the baryons and antibaryons , given in terms of the effective energy , @xmath22 , and the effective chemical potential , @xmath23 . @xmath24 is the effective nucleon mass and @xmath25 is the baryon number density after subtracting out the vacuum contribution . the spin - isospin degeneracy factor is @xmath26 for symmetric nuclear matter . in the expression for the energy density arising from the scalar meson sector , the field dependent effective sigma mass , @xmath27 , satisfies the gap equation in terms of the renormalised parameters as @xmath28 where @xmath29 where @xmath30 . the effective meson mass @xmath31 is determined through a self consistent solution of eq . ( [ mm2 ] ) . in eq . ( [ vph0 ] ) , @xmath32 and @xmath33 are the expressions as given by eqs . ( [ mm2 ] ) and ( [ if ] ) with @xmath34 . we might note here that the gap equation given by eq . ( [ mm2 ] ) is identical to that obtained through resumming the daisy and superdaisy graphs @xcite and hence includes higher order corrections from the scalar meson field in a self - consistent manner . extremisation of the thermodynamic potential , @xmath35 , with respect to the meson fields @xmath36 and @xmath37 yields the self consistency conditions for @xmath36 ( and hence for the effective nucleon mass @xmath38 ) and for the vector meson field @xmath37 . we now examine the medium modification to the masses and decay widths of the @xmath0 and @xmath1 mesons including the quantum correction effects in hot nuclear matter in the relativistic random phase approximation . the interaction vertices for these mesons with nucleons are given as @xmath39 where @xmath40 or @xmath41 , @xmath42 is the free nucleon mass , @xmath8 is the nucleon field and @xmath43 or @xmath44 , @xmath45 being the pauli matrices . @xmath46 and @xmath47 correspond to the couplings due to the vector and tensor interactions for the corresponding vector mesons to the nucleon fields . the vector meson self energy is expressed in terms of the nucleon propagator , @xmath48 modified by the quantum effects . this is given as @xmath49,\ ] ] where @xmath50 is the isospin degeneracy factor for nuclear matter , and @xmath51 represents the meson - nucleon vertex function . the vector meson self energy can be written as the sum of two parts @xmath52 where @xmath53 is the contribution arising from the vacuum polarisation effects , described by the coupling to the @xmath54 excitations and @xmath55 is the density dependent contribution to the vector self energy . for the @xmath0 meson , the tensor coupling is generally small as compared to the vector coupling to the" +"seeing a quantum effect , and even making practical use of it , does not necessarily imply recognising it as such . magnetic compasses have been around for millenia , but quantum nature of ferromagnetism could not be understood till the discovery of the electron spin and the pauli principle . more than forty years elapsed between stewart s and kirchhoff s experiments with thermal radiation and planck s dissertation . already in the 20th century , it took three years for einstein to come up with a quantum explanation of lenard s experiments . clearly there must exist certain _ mathematical patterns _ in quantum equations of motion allowing one to look at the quantum without recognising it . an immediate reservation is in place here . this paper concerns , and is limited to , phase - space formulation of quantum electrodynamics based on the time - normal operator ordering @xcite . this is only one example in the multitude of analogies existing between the quantum and classical mechanics ( see , e.g. , @xcite ) . our work should be kept distinct from attempts to modify quantum electrodynamics by making arbitrary physically motivated assumptions about properties of matter ( cf . @xcite ) , as well as from attempts to imitate quantum behaviour in classical stochastic electrodynamics ( cf . @xcite ) . another well established tradition is applying methods of quantum field theory to classical statistical mechanics @xcite . worth mentioning are also attempts to implement classical mechanics in the hilbert space , see @xcite and references therein . the result of this paper in a nutshell is that _ quantum electrodynamics and classical stochastic electrodynamics share their macroscopic dynamical structure . _ more specifically , all relations for generalised phase - space quasi - distributions @xcite we obtain in this paper lack planck s constant and , _ ipso facto _ , coincide with the corresponding relations of the classical stochastic electrodynamics for probability distributions . this lack of planck s constant is exactly the aforementioned mathematical pattern . one way of formulating our results is that truly quantum dynamics is limited to microscopic conditions of indistinguishability and/or equations of motion of matter . for purposes of this paper , _ macroscopic _ refers to electromagnetic interactions under conditions of distinguishability . etymologies aside , we associate `` macroscopic '' and `` microscopic '' with `` distinguishable '' and `` indistinguishable '' , and not with `` large '' and `` small '' . `` distinguishability '' has its standard meaning ( formalised as commutativity of relevant dynamical variables in the interaction picture ) . on the commonly used term _ mesoscopic _ see endnote @xcite ; we treat macroscopic and mesoscopic as synonyms . the logic of the paper revolves around two concepts : `` obscured macroscopic view '' and `` doing quantum electrodynamics while thinking classically '' . the former refers to a closed albeit , strictly speaking , phenomenological quantum dynamical framework confined to the electromagnetic field and current operators . the latter expresses the critical property of such framework : on rewriting it in the so - called _ response picture _ @xcite , planck s constant drops out . this is another manifestation of the said mathematical pattern . any relation within `` obscured macroscopic view '' may therefore be obtained by formal quantisation of its classical counterpart . we stress that `` obscured macroscopic view '' is not an approximation , nor is it a modification of conventional quantum mechanics . it is a _ voluntary limit _ we impose on information extracted from a microscopic theory . it does not impose any restrictions on the theory itself , except that it be consistent with conventional quantum electrodynamics . implications of these results , with a multitude of specifications and reservations , are discussed at length in the paper . here we allow ourselves only a brief comment so as to clarify our motivation . particulars aside , quantum measurement is interaction of classical apparata with a quantum system . nice as it may sound , this definition has two obvious problems . classical apparata in the strict meaning of the term do not exist in nature , and it is not at all clear which laws quantum or classical should govern such interaction . both problems disappear if we limit `` measurement '' to electromagnetic interaction of an observer e.g . , a human being with the rest of the world . `` obscured macroscopic view '' is a formal expression of limitations of such `` electromagnetic observer '' . the difference between the classical and the quantum for such observer is _ only _ in whether currents he / she sees may or may not be _ phenomenologically _ interpteted as stochastic c - numbers . if such interpretation happens to be possible for some macroscopic quantum system , the latter becomes phenomenologically indistinguishable from a classical system . we term such systems classically behaving . `` classical apparata '' are classically behaving quantum systems , i.e. , _ inherently quantum _ systems which _ appear classical _ to the observer . their interaction with other quantum systems is governed by laws of quantum electrodynamics , which in this case are structurally identical with classical electrodynamics . if all devices involved behave classically , the whole situation reverts to classical electrodynamics . in particular , the classical world we perceive in everyday life is a collection of classically behaving quantum systems . as we demonstrate in this paper , these leading considerations are fully justified by the formal structure of quantum electrodynamics . the goal of this paper is twofold . firstly , we extend the earlier analyses @xcite to distinguishable matter subsystems . we show that the _ formal _ response characterisation of a solitary electromagnetic device @xcite becomes its _ physical _ characterisation as a radiation scatterer were this device interacting electromagneticaly with other macroscopic devices . this proves overall physical consistency of the response viewpoint . secondly , we establish the connection between our approach and the conventional phase - space techniques , making all results , the old as well as the new , intuitive . to this end we reformulate everything in terms of _ conditional p - functionals _ @xcite ; these quantities generalise both _ conditional probability distributions _ of classical stochastics and _ quasiprobability distributions _ of the conventional phase - space techniques , to arbitrary nonlinear non - markovian bosonic quantum systems . our analyses imply generalisation of the conventional phase - space techniques , firstly , beyond the resonance , or rotating wave , approximation ( rwa ) , and , secondly , to quantum response problems . coherent states of the harmonic oscillator , which traditionally serve as an entry point to phase - space approaches , were introduced by schrdinger as early as 1926 @xcite . that quantum dynamics of free bosonic systems maps to classical dynamics irrespective of the quantum state was firstly noticed by feynman in his review on path integrals @xcite . this understanding was instrumental in developing quantum theory of photodetection by glauber @xcite . glauber s theory was initially formulated for free electromagnetic fields , then extended to interacting fields by kelley and kleiner @xcite . however , de haan @xcite and later bykov and tatarskii @xcite pointed out that kelley - kleiner s results are limited to the rwa . taking them outside the rwa leads to causality violations ( we associate causality with retardation , cf . also endnote @xcite ) . lifting this restriction by amending the glauber - kelley - kleiner definition is one of the key results of . the critical generalisation is inclusion of response . it establishes a link to a host of powerful ideas , notably , to the real - time quantum field theory , schwinger - perel - keldysh s closed - time - loop formalism @xcite , and , last but not least , to relativistic quantum field theory @xcite . ( this link was a subject of @xcite . ) from a physical perspective , it allows one to make propagation of quantum signals in space - time the guiding principle of the whole investigation . in particular , propagation of the electromagnetic field underlies the aforementioned amendment of the concept of time - normal ordering . it also reveals the inherent link between operator noncommutativity and response @xcite . the pivotal formal point of these analyses is that the description of a quantum system in terms of time - normal averages of heisenberg operators conditional on external sources turns out to be equivalent to the closed - time - loop framework . this kind of description was termed in @xcite _ response formulation _ of a quantum system ( also _ response picture _ , _ response viewpoint _ , or _ response characterisation _ ) . the said equivalence was proven in @xcite for interacting bosons and in @xcite for interacting fermions ( see also endnote @xcite ) . the closed - time - loop formulation is the most general formal framework known in quantum field theory . _ ipso facto _ , our approach may be seen as an ultimate generalisation of the phase - space techniques in quantum electrodynamics ( cf . endnote @xcite ) . its ability to tackle relativistic problems with renormalisations was demonstrated in @xcite . the way the paper is structured reflects our wish to make the results intuitive . `` obscured macroscopic view '' as a formal viewpoint is mostly relegated to appendices . in the main body of the paper , we proceed by `` doing quantum electrodynamics while thinking classically '' . we start from a brief overview of the results in . in , we develop the `` classical yardstick '' : a collection of general formulae , describing properties of devices and their interactions in classical stochastic electrodynamics . quantum mechanics starts in , which summarises formal definitions . conditional p - functionals are introduced in . the conjecture that classical formulae of are in fact _ exact _ relations for p - functionals is verified in and [ ch:91rj ] . in , we review the formal approach , concentrating on the interplay of the formal viewpoint and approximations . the results are discussed in . in appendix [ ch : reg ] we briefly touch upon the role of causality and regularisations in the classical electromagnetic self - action problem . appendix [ ch : qr ] summarises the results `` imported '' from earlier papers . in appendix [ ch : lm ] , we outline redefinitions allowing one to exclude passive linear devices ( mirrors etc . ) from explicit consideration . appendices [ ch:2dc ] and [ ch : phdet ] provide formal support to `` pictorial derivations '' in . in this paper we concern ourselves with the _ formal structure _ of quantum electrodynamics . rather than attempting to calculate something measurable , we look at restrictions measurable quantities must obey , assuming the only means of accessing the world is the electromagnetic interaction . moreover , we are only interested in relations which are independent of any particulars of nonelectromagnetic nature . this greatly limits the kind of question we are able to ask . consider for instance electromagnetic interaction of two devices depicted schematically in . for the time being , ignore hats and think about the devices as classical electromagnetic scatterers . in any real problem , there must exist microscopic dynamical models allowing one to calculate properties of the devices . these models necessarily rely on information about properties of matter , which is by itself nonelectromagnetic ( e.g. , the dirac equation in spinor qed , or various models in solid state theory ) . within `` obscured macroscopic view '' , we" +"when the high energy photons emitted by the x - ray source arrive to the earth , they have been scattered by the interstellar dust grains . therefore many galactic x - ray sources are observed to have faint and diffuse halos . this effect and its possible application was first discussed by overbeck ( 1965 ) , and the x - ray halo was first detected with einstein observatory ( rolf 1983 , catura 1983 ) . the investigation of the shape and strength of the haloes was done by several authors ( e.g. mauche & gorenstein 1986 , predehl & schmitt 1995 ) based on the data of einstein and rosat . as the photons in the halo travel through longer paths than the photons in the point source , any intensity variation in the the source induces a delayed signal in the halo . it has been suggested by trmper and schnfelder ( 1973 , hereafter ts1973 ) that this effect can be uesd to determine the distance of variable galactic x - ray sources . although the method is very simple , the first successful application was realized by predehl ( 2000 ) for a x - ray binary cyg x-3 almost 30 years later . they obtained the distance of @xmath0 kpc to the source . the difficulty of the method is that it is hard to distinguish the halo from the image induced by the point spread function of the instrument until the chandra x - ray observatory provides us the high resolution image of x - ray sources . the shape and strength of the halo depend on the distance to the x - ray source , the geometric distribution and the physical properties of the interstellar dust grains ( hayakawa ( 1970 ) , mathis & lee ( 1991 ) , and predehl & klose ( 1996 ) ) . the differential scattering cross section of x - ray photons in interstellar dust is ( predehl , 2000 ) @xmath1 where @xmath2 is the size of the dust grains ( in @xmath3 m ) , @xmath4 is the energy of x - ray ( in kev ) , and @xmath5 is the scattering angle ( in arc min ) . following ts1973 , we obtain the time delay of a scattered photon compared with an unscattered photon is ( see fig . 1 ) @xmath6 where @xmath7 is given in kpc , @xmath8 in arcsec . given the dust density distribution along the line of sight @xmath9 , the time delay distribution function @xmath10 can be calculated . as pointed by predehl & schmitt ( 1995 ) , we can assume @xmath9 is a constant . thus @xmath11 ^ 2})}{t+1.15d\theta^2}{\rm d}t{\rm d}\theta\ ] ] for a viable point source with light - curve @xmath12 , the normalized light - curve in the halo is @xmath13 where @xmath14 is the possible maximal time delay . in ts1973 , @xmath12 and @xmath15 are compared directly to determine distance . suppose the light - curve @xmath16 of the point source and the light - curve @xmath17 of the halo at @xmath18 radius are stationary random signals , @xmath19 and @xmath20 are their fourier transformation respectively . it is easy to show that @xmath21 where @xmath22 is the normalized integral transformation of the signal arrival time distribution function @xmath10 . denote the power density spectrum of the point source and the halo as @xmath23 and @xmath24 , we get @xmath25 given the power density spectra of the point source and the halo at different radius , @xmath26 and @xmath27 are easy to know , and @xmath7 can thus be determined by fitting equation ( 3 ) . 1.8 in now we apply this method to the chandra data of x - ray binary cyg x-3 . cyg x-3 is an eclipsing x - ray binary with an orbital period of 4.8 hours ( brinkman et al . cyg x-3 was observed with the high energy transmission grating spectrometer ( hetgs ) on board of chandra on october 20 , 1999 , with a total time of 12.3 ksec , starting at 01:11:38 ut . the observation covered the binary phases from -0.3 to + 0.4 . we only use the zeroth order data in this study . because the image of the point source is severely damaged by the pileup effect , we can only campare the power density spectra at different and radius . the theoretical difference of the power density spectrum of the halo at 2 arcsec and 4 arcsec in 5.0 - 7.0 kev energy band are shown in fig . then we calculate @xmath28)/h^2(\omega,\theta=[2^{\prime\prime},4^{\prime\prime}])$ ] in 5.0 - 7.0 kev energy band , the result shows in fig . 3 . because the error bar of the data in fig . 3 is very big , it is hard to fit the data with theoretical curves . for simplicity , we fit the data with a exponential curve . the turning point of the fitting curve lies at about 0.001 hz , and the corresponding value of @xmath7 is 9 kpc . according to fig . 3 , it seems the real turning point should small than 0.002 hz , so we estimate @xmath7 is at least 5 kpc . 1.7 in our result is consistent with previous estimate on the distance of cyg x-3 . predehl et al . ( 2000 ) used ts1973 method and obtained @xmath0 kpc , dickey ( 1983 ) found a lower limit of 9.2 kpc 1 using 21 cm wavelength absorption data , predehl & schmitt ( 1995 ) derived 8 kpc as distance through the galactic dust layer from their comparison of x - ray scattering and absorption . our method and ts1973 method both determine the geometric distance instead of physical distance . the physical distance depend on the estimation of many physical parameters , i.e. , absorption optical depth . the uncertainties of the geometric distance determination come mainly from the dust density distribution along the line of sight . in principle , it can be solved by carefully fitting the shape and strength of the halo . in ts1973 method the x - ray source must have relatively obvious variations in the time interval comparable to the delay time ( see fig . 4 . in predehl et al . 2000 ) . but in our method this requirement is not needed . although the chandra observatory has high resolution , its effective area is relatively small , therefore the count rate of the cyg x-3 halo is not high enough for good statistical study with our method . the future x - ray satellites such as _ constellation - x _ will provide us with high count rate data , and our method can be applied to many more galactic variable x - ray sources . * acknowledgement : * this study is supported in part by the special funds for major state basic research projects and by the national natural science foundation of china . snz also acknowledges supports by nasa s marshall space flight center and through nasa s long term space astrophysics program . 10 brinkman , a.c . , _ _ iau circ . _ * 2446 * ( 1972 ) catura , r. c. , _ astrophys . j. _ * 275 * , 645 ( 1983 ) dickey , j.m . , _ astrophys . j. _ * 273 * , l71 ( 1983 ) hayakawa , s. , _ prog . _ * 43 * , 1224 ( 1970 ) mathis , j.s . , lee c .- w . , _ astrophys . j. _ * 376 * , 490 ( 1991 ) mauche , c.w , gorenstein p. , _ astrophys . j. _ * 302 * , 371 ( 1986 ) overbeck , j. w. , _ astrophys . j. _ * 141 * , 864 ( 1965 ) predehl , p. , schmitt , j.h.m.m . , _ _ * 293 * , 889 ( 1995 ) predehl , p. , klose , s. , _ astro . astrophys . _ * 306 * , 283 ( 1996 ) predehl , p. , burwitz , v. , paerels f. , trmper j. , _ astro . _ * 357 * , l25 ( 2000 ) rolf , d. p. , _ nature _ * 302 * , 46 ( 1983 ) trmper , j. , schnfelder , v. , _ astro . astrophys . _ * 25 * , 445 ( 1973 )" +"stable compounds@xcite formed by fe and n , such as @xmath1-fe@xmath2n and @xmath3-fe@xmath4n , or quasi - stable@xcite like @xmath5-fe@xmath6n have been known for some time . on the other hand , almost nothing was reported about fen until the work of heiman _ et al._@xcite , where for the first time , they synthesized fe@xmath7n@xmath8 with 0.4 @xmath9 0.75 . in this work fen was found to be ferromagnetic . successive studies found fen in nacl - type crystal structure@xcite , and non - ferromagnetic at room temperature@xcite . more recent works are in contradiction with the earlier ones : morita _ et al._@xcite reported fen antiferromagnet at temperatures below 100 k. moreover , suzuki _ et al._@xcite determined the fen structure to be of zns fcc type . they also found their sample to exhibit a mictomagnetic character that was suggested be related to the antiferromagnetism of fen . regarding the structure , it seems clear that fen can assume both zincblende and rocksalt structure , depending on the sample history , and both of them may contain some deficiencies of n atoms . regarding magnetic properties , recent mssbauer spectroscopy measurements suggested that nacl - type fen is antiferromagnetic@xcite , with nel temperature around room temperature . however , mssbauer spectroscopy is not able to determine completely magnetic ordering . for both structural and magnetic properties ab initio calculations are suited to furnish a prediction about the ground state of fen , and to help guide understanding of experimental results . here we investigate the relative stability of paramagnetic ( pm ) , ferromagnetic ( fm ) and some possible antiferromagnetic ( afm ) phases of nacl - type fen that have been observed or suggested for other transition - metal nitride ( or oxide or carbide ) compounds . compared to other transition - metal nitrides ( tmns ) , it has been noticed@xcite that nacl - type fen shows electronic properties close to those of crn that we recently investigated@xcite , e.g. the fermi energy falls exactly on a pronounced peak of the density of states , mainly formed by fe @xmath10-like flat bands . in ref . the authors come to the conclusion , on the basis of the rigid band model to evaluate the dos and the stoner condition of ferromagnetism , that only crn , fen and con in rocksalt phase are likely to be stabilized by magnetic ordering . comparison with crn is particularly interesting because it undergoes a cubic - to - orthorhombic transition accompanying the pm to afm ordering at a nel temperature close to the room temperature , with afm phase formed by double ferromagnetic sheets compensating along the [ 110 ] direction**???**. the structural distortion is decisive in determining the most stable among the different afm phases , and stress relief is likely to be the ultimate driving force towards distortion . if such an involved mechanism of magnetic - ordering is driven by the high dos at fermi level , it could be argued that a similar magnetic ordering occurs for fen as well . thus , for possible afm phases , we decide to consider here the [ 110]-double and single sheet afm arrangements ( indicated as afm@xmath11}$ ] and afm@xmath12}$ ] , respectively and described fully in ref.@xcite ) , as well as the afm@xmath13}$ ] phase ( very common for nacl - type transition metal oxides ) , consisting of single ferromagnetic sheets alternating along the [ 111 ] direction . equilibrium lattice constants , energies , and magnetic moments are presented for all the considered phases . also , band structures and density of states ( dos s ) are presented for pm and fm phases . our local - spin - density calculations are performed in a plane - wave and ultrasoft pseudopotential framework@xcite . use of ultrasoft pseudopotentials allow us to obtain well converged results for a cutoff energy equal to 30 ryd . we used sets of 10 to 110 special k - points ( depending on the structure ) for the self - consistent calculations , up to 280 k - points to evaluate the dos . experimentally it was found for the lattice constant of fen in rocksalt and zincblende phase @xmath14=8.5 bohr@xcite and @xmath15=8.1 - 8.2 bohr @xcite , respectively . this result is somewhat surprising ; indeed , assuming the same anion - cation bond length in the two phases , the relation between lattice constants would be @xmath16 . although this crude approximation considerably overestimates the actual difference between the two structures , it is generally true that in most cases the rocksalt phase have larger volume . doubts about the measurements are confirmed by a recent theoretical work@xcite where structural properties for transition metal nitrides are calculated . they found for @xmath15 a value in good agreement with experiments , but a much smaller @xmath17 7.5 bohr in the paramagnetic phase . the discrepancy with experiment is so large that it seems unlikely it could be due to different magnetic orderings . also , in ref . the equilibrium lattice constant for other phases ( ferromagnetic and a couple of antiferromagnetic phases ) was evaluated , but no relevant changes on @xmath14 were found . finally , the value @xmath17 7.5 bohr is consistent with that of other rocksalt tmn structures . for instance , experiments assign to afm crn a value @xmath17 7.8 bohr , and we should expect for fen a somewhat smaller lattice constant . to try to explain the disagreement with experiments we consider here other afm phases . in particular , among the afm phases examined in ref . , the afm@xmath18}$ ] was not taken into account . the pm to afm@xmath11}$ ] transition is found to produce , for crn , a large increase of lattice constant@xcite ( @xmath19 2% ) , although not large enough to account for the discrepancy with experiments of fen , and the largest energy gain with respect to the pm phase . in table [ struct ] we report our calculated values of @xmath14 for the corresponding magnetic orderings . evidently , contrary to what happens for crn , the structure of fen is basically unaffected by magnetic ordering , and only a 0.4% increase of @xmath14 is found in the fm phase with respect to the pm . our results are in substantial agreement with ref . ( they found @xmath20=7.47 and 7.54 for pm and afm phases , respectively ) . from our calculations , it results that nacl - type fen is ferromagnetic . the energy gain of fm phase with respect to the pm is less than 0.1 ev per formula unit , i.e. significantly smaller than in case of crn . also , the competition between fm and the examined afm phases is very close ( energy differences are few hundredths of ev ) . to be confident about the precision of our calculations , we evaluated the fm - afm energy differences by performing fm calculations in the same symmetry of all the afm structures considered , and tested the differences for sets of special k - points of increasing size . we conclude that , among the afm phases , the lowest in energy is afm@xmath12}$ ] , also the lowest among the cubic phases of crn@xcite . in that case , the orthorhombic [ 110 ] shear distortion of crn produces a further energy gain for the afm@xmath11}$ ] structure ( anisotropic in the ( 100 ) plane due to magnetic ordering ) that causes the latter to be the most stable phase overall . to investigate the effect of planar distortion on fen we applied the same distortion experimentally observed for crn ( i.e. a @xmath192% reduction of the bisection angle at the squared base of the tetragonal cell . surprisingly , we find very little change in the energy with respect to the cubic afm@xmath11}$ ] phase ( the increase is just @xmath19 2 mev ) . thus , notwithstanding the similarity of dos at fermi level , crn and fen are stabilized by very different magnetic order and structure . in table [ struct ] we report the magnetization @xmath21 ( per formula unit , i.e. per couple fe - n ) for the considered phases of fen . the fm phase has the highest magnetization ( 1.65 @xmath22 ) , of which @xmath19 0.15 @xmath22 comes from polarization of n , and @xmath19 1.5 @xmath22 from polarization of fe . for crn the magnetization is more that 2 @xmath22 per formula unit . also , the charge transfer is different . for fen it is equal to about one electron , so that the approximate ionic configuration fe@xmath23n@xmath24 can be deduced , i.e. fe is near a @xmath25 configuration . in case of crn , the charge transfer is larger ( close to 2 electrons ) , due to the higher electronegativity of fe with respect to cr . i.e. to the smaller electronegativity difference with n. the higher covalency of fen contributes to it having a smaller lattice constant , whereas crn has larger ionicity and polarization . in ref . it is argued that for crn the energy gain from the planar distortion is due to a relief of tensile stress stored in the bonds between metal atoms with antiparallel spins . this stress can be conveniently defined as the excess stress produced by a transition from the afm@xmath12}$ ] phase ( where there is no stress by symmetry ) and the afm@xmath11}$ ] cubic phase with the same lattice constant . the transition produces a planar anisotropic stress , whose component @xmath26}$ ] is tensile , i.e. the spin - antiparallel metal atoms tend to get closer each other . in light of our results for fen , we speculate that this magnetic order - derived stress is sensitive to the magnitude of magnetization . of course , the different bond length ( slightly larger for crn than for fen ) plays a role as well and could justify in itself a different behavior . in figure [ dos_pm ] the dos for the pm phase of fen is shown . in this energy region , the total dos ( top panel ) is almost completely made up by d states of fe and p states of n ( bottom panel ) . the d - like dos shows two high peaks close to the fermi energy ( e@xmath27 ) . the lowest in energy is completely occupied and is composed by a mixture of 75% @xmath0-type and 25% @xmath28-type character . it is this peak which falls at e@xmath27 in paramagnetic crn@xcite ( a rigid band model works well for the pm phase of this system ) . the second peak in the d dos is entirely @xmath0 in character , and is centered at e@xmath27 . the peaks located between -8 ev and -4 ev are mostly n p , with a mixture of @xmath0-type and ( predominantly ) @xmath28-type states . the n p - like dos gives an appreciable contribution to the dos at the fermi energy as well , unlike crn for which only d - type states contribute . this dos peak at e@xmath27 arises from a strong @xmath29 antibonding band . the effect of fm ordering is easily visible in figure [ dos_fm ] . now the fe d - like dos ( middle panel ) is shown decomposed in @xmath0 and @xmath28 states . the two d - type peaks are now split by an exchange splitting of roughly 1.6 ev . after this splitting both peaks in the spin up channels are completely occupied , whereas the upper peak of the spin down channel is empty . thus , 3 electrons per fe atom saturate almost completely three @xmath30 states , and @xmath19 1.5 electron charge" +"gas giants form in protoplanetary disks , through core accretion followed by runaway gas accretion , or through gravitational instabilities @xcite . in the core accretion scenario , the elemental compositions of gas giant gaseous envelopes or atmospheres are determined by the composition of the disk gas from which the envelope is accreted , by subsequent accretion of icy planetesimals , and by core - envelope interactions @xcite . in this letter we show how snowlines in conjunction with pebble drift affect the c / o and c / h ratios of disk gas , and further the compositions of of gas giant atmospheres forming through core accretion . considering a core accretion idealized scenario , where the core is composed purely of disk solids and the envelope purely from disk gas , the gaseous envelope will have a high c / o ratio and a substellar c / h ratio if it is accreted in between the water and co snowlines @xcite . at the water and co@xmath0 snowlines the gas is ( preferentially ) depleted of oxygen , resulting in a supersolar gas - phase c / o ratio and subsolar o / h and c / h ratios . this motivated @xcite to predict that gas giants that form through the core accretion scenario at large separations should have a c / o ratio close to unity in their envelopes , and a substellar c / h ratio . in reality pollution by pebbles and planetesimals accreting with the gas or at later times is bound to take place , and this process and migration will affect the elemental atmospheric ratios ( see 4 ) . both the c / o ratio and the c / h ratio ( or metallicity ) have large effects on the atmospheric chemistry of gas giants @xcite . observations of gas giant atmospheric chemical compositions may thus be used to constrain their elemental composition , and further their formation mode and location . in the solar system , the atmospheres of both jupiter and saturn appear to be enhanced in c / h ( and n / h ) relative to solar by factors of a few @xcite . the c / o ratio remains in question in the solar system gas giants , but may become resolved when juno measures the water content of jupiter @xcite . the c / o ratio has been constrained in a number of gas giant exoplanet atmospheres and several appear to contain supersolar c / o @xcite , though some of the early results are contested ( e.g. * ? ? ? the metallicity of a few extrasolar gas giants have been retrieved as well , and the result is a range of inferred c / h ratios @xcite . of especial interest for this letter is the retrieval of a c / o ratio close to unity and a supersolar c / h in the large - separation gas giants hr 8799b and c@xcite , which is at odds with the predictions from @xcite . the prediction of substellar gas - phase c / h in the outer disk was based on a static disk model , however , while in reality disks are dynamical systems that experiences large - scale redistributions of gas and solids . in this letter we explore how the redistribution of volatiles that accompanies grain growth and subsequent pebble drift affect the elemental composition of the gas in the planet forming zone of disks . we use a simple toy model to demonstrate the importance of this effect and present a new set of qualitative predictions on the c / o and c / h ratios in gas giants assembling at different disk radii . the framework for our toy model is a disk where the distribution of solids is regulated by settling , growth and drift . grain growth through coagulation is efficient up to cm - scales or pebble sizes and takes place on time scales of thousands of years at 1 au @xcite . in the outer disk , grain growth occurs on longer time scales , tens of thousands of years , but this is still short compared to disk lifetimes @xcite . once formed , pebbles are expected to rapidly drift inward due to gas drag , resulting in a major redistribution of solids from the outer to the inner disk . this scenario is confirmed by observations of disks with mm - to - cm sized pebbles confined to the inner 10s of au , while gas and small , micro - sized dust grains extend to 100s of au @xcite . why drift of pebbles stops or slows down at 10s of aus in these disks is not immediately clear , but may be due to the presence of sub - structure ( e.g. * ? ? ? * ; * ? ? ? * ) . based on these theoretical and observational constraints , and on the insights from @xcite , we imagine the scenario outlined in cartoon - form in fig . [ fig : cartoon ] . the disk forms with gas and solids ( in the form of bare and icy dust grains ) initially co - located . the dust grain composition is set by sublimation and condensation rates of different volatiles , which are temperature and therefore disk radius dependent . beyond the water snowline , the grains are covered by water ice , and further outward also by co@xmath0 and co ice . in between the water and co snowlines the gas is depleted in oxygen with respect to carbon , resulting in a supersolar c / o ratio . as the icy grains coagulate to form pebbles they drift rapidly inward @xcite , depleting the outer disk of solids . pebbles that form exterior to the co snowline , which is located at 20 - 60 au around solar - type stars @xcite , and drift inward deplete the outer disk of co ice @xcite as well as more refractory solids . if co - ice covered pebbles drift across the co snowline and sublimate some distance interior to it @xcite , the inner disk will become enhanced in co vapor , locally enhancing the c / h ( and o / h ) ratio above the expected value for a static disk . in this letter we only consider the effects of co redistribution in detail , but the process can be generalized to other volatiles . in particular , icy pebbles that drift past the co@xmath0 snowline will result in a second disk region with a c / h and c / o excess in the gas . following sublimation , co will be distributed over some disk region due to diffusion . diffusion has been shown to have a large effect on elemental ratios : @xcite recently showed that the faster diffusion of water compared to co interior to the water snowline results in an increased c / o ratio in the inner disk . in general diffusion rates depend on concentration gradients , and are therefore especially efficient for species x close to the x condensation line . the level of c / h excess in the disk gas interior to the co snow - line will therefore depend on how far the pebbles drift inward of the co snowline before sublimating , on the diffusion efficiency , and on the fraction of co vapor that following back - diffusion condenses out on grains that grow and drift back into the sublimation zone . the relative rates of these different processes are likely time dependent and thus the level of achieved c / h excess in the inner disk will vary across both space and time . in the following section we use a small set of toy models to evaluate possible levels of c / h enrichments interior to the co snowline when pebble drift redistribute co from the outer to the inner disk and diffusion spreads out the sublimated co vapor figure [ fig : model ] shows our disk toy models : the adopted initial dust ( refractory solids ) and co distributions , different redistributions of solids from the outer disk , and their impacts on c / h gas - phase ratios assuming different levels of co diffusion . our initial disk model is a recent variation of the minimum mass solar nebula ( mmsn ) density and temperature profile . we assume a gas surface density of @xmath1 g @xmath2 and temperature of @xmath3 k @xcite between 0.1 and 200 au . initially the dust follow the gas distribution with a mass ratio of 1/100 ( not including volatile mantles ) . the initial co column density is set such that the total ( solid / ice+gas ) co abundance in number of molecules per h nuclei is @xmath4 at each disk radius , corresponding to a co / dust mass ratio of 0.42 . this is shown in the upper left panel of fig . [ fig : model ] , labeled m0 . to calculate snowline locations and c / h gas ratios in the disk we adopt the same silicate , carbon grain , h@xmath0o , co@xmath0 and co abundances and sublimation temperatures as in @xcite , except for a slightly elevated co sublimation temperature of 25 k. the resulting h@xmath0o , co@xmath0 and co midplane snowline locations are at @xmath50.7 , 9 and 39 au respectively . across the disk the c / h ratio is calculated by a balance between freeze - out and sublimation of these species at each disk radius . the lower left panel in figure [ fig : model ] shows the expected drops in c / h gas - phase abundances at the co@xmath0 and co snowlines in the static disk , where substantial amounts of carbon become depleted into the solids . c / h is @xmath6% of the solar value in between the co@xmath0 and co snowlines . we then simulate the effects of dust grain growth and drift on the dust surface density and further on the total co surface density by moving a fraction of the solids located exterior to 40 au into the inner disk . the 40 au radius is somewhat arbitrary the sizes of observed pebble disks range from 15 of au and upward @xcite . we opt to put it close to the co snowline , since sublimation lines are proposed to cause disk sub - structure ( e.g. * ? ? ? * ) , and thus to slow down drift locally . the fraction of redistributed solids is either 20% ( model 1/m1 ) , appropriate at ` early ' times , or 99% ( model 2/m2 ) , characteristic of mature disks where the outer disks have been emptied of pebbles and only micron - sized grains remain . for simplicity , the pebbles are re - distributed such that a constant surface density of refractory grain mass are added to each disk radius interior to 40 au ( fig . [ fig : model ] top panels ) the adopted redistributed dust profile have a little effect on the output c / h ratio . the gas - solid balance of water and co@xmath0 is then recalculated using the new surface density of solids assuming a constant h@xmath0o / co@xmath0/refractory solids ratio throughout the disk . this is a reasonable assumption exterior to the co@xmath0 snowline ( the region of interest for this paper ) , since the pebbles originate beyond the co snowline and thus all available h@xmath0o , co@xmath0 and co in the outer disk are brought with the pebbles as they drift . we treat co differently than water and co@xmath0 , since the drifting pebbles and co decouple where co mantles sublimate , which happens somewhere between" +"most of the games represent simplified real - life situations and help us to find an optimum decision ( action ) . due to the simplifications the players have only a few options to choose and the corresponding incomes are quantified by a payoff matrix allowing us to apply the tools of mathematics . the theory of games has been used successfully both in economics and political decisions since the pioneering work of von neumann and morgenstern @xcite . subsequently the concept of payoff matrix is adopted by biologists to quantify the effect of interactions of species on their fitness ( characterizing the capability to create offspring ) in the mathematical models of darwinian evolution @xcite . since that time the evolutionary game theory provides a general mathematical framework for the investigation of multi - agent systems used widely in economy and other social sciences where imitation is substituted for the offspring creation @xcite . in traditional game theory selfish and intelligent individuals try to maximize their own payoff irrespective of others . in evolutionary game theory players repeat the games and sometimes imitate ( adopt ) the neighbor s strategy if the neighbor received a higher score . it turned out that assuming local interactions among players the imitation supports the maintenance of altruistic behavior even for prisoner s dilemma games where the individual interest is in conflict with the common one and the selfish individual behavior drives the well - mixed community into a state ( called `` tragedy of the commons '' ) with players exploiting ( instead of helping ) each other @xcite . in parallel with theoretical investigations game theory is also used to study human and animal behaviors experimentally @xcite . these experiments have motivated the extension of evolutionary games to study the effect of different types of mutual help , e.g. , charity @xcite , inequality ( inequity ) aversion @xcite , emotions @xcite including juvenile - adult interactions @xcite . in generally , the modelling of human decision dynamics is one of the most important open problems in the behavioral sciences @xcite . the examples mentioned raise the possibility that a player tries to optimize not only personal but her local neighborhood s payoff as well . motivated by this option we consider the simplest case and introduce a collective pairwise strategy update rule providing that two randomly chosen neighbors upgrade their strategy simultaneously in order to increase their summarized payoff each coming from games with all their neighbors on the spatial system . this way of strategy update can be considered as an extension of cooperative games toward the spatial evolutionary games . originally , in cooperative games groups of players ( coalitions ) may perform coordinated behavior within the group to enhance the group s payoff . on the other hand , the present model implies a connection between the theory of kin selection @xcite and spatial models of viscous population of altruistic relatives helping each other @xcite . as a consequence of the proposed strategy update rule , it will be shown that the previously mentioned tragedy of the commons state can be avoided even in the hard condition of prisoner s dilemma game . in the latter case both analytical and numerical approaches indicate the existence of an ordered structure of cooperator and defector players on square lattice at sufficiently low noise level . ( this arrangement of alternative strategies resembles the sublattice ordering of anti - ferromagnetic ising model . ) it is worth mentioning that similar formation of strategies was also reported by bonabeau _ _ @xcite and by weisbuch and stauffer @xcite within the framework of social models . to explore and identify the exclusive consequence of the proposed strategy update rule , we will compare the results with the outcomes of two previously applied dynamical rules . these are the imitation of a better neighbor and the so - called myopic strategy update rules . the present work is structured as follows . in sec . [ sec : models ] we define the spatial evolutionary games with the mentioned dynamical rules . the main results for these types of dynamical rules are compared for the anti - coordination game in sec . [ sec : acg ] . subsequently we will discuss the weak prisoner s dilemma games with using monte carlo ( mc ) simulations and mean - field analysis . in sec . [ sec : robus ] we present and compare the mc results for the three dynamical rules within a relevant region of payoff parameters describing social dilemmas @xcite . as the dynamical rules influence significantly the sublattice ordering process therefore some aspects of domain growth are considered numerically in sec . [ sec : domgr ] . finally we summarize the main results in sec . [ sec : conc ] . in the studied models each player follows one of the pure cooperate or defect ( @xmath1 or @xmath2 ) strategies . according to pairwise interaction a player s payoff is calculated by means of @xmath3 payoff matrix . for a given pair of equivalent players the possible strategy dependent payoffs are given by the payoff matrix as @xmath4 where @xmath5 ( @xmath6 ) is received by the @xmath1 ( @xmath2 ) player if her co - player follows the same strategy . on the other hand , if the players choose opposite strategies the @xmath1 players receive @xmath7 while @xmath2s are rewarded by @xmath8 . the anti - coordination ( ac ) game will be considered when @xmath9 and @xmath10 . in this case the players receive the maximum payoff if they choose opposite strategies . for the social dilemmas we also use a rescaled payoff matrix @xcite in such a way that @xmath11 and @xmath12 , that is , the mutual choice of @xmath1 is better for both players . despite it the players can favor the choice of @xmath2 if either @xmath13 or @xmath14 where @xmath15 refers to the temptation to choose defection and @xmath16 is the sucker s payoff . for the prisoner s dilemma ( pd ) both conditions are satisfied and the players are enforced to choose @xmath2 yielding the second lowest individual income for them . the hawk - dove , in short hd ( also called as snowdrift or chicken ) game describes the situation when @xmath17 and @xmath18 while the stag - hunt ( sh ) game corresponds to the case @xmath19 and @xmath20 . the fourth quadrant of the @xmath21 parameter plane is represented by the harmony ( h ) game where mutual @xmath1 is the best solution for the players . in the mentioned four quadrants of the @xmath21 plane the two - person one - shoot games have different set of nash equilibria @xcite . in the present spatial models players are located on the sites @xmath22 of a square lattice consisting of @xmath23 nodes under periodic boundary conditions . initially each player follows an @xmath24 or @xmath2 strategy chosen at random . the payoff @xmath25 is collected from the mentioned matrix games with her four nearest neighbors . according to the proposed pairwise collective strategy update the evolution of strategy distribution is based on the following protocol . first , we choose two neighboring players ( @xmath22 and @xmath26 ) at random and we evaluate their payoff ( @xmath25 and @xmath27 ) depending on their own @xmath28 , @xmath29 , and also on the neighboring strategies . subsequently we evaluate the payoff @xmath30 and @xmath31 assuming that the given players follow randomly chosen @xmath32 and @xmath33 strategies while the neighborhood remains unchanged . as a consequence of randomly chosen @xmath32 , @xmath33 strategy pair , there are cases when only one ( or none ) of the two players will modify her strategy . notice , however , that this strategy choice allows the pair of players to select all the possible four strategy pairs . finally the strategy pair , @xmath32 and @xmath33 , is accepted simultaneously with a probability @xmath34}\ ; , \label{eq : pwc}\ ] ] where @xmath35 characterizes the average amplitude of noise disturbing the players rational decision . the results of the above evolutionary process will be contrasted with the consequence of two other dynamical rules used frequently in previous studies @xcite . if the evolution is controlled by stochastic imitation of the more successful neighbor then player @xmath22 adopts the neighboring strategy @xmath29 with a probability @xmath36}\ \label{eq : imit}\ ] ] dependent on the current payoff difference between players @xmath22 and @xmath26 . besides it , we also study a so - called myopic strategy update when a randomly chosen player @xmath22 changes her strategy @xmath28 to a random strategy @xmath32 with a probability @xmath37}\ \ , \label{eq : myop}\ ] ] where @xmath25 and @xmath30 are the income of player @xmath22 when playing @xmath28 and @xmath32 for the given neighborhood . notice that the latter strategy update is analogous to the glauber dynamics used in the kinetic ising models @xcite . consequently , for symmetric payoff matrices , @xmath38 , ( or potential games ) the myopic strategy update drives the spatial system into a thermal equilibrium ( at temperature @xmath35 ) that can be described by the boltzmann statistics @xcite . this means that an anti - ferromagnetic ordering process is expected for the ac games with myopic strategy update when decreasing the noise parameter @xmath35 . motivated by the above mentioned connection to the ising model , we first consider the anti - coordination game and study the consequences of different strategy update rules . the presented results of mc simulations were obtained typically for @xmath39 size but we used significantly larger system size in the vicinity of the critical transitions to suppress undesired fluctuations . during the evolution we have determined the average portion @xmath40 of players following the @xmath1 strategy in the stationary state . to describe the expected anti - ferromagnetic ordering the square lattice is divided into two sublattices ( @xmath41 and @xmath42 ) on the analogy of white and black boxes on the chessboard . in fact two equivalent types of completely ordered structure exist in the limit @xmath43 . for both cases the @xmath1 and @xmath2 strategies are present with the same frequency ( @xmath44 ) . in the first ( second ) case all the @xmath1 strategies are located on the sites of sublattice @xmath41 ( @xmath42 ) . the sublattice ordering will be characterized by an order parameter @xmath45 where @xmath46 and @xmath47 denote the portion of @xmath1 strategy in the sublattices @xmath41 and @xmath42 . in a finite system the sublattice ordering develops throughout a domain growing process within a transient time . starting with myopic strategy update , defined by eq . [ eq : myop ] , the mc data coincide with the exact results of ising model @xcite if the noise parameter ( temperature in the latter case ) is rescaled by a factor of 2 . accordingly , a long - range ordered state appears in the zero noise limit where cooperator and defector players form a chessboard - like pattern . the order parameter @xmath48 varies from 1 to 0 if @xmath35 is increased from 0 to @xmath49 and @xmath50 if @xmath51 , as illustrated in fig . [ fig : ising ] . when considering the analogy between the kinetic ising spin systems and evolutionary ac games one should keep in mind that the glauber dynamics @xcite favors spin flips decreasing the total energy and the opposite flips are generated by the external noise ( temperature ) . on the contrary , for the evolutionary games the myopic individuals wish to increase their own payoff and the opposite decision is caused by noisy effects . the necessity of the temperature rescaling is related to the fact that in the kinetic ising model for glauber dynamics the individual spin flips" +"since its discovery by stephenson ( 1986 ) , the remarkable field star bp psc (= sth@xmath3 202 ) has been classified as a classical t tauri star ( ctts ) on the basis of its strong h@xmath3 and forbidden line emission . the discovery by zuckerman et al . ( 2008 ; hereafter zms08 ) of an orbiting , dusty circumstellar disk and an enormous ( pc - scale ) system of highly collimated outflows ( jets ) would appear , at first glance , to provide strong support for such a ctts classification . however , as noted by zms08 , it is not at all clear that bp psc is a pre - main sequence ( pre - ms ) star . first , although its jet system resembles those of cloud - embedded young stellar objects , bp psc is located at high galactic latitude , far from any known star forming cloud . furthermore , unlike the rare ( though increasingly scrutinized ) `` isolated , '' ctts systems within @xmath4 pc ( torres et al . 2008 ) the best - known examples being tw hya ( kastner et al . 1997 ; zuckerman & song 2004 ; and references therein ) and v4046 sgr ( kastner et al . 2008b ; rodriguez et al . 2010 ; and references therein ) bp psc is not associated with any known sparse group of young stars ( zms08 ) . second , its photospheric li abundance appears to be anomalously weak for a k - type pre - ms star of age @xmath5 myr , and its gravity - sensitive photospheric absorption lines also call into question such a classification ( zms08 ) . third , the mm - wave molecular spectrum of its circumstellar disk specifically , its weak cn and hco@xmath6 emission is atypical of the disks of low - mass , pre - ms stars ( kastner et al . 2008a ) . in light of the first two considerations , zms08 proposed that bp psc is most likely a first - ascent giant at a distance @xmath7 pc . they speculated that the bp psc disk / jet system might therefore be the result of a recent , catastrophic interaction in which a low - mass companion star ( or perhaps giant planet ) had been consumed by bp psc . though somewhat exotic , a similar ( companion engulfment ) scenario may also apply to the first - ascent giant star tyc 4144 329 2 ( melis et al . 2009 ) : the post - ms nature of tyc 4144 329 2 is well - established , yet ( like bp psc ) this star is evidently actively accreting gas from a dusty circumstellar disk . low - mass , pre - ms stars are highly luminous x - ray sources , with typical ( 0.38.0 kev ) x - ray luminosities @xmath8 \stackrel{>}{\sim } 29.5 $ ] and x - ray to bolometric luminosity ratios in the range @xmath9 to @xmath10 ( e.g. , preibisch & feigelson 2005 ; gdel et al . hence , x - ray observations are diagnostic of stellar youth . furthermore , in rare cases , tts jet systems may yield shocks energetic enough to produce x - rays , yielding insight into physical conditions within the jets ( e.g. , kastner et al . 2005 ; guedel et al . 2005 , 2007b ) . here , we report the results of _ chandra _ x - ray observatory observations of bp psc intended to determine whether bp psc and/or its jet system emit x - rays and , thereby , to better understand the nature of this unusual system . _ chandra _ observed bp psc in 2009 january , with the advanced ccd imaging spectrometer ( acis ) as the detector . due to spacecraft thermal constraints , the observation was obtained in two pieces of duration 10.15 and 65.4 ks ( obsids 8900 and 10856 , respectively , on 2009 jan.12 and 13 ) , for a total exposure time of 75.5 ks . data were obtained with acis ccds s1 , s2 , s3 , s4 , i2 , and i3 active . each ccd has a @xmath11 field of view with 0.49@xmath12 pixels , and is sensitive to photons in the energy range 0.58.0 kev ( with some additional sensitivity down to 0.3 kev , for back - illuminated ccd s3 ) . the telescope was pointed such that bp psc was positioned at the nominal aimpoint of ccd s3 , @xmath13 from the s2-s3 chip boundary . the merged event data from the two exposures were subject to standard processing , filtering , and calibration ( via _ chandra _ x - ray center ( cxc ) acis pipeline v7.6.1 and caldb v3.5.1 ) . we ran the cxc ( ciao ) source detection tool ` celldetect ` on the filtered event list , restricted to ccds s2 and s3 ( the other active ccds lie far off the best focal surface ) . we find 26 sources , including bp psc itself ( 3.1 ) , were detected at a significance @xmath14 ( using poisson statistics ) on these two ccds ( fig . [ fig : bppscimage ] , right ) . four of these s2 and s3 sources lie within @xmath15 of denis near - ir sources ; two of the four ( bp psc itself and an x - ray source detected on ccd s2 ; 3.3 ) are also 2mass sources . based on the @xmath16 x - ray sources that lie within @xmath15 of guide star catalog stars ( not including the bp psc source ) , we estimate the absolute astrometric accuracy of the two - part _ chandra _ pointing to be @xmath17 . in fig . [ fig : bppscimage ] we display the wide - field h@xmath3 image originally published in zms08 alongside the broad - band ( 0.58.0 kev ) _ chandra_/acis image of the same field surrounding bp psc . the comparison reveals that _ chandra _ has detected a faint , point - like x - ray source at the position of bp psc . source detection indicates a background - subtracted count rate of 0.24@xmath180.07 ks@xmath19 for this source , or @xmath20 source photons detected during the @xmath21 ks exposure . the bp psc x - ray source lies at j2000 coordinates @xmath2223:22:24.72 , @xmath2302:13:41.66 , with a positional uncertainty that is dominated by the estimated astrometric accuracy ( @xmath180.2@xmath12 ) . given the uncertainties , this x - ray position is precisely coincident with that of the 2mass position of bp psc ( @xmath2223:22:24.70 , @xmath2302:13:41.40 ) as well as with the centroid of submillimeter continuum emission from bp psc ( @xmath2223:22:24.72@xmath180.02 , @xmath2302:13:41.55@xmath180.2 ; zms08 ) . analysis of photon arrival times ( via a kuiper test against a poisson process ; press et al . 1992 ) yields no evidence that the bp psc source is variable , although we are unable to rule out source variability . given the small number of photons detected , it is not reasonable to attempt to deduce the characteristic source temperature @xmath24 and line - of - sight absorbing column @xmath25 and , hence , intrinsic source flux @xmath26 via standard x - ray spectral analysis . however , useful constraints on @xmath25 and @xmath26 can be obtained via the median energy of the detected source photons . specifically , feigelson et al . ( 2005 ) demonstrated that orion nebula cluster ( onc ) pre - ms star x - ray sources detected by _ chandra_/acis - i display a relatively tight correlation between median x - ray energy and @xmath25 . getman et al . ( 2010 ) refined and further generalized the feigelson et al . ( 2005 ) results , demonstrating ( via spectral simulations ) that the relationship between median x - ray energy and @xmath25 should in principle apply to any source that can be modeled in terms of two - temperature optically thin thermal plasma emission suffering intervening absorption , and is applicable over a wide range of intrinsic source luminosity ( i.e. , for @xmath27 from @xmath28 to @xmath29 erg s@xmath30 ) . as the getman et al . analysis was carried out for sources detected on the front - illuminated acis ccds ( i0-i3 ) , which have lower qe than ccd s3 at low energy ( i.e. , photon energies @xmath31 kev ) , application of the getman et al.methods might result in an underestimate in the value of @xmath25 obtained via the median photon energy of a source on s3 . this is unlikely to be an important effect for a source as hard as that detected toward bp psc in 2009 , however , especially given the overall degradation in the soft ( @xmath32 kev ) x - ray sensitivity of acis in the decade since _ chandra _ s launch , to determine the median detected photon energy for the bp psc source , we applied the ( ae ) software package ( broos et al . 2010 ) to extract and analyze the source photons . doing so , we find the median background - subtracted photon energy of the bp psc source in the 0.58.0 kev energy band is 3.47@xmath180.33 kev . this median energy corresponds to an absorbing column @xmath33 = 22.9\pm0.2 $ ] , based on the `` best model family '' determined from the getman et al . ( 2010 ) statistical spectral analysis method ( we display the ae - extracted x - ray spectral energy distribution of bp psc , overlaid with the getman et al . `` best model family '' spectral model , in fig . [ fig : bppsc_spec ] ) . the getman et al . ( 2010 ) method yields an estimated apparent ( measured ) broad - band flux of @xmath34 erg @xmath35 s@xmath19 ( 0.58.0 kev ) , corresponding to an intrinsic flux @xmath36 erg @xmath35 s@xmath19 . the measured and intrinsic hard - band ( 2.08.0 kev ) fluxes are @xmath37 erg @xmath35 s@xmath19 and @xmath38 erg @xmath35 s@xmath19 , respectively . although the statistical error on the broad - band intrinsic flux ( @xmath26 ) is small ( @xmath39% ) , the value of @xmath26 is uncertain by almost a factor of 5 ( and the hard - band intrinsic flux is uncertain by a factor @xmath402 ) , due to systematic uncertainties in determining the generic spectral model that best describes the bp psc source ( see getman et al . 2010 , their fig . 1 ) . however , the foregoing estimates for apparent and intrinsic flux are consistent with those we obtained via simple simulations to match the bp psc source acis - s3 count rate using absorbed thermal plasma models ranging in temperature from @xmath41 to 3.0 kev a range typical of coronal sources with median photon energies similar to that of bp psc ( feigelson et al . 2005 ; also see 4 ) assuming @xmath42 @xmath35 . from the preceding results for @xmath25 and @xmath26 , we estimate that the x - ray luminosity of the bp psc source is @xmath43 erg s@xmath19 where @xmath44 is the distance in pc . adopting a bolometric luminosity @xmath45 erg s@xmath19 for the star ( zms08 ) , and allowing for the ( large ) systematic errors in @xmath26 obtained via the getman et al . ( 2010 ) method , we conservatively conclude that @xmath0 lies in the range @xmath1 to @xmath2 , with a best estimate of @xmath46 . as is apparent from inspection of fig . 1 , no diffuse x - ray emission is associated with the jets and bow - shock - like herbig" +"in the last two decades several experiments have provided strong evidence in favor of the neutrinos oscillation hypothesis . in the so called _ atmospheric sector _ the flavor conversion was first established by super - kamiokande@xcite and further by macro@xcite and soudan-2@xcite experiments . further confirmation was more recently obtained by the k2k@xcite and minos@xcite long - baseline experiments . however a two fold question is still unanswered , does the oscillation scenario correspond to the simple 3-flavor expectation or not ? which is related to the still unobserved direct appearance of one flavor to another , in particular to the highly expected @xmath0 oscillation . answer to this two - fold question is relevant mainly to proceed towards the next steps in the clarification of the leptonic sector of the particle model . after a brief reminder of the physics behind we will assay to focus on the main points which brings us to the present knowledge about neutrino mixing . the recent history provided the scenario in which the neutrino oscillation framework was settled . still new questions opened up and these bring us directly into the future . next we will shortly report on the present results from short - base - line ( sbl ) experiment , mainly the miniboone@xcite experiment , and the long - base - line ( lbl ) experiments , namely minos and opera@xcite . finally some physics expectations for the near future after a personal discussion of the very recent opera results@xcite will be drawn . the issue of the lepton mixing is far from being understood and even generally described as it occurs in the quark sector . in particular the generic three questions on the reason the leptons mix themselves , the details of the way they actually mix and which are the mechanisms which underlay their mixing , arize . in 1998 a new history for neutrinos began as a sort of second life with the double discovery that ( a ) they oscillate@xcite then owing a mass after 41 years from the initial idea of b. pontecorvo in 1957@xcite and ( b ) they mix themselves in a peculiar way after the void result by chooz@xcite . the chooz experiment took data in 1997 - 98 at a distance of about 1 km from a nuclear power plant of two reactors in france . it aimed to observe @xmath1 ( actually antineutrinos ) oscillations . after a collection of 2991 @xmath2 candidates chooz put an upper limit on the direct observation of @xmath3 events . at that time the limit was set as @xmath4 with a systematic error of 2.7% . the low error was due to the possibility for chooz to measure the backgrounds before the switching on of the reactors . in 2002 the kamland experiment@xcite repeated the measure in a site in japan where many reactors were present , close and far away from the detector . the distribution of the @xmath2 flux coming from the reactors is displayed in fig . [ fig1.2](a ) , with an average distance of 150 km from the reactor . differently from chooz , kamland obtained a positive result in term of disappearance of @xmath2 flux . the beautiful oscillation pattern is shown in fig . [ fig1.2](b ) . # 1 ( # 1 ) mainly after kamland ( and a rather contemporary result in the _ solar _ neutrino sector by the sno experiment@xcite ) the increase in the oscillation neutrino studies was extremely rapid and huge bringing to a re - interpretation of the chooz result in term of oscillations of flavour eigenstates . the old idea of mixing matrix by maki et al . in 1962@xcite was revitalized , similarly to what was made by cabibbo@xcite in 1963 for the quark sector . the standard parametrization of a mixing matrix at 3 components is therefore realized via the usual 3 euler rotations , leaving us with 3 angles , @xmath5 , @xmath6 , @xmath7 , and a phase @xmath8 . moreover in case of a majorana picture two more phases are present , @xmath9 and @xmath10 . to emphasize the key point it comes out quite naturally to simply establish a similar way of mixing for quarks and leptons . of course other more complex scenarios , where more than 3 eigenstates appear , are possible . more neutrinos states are compatible with the present knowledge of the lepton physics , in particular one or more _ sterile _ neutrinos@xcite may be included . this is a fundament question since it may or it may not en strength parallelism between quarks and leptons . the complete description of the formalism may be found in [ ] , while several fits have been performed to take into account the whole set of measurements . still fundamental questions remain unanswered . the first question relates to the mass ordering of the neutrino mass eigenstates . does the mass scale ordering of @xmath11 , @xmath12 , @xmath13 ( as defined by the parametrization ) follows the same ordering of @xmath14 , @xmath15 , @xmath16 ? as the measured oscillation pattern is described only in term of @xmath17 and @xmath18 the exact order is not identified yet , neither it is the absolute mass scale . are the 3 masses just below the present neutrino mass absolute limit ( less than 1 ev ) or are they some order of magnitude smaller ? more and more unanswered questions come up as we put a closer look to the measured quantities . for example in table [ tab1 ] the present values of the mixing matrix components for quarks , @xmath19 , and for leptons , @xmath20 are compared . the underlying pattern is clearly different and we finally conclude that the lepton mixing is weird s angles have been done . see for example ref . . ] . [ tab1 ] also the present knowledge of the errors is largely different in the quark and lepton sector . see e.g. ref . for an up - to - date report on the error measurements , to be compared with the extremely well known values of the quark mixing matrix@xcite . to illustrate the importance of the size of the errors we may look at fig . [ figiss ] taken from ref . 43 ) , which shows the large region for the possible values of the top angle of the lepton unitarity triangle . the degenerate case , @xmath21 , corresponding to the bottom horizontal line , is also still allowed by the present measurements . more and exhaustive discussions may be found in ref . . in summary we may conclude that the lepton mass mixing matrix might be technically similar to the quark one even if it shows a quite different pattern and it is at present rather poor known . we like to conclude this section by using the same wording of w. buchmller at eps09 conference@xcite : `` right - handed neutrinos have been found ; no exotics have been found ( yet ) '' . therefore as a whole it follows that we have to be prepared to the unexpected ! currently the lepton scenario illustrated in the previous section is the only one which is receiving attention by experimental investigation and mostly phenomenological investigation too . other theoretical possibilities like e.g. the nsi , non - standard - interactions@xcite , are in our judgement not so appealing and remains at the level of generic phenomenological models . therefore a not so long list of unknowns have to be identified and measured : the 3 mixing angles ( @xmath5 , @xmath7 and @xmath6 ) , the 2 neutrino squared mass differences ( @xmath17 , @xmath18 ) , the sign of one the two mass differences ( @xmath22 ) , a cp phase ( @xmath8 ) , the absolute neutrino mass scale and their nature ( dirac or majorana ) , the total number of neutrino ( are there more than 3 neutrinos ? ) , not at last forgetting the detection of the undergoing source of the oscillation . the latter question corresponds to the detection of a direct appearance signal , that is the observation of the @xmath16 appearance for the atmospheric oscillation ( and the @xmath14 for the solar one ) providing a direct measurement of the lepton flavor violation ( lfv ) process . most of the above items may be investigated at long - base - line experiments by excluding the investigation of the fundamental nature of the neutrinos and their absolute mass scale . the physics prospects are raveled by the `` presence '' of internal puzzles in the experimental side . in particular the recent results from miniboone are not able to disentangle the somewhat old and controversial result by lsnd@xcite . the original result from lsnd ( see fig . [ figlsnd ] ) of the @xmath23 observation could not be phenomenologically arranged in the 3 neutrino standard scenario . miniboone@xcite looked for the oscillation in either the neutrino or the antineutrino modes . in the neutrino mode it is able to rule out the result by lsnd as oscillation while observing an unexplained excess in a energy region below that of lsnd . in the antineutrino mode no similar excess is observed while the ruling out of lsnd is not gained . [ figminiboone ] ( a and b ) as extracted by ref . shows the miniboone results . as a matter of fact to the author the experimental situation is rather confused . more experimental facts are needed and the question whether the ongoing two lbl experiments minos and opera may help turns out to be fully relevant . the minos experiment@xcite is constituted by two similar apparata , the near and the far detectors , made of scintillator strips and a toroidal spectrometer . this layout allows the minimization of several uncertainties like the neutrino flux from the numi beam and the extrapolation via monte carlo of the unoscillated @xmath15 spectrum from near to far sites . a very detailed analysis allows to reconstruct the energy of the interacting neutrinos ( fig . [ figminos ] ) and estimate the percentage of disappeared neutrinos@xcite . from the later minos extracts the oscillation parameters in the assumption of 2 flavor oscillation mode ( fig . [ figminos1 ] from the analysis in [ ] ) . since we will discuss in the next section the opera experiment it is worthwhile to outline the twofold character of the minos analysis , the `` rate '' and the `` shape '' . as opera will be able to deal only with `` rates '' , the latter significance power has to be compared with the corresponding one by minos which turned out to be rather poor ( fig . [ figminos2 ] ) . the disappearance mode can be complementary studied in minos with the appearance of electron @xmath24 . first results reported were indicative of a possible @xmath14 appearance : 35 events from @xmath14 interactions were observed against an expected background of @xmath25 , corresponding to a 1.5 excess@xcite . however very recent results ( released after the conference time ) with an increased statistics washed out that indication@xcite . it seems that the new dedicated experiments for the @xmath7 measurement have to be waited for ( see the related contributions to these proceedings ) . we will now discuss at length the opera experiment since the very recent on may 31@xmath26 2010 release of new results ( see next section ) corresponds to a relevant new contribution in the neutrino physics . the opera experiment@xcite has been designed to observe the @xmath27 appearance in the cngs @xmath28 beam@xcite on an event by event basis . the @xmath27 signature is given by the decay topology of the short - lived" +"more than thirty years after the discovery of radio pulsars , the problem of understanding the properties of condensed matter in the interior of neutron stars ( nss ) has remained largely unsolved . a promising way to obtain constraints on the equation of state of nss is represented by the study of thermal radiation ( peaking at x - ray energies ) from their surfaces . the observed spectra are expected to show , as a characteristic signature of radiative transfer effects induced by the atmosphere surrounding the ns , several absorption features . these , if correctly deciphered , could unveil the ns physics . however , no such features were ever detected in the x - ray spectrum of a neutron star until recently , when chandra and xmm - newton observed the radio - quiet ns 1e 1207.45209 . this peculiar source ( bignami et al.1992 ; mereghetti et al.1996 ) , located close to the center of the high galactic latitude ( @xmath0 ) supernova remnant g296.5 + 10.0 , was securely identified as a ns when fast pulsations ( p@xmath1424 ms ) were detected by chandra ( zavlin et al.2000 ) ; a second chandra observation led to the discovery of two broad absorption features in its x - ray spectrum ( sanwal et al . 2002 ) . here we report on an xmm - newton observation ( 30 ksec ) performed on 2001 , december . the high throughput of the epic instrument allowed for a deeper study of the phenomenology of 1e 1207.45209 . see mereghetti et al.(2002 ) for more details . we measured a period of 424.13084@xmath20.00046 ms , implying a surprisingly low value of the period derivative , @xmath3=(1.98@xmath20.83)@xmath410@xmath5 s s@xmath6 , in agreement with ( but more accurate than ) the chandra estimate ( pavlov et al . 2002 ) . the pulse shape does not present any significant energy dependence ( see fig.1 ) , at variance with the findings of pavlov et al.(2002 ) , who reported some evidence for a phase shift of 0.4@xmath70.6 between the energy bands 0.3 - 1.0 and 1.0 - 1.7 kev . if the latter result is confirmed , it might imply a time - variable light curve . the spectrum of 1e 1207.4 - 5209 is characterized by two broad absorption features at 0.7 and 1.4 kev ( sanwal et al.2002 ) . figure 2 presents the results of the analysis of the epic pn spectrum by showing the residuals obtained with different models . * panel 1 : a simple blackbody fits is clearly inadequate * panel 2 : the weakly - magnetized hydrogen atmosphere model by zavlin et al.(1996 ) , although possibly inappropriate to the case of 1e 1207.4 - 5209 ( inferred b@xmath8 g ) , gives residuals very similar to the blackbody fit . * panel 3 : models of ns atmospheres with solar abundance ( gnsicke et al.2002 ) give unacceptable fits , since the predicted features are much narrower than the observed ones . the same is true for fe composition . * panel 4 : acceptable fits required the inclusion of two absorption lines , that we modeled for simplicity as gaussian lines : here we give the residuals to a blackbody@xmath9lines fit . * panel 5 : a further improvement was obtained by adding a power law : we believe that this reflects the shortcomings of other models alone to reproduce the low - energy part of this complex spectrum , rather than being evidence for a distinct non - thermal component . * panel 6 : for completeness , the residuals to an hydrogen atmosphere@xmath9lines fit are shown here . the plots in panels 4@xmath76 show that the broad feature at 0.7 kev is not well described by a single gaussian line . significant substructures suggest that the feature may be due to the blending of several narrower lines . the epic pn data were divided in four subsets corresponding to the phase intervals shown in fig.1 . the resulting spectra provide striking evidence of pulse - phase variations of the spectral features . this is clearly shown in fig.3 : we have fitted a blackbody+power law model after excluding the energy bands corresponding to the features . the residuals on the overall energy range show that the line at 1.4 kev is more pronounced during the minimum and the rising part of the pulse profile , while it is almost unvisible during the pulse peak . the feature below 1 kev presents a significant variation in shape , possibly due to different contributions of several narrower lines during the various phase intervals . our xmm - epic observation of 1e 1207.4 - 5209 has shown new , crucial details of the phenomenology of this puzzling source . the timing analysis yielded a very low value for the period derivative . the resulting characteristic age , @xmath10 kyrs , turns out to be much higher than the age of the host supernova remnant,@xmath11 10 kyears . this discrepancy can be settled by supposing that the ns was born with a spin period very similar to the observed one . most important , the spectral analysis has revealed that the absorption features have significant substructure and are phase - dependent . this strongly supports an interpretation in terms of atomic transitions in the neutron star atmosphere , different regions with different physical conditions being responsible for the emission visible at different phases . the actual chemical composition of the atmosphere is an open problem : sanwal et al.(2002 ) proposed once ionized helium in a superstrong magnetic field ( @xmath12 g , hardly conciliable with the value inferred from the pulsar spin parameters ) ; we prefer an interpretation in terms of heavier elements in a more conventional ( @xmath13 g ) magnetic field . indeed , hailey & mori ( 2002 ) suggested that the lines could be produced by he - like oxigen or neon , predicting the presence of substructures in the broad features . a second , very deep ( 250 ksec ) xmm observation of 1e 1207.4 - 5209 has now been successfully performed ( august 2002 ) . the new data will allow for a more detailed analysis of phase - resolved spectra . this will yield important and maybe conclusive information on the atmosphere composition , hopefully providing firm constraints on the other neutron star parameters . bignami g.f . , caraveo p.a . & mereghetti s. 1992 , apj 389 , l67 . gnsicke b.t . , braje t.m . & romani r.w . 2002 , a&a , 386 , 1001 . hailey c. j. & mori k. , 2002 , apjl accepted , astro - ph/0207590 mereghetti s. , bignami g.f . & caraveo p.a . 1996 , apj 464 , 842 . mereghetti s. , de luca , a. , caraveo , p.a . , mignani , r.p . , beker , w. and bignami , g.f . , 2002 , apj accepted , astro - ph/0207296 pavlov g.g . 2002 , apj 569 , l95 . sanwal d. , pavlov g.g . , zavlin v.e & teter m.a . 2002 , apj 574 , l61 . zavlin v.e . , pavlov g.g . & shibanov yu.a . 1996 , a&a 315 , 141 ." +"the mechanism by which a large class of proteins folds spontaneously into a unique globular shape @xcite has remained elusive . significant new insight was gained over the last few years from the studies of minimal protein models . for instance , energy landscape theory and funnel concept @xcite proved to be powerful tools for description of the general characteristics of folding not only in minimalistic protein models but also for real proteins @xcite . however , many questions on the details of the folding process remain to be solved . for instance , folding of proteins involves one or more transitions between different thermodynamic states . the role of these transitions in the folding process is an active area of research . an important example for these transitions is the formation of secondary structure elements . for the case of @xmath0-helices it is long known that there is a sharp transition towards a random coil state when the temperature is increased . the characteristics of this so - called helix - coil transition have been studied extensively @xcite , most recently in refs . @xcite . in this paper , we research the relation between helix - coil transition and folding . for this purpose , we have studied an artificial peptide , ala@xmath1-gly@xmath2-ala@xmath1 , in a detailed representation where the interactions between all atoms are taken into account . multicanonical simulations @xcite with large statistics are used to evaluate the free energy landscape of our peptide at different temperatures . the encountered transitions are further investigated by partition zeros analysis which allows to characterize `` phase transitions '' in small systems @xcite . quantities such as the energy , specific heat , helicity and susceptibility were calculated as function of temperature . we have neglected in the simulations the interaction of our artifical peptide with the surrounding solvent . while this is certainly a crude approximation , it allows us not only to relate our results to our previous studies on helix - coil transition in poly - alanine that also relied on gas - phase simulations @xcite , but also to study the extend to that secondary structure formation and folding are determined by intrinsic properties of the peptide . our data suggest that the peptide in gas - phase folds in a two - step process : in a first step two @xmath0-helices are formed in what amounts to a first order transition . afterwards these helices re - arrange themselves into a u - like structure . the second step has the characteristics of a second order transition . our investigation of ala@xmath1-gly@xmath2-ala@xmath1 is based on a detailed , all - atom representation of that peptide . the interaction between the atoms is described by a standard force field , ecepp/2,@xcite ( as implemented in the program package smmp @xcite ) and is given by : @xmath3 here , @xmath4 ( in ) is the distance between the atoms @xmath5 and @xmath6 , and @xmath7 is the @xmath8-th torsion angle . the peptide bond angles were set to their common value @xmath9 . we do not include explicitly the interaction of the peptide with the solvent into our simulations and set the dielectric constant @xmath10 equal to 2 . since the charges at peptide termini are known to reduce helix content @xcite , we removed them by taking a neutral nh@xmath11 group at the n - terminus and a neutral cooh group at the c - terminus . simulation of detailed protein models where the interaction between all atoms are taken into account are extremely difficult . this is because the various competing interactions within the molecule lead to an energy landscape characterized by a multitude of local minima separated by high energy barriers . hence , in the low - temperature region , canonical monte carlo or molecular dynamics simulations will tend to get trapped in one of these minima and the simulation will not thermalize within the available cpu time . one example of the new and sophisticated algorithms @xcite that allow to overcome this difficulty are _ generalized - ensemble _ techniques @xcite , and it is one of these techniques , multicanonical sampling @xcite , that we used for our investigations . in the multicanonical algorithm @xcite conformations with energy @xmath12 are assigned a weight @xmath13 . here , @xmath14 is the density of states . a simulation with this weight will lead to a uniform distribution of energy : @xmath15 this is because the simulation generates a 1d random walk in the energy space , allowing itself to escape from any local minimum . since a large range of energies are sampled , one can use the reweighting techniques @xcite to calculate thermodynamic quantities over a wide range of temperatures @xmath16 by @xmath17 where @xmath18 stands for configurations . note that unlike in the case of canonical simulations the weights @xmath19 are not a priori known . instead estimators for these weights have to be determined by an iterative procedure @xcite . in our case we needed 500,000 sweeps for the weight factor calculations . all thermodynamic quantities were then estimated from one production run of @xmath20 monte carlo sweeps which followed 10,000 sweeps for thermalization . our simulations were started from completely random initial conformations ( hot start ) and one monte carlo sweep updates every torsion angle of the peptide once . at the end of every 10th sweep we stored the ecepp/2 energies @xmath21 and @xmath22 of the conformation , the corresponding number @xmath23 of helical residues and end - to - end distance @xmath24 . here , we follow previous work @xcite and consider a residue as helical if its backbone angle @xmath25 are within the range @xmath26 . using the results of our generalized - ensemble simulation , we explored for various temperatures the free energies @xmath27 here , @xmath28 is the probability to find a peptide conformation with values @xmath29 , @xmath24 ( at temperature @xmath16 ) . we chose the normalization so that the lowest value of @xmath30 is set to zero for each temperature . we finally used that the multicanonical algorithm allows us to calculate estimates for the spectral density : @xmath31 we can therefore construct the corresponding partition function for our all - atom model of ala@xmath1-gly@xmath2-ala@xmath1 from these estimates by @xmath32 with @xmath33 the inverse temperature , @xmath34 . the complex solutions of the partition function determine the critical behavior of the model and were also studied by us . our peptide , ala@xmath1-gly@xmath2-ala@xmath1 , is build up out of two chains of each 10 alanine residues connected by 5 glycine residues . in previous work @xcite we could show that polyalanine has a pronounced transition between a disordered coil phase and an ordered state in which the polymer forms an @xmath0-helix . for this reason , we expect formation of @xmath0-helices in our peptide , and the average number of helical residues @xmath35 is therefore one of the quantities that we have measured . @xmath35 is displayed in fig . 1 as a function of temperature , and we observe in this plot two temperature regions . at high temperature , few residues are found with backbone dihedral angles @xmath25 typical for an @xmath0-helix . on the other hand , at low temperatures we observe helix - formation , and almost all of the alanine residues are part of an @xmath0-helix , i.e. have backbone dihedral angles @xmath25 in the range ( @xmath36 ) . the transition between the two temperature regions is sharp indicating the existence of a helix - coil transition . the transition temperature @xmath37 can be determined from the corresponding peak in the susceptibility @xmath38 which is ploted in the inset of fig . 1 , and we find the transition temperature @xmath39 k. in previous work @xcite we could show that in polyalanine the formation of @xmath0-helices is related to a gain in potential energy . for this reason , we display in fig . 2 the average total ecepp/2 energy @xmath40 and the thermodynamic averages of partial energies @xmath41 , @xmath42 , @xmath43 and @xmath44 of ala@xmath1-gly@xmath2-ala@xmath1 as a function of temperature . as expected , we observe around our transition temperature @xmath37 a sharp decrease in the potential energy @xmath40 that is due to a corresponding decrease in the coulomb energy @xmath41 , lennard - jones energy @xmath42 and hydrogen - bond energy @xmath43 . the change in @xmath40 with temperature can be described by the specific heat @xmath45 which we display in fig . a pronounced change in energy with temperature corresponds to a peak in the specific heat . as one can see from fig . 3 , we observe indeed a pronounced peak in the specific heat at a temperature @xmath46 k that is consistent with @xmath47 k , the temperature where the peak in the susceptibility is located . combining both values we obtain as our final estimate for the helix - coil transition temperature @xmath48 . however , we find in fig . 3 also a second , smaller peak in the specific heat at the lower temperature @xmath49 k indicating yet another transition . the sharp decrease in potential energy corresponding to this second peak is clearly visible in fig . 2 for the total energy @xmath40 , however , not for all of the partial energies . only the lennard - jones term @xmath42 exhibits also a signal for the second transition at @xmath50 . this energy term depends strongly on the overall size of the molecule and the change in this quantity indicates a transition between extended and compact structures . hence , we conjecture that the second peak in specific heat at the lower temperature @xmath50 is related to a transition between extended and compact structures . a possible measure for such a change is the average end - to - end distance @xmath51 . we define here @xmath52 as the distance between n of ala@xmath53 and o of ala@xmath54 , and plot this quantity in fig . 4 . we observe that this quantity decreases with decreasing temperature . below the helix - coil transition @xmath37 the decrease slows down and the curve becomes almost flat at a value of @xmath55 indicating that there is little further change in the compactness of the molecule . however , at temperature @xmath50 the end - to - end distance decreases again sharply towards a new value @xmath56 . hence , @xmath50 marks the folding of the molecule into a defined compact structure with the two terminal ends of the peptide close together . the transition between extended and a more compact structure can also be seen when we display the free energy landscape of our peptide as a function of helicity @xmath23 and end - to - end distance @xmath24 . at the temperature @xmath57 k ( which is essentially the helix - coil transition temperature @xmath58 k ) the free energy landscape ( displayed in fig . 5a ) is flat over a large range of values of @xmath23 and @xmath24 . the @xmath59 contour line surrounds a region where the helicity can take values between @xmath60 and the end - to - end distance values between @xmath61 , allowing the system to move freely between extended and compact configurations , and between helical and coil configurations . on the other hand , at the second and lower temperature @xmath62 k ( which is essentially the folding transition temperature @xmath49 k ) the free energy grows rapidly with decreasing helicity @xmath23 favoring configuration in a small strip with @xmath63 . hence , the plot of the free energy landscape in fig . 5b is limited to values @xmath64 of the helicity . here , two regions of minimal free energy can be seen ( marked by the 3 @xmath65 contour lines ) . the first minima is found at values of @xmath24" +"progressive improvements of detectors since the pioneering efforts in the 1960s have led to improved measurements of the spectrum of the electronic component and positron fraction by the fermi , hess , atic , and pamela instruments [ 1 - 5 ] . these measurements have stimulated great excitement , not only because of their importance to cosmic ray studies , but also because of the possible interpretation of some of the features from signals from the annihilation of dark matter in the galaxy . we reproduce the observed total electronic spectrum @xmath1 and the positron fraction @xmath2 in fig . [ hess ] and fig . [ pam ] respectively . in section ii , we show that these observations help us in distinguishing between the leaky box @xcite and the nested leaky box models @xcite . it is the difference in the kinematics of the reactions producing secondary ` light ' nuclei and positrons that helps in distinguishing amongst these models . we show that the positron fraction observed by pamela may be fit well with the nested leaky box model . we begin section iii by deriving the spectrum of electrons resulting from direct acceleration in the cosmic ray sources by subtracting the secondary electrons and positrons from the spectrum of the total electronic component . after this , the rest of the section is devoted to a discussion of this primary electron spectrum in terms of a set of discrete sources of cosmic rays sprinkled throughout the galaxy . the analysis indicates that we need the closest source to be no more than @xmath3 200 pc from the solar system , which in turn implies that there are about 5000 sources accelerating cosmic rays in the galaxy . the contrast between the spectra expected from a discrete set of sources and from sources spatially distributed smoothly throughout the galaxy plays an important role in analyzing signatures from the annihilation of dark matter in the galaxy . this aspect is discussed in section iv . it would be appropriate to note here that the theoretical considerations of cosmic ray transport with exponential pathlength distributions @xcite@xcite and its analysis in terms of a set of discrete sources sprinkled over the galaxy @xcite@xcite started three or four decades ago . the recent improved measurements constitute a testing ground for these early ideas on cosmic ray physics . and @xmath4.,width=240 ] gev.,width=240 ] the observations of decreasing ratios of secondaries to primaries like b / c and ( v+ti+sc)/fe with increasing energy per nucleon in cosmic rays could be incorporated into the original leaky box model ( a and b ) @xcite by letting the mean residence time @xmath5 depend on energy in such a way as to reproduce the observations @xcite . a viable alternative to this idea was the nested leaky box model ( c ) @xcite in which the energy dependant part of the ratio ( proportional to @xmath6 ) was attributed to the spallation in the matter constrained in a cocoon - like region surrounding the sources and the resident time in the galaxy @xmath7 was assumed independent of energy . with observations of the ratios limited to a finite range of energies , it became customary to extrapolate the residence times as a simple power law , decreasing as @xmath8 . even though the observations to date allow @xmath9 beyond some tens of gev / n , this alternative had not been discussed earlier . these three possibilities and their corresponding fit to the secondary to primary ratios are shown in fig . [ bc ] for the b / c ratio . the ( v+ti+sc)/fe ratio can be fit similarly . the three models presented here are characterized by mean residence times as noted below : . a(e)&~_0e^- , e>2 gev / n .. ll _ b(e ) & ~_a(e ) , e10 gev / n + & ~_g~x , e10 gev / n .. ll _ s(e)&~_b(e)-_g , e10 gev / n + & ~_g~x , e10 gev / n .where @xmath10 is a constant . consider now the injection of cosmic rays by sources with the spectral form q(e)~q_0e^-cm^-3s^-1sr^-1gev / n^-1.when spallation and energy loss during transport could be neglected , the three models led to the following equilibrium spectra of cosmic rays in the galaxy : [ eq : f ] ll f_a&~q_0_0e^-(+ ) + f_b&~q_0_0e^-(+ ) , e10 gev + & ~q_0_ge^- , e10 gev + f_c&~q_0_ge^- . note that @xmath11 does not depend upon @xmath6 @xcite . unless @xmath12 itself is a function of energy so that eq . 5b reproduces the observed spectra of the nuclear component that is a simple power law , model b is not viable . model a requires @xmath13 and predicts increasing anisotropy with energy of cosmic rays , and model c requires @xmath14 and generates constant anisotropy at all energies . the observations of the positron fraction provides a clear way of choosing amongst these three models . the reason for this is related to the fact that in the spallation process that generates the secondary cosmic ray nuclei like b in collisions of the primary c nuclei , the daughter nuclei will emerge with the same energy per nucleon as the parents . on the other hand , the production of positrons proceeds through the production of mesons ( mainly pions ) in the collision of the primary nuclei which follow the decay chain @xmath15 , followed by @xmath16 . in this process , the positrons and the secondary electrons carry , on the average , only a small fraction @xmath17 of the energy / nucleon of the primary . as a consequence of this , the production spectrum of positrons ( and secondary electrons ) in all the three models are nearly identical . the fact that low energy cosmic rays spend more time in the cocoon surrounding the sources plays no role as the @xmath18 and @xmath19 secondaries are generated only by the high energy part of the nucleon spectrum . now the equilibrium spectrum of secondary @xmath18 and @xmath19 predicted by the three models simply follow the product of the production rate , @xmath20 and the residence time @xmath21 at low energies . at very high energies , all the models predict steeper spectra @xmath22 : @xmath23 where @xmath24 and @xmath25 is defined in eq . 10 . in fig . [ pam ] we show the positron fraction r(e)=f_n+(e)/f_t(e)with the positron spectrum @xmath26 as given in eq . 6 for the three models , and the spectrum of the total electronic component is taken to be the smooth fit to the data shown in fig . note that only model c provides a good fit over the entire range of the pamela observations . thus , the observed positron fraction resolves the degeneracy amongst models developed to understand the nuclear secondaries and suggests that the nested leaky box model may provide a closer approximation to cosmic ray transport in the galaxy @xcite . the nucleonic component in the primary cosmic rays consists mainly of protons with a small fraction of neutrons which come in bound to he and other nuclei . as a consequence , the production of positrons is favored over that of electrons in cosmic ray secondaries : q_n-(e)/q_n+(e)0.5 - 0.8.the lower value of @xmath27 is favored by the theoretical estimates based on the data on nuclear interactions obtained at accelerators @xcite , and the larger value is favored by the observations of the @xmath28 ratio generated by cosmic rays in the atmosphere @xcite . the loss of energy by energetic cosmic ray electrons due to inverse compton scattering and synchrotron emission in the magnetic fields prevalent in the propagation volume is given by de / dt =- be^2;@xmath29 noting that the scattering of starlight by the very high energy electrons is described by the klein - nishina formula , the effect of starlight may be neglected , and only the microwave background contributes to @xmath30 in eq . 10 . taking @xmath31 and @xmath32 , we get @xmath33 . adopting the nested leaky box model , the spectrum of the secondary positrons and electrons is given by @xcite @xmath34 in fig . [ hess ] , we show the total secondary component @xmath35 , with the normalization for @xmath36 determined from a smooth fit to the pamela data and @xmath37 , i.e. @xmath38 . we also show the secondary component for @xmath39 . subtracting this ( for @xmath40 ) from the total spectrum of the electronic component , we get the spectrum due to the sources , g_e(e)=f_t(e)-f_n+(e)(1+),which is displayed in figs . [ single ] and [ sum ] . in an attempt to understand this spectrum , we assume diffusive transport of cosmic rays and write the differential equation describing the transport as dn / dt-^2n+n/=q.note that here we have simplified the form of the green s function by introducing an escape term @xmath41 in place of the boundary condition demanding that the cosmic ray density vanish at the planar surfaces of the thick cosmic ray disk of the galaxy . the green s function is given by g(r , t)=(4t)^-3/2exp(--).this along with the subsidiary eq . 9 is adequate to describe the transport of the electronic component of cosmic rays . note that for a smooth and uniform distribution of sources @xmath42 , the green s function in eq . 14 integrates to the simple leaky box model . compared to the _ primary _ electron spectrum.,width=240 ] compared with the _ primary _ electron spectrum . their difference ( thick line ) is shown.,width=240 ] suppose we have a source situated at a distance @xmath43 which is continuously emitting cosmic ray electrons with a spectrum ll q&~ q_0e^- , e < e_x + & ~ 0 , ee_x , the observed spectrum is given by ll f_d(e , r_i)= & + ^_0q_0e^-(1-bet)^-2g(r_i , t)dt . & we display in fig . [ single ] this spectrum for various values of @xmath43 . note that for @xmath44 , @xmath45 , and @xmath46 , one can obtain a reasonable fit to the high energy part of the primary electron spectrum g(e ) . however , it is appropriate to add the contributions of all the sources situated at different distances to obtain their net contribution @xmath47 to @xmath48 . assuming that the @xmath49 source is at an average distance of @xmath50 , we sum their contributions and compare with the primary electron spectrum @xmath48 in fig . we see that irrespective of the choice of parameters , the high energy part of @xmath48 is not reproduced by the theoretical expectation @xmath47 . this difference becomes particularly large for @xmath51 much larger than @xmath52 . thus we may expect that the distance to the nearest source and the typical spacing between the sources is @xmath52 . the difference between the contribution of the discrete sources @xmath47 and the fit to @xmath48 is also shown in fig . [ sum ] , and the difference @xmath53 with the data points is shown in fig . [ conteloss ] . the narrow spectral feature displayed in figs . [ sum ] and [ conteloss ] has been ascribed _ in toto _ or in part to products of dark matter annihilation ( see @xcite for references ) . in this section , we discuss two input spectra , one a @xmath54-function in energy and the other a flat spectrum @xmath55 , such as that expected for acceleration at planar shocks of high mach number . here , the injection spectrum @xmath58 , the spectrum after time @xmath59 , @xmath60 ( without leakage ) , and @xmath61 for a spatially smooth source and leakage lifetime @xmath7 are given by q(t=0,e_a)=(e(t=0)-e_a),f_1(e)=(-e_a),f_c = exp-().the spectrum @xmath61 peaks at @xmath62 for @xmath63 , and there is no sharp peak at @xmath64 ( see fig . [ conteloss ] )" +"stars and gas in galaxies interact continuously through the exchange of matter and energy . it is this process that drives galactic evolution and that determines many of their observed characteristic properties . low - mass stars have a limited effect on their environment by generating wind - blown bubbles and planetary nebulae . high - mass stars , on the other hand , disturb the dynamics of the surrounding interstellar medium on larger , that is galactic scales through their ionizing photons which destroy molecular material and through supernova explosions which act as point sources of thermal and kinetic energy input and which drive galactic chemical evolution . the most violent events are multiple supernova explosions that erupt on timescales of order @xmath0 yrs in young massive clusters ( ymcs ) and that can completely change the morphology and evolution of a galaxy by blowing its gas and metals out into intergalactic space . star formation in galaxies is a non - linear process which in details is not understood up to now ( for a recent comprehensive review see mac low & klessen 2004 ) . ordinary spiral galaxies , like the milky way , `` burn '' stars at a low , self - regulated rate . although a large fraction of their visible gas is condensed in cold molecular clouds with masses that by far exceed their thermal jeans mass , star formation turns out to be surprisingly inefficient ( blitz & shu 1980 ) . for example , the milky way with a total molecular gas mass of order @xmath1 and molecular cloud densities of order 100 @xmath2 , corresponding to collapse timescales of @xmath3 yrs , could in principle form stars with a rate of @xmath4 m@xmath5/yr , which is a factor of 1000 larger than observed . irregular supersonic motions ( so called `` molecular cloud turbulence '' ) have been detected in most cloud complexes ( larson 1981 , elmegreen & falgarone 1996 ) and are considered as the main source for their stability . however numerical hydrodynamical simulations consistently show that supersonic , highly compressible turbulence dissipates on timescales that are smaller than their collapse timescale ( stone et al . 1998 ; mac low et al . 1998 ) . in addition , no driver of molecular cloud turbulence has ever been found which on the one hand efficiently suppresses star formation on small scales while , at the same time , stabilizing giant molecular clouds on the large scales ( heitsch et al . 2001 ) . magnetic fields are not strong enough to stabilize a giant molecular cloud either , although they might play an important role on scales of molecular cloud cores , regulating their collapse and angular momentum distribution and by this also affecting the stellar initial mass function and multiplicity ( shu et al . 1987 , mouschovias 1991 , crutcher 1999 ) . kornreich & scalo ( 2000 ) argued that large - scale interstellar shocks , identified with supernova remnants or superbubbles , provide an energy source for molecular cloud turbulence . when the shock passes through a cloud with an internal density gradient , vortical motions are generated that resemble turbulent motions . still , it has not yet been demonstrated that such a scenario can explain the detailed observed structures and velocity fields in molecular clouds . the virialized , long - lived molecular cloud scenario also leads to a post - t tauri problem ( herbig 1978 , hartmann 2000 , hartmann et al . 2001 ) : the age spread of young stellar populations in filamentary cloud complexes like taurus are typically 1 - 3 myrs which is considerably smaller than their lateral crossing times that are of order 2 - 3 @xmath6 yrs . these arguments have motivated scientists to explore an alternative scenario , where molecular clouds never achieve a dynamical equilibrium state of turbulent support . they instead form from the turbulent , diffuse interstellar medium with their irregular motions and clumpy substructures already being imprinted at the time of formation ( larson 1981 , elmegreen 2000 ; hartmann 2003 ) . star formation then is an initial condition problem , rather than determined by the gravitational fragmentation of an initially driven , turbulent equilibrium state ( klessen & burkert 2000,2001 , bate et al . 2003 ) . in this case , the important question is not to identify the source of stability and turbulent driving in dense clouds , but instead to investigate the various processes that play a role when molecular clouds form . giant molecular clouds are one of the most massive objects in galaxies . how molecular gas manages to accumulate into such large entities with masses of @xmath7 before condensing into stars and which processes lead to their internal kinematics and density distribution is still unclear ( pringle et al . 2001 ) . hartmann et al . ( 2001 , see also scalo & chappell 1999 , ballesteros - paredes et al . 1999 , vzquez - semadeni et al . 2003 ) suggested that filamentary cloud complexes could form from large - scale colliding gas flows ( see also klessen et al , this volume ) . most of the stellar energy input into the diffuse interstellar medium arises from supernovae ( wada & norman 2001 ) which drive large - scale turbulent flows with characteristic velocities of order 10 km / s . superbubbles , resulting from multiple supernovae in young massive clusters lead to supersonic large - scale flows with an extent of 150 pc ( mc cray & kafatos 1987 ) . when such flows collide , it takes of order @xmath8 yrs to accumulate enough material to form a giant molecular cloud in the post - shock gas . as the age spread of young stars is a factor of 5 smaller , star formation needs to be suppressed during this stage . hartmann et al . ( 01 ) argue that this is indeed likely , as the conditions for efficient molecular hydrogen formation require a minimum column density of order @xmath9 @xmath10 for shielding from the interstellar radiation field to be effective . prior to that , the dense hi slabs would still be invisible . figure 1 shows the results of a numerical calculation of two converging hi gas flows which collide with mach 1 , leading to a compressed and cooling dense slab ( burkert , 2004 in preparation ) . a cooling instability ( burkert & lin 2000 , kritsuk & norman 2002 ) , combined with a thin slab instability ( vishniac 1999 ) enhances small density fluctuations in the incoming hi , leading to a clumpy , irregular density distribution with internal irregular velocities , embedded in a hotter environment of compressed hi gas . during the early build - up phase the internal irregular motions , powered by the kinetic energy of the colliding gas flows can stabilize the dense clumps against gravitational collapse ( koyama & inutsuka 2002 ) . after @xmath11 yrs a filamentary , highly structured cold cloud complex has formed that resembles observed molecular cloud regions well ( fig . 2 ) . now gravity becomes dominant and stars begin to form . within the framework of this scenario , the low rate of star formation in the milky way is a combination of the timescale of molecular cloud formation ( @xmath8 yrs ) , coupled with a low star formation efficiency of order a few percent . note also , that star formation regulates itself as the rate of formation of new sites of star formation , as well as their substructures will be determined by flows that are generated by previous generations of stars . ( 0,220 ) ( 75 . , 0.)=7.7 cm ( 0,160 ) ( 40 . stars tend to form preferentially in clusters ( lada & lada 2003 , tan & mckee , this volume ) . still , massive clusters with masses exceeding @xmath12 are rare in quiescently evolving , self - regulated galactic environments , like the milky way . larsen ( 2002 ) estimates that only @xmath13 % of normal spirals have clusters as bright as @xmath14 . the situation is different in star burst regions which typically contain swarms of ymcs and super - star clusters that might even represent the progenitors of globular clusters ( whitmore & schweizer 1995 , ashman & zepf 1991 ; see however tenorio - tagle et al . ymc - formation therefore seems to require unusual conditions that are found in perturbed galactic environments ( keel & borne 2003 ) . interestingly , ymcs follow the same universal mass function @xmath15 as molecular clouds , independent of environment . this can be explained if ( a ) the probability to form a massive stellar cluster and ( b ) the star formation efficiency , that is the fraction of cloud mass that condenses into cluster stars , is independent of cloud mass ( elmegreen & efremov 1997 ) . as massive clouds are found both in quiescent as well as in perturbed galaxies , ymcs could in principle form everywhere and one might at first not expect to find a dependence of the number of ymcs on environment , in contradiction with the observations . there exists however strong evidence that the star formation efficiency depends on environment , even if it is independent of cloud mass for a given environment . solomon et al . ( 1997 ) and solomon ( 2000 ) find that in starburst regions with high star formation efficiencies ( sfe @xmath16 0.1 ) the fraction of gas at high densities of @xmath17 is of order 10% , which is a factor of 10 higher than in unperturbed galaxies like the milky way with typical values of sfe @xmath16 1% . the star formation efficiency therefore seems to be correlated with the fraction of gas at high densities : @xmath18 where m@xmath19 is the total mass of molecular gas with densities above n = @xmath20 @xmath2 and m@xmath21 is the total cloud mass . in quiescent regions with sfe @xmath16 0.01 ymcs with stellar masses m@xmath22 @xmath23 m@xmath5 can only form from clouds with masses exceeding m@xmath21 @xmath24 m@xmath5 . in perturbed environments with sfe @xmath25 , on the other hand , a much larger fraction of clouds will form ymcs , as the limiting lower mass for ymc formation is m@xmath26 m@xmath5 . again , molecular cloud formation in converging gas flows might be an important mechanism to explain the large fraction of dense gas in starburst regions as well as their high star formation rates . in perturbed galactic environments , as for example in merging galaxies , the relative velocites of colliding gas flows are @xmath27 100 km / s , one to two orders of magnitude larger than in unperturbed disks . colliding flows with such a high relative velocity lead to exceptionally high compression of the cooling and fragmenting slabs and , by this , to a larger gas fraction at high densities than in unperturbed galactic environments . in addition , due to the large inflow velocities , the timescales for accumulating @xmath28 m@xmath5 of gas is reduced by 1 - 2 orders of magnitudes , leading to molecular cloud formation timescales , less than @xmath0 yrs . both , the high star formation efficiencies in combination with the strongly reduced molecular cloud formation timescales could explain why the star formation rates in perturbed galacies are orders of magnitudes higher than in unperturbed regions . more theoretical work is required in order to understand all aspects of this model in details . the evolution of multiple supernova remnants that form from an ob association of 10 to 1000 massive stars in ymcs has been summarized by mac low ( 1996 ) . the most massive" +"far - infrared astronomy is largely the preserve of telescopes borne on satellites , balloons and aircraft . the infra - red astronomical satellite , iras ( beichman et al . , 1988 ) operated at wavelengths as long as 100 @xmath0 m . the kuiper airborne observatory , kao ( cameron , bader & mobley 1971 ; harvey 1979 ) , the infrared space observatory , iso ( kessler et al . , 1996 ) , and the spitzer space telescope ( werner et al . , 2004 ) were designed to operate out to 200 @xmath0 m . a number of planned missions such as herschel and planck aim to cover still longer wavelengths . however , a problem with all such airborne and satellite telescopes is that they are unlikely to be as large as telescopes that can be built on the ground . consequently , airborne and orbiting telescopes do not have the angular resolution of comparable ground - based instruments . therefore , any instruments that can be operated from the ground at these wavelengths and mounted on large telescopes will automatically have a resolution advantage . only a limited number of previous ground - based astronomical observations have been made at far - infrared wavelengths . this is because the atmosphere is largely opaque in this regime . however , spectral measurements of the atmosphere , coupled with detailed modelling of atmospheric properties , have shown that there are some small windows that do open up across this range on very high , dry sites under good conditions . one such window is that at 200 @xmath0 m , corresponding to a frequency of 1.5 thz . ( 70,60 ) ( -16,-43 ) previous ground - based measurements at this frequency have only been made spectroscopically . no previous ground - based imaging camera has been built to work at this frequency . the spectroscopic observations include fourier transform spectrometer ( fts ) measurements at pampa la bola in chile ( matsuo , sakamoto & matsushita 1998 ; matsushita et al . , 1999 ) . these latter authors derived measurements relating the optical depths in different atmospheric pass - bands , including that at 200 @xmath0 m . ground - based fts measurements at mauna kea in hawaii have been carried out by a number of groups ( e.g. serabyn & weisstein 1996 ; serabyn et al . , 1998 ; pardo et al . , 2004 ) all have confirmed the existence of an atmospheric window at 200 @xmath0 m , albeit with varying levels of transmission , depending upon the conditions . paine et al . , ( 2000 ) carried out similar fts measurements at both mauna kea in hawaii and at chajnantor in chile and measured the atmospheric transmission from about 300 to 3000 ghz . they measured the 1.5-thz window and found significant transmission in the wave - band of interest at both locations . other work at this frequency has included plans for a heterodyne system to operate at the south pole by a group who have made fts sky measurements , broadly confirming the above - mentioned results ( chamberlin et al . , 2003 ; gerecht et al . , 2003 ) . in this paper , we present the results from the first commissioning run of the two hundred micron photometer ( thumper ) at the james clerk maxwell telescope ( jcmt ) . this instrument is a prototype camera built at cardiff university to demonstrate the viability of carrying out high - resolution broad - band imaging at 200 @xmath0 m from the ground . ( 70,60 ) ( -16,-43 ) thumper consists of a 7-channel array of photoconductor pixel elements arranged on a hexagonal grid ( ward - thompson et al . , 2002 ; walker et al . , 2003 ; evans et al . , 2005 ) . this is designed to match the layout of the central pixels in the sub - millimetre common user bolometer array , scuba ( holland et al . , 1999 ) , when placed at the nasmyth focus of the james clerk maxwell telescope ( jcmt ) on mauna kea , hawaii . this is at an altitude of 4092 m , and is one of the best sites for sub - millimetre observations in the world . the thumper detectors are photo - conductors made from gallium - doped germanium ( in the ratio ge : ga @xmath3 10@xmath6:1 ) crystal semi - conductors , which have been stressed to move their peak responsivities into the 200-@xmath0 m waveband ( walker et al . , 2003 ; walker 2004 ) . figure [ crystals ] shows a typical crystal responsivity as a function of frequency . the lighter line to the right shows the natural crystal response . the heavier line to the left shows the response after the crystal has been mounted in the camera and stressed to its optimal value . a series of filters matches the band - pass of the instrument to the atmospheric window . figure [ filters ] shows the combined band - pass filtering of the system . a drawing of one of the stressing blocks is shown in figure 3(a ) . the crystals are mounted in the integrating cavities on the front of the stressing block ( on the left of figure 3(a ) ) and a stressing rod is pushed up into the rear of the block ( on the right of figure 3(a ) ) using a stressing screw . this in turn operates a lever which applies the stress downwards through the line of crystals by means of further stressing rods . ( 140,120 ) ( -46,0 ) ( 46,0 ) ( -46,-63 ) ( 46,-63 ) there are three stressing blocks . the centre block holds three crystals and the two side blocks hold two crystals each , such that when the three blocks are fixed together , as in figure 3(b ) , the crystals make a hexagonal arragement . the crystal integrating cavities are coupled to the telescope by individual feed - horns , as shown in figure 3(b ) , with a resolution of 14 arcsec , as for the scuba 850-@xmath0 m array ( holland et al . , 1999 ) . the thumper focal plane array can also be adjusted to match the scuba 450-@xmath0 m array if desired , although this mode was not used on this occasion . we chose not to make the feed - horns diffraction - limited on the telescope because the dish surface accuracy is too low to provide a significant fraction of the total incident power in a diffraction - limited beam at this wavelength . the focal plane array is mounted in a stand as shown in figure 3(c ) and the filter stack attached to the front of the array as seen in figure 3(d ) . the whole array is cooled to liquid helium temperature ( 3.7 k at jcmt ) in a long hold - time cryostat , built by queen mary college instruments ( now based at cardiff university ) and thomas keating ltd . the system detector quantum efficiency ( dqe ) was measured in the laboratory . calculations were performed based upon the optical set - up of the instrument at the telescope , including estimates of the dish surface accuracy . incorporating all of these factors we estimated before going to the telescope that the noise equivalent flux density ( nefd ) of the jcmt - thumper arrangement should be @xmath35070 jy ( 1@xmath5 1s walker 2004 ) . the cryostat was mounted on the right nasmyth platform of the jcmt . two lenses , made of high - density polyethylene , were used to bring the beam from the telescope to the f/5.75 focus required by thumper ( walker et al . the instrument was commissioned during director s discretionary time in two 4-night observing runs on 2005 march 20 - 23 , and 2005 april 6 - 9 . optical alignment and instrument setup were carried out prior to this . data acquisition was carried out via a stand - alone computer operating the labview software system ( laboratory virtual instrument engineering workbench ) . only one of the scheduled nights was good enough for astronomical observations at this wavelength , 2005 april 9 , when our observing was scheduled from 01.30 to 09.30 hawaiian standard time ( ut 11.30 to 19.30 ) . data from that night are presented in this paper . ( 70,60 ) ( -16,-43 ) the 200-@xmath0 m ( 1.5 thz ) atmospheric window is much narrower in wavelength than the more commonly used sub - millimetre windows , and has much lower transmission . we modelled this window , along with neighbouring windows , using the cardiff - developed software package fetch ( araujo et al . , 2001 ; hayton et al . , this is a fast , highly flexible line - by - line , layer - by - layer , radiative transfer model that uses the latest high - resolution transmission ( hitran ) molecular spectroscopic database ( 2004 version ) to calculate the atmospheric transmission as a function of frequency ( rothman et al . , 2003 ; 2005 ) . we found that the window extends from 1428 to 1588 ghz ( 189210 @xmath0 m ) , with peak transmission at 1486 ghz ( 202 @xmath0 m ) . the reason why the peak wavelength is not centred in the window is that there is an absorbtion line directly in the centre of the window . ( 70,60 ) ( -16,-43 ) figure [ atmos ] shows the result of the detailed model calculations of the transmission across the whole of this part of the spectrum , assuming that the atmospheric precipitable water vapour ( pwv ) content is 0.5 mm . the more familiar window at 850 ghz ( 350 @xmath0 m ) can be seen , along with the small transmission window just opening at 1.5 thz ( 200 @xmath0 m ) . the peak transmission is low , but nonetheless useable for part of the time . this calculation is consistent with the measurements of paine et al . ( 2000 ) , under better atmospheric conditions in chajnantor , chile see their figure 3 . on the occasions when the sky was totally opaque we measured the relative responsivity of the seven channels by measuring the sky emission at zenith . this is essentially a flat , extended source , and allowed us to make a flat - field of our focal plane array . this remained remarkably constant , and was also consistent with our sensitivity measurements made in the laboratory . during the times when we could carry out astronomical observations we calibrated the sky transmission using the method of sky - dipping . this entails measuring the sky emission at several positions between zenith and horizon , and modelling the profile as a function of zenith distance , z. the emission is predicted to have the form @xmath7 , and hence a fitting routine can be used to calculate the optical depth , @xmath1 . figure [ skydip ] shows the result of a typical sky - dip . on the x - axis is plotted zenith distance z from 90@xmath8 to 0@xmath8 , while the y - axis gives the emission measured from the sky at a given value of z , normalised to the peak emission at 90@xmath8 . the data - points with error - bars are shown connected by a dashed line , while the solid line shows the model fit to the data for an optimised value of the optical depth , @xmath1 . throughout our observations , the jcmt water vapour monitor" +"most spiral galaxies have rather sharp edges in their stellar disks . the situation for the milky way is unclear . the disk of our galaxy is well represented by an exponential density profile @xcite , with some evidence for a stellar disk cut - off at a radius of @xmath1 kpc towards the anticentre region @xcite , but other claims for a warped and flaring stellar disk out to 23 kpc . based upon the scaling relation established by other galaxies , the radial cut off should be between 10 and 25 kpc @xcite . here we report observations of `` clump red giant '' stars , which are good distance indicators @xcite , along 10 lines of sight in the disk of the milky way . the data reveal an edge to the disk at @xmath2 kpc . why there should be a sharp edge to the stars , while the gas profile is much more extended and does not show such an edge , remains unclear , but a critical test would be the measurement of the gas and star density in situ @xcite . there are two new deep surveys of the milky way disk in the near - infrared : the ukidss galactic plane survey ( gps ) , that is mapping the northern disk @xcite , and the vista variables in the _ va lctea _ ( vvv ) survey , that is mapping 520 square degrees in the southern disk and bulge of our galaxy @xcite . while previous observations in the galactic plane have been limited by crowding , source dimness , and interstellar extinction , these new public surveys allow us to pierce through the whole disk , reaching red giants in the horizontal branch ( clump giants ) located at the other side of our galaxy for the first time in different near - ir pass - bands . the vvv survey observes in the @xmath3 ( 0.87 microns ) , @xmath4 ( 1.02 microns ) , @xmath5 ( 1.25 microns ) , @xmath6 ( 1.64 microns ) , and @xmath7 ( 2.14 microns ) bands , while the ukidss - gps is observing in the @xmath5 ( 1.25 microns ) , @xmath6 ( 1.64 microns ) , and @xmath8 ( 2.14 microns ) bands ; with the photometry uniformly calibrated in the 2mass system @xcite . clump giants are excellent tools to study the structure of our galaxy because of two main reasons , discussed below : ( i ) they are good distance indicators , and ( ii ) they are good tracers of the mass in the disks of galaxies . the ukidss - gps and vvv surveys give the largest homogeneous census of clump giants out to well beyond the extent of the milky way stellar disk . the limiting dophot @xcite magnitude of single epoch vvv images processed by the cambridge astronomical survey unit ( casu ) pipeline v1.0 is @xmath9 in the disk fields , and the dophot photometry on the combined epochs allow to reach approximately @xmath10 mag , and @xmath11 mag ( fig . [ cmd ] ) , slightly fainter than the ukidss - gps , and much fainter than the near - ir surveys 2mass and denis , for which the limit is @xmath12 mag @xcite . the distance probed along the line of sight depends on the reddening of the fields . for example , in disk fields with low extinction ( @xmath13 mag ) the ukidss - gps and vvv surveys would see clump giants beyond 50 kpc . therefore we can search for the edge of the disk of our galaxy using well calibrated standard candles . the clump giants with known parallaxes measured by the hipparcos satellite are the best collectively calibrated standard candles @xcite . figure [ cmd ] shows a colour - colour and colour - diagram magnitude for the vvv field d003 . in order to select the giant stars a colour cut was applied in the @xmath7 @xmath14 ( @xmath15 ) , as shown in left - hand and central panels of fig . not all selected stars are clump giants , but the presence of sub - giant branch and red - giant branch stars , or even main - sequence stars at fainter magnitudes , contribute to the smooth underlying background . these different population do not affect the location of any sharp edges of the stellar distribution , which can however be well defined by the clump giants . the effect of reddening in the selection of clump giants was also tested using different selection criteria both in the colour - magnitude and colour - colour diagrams , finding consistent results . an accurate @xmath8-band calibration of the red clump giant luminosity was obtained and applied to the red giant clump of the galactic bulge @xcite , and of the large magellanic cloud @xcite . our magnitudes are in the 2mass magnitude system , and we transformed the @xmath8-band magnitudes of clump giants of hipparcos @xcite to @xmath7 magnitudes using @xmath16 . the resulting zero point differences should be less than 0.02 magnitudes @xcite . for the ks photometry , the distance modulus to a red clump giant in the outer disk would be : @xmath17-m_{k_{\rm s}}\]]where we adopted @xmath18 , @xmath19 and @xmath20 as the mean values for the red clump giants of the milky way disk @xcite . there should be negligible metallicity dependence of these mean values because we are looking at a stellar population of the milky way disk that should be similar to that of the solar neighbourhood where hipparcos distances of clump giants were calibrated . adopting these means magnitudes and colours , and the reddening coefficients @xcite yields : @xmath21 using this equation we computed the distance modulus ( and distance in kpc ) for every single clump giant candidate in the fields . for the ukidss - gps @xmath8-band data the computations are the same , but with @xmath22 , @xmath23 and @xmath24 . in order to determine the disk edge we computed the distribution in distance for the clump giants in each field . thus we coadded the distance distribution of fields located above and below the plane at same galactic longitude . the coadded distance distribution for each longitude was analyzed non - parametrically using the local likelihood density estimation method @xcite . finally , the derivative method was applied for the distribution curve . this method is simple and robust , and can be used to detect the structures in the distance distribution . we defined as the disk edge the outermost point of minimum derivative in each case . the uncertainties were calculated with a monte carlo procedure , assuming poisson errors . the uncertainties due to the photometric errors do not produce any trend in the calculations and are much smaller than the statistical error . the resulting distance distributions along different lines of sight are shown in fig . [ dist ] . in all fields there is a density drop in the clump giant distribution at a corresponding galactocentric distance of about 13.9 kpc ( assuming @xmath25 kpc ) , as listed in table [ table ] . we first noticed the sharp termination of the clump giant distribution in the color - magnitude diagram of the vvv field d001 ( @xmath26 ) , a very heavily reddened area located in the outskirts of the carina star forming region @xcite . similar behavior is also found in ukidss - gps data for different galactic longitudes @xcite . we studied low - extinction fields across the milky way disk ( see table [ table ] ) . when these were available , we selected pairs of fields located above and below the plane at the same galactic longitude , in order to account for the galactic warp , because if the disk is warped , the line of sight can leave the stellar disk before this ends . for example , at @xmath27 the mean warp location is @xmath28 below the plane @xcite , so the selected vvv field d003 is conveniently located to probe the full extent of the disk . at most other longitudes explored here the warp is absent , with the mean plane being at @xmath29 ( fig . [ map ] ) . we have also explored a few other ukidss - gps fields located at inner longitudes that yield lower distances . these fields with @xmath30 were discarded because they are heavily reddened and crowded , and the photometry is not as deep as the rest , presumably due to enhanced contamination from the near - side of the inner bar . systematic errors such as variations of the reddening law have not been included . it is important to note that the present results are independent of models . they rely on basic assumptions such as that the hipparcos stellar sample is representative of the entire the milky way disk , and that clump giants are reliable distance indicators and tracers of the old and intermediate age populations . however , the besanon galactic model with a scale - length of 2.4 kpc , including a flaring and warped outer disk , with a disk cutoff at @xmath31 kpc seems to reproduce well the observed distance distributions ( see fig.[model ] ) . data and model show the same features , with a sharp increase , the peak around 5 kpc and the exponential decrease . the edge is detected in the data and model at the expected place within the errors [ @xmath32 kpc ( corresponding to @xmath33 kpc ) , and @xmath34 kpc ( @xmath35 kpc ) , respectively ] . a few studies have discussed the edge of the milky way towards the anticentre region previously . the old galactic disk apparently does not extend beyond 14 kpc on the basis of optical @xmath36 vs. @xmath37 colour - magnitude diagrams and star counts @xcite , which does not contradict the presence of other more distant young stars . models of the cobe - dirbe infrared emission maps yield that the edge of the disk is at 4 kpc from the sun ( assuming @xmath38 kpc , * ? ? ? denis star counts reveal the cut off of the stellar disk at a galactocentric distance of @xmath39 kpc . in contrast , star counts from 2mass reveal no radial disk truncation at 14 kpc . again , the depth of 2mass is not enough to reach large distances , which is possible with the vvv and ukidss - gps survey that reach 3 - 4 magnitudes fainter . more recently , it was found that the 2mass star counts are best fit if the external disk is truncated at 12 - 14 kpc , while early a - type stars in the anticentre from the iphas survey reveal an exponential disk out to 13 kpc , with a steeper decline beyond that distance @xcite . most of the previous evidence for cutoffs in the stellar distribution has been acquired at the anticentre fields . the present deep exploration of different fields in three galactic quadrants finds consistent results . even though we interpret this termination of the clump giant distribution as a truncation , we note that a break in the slope of the distribution would also be consistent with the data . it is difficult to measure the sharpness of the cutoff , because the number of stars drop rapidly with distance , but as the surveys progress , we will have more fields in order to explore this issue . this does not mean that one could not find other young stellar sources beyond the distance that we measure . there are stars detected beyond the edge of the old stellar disk . for example , there is a population of distant young" +"in an informative display of supernovae light curves ( fig.1 in physics today , july 2007 , p 17 ) it was clear that sn2006gy was about `` 10 times brighter than the peak luminosity of type ia '' . implied was a total radiated energy `` two orders of magnitude '' greater than ordinary supernovae . the first question that naturally arises is : with what certainty is its distance from the observer known ? the smith et al . paper@xmath0 mentions that the galaxy in which sn2006 appears is a `` minor member of the perseus cluster '' . indeed it is , ngc 1260 , with a redshift of 5703 km / sec . but readers who are familiar with the sky recognize this as the perseus - pisces cluster which extends over large regions of the sky . in fact it extends in filaments over about 90 degrees in angle which would require a structure of startlingly large size at its redshift distance of 74 mega parsecs . detailed information on this large region is available from the long term cataloguing work done by fritz zwicky and his associates . the galaxies in this large region down to the classification limit of the palomar 18-inch schmidt are shown in arp@xmath1 figs . the strongest line of galaxies , however , consists mostly of e s and s0 s originating from the large sb ( ngc 891 ) and ending on ngc 1260 and the supernova sn2006gy . all the galaxies with redshifts @xmath2 as given in ned are shown here in figure 1 . in the eastern end of the perseus - pisces filament ( from the ned catalogue courtesy d. carosati ) . note that the subclusters are elongated along the filament and the filament appears to start at ngc 891 . [ fig1],width=566 ] although the galaxies in the line originating in ngc 891 are predominantly in the 5300 to 5700 km / sec range of redshift , the redshift of ngc891 itself is only cz = 528 km / sec . it is intriguing to note that it would imply a distance closer by a factor 10 and luminosity smaller by about a factor of 100 for the supernova if its progenitor had been ejected out of ngc 891 along with some of the higher redshift material . in fact there are 13 smaller galaxies within 5 deg of ngc 891 with redshifts @xmath3 . one could take the least radical position that sn2006gy ocurred in such a companion that was faint enough to escape spectroscopic measurement . the near proximity ( 1 ) to ngc 1260 would then be an accident . but i believe there is enough evidence that large galaxies like ngc 891 eject material which becomes higher redshift companions that i would argue for the ejection of the supernova progenitor in that process . that ngc 891 could have ejected the extremely active radio , x - ray , infra red galaxy perseus a ( ngc 1275 ) is suggested by the elongation of the perseus a cluster back along the line to ngc 891 . moreover the ngc 891 minor axis is only about 18 deg . off the line to per a. of course the low redshift material which gave rise to the supernova would have had to have been entrained along with the ejection of the higher redshift cluster galaxies . that companion galaxies have an ejection origin along the minor axes of edge on disk galaxies was first pointed out by holmberg@xmath4 whose observations demonstrated in 1969 preferential alignment along minor axes of disk galaxies . it was then demonstrated by arp@xmath5 and lpez corredoira and gutirrez@xmath6 that companions came out in a cone with half opening angle about 35 degrees and quasars within @xmath7 degrees . as mentioned , the minor axis of ngc 891 is aligned with the nearest galaxies in fig 1 and to within about 18 deg . of the perseus cluster to the east . as for entraining low redshift material from the parent there are now a number of cases where smaller dwarfs are considered to be physical companions which have arisen as fragments from disturbed regions of parent galaxies . a good example of this is ngc 5985 in fig.2 where this seyfert galaxy has ejected a quasar but only 2.4 arcsec from it is attached a dwarf with the same small redshift as the big , low redshift , parent galaxy . , width=529 ] but perhaps the strongest argument for the ejection origin of the perseus cluster extending eastward from ngc 891 is the study of the 20 brightest galaxies in apparent magnitude north of declination = 0 deg . of the 14 that are uncrowded by nearby bright galaxies , a total of 13 have well marked lines and concentrations of fainter , higher redshift galaxies@xmath1 . figure 3 shows the range in redshift of the lines of fainter galaxies which are strongly associated with almost every bright galaxy in the sky . this 1990 study was followed by a 2001 study of 14 examples of higher redshift abell clusters which were paired and aligned across bright apparent magnitude galaxies@xmath8 . , width=491 ] if such strong ejections take place it is reasonable to expect some of the material of the ejecting galaxy to be carried along with it . along with ejected gas and plasma which is observed we only need to include a few old stars or groups of stars among which to find the very occasional supernova . supernovae of type ia are much discussed today because of their interpretation in terms of a universe that is expanding faster now than in the past - in other words , dark energy. but if their luminosity is over estimated the sole reason for this radical postulate falls . if the distance to sn2006gy is strongly overestimated this may also effect to some extent the models of supernovae on which dark energy has been hypothesized . generally one could reason that objects at appreciably large distances tend to be younger because of the look - back time . younger objects tend have built up less metal abundance which in turn lowers the luminosity of objects like cepheid variables . if intrinsic redshifts of younger material is operative , galaxies like the perseus cluster would need low particle masses@xmath5 to explain their apparent association with ngc 891 . the smaller elementary particle masses would give smaller luminosities of objects in those galaxies . all of these effects would combine in the direction of making the hubble constant appear lower in the past and lead to the impression that it was speeding up at present . ironically , if we move sn2006gy to this closer distance it could reinstate supernovae i as , at least , approximate distance indicators . n. smith et al . j. and http://arxiv.org/abs/astro-ph/0612617 ( version 3 ) ." +"stars at the very bottom of the main sequence have been a very popular topic of research during the last few years , including in studies of stellar activity . fleming , schmitt , & giampapa ( 1995 ) demonstrated that fully - convective m dwarfs , i.e. those with masses less than 0.3 m@xmath3 , exhibit high levels of coronal activity , although at that time , virtually no x - ray detections had been made of stars less massive than vb 8 and lhs 3003 ( both type m7 . ) the star vb 10 ( a.k.a . gl 752 b , lhs 474 ; type m8 ) appeared to have been marginally detected once by the einstein high resolution imager and was catalogued by barbera et al . then linsky et al . ( 1995 ) reported the detection of a large amplitude flare on vb 10 in the far uv using the goddard high resolution spectrograph . more recently , neuhauser & comron ( 1998 ) have detected x - ray emission from a very young brown dwarf in chameleon . this confirms that activity does exist for the very lowest mass stellar ( or substellar ) configurations . we have used the rosat high resolution imager ( hri ) to reobserve vb 10 , which was not detected by the rosat position sensitive proportional counter ( pspc ) during either the all - sky survey or a 7.3-ksec pointed observation ( fleming et al . 1993 ) . by obtaining a deeper exposure , we hoped to discover the nature of the vb 10 corona , detect its quiescent x - ray luminosity , and compare its level of coronal activity to that of the more massive m dwarfs . we have succeded in detecting x - ray emission from vb 10 , but only during a brief flare similar to the one observed by linsky et al . ( 1995 ) at ultraviolet wavelengths . in this paper , we present the latest rosat data on vb 10 . section 2 contains a description of the observations and data analysis . in section 3 , we discuss a hypothesis to account for the stark contrast between the flare and non - flare x - ray flux values , including the possibility of a total lack of @xmath2 k coronal plasma about vb 10 . the star vb 10 was observed during the period of 1997 october 27 - 31 for a total of 21,992 sec with the rosat hri ( zombeck et al . 1990 ) . the total image is shown in fig . 1a . the one obvious x - ray source seen in fig . 1 is positionally coincident with the star wolf 1055 ( type m3.5 ve ) , which has a common proper motion with vb 10 . at the position of vb 10 , which is marked in fig . 1a , there is only a marginal detection . however , when the data are separated into their individual observation intervals ( obis ) , we find that all of the photons in the vb 10 detection are contained within one single obi ( figs . 1b and 1c ) . this particular obi , which began on ut 1997 october 29 at 3:05:24 and ended at 3:25:43 , had an effective total exposure time of 1,138 sec . within an extraction radius of @xmath4 around the optical position of vb 10 , 11 photons were detected . by examining the rest of the image , we determined that the density of background photons for this obi was 0.0024 cts arcs@xmath5 . the solid angle of our extraction circle about vb 10 was 452.4 arcs@xmath6 , which means that we would expect one photon in the extraction circle to be from the background . therefore , with 10 source photons , the mean count rate over the entire obi is @xmath7 cts s@xmath1 ( this includes a deadtime and vignetting correction factor of 1.017 . ) of course , to get a better idea of the flare duration and flux , one needs to look at the temporal distribution of the source photons throughout the observation . in fig 2 , we show a histogram in arrival time for the 11 photons contained within the source extraction radius . remember , we do not know which one is the background photon . the histogram is binned in 3-minute ( 180 sec ) intervals over the nearly 20-minute observation . one can see that 5 photons arrived in the first 3 minutes of the observation , 5 photons arrived during the last 8 minutes , with the remaining photon arriving in between . the data are consistent with there being only one flare which is tailing off during our observation . in this case , the flare duration is at least 20 minutes and @xmath8 cts s@xmath1 ( 5 photons in 3 minutes ) represents a lower limit to the peak count rate . in order to get the x - ray luminosity , we adopt a conversion factor of @xmath9 ergs cm@xmath5 cnt@xmath1 . this comes from table 10 of david et al . ( 1999 ) , the rosat hri calibration report ( cambridge : sao ) ] , for a raymond - smith spectrum of 0.5 kev and negligible interstellar absorption . this yields an apparent energy flux , @xmath11 ergs cm@xmath5 s@xmath1 for the mean count rate . at a distance of 5.74 pc , this gives us a luminosity , @xmath12 ergs s@xmath1 . again , this is just a mean luminosity for the observation . the peak flare luminosity would be at least @xmath13 ergs s@xmath1 . we have also analyzed the remaining 20,854 sec of our hri observation , in which no x - ray source was detected at the position of vb 10 . using the non - detection analysis software in midas / exsas , we have calculated a @xmath14 ( i.e. 99.7% confidence ) upper limit of @xmath15 cts s@xmath1 . this translates into @xmath14 upper limits on the apparent x - ray flux and x - ray luminosity of @xmath16 ergs cm@xmath5 s@xmath1 and @xmath17 ergs s@xmath1 , respectively , for vb 10 outside of flare . these are upper limits on any quiescent emission , if it exists . all of the numbers presented in this section have been tabulated in table 1 . lclllr flare ( mean ) & 1.14 & @xmath18 & @xmath19 & @xmath20 & @xmath21 flare ( peak ) & 0.18 & @xmath22 & @xmath23 & @xmath24 & @xmath25 non - flare & 20.85 & @xmath26 & @xmath27 & @xmath28 & @xmath29 this x - ray flare on vb 10 is reminiscent of the far - uv flare which was detected on vb 10 by linsky et al . these authors observed c ii , iv and si iv emission lines only during the last five minutes of an hour - long exposure taken with the ghrs onboard hst . they concluded that the flare which they had observed indicated increased magnetic heating rates for low - mass stars near the hydrogen - burning mass limit . in both the uv and rosat x - ray observations , quiescent ( i.e. non - flare ) emission was never detected from vb 10 . for the uv flare , the emission line fluxes were an order of magnitude greater than the upper limits placed on the non - flare emission by linsky et al . ( 1995 ) . for this most recent x - ray flare , the contrast is even greater . the peak flare luminosity is _ at least _ more than two orders of magnitude greater than the non - flare value . for ease of comparison to more massive m dwarfs , we will normalize l@xmath30 by l@xmath31 , which for vb 10 is @xmath32 ergs s@xmath1 based on the absolute k magnitude measured by leggett ( 1992 ) and the bolometric correction of veeder ( 1974 ) . this gives us log ( l@xmath30/l@xmath33 for the peak of the flare and log ( l@xmath30/l@xmath34 outside of flare . using the data of fleming et al . ( 1995 ) for the late ( later than m5 ) , presumably fully - convective m dwarfs within 7 pc of the sun , we find that these star have values of log ( l@xmath30/l@xmath31 ) which are typically @xmath35 . but during flares ( e.g. az cnc ; fleming et al . 1993 ) , these stars can reach values of ( l@xmath30/l@xmath36 to @xmath37 . therefore , the magnitude of the flare on vb 10 is completely consistent with that of flares on more massive m dwarfs . in fig . 3 we display a plot of normalized x - ray luminosity versus absolute visual magnitude for all known m dwarfs within 7 pc that are later than m5 , based on data from a volume - limited survey by fleming et al . inspection of fig . 3 reveals the sharp contrast between the upper limit to the non - flare x - ray emission in vb 10 and the x - ray emission levels of other late dme stars . in particular , the upper limit for vb 10 is 1 - 2 orders of magnitude less than that detected in the late dme stars . it is comparable to the upper limit for gj1002 in fig . 3 , a quiescent dm5.5 star that does not exhibit h@xmath38 emission nor any reported flare activity . by contrast , vb 10 is a known flare star with ( variable ) h@xmath38 line emission in its spectrum . while one can not build a theory based on one observation , we can not help but speculate that our result for vb 10 does indeed reflect a decline in coronal heating efficency near the h - burning mass limit . but somehow these stars are still able to flare . we do not understand in detail the mechanisms that give rise to energetic , transient outbursts identified as `` flares '' in the sun and late - type stars . however , flares do appear to be the result of instabilities that return stressed systems toward configurations that are characterized by lower potential energy ( rosner & vaiana 1978 ) . since we do not have an x - ray spectrum , we can not verify through modeling that the observed emission in vb 10 is consistent with the presence of loop - like magnetic structures . however , the energetics of the event suggest the possible occurrence of a large volume of flare plasma , implying the presence of large - scale magnetic structures in the atmosphere . in particular , we can crudely estimate the plausible range of spatial scales that characterize the flare event in the following manner . in the absence of an actual energy spectrum ( such as the pulse - height spectra that were produced by the now - defunct rosat pspc ) , we assume some plausible flare plasma parameters . based on x - ray observations of other flare events on m dwarfs , we adopt a flaring temperature of @xmath39 10@xmath40 k. we note that a large flare event recorded by the rosat pspc on a late m dwarf star was well - described by a thermal plasma model fit characterized by a temperature of 2 4 @xmath41 10@xmath40 k ( sun et al . 1999 ) . utilizing the xspec analysis package combined with the observed flux from the hri and the adopted temperature yields a differential emission measure at the flare maximum of em @xmath42 @xmath43 . the corresponding volume emission measure is @xmath44 where r@xmath45 = 0.102 r@xmath46 ( linsky et al . 1995 ) . given" +"methanol masers are commonly found in massive star - forming regions , with more than twenty different centimetre and millimetre wavelength masing transitions discovered to date ( e.g. , * ? ? ? all methanol maser transitions do not share the same behaviour . empirically , they form two classes @xcite . class i methanol masers ( e.g. at 36 , 44 , 84 , and 95 ghz ) usually occur in multiple locations across the star - forming region scattered around an area up to a parsec in extent ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? in contrast , class ii methanol masers ( e.g. at 6.7 , 12 and 107 ghz ) reside in the close vicinity of exciting young stellar objects ( ysos ) and are typically found as a single cluster of emission at arcsecond resolution ( e.g. , * ? ? ? theoretical calculations are able to explain this empirical classification and strongly suggest that the pumping process of class i masers is dominated by collisions with molecular hydrogen , in contrast to class ii masers which are pumped by radiative excitation ( e.g. * ? ? ? * and references therein ) . the morphology of class i methanol masers has recently become the focus of high angular resolution studies aimed at searching for associations with other phenomena commonly observed in regions of high - mass star - formation ( e.g. , * ? ? ? * ) . the common consensus is that the majority of class i masers trace interface regions between outflows and molecular gas , although direct observational evidence of this has been obtained for a limited number of sources only ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? the alternative scenarios involving cloud - cloud collisions ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) as well as the interaction of expanding hii regions with the ambient molecular environment @xcite may also be realised in some sources . the common point of all these scenarios is the presence of shocked gas , where the physical conditions are favouring class i methanol masers ( see the discussion in section [ hv_discussion ] below ) . apart from the outflow associations cited above ( based on the 2.12-@xmath2 m h@xmath4 emission , which is a well known shock tracer ) , @xcite reported association of some class i maser spots with the extended features showing a prominent excess of the 4.5-@xmath2 m emission in the images obtained with the spitzer space telescope s infrared array camera ( irac ) , also known as extended green objects ( egos ; * ? ? ? * ) or `` green fuzzies '' @xcite . the excess of the 4.5-@xmath2 m ( irac band 2 ) emission could be a result of shock excitation of molecular hydrogen and carbon monoxide in protostellar outflows @xcite . it is worth noting that @xcite demonstrated statistically the presence of an ego in the vicinity of a large fraction of class i methanol masers at low angular resolution ( single dish positions ) . to increase the number of class i masers studied at high angular resolution and to compare the morphologies observed in different maser transitions we carried out an interferometric survey at 36 and 44 ghz of all class i masers previously reported in the literature and located south of declination @xmath035 . in this letter , we present a study of g309.38@xmath00.13 , an especially interesting source from the survey . it represents the level of morphological and kinematical complexity encountered for the majority of sources observed in the survey , but it has a distinct high - velocity maser feature at 36-ghz , which was quite unexpected ( see e.g. , * ? ? ? * ; * ? ? ? this maser is found in an area devoid of bright radio - continuum emission , but near infrared sources which are presumably embedded stars . it is located approximately 20offset from the prominent hii region gum 48d at the heliocentric distance of about 3.5 kpc ( for further information on the region see * ? ? ? 0.13 region . the emission in 8.0 , 4.5 and 3.6 @xmath2 m irac spitzer bands is shown as red , green and blue , respectively . the filled red circles show the fitted position of the strongest spectral component at each location , while the weaker components are shown by yellow crosses ( all components are given in table [ fit_results ] ) . the location of a class ii 6.7-ghz methanol maser @xcite is shown by the white cross . the contours show the maximum of the 36-ghz emission across all spectral channels . the levels are 5 , 15 , 50 and 90 per cent of the peak 36-ghz flux density of 16.1 jy . low level artefacts in the top right corner are caused by the primary beam correction . ] observations were made with the australia telescope compact array ( atca ) in may 2007 as part of the interferometric survey of southern class i methanol masers at 36 and 44 ghz ( project code c1642 ) . the source was observed using the hybrid h214c array configuration in a few 3 minute cuts ( four cuts at 36 ghz and six at 44 ghz ) spread in hour angle for better uv - coverage . we did not use , for imaging , the data from the ca06 antenna ( located about 4.5 km to the west of the other 5 antennas ) . the remaining antennas provided baselines ranging from 82 to 240 m. the position of the phase and pointing centre was @xmath52601 , @xmath6181166 . we used reference pointing procedures and determined corrections using the continuum source 1414 - 59 ( which served also as a phase calibrator ) . from the statistics of pointing solutions the reference pointing accuracy was estimated to be 48@xmath726 . this accuracy affects the accuracy of flux density measurements , particularly for sources of emission which are offset from the pointing centre . the positional accuracy of the maser locations depends on the quality of the phase calibration and is believed to be better than 0.5 arcsec . the absolute flux density scale was bootstrapped from observation of uranus ( assumed flux densities were 1.38 and 1.98 jy at 36 and 44 ghz respectively ) . we estimate the flux scale to be accurate to about 20% . the correlator was configured to split 8 mhz bandwidth into 1024 spectral channels . the resulting spectral resolution and velocity range covered are given in table [ obsdetails ] along with other observing parameters . most columns of table [ obsdetails ] are self - explanatory and include , in addition to above , the molecular transition and its rest frequency ( adopted from * ? ? ? * ) , full width at half maximum ( fwhm ) and position angle ( p.a . ) of the synthesised beam reflecting the spatial resolution , as well as the size of the primary beam which determines the field of view . the 1@xmath8 rms noise given in the seventh column is a median value of rms noise levels obtained for each individual spectral plane of the image cube prior to the primary beam correction ( i.e. with constant noise across the field of view ) . scaled up with the primary beam , it represents the 1@xmath8 detection limit of these observations at a particular location . it is worth mentioning , however , that the ability to detect weak features is notably reduced within the velocity range of strong emission due to dynamic range limitations , which were largely a result of sparse uv - coverage . we estimate the dynamic range ( the ratio of peak flux to rms noise in the image ) to be about 90 and 400 for the 36 and 44-ghz image cubes , respectively . the uncertainty of the radial velocity corresponding to the rest frequency uncertainty is given in the ninth column of table [ obsdetails ] . [ cols=""<,>,^,<,^,^,^,>,^ , > "" , ] the blue - shifted spectral component corresponding to location e is a remarkable feature of this maser source . more commonly , the observed velocities of class i methanol masers are no more than a few km s@xmath3 from the velocity of the ambient molecular cloud , and the velocity dispersion is low ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . the notable exception with a high velocity dispersion is g1.6@xmath00.025 , which has emission components at radial velocities ranging from 0 to 160 km s@xmath3 @xcite however , unlike g309.38@xmath00.13 , the emission in g1.6@xmath00.025 corresponds to distinct , but interacting , molecular clumps detected also in a number of thermal transitions of various molecules @xcite . the large velocity difference between individual clumps reflects a violent environment and the exceptional kinematics in the vicinity of the galactic centre . in contrast , the g309.38@xmath00.13 region is close to the tangential direction of the sagittarius - carina arm ( see figure 5 of * ? ? ? * ) where the extreme velocity of e ( @xmath080 km s@xmath3 ) makes an association with an unrelated molecular cloud highly unlikely . this is corroborated by the @xmath9co brightness temperature limit of 0.1 k at the radial velocities below @xmath070 km s@xmath3 obtained with the 4-m nanten telescope @xcite . this limit is two orders of magnitude lower than the peak @xmath9co brightness temperature observed near @xmath050 km s@xmath3 in the g309.38@xmath00.13 region ( nearest @xmath10co clump mass is about 10@xmath11 m@xmath12 ; * ? ? ? * ) , which is close to the velocities of most of the maser spots . we conclude that the high - velocity 36-ghz maser in e most likely reflects the presence of a molecular outflow , rather than a separate molecular cloud projecting onto the same location by chance . the area around b and e is characterised by the presence of shocked gas traced by a strong ego ( fig . [ glm_mas_overlay ] ) . this supports the idea that an outflow is present . the close spatial location of b and e and the presence of the class ii methanol maser ( which indicates the presence of a high - mass yso ) in the vicinity both suggest that the outflow axis is close to the line of sight . as mentioned earlier , the interaction between outflows and the ambient material is believed to be responsible for the majority of class i methanol masers . the production of methanol by purely gas - phase chemical reactions is quite inefficient , but the passage of weak shocks is expected to release methanol from the grain mantles ( e.g. , * ? ? ? enhanced methanol abundance arising from shocks driven by outflows into the ambient cloud has also been confirmed observationally ( e.g. , * ? ? ? * ; * ? ? ? in addition , outflows compress the medium , which makes collisions more frequent and the pumping mechanism more efficient . however , methanol is expected to survive sputtering and desorption of grain mantles only if the shocks are relatively mild , i.e. at shock velocities not greatly exceeding 10 km s@xmath3 @xcite . therefore , the detection of a maser feature offset by 30 km s@xmath3 with respect to the velocity of the ambient gas is somewhat surprising . this discrepancy can be resolved if the outflow interacts with a" +"gravitational lensing is an important phenomenon to survey dark and compact objects and to confirm gravitational theories from a solar system scale to a cosmological scale . gravitational lensing has been investigated mainly under a quasi - newtonian approximation or a weak - field approximation @xcite but gravitational lensing over the quasi - newtonian approximation also has been studied @xcite . darwin pointed out that faint images near the circular orbit of a light ray called light sphere or photon sphere @xcite appear in the schwarzschild spacetime in 1959 @xcite and the gravitational lensing phenomena have been revived several times . the gravitational lensing by a light sphere in various black hole @xcite , naked singularity @xcite , and wormhole spacetimes @xcite has been also investigated . recently , ligo has reported a gravitational - wave event gw150914 @xcite and it has shown the existence of heavy stellar - mass black holes with the mass @xmath0 in nature @xcite . black holes are becoming an important target in astronomy and astrophysics and gravitational lensing by black holes will be an important tool to research dim and isolated black holes . holz and wheeler @xcite proposed to survey retrolensing caused by sun lights which reflected by a light sphere of a stellar - mass black hole near the solar system in 2002 . a black hole in galactic center as a retrolens @xcite , wormholes as retrolenses @xcite , and the effect of the rotation @xcite and the electrical charge @xcite of a black hole on the magnification were also studied . in ref . @xcite , bozza considered gravitational lensing effects of light rays passed near a light sphere in a general static and spherical symmetric spacetime and provided a formula of the deflection angle in a strong deflection limit . the deflection angle in the strong deflection limit describes a fundamental feature of a light sphere and the relations between the deflection angle in the strong deflection limit and the quasinormal modes @xcite and the high - energy absorption cross section @xcite were also discussed . eiroa and torres @xcite and bozza and mancini @xcite showed that the deflection angle in the strong deflection limit is useful to obtain retrolensing light curves in the general static and spherical symmetric spacetime . considering the difference of observables between a schwarzschild black hole and the other black holes is important to check whether a observed non - rotating black hole really can be described by the schwarzschild black hole . the reissner - nordstrm black hole solution is one of useful and simple black hole solutions for the purpose even though black holes in nature would be almost electrically neutralized . the deflection angle in the strong deflection limit in the reissner - nordstrm black hole spacetime has been obtained numerically by eiroa _ _ in ref . bozza investigated the deflection angle in the strong deflection limit in the reissner - nordstrm black hole spacetime and pointed out an integral in the deflection angle can not be calculated analytically in ref . the integral was calculated numerically and the expansion of the integral in power of the electrical charge was calculated analytically @xcite . in this paper , we revisit the deflection angle in the strong deflection angle in the reissner - nordstrm spacetime and investigate the effect of the electrical charge on retrolensing light curves and the separation of a double image . we revise a strong deflection limit analysis investigated by bozza @xcite to obtain the deflection angle in the strong deflection limit in the reissner - nordstrm black hole spacetime analytically . this paper is organized as follows . in sec . ii we investigate the deflection angle in the strong deflection limit in the reissner - nordstrm spacetime and obtain it analytically without the expansion in power of an electrical charge . in sec . iii we review retrolensing and investigate the effect of an electrical charge on retrolensing light curves and a double image by a retrolens in the reissner - nordstrm spacetime . in sec . iv we conclude our results . in this paper we use the units in which the light speed and newton s constant are unity . in this section , we calculate the deflection angle @xmath1 of a light ray in a strong deflection limit in the reissner - nordstrm spacetime in a following form : @xmath2 where @xmath3 is the impact parameter of the light ray , @xmath4 is the critical impact parameter of the light ray , @xmath5 is a positive function of @xmath6 which is the ratio of the electrical charge @xmath7 to the arnowitt - deser - misner mass @xmath8 of a reissner - nordstrm black hole , and @xmath9 is a function of @xmath6 .. recently , however , tsukamoto pointed out that the order of the error term should be read as @xmath10 . see ref . @xcite for the details . ] the line element in the reissner - nordstrm spacetime is given by @xmath11 where @xmath12 . there are time translational and axial killing vectors @xmath13 and @xmath14 because the spacetime is a static and spherical symmetric spacetime , respectively . if @xmath15 is satisfied , an event horizon exists at @xmath16 , where @xmath17 please note that @xmath16 is the largest positive solution of the equation @xmath18 . we concentrate on the black hole spacetime . a light sphere exists at @xmath19 , where @xmath20 is given by @xmath21 the radius of the light sphere @xmath20 is the largest positive solution of an equation @xcite @xmath22 where @xmath23 is the differentiation with respect to the radial coordinate @xmath24 . note that @xmath25 the trajectory of a light ray is described by @xmath26 where @xmath27 is the wave number of the light ray and the dot denotes the differentiation with respect to an affine parameter parameterizing the null geodesic . the conserved energy @xmath28 and angular momentum @xmath29 of the photon given by @xmath30 and @xmath31 respectively , are constant along the null geodesic . we assume that @xmath28 is positive . we define the impact parameter @xmath3 of a light ray as @xmath32 we can assume @xmath29 and @xmath3 are positive without loss of generality as long as we consider one light ray . we assume @xmath33 without loss of generality . from eq . ( [ eq : trajectory1 ] ) , the trajectory equation in the reissner - nordstrm spacetime is given by @xmath34 and it is expressed as @xmath35 where @xmath36 is the effective potential for the motion of the photon defined as @xmath37 the motion of the photon is permitted in a region where @xmath36 is non - negative . since the effective potential @xmath36 in the limit @xmath38 becomes @xmath39 a photon can exist at @xmath40 . we consider that a photon comes from infinity , is reflected by a black hole at the closest distance @xmath41 , and goes to infinity . since @xmath42 vanishes at the closest distance @xmath41 , from eqs . ( [ eq : trajectory3 ] ) and ( [ eq : v ] ) , we obtain a relation between the impact parameter @xmath3 and the closest distance @xmath43 as @xmath44 where @xmath45 . hereafter subscript @xmath46 denotes the quantities at the closest distance @xmath41 . we define the critical impact parameter @xmath4 as @xmath47 we call the limit @xmath48 or @xmath49 strong deflection limit . the impact parameter @xmath50 can be expanded in power of @xmath51 as @xmath52 from the derivative of the effective potential @xmath36 with respect to the radial coordinate @xmath24 given by @xmath53 and eqs . ( [ eq : rm2 ] ) and ( [ eq : trajectory3 ] ) , we obtain @xmath54 and @xmath55 thus , in the strong deflection limit @xmath48 or @xmath49 , a photon with the impact parameter @xmath49 almost stops in the radial direction near outside the light sphere at @xmath19 and the orbit of the photon winds around the light sphere . the trajectory equation ( [ eq : trajectory2 ] ) can be rewritten as @xmath56 and then the deflection angle @xmath57 of the light ray is obtained as @xmath58 where @xmath59 by introducing a variable @xmath60 defined as } $ ] defined by @xmath61}\equiv \frac{-g_{tt}(r)+g_{tt}(r_{0})}{1+g_{tt}(r_{0})}\ ] ] in our notation . ( 10 ) and ( 11 ) in @xcite . the difference between @xmath60 and @xmath62}$ ] is discussed in sec . iv in this paper . ] @xmath63 @xmath64 can be rewritten as @xmath65 where @xmath66 where @xmath67 @xmath68 @xmath69 and @xmath70 since @xmath71 and @xmath72 in the strong deflection limit @xmath48 become @xmath73 and @xmath74 respectively , the order of the divergence of @xmath75 is @xmath76 . we separate @xmath64 into two parts , i.e. , a divergent part @xmath77 and a regular part @xmath78 : @xmath79 . the divergent part @xmath77 is defined as @xmath80 where @xmath81 the divergent part @xmath77 can be integrated and we obtain @xmath82 using eq . ( [ eq : b2 ] ) , @xmath83 in the strong deflection limit @xmath48 or @xmath84 is expressed as @xmath85 where @xmath5 is given by @xmath86 one sees that @xmath5 is the factor in the deflection angle in the strong deflection limit ( [ eq : deflection0 ] ) later . the regular part @xmath87 is defined by @xmath88 where @xmath89 since we are interested in the deflection angle in the strong deflection limit @xmath48 , we consider @xmath90 we can integrate @xmath78 in the strong deflection limit @xmath48 or @xmath84 analytically and obtain it as @xmath91 \nonumber\\ & & + o((b - b_{c})\log ( b - b_{c})).\end{aligned}\ ] ] thus , the deflection angle @xmath92 in the strong deflection limit @xmath49 is given by @xmath93 where @xmath5 and @xmath9 are obtained as @xmath94 and @xmath95 -\pi , \nonumber\\\end{aligned}\ ] ] respectively . figure [ parameter ] shows @xmath96 , @xmath97 , @xmath5 , and @xmath9 as the functions of @xmath6 . . the ( red ) solid , ( green ) dashed , ( blue ) dash - dotted , and ( purple ) dotted curves denote @xmath96 , @xmath97 , @xmath5 , and @xmath9 , respectively.,width=264 ] when the black hole has no charge ( @xmath98 ) , we obtain @xmath99 , @xmath100 , and @xmath101-\pi$ ] . they are equivalent to a well - known result in refs . @xcite in the schwarzschild spacetime . when the black hole has the maximal charge ( @xmath102 ) , we obtain @xmath103 , @xmath104 , and @xmath105-\pi$ ] . in @xcite , @xmath5 in the reissner - nordstrm spacetime was obtained as , in our notation , @xmath106 using eq . ( [ eq : rm2 ] ) , one shows that eq . ( [ eq : abar2 ] ) is equivalent to eq . ( [ eq : abar1 ] ) . in this section , we review retrolensing following ref . @xcite and then we investigate retrolensing in the reissner - nordstrm spacetime . we consider that the ray of the sun @xmath107 is reflected by the light sphere @xmath29 of a black hole with a deflection angle @xmath1 and reaches an observer @xmath108 . the observer sights an image @xmath109 with an image angle @xmath110 . the lens configuration is shown in fig . [ lens_configuration ] . is reflected by a light sphere @xmath29 of a black hole with a deflection angle @xmath1 and reaches an observer @xmath108 . the observer sights an image @xmath109 with an image angle @xmath110 . @xmath111 is a source angle defined @xmath112 . @xmath113 is an angle between a line @xmath114 and the light ray at @xmath107.,width=264 ] we solve a lens equation proposed by ohanian @xcite , @xmath115 where @xmath111 is a source angle @xmath112 defined in a range @xmath116 and @xmath113 is an angle between a line @xmath114 and the light ray at @xmath107 ." +"in recent months the wmap satellite has provided the clearest picture of temperature fluctuations in cosmic microwave background ( cmb ) to date @xcite . the power spectrum of these fluctuations is a sensitive function of the cosmological parameters , such as the total energy density , matter density , baryon density , hubble constant and others . the emerging model was convincingly confirmed : the universe is spatially flat , consisting mostly of `` dark energy '' that behaves like a cosmological constant , about 23% dark matter , and about 4% baryons . the sum of the neutrino masses is limited to be less than 0.7 ev , much more strict than the bound from terrestrial laboratories . the compton scattering optical depth implies an early reionization at redshift @xmath0 . these results will improve , as the wmap team plans to take at least 4 years of data . several profound questions arise from these results . to start , the nature of the dark matter and the dark energy are completely unknown . we understand the 4% in baryons , but the other 96% is a mystery . furthermore , there is an indication of a deficit of power on the largest scales ( in e.g. the quadrupole and octupole moments ) , but the meaning of this unclear . a finite universe is one among many unlikely possibilities . the snap satellite@xcite has been proposed to study the nature of the dark energy by measuring the hubble diagram ( redshift distance relation ) using type ia supernovae ( snia ) as standard candles , as has been done from the ground . ground based measurements of this kind have already shown that there is a large density of dark energy . the snap team hopes to study the equation of state @xmath1 of this material . a satellite is required to significantly extend the ground based results , as a large number of snia with redshifts @xmath2 is required : this tests the universe in its decelerating phase . the wavelengths of interest are redshifted into the infrared , thus the necessity of a space based instrument . furthermore , the exact nature of the progenitors of snia is unknown . a large sample can be split into many subsamples to study systematic effects . snap is fundamentally a large survey telescope , and should have a broad science reach . big bang nucleosynthesis ( bbn)@xcite tries to explain the primordial abundances of light elements , in particular the stable isotopes of hydrogen , helium and lithium . as a function of only the baryon to photon ratio , these abundances can be calculated by tracking the network of nuclear reactions in the hot big bang . the primordial abundance of deuterium depends sensitively on the one free parameter , thus deuterium measurements can provide an accurate assessment of the cosmological baryon density . lyman-@xmath3 clouds obscuring distant quasars presumably consist of predominantly unprocessed gas , and thus reflect primordial abundances . with the right column depth of hydrogen ( not so small that deuterium is unobservable , and not so large so that the damping wings of hydrogen cover the deuterium line ) , the primordial deuterium abundance is measured . at present , the implied baryon density is fully consistent with the wmap value , with comparable errors . to go further , many more such systems would be needed . suitable systems are currently found at the rate of one per year , so for now progress on the baryon density will come from cmb measurements . cosmological observations have the potential to probe planck - scale physics@xcite . inflationary theories usually predict that observable wavelengths ( e.g. galaxy and cluster scales ) originated during inflation as sub - planck fluctuations . thus , inflation can in principle probe quantum theories of gravity such as superstring theory . with not overly optimistic assumptions , a 1% modulation of the cmb fluctuations might be produced by planck - scale physics during inflation , detectable in the next decade or two . the standard cosmological model requires that 23% of the energy density in the universe is some form of non baryonic nearly collisionless clustering matter . a new stable particle would fit the bill , as has been known for several decades . in this regard the dark matter problem is more tractable than the dark energy problem dark matter `` looks like '' something we understand , while dark energy is completely mysterious . two possible candidates for dark matter have survived numerous tests and remain viable . the first is the lightest superpartner in supersymmetric extensions to the standard model , which is naturally stable , weakly interacting , and electrically neutral . the second is the axion , arising in a compelling solution to the strong cp problem . weakly interacting massive particles ( wimps ) , such as those in supersymmetric models can be detected in sensitive low background experiments by their rare scattering from atomic nuclei . the nuclear recoil deposits energy , which in principle is detectable . two such detectors currently running are cdms and dama . cdms@xcite uses germanium and silicon detectors . these are sensitive to both phonons and ionization . the ratio of these two signals powerfully discriminates against background , as nuclear recoils exhibit much lower ionization that most backgrounds ( electrons and gamma rays ) . cdms - i ran in a shallow site at stanford , and the final wimp exclusion results are now available . cdms - ii is currently running in the soudan mine , with new results anticipated by the end of 2003 . the dama@xcite detector uses nai scintillators . they do not have the background rejection capabilities of cdms , but instead rely on the annual modulation of the wimp signal : as the earth orbits the sun , its relative velocity with respect to the wimp `` wind '' is modulated by several tens of km s@xmath4 , leaving a rate modulation of a few percent . in the 4-year data such a modulation is seen , though the implied mass and cross section are nearly ruled out by other experiments ( cdms , edelweiss , zeplin ) . three more years of data have been released since the conference , and the modulation signal is strengthened . furthermore , the successor experiment libra is being installed now . the future of wimp searches requires that ton - scale detectors be constructed . the xenon proposal@xcite to use a two - phase detector for both scintillation light and ionization is a promising possibility for scalability to a one ton target mass . background can again be rejected by the lower levels of ionization from nuclear recoils relative to electronic processes . small prototypes are currently being tested . the construction of a 10 kg prototype is well underway . the goal is to build a 100 kg module ; with this a ton - scale detector could feasibly be built in the next decade . axions in the range micro- to milli - ev remain a viable dark matter candidate . they require a vastly different experimental approach : conversion to microwave photons in a magnetic field . these photons are then detected with with what is essentially a very sensitive radio receiver . the axion dark matter experiment admx is ongoing , already scanning deep in the allowed model range@xcite . upgraded receivers using squid amplifiers are on the way . as light pseudoscalars , axions have a bounded parameter space , as their interactions are essentially the same as neutral pions . the lowest allowed axion - photon couplings are within reach . energetic cosmic ray nuclei are an important probe of high energy processes in astrophysics@xcite . supernova blast waves are capable of accelerating protons to energies of 10@xmath5 ev , the `` knee '' in the spectrum where the power law shifts to a steeper value . very puzzling are the ultra high energy cosmic rays with energies in excess of 10@xmath6 ev . various acceleration mechanisms have been proposed , involving fr ii galaxies , interacting galaxies , jets in radio sources ( with lorentz factor 10 ) , gamma ray bursts ( with lorentz factor 300 ) , and others . top - down models have also been considered : uhecrs may arise in the decay chains of supermassive particles . whichever mechanism produces uhecrs , they must originate cosmologically nearby , within roughly 100 mpc . the gzk cutoff operates for nuclei above 10@xmath6 ev / a , where the threshold for pion photoproduction on the cmb is exceeded . uhe photons have a similar cutoff at lower energy , at the pair production threshold . the nature of the observed events above 10@xmath6 ev is unknown , and difficult to determine experimentally . nuclei such as iron , protons , photons , and neutrinos are all possibilities . the experimental situation in uhecrs is quite promising . the hires experiment@xcite consists of two air fluorescence detectors situated 12.6 km apart , allowing stereoscopic viewing of the air showers induced in the atmosphere . the dataset exhibits the gzk cutoff , though at low significance . the data are in agreement with agasa , the japanese particle detector , and the agasa data does not exhibit the cutoff . the relative calibration between air fluorescence and particle detectors is uncertain ; the flash collaboration@xcite at slac expects to measure this to better than 10% accuracy . hires does not see the clustering visible in the agasa data , though again the experiments are consistent . this of course dilutes the agasa evidence for clustering . the collaboration expects three more years of data to be taken , which may clear up the situation . the plan for the pierre auger project@xcite is to use both particle detectors ( with 100% duty cycle ) and air fluorescence detectors ( with 10% duty cycle ) . the project promises greatly enhanced statistics and cross - correlation between the two methods . two sites are planned : one in argentina to be fully operational in 2004 , and one in the northern hemisphere . 3000 events per year per site above 10@xmath7 ev are expected , with 30 per year per site above @xmath8 ev . the comparison of the two detector types will allow more accurate energy measurements , and furthermore the identification of the primary will be more certain ( e.g. proton vs. fe ) . at the southern site , a mountain range will act as a neutrino converter for low altitude primaries , so uhe neutrinos can be studied as well . at energies below 1 tev , the alpha magnetic spectrometer ( ams)@xcite will measure the spectra of cosmic ray species with higher accuracy that has been possible . of particular interest are several exotic possibilities , including antinuclei , dark matter , and quark matter `` strangelets '' . ams-01 , which flew on the space shuttle , placed limits on the antihelium to helium ratio of @xmath9 . ams-02 will be installed on the international space station as early as 2005 . with three years of data , the sensitivity to antihelium will be improved to @xmath10 . ams is sensitive to dark matter since annihilations in the galactic halo may produce anomalous levels of antiprotons and positrons at low to moderate energies , though very low energy particles are difficult to study because of the geomagnetic cutoff . ams will have some sensitivity to photons in the sub - tev range as well . a final possibility is the search for stable strangelets . they would be easily identified by their anomalous charge to mass ratios . overall , ams is a high statistics cosmic ray experiment , and will advance our" +"investigation of astrophysical origins of the elements is a important task of modern astrophysics . the elements more heavier than iron - group elements are mainly produced by slow neutron - capture process ( s - process ) and rapid neutron - capture process ( r - process ) @xcite . the s - process contains two categories : the weak s - process and the main s - process . the weak s - process mainly produces the lighter neutron - capture elements ( e.g. , sr ) and occurs in massive stars @xcite . the contribution of s - process to the heavier neutron - capture elements ( e.g. , ba ) is due to the main s - process . the low - mass and intermediate - mass agb stars are usually considered to be the sites in which the main s - process occur @xcite . by subtracting the s - process abundances from the solar system abundances , @xcite derived the r - process abundances , which are called as residual r - process abundances "" . there are many evidences supporting that sne ii are the sites of the r - process nucleosynthesis @xcite . because of the large overabundance of r - process element eu ( [ eu / fe]@xmath0 ) , the two main r - process stars "" cs 22892 - 052 and cs 31082 - 001 arouse special attention : their abundance patterns of the heavier neutron - capture elements fitted the r - process pattern of solar system very closely @xcite . however , their lighter neutron - capture elements ( i.e. , from rb to ag ) are too defficient to agree with the residual r - process abundances "" @xcite . this implies that , for explaining the r - process abundances of the solar system , another process , referred to as the lighter element primary process "" @xcite or weak r - process "" @xcite , is required . by comparison , the abundance patterns of weak r - process stars , hd 122563 and hd 88609 , show excess of lighter neutron - capture elements and defficiency of heavier neutron - capture elements , which are obviously different from the patterns of the main r - process stars @xcite . based on the abundance analyze of metal - poor stars , @xcite found that the weak r - process abundance pattern is uniform and unique . @xcite have performed the r - process calculations . they found that the main r - process abundances can only be matched under the conditions of high neutron densities ( @xmath1 ) . on the other hand , their calculations indicate that smaller neutron number densities ( @xmath2 ) could reproduce the weak r - process abundances . recently , @xcite found that the abundances of neutron - capture elements in all metal - poor stars , including main r - process stars and weak r - process stars , contain the contributions of two r - processes . the element germanium is in the transition between the iron group elements and neutron - capture elements . to date , the quantitative contributions of germanium ( ge , @xmath3 ) from various astrophysical scenarios are rarely known in the studied metal - poor stars . traditionally , ge ( @xmath4 ) has been considered as one of the lightest neutron - capture elements @xcite . it is thought to be produced through the s - process and r - process . based on chemical evolution calculations , @xcite reported that about 12% of ge abundance in the solar system is produced in the agb stars . on the other hand , about 43% of the ge abundance has been produced by the weak s - process via neutron captures through the @xmath5 reaction in massive stars @xcite and around 45% of the ge abundance belong to residual r - process abundance "" @xcite . note that the r - process abundances in solar system are derived through subtracting the s - process abundances from total abundances of solar system @xcite . adopting updated neutron - capture cross sections , @xcite presented new weak s - process calculations for a massive star with 25 m@xmath6 at solar metallicity . they found that ge is one of the most abundant s - elements in the he core and the c shell of the massive star and speculated that the weak s - process is responsible for about 80% of ge abundance in the solar system . however , they point out that their calculated results can not be regarded as the weak s - component of the solar system , because the results come from only one stellar model . they suggested that , for deriving the weak s - component , the contributions from massive stars with various masses must be considered . in this case , the averaged yields weighted by the initial mass function ( imf ) should be more effective than the yields of individual massive star ( e.g.,@xcite ) . furthermore , based on the observed [ ge / fe ] ratios of the metal - poor stars , they estimated that the contribution from the primary - like yields produced in massive stars to the solar germanium is about 5%-8% . recently , @xcite reported that large variations in weak s - process yields could occur since the rotating of the metal - poor massive stars . based on the abundance analysis of neutron - capture elements for metal - poor stars , @xcite found that the abundances of the third r - process peak elements correlated with the abundances of the r - process element eu , implying a common origin or site for r - process nucleosynthesis of heavier ( z @xmath7 56 ) elements . on the other hand , the ge abundances correlated with the fe abundances well . they estimated that the observed relation is [ ge / h]@xmath8 [ fe / h]@xmath9 , which is lower than the ratio of the solar system about 0.8 dex . the abundance relation between ge and fe would mean that an explosive process or charged - particle process , rather than neutron - capture process , would be responsible for the production of ge at low metallicities @xcite . recently , @xcite and @xcite analyzed the abundances of the metal - poor star hd 108317 and found that the abundances can not be matched by the s - process pattern or by the scaled residual r - process "" pattern of the solar system . hd 108317 shows overabundance of the heavier neutron - capture elements from eu to pt , but the discovery that ge , which is one of the lightest neutron - capture element , is deficient is puzzling . the ge abundance of hd 108317 is about 1.2 dex lower than that of scaled ge residual r - process abundance "" in the solar system . they proposed that the elements heavier than ge ( i.e. , as and se ) should be the point where the r - process turns on . @xcite point out that the observed ge abundance in metal - poor stars should serve as the key conditions in constraining the r - process nucleosynthesis . obviously , understanding of the astrophysical origins of ge abundance in our galaxy is a challenging task @xcite . in this paper , based on the abundance approach for metal - poor stars presented by @xcite , we calculate the relative contributions from the individual neutron - capture process to the abundances of metal - poor stars in which ge abundances have been observed . in section 2 , we extract abundance clues of the weak r - process and main r - process for ge from weak r - process star hd 122563 and main r - process star cs 31082 - 001 . in section 3 , based on the observed abundances , we derived the abundances of weak r - process and main r - process for ge element . the calculated results are discussed in section 4 and section 5 . in section 6 , the astrophysical origin of residual abundance "" of ge was investigated . our conclusions are given in section 7 . the element germanium is in the transition between charged - particle synthesis of the iron - group elements and neutron - capture synthesis of heavier elements . there are 19 stars that have been observed for ge abundance . the values of log@xmath10(ge ) , log@xmath10(fe ) and log@xmath10(eu ) @xcite for the sample stars are listed in table 1 . the standard definitions of elemental abundances and abundance ratios are used throughout the paper . for element x , the abundance is defined as the logarithm of the number of atoms of element x per @xmath11 hydrogen atoms , log@xmath12=log@xmath13 + 12.0 . the abundance ratio relative to the solar ratio of element x and element y is defined as [ x / y]=log(@xmath14)-log(@xmath15 . the ratios of [ ge / h ] , [ fe / h ] and [ eu / h ] have been rescaled to corresponding solar logarithm abundances of log@xmath10(fe)=7.50 , log@xmath10(eu)=0.54 and log@xmath10(ge)=3.62 @xcite . in this section , we wish to compare the observed ge abundances of the metal - poor stars which are formed in the interstellar medium ( ism ) with the yields of the massive stars to investigate the astrophysical origin of ge . in this case , the averaged yields weighted by imf should be more effective than the yields of individual massive star . the solid lines in figure 1 ( a ) and ( b ) show the averaged yields of massive star with a mass range from 10 m@xmath6 to 100 m@xmath6 for zero metallicity ( standard mixing of 0.1 , explosion energy of 5.0 ( @xmath16ergs ) ) presented by @xcite , which have been weighted by the salpeter initial mass function ( imf ) and scaled to the fe abundances of the weak r - process star hd 122563 and main r - process star cs 31082 - 001 , respectively . the observed elemental abundances of hd 122563 @xcite and cs 31082 - 001 @xcite marked by filled circles are also shown to facilitate comparison . the scaled imf - weighted yields of massive stars with a mass range from @xmath17 to @xmath18 for zero metallicity presented by @xcite ( see their table 3 ) are also plotted in figure 1(a ) and ( b ) by dashed lines . from the figure we can see that the scaled ge abundances are lower than the ge abundances of the weak r - process star hd 122563 ( [ ge / fe]=-0.9 ) and main r - process star cs 31082 - 001 ( [ ge / fe]=-0.63 ) about 1.0 dex and 1.3 dex respectively . note that the ratio of [ ge / fe]=-0.9 listed in table 1 corresponds to that the scaled ge abundance is lower than the observed ge abundance about 1.0 dex . because the observed ratios of [ ge / fe ] in the metal - poor stars ( [ fe / h]@xmath19 ) lies in the range of @xmath20 @xcite , for the other metal - poor stars , the scaled ge abundances produced in the massive stars are lower than the observed ge abundances about 0.7 dex at least . the compared results mean that the ge abundances in the metal - poor stars would not be produced as the primary - like yields in the massive stars . obviously , another process , which is responsible for the ge abundances in the metal - poor stars , is needed . because hd 122563 is a weak r - process star and cs" +"exact duality transformations for statistical mechanical systems with many degrees of freedom have provided a rich source of insights and alternative computational methods over the years @xcite . as lattice regularized quantum theories share much of the essential structure of lattice statistical mechanical models , it is natural to investigate analogous duality transformations . indeed , applications of duality to quantum fields on the lattice continues to grow ; recent examples include @xcite . in the present work , we shall focus on pure yang - mills theory as we expect it will be instructive to construct dual algorithms in this case before proceeding to dynamical fermions in the dual . for lattice gauge theory ( lgt ) with abelian groups such as @xmath6 and @xmath7 , it is well understood how to construct dual models useful for practical computations @xcite . however , dual simulations with non - abelian gauge groups have presented a greater challenge . the main difficulties have been the definition of the dual model in terms of practically computable amplitudes and the construction of an ergodic set of moves that can be used with a markov chain monte carlo method ( e.g. the metropolis algorithm ) . following some initial results on amplitudes for non - abelian lattice models in the specific case of @xmath8 and @xmath9 in @xcite , a procedure for obtaining non - abelian dual models in four and higher dimensions on the lattice was given by halliday and suranyi @xcite . more recently , a new mathematical framework for understanding the non - abelian dual transformation was constructed , the lattice spin foam formulation @xcite . with regard to numerical simulations , the spin foam approach is helpful for computing amplitudes ( particularly in the four - dimensional case @xcite ) as it gives an explicit prescription for the dual amplitudes in terms of spin networks . these spin networks can in turn be reduced in complexity from their initial definition by the use of diagrammatic recoupling methods @xcite , thus avoiding the typically explosive proliferation of tensorial algebra that would otherwise ensue . the spin foam construction also makes more transparent the distinction between irrep labels associated to plaquettes and intertwiner labels that are naturally associated to edges , as well as the admissibility constraints between these quantities necessary for a non - zero amplitude . in @xcite , these features were applied to the three dimensional case with @xmath9 , resulting in an explicit algorithm that was validated against conventional results . further details on the development and current status of this area can be found in @xcite . the present work may be viewed as a follow - up in four dimensions to the previous results in three dimensions that includes @xcite as well as earlier work by hari dass _ et al . _ @xcite . in the three - dimensional case , an explicit amplitude was known from @xcite and the primary challenge was finding an ergodic set of moves . in the present case , the four - dimensional ( hyper - cubic ) vertex amplitude is a non - trivial function of 48 spin variables , and it was nt until recently that a practical algorithm for this vertex amplitude @xcite was available . in this paper , we construct a set of ergodic moves ( detailed in the appendix ) which when combined with the amplitude of @xcite allow us to perform the first metropolis algorithm simulations of dual @xmath0 in four dimensions . we emphasize that the primary purpose of the present work was to validate the dual algorithm and its implementation against a conventional algorithm , in order to understand its performance over a range of couplings and to evaluate the severity of the sign problem in a simple setting . efforts to extend the methods to more observables such as wilson or polyakov loops are presently underway by the author . this paper is organized as follows . in section 2 , we briefly summarize the form of the dual model for an @xmath0 lattice gauge theory and define the observable to be computed . in section 3 , we describe how a conventional lattice code was constructed and used to compute expectation values of an appropriately chosen effective observable . section 4 summarizes the results obtained with the dual algorithm . the paper is concluded with some discussion of the sign problem and other features of the dual algorithm in section 5 . details of the moves that define the dual algorithm are provided in the appendix . in the present section we shall briefly review some essential features of the dual spin foam model in order to describe the simulations performed and results obtained . the reader is referred to @xcite for a derivation of spin foam duality motivated by simulations with @xmath9 in three dimensions ; its adaption to the present case of four dimensions can be found in @xcite . a general derivation of spin foam models can be found in @xcite . in a dual spin foam model , the continuous group - valued variables of the conventional theory are replaced by discrete labels . the plaquettes of the lattice are labelled by irreducible unitary representations of @xmath0 , typically taken as the half - integers ( although whole integers are sometimes used in diagrammatic methods ) . for a given plaquette labelling , each edge carries an intertwiner label , corresponding to one of a complete basis of maps that intertwine the irreps on plaquettes that intersect the edge . if an appropriate set of conditions is satisfied , than a particular labelling of plaquettes by irreps and edges by intertwiner labels is said to form an _ admissible _ spin foam . further details on these variables and the admissibility constraints among them are given in the appendix . as our present motivation is to evaluate the correctness and efficiency of the dual algorithm relative to the conventional formulation , we chose an observable that is particularly simple to compute in the dual model . such an observable is provided by the average value of the spin at a plaquette @xmath10 : @xmath11 where @xmath12 are the admissible spin foams , and @xmath13 is the dual amplitude , as reviewed in appendix [ sec : alg_append ] . the observable @xmath14 is the spin label assigned by spin foam @xmath15 to plaquette @xmath16 . the subscript @xmath17 on the lhs indicates evaluation of the observable against the dual ( as opposed to conventional ) amplitude @xmath13 . in section [ sec : conventional ] , we will describe how to define and compute the same observable within the conventional lgt framework . for concreteness , we define here precisely which amplitudes were used to generate the results given in section [ sec : results ] . in terms of the spin foam amplitude @xmath13 defined in equation ( [ eqn : partfun ] ) of the appendix , the vertex and edge amplitudes @xmath18 and @xmath19 are those defined in @xcite . the plaquette amplitude @xmath20 used comes from the _ heat kernel _ action , defined as follows : [ defn : heatkernel ] let @xmath21 and @xmath22 . let @xmath23 be the solution to the differential equation @xmath24 at @xmath25 , with initial condition @xmath26 . then the action @xmath27 defined implicitly by @xmath28 is known as the heat kernel action @xcite . it can be shown that the character expansion of the heat kernel action for @xmath0 is of the form @xmath29 where @xmath30 is the quadratic casimir eigenvalue associated to the @xmath31th representation ; for @xmath0 , @xmath32 . as the @xmath33 are absorbed into the vertex and edge amplitudes of the dual model , by inspection of ( [ eqn : hk_expansion ] ) the plaquette amplitude @xmath20 in equation ( [ eqn : partfun ] ) associated with the heat kernel action is thus @xmath34 ; the reader is referred to @xcite for further details . as we are working with a mathematically exact transformation between the conventional and dual forms of the lattice gauge theory , it is possible to validate the correctness of the dual algorithm by computing the same expectation value on both sides of the duality . we believe it is important to do so for several reasons . the dual vertex amplitude we make use of is relatively complex in both its derivation and final form @xcite . assuming that a dual amplitude has been correctly derived and implemented , one would also like to verify that the algorithm constructed ( see the appendix ) is in fact ergodic and capable of realizing convergence of expectation values with comparable time and resources to that of a conventional code . agreement within statistical error of conventional and dual results , while not constituting proof of a correct dual algorithm , strongly indicates its correctness . such testing is particularly valuable as the dual code is further optimized . given an observable and its expectation value defined in terms of the dual model , one can derive the effective observable whose expectation value is equal when evaluated with respect to the original conventional model . explicitly , we seek a function @xmath35 such that @xmath36 where we have introduced a character expansion in the second line to better show the relation with the dual observable . we next recall from section [ sec : spinfoamsims ] the dual observable of interest @xmath37 based on the above we introduce the following proposal for @xmath38 : @xmath39 the above can be checked by substituting into the second line of equation ( [ eqn : effectdef ] ) and comparing to the second line of equation ( [ eqn : charsumj ] ) . given the above , it is useful to be able to readily compute the character expansion components @xmath40 of the action in order to compute the `` re - weighted '' numerator of ( [ eqn : effectformula ] ) . the heat kernel action used in the present simulations has a simple form ( see definition [ defn : heatkernel ] ) in which character coefficients can be rapidly evaluated . we note in passing that the division by part of the original amplitude as is done in ( [ eqn : effectformula ] ) in general may produce numerical problems , as convergence is better when observables are well correlated with the amplitude . in practice , for this particular case we have found good convergence ( low variation of independent runs ) of simulations for this effective observable . several sets of computations were performed in order to confirm the correctness of the algorithm and evaluate the computational performance of the dual simulations as currently implemented . these are described in the subsections below ; we first make some general comments . prior to computing the observable @xmath41 , the conventional code was validated against published curves appearing in @xcite , which we selected because those simulations used the same heat kernel action employed in the present work . due to the computational cost of the vertex amplitude at higher spins , for the simulations described below the series appearing in ( [ eqn : effectdef ] ) are cut off at a relatively low spin @xmath42 ; however , because the cut - off is applied to both conventional ( as a truncation of the character expansion ) and dual forms , a direct comparison can still be made , and posible errors in the ( considerably more complex ) dual code can be detected . while low cut - off simulations can be quite accurate in the strong coupling regime , they begin to break down at the weaker coupling scales of interest . further optimizations of the vertex amplitude underway by the author should allow for higher" +"the effect of random defects on the properties of solids is an important area in the study of materials . defects are ubiquitous in solids @xcite . either formed naturally during their preparation or artificially engineered , they may profoundly affect their physical properties . chemical reactions , phase transitions or plastic deformations during the formative stage may leave their imprints as defects . these defects may be local , like vacancies @xcite , substitutional impurities @xcite or adatoms @xcite . defects can also be extended , like dislocations , stacking faults , twins and grain boundaries . extended defects have been visualized by stm images @xcite . it is important therefore to set up a first - principles , essentially parameter free , theoretical methodology for the signature of random defects , and to distinguish , in particular , the role of disorder . local random defects has been thoroughly studied using sophisticated mean - field approaches like the itinerant coherent potential approximation ( icpa ) @xcite , the travelling cluster approximation ( tca)@xcite , both derived from the parent formalism : the augmented space formalism ( asf ) @xcite . however , most of the work on extended defects have involved super - cell methods . these works look at essentially periodic arrays of defects with disorder stretching only over the finite super - cell @xcite . long ranged disorder is not accessible to these reciprocal space based methods . none of the supercell methods can accurately capture the disorder induced smearing of the density of states due to the self - energy arising out of scattering of bloch waves by configuration fluctuations . this ` life - time ' effect is experimentally accessible through neutron scattering and has been found to be strongly dependent both on the energy e and the wave - vector @xmath0 . in this work we shall propose a fully real space technique , where the structure and hamiltonian of the relaxed defected lattice goes as an input into a recursive algorithm which gives us the electronic structure carrying the signatures of disorder . although the application will be to a specific problem , the method is general enough to be applied in any solid carrying random extended defects . electronic structure of low - dimensional solids with extended defects have been addressed earlier @xcite . let us quote shirodkar and waghmare @xcite : _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ our work , along with other work @xcite has involved a _ periodic array _ of sw defects , whereas sw defects are _ randomly distributed _ in a real sample . "" _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ the authors go on to remark that although this disorder may not affect the vibrational spectrum significantly , the electronic structure obtained from a periodic array of sw defects needs to be interpreted with care . our real space recursion approach @xcite makes no appeal to lattice translational symmetry and is thus ideal for studying topological disorder and its effect on electronic structure . the illustration of this point is the justification of our proposed methodology and the main focus of this communication . early in the seventies heine and co - workers introduced @xcite the recursion method based on a fully real space technique to deal with lattices without any translation symmetry . the essential inputs are the geometry of the lattice and a tight - binding , sparse hamiltonian . as an example , and in view of our later applications , let us look at a honeycomb lattice and map its vertices onto the set of positive integers . the mapping is not unique , but necessarily one - to - one ( fig.[fig5 ] ) . the geometry of the lattice is uniquely described by a connectivity matrix @xmath1 which gives us the @xmath2-th neighbour of the vertex labelled as @xmath3 . the central panel of fig.[fig5 ] shows a model in which up to third neighbour overlaps are taken into account . the connectivity matrix is : c(n , m ) = ( c|ccc|cccccc|ccc 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11&12&13 + 2 & 9 & 10 & 1&3&4&12 & 11& & &5&8 & + 3 & 6&5 & 1&11&4&2 & 13 & & & 7&10 & + 4&7 & 8 & 1 & 3 & 12&2&13& & &6&9 & + ) [ map ] the tight - binding hamiltonian can be written as : h = _ n__p_n + _ nm _ t_(n - m ) t_n , m here , @xmath4 and @xmath5 are projection and transfer operators on the tight - binding basis labelled by @xmath6 , where @xmath3 is the vertex label and @xmath7 all other possible degrees of freedom associated with it . similarly , we describe a honeycomb lattice with a structural defect shown in the right most panel of fig.[fig5 ] . we label the distorted sites say with a label @xmath8 , then whenever @xmath9 , @xmath10 and otherwise @xmath11 . with this recursion method , we shall study the representations of the green operator or the resolvent of the hamiltonian , @xmath12 where @xmath13 is a complex variable . most physically measurable quantities describing the electronic properties of a solid are related to different matrix elements of * g*(z ) . in particular , the local ( atom projected ) density of states ( ldos ) @xmath14 and the total densities of states ( tdos ) @xmath15 : @xmath16 where n is the number of atoms in the system . it would be interesting to note that although the super - cell based methods can easily access both the band projected partial density of states ( pdos ) and the total density of states ( tdos ) , it is only the real - space based methods that can give is a single atom or an atomic cluster projected _ local _ densities of states ( ldos ) . in this basis the representation of the hamiltonian is a matrix of infinite rank . the solution of the kohn - sham equation of an electron in this system can be simplified enormously if the hamiltonian has lattice translation symmetry . in that case the bloch theorem introduces the quantum label @xmath0 and reduces the effectively infinite rank matrix representation of the hamiltonian to a manageable finite rank equal to the number of bands ( in this case two ) . consequently , crystalline systems are always studied in this bloch representation . but in disordered systems , particularly where the disorder is a topological distortion of the lattice and these defects are distributed randomly throughout it , such periodicity is absent and the reciprocal space representation is no longer strictly valid . in such situations we need to look for real - space based techniques . calculation of the resolvent requires inversion of a matrix of infinite rank . haydock @xcite proposed a technique to do so . we start from a suitable vertex at @xmath17 . it essentially involves generation of a new basis through a three term recurrence relation : @xmath18 _ n _ n^2 haydock @xcite showed that the matrix element of the resolvent may be written as a continued fraction . @xmath19 right at the start we emphasized that we have chosen a real space algorithm over mean - field and supercell approaches , because we do not wish to introduce artificial periodicity and confine randomness over a finite volume . but the problem with any numerical calculation is that we can deal with only a finite number of operations . in the recursion algorithm , we can go up to a finite number of steps leading to exactly what we wish to avoid . the analysis of the asymptotic part of the continued fraction then is of prime interest to us . this is the termination "" procedure in which the asymptotic behaviour is assessed from the way the coefficients @xmath20 behave as @xmath21 . different terminators have been discussed in detail by haydock and nex @xcite , luchini and nex @xcite , beer and pettifor @xcite and in considerable depth by viswanath and muller @xcite . the terminator which describes the asymptotically far environment must satisfy certain basic properties : this termination process is a delicate mathematical approximation . we would like to maintain the herglotz analytic properties of the resolvent after termination . a function t(z ) is called herglotz if : 1 . all singularities of t(z ) lie on the real z - axis . singularities of t(z ) form a bounded set . i m t(z)@xmath22 0 if i m z @xmath23 0 ; i m t(z ) @xmath24 0 if i m z @xmath25 0 . re t(z ) @xmath26 0 as re z @xmath27 the next step is to analyze our resolvent to locate singularities on its compact spectrum . majority of resolvents with bounded spectra have singularities at the band edges . the termination of continued fractions describing spectral densities with compact support and singularities except at the band edges have been described in detail in earlier works @xcite . the best illustration of this technique is to apply it to an interesting material where alternative methods always leads to problems of one sort or another . we have chosen to study graphene with random stone - wales defects . in this work , we shall be interested in intrinsic extended structural defects like stone - wales ( sw ) defects @xcite in graphene . the study of graphene , the two - dimensional allotrope of carbon is an area of intense interest to both theoretical and experimental researchers for various reasons . the first is the possible technological applications of graphene@xcite . second , graphene seems to defy the theorem of mermin and wagner @xcite and form a stable two - dimensional structure . finally , the electrons in graphene behave like massless charged particles , something not encountered in our three dimensional world @xcite ." +"since its discovery @xcite , the black - hole candidate ( bhc ) has been observed to spend long periods in outburst . although historically it was found to be mainly in the hard state ( maejima et al . 1984 ; ilovaisky et al . 1986 ; miyamoto et al . 1991 ) , since the launch of the source has been monitored and complete sets of transitions have been observed and studied ( belloni et al . 2005 ; zdziarski et al . 2004 ; del santo et al . 2008 ) . unlike the bhc prototype cyg x1 , for which spectral state transitions are directly correlated with luminosity , shows hysteresis in its relation between x - ray luminosity and spectral state @xcite , as also observed in other bhc in low - mass binary systems ( lmxb ; maccarone & coppi 2003 ; smith , heindl & swank 2002 ) . it was observed that hard - to - soft state transitions during the rise phase occurs at higher luminosities than the soft - to - hard transitions during the decline phase ( smith , heindl & swank 2002 ; zdziarski et al . 2004 ) . _ cgro _ , _ ginga _ and data from collected in the period 1987 - 2004 have been analysed by zdziarski et al . these authors reported on long term variability and spectral correlations for the @xmath115 outbursts of that occurred in this period . furthermore , in that work a lower limit for the source distance at 7 kpc was provided . the 2002/2003 outburst ( smith et al . 2002a ; nespoli et al . 2003 ; buxton & bailyn 2004 ) was followed with in detail through timing and hardness - ratio ( hr ) analysis @xcite . these authors described hysteresis in term of the source s evolution through a hardness - intensity diagram ( hid ) . belloni et al . ( 2005 ) also introduced new definitions for the different sub - states observed during state transitions : the hard - intermediate ( hims ) and the soft - intermediate states ( sims ; see also homan & belloni 2005 ; belloni 2005 ) . for a description of historical and alternative states classification see tanaka & lewin ( 1995 ) , van der klis ( 1995 ) and a more recent review by mcclintock & remillard ( 2006 ) . during the 2002/2003 outburst , close to the transition to the sims ( on 2002 may 17th @xcite ) , a rapid ( hours ) bright radio flare was observed @xcite which led to the formation of a large - scale relativistic jet @xcite . fender , belloni & gallo ( 2004 ) associated this flare and subsequent matter ejections with the crossing of the so - called jet - line , i.e. the hims - sims transition as reported by nespoli et al . ( 2003 ) . during this hims - sims transition showed fast changes in its timing properties , but almost none in the 3 - 20 kev energy spectrum @xcite . in february 2004 a new outburst started , which reached a significantly lower peak flux than the 2002/2003 outburst ( buxton et al . 2004 ; smith et al . 2004 ; belloni et al . 2004 ; kuulkers et al . 2004 ) . to get broad - band coverage during the expected hims - sims spectral transition , simultaneous and observations were made . belloni et al . ( 2006 ) combined data from pca , hexte and ibis , and obtained good quality broad - band ( 3 - 200 kev ) energy spectra before and soon - after the transition . these spectra indicated steepening of the hard , high - energy component . also , the high - energy cut - off that was present at @xmath170 kev before the transition was not detected later . therefore , although spectral parameters at lower energies do not change abruptly through the transition , the energy of the cut - off increases or disappears rather fast ( within 10 hours ) . the power spectra before and after the transition showed significant differences ( see belloni et al . 2005 ; belloni 2008 ) : from strong band - limited noise and type - c qpo to much weaker noise and type - b qpo ( for a description of the properties of different types of qpo , see casella , belloni & stella 2005 ) . in 2006 monitoring of revealed low - level x - ray activity ( bezayiff & smith 2006 ; swank et al . 2006 ) until december , when a new strong outburst started @xcite . miller et al . ( 2007 ) triggered a public too campaign on which started on january 30th ( caballero - garcia et al . 2007a - e ) . we activated our campaign with the aim to follow the source through a hims - sims transition . unfortunately , we did not observe the main transition , as we did in 2004 , but managed to capture a secondary transition . in this paper , we report the results of the timing and spectral analysis of our data from 2007 march 46 and of the quasi - simultaneous interval of the public data ." +"a giant x - ray outburst of ngc5905 was discovered during the ( trmper 1983 ) survey observation ( bade , komossa & dahlem 1996 ) . ngc5905 showed a high countrate during this first observation . the countrate then declined by at least a factor of several within months and was down by a factor @xmath0100 two years later . the x - ray spectrum during the outburst was very soft ( with photon index @xmath1 when fit by a powerlaw ) . during quiescence , the spectrum is flatter ( @xmath2 ) . the outburst luminosity is of the order of @xmath3 several @xmath4 erg / s ; much _ higher _ than observed in _ non - active _ spiral galaxies ( e.g. , fabbiano 1989 , vogler 1997 ) . new hri data were taken in 1996 with an exposure time of 76 ksec . these show a further decline by a factor @xmath02 in flux with respect to the last pspc observation . the long - term x - ray lightcurve is displayed in fig optical observations are an important supplement to the x - ray data . the two most important questions are ( i ) is there a simultaneous optical outburst , and ( ii ) does the optical spectrum of ngc5905 show any signs of seyfert activity ? we have used photographic plates taken at _ sternwarte sonneberg _ to produce a long - term optical lightcurve ( between years 1962 and 1995 ) of the nucleus of ngc5905 and searched the plates taken quasi-_simultaneously _ to the x - ray outburst for a correlated optical outburst . the factor @xmath0100 variability seen in x - rays would corresponds to 5@xmath5 in the optical spectral region in the variable component . the optical brightness of ngc5905 is found to be _ constant _ within the errors on long terms as well as near the x - ray outburst ( fig . 2 ) , placing strong constraints on outburst scenarios . we have taken high - resolution post - outburst optical spectra ( about 6 years after the x - ray outburst ) at the 3.5 m telescope of calar alto . these show the same spectral characteristics as the pre - outburst spectrum of ho et al . ( 1995 ) and classify the galaxy as hii - type . if a high - ionization emission - line component was present during outburst , it had already declined below detectability . we carefully searched for other signs of _ permanent _ seyfert activity none are revealed . this is another important constraint for outburst models and , at present , makes ngc5905 the only non - active galaxy among the x - ray outbursting ones . the major characteristics to be explained by outburst models are * short duration , extremely soft spectrum , giant amplitude ( a factor @xmath6 100 ) and huge peak luminosity of the x - ray outburst * no detected simultaneous change in optical brightness * the optical spectrum is that of an hii - type galaxy with _ no _ signs of _ permanent _ seyfert activity we in turn discuss several outburst scenarios ( for details see komossa & bade 1998 ) . the outburst x - ray luminosity by far exceeds that of individual supernovae . those observed in x - rays range between @xmath7 and a few @xmath8 erg / s ( e.g. , schlegel 1995 , immler & pietsch 1998 ) ; the x - ray brightest reached @xmath9 erg / s ( fabian & terlevich 1996 ) . the possibility of ` buried ' supernovae ( sn ) in _ dense _ molecular gas was studied by shull ( 1980 ) and wheeler et al . ( 1980 ) . in this scenario , x - ray emission originates from the shock , produced by the expansion of the sn ejecta into the ambient interstellar gas of high density . since high luminosities can be reached this way , and the evolutionary time is considerably speeded up , an sn in a dense medium may be an explanation for the observed x - ray outburst in ngc5905 . assuming the observed outburst luminosity of ngc5905 to be the peak luminosity and using the analytical estimates of shull and wheeler et al . for the evolution of temperature , radius and luminosity of the shock , @xmath10 @xmath11 @xmath12 results in a density of the ambient medium of @xmath13 but is inconsistent with the observed softness of the spectrum : the expected temperature is @xmath14 k , compared to the observed one of @xmath15 k. therefore , an sn in dense medium is an unlikely explanation of the observed x - ray outburst . additionally , fine - tuning in the column density of the surrounding medium would be required in this scenario in order to prevent the snr from being completely self - absorbed . large magnification factors of the source brightness can be reached by gravitational lensing ( gl ) if the observer , lens , and source ly nearly exactly on a line . lensing was , e.g. , discussed as a possibility to explain the observed variability in bl lac objects ( e.g. , ostriker & vietri 1985 ) . being independent of photon energy , gl predicts the same magnification factor at optical wavelengths as in x - rays . given the non - detection of optical variability simultaneous to the x - ray outburst the gl scenario is very unlikely . as to the question of whether the observations may have represented the x - ray afterglow of a gamma - ray burst ( grb ) , we note that no grb has been detected in the time around the x - ray outburst ( july 1215 , 1990 ) of ngc5905 ( the 2 reported grbs nearest in time , of july 8 , 1990 , have different positions ; castro - tirado 1994 on the basis of granat / watch data ) . the possibility remains that the grb escaped detection or that it was not beamed towards us and only the isotropic afterglow was seen . if a massive bh _ with an accretion disk _ exists in the center of ngc5905 , it usually has to accrete with low accretion rate or radiate with low efficiency , to account for the comparatively low x - ray luminosity of ngc5905 in quiescence . an accretion disk instability may then provide an explanation for the observed x - ray outburst . thermally unstable slim accretion disks were studied by honma et al . ( 1991 ) , who find the disk to exhibit burst - like oscillations for the case of the standard @xmath16 viscosity description and for certain values of accretion rate . using the estimate for the duration of the high - luminosity state ( honma et al . ; 4.8 ) , and a duration of the outburst of less than 5 months ( the time difference between the first two observations of ngc5905 ) , a central black hole of mass in the range @xmath17 could account for the observations . the burst - like oscillations are found by honma et al . only for certain values of the initial accretion rate . a more detailed quantitative comparison with the observed outburst in ngc5905 is difficult , since the behavior of the disk is quite model dependent , and further detailed modeling would be needed . the idea of tidal disruption of stars by a supermassive black hole ( smbh ) was originally studied as a possibility to fuel agn ( hills 1975 ) , but was dismissed later . peterson & ferland ( 1986 ) suggested this mechanism as possible explanation for the transient brightening of the heii line observed in a seyfert galaxy . tidal disruption was invoked by eracleous et al . ( 1995 ) in a model to explain the uv properties of liners , and was suggested as possible outburst mechanism for ic3599 ( brandt et al . 1995 , grupe et al . 1995 ) . rees ( 1988 , 1990 ) proposed to use individual such events as tracers of smbhs in nearby _ non - active _ galaxies . the debris of the disrupted star is accreted by the bh . this produces a flare , lasting of the order of months , with the peak luminosity in the opt - uv , euv or soft x - ray spectral region . the luminosity emitted if the bh is accreting at its eddington luminosity can be estimated by @xmath18 erg / s . in case of ngc5905 , a bh mass of at least @xmath19 m@xmath20 would be required to produce the observed @xmath21 , and a higher mass if @xmath21 was not observed at its peak value . the decline in luminosity after the maximum in the tidal disruption scenario scales as @xmath22 ( rees 1990 ) . the observed long - term x - ray lightcurve of ngc5905 is given in fig we favour the scenario of tidal disruption of a star because it can account for the high outburst luminosity , seems to require least fine - tuning , and the long - term x - ray lightcurve shows a continuous fading of the source over the whole measured time interval . however , we also caution that many theoretical details of the tidal disruption process are still rather unclear . we performed a search for further cases of strong x - ray variability ( komossa 1997 ) using the sample of nearby galaxies of ho et al . ( 1995 ) and survey and archived pointed observations . we do not find another object with a factor @xmath0100 amplitude , but several sources are discovered to be strongly variable ( with maximal factors ranging between @xmath010 and 20 in the mean countrates ) : ngc3227 , ngc4051 , and ngc3516 . it is a pleasure to thank the _ sternwarte sonneberg _ for the kind hospitality and g. richter additionally for valuable help in the assessment of the photographic plates . st.k . acknowledges support from the verbundforschung under grant no . the project is supported by the german bundesministerium fr bildung , wissenschaft , forschung und technologie ( bmbf / dlr ) and the max - planck - society . bade n. , komossa s. , dahlem m. , 1996 , a&a 309 , l35 brandt w.n . , pounds k.a . , fink h. , 1995 , mnras 273 , l47 castro - tirado a. , 1994 , thesis , copenhagen univ . eracleous m. , livio m. , binette l. , 1995 , apj 445 , l1 fabbiano g. , 1989 , ara&a 27 , 87 fabian a.c . , terlevich r. , 1996 , mnras 280 , l5 grupe d. et al . , 1995a , b , a&a 299 , l5 and a&a 300 , l21 hills j.g . , 1975 , nature 254 , 295 ho l.c . , filippenko a.v . , sargent w.l.w . , 1995 , apjs 98 , 477 honma f. , matsumoto r. , kato s. , 1991 , pasj 43 , 147 immler s. , pietsch w. , 1998 , astron 319 , 27 komossa s. , 1997 , thesis , lmu mnchen komossa s. , fink h. , 1997 , in _ accretion disks new aspects _ , e. meyer - hofmeister , h. spruit ( eds ) , lecture notes in physics 487 , 250 komossa s. , bade n. , 1998 , a&a , subm . ostriker j.p . , vietri m. , 1985 , nature 318 , 446 peterson b. , ferland g.j . , 1986 , nature 324 , 345 piro l. et al . , 1988 , apj 325" +"evolutionary algorithms ( eas ) have been successfully used in the areas of music and art @xcite . in this application area the primary aim is to evolve artistic and creative outputs through an evolutionary process @xcite . the use of evolutionary algorithms for the generation of art has attracted strong research interest . different representations have been used to create works of greater complexity in 2d and 3d @xcite , and in image animation @xcite . the great majority of this work relates to using evolution to produce a final artistic product in the form of a picture , sculpture or animation . the focus of study in this paper is how ea processes can be mirrored in image transitions . past work studying the use of eas for image transitions includes work by sims @xcite which described methods for cross - dissolving of images by changes in an expression genotype . furthermore , deep neural networks have recently been used to create artistic images @xcite . banzhaf @xcite used interactive evolution to help determine parameters for image morphing . furthermore , karungaru @xcite used an evolutionary algorithm to automatically identify features for morphing faces . our work differs from previously mentioned work in our focus on the direct link between the evolutionary process and image transitions they produce . we use well - known random processes for the evolutionary image transition process . the key idea in this work is to use the evolutionary process _ itself _ in an artistic way . ( sydney opera house ) and target image @xmath0 ( eiffel tower),title=""fig : "" ] ( sydney opera house ) and target image @xmath0 ( eiffel tower),title=""fig : "" ] the transition process used in this work consists of evolving a given starting image @xmath1 into a given target image @xmath0 by random decisions . considering an error function which assigns to a given current image @xmath2 the number of pixels where it agrees with @xmath0 and maximizes this function boils down to the classical onemax problem for which numerous theoretical results on the runtime behaviour of evolutionary algorithms are available @xcite . we use the insights obtained in such studies and show how different processes have an influence on evolutionary image transition . furthermore , we are optimistic that the visualization of evolutionary algorithms through image transition may be of independent interest to researchers working on evolutionary computation as it provides a new mechanism of visualizing an evolutionary process . using mutations where in each step exactly one uniformly at random chosen pixel may flip to the target , leads to the coupon collector process @xcite which significantly slows down when being close to the target . it has been shown in @xcite that an asymmetric mutation operator moves at a constant speed towards the target and thereby avoids the slow - down due to the coupon collector s effect . we use a simple ( 1 + 1 ) ea together with this asymmetric mutation operator as our baseline algorithm for evolutionary image transition . another important topic related to the theory of evolutionary algorithms are random walks @xcite . we consider random walks on images where each time the walk visits a pixel its value is set to the value of the given target image . by biasing the random walk towards pixels that are similar to the current pixel we can study the effect of such biases which might be more interesting from an artistic perspective . after observing these two basic random processes for image transition , we study how they can be combined to give the evolutionary process additional interesting new properties . we study the effect of running random walks for short periods of time as part of a mutation operator in a ( 1 + 1 ) ea . furthermore , we consider the effect of alternating different mutation operators over time . our results show that the area of evolutionary image transition based on different well studied random process provides a rich source of artistic possibilities with strong potential for further exploration . the outline of the paper is as follows . in section [ sec2 ] , we introduce the evolutionary transition process and examine the behaviour of simple evolutionary algorithms for image transition in section [ sec : asym ] . section [ sec3 ] studies how variants of random walks can be used for the image transition process . in section [ sec4 ] , we examine the use of random walks as part of mutation operators and study their combinations with pixel - based mutations during the evolutionary process . finally , we finish with some concluding remarks . * let @xmath1 be the starting image and @xmath0 be the target image . * set x:=s . * evaluate @xmath3 . * while ( not termination condition ) * * obtain image @xmath4 from @xmath2 by mutation . * * evaluate @xmath5 * * if @xmath6 , set @xmath7 . we consider an evolutionary transition process that transforms a given image @xmath2 of size @xmath8 into a given target image @xmath0 of size @xmath8 . our goal is to study different ways of carrying out this evolutionary transformation based on random processes from an artistic perspective . we start our process with a starting image @xmath9 . our algorithms evolve @xmath1 towards @xmath0 and has at each point in time an image @xmath2 where @xmath10 . we say that pixel @xmath11 is in state @xmath12 if @xmath13 , and @xmath11 is in state @xmath14 if @xmath15 . for our process we assume that @xmath16 as pixels with @xmath17 can not change values and therefore do not have to be considered in the evolutionary process . to illustrate the effect of the different methods presented in this paper , we consider the sydney opera house as the starting image and the eiffel tower as the target image ( see figure [ fig : opera ] ) . the fitness function of an evolutionary algorithm guides its search process and determines on how to move between images . therefore , the fitness function itself has a strong influence on the artistic behaviour of the evolutionary image transition process . an important property for evolutionary image transition should be that images close to the target image get a higher fitness score . we measure the fitness of an image @xmath2 as the number of pixels where @xmath2 and @xmath0 agree . this fitness function is isomorphic to that of the onemax problem when interpreting the pixels of @xmath1 as @xmath18 s and the pixels of @xmath0 as @xmath19 s . formally , we define the fitness of @xmath2 with respect to @xmath0 as @xmath20 we consider simple variants of the classical ( 1 + 1 ) ea in the context of image transition . the algorithm is using mutation only and accepts an offspring if it is at least as good as its parent according to the fitness function . the approach is given in algorithm [ alg : ea ] . using this algorithm has the advantage that parents and offspring do not differ too much in terms of pixel which ensures a smooth process for transitioning the starting image into the target . furthermore , we can interpret each step of the random walks flipping a visited pixel to the target outlined in section [ sec3 ] as a mutation step which according to the fitness function is always accepted . we consider a simple evolutionary algorithm that have been well studied in the area of runtime analysis , namely variants of the classical ( 1 + 1 ) ea . as already mentioned , our setting for the image transition process is equivalent to the optimization process for the classical benchmark function onemax . our aim is to demonstrate how the progress of these processes are mirrored in the transition of images . the standard variant of the ( 1 + 1 ) ea flips each pixel with probability @xmath21 where @xmath22 is the total number of pixels in the given image . using this mutation operator , the algorithm encounters the well - known coupon collector s effect which means that additive progress towards the target image when having @xmath23 missing target pixels is @xmath24 @xcite . * obtain @xmath4 from @xmath2 by flipping each pixel @xmath11 of @xmath2 independently of the others with probability @xmath25 if @xmath26 , and flip @xmath11 with probability @xmath27 if @xmath15 , where @xmath28 and @xmath29 are constants . in order to avoid the coupon collector s effect , we use the asymmetric mutation operator introduced and theoretically analyszed in @xcite . jansen and sudholt @xcite have shown that the ( 1 + 1 ) ea using asymmetric mutation optimizes onemax in time @xmath30 which improves upon the usual bound of @xmath31 when using standard bit mutations . in order to apply this asymmetric mutation to our image transition process we make the process of flipping pixels dependent on the number of pixels of @xmath2 that are in the same state as @xmath11 . we denote by @xmath32 the number of pixels where @xmath2 and @xmath0 agree . similarly , we denote by @xmath33 the number of pixels where @xmath2 and @xmath1 agree . each pixel is starting state @xmath12 is flipped with probability @xmath25 and each pixel in target state @xmath14 is flipped with probability @xmath27 . the mutation operator is shown in algorithm [ alg : asym ] . the mutation operator differs from the one given in @xcite by the two constants @xmath34 and @xmath35 which allows the determination of the expected number of new pixels from the starting image and the target image , respectively . the choice of @xmath34 and @xmath35 determines the expected number of pixel in the starting state and target state to be flipped . to be precise , the expected number of pixel currently in starting state @xmath12 to be flipped is @xmath36 and the number of pixels in target state @xmath14 to be flipped is @xmath37 as long as the current solution @xmath2 contains at least that many pixel of the corresponding type . in @xcite the case @xmath38 has been investigated which ensures at each point in time an additive drift of @xmath39 . using different values for @xmath34 and @xmath35 allows us to change the speed of transition as well as the relation of the number of pixels switching from the starting image to the target and vice versa while still ensuring that there is constant progress towards the target . all experimental results in this paper are shown for the process of moving from the starting image to the target image given in figure [ fig : opera ] where the images are of size @xmath40 . the algorithms have been implemented in matlab . in order to visualize the process , we show the images obtained when the evolutionary process reaches 12.5% , 37.5% , 62.5% and 87.5% pixels of target image for the first time . we should mention that all processes except the use of the biased random walk are independent of the starting and target image which implies that the use of other starting and target images would show the same effects in terms of the way that target pixels are displayed during the transition process . for our experiments with ( 1 + 1 ) ea@xmath41 , we set @xmath42 and @xmath43 which allows both a decent speed for the image transition process and enough exchanges of pixels for an interesting evolutionary process . we should mention that obtaining the last pixels of the target image may take a long time compared to the other progress steps when using large values of @xmath35 . however , for image transition , this only effects steps when the are at most @xmath37 source pixels remaining in the image ." +"one of the spectacular predictions of quantum electrodynamics is the emergence of forces that arise purely from quantum fluctuations of the electromagnetic vacuum @xcite . also known as london - van der waals @xcite or casimir forces @xcite in different regimes , these forces are often dominant at short distances and can give rise to undesirable effects in nanoscale systems , such as nanomechanical stiction @xcite . these forces have also attracted increasing attention in the fields of atomic physics and quantum optics . in particular , significant efforts have been made in recent years to interface cold atoms with the evanescent fields of dielectric micro- and nano - photonic systems @xcite . these systems are expected to facilitate strong , tunable interactions between individual atoms and photons for applications such as quantum information processing @xcite and the investigation of quantum many - body physics @xcite . in practice , efficient atomic coupling to the evanescent fields of the nanophotonic systems requires that atoms be trapped within sub - wavelength distances of these structures . at these scales , quantum vacuum forces can overwhelm the forces associated with conventional optical dipole traps , typically resulting in a loss of trap stability at distances @xmath0 nm from dielectric surfaces . given the ability to engineer the properties of nanophotonic structures , an interesting question arises as to whether such systems could be used to significantly modify vacuum forces , perhaps changing their sign from being attractive to repulsive , or even creating local potential minima . the strength of nanoscale vacuum forces should lead to unprecedented energy and length scales for atomic traps , which would find use beyond nanophotonic interfaces , such as in quantum simulation protocols based upon ultracold atoms @xcite and control of inter - atomic interactions @xcite . here we propose a novel mechanism in which engineered vacuum forces can enable the formation of a nanoscale atomic trap . while a recent no - go theorem @xcite forbids a vacuum trap for atoms in their electronic ground states , tailored nanophotonic systems can yield strong repulsive potentials for atomic excited states . we show that a weak external optical field can give rise to an overall trapping potential for a dressed state . remarkably , absent fundamental limits on the losses of the surrounding dielectric structure , the fraction of excited - state population in the dressed state can become infinitesimal , which greatly enhances the trapping lifetime and stability . we identify and carefully analyze the actual limiting mechanisms . while we present calculations on a simple model where analytical results can be obtained , we also discuss the generality of our protocol to realistic systems such as photonic crystal structures . the no - go theorem for non - magnetic media states that a dielectric object in vacuum can not be stably trapped with vacuum forces for any surrounding configuration of dielectric objects , provided that the system is in thermal equilibrium @xcite . in analogy with earnshaw s theorem , which prohibits trapping of charged objects with static electric potentials , at best one can create a saddle - point potential ( see , _ e.g. _ , ref . @xcite involving metal particles and ref . @xcite for a hybrid vacuum / optical trap for atoms ) . for dielectric objects , potential loopholes involve embedding the system in a high - index fluid @xcite , or using blackbody radiation pressure associated with strong temperature gradients @xcite . applied to atoms , this theorem essentially forbids stable vacuum trapping near a dielectric structure when the atom is in its electronic ground state . no such constraint exists for atoms in their excited states @xcite , although the robustness of any possible trap would be limited by the excited state lifetime . here , we show that an atom only weakly dressed by its excited state can be trapped by properly tailoring the dispersion of the underlying structure . we begin by briefly reviewing how quantum vacuum fluctuations give rise to forces on the ground and excited states . within an effective two - level approximation of an isotropic atom with ground and excited states @xmath1 ( see appendix for description of how isotropy is incorporated into the model ) , the interaction between the electromagnetic field and an atom at position @xmath2 is given by the dipole hamiltonian @xmath3 . following a complete decomposition of the electric field into its normal modes @xmath4 , one can write @xmath5 , where @xmath6 . the energy non - conserving terms ( @xmath7 and @xmath8 ) enable an atom in its ground state @xmath9 to couple virtually to the excited state and create a photon , @xmath10 , which is subsequently re - absorbed . the corresponding frequency shift for the ground state within second - order perturbation theory is @xmath11 , where @xmath12 is the unperturbed atomic transition frequency . this shift results in a mechanical `` vacuum '' potential when translational symmetry is broken due to dielectric surfaces . using a quantization technique for electrodynamics in the presence of dispersive dielectric media , the shift can be expressed in terms of the scattered component of the dyadic electromagnetic green s function evaluated at imaginary frequencies @xmath13 @xcite ( see appendix ) , _ g()=_0^dug_(,,iu ) , where @xmath14 is the free - space spontaneous emission rate of the atom . a similar process can occur for an atom in its excited state @xmath15 , in which the atom virtually emits and re - absorbs an off - resonant photon ( @xmath16 ) . however , the excited state is unique in that it can also emit a resonant photon . the total excited state shift is given by @xcite _ e()=--g_(,,_0).[eq : omegae ] the first term on the right arises from off - resonant processes , while the second term can be interpreted as the interaction between the atom and its own resonantly emitted photon . naturally , the dielectric environment can modify the spontaneous emission rate as well , ( ) = _ 0+g_(,,_0).[eq : gamma ] note that the modified emission and resonant shifts are complementary in that they emerge from different quadratures of the green s function . the versatility of micro- and nanophotonic systems has already been exploited to greatly modify emission rates of atoms and molecules in a variety of contexts @xcite . we propose that these same systems can be used to tailor excited - state potentials in order to facilitate vacuum trapping . of course , the excited - state shift can be affected by coupling to even higher electronic levels . however , since our goal is to engineer giant resonant shifts of @xmath17 , the off - resonant couplings to higher - lying states yield only minor corrections and consequently are ignored here . in what follows , we present a simple model system that enables one - dimensional trapping in a plane parallel to a semi - infinite dielectric slab , as illustrated in fig . [ fig : schematic ] . the use of a homogeneous dielectric ( as opposed to , _ e.g. _ , a photonic crystal ) greatly simplifies the calculation and enables one to understand the relevant trap properties analytically , although we later argue why the qualitative features should still hold in more complex geometries . in the dielectric slab model , dispersion engineering will be realized via the frequency - dependent electric permittivity @xmath18 . while this particular system achieves a one - dimensional trap along @xmath19 , our electrodynamic calculations are performed in three dimensions . enables large repulsion in the excited state @xmath20 , in contrast to the attractive vacuum potential experienced by an atom in its ground state . an overall trapping potential normal to the surface ( along @xmath19 ) can be generated by driving the atom with an external laser of frequency @xmath21 , which is greater than the natural resonance frequency @xmath12 of the atom . the laser comes into local resonance with the atom at @xmath22 . an atom far from @xmath22 is unaffected by the largely detuned field and feels an attractive force @xmath23 toward the dielectric interface . b ) the atom comes closer to local resonance with the laser as @xmath24 . this creates an atomic dressed state , whose excited state component yields a net repulsive force on the atom . c ) a slowly moving atom experiences the adiabatic dressed state potential @xmath25 shown in red , which characterizes the position - dependent mixing between ground and excited states . the minimum of the dressed potential is located at @xmath26.[fig : schematic],width=491 ] a short - distance expansion of the green s function , valid for sub - wavelength scales , shows that the excited - state emission rate @xmath27 and resonant contribution @xmath28 to the shift are given by & & ( ) , [ eq : gammageneral ] + & & -(),[eq : omegaegeneral ] where the permittivity @xmath29 is evaluated at the atomic resonance frequency , @xmath19 is the distance from the surface , and @xmath30 is the resonant free - space wavevector . a large repulsive potential is generated when @xmath31 , which is analogous to the interaction between a classical dipole at position @xmath19 and its large induced image dipole in the dielectric . the modified spontaneous emission rate originates from the absorption or quenching of the atomic emission due to material losses . we choose a drude model , @xmath32 , as a simple dielectric function . note that this function satisfies kramers - kronig relations ( causality ) , as a choice of a non - causal function could result in an apparent violation of the no - go theorem @xcite as well . in the limit of vanishing material loss parameter @xmath33 , the system passes through @xmath34 at the plasmon resonance frequency @xmath35 . the system is conveniently parameterized by the quality factor @xmath36 and a dimensionless detuning @xmath37 . then , for large @xmath38 and @xmath39 , @xmath40 and @xmath41 . the dispersion and dissipation scale like @xmath42 and @xmath43 , respectively . thus , for high @xmath38 , it is possible to choose detunings where the atom still sees significant repulsive forces , but where spontaneous emission into the material is not significantly enhanced ( in addition to material - induced emission of eq . ( [ eq : gammageneral ] ) , there still is emission into free - space at a rate @xmath44 ) . this scaling behavior is in close analogy with conventional optical trapping of atoms , where simultaneously using large trapping intensity and detuning maintains reasonable trap depths but suppresses unwanted photon scattering . the ground - state shift for atomic frequencies @xmath45 and in the near - field is given by @xmath46 . we now describe how a trap can form for an atom subject to these potentials , and in the presence of a weak driving laser of frequency @xmath21 and rabi frequency @xmath47 ( see fig . [ fig : schematic ] ) . for conceptual simplicity , we choose the rabi frequency to be spatially uniform , such that all atomic forces are attributable to the vacuum potentials alone . qualitatively , the strong position dependence of the ground and excited state frequencies causes the laser to come into resonance with the atom at a single , tunable point @xmath48 . under certain conditions ( described in detail later ) , an atom starting at position @xmath49 will be far detuned , such that it is essentially in the ground state and is attracted by the pure ground - state potential . however , moving closer to @xmath22 brings the atom closer to resonance . the dressing of the atom with a small fraction of excited state population causes a repulsive barrier to form" +"simultaneous planning localization and mapping ( splam ) or active slam has been a popular area of research over the years @xcite . the main theme is to compute a set of control actions for the mobile robot such that either the uncertainty of the robot or the combined uncertainty of robot and map states are bounded . traditionally , splam frameworks have been approached through either model predictive control @xcite or information gain @xcite paradigms . in recent times , belief space planning paradigms have tended to compute the control law in continuous domain @xcite taking a leaf out of slam frameworks that model it as a least squares problem @xcite . however , all of the above works assume the availability of immediate range data and uncertainty estimates for the map . some of them , such as @xcite , also assume the availability of dense range data transposed to an occupancy grid map . in contrast , in a monocular slam setting , the following complexities get accrued : * sparse depth estimates , which are highly inaccurate in textureless or low texture scenes * degeneracies in camera motion estimation such as in planar scenes or for in - place rotation of the camera * highly non linear nature of the camera projection operation since a monocular camera is not a depth sensor but a projective sensor [ cols= "" < , < "" , ] in this paper , we proposed a reinforcement learning based slam - safe navigational planner that learns to identify robot motions that can lead to failures in slam pose estimation and avoid such motions during trajectory planning . the method was expected to generate trajectories that have minimal failures and pose estimation errors over varying maps . through various experiments we have proven the effectiveness of a slam - safe planner that predicts failures and executes recovery actions to continue the navigation task . in terms of learning slam - safe behaviour , our method showed an increase in performance by about 50% as compared to supervised learning methods . in terms of slam recovery during trajectory planning , our methods showed about 70% improvement in comparison with a state - of - the - art trajectory planner and about 45% in comparison with supervised learning based planners . autonomous navigation with a monocular camera has always been challenging due to reasons mentioned earlier . this paper establishes that a rl framework is able to learn precisely those actions resorted by humans when they use a handheld camera or teleoperate a robot for slam . for example this involves slow transitions to newer scenes avoiding sharp turns by repeated back and forth motions , which was well captured by the learning framework . leung , cindy , shoudong huang , and gamini dissanayake . `` active slam using model predictive control and attractor based exploration . '' _ in intelligent robots and systems , 2006 ieee / rsj international conference on , pp . 5026 - 5031 . ieee , 2006 . _ leung , cindy , shoudong huang , ngai kwok , and gamini dissanayake . `` planning under uncertainty using model predictive control for information gathering . '' _ robotics and autonomous systems 54 , no . 11 ( 2006 ) : 898 - 910 . _ harvard indelman , vadim , luca carlone , and frank dellaert . `` planning in the continuous domain : a generalized belief space approach for autonomous navigation in unknown environments . '' _ the international journal of robotics research 34 , no . 7 ( 2015 ) : 849 - 882 . _ charrow , benjamin , gregory kahn , sachin patil , sikang liu , ken goldberg , pieter abbeel , nathan michael , and vijay kumar . `` information - theoretic planning with trajectory optimization for dense 3d mapping . '' _ proceedings of the robotics : science and system ( rss ) ( 2015 ) . _ klein , georg , and david murray . `` parallel tracking and mapping for small ar workspaces . '' _ in mixed and augmented reality , 2007 . ismar 2007 . 6th ieee and acm international symposium on , pp . 225 - 234 . ieee , 2007 . _ gopalakrishnan , balasubramanian , arun kumar singh , and k. madhava krishna . `` time scaled collision cone based trajectory optimization approach for reactive planning in dynamic environments . '' _ in intelligent robots and systems ( iros 2014 ) , 2014 ieee / rsj international conference on , pp . 4169 - 4176 . ieee , 2014 . _ koenig , nathan , and andrew howard . `` design and use paradigms for gazebo , an open - source multi - robot simulator . '' intelligent robots and systems , 2004.(iros 2004 ) . proceedings . 2004 ieee / rsj international conference on . 3 . ieee , 2004 ." +"symbiotic stars are binary systems in which a compact object accretes from red giant , the wind of which forms a dense nebula around the binary . the nebula is ionized by the hot compact source , which is usually a white dwarf @xcite . among the known symbiotic stars @xcite , four objects have shown recurrent nova ( rn ) eruptions : t crb , rs oph , v3890 sgr and v745 sco . these eruptions are triggered by a thermonuclear runaway on the white dwarf ( wd ) surface after accretion of a critical amount of h rich material from the companion . @xcite suggested that during quiescence , the x - ray emission from rn could originate in the boundary layer of an accretion disc that was reconstructed around the wd after the outburst . therefore , x - ray observations should allow one to determine a lower limit for the accretion rate . the low x - ray luminosity measured in 350 novae and recurrent novae in quiescence @xcite imply a low accretion rate , inconsistent with the observed recurrence times . for example , in the case of rs oph @xcite , the short recurrence time of @xmath120 years requires an accretion rate of @xmath110@xmath2 m@xmath3/yr , inconsistent with measured x - ray fluxes . this inconsistency is known as the missing boundary layer problem "" . t crb is a well known recurrent nova with recorded outbursts in 1866 and 1946 . its quiescent - state hard x - ray emission ( e@xmath4 @xmath1 100 kev ) was first revealed during a 9 month @xmath5 survey @xcite . two additional @xmath5/xrt observations were analyzed by @xcite , who reported highly absorbed emission that was well fit with a cooling flow model with @xmath6=23.1 kev . the absorber consisted of components that both fully covered and partially covered the hard x - ray source . here we describe suzaku x - ray imaging spectrometer ( xis ) and hard x - ray detector ( hxd ) observations of the recurrent nova t crb performed on september 6 , 2006 . on september 6th 2006 , the astro - e2/suzaku x - ray observatory performed a 46 ks ( go ) observation of t crb ( obsid 401043010 start time 22:44:21 ut ) . we reduced the data according to standard procedures using the software package heasoft 6.2 . after determining the xis background count rate from a nearby blank region , we extracted spectra and light curves for the xis and hxd detectors . we extracted two sets of light curves for each detector one with a bin size of 360 s ( used to search for stochastic bright variations ) and the other grouping photons every 8 s. we used the light curve with the smaller time bins for power spectrum analysis . visual inspection of the extracted spectrum showed prominent fe lines around @xmath16.5 kev . as these lines are an indication of the presence of thermal emission from a plasma with temperatures @xmath110@xmath7 k , we first attempted to fit the spectrum with a single - temperature plasma plus neutral absorption . but no satisfactory fit was obtained . even using more complex absorbers , such as an absorber that only partially covers the source , or absorption from an ionized plasma , did not produce acceptable fits . we did , however , find acceptable fits ( @xmath8=1.07 ) for a multi - temperature , cooling flow plasma model ( @xmath9 ) . the model required a complex absorber consisting of one absorbing system that fully covered the source [ n@xmath10 @xmath11 , which includes interstellar absorption of 0.047@xmath12@xmath11 ] and and another that only partially covered the source [ n@xmath14 @xmath1510@xmath16 @xmath11 , partial covering fraction of 0.68@xmath17 . the minimum temperature of the cooling - flow model is consistent with the smallest value allowed by the _ mkcflow _ model ( @xmath18=0.0808 kev ) , and the maximum temperature is @xmath18=57.4@xmath19 kev . we also added a gaussian emission - line profile to the model to account for the fe k@xmath20 fluorescence line . figure [ fig : spectrum ] shows the spectra from the xis and hxd detectors , with the cooling - flow model overplotted . to estimate the parameters for the fe lines , we used a simple powerlaw fit to establish the continuum level , and then fit the fe k@xmath20 , fe xxv and fe xxvi emission lines with three gaussian profiles ( see fig . [ fig : spectrum ] , right panel ) . the equivalent widths obtained were 185@xmath21 , 135@xmath22 and 151@xmath23 ev respectively . we examined the xis time series binned at 360 s ( figure 2 ) and found significant stochastic variability above the level expected from poisson noise . the fractional amplitude of the stochastic variations , represented as the ratio between the measured rms variation , @xmath24 , and that expected from poisson fluctuations alone , @xmath25 , is 3.75 . in the case of hxd light curve , no stochastic variations were found above the poisson level . although by eye there appears to be a periodic ( or quasi - periodic ) variation in the light curve at a period of around 100 minutes , we did not detect a statistically significant oscillation at this period in our preliminary lomb - scargle analysis ( taking into account the underlying broadband continuum power ) of the xis and hxd light curves . hard x - ray emission with energy up to 100 kev is observed from the dwarf nova ss cyg in quiescence @xcite . dwarf novae observed with xmm-@xmath26 in quiescence also display spectra with energies up to @xmath112 kev @xcite . for low accretion rates ( @xmath27 3@xmath1510@xmath28 m@xmath3/yr ) , @xcite showed that the most internal part of an accretion disc around a 1 m@xmath3 wd , the boundary layer , radiates as an optically thin plasma at @xmath1 10 kev . the hardness of the x - ray emission detected from t crb strongly suggest that it comes from the accretion region closest to the wd . from the spectral model fitted , the accretion rate is @xmath29 @xmath14.2@xmath1510@xmath28 m@xmath3 yr@xmath30 ( @xmath31/1 kpc)@xmath32 . the detection of rapid flickering , which typically emanates from regions close to the wd , supports an accretion origin for the detected emission . moreover , the cooling - flow spectral model , as with boundary layer emission from non - magnetic cataclysmic variables ( cvs ; * ? ? ? * ) and other accreting high - mass white dwarfs @xcite , provides a natural context for the flickering . the ew of the neutral fe k@xmath20 line suggests that the x - ray source is surrounded by large amounts of neutral material @xcite . reflection of radiation off of the wd surface can also contribute to the formation of this line . from @xcite , the ew of the fe k@xmath20 line when a 2@xmath33 source reflects bremsstrahlung photons with @xmath110 kev is 100 - 200 ev . therefore the intense fe k@xmath20 line is consistent either with large amounts of neutral material , as with rt cru and cd -57 3057 @xcite , or with reflection from the surface of the wd . using the suzaku x - ray satellite , we observed hard - x - ray emission from the recurrent nova t crb in quiescence . assuming that a more detailed timing analysis confirms the lack of periodic variations , the presence of flickering on a timescale of minutes and the cooling - flow type spectrum suggest that the accretion onto the wd proceeds through a disc with an optically thin boundary layer . t crb is the first recurrent nova to show hard - x - ray emission from a boundary layer during quiescence . barlow e. j. , knigge c. , bird a. j. , dean a. , clark d. j. , hill a. b. , molina m. , sguera v. , 2006 , mnras , 372 , 224 belczysky , k , mikoajewska , j. , munari , u. , ivison , r.j . and friedjung , m. , 2000 , a&as,@xmath34,407 george i. , fabian a. , 1991 , mnras , 249 , 352 hachisu i. & kato m. , 2001 , apj , 558 , 323 hachisu , i. , kato , m. , luna , g. j. m. , 2007 , apjl , inoue h. , 1985 , sp . , 40 , 317 kennea , j. & mukai , k. , sokoloski j. , 2007 in prep . kenyon , s. j. , _ the symbiotic stars _ , 1986 , cambridge university press luna , g. j. m. & sokoloski j. l. , 2007 , apj , _ in press _ mukai k. , kinkhabwala a. , peterson j. r. , kahn s. m. , paerels f. , 2003 , apj , 586 , 77 narayan r. & popham r. , 1993 , nature , 362 , 820 nelson t. , orio m. , cassinelli j. , still m. , leibowitz e. , mucciarelli p. , 2007 , apj , in press orio m. , 1993 , a&a , 274 , l41 orio m. , covington j. , gelman h. , 2001 , a&a , 373 , 542 pandel d. , crdova f. a. , mason k. o. , priedhorsky w. c. , 2005 , apj , 626 , 396 smith r. , mushotzki r. , mukai k. , kallman t. , markwardt c. , tueller j. , 2007 , pasj , _ submetido _ sokoloski , j. l. , luna , g. j. m. , mukai , k. , kenyon , s. j. , 2006 , nature , 442,276 tueller , j. , barthelmy , s. , burrows , d. , falcone , a. , gehrels , n. , grupe , d. , kennea , j. , markwardt , c. b. , mushotzky , r. f. , skinner , g. k. , _ the astronomer s telegram _ , 669" +"it has long been recognized that highly luminous ( @xmath0 erg s@xmath1 ) x - ray sources in the cores of globular clusters are grossly overrepresented with respect to the general galactic population ( katz 1975 ; clark 1975 ) : clusters contain @xmath2 of the galaxy s mass , but @xmath3 of the low - mass x - ray binary ( lmxb ) sources . a variety of lines of evidence tell us that these objects are neutron stars in very close binary systems , but the precise mechanisms which enhance their formation in clusters , and protect them from disruption thereafter , are obscure . essentially all of the bright cluster sources are also x - ray bursters , frequently emitting @xmath4 in just a few seconds . close binaries also have a profound effect on cluster dynamics : just a few such objects in a cluster have a store of orbital kinetic energy which can equal or exceed the orbital energy of all @xmath5 single cluster stars . thus the study of these rare and odd objects also has important macroscopic implications for the dynamical evolution of clusters ( elson et al . 1987 , hut et al . 1992 ) . considerable recent progress in the understanding of the intense bursting x - ray sources in globular cluster cores is in large part due to _ hubble space telescope _ ( _ hst _ ) identifications and follow - on studies of optical / uv counterparts , and to the realization that at least two of the cluster sources are exotic , ultra - short period double - degenerate binary systems : @xmath6 min for x1820303 in ngc6624 ( stella et al . 1987 ; anderson et al . 1997 ) and @xmath7 min for x1850087 in ngc6712 ( homer et al . 1996 ) . the optical / uv studies with _ hst _ have in one sense proven highly successful : a plausible optical counterpart has been identified and/or studied in detail in each of the clusters carefully scrutinized thus far . however , the diversity in properties of the six counterparts now identified is enormous , with optical luminosities ranging from @xmath8=6 to @xmath8=1 , and confirmed binary orbital periods ranging from 11 min to 17 hr . the only optical counterpart candidate thus far for x1832330 in ngc6652 was advanced by deutsch et al . ( 1998b ; hereafter paper i ) . the object , denoted star 49 , exhibits a uv excess in the _ hst _ data similar to other known lmxb optical counterparts , and similar absolute magnitude to the optical counterpart of the lmxb in ngc1851 . however , the region surveyed in paper i does not completely cover the _ rosat _ x - ray error circle derived in that work , and the images are not very deep . furthermore , the position of star 49 is discrepant at the @xmath9 level with the x - ray coordinates . for these reasons , paper i suggests that while star 49 is the best candidate for the optical counterpart , its identification remains tentative . since the initial search for the optical counterpart and discovery of star 49 in paper i , additional wfpc2 observations have become available in the _ hubble data archive_. here we discuss three orbits of f555w ( v ) and f814w ( i ) imaging data obtained on 1997 september 5 , as well as one orbit of f555w , f439w ( b ) , and f218w imaging data obtained on 1995 september 13 . in the former observation , seventeen @xmath1020 s f555w and f814w exposures were taken on the first orbit , twelve 160 s f555w exposures on the second orbit , and twelve 160 s f814w exposures on the third . for the latter observation , fine lock was not achieved and the stellar images are elongated , the cluster is miscentered on the ccds , and the f218w exposures failed completely . the retake data for this failed observation were successful , and are discussed in paper i , but did not include the proposed optical counterpart . the early , poor quality data , however , do actually include star 49 , are usable , and will be briefly discussed here as they were overlooked in paper i. all these data were acquired during unrelated programs to study the cluster ngc6652 itself . despite the suboptimal sampling of the wfpc2 _ wide field _ ccds , on which the optical counterpart falls in these observations , the cluster is sufficiently sparse and star 49 sufficiently unblended that aperture photometry is entirely adequate to measure magnitudes for this object and a set of nearby comparison stars . aperture corrections are taken from table 2(a ) in holtzman et al . ( 1995b ) . the photometric measurements have not been corrected for geometric distortions , nor is any correction for charge transfer efficiency losses ( holtzman et al . 1995b ) applied ; for most of the images , these effects should contribute errors of only a few percent . we use the photometric zero points for the stmag system from table 9 ( @xmath11 ) in holtzman et al . ( 1995a ) . systematic errors for all magnitudes due to uncertainties in detector performance and absolute calibration are @xmath105% . five nearby reference stars also photometered show no variability to the limit of the derived uncertainties ; three of the five are of comparable brightness of star 49 . for star 49 itself , variability is suggested in the 1995 epoch observations , and large amplitude variability is clearly evident in the 1997 epoch observations . this large - amplitude variability , when coupled with the uv excess demonstrated in paper i , lends considerable confidence that this object is the correct identification of the optical counterpart to x1832330 . from the three orbits of f555w and f814w observations , we find @xmath12 and @xmath13 . to create a single light curve of all the data , we subtract 0.4 mag from @xmath14 to create approximately filter - independent magnitudes . this result is searched for periodic components using algorithms described in horne & baliunas ( 1986 ) . in fig . 1a we show the fourier transform with the clean algorithm ( roberts et al . 1987 ) applied to remove the effects of the window function . we find the strong peak seen at @xmath15 min to have 99.5% significance , based on the original ( i.e. prior to cleaning ) periodogram , using methods in horne & baliunas ( 1986 ) . in fig . 1b we show the entire light curve ( @xmath16 , @xmath17 ) for the three orbit observation . uncertainty bars are provided for each datapoint , although they are sometimes smaller than the symbols themselves . a non - linear least squares fitting algorithm is used to determine the best fit sinusoid , which is overplotted on the light curve . the result is a best - fit period @xmath18 min , semi - amplitude @xmath19 mag , and mean magnitude @xmath20 . the sinusoid does describe the broad trends in the data quite well , but clearly a large amount of aperiodic flickering is also evident . in fig . 1c we show the light curve averaged into 10 phase bins . photometric uncertainties are smaller than the symbols . a few points deviate significantly from the sinusoid fit , most likely due to the strong flickering and small amount of data . during 1998 november 2830 , we obtained @xmath21 ks of x - ray observation on x1832330 with _ rossi x - ray timing explorer_. the data are processed through the standard _ ftools _ package to obtain a calibrated light curve . two type i x - ray burst events are evident , confirming the bursting nature of this source first reported by in t zand et al . ( 1998 ) with _ bepposax _ observations . after background subtraction , we measure a persistent countrate @xmath22 s@xmath1 , which is @xmath23 mcrab , similar to fluxes reported previously for this object . a search of the background - subtracted light curve reveals no significant periodicities , except for some power at half the _ rxte _ orbital period , apparently induced by the calculated background model . in particular , there does not appear to be any significant power at the 43.6 min optical period . the rms scatter in the x - ray light curve is consistent with poisson noise ; we find no evidence for flickering , which might be expected based on our optical observations . however , as the x - ray and optical observations were made over a year apart , no firm conclusions can be drawn from the lack of x - ray flickering . a further analysis of the light curve , spectra , and bursts in these x - ray data will be discussed elsewhere . mukai & smale ( 2000 ) present an x - ray observation of x1832330 from a 1996 _ asca _ observation . they also find no periodic x - ray modulation , but they do provide evidence for x - ray variability with a similar timescale as the flickering seen in our optical light curve . the peak in the periodogram of the optical data has 99.5% significance , indicating that it is quite improbable that uncorrelated , gaussian noise would randomly generate such a strong periodic signal . however , the evident scatter in the photometry is not due to measurement uncertainties , but rather an inherent flickering in the source , and this behavior is likely to produce significantly correlated `` noise '' . thus the formal significance calculation for the periodicity may overestimate the actual confidence . our derived period is close to , but statistically different from , half the _ hst _ orbital period . two further tests increase our confidence that this behavior is not an artifact of the _ hst _ orbit . as noted in 2.1 , several stars near to and of similar magnitude to star 49 have been measured from the same data , and show no variability at this or other periods . we have also randomized the association of observation times versus magnitudes for star 49 and rereduced the data . although periods due to incomplete removal of the window function should then remain , as the observing times are identical in these randomized data and in the original observations , the resulting periodograms show no significant power at 43 min . we find that only @xmath24 of 10000 trials show a peak at any frequency as high as the 43 min one . although the marked variability we report here adds confidence to the identification of star 49 with the x - ray source , the mediocre agreement of the x - ray position with the object still leaves some uncertainty . this issue will almost surely be settled by a scheduled observation by the _ chandra x - ray observatory _ , which should yield a highly accurate position . however , if we accept that our observed optical variations in star 49 are indeed periodic , there are few alternatives to identifying this object as a lmxb , given its measured characteristics , irrespective of the issues of the x - ray position . the most extreme sx phe stars , for example , have periods less than 1 hr , but do not display the marked flickering we observe , so stellar pulsation seems implausible . if the period is instead orbital , the flickering implies a mass - transfer system . however , no classical cataclysmic variables ( cvs ) are known with periods less than 1 hr , and" +"eta carinae is a rarity among the rarities that constitute massive stars in the short , unstable luminous blue variable ( lbv ) phase . the nature and fate of the central object are still the subject of intense debates , although consensus seems to exist around an eccentric massive binary scenario , as initially proposed by @xcite . this scenario is supported by multi - wavelength observations from x - rays @xcite to radio wavelengths @xcite . the ultraviolet and optical spectra are strongly dominated by the dense wind of the primary star ( hereafter @xmath1 ) , hinting that most of the luminosity of the system ( @xmath2 , @xcite ) comes from @xmath1 ( * ? ? ? * ; * ? ? ? * ; * ? ? ? * hereafter g12 ) . recent spectroscopic analysis suggests that @xmath1 has a mass - loss rate of @xmath3 and wind terminal velocity of @xmath4 ( g12 ; see also @xcite ) . the companion star ( hereafter @xmath5 ) has yet to be observed directly , with only indirect constraints available on its temperature and luminosity ( @xmath6 and @xmath7 ; @xcite ) , and wind properties ( @xmath8 and @xmath9 ; e.g. , @xcite ) . eta car has interested astronomers ever since its dramatic brightness increase in the 1830s . this eruptive event caused the ejection of tens of solar masses of material @xcite , enshrouding the central object within a dusty nebula ( the homunculus ) . the expanding dust residing in the homunculus scatters light emitted by the central source . the 3d determination of the homunculus shape @xcite allows one to relate the scattered light at a given position in the homunculus to a line - of - sight that views the stellar system from a certain latitude ( * ? ? ? * hereafter s03 ) and azimuth . in the context of a binary , this implies that different positions in the homunculus see the binary as if viewed from different orbital inclinations @xmath10 and longitudes of periastron @xmath11 ( fig . [ offsetpos ] ) . spatially resolved observations of eta car show that , during most phases of the orbital cycle , h and spectral lines are latitude dependent . the p cygni absorption is stronger in spectra taken around the pole of the homunculus se lobe than in the spectra of the central object ( * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * k. nielsen 2009 , priv . the p cygni absorption seems to extend to higher velocities in spectra reflected off the homunculus se pole , which , combined with the stronger absorption , has been interpreted as evidence for a denser , faster polar wind generated by the rapid rotation of @xmath1 . the latitudinal dependence of h and seems to be less pronounced around periastron , suggesting that @xmath1 s wind becomes more spherical . however , h and lines , which are formed in the wind of @xmath1 , are extremely affected by the presence of a cavity created by @xmath5 . this cavity arises naturally in hydrodynamical models as a consequence of the carving of the wind of @xmath1 by the fast , thin wind of @xmath5 @xcite . taking into account the presence of the low - density cavity , two - dimensional ( 2d ) radiative transfer models of eta car show that h and lines become latitude- and azimuth - dependent . this occurs because of the varying amount of primary wind material towards different latitudes and azimuths . these models reproduce the absence of p cygni absorption in h@xmath0 and lines in spectra seen in the direct view to the central object ( which is viewed through the rarified cavity ) , _ without _ evoking rapid rotation of @xmath1 . can we still consider @xmath1 as a rapid rotator and prototype of massive stars with dense polar winds ? the goal of this letter is to investigate the origin of the observed latitudinal and azimuthal dependencies of @xmath1 s wind and , in particular , whether they can be explained by the presence of a wwc cavity in the wind of @xmath1 . to illustrate our findings , we focus on archival _ hst_/stis observations obtained around apastron ( 2000 mar 20 , orbital phase @xmath12 . ] , @xmath13 aperture ) and periastron ( 1998 mar 20 , @xmath14 , @xmath15 aperture ) . both datasets were acquired with the g750 m grating , covering the region around h@xmath0 with @xmath16 . the spectra were extracted using custom idl routines using an aperture of 6 half - pixels ( 0152 ) on the central object and close to the weigelt blobs ( wbs ; @xcite , located 015030 nw of the central source ) , and 12 half - pixels elsewhere . the spectra were corrected for the velocity shift introduced by the dust scattering using narrow forbidden lines as proxies , following @xcite . this technique could not be applied to the offsets at 5ne and 4sw , and the profiles were aligned on the _ red _ side of h@xmath0 , where the influence from @xmath5 is minimized . note that this does not affect our conclusions . we refer the reader to e.g. for details about the observations and data reduction . the aforementioned observations are analyzed using the 2d radiative transfer models of eta car from . the 2d models take into account @xmath1 and the presence of a rarified wwc cavity and a dense wind - wind interacting region , corresponding to the post - shocked primary wind . we refer the reader to for an extensive discussion about the impact of the wind - wind collision ( wwc ) cavity on the spectrum , and to their table 2 for the full model parameters . we assume an orbital orientation with @xmath17 , @xmath18 , @xmath19 @xcite , and half - opening angle of the cavity of @xmath20 . this corresponds to the direct view of the central source . since offset positions in the homunculus see the binary system under different vantage points , 2d models with different @xmath10 and @xmath11 were computed for each offset analyzed here . for visualization purposes , we also present 3d renderings of smoothed particle hydrodynamics ( sph ) simulations of the eta car binary system , similar to those presented in @xcite . we first investigate the strong latitudinal changes in line profiles around apastron . in the wwc cavity scenario , the latitudinal variations of line profiles depend on the amount of primary wind material towards a certain latitude . this is regulated mainly by the size of the line formation region compared to the distance of the wwc apex to @xmath1 , meaning that certain lines ( h@xmath0 , ) are more affected by the cavity than others ( e.g. , higher balmer lines ) . for brevity , we present here results for h@xmath0 , which is formed at a distance of @xmath21 au from @xmath1 . similar conclusions would be obtained for h@xmath22 and lines . figure [ latiap]c , d presents the observed and 2d model spectra of eta car for different viewing angles , corresponding to a direct view of the stellar system ( black line ) , a view from the homunculus se pole ( light blue ) , and from the homunculus equator towards the wbs ( red ) . our 2d models qualitatively reproduce the observed variation of h@xmath0 with latitude , suggesting that the latitudinal changes can be explained by the presence of the wwc cavity . for viewing angles corresponding to line - of - sights that view @xmath1 through the rarified cavity , there is little or no p cygni absorption because of the reduced density within the cavity . this drastically reduces the @xmath23 level population of h , reducing the h@xmath0 absorption . this is the case for the direct view to the central source or to the homunculus equator towards the wbs ( fig . [ latiap]a ) . there is also a fair quantitative agreement between observations and 2d models at these two positions . for line - of - sights that cross the undisturbed wind of @xmath1 , such as for the spectra reflected on the homunculus se pole , the population of the @xmath23 energy level of h is unchanged in our model compared to a spherically symmetric case . this results in stronger absorption of the stellar continuum in spectra scattered off the homunculus se pole than in spectra of the direct view to the central source , in agreement with the observations . however , our 2d model overestimates the amount of p cygni absorption seen in spectra scattered off the homunculus se pole , and underestimates the maximum velocity of p cygni absorption in h@xmath0 by @xmath24 ( blue lines in fig . [ latiap]c , d ) . our favored explanation for these discrepancies is that the polar regions of @xmath1 s wind could be mildly photoionized by @xmath5 @xcite . this effect is not included in our 2d models and would reduce the population of the @xmath23 energy level of h and thus the amount of h@xmath0 absorption . in addition , photoionization by @xmath5 would likely change the driving of the wind of @xmath1 , perhaps allowing it to reach velocities slightly higher than regions of @xmath1 s wind not affected by @xmath5 . alternatively , a wrong choice of stellar and wind parameters could also be the culprit , e.g. a _ lower _ @xmath25 over the poles would be needed to produce less absorption in h@xmath0 , but the fit to the uv and optical emission lines would be significantly worse . in addition , we can not rule out that the observations do not correspond to the pure polar spectrum , with the intrinsic p cygni absorption being diluted by continuum and h@xmath0 emission from the ejecta in the inner arcsecond . lastly , we can not preclude that the wind is slightly faster at the pole because of rapid rotation , although our 2d cavity models suggest that @xmath26 over the pole would be much smaller ( @xmath27 ) than previous observational estimates . we turn our attention to azimuthal variations observed in scattered light off the homunculus around apastron . these would not be expected in a single rapid rotator scenario , while a wwc cavity intrinsically produces azimuthal density variations ( fig . [ aziap]a ) . therefore , this crucial difference could allow one to distinguish between the two scenarios . figure [ aziap]c presents the h@xmath0 line profiles scattered off the homunculus equator , around the wbs ( red ) , 5ne ( orange ) , and 4sw ( purple ) . these positions probe different azimuths , as if the system were viewed from @xmath28 , but different @xmath11 . the corresponding synthetic h@xmath0 line profiles from our 2d models are shown in fig . [ aziap]d . our 2d model qualitatively explains the variations in strength of the p cygni absorption as a function of azimuth for an orbital orientation with @xmath29 , @xmath30 , and @xmath20 . lower values of @xmath11 would be allowed for larger @xmath0 . the changes in the p cygni absorption occur because of the variation of primary wind material at different azimuths in the equatorial regions . line - of - sights that view the system down the wwc cavity have little primary wind material between the observer and @xmath1 . this causes less absorption in h@xmath0 . this is the case for the spectra scattered off the wbs ( red ) and at 4sw ( purple ) ." +"the spin orbit coupling ( soc ) , which describes the interaction between the spin and orbit degrees of freedom of a particle , has not only generated many interesting quantum phenomena in modern physics ranging from the nuclear physics to condensed - matter physics , and but also become an important resource for realizing fault - tolerant topological quantum computing @xcite . by controlling the external lasers , the different kinds of socs have been proposed to be simulated in the trapped bose - einstein condensates ( becs ) with the neutral atoms @xcite . especially , in recent experiment at nist , the equal rashba and dresselhaus socs has been realized successfully in the ultracold @xmath0rb atoms by a couple of raman lasers @xcite . attributed to this pioneer experiment , the investigation of soc - driven becs has attracted much attentions . moreover , rich many - body phenomena with no analogy in condensed - matter physics ( in becs , all ultracold atoms can occupy the same quantum state ) have been predicted by considering the ground - state properties larson2009,wc , wu , yip2011,yp , yp2,ss , xxu , zhu , hu , zhangdw , zhangdw2,ozawa , deng , weizheng2012,zhai2012,shenoy2012,zfxu , fialko , jr2012 . for example , in the presence of the equal rashba and dresselhaus socs , the bec is made up of two non - orthogonal dressed atom spin states carrying different momenta . furthermore , the interaction between these spin states are modified , driving a quantum phase transition from a spin - mixed state to a phase - separated state @xcite . in fact , even if the effective atom interaction governed by both the inter- and intra- spin interactions is not taken into account , a quantum phase transition from a separate phase ( sp ) to a single minimum phase ( smp ) can also occur @xcite . in very recent experiment , this new quantum phase transition has been observed by measuring the amplitude ratio of spin and momentum oscillation @xcite . it has been known that quantum phase transitions governed by the ground - state energies occur at absolute zero temperature @xcite . however , it is unattainable experimentally due to the third law of thermodynamics , i.e. , any system must work at a finite temperature . thus , it is crucially important to investigate the thermodynamic properties to fully understand the fundamental physics for a given system . for instance , in the framework of finite - temperature theory , the system s real evaluation can be described more accurately and some important physical quantities such as the specific heat , the entropy and the free energy , which have no zero temperature correspondence , can be explored . more importantly , some exotic phenomena driven only by thermal fluctuations can be revealed @xcite . motivated by the experimental developments and the third law of thermodynamics , we , for the first time , develop a quantum field approach to reveal the thermodynamic properties of the trapped bec with the equal rashba and dresselhaus socs . our main results are given as follows : ( i ) in the experimentally - feasible regime , the phase transition from the sp to the smp can be driven by the tunable temperature . moreover , the corresponding critical temperature is derived exactly and is independent of the trapped potential . ( ii ) we find that the specific heat has a large jump at the critical temperature . this step behavior is quite different from that of the atom population , which varies smoothly when crossing the critical point . it implies that the temperature - driven phase transition can be well detected by measuring the specific heat . ( iii ) in the different phases , the analytical expressions for the specific heat and the entropy are also given . in the smp , the specific heat as well as the entropy are governed only by the rabi frequency . however , in the sp , the strong soc modifies the energy structure and thus the thermodynamic statistics . at lower temperature , we find that the specific heat and the entropy in such phase are determined only by the soc strength . ( iv ) finally , the effect of the effective atom interaction is also addressed . in the smp , no collective excitations can be found in soc - driven bec and thus the effective atom interaction does not affect the thermodynamic properties . however , in the sp with soc - induced macroscopic excitations , this effective atom interaction affects dramatically on the critical temperature as well as the other thermodynamic quantities . for example , for the repulsive atom interaction , the critical temperature decreases , and vice versa . figure 1 shows the experimental scheme about how to create soc in the trapped bec with the ultracold @xmath0rb atoms at nist @xcite . in their experiment , the bec is trapped in the @xmath1 plane through a strong confinement with frequency @xmath2 along the @xmath3 direction . in the large detuning @xmath4 , the momentum - sensitive coupling between two hyperfine ground states @xmath5 and @xmath6 is constructed by a pair of raman lasers with rabi frequencies @xmath7 and @xmath8 incident at a @xmath9 angle from the @xmath10 axis , as illustrated in fig . 1(a ) . in the dressed - state basis @xmath11 and @xmath12 , where @xmath13 and @xmath14 are the wavevectors of the raman lasers , an effective soc , which is identical to the one - dimensional equal rashba and dresselhaus socs in condensed - matter physics , can be achieved . moreover , the corresponding hamiltonian with the atom - atom collision interaction can be written from the coupled gross - pitaevskii equations as @xcite @xmath15here , @xmath16 is a harmonic trap mode with @xmath17 and @xmath18 being the atom mass . @xmath19 reflects the experimentally - measurable population between the different spin components . @xmath20 is the trapped frequency in the @xmath10 direction . @xmath21 is the effective rabi frequency . @xmath22 with @xmath23 being the soc strength , where @xmath24 is the wavelength of the raman laser . the effective atom interaction @xmath25 is proportional to @xmath26 , where @xmath27 and @xmath28 are the inter- and intra- spin interaction constants with @xmath29 and @xmath30 being the _ s_-wave scattering lengths and @xmath31 . @xmath32 is the total atom number . if defining the number - dependent trapped frequency @xmath33 and the effective soc strength @xmath34 , hamiltonian ( [ h1 ] ) can be rewritten in the rotating frame as ( @xmath35 henceforth)@xmath36 in the following discussion , we focus mainly on hamiltonian ( [ h2 ] ) , in which @xmath37stands for the atom population . before proceeding , we estimate the relative parameters under current experimental conditions @xcite . in the experiment of nist , the tunable trapped frequency @xmath20 is of the order of 10 hz , and correspondingly , the number - dependent trapped frequency @xmath38 is of the order of mhz for @xmath39 . parameter @xmath40 is of the order of khz for @xmath41 nm . the effective rabi frequency @xmath42 can range from zero to the order of mhz . in addition , since @xmath43 @xmath44 and @xmath45 @xmath46 with @xmath46 being the bohr radius , we have @xmath47 and thus @xmath48 . it means that the effective atom interaction need not be taken into account in the nist s experiment . it should be pointed out that this effective atom interaction can be well controlled through feshbach resonance @xcite . moreover , its magnitude can reach the order of mhz near the feshbach resonant point . finally , we will take @xmath49 , which is of the order of khz , as the natural unit of the energy for simplicity . a key step to extract the thermodynamic properties of the soc - driven becs is to obtain the partition function of hamiltonian ( [ h2 ] ) @xcite . here we develop a quantum field approach , i.e. , an imaginary - time ( @xmath50 ) functional path - integral technique , to arrive at the target . we first rewrite the collective spin operators in the representation of the grassmann fermi fields , namely , @xmath51 , and @xmath52 , where the fermi operators @xmath53 and @xmath54 satisfy the anticommutator relations @xmath55 . furthermore , we transform the harmonic trap mode @xmath56 into a single mode bosonic field @xmath57 . as a consequence , the partition function is obtained by@xmath58 \exp \left [ -a(\tau ) \right ] . \label{pfc}\]]in eq . ( [ pfc ] ) , @xmath59=d[\psi , \psi ^{\ast } , \mu , \mu ^{\ast } , \nu , \nu ^{\ast } ] $ ] is the path integral measure . the euclidean action is given by @xmath60 , \label{aa}\]]where @xmath61 , @xmath62 with @xmath63 being the boltzmann constant and @xmath64 being the system s temperature , and @xmath65 . \label{hf}\ ] ] since hamiltonian ( [ h2 ] ) has two degrees of freedom including the spin and orbit cases , it is very difficult to directly discuss the partition function to extract its fundamental thermodynamic properties . the usual method is that we eliminate one degree of freedom by integrating the euclidean action @xmath66 @xcite . without the effective atom interaction ( @xmath67 ) , the euclidean action @xmath66 is a quadric term and the corresponding integral is gaussian . it means that in this case we can integrate over the grassmann fermi fields and then obtain the partition function of the bosonic mode . however , for nonzero @xmath25 ( @xmath68 ) , the integral in the euclidean action @xmath66 is not gaussian and thus the corresponding integral is hard to be solved directly . here we introduce an auxiliary field @xmath10 to circumvent this difficult . based on this auxiliary field @xmath10 , we have @xcite @xmath69\propto \int \left [ d\eta \right ] \exp \{\int_{0}^{\beta } d\tau \lbrack \frac{1}{q}x^{\ast } x-\sqrt{\frac{1}{n}}% \sum_{i=1}^{n}(x+x^{\ast } ) ( \mu _ { i}^{\ast } \mu _ { i}-\nu _ { i}^{\ast } \nu _ { i})]\}. \label{me}\ ] ] in analogy of the mean field approximation , the value of auxiliary field @xmath10 determines @xmath70 , as will be shown . substituting the formula about the auxiliary field @xmath10 into the euclidean action @xmath66 yields@xmath71where @xmath72@xmath73 , \label{az}\]]and @xmath74 \label{green}\]]with @xmath75 for the effective euclidean action @xmath66 in eq . ( [ action ] ) , we can integrate over the grassmann fermi fields , i.e. , the degree of freedom for the spin , and then obtain @xmath76 , \label{fact}\]]where @xmath77 and @xmath78 . finally , by means of the standard stationary phase approximation , namely , @xmath79 and @xmath80 , the required @xmath81 and @xmath82 , which play a crucial role in determining thermodynamic properties of hamiltonian ( [ h2 ] ) , can be obtained by @xmath83where @xmath84it should be noticed that in the derivation of eq . ( [ eeq ] ) we focus on the constant path that @xmath81 is not influenced by @xmath85 , namely , @xmath86 @xcite . according to eq . ( [ eeq ] ) we have@xmath87equation ( [ main1 ] ) shows clearly that there exist a trivial solution @xmath88 , and the nontrivial solutions @xmath89 and @xmath90 when @xmath91 . moreover , these nontrivial solutions are governed by the nonlinear equation @xmath92=\tanh ( \beta \zeta _ { 0}/2)$ ] , where @xmath93 . with the help of the stable condition at the equilibrium points , we can obtain the required solutions of both @xmath81 and @xmath82 and thus reveal the thermodynamics of hamiltonian ( [ h2 ] ) @xcite . and the temperature @xmath64 without the effective atom interaction ( @xmath67 ) , where the effective trapped frequency @xmath94" +"coin flipping had been already known to ancient romans as a way to decide an outcome @xcite . more recently , scientists inspired by this old question , how unbiased the real ( physical ) coin is , have been studying coin dynamics , see e.g. @xcite . previous studies have mainly focused on the dynamics of the flying coin assuming that it does not bounce and finding the effects of angular momentum on the final orientation . partial analysis in combination with numerical simulations of the bouncing effects has been done by vulovic and prange @xcite . it appears that this is the only reference that addressed the effect of bouncing on coin tossing . on the other hand , there is a well developed theory of mathematical billiards : classical dynamics of a particle moving inside a bounded domain . the particle moves along straight line until it hits the boundary . next , the particle reflects from the boundary according to the fermat s law . the billiard problem originally appeared in the context of boltzman ergodic hypothesis @xcite to verify physical assumptions about ergodicity of a gas of elastic spheres . however , various techniques in billiard dynamics turned out to be useful beyond the original physical problem . the so - called unfolding technique ( which is used in this paper ) allows one to obtain estimates on the maximal number of bounces of a particle in a wedge . one could expect that the bouncing coin dynamics could be interpreted as a billiard ball problem . in this paper we consider a simpler system ( with fewer degrees of freedom ) which we call the dumbbell . the bouncing coin on a flat surface , restricted to have axis of rotation pointing in the same direction , can be modeled as a system of two masses connected with a weightless rod . the dumbbell dynamics that is studied in this article is a useful model to initiate investigation of this potentially useful relation . another motivation for the dumbbell dynamics comes from robotics exploratory problems , see _ e.g. _ @xcite . consider an automated system that moves in a bounded domain and interacts with the boundary according to some simple laws . in many applications , it is important to cover the whole region as _ e.g. _ in automated vacuum cleaners such as roomba . then , a natural question arises : _ what simple mechanical system can generate a dense coverage of a certain subset of the given configuration space_. the dumbbell , compared to a material point , has an extra degree of freedom which can generate more chaotic behavior as _ e.g. _ in sinai billiards . indeed , a rapidly rotating dumbbell will quickly `` forget '' its initial orientation before the next encounter with the boundary raising some hope for stronger ergodicity . in this paper , we study the interaction of a dumbbell with the flat boundary . this is an important first step before understanding the full dynamics of the dumbbell in some simple domains . by appropriately rescaling the variables , we obtain an associated single particle billiard problem with the boundary corresponding to the collision curve ( which is piecewise smooth ) in the configuration space . the number of collisions of the dumbbell with the boundary before scattering out depends on the mass ratio @xmath0 . if this ratio is far from 1 , then the notion of adiabatic invariance can be introduced as there is sufficient time scales separation . we prove an adiabatic invariant type theorem and we describe under what conditions it can be used . finally , we estimate the maximal number of bounces of the dumbbell with the flat boundary . + * notation : * we use some standard notation when dealing with asymptotic expansions in order to avoid cumbersome use of implicit constants . + @xmath1 for some @xmath2 + @xmath3 + @xmath4 + let us consider a dumbbell - like system , which consists of two point masses @xmath5 , @xmath6 , connected by weightless rigid rod of length @xmath7 in the two - dimensional space with coordinates @xmath8 . the coordinates of @xmath5 , @xmath6 , and the center of mass of the system are given by @xmath9 , @xmath10 , and @xmath11 , respectively . let @xmath12 be the angle measured in the counterclockwise direction from the base line through @xmath5 and to the rod . we also define the mass ratios @xmath13 and @xmath14 which correspond to the distance from the center of mass to @xmath6 and to @xmath5 , respectively . the dumbbell moves freely in the space until it hits the floor . in this system , the velocity of the center of mass in @xmath15 direction is constant since there is no force acting on the system in @xmath15 direction . thus , we may assume without loss of generality that the center of mass does not move in @xmath15 direction . with this reduction , the dumbbell configuration space is two dimensional with the natural choice of coordinates @xmath16 . the moment of inertia of the dumbbell is given by @xmath17 introducing the total mass @xmath18 , we can write the kinetic energy of the system as @xmath19 using the relations , @xmath20 @xmath21 we find the velocities of each mass @xmath22 @xmath23 by rescaling @xmath24 , we rewrite the kinetic energy @xmath25 by hamilton s principle of least action , true orbits extremize @xmath26 since the kinetic energy is equal to the that of the free particle , the trajectories are straight lines between two collisions . when the dumbbell hits the boundary , the collision law is the same as in the classical billiard since in @xmath27 coordinates the action is the same . using the relations @xmath28 we find the boundaries for the dumbbell dynamics in the @xmath29-@xmath12 plane : @xmath30 @xmath31 the dumbbell hits the floor if one of the above inequalities becomes an equality . therefore , we take the maximum of two equations to get the boundaries : @xmath32 . \end{aligned}\ ] ] note that this boundary has non - smooth corner at @xmath33 . this is the case when the dumbbell s two masses hit the floor at the same time . we will not consider this degenerate case in our paper . now we will derive the collision law for the case when only @xmath5 hits the boundary . we recall that given vector @xmath34 and a unit vector @xmath35 the reflection of @xmath34 across @xmath35 is given by @xmath36 here and in the remainder of the paper , @xmath37 are defined as the corresponding values right before the collision and @xmath38 are defined as the corresponding values right before the next collision . according to the collision law , the angle of reflection is equal to the angle of incidence . in our case , @xmath35 is the normal vector to the boundary @xmath39 so that @xmath40\\ \vv_-&= \left[\yd_- , \pdm\right]=\left[\sqrt{m / i } \ , \ydm , \pdm\right].\end{split}\ ] ] then , using ( [ eq : ref ] ) , we compute @xmath41 $ ] . in this way , we express the translational and the angular velocities after the collision in terms of the velocities before @xmath5 hits the floor . changing back to the original coordinates , we have @xmath42 the bouncing law for the other case , when @xmath6 hits the boundary can be obtained in a similar manner : we switch @xmath43 and @xmath44 , replace @xmath45 and @xmath46 with @xmath47 and @xmath48 , and replace @xmath49 with @xmath50 . consider the case when @xmath51 and @xmath5 rotates around @xmath6 with high angular velocity @xmath52 and assume that the center of mass has slow downward velocity compared to @xmath52 . since multiplying velocities @xmath53 by a constant does not change the orbit , we normalize @xmath54 to be of order 1 , then @xmath55 is small . consider such dumbbell slowly approaching the floor , rotating with angular velocity of order 1 , _ i.e. _ @xmath56 . at some moment the small mass @xmath5 will hit the floor . if the angle @xmath57 ( or sufficiently close to it ) , then the dumbbell will bounce away without experiencing any more collisions . this situation is rather exceptional . a simple calculation shows that @xmath58 will be generically of order @xmath59 for our limit @xmath60 . in this section we assume this favorable scenario . for the corresponding set of initial conditions , we obtain an adiabatic invariant ( nearly conserved quantity ) . we start by deriving approximate map between two consecutive bounces . [ fig2 ] [ lemma_bounce ] let @xmath61 , @xmath62 and assume @xmath5 bounces off the floor and hits the floor next before @xmath6 does . then there exist sufficiently small @xmath63 such that if @xmath64 and @xmath65 , the collision map is given by @xmath66 @xmath67 we prove ( [ eq : phi ] ) in two steps . we first show that @xmath68 using the expression for @xmath69 in ( [ eq : law ] ) . we have , @xmath70 for sufficiently small @xmath71 , @xmath72 implies @xmath73 . it follows that @xmath74 observe from the figure 2 that @xmath75 . thus , @xmath76 where @xmath77 using that @xmath78 , we obtain @xmath79 combining the results , we have @xmath80 this completes the proof for ( [ eq : phi ] ) . + let @xmath81 be the time between the two consecutive collisions of @xmath5 . then @xmath82 . the angular distance that @xmath5 traveled is given by @xmath83 where @xmath84 and @xmath85 are the error estimates for the taylor series expansion and are given explicitly by @xmath86 since @xmath5 can travel at most @xmath87 between two collisions , @xmath81 is bounded by @xmath88 . also note that @xmath84 and @xmath85 contain the factor @xmath89 and @xmath43 respectively . we finish the proof for ( [ eq : dist ] ) by computing , @xmath90 under the same assumptions as in lemma [ lemma_bounce ] with the exception @xmath91 for @xmath92 and @xmath93 , the variables after the collision are given by the similar equations to ( [ eq : phi ] ) and ( [ eq : dist ] ) but with different error terms . @xmath94 @xmath95 when computing the error terms , use @xmath96 . now , we can state the adiabatic invariance theorem for the special case when the light mass hits the floor and the dumbbell is far away from the vertical position : @xmath97 . [ ai_theo ] suppose right before the collision @xmath98 and @xmath99 . then there is @xmath100 such that if @xmath101 , @xmath102 , then there exists an adiabatic invariant of the dumbbell system , given by @xmath103 , where @xmath104 . in other words , @xmath105 after @xmath106 collisions . we prove this by finding @xmath107 that satisfies @xmath108 when @xmath109 and @xmath71 is sufficiently small , it follows from ( [ eq : dist ] ) that , @xmath110 then , we have @xmath111 therefore , @xmath107 satisfies @xmath112 provided @xmath113 the solution of the above equation is given by @xmath114 let @xmath115 and let @xmath116 and @xmath117 be the angular velocity and the distance after @xmath118 collision . then , we have @xmath119 adiabatic invariant has a natural geometric meaning : angular velocity times the distance traveled by the light mass between two consecutive collisions . now , we state the theorem for a realistic scenario when a rapidly rotating dumbbell scatters off the floor . let the dumbbell approach the floor from infinity with . there exists @xmath120 such that if @xmath121 , @xmath122 , @xmath123 then , after @xmath124 bounces the dumbbell will leave the floor after the final bounce by @xmath5 with @xmath125 . the adiabatic" +"the preparation of many - particle entangled states is becoming a fundamental task in modern quantum physics . entanglement lies at the heart of quantum communication and quantum information and is also a fundamental resource in precision spectroscopy . with recent advances in the manipulation of trapped ions and neutral atoms , there has been significant progress in the preparation of many - body entanglement states in atomic gases @xcite . such systems therefore offer rich opportunities to investigate new physics with both practical and fundamental applications . here we propose an interferometric method that uses the entanglement that emerges during the many - body dynamics between interacting spinor atoms to perform precision measurements of their interatomic interaction strength , usually parameterized by the @xmath3-wave scattering length . our method is a many - body generalization of the technique reported in ref . @xcite , where information of the scattering properties was obtained by using the entanglement dynamics in pairs of atoms trapped in the ground state of a potential well . a precise determination of the scattering properties has broad and important applications beyond atomic physics . for example , ref . @xcite shows that such type of measurements might be useful for fundamental physics , as by monitoring the scattering length on the @xmath4 level one could detect variation in the electron to proton mass ratio on the level of @xmath5 . standard ramsey spectroscopy starts with a system of @xmath0 non - interacting spin @xmath1 particles initially prepared in the same internal state . subsequently , a ramsey pulse prepares it in a coherent superposition of the two internal states and the system is let to evolve freely for a time during which a relative phase accumulates , @xmath6 , due to the energy splitting between the two states . the latter is then decoded by using a second ramsey pulse which maps the phase onto a population difference , thus allowing to perform precision measurements of the atomic transition frequency . the statistical fluctuations associated with a finite sampling yields a lower limit in the phase accuracy @xmath7 called the shot noise limit @xcite . the heisenberg uncertainty principle , however , allows for phase accuracies consistent with the basic principles of quantum mechanics , as low as @xmath8 , called the heisenberg limit . the latter can be achieved by using initially entangled atoms instead of a polarized sample @xcite . here we propose a spectroscopy technique which aims to measure the atomic interaction parameters arising form two - body collisions by using similar ramsey spectroscopic ideas , but applied to interacting atoms instead of non - interacting ones . the many - body interactions during the free evolution build in quantum mechanical correlations between the atoms and generates a large amount of entanglement even from an initially uncorrelated sample @xcite . this scheme provides a resolution which is fundamentally limited to @xmath2 , a factor of @xmath0 smaller than the heisenberg limit achievable with non - interacting atoms . moreover , for initially uncorrelated atoms the sensitivity scales as @xmath9 , implying a gain in resolution by a factor of @xmath10 with respect to the classical shot noise resolution . a more general analysis of beyond - heisenberg scaling for multi - body collisions or tensor - field interactions has been derived in ref . @xcite . many - particle entangled states , however , are difficult to prepare and maintain since they are extremely fragile : in practice , noise and decoherence rapidly collapse entangled states into classical statistical mixtures . for example in standard ramsey spectroscopy decoherence destroys the potential gain provided by entanglement , and , when it is taken into account both initially uncorrelated and maximally entangled states provide the same shot noise resolution @xcite . here we show that decoherence degrades the sensitivity of our method to @xmath11 for initially entangled atoms and to @xmath12 for initially uncorrelated ones . this scaling is interesting as it demonstrates that the entanglement build up by the many - body interactions helps , even with decoherence , to keep the sensitivity achievable with initially squeezed atoms above the maximally achievable with initially uncorrelated particles . we also discuss physical implementation of our scheme using a ) spinor bose- einstein condensates and b ) fermionic atoms loaded in optical lattices and compare and contrast the advantage and disadvantages of these two possible set - ups . the paper is organized as follows . in sec . ii we present our interferometry method based on the many - body collective dynamics . in sec . iii we apply it to initially uncorrelated states and derive the type of initially entangled states that lead to heisenberg - limited sensitivity . in this section we also propose a way to generate such states . in sec . iv we include the effect of decoherence . in sec . v we discuss the experimental implementation of the interferometry method using spinor condensates and cold fermionic atoms in optical lattices and discuss possible technical limitations . finally we conclude in sec . vi . let us consider a collection of @xmath0 spin-1/2 interacting particles described by the hamiltonian @xmath13 we used @xmath14 to denote the collective spin operators of the @xmath0 atoms : @xmath15 , where @xmath16 and @xmath17 is a pauli operator acting on the @xmath18 atom . we set @xmath19 . our interferometric technique follows the same ideas used in standard ramsey spectroscopy , but replaces the free evolution of the atoms by evolution with @xmath20 and the goal is to estimate @xmath21 as accurately as possible . we start with the initial state @xmath22 and apply a @xmath23 rotation to all particles about the y axis , @xmath24 . after letting the system evolve for time @xmath25 under @xmath20 , @xmath26 , a second @xmath27 pulse is applied , @xmath28 . finally the collective spin is measured @xmath29 . if this scheme is repeated during a total time @xmath30 the achievable sensitivity is given by @xmath31 with variance @xmath32 . in contrast to standard ramsey spectroscopy , which is fundamentally limited by the heisenberg exclusion principle to @xmath33@xcite per realization , the fundamental limit of this scheme is @xmath34 . this follows from an application of the time - energy uncertainty principle : @xmath35 where @xmath36 is the variance of the hamiltonian and @xmath37 is the variance in estimating time from a measurement on the system . can be used to determine time with an uncertainty @xmath38 the time - energy uncertainty can be reexpressed as @xmath39 , where @xmath40 . we can establish an upper limit @xmath41 from @xmath42 is @xmath43 . this implies @xmath44 and therefore a fundamental uncertainty in determining @xmath45 after a time @xmath25 of : @xmath46 spectroscopy ------------ let us start by outlining the basic properties of @xmath20 . it commutes with @xmath47 and @xmath48 , so a good basis to describe the dynamics is the one spanned by the collective angular momentum eigenstates . in the @xmath49 dimensional hilbert space , there are @xmath50 orthogonal fully symmetric states which we denote by @xmath51 that satisfy : @xmath52 , and @xmath53 with @xmath54 . we refer to the @xmath55 states as the @xmath56 manifold . the quantum numbers @xmath57 and @xmath58 are conserved during the dynamics , and therefore , if the initial state @xmath59 belongs to @xmath56 , then the subsequent evolution of the system only takes place within @xmath56 . first , consider the case when the initial state is fully polarized along @xmath60 : @xmath61 . after the first @xmath23 pulse it becomes @xmath62 . the effect of @xmath20 on the state is to imprint a phase @xmath63 to each @xmath64 component . in the limit of many atoms @xmath65 we may approximate the sums by integrals assuming @xmath66 is a continuous variable and to replace the binomial coefficient by a gaussian distribution with the same width . in this limit @xmath67 and @xmath68 become @xmath69 where we used the notation @xmath70 . the time evolution of the signal is a series of equally spaced gaussian pulses ( see fig . [ fig1 ] ) . as the system evolves , at first the different accumulated phases lead to a collapse of @xmath71 . for the initial coherent state in consideration . the collapse time , which depends on its variance , is @xmath72 . the evolution continues and at @xmath73 all the different components rephase inducing a perfect revival of the initial state , now with opposite polarization:@xmath74 . using eqs . ( [ jz ] ) and ( [ jz2 ] ) one can show that the optimal sensitivity is reached at the points with maximal signal intensity , @xmath75 . it scales as @xmath9 ( see fig . [ fig1 ] ) : @xmath76 entangled atomic states ( e.g. spin squeezed states ) potentially allow to significantly improve the sensitivity in precision measurements . for example , consider the initial state@xmath77 \right ) } { \sqrt{1+a^{2 } } } . \label{inisquee}\ ] ] here @xmath78 is a real number of order unity and @xmath0 is assumed to be even and large . the probability distribution of @xmath79 in the @xmath80 basis is plotted in the inset of fig.[fig2 ] . for even @xmath58 values , the amplitudes are almost constant ( except for those with @xmath81 close to @xmath82 ) , and for odd @xmath58 values they are proportional to @xmath83 . @xmath84 is a highly squeezed state with reduced variance in the @xmath60 direction : @xmath85 . using properties of the wigner rotation functions , it is possible to show that : @xmath86}{n ( \chi t-\pi/2 + k\pi ) } , \label{jzs } \\ \langle \hat{j}_x^2\rangle_\psi^a & = & n^2a\sum_{k=0 } \left(\frac{% j_1[2n(\chi t- k \pi/2]}{(2n ( \chi t- k\pi/2))}\right ) + b , \label{jz2s}\end{aligned}\ ] ] with @xmath87 and @xmath88 . as shown in fig . [ fig2 ] the system starts at @xmath89 with @xmath90 , and during the time evolution @xmath91 grows while oscillating . at @xmath92 the signal reaches a maximum and vanishes again at @xmath93 . then it evolves with opposite polarization until it returns to the initial state at @xmath94 . using eqs . ( [ jzs ] ) and ( [ jz2s ] ) , the optimal sensitivity can be shown to be reached at @xmath95 , with @xmath96 an odd integer ( see fig.[fig3 ] ) : @xmath97 these states lead to @xmath98 sensitivity . the best accuracy is obtained for @xmath99 , in which case @xmath100 . note , however , that estimating @xmath101 by measuring @xmath102 might be experimentally impractical due to the fact that not only the signal vanishes at @xmath95 ( regardless of the value of @xmath78 ) but also @xmath103 is very sharply peaked at @xmath95 and hence very sensitive to small variations of @xmath104 . to overcome this limitation we propose , following the ideas exposed in ref . @xcite , to measure @xmath105 instead of @xmath102 . in contrast to @xmath102 , the average square signal does not vanishes for finite @xmath78 ( it goes like @xmath106 ) and , as shown in fig . [ fig3 ] , measuring @xmath101 by means of @xmath107 provides the same @xmath2 accuracy with the advantage of a broader profile around the optimal value which becomes slightly shifted from @xmath108 . we calculated @xmath103 numerically according to eq . ( [ sig ] ) but replacing @xmath102 by @xmath109 . this idea , however , has the drawback that @xmath110 diverges exactly at @xmath108 . nevertheless as shown in fig . 3 this is a extremely narrow divergency and almost a one point behavior . let us now discuss how to generate states of the form given by eq.([inisquee ] ) . these states are highly squeezed , and a robust method to generate them can have also applications in heisenberg" +"rr lyrae , as well as classical cepheids , are considered standard candles for estimating stellar distances in the milky way and to local group galaxies . they are produced in old stellar populations , and hence they provide important information for an understanding of the age , structure and formation of their parent stellar systems . as typical population ii stars , rr lyrae are abundant in globular clusters and have been the subject of a huge number of studies for more than a century . although the pulsation theory explains quite well the connection between most of the involved physical quantities ( van albada & baker 1971 ; caputo , marconi & santolamazza 1998 ) , the dependence of intrinsic luminosity on metal content has been the subject of debate for nearly three decades ( see smith 1995 for a review ) . only recently the slope of the luminosity - metallicity relation m@xmath2-[fe / h ] seems to be converging towards a value @xmath30.20 - 0.23 that appears to be `` universal '' as supported by the most accurate studies of field rr lyrae stars in the milky way ( fernley et al . 1998 ; chaboyer 1999 ) and in the large magellanic cloud ( lmc , gratton et al . 2004 ) , and globular clusters in m31 ( rich et al . 2005 ) . near infrared observations of variable stars present several advantages over optical investigations : a smaller dependence on interstellar extinction and metallicity , a smaller pulsational amplitude and more symmetrical light curves , and hence good mean magnitudes . in the last 20 years the calibration of the rr lyrae period - ir luminosity relation ( pl@xmath0 ) has been the subject of several empirical and theoretical investigations ( see sect . [ method ] ) , but there still remains some degree of uncertainty on the dependence of @xmath4 on period and metallicity . to solve the problem of the dependence of @xmath4(rr ) on these physical quantities , a large sample of rr lyrae stars is needed , spanning a wide range of [ fe / h ] , for which accurate k and [ fe / h ] measurements are available . in this paper we present an accurate analysis of the infrared photometric properties of 538 rr lyrae variables ( 376 rrab and 162 rrc ) in 16 globular clusters ( gc ) with @xmath5<-0.9 $ ] . this more than doubles the number of stars used in the previous largest study of this type ( nemec , linnell nemec & lutz 1994 ) . by means of such a large database we calibrated the pl@xmath0 relation constraining its dependence on period and metallicity on a strictly observational basis . in 2 we describe the sample of rr lyrae stars and the used photometric ir datasets . 3 is devoted to the description of the adopted method to calibrate the pl@xmath0 relation . in 4 we use the derived pl@xmath0 relation to estimate the distance to the calibrator gcs and to a sample of field rr lyrae stars in the lmc , and compare the results with the previous determinations in literature . finally , we summarize our results in 5 . the data used in the present analysis consist of k photometry for the central regions of 9 gcs ( m4 , m5 , m15 , m55 , m68 , m92 , m107 and @xmath6 cen ) derived from a set of images secured at the telescopio nazionale galileo ( tng , canary islands ) , using the near - ir cameras arnica , and at the european southern observatory ( eso , la silla ) , using the near - ir camera irac-2 and sofi . a detailed description of the data reduction and calibration procedure can be found in ferraro et al . ( 2000 ) , valenti et al . ( 2004 ) , valenti , ferraro & origlia ( 2004 ) and sollima et al . all measured instrumental magnitudes were transformed into the two - micron all - sky survey ( 2mass ) photometric system . to extend our analysis to the outer regions of these clusters , we correlated our catalogs with the database obtained by 2mass that extends to a wide area up to 15 from the cluster centers . the 2mass k photometry for 5 additional gcs ( m22 , ngc 3201 , ngc 5897 , ngc 6362 and ngc 6584 ) was also considered . for each cluster we identified a large number of variable stars by cross - correlating the ir catalog with the most comprehensive catalog of gc variable stars available in literature ( clement et al . . since the adopted k magnitudes are the average of repeated exposures and the k light curves of rr lyrae variables have a fairly sinusoidal low amplitude shape , we assumed our k magnitudes as the mean magnitudes of the identified variables . note that the individual k values from different datasets generally agree within less than 0.1 mag . so , we assumed @xmath70.1 mag as a plausible error to attach to the mean k magnitudes used in the following analysis . in addition , we considered the k photometry of rr lyrae stars taken by longmore et al . ( 1990 , for variables in the clusters m3 , m4 , m5 , m15 , m107 and ngc 3201 ) , storm et al . ( 2004 , ic4499 ) , butler ( 2003 , m3 ) , dallora et al . ( 2004 , reticulum ) and del principe et al . ( 2005 , m92 ) . all magnitudes were reported to the homogeneous photometric system of 2mass using the transformation equations provided by carpenter ( 2001 ) . table 1 lists for each calibrator gc the metallicity ( in the carretta & gratton 1997 scale ) and the reddening coefficient e(b - v ) from ferraro et al . ( 1999 ) together with the number of rr lyrae considered in the present analysis . [ summ ] .the sample of calibrator gcs . metallicities are in the cg scale . [ cols=""<,^,^,^,>"",options=""header "" , ] from an accurate analysis of 538 rr lyrae variables in 16 gcs using infrared ( k - band ) photometry we derive a pl@xmath0 relation based on purely observational constraints . the derived dependences of the k magnitude on period and metallicity are in good agreement with those estimated by previous empirical studies . we confirm that the metallicity coefficient is about 2 - 3 times smaller than that predicted by theoretical models , as it was found in all previous empirical analyses . the zero point of the calibration has been tied to the trigonometric parallax of rr lyr measured with hst by benedict et al . this calibration has been used to derive the distances to the 16 calibrator gcs considered in this analysis . as a further check , this relation has been applied to rr lyrae stars in a few central fields in the lmc yielding a distance modulus @xmath8 , in good agreement with the most recent determinations based on cepheid variables ( persson et al . , 2004 ; gieren et al . , 2005 ) . this research was supported by the ministero dellistruzione , universit e ricerca . we warmly thank paolo montegriffo for assistance during catalogs cross - correlation . we also thank santino cassisi and the anonymous referee for their helpful comments and suggestions . benedict g. f. et al . , 2002 , apj , 581 , 115 bono g. , caputo f. , castellani v. , marconi m. , 2001 , mnras , 326 , 1183 bono g. , caputo f. , castellani v. , marconi m. , storm j. , deglinnocenti s. , 2003 , mnras , 344 , 1097 borissova j. , minniti d. , rejkuba m. , alves d. , cook k. h. , freeman k. c. , 2004 , a&a , 423 , 97 butler d. j. , 2003 , a&a , 405 , 981 caputo f. , marconi m. , santolamazza p. , 1998 , mnras , 293 , 364 carney b. w. , storm j. , jones r. v , 1992 , apj , 386 , 663 carpenter j. m. , 2001 , aj , 121 , 2851 carretta e. , gratton r. g. , 1997 , a&as , 121 , 95 carretta e. , gratton r. g. , clementini g. , fusi pecci f. , 2000 , apj , 533 , 215 catelan m. , pritzl b. j. , smith h. , a. , 2004 , apj suppl . ser . , 154 , 633 chaboyer b. , 1999 in `` post - hipparcos cosmic candles '' , kluwer ac . , a. heck , f. caputo eds . , 237 , 111 clement c. et al . , 2001 , aj , 122 , 2587 clementini g. , carretta e. , gratton r. , merighi r. , mould j. r. , mccarthy j. k. , 1995 , aj , 110 , 2319 clementini g. , gratton r. , bragaglia a. , carretta e. , di fabrizio l. , maio m. , 2003 , aj , 125 , 1309 dallora m. et al . , 2004 , apj , 610 , 269 del principe m. , piersimoni a. m. , bono g. , di paola a. , dolci m. , marconi m. , 2005 , aj , 109 , 2714 detre l. , szeidl b. , 1973 , ibvs , 764 fernley j. , skillen i. , burki g. , 1993 , a&as , 97 , 815 fernley j. , skillen i. , carney b. w. , cacciari c. , janes k. , 1998 , mnras , 293 , 61 ferraro f. r. , messineo m. , fusi pecci f. , de palo m. a. , straniero o. , chieffi a. , limongi m. , 1999 aj , 118 , 1738 ferraro f. r. , montegriffo p. , origlia l. , fusi pecci f. , 2000 , aj , 119 , 1282 frolov m. s. , samus n. n. , 1998 , astl , 24 , 171 gieren w. , storm j. b. , thomas g. iii , fouqu p. , pietrzyski g. , kienzle f. , 2005 , apj , 627 , 224 gratton r. g. , bragaglia a. , clementini g. , carretta e. , di fabrizio l. , maio m. , taribello e. , 2004 , a&a , 421 , 937 gratton r. g. , bragaglia a. , carretta e. , clementini g. , desidera s. , grundahl f. , lucatello s. , 2003 , a&a , 408 , 529 jones r. v. , carney b. w. , latham d. w. , 1988 , apj , 332 , 206 jones r. v. , carney b. w. , storm j. , latham d. w. , 1992 , apj , 386 , 646 jones r. v. , carney b. w. , fulbright j. p. , 1996 , pasp , 108 , 877 kazarovets e. v. , samus n. n. , durlevich o. v. , 2001 , inf . bull . variable stars , 5135 , 1 liu t. , janes k. a. , 1990 , apj , 354 , 273 longmore a. j. , dixon r. , skillen i. , jameson r. f. , fernley j. a. , 1990 , mnras , 247 , 684 nemec j. m. , linnell nemec a. f. , lutz t. e. , 1994 , aj , 108 , 222 persson s. e. , madore b. f. , krzemiski w. , freedman w. l. , roth m. , murphy d. c. , 2004 , aj , 128 , 2239 rey s. c. , lee y. w. , joo j. m. , walker a. , baird s. , 2000 , aj" +"in this paper , we propose a simple distributed scheduling algorithm that provides weighted fairness in ieee 802.11 @xcite wireless networks , despite the unpredictability of the 802.11 mac layer and physical channels . in 802.11 wireless networks , mac - layer contention , dynamics and bandwidth allocation are hard to predict . for such networks , the fixed - point model in @xcite gives a method for computing the long - term throughput of the binary exponential backoff ( beb ) algorithm @xcite . however , the short - term dynamics and unfairness are quite unpredictable . in a certain period , a station may randomly backoff more than others , and therefore have a smaller chance of winning the channel , which in turn makes that station backoff even more . meanwhile , the beb amplifies the unfairness caused by the impairments of the wireless channels . this aggravation is an unintentional side effect of beb that was designed to reduce collisions , not to guarantee fairness . the following two effects cause the unfairness : * _ capture : _ capture occurs when the signals from different transmitters have very different strengths at a receiver @xcite . for instance , a ratio of 2 in distances from the stations to the ap can lead to approximately a ratio of 16 in received signal strengths . when more than one station transmit packets to the ap at the same time , the ap may be able to capture and correctly decode the packet from the closer station , while ignoring the other packets . this effect increases the aggregate throughput since the ap receives one packet even when multiple transmissions overlap in time . however , capture may result in unfairness since the stations that are further away backoff more with the beb algorithm , and consequently obtain much less throughput than closer stations @xcite . * _ channel errors : _ in addition to packet collisions , channel errors are another important cause of packet loss . a more lossy channel to the ap drops more packets because of channel errors . the transmitting station interprets all packet losses as collisions and doubles its contention window . accordingly , the beb algorithm magnifies the asymmetry of the lossy channels . to alleviate this problem , reference @xcite describes a way to differentiate the two kinds of packet losses ( due to collisions or channel errors ) . the algorithm proposed in this paper provides a simpler solution . with a more complicated mac , ieee 802.11e @xcite provides differentiated service ( diffserv ) , by adopting different minimum contention windows ( @xmath0 ) and inter - frame spaces ( ifs ) for different service classes such as voice , video and data . this protocol provides relative performance differentiation among different classes : the classes with smaller @xmath0 and ifs have a relative priority over others . to evaluate the performance of 802.11e , reference @xcite provides a simulation study ; while reference @xcite uses an analytical model ( a markov chain ) to find the saturated throughput of 802.11e . however , the model there is quite complicated , indicating that the `` amount '' of relative priority is hard to quantify and control . for instance , it is not clear how much more bandwidth the protocol gives to video with a particular setting of @xmath0 and ifs , nor how to adjust the amount of priority by varying these parameters . in this paper , we describe a simple , easy to implement , distributed fair scheduling algorithm that we call vls , for``variable - length scheduling , '' to cope with the above problems . vls provides exact weighted fairness despite the unpredictability of the 802.11 mac layer and physical channels . in this section , we assume that there is only one collision domain . that is , each station can sense the transmissions of other stations . ( we consider the case of multiple collision domains in section [ sec : vls - in - multiple - cd ] . ) there are two versions of the scheduling algorithm : without and with an access point ( ap ) . the latter is an adaptation of the former that utilizes the ap to simplify the algorithm . the algorithm is based on the concept of `` virtual slot . '' by definition , a station sees a virtual slot when it senses a collision , a burst of transmissions ( i.e. , one data - ack exchange , or a series of data - ack exchanges separated by sifs ) , or when it transmits a burst of packets itself . mini - slots are not counted as virtual slots . in other words , a station counts a virtual slot whenever if senses the channel as `` idle '' for an interval equal to difs ( difs@xmath1sifs @xcite ) and is involved in a contention process ( i.e. , when the station s backoff counter goes down until it transmits a packet or senses other transmissions ) . in fig . [ fig : virtual - slots ] , for example , there are 3 virtual slots . `` virtual slots '' are similar to `` busy slots '' except that a burst of transmissions is counted as one `` virtual slot . '' virtual slots . ( there are 3 virtual slots in this figure.),width=316 ] the notion of `` virtual slot '' is particularly useful because every station in a single collision domain sees the same number of virtual slots , assuming that the stations are always backlogged . ( if not , the station starts the algorithm only when it has a backlog and stops it when its backlog is cleared . ) therefore , virtual slots can serve as a `` clock '' for scheduling . we design the distributed algorithm as follows . * each station @xmath2 is assigned a `` weight '' @xmath3 @xcite . ( if there are multiple flows outgoing from station @xmath2 , then let @xmath3 be the sum of the weights of all individual flows . ) and each station @xmath2 keeps track of a value @xmath4 that is initially equal to 1 . * if station @xmath2 gets an ack after it transmits a packet , it keeps transmitting a burst of @xmath5 packets separated by sifs and then resets @xmath4 to the value 1 . * if it does not get an ack after it transmits a packet , or if it does not get to transmit ( i.e. , it does not win a contention ) , station @xmath2 increments @xmath4 by one whenever it sees a virtual slot . for example , fig . [ fig : vls_2sta ] shows the process with 2 stations with weights @xmath6 and @xmath7 respectively . in the figure , each block represents a virtual slot ( aligned across different stations ) . the number in each block indicates the transmission length in that virtual slot . ( note that the size of a block here does not reflect the actual length of the virtual slot . ) assume station 1 starts transmission with the 1st virtual slot , while station 2 starts transmission with the 2nd . variable - length scheduling . ( @xmath6 , @xmath7 are the weights . each block represents a variable - length virtual slot . the number in a block indicates the transmission length.),width=316 ] in a time period when station @xmath2 is backlogged , we can see that the total number of packets it has transmitted is equal to the number of virtual slots it has seen so far times the weight @xmath8 . ( so station @xmath2 _ virtually _ transmits @xmath8 packets per slot . this is why we use the name `` virtual slot '' . ) since all stations see the same virtual slots , the bandwidth allocation is weighted fair . that is @xmath9 is the same for all the stations where @xmath10 is the average rate of packets that station @xmath2 transmits . note that vls guarantees the weighted fairness , no matter what happens in the mac and physical layers . thus , vls automatically adjusts for the randomness of the mac protocol and the asymmetry of the physical channels . in a wireless lan with an ap , the above algorithm can be adapted so that the client stations need not count the virtual slots . in this variation , the ap counts the virtual slots for the stations and piggybacks that count in the mac - layer acks to the stations . the algorithm works as follows . * the ap keeps counting the virtual slots . it increments the count ( @xmath11 ) for each virtual slot . * a station can start and stop the algorithm at any time . when station @xmath2 starts , it contends for the channel and sends the first @xmath8 packets to the ap . in one ack , the ap piggybacks the current value of @xmath12 , denoted as @xmath13 . the next time station @xmath2 wins the channel , it sends @xmath8 packets first . the ap , again , piggybacks the current value of @xmath12 , denoted as @xmath14 . then , the station sends @xmath15 more packets in the burst . since @xmath16 , station @xmath2 sends at least @xmath8 packets per burst . suppose that , at each virtual slot , every station @xmath17 has a probability @xmath18 of winning the channel . then on average , station @xmath17 accumulates @xmath19 units of `` credit '' before it wins the channel ( since the average number of virtual slots it waits for is @xmath20 ) . it can then spent the credits by transmitting ( on average ) @xmath19 packets . when the number of active stations @xmath21 increases in a wireless networks , @xmath18 decreases ( approximately @xmath22 ) . as a result , the average burst length increases , thus causing more delays for all the stations . to avoid this effect , we define a system - wide parameter @xmath23 , called `` _ speed of the clock _ '' , and we modify the protocol as follows : * instead of transmitting @xmath24 packets in a burst as in subsection [ sub : distributed - algorithm ] , station @xmath2 transmits @xmath25 packets . if @xmath25 is not an integer , then it transmits @xmath26 packets , and saves the extra credits @xmath27 for the next time . essentially , @xmath28 controls the speed of clock in the whole network . ( therefore , the delay is proportional to @xmath28 . ) * the stations can adjust the value of parameter @xmath28 in several different ways : * * if station @xmath2 knows the number of backlogged stations @xmath21 , then it can choose @xmath29 and broadcast @xmath30 to the network . the other stations will then follow the parameter . * * common tcp flows are usually not sensitive to the burst length and delay . but if a station ( say , station @xmath2 ) has delay - sensitive flows and some other stations burst lengths are causing too much delay to it , it computes a new value of @xmath30 and broadcasts it to the network . ( assume the current average delay for station @xmath2 is @xmath31 , and its targeted delay is @xmath32 , then set @xmath33 , where @xmath34 is the current parameter of the system . ) * * if the network has an ap , the ap can act as a controller to adjust @xmath28 . * * if there are more than one stations broadcasting @xmath30 , each station follow the lowest @xmath30 it has received ( i.e. , @xmath35 ) . * further details about the implementation of" +"the identification and study of very cool white dwarf ( wd ) stars is important for understanding the evolution of wds , their luminosity function , their space density , and their total formation rate . this study is particularly important for wds in the galactic halo , because they are sufficiently old that most are expected to have cooled to very low temperatures @xcite . until recently , the coolest wds known had temperatures @xmath04000 k ( bergeron et al . 1997 ; leggett et al . the discovery @xcite of two wds that definitely have temperatures below 4000 k has shown that such cool wds do exist and has added impetus for further searches . very cool wds will have molecular hydrogen in their atmospheres if any hydrogen is present . in these high - density atmospheres , collisions can induce a temporary electric dipole moment in the hydrogen molecules . calculations predict ( borosow et al . 1989 ; lenzuini et al . 1991 ; saumon et al . 1994 ; borosow et al . 1997 ) a high opacity at infrared wavelengths , referred to as collision - induced absorption ( cia ) . this opacity produces a spectral energy distribution with greatly depressed red / infrared flux that should result in distinctive colors ( bergeron et al . 1995a ; bergeron et al . 1997 ; hansen & phinney 1998 ; hansen 1998 ; hansen 1999 ; saumon & jacobson 1999 ; chabrier 1999 ) . the sloan digital sky survey ( sdss ) @xcite should be especially effective at identifying such stars @xcite . this survey is obtaining deep ccd images of 10,000 deg@xmath1 of the north galactic cap in five photometric bands ( @xmath2 , @xmath3 , @xmath4 , @xmath5 , and @xmath6 ) to a limiting magnitude @xmath7 see fukugita et al . ( 1996 ) and appendix a of fan et al . ( 2001 ) for details of the photometric system . this paper describes the first such star found by sdss in its commissioning data . this star appears to have stronger cia and , therefore , is probably cooler than the two previously known sub-4000 k wds . in addition , the rediscovery of lhs 3250 , previously the wd with strongest cia , is reported . both ( re)discoveries indicate that sdss can find other similar stars . imaging data from the sdss 2.5 m telescope and its survey camera @xcite now include most of the equatorial stripe with @xmath8 and outside of the galactic plane , as well as a number of scans away from the equator . the two stars reported here are a new white dwarf , sdssp j133739.40 + 000142.8 ( hereafter referred to as sdss 1337 + 00 ; `` p '' indicates that the coordinates are preliminary ) , and lhs 3250 @xcite . they were imaged on 1999 march 21 and 2000 april 04 , respectively . their positions , proper motions , and magnitudes are given in table 1 magnitudes are on the ab system ( lupton et al . 1999 ) , and errors are internal . only preliminary colors and magnitudes are available , until the sdss photometric system has been established ; @xmath9 and @xmath10 are used to designate these preliminary values . final magnitudes and colors are not likely to change by much more than a few hundredths . note , the difference between @xmath11 magnitudes and traditional logarithmic magnitudes is negligible at these magnitudes well above the survey limits . ] . a finding chart for sdss 1337 + 00 is shown in figure 1 . the proper motion is derived from the sdss position and the position in the usno - a2.0 catalog @xcite measured on the palomar observatory sky survey o and e plates taken in 1952 . for comparison , table 1 also includes data taken from the literature @xcite for the cool wd wd0346 + 246 . magnitudes in the sdss system and in the johnson / cousins / cit system are included in table 1 , where some of the values not observed directly have been transformed from the other system using predicted relations for normal stars @xcite . these estimated values are probably accurate to better than 0.1 mag . the @xmath12 magnitude limit for sdss 1337 + 00 was kindly obtained by f. vrba with the usno 1.55 m telescope and aladdin insb array detector . the colors of sdss 1337 + 00 and lhs 3250 are highly unusual , as shown in figure 2 . they are plotted along with a sample of normal wds with synthesized sdss colors @xcite , and with observed j magnitudes @xcite . the two curves show the colors of h and he wd model atmospheres @xcite with log @xmath13 ( kindly calculated and made available to us by pierre bergeron ) . the deviation of the spectral energy distributions of these two stars from normal white dwarfs and non - degenerate stars is dramatic . 1337 + 00 has colors in figure 2(b ) and 2(c ) even more extreme than those for lhs 3250 . spectroscopic `` plates '' ( exposures with fiber configurations covering the 3-degree field of view ) are taken by sdss after imaging data are available objects ( primarily galaxies and qso candidates ) are selected for observation based on their image morphology and colors . qsos with redshift @xmath14 have @xmath15 colors @xcite similar to those predicted for very cool wds . objects with such colors will be selected as high - redshift qso candidates , and those brighter than @xmath16 will be given high priority for spectroscopic observation as qso targets . they also will be selected as cool - wd candidates , but given lower priority for spectra . both sdss 1337 + 00 and lhs 3250 were allocated fibers as qso candidates . the two sdss fiber spectrographs cover 3800 - 9200 at a spectral resolution of 1800 . the exposure time is 45 min under optimum observing conditions , or more as necessary to reach a target s / n . the spectra are extracted and calibrated with an automated software pipeline ( frieman et al . 2001 , in preparation ) . the spectra of sdss 1337 + 00 and lhs 3250 were taken on 2000 may 07 ( plate 0299 , 75 min exposure ) and 2000 may 28 ( plate 0349 , 90 min exposure ) , respectively . they have been smoothed to 6 resolution , and are shown in figure 3 . the spectrum of lhs 3250 has been scaled to match that of sdss 1337 + 00 for ease of comparison ; it agrees quite well with the spectrum previously published @xcite . there are no significant features in the spectrum of either star . the spectra show that sdss 1337 + 00 has relatively less flux at red - infrared wavelengths , consistent with the colors shown in figure 2 . the low flux at red - infrared wavelengths in sdss 1337 + 00 appears similar to that in lhs 3250 but more pronounced . the most viable explanation is that we are seeing cia from molecular hydrogen @xcite . less extreme cia is also seen in wd0346 + 246 @xcite , and possibly in lhs 1126 @xcite and f351 - 50 @xcite . the discovery of cia in these stars represents a striking confirmation of the qualitative trends expected from theoretical model atmospheres @xcite . figure 4 compares the spectrum of sdss 1337 + 00 with models of pure hydrogen atmospheres at three cool temperatures . the discrepancy between the models and the observed spectrum is most likely the result of missing opacities in the theoretical models , as well as the likelihood of the admixture of helium into the hydrogen atmosphere to provide additional h@xmath17-he cia @xcite . improvements to both the atmosphere models and the theoretical opacity inputs are underway . for example , new models with low temperatures and mixed ( helium - dominated ) composition @xcite show the sensitivity of cia and the output spectrum to the input assumptions . however , these new models only explore a few compositions out of many plausible possibilities ; they still do not give improved fits to the spectra in figure 2 . until further improved models are available , we can only deduce broad constraints on the effective temperature . the fact that the h@xmath17 cia is strong suggests the objects are somewhat cooler than 4000 k. while temperatures below 3000 k can not be ruled out , such low temperatures imply cooling ages for some ranges of mass that exceed reasonable estimates for the age of the galaxy ( see section 4 ) , so a temperature range 3000 - 4000 k is suggested . much recent attention has been devoted to the existence of halo wds , motivated by microlensing @xcite and optical @xcite observations , and a few wds are known to be halo stars @xcite . are these two very cool wds part of the halo population ? the proper motion and distance of wd0346 + 246 give a tangential velocity of 175 km s@xmath18 , indicating that star is indeed a halo object @xcite . however , the proper motion of lhs 3250 is smaller ( v@xmath19 = 81 km s@xmath18 ) and is consistent with membership in either the disk or the halo ; meanwhile , its luminosity is not as low as expected for a presumably very old halo wd . the proper motion of sdss 1337 + 00 is smaller yet . if it has an absolute magnitude similar to that of lhs 3250 ( @xmath20 = 15.7 ) , then its distance will be about 54 pc and v@xmath19 will be 46 km s@xmath18 . alternatively , if it has the lower luminosity ( @xmath21 ) expected for a conventional , 0.6-@xmath22 wd cooling to a temperature where cia becomes strong , then its distance will be about 20 pc and v@xmath19 will be only 17 km s@xmath18 . in either case ( pending a parallax measurement ) , these two coolest wds do not have the properties expected for halo stars . to properly constrain the nature of these objects , we must consider not only wds with conventional c / o cores , but also the known population of low mass ( @xmath23 or less ) helium core wds found in binaries @xcite . such objects are the result of truncated stellar evolution in close binaries @xcite and cool more slowly ( for similar masses ) as a result of the increased heat capacity of the helium core . figure 5 shows the cooling time for wds with hydrogen atmospheres ( hansen 1999 ; see also benvenuto & althaus 1999 , chabrier et al . 2000 , salaris et al . conventional wds ( @xmath24 ) require ages @xmath258.5 gyr to cool to 4000 k. wds more massive than average can cool somewhat faster at late times due to the earlier onset of core crystallization . the aforementioned low mass helium core wds can potentially cool below 4000 k much faster . a 0.23 @xmath22 helium core wd may cool below 4000 k in @xmath06 gyr . ( note that very low mass wds may possess thick hydrogen envelopes and thus will cool more slowly , with a contribution to their luminosity from residual hydrogen burning @xcite . if true , this will cause the curves shown in figure 5 to turn upwards again below @xmath26 . ) further progress requires that we determine a temperature or a radius , because the luminosity is known ( or soon will be , after the parallax of sdss 1337 + 00 is measured ) . the radius varies from @xmath27 cm for the @xmath28 model , to @xmath29 cm for the" +"very unstable nuclei with unusual ratios of neutron number ( @xmath2 ) to proton number ( @xmath5 ) are currently the subject of intense theoretical and experimental work . a particularly important issue is the effect on nuclear properties of a large neutron excess and the accompanying low - lying continuum of excited states . in ground states these conditions sometimes lead to halos , thick skins , and changes in magic numbers . less is known about excited states , which we study here by calculating transition strengths and densities . most of the work on excited states is in light neutron - rich nuclei ; a low - energy strength - function peak has been studied for years . recent work @xcite has focused on enhanced @xmath4 strength in nuclei like @xmath6li or in neutron - rich oxygen isotopes @xcite . but in heavier nuclei , calculations are more spotty . several groups have calculated the isovector ( iv ) @xmath4 strength functions , or photoabsorption cross sections , in the ca isotopes @xcite . references @xcite predict a small peak at around @xmath7 mev in @xmath8ca . the first paper also calculates the strength function in @xmath9ca , finding no low - energy peak , but ref . @xcite , a calculation based on density - functional theory , finds a very broad bump at @xmath1010 mev . it is not clear , therefore , at what value of @xmath2 the low - energy strength is first discernible . the method we use here , the quasiparticle random phase approximation ( qrpa ) , has been applied mainly to selected @xmath4 excitations in particular isotopes of o , ca , and ni ; one example is ref.@xcite , which asserts that the low - energy excitations reflect strong particle - particle ( dineutron "" ) correlations . references @xcite show extensive and systematic qrpa calculations of photoabsorption cross sections , but focus primarily on radiative neutron - capture cross sections . the relativistic qrpa @xcite has been applied more with an eye to nuclear structure issues ( for a recent review , see ref . @xcite ) , asserting , for example , that low - lying isoscalar ( is ) @xmath4 states exhibit toroidal flow . references @xcite go beyond rpa , altering details of predicted low - lying strength . other channels have been discussed less than the iv @xmath4 . the authors of ref . @xcite calculate @xmath3 strength functions in ca isotopes up to the neutron drip line , finding an enhancement at low energy in @xmath8ca . reference @xcite examines transition strengths in the @xmath3 , @xmath4 , and @xmath1 channels near the neutron drip line , finding , for example , a sharp @xmath1 peak near @xmath11 in @xmath12ni . the above represents a considerable amount of work on excitations in exotic nuclei . its range and results can be summarized , roughly , as follows : 1 ) most of the calculations are for spherical nuclei , and the iv @xmath4 channel has been studied the most . 2 ) a low - energy peak grows as @xmath2 increases . 3 ) the low - energy excitations do not seem collective in the @xmath4 channel ( e.g. ref . @xcite ) , i.e. they do not contain more than a few particle - hole or two - quasiparticle configurations . 4 ) the corresponding transition densities have long neutron tails extending beyond the bulk nuclear radius . 5 ) the neutron skin thickness is correlated with the amount of low - energy strength @xcite . 6 ) calculations reproduce measurements of the amount of low - energy strength fairly well if they include many - particle many - hole correlations @xcite . most of this work has focused on nuclei right at the drip line and , as already noted , has emphasized the iv @xmath4 channel . it is still not known whether theory makes similar predictions for other neutron - rich nuclei , or to what extent the properties of the low - energy peaks vary from one multipole to another . the purpose of this paper , therefore , is to calculate strength functions in as many nuclei as possible , in all multipoles up to @xmath1 , and investigate how the properties of the strength functions vary as @xmath2 and the multipolarity change . we use the qrpa with skyrme density functionals ( which we refer to as interactions from here on ) and volume - type delta pairing interactions . currently , the qrpa is the most sophisticated method that can be used systematically for resonances of all energies in heavy nuclei without assuming that part of the nucleus forms an inert core . here we will display results of qrpa calculations for ca , ni , and sn isotopes from the proton drip line to the neutron drip line , describing the corresponding strength functions and transition densities in detail . we will also examine whether results depend on which skyrme interaction we use , so that we can identify important measurements / nuclei that will help distinguish among them . section [ sec : calculation ] below describes our method . section [ sec : strength function ] shows strength functions in the three isotopic chains and looks for @xmath13-dependent trends in their behavior . section [ sec : transition density ] discusses transition densities to states in low - lying peaks . section [ sec : conclusion ] is a conclusion . our approach to the qrpa is described in detail in ref . @xcite , and we discuss it here only briefly . the starting point is a coordinate - space hartree - fock - bogoliubov ( hfb ) calculation , carried out with the code used in refs . the code outputs quasiparticle wave functions , with spherical symmetry assumed . it takes the continuum into account by placing the nucleus in a 20-fm box . we use as large a single - particle space as possible and solve the hfb equations accurately , so as to ease the removal of spurious states from the qrpa and satisfy sum rules . we diagonalize the hfb density matrix to obtain a set of canonical states as many as there are quasiparticle states that make up our qrpa basis . the qrpa - hamiltonian matrix then contains off - diagonal elements from the quasiparticle one - body hamiltonian as well as the matrix elements of the residual two - body interaction . the two - body matrix elements are functional derivatives of the energy with respect to the density and pairing tensor , after diagonalizing the qrpa hamiltonian , we use the eigenvectors to obtain strength functions @xcite and transition densities ( see appendix ) . we can not handle an infinite number of canonical quasiparticle states , and so truncate our basis in the following way : for @xmath14 the maximum single - particle angular momentum @xmath15 is 15/2 , and for @xmath16 @xmath15 is 21/2 . if the ground state has a finite pairing gap in the hfb calculation we truncate the canonical quasiparticle basis in the qrpa by omitting states with very small occupation probability @xmath17 . in the @xmath18 and @xmath4 channel we keep states with @xmath19 , and in the @xmath20 channel we keep those with @xmath21 . if the mean field has no pairing we use the hartree - fock energy to truncate ; in the @xmath18 and @xmath4 channels we keep single - particle states with energy @xmath22 mev , and in the @xmath20 channel we keep those with @xmath23 mev . in the hfb calculations we always cut off the quasiparticle spectrum at 200 mev . the largest qrpa - hamiltonian matrix that we encounter here ( in the @xmath4 channel for sn near the neutron drip line ) is about 14,000 , and the minimum is about 2,000 ( in the @xmath3 channel for ca near the proton drip line ) . and @xmath24 mev were used for the @xmath1 channel , and then the maximum dimension of the hamiltonian matrix was about 20,000 . ] the separation of spurious excitations from physical states is as complete as in ref . @xcite in most of cases . we use 3 skyrme interactions : skm@xmath25 , sly4 , and skp . our pairing interaction has zero range with no density dependence ( this is `` volume pairing '' ) . for reasons we do not understand , we can not obtain solutions of the hfb equation with skp for ca and ni isotopes . the other interactions give solutions that are unstable against qrpa quadrupole vibrations for isotopes with : @xmath26 in ni ( skm@xmath25 ) ; @xmath27 ( skm@xmath25 ) and @xmath28 , @xmath29 ( sly4 ) in sn , and so we do not discuss these nuclei . strength functions are important because they capture information about all excited states and can often be measured . we define the strength functions through the transition operators @xmath30 : @xmath31 @xmath32 : @xmath33 @xmath34 : @xmath35 where @xmath36 is total - nucleon number , and @xmath37 is a single - particle index . the upper limit for @xmath5 ( @xmath2 ) on a summation sign means that the sum is over protons ( neutrons ) . in the next few sections we show the strength functions , with spurious states removed , produced by skm@xmath25 , and discuss those produced by the other skyrme interactions when appropriate . we then display energy - weighted sums ( up to several different energies ) produced by all our interactions , in all isotopes . figures [ fig : str_ca_0+][fig : str_sn_0 + ] show the is and iv strength functions in the @xmath18 channels . in ca ( fig.[fig : str_ca_0 + ] ) , most of the functions are smooth except for small low - energy spikes in several nuclei and the large low - energy peaks in @xmath39ca . the is giant resonances peak at @xmath40 mev for @xmath41ca and gradually move to 15 mev by @xmath42ca . as @xmath2 approaches the neutron drip line , a peak near @xmath11 grows , becoming quite large at the drip line . the iv giant resonance is broad in the light isotopes and develops a low - energy component as @xmath2 increases , apparently increasing the summed strength . the larger peak varies only slightly in energy over the same range of @xmath2 . near the drip line the low - energy iv strength develops a peak that exactly mirrors the is peak , indicating that the strength in both channels is produced solely by neutrons this distinct low - energy bump seems to appear first at 10 mev in @xmath43ca . this nucleus is not as short - lived as the isotopes near the drip line ; perhaps the appearance of the low - energy mode is experimentally testable . the same nucleus marks the beginning of the low energy peak when we use sly4 . the @xmath2 dependence of the strength function of ni ( fig . [ fig : str_ni_0 + ] ) is similar in many ways to that of ca ; the energy of the is giant - resonance energy , for example , falls in a similar way past @xmath44 . a large low - energy peak again develops near the neutron - drip line , though not as dramatically as in ca , and with the complication that the strength shrinks after @xmath45ni . this peak first is noticeable in both the is and iv channel at 6 mev in @xmath46ni , here and in calculations with sly4 . this example and that in ca suggest more generally that the nucleus with 2 neutrons outside a closed shell will mark the appearance of the low - energy peak ." +"sequence https://oeis.org/a000975[a000975 ] in the online encyclopedia of integer sequences ( oeis ) @xcite starts out 1 , 2 , 5 , 10 , 21 , 42 , 85 , . throughout this paper we denote this sequence as sequence @xmath0 and the @xmath1th term of this sequence as @xmath2 , written in function notation . the oeis defines this sequence recursively as follows . * characterization 1 : * \1 . @xmath3 , \2 . @xmath4 , and \3 . @xmath5 . thus to get the next term we either double the preceding value or double it and add 1 . but doubling is the same as appending a 0 in base 2 , while doubling and adding 1 is the same as appending a 1 in base 2 . this provides a second characterization . * characterization 2 : * for @xmath6 , @xmath2 is the number whose binary representation has length @xmath1 and consists of alternating ones and zeros . we illustrate this characterization in table 1 . @xmath7 if we add @xmath2 to @xmath8 , the binary representation of the sum is a string of @xmath1 ones , with value @xmath9 . this gives us our third characterization . * characterization 3 : * \1 . @xmath3 , and \2 . @xmath10 for @xmath11 . alternatively , if we subtract @xmath12 from @xmath2 , most of the ones in the binary representations cancel , leaving @xmath13 . this gives us yet another characterization . * characterization 4 : * \1 . @xmath14 , \2 . @xmath15 , and \3 . @xmath16 for @xmath17 . there are several standard methods for obtaining a closed form expression for @xmath2 . we present a rather unusual derivation . recall that the binary representation of the fraction @xmath18 is @xmath19 multiplying this value by @xmath20 moves the binary point @xmath1 places to the right . rounding down then truncates this expression , yielding @xmath2 , according to characterization 2 , and giving us our next characterization . * characterization 5 : * @xmath21 for all @xmath22 . other expressions are @xmath23{0pt}{10pt}}{\textstyle 3 \rule{0pt}{9pt}}&\mbox{if $ n$ odd}\\ \ \\ \frac{\textstyle 2^{n+1 } -2 \rule[-3pt]{0pt}{10pt}}{\textstyle 3 \rule{0pt}{9pt}}&\mbox{if $ n$ even } \end{array } \right.\\ \ \\ \ \\ & = & \frac{2^{n+2 } - 3 - ( -1)^n}{6}.\end{aligned}\ ] ] it is an easy exercise to prove that all these characterizations of @xmath2 are equivalent . we observe that @xmath2 is even or odd exactly when @xmath1 is even or odd , respectively . why do we care about a particular sequence ? often it is because the sequence occurs as the answer to some counting problem . the oeis lists several places where the values in sequence https://oeis.org/a000975[a000975 ] occur . here are some of the more interesting . * occurrence 1 : * @xmath2 is the number of moves needed to solve the @xmath1-ring chinese rings puzzle ( baguenaudier ) if the rings are moved one at a time . see , for example , ( * ? ? ? * chapter 1 ) . figure [ rings ] shows the state graph for the 4-ring puzzle . the 16 vertices represent the possible states of the puzzle , and two vertices are joined by an edge if the two corresponding states are one move apart . the labels on the vertices denote the positions of the 4 rings in that state , with 0 representing a ring that is off the sliding bar and 1 a ring that is on . it is easy to confirm that the state graph for the @xmath1-ring puzzle is a path of length @xmath24 from the state labeled @xmath25 to the state labeled @xmath26 . the sub - path from state @xmath25 to state @xmath27 constitutes an optimal solution of the @xmath1-ring puzzle , while the sub - path from state @xmath27 to state @xmath26 represents an optimal solution of the @xmath28-ring puzzle . the number of moves in an optimal solution to this puzzle thus satisfies characterization 3 of sequence @xmath0 . figure [ rings ] also illustrates a related occurrence of our sequence . * occurrence 2 : * @xmath2 is the distance between a string of @xmath1 zeros and a string of @xmath1 ones in the standard @xmath1-bit binary gray code . again , see , for example , ( * ? ? ? * chapter 1 ) . a special case of a problem posed by donald knuth @xcite and solved by o. p. lossers @xcite provides our next occurrence * occurrence 3 : * @xmath2 is the number of ways to partition a set of @xmath29 people sitting around a circular table into three affinity groups with no two members of a group seated next to each other . we illustrate this occurrence in figure [ dk ] , showing the @xmath30 partitions of six people into three affinity groups . for concreteness we assign the names a and b to the affinity groups of the people at the bottom left and bottom right , respectively . following @xcite , we note that there are @xmath9 strings of length @xmath29 that start with ab , contain all the letters a , b , and c , and have no two adjacent letters the same . if such a string ends in either b or c , it can be wrapped into a circle to represent an affinity partition of @xmath29 people . if such a string ends in a , the a can be deleted and the shortened string will represent an affinity partition of @xmath31 people . the number of affinity partitions of @xmath29 people is thus another problem that satisfies characterization 3 of sequence @xmath0 . equivalently , @xmath2 is the number of different 3-colorings for the vertices of all triangulated @xmath32-gons if the colors of the two base vertices are fixed . antti karttunen has suggested that our sequence https://oeis.org/a000975[a000975 ] serves as a link between sequences https://oeis.org/a0000217[a0000217 ] ( the triangular numbers ) and https://oeis.org/a048702[a048702 ] ( the even length binary palindromes divided by 3 ) in the oeis . the triangular numbers , which we represent by @xmath33 , are well - known : @xmath34 . the even length binary palindromes , denoted @xmath35 , ( sequence https://oeis.org/a048701[a048701 ] in the oeis ) , are less well known . we illustrate the sequence @xmath36 in table [ pal ] . @xmath37 the proposal of karttunen is that the values @xmath38 serve as the indices @xmath1 where @xmath33 and @xmath36 agree , as illustrated in table [ blue ] . @xmath39{0pt}{15pt}\\ \hline t(n)&{\bf \color{blue}1}&{\bf \color{blue } 3}&6&10&{\bf \color{blue } 15}&21&28&36&45&{\bf \color{blue } 55}&66&78&91&105&120 \rule[-5pt]{0pt}{15pt}\\ \hline p(n)/3&{\bf \color{blue } 1}&{\bf \color{blue } 3}&5&11&{\bf \color{blue } 15}&17&21&43&51&{\bf \color{blue } 55}&63&65&73&77&85 \rule[-5pt]{0pt}{15pt } \end{array}\ ] ] for any positive integer @xmath1 let @xmath40 . then the binary representation of @xmath1 is @xmath41 bits long , and @xmath35 satisfies @xmath42 where @xmath43 is the binary reversal of @xmath1 ( sequence https://oeis.org/a030101[@xmath44 in the oeis ) . for example , when @xmath45 we have @xmath46 and @xmath47 , so @xmath48 this lemma follows immediately from the definition of @xmath35 . for all @xmath6 , we have @xmath49 if and only if @xmath50 for some positive integer @xmath41 . first suppose @xmath50 where @xmath41 is odd . then we know that @xmath51 @xmath1 is @xmath41 bits long , and @xmath52 . we have @xmath53 now suppose @xmath50 where @xmath41 is even . then we know that @xmath54 @xmath1 is @xmath41 bits long , and @xmath55 . we have @xmath56 next suppose @xmath57 . then @xmath1 is @xmath41 bits long , and @xmath58 finally , suppose @xmath59 . then @xmath1 is @xmath41 bits long , and @xmath60 reinhard zumkeller has conjectured that our sequence @xmath0 is related to the sequence https://oeis.org/a265158[a265158 ] in the oeis . we denote this sequence as @xmath61 and its @xmath1th term as @xmath62 . the sequence is defined by \1 . @xmath63 , \2 . @xmath64 for @xmath22 , and \3 . @xmath65 for @xmath22 . the first few values of this sequence are displayed in table [ b ] . @xmath66{0pt}{12pt}\\ \hline 1&1\;&9&2\;&17&4\;&25&0\;\rule{0pt}{11pt}\\ 2&2\;&10&2\;&18&4\;&26&0\;\\ 3&0\;&11&0\;&19&1\;&27&0\;\\ 4&4\;&12&0\;&20&4\;&28&0\;\\ 5&1\;&13&0\;&21&1\;&29&0\;\\ 6&0\;&14&0\;&22&0\;&30&0\;\\ 7&0\;&15&0\;&23&0\;&31&0\;\\ 8&8\;&16&16\;&24&0\;&32&32\ ; \end{array}\ ] ] a notable property of this sequence is that it contains long runs of zeros . zumkeller conjectures that the lengths of the record runs of zeros in sequence @xmath61 are exactly the values found in sequence @xmath0 . the run lengths themselves form sequence https://oeis.org/a264784[a264784 ] , with values * 1 * , * 2 * , * 5 * , * 10 * , 1 , * 21 * , 2 , * 42 * , 1 , 1 , 5 , 1 , * 85 * , 2 , 2 , 10 , 2 , * 170 * , 1 , 1 , 1 , 5 , 1 , 1 , 5 , 1 , 21 , 1 , 1 , 5 , 1 , * 341 * , 2 , 2 , 2 , 10 , 2 , 2 , 10 , 2 , 42 , 2 , 2 , 10 , 2 , * 682 * , 1 , 1 , 1 , 1 , 5 , 1 , 1 , 1 , 5 , 1 , 1 , 5 , 1 , 21 , 1 , 1 , 1 , 5 , 1 , 1 , 5 , 1 , 21 , 1 , 1 , 5 , 1 , 85 , 1 , 1 , 1 , 5 , 1 , 1 , 5 , 1 , 21 , 1 , 1 , 5 , 1 , * 1365 * , . we will refer to this sequence of run lengths as sequence @xmath67 , with entries @xmath43 . we confirm a few facts about sequence @xmath61 . @xmath68{0pt}{5pt}\\ 2 & \mbox { if $ k$ is even}\rule{0pt}{15pt } \end{array}\right.\ ] ] the proof is by induction on @xmath41 . for @xmath69 we have @xmath70 let @xmath41 be an even positive integer , and suppose that the lemma is true for smaller values of @xmath41 . we have @xmath71 now let @xmath72 be an odd integer , and suppose that the lemma is true for smaller values of @xmath41 . we have @xmath73 @xmath74 for @xmath75 . for @xmath41 even we have @xmath76 once the case @xmath41 even is established , the case @xmath41 odd follows . @xmath77 note that lemmas 4.1 and 4.2 together imply that for all @xmath75 there is a run of zeros in sequence @xmath61 beginning at index @xmath78 . @xmath79 for all @xmath80 . the proof is by induction on @xmath41 . for @xmath81 we have @xmath82 . now assuming the lemma is true for all values smaller than some @xmath83 , we have @xmath84 for every @xmath75 we have @xmath85 for @xmath86 . these values form a run of zeros of length @xmath87 in @xmath62 , and these are the runs of record length . we again use induction on @xmath41 . for @xmath88 we consider @xmath1 such that @xmath89 , or @xmath90 . now @xmath91 so the claim is true in this case . we now consider the claim for some @xmath92 and assume the claim is true for smaller values of @xmath41 . we know from lemma 4.2 that @xmath93 for @xmath94 , so we need consider only those @xmath1 such that @xmath95 . if @xmath1 is even , this implies @xmath96 , so by the induction hypothesis we have @xmath97 if @xmath1 is odd , it can still be shown that @xmath98 , so the induction hypothesis yields @xmath99 for all @xmath75 , then , we have a run of zeros in sequence @xmath62 starting at @xmath100 and ending at @xmath101 , of length @xmath102 . that these are precisely the runs of record length follows from the fact that @xmath103 for all @xmath80 and that" +"the last seven years have been a very exciting time for string theory . a new understanding of nonperturbative features of string theory , such as d - branes , has led to exciting new developments relating string theory to physically interesting systems such as black holes and supersymmetric gauge field theories , as well as to a new understanding of the relationship between yang - mills theories and quantum theories of gravity . despite remarkable progress in these directions , however , a consistent nonperturbative background - independent formulation of string theory is still lacking . this situation makes it impossible at this point , even in principle , to directly address cosmological questions using string theory . string field theory is a nonperturbative approach to string theory which holds some promise towards providing a background - independent definition of the theory . these lecture notes give an introduction to string field theory and review some recent work which incorporates d - branes into the framework of string field theory . this work shows that string field theory is a sufficiently robust framework that distinct string backgrounds can arise as disconnected solutions of the theory , at least for open strings . it remains to be seen whether this success can be replicated in the closed string sector . in this section we review briefly the situation in string theory as a whole , and summarize the goals of this set of lectures . in section 2 we review some basic aspects of d - branes . in section 3 , we describe a particular d - brane configuration which exhibits a tachyonic instability . this tachyon can be seen in the low - energy super yang - mills description of the d - brane geometry . this field theory tachyon provides a simple model which embodies much of the physics of the more complicated string field theory tachyon discussed in the later lectures . in section 4 we give an introduction to witten s cubic bosonic open string field theory and summarize the conjectures made by sen in 1999 , which suggested that the tachyonic instability of the open bosonic string can be interpreted in terms of an unstable space - filling d - brane , and that this system can be analytically described through open string field theory . section 5 gives a more detailed analytic description of witten s cubic string field theory . in section 6 we summarize evidence from string field theory for sen s conjectures . section 7 contains a brief review of some more recent developments . section 8 contains concluding remarks and lists some open problems . much new work has been done in this area since these lectures were presented at valdivia in january 2002 . except for a few references to more recent developments in footnotes and in the last two sections , these lecture notes primarily cover work done before january 2002 . previous articles reviewing related work include those of ohmori @xcite , de smet @xcite , and arefeva _ et al . an expanded set of lecture notes , based on lectures given by the author and barton zwiebach at tasi 01 , will appear in @xcite ; the larger set of notes will include further details on a number of topics . to understand the significance of developments over the last seven years , it is useful to recall the situation of string theory as it was in early 1995 . at that time it was clearly understood that there were 5 distinct ways in which a supersymmetric closed string could be quantized to give a microscopic definition of a theory of quantum gravity in ten dimensions . each of these approaches to quantizing the string gives a set of rules for calculating scattering amplitudes between on - shell string states which describe gravitational quanta as well as an infinite family of massive particles in a ten - dimensional spacetime . these five string theories are known as the type iia , iib , i , heterotic @xmath0 , and heterotic @xmath1 superstring theories . while these string theories give perturbative descriptions of quantum gravity , in 1995 there was little understanding of nonperturbative aspects of these theories . in the years between 1995 and 2000 , several new ideas dramatically transformed our understanding of string theory . we now briefly summarize these ideas and mention some aspects of these developments relevant to the main topic of these lectures . * dualities : * the five different perturbative formulations of superstring theory are all related to one another through duality symmetries @xcite , whereby the degrees of freedom in one theory can be described through a duality transformation in terms of the degrees of freedom of another theory . some of these duality symmetries are nonperturbative , in the sense that the string coupling @xmath2 in one theory is related to the inverse string coupling @xmath3 in a dual theory . the web of dualities relating the different theories gives a picture in which , rather than describing five distinct possibilities for a fundamental theory , each of the perturbative superstring theories appears to be a particular perturbative limit of some other , as yet unknown , underlying theoretical structure . * m - theory : * in addition to the five perturbative string theories , the web of dualities also seems to include a limit which describes a quantum theory of gravity in eleven dimensions . this new theory has been dubbed `` m - theory '' . although no covariant definition for m - theory has been given , this theory can be related to type iia and heterotic @xmath1 string theories through compactification on a circle @xmath4 and the space @xmath5 respectively @xcite . for example , in relating to the type iia theory , the compactification radius @xmath6 of m - theory becomes the product @xmath7 of the string coupling and string length in the 10d iia theory . thus , m - theory in flat space , which arises in the limit @xmath8 , can be thought of as the strong coupling limit of type iia string theory . it is also suspected that m - theory may be describable as a quantum theory of membranes in 11 dimensions @xcite , although a covariant formulation of such a theory is still lacking . * branes : * in addition to strings , all five superstring theories , as well as m - theory , contain extended objects of higher dimensionality known as `` branes '' . m - theory has m2-branes and m5-branes , which have two and five dimensions of spatial extent ( whereas a string has one ) . the different superstring theories each have different complements of d - branes as well as the fundamental string and neveu - schwarz 5-brane ; in particular , the iia / iib superstring theories contain d - branes of all even / odd dimensions . the branes of one theory can be related to the branes of another through the duality transformations mentioned above . through an appropriate sequence of dualities , any brane can be mapped to any other brane , including the string itself . this suggests that none of these objects are really any more fundamental than any others ; this idea is known as `` brane democracy '' . * m(atrix ) theory and ads / cft : * one of the most remarkable results of the developments just mentioned is the realization that in certain space - time backgrounds , m - theory and string theory can be completely described through simple supersymmetric quantum mechanics and field theory models related to the low - energy description of systems of branes . the m(atrix ) model of m - theory is a simple supersymmetric matrix quantum mechanics which is believed to capture all of the physics of m - theory in asymptotically flat spacetime ( in light - cone coordinates ) . a closely related set of higher - dimensional supersymmetric yang - mills theories are related to string theory in backgrounds described by the product of anti - de sitter space and a sphere through the ads / cft correspondence . it is believed that these models of m - theory and string theory give true nonperturbative descriptions of quantum gravity in space - time backgrounds which have the asymptotic geometry relevant to each model . for reviews of m(atrix ) theory and ads / cft , see @xcite . the set of ideas just summarized have greatly increased our understanding of nonperturbative aspects of string theory . in particular , through m(atrix ) theory and the ads / cft correspondences we now have nonperturbative definitions of m - theory and string theory in certain asymptotic space - time backgrounds which could , in principle , be used to calculate any local result in quantum gravity . while these new insights are very powerful , however , we are still lacking a truly background - independent formulation of string theory . the goal of these lectures is to describe progress towards a nonperturbative background - independent formulation of string theory . such a formulation is needed to address fundamental questions such as : what is string theory / m - theory ? how is the vacuum of string theory selected ? i.e. _ , why can the observable low - energy universe be accurately described by the standard model of particle physics in four space - time dimensions with an apparently small but nonzero positive cosmological constant ? ) , and other questions of a cosmological nature . obviously , aspiring to address these questions is an ambitious undertaking , but we believe that attaining a better understanding of string field theory is a useful step in this direction . more concretely , in these lectures we will describe recent progress on open string field theory . it may be useful here to recall some basic aspects of open and closed strings and the relationship between them . closed strings , which are topologically equivalent to a circle @xmath4 , give rise upon quantization to a massless set of spacetime fields associated with the graviton @xmath9 , the dilaton @xmath10 , and the antisymmetric two - form @xmath11 , as well as an infinite family of massive fields . for the supersymmetric closed string , further massless fields associated with the graviton supermultiplet appear these are the ramond - ramond @xmath12-form fields @xmath13 and the gravitini @xmath14 . thus , the quantum theory of closed strings is naturally associated with a theory of gravity in space - time . on the other hand , open strings , which are topologically equivalent to an interval @xmath15 $ ] , give rise under quantization to a massless gauge field @xmath16 in space - time . the supersymmetric open string also has a massless gaugino field @xmath17 . it is now understood that generally open strings should be thought of as ending on a dirichlet @xmath12-brane ( d@xmath12-brane ) , and that the massless open string fields describe the fluctuations of the d - brane and the gauge field living on the world - volume of the d - brane . it may seem , therefore , that open and closed strings are quite distinct , and describe disjoint aspects of the physics in a fixed background space - time containing some family of d - branes . at tree level , the closed strings indeed describe gravitational physics in the bulk space - time , while the open strings describe the d - brane dynamics . at the quantum level , however , the physics of open and closed strings are deeply connected . indeed , historically open strings were discovered first through the form of their scattering amplitudes @xcite . looking at one - loop processes" +"the universe is not matter - antimatter symmetric ; as shown by primordial nucleosynthesis measurements , the baryon density to entropy density ratio @xmath1 is constrained to be about @xmath2 @xcite . the necessary ingredients for a theory to explain this asymmetry are the sakharov criteria : baryon number violation , c and cp violation and non - equilibrium conditions @xcite . electroweak baryogenesis is an attractive mechanism with the best chance of verification through traditional collider experiments @xcite . the central feature of electroweak baryogenesis is spontaneous symmetry breaking . at high temperatures , the vaccum expectation value of the higgs field is zero but as the universe cools down over time , a second minimum appears in the potential at @xmath3 . the universe undergoes a phase transition , from a `` symmetric '' phase where @xmath4 to the `` broken '' phase where @xmath3 . if the phase transition is second order , which means that no potential barrier exists , then the universe is approximately in equilibrium throughout the transition and no baryogenesis can result ( since the third sakharov criterion is violated ) . if the phase transition is first order , then the phase transition occurs through quantum tunneling . as the universe cools , the probability of making a transition from symmetric to broken phase grows and when the transition occurs at a certain point in space , a bubble of broken phase forms and expands . because of its first order nature , the phase transition does not occur throughout the whole universe at the same time , resulting in non - equilibrium conditions . the baryon asymmetry is generated as the wall of the expanding bubble passes through points in space . particles in the unbroken phase close to the wall interact with the changing higgs field profile in the wall and the presence of cp - violating couplings produces source terms for participating particles . different chiralities couple with different strength when cp is violated and a difference occurs in the reflection and transmission probabilities for the two different chiralities . due to rapid gauge , yukawa and strong sphaleron interactions , the cp - violating source terms are translated into a net left handed weak doublet quark density which is finally converted into a baryon asymmetry by weak sphaleron decays . the asymmetry then diffuses through the bubble wall into the broken phase where the weak sphaleron interactions are exponentially suppressed . subsequent washout of the baryon asymmetry can therefore be kept under control provided the first order phase transition is strong enough . the standard model satisfies the three sakharov criteria , but it can not generate the required value of @xmath1 . this is because the only source of cp violation in the sm comes from the phase @xmath5 in the ckm quark mixing matrix . the baryon asymmetry is @xmath6 , but this value is suppressed by flavor mixing factors @xcite and the resulting asymmetry can not be too large . therefore , the phase transition has to be strongly first order to avoid washing out the produced baryon number , which translates into the criterion @xmath7 @xcite . however , in the standard model , the phase transition is too weakly first order to prevent washout , unless the sm higgs mass is less than 50 gev , far below the present experimental limit @xcite . the situation can be improved in the minimal supersymmetric standard model ( mssm ) as the light right handed top squark contribution to the temperature dependent effective potential can push the value of @xmath8 up to acceptable values even for light higgs masses allowed by experimental searches @xcite . also , supersymmetric extensions of the sm include additional sources , which in general can further enhance the possibilty of baryon asymmetry production during the electroweak phase transition . as a result , a specific region in the mssm parameter space corresponding to a heavy cp - odd higgs boson , a light cp - even higgs boson , a light right - handed stop and a heavy left - handed stop can provide a plausible framework for electroweak baryogenesis . the cp - violating interactions in the mssm arise in the complex phases of the soft supersymmetry breaking terms in the lagrangian and in the phase of @xmath9 . since the largest contributions come from charginos and neutralinos @xcite and less importantly from the right handed stops , only the gaugino mass phases @xmath10 , @xmath11 and @xmath12 , the phase of @xmath9 and the phase of the stop trilinear parameter @xmath13 are relevant for baryogenesis . these phases have to be small , typically @xmath14 , if they are considered individually with sparticle masses @xmath15(tev ) , otherwise they induce contributions to the electric dipole moments ( edms ) of the neutron and electron exceeding experimental limits @xcite . however , these constraints can be avoided if relations among soft breaking parameters ensure cancellations of individual contributions to the edms @xcite . in the most general case this possibility leads to models with light superpartner spectra and cp - violating phases of @xmath15(1 ) @xcite . remarkably , string motivated scenarios with non - universal gaugino masses can be described where such edm cancellations occur naturally as a result of the sm embedding on five - branes @xcite . different methods of calculating the baryon asymmetry , using both classical and quantum boltzmann equations , have produced the required asymmetry , provided that @xmath16 @xcite in agreement with the experimental limits on the edms of the electron and neutron , when the other mssm phases are taken to be zero . in this paper we assume that large phases are allowed by the cancellation mechanism and at the same time the right handed stop is light enough to significantly modify the finite temperature higgs potential . all other sfermions are heavier and their contribution to the higgs potential is boltzmann suppressed . we briefly review the generation of the baryon asymmetry and the phase dependence factorization emphasizing the significance of the @xmath17 phase combination . in the large phase scenario it is then possible that the amount of baryon asymmetry generated at the phase transition is @xmath18 larger than what is observed . we solve the full quantum boltzmann equations to extract the cp violating source terms which also provides enhancement compared to classical boltzmann equations due to quantum memory effects @xcite . it is necessary to wash out some of the asymmetry ; therefore the constraint @xmath7 can be relaxed . we reevaluate the washout calculation using the effects of requiring some washout to occur and derive our limits for the light higgs mass and the right handed stop based on electroweak baryogenesis . we are able to show that even in the one - loop approximation for the temperature dependent effective higgs potential the light higgs mass upper limit can be pushed up to 115 gev without invoking negative values of the right handed stop soft breaking mass parameter @xmath19 , which can lead to color - breaking global minima and scalar potential instability @xcite . in order to calculate the baryon asymmetry of the universe , one has to start with a self - consistent computation of the cp - violating sources resulting from particle interactions with the changing higgs profile in the bubble wall . we follow the procedure of reference @xcite , which uses the closed - time - path formalism of finite - temperature field theory to derive quantum boltzmann equations for higgsinos and stops . quantum memory effects resulting from correct treatment of particle propagation in the plasma strengthen the non - equilibrium character of the the particle scattering off the bubble wall and produce larger source terms . the dominant sources of cp - violation that are relevant to the electroweak baryogenesis scenario comes from the interactions of the higgs fields with charginos and neutralinos . these interactions couple the higgsino and gaugino components of charginos and neutralinos and involve potentially large cp - violating phases originating from the mixing . for the charginos , the cp - violating lagrangian in the symmetric phase is @xmath20 the cp - violating phases @xmath21 and @xmath11 are introduced by switching to the basis of mass eigenstates in the broken phase ( see appendix ) . following the steps in @xcite to generate the cp - violating source term in the boltzmann equation , we obtain for any point @xmath22 inside the bubble wall @xmath23 where @xmath24 and @xmath25 characterizes the temporal variation of the higgs profile @xmath26 as the wall passes through point @xmath22 . @xmath27 is a temperature dependent phase - space integral ( the explicit form can be found in @xcite ) and includes information about thermal behavior of the winos and higgsinos in the high temperature plasma . the neutralino cp - violating interactions are @xmath28 + h.c.\ ] ] following the same steps as in the chargino case , we find the source term @xmath29 we can combine the source terms for the charginos and neutralinos to obtain the total source term for higgsinos @xmath30 where @xmath31 . here we emphasize that the source dependends on the full physical ( reparametrization invariant ) combinations of the phases @xmath32 and @xmath33 which factorize from the rest of the source term . in this sense our considerations are independent of the particular details going into the calculation of the higgsino thermal production rate . the phase space integrals @xmath27 and @xmath34 exhibit strong resonant behavior leading to a maximum for @xmath35 ( @xmath36 ) @xcite . in terms of the soft breaking parameters the enhancement occurs when the gaugino masses @xmath37 or @xmath38 are close in value to the higgsino mass parameter @xmath9 . for similar reasons it is easy to understand why the right handed stop contribution to the cp - violating source is always subdominant . the corresponding phase - space integral @xmath39 is typically far away from its maximum as @xmath40 in our framework and the stop source can therefore be neglected . the baryon asymmetry can be directly related to the higgsino source by solving a set of coupled diffusion equations for the higgs and higgsino , top and stop , and the first two generation quark and squark densities @xcite . we assume that strong sphaleron transitions and interactions induced by the top yukawa coupling are very fast , allowing us to reduce the number of relevant equations to the diffusion equations for higgses and higgsinos and baryon number . they can be solved analytically , with the result @xmath41 where @xmath42 is an effective diffusion constant , @xmath43 is the weak sphaleron transition rate , and @xmath44 is the velocity of the bubble wall . the coefficient @xmath45 is determined by boundary conditions to be @xmath46 where @xmath47 and @xmath48 is an effective decay constant . once the phase transition has occurred , weak sphaleron transitions tend to erase any asymmetry that has been created . in the broken phase , the weak sphaleron rate is @xcite @xmath49 where @xmath50 and @xmath51 @xmath52 is a constant in the range @xmath53 . the differential equation satisfied by @xmath54 in the broken phase is @xmath55 where c is a number of @xmath15(1 ) @xcite and we take @xmath56 absorbing the uncertainty into the uncertainty of @xmath52 and @xmath57 . solving ( 14 ) we get @xmath58 the traditional bound is found by assuming that all of the washout happens at @xmath59 , which amounts to saying that the integral in equation ( 3.5 ) is equal to the value of the integrand at @xmath59 . however , we want to evaluate the integral more carefully , and in the process derive a new bound . since we do not have an analytic formula for @xmath60 , we need to examine the integrand to see if we" +"the bogoliubov de gennes ( bdg ) equation and the gap equation describe spatially inhomogeneous states in various kinds of condensed matter systems , such as superconductors@xcite , polyacetylene@xcite , and ultracold atomic fermi gases . the equivalent equations also appear in the mean field theory of the nambu jona - lasinio ( njl ) or the chiral gross neveu ( gn ) model in high - energy physics@xcite . + it is generally a difficult problem to obtain a self - consistent exact solution satisfying not only the bdg equation but also the gap equation , and only a few analytic examples were known so far such as the one- and two - kink ( polaron in polyacetylene ) solutions @xcite and the real@xcite and complex@xcite kink - crystals . recently , the present authors have determined the most general self - consistent solutions under uniform boundary conditions@xcite . the solutions describe @xmath0-soliton states , in which their positions are arbitrary but their phase shifts must be discretized . more recently , these solutions have been generalized to the time - dependent case@xcite . in this paper , we show several complementary results , which were absent in the previous our work . first , we prove _ directly from the gap equation _ that the self - consistent soliton solutions need to have reflectionless potentials , using the form of jost solutions derived from the riemann - hilbert approach@xcite . in the preceding works , this fact was proved by the functional derivative with respect to the reflection coefficient@xcite . our derivation will be more comprehensive because we can see directly how the reflection coefficient vanishes . next , we give the self - consistent condition of the system consisting of only right - movers , which is more used in high - energy physics . the resultant condition is consistent with the time - independent case of the recent work@xcite . ( color online ) schematic of the andreev approximation . the left ( right ) figure shows the dispersion relation before ( after ) the andreev approximation . the red dashed line represents the dispersion relation of free particles and holes and the blue solid line represents the dispersion relation of quasiparticles in the gapped system . ] the one - dimensional bdg system is given by the bdg equation and the gap equation as a self - consistent condition @xmath1 where @xmath2 with a fermi momentum @xmath3 and a magnetic field @xmath4 . in this paper we only consider the case @xmath5 . following the andreev approximation , we linearize the dispersion relation around the fermi points by substituting @xmath6 near the right and left fermi point @xmath7 and ignoring second - order derivatives ( see fig . [ fig : andapp ] ) . moving to the new unit with @xmath8 , we obtain the bdg equation for the right- and left - movers @xmath9 and the gap equation @xmath10 if we consider the system consisting of only right - movers , the fundamental equations are given by @xmath11 which corresponds to the njl or the chiral gn model@xcite . + henceforth , when we cite eq . ( x ) from our letter @xcite , we write it as eq . similarly , eq . ( y ) in the supplemental material of our letter @xcite is written as eq . we assume that the gap function @xmath12 satisfies the finite - density boundary condition ( s.2 ) . since the solution of the bdg equation for left - movers is expressed by the one for right - movers [ eq . ( l.21 ) ] , we can write down the gap equation only using the quantities of right - movers , and we always do so and omit the subscript r hereafter . + we use the same definitions of right and left jost solutions @xmath13 and the transition coefficients @xmath14 and @xmath15 in ( s.10)-(s.17 ) , where @xmath16 is a uniformizing variable defined by @xmath17 and @xmath18 [ eq . ( l.10 ) ] . in order to fit the notations with ref . @xcite , we define the scattering states @xmath19 and bound states @xmath20 using the left jost solution as follows : @xmath21 where @xmath22 is a discrete eigenvalue satisfying @xmath23 , and @xmath24 is a normalization constant of the @xmath25-th bound state ( see ref . @xcite for more detail ) . we also write @xmath26 and @xmath27 . if @xmath12 is a reflectionless potential , they reduce to ( l.18 ) and ( l.19 ) with the linear equation ( l.13 ) , or equivalently , ( s.83 ) and ( s.84 ) with ( s.79 ) . the asymptotic form of scattering states are given by @xmath28 s^{-1}\end{pmatrix}\mathrm{e}^{\mathrm{i}k(s)x } & \!\!(x\rightarrow-\infty ) \\ \mathrm{e}^{\mathrm{i}\theta\sigma_3}\left[a(s)^ * \begin{pmatrix } 1 \\[-0.75ex ] s^{-1}\end{pmatrix}\mathrm{e}^{\mathrm{i}k(s)x}-b(s)\begin{pmatrix}s^{-1 } \\[-0.75ex ] 1 \end{pmatrix}\mathrm{e}^{-\mathrm{i}k(s)x}\right]&\!\!(x\rightarrow+\infty ) . \end{cases } \label{eq : reful301 } \end{aligned}\ ] ] the transmission and reflection coefficients are defined by @xmath29 and @xmath30 . + for a system with both right- and left - movers described by eqs . ( [ eq : bdglr01 ] ) and ( [ eq : bdglr02 ] ) , we consider the same occupation state considered in ref . @xcite . as we derive in the next section , the gap equation in the infinite - length limit is given by @xmath31\frac{\mathrm{d}s}{2\pi}\left ( \frac{m}{2}\left ( u(x , s)v(x , s)^*+r(s)^*u(x , s)^2 \right)-\frac{\delta(x)}{2s } \right)\ ! , \label{eq : gapeqforlr } \end{aligned}\ ] ] which gives the generalization of eq . ( l.27 ) with a non - vanishing reflection coefficient @xmath32 . for a system with only right - movers described by eq . ( [ eq : bdgr01 ] ) , we also consider the similar occupation state , in which the negative - energy scattering states are completely filled and positive ones are empty , and the bound states are filled partially . writing the filling rate of the @xmath33-th bound state as @xmath34 , we obtain the following gap equation in the next section : @xmath35 in this section , we derive the gap equation in the infinite - volume limit . in order to avoid the mathematical difficulty of infinite systems , we first treat the finite system with the length @xmath36 in the interval @xmath37 $ ] , and take the limit @xmath38 . to include the effect of solitons phase shifts , we consider the following `` twisted '' periodic boundary condition : @xmath39 we note , however , that the final expression eq . ( [ eq : gapssinf01 ] ) below does not depend on the detail of the boundary condition . we assume that @xmath36 is sufficiently large and hence the asymptotic form of the left jost solution ( [ eq : reful301 ] ) can be used in the substitution at @xmath40 . then , after a straightforward calculation , we obtain a set of discretized scattering eigenstates satisfying the boundary condition ( [ eq : reful303 ] ) , which is given by @xmath41 with the discretization condition @xmath42 now we move to the derivation of the gap equation in the infinite - length limit . since @xmath43 , the relation , @xmath44 , follows . when @xmath36 is sufficiently large , the wavenumbers of discretized eigenstates are given by @xmath45 with an integer @xmath0 . therefore the sum is replaced by @xmath46 thus , the contribution of positive- ( negative- ) energy scattering states to the gap equation can be evaluated as @xmath47 to obtain the last line , we have used eq . ( [ eq : reful203 ] ) and the relations @xmath48 and @xmath49 , which can be shown using the relations @xmath50 and @xmath51 valid for real @xmath52 . using the expression ( [ eq : gapssinf01 ] ) , and following the same discussion in ref . @xcite , we obtain the gap equation ( [ eq : gapeqforlr ] ) . by a similar procedure , we also obtain eq . ( [ eq : gapeqforr ] ) for a system with only right - movers . the gelfand - levitan - marchenko ( glm ) equation , which determines the kernel @xmath53 of the integral representation for the left jost solution [ eq . ( s.40 ) ] , is given by eqs . ( s.59)-(s.62 ) . if we rewrite them in the matrix form using the relation ( s.43 ) , we obtain @xmath54 with @xmath55 . following the result of the riemann - hilbert approach @xcite , the kernel @xmath53 can be written as @xmath56 by substituting eq . ( [ eq : rhk01 ] ) into the integral representation of @xmath57 [ eq . ( s.40 ) ] , and recalling the notations for scattering and bound states introduced in eq . ( [ eq : reful401 ] ) , we obtain @xmath58\mathrm{e}^{\mathrm{i}k(s)x } \label{eq : rhscat001 } \\ \intertext{and } \begin{pmatrix } f_j(x ) \\ s_jf_j(x)^ * \end{pmatrix}&=-\left [ \begin{pmatrix } 1 \\ s_j \end{pmatrix}+\int_{-\infty-\mathrm{i}0}^{\infty-\mathrm{i}0}\frac{\mathrm{d}\zeta}{2\pi\mathrm{i } } r(\zeta)^*\begin{pmatrix } u(x,\zeta ) \\ v(x,\zeta ) \end{pmatrix}\frac{\mathrm{e}^{\mathrm{i}k(\zeta)x}}{(1-\zeta s_j^{-1})}\right . \nonumber \\ & \qquad\qquad\qquad\qquad\qquad \left . + \frac{2\mathrm{i}}{m}\sum_l\begin{pmatrix}f_l(x ) \\ s_lf_l(x)^*\end{pmatrix}\frac{e_l(x)}{s_l - s_j^{-1 } } \right]e_j(x ) . \label{eq : rhbound001 } \end{aligned}\ ] ] here , we have used the relation @xmath59 for real @xmath60 . note that eqs . ( [ eq : rhscat001 ] ) and ( [ eq : rhbound001 ] ) provide a closed set of equations for left jost solutions expressed without using the kernel @xmath53 . using the relation @xmath61 ( prop . 2 of supplemental material of ref . @xcite ) and eq . ( [ eq : rhk01 ] ) with changing variable @xmath62 , we obtain @xmath63 when @xmath64 , eqs . ( [ eq : rhscat001 ] ) , ( [ eq : rhbound001 ] ) and ( [ eq : rhgap01 ] ) reduce to eqs . ( l.19 ) , ( l.13 ) , and ( l.14 ) . using the first components of eqs . ( [ eq : rhscat001 ] ) and ( [ eq : rhbound001 ] ) and eq . ( [ eq : rhgap01 ] ) , after a little long calculation , we obtain @xmath65 for real @xmath16 . here @xmath66 is defined by @xmath67 ( see ref . @xcite for more detail ) . using eq . ( [ eq : afterlong01 ] ) and the formulae @xmath68,\quad \int\frac{(1-\zeta^2)\mathrm{d}s}{(s-\zeta)(1-\zeta s)}=\log\frac{s-\zeta}{1-\zeta s } , \end{aligned}\ ] ] we obtain @xmath69+\frac{m}{2}\int_{-\infty}^\infty\frac{\mathrm{d}s}{2\pi}r(s)^*u(x , s)^2\left [ \frac{\log s^2}{\mathrm{i}\pi}-\operatorname{sgn}s \right ] . \end{aligned}\ ] ] because of linear independence of @xmath70 s and @xmath71 s , we finally obtain @xmath72 for @xmath73 and any real @xmath16 , and we thus conclude the reflectionless property @xmath74 . on the other hand , for the system with only right - movers , the gap equation [ eq . ( [ eq : gapeqforr ] ) ] becomes @xmath75+\frac{m}{2}\int_{-\infty}^\infty\frac{\mathrm{d}s}{2\pi}r(s)^*u(x , s)^2\left [ \frac{\log s^2}{2\mathrm{i}\pi}+h(-s ) \right ] , \end{aligned}\ ] ] where @xmath76 is the heaviside step function . thus the self - consistent condition is given by @xmath77 for @xmath73 and any real @xmath16 . the result @xmath78 is consistent with the recent work@xcite . in this paper , we have proved that the self - consistent soliton solutions must have reflectionless potentials . combining this paper and our previous work@xcite , we can provide the fully self - contained derivation of static self - consistent solutions under the uniform boundary condition . one of future problems is to generalize the solutions with modulated background , using the solution recently obtained in ref . @xcite . p. g. de gennes , _ superconductivity of metals and alloys _ ( westview , 1999 ) . h. takayama , y. r. lin - liu , and k. maki , phys" +"atlas ( _ a toroidal large acceptance spectrometer _ ) is one of two multi - purpose particle detector experiments designed to explore physics produced at the energy frontier with colliding proton beams at the lhc . built around one of the crossing points for lhc beams , atlas utilizes a highly granular , multi - layered detector construction , based on nearly hermetic @xmath0 geometry with respect to the collision region . the inner tracking volume , immersed in a 2 t solenoidal magnetic field , begins just a few centimeters away from the proton beam axis , extends to a radius of 1.1 meters , and is seven meters in length along the beam pipe . its basic function is to track charged particles by detecting their interactions with the detecting media at discrete points with high precision , revealing detailed information about the type of particle and its momentum . the inner tracker is comprised of three sub - detector layers , nested from the interaction point to the periphery : a silicon pixel detector , a semi - conductor tracker , and a transition radiation tracker . the operational conditions impose stringent requirements on the overall pixel detector design . the expected dose for the innermost layer is assumed to reach 500 kgy within approximately five years of lhc operation . minimum amounts of materials are used for all elements of the pixel detector in order to reduce multiple scattering and secondary interactions . being the innermost tracking sub - system , the pixel detector provides excellent impact parameter resolution and low occupancy per readout channel . its design defines the ability of atlas to identify and reconstruct secondary vertices from the decay of long - lived particles containing heavy quarks , or for flavor - tagging of jets with extremely high overall track multiplicity per event . in addition , the pixel detector provides excellent spatial resolution for reconstructing primary vertices close to the proton - proton interaction region within the detector , with multiple interactions being common at full lhc design luminosity of @xmath1 . the atlas silicon pixel detector ( fig.[fig:01_pixel_overview ] ) contains approximately 80 million readout channels in total . the mechanical detector layout consists of three concentric cylindrical layers located respectively at radii of @xmath2 , @xmath3 and @xmath4 from the beam axis , and two symmetrical end caps with three disks in each , attached to both sides of the barrel region . such layout ensures the design requirement of having at least three pixel hits in the pseudorapidity range of @xmath5 . the 1744 identical pixel modules , each measuring roughly as two centimeters by six centimeters , provide a total sensitive area of @xmath6 . the modules are located on lightweight carbon support structures , with integrated @xmath7 active bi - phase evaporative cooling in place , in order to keep modules at the desired operational temperature of about @xmath8c to minimize irradiation effects and noise . the identical mechanical supports in the barrel layers are called staves . the three barrel layers are built respectively with 22 , 38 , and 52 staves , each holding 13 pixel modules . the disks are made up of sector structures , with each sector holding six modules . each complete disk is comprised of eight sectors . fully assembled , the pixel detector is sized @xmath9 in diameter by 1.3 m in longitude , weighting only 4.5 kg . a more detailed description of the atlas pixel detector can be found in @xcite,@xcite . the basic building block of the active part of the pixel detector is a pixel module ( fig.[fig:02_pixel_module ] ) that is composed of silicon sensors , front - end electronics , and flex - hybrids with integrated control circuits @xcite . all modules are functionally identical at the sensor and at the integrated circuit levels , but differ somewhat in design of the connection points for barrel modules and for disk modules . in order to achieve the nominal design specifications on impact parameter resolution of @xmath10 in the @xmath11 direction , the nominal pixel size is 50 microns in the @xmath12 direction and 400 microns in @xmath13 ( barrel region , along the beam axis ) or @xmath14 ( disk region ) . there are 46,080 pixel electronics channels in each module , being read out by 16 front - end ( _ fe _ ) chips , arranged in 2 columns of 8 chips , which are attached to the sensor pixels by either in or pbsn bump bonds . approximately 13% of the 47232 physical pixels on each sensor have slightly larger dimensions of @xmath15 to allow for a contiguous sensitive area between the fe chip boundaries in the longitudinal pixel direction . in the transverse direction , @xmath16 pixels under each of the two adjacent chips can not be covered by active pixel circuitry . these special pixels are interconnected , or _ ganged _ by the conductive traces on the sensor , with one of @xmath17 neighboring electronics pixels on top of the columns , as is illustrated in fig.[fig:03_ganging ] . the resulting hit ambiguity is resolved by the off - line pattern recognition algorithm @xcite . sensors are the sensitive part of the pixel detector used for charged particle detection , and their function can be loosely compared to microscopic solid - state ionization chambers . the atlas pixel sensors are arrays of bipolar diodes placed on a high resistivity , @xmath18 thick @xmath19-type bulk , with @xmath20 implants on the readout side , and a @xmath21 junctions on the other side of the sensor . the oxygen - enhanced silicon , so - called _ diffusion - oxygenated float zone _ ( _ dofz _ ) , is used , as it has been proven to provide more tolerance to irradiation than the standard float - zone silicon @xcite . the sensors are operated in reverse bias , with full depletion voltages ranging from @xmath22 to @xmath23 , depending on the @xmath21 junction conditions , determined by the irradiation damage . each of the fe readout chips of the atlas pixel detector contains 2880 individual readout cells . there is an analog and a digital circuitry in every pixel cell . the charge created in a pixel by a traversing charged particle is collected and amplified by in - cell charge - sensitive preamplifier in the analog part of a cell s electronics . to reduce the data volume transferred out of the detector , only those hits that produce a charge above an individually adjustable predefined threshold , are read out . the individual threshold level is set in a discriminator at the output of each cell s preamplifier . the hits above threshold are digitized before they are collected in a memory buffer at the front - end chip periphery , including the hit address , the signal s leading and trailing edge time - stamps , and the collected charge measurement determined by the _ time - over - threshold _ ( _ tot _ ) , and stored there for up to @xmath24 . pixel cells are being read - out in columns , with each double - column operated by a separate _ controller end - of - column _ ( _ ceu _ ) unit . the readout buffers with 64-hit capacity are available within each ceu . if the time - stamp of the hit matches with a level-1 trigger signal , the hit is flagged for readout and sent to the _ module controller chip _ ( _ mcc _ ) , located on a flex - hybrid printed circuit board , glued to the back of the sensor . the mcc manages _ timing , trigger and control _ ( _ ttc _ ) signals to the front end chips . the mcc can replicate a trigger signal up to 15 times , which allows for readout windows of up to @xmath25 . the flex - hybrid circuit of the pixel sensor also houses the decoupling capacitors and the _ negative thermal coefficient _ ( _ ntc _ ) sensor for temperature measurement . the barrel modules possess an additional flexible layer - a _ pigtail _ , with a connector for a low - mass cable . this low - mass cable connects modules to the _ patch panel _ ( _ pp _ ) , while the disk modules are connected without using the pigtails @xcite . in the atlas pixel detector , optical communication links are used to pass on data and control signals between modules and off - detector readout electronics . the overall schematics of the optical readout communication links is presented in fig.[fig:04_optolinks ] . the optical links are custom made , and are implemented using commercial - grade , expitaxial silicon - based pin diodes for the optical receivers as well as _ vertical cavity surface emitting laser _ ( _ vcsel _ ) arrays bare die , with custom - designed integrated readout control circuits . on - detector optical communication is realized by means of the optical link boards ( the @xmath26 ) , and via the _ back of crate _ ( _ boc _ ) communication cards on the off - detector end . the transmission of the signals from the detector modules to the opto - boards uses _ low voltage differential signaling _ ( _ lvds _ ) electrical connections . these serial connections link the mcc with the _ vcsel driver chips _ ( _ vdc_s ) and the _ digital optical receiver integrated circuits _ ( _ doric_s ) , instrumented on the opto - board pcbs made with beryllium oxide . the communication with each detector module uses individual fibers : one for the downlink and one ( or two for the b - layer boards ) for the uplinks . about @xmath27 of radiation - resilient clear optical fibers interconnect 132 boc cards located in racks inside the atlas cavern , and 272 opto - boards on the detector side . the number of connections per boc depends on the readout speed , which at the full lhc luminosity is designed to be @xmath28 for the b - layer , @xmath29 for the layer-1 and the disks , and @xmath30 for the layer-2 modules . trigger , clock , commands and configuration data travel on the downlink , while event data and configuration read - back data travel on the uplink(s ) . on the downlink , a _ bi - phase mark _ ( _ bpm _ ) encoding is used to send a @xmath30 control stream on the same channel as the @xmath31 bunch crossing clock . decoding of the bpm channel within the doric recovers both the data stream and the clock signal . the use of individual links for every module permits the adjustment of the timing used to associate the hit to a bunch crossing . the timing adjustment is accomplished by changing the delay of the transmitted signal with respect to the phase of the lhc machine reference clock received in the boc @xcite . the differential data output of the module is converted into single - ended current signals in the vdc , driving each vcsel array . output power of the laser arrays is controlled by the @xmath32 voltage , which has the same value for all channels on each opto - board . data are received by the rx plug - in of the boc on the off - detector side , where the phase between the data and the sampling clock are being adjusted for every communications channel @xcite . it was found that the opto - boards require to be maintained at a certain operating temperature for stable , error - free operation . a special system of" +"x - rays from cool stars are a manifestation of magnetic fields generated by the internal dynamos . this by now classical view has not changed despite the discovery of new x - ray phenomenology and the development of new theoretical concepts with which to explain the production of x - rays around stars ( e.g. , accretion , outflows , fluorescence , etc ) . however , with increasing detector sensitivities and the advent of high - resolution spectroscopy , `` stellar environmental issues '' have become of central interest in the area of pre - main sequence stars . the interplay between accretion disks and stellar magnetic fields leads to disk instabilities , ionization and heating of circumstellar material , chemical reactions in cool molecular gas , accretion flows from the disk to the star , outflows , and jets , in all of which x - rays either play a key role or at least provide important diagnostic access . limitations of present - day instrumentation are , however , evident . the following sections summarize selected topics of x - rays from cool stars that have been addressed in recent years using high - resolution spectroscopy from _ xmm - newton _ and _ chandra_. to derive location , structure , and extent of stellar magnetic fields , only radio interferometric methods are available for direct imaging , with their own severe limitations . x - ray photometric studies have made use of rotational modulation or of eclipses ( e.g. , @xcite ) . while appealing for specific studies of individual objects , such methods are constrained to exceptional cases or the fortuitous eclipse geometry of binaries , and are complicated by intrinsic variability ( flares , new emerging flux ) or the superposition of x - rays from two objects . on the other hand , x - ray spectroscopic density measurements have opened a new avenue toward assessing coronal structure . he - like triplets show ratios between the `` forbidden '' and the `` intercombination '' line fluxes that are sensitive to the electron density @xmath0 , the forbidden line being suppressed in high - density environments @xcite . under coronal temperature and density conditions , transitions of cv , nvi , ovii , neix , mgxi , and sixiii are diagnostically useful , with some caveats . first , the density - sensitive range for the latter two exceeds @xmath1 @xmath2 , values that are probably uncommon to most solar - like stellar coronae . second , the densities to which he - like transitions are sensitive increases with the formation temperature of the ion . low densities can not be explicitly measured in very hot plasmas . and third , the maximum formation temperatures of all ions mentioned above are in the range of 110 mk , while active stars reveal dominant electron temperatures up to several tens of mk ( e.g. , @xcite ) . several fe lines are also sensitive to @xmath0 ( e.g. , prominent lines of fexvii and fexxi ; @xcite ) although blends and inaccuracies in the atomic physics parameters make their application challenging . fe lines were already accessible to euv spectroscopy performed by the euve satellite @xcite . triplet flux ratios measured in low - activity stars point to densities common to the solar corona , i.e. , @xmath3 @xmath2 ( e.g. , @xcite ) at temperatures of a few mk . magnetically active main - sequence stars show trends toward higher @xmath0 , typically of a few times @xmath4 @xmath2 , in the cool plasma as diagnosed for example by ovii @xcite while several subgiant active binaries indicate @xmath0 below the low - density limit of o vii @xcite . a rather surprising - and to the present day controversial - result have been indications for _ very high _ @xmath0 ( @xmath5 @xmath2 ) derived from ions forming in _ hot _ plasma ( e.g. , mgxi , sixiii , and fexxi ; see , e.g. , @xcite , and the work referring to euve summarized in ref . the controversies are the following : @xmath6 contradicting measurements using different instruments ; lines that should appear in high - density environments , and some of which were indeed reported from euve spectroscopy , are not present in high - resolution spectra obtained by _ chandra _ , indicating much lower @xmath0 ( @xcite , see fig . [ fig : ness04_f5a ] ) . @xmath6 most high - density measurements straddle the low - density limit of the respective ion . this circumstance makes the measurements extremely vulnerable to inaccuracies in the atomic physics tabulations , and to unrecognized blends in some of the lines . slight modifications then have a dramatic effect on the implied @xmath0 , as can be nicely seen in the analysis presented by ref . this work concluded , from a detailed study of the _ chandra _ hetg spectrum of capella , that @xmath0 measured by the most reliable fexxi line ratio , @xmath7 , is compatible with the low - density limit of this diagnostic ( i.e. , @xmath8 @xmath2 ) . the similarity among the high density values just slightly above the low - density limits for a _ wide variety of stars _ points to a problem in the atomic physics tabulations , while the true densities remain below the low - density limit @xcite . -0.5truecm -0.8truecm -0.7truecm @xmath6 some @xmath0 measurements tend to be systematically different between ionization stages that have similar formation temperatures . in a study of the active binary @xmath9 crb , for example , densities derived from he - like triplets , fexxi and fexxii reaches up to a few times @xmath10 @xmath2 whereas mgxi suggests @xmath11 @xmath2 @xcite . @xmath6 blends , perhaps from as of yet unrecognized lines , may bias the measured line - flux ratios systematically . the resolution of this issue requires very high spectral resolution . detailed studies for the neix triplet and for the mgxi and sixiii triplets are available @xcite . if the density trend described above is real , then coronal loop pressures should vary by 34 orders of magnitude . this obviously requires different magnetic loop systems for the different pressure regimes , with a tendency that hotter plasma occupies progressively smaller volumes @xcite . -0.5truecm -0.8truecm -0.7truecm the most comprehensive surveys of stellar coronal @xmath0 measurements are those given by refs . @xcite and @xcite . these studies concluded that the surface filling factor ( derived from the emission measure , the measured @xmath0 , and a realistic coronal scale height ) of magnetic loops containing _ cool _ x - ray emitting material increases from inactive to moderately active stars but then `` saturates '' at levels of about ten percent ( fig . [ fig : ness04_f13a ] ) . in the most active stars , hot coronal loops are added , with a sharply increasing filling factor . this trend may be a consequence of increasing magnetic interaction in the corona . as one moves from low to intermediate activity levels , more magnetic flux increases the number of active regions . as the packing of active regions becomes denser , more frequent interactions between magnetic features induce more flare - like processes . the increased luminosity , the higher temperatures and the higher densities are then all a consequence of increased flaring and chromospheric evaporation in active regions @xcite . in general , the inversion problem from line flux ratios to density is degenerate , however . the simplest solution usually quoted , namely a plasma at constant density , is the least plausible one . realistic coronae reveal a distribution of electron densities , with infinitely many distributions resulting in the same line flux ratios . the ratio - derived densities are not even linear averages across the emitting volume because of the @xmath12 dependence of the line fluxes . denser volumes contribute disproportionately more x - rays than low - density volumes . the flux ratios thus provide information on possible distributions of volume in density @xcite . -0.1truecm -0.8truecm -0.6truecm doppler information from x - ray spectral lines may open up new ways of imaging coronae of stars as they rotate , or as they orbit around the center of gravity in binaries . first attempts are encouraging although the instrumental limitations are still severe . @xcite reported doppler shifts with amplitudes of @xmath13 km s@xmath14 in x - ray lines of hr 1099 . amplitudes and phases clearly agreed with the line - of - sight orbital velocity of the subgiant k star , thus locating the bulk of the x - ray emitting plasma on the latter rather than in the intrabinary region . periodic line _ broadening _ in yy gem , on the other hand , suggests that both components are similarly x - ray luminous @xcite which is expected because the two m dwarf components show nearly identical fundamental properties @xcite found doppler motions in ar lac to be compatible with coronae on both companions if the plasma is close to the photospheric level . for the contact binary 44i boo , periodic line shifts corresponding to a total net velocity change over the full orbit of 180 km s@xmath14 were found @xcite . from the amplitudes and the phase of the rotational modulation @xcite , the authors concluded that two dominant x - ray sources , one very compact and one extended , were present , both being located close to one of the stellar poles of the larger companion . -0.1truecm -0.8truecm -0.6truecm a comprehensive study involving line shifts and broadening has been presented for the algol binary @xcite . periodic line shifts corresponding to a quadrature velocity of 150 km s@xmath14 clearly prove that the x - rays are related to the k subgiant ( fig . [ fig : chung04_f4 ] ) . however , the amplitude of the shifts indicates that the source is slightly displaced toward the b star , which may be the result of tidal distortions of the k star . excess line broadening ( above thermal and rotational broadening , fig . [ fig : chung04_f6 ] ) can be ascribed to a radially extended corona , with a coronal scale height of at least one stellar radius , which is consistent with expected scale heights of hot coronal plasma on this star . it is quite well established that the solar corona and the solar wind show elemental compositions at variance with the composition of the solar photosphere . in the solar corona , elements with a first ionization potential ( fip ) above @xmath15 ev ( e.g. , c , n , o , ne , ar ) show photospheric abundance ratios with respect to hydrogen , while elements with a smaller fip ( e.g. , si , mg , ca , fe ) are overabundant by a factor of a few ( `` fip effect '' , @xcite ) . current thinking is that a fractionation process , probably involving electric and/or magnetic fields , waves , or pressure gradients , occurs at chromospheric levels where low - fip elements are predominantly ionized and high - fip elements are predominantly neutral ( e.g. , @xcite ) . ions and neutrals can be affected differently by electric and magnetic fields . first recognition of coronal abundance anomalies date back to the earliest stellar spectral x - ray observations ( see summary in @xcite ) . clarification of trends with fip , however , required high - resolution grating spectroscopy . early observations with _ xmm - newton _ uncovered a new , systematic fip - related bias in magnetically active stars : _ low - fip abundances are systematically depleted with respect to high - fip elements _ ( @xcite ; fig ." +"given an undirected graph @xmath0 with a set @xmath1 of vertices and an edge set @xmath2 , the bandwidth coloring problem ( bcp ) is to assign a color @xmath3 ( @xmath4 ) to each vertex @xmath5 ( @xmath6 ) such that for each edge @xmath7 the difference between the colors of vertices @xmath5 and @xmath8 must be larger than or equal to the associated edge weight @xmath9 , i.e. , @xmath10 . the objective of bcp is to minimize the number of the colors used , @xmath11 . it is obvious that bcp is a generalization of the classical vertex coloring problem ( vcp),which results in the case where @xmath12 for all distinct pairs @xmath13 . the bandwidth multicoloring problem ( bmcp ) is a generalization of bcp , where each vertex @xmath5 is associated with a positive integer @xmath14 and each edge @xmath7 is associated with an edge weight @xmath9 . bmcp aims to assign @xmath14 distinct colors from 1 to @xmath11 to each vertex @xmath5 ( @xmath6 ) , such that for each edge @xmath7 the difference between the colors of vertices @xmath5 and @xmath8 must be at least the associated edge weight @xmath9 . moreover , for @xmath15 , the difference between any two colors of vertex @xmath5 must be at least @xmath16 , which is the weight of the loop edge of vertex @xmath5 . like bcp , bmcp aims to minimize the number of the colors used , @xmath11 . one can observe that bcp is a special case of bmcp with @xmath17 for all vertices . in addition to their theoretical significance as np - hard problems , bcp and bmcp have a number of relevant real - world applications . for example , the fixed spectrum frequency assignment problem ( fs - fap ) @xcite can be viewed as a simple variant of bcp and the minimum span frequency assignment problem ( ms - fap ) is equivalent to bmcp considered here @xcite . in addition , some other variants of bmcp have also been used to model the corresponding frequency assignment problems in the literature @xcite ( see @xcite for more details about the frequency assignment problems ) . as mentioned in @xcite , bmcp can be converted into bcp by splitting each vertex @xmath5 into a clique with @xmath14 vertices , where each edge of the clique has an edge weight @xmath16 that corresponds to the weight of the loop edge of vertex @xmath5 in the original graph ( see @xcite for an example ) . the resulting new graph has @xmath18 vertices . thus , any approach for bcp can be applied to bmcp directly . for this reason , we focus on solving bcp in this paper . a large number of solution approaches have been reported in the literature . in 1998 , dorne and hao proposed a tabu search algorithm for the t - coloring problem and the set t - coloring problem which are a generalization of bcp and bmcp @xcite . in 2002 , phan and skiena proposed a general heuristic @xcite , called discropt for solving the vertex coloring problem and bcp , and prestwich proposed a hybrid algorithm that combines a local search with constraint propagation for solving bcp and bmcp , called fcns @xcite . subsequently , an extended version of fcns was developed by the same author @xcite . in @xcite , lim et al . developed two hybrid algorithms for solving vcp and its generalizations . in @xcite , chiarandini investigate several stochastic local search algorithms for the set t - coloring problem . in 2008 , malaguti and toth reported an effective evolutionary approach for bcp and bmcp @xcite . recently , mart et al . developed several heuristic approaches for bcp using memory structures in both constructive and improvement methods @xcite . in a very recent work @xcite , lai and l developed a multistart iterated tabu search ( mits ) algorithm for bcp and bmcp . in addition , some other heuristic algorithms were also proposed in the literature to solve ms - fap which is equivalent to bmcp , such as tabu search @xcite , genetic algorithms @xcite , and constraint programming approaches @xcite . recently , path relinking ( pr ) @xcite has attracted special attention in the community of combinatorial optimization , and shows outstanding performances in solving a number of difficult problems , such as unconstrained binary quadratic optimization @xcite , multiple - level warehouse layout @xcite , and flow shop sequencing @xcite . in this paper , we devise a new pr algorithm for the bcp and bmcp problems , which integrates a tabu search ( ts ) algorithm ( for local optimization ) with the population based pr framework . the proposed pr algorithm is assessed on two sets of 66 benchmark instances commonly used in the literature and shows remarkable performances compared to the current best solution methods . the rest of this paper is organized as follows . in section [ pr ] , we describe in detail the pr algorithm proposed in this paper . in section [ results ] , we show our computational results compare them with several best performing algorithms from the literature . in section [ discussion ] , we investigate some key ingredients of the pr algorithm , before concluding the paper in section [ discussion ] . the pr algorithm presented in this paper is a hybrid population algorithm that combines path relinking and local search to achieve a desirable tradeoff between intensification and diversification . the effectiveness of the pr algorithm depends mainly on three components : the pr population scheme , the path relinking procedure , and the local search method . we explain in this section the ingredients of our proposed pr algorithm designed for bcp . bcp can be considered from the point of view of constraint satisfaction by solving a series of @xmath11-bcp problems aiming at searching for a @xmath11-coloring ( @xmath11 being fixed ) that satisfies all edge constraints . starting from a large enough initial @xmath11 , our algorithm seeks to solve the @xmath11-bcp problem , i.e. to find a legal @xmath11-coloring . a @xmath11-coloring is legal if all the edge constraints of bcp are satisfied and is illegal , otherwise . as soon as the @xmath11-bcp problem is solved for the current @xmath11 value , we set @xmath11 to @xmath19 and solve again the new @xmath11-bcp problem . the process is repeated until no legal @xmath11-coloring can be found . therefore , the presented pr algorithm only considers the @xmath11-bcp problem . in general , a combinatorial optimization problem can be represented as a 2-tuple @xmath20 , where @xmath21 represents the search space and @xmath22 represents the objective function defined on @xmath21 . as stated in @xcite , for the @xmath11-bcp problem , the search space @xmath21 can be defined as the set of all possible @xmath11-colorings , including legal and illegal @xmath11-colorings . it should be noted that the same search space is also used for the studies of vertex coloring problem in for instance @xcite . moreover , for a @xmath11-coloring , we define the objective function of the @xmath11-bcp problem as the summation of all constraint violations induced by the @xmath11-coloring . specifically , let @xmath23 be a @xmath11-coloring , the objective function @xmath24 used in this study is written as : @xmath25 where @xmath9 is the edge weight for edge @xmath26 , and @xmath27 and @xmath28 respectively represent colors of vertices @xmath5 and @xmath8 . therefore , a solution @xmath23 with @xmath29 corresponds to a legal @xmath11-coloring . as mentioned above , our pr algorithm falls into the class of population algorithms and consists of four main components : population initialization , local search method , path relinking procedure , and population update . algorithm [ algo_pr ] describes in detail the framework of our pr algorithm . in the algorithm , @xmath30 and @xmath31 respectively represent the best solution found so far and the worst solution in the population in terms of objective function value , @xmath32 is the set of solution pairs @xmath33 and is initially composed of all the possible solution pairs @xmath33 in the population . the pr algorithm starts with an initial population @xmath34 ( line 4 ) which includes @xmath35 different solutions , where each of them is randomly generated and then optimized by the tabu search procedure to reach a local optimum . subsequently , the algorithm enters a while loop ( lines 11 to 25 ) , and at each iteration a solution pair is randomly selected from @xmath32 , and then the path relinking procedure ( line 14 ) and tabu search procedure ( line 15 ) are applied to generate two new offspring solutions . more specifically , for the selected solution pair @xmath33 , two offspring solutions @xmath36 and @xmath37 are generated by building paths from the initial solution @xmath38 to the target solution @xmath39 as well as from @xmath39 to @xmath38 , and then @xmath36 and @xmath37 are respectively optimized by the tabu search procedure . after that , a population update criterion is used to decide whether the obtained solutions should be inserted into the population ( lines 19 to 20 ) . the @xmath32 is updated as follows . first , the solution pair @xmath33 is removed after it has been chosen from @xmath32 for the path relinking procedure ( line 13 ) . second , after the population update , once a reference solution @xmath36 replaces the worst solution @xmath31 in the population , all the solution pairs containing @xmath31 are removed from @xmath32 and all the solution pairs that can be generated by combining @xmath36 with other solutions in the population are added into @xmath32 ( lines 21 to 22 ) . the while loop ends when @xmath32 becomes empty , then the population is recreated ( lines 4 to 7 ) and the above while loop is repeated if the stopping condition is not satisfied . there are several stopping criteria that can be employed for the pr algorithm , such as the maximum number of iterations , the maximum number of iterations during which the best solution can not be improved , the maximum timeout limit , and so on . in this study , our pr algorithm stops when a legal solution ( @xmath11-coloring ) is found or the timeout limit is reached . the pr algorithm presented in this paper has several specific features . first , each solution pair @xmath33 is used to generate two paths by the path relinking procedure : one is from @xmath38 to @xmath39 , the other is from @xmath39 to @xmath38 . therefore , each selected solution pair will generate two new offspring solutions by the path relinking procedure . second , when @xmath32 is empty , we rebuild the population while retaining the best solution @xmath40 in the new population ( lines 4 to 7 ) . in the following subsections , we describe in detail each main component of our pr algorithm . from scratch , an initial population is constructed as follows . we first generate @xmath41 random solutions , where each variable ( or vertex ) of each solution is assigned a random color from 1 to @xmath11 . then , for each generated solution , the tabu search method ( see section [ subsec_ts ] ) is used to optimize it to a local optimum . finally , we choose the first @xmath35 best solutions to form the initial population . * input * : problem instance @xmath42 , the number of colors ( @xmath11 ) , the size of population ( @xmath35 ) * output * : the best @xmath11-coloring @xmath40 found and @xmath43 @xmath44 @xmath45 population_initialization(@xmath46 ) /@xmath47 section [ subsec_initialization_population ] @xmath47/ @xmath48 @xmath49 @xmath50 @xmath51 randomly pick a solution pair @xmath52 @xmath53 @xmath54 ," +"between 2004 and 2005 , three groups propelled graphene to the foreground @xcite . they brought it from the theoretical to the real experimental world by synthetizing it for the first time . indeed , since the pioneering work of wallace in 1947 @xcite very exotic properties had been forcast for this material that remained untested . 3 years after its first synthesis , graphene is up to its promises : room temperature quantum hall effect has been evidenced @xcite together with large coherence length and high electronic mobility @xcite . furthermore , these fundamental properties give a high application potential to graphene , especially in nanoelectronics ( qbits , transistors ) @xcite . outstanding electronic properties @xcite together with a high potential for application explain why graphene is becoming the new star of condensed matter physics . graphene is the name given to one isolated plane of carbon atoms arranged on a honeycomb lattice . the unit cell contains two equivalent carbon atoms ( named a and b ) . the interaction with this pecular lattice makes electrons behave like relativistic massless fermions governed by a dirac like equation . indeed the band structure of graphene shows two bands with a linear dispersion that cross at the fermi level . the crossing point is called the dirac point . the anomalous quantum hall effect of graphene for example is a direct consequence of this band structure . two ways are used to synthetize high crystalline quality samples : either from mechanical exfoliation of highly oriented pyrolitic graphite ( hopg ) @xcite or from sublimation of si from 4h or 6h sic surface @xcite . we focus here on epitaxial graphene on sic since then graphene is directly grown on a substrate and this approach is the only one that could lead to mass production for nanoelectronics needs . it has been shown to produce from few layers of graphite ( flg ) to one unique graphene layer @xcite . high quality graphene is required for transport properties and the development of nanoelectronic applications @xcite . the mastering of the interface morphology is then a priority . the main question one has to answer is how the sic substrate impacts the graphene unique structure . indeed , angle resolved photoelectron spectroscopy ( arpes ) @xcite and transport measurements @xcite showed that the system morphology has a strong effect on the electronic structure of the flg . the crystalline structure of the system has been approached by different techniques ( x - ray diffraction @xcite , low energy electron diffraction ( leed ) @xcite , core level shift ( cls ) @xcite and scanning tunneling microscopy ( stm ) @xcite ) . the existence of a @xmath0 ( hereafter 6r3 ) cell common to the sic substrate and the graphene is rather well established for the si - terminated surface . the c - terminated case is not so clear but the interface geometry does not seem to involve the 6r3 cell and calculations with this geometry are given here only for direct comparison . ab initio calculations using a highly simplified geometry for the interface ( a @xmath1 cell , hereafter r3 ) have established the bufferlayer role of the first c layer that electronically decouples the graphene planes from the substrate @xcite . here we address the actual @xmath0 cell and on the basis of extensive ab initio calculations supported by scanning tunneling experiments we demonstrate that the substrate has a strong effect on the first two carbon layers . the interface c buffer layer is strongly distorted so that it can not be seen as a graphene layer but it should instead be considered as the very beginnings of graphene . its actual structure is elucidated at the atomic scale . moreover , ripples are shown to be generated in the otherwise graphene like second plane . calculation and experimental details are given in part ii . the third part presents the ab initio results for both si- and c - terminated faces , for the buffer layer and for the first actual graphene layer . stm results are compared to ab initio calculations in part iv . ab initio calculations have been performed whithin the density functionnal theory using the code vasp @xcite . ultra soft pseudopotentials ( uspp ) @xcite have been used with a plane wave basis cutoff equal to 211 ev ; the uspp have been extensively tested , especially , the c - short uspp was shown to correctly reproduce the band structure of graphene , graphite and bulk and surfaces of different sic polytypes @xcite . the perdew and wang @xcite formulation of the general gradient approximation is used . brillouin zone integration is performed using the @xmath2 point . calculations have been performed with one or two carbon layers on the si - terminated and c - terminated surfaces of sic . the graphene and the ( 0001 ) sic lattices are nearly commensurate with a 6r3 common cell with respect to sic or a 13x13 cell with respect to graphene . in the following , periodicity expressed with respect to sic ( graphene ) will be referred to -sic ( -g ) for clarity . the calculations are performed in the actual 6r3-sic interface geometry . we used complete and flat graphene layers as a starting point for all the c planes above the sic substrate . this is to account for the arpes results that demonstrated the existence of the @xmath3 bands skeleton for the interface c layer @xcite : these bands are related to the presence of a well developped honeycomb like lattice . when an additional graphene layer is added , the converged geometry of the interface c layer remains unchanged and forms the so - called bufferlayer . the starting buffer layer system ( 1 c layer on sic ) was described by a supercell formed of 4 sic bilayers plus one layer of c atoms arranged on a honeycomb lattice . h atoms are bound to the second sic surface to passivate it and the whole cell contains 1310 atoms . the atomic positions where relaxed so that residual forces on the atoms are lower than 0.015 ev / . the same cell with an additional graphene layer would be too large to keep the computational time within a reasonnable value ( several months had already been necessary to reach convergence for each system ) and we had to restrict the cell to two sic bilayers , the buffer layer and the graphene layer ( 1216 atoms ) . atoms in the lower sic bilayer and the subsequent c plane are kept fixed to bulk positions . because of the limited number of planes used to describe the substrate , forces could not be zeroed in these 3 layers that remain constrained . however , forces in the above graphene , buffer layer and last sic plane could be relaxed to negligible values and the calculation that started from two flat honeycomb lattices reproduces the buffer layer geometry found with the first cell . stm experiments were performed at room temperature , in ultra - high vacuum , using a home made microscope . graphitization of n - type ( nitrogen 1x@xmath4 @xmath5 ) 6h - sic(0001 ) substrates was achieved by successive annealing into uhv , controlled by leed and auger spectroscopy . experiments were done first on the buffer layer surface , and second on a mixed surface with mono- and bilayer graphene areas . the details of the growth process and the determination of layer thickness have been discussed elsewhere @xcite . we used the symmetric stm atomic contrast to identify areas corresponding to monolayer graphene . results have been checked on 2 different substrates with different tips and at different temperatures . fig.1a shows a large scale image of the ab initio total charge density of an uncovered buffer layer ( the picture is identical when it is covered by a graphene layer ) . it has three main characteristics : i ) an obvious apparent 6x6-sic modulation ii ) the 6r3-sic periodicity iii)low regions , separated by boundaries , that form nanograins with an unexpected local 2x2-g symmetry . this gives a mosaic structure to the buffer layer . the 6x6-sic modulation is strongly apparent ( cell in red in fig.1a ) because it is related to the bright spots of fig.1a and fig.1b . it is not a real reconstruction since it is not compatible with translationnal symmetry within the buffer layer : fig.1a and fig.1b show that the local environment of the atoms at the 6x6-sic bright spots is not the same . the 6r3-sic periodicity ( cell in blue in fig.1a ) corresponds to the sic and graphene common cell . it is imposed by the calculation . the mosaic pattern is composed of grains of more or less irregular hexagonal shape , 20wide . the origin of the mosaic structure comes from the superposition of the c honeycomb and sic lattices @xcite . the two lattices do not adjust to each other . the grains ( dark area ) corresponds to regions where the sic and honeycomb lattices match ( in a local 2x2-g or r3-sic symmetry ) . si - c bonds are formed there . it generates the small hexagonal patterns of fig.1a . the local 2x2-g patterns are shifted in adjacent grains , the boundaries also accomodate for this shift . atoms that are not in registry lay higher above the substrate and form boundaries ( light area ) . the fourier transform of the charge density map of the free buffer layer ( fig.1d ) and of the buffer layer covered with a graphene layer ( not shown ) are identical . apart from the 1x1-g graphene and the 6x6-sic spots , one remarkable feature of this ft image is the rather intense spots located around midway from the 1x1-g spots ( but off - axis ) . these spots are also found in the ft of the stm images as shown below . they belong to the reciprocal lattice of the 6r3-sic . their intensity is locally enhanced ( in k - space ) by the presence of small grains with local 2x2-g ( or r3 -sic ) symmetry . we call them 2x2-g spots in the following . additionally , one remarks that the first order spots of the 6r3 reconstruction are missing at the centre of fig.1d ( although higher order spots of the 6r3 are present ) @xcite . the corrugation of the buffer layer is rather large with a lower to upper atom height difference close to 0.12 nm ( fig.1f ) . in contrast to previous models proposed for the buffer layer @xcite , the present structure directly comes from atomic relaxation during ab initio calculation starting from a flat carbon honeycomb lattice on top of the sic surface in the actual 6r3-sic common cell . the resulting morphology is in agreement with cls data that evidence the existence of 2 types of c atoms that are bound or not to si atoms @xcite . ab initio calculations in the 2x2-g structure @xcite demonstrated that the interface c layer has not the electronic structure of graphene but acts as a bufferlayer since it allows growth of subsequent c planes with graphene like dispersion . the present calculations , performed in the actual interface geometry , support this results . it demonstrates that part of the interface layer indeed has the simple 2x2-g geometry . it also further evidences the buffer role of the first c layer since a second c layer , on top of it , presents a ( wavy ) honeycomb lattice . the nanostructuration induced by the substrate in the bufferlayer propagates to the ontop graphene layer . it generates ripples that show up as a 6x6 modulation of the honeycomb lattice in" +"the cosmic microwave background explorer ( cobe ) detection of large angle cmb anisotropy ( smoot et al . 1992 ) has sparked a drive to measure the anisotropy on smaller angular scales with the goal of determining crucial information about the density and expansion rate of the universe , the nature of dark matter , and the spectrum of primordial density perturbations . cobe dmr observations were basically unaffected by extragalactic foreground sources ( banday et al . 1996 , kogut et al . 1994 ) due to the large beam size ( @xmath1 fwhm ) . because the contribution of a point source increases with the inverse of the beam area , observations at higher angular resolution are more sensitive to extragalactic foregrounds , including radio galaxies , bright infrared galaxies ( gawiser & smoot 1997 ) , high - redshift infrared galaxies ( blain et al . 1998 , gawiser , jaffe , & silk 1998 , hereafter gjs ) , and the sunyaev - zeldovich effect from galaxy clusters ( aghanim et al . 1997 ) . estimates of extragalactic foreground confusion are critical as many ground - based , balloon - borne , and satellite experiments ( map , planck surveyor ) plan to study cmb anisotropies at angular scales from 5@xmath2 to @xmath3 , and preliminary results are already available ( e.g. netterfield et al . 1997 , scott et al . 1996 ) . to evaluate the impact of known radio sources on cmb anisotropy observations , we use flux data from a variety of catalogs ( see @xmath42 ) , including recent measurements , to construct models of source spectra as a function of frequency . we analyze simulated skymaps at frequencies from 10 to 300 ghz to determine the expected contribution of radio galaxies to foreground confusion of cmb temperature anisotropy . this information will be useful when choosing frequencies and regions of the sky to observe cmb fluctuations on small angular scales . this work represents a significant improvement over previous efforts ( toffolatti et al . 1995 , 1998 , franceschini et al . 1989 ) which depended upon galactic evolution models to predict the contribution of simulated radio sources at microwave frequencies . our catalog contains detailed observations of known sources and hence can be used to make a spatial template for masking out their emission , and we believe that this phenomenological approach will lead to greater accuracy in predicting source counts and the overall level of foreground anisotropy . the discrete radio sources used in this project were compiled from a number of separate catalogs . our current catalog includes flux measurements and their corresponding errors at multiple frequencies for 2207 sources . we have focused our attention on obtaining all available radio observations at millimeter and sub - millimeter wavelengths , resulting in 5766 observations of 758 different sources at 90 ghz , 890 observations of 229 different sources from 100 - 200 ghz , and 2628 observations of 309 different sources at frequencies above 200 ghz . the sources are roughly isotropic in distribution , except for a significantly greater number of sources in the northern celestial hemisphere due to the anisotropic distribution of radio telescopes on earth . in addition , there are noticeably fewer observations within @xmath5 of the galactic plane and the celestial north pole due to the difficulty of observing extragalactic radio sources in those locations . our catalog includes the full - sky 5 ghz - selected 1 jy sample of khr et al . we add high - frequency ( @xmath6 ghz ) measurements ( steppe et al . 1988 , 1992 , 1995 ; tornikoski et al . 1996 ; kreysa 1998 ; antonucci , barvainis , & alloin 1990 ; beichman et al . 1981 ; chini et al . 1989 ; gear et al . 1994 ; edelson 1987 ; holdaway , owen , & rupen 1994 ; knapp & patten 1991 ; landau et al . 1980 , 1983 , 1986 ; lawrence et al . 1991 ; nartallo et al . 1997 ; owen et al . 1978 ; owen , spangler , & cotton 1980 ; stevens , robson , & holland 1996 ; chandler 1995 ; vla memo#193 ) and centimeter - wavelength observations ( herbig and readhead 1992 ; patnaik 1992 ; wiren et al . 1992 ; stanghellini et al . 1997 ; perley 1982 ; cotton 1980 ; aller et al . 1985 ; vla calibrator manual ) . an updated version of the catalog with more detail will be described by gawiser , sokasian , & smoot ( 1998 , hereafter gss ) . some extragalactic radio sources have complex spectra which can not be approximated by simple functional forms due to emission from both compact and extended structures which dominate at different frequencies . in most radio galaxies , the emission comes from radio lobes located symmetrically around the core . the dominant emission mechanism , synchrotron , can be well approximated by a simple power law , @xmath7 with a flux spectral index , @xmath8 , typically between 0.5 and 1.0 ( platania et al . 1997 ) . some radio sources have compact active nuclei which generate flat - spectrum radio emission . the spectra of these sources can be inverted ( @xmath9 ) for most of the radio frequency range due to self - absorption of the lower frequency emission . attempts to fit the observational data have yielded a variety of results . the central engine of a typical active galaxy may consist of a supermassive black hole surrounded by an accretion disk and accelerating a jet of relativistic particles perpendicular to the disk plane ( e.g. urry & padovani 1991 ) . bttcher et al . ( 1997 ) proposed a model in which the inverted spectrum of ngc 3031 is assumed to be the emission of a jet component , becoming optically thin to the radio emission of a monoenergetic pair plasma at decreasing frequencies as it moves outward and expands . for sources which lack direct high - frequency observations , we avoid trying to determine the nature of the emission mechanism instead , we use a phenomenological approach based on the expectation that the spectra of most radio sources approach power law behavior at frequencies higher than @xmath10 ghz ( verschuur & kellerman 1988 ) . this power law may then be used to extrapolate the spectrum to typical cmb observation frequencies . a previous phenomenological approach ( tegmark & efstathiou 1996 ) extrapolated 1.4 ghz source counts by assuming flat - spectrum emission for all sources . our method has the advantages of using the actual source locations , which can be turned into templates for masking the brightest pixels on the sky . to determine if there is any spectral index clustering , we use sources that have been measured near 1.4 , 10 , and 90 ghz and plot each source s spectral index from 1.4 ghz to 10 ghz versus its index from 10 ghz to 90 ghz in figure 1 . there is a vague clustering of bright sources ( circles ) consistent with the notion that the brightest sources selected at low frequencies tend to have steep spectra . the overall scatter of source spectra in figure 1 shows that it is wrong to categorize radio sources into template spectra or a narrow spectral index range . this motivates us to fit the spectra of each source individually . to determine the frequency beyond which a power law ( a line on a log - log plot ) can be fitted to the spectra of a given source , we use an iterative model which starts with the best - fit line to the three highest frequency data points and repeatedly includes the next highest frequency data point to the set to which it fits a line . the fitting stops when the reduced @xmath11 starts to get worse or becomes acceptable ( @xmath12 ) . there is little evidence that inverted spectra are common past 30 ghz ( steppe et al . 1995 , stanghellini et al . 1997 ) , so we set the few inverted ( @xmath13 ) high - frequency spectra in the catalog to flat ( @xmath14 ) spectra . these inverted spectra appear to result from variable sources being observed at different epochs at different frequencies , and we find that most of the sources with @xmath15 in figure 1 based on their mean 10 and 90 ghz fluxes are better fit by an @xmath13 power - law when all observations are taken into account . the average high - frequency spectral index was 0.5 with 27% of the sources in our catalog having steep spectra ( @xmath16 ) , and 37% having flat spectra ( @xmath17 ) . to check the accuracy of this technique , we ran our extrapolation method on sources with observations at 90 , 150 , and 230 ghz while ignoring the observations above certain frequencies and then compared the measured fluxes with the extrapolated fluxes . the results ( table 1 ) show that the extrapolation method works best when there is at least one measurement at 20 ghz or greater , as expected since many spectra become power - law past 5 ghz . table 1 shows that on average we overpredict the flux at 90 ghz by a factor of 1.6 , even when measurements above 20 ghz are used . however , the median such error factor is only a factor of 1.1 overestimate , so we have roughly an equal number of over- and under - estimates . this is no longer the case at 230 ghz , where even the median error factor is 1.9 ; our extrapolation method is overestimating the typical flux due to flat spectra falling off to more typical synchrotron spectra at frequencies around 100 ghz ( gear et al . it is difficult to predict how far this fall - off will last , as thermal emission from low levels of dust in these radio - bright galaxies are expected to dominate their spectra by 500 ghz , except for the bl lacs which have flat spectra up to infrared wavelengths ( knapp & patten 1991 , chini et al . 1989 , landau et al . we therefore only trust our extrapolation in the range that has been tested , up to a maximum frequency of 300 ghz . as the radio sources that have been observed at 30 - 300 ghz were selected at lower frequencies for brightness and flat spectra , our errors are only good estimates for this type of radio sources . this selection effect is not a great concern , however , as those are exactly the type of radio sources that threaten cmb anisotropy observations . when interpolation is required , we use a cubic spline which passes through the mean fluxes at the observed frequencies . we visually inspected all 2207 sources to check the algorithm and eliminate any serious errors or outliers . for planned cmb anisotropy experiments , an additional concern is that the flat - spectrum radio sources can vary by up to a factor of ten in flux since their emission comes from a compact , active core . typical variations occur on timescales of one month to one year , although the overall spectrum shape is often preserved for a decade or longer ( tornikoski et al . we use the scatter in the observed fluxes of a source at each frequency to estimate the typical range of variability , which yields an error bar on the source s flux at that frequency about the mean of all observations . because the variations are not periodic , there is little more that can be done , unless" +"rna is an important biopolymer critical to all living systems @xcite and may be the crucial entity in prebiotic evolution @xcite . like for dna , there are four types of nucleotides ( or bases ) a , c , g , and u which , when polymerized can form double helical structures consisting of stacks of stable watson - crick pairs ( a with u or g with c ) . however unlike a long polymer of dna , which is often accompanied by a complementary strand and forms otherwise featureless double helical structures , a polymer of rna usually `` operates '' in the single - strand mode . it bends onto itself and forms elaborate spatial structures in order for bases located on different parts of the backbone to pair with each other , similar conceptually to how the sequence of an amino acid encodes the structure of a protein . understanding the encoding of structure from the primary sequence has been an outstanding problem of theoretical biophysics . most theoretical work in the past decade have been focused on the problem of protein folding , which is very difficult analytically and numerically @xcite . here , we study the problem of rna folding , specifically the formation of rna _ secondary structures_. for rna , the restriction to secondary structures is meaningful due to a separation of energy scales . it is this restriction that makes the rna folding problem amenable to detailed analytical and numerical studies @xcite . there exist efficient algorithms to compute the exact partition function of rna secondary structures @xcite . together with the availability of carefully measured free energy parameters @xcite describing the formation of various microscopic structures ( e.g. , stacks , loops , hairpins , etc . ) , the probable secondary structures formed by any given rna molecule of up to a few thousand bases can be obtained readily . on the experimental side , rna molecules of @xmath1 @xmath2 bases in length are available . furthermore , the restriction to secondary structures can be physically enforced in a salt solution with monovalent ions , e.g. , @xmath3 , so that controlled experiments are in principle possible @xcite . in this work , we are not concerned with the structure formed by a specific sequence . instead , we will study the statistics of secondary structures formed by the ensemble of _ long _ _ random _ rna sequences ( of at least a few thousand bases in length in practice ) . such knowledge may be of value in detecting important structural components in messenger rnas which may otherwise be regarded as random from the structural perspective , in understanding how functional rnas arise from random rna sequences @xcite , or in characterizing the response of a long single - stranded dna molecule to external pulling forces @xcite . more significantly from the theoretical point of view , the rna secondary structure problem presents a rare tractable model of a random heteropolymer where concrete progress can be made regarding the thermodynamic properties @xcite . nevertheless , there are many gaps in our understanding . this paper is a detailed report of our on - going effort in this regard . it provides a self - contained introduction of the random rna problem to statistical physicists as a novel problem of disordered systems , and depicts several approaches we have tried to characterize this system . the manuscript is organized as follows : in sec . [ sec_secondarystructure ] , we provide a detailed introduction to the phenomenology of rna secondary structure formation . we review the key simplifications which form the basis of efficient computing as well as exact solutions in some cases . we also review the properties of the molten phase "" , which is the simplest possible phase of the system assuming sequence disorder is not relevant . in sec . [ sec_randomnesshight ] , we consider the effect of sequence disorder at high temperatures . we show numerical evidence that the random rna sequence is in the molten phase at sufficiently high temperatures , and support this conclusion by solving the two - replica system which can be regarded as a perturbative study on the stability of the molten phase . in sec . [ sec_randomnesslowt ] , we provide a scaling argument , and show why the molten phase should break down at low enough temperatures . this is followed by a detailed numerical study of the low temperature regime . we apply the droplet picture and characterize the statistics of large - scale , low - energy excitations of the secondary structures from the ground state structure . our results support the existence of a very weak ( i.e. , marginal ) glass phase characterized by logarithmic excitation energies . finally , we describe the intermediate temperature regime where the system makes the transition from the glass phase to the molten phase . the solution of the two - replica problem is relegated to the appendices . we present two approaches : in appendix [ app_intuitive ] , we provide a mapping of the two - replica problem to the denaturation of an effective single rna in @xmath0-dimensional embedding space ; this approach highlights the connection of the rna problem to the self - consistent hartree theory and should be most natural to field theorists . in appendices [ app_solution ] and [ app_derivez1 ] , we present the exact solution . it is hoped that the two - replica solution may be helpful in providing the intuition needed to tackle the full @xmath4-replica problem . the secondary structure of an rna describes the configuration of base pairings formed by the polymer . if the pairing of the @xmath5 and @xmath6 bases in a polymer of @xmath7 total bases is denoted by @xmath8 with @xmath9 , then each secondary structure @xmath10 is defined by a list of such pairings , with each position appearing at most once in the list , and with the pairs subject to a certain restriction to be described shortly below . each such structure can be represented by a diagram as shown in fig . [ fig_diagrams ] , where the solid line symbolizes the backbone of the molecule and the dashed lines stand for base pairings . the structure shown can be divided into _ stems _ of consecutive base pairs and _ loops _ which connect or terminate these stems . in naturally occurring rna molecules , the stems typically comprise on the order of five base pairs . they locally form the same double helical structure as dna molecules . however , while the latter typically occur in complementary pairs and bind to each other , rna molecules are mostly single - stranded and hence must fold back onto themselves in order to gain some base pairings . by a secondary structure , one often considers only the restricted set of base pairings where any two base pairs @xmath8 and @xmath11 in a given secondary structure are either independent , i.e. , @xmath12 , or nested , i.e. , @xmath13 . this excludes the so - called pseudo - knots ( as exemplified by fig . [ fig_pseudoknot ] ) and makes analytical and numerical studies much more tractable . for an rna molecule , the exclusion of pseudo - knots is a reasonable approximation because the long pseudo - knots are kinetically difficult to form , and even the short ones occur infrequently in natural rna structures @xcite . the latter is due to their relatively low binding energies for short sequences and the strong electrostatic repulsion of the backbone because the polymer backbone is highly charged and pseudo - knotted configurations increase the density of the molecule , their formation can be relatively disfavored in low salt solution . similarly , the tertiary structures which involve additional interactions of paired bases are strongly dependent on electrostatic screening and can be turned off "" experimentally by using monovalent salt solution @xcite . indeed , the pseudo - knots are often deemed part of the tertiary structure of an rna molecule . throughout this study , we will exclude pseudo - knots in our definition of secondary structures . without the pseudo - knots , a secondary structure can alternatively be represented by a diagram of non - crossing arches or by a mountain "" diagram as shown in fig . [ fig_strreps ] . : in ( a ) the solid line symbolizes the stretched out backbone of the molecule while the dashed arches stand for the base pairs formed . due to the no pseudo - knot constraint two arches never cross . ( b ) shows an equivalent representation as a `` mountain diagram '' . it is a line derived from the arch diagram by going along the backbone from left to right and going one step up for every beginning arch , horizontally for each unbound base , and one step down for each ending arch . such a mountain always stays above the baseline and comes back to the baseline at base @xmath7 . ] in order to calculate boltzmann factors within an ensemble of secondary structures , we need to assign an energy @xmath14 $ ] to each structure @xmath10 . each secondary structure can be decomposed into elementary pieces such as the stems of base pairs and the connecting loop regions as shown in fig . [ fig_diagrams ] . a common approach is to assume that the contributions from these structural elements to the total energy are independent of each other and additive . within a stem of base pairs , the largest energy contribution is the _ stacking energy _ between two adjacent base pairs ( g - c , a - u , or g - u ) , and the total energy of the stem is the sum of stacking energies over all adjacent base pairs . since each secondary structure is defined as a _ single _ state in our ensemble , it is necessary to integrate out all other microscopic degrees of freedom of the bases within a given secondary structure and use an effective energy parameter for each base stacking . the most convenient one to use is the gibbs free energy of stacking @xcite , which contains an enthalpic term due to base stacking , and an entropic term due to the loss of single - stranded degrees of freedom ( as well as the additional conformational change of the backbone and even the surrounding water molecules ) due to base pairing . the magnitudes of these stacking free energies actually depend on the identity of all four bases forming the two base pairs bracketing the stack and are dependent on temperature themselves . while their typical values are on the order of @xmath15 at room temperature , the enthalpic and entropic contributions are each on the order of @xmath16 . thus , upon moderately increasing the temperature from room temperature to about @xmath17 , the stacking free energies become repulsive and the rna molecule denatures . the stacking free energies account for most but not all of the entropic terms for a given secondary structure . there is an additional ( logarithmic ) `` loop energy '' term associated with the entropy loss of each _ closed loop _ of single - stranded rna formed by the secondary structure , as well as the energy necessary to bend the single strand . all of these energy parameters have been measured in great detail @xcite . when incorporated into an efficient dynamic programming algorithm ( to be described below ) , they can rather successfully _ predict _ the secondary structures of many rna molecules of up to several hundred bases in length @xcite . in this paper , we investigate the statistical properties of long ," +"nonlinearities are important in optical systems since they enable us to manipulate light by light . especially , nonlinearities sensitive to single photons are necessary for quantum optical applications such as optical quantum computation @xcite , entanglement generation @xcite , and quantum non - demolition measurements @xcite . in particular , strong nonlinearities are indispensable for quantum computation , since conditional operations at the single photon level are required to realize elementary gate operations . however , conventional optical media require very high photon densities to obtain significant nonlinear effects @xcite . single atom cavity quantumelectrodynamics may offer a possible solution @xcite . in particular , a cavity can focus all the light in an input beam on a single atom , effectively creating a situation where a single atom is coupled to a one - dimensional light field @xcite . such a one - dimensional atom is an ideal device for the non - linear manipulation of few photon pulses . it is therefore of great interest to investigate the response of a one - dimensional atom to one- and two - photon input pulses . there are many theories for such atom - cavity systems @xcite . however these theories usually eliminate the quantum state of the field outside the atom - cavity system and therefore the analysis of the precise spatiotemporal coherence of the input and output photon pulses can not be achieved . in our previous work , we have therefore presented a theory for one- and two - photon pulses that includes the propagation to and from the system in a bad - cavity regime @xcite , based on a one - dimensional model of light - atom interaction @xcite . in these studies , we focused on the changes of the photon - photon correlations in time @xcite and in frequency @xcite . in this paper , we study the effect of the non - linear interaction with the one - dimensional atom on the shape of one- and two - photon wavefunctions using gaussian input pulses of different pulse lengths . for this purpose , we first introduce an analysis of the interaction in terms of absorption and transmission processes in section [ sec : level2 ] . the characteristic time scale defining the response of the atom is given by the dipole relaxation time @xmath0 . in section [ sec : level3 ] , we then analyze the interaction processes for a long pulse length of @xmath1 in terms of pulse amplitude and pulse delay time . from these results , we can estimate that a maximal non - linear effect should be obtained for a pulse length equal to the dipole relaxation time of the atom . in section [ sec : level4 ] , we therefore analyze the corresponding interaction processes for a short pulse length of @xmath0 , confirming the dominance of the non - linear effect throughout the short two - photon pulse . the results of the analysis are summarized and discussed in section [ sec : level5 ] . the model of a single two - level atom in one - dimensional free space is shown in figure . [ fig : figure1](a ) . in this model , an incoming one - photon or two - photon wavepacket interacts with the atom locally , and the output wavepacket is then emitted into the output field . the physical realization of this model can be implemented by a two - level atom coupled with a single mode of a one - sided cavity in the bad cavity regime @xcite . the cavity geometry is shown in figure . [ fig : figure1 ] ( b ) . the input field of the one - dimensional free space shown in figure . [ fig : figure1 ] ( a ) corresponds to the input of the one - sided cavity in figure . [ fig : figure1 ] ( b ) . likewise , the output field in figure . [ fig : figure1 ] ( a ) corresponds to the output of the one - sided cavity in figure . [ fig : figure1 ] ( b ) . here , we assume that the spontaneous emission rate through the cavity mode is much larger than the spontaneous emission rate through non - cavity modes . in terms of the conventional cavity quantum electrodynamics parameters , this regime is characterized by @xmath2 , where @xmath3 is the cavity damping rate through the left mirror , @xmath4 is the dipole coupling between the atom and the cavity mode and @xmath5 is the rate of spontaneous emission into the non - cavity modes . since the cavity damping rate @xmath3 is much faster than the dipole coupling @xmath4 , the method of adiabatic elimination can be applied to the time evolution of the cavity field @xcite . this means that the interaction between the atom and the outside field through the cavity field can be expressed by an effective dipole relaxation rate @xmath6 . the dipole relaxation rate @xmath7 describes the dipole damping caused by emissions through the left mirror of the cavity , and the corresponding rate of spontaneous emission through the cavity is equal to @xmath8 @xcite . in our case , we assume that the rate of spontaneous emission into the non - cavity modes @xmath5 is negligible ( @xmath9 ) . nearly all emissions from the atom can then be confined to the cavity and 2@xmath7 is the total spontaneous emission rate of the excited atom in the cavity . in present cavity designs , this can be realized by exploiting the purcell effect . for example , in the case of turchette et al.s experiment @xcite , the cavity parameters indicate that about 80% of the sponaneous emission from the atom is emitted through the single cavity mode . ( 0,0 ) ( -10,160)(a ) ( 270,160)(b ) ( a ) schematic of a two - level atom in one - dimensional free space and ( b ) physical realization of the one - dimensional atom using an atom - cavity system . an incoming one - photon or two - photon wavepacket interacts with the atom locally , and the output wavepacket is then emitted into the output field . the input field of the one - dimensional free space shown in ( a ) corresponds to the input of the one - sided cavity in ( b ) . likewise , the output field of the one - dimensional free space shown in ( a ) corresponds to the output of the one - sided cavity in ( b).,title=""fig:"",width=340 ] ( a ) schematic of a two - level atom in one - dimensional free space and ( b ) physical realization of the one - dimensional atom using an atom - cavity system . an incoming one - photon or two - photon wavepacket interacts with the atom locally , and the output wavepacket is then emitted into the output field . the input field of the one - dimensional free space shown in ( a ) corresponds to the input of the one - sided cavity in ( b ) . likewise , the output field of the one - dimensional free space shown in ( a ) corresponds to the output of the one - sided cavity in ( b).,title=""fig:"",width=245 ] in the following , we investigate the effect of the one - dimensional atom on one and two - photon input pulses of different pulse length . for this purpose , we have to formulate the quantum states for a given input pulse shape for both one photon and two photon cases . if the real space representation for the one - photon state reads , @xmath10 the two - photon state can be expressed as the product state @xmath11 the light pulses characterized by the above input states are propagating at the velocity of light in the input field of the schematic shown in figure . [ fig : figure1](a ) . to simplify the expression , the spatial coordinates , @xmath12 and @xmath13 , therefore represent a coordinate system moving at the velocity of light . the indices 1 and 2 of @xmath12 and @xmath13 in eq . ( [ eq : spatialinput ] ) identify the two particles . the spatial features of the probability amplitudes given by the wavefunction @xmath14 correspond to the spatial features of the pulse mode a. thus , the wavefunction @xmath15 characterizes the single mode two - photon wavefunction , where the wavefunctions of both particles overlap perfectly . in our previous work @xcite , we derived the unitary time evolution operator in the hilbert spaces for the one photon component and the two photon component by solving the schrdinger equation of the interaction between a one - dimensional field and a single atom . the output one - photon state in the far field can then be obtained by convoluting the one - photon input wavefunction @xmath16 with the matrix description of the unitary operator in real space , @xmath17 @xmath18 the matrix elements @xmath19 are given by @xmath20 likewise , the output two - photon state in the far field can be obtained by a linear convolution , @xmath21 @xmath22 the matrix elements @xmath23 are given by @xmath24 where the contribution of the non - linear photon - photon interaction is given by @xmath25 . \label{eq : nonlineffect}\end{aligned}\ ] ] the output wavefunctions @xmath26 and @xmath27 describe the spatial feature of the output states in the far field of the atom shown in figure . [ fig : figure1 ] ( a ) . note that the spatiotemporal features of the input one - photon and two - photon wavefunctions are generally not preserved in the output due to the atomic response described by the matrix elements @xmath28 and @xmath29 . the matrix element of the time evolution @xmath28 in eq.([eq : onemat ] ) can be expanded in terms of two interaction processes , @xmath30 where the two processes are ( i ) single photon transmission without absorption , given by @xmath31 and ( ii ) single photon reemission after absorption , given by @xmath32 the output one - photon wavefunction @xmath26 can thus be interpreted as the result of quantum interference of the two processes , @xmath33 where the components are given by @xmath34 in the same way , the matrix element of the time evolution @xmath35 can be expanded in terms of three interaction processes . process ( 1 ) is the transmission of both photons without absorption . process ( 2 ) is the transmission of one photon without absorption and the absorption and reemission of the other photon . process ( 3 ) is the absorption and reemission of both photons . in the following , we will refer to process ( 1 ) as the transmission process , to process ( 2 ) as the one photon absorption process , and to process ( 3 ) as the two photon absorption process . the transformation of the two - photon wavefunction can then be written as @xmath36 the components of @xmath35 read @xmath37 note that the non - linear contribution @xmath38 only occurs in the two photon absorption process . this is because the non - linearity is due to the saturation of the two - level atom , which prevents the absorption of two photons at the same time . likewise , the output wavefunction @xmath39 can be expanded as @xmath40 where the @xmath41 are given by @xmath42 this analysis will be convenient to understand the origin of the statistical properties of the output photons . in the next section , these results are applied to the cases of gaussian one - photon and two - photon input wavepackets . the dependence of the coherent spatiotemporal correlations between the output" +"in the standard big bang cosmology , the amount of heavy elements synthesized in the universe until the decoupling of matter from primordial radiation is negligibly small ; i.e. , @xmath6 where @xmath7 is the mass fraction of heavy elements ( wagoner , fowler , & hoyle 1967 ) . on the other hand , gas clouds in the present - day galaxies have an appreciable amount of heavy elements @xmath8 ; e.g. , the solar heavy element abundance is @xmath9 . this means that chemical and thermal properties of gas clouds in primeval galaxies at high redshift are significantly different from those in the present - day galaxies . just after the recombination of the universe , the hydrogen gas could be in atomic phase at a temperature of @xmath10 k. then the formation of primordial hydrogen molecules can proceed through the gas phase reaction ( e.g. , peebles & dicke 1968 ) . since the rotational and vibrational transitions in hydrogen molecules can cool the gas further , the first generation stars can be born in such gas clouds at redshift @xmath11 - 30 . since the temperature is still much higher than a typical kinetic temperature of molecular gas clouds in the present - day galaxies ( e.g. , @xmath11 k ) , the initial mass function ( imf ) in primeval galaxies may be different from that in the present - day galaxies ; i.e. , a salpeter - like imf ( salpeter 1955 ; scalo 1986 ) . therefore , one of fundamental questions on the star formation in primeval galaxies is ; `` what kind of stars ( i.e. , population iii stars ) were made in such extremely metal deficient gas clouds ? "" [ matsuda , sato , & takeda 1969 ; yoneyama 1972 ; yoshii & saio 1986 ( hereafter ys86 ) ; silk 1977a ; tegmark et al . 1997 ; nakamura & umemura 1999 , 2001a , 2001b ; bromm et al . 1999 , 2001 , 2002 ; coppi et al . 2001 ] . applying the opacity - limited fragmentation theory [ the fragmentation of gas clouds due to the gravitational instability continues until the fragments become to be optically thick to the cooling radiation ( silk 1977b , 1977c ) ] , ys86 first derived an imf for a hydrogen - helium gas cloud . they found that typical masses of the first - generation stars are from several @xmath0 to 10 @xmath0 . nakamura & umemura ( 1999 ) obtained similar results based on their one - dimensional hydrodynamical calculations together with nonequilibrium processes for hydrogen molecule formation . abia et al . ( 2001 ) pointed out that the very large c and n enhancements observed in the extremely metal - poor stars in our galaxy favor a population iii imf peaked at intermediate - mass stars . recently , on one hand , some groups investigated the collapse and fragmentation of primordial , metal - free gas by numerical simulations ( abel , bryan , & norman 2000 , 2002 ; bromm et al . 1999 , 2001 , 2002 ; coppi et al . they showed that the first generation gaseous clumps have masses of @xmath12 which corresponds to the jeans mass of the gas with temperature @xmath13 a few 100 k and the density @xmath14 . as bromm et al . ( 2002 ) assumed , if the clump masses are indicative of the final stellar mass , population iii stars may be more massive than @xmath15 . nakamura & umemura ( 2001a , 2001b ) have developed their hydrodynamical simulations and found that the initial mass function of population iii stars may be bimodal with peaks of @xmath16 @xmath17 and @xmath18 . the mass depends on the initial density and the initial fraction of molecular hydrogen ( @xmath19 ) ( nakamura & umemura 2001b ) . if @xmath20 is larger than @xmath21 for low - density ( @xmath22 @xmath23 ) , the effective hd cooling makes the high mass peak small to @xmath24 . however , if @xmath20 is smaller than @xmath21 , very massive stars with @xmath25 are formed preferentially . in this way , the mass of first - generation stars is controversial . it seems also hard to examine observationally which mode is more feasible ; i.e. , population iii stars are either intermediate - mass star or very massive ones . if most population iii stars are as massive as @xmath25 , they could explode quickly and then contribute to the chemical enrichment of either galaxies or intergalactic medium or both ( e.g. , madau , ferrara , & rees 2001 and references therein ) . since usual population ii stars could be formed in cold gas clouds polluted chemically by first population iii stars , we can not examine observationally whether or not such very massive stars were really formed in the primordial gas clouds . furthermore , according to nakamura & umemura ( 2001a ) , proto - galactic clouds with a higher density tend to form intermediate - mass stars . if such proto - galactic systems are present , their evolution can be governed by evolution of the intermediate - mass stars whose lifetime is @xmath26 yr , being much longer than those of very massive stars . we investigate what happens and follows in such bursts of formation of intermediate - mass stars and discuss effects on the further evolution of galaxies , adopting the imf of ys86 . in particular , intermediate - mass stars experience inevitably the planetary - nebula - nucleus ( pnn ) phase , providing a lot of high - energy photons ( e.g. , vassiliadis & wood 1994 ) . therefore , it is expected that the galaxies appear to be luminous emission - line galaxies during the pnn phase . we discuss how they look and compare our model results with observations of some interesting high - redshift galaxies . in many previous galaxy evolution models , it has been often assumed that stars are formed with a salpeter - like initial mass function ( imf ) in a galaxy ; @xmath27 where @xmath28 is the stellar mass in units of @xmath0 and @xmath29 is a normalization constant determined by the relation @xmath30 which leads to @xmath31 in this formulation , there are three free parameters ; the power index ( @xmath32 ) , and the upper and lower mass limits of the imf ( @xmath33 and @xmath34 ) . in order to describe the evolution of the solar neighborhood , one adopts conventionally @xmath32 = 1.35 , @xmath35 , and @xmath36 or @xmath37 . however , it is highly uncertain whether or not this salpeter - like imf is applicable to the star formation history in primeval galaxies . ys86 investigated the imf for a hydrogen - helium gas cloud in detail based on the opacity - limited fragmentation theory . they found that typical masses of the first - generation stars are from several @xmath0 to 10 @xmath0 , depending on the assumed mass - luminosity relation for protostars derived by silk ( 1977c ) ; assuming that the opacity sources within the protostar is due to grains , he obtained the protostar luminosity @xmath38 where @xmath39 and @xmath40 . since this equation can not be applicable to the luminosity of stars with @xmath41 , ys86 treated @xmath42 as well as @xmath43 as free parameters in the ranges @xmath44 and @xmath45 . then ys86 found that the mass at the peak of the imf is @xmath46 for @xmath40 and @xmath1 for @xmath47 . another important conclusion in ys86 is that stars more massive than these peaks are formed less efficiently than those expected from the salpeter imf with @xmath48 . in addition , stars less massive than these peaks are also formed less efficiently than those expected from the same salpeter imf ( see figure 3 in ys86 ) . therefore , the imfs derived by ys86 are significantly different from the salpeter imfs . we therefore adopt the imfs of ys86 and investigate luminosity and spectral evolution of galaxies for various sets of the parameters . for convenience , we present a parametric form of the ys86 imf in the mass range between 1 @xmath0 and 60 @xmath0 for @xmath40 ( ys86a ) , @xmath49 and that for @xmath47 ( ys86b ) , @xmath50 here the above numerical coefficients are determined by the following normalization for each case , @xmath51 in figure 1 , we show the shapes of imf which we use in this paper . since the massive end slope of ys86a imf is steepest , the number of massive stars ( @xmath52 ) is smallest among the three , although the number of intermediate - mass star exceeds that of salpeter imf . prior going to investigating the luminosity and spectral evolution of galaxies using the ys86 imfs given in equations ( 5 ) and ( 6 ) , we estimate how populous intermediate - mass stars are in the ys86 imfs with respect to those expected from usual salpeter - like imfs . since it is expected that the most spectacular effect of intermediate - mass enhanced star formation is brought by a number of luminous pnns with very high temperature @xmath53 k ( e.g. , vassiliadis & wood 1994 ) . since the mass of such high - temperature pnn progenitors lies in a range between @xmath54 and @xmath55 , we estimate how many stars within this mass range are formed . if we adopt a salpeter imf , the number of stars with a mass range @xmath56 formed in the gas with 1 @xmath0 is estimated as @xmath57 using @xmath29 given in equation ( 3 ) , we re - write equation ( 8) as @xmath58 taking @xmath59 and @xmath60 , we obtain the numbers for the following two cases ; 1 ) @xmath32 = 1.35 , @xmath35 , and @xmath36 , and 2 ) @xmath32 = 1.35 , @xmath61 , and @xmath36 ( see table 1 ) . if we adopt a ys86 imf , we can estimate the number of stars with a mass range @xmath62 by integrating equations ( 5 ) and ( 6 ) for @xmath47 and @xmath63 , respectively . the results are shown in table 1 . we also show the number if all stars have a mass of 5 @xmath0 ; i.e. , the imf is described as a @xmath64 function with @xmath65 . as shown in table 1 , the number of intermediate - mass stars with @xmath66 @xmath55 for the ys86 imf with @xmath47 is nearly the same as that for the salpeter imf with @xmath61 . however , that for the ys86 imf with @xmath40 is larger by a factor of 2.4 than that for the salpeter imf with @xmath61 . for both cases , the ratio of the number of intermediate - mass stars with @xmath67 @xmath68 for ys86 imfs to that for salpeter imf is within a factor of 3 . if stars with mass of @xmath55 are only formed , the number is larger by a factor of 15 than that for the salpeter imf with @xmath61 ( see section 3 ) . in this section , we show the evolution of bolometric luminosity , ionizing photon production rate , and emission line ratios of population iii star clusters with the ys86 imfs . we adopt the @xmath69 yr burst model as the star formation history . we calculate the spectral energy distributions ( seds ) of star clusters by using the evolutionary population synthesis code pegase2 ( fioc & rocca - volmerange 1997 , 2000 ) . although the code can be used to calculate the photometric evolution of galaxies being the effect of the chemical evolution into account , we calculate that of a single metallicity population with @xmath70 ;" +"the rapid development and improvement of ultra - intense laser pulses have opened new areas of physics for fundamental research and have also enabled novel technological applications . relativistically intense ( @xmath0 w/@xmath1 ) laser pulses readily ionize matter converting it into a plasma . the interaction with the plasma electrons is the primary channel for the energy transfer from the laser pulse , providing the basis for a wide range of phenomena and applications . specifically , generation of copious relativistic electrons is the key to x - ray @xcite and secondary particle sources , such as energetic ions @xcite , neutrons @xcite , and positrons @xcite . it is therefore critical to understand what controls the generation of relativistic electrons in relevant regimes of laser - plasma interactions . it is well recognized that the regime in which a relativistically intense laser pulse irradiates a sub - critical plasma is optimal for generating relativistic electrons . the pulse can propagate through such a plasma , which enables an extended interaction length with the electrons . in experiments aimed at x - ray generation , this regime is deliberately achieved by using an expanding gas jet @xcite . this regime can also naturally arise in experiments with solid density targets irradiated by a powerful laser pulse due to the presence of a prepulse @xcite . the prepulse often delivers a considerable amount of energy , causing the front of the target to expand and form an extended subcritical preplasma prior to the arrival of the main pulse . the important role played by the interaction of the main pulse with the preplasma in generating an energetic electron population in experiments with initially solid - density targets was however not immediately recognized . this is in part due to the fact that in some setups the role of the prepulse can also be detrimental . it is the case in experiments aimed at ion acceleration , where the pre - expansion at the surface of a thick bulk target caused by the prepulse significantly reduces the effectiveness of ion acceleration @xcite . recently , the focus of the ion acceleration research has markedly shifted towards those regimes in which the target becomes transparent to the main relativistically intense pulse and the electron acceleration and heating can be fully utilized @xcite . such a regime is achieved by employing an initially ultra - thin target that significantly expands during the pre - pulse and forms a relativistically transparent plasma extending many wavelengths along the direction of the laser beam propagation . the same regime has also been used to generate energetic electrons that are subsequently converted into a short neutron beam @xcite . how energetic electrons are generated strongly depends on the duration of the main laser pulse . in most setups aimed at producing secondary particle sources , the laser pulse irradiates the plasma over a time period that is longer than the characteristic electron response time . this regime is the opposite to the regime used for the wakefield acceleration @xcite . as a consequence , the laser pulse establishes a quasi - steady - state structure in the plasma that slowly evolves on an ion time scale @xcite . by expelling some of the electrons radially , the laser creates a positively charged elongated channel in the plasma with quasi - static transverse and longitudinal electric fields . new electrons are continuously injected into the channel , typically through the channel opening @xcite , and then get accelerated and pushed forward by the laser pulse in the presence of the quasi - static fields . the described regime is often broadly referred to as the direct laser acceleration regime . in terms of applications , it is critical to know what controls the electron energy gain . early work on the topic @xcite indicated that the transverse static electric field can be beneficial for enhancing the electron energy gain beyond what is expected from a single electron irradiated by a plane wave in a vacuum . recently , there has been a renewed interest in the direct laser acceleration of electrons , as experimental groups shift their focus to regimes of relativistic transparency and also try to optimize the preplasma conditions using multiple laser pulses @xcite . recent simulation results have also demonstrated that the direct laser acceleration can be important in the context of the laser wakefield acceleration @xcite . in this paper , we examine the role played by transverse and longitudinal quasi - static electric fields present in a plasma channel in enhancing the electron energy gain from the laser pulse . we also address the role of electron injection into the laser beam and the limitations imposed by the super - luminosity of the laser field that is induced by the channel . this paper is based on a body of work performed by us over the last couple of years @xcite and is designed to serve in part as an overview of some novel aspects of the direct laser acceleration . here we focus on illustrating the key qualitative concepts and phenomena , while providing references to those publications where one can find more detailed technical analysis . the nature of the laser - plasma interaction strongly depends on the amplitude of the irradiating laser pulse and on the electron density of the irradiated plasma . it is convenient to use a dimensionless parameter @xmath2 to quantify the impact of a laser pulse with electric field amplitude @xmath3 and frequency @xmath4 on electron motion . here @xmath5 is the speed of light and @xmath6 and @xmath7 are the electron charge and mass . the parameter @xmath8 is often referred to as the normalized laser amplitude . it is roughly the ratio of the transverse electron momentum induced by the oscillating laser electric field to @xmath9 . therefore , a laser pulse with a normalized amplitude of @xmath10 would induce relativistic electron motion . the electron density in the plasma determines whether the laser pulse can propagate into the plasma and accelerate plasma electrons . the cut - off for a pulse with @xmath11 occurs at a critical density , @xmath12 for which the electron plasma frequency @xmath13 becomes equal to the frequency of the laser pulse . at laser amplitudes @xmath10 , the plasma can become relativistically transparent at electron densities exceeding the critical density @xmath14 . the adjusted critical density in this case depends on the amplitude of the irradiating laser pulse , because the effect is caused by the relativistic motion of electrons in the strong field of the laser . the optimal regime for generating copious relativistic electrons is then the regime in which a relativistic amplitude laser pulse @xmath15 irradiates an extended sub - critical plasma @xmath16 . in order to illustrate the key features of the laser - plasma interaction in this regime , we have performed a two - dimensional ( 2d ) particle - in - cell ( pic ) simulation whose results are shown in fig . [ fig:2d_example ] . in this simulation , a uniform sub - critical plasma with initial electron density @xmath17 is irradiated by a laser beam with wavelength @xmath18 @xmath19 m whose amplitude ramps up to @xmath20 and then remains constant . the laser pulse propagates along the @xmath21-axis and it is linearly polarized , with the laser electric field polarized in the @xmath22-plane . the ions were kept immobile in this simulation to distinguish more clearly the effect of the long laser pulse . detailed parameters of the simulation are given in appendix [ appendix_1 ] . as the pulse enters the plasma , its ponderomotive force begins to expel some of the electrons out of the laser pulse in the transverse direction producing a channel . the un - neutralized ion charge generates a counteracting force that , in the example shown in fig . [ fig:2d_example ] , prevents the channel from becoming fully evacuated . the laser pulse produces and maintains a steady - state channel if the pulse duration exceeds the characteristic electron response time . the snapshot of the electron density in fig . [ fig:2d_example ] taken at 1 ps illustrates such a channel . the positively charged elongated channel generates quasi - static transverse and longitudinal electric fields shown in the lower - left panel of fig . [ fig:2d_example ] . the fields have been averaged over ten laser periods and they are normalized to the electric field amplitude @xmath3 of a plane wave with @xmath20 , which is essentially the amplitude of the electric field in the laser pulse . the time - averaged electric fields are relatively small compared to the amplitude of the oscillating laser electric field that is also present in the channel . once the steady - state channel structure is established , new electrons are continuously injected into the channel through the opening . this is particularly clear from the snapshot of the time - averaged current density , whose absolute value is shown in the upper - right panel of fig . [ fig:2d_example ] . the injected electrons are accelerated and pushed forward by the laser pulse , producing a steady - state electron current in the channel . this current generates a quasi - static transverse magnetic field directed in and out of the plane of the simulation ( along the @xmath23-axis ) . the return current flowing outside of the channel causes for the magnetic field to be localized inside the channel , as shown in the lower - right panel of fig . [ fig:2d_example ] . the plotted time - averaged field is normalized to the magnetic field amplitude @xmath24 of a plane wave with @xmath20 . the quasi - static magnetic field is also relatively weak in this regime , as it is less that 1% of the magnetic field in the laser pulse . . color - coded is the electron longitudinal momentum . ] the presented example illustrates that , in a sub - critical plasma irradiated by a long laser pulse , electron acceleration takes place in a positively charged channel in the presence of extended transverse quasi - static electric and magnetic fields and a localized quasi - static longitudinal electric field . these fields are relatively small compared to the fields in the laser pulse , not exceeding a few percent . it is then somewhat unexpected that , for example , the transverse electric field can significantly enhance the electron energy gain @xcite . as we show in the following sections , the transverse and longitudinal electric fields can synergistically enhance the electron energy gain , with a well - pronounced threshold , well beyond the energy gain that one would expect in the absence of these fields . in order to provide the context for the discussion of the electron acceleration in the channel , we briefly review the key features of the electron motion in a vacuum where no static electric or magnetic fields are present . specifically , we consider a single electron that is initially at rest . it is irradiated by a plane electromagnetic wave whose normalized amplitude gradually increases from zero to @xmath8 . in what follows , we refer to this regime as the vacuum regime . the electron moves according to the following equations : @xmath25 , \label{main_eq:1 } \\ & & \frac{d { \bf{r}}}{d t } = \frac{c}{\gamma } \frac{{\bf{p}}}{m_e c } , \label{main_eq:2}\end{aligned}\ ] ] where @xmath26 is the relativistic factor , @xmath27 and @xmath28 are the electron position and momentum , and @xmath29 is the time . in the regime under consideration , @xmath30 and @xmath31 are the electric and magnetic fields of the wave . it is convenient to express these fields in terms of a normalized vector potential @xmath32 , @xmath33 . \label{b_wave}\end{aligned}\ ] ] in the case" +"the only known method to exchange secret information through a communication channel in a proven secure way , is to use the so - called one - time pad ( for a good review of both classical and quantum cryptography , see @xcite ) . in this technique , the data , which is represented by a string of bits , is combined with a random string of bits of equal length called the key , and is then sent through the communication channel . the randomness of the key ensures that the encoded message is also completely random and as such totally unintelligible to a potential eavesdropper . the safety of the transmission is thus entirely dependent on the safety of the key , which has to be secret and shared just by both legitimate users . moreover , safety can be guaranteed only if the key is used once , and then discarded . the problem is therefore how to distribute the random key between users in a secure way . classically , the only possibility is either through personal meetings , or through a trusted courier , which makes the technique rather expensive , and not practical for many applications . therefore , most practical cryptographic systems nowadays rely on different principles @xcite . however , these can not really _ guarantee _ the safety of the transmission , but rely on a weaker property of the system , namely that it is _ computationally _ safe . this means that the system can be broken in principle , but that the computation time required to do so is too long to pose a real threat . the main problem with this approach is that its safety could be destroyed by technological progress ( faster computers ) or mathematical advances ( faster algorithms or future theoretical progress in computation theory ) . another technique , whose safety does not rely on computing abilities , and which was only recently developed , is quantum cryptography ( for an introduction , see @xcite ) . in quantum cryptography , the two users , generally referred to as alice ( the sender ) and bob ( the receiver ) , have two kinds of communication channels at their disposal . one is a classical public channel , which can be overheard by anybody , but can not be modified ; and the second is a quantum channel , whose main characteristic is that any attempt at eavesdropping will create errors in the transmission . the quantum channel will be used to transmit the secret key , and the classical public channel will be used to exchange information and to send the encoded message . in principle , this is sufficient to ensure the safety of a transmission : alice and bob exchange a series of bits over the quantum channel , and then use part of the transmission to test for eavesdropping . if they find any discrepancy between their strings , they can infer that an eavesdropper , usually referred to as eve , was listening and that their transmission is not secret . if they detect no errors , they can assume that the key is safe . by testing a large proportion of their initial string , they can attain any safety level they wish . unfortunately , quantum channels are very sensitive devices , and due to the imperfections of the channels and of the detectors , some errors will always be unavoidable . the problem facing alice and bob is therefore , for a given error rate , to estimate the amount of information that may have leaked to eve , and decide on the safety of the transmission . this of course depends on both the particular system used by alice and bob , and on the eavesdropping strategy adopted by eve . a safer system is a system for which the amount of information that may have leaked to eve is lower . if the information leaked to eve is not too high , alice and bob can use classical information processing techniques to reduce it to approximately zero , at the expense of shortening their strings @xcite . at present , there exist three different quantum cryptographic systems . the first one relies on the transmission of single photons randomly polarized along four directions @xcite . as single photons are difficult to produce experimentally , a slight modification of this system , using weak pulses instead of single photons , was the first one to be implemented in practice @xcite . the second system , which is conceptually the simplest , uses only two non - orthogonal quantum states @xcite . its implementation relies on weak coherent pulses , with a phase difference between them @xcite . the third system is based on the creation of pairs of epr correlated photons @xcite . one of its potential advantages is that the correlations are between single photons and not weak pulses , which can be a great advantage , as we shall emphasize later . however , creation and transmission over long distances of epr correlated pairs is technologically more difficult , and it is not clear yet whether this will prove practical @xcite . in this work , we focus on quantum cryptographic schemes implemented with weak pulses of coherent light . we compare the safety of the first and the second of these quantum cryptographic systems , and present a new system , which is a symbiosis of both , and for which the safety can be significantly increased . in section [ 4 ] , we analyze the first system , referred to as 4-states system . in section [ 2 ] , we turn to the second one , named 2-states system , and present a new implementation . we introduce our new 4 + 2 system in section [ 4 + 2 ] , and show that it is more sensitive to eavesdropping than the two previous ones . in section [ lossy ] , we show the dangers associated with a lossy transmission line , and conclude in section [ conclusion ] . this protocol was developed by bennett et al . the sender , alice , chooses at random one out of four states , e.g. for polarized photons : , , or , and sends it to the receiver , bob . the two states and stand for bit value ` 0 ' , while the other two , and , stand for ` 1 ' . bob chooses , also at random , a basis , or , in which he measures the polarization . when his basis corresponds to alice s , his bit should be perfectly correlated with hers , whereas when his basis is the conjugate , there is no correlation between his result and alice s original choice . by discussing over the public channel , alice and bob agree to discard all the instances where they did not use the same basis ( half of the total on average ) . the result is what we call the sifted key , which should be two perfectly correlated strings , but which may contain errors . the two fundamental properties of this protocol are : * the choice of basis is completely hidden from the other protagonist ( the two bases correspond to the same density matrix ) , as well as from any mischievous eavesdropper , eve ; * when alice and bob use different bases , there is no correlation between their bits . the first one , ( i ) , ensures that , as the eavesdropper eve can not know which basis was used , she will unavoidably introduce errors . the second one , ( ii ) , is not really necessary , but is preferable , as it reduces the information available to eve to a minimum @xcite ( 25 % for each photon on which she eavesdropped ) . there have been various works analyzing eavesdropping strategies , calculating the information available to eve as a function of the error rate and developing information processing techniques to reduce it to any required level @xcite . one technical difficulty with this scheme is that in principle it should be implemented by means of single photons @xcite . as these are difficult to generate experimentally , existing schemes rely on weak pulses of coherent or thermal light , with much less than one photon per pulse on average @xcite . this ensures that the probability of having two or more photons in a pulse remains very small . this strategy reduces the transmission rate ( recent experiments use about one tenth of a photon per pulse ) , while providing no advantage to an honest participant . more precisely , if alice and bob use coherent pulses @xmath0 , the transmission rate @xmath1 is given by : @xmath2 where the factor @xmath3 comes from the fact that half of the transmissions had to be discarded ( when alice and bob used different bases ) . in fact , even for these weak pulses , the probability of having two or more photons per pulse may not always be neglected ( for the above pulses , one out of twenty non - zero pulses will have two photons ) . we shall show in section [ lossy ] how to take this into account . in order to get quantitative results , we shall assume that eve uses the intercept / resend strategy : she intercepts the pulses , attempts to gain as much information as possible , and sends to bob a new pulse , prepared according to the information she obtained . moreover , we shall assume that she eavesdrops in the bases used by alice and bob , or . this is the intercept / resend strategy which provides her with the most information on the sifted key @xcite . however , it is not yet known whether this is the optimal strategy . it is easy to see that , when eve eavesdrops on a fraction @xmath4 of the transmissions , the error rate created is @xmath5 ( when eve uses the correct basis , she does not introduce any error , while she creates a 50% error rate when she uses the wrong basis ) , and that the information she obtained is @xmath6 ( she has total information when she used the correct basis , and none when she used the wrong one ) . moreover , the scheme is completely symmetric , so that eve shares the same information with alice and with bob . therefore , we can write the mutual information shared by alice and eve and shared by eve and bob as a function of the error rate @xmath7 : @xmath8 in this system , the intensity of the weak pulses , or equivalently the transmission rate @xmath1 defined in ( [ t4 ] ) has no influence . in the following , we will compare ( [ i4 ] ) to the information obtained by eve for the other two systems . in this protocol @xcite , alice chooses between only two non - orthogonal states , and sends one to bob . as these are not orthogonal , there is no way for bob to decode them deterministically . however , by means of a generalized measurement , also known as _ positive operator valued measure _ or povm @xcite , he can perform a test which will sometimes fail to give an answer , and at all other times give the correct one . in essence , instead of having a binary test ( with results 0 or 1 ) , which will unavoidably create errors when the two states are not orthogonal , bob has a ternary system , with possible results" +"symmetry is one of the basic principles that penetrate all of physics : from classical to quantum physics @xcite ; from statistical or condensed matter physics to particle physics @xcite ; and from relativity to gauge field theory . thus we see a wide range of symmetries : from external ( space - time ) to internal ones ; and from discrete to continuous ones . this is partly because geometry is an indispensable element to describing physics . and a natural algebraic language to express geometrical symmetry is group theory . @xcite classical mechanics is widely known to have close relations between symmetries and lagrangians or hamiltonians.@xcite since quantum mechanics and field theory are , in some respects , modeled and devised after classical mechanics , we see that not a few methods and notions , including symmetry , in quantum mechanics and field theory resemble those in classical mechanics . and thus symmetry plays a crucial role also in quantum physics . or we can interpret that although `` the physical world is quantum mechanical'',@xcite the quantum feature are somewhat transmitted to the classical world ; and through the latter we may try to grasp the former . of course since we are not able to capture all nature by classical analogies , there are sometimes discrepancies between quantum symmetries and classical ones . @xcite now , one of the typical mathematical tools that relate classical states with quantum ones is coherent states ( cs ) . @xcite it was originally devised by schrdinger @xcite as the states having classical `` particle '' nature . the state exhibits a wave packet whose center moves along with the classical trajectory with minimum uncertainty ; thus it shows classical nature . the original cs which is called canonical cs is , in the light of quantum optics , generated by displacing , or driving , the vacuum , i.e. the zero photon state . @xcite later cs have been developed in a wide variety of directions . viewed from a general framework , we may take up the following three subjects among the evolutions . first , cs have been extended to wider classes . a systematic way to broaden cs is constructing cs in terms of unitary irreducible representations of lie groups due to perelomov.@xcite in the approach , cs is defined by operating a unitary operator related to a physical system being considered on a `` fiducial vector ( fv ) '' , which we denote @xmath4 . from this point of view , for the canonical cs the unitary operator is a displacement operator and a fv is the ground state or vacuum . similarly , the spin cs can be constructed by operating a rotation operator on a fv ; the fv is conventionally taken as @xmath5 or @xmath6 : the highest or lowest eigenvectors of @xmath2 . we may perform the procedures to other lie groups , which automatically produces cs for the corresponding lie groups . schur s lemma coming from irreducibility always ensures the overcomplteness of cs . second , since cs enjoy overcomplete relations , `` coherent state path integrals ( cspi ) '' , i.e. , path integrals ( pi ) via cs , have been developed.@xcite such cspi have been pushing the method of pi forward strongly . and besides cspi turned out to be closely related to geometric phases @xcite ; in fact it is remarkable that geometric phases follow from the topological terms of phase space pi or cspi naturally . @xcite third , following the fruits of the above two developments , cs and cspi with arbitrary fv have been explored . @xcite in the case cs are obtained by operating a unitary operator on an _ arbitrary _ fv : for the canonical cs a fv is arbitrary superpositions of the fock number states ; and for the spin cs arbitrary superpositions of @xmath7 : a general eigenvector of @xmath2 . we found that , as mentioned in ref . , the canonical cs evolving from arbitrary fv@xcite turned out to be an arbitrary superposition of displaced number states having no classical analogues . similarly , we may regard spin cs evolving from a general fv other than the conventional one as quantum states without classical analogues . it is true that cs with the conventional fv are closest to classical states and have useful properties . @xcite however , recent technologies enable us to prepare quantum states which have no classical analogues ; the typical one is the squeezed states of light . @xcite we certainly regard the evolutions plausible since experimental developments due to high technologies have often created opportunities to reconsider nature . in this respect we may take cs evolving from a generic fv as the mathematical tools , or a sort of new language , for describing non - classical quantum states . and thus what we have done in refs . and is constructing new quantum states and investigating the dynamics : i.e. , the time evolutions of the quantum states . we can interpret the attempts as extending both cs due to schrdinger - klauder - glauber - perelomov and pi due to dirac - feynman - klauder - kuratsuji - suzuki . in the previous paper,@xcite hereafter referred to as * i * , we have developed a basic formulation of the su(2 ) , i.e. spin , cs based on arbitrary fv and of their pi . the cs and cspi are labeled by a full set of three euler angles @xmath8 . since the present paper flows directly out of * i * , we will look back the previous results concisely . in * i * we found out that the lagrangian in the action appeared in the pi expression were composed of two parts : the topological term related to geometric phases and the dynamical one originating from a hamiltonian . and the former is again split into two parts : one is the monopole type part which is the generalization of that of balachandran _ et al._@xcite and the other represents the effect of entanglements between neighboring components of a fv . such interweaving components of a fv appear in the dynamical term as well . the monopole is fictitious in that it does not represent a real physical monopole having a magnetic charge ; instead it stems from the topological or geometric phase terms . however , mathematical descriptions seem quite common to both real and fictitious monopoles . and we have confirmed the pi form by demonstrating from discrete pi to continuous ones . moreover , it has been proved that the generic spin cspi contract to the general canonical cspi in the high spin limit . at first sight it seems that we are free to choose fv ; there are no restrictions on fv and we may take an arbitrary fv . however , when a lagrangian varies at most a total derivative under a certain gauge transformation and possesses a sort of semiclassical symmetry , a full quantum state with an arbitrary fv does not always preserve the related symmetry . in the case , when a fv @xmath4 can not be reached from @xmath7 via @xmath9 , we find some strange feature : semiclassical orbits do not always represent exact quantal evolutions . it is stone who first observed that there does exist one of the central problems at the point viewed from a general framework of cs with arbitrary fv . he raised the problem in a paper@xcite commenting on the precursory version of * i * @xcite ; moreover , he went further enough to propose a criterion under which the cs capture full quantal evolutions . according to that , an arbitrary fv is not always realized and that there may be restrictions on fv so that quantum evolutions are consistent with the semiclassical ones which has an original symmetry . actually , the fv have to be identical with @xmath7 or on the orbits of @xmath7 under the action of @xmath10 . and , as stone precisely pointed out , the problem is deeply related to the charge quantization of monopoles . in this article we consider the problem posed in ref . from the general framework of spin cspi developed in * i*. as mentioned earlier , we have demonstrated the process of going from the discrete pi to the continuous pi in * i * ; we have also showed that the spin cspi contract to the canonical cspi . so the pi expressions in * i * are quite all right and are not responsible for not bringing the restriction on fv . then one might wonder from where the restriction comes . we will approach the riddle in the light of the `` gauge symmetry '' associated with the invariance of lagrangian appeared in the spin cspi in * i*. so the present article is also concerned with `` symmetry '' . it will be one of the early attempts that relate cs and cspi with symmetry , especially gauge symmetry . the plan of the paper is as follows . first , we look back the spin(su(2))cspi based on arbitrary fv in @xmath11 [ sec : spincspi ] . next , using the formulation of the spin cspi , we discuss general properties of a lagrangian in the light of gauge symmetries in @xmath11 [ sec : symlagfv ] . next , in @xmath11 [ sec : lags ] we demonstrate , using simple examples , the relations between types of fv and semiclassical as well as full quantal dynamics . we then look over several real examples of lagrangians in order to see the relations between hamiltonians , fv and gauge symmetries of the whole lagrangians . main results are presented as theorems and proved in @xmath11 [ sec : gentheorems ] . theorem [ th : typefv ] gives the central result concerning the restriction on fv in the full quantum picture . we find that gauge symmetries bring restrictions on fv and thus on the form of cs . we look into the situation much deeper by investigating the generator of the symmetry transformation in theorem [ th : gform ] . next , we revisit the gauge symmetries in the light of a new kind of isotropy subgroups due to ref . in @xmath11 [ sec : anotherviewscevolvs ] ; and we see the correspondence between the approach and that in @xmath11 [ sec : symlagfv ] and @xmath11 [ sec : lags ] . finally we summarize the results in @xmath11 [ sec : discussion ] . there we also discuss the related topics that we view in a future prospect . let us recall the results in * i*. first , we define the spin(su(2))cs , @xmath12 , evolving from an arbitrary fv @xmath4 as : @xmath13 the fv @xmath4 is represented by : @xmath14 hereafter @xmath15 stands for @xmath7 . from ( [ eqn : cs1 ] ) and ( [ eqn : spinfv ] ) we obtain @xmath16 see ( * i * - 19 ) ) denotes eq . ( @xmath17 ) in * i*. ] for the explicit form of @xmath18 which we do not need in the present paper . we called @xmath18 the `` rotated spin number state '' in * i * where we saw that it corresponded to the `` displaced number state '' in the general canonical cs . @xcite then the quantum time evolution of a physical system with a hamiltonian @xmath19 in terms of @xmath12 is given by the propagator : @xmath20 \ } \ , { \cal d } [ { \bf\omega}(t ) ] , \label{eqn : pi}\ ] ] where @xmath21 \equiv \int_{t_i}^{t_f } \bigl [ \ { { \left\langle \bf\omega\right\vert } } i \hbar \frac{\partial}{\partial t } {" +"the study of spin dynamics in ultrathin ferromagnets is of fundamental interest , since new physics arises in these materials that has no counterpart in bulk magnetism . examples are provided by relaxation mechanisms evident in ferromagnetic resonance and brillouin light scattering studies,@xcite and also for the large wave vectors probed by spin polarized electron loss spectroscopy ( speels).@xcite of course , by now the remarkable impact of ultrathin film structures on magnetic data storage is very well known , and other applications that exploit spin dynamics in such materials are envisioned . thus these issues are important from a practical point of view as well as from that of fundamental physics . theoretical studies of the nature of spin waves in ultrathin films adsorbed on metal substrates have been carried out for some years now , along with comparison with descriptions provided with the heisenberg model.@xcite in this paper , we extend the earlier theoretical treatments to include the influence of spin orbit coupling on the spin wave spectrum of ultrathin films . this extension is motivated by a most interesting discussion of the ground state of the mn monolayer on the w(110 ) surface . a nonrelativistic theoretical study of this system predicted that the ground state would be antiferromagnetic in character.@xcite this prediction was confirmed by spin polarized scanning tunneling microscope studies of the system.@xcite however , recent experimental stm data with a more sensitive instrument showed a more complex ground state , wherein the ground state is in fact a spin density wave.@xcite one can construct the new state by beginning with the antiferromagnet , and then superimposing on this a long wavelength modulation on the direction of the moments on the lattice . the authors of ref . argued that the lack of reflection symmetry of the system in the plane of the film activates the dzyaloshinskii moriya ( dm ) interaction , and the new state has its origin in this interaction . they also presented relativistic and ab initio calculations that gave an excellent account of the new data . the reflection symmetry is broken simply by the presence of the substrate upon which the film is grown . this argument to us is most intriguing , since one can then conclude that the dm interaction must be active in any ultrathin ferromagnet ; the substrate is surely always present . the dm interaction has its origin in the spin orbit interaction , which of course is generally very weak in magnets that incorporate the 3d transition elements as the moment bearing entities . however , in the case of the mn monolayer on w(110 ) hybridization between the mn 3d and the w 5d orbitals activates the very large w spin orbit coupling , with the consequence that the strength of the dm interaction can be substantial , as illustrated by the calculations presented in ref . . one may expect to see substantial impact of the dm interaction in other ultrathin magnets grown on 5d substrates , and possibly 4d substrates as well . we have here another example of new physics present in ultrathin magnets that is not encountered in the bulk form of the material from which the ultrathin structure is fabricated . the purpose of this paper is to present our theoretical studies of spin orbit effects on spin waves and also on the dynamic susceptibility of a much studied ultrathin film / substrate combination , the fe monolayer and bilayer on w(110 ) . we find striking effects . for instance , when the magnetization is in plane , as we shall see the dm interaction introduces a term linear in wave vector in the dispersion relation of spin waves . thus the uniform spin wave mode at zero wave vector acquires a finite group velocity . we find this to be in the range of @xmath0 cm / sec for the fe monolayer on w(110 ) . furthermore , left / right asymmetries appear in the speels response functions . thus , we shall see that spin orbit coupling has clear effects on the spin excitations of transition metal ultrathin ferromagnets grown on 5d substrates . we comment briefly on the philosophy of the approach used here , and in various earlier publications.@xcite numerous authors proceed as follows . one may generate a description of the magnetic ground state of the adsorbed films by means of an electronic structure calculation based on density functional theory . it is then possible to calculate , within the framework of an adiabatic approximation , effective heisenberg exchange integrals jij between the magnetic moments in unit cell i and unit cell j. these may be entered into a heisenberg hamiltonian , and then spin wave dispersion relations may be calculated through use of spin wave theory . it has been known for decades@xcite that in the itinerant 3d magnets , effective exchange interactions calculated in such a manner have very long range in real space . thus , one must include a very large number of distant neighbors in order to obtain converged results . this is very demanding to do with high accuracy for the very numerous distant neighbors , since the exchange interactions become very small as one moves out into distant neighbor shells . at a more fundamental level , as noted briefly above , discussions in earlier publications show that in systems such as we study here , the adiabatic approximation breaks down badly , with qualitative consequences.@xcite first , spin wave modes of finite wave vector have very short lifetimes , by virtue of decay into the continuum of particle hole pairs ( stoner excitations ) even at the absolute zero of temperature@xcite whereas in heisenberg model descriptions their lifetime is infinite . in multi layer films , the earlier calculations show that as a consequence of the short lifetime , the spectrum of spin fluctuations at large wave vectors contains a single broad feature which disperses with wave vector in a manner similar to that of a spin wave ; this is consistent with speels data on an eight layer film of co on cu(100).@xcite this picture stands in contrast to that offered by the heisenberg model , in which a film of n layers has n spin wave modes for each wave vector , and each mode has infinite lifetime . the method developed earlier , and extended here to incorporate spin orbit coupling , takes due account of the breakdown of the adiabatic approximation and also circumvents the need to calculate effective exchange interactions in real space out to distant neighbor shells . we work directly in wave vector space through study of the wave vector and frequency dependent susceptibility discussed below , denoted as @xmath1 . the imaginary part of this object , evaluated for @xmath2 and considered as a function of frequency @xmath3 for fixed wave vector @xmath4 provides us with the frequency spectrum of spin fluctuations on layer @xmath5 for the wave vector chosen . spin waves appear as peaks in this function , very much as they do in speels data , and in a manner very similar to that used by experimentalist we extract a dispersion relation for spin waves by following the wave vector dependence of the peak frequency . we never need to resort to a real space summation procedure over large number of neighbors , coupled by very tiny exchange couplings . the spin wave exchange stiffness can be extracted either by fitting the small wave vector limit of the dispersion relation so determined , or alternatively by utilizing an expression derived earlier@xcite which once again does not require a summation in real space . we comment on another feature of the present study . in earlier calculations,@xcite as in the present paper , an empirical tight binding description forms the basis for our description of the electronic structure . within this approach , referred to as a multi band hubbard model , we can generate the wave vector and frequency dependent susceptibility for large systems . in the earlier papers , effective tight binding parameters were extracted from bulk electronic structure calculations . the present studies are based on tight binding parameters obtained directly from a rs - lmto - asa calculation for the fe / w(110 ) system . we also obtain tight binding parameters by fitting kkr based electronic structure calculations for the ultrathin film / substrate combinations of interest . we find that spin waves in the fe / w(110 ) system are quite sensitive to the empirical tight binding parameters which are employed , though as we shall see the various descriptions provide very similar pictures of the one electron local density of states . we note that udvardi and szunyogh@xcite have also discussed the influence of spin orbit coupling on the dispersion relation of spin waves in the fe monolayer on w(110 ) within the framework of the adiabatic approach discussed above , where exchange interactions and other magnetic parameters are calculated in real space . we shall discuss a comparison with our results and theirs below . there are differences . most particularly , we note that in fig . 3 , the authors of ref . provide two dispersion curves for propagation perpendicular to the magnetization , whereas in a film such as this with one spin per unit cell there can be only one magnon branch . additionally and very recently , bergmann and coworkers@xcite investigated within an adiabatic approach finite temperature effects on the magnon spectrum of fe / w(110 ) . in section ii , we comment on our means of introducing spin orbit coupling into the theory . the results of our calculations are summarized in section iii and concluding remarks are found in section iv . the formalism for including spin orbit coupling effects in our description of spin dynamics is quite involved , so in this section we confine our attention to an outline of the key steps , and an exposition of the overall structure of the theory . our starting point is the multi band hubbard model of the system that was employed in our earlier study of spin dynamics in ultrathin ferromagnets . the starting hamiltonian is written as@xcite @xmath6 where @xmath7 and @xmath8 are site indices , @xmath9 refer to spin , and @xmath10 to the tight binding orbitals , nine in number for each site , which are included in our treatment . the coulomb interactions operate only within the 3d orbitals on a given lattice site . the film , within which ferromagnetism is driven by the coulomb interactions , sits on a semi - infinite substrate within which the coulomb interaction is ignored . in our empirical tight binding picture , the spin orbit interaction adds a term we write as @xmath11 \label{hamilt_so}\ ] ] where @xmath12 is the angular momentum operator , @xmath13 is the local spin - orbit coupling constant , @xmath14 and @xmath15 . we assume that the spin orbit interaction , present both within the ferromagnetic film and the substrate , operates only within the 3d atomic orbitals . a convenient tabulation of matrix elements of the orbital angular momentum operators is found in ref . . information on the spin waves follows from the study of the spectral density of the transverse dynamic susceptibility @xmath1 as discussed above . from the text around eq . ( 1 ) of ref . , we see that this function describes the amplitude of the transverse spin motion ( the expectation value of the spin operator @xmath16 in the layer labeled @xmath5 ) to a fictitious transverse magnetic field of frequency @xmath3 and wave vector @xmath4 parallel to the film surface that is applied to layer @xmath17 of the sample . the spectral density , given by @xmath18 , when multiplied by the bose einstein function @xmath19^{-1}$ ] is also the" +"soft x - ray transients ( sxts ) are compact binary systems in which a low - mass secondary ( either a main - sequence star or a subgiant ) transfers mass via roche - lobe overflow onto a black hole ( bh ) or neutron star ( ns ) primary ( see reviews by tanaka & lewin 1995 ; van paradijs & mcclintock 1995 ; white , nagase & parmar 1995 ) . sxts have highly variable luminosities . they spend most of their lifetimes in a low luminosity quiescent state , but occasionally undergo dramatic outbursts during which both the optical and x - ray emission increase by several orders of magnitude ( e.g. chen , shrader & livio 1997 ; kuulkers 1998 ) . ns sxt outbursts typically occur every 1 - 10 years and last for several weeks , while bh sxt outbursts are typically separated by 10 - 50 years ( or perhaps longer ) and last for several months ( see chen et al . 1997 ) . a variety of observations ( see e.g. tanaka & shibazaki 1996 ) indicate that , near the peak of an outburst , sxts accrete matter via a standard thin disk ( shakura & sunyaev 1973 ) , so that there is little doubt that the accretion is radiatively efficient during this phase . the situation is more complex in quiescence . the spectra of quiescent bh sxts do not resemble that of a thin disk , and the accretion rates inferred from the observed x - ray luminosities disagree by orders of magnitude with the predictions of the standard disk instability model for quiescent disks ( e.g. lasota 1996 ) . narayan , mcclintock & yi ( 1996 ) and narayan , barret & mcclintock ( 1997 ) showed that the observations of quiescent bh sxts can be explained by a two - component accretion flow model consisting of an inner hot advection - dominated accretion flow ( adaf ; narayan & yi 1994 , 1995a ; abramowicz et al . 1995 ; ichimaru 1977 ; see narayan , mahadevan & quataert 1998 and kato , mineshige & fukue 1998 for reviews of adafs ) surrounded by an outer thin disk . in the recent version of this model described in narayan et al . ( 1997a ) , only the inner adaf contributes to the observed optical , uv and x - ray emission of the system . the outer thin disk acts mainly as a reservoir which accumulates mass until the next outburst is triggered . in quiescence , the emission of the disk is primarily in the infrared ; this radiation is hardly seen as it is swamped by the emission of the secondary ( see narayan et al . 1996 , 1997a and lasota , narayan & yi 1996 for details ) . a key feature of the narayan et al . ( 1996 , 1997a ) model of quiescent bh sxts is the low radiative efficiency of the adaf . in these flows , the bulk of the viscously dissipated energy is stored in the gas and advected with the flow into the black hole ( narayan & yi 1995b ; abramowicz et al . 1995 ; narayan et al . 1996 , 1997a ) . this explains the unusually low luminosities of bh sxts . by contrast , in ns sxts all the advected energy is expected to be radiated from the neutron star surface , resulting in a much higher radiative efficiency of the accretion flow even in the presence of an adaf ( narayan & yi 1995b ) . motivated by this fundamental distinction between black hole and neutron star systems , narayan , garcia & mcclintock ( 1997 ) and garcia et al . ( 1998 ) compared the outburst amplitudes of bh sxts and ns sxts as a function of their maximum luminosities and showed that the observations reveal systematically lower relative luminosities in bh sxts . they argued that this constitutes a confirmation of the presence of an event horizon in bh sxts . the argument was challenged by chen et al . ( 1998 ) . in this paper , we attempt to develop a physical understanding of the difference in quiescent luminosities between ns and bh sxts . we first show , in 2 , that there is indeed a significant difference in the observed quiescent luminosities of the two classes of objects , in contrast to the claim of chen et al . we then use binary evolution models in 3 to estimate mass transfer rates in sxts . we combine these estimates with the adaf+thin disk accretion scenario , taking into account the presence of an event horizon in bh systems and a reradiating surface in ns systems , to determine the expected x - ray luminosities in quiescence ( 4 ) . the model predictions agree well with the observations of quiescent bh sxts . however , the model substantially overestimates the luminosities of quiescent ns sxts . in 5 we show that the ns sxt data can be reconciled with the predictions of the model if we take into account the `` propeller effect '' ( illarionov & sunyaev 1975 ) , whereby the magnetosphere of a rapidly rotating neutron star prevents much of the accreting material from reaching the surface of the neutron star . in 6 we show that an adaf model with a moderate wind and a somewhat less efficient propeller ( in ns sxts ) , is also consistent with the observed quiescent luminosities of bh and ns sxts . finally , in 7 we discuss possible limitations and extensions of this work and in 8 we summarize the main results . in table [ tab : systems ] , we list key parameters of several ns and bh sxts : the orbital period @xmath0 , the distance @xmath1 , the quiescent x - ray luminosity @xmath2 in the @xmath3 kev x - ray band , and the mass @xmath4 ( in solar units ) of the compact primary . since our main interest is in the quiescent emission , we list only systems for which there exist reliable measurements of @xmath2 . the values of @xmath2 are taken from narayan et al . ( 1997b ) and garcia et al . ( 1998 ) , except for the bh sxt h1705 - 250 ( see below ) . in selecting the systems listed in table [ tab : systems ] , we were careful to avoid any possible confusion between bh and ns sxts , since this would make a comparison between the two sets of objects less reliable . thus , we limit our sample to the eight bh candidates that have firm _ dynamical _ lower limits on the mass of the primary ( e.g. mcclintock 1998 ) . ( note that this is not true for several so - called bh `` candidates '' of chen et al . 1998 , which seriously weakens their arguments . ) similarly , there is firm evidence that the five systems listed in table [ tab : systems ] as ns sxts contain ns primaries , based on the detection of type i x - ray bursts ( e.g. narayan et al . 1997b ; chen et al . 1997 ) . here we report a new and improved luminosity limit for h1705 - 250 ( = nova oph 77 ) based on the asca observation of 18 september 1996 , which we extracted from the heasarc archive . the exposure time was 31 ks , but unfortunately the target was near the chip boundaries which limits the effective area . the 4@xmath5 upper limit is @xmath6 c s@xmath7 , which corresponds to an x - ray flux @xmath8ergs s@xmath7@xmath9 . assuming a distance of 8.6 kpc , @xmath10ergs s@xmath7 . luminosities can be expressed in units of the eddington luminosity , @xmath11 where @xmath4 , the mass of the compact object in solar units , is listed in table [ tab : systems ] . for a standard radiative efficiency of @xmath12 % , the eddington luminosity corresponds to a mass accretion rate of @xmath13 in this section , we use both absolute luminosities and eddington - scaled luminosities in a system is not well known ( eq . [ [ eq : ledd ] ] ) . this is for instance the case of the bh sxt j1655 - 40 . orosz & bailyn ( 1997 ) estimate that @xmath14 in this system , while phillips et al . ( 1999 ) claim that @xmath4 could be as low as @xmath15 since it is not clear which is the more appropriate quantity for comparisons . our calculations in 3 suggest that the mass transfer rates in ns and bh sxts are similar when expressed in units of @xmath16 , especially at short orbital periods . thus , eddington - scaled luminosities might be more appropriate to compare the two classes of objects at short periods ( where most of the data lie ) . however , this argument is not very strong . therefore , we also show absolute luminosities , expressed in units of @xmath17 erg s@xmath7 ( which is roughly the luminosity expected from an object accreting at @xmath18 g s@xmath7 with a radiative efficiency of @xmath12 % ) . finally , the ratio @xmath19 ( which is independent of the distance @xmath1 ) is used for comparison with previous investigations of the luminosity difference between bh and ns sxts . the values of @xmath20 , the outburst peak luminosity , are taken from garcia et al . ( 1998 ) . in figure [ fig : lumtot ] , we show the quiescent luminosities of the bh and ns systems listed in table [ tab : systems ] as a function of their orbital periods @xmath0 . the open circles correspond to ns sxts and the filled dots correspond to bh systems . luminosity upper limits ( indicated by downward arrows ) are shown for five sxts , all of which are bh systems . the orbital period of the ns sxt h1608 - 52 is uncertain ( see table [ tab : systems ] ) and its location in figure [ fig : lumtot ] is indicated by dashed circles . among the undetected sxts , we choose to include in our sample only those systems that have been observed for more than 10 ks ( see table [ tab : systems ] herein , and also table 1 in narayan et al . 1997b ) , which therefore have flux limits @xmath21 ergs s@xmath7 with current x - ray satellites ( 0.5 - 10 kev ; rosat / asca ) . the argument for using @xmath0 along the horizontal axis of figure [ fig : lumtot ] is as follows . for any binary system with a low mass secondary , and transferring mass via roche - lobe overflow , the density of the secondary essentially determines @xmath0 . at a given @xmath0 , a bh sxt and a ns sxt will have similar secondaries , so that the mass transfer characteristics are likely to be similar . thus a reliable comparison of the radiative efficiencies of their accretion flows would be possible . in contrast , if we were to compare the quiescent luminosities of a bh sxt and a ns sxt with quite different @xmath0 , a difference in the mass transfer rates ( see 3 ) could mask actual differences in the radiative efficiencies of the accretion flows . this point , which is the motivation for the calculations in 3 , was first emphasized by lasota & hameury ( 1998 ) . figure [ fig : lumtot ] strongly suggests that bh sxts are fainter than ns sxts . this is especially true" +"as the paradigmatic discrete - time realization of brownian motion and diffusive processes , whose theory was formulated in the pioneering work by einstein @xcite and smoluchowski @xcite published in beginning of the last century , random walks have received a considerable amount of attention @xcite , uncovering their wide range of distinct applications . thus far , random walks are still an active area of research @xcite . however , due to the complexity and variety of real media , theory of random walks on general graphs ( networks ) is not yet available . for this reason , studying random walks occurring on simple structures is a matter of exceptional importance . fractal structures , in particular deterministic fractals , are valuable media in this content @xcite , because their properties can be exactly studied . among various deterministic fractals @xcite , the t - fractal ( t - graph ) @xcite is a typical candidate for exactly solvable model , and a plethora of issues for random walks on this fractal have been studied @xcite . a simple analytical approach was proposed in @xcite , showing that random walks on the t - graph can be mapped onto diffusion on a comb structure . the asymptotic behavior of the moments of the first - passage time and survival probability for random walks on the t - graph was computed in @xcite . particularly , random walks performed on the t - graph with a single trap were extensively studied by many groups @xcite , revealing some scaling relations and dominating behavior . despite the fact that these investigations uncovered many unusual and exotic features of the t - graph , providing useful insight into understanding random walks on this fractal , they did not give a complete picture of random - walk dynamics on the t - fractal , since in these studies , only one special trap was considered . it was shown that in some real networks , any node may be looked as a trap , and the location of traps strongly affects the behavior of random walks @xcite . irrespective of its obvious importance and ubiquity , this issue has not been addressed for the t - graph . in this paper , using the connection between the random walks and electrical networks @xcite , we investigate random walks on the t - graph . the random walk process addressed here may be considered as the trapping problem with the perfect trap uniformly located at all nodes . we derive analytically an exact formula for the mean first - passage time ( mfpt ) averaged all pairs of nodes , which characterizes the efficiency of random walks on the t - graph . we show that the location of trap has no qualitative effect on the scaling for mfpt . we expect that our analytical method can be applied to some other deterministic media , and that our results can lead to deeper insights to random walks on the t - graph . the t - graph is built in an iterative way @xcite . we denote by @xmath0 ( @xmath1 ) the t - graph after @xmath2 iterations . note that henceforth we will also call the number of iterations as generation of the t - graph . the construction of the t - graph starts from ( @xmath3 ) two nodes connected by an edge , which corresponds to @xmath4 . for @xmath5 , @xmath0 is obtained from @xmath6 by performing the operation illustrated in fig . [ cons ] . according to the construction algorithm , at each generation , the number of edges in the system increases by a factor of @xmath7 . thus , we can easily obtain that at generation @xmath2 , the total number of edges in @xmath0 is @xmath8 . since the t - graph is a tree , the total number of nodes in @xmath0 is @xmath9 . figure [ net ] shows schematically the structure of @xmath10 . the t - graph is a fractal with the fractal dimension and random walk dimension being @xmath11 and @xmath12 , respectively . the spectral dimension of the t - graph is @xmath13 . note that for a general connected graph , the spectral dimension governs the longtime behavior of a random walk on the graph at a deep level . for example , when a walker originating at a given node @xmath14 of the graph , the probability @xmath15 for returning back to @xmath14 , at long time @xmath16 , obeys the relation @xmath17 @xcite . again for instance , for an infinite graph with the spectral dimension @xmath18 , a walker starting from a given node will return back to the node almost surely over the course of time . the phenomenon of a random walk on such a graph is called persistence "" . since the spectral dimension @xmath19 for the t - graph , a random walk on such a graph is persistent . to facilitate the description in what follows , we define the central node in fig . [ net ] as the innermost node , and we call those nodes farthest from the central node as outermost nodes . then , the t - graph can be alteratively constructed in another method , see fig . [ copy ] . given the generation @xmath2 , @xmath20 may be obtained by joining three copies of @xmath0 , denoted as @xmath21 , @xmath22 , and @xmath23 , respectively . in other words , to get @xmath20 one can merge together separate outermost nodes of the three replicas of @xmath0 . in the process of joining , the three outermost nodes are emerged into a single new node , which becomes the innermost node of @xmath20 . , which is obtained by joining three copies of @xmath0 , consecutively represented as @xmath21 , @xmath22 , and @xmath23 , respectively . in this section , we investigate a minimal model for discrete - time random walks of a particle on the t - graph @xmath0 . at each time step , the walker moves from its current location to any of its nearest neighbors with equal probability . a key quantity characterizing such a random walk is the first - passage time ( fpt ) , in terms of which many other quantities can be expressed . we are interested in the mean first - passage time ( mfpt ) between two distinct nodes , averaged over all pairs . it is well - known that the random walks addressed here can be described by the processes of markov chains @xcite , the fundamental matrices corresponding to which can be used to express the fpt between any pair of nodes . however , the fundamental matrix method for computing the mfpt in @xmath0 requires computing the inversion of @xmath24 matrices of size @xmath25 , making it prohibitively difficult to calculate the quantity concerned for all but small networks . to bring down the high computational demands the fundamental matrix method makes , one can apply the method of the pseudoinverse of the laplacian matrix @xcite for the graph @xmath0 that random walks are performed on , which allows to compute the fpt between two arbitrary nodes directly from the network topology and requires inversion of a single @xmath26 matrix . the elements @xmath27 of the laplacian matrix @xmath28 for graph @xmath0 are defined as follows : @xmath29 if the pair of two different nodes @xmath14 and @xmath30 is connected by a link , otherwise @xmath31 ; while @xmath32 ( i.e. , degree of node @xmath14 ) . then , the pseudoinverse of the laplacian matrix @xmath28 is @xcite @xmath33 where @xmath34 is the @xmath35-dimensional one "" vector , i.e. , @xmath36 . let @xmath37 denote the fpt for a walker in the t - graph @xmath0 , starting from node @xmath14 , to arrive at node @xmath30 for the first time . since the graph @xmath0 is connected , the pseudoinverse matrix @xmath38 is well defined and the entries @xmath39 can be applied to express the fpt @xmath37 as follows @xcite : @xmath40 where @xmath41 is the @xmath42 entry of the diagonal of the laplacian matrix @xmath28 as defined above . then the sum , @xmath43 , for the fpt between two nodes over all node pairs in graph @xmath0 reads @xmath44 and the mfpt , @xmath45 , is @xmath46 the quantity of mfpt @xmath45 is very important since it measures the efficiency of the random walks on @xmath0 : the smaller the value @xmath45 , the higher the efficiency , and vice versa . equations ( [ hitting01 ] ) and ( [ hitting03 ] ) show that the problem of calculating @xmath47 is reduced to determining the elements of the pseudoinverse matrix @xmath38 , whose complexity is that of inverting an @xmath48 matrix , it can be easily obtained by utilizing a standard software package , mathematica 5.0 . however , since @xmath35 increases exponentially with @xmath2 , for large @xmath2 , it becomes difficult to obtain @xmath45 through direct calculation using the pseudoinverse matrix , because of the limitations of time and computer memory . therefore , one can compute directly the mfpt only for the first generations , see fig . fortunately , the particular construction of the t - graph and the connection @xcite between effective resistance and first - passage time allow us to calculate analytically the mfpt to obtain an explicit formula . details will be given below . ( color online ) mean first - passage time @xmath45 as a function of the iteration @xmath2 on a semilogarithmic scale . the red squares are the numerical results obtained by direct calculation from eqs . ( [ hitting01 ] ) and ( [ hitting03 ] ) , while the full blue squares represent the exact values from eq . ( [ hitting07 ] ) , both of which agree with each other . ] in the following text , we will use the connection between the electrical networks and random walks to derive the closed - form expression for mfpt @xmath45 , avoiding the computation process for inverting any matrix . given a graph , the underlying electrical network @xcite can be obtained by replacing each edge of the original graph with a unit resistor . the effective resistance between any node pair @xmath14 and @xmath30 is defined as the voltage when a unit current enters one node and leaves the other . it has been proved that the effective resistance is a distance measure , so the quantity is also called resistance distance @xcite . thus , we can view @xmath0 as a resistor network by considering all edges of @xmath0 to be unit resistors . previous work @xcite showed that many problems on a resistor network are closed related to the classic random walks on the original graph . for example , the computation of effective resistance between two nodes in a resistor network can be expressed by the fpt between the two nodes on the corresponding network : for an arbitrary connected graph , the effective resistance @xmath49 between a pair of nodes @xmath14 and @xmath30 is equal to @xmath50 , where @xmath51 is the total number of edges in the graph , and @xmath52 is the expected time for a walker starting at node @xmath14 to first reach @xmath30 . in fact , @xmath53 is the average time that a walker , originating at node @xmath14 , will take to hit node @xmath30 and go back to @xmath14 , and it is often called commute time @xcite between @xmath14 and @xmath30 denoted as @xmath54 , i.e. , @xmath55 . according to the close relation between commute time and effective resistance , we have that for @xmath0 , the effective resistance @xmath56 between a pair of nodes @xmath14 and @xmath30 is @xmath57 ," +"the phase space of stckel potentials is completely occupied by four major families of regular orbits : the boxes , and the three families of tubes ( @xcite ; @xcite ) . roughly the same is true in many nonrotating triaxial potentials corresponding to mass models with smooth cores : most of the orbits have shapes that can be identified with one of the four families of regular orbits in stckel potentials ( @xcite ) . however the situation is very different in triaxial models with divergent central densities , or cusps . while the tube orbits are not strongly affected by cusps , the boxlike orbits orbits with stationary points and filled centers are often rendered stochastic , except when they are associated with a resonant orbit that avoids the center ( @xcite ; @xcite ; @xcite ; @xcite ) . kormendy pointed out already in 1985 that many early - type galaxies and bulges have central brightness profiles that deviate slightly but systematically from that of an isothermal core . the significance of this deviation was not recognized for ten more years , however , due to an optical illusion associated with projection onto the plane of the sky . a luminosity density profile that varies as @xmath7 at small radii generates a power - law cusp in projection only if @xmath8 . when @xmath9 , the surface brightness exhibits a curving , logarithmically - divergent central profile ( e.g. @xcite , fig . 1 ) , and for @xmath1 the central surface brightness is finite . the observed brightness profile of a galaxy like m87 , which has a cusp with @xmath10 ( @xcite ) , differs only subtly from that of a galaxy with an isothermal core ( @xcite ) . this is true in spite of the fact that the cusp in m87 is well resolved from the ground . thus even if galaxies were distributed uniformly over @xmath3 , their central brightness profiles would appear to fall into one of two distinct categories : the `` cores '' ( @xmath11 ) and the `` power - laws '' ( @xmath8 ) . just such a dichotomy was proposed following the first nuclear brightness measurements from hst ( @xcite ; @xcite ) . merritt & fridman ( 1995 ) suggested that the centers of _ all _ early - type galaxies , including the core galaxies , might contain power law cusps in the space density . they used a nonparametric deprojection algorithm to confirm this hypothesis for six galaxies observed with hst . gebhardt et al . ( 1996 ) subsequently reanalyzed the full sample of 42 early - type galaxies observed by lauer et al . ( 1995 ) and verified the power - law nature of the deprojected cusps in each case . they also confirmed a tendency , noted earlier by kormendy ( 1985 ) , for the brightest galaxies to have the shallowest cusps . most of the theoretical work on orbital motion in triaxial potentials has focused on mass models with cores , @xmath12 , or with steep cusps , @xmath13 . but galaxies with cores probably do not exist ; and only the faintest ellipticals , @xmath14 , have cusps that are predictably as steep as @xmath15 . here we present the first detailed study of periodic orbits in triaxial models with weak cusps , @xmath16 , characteristic of bright elliptical galaxies . the value @xmath9 is a natural one for separating `` weak '' from `` strong '' cusps , since a central density that increases more rapidly than @xmath17 implies a divergent central force . for instance , a spherical galaxy with dehnen s ( 1993 ) density law @xmath18 has a gravitational force @xmath19 dehnen s law , with @xmath13 ( @xcite ) and @xmath9 ( @xcite ) , has been shown to accurately describe the brightness profiles of a number of early - type galaxies . the triaxial generalization of dehnen s law , @xmath20 @xmath21 was presented by merritt & fridman ( 1996 ) , who derived expressions for the gravitational potential , force and force gradients for @xmath22 . our primary concern here is with the closed `` boxlets '' , the low - order resonant orbits that act as parents of the boxlike orbits in non - integrable triaxial potentials . most important is the @xmath2- ( long- ) axis orbit , which generates the box orbits in stckel potentials . its instability usually occurs through the bifucation of a @xmath23 resonant orbit , or `` banana . '' ( we adopt miralda - escud & schwarzschild s ( 1989 ) scheme for labeling the closed boxlets ; their figure 4 illustrates the different types . ) higher - order resonances produce the `` fish '' ( @xmath24 ) and `` pretzel '' ( @xmath25 ) orbits . boxlets corresponding to each resonance are expected to exist in all three of the principal planes of a triaxial model , at least at certain energies and for certain values of the model axis ratios . however little is known about the dependence of boxlet stability on model parameters . in particular , the vertical stability of the closed boxlets has been very little explored . in the present paper , we locate and test the stability of the axial orbits , the bananas , and the fish as a function of the three parameters that define dehnen s models : the cusp slope @xmath3 ; the short - to - long axis ratio @xmath26 ; and the degree of triaxiality , expressed in terms of @xmath27 . @xmath28 corresponds to oblate - axisymmetry , and @xmath29 to prolate - axisymmetry . for each set of model parameters , we present results as a function of energy ; thus we explore a four - dimensional parameter space for each of the orbit families . a total of approximately @xmath30 orbits were investigated . the numerical scheme for evaluating the stability of the boxlets is presented in 2 . the results for the axial orbits , the bananas and the fish are presented in 3 , 4 and 5 respectively . our results are summarized in 6 . there is increasingly strong evidence for dark mass concentrations , possibly supermassive black holes , at the centers of many early - type galaxies ( @xcite ) . we ignore the ( possibly substantial ) effect that such singularities would have on the behavior of boxlike orbits : partly because the universality of central black holes has not yet been established ; and partly because the behavior of orbits in triaxial galaxies with cusps provides an essential first step toward understanding the additional effects of a central black hole . we applied a numerical version of the standard floquet - liapunov theory ( @xcite ; @xcite ) to evaluate the stability of the lowest - order periodic orbits in dehnen s model potential . our approach was similar to that of earlier studies ( e.g. @xcite ; @xcite ) , with one difference . instead of integrating a set of orbits whose initial conditions were offset by small , finite amounts from those of the closed orbit , we integrated the linearized equations corresponding to a set of infinitesimal perturbations about the closed orbit . our results are therefore strictly independent of the numerical amplitude of the perturbation . let @xmath31 , @xmath32 be the parametric representation of a closed orbit . the equations of motion are @xmath33 a nearby orbit has coordinates @xmath34 , @xmath35 . for small @xmath36 and @xmath37 , the equations of motion are @xmath38 subtracting equations ( [ motion ] ) from equations ( [ linmotion ] ) , we have @xmath39 or @xmath40 the second derivatives of the potential , @xmath41 , are taken along the closed orbit whose period is @xmath42 . expressions for the @xmath41 are given by merritt & fridman ( 1996 ) . the stability of the closed orbit is then determined by the eigenvalues of the monodromy matrix @xmath43 , where @xmath44 and @xmath36 has been redefined to include velocities . we computed the elements of @xmath43 by numerically integrating the six linearized equations of motion ( [ matrix ] ) , starting from unit perturbations in each of the coordinates . a 7/8th order , variable timestep integrator the routine dopri8 of hairer et al . ( 1987 ) was used . initial conditions for the non - axial closed orbits were found by an iterative newton method , and precise orbital periods were calculated using the scheme of hnon ( 1982 ) . two of the eigenvalues of @xmath43 are guaranteed to be unity ; these correspond to eigenvectors lying along the closed orbit . the remaining four eigenvalues satisfy @xmath45 , @xmath46 ; the stability of the closed orbit is determined by the parameters @xmath47 , @xmath48 , with @xmath49 denoting instability ( @xcite ) . for orbits that lie in a symmetry plane , @xmath50 and @xmath51 correspond to perturbations in the orbital plane and perpendicular to the orbital plane , or vice versa . for the simplest orbits , the full set of six perturbation equations is not required ; for instance , the stability of the axial orbits can be evaluated using just four independent perturbations . axial orbits presented one complication , however . while the gravitational force @xmath52 is everywhere finite in dehnen models with @xmath1 , the second derivatives of the potential diverge at the origin as @xmath53 , @xmath45 , etc . integrations using an algorithm based on finite - amplitude perturbations were carried out for some orbits and compared to the results of the linearized code . finally , numerical surfaces of section were constructed for a few models and compared to the results from the stability calculations . all orbits in a given model were assigned energies from a discrete grid , consisting of 20 energy values that corresponded to the values of the potential on the @xmath2-axis of a set of ellipsoidal shells with the same axis ratios as the density that divide the model into 21 sections of equal mass . thus , shell 1 encloses @xmath54 of the total mass , shell 2 encloses @xmath55 , etc . henceforth units are adopted such that @xmath56 . the long- ( @xmath2- ) axis orbit is stable at all energies in integrable triaxial potentials and acts as the parent of the box orbits ( @xcite ; @xcite ) . in more general triaxial potentials , like the ones considered here , the @xmath2-axis orbit becomes unstable at high energies when its frequency of oscillation falls to @xmath57 the average oscillation frequency of a perturbation in the direction of the short or intermediate axis ( @xcite ) . a bifurcation then occurs , with the @xmath23 @xmath4 or @xmath5 banana orbit branching off . a similar bifurcation occurs from the intermediate ( @xmath58- ) axis orbit , producing the @xmath6 banana . nearer the center , the @xmath58- and @xmath59-axis orbits become unstable at the bifurcation points of the @xmath60 loop orbits . in models with a harmonic core , the loop orbits first appear just outside of the core ( @xcite ) . the @xmath5 loop is the parent of the short - axis tubes , and the @xmath6 loop is the parent of the long - axis tubes . the @xmath4 loop is generally unstable and generates no families of regular orbits ( @xcite ) . in models without cores , the loops and their associated tube orbits may exist all the way into the center . figures 1 and 2 display the stability diagrams for the @xmath2- and @xmath58- axis orbits in dehnen s potential , for three values of @xmath61 and four values of @xmath3 ; a total of 4104 orbits are displayed in each figure . four cases" +"living organisms are not passive objects which filter out blindly the modifications of the environment in which they live . on the contrary , both unicellular and multicellular organisms are biochemical systems that receive information from different environmental sources , process this information , and consequently make decisions . these actions allow them to adapt their behavior to the information received . the existence of different input signals thus explains why cells with identical genetic content may sometimes behave differently . the net effect of this information - relay process is the activation or inhibition of key regulatory elements that commit the cell to perform specific tasks , such as taking nutrients , secreting chemicals , proliferating , or communicating with other cells in a tissue . in this way , the cellular signaling machinery @xcite acts as a decision - making device that maps the large number of inputs signals to a reduced set of behaviors characterized by specific outputs @xcite . all these physiological processes are implemented in the cell by signal transduction networks composed of large numbers of interacting proteins . many of these networks receive information about conditions outside the cell , which activate receptor proteins located at the membrane ( see fig . [ fig : celldiagram ] ) . the activation of these receptors triggers a cascade of downstream biochemical reactions that ultimately modify the state of the cell , by controlling both dna expression and protein levels . hence , signaling pathways integrate the signals coming from the environment , and define the response of the cell to the particular external situation in which it is living . these signaling routes have traditionally been studied as isolated cascades which do not interact with each other very strongly . however , it is well known that the different signaling pathways are interconnected , and recent studies have shown that this feature can not be neglected @xcite . in other words , one ought to refer to signaling networks , rather than signaling pathways . the fact that cells process information using an entire network of protein interactions means that the dynamical behavior can be much richer than the one obtained if signaling paths were uncoupled @xcite . , scaledwidth=41.0% ] these complex signal transduction processes must work reliably even in the presence of a substantial amount of environmental noise . indeed , the level of extracellular molecules representing a given external signal is likely to fluctuate in time . more fundamentally , non - saturating levels of external signals will induce stochastic activation of their receptors , leading to random fluctuations that are transmitted down the signaling network and are bound to interfere with its information - processing tasks . the question then arises , whether signaling networks have evolved to filter out the unavoidable levels of noise existing in the extracellular milieu @xcite , or to use it in a constructive manner @xcite . in fact , a large body of evidence has been gathered in the last decades within the fields of statistical and nonlinear physics , showing that random fluctuations can be a source of order ( both temporal and spatial ) in nonlinear systems @xcite . a well - established example of such a constructive influence of noise is _ stochastic resonance _ , a process through which an information - carrying signal ( periodic or non - periodic ) is amplified by an optimal amount of noise acting on the system ( internally or externally ) @xcite . this mechanism was initially proposed by @xcite as an explanation of the occurrence of ice ages in earth s climate ( where the signal to be amplified corresponds to periodic variations in the amount of energy received by the earth from the sun , and the noise arises from all other contributions to climate fluctuations ) . after successful experimental demonstrations in lasers @xcite and in chemical systems @xcite , interest in this phenomenon grew and extended to biological systems , namely sensory neurons , where the phenomenon was amply demonstrated @xcite . stochastic resonance arises in neuronal systems due to their excitable character @xcite . specifically , the noise - induced enhancement originates from the fact that neurons are threshold devices , and noise helps a time - varying ( or space - varying ) signal to surpass this threshold in a manner that is correlated with the signal itself @xcite . this mechanism can act even if there is no external input signal acting upon the system , with noise extracting instead an internal temporal ( or spatial ) scale existing within the system s dynamics . this latter mechanism is called _ stochastic coherence _ @xcite , or more commonly _ coherence resonance _ @xcite , and has been suggested to exist in genetic oscillators @xcite . there are other examples of the constructive effects of noise beyond stochastic resonance and stochastic coherence . most notably , noise has been seen to induce transitions , both in time @xcite and in space ( in that case one speaks of noise - induced _ phase _ transitions ) @xcite . in those situations , the statistical properties of the system change when noise is varied beyond a certain critical threshold , so that new states appear as a result of random fluctuations . experimental preliminar evidence of this type of behavior in genetic systems has been presented by @xcite , but there is still much work to do in this direction . in the context of cellular signaling , it is appealing to think that environmental noise might be used by the cell in a constructive manner , similarly to what happens in stochastic resonance , to detect and amplify information - carrying signals . preliminary theoretical evidence in this direction has been recently presented @xcite . however , the implication of this type of mechanism on signal integration processes is still an open question . in fact , despite the effort made during decades , signal integration is far from being completely understood . one of the reasons behind this problem is that a detailed theoretical description of a cell is proving difficult , because cells are extremely complex objects . the chemistry of cells operates at multiple levels , spanning for instance signaling interactions , genetic expression , and metabolism , and each of these levels of operation is mediated by many chemical species that interact in a strongly nonlinear manner , forming highly complex dynamical webs . in this paper , we discuss work that moves away from classical signaling studies that focus on only one ligand , and examine instead the effects of multiple ligands upon the same cell , in the presence of external noise . in particular , we consider whether the ability of cells to integrate signals from one or more sources of information is altered when other input signals provide a chattering environment . to study this problem , we consider a dynamic description of the signaling network of a typical human cell a fibroblast in terms of a previously derived boolean model @xcite . boolean models describe the activity of the different proteins involved in the network in a binary way , as being on or off , and are iterated in order to update the protein activity states according to logical rules acting in each node . even though there is no well defined time scale in this type of model , boolean models have been shown to reproduce ordered sequences of cellular events @xcite . the model we use was constructed manually by @xcite using the large body of scientific literature available for this type of cell , and it represents one of the largest signaling network models currently available . despite representing a simplified view of the real network , it offers a good balance between a realistic description and a model simple enough to be studied theoretically . indeed , this model was shown to reproduce experimental results satisfactorily @xcite . using this model , we explore systematically , by means of numerical simulations , the effect of a chattering environment in the integration of input signals . as described above , we use a boolean model of signal transduction to study signal integration in varying environments . this choice is appropriate for our purposes , since it defines the level of activity of the molecules that compose the signaling network . boolean networks ( bn hereafter ) were introduced by @xcite as sets of dynamical units , called _ nodes _ , which are connected with each other by interaction _ edges_. the state of every node @xmath0 at each discrete time @xmath1 , @xmath2 , is either on ( @xmath3 ) or off ( @xmath4 ) , and all nodes are updated according to a set of node - specific logic rules that define the dynamics of the system . for signaling networks , the state of each node corresponds to the level of activity of a specific protein , and edges represent their interactions . we will consider two types of nodes , determined by their definition : _ input _ nodes and _ internal _ nodes . on the one hand , the state of _ input _ nodes is independent from the state of other nodes of the network and determined externally . these nodes represent signals outside the cell ( i.e. the external environment ) , and may evolve deterministically ( for instance , being maintained to a fixed value of activity or oscillating at a specific periodicity ) or stochastically . here we set these states using random value sequences . on the other hand , every _ internal _ node @xmath0 has an associated logic rule , @xmath5 , which determines the new state @xmath2 at time @xmath1 from the states of its @xmath6 incident nodes at time @xmath7 ( note that @xmath8 may include the node @xmath0 itself ) : @xmath9 [ fig : network ] the fibroblast signal transduction network analyzed in this paper @xcite consists of nine input nodes and 130 internal nodes interconnected by a dense web of interactions ( see fig . [ fig : network]a ) . the input layer contains cytokines ( il1/tnf-@xmath10 ) , growth factors ( egf ) , extracellular matrix components ( ecm ) , oxidative stress , a calcium pump and different g protein - coupled receptor ligands . @xcite chose six of the 130 internal nodes to be _ outputs _ of the network ( the proteins akt , erk , rac , cdc42 , sapk and p38 ) . the motivation for choosing these six output species was their role in regulating specific cellular processes : apoptosis ( akt ) , gene transcription ( erk ) , cytoskeletal regulation ( rac and cdc42 ) , and cellular stress ( sapk and p38 ) . the activity of every input node @xmath0 has been implemented as a stochastic sequence in which each state ( 0 or 1 ) derives from an independent draw of a bernoulli distribution with success probability equal to @xmath11 ( where @xmath11 is held constant within each run ) . in this way , the parameter @xmath11 is what we define as the _ chatter level _ for node @xmath0 . the produced sequences of states , @xmath2 , show an intrinsic variability , which is maximal at @xmath12 , and decreases monotonically when @xmath11 approaches to 0 and 1 . here we calculate the bernoulli draws with a standard mersenne twister pseudo - random number generator @xcite . we are interested in the average activity of each node @xmath13 over time and over multiple realizations ( which might correspond to different cells in a population ) : @xmath14 note that , for input nodes and sufficiently long dynamical evolutions , @xmath15 . to illustrate this procedure , the upper panel in" +"this review article is concerned with fermionic property of heavy ions ( many - nucleon systems with the size up to several 10-femtometers ) colliding at the energy of a few mev per nucleon . in the following , we refer to those collisions as low - energy heavy - ion collisions . fusion is not necessarily achieved in the low - energy heavy - ion collisions , neither is fragmentation . reaction dynamics and the resulting products can be drastically different depending on the impact parameter , the mass of colliding ions , and so on . therefore , the reaction mechanism of low - energy heavy - ion collisions is worth investigating to understand the production of chemical elements . this is deeply concerned with an open problem as for the existence and the origin of chemical elements including their production mechanism . charge equilibrium in heavy - ion reactions means the states with the proton - neutron ratio corresponding to the average of the two colliding ions , and charge equilibration is the process leading towards charge equilibrium . the chemical property of final products can be different depending on whether charge equilibration appears or not , being determined by the number of protons . there is a relatively long research history for the charge equilibration . in fact many experiments of low - energy heavy - ion collisions were carried out in the 1960 s . in those experiments most of the final products were reported to be in charge equilibrium , even when the fragmentation takes place @xcite . there should not be any restrictions to the proton - neutron ratio of the final products if the final product forms a kind of stable bound system , so that these experimental results can not be trivially understood . one of the most important features of charge equilibration is its rapidness taking as much as a few 10@xmath0 s @xcite . this time scale is actually short in the order of magnitude compared with the typical reaction time of low - energy heavy - ion collisions ( 1000 fm / c @xmath1 10@xmath2 s ) , so that charge equilibration has been recognized as an inevitable and dominant process in low - energy heavy - ion reactions . the relation between charge equilibration and the isovector giant dipole resonance has been studied relatively well because of the correspondence in their time scales , but no decisive conclusion has ever been obtained . indeed , including the question of `` when does charge equilibration take place ? '' , many things could not be explained merely by the isovector giant dipole resonance . for the theoretical research on the relation between charge equilibration and the isovector giant dipole resonance , the importance of dipole mode to charge distribution of a fissioning nucleus was pointed out by hill - wheeler @xcite in the 1950 s . research on charge equilibration using time - dependent mean field calculations were started in the 1970 s ( bonche - ng @xcite ) . recently research based on three - dimensional time - dependent mean field calculations was carried out by simenel - chomaz - de france @xcite . in this article , based on ref . @xcite , the unknown relation between charge equilibration and the zero sound propagation is presented . it leads to a rather universal recognition of zero sound propagation in femto - scale quantum liquids , which can not necessarily be reduced to the giant dipole resonance . let us denote a many - particle wave function by @xmath3 . it is assumed to satisfy @xmath4 where @xmath5 denotes the hamiltonian operator . the solution can be represented by @xmath6 under a suitable boundary condition , if @xmath5 does not depend on @xmath3 . let the corresponding probability density be @xmath7 , and begin with the classic theory of sound propagation inside gases . readers may wonder why sound propagation is related to charge equilibration , it will be clarified step by step . let the equilibrium probability density be @xmath8 . if the fluctuation is added to the equilibrium : @xmath9 a force arises from the gradient pressure . here the essential property of sound propagation is extracted from the simplified linearized analysis . the equation of motion is given by @xmath10 where @xmath11 and @xmath12 denote the velocity and the pressure , respectively . the pressure @xmath12 depends on both @xmath13 and the entropy @xmath14 . on the other hand , the equation of continuity is given by @xmath15 the right hand side is approximated by @xmath16 to the lowest order . after differentiating this equation by @xmath17 , an equality is derived together with the divergence of eq . ( [ eq2 - 1 ] ) . if we further assume that @xmath12 is expanded with respect to @xmath18 at a fixed entropy , the lowest order contribution brings about @xmath19 this is a wave equation for @xmath18 , where @xmath20 represents the propagation speed of the density . for example , @xmath20 is given by @xmath21 for the perfect fermi gas in its ground state ( @xmath22 ) , where @xmath23 means the fermi velocity . this type of propagation is called first sound , which provides a picture for particles propagating with changing density . on the other hand , we should pay attention to the propagation of particle without changing density . this type of propagation is called zero sound , which has a finite frequency even when the wave number is equal to zero ( cf . zero point vibration ) . to understand zero sound , the linear response is considered for a given external field @xmath24 : @xmath25 where @xmath26 denotes the number density operator . in particular , if we restrict ourselves to the impulsive perturbation @xmath27 , the linear response is @xmath28^{-1 } -1 \right ) , \end{array}\ ] ] where @xmath29 denotes the retarded generalized dielectric function . the resonance frequency can be calculated by the pole of the integrand of the right hand side . eventually we assume the phonon dispersion relation ( @xmath30 ) , which reproduces the frequency of propagating wave , and is nonzero even when the wave number is equal to zero : @xmath31 then the resonance frequency is obtained . consequently the dispersion relation at long wave length becomes @xmath32 where @xmath33 ; @xmath34 and @xmath35 denote the mass and the fermi wave number , respectively . note that this relation is the representation in momentum space . the lower - limit of the velocity for zero sound is the fermi velocity , because the non - damping mode can only exist when @xmath36 ( see the denominator inside the logarithmic function ) . if @xmath37 is assumed in the limit @xmath38 , the left hand side becomes @xmath39 , and the propagation velocity of zero sound is represented using @xmath40 . for the weak - coupling limit ( @xmath41 ) : @xmath42 and for the strong - coupling limit ( @xmath43 ) : @xmath44 this shows that the propagation velocity of zero sound is almost equal to @xmath23 in the weak - coupling limit . it is just @xmath45 times faster than the previously seen first sound velocity of the perfect fermi gas . a rather general discussion shows that zero sound is faster than first sound @xcite . roughly speaking , the matter waves without changing density propagate more easily than those with changing density , because the change in density possibly leads to the appearance of larger restoring force . zero sound provides a picture of particle exchange within a quite short time ( but not instantaneous ) . two different sound propagations in fermi liquids have been discussed in terms of whether they entail the density change or not . in particular there exists zero sound in fermionic many - body system , which is different from and faster than the ordinary sound . zero sound has been known to arise from the collective dynamics of the fermionic many - body systems . all the collective dynamics is actually based on the propagation of zero sound , while there are various representations ( various modes ) for the collective dynamics . one distinct difference between zero and first sounds is their relation to collisions between particles . first sound appears when the states are in local thermal equilibrium . this corresponds to the situation when the mean interparticle collision time is sufficiently smaller than the oscillation period of the propagating wave . meanwhile zero sound is associated with the collective excitation mode , which disappears when there are many collisions between particles . this corresponds to the situation when the mean interparticle collision time is larger than the oscillation period of the propagating wave . although such a collisionless energy regime is expected to be realized due to the pauli principle , its validity should be confirmed for an individual physical system . consequently zero sound is expected to be important to low - energy phenomena , while first sound becomes effective at higher energies . for the usage of the terminology low and high energies , we had better note that both sounds are scaled by @xmath23 ( i.e. fermi energy ) . for more details of sound propagation , see sec . 5 of ref . @xcite . as a theoretical research on the zero sound in fermionic many - body systems , landau s fermi liquid theory @xcite is well known , where zero sound propagation was actually seen in liquid @xmath46he @xcite . however , there is no guarantee that such a sound plays a role in heavy - ion reactions . there are two essential differences between heavy - ion reactions and the @xmath47he case ; the physical system consists of finite numbers of nucleons , and the event is accomplished within a finite time interval . that is to say , both size and time are highly restricted in heavy - ion reactions . indeed , in the context of many - nucleon systems , the main interest of zero sound propagation was not in heavy - ion reactions but in nuclear vibrations ( for example , see ref . @xcite ) . in the following the mechanism of charge equilibration is discussed with respect to whether it is achieved by nucleon propagation with or without changing density . as an example of fermionic many - body systems , we consider a many - nucleon system . there are two types of nucleons , that is , protons and neutrons . charge equilibration is the mixing of protons and neutrons due to the time evolution , therefore it is a kind of chemical mixing . apart from such a chemical equilibration , there are several kinds of equilibration in heavy - ion reactions , that is , mass equilibration , momentum equilibration , and thermal equilibration . among them charge equilibration ( chemical equilibration ) has drawn special attention because of its crucial role in the synthesis of chemical elements . let us consider the collision of two ions . the existence of an upper energy limit for charge equilibration has been pointed out by iwata - otsuka - maruhn - itagaki @xcite for the first time . the limit is presented by a formula explaining both experiments and numerical calculations based on microscopic three - dimensional time - dependent mean - field theory . furthermore , the upper energy limit has been concluded to be determined by the fermi energy . @xmath48 } % \vspace{2.5 mm } \nonumber \\ \displaystyle \frac{e_{lab}}{a } = \frac{\hbar^2 ( 3 \pi^2 \rho_{\rm min})^{2/3}}{2 m } + \frac{e^2 z_1 z_2}{4 \pi \epsilon_0 r_0 } \frac{a_1 + a_2 } { a_1 a_2 ( a_1^{1/3}+a_2^{1/3 } ) } , \end{array}\ ] ] @xmath49 where @xmath50 identifies the two colliding ions , and @xmath51 means the" +"the magnetocentrifugal mechanism is the leading candidate for producing the jets and winds observed around young stellar objects . the basic principle is relatively simple , and has been understood for a long time @xcite . it envisions parcels of fluid element being lifted off and accelerated centrifugally along rapidly rotating open magnetic field lines anchored firmly on an accretion disk . beyond a certain point where the energy densities in the bulk flow motion and magnetic field are comparable , the field lines can no longer enforce rigid rotation , and the field becomes increasingly toroidal . it is the `` hoop stress '' associated with the toroidal field that is thought to be responsible for the wind collimation and jet production . the quantitative properties of the jet expected from this mechanism are poorly determined however , even though the mhd equations that govern the wind structure and jet formation are well known . our understanding of the jet properties has been hampered to a large extent by the mathematical difficulties associated with obtaining wind solutions . there are two basic approaches in obtaining wind solutions . the first is to solve for the steady - state wind structure directly from the time - independent mhd equations . these equations can be cast into a second order partial differential equation ( the grad - shafranov equation ) . it is well known that , for a cold wind that we are interested in here , the equation changes its type from being elliptic inside the fast ( magnetosonic ) surface to hyperbolic outside . computationally , the structure of the inner part of the wind inside the fast surface can be solved first by relaxation , and that beyond the fast surface later by the method of characteristics @xcite . the fact that the position of the fast surface , where the poloidal flow speed matches the fast magnetosonic speed , is unknown a priori poses a problem . to obtain a converged solution , one needs to have a good initial guess of the fast surface position , which is generally difficult to obtain . a more flexible approach is to numerically follow the time evolution of a wind to steady - state , if such a state exists . this approach has been taken by several groups @xcite . it is also the approach that we took @xcite . our simulations are based on the zeus mhd code , and treat the keplerian disk as a ( lower ) boundary , on which an open magnetic field of a prescribed distribution is anchored and from which cold material is injected into the wind at a prescribed rate . a novel feature of our simulation is the treatment of the region near the rotation axis , where the magnetocentrifugal mechanism is ineffective . the reason is that to launch a cold parcel of fluid element centrifugally from a keplerian disk the field line must incline an angle of at least @xmath0 away from the disk normal @xcite . this condition is not met in the axial region since the field line along the axis must be exactly vertical by symmetry . in reality , the axial region may be filled with a normal stellar wind from the central object or bundles of open field lines from the stellar magnetosphere . we are thus motivated to inject a light fluid with little mass flux at a speed fast enough to escape from the potential well along those field lines that fail to operate magnetocentrifugally . the light axial flow provides a plausible inner boundary to the magnetocentrifugal disk - wind , the focus of our investigation . a typical example of the steady - state disk - wind solutions obtained from time - dependent simulations is given in fig . the wind is driven off all of the ( equatorial ) disk surface . flow acceleration is apparent along all field lines except those near the axis where a fast initial injection is imposed . note that the field ( and stream ) lines collimate gradually , as expected . what was not expected was the great care that went into designing the shape of the simulation box , so that a steady state could be reached at all . if we were to cut the box shown in fig . [ fig1 ] in half or to elongate the box horizontally instead of vertically , and restart the simulation with the same initial and boundary conditions , the wind would become chaotic . the sensitive solution dependence on the simulation box has also been noted by others @xcite . it is a major concern for the time - dependent approach to finding disk - wind solutions . we believe that the simulation box dependence described above comes from the fact that a large fraction of the wind remains completely sub fast - magnetosonic in the computational domain , as shown in lower - right corner of fig . information on the sub - fast outer boundary can propagate upstream all the way to the disk surface and interfere with the wind launching . the reason for the region to remain sub fast is simple : the wind coming off the outer part of the disk encounters the edge of the simulation box too soon ; it simply does not have enough room to get accelerated to the fast speed . this situation remains as long as the wind is driven off from _ all _ of the ( equatorial ) disk plane ( as assumed in fig . [ fig1 ] and other previous time - dependent disk - wind simulations ) regardless of the box size . it motivates us to restrict the wind launching to only the inner region of an accretion disk , and focus on inner - disk driven winds for which the simulation box dependence disappears . physically , the wind launching may be limited to the inner region of a protostellar disk where the temperature is high enough ( greater than @xmath1 k ) that thermal ionization of alkali metals can provide enough charges to couple the magnetic field to the disk matter . for typical parameters , this occurs inside a radius of order 1 au . numerically , we set up the simulation as sketched in fig . [ fig2 ] . to fill all available space above ( and below ) the equatorial plane , we demand the last field line anchored at the outer radius of the launching region @xmath2 to lie exactly on the equatorial plane . wind plasma sliding along this last ( horizontal ) field line will become super fast - magnetosonic in the computational realm , provided that the size of the simulation box is sufficiently large . once the whole fast surface is completely enclosed inside the simulation box , the size and shape of the box would have minimal effects on the structure of the wind , especially near the launching surface , since information can not propagate upstream in a super fast region . in this way , we should be able to study the wind structure up to arbitrarily large distances from the source region , limited only by computer time . for illustration , we consider a specific example . we adopt as the launching conditions on the disk a power - law distribution of the vertical field strength with radius as @xmath3 and a mass injection rate ( per unit area ) @xmath4 between 0.1 and 0.8 au . the inner radius is chosen to mimic the disk truncation radius due to the stellar magnetosphere . inside this radius , we inject a fast light flow as described earlier . at the edge of the wind launching region , taken to be @xmath5 au for simplicity , we impose the condition that @xmath6 since the last field ( and stream ) line must be horizontal . a cubic polynomial is used to connect smoothly the values of @xmath7 ( or @xmath8 ) between 0.8 and 1 au . as before , we follow the time evolution of the wind numerically to a steady state . the steady wind solution , from the launching surface ( inside 1 au ) all the way to a large distance of @xmath9 au , is displayed in fig . [ fig3 ] on two scales . au ( _ bottom panel _ ) box . the fast surface ( _ dashed line _ ) is also plotted in the smaller box . the streamlines divide the wind into 10 zones of equal mass flux , with a total mass flux of @xmath10yr@xmath11 per side of the disk . the gray scale shows the log of the hydrogen number density , with three shades per decade . the density contours correspond to @xmath12 , @xmath13 , @xmath14 and @xmath15 in units of @xmath16 . ] au ( _ bottom panel _ ) box . the fast surface ( _ dashed line _ ) is also plotted in the smaller box . the streamlines divide the wind into 10 zones of equal mass flux , with a total mass flux of @xmath10yr@xmath11 per side of the disk . the gray scale shows the log of the hydrogen number density , with three shades per decade . the density contours correspond to @xmath12 , @xmath13 , @xmath14 and @xmath15 in units of @xmath16 . ] several features are worth noting . first , the fast surface shown in the smaller box closes on the equatorial plane , as advertised . this closure enabled us to continue the wind solution on to large distances without having to worry about the effects of box size . second , the wind speed is anisotropic , with a value roughly 3 times higher in the axial region than in the equatorial region . the anisotropy appears to be even stronger in density , which is stratified more or less cylindrically ( or jet - like ) near the rotation axis , as expected . in the more equatorial region , the density contours bulge outward prominently , retaining some memory of the nearly horizontal shape of the initial density contour . this non - cylindrical shape of density contours is significant because the wind emission in forbidden lines such as [ sii]@xmath176716,6731 is sensitive to the density @xcite , and the shape of the jet may resemble to a zeroth order the shape of the density contour at some fiducial value . we choose to represent the outer boundary of a `` jet '' by a fiducial density contour of @xmath12 @xmath16 ( the outermost contour in the larger box of fig . [ fig3 ] ) . the `` jet '' so defined has a width of @xmath18 au at a height of @xmath9 au , comparable to that observed in hh 30 jet . the bulging out at the `` jet '' base is not observed , however . furthermore , the `` jet '' contains only about a quarter of the total wind mass flux , making its formation rather inefficient . these undesirable `` jet '' features demonstrate that not all combinations of the launching conditions are capable of producing cylindrical jets that contain the majority of the wind mass flux . we find that one way to improve the jet shape _ and _ increase its mass flux fraction is to make the mass injection rate @xmath8 on the disk decrease more steeper with radius . the details will be presented in a forthcoming paper . to summarize , by limiting the wind launching to the inner part of an accretion disk , we are able to obtain using time - dependent simulation steady - state wind solutions that extend from the launching surface to large distances . combined with a detailed calculation" +"thermodynamics is an integral cornerstone of our understanding of the physical world , where the core principles are based on the existence of a thermal equilibrium . for systems driven out - of - equilibrium , the governing principles are much less understood ; see _ e.g. _ @xcite . it is extremely difficult to address such questions in a strongly coupled quantum system . first , given a microscopic description , conventional perturbative techniques are inadequate at strong coupling . second , conceptual insights that may lead to an effective description are also lacking . in recent years , the ads / cft correspondence@xcite , more generally the gauge - gravity duality@xcite , has emerged to be an extremely powerful tool to address aspects of strongly coupled physics . string theory provides a large class of concrete examples where this correspondence is precise . many of these examples correspond to a strongly coupled conformal or a scale - invariant field theory and is naturally equipped in describing quantum criticality . however , criticality is not necessary . the duality works for generic large-@xmath0 gauge theories with a running coupling constant@xcite , or a confining gauge theory@xcite . in this article , we will use the gauge - gravity duality to explore an emerging principle for a system driven out - of - equilibrium . we will consider a non - equilibrium steady - state ( ness ) situation within a probe sector which is kept in contact with a large background at some given temperature @xmath1 . the ness in the probe sector is induced by introducing a constant external electric field @xmath2 that drives a constant current . we will argue that _ all modes _ in this probe sector experience an effective temperature , denoted by @xmath3 , with respect to which it has a purely thermal behaviour . we will also argue that for conformal systems this effective temperature is always larger than the background temperature : @xmath4 . by virtue of the probe limit , the heat flow between the probe sector and the background is suppressed . for critical systems , @xmath3 depends only on three ingredients : ( i ) dimensionality @xmath5 , ( ii ) the global symmetry group @xmath6 and ( iii ) how ness is induced , _ i.e. _ , @xmath2 . for gapped systems , or systems with a running coupling constant , there may be additional dependences on the beta function of the gauge coupling or other dimensionful parameters in the system . the existence of the unique effective temperature @xmath3 is , nonetheless , ubiquitous . in generic situations one can verify that @xmath7 . however , there may be special cases when this is not true , see _ e.g. _ the consequences of this are rather profound : it allows us to define thermodynamics with an effective entropy , obtain a fluctuation - dissipation relation and recover an _ otherwise thermal _ physics for the ness . in this article , we will discuss the main results for a broader perspective and a technically detailed account will appear elsewhere@xcite . in the most familiar example of the ads / cft correspondence @xmath8 for a boundary theory in @xmath5 spacetime dimensions@xcite . in all known examples , the gravity description emerges from the closed string sector . this is typically described by a @xmath9-dimensional geometry of the freund - rubin type : _ e.g. _ ads@xmath10 , where ads@xmath11 denotes the anti - de sitter space in @xmath12-dimensions and @xmath13 denotes a compact manifold . the symbol @xmath14 denotes a warped product geometry . this geometry and the various matter fields are sourced by a collection of a large number of branes , which equivalently gives rise to the adjoint sector of the dual large-@xmath0 , @xmath15 gauge theory . a finite non - zero temperature is realized as the presence of an event horizon in the geometry . the corresponding hawking temperature can be obtained by demanding regularity of the euclidean metric with a compact time direction . we introduce probe degrees of freedom in the background of a thermal adjoint sector , which transform under the fundamental representation of the @xmath15 gauge group . in the full @xmath9-dimensional geometry , this can be achieved by introducing probe branes of appropriate dimensions , which amounts to introducing open string degrees of freedom in the closed - string background . the details of the probe embedding depend primarily on three factors : ( i ) dimensionality , ( ii ) stability of the embedding and ( iii ) the physics we want to realize . this was pioneered in @xcite . clearly , the full details of the @xmath9-dimensional background play a crucial role in such embeddings and each case needs to be studied individually . for simplicity , however , we will abstract away from this detailed constructions and focus on a _ reduced _ description for the probes@xcite . let us begin with a background @xmath12-dimensional metric , in the string frame , of the general form @xmath16 where we assume that the metric functions depend on only one co - ordinate @xmath17 , which is the radial direction . in our convention , @xmath18 is the boundary of the bulk spacetime . the dual field theory lives in the @xmath19-plane . furthermore , we collectively represent the compact manifold by @xmath20 . in this background we introduce @xmath21 number of probe d@xmath22-branes which wrap @xmath23 and @xmath24 of the remaining space - directions ( along with @xmath25 of the compact directions ) . the dynamics of these probes is determined by the dirac - born - infeld ( dbi ) action@xcite @xmath26 + f \right]\right)^{1/2 } , \label{dbi } \\ & = & - n_f t_p \int d^{p+1 } \xi \ , l_{\rm dbi } \ , \\ { \rm with } \quad 1 & = & \left(2 \pi \alpha'\right ) \ , \end{aligned}\ ] ] where @xmath27 denotes the tension of the d@xmath22-brane , @xmath28 denotes the collective coordinates on the brane worldvolume ( including the compact directions ) , @xmath29 is the dilaton field , @xmath30 $ ] denotes the pull - back of the background metric : @xmath31_{ab } = \frac{\partial x^\mu}{\partial \xi^a } \frac{\partial x^\nu}{\partial \xi^b } \ , g_{\mu\nu } \end{aligned}\ ] ] and @xmath32 represents a gauge field on the probe worldvolume . for simplicity , we will assume that @xmath30 $ ] is trivial , _ @xmath33 = g \right |_{\rm worldvolume}$ ] , which means that we assume @xmath34 minimizes the probe worldvolume . here , the subscript @xmath35 denotes the classical profile . note that we have implicitly assumed that the background has vanishing ns - ns two - form . this is chosen for convenience , and a non - vanishing ns - ns two - form will not modify the qualitative physics which we will discuss in this article . the steady - state physics can be induced by having a gauge field on the worldvolume @xmath36 where @xmath2 denotes the electric field along @xmath37-direction and @xmath38 is a function that needs to be determined from the equation of motion . since the dbi lagrangian depends only on @xmath32 , it is a functional of @xmath39 only . thus we immediately get an integral of motion , which we call @xmath40 @xmath41 the above definition of @xmath40 yields the equation of motion for @xmath42 , which can be solved to obtain @xmath43 evidently , the solution for @xmath42 has a sign ambiguity . this can be fixed by demanding an ingoing "" boundary condition at the horizon@xcite , which means that the energy - momentum flows into the horizon . using this , the on - shell dbi lagrangian is obtained to be @xmath44^{1/2 } .\label{lagon}\end{aligned}\ ] ] in general , because of the square - root expressions , the on - shell dbi lagrangian may not be real - valued for all values of @xmath17 . the reality condition demands that the numerator and the denominator change sign at the same radial location @xmath45 . these conditions in turn determine the constant @xmath40 as a function of @xmath45 : @xmath46 here @xmath45 is obtained by solving ( [ ustar ] ) and , as observed by the bulk geometry , is a completely unremarkable position . we will see that this @xmath45 will play the key role for the open string degrees of freedom . following @xcite it can be shown that the constant @xmath40 is proportional to the boundary current driven by @xmath2 and consequently we can define a conductivity , @xmath47@xcite . so far we have discussed the classical profile of the probe brane . let us now discuss the physics of the fluctuation modes on the probe . from the perspective of the dual field theory , these fluctuations are of three kinds : ( i ) scalar , ( ii ) vector and ( iii ) spinor . the scalar fluctuations are the transverse fluctuations of the probe brane embedding : @xmath48 where @xmath49 denotes the classical profile of the probe and @xmath50 represents the collective transverse fluctuations . the vector fluctuations correspond to the fluctuations of the classical gauge field on the probe @xmath51 where @xmath52 is the classical gauge field on the probe in equation ( [ classgauge ] ) . finally , the spinors come from a supersymmetric counter - part of the dbi action in ( [ dbi ] ) , which schematically consists of a standard volkov - akulov type term @xmath53\right)^{1/2 } , \label{dbi2}\end{aligned}\ ] ] where @xmath54 + f$ ] and the @xmath55 matrices satisfy anti - commutation relation with respect to @xmath30 $ ] : @xmath56_{ab } \ .\end{aligned}\ ] ] more precisely , the quadratic fluctuation term on a given d@xmath22-probe brane can be read of from @xcite . the computation of fluctuation modes around a particular classical brane configuration will involve inverting the matrix @xmath57 , which can then be decomposed into a symmetric and an anti - symmetric part : @xmath58 + f^{(0 ) } \right)^{-1 } \right)^{ab}= \s^{ab } + \a^{ab } \ .\end{aligned}\ ] ] it can be showed that@xcite @xmath59 + f^{(0 ) } } \cdot p[g ] \cdot \frac{1}{p[g]-f^{(0)}}\right)^{ab } \ , \label{osmmet } \\ \s_{ab } & = & p[g]_{ab } - \left ( f^{(0 ) } \cdot p[g]^{-1 } \cdot f^{(0 ) } \right)_{ab } \ , \\ \a^{ab } & = & - \left(\frac{1}{p[g]+ f^{(0 ) } } \cdot f^{(0 ) } \cdot \frac{1}{p[g]-f^{(0)}}\right)^{ab } \ .\end{aligned}\ ] ] the indices are now raised and lowered with respect to the effective metric denoted by @xmath60 , which also determines the kinetic terms for the corresponding fluctuation modes . thus , the fluctuations are governed by lagrangians which take the following schematic form : @xmath61 in @xmath62 we have redefined the gamma matrices by : @xmath63 also in ( [ fscalar])-([fspinor ] ) , @xmath64 denotes an overall constant , the details of which is not relevant for us . the fields @xmath50 , @xmath65 and @xmath66 represent the various fluctuation modes and the indices @xmath67 represent the worldvolume coordinates on the probe . we have shown only the kinetic parts of the fluctuation lagrangian ; since other potential terms will not affect our conclusions . the key observation is that all these modes perceive an effective metric , denoted by @xmath60 , which is different from both the background metric @xmath68 and the induced metric @xmath30 $ ] . this is the so called _ open string metric_@xcite , which governs the dynamics of open string degrees of freedom propagating in a background geometry with an anti - symmetric @xmath69-form . the open string data , in terms of the closed string data , is given by@xcite @xmath70_{ab } - \left(f^{(0 ) } \cdot p[g]^{-1 } \cdot f^{(0" +"spiral disks form as a result of complex interactions of star formation , accretion , and gas . these processes are recorded in a galaxy s stellar component . the stellar metallicity , in particular , encodes information on a galaxy s overall chemical enrichment resulting from its history of star formation , gas accretion , and gas outflows . spiral galaxies are commonly thought to form `` inside out '' with the inner regions forming earliest ( e.g. * ? ? ? * ) . this effect has been observed by measuring a decreasing age with increasing radius in some nearby galaxies ( e.g. * ? ? ? * ; * ? ? ? a metallicity gradient is a natural consequence of inside out growth . observationally , present - day metallicity gradients can be measured using hii regions or the atmospheres of young stars . studies of the present - day metallicity gradients in the milky way and other nearby spirals do show lower metallicities at larger radii ( e.g. * ? ? ? * ; * ? ? ? * ) . to measure metallicity gradients not at the present - day , but in the past , one must analyze stellar metallicities as a function of age . the simultaneous measurement of age and metallicity is non - trivial , but can be done using either the observations of resolved stars or using integrated spectra . recently , the califa survey @xcite used integral field spectroscopic data to study both the present - day and the mean stellar metallicity gradients in a large sample of galaxies @xcite . the mean mass - weighted stellar metallicity gradient found among the califa galaxies is relatively shallow , @xmath3 dex / r@xmath4 , where r@xmath4 is the disk effective radius @xcite . the galaxies in this califa subsample are very similar to m31 in hubble type and luminosity . similar results based on photometric modeling were also found by @xcite for spiral galaxies in the virgo cluster . in both studies , there is no clear dependence on hubble type for spiral galaxies . in the milky way , the best gradients utilize measurements of 1000s of individual stars from large surveys ( e.g. sdss ) and found a gradient of @xmath5 - 0.06 dex / kpc @xcite . in addition to the smooth gradients in metallicity , distinct metallicity structures are visible within galaxies . metallicity substructure in the halos of galaxies have been linked to galactic merger events ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? within the disks of galaxies , structures with distinct metallicity signatures can arise due to bars , bulges and other dynamical structures @xcite . the ability to resolve individual stars all at the same distance makes andromeda a unique object with which to study massive galaxy disks . distance is the main source of uncertainty within the milky way and large - scale morphology observations are largely restricted to the solar neighborhood . in contrast , stars can be resolved with ease at a wide range of radii in andromeda . the panchromatic hubble andromeda treasury ( phat ; * ? ? ? * ) survey recently observed 117 million stars over a third of andromeda , providing a unique database for studying andromeda s stellar populations @xcite . in this paper , we present a detailed analysis of the metallicities of andromeda s red giant branch ( rgb ) stars using phat photometry . previous work on the rgb metallicities in andromeda have focused on the halo with limited information in the disk of the galaxy @xcite . for this study , we assume the following parameters : the center of m31 is at ra=10.68458and dec=1.2692@xcite ; m31 position angle and inclination angle are respectively 38and 74@xcite ; the distance modulus is 24.45@xmath60.05 mag or 776@xmath618 kpc ( mean distance , see @xcite for discussion ) . due to the small uncertainty in m31 s distance , and the primary dependence of the rgb metallicity on color and not luminosity , the distance uncertainty should have little effect on the analysis we present in this paper . the foreground extinction is @xmath7 0.17 mag @xcite ; m31 s effective radius is 8.9@xmath60.8 kpc @xcite . the paper is structured as follows : in section [ sec : data ] , we explain our data sources , including the rgb star photometry and dust extinction measurements . in section [ sec : principles - of - metallicities ] , we discuss our method for estimating metallicities from isochrone models and the uncertainties caused by photometric crowding and dust extinction . we present and discuss our results on andromeda s metallicity gradient and a metal rich structure associated with the bar in section [ sec : results ] . the phat survey observed approximately 117 million stars with the hubble space telescope ( hst ) in ultraviolet ( f275w and f336w ) , optical ( f475w and f814w ) , and infrared ( f110w and f160w ) filters using the wfc3/uvis , acs / wfc and wfc3/ir hst camera , respectively . the camera pointing angles divided the survey into 23 bricks each consisting of 18 overlapping ir - fields defined from the wfc3/ir camera footprint ( for details see @xcite ) . 3.4@xmath8 stars . the red clump is visible at @xmath9 and @xmath10 24.3 mag . the black dashed line indicates the rgb selection box used for this paper ( see section [ sec : completeness - limit ] ) . color indicates the metallicity . the three color lines plot padova parsec1.2s isochrones at @xmath11=$]-2.0 , 0.0 , and 0.6 dex ( in violet , orange , and yellow , respectively ) at a fiducial age of 4 gyr . the black star marks an example from our data sample at a deprojected radius of 6.1 kpc whose interpolated metallicity estimate is 0.033 dex ( see section [ sec : metallicities ] ) . the black arrow indicates 1 mag of dust extinction in @xmath12 band . extinction causes stars metallicities to be overestimated as discussed at length in section [ sec : dust - impact ] . ] two versions of the photometry are publicly available . first , there is camera - by - camera photometry derived separately on the pairs of filters in each camera producing a uv , optical , and infrared catalog that are then merged together to form a single six - filter catalogcamera - by - camera photometry can be downloaded at http://archive.stsci.edu/prepds/phat/datalist.html ] @xcite . second , the `` six - filter photometry '' is derived across all filters simultaneouslysix filter photometry can be downloaded at http://archive.stsci.edu/missions/hlsp/phat/ ] @xcite . in both versions , each star is parameterized by a position and magnitude , magnitude error , signal - to - noise ratio , crowding , and sharpness for each filter . sharpness parameterizes the shape of each source relative to the point spread function ; and , crowding parameterizes the brightness of nearby sources . in this paper , we use the optical camera - by - camera photometry to derive rgb metallicity estimates . the primary reason for using the camera - by - camera photometry over the six filter photometry is the availability of extensive artificial star tests ( also publicly available from mast archive ) . these artificial star tests allow us to understand the photometric completeness and bias ( see section [ sec : artificial - star - tests ] ) . the optical color of rgb stars also is more sensitive to the metallicity relative to the ir photometry , while the uv photometry suffers from significant incompleteness for even the brightest rgb stars . the smaller effect of dust extinction on the ir data makes it logical to include this data in our analysis , however , artificial stars are only available for the two - camera photometry in the ir , and this data is significantly shallower and crowding limited than the optical data ( see figure 11 of * ? ? ? * ) . the six filter photometry is significantly deeper in the ir due to the ability to use the optical data to determine the positions of stars , but it is not computationally feasible to run artificial star tests over the full phat footprint for the six band photometry @xcite . we create an optical only ( @xmath13 and @xmath14 ) photometric catalog with uniform coverage from the individual acs / wfc field images . this involves two primary steps : defining non - overlapping spatial regions , and filling in the chip gaps of each individual field . the boundary of each field is first defined using a grid of non - overlapping regions that roughly follow the individual wfc3/ir field footprints . we additionally crop bricks 9 and 12 , which overlap with neighboring bricks , because of orientation differences described in section 3.5 of @xcite . the phat tiling scheme allows us to use neighboring acs / wfc fields to fill in the chip gap of each acs / wfc field . thus , our final catalog has uniform spatial coverage over the full phat survey region but does not make use of multiple overlapping observations . this same catalog creation process is also used to deal with chip gaps in the the six - filter photometry as described in @xcite . we apply quality cuts on our photometry . the cuts use signal - to - noise , sharpness , and crowding in the f475w and f814w filters for each star . we use the same parameterization which defines `` gst '' ( good star ) cuts from @xcite by applying all of the following equations : @xmath15 + the variables correspond to the names given in the data files . for example , @xmath16 , @xmath17 , and @xmath18 respectively correspond to the signal - to - noise , sharpness , and crowding parameters for the @xmath13 filter . we correct the magnitudes in @xmath13 and @xmath14 for foreground extinction using @xmath70.17 mag @xcite . this extinction in @xmath19 is converted to @xmath13 and @xmath14 extinctions by multiplying with @xmath20 equal to 1.19119 and 0.60593 , respectively taken from http://stev.oapd.inaf.it/cgi-bin/cmd ] . the corrected photometry is indicated by a subscript zero ( _ e.g. _ @xmath21 ) . in addition to the `` gst '' cuts , we require that @xmath22 to remove stars with higher photometric bias and lower completeness . the foreground reddening correction is applied before this brightness cut . after applying the spatial and photometric cuts our sample contains @xmath57.0@xmath23 stars . in figure [ fig : data - selection - cmd ] , we present the optical color - magnitude diagram after quality cuts and foreground extinction corrections . this color - magnitude diagram ( cmd ) shows the stellar density prior to the magnitude cut in gray scale contours . the red - clump and bump of early - agb stars are both visible as peaks in the density below our selection region . the dashed area shows the selection region in which we determine rgb metallicities . in this paper , we estimate metallicities for rgb stars from their positions in the cmd . isochrones at a range of metallicities are shown in figure [ fig : data - selection - cmd ] , showing that stars of different metallicities are clearly separated in color ; we use this information to infer metallicities after considering a number of subtleties that can affect this measurement ( section [ sec : principles - of - metallicities ] ) . dust extinction has a significant impact on the observed photometry and thus our metallicity estimates . we discuss this in more detail in section" +"it is now well accepted that the giant planets of the solar system did not have the current orbits when the gas was removed from the protoplanetary disk . the first work showing that the planets had to migrate while interacting with the remaining planetesimal disk was @xcite . this work demonstrated that , in the planetesimal scattering process , on average saturn , uranus , and neptune gain angular momentum and thus migrate outwards , while jupiter loses angular momentum and moves inwards . since then , the process of planetesimal - driven migration was considered to be a fundamental one in shaping the current structure of the solar system . @xcite showed that planetesimal - driven migration can explain the origin of the orbit of pluto and of the resonant populations of kuiper belt objects . however , it appeared soon that planetesimal - driven migration alone is a process too smooth to explain several aspects of the kuiper belt s orbital distribution , e.g. the orbital excitation of the non - resonant objects . @xcite was the first paper showing that a dynamical instability of the giant planets could lead to a global orbital excitation of the kuiper belt , while delivering the giant planets on final orbits roughly similar to the current ones . building on these results , the so - called _ nice model _ @xcite combined the processes of planetesimal - driven migration and dynamical instability into a new global scenario . it suggested that the planets jupiter , saturn , uranus , and neptune formed in a compact configuration with jupiter around 5.45 au , saturn slightly interior to the 2:1 mean motion resonance ( mmr ) with jupiter ( @xmath3 @xmath4 8.65 au ) , and the initial semimajor axes of the ice giants ( uranus and neptune ) in the ranges 1113 au and 13.517 au . the planets were surrounded by a disk of leftover planetesimals , accounting for a total of about 35 @xmath5 , from @xmath016 to 30 au ( where @xmath6 is the mass of the earth ) . in this model the planets interacted with the planetesimal disk and , by planetesimal - driven migration , their mutual separations slowly increased . when jupiter and saturn crossed their mutual 2:1 mmr the full system of the giant planets became unstable and spread further through mutual close encounters . in particular , uranus and neptune were scattered onto orbits with relatively large eccentricities and semimajor axes , which crossed the original trans - neptunian disk . then , following a phase of dynamical friction caused by their interaction with the disk , the orbits of uranus and neptune damped in eccentricity and inclination . a residual planetesimal - driven migration placed the planets on orbits fairly similar to the current ones @xcite . the nice model had great success in explaining many features of our solar system , as : the capture of jupiter s trojans @xcite , the capture of the irregular satellites of the giant planets @xcite , the absence of regular moons beyond oberon s orbit at uranus @xcite , to cite a few . moreover , it was shown that , provided the inner edge of the trans - neptunian disk was at an appropriate distance from the original orbit of neptune , the giant planet instability could have occurred after hundreds of my of evolution , potentially explaining the origin of the so - called late heavy bombardment ( lhb ) of the terrestrial planets @xcite . however , the original version of the nice model presented a major problem ; the initial configuration of the planets was chosen in an ad hoc manner . @xcite performed hydrodynamical simulations of the evolution of the giant planets when they were still embedded in a disk of gas and found that the planets should have acquired a fully resonant configuration , with jupiter and saturn preferentially locked in their mutual 3:2 mmr with jupiter at @xmath05.4 au , saturn and uranus ( ice i ) in the 3:2 mmr , and uranus ( ice i ) and neptune ( ice ii ) in the 4:3 mmr ( although other resonant configurations are also possible ) . the authors also concluded that such a multi - resonant system is compatible with a subsequent evolution similar to that described in @xcite , although the instability in this case happens when a pair of planets leave the original resonant configuration , rather than when jupiter and saturn cross their 2:1 mmr . @xcite investigated whether , under some conditions , this initial multi - resonant configuration could still lead to a _ late _ giant planet instability , in order to explain the putative lhb as in the original @xcite paper . they found that late instabilities are possible , provided that the inner edge of the disk is several au s beyond the outermost planet and about 1,000 pluto - sized planetesimals are embedded in the disk , so to produce an important dynamical self - stirring of the planetesimals population . during the dynamical instability of the giant planets , several dynamical paths are possible , even when restricting the evolutions to those leading to final planetary orbits similar to the current ones . the actual dynamical evolution of the giant planets at the instability time can be constrained by investigating the consequences on the other components of the solar system : the terrestrial planets and the small body populations . the terrestrial planets and the asteroid belt give similar constraints , as investigated in @xcite and @xcite . if the orbits of jupiter and saturn migrate away from each other smoothly and slowly , as in planetesimal - driven migration , the @xmath7 secular frequency ( dominant in the precession of jupiter s longitude of perihelion ) decreases slowly in value and becomes very similar for some time to the @xmath8 secular frequency , dominant in the precession of mercury s perihelion . as a consequence , the orbit of mercury is destabilized @xcite . similarly , the @xmath9 secular frequency , dominant in the precession of saturn s perihelion , as it slows down becomes equal to the frequencies characterizing the precession of the asteroids at low inclination in the inner asteroid belt , so that this region becomes severely depleted @xcite . both papers concluded that the ratio of the orbital periods of jupiter and saturn @xmath10 had to evolve almost discontinuously from @xmath11 to @xmath12 ( the current value is @xmath13 ) . this happens if jupiter and saturn encounter another planet ( uranus or neptune or a third planet of comparable mass ) . the sequence of encounters causes a divergent jump in the semimajor axes of the orbits of jupiter and saturn , and therefore a jump in the @xmath14 ratio . this scenario is commonly known as the _ jumping - jupiter _ model . notice that if the giant planet instability occurred early , the terrestrial planets were possibly not yet fully formed and therefore the constraint on the evolution of @xmath7 relative to @xmath8 does not apply @xcite . however , the constraint set by the asteroid belt is still valid , supporting the need for a _ jumping - jupiter _ evolution regardless of the time of the instability @xcite . given that in a _ jumping - jupiter _ evolution the planet that encounters jupiter is often ejected onto a hyperbolic orbit , @xcite and @xcite suggested that the solar system had originally a third ice giant planet with a mass comparable to uranus or neptune . this scenario increases the probability that a _ jumping - jupiter _ evolution ends with four planets near their current orbits , once the putative fifth planet is ejected after its encounter with jupiter . then , @xcite considered many different initial multi - resonant configurations for jupiter , saturn , uranus , neptune , and the rogue fifth planet , and determined for each of them the probability that the @xmath14 ratio had a jump across the 2.12.3 range and the final planets reached orbits compatible with those of our current solar system . the successful simulations of @xcite have then been used to investigate again the capture of the trojans of jupiter @xcite , the capture of irregular satellites at jupiter @xcite , the excitation of the inclination of the moon iapetus at saturn @xcite , the evolution of the asteroid main belt and of its collisional families @xcite . they have also been shown to be compatible with the survival of the galileans satellites @xcite , despite of the encounters of jupiter with the ejected planet . however , when investigating the dynamical sculpting of the kuiper belt , @xcite and @xcite realized that , of all possible evolutions of neptune consistent with the five - planet _ jumping - jupiter _ model , only some are consistent with the current orbital structure of the trans - neptunian population . in order to get the correct inclinations of the hot population of the kuiper belt objects ( kbo ) , @xcite found that neptune should have migrated more that 5 au from its original resonance by planetesimal - driven migration before that the planets became unstable . this migration should have occurred on a timescale @xmath15 @xmath16 10 my , with the planet on a quasi - circular planar orbit ( @xmath17 0.1 and @xmath18 ) to avoid excessive orbital excitation of the cold classical belt , in the @xmath04245 au region . the planetary instability should have happened when neptune was already at 28 au @xcite in order to explain the so - called _ kernel _ of the cold kuiper - belt ( a clump of objects around 44 au ; @xcite ) . in this case the _ kernel _ would have formed from objects transported outwards in the 2:1 mmr with neptune and released from the resonance when neptune s orbit had a jump of about 0.5 au in semimajor axis , due to a close encounter with another planet . finally , in order to reproduce the observed ratio between the resonant and non - resonant kuiper belt populations , @xcite concluded that the planetesimal - driven migration of neptune should have been characterized by several small amplitude jumps , as those caused by a population of 1,0004,000 pluto - size objects in the disk . the brief review reported above , sets the context that motivated the study reported in this paper . it is clear that the work by @xcite needs to be revisited to test which initial resonant configurations are the most compatible with the new constraints on the dynamical evolution of neptune . this is done in the first part of the paper ( section [ early ] ) . in the second part of the paper ( section [ late ] ) we investigate whether the initial configurations selected in the first part of the work can lead to a _ late _ planetary instability , while still showing an evolution of neptune consistent with kuiper belt constraints . the possibility of a _ late _ instability is far from trivial . in fact , in order to exhibit a long - range planetesimal - driven migration before the planet instability , neptune needs to be embedded in the planetesimal disk . but in this case , neptune would start migrating away from the other planets from the very beginning of the simulation ( corresponding to the gas - removal time ) . this is likely to lead to an instability after just a few 10s of my . if instead the planetesimal disk is relatively far from neptune , the planet can be extracted from its initial resonance at a _ late _ time as in @xcite , but the instability is" +"the recent appearance of tags in large online datasets represents a significant innovation in categorisation @xcite . tags allow multiple categories for each item , and tagging can be done in a bottom - up approach , in a parallel manner , by several users simultaneously @xcite . this feature allows the tagging of huge datasets in a reasonable time . in contrast , traditional hierarchical categorisation typically allows one category per item , and it is done by a few experts , slowing down the process . also , available categories are restricted in traditional expert - made hierarchies , while user given tags are usually allowed to take any expression deemed relevant by the user . although there is no prescribed structure between the tags , it is a reasonable assumption that tags are attached to objects according to hidden hierarchical relations , e.g. , `` poodle '' is usually considered as a special case of `` dog '' . consequently , it is an interesting non - trivial task to extract this implicit hierarchy from the co - appearance of tags solely . indeed , a number of different methods have already been proposed in the literature , such as aggregation of user - defined shallow hierarchies for obtaining a global hierarchy @xcite , integration of information from as many sources as possible @xcite , using a probabilistic criterion to define parent - child relations @xcite , applying pairwise similarities to centrality - ordered tags @xcite , or building up the hierarchy from bottom up based on the z - score between the tags @xcite . beside the organisation of different keywords or categories describing a given topic , signs of hierarchy are prevalent in a very wide range of systems . among others , the transcriptional regulatory network of escherichia coli @xcite , the dominant - subordinate hierarchy among crayfish @xcite , the leader - follower network of pigeon flocks @xcite , the rhesus macaque kingdoms @xcite , neural networks @xcite , technological networks @xcite , social interactions @xcite , urban planning @xcite , ecological systems @xcite , and evolution @xcite all show signs of hierarchical organisation . different approaches were introduced to uncover hierarchy in networks , including the introduction of hierarchy measures @xcite , statistical inference of hierarchy @xcite and construction of hierarchical network models @xcite . here we analyse the hierarchies obtained for the scientific keywords from the web of science @xcite by applying a recent generalisation of the method given in ref.@xcite presented in @xcite . we treat the set of author given tags and the set of repository given tags separately , resulting in two alternative hierarchies . these are compared to each other and also to the 3-level classification of categories given by the web of science . the organisation of the paper is the following : in sect . [ s : pre ] we introduce the tag hierarchy construction methodology and describe the datasets to which it is applied . the obtained hierarchies are presented in sect . [ s : results ] , while the results are discussed in sect . [ s : concl ] . in order to obtain a tag hierarchy , we will follow the method described in @xcite and @xcite , for which a quick overview is provided here . given a set of objects and each object having a set of tags , the goal is to construct a hierarchy , i.e. , a directed acyclic graph ( dag ) of the tags , where links are directed from more general concepts to more special ones . our method constructs a hierarchy in two steps : first the tags are ordered , defining which tag should be placed higher in the hierarchy and which lower , then for each tag an appropriate parent is chosen . note , that in the second step here we allow to choose more than one parent for a tag , hence the resulting hierarchy can be more complex than a simple tree . for the reader who is not familiar with the method @xcite we briefly summarize the main steps below . first we rank first the tags according to the eigenvector centrality of the tag - coappearence graph . nodes in the co - appearance graph correspond to the tags , and links represent the co - appearances of the tags on the same object . the weights of the links are given by the number of co - appearances . however , when calculating the eigenvector centrality , links having a z - score below a certain threshold value are neglected . the z - score is calculated as the observed number of objects where the two tags co - appear minus the expected number co - occurrences when tags are randomly shuffled . the z - score is normalized by the standard deviation of random co - occurrences , @xmath0 where @xmath1 is the number of times tags @xmath2 and @xmath3 co - appear , @xmath4 and @xmath5 are the expected value and standard deviation , respectively , for randomly reshuffled tags . in the second step the hierarchy is built according to a bottom - up approach , i.e. , we look for parents at each tag @xmath2 in ascending order of their eigenvector centrality . we choose a tag to be the first parent of @xmath2 , when it has higher eigenvector centrality than @xmath2 and has maximal score among possible parents . the score here is the sum of the z - scores of the links between the candidate parent and the descendants of @xmath2 , and between @xmath2 itself . note , that by aggregating the descendants z - scores , we take into account much more information than any pairwise similarity metric can provide . finally , we allow further parents if they have links to @xmath2 with at least as high z - score as the first parent . we study the keywords of scientific papers between 1975 and 2011 obtained from the web of science . the dataset contains 35 371 214 papers , which are tagged by three type of tags . the first type ( heading ) gives a very broad categorisation of the paper , there are only 5 tags of this type : ` arts & humanities ` , ` life sciences & biomedicine ` , ` multidisciplinary science & technology ` , + ` physical sciences ` and ` social sciences ` . the second type ( category ) has 251 more fine - grained scientific areas like ` chemistry , analytical ` or ` engineering , geological ` . tags of the third type are chosen from two sets of specific phrases . one set is composed from the keywords which originated from the authors of the papers . the other set is given by the web of science service , and targeted as complementary to the author - given keywords . we will refer to the first keywords as _ authorkeywords _ and to the other as _ woskeywords_. there are a huge number of third - type - tags : the _ woskeywords _ set contains 2 245 143 phrases and the _ authorkeywords _ set contains 6 891 089 , which are very specific , like ` zygapophyseal arthritis ` or ` h-3 -r - alpha - methylhistamine binding ` . although these keywords are aimed to be complementary on the level of individual papers , still 883 836 of them appear both in the set of _ woskeywords _ and _ authorkeywords_. finally , we note that the web of science does not define any hierarchical relations between the tags , i.e. , the ancestors or descendants of the tags are not given in the data set , only the categorization into the three major types is provided . the aim here is to apply the methodology of sec . [ s : pre_meth ] to the data described in sec . [ s : pre_data ] , in order to study the differences and similarities of hierarchies resulting from tags given by independent individuals and from tags given by a repository . in the first case the input of the hierarchy reconstruction is given by heading , category and _ authorkeyword _ tags , while in the second case the heading , category and _ woskeywords _ tags . note that the general and intermediately general type tags are common in both datasets , and these tags are given by the repository management system . the difference between the independent tagging and centrally managed tagging comes from the most numerous third level tags . we compare below the hierarchies of the two taggings . first we compare the upper most part of the reconstructed dags . then the hierarchy level occupation statistics of the dags are compared for each tag types . finally the horizontal ( branching ) structures of the dags are analysed . in the reconstructed hierarchies obtained from our method both dags had 4 dominant roots at the highest level of the hierarchy , being the ancestors of @xmath6-@xmath7 of the available tags . the dags contain several other non - dominant roots , corresponding to tiny connected components which cover only @xmath8-@xmath9 of the tags . the four dominant roots coincide with the heading type tags except ` multidisciplinary science & technology ` , which appears as a child of ` physical sciences ` . next , we compare the vertical structures of the two dags by analysing the hierarchy level distribution of different tag types . a technical difficulty arises from the fact that a tag may belong to more roots , thus it can have more level values depending on the root from which it is counted . here we classify tags to hierarchy levels according to their closest root , i.e. , from the possible level numbers we associate the highest possible level to each tag . the resulting level distributions are shown on fig . [ f : levels ] . they indicate that the position in the dag correlates strongly with the heading - category-(author / wos)keyword classification , i.e. , the reconstruction is consistent with the a priori classification of the tags in this respect . however , it is interesting to note , that while tags from different types mostly appear below each other in the expected order , tags from the _ same _ type also appear below each other the reconstruction finds structure within the types . the third aspect is the horizontal similarity of the dags . here we analyse whether common members of the dags are in similar horizontal position , i.e. , having similar descendant subgraphs . since the dags are constructed from the same header and category type tags and the two different keyword tags , we compare the horizontal structure of the two dags in two ways : i ) first we restrict the analysis only for those tags , that are common in the two dags ( header , category and common keywords ) ii ) secondly we restrict the analysis even more , considering only the header and category type tags , that are common by definition of the dags . for the first case , where we compare the horizontal position of the common keywords / categories / headers of the two dags , we calculated the linearised mutual information - based similarity of @xcite . the result shows huge dissimilarity with @xmath10 for the mutual information . a sample of the dags is shown on fig . [ f : reduced2common ] , around `` vegetation response '' . in both dags , related tags appear below the chosen tag , however , according to fig . [ f : reduced2common ] , descendants in one dag differ from descendants in the" +"macroscopic objects in contact with an ionized gas acquire a negative charge because the influx of electrons from the plasma outruns the influx of ions . the collection of electrons at the wall ( boundary of the object ) gives rise to a repulsive coulomb potential which reduces the electron influx until the wall charge reaches a quasi - stationary value . as a consequence of the electron accumulation at the wall an electron depleted region , the plasma sheath , is formed adjacent to the wall . most of the voltage driving the discharge drops across the sheath . wall charges may however not only affect the spatial structure of the plasma but also surface - supported elementary process such as electron - ion recombination and secondary electron emission , which are particularly important in dusty plasmas,@xcite dielectric barrier discharges,@xcite and solid - state based micro - discharges.@xcite a macroscopic description of the plasma - induced wall charge , sufficient for the modeling of the plasma sheath , @xcite is clearly insufficient for quantifying the effect wall charges might have on these processes . a microscopic description of the plasma - induced wall charge and the potential across the plasma - wall interface it leads to is required . traditionally , plasma walls are treated as perfect absorbers.@xcite irrespective of the microscopic interaction , all electrons and ions impinging on the wall are assumed to recombine instantly . from this model only the wall potential just outside the wall can be obtained . this is the potential that balances the electron and ion influx at the wall . a first , qualitative step going beyond this model was taken by emeleus and coulter,@xcite who envisaged the wall charge as a two - dimensional surface plasma coupled to the bulk plasma via electron - ion wall recombination . no attempt was however made to put this appealing idea onto a formal basis . later the notion of a two - dimensional surface charge was developed further by behnke and coworkers@xcite utilizing phenomenological rate equations for the electron and ion surface densities . in these equations , the microphysics at the wall is encapsulated in surface parameters , such as , electron and ion sticking coefficients , electron and ion desorption times , and an electron - ion wall recombination coefficient . in principle these parameters can be calculated . assuming , for instance , plasma electrons to ad- and desorb in the long - range image potential of the wall we calculated in our previous work electron sticking coefficients and electron desorption times for uncharged metallic @xcite and dielectric surfaces . @xcite we also made a first attempt to estimate these two quantities for charged dielectric plasma walls @xcite and proposed a physisorption - inspired microscopic charging model for dust particles in a gas discharge . @xcite in this work , we shift gears and focus on the potential and charge distribution across the plasma - wall interface after the quasi - stationary wall charge ( electron adsorbate in the notation of our previous work @xcite ) has been established . in other words , we extend the modeling of the plasma sheath @xcite to the region inside the solid and calculate the plasma - induced modifications of the potential and charge distribution of the surface . although knowing the potential and charge distribution across the interface may not be of particular importance for present day technological plasmas , it is of fundamental interest from an interface physics point of view . in addition , considering the plasma wall as an integral part of the plasma sheath may become critical when the miniaturization of solid - state based plasma devices @xcite continues . in the model outlined below we specifically consider a dielectric wall and treat the plasma - induced quasi - stationary wall charge , that is , the surplus charge on top of the charge distribution of the bare , free - standing surface , as an electron surface layer of a certain extent , which is trapped by and in thermal equilibrium with the wall . in order to determine the chemical potential , width , and spatial position ( relative to the crystallographic interface ) of the electron surface layer , which depend on surface as well as plasma parameters , we employ a one - dimensional model for a graded interface between a collisionless plasma sheath and a dielectric surface which is assumed to be a perfect absorber , that is , the wall potential balances at a certain distance from the crystallographic interface the electron and the ion influx from the plasma . the model of a graded interface encompasses two important ingredients : the surface dipole of the bare surface responsible for the offset of the conduction band minimum to the potential just outside the dielectric and the long - range image potential . the former accounts for the charge re - distribution of the free - standing , uncharged surface arising from the truncation of the crystal and the latter supports polarization - induced external surface states ( image states ) , first predicted for liquid helium @xcite and later studied for metallic and dielectric surface with negative electron affinity @xcite , which may trap the electron surface layer in front of the crystallographic interface . originally proposed by stern for the interface between two dielectrics,@xcite and later on used by others for semiconductor heterojunctions @xcite and electron trapping in nanopores,@xcite the graded interface model also guarantees continuity of the electrostatic potential across the plasma - wall interface . the model thus allows us to study the spatial distribution of the plasma - induced wall charge across the interface . to insert the surplus charge into the interface we follow tkharev and danilyuk @xcite and minimize , in the spirit of density functional theory , @xcite the grand canonical potential of wall - thermalized excess electrons we also investigate how the electron surface layer merges with the neutral bulk of the dielectric which we describe with the model of an intrinsic semiconductor . various improvements of the model are conceivable but the increased mathematical complexity would mask the general ideas we would like to convey . for instance , the model of a collisionless sheath could be replaced by more realistic models . @xcite going beyond the perfect absorber model , on the other hand , is an unsolved problem . it would require the inclusion of electron desorption , electron sticking , and electron - ion recombination , with the respective coefficients to be self - consistently calculated for the quasi - stationary electron adsorbate at the wall . replacing the graded interface by an ab - initio theory for the surface , for instance , along the lines given in refs . @xcite , possibly taking ad - layers of the host gas atoms or molecules as well as impurities and imperfections into account , is desirable but at the present stage of the investigation impractical . it would require an expensive atomistic characterization of the plasma - wall interface , either experimentally via various surface diagnostics or theoretically via ab - initio simulations . as long as the atomistic details affect however only the off - sets of the dielectric constant , the electron affinity , and the effective mass , the graded interface model already incorporates these details by a suitable parameterization . what is not well described is the non - universal region a few atomic units below and above the crystallographic interface . in particular , intrinsic surface states ( shockley and tamm states @xcite ) and additional surface states which may arise from the short - range surface potential due to impurities , imperfections , and ad - layers are not included . if unoccupied these states could trap the electron surface layer in the vicinity of the interface even for surfaces with positive electron affinity where image states are absent and can not trap the surplus charge in front of the surface . the remaining paper is structured as follows . in sec . [ electron surface layermain ] we first construct a crude model for the plasma - induced electron surface layer at the interface between a plasma and a dielectric wall . it does not account for the merging of the electron surface layer with the bulk of the dielectric . as long as the primary interest is in the region close to the crystallographic interface and the band gap of the dielectric is large enough , the crude model is sufficient . section [ negativescr ] describes a refinement of the model which enables one to also investigate the cross - over of the electron surface layer to the bulk of the dielectric . this is particularly important for dielectrics with small energy gaps . numerical results for the potential and the electron distribution are given in section [ results ] and a short summary is formulated in sec . [ summary ] . as depicted in fig . [ figure1 ] , we consider an ideal , planar interface at @xmath2 with the dielectric occupying the half - space @xmath3 and the discharge occupying the half - space @xmath4 . chemical contamination and structural damage due to the burning gas discharge are discarded . at the moment we focus on the physical principles controlling the electronic properties of the plasma - wall interface . in the model we propose the plasma - induced wall charge to be treated as an electron surface layer ( esl ) which is an interface specific electron distribution on top of the charge re - distribution due to the truncation of the solid . the esl is assumed to be thermalized with the solid and to stretch from the plasma sheath over the crystallographic interface to the bulk of the dielectric . the boundary between the esl and the plasma sheath is located in front of the surface at @xmath5 . it is the position where the attractive force due to the surface potential @xmath6 and the repulsive force due to the sheath potential @xmath7 balance each other . thus , @xmath8 is given by @xmath9 it gives the position of an effective wall for plasma electrons and ions at which , for instance , the flux balance condition of the perfect absorber model , @xmath10 , with @xmath11 and @xmath12 , respectively , the electron and ion flux towards the dielectric surface , has to be fulfilled . for @xmath13 an electron is attracted to the surface and thus contained in the esl while for @xmath14 it is repelled back into the plasma . on the solid side , for @xmath3 , the esl is bounded because of the shallow potential well formed by the restoring force from the positive charge in the plasma sheath . in this section we will outline the essential building blocks of the esl model . putting together concepts from plasma as well as surface physics a detailed , self - contained account seems to be helpful . in the traditional view , electrons missing in the positive space charge region in front of the plasma wall accumulate on the wall and give rise to a wall potential . for the construction of our one - dimensional interface model we need the total number per unit area of missing sheath electrons ( that is , the total surface density of missing sheath electrons ) as a function of the wall potential because it is this number of electrons which can be distributed across the esl . hence , we require a model for the plasma sheath . for simplicity , we use a collisionless sheath @xcite , more realistic sheath models @xcite make no difference in principle . in the collisionless sheath electrons are thermalized , that is , the electron density @xmath15 , with @xmath16 the potential ," +"the observation of a valley of stability and the search for mass formulae belong to the oldest subjects studied in nuclear physics @xcite and continue to be of great interest today @xcite . given the neutron and proton numbers @xmath6 and @xmath7 as independent variables and the corresponding atomic number , @xmath8 terms such as volume energy @xmath9 , surface tension @xmath10 coulomb energy @xmath11 symmetry energy @xmath12 _ etc . _ , flourish in the literature , and a great deal of attention has been dedicated to the consideration of finer corrections , such as , for instance , terms @xmath13 and @xmath14 that account for shell and pairing effects , respectively , and further correlations . this work is motivated by the observation that the dominant terms , such as @xmath15 @xmath16 and @xmath17 , define a notoriously _ concave _ energy surface . upper and lower bounds to nuclear binding energies can be deduced from such a concavity , provided that deviations from concavity , possibly induced by subdominant terms like @xmath10 @xmath18 @xmath19 _ etc . _ , can be corrected . for the sake of simplicity this paper first considers only sequences of isotopes and , thus , takes advantage of concavity with respect to @xmath6 only ; @xmath7 is frozen . in section 2 we begin with a theory at zero temperature and show how elementary , invertible transformations of data can generate truly concave patterns . this is obtained by an analysis of the table of second differences between binding energies , then by a removal of the pairing energy , and finally by an _ ad hoc _ , but minimal , parabolic term added to the nuclear energies , if necessary . since concavity is also a property of several thermodynamical functions , an extension of the zero temperature analysis to finite temperatures is in order . in section 3 we discuss properties of that grand potential , @xmath20 which can be deduced from the experimental data after their tuning . other thermodynamical functions are also considered , and their concavity is tested . bounds are found , and an error bar for predictions is estimated . a generalization to concavity with respect to both @xmath6 and @xmath7 is briefly studied in section 4 . an additional motivation for our investigation of concavity properties is the need , in density functional theories , of concavity , if the universality @xcite of a density functional must be obtained . a solution will be shown . finally , a discussion and conclusion are given in section 5 . our argument is best illustrated numerically , by using a sequence of isotopic ground - state binding energies , @xmath21 we choose to work with the tin isotopes ( sn ) , because they provide a large number of known isotopes for testing our method . in addition , in section 3 , we will extend our approach to finite temperatures using a grand potential , which requires that a sufficiently large number of excited states are also known . for instance , a table of @xmath22 ground - state bindings for the tin isotopes from @xmath23sn to @xmath24sn reads , in kev , \ { 934571 , 942744 , 953531 , 961274 , 971574 , 979120 , 988684 , 995627 , 1004954 , 1011438 , 1020546 , 1026716 , 1035529 , 1041475 , 1049963 , 1055696 , 1063889 , 1069439 , 1077345 , 1082676 , 1090293 , 1095540 , 1102851 , 1105320 , 1109239}. despite a standard linear trend because of a `` not too much fluctuating average energy per nucleon '' , this list is not making a smooth pattern , even less of a concave one . the full line in fig . 1 , where , for graphical convenience , we have added to each @xmath25 a constant term , @xmath26 mev and a linear term , @xmath27 mev , shows the amount of irregularity in the pattern . the main source of irregularity is , obviously , the pairing effect . if it can be removed , concavity emerges . concavity for a sequence of isotones is not a surprise , because of the @xmath28 nature of the coulomb term . for a sequence of isotopes , however , there is no such obviously quadratic term available , notwithstanding the empirical modelization of a symmetry energy @xmath29 our choice of sn , because of its long isotope sequence , illustrates this concavity more dramatically . most energies stated in this paper are in units of kev . our data come from ref . @xcite . see also @xcite . these sources usually quote the binding energy per nucleon instead of the total binding energy itself and such values per nucleon are given to varying numbers of significant figures , from six to seven for the sn isotopes @xcite that we consider . consequently , we quote and use all our binding energies to six or seven significant figures . our values are generally accurate to the order of two to three kev near the center of the sequence , and tens of kev at both ends for the sn isotopes . see , in particular , @xcite for error bars . the staggering effect is clear from the @xmath30 first differences , @xmath31 \{-673 , -3287 , -243 , -2800 , -46 , -2064 , 557 , -1827 , 1016 , -1608 , 1330 , -1313 , 1554 , -988 , 1767 , -693 , 1950 , -406 , 2169 , -117 , 2253 , 189 , 5031 , 3581 } , see fig . the list of @xmath32 second differences ( sds ) , @xmath33 \{-2614 , 3044 , -2557 , 2754 , -2018 , 2621 , -2384 , 2843 , -2624 , 2938 , -2643 , 2867 , -2542 , 2755 , -2460 , 2643 , -2356 , 2575 , -2286 , 2370 , -2064 , 4842 , -1450 } , is insensitive to the constant and linear terms we used for graphical convenience . it gives estimates of the `` curvatures '' of the pattern . it turns out to be far from containing only positive numbers . the nonconnected points shown in fig . 3 represent this pattern of sds . a systematic oscillation , reflecting the staggering effect , is found . alternating signs are obviously due to the gains of binding for even sn nuclei because of pairing . the oscillation between sds centered at odd and even nuclei has , roughly speaking , a constant amplitude . notice , however , the maximum in the list , @xmath34 due to the shell closure at @xmath35sn . add now to each _ even _ nucleus energy a fixed number , for example @xmath36 kev , to tentatively suppress the increase of binding due to pairing . the resulting list of sds is attenuated by an amount equal to @xmath37 , as illustrated by the full line in fig . the attenuated list reads , \{-114 , 544 , -57 , 254 , 482 , 121 , 116 , 343 , -124 , 438 , -143 , 367 , -42 , 255 , 40 , 143 , 144 , 75 , 214 , -130 , 436 , 2342 , 1050}. all numbers are now significantly smaller than their partners in the previous list of sds , except for the smaller , but still large maximum at @xmath35sn . this maximum is positive , however , and causes no difficulty for concavity . the interesting point is rather the most negative number in the list , namely @xmath38 kev . all negative curvatures can be converted into positive ones if we add to every energy an artificial , parabolic correction , @xmath39 with @xmath40 kev . incidentally , the lowest point , @xmath41 of the `` added parabola '' is arbitrary , because sds will increase by just a constant , namely twice the coefficient @xmath42 of the @xmath43 term . after this @xmath44 kev shift , the whole sequence of sds becomes positive , \{36 , 694 , 93 , 404 , 632 , 271 , 266 , 493 , 26 , 588 , 7 , 517 , 108 , 405 , 190 , 293 , 294 , 225 , 364 , 20 , 586 , 2492 , 1200 } , see the dashed line shown in fig . 3 . in short , a `` concavity ensuring '' manipulation for the isotope energies consists in replacing each energy @xmath25 by @xmath45 + p \times ( a - a_0)^2 + 115000 + 7500\ , a.$ ] ( we recall that the terms which we have added are here just for graphical , and later , numerical convenience ; they do not influence the theory . ) with @xmath46 @xmath40 and @xmath41 the list of such tuned energies @xmath47 ( shown by the nonconnected dots in fig . 1 ) reads , \{17479 , 13831 , 10219 , 7301 , 4476 , 2055 , 266 , -1252 , -2504 , -3263 , -3996 , -4141 , -4279 , -3900 , -3413 , -2521 , -1439 , -64 , 1605 , 3499 , 5757 , 8035 , 10899 , 16255 , 22811}. the choice of the two parameters , p=1250 kev and p=75 kev , is empirical : one looks for a pairing correction leading to a modest , if not minimal , parabolic correction inducing concavity . other choices for @xmath48 are possible , but , obviously , within a small range around @xmath49 and @xmath50 furthermore , such parameters must be readjusted for different regions of the table of nuclei , but it is again obvious that readjustments will be moderate ; for instance , the order of magnitude for pairing will always be around @xmath51 to @xmath52 mev . analyzing short sequences obviously leaves fewer negative sds to be compensated by the artificial , parabolic term , and , hence should induce smaller values of @xmath53 for this reason , we would expect short sequences to give often better extrapolations . once concavity is obtained , it is straightforward that extrapolations from two points on the concave pattern allow predictions of lower bounds to nuclear energies and interpolations give upper bounds . then , from such bounds for energies @xmath54 one recovers bounds , of strictly the same quality , for the physical energies @xmath55 this obtains by subtracting from each @xmath56 bound its `` tuning term '' . assume now that @xmath23sn were unknown and one had done a brute force extrapolation , @xmath57 compared with @xmath58 this prediction underbinds @xmath23sn by @xmath59 kev . consider rather @xmath60 to be compared with @xmath61 a slight overbinding , by 36 kev , is found . although this small error is likely accidental , it is clear that systematic lower bounds will be found . naturally , once a value for @xmath47 is predicted , one recovers as good an estimate for @xmath25 after removing the `` concavity manipulation terms '' , which are known explicitly . in the present case , the tuning of the data added @xmath62 to @xmath63 the same @xmath62 must be subtracted from that value , @xmath60 extrapolated from the concave pattern , yielding a final result of @xmath64 to be compared with @xmath58 which obviously exhibits the same slight overbinding , @xmath65 kev . based on the data in @xcite , the experimentally measured energy for @xmath23sn has an error bar @xmath66 kev ; hence , in this case , the experimental error bar and the uncertainty in our theoretical value have the same order of magnitude . if @xmath35sn were unknown , the brute force extrapolation gives , @xmath67 to be compared with @xmath68 showing an underbinding equal to @xmath69 kev , clearly failing to reproduce the shell closure effect . now , from the concave pattern ," +"in these days , interference management is one of the most important issues in wireless communication systems . in order to obtain high spectral efficiency , many interference management techniques have been proposed and studied . for the two - user interference channel , the capacity region is already known for weak and strong interference regions in @xcite and @xcite . for the moderate region , the capacity region is still unknown , but there are some works that the capacity regions can be achieved by rate - splitting within one bit @xcite . the authors in @xcite also proved that the optimal generalized degrees of freedom are achievable using the rate - splitting scheme . compared to the two - user interference channel , the general @xmath0-user interference channel have not been much known yet . many researchers have studied degrees of freedom ( dof ) to understand the asymptotic capacity because of the difficulty of finding the exact capacity region . for the @xmath0-user interference channel , the dof was shown to be upper bounded by @xmath2 in @xcite . the authors in @xcite showed that this upper bound can be achieved by the interference alignment ( ia ) scheme that all interfering signals from other transmitters are aligned in the same dimension to independently decode the desired signals at the receivers . this scheme operates in high snr to guarantee independence between the desired signal dimension and the interference aligned dimension . in order to operate in any finite snr , @xcite proposed ergodic ia that all interfering signals are perfectly cancelled out by properly choosing two time indices . using ergodic ia , each user can achieve half the interference - free ergodic capacity . the ia schemes generally require perfect channel state information ( csi ) . in rapidly time varying channels , however , channel state information becomes outdated due to feedback delay . in other words , it is impractical to assume that transmitters have perfect knowledge of current channel state information . in order to solve this problem , recent studies @xcite focus on exploiting imperfect channel state information no channel state information at transmitter ( csit ) or delayed feedback information . it was shown in @xcite that @xmath3 dof is achievable for the three - user interference channel with delayed csit and @xmath4 dof is achievable for the three - user interference channel with delayed output feedback without csit . more generally , @xcite showed that @xmath5 dof is achievable for the @xmath0-user interference channel @xmath6 with delayed csit and @xmath7 dof is achievable for the @xmath0-user interference channel with delayed output feedback without csit . in this paper , we assume two delayed feedback scenarios as follows . ( i ) _ delayed channel information at transmitter _ : in this scenario , nothing but the past channel information is given at the transmitter . the channel information implies either channel state information or time index information . output feedback is not assumed in this case . ( ii ) _ delayed output feedback without csit _ : in this scenario , nothing but the past output feedback information is given at the transmitter and the channel information is not available at the transmitter . we devise effective interference management strategies in the @xmath0-user interference channel for these two scenarios . the proposed schemes are developed in the framework of ergodic ia @xcite and enables interference - free decoding of the desired message at the receiver . it is shown that the proposed strategies achieve @xmath8 dof in the @xmath0-user interference channel for the scenarios of the delayed channel information and the delayed output feedback without csit . the proposed schemes achieve higher dof than the retrospective ia @xcite in the @xmath0 user interference channel with the same assumptions of delayed feedback . the received signal in the @xmath0-user interference channel is given by @xmath9 where @xmath10^t$ ] , the transmitted signal vector @xmath11 @xmath12^t\in \mathbb{c}^{k \times 1 } $ ] with power constraint @xmath13 , @xmath14 represents the time varying fading channel matrix and is given by @xmath15.\end{aligned}\ ] ] where @xmath16 denotes the channel coefficient from transmitter @xmath17 to receiver @xmath18 and is an independent and identically distributed ( i.i.d . ) complex gaussian random variable with distribution @xmath19 . at receivers , full channel state information is assumed to be available , i.e. , csir . the element of the additive white gaussian noise vector @xmath20^t$ ] is assumed to follow complex gaussian distribution @xmath21 . the ergodic ia @xcite requires perfect knowledge of channel state information at the transmitter ( csit ) . for a @xmath0-user interference channel , @xmath22 total dof can be achieved in an ergodic sense if the channel is time varying . contrary to other ia techniques , the ergodic ia works for infinite snr as well as any finite snr since interfering signals are canceled out when the channel matrices at two different time instants satisfy a certain condition . specifically , let @xmath23 and @xmath24 be the time instants ( or time indices ) at which the the channel matrices satisfy the following relationship : @xmath25\label{eq : channel1}\\ \textbf{h}(t_2 ) & = c(t_2)\cdot\left [ \begin{array}{ccc } h_{11}(t_1 ) & \cdots & -h_{1k}(t_1 ) \\ \vdots & \ddots & \vdots~ \\ -h_{k1}(t_1 ) & \cdots & h_{kk}(t_1 ) \\ \end{array } \right ] \label{eq : channel2}\end{aligned}\ ] ] where @xmath26 is a complex valued constant and @xmath27 , @xmath28 , @xmath29 , @xmath30 . at the time @xmath24 , the message which was previously sent at the time @xmath23 is again sent from the transmitter . in other words , the transmitted signal vector @xmath31 is equal to @xmath32 . to decode the message , receiver @xmath33 adds the received signals at @xmath23 and @xmath24 and constructs a sufficient statistics for the message @xmath34 as @xmath35 then , the achievable rate is determined by @xmath36 where @xmath37 , @xmath38 . correspondingly , the total @xmath2 dof is achievable @xcite . contrary to the existing ergodic ia , we assume only full csir and imperfect or partial csit by feedback delay . specifically , all receivers feed either channel state information or time indices back to the transmitters . each transmitter can not use the current channel information but can use the outdated channel information due to feedback delay . in this subsection , we propose a new strategy to achieve high dof when the receivers feed csi back to the transmitters . to effectively establish the concept of the proposed scheme , we start from the three - user interference channel , i.e. , @xmath39 . three - user interference channel with delayed csit can achieve total @xmath40 dof by ergodic ia . the proposed ergodic ia is carried out over two phases : _ transmission phase 1 _ : transmission phase 1 for data transmission is continued until @xmath24 . at each time until @xmath24 , new messages are continuously transmitted . for the time @xmath23 and @xmath41 at which the channel condition in ( [ eq : channel1 ] ) and ( [ eq : channel2 ] ) is satisfied , the received signals are given by @xmath42 due to delayed csit , the transmitters can not recognize what the current channel states are so that they can not send the same message of @xmath23 at @xmath24 as in the conventional ergodic ia . thus , they just send independent messages at @xmath23 and @xmath24 . after the channel changes , the transmitters can figure out that the channel condition in ( [ eq : channel1 ] ) and ( [ eq : channel2 ] ) is satisfied at the previous time @xmath24 due to delayed csi feedback . then , transmission phase 2 is entered . _ transmission phase 2 _ : if the previous time was @xmath24 , the transmitters send the following signals at time @xmath43 , respectively : @xmath44 after transmission phase 2 is completed , the transmission mode goes back to transmission phase 1 . each receiver adds its received signals at @xmath23 and @xmath24 and constructs the following variables . @xmath45 _ decoding at receiver 1 _ : using the received signal at @xmath46 and @xmath47 , receiver 1 removes the interfering signals from the other senders in ( [ eq : rx1 ] ) . then , we have an equation for @xmath48 . using another equation for @xmath49 received at @xmath50 , receiver 1 can decode both @xmath51 and @xmath52 . _ decoding at receiver 2 _ : similarly , receiver 2 removes the interfering signals in ( [ eq : rx2 ] ) using the received signal at @xmath50 and @xmath47 and decodes @xmath53 and @xmath54 using the received signal at @xmath46 and ( [ eq : rx2 ] ) . _ decoding at receiver 3 _ : similarly , receiver 2 removes the interfering signals in ( [ eq : rx3 ] ) using the received signal at @xmath50 and @xmath46 and decodes @xmath55 and @xmath56 using the received signal at @xmath47 and ( [ eq : rx3 ] ) . according to the decoding procedure , the proposed scheme enables each receiver to decode its 2 messages in 5 symbol times . that is , total 6 messages are decodable over 5 symbol times and hence total 6/5 dof is achievable . total @xmath8 dof is achievable in a @xmath0-user interference channel with delayed csit by ergodic ia . for a @xmath0-user interference channel , two independent messages sent at time @xmath23 and @xmath24 are decoded at each receiver over @xmath57 symbol times . as in the three - user interference channel , the time @xmath23 and @xmath24 correspond to transmission phase 1 . if the transmitters realize the channel matrix at time @xmath24 satisfies the condition in ( [ eq : channel1 ] ) and ( [ eq : channel2 ] ) , transmission phase 2 starts . then , transmitter @xmath33 , @xmath58 , sends the signal @xmath59 at time @xmath60 . similarly to the three - user interference channel , each receiver can decode its two messages over @xmath57 symbol times . therefore , total @xmath8 dof is achievable in a @xmath0-user interference channel by the proposed ergodic ia . [ fig : p1 ] shows the achievable dof by the proposed ergodic ia ( solid line ) and the retrospective ia @xcite ( dashed line ) with delay csit according to the number of users in a @xmath0-user interference channel . the total achievable dof by the retrospective ia is @xmath61 . it starts from @xmath62 for a three - user case and converges to @xmath63 as @xmath0 goes to infinity . on the other hand , the total achievable dof by the proposed ergodic ia starts from @xmath40 and converges to @xmath64 . if the receivers feed the time indices at which the condition in ( [ eq : channel1 ] ) and ( [ eq : channel2 ] ) is satisfied , total achievable dof is the same as the case that delay csit is used . total achievable dof by the proposed ergodic ia with delay time index feedback in a @xmath0-user interference channel is @xmath8 . the strategy in section [ kudcsit ] can be applied . instead of using the channel state information ( i.e. , channel matrix ) to find the time @xmath23 and @xmath24 at which the condition in ( [ eq : channel1 ] ) and ( [ eq : channel2 ] ) is satisfied , the receivers send the time indices @xmath23 and @xmath24 since receivers can find them by the assumption of full csir . after receiving the time indices , the transmitters realize that the previous time was @xmath24 and enter into transmission phase 2 . in this section , we assume full csir and delayed output feedback . the received signals" +"resonant inelastic x - ray scattering ( rixs ) is a technique that matures rapidly due to the recent increase in brilliance of the new generation synchrotron x - ray sources , where high flux photon beams with energies that are tunable to resonant edges are now becoming widely available @xcite . the probability for x - rays to be scattered from a solid state system can be enhanced by orders of magnitude when the energy of the incoming photons is in the vicinity of an electronic eigenmode a resonant edge of the system . rixs experiments are performed on e.g. the k - edges of transition metal ions , where the frequency of the x - rays is tuned to match the energy of an atomic @xmath1-@xmath2 transition , which is around 5 - 10 kev @xcite . at this resonant energy a @xmath1 electron from the inner atomic core is excited into an empty @xmath2 state , see fig . 1 . it is a well - known fact that the @xmath1 core - hole that is created has an ultrashort lifetime , of the order of femtoseconds . the reason is that the core - hole has a very high energy and is prone to decay via all sorts of radiative and non - radiative processes , severely cutting down the efficiency of rixs . in theoretical treatments of rixs this life - time effect is normally introduced as a core - hole broadening and disregarded from that point on . in a previous study @xcite , however , we have shown that from the theory perspective there is a great advantage of the very short lifetime of the core - hole . the ultrashort lifetime implies that for the other electrons in the system particularly for the slow ones that are close to the fermi - energy the core - hole potential is almost an instantaneous delta - function in time . this allows for a systematic expansion of the scattering cross section in terms of the lifetime , for which we present a detailed derivation and various generalizations in this paper . we shall see that the most important consequence of the ultrashort core - hole lifetime is that for indirect rixs the effective scattering cross section is proportional to the charge structurefactor @xmath0 and the longitudinal spin structure factor that is associated with it . the indirect rixs process is shown schematically in fig . 1 . in transition metal systems the photo - electron is promoted from a @xmath1 core - orbital to empty @xmath2 states that are far ( 10 - 20 ev ) above the fermi - level . so the x - rays do not cause direct transitions of the @xmath1 electron into the lowest @xmath3-like conduction bands of the system . still rixs is sensitive to excitations of electrons near the fermi - level . the coulomb potential of @xmath1 core - hole causes e.g. very low energy electron - hole excitations in the valence / conduction band : the core - hole potential is screened by the valence electrons . when the excited @xmath2-electron recombines with the @xmath1 core - hole and the outgoing photon is emitted , the system can therefore be left behind in an excited final state . experimentally the momentum @xmath4 and energy @xmath5 of the elementary excitation is determined from the difference in energy and momentum between incoming and outgoing photons . since the excitations are caused by the core - hole , we refer to this scattering mechanism as _ indirect _ resonant inelastic x - ray scattering ( rixs ) . at present energy resolutions of about 100 mev can be reached . in the near feature it seems experimentally feasible for rixs to become sensitive to the low energy excitations of the solid , where excitation energies are of the order of room temperature . recently it has been shown that also magnetic excitations , magnons , can be measured in rixs @xcite . other interesting low - lying electronic excitations that potentially can be probes by rixs are , for example , collective features such as plasmons , orbitons , excitons , but also single - particle - like continua related to the band structure . rixs provides a new tool to study these elementary excitations . for the interpretation of spectroscopic data , it is very important to express the scattering cross section for a technique in terms of physical correlation functions . in this paper , we derive in detail the dynamical correlation function that is measured in indirect resonant inelastic x - ray scattering . for local core - hole potentials and ultrashort lifetimes , the dynamical correlation function turns out to be a linear combination of the charge density and longitudinal spin density response function . we show that for a single band system the actual linear combination that is measured depends on the energy of the incoming photons and we determine the precise energy dependence of its coefficients . a sum - rule is derived and we generalize these results to the case of finite temperature and for multiband systems . the kramers - heisenberg formula @xcite for the resonant x - ray scattering cross section at finite temperature is @xmath6 where @xmath7 and @xmath8 denote the final and initial state of the system , respectively . the sum is over all final states and the brackets denote the statistical average over initial states @xmath8 for a temperature @xmath9 . the momentum and energy of the incoming / outgoing photons is @xmath10 and @xmath11 and the loss energy @xmath12 is equal to the energy difference between the final and initial state @xmath13 . in the following we will take the groundstate energy of our system as reference energy : @xmath14 . the scattering amplitude @xmath15 is given by @xmath16 where @xmath17 the resonant energy , @xmath18 denotes the intermediate states and @xmath19 the ( dimensionless ) dipole operator that describes the excitation from initial to intermediate state and the de - excitation from intermediate to final state . the energy of the incoming x - rays with respect to the resonant energy is @xmath20 ( this energy can thus either be negative or positive : @xmath21 ) and @xmath22 is the energy of intermediate state @xmath23 with respect to the resonance energy . in the intermediate state a core - hole and a photo - excited electron are present . when we take the coulomb interaction between the intermediate state core - hole and the valence band electrons into account , we obtain a finite inelastic scattering amplitude . in that case there is a non - zero probability that an electron - hole excitation is present in the final state , see fig.1 . the intermediate state , however , is not a steady state . the highly energetic @xmath1 core - hole quickly decays e.g. via auger processes and the core - hole life - time is very short . the heisenberg time - energy uncertainty relationship then implies that the core - hole energy has an appreciable uncertainty . this uncertainty appears in the formalism above as the core - hole energy broadening @xmath24 which is proportional to the inverse core - hole life - time , which is of the order of electron volts as the lifetime is ultrashort , of the order of femtoseconds . note that the life - time broadening only appears in the intermediate states and not in the final or initial states as these both have very long life times . this implies that the core - hole broadening does not present an intrinsic limit to the experimental resolution of rixs : the loss energy @xmath5 is completely determined by kinematics . when the incoming energy of the x - rays is equal to a resonant energy of the system @xmath25 and we see from eqs . ( [ eq : kramers],[eq : amplitude ] ) that the resonant enhancement of the x - ray scattering cross section is @xmath26 , which is @xmath27 for a transition metal k - edge @xcite . in a resonant scattering process , the measured system is generally strongly perturbed . formally this is clear from the kramers - heisenberg formula ( [ eq : kramers ] ) , in which both the energy and the wavefunction of the intermediate state where a potentially strongly perturbing core - hole is present appear . this is in contrast with canonical optical / electron energy loss experiments , where the probing photon / electron presents a weak perturbation to the system that is to be measured . to calculate rixs amplitudes , one possibility is to numerically evaluate the kramers - heisenberg expression . to do so , all initial , intermediate and final state energies and wavefunctions need to be known exactly , so that in practice a direct evaluation is only possible for systems that , for example , consist of a small cluster of atoms @xcite . in this paper , however , we show that under the appropriate conditions we can integrate out the intermediate states from the kramers - heisenberg expression . after doing so , we can directly relate rixs amplitudes to linear charge and spin response functions of the unperturbed system . for non - resonant scattering , one is familiar with the situation that the scattering intensity is proportional to a linear response function , but for a resonant scattering experiment this is a quite unexpected result . let us proceed by formally expanding the scattering amplitude in a power series @xmath28 where we introduced the matrix elements @xmath29 the formal radius of convergence of this power series is given by @xmath30 , so that the series is obviously convergent when the incoming x - ray energy is e.g far enough below the resonance , i.e. when @xmath31 . but also at resonance , when @xmath32 the series is convergent for intermediate energies that are smaller than the core - hole broadening @xmath24 . thus this expansion is controlled for ultrashort core - hole lifetimes , which implies that @xmath24 is large . in the following we will be performing re - summations of this series . we denote the denominator of the expansion parameter @xmath33 by the complex number @xmath34 , so that @xmath35 where @xmath36 is the hamiltonian in the intermediate state . we thus obtain the following series expansion for the resonant cross section @xmath37 we will first calculate the resonant x - ray cross section at zero temperature in the case where the valence and conduction electrons are effectively described by a single band of spinless fermions : spin , and orbital degrees of freedom of the valence electron system are suppressed . physically this situation can be realized in a fully saturated ferromagnet . the final and initial states of the system are determined by a hamiltonian @xmath38 that describes the electrons around the fermi - level . the generic form of the full many - body hamiltonian is @xmath39 where @xmath40 and @xmath41 denote lattice sites with lattice vectors @xmath42 and @xmath43 . note that the sum is over each pair @xmath44 once , with @xmath44 ranging from 1 to @xmath45 , where @xmath45 is the number of sites in the system . the hopping amplitudes of the valence electrons are denoted by @xmath46 and the @xmath47-operators annihilate / create such electrons . the coulomb interaction between valence electrons is @xmath48 , as the coulomb interaction only depends on the relative distance between two particles . the intermediate states are eigenstates of the hamiltonian @xmath49 , where @xmath50 accounts for the coulomb coupling between the intermediate state core - hole and the valence electrons : @xmath51 where @xmath52 creates a core - hole on site @xmath40 . we assume that the core - hole is fully localized" +"many networks in nature and technology are sparse , _ i.e. _ , the average node degree is much smaller than the total number of nodes @xmath0 @xcite . widely studied classes of networks , such as regular grids , random graphs , and scale - free networks , are maximally sparse , as the average node degree remains finite as @xmath1 . however , in other examples of real sparse networks , such as the internet , the average node degree grows , albeit very slowly , with system size . motivated by this observation , we introduce a simple network growth mechanism of copying that naturally generates sparse networks in which the average node degree diverges logarithmically with system size . we dub these log - networks . related results appear in previous investigations of related models @xcite , while models where a slowly increasing ratio of links to nodes is imposed externally have also been considered @xcite . to motivate the copying mechanism for log - networks let us recall the growing network with redirection ( gnr ) @xcite . the gnr is built by adding nodes according to the following simple rule . each new node initially selects an earlier `` target '' node at random . with a specified probability a link from the new node to the target node is created ; with a complementary probability , the link is re - directed to the ancestor node of the target . although the target node is chosen randomly , the redirection mechanism generates an effective preferential attachment because a high - degree node is more likely to be the ancestor of a randomly - selected node . by this feature , redirection leads to a power - law degree distribution for the network . the gnr thus provides an appealingly simple mechanism for preferential attachment , as well as an extremely efficient way to simulate large scale - free networks @xcite . the growing network with redirection is a simplification of a previous model @xcite which was proposed to mimic the copying of links in the world - wide web . in this web model , a new node links to a randomly - chosen target node and also to its ancestor nodes ( subject to a constraint on the maximum number of links created ) . in the context of citations , copying is ( regrettably ) even more natural , as it is easier merely to copy the references of a cited paper , rather than to look at the original references @xcite . as the literature grows , the copying mechanism will necessarily lead to later publications having more references than earlier publications . in the following sections , we analyze a growing network model with copying ( gnc ) . we consider a model with no global bound on the number of links emanating from a new node . we shall see that this simple copying mechanism generates log - networks . we will use the master equation approach to derive basic geometric properties of the network . we then compare our prediction about the logarithmic growth of the average degree with data from physical review citations . we now define the gnc model precisely . the network grows by adding nodes one at a time . a newly - introduced node randomly selects a target node and links to it , as well as to all ancestor nodes of the target node ( fig . [ c ] ) . if the target node is the initial root node , no additional links are generated by the copying mechanism . if the newly - introduced node were to always choose the root node as the target , a star graph would be generated . on the other hand , if the target node is always the most recent one in the network , all previous nodes are ancestors of the target and the copying mechanism would give a complete graph . correspondingly , the total number of links @xmath2 in a network of @xmath0 nodes can range from @xmath3 ( star graph ) to @xmath4 ( complete graph ) . notice also that the number of outgoing links from each new node ( the out - degree ) can range between 1 and the current number of nodes . we now study geometric properties of the gnc model by the master equation approach . we determine how the total number of links @xmath5 grows with @xmath0 , as well as the in - degree , out - degree , and the joint in / out - degree distributions . let @xmath6 be the average value of the total number of links in a network of @xmath0 nodes . if a newly - introduced node selects a target node with @xmath7 ancestors , then the number of links added to the network will be @xmath8 . therefore the average total number of links satisfies @xmath9 the factor @xmath10 in the first line assures that a target node @xmath11 is selected uniformly from among all @xmath0 nodes , and we obtain the second line by employing the sum rule @xmath12 . dividing eq . ( [ ln ] ) by @xmath13 gives @xmath14 and then summing both sides from 1 to @xmath3 gives the solution @xmath15 here @xmath16 is the harmonic number . ( for concreteness , we assume that the network starts with a single node , so that @xmath17 . ) using the asymptotics of the harmonic numbers @xcite we find @xmath18 where @xmath19 is the euler constant . the leading asymptotic behavior of @xmath20 can also be obtained more easily from eq . ( [ ln ] ) by taking the continuum approximation and solving the resulting differential equation . for @xmath21 realizations of a gnc of @xmath22 sites . shown are both the raw data and the result of averaging the data over a 1% range . for this value of @xmath0 , the mean number of links is 6485.56 , while eq . ( [ ln - sol - asymp ] ) gives 6485.47 . , scaledwidth=45.0% ] thus we conclude that the average degree of the network grows logarithmically with the system size ; that is , the copying mechanism generates a log - network . this simple phenomenon is one of our major results . we now briefly discuss the probability distribution of the total number of links @xmath23 for a network of @xmath0 nodes . simulations show that the distribution is asymmetric and quite broad ( fig . [ pl ] ) . to understand the origin of the asymmetry , notice that both the extreme cases of the star graph ( @xmath24 ) and the complete graph ( @xmath25 ) each occur with probability @xmath26 because each new node must select one specific target node . therefore the distribution of the total number of links vanishes much more sharply near the lower cutoff . near the peak however , the distribution @xmath23 is symmetric about the average . more precisely , when the deviation from the average @xmath27 is of the order of @xmath28 ^ 2\,p_n(l)}$ ] , the distribution approaches a symmetric gaussian shape . the value of the standard deviation as @xmath1 is @xmath29 as derived in appendix [ ap ] . the relative width of the distribution is measured by the standard deviation @xmath30 divided by the average @xmath6 ; this ratio approaches zero as @xmath31 when @xmath1 , so that fluctuations die out slowly . this slow decay of fluctuations explains why the distribution ( fig . [ pl ] ) remains wide for large @xmath0 and why it looks asymmetric near the peak . the gnc model can be extended to allow for wider copying variability . for example , instead of linking to one initial random target node , we can link to @xmath32 random initial targets . further , we can link to each target node with probability @xmath33 and to each of the corresponding ancestors with probability @xmath34 . for this general @xmath35 model , the analog of eq . ( [ ln ] ) is @xcite @xmath36 which reduces to @xmath37 in the continuum approximation . the asymptotic growth of the average total number of links crucially depends on the parameter @xmath38 : @xmath39 thus incomplete copying leads to an average node degree that is independent of @xmath0 when @xmath40 , while marginal logarithmic dependence is recovered when @xmath41 . there is also a pathology for @xmath42 , as the number of links in the network would exceed that of a complete graph with the same number of nodes . in this case , it is not possible to accommodate all the links specified by the copying rule without having a multigraph , _ i.e. _ , allowing for more than one link between a given pair of nodes . we now present empirical data from the citation network of physical review to test whether the average degree of these networks grows with time , and if so , whether the growth is consistent with log - networks . data from all issues of physical review journals is available , encompassing a time span of 110 years @xcite . from this data , we have the following evidence that citations may be described as a log - network . specifically , the average number of references in the reference list of each physical review paper grows systematically with time and is consistent with a linear increase ( fig . [ ref - compare ] ) . additionally , the number of physical review papers published in a given year roughly grows exponentially with time @xcite . thus the cumulative number of physical review papers up to a given year also grows exponentially . as a result , the number of references should grow logarithmically with the total number of available papers . this behavior is reasonably consistent with the data of fig . [ ref - compare ] . ) . also shown as a smooth curve is the logarithm of the cumulative number of physical review papers that were published up to each year . the value 5 is subtracted from the latter data to make the two datasets lie in the same range.,scaledwidth=45.0% ] in a related vein , the average number of coauthors per paper has grown slowly with time , due in part , to the growing trend for collaborative research and the continuing ease of long - distance scientific interaction . while co - authorship and other collaboration networks have recently been investigated ( see , _ e.g. _ , @xcite ) , the analysis has primarily been on network properties at a fixed time . there is , however , one study of the number of mathematics papers with 1 , 2 , and more authors since 1940 @xcite . this data shows that the fraction of singly - authored papers is decreasing systematically , while the number of multiple - authored papers is steadily growing . thus it should be interesting to track the time dependence of the number of co - authors in scientific publications from the current studies of collaboration networks . interestingly , the internet and the world wide web exhibit certain similarities with log - networks . for example , the total number of links exceeds the total number of nodes in the world wide web by about an order of magnitude @xcite . similarly for the internet , specifically for the autonomous systems ( as ) graph , the average number of links per node is also growing slowly but systematically with time @xcite . qualitatively these behaviors are consistent with our expectations from log - networks . it is not still possible to reach definitive conclusions about the precise growth rate on @xmath0 since the available data for the as" +"the quantization of polarized gravitational cylindrical waves has received a lot of attention in recent years @xcite . this is partly due to the fact that this system provides a tractable , yet non - trivial , reduction of full general relativity and hence is an ideal framework to explore several issues involved in the quantization of gravity . some intriguing phenomena , related to the existence of large quantum gravity effects , have been discussed by studying precisely this model @xcite . it has also been argued that some manifestations of quantum gravity , such as the smearing of light cones are , indeed , present and can be understood in this simplified setting @xcite . one of the interesting points behind the obtained results is the realization of the fact that the physical hamiltonian is a function of the free field hamiltonian for a 2 + 1 dimensional , axially symmetric , massless scalar field evolving in an auxiliary minkowski background @xcite . as we show in the first section of the paper , this free hamiltonian naturally appears when one linearizes the system , thus suggesting that , in a precise sense , it can be considered as the free part of an interacting model . however the full interacting hamiltonian is obtained by adding a very specific type of terms to the free part , namely , just functions of it . here we plan to explore the consequences of this functional relation between the two physically relevant hamiltonians for the system and explore how this affects the causal structure of quantum spacetime . to this end we will pay attention to the smearing of the light cones due to quantum gravity effects within the framework of linearly polarized cylindrical waves . instead of considering the full information encoded in the metric tensor we will concentrate on the causal structure provided by light cones . an interesting , albeit somewhat indirect way , to look at this structure is to study the commutators of field operators at different spacetime points . these are the basic objects to discuss the commutativity of observables and the microcausality of the model ; conventionally , a physical model should be such that observables commute for space - like intervals . this has been discussed in the standard perturbative quantum field theory framework for simple examples such as scalar or fermion fields ( see e.g. @xcite ) . in fact , microcausality is one of the key conditions to prove such important results as the spin - statistics theorem @xcite . here we will use the commutator of the scalar field that describes linearly polarized cylindrical waves as a way to get information about the causal structure of quantum spacetime . as we show later it is possible to give exact expressions for this commutator both for the evolution provided by the free and the full physical hamiltonians . we will use these expressions to study in a quantitative way the smearing of the light cones as a function of the three - dimensional gravitational constant and explore some physical issues , in particular the appearance of singularities as a consequence of having a hamiltonian bounded from above @xcite . the rest of the paper is structured as follows . in sec . [ lingrav ] we discuss how the free hamiltonian is derived from the linearized cylindrical wave model . [ evolutions ] deals with the classical and quantum dynamics of cylindrical gravitational waves under the evolution provided both by the free hamiltonian and the physical hamiltonian . we will pause here to discuss and compare on a familiar example ( the harmonic oscillator ) the main features of the time evolution defined by functionally related hamiltonians , both from the classical and the quantum points of view . this will provide valuable insights for the problem considered in this work . [ microcausality ] is devoted to the study of microcausality . we will look at the main features of the field commutators and study the smearing of the light cones due to quantum gravitational effects . we end the paper with a discussion of the main results and perspectives for future work . linearly polarized cylindrical waves in general relativity can be described by the spacetime metric @xcite : @xmath0 where @xmath1 is the coordinate of the symmetry axis and @xmath2 is the three - metric @xmath3 from this three - dimensional point of view , @xmath4 and @xmath5 correspond to polar coordinates , @xmath6 is the radial component of the shift vector and @xmath7 is the lapse function . all metric functions ( @xmath8 , @xmath9 , @xmath7 , and @xmath6 ) depend only on the time and radial coordinates , @xmath10 and @xmath11 . unless otherwise stated , we adopt a system of units such that @xmath12 , where @xmath13 is the speed of light , @xmath14 is planck constant , and @xmath15 is the effective newton constant per unit length in the direction of the symmetry axis @xcite . in these units , the gravitational action of the system has the form @xcite @xmath16,\ ] ] where the dot denotes the derivative with respect to @xmath10 , the @xmath17 s are the momenta canonically conjugate to the metric variables and @xmath18 is the total hamiltonian @xmath19.\end{aligned}\ ] ] the first term is a boundary contribution at infinity [ @xmath20 and the second term is a linear combination of the hamiltonian constraint @xmath21 and the ( radial ) diffeomorphisms constraint @xmath22 : @xmath23 , \nonumber\\ c^r&=&e^{-\gamma}\left(-2p^{\prime}_{\gamma}+ p_{\gamma}\gamma^{\prime}+p_rr^{\:\prime}+p_{\psi}\psi^{\prime } \right).\end{aligned}\ ] ] the prime denotes the derivative with respect to @xmath11 . the gauge freedom associated with these constraints can be removed by imposing , respectively , the gauge fixing conditions @xcite @xmath24 on the other hand , the lagrangian form of the action can be obtained from the relations between momenta and time derivatives of the metric provided by the hamilton equations , @xmath25 from a three - dimensional perspective , the system describes an axially symmetric model consisting of a scalar field @xmath26 coupled to gravity @xcite , the line element being ( [ 3met ] ) . a particular classical solution is a vanishing scalar field in three - dimensional minkowski spacetime or , equivalently , minkowski spacetime in four dimensions . in this solution , @xmath27 and @xmath28 , whereas the rest of metric fields and momenta vanish ( i.e. @xmath29 ) . in this section , we will consider this solution as a background and discuss first - order perturbations around it . in other words , we will analyze the linearized theory of gravity around this minkowski spacetime , as it is usually done in the perturbative , quantum field theory approach to gravity . in order to expand the metric fields around the classical solution , let us call @xmath30 up to first - order terms in the fields , the expression of the three - metric becomes @xmath31 while the four - dimensional metric is given by @xmath32 here , it is understood that the product of @xmath26 with any other metric field vanishes in the perturbative order considered . on the other hand , regularity on the axis of symmetry imposes the following conditions : @xmath33 in order to discuss the linearized gravitational system , we must keep up to quadratic terms in the fields in the action ( [ act ] ) . a straightforward calculation leads to the result @xmath34,\nonumber\\ \bar{\cal h}&=&\int_0^\infty dr \left [ \frac{p_{\psi}^2}{2r}+\frac{r\,(\psi^{\prime})^2}{2}-p_{\gamma } p_{\bar{r}}+\bar{n}\bar{c}+n^r\bar{c}^r\right]\nonumber\\ & & + ( 2-\gamma_{\infty})\,\bar{r}^{\,\prime}(r\rightarrow\infty).\end{aligned}\ ] ] here , @xmath35 is the momentum canonically conjugate to @xmath36 , and the linearized constraints are : @xmath37 the diffeomorphisms gauge freedom can be fixed just like in the cylindrical reduction of general relativity , namely , by demanding that @xmath38 coincides with the radial coordinate @xcite . we thus impose the gauge fixing condition @xmath39 . it is easily checked that the poisson brackets @xmath40 of this condition with the linearized constraint do not vanish , so that the gauge fixing is admissible . dynamical consistency of the gauge fixing procedure requires , in addition , @xmath41 hence , the shift must be chosen as @xmath42 . finally , the momentum conjugate to @xmath36 is fixed by solving the diffeomorphisms constraint : @xmath43 . in this way , the canonical pair @xmath44 is removed from the set of degrees of freedom . the action of the resulting reduced model is @xmath45.\end{aligned}\ ] ] here , @xmath46 is the hamiltonian constraint of the reduced linearized system , and @xmath47.\ ] ] remarkably , the condition employed to eliminate the hamiltonian gauge freedom in full cylindrical gravity @xcite can be used as well to fix the corresponding gauge in the linearized theory . the gauge fixing @xmath48 is acceptable , because the poisson brackets of @xmath49 and @xmath50 differ from zero . in addition , consistency of the chosen gauge demands the vanishing of @xmath51 therefore , @xmath52 has to be independent of the radial coordinate . actually , we can set @xmath53 by demanding that the total lapse equals the unity at spatial infinity . on the other hand , taking into account the regularity condition ( [ reg ] ) , the solution to the hamiltonian constraint is simply @xmath54 . this allows us to remove the canonical pair @xmath55 from the system and arrive at a constraint - free model in linearized gravity . the degrees of freedom of this system are the field @xmath26 and its momentum . the reduced action is @xmath56.\end{aligned}\ ] ] note that @xmath57 , given in eq . ( [ ham0 ] ) , is the hamiltonian of a massless scalar field with axial symmetry in three - dimensions . furthermore , in the gauge that we have selected , the three - dimensional metric of the linearized gravitational theory is exactly that of minkowski spacetime and contains no physical degrees of freedom . the scalar field @xmath26 determines the norm of the killing vector @xmath58 , and appears in the four - dimensional metric of the gauge - fixed , linearized model in the form ( [ metlin ] ) , but with @xmath59 substituted by the flat metric @xmath60 where we have renamed @xmath61 the time coordinate of the reduced system . summarizing , the perturbative description provided in linearized gravity for cylindrical waves with linear polarization around four - dimensional minkowski spacetime is equivalent to a massless scalar field with axial symmetry in a three - dimensional flat background . the dynamics of this field is dictated by the free hamiltonian @xmath57 , which generates the evolution in the minkowskian time @xmath61 . it is worth noticing that the action and metric of the gauge - fixed model in linearized gravity reproduce in fact the results that one would obtain from the gauge - fixed model in full cylindrical gravity by working just in the first perturbative order , i.e. , by keeping in the action and metric , respectively , up to quadratic and linear terms in the field @xmath26 and its momentum . in this sense , the gauge fixing and linearization procedures commute . one of the significant features of gravitational cylindrical waves is the existence of two distinct , physically relevant hamiltonians ( or equivalently two distinct time coordinates ) to define both the classical and quantum evolution . one is the hamiltonian @xmath57 [ given in eq . ( [ ham0 ] ) ] that generates the dynamics in the linearized gravitational theory ; the other is the hamiltonian @xmath62 that provides the energy per unit length along the symmetry axis in general relativity @xcite . in fact , they are functionally dependent , since @xmath63 . in order to gain insight into the relation that can be established between the dynamics associated with these two different hamiltonians , we open this section by discussing" +"under the influence of gravity , the initially - small fluctuations in the primordial density field grow to become the hierarchical and nonlinear structures observed today . we can study the late - time clustering of matter by evolving a density field described by an initial power spectrum and comparing the simulated structures to observed galaxies in a statistical way . however , if we were able to undo the smearing effects of nonlinear evolution and reverse the formation of structure , we would be able to reconstruct the primordial power spectrum from an observed distribution of galaxies . many reconstruction methods have been developed @xcite , from simple linear reconstruction to more complex methods , with varying degrees of success ( see @xcite for a comparative review ) . for example , monge - ampre - kantorovitch ( mak ) reconstruction @xcite was successfully able to reproduce the observed velocity field of the local group @xcite . a reconstruction method that uses the linear zeldovich approximation of the lagrangian displacement has also been proposed to enhance the measurement of baryon acoustic oscillations ( baos ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? the displacement field is a crucial quantity in most of these methods , and is of interest in its own right . there is reason to believe that a logarithmic transformation of the density field may aid estimation of the displacement field . the mass distribution has been successfully described by a lognormal field that evolved from gaussian initial conditions @xcite , with some evidence for a skewed lognormal field in the nonlinear regime @xcite . more recently , it has been found that the power spectrum of the log - transformed density field contains more fisher information than the usual power spectrum at small scales by up to a factor of @xmath110 @xcite . a modified logarithmic transform has also been shown to increase the precision of the power spectrum of the nonlinear weak lensing convergence field @xcite . the log - transformed density field is also more effective in constraining cosmological parameters than the standard density field when using the power spectrum @xcite . this paper investigates the effect of a logarithmic transform of the density field on the relation between the density and displacement fields . we do this by measuring the divergence of the displacement field , which in linear theory is proportional to the negative density contrast @xmath3 , using both eulerian and lagrangian techniques in a cosmological @xmath0-body simulation . we compare the linear and logarithmic approaches and evaluate their dependence on redshift and smoothing scale , both of which affect the applicability of linear theory . the linear and logarithmic approximations for the displacement field are derived in section [ sec : reconstruction ] , and three methods of measuring the divergence of the displacement field and the density field are presented in section [ sec : results ] . concluding remarks are given in section [ sec : conclusion ] . in this section , we compare the linear approximation of the continuity equation to a logarithmic approximation . the large - scale dynamical evolution of structure is described by the zeldovich approximation @xcite , @xmath4 where @xmath5 is the comoving eulerian coordinate , @xmath6 the lagrangian coordinate , @xmath7 the displacement , @xmath8 the linear growth function , and @xmath9 the gravitational potential . the linear poisson equation relates the density contrast , @xmath10 , to the gravitational potential by @xmath11 , thus the divergence of the linear zeldovich displacement can be related to the density contrast : @xmath12 the time derivative of the zeldovich approximation in expanding coordinates ( @xmath13 , where @xmath14 is the physical coordinate ) allows us to relate this expression to the continuity equation . we first note that the derivative consists of two components , @xmath15 , where the first component describes the rate of expansion and the second the peculiar velocity of galaxies ( or mass particles ) : @xmath16 . the continuity equation can be written as ( see , e.g. , * ? ? ? * p 48 ) @xmath17 = 0.\ ] ] to first in @xmath3 order this becomes @xmath18 thus we have @xmath19 and have recovered equation [ eqn : divdel ] . the continuity equation ( eqn . [ eqn : continuity ] ) may also be simplified by keeping the @xmath20 together , resulting in a logarithmic derivative of @xmath20 : @xmath21 this gives a logarithmic expression for the divergence of the lagrangian displacement , @xmath22 where the @xmath23 term appears because @xmath24 is not a zero - mean - field , so we must take into account a non - zero integration constant . we find that this constant is well - approximated by the rather natural value of @xmath25 . we now may compare the linear relation , given by eqn . [ eqn : divdel ] , to the logarithmic relation , given by eqn . [ eqn : divlnd ] . we measure the density field and @xmath26 in a 200 h@xmath2mpc , @xmath27 particle gadget @xcite cold dark matter simulation with standard @xmath28cdm cosmology ( @xmath29 ) . we use three different methods : a grid - based cloud - in - cell ( cic ) smoothing plus a fourier - space estimation of the divergence ( section [ sec : cic ] ) ; an adaptive smoothing using a smoothed particle hydrodynamics ( sph ) kernel , combined with a fourier - space divergence calculation ( section [ sec : sph ] ) ; and a geometrical delaunay tessellation estimation of both the density and the divergence ( section [ sec : dtfe ] ) . we find that each of these methods achieves differing degrees of success based on the nature of the length - scales involved : the cic method is an eulerian , mass - weighted scheme ; the delaunay tessellation is a lagrangian , volume - weighted scheme ; and the adaptive mesh method is a hybrid , featuring a lagrangian kernel with interpolation onto an eulerian grid . we discuss each in turn below . the cic method smooths an arbitrary distribution of particles onto a regularly - spaced grid by placing a `` cloud '' having the volume of a grid cell around each particle , so that a particle contributes to the average of multiple nearby cells based on the fraction of its volume contained in these cells . using this weighting scheme , we calculate the density and displacement fields in real space for both @xmath30 and @xmath31 cells , where the displacement @xmath7 is the final ( @xmath32 ) minus initial ( @xmath33 ) particle positions . in the case of @xmath31 cells at @xmath32 , there is only one cell containing zero particles ; we set its value to the average value in the surrounding cells . to avoid cells with zero particles , this is the finest grid we use , given the resolution of the simulation . the divergence of the displacement can then easily be calculated in fourier space , where the derivatives become simple multiples of @xmath34 . we note here that bao reconstruction methods also calculate the linear zeldovich displacement in fourier space , which they multiply by a smoothing function @xmath35 : @xmath36 ; for example , a gaussian smoothing function would take the form @xmath37 . we do not apply an extra smoothing function in fourier space , but note that the size of the grid cells gives the effective smoothing length of the both the density and displacement fields . in our simulations , a @xmath30 cell grid has a length of 3.1 h@xmath2mpc and a @xmath31 cell grid has length 1.6 h@xmath2mpc , while the reconstruction methods have @xmath38 = 5 , 10 , and 20 h@xmath2mpc , with @xmath38=10 h@xmath2mpc performing the best @xcite . in figure [ fig : divcic4z ] we show a two - dimensional histogram of @xmath26 versus @xmath3 and @xmath24 at four different redshifts , for a cell size of 1.6 h@xmath2mpc and with a slope of -1 plotted for reference . the color scale is logarithmic so that the outlying cells can be seen , though the furthest outliers ( especially at low-@xmath39 ) extend beyond the range of the plot . at @xmath40 , the nonlinear clustering of matter has only begun for the initially highest - density peaks , so both the linear and logarithmic relations have slopes near -1 and are very tight . at @xmath41 there is more scatter , and the linear relation begins to deviate very slightly from a slope of -1 for the majority of cells ( shown in black in the plot ) and to develop a high @xmath3 tail . this trend continues at @xmath42 , with increased scatter in both the logarithmic and linear relations , and with the linear relation deviating from a slope of -1 . finally , by @xmath32 the linear relation deviates drastically from a slope of -1 while the logarithmic relation does very well , though with much scatter . ( left ) and @xmath43 ( right ) , calculated using cic smoothing for a cell size of 1.6 h@xmath2mpc at 4 different redshifts . a slope of -1 through the origin is plotted for reference . the color scale is logarithmic and gives the number of cic cells in each histogram bin.[fig : divcic4z ] ] it is not unexpected that the linear relation does not hold , since 1.6 h@xmath2mpc is by no means in the linear regime , but the fact that the logarithmic relation holds so well echoes the results of @xcite and others that the logarithmic transform of the density field increases the information content of the matter power spectrum in the weakly nonlinear regime . when the cic cell size is increased to 12.5 h@xmath2mpc , both the linear and logarithmic relations become very tight , though the logarithmic approximation continues to do slightly better . figure [ fig : divz0 ] is the same as figure [ fig : divcic4z ] but at @xmath32 , showing the cic method for cell sizes of 1.6 h@xmath2mpc and 12.5 h@xmath2mpc , along with the two other methods discussed in the next sections . ( left ) and @xmath43 ( right ) at @xmath32 , calculated using cic smoothing for a cell size of 12.5 h@xmath2mpc ( top ) and 1.6 h@xmath2mpc ( upper middle ) , adaptive sph - like smoothing with a cell size of 1.6 h@xmath2mpc ( lower middle ) , and the delaunay tessellation field estimator ( dtfe ) method ( bottom ) . a slope of -1 through the origin is plotted for reference . the color scale is logarithmic and gives the number of cells ( cic and sph ) or particles ( dtfe ) in each histogram bin.[fig : divz0 ] ] we also try an adaptive smoothing technique , described by @xcite , on both the density and the displacement fields . we assume that each particle @xmath44 traces some physical quantity @xmath45 . for the purpose of this paper , @xmath45 will be either a particle count or the displacement vector @xmath46 between the final and initial particle positions . we sample the adaptively - smoothed field onto a three - dimensional grid , with grid sites denoted by the integers @xmath47 . at each grid site we define the smoothing radius @xmath48 which corresponds to half the distance from the grid site to the @xmath49-th particle , where @xmath49 is defined as : @xmath50 and @xmath51 is the number of particles binned on the grid site @xmath47 . following @xcite , we conservatively set @xmath52 , corresponding to the typical number of" +"whenever a group of autonomous software agents or robots needs to decide on a joint course of action in a fair and satisfactory way , they need to aggregate their preferences . a common way to achieve this is to use voting rules . voting rules are studied in detail in social choice theory and are coming under increasing scrutiny from computer scientists who are interested in their computational properties or want to utilize them in multiagent systems ( see , * ? ? ? * ; * ? ? ? * ) . in social choice theory , voting rules are usually compared using desirable properties ( so - called axioms ) that they may or may not satisfy . there are a number of well - known impossibility theorems among which arrow s impossibility is arguably the most famous which state that certain axioms are incompatible with each other . these results , which show the non - existence of voting rules that satisfy a given set of axioms , are important because they clearly define the boundary of what can be achieved at all . this applies to the explicitly stated axioms as well as implicit ones such as boundaries on the number of voters or alternatives . for instance , if there are only two alternatives , arrow s theorem does not apply and there are many voting rules , including majority rule , that satisfy the conditions used in arrow s theorem . one impossibility that requires unusually high bounds on the number of voters and alternatives is moulin s _ no - show paradox _ @xcite , which states that the axioms of condorcet - consistency and participation are incompatible whenever there are at least 4 alternatives and 25 voters . moulin proves that the bound on the number of alternatives is tight by showing that the maximin voting rule ( with lexicographic tie - breaking ) satisfies the desired properties when there are at most 3 alternatives . the tightness of the more restrictive condition on the number of voters was left open , however . the goal of this paper is to give tight bounds on the number of voters required for moulin s theorem and related theorems that appear in the literature . to achieve this , we encode these problems as formulas in propositional logic and then use sat solvers to decide their satisfiability and extract minimal unsatisfiable sets ( muses ) in the case of unsatisfiability this approach is based on previous work by @xcite , @xcite , @xcite , and @xcite . however , it turned out that a straightforward application of this methodology is insufficient to deal with the magnitude of the problems we considered . several novel techniques were necessary to achieve our results . in particular , we extracted knowledge from computer - generated proofs of weaker statements and then used this information to guide the search for proofs of more general statements . as mentioned above , moulin s theorem uses the axioms of condorcet - consistency and participation . condorcet - consistency goes back to one of the most influential notions in social choice theory , namely that of a _ condorcet winner_. a condorcet winner is an alternative that is preferred to any other alternative by a majority of voters . the marquis de condorcet , after whom this concept is named , argued that , whenever a condorcet winner exists , it should be elected @xcite . a voting rule satisfying this condition is called _ condorcet - consistent_. apart from the intuitive appeal of this condition , condorcet - consistent rules are more robust to changes in the of feasible alternatives and less susceptible to strategic manipulation than other voting rules ( such as borda s rule ) ( see , * ? ? ? * ; * ? ? ? * ) . while the desirability of condorcet - consistency as that of any other axiom has been subject to criticism , many scholars agree that it is very appealing if not indispensable and a large part of the social choice literature deals exclusively with condorcet - consistent voting rules @xcite . _ participation _ was first considered by @xcite and requires that no voter should be worse off by joining an electorate , or alternatively that no voter should benefit by abstaining from an election . the desirability of this axiom in any context with voluntary participation is evident . all the more surprisingly , @xcite have shown that single transferable vote ( stv ) , a common voting rule , violates participation and referred to this phenomenon as the _ no - show paradox_. @xcite , perhaps even more startlingly , proved that no condorcet - consistent voting rule satisfies participation when there are at least 25 voters . we leverage sat solving to obtain an elegant human - readable proof of moulin s result that requires only 12 voters . while computer - aided solving techniques allow us to tackle difficult combinatorial problems , they usually do not provide additional insight into these problems . somewhat surprisingly , the computer - aided proofs we found possess a certain kind of symmetry that has not been exploited in previous proofs . moreover , the sat solver is able to construct a condorcet - consistent voting rule that satisfies participation as well as a number of other desirable properties for up to 11 voters , proving the optimality of the above bound . this computer - generated voting rule is compatible with the maximin voting rule in 99.8% of all cases and , in contrast to maximin , only selects alternatives from the top cycle . as a practical consequence of our theorem , strategic abstention need not be a concern for condorcet - consistent voting rules when there are at most 4 alternatives and 11 voters , for instance when voting in a committee . we also use our techniques to provide optimal bounds for related results about set - valued and probabilistic voting rules @xcite . in particular , we give a tight bound of 17 voters for the optimistic preference extension , 14 voters for the pessimistic extension , and 12 voters for the stochastic dominance preference extension . these results are substantial improvements of previous results . for example , the previous statement for the pessimistic extension requires an additional axiom , at least 5 alternatives , and at least 971 voters @xcite . our results are summarized in . lccccccccccccccccccccccccc & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 & 21 & 22 & 23 & 24 & 25 + condorcet & & & & + maximin & & + kemeny & & + optimistic & & + pessimistic & & + strong sd & & + + [ cols= "" < , < , < , < , < "" , ] the no - show paradox was first observed by @xcite for the stv voting rule . @xcite and @xcite investigate how frequently this phenomenon occurs in practice . the main theorem addressed in this paper is due to @xcite and requires at least 25 voters . this bound was recently brought down to 21 voters by @xcite . simplified proofs of moulin s theorem are given by @xcite and @xcite . @xcite and @xcite strengthen moulin s theorem by weakening condorcet - consistency and participation , respectively . @xcite prove variants of moulin s theorem for set - valued voting rules based on the optimistic and the pessimistic preference extension . @xcite defines a weaker notion of participation in the context of set - valued voting rules and shows that all common condorcet extensions except the maximin rule and young s rule violate this property . @xcite notes that `` a practical question , which has not been dealt with here , refers to the number of candidates and voters that are necessary to invoke the studied paradoxes '' @xcite . when assuming that voters have incomplete preferences over sets or lotteries , participation and condorcet - consistency can be satisfies simultaneously and positive results for common condorcet - consistent voting rules have been obtained by @xcite and @xcite . abstention in slightly different contexts than the one studied in this paper recently caught the attention of computer scientists working on voting equilibria and campaigning @xcite . the computer - aided techniques in this paper are inspired by @xcite , who reduced well - known impossibility results from social choice theory such as arrow s theorem to finite instances , which can then be checked by a sat solver . this methodology has been extended and applied to new problems by @xcite , @xcite , and @xcite . the results obtained by computer - aided theorem proving have already found attention in the social choice community @xcite . more generally , sat solvers have also proven to be quite effective for other problems in economics . a prominent example is the ongoing work by @xcite in which sat solvers are used for the development and execution of the fcc s upcoming reverse spectrum auction . in some respects , our approach also bears some similarities to _ automated mechanism design _ ( see , * ? ? ? * ) , where desirable properties are encoded and mechanisms are computed to fit specific problem instances . let @xmath0 be a set of @xmath1 alternatives and @xmath2 be a set of @xmath3 voters . whether no - show paradoxes occur depends on the exact values of @xmath1 and @xmath3 . by @xmath4 we denote the set of _ electorates _ , non - empty subsets of @xmath2 . for many of our results , we will take @xmath5 , and we use the labels @xmath6 for arbitrary elements of @xmath0 . a _ ( strict ) preference relation _ is a complete , antisymmetric , and transitive binary relation on @xmath0 . the preference relation of voter @xmath7 is denoted by @xmath8 . the set of all preference relations over @xmath0 is denoted by @xmath9 . for brevity , we denote by @xmath10 the preference relation @xmath11 , eliding the identity of voter @xmath7 , and similarly for other preferences . a _ preference profile _ @xmath12 is a function from an electorate @xmath13 to the set of preference relations @xmath9 . the set of all preference profiles is thus given by @xmath14 . for the sake of adding and deleting voters , we define for any preference profile @xmath15 with @xmath16 , and @xmath17 , @xmath18 @xmath19 if the identity of the voter is clear or irrelevant we sometimes , in slight abuse of notation , refer to @xmath20 by @xmath21 , and write @xmath22 instead of @xmath23 . if @xmath24 voters with the same preferences @xmath8 are to be added or removed , we write @xmath25 and @xmath26 , respectively . the _ majority margin _ of @xmath12 is the map @xmath27 with @xmath28 . the majority margin can be viewed as the adjacency matrix of a _ weighted tournament _ @xmath29 . we say that a preference profile @xmath12 _ induces _ the weighted tournament @xmath29 . an alternative @xmath30 is called _ condorcet winner _ if it wins against any other alternative in a majority contest , if @xmath31 for all @xmath32 . conversely , an alternative @xmath30 is a _ condorcet loser _ if @xmath33 for all @xmath32 . our central object of study are _ voting rules _ , functions that assigns every preference profile a socially preferred alternative . thus , a voting rule is a function @xmath34 . in this paper , we study voting rules that satisfy _ condorcet - consistency" +"coexistence between the spin - singlet superconducting order parameters and spin - triplet one is the essential feature of noncentrosymmetric superconductors ( ncs)@xcite . the absence of spatial inversion symmetry leads to spin - orbit coupling large enough to mix the spin - singlet component and spin - triplet one . the amplitude of the spin - singlet component @xmath0 and that of the spin - triplet one @xmath2 is a material parameter determined by the amplitude of spin - orbit coupling . the rashba type spin - orbit coupling induces the helical @xmath1-wave spin - triplet order parameter which is the topologically nontrivial superconducting state @xcite . there have been several studies on superconducting properties coexisting of the spin - singlet @xmath5-wave and the spin - triplet helical @xmath1-wave symmetries @xcite . it is known that topologically protected states with linear dispersion appear at a surface of a ncs for @xmath6 . recent papers , however , have suggested a mixed order parameter spin - singlet @xmath7-wave and spin - triplet @xmath1-wave symmetries @xcite which has been proposed for the interfacial superconductivity @xcite . such pairing symmetry results in dispersionless surface bound state at the fermi level . a similar flat zero - energy surface states has also discussed in a ncs very recently @xcite . physical values originated from the bulk region of a superconductor such as the specific heat and spin susceptibility @xcite are expected to be interpolated from those in the two limits : the pure spin - singlet case and the pure spin - triplet one . an open question is how physical values governed by the surface bound states behave as a function of the relative amplitude between @xmath2 and @xmath0 . the present paper addresses this issue . the surface bound states of unconventional superconductors have been theoretically discussed in heavy fermionic superconductors @xcite , the polar state of @xmath8he @xcite , and high-@xmath9 cuprates @xcite . experimentally , the presence of the surface bound states have been observed as the zero - bias anomaly @xcite of the scanning tunneling spectroscopy ( sts ) of hole - doped @xcite and electron - doped @xcite high-@xmath9 cuprates . the zero - bias anomaly has been observed also in the differential conductance of ramp - edge junctions of hole - doped high-@xmath9 cuprates @xcite and grain boundary junction of electron - doped high-@xmath9 cuprates @xcite . the presence of the surface bound states has been reinterpreted since the proposal for new classification of matter @xcite . the surface bound states at the zero energy are necessary to naturally connect a nontrivial topological integer number inside of an unconventional superconductor with the trivial topological number outside of the superconductor . the dispersion of the subgap states depends on the type of the topological number defined in superconductors . the chiral or helical superconductors give rise to dispersive surface bound states @xcite . on the other hand , dispersionless zero - energy states are formed under @xmath10- and @xmath11-wave symmetries . in direct current josephson effect , the surface bound states result in large @xmath12 values and the deviation of current - phase relationship from the sinusoidal function at low temperature @xcite , where @xmath13 is the critical josephson current , @xmath14 is the normal resistance of a junction , and @xmath15 is the amplitude of pair potential at the zero temperature . such behavior is called low - temperature anomaly of josephson current and is known to be sensitive to spectra of surface bound states @xcite . so far the josephson effect between @xmath5-wave superconductor and a ncs has been reported @xcite . the low - temperature anomaly of the josephson current has never been discussed yet . in this paper , we theoretically calculate the josephson current between two ncs s @xcite based on a current formula @xcite in terms of the andreev reflection coefficients of junctions . we assume a order parameter which is a mixture of the spin - singlet @xmath5-wave and the spin - triplet helical @xmath1-wave symmetries . we call such states as @xmath16 mixture . for @xmath17 , the josephson current saturates at low temperature as is described by the ambegaokar - baratoff formula @xcite . on the other hand for @xmath18 , the josephson current increases logarithmically with decreasing temperature ( @xmath19 ) . the interfacial bound state causes the low - temperature anomaly . the characteristic behavior of the josephson current does not changes gradually as a function of the relative amplitude between @xmath2 and @xmath0 . the critical point @xmath20 clearly divides the qualitative feature of josephson current . in addition to @xmath16 mixture , we also consider two types of mixed order parameter between the spin - singlet @xmath21-wave and the spin - triplet helical @xmath1-wave symmetries . we call such state as @xmath22 mixture . the feature of josephson current are well characterized by the relative amplitude between @xmath2 and @xmath0 . in some cases , the josephson current increases as @xmath23 with decreasing temperature due to dispersionless zero - energy state . we will discuss the physics behind such clear qualitative change of the josephson effect in terms of topologically protected zero - energy surface states . it is known that excitation of such surface bound states on superconductor are characterized by the majorana fermion @xcite . unusual phenomena peculiar to the majorana fermion has been suggested theoretically @xcite . this paper is organized as follows . in sec . ii , we discuss a theoretical model of josephson junction consisting two ncs s . in sec . iii , we show the calculated results of josephson current for @xmath16 and @xmath22 mixtures . we summarize this paper in sec . let us consider a josephson junction between two ncs s as shown in fig . [ fig1 ] , where the electric current flows in the @xmath24 direction and the junction width in the @xmath25 direction is @xmath26 . we apply the periodic boundary condition in the @xmath25 direction . the bogoliubov - de gennes ( bdg ) hamiltonian in momentum space reads @xmath27 , \label{bdg}\\ \hat{h}(\boldsymbol{k})= & \xi_{\boldsymbol{k } } \hat{\sigma}_0 + \lambda\boldsymbol{g}\cdot\hat{\boldsymbol{\sigma } } , \\ \xi_{\boldsymbol{k}}=&\frac{\hbar^2\boldsymbol{k}^2}{2 m } -\mu,\end{aligned}\ ] ] where @xmath28 for @xmath29 are the pauli matrices , @xmath30 is the unit matrix in spin space , @xmath31 is the wavenumber in the @xmath32 direction , @xmath33 is the fermi wave number , @xmath34 is the chemical potential , and @xmath35 is amplitude of the spin - orbit interaction . in this paper , we assume that @xmath36 . we consider the rashba type spin - orbit coupling reflecting the noncentrosymmetry along the @xmath37 direction ( i.e. , @xmath38 ) . correspondingly , we choose the @xmath39-vector in the pair potential as @xmath40 as discussed in ref . . as a consequence , the spin - triplet part of the pair potential has the helical @xmath1-wave symmetry . in this paper , we consider three types of mixed order parameter as follows @xmath41 where @xmath42 is the incident angle of a quasiparticle as shown in fig . [ fig1 ] and @xmath43 . the first one consists of @xmath5-wave singlet and helical @xmath1-wave triplet components . the pair potential of @xmath22 ii is the order parameter discussed in the interfacial superconductivity @xcite . although the pair potential of @xmath22 i may not have a relation to any materials , we consider it for theoretical interest . the energy eigen values of eq . ( [ bdg ] ) are @xmath44 with @xmath45 and @xmath46 to represent the wave function of a quasiparticle , we need another values of the pair potential defined by @xmath47 @xmath48 the wave function in the left superconductor is obtained as @xmath49 \left [ \begin{array}{c}a_+ \\ a_-\end{array } \right ] e^{ik_xx } + \left[\begin{array}{cc } \tilde{v}_+ & \tilde{v}_- \\ ie^{-i\gamma}\tilde{v}_+ & -ie^{-i\gamma}\tilde{v}_- \\ -ie^{-i\gamma } \tilde{u}_+ & ie^{-i\gamma } \tilde{u}_-\\ \tilde{u}_+ & \tilde{u}_- \end{array } \right ] \left [ \begin{array}{c}b_+ \\ b_-\end{array}\right ] e^{-ik_xx } \right.\nonumber\\ & \left.+ \left[\begin{array}{cc } \tilde{u}_+ & \tilde{u}_- \\ ie^{-i\gamma}\tilde{u}_+ & -ie^{-i\gamma}\tilde{u}_- \\ -ie^{-i\gamma } \tilde{v}_+ & ie^{-i\gamma } \tilde{v}_-\\ \tilde{v}_+ & \tilde{v}_- \end{array } \right ] \left [ \begin{array}{c}a_+ \\ a_-\end{array}\right]e^{-ik_xx } + \left[\begin{array}{cc } { v}_+ & { v}_- \\ -ie^{i\gamma}{v}_+ & ie^{i\gamma}{v}_- \\ ie^{i\gamma } { u}_+ & -ie^{i\gamma } { u}_-\\ { u}_+ & { u}_- \end{array } \right ] \left [ \begin{array}{c}b_+ \\ b_-\end{array}\right]e^{ik_xx } \right]e^{ik_yy } , \\ & u_\pm = \sqrt { \frac{1}{2}\left(1+\frac{\omega_\pm}{e}\right ) } , \ ; v_\pm = \sqrt{\frac{1}{2}\left(1-\frac{\omega_\pm}{e}\right)}s_\pm , \ ; \tilde{u}_\pm = \sqrt{\frac{1}{2}\left(1+\frac{\tilde{\omega}_\pm}{e}\right)},\ ; \tilde{v}_\pm = \sqrt{\frac{1}{2}\left(1-\frac{\tilde{\omega}_\pm}{e}\right ) } \tilde{s}_\pm , \\ & \omega_\pm= \sqrt { e^2- \delta_\pm^2 } , \ ; \tilde{\omega}_\pm=\sqrt{e^2- \tilde{\delta}_\pm^2 } , \ ; s_\pm= \frac { \delta_\pm}{|\delta_\pm| } , \ ; \tilde{s}_\pm= \frac { \tilde{\delta}_\pm}{|\tilde{\delta}_\pm| } , \ ; \check{\phi}_{j}=\text{diag}\left\ { e^{i\varphi_j/2},e^{i\varphi_j/2 } , e^{-i\varphi_j/2},e^{-i\varphi_j/2 } \right\},\end{aligned}\ ] ] where @xmath50 and @xmath51 are the amplitudes of incoming waves , @xmath52 and @xmath53 are the amplitudes of outgoing waves , and @xmath54 for @xmath55 or @xmath56 is the macroscopic phase of a superconductor . in the same way , the wave function in the right superconductor is represented by @xmath57 \left [ \begin{array}{c}c_+ \\ c_-\end{array } \right ] e^{ik_xx } + \left[\begin{array}{cc } \tilde{v}_+ & \tilde{v}_- \\ ie^{-i\gamma}\tilde{v}_+ & -ie^{-i\gamma}\tilde{v}_- \\ -ie^{-i\gamma } \tilde{u}_+ & ie^{-i\gamma } \tilde{u}_-\\ \tilde{u}_+ & \tilde{u}_- \end{array } \right ] \left [ \begin{array}{c}d_+ \\ d_-\end{array}\right ] e^{-ik_xx } \right]e^{ik_yy},\label{psi_right}\end{aligned}\ ] ] with @xmath58 and @xmath59 being amplitudes of outgoing waves . at the junction interface , we introduce the potential barrier described by @xmath60 . throughout this paper , we fix @xmath61 , which leads to the transmission probability of the insulating barrier @xmath62 being about 0.01 . by eliminating @xmath58 and @xmath59 using a boundary condition , it is possible to obtain the reflection coefficients , @xmath63 = \left [ \begin{array}{cc } \hat{r}_{ee } & \hat{r}_{eh } \\ \hat{r}_{he } & \hat{r}_{hh } \end{array}\right ] \left [ \begin{array}{c } a_+ \\ a_- \\ b_+ \\ b_- \end{array } \right].\end{aligned}\ ] ] the josephson current can be calculated based on a formula @xcite after applying the continuation @xmath64 , @xmath65 \hat{r}_{he } - \left [ \begin{array}{cc}\frac{\tilde{\delta}_+}{\tilde{\omega}_{n+ } } & 0 \\ 0 & \frac{\tilde{\delta}_-}{\tilde{\omega}_{n- } } \end{array } \right ] \hat{r}_{eh } \right],\end{aligned}\ ] ] with @xmath66 and @xmath67 . we introduce a parameter @xmath68 to tune the mixing rate between the spin - singlet and spin - triplet components as @xmath69 where the dependence of @xmath70 on temperature @xmath19 is described by the bcs theory . the energy spectra of subgap state at a surface of ncs is calculated from eq . ( [ psi_right ] ) with a boundary condition @xmath71 . at first , we summarize the energy spectra of subgap state at a surface of superconductor in fig.[fig2 ] . at @xmath72 , ( b ) : @xmath73 i at @xmath74 , ( c ) : @xmath73 i at @xmath75 , ( d ) : @xmath22 ii at @xmath74 , and ( e ) : @xmath22 ii at @xmath75 . the horisontal axis @xmath76 corresponds to @xmath77 . , width=340 ] in @xmath16 mixture , energy of bound state satisfies @xmath78 it has been already known that the surface bound state is absent for @xmath79 , whereas the surface bound states with the linear dispersion exist for @xmath79 as shown in ( a ) . in @xmath22 i mixture , energy of the surface bound state satisfies @xmath80 the equation has two solutions . the first one is @xmath81 which is allowed for @xmath82 as shown in fig . [ fig2](b ) . the dispersionless zero - energy bound states are a direct consequence of the @xmath21-wave symmetry @xcite . therefore such flat zero - energy state is absent for @xmath83 . the second solution is given by @xmath84 for @xmath85 as shown in fig . [ fig2](b ) and ( c ) ." +"magnetic fields are unexpected in hot , massive stars due to the lack of convection in their outer envelopes . however , a small number of massive b stars host strong , organized magnetic fields , such as the chemically peculiar he strong stars like the archetypical star @xmath0 ori e and the recently discovered b2v star hr 7355 ( oksala et al . 2010 ; rivinius et al . these stars are rapidly rotating and host strong magnetic fields that are coupled to a co - rotating magnetosphere ( townsend , owocki , groote 2005 ) . twenty - one high - resolution ( @xmath1 ) observations of the variable b2v star hr5907 were obtained with the espadons spectropolarimeter at the canada - france - hawaii telescope between february and august 2010 . these initial observations clearly show the presence of zeeman signatures in the circular polarization , stokes @xmath2 least - squares deconvolved ( lsd ) , mean line profiles , indicative of a magnetic field . we have also obtained six low - resolution eso - vlt fors polarimetric observations in addition to 27 uves observations in april 2010 to follow up the espadons observations and to further study the line - profile variability . equivalent width measurements ( right ) for hr5907 . different colours correspond to the different instruments ( red = espadons , blue = fors , green = uves).,width=600 ] using hipparcos photometry , we find a single - wave period of @xmath3d ( see fig . [ sidebyside ] ) , which differs from the double - wave photometric light curve of hr7355 or @xmath0 ori e , likely indicating a different geometry of the magnetic field . from our longitudinal magnetic field measurements , we confirm this period , which we take to be the rotational period of this star ( see fig . [ sidebyside ] ) , making it the fastest rotating , non - degenerate , magnetic massive star ! however , the period is sufficiently imprecise that the relative phasing between our current data and the hipparcos data can be offset by so much as 0.5 cycles . therefore , we have adopted a period of 0.50833d so that the relative phasing between the photometric minimum and the peak of the longitudinal field curve differs by 0.5 cycles - consistent with the predictions of semi - analytical models for a rotationally supported magnetosphere ( townsend 2008 ; townsend & owocki 2005 ) . from nlte model fits to the espadons spectra ( shown in fig . [ nlte_fit ] ) , we find that @xmath4kk , @xmath5 , and @xmath6kms@xmath7 . in addition to the photometric and magnetic periodicity , we also find that h@xmath8 varies with the same period , as illustrated by the equivalent width variations shown in fig . [ sidebyside ] . h@xmath8 shows line profile variations of emission extending to high velocities , as shown in fig . [ ha_dyn ] . the double - lobed pattern and equivalent width variations strongly suggests that hr5907 hosts a structured magnetosphere similar to @xmath0 ori e and hr7355 consisting of co - rotating , magnetically confined clouds of stellar wind plasma . ( black ) profiles for different nights compared to a nlte model profile ( red ) . * right : * phased residual h@xmath8 variations relative to the nlte model.,title=""fig:"",width=268 ] ( black ) profiles for different nights compared to a nlte model profile ( red ) . * right : * phased residual h@xmath8 variations relative to the nlte model.,title=""fig:"",width=268 ] + assuming rigid rotation , we infer that the inclination @xmath9 . from fits to the longitudinal field curve shown in fig . [ sidebyside ] we estimate that hr5907 hosts a mainly dipole magnetic field , with a strength at its pole of @xmath10 kg , and a magnetic axis nearly aligned with the rotation axis . preliminary fits of a dipole model to the lsd profiles at each individual phase seems to confirm this estimate , as shown in fig . [ lsd_fits ] . also included in fig . [ lsd_fits ] is an illustration of how the magnetic field and circumstellar environment of a star with a similar rotation rate and similar magnetic field configuration would appear edge - on . currently , the inclination is poorly constrained , which results in a large possible range for the dipole field strength . however , using the predictions of the rigidly rotating magnetosphere model ( townsend & owocki 2005 ) , we expect to better constrain the geometry of hr5907 based on the variations shown in fig . [ sidebyside ] . kg and @xmath11 ( red ) to the observed lsd stokes @xmath2 ( top ) , diagnostic null ( middle ) and unpolarized stokes @xmath12 profile ( bottom ) of hr5907 ( black ) . * right : * illustration of the magnetic field and circumstellar environment for a star with a rotation rate and magnetic field geometry similar to hr5907 ( image courtesy of r.h.d . townsend).,width=499 ] oksala et al . , 2010 , _ mnras _ , 405 , l510 rivinius et al . , 2010 , _ mnras _ , 405 , l46 townsend , r.h.d . , owocki , s.p . , 2005 , _ apj _ , 630 , l81 townsend , r.h.d . , owocki , s.p . , groote , d. , 2005 , _ apj _ , 630 , l81 townsend , r.h.d . , 2008 , _ mnras _ , 389 , 559" +"galaxy clusters form via mergers of smaller subunits . such mergers dissipate a large fraction of the subclusters vast kinetic energy through gas dynamic shocks , heating the intracluster gas and probably accelerating high energy particles ( e.g. , sarazin 2001 and references therein ) . shocks contain information on the velocity and geometry of the merger . they also provide a unique laboratory for studying the intracluster plasma , including such processes as thermal conduction and electron - ion equilibration ( e.g. , shafranov 1957 ; takizawa 1999 ) . some exploratory uses of x - ray data on cluster shocks were described by markevitch , sarazin , & vikhlinin ( 1999 ) . while many merging clusters exhibit recently heated gas ( e.g. , henry & briel 1995 ; markevitch et al . 1999 , furusho et al . 2001 and references in those works ; neumann et al . 2001 ) , so far only two candidate merger shock fronts were observed . one is a mild x - ray brightness edge , apparently a shock with a mach number near 1 , preceding the prominent `` cold front '' in a3667 ( vikhlinin , markevitch & murray 2001 ) . another is a hot region in front of the a665 core ( markevitch & vikhlinin 2001 , hereafter mv ) which shows no clear density jump perhaps because of an unfavorable viewing geometry . the observation of e presents the first clear example of a cluster bow shock . this @xmath2 cluster was discovered by tucker , tananbaum , & remillard ( 1995 ) as an ipc extended source . from data , tucker et al . ( 1998 , hereafter t98 ) derived a temperature around 17 kev , making this system one of the hottest known ( see also yaqoob 1999 ; liang et al . 2000 , hereafter lhba ) . data showed that e is a merger ( t98 ) . it also hosts the most luminous synchrotron radio halo ( lhba ) . below we present results from the observation of e performed in october 2000 . we use @xmath3 and @xmath4 , @xmath5 ; @xmath6 mpc at the cluster redshift . confidence intervals are 90% for one - parameter , unless specified otherwise . ( 0,14.2)(18.5,24 ) ( -0.1,24.0)=9.4 cm ( 9.2,24.0)=9.4 cm ( 8.2,23.3)a ( 17.6,23.3)b ( -0.1,15.3 ) = 3.5 mm fig . 1.(_a _ ) acis 0.55 kev image . pixels are 4 ; linear scale is for @xmath7 . ( _ b _ ) grayscale shows optical @xmath8-band image from eso ntt ( courtesy of e. falco and m. ramella ) . contours , spaced by a factor of 2 , show the smoothed acis image . the western part of the outer contour is approximately at the shock position . a number of well - matched point sources shows that the coordinates are accurate . e was observed by acis - i at the focal plane temperature of @xmath9c for a useful exposure of 24.3 ks . to derive the gas temperature for a given region of the cluster image , the telescope and detector response were modeled as described in mv . the acis background rate did not vary during the exposure , but was higher than expected by a factor of about 1.3 , most likely due to anomalous `` space weather '' . this required special background modeling . to do this , we extracted a spectrum from the acis - i region outside an @xmath10 ( @xmath11 mpc ) circle centered on the cluster , which should be free of cluster emission . point sources were excluded . the observed excess over the nominal background was well - modeled in the @xmath12 kev band by the sum of two power laws @xmath13 with photon indices @xmath14 and @xmath15 ( dominant below and above @xmath16 kev , respectively ) originating inside the detector , i.e. , without applying mirror effective area and ccd efficiency to the model . such a background anomaly in the acis - i chips is rare and not yet understood . we assumed that this component is distributed uniformly over the detector , and added it ( normalized by solid angle ) to the nominal background spectra . high - energy residuals in the overall cluster fit indicated that the normalization of the corrected background required an additional 10% increase ( perhaps indicating some spatial nonuniformity of the excess ) , which we applied to the spectra from all cluster regions . to make a @xmath17 kev image for the gas density analysis , we compared the observed background rate far from the cluster to the nominal model background ( without the above additional component ) and derived a correction factor of 1.35 for this wide band , which was applied to the model background image . this is of course consistent with the above spectral correction . a 10% background uncertainty was included in deriving the confidence intervals for all quantities . this approximate background modeling is adequate for our present qualitative study . to minimize the effects of calibration uncertainties , the spectra were extracted in the @xmath18 kev energy band , excluding the @xmath19 kev interval around the mirror ir edge . the acis image of the cluster is shown in fig . 1_a_. it shows a `` bullet '' apparently just exiting the cluster core and moving westward . this subcluster was previously seen in the data ( e.g. , t98 ) , but the high resolution image makes its nature and direction of motion clear . the bullet is preceded by an x - ray brightness edge that resembles a bow shock . to determine whether it is indeed a shock ( and not a `` cold front '' , e.g. , markevitch et al . 2000 ; vikhlinin et al . 2001 ) , below we derive the gas temperatures on both sides of the feature ( see [ sec : tmap ] ) . figure 1_b _ shows x - ray contours overlaid on an optical image . a subcluster of galaxies ( e.g. , barrena et al . 2001 ) is seen leading the x - ray bullet , which is apparently swept back from the galaxies by the ram pressure of the ambient cluster gas . we first fit an overall cluster spectrum within @xmath20 ( @xmath21 mpc ) as described in [ sec : analysis ] using the kaastra ( 1992 ) plasma model . we obtain @xmath22 kev and an abundance of @xmath23 solar , fixing the absorption at @xmath24 as derived by lhba from radio and pspc data . this temperature agrees with their + fit of @xmath25 kev and is consistent with the @xmath26 kev fit by t98 . if @xmath27 from dickey & lockman ( 1990 ) is used instead , we obtain @xmath28 kev . when @xmath29 is fit as a free parameter , it is consistent with both those values ; the present low - energy acis - i calibration is not reliable for measuring @xmath29 independently . below we fix @xmath30 . within the @xmath31 mpc aperture , the cluster s 0.55 kev ( rest - frame ) luminosity is @xmath32and @xmath33 . figure 2 shows a temperature map made by dividing the cluster image into several regions and fitting their temperatures and abundances as above . despite large uncertainties , the map shows that the gas outside the shock feature ( region _ p _ ) is cooler , or at least not hotter , than that inside ( region _ s _ ) , confirming that it is indeed a shock front . the temperature at the tip of the bullet is low ( @xmath34 kev ) and is likely to have been the temperature of the subcluster . the hottest region of the cluster is its southeastern x - ray brightness elongation . the optical image shows several large galaxies in that area , suggesting that this is the main merger site . as seen in fig . 3 , this also is where the radio halo is enhanced ( lhba ) . the halo also extends to the western shock front . a spatial correlation between the halo brightness and the local gas temperature ( in addition to the general similarity to the x - ray brightness , e.g. , lhba ; govoni et al . 2001 ) was noticed by mv in two other merging clusters and supports the merger shock origin for the relativistic halo electrons ( e.g. , tribble 1993 ) . the temperature map confirms that the western x - ray brightness edge is a shock front . we can derive its mach number from either the temperature or density jump across the front using the rankine - hugoniot shock adiabat . figure 4_a _ shows an x - ray brightness profile in a 120 sector centered on the bullet s center of curvature and directed along its apparent motion . there are two brightness edges whose shapes indicate spherical gas density discontinuities in projection . we fit this profile by the projection of a gas density model consisting of two power laws @xmath35 centered on the bullet representing the bullet gas and the shock region , respectively . these are immersed in a @xmath36-model centered on the main cluster ( region _ j _ ) representing the outer , undisturbed gas . all components are spherically symmetric around their respective centers ; it is an adequate assumption in the sector of interest . free parameters are the three slopes , two jump amplitudes and two jump radii . a reasonable range of core radii and center positions for the @xmath36-model was explored ( obviously , these can not be restricted by the fit ) and found to have a small effect on our main interesting parameter , the density jump at the shock . its confidence interval includes this modeling uncertainty . the observed temperature difference has a negligible effect on the derived density . ( 0,8.9)(9,24.3 ) ( 0.0,24.0)=8.7 cm ( -0.04,19.7)=8.7 cm ( -0.1,11.3 ) = 3.5mmfig . 2.projected gas temperature map ( colors ) overlaid on the x - ray brightness contours from fig . 1_b_. temperatures for individual regions are shown in lower panel ( region _ b _ is the tip of the bullet , unmarked in the map for clarity . this region appears smaller than the bullet in the contour plot because of smoothing ) . errors in this figure are @xmath37 . the horizontal line shows the cluster average temperature . the best - fit density model is shown in fig . 4_b _ ; it describes the brightness profile in fig . 4_a _ well . the best - fit radial slopes are @xmath38 for the bullet and @xmath39 for the shock region ; @xmath40 assuming a core - radius of @xmath41 kpc . the density jumps by factors of @xmath42 at the bullet edge and @xmath43 at the shock front . figure 4_b _ also shows an approximate pressure profile ( the density model times the temperatures from fig.2 ) . the approximate pressure continuity at the first jump indicates that the bullet boundary is a `` cold front '' , or contact discontinuity , similar to those recently discovered in other clusters . as expected , there is a large pressure increase at the shock front . a density jump of @xmath43 at the shock corresponds to a mach number @xmath44 ( @xmath45 at 90% ) for a @xmath46 gas and a one - dimensional shock ( strictly speaking , the latter approximation applies only along the direction of the motion , but we can use it as a qualitative estimate for our wide sector ) . the observed temperature jump from @xmath47 kev to @xmath48 kev corresponds to @xmath49 (" +"ever since the foundation of modern cosmology based on general relativity , there have been attempts to determine the cosmological parameters of our universe . gravitational lensing has been recognized as one of several such tools . for example , the results of radio surveys for gravitational lenses have recently been used to place significant constraints on cosmological models ( falco et al . it has also been realised that observations of supernovae at high redshift can be used for this purpose ( goobar & perlmutter @xcite ) , in particular for determining the value of the cosmological constant . in fact , several collaborations with this in mind are in progress , and the first sets of data show an intriguing hint of a non - vanishing cosmological constant in a universe consistent with having a flat geometry ( see , e.g. , riess et al . @xcite ; perlmutter et al . although the two groups which have published results mutually agree on the best - fit parameters , it is important to note that the effects of geometry are small ( on the order of half a magnitude ) , and the need to go to even higher redshift to get larger effects is obvious . when observing such distant sources , at redshift greater than unity , it is necessary to estimate the effects of lensing due to inhomogeneities in the matter distribution . this will be of growing importance when supernovae at very high redshifts become accessible , e.g. , with ngst , the next generation space telescope ( miralda - escud & rees @xcite ; dahln & fransson @xcite ) or with the dedicated supernova search satellite , snap ( perlmutter et al . , private communication ) . the literature on gravitational lensing is quite rich . much of the history and developments up to the early 1990s can be found in the excellent textbook by schneider , ehlers & falco ( @xcite ) . a new method for examining lensing effects has recently been proposed by holz & wald ( @xcite ; hw ) , one which has the virtue of lending itself easily to numerical calculations . in that work it is also shown that given a large and deep enough sample of standard candle supernovae , one may in principle distinguish between different matter distributions in the galactic halos responsible for the lensing . in particular the case of point masses gives a quite different distribution of magnifications ( or de - magnifications ) compared to the case of singular isothermal spheres ( see also metcalf & silk @xcite ) . the method of hw can be summarized as follows : first , a friedmann - lematre ( fl ) background geometry is selected . inhomogeneities are accounted for by specifying a matter distribution in cells which have an average energy density equal to that of the underlying fl model . following the history of observed light from a distant source , a light ray is traced backwards to the desired redshift by being sent through a series of cells , each time with a randomly selected impact parameter with respect to the matter distribution in the cell . between each cell , the fl background is used to update the scale factor and the expansion rate . by using monte carlo techniques to trace a large number of such light rays , statistics for the apparent luminosity of an ensemble of sources at a given redshift is obtained . the purpose of this paper is to generalize the method of hw in a number of ways and to investigate some issues related to the different lensing signatures in the luminosity distribution of supernovae caused by different mass distributions of the intervening lens population . the outline is as follows . in sect . [ sec : cosmodel ] it is demonstrated how the hw method can be generalized from matter in dust form to perfect fluids with pressure . [ sec : area ] is concerned with the interpretation of results as probability distributions . [ sec : devi ] presents the geodesic deviation and in sect . [ sec : hwsummary ] , we summarize and discuss some of the conceptual issues in the analysis of hw . in sect . [ sec : nfw ] , we include the possibility of using the more realistic halo matter distribution proposed by navarro et al . ( @xcite ; nfw ) based on their n - body simulation results , and in sect . [ sec : massdist ] we discuss the mass distribution of lensing galaxies . by using realistic density profiles and mass distributions of dark matter halos , we can obtain high accuracy results on gravitational lensing without the need of using the extensive full data sets of n - body simulations , as in some other methods ( wambsganss et al . @xcite ; premadi et al . @xcite ; jain et al . one strength of our ray - tracing monte carlo method is further that it can be continuously refined as more observational information , e.g. , on galaxy distributions is obtained . also , effects such as absorption by dust and other possibly @xmath0-dependent effects can be straightforwardly added to the algorithm . in sect . [ sec : results ] , some results from the generalizations of the method of hw are presented as luminosity distributions . in sect . [ sec : limit ] , we investigate some limitations of the numerical implementation of the method and in sect . [ sec : mi ] , we discuss multiple images . [ sec : cc ] investigates different consistency checks , sect . [ sec : formula ] contains convenient analytical fits to our numerical results and the paper is concluded with a discussion in sect . [ sec : disc ] . the starting point of hw is a newtonianly perturbed fl universe . the line element of robertson - walker form is then @xmath1 where @xmath2 is the scale factor , and @xmath3 is a constant - curvature three - geometry , for which @xmath4 indicates the sign of the curvature . ( we use geometrized units such that @xmath5 ) . the perturbation @xmath6 is assumed to satisfy a number of properties that will be employed when determining dominant terms . firstly , @xmath7 , reflecting that @xmath6 indeed is a perturbation . secondly , inhomogeneities are assumed to be significant , so that @xmath8 is small compared to spatial derivatives . thirdly , second - order spatial derivatives will be assumed to dominate over products of first - order ones ( e.g. , @xmath9 ) . in this paper , we have generalized the treatment of hw so that the matter content of the model can be taken to be a number of perfect fluids : @xmath10 where @xmath11 is the stress - energy tensor , @xmath12 is the energy density , @xmath13 the pressure of fluid @xmath14 , @xmath15 is the ( normalized ) fluid four - velocity , and @xmath16 is the metric corresponding to the line element ( [ eq : line - element ] ) . cosmologically reasonable equations of state are linear barotropic ones : @xmath17 . in this paper , the @xmath18 s are constants with @xmath19 . however , it is straightforward to allow for the equations of state to evolve with redshift , i.e. , @xmath20 . hw considered dust models with a cosmological constant , which corresponds to a two - fluid model , the first fluid having @xmath21 , and the second fluid homogeneously distributed with @xmath22 and @xmath23 . the field equations , corresponding to eqs . ( hw7,8 ) , become + _ the friedmann equation : _ @xmath24 _ the raychaudhuri equation : _ @xmath25 where the definitions of the hubble scalar @xmath26 and deceleration parameter . ] @xmath27 have been made explicit , and where @xmath28 denotes the spatial projection of contracted covariant derivatives . the pressure does not enter the friedmann equation , i.e. , the hubble scalar is entirely given by the energy densities and the curvature . the deceleration , on the other hand , is affected by the presence of pressure . comparing the above field equations with the field equations for the corresponding fl background ( with averaged densities and pressures @xmath29 , @xmath30 ) it can be shown [ eq . ( hw11 ) ] that @xmath6 satisfies a poisson equation @xmath31 , where @xmath32 , while @xmath33 vanishes . thus , the pressures result in homogeneous contributions , and the specification of an equation of state only makes sense in terms of the averaged energy density : @xmath34 . from the field equations for the background model follows + _ the energy conservation equation : _ @xmath35 if the fluids are assumed to couple only to gravity , they will be separately conserved , and each component in the sum of eq . ( [ eq : ec ] ) vanishes . note that it is only for dust ( @xmath36 ) that the mass within a volume co - moving with the hubble flow is constant ( @xmath37 ) . for other types of matter , the mass varies with time because of the work done by the pressure . also note that @xmath38 results in a constant energy density . thus , a homogeneously distributed fluid with @xmath38 is equivalent to a cosmological constant , or in terms of quantum field models , to vacuum energy . it is convenient to introduce density parameters @xmath39 which depend on time and therefore on redshift . assuming the above discussed equations of state the time dependence is governed by the following set of conservation equations ( see , e.g. , goliath & ellis @xcite ) @xmath40\omega_ih .\ ] ] hw proceed by performing a number of coordinate transformations to co - moving coordinates on isotropic form , eq . the inclusion of pressure results in a modification of this line element : @xmath41 dt^2 \nonumber \\ & + & \left[1 - 2\phi\right](dx^2+dy^2+dz^2 ) , \end{aligned}\ ] ] where @xmath42 , and the effective potential @xmath43 satisfies the poisson equation @xmath44 the lookback time of an event at redshift @xmath45 is the time difference ( with respect to the coordinate @xmath46 ) between the event and the present . by using @xmath47 , we get a relation between the lookback time and the redshift for a fl universe : @xmath48 to obtain @xmath49 , the friedmann equation , eq . ( [ eq : fe ] ) , is expressed in terms of redshift and the present densities @xmath50 . to do so , first note that the energy conservation equation , eq . ( [ eq : ec ] ) , together with the equation of state gives @xmath51 the hubble scalar can then be expressed @xmath52 where we introduced the curvature density parameter @xmath53 the luminosity distance to the event at redshift @xmath45 is given by a similar expression ( see , e.g. , bergstrm & goobar @xcite ) @xmath54 note that , when @xmath55 , the present scale factor can be expressed [ using ( [ eq : ook ] ) ] as @xmath56 . consider a narrow ( strictly speaking ; infinitesimal ) ray bundle connecting a source and an observer as depicted in fig . [ fig : focusing ] . the ray bundle can be focused either at the source or the observer . the relevant quantity when determining luminosity distances is the ratio of the area of a beam and the solid angle it subtends . of course , the smaller the distance , the brighter the source . in the method of hw , a beam focused at the observer with infinitesimal @xmath57 is integrated backwards using the" +"the successful operation of lep has allowed a precise measurement of fermion pair production , @xmath1 , at centre of mass energies near the z resonance . the mass and the total and partial widths of the z boson have been determined with excellent accuracy . the standard model@xcite is confirmed with high precision by the experimental results of l3@xcite and other experiments@xcite . in these analyses , the contribution of the interference between the photon and the z boson exchange amplitudes is fixed to the standard model expectation . in this paper , we use an s matrix@xcite approach to determine the contributions of @xmath0/z interference and z boson exchange , thus reducing the number of theoretical assumptions . at centre of mass energies well above the z resonance , the reduced importance of z boson exchange allows the determination , in particular , of @xmath0/z interference with enhanced precision . the running of lep in 1997 and 1998 at energies of 182.7 and 188.7 , together with a tenfold increase of integrated luminosity at high energy compared to our previous s matrix analysis@xcite , improves substantially the sensitivity to the s matrix parameters . similar analyses have been performed by the delphi and opal collaborations@xcite . measurements of cross sections and forward backward asymmetries for the reactions @xmath1 , have been performed with the l3 detector@xcite at centre of mass energies , @xmath2 , in the vicinity of the z resonance@xcite and at 130.0 , 136.1 , 161.3 , 172.3 , 182.7 and 188.7 @xcite . at energies greater than 130 both leptons of the @xmath3 final state are required to be in the range @xmath4 , where @xmath5 is the angle between the incoming electron and the outgoing lepton . muon- and tau pair candidates are selected by the cuts @xmath6 and @xmath7 , respectively , for both final state leptons . hadron events are selected in the full solid angle . in total , 27470 hadron events and 9417 lepton pair events are selected . these correspond to an integrated luminosity of 258.7 pb@xmath8 . for centre of mass energies in the vicinity of the z resonance , the sensitivity to photon exchange and @xmath0/z interference is suppressed due to the large z exchange cross section . therefore , a minimum effective centre of mass energy , @xmath9 , or a maximum acollinearity angle in the bhabha channel , are required to select events without substantial energy loss due to initial state radiation . the remaining event samples at @xmath10 contain , in total , 7785 hadron and 7704 lepton pair events . the details of the analyses such as selection procedures , efficiencies , background contributions , measured cross sections and forward backward asymmetries , together with the statistical and systematic uncertainties , are discussed in references , , and . standard model expectations are calculated using the zfitter@xcite and topaz0@xcite programs with the following values@xcite for the z boson mass , , the top quark mass , , the higgs boson mass , , the electromagnetic coupling constant , @xmath11 , and the strong coupling constant @xmath12 : @xmath13 the results of our analysis are not sensitive to the uncertainties on these parameters . at energies above the z resonance , the theoretical uncertainties on the predicted cross sections are estimated to be 0.5%@xcite except for the predictions for large angle bhabha scattering which have a larger uncertainty of 2%@xcite . uncertainties on the forward backward asymmetries are smaller and negligible compared to the statistical uncertainties of the measurements . the theoretical uncertainties are propagated into the systematic uncertainty on our results . the measurements of cross sections and forward backward asymmetries are analysed in the framework of the s matrix ansatz . the programs smatasy@xcite , together with zfitter and topaz0 , are used for the calculation of the theoretical predictions and qed radiative corrections to the cross sections and forward backward asymmetries . the lowest order total cross section , @xmath14 , and forward backward asymmetry , @xmath15 , + for @xmath16@xcite are : @xmath17 , \qquad\mathrm{where}~a=\mathrm{tot , fb } , \nonumber\\ a^0_{\mathrm{fb}}(s ) & = & \frac{3}{4 } \frac{\sigma^0_{\mathrm{fb}}(s)}{\sigma^0_{\mathrm{tot}}(s ) } , \qquad\mathrm{with}~\sigma^0_{\mathrm{fb}}=\frac{4}{3}\left(\sigma_\mathrm{f}-\sigma_\mathrm{b}\right).\end{aligned}\ ] ] the s matrix ansatz defines the z resonance using a breit wigner denominator with an @xmath18independent width . in other approaches , a breit wigner denominator with an @xmath18dependent width is used , which implies the following transformation of the values of the z boson mass and width@xcite : @xmath19 and @xmath20 . in the following , the fit results are quoted after applying these transformations . the s matrix parameters @xmath21 , @xmath22 and @xmath23 give the z exchange , @xmath0/z interference and photon exchange contributions for fermions of type @xmath24 , respectively . for hadronic final states the parameters @xmath25 , @xmath26 and @xmath27 are sums over all produced quark flavours . in figure [ fig : ha_xsec ] the measured hadronic cross sections are compared to the theory predictions for different values of @xmath26 . the s matrix parameters are determined in a @xmath28 fit to our published measurements@xcite at centre of mass energies of 130 to 189 , using our results of s matrix fits to the z peak data@xcite as constraints . as a cross check , a fit to all cross section and asymmetry measurements is performed , which gives identical results . correlations between measurements taken close to the z resonance and measurements at high centre of mass energies are estimated and their influence on the fit results is found to be negligible . correlations between different measurements at high centre of mass energy are taken into account in the fits . the photon exchange contributions , @xmath23 , are fixed in the fits to their qed predictions . the fit results do not depend on the uncertainty on @xmath29 . the fitted s matrix parameters for electrons , muons , taus and hadrons , and their correlations , are listed in tables [ tab : smat_pars ] , [ tab : smat_corr8 ] and [ tab : smat_corr16 ] . the fits are performed with and without the assumption of lepton universality . the parameters obtained for the individual lepton types are compatible with each other and support this assumption . a large correlation is observed between the mass of the z boson and the hadronic @xmath0/z interference term , @xmath26 . this correlation causes an increase in the uncertainty on @xmath30 with respect to fits where the hadronic @xmath0/z interference term is fixed to its standard model prediction . the value of this correlation is reduced from -0.95 when using z peak data alone@xcite to -0.57 . under the assumption of lepton universality the fitted hadronic @xmath0/z interference term is : @xmath31 this value agrees with the standard model prediction of 0.21 and improves significantly the precision of our previous s matrix analyses@xcite . the theoretical uncertainty is due to the uncertainty of 0.5% on the calculation of cross sections for @xmath32 130 of the zfitter program . for the leptonic @xmath0/z interference terms we obtain similar improvements . the fitted value for is : @xmath33 the contribution to the uncertainty due to the @xmath0/z interference is separated from the rest of the experimental uncertainty . it is reduced significantly with respect to our previous results@xcite . again , the theoretical uncertainty is due to the limited precision of the cross section calculations with the zfitter program . figure [ fig : mz_jhad ] shows the 68% confidence level contours in the ( @xmath30 , @xmath26 ) plane for the data taken at the z pole and after including the 130189 measurements . the improvement resulting from the inclusion of the high energy measurements is clearly visible . our measurement of the hadronic interference term agrees with results from data taken at energies below the z resonance@xcite . adding these low energy measurements to the fits , we obtain : @xmath34 with a correlation coefficient of -0.40 between these quantities . in summary , we use the s matrix framework to analyse data taken at the z resonance and at higher centre of mass energies . our measurements provide an improved determination of the @xmath0/z interference terms and the z boson mass . all parameters show good agreement with the standard model predictions . we wish to express our gratitude to the cern accelerator divisions for the excellent performance of the lep machine . we acknowledge the contributions of the engineers and technicians who have participated in the construction and maintenance of this experiment . glashow , nucl . * 22 * ( 1961 ) 579 ; s. weinberg , phys . * 19 * ( 1967 ) 1264 ; a. salam , `` elementary particle theory '' , ed . n. svartholm , ( almqvist and wiksell , stockholm , 1968 ) , 367 m. veltman , nucl . phys . * b 7 * ( 1968 ) 637 ; g.m . t hooft , nucl . * b 35 * ( 1971 ) 167 ; g.m . t hooft and m. veltman , nucl . phys . * b 44 * ( 1972 ) 189 ; nucl . phys . * b 50 * ( 1972 ) 318 l3 collab . , m. acciarri , measurements of cross sections and forward - backward asymmetries at the z resonance and determination of electroweak parameters , preprint cern - ep/2000 - 022 , cern , 2000 , accepted by e. phys . j. c aleph collab . , r. barate , e. phys . j. * c 14 * ( 2000 ) 1 delphi collab . , p. abreu , cross - sections and leptonic forward - backward asymmetries from the z@xmath35 running of lep , preprint cern - ep-2000 - 037 , cern , 2000 , accepted by e. phys . j. c opal collab . , r. akers , z. phys . * c 61 * ( 1994 ) 19 sld collab . , k. abe , phys . * 73 * ( 1994 ) 25 ; sld collab . , k. abe , phys . rev . lett . * 78 * ( 1997 ) 2075 sld collab . , k. abe , phys . * 79 * ( 1997 ) 804 a. leike , t. riemann and j. rose , ( 1991 ) 513 ; + t. riemann , ( 1992 ) 451 l3 collab . , m. acciarri , phys . lett . * b 407 * ( 1997 ) 361 delphi collab . , p. abreu , e. phys . j. * c 11 * ( 1999 ) 383 opal collab . , k. ackerstaff , e. phys . j. * c 2 * ( 1998 ) 441 l3 collab . , b. adeva , nucl . . meth . * a 289 * ( 1990 ) 35 ; m. acciarri , nucl . meth . * a 351 * ( 1994 ) 300 ; m. chemarin , nucl . inst . meth . * a 349 * ( 1994 ) 345 ; a. adam , nucl . . meth . * a 383 * ( 1996 ) 342 ; g. basti , nucl . inst . meth . * a 374 * ( 1996 ) 293 ; i.c . brock , nucl . a 381 * ( 1996 ) 236 l3 collab . , m. acciarri , phys . * b 370 * ( 1996 ) 195 l3 collab . , m. acciarri , phys . lett . * b 479 * ( 2000 ) 101 zfitter version 6.21 is used . + d. bardin , preprint hep - ph/9908433 ; ( 1989 ) 493 ; ( 1991 ) 1 ; ( 1991 ) 290 . for the comparison with our measurements , the following zfitter flags have been changed from their default values : ` finr ` @xmath36 ," +"since the fulde - ferrell - larkin - ovchinnikov ( fflo ) superconducting / superfluid phase , which is a condensate of cooper pairs with finite center of mass momentum and the spatially modulated order parameter @xcite , was proposed in the 1960s , the theoretical and experimental studies have been conducted in a variety of areas , ranging from heavy fermions @xcite , dense quark matter @xcite , ultracold atomic gases @xcite , and so forth . this unconventional pairing state can be realized by pairing the particles on different fermi surfaces that are mismatched in spin - polarized systems @xcite , as well as by pairing the particles on a single fermi surface that is deformed by breaking the spatial inversion symmetry @xcite . however , the region occupied by the fflo phase in the @xmath1 phase diagram of ultracold fermions is typically small in 2 and 3 dimensions and becomes diminished with increasing temperature @xcite . in the 1d ultracold atomic fermi gas with spin imbalance , on the other hand , the fflo phase occupies a much larger portion of the phase diagram @xcite , although both the fflo phase ( with spin imbalance ) and the conventional bardeen - cooper - schrieffer ( bcs ) superfluid phase ( with equal number of up and down spins ) are only power law ordered in 1d even at @xmath1 . starting from the bethe ansatz equations @xcite , one finds that the 1d polarized fermi gas can host an unpolarized uniform superfluid phase , an fflo superfluid phase , a fully - polarized normal phase , and the vacuum . although in 1d the fflo phase occupies a large region of the @xmath1 phase diagram , the study of 1d system in the frame of mean - field theory is problematic . this is because the pair fluctuations become significant with the reduced dimensionality and true long - range order in 1d is completely destroyed by the mermin - wagner theorem but has only power - law correlations in the thermodynamic limit @xcite . also , experimental investigations of the superfluid phases are hard since the transition temperature @xmath2 of the 1d superfluid is zero . in order to overcome these technical difficulties peculiar to pure 1d systems , the two - dimensional array of 1d atomic `` tubes '' @xcite has been proposed as a model of quasi-1d fermi gas , where atoms are allowed to move freely in one direction and tightly confined in the transverse motion @xcite . in this weakly coupled 1d system the atomic motion is gas - like in the axial direction but the weak coupling in the transverse lattice plane stabilizes the long - range superfluid order . the stabilization of the long - range order allows the use of mean field theory while the anisotropy between the couplings in the axial direction and the transverse plane still reveals the behavior specific to 1d . in this model , the mean - field study shows that the parameter space of the fflo superfluid phase is enhanced in a spin - polarized quasi-1d fermi gas as the confinement of the atomic motion in the transverse directions is enhanced ( that is , as the system becomes more and more 1d - like ) . in addition , this model allows one to investigate the behavior of the system during the crossover from the 3d to 1d regimes by increasing the optical lattice strength that controls the transverse hopping between the tubes . the presence of spin - orbit coupling ( soc ) and external zeeman fields in otherwise uniform @xmath0-wave superfluids / superconductors is another topic of great current interest . these effects in combination with long - ranged superfluid order can produce interesting phases such as non - centrosymmetric superconductors @xcite and nonuniform superfluids in ultracold systems @xcite . in addition to these rich quantum phases , the combination of soc and a suitably directed zeeman field allows one to take a further step towards novel quantum states , the topological superconducting / superfluid phases @xcite . in solid state systems , spin - orbit coupled semiconducting thin films and nanowires with proximity induced @xmath0-wave superconductivity and a zeeman field can host novel non - abelian topological states with the order parameter defects such as the vortex cores and the sample edges supporting localized topological zero - energy excitations called majorana fermions @xcite . since the soc and zeeman field in @xmath0-wave superfluids induce topological superfluid phases in 1d with majorana fermion end states , while at the same time the crossover from 3d to quasi-1d in the presence of a zeeman field enhances the stability of the fflo phase , it is a natural question to ask what is the precise behavior of the system as it crosses over from 3d to 1d but in the presence of both spin - orbit coupling and a zeeman field . in particular , we ask which of the two phases between the ( a ) topological uniform superfluid ( that contains the majorana fermion end states and an otherwise gapped spectrum ) and ( b ) the fflo non - uniform superfluid ( that contains non - zero center of mass momentum cooper pairs and may be gapless ) is preferred as the system crosses over from 3d to quasi-1d in the presence of both zeeman field and soc . in this paper we address this question by calculating the @xmath1 phase diagram of a set of parallel 1d `` tubes '' arranged in a 2d lattice in the presence of a zeeman field and an additional rashba type spin - orbit coupling . in this paper , we consider the mean - field theory of the above quasi-1d fermi gas under the effective zeeman field together with synthetic spin - orbit coupling , and show that the @xmath1 phase diagram can host both the uniform superfluid state with zero center of mass momentum cooper pairs , the uniform topological superfluid with majorana fermions edge states , and a fflo state with non - zero center of mass momentum cooper pairs . most importantly , we find that the uniform topological superfluid and the fflo state occur in distinctly different regimes of the ( zeeman field - soc ) phase diagram ( see fig . [ fig-1 ] ) ) . from the uniform ( non - topological ) superfluid state the fflo state is the leading instability at high enough zeeman fields but only for small values of the spin - orbit coupling . for larger values of the soc , the fflo phase disappears from the phase diagram and the uniform non - topological superfluid state transitions into a uniform _ topological _ superfluid state for high values of the zeeman field . this result will be experimentally very useful because it clearly separates the two interesting unconventional superfluid phases topological superfluid and fflo into distinct regimes of the phase diagram as the system crosses over from 3d to 1d with the tuning of the transverse lattice . the emergence of the fflo phase with the zeeman field for small values of the spin - orbit coupling is easily understood from the fact that the dominant instability of the system as it crosses over to 1d in the presence of a zeeman field ( but no soc ) is to the fflo phase . for small soc this instability persists and the system moves into the fflo phase beyond a critical value of the zeeman field via a first order phase transition . the soc disfavors the fflo phase , however , since it creates a mixing of the spins in the same band , thus increasing the tendency of the system to create spin - singlet @xmath0-wave pairs from the same band ( note that , for symmetric fermi surfaces , the fflo phase is a result of pairing between electrons from the different spin - split bands ) . with increasing values of the soc the system transitions from the fflo phase to the uniform superfluid phase ( in fig . [ fig-1 ] moving horizontally for a high enough zeeman field ) finally entering into the topological superfluid phase with majorana fermions at a second order topological quantum phase transition ( tqpt ) . we find that the fflo phases are gapless ( see fig . [ fig-2](a ) ) , while the uniform topological superfluid phase is gapped ( see fig . [ fig-2](b ) ) in the bulk but with zero energy majorana fermion excitations at the ends of the 1d tubes . in addition to these interesting phases , within the fflo phase itself we find a topologically distinct fflo phase ( indicated as fflo-2 in fig . 1 ) setting in at higher values of the zeeman field . this new fflo phase is characterized by a non - trivial value of a certain relevant topological invariant known as pfaffian invariant for 1d systems that usually signals , in the presence of a gapped spectrum , the emergence of a topological phase with majorana fermion edge states . in contrast to the uniform topological superfluid state ( shown as uts in fig . 1 ) with majorana fermions end states , however , we find that the spectrum in both topologically distinct fflo phases ( fflo-1 and fflo-2 ) is gapless . a full characterization of these topologically distinct fflo states is beyond the scope of the present paper and will be taken up in a future publication . the system we consider in this paper is an array of quasi-1d fermi gas with two hyperfine states , @xmath3 , @xmath4 , confined by a wide trapping potential @xmath5 . to create the two - dimensional lattice of 1d tubes , we include optical lattice potential , @xmath6 $ ] , with lattice spacing @xmath7 and depth @xmath8 . the latter breaks the 3d cloud apart into an array of parallel tubes aligned along one direction . we choose the axis of a tube as @xmath9 direction . this model of two - dimensional array of 1d tubes has been studied for the fflo superfluid phases in the quasi-1d spin - polarized fermi gas . with sufficiently low density and strong enough @xmath10 , the particle motion along the tubes ( @xmath9 direction ) is well described by a parabolic dispersion with a single - band tight - binding dispersion for the @xmath11 motion @xcite . in this paper , we will ignore the trapping potential @xmath12 and discuss the spatially homogeneous quasi-1d system to simplify the analysis . the spatial dependence of the physical quantities in a smooth trapping potential can be obtained by the local density approximation ( lda ) by replacing the chemical potential of each spin state @xmath13 , while the difference of the chemical potential @xmath14 to be held spatially constant . without the trapping potential @xmath12 , we consider the two - dimensional optical lattice with constant lattice depth @xmath15 comprised of @xmath16 tubes , each of which has length @xmath17 along the @xmath9 direction . within this model , we include the rashba type of spin - orbit coupling along the @xmath9 direction @xmath18 and the zeeman splitting @xmath19 , where @xmath20 and @xmath21 are the pauli matrices . then , we write the single particle hamiltonian of spin - orbit coupled quasi-1d fermi gas as h_0 = _ , s , s^ c_s^c_s^ , where @xmath22.$ ] here , @xmath23 is the transverse hopping between the nearest neighbor tubes , and @xmath24 is the atomic mass with letting @xmath25 . @xmath26 and @xmath27 are the spin - orbit coupling and zeeman splitting strength , respectively . @xmath28 is unconstrained in the thermodynamic limit , while @xmath29 and @xmath30 is in the brillouin zone : @xmath31 and @xmath32 . thus , @xmath33 describes the single" +"massive multiple - input multiple - output ( mimo ) ( also known as large - scale mimo ) is considered as one of the most promising technologies for next generation wireless communication systems @xcite , since it can provide very high spectral and energy efficiencies . besides , for massive mimo systems , the effects of small - scale fading and interference can be significantly reduced with linear signal processing , such as maximal - ratio transmission ( mrt ) and zero - forcing ( zf ) @xcite . the performance of massive mimo single / multi - cell downlink systems has been widely studied in the literature . in @xcite , the asymptotic signal - to - interference - plus - noise - ratio ( sinr ) for linear precoding in single - cell _ frequency - division - duplex _ ( fdd ) systems was derived based on which the optimization of the user number was investigated . in @xcite , the power scaling , i.e. , how fast the transmission power can decrease with the antenna number while maintaining a certain sinr level , for multi - cell _ time - division - duplex _ ( tdd ) systems was given based on asymptotic sinr analysis , where the pilot contamination was shown to be the only performance limit . in @xcite , capacity lower bounds and energy efficiency of mrt and zf in single - cell tdd systems were studied and compared with each other . in the parallel field of uplink systems , similar results were derived in @xcite , @xcite . these works mainly focus on the derivations of asymptotically deterministic expression for the sinr , and the performance analysis only consider some special cases , e.g. , the constant or linearly increasing user number with respect to the base station ( bs ) antenna number , the power scaling for perfect or imperfect channel state information ( csi ) with equal training and transmission power and constant user number . recently , along this route , the performance improvement for using coherent detection based on the dedicated downlink channel estimation was shown in @xcite , especially for large but finite antenna numbers . meanwhile , the impact of other practical factors such as channel aging @xcite , hardware limits @xcite , and rician fading @xcite on the performance of massive mimo systems was studied . however , a comprehensive scaling law analysis for multi - cell multi - user massive mimo is still missing in existing works . another important problem in the performance analysis of massive mimo is when the derived asymptotic results are applicable in practical systems . while many works derived deterministic sinr approximations via calculating the expected value of the sinr or its compenents , the analysis on whether the instantaneous sinr becomes asymptotically deterministic and converges to the derived expressions is sometimes missing . in @xcite , this problem was studied through the so called massive mimo efficiency for the ideal situation that the noise , channel estimation error , and interference are negligible compared with pilot contamination , where the dependence of the massive mimo efficiency on the ratio of spatial degrees of freedom / antenna number to the user number and the product of antenna number and transmit power was shown by simulations . in @xcite , via simulations , the convergence speed of the strong law of large numbers with respect to the antenna number and the convergence of the sinr of mrt and zf to their expected values were both analyzed for fixed ratio of antenna number to user number . it was shown that the sinr of mrt has slower convergence than that of zf , while the explicit relationship between the convergence speed and important parameters , i.e. , antenna number , user number , transmit power , and channel training energy ( csi quality ) , is missing . in this work , by drawing lessons from the analyzing method and the mean square convergence definition in @xcite , we provide a comprehensive performance scaling law analysis for multi - cell multi - user tdd massive mimo downlink systems with channel spatial correlation , csi error , and pilot contamination and investigate the applicability of the derived asymptotic scaling law in practical systems with large but finite antenna numbers . extensive simulations are also conducted to validate the analytical results . our main new contributions are summarized as follows . * we consider a multi - cell multi - user massive mimo network with correlated channel model , csi error , and pilot contamination . in dealing with pilot contamination , recent advancements in pilot contamination elimination ( pce ) @xcite is also considered , while in existing works it is treated as a constant bottleneck of massive mimo . an approximate model for the pce effect is proposed . * a lower bound on the system sum - rate is derived based on which a general performance scaling law is obtained . the result reveals the effect and joint interaction of extensive network parameters , i.e , the channel training energy , the transmission power , and the user number . in the scaling - law analysis , a general model is used where the parameters have continuous scaling exponents with respect to the number of bs antennas , while in most existing work , only a few discrete values for the power scaling exponent , e.g. , @xmath0 ; @xmath1 ; @xmath2 , are allowed . * to understand the applicability of the derived scaling law in practical systems with large but finite antenna number , the effect of antenna number on its accuracy is analyzed and evaluated by simulations . * we conduct quantitative analysis on the asymptotically deterministic property of random instantaneous sinr using the mean square convergence . sufficient conditions for the instantaneous sinr to be asymptotically deterministic are given , from which the tradeoff among different parameter scales is discovered . in @xcite , the performance scaling law for multi - user massive mimo relay networks was extensively studied . while our work adopts the mean square convergence idea and the sinr analysis method from @xcite , it is fundamentally different in both network model and channel model . we consider the multi - cell multi - user massive mimo downlink networks with a general spatially correlated channel model . furthermore , as crucial issues for multi - cell systems , the pilot contamination and pce are taken into account in our work . as a result , the corresponding derivation procedures and analytical results are significantly different . in addition , the analysis on the effectiveness of the derived scaling law for practically large but finite antenna numbers is completely new . the remaining of the paper is organized as follows . in section ii , the channel model and system model including both the multi - cell channel estimation with pilot contamination and the downlink transmission with mrt are introduced . section iii shows the performance scaling law result , discussions on typical network scenarios , and the analysis on the applicability to practical systems with large but finite antenna numbers . in section iv , sufficient conditions for the sinr to be asymptotically deterministic are derived . section v shows simulations and conclusions are provided in section vi . in this paper , bold upper case letters and bold lower case letters are used to denote matrices and vectors , respectively . for a matrix @xmath3 , its conjugate transpose , transpose , and trace are denoted by @xmath4 , @xmath5 and @xmath6 , respectively . @xmath7 and @xmath8 are the mean and variance operators . @xmath9 means equivalence in probabilistic distribution . the notation @xmath10 means that when @xmath11 , @xmath12 and @xmath13 have the same scaling with respect to @xmath14 , in other words , for large @xmath14 , there exists positive constants @xmath15 and @xmath16 , such that @xmath17 . consider a multi - cell multi - user massive mimo network consisting of @xmath18 cells with one @xmath14-antennas bs and @xmath19 scheduled single - antenna users in each cell . the bss and users are assumed to operate a tdd protocol with universal frequency reuse . the uplink spatially correlated channel from user @xmath20 in cell @xmath21 to the antennas of bs @xmath22 in cell @xmath22 can be written as @xmath23 where @xmath24 is the channel correlation matrix and @xmath25 is the independent fast - fading channel vector . the following assumptions on @xmath24 are made by taking into consideration the pilot contamination , pce , and tractability analysis . the set @xmath26 denotes the index set of all cells having pilot contamination to cell @xmath22 while @xmath27 denotes the index set of remaining cells whose pilot contamination is eliminated . we assume that for all @xmath28 and @xmath29 , @xmath30 where the channel direction matrix @xmath31 is an @xmath32 unitary matrix and @xmath33 with @xmath34 $ ] indicates the channel correlation level . for example , elements of the channel vector become independent and identically distributed ( i.i.d . ) when @xmath35 . also , @xmath36 is the pass - loss fading factor where @xmath37 and @xmath38 . the parameter @xmath39 denotes the large - scale fading between different cells and the intra - cell one is normalized to @xmath1 . for @xmath40 , the pilot contamination from cell @xmath21 to cell @xmath22 is eliminated by using the spatial information in channel correlation matrix . thus we have @xmath41 this channel model considers both the channel correlation and the inter - cell pass - loss fading . it is similar to the one used in ( * ? ? ? * section iii ) where motivations and justifications for this model can be referred to . new feature of the modeling in and is that the possible effect of pce , i.e. , the bss schedule users with relatively less pilot contamination for channel training and transmission , can be embodied . in @xcite , several efficient methods by exploiting the statistical channel information have been proposed to alleviate the pilot contamination due to the pilot reuse among @xmath42 cells @xcite , @xcite . generally speaking , the overlap among users channel directions can be in any degree leading to different pilot contamination level @xcite . for explicit analytical results , in , we assume that channels from both users in cell @xmath22 and users in other cells with pilot contamination to cell @xmath22 have the same @xmath3 matrix , while in other cells , pilot contamination is eliminated by having the orthogonal channel directions as shown in . this is a discretization approximation to show the average effect of pce and the extension to the case of more general channel direction distribution is left for future research . in the uplink training phase , users in cell @xmath21 transmit mutually orthogonal pilot sequences which are reused by users in other cells . denote the length of the pilot sequence as @xmath43 ( @xmath44 for reliable performance @xcite ) . assume that all @xmath19 users in each cell use the same training power @xmath45 . define @xmath46 which is the channel training energy . by correlating the received training signals with the pilot sequence of user @xmath47 , bs @xmath21 has the observation @xmath48 as @xmath49 where @xmath50 is the local noise . with the minimum - mean - squared - error ( mmse ) estimation @xcite , the estimate @xmath51 is given as @xmath52 we assume that all the @xmath42 cells have the same pilot contamination level , i.e. , @xmath53 $ ] for all @xmath21 . by defining @xmath54 and utilizing , , we have @xmath55 , for @xmath56 where @xmath57 from , it can be shown that @xmath58 this will be utilized to simplify the derivations in later parts . define @xmath59 , which" +"the tunability in size , shape , and electron number of semiconductor quantum dots ( qd ) provides numerous technological applications as well as interesting many - electron physics . @xcite in actual qd devices , the effects induced by impurities or donor scattering centers may be remarkable . in most cases , irregularities in samples have only an indirect influence on the many - body structure , complicating the identification of the origin behind the peculiar behavior in the measured characteristics of qd s . a clean quantum dot typically shows single - electron energy levels reminiscent of the well - known fock - darwin ( fd ) energy spectrum corresponding to a parabolic confining potential . @xcite adding external impurities into the qd breaks the circular symmetry of the system , leading to avoided crossings and liftings of the degeneracies in the single - electron energy spectrum . this was demonstrated by halonen _ et al . _ , @xcite who studied theoretically qd s distorted by repulsive gaussian scattering centers . however , even if clear traces of the fd spectrum have been obtained experimentally in both lateral @xcite and vertical @xcite quantum dots , there is , to the best of our knowledge , no direct experimental evidence of repulsive impurities present in qd structures . instead , states bound to hydrogenic impurities , probably arising from si dopant atoms in the gaas quantum well , were found already by ashoori and co - workers @xcite in their pioneering single - electron tunneling experiment . these impurities have been suggested to be sources of pair - tunneling states , theoretically analyzed with a superimposed attractive @xmath0-type potential . @xcite theoretically , the distortion of the circular symmetry makes the many - electron problem particularly complex to solve , especially in the presence of an external magnetic field . in the above - mentioned study , halonen _ et al . _ @xcite applied exact diagonalization up to three electrons and focused on the effects of impurities on the energy levels and optical absorption spectra . recently , gl and co - workers @xcite performed diffusion quantum monte carlo ( dmc ) calculations on qd s distorted by randomly distributed gaussian scatterers and studied the energetics up to ten electrons . they found that in these systems the transitions between the many - body states are considerably less pronounced than in clean dots . hirose and wingreen @xcite have used the spin - density - functional theory ( sdft ) to examine the energies and spin states in disordered qd s as a function of the interaction strength in zero magnetic field . besides additional scatterers , non - circular qd s have attracted general interest in connection with the chaotic properties @xcite or the behavior in the high magnetic field limit . @xcite in this paper we present a measured single - electron transport spectrum where avoided crossings and lifted degeneracies are clearly observable . we reproduce the spectrum with an appropriate model potential , showing that the unexpected effects in the spectrum result from a negatively charged coulombic impurity located near the qd . the many - electron properties studied by the sdft reflect the strongly distorted single - electron spectrum . the variation of the impurity location shows the stability of the maximum - density droplet ( mdd ) and the screening of the impurity by electrons . the outline of this paper is as follows . in sec . [ sec1 ] we briefly describe the fabrication of the sample and report the transport measurement . in sec . [ sec2 ] the theoretical model describing the physical system is given and the single - electron calculations are compared to the experiment . in sec . [ sec4 ] the many - electron properties , i.e. , chemical potentials , mdd stability , and total magnetization are studied with the sdft . the paper is summarized in sec . the heterostructure consists of a 10 nm wide gaas quantum well sandwiched between two al@xmath1ga@xmath2as - tunneling barriers of @xmath3 and @xmath4 nm , see fig . [ sample ] . the contacts are formed by @xmath5 @xmath6 m thick gaas layers highly doped with si up to @xmath7 @xmath8 and separated from the active region by 7 nm thin spacer layers of undoped gaas . our sample was defined as a mesa of 40 @xmath6 m size . we carried out direct - current measurements of the current - voltage ( i - v ) characteristics in a he@xmath9-refrigerator at 350 mk base temperature in magnetic fields up to @xmath10 t. figure [ exp_spectrum ] t.,width=321 ] shows the resulting transport spectrum of a quantum dot formed in a local potential minimum . the black lines @xmath11 correspond to high differential conductance @xmath12 . they trace the position of the single - electron energy states @xmath13 of the spectrum according to a relation @xmath14 where the energy - voltage conversion factor @xmath15 equals 0.4 , determined from measurements of the broadening of the step edge with temperature , and the onset voltage is fitted to be @xmath16 mv . the energy levels @xmath11 in the transport spectrum can be interpreted as single - particle levels of a local , presumably a grown - induced potential minimum in the gaas quantum well of our device . the lowest fd band is clearly visible , and one can also observe higher excited states . in contrast to ordinary fd energy levels , we are able to observe broken energy degeneracies at @xmath17 t and strong anticrossing effects in the spectrum . we expect the quantum well confined in the gaas layer to have a negligible degree of freedom for electrons in the vertical direction . our model system is thus strictly two - dimensional and defined to be located on the @xmath18 plane . the single - electron hamiltonian is written as @xmath19 ^ 2 + v_{\rm conf}({\mathbf r})+v_{\rm imp}({\mathbf r}),\ ] ] where we use the effective - mass approximation with @xmath20 , which is the typical value for electrons moving in gaas . in a symmetric gauge the vector potential reads as @xmath21 , giving the external magnetic field @xmath22 perpendicular to the qd plane . the zeeman energy is omitted in eq . ( [ hami1 ] ) since the spin splitting @xcite is not visible in the energy levels shown in fig . [ exp_spectrum ] for the magnetic fields applied . the confining potential @xmath23 is expected to be parabolic near the center of the dot . however , we soften the edges of the dot by changing the sign of the paraboloid at a certain cusp radius @xmath24 , giving @xmath25 , & r > r_c , \end{array } \right.\ ] ] where the parameter @xmath26 defines the strength of the rounding term . as shown below , the softening of the confinement is crucial in obtaining a good agreement with the experimental energy spectrum . we expect the impurity to be described by a negatively charged particle located in the vicinity of the quantum well . the impurity potential can thus be written in a coulombic form as @xmath27 where @xmath28 is the ( negative ) charge of the impurity particle , @xmath29 describes the `` dielectricity '' between the impurity and the electrons in the qd , and @xmath30 and @xmath31 are the lateral and vertical distances of the impurity from the qd center , respectively . figure [ vex ] shows the total external confinement of the model system , @xmath32 , and a sketch of the expected configuration . to calculate the single - electron spectrum , we solve the discretized eigenvalue problem @xmath33 ( @xmath34 ) numerically on a 2d point grid using a rayleigh quotient multigrid method . @xcite figure [ spectra ] shows the ) of a gaas / algaas qd and the calculated single - electron energies ( dashed lines ) corresponding to the model potential shown in fig . [ vex](a).,width=302 ] resulting spectrum ( dashed lines ) compared to the experimental data ( repeated from fig . [ exp_spectrum ] ) . the energies are converted to voltages according to eq . ( [ conv ] ) , and the model parameters are adjusted ( see the discussion below ) until the agreement between the experiment and the model is as good as possible . the simulation places the avoided crossings between the energy levels very close to the correct positions . there are still considerable deviations in the 5th and 6th levels but , for example , the 7th level agrees almost perfectly through the magnetic - field regime presented . the differences at high fields between the experimental data and the simulation result from the shift of the chemical potential of the emitter to higher energies with increasing magnetic field . in calculating the energy spectrum shown in fig . [ spectra ] , we optimize the potential parameters corresponding to the best possible fit to the experimental data . the confinement is then defined by @xmath35 mev , @xmath36 nm , and @xmath37 , and the impurity parameters are given by @xmath38 , @xmath39 nm , and @xmath40 nm . there is naturally some uncertainty in the parameters . however , for this particular sample we find the following characteristic features in the model potential : ( i ) the @xmath29-reduced impurity charge is so large that it indicates a multiple charged particle distorting the qd . ( ii ) the impurity is located very close to the qd plane , probably lying in the 10 nm thick gaas layer ( see fig . [ sample ] ) . ( iii ) the confining potential is approximately three times larger than the values typically used ( @xmath41 mev ) for modeling parabolic qd s . this is due to the grown - induced formation of the qd in the absence of gates around the sample . ( iv ) for the same reason , the confinement becomes softer toward the edges of the dot . hence , the rounding at @xmath42 in @xmath43 is required to compress the highest states in agreement with the experimental spectrum . to clarify the sensitivity of the single - electron spectrum on the shape of the model potential , we compare in fig . [ single ] the eigenenergies given by the chosen model ( thick lines ) to those of a model qd without the rounded edges ( thin lines ) and to those of a corresponding clean model dot without @xmath44 but with the rounding term ( dashed lines ) . the level repulsion is clearly induced by the coulombic impurity that breaks the circular symmetry of the qd and mixes the fd levels of different orbital quantum numbers . a statistical analysis of the energy - level spacings would enlighten the quantum chaotic properties @xcite of the system but it is not included in this study . in the high - field limit , however , the system becomes integrable and the eigenstates condense into landau levels . the rounding term in @xmath43 has the strongest influence on the levels with the highest angular momenta , and the cusp at @xmath24 induces also a weak decoupling of the degeneracies at @xmath17 t. we remark that the eigenenergies for the clean case are lifted in fig . [ single ] by @xmath10 mev for clarity . the coulombic impurity in the vicinity of the qd thus has a strong effect on the eigenenergies . this tendency is also apparent in the many - electron properties studied below . next we study situations that the quantum dot described by the best fitting parameters above contains up to six interacting electrons . even if the many - electron case has not yet been experimentally realized for this particular qd ," +"one of the most remarkable observational results in the last three decades in cosmology is the lack of the gunn peterson trough in the spectra of high redshift quasars and galaxies . this finding implies that the intergalactic medium ( igm ) is highly ionized at least out to @xmath5 , the redshift of the most distant known quasars and galaxies ly@xmath6 emission lines , implying @xmath7 ( see discussion below ) . ] . since the primeval plasma recombined at @xmath8 , its subsequent ionization requires some form of energy injection into the igm , naturally attributable to astrophysical sources . the two most popular examples of such sources are an early generation of stars , residing in sub galactic size clusters ( hereafter `` mini galaxies '' ) , or accreting massive ( @xmath9 ) black holes in small ( @xmath10 ) halos ( hereafter `` mini quasars '' ) . reionization is interesting for a variety of reasons . first , the most fundamental questions are still unanswered : what type of sources caused reionization , and around what redshift did it occur ? how were the reionizing sources distributed relative to the gas ? what was the size , geometry , and topology of the ionized zones , and how did these properties evolve ? second , and more directly relevant to the topic of this review , reionization leaves distinctive signatures on the cosmic microwave background ( cmb ) through the interaction between the cmb photons and free electrons . although it may complicate the extraction of cosmological parameters from cmb data , this `` contamination '' could yield important information on the ionization history of the igm . through reionization , the cmb is a useful probe of nonlinear processes in the high redshift universe . thomson scattering from free electrons affects the cmb in several ways . because the scattering leads to a blending of photons from initially different lines of sight , there is a damping of the _ primary _ temperature anisotropy . on the other hand , a new _ secondary _ anisotropy is generated by what can be thought of as a doppler effect : as photons scatter off free electrons , they pick up some of their peculiar momentum . finally , the polarization dependence of the thomson cross section creates new polarization from the initially anisotropic photon field . the inhomogeneity of reionization affects these processes in two different ways . first , the inhomogeneity of the medium affects how the _ mean _ ionization fraction evolves with time . this is important since the damping , doppler and polarization effects all occur even in the idealized case of spatially homogeneous reionization . secondly , the spatial fluctuations in the ionization fraction can greatly enhance the contribution from the doppler effect at small angular scales . polarization and damping are much less influenced by the inhomogeneity , as we will see below . the aim of the present review is to summarize our current knowledge of reionization , describe the possible connections to the cmb , and assess what we can hope to learn about the high redshift igm from forthcoming observations of the cmb anisotropies . if the igm was neutral , its optical depth to ly@xmath6 absorption would be exceedingly high : + @xmath11^{3/2}$ ] , wiping out the flux from any source at observed wavelengths shorter than @xmath12 . the spectra of high redshift quasars and galaxies reveal ly@xmath6 absorption by numerous discrete ly@xmath6 forest clouds , separated in redshift , rather than the continuous gunn peterson ( gp ) trough expected from a neutral igm . the detection of the continuum flux in between the ly@xmath6 clouds implies that @xmath13 is at most of order unity , or , equivalently , an upper limit on the average neutral fraction of @xmath14 . the intergalactic medium is therefore highly ionized . note that there is no sharp physical distinction between the intergalactic medium and the low column density ( @xmath15 ) ly@xmath6 forest ( reisenegger & miralda - escud 1995 ) . these ly@xmath6 clouds fill most of the volume of the universe , are highly ionized , and account for most of the baryons ( implied by big bang nucleosynthesis ) at high redshift ( weinberg et al . 1997 ; rauch et al . 1997 ) . the energy requirement of reionization can easily be satisfied either by the first mini galaxies or mini quasars . nuclear burning inside stars releases several mev per hydrogen atom , and thin disk accretion onto a schwarzschild black hole releases ten times more energy , while the ionization of a hydrogen atom requires only 13.6 ev . it is therefore sufficient to convert a fraction of @xmath16 of the baryonic mass into either stars or black holes in order to ionize the rest of the baryons in the universe . in a homogeneous universe , the ratio of recombination time to hubble time in the igm is @xmath17^{-3/2}$ ] so that each h atom would only recombine a few times at most until the present time . unless reionization occurred at @xmath18 , recombinations therefore would not change the above conclusion , and the number of ionizing photons required per atom would be of order unity . based on three - dimensional simulations , gnedin & ostriker ( 1997 ) argued that the clumpiness of the gas increases the average global recombination rate by a factor @xmath19 ( the averages are taken over the simulation box ) . this would imply a corresponding increase in the necessary number of ionizing photons per atom . however , in a more detailed picture of reionization in an inhomogeneous universe ( gnedin 1998 , miralda - escud et al . 1999 ) , the high - density regions are ionized at a significantly later time than the low density regions . if this picture is correct , then one ionizing photon per atom would suffice to reionize most of the volume ( filled by the low - density gas ) ; recombinations from the high - density regions would only contribute to the average recombination rate at a later redshift . the reionization redshift can be estimated from first principles . in the simplest picture [ first discussed by arons & wingert ( 1972 ) in the context of quasars ] , a homogeneous neutral igm is percolated by the individual hii regions growing around each isolated uv source . the universe is reionized when the ionized bubbles overlap , i.e. when the filling factor of hii regions reaches unity . several authors studied this problem ( carr et al . 1984 , couchman & rees 1986 , fukugita & kawasaki 1994 , meiksin & madau 1993 ; shapiro et al . 1994 , tegmark et al . 1994 ; aghanim et al . 1996 ; haiman & loeb 1997 ) . specifically , haiman & loeb ( 1998a ) have used the press schechter formalism to describe the formation of halos that potentially host ionizing sources , in order to estimate the redshift at which overlap occurs . in this study , star and quasar black hole formation was allowed only inside halos that can cool efficiently via atomic hydrogen , since molecular hydrogen would be photodissociated earlier , as argued by haiman , abel & rees ( 1999 ) and haiman , rees & loeb ( 1997 ) . this requirement translates to a minimum virial temperature of @xmath20k , or halo masses above @xmath21^{-3/2}$ ] ( see fig . [ fig : bubbles ] ) . for both types of sources , the total amount of light they produce was calibrated using data from redshifts @xmath22 . the efficiency of early star formation can be estimated from the observed metallicity of the intergalactic medium ( songaila & cowie 1996 , tytler et al . 1995 ) , utilizing the fact that these metals and the reionizing photons likely originate from the same stellar population . similarly , the efficiency of black hole formation inside early mini quasars can be constrained to match the subsequent evolution of the quasar luminosity function at redshifts @xmath22 ( pei 1995 ) . these assumptions generically lead to a reionization redshift @xmath23 . the uncertainty in the redshift reflects a range of cosmological parameters ( @xmath24 ) , cdm power spectra ( @xmath25 , @xmath26 ) , and efficiency parameters for the production and escape fraction of ionizing photons . in the stellar reionization scenario , the predicted redshift could be above or below this range , if the initial mass function was strongly biased ( relative to scalo 1986 ) towards massive or low - mass stars . although the naive picture of overlapping hii spheres may give a good estimate for the `` overlap redshift '' , it is likely to be a crude and incomplete description of the real process of reionization . the ionizing sources are expected to be located in the highly overdense regions that form the complex large scale structure of the universe - along filaments or sheets , or at their intersections ( see fig . [ fig:3d ] ) . the ionizing radiation will have to cross the local dense structures before propagating into the igm , which itself has significant density fluctuations . several important consequences of these inhomogeneities can be noted . first , reionization could occur `` outside - in '' ( miralda - escud et al . 1999 ) , if the radiation from a typical source escapes through a relatively narrow solid angle from its host , without causing significant local ionization . in this case , the low density regions could be ionized significantly earlier than the high density regions . an important effect in this case could be the shadowing of ionizing radiation by the dense concentrations within the igm . the same type of shadowing effect was found to be important at low redshift . based on the number of ly@xmath6 absorbers , madau , haardt & rees ( 1998 ) have concluded that as much as @xmath27% of the uv flux is absorbed by these systems . the redshift at which the igm becomes optically thin to the ionizing continuum is therefore significantly delayed relative to the overlap epoch , when the ionized zones first percolate . an alternative possibility is that the ionizing sources are densely spaced along filaments , and their radiation ionizes most of the dense filament before escaping into the igm . in this `` inside - out '' case , the description of ionized zones surrounding their host source would be more applicable . an important feedback during and after reionization is that the newly established uv background can photo evaporate the gas from small ( @xmath28 ) halos ( shapiro , raga & mellema 1997 ; barkana & loeb 1999 ) . a related point , important for the detection of the gp trough , is that at the time of overlap of the hii zones , each individual hii region could still have a non negligible ly@xmath6 optical depth , due to its residual hi fraction . the gp trough therefore disappears only from the spectra of individual sources located below the later redshift when the average ly@xmath6 optical depth of the igm drops below unity ( haiman & loeb 1998b ; miralda - escud et al . 1999 ; shapiro et al . finally , the inhomogeneity of the reionized igm leads to generation of anisotropies in the cmb which are strongly suppressed in the homogeneous case , as we shall see below . reionization is now also being addressed by three - dimensional simulations , which can eventually shed light on some of the above issues . the first such studies approximated radiative transfer by assuming an isotropic radiation field , but were able" +"no hair conjecture @xcite demands the non existence of any information other than mass , charge and angular momentum of a black hole . there are reports for and against the existence of scalar hair . in order to prove the no - hair conjecture , no - hair theorems had been established by coupling the classical fields with the einstein gravity @xcite . it had been shown that the scalar field would be trivial if one demands a regular horizon at a finite distance from the center of the black hole and also that stationary black hole solutions are hairless in a variety of cases , coupling different classical fields to gravity @xcite . another calculation @xcite showed that the static spherically symmetric exterior solutions of the gravitational field equations in a wide class of scalar tensor theories would essentially reduce to the well known schwarzschild solutions once the event horizon had hidden the singularity . the above work was extended to charged black holes and consolidated the non - existence of hair @xcite . as a weak interpretation of scalar hair , nontrivial scalar field solution in terms of conserved charges was mooted @xcite . using this ideology , scalar hair was reported in asymptotically anti - de sitter space time and asymptotically flat space time and it is widely believed that black holes with scalar hair generally exist when the scalar potential has negative region @xcite . there is no regular black hole solution when the scalar field is massless or has a `` convex '' potential . it is widely reported that there are no static asymptotically flat and asymptotically ads black holes with spherical scalar hair if the scalar field theory , when coupled to gravity , satisfies the positive energy theorem @xcite . a charged de sitter black hole in the einstein - maxwell - scalar-@xmath0 system possesses only unstable solutions @xcite . but an unexpected development of scalar hair in ads black hole with minimal @xcite as well as nonminimal @xcite coupling of scalar field , demanded a heuristic study of scalar hair @xcite . as a strong interpretation , black hole has hair if there is a need to specify quantities other than the conserved charges defined at asymptotic infinity in order to characterize completely a stationary black hole solution @xcite . efforts were done to reveal strong hair @xcite and they came up with a scalar solution conformally coupled to einstein s gravity through a metric for extremal case . eventhough innocuous , the solution has a divergence at the horizon . it is given as , @xmath1 with @xmath2 . ( 1 ) is characterized by the adm mass , @xmath3 and scalar charge , @xmath4 . but in eq . ( 1 ) , @xmath5 blows up at the horizon , which is against the principle that @xmath5 shall be finite everywhere@xcite . in another attempt , a four dimensional solution of the einstein equation with a positive cosmological constant coupled to a massless self interacting conformal scalar field was put forwarded @xcite . the scalar solution in that case is , @xmath6 but eq . ( 2 ) does not give any information other than mass of black hole and the cosmological constant . hence strong interpretation of scalar hair is not guaranteed . the motivation of the present work is to know whether a strong interpretation of the scalar hair can be possible in a static ( 3 + 1 ) black hole , which requires a nontrivial solution of scalar field in the vicinity of black hole with regular horizon . in this paper , we report a nontrivial black hole solution of a massive but self interacting scalar field showing no divergence at the horizon and asymptotically falling to the vacuum value . the proposed metric shows trace of scalar charge . whether a nontrivial scalar solution and a metric with a horizon are mutually compatible has been the objective of scalar hair investigation . many contend that only when the solution is trivial that a metric with a horizon is established and for a nontrivial solution , the singularity will become naked . the criterion of scalar hair is the coexistence of nontrivial solution and a proper metric ( having horizon and temperature ) that holds the trace of scalar field . the scheme of the paper is as follows . in sec . ii , nontrivial scalar hair solution is obtained . in sec . iii , the metric of the hairy black hole is obtained . iv discusses thermodynamics of black hole . the conclusion is given in section v. a nontrivial radial solution of a scalar field , whose source is a scalar double well potential , in the vicinity of the static ( 3 + 1 ) black hole will be discussed in this section . we will restrict our consideration to the conformally coupled case . consider the action , @xmath7,\end{aligned}\ ] ] where @xmath8 is a massive , self interacting and conformally coupled scalar field . for a ( 3 + 1 ) case , @xmath9 . a double well potential given by the equation , @xmath10 has been introduced in the action given by eq . ( 3 ) . , with , @xmath11 and @xmath12 . , width=302 ] the potential well is shown in fig . ( 1 ) . in fig . ( 1 ) , @xmath13 has global minima at @xmath14 and a local maximum at @xmath15 . the scalar field equation is given by , @xmath16 where @xmath17 is the laplace - beltrami operator and @xmath18 represents the ricci scalar . the stress energy tensor of scalar field under gravity can be shown by the relation , @xmath19\phi^2 \\ \\ + \frac14g_{\mu \nu } \mu^2(\phi-\phi_0)^2-\frac 18g_{\mu \nu } \delta ^2(\phi-\phi_{0})^4-\frac18g_{\mu\nu}\frac{\mu^4}{\delta^2 } , \end{array}\ ] ] with , @xmath20 here @xmath21 represents a co - variant derivative . for a static and spherically symmetric space time , the @xmath22 component of scalar stress energy tensor is given as , @xmath23 and the @xmath24 component of stress energy tensor is given as , @xmath25 the metric of a static ( 3 + 1 ) black hole may be given as , @xmath26 in the above metric , @xmath27 is a function of @xmath28 only and @xmath29 . here , @xmath30 is an arbitrary function of @xmath31 . there is no loss of generality in setting @xmath32 , since it can be absorbed in the definition of @xmath31 , i.e. , by replacing @xmath33 by @xmath34 . with this redefinition of the time coordinate , @xmath35 . then , @xmath36.\ ] ] we know that black hole is a thermodynamical system with a temperature and its thermal radiation is characterized by renormalized stress - energy tensor @xcite . the gravitational effect of heat radiation , characterized by its gravitationally induced renormalized stress - energy tensor , is constructed on real euclidean section of the black hole geometry with its ( euclidean ) time coordinate identified with period @xmath37 ( for s.b.h ) , so as to eliminate singularity at the horizon . applying eq . ( 11 ) in einstein s equation @xmath38 , we get , @xmath39 the concept of scalar hair is applicable only in a static black hole . from eq . ( 12 ) , we get , @xmath40 eq . ( 13 ) is a co - variant differential equation . in the above scalar field equation , properties such as mass and self interaction terms of scalar field do not come explicitly . in eq . ( 13 ) , @xmath41 can be written in the ordinary derivative as , @xmath42 where @xmath43 is the usual christoffel symbol and @xmath44 runs from @xmath45 . in the above case , all the christoffel symbols except @xmath46 are zeroes and @xmath47 . now , eq . ( 13 ) gets modified as , @xmath48=0.\ ] ] in quest of scalar hair , the general principle is to find a nontrivial solution which is compatible with a proper metric . so we propose a solution of the form , @xmath49+\phi_{0},\ ] ] where @xmath50 is the asymptotic value of scalar field , @xmath51 is a constant which may be derived from mass of black hole and scalar field . it can be shown that @xmath52+\phi_{0}=\frac{a}{r}+\phi_0 $ ] . nontrivial solution of scalar field have been proposed by many people earlier but never extended it to the concept of scalar hair @xcite . by substituting eq . ( 16 ) in eq . ( 15 ) , we get , @xmath53 our primary aim is to evolve a metric with function @xmath54 , which is equal to zero at the horizon and equal to @xmath55 @xmath56 in the asymptotic limit . in eq . ( 17 ) , @xmath50 is a very small field constant , @xmath57 is zero at the horizon and @xmath58 is zero in the asymptotic limit . so the term , @xmath59 is extremely small through out the space and hence may be neglected . ( 17 ) can be rewritten as , @xmath60 from eq . ( 18 ) , we can determine the metric function which is given in the sec.111 . the profile of eq . ( 16 ) shows that the field has a finite value @xmath61 at the horizon and then falls to the asymptotic value @xmath50 . the variation of @xmath5 against @xmath28 is shown in fig . ( 2 ) . with @xmath62 and @xmath12.,width=302 the form of metric , which is compatible with the scalar solution , will be determined . since @xmath63 , eq . ( 18)becomes , @xmath64 by introducing a transformation of the type @xcite , @xmath65 we get from eq . ( 19 ) , @xmath66 where @xmath67 is a radial function . integrating eq . ( 21 ) , @xmath68 in the asymptotic limit @xmath69 and hence @xmath70 . putting the asymptotic value of @xmath5 as @xmath71 , we can obtain , @xmath72 thus from eqs . ( 20 ) and ( 23 ) we find , @xmath73 eq . ( 24 ) represents the metric function which is compatible with the scalar solution @xmath52+\phi_{0}=\frac{a}{r}+\phi_0 $ ] . in the asymptotic limit the metric function , @xmath74 coincides with those of sbh and rn black holes . denoting the field at the horizon as @xmath75 , the radius of the horizon can be obtained as : @xmath76 in eq . ( 24 ) , @xmath77 can be expanded as a series if @xmath78 and it is true in the present case . therefore , @xmath79 the metric function then may be written as a series as , @xmath80 in eq . ( 28 ) , let @xmath81 . the metric function gets modified as , @xmath82 the above mentioned metric is in unison with a recent work@xcite . ( 28 ) may be written in a concise form as , @xmath83.\ ] ] when @xmath84 , we have the schwarzschild like black hole : @xmath85 in this case , @xmath86 . the radius of horizon is @xmath87 . when @xmath88 , we have the extremal case similar to extremal rn black hole . the metric function is reduced to , @xmath89 ^ 2 \\\\ = ( 1-\frac{b}{r})^2 . \end{array}\ ] ] in the extremal case , @xmath90 , which gives the maximum value of @xmath91 . the radius of horizon is @xmath92 . when @xmath93 , @xmath94 and @xmath95 . when @xmath96 , @xmath97 and @xmath98 . it is obtained that the horizon s radius increases and decreases with diminishing magnitude as @xmath99 increases . we can thus introduce more types of black holes by putting @xmath100 . but as the series progress , the series very quickly diminishes . the variation of scalar field @xmath5 against @xmath28 for different black holes are shown in fig" +"physics in extremely high energy regions is particularly of interest to particle physicists . one of the promising idea in the realm of high energy physics is the idea of supersymmetry ( susy ) ( see for instance [ 1 ] and references therein ) . this is a symmetry that relates or mixes ( unites ) fermions and bosons . supersymmetry has the potential to solve some outstanding mysteries in particle physics . one important problem that stands out is called the _ hierarchy problem_. it is believed that the mass of the higgs boson , @xmath2 , is much smaller than the fundamental planck mass , @xmath3 gev/@xmath4 . on the other hand , when we discuss gravity in the context of the quantum field theory , it is expected that there is a minimal measurable length that restricts resolution of adjacent spacetime points up to the planck length . this is actually a common address of all quantum gravity candidates ( see [ 2 ] and references therein ) . incorporation of this idea in quantum field theory provides a theory that is naturally regularized in the ultra - violate regime [ 3,4,5 ] . recently in the context of the doubly special relativity it has been revealed that a test particle s momentum can not be arbitrarily imprecise leading nontrivially to the result that there is a maximal momentum for test particles [ 6 ] . this idea can be explained also through modified dispersion relations as a phenomenological outcome of foam - like structure of spacetime at the planck scale [ 7,8 ] . string theory which has a characteristic scale @xmath5 , is one of the most successful theoretical framework which overcomes the difficulty of ultra - violet divergence in quantum theory of gravity . therefore , if we construct a field theory which captures some stringy nature and/or includes stringy corrections , it would play a pivotal role in investigating physics in high energy regions even near the planck scale . one way to discuss these corrections is deforming the standard heisenberg uncertainty principle to a generalized uncertainty principle ( gup ) . a gup that predicts a minimal observable length can be written as follows @xmath6 this gup leads to the following algebraic structure @xmath7=i\hbar(1+\beta^{2}p^{2})\ ] ] where @xmath8 . if gup is realized in a certain string theory context , @xmath9 takes a value of the order of the string scale , @xmath10 . in the presence of both minimal length and maximal momentum , the gup can be given as follows @xmath11 in this framework the following algebraic structure can be deduced [ 9 ] @xmath12=i\hbar(1-\beta p+2\beta^2 p^2)\,.\end{aligned}\ ] ] in this context , we can define the generalized momentum operator as @xmath13 with these preliminaries , in this paper we construct a quantum theory of free fermion fields based on the deformed heisenberg algebra ( 4 ) . we respect the supersymmetry in this context as a guiding principle . this is because string theory contains this symmetry and it provides a useful tool to understand physics in ultra - violet regime . because of existence of natural cutoffs as minimal length and maximal momentum , the supersymmetry is deformed in this context . from the fermionic part of the system , we propose an action of fermionic field based on the gup in a spacetime with arbitrary number of dimensions . we construct the deformed supersymmetric algebra in this context . finally , we compute some scattering amplitudes such as the pair annihilation amplitude to see how these important quantities can be calculated in the presence of natural cutoffs . we note that experimental limits and the general phenomenology perspective on this issue are not discussed here . one can see ref . [ 10 ] for this purpose . we note also that while the study of susy in relation to gup is a relatively young subject , a bit more has been done for other quantum - spacetime intuitions . for instance , in ref . [ 11 ] the authors have studied the basic twist quantization of @xmath14 and kappa - deformation of @xmath15 superconformal mechanics . the organization of the paper is as follows : in section 2 we construct a scalar field theory based on the gup ( 4 ) . section 3 is devoted to the issue of supersymmetry in the presence of natural cutoffs as minimal length and maximal momentum . in section 4 we compute scattering amplitude of the pair annihilation in the presence of natural cutoffs . the paper follows by a summary and conclusion in section 5 . generalization of the heisenberg algebra to @xmath16-dimensions , where rotational symmetry is preserved and there are both a minimal length and maximal momentum as natural cutoffs , is as follows @xmath17}=i\hbar ( 1-\beta \textbf{p}+2\beta^2 \textbf{p}^2)\delta_{ij } } , \end{aligned}\ ] ] here @xmath18 and @xmath19 run from @xmath20 to @xmath16 , where in three dimensions @xmath21 that @xmath22 , @xmath23 and @xmath24 are unit vectors of cartesian coordinates and @xmath25 . hereafter , we use indices @xmath18 and @xmath19 for spatial coordinates and @xmath26 and @xmath27 for all spacetime coordinates . now the jacobi identity determines the full algebra of the theory which is given as follows ( see the work by k. nozari and a. etemadi in ref . [ 6 ] ) @xmath17}=i\hbar ( 1-\beta \textbf{p}+2\beta^2 \textbf{p}^2)\delta_{ij } } , \end{aligned}\ ] ] @xmath28=0},\end{aligned}\ ] ] @xmath29 = -i \beta \hbar\ ( 4 \beta - \frac{1}{\textbf{p}})\ ( 1 - \beta \textbf{p } + 2\beta^2 \textbf{p}^2)\ \textbf{l}_{ij}\,.\end{aligned}\ ] ] the presence of the @xmath30 is a trace of the existence of the maximal momentum in this setup . note also that eq . ( 9 ) reflects the noncommutative nature of the spacetime manifold in planck scale . here @xmath31 are angular momentum like operators defined as @xmath32 since operators @xmath33 s commute with each other and we have not assumed the existence of a minimal uncertainty in momentum ( see ref . [ 12 ] for possible extension in this regard ) , we can construct our theory in momentum space representation . in momentum space representation , momentum operators are diagonalized simultaneously and we do not distinguish eigenvalues of momentum @xmath34 from operator @xmath35 . in which follows , we set @xmath36 for simplicity . the lagrangian in @xmath37 dimensional spacetime and in the presence of a minimal observable length and a maximal momentum can be written as follows @xmath38\phi(\textbf{p},t)}\end{aligned}\ ] ] where @xmath39 note that the difference from ordinary quantum field theory is the extra prefactor @xmath40 in the lagrangian . using the bjorken - johnson - low prescription , from behavior of @xmath41-product through the following relations @xmath42 @xmath43 where @xmath44 we obtain @xmath45 = i\hbar(1-\beta \textbf{p}+2\beta^2 \textbf{p}^2 ) \delta(\textbf{p}+\textbf{p}')}\end{aligned}\ ] ] where @xmath46 in this relation , @xmath47 where @xmath48 is an arbitrary even function whose explicit form has no influence on the arguments . one can see from equation ( 13 ) that a deformation prefactor , @xmath49 , of heisenberg algebra in the first quantization ( 6 ) also appears in canonical commutation relation of the second quantized field theory . in the fermion field case , we encounter a difficulty in the construction of the second quantized hilbert space which dose not appear in a scalar field system . in which follows we use the idea of supersymmetry to construct a quantized field theory of fermions . in fact , we construct a quantum field theory of fermions , which is consistent with the above scalar field theory , and by using supersymmetry prescription with a minimal length and maximal momentum scale . supersymmetric quantum field theory with minimal length has been studied by shibusa [ 13 ] . in which follows , we generalize the pioneer work of shibusa to the more general case that there are both minimal length and maximal momentum as natural cutoffs . as we have mentioned in the introduction , supersymmetry proposes that to each fermion there exists a boson and vice versa . thus in two and three - dimensional spacetime , a system with a real scalar and a majorana fermion has a special symmetry between a boson and a fermion , namely susy . following ref . [ 13 ] , our notation for two and three - dimensional spacetime is as follows : in those dimensional spacetime ( with signature @xmath50 or @xmath51 ) the lorantz group has a real ( majorana ) two - component spinor representation @xmath52 . for instance , in three - dimensional spacetime , we define a representation of gamma matrices by pauli matrices as follows [ 13 ] : @xmath53 @xmath54 we note that the spinor indices in this case are lowered or raised by charge conjugation matrix @xmath55 and its inverse matrix @xmath56 . the generalized supersymmetric algebra in the presence of a minimal length and a maximal momentum and its action on a scalar field @xmath57 , a majorana fermion @xmath58 and an auxiliary field @xmath59 with parameter @xmath60 is as follows @xmath61=2\upsilon\bar{\epsilon}_1\gamma^a\epsilon_2p_a,\end{aligned}\ ] ] @xmath62 @xmath63 @xmath64\psi(p , t)},\end{aligned}\ ] ] where @xmath65 and @xmath66 are functions of gup deformation parameter @xmath9 and momentum . these factors reduce to unity in the limit of @xmath67 and will be determined later by consistency condition . the closeness of algebra requires @xmath68 now the supersymmetric lagrangian can be written as a sum of separate lagrangians , that is , @xmath69 where @xmath70 , @xmath71 and @xmath72 are bosonic , fermionic and auxiliary fields lagrangian respectively . following [ 13 ] , we generalize the lagrangian by introduction of factors @xmath73 , which are functions of deforming parameter @xmath9 and momentum . these functions can be determined as follows . starting with lagrangian @xmath74 where @xmath16 is the number of the spatial coordinates . by integrating out the field @xmath59 , we obtain the lagrangian for the scalar and majorana fields as follows @xmath75 on the other hand , the invariance of the lagrangian ( 21 ) under supersymmetry variation ( 17)-(19 ) in the presence of the minimal length and maximal momentum leads to @xmath76 @xmath77 @xmath78 using the conditions ( 20 ) and ( 23 ) , only @xmath79 and @xmath80 need to be determined . note also that factor @xmath81 can be absorbed into normalization of @xmath59 . in which follows we set @xmath82 for @xmath59 to be an auxiliary field . noether s current for supersymmetric lagrangian ( 22 ) can be calculated and the supersymmetric charge is obtained to be @xmath83 now the hamiltonian of this system can be written as follows @xmath84 using the bjorken - johnson - low prescription , from behaviors of @xmath85-product between fields , as has been explained in the previous section , we obtain canonical relations as follows @xmath86=i{\zeta_1}^{-1}\delta(p+q),}\end{aligned}\ ] ] @xmath87 therefore , the hamiltonian ( 25 ) now can be written as follows @xmath88 where @xmath89 and @xmath90 . there is another condition that can be used to determine @xmath91 and @xmath92 and comes from the free energy of the supersymmetric vacuum . from algebra ( 16 ) , the supersymmetric state has zero energy @xmath93- \frac{1}{4}{tr}_f\ln \big[\zeta_1(e^2+\textbf{p}^2+m^2)\big],}\end{aligned}\ ] ] where @xmath94 and @xmath95 represent trace in bosonic and fermionic hilbert space respectively . this relation leads to the following condition @xmath96 finally we can write @xmath97 as one can read from ( 11 ) . thus we have @xmath98 @xmath99 @xmath100 therefore , we have constructed the quantized field of fermions as follows @xmath101 in consequence , the supersymmetric algebra in the presence of both minimal length and maximal momentum is deformed from the usual one as follows @xmath102=2(1-\beta \textbf{p}+2\beta^2 \textbf{p}^2)^{-\frac{1}{2}}\bar{\epsilon}_1\gamma^a\epsilon_2p_a.}\end{aligned}\ ] ] these results can be generalized to higher dimensions easily . finally we note that the lagrangian now takes the following form @xmath103\psi(p , t)\big \}.}\end{aligned}\ ] ] we" +"protein aggregation is linked to neuro - degenerative afflictions such as alzheimer s and parkinson s disease . @xcite another classic example of a linearly self - assembling system is the polymerization of actin fibrils and microtubules in living cells that help cells to control their mechanics . @xcite it is the importance of the aggregation of proteins in a wider biological context that has motivated many theoreticians and experimentalits to study equilibrium @xcite and kinetic aspects of it . @xcite although decades of theoretical and experimental investigation has contributed to deeper understanding of how proteins self - assemble into polymer - like objects _ in vitro _ , relatively little is known as to what happens _ in vivo _ , that is , at the cellular scale . almost all of the theoretical work is restricted to using deterministic rate equations to study the kinetics of linear self - assembly . even experimentally , studying stochasticity in protein aggregation turns out to be challenging . @xcite this is because given the mesoscopic nature of the biology of the cell , the stochasticity is arguably mainly due to statistical number fluctuations of assemblies of a certain size . as cells are small in volume ( pico litre to femto litre ) , the number of molecules aggregating is also relatively small , that is , on the scale of typical _ in vitro _ experiments , causing fluctuations to play a significant role in the kinetics as well as in equilibrium . the latter expresses itself in large deviations from mean length distributions . @xcite the kinetics of self - assembly of protein monomers into polydisperse polymer - like objects , i.e. , the time evolution of the polymer length distribution , can take place via a host of different molecular pathways . examples include _ monomer addition and removal _ , _ scission and recombination _ , _ secondary nucleation _ and so on , see fig @xcite in principle , all these pathways are active during the time course of aggregation , but the predominance of one or more pathways may depend on the specific chemistry of a particular system . due to the highly nonlinear nature of the dynamical equations that describe these pathways , it is extremely difficult to study the kinetics of even a single pathway analytically , let alone a combination of several of them . to study the _ stochastic _ nature of self - assembly , one would be required to include the effects of thermal noise that might depend on a plethora of rate constants and thermodynamic parameters . @xcite deducing the properties of the noise from microscopic rate equations , i.e. , by making use of the fluctuation - dissipation theorem , is not trivial , again due to the complexity of the involvement of multiple molecular pathways . all of the above - mentioned challenges limits the applicability of analytical tools available to study the kinetics of protein aggregation . @xcite given the challenges and limitations of the rate - equations approach , we study in this work the kinetics of nucleated linear self - assembly using the method of kinetic monte carlo , hereafter referred to as kmc . kmc is a computer simulation technique used to study markov processes . @xcite protein aggregation can be cast in to the form of a markov process , where a monomer becomes a dimer , a dimer becomes a trimer , and so on . this is exactly the same principle on which rate - equation approaches are based upon . the advantage of kmc is that it is inherently stochastic and hence we do not need to know the nature of thermal noise _ a priori_. in fact , the results obtained from this technique can be used to characterise this kind of noise and its dependence on the model parameters . stochastic simulation techniques have been widely employed to study colloidal aggregation kinetics . @xcite colloidal aggregation resembles protein self - assembly closely in terms of the governing rate equations . the characteristic feature of a lag phase present in nucleated self - assembly has also been found in computational studies of reversible colloidal aggregation . @xcite in this paper we explore the stochastic nature of the kinetics of protein polymerization in small volumes , and study the effect of statistical number fluctuations . we study the aggregation kinetics for small volumes not for one pathway but for no fewer than nine of them discussed in more detail in section ii . the pathways we consider are _ end evaporation and addition _ @xcite , _ scission and recombination _ @xcite , _ secondary nucleation _ @xcite , _ two - stage nucleation _ @xcite , and combination thereof . for the _ scission and recombination _ molecular pathway , the forward and backward rate constants in principle depend on the length of the polymer chains . hence , to probe the impact of length - dependent rate constants , we use hill s model . @xcite although hill s model is valid only for long rigid rod like polymers , we neverthless use it to study if any kind of length dependence of the rate constants can alter the scaling of the lag time with system volume . to quantify the stochastic behavior of the polymerization kinetics , we focus specifically on the lag time associated with the time evolution of the polymerized mass fraction . we provide the simulation details in section iii . in section iv , by doing an exhaustive study for various combinations of molecular pathway , we show that the lag time for the polymerized mass fraction is inversely proportional to the system size in the limit of large volumes albeit that there are corrections to that , that do depend on the specific assembly pathway . @xcite finally , in section v , we conclude the article and discuss our main findings . the molecular pathway determines the relevant time scales in reversible polymerization kinetics . @xcite hence , if we are interested in the stochastic kinetics of the protein aggregation , it makes sense to study the system size dependence of a variety of molecular pathways . in this work we choose the most widely accepted and dominant kinetic pathways as far as the study of protein polymerization is concerned . @xcite we focus on ( i ) _ end evaporation and addition _ , ( ii ) _ scission and recombination _ , ( iii ) _ monomer - dependent secondary nucleation _ , and ( iv ) _ two - stage nucleation _ , and combinations of these pathways . in our description , all these reaction pathways have two things in common , which is that they all are nucleated with nucleus size @xmath0 and that they are _ reversible_. primary nucleation is thought of as the coming together of a minimum of @xmath0 monomers to form the smallest stable polymer . of these pathways seemingly the most obvious to consider is that of _ end evaporation and addition _ , given the linear structure of the aggregates of proteins . in it , growth or shrinkage of an aggregate is possible only by adding or removing a single monomer from either end . @xcite although _ end evaporation and addition _ is the most plausible choice to describe the kinetics of the evolution of length distributions of aggregates , fragmentation and recombination of polymers must be important if the self - assembly is nucleated . for a nucleated self - assembling system , the _ end evaporation and addition _ pathway requires each polymer formed to cross a nucleation barrier , which slows down the assembly process significantly . instead , in _ scission and recombination _ kinetics the polymers can bypass the nucleation barrier by breaking already existing filaments and creating new nucleation centers that then can grow . hence , it is sensible to study scission - recombination in combination with end evaporation and addition , which is why this is one of the combined schemes that we investigate . the forward and backward rate constants for all pathways could be length dependent , in particular for the scission - recombination pathway . indeed , shorter polymers should recombine faster than longer ones if the reaction is diffusion limited , and longer ones plausibly have a higher probability of breaking within a certain amount of time than shorter ones . we do take into account the length dependence of the rate constants for the _ scission and recombination _ pathway by invoking hill s rate constants . @xcite hill derived the forward and backward rate constants in the limit of diffusion - limited aggregation that are valid only for long rigid rods . hill s rate constants are not entirely consistent with the thermodynamics of nucleated self - assembly , and alternative ones have been derived in the context of the radical polymerization with more accurate length dependent rate constants these seem to suffer from the same problem . @xcite as our aim is to find out if any kind of length dependence of the rate constants alters the dominant scaling of the lag time as a function of system volume , we make an arbitrary choice of using hill s model . we study both kinds of scission - recombination pathway , i.e. , with and without length dependence of the rate constants . the pathways of _ end evaporation and addition _ and of _ scission and recombination _ have proven to apply to the polymerisation of actin and tubulin filaments , but the time scales obtained from these pathways can not explain other types of protein aggregation , such as that of sickle hemoglobin . @xcite sickle cell hemoglobin shows relatively rapid polymerization kinetics in comparison to predictions from _ end evaporation and addition _ and _ scission and recombination _ kinetics . to successfully explain the rapid polymerization observed in sickle cell hemoglobin , surface - catalysed or secondary nucleation has been included in several studies . @xcite secondary nucleation is also found to be relevant in the context of amyloid fibrillation . @xcite recalling that primary nucleation concerns the conversion of a cluster of monomers into a stable polymer of shortest length , @xcite in secondary nucleation a critical number @xmath0 of monomers may first form an unstable cluster that next transforms into a stable cluster , which in turn facilitates the elongation process . clearly , molecules may polymerize via a combination of molecular pathways . in this work we perform an exhaustive study of stochastic aggregation kinetics allowing for several combinations of pathway , and study how the resulting kinetics are affected by the system size . the pathways we study are listed in table i. mathematically , reversible polymerization can be represented by an infinite set of rate equations for all allowed chemical reactions . indeed , a monomer reacts with a monomer to form a dimer , a dimer reacts with a monomer to form a trimer and so on . let us first translate each pathway of table i into a set of chemical reactions and write the corresponding rate equation for the polymers as state given the present state @xmath1 & reaction rate + primary nucleation & & .possible molecular aggregation steps by which a polymer length distribution can change , considered in this work . assuming the present state to be @xmath2 , where @xmath3 is the number of monomers and @xmath4 the number of polymers of length @xmath5 , the states following the corresponding reactions are indicated . notice that for secondary nucleation we do not have a backward reaction . this is because @xmath6 is a polymer of size greater than the stable nucleus of size @xmath0 , that then can disintegrate via monomer removal or scission . also" +"systematic investigations of a(@xmath10 ) reactions at saclay , nikhef , mainz and bates have produced an impressive amount of data for various target nuclei @xcite . for the sake of minimizing the uncertainties with respect to the reaction mechanism , a large fraction of these investigations were done under or close to quasi - elastic kinematics ( bjorken @xmath11 1 ) . these data sets highlight at the same time the success and the limits of the independent - particle - model ( ipm ) for atomic nuclei @xcite . indeed , after corrections for final - state interactions and coulomb distortions of the electron probe , the shape of the deduced proton momentum distributions are systematically in line with the predictions of modern formulations of the nuclear ipm . on the other hand , below the fermi momentum the absolute magnitude of the deduced momentum distributions are systematically , i.e. independent of the nucleon momentum , lower than ipm predictions . to cut a long story short , the major conclusion from this world - wide @xmath5 effort seems that an appropriate non - relativistic picture of the nucleus is roughly compatible with _ 70% mean - field behaviour and 30% `` correlations '' _ an observation which is still frequently ignored in various nuclear structure calculations and model developments . the energy of the available electron beams with a large duty factor ( @xmath12 1 gev ) made that most of this aforementioned @xmath5 work was done at four - momentum transfers of the order @xmath13 0.2 ( gev / c)@xmath3 . with the advent of the tjnaf and an upgraded mainz electron facility higher values of @xmath2 come into reach of experimental exploration . amongst the major physics goals motivating exclusive ( @xmath10 ) measurements from finite nuclei at higher momentum transfer ( @xmath14 ( gev / c)@xmath3 ) one can mention the following ones . the higher @xmath2 conditions and unmistakingly smaller distance scales probed should make it feasible to achieve a better understanding of the short - range mechanisms in nuclei . at the same time , one could hope to find experimental evidence for the onset of quark and gluon degrees of freedom . presumably , the most convincing evidence pointing into that direction could come from measurements for processes that are fairly well understood at lower @xmath2 ( like ( @xmath10 ) at x=1 ) and turn out to be completely at odds with meson / baryon models when higher @xmath2 regimes are entered . another challenge for ( @xmath10 ) measurements at higher momentum transfers is the question whether available relativistic models can succeed in producing a better agreement with the data sets than the non - relativistic ones and if so , which dynamical degrees of freedom make them to be substantially different from what is commonly implemented in the non - relativistic nuclear many - body models . another fundamental question that has received a great share of attention for many years , is the question whether the nucleon properties ( like electromagnetic form factors e.g. ) are modified in the nuclear medium . this information is of unvaluable importance for models that embark on the ambitious program of understanding nuclei in terms of quark and gluon degrees of freedom @xcite . a challenging but at the same time rather ambiguity - free way of probing the medium - dependent form factors , are double polarization observables from a(@xmath0 ) measurements @xcite . indeed , double polarization observables are conceived to be rather insensitive to ambiguities with respect to the final state interactions ( fsi ) that affect most of the other a(@xmath10 ) observables . other effects that are recognized to possibly complicate the interpretation of double polarization observables in terms of medium - dependent nucleon form factors are gauge ambiguities , channel - couplings and two - body current effects . whereas the first two sources of possible dilutions were extensively studied by kelly @xcite and found to produce very small corrections , the two - body current effects are not well studied for finite nuclei . earlier efforts to study the role of two - nucleon currents in exclusive a(@xmath10 ) reactions from finite nuclei ( a@xmath154 ) include the pioneering work of suzuki @xcite , the systematic investigations by the pavia group @xcite and the @xmath16he(@xmath10 ) studies as e.g. reported in refs . @xcite . in order to make their calculations computationally more attractive , the results of the pavia group were obtained with a two - body current operator that was formally reduced to an effective one - body one . this approximation adopts a fermi - gas picture for the residual nucleus that allows to integrate out the coordinates of the second nucleon that gets involved in the photoabsorption process . for the work presented here , we treat the two - body currents in their full ( non - relativistic ) complexity and deal with the multi - dimensional integrals that automatically occur when several nucleons get involved in the ( virtual ) photoabsorption process . a similar sort of exact treatment was earlier adopted in our work reported in references @xcite . there it was found that the effect of the two - body currents on the a(@xmath10 ) cross sections , just as the role of the coupled - channel effects , is gradually decreasing with increasing momentum transfer . this conforms to the findings with respect to the momentum - transfer dependence of the two - body current effects in the d(@xmath10)n and @xmath16he(@xmath10 ) @xcite . nevertheless , even at the highest momentum transfer considered in ref . @xcite ( q=600 mev / c ) the cross sections were predicted to be substantially affected by the two - body currents . in this work the role of meson - exchange and isobar degrees of freedom in a(@xmath0 ) and a(@xmath1 ) is investigated in a wide range of four - momentum transfers ( 0.2 @xmath170.8 ( gev / c)@xmath3 ) . special emphasis is placed on the recoil polarization observables as they open perspectives to investigate possible medium modifications of the nucleon properties . the calculational framework will be introduced in section [ sec : model ] . in section [ sec : observ ] the adopted conventions for the ( @xmath0 ) observables will be introduced . the model for the bound and scattering states is described in section [ sec : fsi ] . in section [ sec : current ] the model assumptions with respect to the one- and two - body current operators will be summarized . the results of the calculations are contained in section [ sec : results ] . our conclusions are summarized in section [ sec : conclusions ] . we consider processes in which a longitudinally polarized electron impinges on a nucleus and induces the following reaction @xmath20 to occur . for such a process the cross section reads in the one photon exchange approximation @xmath21 \biggr ] \ ; , \label{eq : eep}\end{aligned}\ ] ] where @xmath22 is the recoil factor @xmath23 and @xmath24 the mott cross section @xmath25 the electron kinematics is contained in the kinematical factors @xmath26 whereas the structure functions are defined in the standard fashion @xmath27 & w_{tt}= 2 { \cal r}e \left [ \left ( j_{-1}^{fi } \right)^ * \left ( j_{+1}^{fi } \right ) \right ] \\ w_{lt}^ { ' } = -2 { \cal r}e \left [ \left ( j_{0}^{fi } \right)^ * \left ( j_{+1}^{fi } \right ) + \left ( j_{0}^{fi } \right)^ * \left ( j_{-1}^{fi } \right ) \right ] & w_{tt}^ { ' } = \left ( j_{+1}^{fi } \right)^ * \left ( j_{+1}^{fi } \right ) - \left ( j_{-1}^{fi } \right)^ * \left ( j_{-1}^{fi } \right ) \ ; . \\ \end{array}\ ] ] the above definitions for the structure functions and the kinematical variables correspond with those of ref . we remind that apart from a negligible parity - violating component , the structure function w@xmath28 vanishes identically and the w@xmath29 in coplanar kinematics if no recoil polarization is determined . a new set of observables comes into reach of experimental exploration when performing polarimetry on the ejected hadron . this results in knowledge about the spin orientation of the ejectile and as e.g. illustrated in neutron form factor studies represents a powerful tool to address fundamental physical quantities . the formal framework for the electroproduction of polarized nucleons from nuclei is outlined in great detail in refs . @xcite and will not be repeated here . here , we only review some basic concepts which mainly serves at introducing the conventions adopted . for the results presented below , the polarization of the escaping nucleon is expressed in the so - called barycentric reference frame that is defined by the following set of unit vectors ( fig . [ fig : reffram ] ) @xmath30 note that for coplanar kinematics @xmath31 determines the y axis of the reference frame . the escaping nucleon polarization observables can be determined through measuring * ratios*. the _ induced polarization _ can be addressed with unpolarized electrons ( i = n , l , t ) @xmath32 whereas the _ polarization transfer _ also requires polarized electron beams ( i = n , l , t ) @xmath33 - \left [ \sigma ( h=1,s_{n}^{i}= \downarrow ) - \sigma ( h=-1,s_{n}^{i}= \downarrow ) \right ] } { \left [ \sigma ( h=1,s_{n}^{i}= \uparrow ) + \sigma ( h=-1,s_{n}^{i}= \uparrow ) \right ] + \left [ \sigma ( h=1,s_{n}^{i}= \downarrow ) + \sigma ( h=-1,s_{n}^{i}= \downarrow ) \right ] } \ ; , \label{eq : trans}\end{aligned}\ ] ] where @xmath34 denotes that the ejected hadron is spin - polarized in the positive i direction ( i=(n , l , t ) ) and @xmath35 is the helicity of the electron impinging on the target nucleus . @xmath36 is a shorthand notation for the differential cross section for an electrodisintegration process initiated by an electron with helicity @xmath35 and for which the ejectile is detected with a spin polarization characterized by @xmath37 . throughout this work we adopt relativistic kinematics . for the model calculations presented here , the bound and scattering states are produced by solving a schrdinger equation with a mean - field potential that is obtained from a hartree - fock calculation . the latter are performed with an effective nucleon - nucleon force of the skyrme type . the mean - field potential includes central , spin - orbit and coulomb terms . this model does not require any empirical input with respect to the inital and final - state potentials . moreover , the orthogonality condition between the initial and final states is obeyed and gauge invariance is preserved at the one - body current level . a drawback of the model is that the inelastic processes , which are commonly accounted for through imaginary parts in the final - state potential , are only partially included . the major impact of the rescattering processes in exclusive ( @xmath10 ) is generally conceived , however , to be a mere reduction of the absolute cross section . in the kinematics regime of interest here , the reduction factor can be estimated from nuclear transparency @xmath5 measurements as they were recently performed at tjnaf for various target nuclei @xcite . the differential cross section , the various structure functions and polarization observables are all calculated starting from the following set of transition matrix elements @xmath38 where @xmath39 and @xmath40 refer to the quantum states of the target and residual a-1 nucleus and @xmath41 denotes the spin projection of the ejectile along the z - axis . the latter is chosen to coincide with the direction of the momentum transfer @xmath42 . when calculating the induced and transverse polarizations as defined in eqs ." +"justification logic is a family of logics of justified beliefs . where epistemic modal logic treats formulas of the form @xmath1 with the intended meaning that an agent knows / believes @xmath2 , in justification logic we consider formulas of the form @xmath3 with the intended meaning that @xmath4 is a justification for @xmath2 - or that the agent has justification @xmath4 for @xmath2 . the first justification logic was lp , the logic of proofs , and appeared in @xcite by artemov , but it has since developed in a wide system of explicit epistemic logics with notable complexity properties that significantly differ from the corresponding modal logics : while every single - agent justification logic whose complexity has been studied has its derivability problem in @xmath5 ( the second level of the polynomial hierarchy ) , the corresponding modal logics have -complete derivability problems . furthermore certain significant fragments of these justification logics have an even lower complexity- , or even in some cases . for an overview of justification logic see @xcite . for an overview of complexity results of ( single - agent ) justification logic , see @xcite . in epistemic situations we often have multiple agents , so as it is the case with modal logic , there is a need for a multi - agent justification logic . in @xcite , yavorskaya presents two - agent variations of lp . these logics feature interactions between the two agents justifications : for @xmath6 , for instance , every justification for agent 1 can be converted to a justification for agent 2 for the same fact and we have the axiom @xmath7 , while @xmath8 comes with the extra axiom @xmath9 , so agent 2 is aware of agent 1 s justifications . in @xcite , we extended yavorskaya s logics to two - agent variations of other justification logics , as well as to combinations of two different justification logics . we then gave tableau procedures to prove that most of these logics were in the second step of the polynomial hierarchy , an expected result which mimics the ones for single - agent justification logics from @xcite . for some cases , however , we were able to prove -completeness , which was a new phenomenon for justification logic . in this paper we continue our work from @xcite . we provide a general family of multi - agent logics . each member of this family we call @xmath10 , where @xmath11 are parameters of the logic . for @xmath10 we consider @xmath12 agents and the interactions between the agents justifications are described by binary relations on agents , @xmath13 and @xmath14 . furthermore , not all agents are equally reliable : @xmath15 and @xmath16 are sets of agents , all agents in @xmath15 have consistent beliefs and all agents in @xmath16 have true beliefs . these concepts are made precise in section [ multidefinitions ] . it is our goal to provide a flexible system capable of modelling situations of many diverse agents , or diverse types of justifications , allowing for reasonably general interactions among their justifications . for this family of logics we provide semantics and a general tableau procedure and then we make observations on the complexity of the derivation problem for its members . in particular , we demonstrate that all logics in this family have their satisfiability problem in - under reasonable assumptions . this family demonstrates significant variety , as it also includes - and -complete members , while of course some of its members have their satisfiability problem in @xmath17 . this is a somewhat surprising result , as all single - agent justification logics whose complexity is known have their satisfiability problem in @xmath17 . this paper is organised as follows . in section [ multidefinitions ] , we give the base definitions of the syntax , axioms and semantics for each logic in the family . then we reintroduce the star calculus , an invaluable tool , and our first complexity results , mirroring the ones for single - agent justification logic ( see @xcite ) . the version of the star calculus we provide is somewhat different than the usual ones in that it is based on a given frame . if the frame includes a single world , we get the usual , more familiar version . in section [ tableaux ] we give general tableau rules for each of our logics . naturally , the rules are parameterized by the logic s parameters , including the interactions between the agents , so special attention is given in that section to these interactions . we then go on and further optimize the tableau procedure with respect to the number of world - prefixes it produces ; this results in a @xmath17 upper bound for the satisfiability of a general class of logics . in this section we present the system we study in this paper , its semantics and the basic tools we will need later on . most of the proofs for the claims here can be adjusted from the one- or two- agent versions of justification logic . the reader can see @xcite or @xcite for an overview of single - agent justification logic and @xcite for a two - agent version of this system . in this paper , if @xmath18 , @xmath19 $ ] will be the set @xmath20 . for every @xmath21 , the justification terms of the language @xmath22 will include all constants @xmath23 and variables @xmath24 and if @xmath25 and @xmath26 are terms , then the following are also terms : @xmath27 , [ t_1\cdot t_2 ] , ! t_1 $ ] . the set of terms will be referred to as @xmath28 . we also use a set @xmath29 of propositional variables , or sentence letters . these will usually be @xmath30 . formulas of the language @xmath22 include all propositional variables and if @xmath31 are formulas , @xmath32 $ ] and @xmath4 is a term , then the following are also formulas of @xmath22 : @xmath33 . the remaining propositional connectives , whenever needed , are treated as constructed from @xmath34 and @xmath35 in the usual way . the operators @xmath36 and @xmath37 are explained by the following axioms . intuitively , @xmath38 applies a justification for a statement @xmath39 to a justification for @xmath40 and gives a justification for @xmath41 . using @xmath42 we can combine two justifications and have a justification for anything that can be justified by any of the two initial terms - much like the concatenation of two proofs . finally , @xmath37 is a unary operator called the proof checker . given a justification @xmath4 for @xmath2 , @xmath43 justifies the fact that @xmath4 is a justification for @xmath2 . let @xmath18 , @xmath44 $ ] and @xmath45^{2}$ ] . the logic @xmath46 is the logic with modus ponens as a derivation rule and the following axioms : propositional axioms : : : finitely many schemes of classical propositional logic ; application : : : @xmath47 \colon_{i } \ ! } \psi)$ ] ; concatenation : : : @xmath48 \colon_{i } \ ! } \phi$ ] , @xmath49 \colon_{i } \ ! } \phi$ ] ; @xmath16-factivity : : : for every @xmath50 , @xmath51 ; @xmath15-consistency : : : for every @xmath52 , @xmath53 ; @xmath13-verification : : : for every @xmath54 , @xmath55 ; @xmath14-conversion : : : for every @xmath56 , @xmath57 , where in the above , @xmath2 and @xmath58 are formulas in @xmath22 , @xmath59 are terms and @xmath60 $ ] . @xmath16-factivity and @xmath15-consistency are the usual factivity and consistency axioms for every agent in @xmath16 and @xmath15 respectively . positive introspection is seen as a special case of @xmath13-verification - in this context , if agent @xmath61 has positive introspection , then @xmath62 . a constant specification for @xmath63 is any set @xmath64\}.\ ] ] we say that axiom @xmath40 is justified by a constant @xmath65 for agent @xmath61 , when @xmath66 . a constant specification is : _ axiomatically appropriate with respect to @xmath67 $ ] _ if for every @xmath68 , each axiom is justified by at least one constant , _ schematic _ if every constant justifies only a certain number of schemes from the ones above ( as a result , if @xmath65 justifies @xmath40 for @xmath61 and @xmath41 results from @xmath40 and substitution , then @xmath65 justifies @xmath41 for @xmath61 ) and _ schematically injective _ if it is schematic and every constant justifies at most one scheme . let @xmath69 be the smallest set such that @xmath70 and for every @xmath71 , it is the case that for every @xmath72 $ ] , @xmath73 . @xmath74 is @xmath75 , where @xmath76 just outputs all elements of @xmath69 . @xmath77 is consistent : just map each formula to the propositional formula that is the result of removing all terms from the original one ; then , all axioms are mapped to propositional tautologies and modus ponens preserves this mapping . we now introduce models for our logic . in the single - agent cases , m - models ( introduced in @xcite ) and f - models ( introduced in @xcite ) are used ( also in @xcite for two - agent logics ) and they are both important in the study of complexity issues . in this paper we are mostly interested in f - models , which we will usually just call models . these are essentially kripke models with an additional machinery to accommodate justification terms . let @xmath78 . then , an f - model @xmath79 for @xmath80 is a quadruple @xmath81 } , ( { { \mathcal{a}}}_i)_{i \in [ n]},{\mathcal{v}})$ ] , where @xmath82 is a set , for every @xmath83 $ ] , @xmath84 is a binary relation on @xmath85 , @xmath86 and for every @xmath83 $ ] , @xmath87 . @xmath85 is called the _ universe _ of @xmath79 and its elements are the worlds or states of the model . @xmath88 assigns a subset of @xmath85 to each propositional variable , @xmath89 , and @xmath90 assigns a subset of @xmath85 to each pair of a justification term and a formula . furthermore , @xmath91}$ ] will often be seen and referred to as @xmath92\times tm \times l_n { \longrightarrow}2^{w}$ ] and @xmath93 is called an admissible evidence function . additionally , @xmath93 must satisfy the following conditions : application closure : for any @xmath83 $ ] , formulas @xmath31 , and justification terms @xmath94 , + @xmath95 sum closure : for any @xmath83 $ ] , formula @xmath2 , and justification terms @xmath94 , + @xmath96 @xmath97-closure : for any formula @xmath71 , @xmath98 . @xmath13-verification closure : if @xmath54 , then @xmath99 @xmath14-conversion closure : if @xmath56 , then @xmath100 @xmath13-distribution : for any formula @xmath2 , justification term @xmath4 , @xmath54 and @xmath101 , if @xmath102 and @xmath103 , then @xmath104 . the accessibility relations , @xmath105 , must satisfy the following conditions : * if @xmath106 , then @xmath105 must be reflexive . * if @xmath107 , then @xmath105 must be serial ( @xmath108 ) . * if @xmath109 , then for any @xmath110 , if @xmath111 , we also have @xmath112 . has positive introspection ( i.e. @xmath113 ) , then @xmath105 is transitive . ] * for any @xmath56 , @xmath114 . truth in the model is defined in the following way , given a state @xmath115 : * @xmath116 and if @xmath89 is a propositional variable , then @xmath117 iff @xmath118 . * if @xmath31 are formulas , then @xmath119 if and only if @xmath120 , or @xmath121 . * if @xmath2 is a formula and @xmath4 a term , then @xmath122 if and only if @xmath103 and @xmath123 for all @xmath124 such that @xmath125 . a formula @xmath126 is" +"single molecule biomechanical experiments allow to measure the forces generated by biomolecules and their response to applied forces @xcite . for `` passive '' biopolymers , that do not produce active movement against load , the resulting force - extension curves provide a probe of the nonlinear elasticity of the chains and its relationship to configurational changes . such studies were carried out for single stranded and double stranded dna @xcite , for the muscle protein titin @xcite , the extracellular matrix protein tenascin @xcite , the polysaccharides dextran @xcite and xanthan @xcite , as well as the synthetic polymer poly(ethylene - glycol ) @xcite . theoretical modeling of the elastic behavior of these polymers is often hampered by lack of detailed knowledge concerning the configurations involved and the relevant interactions . a direct and detailed confrontation between experiment and theory is however possible for the case of homopolypeptides capable of forming an @xmath4-helix . in this case the molecular configurations are well understood . furthermore , one can relate the elastic force law to the known zimm - bragg parameters that characterize the helix - coil transition of the free polypeptides . as we shall discuss , the extension force law of a long polypeptide just above the melting temperature of the helix , @xmath0 , exhibits two plateaus . both are associated with a coexistence of helical and coil domains . the low - tension plateau is due to helix formation induced by the chain extension and the accompanying loss of configurational entropy . the second , high - tension plateau is due to the extension induced melting of the helices when the end - to - end length exceeds the length of the fully helical chain . for @xmath5 only the second plateau survives but the force law for weak extensions exhibits a `` quasi plateau '' _ i.e. , _ a regime with a weak slope that is not associated with a coexistence . this last regime is due to the facile alignment of the long persistent regions in the helix . in the following we analyze the force laws , their dependence on temperature and the corresponding population distribution of helical and coil segments . while we are unaware of single molecule experiments on this system , similar behavior was observed experimentally on fibers of collagen during the 1950s @xcite . two different treatments of this problem were recently advanced @xcite . in the present article we present a unified analysis of the problem , tracing the physical origins of the disagreements between the force laws obtained in the two earlier publications and analyzing their range of validity . our treatment is distinctive in that it is based on free energy argument instead of the customary transfer matrix approach @xcite . this free energy argument allows to recover the results of the transfer matrix method but is physically transparent and relatively simple mathematically . within this approach we consider the extension of a very long homopolypeptide capable of forming @xmath4-helices . the discussion is limited to quasi - static extension assuming that the rate of equilibration of the configurations of the chain is much faster than the rate of extension . two models are explored . in one , the helical domains are viewed as rigid rods while in the second , they are modeled as semiflexible chains . for each model we present a rigorous derivation of the corresponding force law allowing for the polydispersity of the helical and coil domains and the associated mixing entropy ( see fig . [ multi ] ) . in addition , we explore two useful approximations allowing for simplified calculations of the force law . in one approximation , the mixing entropy of the helices and domains is neglected and the plateau is associated with coexistence of one helical domain with one coil domain ( see fig . [ phases ] ) . within this `` diblock '' or `` @xmath6 '' approximation the coexistence regimes involve a first order phase transition . in spite of this erroneous conclusion , this approximation correctly identifies the important length and force scales in the problem . the second , mean field approximation , neglects the direct coupling of the distribution of domains sizes and the applied tension . as we shall see , this approximation is actually exact when the helical domains are modeled as long semiflexible chains . the problem and the analysis are of interest from a number of perspectives . homopolypeptides are the simplest representatives of helicogenic molecules . in this case it is not necessary to allow for the sequence heterogeneity which affects the elasticity of heteropolypeptides . nor is it necessary to consider the long range interaction that occur in multiple helices . as a result , the number of parameters invoked in the theory is smaller and the mathematical analysis is simpler . the force laws obtained are determined by known zimm - bragg parameters with no adjustable parameters . accordingly this system enables a direct comparison between experiment and theory . in this juncture it is important to note the availability of synthetic methods for producing long polypeptides with a well defined architecture @xcite . furthermore , the formalism described provides a convenient basis for the analysis of more complex helicogenic polymers such as dna and collagen . from a polymer science point of view the elasticity of homopolypeptides is of interest because it reflects the effects of internal degrees of freedom arising from intrachain self - assembly . the study of these systems enables the exploration of the distinctive non - linear force laws that are the signatures of such intrachain self - assembly . finally , this elasticity plays a role in the stabilization of the helical state of grafted polypeptides @xcite . in turn this is of importance for the function of fusogenic polypeptides and the design of surfaces that favor spreading and growth of cells @xcite . the paper is organized as follows . in section ii we introduce the free energy argument _ via _ an analysis of the helix - coil transition in free , undeformed homopolypeptides . a semiquantitative analysis of the effect of extension is presented in section iii . two approaches are used . one focuses on the intersections of the free energy curves of a pure coil and a pure helix as a function of the end - to - end distance , @xmath2 . as we shall see , each intersection is a rough diagnostic for a transition between the two configurations and for the occurrence of a plateau in the force law . the second , more quantitative approach is the diblock or @xmath6 approximation . within this approximation the homopolypeptide is assumed to consist of two domains , a helix and a coil , and the mixing entropy associated with the polydispersity of the helical and coil domains is set to zero , @xmath6 . finally , in section iv we present a rigorous analysis of the force laws allowing for the polydispersity of the coexisting helices and coil domains . as stated earlier , we implement this analysis for two models . in one the helical domains are viewed as rigid rods and in the second as semiflexible chains described by the worm like chain ( wlc ) model . in this section we also examine the validity of the mean field approximation introduced in @xcite . within this approximation , the explicit coupling between the tension and the distribution of domain sizes is ignored . as we shall see , it recovers the exact result when the helices are semiflexible _ i.e. , _ when the persistence length of the helices is finite and the helical domains are large . the analysis of the rigid helices model recovers the results obtained by tamashiro and pincus @xcite using a transfer matrix formalism . a comparison between the two models and an outline of some open problems are presented in the discussion . it is helpful to first summarize the main features of the helix - coil transition of free polypeptides in the absence of imposed extension . we will consider only homopolypeptides , consisting of a single type of amino acid residues , in order to avoid complications introduced by sequence of different residues found in heteropolypeptides . our discussion focuses on the case of long chains where the degree of polymerization of the polymer @xmath7 is large , @xmath8 . to this end we first discuss the zimm - brag parameters and then introduce the free energy analysis of the transition . as we shall see , this is equivalent to the transfer matrix formalism @xcite that is traditionally used to analyze the transition @xcite . our discussion focuses on helicogenic polypeptides that are capable of assuming two configurations : a random coil and an @xmath4-helix . in the coil state the monomers are free to rotate thus leading to a small kuhn length with typical value of @xmath9 corresponding to the length of few monomers . for simplicity we will identify the kuhn length with the span of a single monomer , @xmath10 . the helical configuration involves hydrogen bonds between residues @xmath11 and @xmath12 . this constrains the orientation of the three intermediate monomers . as a result the persistence length @xmath13 of the helical configuration is large , of order @xmath14 . at the same time the projected length of a monomer along the axis of the helix decreases to @xmath15 . the length of the polypeptide in a helical configuration is thus smaller than the span of a fully extended coil by a factor of @xmath16 @xcite . the homopolypeptides are modeled as a two state system . each monomer can exist either in a helical or a coil state . choosing the coil state as a reference state , the excess free energy @xmath17 of a monomer within a helical domain reflects two contributions . first is the change in enthalpy upon formation of an intrachain @xmath18-bond , @xmath19 . the second is associated with the loss of configurational entropy , @xmath20 , in the helical state . altogether @xmath21 the enthalpy term favors the helical state while the entropy term favors the coil state . thus , at low temperatures the free energy @xmath17 is negative and the helical configuration is preferred while at high temperatures @xmath17 is positive and the coil state is dominant . the two terms are comparable at @xmath22 when @xmath23 . @xmath0 provides an approximate value for the melting temperature of the @xmath4-helix . an additional parameter is needed to describe the helix - coil transition . the number of @xmath18-bonds in a helical domain consisting of @xmath24 monomers is @xmath25 . it is thus necessary to allow for the special state of the terminal monomers of the helical domain . these two monomers lose their configurational entropy with no gain due to the formation of @xmath18-bonds . each of the terminal bonds is thus assigned an excess free energy of @xmath26 with respect to the coil state . in the following we will use @xmath27 measured with respect to the helical state , that is @xmath28 as we shall discuss later , this definition is consistent with the known experimental results . clearly , this definition is consistent with the traditional one when the coil state is used as a reference . @xmath27 plays the role of an interfacial free energy associated with the boundary between helix and coil domains . this term makes the helix - coil transition cooperative since it favors the formation of large domains . it is customary to describe the helix - coil transition in terms of the zimm - bragg parameters @xcite : @xmath29 where @xmath30 is the boltzmann constant . the @xmath31 dependent @xmath32 represents the boltzmann factor associated with adding one monomer to a helical domain ." +"recently , motivated by the lifshitz model in condensed matter physics , hoava proposed a power counting renormalizable theory for ( 3 + 1)-dimensional quantum gravity @xcite . this theory , denoted as hoava - lifshitz gravity , is believed to be the potential ultraviolet ( uv ) completion of general relativity ( gr ) . in the infrared ( ir ) limit ( setting the parameter @xmath1 in the action ) , it recovers gr . hoava - lifshitz gravity admits a lifshitz scale - invariance in time and space , exhibiting a broken lorentz symmetry at short scales , while at large distances higher derivative terms do not contribute , and the theory reduces to standard gr . since then various properties and characteristics of the hoava gravities have been extensively analyzed , ranging from formal developments @xcite , cosmology @xcite , dark energy @xcite and dark matter @xcite , spherically symmetric solutions @xcite , and its viability with observational constraints @xcite were also explored . although a generic vacuum of the theory is the anti - de sitter one , particular limits of the theory allow for the minkowski vacuum . in this limit post - newtonian coefficients coincide with those of pure gr . thus , the deviations from conventional gr can be tested only beyond the post - newtonian corrections , that is for a system with strong gravity at astrophysical scales . in this work , we consider the stability of the einstein static universe in hoava - lifshitz gravity , with a ` soft ' violation of the detailed balance condition ( recently , the stability of the einstein static universe in hoava - lifshitz gravity satisfying the detailed balance condition was analyzed @xcite ) . the presence of the respective term in the action which represents a ` soft ' violation of the ` detailed balance ' condition modifies the ir behavior . note that this ir modification term , with an arbitrary cosmological constant , represent the analogs of the standard schwarzschild(a)ds solutions , which were absent in the original hoava model . the analysis of the static einstein universe is motivated by the possibility that the universe might have started out in an asymptotically einstein static state , in the inflationary universe context @xcite . on the other hand , the einstein cosmos has always been of great interest in various gravitational theories . in gr for instance , generalizations with non - constant pressure have been analyzed in @xcite . in brane world models , the einstein static universe was investigated in @xcite , while its generalization within einstein - cartan theory can be found in @xcite , and in loop quantum cosmology , we refer the reader to @xcite . in the context of @xmath2 modified theories of gravity , the stability of the einstein static universe was also analyzed by considering homogeneous perturbations @xcite . by considering specific forms of @xmath2 , the stability regions of the solutions were parameterized by a linear equation of state parameter @xmath0 . contrary to classical gr , it was found that in @xmath2 gravity a stable einstein cosmos with a positive cosmological constant does indeed exist . thus , in principle , modifications in @xmath2 gravity stabilize solutions which are unstable in gr . furthermore , in @xcite it was found that only one class of @xmath2 theories admits an einstein static model , and that this class is neutrally stable with respect to vector and tensor perturbations for all equations of state on all scales . these results are apparently contradictory with those of ref . @xcite . however , in a recent work , homogeneous and inhomogeneous scalar perturbations in the einstein static solutions were analyzed @xcite , consequently reconciling both of the above works . in the context of modified theories of gravity , the stability of the einstein static universe in @xmath3 gauss - bonnet modified gravity was also analyzed @xcite . in particular , by considering a generic form of @xmath3 , the stability regions of the einstein static universe were parameterized by the linear equation of state and the second derivative @xmath4 of the gauss - bonnet term . it was shown that stable modes for all equation of state parameters @xmath5 exist , if the parameters of the theory are chosen appropriately . thus , the results show that perturbation theory of modified theories of gravity present a richer stability / instability structure than in gr . thus , it is the purpose of the present paper to consider the stability of the einstein static universe by considering linear homogeneous perturbations in hoava - lifshitz gravity . indeed , this analysis is particularly important as the higher derivative terms in the action contributes with a @xmath6 term in the modified friedman equations . this contribution becomes dominant for small @xmath7 , and as mentioned above motivates this analysis , due to the possibility that the universe might have started out in an asymptotically einstein static state , in the inflationary universe context @xcite . on the other hand , the cosmological solutions of gr are recovered at large scales . it is shown that a large class of einstein static universes exist that are stable with respect to linear homogeneous perturbations . this paper is outlined in the following manner : in sec . [ sec : ii ] , we briefly review the action and field equations of hoava gravity , and the respective modified friedman equations . in sec . [ sec : iii ] , we consider linear homogeneous perturbations in the context of the einstein static universe in hoava gravity , and analyze the respective stability regions . in sec . [ sec : concl ] , we conlcude . using the adm formalism , the four - dimensional metric is parameterized by the following @xmath8 where @xmath9 is the lapse function , @xmath10 is the shift vector , and @xmath11 is the 3-dimensional spatial metric . in this context , the einstein - hilbert action is given by @xmath12 where @xmath13 is newton s constant , @xmath14 is the three - dimensional curvature scalar for @xmath11 , and @xmath15 is the extrinsic curvature defined as @xmath16 where the overdot denotes a derivative with respect to @xmath17 , and @xmath18 is the covariant derivative with respect to the spatial metric @xmath11 . consider the ir - modified hoava action given by @xmath19\ , , \label{haction}\end{aligned}\ ] ] where @xmath20 , @xmath21 , @xmath22 , @xmath23 , @xmath24 and @xmath25 are constant parameters . @xmath26 is the cotton tensor , defined as @xmath27 note that the last term in eq . ( [ haction ] ) represents a ` soft ' violation of the ` detailed balance ' condition , which modifies the ir behavior . this ir modification term , @xmath28 , generalizes the original hoava model ( we have used the notation of ref . @xcite ) . note that now these solutions with an arbitrary cosmological constant represent the analogs of the standard schwarzschild-(a)ds solutions , which were absent in the original hoava model @xcite . the fundamental constants of the speed of light @xmath29 , newton s constant @xmath13 , and the cosmological constant @xmath30 are defined as @xmath31 consider the homogeneous and isotropic cosmological solution given by the following metric @xmath32 \ , , \label{einst : metric2}\end{aligned}\ ] ] where @xmath33 corresponds to a closed , flat , and open universe , respectively . we assume that the matter contribution takes the form of a perfect fluid , with @xmath34 and @xmath35 the energy density and the pressure , respectively , so that the modified friedman equations in hoava gravity take the following form @xcite @xmath36\ , , \label{hfieldeq1 } \\ \frac{\ddot{a}}{a}&=&\frac{\kappa^2}{6(3\lambda-1 ) } \left[-\frac{1}{2}(\rho+3p ) + \epsilon \frac{3\kappa^2\mu^2}{8(3\lambda-1)}\left(\frac{k^2}{a^4 } -\lambda_w^2\right)\right]\ , , \label{hfieldeqs}\end{aligned}\ ] ] where @xmath37 . the analytic continuation @xmath38 for the ds case , i.e. , @xmath39 , is considered @xcite , and the upper ( lower ) sign denotes the ads ( ds ) case . it is interesting to note that the higher derivative term appearing in the action ( [ haction ] ) contributes with a @xmath6 term , and only exists for @xmath40 . this term dominates for low values of @xmath7 , and the general relativistic cosmological solutions are recovered for large scales . for the einstein static universe , @xmath41 and @xmath42 , the ricci scalar becomes @xmath43 , ( note that for @xmath44 , gr is obtained in the ir limit ) . furthermore , we consider a linear equation of state , @xmath45 , so that the field equations in this case are expressed in the following manner @xmath46}{6(1+w)^2(3\lambda-1)}\ , , \label{hfieldeqs2a } \\ \lambda_w a_0 ^ 2 & = & \frac{(1 + 3w)\mp\sqrt{4 - 6a_0 ^ 2 ( 1+w)(1 + 3w)\varpi } } { 3(1+w)}\ , , \label{hfieldeqs2}\end{aligned}\ ] ] where @xmath47 and @xmath48 are the unperturbed energy density and isotropic pressure , respectively . note that it is useful to introduce the dimensionless parameters @xmath49 and @xmath50 . these relationships are useful to be written in this form , as one has a first glance at the existence issue that @xmath47 and @xmath51 should be real , which imposes the following condition @xmath52 the above inequality needs to be analyzed for the three cases @xmath53 , @xmath54 and @xmath55 which places restrictions on the allowed values of @xmath56 . however , as we are primarily interested in a physically reasonable einstein static universe , we will furthermore require positivity of the energy density , @xmath57 . to further simplify the subsequent analysis , we will also assume @xmath58 . these useful conditions imply the following existence conditions for the upper sign of eq . ( [ hfieldeqs2a ] ) : @xmath59 which are depicted in the left plots of figs . [ fig1 ] and [ mfig1 ] , respectively . for the lower sign , of eq . ( [ hfieldeqs2a ] ) , we find : @xmath60 which are depicted in the right plots of figs . [ fig1 ] and [ mfig1 ] , respectively . the above inequalities with the upper and lower signs , and with @xmath61 , are represented graphically in fig . [ fig1 ] , and with @xmath62 in fig . [ mfig1 ] , respectively . note that there are many configurations which allow for an einstein static universe . this is in contrast with other modifications of gr , such as @xmath2 modified gravity , where there exists a unique background einstein static universe for every choice of @xmath2 . parameter space for the specific case of @xmath63 . the left panel shows the existence regions for the upper sign of eq . ( [ hfieldeqs2a ] ) , while the right panel is for the lower sign . the different shades of gray correspond to the different inequalitites.,title=""fig:"",scaledwidth=45.0% ] parameter space for the specific case of @xmath63 . the left panel shows the existence regions for the upper sign of eq . ( [ hfieldeqs2a ] ) , while the right panel is for the lower sign . the different shades of gray correspond to the different inequalitites.,title=""fig:"",scaledwidth=45.0% ] parameter space for the specific case of @xmath64 . the left panel shows the existence regions for the upper sign of eq . ( [ hfieldeqs2a ] ) , while the right panel is for the lower sign . the different shades of gray correspond to the different inequalitites.,title=""fig:"",scaledwidth=45.0% ] parameter space for the specific case of @xmath64 . the left panel shows the existence regions for the upper sign of eq . ( [ hfieldeqs2a ] ) , while the right panel is for the lower sign . the different shades of gray correspond to the different inequalitites.,title=""fig:"",scaledwidth=45.0% ] in what follows , we analyze the stability against linear homogeneous" +"the origin of ultra - high - energy ( uhe ) cosmic rays ( crs ) , that is of cosmic particles with energies @xmath0 ev , is presently unknown . however , there are numerous hints , both in data and in theory , which might help to constrain possible models of uhecr sources . in particular , the observation @xcite of the spectrum steepening consistent with the greisen zatsepin kuzmin @xcite ( gzk ) cutoff , together with the global isotropy of the arrival directions ( see e.g. @xcite ) and the fact that the uhe particles are not expected to be confined by the milky - way magnetic field ( see e.g. @xcite ) suggest that the bulk of cosmic rays at these energies have extragalactic origin . next , the lack of clustering of arrival directions at small scales is a powerful tool @xcite to constrain the number density of sources . in recent data of the pierre auger observatory ( pao ) , no evidence for clustering at @xmath1 ev is seen @xcite which translates into the number density of @xmath2 sources per cubic megaparsec , which means that sources of these extreme particles should not be exceptional and , most probably , some of them should be located relatively nearby . the latter fact gets further , though limited by statistical significance , support from the shape of the gzk feature in the spectrum which does not seem to be very sharp ( cf.ref . @xcite ) . on the other hand , it is a nontrivial task to find particular astrophysical objects which could serve as uhecr accelerators . even without a detailed modelling of the acceleration process , a number of simple estimates rule out many classes of potential sources . these simple criteria include in particular the geometrical ( hillas ) criterion @xcite and estimates of radiative energy losses of particles being accelerated ( see e.g. refs . analysis of the modern astrophysical data demonstrates @xcite that the combination of these constraints leaves just a few candidate classes of sources capable of acceleration of particles to uhe energies . leaving aside large - scale structures where interaction losses are expected to suppress the energy gain , the conventional diffusive ( e.g. , relativistic or non - relativistic shock ) acceleration may work only in ultrarelativistic jets , hot spots and lobes of exceptional active galaxies ( powerful radio galaxies and blazars ) which are not that abundant in the nearby universe . for very special field configurations when synchrotron losses are suppressed and the curvature radiation dominates , possible acceleration sites include also gamma - ray bursts ( grbs ) and immediate neighbourhood of supermassive black holes ( smbhs ) in the galactic nuclei . while it is unclear whether these field configurations may be present in grbs , recent icecube results disfavour the grb scenario anyway @xcite ( see however ref . @xcite ) . at this level of reasoning , the smbh environment remains a viable option . a natural assumption is that numerous uhecr sources are not identical there should be less and more powerful accelerators where the maximal energies , injection spectra and fluxes of accelerated particles are different . until now , numerous attempts to model the sources of uhecrs and to confront theoretical predictions with experiments often assumed that these parameters are fixed once and for the entire universe ( see e.g.refs . @xcite and numerous other works ; see however ref . @xcite where acceleration in non - identical jets was considered ) . while , for numerous sources , the assumption of equal fluxes is well justifiable ( in the sence that only the mean flux of a large sample of sources is important and this mean flux does not vary significantly from one region in the universe to another ) and the injection spectrum is often fixed by the acceleration model , the maximal energies are expected to vary significantly . as it was recognised in ref . @xcite , these variations affect the observable spectrum seriously . in this work , we attempt to present a toy model of numerous and different sources of uhecrs and , within certain assumptions , to confront it with the experimental data . to this end , we choose a simple toy model of particle acceleration in the immediate vicinity of smbh put forward in refs . the reason to choose this particular model is twofold . first , unlike many other models , it allows @xcite for uhecr acceleration in numerous nearby sources . second , as we will see below , within some realistic assumptions , the acceleration capabilities of a source are determined by a single parameter , the smbh mass . at the same time , the demography of smbhs is well studied by astrophysicists and we take this advantage to describe the population of sources easily . the rest of the paper is organized as follows . in sec . [ sec : bh ] , we give a brief review of the acceleration model of refs . @xcite and make a bridge between the parameters which determine the maximal energy of accelerated particles and the smbh mass . in sec.[sec : population ] , we discuss the astrophysical data on the smbh population , merge them with the acceleration model , calculate the spectrum of uhecrs with the account of propagation from source to the observer and compare it with the experimental cosmic - ray data . we obtain a good agreement with the observed spectrum by fitting the spectrum with only two continuous parameters , the overall normalization and a single free parameter of the model . [ sec : constraints ] demonstrates that the population model of sec . [ sec : population ] satisfies simple observational constraints : it does not produce too much secondary gamma rays , it results in an acceptable number density of sources and , with the best - fit normalization , it does not require enormous luminosity of a single source . we give our conclusions and discuss our results in sec . [ sec : concl ] . a toy model of particle acceleration in the black - hole magnetosphere was proposed by neronov et al . @xcite . let us briefly discuss the model and its parameters . assume that a stationary rotating black hole without electric charge is embedded into the external magnetic field , homogeneous at the horizon distance scale . in general , the magnetic field is inclined at some angle @xmath3 with respect to the black - hole rotation axis . there is a well - known exact solution of maxwell s equations in the kerr metric for each inclination angle @xmath3 of an asymptotically homogeneous magnetic field @xcite . for instance , if @xmath4 , then a rotation - induced electric field is parallel to the magnetic one on the symmetry axis and its direction depends on the directions of both the magnetic field and the black hole s rotation velocity . thus in the region near the rotation axis , particles moving along magnetic lines are accelerated by the electric field . in this case , radial components of the electric and magnetic fields in units @xmath5 in locally non - rotating frame in boyer - lindquist coordinates on the symmetry axis are : @xmath6 @xmath7 where @xmath8 is the black hole s mass , @xmath9 is its angular momentum per unit mass , @xmath10 is the radial coordinate and @xmath11 is the external homogeneous magnetic field . neglecting for the moment the energy losses , the maximal energy gain of the accelerating particle with a charge @xmath12 is determined by the available potential difference in the region along the rotation axis , @xmath13 @xmath14 is the radius of the black - hole horizon where particle acceleration starts while @xmath15 limits the size of the region along the rotation axis , where acceleration is possible ( in ref . @xcite , it is called `` the vacuum gap '' due to the absence of numerous charged particles in this region except of the single test particle being accelerated , which does not change the electromagnetic field ) . of course , one can rewrite eq . ( [ eq:2 ] ) for the potential difference and @xmath16 in terms of the distance - averaged electric field @xmath17 , @xmath18 @xmath19 where @xmath20 . by making use of eq . ( [ eq:1 ] ) one obtains @xmath21 @xmath22.\ ] ] it is easy to see that the expression in square brackets equals to @xmath23 and therefore is always negative for any value of @xmath24 ( remember that the angular momentum per unit mass @xmath25 varies between zero and @xmath8 ) . thus for parallel magnetic field and angular momentum , @xmath26 and the radial component of the electric field @xmath27 on the black - hole rotation axis is negative . so if there are negative charges near the rotation axis , they will be accelerated away from the black hole . according to eq . ( [ eq:4 ] ) the difference between their energies at @xmath15 and @xmath28 is positive , so they gain energy while moving along the rotation axis away from the black hole . in the opposite case , when the magnetic field and angular momentum are antiparallel , the radial component of the electric field on the black hole rotation axis is positive . so positive - charge particles , situated near the rotation axis , are accelerated away from the black hole ; according to eq . ( [ eq:4 ] ) , the energy gain in this case is positive for the positive - charge particles . in ref . @xcite , a simple expression @xmath29 rather than eq . ( [ eq:4 ] ) was used ; however , more precisely , eq . ( [ eq:4 ] ) implies @xmath30 . the dependence of @xmath31 from the angular momentum @xmath25 for different @xmath24 is shown in fig . [ f_1 ] . dependence of the normalized maximal energy @xmath32 from the angular momentum @xmath25 of the black hole with mass @xmath8 for different values of the vacuum - gap size @xmath24 ( curves labeled by values of @xmath33 ; see the text for definitions of parameters ) . , scaledwidth=48.0% ] for black holes with angular momentum @xmath34 and @xmath35 , we have @xmath36 ; however , for slowly rotating black holes , @xmath37 , @xmath38 varies from zero to @xmath39 . hereafter , @xmath40 denotes the schwarzschild radius . however , the precise value of @xmath16 is often irrelevant since particles can not achieve this maximal energy because of inevitable energy losses associated with the accelerated motion of the particle . the particle energy is determined by the balance between the energy losses and the energy gain per unit time , @xmath41 it was shown in ref . @xcite that protons can be accelerated to the energies of about @xmath42 ev only if the magnetic field is almost aligned with the rotation axis . in this case , only the curvature radiation is relevant for an accelerated particle , and not the synchrotron one . we should also note here that we do not consider energy losses related to interactions of accelerated particles in the source . the maximal energy of an accelerated particle is @xmath43 @xmath44 where @xmath11 is the external magnetic field , @xmath45 is the curvature radius of magnetic - field lines , @xmath12 is the particle charge , @xmath46 is the particle mass ( @xmath47 is the atomic number and @xmath48 is the nucleon mass ) and @xmath49 is a coefficient between the electric field and the external magnetic field , @xmath50 ( see eq . ( [ eq:1 ] ) ) . note that @xmath49 is a function" +"random matrix theory ( rmt ) has been applied in surprisingly many fields of physics and mathematics . we have proposed in a recent letter @xcite its application to transfer matrices of lattice models in classical statistical mechanics . in a preceding paper @xcite , referred to hereafter as paper i , we have given the details of this rmt analysis applied to the general eight - vertex model . we have numerically shown that the integrability of the model can be seen on the statistical properties of the entire spectrum of transfer matrices of vertex models . using this as a criterion for integrability , we have located all the known integrable varieties in the parameter space . in this paper we continue this work with the study of spin models . many aspects have already been presented in paper i , so we will recall below only the basic ideas of the rmt analysis with emphasis on the points which are specific to spin models . an important area of application of rmt is the characterization of chaos @xcite . one can describe the fluctuations of energy spectra of chaotic systems with some ensembles of rmt , while the spectra of regular systems show the characteristics of independent numbers ( poissonian ensemble ) . in classical ( hamiltonian ) mechanics , the notions of regular and chaotic dynamics coincide with the notions of integrability and non - integrability . but in quantum mechanics the notions of chaos and integrability are less precise ; one nowadays adopts the criterion of rmt as a definition of quantum chaos . for models of quantum statistical mechanics one can adopt a definition of integrability related to the bethe ansatz : an integrable system is a system for which a complete set of eigenstates having the bethe ansatz form exists . for a classical statistical mechanics model , the notion of integrability is generally related to the yang baxter equations . for example , solving the yang baxter equations for the symmetric eight - vertex model ( also called the baxter model ) allows to build a one - parameter family of commuting transfer matrices , and finally to compute the free energy of the model @xcite . the spin version of the yang - baxter equations are the star - triangle equations which have been introduced earlier @xcite . solving these star - triangle equations also allows to construct an infinite family of commuting transfer matrices . we note that a vertex model can be turned into a spin model with many - spin interactions ( irf model ) ( see for example @xcite ) . in this paper , we treat spin models including only two - spin interactions , possibly coupled to an external field , and by integrable we mean yang - baxter integrable as well as star - triangle integrable . the spectrum of an integrable system , after a suitable treatment , has been shown to have many properties of a set of random _ independent _ numbers ( poissonian behavior ) , while the spectrum of a chaotic system is described quite accurately by the spectrum of matrices of statistical ensembles . the choice of the proper ensemble depends on very general symmetry properties of the model under consideration . for a time reversal symmetric model this ensemble is the gaussian orthogonal ensemble ( goe ) @xcite . this classification scheme has been applied succesfully to quantum spin models in one dimension @xcite and on two - dimensional lattices @xcite . for a classical lattice spin model , the energy spectrum is usually very simple . ( for an ising model this spectrum contains all the possible numbers of violated bonds i.e. the set of integers @xmath0 $ ] where @xmath1 is the number of bonds ; the physical properties of the model are contained in the degeneracies , its statistical properties have been studied in ref . therefore the analysis has to be performed on another quantity . the transfer matrix is such an operator ( related to the hamiltonian ) which describes completely the thermodynamic properties of a system including the size effects @xcite , and we will perform the rmt analysis on its spectrum . it has already been shown in paper i and in @xcite that the notion of yang baxter integrability coincides with a poissonian spectrum , and that nonintegrable spectra are described by goe matrix spectra . to perform this rmt analysis in its usual form , one needs to deal with a real spectrum . for spin models and when the interactions are nonchiral ( symmetric ) , this can be achieved using the so - called row - to - row ( or layer - to - layer in higher dimension ) transfer matrix as explained below . we also have studied the spectra in the nonphysical regime where the boltzmann weights are not positive . indeed , most of the analytical results concern varieties in the entire parameter space including the region where the boltzmann weights are negative . in this region , even row - to - row transfer matrices can have complex eigenvalues . the necessary changes in the analysis will be briefly discussed . the plan of this paper is the following . in sec . [ s : numeric ] we recall the numerical methods of the rmt analysis with a special emphasis on the specificity of the spin models we investigate . in sec . [ s : results ] we present the numerical results , succesively of the two - dimensional ising model in absence of magnetic field ( a paradigm of an integrable system ! ) , the same two - dimensional ising model in a magnetic field , the three - dimensional ising model ( a paradigm of nonintegrable system ! ) , and the three - state potts model . the three - state potts model provides an example of a point which is integrable and critical at the same time . by contrast , the three - dimensional ising model provides a nonintegrable , but critical , point . finally , we investigate a nonphysical self - dual point of the three - state potts model . this is a first attempt to study complex spectra in the context of this statistical analysis of transfer matrices . we conclude in sec . [ s : conclusion ] with a discussion . the machinery of random matrix theory has been explained in details in paper i. it consists in five distinct steps : * the first one is to choose a representation basis for the operator and to construct the corresponding matrix ; * the second step consists in finding the parameter - independent stable subspaces and find the matrices representing the operator in each of these subspaces ; * the third step is to diagonalize each matrix ; * the fourth step is to ` unfold ' each spectrum ; * and in the fifth step all the spectral quantities are computed . in this section , we briefly discuss these five points and give the details which are specific to the spin models studied in this paper . \(i ) we use the transfer matrix formalism , where the lattice is built up adding identical `` generating sub - lattices '' . these generating sublattices can be rows for two - dimensional models or rectangular layers for three - dimensional lattices . for spin models , it is well known that this transfer matrix can be factorized as : @xmath2 where @xmath3 contains the interactions between two generating sub - lattices and @xmath4 contains the interactions inside a generating sub - lattice ; @xmath4 is usually a diagonal matrix . @xmath5 are the coupling constants in the different directions , we assign the direction 1 to be the direction in which the lattice grows . for each case we study in this paper , the precise form of @xmath4 and @xmath3 are given in the corresponding section . in the form ( [ e : transfer ] ) the transfer matrix is a symmetric matrix if the interaction between the two layers and thus the matrix @xmath3 is symmetric . if the boltzmann weights are real positive , the entries of the transfer matrix are also real positive . in this case of a real and symmetric ( transfer ) matrix the spectrum is real so that the methods for the statistical analysis presented in paper i apply . \(ii ) to find the parameter independent subspaces one needs to know the symmetries of the generating sub - lattices . for the transfer matrix of a @xmath6-dimensional hyper - cubic lattice these generating sub - lattices are @xmath7-dimensional lattices . for the square lattice , the generating sub - lattice is a periodic chain . as explained in paper i the symmetry group is the dihedral group @xmath8 . for a three - dimensional cubic lattice we use a square lattice as the generating sub - lattice . for an isotropic square lattice the automorphy group has been detailed in @xcite ( with emphasis on the atypical case @xmath9 ) . it is a large group which leads to consequent size reduction ( see sec . [ ss : ising3d ] ) . in addition to these space symmetries there is a ` color symmetry ' when no field is applied . this symmetry reflects the fact that the hamiltonian is invariant under a permutation of the possible values of the spin variables ( i.e. spin reversal symmetry for the ising model ) . for a @xmath10-state model , this is a @xmath11 symmetry ; in this paper we work with @xmath12 and @xmath13 . this ` color - symmetry ' commutes with the space symmetries . \(iii ) the diagonalization of the blocks is done numerically using standard procedures of the lapack library . we note that the block - diagonalization of step ( ii ) requires more numerical effort ( cpu time ) than the diagonalization of one block . \(iv ) the unfolding procedure is the same as the procedure detailed in paper i. it produces the unfolded eigenvalues @xmath14 from the raw eigenvalues @xmath15 . the spectra of spin and vertex models are quite similar . however , we also have analyzed _ complex _ spectra . in that case the eigenvalues are seen as points in the plane ( and not on a line ) the local density of which has to be made constant . to unfold complex spectra we follow the procedure described in chap . 8.6 of ref . @xcite . \(v ) the spectral analysis is performed on the same quantities as in paper i. these are the level spacing distribution @xmath16 of the differences between two consecutive unfolded eigenvalues @xmath17 ( for a nonintegrable model , the eigenvalue spacing distribution is very close to the wigner surmise for the goe : @xmath18 in contrast , with the exponential @xmath19 for a set of independent eigenvalues for an integrable model ) ; the spectral rigidity : @xmath20 where @xmath21 is the integrated density of unfolded eigenvalues and @xmath22 denotes an average over @xmath23 ; another quantity of interest is the number variance @xmath24 defined as the variance of the number of unfolded eigenvalues in an interval of length @xmath25 : @xmath26 ^ 2 \right\rangle_{\varepsilon},\ ] ] where the brackets denote an averaging over @xmath27 . the expected behavior in the limiting cases of independent numbers and of goe spectra has been recalled in paper i ; for more details see for example refs . @xcite . we also recall the parametrized probability distribution we use to interpolate between the poisson law and the wigner law : ( * ? ? ? 16.8 ) : @xmath28 with @xmath29^{1+\beta}$ ] . the interpolation parameter @xmath30 proved itself to be" +"we choose as the starting point of the present work the fundamental problem of channel simulation . roughly speaking , this problem asks when a communication channel @xmath1 from alice ( a ) to bob ( b ) can be used to simulate another channel @xmath2 , also from a to b ? @xcite this problem has many variants according to the resources available to a and b. in particular , the case when a and b can access unlimited amount of shared entanglement has been completely solved . let @xmath3 denote the entanglement - assisted classical capacity of @xmath1 @xcite . it was shown that , in the asymptotic setting , to optimally simulate @xmath2 , we need to apply @xmath1 at rate @xmath4 @xcite . in other words , the entanglement - assisted classical capacity uniquely determines the properties of the channel in the simulation process . furthermore , even with stronger resources such as no - signalling correlations or feedback , this rate can not be improved otherwise we would violate causality , see @xcite for a discussion . here we are interested in the zero - error setting @xcite . it is well known that the zero - error communication problem is extremely difficult , already for classical channels . indeed , the single - shot zero - error classical communication capability of a classical noisy channel equals the independence number of the ( classical ) confusability graph induced by the channel , and the latter problem is well - known to be np - complete . the behaviour of quantum channels in zero - error communication is even more complex as striking effects such as super - activation are possible @xcite . the most general zero - error simulation problem remains wide open . to overcome this difficulty , many variants of this problem have been proposed . the most natural way is to introduce some additional resources and see how this changes the capacity . indeed , extra resources such as classical feedback @xcite , entanglement @xcite , and even a small ( constant ) amount of forward communication @xcite , have been introduced . it has been shown these extra resources can increase the capacity , and generally simplify the problem . in particular , it was shown that even for classical communication channel , shared entanglement can strictly increase the asymptotic zero - error classical capacity @xcite . however , determining the entanglement - assisted zero - error classical capacity remains an open problem even for classical channels . more powerful resources are actually required in order to simplify the problem . @xcite introduced classical no - signalling correlations into the zero - error communication for classical channels , and showed that the well - known fractional packing number of the bipartite graph induced by the channel , gives precisely the zero - error classical capacity of the channel . previously , it was known by shannon that this fractional packing number corresponds to the zero - error classical capacity of the channel when assisted with a feedback link from the receiver to the sender and when the unassisted zero - error classical capacity is not vanishing @xcite . for general background on graph theory see @xcite , and for `` fractional graph theory '' the delightful book @xcite . another major motivation for this work is to further explore the connection between quantum information theory and the so - called `` non - commutative graph theory '' suggested in @xcite . such a connection has been well - known in classical information theory . in @xcite , shannon realized that the zero - error capacity of a classical noisy channel only depends on the confusability graph induced by the channel . he further pointed out that in the presence of classical feedback , the zero - error capacity is completely determined by the bipartite graph of possible input - output transitions associated with the channel . thus it makes sense to talk about the zero - error capacity of a ( bipartite ) graph . the notion of non - commutative graph naturally occurs when we use quantum channels for zero - error communication . for any quantum channel , the non - commutative graph associated with the channel captures the zero - error communication properties , thus playing a similar role to confusability graph . most notably , this notion also makes it possible to introduce a quantum lovsz @xmath0 function to upper bound the entanglement - assisted zero - error capacity that has properties quite similar to its classical analogue @xcite . very recently , it was shown that the zero - error classical capacity of a quantum channel in the presence of quantum feedback only depends on the kraus operator space of the channel @xcite . in other words , the kraus operator space plays a role that is quite similar to the bipartite graph . now it becomes clear that any classical channel induces a bipartite graph as well as a confusability graph , while a quantum channel induces a non - commutative bipartite graph and a non - commutative graph . the new insight is that we can simply regard a non - commutative ( bipartite ) graph as a high - level abstraction of all underlying quantum channels , and study its information - theoretic properties , not limited to zero - error setting . this leads us to a very general viewpoint : graphs as communication channels . for instance , we can define the entanglement - assisted classical capacity of a non - commutative bipartite graph as the minimum of the entanglement - assisted classical capacity of quantum channels that induce the given kraus operator space . it was shown that this quantity enjoys a number of interesting properties including additivity under tensor product and an operational interpretation as a sort of entanglement - assisted conclusive capacity of the bipartite graph @xcite . it remains a great challenge to find tractable forms of various capacities for non - commutative ( bipartite ) graphs . in this paper we consider a more general class of quantum no - signalling correlations described by two - input and two - output quantum channels with the no - signalling constraints . this kind of correlations naturally arises in the study of the relativistic causality of quantum operations @xcite ; see also the more recent @xcite . distinguishability of these correlations from an information theoretic viewpoint has also been studied @xcite . we provide a number of new properties of these correlations , and establish several structural theorems of these correlations . then we generalize the approach of @xcite to study the zero - error classical capacity of a noisy quantum channel assisted by quantum no - signalling correlations , and the reverse problem of perfect simulation . we show that both problems can be completely solved in the one - shot scenario , revealing some nice structure : 1 . the answers are given by semidefinite programmes ( sdps , cf . @xcite ) ; 2 . at the same time they generalize the results of cubitt _ et al . _ @xcite ; 3 . for the simulation , the question is really how to form a constant channel by a convex combination of the one we want to simulate and an arbitrary other quantum channel , and the number of bits needed is just @xmath5 , where @xmath6 is the probability weight of the target channel in the convex combination ( throughout this paper , @xmath7 denotes the binary logarithm ) ; 4 . for assisted communication , there is an analogous problem of convex - combing a certain channel from b to a which has some kind of orthogonality relation with the given channel from a to b , with another one to form a constant channel . if the target channel has weight @xmath6 , then the number of bits sent is again @xmath5 . most interestingly , the solution to the communication problem only depends on the kraus operator space of the channel , not directly on the channel itself . for the simulation problem , the solution is given by the conditional min - entropy @xcite of the channel s choi - jamiokowski matrix , and is actually additive , thus also gives the asymptotic cost of simulating the channel . if we are interested in simulating the cheapest channel contained in the kraus operator space , we obtain an sdp in terms of the projection of the choi - jamiokowski matrix . both the capacity and the simulation sdps are in general not known to be multiplicative under the tensor product of channels , thus we do not know the optimal asymptotic simulation cost . we then focus on the asymptotic zero - error classical capacity and simulation cost assisted with quantum no - signalling correlations . this requires determining the asymptotic behaviour of a sequence of sdps . in general the one - shot solution does not give the asymptotic result , since the corresponding sdp is not multiplicative with respect to the tensor product of channels . a simple formula for the asymptotic channel capacity remains unknown . however , for the special cases of classical - quantum ( cq ) channels , we find that the zero - error capacity is given by the solution of a rather simple sdp suggested earlier by harrow as a natural generalization of the classical fractional packing number @xcite , which we call _ semidefinite packing number_. this result has two interesting corollaries . first , it implies that the zero - error classical capacity of cq - channels assisted by quantum no - signalling correlations is additive . second , and more importantly , we show that for a classical graph @xmath8 , the celebrated lovsz number @xmath9 @xcite , is actually the minimum zero - error classical capacity of any cq - channel that has the given graph as its confusability graph . in other words , lovsz @xmath0 function is the zero - error classical capacity of a graph assisted by quantum no - signalling correlations . to the best of our knowledge , this is the first information theoretic operational interpretation of the lovsz number since its introduction in 1979 . previously , it was known that it is an upper bound on the entanglement - assisted zero - error classical capacity of a graph @xcite . it remains unknown whether the use of quantum no - signalling correlations could be replaced by shared entanglement . the asymptotic simulation cost for kraus operator spaces associated with cq - channels is rather simpler , and is actually given by the one - shot simulation cost . before we proceed to the technical details , it may be helpful to present an overview of our main results . let @xmath1 be a quantum channel from @xmath10 to @xmath11 , with a kraus operator sum representation @xmath12 where @xmath13 . let @xmath14 denote the kraus operator space of @xmath1 . the choi - jamiokowski matrix of @xmath1 is given by @xmath15 , where @xmath16 and @xmath17 are isomorphic hilbert spaces , @xmath18 ( @xmath19 ) is orthonormal basis over @xmath16 ( @xmath17 , resp . ) , and @xmath20 is the unnormalized maximally entangled state over @xmath21 . recall that @xmath22 . let @xmath23 denote the projection onto the support of @xmath24 , which is the subspace @xmath25 , sometimes called the choi - jamiokowski support of @xmath26 ( or of the channel ) . it is worth noting that many results below can be defined on any matrix subspace @xmath26 , not just those corresponding to a quantum channel @xmath1 . however , we have to make sure that @xmath26 is actually corresponding to some quantum channel @xmath1 . this puts an additional constraint on @xmath26 . more precisely" +"as is well - known , the logical theory @xmath5 , sometimes called presburger arithmetic , is decidable @xcite . bchi @xcite showed that if we add the function @xmath6 , for some fixed integer @xmath7 , where @xmath8 , then the resulting theory is still decidable . this theory is powerful enough to define finite automata ; for a survey , see . as a consequence , we have the following theorem ( see , e.g. , @xcite ) : there is an algorithm that , given a proposition phrased using only the universal and existential quantifiers , indexing into one or more @xmath9-automatic sequences , addition , subtraction , logical operations , and comparisons , will decide the truth of that proposition . [ one ] here , by a @xmath9-automatic sequence , we mean a sequence @xmath10 computed by deterministic finite automaton with output ( dfao ) @xmath11 . here @xmath12 is the input alphabet , @xmath13 is the output alphabet , and outputs are associated with the states given by the map @xmath14 in the following manner : if @xmath15 denotes the canonical expansion of @xmath16 in base @xmath9 , then @xmath17 = \kappa(\delta(q_0 , ( n)_k))$ ] . the prototypical example of an automatic sequence is the thue - morse sequence @xmath18 , the fixed point ( starting with @xmath19 ) of the morphism @xmath1 , @xmath20 . it turns out that many results in the literature about properties of automatic sequences , for which some had only long and involved proofs , can be proved purely mechanically using a decision procedure . it suffices to express the property as an appropriate logical predicate , convert the predicate into an automaton accepting representations of integers for which the predicate is true , and examine the automaton . see , for example , the recent papers . furthermore , in many cases we can explicitly enumerate various aspects of such sequences , such as subword complexity . beyond base @xmath9 , more exotic numeration systems are known , and one can define automata taking representations in these systems as input . it turns out that in the so - called pisot numeration systems , addition is computable , and hence a theorem analogous to theorem [ one ] holds for these systems . see , for example , . it is our contention that the power of this approach has not been widely appreciated , and that many results , previously proved using long and involved ad hoc techniques , can be proved with much less effort by phrasing them as logical predicates and employing a decision procedure . furthermore , many enumeration questions can be solved with a similar approach . we have implemented a decision algorithm for one such system ; namely , fibonacci representation . in this paper we report on our results obtained using this implementation . we have reproved many results in the literature purely mechanically , as well as obtained new results , using this implementation . the paper is organized as follows . in section [ fibrep ] , we briefly recall the details of fibonacci representation . in section [ proofsf ] we report on our mechanical proofs of properties of the infinite fibonacci word ; we reprove many old results and we prove some new ones . in section [ finitefib ] we apply our ideas to prove results about the finite fibonacci words . in section [ rotefib ] we study a special infinite word , the rote - fibonacci word , and prove many properties of it , including a new avoidability result . in section [ other ] we look briefly at another sequence , the fibonacci analogue of the thue - morse sequence . in section [ additive ] we apply our methods to another avoidability problem involving additive squares . in section [ enumer ] we report on mechanical proofs of some enumeration results . some details about our implementation are given in the last section . let the fibonacci numbers be defined , as usual , by @xmath21 , @xmath22 , and @xmath23 for @xmath24 . ( we caution the reader that some authors use a different indexing for these numbers . ) it is well - known , and goes back to ostrowski @xcite , lekkerkerker @xcite , and zeckendorf @xcite , that every non - negative integer can be represented , in an essentially unique way , as a sum of fibonacci numbers @xmath25 , subject to the constraint that no two consecutive fibonacci numbers are used . for example , @xmath26 . also see @xcite . such a representation can be written as a binary string @xmath27 representing the integer @xmath28 . for example , the binary string @xmath29 is the fibonacci representation of @xmath30 . for @xmath31 , we define @xmath32_f : = \sum_{1 \leq i \leq n } a_i f_{n+2-i}$ ] , even if @xmath27 has leading zeroes or consecutive @xmath33 s . by @xmath34 we mean the _ canonical _ fibonacci representation for the integer @xmath16 , having no leading zeroes or consecutive @xmath33 s . note that @xmath35 , the empty string . the language of all canonical representations of elements of @xmath36 is @xmath37 . just as fibonacci representation is the analogue of base-@xmath9 representation , we can define the notion of _ fibonacci - automatic sequence _ as the analogue of the more familiar notation of @xmath9-automatic sequence . we say that an infinite word @xmath38 is fibonacci - automatic if there exists an automaton with output @xmath39 that @xmath40 for all @xmath41 . an example of a fibonacci - automatic sequence is the infinite fibonacci word , @xmath42 which is generated by the following 2-state automaton : ( q_0 ) @xmath43 ; ( q_1 ) [ right = of q_0 ] @xmath44 ; ( q_0 ) edge [ loop above ] node 0 ( ) ( q_0.10 ) edge node 1 ( q_1.170 ) ( q_1.190 ) edge node 0 ( q_0.350 ) ; to compute @xmath45 , we express @xmath46 in canonical fibonacci representation , and feed it into the automaton . then @xmath45 is the output associated with the last state reached ( denoted by the symbol after the slash ) . another characterization of fibonacci - automatic sequences can be found in @xcite . a basic fact about fibonacci representation is that addition can be performed by a finite automaton . to make this precise , we need to generalize our notion of fibonacci representation to @xmath47-tuples of integers for @xmath48 . a representation for @xmath49 consists of a string of symbols @xmath50 over the alphabet @xmath51 , such that the projection @xmath52 over the @xmath46th coordinate gives a fibonacci representation of @xmath53 . notice that since the canonical fibonacci representations of the individual @xmath53 may have different lengths , padding with leading zeroes will often be necessary . a representation for @xmath54 is called canonical if it has no leading @xmath55 $ ] symbols and the projections into individual coordinates have no occurrences of @xmath56 . we write the canonical representation as @xmath57 . thus , for example , the canonical representation for @xmath58 is @xmath59[1,0][0,0][0,1][0,0][1,0]$ ] . thus , our claim about addition in fibonacci representation is that there exists a deterministic finite automaton ( dfa ) @xmath60 that takes input words of the form @xmath61^ * ( x , y , z)_f$ ] , and accepts if and only if @xmath62 . thus , for example , @xmath60 accepts @xmath63[1,0,0][0,1,0][1,0,1]$ ] , since the three strings obtained by projection are @xmath64 , which represent , respectively , @xmath65 , @xmath66 , and @xmath67 in fibonacci representation . this result is apparently originally due to berstel @xcite ; also see . since this automaton does not appear to have been given explicitly in the literature and it is essential to our implementation , we give it here . the states of @xmath60 are @xmath68 , the input alphabet is @xmath69 , the final states are @xmath70 , the initial state is @xmath71 , and the transition function @xmath72 is given below . the automaton is incomplete , with any unspecified transitions going to a non - accepting dead state that transitions to itself on all inputs . this automaton actually works even for non - canonical expansions having consecutive @xmath33 s ; an automaton working only for canonical expansions can easily be obtained by intersection with the appropriate regular languages . the state @xmath19 is a `` dead state '' that can safely be ignored . .transition table for @xmath60 for fibonacci addition [ cols=""^,^,^,^,^,^,^,^,^"",options=""header "" , ] we use the predicate @xmath73[i][i+n]=0 ) \wedge ( \forall j < i\ ( \exists t<2n \ ( { \bf f}[j+t]\not= { \bf f}[i+t]))).\ ] ] to create the matrices and vectors . @xmath74 infinitely often and @xmath75 infinitely often . more precisely @xmath74 iff @xmath76 or @xmath77 for @xmath78 , and @xmath75 iff @xmath79 for @xmath78 . for the first statement , we create a dfa accepting those @xmath34 for which @xmath74 , via the predicate @xmath80[i][i+n]=0 ) \wedge ( \operatorname{fab}[n][j][j+n]=0 ) ) \implies ( \forall t<2n \ ( { \bf f}[j+t ] = { \bf f}[i+t])).\ ] ] the resulting @xmath67-state automaton accepts the set specified . for the second result , we first compute the minimal polynomial of the matrix @xmath81 of the linear representation . it is @xmath82 . this means that , for @xmath83 , we have @xmath84 where , as usual , @xmath85 and @xmath86 . solving for the constants , we determine that @xmath87 for @xmath24 , as desired . to show that these are the only cases for which @xmath75 , we use a predicate that says that there are not at least three different factors of length @xmath88 that are not abelian squares . running this through our program results in only the cases previously discussed . finally , we turn to abelian cubes . unlike the case of squares , some orders do not appear in @xmath3 . the fibonacci word @xmath3 contains , as a factor , an abelian cube of order @xmath16 iff @xmath34 is accepted by the automaton below . , width=624 ] theorem [ fibr ] has the following interesting corollary . let @xmath89 be an arbitrary morphism such that @xmath90 . then @xmath91 is an infinite fibonacci - automatic word . from theorem [ fibr ] we see that there is a predicate @xmath92 which is true if @xmath93|_0 $ ] and false otherwise , and this predicate can be implemented as a finite automaton taking the inputs @xmath16 and @xmath94 in fibonacci representation . suppose @xmath95 and @xmath96 . now , to show that h(*f * ) is fibonacci - automatic , it suffices to show that , for each letter @xmath97 , the language of `` fibers '' @xmath98 = a \}\ ] ] is regular . to see this , we write a predicate for the @xmath16 in the definition of @xmath99 , namely @xmath100)| ) \ \wedge \ \operatorname{zc}(m , r_0 ) \ \wedge \ ( r_0+r_1=m ) \wedge \\ ( r_0 |w| + r_1 |x| = q ) \ \wedge \ ( ( { \bf f}[m]=0 \ \wedge \ w[n - q ] = a ) \ \vee \ ( { \bf f}[m ] = 1 \ \wedge\ x[n - q ] = a ) ) .\end{gathered}\ ] ] notice that the predicate looks like it uses multiplication , but this multiplication can be replaced by repeated addition since @xmath101 and @xmath102 are constants here . unpacking this predicate we see that it asserts the existence of @xmath103 , @xmath104 , @xmath105 , and @xmath106 having the meaning that * the @xmath16th symbol of h(*f * ) lies inside the block @xmath107)$ ] and is in fact the @xmath108th symbol in the block ( with the first symbol being" +"distributed computing provides an effective means of utilizing a network of limited capacity quantum computers . by connecting a network of limited capacity quantum computers via classical and quantum channels , a group of small quantum computers can simulate a quantum computer with a large number of qubits . this approach is useful for the development of quantum computers because the earliest useful quantum computers will most likely hold only a small number of qubits . this constraint limits the usage of such quantum computers to small problems . we propose that distributed quantum computing ( dqc ) is a possible solution to this problem . furthermore , even if one could construct a large quantum computer , the distributed computing model can still provide an effective means of increasing computational power . by a distributed quantum computer , we mean a network of small quantum computers , connected by classical and quantum channels . each quantum computer ( or node ) has a register that can hold only a limited number of qubits . each node also possesses a small number of channel qubits which can be sent back and forth over the network . a qubit in a register can freely interact with any other qubit in the same register . it also can freely interact with channel qubits that are in the same node . to interact with qubits on a remote computer , the qubits have to be teleported or physically transported to the remote computer , or have to interact via non - local operations . indeed , distributed quantum computing can simply be implemented by teleporting or physically transporting qubits back and forth . a more efficient implementation of dqc has been proposed by eisert et al @xcite using a non - local cnot gate . since the control not gate ( cnot ) together with all one - qubit gates is universal @xcite , a distributed implementation of any unitary transformation reduces to the implementation of non - local cnot gates . eisert et al also prove that one shared entangled pair ( ebit ) and two classical bits ( cbits ) are necessary and sufficient to implement a non - local cnot gate . in this paper , we present two primitive operations , cat - entangler and cat - disentangler , which in turn can be used to implement non - local operations , e.g. a non - local cnot and quantum teleportation protocol . the cat - entangler and cat - disentangler can be implemented using only local operation and classical communication ( locc ) , assuming that an entanglement has already been established . we show how to establish an entangled pair between two nodes , and use entangled pairs to efficiently create a generalized ghz state . furthermore , we present procedures which allow us to reuse channel qubits in a sequence of non - local operations . to implement a non - local cnot gate , first an entangled pair must be established between two computers . then the cat - entangler transforms a control qubit @xmath0 and an entangled pair @xmath1 into the state @xmath2 , called a `` cat - like '' state . this state allows two computers to share the control qubit . as a result , each computer now can use a qubit shared within the cat - like state as a local control qubit . after completion of the control operation , cat - disentangler is then applied to disentangle and restore the control qubit from the cat - like state . finally , the channel qubits are then be reset so that the entangled pair can be re - established . to teleport an unknown qubit to a target qubit , we begin by establishing an entangled pair between two computers . then we apply the cat - entangler operation to create a cat - like state from an unknown qubit and the entangled pair . after that , we apply a slightly modify cat - disentangler operation to disentangle and restore the unknown qubit from the cat - like state into the target qubit . finally , we reset the channel qubits . in other words , quantum teleportation can be considered as a composition of the cat - entangler operation followed by the cat - disentangler operation . the cat - entangler and cat - disentangler operations can be extended to a multi - party environment by replacing the entangled pair with a generalized greenberger - horne - zeilinger ( ghz ) state ( also called a cat state ) expressed as @xmath3 . the state @xmath4 ( also called a cat - like state ) can be created using only locc . a cat - like state can be used to share a control qubit between multiple computers , allowing each computer to use a qubit shared within the cat - like state as a local control line . in many cases , this idea leads to an efficient implementation of multi - party control gates . in addition , a parallel implementation of some unitary transformations can also be realized . before performing any non - local operation , an entanglement between computers must be established . moreover , the entanglement has to be refreshed after its use . brennen , song , and williams address this issue in a lattice model quantum computer using entanglement swapping @xcite , which can be used to establish and refresh entanglement between two qubits . the multiple entanglement swapping @xcite can create a generalized ghz state , which is used by multiple computers . we address these same issues for the quantum network model by showing how to establish two entangled pairs by sending two qubits , one in each direction . asymptotically , this is equivalent to establishing one entangled pair at the cost of sending one qubit . furthermore , we show how to convert a number of entangled pairs into a generalized ghz state , which in turn is used to distribute control over multiple computers . we also address refreshing entanglement by observing that measurements , made during the primitive operations , provide crucial information for resetting channel qubits to @xmath5 . hence , channel qubits can be re - entangled with other channel qubits at a later time . the idea of using a cat - like state to distribute control qubits is discussed in section [ sec : dist - ctrl ] . next , the cat - entangler and cat - disentangler are presented . after that , we use these operations to construct non - local cnot and teleportation operations . section [ sec : ctrl - gates ] discusses various constructions of non - local control gates in different situations . issues related to establishing and refreshing entanglement are addressed in section [ sec : impt - em ] via constructing entangling gates . finally , an example of a distributed version of the quantum fourier transform is presented in section [ sec : fourier ] . we adopt the notation found in @xcite . for any one - qubit unitary matrix @xmath6 , and integer @xmath7 , the operator @xmath8 which acts on @xmath9 qubits , is defined as @xmath10 for all @xmath11 , where `` @xmath12 '' denotes logical ` and . ' in other words , @xmath8 is an @xmath13-fold control-@xmath14 gate . for example , if @xmath15 then @xmath16 is the cnot gate , and @xmath17 is the toffoli gate . more detailed discussion about this notation can be found in @xcite . this diagram represents an entangling gate , denoted by @xmath18 . this gate can be locally implemented using a hadamard gate and a cnot gate , as shown . a distributed version of the entangling gate is discussed in section [ sec : impt - em ] . ] to reduce the complexity of diagrams , we introduce a diagram for an entangling gate , called an @xmath18 gate , as shown in figure [ fig : entan - gate ] . two qubits are entangled by this @xmath18 gate . in particular , if the input state is @xmath19 , the output state will be @xmath20 . the entangling gate @xmath18 can be generalized to an @xmath13-fold entangling gate , denoted by @xmath21 , which creates the cat state @xmath22 upon the input state @xmath23 . the @xmath24 gate is illustrated in figure [ fig : ghz - gate ] . this diagram represents a generalized entangling gate for 3 qubits , denoted by @xmath24 . it creates the ghz state if the input is the state @xmath25 . this gate can be locally implemented by a hadamard gate and two cnot gates , as shown . ] finally , figure [ fig : swap - gate ] shows a diagram for the swap gate . section [ sec : impt - em ] discusses the distributed implementations of the @xmath21 gate and the swap gate . a swap gate . the discussion of distributed implementation of this gate can be found on section [ sec : dist - swap ] ] in this section , we discuss how a cat - like state can distribute control over multiple computers . _ this is the key idea of the construction of non - local interaction presented in this paper . _ we will demonstrate this idea using the simplest control gate , i.e. , the cnot gate . the cnot gate @xmath26 is defined on a two - qubit system as follows : for any control qubit @xmath27 and target bit @xmath28 , @xmath29 we assume that a cat - state @xmath30 has already been shared between multiple computers . then cat - entangler can be used to transform a control qubit and a cat - state into a cat - like state . as a result , equation [ eqn : samp_ctrl ] becomes @xmath31 which can be rewritten as @xmath32 equations [ eqn : multi_ctrl ] and [ eqn : dist_ctrl ] show that we can use any qubit , shared in the cat - like state , as a control line . for example , the two circuits in figure [ fig : eqv - ctrl ] have an equivalent effect on the target bit , assuming that the state of lines one and two is the cat - like state @xmath33 . since line one and line two are in the state @xmath34 , the target qubit @xmath28 can be controlled by either line one or two . ] given a qubit @xmath35 and a generalized ghz state @xmath36 , created by an entangling gate @xmath37 , one can create a cat - like state @xmath38 with the above circuit . ] a cat - entangler is shown in figure [ fig : create - ctrl ] . the box labeled by @xmath39 is a standard basis measurement . since a result of the measurement ( represented by a dotted line ) is a classical bit , we can distribute and reuse the result to control many @xmath40-gates at the same time . [ thm : dist - ctrl ] given a qubit @xmath41 and an @xmath13-fold cat state @xmath42 , a cat - like state @xmath43 can be created by a cnot gate , local operations ( i.e. , one measurement and @xmath40-gates ) , and classical communication . proof : a quantum circuit that creates an @xmath13-fold cat - like state can be generalized from the circuit shown in figure [ fig : create - ctrl ] . assume that an m - fold ghz state is created by a @xmath21 gate . at point a , after applying the cnot gate , the state of the circuit is @xmath44 after the measurement , the state is either @xmath45 or @xmath46 where the underlined qubit is" +"lorentz symmetry is a fundamental feature of modern descriptions of nature . lorentz transformations include both spatial rotations and boosts . therefore , experimental investigations of rotation symmetry provide important tests of the framework of the standard model of particle physics and single - metric theories of gravity @xcite . in particular , the minimal su(3)@xmath4su(2)@xmath4u(1 ) standard model successfully describes particle phenomenology , but is believed to be the low energy limit of a more fundamental theory that incorporates gravity . while the fundamental theory should remain invariant under lorentz transformations , spontaneous symmetry - breaking could result at the level of the standard model in violations of local lorentz invariance ( lli ) and cpt ( symmetry under simultaneous application of charge conjugation , parity inversion , and time reversal ) @xcite . clock comparisons provide sensitive tests of rotation invariance and hence lorentz symmetry by bounding the frequency variation of a given clock as its orientation changes , e.g. , with respect to the fixed stars @xcite . in practice , the most precise limits are obtained by comparing the frequencies of two co - located clocks as they rotate with the earth ( see fig . [ f.lliearth ] ) . atomic clocks are typically used , involving the electromagnetic signals emitted or absorbed on hyperfine or zeeman transitions . we report results from two new atomic clock tests of lli and cpt : 1 . using a two - species @xmath0xe/@xmath1he zeeman maser @xcite we placed a limit on cpt and lli violation of the neutron of nearly @xmath2 gev , improving by more than a factor of six on the best previous measurement @xcite . we employed atomic hydrogen masers to set an improved clean limit on lli / cpt violation of the proton , at the level of nearly @xmath3 gev . our atomic clock comparisons are motivated by a standard model extension developed by kosteleck and others @xcite . this theoretical framework accommodates possible spontaneous violation of local lorentz invariance ( lli ) and cpt symmetry , which may occur in a fundamental theory combining the standard model with gravity . for example , this might occur in string theory @xcite . the standard model extension is quite general : it emerges as the low - energy limit of any underlying theory that generates the standard model and contains spontaneous lorentz symmetry violation @xcite . the extension retains the usual gauge structure and power - counting renormalizability of the standard model . it also has many other desirable properties , including energy - momentum conservation , observer lorentz covariance , conventional quantization , and hermiticity . microcausality and energy positivity are expected . this well - motivated theoretical framework suggests that small , low - energy signals of lli and cpt violation may be detectable in high - precision experiments . the dimensionless suppression factor for such effects would likely be the ratio of the low - energy scale to the planck scale , perhaps combined with dimensionless coupling constants @xcite . a key feature of the standard model extension of kosteleck _ et al . _ is that it is at the level of the known elementary particles , and thus enables quantitative comparison of a wide array of tests of lorentz symmetry . in recent work the standard model extension has been used to quantify bounds on lli and cpt violation from measurements of neutral meson oscillations @xcite ; tests of qed in penning traps @xcite ; photon birefringence in the vacuum @xcite ; baryogenesis @xcite ; hydrogen and antihydrogen spectroscopy @xcite ; experiments with muons @xcite ; a spin - polarized torsion pendulum @xcite ; observations with cosmic rays @xcite ; and atomic clock comparisons @xcite . recent experimental work motivated by this standard model extension includes penning trap tests by gabrielse _ et al . _ on the antiproton and h@xmath5 @xcite , and by dehmelt _ _ on the electron and positron @xcite , which place improved limits on cpt and lli violation in these systems . also , a re - analysis by adelberger , gundlach , heckel , and co - workers of existing data from the `` et - wash ii '' spin - polarized torsion pendulum @xcite sets the most stringent bound to date on cpt and lli violation of the electron : approximately @xmath6 gev @xcite . the design and operation of the two - species @xmath0xe/@xmath7he maser has been discussed in recent publications @xcite . ( see the schematic in fig . [ f.dngmschem ] . ) two dense , co - located ensembles of @xmath7he and @xmath0xe atoms perform continuous and simultaneous maser oscillations on their respective nuclear spin 1/2 zeeman transitions at approximately 4.9 khz for @xmath7he and 1.7 khz for @xmath0xe in a static magnetic field of 1.5 gauss . this two - species maser operation can be maintained indefinitely . the population inversion for both maser ensembles is created by spin exchange collisions between the noble gas atoms and optically - pumped rb vapor @xcite . the @xmath0xe/@xmath7he maser has two chambers , one acting as the spin exchange `` pump bulb '' and the other serving as the `` maser bulb '' . this two chamber configuration permits the combination of physical conditions necessary for a high flux of spin - polarized noble gas atoms into the maser bulb , while also maintaining @xmath7he and @xmath0xe maser oscillations with good frequency stability : @xmath8 nhz stability is typical for measurement intervals of @xmath9 hour @xcite . ( a single - bulb @xmath0xe/@xmath7he maser does not provide good frequency stability because of the large fermi contact shift of the @xmath0xe zeeman frequency caused by @xmath0xe - rb collisions @xcite . ) either of the noble gas species can serve as a precision magnetometer to stabilize the system s static magnetic field , while the other species is employed as a sensitive probe for lli- and cpt - violating interactions or other subtle physical influences . ( for example , we are also using the @xmath0xe/@xmath7he maser to search for a permanent electric dipole moment of @xmath0xe as a test of time reversal symmetry ; hence the electric field plates in fig . [ f.dngmschem ] . ) we search for a signature of lorentz violation by monitoring the relative phases and zeeman frequencies of the co - located @xmath7he and @xmath0xe masers as the laboratory reference frame rotates with respect to the fixed stars . we operate the system with the quantization axis directed east - west on the earth , the @xmath7he maser free - running , and the @xmath0xe maser phase - locked to a signal derived from a hydrogen maser in order to stabilize the magnetic field . to leading order , the standard model extension of kosteleck _ et al . _ predicts that the lorentz - violating frequency shifts for the @xmath7he and @xmath0xe maser are the same size and sign @xcite . hence the possible lorentz - violating frequency shift in the free - running @xmath1he maser ( @xmath10 ) is given by : @xmath11,\ ] ] where @xmath12 is the sidereal - day - period modulation induced in both noble gas zeeman frequencies by the lorentz - violating interaction , and @xmath13 is the ratio of gyromagnetic ratios for @xmath1he and @xmath0xe . we acquired 90 days of data for this experiment over the period april , 1999 to april , 2000 . we reversed the main magnetic field of the apparatus every @xmath14 days to help distinguish possible lorentz - violating effects from diurnal systematic variations . in addition , we carefully assessed the effectiveness of the @xmath0xe co - magnetometer , and found that it provides excellent isolation from possible diurnally - varying ambient magnetic fields , which would not average away with field reversals . furthermore , the relative phase between the solar and sidereal day evolved about @xmath15 radians over the course of the experiment ; hence diurnal systematic effects from any source would be reduced by averaging the results from the measurement sets . we analyzed each day s data and determined the amplitude and phase of a possible sidereal - day - period variation in the free - running @xmath7he maser frequency . ( see fig . [ f.dngmdata ] for an example of one day s data . ) we employed a linear least squares method to fit the free - running maser phase vs. time using a minimal model including : a constant ( phase offset ) ; a linear term ( larmor precession ) ; and cosine and sine terms with sidereal day period . for each day s data , we included terms corresponding to quadratic and maser amplitude - induced phase drift if they significantly improved the reduced @xmath16 @xcite . as a final check , we added a _ faux _ lorentz - violating effect of known phase and amplitude to the raw data and performed the analysis as before . we considered our data reduction for a given sidereal day to be successful if the synthetic physics was recovered and there was no significant change in the covariance matrix generated by the fitting routine . using the 90 days of data , we found no statistically significant sidereal variation of the free - running @xmath7he maser frequency at the level of 90 nhz ( two - sigma confidence ) . kosteleck and lane report that the nuclear zeeman transitions of @xmath0xe and @xmath7he are primarily sensitive to lorentz - violating couplings of the neutron , assuming the correctness of the schmidt model of the nuclei @xcite . thus our search for a sidereal - period frequency shift of the free - running @xmath7he maser ( @xmath17 ) provides a bound to the following parameters characterizing the magnitude of lli / cpt violations in the standard model extension : @xmath18 here @xmath19 denotes spatial indices in a non - rotating frame , with @xmath20 and @xmath21 oriented in a plane perpendicular to the earth s rotation axis and we have taken @xmath22 . the parameters @xmath23 , @xmath24 , and @xmath25 describe the strength of lorentz - violating couplings of the neutron to possible background tensor fields . @xmath23 and @xmath25 correspond to couplings that violate both cpt and lli , while @xmath24 corresponds to a coupling that violates lli but not cpt . all three of these parameters are different linear combinations of fundamental parameters in the underlying relativistic lagrangian of the standard model extension @xcite . it is clear from eqn . ( [ e.dngmkosshift ] ) that the @xmath0xe/@xmath7he clock comparison is primarily sensitive to lli / cpt violations associated with the neutron parameter @xmath23 . similarly , the most precise previous search for lli / cpt violations of the neutron , the @xmath26hg/@xmath27cs experiment of lamoreaux , hunter _ @xcite , also had principal sensitivity to @xmath23 at the following level @xcite : @xmath28 in this case , the experimental limit , @xmath29 , was a bound of 110 nhz ( two - sigma confidence ) on a sidereal - period variation of the @xmath26hg nuclear zeeman frequency , with the @xmath27cs electronic zeeman frequency serving as a co - magnetometer . therefore , in the context of the standard model extension of kosteleck and co - workers @xcite , our @xmath0xe/@xmath7he maser measurement improves the constraint on @xmath23 to nearly @xmath2 gev , or more than six times better than the @xmath26hg/@xmath27cs clock comparison @xcite . note that the ratio of this limit to the neutron mass ( @xmath30 ) compares favorably to the dimensionless suppression factor @xmath31 that might be expected to govern spontaneous symmetry breaking of lli and cpt originating at the planck scale . we expect more than an order of magnitude improvement in sensitivity to lli / cpt violation of the neutron using a new device recently demonstrated in" +"recent growth of the interest in complexes of domain walls ( dws ) in quasi-1d ferromagnets is due to hopes for miniaturization of information registers and logical devices based on magnetic nanowires , @xcite , and nanorings @xcite . currently , the main technological effort is focused on the ( straight or curved ) magnetic nanostripes whose spin structure is more complex than described within the 1d idealization . it is because nanostructures of the best quality are obtained in this form using lithography methods @xcite . mutual interactions of the dws influence the stability of a record of bits encoded in a string of the magnetic domains @xcite . in the present paper , i study interactions of dws in ferromagnetic stripes of nonzero thickness including two regimes of the stripe widths ; narrow stripes correspond to the so called transverse dws while wider stripes to the so called vortex dws @xcite . it is shown that both kinds of the dws are exact stationary solutions to the landau - lifshitz - gilbert ( llg ) equation in 2d ( different realizations of the cross - tie dw @xcite ) , however , their orientations in the stripe plane are distinguished by different boundary conditions . both transverse and vortex dws are characterized by two features ; a chirality ( the direction of magnetization rotation in the stripe plane ) which is clockwise or counterclockwise one and a polarity ( the direction of magnetization alignment in a vortex / halfvortex center ) which is positive or negative one @xcite . pairs of the dws of the opposite ( like ) both the chiralities and polarities are found to constitute exact stationary solutions to llg in the absence of external field , hence , they do not interact . the interactions of the dws of opposite chiralities and of like polarities ( as well as of like chiralities and of opposite polarities ) are studied within a perturbation calculus previously developed with relevance to dws in 1d ferromagnetic wire and in critical systems @xcite . evaluating the dependence of energy of the two - dw systems on the distance between the dws , i analyze the creation of stationary bound states of two dws ( magnetic bubbles ) . in the presence of an external magnetic field , even dws of the opposite chiralities and polarities ( of like chiralities and polarities ) interact . the field - induced collision of such dws is studied applying a method developed to 1d systems in @xcite . for this aim , an extension of the ( dissipative ) evolution equation of magnetization is performed in a way to describe the dynamics in the limits of large positive and large negative values of time . the collision is found to be accompanied by the reflection of the dws , hence , by the creation of stable magnetic bubbles . in section ii , the single dw solutions to the llg equation in magnetic stripes are analyzed . the interactions of the transverse and vortex dws of opposite chiralities and of like polarities ( as well as of like chiralities and of opposite polarities ) are investigated within the perturbation calculus in section iii while the field - induced collisions of the dws of opposite ( like ) chiralities and polarities are studied in section iv . main conclusions are summarized in section v. i consider stationary dw solutions to the llg equation in 2d @xmath0 the first term on the r.h.s . of ( [ llg ] ) relates to the exchange interactions while the second ( zeeman ) term depends on the external magnetic field @xmath1 , thus , @xmath2 denotes the gyromagnetic factor . the constant @xmath3 determines strength of the easy - axis anisotropy and @xmath4 indicates the long axis of the stripe . in nanomagnets with structural disorder ( permalloys are the most popular materials for nanostripes ) , the effective spin anisotropy is dominated by dipolar interactions , hence , it is a shape dependent and mainly surface effect . then , for stripes of big enough cross section , the bulk anisotropy is negligible , @xmath5 , where @xmath6 denotes the stripe width . since ( [ llg ] ) is valid only when the constraint @xmath7 is satisfied , one writes equations of the unconstrained dynamics equivalent to ( [ llg ] ) . introducing @xmath8 , one represents the magnetization components using a pair of complex functions @xmath9 , @xmath10 . the relation between the primary and secondary dynamical variables @xmath11 ensures that @xmath7 . inserting ( [ transform ] ) into ( [ llg ] ) leads , following the hirota method for solving nonlinear equations @xcite , to @xmath12&&f^{*}\cdot g \nonumber\\ -&&\left(\gamma h_{x}+\beta_{1}\right)f^{*}g=0 , \nonumber\\ \left[-{\rm i}d_{t}-j(d_{x}^{2}+d_{z}^{2})+\alpha d_{t}\right]&&f^{*}\cdot g \nonumber\\ + & & \left(-\gamma h_{x}+\beta_{1}\right)f^{*}g=0 , \label{secondary - eq}\\ ( d_{x}^{2}+d_{z}^{2})g\cdot g=0,\hspace*{3em}&&(d_{x}^{2}+d_{z}^{2})f^{*}\cdot f^{*}=0 , \nonumber\end{aligned}\ ] ] where @xmath13 , @xmath14 , @xmath15 denote hirota operators of differentiation @xmath16 for @xmath17 , stationary single - dw solutions to ( [ secondary - eq ] ) take the form @xmath18 where @xmath19 and @xmath20 . i denote @xmath21 , @xmath22 . assuming one of the dw ends to be centered at @xmath23 , ( then @xmath24 ) , the relevant magnetization profile [ the single - dw solution to ( [ llg ] ) ] is written explicitly with @xmath25 , \nonumber\\ m_{x}(x , z)&=&-m{\rm tanh}[k^{'}x+q^{'}z ] . \label{profile1}\end{aligned}\ ] ] i assume @xmath26 since , in the case @xmath27 , the dw states are similar to dws in 1d and can not exist in absence of the bulk anisotropy @xcite . defining @xmath28 , following ( [ condition_1 ] ) , one finds @xmath29 and @xmath30\}$ ] . also , i assume the magnetization alignments on both the stripe edges to be similar , the ordering is symmetric with respect to the line @xmath31 . it leads to the condition @xmath32 where @xmath33 and , finally , to @xmath34\}$ ] . ( 175,143 ) ( 0,-5 ) additional boundary condition is related to minimization of the surface ( magnetostatic ) energy and it discriminates between different values of @xmath35 , @xmath36 , and @xmath37 . i evaluate the dependence of the energy of the dw on these parameters using the hamiltonian @xmath38 , where @xmath39 , \nonumber\\ { \cal h}_{z}&=&-\gamma{\bf h}\cdot{\bf m } , \label{hamiltonian}\end{aligned}\ ] ] ( @xmath40 denotes its zeeman part ) . total energy of the dw @xmath41 is the sum of the bulk energy @xmath42 , defined by @xmath43 , and of the boundary energy @xmath44 . the contribution @xmath44 is determined referring to a theorem by carbou who proved that the magnetostatic energy of any ferromagnetic element of finite thickness @xmath45 ; @xmath46 tends to @xmath47 with @xmath48 , @xcite . here , @xmath49 denotes the surface of the bulk ferromagnet and @xmath50 denotes the boundary of the base of its solid , @xmath51 is normal to the magnet surface , @xmath52 denotes the unitary vector outward to the line of the base boundary . the coefficient @xmath53 scales with @xmath45 and with a diameter @xmath6 following @xmath54 $ ] , ( with relevance to a stripe , @xmath6 represents its width @xcite ) . writing the formula for @xmath44 , one has to notice that , the carbou theorem is not strictly applicable to systems with open boundaries , ( infinite stripes ) , however , it shows some tendency in ordering at the stripe edges . in particular , it indicates that the magnetostatic interactions in flat magnets induce more than one hard directions of magnetization parallel to the main plane . i propose to effectively describe the magnetostatic energy in the form of an integral over the stripe edge @xmath55_{z=0}{\rm d}x , \label{e_b}\end{aligned}\ ] ] where , in contrast to @xcite , the effect of anisotropy relating to the long axis of the stripe is included via the term depending on @xmath56 . by analogy to systems with boundaries of finite length that satisfy the carbou theorem , this coefficient is expected to scale with the stripe width following @xmath57 . more detailed estimation of @xmath44 is performed in appendix a , ( see also @xcite ) . inserting ( [ profile1 ] ) into the hamiltonian ( [ hamiltonian ] ) , one arrives at @xmath58+\frac{\pi^{2}n^{2}}{w^{2}}}. \label{e_0}\end{aligned}\ ] ] estimating @xmath44 , i divide it into two parts @xmath59 ; @xmath60}\right\}{\rm d}x , \nonumber\\ e_{b2}(\varphi,\theta , n)&\equiv&\frac{2m^{2}}{\lambda_{2}}\int_{-\infty}^{\infty } { \rm sin}^{2}\left\{\varphi-\frac{n\pi\tan(\theta)x}{w[1+\tan^{2}(\theta)]}\right\ } \nonumber\\ & & \times{\rm sech}^{2}\left\{\frac{n\pi x}{w[1+\tan^{2}(\theta)]}\right\}{\rm d}x . \label{boundary_energy}\end{aligned}\ ] ] the minimization of @xmath61 leads to @xmath62 independently of other parameters of the dw . it corresponds to the presence of halfvortices ( halfantivortices ) at the stripe edges ( as shown in fig . 1 ) . in the regime of narrow stripes @xmath63 , @xmath64 , ( @xmath65 is small , thus , @xmath66 dominates over @xmath44 ) , via minimization of @xmath67 the smallest possible value of @xmath36 is preferable while the minimization of both the energy components @xmath67 , @xmath68 leads to the preferred values of the angle @xmath69 . increase of the stripe width @xmath6 with fixed thickness @xmath45 results in the transition to the regime @xmath70 . furthermore , as mentioned previously , for soft - magnetic alloys , @xmath3 is negligibly small , @xmath5 , thus , from ( [ e_0 ] ) , @xmath71 is independent of @xmath6 , and @xmath44 becomes comparable to @xmath66 . for this case , via the minimization of @xmath72 , the biggest possible value of @xmath73 and the smallest value of @xmath36 are preferable , whereas , for @xmath74 , the minimization of @xmath75 indicates big values of @xmath36 to be preferable . hence , the transition from the dw state of @xmath76 , @xmath69 to a state of @xmath77 , @xmath78 takes place with increase of @xmath6 . for @xmath77 , the condition @xmath79 has to be satisfied in order to @xmath80 . the state @xmath76 and @xmath69 corresponds to @xmath81 , @xmath82 , @xmath83 and it is called a _ transverse dw_. with relevance to the state @xmath77 , i take @xmath84 , ( the shape anisotropy does not affect the dynamical equation while it is completely included in the boundary condition , the minimization of @xmath44 ) , and @xmath85 to be close to its infimum @xmath86 . the resulting magnetization structure corresponds to @xmath87 and one calls it a _ vortex dw_. the polarity of vortex ( transverse ) dw , ( the magnetization orientation in the center of vortex / halfvortex , parallel or antiparallel to @xmath88 axis ) , is determined by value of @xmath35 while @xmath89 determines its chirality , ( the magnetization rotation in the stripe plane , clockwise or anticlockwise to @xmath88 axis ) . let me analyze the interaction of transverse ( vortex ) dws within a perturbation calculus developed earlier with relevance to the interactions of dws in 1d ferromagnet @xcite . in the present section , i focus on the systems whose interacting dws are of opposite chiralities and of like polarities ( or of like chiralities and of opposite polarities ) visualized in fig . i refer to the remaining cases ( the dws of opposite chiralities and polarities as well as the dws of like chiralities and polarities ) in the next section . ( 175,24 ) ( 0,-5 ) locally , in the vicinity of the center of @xmath90th dw , ( @xmath91 ) , one can write the magnetization in the form @xmath92 where @xmath93 denotes the stationary single - dw solution to ( @xmath94 ) @xmath95\ } } \nonumber\\ & & \times { \rm sech}\{\sigma_{j}[k^{'}(x - x_{0j})+q^{'}z]\ } , \nonumber\\ m_{x}^{(j)}(x , z)&=&-m{\rm tanh}\{\sigma_{j}[k^{'}(x - x_{0j})+q^{'}z]\ } \label{single_dw_int}\end{aligned}\ ] ] while @xmath96 denotes a perturbation due the presence of another dw . here @xmath97 , @xmath98 , @xmath99 , and" +"it is well known that , studying the spatial structures and dynamics of globular clusters ( gcs ) is of great importance for understanding both their formation condition and dynamical evolution within the environment of their galaxies @xcite . for example , these clusters are ideal laboratories for detailed studies on two - body relaxation , mass segregation , stellar collisions and mergers , and core collapse @xcite . the correlations of structures with galactocentric distance can provide information on the role of the galaxy tides towards the clusters , while the distribution of ellipticity can shed light on the primary factor for cluster elongation . in addition , comparisons of structures of gcs located in different environment of galaxies offer clues to differences in the early formation and evolution of the galaxies or in their subsequent accretion histories @xcite . the `` fundamental plane '' for clusters in parameter space reflects universal cluster formation conditions , regardless of their host environments @xcite . the structural and dynamical parameters of clusters are often determined by fitting the surface brightness profiles to structure models , combined with mass - to - light ratios estimated from velocity dispersions or population - synthesis models . an accurate and well resolved density profile can be obtained by studying the distribution of integrated light coupling with star counts @xcite . several models are often used in the fits : the empirical , single - mass , modified isothermal spheres @xcite ; the isotropic multi - mass models @xcite ; the anisotropic multi - mass models @xcite ; the power - law surface - density profiles @xcite . the nearest large gc system outside the milky way ( mw ) is that of m31 , with a distance of @xmath1 kpc from us @xcite . it is so close to us that most gcs in it can be well resolved with _ hubble space telescope _ ( _ hst _ ) . @xcite first estimated core radii for several clusters in m31 , and subsequently , a number of studies @xcite focused on the internal structures of m31 gcs , including the core radius , half - light radius , tidal radius , and ellipticity , using the images from large ground - based telescopes and _ @xcite derived structural and dynamical parameters for 34 m31 gcs , and construct a comprehensive catalog of these parameters for 93 m31 gcs with corrected versions of those in a previous study @xcite . combined with the structures and dynamics for clusters from the mw , magellanic clouds , the fornax dwarf spheroidal , and ngc 5128 , these authors found the gcs have near - universal structural properties , regardless of their host environments . @xcite found that bright young clusters in m31 are larger and more concentrated than old ones , and are expected to dissolve within a few gyr and will not survive to become old gcs . with measurements of structural parameters for 13 extended clusters ( ecs ) in the halo regions of m31 , @xcite presented that the faintest ecs have magnitudes and sizes similar to palomar - type gcs in the mw halo . @xcite measured structures and kinematics for 10 newly discovered gcs in the outer halo of m31 , and found that they have larger ellipticities than most of gcs in m31 and the mw , which may be due to galaxy tides from satellite galaxies of m31 or may be related to the merger and accretion history that m31 has experienced . using the same sample clusters in @xcite , @xcite found that some gcs in m31 exhibit cuspy cores which are well described by @xcite models . these authors also confirmed the exist of luminous and compact globulars at large galactocentric radii of m31 , with no counterparts found in the mw . the last three studies extended the structural analysis of clusters in m31 out to @xmath2 kpc , providing important information on the accretion history of m31 outer regions . in this paper , we determined structures and kinematics for 79 clusters in m31 by fitting several structural models to their surface brightness profiles . this paper is organized as follows . in section 2 , we present the _ hst _ observations for the sample clusters , and the data - processing steps to derive the surface brightness profiles . in section 3 , we determine structures and kinematics of the clusters and make some comparisons with previous studies . a discussion on the correlations of the derived parameters is given in section 4 . finally , we summarize our results in section 5 . _ hst _ has imaged a large fraction of globular clusters ( gcs ) in m31 . @xcite used _ hst_/wide field planetary camera 2 ( wfpc2 ) images to measure ellipticities , position angles , and best - fit @xcite model ( hereafter `` king model '' ) parameters for a large sample of m31 gcs . @xcite determined structures and kinematics for m31 gcs by fitting surface brightness profiles to different models , however , for all the gcs but g001 studied in @xcite , only king model was used . in addition , there were some clusters located at the edges of the images or observed with only one filter . with updated observations by _ hst _ , new data can be derived for them now . so , we decided to re - estimate the structure parameters for these gcs in @xcite . however , @xcite determined structures for g001 using three models and new observation , while @xcite determined structure parameters for five clusters ( b315 , b318 , b319 , b368 , and b374 ) using updated _ hst _ data . in addition , there is no new observation for b077 , which is at the edges of the _ hst _ images . we also noticed that bh20 and bh21 had been classified as stars , while bh24 a galaxy @xcite , which would not be discussed again in this paper . the remaining 69 clusters from @xcite would be included in the sample . @xcite estimated metallicities , distance moduli and reddening values for 10 newly - discovered halo gcs in m31 using the acs / wide field camera ( wfc ) images . although @xcite and @xcite determined structures for the 10 gcs , @xcite only used king model , while @xcite presented few structure parameters . so , we re - estimated the structure parameters for these gcs . finally , there are 79 clusters in our sample . we obtained the combined drizzled images from the hubble legacy archive . the images in the bandpass close to @xmath3 band ( f555w or f606w ) and @xmath4 band ( f814w ) were preferred , otherwise the images of f300w , f435w or f475w were selected . the images with high resolution were preferentially adopted ( wfpc2/pc or acs / wfc ) , followed by those obtained with wfpc2/wfc . figure 1 shows the spatial distribution for the sample gcs . the data analysis procedures to measure surface brightness profiles of clusters have been described in @xcite . when the center positions of these clusters were determined using the imcentroid task in iraf , the ellipse task was run in two passes to derive the surface brightness profiles . the ellipse showed inability to converge for several individual clusters . in these cases we first smoothed the images with a boxcar filter @xcite , and then ran the ellipse to derive the density profiles . the overall ellipticity and position angle ( pa ) were determined by averaging the ellipse output in the first pass , with the errors estimated as the standard deviation of the mean . several clusters ( b330 , b468 , bh04 , bh11 , bh29 , and nb39 ) showed errors of p.a.s larger than 15 degrees . we checked the images for these clusters , and found that the random fluctuations due to individual stars @xcite may account for the high errors , leading to a more difficult business for accurate measurements of pas table 1 lists the average ellipticity , p.a . and some additional integrated data for the sample clusters . considering that the metallicities for young ( @xmath5 gyr ) and old clusters are quite different , first , we averaged the ages for the sample 79 clusters from several previous studies @xcite to distinguish young from old clusters . of which , there are 13 clusters ( bh23 , bh29 , nb39 , and the 10 gcs from * ? ? ? * ) with no available age values in the literatures , and we assumed them as old ones . finally , there are six young clusters ( b097d , b324 , bh05 , bh12 , dao38 , and m091 ) in our sample , all of which are from @xcite . for the 69 gcs from @xcite , the metallicities with uncertainties from @xcite were preferentially adopted as our reference , followed by those of @xcite for old clusters , while the solar metallicity was assumed for young clusters @xcite . the reddening values were from @xcite , while the other integrated data were from rbc v.5 @xcite . for the 10 gcs from @xcite , we used the integrated data presented in @xcite , including the @xmath6 magnitudes , galactocentric distances , reddening values , and metallicities ( see * ? ? ? * and references therein ) . in addition , @xmath7 magnitudes for six of the 10 gcs are from rbc v.5 . old clusters with no metallicity measurements are assigned with a mean m31 gc metallicity of [ fe / h]@xmath8 @xcite , while the uncertainties of [ fe / h ] are assumed to be 0.6 as for the standard deviation of the metallicity distribution of the m31 gc system @xcite . clusters with no reddening values are assigned with the galactic reddening in the direction of m31 of @xmath9 @xcite . raw output from package ellipse is in terms of counts s@xmath10 pixel@xmath10 , which needs to multiply by a number ( 400 for acs / wfc , 100 for wfpc2/wfc , and 494 for wfpc2/pc ) to convert to counts s@xmath10 arcsec@xmath10 . a formula was used to transform counts to surface brightness in magnitude calibrated on the vegamag system , @xmath11 as noted by @xcite , occasional oversubtraction of background during the multidrizzling in the automatic reduction pipeline led to `` negative '' counts in some pixels , so we worked in terms of linear intensity instead of surface brightness in magnitude . with updated absolute magnitudes of the sun @xmath12 ( c. willmer , private communication ) listed in table 2 , the equation for transforming counts to surface brightness in intensity was derived , @xmath13 converting from luminosity density in @xmath14 to surface brightness in magnitude was done according to @xmath15 table 2 presents the zeropoints , conversion factors , and coefficients used in these transformations for each filter . table 3 gives the final , calibrated intensity profiles for the 79 clusters but with no extinction corrected . the reported intensities are calibrated on the vegamag scale . column 7 gives a flag for each point , which has the same meaning as @xcite and @xcite defined . the points flagged with``ok '' are used to constrain the model fit , while the points flagged with `` dep '' are those that may lead to excessive weighting of the central regions of clusters ( see * ? ? ? * ; * ? ? ? * for details ) . in addition , points marked with `` bad '' are those individual isophotes that deviated strongly from their neighbors or showed irregular features , which were deleted by hand . the point - spread function (" +"we are concerned with the problem of speaker detection , where an automatic speaker recognizer is used to decide whether or not the voice of a designated target speaker is present in a given speech segment . current speaker recognition algorithms output uncalibrated _ scores _ , which have to be processed through a calibration stage before cost effective decisions can be made . this paper deals with the problem of designing the calibration stage . we implement the calibration stage in the form of a discriminative model , say @xmath0 , which outputs a posterior probability that the target speaker spoke the speech segment : @xmath1 . the trial score , @xmath2 , is computed by the speaker recognizer as a function of the target speaker and the speech segment . this posterior can be used in a straight - forward , standard way to make minimum - expected - cost bayes decisions . we shall take as the baseline discriminative model prior - weighted logistic regression @xcite , which has become a standard recipe for calibration in speaker recognition , with implementations available in the focal @xcite and bosaris @xcite toolkits . logistic regression is the minimization of the expected value of a special cost function , known as the _ logarithmic proper scoring rule_. we are interested here in generalizing this recipe by modifying the cost function . our motivation derives from @xcite , where it was demonstrated that a modified logistic regression that ignores scores below a suitable threshold can benefit applications with low false - alarm rate requirements . in this work we limit ourselves to cost functions which are _ proper scoring rules _ @xcite . we expand on our previous work @xcite , to demonstrate theoretically and experimentally that we can tailor proper scoring rules to target the low false - alarm region . given a database of supervised trials , the sum over trials of a proper scoring rule forms an objective function that can be used to simply evaluate the goodness of a recognizer with probabilistic output , and indeed also to facilitate discriminative training of such recognizers . we restrict ourselves to _ binary _ proper scoring rules , a family of special cost functions of the form @xmath3 , which evaluates the goodness of the recognizer output @xmath4 , for a trial where hypothesis @xmath5 is true . we use the notation @xmath6 for a trial where the target speaker spoke and @xmath7 for one where some other speaker spoke . in what follows it will be convenient to work with recognizer outputs in the form of posterior probabilities : @xmath8 , where @xmath2 is the uncalibrated trial score and @xmath0 is the calibration model . later we show how to adapt this to recognizer outputs in likelihood - ratio form . a binary proper scoring can be seen as a _ model of an application _ of a detector or more generally , a mixture of such applications . an application , @xmath9 , is represented by a cost function @xmath10 , which maps outcomes to real - valued consequences . the outcome is composed of the decision , @xmath11 , and the true hypothesis , @xmath12 . the sets from which decisions are chosen may differ between applications , for example @xmath13 , or @xmath14 , and so on . our application model assumes that the detector output , @xmath4 , is used to make a minimum - expected - cost bayes decision : @xmath15 the associated _ proper scoring rule _ is defined as the cost of this decision @xcite : @xmath16 a convex combination of proper scoring rules is still a proper scoring rule , in the sense that it can be derived via from a suitably constructed cost function that represents a mixture of different applications @xcite . although applications may be defined via a large variety of cost functions , all of this variety can be conveniently represented in a surprisingly simple form @xcite . all binary proper scoring rules can be expressed in the form : @xmath17 where @xmath18 , @xmath19 and @xmath20 . the constants @xmath21 do nt play any useful role in the bayes decision framework and may be set to @xmath22 and @xmath23 without loss of generality @xcite . the weighting distribution @xmath24 can be very general , including smooth functions , step functions or even impulses . the impulse @xmath25 represents a single , _ simple application _ , with binary decisions in @xmath13 , a cost function with penalties @xmath26 and @xmath27 and the bayes decision threshold at @xmath28 . a sum of impulses represents a discrete mixture of applications , while a smooth function represents a continuous mixture over a continuous spectrum of applications . the important point here is that all bayes decision applications ( or mixtures of applications ) can be represented by via a suitable choice of @xmath24 . here we build an objective function , for training or evaluation , out of a proper scoring rule , @xmath29 . the proper scoring rule models the cost of making a bayes decision in a single detection trial . to turn this into an objective function , we take the _ expected _ cost over a whole supervised database . we form this expectation via two hypothesis conditional averages , weighted by a synthetic class prior ( usually different from the database proportions ) , of the form @xmath30 , @xmath31 . the expected cost is : @xmath32 where @xmath33 is the recognizer s posterior for trial @xmath34 ; @xmath35 is a set of @xmath36 target trial indices ; and @xmath37 a set of @xmath38 non - target indices . now , we relieve the calibrator of the ( implicit ) responsibility to have a hypothesis prior and to produce posteriors . instead , we require it to output _ log - likelihood - ratios _ , denoted @xmath39 . since the prior is already fixed as a parameter of the objective , the recognizer s posterior is given by bayes rule as : as the ratio of two generative likelihoods adds no value . instead should be taken as the definition of @xmath39 . ] @xmath40 where @xmath41 is prior log odds and @xmath42 is the logistic sigmoid : @xmath43 after some manipulation , we can express the functions of @xmath33 in as functions of @xmath39 instead : @xmath44 where @xmath45 is a translated and modulated version of @xmath24 , where the modulation factor : @xmath46 is a raised and scaled sigmoid . if @xmath24 is normalized , then @xmath47 is normalizable in the sense : @xmath48 . the integrals in can be interpreted as averaging over all possible cost functions , where @xmath24 determines the relative importance of different cost functions . in our construction of the objective function , we inherit this averaging over cost functions , but we seem to have fixed the prior at @xmath49 . since different applications of a speaker detector can be expected to have different priors , should we not also average over @xmath49 ? we can , but it adds no generality , because this would effectively just replace @xmath47 in by some other normalized / normalizable weighting distribution , say @xmath50 . we can now reformulate our objective function in its most general form as : @xmath51 where @xmath52 we now have a general objective function , parametrized by @xmath50 , which effectively determines the relative weighting over a mixture of different applications , each of which can have a different cost function and target prior . notice that @xmath53 is just the log - likelihood - ratio threshold . simple @xmath54/@xmath55 applications use a single threshold , while more complex applications ( or mixtures ) have multiple thresholds . thus , the combination of application costs in is accomplished via representing applications by their thresholds . here we introduce a practical choice for the weighting distribution , @xmath50 and show how it is used for calibration . since calibration involves optimization , smooth differentiable distributions are easier to work with . it is also desirable that the integrals have closed - form solutions . to this end , we adopt a 2-parameter ( here @xmath56 ) family of proper scoring rules proposed in @xcite . this family is effectively augmented by a third parameter , @xmath57 , via the prior - weighting in . this gives @xmath58 : @xmath59 where @xmath60 ; @xmath61 is defined in ; @xmath62 ensures the distribution is normalized ; and @xmath63 is the beta distribution , transformed to log - odds domain : @xmath64 and @xmath65 is the beta function . when @xmath66 , then using @xmath67 in gives closed - form solutions , which can be plugged into , with @xmath68 and @xmath69 . while this recipe is practically realized via and , a theoretical interpretation is given by and , because for this parametrization we have @xmath70 . we exploit this in figure [ fig : omega ] , where we plot for several values of the parameters . parameters @xmath56 control left and right tails respectively when they are increased tails become thinner and the distributions become narrower ( higher modes ) . location is indirectly controlled by @xmath41 , but this depends on @xmath56 . for the case @xmath71 , the distribution is _ invariant _ to @xmath41 . for @xmath72 , the mode shifts only as far as @xmath73 , while the distribution is considerably widened . however , when @xmath74 , the mode shifts close to @xmath75 and the widening is less dramatic . we show in our experiments below that when we target applications with high thresholds ( low false - alarm rate ) , then the effective shifting allowed by @xmath74 leads to better performance than the halfway shifted and stretched version given by the baseline logistic regression solution with @xmath72 . here we list some solutions for the integrals in , which we used in our experiments . the _ boosting rule _ @xcite , with @xmath71 : @xmath76 the _ logarithmic rule _ , with @xmath72 , forms the objective function for logistic regression and is our baseline : @xmath77 the parametrization @xmath78 gives ( up to scaling ) , the objective @xmath79 , proposed in @xcite for the evaluation of goodness of recognizers with likelihood - ratio output . the _ brier rule _ @xcite , with @xmath80 : @xmath81 an _ asymmetric _ rule , with @xmath82 : @xmath83 we assume that our recognizers output uncalibrated scores . let the score for a trial @xmath34 be denoted @xmath84 . we then apply a parametric ( affine ) calibration transformation : @xmath85 the calibration parameters @xmath86 need to be trained on a calibration training database . for training purposes , we choose and fix the parameters @xmath87 and then minimize the objective w.r.t . @xmath86 . in the special case @xmath72 such training is known as logistic regression . since the objective and the calibration transformation are differentiable , one can obtain the gradient w.r.t . @xmath86 by backpropagation and then use any of a variety of well - known unconstrained numerical optimization algorithms . for this work , we used bfgs @xcite . we performed calibration experiments on scores from a single speaker recognizer ( an i - vector plda system ) , which was part of the abc submission @xcite to the nist sre12 speaker recognition evaluation . several calibration transformations of the form were trained ( separately for males and females ) on a large development set with multiple microphone and telephone speech segments of 2019 speakers from sre04 , 05 , 06 , 08 and 10 . this gave about 120 million scores for calibration training . the different calibration transformations were obtained by using different objective function parameters , @xmath87 . we tested the goodness of these calibrators on the nist" +"stripped supernovae ( sne ) and long - duration gamma - ray bursts ( long grbs ) are nature s most powerful explosions from massive stars . they energize and enrich the interstellar medium , and , like beacons , they are visible over large cosmological distances . however , the mass and metallicity range of their progenitors is not known , nor the detailed physics of the explosion ( see reviews by @xcite and @xcite ) . stripped - envelope sne ( i.e , sne of types iib , ib , and ic , e.g. , @xcite ) are core - collapse events whose massive progenitors have been stripped of progressively larger amounts of their outermost h and he envelopes ( fig . [ fig1 ] ) . in particular , broad - lined sne ic ( sne ic - bl ) are sne ic whose line widths approach 20,000@xmath030,000 @xmath1 around maximum light ( see below ) and whose optical spectra show no trace of h and he . for the last 15 years , the exciting connection between long grbs and sne ic - bl , the only type of sne observed accompanying long grbs ( for reviews , see @xcite ) , and the existence of many more sne ic - bl _ without _ grbs raises the question of what distinguishes sn - grb progenitors from those of ordinary sne ic - bl without grbs . viewing angle effects are probably not the reason why those sne ic - bl did not show an accompanied grbs @xcite and based the same radio upper - limits , only @xmath2 1% of sne ib / c appear to be accompanied by grbs @xcite . one promising line of attack is to investigate what sets apart sne ib / c * with * grbs from those * without * grbs to elucidate the conditions and progenitors of these two types of explosions . while of course there are numerous possible avenues ( for a recent review see e.g. , @xcite ) , i will here adopt a two - thronged approach , given the short amount of time : first , i focus on comparing the optical spectra of sne ib / c with and without grbs , since early - time optical spectra are used for identifying the spectral features of different explosions and probe the bulk of the ejected stellar material , in particular the outermost layers . secondly , i present a meta - analysis of published measured metallicities at the explosion site of sne ib / c with and without grbs . metallicity is expected to strongly impact the lives and deaths of stars due to the metallicity dependence of mass loss ( e.g. , @xcite ) and its subsequent link to rotation and angular momentum content of the stellar core . the main thrust of my talk is that now a number of different groups , including ours , have contributed to gathering large data - sets , whose analysis can to lead to robust statistical conclusions and interesting insights into different populations of sne with and without grbs . while the observational hallmark of a sn ic - bl is , by the definition , its high expansion velocity ( which , when modeled in combination with light curves , yields high energies , sometimes above @xmath3 erg , i.e. 10 times more than the canonical ccsn , and thus motivated some to call them `` hypernovae '' ) , there are debates within the community whether such sne ic - bl can be robustly distinguished from `` normal '' sne ic and whether there are systematic differences between sne ic - bl with and without grbs . prior work involving synthetic models based on monte carlo radiative transfer codes ( @xcite and reference therein ) , while important , has included only a few normal sne ic and a few sn ic - bl without grbs , thus not yet providing a large sample . here we are using the spectra from the cfa sample of stripped sne ( modjaz et al . in prep ) , as well as those from the literature ( see references in modjaz et al . in prep ) to compare the absorption velocities as traced by fe ii @xmath45169 of different kinds of sne ic . spectral synthesis studies have shown that this and other fe lines are good tracers of the photospheric velocity , since they do not saturate @xcite . with the largest sample of spectra to date , we find that sn ic - bl * with * grbs have the * highest * absorption velocities ( 25,000@xmath035,000 @xmath1 at maximum v - light ) , while sne ic - bl * without * grbs have * lower * velocities ( between 15,000@xmath025,000 @xmath1 at maximum v - light ) , and normal sn ic have the lowest absorption velocities ( 8,000@xmath015,000 @xmath1 ) . of course , we caution that because of sever blending , specifically in sne ic - bl , the fe ii @xmath45169 line could be blended with other nearby lines in a manner such that it may compromise the velocity measurements . however other , more isolated , lines ( e.g. si ii ) also indicate high velocities for sn ic - bl . = 8.9 ( levesque et al . 2010a ) . , width=345 ] since direct sn ib / c progenitor detection attempts via deep pre - explosion images have not been successful @xcite and are impossible for grbs , we employ a complimentary approach : we study the host galaxy environments in order to discern any systematic trends as a function explosion type that may characterize their stellar progenitors . specifically , massive stars at different metallicities are expected to live and die differently , due to the metallicity dependence of mass loss and its subsequent link to rotation and angular momentum content of the stellar core ( e.g. , @xcite ) . since the early work on grb host metallicities and their comparison with sdss galaxies as well as with sn galaxies , the field of environmental metallicity studies has experienced a tremendous growth ( see discussions in e.g. , levesque et al . 2010a , @xcite and references therein , as well as contributions in this volume ) . here , we outline the recipe for state - of - the - art metallicity analysis , specifically of the oxygen abundance from nebular hii region emission lines , first formalized in @xcite : 1 ) in order to probe the natal oxygen abundance , obtain spectra at the position of the sn or grb ( because of metallicity gradients in spiral galaxies ) ; 2 ) include only sne with secure sn i d ( i.e. , ideally from multi - epoch sn spectra to monitor for any potential classification changes ) and also ( only ) from untargetted surveys in order to mitigate any selection effects ; 3 ) employ spectrographs with a large wavelength range in order to observe emission lines ( from [ oii ] @xmath43727 to h@xmath5 and [ nii ] @xmath46584 ) as to compute abundances in different diagnostics , since there are systematic differences between different diagnostics @xcite ; 4 ) remove stellar absorption in spectra when necessary , and 5 ) obtain good handle on uncertainty budget and propagate line flux and reddening uncertainties into abundance measurement errors via monte carlo simulations . while recently different groups have arrived at different conclusions about whether there is a statistically significant trend of metallicity with stripped sn subtype ( @xcite , see also proceedings by anderson , leloudas in this volume ) , not all measured metallicities reported in the anderson and leloudas et al samples are at the position of the sne . thus , we conducted a meta - analysis of all samples @xcite with the best - possible quality - control and following the above state - of - the - art recipe , now that we have larger samples to draw from : we only included oxygen abundance measurements at the exact sn explosion sites ( within the slit ) of sne with solid ids and also from untargeted surveys , to have the best handle possible on the natal metallicity estimates of sne with well - determined sn types over a large metallicity baseline , the ultimate goal of the study . figure [ oxyfig ] shows the result of our metal - analysis , namely the cumulative distributions of local metallicities for different types of stripped ccsne ( sne ib , ic , ic - bl without grbs , sne ic - bl with grbs ) from the combined samples . we find that with a combined and large sample size , the sites of sne ic do indeed have higher oxygen abundances than sne ib , and with a higher statistical significance than in the individual samples . there is only a 0.1% ( 2% ) probability in the pp04-n2 ( pp04-o3n2 ) scale that the oxygen abundances of the 19 ( 17 ) sne ib and of 20 ( 18 ) sne ic are drawn from the same parent population , which are different on average by @xmath20.2 dex . here we have taken advantage of the power of statistics by combining the hard work of three different groups . in addition , sn ic - bl with grbs still prefer , on average , more metal - poor environments than those without grbs ( see fig . 2 in @xcite ) , with the grb metallicity - luminosity relation offset to lower metallicities , but without a cut - off metallicity above which grb production would be suppressed ( levesque et al . 2010b ) . since the host galaxies of both samples span similar range in galaxy luminosity ( i.e , . even to luminous grb host galaxies of @xmath6 mag ) , dust effects are most likely not the reason for the offset to low metallicity . however , while these results are intriguing , the next step is to conduct a thorough and extensive host galaxy study with a large single - survey , untargeted , spectroscopically classified , and homogeneous collection of stripped sne , something we are currently undertaking with the palomar transient factory ( ptf ) . m.m . acknowledges current support from the nyu advance women - in - science travel grant funded by the nsf advance - paid award number hrd-0820202 and prior support from hubble fellowship grant hst - hf-51277.01-a ." +"the physics of many 1 + 1 dimensional lattice models at criticality is captured in the continuum limit by two - dimensional conformal field theory ( 2d cft ) . as a result , one can numerically extract the conformal data , for instance scaling dimensions of the primary operators from the scaling of the two - point correlation functions in the critical lattice model , see @xcite for the standard reference . on the other hand , measures of entanglement proved to be useful quantities for exploring the critical points of many - body systems . for example , in the ground state of a critical chain , the entanglement entropy of a block of spins has a universal logarithmic scaling with the size of the block that is proportional to the central charge @xcite . this provides an efficient numerical way to obtain the central charge of the cft that governs the critical point , see refs . @xcite for review . it is then natural to ask if entanglement measures in excited states can be used to extract more cft data , such as for instance the modular s or t matrices or quantum dimensions , numerically . in rational cfts local elementary excitations are catalogued into finite number of conformal families containing primary operators and their descendants . the simplest excited states can then be obtained by inserting local cft operators at some spatial points . in such states , one can study how the local operator changes the structure of entanglement in the ground state . more precisely , it is possible to compute the time evolution of the change in rnyi entropies for a reduced density matrix of a single interval due to the operator insertion @xcite see ref . @xcite for some results in various cft setups and ref . @xcite for entanglement in a related class of globally excited states . in 2d cft this analysis can be preformed analytically and rnyi entropies detect an increase in entanglement equal to the logarithm of the quantum dimension of the conformal family @xcite . having such a clear and elegant prediction from the cft , it is then natural to wonder if and how the logarithms of quantum dimensions are reproduced on the lattice . in this article we initiate such program for the simplest case of the critical ising chain . the advantage of the ising model is that it is exactly solvable and the action of a family of local operators can be efficiently simulated for large system sizes . the main subtle point of this analysis is the identification between the cft operators and their lattice counterpart . in fact , there are only few models where such map is well established see for instance the discussion in @xcite and a general belief is that a given lattice operator corresponds in the continuum to a primary operator plus its descendants . in the case of the two - point functions these extra contributions from descendants lead to corrections that are suppressed as higher powers with the distance . in this work , given a well established identification for the ising model operators , we will be able to check the contribution form this non - unique identification to the physics of entanglement propagation . we will see that for truly local operators on the lattice like the ising spin we recover the cft answer , but for operators with non - local support like ising energy the subleading contributions modify the leading answer and lead to a mismatch . the computations of rnyi entropies in cft are done using the replica method that , for excited states , boils down to calculation of correlation functions on complicated riemann surfaces . even for states locally excited by more than a single operator such objects are notoriously difficult to compute analytically and features of entanglement measures in this class of states remain unexplored . similarly , measures of distance between quantum states like , e.g. , relative entropy for locally excited states require the access to higher - point correlators @xcite . in this work , we will further explore the ising model to shed a new light in these directions by numerically performing the time evolution of the relative entropy , as well as rnyi entropies in more general states excited by multiple local operators . this paper is organized as follows . in section [ sec : cft ] we summarize the relevant results from the two dimensional cft . in section [ sec : num ] we present our main numerical results for the evolution of entanglement in the critical ising model in states excited by single local operators . in section [ sec : gen ] we consider the evolution away from the critical point , as well as more general operator excitations . in section [ sec : rel ] we present the evolution of the relative entropy after local operator excitation in this model . finally , we conclude and present the details of our numerical approach in the appendix [ numer ] . in this section we briefly review the existing results for the evolution of rnyi entropies in locally excited states in 2d cfts and then show some details of the computation for the ising cft . finally , we discuss the minor modifications that appear for the cfts on the cylinder that , in the following sections , we will be comparing to numerics from the periodic chain . let us start with a 2d cft on the real line and a state excited by a local operator @xmath0 at distance @xmath1 from the entangling interval @xmath2 $ ] , as presented pictorially on fig . [ fig : schematic ] . the density matrix is given by ( t)&=&ne^-ite^-(0,-l)|00|^(0,-l)e^-e^it & & n(w_2,|w_2)|00| ^(w_1,|w_1 ) , [ denmat ] where the insertion points of the local operators are defined as & & w_1=i(-it)-l , w_2 = -i(+it)-l , + & & |w_1=-i(-it)-l , |w_2=i(+it)-l . [ points ] the factor of @xmath3 is the uv regulator for the local operators and we take @xmath4 at the end of the computation . the normalization @xmath5 ensures that the trace of the density matrix is equal to 1 . + using the replica trick , we can compute how a family of rnyi entropies @xmath6 , indexed by integer @xmath7 , changes due to the local operator insertion . the answer to this question is expressed in terms of the logarithm of the ratio @xcite s_a^(n ) , [ eq : delta ] where the correlator in the numerator is computed on the @xmath7-sheeted surface @xmath8 with cuts on each copy corresponding to interval @xmath9 , and the two - point function in the denominator is on a single sheet @xmath10 with an interval cut @xmath9 . for a detailed derivation and further illustrative explanations see @xcite . in 2d cft , one can apply a conformal map from @xmath8 to a complex plane and evaluate the correlators explicitly . it turns out that the answer is universal and the increase in the rnyi entanglement entropies is equal to a constant that is the same for all the members of a conformal family , i.e. primary operators and their descendants @xcite . in rational cfts this constant is equal to the logarithm of the quantum dimension of the local operator @xcite which is defined as d_a=,[qdim ] where @xmath11 denotes the elements of the modular s - matrix of the cft , see e.g. ref . @xcite . in this work we focus on the 2d ising model which is the @xmath12 minimal model with three primary operators : the identity @xmath13 , the energy @xmath14 with conformal dimensions @xmath15 @xmath16 and the spin @xmath17 with @xmath18 @xmath19 , where @xmath20 marks the total scaling dimensions . + the modular s - matrix of the ising model is given by s= ( ccc 1 & 1 & + 1 & 1 & - + & - & 0 + ) , so the three quantum dimensions are d_=d_=1,d_=. this way , at criticality , only excitations with primary @xmath17 can non - trivially change the entanglement in the vacuum state , and for all the rnyi entropies we have @xcite s^(n)_a=. the standard , chiral ( anti - chiral ) descendants are obtained by either acting on the primary operators with chiral ( anti - chiral ) derivatives @xmath21 ( @xmath22 ) or taking the operator product expansion ( ope ) of the primary operators with the energy momentum tensor . such descendants increase the entropies by the same amount as the primaries . if we however act with the linear combination of the two derivatives , there is an additional contribution to the entropy equal to @xmath23 @xcite . we will see this in case of the spatial derivative @xmath24 acting on @xmath25 , which we consider in sec . [ sec : num ] c. .,width=264 ] in order to compare the cft results with numerics we have to take into account finite size of the system , @xmath26 . in the cft computation it enters through the invariant cross - ratios . let us , for simplicity , consider the change in the second renyi entropy @xmath27 that requires the correlator on two cylinders . the correlators entering are computed using a composition of the conformal map @xmath28 from each cylinder to the plane with a cut and the uniformization map @xmath29 . after some standard cft manipulations , the change in the entropy can be written as s^(2)_a=-(|z(1-z)|^4h_^_(z,|z)),[secren ] where @xmath30 is the canonical 4-point function on the complex plane with operators @xmath31 inserted at @xmath32 and the cross - ratios are defined as z=,|z= , with @xmath33 , @xmath34 and similarly for @xmath35 . from the conformal map , we can also show that @xmath36 and @xmath37 ( similarly for @xmath35 ) . once we plug the insertion points of the operators , in the @xmath4 limit , the cross - ratios become periodic functions of time , as shown on fig . [ fig : cr1 ] . the difference with the cft on the infinite line is that in one cycle of time equal to @xmath26 , both @xmath38 and @xmath35 reach their maximal value of @xmath39 . more precisely , @xmath40 in the time @xmath41=[l+\alpha n , l+l+\alpha n]$ ] and zero outside , whereas @xmath42 inside @xmath43=[n-(l+l)+\alpha n , n - l+\alpha n]$ ] and zero outside , for integer period @xmath44 . in order to extract the increase in the second rnyi entropy analytically in the @xmath4 limit , we simply take the limit of @xmath45 or @xmath46 in in the appropriate time intervals . let us focus on the explicit example of the ising model . for the @xmath17 operator , from the fusion rule @xmath47 , the correlator can be decomposed as @xcite ^_(z,|z)=(c^1_)^2|^_(1|z)|^2+(c^_)^2|^_(|z)|^2 , with the three - point coefficients @xmath48 and @xmath49 , as well as the conformal blocks ^_(1|z)=,^_(|z)=. we can then check that that the non - zero contribution in the two time intervals comes from the identity block and is equal to @xmath50 , in accordance with the modular s - matrix elements . this behavior is naturally explained from the quasi - particle picture where left and right moving sets of quasi - particles propagate from the insertion point of the operator and , on the circle , there are two time intervals where either left or right particles are inside the entangling interval @xmath9 . on the other hand , for the @xmath14 excitation , using the fusion @xmath51 , we can write the correlator as ^_(z,|z)=(c^1_)^2|^_(1|z)|^2 , with @xmath52 and conformal block ^_(1|z)=. clearly , inserting the cross - ratios and taking @xmath4 yields @xmath53 for all times . this suggests that the quasiparticles produced by" +"the transformation of photometric observations from one filter system to another is rarely a trivial task . this is especially true for observations of cool giants at near - ir wavelengths because of the presence of very deep molecular absorption bands both in the stars themselves ( eg . co and h@xmath2o ) and in the earth s atmosphere ( eg . co@xmath2 and h@xmath2o ) . examples of such transformations may be found in bessell & brett ( 1988 ) and elias et _ al . _ ( 1983 ) . because of these molecular bands the transformation equations can be dependent not only on stellar color , but also on absolute luminosity and stellar metallicity . for the hubble space telescope ( hst ) near infrared camera and multi - object spectrograph ( nicmos ) filters on camera 2 ( nic2 ; @xcite ) that have been used as pseudo-@xmath3 filters , the transformation to a standard ground - based system presents a particularly difficult case . this is because the commonly used nic2 filters ( f110w for @xmath4 , f160w for @xmath5 , and f222 m for @xmath6 ) differ significantly from the commonly used ground - based filters ( @xcite ) ; also there are no telluric absorption features in hst observations . nonetheless , many scientific programs , including our own , will require accurate ( uncertainties no worse than a few percent ) knowledge of these transformations . in order to derive accurate color transformations , we devoted two orbits of one of our observing programs ( go-7826 ) to gathering observations of cool , metal rich giants that have extensive ground - based observations on the cit / ctio system . these giants are all in the baade s window field of the galactic bulge . the brighter ones and a few of the fainter ones had previously been observed with the same single channel photometric system that was used to establish the cit / ctio grid of southern standards ( @xcite ; @xcite ) . the remainder of the fainter stars had previously been observed with a nicmos array by tiede et _ al . _ ( 1995 ) . this paper presents our hst - nicmos observations of these previously observed bulge giants which span the color range of @xmath0 . section two outlines our observations ; the reduction procedures are discussed in section three . a comparison with ground - based measurements and the color transformations are in section four . the final section is a brief summary . the targets were originally observed on 1998 , august 19 with hst , but problems encountered while traversing the south atlantic anomaly caused a loss of tracking . thanks to the gracious reallotment of time by the telescope time review board ( ttrb ) , our fields were reobserved on 1998 , october 28 . of the first observation attempt , we were only able to confidently salvage the observations of the first target , thus our quoted bw1 measurements are actually the average of measurements made on both visits . our observations consist of eight pointings in baade s window ( henceforth referred to as bw1-bw8 ) , from which we have obtained measurements of 19 stars previously observed from the ground . we will refer to these stars as `` standard '' stars . the first field ( bw1 ) is a small part of the `` bw4b '' field observed by @xcite ( see fig . this field is fairly rich , and includes 12 stars observed by tiede et _ al . _ ( 1995 ) . the remaining 7 fields ( bw2-bw8 ) are of single stars observed previously by frogel & whitford ( 1987 ) . the coordinates of each field are given in table 1 . our observations were taken with the nicmos camera 2 ( nic2 ) which has a plate scale of @xmath7 00757 pixel@xmath8 giving nic2 a field of view of 194 on a side ( 376 arcsec@xmath9 ) . the nicmos focus was set at the compromise position 1 - 2 , which optimizes the focus for simultaneous observations with cameras 1 and 2 . each field was observed in three filters : f110w ( @xmath10 ) , f160w ( @xmath11 ) , and f222 m ( @xmath12 ) , using a spiral dither pattern with 4 positions ( see section 4 for a discussion of the filters ) . we used 04 steps on bw1 to maximize the size of the overlapping field , and 5 0 steps on bw2-bw8 to minimize the effects of residual images from the bright stars . all of our observations used the multiaccum mode ( @xcite ) because of its optimization of the detector s dynamic range and cosmic ray rejection . the bw1 field used the predefined sample sequences step2 , step8 and step16 with 12 , 11 , and 14 samples in @xmath4 , @xmath5 , and @xmath6 respectively , yielding exposure times of 18 , 48 , and 128 seconds . fields bw2-bw8 implemented the multiaccum sample sequence scamrr , designed for fast temporal sampling with a single camera , which performs a nondestructive read every 0.203 seconds , yielding typical exposure times of 0.41 seconds for each of the four dither positions . table 1 lists the total exposure times in each filter for all targets . cosmic ray ( cr ) rejection using the multiaccum mode requires many intermediate reads . since most of our targets are of bright stars , our required exposure times were very short with only two to four intermediate reads during each exposure , an inadequate number for effective cr rejection . we therefore rely on the four dither positions for cr and bad - pixel rejection . c c c r r r bw1 & 18 03 49.9 & -30 02 06.6 & 71.76 & 191.80 & 511.68 + bw2 & 18 03 52.6 & -30 01 23.1 & 1.64 & 1.64 & 1.64 + bw3 & 18 03 46.1 & -29 59 12.5 & 1.64 & 1.64 & 1.64 + bw4 & 18 03 34.1 & -29 59 58.5 & 2.44 & 1.64 & 1.64 + bw5 & 18 03 46.1 & -30 02 23.6 & 1.64 & 1.64 & 1.64 + bw6 & 18 03 44.3 & -30 03 41.7 & 3.24 & 1.64 & 1.64 + bw7 & 18 03 43.7 & -30 05 15.8 & 3.24 & 1.64 & 1.64 + bw8 & 18 03 33.3 & -30 05 21.4 & 1.64 & 1.64 & 1.64 + our data were reduced using three different techniques . the first technique was the standard stsci pipeline . afterwards we performed our own reductions with the nicred v. 1.8 package dated 01/29/99 ( @xcite , @xcite ) , and with the stsci pipeline using the iraf nicproto package ( may 1999 ) to eliminate any residual pedestal . all the reductions use flat fields and dark frames provided by stsci , although we generated our own bad pixel masks for the nicred and nicproto reductions . not too surprisingly , all of these methods give similar photometric results , with no apparent systematic deviations and typical dispersions of @xmath13 magnitudes . although the images produced by nicred appear cleaner in terms of crs and bad pixels , all of our photometric measurements have been made off the frames reduced with the stsci pipeline and iraf nicproto package . aperture photometry was performed according to the guidelines set down by stsci ` ( http://www.stsci.edu/ftp/instrument_news/nicmos/nicmos_doc_phot.html ) ` for point - sources observed with nic2 . in our case we used the iraf phot routine with a 05 aperture and a @xmath14 sky annulus placed directly outside the aperture , assuming a nic2 plate scale of 00757 pixel@xmath8 . the measured count rate of each star was multiplied by 1.15 to correct to an infinite aperture , and then converted to flux using the nicmos photometric keywords released december 1 , 1998 , obtained from ` http://www.stsci.edu/ftp/instrument_news/nicmos/nicmos_phot/keywords.html ` , and listed in table 2 . finally the fluxes were converted to magnitudes using the parameters shown in table 2 . ( note that the photzpts in table 2 are _ not _ those given by stsci , but have been calculated to force the transformation to the cit / ctio system to be zero at zero ( @xmath15 ) color , as can be seen in eqn . one should also note that there are several methods of converting dn to magnitudes . two ways are to use either photflam & photzpt or photfnu & zp(vega ) , which are not equivalent and give different magnitudes ( because of a zero - point shift ) . we present our nicmos magnitudes ( ie . @xmath16 , @xmath17 , @xmath18 ) as obtained using photfnu & zp(vega ) so that we can directly compare our observations with the stsci standards ( see table 4 ) , but we have calculated the transformations for both methods ( eqns . 4 - 7 ) . another method , and the easiest of these presented , is to use our transformations to go directly from instrumental magnitudes to cit / ctio magnitudes ( see eqns . 8 - 9 ) . c c c c c f110w & 4.292364e-19 & 23.566 & 1.823290e-6 & 1898 + f160w & 2.406112e-19 & 24.546 & 2.070057e-6 & 1113 + f222 m & 3.217631e-19 & 26.131 & 5.280848e-6 & 653 + our measurements of the faint stars in our bw1 field are compared with the observations of tiede et _ al . _ ( 1995 ) . their observations were made on the 2.5 m dupont telescope at las campanas observatory with the ircam ( @xcite ) , which used a @xmath19 hgcdte nicmos 3 detector with a plate scale of 0.348 arcseconds pixel@xmath8 . their measurements were calibrated from 11 stars measured previously with single - channel photometry ( @xcite the same system used for the ground - based measurements of the stars in bw2-bw8 ) to the cit / ctio system ( @xcite , 1983 ) . these measurements have reported average errors given in fig . 3 of @xcite ( @xmath20 ) , and calibration errors of @xmath21 , @xmath22 , @xmath23 magnitudes . our measurements of the single stars in fields bw2-bw8 are compared with the measurements of frogel & whitford ( 1987 ) . these were obtained on the ctio 4 m and the d3 insb system , and transformed to the cit / ctio standard system . note that their published table 1 is corrected for reddening and extinction by @xmath24 , @xmath25 , and @xmath26 , while our values are uncorrected . in figure 2 we have plotted the difference between the ground - based measurements and our nicmos photfnu & zp(vega ) calibrated measurements against color for each filter . these plots show that a color term is required to bring the nicmos data into agreement with ground - based observations . by applying a linear fit to the data , giving stars fainter than @xmath27 half weight ( points with @xmath28 ) , we have calculated the appropriate transformations ( eqns . 4 - 9 ) . as discussed in section 3 , stsci supplies two sets of keywords for converting count rates to magnitudes . to eliminate confusion , equations 1 - 3 explicitly state how the magnitudes used in calculating our transformations were determined . @xmath29 where cr@xmath30 is the count rate measured in a 05 aperture . using the photfnu & zp(vega ) keywords to calculate @xmath31 : @xmath32 @xmath33 using the photflam & _ our _ photzpt ( from table 2 ) to calculate @xmath31 : @xmath34 @xmath35 going directly from raw instrumental nicmos magnitudes : @xmath36 @xmath37 these transformations are required due to the differences between cit /" +"based on studies of the morphology - density relation in clusters ( dressler 1980 ) and groups ( wilman et al . 2009 ) , it has been suggested that lenticular ( s0 ) galaxies may be the descendants of spirals that have undergone some evolutionary process ( e.g. ram pressure stripping , galaxy harrassment , gas starvation and/or mergers ) . recent investigations of s0s have studied their metallicity gradients ( bedregal et al . 2011 ) , tully - fisher relation ( bedregal , aragon - salamanca & merrifield 2006 ) and stellar populations ( aragon - salamanca , bedregal & merrifield 2006 ) . however , the origin of s0s is still a subject of much debate ( e.g. kormendy & bender 2012 ) . the internal kinematics of galaxies are a key tool to understanding their structure and formation histories , and s0s are no exception . for example , the kinematics will be largely unaffected if s0s were formerly spirals that have been simply stripped of gas or if they were involved in a relatively minor merger . although half of the stellar mass within a galaxy lies within one effective radius ( r@xmath3 ) , more than 90% of the _ total _ mass and angular momentum does not ( romanowsky & fall 2012 ) . thus in order to examine the internal kinematics and total mass of early - type galaxies one must probe well beyond 1 r@xmath3 . elliptical and s0 ( early - type ) galaxies often lack the significant quantities of extended hi gas commonly found in spirals , so the kinematic tracers are the galaxy starlight itself , planetary nebulae ( pne ) and globular clusters ( gcs ) . using the underlying starlight of a galaxy to probe its stellar kinematics is perhaps the preferred method , however the surface brightness of a galaxy declines rapidly with increasing radius so it is very difficult to obtain high quality spectra beyond a few effective radii without a large investment of 8m - class telescope time ( coccato et al . 2010 ) or using deep single pointings ( weijmans et al . pne and gcs have the advantage that they are ubiquitous in the halos of early - type galaxies out to large galactocentric radii ( 510 r@xmath3 ) . although there have been several studies of pne and gc system kinematics in early - type galaxies , very few studies have directly compared them to each other , or to results from galaxy starlight over a common radial range . luminous pne are the end product of low mass stars . however , there is still debate as to whether they arise from normal single - star evolutionary processes or from mass transfer in a binary star system ( ciardullo et al . 2005 ) in the former case , the pne observed in early - type galaxies would have an age of @xmath01.5 gyr , and in the latter case they could be as old as 10 gyr . coccato et al . ( 2009 ) showed that the radial surface density of pne follows the galaxy starlight in early - type galaxies and that they are useful probes of galaxy kinematics . however , ellipticals with embedded thick disks and s0 galaxies may contain two subpopulations of pne , one associated with the disk and one with the bulge , as seen for spiral galaxies ( nolthenius & ford 1987 ; hurley - keller et al . 2004 ) . not accounting for the different kinematics of these distinct pne subpopulations could lead to misleading results as illustrated recently by cortesi et al . ( 2011 ) for the lenticular galaxy ngc 1023 . furthermore , dekel et al . ( 2005 ) suggested that an intermediate - aged population of pne may have ` contaminated ' the pne velocity dispersions of some galaxies in the early - type sample of romanowsky et al . ( 2003 ) and hence impacted the resulting mass analysis . the globular cluster ( gc ) systems of all large galaxies , irrespective of hubble type , generally consist of two subpopulations blue ( or metal - poor ) and red ( or metal - rich ) . both of these subpopulations are thought to have ages @xmath4 10 gyr and hence trace old stellar populations ( for a review of gc system properties see brodie & strader 2006 ) . the blue subpopulation is associated with galaxy halos ( forte et al . 2005 ; forbes et al . 2012 ) whereas the red subpopulation has been shown to share many properties with the spheroid / bulge stars of early - type galaxies ( strader et al . 2011 ; forbes et al . 2012 ) , including their kinematics ( pota et al . we note that the association of red gcs with the bulge and not with a thin disk component extends to spiral galaxies , including our own ( minniti 1995 ; cote 1999 ) and the sombrero ( forbes , brodie & larsen 2001 ) . to better understand the issues discussed above it is important to directly compare different kinematic tracers for the same galaxy . here we combine starlight , pne and gc data for an archetype lenticular galaxy ngc 2768 and directly compare these different kinematic tracers in the same galaxy . the galaxy is a nearby , near edge - on s0 ( sandage , tammann & van den bergh 1981 ) , although we note that it was originally classified as an e6 in the rc3 catalogue . according to wikland et al . ( 1995 ) is it an isolated galaxy however it has also been classified as part of the lyon group of galaxies ( lgg ) 167 ( garcia 1993 ) . it reveals ionised gas and a minor axis dust lane ( kim 1989 ) . the central ionised gas and stars are known to have different kinematics ( fried & illingworth 1994 ) suggesting an external origin for the gas . ngc 2768 is a rare example of an early - type galaxy with detectable co emission ( wikland et al . 1995 ) and the host of a calcium - rich supernova type ib ( filippenko & chornock 2000 ) . the effective radius of the galaxy is 1.06 arcmin ( proctor et al . 2009 ; cappellari et al . 2011 ) . for a distance of 21.8 mpc ( cappellari et al . 2011 ) , this corresponds to 6.7 kpc . using a new technique to extract integrated kinematic information of the underlying galaxy starlight from a multi - slit spectrograph , proctor et al . ( 2009 ) presented 2d stellar kinematics for ngc 2768 out to @xmath03 r@xmath3 . here we have carried out a re - analysis of the proctor et al . galaxy data after re - defining the sky scaling index continuum passbands to avoid any strong spectral features associated with the galaxy , as well as any skylines in order to refine the sky subtraction ( see foster et al . 2009 for more details ) . the resulting velocity and velocity dispersion profiles are similar to those published in proctor et al . ( 2009 ) . the total number of positions with stellar kinematics available are 104 and our full dataset is given in table 1 of the appendix . velocity data for 315 pne in ngc 2768 were acquired using the pn.s spectrograph ( douglas et al . 2002 ) in 2007 and are available at : www.strw.leidenuniv.nl/pns/ details of the data reduction procedure and analysis can be found in cortesi et al . ( 2011 , 2012 in prep . ) . following coccato et al . ( 2009 ) , a uniform magnitude cut has been applied and radial incompleteness tests carried out . thus each bin of the pne surface density distribution is complete to a given magnitude and has been statistically corrected for any radial incompleteness . all are spectroscopically confirmed . the pne data reach out to @xmath05r@xmath3 . the radial surface density distribution and velocity data for gcs comes from the imaging and spectroscopy of pota et al . briefly , imaging from hst allows us to model and subtract the galaxy light , and hence detect gcs in the galaxy inner regions with little or no radial incompleteness . the resulting surface density distribution for over 500 gcs is a combination of hst data in the inner regions and subaru data in the outer regions , with a background level subtracted . blue and red gcs were separated according to the local minimum of their bimodal colour distribution , i.e. at r z = 0.56 ( pota et al . 2012 ) . follow - up keck spectroscopy returned 112 kinematically - confirmed blue and red gcs ( pota et al . the blue gcs , associated with galaxy halos ( forbes et al . 2012 ) , were found not to rotate ( pota et al . 2012 ) . here we only consider further the 62 gcs from the red subpopulation . for these gcs the mean velocity is 1353 @xmath5 3 kms @xmath6 in excellent agreement with the galaxy systemic velocity of 1353 km s @xmath6 ( cappellari et al . the red gcs reach out to @xmath04 r@xmath3 and we henceforth assume they are all associated with the bulge of the galaxy ." +"the control and detection of single spins is of considerable recent interest . a particularly interesting method of detecting a single spin on a surface is possible by a scanning tunneling microscope ( stm ) @xcite . the technique has been initiated and developed by y. manassen and various collaborators @xcite . it is based on monitoring the noise , i.e. the stm current - current correlations , and observing a signal at the expected larmor frequency , a signal that is sharp even at room temperature . the larmor frequency is also seen in an electron spin resonance ( esr ) experiment with many spins , in contrast , the esr - stm method observes a single spin and furthermore , the system is static , no oscillating field is applied as in esr . the observed frequency is found to vary linearly with the applied magnetic field , confirming that the stm has detected an isolated spin on the surface . this phenomenon was first demonstrated on oxidized si(111 ) surface @xcite and then on fe atoms @xcite on si(111 ) as well as on a variety of organic molecules on a graphite surface @xcite and on au(111 ) surfaces @xcite . recent extensions have resolved two resonance peaks on oxidized si(111 ) @xmath0 surface corresponding to site specific @xmath1 factors @xcite as well as to observation of hyperfine coupling @xcite . we further note that the spatial dependence of the signal shows a non - monotonic contour plot , i.e. the signal is elongated and is maximal at @xmath2 nm on either side of a minimum point @xcite . the theoretical understanding of the esr - stm effect is not settled @xcite . the emergence of a finite frequency in a steady state stationary situation is a non - trivial phenomenon . an obvious mechanism for coupling the charge current to the spin precession is spin - orbit coupling @xcite . it was shown that an esr signal is present in the noise with spin - orbit coupling when the leads are polarized , either for a strong coulomb interaction @xcite or for the non - interacting case @xcite , and even in linear response @xcite . however , the experimental data @xcite involves a small field of @xmath3 g corresponding to a larmor frequency of @xmath4mhz , i.e. @xmath5 relative to a lead s bandwidth . it was found in these spin - orbit models @xcite that the signal vanishes when the lead polarization vanishes , or when the lead and dot polarization are parallel , as for a uniform magnetic field . it was argued that an effective spin polarization is realized as a fluctuation effect either for a small number of electrons that pass the localized spin in one cycle @xcite or due to 1/f magnetic noise of the tunneling current @xcite . it was further shown that spin - orbit coupling in an asymmetric dot can yield an oscillating electric dipole , possibly affecting the stm current @xcite . in the present work we follow a recently proposed model that allows for an esr - stm phenomena with non - polarized leads @xcite . the model assumes an additional direct tunneling between the tip and the substrate in parallel to tunneling via the dot s states , i.e. a nanoscopic interferometer . the numerical study @xcite shows that the interference of the direct current and that via the spin has an esr signal in the noise , a signal that increases with the direct tunneling . this model is motivated by studies of quantum dots with spin - orbit @xcite and by stm studies of a two - impurity kondo system that shows a significant direct coupling between the tip and substrate states @xcite . similar models including a aharonov - bohm phase have been studied @xcite . the nanoscopic interferometer model is consistent with the unusual non - monotonic contour plot @xcite , i.e. the signal is maximized when the stm tip is not directly on the spin center but slightly away , so as to maximize an overlap with a surface state of the substrate . in the present work we consider non - polarized leads , as relevant to the experimental setup , and evaluate the noise analytically in the stationary system , in accord with the numerical results for this case . the analytic results clarify the physical processes of the resonance phenomenon and allow us to discuss the esr - stm effect for a broad range of parameters , as in the conclusion section below . the paper is organized as follows . in sec.ii we introduce the hamiltonian of the system and present the results for direct tunneling : effective action , the current and the current noise power spectrum . sec . iii contains the effective action of the dot and the expression for the current flow through dot . iv reflects our principal result : the resonance part of the current spectral density . the results are illustrated by figs 1,2 . finally our conclusions are contained in sec.v . the appendices a , b , c give various details of the calculations . the hamiltonian of the system describes direct tunneling through the dot between left ( l ) and right ( r ) leads as well as l - r tunneling via the dot states , @xmath6 where the lead hamiltonians are @xmath7 , @xmath8 , @xmath9 is the spin and @xmath10 are the continuum states . the dot hamiltonian is @xmath11 with @xmath12 , @xmath13 is the mean position of the dot levels and @xmath14 is the applied magnetic field that includes the @xmath1 factor and the bohr magneton . we assume that the dispersions @xmath15 of the lead electrons are spin independent , justified by the small ratio @xmath5 of the larmor frequency and a typical electron bandwidth . a general spin - orbit coupling involves unitary matrices that can be parameterized @xcite by two angles @xmath16 . the angle @xmath17 appears in the hamiltonian for the direct tunneling @xmath18 the spin dependent form in @xmath19 is required by time reversal . the angle @xmath20 appears in the tunneling via the dot as a spin rotation in the @xmath21 lead , while the @xmath22 lead is diagonal in spin @xmath23+h.c.\ ] ] where @xmath24 we note that special cases of this parameterization have been used in related models @xcite . to calculate the current and the noise we use the keldysh formalism @xcite and include in the action a quantum source field @xmath25 that couples to the total current . the source term has the form @xmath26 where @xmath27 is a pauli matrix in the rotated keldysh space . the total action is @xmath28 where @xmath29 corresponds to @xmath30 , i.e. tunneling via the dot @xmath31 and @xmath32 is the action of the dot @xmath33 @xmath34 is the green s function ( gf ) of the noninteracting dot in the rotated keldysh representation that has the form @xmath35 with retarded ( @xmath21 ) , advanced ( @xmath36 ) and keldysh ( @xmath37 ) indices as superscripts . the current via the dot @xmath38 is chosen as a symmetric combination of the current from the left lead to the dot @xmath39 and that from the dot to the right lead @xmath40 . in general a linear combination of these currents is needed , depending on various capacitances @xcite . we expect that the resonance effect is dominated by single occupancy of the dot and the latter two currents are equal . indeed we check below that our results for the resonance term do not depend on which linear combination is used . furthermore , the numerical study @xcite used @xmath39 for the noise evaluation with results consistent with our analytic ones . here and below the dot electron operator @xmath41 becomes a vector in spin space ( and keldysh space ) . the gf @xmath42 are diagonal in spin space and in terms of a fourier energy variable @xmath43 are given by @xmath44 with the limit @xmath45 . the part of the action @xmath46 which contains the leads and the direct lr tunneling is @xmath47\,.\label{sw}\end{aligned}\ ] ] here @xmath48 , @xmath49 are vectors and pauli matrices , respectively , in lr ( left - right ) space , the gfs of the leads @xmath50 are diagonal in lr space and @xmath51 present a constant matrix in momentum k , k space . fermion operators and gf as well the quantum source field @xmath52 acts in the rotated keldysh space . the voltage @xmath53 between the leads is assumed small relative to the bandwidths , hence the density of states @xmath54 are taken as constants . the gf @xmath55 has the structure of eq . ( [ g0 ] ) and its momentum integrated forms @xmath56 are @xmath57 where @xmath53 is the voltage difference between the lr leads and @xmath58 . to cope with scattering of electrons due to the tunneling we shift the operators @xmath48 so as to cancel the linear coupling to @xmath59 in eq . ( [ st ] ) . this adds a term of the form @xmath60 to the dot action and then the effective action separates into two independent parts @xmath61 . the total generating functional @xmath62 , as a function of the source field , is therefore factorized into @xmath63 . we consider now the @xmath46 part of the effective action . inverting @xmath64 by using blockwise matrix inversion we obtain @xmath65 here @xmath66 , @xmath67 and the coupling parameter @xmath68 the electron transport and noise calculations involve only the integrated gf of eq . ( [ g ] ) . direct integration over electron operators @xmath69 yields @xmath70=\exp[\tr\ln g^{-1}]$ ] . the direct current @xmath71 and related noise power are defined as derivatives with respect to the source field ( taking @xmath72 after derivatives is implied ) @xmath73 we obtain the textbook results @xcite for noise and transport current through a contact with transmission probability @xcite @xmath74 and reflection coefficient @xmath75 ( details in appendix a ) , the conductance is then @xmath76 . the effective action of the dot includes the @xmath77 term from the integration over the lead fermions . it is expressed ( in keldysh space ) in terms of various gfs @xmath78 as listed in eq . ( [ gbar ] ) and in terms of the noninteracting dot gf eq . ( [ g0 ] ) as @xmath79\label{q}\end{aligned}\ ] ] the matrix @xmath80 is @xmath81=@xmath82 where @xmath83 , @xmath84 and @xmath85 are pauli matrices in spin space . here we introduce the tunneling widths : @xmath86 . taking @xmath72 and inverting @xmath87 we find the gfs of the dot interacting with the leads ( see appendix a ) . as we find below , the resonance contribution to the noise is related to terms that involve the matrices @xmath88 ( or @xmath89 in eq . ( [ c5 ] ) ) . we note therefore that the result for the resonance term does not depend on which combination of currents @xmath39 and @xmath40 ( determining the source terms @xmath90 in ( [ q ] ) ) are used . integrating out the dot fermions @xmath41 with the action ( [ sd ] ) we arrive at the generating functional @xmath91 $ ] which depends on the vertex function @xmath77 . similar to ( [ dz ] ) the current through the dot is @xmath92\label{id}\end{aligned}\ ] ] performing calculations for the case of equal tunneling widths @xmath93 ( see appendix b ) we obtain the current : @xmath94 where @xmath95 \delta^{(-)}_{\epsilon}\label{jd3}\end{aligned}\ ] ] here @xmath96 and @xmath97 . the trace in the last equation ( [ jd3 ] ) is @xmath98 & = & \sum_{\sigma}[-\frac{\sin^2\phi \cos^2\theta/2}{\bar{\gamma } } img^r_{\sigma}(\epsilon)+\nonumber\\ & & \sin^2(\theta/2 ) g^r_{\sigma } g^a_{-\sigma}]\label{tr}\end{aligned}\ ] ] presents two different scattering processes . the first term with @xmath99 appears also" +"classical globular clusters are prominent objects with respect to the surrounding fields . in recent years , however , low luminosity globular clusters have been identified or discovered in the galaxy . these include obscured or field contaminated objects , or a combination of these factors ( e.g. @xcite , and references therein ) . @xcite recently found glimpse - c02 , an extremely obscured and metal rich globular cluster , * which was almost simultaneously detected by @xcite . * pfleiderer2 was found by @xcite and has been also referred to as pwm2 . the cluster center is located at ( j2000 ) @xmath3 , @xmath4 , with galactic coordinates @xmath5 , @xmath6 . the angular size is @xmath7 , as seen on dss / xdss images . in sect . [ obs ] the observations and reductions are described . in sect . [ decont ] we describe the decontamination procedures . colour magnitude diagrams ( cmd ) are presented and fundamental parameters derived in sect . the cluster structure is studied in sect . [ struc ] . concluding remarks are given in sect . [ conclu ] . pfleiderer2 was observed on 2008 june 5 , 6 , with the 3.58 m galileo telescope ( tng ) at la palma , equipped with the dolores spectrograph focal reducer . a eev 4260 ccd detector with @xmath8 pixels , of pixel size 13 @xmath9 m was used . a pixel corresponds to @xmath10 on the sky , and the full field of the camera is @xmath11 . the log of observations is provided in table 1 . in fig . [ fig1 ] is shown a 420 sec full field @xmath12 image of pfleiderer2 , showing a rather prominent cluster . rrrrrrrrr v & 5 - 6/06/2008 & 600 & 1.1 & 1.2 & + i & & 30 & 1.2 & 1.2 & + i & & 420 & 1.1 & 1.2 & + v & 6 - 7/06/2008 & 30 & 1.6 & 1.7 & + v & & 900 & 1.6 & 1.6 & + b & & 60 & 1.5 & 1.5 & + b & & 20 & 1.4 & 1.5 & + b & & 900 & 1.4 & 1.4 & + b & & 60 & 1.4 & 1.4 & + the calibration was performed using 3 different landolt ( 1983 , 1992 ) standard fields observed in bvi , the first night ( pg1633 + 099 , sa 113337 , pg 2213 - 06 ) with different exposure times and in different positions . we checked shutter time dependence and zero point variations across the field . in the second night ( june 6th ) five additional @xcite fields have been observed ( pg 1323 - 086 , pg1528 + 062 , pg1633 + 099 , sa113 337 , pg 2213 - 06 ) . the airmass corrections of 0.15 in v , 0.25 in b and 0.07 in i , have been done using the standard values given for la palma in clear nights ( with no dust in the atmosphere ) , available at the dolores webpagepalma@xmath13sky.html ] the derived calibration equations are : v = 28.44 - 0.06(v - i)+v i = 28.28 - 0.07(v - i)+i b = 28.59 + 0.12(b - v)+b v = 28.43 - 0.06(b - v)+v where the zero points are calculated for 10s exposures at 1.15 airmasses , with an aperture of @xmath14 . the bvi are instrumental magnitudes ( counts in adus , gain 1 e-/adu ) . bvi are the calibrated magnitudes . the zero points were remarkably stable and identical in the two nights . no shutter time effects have been detected at the 0.01 mag . level in the exposure range of our images ( from 1 to 30 s ) . in the @xmath15 pixels central area the standard stars showed a very good uniformity , but their flux rapidly decreased at the frame corners . the repeated measurements of the standard stars across the field have been used to separate the contribution of the sky concentration from the flat field , including the decrease of sensitivity of the system ( possibly due to some vignetting ) at the edge . measurements performed with different apertures excluded the possibility that the loss of light at the edges was due to degradation of the psf . the ccd frame reductions were performed using a slightly more complex procedure than the standard flat field division . this was needed due to the analysis of the standard star fluxes across the field , compared to the background brightness , and showed a sky flux excess in an area roughly corresponding to the central 500 pixels . this excess is interpreted as the effect called `` sky concentration '' ( @xcitecalibration.ps ] ) . this is known to be caused by internal reflections and it is color dependent . in our images it reached about 6% in i , 5% in v ( fig . [ fig2 ] ) and it was almost negligible in b. if the light concentration is not removed from the flatfields , it causes a systematic photometric error across the field of the same amount . the light loss at the edges was instead almost constant with the colors , up to 5% from center to corner . the flatfielding ( after bias correction ) was performed in four main steps : ( 1 ) a map of sky concentration was prepared using the standard stars , compared to the sky level ; ( 2 ) the contribution of the light concentration was extracted from the flatfields and smoothed ( fig . [ fig2 ] ) ; ( 3 ) the light concentration was scaled to the value of the sky images and subtracted ; ( 4 ) the flatfield obtained after removing the light concentration was used to correct the high frequencies and sensitivity variations ( including vignetting ) . the corrected images have been processed using daophot ii and allstars ( @xcite ; @xcite ) . the software is available in midas for the instrumental photometry of individual stars , and it was converted into the standard johnson - cousins system , defined from the landolt stars , using the above calibration equations . the conversion from the instrumental ( psf convolved ) magnitudes to the calibrated ones revealed an additional problem related to the image quality variation across the field . this produces a variable aperture correction , changing with time and filter . in pfleiderer2 images it was of the order of 0.02 magnitudes , with a peak around 0.04 magnitudes at the extreme corners . for this reason we adopted the aperture correction established from stars located in the central 200 pixels which is representative of most of the image within about 1% to 2% . the resulting calibration accuracy , taking into account the uncertainties in the calibration equations ( @xmath160.01 mag ) , the flatfield procedure ( an additional 0.01 - 0.02 mag ) and the aperture corrections ( 0.02 mag ) , is estimated to be within @xmath17 in a single filter . the relative photometric errors have been derived from short exposures ( 15s in v and 10s in i ) frame to frame images . the errors are 0.03 mag for 14 @xmath18 v @xmath18 16.5 , increasing to about 0.2mag at v=20.5 . in order to have the errors for our deep 600s exposures , they must be scaled to the corresponding magnitudes . the 600 sec images imply a factor 40 larger in exposure times , and the corresponding error values can be estimated from the ones given above . field - stars are an important contaminant of cmds in rich fields , especially near the disk and bulge . the decontamination algorithm employed here is based on a three - dimensional routine designed for the wide - field photometry of 2mass data , as developed in @xcite , @xcite and @xcite . in the present case we adapted the original algorithm to work with photometry obtained with a large telescope and a single color . for clarity , we recall the basic procedures . the algorithm divides the whole magnitude and color ranges into a grid of cmd cells . for a given cluster extraction and comparison field , it estimates the relative number densities of probable field and cluster stars present in each cell . the estimated number of field stars is subsequently subtracted from each cell . * decontamination results for different cluster / field contrasts are given and discussed in the above cited papers . the reference cell dimensions are @xmath19 and @xmath20 . however , to minimize spurious results , several runs of the decontamination procedure are used , with different input parameters . * in the present paper , different cell sizes are considered , with @xmath21 and @xmath22 taken from 0.5 , 1.0 and 2.0 times the reference values . also , the cell grid is shifted by -1/3 , 0 and + 1/3 of the respective cell size in both the colour and magnitude axes . taking together all the grid / cell size setups , we are left with 81 different and independent decontamination combinations . stars are ranked according to the number of times they survive each run . finally , only the highest ranked stars are considered as cluster members and transposed to the respective decontaminated cmd . in the case of pfleiderer2 , the decontaminated stars have a survival frequency above @xmath23 . we note that the two bright and red stars ( figs . [ fig6 ] and [ fig7 ] ) are among those with @xmath24 , which implies that the observed field is scarcely populated of stars with similar colour and magnitude . in fig . [ fig3 ] we investigate the surface density ( @xmath25 , in units of @xmath26 ) distribution of pfleiderer2 both with the observed ( left panels ) and decontaminated ( right ) photometry . we also include the respective isopleth surface maps ( bottom panels ) , which show a rather circular geometry in the stellar distribution around the center of pfleiderer2 . as expected , the cluster is much more contrasted in the decontaminated data . fig . [ fig4 ] shows the @xmath27 vs. @xmath28 cmd of essentially the full field ( r @xmath18 1000 pixels , or r @xmath18 4.2 ) * around pfleiderer2 , reaching the photometric limit of @xmath29 . as anticipated in sect . [ decont ] , field contamination is dominant in this direction . a few bright and red stars show up at @xmath30 and @xmath31 , which might suggest a metal - rich cluster . * the fit of padova isochrones ( @xcite ) to the v vs. v - i cmd of pfleiderer2 is shown in figs . [ fig5]a , b for extractions of r @xmath18 10 and 30 . a tilted red giant branch ( rgb ) is seen , together with a clump of stars at @xmath32 and @xmath33 , compatible with a red horizontal branch ( hb ) . a tilted rgb is indicative of a high metallicity as discussed in @xcite . we also note that the spread across the diagram is due to differential reddening . the fit of the isochrones to the cluster sequences in these figs . required a high metallicity of z=0.019 ( [ fe / h]@xmath340.0 ) . it might be one of the most metal - rich globular clusters in the galaxy . the age estimated is 10@xmath12 gyr , compatible with a globular cluster . this leads to a reddening of e(v - i)=1.34 . assuming e(v - i)/e(b - v)=1.33 ( @xcite ) , we get e(b - v)=1.01@xmath10.15 , which corresponds to a@xmath35 = 3.13 . this" +"the present contribution focuses on the dynamics of particles and their accumulation in electro - osmotic flow through micro - channel junctions which are a basic element of microfluidic systems . this work thus extends previous studies @xcite that focused on describing the interesting hydrodynamic behavior , wherein beyond a critical level of external - field intensity , vortices are observed to appear within the flow around ( sharp ) corners of micro - channel junctions . the generation of such vortices is potentially useful in certain applications as a means to enhance and control micro - fluid mixing @xcite . in other situations the appearance of vortices may need to be suppressed so as to avoid accumulation of suspended particles leading to the eventual jamming of the device @xcite . in linear electro - osmosis , when the equilibrium zeta potential is uniform and independent of the external field , the resulting flow is irrotational . however , the small yet finite polarizability of the walls gives rise to an additional , non - linear , electro - kinetic mechanism termed induced - charge electro - osmosis ( iceo ) @xcite . when an external field is applied to the system , it sets off within the electrolyte solution transient ohmic currents which create a non - uniform charge cloud near the walls . thus , a non - uniform distribution of induced zeta potential is established whose magnitude is proportional to the external - field intensity . the helmholtz - smoluchowski slip velocity at the fluid - solid interface resulting from the interaction of the electric field and the induced - charge cloud is non - linear in the applied field and generates an electro - osmotic flow which is not necessarily irrotational . thamida & chang @xcite pointed out that the above mechanism produces opposite polarization of the respective upstream and down - stream faces of the corner . furthermore , for a sufficiently strong external field this iceo not only dominates the local flow near the corner but produces downstream macro - scale vortices as well @xcite . thamida & chang @xcite also observed that an interesting colloid accumulation occurs at the corner , however no attempt was made to address this particle trapping mechanism either theoretically or experimentally . as will be shown herein , the rapid trapping occurs due to a combination of the short range dep trapping force and the long - range induced electro - osmotic flow which feeds the particles . previous studies have examined particle trapping and separation based on insulator - based dielectrophoresis ( idep ) using sharp tips among other geometries @xcite . however , in contrast to the current study , these works have treated such structures as insulators and as a result induced electrokinetic effects , emanating from the finite but small dielectric polarizability of the wall materials , were overlooked . nevertheless , efficient trapping via the combination of a short range dep force and far - field hydrodynamics has been shown for a variety of flow generation mechanisms . ac electroosmosis ( aceo ) , which uses electrodes embedded within the microchannel , has attracted a lot of attention as means for vortex generation and particle trapping through hydrodynamic forces that focus the particles into the stagnation point of the vortices @xcite . additionally , similar accumulation has recently been demonstrated @xcite at the stagnation points of electro - osmotic vortices of the second kind formed at the interface of a microchannel and a wide nanoslot . it is thus the focus of the current study to provide for the first time a thorough explanation , based on both theory and experiments , for the rapid particle trapping due to the combined forces of the dep and iceo vortex at the corner of a microchannel . in the following , we describe the experimental methods in sec . 2 , the theoretical model in sec . 3 , the results and discussion in sec . 4 and concluding comments in sec . 5 a l - junction microchannel connected to two reservoirs at opposite ends ( fig . [ fig : the flow system](a ) ) ] with a depth ( normal to the plane of view ) of 120 m was fabricated from pdms ( polydimethylsiloxane , dow - corning sylgard 184 ) using a rapid prototype technique @xcite . we used a high resolution ( 3 mm ) chrome mask for the creation of the master . the radii of curvature of the corner is estimated to be ~6 m the channel was then sealed by a pdms coated ( 30 m thick ) microscope glass slide , using a plasma bonding process @xcite . two large ( 19 mm diameter ) reservoirs were inserted into the pdms inlets so as to minimize possible pressure driven flow due to induced pressure head and to allow the introduction of platinum wire electrodes ( fig . ( [ fig : the flow system])b ) . a high voltage dc power supply ( stanford research systems ps350 ) was connected to the platinum wire electrodes ( 0.5 mm platinum wire , sigma - aldrich ) . an electrolyte solution of 10 ^ -5^[m ] potassium chloride ( conductivity @xmath0 ms / cm ) was seeded by negatively charged fluorescently tagged tracer particles ( fluoro - max , thermo - scientific ) of various sizes ( 0.48 , 1 and 2 mm ) and volumetric concentrations of ( 0.0025% , 0.01% , 0.04% respectively ) . the particles were visualized dynamically using a spinning disc confocal system ( yokugawa csu - x1 ) connected to a camera ( andor ixon3 ) and installed on an inverted microscope ( nikon ti eclipse ) . prior to the sudden application of the external field the system was equilibrated to minimize initial pressure driven flow . here we extend the theoretical analysis of yossifon et al . @xcite for iceo around a sharp corner to include dep forces acting on particles . for brevity , in deriving the latter hydrodynamic contribution to the particle motion we will closely follow their derivation , skipping the details and showing only the main results . the current problem for the l - junction differs from that of the t - junction microchannel configuration of yossifon et al . 2006 @xcite only in that the mid - narrow channel symmetry line is replaced by a wall ( i.e. we apply an electroosmotic slip velocity instead of a symmetry condition at @xmath1 boundary , see fig . [ fig : the - l - junction - configuration . ] ) . the l - junction configuration ] it is noted that for a low - conductivity electrolyte , electrothermal effects stemming from joule heating ( which scales linearly with the conductivity ) become minimal @xcite . moreover , for the current geometry , it may also be shown that any inplane temperature gradients ( which would potentially control the 2d electrothermal forcing ) resulting from such minimal joule heating , would be negligible as most of the generated heat dissipate through the bottom slide which has minimum thermal resistance . the introduction into the problem of a small but finite wall dielectric constant @xmath2 , necessitates the simultaneous calculation of both @xmath3 and @xmath4 , the electrostatic potentials within the fluid and wall domains , respectively . on the microscale of the electric double layer these potentials are coupled through the boundary conditions imposing continuity of the potential and specifying the jump in electric displacement across the true solid - liquid interface @xcite . the thin - double - layer approximation was previously extended by yossifon et al . 2006 @xcite to account for the electric - field leakage through the wall for an arbitrary value of the dielectric constants ratio @xmath5 , to obtain an appropriate macro scale boundary condition for a symmetric electrolyte solution relating @xmath3 just outside the double layer and @xmath4 at the surface of the wall @xmath6 the dimensionless robin - type boundary condition ( [ eq : robin cond . on wall-1 ] ) is formulated in terms of the dimensionless electric potentials @xmath3 , @xmath4 and the equilibrium zeta - potential @xmath7 normalized by @xmath8 , wherein @xmath9 is the width of the narrow channel and @xmath10 is the magnitude of the externally applied electric field within the narrow channel far from the junction . here @xmath11 denotes the derivative in the direction normal to the wall pointing into the fluid domain . appearing in ( [ eq : robin cond . on wall-1 ] ) is the parameter @xmath12 , wherein @xmath13 is the ( presumed small ) debye length , which represents the thickness of the electric double layer . under this macro scale boundary condition ( 1 ) the dimensionless electric potentials within the bulk fluid and within the wall both satisfy the laplace equation . in addition , the potential within the bulk fluid satisfies the neumann - type boundary condition @xmath14 applied on the channel walls ( @xmath15 and @xmath16 in fig . [ fig : the - l - junction - configuration . ] ) . these boundary conditions are supplemented by the requirements that@xmath17 within the narrow channel far from the junction ( @xmath18 ) ( see fig . [ fig : the - l - junction - configuration . ] ) and by conservation of electric - field flux @xmath19 far from the junction within the wider channel ( @xmath20 ) , as well as appropriate far field ( @xmath21 ) decay conditions within the wall domain . the problems governing @xmath3 and @xmath4 are thus decoupled and may be solved recursively . making use of the schwartz - christoffel ( e.g. milne - thomson @xcite ) transformation @xmath22,\label{eq : sc mapping 1}\ ] ] and @xmath23 the physical complex @xmath24 plane is mapped onto the upper half of the @xmath25 plane , to obtain for a 2d potential of a point charge located at @xmath26 @xmath27 wherein @xmath28 denotes the real part . expanding ( [ eq : sc mapping 1],[eq : sc mapping 2 ] ) and ( [ eq : point charge potential in mapped plane ] ) for @xmath29 ( corresponding to @xmath30 ) one obtains the following potential function : @xmath31 which holds in the vicinity of the corner @xmath32 . once @xmath3 is known , one can calculate @xmath4 to satisfy laplace s equation within the wall domain and ( [ eq : robin cond . on wall-1 ] ) from which we find the total zeta potential to be @xmath33 wherein @xmath34 denotes the induced zeta potential . on the channel walls ( @xmath16 ) opposite from those forming the corner ( @xmath15 ) the latter effect is negligible and it is assumed that @xmath35 . the fluid velocity @xmath36 and pressure @xmath37 are normalized by @xmath38 and @xmath39 , respectively , where @xmath40 denotes the dynamic viscosity of the electrolyte solution and @xmath41 is the permittivity of vacuum . the quasi - steady , small - reynolds number flow of the bulk electro - neutral fluid is governed by the continuity equation @xmath42 and the stokes equation @xmath43 . on the channel walls ( @xmath15 and @xmath16 in fig . [ fig : the - l - junction - configuration . ] ) @xmath36 satisfies the vanishing of the fluid velocity normal to the wall and the helmholtz - smoluchowski slip velocity @xcitecondition @xmath44 where the subscript @xmath45 denotes the vector component tangent to the wall . far upstream and downstream of the corner the pressure and fluid - velocity vector become uniform across the channel . we therefore choose to present the velocity field as the sum of the linear electro - osmotic flow ( eof ) and induced contributions @xmath46 the first term on the right - hand side" +"despite the differences in their compositions , structures and mechanisms of formation , the giant planets of our solar system have one common feature . they all host irregular satellites . thanks to wide field charge - coupled - devices ( ccds ) , the past few years have witnessed the discovery of a large number of these objects [ see @xcite for a comprehensive review ] . at the time of writing of this article , 108 irregular satellites have been discovered , of which 55 belong to jupiter , making the jovian satellite system the largest among all planets . due to its proximity , the irregular satellites of jupiter have been the subject of extensive observational and theoretical research . many of the dynamical characteristics of these objects , such as their orbital stability , dynamical grouping and their collision probability have long been studied @xcite . there is , however , one interesting feature in the distribution of jovian irregulars that has not yet been fully understood . as shown by @xcite , the region extending from the orbit of callisto , the outermost galilean satellite at 26 jupiter - radii @xmath0 , to the periastron of themisto @xmath1 , jupiter s innermost irregular satellite , is void of irregulars . observations suggest the presence of similar void regions around all four giant planets . table 1 and figure 1 show this in more detail . as seen from figure 1 , satellite void regions also exist _ between _ the currently known irregular satellites of the giant planets . theoretical studies have indicated that there may be two possible scenarios for the existence of such void regions ; ejection from the system due to mutual interactions with other irregular satellites and , in the case of satellites that are the remnants of collisions , clustering around their parent bodies @xcite . the focus of this paper is , however , on the lack of irregular satellites in the _ boundary _ between regulars and irregulars . we are interested in understanding of why no irregular satellite exists between the outermost galilean satellite and jupiter s innermost irregular one . the lack of irregular satellites in the boundary between regulars and irregulars may be attributed to the distribution of the orbits of the latter bodies . since irregular satellites appear to have been captured from heliocentric orbits , it may be natural to expect them to preferably have large semimajor axes , and therefore not to exist in close orbits . proving this to be so would be an important contribution to the subject , but , unfortunately , none of the models of capture is sufficiently specific to be used in this way . the n - body capture model of @xcite does roughly match the distribution of irregular satellites of some planets , but not of jupiter . in this paper , we examine the possibility of a dynamical origin for the existence of this satellite - void boundary region . the origin of irregular satellites and the mechanisms of their capture remain unknown . the high values of the orbital inclinations and eccentricities of these objects imply an origin outside the primordial circumplanetary disk from which the regular satellites of giant planets were formed . it is believed that irregular satellites were formed elsewhere and were captured in their current orbits @xcite . the capture of irregular satellites might have occurred during and/or after the formation of the regular satellites of the giant planets . given that the latter objects are formed through the collisional growth of small bodies in a circumplanetary disk @xcite , the orbits of captured irregulars might have been altered by perturbations from these objects during their formation and after they are fully formed . in the case of jovian irregulars , the migrations of ganymede and callisto @xcite have also had significant effects on the dynamics of irregular satellites . in this paper we study the dynamics and stability of irregular satellites between callisto and themisto . we present the details of our model in 2 , and an analysis of the results in 3 . section 4 concludes this study by reviewing our study and discussing its limitations . we numerically integrated the orbits of several hundred test particles in a region interior to the orbit of themisto , the innermost jovian irregular satellite . we assumed that the regular satellites of jupiter were fully formed and studied the perturbative effects of the galilean satellites on the dynamics of small objects in their vicinities . we considered a system consisting of jupiter , the galilean satellites , and 500 test particles uniformly distributed between 30 and 80 jupiter - radii . the initial orbital elements of the test particles were chosen in a systematic way as explained below . \1 ) at the beginning of each simulation , test particles were placed in orbits with semimajor axes starting at @xmath2 and increasing in increments of 0.1@xmath3 . \2 ) for each initial value of the semimajor axis of a test particle @xmath4 , the initial orbital eccentricity @xmath5 was chosen to be 0 , 0.2 , 0.4 , and 0.6 . this choice of orbital eccentricity matches the range of the current values of the orbital eccentricities of jovian irregulars , as shown in figure 1 . \3 ) the initial orbital inclinations of test particles @xmath6 were varied between @xmath7 and @xmath8 in steps of @xmath9 . as shown by figure 2 , irregular satellites are absent at inclinations between @xmath10 and @xmath11 due to perturbations resulting from the kozai resonance @xcite . in choosing the initial orbital inclinations of these objects , we made a conservative assumption and considered the region of the influence of kozai resonance to be between @xmath12 and @xmath13 . we did not integrate the orbits of the test particles for @xmath14 and @xmath13 . \4 ) since we were interested in studying the effects of the perturbations of regular satellites on the variations of the orbital eccentricities and inclinations of test particles , we considered the initial values of the argument of the periastron , longitude of the ascending node , and the mean - anomaly of each test particle to be zero . this is an assumption that was made solely for the purpose of minimizing the initial - value effects . we numerically integrated the orbits of the galilean satellites and the test particles of our system for different values of the test particles orbital eccentricities and inclinations . simulations were carried out for 10 myr using the n - body integration package mercury @xcite . since the objects of our interest are close to jupiter , we neglected the perturbation of the sun and considered jupiter to be the central massive object of the system . this assumption is consistent with the findings of @xcite , who have shown that around a giant planet with a hill radius @xmath15 , the gravitational force of the sun destabilizes the orbit of prograde irregular satellite at distances larger than 0.53@xmath15 and those of the retrograde irregulars at distances beyond 0.69@xmath15 . for jupiter , these values translate to 389@xmath3 for prograde irregulars and 507@xmath3 for retrograde ones . we carried out all integrations with respect to jupiter with timesteps equal to the 1/20 of the orbital period of io . to study the relation between the orbital parameters of test particles and their stability , we determined the lifetime of each particle , considering ejection from the system and collision with other bodies . we considered a particle to be ejected when it reached a distance of 2000@xmath3 or larger from the center of jupiter . a collision , on the other hand , occurred when the distance between a particle and a galilean satellite became smaller than @xmath16 , or the particle s closest distance to the center of jupiter became smaller than jupiter s radius . here , @xmath17 and @xmath18 represent the semimajor axis and mass of a galilean satellite , and @xmath19 is the mass of jupiter . figure 3 shows the graphs of the test particles lifetimes in terms of their initial semimajor axes for particles in two coplanar systems . the graph at the top corresponds to particles initially in circular orbits , and the one at the bottom shows the lifetimes of particles with initial eccentricities of 0.2 . the positions and lifetimes of the regular satellites of jupiter and the orbit of themisto are also shown . as shown by the upper graph , test particles in circular orbits are mostly stable ( for the duration of integrations ) except for a few that are close to callisto . the region of stability , however , becomes smaller ( instability progresses toward larger distances ) in simulations in which the initial eccentricities of test particles are larger . this can be seen more clearly in figure 4 where from the graphs of figure 3 , only the regions between @xmath2 and @xmath20 are shown . the islands of instability , corresponding to mean - motion resonances with callisto ( indicated by the subscript c ) and ganymede ( indicated by the subscript g ) are also shown . the migration of unstable regions to larger distances in systems where test particles were initially in eccentric orbits was observed in all our simulations . figure 5 shows another example of such a system . in this figure , the lifetimes of test particles with initial eccentricities of 0.4 and initial inclinations of 20@xmath21 are shown . the unstable region extends to distances beyond their corresponding regions in figures 3 and 4 . we also simulated the dynamics of test particles having orbital inclinations larger than 90@xmath21 ( retrograde orbits ) . as shown by figure 2 , the number of irregular satellites is larger at these angles implying that retrograde orbits have longer lifetimes @xcite . our simulations also show that retrograde orbits are more stable than their corresponding prograde ones . figure 6 shows this for two sets of test particles . the particles in black correspond to a system in which @xmath22 and @xmath23 . the particles in red correspond to a system with similar orbital eccentricity , but with @xmath24 . as expected , the particles on retrograde orbits are more stable and maintain their orbits for longer times . the fact that the region of instability of test particles , having a given semimajor axis , expands by increasing the initial values of their orbital eccentricities can be attributed to the interactions of these particles with jupiter s regular satellites . given that the orbits of jovian regulars are almost circular , an eccentric orbit for a test particle implies a smaller periastron distance for this object , and consequently a closer approach to the system s regular moons . instability occurs when the perturbative effects of regular satellites disturb the motion of a test particle in its close approach . the outer boundaries of the influence zones and @xmath25 , where the dynamics of a small object is primarily affected by the gravitational force of the satellite . ] of the galilean satellites ( table 2 ) mark the extent of these perturbations . particles with periastron distances beyond these boundaries , i.e. , @xmath26 , will more likely have longer lifetimes . figure 7 shows the boundaries of the stable and unstable test particles for all galilean satellites . the initial positions of test particles with @xmath27 equal to ( 0,0 ) , ( 0.2,0 ) , ( 0.4,40 ) , ( 0.4,140 ) , ( 0.6,60 ) , and ( 0.6,120 ) , are also shown . the stable particles are shown in black and unstable ones are in red . as shown here , particles with higher initial orbital eccentricities penetrate the influence zones" +"two - photon states with specific continuous variable - entanglement properties are required for a number of quantum - information - processing applications . in particular , pure - state single photons , crucial for applications relying on interference between independently prepared single photons , such as quantum computing with linear optics @xcite , entanglement swapping @xcite , and teleportation @xcite , can be heralded only from _ factorable _ photon pairs , where no correlations exist between the constituent single photons @xcite . let us note that factorability may be imposed by postselecting an appropriate subensemble of photon pairs through spectral and/or spatial filtering ; this can be done only at the cost of a typically drastic reduction in count rate and source brightness . scalable quantum - information processing requires the elimination of this type of postselection . it has furthermore been shown that , for quantum - information applications involving multiple - pair generation resulting from high - gain parametric down - conversion , spectral or spatial filtering is likewise ineffectual . @xcite . in addition , the coexistence of factorability and a large generated bandwidth is important for some applications , such as the generation of ultrashort fourier - transform - limited heralded single photons @xcite . the process of spontaneous parametric down - conversion represents a well - established method for the generation of photon pairs , leading to unparalleled flexibility in the resulting continuous - variable entanglement properties . indeed , the nonlinear crystal dispersion characteristics in conjunction with temporal and spatial structure in the pump beam may be exploited to engineer the type and degree of correlations present in spectral and transverse wave - vector degrees of freedom _ at the source _ , thus eliminating the need for photon pair filtering . the use of a broadband pump is essential in the context of the generation of photon pairs with spectrally engineered properties ; indeed , a monochromatic pump can access only a one - dimensional subspace of signal - idler frequency space , which precludes certain states of interest . previous work has established the central role that is played by group velocity mismatch terms between the three fields involved in parametric down - conversion ( pump , signal , and idler ) in the determination of the resulting photon pair properties . thus , in ref . @xcite , it was shown that if the pump pulse propagates at a higher group velocity than one of the generated photons but lower than the conjugate generated photon , then it becomes possible to emit factorable photon pairs . an important limitation of this technique is that the group velocity condition which must be satisfied occurs only for specific materials , at specific spectral ranges @xcite , typically in the infrared where single - photon detection is unfortunately not well developed . a number of techniques have been proposed and in some cases implemented which enable effective control over the photon pair entanglement properties in the spectral domain unconstrained by material dispersion . in one such technique , the effective group velocities experienced by the three fields involved are modified by a pair of diffraction gratings placed before and after the nonlinear crystal so as to generate photon pairs with tunable spectral characteristics @xcite . alternatively , the spectral content of two photon states may be restricted to the modes supported by a nonlinear cavity which leads , for a short , high - finesse cavity , to factorable , narrowband photon pair generation @xcite . likewise , on the one hand a transversely pumped source where signal and idler photons are emitted in a counterpropagating waveguided geometry @xcite and on the other hand noncollinear parametric down - conversion ( pdc ) where a specific relationship between transverse and longitudinal phase matching is attained @xcite can both lead to states with spectrally engineered properties . another route is the use of crystal superlattices , where the dispersion in short crystal segments is compensated by birrefringent compensators , permitting two - photon states with a wide range of possible spectral entanglement characteristics @xcite . previous theoretical work has explored the use of non linear photonic crystals in the context of the process of spontaneous parametric down - conversion . in particular , refs . @xcite study the potential of semiconductor - based nonlinear one - dimensional photonic crystals to yield phase - matching properties appropriate for the generation of polarization - entangled photon pairs . likewise , it has been shown that even a short one - dimensional photonic crystal is capable of generating a considerable photon pair flux due to field localization in such structures @xcite . in this paper we study the potential of exploiting the properties of one - dimensional nonlinear photonic crystals in order to generate photon pairs with engineered spectral entanglement properties . we concentrate on type - ii , frequency degenerate , collinear pdc . collinear operation is important because it permits pdc in a waveguided geometry , which leads to larger generation rates as well as to effective control over the transverse spatial structure of the emitted light , crucial for efficient single - mode fiber coupling and for spatial mode matching in interference experiments @xcite . type - ii operation for which the signal and idler photons are orthogonally polarized is important because it enables efficient photon pair splitting . we show that a weak index of refraction modulation present in an otherwise standard birefringent nonlinear crystal can be exploited to attain the group velocity conditions , in addition to basic phase matching , required for factorable photon pair generation . in this paper we analyze the generation of photon pairs by the process of parametric down - conversion in a @xmath0 material characterized by a spatial periodicity in its linear optical properties . in particular , we study pdc produced by a nonlinear photonic crystal ( nlpc ) based on a standard bulk nonlinear crystal with uniaxial birefringence which has been modified from its natural state by an appropriate physical mechanism so as to yield a periodic variation of the index of refraction for both polarizations , while maintaining the nonlinearity constant throughout the crystal thickness . concretely , within one period of the resulting bragg grating , we assume that the index of refraction for the ordinary ( @xmath1 ) and the extraordinary ray ( @xmath2 ) are given by @xmath3 this unit cell is assumed to be replicated throughout the crystal length . here , @xmath4 represents the bragg period and @xmath5 is the duty cycle . we refer to such a material as a one - dimensional nonlinear photonic crystal . figure [ fig : bragg ] shows a crystal schematic where @xmath6 indicates zones characterized by indices of refraction @xmath7 and @xmath8 and @xmath9 indicates zones characterized by indices of refraction @xmath10 and @xmath11 . we assume that in zones @xmath6 the crystal has been left in its natural state , while in zones @xmath9 it has undergone index change . for simplicity , we assume that zones @xmath6 and @xmath9 are of equal length ( leading to an @xmath12 duty cycle ) and we likewise assume that the permittivity contrast @xmath13 , equivalent to the index square contrast , is frequency independent , . [ fig : bragg],width=288 ] @xmath14}{\epsilon_{\mu1}(\omega)+\epsilon_{\mu2}(\omega ) } = \frac{n_{\mu 1}(\omega)^2-n_{\mu 2}(\omega)^2}{\overline{n}_\mu(\omega)^2},\ ] ] where @xmath15/2.\ ] ] with @xmath16 . throughout this paper we will assume that propagation of the three fields involved is normal to each of the interfaces between zones @xmath6 and @xmath9 . under these conditions , such a material can exhibit , for each of the polarizations , a so - called photonic band gap centered at each of the bragg wavelengths @xmath17 where @xmath18 , and where @xmath16 . within each band gap , for a sufficient crystal thickness , light is efficiently reflected , while for frequencies outside the band gap , light propagates in the form of so - called bloch waves which can be written as @xmath19\}.\ ] ] here , @xmath20 is the bloch envelope , which exhibits a spatial periodicity matching that of the material , i.e. , @xmath21 , while @xmath22 represents the bloch wave number . note that , for a continuous material without bragg grating , the bloch envelope reduces to a constant , and therefore the bloch wave reduces to a plane wave . following a coupled - mode analysis where the spatial periodicity in the permittivity is assumed to be well represented by a weak perturbation to the material permittivity , it can be shown that the bloch wave number in the vicinity of @xmath23 can be expressed as @xcite @xmath24 here , @xmath25 represents the coupling coefficient between the forward and backward waves @xmath26\alpha \overline{k}_\mu(\omega)/ ( 4 \pi m),\ ] ] and @xmath27 represents the bragg phase mismatch between these two waves , @xmath28 where @xmath29 characterizes the underlying material dispersion ; note that eq.([ec : lambda_bragg ] ) follows from the condition @xmath30 . a photonic band gap appears when @xmath31 and its effects become appreciable for @xmath32 . the band gap boundaries @xmath33 and @xmath34 are obtained by solving for the frequencies such that the argument of the square root in eq.([ec : wavenumber ] ) vanishes . for a forward - propagating wave , the minus sign in front of the square root in eq.([ec : wavenumber ] ) should be used for @xmath35 while the plus sign should be used for @xmath36 . let us note that for a @xmath37 duty cycle , eq.([ec : couple_coef ] ) tells us that , even order band gaps ( @xmath38 ) are suppressed . in what follows , we will concentrate on first order ( @xmath39 ) band gaps , though the analysis below could be employed for any order . in particular , for practical implementations it may be challenging to fabricate the required bragg gratings with periods in the region of hundreds of nanometers compatible with modified dispersive characteristics in the visible ; alternatively , it is possible to use longer periods , together with higher - order band gaps . the dispersive properties of nplcs are characterized by the function @xmath22 , where from this point we omit the order superscript . for propagating waves at frequencies in the vicinity of the band gap boundaries , @xmath22 can differ substantially from the underlying material dispersion relation @xmath40 . in particular , group velocities can be strongly reduced , while group velocity dispersion terms ( as well as higher - order frequency derivatives of the wavenumber ) can increase markedly , from their values associated with material - only dispersion . in order to illustrate these effects , let us consider a specific example of a one - dimensional nlpc , based on a @xmath41-barium - borate ( bbo ) crystal . we assume that the bragg period is given by @xmath42 nm with a @xmath12 duty cycle , the angle subtended by the pump and the optic axis ( to be referred to as the propagation angle ) is @xmath43 , and the permittivity contrast is @xmath44 . figure [ fig : dispersion ] shows the resulting dispersive properties . figure [ fig : dispersion ] ( a ) shows , for each of the two polarizations , a plot of the bloch wave number @xmath22 , showing clearly a band gap for each of the polarizations , within which @xmath22 becomes complex - valued . figure [ fig : dispersion ] ( b ) shows a plot of the group velocities for each of the two polarizations , exhibiting a marked reduction near the band gap boundaries . figure [ fig : dispersion ] ( c ) shows the first frequency derivative of @xmath22 , or the reciprocal group velocity . finally , figure [ fig : dispersion ] ( d )" +"coupled chaotic systems are recently calling much attention due to the verification that they may be useful to the understanding of natural systems in a variety of fields as in ecology @xcite , in neuroscience @xcite , in economy @xcite , and in lasers @xcite . it has been verified that despite of the higher dimensionality of a coupled chaotic system , the coupling among the elements might make them to synchronize @xcite , reducing the dynamics of the system to a few degrees of freedom . in this work , we focus our attention in the phenomenon of phase synchronization ( ps ) , which describes the appearance of a phase synchronous behavior between two interacting chaotic systems @xcite , i.e. , given two chaotic systems , their phase difference remains bounded , despite of the fact that their amplitudes may be uncorrelated . this phenomenon is particularly interesting since it can arise from a very small coupling strength . its presence was reported in a variety of experimental systems . it was experimentally demonstrated in electronic circuits @xcite , and latter in electrochemical oscillators @xcite . it was found in plasma @xcite , in the chua s circuit @xcite , and there were also found evidences of phase synchronization in communication processes in the human brain @xcite . to detect ps in a real - time experiment , one has to measure the phase of the chaotic trajectory @xcite . however , the phase is not always an easily accessible information . to overcome this difficulty , it is important to understand fundamental properties of phase synchronous systems , that could be experimentally easily verified . for chaotic systems that are phase synchronized with a periodic forcing @xcite , it was reported that a stroboscopic map of the trajectory was a subset of this attractor and occupies only partially the region delimitated by a projection of the attractor . this property was used to detect in a real - time experiment phase synchronization between the chua s circuit and a sinusoidal forcing @xcite . this approach of detecting phase synchronization through the stroboscopic map can be extended for coupled chaotic oscillators , in a formal way . the stroboscopic map is generalized to the * conditional poincar map*. given two oscillators , at least one being chaotic , the conditional poincar map is constructed by collecting points in one oscillator at the moment at which some event happens in the other one . if the set of discrete points generated by this conditional map does not visit any arbitrary region of a especial projection of the chaotic attractor , we call this set a * p - set*. this property of the conditional poincar map is called non - transitivity @xcite , i.e. , an initial condition under the conditional poincar map does not visit everywhere in a subspace of the attractor . alike the stroboscopic maps of oscillators that are in phase synchrony with a forcing , the conditional poincar maps of coupled chaotic oscillators , in ps , also only partially occupy a projection of the attractor . in this work , we show how the conditional poincar map can be used to detect ps , without actually having to measure the phase . for phase - coherent oscillators , a special type of p - set , that we call ps - set ( phase synchronization set ) , conversely , its existence also implies ps . we illustrate our findings and ideas with numerical and experimental analyzes in the forced chua s circuit , and the coupled rsller oscillator @xcite . further , we extend these results to non - phase coherent attractors . finally , we also introduce a phase of a chaotic trajectory to be a quantity related to the amount of rotation of the tangent vector . this definition can be used to chaotic attractors , independently whether they have phase - coherent or non phase - coherent dynamics . this work is organized as follows : in sec . [ sec : phase ] , we define a way to measure the phase of a chaotic flow , and discuss the relation between the average returning time and the average angular frequency . in sec . [ sec : ps ] , we discuss the conditions for ps states and , in sec . [ sec : chua ] , we describe the phenomenon of ps in the forced chua s circuit . we introduce the notion of a conditional poincar map in sec . [ cpm ] and the p - sets ( as well as the ps - sets ) in sec . [ p - sets ] . in sec . [ sec : bsc ] , we show how ps can be found by the detection of these sets in the forced chua s circuit and in sec . [ sec : bsr ] , for the coupled rssler oscillator . further , in sec . [ extension ] , we discuss the extension of these ideas to a class of non - coherent oscillators . in sec . [ sec : cr ] , we make some remarks and the conclusions of this work . in appendix a , we formally introduce the conditional poincar map and the p - set , and in appendix b , we show that for coherent dynamics the ps - sets exist if , and only if , there is ps . in other words , ps implies ps - sets and vice - versa . the phase of a chaotic attractor in a projection @xmath0 ( a subspace ) is defined to be the amount of rotation of the tangent vector in this projection , and can be represented by an integral function of the type @xmath1 with @xmath2 being an infinitesimal displacement of the tangent vector of the flow , from time @xmath3 to time @xmath4 , and @xmath5 . note that in eq . ( [ fase ] ) , we are measuring the amount of rotation , per unit time , of a projection of the tangent vector of the flow , on the same subspace @xmath0 where the phase is defined . we call this subspace @xmath6 . the attractor @xmath7 , projected on the subspace @xmath6 is regarded as @xmath8 . the instantaneous angular frequency of the trajectory in @xmath8 , named @xmath9 is given by @xmath10 . so , from eq . ( [ fase ] ) , @xmath11 and , the average angular frequency @xmath12 is @xmath13 @xmath14 represents the average . equation ( [ natural_frequence_2 ] ) can be put into the form @xmath15 = @xmath16 . whenever a poincar section can be defined , the average period of the chaotic attractor on the subspace @xmath6 is calculated by @xmath17 where @xmath18 , and @xmath19 represents the time at which the trajectory in the subspace @xmath6 makes the @xmath20-th crossing with this poincar section . we introduce @xmath21 to be the average displacement of the phase for a typical period as @xmath22 with @xmath23 being the phase associated to the subspace @xmath6 at the moment that the @xmath24-th crossing between the trajectory and the poincar section happens . thus , we can put eq . ( [ natural_frequence_2 ] ) as @xmath25 for the forced chua s circuit , the subspace @xmath26 is defined by a suitable projection of the circuit variable . we have that @xmath27 . so , eq . ( [ natural_frequence_1 ] ) can be written as @xmath28 . for the coupled rssler oscillator , the quantities in eq . ( [ natural_frequence_1 ] ) can be calculated in two subspaces , one associated to the variables of one rssler , the subspace @xmath26 , and the subspace @xmath29 , associated to the variables of the other rssler system . as shown in @xcite , @xmath30 might slightly differs from @xmath31 , and thus , @xmath32 . ( [ natural_frequence_2 ] ) and ( [ natural_frequence_1 ] ) relate the average period , the average angular frequency , and the phase of a chaotic trajectory . this shows that the average period ( recurrence ) and the average angular frequency are intimately connected in phase coherent chaotic systems , and both these quantities can be calculated from the phase . having defined phase , ps exists whenever the following condition is satisfied @xmath33 the minimal bound for the phase difference , @xmath30 , in terms of the phase as defined by eq . ( [ ps ] ) , was theoretically estimated in ref . @xcite . equation ( [ ps ] ) means that the phase difference between the two coupled systems is always bounded , and @xmath34 is a rational constant @xcite . also , @xmath35 in this work , we will consider cases for @xmath34=1 . otherwise , a simple change of variables could eliminate this constant from eq . ( [ nc ] ) . for the forced chua s circuit @xmath36 , with @xmath37 , representing the angular frequency of the forcing . there is ps , if @xmath38=@xmath39 . therefore , @xmath40=@xmath41 . for the coupled rssler , if ps exists , @xmath42 = @xmath43 , @xmath44=@xmath45 , and @xmath46=@xmath47 , and therefore , we could have in the right term of eq . ( [ ps ] ) @xmath48 , instead of @xmath49 . the circuit is represented by : @xmath50 where @xmath51 , @xmath52 , and @xmath53 represent , respectively , the tension across two capacitors and the current through the inductor ( see @xcite for more details ) , @xmath39 and @xmath54 are the angular frequency and the amplitude of the forcing , respectively . the piecewise - linear function , @xmath55 , is given by : @xmath56\ ] ] where we have chosen the parameters @xmath57=0.1 , @xmath58=0.574 , @xmath59=1 , @xmath60=1/6 , @xmath61=-0.5 , and @xmath62=-0.8 , such that we obtain a rssler - type attractor , for @xmath54=0 . to calculate the phase of the chaotic trajectory , we first define the subspace @xmath26 to be given by the pair of variables @xmath63 , and then , we use eq . ( [ fase ] ) . in fig . [ ps_fig6 ] , we show the difference between the phase of the chaotic circuit [ as calculated by eq . ( [ fase ] ) ] and the phase of the forcing , @xmath64 . in ( a ) , the phase difference is bounded and the average period of the chaotic attractor , defined as the average recurrence time of trajectories that cross the section @xmath65 , is equal to @xmath66=3.57015 , which is equal to 1/f , since @xmath67=0.2801 . the average angular frequency can be calculated using eq . ( [ natural_frequence_1 ] ) , which gives us @xmath68=1.75992 . or , from eq . ( [ natural_frequence_2 ] ) , which gives us @xmath38=1.75992 . note that the average growing of the phase [ calculated by eq . ( [ fase ] ) ] for a typical average period is @xmath69 which is @xmath31 . in fig . [ ps_fig6](b ) , we have that @xmath70=3.57006 which is different from @xmath41 , since @xmath67=0.279 . so , in ( b ) there is no ps , and consequently inequality ( [ ps ] ) is not satisfied . in ref . @xcite , we detected @xmath71 experimentally in the forced chua s circuit , whenever stroboscopic maps could be constructed for a time interval equal to @xmath72 , such that this map , projected into the same subspace considered to calculate the phase , does not occupy the region occupied by the attractor projected on the same subspace . to understand this technique , we assume that @xmath73 , the phase of the chaotic trajectory , is the angle" +"the lepton flavor violating ( lfv ) neutrinoless conversion of a bound 1s - muon to electron in the field of a nucleus @xcite-@xcite @xmath10 is known as one of the best probes to search for the hypothetical muon and electron flavor non - conservation @xcite . so far , the experiments @xcite-@xcite seeking for @xmath11 conversion events have only succeeded to put upper bounds on the branching ratio @xmath12 i.e. the ratio of the muon - electron conversion rate relative to the total rate of the ordinary muon capture . the best upper limits have been extracted at psi by the sindrum ii experiments in the values ( at 90% confidence level ) @xmath13 @xmath14 these limits are improvements over the previous limits set at triumf @xcite a decade ago using the same targets . at present , two @xmath1 conversion experiments are launched , the ongoing experiment at psi using @xmath3ti target @xcite , and the planned meco experiment at brookhaven @xcite using @xmath5al target . the expected sensitivity on @xmath2 in the psi experiment is @xmath15 while in the brookhaven experiment it will be roughly @xmath16 which implies an improvement over the existing limits by about four orders of magnitude . the meco experiment is going to be conducted in a new @xmath17 beam line at the ags , where the muons are produced using a pulsed proton beam @xcite . the proton energy will be chosen in the range of 8 - 20 gev to optimize the @xmath18 flux per unit time . furthermore , the number of electrons with energy @xmath19 mev , equal to the energy for the coherent peak in @xmath5al , is very much suppressed . this is in contrast with the case of @xmath20 , where the electron flux from @xmath21 decay is peaked at the energy of the electrons from @xmath22 . for such experiments the knowledge of nuclear transition matrix elements for all accessible @xmath23 channels of the targets employed are of significant importance @xcite-@xcite . in this work we use the transition matrix elements calculated for the aforementioned isotopes in the coherent mode to constrain the lepton flavor violating parameters of various lagrangians predicting this exotic process ( e.g. scalar and vector couplings , neutrino mixing angles and masses @xcite-@xcite , supersymmetric r - parity violating couplings @xcite-@xcite etc . ) . to this aim the recent experimental data and the expected sensitivity of the meco experiment . as is well known , only the coherent rate can be measured because it is free from background events from bound muon decay and radiative muon capture followed by a fully asymmetric @xmath24 pair creation @xcite . on the other hand , previous studies of @xmath1 conversion rates @xcite-@xcite have shown that for all mechanisms the coherent mode dominates the process ( [ reaction ] ) which means that this is the most important channel . the incoherent reaction leading to excited nuclear states is suppressed due to pauli blocking effects and it is much harder to calculate but its knowledge is also useful in order to determine the experimentally interesting quantity of the ratio of the coherent to the total @xmath6 rate ( see refs . @xcite-@xcite ) . the family quantum numbers @xmath25 , @xmath26 , @xmath27 are conserved within the standard model ( sm ) in all orders of perturbation theory . however this is an accidental consequence of the sm field content and gauge invariance . physics beyond the sm can easily spoil this property . processes like @xmath11 conversion , which is forbidden in the standard model by muon and electron quantum number conservation , play an important role in the study of flavor changing neutral currents and possible physics beyond the sm . on the particle physics side @xcite , there are many mechanisms of the @xmath11 conversion constructed in the literature ( see @xcite-@xcite and references therein ) . all these mechanisms fall into two different categories : photonic and non - photonic . mechanisms from different classes significantly differ from the point of view of the nucleon and nuclear structure calculations . this stems from the fact that they proceed at different distances and , therefore , involve different details of the structure . the long - distance photonic mechanisms are mediated by the photon exchange between the quark and the @xmath11-lepton currents . these mechanisms resort to the lepton - flavor non - diagonal electromagnetic vertex which is presumably induced by the non - standard model physics at the loop - level . the @xmath11 lepton - flavor violating loop can appear as the @xmath28 loop [ fig.1(a ) ] with the massive neutrinos @xmath29 and the loop with the supersymmetric particles such as the neutralino(chargino)-slepton(sneutrino ) [ fig.1(d ) ] . in the r - parity violating susy models there are also lepton - slepton and quark - squark loops generated by the superpotential couplings @xmath30 and @xmath31 respectively . the short - distance non - photonic mechanisms contain heavy particles in intermediate states and can be realized at tree level [ fig.2 ] , at 1-loop - level [ fig.1(a , b , d , e ) ] or at the level of box diagrams [ fig.1(c ) ] . the tree - level diagrams can be constructed in the r - parity violating susy models with the virtual z - boson , squarks @xmath32 and sneutrinos @xmath33 [ fig.2 ] . the 1-loop diagrams of the non - photonic mechanisms include the diagrams similar to those for the photonic mechanisms but with the z - boson instead of the photon [ fig.1(a , d ) ] as well as additional z - boson couplings to the neutrinos and neutralinos [ fig.1(b , e ) ] . the box diagrams are constructed of the w - bosons and massive neutrinos [ fig.1(c ) ] as well as similar boxes with neutralinos and sleptons or charginos and sneutrinos . our purpose is to calculate the contribution of the above - described mechanisms to the @xmath6 conversion branching ratio ( [ def1 ] ) . at the first step we construct the effective @xmath6 conversion hamiltonian for these mechanisms in terms of nucleon degrees of freedom of a nucleus involved in the process this will allow us to accomplish the calculation of @xmath2 by applying the conventional nuclear structure methods using non - relativistic impulse approximation . for the photonic diagrams of fig . 1(a , d ) the hadronic vertex represents the usual nucleon electromagnetic current @xmath34 @xmath35 is the nucleon isospin doublet @xmath36 with @xmath37 , @xmath38 being the proton and neutron spinors . in the case of the non - photonic mechanisms of fig . 1 the hadronic currents are either the sm neutral currents coupled to z - boson [ fig . 1(a , b , d , e ) ] or the effective currents derived after an appropriate fierz transformation from the effective operators of the box diagrams [ fig . 1(c ) ] involving heavy particles . these currents can be written in terms of the nucleon doublet field as @xmath39 n \qquad ( non - photonic ) \label{3.1.4}\ ] ] where @xmath40 , @xmath41 represent the vector , axial vector static nucleon form factors ( @xmath42 ) and the parameters @xmath43 , @xmath44 , @xmath45 , for the models adopted take the values given in ref . the parameter @xmath43 is defined as @xmath46 , with @xmath47 @xmath48 the isoscalar ( isovector ) couplings at the quark level . we should note that , in general , the parameters @xmath43 , @xmath49 and @xmath50 are functions of @xmath51 . for example , in the case of z - exchange we have @xmath52 . the corresponding leptonic currents for the photonic and non - photonic mechanism of figs . 1 are given in ref . @xcite . in the minimal susy model with a most general form of r - parity violation ( for review see , for instance , @xcite ) all the possible tree - level diagrams for the @xmath6 conversion process are shown in fig . 2 @xcite,@xcite . to write down the low - energy @xmath11 conversion lagrangian at quark level one starts from the well known r - parity violating superpotential and integrates out heavy intermediate fields . for the diagrams of fig . 2 the corresponding 4-fermion low - energy effective lagrangian at the quark level takes the form @xcite ( first order of perturbation theory ) @xmath53 \nonumber \\ & & + \frac{g_f}{\sqrt{2}}\left [ \bar\eta_{r}^{di}j_{dr(i)}j_{l } + \bar\eta_{l}^{di}j_{dl(i)}j_{r}\right ] . \label{eff - q}\end{aligned}\ ] ] ( @xmath54 runs over generations so that @xmath55 with @xmath56 and @xmath57 ) where the coefficients @xmath58 contain the @xmath59 susy parameters @xcite . the color singlet currents @xmath60 and @xmath61 at the quark level are written as @xmath62 where @xmath63 . the leptonic currents are written as @xmath64 at the next step we rewrite eq . ( [ eff - q ] ) , specified at the quark level , in terms of the nucleon degrees of freedom . this is usually achieved by utilizing the on - mass - shell matching condition @xcite and gives @xmath65 . \label{nucl1}\ ] ] where now the hadronic ( nucleon ) currents are @xmath66 \,n , \label{nucur } \\ j^{\pm } & = & \bar{n}\,\,\left [ ( \alpha _ { \pm s}^{(0)}+\alpha _ { \pm s}^{(3)}\tau _ { 3})+(\alpha _ { \pm p}^{(0)}+\alpha _ { \pm p}^{(3)}\tau _ { 3})\gamma _ { 5}\right ] \,n , \nonumber\end{aligned}\ ] ] the coefficients @xmath67 , with @xmath68 , in eq . ( [ nucur ] ) include the nucleon form factors ( functions of the momentum transfer @xmath69 ) for scalar , vector , axial vector and pseudoscalar contributions , respectively ( for their definition see ref . @xcite ) . since , however , the maximum momentum transfer @xmath69 in @xmath1 conversion is much smaller than the typical scale of nucleon structure ( @xmath70 , with @xmath71 , the muon mass ) , we can safely neglect the @xmath69-dependence of the nucleon form factors . one of the most interesting quantities in @xmath6 conversion , both from theoretical and experimental points of view , is the branching ratio @xmath2 defined in eq . ( [ def1 ] ) . the expression which gives @xmath2 in the case of the dominant coherent channel has been written as @xcite @xmath72 where @xmath73 is nearly independent of nuclear physics @xcite and contains the flavor - violating parameters mentioned before . thus , e.g. for photon - exchange @xmath73 is given by @xmath74 this expression contains the electromagnetic form factors @xmath75 , @xmath76 , @xmath77 , @xmath78 parametrized in a specific elementary model @xcite . the function @xmath79 of eq . ( [ iii.2 ] ) includes about all the nuclear information . by assuming that the total rate of the ordinary muon capture rate is described by the goulard - primakoff function @xmath80 , @xmath79 is defined as @xmath81 where @xmath82 . thus , the nuclear aspects of the @xmath23 branching ratio @xmath2 are mainly included in the matrix elements @xmath83 @xcite , which in the proton - neutron representation , are written as @xmath84 in general , the transition matrix elements @xmath85 in eq . ( [ me2 ] ) depend on the final nuclear state populated during the @xmath11 conversion . for ground state to ground state transitions ( @xmath86 ) in spherically symmetric nuclei the following integral representation is valid @xmath87 where @xmath88 the zero order spherical bessel function and @xmath89 the proton ( p ) , neutron ( n ) nuclear density normalized to the atomic number @xmath90 and neutron number @xmath35 of the participating nucleus , respectively . the space dependent part of the muon wave function @xmath91 , a spherically symmetric function , can be obtained by solving numerically the schrdinger and dirac" +"increasing interest is attracted by modified versions of general relativity @xcite . they have been proposed as serious alternatives to einstein s theory of gravitation , and could be used to describe more accurately the observed accelerated expansion of our universe @xcite . in addition , it has been shown @xcite that it is actually possible to reconstruct the explicit form of the postulated curvature function @xmath0 , from the universe expansion history . it is quite well known that modified versions of general relativity are mathematically equivalent to scalar fields models ( see e.g. @xcite ) , meaning that a solution in a modified gravity model can always be mapped into a solution of the corresponding scalar field theory . in spite of this mathematical correspondence , physical equivalence does not always follow . in fact , two corresponding solutions of two equivalent theories can actually exhibit rather different physical behaviors . furthermore , it is not necessary , in order to justify modified gravity , to do it by always using this relation with scalar field theories . because of the new situation , in the following we will disregard this mathematical equivalence and do consider in our analysis modified gravity as an independent theory aiming directly at some measurable physical properties . what is more , in our treatment modified gravity will in fact be viewed just as a different classical theory of gravitation . although other models have been considered @xcite with the gauss - bonnet scalar in the action , here we shall restrict our attention to pure @xmath0 models . as often discussed , there are limitations on the function @xmath0 when trying to construct a theory which is in agreement with the very precise solar system tests carried out so far , as well as with all the known cosmological bounds @xcite . recently , different models of that kind have been studied @xcite , the last three of them having been reported to pass all solar system tests ; in addition , they exhibit a number of very interesting features . in @xcite possible newton law corrections to such models have been considered . we present here an analysis of the models above based on the study of pure schwarzschild and also schwarzschild - de sitter black holes ( sbh , sdsbh ) , calculated through use of the noether charge method . we start with a discussion of two examples considered in @xcite and go over to study more recent ones @xcite . the direct confrontation of basic quantities , as the black hole entropy , with the well established , classical ( einsteinian ) result can offer a further insight into the construction of a general @xmath0 theory . we start with a short review of modified @xmath0 gravity and the noether charge method to compute the bh entropy and then calculate the bh entropy for the models in refs . @xcite . after that , we extend our analysis to the models @xcite , taking due care of the sign of the bh entropy and also discussing the stability conditions as well as the existence of a schwarzschild bh solution . we conclude by providing a brief comparison of the different models considered . the action for @xmath0 gravity ( see e.g. @xcite for a review ) is @xmath1 with @xmath0 a generic function . as discussed in @xcite , in order to give rise to a realistic cosmology this function needs to fulfill some limiting conditions . however , for the moment we can ignore them , because they do not affect the considerations which will follow . the equations of motion for this theory , in the presence of matter , are @xmath2 where @xmath3 is the matter stress energy tensor . contracting the indices in the last equation , we obtain the relation @xmath4 since we are interested in the study of the schwarzschild solution ( in the case when there is a @xmath5 solution ) or either in schwarzschild - de sitter black holes , we restrict our reasoning to the case of metric tensors with constant scalar curvature in the vacuum . in that case , we simply have @xcite @xmath6 for completeness , let us recall that , in order to build a realistic modified gravity , @xmath0 needs satisfy the two conditions : @xmath7 the first condition corresponds to the existence of an effective cosmological constant at high curvature . the second one allows for vacuum solutions , as for example minkowski or schwarzschild space - times . then , although an effective cosmological constant exists , vacuum solution are preserved and it is legitimate to study them also in a large scale universe with nonzero @xmath8 . moreover , in order to give rise to stable solutions @xcite , the following additional condition needs to be fulfilled : @xmath9/f''(r ) > r.\ ] ] we can now consider the schwarzschild - de sitter metric , a spherically symmetric solution of ( [ eq2 ] ) with constant curvature @xmath10 ( see @xcite ) @xmath11 where @xmath12 and @xmath13 . we will use the noether charge method , as discussed in @xcite , in order to calculate the entropy for the schwarzschild - de sitter bh . the entropy formula reads @xmath14 and the integration is made on the external horizon of events surface . in the case of constant curvature , for a generic modified theory , the result is @xmath15 a_h/4g,\ ] ] where @xmath16 is the area of the bh horizon . this enables us to calculate the bh entropy for a generic @xmath0 theory . we must here stress the fact that the requirement of positive black hole entropy simply avoids the appearance of ghost or tachyon fields in the corresponding scalar field theory . then a negative entropy is simply a footprint of some instabilities in the einstein frame . what is new in this picture is that we do not need to involve the ( mathematical ) equivalence of these models in order to give a physically meaningful interpretation of such constrain . in order to illustrate the method with explicit examples of entropy calculation , we analyze here two modified gravity models that appeared some time ago and which have been quite successful up to now . in those models no @xmath5 solution occurs . the first one , introduced in @xcite , is given by @xmath17 with @xmath18 . the condition to obtain a sdsbh ( namely , @xmath19 ) leads to @xmath20 \nonumber \\ & & \hspace*{10 mm } = 2 \left [ - a\left(r_0 - \lambda_1 \right)^{-n } + b \left ( r_0 - \lambda_2 \right)^m \right],\end{aligned}\ ] ] so that we have for the entropy @xmath21.\ ] ] thus the sdsbh entropy is positive for all @xmath22 . the second model , studied in @xcite , is defined by @xmath23 this modified gravity model does not admit vacuum solutions , thus we can calculate the entropy for the sdsbh . the ricci scalar is such that it satisfies the relation @xmath24 the sdsbh entropy is given by @xmath25 and turns out to be positive for all values of @xmath26 . we now analyze three recent models @xcite which have been proven to comply with the solar - system as well as with other cosmological parameter constraints . their respective authors have given a complete discussion of each model , taking care to provide a range for the free parameters contained in the @xmath0 function , and have also produced stable solutions . here we just want to stress , with the help of these examples , how the corresponding bh entropy calculation offers a further tool in order to confront each of those modified gravity theories with einstein s general relativity , given the fact that the presence of spherically symmetric bh solutions is a necessary element of all local tests . in this model @xcite ( with @xmath27 ) we have @xmath28 in @xcite , @xmath29 is chosen such that , at cosmological scale , @xmath30 at the present epoch , and @xmath0 satisfies the condition @xmath31 for @xmath30 . this also ensure that solutions with @xmath30 are stable . moreover the requirement that @xmath32 at fixed @xmath33 gives a cosmological constant , in both cosmological and local tests of gravity . in spite of this fact , since @xmath34 , this theory admits the schwarzschild solution ( i.e. @xmath5 ) . by the way we note that the stability condition for the vacuum solution is not satisfied unless @xmath35 and @xmath36 . therefore , except of this case , vacuum solutions ( than also sbh ) are unstable . note also that @xmath35 corresponds to a lagrangian @xmath37 for small @xmath8 , so it is associated with a correction to the gravitational coupling constant for small @xmath8 , giving an effective @xmath38 ( see @xcite ) . the entropy formula gives for the sds metric @xmath39 the entropy for the schwarzschild solution is @xmath40 then , in the only stable case , with @xmath35 and @xmath36 , a correction to the classical einstenian bh entropy is found . from ( [ entropyhu ] ) it also follows that , for sds bh with @xmath41 , the entropy is positive and corrections to its einstenian value are of order @xmath42 . in this model @xmath0 is @xcite @xmath43^{-n } -1 \right\},\ ] ] from where @xmath44^{-n-1}.\ ] ] note that in this case @xmath45 an thus , although this model admits a sbh solution , it is unstable together with all its vacuum solutions . in @xcite the author limits his analysis to solutions that satisfy the following stability conditions @xmath46 we can therefore consider the sdsbh solutions , with curvature @xmath10 given by @xmath47^{-n-1 } + 1 \right\}\nonumber \\ & & \hspace*{10 mm } = - 2 \lambda c \left [ \left ( 1+(r_0/c)^2 \right)^{-n } -1 \right],\end{aligned}\ ] ] that satisfies also ( [ stabilitistarobinski ] ) . in this case , the entropy is just @xmath48^{-n-1 } \right\}.\ ] ] therefore , in this case a _ non trivial _ correction of the sdsbh entropy is found . we just stress the fact that the sbh solutions have classical entropy but are _ unstable _ , and that the sdsbh ones have a modified entropy which , under the limitations stated in @xcite , is strictly positive . here @xmath0 is given by @xcite @xmath49/2a\ ] ] and @xmath50/2.\ ] ] this model admits a sbh solution . the entropy for the sdsbh is simply @xmath51 a_h/8g.\ ] ] we can use the stability condition given in @xcite , @xmath52 , to obtain @xmath53 for the sbh , the stability condition is just @xmath54 . moreover , being @xmath31 for all @xmath8 , in this model the vacuum solutions are always stable and there are no substantial corrections to the classical result . it is interesting to put together all three models and explicitly compare the behavior of the function @xmath0 , in particular , the stability of the euclidean limit and the asymptotic behavior at large curvature . to simplify the comparison , we do not play with the values of the different parameters and set all coefficients equal to 1 and the curvature powers equal to 2 or 4 . for the case of the hu - sawicki model , with @xmath55 being @xmath56 , the corresponding plot is given in fig . 1 . for the case of the starobinsky model , with @xmath57 being @xmath58 , we obtain fig . 2 . and for the case of the appleby - battye model , with @xmath59 being @xmath60 and @xmath61 , fig . 3 . in a first comparison of these different models , we note that the one of starobinsky , as remarked by the author himself @xcite , has unstable vacuum solutions" +"the theoretical framework of physics has evolved enormously since the time of newton , but one notable invariant , so pervasive as to be effectively invisible , is the one - dimensionality of time . while time and space have been amalgamated into a composite known as _ spacetime _ in the wake of relativity theory , and while modern superstring theories follow the kaluza - klein theory in postulating more than three _ space _ dimensions , time itself has remained one - dimensional . indeed , very little work has been devoted to the study of multiple time dimensions . yet one might like to know more about physics with multiple times for at least two reasons : * it s not at all clear we can be confident that our world has a single time dimension unless we know what a world with multiple times looks like . kant thought such a world was inconceivable . but kant also thought that space must be three - dimensional and euclidean @xcite . * problems connected with the interpretation of quantum mechanics , the construction and interpretation of a quantum theory of gravity , and the origin of cosmological time asymmetry all suggest the need for a new conceptual framework . these questions motivate recent work of walter craig and myself @xcite , work which explores , from a mathematical perspective , the features one might expect in a theory with multiple time dimensions . the results are surprising , undermining as they do the conventional wisdom that such theories are plagued by instabilities @xcite or are hopelessly unpredictive @xcite . as i ll show , theories in multiple time dimensions allow a meaningful sense of determinism , while giving rise to intriguingly nonlocal constraints on initial data . furthermore , the way in which these sorts of constraints arise , from a reconception of the structure of the spacetime background , suggests heretofore unexplored ways of extending physical theory . the special theory of relativity brought with it the relativity of simultaneity , which in turn prompted a reimagining of space and time as _ spacetime _ , a four - dimensional manifold of points @xmath0 equipped with a metric @xmath1 , the latter giving the distance between pairs of nearby points . if the square of the distance is positive , then the distance is spatial , and if it s negative , the distance is temporal . we say that the _ signature _ of the metric on a 4-dimensional manifold @xmath2 metric is @xmath3 if three of the directions are spatial and one is temporal .. ] the signature of a 5-dimensional metric with four space dimensions and one time dimension is thus @xmath4 , whereas a metric with three space and two time dimensions has signature @xmath5 . thus it is straightforward to characterize spacetimes with any given number of space and time dimensions . matter generally takes the form of either particles or fields , though extended objects such as strings and membranes are also possible . the focus here will be on fields , in particular the massless scalar field @xmath6 described by the ` wave equation ' @xmath7 this is a simple equation in three space dimensions and one time dimension which describes many phenomena of interest , most notably the propagation of the components of the electromagnetic field ( thus the behavior of light ) . there is a ` well - posed ' initial value problem for this equation . what this means is that if we are given sufficient information about the field at a given time , a stable solution of the equation exists , and it is unique . in other words , the initial data completely determine the data at all other times , and do so in such a way that small errors in the specification of the initial data do not lead to uncontrollable errors in the solution . in the usual case , in which the initial data lies on a hypersurface of codimension one ( meaning a hypersurface of dimension one less than the total dimension of spacetime ) , the initial value problem is called the cauchy problem . because the equation contains only second derivatives , the appropriate initial data for the cauchy problem consist of the field and its first normal derivative at each point . ( the ` normal ' derivative is the derivative perpendicular to the hypersurface , which is the derivative in the time direction . ) this is given by the functions @xmath8 ( where @xmath9 stands for @xmath10 ) . the statement that the cauchy problem for the wave equation is well - posed means that , given appropriately differentiable functions @xmath11 and @xmath1 representing the relevant properties of the field at some time , a unique , stable solution exists for all times . the generalization of the wave equation to a spacetime with @xmath12 space dimensions and @xmath13 time dimensions is the ` ultrahyperbolic ' equation@xmath14 where @xmath15 and @xmath16 and where both @xmath12 and @xmath13 are greater than @xmath17 . let s now investigate the status of the initial value _ problems _ for this equation , where i say problems rather than problem in recognition of the fact that the meaning of initial is up for grabs in the presence of more than one time dimension . it has long been known ( to those who know it ) that the ordinary cauchy problem for equation ( [ ultra])the initial value problem on a surface of codimension one , i.e. dimension @xmath19 is not well - posed . it was shown by courant @xcite , using the mean - value theorem of asgeirsson , that solutions of the equation do not exist for arbitrary choices of initial data@xmath20 where @xmath21 and @xmath15 as before . this is perhaps unsurprising , given that the initial hypersurface is a ` mixed ' hypersurface@xmath22 , extended not only in @xmath12 space dimensions but also in @xmath23 time dimensions . therefore , it is traversed by lightlike lines , so - called ` characteristics ' along which one expects disturbances in the field to propagate . initial.png + initial data on a mixed hypersurface ( dashed lines represent lightlike lines ) . it might be thought that there is an additional obstacle to well - posedness , that just as ( global ) solutions do not exist at all for some initial data , other data are consistent with _ multiple _ solutions , conflicting with the uniqueness requirement . however , this is not the case : the holmgren - john uniqueness theorem guarantees that cauchy data on our mixed hypersurface uniquely determine the solution everywhere , as long as that initial data is consistent with _ some _ solution . indeed , it tells us that domains of dependence and influence are compact , so that we only need to know the solution on a compact region @xmath24 of the cauchy surface in order to determine the solution at a given point @xmath25 off the surface . tlike3.png + data in @xmath24 on a mixed hypersurface determines data out to @xmath25 . this holds true even for mixed surfaces in ordinary spacetime ( replace @xmath9 with @xmath26 @xmath27 @xmath28 with @xmath29 , and @xmath30 with @xmath31 in the figure above ) . the absence of a well - posed initial value problem is tantamount to a lack of any sort of practical predictability , and it has been argued that observers _ qua _ information processors could not even exist in such a universe , as they would be unable to engage in any meaningful action in response to information gleaned about their environment . thus it has been argued that universes with more than one time dimension are not meaningful possibilities @xcite . however , recent work of walter craig and myself @xcite shows that this judgment is too hasty . imposition of a constraint on the initial data yields a well posed cauchy problem after all . for those unfamiliar with the notion of a constraint , consider maxwell s theory of electromagnetism . the values of the electric and magnetic fields at a given time uniquely determine the evolution of the field . but given arbitrary initial data , which is to say arbitrary electric and magnetic fields at some time , a solution to the maxwell equations of motion will not , in general , exist . fortunately , maxwell s theory comes with two constraints , gauss s law for electricity @xmath32 and for magnetism @xmath33 . initial @xmath25 ( electric ) and @xmath34 ( magnetic ) fields satisfying these constraints _ do _ give rise to unique global solutions . with the imposition of the constraints , the initial value problem is indeed well - posed . the situation turns out to be similar for the ultrahyperbolic equation . there is a constraint on the initial data such that all and only data satisfying the constraint lead to a ( stable ) solution . the constraint is most straightforwardly specified in terms of the fourier transforms of the initial data @xmath35 and @xmath36 . it consists simply of the requirement that the domains of @xmath37 and @xmath38 be restricted to the region @xmath39 the inverse fourier transforms @xmath40 of such functions then correspond to the allowable sets of initial data . with the imposition of the constraint ( [ constraint ] ) , the problem is well - posed . the constraint ( [ constraint ] ) has an interesting property : it is nonlocal , in that it establishes nontrivial correlations between the values of the field at different points on the hypersurface . below we have an illustration of this on a surface spanned by one space and one time dimension : courant @xcite shows that the field in @xmath41 uniquely determines the field in @xmath24 . tlike3d.png + @xmath41 determines @xmath24 . the nonlocality here is causally benign , since there is no sense in which changes in one region bring about instantaneous changes in the larger region ; it is a version of what i refer to in @xcite as nonlocality without nonlocality . i ll have more to say about the potential physical significance of such nonlocal constraints toward the conclusion of this essay . we ve seen , then , that many of the features one physics with one time dimension remain in the transition to multiple time dimensions , when the initial value problem is understood as a cauchy problem . * the initial value problem is well - posed , albeit in the company of a novel , nonlocal constraint . * the domains of dependence are compact , as shown by the holmgren - john uniqueness theorem . * furthermore , there is a well - defined energy functional a hamiltonian which is conserved with respect to the chosen time . let s now move on and look at other versions of the initial value problem , corresponding to other notions of initial in the presence of multiple times . in ordinary physics with a single time dimension , determinism means that the state of the system at one time determines the state at other times . for a field theory , the initial data are naturally given on a hypersurface of codimension one , meaning one fewer dimension than the entire spacetime . the construction of the cauchy problem in the previous section simply carries this over to a spacetime with multiple times , giving data again on a hypersurface of codimension one , the difference being that the hypersurface is mixed , rather than purely spacelike . but one might suppose that a more natural way to give initial data in a theory with multiple times is to give it on a surface of" +"the subject of deformed quantum field theories has attracted renewed attention in recent years due to their natural appearance in string theory . initial studies were devoted to theories on non - commutative spacetime in which the commutator of the spacetime co - ordinates becomes non - zero . more recently@xcite-@xcite , non - anticommutative supersymmetric theories have been constructed by deforming the anticommutators of the grassmann co - ordinates @xmath1 ( while leaving the anticommutators of the @xmath2 unaltered ) . consequently , the anticommutators of the supersymmetry generators @xmath3 are deformed while those of the @xmath4 are unchanged . non - anticommutative versions of the wess - zumino model and supersymmetric gauge theories have been formulated in four dimensions@xcite and their renormalisability discussed@xcite-@xcite , with explicit computations up to two loops@xcite for the wess - zumino model and one loop for gauge theories@xcite@xcite . more recently still , non - anticommutative theories in two dimensions have been considered . on the one hand , non - anticommutative versions of particular non - linear @xmath5-models have been constructed ( by dimensional reduction from four dimensions)@xcite and the one - loop corrections computed@xcite ; on the other hand , a non - anticommutative version of the general @xmath6 khler @xmath5-model has been constructed directly in two dimensions , initially in refs . @xcite but then given an elegant reformulation in refs . the one - loop divergences for this model were computed in ref . @xcite , where it was found convenient to introduce differential operators implementing the deformed supersymmetry algebra acting on the component fields . in this article we return to a closer examination of the non - anticommutative wess - zumino model in four dimensions . firstly , we show how analogues of the differential operators introduced in ref . @xcite may easily be constructed to implement the non - anticommutative supersymmetry algebra for this model in its component formulation . next we re - examine the two - loop calculation first performed in ref . @xcite , showing that to correctly obtain results for the theory where the auxiliary fields have been eliminated from those for the uneliminated theory , it is necessary to include in the classical action separate couplings for all the terms which may be generated by the renormalisation process . we show that ( at least up to two - loop order ) the results obtained when we eliminate the auxiliary field after renormalisation are equivalent to those obtained when we eliminate the auxiliary fields before quantisation . we follow the analysis of ref . @xcite in determining differential operators which represent the supersymmetry algebra in the undeformed and deformed cases . the supersymmetry charges are q_=,_= -+2i^ _ , where _ & = & ^ _ , y^&=&x^+i^^ _ ^. [ eq : ydef ] they satisfy the algebra \{q_,q_}=0 , & & \ { _ , _ } = 0,\{_,q_}&=&2i_.[eq : undefcom ] the superfields have expansions in terms of component fields given by & = & + 2+^2 f , + & = & + 2 - 2i^_+^2 , [ compexp ] where the component fields are functions of @xmath7 , as defined in eq . ( [ eq : ydef ] ) . it is useful to represent the charges @xmath4 , @xmath3 by differential operators @xmath8 , @xmath9 acting on the fields , i.e. & = & q_,&=&^0_[eq : undefopa ] ( with similar expressions for @xmath10 ) where q_&= & _ + f -i[_]+i [ _ ^ ] , [ eq : undefopba ] + 1_^0&= & _ - -i [ _ ] -i[_^ ] . [ eq : undefopbb ] the superscript `` 0 '' is in anticipation of a different form for @xmath11 in the deformed case ; while @xmath8 , on the other hand , will be unchanged . our convention will be that a derivative or other operator acts on everything to its right , unless enclosed in square brackets . ( by the way , note that _ = - . ) in this section we repeat the analysis of the previous section for the case of deformed supersymmetry . for the deformed version we take \{^,^}=0 , \{^,^}=c^. the charges then satisfy the algebra \{q_,q_}=0 , & & \ { _ , _ } = -4c^ _ _ , \{_,q_}&=&2i_.[eq : acomm ] the non - anticommutativity is implemented at the level of superfields by introducing the moyal @xmath12-product , which satisfies ^*^&=&-12^^2 + 12c^,^*^2&=&c^_,^2*^2&=&-c . we now wish to construct differential operators @xmath11 representing the effects of @xmath3 in the deformed case in a similar manner to eq . ( [ eq : undefopa ] ) , extending @xmath9 given in eq . ( [ eq : undefopbb ] ) for the undeformed case . ( as mentioned before , the operators @xmath8 are unchanged by the deformation . ) we start by examining the effects of @xmath3 on powers of @xmath13 alone , since mixed products of @xmath13 and @xmath10 present additional complications . defining i_r^(n)(,f)=_-12 ^ 12d()^r ( + f)^n it is straightforward to show using the methods of ref . @xcite that ^n_*= ( 1+q -14 ^ 2 q^2)(i_0^(n)-q^2i_1^(n ) ) , [ suppot ] where @xmath14 denotes the @xmath12-product of @xmath15 @xmath13 s . then acting on @xmath14 , @xmath3 is represented by ^_=^0 _ -i(qc)_+4i ( -q^2[_q^]+_q^+ [ _ q^ ] ) . [ eq : fullq ] here i_0^(n)&=&i_1^(n),i_1^(n)&= & i_2^(n)-i_0^(n).[eq : orels ] these properties are guaranteed by the following definitions : & = & _ r=1^a_r ( ) ^r ( 4f)^2r-1,&=&_r=1^(2r-1)a_r ( ) ^r ( 4f)^2r-2,where the @xmath16 must satisfy for each @xmath17@xcite _ r=0^n-1= , the first few being given by a_1= , a_2=-,a_3=. to check that the operators in eq . ( [ eq : fullq ] ) do indeed represent the operators @xmath3 according to _ * = ^_^n _ * ( where @xmath18_*$ ] represents the commutator evaluated using @xmath12-products ) we need to use eqs . ( [ eq : orels ] ) in conjunction with _ ^0i_r^(n ) = -i [ _ q^]i_r+1^(n).[eq : idsa ] of course it is not sufficient to reproduce the effects of @xmath3 on @xmath12-products of @xmath13 alone ; we saw in the two - dimensional case that it was necessary to consider the effect on deformed versions of general polynomials in @xmath13 and @xmath10 , such as the khler potential . in the case of the four - dimensional wess - zumino model , to investigate the divergence structure it would be sufficient to consider only the effects of @xmath3 on cubic superpotentials in either @xmath13 or @xmath10 , or on @xmath19 . however , in general , if one were interested in contributions to the effective action , one would need once again to consider deformed versions of general polynomials ; and so we shall again take the khler potential as an example . for an undeformed khler potential k[,]=_n , mk_n , m^n^m , the natural definition of the deformed khler potential is k_*[,]=_n , mk_n , m[^n^m ] _ * , where @xmath20_*$ ] represents the symmetrised @xmath12-product of @xmath15 @xmath13 s and @xmath21 @xmath10 s . it can be shown that k_*[,]&= & ( 1+q-14 ^ 2 q^2)&&&&-^2 q^2()^2 k_0(,f , ) , [ kstar ] where k_m(,f,)=_-12 ^ 12d()^m k(+ f , ) . here a prime denotes the part of the operator containing derivatives with respect to the chiral ( but not the anti - chiral ) fields , and correspondingly a double prime denotes the part of the operator containing derivatives with respect to the anti - chiral ( but not the chiral ) fields . moreover , _ = [ _ ] + [ _ _ ] + [ _ ] , with a similar expression for @xmath22 . the corresponding version of the operator representing @xmath3 is @xmath11 defined by _ & = & ^0 _ -i(qc)_- ( _ q^q^2 + _q^q^2)&&+4i ( -q^2[_q^]+_q^+ [ _q^ ] ) . [ eq : fullqa ] we can verify that these operators do indeed implement the operators @xmath3 according to _ * = _ k _ * , using the analogue of eq . ( [ eq : orels ] ) for the khler potential , k_0&=&k_1,k_1&= & k_2-k_0[eq : orelsa ] together with the analogue of eq . ( [ eq : idsa ] ) , _ ^0k_r =- i[_q^ ] k_r+1,q^_k_0=q^_k_1=0 . moreover , it is easy to check that the operators @xmath8 in eq . ( [ eq : undefopba ] ) and @xmath11 in eq . ( [ eq : fullqa ] ) satisfy the anticommutation relations of eq . ( [ eq : acomm ] ) , using = -i[_q^ ] ( which implies [ _ ^0 , ] = -i[_q^ ] ) . the kinetic part of the standard wess - zumino model may be obtained as in ref . @xcite from eq . ( [ kstar ] ) taking simply @xmath23=\phi\phibar$ ] , s_kin&=&d^4xd^2d^2 = d^4x q^2 ^ 2&=&d^4x ( ^_+i^ _ + f ) , [ inva ] so we see that the kinetic terms are undeformed . we see from eq . ( [ suppot ] ) that the holomorphic potential terms are given by s_w = -d^4xd^2 [ 12 m _ * ^2 + 16y_*^3 ] = 14d^4x q^2[12mi_0^(2)+16yi_0^(3 ) ] [ invb ] which leads to s_w = d^4x [ 12m(^2-f)+12y(^2-f^2)+ 16y(c ) f^3 ] . since @xmath24 , the antiholomorphic potential terms are given by s_w = -d^4xd^2 [ 12 ^ 2 + 16 ^ 3 ] = 14d^4x ^2[12 ^ 2 + 16 ^ 3 ] [ invc ] which leads to s_w= d^4x [ 12(^2-)+12(^2 -^2 ) ] , with no deformation ( the deformed part of @xmath25 in eq . ( [ eq : fullqa ] ) having no effect on a function of @xmath26 ) . the full classical @xmath27 action is therefore s&=&d^4x ( ^_+i^ _ + f -gf-&&+12y^2 + 12 ^ 2 + 12m^2 + 12 ^ 2 + 16 y(c ) f^3 ) , [ defact ] where @xmath28 . this action was first derived in ref . @xcite by taking the standard undeformed ( @xmath29 ) action in superfields and replacing ordinary products by moyal @xmath12-products . in the undeformed case , expressions like those in eqs . ( [ inva ] ) , ( [ invb ] ) and ( [ invc ] ) in terms of @xmath8 and @xmath30 encapsulate the supersymmetry of the undeformed action @xmath31 due to the nilpotency of @xmath8 , @xmath11 and the fact that @xmath8 , @xmath9 annihilate functions of @xmath26 , @xmath32 , respectively , leading to q_s_0=^0_s_0=0 . in the deformed case , although q_s_kin= _ s_kin = q_s_w= q_s_w = _ s_w=0 , it is not the case that @xmath33 ; indeed it is no longer the case that @xmath34 either . it is only the tranformations generated by @xmath4 that are a symmetry of the deformed action with potential . it is worth mentioning that in the two - dimensional case ( where we considered only the kinetic part of the action derived from the khler potential ) , despite our classical action being annihilated by @xmath35 and @xmath25 , the divergent quantum corrections were only annihilated by @xmath35 . in fact it is only for simple linear field transformations that one can prove that an invariance of the classical action results in a similar invariance of the quantum corrections ; for non - linear gauge transformations the quantum invariance is encapsulated in ward identities , and for transformations such as our deformed @xmath11 some other formulation may be possible . in this section we discuss the renormalisation of the non - anticommutative wess - zumino model up to two loops . two - loop calculations for this model were first" +"qcd processes provide signals to test theoretical calculations and models and contribute major backgrounds to many measurements . thus , their detailed understanding and modeling is of crucial importance . production of isolated photons at large @xmath0 provides one of the cleanest and most accurate tests of perturbative qcd ( pqcd ) . such photons originate primarily from hard collisions of partons ( quark - gluon or quark - antiquark ) and are thus sensitive to the parton distribution functions ( pdfs ) . consequently , they can help constrain pdfs ( especially the large-@xmath1 gluon distribution ) independently of the high-@xmath0 jet production . such constraints can reduce ambiguities in interpreting results on high-@xmath0jet production in terms of new physics . isolated photon samples also provide indispensable calibration of the recoiling jets . d0 presented the first measurement of the inclusive isolated photon cross section in run 2 of the tevatron @xcite . the photon spectrum , obtained using 326 pb@xmath2 , spans @xmath0= 23300 gev/@xmath3 and @xmath4 , significantly extending the reach observed in run 1 . the measurement agrees well with next - to - leading order ( nlo ) pqcd calculation @xcite over six orders of magnitude , fig . [ fig : d0-photons](left ) . the data / theory ratio , presented in the right panel , shows that the theoretical scale dependence and pdf uncertainties are comparable to the experimental error bars . further improvements in theoretical predictions are desired to reduce the level of sensitivity to the choice of pqcd scales in order to fully exploit the potential of this measurement for constraining pdfs with the help of much larger data samples already available . = 2.5 in = 2.5 in measurements of the inclusive jet cross section provide tests of pqcd and sensitivity to new physics by probing distances down to @xmath5 m. results at large rapidities are particularly important for constraining pdfs in a kinematic region where no effects from new physics are expected . cdf obtained the first measurement in run 2 of inclusive jet cross section in five rapidity regions using the longitudinally - invariant @xmath6 algorithm and @xmath7 fb@xmath2 of data @xcite . figure [ fig : cdf - kt](left ) shows the results for the size parameter @xmath8 for jets with @xmath0@xmath9 gev/@xmath3 and @xmath10 . the right panel shows the data ratio to nlo theory @xcite and displays the experimental and theoretical uncertainties . the former are dominated by the jet energy calibration and the latter by the qcd scale and pdf variations . the theoretical calculations include corrections for non - perturbative effects related to the underlying event and hadronization process . these corrections are essential to obtain good agreement between data and theory . similar level of agreement has been found for central jets ( @xmath11 ) using values of @xmath12 and 1.0 and the corresponding corrections . these results demonstrate veracity of the @xmath6 algorithm in the hadron - collider environment within the range of the measurement . for the most forward rapidity bin ( @xmath13 ) the experimental uncertainty is smaller than the one due to pdfs , hence this measurement is expected to further constrain large-@xmath1 pdfs in future global fits . similar conclusions have been reached by cdf and d0 for the inclusive jet cross section measurements using the midpoint cone algorithm ( not shown ) . here corrections for soft effects are smaller than for @xmath6 algorithm but non - negligible at the current level of precision . = 2.in correlations in the azimuthal angle @xmath14 between the two leading jets in an event provide a clean and simple probe of radiation effects . in the absence of radiation @xmath14= @xmath15 . soft radiation causes small deviations from @xmath15 while @xmath14 significantly lower than @xmath15 indicates the presence of hard radiation , such as additional jets with high @xmath0 . the proper description of multi - parton radiation is crucial for a wide range of precision measurements as well as for searches for new physical phenomena at tevatron and lhc . d0 results @xcite for @xmath14 correlations between central jets ( @xmath16 ) are presented in fig . [ fig : d0-deltaphi ] in four ranges of leading - jet @xmath0 . since the data are sensitive to a range of jet multiplicities , they provide a test of recent monte carlo approaches that combine exact lo pqcd matrix elements for multi - parton production with parton - shower models and of the associated `` matching '' prescriptions imposed to avoid double - counting of equivalent parton configurations . two such generators , alpgen @xcite ( not shown ) and sherpa @xcite , are in good agreement with data , thus enhancing confidence in their applications to other processes . the data are also well described by nlo pqcd for three - jet production @xcite , and by herwig @xcite with default parameters . distributions from pythia @xcite are sensitive to the value of a parameter which controls the maximum allowed virtuality in the initial - state shower . the shaded bands in fig . [ fig : d0-deltaphi](right ) show the range of predictions when this parameter is varied by a factor of four . the optimal value of 2.5 has been incorporated in the recent tunes dw and dwt of pythia parameters @xcite . = 2.in = 2.in production of w and z bosons in association with jets constitutes an important background to top - quark production and in the searches for new physics , including production of the higgs boson and supersymmetric particles . thus an accurate modeling of this process is essential . the presence of w / z ensures high @xmath17 and facilitates tests of pqcd and monte carlo tools for configurations with multiple soft jets . d0 compared predictions from pythia and sherpa to various distributions in z/@xmath18+jets events using 950 pb@xmath2of data @xcite . data selection required two electrons with @xmath0@xmath19 gev/@xmath3 and @xmath20 within a di - electron mass window of 70100 gev , and jets with @xmath0@xmath21 gev/@xmath3 . pythia was found to underestimate the production rate of higher jet multiplicities , fig . [ fig : d0-zjets](left ) . sherpa provides a good description of jet multiplicity ( right panel ) , and all kinematic distributions studied , including @xmath0 distributions of the z and of 1@xmath22 , 2@xmath23 and 3@xmath24 leading jets , as well as @xmath14 and @xmath25 angular distributions between the jets . significant differences with data have been observed for pythia distributions . = 2.5 in = 2.5 in using 320 pb@xmath2 of data cdf performed @xcite shape comparisons between w+jets production ( up to four jets ) with predictions from alpgen interfaced to pythia for showering and hadronization . jets were corrected to hadron level and kinematic cuts imposed to reduce model dependence on acceptance and efficiency . data selection required a good - quality electron candidate with @xmath0@xmath26 gev/@xmath3 , missing transverse energy @xmath27 gev , and @xmath28 cone jets with @xmath0@xmath29 gev/@xmath3 and @xmath30 . reasonable agreement is observed for the jet @xmath0 distributions ( fig . [ fig : cdf - wjets](left ) ) , @xmath31 between jets in w+2jets sample ( fig . [ fig : cdf - wjets](right ) ) , and dijet invariant mass ( not shown ) . = 2.5 in = 2.5 in ten years after its discovery top quark is intensely studied at the tevatron . its surprisingly large mass makes it the only fermion having the yukawa coupling near unity implying its large contribution to the radiative corrections to the higgs mass . this leads to speculation that electroweak symmetry breaking mechanism may be probed through studies of its production and properties . consequently , every aspect of top - quark physics experimentally accessible is vigorously scrutinized at the tevatron . the standard model ( sm ) predicts that at the tevatron top quarks are primarily produced in pairs through the strong force by @xmath32 annihilation 85% of the time and by gg fusion 15% of the time . the predicted cross section is @xmath33 pb for @xmath34 gev @xcite . in sm , top quarks decay @xmath35100% to wb , and hence t@xmath36 events are classified according to the decay modes of the w s . in dilepton events both w s decay into e or @xmath37 . this channel has a low branching fraction ( @xmath38% ) but is very clean . a recent extension of the dilepton analysis selects candidate events requiring an isolated track instead of one of the leptons . this improves selection efficiency and enlarges the event sample at the cost of additional backgrounds . the channel when one w decays to e or @xmath37 and the other to quarks is called lepton+jets . it has a higher branching fraction ( @xmath39% ) but also receives higher backgrounds . since it provides a large but still fairly pure sample of top quarks , it facilitates some of the best measurements in top physics . decays of both w s to quarks result in the all - hadronic channel , which has the largest branching fraction ( @xmath40% ) but also the highest background from qcd multi - jet production . the b - tagging information is essential for background suppression in this channel . it also helps to reduce backgrounds in the lepton+jets channel . analyses based on decay modes involving @xmath41 leptons are especially difficult and are only now becoming developed . due to the presence of w s and jets in top decays , good understanding and simulation of qcd w / z+jets and multijet production is indispensable in top - quark measurements . one of the best measurements of t@xmath36 cross section has been obtained by cdf using the lepton+jets channel and 695 pb@xmath2 of data @xcite . while the traditional analyses in this channel have used selections based on topological variables to enhance t@xmath36 signal , this measurement employs b - tag information to reduce backgrounds . events are required to have one isolated electron or @xmath37 with @xmath0@xmath26 gev/@xmath3 and @xmath26 gev , at least three jets with @xmath0@xmath21 gev/@xmath3 within @xmath30 and the total scalar sum of transverse energies of all objects in the event @xmath42 gev ( including jets with @xmath0@xmath43 gev/@xmath3 and @xmath44 ) . the last requirement is dropped for the double - tagged sample . as illustrated in fig . [ fig : cdf - ttxs - lj](left ) , the events in the `` w+3 jet '' and `` w+@xmath454jet '' bins are relatively background free and dominated by t@xmath36 contribution when one b - tag is required . the resulting cross section is @xmath46 pb . the uncertainty is dominated by systematics , and its largest component comes from b - tagging . when two b - tags are required , the sample statistics is reduced but t@xmath36purity improves even further . it is noteworthy that the cross section measurement using the double - tagged sample alone has achieved a @xmath47 significance : @xmath48 pb . = 2.3 in = 2.3 in cdf and d0 are developing a variety of techniques to examine t@xmath36 decays into the all - hadronic final state . a novel analysis from d0 @xcite , based on 360 pb@xmath2 , selects six - jet events with at least 2 jets having @xmath0@xmath49 gev/@xmath3 and tagged as b - jets with a secondary - vertex tagging algorithm . the remaining jets are required not to be b - tagged , two of them to have @xmath0@xmath50 gev/@xmath3 and the rest @xmath0@xmath51 gev/@xmath3 . all jets are required to be within @xmath52 . as no events have been rejected based on the presence of high-@xmath0 leptons or , this sample includes contributions from the all - hadronic channel , the @xmath41 channel with hadronic @xmath41 decays , and the other t@xmath36 decay channels" +"in his classical paper on quantisation of magnetic poles dirac ( 1931 ) remarked that `` non - euclidean geometry and non - commutative algebra , which were at one time considered to be purely fictions of the mind and pastimes for logical thinkers , have now been found to be very necessary for the description of general facts of the physical world . it seems likely that this process of increasing abstraction will continue in the future and that advance in physics is to be associated with a continual modification and generalisation of the axioms at the base of the mathematics rather than with a logical development of any one mathematical scheme on a fixed foundation . '' in accordance with this principle , the present paper further extends the work of dirac by exploring the ` dequantisation ' of magnetic poles . diverse and numerous versions of the magnetic pole construction and the associated charge quantisation condition of dirac ( 1931 , 1948 ) have appeared in the literature , but the basic model can be most concisely and accurately formulated in terms of the hopf fibration ( wu & yang 1975 ; trautman 1977 ; yang 1977 ) . from a mathematical viewpoint , the rationale is as follows . the monopole potential is modelled as a connection @xmath0 on a nontrivial principal @xmath1-bundle @xmath2 over a subset of minkowski space . a charged matter field interacting with the monopole is accordingly modelled as a section of a vector bundle @xmath3 associated with @xmath2 via the representation @xmath4 of @xmath1 on a complex vector space . since @xmath0 then induces the connection @xmath5 on @xmath3 , the integer @xmath6 can be identified with the electric charge of the matter field ( see urbantke 2003 for a detailed account of the description of a magnetic monopole in the language of the hopf fibration ) . however , following the spirit of dirac , if we describe the monopole by a more general mathematical scheme , then the interaction of matter fields and magnetic poles _ with arbitrary real charges _ can also be modelled in a consistent manner . the present paper introduces a new sheaf - theoretic framework permitting an explicit construction of arbitrarily charged magnetic monopoles . this framework is likewise applied to generic @xmath1-bundles and also yields , as a by - product , the notion of a quasispin structure defined on arbitrary space - times . the results suggest that topological quantisation in general can be viewed from a more flexible perspective . although magnetic monopoles have not been observed experimentally , one important physical consequence of the present model is that their detection would not necessarily imply the quantisation of electric charge . likewise , an observed violation of charge quantisation would not necessarily imply the nonexistence of magnetic monopoles . furthermore , grand unified theories require the existence of magnetic monopoles , and , according to conventional field theory described in terms of manifolds this necessarily implies charge quantisation , hence , the detection of nonintegral electric charge would indicate that the present scheme , based on sheaves rather than manifolds , may be physically more realistic . also , a sheaf construction permits the global description of fermion fields on lorentzian manifolds possessing no conventional spin structure , as an alternative to the cumbersome machinery of khler fermions . the paper is organised as follows . in [ sec:2 ] we present a very brief sketch of sheaf theory for the benefit of readers less acquainted with the subject . this is intended to provide the bare minimum of information necessary for following the ensuing discussion ; for further details on sheaf theory , see , e.g. , bredon ( 1997 ) , kultze ( 1970 ) , or wells ( 2008 ) . in [ sec:3 ] we develop the basic mathematical machinery used in later sections . the key idea here is the construction of a principal @xmath7-sheaf bundle which generalises the conventional notion of a principal bundle . in [ sec:4 ] we prove that equivalence classes of principal @xmath8-bundles can , under certain hypotheses , be mapped injectively into equivalence classes of @xmath7-sheaf bundles . this implies that the dirac sheaf bundle constructed in [ sec:5 ] does indeed constitute a generalisation of the conventional dirac monopole . the spherically symmetrical connection and curvature of the dirac sheaf bundle are constructed in [ sec:6 ] , demonstrating that the magnetic charge of this model can assume arbitrary real values . the interaction of the generalised monopole with a charged matter field is considered in [ sec:7 ] . dequantisation of more general @xmath1 bundles is considered in [ sec:8 ] , with particular attention to gravitational and electromagnetic instantons . in [ sec:9 ] the basic machinery developed earlier is applied to spin structures and dirac operators . in [ sec:10 ] the paper concludes with a brief discussion of possible implications in diverse areas of physics . the concept of a sheaf over a manifold @xmath9 provides a way of interpolating local data and global data on x. we begin with the definition of a presheaf . a _ presheaf _ @xmath10 on @xmath9 is a functor assigning , to each open @xmath11 , a group @xmath12 , abelian or otherwise , such that for each @xmath13 the restriction map @xmath14 , @xmath15 , defines a homomorphism and such that @xmath16 for @xmath17 . an element @xmath18 is referred to as a _ section _ of @xmath12 over @xmath19 . the restriction of @xmath20 on @xmath13 is thus given by @xmath21 . the sections @xmath18 and @xmath22 are said to be _ equivalent _ at @xmath23 if there is a neighbourhood @xmath24 of @xmath25 such that @xmath26 . the equivalence class containing @xmath18 is called the _ germ _ of @xmath27 at @xmath25 , and the set of all such germs for any fixed @xmath25 is denoted by @xmath28 . the disjoint union @xmath29 of all the sets @xmath28 provides local information about the structure of @xmath10 . however , information concerning global structure has been lost , since we have discarded relations between the @xmath28 for varying @xmath25 . to retrieve some global structure , we introduce a topology in the following manner . for a fixed @xmath18 the set of all germs @xmath30 for @xmath31 is taken to be an open set in @xmath29 , and the topology of @xmath32 is defined as that generated by these open sets . the projection @xmath33 mapping @xmath28 into @xmath25 has the property that for any point @xmath34 with @xmath35 there is a neighbourhood @xmath36 for @xmath18 and @xmath37 such that the restriction @xmath38 is a homeomorphism onto a neighbourhood of @xmath39 . these ideas can be summarised as follows : a _ sheaf _ of groups on @xmath9 is a pair @xmath40 such that * @xmath29 is a topological space ( in general , not hausdorff ) ; * @xmath41 is a local homeomorphism of @xmath29 onto @xmath9 ; * each @xmath42 , @xmath43 , is a group called the _ stalk _ of @xmath29 at @xmath25 ; and * the group operations are continuous with respect to the relative topology on the subset @xmath44 of @xmath45 . [ def:1 ] for @xmath11 , a continuous map @xmath46 such that @xmath47 is called a _ section _ of @xmath32 over @xmath19 . the totality of such @xmath27 will be denoted @xmath48 . note that every element of the group @xmath12 specified by the presheaf functor naturally determines an element of @xmath48 , but the converse is only true locally . some of the key properties of a sheaf are as follows . if @xmath49 is an open covering of an open set @xmath50 , and if @xmath51 are such that @xmath52 . furthermore , if @xmath53 are such that latexmath:[$\sigma_\alpha|_{u_\alpha\cap u_\beta } = \sigma_\beta there exists an element @xmath18 with @xmath55 for all @xmath56 . the first property implies that if the restrictions of a pair of sections always agree , then the two sections are identical thus a section over @xmath19 is determined by the totality of its restrictions to subsets of @xmath19 . the second property , somewhat complementary to the first , implies that if pairs of sections always agree on their overlapping regions then global section can be constructed from the local data thus a section over @xmath19 may be assembled from consistent local sections on subsets of @xmath19 . a sheaf @xmath29 contains localised information concerning the topological space @xmath9 . global information about @xmath9 can then be extracted from @xmath29 by consideration of exact sequences , quotients , and so on . given two sheaves @xmath29 and @xmath57 over @xmath9 , a sheaf homomorphism @xmath58 is a continuous map such that the stalk map @xmath59 is a homomorphism of @xmath60 into @xmath61 for each @xmath43 . a sequence of sheaf homomorphisms of the form @xmath62 such that the corresponding sequence of stalk maps is exact for all @xmath43 is called a short exact sequence of sheaves . evidently , exactness is a local property . given a short exact sequence of sheaves , the induced sequence @xmath63 is exact at @xmath64 and @xmath65 , but in general not at @xmath66 . that is to say , the local exactness of a sequence does not imply exactness with respect to the global sections over @xmath9 . the measure of inexactness at @xmath66 can then be characterised by cohomology . recall that in the cohomology theories of @xmath9 one computes @xmath67 where @xmath8 is an abelian group . in sheaf cohomology the coefficients are not elements of a fixed group @xmath8 but are , rather , local sections of some sheaf @xmath29 over @xmath9 . more precisely , let @xmath68 be an open covering of @xmath9 . for any @xmath69 such that @xmath70 , we define the set of @xmath71-cochains by @xmath72 . for any @xmath73 define the coboundary operator @xmath74 by @xmath75 where @xmath76 and @xmath77 is the sheaf restriction map . these coboundary operators define a complex @xmath78 and the cohomology groups of this complex are then defined in the usual manner : @xmath79 passing to a direct limit over progressively finer coverings , we obtain the sheaf cohomology groups @xmath80 . the reader will notice that the definitions in this section run parallel , _ mutatis mutandis _ , to the conventional definitions in the theory of fibre bundles . the @xmath7-sheaf plays the role of a trivial and the @xmath7-sheaf bundle that of a generally nontrivial fibre bundle . let @xmath9 and @xmath81 be topological spaces and @xmath82 a sheaf of groups over @xmath9 . @xmath7-sheaf _ over @xmath9 is a triple @xmath83 such that * @xmath41 is a local homeomorphism of @xmath81 onto @xmath9 ; * for each @xmath84 , the stalk @xmath85 operates ( by left action ) upon @xmath86 ; and * if @xmath87 is equipped with the relative topology in @xmath88 , then the mapping @xmath89 defined by @xmath90 is continuous . [ def:2 ] for any subset @xmath91 , the obvious restriction maps define a @xmath92-sheaf @xmath93 over @xmath0 . in the sequel , when @xmath0 is clearly understood , we shall , for brevity , use the term @xmath7-sheaf in place of @xmath94-sheaf . we call @xmath29 a _ principal @xmath7-sheaf _ if @xmath95 and @xmath7 operates by left translation . given two @xmath7-sheaves @xmath96 and @xmath97 over @xmath9 , a continuous map @xmath98 will be called a _ @xmath7-sheaf map _ of @xmath29 into @xmath57 provided * @xmath99 ; and * for each @xmath84 , the induced map @xmath100 satisfies @xmath101 for all @xmath102 and @xmath103 . [ def:3 ] again , if @xmath104 , then a @xmath105-sheaf map will , for brevity , be called a @xmath7-sheaf map when the restriction is clearly understood . a _ @xmath7-sheaf isomorphism _" +"the presence and location of corotation resonances in barred spiral galaxies is important for several reasons . first , resonances are required by density wave theory , so their existence would be evidence that supports the theory . second , the corotation resonance of a bar is related to the ability to transfer angular momentum outwards , or material inwards . this is the main process that drives the secular evolution of a galaxy . also , resonances can scatter stellar orbits and cause disk heating . finally , the corotation radius of barred galaxies is related to the bar pattern speed . fast bars may indicate low concentration central dark matter halos due to decreased dynamical friction ( debbatista & sellwood 2000 ) . current methods of measuring corotation resonance ( cr ) radii and/or bar pattern speeds , e.g. , computer simulations ( rautiainen et al . 2008 ; treuthardt et al . 2012 ) , the tremaine - weinberg method ( tremaine & weinberg 1984 ; hereafter tw ) , etc . , require extensive computer and telescope time , the presence of specific morphological features , or other limiting factors . the tw method directly measures the bar pattern speed , but it requires a lot of telescope time . also , it is only useful on galaxies where the bar major axis and galaxy major axis are offset by 45@xmath9 , or as close to 45@xmath9 as possible . this severely limits the number of galaxies you can analyze with the tw method . therefore , other methods have been found to estimate the bar pattern speed , such as the dimensionless parameter @xmath5 , which estimates the relative bar pattern speed . @xmath5 is defined as the bar corotation radius divided by the bar radius , @xmath10 . when finding the relative bar pattern speed , the focus is on determining the radius of the bar s corotation resonance . rather than make use of tw , it would be beneficial to have a faster , cheaper , but reliable method for determining corotation resonance radii and relative bar pattern speeds . puerari & dottori ( 1997 ; hereafter pd ) present such a method . in this study , we use the pd method to measure the cr radii and relative bar pattern speed of 15 barred spiral galaxies that already have cr measurements elsewhere in the literature . resonances are predicted by density wave theory , which was originally proposed by lin & shu ( 1964 ) . further developments of the theory have led to the modal theory of spiral structure ( e.g. , bertin et al . 1989a , b ; bertin 1993 ; bertin & lin 1996 ) . in these models , the spiral density wave has a pattern speed which is independent of the orbital speeds of stars and gas in the disk . if the relative velocities between the gas and the density wave are supersonic , a shock front may be formed ( roberts 1969 ; binney & tremaine 2008 ) . the shock compresses the gas , which after a time delay leads to star formation on the side of the arm opposite the shock front ( seigar & james 2002 ) . when observed in the near - infrared , about two - thirds of all disk galaxies seem to have a bar - like structure with their own pattern speeds ( seigar et al . 1998 ; eskridge et al . 2000 ; hernandez et al . 2005 ) . in barred - spiral galaxies , the bar forcing influences the spiral arm amplitudes . specifically , salo et al . ( 2010 ) found a strong correlation between the local tangential bar torque , @xmath11 , and the local spiral arm amplitude , @xmath12 , out to 1.5 bar lengths . this suggests that the inner portions of spiral arms may be either a continuation of the bar mode or they are driven by bar forcing itself . further out , the spirals are most likely independent modes , and the disk pattern speed becomes the dominant factor . the radius where the angular velocity of the stars is equal to a pattern speed is called a corotation radius . according to contopoulos ( 1980 ) , the radius of the bar can not be larger than its corotation radius , or the bar would not be self - sustaining ( i.e. , it simply would not exist ) . note that buta & zhang ( 2009 ) find some bars that are larger than their cr radii , but this is considered controversial . beckman & cepa ( 1990 ) showed that azimuthal color profiles of galaxies can be a useful tool in studying spiral galaxies . phase shifts in the profiles of the @xmath13 and @xmath14 band can highlight star - forming regions in galaxies . pd expanded on the findings of beckman & cepa ( 1990 ) by showing that phase crossings of the @xmath13 and @xmath14 bands indicate a corotation radius . the motion of the spiral density wave creates a shock front inducing star formation . because new stars are bluer than older stars , the side of the spiral arm with the shock front should be bluer . inside corotation the material speed is greater than the bar pattern speed . this means that the inner edge of the spiral pattern is bluer than the outer edge . this is because gas clouds enter the density wave and create a shock front as they enter . bright , blue , newly formed stars then appear downstream of this shock . outside corotation the bar pattern speed is faster and the color of the two sides switch . at corotation the bar pattern speed and material speed are equal . at this radius the shock wave switches sides . we refer the reader to pd ( their figure 1 ) to see how the shock front would switch sides at the cr . pd describes the photometric method for determining corotation radius and included two example galaxies , ngc 7479 and ngc 1832 . aguerri , beckman & prieto ( 1998 ) reported the cr , determined by using the pd method , for 10 galaxies . during the next decade , references were made to the pd method ( e.g. , aguerri et al . 2000 ; rautiainen , salo & laurikainen 2008 ) but its usage was absent from the literature . martnez - garca et al . ( 2009a ) reported their results on the relationship between color gradients and pattern speed . they found that 10 out of the 13 barred and non - barred spiral galaxies in their sample showed color gradients that matched the theoretical predictions . martnez - garca et al . ( 2009b ) describe the effect non - circular motions have on the azimuthal color gradient . the initial assumptions for the formation of a color gradient involved the collision of a spiral density wave and the disc material , whose orbital velocities decrease with radial distance . martnez - garca et al . ( 2009b ) showed that legitimate color gradients could form in galaxies even if the disc material moved in non - circular orbits . finally , martnez - garca & puerari ( 2014 ) reported results using the pd method on 9 nearby spiral galaxies . instead of using optical wavebands , they used hi , co , 24-@xmath15 m , and fuv wavebands . they were able to find phase shifts . as noted in previous work by martnez - garc et al . ( 2009a ) , color gradients are common in spiral arms . although the gradients do not always occur across a large enough radial range to be sufficient for finding resonance locations , martnez - garca & gonzlez - lpezlira ( 2013 ) found that at least 50% of their studied objects did have a sizeable region of color gradients in the spiral arms . martnez - garca & puerari ( 2014 ) showed that the phase shifts discovered in two arm spirals are different for the two arms . however , they were looking for the spiral arm pattern speed . in this paper , we focus on the bar pattern speed , which occurs very near the end of the bar which is more symmetrical in nature . an alternative theory of spiral structure , particularly in barred galaxies , is refered to as manifold theory ( romero - gmez et al . 2006 ; romero - gmez et al . 2007 , athanassoula et al . 2009a , b ; athanassoula et al . 2010 ) . these authors studied the orbits of individual particles . athanassoula summarizes one of the differences between manifold and spiral density wave theory as : `` in density wave theory , the arms are loci of density maxima . particles should thus traverse the arms , but stay longer in the arm than in the interarm region ( lin & shu 1964 ) . this is totally different from our manifold theory , where spiral arms should be a bundle of orbits guided by the manifolds , so that particles should move along the arms rather than across them '' ( athanassoula 2012 ) . if the stars or particles travel along the arms instead of across them , then any age gradients or color gradients should also be along the arms instead of across them . therefore , if we could show many examples of age gradients across spiral arms , this would favor density wave theory over manifold theory . as well as the pd method , multiple methods for finding the @xmath16 have been developed . a few example methods are listed below . * morphological , e.g. , rings ( patsis et al . 2003 ) : the rings of galaxies can be related to resonances locations . the nuclear , inner , and outer rings can be linked to the inner lindblad resonance , inner ultraharmonic resonances , and outer lindblad resonances . * computer modeling , e.g. , sticky - particle ( rautianien et al . 2008 ; treuthardt et al . 2012 ) or hydrodynamics ( lin , yuan & buta 2008 ) : virtual particles are used to simulate the response of gas clouds in a gravitational potential . * phase shift between potential and density ( zhang & buta 2007 ) : a method for determining the corotation radii and pattern speed of galactic density waves using the azimuthal phase shift between the potential and density wave patterns . in this paper , we use the results of our pd analysis and compare them to the latter two methods described above . we do not make any comparisons with the first method , since the method has large uncertainties . this paper is organized as follows : section 2 describes the dataset and methods used ; section 3 presents the corotation radii that we have determined ; section 4 presents and discusses our results ; and in section 5 we summarize our main conclusions . [ efigi ] [ cols= "" < , < , < , < , < , < "" , ] two of the 57 galaxies had 3 major phase crossings . all three crossings are shown in figures 3 and 4 . the third phase crossing might correspond to the spiral arm pattern speed ( cepa & beckman 1990 , their figure 1 ) . the pixel scale ( in @xmath17/pixel ) for pgc 37091 is 0.32 . the difference between cr2 and cr is @xmath18 pixels or @xmath19 and the difference between cr3 and cr is @xmath20 . the pixel scale for pgc 42575 is 0.51 . the difference between cr2 and cr is" +"the stability and structure of nuclei at the upper end of the nuclear chart is a hot topic in contemporary nuclear physics . it is a challenging task to answer which heavy nuclides may exist and what properties they may have . therefore strong efforts have been made in the experimental developments as well as in the theoretical description of super - heavy elements ( she s ) . in the last decades a huge progress in the synthesis of new elements has been achieved in world leading laboratories like the gsi , darmstadt @xcite , jinr , dubna @xcite , and riken , tokyo @xcite . the first she s with @xmath2 and @xmath3 were produced in cold fusion reactions . in these experiments , involving neutron rich projectiles and spherical targets ( @xmath4pb or @xmath5bi ) , weakly excited compound nuclei were produced which cooled down by the emission of only one or two neutrons . further experimental progress in the synthesis of the heaviest elements was achieved by hot fusion reactions in which targets of deformed actinide were bombarded with the doubly - magic nucleus @xmath6ca . the compound nucleus created in this way was more excited and three or more neutrons were emitted . these reactions succeeded in the synthesis of new elements up to @xmath7 and @xmath8 @xcite . the first observation of the element 117 was possible lately @xcite using a radioactive @xmath9bk target . new possibilities for the synthesis of new isotopes will be opened in heavy ion collisions with radioactive ion beams @xcite . nowadays , many other laboratories are involved in the exploration of she s . thus the experimental groups from berkeley @xcite , ganil @xcite , livermore @xcite , jyvskyl @xcite , and oak ridge @xcite are working in this direction . they would bring in the nearest future further information on the stability and properties of the she s and an independent verification of the existing data . in a parallel way to the experimental efforts , the properties of the she s have been also investigated in various nuclear models . a proper description of trans - fermium nuclei is a great challenge for any theoretical model . usually , the parameters of the theories on atomic nuclei are adjusted to the stable isotopes and then extrapolated to the region of heavier systems . therefore many tries in different theoretical approaches are performed to foresee the stability and the structure of the heaviest nuclei . a detailed review of the theoretical analysis of she s can be found in ref . the first theoretical investigations on the stability of heavy nuclei were made in the 60 s . it was noticed that shell effects could stabilize nuclei heavier than those known at that time @xcite . calculations made in the macroscopic - microscopic model with strutinsky shell correction predicted the island of stability "" . large values of shell energies were obtained at @xmath10 for prolate deformed nuclei and @xmath11 for spherical ones @xcite . in the last decades many calculations have been made providing more and more precise predictions . the fission barriers and the ground state properties were calculated using macroscopic - microscopic methods with large range of deformation parameters and nuclear shapes , including reflection and axial symmetry breaking @xcite . self - consistent methods also provided many results on fission barriers and half - lives . important results have been obtained in the relativistic mean - field ( rmf ) @xcite , the hartree - fock ( hf ) approach with skyrme forces @xcite and the hartree fock - bogoliubov ( hfb ) theory with gogny forces @xcite . the first calculations of fission barriers were performed in the axial and reflection symmetric regime but later all relevant deformations were considered in the minimization of the energy . it is well known that the liquid drop model does not predict a fission barrier in the heaviest nuclei and that the stability of the trans - fermium nuclei is achieved by the shell effects . the self - consistent quantum mechanical methods ( rmf , hf and hfb ) as microscopic theories are the perfect tools for the analysis of she s . moreover , in the self - consistent calculations all possible shapes of a nucleus are considered in the minimization process . in contrast , the most of the macroscopic - microscopic models are restricted to some pre - defined classes of deformations and only optimal shapes "" @xcite allow to obtain any configuration of a nucleus . therefore they are very suitable to describe large deformations of nuclei around the scission point . a degree of freedom which plays an important role along the fission path are the pairing correlations @xcite . since in the hfb theory the particle - hole and the particle - particle matrix elements are treated on the same footing , the proper consideration of pairing along the whole fission path is guaranteed . this method has been successfully applied in many aspects of low energy nuclear physics , in particular in the description of fission barriers of heavy nuclei @xcite . another theoretical quest was to discover a semi - empirical formula describing @xmath1 emission half - lives @xcite . these investigations are very important as @xmath1 radioactivity is the dominant decay channel in many she s . the purpose of this article is to perform a systematic study of she s with respect to their stability and ground state properties in the framework of the hfb theory with the density dependent finite range gogny force and the d1s parametrization . in our analysis we include the region of the well known fermium ( fm , @xmath12 ) and nobelium ( no , @xmath13 ) elements to compare our predictions with the available experimental data . we show results for the heavier even - even nuclei rutherfordium ( rf , @xmath14 ) , seaborgium ( sg , @xmath15 ) , hassium ( hs , @xmath16 ) , darmstadtium ( ds , @xmath17 ) and copernicium ( cn , @xmath18 , which was named two years ago @xcite ) . heavier elements with @xmath19 , without given name so far , are also considered . we limit our study to @xmath20 isotopes . these nuclei are nowadays in the main stream of interest of experiments with she s . a large amount of information on nuclear structure and stability can be obtained from properties of the ground states of the she s . consequently , we start our investigation with the description of the ground state characteristics . deformations , pairing energies and two - nucleon separation energies are analyzed and collated with the single - particle energy level scheme . the ground state energies can be used to evaluate the @xmath21 values which are necessary to calculate the probability of @xmath1 emission - one of the dominant decay modes in she . a competing process to @xmath1 decay is the spontaneous fission . to analyze this mode we determine the fission barriers for all mentioned she s as a function of the quadrupole moment @xmath22 . the calculations were performed in an axial basis , although we are aware of the non - axial effects on the height of the barrier and we discuss them in a few selected cases . the impact of the octupole deformation on the potential energy along the fission path is crucial in the determination of fission barriers of she s . this is taken into account by allowing non - reflexion symmetrical shapes . the calculations were performed in a large deformed harmonic oscillator basis paying special attention to the proper optimization of the oscillator lengths and to the convergence of the calculations with the size of the basis . next , using the wkb approximation , we calculate the fission half - lives . finally , the comparison of the half - lives for @xmath1 decay and spontaneous fission allows to predict the stability of the heaviest nuclei . this article is organized as follows . in sec . ii we briefly describe the constrained hartree - fock - bogoliubov calculations . the description of the ground - state properties of she s is shown in sec . iii , fission barriers in sec . half - lives of she s are discussed in sec . v. finally , sec . vi contains a summary and some concluding remarks . in our research we will apply the self consistent hartree - fock - bogoliubov theory with the finite range density dependent gogny force . in the numerical applications we use the d1s @xcite parameterization of the gogny interaction . the d1s parameters were adjusted @xcite to give a better surface energy term ( crucial for a proper description of the fission phenomenon ) . the choice of the gogny force with the d1s parameterization is based on the fact that whenever this interaction has been used to describe low energy nuclear structure phenomena an , at least , reasonable agreement with experiment has been obtained . this degree of agreement has been obtained both for calculations at the mean field level and beyond @xcite . in the microscopic hfb calculations we have used the computer code presented in ref . @xcite , see also @xcite where special attention was paid to an accurate computation of the matrix elements of the gogny interaction for very large basis like the one used in this paper . the self - consistent equations have been solved by expanding the quasiparticle creation and annihilation operators on finite bases of axially symmetric deformed harmonic oscillator ( ho ) eigenfunctions . the size of the bases used depends upon two parameters , @xmath23 and @xmath24 , which are related to the allowed range of the ho quantum numbers through the relation @xmath25 along the perpendicular direction we take @xmath23 shells , ( i.e. @xmath26 shells depending on the value of @xmath27 . in the present study we have used @xmath28 , a value which is suited for the elongated shapes along the @xmath29 direction typical of the fission process , and @xmath30 . other parameters characterizing the ho bases are the oscillator lengths @xmath31 and @xmath32 . these two quantities have been determined , for each calculated wave function , as to minimize the hfb energy . in order to study the different paths to fission , in our calculations we have used as constraints the axial quadrupole ( @xmath22 ) and octupole ( @xmath33 ) moments , with @xmath34 . higher multipolarities are adjusted in the self - consistent process to minimize the energy . to study the impact of triaxiality effects we have also carried out calculations for a few nuclei where the axial symmetry requirement was released but the left - right symmetry was imposed . in the calculations the coulomb exchange energy has been treated in the slater approximation @xcite . additionally , the coulomb and the spin - orbit contributions to the pairing field have been neglected . finally , the two body kinetic energy correction ( 2b - kec ) is not included in the variation process because , for heavy nuclei , it remains almost constant for most of the physical configurations . as this term was included in the fitting of the force , we have to include its contribution at the end of the calculation in order to obtain reasonable binding energies . see also @xcite for a detailed discussion of the relevance of neglected or approximated terms in these calculations . we have also subtracted from the hfb energy the rotational energy corrections ( rec ) stemming from the restoration of the rotational symmetry . this correction has a considerable influence on the energy landscape ( and therefore on the height of the fission barriers ) as it is somehow proportional to the degree of symmetry" +"the model of quantum lattice bose gas has a long history and has been suggested initially for conventional superconductors @xcite , quantum crystals such as @xmath4he where superfluidity coexists with a crystalline order.@xcite afterwards , the bose - hubbard ( bh ) model has been studied as a model of the superconductor - insulator transition in materials with local bosons , bipolarons , or preformed cooper pairs.@xcite two - dimensional bh models have been addressed as relevant to describe the superconducting films and josephson junction arrays . the most recent interest to the system of hard - core bosons comes from the delightful results on bose - einstein ( be ) condensed atomic systems produced by trapping bosonic neutral atoms in an optical lattice . @xcite the progress in boson physics generates an especial interest around nonlinear topological excitations ( skyrmions , vortices ) which play an increasingly significant role in physics . one of the fundamental hot debated problems in bosonic physics concerns the evolution of the charge ordered ( co ) ground state of 2d hard - core bh model ( hc - bh ) with a doping away from half - filling . numerous model studies steadily confirmed the emergence of `` supersolid '' phases with simultaneous diagonal and off - diagonal long range order while penrose and onsager @xcite were the first showing as early as 1956 that supersolid phases do not occur . the most recent quantum monte - carlo ( qmc ) simulations @xcite found two significant features of the 2d bose - hubbard model with a screened coulomb repulsion : the absence of supersolid phase at half - filling , and a growing tendency to phase separation ( co+bs ) upon doping away from half - filling . moreover , batrouni and scalettar @xcite studied quantum phase transitions in the ground state of the 2d hard - core boson hubbard hamiltonian and have shown numerically that , contrary to the generally held belief , the most commonly discussed `` checkerboard '' supersolid is thermodynamically unstable and phase separates into solid and superfluid phases . the physics of the co+bs phase separation in bose - hubbard model is associated with a rapid increase of the energy of a homogeneous co state with doping away from half - filling due to a large `` pseudo - spin - flip '' energy cost . hence , it appears to be energetically more favorable to `` extract '' extra bosons ( holes ) from the co state and arrange them into finite clusters with a relatively small number of particles . such a droplet scenario is believed to minimize the long - range coulomb repulsion . however , immediately there arise several questions . whether a simple mean - field approximation ( mfa ) and classical continuum model can predict such a behavior ? what is the detailed structure of the co+bs phase separated state ? what are the main factors governing the essential low - energy and long - wavelength physics ? is it possible to make use of simple toy models ? are there the analogies with fermion hubbard model ? the behavior of the latter under doping away from half - filling is extensively studied in last decade in frames of stripe scenario which implies that doping may proceed through the formation of stripes , or charged domain walls being specific topological solitons in nel antiferromagnets . in particular , emery and kivelson @xcite argued that the phase separation reflects a universal tendency of the correlated antiferromagnet to expel the doped holes . white and scalapino @xcite showed that the pure 2d t - j model , in the small - j / t regime and with dopings near @xmath5 , has a striped ground state . in general , the topological phase separation is believed to be a generic property of 2d fermion hubbard model . in the paper we present a topological scenario of co+bs phase separation in 2d hc - bh model with inter - site repulsion . the extra bosons / holes doped to a checkerboard co phase of 2d boson system are believed to be confined in the ring - shaped domain wall of the skyrmion - like topological defect which looks like a bubble domain in an easy - axis antiferromagnet . this allows us to propose the mechanism of 2d _ topological _ co+bs _ phase separation _ when the doping of the bare checkerboard co phase results in the formation of a multi - center topological defect , which simplified pseudo - spin pattern looks like a system of bubble co domains with bose superfluid confined in charged ring - shaped domain walls . the rest of the paper is organized as follows . in sec.ii we give a short overview of the conventional hc - bh model in frames of a pseudo - spin formalism and mfa description . in sec.iii we show that the doping in 2d hc - bh system can be accompanied by the formation of a topological defect like a single or multi - center skyrmion . we present the scenario of the essential low - energy physics for the topologically doped hc - bh system . in sec.iv we address a simple model of nanoscopic bubble - like domain in a checkerboard co phase for a discrete square lattice that allows us to demonstrate a subtle microscopic structure of such a center with a multi - component order parameter . the hamiltonian of hard - core bose gas on a lattice can be written in a standard form as follows : @xmath6 where @xmath7 is the projection operator which removes double occupancy of any site , @xmath8 , @xmath9 the chemical potential determined from the condition of fixed full number of bosons @xmath10 or concentration @xmath11 $ ] . the @xmath12 denotes an effective transfer integral , @xmath13 is an intersite interaction between the bosons . here @xmath14 are the pauli creation ( annihilation ) operators which are bose - like commuting for different sites @xmath15=0,$ ] if @xmath16 @xmath17=1 - 2n_i$ ] , @xmath18 ; @xmath19 is a full number of sites . it is worth noting that near half - filling ( @xmath20 ) one might introduce the renormalization @xmath21 , or neutralizing background , that immediately provides the particle - hole symmetry . the model of hard - core bose - gas with an intersite repulsion is equivalent to a system of spins @xmath22 exposed to an external magnetic field in the @xmath23-direction . for the system with neutralizing background we arrive at an effective pseudo - spin hamiltonian @xmath24 where @xmath25 , @xmath26 , @xmath27 , @xmath28 . in a linear approximation the hamiltonian for the coupling with an electromagnetic field reads as follows @xmath29_{z}-\frac{1}{2}(\phi _ { j}-\phi _ { i})^{2}({\hat { \bf s}_{i}}\cdot { \hat { \bf s}_{j}}));\ ] ] @xmath30 where @xmath31 is the vector - potential , and integration runs over line binding the @xmath32 and @xmath33 sites ; @xmath34_{z}=\frac{i}{2}(\hat b_{i}^{\dagger}\hat b_{j}-\hat b_{i}\hat b_{j}^{\dagger}),\ ] ] however , the pseudo - spins are assumed to lie in @xmath35 plane . then the boson current density operator one may represent to be a sum of the paramagnetic @xmath36_{z},\end{aligned}\ ] ] and diamagnetic @xmath37 terms , respectively . below we make use of a conventional two - sublattice mfa approach . for the description of the pseudospin ordering to be more physically clear one may introduce two vectors , the ferromagnetic and antiferromagnetic ones : @xmath38 where @xmath39 . for the plane where these vectors lie one may introduce two - parametric angular description : @xmath40 . the hard - core boson system in a two - sublattice approximation is described by two diagonal order parameters @xmath41 and two complex off - diagonal order parameters @xmath42 and @xmath43 . the complex superfluid order parameter @xmath44 is determined by the in - plane components of ferromagnetic vector : @xmath45 , @xmath46 being the length of the in - plane component of ferromagnetic vector . so , for a local condensate density we get @xmath47 . it is of interest to note that in fact all the conventional uniform @xmath48 states with nonzero @xmath49 imply simultaneous long - range order both for modulus @xmath50 and phase @xmath51 . the in - plane components of antiferromagnetic vector @xmath52 describe a staggered off - diagonal order . it is worth noting that by default one usually considers the negative sign of the transfer integral @xmath12 , that implies the ferromagnetic in - plane pseudospin ordering . the model exhibits many fascinating quantum phases and phase transitions . early investigations predict at @xmath48 charge order ( co ) , bose superfluid ( bs ) and mixed ( co+bs ) supersolid uniform phases with an ising - type melting transition ( co - no ) and kosterlitz - thouless - type ( bs - no ) phase transitions to a non - ordered normal fluid ( no).@xcite the detailed mean - field and spin - wave analysis of the uniform phases of 2d hc - bh model is given by pich and frey.@xcite mfa yields for the conventional uniform supersolid phase @xcite @xmath53 with a constant chemical potential @xmath54 . it should be noted that the supersolid phase appears to be unstable with regard to small perturbations in the hamiltonian . the mean - field energy per site of the uniform supersolid phase is written as follows : @xmath55 where @xmath56 . the cost of doping both for co and co+bs phase appears to be rather high as compared with an easy - plane bs phase at half - filling where the chemical potential turns into zero.@xcite magnetic analogy allows us to make unambiguous predictions as regards the doping of bh system away from half - filling . indeed , the boson / hole doping of checkerboard co phase corresponds to the magnetization of an antiferromagnet in @xmath23-direction . in the uniform easy - axis @xmath57-phase of anisotropic antiferromagnet the local spin - flip energy cost is rather big . in other words , the energy cost for boson / hole doping into checkerboard co phase appears to be big due to a large contribution of boson - boson repulsion . however , the magnetization of the anisotropic antiferromagnet in an easy axis direction may proceed as a first order phase transition with a `` topological phase separation '' due to the existence of antiphase domains.@xcite the antiphase domain walls provide the natural nucleation centers for a spin - flop phase having enhanced magnetic susceptibility as compared with small if any longitudinal susceptibility thus providing the advantage of the field energy . namely domain walls would specify the inhomogeneous magnetization pattern for such an anisotropic easy - axis antiferromagnet in relatively weak external magnetic field . as concerns the domain type in quasi - two - dimensional antiferromagnet one should emphasize the specific role played by the cylindrical , or bubble domains which have finite energy and size . these topological solitons have the vortex - like in - plane spin structure and often named `` skyrmions '' . the classical , or belavin - polyakov ( bp ) skyrmion @xcite describes the solutions of a non - linear @xmath58-model with a classical isotropic 2d heisenberg hamiltonian and represents one of the generic toy model spin textures . it is of primary importance to note that skyrmion - like bubble domains in easy - axis layered antiferromagnets were actually observed in the experiments performed by waldner,@xcite that were supported later by different authors ( see , e.g. refs . ) . although some questions were not completely clarified and remain open until now , @xcite the classical and quantum @xcite skyrmion - like topological defects are believed to be a genuine element of essential physics both of ferro- and antiferromagnetic 2d easy - axis systems . the magnetic analogy seems to" +"ever since landau@xcite suggested that the electron can be trapped by the deformable lattice , strongly coupled electron - phonon systems have been the subject of intensive examination . besides the investigations of those systems in which the lattice is coupled to the whole electronic band , there has been significant interest in the physics of a single polaron , in which the electron and the associated lattice deformation form a quasi - particle , spatially and spectrally decoupled from the rest of the system . lattice degrees of freedom make even a single polaron problem a many - body one . the analytical and numerical examinations of most electron - phonon models are thus difficult . for this reason , even the simple holstein model@xcite ( suggested in 1959 ) is still being investigated in recent works . various methods have been proposed in order to calculate the polaron ground state of the holstein model . almost exact results ( except for the adiabatic limit ) have been obtained with the quantum monte carlo calculations,@xcite the global - local method,@xcite the density matrix renormalization group method,@xcite and some exact diagonalization methods.@xcite the main goal of this paper is to determine the elements important for the qualitative description of the polarons in the whole range of electron - phonon coupling . some of them , although already known , are found to be better understood when supplemented with additional details . the ground state of the holstein system changes from the delocalized polaron state , in which the electron is nearly free , to the small and self - trapped polaron state , as the electron - phonon coupling @xmath0 increases . these two opposite limits are usually identified as the weak and strong coupling regime , respectively . in the weak coupling regime the influence of the small lattice deformation on polaron dynamics is very small , which makes the energies of polaron and electron hopping to neighboring sites similar , @xmath1 . the exact ground state is an eigenstate of the system momentum , regardless of the coupling.@xcite therefore the polaron ground state is delocalized for all parameters . however , in the strong coupling regime @xmath2 becomes negligible , leading to _ self - trapped _ polaron states . according to ref . , the dynamics of the small self - trapped polaron can be separated into two time scales . on the short time scale , the lattice deformation is centered at some lattice site , and the electron can virtually hop among the neighboring lattice sites . only after a certain number of such events ( of the order @xmath3 ) , the polaron as a whole tunnels to a new central site . the localized polaron states thus may lead to a very accurate estimation of the polaron ground state energy in the strong coupling regime . accordingly , for the self - trapped polarons , an exact diagonalization method of calculating the localized polaron states , rather than the translationally invariant ones , can be used . by comparison to the results of other methods , it is shown that this approach introduces only minor errors in the ground state energy of the self - trapped polaron . moreover , the localized polaron functions permit , unlike the translationally invariant ones , a separate analysis of the electron and phonon properties of the polaron . the local electron density , the mean lattice deformation , and the on - site zero point motions of the self - trapped polarons can be calculated in this way . in the crossover ( intermediate ) regime , which is between the weak and the strong coupling regime , no known perturbation calculation converges , which complicates the discussion of the polaron nature . although it has been proved that the change of the polaron ground state with @xmath0 is smooth,@xcite the physics of the rapid crossover between two opposite limits of the electron - phonon coupling , in the small interval of @xmath0 s , is not completely clear . in ref . it has been claimed that the phonon excitation associated with the first excited state of the system is uncorrelated to the electron in the weak coupling regime , while it is confined to the electron in the strong coupling regime . the transition occurs in the crossover regime in which , in addition , the energy difference between the ground and excited states becomes small . in the present paper , the excited polaron states are treated by the new method which uses variational approach in order to define and solve the generalized eigenvalue problem . even if this method does not converge systematically , it does provide new results concerning the nature of the polaron ground and first excited state . the holstein hamiltonian reads @xmath4 it describes the tight - binding electrons in the nearest - neighbor approximation , coupled to one branch of dispersionless optical phonons . @xmath5 is the creation operator for the electron of spin @xmath6 at lattice site @xmath7 , and @xmath8 is the creation operator for the phonon . @xmath9 is the transfer ( hopping ) integral of the electron . @xmath10 and @xmath0 are the phonon and the electron - phonon coupling energies , respectively . the holstein hamiltonian depends only on two ratios of relevant energy parameters : @xmath11 and @xmath12 , i.e. , the results will use @xmath10 as the energy unit . it is often convenient to express the lattice vibrations in terms of the nuclei space and momentum coordinates , @xmath13 where @xmath14 and @xmath15 are space and momentum uncertainties of the harmonic oscillator ground state . @xmath16 is the mass of a nucleus and @xmath17 denotes the spring constant , @xmath18 . by noting that the electron - lattice displacement coupling constant @xmath19 , in @xmath20 , is independent of @xmath16 , an alternative set of holstein hamiltonian parameters can be introduced , @xmath21 which is convenient for the discussion of the adiabatic regime @xmath22 . here , @xmath23 is the electron effective mass and @xmath24 is the lattice constant . it is worth noting that @xmath9 and @xmath25 ( the binding energy of the polaron for @xmath26 ) are independent of @xmath16 and thus they are the only parameters relevant in the adiabatic limit . by using standard conventions for @xmath27 and @xmath28 , @xmath29 eq . ( [ h0 ] ) can be rewritten in momentum space and separated in two mutually commuting parts , @xmath30 , @xmath31 where @xmath32 , @xmath33 , and @xmath34 . the part which involves only the @xmath35 phonon mode , @xmath36 , can easily be transformed into the diagonal form , by using the unitary operator @xmath37 , @xmath38 where @xmath39 . any eigenstate of @xmath40 , @xmath41 , has the same mean total lattice deformation , @xmath42 , @xmath43 which is independent of @xmath9 . since the @xmath35 part of the hamiltoniancommutes with @xmath44 , it can be concluded that eq . ( [ xtot ] ) is also valid for all eigenstates of the total holstein hamiltonian . the phonon part of these eigenstates can be represented in the form of a direct product of two groups of states , the first one includes @xmath45 phonon modes , while the second includes only the @xmath35 phonon mode . this is useful because one can always check approximate computations by calculating @xmath46 , or include this property in the computation itself . this specific property of the @xmath35 mode is not restricted to the particular dimension of the system , nor to the number of electrons . moreover , it can also be found in some other models in which the electron - phonon coupling consists of the lattice deformation linearly coupled to the local electron density . a hint in this direction was reported for the first time in ref . . the total momentum of the system , @xmath47 , is the sum of the electron and phonon momenta , @xmath48 and it commutes with the hamiltonian . in the present treatment , only the low energy polaron states ( the low lying states of the system for which the electron and lattice part of the wave function are spatially bound ) , are explicitly calculated . in this case , the total momentum @xmath49 of the system is also the polaron momentum . the eigenstate computations reported here are based on the variational approach . still , from the physical and mathematical point of view , there are significant differences among them . each method is therefore described separately in the present section . it is important to notice that two qualitatively different kinds of polaron functions are employed , the _ localized _ ones and the _ translationally invariant _ ones . the primary objective of the methods with localized functions are self - trapped polaron states , i.e. , the strong coupling regime . on the other hand , translationally invariant states are devised in the first place with the weak coupling and crossover regime in mind . the methods with a small number of variational parameters are meant to help in understanding the basic properties of the polarons in different regimes of the holstein model . again , the methods with a very large number of variational parameters are necessary to obtain accurate results for the polaron states . let us start with a simple localized polaron wave function formed as a product of the electron and the lattice part , centered at the lattice site @xmath51 , @xmath52 here , @xmath53 is the normalized electron function at site @xmath54 , @xmath55 , while @xmath56 denotes the coherent state operator acting on site @xmath57 , with a complex amplitude , @xmath58 , @xmath59 it is easy to see that operator @xmath56 shifts the space and momentum coordinates of lattice vibration at a site @xmath57 by @xmath60 and @xmath61 , respectively , @xmath62 } e^{[-i2\re(\xi_m)x_0\hat p_{j+m}/\hbar]}\\ & \times&e^{[i\re(\xi_m)\im(\xi_m)]}\;.\end{aligned}\ ] ] the variational energy of the state ( [ iafunction ] ) , @xmath63 , is independent of @xmath51 , and is given by @xmath64 the minimization of the energy with respect to @xmath65 establishes a simple relationship between the lattice mean deformation and electron density @xmath66 , @xmath67 so that only the equation for @xmath53 has to be solved . the well known approximate solution to this problem is the large holsteinpolaron@xcite valid in the long wave limit , @xmath68 the numerical scheme suggested in ref . , and denoted here by @xmath50 ( @xmath50 for localized ) , is not restricted to long waves , and is used here in order to obtain the exact minimum of eq . ( [ iaenergy ] ) . the energy , henceforth referred to as @xmath69 , depends only on two relevant hamiltonianparameters , @xmath9 and @xmath70 , and therefore @xmath69 and @xmath71 are both independent of @xmath16 . for this reason eq.([locking ] ) is sometimes referred to as the adiabatic locking of electron and lattice coordinates . it is noteworthy that the lattice part of the function @xmath72 is a simple product of coherent states with real amplitudes . consequently , the state of the lattice at some site is defined by the ground state of the displaced harmonic oscillator . the mean lattice deformation @xmath71 corresponds to the equilibrium position of that oscillator , while the lattice zero point motion is approximated in eq . ( [ iafunction ] ) by that of the free lattice . next , we shall study a translationally invariant solution composed of a linear superposition of the localized states ( [ iafunction ] ) , @xmath75 @xmath76 describes the polaron state with the momentum @xmath49 . a similar type of function was first proposed by toyozawa.@xcite in the present work , @xmath77 is used so that the mean total" +"recently , we have shown that layered sine - gordon type models are probably not suitable for the description of josephson - coupled layered superconductors , because the linear , confining potential that binds the vortices together can not be obtained from the interaction of the topological excitations of the model , no matter how the interlayer interaction term is chosen @xcite . on the other hand , vortex dominated properties of high @xmath0 layered superconductors and other types of layered materials , e.g. superconducting sandwiches , have already received a considerable amount of attention ( see , e.g. , refs . @xcite ) , and the intuitively obvious connection of sine - gordon models to these materials makes one wonder if at least , a restricted applicability of the layered , field - theoretical model persists . we also observe that recently , there is an increasing interest in the literature @xcite in constructing sine gordon type field theoretical models in order to understand better the vortex dynamics in layered superconducting systems . our aim in this paper to follow this route by constructing a two - dimensional multi - layer sine - gordon type model which can be used to describe the vortex behaviour of magnetically as opposed to josephson - coupled layered superconductors , and to contrast and enhance our recent investigation @xcite . in a two - dimensional ( 2d ) isolated superconducting thin film , the pearl vortices @xcite are naturally identified as the topological excitations and can be considered as the charged analogues of the vortices in a 2d superfluid which generate the kosterlitz thouless berezinski ( ktb ) phase transition @xcite . the logarithmic interaction between the vortices of the superfluid extends to infinity and as a consequence they remain bound below the finite ktb transition temperature ( @xmath1 ) and dissociate above it @xcite . since the pearl vortices carry electric charge , they always remain unbound due to the screening length @xmath2 generated by the electromagnetic field which cuts off the logarithmic interaction @xcite and leads to the absence of any ktb phase transition . however , for realistic finite 2d superconducting films where the lateral dimension of the film can be smaller then the screening length @xmath3 the ktb transition can be restored @xcite . this constitutes an intrinsic finite size effect . in layered materials , the interlayer coupling modifies the 2d picture and leads to new types of topological defects . if the layers are coupled by josephson coupling ( like for many htsc materials ) , the vortex - antivortex pairs on the same layer interact with each other via a logarithmic term for small distances but they feel a linear confining potential for large distances ( see e.g. @xcite and references therein ) . the vortices in neighboring layers always interact via a linear potential which can couple them by forming vortex loops , rings , or vortex `` strings '' piercing all layers . if the layers are coupled by purely magnetic interaction ( e.g. in artificially produced superlattices where the cooper pair tunneling between the superconducting layers is suppressed by relatively large insulating layers ) the topological defects for a system which consists of infinitely many layers are pancake vortices @xcite which undergo a ktb phase transition at @xmath1 . as explained e.g. in ref . @xcite , the josephson coupling can be essentially neglected when the confinement length , i.e. the length scale at which the linear confining potential due to the josephson coupling dominates over the logarithmic interaction due to magnetic effects , is pushed beyond the effective screening length for the logarithmic interaction among vortices . this situation is present when the tunneling between the superconducting layers is suppressed by relatively large insulating layers , and a proposal for a experimental realization has recently been given @xcite . for a finite number @xmath4 of magnetically coupled layers , the pearl type vortex stack @xcite is broken up into a number of coupled pancake vortices of fractional flux @xcite , and this configuration undergoes a ktb - type phase transition at a layer - dependent temperature @xmath5 which is connected with the dissociation of the stack . this result has been obtained on the basis of the entropy method first introduced in the ground - breaking work @xcite . recently , a real space renormalization - group ( rg ) analysis of the case @xmath6 has been performed in ref . @xcite using the dilute gas approximation . a priori , it appears to be rather difficult to generalize this rg analysis for @xmath7 layers . in general , the ginzburg landau ( gl ) theory @xcite provides us with a good theoretical framework in which to investigate the vortex dynamics in thin films and in layered materials . several equivalent models , like field - theoretical , statistical spin models and a gas of topological defects have also been used to consider the vortex properties of films and layered systems . the 2d - gl , 2d - xy and the 2d coulomb gas models ( see e.g. @xcite and references therein ) are considered as the appropriate theoretical background for the vortex dynamics of superfluid films . the field theoretical counterpart is the 2d sine - gordon ( sg ) model @xcite . both kinds of these models belong to the same universality class and produce the ktb phase transition . for superconducting films one has to consider the 2d - gl model in the presence of electromagnetic interactions @xcite or the equivalent gas of topological excitations , the 2d yukawa gas @xcite . the corresponding field theory is the 2d - sg model with an explicit mass term , the massive 2d - sg model @xcite . for josephson - coupled layered superconductors in the case of very large anisotropy one should investigate the layered gl model including the josephson coupling between the layers @xcite ( i.e. the lawrence - doniach model @xcite ) . in case of not too large anisotropy on can use the anisotropic , continuous gl theory @xcite which can be mapped onto the isotropic gl model by an appropriate rescaling method @xcite . the corresponding spin model is the 3d - xy model @xcite and the equivalent gases of topological excitations are the layered vortex @xcite or vortex - loop @xcite gases . there are attempts in the literature to construct the field theoretical countpart of the isotropic model @xcite . in case of strong anisotropy , the layered sine gordon ( sg ) model @xcite has been proposed as a candidate model where the interlayer interaction between the topological defects has been described by a mass matrix which couples the sg fields @xmath8 where @xmath9 and @xmath10 ( n=1, ... ,n ) are one component scalar fields . recently , we showed in ref . @xcite that the layered sg model with the above mass matrix is not apropriate for the description of vortex dynamics of josephson coupled layered superconductors . in case of purely magnetically coupled layered systems , the layered gl model has to be used but excluding the josephson coupling . although the interaction potentials between the topological defects of magnetically coupled layered systems are given in refs . @xcite , no field theoretical model has been proposed for the description of vortex dynamics in a finite system of magnetically coupled superconductors . here , our aim is to open a new platform for considering the vortex dynamics of magnetically coupled layered systems by constructing a multi - layer sine gordon ( mlsg ) type field theoretical model where the two - dimensional sine gordon ( 2dsg ) fields characterizing the layers are coupled by an appropriate general mass matrix , @xmath11 by the exact mapping of the mlsg model onto an equivalent gas of topological defects , we recover the interaction potential given in refs . @xcite and , hence , prove the applicability of the model . we analyse the phase structure of the mlsg model by a differential renormalization group ( rg ) method performed in momentum space , which is in general easier to perform than that in real space , and determine the layer - dependence of @xmath12 . in our field theoretical rg approach , the rg flow can be calculated in one step for an arbitrary number of layers , and the study of the intrinsic finite size effect of thin film superconductors @xcite and of finite layered systems is facilitated . this paper is organized as follows . in sec . [ sec2 ] , we define the multi - layer sine gordon model and show by its exact mapping onto the equivalent gas of topological excitations that it is suitable to describe the vortex dominated properties of magnetically coupled layered superconductors . in sec . [ sec3 ] , a renormalization group analysis of the multi - layer sine gordon model is performed within the framework of the wegner houghton renormalization group method , in momentum space for general @xmath4 , and with a solution that spans the entire domain from the ultraviolet ( uv ) to the infrared ( ir ) . the layer - number dependence of the critical temperature of the multi - layer sine gordon model is determined by using the mass - corrected linearized rg flow . conclusions are reserved for sec . the multi - layer sine gordon ( mlsg ) model consists of @xmath4 coupled two - dimensional sine gordon ( 2d - sg ) models of identical `` frequency '' @xmath13 , each of which corresponds to a single layer described by the scalar fields @xmath10 @xmath14 . its euclidean bare action ( we imply here the sum over @xmath15 ) @xmath16 = \int { \rm d}^2 r \biggl [ { \frac{1}{2}}(\partial_{\mu } \underline\varphi)^{\rm t } ( \partial_{\mu } \underline\varphi ) + v ( \underline\varphi ) \biggr ] \end{aligned}\ ] ] contains the interaction terms @xmath17 with the @xmath18 multiplet @xmath19 . we can choose the fugacities @xmath20 without loss of generality , ensuring that the zero - field configuration is a local minimum of the action ( see chap . 31 of ref . the mass - matrix describes the interaction between the layers and is chosen here to be of the form @xmath21 where @xmath22 is the strength of the interlayer interactions , and the @xmath23 are free parameters . as will be explained below , any choice with @xmath24 for all @xmath25 reproduces exactly the same layer - dependence of @xmath12 as found in refs . @xcite . in this case , the layers can be assumed to be equivalent and , as a consequence , the fugacity @xmath26 for @xmath27 . the most obvious choice fulfilling @xmath24 , namely @xmath28 for all @xmath25 , reproduces the interlayer interaction between pancake vortices given , e.g. , in eq . ( 89 ) of ref . @xcite , and we will restrict our attention to this choice in the following . the mlsg model has a discrete symmetry under the shift of the field variable @xmath29 with @xmath30 where the `` last '' integer @xmath31 is fixed but all the other integers @xmath32 ( @xmath33 ) can be chosen freely ( to see this , one just diagonalizes the mass - matrix ) . the single non - vanishing mass eigenvalue is @xmath34 , and hence the model possesses @xmath35 massless 2d - sg fields and a single massive 2d - sg field . after the diagonalization of the mass matrix by a suitable rotation of the fields , the model thus is invariant under the independent separate shifts of @xmath35 massless fields , but the explicit mass term of the single massive mode breaks the periodicity in the `` massive '' direction of the @xmath4-dimensional internal space . one crucial observation is that the partition function of the mlsg model" +"recent experimental research of diffusion and trapping of single particles of @xmath0- and nm - scales in confined liquid films @xcite show that this process presents non - trivial behavior considerably different from a usual brownian diffusion in a bulk due to strong interaction of ultrathin fluid matrix with a base solid interface . the detailed single - molecule tracking detects the dependence of diffusivity on a distance of layer from the interface . it should be noted that a majority of evaluated experiments deals with the study of hydrodynamic interaction of colloid particles with a rigid wall that leads to change of both vertical and horizontal diffusivities @xcite . however , the very important parameter of such a system is a particle s size @xcite . it has been found @xcite that the experiments with micrometer - scale spherical particles diffusing in a uniform fluid close to the wall quite satisfactory admit the two - dimensional depth - dependent anisotropic diffusion approach of @xcite . at the same time , it was mentioned @xcite that particle size change from @xmath0-m to nm scales leads to large deviations from hydrodynamic theory . particularly , in the experimental work @xcite it was demonstrated that observed vertical diffusion coefficient is smaller . the discussion in @xcite attributes this fact to the prevalence of intermolecular forces over hydrodynamical ones for such scales . from this point of view , very important experimental study was evaluated in the work @xcite , where extremely small ( molecular - size ) markers were traced . it has bean detected there that the lateral diffusion is anomalous ( superdiffusion ) for short times and crosses over to normal diffusion for long times . this phenomenon was discussed in a connection with the fact that fluids close to wetted interfaces are know to form a layered structure . the motion of molecules in such layered structures can be described within the following random walk picture . the layers close to the interface are practically frozen and the lateral motion in these layers is slow . however , particles can diffuse ( jump ) vertically to layers , where the random walks are faster . thus , the transient diffusive behavior is based on a coexistence of these vertical and lateral jumps . note that the process of molecular diffusion in a wetting layer differs from the one of macroscopic particles near the wall which can be described using the hydrodynamical picture @xcite , _ vide infra_. in what follows we adopt a coarse - grained description and consider the continuous model of layered diffusion : the particle performs diffusive motion in @xmath1-direction . the properties of this motion are independent on the particle s lateral position due to translational symmetry of the fluid layer in this direction , while the properties of diffusion in @xmath2-direction depend on the particle s distance from the surface ( i.e. on its @xmath1-coordinate ) . our model thus corresponds to a one of the layered system . the models of layered diffusion correspond to cases when the properties of motion in one ( @xmath1 ) direction ( normal to layers ) do not depend on the coordinate @xmath2 , while the motion within layers ( in @xmath2-direction ) depends on @xmath1 . the properties of motions in @xmath2 and @xmath1-directions differ , defining different models of layered diffusion : thus the combination of continuous drift in @xmath1 with random velocity model in @xmath2 defines taylor s model of `` diffusion by continuous motions '' @xcite , the combination of diffusion in @xmath1 with the same random velocity model in @xmath2 defines a superdiffusive matheron de marsily model @xcite , and combination of diffusion in @xmath1 with transport with deterministic mean velocity proportional to @xmath1 defines the model of diffusion in a shear flow introduced by novikov @xcite . more general @xmath1-dependences of @xmath2-velocity define a class of models in @xcite . the model of a layered system is not limited to hydrodynamical situations . thus , a similar model was recently used for modeling of superdiffusion in a small world network @xcite . namely , the set of slow walks along a regular background lattice and fast jumps along `` short links '' was replaced by the set of simple diffusion equations with the hierarchy diffusion coefficients depending on the distance between background nodes . a simple model described here adds an interesting example to the theory of diffusion in layered systems and gives rise to an effective equation of the batchelor s type for lateral diffusion . due to symmetry in the directions parallel to the surface , it is enough to consider one lateral coordinate , which is denoted @xmath2 in what follows . for this reason we consider 2d picture at first . then we discuss the generalization on 3d case , which is quite straightforward . our model corresponds thus to a particle performing diffusion in @xmath2 and @xmath1-directions , where the properties of the vertical diffusion ( in @xmath1-direction ) do not depend on @xmath2 . on a coarse - grained level ( the steps of a random walk are not resolved ) this model is described by a pair of langevin equations @xmath3 with @xmath4 and @xmath5 being the diffusion coefficients in @xmath1- and in @xmath2-directions , and @xmath6 , @xmath7 being gaussian white noises with zero mean and correlation property given by @xmath8 . note that according to eqs . ( [ motiony ] ) and ( [ motionx ] ) the motion in @xmath1 is independent on the motion in @xmath2-direction , while the motion in @xmath2 does depend on the actial @xmath1-coordinate through @xmath5 and thus depends on the prehistory of @xmath1-motion . the random variables @xmath2 and @xmath1 are not independent . the evolution of two - dimensional joint probability density @xmath9 for marker s position is then described by the fokker - planck equation corresponding to the equation of anisotropic diffusion : @xmath10 the dirac delta function @xmath11 is used as an initial condition . we are interested only in the time dependence of marginal distribution of @xmath2 , which is experimentally accessible @xcite . we note that although the situation with molecular tracer discussed here is different from the case of motion of a massive particle in a quiescent fluid , as discussed e.g. in @xcite , since a molecular motion is never underdamped . however , the final equation is exactly of the form obtained in this work , due to the fact that it is the only form corresponding to thermodynamical equilibrium ( in the absence of external forces ) in a stationary state . although eq.([init_eq ] ) itself does not have to possess a solution which factorizes into a product of functions which depend only on one of the two co - ordinates , the solution of our physical problem given by eqs.([motiony ] ) , ( [ motionx ] ) has to factorize : @xmath12 , although @xmath2 and @xmath1 are not independent . the physical reason for this is as follows . first let us remark , that while the two arguments @xmath2 and @xmath1 of @xmath9 are the values of the corresponding random variables @xmath2 and @xmath1 , its third argument , time , is not a random variable but essentially an additional condition : @xmath13 is a conditional joint probability of @xmath2 and @xmath1 provided their measurement took place at time @xmath14 . note now that according to eq.([motiony ] ) the motion in @xmath1 direction is independent on @xmath2 , and moreover the initial condition for this motion in @xmath1 does not depend on @xmath2 . therefore the conditional probability of @xmath1 given @xmath2 is essentially a non - conditional one : @xmath15 . according to bayes theorem @xmath16 : the @xmath2 and @xmath1-displacements are _ conditionally independent _ @xcite . rewriting it in our initial notation we get @xmath17 independently on whether this discussion is convincing or not , one can always prove that the final solutions obtained by the separation ansatz are indeed the solutions of eq.([init_eq ] ) , i.e. that the product of eq.([sol1infy ] ) and eq.([sol1infx ] ) indeed solves eq.([init_eq ] ) in an unbounded system with @xmath18 , and that the product of eq.([sol1 ] ) and of a symmetric gaussian in @xmath2 with the dispersion given by eq.([msd ] ) solves it for a layer of a finite thickness , as they indeed do . integrating both parts of eq.([init_eq ] ) with respect to @xmath2 we obtain the equation for @xmath19 : @xmath20 inserting eq.([separation ] ) into eq.([init_eq ] ) and integrating over @xmath1 we obtain @xmath21 \frac{\partial^2 p_x}{\partial x^2 } , \label{eq_u_y}\ ] ] with @xmath22 being the film s thickness , i.e. the one - dimensional batchelor s equation @xcite @xmath23 with time - dependent diffusion coefficient @xmath24 note that this batchelor s equation arises here not as the mean - field type approximation , but as an exact equation for the corresponding marginal probability density . introducing a new variable @xmath25 allows to reduce eq . ( [ batchelor ] ) to the simple diffusion equation @xmath26 note that the change of variables from @xmath14 to @xmath27 is always possible within the model since the effective diffusion coefficient @xmath28 given by eq.(8 ) is always non - negative and therefore its integral over time is a monotonically growing ( and therefore invertible ) function . from this it follows that the corresponding probability density is gaussian with a mean square displacement ( msd ) @xmath29 . in a 3d system uniform in @xmath30 coordinates with @xmath31 still depending on the vertical @xmath1 position , the system of eqs . ( [ motiony])([motionx ] ) is supplemented by @xmath32 thus , from the eqs . ( [ motiony])([motionx ] ) , ( [ motionz ] ) and the symmetry in the directions parallel to the surface , it follows that the three - dimensional joint probability density @xmath33 satisfies the equation : @xmath34 + d_y\frac{\partial^2 p}{\partial y^2}. \label{init_eq3d}\ ] ] as before , all displacements are conditionally independent and the three - dimensional joint probability density will be factorized as @xmath35 the equation for @xmath36 has exactly the form of the eq . ( [ px ] ) . finally , since the motions in both lateral directions are independent , the resulting msd is @xmath37 in other words , it is simply two times larger then in 2d case , and the definition of @xmath27 follows from the eq . ( [ d ] ) as above . at first , we consider an idealized situation : the half - plane corresponding to the film of infinite thickness @xmath38 . in this case the solution of eq . ( [ eq_u_x ] ) is the gaussian @xmath39 thereafter , one needs to determine the vertical dependence of the horizontal component of the diffusion coefficient . as it will be shown below , the experimental data are well - fitted by a linear dependence @xmath18 . under this condition , the substation ( [ sol1infy ] ) into ( [ d ] ) gives @xmath40 therefore , the averaged lateral mean - square displacement corresponds to the superdiffusion : @xmath41 and the corresponding distribution of lateral positions is given by a gaussian @xmath42{(64/9)\pi k^2d_y^3t^3}}. \label{sol1infx}\ ] ] as it was discussed above , in 3d case additional multiplier @xmath36 in the eq . ( [ 3dfactorization ] ) will have exactly the same form as ( [ sol1infx ] ) with replacing @xmath43 , and msd @xmath44 is given by twice the expression ( [ msdinfthick ] ) . now let us consider the realistic situation , when the thickness @xmath22 is finite . in such a case the equation ( [ eq_u_x ] ) with impenetrable boundaries has a standard solution in the form of the eigenfunction" +"almost a century ago , schottky pointed out that if electrons are emitted as discrete particles independently of each other , current fluctuations are to be expected with the noise power : @xmath0 , with @xmath1 the elementary charge and @xmath2 the mean current . @xcite this phenomenon , called the `` shot effect '' by schottky , was later observed in vacuum tubes @xcite in nice agreement with his prediction . during the last two decades , the shot effect ( now called shot noise ) has been discovered and intensively studied in mesoscopic phase - coherent conductors . @xcite in a quantum point contact ( qpc ) , for instance , the current - noise power was found to be @xmath3 , where @xmath4 is the transmission probability ( for one - channel transmission ) . in this formula , the noise is suppressed by the factor @xmath5 relative to the schottky result , thereby predicting zero noise for perfect transmission ( see experimental evidence @xcite ) . in both cases , in qpcs and vacuum tubes , the granularity of charge is manifested in the shot noise , although the source of randomness is different : @xcite in qpc , the randomness appears in the transmission process due to the quantum partitioning between the incoming and outgoing states ( the incoming carriers are noiseless ) . in contrast , in vacuum tubes , the randomness is an inherent property of the emitter caused by thermal fluctuations . an interesting question then arises : is it possible to observe the quantum partition noise in electron emission , in the same way as in qpcs , with the noise power suppressed below the @xmath6 value ? the related question whether the shot noise in schottky s vacuum tube is classical has been addressed recently by schnenberger , oberholzer , sukhorukov , and grabert . @xcite the authors showed that for the vacuum tube parameters typical for the earlier stages of development of vacuum electronics , @xcite the quantum partitioning in electron emission is absent , and consequently the shot noise observed in schottky s vacuum tubes is classical . in this paper we show that in new generation electron emitters , scaled down to the nanometer dimensions , shot noise much smaller than the schottky noise , due to a quantum partitioning effect , is observable . moreover , two different sources of randomness thermal agitations and quantum partitioning may act together governing the electron emission noise . @xcite a rapidly growing field of nanoscale electronics suggests to us various examples of electron emitters in which this phenomenon may be tested : the nanotube field emitters , @xcite the composite emitters coated by wide - band - gap , low - work - function , and/or negative - electron - affinity materials , @xcite diamondlike emitters , @xcite among others . we start by considering the electron emission as a quantum scattering problem within the landauer - bttiker framework . the transverse and longitudinal motion of electrons are assumed to be separable , so that one can specify the quantum channels associated with transverse modes , and define the scattering states . the equation for the mean current in a phase - coherent conductor attached to two electron reservoirs with different chemical potentials reads @xcite @xmath7 where @xmath8 are the energy distribution functions at the left ( @xmath9 ) and right ( @xmath10 ) reservoirs , @xmath11 is the matrix of the transmission amplitudes , @xcite and the trace is taken over all the transmission channels at energy @xmath12 . for definiteness , the left reservoir is considered as an emitter , and the right reservoir , to which an external positive bias is applied , as a collector . we assume that the `` quantum conductor '' between the two reservoirs could also be a vacuum gap . at the surface of the emitter between the emitter - vacuum or emitter - semiconductor interface a potential barrier exists , which limits the current and scatters the emitted electrons ( only elastic scattering is assumed ) . thus the transmission matrix @xmath11 is referred to the scattering on the potential barrier . the zero - frequency current - noise power for a two - terminal quantum conductor is given by @xcite @xmath13 \ , { \rm tr}({\bf t}^{\dag}{\bf t}{\bf t}^{\dag}{\bf t } ) \\ + [ f_l ( 1 - f_r ) + f_r ( 1 - f_l ) ] \ , [ { \rm tr}({\bf t}^{\dag}{\bf t } ) - { \rm tr}({\bf t}^{\dag}{\bf t}{\bf t}^{\dag}{\bf t } ) ] \},\end{gathered}\ ] ] with @xmath14 the unit of conductance . for sufficiently high biases , all the states in the collector at energies corresponding to the occupied states at the emitter ( that contribute to the emission ) . hence one can take @xmath15 . in this case , the steady - state emission current in the basis of eigen - channels becomes @xmath16 where @xmath17 are the transmission probabilities associated with @xmath18 quantum channels at energy @xmath12 . hereafter , we drop the subindex @xmath9 at the occupation numbers @xmath19 , since only the emitter contact contributes to the current and noise . the noise power ( [ stwo2 ] ) for the unidirectional injection becomes @xmath20 \nonumber \\ & \equiv s_i^{\rm em } + s_i^{\rm part}.\end{aligned}\ ] ] this formula describes the spectral density of current fluctuations of an electron emitter . it unifies two sources of randomness : ( i ) the probabilistic occupation of states in the emitter ( through the function @xmath19 ) and ( ii ) the probabilistic reflection and transmission at the interface barrier ( through the probabilities @xmath21 ) . the first source of randomness is intimately related to intrinsic thermal agitations of the emitter and can be associated with the first term in eq . ( [ sone ] ) . since @xmath22 , this term is related to a thermal broadening of the occupation numbers at the fermi level . note that it vanishes at zero temperature , but dominates in the absence of partitioning when all transmission coefficients @xmath21 are either @xmath23 or @xmath24 , and hence can be interpreted as the _ emission shot noise_. the second source of randomness associated with the last term in eq . ( [ sone ] ) is caused by quantum partitioning and the fact that charge is carried by discrete portions ( shot effect ) . it only contributes for transmission probabilities @xmath25 , it does not vanish at zero temperature , and can be called the _ partition shot noise_. it is clear that both noise sources act together and can not be separated , in general . @xcite for future analysis , it is convenient , however , to introduce the notations for the emission noise @xmath26 and the partition noise @xmath27 according to the above discussion . equation ( [ sone ] ) can be used to calculate the noise power of the emitter with an arbitrary number of quantum channels . the problem can be simplified by assuming that the interface of the emitter is plane and its transversal area is large compared with wavelength ( a large number of channels ) . then , the summation over the transverse channels can be replaced by integration over the transversal energy @xmath28 , which can be performed giving @xmath29\ , \ln[1+e^{(e_f - e)/k_bt}]\ , de \right\},\end{gathered}\ ] ] where @xmath30 is the sharvin conductance , @xmath31 is the fermi energy , @xmath32 is the cross sectional area , and @xmath33 is the transmission probability at the longitudinal energy @xmath34 . now , we can verify eqs . ( [ sone ] ) and ( [ si_fd ] ) for two practical cases : thermionic emission and field emission . when the potential barrier is wide on the scale of the wavelength , one can neglect tunneling . in this case , an appreciable emission current can be achieved , for instance , by heating the emitter , so that thermally excited electrons escape above the barrier . the transmission probability takes the values 1 for @xmath35 and 0 for @xmath36 , where @xmath37 is the barrier height ( quantum reflection for overbarrier electrons is negligible for a sufficiently smooth potential ) . thus the partition term vanishes and the noise contains only the emission ( thermionic ) contribution : @xmath38 where the summation is taken for open channels only . for wide multichannel emitters with equilibrium fermi - dirac electrons [ see eq . ( [ si_fd ] ) ] , eq . ( [ sone_em ] ) is reduced to @xmath39.\ ] ] this formula gives the @xmath6 schottky value , whenever @xmath40 , which is a condition for a nondegenerate maxwell - boltzmann injection ( richardson - laue - dushman regime of thermionic emission @xcite ) . for a degenerate injection , @xmath41 , the noise is suppressed below the schottky value by the factor @xcite @xmath42 , where @xmath43 , and @xmath44 is the fermi - dirac integral of index @xmath45 . this suppression is caused by fermi correlations imposed by the pauli exclusion principle ( see ref . for the details ) . note that for metallic cathodes used in vacuum tubes , @xcite the work function is about 4 ev , which is much larger with respect to @xmath46 , so that only nondegenerate injection with the full shot noise is possible , @xcite as was observed in the experiment . @xcite the potential barrier at the emitter can be narrowed by applying a strong electric field , so that electrons can be pulled out from the cold emitter via quantum tunneling . @xcite in this case , the partition noise is expected to be the dominating source of noise : @xmath47 by applying this formula again to fermi - dirac electrons in a wide emitter under the condition @xmath48 , we obtain the noise which is independent of temperature , @xmath49\ , \left(1-\frac{e}{e_f}\right)\ , de.\end{aligned}\ ] ] in the fowler - nordheim regime of field emission , @xcite when the fermi energy of the emitter is much below the barrier top , the transmission probability for electrons at the fermi level ( which mostly contribute to the emission ) is small , @xcite @xmath50 . it can be verified that in this regime , eq . ( [ si_fd0 ] ) gives the schottky @xmath6 law . summarizing these two examples , one can conclude that the schottky noise , which is the noise produced by independently injected electrons ( poissonian process ) , may occur under two physically different conditions : @xcite ( i ) the low occupation numbers , @xmath51 , when electrons are initially poissonian and remain poissonian after passing the barrier with whatever probability ; ( ii ) the low transmission probability , @xmath50 , when the incoming electrons may be initially noiseless , but after tunneling through the barrier , the outgoing flow becomes diluted and obeys a poissonian statistics . although in both cases , the noise power is given by the schottky law @xmath0 , in the former case its value is sensitive to the temperature , while in the latter case it is not . this fact may be used in the experiment to distinguish these two mechanisms . now it is clear under which conditions one should expect a deviation from the @xmath6 law . it is the case when both the occupation numbers @xmath19 and the transmission probabilities @xmath4 are not small with respect to 1 . this is precisely the situation that may occur in novel field emitters . the requirements of strong electric currents under low voltages led research interests towards low - work - function materials ( low potential barriers ) and sharp emitter tips ( narrow potential barriers ) . for instance , extremely high electric" +"the recent development in the autonomy and the capabilities of mobile robots greatly increases the number of applications suitable for a team of autonomous agents . particular interest has been received by those tasks requiring continual execution , such as the monitoring of oil spills @xcite , the detection of forest fires @xcite , the track of border changes @xcite , and the patrol ( surveillance ) of an environment @xcite . the surveillance of an area of interest requires the robots to continuously and repeatedly travel the environment , and the challenging problem consists in scheduling the robots trajectories so as to optimize a certain performance criteria . the reader familiar with network location , multiple traveling salesman , or graph exploration problems may observe a close connection with the patrolling problem we address , e.g. , see @xcite . it is worth noting , however , that these classical optimization problems do not capture the repetitive , and hence dynamic , aspect of the patrolling problem , nor the synchronization issues that arise when a timing among the visits of certain zones is required . a precise formulation of the patrolling problem requires the characterization of the robots capabilities , of the environment to be patrolled , and of the performance criteria . in this work , we assume the robots to be identical and capable of sensing and communicating within a certain spatial range , and of moving according to a first order integrator dynamics with bounded speed . we represent the environment as a graph , in which the vertices correspond to physical and strategically important locations , and in which the edges denote the possibility of moving and communicating between locations . we assume that , when a robot is placed at each of the graph vertices , the union of the sensor footprints provides complete sensor coverage of the environment . regarding the performance criteria of a patrolling trajectory , we consider ( i ) the time gap between any two visits of the same region , called _ refresh time _ , and ( ii ) the time needed to inform the team of robots about an event occurred in the environment , called _ latency_. loosely speaking , refresh time and latency reflect the effectiveness of a patrolling team in detecting events in the environment and in organizing remedial actions . for both the refresh time and latency optimization problem , we focus on the worst case analysis , even though the average refresh time and the average latency cases are also of interest . notice that for the latency to be finite , the motion of the robots needs to be synchronized . for instance , if two robots are allowed to communicate only when they simultaneously occupy two adjacent vertices of the graph , then they need to visit those vertices at the same time in a finite latency trajectory . the patrolling problem is receiving increasing attention because of its fundamental importance in many security applications , e.g. , see @xcite . although many solutions have been proposed , the problem of designing minimum refresh time and latency team trajectories for a general environment is , to date , an open problem . almost all traditional approaches rely on space decomposition , and traveling salesperson tour computation @xcite . in @xcite an empirical evaluation of existing patrolling heuristics is performed . in @xcite two classes of strategies are presented , namely the cyclic- and the partition - based strategy . in the cyclic - based strategy , the robots compute a closed route through the viewpoints , and travel repeatedly such route at maximum speed . clearly , in the case of a single robot , if the tour is the shortest possible , then the cyclic - based strategy performs optimally with respect to the refresh time and latency criteria . in the partition - based strategy , the viewpoints are partitioned into @xmath0 subsets , being @xmath0 cardinality of the team , and each robot is responsible for a different set of viewpoints . to be more precise , each robot computes a closed tour visiting the viewpoints it is responsible for , and it repeatedly moves along such tour at maximum speed . still in @xcite , the two classes of strategies are compared , and it is qualitatively shown that cyclic - based strategies are to be preferred whenever the ratio of the longest to the shortest edge of the graph describing the environment is small , while , otherwise , partition - based policies exhibit better performance . in @xcite and @xcite , an efficient and distributed solution to the perimeter patrolling problem for robots with zero communication range is proposed . by means of some graph partitioning and graph routing techniques , we extend the results along these directions , e.g. , by considering the case of a nonzero communication range for the perimeter patrolling , and by characterizing optimal strategies for different environment topologies . an important variant of the patrolling problem is known as persistent surveillance , e.g. , see @xcite . differently to our setup , a dynamically changing environment is considered for the persistent surveillance problem , and performance guarantees are offered only under a certain assumption on the rate of change of the regions to be visited . it is worth mentioning that a different approach to the design of patrolling trajectories relies on the use of pebbles or chemical traces to mark visited regions , e.g. , see @xcite . these techniques , although effective even without a global representation of the environment , and with severe communication constraints , do not explicitly deal with the optimality of the patrolling trajectories , and they represent therefore a complementary area of research with respect to this work . the main contributions of this work are as follows . we introduce and mathematically formalize the concept of refresh time and latency of a team trajectory , and we formally state the patrolling optimization problem . we propose a procedure to build a graph ( roadmap ) to represent the topological structure of the area to be patrolled , and we study separately the case of a chain , tree , and cyclic ( not acyclic ) graph . we exhaustively discuss the case of a chain roadmap . first , we characterize a family of minimum refresh time and latency team trajectories , which can be computed by optimally partitioning the chain graph among the robots . second , we derive a centralized polynomial time algorithm to compute an optimal partition , and , ultimately , to design an optimal team trajectory . our partitioning procedure is based upon a bisection method , and it is also amenable to distributed implementation . third , we develop a distributed procedure for the robots to converge and synchronize along an optimal trajectory , so as to minimize the refresh time and latency criteria . fourth and finally , we test the robustness of our methods through a simulation study . when the roadmap has a tree or cyclic structure , we focus on the refresh time optimization problem , and we do not consider the latency optimization nor the design of distributed algorithms . for the case of a tree roadmap , we reduce the minimum refresh time patrolling problem to a known graph optimization problem . we show that the computational complexity of the minimum refresh time patrolling problem is polynomial in the number of vertices of the roadmap , and , under the assumption of a fixed and finite number of robots , we identify a polynomial time centralized algorithm to compute a minimum refresh time team trajectory . for the case of a cyclic roadmap , we show that the patrolling problem is an _ np - hard _ optimization problem . we propose two approximation algorithms , and we characterize their performance . the first approximate solution is extremely easy to compute , but its performance depends upon the ratio between the longest and the shortest edge in the graph representing the environment . the second approximation algorithm is based on a polynomial time path - covering procedure , and it allows us to compute a team trajectory whose refresh time is within a factor of @xmath1 from the minimum refresh time for the given environment ( cf . [ fig : path_cover ] for an example ) . to the best of our knowledge , this algorithm is the first constant factor approximation algorithm for the _ np - hard _ minimum refresh time patrolling problem . a preliminary version of this work appeared in @xcite . with respect to the latter manuscripts , in this current work we introduce and solve the latency optimization problem , we perform a numerical study to analyze the robustness of our algorithmic procedures , and we improve the presentation of the results on the refresh time optimization problem . the rest of the paper is organized as follows . the notation and the problem under consideration are in section [ sec : prob_set ] , where we also show that the patrolling problem is , generally , computationally hard . section [ sec : refr_time ] , [ sec : latency ] , and [ sec : distr_alg ] contain our results for the patrolling of a chain environment . we characterize a minimum refresh time and latency team trajectory , and we derive a centralized and a decentralized algorithm for its computation . in section [ sec : simulations ] we perform a simulation study to show some robustness and reconfigurability properties of our distributed procedure . section [ sec : tree_patrol ] contains our results for the patrolling of a tree environment . we describe a minimum refresh time team trajectory on a tree roadmap , and we characterize the complexity of computing an optimal solution . section [ sec : heurist ] deals with the general case of cyclic environment , and it contains our approximation procedures . our conclusion and final remarks are in section [ sec : future_work ] . we will be using the standard motion planning notation , and we refer the reader to @xcite for a comprehensive treatment of the subject . we are given a team of @xmath2 identical robots , capable of sensing , communicating , and moving in a connected environment . we make the following combined assumptions on the robot capabilities and on the environment to be patrolled . regarding sensing , we assume that the environment can be completely covered by simultaneously placing a robot at each of a set of @xmath3 _ viewpoints _ in the configuration space . in other words , if @xmath4 robots were available and placed at the @xmath5 viewpoints , then the union of the sensors footprint of the robots would provide complete sensor coverage of the environment . we assume that each viewpoint is required for complete sensor coverage . finally , we assume @xmath3 so that at least one robot needs to visit more viewpoints for the entire environment to be monitored over time . regarding communication , we associate an undirected graph @xmath6 with the environment , whose vertices are the @xmath5 viewpoints , and in which there is an edge between two vertices if two robots placed at those viewpoints are able to communicate to each other . we assume that @xmath6 is connected . in what follows we design cooperative patrolling algorithms with sporadic communication , in the sense that two robots are required to communicate only when they occupy adjacent vertices . the occurrence of additional communication links can be easily incorporated into the algorithms and can not decrease their performance . regarding motion , we assume that the robots are holonomic , i.e. , they are modeled as first order integrators and move" +"in the late 70 s , montonen and olive discovered that a given four dimensional gauge theory might be described using different sets of elementary fields @xcite . the fields in one of this set create the standard perturbative spectrum of the theory ( photon , w bosons , quarks , ) , while the fields in the `` dual '' set correspond to the solitonic states ( dyons ) . an example of such a phenomenon was observed even before in some two dimensional theories @xcite . since then , a natural and exciting question arose : can we find theories where the description in terms of the solitonic states is the same ( same field content and symmetries in the lagrangian ) as the description in terms of the perturbative states ? answering this question requires to understand the strong coupling behaviour of the gauge theories under study , since exchanging electrically charged perturbative states with magnetically charged solitonic states amounts to inverting the gauge coupling constant due to the dirac quantization condition . this was out of reach in the 70 s , though some important progress was made . first , it was realized that the natural arena for electric - magnetic duality was yang - mills theories with extended supersymmetries @xcite . second , it was pointed out that in order to have dyons of spin 1 , which could be the dual of the w bosons , @xmath1 supersymmetry seemed to be required @xcite . actually , an exact electric - magnetic duality , combined with the dirac quantization condition , implies that the @xmath8 function must vanish . this is indeed the only case where the electric coupling @xmath9 and the magnetic coupling @xmath10 , being constant , have the same behaviour under the renormalization group flow . the @xmath1 theory is known to be conformally invariant at the quantum level , perturbatively @xcite as well as non - perturbatively @xcite . at the perturbative level , this property is shared with some @xmath2 theories @xcite , which are believed to be finite even non - perturbatively at least when the rank of the gauge group is one . the latter theories are strongly believed to have , together with the @xmath1 theory , an exact electric - magnetic duality symmetry ; we will study them below . there are various ways to test these duality conjectures . one of them , advocated in @xcite , consists of looking at the ( hyper)elliptic curve from which the low energy physics can be deduced , and check whether some sensible duality transformations can be defined in order to insure exact electric - magnetic duality symmetry . another approach has been to look at the free energy @xcite . but the most popular test certainly is to determine the content of a particular sector of the hilbert space , the bps sector , and to check whether it is compatible with duality @xcite . to study solely the bps states is not too restrictive . actually , all the perturbative and known stable solitonic states are bps states . moreover , this is in general a very accurate test . for instance , it is well known that the bps spectra of the asymptotically free @xmath2 theories certainly do not have the same symmetries as the associated ( hyper)elliptic curve . there are also some technical reasons to study the bps spectra . an exact quantum mass formula is known for these states , stemming from the fact that they lie in small representations of the supersymmetry algebra and thus saturate the bogomolnyi bound @xcite . the semiclassical quantization can give reliable results when one can go continuously from weak coupling to strong coupling without altering the stability of the states , which is the case for instance in the @xmath1 theory . and , what is maybe their most intriguing property , it seems that the bps spectra can be computed completely once one knows the low energy structure of the theory , that is all the information about these spectra seems to be contained , in a very hidden way , in the ( hyper)elliptic curve . in this paper , i will study in detail the bps spectra of two @xmath2 theories having zero @xmath8 function . the first one will be the so(3 ) gauge theory with one flavour of bare mass @xmath11 , which reduces to the @xmath1 theory when @xmath12 , and the second one will be the su(2 ) gauge theory with four hypermultiplets whose bare masses will be taken to be @xmath13 , @xmath14 . the fact that these seemingly very different theories can be treated in parallel stems from the fact that their low energy effective action are formally identical . i will use a method whose spirit originated in @xcite and which is completely understandable in the framework of non perturbative field theory la seiberg - witten @xcite . this will lead to a natural and rigorous proof that the spectra of both the @xmath1 and the @xmath2 theories are self - dual when the bare masses are zero . we will also see how the duality can still work in the massive theories though , as it will be shown , the spectra are no longer in general self - dual _ at a given point _ in the moduli space . the plan of the paper is as follows . in section 2 some generalities on the theories under study are recalled . particular emphasis is put on the quantum numbers carried by the solitonic states , as suggested by a semiclassical analysis , and it is explained why they are compatible with an exact duality symmetry . in section 3 , after a short presentation of the seiberg - witten curves whose exactitude will be our unique , very mild hypothesis , some of the physical ideas which are at the basis of the present work are presented . this leads to a limpid understanding of _ why _ states having any magnetic charges must exist in the theory , and also gives a flavour of what the spectra in the massive cases look like . it appears that in some regime , the magnetic charge is quantized much as if it were a periodic variable , while only one value of the electric charge is allowed . though the spectrum does not appear in general as being self - dual at a given point in moduli space , it is argued that it is nevertheless perfectly compatible with an exact s duality of the massive theories . it is also pointed out that semiclassical reasonings might be able to account for the curious disappearance of all but very few states in some regions of moduli space , a phenomenon first discovered in @xcite at strong coupling . in order to prove the complete sl@xmath15 invariance of the spectra , the consideration of theories with non zero bare @xmath16 angle is needed . this is done in section 4 . we also discuss the appearance of superconformal points in some particular theories . in section 5 , the uniqueness of the states is proven , as required by duality . in section 6 , a general presentation of the curves of marginal stability , across which the bps spectra may be discontinuous , these curves are then used in section 7 to rigorously establish the existence of all the @xmath0 states , for @xmath3 and @xmath4 relatively prime integers , in the massless theories . finally , in section 8 , a general physical argument is presented which shows that the theories under study must have at least an exact @xmath5 duality symmetry . in particular , the bps spectra of the _ massless _ theories must be invariant under the monodromy group @xmath5 of the _ massive _ theories . we then deduce that the vector @xmath6 states exist in the massless @xmath7 theory . in appendix a , the computation of the seiberg - witten periods is presented , and in appendix b the curves of marginal stability are used to prove the existence of some particular states required by duality in the massive theories . as already noted in the introduction , one easy way to check whether a given theory may be , or can not be , self - dual , is to look at the quantum numbers carried by the states which are supposed to be transformed into each other by an electric - magnetic rotation . for example , the w bosons must be the dual of a charged particle having spin one in the one monopole sector . the very existence of such a spin one solitonic state is already a non trivial test of duality and was proven in @xcite . the main goal of this paper will be to extend this kind of result to all the electric and magnetic quantum numbers . in addition to the electric and magnetic charges , there is another abelian quantum number , which we will call the @xmath17 charge , which plays an important r^ ole , since it also appears in the central charge of the supersymmetry algebra and thus in the bps mass formula . the aim of this section is to explain the relations that may exist between these quantum numbers , and also to discuss the way one should compute the @xmath17 charges . the theory whose matter content is one @xmath2 adjoint `` quark '' hypermultiplet will be called hereafter the so(3 ) theory . this matter multiplet consists in two chiral @xmath18 superfields @xmath19 , which correspond in terms of ordinary fields to one dirac spinor @xmath20 and two complex scalars @xmath4 and @xmath21 in the adjoint representation of the gauge group . the microscopic lagrangian also contains one yang - mills @xmath2 multiplet ( one vector field @xmath22 , two majorana spinors @xmath23 and @xmath24 and one complex scalar @xmath25 ) . when the bare mass @xmath11 of the matter multiplet is zero , we recover the @xmath1 theory . when @xmath26 , the moduli space of vacua is a coulomb branch where the gauge symmetry is spontaneously broken down to u(1 ) by a non zero higgs vacuum expectation value , @xmath27 . when @xmath12 and @xmath1 , we have other equivalent coulomb branches , permutted by the su(4)@xmath28 symmetry , corresponding to the other scalar fields having a vev . in addition to the u(1)s associated to the electric @xmath29 and magnetic @xmath30 charges , the theory has an abelian u(1 ) global symmetry @xmath31 , @xmath32 , with corresponding charge @xmath17 . classically , the central charge of the supersymmetry algebra is @xmath33 where @xmath9 is the gauge coupling constant . semiclassically , the electric charge @xmath29 is @xmath34 , @xmath35 integer , up to terms coming from cp violation ( like a standard witten term proportional to the bare @xmath16 angle ) . the magnetic charge is given by the dirac quantization condition , @xmath36 for an integer @xmath37 . we will loosely call in the following the integers @xmath35 and @xmath37 the electric and magnetic charges . the mass of a bps state @xmath38 will then be @xmath39 for instance , an elementary quark @xmath40 has a tree level mass @xmath41 . the exact quantum formula for @xmath42 can be found . it was shown in @xcite that it can be cast in the form @xmath43 here @xmath44 is the dual variable of @xmath45 and can be , at least in principle , computed very explicitly as a function of a gauge invariant coordinate @xmath46 on the moduli space ( @xmath46 is @xmath47 up to a constant ) @xcite . at the tree level , we have @xmath48 , where @xmath49 is a very convenient combination of the gauge coupling @xmath9 and the" +"given a curve @xmath4 , we consider the geometric flow @xmath5 where @xmath6 is the curvature and @xmath7 the binormal component of the frenet - serret formulas @xmath8 the flow can be expressed as @xmath9 where @xmath10 is the usual cross - product , @xmath11 is the time , and @xmath12 is the arc - length parameter . it appeared for the first time in 1906 in the ph . d. thesis of da rios @xcite and was rederived in 1965 by arms and hama @xcite as an approximation of the dynamics of a vortex filament under the euler equations . this model is usually known as the vortex filament equation ( vfe ) ; we refer the reader to @xcite and @xcite for an analysis and discussion of its limitations . equations and are also known as the binormal equation and the localized induction approximation ( lia ) , respectively . some of their explicit solutions are the line , the circle , and the helix . since the tangent vector @xmath13 remains with constant length , we can assume that @xmath14 , for all @xmath11 . differentiating , we get the so - called schrdinger map equation onto the sphere : @xmath15 which is a particular case of the landau - lifshitz equation for ferromagnetism @xcite . equation can be rewritten in a more geometric way as @xmath16 where @xmath17 is the covariant derivative , and @xmath18 is the complex structure of the sphere . written in this way , can be generalized to more general definition domains and images , as in @xcite , where the hyperbolic plane @xmath19 was chosen as the target space . a relevant step forward in the understanding of was given by hasimoto in @xcite , where a transformation ( see section [ s : hasimoto ] ) that relates and with the nonlinear schrdinger ( nls ) equation was introduced : @xmath20 equation is time reversible , i.e. , if @xmath2 is a solution , so is @xmath21 . bearing in mind this fact , an important property of ( and , hence , of ) is that it has a one - parameter family of regular self - similar solutions that develop a corner - shaped singularity at finite time . this was proved in @xcite for the euclidean case , and in @xcite for the hyperbolic case . the self - similar solutions are written in the form @xmath22 as was proved by buttke in @xcite , @xmath23 is a smooth curve characterized by the geometric properties @xmath24 with @xmath25 being a constant . therefore , the shape of @xmath23 is the one of a hairpin : it looks like a segment of a circle of radius @xmath26 close to the origin , that becomes two helicoidal curves with a bigger pitch for bigger @xmath27 , and that winds around two different lines @xcite . buttke also studied numerically these self - similar solutions . later on , in @xcite , a careful numerical study of those solutions for both the euclidean and the hyperbolic cases was done . on the one hand , the authors reproduced numerically in @xcite the formation of the corner - shaped singularity , and , on the other hand , they started with a corner - shaped initial datum , recovering numerically the self - similar solutions ; in all cases , the correct choice of boundary conditions was shown to be vital . furthermore , they gave numerical evidence that fractality phenomena appeared in ( see figure 2.6 in p. 1059 of @xcite ) , if , for instance , fixed boundary conditions were imposed on the tangent vector @xmath28 . remark that the relationship between fractals and the schrdinger map equation is not new ; indeed , in @xcite , an aortic valve model was proposed , in order to study the apparent fractal character of the valve s fiber architecture . instead of @xmath2 , the authors wrote @xmath29 , where @xmath30 , which corresponds to our time , is such that the curves @xmath31 are the fibers . after imposing fixed boundary conditions at @xmath32 , they showed that the curves @xmath33 have a fractal character . besides , the fractal dimension of those curves was calculated numerically in @xcite . it is well known that this fractal behavior already occurs at the linear level , as can be easily seen when solving numerically the free schrdinger equation @xmath34 with an initial datum that is piecewise constant as the sign function in , say , @xmath35 $ ] , and then extended by periodicity . the trigonometric series associated to these problems have been extensively studied and , as we will see later , the behavior at rational times modulo @xmath36 is completely different to that at irrational ones . in @xcite , berry and goldberg made a far - reaching connection of this behavior with the so called talbot effect in optics . in @xcite and in @xcite , the authors used to model the talbot effect and showed that at rational times the solution can be obtained as a finite overlapping of translates of the initial datum , while at irrational times the images have a fractal profile . also in @xcite , a conjecture was made about the dimensions of those fractals . as far as we know , the only available results on the nonlinear setting are the recently ones obtained by erdoan and tzirakis @xcite ( see also @xcite ) in the cubic nonlinear schrdinger equation ( i.e. equation , with @xmath37 ) , for the initial data given by piecewise continuous functions . this means that the data are `` almost '' in the sobolev class @xmath38 , that is subcritical with respect to the one determined by the scaling of the equation ( i.e. @xmath39 ) . this typically implies that the nonlinear potential can be seen as an external force . then , its contribution is computed using duhamel s integral , which has a regularizing effect . as a consequence , the fractal behavior is due to the linear part of the solution . at this point , the available results for the linear theory are used ( see @xcite and @xcite ) . more recently , erdoan and tzirakis , in collaboration with chousionis , have also studied in @xcite the schrdinger map equation , but still with subcritical initial conditions . in this paper , we are interested in filaments with corners . this means to consider delta functions as the initial data for or piecewise continuous functions as the initial data for . therefore , we work with data in critical spaces and the problem turns out to be much more involved . the case of an infinite curve with just one corner and that is otherwise smooth has been studied in the sequence of papers @xcite by banica and vega . one of the conclusions is that is in fact ill - posed for this type of initial conditions , so that is also ill - posed if it is understood in a classical sense . however , after introducing appropriate function spaces and using the appropriate definition of solution , it is proved that and are well - posed for this type of initial condition . more concretely , the velocity at the point where the corner is located is determined by the self - similar solution that at time zero has a corner with the same angle . in fact , in @xcite it was proved that there exists just one self - similar solution with this property . even if the solutions of for an initial datum with a corner are well understood , nothing had been done for more general initial data with several corners , in particular , polygons . nevertheless , in two recent papers @xcite by jerrard and smets , they prove a global existence theorem that allows to consider such types of initial data . moreover , they simulate numerically the evolution of the unit square at different times , suggesting that the solution could become again polygonal ; indeed , at a certain time , the square seems to reappear , but with the axes turned by a @xmath40-angle with respect to the initial ones . in the following pages , we will show not only that these observations are correct , but that , given a regular planar polygon with @xmath41 sides as the initial datum , another polygon is obtained at times of the form @xmath42 , @xmath43 . in fact , we will give a complete description of this polygon ; in particular , and except for @xmath44 , we will see that it is a skew polygon with @xmath45 sides ( if @xmath46 odd ) , or @xmath47 sides ( if @xmath46 even ) . one could wander what , if any , is the connection of these solutions with real fluids . of course , one can not expect anything at the quantitative level , because da rios and arms and hama s approximations are based first in a truncation of the biot - savart integral and then in a renormalization of the time variable . however , using vfe as an approximation of the evolution of real filaments can not be ruled out at the qualitative level , even with data as singular as the ones we consider . in fact , in @xcite , the similitude between the self - similar solutions and a flow traversing a triangular wing is pointed out ( see figure 1.1 in p. 1051 of that paper ) . in the concrete case of the solutions considered in this article , we could ask if the macroscopic effect of the turning axes mentioned above can be seen in the dynamics of real fluids . it appears that this is something quite well documented for noncircular jets . it was first observed when the nozzle has an elliptic shape and , later on , seen for shapes given by a rectangle , a square , and an equilateral triangle among others . the interest of considering nozzles with corners started in the mid 80 s and has received considerable attention since then . we refer the reader to the survey @xcite , where the papers related to the above observations can be found , together with a detailed analysis on how sensitive the axes - turning phenomenon is to the initial geometric conditions ; and several numerical experiments are also reviewed . it has to be understood that , at the numerical level , the corners are always effectively rounded and , in real experiments , the corners are immediately smoothed out once the jet leaves the nozzle , due to viscosity effects . this is consistent with the behavior of the self - similar solutions mentioned above , because the initial corner evolves into a smooth curve with the shape of a hairpin . furthermore , the appearance of smooth polygonal structures with more angles has been appreciated for nozzles with the shape of an equilateral triangle ( see ( * ? ? ? * figure 6 ) ) . also in ( * ? ? ? * figure 10 ) , while in @xcite it is said `` ... a consistent eightfold distribution pattern is also suggested ... '' for square nozzles . similar results are obtained in the numerical simulations of @xcite ( see figure 8 in p. 9 , and p. 11 , where the @xmath48-degree `` flip - flop '' in the case of an equilateral triangle is emphasized ) . we think it would be worth studying in more detail whether or not these more complicated polygonal structures appear in noncircular jet flows . the structure of this paper is as follows . in section [ s : hasimoto ]" +"the storage and transmission of quantum states in a decohering environment is unavoidable in quantum computation and quantum communication @xcite . the conceptual device of a quantum channel is very useful in addressing the issues of such a transmission @xcite and to analyze decoherence related questions in quantum cryptography @xcite and quantum teleportation @xcite . a general quantum operation on an @xmath1-dimensional quantum system is a completely positive map . such a map defines a quantum channel for the given system and can be formally represented by its operator sum representation @xcite . one can also look at this general quantum evolution using affine transformations for the channel @xcite . in an explicit model for this evolution , the system is considered as a part of a larger closed system undergoing unitary evolution . the part of this larger system that we are not interested in can be thought of as the environment , which when traced over , gives us the dynamics of the effective sub - system . the environment can in general be very large . however , it turns out that in order to achieve the most general evolution for a system with an @xmath1-dimensional hilbert space , we need an environment which is of dimensions @xmath2 ( if we allow the most general unitary evolution of the total system and assume that the initial state of the environment is pure ) @xcite . therefore , to simulate the most general evolution of a single qubit , at least a four - dimensional ( two - qubit ) environment is required . however if we allow the initial state of the environment to be a mixed state , there is a possibility of achieving such a simulation by employing a smaller environment . this reduction in the dimension of the hilbert space is desirable for performing actual simulations of open quantum systems @xcite . along these lines , an argument based on counting the number of independent parameters suggests that a one - qubit mixed state environment might be sufficient to simulate the most general quantum evolution of a single qubit @xcite . further investigations in this direction have revealed that there are counter - examples to the above conjecture , and there are single qubit channels which can not be simulated by one qubit in the environment @xcite . we investigate this question in detail via a different route and compute the set of affine transformations for this class of channels analytically , employing the canonical form for two - qubit unitary operators @xcite . restricting ourselves to generalized depolarizing channels , we show that a sizable volume ( namely @xmath3 ) of these channels can not be simulated by a one - qubit mixed state environment . further , we show that the counter example of the two - pauli channel found by terhal et . al . is a special case of our results . the material in this paper is arranged as follows : in section [ one - qubit - channel ] , we explain how a one - qubit mixed state environment can be considered for the simulation of a single qubit channel and the significance of modeling the channel using such an environment . we consider the two - qubit unitary required for the simulation of such a channel and discuss how this class of channels could be a candidate that could occupy a sizable volume in the space of single - qubit channels . at the end of this section , the expression for the affine transformation for a general single qubit channel modeled using a one - qubit mixed state environment is obtained . in section [ depolarizing - channel ] we take up the special case of generalized depolarizing channels . the affine transformation for this case is obtained by setting the shift of the bloch sphere origin to zero in the general expression for affine transformation developed in section [ one - qubit - channel ] . these channels are classified by computing their singular values . from the structure of these singular values and the analysis of all the possible cases the volume occupied by the generalized depolarizing channels simulated by a one - qubit mixed state environment is computed and compared to the total volume of generalized depolarizing channels . the section concludes with a discussion of the two - pauli channel considered as a special case of generalized depolarizing channels and it is shown that it can not be simulated by a one - qubit mixed state environment . section [ conclusions ] contains some concluding remarks . in the model for the one - qubit channel that we consider , we allow the qubit of interest to interact with only one environment qubit . the interaction unitary is allowed to be the most general two - qubit unitary and the environment qubit is a general mixed state . this channel is schematically depicted in figure ( [ channel ] ) . for the purpose of characterizing the channel , we consider the system qubit to be in a general pure state ( a point on the bloch sphere ) given by @xmath4 where @xmath5 varies from 0 to @xmath6 and @xmath7 varies from 0 to 2@xmath6 . the environment qubit is assumed to be in a general mixed state for which we choose a particular parameterization as follows : @xmath8 where @xmath9 corresponds to a maximally mixed state and @xmath10 corresponds to a general pure state given by @xmath11 where @xmath12 varies from @xmath13 to @xmath6 and @xmath14 varies from @xmath13 to @xmath15 . therefore , the environment state can be thought of as a mixture of a completely mixed state and a pure state . the parameter @xmath16 indicates the degree to which the state is mixed . by varying @xmath17 from @xmath18 to @xmath13 , we can go from a pure to a maximally mixed state of the environment . implementation of a one - qubit channel using a single qubit mixed state environment . the system is taken to be in a pure initial state @xmath19 while the environment is in a mixed state @xmath20 . the interaction takes place via the two - qubit unitary @xmath21 and the environment qubit is discarded after the interaction . ] the interaction that takes place between the system qubit and the environment qubit corresponds to a general unitary operator in the four - dimensional ( two - qubit ) hilbert space . this most general unitary which is an @xmath22 transformation has fifteen independent parameters . however , it has been shown that an arbitrary two - qubit unitary can be decomposed into local unitaries on each qubit sandwiching a non - trivial interaction unitary . this interaction unitary @xmath21 belongs to a three - parameter family of transformations @xcite . @xmath23 this is pictorially shown in figure [ u4-fig ] . this three - parameter family of interaction unitaries has the power to entangle or unentangle the qubits involved . this family finds a simple diagonal representation in the special bell basis , namely @xmath24 where @xmath25 for @xmath26 are the special bell basis vectors @xcite . the number of independent parameters @xmath27 can be reduced to three by a global phase change . this transformation matrix can be readily transformed into the product basis @xmath28 to obtain @xmath29 where @xmath30 we are considering a quantum channel for a single qubit with another qubit acting as the environment and a general unitary transformation ( described above ) providing the interaction between the two qubits . it is easy to see that the properties of the channel do not change with the local unitary transformations @xmath31 and @xmath32 . therefore , for the analysis of the family of such channels , the interaction unitary that needs to be considered is the three - parameter family given in ( [ ch9_t ] ) . the final output state of the system @xmath33 emerging from the channel after the action of @xmath21 is obtained by tracing over the environment qubit . schematic diagram for a two - qubit unitary . the local unitaries @xmath34 together with @xmath21 , which is diagonal in the special bell basis , provide a decomposition of a general @xmath22 transformation . ] mathematically , a one - qubit channel can be described in a number of ways , and we find it useful to picture it in terms of an affine transformation of the bloch sphere . the quantum states of a single qubit on the bloch sphere can be represented as follows : @xmath35 where the @xmath36 s are pauli matrices , and @xmath37 is a 3-component real vector . for pure states @xmath38 , and for mixed states @xmath39 . any arbitrary trace - preserving quantum operation on ( [ ch1_t ] ) is given by a map of the form @xmath40 , with the new vector determining @xmath41 given by @xmath42 where @xmath43 are the nine components of a @xmath44 real matrix @xmath45 and @xmath46 are the three components of a constant real column vector @xmath47 . this map , called the affine map , maps the bloch sphere ( including its interior ) onto a shifted ellipsoid with its major axis less than @xmath48 @xcite , the total number of independent parameters defining this map are twelve . the matrix @xmath45 amounts to a combination of proper rotations and contractions in different directions of the vectors on the bloch sphere . the vector @xmath47 corresponds to a shift in the origin of the bloch sphere . two channels which differ from each other by a unitary transformation of the qubit before and after the action of the channel are identical . thus , we can utilize this freedom of performing arbitrary proper rotations of the bloch sphere before and after the channel action to simplify the affine transformations for the channel . this converts the matrix @xmath45 into a ` singular - value ' form with singular values appearing along the diagonal . @xmath49 where @xmath50 and @xmath51 are real orthogonal matrices with unit determinant and @xmath52 is a diagonal matrix with the squares of its three diagonal elements given by the eigen values of the positive semi - definite matrix @xmath53 . the shift vector @xmath47 is mapped onto another such vector under these two proper rotations . after utilizing this freedom through the action of @xmath50 and @xmath51 , the number of independent parameters for single qubit channels is clearly six : namely the three singular values of the matrix @xmath52 , plus the three components of the vector @xmath47 . there is a further restriction of complete positivity on the allowed affine transformations ; however , that does not reduce the number of independent parameters @xcite . these affine transformations provide us with a complete description of one - qubit channels . we now turn to an explicit calculation to obtain the affine transformation given in equation ( [ ch2_t ] ) for the class of channels simulatable by a one - qubit mixed state environment described in figure ( [ channel ] ) ( taking a general initial system state @xmath54 to @xmath55 ) . for this purpose , we consider six points on the input bloch sphere corresponding to the eigen states of the operators @xmath56 and @xmath57 and calculate the output density matrix for each of these points . at the end of this lengthy algebraic calculation , the affine transformation turns out to be @xmath58 the corresponding shift is @xmath59 this affine transformation gives a parameterization of all the channels simulated by a one - qubit mixed state environment . we have thus obtained a closed form expression for the complete class of channels for a single qubit simulated by a one - qubit environment . this class of channels is a six - parameter family" +"according to the standard big bang nucleosynthesis ( sbbn ) , the most abundant elements in the aftermath of the big bang were hydrogen and helium with very small traces of deuterium and lithium . these elements make up the so called pop iii or _ primordial _ chemical composition . all the heavier elements present today had to be produced in the course of the evolution of several generations of stars . in order to understand the physics of the early universe , there is a need of having appropriate and accurate material functions at hand , in particular opacities for a sbbn chemical compositions . there is a large body of literature available with opacity calculations for metal - free ( z=0 ) h / he mixtures , starting with the paczynski i - vi mixtures ( * ? ? ? * hereafter ) , the calculations of ( * ? ? ? * hereafter ) and ( * ? ? ? * hereafter ) , and more recently ( * ? ? ? * hereafter ) . these calculations were restricted to temperatures between @xmath3 and @xmath4 . specific metal - free opacity sets have been calculated by the op project ( * ? ? ? * @xmath5 ) and opal ( * ? ? ? * ; * ? ? ? * @xmath6 ) . more recently , opal calculations have been extended @xcite to @xmath7 and densities is a parameter which replaces the density in order to keep opacity tables in rectangular format when spanning many decades in temperature ( for more details see appendix [ sect : tblfmt ] ) ; @xmath8 @xmath9 with the main application for cno enhanced opacities in stellar evolution . all these opacity calculations , however , only considered pure hydrogen / helium mixtures with no metals ( mass fraction @xmath10 ) , but different ratios @xmath11 of the mass fractions of hydrogen ( @xmath12 ) and helium ( @xmath13 ) . it has been argued that due to the assumed very small abundances of deuterium and lithium these element do not play any significant role in the opacities and thus in the evolution of pop iii objects . moreover , while there are good low - temperature opacities available for a solar chemical composition ( e.g. * ? ? ? * ) , zero - metallicity opacity tabulations have been restricted to temperatures above @xmath14 so far . in this paper we present calculations of both , rosseland and planck mean opacities for primordial matter including all the three elements ( hydrogen , helium , and lithium ) including deuterium isotope and present their absorption properties . in sect . [ sect : matter ] we discuss the quantitative composition of primordial matter at a given temperature and density . we then describe the relevant absorption processes ( sect.[sect : absproc ] ) and present our rosseland and planck mean opacities ( sect . [ sect : rossplanck ] ) . here , we also assess the influence of lithium on the opacity for different lithium contents . before we compare our results to previous tabulations ( sect.[sect : compare ] ) , we give analytic calculations for the molecule formation timescale in sect . [ sect : chemequilibrium ] in order to estimate the time needed to reach chemical equilibrium which is one of the underlying assumptions in our calculations . finally , we summarize our conclusions in sect . [ sect : conclusion ] . primordial matter as created in the sbbn consists of hydrogen ( h ) , helium ( he ) , deuterium ( d ) , and lithium ( li ) . before wmap@xcite , the observed abundances of these elements have been used to constrain the baryon - to - photon ratio . in the framework of a @xmath15cdm cosmology wmap provided the value this parameter with high accuracy . while the abundances of h and he were fairly well known for some time , the uncertainties in the determination of the abundances of d and li were significantly reduced . now , the d abundance as derived from cosmological parameters is consistent with direct observations , while the observed li abundance still lacks a factor of 3 compared to the sbbn results . this may indicate either systematic effects in the observations or new physics ( for an in - depth discussion of this issue , see * ? ? ? we summarize the resultant abundances according to sbbn and wmap in table [ tbl : abundances ] ( after * ? ? ? * ) and take them as our _ fiducial _ pop iii mixture . for later comparison purposes we define also a li - free mixture in table [ tbl : abundances ] . .sbbn concordance abundances @xcite from first - year wmap results [ cols=""<,^,^"",options=""header "" , ] the match with the opacities ( fig . [ fig : comparisons]a ) is good as long as @xmath16 is the dominant absorption mechanism . for low temperatures , the deviations are due to the use of cia data of @xcite and @xcite while we use the more recent borysow data . the deviations at higher temperatures and densities are due to the influence of the stark broadening of h lines which have been neglected in the calculation . the comparison with @xcite is done for both rosseland and planck means ( fig . [ fig : comparisons]b&c ) . at higher temperatures and densities the deviations in the rosseland mean are again due to stark broadened h lines . for lower temperatures the deviations are only in the 20 - 30 % range , much smaller than with respect to . this is due to their use of the partially newly available cia data of @xmath17 and @xmath18 collisions for the roto - vibrational and roto - translational transitions while still having to use extrapolations for the overtones ( using data by * ? ? ? * ) . for the planck means the differences are considerably higher . this is due to the linearity of planck averaging which prefers peaks in the opacity ( cia at low temperatures , h lines at higher temperatures and lower densities ) . the comparison to the opal opacities for the grevesse & noel chemical composition at z=0 shows a much better concordance over a larger temperature range ( fig . [ fig : comparisons]d&e ) . in the high - temperature limit ( @xmath19 ) the rosseland mean opacities are consistent at the 10% level ( stark broadening ) . for the very highest temperatures , deviations are due to the approximation of the statistical weight of h by the ground state which no longer is true . at lower temperatures we again have a 10 - 20% deviation due to cia . while the inclusion of stark broadening for the rosseland means shows a good consistence with the opal data , there are deviations in the planck means . these differences are due to our coarse frequency grid which does not correctly trace all the peaks of the hydrogen lines . the comparison to the data in fig . [ fig : comparisons]f shows an overall good agreement with our data . the discussion is analogous to the opal comparison . except that now we are consistent at the 10% level accuracy for lower temperatures due to their use of @xmath20 , @xmath21 and more recent @xmath17 and @xmath18 cia data . at densities @xmath22 and temperatures @xmath23 there are , however , important differences . these are due to s use of two different approaches to calculate the @xmath24 abundance in order to overcome machine accuracy problems . in their @xmath25 dominated regime , they take a dissociation energy of @xmath26 whereas we take @xmath27 ( following * ? ? ? * ) . in our calculations , we do not find any problems regarding machine accuracy . the second reason for the deviations is probably due to the difference in @xmath28 absorption coefficients where we use the @xcite data while they use @xcite . rosseland and planck mean opacities for primordial matter have been calculated using the most recent available data for the absorption mechanisms . we tabulate the opacity data in tables e1 , e2 and e3 , for a temperature range @xmath29 and @xmath30 for our pop iii matter composition ( cf . table [ tbl : abundances ] ) . these are the first pop iii opacity tables for temperatures @xmath31 . in order to make application as easy as possible , we provide two sets of planck opacities : planck means including only continuum absorption and those including molecular lines . higher resolution tables including routines for bicubic interpolation tables are available from the authors upon request . it has been shown ( see sect . [ sect : rossplanck ] and [ sect : quantlithium ] ) that the small number fraction of li leads to a significant change in the opacity values at temperatures @xmath32k compared to a pure h / he mixture . the differences can reach up to 2 orders of magnitudes . there are four processes which change the opacity : as an alkali metal , li gets ionized at comparatively low temperatures . it therefore increases the number of available electrons considerably . they increase the thomson scattering contribution to the rosseland mean at low densities while increasing the @xmath33 absorption at higher densities . for both the planck continuum and line case only the @xmath33 absorption at low densities ( no scattering ) is enhanced . in the presence of metals ( e.g. lithium ) @xmath34 is being destroyed . as @xmath34 is the most abundant positive ion at temperatures around @xmath35 and densities @xmath36 it influences the opacity indirectly in changing the chemical equilibrium when being destroyed . furthermore , in part it shows up directly via bound - bound transitions of @xmath34 at intermediate densities . for higher densities this is being drowned by the indirect increase of the @xmath33-absorption . the planck means including line absorption are changed due to absorption by atomic li and molecular lih . for atomic li the most important transition is the @xmath37 feature . the planck function , however , is most sensible to features at @xmath37 for temperatures of approx . @xmath38 , a temperature at which li is ionized , at the latest . absorption via this transition is still important at temperatures around @xmath39 because the corresponding einstein coefficient is very large compared to the quadrupole transitions of molecular and atomic h. at temperatures @xmath40 the influence of @xmath25 is ceasing as the lowest lying transition of @xmath25 has an equivalent temperature of @xmath41 . for lower temperatures either @xmath42 or @xmath43 contribute to the opacities . , however , has got a larger dipole moment and thus has got much larger einstein coefficients and transitions at much lower temperatures ( as low as @xmath44 ) . a critical point in primordial chemistry is the formation of molecules . formation times have been calculated for @xmath25 , @xmath42 and @xmath43 . for densities @xmath45 molecule formation proceeds within one free - fall time ( except @xmath42 , which does not play any significant role in the pop iii case ) . hence the calculation is valid for densities larger than that , provided the free - fall time scale being the shortest timescale relevant , other than the chemical . we give values for densities as low as @xmath46 for numerical convenience . in comparison to previous calculations we find a good agreement of our results when neglecting the newly added absorption mechanisms and the contributions of li . based on our new opacities the influence of li on the different stages of pop iii star formation and evolution can now be assessed" +"the nature of anomalous x - ray pulsars ( axps ) has been a mystery since the discovery of the first example ( 1e 2259 + 586 ) nearly 20 years ago ( @xcite ) . the properties of axps can be summarized as follows ( see also @xcite ) : they exhibit x - ray pulsations in the range @xmath4512 s ; they have pulsed x - ray luminosities in the range @xmath5 erg s@xmath2 ; they spin down regularly within the limited timing observations available , with some exceptions ; their x - ray luminosities are much greater than the rate of loss of rotational kinetic energy inferred from the observed spin - down ; they have spectra that are characterized by thermal emission with @xmath6 kev , with evidence for a hard tail in some sources ; they are found in the plane of the galaxy ; and two of the six certain members of the class appear to be located at the geometric centers of apparent supernova remnants ( @xcite ) . soft gamma repeaters also exhibit axp - like pulsations in quiescence ( e.g. @xcite ) . mereghetti & stella ( 1995 ) suggested that axps are accreting from a low mass companion . however increasingly this model has become difficult to reconcile with observations . the absence of doppler shifts even on short time scales ( e.g. @xcite ) , the absence of a detectable optical / ir companion or accretion disk ( see @xcite ) , the apparent associations with supernova remnants , the apparent steady spin down within the limits of current observations ( e.g. @xcite ) , and axp spectra that are very different from those of known accreting sources , all argue against an accretion origin for the x - rays . recently , it has been argued that the axps are young , isolated , highly magnetized neutron stars or `` magnetars '' ( @xcite ) . evidence for this is primarily the inferred strength of the surface dipolar magnetic field required to slow the pulsar down _ in vacuo _ : @xmath7 g. the spin - down ages in this model , inferred assuming small birth spin periods , are in the range of @xmath48200 kyr . this suggested youth is supported by the two apparent supernova remnant associations . additional circumstantial supporting evidence comes from axps location close to the galactic plane , consistent with their being isolated neutron stars near their birth place , as well as from interpreting apparent deviations from spin - down as glitches ( @xcite ) similar to those seen in radio pulsars ( e.g. @xcite ) . recently , deviations from simple spin - down have been suggested , under the magnetar hypothesis , to be due to radiative precession , originating in the asphericity of the neutron star produced by the strong magnetic field ( @xcite ) . one way to test both the magnetar and accretion models is through timing observations . the spin down of some axps has been monitored by considering the measured frequency at individual epochs ( e.g. @xcite ) . however those measurements have been sparse and are only marginally sensitive to spin irregularities on time scales of weeks to months , relevant to glitches or accretion torque fluctuations . further , high - precision determination of the spin evolution over a long baseline is necessary to look for `` timing noise '' as is seen in many young radio pulsars ( e.g. @xcite ) , to obtain a reliable measurement of a braking index , and to search for precession ( @xcite ) . whether such high precision is possible to achieve with axp timing has not , until now , been established . here we report on x - ray monitoring observations made with the _ rossi x - ray timing explorer _ ( _ rxte _ ) in which , for the first time , we determine high - precision spin parameters using long - term phase - coherent timing of two axps . the sources , 1rxs j170849.0@xmath0400910(@xcite ) and 1e 2259 + 586 ( @xcite ) have periods of 11 s and 7 s , respectively . the _ rxte _ axp monitoring project is part of a larger effort to time coherently several axps . results for other sources will be presented elsewhere . our observations were made using the _ rxte _ proportional counter array ( pca ) ( @xcite ) . the detector consists of five identical multi - anode proportional counter units ( pcus ) each containing a front propane anticoincidence layer followed by several xenon / methane layers . the detector operates in the 260 kev range , with a total effective area of @xmath46500 @xmath8 and a 1@xmath9 field of view . in addition to the standard data modes , data were collected in the goodxenonwithpropane mode , which records the arrival time ( 1 @xmath10s resolution ) and energy ( 256-channel resolution ) of every unrejected xenon event as well as all of the propane layer events . to maximize the sensitivity to the targets , which have soft spectra , we restricted the analysis to unrejected events in the top xenon layer of each pcu and chose an optimal energy range for each source : absolute channels 614 ( 2.55.4 kev ) for 1rxs j170849.0@xmath0400910 and absolute channels 624 ( 2.59.1 kev ) for 1e 2259 + 586 . the observations were reduced using mit - developed software for handling raw spacecraft telemetry packet data . data from the different pcus were merged and binned at 62.5 ms and 31.25 ms resolution for 1rxs j170849.0@xmath0400910 and 1e 2259 + 586 , respectively . the data were then reduced to barycentric dynamical time ( tdb ) at the solar system barycenter using the source positions in table 1 and the jpl de200 solar system ephemeris ( @xcite ) and stored on disk as one time series per observing epoch . our strategy for attempting phase - coherent timing of these sources made use of standard radio pulsar techniques . pulse phase at any time @xmath11 can be expressed as @xmath12 where @xmath13 is a reference epoch , and @xmath14 and @xmath15 are the spin frequency and its time derivative . phase - coherent timing amounts to counting all pulses over the entire observing span . to achieve this , uncertainties in the first - gues spin parameters @xmath14 and @xmath15 must be sufficiently small that the discrepancy between observed and predicted arrival time differ by only a fraction of the period . to achieve this goal , we observed each source at two closely spaced epochs ( i.e. within one day ) , then at a third epoch several days later . this spacing was chosen to determine an initial @xmath14 , by absolute pulse numbering , of sufficient precision to predict @xmath16 for the next observation roughly one month later . subsequent monitoring was done at roughly one month intervals . once phase connection was achieved with the @xmath46 months of monitoring data , we also included public _ rxte _ archival data . for 1rxs j170849.0@xmath0400910 , the total data set consists of 19 arrival times obtained between 1998 january 13 and 1999 may 26 . for 1e 2259 + 586 , we have 33 arrival times obtained between 1996 september 29 and 1999 may 12 . our procedure included the following steps . the first barycentered , binned time series for the closely spaced set of three observations were folded at the best - estimate period determined via fourier transform , using a unique reference epoch . the folded pulse profiles were cross - correlated with a high - signal - to - noise template in the fourier domain and the phase offsets were recorded . we suppressed high - order harmonics in the pulse profile using a frequency - domain filter to avoid contamination by bin - to - bin poisson fluctuations . a precise @xmath14 was then determined by demanding that an integer number of pulses occur between each observation . profiles were then re - folded , still with respect to a fixed epoch , using the improved @xmath14 . after each new observation , this process was repeated , also including the effect of @xmath15 . phase residuals were examined to verify that there were no missed pulses , then fit with a quadratic function to determine the optimal @xmath14 and @xmath15 . uncertainties on measured pulse phases were determined using monte carlo simulations . we verified this procedure and its results by extracting absolute average pulse arrival times in tdb at the solar system barycenter from the optimally folded profiles , and using the tempo pulsar timing software package ( http://pulsar.princeton.edu/tempo ) , in common use in radio pulsar timing . best fit @xmath14 and @xmath15 for each source are given in table [ ta : parms ] . these values were measured with @xmath17 fixed at zero . corresponding arrival time residuals are shown in figures 1 and 2 . in both cases , the rms residual is @xmath40.01@xmath18 , where @xmath19 . we also tried fitting for @xmath17 ; the results are given in table [ ta : parms ] . for 1e 2259 + 586 , the fitted @xmath17 is consistent with zero ; we provide a @xmath20 upper limit . for 1rxs j170849.0@xmath0400910 , the fitted @xmath17 is marginally significant at the 4@xmath21 level ; however , a fit omitting only the first point reduces the significance to 2.6@xmath21 . we therefore quote the current best - fit value in parentheses only ; further timing observations will decide if the observed @xmath17 is truly significant . using a very simple spin - down model , we have maintained phase coherence for1rxs j170849.0@xmath0400910 and 1e 2259 + 586 with phase residuals of only @xmath41% , comparable to or smaller than those measured for most radio pulsars ( e.g. @xcite ) . this demonstrates that these axps are extremely stable rotators . this stability is consistent with the magnetar hypothesis because isolated rotating neutron stars are expected to spin - down with great regularity , as is seen in the radio pulsar population . we can compare our pulse ephemerides with past period measurements to see whether there have been a deviation from a simple spin - down law . for 1rxs j170849.0@xmath0400910 , only two previous period measurements have been reported ( @xcite ) . the pulse parameters listed in table [ ta : parms ] , extrapolated to the epochs of the previous observations , agree with the published values within uncertainties . thus , the spin - down has been regular for at least 1.4 yr prior to the commencement of our observations . for 1e 2259 + 586 , spin frequencies have been measured occasionally since 1978 ( see baykal & swank 1996 and references therein ) . figure [ fig : freq2259 ] shows the differences between previously measured spin frequencies and those predicted by our timing ephemeris ( table [ ta : parms ] ) . the error bars represent the published one standard deviation measurement uncertainties . our measured @xmath15 is not consistent with the long - term @xmath15 : all observed frequencies were significantly larger than predicted by the extrapolation of the current @xmath14 and @xmath15 . a least squares fit to the data shown in figure [ fig : freq2259 ] gives @xmath22 hz s@xmath2 , though the linear fit is poor because of apparent short - time - scale fluctuations . thus , the current value of @xmath15 , measured over the past 2.6 yr , is smaller than that of the long - term trend by @xmath23% . melatos ( 1999 ) suggests that the large magnetic field inferred in the magnetar model should result in significant deviations from sphericity of the" +"in recent years , a great deal of attention has been focused on fractional differential equations due to well describing many physical processes and phenomenons @xcite . very limited analytical methods , such as the fourier transform method , the laplace transform method and the green function method are used to solve the very special fractional differential equations . so to seek numerical methods is the center task for studies of fractional differential equations @xcite . in the history of numerical methods for fractional differential equations , liu et al . @xcite , and meerschaert and tadjeran @xcite are the first ones that developed the finite difference methods for fractional partial differential equations . the galerkin finite element methods for fractional partial differential equations is proposed by ervin and roop , for the stationary space fractional partial differential equations with two - sided riemann - liouville derivatives . they first presented a rigorous analysis of the well - posedness of the weak formulation in the framework of fractional sobolev spaces @xcite . generally speaking , one of key issues of approximating fractional differential equations is how to numerically discretice the fractional derivatives . although there have existed some studies on numerical approximations of factional integrals and fractional derivatives , high - order scheme for time fractional derivatives have not been throughly solved . this paper aims to construct new and effective the second - order mid - point approximate formula for time riemann - liouville derivative . then the established scheme is applied to time fractional cable equations in one and two space dimensions . from bibliography available , there have existed numerical studies for the fractional cable equations . for example , langlans et al . @xcite developed two implicit finite difference schemes with convergence orders @xmath12 and @xmath13 . hu and zhang proposed two implicit compact difference schemes , where the first scheme was proved to be stable and convergent with order @xmath14 by the energy method @xcite . in @xcite , quintana - murillo and yuste constructed an explicit numerical scheme for fractional cable equation which includes two temporal riemann - liouville derivatives , where they showed the stability and convergence conditions by using the von neumann method . zhuang et al . @xcite considered the one - dimensional time fractional cable equation by using the galerkin finite element method , in which the proposed method was based on a semi - discrete finite difference approximation in time and galerkin finite element method in space . the spectral method for fractional cable equation was discussed by lin et al . @xcite , where the detailed theoretical analysis was provided . as far as we know , the computational efficiency for time fractional cable equation is not high yet . besides , the high - dimensional time fractional cable equations seen not to be studied . here , we study the fractional cable equation in two space dimensions where the fractional derivative is approximated by the derived method in this paper . the unconditional stability and convergence of the established numerical algorithms are presented by the energy method . the reminder of the paper is constructed as follows . in section 2 , we establish a new second - order approximation formula for riemann - liouville derivatives . then two high - order finite difference schemes for the fractional cable equations in one and two space dimensions are proposed in sections 3 and 4 , respectively . numerical experiments are displayed in section 5 , where are in line with the theoretical analysis . remarks and conclusions are included in the last section . in the section , we propose a new second - order approximation formula for computing riemann - liouville derivatives . @xcite let @xmath15 . for given @xmath16)$ ] , its riemann - liouville derivative of order @xmath17 with lower limit @xmath18 is defined as follows @xmath19 @xcite suppose @xmath17 , @xmath20 . then the fourier transform of @xmath21-th riemann - liouville derivative of @xmath22 is @xmath23 where @xmath24 denotes the fourier transform of @xmath22 . now , we start to develop the second - order numerical approximation formula . [ th:3.1 ] denote @xmath25 define the following difference operator @xmath26 where @xmath8 is temporal stepsize . if @xmath27 , then one has @xmath28 as @xmath29 . here @xmath30 are the expansion coefficients of @xmath31 , that is , @xmath32 where @xmath33 taking the fourier transform on both sides of equation ( 1 ) then combining with equation ( 3 ) , one has @xmath34 where @xmath35 . note that @xmath36 and @xmath37 so , there exists a constant @xmath38 such that @xmath39 . then @xmath40 by using lemma 2.1 . hence , one has @xmath41 all this ends the proof . * remark : * if @xmath22 is suitably smooth and has compact support for @xmath42 , then riemann - liouville derivative @xmath43 coincides with @xmath44 . denote @xmath45 } \varpi_{\ell}^{(\alpha)}u\left(t-\ell\tau\right ) . \end{array}\ ] ] then the corresponding numerical approximation formula ( 2 ) is reduced to @xmath46 that is , @xmath47 the coefficients @xmath48 @xmath49 in equation ( 3 ) can be expressed as follows , @xmath50 where @xmath51 for convenience , take the place of @xmath21 in @xmath3 by @xmath52 which can not cause confusion , where @xmath53 . it is easy to get the following theorem . the coefficients @xmath54 can be computed recursively by the formulas . @xmath55,\;\ell\geq2 . \end{array}\right.\ ] ] the coefficients @xmath56 are nonpositive if @xmath57 where @xmath53 , that is , @xmath58 if @xmath57 , where @xmath53 . for @xmath59 and @xmath57 , one has @xmath60 g_{0}^{(1-\alpha ) } g_{\ell}^{(1-\alpha)}+\left[\frac{2-\alpha}{4 - 3\alpha}+\left(\frac{2-\alpha}{4 - 3\alpha}\right)^{\ell-1}\right]g_{1}^{(1-\alpha ) } g_{\ell-1}^{(1-\alpha)}\right.\vspace{0.2 cm}\\&&\displaystyle\left.+\sum\limits_{m=2}^{\ell-2 } \left(\frac{2-\alpha}{4 - 3\alpha}\right)^m g_{m}^{(1-\alpha ) } g_{\ell - m}^{(1-\alpha)}\right\}\left(\frac{4 - 3\alpha}{2(1-\alpha)}\right)^{1-\alpha}\vspace{0.2 cm}\\ & \leq&\displaystyle\left\{\left[1+\left(\frac{2-\alpha}{4 - 3\alpha}\right)^\ell\right ] g_{0}^{(1-\alpha ) } g_{\ell}^{(1-\alpha)}+\left[\frac{2-\alpha}{4 - 3\alpha}+\left(\frac{2-\alpha}{4 - 3\alpha}\right)^{\ell-1}\right]g_{1}^{(1-\alpha ) } g_{\ell-1}^{(1-\alpha)}\right.\vspace{0.2 cm}\\&&\displaystyle\left.+ g_{2}^{(1-\alpha ) } g_{\ell-2}^{(1-\alpha)}\sum\limits_{m=2}^{\infty } \left(\frac{2-\alpha}{4 - 3\alpha}\right)^m \right\}\left(\frac{4 - 3\alpha}{2(1-\alpha)}\right)^{1-\alpha } \vspace{0.2 cm}\\ & = & \displaystyle\left\{\left[1+\left(\frac{2-\alpha}{4 - 3\alpha}\right)^\ell\right ] \left(1-\frac{2-\alpha}{\ell}\right ) + \left[\frac{2-\alpha}{4 - 3\alpha}+\left(\frac{2-\alpha}{4 - 3\alpha}\right)^{\ell-1}\right](\alpha-1)\right.\vspace{0.2 cm}\\&&\displaystyle\left.- \frac{\alpha(\ell-1)(2-\alpha)^2}{4(4 - 3\alpha)(\alpha+\ell-3 ) } \right\}\left(\frac{4 - 3\alpha}{2(1-\alpha)}\right)^{1-\alpha}g_{\ell-1}^{(1-\alpha ) } \vspace{0.2 cm}\\ & \leq&\displaystyle\left\{\left[1+\left(\frac{2-\alpha}{4 - 3\alpha}\right)^\ell\right ] \left(1-\frac{2-\alpha}{\ell}\right ) + \left[\frac{2-\alpha}{4 - 3\alpha}+\left(\frac{2-\alpha}{4 - 3\alpha}\right)^{\ell-1}\right](\alpha-1)\right.\vspace{0.2 cm}\\&&\displaystyle\left.- \frac{\alpha(\ell-1)(2-\alpha)^2}{4(4 - 3\alpha)(\alpha+\ell-3 ) } \right\}\left(\frac{4 - 3\alpha}{2(1-\alpha)}\right)^{1-\alpha}g_{\ell-1}^{(1-\alpha)}\vspace{0.2 cm}\\&&\displaystyle + \frac{3(1-\alpha)}{2}\left[\left(\frac{2-\alpha}{4 - 3\alpha}\right)^{\ell}-\left(\frac{2-\alpha}{4 - 3\alpha}\right)^{4}\right]g_{\ell-1}^{(1-\alpha ) } \vspace{0.2 cm}\\ \end{array}\ ] ] @xmath61 here @xmath62 , \end{array}\ ] ] and @xmath63 . \end{array}\ ] ] it is somewhat tedious but easy to check that @xmath64 and @xmath65 are increasing with respect to @xmath66 . hence , @xmath67 and @xmath68 noticing that @xmath69 for @xmath59 and @xmath70 gives @xmath71 all this completes the proof . the coefficient @xmath56 are increasing with respect to @xmath72 , where @xmath53 , that is , @xmath73 if @xmath74 , where @xmath53 . here , we use mathematical induction to prove this theorem . let @xmath75 from equation ( 5 ) , one easily knows that @xmath76 . now suppose that the conclusion holds for @xmath77 , that is @xmath78 then for @xmath79 , according to theorems 2.3 and 2.4 , one gets @xmath80 \vspace{0.2 cm}\\ & \geq&\displaystyle\frac{1}{(k+1)(4 - 3\alpha)}\left[2(k+\alpha-1)(3 - 2\alpha ) + ( 2-\alpha)(3 - 2\alpha - k)\right.\vspace{0.2 cm}\\&&\displaystyle\left.-(k+1)(4 - 3\alpha)\right]\varpi_{k}^{(1-\alpha ) } \vspace{0.2 cm}\\ & = & \displaystyle\frac{2(1-\alpha)(\alpha-2)}{(k+1)(4 - 3\alpha)}\varpi_{k}^{(1-\alpha)}\geq0 . \end{array}\ ] ] the proof is thus completed . in this section , we study the following one - dimensional cable equation @xmath81 , \end{array}\eqno(6)\ ] ] with initial condition @xmath82 , \end{array}\eqno(7)\ ] ] and boundary value conditions @xmath83 , \end{array}\eqno(8)\ ] ] where @xmath84 , @xmath85 and @xmath86 are two constants , @xmath87 , @xmath88 and @xmath89 are suitably smooth functions . firstly , denote @xmath90 , @xmath91 , @xmath92 and @xmath93 , where @xmath94 are the uniform spatial and temporal mesh sizes respectively , and @xmath95 are two positive integers . let @xmath96 be defined on @xmath97 . in addition , define the following first- and second - order difference operators as , @xmath98 and fourth - order compact difference operator @xmath99 as , @xmath100 where @xmath101 is the unit operator . now we turn to derive an effective finite difference scheme for solving equation ( 6 ) , together with initial and boundary value conditions ( 7 ) and ( 8) . consider equation ( 6 ) at point @xmath102 @xmath103 applying the second - order central difference formula @xmath104 and second - order approximation formula ( 4 ) to the above equation ( 9 ) , one gets @xmath105 acting the operator @xmath99 on both sides of ( 10 ) and noticing @xmath106 one has @xmath107 in which there exists a positive constant @xmath108 such that @xmath109 . omit the local truncation error @xmath110 and denote the numerical solution of @xmath111 by @xmath112 . one can establish the following high - order compact difference scheme for equation ( 6 ) , together with ( 7 ) and ( 8) , @xmath113 @xmath114 @xmath115 for arbitrary vectors @xmath116 , we introduce the following inner products and the corresponding norms , @xmath117 it is easy know @xmath118 . next several lemmas are listed which will be used later on . @xcite [ lem.3.1 ] if @xmath119 , @xmath120 , then the following young s inequality holds , @xmath121 where @xmath122 , @xmath123 , @xmath124 and @xmath125 . ( gronwall s inequality @xcite ) [ lem.3.2 ] assume that @xmath126 and @xmath127 are nonnegative sequences , and the sequence @xmath128 satisfies @xmath129 where @xmath130 . then the sequence @xmath128 satisfies @xmath131 @xcite [ lem.3.3 ] for any grid function @xmath132 , one has @xmath133 [ lem.3.4]for any grid function @xmath132 , there exists a symmetric positive difference operator denoted by @xmath134 , such that @xmath135 obviously , the corresponding matrix of operator @xmath99 is given by @xmath136 obviously , @xmath137 is real symmetric and positive definite . hence , there exists a symmetric positive matrix denoted by @xmath138 such that @xmath139 where @xmath134 is the associate operator of matrix @xmath138 . therefore , the proof is ended . [ lem.3.5 ] for any mesh function @xmath140 , it holds that @xmath141 for @xmath59 , where @xmath21 denotes @xmath142 or @xmath143 . firstly , we have @xmath144 letting @xmath145 and noticing @xmath146 , one has @xmath147 where matrices @xmath148 and @xmath149 are @xmath150 and @xmath151 by the grenander - szeg theorem @xcite , if the generating function of matrix @xmath152 is nonnegative , then matrix @xmath152 is positive semi - definite . so , we only consider the generating function of matrix @xmath152 which is @xmath153 where @xmath154 because @xmath155 is a real value and even function , we only consider the case of @xmath156 $ ] for @xmath155 . from the above formula , it is easy to know that only function @xmath157 needs to be studied for @xmath59 . let @xmath158,\;\alpha\in(0,1 ) . \end{array}\ ] ] one has @xmath159 ^ 2+\left[(2-\alpha)\sin(x)\right]^2}\geq0 \end{array}\ ] ] which implies that @xmath160 is an increasing function with respect to @xmath161 . and @xmath162 hence , @xmath163 it immediately follows that @xmath164 so the proof is completed . in the following , the first step is to prove the solvability of finite difference scheme ( 11 ) , together with ( 12 ) and ( 13 ) . the finite difference scheme ( 11 ) , together with ( 12 ) and ( 13 ) is uniquely solvable . consider the homogeneous form of system ( 11 ) , @xmath165 taking the inner product of ( 11 ) with @xmath166 gives @xmath167 it follows from lemma [ lem.3.3 ] that @xmath168 that is , @xmath169 . this finishes the proof . now , we give the stability result . the finite difference scheme ( 11 ) , together with ( 12 ) and ( 13 ) is unconditionally stable with respect to the initial value . let @xmath112 and @xmath170 be the solutions of the following two equations , respectively , @xmath171 and @xmath172 denote" +"the outbreak of ebola virus disease ( evd ) in west africa 2014 revealed many challenges in predicting and controlling the spread of infectious diseases . these challenges are partly related to the mathematical modeling of the dynamics of the epidemic . providing accurate predictions appeared to be extremely difficult . to address these challenges , several new models have been suggested each providing quite different results , for example @xcite . we also note that different aspects of possible control have been intensively studied in the literature including distribution strategies for vaccination and antibiotic programs @xcite as well as travel restrictions @xcite . in this paper we concentrate on the development of models that are well suited to the control of an outbreak . the most commonly studied models in this area deal with temporal networks @xcite where several different models have been suggested . in @xcite the 1995 ebola outbreak in congo is considered using an seir model whereby control intervention , performed at time @xmath0 is described by the transmission coefficient @xmath1 defined by @xmath2 if @xmath3 and @xmath4 for @xmath5 where @xmath6 is the initial transmission rate that would remain stable without the intervention . our paper models and studies an alternative control mechanism to decrease in the transmission of infection based on the model developed in @xcite where the transmission of infection depends mainly on two parameters : the transmission rate @xmath6 and the average time of isolation @xmath7 in contrast to @xcite we assume that the transmission rate @xmath6 does not change over the whole period under consideration . the main dynamic parameter in our model is @xmath8 and all the intervention measures are directed at decreasing @xmath8 and consequently reducing the spread of infection . the average time to hospitalization can be used for the average time of isolation @xmath9 although the isolation of infectious population is not exactly the same as hospitalization "" . clearly , as the disease progresses hospitals become short on beds ( as well as staff and supplies ) required to isolate and treat all newly infected individuals . as a result , the number of infected population can grow exponentially . this was the case for the ebola virus epidemic in west africa ( guinea , sierra leone and liberia ) where the spread of infection was highly dangerous during june - november 2014 when the capacity for treating ebola patients was insufficient . it was reported @xcite that during this period ... many clinics and hospitals in all three of the countries worst hit by ebola have effectively been shut down "" . after rapidly building new infrastructure and increasing the capacity of beds the outbreak slowed down significantly . starting from january 2015 , the epidemic has moved to the ending phase that involves ensuring capacity for case finding , case management , safe burials and community engagement "" ( @xcite - who , ebola situation report , 28 jan 2015 ) . note that in @xcite the hospitalization rate was the parameter showing the greatest change . addressing these issues , this paper suggests new mathematical models that can be used to increase the efficiency of available resources . the main goal here is to keep the model as simple as possible and , at the same time , to have measurable control variables . note that there are many useful control measures that have been intensively studied by introducing more detailed "" mathematical models , however such models have less predictive capabilities ( due to overfitting ) . prediction is crucial when considering future planning periods . the main component in the suggested model is the optimal distribution of bed capabilities across countries / regions . this is a very important and difficult problem that requires an accurate prediction of the dynamics of infected population in each region . for example , evaluating the situation of the ebola outbreak , who s ebola situation report on 14 jan 2015 @xcite notes that each of the intense - transmission countries has sufficient capacity to isolate and treat patients , with more than 2 treatment beds per reported confirmed and probable case . however , the uneven geographical distribution of beds and cases , and the under - reporting of cases , means that not all evd cases are isolated in several areas . "" in @xcite a new model is introduced to study the dynamics of epidemics by considering the average time for isolation ( denoted by @xmath8 ) of infectious population as a time - dependent parameter . this model is derived from the well studied @xmath10 ( susceptible - infectious - recovery ) model ( e.g. @xcite ) and is similar to models based on transmission rates from infectious population at different generations ( e.g. @xcite ) . the use of time - dependent parameter @xmath8 enables the analysis of future scenarios by considering possible changes in @xmath7 in this paper we extend this approach by developing practical and efficient optimal control models . we denote by @xmath11 the number of infected cases at @xmath12 ( in days ) . assuming that the natural death rate of population ( @xmath13 ) is zero , the equation for @xmath11 is as follows ( see @xcite for more details ) @xmath14 here @xmath15 is the death rate due to disease ; @xmath16 is the average latent period ( in days ) for infected individuals to become infectious ; @xmath8 is the average infectiousness period ( in days ) ; it is the average time required for isolation ( time to hospitalization ) ; and @xmath6 is the transmission rate . moreover , @xmath17 is a gamma ( cumulative ) distribution function ( with p.d.f - @xmath18 ) for deaths due to disease . the fraction @xmath19 in this case represents the proportion of remaining infected cases @xmath20 after @xmath21 days . the sum @xmath22 defines the number of `` active '' infectious population at time @xmath23 it represents the number of infectious population that are not yet isolated and therefore it is the only source of secondary infections . ( for the sake of simplicity we do not consider infections in hospitals and death ceremonies ) . then by setting @xmath24 we obtain model ( 1 ) in @xcite where @xmath13 ( the natural death rate ) in our case is zero . the basic reproduction number @xmath25 is calculated by considering the stationary states in ( [ x ] ) : @xmath26.\ ] ] there are three main parameters in ( [ x ] ) - @xmath27 and @xmath7 the results obtained in @xcite show that this model provides quite good approximation to the total number infected cases and deaths during the current ebola epidemic if @xmath8 is a piecewise constant function ( in fact , constant over consequent subintervals with durations 2 - 3 months ) and the parameters @xmath15 and @xmath6 are constant over the whole period . these results help us to predict the dynamics of an infected population at future time intervals by keeping the values of @xmath15 and @xmath6 unchanged ( estimated from the previous period ) and considering different possible changes in @xmath7 in this case the major strategy of preventive intervention is the achievement of some decrease in @xmath8 that according to ( [ r ] ) is equivalent to decreasing the effective reproduction number . this approach is implemented below by introducing an optimal control models where the average time to hospitalization @xmath8 is the key variable . according to the results of data fitting mentioned above , it is sufficient to let @xmath8 be constant on quite long time intervals ( months ) . + * control @xmath28 . * therefore , we define @xmath29 as a control variable by assuming that it is piece - wise constant with integer values ( days ) . for the sake of simplicity let @xmath30 , ~ j = 1 , 2 , \cdots , p.\ ] ] it is reasonable to assume that @xmath31 where @xmath32 is the minimal number of days required to isolate infectious population . + * trajectory @xmath33 . * given control @xmath28 we define trajectory @xmath34 as follows @xmath35 in this formula the sum @xmath36 represents the number of infectious individuals that are not yet isolated . considering the average length of hospital stay ( in days ) , the number of hospitalized cases at @xmath37 can be calculated as @xmath38 note that , recent studies ( see for example @xcite ) show that @xmath39 is around 6.5 days . in this section we provide some numerical experiments based on data from guinea , sierra - leon and liberia . we consider the cumulative number of infectious cases and deaths denoted by @xmath40 and @xmath41 respectively . they can be calculated as here @xmath44 is the death rate of infectious population in generation @xmath45 and @xmath46 is a large number . parameters of the gamma distribution function @xmath47 are taken from @xcite where @xmath48 with mean value 7.5 . moreover , we set @xmath49 and @xmath50 as in @xcite . in the considered model ( [ xrt ] ) there are only three parameters @xmath15 and @xmath6 ( constants ) and a piece - wise constant control function @xmath29 that need to be optimized to fit data - the total number of infectious population and deaths . the aim here is to show that there exists a control @xmath29 such that the corresponding trajectory @xmath11 fits data well . + we consider three consequent intervals @xmath51 $ ] @xmath52 for each country and find optimal values @xmath53 @xmath6 and @xmath54 @xmath52 where @xmath55 the results are presented in table [ table_r_k ] . the last time point @xmath56 is 01-mar-2015 . the values of @xmath57 are as follows : 22-march , 23-may , 20-july and 04-dec-2014 for guinea ; 27-may , 20-june , 20-august and 04-dec-2014 for sierra leone ; and 16-june , 20-july , 07-sept and 04-dec-2014 for liberia . each interval @xmath58 has its own reproduction number @xmath59 that defines the shape of the best fits presented in figure [ fig02 ] . data were retrieved from the who website @xcite for the cumulative numbers of clinical cases ( confirmed , probable and suspected ) collected till 1 march 2015 . the global optimization algorithm dso in global and non - smooth optimization ( ganso ) library @xcite is applied for solving optimization problems in this section as well as in section [ example ] . .results of best fits : the ( effective ) reproduction numbers @xmath59 and average times to hospitalization @xmath54 ( in days ) for different intervals @xmath60 @xmath61 the optimal values for @xmath15 and @xmath6 are also provided ; they are constant for a whole period [ cols=""^,^,^,^,^,^,^"",options=""header "" , ] 99 c.l . althaus . estimating the reproduction number of ebola virus ( ebov ) during the 2014 outbreak in west africa . , 2014 ( http://currents.plos.org/outbreaks/article/estimating-the-reproduction-number-of-zaire-ebolavirus-ebov-during-the-2014-outbreak-in-west-africa/ ) . g. chowell , n. w hengartner , c. castillo - chavez , p.w . fenimore , and j.m . the basic reproductive number of ebola and the effects of public health measures : the cases of congo and uganda . , 229(1):119126 , 2004 ." +"active magnetic bearings ( ambs ) are being employed in a variety of rotating machines ( e.g. , compressors , milling spindles , and flywheels ) in place of conventional mechanical bearings . due to the non - contact nature of the magnetic bearings and rotor , ambs have the unique ability to suspend loads with no friction , operate rotors at higher speeds , and operate in applications where the use of lubricants is prohibited . since ambs can be actively controlled , they offer other potential advantages over mechanical bearings , viz . , the elimination of vibration through active damping , the adjustment of the stiffness of the suspended load , and the automatic balancing of rotors . ambs are normally operated with all electromagnets active at all times . an alternative mode of operation is to activate only one electromagnet along each direction at any given time . although posing more difficulty to the control design , this switching operation prevents opposing electromagnets from producing counteracting forces , and thus helps reduce power consumption . typically , an amb is operated by introducing a sufficiently high , fixed magnetic flux in each electromagnet , which is referred to as the _ bias flux_. the bias value is normally set to a fraction of the saturation flux of the electromagnet . this procedure facilitates the design of the amb ` control ' flux , which is superimposed on the bias flux . specifically , this conservative practice allows the system to be modeled by a controllable linear system , thus , enabling the use of linear control design techniques ; see for example @xcite . although the bias flux facilitates the control synthesis , it increases electric power losses in the amb system , causing rotor heating and affecting the machine efficiency . while lowering or eliminating the bias flux is desirable in order to minimize power losses , it enhances the amb system nonlinearities and may lead to a control saturation or singularity . due to these conflicting objectives , the design of amb controllers with reduced power loss is a challenging problem . in this paper , we consider the problem of low - bias control of ambs operating in the switching mode with the constraint that the input voltages are amplitude limited . this problem was previously addressed in @xcite using the nested saturation design method of teel @xcite . in addition , an optimal solution was sought to the power - loss minimization problem under voltage saturation in @xcite . ( a comprehensive literature review of low- , asymptotic - zero- , and zero - bias amb controllers _ without _ voltage saturation can be found in @xcite . ) here , we pursue a different approach to stabilizing the amb model of @xcite . namely , we use a _ forwarding - like _ method @xcite to design a control law of arbitrarily small amplitude that renders the amb system globally asymptotically stable ( gas ) to the origin . the main differences between our approach and @xcite are : ( i ) we allow the use of different saturation functions ( both ` hard ' and ` soft ' ) , thus providing more flexibility in the control implementation , and ( ii ) we provide an explicit construction for a ` global ' control lyapunov function ( clf ) for the system . this contrasts with the result of @xcite , which relies on the standard ` hard ' saturation and whose lyapunov - like function is only an ` asymptotic ' clf for the system , i.e. , a clf only when the system operates in a certain region of the state space . the rest of this paper is organized as follows . in section [ model ] , we introduce the amb model and motivate our stabilization problem . in section [ sec3 ] , we prove a lemma that constructs a stabilizing controller of arbitrarily small amplitude and a clf for a three - dimensional chain of integrators . in section [ sec4 ] , we use our lemma to construct a clf and corresponding stabilizing feedback for the amb model . we provide a numerical example in section [ sec5 ] , and we close in section [ sec6 ] with a summary of our work . the original nonlinear electromechanical model of the one degree - of - freedom amb system shown in figure 1 below can be subdivided into the mechanical subsystem dynamics , the magnetic force equation , and the electrical subsystem dynamics . the mechanical subsystem is governed by @xmath0 where @xmath1 is the rotor mass , @xmath2 represents the position of the rotor center , @xmath3 is the magnetic flux in the @xmath4th electromagnet , @xmath5 denotes the force produced by the @xmath4th electromagnet , given by @xcite @xmath6 @xmath7 is the permeability of air , and @xmath8 is the cross - sectional area of the electromagnet . the electrical subsystem is governed by the equations @xcite @xmath9 where @xmath10 denotes the number of coil turns in the electromagnet , @xmath11 is the resistance of the @xmath4th electromagnet coil , @xmath12 is the input control voltage of the @xmath4th electromagnet , @xmath13 is the current in the @xmath4th electromagnet which is related to the flux according to @xcite @xmath14 and @xmath15 is the nominal air gap . in this paper , we use the new form proposed in @xcite for the amb dynamics in the switching mode of operation . we only outline the model derivation here , and refer the reader to @xcite for the details and justification . consider that the flux is given by @xmath16 where @xmath17 is the constant _ bias _ flux and @xmath18 is the _ control _ flux . generalized _ control flux be defined as @xmath19 and consider the voltage switching strategy @xmath20 where @xmath21 is the _ generalized _ control voltage . based on ( [ flux])-([switch ] ) , the amb model ( [ mech])-([elec ] ) has the equivalent form @xmath22 where @xmath23 and the coil resistance was neglected for simplicity . now , consider that the input voltages to the original amb model are amplitude limited , i.e. , @xmath24 , @xmath25 where @xmath26 is the known limit . defining the states @xmath27 , @xmath28 , and @xmath29 and the change of input @xmath30 , the above model becomes @xmath31 where @xmath32 and @xmath33 , with the input constraint @xmath34 . our goal in this work is to design a feedback control law @xmath35 , satisfying the above saturation constraint , such that @xmath36 is gas where @xmath37 . the gas property means there is a continuously differentiable ( @xmath38 ) function @xmath39 that is radially unbounded and zero only at the origin , and for which the derivative @xmath40 along all trajectories of the system in closed - loop with the controller @xmath35 is negative definite . a function @xmath41 satisfying these requirements for some feedback @xmath35 is called a clf for ( [ xdot amb ] ) @xcite . see @xcite for a discussion on the relation between the global asymptotic stability of @xmath42 and the stability of the original amb states . in the following lemma , we use a forwarding - like approach based on @xcite to construct a clf and corresponding stabilizing state feedback of arbitrarily small amplitude for a three - dimensional chain of integrators . we let @xmath43 denote the standard saturation projecting @xmath44 onto @xmath45 $ ] , i.e. , @xmath46 when @xmath47 and @xmath48 otherwise . however , see remark 1 below for a version of our construction where the hard saturation @xmath43 is replaced by a smoother function . [ mainlemma ] consider the chain of integrators @xmath49 where @xmath50 is the control input . let @xmath51 be given and @xmath52 define the change of variables @xmath53 and the functions @xmath54 g(z_{1},z_{2},z_{3 } ) & = & \frac{\delta } { c_{1}}\sigma ( z_{1})+4\left ( 1+u(z_{2},z_{3})\right ) \nonumber \\ & & \times \left ( z_{3}+\sigma ( z_{2})\right ) -\frac{\delta } { 2}\left ( z_{2}+z_{3}\right ) . \label{g}\end{aligned}\ ] ] then the function @xmath55 is a clf for ( [ chain ] ) since its derivative along the trajectories of system ( [ chain ] ) in closed loop with the control @xmath56 is negative definite . in particular , the bounded control ( [ ubar ] ) renders ( [ chain ] ) gas to the origin . the saturation function @xmath43 from lemma [ mainlemma ] is lipschitz continuous but not continuously differentiable . we chose this hard saturation for simplicity of analysis . however , one can prove a similar result with smoother saturation functions . for example , if one instead chooses the @xmath57 function @xmath58 \\ \mathrm{sign}(s)\left [ 1+\frac{1}{\pi } \tan ^{-1}\left ( \pi \left ( \left| s\right| -1\right ) \right ) \right ] \quad \mathrm{if}\;|s|>1 , \end{array } \right . \label{sigma}\]]then the only change in the statement of lemma [ mainlemma ] is to the right - hand side of the inequality ( [ delta cond ] ) . the proof for this saturation is similar to the proof we give below . condition ( [ delta cond ] ) in lemma [ mainlemma ] allows cases where @xmath59 is arbitrarily large and @xmath60 is as small as desired , as well as cases where @xmath61 is arbitrarily small , including the case where @xmath62 $ ] . we use ( [ z ] ) and @xmath63 , where @xmath64 is the new control input , to transform ( [ chain ] ) into @xmath65 we first perform a lyapunov - type analysis on the @xmath66-subsystem using the function @xmath67 where @xmath68 was defined in ( [ uu ] ) . by separately considering the cases where @xmath69 and @xmath70 , one can easily verify that ( [ v1 ] ) is positive - definite and radially unbounded for @xmath71 . in fact , if @xmath70 , then @xmath72 on the other hand , if @xmath69 , then @xmath73 , so @xmath74 the time derivative of ( [ v1 ] ) along the trajectories of the @xmath66-subsystem is given by @xmath75 \alpha . \label{v1dot1}\end{aligned}\ ] ] since @xmath76 and @xmath77 @xmath78 give @xmath79 ( [ v1dot1 ] ) becomes @xmath80 \alpha . \label{v1dot2}\end{aligned}\ ] ] we now distinguish between two cases : 1 . then @xmath81 , @xmath82 , and since @xmath83 , we get @xmath84 \alpha . \label{v1dot3}\end{aligned}\ ] ] 2 . then @xmath85 sign@xmath86 , @xmath87 , and @xmath88 + since @xmath83 , applying ( [ integral ] ) to ( [ v1dot2 ] ) again yields ( [ v1dot3 ] ) . thus ( [ v1dot3 ] ) holds for all @xmath89 . finally , we perform a lyapunov - type analysis on the whole system ( [ zdot ] ) using the positive definite radially unbounded function @xmath41 from ( [ clf ] ) . since @xmath90 , where @xmath91 was defined in ( [ v1 ] ) , it follows from ( [ v1dot3 ] ) that the time derivative of ( [ clf ] ) along the system trajectories satisfies @xmath92 \alpha . \label{vdot1}\end{aligned}\ ] ] we again distinguish between two cases : 1 . then @xmath93 , so ( [ vdot1 ] ) gives @xmath94 \alpha . \label{vdot2}\end{aligned}\ ] ] 2 . . then ( [ integral ] ) holds and since @xmath95 and @xmath96 , we again get ( [ vdot2 ] ) . thus , ( [ vdot2 ] ) holds for all @xmath89 . using @xmath97 and ( [ g ] ) , ( [ vdot2 ] ) becomes @xmath98 by separately considering the cases @xmath99 @xmath100 and @xmath101 , i.e. , @xmath40 is negative definite . one can easily verify that the origin is a unique equilibrium point of ( [ zdot ]" +"the dynamics of micron and nanoscale cantilevers are important to a wide variety of technologies . for example , the invention of the atomic force microscope ( afm ) @xcite , which relies upon the dynamics of a cantilever a few hundred microns in length , has revolutionized surface science paving the way for direct measurements of intermolecular forces and topographical mappings with atomic precision for a broad array of materials including semiconductors , polymers , carbon nanotubes , and biological cells @xcite ( see @xcite for current reviews ) . in conventional dynamic atomic force microscopy the cantilever is used to measure the force interactions between the cantilever tip and sample . cantilevers smaller than conventional afm have also been used to unfold single protein molecules with improved force and time resolution @xcite . it has also been proposed to exploit the inherent thermal motion of small cantilevers to make dynamic measurements of single molecules @xcite . a passive undriven cantilever placed in a viscous fluid will exhibit stochastic oscillations caused by the thermal bombardment of fluid molecules by brownian motion . in fact , measuring the thermal spectra of the cantilever is a commonly used afm calibration technique @xcite . in all of these applications the ultimate force sensitivity of a particular measurement is limited by the inherent thermal noise of the experimental system . there are at least two ways to improve upon this limitation : ( i ) make the cantilevers smaller @xcite , ( ii ) use correlated measurements of multiple cantilevers @xcite . uniformly decreasing the dimensions of a cantilever results in the favorable combination of decreasing the cantilever s equivalent spring constant while increasing its resonant frequency yielding improved force sensitivity and time resolution . by measuring the cross - correlations between two cantilevers in fluid the independent fluctuations of the two do not contribute , leaving only the smaller correlated fluctuations due to coupling through the fluid . this type of approach has been used to measure femtonewton forces on millisecond time scales between two micron scale beads placed in separate optical traps ( an improvement of a hundredfold from prior measurements ) @xcite . the ability to significantly increase the force resolution by making correlated measurements has yet to be exploited for micron and nanoscale cantilevers . the magnitude of the fluid coupled noise will depend upon the spacing and exact geometries of the cantilevers . combining ( i ) and ( ii ) and measuring the correlations of multiple nanoscale cantilevers offer the potential for experimental measurements with unprecedented force and time resolution @xcite . as experimental measurement continues to push toward the stochastic limit it is important that we build a physical understanding of the stochastic dynamics of micron and nanoscale cantilevers for the precise conditions of experiment including complex cantilever geometries @xcite , the effects of nearby walls @xcite , and the fluid - coupled dynamics of multiple cantilevers in an array configuration @xcite . although micron and nanoscale cantilevers exhibit stochastic motion due to the thermal motion of matter the elastic structures are still large compared to individual fluid molecules and the equations of continuum mechanics remain valid . in what follows we are concerned with situations where the knudsen number ( the ratio of the mean free path of the fluid particles to the width of a cantilever ) remains sufficiently small so that this statement remains true . this means that the fluid is described by the usual navier - stokes equations with no - slip and stress continuity boundary conditions at the solid surfaces . the navier - stokes equations governing the motion of an incompressible fluid , and written in nondimensional form , are @xmath0 where @xmath1 is the fluid velocity , @xmath2 is the pressure , and @xmath3 is time . there are two inertial terms on the left hand side of eq . ( [ eq : ns ] ) multiplied by the nondimensional parameters @xmath4 and @xmath5 . the strouhal number @xmath6 plays the role of a frequency based reynolds number expressing the ratio between local inertia forces and viscous forces where @xmath7 and @xmath8 are characteristic length and time scales , respectively . the velocity based reynolds number @xmath9 expresses the ratio between convective inertial forces and viscous forces . micron and nanoscale cantilevers are characterized by high oscillation frequencies and small oscillation amplitudes . in this case @xmath10 so that the nonlinear convective inertial term @xmath11 is negligible and the equations become linear . however , the strouhal number , @xmath12 ( using the half - width @xmath13 as the appropriate length scale ) is often not negligible . as a result , the local inertia term must be kept in eq . ( [ eq : ns ] ) making the analysis more difficult . in addition , experimentally motivated cantilevers are often of complex geometry , near surfaces , or in an array configuration with multiple cantilevers in close proximity . these difficulties have led to the development of a thermodynamic approach to calculate the stochastic dynamics of micron and submicron scale cantilevers for the precise conditions of experiment ( discussed below ) @xcite . in the following it is assumed that @xmath5 is negligible , and we leave off the subscript denoting @xmath14 by @xmath15 . the fluid equations are coupled with the governing equations of elasticity , @xmath16 where @xmath17 is the stress tensor , @xmath18 is the cantilever density , and @xmath19 is the cantilever deflection . equations ( [ eq : ns]),([eq : mass ] ) , and ( [ eq : beam ] ) represent the governing deterministic continuum equations . if one considers lengths scales on the order of a few atomic lengths these equations would include stochastic terms @xcite . this represents a difficult fluid - solid interaction problem governing the stochastic cantilever dynamics . a brute force molecular dynamics approach which would resolve the stochastic motion of all of the fluid and solid molecules is computationally prohibitive however , the system is always near equilibrium permitting a much more accessible thermodynamic based solution strategy . the paper is organized as follows . a very general thermodynamic approach , valid for complex geometries as well as for arrays of closely spaced cantilevers , is discussed in section [ section : thermodynamic_approach ] . analytical theory based upon the thermodynamic approach , valid for long slender cantilevers , is discussed in section [ section : analytical_theory ] . in section [ section : micron_scale_beam ] a micron scale cantilever , similar to an atomic force microscope , is explored and in section [ section : nanoscale_cantileves ] the stochastic dynamics of an array of experimentally motivated nanoscale cantilevers are quantified using the thermodynamic approach with deterministic finite element numerical simulations to generate results for the precise conditions of experiment . a general discussion of the approach can be found in ref . @xcite . . in the thermodynamic approach of section [ section : thermodynamic_approach ] a step force @xmath20 is removed from the cantilever on the left and the deterministic cantilever deflections @xmath21 and @xmath22 are calculated.,width=288 ] the thermodynamic approach discussed here is based upon the fluctuation - dissipation theorem which states that for equilibrium systems the manner in which the system returns from a linear macroscopic perturbation is related to time correlations of equilibrium microscopic fluctuations @xcite . underlying this statement is the fact that equilibrium fluctuations and the dissipation of the system responding to a macroscopic perturbation are governed by the same physics . for the case of miniature elastic objects in a fluid the dissipation is dominated by the fluid viscosity and the fluctuations by the motion due to the bombardment by the fluid molecules . in what follows , we assume that all of the dissipation comes from the fluid and that elastic dissipation in the cantilever is negligible . this assumption , however , is not required and other sources of dissipation could be included if desired . the essence of our approach is to calculate the dissipation _ deterministically _ and to use the fluctuation - dissipation theorem to determine the cantilever s dynamics . the approach is exact and the only assumptions that have been made are classical dynamics and linear perturbations from equilibrium . the deterministic calculation of the dissipation can come from analytical theory , simplified models , or from detailed numerical simulations . the major benefit of this approach is that the deterministic calculations are straightforward , not computationally prohibitive , and methods of calculation are sophisticated and readily available . we will introduce the use of the thermodynamic approach for the case of two opposing cantilevers as shown in fig . [ fig : adjacent ] . consider one dynamical variable to be the stochastic displacement of the cantilever on the left @xmath23 where @xmath23 is a function of the microscopic phase space variables consisting of @xmath24 coordinates , @xmath25 , and conjugate momenta , @xmath26 , of the system and @xmath27 is the number of particles in the system . the statistical treatment that follows determines the ensemble average of the cantilever deflections @xmath23 over all experimental possibilities . for the undisturbed equilibrium system the ensemble average , and correlations , are denoted as @xmath28 . we now take the system to a prescribed macroscopic excursion from equilibrium and observe how the system returns to equilibrium . the macroscopic cantilever deflection as it returns to equilibrium from a prepared initial condition will be denoted as @xmath21 . for clarity of presentation , lower case variables are reserved for stochastic quantities and upper case variables are for deterministic quantities . the connection between the stochastic and deterministic quantities is particularly straightforward when the excursion from equilibrium is achieved through the application of a step force some time in the distant past that is removed at time @xmath29 , i.e. the force given by , @xmath30{cc}f_1 & \text{for } t \le 0\\ 0 & \text{for } t > 0 . \end{array } \right . \label{eq : step_force}\ ] ] the applied force should be conjugate to the variable for which the fluctuations are to be calculated . for the cantilever system under consideration here , to determine the fluctuations of the tip displacements , the force is applied to the tip of the left cantilever . the step force couples with the cantilever deflection @xmath23 and the full hamiltonian of the system @xmath31 is given by , @xmath32{cc}h_0 + \delta h & \text{for } t \le 0\\ h_0 & \text{for } t > 0 \end{array } \right . \label{eq : hamiltonian}\ ] ] where @xmath33 and @xmath34 is the unperturbed hamiltonian . for small perturbations , @xmath20 , the quantity @xmath35 will also be small , and the results are greatly simplified . the nonequilibrium ensemble average @xmath21 is given by , @xmath36 where @xmath37 , @xmath38 is boltzmann s constant , and @xmath8 is the absolute temperature . in eq . ( [ eq : noneq_ave ] ) the notation @xmath23 is used to represent the value of @xmath39 evaluated at the phase space coordinates that have evolved from the values @xmath40 and @xmath41 at time @xmath29 @xcite . in the limit of linear perturbations , @xmath42 , this simplifies to , @xmath43 where an equilibrium ensemble average is given by , @xmath44 if we now assume that @xmath39 and @xmath45 have the equilibrium average @xmath46 subtracted and recall that @xmath47 , we have our desired result , @xmath48 which can be rearranged to yield , @xmath49 the analysis is similar for the cross correlations of the deflections for two cantilevers in an array , @xmath50 where @xmath51 is the displacement of tip 2 arising from the step force @xmath20 applied to tip 1 . it is interesting to highlight that the cantilever motions are indeed correlated as indicated by eq . ( [ eq : cross" +"in this article we extend previous work which combined the two fields of quantum information and ultra - cold bosons to propose a method for the fabrication of spatially isolated entangled atomic populations @xcite . we do this by comparing the performance of a three - well bose - hubbard system @xcite to that of an optical beamsplitter for the production of spatially separated output modes , using well - known criteria @xcite . in particular , we consider the quadrature based criteria @xcite which were not considered in the earlier paper . the field of ultra - cold bosons has seen much experimental and theoretical investigation since the successful bose condensation of bosonic atoms . for atoms trapped in an optical lattice , one investigative technique uses the bose - hubbard model . this model , from condensed matter physics , was originally shown by jaksch @xcite to provide an accurate description of bosonic atoms trapped in a deep optical lattice . in this work we use a three well bose - hubbard model to propose and analyse the entangling properties of a quantum atom optical mode splitter and recombiner . we show that this can split an initial condensate in the central well into two separated entangled condensates , with the detection of the entanglement being sensitive to both the initial quantum state of the condensate in the central well , and to the actual criteria used . we then examine and compare a quantum optical beamsplitter with one vacuum input with regard to the same correlations and input quantum states . the area of continuous - variable entanglement is very active @xcite , with many criteria having been developed to signify the presence of inseparability and entanglement , especially in bipartite systems . many of these only apply fully to gaussian systems and gaussian measurements . the most commonly used measurements are those developed by duan @xcite and simon @xcite , using combinations of quadrature variances . more recently , teh and reid have shown the degree of violation of these inequalities that is necessary to demonstrate not just inseparability , but genuine entanglement @xcite , as these are only necessarily the same property for pure states . the criteria we use in this work fall into two categories . those in the first category were developed by hillery and zubairy @xcite and expanded on by cavalcanti @xcite to cover multipartite entanglement , steering , and violations of bell inequalities . as shown by he @xcite , the hillery and zubairy criteria are well suited to number conserving processes such as those of interest here . the second category are quadrature based criteria , originally developed by duan @xcite and simon @xcite for inseparability and entanglement , and by reid @xcite for demonstrations of the einstein - podolsky - rosen ( epr ) paradox @xcite . multi - mode entanglement in bose - einstein condensates ( bec ) has been predicted and examined in the processes of molecular dissociation @xcite , four - wave mixing in an optical lattice @xcite , and in the bose - hubbard model @xcite . in the latter case the separation of the modes is produced by the tunneling between wells , in both the continuous @xcite and pulsed tunneling configurations @xcite . the quantum correlations necessary to detect entanglement can in principle be measured using the interaction with light @xcite , or by homodyning with other atomic modes @xcite . we note here that the entanglement we are examining is a collective property between atomic modes which are spatially separated , and is not between individual atoms @xcite . this point , which is unavoidable for indistinguishable bosons , has previously been raised by chianca and olsen @xcite , and was recently put on a formal basis , using the language of quantum information theory , by killoran @xcite . we will follow the approach taken by milburn @xcite , generalising this to three wells @xcite , and solving either the heisenberg equations of motion or the fully quantum positive - p phase space representation @xcite equations , depending on whether there is a collisional interaction present or not . we consider these to be the most suitable approaches here because they are both exact , allow for an easy representation of mesoscopic numbers of atoms , can be used to calculate quantum correlations , and can simulate different quantum initial states @xcite . just as importantly , both calculations scale linearly with the number of sites and can in principle deal with any number of atoms . one disadvantage of the positive - p representation is that the integration can show a tendency to diverge at short times for high collisional nonlinearities @xcite . as long as the procedures followed to derive the fokker - planck equation for the positive - p function are valid @xcite , the stochastic solutions are guaranteed to be accurate wherever the integration converges . with all the results shown here , the solutions were found without any signs of divergences . the system is very simple , with three potential wells in a linear configuration . each of these can contain a single atomic mode , which we will treat as being in the lowest energy level . atoms in each of the wells can tunnel into the nearest neighbour potential , with tunneling between wells @xmath1 and @xmath2 , and @xmath2 and @xmath3 . with all the population initially in the middle well , the system acts as a time dependent mode splitter and recombiner . with the @xmath4 as bosonic annihilation operators for atoms in mode @xmath5 , @xmath6 representing the coupling between the wells , and @xmath7 as the collisional nonlinearity , we may now write our hamiltonian . following the usual procedures @xcite , we find @xmath8 for the case where the collisional interaction between the atoms is set to zero , we find that an analytical solution of the heisenberg equations of motion for the system operators is possible . the heisenberg equations of motion are found as @xmath9 = \left[\begin{array}{cccccc } 0 & 0 & -ij & 0 & 0 & 0 \\ 0 & 0 & 0 & ij & 0 & 0 \\ -ij & 0 & 0 & 0 & -ij & 0 \\ 0 & ij & 0 & 0 & 0 & ij \\ 0 & 0 & -ij & 0 & 0 & 0 \\ 0 & 0 & 0 & ij & 0 & 0 \end{array}\right ] \times \left [ \begin{array}{c } \hat{a}_{1}(0 ) \\ \hat{a}_{1}^{\dag}(0 ) \\ \hat{a}_{2}(0 ) \\ \hat{a}_{2}^{\dag}(0 ) \\ \hat{a}_{3}(0 ) \\ \hat{a}_{3}^{\dag}(0 ) \end{array } \right ] . \label{eq : heisenberg}\ ] ] this set of linear operator equations is readily solved , having the solutions @xmath10 where we have made the substitution @xmath11 for reasons of notational elegance . these equations allow us to find analytical expressions for all the correlations of interest , as we shall do further on in the article . we can also solve the heisenberg equations in terms of @xmath12 and @xmath13 , the quadrature operators . setting @xmath14 we find @xmath15 which then allow us to find solutions for any correlations written in terms of these quadratures . examples of these are the quadrature squeezing @xcite and reid epr correlations @xcite . in this case ( @xmath16 ) , it is not obvious how to solve the equations of motion analytically . we will therefore use the positive - p representation @xcite , which allows for exact solutions of the dynamics arising from the hamiltonian of eq . [ eq : ham ] , in the limit of the average of an infinite number of trajectories of the stochastic differential equations in a doubled phase - space . in practice we obviously can not integrate an infinite number of trajectories , but have used numbers large enough that the sampling error is within the line thicknesses of our plotted results . following the standard methods @xcite , the set of it stochastic differential equations @xcite are found as @xmath17 where the @xmath18 are standard gaussian noises with @xmath19 and @xmath20 . as always , averages of the positive - p variables represent normally ordered operator moments , such that , for example , @xmath21 . we also note that @xmath22 only after taking averages , and it is this freedom that allows classical variables to represent quantum operators . as well as the populations in each well , we can also calculate any type of operator products that we desire , analytically in the case without interactions . beginning with only the middle well occupied , we find the analytic non - interacting solutions for the numbers in each well , @xmath23 on the scale of fig . [ fig : populations ] , which shows numerical solutions , the above are indistinguishable from the stochastic solutions for @xmath16 . , @xmath24 , and @xmath25 , with @xmath26 . the atoms in the centre well begin in a fock state , although an initial coherent state leads to indistinguishable results . the results shown are the average of @xmath27 stochastic trajectories . the non - interacting analytical results are indistinguishable on this scale . the quantities plotted in this and subsequent plots are dimensionless . ] the next class of correlations we calculate are the number variances , including the number difference between the populations of wells @xmath1 and @xmath3 . in terms of the operators , these are @xmath28 in the non - interacting case and with only the middle well initially occupied , we find @xmath29 these results , for initial fock and coherent states in the middle well , are shown in fig . [ fig : erwinvar1 ] and fig . [ fig : erwinvar2 ] . , for an initial fock state of @xmath30 atoms in the middle well . we see that all variances are periodic in the non - interacting case . ] , for an initial coherent state of @xmath30 atoms in the middle well . we see that the maximum variances are much larger than in fig . [ fig : erwinvar1 ] , and that all variances are periodic in the non - interacting case . ] the second correlation is an entanglement measure adapted from an inequality developed by hillery and zubairy , who showed that , considering two separable modes denoted by @xmath31 and @xmath5 @xcite , @xmath32 with the equality holding for coherent states . the violation of this inequality is thus an indication of the inseparability of , and entanglement between , the two modes . cavalcanti @xcite have extended this inequality to provide indicators of epr steering @xcite and bell violations @xcite . we now define the correlation function @xmath33 for which a positive value reveals entanglement between modes @xmath1 and @xmath3 . we easily see that @xmath34 gives a value of zero for two independent coherent states and a negative result for two independent fock states . this inequality , and the epr - steering development of it , have been shown to detect both inseparability and asymmetric steering in a three - well bose - hubbard model under the process of coherent transfer of atomic population ( ctap ) @xcite . in our non - interacting case , with all population initially in well @xmath2 , we find the analytic result @xmath35 , \label{eq : hzanalytic}\ ] ] so that this measure detects entanglement whenever the initial population in the middle well is in a sub - poissonian state , with the measure being maximised for a number state . the signature of entanglement identically vanishes for an initial coherent state , which is to be expected since our system is somewhat analogous to a beamsplitter , with linear couplings between the modes @xcite . cavalcanti @xcite further developed the work" +"the quantum dynamics of photosynthesis have , quite naturally , attracted a lot of attention recently . understanding if and how nature exploits quantum ( de)coherence would have tremendous scientific and technological impact . for what follows , photosynthesis can be simply visualized as a two - step process : ( i ) light harvesting and ( ii ) photochemical processing . light harvesting molecules absorb the incident photon and guide the subsequent excitation to the photosynthetic reaction center ( rc ) . it is there where the photochemistry takes place , transforming the initial electronic excitation in a transmembrane proton pump that further drives the life - sustaining chemistry . regarding step ( i ) , quantum coherence effects in light harvesting complexes ( time scale of 1 - 500 fs ) have been addressed theoretically and experimentally @xcite . we will here focus on step ( ii ) , i.e. on reaction center quantum dynamics ( time scale of 1ps - 10 @xmath1s ) schematically depicted in figure [ cidnp](a ) . photosynthetic reaction centers exhibit a cascade of electron transfer reactions , starting from a photo - excited donor - acceptor dyad pi ( chlorophyl - type molecules ) and shelving the electron further apart to quinones ( q@xmath2 , q@xmath3 ) , producing a long - lived charge - separated state driving the transmembrane proton pump . in each of those steps there is a radical - ion pair formed , further perplexing the dynamics , as radical - ion pairs ( rps ) exhibit intricate magnetic field effects @xcite . radical - ion pairs @xcite are biomolecular ions created from the photo - excited dyad @xmath4pi . they have two unpaired electrons ( denoted by the two dots in figure [ cidnp ] ) and any number of magnetic nuclei . the magnetic nuclei of the donor and acceptor molecular ions couple to the ion s unpaired electron via the hyperfine interaction . this coupling , along with several other intra - molecule magnetic interactions , leads to singlet - triplet ( s - t ) mixing , i.e. a coherent oscillation of the total electronic spin , also affected by the electrons zeeman interaction with the external magnetic field . a spin - dependent charge recombination terminates the coherent s - t mixing and leads to the reaction products , either the original neutral dyad pi ( singlet product ) or a triplet intermediate ( @xmath5pi ) . as shown in figure [ cidnp](b ) , singlet ( triplet ) radical pairs recombine at the singlet ( triplet ) recombination rate , denoted by @xmath6 ( @xmath7 ) . triplet products may close the reaction cycle by intersystem - crossing into the singlet diamagnetic ground state at a rate @xmath8 . , of the two unpaired electrons with each - other , the magnetic nuclei and the external magnetic field . these magnetic interactions in long - lived charge - separated states ( where the long lifetime is either due to the absence of quinones or due to the large spatial separation of secondary radical - pairs ) give rise to singlet - triplet conversion and spin - dependent recombination , further perplexing the dynamics of the whole reaction . figure adapted from @xcite.,width=8 ] it is apparent from figure [ cidnp ] that when the lifetime of the charge - separated states ( which increases with separation ) is long enough that magnetic - field effects ( with typical timescale of e.g. s - t mixing on the order of 0.1 - 1 @xmath1s ) have time to build up , radical - pair spin dynamics get convolved into the reaction center dynamics . one aspect of this interrelation pervading a large number of photosynthetic reaction centers is chemically induced dynamic nuclear polarization [ 13 - 20 ] , the enhancement ( by several orders of magnitude ) of the ground state ( pi ) nuclear spin polarization resulting from the rp spin dynamics . cidnp has emerged as a rather universal signature of spin order in photosynthetic reaction centers @xcite and its possible operational significance for photosynthesis is still an open fundamental question . cidnp is based on nuclear spin sorting , to be shortly explained , taking place in radical - pair reactions . regarding solid - state cidnp in particular , three main mechanisms have so far been known to produce cidnp signals , the three - spin - mixing ( tsm ) @xcite , the differential decay ( dd ) and the differential relaxation ( dr ) mechanism @xcite . the first is a coherent mechanism resulting from particular magnetic interactions within the rp , while the second is about a nuclear spin imbalance brought about by different recombination rates @xmath9 . the last mechanism ( dr ) will not be relevant for the following discussion . we will here demonstrate that there is yet another , completely unanticipated mechanism at work _ at the fundamental quantum dynamical level of rp reactions_. it is due to the inherent quantum measurement of the rp s spin state continuously going on in the rp as part of its very charge recombination process . the decoherence caused by this `` internal '' quantum measurement is responsible for a new kind of nuclear spin sorting , particularly efficient at low fields , and completely unrelated to other low - field cidnp studies @xcite . this new mechanism is ubiquitous , as it is largely independent of the particular magnetic interactions in the radical pairs , and thus opens a new venue towards exploring the biological significance of cidnp - induced spin order in natural ( earth s field ) photosynthesis . in the following we will ( i ) briefly explain the basics of cidnp signal generation for the general reader and ( ii ) recapitulate the recent progress in understanding the fundamental quantum dynamics of radical - ion - pair reactions . combining ( i ) and ( ii ) , we will then explain the quantum measurement corrections to cidnp . before proceeding , we just mention a classical analog of the effect to be discussed , shown in figure [ analog ] . we consider an ensemble of coupled pendulums oscillating in the anti - symmetric mode . the ensemble average of the sum of their displacements is @xmath10 at all times . however , if the `` environment '' perturbs the system , e.g. with random kicks , while the ensemble population decays we will observe a non - zero total displacement rising to a maximum and decaying to zero , following suit with the population decay . this displacement is the analog of the radical - pair nuclear spin to be discussed in the following . the non - zero value of the nuclear spin stems from the particular `` environment '' pertaining to radical - pairs , singlet - triplet dephasing , which produces a nuclear spin imbalance along the reaction . coupled pendulums oscillating out of phase ( anti - symmetric mode ) . the number of such systems @xmath11 is a decaying function of time . while they oscillate , the pendulums are perturbed by the `` environment '' , which is here assumed to produce dephasing kicks at random times . ( b ) for the particular stochastic simulation shown here , every kick from the environment was taken to initialize the amplitude of pendulum 1 to unity and of pendulum 2 to zero . in the absence of the perturbation , all coupled pendulums would be continuously oscillating out of phase , and the ensemble average of the sum of their displacements away from equilibrium , @xmath12 , would be constantly zero . in the presence of the dephasing kicks , however , a non - zero displacement is shown to build up , to later on decay to zero due to the total population decay.,width=8 ] consider radical - ion pairs with just one nucleus coupled to the electron of e.g. the donor . at time @xmath13 the radical - ion pairs start out in the electronic singlet state , while the nuclear spins are thermally polarized , which for protons at earth s field corresponds to a polarization of about @xmath14 , practically taken to equal zero . thus , in the ensemble of radical - ion pairs half will have the nuclear spin in the @xmath15 state , while in the other half the nuclear spin will initially be in the @xmath16 state . the local magnetic field seen by the donor electron will be the external field plus the nuclear magnetic field , while the acceptor electron will only experience the external magnetic field . it is this difference in local magnetic fields experienced by the two electrons that results in a difference in their larmor frequencies , and hence induces the coherent singlet - triplet conversion . consequently , in the first half radical pairs ( with a @xmath15 nuclear spin ) the larmor precession frequency of the donor electron , and thus the s - t mixing frequency , will be slightly higher than in the other half ( due to the opposite contribution of the nuclear spin ) , hence the coherently formed triplet radical pairs will have their nuclear spins predominantly in the @xmath15 state , leaving the singlet radical pairs with an opposite nuclear polarization . while the nuclear spins are thus sorted among singlet and triplet rps , and unless there is a coherent mechanism like tsm producing net nuclear polarization , the expectation value @xmath17 of the z - component of the single nuclear spin under consideration is still zero . here @xmath18 is the spin density matrix of the radical pair , describing the electron and nuclear spin degrees of freedom altogether , and @xmath19 is the direction of the external magnetic field . according to the traditional understanding of the radical - pair mechanism and the concomitant cidnp signal generation , for this nuclear spin sorting to result in a diamagnetic ground state with net nuclear polarization , and in the absence of any coherent mechanism like tsm , the differential decay mechanism ( dd ) should be at play in order to observe nonzero cidnp signals . in the following we will indeed consider a magnetic hamiltonian that _ does not _ exhibit the tsm mechanism , and we will also take @xmath20 , so that the dd mechanism is not operational . hence according to the traditional theory of rp spin dynamics , no cidnp signal should be expected . we are then going to show that the opposite is actually true . to illustrate the above considerations , we consider a radical pair with one spin-1/2 nucleus _ isotropically _ coupled to the donor electron . in figure [ traces](a ) we display the undisturbed spin state evolution brought about _ just _ by the magnetic hamiltonian @xmath21 , where @xmath22 is the electron spin larmor precession frequency in the external magnetic field defining the z - axis and @xmath23 the donor - electron hyperfine coupling with the donor nuclear spin ( in units of frequency ) . what is plotted in figure [ traces](a ) is the spin state s singlet character , given by the expectation value of the singlet projection operator , @xmath24 , and assuming an rp with infinite lifetime ( in other words so far we take the recombination rates to be @xmath25 ) . what figure [ traces](a ) displays are the singlet - triplet oscillations brought about by @xmath26 . the nuclear spin , @xmath27 , of singlet and triplet rps is given by @xmath28 and @xmath29 , respectively , and displayed in figure [ traces](b ) . the previous considerations regarding nuclear spin sorting are easily visualized by noting in figure [ traces](b ) that although @xmath30 and @xmath31" +"two observations of with the rosat pspc resulted in the detection of x - ray emission from 25 members of this old open cluster ( belloni et al . 1993 , 1998 ) . the x - ray emission of many of these sources is readily understood . for example , the x - ray emission originates in deep , hot atmospheric layers in a hot white dwarf ; is due to mass transfer in a cataclysmic variable ; and is caused by magnetic activity in two contact binaries and several rs cvn - type binaries . however , belloni et al . ( 1998 ) point out several x - ray sources in for which the x - ray emission is unexplained . all but one of these objects are located away from the isochrone formed by the main sequence and the ( sub)giant branch of ( fig . [ cmd ] ) . in this paper we investigate the nature of the x - ray emission of these stars through low- and high - resolution optical spectra . in particular , we investigate whether the emission could be coronal as a consequence of magnetic activity , by looking for emission cores in the h&k lines . tidal interaction in a close binary orbit is thought to enhance magnetic activity at the stellar surface by spinning up the stars in the binary . therefore , we also derive projected rotational velocities with the crosscorrelation method . finally , we study the h@xmath0 profile as a possible indicator of activity or mass transfer . the observations and the data reduction are described in sect . 2 , and the analysis of the spectra in sect . comparison with chromospherically active binaries is made in sect . a discussion of our results is given in sect . 5 . in the remainder of the introduction we give brief sketches of the stars studied in this paper ; details on many of them are given by mathieu et al . the stars are indicated with their number in sanders ( 1977 ) , and are listed in table [ tab1 ] . l@l@l@l@l@l@l i d & @xmath1 & @xmath2-@xmath1 & sp.type & @xmath3 & @xmath4 & ctrate + & & & & ( d ) & & ( s@xmath5 ) + + + s1040 & 11.52 & 0.87 & g4iii & 42.83 & 0.027(28 ) & 0.0050(6 ) + s1063 & 13.79 & 1.05 & g8iv & 18.39 & 0.217(14 ) & 0.0047(6 ) + s1072 & 11.32 & 0.61 & g3iii iv & 1495 . & 0.32(7 ) & 0.0013(3 ) + s1082 & 11.25 & 0.42 & f5iv & & & 0.0046(6 ) + s1113 & 13.77 & 1.01 & & 2.823 & 0.031(14 ) & 0.0047(6 ) + s1237 & 10.78 & 0.94 & g8iii & 697.8 & 0.105(15 ) & 0.0010(3 ) + s1242 & 12.72 & 0.68 & & 31.78 & 0.664(18 ) & 0.0007(2 ) + s1063 and s1113 are two binaries located below the subgiant branch in the colour - magnitude diagram of . their orbital periods , 18.4 and 2.82 days respectively , are too long for them to be contact binaries ; also they are too far above the main sequence to be binaries of main - sequence stars . in principle , a ( sub)giant can become underluminous when it transfers mass to its companion , as energy is taken from the stellar luminosity to restore hydrostatic equilibrium ( e.g. kippenhahn & weigert 1967 ) . however , mass transfer through roche lobe overflow very rapidly leads to circularization of the binary orbit , whereas s1063 has an eccentricity @xmath6 . the orbit of s1113 is circular , so mass transfer could be occurring in that system . for the moment , the nature of these binaries is not understood . in both , pasquini & belloni ( 1998 ) observed emission cores in the h&k lines . s1063 is reported to be photometrically variable with @xmath7 0.10 mag ( rajamohan et al . 1988 ; kaluzny & radczynska 1991 ) , but no period is found . for s1113 , photometric variability with a period of 0.313 days and a total amplitude of 0.6 mag was claimed by kurochkin ( 1960 ) , but this has not been confirmed by kaluzny & radczynska ( 1991 ) , who find variability with only 0.05 mag . s1063 is the only star in our sample that shows significantly variable x - ray emission ( between 0.0081 and 0.0047 cts s@xmath5 ; belloni et al . 1998 ) . s1072 and s1237 are binaries with orbital periods of 1495 and 698 days , and with eccentricities @xmath8 and 0.105 , respectively . the colour and magnitude of s1072 can not be explained with the pairing of a giant and a blue straggler , since this is not compatible with its @xmath9 photometry ( nissen et al . 1987 ; mathieu & latham 1986 ) , nor with superposition of three subgiants , since this is excluded by the radial velocity correlations ( mathieu et al . the absence of the 6708 lithium feature in the spectrum of s1072 indicates that the surface material has undergone mixing ( hobbs & mathieu 1991 ; pritchett & glaspey 1991 ) . s1237 could be a binary of a giant and a star at the top of the evolved main sequence ( janes & smith 1984 ) ; high - resolution spectroscopy should be able to detect the main - sequence star in that case ( mathieu et al . 1990 ) . the wide orbits and significant eccentricities appear to exclude both mass transfer and tidal interaction as explanations for the x - ray emission . s1242 has the largest eccentricity of the binaries in our sample , at @xmath10 in an orbit of 31.8@xmath11days . its position on the subgiant branch is explained if a subgiant of 1.25@xmath12 has a secondary with @xmath13 ( mathieu et al . k line emission is reported by pasquini & belloni ( 1998 ) . photometric variability with a period of 4.88@xmath11days and amplitude of 0.0025 mag has been found by gilliland et al . we note that this photometric period corresponds to corotation with the orbit at periastron , which suggests that the x - ray emission may be due to tidal interaction taking place at periastron . the binary would then be an interesting example of a system in transition from an eccentric to a circular orbit . indeed , according to the diagnostic diagram of verbunt & phinney ( 1995 ) a giant of 1.25@xmath12 with a current radius of @xmath14 ( as derived from the location of s1242 in the colour - magnitude diagram ) can not have circularized an orbit of 31.8days . s1040 is a binary consisting of a giant and a white dwarf . the progenitor of the white dwarf circularized the orbit during a phase of mass transfer ( verbunt & phinney 1995 ) ; as a result the mass of the white dwarf is very low ( landsman et al . the white dwarf is probably too cool , at 16160@xmath11k , to be the x - ray emitter . indications for magnetic activity are h&k ( pasquini & belloni 1998 ) and ( @xmath15 2800 , landsman et al . 1997 ) emission lines . if the x - rays are due to coronal emission of the giant , this must be the consequence of the past evolution of the binary , since the giant is too small for significant tidal interaction to be taking place in the current orbit . s1082 is a blue straggler . photometric variability of 0.08 mag within a few hours was observed by simoda ( 1991 ) . goranskii et al . ( 1992 ) found eclipses with a total amplitude of 0.12 mag and a binary period of 1.07 days ; however , the radial velocities of the star do not show this period , and vary by about 2 km s@xmath5 , far too little for a 1day eclipsing binary ( mathieu et al . landsman et al . ( 1998 ) detect a significant excess at 1520 with the ultraviolet imaging telescope , and ascribe this to a hot , subluminous secondary . such a secondary was suggested already by mathys ( 1991 ) on the basis of a broad component in the d and absorption lines . optical spectra were obtained on february 28/29 , 1996 with the 4.2 m william herschel telescope on la palma , under good weather conditions ( seeing @xmath16 until 4@xmath1730 ut , @xmath18 thereafter ) . in addition to the x - ray sources in we observed two ordinary member giants of , s1288 and s1402 , for comparison . furthermore one flux standard and three velocity standards were observed . the blue high - resolution spectra of s1113 were obtained on april 7/8 , 1998 with the same telescope through a service observation ( seeing 12@xmath19 ) . a log of the observations is given in table [ tab11 ] . llrlrlr i d & & & + & & & + & ut & & ut & & ut & + & & & & & & + + + + s1040 & 02:43&60 & 22:03&600 & 00:46&300 + s1063 & 02:30&180 & 20:51&1200 & 00:11&1200 + & & & 21:15&1200 & 00:33&600 + & & & 21:37&1200 + s1072 & 02:49&60 & 22:24&360 & 01:01&240 + s1082 & 02:39&60 & 20:39&300 & 00:01&360 + & & & 23:24&600 & 01:41&360 + & & & & & 04:11&360 + s1113 & 03:01&180 & 22:37@xmath20 & 900 & 03:36&1200 + & & & 22:58@xmath20 & 900 & 03:58&600 + s1237 & 02:46&60 & 22:16&300 & 00:54&180 + s1242 & 02:55&120 & 22:33&1500 & 01:08&900 + + + s1288 & 02:58&60 & 23:12&600 & 01:33&300 + s1402 & 02:52&60 & 23:01&450 & 01:26&240 + + + & 02:21&80 & 23:42&600 & 01:57&600 + & 03:13&80 + & 04:43&480 + + + & & & 06:04 & 90 & 05:13&45 + & & & 05:55&100 & 05:42&50 + & & & & & 05:34&45 + all spectra have been reduced using the image reduction and analysis facility ( iraf ) . low - resolution spectra were taken with the isis double - beam spectrograph ( carter et al . the blue arm of isis was used with the 300 lines per mm grating and tek - ccd , resulting in a wavelength coverage of 3831 to 5404 and a dispersion of 1.54 per pixel at 4000 . the red arm , combined with the 316 lines per mm grating and eev - ccd , covered a wavelength region of 5619 to 7135 with a dispersion of 1.40 per pixel at 6500 . the format of the frames is 1124 @xmath21 200 pixels which includes the under- and overscan regions . for the object exposures the slit width was set to @xmath22 . flatfields were made with a tungsten lamp while cuar and cune lamp exposures were taken for the purpose of wavelength calibration . for the isis - spectra , basic reduction steps have been done within the iraf ccdred - package . these steps include removing the bias signal making use of the under- and overscan regions and zero frames , trimming the frames to remove the under- and overscan , and flatfielding to correct for small pixel - to - pixel gain variations . the remaining reduction has been done with iraf specred - package tasks . with the optimal extraction algorithm ( horne 1986 ) the two dimensional images are reduced to one dimensional spectra . next , the spectra are calibrated in wavelength with the arc frames . a dispersion solution is found by fitting third ( blue ) and fourth" +"since any experiment on a superfluid fermi gas is done in trap potential@xcite , it is interesting to explore physical phenomena originating from this spatial inhomogeneity . an example is surface oscillations observed in a @xmath2li superfluid fermi gas@xcite . another example is the phase separation observed in a @xmath2li fermi gas with spin imbalance@xcite , where the spin - balanced superfluid region in the trap center is spatially surrounded by excess atoms . in addition to these macroscopic phenomena , the spatial inhomogeneity can also affect microscopic superfluid properties . noting that a trap potential breaks the spatial inversion symmetry when the inversion center is taken to be away from the trap center , we expect that the parity becomes no longer a good quantity to classify the spatial structure of a cooper pair , leading to the admixture of even and odd parity symmetry . since a pair wavefunction is always antisymmetric with respect to the exchange of two fermions , this naturally leads to the mixing of spin - singlet and spin - triplet state . when this phenomenon occurs , the @xmath0-wave superfluid state is accompanied by a triplet cooper pair amplitude , in addition to the ordinary singlet component . ( the cooper pair amplitude is symbolically written as @xmath3 , where @xmath4 is an annihilation operator of a fermi atom with pseudospin @xmath5 . ) the purpose of this paper is to theoretically explore this possibility in a trapped @xmath0-wave superfluid fermi gas . using symmetry considerations , we prove that this phenomenon may occur , when a spin rotation symmetry of this system is also broken , in addition to the broken inversion symmetry by a trap potential . in a two - component fermi gas , this additional condition is realized , when two species feel different trap potentials or chemical potentials , or when they have different atomic masses . although this is a necessary condition , we numerically confirm that a triplet pair amplitude is really induced under this condition , within the mean - field theory for a model two - dimensional lattice fermi superfluid in a harmonic trap . in considering a triplet pair amplitude , one should note that the appearance of this quantity does not immediately mean the realization of a triplet superfluid state . actually , the system is still in the @xmath0-wave superfluid state , as far as the system only has an @xmath0-wave interaction . this is simply because the symmetry of a fermi superfluid is fully determined by the symmetry of the superfluid order parameter , which is essentially given by the product of a pairing interaction and a pair amplitude . for example , an @xmath0-wave superfluid fermi gas with a contact type @xmath0-wave pairing interaction @xmath6 ( @xmath7 is characterized by the ordinary @xmath0-wave superfluid order parameter , @xmath8 which is finite when the pair amplitude @xmath9 has the @xmath0-wave component . the odd - parity component does not contribute to @xmath10 in eq . ( [ eq.1 ] ) . however , for an @xmath0-wave superfluid fermi gas with both the singlet and triplet pair amplitude , when one suddenly changes the @xmath0-wave pairing interaction to a triplet ( and odd parity ) one @xmath11 , while the @xmath0-wave superfluid order parameter in eq . ( [ eq.1 ] ) immediately vanishes due to the vanishing @xmath0-wave interaction ( @xmath12 ) , the product of the triplet interaction and the triplet component in the pair amplitude @xmath9 ( which is assumed to have already existed in the @xmath0-wave state ) immediately gives a finite triplet superfluid order parameter , @xmath13 when the triplet interaction @xmath11 is chosen so that the momentum summation in eq . ( [ eq.2 ] ) can be finite . in an ultracold fermi gas , the change of the interaction is possible by using a tunable interaction associated with a feshbach resonance@xcite . then , by definition , one obtains a triplet superfluid fermi gas characterized by the superfluid order parameter @xmath14 in eq . ( [ eq.2 ] ) , at least just after this manipulation . this makes us expect that , when one can induce a @xmath1-wave pair amplitude in an @xmath0-wave superfluid fermi gas , a @xmath1-wave superfluid fermi gas may be realized . this possibility has recently been discussed by one of the authors@xcite , where a @xmath1-wave pair amplitude is induced by a synthetic spin - orbit interaction@xcite . the present paper provides another source of @xmath1-wave pair amplitude , without using an artificial gauge field . the admixture of singlet and triplet cooper pairs has recently attracted much attention in the field of non - centrosymmetric superconductivity@xcite , where a crystal lattice with no inversion center causes this phenomenon . in this field , it has been pointed out that this admixture may be the origin of the anomalous temperature dependence of the penetration depth observed in li@xmath15pt@xmath16b@xcite . thus , an @xmath0-wave superfluid fermi gas with a triplet pair amplitude would be also helpful to the study of this electron system . this paper is organized as follows . in sec.ii , we clarify the necessary condition for a triplet cooper pair amplitude to appear in a trapped @xmath0-wave superfluid fermi gas . in sec.iii , we numerically evaluate how large a triplet pair amplitude is induced under the condition obtained in sec.ii . in this section , we treat a superfluid fermi gas loaded on a two - dimensional square lattice , within the mean - field theory . throughout this paper , we take @xmath17 , for simplicity . we consider a three - dimensional @xmath0-wave superfluid fermi gas , described by the hamiltonian , @xmath18 . \label{eq.3}\ ] ] here , @xmath19 is a fermion field operator with pseudospin @xmath5 , describing two atomic hyperfine states . @xmath6 @xmath20 is a contact - type @xmath0-wave pairing interaction . @xmath21 is a one - particle hamiltonian density , consisting of a kinetic term and a potential term , detailed expression of which will be given later . we assume that the system is in the ordinary @xmath0-wave superfluid state with the @xmath0-wave superfluid order parameter , @xmath22 we also assume that any other spontaneous symmetry breaking is absent ( such as the triplet superfluid state ) . in this model superfluid , we consider the spin - triplet cooper - pair amplitude , given by @xmath23 & ~~(s_z=0 ) , \\ \langle\psi_\downarrow({\bm r})\psi_\downarrow({\bm r}')\rangle & ~~(s_z=-1 ) , \end{array } \right . \label{eq.6}\end{aligned}\ ] ] where @xmath24 denotes the @xmath25-component of the total spin of each pair amplitude . the triplet pair amplitude in eq . ( [ eq.6 ] ) does not contribute the @xmath0-wave superfluid order parameter @xmath26 in eq . ( [ eq.4 ] ) , because @xmath27 . the spin - singlet pair amplitude , @xmath28 , \label{eq.5}\ ] ] only contributes to eq . ( [ eq.4 ] ) . we first prove that the broken spatial inversion symmetry is necessary for a triplet pair amplitude to appear in an @xmath0-wave superfluid fermi gas . for this purpose , we conveniently introduce the inversion operator @xmath29 with respect to the inversion center @xmath30 . the field operator is transformed under this operation as @xmath31 where @xmath32 . the inverted hamiltonian @xmath33 is then given by @xmath34 . \label{eq.8}\end{aligned}\ ] ] when the one - particle hamiltonian density @xmath21 has the symmetry @xmath35 , this system is invariant ( @xmath36 ) under this symmetry operation . on the other hand , the triplet pair amplitude @xmath37 in eq . ( [ eq.6 ] ) with the center of mass position @xmath38/2 $ ] is transformed as , @xmath39 where @xmath40 is the relative coordinate . we also find @xmath41 . that is , the triplet pair amplitude @xmath42 vanishes , when the system has the inversion symmetry ( @xmath36 ) with respect to the inversion center @xmath38/2 $ ] . thus , the broken inversion symmetry is necessary for a triplet pair amplitude to appear . for the singlet pair amplitude in eq . ( [ eq.5 ] ) , this symmetry operation simply gives @xmath43 . as expected , this quantity may be finite . the one - particle hamiltonian density @xmath21 in the ordinary uniform fermi gas has the form @xmath44\delta_{\alpha,\alpha ' } , \label{eq.10}\ ] ] where @xmath45 , @xmath46 is an atomic mass , and @xmath47 is the fermi chemical potential . equation ( [ eq.10 ] ) has the symmetry property , @xmath35 , with respect to @xmath48 for an arbitrary @xmath30 . to conclude , any triplet pair amplitude is not induced . in the presence of a harmonic trap , the one - particle hamiltonian density becomes inhomogeneous as @xmath49 \delta_{\alpha,\alpha ' } , \label{eq.11}\ ] ] so that it does not have the inversion symmetry except at @xmath50 . however , when we consider the @xmath0-wave superfluid state in this trapped case , any triplet pair amplitude is not actually induced ( although we do not explicitly show the result here ) . of course , since the condition obtained from the inversion symmetry is a _ necessary _ condition , the broken inversion symmetry does not guarantee the appearance of a triplet pair amplitude . in this regard , we point out that the vanishing triplet pair amplitude in the trapped case is due to the fact that this system still has a rotation symmetry in spin space . to see this , we next consider the spin rotation of the field operator , given by @xmath51 here , @xmath52 describes the spin rotation around the unit vector @xmath53 with the angle @xmath54 , and @xmath55 , where @xmath56 ( @xmath57 are pauli matrices . ( as usual , we take the spin quantization axis in the @xmath58-direction . ) for the three @xmath59 rotations "" specified by @xmath60 , @xmath61 , @xmath62 , eq . ( [ eq.12 ] ) can be written as , @xmath63 where we have used the formula @xmath64 . under the @xmath59-rotation , the hamiltonian in eq . ( [ eq.3 ] ) is transformed as @xmath65 \nonumber \\ & = & \int d{\bm r } \bigl [ \sum_\alpha \psi^\dagger_\alpha({\bm r } ) \left ( \sigma_j{\hat h}({\bm r})\sigma_j \right)_{\alpha,\alpha ' } \psi_{\alpha'}({\bm r } ) -u_s \psi^\dagger_\uparrow({\bm r } ) \psi^\dagger_\downarrow({\bm r } ) \psi_\downarrow({\bm r } ) \psi_\uparrow({\bm r } ) \bigr ] . \label{eq.14}\end{aligned}\ ] ] here , @xmath66 . thus , one has @xmath36 , when @xmath67=0 \label{eq.15}\ ] ] is satisfied . while the singlet pair amplitude in eq . ( [ eq.5 ] ) remains unchanged under these @xmath59-rotations , the triplet component is transformed as @xmath68 for example , when we set @xmath69 , eq . ( [ eq.16 ] ) means that @xmath70 , when @xmath71=0 $ ] . ( the other two components with @xmath72 are not excluded in this case . ) when the system invariant under all the @xmath59-rotations ( @xmath73 ) , any triplet pair amplitude is not induced . to conclude , the broken spin rotation symmetry characterized by @xmath74 is necessary for a triplet pair amplitude to be induced in a trapped @xmath0-wave superfluid fermi gas . this is the reason why the model case described by eqs . ( [ eq.3 ] ) and ( [ eq.11 ] ) is not accompanied by any triplet pair amplitude . the broken spin rotation symmetry is realized , when the strength of trap potential @xmath75 in eq . ( [ eq.11 ] ) depends on spin ( @xmath76 ) . in this case , the one - particle hamiltonian @xmath66 can be written as @xmath77 + { k_\uparrow - k_\downarrow \over 4}r^2\sigma_z . \label{eq.17}\ ] ] equation ( [ eq.15 ] ) is then satisfied only when @xmath78 . thus , we find" +"due to its use in thin film transistor ( tft ) applications pentacene is continuing to enjoy being the subject of extensive research . since most tft s employ sio@xmath2 as the dielectric layer , initial studies on pentacene focused mainly on gaining a thorough understanding of structural @xcite and electronic @xcite properties of thin films of this molecule on sio@xmath2 surfaces and in turn achieving the best device performance by optimizing @xcite these properties . as a result of this heavy research effort in the last decade , fabricating pentacene tft s with hole mobilities of more than 1 @xmath3/vs have become an almost routine process @xcite . nevertheless there are still , fundamental issues to be resolved such as the dependence of the charge mobility on the film thickness @xcite and areas open to improvement like modification of the substrate surfaces with buffer layers @xcite or the pentacene itself with functional groups @xcite . another very critical but relatively less well understood subject is the growth mechanism of pentacene films on metal substrates . understanding the pentacene film growth on gold and silver surfaces is particularly important since these metals constitute the electrode material in most tft s and the device performance is directly related to the charge transfer efficiency between the electrodes and the organic film . though both experimental @xcite and theoretical @xcite research in this field has been recently intensified , there are contradictory results in the literature and the growth modes of pentacene thin films on au(111 ) and ag(111 ) surfaces are continuing to be a matter of debate . this is mostly due to the relatively strong ( when compared with sio@xmath2 ) interaction of the metal surfaces with the pentacene molecule . as a result of this strong interaction pentacene adopts many different monolayer and multilayer phases on metal surfaces which are energetically and structurally very close to each other . for example on au(111 ) several different low density monolayer phases and an identical full coverage phase have been reported by different groups @xcite . however , in case of the multilayers while kang et al . @xcite report a layer by layer growth of lying down pentacene molecules , beernink et al . @xcite report strong dewetting starting from the second layer and growth of bulk like pentacene crystals . for pentacene films on ag(111 ) surfaces , while eremtchenko et al . @xcite and dougherty et al . @xcite report a bilayer film formation , where an ordered ( second ) layer ( which follows the symmetry of the ag(111 ) surface ) forms on top of a disordered ( 2d gas phase ) first layer at room temperature , kfer et al . @xcite report the formation of bulk - like pentacene structures immediately after the first monolayer . so on both surfaces the growth mechanism of pentacene films is still not completely clear . in addition , if the above mentioned 2d gas phase mechanism for ag(111 ) is really correct then questions like `` why does pentacene behave completely differently on seemingly similar surfaces , ag(111 ) and au(111 ) ? '' and `` how does the symmetry of the substrate affect the bilayer film structure ? '' arise . in spite of this richness of experimental studies and points in need of clarification , pentacene films on ag(111 ) or au(111 ) surfaces have not , yet , been studied theoretically . theoretical work regarding pentacene films were mostly performed on other metal surfaces , such as cu(001 ) @xcite , cu(110 ) @xcite , ag(110 ) @xcite , at semi - empiric level and al(100 ) @xcite , cu(100 ) @xcite , cu(119 ) @xcite , fe(100 ) @xcite , au(001 ) @xcite at dft level . these studies in general addressed two points concerning the first layer of pentacene film / molecule : ( 1 ) determination of the most stable adsorption site / geometry , and ( 2 ) determination of the strength of electronic interaction / coupling between the substrate and the molecule . in these studies either the most stable configuration was found to be pentacene lying flat on the surface @xcite or the calculations were started with this assumption . in terms of the electronic interactions , the dft studies performed using gga functionals found considerable aromatic-@xmath4-system metal substrate interaction @xcite on cu surfaces , hinting at chemisorption . on au(111 ) @xcite and al(100 ) @xcite however , while lda functionals resulted in strong interactions , in the form of broadening and splitting of @xmath4-molecular orbitals , gga functionals are reported to result in much weaker interactions , in accord with a physisorption mechanism . theoretical studies concerning the further stages of pentacene film growth on metal surfaces , however , like second layer structure / energetics or the thin film crystal / electronic structure , are very few and at semi - empiric level @xcite . instead , theoretical works regarding pentacene films are primarily focused on the electronic structure of different pentacene polymorphs observed mainly on sio@xmath2 surfaces , one being the famous `` thin film phase '' @xcite . hence , a theoretical study of growth mechanism and electronic properties of pentacene films on ag(111 ) and au(111 ) may , ( 1 ) help resolve the experimental contradictions mentioned above and ( 2 ) fill a gap in the theoretical literature and enable a comparison of these systems with other pentacene films . as a first attempt to this end , here we present the results of our work on the structural and electronic properties of monolayer and multilayer films of pentacene on ag(111 ) at dft level . first we discuss full coverage monolayer film in the light of experimental results . we compare the adsorption geometries and the corresponding density of states we found with the experimental results reported so far . then we present our results regarding two and three monolayers of pentacene film and discuss how the crystal and electronic structure of the ag(111)/pentacene interface and the film evolves with coverage . we conclude with an overall summary and discussion of the results . we performed total energy density functional theory ( dft ) calculations using the projector - augmented wave ( paw ) method @xcite within the generalized gradient approximation ( gga ) by employing the perdew ernzerhoff ( pbe ) @xcite exchange correlation energy functional as implemented in the vienna ab initio simulation package ( vasp ) @xcite . for consistency , we used a kinetic energy cutoff of 370 ev for the plane wave expansion of single particle wavefunctions in all the calculations . electronic ground states has been determined by requiring a total - energy convergence up to a tolerance value smaller than 0.1 mev . we used a conjugate - gradient algorithm , in all geometry optimization calculations , based on the reduction in the hellman feynman forces on each constituent atom to less than 10 mev / . we examined two previously known polymorphs of pn lattice : the bulk @xcite and the thin film @xcite phases . bulk phase corresponds to a triclinic unit cell which contains two c@xmath5 formulae with a set of parameters : @xmath6 , @xmath7 , @xmath8 , @xmath9 , @xmath10 , and @xmath11 @xcite . our calculated values of @xmath6 , @xmath7 , @xmath8 , @xmath12 , @xmath10 , and @xmath13 shows a very good agrement with the experimental results of campbell _ et al . _ for the thin film phase , we obtained an orthorhombic unit cell with @xmath14 , @xmath15 , and @xmath16 . these parameters agree with parisse _ @xcite theoretical results of @xmath17 , @xmath18 , and @xmath19 except for the last one , corresponding to the longitudinal size of the unit cell . we calculated the length of an isolated molecule to be 14.5 . therefore , the disagreement , in this phase , stems from the pn pn separation in the multilayers . in order to compare the predictions of different dft functionals with the experimental results for key structural and electronic parameters like the lattice constants and binding energies , we repeated our calculations using pw91 @xcite parametrization within both generalized gradient and local density approximations ( lda ) . we calculated the lattice parameter of the silver _ ccp _ bulk structure in @xmath20 symmetry group to be 4.00 , 4.15 , and 4.17 using lda - pw91 , gga - pw91 , and gga - pbe functionals respectively . these compare well with the experimental @xcite value of 4.09 , slightly better than the previous theoretical @xcite result of 4.20 . the ag(111 ) surface has been modeled in a four - layer slab geometry separated from their periodic images by @xmath2115 of a vacuum space and 3@xmath226@xmath221 grid for the cases of 1ml to 4ml deposition , whereas in the cases of isolated pn adsorption a larger cell is needed and therefore a three - layer - slab geometry for the ag(111 ) surface and 1@xmath222@xmath221 grid was used . for this metallic system , the number of layers has been found to be sufficiently large to represent the ag(111 ) surface structure such that the geometry optimization calculations do not disturb the subsurface layer atoms from their bulk lattice positions . in order to study the formation of ordered pn layers on ag(111 ) we first considered a single pn on the surface . isolation of the molecules was achieved by using a 8@xmath225 silver surface unit cell which sets 9.5 tip - to - tip and 7.9 side - to - side separations between the periodic images . we determined the minimum energy pn / ag(111 ) geometry by investigating all possible adsorption sites with a number of orientations , compatible with the lattice symmetry , at each site as shown in [ fig1 ] . ( labeling conventions are described in figure caption . ) in addition to these planar cases we also investigated the possibility of standing - up adsorption configurations which appeared to be around 0.15 ev less favorable than the planar ones . in geometry optimization calculations pn develops a weak interaction with ag(111 ) wherever it is initially placed on the surface . in fact , as presented in [ table1 ] , the comparison of the total energies of these adsorption cases show differences which are no greater than 36 mev from each other . the flatness of the potential energy surface ( pes ) is indicated by the existence of such small barriers which might make pn diffusion over the surface possible in agreement with the experimental observations that the contact layer pn molecules are mobile at the pn / ag(111 ) interface @xcite . similarly , during image acquisition stm tip has been observed to drag pn molecules which are physisorbed on au(111 ) @xcite . .calculated values for geometrical and electronic structure of pn / ag(111 ) systems shown in [ fig1 ] . the lateral height of isolated pn molecule from the ag(111 ) surface @xmath23 in , the binding energy @xmath24 and the relative total energy @xmath25 in ev . [ cols=""<,^,^,^ "" , ] the flat and tilted pentacene configurations above the first layer has also been considered for the 3ml and 4ml initial structures . the difference in the total energies has been calculated to be 0.127 ev and 0.125 ev in favor of the tilted molecules on the first layer for 3ml and 4ml cases , respectively . therefore , bulk - like pentacene formation on ag(111 ) surface above the contact layer is more preferable than flat lying multilayers . in the case of multilayers , the separation of the top layer from the layer underneath is 3.6 and all the inner interlayer distances become 3.5 while the height of the contact layer converges to a value of 3.7" +"granular materials constitute the raw materials in a huge number of human activities as in agriculture , the mining industry , pharmaceutics and are at the heart of the matter in several ecological concerns as desertification by eolian erosion or avalanches . therefore , explaining a few current granular processes , such as storage , transport , or collapse , is a real economical challenge . furthermore , packings of spheres which is the simplest model for granular medium , have a great fundamental interest for physicists : hard sphere systems are indeed a common description of simple liquids @xcite ; moreover grains can behave , according to the external conditions , more or less like a solid , a liquid or a gas @xcite . this great variety of behaviors for a banal heap of grains makes granular mechanics a rich area of investigation only partially clarified at the moment . it is now a well - known result @xcite ( although there is no theoretical explanation for it ) that a disordered static packing of equal hard spheres can cover a large range of volume fraction , approximately from 56 @xmath0 , the random loose packing ( r.l.p . ) , to 64 @xmath0 , the random close packing ( r.c.p . ) . for a regular arrangement , the packing fraction can reach up to 74 @xmath0 which corresponds to the densest structures , namely the hexagonal compact ( h.c . ) and the face - centered cubic ( f.c.c . ) crystals . + as thermal energy ( @xmath1 t ) plays no role , because it is insignificant compared to the gravitational energy of a macroscopic grain , each packing of spheres is a metastable configuration which can persist as long as there is no external excitation . in this frame , the issues of compaction of grains under vertical taps are a practical way to study the succession of jumps from a metastable equilibrium to another one . the initial packing is quite loose and can progressively reach a nearly stationary configuration ( steady state ) evaluated through its average volume fraction . some experiments done in chicago @xcite have studied the influence of the tapping intensity on the steady - state value and the dynamics of the compaction , which is approximately inverse of the logarithm of the number of taps . the experimental set - up is a thin tube of diameter d=1.88 cm filled to about an 80 cm height with monodisperse , spherical soda - lime glass beads ( of diameter d=1 , 2 or 3 mm ) . the tube is shaken by an electromagnetic exciter delivering vertical taps , each of them consisting of an entire cycle of a sine - wave of frequency f = 30 hz . the excitation strength is parameterized by @xmath2 , the ratio between the measured acceleration peak and the gravitational acceleration g. moreover , several numerical and theoretical works @xcite , most of them dealing with the notions of free volume and geometric constraint , found the same kind of behavior as obtained experimentally and some of them @xcite have pointed out structural ageing effects , as typically observed in glassy systems . so a parallel might exist between this granular compaction and the dynamics of out - of - equilibrium systems as glasses . + in this work , we used a simple model to simulate the compaction of a packing of monosize spheres submitted to vertical taps . we did not try to make a realistic description of the quite complex succession of collisions in a shaken packing : we have kept as the only ingredient of the model the geometric constraint between hard spheres , which is believed to be the principal origin of the compaction . despite the fact that we deliberately forgot the mechanical dimension of the problem , the model is able to reproduce qualitatively the experimental results of the chicago group and some further results in agreement with different numerical and theoretical studies . as the model seems to capture the physics of the problem , it is then possible to go beyond a global analysis . indeed , as a three - dimensional packing of hard spheres , our description has the quite interesting asset that it is very close to a real granular medium . so , contrary to almost all the previous works which deal only with a macroscopic probe ( i.e. the average density in all or part of the packing ) , our model can provide us with realistic information on the local structure of a packing and its evolution under compaction by taps . + the paper is organized as follows . a detailed description of the model is presented in section ii . section iii is devoted to the global analysis of compaction ( logarithmic dynamics , hysteresis effect , and ageing behaviors ) . in section iv , the local analysis of the packings is described with the use of density profiles and size and volume distributions of the pores . our conclusions and perspectives end the paper in section v. the model proposed here is purely geometric and deals only with the steric constraint , neither friction nor contact law between the spheres or with the walls is introduced . + the different sequences of tapping were initialized from a relatively loose packing obtained by a steepest - descent algorithm simulating a sequential gravitational deposition @xcite . we worked with packings of 4096 spheres of radius r piled up in a square - box of dimension l = 32r . concerning the vertical walls , we used both periodic boundary conditions ( p.b.c . ) and fixed boundary conditions ( f.b.c . ) i.e. impassable vertical planes . the top of the box is open whereas the bottom is a fixed impassable plane . + a tap is decomposed in two stages : first a vertical dilation and then a gravitational redeposition . + the first stage corresponds to the external excitation which will enable the packing to move from a metastable equilibrium to another one . we used the simplest way to simulate the tap by applying an uniform dilation @xmath3 to the whole packing ( z @xmath4 z(1+@xmath3 ) ) . this reduction is certainly far from a real tap but we assume that the way of dilating the packing is less important than the result of the dilation : a significant increase of the average free - volume of the spheres which will allow collective rearrangements during the second stage , the redeposition of the packing . + this redeposition procedure must be non - sequential in order to permit such collective behaviors ; so we use a monte - carlo algorithm to discretise the motion of the spheres : a great number of small displacements are computed . an individual movement procedure is structured as follows : a sphere , randomly chosen , is submitted to a small random displacement ; if this displacement creates no interpenetration with another sphere or with the walls ( according to the boundary conditions ) , it is accepted otherwise it is rejected . because of this binary schema , two neighboring spheres can not be exactly in contact but , after a sufficient time , they get very close to contact . figure [ algorithm ] shows a typical displacement : the values of the polar angle @xmath5 and of the displacement d are strictly randomly chosen respectively between 0 and 2@xmath6 and between 0 and @xmath7 , whereas the choice of the angle @xmath8 follows a random distribution centered on zero to mimic the effect of gravity . we used the following gaussian distribution of width @xmath9 truncated beyond @xmath6/2 in order to orientate all the displacements down to the bottom of the box . @xmath10 the choice of the distribution does not seem to be restrictive : some attempts with a poissonian and a linear distribution give qualitatively the same phenomenology ; the pertinent parameter is the width @xmath9 . + with such an algorithm , agitation will persist indefinitely . so we regularly test the packing during the redeposition process . the variable checked is @xmath11z@xmath12 , the average altitude of the packing that is the average potential energy of the spheres . the redeposition is stopped when the relative variation of @xmath11z@xmath12 becomes smaller than a threshold @xmath13 . the choice of @xmath11z@xmath12 is motivated by its easy evaluation during the process and by its possible link with a statistical mechanics approach . + this simulation is rather close to the one proposed by barker and mehta @xcite but with some differences especially concerning the way of introducing gravity and the end of the redeposition stage . + + the model uses four parameters : @xmath7 , @xmath13 , @xmath9 and @xmath3 . the two first ones have a direct effect on the simulation time . the smaller @xmath13 , the longer the simulation time ; still , @xmath13 must be small enough if we want the redeposition to be nearly completed . the parameter @xmath7 has to be optimised . a very small value of @xmath7 allows almost all of the displacements to be accepted but the effect on the redeposition is very slight and the packing is therefore nearly frozen . on the contrary , for a large value of @xmath7 , almost of all the displacements are refused and , once again , the packing evolves very slowly . in this study , we used the intermediate value @xmath7 = r/5 . + @xmath9 has a significant effect on the packing behavior : a very small @xmath9 induces a decompaction whereas a large value decreases the efficiency of the compaction . we found @xmath9 = @xmath6/4 as the optimised value giving rise to the maximal compaction rate . + the last parameter , @xmath3 , corresponds to the external excitation induced in the packing . this is our control parameter . the value of @xmath3 can be estimated from experimental results concerning the dilation of a vertically shaken sand heap @xcite : @xmath3 = @xmath14h / h @xmath15 5/500 @xmath16 . we can also try to link roughly @xmath3 to the experimental control parameter , the dimensionless acceleration @xmath2 = a@xmath17/g where a and @xmath18 are , respectively , the amplitude and the frequency imposed to the bottom of the heap . in first approximation , if we neglect the loss of energy in the packing , a particle at the top of the heap ( z(0 ) = h ) acquires an initial speed @xmath18a and achieves a ballistic flight . its maximal altitude is @xmath19 and then it comes : @xmath20 as @xmath21 is linked to @xmath2 , we will use it as our control parameter to quantify the strength of the tapping process . + with this , it is possible to compare the results of our model with the experimental work of the chicago group and with other numerical and theoretical models , almost all of them dealing only with a global description of the granular system . this global analysis is achieved with different average values . we did not use a direct evaluation of the packing fraction from the number of spheres in a reference volume because wether boundary effects are significant or , for a smaller volume , the statistics become too poor . moreover , the choice of the reference volume is not unique : it can be , for example , the space that contains all the spheres or the smaller one that contains only the centers of the spheres . to avoid being partial , we evaluate the packing fraction by averaging the surface packing fraction , @xmath22 , calculated on many horizontal cuts . this measure is permissible because of the following stereologic result : the" +"the radio - loud gravitational lenses b1600 + 434 and b1608 + 656 were discovered in the cosmic lens all sky survey @xcite . b1608 + 656 was also discovered independently by @xcite . b1600 + 434 is a two image system separated by 14 with source redshift @xmath9 @xcite . the lens galaxy of b1600 + 434 is an edge - on early - type spiral galaxy at @xmath10 @xcite . b1608 + 656 is a four image system about 21 across with a source redshift at @xmath11 @xcite and a lens redshift at @xmath12 @xcite . the lens of b1608 + 656 consists of two interacting elliptical galaxies within the einstein ring . in addition , _ hst _ observations have detected extended images of the agn host galaxies in both systems @xcite . one of the important applications of gravitational lenses is to constrain the hubble constant @xcite or alternatively , the dark matter distribution in the lens galaxy , through time - delay measurements between the lensed images . the time - delays in both b1600 + 434 and b1608 + 656 have been measured @xcite . modeling of the two gravitational lenses has been carried out by several studies ( e.g. , koopmans & fassnacht 1999 ; koopmans et al . 2003 ; kochanek 2002 , 2003 ) . in most studies , there are model degeneracy problems in that a number of models can reproduce the limited number of constraints and predict different hubble constant values based on each time delay measurement . therefore , it is important to map the mass distribution close to the lens galaxy with other independent methods to better constrain the lens models . in many lenses , galaxy groups or clusters close to the lenses provide non - negligible contribution to the lens potential @xcite . x - ray observations are particularly important in this respect because they can accurately constrain the positions and masses of the galaxy groups or clusters . in particular , the centroid of the x - ray emission from the intracluster gas provides a more accurate measurement of the cluster s position than optical studies . x - ray clusters or groups have been observed in the lenses rx j0911.4 + 0551 , q0957 + 561 , b1422 + 231 , and pg 1115 + 080 @xcite . the superb angular resolution of _ chandra _ also allows us to resolve the lensed quasar images if they are separated by more than 05 . thus , besides constraining the properties of galaxy groups or clusters , x - ray observations of gravitational lenses can also be used to constrain the sizes of quasar x - ray emission regions @xcite , to measure ultra - short time delays between lensed images @xcite , and to study the interstellar medium of the lens galaxies ( e.g. , dai et al . in addition , the flux magnification provided by gravitational lensing facilitates studies of objects that are intrinsically x - ray faint , such as broad absorption line quasars @xcite and high redshift quasars @xcite . in this paper , we present results from _ chandra _ observations of b1600 + 434 and b1608 + 656 . we discuss the data acquisition and processing in @xmath132 , the spectral properties of the lensed quasars in @xmath133 , our limits on the presence of x - ray luminous groups or clusters in @xmath134 , and the serendipitous sources in the fields in @xmath135 . we assume cosmology with @xmath14 , @xmath15 , and @xmath16 throughout the paper . we observed b1600 + 434 and b1608 + 656 with the advanced ccd imaging spectrometer ( acis ; garmire et al . 2003 ) onboard _ chandra _ @xcite for @xmath17 ks and @xmath18 ks on 2003 october 7 , and 2003 september 21 , respectively . the data were taken continuously with no interruptions during each observation , and there were no significant background flares during the observations . both gravitational lenses were placed on the back - illuminated acis - s3 chip , where the aim points of the observations are located , and the data were taken in the timed / vfaint mode . b1600 + 434 was placed near the aim point of the observation ( @xmath198 off - axis ) and b1608 + 656 was placed much further from the aim point about @xmath1975 off - axis . the latter lens was shifted off - axis to ensure a galaxy clump in the _ hst _ images would stay in the field . this configuration was used to maximize the sensitivity for detecting nearby galaxy groups or clusters that might contribute to the lensing and affect estimates of the hubble constant . the data were reduced with the ` ciao 3.1 ` software tools provided by the _ chandra x - ray center _ ( cxc ) . we improved the image quality of the data by removing the pixel randomization applied to the event positions in the cxc processing and by applying a subpixel resolution technique @xcite . in the data analysis , only events with standard _ asca _ grades of 0 , 2 , 3 , 4 , and 6 were used . we first discuss the x - ray properties of the lensed quasars in both lens systems . the imaging and spectral analysis are discussed in @xmath13[sec : img ] and @xmath13[sec : spec ] and the x - ray flux ratios of the lensed images are estimated in @xmath13[sec : fr ] . we analyzed images limited to the 0.28 kev band where we detected a total of 332 and 84 net events for b1600 + 434 and b1608 + 656 , respectively . the raw and smoothed _ chandra _ images of b1600 + 434 and b1608 + 656 are shown in figure [ fig : img ] . both of the raw images are binned with a bin size of 015 . the smoothed images are generated by binning the images with a bin size of 01 for both lenses and then were smoothed with gaussians of width @xmath20 02 and @xmath20 03 for b1600 + 434 and b1608 + 656 , respectively . in b1600 + 434 we detected both lensed images . the measured image separation ( 135@xmath21005 ) is consistent with the separation measured in the cfa - arizona space telescope lens survey ( castles ) _ hst _ observations . the situation is more complicated in b1608 + 656 due to the large number of images with smaller minimum separations , but also because the count rate of the lens is lower . the relatively larger off - axis angle does not degrade the point spread function ( psf ) very much . we simulated the psf using the ` chart ` @xcite and ` marx ` @xcite tools and found the 50% encircled energy contour is of @xmath1905 radius as opposed to @xmath1904 on axis . three out of four lensed images are clearly detected . image b is well separated , but images a and c are merged . we fit the image assuming there are three point images of a , b , and c constraining the relative quasar position to match the castles @xmath22-band relative position and using the above mentioned psf model . however , we are unable to obtain a stable solution . this may be due to the low count - rate of the source or it may indicate that the images are not point sources . we note that there are some x - ray events about 1 northwest to image a and we are unable to determine whether these events belong to image a or from other unidentified sources . the _ hst _ images do not show any source at the corresponding position other than part of the einstein ring image of the host galaxy . image d is not detected by the _ chandra _ observation . the non - detection of image d could be caused by small number statistics additional absorption is not required to mask the image . we extracted spectra for each quasar using the ` ciao ` tool ` psextract ` and fit them using ` xspec v11.3.1 ` @xcite within the 0.48 kev observed energy range . we note that in ` ciao 3.1 ` the recently observed decline in the low energy quantum efficiency of acis , possibly caused by molecular contamination of the acis filters , is already accounted for by the ` psextract ` tool . therefore , we did not perform any other corrections beyond that . we extracted both the combined spectrum of both images within a circle with 5 radius about the centroid of the combined image and individual spectra of images within 07 radius circles about the centroids of images a and b , respectively . we extracted the background spectrum within an annulus with inner and outer radii of 10 and 30 . we fitted the spectra of b1600 + 434 with a series of models summarized in table [ tab : spec ] . we first modeled the spectrum as a power - law modified by galactic absorption . this model gives a reasonable fit with @xmath23 for 18 degrees of freedom ( dof ) . however , the column density obtained for galactic absorption , @xmath24 @xmath25 , is much higher than the expected @xmath26 @xmath25 @xcite . this exercise indicates that additional absorption components are needed to interpret the spectrum . these additional absorption components can be either intrinsic to the quasar , located in the quasar host galaxy , or in the lens galaxy . we found that adding a neutral absorption component at the redshift of either the quasar or the lens can produce an acceptable fit with @xmath27 for 18 dof and @xmath28 for 18 dof , respectively , for absorption at the quasar and lens redshifts . the absorption column densities obtained are @xmath29 @xmath25 and @xmath30 @xmath25 for absorption at the quasar or lens redshift , respectively . the combined spectrum and the best fit model with absorption at the lens redshift are shown in figure [ fig : spec]a . the estimate of the intrinsic photon index is around @xmath31 for both models with observed 0.48 kev band flux of @xmath3210@xmath33 , and lensed , unabsorbed x - ray luminosities in the 210 kev and 120 kev band rest frame of @xmath3410@xmath35 and @xmath410@xmath5 , respectively . we note that the lensing magnification must be included in order to obtain the unlensed luminosity . @xcite interpreted the wavelength dependence of the image flux ratios as due to @xmath8 of differential extinction obscuring image b. we also see in the spectra of the image that image b has proportionally less soft x - ray emission so that differential absorption must be intrinsic to the lens . to estimate this differential absorption we simultaneously fit the individual spectra of images a and b constrained to have the same intrinsic power - law photon index and galactic absorption column density but allowed to have different absorption column densities at the redshift of the lens . the best fit model is shown in figure [ fig : spec]b . this model also results in acceptable fit with a @xmath36 for 12 dof as compared to @xmath37 for 13 dof if we do not allow for differential absorption . the improvement of the fit by allowing for differential absorption is significant at the 90% confidence level according to the f - test indicating that the x - ray data are consistent with , but do not require , column density variations . the photon index obtained in this fit is slightly steeper than for the previous fits in part because the small extraction regions used to obtain individual spectra of the images" +"the central topic of this paper is the discussion of pseudocontinuability for schur functions in the unit disk . pseudocontinuability is a particular type of meromorphic continuation for functions from the meromorphic nevanlinna class in the unit disk . this concept originated in shapiro s papers @xcite , @xcite and was then systematically discussed a little bit later in the context of invariant subspaces for the backward shift in the landmark paper douglas / shapiro / shields @xcite . ( regarding modern treatments of this area we refer the reader to the monographs cima / ross @xcite and ross / shapiro @xcite . ) important applications of pseudocontinuability are contained in the work of d.z . arov on darlington synthesis , @xmath4-inner functions , and related topics ( see , e.g. , @xcite and @xcite ) . a further domain of application of pseudocontinuable functions is rational approximation . this theme which originated from a series of papers by g.ts . tumarkin ( see @xcite , @xcite , and @xcite ) was treated by katsnelson in @xcite . the paper @xcite is recommended for some other reasons too . it contains an extensive historical overview on the investigation of pseudocontinuable functions which also takes into account matrix - valued functions . moreover , the paper @xcite is very well written from the pedagogical point of view . it strongly influenced our approach to introducing pseudocontinuable functions ( see section [ s2 ] ) . the present paper continues recent investigations on several questions of pseudocontinuability of schur functions in the unit disk ( see @xcite and @xcite ) . our main aim is to establish a direct relation between two well - known criteria for pseudocontinuability of non - inner schur functions in the unit disk ( see theorem [ t3.9 ] and theorem [ t4.2 ] ) . the main result of this paper is a new characterization of pseudocontinuability of a non inner schur function @xmath0 in the unit disk . this characterization is expressed in terms of a special orthogonal basis in an @xmath3 space on the unit circle , where @xmath1 is some probability measure on the unit circle which is canonically associated with @xmath0 ( see theorem [ 4.3 ] ) . the paper is organized as follows . in section [ s1 ] , we recall that the set of schur functions in the unit disk stands in bijective correspondences to the set of normalized carathodory functions in the unit disk and to the set of probability measures on the borel @xmath5-algebra of the unit circle . this will give us the possibility to study the pseudocontinuability of a given schur function in terms of the associated normalized carathodory function and in terms of the associated probability measure , respectively . in section [ s2 ] ( influenced by katsnelson @xcite ) , we summarize essential facts on meromorphic functions and the concept of pseudocontinuability which is due to h.s . shapiro . section [ s3 ] contains a function theoretic approach to the study of pseudocontinuability of non - inner schur functions in the unit disk . we will recognize that a function of this class admits a pseudocontinuation if and only if the associated probability measure satisfies the szeg condition and the corresponding szeg function is pseudocontinuable ( see theorem [ t3.9 ] ) . the central theme of section [ s4 ] is an operator theoretic approach to the investigation of pseudocontinuability of non - inner schur functions in the unit disk . the starting point there is the observation that an arbitrary schur function can be represented as a characteristic function of some completely non unitary contraction in a separable complex hilbert space . then the pseudocontinuability of a non - inner schur function @xmath0 can be characterized in terms of the contraction @xmath2 having @xmath0 as its characteristic function . more precisely , the maximal unilateral shifts @xmath6 and @xmath7 contained in @xmath2 and @xmath8 , respectively , have to fulfill certain conditions of mutual interrelations ( see theorem [ t4.2 ] ) . in section [ s5 ] , we start from a probability measure @xmath1 on the borel @xmath5-algebra of the unit circle . the main aim is to construct a unitary colligation @xmath9 , the characteristic function @xmath10 of which coincides with the schur function @xmath11 associated with the measure @xmath1 according to section [ s1 ] . in section [ s6 ] , we consider a probability measure @xmath1 on the borel @xmath5-algebra of the unit circle for which the polynomials are non complete in the space @xmath12 . in this case the question arises as to the existence of a natural completion of the system of orthonormal polynomials in @xmath12 to a complete orthonormal system in @xmath12 . the primary concern of section [ s6 ] is to construct such a natural completion . in the particular case that the measure @xmath1 is associated with a pseudocontinuable non - inner schur function @xmath0 , we will show that the functions obtained by completing the orthonormal system of polynomials are boundary values of functions belonging to the meromorphic nevanlinna class in the unit disk ( see propoisition [ p6.14a ] ) . the goal of section [ s7 ] is to reformulate the characterization of the pseudocontinuability of a non - inner schur function given by theorem [ t4.2 ] in terms of the complete orthonormal system which was created in section [ s6 ] ( see theorem [ 4.3 ] ) . finally , section [ s8 ] is aimed at determining and further clarifying a direct connection between the criteria of pseudocontinuability of a non - inner schur function which were pointed out in theorem [ t3.9 ] and theorem [ t4.2 ] , respectively . let @xmath13 and @xmath14 be the unit disk and the unit circle in the complex plane @xmath15 , respectively . the central object in this paper is the schur class @xmath16 of all functions @xmath17 which are holomorphic in @xmath18 and satisfy @xmath19 . our main aim is to study the phenomenon of pseudocontinuability for functions belonging to @xmath16 . in order to allow for a more effective treatment of this question , we first consider certain important objects that relate bijectively to the class @xmath16 . this is the main content of the present section . let @xmath20 . then the function @xmath21 defined by @xmath22 is holomorphic in @xmath18 and satisfies @xmath23 > 0,\quad \zeta\in\mathbb d,\ ] ] and @xmath24 let @xmath25 be the carathodory class of all functions @xmath26 which are holomorphic in @xmath18 and satisfy @xmath27 \geq 0 $ ] and let @xmath28 in view of , , , and we have @xmath29 it can be easily verified that via a bijective correspondence between the classes @xmath16 and @xmath30 is established . note that from it follows that @xmath31 the class @xmath25 is intimately related with the class @xmath32 of all finite nonnegative measures on the borel @xmath5-algebra @xmath33 of @xmath34 . according to the riesz - herglotz theorem ( see , e.g. , ( * ? ? ? * theorem 2.2.2 ) ) : for each function @xmath35 there exists a unique measure @xmath36 and a unique number @xmath37 such that @xmath38 obviously , @xmath39 $ ] . on the other hand , it can be easily checked that , for arbitrary @xmath36 and @xmath40 , the function @xmath41 , which is defined by the right hand side of ( [ nr.0.3 ] ) , belongs to @xmath25 . if we consider the riesz - herglotz representation ( [ nr.0.3 ] ) for a function @xmath42 , then @xmath43 and @xmath1 belongs to the set @xmath44 of all probability measures belonging to @xmath32 ( i.e. @xmath45 . actually , in this way we obtain a bijective correspondence between the classes @xmath30 and @xmath44 . in the result of the above considerations we obtain special ordered triples @xmath46 $ ] consisting of a function @xmath20 , a function @xmath47 , and a measure @xmath48 which are interrelated in such way that each of these three objects uniquely determines the other two . for that reason , if one of the three objects is given , we will say that the two others are associated with it . based on this procedure , in section [ s3 ] we will characterize the pseudocontinuability of a function @xmath20 in terms of the associated objects @xmath47 and @xmath48 . in this section , we summarize some facts on several classes of meromorphic functions which will be used later . ( a detailed treatment of this subject can be found , e.g. , in duren @xcite and nevanlinna @xcite . ) in particular , we will recall the concept of pseudocontinuation . we will use @xmath49 and @xmath50 to denote the extended complex plane and the exterior of the closed unit disk , respectively , i.e. @xmath51 and @xmath52 . furthermore , the symbol @xmath53 stands for the normalized linear lebesgue - borel measure on @xmath34 . so we have @xmath54 , i.e. @xmath55 . assume that @xmath56 is one of the domains @xmath18 or @xmath50 . let @xmath57 be the nevanlinna class of all functions which are meromorphic in @xmath56 and which can be represented as a quotient of two bounded holomorphic functions in @xmath56 . if @xmath58 ( resp . @xmath59 ) , then a well - known theorem due to fatou implies that there is a set @xmath60 with @xmath61 and a borel measurable function @xmath62 such that @xmath63 for all @xmath64 . in the following , we will continue to use the symbol @xmath65 to denote such a boundary function of a function @xmath66 which belongs to @xmath67 or @xmath68 . there is a standard bijective correspondence between the sets @xmath67 and @xmath68 . in order to describe this we introduce some further notation . let @xmath56 be a nonempty subset of @xmath49 . then @xmath69 denotes that subset of @xmath49 which is symmetric to @xmath56 with respect to the unit circle , i.e. @xmath70 with the usual conventions @xmath71 and @xmath72 . here @xmath73 means the complex conjugate of @xmath74 . if @xmath75 , then @xmath76 stands for the complex - valued function which is defined on @xmath69 by @xmath77 now the bijective correspondence between the sets @xmath67 and @xmath68 can be expressed as follows . [ r2.1 ] if @xmath58 ( resp . @xmath59 ) , then the function @xmath78 belongs to @xmath68 ( resp . to @xmath67 ) and @xmath79 is the boundary function of @xmath78 . [ r2.2 ] let @xmath80 and let @xmath81 not vanish identically in @xmath56 . then the function @xmath82 is @xmath53-integrable and @xmath83 . the set @xmath67 ( resp . @xmath68 ) is obviously an algebra over @xmath84 . the subalgebra of all @xmath58 which are holomorphic in @xmath85 will be designated by @xmath86 . the class @xmath86 can be characterized as the set of all functions @xmath66 which are holomorphic in @xmath85 and which satisfy @xmath87 where @xmath88 for each @xmath89 . if a function @xmath90 admits a representation @xmath91 \,m(dt ) \right\ } , \quad \zeta\in{{\mathbb d}},\ ] ] with some @xmath92 and some borel measurable function @xmath93 satisfying @xmath94 | \,m(dt ) < + \infty,\ ] ] then @xmath95 belongs to @xmath86 and @xmath96 holds @xmath53-a.e . on @xmath97 such functions @xmath95 are called outer functions in @xmath86 . [ r2.3 ] let @xmath95 be an outer function in @xmath86 . then @xmath98 for all @xmath99 and the function @xmath100 is an outer function in @xmath86 as well . moreover , if @xmath101 and @xmath102 are outer functions in @xmath86 , then @xmath103 is an outer function in @xmath86 . an outer function @xmath95 in @xmath86 is called normalized if @xmath104 . [ r2.4 ] let @xmath105 be a function which does not vanish identically in @xmath85 . then @xmath41 is" +"recently we have shown that spontaneous symmetry breaking imposes a fundamental limit for the time that a large spin system can stay quantum coherent . this universal time - scale is @xmath0 , given in terms of the number of microscopic degrees of freedom @xmath1 , temperature @xmath2 , and the constants of planck ( @xmath3 ) and boltzmann ( @xmath4 ) @xcite . we analyzed this quantum decoherence process in terms of the exactly solvable lieb - mattis spin model , which is known to describe a symmetry broken macroscopic antiferromagnet in equilibrium . within this spin model we investigated the dynamical reduction of quantum physics to classical behavior via spontaneous symmetry breaking . the goal of this paper is to present a self - contained , detailed description and explanation of the decoherence process caused by spontaneous symmetry breaking . the fact that spontaneous symmetry breaking can lead to decoherence on a time scale @xmath5 might come as a surprise . for a macroscopic body at room temperature , @xmath6 is of order @xmath7 seconds , which is quite a short time . however , multiplying with avogadro s number @xmath8 , yields @xmath9 seconds , corresponding to a couple of centuries . given all other sources of decoherence for such a large macroscopic body , this is surely not a relevant timescale . however , the mesoscopic quantum qubits of contemporary interest are typically much smaller and the intrinsic coherence time might be reached in the near future . the counterintuitive feature of this intrinsic decoherence mechanism linked to classical equilibrium is that it starts to matter when systems become small . the many - particle qubits that motivate us to study decoherence due to spontaneous symmetry breaking are realized in a number of mesoscopic solid state systems . for instance , by engineering aluminum on a sub - micron length scale , superconducting flux qubits and cooper pair boxes can be manufactured . the flux qubit is a josephson device that can be brought into a quantum superposition of two electrical currents : a left and a right circulating current @xcite . typically this current is carried by @xmath10 cooper pairs . a cooper pair box on the other hand is a superconducting island , containing @xmath11 electrons , which can be brought in superposition of two states with a different number of cooper pairs @xcite . magnetic many - particle qubits are for instance realized in molecular nanomagnets . molecules with large magnetic moments can be brought into a superposition of directions of magnetization . a well studied example is mn@xmath12 acetate , a molecule that contains 12 manganese atoms , coupled together to form a total spin of @xmath13 . the molecule can be brought into a superposition of states with @xmath14 and @xmath15 and coherent rabi - oscillations of the magnetization are observed @xcite . an even larger molecule is ferritin , that contains about 4500 fe@xmath16 ions @xcite . if the total magnetic moment of a ferritin molecule is brought into a coherent superposition , this corresponds to a superposition of @xmath17 spins . for these mesoscopic superconducting and magnetic qubits the limit in coherence due to spontaneous symmetry breaking is relevant . this paper is organized as follows . we first introduce the general notion of spontaneous symmetry breaking and the thin spectrum . we illustrate these concepts by the elementary example of a harmonic crystal that breaks translational symmetry . we then show how the presence of a thin spectrum can cause decoherence . again we clarify the concept by describing a theoretical setup in which we use the crystal as a qubit . after that we switch to the more involved example of the ( non - abelian ) antiferromagnet . we first recapitulate the properties of the lieb - mattis model @xcite and determine its symmetric and symmetry - broken eigenstates . subsequently we will use the model to determine the effect of spontaneous symmetry breaking on quantum coherence . for this purpose we devise a generic gedanken experiment by coupling a two spin singlet state to the macroscopic lieb - mattis antiferromagnet . we calculate the exact time evolution of this many - body quantum superposition . our main result on decoherence follows from the evaluation of the reduced density matrix of the superposition by tracing out the thin states . finally we will then discuss what it reveals regarding spontaneous symmetry breaking in more general heisenberg - like spin hamiltonians . due to the homogeneity of space , the laws of nature possess translational invariance . this invariance implies the classical law of conservation of momentum . likewise , space being isotropic enforces rotational symmetry on the laws of physics , implying conservation of angular momentum . in quantum mechanics the power of symmetry is even greater : the translational and rotational invariance of the laws of nature taken at face value , should imply that any physical quantum object that obeys these laws , has translational and rotational symmetry . however , daily experience shows that this conclusion is nonsensical . if the universe around us and everything in it would be translationally and rotationally invariant , it would look the same at all places and in all directions : we would be surrounded by a `` quantum mist '' , while human observers should be dissolved in this quantum fog as well . however , in the real world translational and rotational symmetry are manifestly broken . the fundamental difference between quantum and classical physics lies in the role of symmetry . dealing with an exact quantum mechanical eigenstate , all configurations equivalent by symmetry should have exactly the same status in principle , while in a classical state one of them can be singled out . in the example above , given that space is translationally invariant , a quantum object should be in an eigenstate of total momentum , being spread out with equal probability over all of space . in the classical limit however it takes a definite position . the explanation of this ` spontaneous symmetry breaking ' as a ramification of the singular nature of the thermodynamic limit is one of the central achievements of quantum condensed matter physics @xcite . one imagines a symmetry breaking ` order parameter field ' @xmath18 ( e.g. , a potential singling out a specific position in space ) . upon sending @xmath18 to zero before taking the thermodynamic limit ( @xmath19 ) one finds the exact quantum groundstate respecting the symmetry . however , taking the opposite order of limits one finds that the classical state becomes fact . although the concept of spontaneous symmetry breaking was originally introduced in the context of quantum magnetism in solid state physics @xcite , spontaneous symmetry breaking is a general phenomenon , that is just as relevant in other fields , including elementary particle physics and cosmology @xcite . let us first consider how spontaneous symmetry breaking arises in a crystalline lattice to continue in the next section with antiferromagnets . consider the textbook example of a harmonic crystal , with the hamiltonian @xmath20 where @xmath21 labels all @xmath1 atoms in the lattice , which have mass @xmath22 , momentum @xmath23 and position @xmath24 . the harmonic potential between neighboring atoms is parameterized by @xmath25 ; it turns out that the results on spontaneous symmetry breaking that follow are equally valid for an - harmonic potentials . let us first identify the collective dynamics which describe the spontaneous symmetry breaking of this short - ranged microscopic hamiltonian . in the standard treatment of the quantum crystal one begins by introducing new coordinates , which are the displacements of atoms from their equilibrium position . then , after a fourier transform the eigenstates of this hamiltonian are easily found . we take a slightly longer route by introducing bosonic phonon operators from the very beginning and diagonalizing the quadratic part of the hamiltonian by performing a bogoliubov transformation at the end . in doing so we do not have to introduce any equilibrium position of the atoms . instead we can keep track of the center of mass motion of the crystal as a whole , and this brings to the fore the thin spectrum in a natural manner . moreover we can use the exact same procedure in the next section to find the collective order parameter dynamics for antiferromagnets . the momentum and position operators are expressed in terms of bosonic operators as @xmath26 so that the commutation relation @xmath27 = i \hbar \delta_{j , j'}$ ] is fulfilled . we choose @xmath28 so that the hamiltonian reduces to @xmath29 and after a fourier transformation @xmath30 , \nonumber \end{aligned}\ ] ] where @xmath31 , @xmath32 and @xmath33 is the lattice constant . this hamiltonian is still not diagonal , since the terms @xmath34 and @xmath35 create and annihilate two bosons at the same time . we get rid of these terms by a bogoliubov transformation ( see appendix ) . after this the hamiltonian in terms of transformed boson operators @xmath36 is @xmath37\nonumber \\ & = & 2 \hbar { \sqrt \frac{\kappa}{m } } \sum_k \sin |ka/2| \left [ n_k + \frac{1}{2 } \right ] , \label{eq : hbeta}\end{aligned}\ ] ] since @xmath38 . this result seems to coincide with the textbook hamiltonian which we would have obtained if we had followed the conventional route of fourier transforming the hamiltonian for the displacements , and then quantizing it . however , the bogoliubov transformation has the advantage that it brings to the fore a rather subtle point . when @xmath39 the excitation energy @xmath40 and the two parameters in the bogoliubov transformation diverge : @xmath41 and @xmath42 . precisely at @xmath43 the canonical transformation is no longer well defined . we therefore should investigate the bosonic terms in the hamiltonian with @xmath43 separately . this zero momentum part of the hamiltonian describes the obvious fact that the crystal as a whole carries a kinetic energy associated with the combined mass of all of its constituents , and is given by @xmath44\end{aligned}\ ] ] where @xmath45 so that @xmath46 where @xmath47 is the total momentum of the entire system , or equivalently , its center of mass momentum . when @xmath1 is large , this hamiltonian has states that are very low in energy . these states in fact form the thin spectrum of the harmonic crystal . we call this part of the spectrum _ thin _ because it contains so few states of such low energy that its contribution to the free energy in the thermodynamic limit completely disappears ( see appendix ) . in turn , this implies that these thin spectrum states do not contribute to any thermodynamically measurable quantities such as for instance the specific heat of the crystal . their effect on the properties of the crystal is thus increasingly subtle , but its existence can nonetheless have profound consequences . in classical systems this thin spectrum is absent : it is quantum mechanics that generates it . about a decade ago the deep meaning of the thin spectrum for interacting quantum systems became clear and consequently its explicit mathematical structure was determined @xcite . the groundstate of the hamiltonian at @xmath48 , which governs the collective behavior of the crystal as a whole , obviously has total momentum zero . it thus has no uncertainty in total momentum and maximum uncertainty in total position : translational symmetry is unbroken . symmetry breaking can occur if we add to the hamiltonian of equation a symmetry breaking field of the form @xmath49 , where the center of mass coordinate is @xmath50 . this yields a harmonic oscillator equation for the collective position coordinate . its well known groundstate wavefunction is @xmath51 this state describes a wave - packet for the center of mass coordinate in real space , which of" +"density functional theory@xcite ( dft ) combined with the generalized gradient approximation ( gga ) for the exchange and correlation functional has become a popular method for studying materials and molecules at the atomic scale . recently , there has been an increasing interest in using uniform real - space grids and finite - difference methods for doing dft calculations@xcite . real - space grids give an unbiased description of the wave functions and the quality of the description can easily be controlled by changing the grid - point density . finite - difference operators are used because the wave function values are given on grid points in real - space , and not in terms of a basis set . by doing all operations in real - space , parallelization can be done by simple domain decomposition@xcite . furthermore , real - space methods can make use of multigrid acceleration schemes@xcite for solving the kohn - sham equations@xcite and the poisson equation . a further advantage of real space methods is the possibility for imposing localization constraints on the wave functions , which is the basis for linearly scaling electronic structure methods@xcite ( order-@xmath0 methods ) . today , one of the most used methods for performing dft calculations is the pseudo potential method using periodic super - cells and plane - wave expansions for the pseudo wave - functions . this method shares with the grid - based methods the properties of unbiased representation of the wave functions and simple control of the quality of a calculation ( by changing the number of plane waves ) . however , there are three major difficulties with a plane - wave representation for the wave functions . 1 ) working with spatially localized wave functions , which is important for order-@xmath0 methods , is difficult with the extended nature of plane waves . 2 ) not all operations involving the wave functions , densities and potentials can be done directly in the plane - wave representation , and fourier transformations to and from real - space must be carried out . transformations between real and reciprocal spaces are highly non - local operations , and therefore difficult to parallelize . 3 ) due to the periodicity of plane waves , the natural boundary conditions for a plane wave calculation is periodic boundary conditions . although all three problems have been addressed@xcite , the suggested solutions are not as simple as for grid - based approaches where all three problems have simple solutions . an advantage of a plane - wave representation for the wave functions is its compactness . the memory footprint of a wave function is typically 10 times larger in a real - space grid representation compared to a plane - wave representation of similar accuracy . for this reason it is important to use soft pseudo wave functions that can be accurately represented on coarse grids . to our knowledge , until now , all applications of grid - based electronic structure calculations have used norm - conserving pseudopotentials . one way to get smoother pseudo wave functions is to relax the norm - conservation of the wave functions and use ultra - soft pseudopotentials@xcite or the projector augmented wave ( paw ) method@xcite . we have decided to use the paw method . the paw method works with soft valence wave functions and , similar to the ultra - soft pseudopotential method , the wave functions need not be normalized . contrary to the ultra - soft pseudopotential method , the paw method is an all - electron method within the frozen core approximation , giving access to the true wave functions and the full electron density . the paw method has been implemented for plane waves by several groups@xcite . we see the combination of real - space grid - based methods and the paw method as an important step towards enabling larger calculations at a level of accuracy which is essentially all - electron in nature . there is a clear trend in electronic structure theory towards larger and more complex systems as for example nanostructures , large ( bio-)molecular complexes and extended defects in real materials . systems which all quickly challenge present day high accuracy dft codes , that are typically limited to at most a few hundred atoms . the great potential of the method presented here lies in the parallelization of the real - space algorithms . this makes it possible to make use of massively parallel computers as has been demonstrated by several other groups@xcite . in this paper , we focus on how to do accurate dft calculations efficiently by using a real - space paw method . we demonstrate the accuracy of our grid - based paw calculations by showing that we are able to reproduce results for atomization energies from all - electron dft calculations . this very stringent test shows that the methodology that we have developed is useful for real applications . the solution of poisson s equation is straightforward using multigrid methods@xcite ( no fourier transformations required ) . solving the kohn - sham equations using multigrid methods is a much more difficult task : keeping the different eigenstates separated and orthogonal to each other can be a problem , and representing the hamiltonian on the coarse grids can also be problematic . we have decided to use the techniques typically used in `` state of the art '' pseudopotential plane - wave calculations@xcite as they have been developed and improved over the the last few decades . for iteratively solving the kohn - sham equations , we use pulay mixing techniques for obtaining the self - consistent density@xcite , subspace diagonalizations , and the residual minimization method@xcite using preconditioning of the electronic gradients for iteratively improving the wave functions . the preconditioning operation is a single multigrid v - cycle using only the kinetic energy operator as an approximate hamiltonian@xcite . in the following section , we will briefly summarize the paw method . then , in section [ grids ] , we will go through the details of our grid - based formulation of the paw formalism . in section [ groundstate ] , we describe how we solve the kohn - sham equations , and the evaluation of atomic forces is discussed in section [ forces ] . section [ generalizations ] describes generalizations of the method to periodic systems with use of brillouin zone sampling . in section [ applications ] we apply the methodology that we have developed to a number of example systems and discuss approximations necessary for realistic calculations . finally , in section [ performance ] we discuss the computational performance of our implementation . the notation we use is close to the one used by p. e. blchl in his papers on the paw method@xcite . we have used hartree atomic units ( @xmath1 ) and we write the equations for the case of a spin - paired and finite system of electrons . the paw method is based on a transformation between smooth pseudo wave functions , @xmath2 , and the true all - electron kohn - sham wave functions , @xmath3 ( @xmath4 is the band index ) . the core states of the atoms , @xmath5 , are frozen . here @xmath6 is an atom index and @xmath7 is a combination of principal , angular momentum , and magnetic quantum numbers respectively ( @xmath4 , @xmath8 and @xmath9 ) . given a smooth pseudo wave function , the corresponding all - electron wave function , which is orthogonal to the set of @xmath5 orbitals , can be obtained through a linear transformation @xmath10 the transformation operator , @xmath11 , is given in terms of atom centered all - electron wave functions , @xmath12 , the corresponding smooth partial waves , @xmath13 , and projector functions , @xmath14 , as @xmath15 the atom centered all - electron wave functions are taken from a calculation of a single atom with spherical symmetry : @xmath16 , where the @xmath17 s are real - valued spherical harmonics ( @xmath18 is a combined index for @xmath8 and @xmath9 ) . a radial cutoff distance , @xmath19 , defining the atomic augmentation sphere is chosen . this radius is similar to a cutoff radius for a pseudopotential . the larger the augmentation sphere , the smoother the pseudo wave functions , but overlap with neighboring augmentation spheres must be avoided . for all all - electron valence states smooth partial waves @xmath20 are constructed . the partial waves must match the corresponding all - electron waves for @xmath21 . in this way , the correction in parenthesis in eq . ( [ transform ] ) is zero outside the augmentation spheres and we will have @xmath22 in this region . notice , that there are no norm - conservation requirements to meet when choosing the shape of @xmath23 inside the augmentation sphere . smooth projector functions must also be defined one for each partial wave : @xmath24 . they must be localized inside the augmentation spheres and satisfy @xmath25 , which for the radial part gives @xmath26 with this construction we have @xmath27 . in principle , an infinite number of projectors and partial waves are required for the paw method to be exact . for practical calculations , a high accuracy data set will need only one or two projector functions for each angular momentum channel of importance . this is similar to an ultra - soft pseudopotential , where a comparable number of projectors is needed . one partial wave is usually taken as the bound valence state , and additional waves can be taken from `` excited states '' solutions to the radial kohn - sham equation at different non - eigenvalue energies . the construction of partial waves and projector functions is described in appendix [ construction ] . > from the atomic frozen core electron density , @xmath28 , a smooth core electron density , @xmath29 , is constructed . it must be identical to @xmath28 for @xmath21 . there is no norm - conservation requirement to meet when choosing the shape of @xmath29 inside the augmentation sphere . the pseudo electron density has contributions from the wave functions and from the atom centered smooth core electron densities : @xmath30 where the @xmath31 s are occupation numbers and @xmath32 is the position of atom @xmath6 . an atomic density matrix ( see eq . ( 22 ) in ref . ) is defined as @xmath33 where @xmath34 the paw formalism defines atom centered all - electron and pseudo electron densities as @xmath35 and @xmath36 respectively . by construction , @xmath37 is identical to the all - electron density , @xmath38 , for @xmath39 and @xmath40 for @xmath41 ( see ref . for details ) . therefore , the true all - electron density can be obtained from the pseudo electron density : @xmath42.\ ] ] again , the correction is zero outside the augmentation spheres . a neutral charge density , @xmath43 , is obtained by adding compensation charges , @xmath44 , inside the augmentation spheres to the pseudo electron density . these charges compensate for the lack of norm - conservation and for the nuclear charge : @xmath45 using localized functions @xmath46 normalized as @xmath47 the compensation charges are constructed with electrostatic multipole moments @xmath48 : @xmath49 the values to be used for the electrostatic multipole moments , @xmath48 , are found by requiring the pseudo charge density , @xmath50 , to have the same electrostatic multipole moments as the all - electron charge density , @xmath51 , where @xmath52 is the nuclear charge density ( @xmath53 is the atomic number ) . this requirement can be expressed as @xmath54 y_l(\hat{\mathbf{r } } ) = 0.\ ] ] inserting eqs . ( [ n ] ) , ( [ nt ]" +"in the present - day view , mergers are a common and important way of building up massive elliptical galaxies . with the presence of supermassive black holes in the centers of most galaxies ( @xcite ; @xcite ; @xcite ) , merger processes are thought to have left signatures on the central structure of the remnant galaxies . @xcite suggest that a binary black hole that is formed by the merger of two galaxies scours the stars from the center of the newly created system as the binary shrinks . the energy liberated by the hardening of the binary evacuates the central part through the ejection of surrounding stars , causing less light in the center . _ hubble space telescope _ ( _ hst _ ) observations of galaxy nuclei see two kinds of behavior in the central light profiles of ellipticals , traditionally classified as `` power - law '' and `` core '' galaxies @xcite . the power - law profiles took their name from their approximation by a single power law at small radii ( @xmath6 or 20 ) . more modern interpretations have emphasized that these profiles can be better understood as the inward continuation of the galaxy s overall srsic profile , usually modified by an additional , nuclear - scale stellar component @xcite . the core galaxy , in contrast , displays a surface brightness profile with a distinct break from a steep outer slope to a shallower inner cusp . core profiles mainly occur in very luminous elliptical galaxies and are considered the result of dissipationless mergers of two galaxies that have central black holes . much numerical work has been done to explore the binary black hole idea . the work of @xcite suggests that the stellar mass ejected from the core is comparable to the mass of the central black hole @xmath0 . @xcite find that core radius roughly doubles after each major merger . @xcite , using isothermal king models , suggest that the core size should scale with the final @xmath0 . simulations performed by @xcite show for the first time that merging two galaxies with steep cusps can result in a merger remnant with a shallow power - law cusp in the inner part ( core ) . @xcite is the first to quantify the magnitude of the mass deficit ( or the mass ejected by the binary ) with respect to the galaxy s merger history . by following the binary evolution up to the stalling radius , he formulates the mass deficit to be @xmath7@xmath0 with @xmath8 is the number of major merger events . an investigation into the post - coalescence stage of the binary suggests that the mass deficit could still be larger . this is because the coalescing binary emits gravitational waves which impart a kick on the merged black hole and eject it from the center . due to dynamical friction , the resulting oscillations of the black hole would gradually damp , returning it to the center of the galaxy and ejecting more stars from the core . this process could increase the mass deficit existing before the binary coalescence by up to 5@xmath0 for a single merger @xcite . several publications in the past have performed function fitting to galaxy profiles in order to quantify the core parameters such as the core size , the deficit in light or mass , and to analyse the correlation between these core properties and @xmath0 or the global properties of the galaxies ( @xcite ; @xcite ; @xcite , kormendy et al . ( 2009 , hereafter kfcb09 ) , kormendy & bender ( 2009 , hereafter kb09 ) , @xcite ; @xcite ; see also @xcite ) . these studies are based on different samples , datasets , approaches , parametrizations , and assumptions , which apparently lead to different , partly systematic , core quantities . the most important difference is the amount of central mass deficit with respect to the black hole mass that can be expected in core galaxies . @xcite and @xcite find an average mass deficit of around twice the black hole mass , @xcite derive central mass deficits of about 0.54 @xmath0 while find their mean mass deficit to be 10.5 @xmath0 . aside from that , each of these studies has a drawback in at least one of three aspects crucial to achieve high accuracy . the first is the radial range of the surface brightness profiles . @xcite , @xcite , and @xcite fit galaxy profiles that extend typically to only 1020 . moreover , it appears that some galaxy profiles in @xcite , which are taken from lauer et al . ( 2005 , hereafter l05 ) , suffer from oversubtraction of the sky that biases the core - srsic fits ( see section [ previousfits ] ) . a full galaxy profile is necessary to properly measure the outer profile , to optimally remove the sky background , and thus to provide better constraints on the light and mass deficit . the second is the determination of the stellar mass - to - light ratio ( @xmath9 ) to convert the light deficit to the mass deficit . in the past studies , either different values are assigned to the galaxies according to their luminosities ( @xcite , ) or a constant value is assumed for all the galaxies in the sample ( @xcite , @xcite ) . this of course introduces additional uncertainties and biases in deriving the mass deficits . the last important aspect lies in the black hole masses , which are mostly derived from outdated black hole - bulge relations , especially the ones between @xmath0 and the velocity dispersion of the host bulge ( @xmath0@xmath3relation ) . the majority of core galaxies are bright massive elliptical galaxies . for this class of galaxies @xcite find that the @xmath10-@xmath11 relation predicts a higher density of massive black holes ( @xmath12 @xmath13 ) compared to the @xmath0@xmath3 relation . furthermore , the @xmath0@xmath3 relation used in these papers also fails to predict the existence of the largest black holes ( @xmath14@xmath13 ) that are found in distant quasars @xcite in the sample of local galaxies . the recent finding of black holes of 10 billion solar masses @xcite , which might be the missing link between the local black holes and the massive distant quasars , further supports the indications that the previous @xmath0@xmath3 relations for massive bright early type galaxies need to be reevaluated ( e.g. , * ? ? ? in addition , most previous studies have used @xmath0 measurements ( or @xmath0@xmath3relations based on @xmath0 measurements ) which did not include dark - matter halos in the modeling . values typically increase by @xmath15% @xcite or 30% ( * ? ? ? * hereafter paper i ) when dark matter is included in the modeling , but the increase can be as large as a factor of 6 when the black hole s sphere of influence is not well resolved @xcite . in the particular sample that we use in this paper , which includes bcgs , we find that the measured black hole mass is on average more than 3 times higher than that predicted by the @xmath0@xmath3 relation ( e.g. @xcite , @xcite , @xcite . in this paper , we combine improved core - property measurements with new measurements and present the analysis of possible relations between the core and black hole mass or the galaxy properties . we use only directly measured black hole masses and consequently avoiding scatter and possible biases inherent in using proxy measurements . we use dynamically - determined , individual stellar mass - to - light ratios ( @xmath2 ) to estimate the mass deficit , instead of relying on a scaling function or a constant value . we also use full galaxy profiles in the fitting and the quantification of the core parameters . our analysis is based on a sample of 20 galaxies ; seven of these galaxies are taken from , in which the black hole masses and @xmath2 are derived taking into account the presence of dark matter halos . for completeness , we add a further 3 galaxies to the sample ; they are not included in the main sample due to the lack of reliable literature sources for the black hole masses . in order to derive the mass deficit , we assume that the original ( pre - scouring ) profile is the extrapolated srsic profile that fits the light distribution at large radii . in section [ themethod ] , we describe the method that we use to identify the core galaxies and to fit the observed surface brightness profiles . in section [ corefitting ] , we present the best - fitting models for each galaxy ; cases where galaxies are best fit with the addition of an outer envelope are discussed in section [ multi - component - fits ] . we compare the fitting results with previous studies in section [ previousfits ] . section [ coredeficit ] presents the details of how the luminosity and mass deficit in the core are computed based on the best - fitting models . the core - related quantities derived in section [ corefitting ] and [ coredeficit ] are compared with the black hole mass , velocity dispersion and galaxy luminosity in section [ bhcore ] . the last section discusses and summarizes the results . all of the photometric profiles examined in this work are quite extended , reaching out to at least 9 kpc . therefore , we base our analysis on a function that is designed to fit not just the inner or the outer part of galaxies , but rather the galaxy as a whole . to identify core galaxies , we follow the criteria in @xcite and @xcite , who define the core as `` a downward deviation from the inward extrapolation of the outer ( srsic ) profile '' . this involves fitting the galaxy in question with both the srsic and the core - srsicfunctions . the srsic profile @xcite is written as : @xmath16 \right\}. \label{sersiceq}\ ] ] @xmath17 is the intensity at @xmath18 , the projected half - light radius . @xmath19 is called the srsic index which describes the shape or curvature of the light profile . the quantity @xmath20 is a function of @xmath19 , defined in such a way that @xmath18 encloses half of the total luminosity . we approximate @xmath21 by using the asymptotic expansion of @xcite , eq . 18 for @xmath22 . many other approximation formulas are available and are summarized in @xcite . for @xmath23 , the srsic function reduces to an exponential function and for @xmath24 , it becomes the de vaucouleurs profile @xcite . the core - srsic function introduced by @xcite and @xcite is expressed as : @xmath25^{\gamma/\alpha}\,{\rm exp}\left[-b_n\left(\frac{r^\alpha+r_b^\alpha}{r_e^\alpha}\right)^{1/n\alpha}\right ] \label{coresersiceq1}\ ] ] with @xmath26 . \label{coresersiceq2}\ ] ] this profile consists of a srsic profile in the outer part , specified by the projected half - light radius @xmath18 and the srsic index @xmath19 , and a power - law profile in the inner part with a slope of @xmath27 . the change from one to another regime occurs at the break radius @xmath28 and the sharpness of the transition is specified by the parameter @xmath29 . higher values of @xmath29 mean sharper transitions . @xmath20 is approximated in the same way as for the srsic function . we summarize four criteria in @xcite that we use to identify core galaxies below . in section [ corefitting ] we examine each criterion . 1 . a characteristic pattern should be visible in the residuals when fitting a srsic profile to an idealized core galaxy . this serves as a qualitative evidence . 2 . a core" +"the nucleation of microscopic crystallites in polymer liquids is profoundly influenced by flow @xcite . this flow - induced crystallization ( fic ) , is a fascinating example of an externally driven , non - equilibrium phase transition , controlled by kinetics . furthermore , fic is ubiquitous in industrial processing of semi - crystalline polymers , the largest group of commercially useful polymers . a fundamental understanding of fic promises extensive control of polymer solid state properties , as virtually every property of practical interest is determined by the crystal morphology . flow can drastically enhance nucleation and trigger the formation of highly aligned , elongated crystals , known as shish kebabs @xcite . recent experiments on entangled polymers , have studied , in detail , shish kebab formation @xcite and the role of blend concentration @xcite , molecular architecture @xcite and molecular relaxation time @xcite . often the most pronounced flow - induced effects occur near the melting point , where quiescent crystallization is immeasurably slow @xcite . the widely postulated mechanism for fic states that flow forces the polymer chains into elongated configurations , which lowers the entropic penalty for crystallization @xcite . however , this hypothesis has yet to be developed into a quantitative molecular model . fic is extremely sensitive to the flow - induced configurations of the non - crystalline chains , so an accurate molecular flow model is an essential prerequisite . unfortunately , most polymer flow models predict only the macroscopic stress tensor and not the full molecular configuration . alternatively , detailed simulations of polymer crystallization have provided much useful information on the growth process @xcite , yet simulating primary nucleation has proven difficult , especially at low undercooling , because of the extremely long nucleation times . at a much higher level of coarse - graining , models based on differential equations either assume an empirical dependence of the nucleation rate on the flow conditions @xcite , the stress tensor @xcite , or the chain stretch @xcite ; or assert that free energy changes under flow can be directly subtracted from the nucleation barrier @xcite . in either case the postulated fic mechanism remains untested . an intermediate level of coarse - graining is required to surmount these difficulties . this letter presents coarse - grained kinetic monte carlo ( mc ) @xcite simulations of anisotropic nucleation in flowing polymers . we compute chain configurations using a recent molecular flow model @xcite that reliably predicts both neutron scattering @xcite and bulk stresses . our simulations predict both enhanced nucleation and elongated shish nuclei . kinetic mc has previously been used to model quiescent crystal growth in dilute polymers @xcite . however , it is particularly suited to nucleation and our algorithm is tractable even at low undercooling , providing an efficient and highly flexible framework to simulate general anisotropic nucleation under external fields . we compute the transient chain configuration of the uncrystallized chains under flow using the glamm model @xcite , with finite chain extensibility included using cohen s approximation @xcite . the chains are divided into @xmath0 sub - chains , each corresponding to an entanglement segment of @xmath1 kuhn steps of length @xmath2 . we take @xmath3 throughout this letter . one deterministic run of the model provides the end - to - end vector @xmath4 , where the ensemble average is for sub - chains of type @xmath5 . the data for an entire transient flow are used later in the nucleation simulations . all flow timescales are in units of the subchain rouse time @xmath6 and @xmath7 is normalized by @xmath8 . deformation of the amorphous chains has two effects on the nucleation kinetics : stretching reduces the entropic penalty for crystallization ; and monomer alignment modifies the probability of compatible alignment with the nucleus . the change in elastic free energy @xmath9 for chains with ensemble average constraints @xmath10 , but locally at equilibrium , can be calculated by statistical mechanics @xcite . although an analytic calculation is not possible for finitely extensible chains , steep free energy gradients in highly stretched chains suppress fluctuations . thus our numerical calculations for uniaxial deformations show that @xmath11 can be accurately approximated by an expression that interpolates between gaussian elasticity @xcite for small @xmath12 and cohen s @xcite approximation with @xmath13 at high stretching , @xmath14 similarly , numerical calculation of the monomer orientation distribution @xmath15 for chains with a constraint @xmath16 are well approximated by using @xmath13 in the expression for @xmath15 derived from a direct constraint on @xmath7 @xcite . @xmath17}{4\pi\sinh(\mathcal{l}^{-1}[\sqrt{{\mathrm{tr } \,}{{\mathbf{f}}}}/n_e ] ) } \cosh\left(\mathcal{l}^{-1}\left[\frac{\sqrt{{\mathrm{tr } \,}{{\mathbf{f}}}}}{n_e}\right]\cos\theta\right ) , \end{array}\ ] ] where @xmath18 is the inverse langevin function and @xmath19 is the angle between the monomer and the principle axis of @xmath16 . each subchain has an individual @xmath20 so is treated as a separate species with concentration @xmath21 . our coarse - grained simulations use the minimal nucleus description required for anisotropic nucleation . the nucleus comprises @xmath22 crystallized `` monomers '' or kuhn steps , arranged in stems , with each stem formed from a single chain ( see fig [ fig : nucfig ] ) . the total number of stems @xmath23 and the number of monomers in each stem is simulated . the arrangement of the monomers within the crystal is not resolved . the nucleus is assumed to be spheroidal with the polar radius @xmath24 parallel to the stems . assigning a crystalline volume of @xmath25 to each monomer and normalizing all lengths by @xmath26 gives the equatorial radius @xmath27 , the volume @xmath28 and thus the polar radius @xmath29 . we also simulate the unit vector @xmath30 parallel to the polar radius . as in classical nucleation theory the nucleus free energy comprises the free energy of crystallization , proportional to the nucleus volume , and a free energy penalty proportional to the surface area @xmath31 . thus the free energy in units of @xmath32 is @xmath33 , where @xmath34 and @xmath35 are the coefficients of the volume and surface area free energies , respectively . we simulate two types of mc moves : addition of a new stem containing one monomer and lengthening of an existing stem by adding a new monomer , each with a corresponding reverse move . as in @xcite we assume that to attach , a monomer must be oriented within a solid tolerance angle @xmath36 of the nucleus orientation . for small @xmath36 , the fraction of monomers within this angle is @xmath37 , where @xmath19 is the angle between the nucleus polar radius and the sub - chain principle strain axis . the stem attachment rate for species @xmath5 is proportional to its melt concentration @xmath38 . in contrast , for stem lengthening only the next monomer along the chain forming the stem can crystallize . the concentration of this monomer at the nucleus surface where the lengthening event occurs is taken to be unity . thus the attachment ( @xmath39 ) and detachment ( @xmath40 ) move rates for stem addition ( @xmath41 ) and stem lengthening ( @xmath42 ) are : @xmath43 where @xmath44 is the time for a monomer attachment attempt , @xmath45 is the fraction of correctly aligned monomers ( normalized to unity in the quiescent limit ) , and the constant @xmath46 has been added to @xmath34 . the free energy change of attaching a new stem of species @xmath5 is @xmath47 where @xmath48 is the flow - induced free energy change in sub - chain @xmath5 . similar calculations give the free energy changes for the other move types . a stem can only be detached if it contains a single monomer . the kinetic mc algorithm requires a sum over all possible move rates . the area available for stem addition moves is @xmath49 , which is taken to be proportional to @xmath50 , and to give spherical nuclei in the quiescent limit . to obey detailed balance the rate of stem removal must be multiplied by @xmath51 , the probability of a given stem being at the nucleus surface . each stem can lengthen or shorten from either the top of bottom . thus the total sum over all possible move rates is : @xmath52 at each kinetic mc timestep one move is performed at random , with the selection probability weighted by the move rate . time is then incremented by a stochastically determined interval @xmath53 , where @xmath54 is chosen uniformly on @xmath55 $ ] @xcite . after each mc step the nucleus orientation @xmath30 is incremented over @xmath56 by brownian dynamics . flow rotates the spheroid nucleus through the jeffery algorithm @xcite . the angular diffusion time @xmath57 scales with both the nucleus volume @xmath22 and aspect ratio @xmath58 following the expressions in @xcite , giving @xmath59 , where @xmath60 depends only on the aspect ratio and we have introduced a dimensionless constant @xmath61 , connecting @xmath57 with the monomer attachment time @xmath44 . as the jeffery algorithm is for newtonian fluids we have neglected non - newtonian effects here . after each time step all @xmath20 values are updated from the glamm model results , and @xmath48 and @xmath62 are recalculated . the parameter @xmath63 sets the ratio of flow and monomer attachment timescales . we use @xmath64 throughout this letter , unless indicated otherwise , although similar results are obtained for any value of @xmath65 . each simulation evolves a single nucleus from a single monomer . the algorithm is especially effective at low undercooling , as for small nuclei the rate sum is small , leading to large time steps . the quiescent free energy landscape can be calculated analytically from @xmath34 and @xmath66 to give a dimensionless nucleation barrier @xmath67 and a critical nucleus of @xmath68 monomers . the simulated nucleation time @xmath69 is the first time the polar and equatorial radii simultaneously exceed the critical radius @xmath70{3n^*/4\pi}$ ] . choosing a larger threshold size for nucleation has little effect on @xmath71 . the results are accurately approximated by @xmath72 . we obtained good statistics for barriers up to @xmath73 in @xmath74hrs on one @xmath75ghz processor , giving a nucleation time of @xmath76 . the nucleation times are poisson distributed , so the nucleation rate can be defined as @xmath77 . under flow , the nucleation kinetics depend on the evolving chain deformation . we define the instantaneous nucleation rate @xmath78 where @xmath79 is the cumulative fraction of runs nucleated at time @xmath80 . for shear rates @xmath81 that are slow compared to the critical nucleus rotation time ( @xmath82 ) alignment effects can be ignored , equivalent to taking @xmath83 . the glamm model predictions for start - up of constant shear at @xmath84 of a @xmath85 melt and the resulting instantaneous nucleation rate are in fig [ fig : nucdata](a ) . the results are independent of the ratio of flow and crystallization timescales for @xmath86 . in fact , fixing the non - crystalline chain configuration to that corresponding to flow time @xmath80 for the entire simulation and plotting the resulting quasi - static nucleation rate against @xmath80 , reproduces the transient results ( fig [ fig : nucdata]a ) . thus nucleation is fully controlled by the instantaneous configuration of the surrounding chains , if @xmath87 . the stretch ratio @xmath88 is the dominant factor determining the nucleation rate , despite variations in flow rate , molecular weight and flow geometry ( fig [ fig : nucdata](b ) ) . this universal result is somewhat surprising as the distribution of stretch along the chain varies considerably with flow conditions , which may be expected to influence nucleation , especially if molecular weight and flow geometry is varied . this result will be useful in deriving simple differential models of fic @xcite as the nucleation rate can be described the expression @xmath89 , where @xmath90 is a fitting constant ." +"minimizers of a submodular function form a distributive lattice , and are compactly represented by a poset ( partially ordered set ) via birkhoff representation theorem . this fact reveals a useful hierarchical structure of the minimizers , and is applied to the dm - decomposition of matrices and further refined block - triangular decompositions @xcite . in this paper , we address such a birkhoff - type representation for minimizers of a _ @xmath0-submodular function_. here @xmath0-submodular functions , introduced by huber kolmogorov @xcite , are functions on @xmath2 defined by submodular - type inequalities . this generalization of ( bi)submodular functions has recently gained attention for algorithm design and modeling @xcite . our main result is to establish a compact representation for minimizers of a @xmath0-submodular function . this can be viewed as a generalization of the above poset representation for submodular functions and ando fujishige s signed - poset representation for bisubmodular functions @xcite . a feature of our representation is to utilize a _ poset with inconsistent pairs ( pip ) _ @xcite , which is a discrete structure having a stronger power of expression than that of a signed - poset . actually a pip is a poset endowed with an additional binary relation ( _ inconsistent relation _ ) , and is viewed as a poset reformulation of 2-cnf . this concept , also known as an _ event structure _ , was first introduced by nielsen plotkin winskel @xcite as a model of concurrency in theoretical computer science , and was independently considered by barthelemy constantin @xcite to establish a birkhoff - type representation theorem for a _ median semilattice_a semilattice generalization of a distributive lattice . a pip was recently rediscovered by ardila sullivant @xcite to represent nonpositively - curved cube complexes ; the term `` pip '' is due to them . our results consist of structural and algorithmic ones , summarized as follows : [ [ structural - results . ] ] structural results . + + + + + + + + + + + + + + + + + + + we show that minimizers of a @xmath0-submodular function form a median semilattice ( lemma 3 ) . by a birkhoff - type representation theorem @xcite for median semilattices , the minimizer set is represented by a pip , where minimizers are encoded into special ideals in the pip , called _ consistent ideals_. pips arising from @xmath0-submodular functions are rather special . we completely characterize such pips ( theorem [ thm : closed_set_and_elementary_pip ] ) , which we call _ elementary_. this representation is actually compact . we show that the size of the elementary pip for a @xmath0-submodular function of @xmath3 variables is @xmath4 ( proposition [ prop : number_of_irreducibles ] ) . [ [ algorithmic - results . ] ] algorithmic results . + + + + + + + + + + + + + + + + + + + + we present algorithms to construct the elementary pip of the minimizers of a @xmath0-submodular function @xmath1 under the following three situations : * a minimizing oracle of @xmath1 is given . * @xmath1 is network - representable . * @xmath1 arises from a potts energy function . for ( i ) , we show that the pip is obtained by calling the minimizing oracle @xmath5 time ( theorem [ thm : alg_oracle ] ) . notice that a polynomial time algorithm to minimize @xmath0-submodular functions is not known for the value - oracle model but is known for the valued - csp model @xcite . our result for ( i ) is applicable to such a case . for ( ii ) ( and ( iii ) ) , we consider an efficiently minimizable class of @xmath0-submodular functions considered in @xcite , where a @xmath0-submodular function in this class is represented by the cut function in a network of @xmath4 vertices and can be minimized by a minimum - cut computation . we show that the pip is naturally obtained from the residual graph of a maximum flow in the network ( theorems [ thm : network_algo ] and [ thm : network_time ] ) . for ( iii ) , we deal with a @xmath0-submodular function @xmath6 obtained from a @xmath0-label potts energy function @xmath7 by adding the @xmath8-label ( meaning `` non - labeled '' ) . such a @xmath0-submodular function , called _ potts @xmath0-submodular _ , is particularly useful in vision applications . indeed , via the _ persistency property _ @xcite , a minimizer of @xmath9 ( an optimal labeling ) is partly recovered from a minimizer of the relaxation @xmath10 . kolmogorov @xcite showed that a minimizer of a potts @xmath0-submodular function can be obtained by @xmath11 calls of a max - flow algorithm performed on a network of @xmath12 vertices . we show that the pip is also obtained in the same time complexity ( theorem [ thm : potts ] ) . in showing this result , we reveal an intriguing structure of the pip for a potts @xmath0-submodular function ( theorem [ thm : pip_potts ] ) , and utilize results @xcite from undirected multiflow theory . we also discuss enumeration aspects for minimizers . maximal minimizers , which are minimizers with a maximal number of nonzero components , are of particular interest from the view of partial optimal labeling . for a potts @xmath0-submodular function , we show that the problem of enumerating all maximal minimizers reduces to the problem of enumerating all ideals of a single poset ( theorem [ thm : enumeration_potts ] ) . this enables us to use an existing fast enumeration algorithm , and leads to a practical algorithm enumerating all maximal partial optimal labeling in actual computer vision problems . we present experimental results for real instances of stereo matching problems . [ [ organization . ] ] organization . + + + + + + + + + + + + + the rest of this paper is organized as follows . in section [ sec : preliminaries ] , we give preliminaries including a birkhoff - type representation theorem between pips and median semilattices . in section [ sec : structure ] , we prove the above structural results . in section [ sec : algorithms ] , we prove the algorithmic results . finally , in section [ sec : application ] , we describe applications and present experimental results . for a nonnegative integer @xmath3 , we denote @xmath13 by @xmath14}}$ ] ( with @xmath15 } } \defeq \varnothing$ ] ) . for a subset @xmath16 of an ordered set , let @xmath17 denote the minimum element in @xmath16 ( if it exists ) . let @xmath18 be the set of real numbers and @xmath19 . for a function @xmath1 from a set @xmath20 to @xmath21 , a _ minimizer _ of @xmath1 is an element @xmath22 that satisfies @xmath23 for all @xmath24 . the set of minimizers of @xmath1 is simply called the _ minimizer set _ of @xmath1 . we assume that posets are always finite , and assume the standard notions of lattice theory , such as join @xmath25 and meet @xmath26 . let @xmath0 be a positive integer . let @xmath27 denote @xmath28 . the partial order @xmath29 on @xmath27 is defined by @xmath30 if and only if @xmath31 for each @xmath32 . consider the @xmath3-product @xmath33 of @xmath27 , where the partial order on @xmath33 is defined as the direct product of @xmath29 and is also denoted by @xmath29 . in this way , @xmath33 and its subsets are regarded as posets . for @xmath34 , the _ support _ of @xmath35 is the subset of indices @xmath36}}$ ] with nonzero @xmath37 , and is denoted by @xmath38 : @xmath39}}}\mathrel{}\middle|\mathrel{}{x_i \neq 0}\right\}}.\end{aligned}\ ] ] a _ @xmath0-submodular function _ @xcite is a function @xmath40 satisfying the following inequality @xmath41 for all @xmath42 . here the binary operation @xmath43 on @xmath33 is given by @xmath44 for every @xmath42 and @xmath36}}$ ] . the operation @xmath45 in is dually defined by changing @xmath46 to @xmath47 in . besides its recent introduction , a @xmath0-submodular function seems to be recognized when bouchet @xcite introduced _ multimatroids_. indeed , a @xmath0-submodular function is a direct generalization of the rank function of a multimatroid , and was suggested by fujishige @xcite in 1995 as a _ multisubmodular function_. it is not known whether @xmath0-submodular functions for @xmath48 can be minimized in polynomial time on the standard oracle model . however , some special classes of @xmath0-submodular functions are efficiently minimizable . for example , kolmogorov thapper ivn @xcite showed that a sum of low - arity @xmath0-submodular functions can be minimized in polynomial time , where the _ arity _ of a function is the number of variables . a nonnegative combination of binary _ basic @xmath0-submodular functions _ , introduced by iwata wahlstrm yoshida @xcite , can be minimized by computing a minimum @xmath49-cut on a directed network ; see section [ sec : network ] . a nonempty subset of @xmath33 is said to be _ @xmath50-closed _ if it is closed under the operations @xmath43 and @xmath45 . from , the following obviously holds . the minimizer set of a @xmath0-submodular function is @xmath50-closed . a key tool for providing a compact representation for @xmath50-closed sets is a correspondence between median semilattices and pips , which was established by barthlemy constantin @xcite . a recent paper @xcite also contains an exposition of this correspondence . a _ median semilattice _ @xcite is a meet - semilattice @xmath51 satisfying following conditions : ms every principal ideal is a distributive lattice . for all @xmath52 , if @xmath53 and @xmath54 exist , then @xmath55 exists in @xmath56 . note that every distributive lattice is a median semilattice . an element of @xmath56 is said to be _ join - irreducible _ if it is not minimum and is not represented as the join of other elements . let @xmath57 denote the set of join - irreducible elements of @xmath56 . next we introduce a _ poset with inconsistent pairs ( pip)_. a pip @xcite is a poset @xmath58 endowed with an additional symmetric relation @xmath59 satisfying the following conditions : ic for all @xmath60 with @xmath61 , there is no @xmath62 with @xmath63 and @xmath64 . for all @xmath65 , if @xmath66 and @xmath67 , then @xmath61 . a pip is also denoted by a triple @xmath68 . the relation @xmath59 is called an _ inconsistent relation_. each unordered pair @xmath69 of @xmath70 is called _ inconsistent _ if @xmath61 . note that every inconsistent pair of @xmath70 is incomparable and has no common upper bound in @xmath70 . an inconsistent pair @xmath69 of @xmath70 is said to be _ minimally inconsistent _ if @xmath71 , @xmath72 and @xmath67 imply @xmath73 and @xmath74 for all @xmath75 . if @xmath69 is minimally inconsistent , the @xmath61 is particularly denoted by @xmath76 . we can easily check the following properties of the minimally inconsistent relation : mic for all @xmath60 with @xmath76 , there is no @xmath62 with @xmath63 and @xmath64 . for all @xmath65 with @xmath71 and @xmath72 , if @xmath77 and @xmath76 , then @xmath78 and @xmath79 . actually , pips can also be defined as a triplet @xmath80 , where @xmath81 is a binary symmetric relation on a poset @xmath58 satisfying the conditions ( mic1 ) and ( mic2 ) . in this definition , the inconsistent relation @xmath59 on @xmath70 is obtained by @xmath82 for every @xmath60 . since both definitions of pips are equivalent , we will use a convenient one . for a pip @xmath70 , an ideal of @xmath70 is said to be _ consistent _ if it contains no ( minimally ) inconsistent pair . let @xmath83 denote the family of consistent ideals of" +"the detection of delayed x - ray , optical and radio emission , `` afterglow '' , following a grb is reasonably described by emission from a spherical relativistic shell , decelerating upon collision with an ambient medium ( waxman 1997a , mszros & rees 1997 , katz & piran 1997 , sari , piran & narayan 1998 ) . a relativistic blast wave is formed and expands through the surrounding medium , heating the matter in it s wake . the observed afterglow is believed to be due to synchrotron emission of relativistic electrons from the heated matter . the surrounding medium will be referred to as interstellar medium ( ism ) , though this may not necessarily be the case . at any given time , a detector receives photons which were emitted at different times in the observer frame , at different distances behind the shock front and at different angles from the line of sight ( los ) to the center of the grb . the properties of the matter are different at each of these points , and so are the emissivity and the frequency of the emitted radiation . early calculations have considered emission from a single representative point ( mszros & rees 1997 , waxman 1997a , sari , piran & narayan 1998 ) . later works included more detailed calculations . synchrotron emission was considered from the shock front ( sari 1998 , panaitescu & mszros 1998 ) , and monochromatic emission was considered from a uniform shell ( waxman 1997b ) . we consider an adiabatic hydrodynamical evolution , and use the adiabatic self similar solution found by blandford and mckee ( 1976 ) for a highly relativistic blast wave expanding into a uniform cold medium , which we will refer to as the bm solution . we neglect scattering , self absorption and electron cooling . self absorption becomes important at frequencies much smaller than the peak frequency , and for slow cooling , electron cooling becomes important at frequencies much higher than the peak frequency , so this should yield a good approximation for the observed flux around the peak . an analysis of the spectrum over a wider range of frequencies was made by sari , piran and narayan ( 1998 ) . in section 2 we derive the basic formula for the observed flux from a system moving relativistically . in section 3 we consider synchrotron emission from a power law electron distribution , and calculate the observed light curve and spectra . we show that both the light curve and the spectra are flat near the peak . this causes difficulty in explaining the shape of the optical peak of grb970508 ( sokolov et . we obtain expressions for the peak frequency at a given observed time , and for the peak flux . in section 4 we consider three alternative magnetic field models . we show that the light curve and the spectra remain flat near the peak in all the cases we considered . in section 5 we calculate the observed light curve and spectra from a locally monochromatic emission . we consider a uniform shell approximation , which was calculated by waxman ( 1997c ) , and compare the light curve and spectra to those obtained for the bm solution . we show that a uniform shell approximation yields results which are considerably different from those obtained for a more realistic hydrodynamics , and very different from those obtained for a realistic emission together with a realistic hydrodynamics . in section 6 we calculate the surface brightness , thus obtaining the observed image of a grb afterglow . as indicated in previous works ( waxman 1997b ) , sari 1998 , panaitescu & mszros 1998 ) , we obtain from detailed calculations , that the image appears brighter near the edge and dimmer near the center , creating a ring near the outer edge . at a given observed time , the contrast between the edge and the center of the image is larger and the width of the ring is smaller at high frequencies , while at low frequencies the contrast is smaller and the width of the ring is larger . we consider a system that is moving relativistically while emitting radiation . we obtain a formula for the flux that is measured by a distant detector ( i.e. @xmath1 where d is the distance to the detector , and l is the size of the area emitting radiation ) . we use a spherical coordinate system and place the origin within the emitting region ( i.e. at the source ) , while the z - axis points towards the detector ( see figure [ fig1 ] ) . the detector is at rest in this frame , and so is the ambient ism . we refer to this frame as the observer frame . consider a small volume element @xmath2 ( where @xmath3 ) and let @xmath4 be the energy per unit time per unit volume per unit frequency per unit solid angle , emitted by the matter within this volume in it s local frame ( note that generally @xmath5 depends on the direction @xmath6 as well as on the frequency , place and time ) . we denote quantities measured in the local rest frame of the matter with a prime , while quantities without a prime are measured in the observer frame . note that @xmath7 is lorentz invariant ( rybici & lightman 1979 ) and @xmath8 , where @xmath0 and @xmath9 are the lorentz factor and the velocity of the matter emitting the radiation , respectively , and @xmath10 is the cosine of the angle between the direction of the velocity of the matter and the direction to the detector , in the observer frame ) . the contribution to @xmath11 from this volume element is given by : @xmath12 ( see figure [ fig1 ] ) . the contribution to the flux at the detector is @xmath13 where @xmath6 is the solid angle seen from the detector , and @xmath14 includes all the contributions from different volume elements along the trajectory arriving at the detector from the direction @xmath6 simultaneously and at the time for which @xmath15 is calculated . consider a photon emitted at time @xmath16 and place @xmath17 in the observer frame . it will reach the detector at a time @xmath18 given by ; @xmath19 where @xmath20 was chosen as the time of arrival at the detector of a photon emitted at the origin at @xmath21 . using @xmath22 , we obtain : @xmath23 where @xmath24 , and later @xmath25 . @xmath26 is taken in the direction @xmath27 at which a photon should be emitted in order to reach the detector , and @xmath28 should be taken at the time @xmath16 implied by equation [ time ] . the contribution of a volume element @xmath29 to the flux observed by a distant observer is @xmath30 , where @xmath31 . since the observer is far away , the direction of emission in the observer frame is almost parallel to the z - axis.,width=491 ] for a spherical expanding system , which emits isotropically in it s local rest frame , one obtains @xmath32 and @xmath33 , so that : @xmath34 note that because of relativistic effects , a jet with an opening angle @xmath35 around the los can be considered locally as spherical ( piran 1994 ) . in order to learn whether the radial integration is important , we calculate the observed flux from emission only along the los . we do this by considering a situation in which at each point the photons are emitted only radially : @xmath36 . note that the correct limit is obtained when the delta function in the direction of the emission is taken in the local frame . since @xmath37 ( rybici & lightman 1979 ) we obtain that : @xmath38 substituting this @xmath26 in equation [ flux j ] we obtain : @xmath39 equation [ prefaf ] is quite general , and includes integration over all space . in the case of grb afterglow , radiation is emitted only from the region behind the shock front . the spacial integration should therefore be taken over a finite volume , confined by the surface of the shock front . we would therefore like to obtain an explicit expression for the radius of the shock @xmath40 as a function of @xmath41 for a given arrival time @xmath18 . in the case of a shell moving with a constant velocity @xmath9 , one obtains from equation [ time ] : @xmath42 if one considers a constant arrival time @xmath18 , this equation describes an ellipsoid , which confines the volume constituting the locus of points from which photons reach the detector simultaneously ( rees 1966 ) . in grbs , most of the matter is concentrated in a thin shell which decelerates upon collision with the ambient medium . when the deceleration of the shell is accounted for , the ellipsoid is distorted . the details of this distortion depend on the evolution of the shock radius @xmath43 ( sari 1998 , panaitescu & mszros 1998 ) . in this paper we consider an adiabatic ultra - relativistic hydrodynamic solution , which implies @xmath44 , where @xmath45 is the lorentz factor of the shock . for this case , equation [ time ] yields : @xmath46 the shape of the volume constituting the locus of points from which photons reach the detector simultaneously resembles an elongated egg ( see figure [ fig2 ] ) , and will be simply referred to as the `` egg '' . the side facing the observer ( the right side in the figures ) will be referred to as the front of the `` egg '' , and the side closer to the origin ( the left side in the figures ) will be referred to as the back of the `` egg '' . we see here the egg - shaped region from which photons reach an observer at a given time @xmath18 . in all the figures of the `` egg '' the observer is located far to the right , and the symmetry axis is the los to the center of the grb . in order to reach the observer simultaneously , photons emitted at different locations should be emitted at different times in the observer frame , according to equation [ time ] . photons that are emitted simultaneously in the observer frame along the dashed - dotted line @xmath47 , reach the observer simultaneously . therefore @xmath47 represents an equal @xmath48 contour line . the location of the shock front at this time of emission is indicated by the solid line @xmath49 , and it s radius @xmath40 appears in the definitions of @xmath50 and @xmath51 . a photon emitted at point a , at a distance of @xmath52 behind the shock front and at a time @xmath53 ( both in the observer frame ) caches up with the shock front at point b , at a later time @xmath54 in the observer frame.,width=491 ] from hydrodynamic considerations , we expect the typical size of the region emitting radiation behind the shock , to scale as : @xmath55 in the observer frame . despite this fact , it is still important to consider the emission from the whole volume of the `` egg '' , whose limits are given by equation [ egg ] . to illustrate this we give a simple example . consider a photon emitted on the los at a distance @xmath56 behind the shock ( point a in figure [ fig2 ] ) at a time @xmath53 in the observer frame , where @xmath57 is the lorentz factor of the matter just behind the shock . this photon will catch up with" +"in this article we study heat diffusion via neutrinos in dense , color superconducting quark matter . recent theoretical works @xcite suggest that quarks form cooper pairs in medium , a natural consequence of attractive interactions destabilizing the fermi surface . this would likely affect the early evolution of neutron stars born through a type ii supernova explosion , where the central role of neutrino diffusion through a strongly - interacting medium has long been postulated on theoretical grounds @xcite . type ii ( core collapse ) supernovae are triggered by the implosion of the inner core of a massive star ( m@xmath1 @xmath2 m@xmath3 ) , when the core mass is on the order of the chandrashekar mass ( m@xmath4 @xmath5 m@xmath3 ) . during the implosion nearly all ( @xmath6% ) of the enormous gravitational binding energy ( @xmath7 ergs ) gained is stored as internal energy of the newly born , proto - neutron star ( pns ) . the subsequent evolution of the proto - neutron star is driven by neutrino diffusion . temporal and spectral characteristics of the neutrino emission depend on the rate at which neutrinos diffuse through the imploded pns which , at this early stage , is composed of hot ( @xmath8 mev ) and dense ( @xmath9 where @xmath10 @xmath11 ) strongly - interacting matter . neutrino emission during this phase is a directly observable feature of a galactic supernova explosion . the few neutrinos detected from sn 1987a indicate that neutrinos of mean energy @xmath12 mev are emitted on a diffusion time scale of about @xmath13 seconds . it is reasonable to expect that neutrino mean free path in the inner , denser regions of the star will strongly influence the temporal characteristics of a supernova neutrino signal . supernova neutrinos can therefore reveal properties of matter at high baryon density , at temperatures substantially lower than those expected in relativistic heavy ion collisions . although the idea of quark pairing in dense matter is not a new one @xcite , it has recently seen renewed interest in the context of the phase diagram of qcd @xcite . model calculations , mostly based on four - quark effective interactions , predict the restoration of spontaneously broken chiral symmetry through the onset of color superconductivity at low temperatures @xcite . for much higher densities color superconductivity is manifest through perturbative gluon exchange @xcite , which can be calculated systematically suggests that the phenomenon is robust . for densities and temperatures relevant to neutron stars , quark matter is therefore expected to be superconducting . models generally predict an energy gap of @xmath14 mev for a typical quark chemical potential of @xmath15 mev . as in bcs theory , the gap will weaken for @xmath16 and at some @xmath17 there is a ( second - order ) transition to a `` standard '' quark - gluon plasma . thus , when cooling from temperatures greater than critical , the formation of a such a gap in the fermionic excitation spectrum in quark matter at high density will influence various neutron star observables if neutron stars contain quark matter in their cores at early time . two examples recently investigated are the effects on magnetic fields @xcite and on the thermal evolution of neutron stars at late time @xcite , when interior temperatures evolve from @xmath18 mev to @xmath19 kev . in this work we shall consider the cooling of quark matter at earlier times , when temperatures pass through the critical @xmath20 . assuming a simplified scenario , we investigate the thermal evolution of the inner core of a proto - neutron star as it cools via neutrino diffusion during its first few seconds . our main finding is that the neutrino mean free path in the superconducting phase has a strong dependence on temperature . an energy gap tends to increase the neutrino mean free paths exponentially when @xmath21 . however in the intermediate regime , when @xmath22 , the temperature dependence is not exponential . from this we predict a uniquely uneven cooling process for simplified pns matter , marked by a slowdown of the cooling rate when the system undergoes a second - order phase transition . this is a consequence of the specific heat being peaked at @xmath0 , a standard characteristic of a phase transition , rather than a large change in the neutrino mean free path . since the energy gap vanishes at this point , the mean free path is _ not _ significantly modified in the neighborhood of @xmath0 . in section ii the neutrino mean free path , always denoted @xmath23 in this work , is computed in a background of superconducting quarks . taking a general , bcs - type model for the energy gap , we relate @xmath23 to in - medium quark polarizations via the differential and total neutrino - quark cross sections . explicit formulae are derived for the imaginary parts of the vector and axial - vector polarizations of a relativistic fermi system with an energy gap . after assuming bcs - type mean field behavior of the gap and the specific heat , in section iii we compute a characteristic time for heat diffusion via neutrino emission from a simple model of superconducting quark matter . we then consider some astrophysical consequences and outline the model s applicability to proto - neutron stars . section iv contains our conclusions . the primary process by which heat escapes a proto - neutron star is neutrino diffusion , and so a significant consequence of color superconductivity in this context will be modified neutrino propagation . while noting that the neutrino production rate will also differ from that of normal matter , in the diffusive regime one can see that the dominant critical behavior will be a change in the _ inelastic _ quark - neutrino cross section , since here neutrino production rates decouple from the transport equation and depend only on the neutrino mean free path . in this section we calculate the differential and total cross sections and then compute the neutrino mean free path in two - flavor quark matter . the magnitude of the superconducting gap , @xmath24 , is taken as arbitrary within a range of values found in recent literature . closely following bcs theory , we assume the gap to be a constant , and calculate the response functions and neutrino cross sections in the weak coupling approximation . the neutral current coupling between neutrinos and quarks , a four - fermion effective interaction for energies @xmath25 , is written as @xmath26 where @xmath27 gev@xmath28 is the fermi weak coupling constant and @xmath29 and @xmath30 are the flavor - specific vector and axial vector coupling constants , respectively . the differential neutrino scattering cross section per unit volume in an infinite and homogeneous system of fermions as calculated in linear response theory is @xcite @xmath31}{\left[1-\exp{\left(-q_0/t\right)}\right ] } ~{\rm im}~(l^{\alpha\beta}\pi_{\alpha\beta } ) \ , , \label{dcross}\end{aligned}\ ] ] where @xmath32 ( @xmath33 ) is the incoming ( outgoing ) neutrino energy . the factor @xmath34^{-1}$ ] maintains detailed balance and the final state blocking of the outgoing neutrino is enforced by the pauli blocking factor , @xmath35 $ ] . the neutrino tensor @xmath36 is given by @xmath37 \,,\ ] ] where the incoming four - momentum is @xmath38 and the momentum transferred to the medium is @xmath39 . the minus ( plus ) sign on the final term applies to neutrino ( anti - neutrino ) scattering . the medium is characterized by the quark polarization tensor @xmath40 . in the case of free quarks , each flavor contributes a term of the form @xmath41 \ , , \label{pi_free}\ ] ] where @xmath42 is the free quark propagator at finite chemical potential and temperature . the outer trace is over color and simplifies to a @xmath43 degeneracy . the inner trace is over spin , and the @xmath44 are the neutrino - quark vertex functions which determine the spin channel . specifically , the vector polarization is computed by choosing @xmath45 . the axial and mixed vector - axial polarizations are similarly obtained from @xmath46 and @xmath47 , respectively . the free quark propagators in eq . ( [ pi_free ] ) are naturally modified in a superconducting medium . as first pointed out by bardeen , cooper , and schrieffer several decades ago , the quasi - particle dispersion relation is modified due to the presence of a gap in the excitation spectrum . in calculating these effects , we will consider the simplified case of qcd with two quark flavors which obey su(2)@xmath48 su(2)@xmath49 flavor symmetry , given that the light @xmath50 and @xmath51 quarks dominate low - energy phenomena . furthermore we will assume that , through some unspecified effective interactions , quarks pair in a manner analogous to the bcs mechanism @xcite . the relevant consequences of this are the restoration of chiral symmetry ( hence all quarks are approximately massless ) and the existence of an energy gap at zero temperature , @xmath52 , with approximate temperature dependence , @xmath53 the critical temperature @xmath54 is likewise taken from bcs theory ; this relation has been shown to hold for perturbative qcd @xcite and is thus a reasonable assumption for non - perturbative physics . breaking the su@xmath55(3 ) color group leads to complications not found in electrodynamics . in qcd the superconducting gap is equivalent to a diquark condensate , which can at most involve two of the three fundamental quark colors . the condensate must therefore be colored . since the scalar diquark ( in the @xmath56 color representation ) appears to always be the most attractive channel , we consider the anomalous ( or gorkov ) propagator @xcite @xmath57 here , @xmath58 are color indices , @xmath59 are flavor indices , @xmath60 is the usual anti - symmetric tensor and we have conventionally chosen 3 to be the condensate color . this propagator is also antisymmetric in flavor and spin , with @xmath61 being the charge conjugation operator . the color bias of the condensate forces a splitting of the normal quark propagator into colors transverse and parallel to the diquark . quarks of color 3 , parallel to the condensate in color space , will be unaffected and propagate freely , with @xmath62 this is written in terms of the particle and anti - particle projection operators @xmath63 and @xmath64 respectively , where @xmath65 . the excitation energies are simply @xmath66 for quarks and @xmath67 for anti - quarks . on the other hand , transverse quark colors 1 and 2 participate in the diquark and thus their quasi - particle propagators are given as @xmath68 the quasi - particle energy is @xmath69 , and for the anti - particle @xmath70 . the appearance of an anomalous propagator in the superconducting phase indicates that the polarization tensor gets contributions from both the normal quasi - particle propagators ( [ s_bcs ] ) and anomalous propagator ( [ a_bcs ] ) . thus , to order @xmath71 , eq . ( [ pi_free ] ) is replaced with the two contributions corresponding to the diagrams shown in fig . [ pol_fig ] , and written @xmath72 + 2 { \rm tr}~[s(p)\gamma_{\alpha } s(p+q)\gamma_{\beta } ] + 2 { \rm tr}~[f(p)\gamma_{\alpha } \bar{f}(p+q)\gamma_{\beta } ] \right\ } \ , . \label{pi_bcs}\ ] ] the remaining trace is over spin , as the color trace has been performed . [ pol_fig](a ) corresponds to the first two terms , which have been decomposed into one term with ungapped propagators ( [ s_0 ] ) and the other with gapped quasi - particle propagators ( [ s_bcs ] ) . fig . [ pol_fig](b ) represents the third , anomalous term . for neutrino scattering we must consider vector , axial , and mixed vector - axial channels" +"most mass in the universe is in the form of dark matter , and most dark matter is gravitationally clustered in the form of halos . dark matter halos are therefore the building blocks of the universe . knowledge of the formation and evolution history of dark matter halos is essential for an understanding of the halos structure and dynamics , as well as the environment that harbors galaxies and clusters . designs for dark matter search experiments also rely on the predicted spatial and velocity distributions of dark matter particles in our own galaxy . according to the theory of structure formation in current cosmological models , dark matter halos arise from tiny primordial fluctuations seeded in the matter and radiation fields in the early universe at , for example , the end of an inflationary era . these small inhomogeneities grow via gravitational instability , with the slightly overdense regions becoming denser and the slightly underdense regions becoming emptier . at a given time , there exists a spectrum of density fluctuations over a wide range of length and mass scales , whose spatial distribution is characterized by the power density in fourier space @xmath0 , the power spectrum . dark matter halos therefore rarely form and evolve in isolation , growing instead by frequent accretion of smaller - mass halos and occasional major mergers with other halos of comparable mass . the earliest theoretical insight into cosmological halo formation came from the spherical radial infall model , which considers an isolated spherical overdense volume and describes the secondary infall of bound but initially expanding collisionless matter onto this region @xcite . if the initial density perturbation spectrum is scale - free and the velocity distribution follows the hubble law , the infall solution is found to approach a self - similar form in an einstein - de sitter universe . the resulting density profile asymptotically approaches @xmath1 with @xmath2 @xcite . the exact value of @xmath3 depends on the index of the initial perturbation spectrum @xmath4 : it is isothermal ( @xmath5 ) for @xmath6 and for @xmath7 steepens to @xmath8 @xcite or @xmath9 @xcite . the collapse of halos therefore retains memory of the initial conditions in the radial infall model . by contrast , modern cosmological n - body simulations find dark matter halos over a wide range of mass scales to follow a density profile that is nearly independent of the initial power spectrum and is shallower near the halo centers ( with @xmath10 ) than that predicted by the radial infall model @xcite . furthermore , the dark matter in the simulated halos is not entirely smoothly distributed spatially ; instead , at least 10% of the halo mass is in the form of hundreds to thousands of smaller , dense satellite halos of varying mass @xcite . thus even though the analytic similarity solutions derived from one - dimensional infall onto a smooth overdensity have provided valuable insight into the evolution of self - gravitating systems , realistic halo formation is clearly more complicated . numerical simulation has been the tool most frequently used in cosmology to study structure formation . it has provided powerful insight and occasionally surprising results ( e.g. universal density profile ) unexplainable by the simulations themselves . our understanding of structure formation can certainly be enhanced if a complementary tool is developed . complementary approaches are also especially needed at this time to help us better understand and perhaps resolve the `` cuspy halo '' and `` dwarf satellite '' problems of the cold dark matter model . in this paper we offer a new perspective on the subject of dark matter halo formation by proposing an approach different from both the radial infall model and n - body simulations . we focus on the phase - space distribution of dark matter in galaxy halos instead of on the motion of a mass shell ( as in infall models ) or the orbit of a simulation particle ( as in n - body ) . we attempt to understand the evolution of the phase - space distribution with a statistical description based on kinetic theory . our method is to be contrasted with the standard method where the individual dark matter particles are described by the collisionless boltzmann equation ; n - body simulations are in essence a monte carlo method for solving this equation . instead , we consider the phase space of dark matter particles in an average halo and develop a cosmological kinetic theory for halo evolution in the presence of a spectrum of density fluctuations . the essential features of our approach are represented by the fluctuation - dissipation theorem for time - dependent stochastic processes . to elaborate on this concept , we recall that stochastic modelling was first developed to explain the brownian motion of pollen particles suspended in a fluid . ( see [ sec : brownian ] for a more detailed discussion . ) this phenomenon is now understood to arise from a fluctuating force on a brownian particle due to many rapid collisions with the molecules in the surrounding fluid . these fluctuations cause successive small changes in the particle velocity , hence to a random walk . the consequence of many such random walks is diffusion , a form of dissipation . due to the large number of molecules , it is impossible to solve the coupled equations of motion for the trajectories of all molecules and the pollen particle in the fluid fortunately , a stochastic treatment suffices . one mathematical prescription is provided by the langevin equation @xcite , which models the forces arising from the fluctuations as a stochastic term that is added to all other deterministic forces in the equation of motion for a particle . an alternative prescription is given by the fokker - planck equation @xcite , which is an equation of motion for the probability density or distribution function of particles undergoing random walks . in this case , the collective changes in the velocities due to the fluctuations in the system are represented by a drift coefficient and a diffusion coefficient arising from the collision terms in the collisional boltzmann equation . stochastic phenomena occur beyond molecular scales . in astrophysics , the best studied example is the evolution of dense stellar systems such as globular clusters @xcite . a star in a globular cluster experiences a fluctuating force from many gravitational two - body encounters and suffers a succession of small velocity changes . the fluctuations in these systems arise from granularity in the mass distribution at the locations of the stars . the fokker - planck approximation is valid for these weak encounters . we explore this example in greater detail and contrast it with our model of galaxy halo evolution in [ sec : globular ] . the key feature common to all of these systems is the presence of stochastic fluctuations that result in dissipation . in the cosmological setting addressed by this paper , the fluctuations arise from cosmological perturbations produced in the early universe . at early times , these perturbations are gaussian and fully characterized by their power spectrum ; at late times , the substructures in halos seen in recent simulations are the nonlinear counterparts of this spectrum of early ripples . these fluctuations scatter particles . if one considers an ensemble of halos , the masses and locations of the substructures ( or their gaussian predecessors ) are random variables . the substructures thereby introduce `` noise '' into the evolution of dark matter halos . as we show in this paper , the result is dissipation in the form of drift and velocity - space diffusion . recent work has explored the use of the fokker - planck equation in cosmological problems . @xcite , for example , searched for steady - state solutions of the fokker - planck equation assuming the fluctuations arise from two - body encounters . it also assumed a simple isotropic phase space distribution dependent only on the total energy and a radial power law form for the potential and density . under these assumptions , @xcite found that @xmath11 was a steady - state solution under the effects of encounters . there was no dynamics in this work , however : the system was assumed to be in collisionless equilibrium and the nature of the clumps producing the collisions was left arbitrary . it also remains to be determined whether galaxy halos , either dark matter or stellar , actually evolve to @xmath12 cusp . @xcite examined the dynamics of halos due to stochastic fluctuations from three different noise processes for the fokker - planck scattering term : the merging clumps were assumed to fly by with constant velocity , to follow decaying orbits due to dynamical friction , or to orbit inside halos . the results of this study were promising and supported the notion that the density profiles of halos were affected by mergers and substructures . the fluctuations in this work , however , were constructed by hand instead of being self - consistently calculated , and the results about a central cusp were inconclusive . our objective here is to construct a kinetic equation in which the drift and diffusion terms are derived from realistic density fluctuations in current cosmological models . we will also retain the full phase space information by , in effect , using @xmath13 without averaging over the angular momentum or radial velocity . we also do not assume collisionless equilibrium ; instead we base our approach on exact dynamics . the organization of this paper is as follows : in 2 , we derive the kinetic equation relevant for the evolution of an average halo , starting with the collisionless boltzmann equation for individual dark matter particles . this procedure gives rise to a collision term on the right - hand side of the kinetic equation . this term represents a correlated force density and arises from fluctuations in the ensemble averaged gravitational potential due to clustering of the matter distribution . in , we introduce the concepts and physical variables needed to apply this equation to cosmological problems . the key step is in relating the phase space density @xmath14 to the probability densities of two standard variables in cosmology : the mass density @xmath15 and velocity @xmath16 . we then focus on the quasi - linear regime in which the fluctuations about the mean density and hubble flow of an isotropic and homogeneous universe are small . this focus allows us to relate @xmath15 and @xmath16 to the density and displacement fields @xmath17 and @xmath18 , which are gaussian random fields in standard cosmological models . we leave the most mathematical part of the paper to appendix [ sec : pgauss ] , where we describe how to use the statistics of constrained gaussian random fields to express the probability densities of 3 in terms of the ( constrained ) means and covariances of the density and displacement fields . the idea of a constrained field is central to this study because our aim is to construct a kinetic theory for dark matter particles that will later reside in a collapsed halo rather than at any random location in the universe . the relevant perturbations are for a density field constrained to have certain properties , e.g. , a specified height or gradient at some point in space . the spectrum for such constrained fields is related but not identical to the familiar linear power spectrum @xmath19 for unconstrained gaussian density fluctuations . in [ sec : fpeq ] , we put the final expression for the correlated force derived in appendix [ sec : pgauss ] back into the kinetic equation , and show that the resulting equation is of the fokker - planck form where one term represents a drift" +"intermediate scale disk galaxies with starbursts are relatively common in the nearby universe . about 5% of galaxies with @xmath017 @xmath1 m@xmath2 @xmath321 have evidence for starbursts . many of these occur in smaller galaxies , produce blue colors and strong emission lines , and are in gas rich systems , as indicated by their relatively large fractional hi content . the more luminous nearby blue starbursts structurally and spectroscopically resemble the faint blue compact narrow emission line galaxies ( cnelgs ) , which become common at redshifts of z@xmath40.3 ( e.g. , guzman et al . they are less well - matched to high redshift blue galaxies , which have a combination of high uv luminosities and huge star formation rates that are not common in nearby extreme starbursts . this difference probably reflects secular evolution in the lives of galaxies ; for example , systems at high redshift may be subject to frequent , strong mergers that trigger hyperactive star formation ( e.g. conselice et al . 2001 in prep ) . nearby starbursts frequently show evidence for being dynamically cool , that is they contain strong spiral arms or bars , features that are found in rotationally supported galactic disks . thus the processes that produced these starburst did not severely disrupt the disk , or the disk reformed during the starburst event . local analogs to the cnelgs include profound starbursts arising from minor perturbations ( see figure 1 ) . moderate interactions ( glancing collisions between equals , minor mergers ) are apparently the sources of many starbursts . evidence for this includes subtle optical structural features such as wisps , faint tails , or moderately disturbed kinematics in starbursts , as well as the more ubiquitous signatures of disturbed hi . furthermore , in some starbursts where an interaction is the likely trigger , the outer regions of the optical disk appear to be relatively symmetric and relaxed . three possible explanations for this behavior are : @xmath5 blue starbursts are commonly associated with disk galaxies : near face - on systems can transmit uv light through areas where the disk has been cleaned out by supershells , supernova , etc . ( e.g. conselice et al . 2000 ) . @xmath5 low inclination disks can mimic the kinematics of low mass galaxies due to their narrow line widths ( homeier & gallagher 1999 ) . some intermediate redshift cnelgs could be low inclination disks of moderate mass rather then extreme dwarf starbursts . @xmath5 undisturbed intermediate mass galaxies , such as extreme late - type and superthin spirals ( e.g. , matthews et al . 1998 ) can be inefficient star - formers and thereby store interstellar gas , the fuel for starbursts , over cosmic time scales . @xmath5 uv - bright regions of starbursts frequently occur in features associated with disks , such as rings or arms ( e.g. conselice et al . 2000 ) which may represent star forming environments not yet accessible to severely disturbed high luminosity starbursts in the distant universe . conselice , c.j . 2000 , aj , 119 , 79 + guzman , r. et al . 1998 , apj , 495 , l13 + homeier , n. & gallagher , j.s . 1999 , apj , 522 , 199 + matthews , l. , van driel , w. , & gallagher , j. 1998 . aj , 116 , 1169 + mihos , c. & hernquist , l. 1996 , apj , 464 , 641 +" +"mixing in fluids plays an important role in nature and technology with implications in areas ranging from geophysics to chemical engineering@xcite . the phenomenon of chaotic advection intensively investigated during the last decade provides a basic mechanism for mixing in laminar flows@xcite . briefly stated , chaotic advection refers to the situation in which fluid elements in a non - turbulent flow follow chaotic trajectories . advection by simple time - dependent two - dimensional flows falls generically under this category . stirring by chaotic motion , with its characteristic stretching and folding of material elements , is able to bring distant parts of the fluid into intimate contact and thus greatly enhances mixing by molecular diffusion acting at small scales . mixing efficiency becomes specially important when the substances advected by the flow are not inert but have some kind of activity . by ` activity ' we mean that some time - evolution is occurring to the concentrations inside advected fluid elements ( produced by chemical reactions , for example ) . for definiteness we will use terms such as chemical fields and chemical reactions , but biological processes , occurring for example when the advected substance is living plankton , can be described formally in the same way . the interaction between the stirring process and the chemical activity can result in complex patterns for the spatial distribution of the chemical fields , which in turn greatly affect the chemical processes@xcite . in addition to the impact on its own chemical dynamics , the spatial inhomogeneities may have important effect on other dynamical processes occurring in the fluid ( for example in the behavior of predators seeking for the advected plankton @xcite ) . an understanding of the structure of these spatial patterns is thus valuable . previous theoretical work concentrated on the temporal evolution of the total amount of chemical products in specific reactions such as @xmath0 or @xmath1 @xcite . in @xcite the same type of reactions were studied in open flows . in a previous paper @xcite some of us considered a class of chemical dynamics characterized by a negative lyapunov exponent in the presence of ( non - homogeneous ) chemical sources . under such chemical processes , reactant concentrations present a tendency to relax towards a local - equilibrium concentration ( the fixed point of the local chemical dynamics ) . this tendency is disrupted by the advection process , which forces fluid elements to visit places with different local - equilibrium states . depending on the relative strength of chaotic advection and relaxation the resulting concentration distribution can be smooth ( differentiable ) or exhibits characteristic filamental patterns that are nowhere differentiable except in the direction of filaments aligned with the unstable foliation induced in the fluid by the chaotic dynamics . the mechanism for the appearance of these singular filaments is similar to the one producing singular invariant measures in dynamical systems @xcite , although here it is affected by the presence of the chemical dynamics : stretching by the flow homogeneizes the pattern along unstable directions , whereas small - scale variance , cascading down from larger scales , accumulates along the stable directions , producing diverging gradients . the strength of the singularities of the concentration field @xmath2 can be characterized by a hlder exponent @xmath3 @xmath4 if the field is smooth ( differentiable ) at @xmath5 , @xmath6 , while for an irregular rough ( e.g. filamental ) structure @xmath7 . in @xcite we focused on the existence of a smooth - filamental transition as time - scales of the system are varied , and also obtained the most probable ( bulk ) value of the hlder exponent . note , however , that the hlder exponent defined by ( [ holder ] ) is a local characteristic of the field , whose value may depend on the position @xmath8 . in this paper we concentrate on such non - uniformities of the filamental chemical field and study how this affects scaling properties of quantities involving spatial averages , which are the more convenient quantities to be observed in experiments . in section [ sec : transition ] we review the results presented in @xcite , namely the smooth - filamental transition and the dominant value of the hlder exponent in closed flows . then we consider the same problem for the case of mixing by open flows ( sect . [ sec : open ] ) . in this case the necessity of a multifractal description becomes manifest , and this motivates the development of a quantitative characterization of the filamental structures in terms of structure functions . this is presented in sect . [ sec : structure ] . scaling exponents appear to be related to the distribution of finite - time lyapunov exponents . we conclude the paper with a summary and discussion . we consider the flow as externally prescribed , thus neglecting any back influence of the chemical dynamics into the hydrodynamics ( the advected substances are chemically active but hydrodynamically passive ) . in this context , the general continuum description of chemical reactions in hydrodynamic flows is given by sets of reaction - advection - diffusion equations . they involve in general multiple components and nonlinear reaction terms . reference @xcite considered the situation in which the chemical kinetics is stable , i.e. there is a local - equilibrium state at each spatial position , determined by the sources and the reaction terms , so that concentrations of fluid particles visiting that position tend to relax to the local - equilibrium value . mathematically this corresponds to the negativity of the lyapunov exponents associated to the chemical dynamical subsystem . it was shown in @xcite that arbitrary chemical dynamics in this class can be substituted by linear relaxation towards local equilibrium at a rate given by the largest ( least negative ) chemical lyapunov exponent . within this restriction , the multiplicity of components is not essential since , except for special types of coupling , linearization leads to simple relations between the different fields . because of the above remarks , and with the aim of keeping the mathematics as simple as possible , we will restrict our considerations in this paper to the simplest chemical evolution : linear decay , at a rate @xmath9 , of a single advected substance . a space - dependent source of the substance will also be included , to maintain a non - trivial concentration field at long times . this chemical dynamics can be considered either as an approximation to more complex chemical or biological evolutions , with maximum chemical lyapunov exponent @xmath10 , or as a description of simple specific processes such as spontaneous decomposition of unstable radicals , decay of a radioactive substance , or relaxation of sea - surface temperature towards atmospheric values @xcite . the validity of our ideas for nonlinear multicomponent situations has been checked for a plankton model in @xcite . the concentration field @xmath11 , when advected by a incompressible velocity field @xmath12 is governed by the equation @xmath13 where @xmath14 is the diffusion coefficient , @xmath9 is the decay rate introduced above and @xmath15 is the concentration input from chemical sources ( negative values representing sinks ) . we restrict our study to the case in which the incompressible velocity field is two - dimensional , smooth , and non - turbulent . chaotic advection is obtained generically if a simple time - dependence , for example periodic , is included in @xmath12 . we assume that diffusion is weak and transport is dominated by advection . thus one expects that the distribution on scales larger than a certain diffusive scale is not affected by diffusion . therefore we consider the limiting non - diffusive case @xmath16 . in this limit the above problem can be described in a lagrangian picture by an ensemble of ordinary differential equations @xmath17 @xmath18-b \hat c,\ ; \label{lagrangec}\ ] ] where the solution of the first equation gives the trajectory of a fluid parcel , @xmath19 , while the second one describes the lagrangian chemical dynamics in this fluid element : @xmath20 $ ] . to obtain the value of the chemical field at a selected point @xmath21 at time @xmath22 one needs to know the previous history of this fluid element , that is the trajectory @xmath19 ( @xmath23 ) with the property @xmath24 . this can be obtained by the integration of ( [ lagranger ] ) backwards in time . once @xmath19 has been obtained , the solution of ( [ lagrangec ] ) is @xmath25 e^{-b \bar t } + \int_0^{\bar t } s[{\bf \hat r}(t ) ] e^{-b ( \bar t - t ) } dt . \label{field}\ ] ] one can obtain the difference at time @xmath22 of the values of the chemical field at two different points @xmath21 and @xmath26 separated by a small distance @xmath27 in terms of the difference @xmath28-c[{{\bf \hat r}}(t),t ] \equiv \delta c[{{\bf \hat r}}(t),t;{\hat{\delta{\bf r}}}(t)]$ ] for @xmath29 , namely : @xmath30 e^{-b \bar t } \nonumber \\ + \int_0^{\bar t } \delta s[{{\bf \hat r}}(t ) ; { \hat{\delta{\bf r}}}(t ) ] e^{-b ( \bar t- t ) } dt \label{deltac1 } \end{aligned}\ ] ] where @xmath31 ( @xmath29 ) is the time - dependent distance between the two trajectories that end at @xmath21 and @xmath26 at time @xmath22 , and @xmath32 , in analogy with @xmath33 , is the difference of the source term at points @xmath19 and @xmath34 . thus we have expressed the behavior of an eulerian quantity @xmath35 in terms of lagrangian quantities , in particular of @xmath36 . further analysis of eq . ( [ deltac1 ] ) requires specification of the behavior of @xmath37 . the signature of chaotic advection is the exponentially growing behavior of this quantity at long times . more precise statements need additional assumptions on the character of the flow . the simplest framework is obtained if we restrict our attention to initial conditions @xmath38 in an invariant _ hyperbolic _ set @xcite . in this case one can identify at each point two directions , the one in which the flow is _ contracting _ @xmath39 and the _ expanding _ direction @xmath40 . they depend continuously on position ( for time - dependent flows there is an additional explicit time - dependence that we do not write down to simplify the notation ) . since @xmath41 and @xmath42 form at each point a vector basis which is not orthonormal , it is convenient to introduce also the dual basis ( @xmath43 ) at each point . chaotic advection manifests in which for most initial separations @xmath44 the long - time behavior of @xmath37 is @xmath45^\dag \cdot { \hat{\delta{\bf r}}}(0)\right| e^{\lambda t}$ ] ( for @xmath46 ) , where @xmath47 is the positive lyapunov exponent of the flow and @xmath48^\dag \cdot { \hat{\delta{\bf r}}}(0)$ ] gives the component of the initial separation along the expanding direction . at long times , the direction of @xmath36 tends to become aligned with the expanding direction of the flow at @xmath19 , @xmath49 $ ] . however , if the initial separation is aligned with the contracting direction at the initial point , @xmath47 should be substituted by @xmath50 , the contractive lyapunov exponent , and @xmath51 by @xmath52 . for incompressible flows one has @xmath53 . in order to analyze ( [ deltac1 ] ) one has to consider the backwards evolution . in this case typical solutions behave , for @xmath54 and large , as @xmath55^\dag\cdot{\hat{\delta{\bf r}}}(0 ) \right| e^{\lambda ' t } = \left| { \bf c}[{{\bf \hat r}}(0)]^\dag\cdot{\hat{\delta{\bf r}}}(0 ) \right| e^{-\lambda t}$ ] so that , also in this backwards dynamics , close initial conditions diverge , and the difference will tend to become aligned with the most expanding direction" +"the pion induced double charge exchange ( dcx ) reaction has been extensively studied @xcite at energies below and around the @xmath7 resonance . however , many questions remain not sufficiently understood , like the angular dependence of the analog transitions at resonance energy @xcite , or the two - peaks structure of the spectra at forward angles that appear in the inclusive dcx process in light nuclei@xcite . there are many reasons for these difficulties . one is the existence of several mechanisms , some of them important , that interfere , and whose evaluation is not simple . another one is the strong distortion of the pion waves at energies around the @xmath7 resonance . finally , for exclusive reactions , dcx processes are very sensitive to small details of the nuclear structure . at higher energies the analysis of dcx reactions is much simpler , mainly , because the @xmath8 cross section is much smaller , reducing the importance of distortion . additionally , the contribution of some of the mechanisms , like dint @xcite and the absorption @xcite mechanism , is expected to decrease rapidly with energy . furthermore , the angular dependence of the single charge exchange @xmath9 reaction is strongly energy dependent . this has the consequence that at certain energies the sequential contribution to the dcx cross section results in deep minima . this result , found for the exclusive reaction in @xcite will be shown here to be a general feature of inclusive dcx for all nuclei . the energies , at which the sequential mechanism is very small , and distortion is probably negligible , offer the best ground for the investigation of some exotic mechanisms , like those involving meson exchange currents @xcite , six - quark bags @xcite , and others involving more than two nucleons @xcite , which , although small around the @xmath7 resonance , are not expected to decrease significantly with energy . we know , from our experience at low energies , how strong is the dependence of the dcx cross section on the nuclear structure for exclusive processes . this dependence is smeared out in the inclusive case , when a sum over all possible final states is done . additionally , inclusive dcx offers the advantage of a much higher yield than exclusive experiments and does not require such a good energy resolution . at present there are no data on inclusive dcx in the energy range above @xmath10 , although some measurements are in progress now @xcite at itep ( moscow ) . these experiments have stimulated the present work . there are , however , some data around .5 gev which will be used to test our model . the calculation presented here is a monte carlo simulation of the reaction . this is most appropriate for a multichannel situation ( i.e. absorption , quasielastic , scx , dcx , @xmath0-production ) that renders a full quantum calculation infeasible . furthermore , similar calculations @xcite describe quite well all @xmath0-nucleus inclusive reactions around the @xmath7-resonance : absorption , quasielastic scattering , single charge exchange , and double charge exchange . at higher energies the wavelength of the pion is shorter and therefore quantum interference effects should be less important . this paper is organized as follows : section 2 presents the basic elements of the variant of the cascade model considered here ( details are given in appendix a ) . in section 3 the results of calculations of pion spectra ( energy and angular distributions ) for the inclusive dcx are presented , and in section 4 the obtained results are discussed . a pion travelling inside a nucleus can be absorbed , can change direction , energy , charge , or even produce more pions . the basic inputs for our simulation will be the probabilities per unit length for each of these channels to happen . how these probabilities are obtained is presented below , in sections 2.2 - 2.4 . details on the simulation will be presented in appendix a. the probability per unit length of quasielastic scattering ( or single charge exchange ) is given by @xmath12 where @xmath13 stands for neutron or proton , @xmath14 is the density of nucleons of type @xmath13 , and @xmath15 is the elementary cross section for the reaction @xmath16 obtained from arndt s phase shifts @xcite . the density of protons is taken from experiment , and the density of neutrons is taken proportional to the density of protons in all results presented in this work . when according with the probabilities of eq . ( 1 ) , a quasielastic scattering took place , we executed the following algorithm . first , we chose randomly a nucleon , of the type @xmath13 , from the fermi sea , then we boosted the @xmath0 and @xmath13 to their center of mass system . finally , we selected the scattering angle ( and therefore energy ) of the outgoing particles using again the experimental cross sections @xcite , and boosted the momenta to the lab . system . when the momentum of the outgoing nucleon in the lab . system is below the fermi level , we consider the event to be pauli - blocked and therefore keep the pion initial charge and momentum unchanged . even if pion absorption is a relatively small effect at high energies ( which one could suggest from the rapid decrease of the pion - deuteron absorption cross section at the energy range from @xmath17 @xcite ) , there is a large number of pions at lower energies which are generated both by the quasielastic rescatterings and the pion production on the nuclear nucleons . the proportion of these pions that eventually comes out of the nucleus is essentially determined by the absorption strength . although pion absorption has been extensively studied at energies below 0.3 gev , little theoretical work has been done about pion absorption by complex nuclei at high energies , and very little experimental information is available . in ref . @xcite the effect of pion absorption on the pion - nucleus elastic and the scx scattering has been studied in the energy range of 250 to @xmath18 . the absorptive part of the pion - nucleus optical potential was calculated within the framework of a many - body field theoretical approach . the model contains both two- and three - nucleon absorption mechanisms and it has been shown to agree quite well to the more complex microscopical model of ref . @xcite in the @xmath7 resonance region . results show a quite weak absorption at high energies , as was expected . another interesting result presented in ref.@xcite is that , whereas in the resonance region three - body - absorption becomes comparable with the two - nucleon mechanism , as the pion energy increases the effects of three - body absorption decrease again , and the two - body mechanism becomes dominant , as is the case at low energy . the probability per unit length of a pion to be absorbed is expressed in terms the imaginary part of the pion self - energy is related to the optical potential as @xmath19 by the equation @xmath20 . the imaginary part of the pion self - energy , related to two - nucleon pion absorption , which has been calculated in @xcite is of the form @xmath21 here , @xmath22 , @xmath23 is the pion momentum in the lab system , @xmath24 is the square of the c.m . energy of a pion of momentum @xmath23 and a nucleon at rest , @xmath25 is the spin - isospin averaged unpolarized @xmath8 cross section , and the momentum of a virtual pion @xmath26 that appears in the model of ref . @xcite is determined as @xmath27 ^ 2 -\,m^2\}^{1/2 } \nonumber\ ] ] which in the nonrelativistic limit actually used in @xcite goes to @xmath28^{1/2 } \nonumber\ ] ] where @xmath29 is the mass of a nucleon . the three - nucleon pion absorption has been calculated @xcite in a similar fashion , and the contribution to the selfenergy is given by @xmath30 with @xmath31^{1/2 } \nonumber\ ] ] and @xmath32,@xmath33 have the same meaning as @xmath24 and @xmath34 , but are evaluated at a kinetic energy of the pion equal to two thirds of the real one ( @xmath35 ) , and @xmath36 @xmath37mb@xmath38mev@xmath39 . the pion selfenergy pieces of eqs . ( 2 ) and ( 3 ) can readily be translated to a probability per unit length by the relation @xmath40 in @xcite ( see , also erratum in @xcite ) , the pion absorption effect on the pion - nucleus scattering at @xmath41 has been estimated using the quasi - deuteron ( qd ) model . taking into account that at energies well above the resonance region the two - body absorption becomes dominant @xcite , it is interesting to compare the outlined above model ( eq.(2 ) ) with the quasi - deuteron model . the imaginary part of the pion selfenergy @xmath42 within the framework of the quasi - deuteron model is given by @xmath43 where @xmath44 and @xmath45 are the densities of protons and neutrons . the kinematical factor @xmath46 is determined as @xmath47 where , @xmath48 and @xmath49 are the @xmath0-nucleus and @xmath0-deuteron reduced masses correspondingly , and @xmath50 is the relativistic transformation factor of the @xmath51 scattering amplitude from the @xmath52-nucleus to the @xmath51 c.m.s . @xmath53^{1/2 } \nonumber\ ] ] here , @xmath54 and @xmath55 are the pion momenta before and after the collision in the @xmath52-nucleus c.m.s . ; @xmath56 and @xmath57 are the pion momenta before and after the collision in the @xmath51 c.m.s . , and @xmath58 and @xmath59 are the total momenta of the @xmath60 subsystem before and after the collision in the @xmath52-nucleus c.m.s . we use here the `` frozen '' approximation which means that @xmath61 and @xmath62 , where @xmath63 is the momentum transfer . the imaginary part of the absorption parameter @xmath64 is given by @xmath65 where @xmath66 is the deuteron density at @xmath67 . so as in @xcite this quantity is calculated using the square - well potential model of a deuteron . the parameter @xmath68 is related to the pion - deuteron total cross section as @xmath69 . the total pion - deuteron absorption cross section at the energy range from @xmath70 to @xmath71 can be obtained from the differential cross section data of @xcite . the energy dependence of @xmath72 can be approximated as @xmath73 where @xmath74 is the pion kinetic energy in the laboratory system ( measured in fm ) , and the parameters @xmath75 are @xmath76 pion production is a determinant feature in the high energy pion nucleus reactions . the inelastic channels have a cross section comparable , or even larger than the elastic channels at energies above 0.6 gev . although two ( or more ) pion production channels are possible at the energies considered , the inelastic cross section is clearly dominated by the single pion production @xcite . in this work the multipion production channels have been ignored . whereas at low energies a considerable amount of data is available for most isospin channels , including differential cross sections , our knowledge is more fragmentary in the energy regime addressed here . data has been taken from compilation @xcite and @xcite , to obtain parametrizations of the @xmath77 total cross sections . then , for each channel , the probability per unit length is given by the equation @xmath78 when , according to this probability , a pion production event of a certain isospin channel has taken place , we proceed in the following way . first , a nucleon of the type @xmath13 is randomly chosen from the fermi sea . then the scattering angles and energies of the outgoing particles" +"we consider the following optimization problem @xmath4},\end{aligned}\ ] ] where @xmath5 is a non - linear function , @xmath6 denotes the response variable , @xmath7 denotes the predictor ( or covariate ) , and the expectation is over the joint distribution of @xmath8 . the above minimization is called a generalized linear problem in its canonical representation , and it is commonly encountered in the statistical learning . celebrated examples include binary classification with smooth surrogate losses @xcite , and generalized linear models ( glms ) such as poisson regression , logistic regression , ordinary least squares , multinomial regression and many applications involving graphical models @xcite . these methods play a crucial role in numerous machine learning and statistics problems , and provide a miscellaneous framework for many regression and classification tasks . the exact minimization of the stochastic optimization problem , requires the knowledge of the underlying distribution of the variables @xmath9 . in practice , however , the joint distribution is not available . therefore , after observing @xmath0 independent data points @xmath10 , the standard approach is to minimize the empirical risk approximation given as @xmath11 in the case of glms , the empirical risk minimization given in is called the maximum likelihood estimation , whereas in the case of binary classification , it is generally referred to as surrogate loss minimization . due to non - linear structure of the optimization task given in , for both problems , the minimization of the empirical risk requires iterative methods . regardless of the problem formulation , the most commonly used optimization method is the newton - raphson method , which may be viewed as a reweighted least squares algorithm @xcite . this method uses a second - order approximation to benefit from the curvature of the log - likelihood and achieves locally quadratic convergence . a drawback of this approach is its excessive per - iteration cost of @xmath12 . to remedy this , hessian - free krylov sub - space based methods such as conjugate gradient and minimal residual are used , but the resulting direction is imprecise @xcite . on the other hand , first - order approximation yields the gradient descent algorithm , which attains a linear convergence rate with @xmath13 per - iteration cost . although its convergence rate is slow compared to that of the second - order methods , its modest per - iteration cost makes it practical for large - scale problems . in the regime @xmath14 , another popular optimization technique is the class of quasi - newton methods @xcite , which can attain a per - iteration cost of @xmath13 , and the convergence rate is locally super - linear ; a well - known member of this class of methods is the bfgs algorithm @xcite . there are recent studies that exploit the special structure of glms @xcite , and achieve near - quadratic convergence with a per - iteration cost of @xmath15 , and an additional cost of covariance estimation . in this paper , we take an alternative approach for minimizing , based on an identity that is well - known in some areas of statistics , but appears to have received relatively little attention for its computational implications in large - scale problems . let @xmath16 denote the true minimizer of the population risk given in , and let @xmath17 denote the corresponding ordinary least squares ( ols ) coefficients defined as @xmath18}^{-1}{\mathbb{e}\left[xy\right]}$ ] . then , under certain random predictor ( design ) models , @xmath19 for logistic regression with gaussian design ( which is equivalent to fisher s discriminant analysis ) , was noted by fisher in the 1930s @xcite ; a more general formulation for models with gaussian design is given in @xcite . the relationship suggests that if the constant of proportionality is known , then @xmath16 can be estimated by computing the ols estimator , which may be substantially simpler than minimizing the empirical risk . in fact , in some applications like binary classification , it may not be necessary to find the constant of proportionality in . our work in this paper builds on this idea . our contributions can be summarized as follows . 1 . we show that @xmath16 is approximately proportional to @xmath17 in the random design setting , regardless of the covariate ( predictor ) distribution . that is , we prove @xmath20 for some @xmath21 which depends on the non - linearity @xmath22 . our generalization uses zero - bias transformations @xcite . we also show that the above relation still holds under certain types of regularization . we design a computationally efficient estimator for @xmath16 by first estimating the ols coefficients , and then estimating the proportionality constant @xmath23 via line search . we refer to the resulting estimator as the scaled least squares ( sls ) estimator and denote it by @xmath24 . after estimating the ols coefficients , the second step of our algorithm involves finding a root of a real valued function ; this can be accomplished using iterative methods with up to a cubic convergence rate and only @xmath25 per - iteration cost . this is cheaper than the classical batch methods mentioned above by at least a factor of @xmath3 . 3 . for random design with sub - gaussian predictors , we show that @xmath26 this bound characterizes the performance of the proposed estimator in terms of data dimensions , and justifies the use of the algorithm in the regime @xmath2 . we demonstrate how to transform a binary classification problem with smooth surrogate loss into a generalized linear problem , and how our methods can be applied to obtain a computationally efficient optimization scheme . we further discuss the canonicalization of the square loss , which may be of independent interest to non - convex optimization community . we propose a scalable algorithm for converting one generalized linear problem to another by exploiting the proportionality relation . the proposed algorithm requires only @xmath27 per each iteration , with no additional cost . we study the statistical and computational performance of @xmath24 , and compare it to that of the empirical risk minimizer ( using several well - known implementations ) , on a variety of large - scale datasets . the rest of the paper is organized as follows : section [ sec::related - work ] surveys the related work and section [ sec::preliminaries ] introduces the required background and the notation . in section [ sec::equivalence ] , we provide the intuition behind the relationship , which are based on exact calculations for the gaussian design setting . in section [ sec::algorithm ] , we propose our algorithm and discuss its computational properties . theoretical results are given in section [ sec::theory ] . in section [ sec::conversion ] , we propose an algorithm to convert one glm type to another . we discuss how a binary classification problem can be cast as a generalized linear problem in section [ sec::binary - classification ] , and in section [ sec::canonicalization ] we propose a method to canonicalize the square loss . section [ sec::experiments ] provides a thorough comparison between the proposed algorithm and other existing methods . finally , we conclude with a brief discussion in section [ sec::discussion ] . as mentioned in section [ sec::intro ] , the relationship is well - known in several forms in statistics . brillinger @xcite derived for models with gaussian predictors using stein s lemma . li & duan @xcite studied model misspecification problems in statistics and derived when the predictor distribution has linear conditional means ( this is a slight generalization of gaussian predictors ) . the relation has led to various techniques for dimension reduction @xcite , and more recently , it has been studied by @xcite in the context of compressed sensing . it has been shown that the standard lasso estimator may be very effective when used in models where the relationship between the expected response and the signal is nonlinear , and the predictors ( i.e. the design or sensing matrix ) are gaussian . a common theme for all of this previous work is that it focuses solely on settings where holds exactly and the predictors are gaussian ( or , in the case of @xcite , very nearly gaussian ) . two key novelties of the present paper are ( i ) our focus on the computational benefits following from for large scale problems with @xmath2 ; and ( ii ) our rigorous finite sample analysis of models with non - gaussian predictors , where is shown to be approximately valid . to the best of our knowledge , the present paper and its earlier version @xcite are the first to consider the relation in the context of optimization . we assume a random design setting , where the observed data consists of @xmath0 random iid pairs @xmath28 , @xmath29 , @xmath30 , @xmath31 ; @xmath32 is the response variable and @xmath33 is the vector of predictors or covariates . we focus on problems where the minimization is desirable , but we do not need to assume that @xmath10 are actually drawn from a particular distribution or the corresponding statistical model ( i.e. we allow for model misspecification ) . @xmath34}.\ ] ] while we make no assumptions on @xmath35 beyond smoothness , note that when the optimization problem is glm , and @xmath35 is the cumulant generating function for @xmath36 , then the problem reduces to the standard glm with canonical link and regression parameters @xmath16 @xcite . examples of glms in this form include logistic regression with @xmath37 , poisson regression with @xmath38 , and linear regression ( least squares ) with @xmath39 . our objective is to find a computationally efficient estimator for @xmath16 . the alternative estimator for @xmath16 proposed in this paper is related to the ols coefficient vector , which is defined by @xmath40^{-1}{\mathbb{e}\left[x_iy_i\right]}$ ] ; the corresponding ols estimator is @xmath41 , where @xmath42 is the @xmath43 design matrix and @xmath44 . additionally , throughout the text we let @xmath45\!=\ ! \{1,2, ... ,m \}$ ] , for positive integers @xmath46 , and we denote the size of a set @xmath47 by @xmath48 . the @xmath46-th derivative of a function @xmath49 is denoted by @xmath50 . for a vector @xmath51 and a @xmath52 matrix @xmath53 , we let @xmath54 and @xmath55 denote the @xmath56-vector and -operator norms , respectively . if @xmath57 $ ] , let @xmath58 denote the @xmath59 matrix obtained from @xmath53 by extracting the rows that are indexed by @xmath47 . for a symmetric matrix @xmath60 , @xmath61 and @xmath62 denote the maximum and minimum eigenvalues , respectively , and @xmath63 denotes the condition number of @xmath64 with respect to @xmath65-norm . we denote by @xmath66 the @xmath67-variate normal distribution , and all expectations are over all randomness inside the brackets . finally , we use @xmath68 and @xmath69 interchangeably , whichever is convenient ( where @xmath70 refers to the big o notation ) . to motivate our methodology , we assume in this section that the covariates are multivariate normal , as in @xcite . these distributional assumptions will be relaxed in section [ sec::theory ] . [ prop::equivalence ] assume that the covariates are multivariate normal with mean 0 and covariance matrix @xmath71 , i.e. @xmath72 . then @xmath16 can be written as @xmath73 where @xmath21 is the fixed point of the mapping @xmath74}^{-1}. \end{aligned}\ ] ] the optimal point in the optimization problem , has to satisfy the following normal equations , @xmath75 } = { \mathbb{e}\left[x_i \dcgf(\)\right]}. \end{aligned}\ ] ] now , denote by @xmath76 the multivariate normal density with mean 0 and covariance matrix @xmath71 . we recall the well - known property of gaussian density @xmath77 . using this and integration by parts on the right hand side of the" +"the understanding of the qcd phase diagram has become one of the most interesting issues in the physics of strong interactions . such phase diagram is relevant to phenomena in the early universe , in the interior of neutron stars and in relativistic heavy ion collisions . already in the seventies it was suggested that there should be two distinct phases : a low temperature and density phase in which quarks and gluons are confined within hadrons and chiral symmetry is broken , and a high temperature and density phase ( the so - called quark - gluon plasma ) in which these particles are deconfined and chiral symmetry is restored . although the possible existence of other phases ( e.g. the color superconducting phase ) was also suggested quite long ago@xcite , this two - phase structure became the standard picture of the qcd phase diagram for more than two decades . in recent years , however , it has been established that at low temperatures and medium densities several other phases might appear ( see e.g. ref.@xcite for recent reviews ) . in particular , for the case of two light flavors it has been shown that there should be a non - negligible region in the qcd phase diagram where strongly interacting matter is a color superconductor ( 2sc phase)@xcite . unfortunately , due to difficulties in dealing with finite chemical potential , ab initio calculations ( as e.g. lattice qcd ) are not yet able to provide a detailed knowledge of the qcd phase diagram@xcite . thus , most theoretical approaches are based on the use of effective models of qcd . among them , the nambu - jona - lasinio model@xcite is one of the most popular . in this model the quark fields interact via local four point vertices which are subject to chiral symmetry . if such interaction is strong enough , chiral symmetry is spontaneously broken at zero temperature and density , and pseudoscalar goldstone bosons appear . it has been shown by many authors that when the temperature and/or density increase , the chiral symmetry is restored@xcite . when effective quark - quark interactions are added to the effective lagrangian other phases also appear@xcite . as an improvement on the local njl model , some covariant nonlocal extensions have been studied in the last few years@xcite . nonlocality arises naturally in the context of several successful approaches to low - energy quark dynamics as , for example , the instanton liquid model@xcite and the schwinger - dyson resummation techniques@xcite . it has been also argued that nonlocal covariant extensions of the njl model have several advantages over the local scheme . several studies@xcite have shown that these nonlocal models provide a satisfactory description of the hadron properties at zero temperature and density . recently@xcite , the characteristics of the chiral phase transition have been investigated within this kind of models . the aim of the present work is to extend such studies to the case in which a superconducting phase can appear . this article is organized as follows . in sec . ii we introduce the model and formalism . our results for some specific nonlocal regulators are presented in sec . iii . in sec . iv we analyze the dependence of our results on the strength of the diquark correlations . finally , in sec . v we give our conclusions . let us begin by stating the euclidean action for the nonlocal chiral quark model in the case of two light flavors and @xmath5 isospin symmetry . for the purpose of the present study it is enough to only consider interactions in the scalar quark - antiquark and quark - quark channels . thus , one has @xmath6 ^ 2 - \frac{h}{2}\ \left [ \bar q(x ) \ i \gamma_5 \tau_2 \lambda_2 \ q_c(x ) \right ] \left [ \bar q_c(x ) \ i \gamma_5 \tau_2 \lambda_2 \ q(x ) \right ] \right\ } \ , \label{action}\end{aligned}\ ] ] where @xmath7 is the current quark mass and @xmath8 and @xmath9 are pauli and gell - mann matrices corresponding to the flavor and color groups , respectively . the delocalized quark fields @xmath10 are defined in terms of the quark fields @xmath11 as @xmath12 where the function @xmath13 is a nonlocal regulator . it can be translated into momentum space , @xmath14 lorentz invariance implies that @xmath15 can only be a function of @xmath16 . hence we will use for the fourier transform of the regulator the form @xmath17 from now on . in addition , in eq.([action ] ) we have used @xmath18 the partition function for the model is defined as @xmath19 where the euclidean action at finite temperature @xmath20 and chemical potential @xmath21 is obtained from eq . ( [ action ] ) by going to momentum space and performing the replacement @xmath22 where @xmath23 are the matsubara frequencies corresponding to fermionic modes , @xmath24 . as in ref.@xcite we are assuming here that the quark interactions only depend on the temperature and chemical potential through the argument of the regulators . to proceed it is convenient to perform a standard bosonization of the theory . thus , we introduce the sigma meson field @xmath25 and the scalar diquark field @xmath26 and integrate out the quark fields . in what follows we will work within the mean field approximation ( mfa ) , in which these bosonic fields are expanded around their vacuum expectation values @xmath27 and @xmath28 and the corresponding fluctuations neglected . within this approximation and employing the nambu - gorkov formalism , the mean field thermodynamical potential per unit volume reads @xmath29 \label{z}\ ] ] where @xmath30 stands for the trace over the dirac , flavor , color and nambu - gorkov bispinor indexes . the inverse propagator @xmath31 is @xmath32 where @xmath33 and @xmath34 . after some straightforward algebra @xmath35 can be more explicitly expressed as @xmath36 \right\ } \label{omega}\end{aligned}\ ] ] where , @xmath37 for finite values of the current quark mass , @xmath35 turns out to be divergent . the regularization procedure used here amounts to define @xmath38 where @xmath39 is the regularized expression for the thermodynamical potential of a free fermion gas , @xmath40 . \label{freeomegareg}\ ] ] the mean field values @xmath41 and @xmath28 are obtained from the coupled pair of gap equations @xmath42 the explicit form of these equations is @xmath43 , \label{gapeq}\end{aligned}\ ] ] where , in addition to the definitions given in eq.([def1 ] ) , we have used @xmath44 it should be noticed that , in general , there might be regions for which there are more than one solution for each value of @xmath20 and @xmath21 . in such regions we identify the stable solution by requiring it to be an overall minimum of the potential . given the thermodynamic potential the expressions for all other relevant quantities can be easily derived . for each flavor the quark - antiquark condensate @xmath45 and the quark density @xmath46 are given by @xmath47 in the case of the quark - quark condensate an extra source term @xmath48 has to be added to the effective action . it is easy to see that this leads to a thermodynamic potential @xmath49 which has the form given in eq.([omega ] ) but where @xmath50 has been replaced by @xmath51 . then , we get @xmath52 finally , a magnitud which is important to determine the characteristic of the chiral phase transition is the chiral susceptibility @xmath53 . it can be calculated as @xmath54 in this section we concentrate on the numerical results obtained for two different regulators often used in the literature : the gaussian regulator and the lorentzian regulator . in each case we have considered @xmath55 , @xmath7 and @xmath56 as input parameters fixed so as to reproduce the phenomenological values of the chiral condensate , pion mass and pion decay constant at vanishing temperature and densities@xcite . moreover , we have set @xmath57 as implied by , for example , oge interactions @xcite . the dependence of our results on this ratio will be discussed in the following section . in this case the regulator is given by @xmath58 where @xmath56 plays the role of a cut - off parameter . we have considered two different sets of parameters . set i corresponds to @xmath59 , @xmath60 and @xmath61 while set ii to @xmath62 , @xmath63 and @xmath64 . although for both sets the zero temperature and density properties mentioned above are well reproduced , in the case of set i the quark propagator has no purely real poles while for set ii it does . thus , following ref.@xcite , set i might be interpreted as a confining one , since quarks can not materialize on - shell in minkowski space . the mean field values @xmath41 and @xmath28 as a function of @xmath21 and @xmath20 are obtained by numerically solving eqs.([gapeq ] ) . the corresponding results as a function of @xmath21 for various values of @xmath20 are displayed in fig.[unos ] , where left panels correspond to set i while right ones to set ii . it can be seen that , for small values of @xmath20 and @xmath21 ( full lines in fig.[unos ] ) , the system is in the chiral phase for which @xmath65 and @xmath66 . if we increase @xmath21 keeping @xmath20 fixed , at some critical value of @xmath21 there is sudden drop of @xmath67 and a simultaneous sudden increase in @xmath68 so that we get into the 2sc phase characterized by @xmath69 and @xmath70 . in particular , the values of the diquark gap at the critical chemical potential and @xmath71 can be found in table 1 . if we repeat the process with a higher value of @xmath20 something similar happens until we reach the triple point "" ( 3p ) . for temperatures slightly higher than @xmath72 ( dashed lines in fig.[unos ] ) the sudden drop in @xmath67 and the increase @xmath68 start to happen at two different values of @xmath21 . between these values of @xmath21 we have @xmath69 and @xmath66 . moreover there is no discontinuity in the behavior of @xmath68 as a function of @xmath21 . for temperatures above the end point "" ( ep ) the discontinuity in @xmath67 also disappears ( dotted lines in fig.[unos ] ) . finally for temperatures above the critical temperature for @xmath73 , @xmath74 , we get @xmath75 for all values of @xmath21 . in the region corresponding to the crossover the transition point is defined by the point at which the chiral susceptibility @xmath53 has a maximum . the positions of the different critical points are summarized in table 1 . also shown in fig.[unos ] are the corresponding quiral @xmath76 and diquark @xmath77 condensates . their behavior is quite similar to those of the mean field values @xmath41 and @xmath28 , respectively . it is worthwhile to mention that the fact that the chiral condensate approaches some positive value for large values of @xmath21 is due to the substraction scheme used to regularize the thermodynamical potential , eq.([omegareg ] ) . in fact , it is not difficult to see that for finite values of @xmath7 the regularized free thermodynamical potential @xmath39 , eq.([freeomegareg ] ) , has such behavior . the corresponding phase diagrams are displayed in fig.[dos ] . again left panels correspond to set i and right ones to set ii . on the other hand , the upper panels correspond to the phase diagrams in the @xmath0 plane and the lower ones to the diagrams in the @xmath78 plane , where the nuclear matter density @xmath79 . in all the cases we have indicated with full lines the first order transition lines , with dashed lines the second order transition lines and with dotted lines the lines corresponding to the crossover between the chiral phase and" +"after the experimental observation of bose - einstein condensate ( bec ) @xcite , there have been many experimental studies to investigate different quantum phenomena in a laboratory previously not accessible for study in a controlled environment , such as , quantum phase transition @xcite , quantum collapse of matter wave under attraction @xcite , four - wave mixing of matter waves @xcite , formation of vortex lattice @xcite , interference of matter waves @xcite , josephson tunneling @xcite , anderson localization @xcite etc . the generation and the dynamics of self - bound large quantum waves have drawn much attention lately . there have been some studies of self - bound matter waves or solitons in one ( 1d ) @xcite or two ( 2d ) @xcite space dimensions . a ( self - bound ) bright soliton travels at a constant velocity in 1d , due to a cancellation of nonlinear attraction and defocusing forces @xcite . the collision between two analytic 1d bright solitons is always elastic @xcite with the solitons emerging after collision without a change of velocity and shape . the 1d soliton has been observed in nonlinear optics @xcite and in bose - einstein condensates @xcite . however , a two- or three - dimensional ( 3d ) soliton can not be realized for two - body contact attraction alone due to collapse @xcite . the 1d bec solitons studied experimentally @xcite are really quasi solitons behaving like real solitons at large velocities . at low velocities a deformation of their shapes is expected upon collision . there have been a few proposals for creating a self - bound 3d matter - wave state which we term a quantum ball . some of these proposals involve an engineering of the atomic scattering length using the feshbach resonance technique to generate dynamically stabilized solitons in 2d and 3d @xcite . others consider extra interactions usually neglected in dilute bec of alkali atoms to create a stationary localized state . in the presence of an additional nonlocal dipolar interaction a 2d bec soliton can be generated @xcite . it has been suggested by maucher _ _ @xcite that in the case of rydberg atoms , off - resonant dressing to rydberg nd states can provide a nonlocal long - range attraction which can form a quantum ball . the collapse instability can be stopped in this case by a repulsive contact interaction . in this paper we demonstrate that a _ very small _ repulsive three - body interaction in the presence of an attractive two - body contact interaction can generate a stable quantum ball . the collapse is stopped in this case by the repulsive three - body interaction . although , some theoretical suggestions for generating a quantum ball , in the presence of a repulsive core in the two - body atomic interaction , seem viable @xcite , so far there has not been success in their experimental realization . nevertheless , there are questions about the dynamics of a quantum ball which are very intriguing . the study of the dynamics of a quantum elementary particle like an electron to determine simultaneously its position and velocity is doomed to failure due to the heisenberg uncertainty relation . on the other hand , for a quantum ball the uncertainty relation is not of concern due to its large mass and it can be traced like a classical object by its position and velocity at each instant . as the quantum ball is self bound it can move like a classical ball obeying newton s first law of motion . however , very little is known about the interaction dynamics of two quantum balls and that of a quantum ball with other objects and we address these questions in this paper . we consider the mean - field gross - pitaevskii ( gp ) equation with the inclusion of a three - body interaction for the study of statics and dynamics of a quantum ball . the quantum balls are bound by an attractive two - body contact interaction in the presence of a repulsive three - body contact interaction . we use the realistic parameters of @xmath0li atoms , in this study , with a negative scattering length corresponding to two - body attraction @xcite . the effect of atom loss due to three - body recombination is included in the study of dynamics . the three body loss rate is not accurately known for this system @xcite for the parameter domain used in this study . we have chosen three - body loss rates that ensure our system does not decay significantly during our dynamical simulations . it is expected that the dynamics of quantum balls will be independent of the details of the mechanism responsible for self binding and we do not believe that the results obtained here are so peculiar as to have no general validity . in fact , a preliminary study revealed similar dynamics for quantum balls made of dipolar atoms @xcite . a stationary quantum ball can be formed for the two - body attraction above a critical value in the 3d gp equation for any finite three - body repulsion . the statical properties of the quantum ball are studied using a variational analysis and a numerical solution of the 3d gp equation . the variational and numerical results are found to be in good agreement with each other . the stability of the quantum ball is established numerically under a small perturbation introduced by changing the three - body interaction by a small amount , while the quantum ball is found to execute sustained breathing oscillation . a quantum ball can move freely without deformation along any direction with a constant velocity . we study the frontal and angular collisions between two quantum balls . only the collision between two integrable 1d solitons is truly elastic @xcite . as the dimensionality of the soliton is increased such collision is expected to become inelastic with loss of energy in 2d and 3d . in the present numerical simulation of frontal collision between two quantum balls , at sufficiently large velocities the collision is found to be quasi elastic when the two quantum balls emerge after collision with practically no deformation and without any change of velocities . unlike classical balls , obeying the newton s laws , there is no change in the directions of motion of the quantum balls after collision . however , upon impact with a rigid impenetrable plane the quantum ball bounces like a classical elastic ball obeying the usual laws of reflection . at small velocities the collision between two quantum balls is inelastic and the quantum balls form a single bound entity in an excited state executing breathing oscillation , which we call a quantum - ball breather . we present the 3d gp equation used in this study in sec . [ ii ] and a variational analysis of the same for an analytic understanding of the formation of the quantum ball . in sec . [ iii ] we present the numerical results for stationary profiles of a quantum ball . we present numerical tests of stability of a quantum ball under a small perturbation . the quasi - elastic nature of collision of two quantum balls at large velocities and the formation of a quantum - ball breather at small velocities are demonstrated by real - time simulation . we end with a summary of our findings in sec . we consider a quantum ball in the presence of a three - body interaction and the mean - field model appropriate for this study . the mean - field gp equation for @xmath1 atoms of mass @xmath2 is @xcite @xmath3 } \phi({\bf r},t ) , \label{eq1}\end{aligned}\ ] ] where @xmath4 is the scattering length , and @xmath5 is the three - body interaction term . the negative scattering length @xmath4 represents two - body attraction and the positive @xmath5 to three - body repulsion . for an analytic understanding of the formation of a quantum ball convenient variational approximation of eq . ( [ eq1 ] ) can be obtained with the following gaussian ansatz for the time - independent stationary wave function @xcite @xmath6,\end{aligned}\ ] ] where @xmath7 , @xmath8 is the width . the energy density corresponding to eq . ( [ eq1 ] ) is given by @xmath9 consequently , the total energy per atom @xmath10 becomes @xmath11 the width @xmath8 of a stationary quantum ball with negative energy corresponds to a global minimum of energy @xmath12 : @xmath13 without the quintic term ( @xmath14 ) the quantum ball of width @xmath15 is tantamount to an unstable towne s soliton @xcite . for stability a non - zero quintic term ( @xmath16 ) is necessary . versus @xmath8 in @xmath17 m for different @xmath1 from eq . ( [ eq6 ] ) for @xmath18 and @xmath19 m@xmath20/s . variational ( b ) @xmath21 and ( c ) @xmath22 phase plots for @xmath18 and @xmath19 m@xmath20/s , respectively , illustrating the regions of formation of a stable and metastable quantum ball obtained from eq . ( [ eq6 ] ) . , title=""fig : "" ] versus @xmath8 in @xmath17 m for different @xmath1 from eq . ( [ eq6 ] ) for @xmath18 and @xmath19 m@xmath20/s . variational ( b ) @xmath21 and ( c ) @xmath22 phase plots for @xmath18 and @xmath19 m@xmath20/s , respectively , illustrating the regions of formation of a stable and metastable quantum ball obtained from eq . ( [ eq6 ] ) . , title=""fig : "" ] versus @xmath8 in @xmath17 m for different @xmath1 from eq . ( [ eq6 ] ) for @xmath18 and @xmath19 m@xmath20/s . variational ( b ) @xmath21 and ( c ) @xmath22 phase plots for @xmath18 and @xmath19 m@xmath20/s , respectively , illustrating the regions of formation of a stable and metastable quantum ball obtained from eq . ( [ eq6 ] ) . , title=""fig : "" ] in the numerical calculation , we use the parameters of @xmath0li atoms , e.g. , @xmath23 @xcite and @xmath24 amu , where @xmath25 is the bohr radius . unlike the 1d case , the 3d gp equation ( [ eq1 ] ) does not have analytic solution and different numerical methods , such as split - step crank - nicolson @xcite and fourier spectral @xcite methods , are used for its solution . we solve the 3d gp equation ( [ eq1 ] ) numerically by the split - step crank - nicolson method using both real- and imaginary - time propagation in cartesian coordinates using a space step of @xmath26 @xmath17 m and a time step of @xmath27 ms in all calculations @xcite . all imaginary - time simulations were performed in a box of size @xmath28 unless otherwise stated . imaginary - time simulation is employed to get the lowest - energy bound state of a quantum ball , while the real - time simulation is to be used to study the dynamics using the initial profile obtained in the imaginary - time propagation @xcite . there are different c and fortran programs for solving the gp equation @xcite and one should use the appropriate one . in the imaginary - time propagation the initial state was taken as in eq . ( [ eq1 ] ) and the width @xmath8 set equal to the variational solution obtained by solving eq . ( [ eq6 ] ) . the convergence will be quick if the guess for the width @xmath8 is close to the final width . , ( b ) energy @xmath29 and ( c ) peak atom density @xmath30 versus the number of @xmath0li atoms @xmath1 in a quantum ball for three different three - body interactions @xmath31 m@xmath20/s , @xmath32 m@xmath20/s , @xmath33 m@xmath20/s ." +"there is growing evidence from nuclear magnetic resonance @xcite , resonant x - ray scattering and diffraction @xcite and scanning tunneling microscopy @xcite that charge ordered states play an important role in underdoped cuprates . in particular , a charge - modulated state with 4 incommensurate wave vectors along the crystalline axes was detected in ybco and in bi - based single and double layer compounds . resonant elastic x - ray scattering showed that the charge order emerges just below the opening of the pseudogap @xcite in underdoped bi2201 @xcite . the formation of the pseudogap , fermi pockets , the appearance of quantum oscillations @xcite and of charge order may thus be intimately related in these systems . it is the aim of this paper to characterize charge ordered states in interacting systems independently of the strength of the interaction . furthermore , the implications of point group and time reversal symmetries as well as the hermiticity of the hamiltonian for the order parameter ( op ) will be taken into account in greater detail than in previous treatments . the microscopic form of the charge op in cuprates is not clear at present . to illustrate this let us consider the following model hamiltonian for electrons on a square lattice which generally is believed to be relevant for cuprates @xcite , @xmath5 @xmath6 denotes the hopping amplitude of electrons between the lattice site @xmath7 and @xmath8 . @xmath9 and @xmath10 are fermionic creation and annihilation operators , @xmath11 spin indices and repeated spin indices are always summed over . the second and third terms in eq . ( [ h ] ) describe antiferromagnetic and coulomb interactions between electrons on neighboring sites @xmath7 and @xmath8 with coupling constants @xmath1 and @xmath12 , respectively . if double occupancies of sites are excluded eq . ( [ h ] ) represents the well - known @xmath0-@xmath1 model for @xmath13 . the interaction terms in eq . ( [ h ] ) give rise to two kinds of charge ops . a hartree - like contraction of the third term yields an op proportional to @xmath14 describing the charge on the site @xmath7 . it may vary from site to site and represents a conventional charge density wave ( cdw ) state . the exchange contractions of the second and third term in eq . ( [ h ] ) yield an op proportional to @xmath15 , where @xmath7 and @xmath8 are nearest neighbor sites . this state may be called a nonlocal cdw or a bond - order wave ( bow ) state @xcite where the cdw acquires an internal degree of freedom because the electron and hole occupy different sites . it has been shown that in the large n limit of the @xmath0-@xmath1 model ( which corresponds to enforcing the constraint of no double occupancies of sites only globally ) the phase diagram consists in the underdoped regime of incommensurate bow states ( at zero doping of the staggered flux phase @xcite as a special case ) @xcite . at the same time the conventional cdw op is zero showing that both kinds of charge order are independent from each other . more recently the bow state has been studied theoretically in more detail @xcite . also models with more than one band @xcite or more complex ops @xcite have been considered . recently a microscopic form for the op in underdoped ybco and bi2201 was proposed @xcite based on experimental data from resonant x - ray scattering . throughout the paper we will assume that the temperature is below the transition temperature to the bow state . the ops are then in general nonzero and their symmetry properties can be studied . we will classify possible ops for bow states by exploiting point - group and time reversal symmetries as well as the hermiticity of @xmath16 . in the appendix it is shown that possible ops for the ground state are basis functions for representations of @xmath17 . if the ground state is non - degenerate in the sense that it does not contain two linearly independent ops the representation is irreducible . if the ground state is degenerate and satifies a two dimensional representation this representation may be irreducible or reducible . in the latter case it is composed of two ops with different symmetries and the degeneracy is not a consequence of symmetry but of coupling constants . in the following we will confine our discussion to ops which form irreducible representations of @xmath17 and exlude accidential degeneracies , additional instabilities or induced higher harmonics @xcite . explicit expressions for the ops will be given for bow states with four wave vectors of the form @xmath18 and the form @xmath19 and @xmath20 . from eq . ( [ h ] ) follows that the bow op has the form of a coupling constant times the matrix element @xmath21 , where @xmath7 and @xmath8 are nearest neighbors . to simplify the nomenclature we will call the modulated part of @xmath21 op in the following . after a fourier transform we obtain , @xmath22 @xmath23 is the vector from the origin to the lattice site @xmath7 . the sum over @xmath24 in eq . ( [ fourier ] ) includes in the plane - wave limit only the wave vectors corresponding to a charge instability of the normal state . they form a star of wave vectors @xmath25 . writing @xmath26 , keeping @xmath27 fixed and performing a fourier transformation with respect to @xmath23 we get @xmath28 the functions @xmath29 are defined by eq . ( [ f ] ) and represent our set of order parameters . if umklapp terms are included the sum over @xmath30 may not only include primary instability vectors of the normal state but higher harmonics with wave vectors @xmath31 where @xmath32 is an integer . they form new stars and cause deviations from the plane - wave limit of the op . because these higher harmonics are important only near the transition to the commensurate phase we will neglect them in the following and restrict ourselves to the plane - wave limit . the symmetry group of the square lattice is @xmath17 . using the notation of ref . @xcite let us denote one of the 8 symmetry transformations by @xmath33 . its action on the order parameter in eq . ( [ f ] ) can be written as @xmath34 where @xmath35 is the 2x2 matrix representing @xmath33 in the two - dimensional direct space . after a fourier transformation with respect to @xmath23 we find that @xmath29 transforms under @xmath33 into @xmath36 , where @xmath37 and @xmath38 belong to the star of wave vectors and to nearest neighbor bonds , respectively . this means that the set of functions @xmath39 forms basis functions for a ( reducible ) representation of @xmath17 . decomposing this reducible representation into irreducible parts the basis function of one of the irreducible representations describes the op of the state corresponding to the global minimum of the free energy . one important feature is that in general both @xmath30 and @xmath27 are transformed under @xmath33 at the same time and not independently from each other . this is a crucial point in our approach . further general properties of the functions @xmath40 are related to time reversal and the hermiticity of the hamiltonian . the operator @xmath41 for time reversal is defined in real space by @xmath42 where the star means conjugate complex . taking fourier transforms on both sides we get , @xmath43 or @xmath44 or , @xmath45 in eqs . ( [ philf2 ] ) and ( [ philf3 ] ) @xmath46 stands for @xmath47 and @xmath27 is fixed in the sums over @xmath23 . @xmath48 is defined by the last equation . some authors interprete the right - hand side of eq . ( [ philf2 ] ) as a fourier transform of @xmath49 which may be written as @xmath50 . the connection to our definition eq . ( [ philf4 ] ) is @xmath51 . in order to avoid confusion we will always use our definition in eq . ( [ philf4 ] ) . using the hermiticity of the hamiltonian the second half of eq . ( [ f ] ) yields @xmath52 @xmath53 denotes the rotation by @xmath54 . ( [ philf4 ] ) implies @xmath55 , which corresponds to the case of integral spin . @xcite applying the frobenius - schur test @xcite to the point group @xmath17 shows that including @xmath41 in the set of symmetry transformations can not produce additional degeneracies of irreducible representations . thus it is convenient to construct first basis functions for irreducible representations of the point group and then to check their behavior under time reversal . in the following we will first consider the case with 4 wave vectors along the diagonals , i.e. , @xmath56 , where @xmath57 lies between 0 and @xmath54 . the four bond directions are denoted by @xmath58 . it is easy to see that the following 8 functions @xmath59 , @xmath60 , @xmath61 , @xmath62 , and @xmath63 yield a reducible representation of @xmath17 . let us denote the linear combinations of the @xmath64 which form basis functions for the corresponding irreducible representations @xmath65 by @xmath66 for the one - dimensional representations @xmath67 one can easily determine the coefficients @xmath68 from the character table of @xmath17 . one finds that each of these representations occurs exactly one time , the corresponding @xmath68 are given in the first 4 lines of table 1 . using again the character table one finds that the remaining 4 functions form 2 two - dimensional representations @xmath69 and @xmath70 . the corresponding @xmath68 are given in the lines 5 - 8 in table 1 . .coefficients @xmath68 [ cols=""^,^,^,^,^,^,^,^,^"",options=""header "" , ] going back to eq . ( [ herm ] ) we note that for the functions @xmath71 the phase factor @xmath72 is always equal to @xmath57 . multiplying eq . ( [ herm ] ) by @xmath68 and summing over @xmath73 we obtain @xmath74 from the character table of @xmath75 follows that @xmath76 is equal to @xmath77 for @xmath67 and equal to @xmath78 for @xmath79 . the solution of eq . ( [ ff ] ) is @xmath80 where the upper sign refers to @xmath81 and the lower sign to @xmath79 , respectively . the real part of @xmath77 , @xmath82 , may assume any real number . for @xmath83 or @xmath54 the four functions @xmath84 form a basis for a reducible representation of @xmath17 which decomposes into @xmath2 , @xmath3 and @xmath4 representations with the basis functions @xmath85 , @xmath86 and @xmath87 , @xmath88 , respectively . ( [ ff ] ) still holds the first two basis functions are real ( imaginary ) and the third and fourth ones imaginary ( real ) for @xmath83 ( @xmath89 ) . included as a special case is the staggered flux phase with wave vector @xmath90 . it has @xmath3 symmetry and a purely imaginary op in agreement with previous conclusions . @xcite let us denote the second set of 8 functions by @xmath91 . each @xmath92 is obtained from @xmath64 by exchanging @xmath93 with @xmath94 and @xmath95 with @xmath96 . the linear space spanned by the functions @xmath97 yields a reducible representation of @xmath17 . decomposing it into its irreducible parts gives one time the representations @xmath98 and two times the representation @xmath4 , exactly as for the first 8 functions @xmath64 . the analogue of eq . ( [ c ] ) reads @xmath99 where the coefficients @xmath68 are the same as in table 1 . the phase factor @xmath72 is for all 8 functions equal to @xmath100 so that eq . ( [ ff ] ) reads @xmath101 with the solution @xmath102 @xmath103 is unrelated to @xmath82 and may assume any real value . this" +"the efficiency of a crystal as a scintillator is parametrized by the light yield ( ly ) , defined as the number of photons emitted per unit of absorbed energy . a remarkable aspect outlined by different studies @xcite is that the @xmath1/@xmath2 ly of a crystal is not constant with the energy deposited inside the lattice . this characteristic , referred to as _ non - proportionality _ , prevents the correct reconstruction of the absorbed energy , affecting the energy calibration . moreover , the ly dependency on energy strongly affects the intrinsic component of the scintillator energy resolution @xcite . events having the same nominal energy can in fact result in multiple depositions differently affected by the _ non - proportionality _ , causing a final broadening of the energy peaks . in recent years great importance has been given to the study of _ non - proportionality _ , because of its correlation with the attainable energy resolution of scintillation crystals @xcite . in order to fully understand this feature , different crystals have been characterized , exciting the scintillation both with @xmath1 rays and charged particles , such as @xmath3s , @xmath2s and ions . in order to characterize the crystal independently from the detector , the ly _ non - proportionality _ has been measured as a relative variation with respect to the ly at the 662 kev @xmath1 line , referred to as _ relative light yield _ ( @xmath4 ) . as the excitation energy lowers , the @xmath4 increases for iodine crystals ( nai and csi for example ) and lowers for oxide crystals ( lso and bgo for example ) @xcite . moreover the @xmath4 is bigger in crystals characterized by worst energy resolution @xcite : as a consequence , the _ non - proportionality _ appears to be the fundamental limit to the attainable scintillators energy resolution . a definite theoretical explanation for the _ non - proportionality _ is not available and in recent years three phenomena have been addressed to as possible causes @xcite : the energy dependence of the relaxation channels , the landau fluctuations of the stopping power and the secondary electrons ( @xmath5-ray ) scattering . these models ascribe the observed _ non - proportionality _ to an actual change in ly , depending on the influence of intrinsic characteristics of crystals on the electrons / holes diffusion inside the lattice . these models generally predicts the behaviour of crystals , but can not give explanation to some particular features , such as the change of @xmath4 obtained with a change in the shaping time chosen for the scintillation pulse @xcite . in particular , the choice of larger shaping times both enhances the intrinsic energy resolution and reduces the @xmath4 . as a consequence , in this paper an in depth study of the _ non - proportionality _ dependence on shaping time is presented , in order to understand how deep this relation is . the compton coincidence technique ( cct ) has been used to measure the @xmath4 of three crystals with different time and light output characteristics ( see table [ cprop ] ) : cdwo@xmath0 , bgo , and nai(tl ) . the point in the application of this technique is that it allows the analysis of the crystal response to electrons @xcite . since the scintillation mechanism is based on the electron diffusion and recombination @xcite , the cct allows an in depth analysis of this phenomenon . .crystal properties table . data were taken from @xcite . [ cols=""^,^,^,^,^"",options=""header "" , ] as previously said , the ly _ non - proportionality _ has been measured as a relative variation with respect to the light yield at the 662 kev @xmath1 line , referred to as _ relative light yield _ ( @xmath4 ) . the obtained variable is given by the following expression : @xmath6 according to the current knowledge @xcite , both the cdwo@xmath7 and bgo crystals should present a negative _ non - proportionality _ , and their @xmath4 should decrease when the deposited energy lowers . on the other hand , the nai(tl ) crystal should be positively non - proportional , thus its @xmath4 should increase when the deposited energy lowers ( see figure [ nonproplit ] ) . crystal digitized by the adc at 60 mhz . ] as reported in @xcite the choice of the shaping time ( st ) used to shape the light signals can change the slope of the _ non - proportionality _ curve . to evaluate the actual effect of st , it has been chosen to apply a digital pulse processing algorithm ( dpp ) to the acquired preamplified scintillator pulses . this strategy allows to check the effects of different shaping times , without acquiring multiple measurements for every configuration . the developed algorithm implements the trapezoidal filtering of the acquired pulses and is based on the procedure adopted in @xcite . the transfer function of the filter , expressed in the z - transform domain , is : @xmath8 where @xmath9 is the number of samples used for rise and decay times , @xmath10 is the number of samples used for the flat top and @xmath11 is the factor responsible for the zero - pole cancellation . since the flat top was affected by noise fluctuations , it has been chosen to use a trapezoidal filter with no flat top , referred to as triangular filter ( see figure [ trapezoidalexample ] ) . in addition to the dpp technique , the digitalized preamplified pulses were also integrated numerically . this operation allows to estimate the amplitude of the light pulse without selecting a defined bandwidth , thus including the majority of the scintillation components . the results obtained for the _ non - proportionality _ behaviour with different sts , for cdwo@xmath7 , bgo and nai(tl ) crystals are reported respectively in figure [ rlycdwo ] , [ rlybgo ] and [ rlynai ] . from these data it can be inferred that the _ non - proportionality _ of scintillation crystals is determined by the st used to process the light signal . choosing a longer shaping time , in fact , causes all the studied crystals to be negatively non - proportional , while choosing a shorter shaping time causes the same crystals to be positively non - proportional . the transition between negative and positive deviation is different for each studied crystal , and it is related to the time characteristics of its scintillation . for example , on one hand the cdwo@xmath7 , which has a main scintillation time constant of @xmath12 @xmath13s , shows negative _ non - proportionality _ for st@xmath1410 @xmath15 . on the other hand the bgo , which has a main time constant of @xmath16 ns , shows negative deviations for st@xmath1450 ns . the obtained results show a clear correlation between the _ non - proportionality _ behaviour with energy and the st chosen to filter the light pulses . the observed behaviour can be explained by a dependence with energy of the involved scintillation component : faster components are predominant at lower energies , while higher energy events are characterized by longer scintillation times . this can be ascribed to an eventual enrolment mechanism of the activation sites in the crystal lattice : on one hand , the deposition of small energies activates just few sites characterized by a short decay time ; on the other hand , an event with higher energy causes the activation of different recombination sites , with both short and long characteristic times . as a consequence it could be inferred a sort of hierarchy between the recombination sites , ruled by the energy of the activation event and by its ionizing potential . the effect of the st is evident , since it causes the _ non - proportionality _ to space in a range between 0.5 and 2.5 . as expected , integrating the preamplifier signal causes the crystal to loose its _ non - proportionality_. ] , all the st@xmath1450 ns give the same effects , and a longer st ( 10 @xmath15 ) return a negative r@xmath17 . at high energies the r@xmath17 is lower than 1 , because the small size of the used bgo crystal ( 2x2x2@xmath18 ) did not allow the complete absorption of the electrons energy . ] and 5@xmath15 cause the observed behaviour to change from the literature studies ( figure [ nonproplit ] ) . ] a detailed study of the _ non - proportionality _ behaviour with energy of three different scintillation crystals ( cdwo@xmath0 , bgo and nai ) has been performed . the relation between _ non - proportionality _ and st has been characterized by the means of a dpp algorithm , which allowed to test different integration times on the same measurement . the obtained results suggest that the _ non - proportionality _ in light yield of scintillation crystals is not an intrinsic characteristics of the crystal itself : as a matter of fact , it depends on which part of the scintillation spectrum is considered in the pulse processing , since different scintillation components are selected by different sts . in the framework of high resolving scintillation detectors , this evidence can be used to tune the analysis strategy for the light pulses , optimizing the spectrometric performances of these crystals . on the other hand , this peculiar characteristics has to be further investigated , in order to enlighten the hidden characteristics of the scintillation mechanism of crystals . m. moszyski and a. syntfeld - kauch and l. swiderski and m. grodzicka and j. iwanowska and p. sibczyski and t. szczniak , _ energy resolution of scintillation detectors _ , _ nucl . instrumention and methods in physics research a _ * 805 * ( 2016 ) 25 - 35 . p. dorenbos and j. t. m. de haas and c. w. e. van eijk , _ non - proportionality in the scintillation response and the energy resolution obtainable with scintillation crystals _ , _ ieee transactions on nuclear science _ * 42 * ( 1995 ) 2190 - 2202 . john d. valentine , brian d. rooney , _ design of a compton spectrometer experiment for studying scintillator non - linearity and intrinsic energy resolution _ , _ nuclear instruments and methods in physics research a _ * 353 * ( 1994 ) 37 - 40 . john d. valentine and brian d. rooney , _ benchmarking the compton coincidence technique for measuring electron response non - proportionality in inorganic scintillators _ , _ ieee transactions on nuclear science _ * 43 * ( 1996 ) 1271 - 1276 . brian d. rooney and john d. valentine , _ scintillator light yield nonproportionality : calculating photon response using measured electron response _ , _ ieee transactions on nuclear science _ * 44 * ( 1997 ) 509 - 516 . n. tsuchida , m. ikeda , t. kamae , m. kokubun , _ temperature dependence of gamma - ray excited scintillation time profile and light yield of gso , yso , yap and bgo _ , _ nuclear instruments and methods in physics research section a _ * 385 * ( 1997 ) 290 - 298 . c. cuesta , m.a . olivn , j. amar , s. cebrin , e. garca , c. ginestra , m. martnez , y. ortigoza , a. ortiz de solrzano , c. pobes , j. puimedn , m.l . sarsa , j.a . villar , p. villar , _ slow scintillation time constants in nai(tl ) for different interacting particles _ , _ optical materials _ * 36 * ( 2013 ) 316 - 320 . m. moszyski , w. czarnacki , w. klamra , m. szawlowski , p. schotanus" +"we present a numerical study of exact breather dynamics in two - dimensional nonlinear schrdinger lattices . this issue fits well with the enduring scientific interests of serge aubry in the many faceted subject of localization and transport in nonlinear macroscopic discrete systems , where serge s outstanding contributions are widely recognized . many ideas and lines of study followed in the investigation reported here have found a source of inspiration in early works of aubry and collaborators , among which the doctoral works of th . cretegny and j.l . marn deserve special mention . the existence and properties of localized solutions in extended discrete systems have atracted interest in a broad range of physical fields @xcite . discrete breathers , sometimes referred to as intrinsic localized modes , are spatially localized and time periodic solutions . these solutions arise in the context of nonlinear discrete systems and are of fundamental interest for varied physical applications such as pulse propagation in nonlinear optics , energy storing and transport in biomolecules , plasma physics , etc ... the existence of discrete breathers in these systems has been proved rigorously @xcite for a number of equations with physical relevance and , contrary to continuous nonlinear equations , their existence can be regarded as a generic feature of these systems . one of the most important class of equations are the so - called _ discrete nonlinear schrdinger lattices _ the existence of discrete breathers has been proven for a wide range of systems belonging to this class of nonlinear difference - differential equations . in particular , the most important example of wide aplicability is the standard nonlinear schrdinger equation . for instance , this equation was employed in @xcite for describing the propagation of localized beams in an array of nonlinear ( kerr type ) waveguides , having experimental validation subsequently reported in @xcite . the study of two - dimensional nonlinear schrdinger lattices has atracted much atention @xcite in recent years due to the new phenomena emerging when the dimensionality of the lattice is increased . some examples of these new features are the existence of vortex - breathers @xcite which supports energy flux , the appearance of an energy threshold for the creation of discrete breathers @xcite and the ubiquity of an instability ( the quasi - collapse ) of some discrete breather solutions leading to a highly localized pulson state @xcite . these theoretical efforts have their counterpart in recent advances in the field of nonlinear optics . the studies of two - dimensional arrays of coupled nonlinear waveguides allow the experimental observation of those effects studied theoretically . specially relevant is the recent experimental breakthrough ( theoretically designed in @xcite ) by fleisher _ et al _ @xcite , where a two - dimensional array of nonlinear waveguides is induced in a photosensitive material . this technique provides a clear experimental verification of the two - dimensional discrete breather existence in this system . in particular , besides the observation of standard discrete breathers , these works reported the first observations of staggered discrete breathers . our study here will focus on the computation of numerically exact dicrete breathers in two - dimensional anisotropic nonlinear schrdinger lattices , _ i.e. _ where the couplings in the two spatial directions are different . the use of shooting methods allow us to find these solutions and analyze their structural and stability properties . both pinned and mobile discrete breathers are studied . in the latter case we will study only the ones whose motion is along one axis of the lattice . the analysis of the numerically exact solutions shed light on some features of the properties and stability of localized solutions reported in previous works . the plan of the paper is as follows : in section [ sec : numerical ] we provide the technical background and details needed for self - contained purposes . first we summarize in [ subsec:1d ] the main conclusions on the dynamics of 1d schrdinger discrete breathers reported in @xcite . a detailed account of the numerical methods ( svd - regularized newton continuation of operator fixed points ) that we have used can be found in that reference . also in [ subsec:1d ] , we discuss briefly the most relevant formal differences with respect to alternative approaches to ( one - dimensional ) exact mobility of discrete breathers , _ e.g. _ those in refs @xcite and @xcite . in subsection [ sec : numerics ] we introduce the two - dimensional anisotropic salerno lattice and provide explanations on the implementation of the numerical procedures used to study the dynamics of 2d discrete breathers . the analysis of the results of our numerics on pinned discrete breathers for anisotropic nonlinear schrdinger lattices is reported in section [ sec : pinned ] . we present the numerical computations of the fixed point norm , as a function of three parameters : breather frequency , transversal coupling , and nonlinearity ( see below ) . they show , as anticipated , the so - called _ quasi - collapse _ transition , associated with the ( well - known ) existence of thresholds for the breather norm in two - dimensional lattices . we present numerically computed sectors of the bifurcation surface . we conclude this section with a brief look at the nonlinear dynamics on the unstable manifold , whose typical trajectories have been called _ pulson _ states . early numerical work on the 2d quasi - collapse phenomena in isotropic lattices was reported in @xcite and @xcite . a two - year - old account of the `` state of knowledge '' on 2d schrdinger lattices can be found in section six of @xcite . in section [ secc : mobile ] we show results on a type of mobile breather , namely those moving along the direction of stronger lattice coupling constant . the structure of each of these mobile exact discrete breathers is that of a localized moving _ core _ superimpossed on a specific extended state of resonant small amplitude radiation , the _ background_. we present here the results of an extensive floquet stability analysis of this type of solutions in two sectors of the three - dimensional parameter space , which clearly show the existence of two different transitions . the tangent space eigenvectors associated to each of the transitions are presented , and the relation of the unstable manifold trajectories to pulson states is analyzed afterwards . we conclude with section [ secc : conclusions ] , where we briefly review the results obtained and illustrate their possible implications for mobility of 2d discrete breathers . the use of numerical tools for the continuation of discrete breather solutions has been widely employed since their existence proof was reported ( see _ e.g _ @xcite ) . in particular , the design of numerical techniques for finding exact mobile breathers based on those employed for the pinned ones has been explored in the recent years @xcite and paves the way to resolving the still open question about discrete breather mobility . here , after reviewing the most important features of 1d mobile breathers in nonlinear schrdinger lattices , we briefly explain how the continuation method is implemented in our system . as was introduced in section [ sec : introduction ] , exact mobility of dicrete breathers in 1d schrdinger nonlinear lattices were numerically studied by the authors in previous works @xcite . in particular , a numerical continuation from the integrable _ ablowitz - ladik lattice _ , a - l , ( where exact mobile breathers can be calculated analytically @xcite ) , @xmath1 to the standard _ discrete nonlinear schrdinger equation _ , dnls , @xmath2 was performed within the so - called _ salerno model _ @xcite , @xmath3 where @xmath4 , @xmath5 and @xmath6 are the parameters accounting for the strength of the nonlinear terms . the above equation includes the former two relevant equations ( [ eq : al ] ) and ( [ eq : dnls ] ) , for ( @xmath7 , @xmath8 ) and ( @xmath9 , @xmath10 ) respectively , providing the desired interpolation needed to develop the continuation scheme . the integrability of equation ( [ eq : al ] ) provides for @xmath11 a two - parametric family of discrete breathers @xmath12\;{\mbox{exp}}[{\mbox{i}}(\alpha(n - x(t))-\omega(t))]\;,\ ] ] where the two parameters @xmath13 $ ] and @xmath14 describe the velocity and internal frequency of the solution @xmath15 the salerno lattice ( [ eq : salerno ] ) , possess two dynamical invariants , namely the hamiltonian , @xmath16 where @xmath17 denotes the complex conjugate of @xmath18 , and the norm @xmath19 in order to find exact mobile discrete breathers in the salerno model we define a ( @xmath20)-resonant solution @xmath21 referred to some time scale @xmath22 such that @xmath23 within the above definition , a mobile breather that translates @xmath24 sites after @xmath25 periods of the internal oscillation will satisfy equation ( [ eq : p - q_resonant ] ) when @xmath26 . in this sense , the continuation focuses on the families of ( @xmath20)-resonant discrete breathers , that is breather solutions with the two characteristic time scales ( corresponding to the breather velocity , @xmath27 , and the internal frequency , @xmath28 ) being commensurate . in all the computations we have used finite lattices with periodic boundary conditions ( pbc ) so that @xmath29 and @xmath30 ( with @xmath31 being the lattice size ) . in the previous works @xcite the authors start from those a - l solutions which are ( @xmath20)-resonant , we discretize ( fine grid ) the path @xmath32 ( with @xmath5 and @xmath6 being positive ) along the salerno model , and go through it computing the corresponding ( @xmath20)-resonant solutions for the pairs @xmath33 . we can choose the path without loss of generality because of the scaling property of equation ( [ eq : salerno ] ) . then , each solution is numerically computed as a fixed point of the map @xmath34 where @xmath35 is the lattice translation operator @xmath36 , and @xmath37 is the @xmath38-evolution map ( @xmath39 ) following the dynamics dictated by equation ( [ eq : salerno ] ) for the corresponding value of @xmath6 ( @xmath40 ) ; _ i.e. _ , @xmath41=\{\phi_{n}(t_{0}+t_b)\}$ ] . the continuation was then performed for a fine grid of frequencies belonging to the family of ( @xmath42)-resonant discrete breathers . the most important conclusion about discrete breathers in these nonlinear schrdinger lattices is that mobility in the non - integrable regime ( @xmath43 ) demands the presence of an extended _ background _ to which the fixed point solution is spatially asymptotic ( @xmath44 ) , _ i.e. _ the solution is exactly written as @xmath45 this expression defines the purely localized component @xmath46 of the solution . the background is a finite linear combination of nonlinear plane waves , @xmath47 $ ] . these plane waves are exact solutions of the salerno model ( [ eq : salerno ] ) being the nonlinear dispersion relation @xmath48\cos k_{j } - 2\nu |a_{j}|^{2}$ ] . the results concerning the characterization of the background are discussed in detail in @xcite , here we briefly summarize the most important features : * the set of `` @xmath49 '' plane waves which take part in the background of a @xmath50resonant discrete breather with internal frequency @xmath51 is derived by the simple selection rule for the wave - numbers @xmath52 @xmath53 _ i.e. _ only the plane waves which are ( @xmath20)-resonant with the internal period of the breather can be components of @xmath54 . the number of solutions of ( [ resonant ] ) fixes `` @xmath49 '' . * the amplitudes @xmath55 of the nonlinear plane waves differ by orders of magnitude ." +"due to its high curie temperature and strong magnetic anisotropy , mnbi has attracted increasing attention in the pursuit of rare - earth - free permanent magnets ( see for example the review by poudyal and liu @xcite ) . advances in the understanding of the properties and processing of this material continue , despite its relatively simple , nias - type crystal structure , and the fact that ferromagnetism in mnbi was first reported over a century ago @xcite . key early studies were preformed by guillaud @xcite . in the 1950 s , this material was considered as a candidate to replace permanent magnets containing cobalt and nickel , and an energy product of 4.3 mgoe was achieved in the resulting `` bismanol '' magnets @xcite . subsequently , energy products as high as 7.7 mgoe have been reported @xcite . mnbi has several promising aspects as a candidate replacement for rare earth magnets . these include : ( 1 ) relatively inexpensive components @xcite , ( 2 ) high ordered moment and saturation magnetization of 0.58 ma m@xmath1 or about 3.5 @xmath2 per mn at room temperature @xcite , ( 3 ) ferromagnetism that persists to 630 k ( about 40 k higher than nd@xmath3fe@xmath4b ) @xcite , ( 4 ) large and uniaxial magnetocrystalline anisotropy energy near 1 mj m@xmath5 at room temperature ( moments along the c - axis ) , which increases upon heating above room temperature @xcite . the observed increase in magnetic anisotropy and coercivity with increasing temperature is perhaps the most interesting , unique , and potentially important property of mnbi . the ferromagnetism in mnbi vanishes abruptly upon heating above 630 k @xcite . importantly , the phase transition that occurs near 630 k is not a typical magnetic transition . this is not technically the curie temperature , and the transition is not directly driven by magnetism . this transitions has been identified as a peritectic decomposition of mnbi . heikes noted that the decomposition products contain a ferromagnetic phase with a curie temperature well below the decomposition temperature of mnbi @xcite . it has since been determined that near 630 k mnbi decomposes into mn@xmath6bi and bi @xcite , both of which are paramagnetic at this temperature . the mn rich phase is an orthorhombic variant of the nias - structure with the excess mn occupying trigonal prismatic interstices similar to those occupied by the bi atoms @xcite . since mnbi is ferromagnetic and the decomposition products are paramagnetic ( at the peritectic temperature ) , application of strong magnetic field has been shown to stabilize mnbi to higher temperatures , up to about 650 k in a 10 tesla magnetic field @xcite . synthesis of high quality single phase samples and in particular large single crystals of mnbi is complicated by the peritectic nature of this reaction , the relatively low temperature at which it occurs ( 630 k ) , and the nearness to the eutectic temperature ( 535 k ) . mnbi can be grown from a melt with excess bi , as first described by adams et al . @xcite by cooling the melt in a magnetic field , textured composites with coaligned mnbi crystallites embedded in a bi matrix have been obtained and studied @xcite . for permanent magnet applications , fine - grained , polycrystalline samples are usually desired . these have been produced from melt - spun and/or mechanically milled material @xcite , and by magnetic separation of mnbi from excess bi in samples produced by powder - metallurgical routes @xcite . magnetic measurements show that the magnetocrystalline anisotropy of mnbi passes through zero and the coercivity of mnbi powders vanishes near 90 k @xcite . these observations are associated with the reorientation of the mn magnetic moment from parallel to perpendicular to the crystallographic c - axis upon cooling . the spin reorientation temperature , @xmath0 , denotes the temperature at which magnetic moment develops a c - component upon heating and the coercivity begins to increase . the rotation of the moments has been oberved in neutron diffraction from mnbi powders @xcite and also nuclear magnetic resonance ( nmr ) experiments @xcite . the nmr results from powders @xcite and magnetization measurements on single crystals @xcite show the rotation away from the _ c_-axis upon cooling begins near 140 k , increases gradually upon further cooing to @xmath0 = 90 k , and then abruptly completes , with the moment flopping discontinuously into the _ ab_-plane . however , neutron diffraction from mnbi powder suggests the moments are not fully in - plane below 90 k @xcite . in the presence of significant magneto - elastic coupling , a response in the crystal lattice to the reorientation of the magnetic moments is expected . signatures of this coupling have been reported in the temperature dependence of the lattice constants of mnbi @xcite . while the hexagonal nias structure type describes the powder x - ray diffraction results at all temperatures , anomalies in both the a and c lattice parameters occur at temperatures near the spin reorientation . recent first - principles calculations have reproduced these magneto - elastic effects , and linked the spin - reorientation to anisotropic thermal expansion @xcite , and in particular to resulting changes in the anisotropic pairwise exchange interactions between bi p - states @xcite . most of the experimental studies performed on mnbi to date have used polycrystalline material . single crystals are better suited for the detailed study of intrinsic and anisotropic properties . here we report the results of our detailed investigation of the structural and physical properties of single crystal mnbi , including x - ray and neutron diffraction , magnetization , heat capacity , and electrical resistivity measurements . in addition to elucidating the intrinsic properties of mnbi , we find significant differences between the behavior of the single crystals and the reported behavior of polycrystalline mnbi in the literature , in particular regarding the spin reorientation . our x - ray diffraction results reveal a symmetry - lowering structural distortion occurs at @xmath0 , and suggest that mnbi adopts an orthorhombic structure at low temperature , similar to mn@xmath6bi but without the excess interstitial mn . this transition is extremely sensitive to strain , and is not observed in powders gently ground from the crystals . the structure change is accompanied by a thermal anomaly which responds strongly to applied magnetic field , and a sharp decrease in electrical resistivity . examination of the anisotropic atomic displacement parameters determined from neutron diffraction analysis shows that the bi vibrations along the @xmath7-axis are enhanced with increasing temperature above the spin reorientation , suggesting a relationship with the well - documented increase in magnetocrystalline anisotropy energy with temperature . x - ray diffraction patterns from mnbi single crystal faces at room temperature . ( a ) diffraction from a face perpendicular to the _ c_-axis . ( b ) diffraction from a face perpendicular to the _ a_-axis . the inset in ( a ) shows a photograph of typical mnbi crystals . the inset in ( b ) shows the room temperature hexagonal crystal structure of mnbi . the lattice constants determined from the reflections shown in the figure are listed in ( b ) . , width=288 ] starting materials for the crystal growths were bi shot ( cominco american , 99.9999% ) and mn pieces ( alfa aesar , 99.95% ) , and the crystal were grown from a flux with excess bi based on the published binary phase diagram @xcite . the mn pieces were lightly ground into a powder and 0.65 g of this material was then immediately combined with 35 g of bi and loaded into an alumina crucible . the 10 ml crucible , covered with an inverted 10 ml `` catch '' crucible half - filled with quartz wool was sealed under vacuum inside a silica ampoule . the ampoule was heated to 1000 @xmath8c at 1 @xmath8c / min , held for 24 h , cooled to 440 @xmath8c at 1 @xmath8c / min , held at 440 @xmath8c for 1 h , and then cooled to 275 @xmath8c at 0.4 @xmath8c / h . at 275 @xmath8c , the excess bi flux was centrifuged into the catch crucible . several mm - cm sized mnbi single crystals were produced via this method , some of which are shown in fig . [ fig : crystals]a . the largest crystal obtained weighed close to 2 g. when exposed to air for hours , crystals developed a visible patina . x - ray diffraction from crystals which had been powdered and then exposed to air for more than 12 hours indicated slow decomposition into mnbi , mno@xmath9 , and bi . x - ray diffraction measurements were conducted with a panalytical xpert pro mpd diffractometer , equipped with an incident beam monochromator ( cu k@xmath10 radiation ) and an oxford phenix closed - cycle helium cryostat . single crystal neutron diffraction was performed at the hb-3a four - circle diffractometer at the high flux isotope reactor at oak ridge national laboratory . a neutron wavelength of 1.003 was used from a bent perfect si-331 monochromator @xcite . the data were collected at the selected temperatures of 5 k , 50 k , 70 k , 90 k , 110 k , 130 k , 150 k , 200 k , 300 k , 350 k , 400 k , and 450 k. at each temperature , more than 330 reflections were collected and used for the refinements . refinements of the x - ray and neutron diffraction data were performed using fullprof @xcite . dc magnetization measurements were performed using a quantum design magnetic properties measurement system and ac measurements were made using a quantum design physical properties measurement system , which was also used for the resistivity and heat capacity measurements . spot - welded pt leads were used for electrical contacts . results of temperature dependent x - ray diffraction measurements from indexed faces of mnbi single crystals . ( a , b ) contour plots of intensity vs diffraction angle and temperature for the 300 and 004 reflections ( h denotes the hexagonal unit cell ) . ( c ) in - plane lattice constants vs temperature for the high temperature hexagonal and low temperature orthorhombic ( denoted by subscript o ) structures . ( d ) the relationship between the high temperature hexagonal and low temperature orthorhombic unit cells . ( e ) c - axis length and primitive unit cell volume vs temperature ( the volume of the c - centered orthorhombic cell is twice the value plotted ) . , width=288 ] a photograph of typical crystals used in this study is shown in fig . [ fig : crystals]a . diffraction from powdered crystals at room temperature confirmed them to be nias - type mnbi ( space group @xmath116@xmath12 ) . the crystal structure is shown in fig . [ fig : crystals]b , along with the lattice constants determined from this room temperature data . diffraction patterns , like those shown in fig . [ fig : crystals ] , from crystal facets were used to identify the hexagonal c - axis ( typically a hexagonal face ) and the a - axis ( typically a rectangular face ) . to examine the lattice response to the spin reorientation , diffraction patterns from crystal faces were collected at temperatures between 300 and 20 k. at 90 k , the sixfold symmetry in the _ ab_-plane is broken , as demonstrated by the splitting of the hexagonal 300 reflection in fig . [ fig : xray]a . such a distortion lowers the unit cell symmetry from primitive hexagonal to _ c_-centered orthorhombic . the temperature dependence of the lattice parameters determined from these measurements" +"existence of a mass gap for a yang - mills theories received a confirmation from recent lattice studies . strong evidence has been obtained both in the spectrum @xcite and for the gluon propagator @xcite . on the other side , theoretical analysis have confirmed this finding @xcite but none of them reached the status of a rigorous proof . anyhow , this fundamental result can be used to perform computations in quantum chromodynamics ( qcd ) at low energies . the reason is that a very good approximation for the gluon propagator in the landau gauge in the deep infrared is a free massive propagator as shown in the aforementioned references . in order to get the gluon propagator in a closed form we need to know what the ground state of a yang - mills theory is . we select a ground state using known exact solutions of the classical equations of motion of the theory @xcite . these solutions have the property to recover an instanton liquid for the ground state @xcite in agreement with the results given in @xcite . we will support our choice by comparing the gluon propagator we obtain with the lattice data at large volume presented in @xcite . having the gluon propagator in closed form for a given gauge opens up the possibility to perform computations at low energies in qcd both at zero and finite temperature . indeed , we have shown in this way that a nonlocal nambu - jona - lasinio ( nnjl ) model describes the low energy phenomenology of hadron physics @xcite . in ref.@xcite , we obtained the critical temperature at zero chemical potential for the chiral transition . this turns out in close agreement with lattice data @xcite and with preceding theoretical computations @xcite . for our aims in this paper we always reduce the nnjl model to a local one . improvements are left for future works but are not needed here . the question of how to correct the njl model is not new @xcite . these authors do an extensive study of the njl model with both an eight quark interaction term and a t hooft correction and for zero and non - zero temperature as well . the effect of a magnetic field is also accounted for . these corrections are not generally motivated in a situation where the role of the njl model is just in the framework of a postulated phenomenological model , even if with great success . the aim of this paper is to provide a sound motivation to the existence of such higher order terms in the njl model deriving them directly from qcd . this is made possible by the gluon propagator yielded in a closed analytical form and by the existence of a mass gap as said above . this means that the njl model has a role as a low energy limit of qcd and obtaining higher order corrections is needed due exactly to this role . as a first application we prove that the eight quark interaction term does not change the critical temperature for the chiral transition . we will assume the chiral approximation from the start with the u and d quarks having zero mass . the analysis will be limited to a two - quark model . in this way , this will appear as a leading order approximation to more realistic computations . it is essential to point out that because we start from qcd , all the parameters of the njl model and its higher order corrections are properly fixed . the paper has the following structure . in sec . [ sec2 ] we introduce a yukawa model with self - interaction and prove how the infrared limit reduces to a njl model with an eight quark correction term . in sec . [ sec2a ] we show that the classical solutions we consider are indeed a minimum for the action . in sec . [ sec3 ] we do the same starting from a two - quark qcd theory in the chiral limit . in sec . [ sec4 ] we discuss the gap equation once all the parameters of the model are properly fixed . in sec . [ sec5 ] we prove that , for this model , the eight quark interaction term does not change the critical temperature of the chiral transition . finally , in sec . [ sec6 ] conclusions are given . let us consider the generating function of the scalar field @xmath0=\int[d\phi]\exp\left[-i\int d^4x\left(\frac{1}{2}(\partial\phi)^2-\frac{\lambda}{4}\phi^4+j\phi\right)\right].\ ] ] one has @xmath1 = -i\int d^4x\left(\frac{1}{2}(\partial\phi)^2-\frac{\lambda}{4}\phi^4+j\phi\right)\ ] ] and we can think to perform a functional taylor series on @xmath2 $ ] @xcite . we have @xmath3 & = & -i\int d^4x\left(\frac{1}{2}(\partial\phi_0)^2-\frac{\lambda}{4}\phi_0 ^ 4\right ) \nonumber \\ w_1[0 ] & = & \left.\frac{\delta w[j]}{\delta j(x_1)}\right|_{j=0 } = -i\int d^4x\left(\partial\phi_0(x)\cdot\partial\left.\frac{\delta\phi(x)}{\delta j(x_1)}\right|_{j=0}\right . \nonumber \\ & & \left.-\lambda\phi_0 ^ 3(x)\left.\frac{\delta\phi(x)}{\delta j(x_1)}\right|_{j=0}+\delta^4(x - x_1)\phi_0(x)\right ) = -i\phi_0(x_1 ) \nonumber \\ w_2[0 ] & = & \left.\frac{\delta^2 w[j]}{\delta j(x_1)\delta j(x_2)}\right|_{j=0 } = -i\int d^4x\left ( \partial\left.\frac{\delta\phi(x)}{\delta j(x_1)}\right|_{j=0 } \cdot\partial\left.\frac{\delta\phi(x)}{\delta j(x_2)}\right|_{j=0}+\partial\phi_0\cdot\partial\left.\frac{\delta^2\phi(x)}{\delta j(x_1)\delta j(x_2)}\right|_{j=0}\right . \nonumber \\ & & -3\lambda\phi^2_0(x)\left.\frac{\delta\phi(x)}{\delta j(x_1)}\right|_{j=0}\left.\frac{\delta\phi(x)}{\delta j(x_2)}\right|_{j=0 } -\lambda\phi_0 ^ 3(x)\left.\frac{\delta^2\phi(x)}{\delta j(x_1)\delta j(x_2)}\right|_{j=0 } \nonumber \\ & & \left.+\delta^4(x - x_1)\left.\frac{\delta\phi(x)}{\delta j(x_2)}\right|_{j=0 } \right ) = -2i\left.\frac{\delta\phi(x_2)}{\delta j(x_1)}\right|_{j=0}=-2i\delta(x_2-x_1 ) % \nonumber \\ % w_3[0 ] & = & \left.\frac{\delta^3 w[j]}{\delta j(x_1)\delta j(x_2)\delta j(x_3)}\right|_{j=0 } = \end{aligned}\ ] ] where use has been made of the equations @xmath4 and integration by parts . then , one has finally @xmath5 = w[0]-i\int d^4xj(x)\phi_0(x)-i\int d^4xd^4x_1j(x)\delta(x - x_1)j(x_1)+o(j^3).\ ] ] now , let us consider the following yukawa model @xmath6 one has @xmath7=\int [ d\bar\psi][d\psi]\left.\exp\left[-i\int d^4x\bar\psi\left(i\slashed\partial - g\frac{\delta}{\delta j}\right)\psi\right]\exp(w[j])\right|_{j=0 } \exp\left[i\int d^4x\left(\bar\eta\psi+\bar\psi\eta\right)\right]\ ] ] and using eq.([eq : w1 ] ) yields @xmath8&=&\int [ d\bar\psi][d\psi]\exp\left[-i\int d^4x\bar\psi\left(i\slashed\partial - g\phi_0\right)\psi - g^2\int d^4y\delta(x - y)\bar\psi(x)\psi(x)\bar\psi(y)\psi(y)\right]\times \nonumber \\ & & \exp\left[i\int d^4x\left(\bar\eta\psi+\bar\psi\eta\right)\right]\end{aligned}\ ] ] that is a non - local nambu - jona - lasinio(njl)-like model in close agreement to @xcite . in order to correct this approximation , we consider the next - to - leading order correction that is @xmath9 & = & \left.\frac{\delta^3 w[j]}{\delta j(x_1)\delta j(x_2)\delta j(x_3)}\right|_{j=0 } = \nonumber \\ & & -i\int d^4x\left[\partial\left.\frac{\delta^2\phi}{\delta j(x_2)\delta j(x_3)}\right|_{j=0}\partial\left.\frac{\delta\phi}{\delta j(x_1)}\right|_{j=0 } + \partial\left.\frac{\delta^2\phi}{\delta j(x_1)\delta j(x_3)}\right|_{j=0}\partial\left.\frac{\delta\phi}{\delta j(x_2)}\right|_{j=0}\right . \nonumber \\ & & + \partial\left.\frac{\delta^2\phi}{\delta j(x_1)\delta j(x_2)}\right|_{j=0}\partial\left.\frac{\delta\phi}{\delta j(x_3)}\right|_{j=0 } + \partial\phi_0\partial\left.\frac{\delta^3\phi}{\delta j(x_1)\delta j(x_2)\delta j(x_3)}\right|_{j=0}\nonumber \\ & & -3\lambda\phi_0 ^ 2\left.\frac{\delta^2\phi}{\delta j(x_2)\delta j(x_3)}\right|_{j=0}\left.\frac{\delta\phi}{\delta j(x_1)}\right|_{j=0 } -3\lambda\phi_0 ^ 2\left.\frac{\delta^2\phi}{\delta j(x_1)\delta j(x_3)}\right|_{j=0}\left.\frac{\delta\phi}{\delta j(x_2)}\right|_{j=0 } \nonumber \\ & & -3\lambda\phi_0 ^ 2\left.\frac{\delta^2\phi}{\delta j(x_1)\delta j(x_2)}\right|_{j=0}\left.\frac{\delta\phi}{\delta j(x_3)}\right|_{j=0 } -6\lambda\phi_0\left.\frac{\delta\phi}{\delta j(x_1)}\right|_{j=0}\left.\frac{\delta\phi}{\delta j(x_2)}\right|_{j=0}\left.\frac{\delta\phi}{\delta j(x_3)}\right|_{j=0 } \nonumber \\ & & -\lambda\phi_0 ^ 3\left.\frac{\delta^3\phi}{\delta j(x_1)\delta j(x_2)\delta j(x_3)}\right|_{j=0 } \nonumber \\ & & \left.+\delta^4(x - x_1)\left.\frac{\delta^2\phi}{\delta j(x_2)\delta j(x_3)}\right|_{j=0 } + \delta^4(x - x_2)\left.\frac{\delta^2\phi}{\delta j(x_1)\delta j(x_3)}\right|_{j=0 } + \delta^4(x - x_3)\left.\frac{\delta^2\phi}{\delta j(x_1)\delta j(x_2)}\right|_{j=0 } \right ] \nonumber \\ & & = 6i\lambda\int d^4x\phi_0(x)\delta(x - x_1)\delta(x - x_2)\delta(x - x_3)\end{aligned}\ ] ] where use has been mad of eq.([eq : conds ] ) and integration by parts . a similar computation yields @xmath10 = \left.\frac{\delta^4 w[j]}{\delta j(x_1)\delta j(x_2)\delta j(x_3)\delta j(x_4)}\right|_{j=0 } = 6i\lambda\int d^4x\delta(x - x_1)\delta(x - x_2)\delta(x - x_3)\delta(x - x_4)\ ] ] where use has been made of the equation @xmath11=0.\ ] ] the functional becomes @xmath12 & = & w[0]-i\int d^4xj(x)\phi_0(x)-i\int d^4xd^4x_1j(x)\delta(x - x_1)j(x_1 ) \nonumber \\ & & + i\lambda\int d^4xd^4x_1d^4x_2d^4x_3\phi_0(x)\delta(x - x_1)j(x_1)\delta(x - x_2)j(x_2)\delta(x - x_3)j(x_3 ) \nonumber \\ & & + \frac{i}{4}\lambda\int d^4xd^4x_1d^4x_2d^4x_3d^4x_4\delta(x - x_1)j(x_1)\delta(x - x_2)j(x_2)\delta(x - x_3)j(x_3)\delta(x - x_4)j(x_4 ) \nonumber \\ & & + o(j^5).\end{aligned}\ ] ] this permits to compute the next - to - leading order correction to the non - local njl - like model we obtained above . the model has now the structure @xmath13 \nonumber\end{aligned}\ ] ] and we observe that odd powers of the current take a @xmath14 contribution . the important conclusion to be drawn is that _ if one knows an exact solution to the equation of motion and the corresponding propagator ( see eq.([eq : conds ] ) ) , the scalar theory is completely solved and the yukawa model reduces to a non - local njl model and its higher order corrections . _ the latter are easy to compute due to the triviality of the scalar theory . to fix the parameters of the theory , we now consider an exact solution @xcite @xmath15 being sn an elliptic jacobi function and @xmath16 and @xmath17 two integration constants . in order for this solutions to hold , the following dispersion relation applies @xmath18 . we recognize here a free massive solution notwithstanding we started from a massless theory . the corresponding 2-point function can be computed immediately yielding @xcite @xmath19 being @xmath20 the mass spectrum is @xmath21 and @xmath22 an elliptic integral , consistently with the idea of a strong coupling expansion . this holds provided one fixes the phase @xmath17 in the exact solution to @xmath23 . this identifies an infinite set of scalar field theories with a trivial infrared fixed point in quantum field theory . these solutions appear really interesting as they provide a strong coupling expansion for eq.([eq : w2 ] ) in inverse powers of @xmath24 . it is very easy to see that the contact limit is obtained by taking @xmath25 in the propagator that provides @xmath26 being @xmath27 a constant having the dimensions of inverse mass squared , taking us to the well - known contact interaction of a njl model . similarly , we note that @xmath28 . our action has now the form @xmath29 . \nonumber\end{aligned}\ ] ] now , by assuming the average of the field @xmath30 to be zero , we recover a standard mean field njl model with a higher order correction @xmath31 . \nonumber\end{aligned}\ ] ] one could ask if the exact solutions we started from to build the expansion for the scalar field are a real minimum for the functional of the field . this , in view of the mapping theorem proven in @xcite , this will immediately apply to the yang - mills equations we exploit in the following sections . that this is so can be seen in the following way . firstly , let us see how the idea works for the free field . one has @xmath32 = \int d^4x\left[\frac{1}{2}(\partial\phi)^2-\frac{1}{2}m^2\phi^2\right].\ ] ] for a given classical solution @xmath14 , we can take a functional taylor series of this as @xmath33+\int d^4x'\left.\frac{\delta{\cal l}}{\delta\phi(x')}\right|_{\phi=\phi_0}\phi(x ' ) + \frac{1}{2}\int d^4x'd^4x''\left.\frac{\delta^2{\cal l}}{\delta\phi(x')\delta\phi(x'')}\right|_{\phi=\phi_0}\phi(x')\phi(x'')+\ldots\ ] ] that becomes @xmath33 -\frac{1}{2}\int d^4x'd^4x\left[\partial^2\delta^4(x - x')+m^2\delta^4(x - x')\right]\phi(x')\phi(x)+\ldots,\ ] ] where use has been made of the condition @xmath34 , due to motion equation . we can now prove that the term originating from the second functional derivative is indeed strictly positive off - shell . let us consider the eigenvalue problem @xmath35 then , one has @xmath36 . it is not difficult to see that @xmath37 as the theory has a lower bound to energy . this means that @xmath33+\frac{1}{2}\int d^4x'd^4x\sum_p(p^2-m^2)\chi_p(x)\chi_p(x')\phi(x')\phi(x)+\ldots.\ ] ] but , @xmath38 are the coefficients of the fourier series for the field in terms of the eigenfunctions @xmath39 and then @xmath33+\frac{1}{2}\sum_p(p^2-m^2)c^2(p)+\ldots={\cal l}[\phi_0]+\frac{1}{2}\sum_p(p^2-m^2)c^2(p)+\ldots.\ ] ] the second term on the lhs must be positive definite for physical reasons and the classical solution is a minimum of the functional . for this it is enough to assume a lower bound on the spectrum for @xmath40 that grants the positivity of the energy . the zero mode is expected due to the translational invariance of the theory . we can use this strategy to show that the classical solutions we use in our analysis are indeed stable solutions . now it is @xmath32 = \int d^4x\left[\frac{1}{2}(\partial\phi)^2-\frac{\lambda}{4}\phi^4\right].\ ] ] then , @xmath33 -\frac{1}{2}\int d^4x'd^4x\left[\partial^2\delta^4(x - x')+3\lambda\phi_0 ^ 2(x)\delta^4(x - x')\right]\phi(x')\phi(x)+\ldots\ ] ] being now @xmath14 given by a solution to @xmath41 ( see @xcite ) . we introduce the set of eigenfunctions @xmath42 so , let us consider @xmath43 being sn a jacobi elliptical function , then the eigenfunctions take the form @xmath44 with" +"this research was supported by basic science research program through the national research foundation of korea(nrf ) funded by the ministry of education(nrf-2011 - 0012073 ) . we define the third and fourth moment variations of financial asset return process and examine the properties of the variations . the third moment variation is defined to be a quadratic covariation between squared return and return process and the fourth moment variation is defined to be a quadratic variation of squared return process . it is demonstrated that the variations can be used as approximations for the third and fourth moments of the return distribution , which are generally hard to measure , under certain conditions . skewness , the third standardized moment , has long been an important topic in financial study and there are numerous evidences that stock return distributions are left skewed under both physical and risk - neutral probability . @xcite extended the capital asset pricing model to incorporate skewness preference . @xcite developed a new methodology for estimating time - varying conditional skewness . @xcite showed that conditional skewness explain the cross - sectional variation of expected returns across assets . in @xcite , cubic and quartic contracts are defined to measure risk - neutral skewness and kurtosis . @xcite developed a garch type option pricing model with inverse gaussian innovations to incorporate conditional skewness . @xcite and @xcite proposes a new definition of realized third moment which satisfies the aggregate property to estimate of the true third moment of long - horizon returns . in addition , kurtosis , the fourth standardized moment , also plays an crucial role in financial studies and it is well known that a financial asset return distribution has larger kurtosis than the gaussian distribution . @xcite proposed a new model for autoregressive kurtosis and showed the evidence of the presence of autoregressive conditional kurtosis . @xcite also indicated a significant presence of conditional skewness and kurtosis . our approaches to examining the high moments of return distribution are based on quadratic variation methods and the motivation stems from the previous researches on the quadratic variation of asset return process . the quadratic variation of an asset return ( or price ) process , the limit of the sum of squared returns , plays a central role in measuring the variance of return , since the expectation of the quadratic variation of return is considered as an estimator of the variance of the return distribution . the realized ( quadratic ) variation , which refers to the finite sum of squared return computed from high - frequency return time series , is an approximation to the quadratic variation . thus , the realized variation of return is an efficient estimator of the variance of return distribution under physical probability . we extend this idea to link newly defined high moment variations and the corresponding quantities of the return distribution . in the previous studies about theory and empirical analysis on high - frequency data , @xcite showed that when underlying process is a semimartingale , the realized variance is a consistent estimator of quadratic variation . @xcite derived the asymptotic distribution of the realized volatility error under stochastic volatility models . @xcite and @xcite introduced realized bipower variation which is robust to rare jumps in estimating integrated variance and tested jump in asset price process . @xcite examined the errors of the realized variance under the presence of market microstructure noise . @xcite studied local - constancy approximation of variance on which econometric literatures of high frequency data often rely . one of the interesting properties of the quadratic variation of the return is that the risk - neutral expectation of the quadratic variation is synthesized by a continuum of european option prices . more precisely , the expectation is represented by an integration formula whose integrand is composed of weighted option prices . for detailed information about such replication techniques , see @xcite and @xcite . thus , one can compare the difference between the variance of return under the physical probability and the risk - neutral probability by computing the realized variance and the synthesized option value . using this method , @xcite show that there exists a variance risk premium which implies that the risk - neutral variance is generally larger than realized variance . the reader may refer to @xcite where the relationship between the variance risk - premium and the higher degree quantities of the return distribution is explained . @xcite investigate the role of jump in explaining the variance risk - premium . see @xcite for the relationship between the realized and risk - neutral volatilities . the synthesized option value is often referred to as a fixed variance swap rate . the fixed variance swap rate is the value in which investors are willing to pay to protect their wealth from variance risk . for more information about variance swap , see @xcite . we show that the risk - neutral expectations of the third and fourth moment variations are composed of synthesized option part of out - of - the - money ( otm ) european options and jump correction parts . our empirical study shows that the option parts of expected third and fourth moment variation are good approximations to expected third and fourth moments of the return distribution , respectively . the fact that the realized high moments variations , computable from high - frequency data , are mimicking the moments of return distribution , ones hard to compute from data , is important to hedge fat - tail risk . to hedge the risk , we propose a new kind of variation swap . the swap is similar with the skew swap introduced in @xcite and @xcite , but the floating leg is defined to be the realized third moment variation of the asset return over a fixed time period . the third moment variation swap can be used to hedge shortfall risk of a financial asset with heavy left tail return distribution . under the third moment variation swap , counterparties exchange the realized third moment variation for a predetermined strike price . the portfolio consisting of the skewed underlying asset and the third moment swap has more gaussian - like symmetric return distribution than the original asset so that one can hedge extreme shortfall risk . the fourth moment variation swap can be applied to an asset with leptokurtic return distribution to hedge fat - tail risk . similarly , the portfolio consisting of the fat - tailed underlying asset and the fourth moment variation swap has more gaussian - like thinner tail return distribution . we employ simulations and empirical studies to examine the performance of the variation swap . the remainder of the paper is organized as follows . section [ sect : moment ] introduce the third and fourth moment variations . in section [ sect : synthesizing ] , we construct a mathematical framework to show that the risk - neutral expectations of third and fourth moment variations are represented by european option prices . in section [ sect : empirical ] , we present empirical studies on s&p 500 index returns and options data . five - minute high frequency data of s&p 500 index series is used to compute realized quadratic variation and covariation . employing some filtering methods on the index option data , we also calculate the risk - neutral expectations of quadratic variations . in section [ sect : swap ] , we explain the variation swaps to deal with tail risk and show interesting examples and empirical studies . section [ sect : concl ] concludes the paper . throughout this paper , we introduce a probability space with a time index set @xmath0 $ ] for some fixed @xmath1 . let @xmath2 be a complete probability space with a filtration @xmath3}$ ] where @xmath4 . the measure @xmath5 is the physical probability measure . all processes introduced in this paper are defined on the probability space and those processes are adapted to the filtration . let @xmath6 denote a semimartingale asset price process and @xmath7 be a corresponding futures price process with maturity @xmath8 . assume that there exists a risk - neutral measure @xmath9 under which every discounted asset price process is a martingale . also we assume @xmath10 $ ] . define the log - return process @xmath11 we are interested in the high order moment properties of return @xmath12 over a fixed time period @xmath13 $ ] , for example , @xmath14 or @xmath15 days , and the analysis are based on quadratic variation methods . the quadratic variation process of a semimartingale @xmath16 is defined by @xmath17_t = x_t^2 - 2 \int_0^t x_u { \mathrm{d}}x_u.\ ] ] the quadratic covariation process of @xmath16 and @xmath18 is defined by @xmath19_t = x_t y_t - \int_0^t x_u { \mathrm{d}}y_u - \int_0^t y_u { \mathrm{d}}x_u.\ ] ] note that for a sequence of partition @xmath20 ranged over @xmath21 $ ] , we have @xmath19_t = \lim_{||\pi|| \rightarrow 0 } \sum_{i } ( x_{t_i } - x_{t_{i-1 } } ) ( y_{t_i } - y_{t_{i-1 } } ) \quad \textrm{in probablity.}\ ] ] for the details , see @xcite . the realized quadratic variation of return , @xmath22_t$ ] , is an unbiased estimator of the variance of the log return @xmath23 under certain conditions @xcite . thus , the realized variation become a conventional measure of the actual variance or the return . we now define the analogous third moment covariation and fourth moment variation by @xmath24 \quad & \textrm { the third moment covariation } \\ [ r^2 ] \quad & \textrm { the fourth moment variation}.\end{aligned}\ ] ] the third moment covariation is the quadratic covariation between return and squared return processes . the fourth moment covariation is the quadratic variation of squared return process . it will be shown that the newly defined variations are closely related to the actual moments . in the later , we will demonstrate that the linear transform of the expectations of the third moment covariation @xmath25_t$ ] and fourth moment variation @xmath26_t$ ] approximate the third and fourth moments of the return distribution over @xmath27 $ ] , respectively . especially , such as in continuous - time stochastic volatility models , by assuming the drift term of return process is zero , the expected moment variations and actual moments are in exact linear relationship . this is the reason that @xmath25 $ ] is called the third moment covariation and @xmath26 $ ] is called the fourth moment variation . consider a partition that @xmath28 . for the notational simplicity , let @xmath29 . then we approximate the following quadratic variations and covariations by @xmath30_t & \approx \sum_{i=1}^{n } ( r_{i } - r_{i-1})^2 \\ [ r , r^2]_t & \approx \sum_{i=1}^{n } ( r_{i } - r_{i-1})(r^2_{i } - r^2_{i-1 } ) \\ [ r^2]_t & \approx \sum_{i=1}^{n } ( r^2_{i } - r^2_{i-1})^2.\end{aligned}\ ] ] since @xmath31 and @xmath32 are semimartingales , the right hand sides of the above equations converge to the corresponding quadratic variations and covariation in probability as the mesh size of partition goes to zero . the finite sums are called the realized ( co)variations and the realized variations are consistent estimators of the corresponding quadratic variations . we will use the realized ( co)variations as proxies for the third and fourth moment of physical distribution of @xmath12 . the each term in the finite summation of the realized variations consists of the powers of log contract . we can rewrite @xmath33 and @xmath34 where @xmath35 . the term in the third moment covariation is replicated by holding one cubic log contract and @xmath36 square log contracts over the period @xmath37 $ ] . similarly , the term in the fourth moment variation is replicated by holding one quartic log" +"recently , localization systems have found widespread application , since they allow to develop a number of new services in both outdoor and indoor environments @xcite . conventional localization systems acquire positional information from a set of observations ; these are usually extracted from noisy wireless signals propagating in harsh environments . unavoidably , this limits the accuracy that can be achieved by such systems . localization accuracy can certainly benefit from the availability of any form of _ a priori _ knowledge . in the technical literature , the sources of prior knowledge commonly exploited are represented by the positions of some specific nodes ( called _ anchors _ ) or by some characteristic of the communication channel ; for instance in @xcite the impact of different factors ( like non - line - of - sight , nlos , propagation and network synchronization ) on localization accuracy have been thoroughly analysed employing cramer - rao bounds ( crbs ) and , when a priori knowledge is available , bayesian cramer - rao bounds ( bcrbs ) . in @xcite multipath propagation in ultra wide band ( uwb ) systems and its effects on time - of - arrival ( toa ) estimation have been investigated by means of crbs or bcrbs . in @xcite crbs and bcrbs for the analysis of cooperative localization techniques have been derived . in recent times , however , some attention has been paid to the possibility of improving accuracy by endowing localization systems with _ map - awareness _ , i.e. , with the knowledge of the _ map _ of the environment in which they operate . specific examples of map - aware algorithms have been developed in @xcite , which propose the adoption of non - linear filtering techniques ( namely , particle filtering and extended kalman filtering ) to embed map - based a priori information in navigation systems . this work evidences that this kind of information plays an important role in improving localization and navigation accuracy ; however , the impact of map - awareness on the performance limits of localization systems is still an open problem . in fact , as far as we know , the technical literature dealing with the fundamental limits of localization accuracy @xcite has not considered this issue yet . in this paper , novel accuracy bounds for map - aware localization systems are developed and their applications to specific environments are analysed . specifically , the bcrb , the extended zik - zakai bound ( ezzb ) and the weiss - weinstein bound ( wwb ) for the above mentioned systems are derived . these bounds , which provide several novel insights into map - aware localization , have the following features : 1 . they are characterized by different tightness / analytical complexity ; 2 . they can be evaluated for any map geometry and , in the cases of the bcrb and the ezzb , admit a closed form for rectangular maps ; 3 . they allow to a ) identify map features ( e.g. , shape , area , etc . ) influencing localization accuracy and b ) quantify such an influence . then , such bounds are evaluated and compared for simple representative environments . our results allow to assess the importance of map - awareness in localization systems in the presence of noisy observations . in particular , they evidence that : 1 . maps should be expected to play a significant role at low signal - to - noise ratios ( snrs ) and in the presence of obstructions ; 2 . in some cases simplified map models can be adopted for localization purposes , since map details have a negligible impact on estimation accuracy . the manuscript is organized as follows . in section [ sec : scenario ] our reference scenario is illustrated and the map model is defined . performance bounds for map - aware localization are derived and evaluated in specific scenarios in sections [ sec : perf_bounds ] and [ sec : num_res ] , respectively . finally , some conclusions are offered in section [ sec : conc ] . _ notations _ : matrices are denoted by upper - case bold letters , vectors by lower - case bold letters and scalar quantities by italic letters . the notation @xmath0 denotes expectation with respect to the random vector @xmath1 ; @xmath2 denotes the trace of a square matrix ; @xmath3 denotes a square matrix with the arguments on its main diagonal and zeros elsewhere ; @xmath4_{i , l}$ ] is the element on the @xmath5-th row and @xmath6-th column of its argument . @xmath7 denotes the @xmath8 identity matrix ; @xmath9 means that the matrix @xmath10 is positive semi - definite . the probability density function ( pdf ) of the random vector @xmath11 evaluated at the point @xmath1 is denoted as @xmath12 , whereas @xmath13 denotes the pdf of a gaussian random vector having mean @xmath14 and covariance matrix @xmath15 , evaluated at the point @xmath1 . @xmath16 denotes the so called indicator function for the set @xmath17 ( it is equal to 1 when @xmath18 and zero otherwise ) . in the following we focus on the problem of localizing a single device , called _ agent _ , in a 2-d environment , i.e. , of estimating its position @xmath19^{t}$ ] , in the presence of the following information : a ) a map representing the a priori knowledge about the environment in which the localization system operates ; b ) an observation vector @xmath20 related to the true position @xmath21 of the agent . in a bayesian framework the map of a given environment can be modelled for localization purposes as a pdf @xmath22 of the random variable @xmath21 , representing the agent position . such a pdf is characterized by a 2-d support @xmath23 having a finite size and consisting of the set of points in the environment not occupied by obstructions ( e.g. , walls , buildings , etc ) . in the absence of other prior knowledge , a natural choice for @xmath22 is a simple uniform model , i.e. , @xmath24 where @xmath25 denotes the area of @xmath23 . this model is referred to as _ uniform map _ in the following and is preferable to other , more detailed , prior models since it can be adopted when only basic knowledge of the environment is available ( e.g. , the floor plan of a building in indoor environments or satellite photos in outdoor environments ) . an alternative statistical model for maps , better suited to mathematical analysis in the bcrb case , is a `` smoothed '' version of ( [ eq : uniform_map ] ) ; this is obtained modifying the uniform pdf in a narrow area around the edges of @xmath23 in order to introduce a smooth transition to zero along the boundaries of its support . note that the adoption of a smoothed uniform model leads to analytical results similar to those found with the uniform model if the transition region is small with respect to the size of @xmath23 . as it will become clearer in the following , for a generic map , a detailed description of the structure of its support @xmath23 should be provided to ease the formulation of the accuracy bounds referring to the map itself . to begin , let us define , for each @xmath26 , the sets @xmath27 and @xmath28 representing the intersection between @xmath23 and an horizontal ( _ h _ ) and vertical ( _ v _ ) line identified by the abscissa @xmath29 and ordinate @xmath30 , respectively . then , let : * @xmath31 and @xmath32 denote the number of connected components of @xmath33 and @xmath34 , respectively ; * @xmath35 and @xmath36 denote the set of the _ odd _ values @xmath37 and @xmath38 @xmath39 , respectively ; * @xmath40 and @xmath41 , with @xmath42 and @xmath43 , denote the length of the connected components of @xmath33 and @xmath34 respectively ; * @xmath44 and @xmath45 denote the set of the _ even _ values @xmath46 and @xmath47 @xmath48 , respectively . * @xmath49 and @xmath50 , with @xmath51 and @xmath52 , denote the length of the connected components of @xmath53 and @xmath54 respectively ( note that @xmath53 and @xmath54 represent the complementary sets of @xmath33 and @xmath34 with respect to @xmath55 ) ; in other words , they denote the horizontal and vertical size of map obstructions , respectively ; * @xmath56 and @xmath57 denote the projection of @xmath23 on the @xmath29 and @xmath30 axis , respectively ; the graphical meaning of these parameters for a specific uniform map is exemplified by fig . [ fig : non_convex_generic_shape ] . in the following , we assume that the localization system is able to acquire a set of noisy observations , collected in a vector @xmath20 and related to the agent position @xmath21 according to a specific statistical model . note that , on the one hand , the results illustrated in sec . [ sub : bcrb ] hold for a general statistical model relating @xmath20 to @xmath21 ; on the other hand , in sec . [ sub : zzb ] and [ sub : wwb ] , it is assumed that @xmath58 for mathematical convenience , where @xmath59 and @xmath60 ( i.e. , @xmath20 is affected by uncorrelated noise ) . it is important to point out that : 1 . the model ( [ eq : obs_model_gaussian ] ) is purposely abstract and does not explicitly refer to a specific localization technique ( e.g. , toa or received signal strength ( rss ) ) or to particular propagation conditions . generally speaking , it is suitable to describe the position estimate @xmath20 generated by a map - unaware and unbiased localization algorithm ; in addition , it leads to useful bounds which unveil the impact of _ map _ modelling ( instead of that of _ observation _ modelling ) on estimation performance ; readers interested in an in - depth analysis on the impact of observation modelling can refer to @xcite . 2 . in principle , the bounds derived in this manuscript can be extended to the case of correlated noise , accounting for the presence of an off - diagonal term @xmath61 in @xmath15 . however , the presence of noise correlation is neglected in the following derivations since : a ) the magnitude of @xmath62 in a real world system depends on several parameters ( the type of measurements processed by the system , the multi - lateration or angulation technique employed , the properties of the propagation channel , etc ) and can not be easily assessed ; b ) our research work evidenced that the presence of noise correlation does not provide significant additional insights on the impact of map - awareness on performance bounds . in this section various bounds about the accuracy of map - aware position estimation are derived and their implications are analysed . given an estimator @xmath63 of @xmath21 based on the observation vector @xmath20 , the bcrb establishes that the bayesian mean square error ( bmse ) matrix @xmath64 satisfies @xmath65 @xcite , where @xmath66 is the bayesian fisher information matrix ( bfim ) associated to the statistical models employed by @xmath63 . this result entails that , for 2-d localization : @xmath67 where @xmath68_{1,1}$ ] , @xmath69_{2,2}$ ] , @xmath70_{1,1}$ ] and @xmath71_{2,2}$ ] . it is not difficult to show that the bfim @xmath66 can be put in the form ( e.g. , see ( * ? ? ? ( 75 ) ) ) @xmath72 where @xmath73^{t}\right\ } \label{eq : bfim_cond}\ ] ] and @xmath74^{t}\right\ } \label{eq : bfim_apriori}\ ] ] represent the contributions originating from the observation vector ( i.e. , the so" +"the accelerated expansion of the universe has now been confirmed by several independent observations including those of high redshift type ia supernovae , and the cosmic microwave background ( cmb ) combined with the large scale structure of the universe @xcite . another way of presenting this kinematic property of the universe is to postulate the existence of a new entity dark energy ( de ) . this latter statement is dynamical in nature and therefore requires some assumptions to be made about the form of gravitational field equations governing the evolution of the ( observed part of the ) universe . although observationally well established , no single theoretical model provides an entirely compelling framework within which cosmic acceleration or de can be understood . indeed , the very many models of de existing in the literature illustrate that its nature is still very much an enigma . at present , all existing observational data are in agreement with the simplest possibility of de being a cosmological constant @xmath2 with @xmath3gev@xmath4 ( inside @xmath5 error bars in the worst case ) . is used throughout the paper . ] this case is internally self - consistent and non - contradictory . the extreme smallness of the cosmological constant expressed in either planck , or even atomic units means only that its origin is _ not _ related to strong , electromagnetic and weak interactions ( in particular , to the problem of the energy density of their vacuum fluctuations ) . where @xmath6 is some characteristic neutrino rest - mass ( the lightest one ? ) suggests that vacuum energy of the interaction responsible for non - zero neutrino rest - masses may be relevant for a non - zero @xmath2 . ] although in this case de reduces to only a single fundamental constant we still have no derivation from any underlying quantum field theory for its small value . within this context it is but natural that other possibilities admitting a ( slightly ) variable dark energy have also been actively studied by the scientific community in recent years . moreover , it is interesting that properties of the currently observed ` late de ' are _ qualitatively _ similar to those of an ` early de ' which is believed to have given rise to accelerated expansion ( inflation ) in the early universe . however in the case of the latter , there are sufficient grounds to support the view that ` early de ' was unstable and , thus , more complicated than a cosmological constant . so , it is natural to conjecture by analogy that the same might also be true of ` late de ' . de models proposed to account for the present cosmic acceleration include : + ( i ) quiessence with @xmath7 , the @xmath2 ( @xmath8 ) is a special member of this class . + ( ii ) quintessence models which are inspired by the simplest class of inflationary models of the early universe and employ a scalar field rolling down a potential @xmath9 to achieve late - time acceleration . quintessence potentials with @xmath10 have the attractive property that approaches a common evolutionary ` tracker path ' from a wide range of initial conditions . + ( iii ) the chaplygin gas model ( cg ) has the equation of state @xmath11 and evolves as @xmath12 where @xmath13 is the redshift , @xmath14 . it therefore behaves like dark matter at early times ( @xmath15 ) and like the at late times . cg appears to be the simplest model attempting to unify de and non - baryonic cold dark matter . + ( iv ) ` phantom ' de ( @xmath16 ) . + ( v ) oscillating de . + ( vi ) models with interactions between de and dark matter . + ( vii ) scalar - tensor de models . + ( viii ) modified gravity de models in which the gravitational lagrangian is changed from @xmath17 to @xmath18 where @xmath17 is the scalar curvature and @xmath19 is an arbitrary function . + ( ix ) dark energy driven by quantum effects . + ( x ) higher dimensional ` braneworld ' models in which acceleration is caused by the leakage of gravity into extra dimensions . + ( xi ) holographic dark energy , etc . + see the reviews @xcite for an exhaustive list of models and references . however , none of these models leads to the reduction of the number of fundamental constants ( parameters in the microscopic lagrangian ) as compared to standard @xmath2cdm . in other words , at the current state - of - the - art , de requires at least one new parameter whose value is set from observations . models with variable de can be broadly divided into two main classes : , in these models de is the energy density of some new , very weakly interacting physical field . ( otherwise dubbed modified gravity models ) . in these models the gravity equations do not coincide with those of einsteinian general relativity . however , it is usually possible to re - write the new equations in the conventional _ einsteinian _ form by transferring all additional terms from the l.h.s . into the r.h.s . of the einstein equations and referring to them as an effective energy - momentum tensor of de ( see sec . 2 below ) . ( precisely this happened to the cosmological constant which originally appeared in the l.h.s . of einstein s field equations but is now felt by many to constitute an effective matter term such as vacuum energy , etc . ) another category , which is even more important from the observational point of view , arises in response to the question whether or not the description of de requires a new field degree of freedom (= a new kind of matter ) . if the answer is in the affirmative then de may be considered as being ` induced ' by other kinds of matter . all physical de models and many geometrical ones belong to this category but there do exist geometrical de models which do not ( for instance the @xmath18 model with the palatini variation of its action ) . faced with the increasing proliferation of de models each with its own physical motivations and assumptions , a concerned cosmologist can proceed in either of two ways : \(i ) test _ every single _ model against observations . \(ii ) try and ascertain properties of dark energy in a _ model independent manner_. in this article , we proceed along route ( ii ) and attempt to review both the successes as well as difficulties faced by methods attempting to reconstruct the properties of dark energy directly from observations in a model independent manner . before attempting to determine its properties , we first need to provide a definition of _ dark energy_. a traditional approach is to use the einstein form of the gravitational field equations [ einst ] r _ - 12g_r = 8 g ( _ a t_^(a ) + t_^de ) as providing a _ definition _ of the effective energy - momentum tensor @xmath20 of de . here , the summation over @xmath21 in the r.h.s . includes all types of matter known from laboratory experiments ( protons , neutrons , photons , neutrinos , etc . ) as well as non - relativistic non - baryonic cold dark matter ( whose energy - momentum tensor is dust - like in the first approximation @xmath22 ) . @xmath23 is the present value of newton s gravitational constant . this definition has a number of advantages : + ( i ) it is simple , well - defined and self - consistent ; + ( ii ) it treats physical and geometrical de on an equal footing ; + ( iii ) in the absence of direct physical interaction between de with known forms of matter or with cold dark matter , the de energy - momentum tensor is conserved : @xmath24 . + one should stress here that using ( [ einst ] ) we automatically ascribe terms describing ( possible ) gravitational interactions between de and non - relativistic matter , as well as the matter energy - momentum tensor multiplied by a change in the effective gravitational constant , to the de energy - momentum tensor . the latter possibility arises , for instance , in scalar - tensor de models . when applied to a homogeneous and isotropic friedmann - robertson - walker ( frw ) cosmological model , eqs . ( [ einst ] ) reduce to two algebraically independent equations : h^2 & = & ( _ a _ a + _ de ) - , [ eq : acc ] + & = & -(_a ( _ a + 3p_a ) + _ de + 3p_de ) [ eq : acc1 ] where @xmath25 is the frw scale factor and the hubble parameter @xmath26 . at late times when radiation may be neglected , one gets [ eq : energy ] _ de = ( 1 - _ m ) where we have omitted the contribution from the curvature term in ( [ eq : acc ] ) for simplicity . @xmath27 is the total density of non - relativistic matter in terms of its critical value . similarly , the expression for the deceleration parameter q - a / ah^2 = x - 1 , x = 1 + z [ eq : decel1 ] ( prime implies differentiation with respect to @xmath28 ) takes the form : p_de = ( q - ) . [ eq : pressure ] dividing ( [ eq : pressure ] ) by ( [ eq : energy ] ) we get the following expression for the _ effective _ equation of state ( eos ) of dark energy ( @xmath29 ) : [ eq : state ] w(x ) = 2 q(x ) - 1 3 ( 1 - _ m(x ) ) . for physical de , the eos makes physical sense . however , this is not so for geometrical de for which the acceleration of the universe is caused by the fact that the field equations describing gravity are not einsteinian . as a specific example of geometrical de consider the widely studied dgp braneworld @xcite for which [ eq : dgp ] h = + , where @xmath30 is a new length scale and @xmath31 and @xmath32 refer respectively to the four and five dimensional planck mass . the acceleration of the universe in this model arises not because of the presence of de but due to the fact that gravity becomes five dimensional on length scales @xmath33 . the contrast between ( [ eq : acc ] ) and ( [ eq : dgp ] ) makes it abundantly clear that for models such as dgp the eos in ( [ eq : state ] ) is an _ effective _ quantity ( @xmath34 ) , which may still be useful for descriptive purposes but which no longer represents any fundamental physical property of an accelerating universe . indeed , instances are known when @xmath35 even when matter itself satisfies the weak energy condition @xmath36 @xcite . it may be instructive to note that , for geometrical de , @xmath1 may show pathological behaviour in certain cases , such as the presence of poles at finite values of redshift , @xmath37 , even though the underlying cosmological model is completely well behaved ( see for instance @xcite ) . for such models , the deceleration parameter @xmath38 and other geometrical parameters prove to be more robust for determining de properties than the eos . we shall return to these important" +"predictions of standard model ( sm ) have so far been in agreement with results of numerous experiments . therefore , sm has been in use to explain many puzzles related to fundamental particles and their interactions . however , there have been a number of fundamental problems ( quark - lepton symmetry , family replication , hierarchy problems , charge quantization etc . ) sm could not deal with . furthermore , masses and mixings of leptons and quarks are fixed by hand . these problems forced physicists to go beyond sm . extra dimensions , supersymmetry ( susy ) , compositeness and so on have been created for solving these problems and to explain the physics underlying them . among these alternative models compositeness has explained the subjects of family replication and quark - lepton symmetry in the best manner according to the theory of compositeness quarks , leptons , gauge bosons need to be composite particles made up of more basic constituents . these basic constituents , in otherwords substructural particles , are named preons . it is assumed that preons are what compose quarks , leptons and gauge bosons . it s also supposed that preons interactions lead to development of many new types of particles such as leptoquarks , leptogluons , diquarks , dileptons and excited fermions . we will be interested in color octet leptons that in the framework of composite models with colored preons @xcite have the same status as the excited leptons . for instance , in the framework of fermion - scalar models , leptons would be a bound state of one fermionic preon and one scalar anti - preon @xmath6 ( both @xmath7 and @xmath8 are color triplets ) , then each sm lepton is thought to accompany with its own color octet partner @xcite . there are many papers about manifestations of excited leptons at high energy colliders whereas color octet leptons are discussed only in a few papers @xcite . resonant production of @xmath0 at future ep colliders have been analyzed in recent paper @xcite , where also current limits on leptogluon masses are briefly discussed . it was shown that the @xmath0 discovery at the lhec simultaneously will determine the compositeness scale . in this paper we will consider indirect manifestation of color octet electrons at the next generation linear colliders : international linear collider ( ilc ) and compact linear collider ( clic ) . in section 2 , we present the interaction lagrangian of the leptogluons as well as signal cross - section for the process @xmath9 via t - channel @xmath0 exchange . the signal and background analysis performed at ilc and clic is given in section 3 . in the last section we give an interpretation of obtained results and concluding remarks . the interaction lagrangian of leptogluons with the corresponding lepton and gluon is given by @xcite : @xmath10 where @xmath11 is field strength tensor for gluon , index @xmath12 denotes the color , @xmath13 is gauge coupling , @xmath14 and @xmath15 are the chirality factors , @xmath16 and @xmath17 denote left and right spinor components of lepton , @xmath18 is the anti - symmetric tensor and @xmath19 is the compositeness scale , which is taken to be equal to @xmath20 . the leptonic chiral invariance implies @xmath21@xmath22 . for numerical calculations we implement this lagrangian into the calchep program @xcite . the cross sections for the process @xmath9 via t - channel @xmath0 exchange at @xmath3 tev are presented in figure 1 . isr and beamstrahlung effects at ilc and clic are calculated with calchep program using parameters given in table i @xcite . .main parameters of ilc and clic . here n is the number of particles in bunch . @xmath23 and @xmath24 are rms beam sizes at interaction point ( ip ) , @xmath25 is the rms bunch length . [ cols=""^,^,^,^"",options=""header "" , ] up to now , we assumed the compositeness scale equal to the mass of color octet electron ( @xmath26 ) . in general case this scale can be decoupled from the mass of new particles . for this reason below we consider limits for the compositeness scale as a function of the color octet electron mass . in this analysis we use @xmath27 @xmath28 and @xmath29 @xmath30 for ilc , clic1 and clic2 , respectively . these values correspond to one year operation with nominal luminosities . in figure 9 , 10 and 11 we plot reachable values of the compositeness scale as a function of @xmath20 for ilc , clic1 and clic2 , respectively . tev and @xmath31 @xmath30 . ] tev and @xmath32 @xmath30 . ] tev and @xmath33 @xmath30 . ] we show that , if @xmath26 ilc will give opportunity for indirect observation of octet electron upto @xmath34 @xmath35 gev during one ( three ) operation with nominal luminosity . corresponding values for clic1 are about @xmath36 gev lower . therefore , both ilc and clic1 will give opportunity to pass essentially the tevatron capacity for color octet electron ( @xmath0 ) search . clic2 will be sensitive to @xmath37 times higher mass values , namely , @xmath0 masses upto @xmath38 ( @xmath39 ) gev could be observed during one ( three ) year operation with nominal luminosity . these values essentially exceed capacity of the lhc to observe color octet electron ( @xmath0 ) via pair production . if the compositeness scale and color octet electron mass are decoupled , observable values of @xmath19 at ilc and clic1 exceeds @xmath20 for @xmath40 gev ( at @xmath41 gev the ratio @xmath42 ) . at the clic2 @xmath19 exceeds mass for @xmath43 gev ( at @xmath44 gev observable @xmath19 is @xmath45 gev ) . this work is supported by tubitak in the framework of the bidep 2218 post - doctoral program ." +"stochastic partial differential equations ( spdes ) , or partial differential equations ( pdes ) with uncertainties , play an important role in many areas of engineering and applied sciences such as turbulence , flows in random media , solid mechanics , filtering , and finance . numerical simulations of spdes are typically based on the monte carlo ( mc ) or the polynomial chaos ( pc ) methods @xcite . in both cases , the long - time simulation of spdes proves to be quite expensive @xcite . in this paper , we extend the pc - based method developed for stochastic differential equations in @xcite to the setting of spdes . the pc method originates from the works @xcite and enables us to expand ( square integrable ) functionals of brownian motion in a basis of hermite polynomials . applications of such a framework to random flows and turbulence theory are examined in @xcite . more recently , works in @xcite combined the pc method with the karhunen loeve ( kl ) expansion @xcite to study structural mechanics problems . the generalized polynomial chaos ( gpc ) developed in @xcite next extends the hermite pc to a set of non - gaussian random parameters . the main advantage of the pc method is that it allows us to propagate stochasticity by providing expansions of quantities of interest in terms of appropriate uncertainties while in effect replacing the stochastic equations by systems of deterministic equations . once these deterministic equations are solved , the statistical properties of the solution can be readily inferred from the coefficients of the expansion , which facilitates uncertainty quantification . in some cases , the pc method can propagate uncertainties with a substantially lower cost than mc methods ; especially for low dimensional uncertainties @xcite ; see also @xcite . however , in cases of high dimensional random parameters , the efficiency of the pc method is reduced because of the large number of terms that appear in the expansion . the presence of a temporal random forcing is a serious challenge to the pc method as the number of stochastic variables increases linearly with time , which hinders the capability of the pc method for long - time computations @xcite . moreover , the optimality of the initial basis typically degrades as time evolves due to the presence of nonlinearities in the equation . these drawbacks were addressed in @xcite . in our previous work @xcite , we proposed the _ dynamical generalized polynomial chaos _ ( dgpc ) method to solve low dimensional stochastic differential equations ( sdes ) driven by white noise . the novelty of the dgpc algorithm is that it utilizes a restart procedure and constructs polynomial chaos expansions ( pces ) dynamically in time by using orthogonal polynomials of the projections of the solution at the current steps and the future random forcing @xcite . this allows the algorithm to keep reasonably sparse random bases , and to mitigate the aforementioned curse of dimensionality and loss of optimality . numerical experiments in that reference illustrate that such a restart procedure has the ability to accurately estimate long - time solutions of sdes ; see the relevant computational and theoretical details in @xcite . although the algorithm performs well for low dimensional sdes , extension to larger systems is challenging and requires serious modifications . in this manuscript , we extend dgpc to the framework of spdes driven by white noise . while solutions to spdes are , in general , high dimensional random fields , they may lend themselves in some cases to low dimensional representations @xcite . armed with this fact , we propose at each restart to use the kl expansion to compress the solution into a representation involving a finite number of random modes , i.e. , a projection onto a lower dimensional manifold . in cases where the modeling equations contain non - forcing random inputs other than brownian forcing , such as a random viscosity , the kl expansion is applied to the solution and the random parameters together so that the algorithm automatically selects the intrinsic variables , which have the largest influence on the solution . since kl expansions are known to be optimal in the mean square sense , at each restart point in time , only a few dominating , most energetic , random modes are chosen and incorporated into pce to represent the future solution . however , the combination of the random kl modes and the random forcing variables brings about high dimensionality . the computational challenges then become : ( i ) computing orthogonal polynomials of arbitrary multivariate distributions ; ( ii ) keeping the number of terms in the expansion as small as possible . the construction of orthogonal polynomials of evolving multivariate distributions is possible by estimating their statistical moments @xcite , which is , in general , a computationally intensive procedure . in this work , we estimate the moments of the solution using its pce through a sampling approach to greatly reduce their computational cost ; see @xcite for a similar sampling methodology . we also show that the method is robust with respect to re - sampling . the second challenge ( ii ) is a major problem for all pc - based methods . the kl decomposition is computationally expensive as it requires solving a large eigenvalue problem . for problems of moderate size , we find that the eigenvalue problem is solved efficiently by using a krylov subspace method . for larger problems , in order to mitigate both memory requirements and computational cost of the kl expansion , we find low - rank approximations to the covariance matrices based on their pc representations and without assembling them . the algorithm leverages randomized projection methods as introduced in @xcite , and uses appropriate random matrices to obtain fast and accurate solutions of large eigenvalue problems . after selecting the dominating modes in the kl expansion , we make use of the sparse truncation technique proposed in @xcite to further reduce the number of terms in a pce . for long - time computations , we also develop an adaptive restart scheme , which adapts the time lag between restarts based on the acuity of the nonlinear effects . the use of compression techniques to exploit intrinsic lower dimensional structures of solutions of spdes is not new and is in fact necessary in many contexts ; see @xcite . the novelty of our approach is that a lower dimensional representation of the solution is learned online and integrated into a pce to integrate future random forcing and represent future solutions . this procedure is computationally viable and the combination of the aforementioned ideas allows us to attain a reasonable accuracy in the long - time evolutions of spdes for a reasonable computational cost . as we are interested in the long - time evolution of spdes , we restrict ourselves here to dynamics with a dissipation mechanism . equilibrium statistics and asymptotic properties of the solutions are relevant in many applications and have been extensively studied in the literature @xcite . based on these motivations , we provide numerical experiments for a 1d randomly forced burgers equation and a 2d stochastic navier stokes ( sns ) system . all equations are driven by white noise and satisfy periodic ( spatial ) boundary conditions . to demonstrate the efficiency of our algorithm , we present both short- and long - time computations . in some cases , we model the viscosity as a random process . statistical moments obtained by the algorithm are compared to the standard mc methods for short times to assess the accuracy of the algorithm . results show promising speed - ups over standard mc methods . we exhibit convergence behavior in terms of the degree of the expansion , the number of random modes retained in the kl expansion , and the ( adaptive ) restart time . in some cases , we provide a purely pce - based numerical verification of the convergence of the process to its invariant measure . the outline of the paper is as follows . section [ sec : kl_pc ] introduces the basic setting for the pc and kl expansions . in the following section , the main algorithm and its implementation details are discussed . numerical experiments are conducted in section [ sec : numerical ] using several settings for the stochastic burgers equation and navier stokes system . some concluding remarks are offered in section [ sec : summary ] . throughout the manuscript , we consider the following time - dependent stochastic partial differential equation ( spde ) driven by the white noise @xmath0 : @xmath1 , \\ & u(x,0,\omega)= u_0(x,\omega ) , \quad x \in g , \ , \omega \in \omega , \end{aligned } \right.\end{aligned}\ ] ] where , for concreteness , @xmath2 is the @xmath3-dimensional torus so that @xmath4 and its derivatives are periodic functions in the variable @xmath5 . the dgpc algorithm may easily be extended to more general boundary conditions and geometries . above , @xmath6 is a possibly non - linear differential operator in the spatial variables . the solution takes values in @xmath7 . in the numerical simulations , the parameters @xmath3 and @xmath8 are set to either @xmath9 or @xmath10 . given a probability space @xmath11 , where @xmath12 is a sample space equipped with the sigma - algebra @xmath13 and the probability measure @xmath14 , we denote by @xmath15 the hilbert space of square integrable random fields on @xmath2 . for a random field @xmath16 , we define the expectation @xmath17 = \int_{\omega } u(x,\omega ) { \mathbb{p}}(d\omega),\ ] ] and the covariance @xmath18 , \quad x , y \in g,\end{aligned}\ ] ] where @xmath19 denotes the transpose . the kl expansion of a time - independent random field @xmath16 with a continuous covariance is as follows : @xmath20 where the eigenvalues @xmath21 are nonnegative , and the eigenfunctions @xmath22 and the mean zero random variables @xmath23 are given by @xmath24 \ , , \phi_l \rangle_{l^2(g)}.\end{aligned}\ ] ] here , @xmath25 denotes the spatial inner product on @xmath2 . the spatial and random modes satisfy bi - orthogonality , i.e. @xmath26 = \delta_{lk}$ ] and @xmath27 , where @xmath28 denotes the kronecker delta function ; see @xcite . the major feature of the kl decomposition is that the truncation after a finite number , denoted by @xmath29 hereafter , of terms is optimal in the @xmath30 sense . how @xmath29 should be chosen obviously depends on the spectrum of the covariance operator . when the process shows a high degree of correlation , then typically @xmath29 may be chosen relatively small due to the rapid decay of the eigenvalues @xcite . this makes the kl expansion a useful dimensionality reduction technique in many applications and will play a crucial role in our algorithm to compress the dimensionality of stochastic solutions of . we assume that the random solution @xmath31 of is a second - order stochastic process for all @xmath32 $ ] , and for simplicity , that the initial condition is deterministic . the pc method for is constructed as follows . given a complete countable orthonormal system @xmath33 $ ] , @xmath34 , we project the brownian motion @xmath35 onto @xmath36 $ ] by defining @xmath37 . then , @xmath38 consists of a countable number of independent and identically distributed standard gaussian random variables , and the convergence @xmath39 ^ 2 \rightarrow 0 , \quad k \rightarrow \infty,\end{aligned}\ ] ] holds for all @xmath40 . basic examples of orthonormal systems are trigonometric functions and wavelets ; see @xcite . the spde solution is a nonlinear functional of brownian motion on the interval @xmath41 $ ] . therefore , the projection onto @xmath42 enables us to consider the solution depending on a countable number of random" +"by far the study of neutron stars has been mainly focused on the relationship between the equation of state ( eos ) of nuclear matter and the observed maximum mass . the connection has been achieved by solving the hydrostatic equilibrium equations based on general relativity . the first generation observed masses exhibited an average value around 1.5 solar masses . this value requires a soft eos that can be easily obtained by introducing new degrees of freedom like hyperons , kaons or quarks accompanied or not by a phase transition . sometimes the softening was so large that the neutron star is predicted to collapse into a black hole , as for the sn1987a @xcite . in the new generation of observations the masses are distributed within a large range , up to 2 solar masses , that requires a stiff eos , i.e. , hadronic matter without new degrees of freedom . since it is hard to imagine pure hadronic matter to sustain the high pressure predicted in the inner core , new scenarios have to be advanced to explain the coexistence , in the phenomenology of neutron stars , of low and high mass spectra . recently @xcite it has been argued that the two observed classes of neutron stars might correspond to two different evolutionary scenarios of neutron stars . in one case , the hot and dense remnant of the supernova explosion rapidly evolves into a hybrid star , where the transition to a quark phase softens the nuclear matter so that @xmath0 ; in the other case a slow evolution could lead the neutron star to a large mass via a mass accreting from the coupling with a white dwarf . from this point of view the destiny of the remnant is strongly affected by the initial conditions , i.e. density , temperature , leptonization degree etc . for instance , if the mass of the remnant is below the mass threshold for quark nucleation the transition to the quark phase is forbidden @xcite . if the mass is slowly accreting the transition is allowed . the role of temperature or other parameters defining the initial state of a new born neutron star has not yet been studied . to investigate the possible phase transition to quark matter in neutron stars , we need also to know the eos of quark matter . although we have in hand the fundamental theory of strong interactions , i.e. , quantum chromodynamics ( qcd ) , we still do not know the true ground state . it is now generally expected that quark matter is in the color - flavor locked phase ( cfl ) @xcite at extremely high densities when the finite current mass of strange quarks becomes unimportant . in the density range from nuclear saturation to cfl , there may exist a rich and varied landscape of phases , e.g. , the 2sc , g2sc , gcfl etc . presently , however , these phases suffer from the so - called chromomagnetic instability problem for both the two- @xcite and three - flavor @xcite cases . on the other hand , experiments show that quarks become asymptotically free rather slowly @xcite . therefore , in the present study we are dealing with the ordinary strange quark matter ( sqm ) @xcite . the special problem in studying the eos of ordinary quark matter is to treat quark confinement in a proper way . in the conventional standard approach , an extra constant term , the famous bag constant @xmath1 , is added to the energy density of the system , which provides a negative pressure to confine quarks within a finite volume , usually called a ` bag ' . the quark mass is infinitely large outside the bag , and a finite constant within the bag . a vast quantity of investigation have been performed within the framework of the bag model @xcite . as is well known , however , particle masses vary with environment . such masses are usually called effective masses . effective masses of hadrons and quarks have been extensively discussed , e.g. , within the nambu - jona - lasinio model @xcite and within a quasi - particle model @xcite . in principle , the density dependence of quark masses should be connected to the in - medium chiral condensates @xcite . taking advantage of the density dependence , one can describe quark confinement without using the bag constant . instead , the quark confinement is achieved by the density dependence of the quark masses derived from in - medium chiral condensates @xcite . the two most important aspects in this model are the quark mass scaling @xcite and the thermodynamic treatment @xcite . both aspects will be reviewed in this paper . in the present contribution , the transition from hadron phase ( hp ) to strange quark phase ( sqp ) in the inner core of a neutron star is investigated within the fully consistent nuclear and quark models . in the hadron sector we adopt the equation of state from brueckner - bethe - goldstone ( bbg ) approach with three - body forces ( tbf ) @xcite . this theory , being a completely microscopic approach , can easily incorporate degrees of freedom such as nucleon resonances [ @xmath2(1232 ) or @xmath3(1440 ) ] , which are expected to appear at higher hadron densities . it is found that the mixed hadron - quark phase can occur , for reasonable values of the confinement parameter , a little above the normal saturation density , and can undergo the transition to pure quark matter at about 5 - 6 times the saturation . this result is quite different from the previous results from nambu - jona - lasinio ( njl ) model in which the mixed quark phase can not appear at neutron - star densities @xcite . afterwards , the influence of the mixed and quark phases on the structure of compact stars is discussed by solving the tolman - oppenheimer - volkov ( tov ) equation and extracting the mass - radius plots for neutron stars . finally , it is shown that the transition to the deconfined phase turns out to be incompatible with the onset of kaon condensation . sqm has been one of the hot topics in nuclear physics since witten s famous stability conjecture @xcite . in many studies , the quark confinement was treated adopting the bag mechanism @xcite . an alternative approach to obtain confinement is based on the density dependence of quark masses @xcite . this mechanism has been extensively applied to investigating the properties of sqm @xcite . in this section , we first give a short review of the two most important aspects , with the main inconsistency of the original model . then we present a fully self - consistent thermodynamic treatment . the properties of sqm will be given in the new treatment . in the present paper , however , the main application of the new approach is the study of the phase transition in compact stars . as mentioned above , the quark confinement in this model is achieved by the density dependence of quark masses . therefore , the first important question is how to determine the quark mass scaling which can reasonably produce confinement . originally , the interaction part of the quark masses was assumed to be inversely proportional to the density @xcite . this linear scaling has been extensively applied to studying the properties of sqm . there are also other mass scalings @xcite . their main drawback is that they are pure parametrizations without any convincing derivation . therefore , a cubic scaling was derived based on the in - medium chiral condensates and linear confinement at both zero @xcite and finite temperature @xcite . this new scaling has been applied to investigate the viscosity of sqm and the damping time scale that is due to the coupling of the viscosity and r mode @xcite , the quark - diquark equation of state and compact star structure @xcite , the properties of strangelets versus the electric charge and strangeness @xcite , and the new solutions for cfl slets @xcite . in the present paper , we use the chirally determined quark mass scaling @xcite to study the phase transition in neutron stars . for this we need a completely self - consistent thermodynamic treatment of the eos of quark matter . the thermodynamic treatment of the system with confinement via the density dependent quark masses has been a long story . originally , the thermodynamic formulism was regarded the same as the constant - mass case @xcite . in this first treatment , the internal pressure can not be zero , and the properties of sqm were rather different from those in the bag model . but it was later pointed out that the difference was caused by the incorrect thermodynamic treatment @xcite . it was found that an additional term is to be added to the pressure and energy expressions @xcite . this second treatment makes it possible sqm to be self - bound . however , two serious problems came out : one is the unreasonable vacuum limits , the other one is the discrepancy between the energy minimum and zero pressure . it was shown that the added term in the pressure , due to the density dependence of quark masses , should not be appended to the energy . after discarding this term in the energy , while keeping it in the pressure , the two inconsistencies mentioned above were immediately removed @xcite . this third treatment has recently been extended to finite temperature @xcite . the thermodynamic formulism in ref . @xcite was also adopted in ref . @xcite , though a different quark mass scaling was used there . a common feature of the last two thermodynamic treatments @xcite , as well as other recent references using this model @xcite , is that they all regard the thermodynamic potential the same as in the fermi gas model . because of the additional term , the pressure becomes obviously not equal to the minus thermodynamic potential density , contradicting the thermodynamic equality @xmath4 for a homogeneous system . one can also easily check that the fundamental differentiation equality @xmath5 for homogeneous systems at zero temperature was not fulfilled in the mentioned references . in the rest of this section , we will present a fully self - consistent thermodynamic treatment of the confinement by density - dependent mass model ( cddm ) . let us consider a quark model with three flavors . denoting the fermi momentum in the phase space by @xmath6 , the particle number densities can then be expressed as @xmath7 and the energy density as @xmath8 equations ( [ nimod ] ) and ( [ emod ] ) are familiar expressions , where the summation index goes over all considered particle types . to let the model be valid for both particles and anti - particles , the particle number density , or accordingly , the fermi momentum , are formally assumed to be negative for anti - particles . therefore , in the upper limit of the integration , the absolute value has to be taken . if the particle masses @xmath9 are constant , the relation between the fermi momenta @xmath6 and the chemical potentials @xmath10 is @xmath11 as is well - known , however , the quark mass depends on density and temperature . in principle , the quark mass scaling should be determined from qcd , which is obviously impossible presently . based on the in - medium chiral condensates , a cubic scaling law was derived at zero temperature @xcite , and it has been recently extended to finite temperature @xcite . at zero temperature , we have the simple cubic" +"the ultracold quantum gases have been the test bed to investigate the many - body physics @xcite . thanks to the versatile advances in the experiments , the interaction strength @xcite , the optical lattice depth , and the dimensionality can be manipulated to study strongly correlated quantum gases . to name a few , the typical atomic systems involve luttinger liquid of one - dimensional ( 1d ) bose gases @xcite , a three - dimensional ( 3d ) bose - mott insulator @xcite , and the superfluid state of two - component fermi gases @xcite . conventional experimental measurements of the atomic many - body systems include the time - of - flight experiment , the noise correlations measurement @xcite , the bragg scattering spectroscopy @xcite , and the in - situ imaging @xcite . recently , we investigate the spectrum of electromagnetically induced transparency ( eit ) @xcite in the strongly correlated atomic systems @xcite as an alternative and non - destructive method @xcite to probe the quantum many - body physics . the eit spectrum is shown to be solely determined by the single - particle green s function of the ground - state atoms . non - trivial many - body effect for the spectrum is predicted @xcite when the atoms are virtually coupled to the low - lying rydberg states @xcite . the single - particle green s function is crucial for many - body systems , from which the observable of any single - particle operator , the ground state energy , and the excitation spectrum can be extracted @xcite . similar to the well - known angle - resolved photoemission spectroscopy ( arpes ) @xcite , where the single - particle green s function is probed to investigate the electronic structure of the surface in the solids , the eit spectroscopy accesses the information of it as well . what differs is the single - particle green s function in arpes is directly measured whereas the eit spectrum involves an integral of the green s function and the functional laser parameters @xcite . a recent proposal of probing spin correlation functions by ramsey interferometry @xcite provides the other direct way to measure the dynamical green s function of the many - body systems . in ultracold atomic systems , matter wave interference patterns are powerful to reveal the many - body physics . for example in two - dimensional ( 2d ) bose - einstein condensate ( bec ) @xcite , the contrast of interference fringes relates to the spatial single - particle green s function @xcite . therefore , the algebraic decay of spatial correlation in the contrast indicates the quasi - long - range order in the system , which can be fully described by green s function . in addition , the second - order correlation function in the interference pattern of two 1d bose gases is also manifested to provide the evidence of luttinger liquid signatures @xcite . on the contrary to the destructive interference method , quantum non - demolition ( qnd ) detection of quantum matter @xcite provides a least destructive measurement . it can be used to effectively map the quantum correlations of the ultracold atoms into light signals , which is similar to our proposed eit scheme in this paper . the common feature of matter wave interference and eit spectrum in probing the quantum many - body physics is that the measurements respectively involve the average and integral of the green s function , making both methods the indirect probes . nevertheless the eit spectroscopy has the advantage of non - destructive probe with well - controlled laser parameters , which may provide more efficient and precise measurements on the ultracold atoms . in this paper , we demonstrate that the dynamical single - particle green s function of the many - body system can be determined by eit spectroscopy . in section ii , we briefly describe the eit susceptibility in terms of the green s function @xcite . then we propose an experimental setup to realize the reconstruction of the single - particle green s function , and also discuss the finite size effect . in section iii , we investigate finite temperature green s function , and demonstrate the reconstruction steps by measuring the frequency moments from the information of eit spectrum . we take 3d mott - insulator and 1d luttinger liquid as two examples . in the last section , we discuss possible application to other many - body systems and summarize . our results suggest a universal determination on the essential single - particle green s function of the ultracold quantum gases in parallel to the arpes in the solids . we consider the conventional eit setup ( @xmath0 type scheme ) as shown in fig . [ fig1 ] . the probe ( @xmath1 ) and control ( @xmath2 ) fields couple the ground state @xmath3 to the other hyperfine ground state @xmath4 and an excited state @xmath5 . the detunings are @xmath6 and @xmath7 for the probe and control fields respectively . they are defined as the differences from the laser central ( @xmath8 ) to the atomic transition frequencies . in the linear response of the probe field , the electric susceptibility is derived as @xmath9 where @xmath10 is the fourier transform of slow - varying @xmath11 , and @xmath12 is the polarization operator calculated by the perturbation of a weak probe field @xcite . in the momentum - frequency space , the electric susceptibility is obtained as ( @xmath13 ) @xcite @xmath14 where @xmath15 is the quantization volume , @xmath16 is the dipole moment of the probe field transition , and @xmath17 is the fourier transform of the green s function @xmath18 at zero temperature @xcite . the functional @xmath19 that includes the laser parameters is @xmath20 where the mixing angle is @xmath21 and the eigenenergies from the unperturbed hamiltonian in the eit setup ( @xmath22 ) is @xmath23 the recoil - energy shifted detuning is @xmath24 , the kinetic energy is @xmath25 , and the recoil momentum is @xmath26 . the chemical potential is @xmath27 , and @xmath28 are the central momenta of the probe and control fields respectively . a phenomenonological spontaneous decay rate ( @xmath29 ) of the excited state can be added by replacing @xmath30 with @xmath31 . note that we assume negligible dephasing rate between the two hyperfine ground states . the above eq . ( [ chi ] ) provides the crucial recipe of the many - body effects on the eit spectrum for generally any strongly correlated ultracold quantum gases @xcite . the nontrivial power - law dependence of the eit spectrum near the resonance is shown for a luttinger liquid , and the significant frequency shift and asymmetric absorption spectrum can be identified for a bose - mott insulator phase @xcite . this non - destructive eit measurement is proposed to detect the fermi paring in a bardeen - cooper - schrieffer ( bcs ) superfluid state of two - component fermi gases @xcite . the gap energy can be also measured from the transparency position @xcite . as long as the single - particle green s function is known , the eit spectrum can be derived . on the other hand , the eit spectroscopy can be an efficient method to extract the single - particle green s function . ] via an eit experiment with a probe pulse . the experiment is conducted with a probe pulse in the ultracold quantum gas with an atomic @xmath0-type configuration : the counter - propagating control ( @xmath32 ) and the probe [ @xmath33 fields in @xmath34 direction couple two hyperfine ground states @xmath3 and @xmath4 with the excited state @xmath5 ( detunings are @xmath7 and @xmath6 respectively ) . @xmath29 is the spontaneous decay rate of @xmath5 . b.s . represents the beam splitter . open circles denote the fiber coupling that guide the reference and transmitted pulses into the temporal interferometry . from the interferometry box , we characterize the output probe pulse @xmath35 . @xmath36 is then extracted by reconstructing green s function from the frequency moment calculation in eit spectroscopy.,width=302,height=181 ] the functional @xmath19 incorporates all the information of the laser parameters in the eit setup , which is well defined . we find that eq . ( [ chi ] ) has a simple form of the convolution between the single - particle green s function and @xmath37 in momentum - frequency space . since the dispersion of the probe field has @xmath38 in the propagating direction , the momentum ( position ) of @xmath39 ( @xmath40 ) is not able to be resolved independently from frequency ( time ) in the eit spectroscopy . we let @xmath39 @xmath41 @xmath42 in eq . ( [ chi ] ) which is valid if the spread of frequency @xmath43 @xmath44 @xmath8 so @xmath45 @xmath46 @xmath47 . we first fourier transform eq . ( [ chi ] ) in frequency space , @xmath48 where @xmath49 and @xmath50 are the inverse fourier transforms ( @xmath51 ) of @xmath52 and @xmath53 respectively with @xmath54 @xmath55 @xmath56 . we may proceed to fourier transform the momentum degree of freedom ( @xmath54 ) above , and derive directly the transverse space and real - time green s function @xmath57 in terms of @xmath58 and @xmath59 where @xmath60 @xmath55 @xmath61 . the validity of the fourier transform in momentum space requires large enough @xmath54 to cover the complete eit spectrum @xmath49 . to estimate the largest possible transverse range of the probe field momentum , it is limited by @xmath62 where @xmath63 is the average transverse atomic distance . in this limit however the probe field suffers from small optical density if the interacting cross section is less than @xmath64 . therefore the probe field can not probe large enough momentum for general quantum degenerate gases ( with the order of @xmath65 nm for a typical density @xmath66 @xmath67 ) , and we can not further fourier transform eq . ( 5 ) . for simplification and to proceed the investigation of green s function retrieval , we choose @xmath68 and eq . ( [ green1 ] ) becomes @xmath69 where due to the limited spatial bandwidth of the eit , we may not resolve directly the transverse dynamical green s function from the eit susceptibility @xmath70 . however we will show in the examples of the next section that we may still extract the dynamical green s function @xmath71 from the information of @xmath70 . the eit spectrum holds much useful information to reconstruct @xmath71 to provide the features that characterize the many - body systems . in addition we note that choosing a different @xmath54 in eq . ( [ green1 ] ) does not improve our reconstruction steps in the examples of section iii , and in general it makes no significant difference than eq . ( [ green ] ) . in fig . [ fig1 ] , we demonstrate an experimental setup to extract the single - particle green s function using eit spectroscopy . we use a spatio - temporal pulse to probe the ultracold quantum gas . the probe pulse goes through a 50:50 beam splitter ( b.s . ) to interact with the atoms , and the reflected one acts as a reference pulse . the transmitted probe pulse is then guided by the fiber to interfere with the reference one . we denote the process as the interferometry box that characterizes the temporal information of the transmitted pulse . this technique of measuring the spatial and temporal electric field @xcite is not new for the ultrafast optical society . the single trace of interferometry is done through the input fiber at the specific position @xmath72 that the electric field @xmath73 can be resolved @xcite . to further resolve the complete" +"as very few gamma - ray burst ( grb ) sources have astronomical counterparts at other wavebands , empirical studies of grbs have been largely restricted to the analysis of their gamma ray properties : bulk properties such as fluence and spectral hardness , and evolution of these properties within a burst event ( fishman & meegan 1995 ) . while bursts exhibit a vast range of complex temporal behaviors , their bulk properties appear simpler and amenable to straightforward statistical analyses . studies fall into two categories : examination of whether grb bulk properties comprise a homogeneous population or are divided into distinct classes ; and search for relationships between bulk properties . both types of study may lead to astrophysical insight , just as the distinction between main sequence stars and red giants and the measurement of a luminosity - mass relation along the main sequence assisted the development of stellar astrophysics early in the century . the most widely accepted taxonomy of grbs is the division between short - hard and long - soft bursts proposed by dezalay et al . ( 1992 ) and kouveliotou et al . ( 1993 , henceforth k93 ) . k93 noticed a bimodality in the burst duration variable @xmath1 ( time within which 90% of the flux arrived ) , suggesting the presence of two distinct types of bursts separated at @xmath2 sec . the short bursts have systematically harder gamma - ray spectra than longer bursts . the two groups seemed indistinguishable in most other bulk properties , although the larger group of long - soft bursts may have a subclass with a different fluence distribution ( i.e. , different @xmath3 ; katz & canel 1996 ) and the groups may have different galactic latitude distributions ( belli 1997 ) . other researchers point to small groups of bursts with distinctive properties such as the soft - gamma repeaters ( norris et al . 1991 ) , two possible classes with differing short - timescale variability ( lamb , graziani & smith 1993 ) , fast - rise exponential - decay bursts ( bhat et al . 1994 ) , and two types of bursts with different ratios of total fluence and @xmath4300 kev fluence ( pendleton et al . 1997 ) . a variety of relationships between burst properties have also been reported . norris et al . ( 1995 ) find an anti - correlation between @xmath1 ( calculated after wavelet thresholding ) and peak intensity , consistent with a cosmological time dilation . however , a positive correlation between @xmath1 and total fluence is also seen which does not agree with the simplest cosmological interpretation ( lee & petrosian 1997 ) . additional reported relationships include : @xmath1 correlated with peak heights ( lestrade 1994 ) , peak energy correlated with peak flux ( mallozzi et al . 1995 ) , and peak duration anticorrelated with gamma - ray energy ( fenimore et al . 1995 ) . most of these studies suffer from a failure to treat all of the bulk property variables in an unbiased and quantitative way . astronomers typically examine univariate or bivariate distributions , sometimes constructing composite variables ( such as hardness ratios ) with pre - determined relationships to include one or two additional variables . but it is quite possible that the complex astrophysics producing grbs will not manifest themselves in simple bivariate plots , just as the division between short - hard and long - soft bursts is not evident in spectral variables alone ( pendleton et al . grb catalogs , like most multiwavelength astronomical catalogs , are multivariate databases and should be treated with multivariate statistical methods that can objectively and effectively uncover structure involving many variables ( feigelson & babu 1997 ) . two previous studies take a fully multivariate approach to understanding grb bulk properties . baumgart ( 1994 ) constructs a neural network taxonomy of 99 grbs from the pvo satellite using 26 variables representing both bulk burst properties and detailed temporal characteristics ( e.g. number of peaks , fractal dimension , wavelet transform crossings ) and finds two or three distinct grb classes . bagoly et al . ( 1997 ) perform principal components and factor analyses of nine bulk property variables using 625 grbs from the batse 3b catalog . they find that the relationships in the database are determined principally by only three variables : an appropriately weighted fluence , a weighted burst duration , and ( to a lesser extent ) flux in the highest energy bin . we note , however , that it can be dangerous to look for correlations prior to classifying ( or establishing the homogeneity of ) the population . while the anticorrelation between hardness ratio and burst duration seen in full samples ( k93 ) may be the manifestation of a single astrophysical process , it may alternatively reflect differences between distinct processes . the latter possibility is suggested by a reported hardness - duration positive correlation within the long - soft class of bursts ( dezalay et al . 1996 ; horack & hakkila 1997 ) . most multivariate analyses thus begin with a study of homogeneity and classification , and then investigate the variance - covariance structure ( i.e. correlations ) within each class . this paper describes a multivariate analysis of grbs from the third batse catalog ( meegan et al . 1996 ) . after defining the sample ( 2 ) , we start with a simple statistical description of the variables and their bivariate relationships for the entire dataset ( 3 ) . we then seek distinct types of clusters in two ways . first , a standard nonparametric agglomerative hierarchical clustering analysis is performed ( 4 ) which reveals three distinct classes . the statistical significance of the third cluster is validated , under gaussian assumptions , with manova tests . second , a parametric maximum likelihood model - based clustering procedure is adopted which reveals the same three groups and indicates strong evidence for the presence for three rather than two groups ( 5 ) . the variance - covariance structure of each group is then examined ( 6 ) . results are synthesized in the discussion ( 7 ) . throughout the paper , we discuss our mathematical techniques to help the reader understand the complexities of multivariate analysis . from the vast literature in this subject , we recommend the following monographs for interested readers : johnson & wichern ( 1992 ) and jobson ( 1992 ) for overviews of applied multivariate analysis ; hartigan ( 1975 ) , jain & dubes ( 1988 ) and kaufman & rousseeuw ( 1990 ) for multivariate clustering algorithms ; murtagh & heck ( 1987 ) and , more briefly , babu & feigelson ( 1996 ) and feigelson & babu ( 1997 ) , for multivariate methodology in astronomy . our sample is drawn from the third catalog of the _ burst and transient source experiment _ ( batse ) on board the compton gamma ray observatory . this 3b catalog has 1122 grbs detected by batse between 1991 april 19 and 1994 september 19 . the catalog is presented and fully described by meegan et al . our database was extracted from the on - line database www.batse.msfc.nasa.gov/data/grb/catalog in may 1996 , which provides many properties of each burst . there are roughly eleven variables of potential astrophysical interest : two measures of location in galactic coordinates , @xmath5 and @xmath6 ; two measures of burst durations , the times within which 50% ( @xmath7 ) and 90% ( @xmath1 ) of the flux arrives ; three peak fluxes @xmath8 , @xmath9 and @xmath10 measured in 64 ms , 256 ms and 1024 ms bins respectively ; and four time - integrated fluences @xmath11-@xmath12 in the 20 - 50 kev , 50 - 100 kev , 100 - 300 kev and @xmath13 kev spectral channels respectively . researchers commonly consider three composite variables : the total fluence , @xmath14 , and two measures of spectral hardness derived from the ratios of channel fluences , @xmath15 and @xmath16 . due to the limitations of available multivariate statistical techniques , we ignore other variables of potential relevance including the heteroscedastic measurement errors of each quantity ( i.e. , errors that differ from point to point ) and truncation values associated with batse triggering operations . of the 1122 listed bursts , 807 have data on all the variables described above . ten bursts listed with zero fluences were eliminated . our sample thus has 797 batse grbs . for some analyses , we also used a subset of 644 bursts with ` debiased ' durations , @xmath17 . here the durations are modified to account for the effect that brighter bursts will have signal above the noise for longer periods than fainter bursts with the same time profiles ( j. norris , private communication ) . statistical analyses in 3 , 4 and 6 were conducted within the statistical analysis system _ sas / stat _ , a very large and widely distributed commercial statistical software package ( sas institute inc . _ sas / stat _ procedures _ cluster _ , _ glm _ , _ princomp _ and _ varclus _ were used . the analysis in 5 was performed with the _ mclust _ software ( banfield & raftery 1993 ; fraley 1998 ) , which is interfaced to the splus statistical package ( splus version 3.4 ; mathsoft , inc . 1996 ) and its extensions . further information is provided at http://stat.washington.edu/fraley/software.html and http://lib.stat.cmu.edu/general/mclust . for multivariate data visualization , we used the xgobi ( swayne , cook & buja 1991 ) program , available from the _ statlib _ software archive at http://lib.stat.cmu.edu/general/xgobi . hypertext links to a variety of public domain software for multivariate analysis , classification and visualization are available at the penn state _ statcodes _ web site , http://www.astro.psu.edu/statcodes . we are faced with a multivariate database of 797 objects and 15 variables ( 11 variables from the catalog , 3 composite variables , and @xmath18 ) . two initial problems are frequently faced in analyses of multivariate databases . first , variables with incompatible units and ranges must be compared . units can be removed by normalization ( e.g. replacing @xmath11 by @xmath19 ) , by standardization ( e.g. replacing @xmath11 by @xmath20 where @xmath21 is the sample standard deviation ) , or by taking logarithms . second , the dimensionality of the problem should be reduced , as many of the variables are closely interrelated either by construction or by astronomical circumstance . although there are no mathematical rules regulating reduction of dimensionality , it can usefully be guided by a correlation matrix showing bivariate relationships and a principal components analysis showing multivariate relationships that are mainly responsible for structured variance in the data . scientific reasoning can also be used to eliminate consideration of variables . we conducted a preliminary examination of data representations , correlation matrices and bivariate plots , and principal components analyses to facilitate choice of variables . when no mathematical preference arose , we selected variables most commonly used by previous researchers to facilitate comparison of results . our choices were as follows . we use log variables , rather than normalized or standardized variables . we kept information on burst fluence and spectra through @xmath22 and hardness ratios rather than through the original fluences @xmath11-@xmath12 . we initially eliminated @xmath8 and @xmath10 from consideration , and later eliminated @xmath9 when we found that its main contribution to the clustering process was noise . we chose to remove the location variables @xmath23 , already established by other researchers to be random for the entire sample , but use them later to test for isotropy of subsamples . the debiased @xmath24" +"graphene , a mono - layer of carbon atoms disposed on an hexagonal lattice was firstly synthesized a decade ago @xcite . however , graphene was not an unknown material , but it was theoretically investigated long time ago by p. r. wallance and others @xcite as a two - dimensional graphite material . the unusual properties of graphene are owing to its dirac - like band structure , where conduction and valence bands touch at six discrete points at the edges of the honeycomb brillouin zone . the relativistic ( dirac ) character of graphene was pointed out by d.p . divincenzo and e.j . mele @xcite before it was created in the lab . in graphene band structure , only two of the six dirac cones are nonequivalent being currently named as k and k points @xcite . the quasiparticle excitations at those points obey linear dirac - like energy dispersion and are responsible for many physical phenomena such as the relativistic quantum hall , the klein tunneling among others @xcite . besides , graphene quasiparticles are chiral fermions with potential applications in the so - called valleytronics @xcite . . for double occupancy the dot level is shifted by an amount @xmath1 that describes the coulomb repulsion . the hybridization @xmath2 depends on energy @xmath3 . we consider undoped graphene electrodes with @xmath4 located at the dirac point . ] one of the successful graphene applications is found when graphene acts as a conductive material attached to a nanostructure to create a single - electron transistor circuitry @xcite . an instance is the particular case of a quantum dot carved in a graphene sheet @xcite . here , typical coulomb blockade phenomenon is observed associated to the transport of charges across the localized dot level @xcite . the linear conductance exhibits peaks at the dot resonances separated by the mean - dot level spacing and electron - electron coulomb repulsion . interestingly , transport of charges in graphene based quantum dots occur at much higher temperatures than in traditional semiconductor dots @xcite . besides , under certain circumstances many - body effects , such as the kondo effect @xcite can be observed @xcite . in reality graphene alters quite strongly kondo physics @xcite . the kondo effect in graphene has been intensively discussed in connection with the magnetic impurity problem in massless dirac fermions . the experimental measurements show that the kondo effect can be induced by lattice vacancies in graphene sheets @xcite . the kondo problem in massless dirac fermion system is indeed a particular case of the pseudo - gap anderson model @xcite where the density of states ( dos ) of conduction electrons is proportional to @xmath5 , with @xmath3 being the energy of conduction electrons and @xmath6 an exponent specific for the material . the massless dirac fermion system corresponds to @xmath7 . there has been a great effort ( theory and experiment ) to describe the kondo effect in dirac - like materials . however , much less attention has received the coulomb blockade regime in which charge fluctuations are the dominant events in transport . coulomb - blockade effects are ubiquitous and govern the transport properties of a large variety of systems : quantum dots @xcite , molecular bridges , carbon nanotubes @xcite , etc . coulomb blockade transport has been investigated extensively in nanostructures attached to metallic contacts . however , when the contacts are made by graphene the coulomb blockade effect is an almost unexplored problem . the goal of this work is to investigate how coulomb blockade effects are altered by the presence of dirac - like fermions . experimentally coulomb blockade oscillations have been reported to occur in graphene quantum dots where the linear conductance oscillates with the dot gate position @xcite . graphene has been revealed as a singular material that exhibits amazing properties in a plenty of fields , namely , electronics , spintronics , optics , etc . a great portion of works has been devoted to the study of its purely electronic properties . in comparison , its thermal properties are poorly investigated . recent measurements show that graphene offers high thermal conductance values @xcite . in this respect , graphene based materials offer new chances to the progress of the cross - field of thermoelectricity . good thermoelectric devices at nanoscale are those where the heat dissipated or wasted is efficiently transformed into useful electricity and vice - versa @xcite . the figure of merit @xmath8 is a coefficient that quantifies the efficiency in the heat - to - electricity ( electricity - to - heat ) conversion process . when the heat is only carried out by electrons then the @xmath8 is proportional to the square of the seebeck ( thermopower ) coefficient or the ratio between the electrical and thermoelectrical linear conductances under the open - circuit condition . the purpose of our work is to analyze the thermoelectric transport through a quantum dot ( or interacting localized level ) coupled to dirac - like electrodes . we are interested in a temperature regime where charge fluctuations are important and therefore we discard the kondo physics . below we develop the theoretical model to describe this system . we will consider the simplest case where different voltages and temperatures are applied across the quantum dot . then , pure electrical , thermal , and cross - conductance responses ( thermoelectric ) are characterized by the electrical ( @xmath9 ) , thermal ( @xmath10 ) , and thermoelectrical ( @xmath11 ) conductances , respectively . our main findings indicate that graphene transistors offer extraordinary high thermoelectrical efficiencies . we report values of @xmath12 . besides , due to the strong energy dependent tunneling rates , graphene interacting quantum dots do not follow the wiedemann - franz law . the paper is organized as follows . in sec . ii , our model for an interacting dot coupled to two dirac - like contacts is introduced . the onsager matrix is computed to describe electrical and heat transports when electrical and thermal biases are applied , and the seebeck and @xmath8 coefficients are defined in addition . since the transport coefficients depend on the dot green s function , it is furthermore calculated employing the equation - of - motion ( eom ) technique @xcite . our results for various transports are thoroughly explained in sec . finally , section iv summarizes the main achievements of this work . we employ an anderson - like model to describe a spin degenerate localized level with strong on - site coulomb interaction which is coupled to two dirac - like electrodes as shown in fig . [ fig:1 ] . the full hamiltonian consists of @xmath13 . the localized level ( dot ) is described by @xmath14 where @xmath15 annihilates ( creates ) an electron with spin @xmath16 in the localized level , @xmath17 denotes the spin - resolved energy level , and @xmath1 represents the strength of the coulomb interaction . here , @xmath18 is the particle number operator for the localized level . the graphene contact hamiltonian reads @xmath19 where @xmath20 is relatively measured with respect to the chemical potential @xmath21 with @xmath22 being the graphene fermi velocity . the chemical potential @xmath21 can be tuned by doping techniques and , hereafter , we consider @xmath4 . we recall that the linear dispersion @xmath23 leads to the linear density of states @xmath24 the hamiltonian then corresponds to the so - called anderson pseudogap model @xcite . here , @xmath25 annihilates ( creates ) a relativistic electron in the contact @xmath26 ( @xmath27 for the left / right contact ) with valley index @xmath28 , wave - vector @xmath29 , and spin @xmath30 . @xmath31 is a cutoff of the momentum such that @xmath32 is the cutoff of the energy . dirac - like quasi - particles are tunnel coupled to the localized level by means of the hybridization hamiltonian @xmath33 where @xmath34 being @xmath35 the area of the graphene unit cell and @xmath36 the tunneling amplitude . in the next step , we compute the transport coefficients by employing the onsager matrix @xcite that connects linearly charge and heat currents with the applied forces , which in our case are the electrical and thermal biases . we aim to investigate such transport coefficients in dirac - like systems when coulomb blockade phenomenon takes place . for such purpose we write down all the onsager matrix elements in terms of the local density of states ( dos ) of the localized impurity . therefore , our description will depend on the approach employed to derive the impurity dos . in the linear response regime , the onsager matrix reads @xmath37 here , @xmath38 and @xmath39 are the charge and heat currents , respectively generated when an electrical bias @xmath40 and a thermal bias @xmath41 are applied to the left and right contacts . for definiteness , we take @xmath42 and @xmath43 where @xmath44 and @xmath45 are the bias and background temperature common to the two graphene flakes . in an explicit manner , the elements of the onsager matrix elements are @xcite @xmath46_{t,\mu } , \\ \mathcal{l}_{12 } & = \frac{e}{ht}\int_{-\infty}^{+\infty } d\varepsilon~ \mathcal{t}(\varepsilon ) ( \varepsilon - \mu ) \left[-\frac{\partial{f(\varepsilon)}}{\partial{\varepsilon } } \right]_{t,\mu } , \\ \mathcal{l}_{22 } & = \frac{1}{ht}\int_{-\infty}^{+\infty } d\varepsilon~ \mathcal{t}(\varepsilon ) ( \varepsilon - \mu)^2 \left[-\frac{\partial{f(\varepsilon)}}{\partial{\varepsilon } } \right]_{t,\mu},\end{aligned}\ ] ] where @xmath47 is the transmission probability . the onsager s coefficients ( @xmath48 ) are now connected to the linear electrical ( @xmath9 ) , thermal ( @xmath10 ) , and thermoelectrical ( @xmath11 ) conductances as @xmath49 it is worthy to define the seebeck coefficient or themopower in terms of the onsager transport coefficients . the seebeck coefficient reads @xmath50 an important remark here is in order . note that for sufficient low temperatures the thermal conductance is dominated by the electronic contribution and therefore we can neglect the phonon contribution . the efficiency of the heat - to - electricity ( or vice - versa ) conversion processes is measured by the figure of merit @xmath8 @xmath51 all transport coefficients are expressed in terms of the transmission coefficient @xmath47 @xmath52 where @xmath53 with @xmath54 ( here , @xmath55 ) . @xmath56 denotes the local dos for the interacting level which can be found as @xmath57 @xmath58 is the retarded green function for the interacting localized level . in the following , we derive a green s function suitable for the coulomb blockade regime . to attain such a goal , we employ the eom technique @xcite followed by a decoupling procedure ( see below ) . we mention that kondo correlation is not included in our decoupling scheme . however , our approach yields an excellent characterization of the transport properties of strongly interacting quantum dots for temperatures larger than the kondo temperature or when the localized level is weakly coupled to the electrodes @xcite . besides , it is known that for zero doped graphene kondo effect is never built . a retarded green s function @xmath59 for fermionic operators @xmath60 and @xmath61 is defined as @xmath62 whose eom in energy space takes the following form @xmath63,b\right>\hspace{-2.3pt}\right>_{\hspace{-2pt}\varepsilon}^{\hspace{-2pt}r } } = \langle\{a , b\}\rangle,\ ] ] with @xmath64 being the hamiltonian under consideration and @xmath65 . for the dot green s function @xmath66 , it is easy to show that @xmath67 the equation for @xmath68 is found to be @xmath69 such that the dot green s function becomes @xmath70 where @xmath71 is the self - energy due to the hybridization between graphene contacts and localized level . the self - energy is evaluated as @xmath72\ ] ] where @xmath73 . in order to get the coulomb blockade solution , we need to calculate the eom for @xmath74 . it is given by @xmath75 \,.\end{gathered}\ ] ] we keep only the correlation @xmath76 on the right" +"spin - charge separation and interaction dependent power laws of correlation functions have been known as non - fermi - liquid behavior of tomonaga - luttinger ( tl ) liquid , which is expected to describe the low energy physics of one dimensional ( 1d ) interacting electron systems @xcite . in the past ten years , experimental evidences for the realization of tl states have been reported in many systems such as carbon nanotube devices @xcite , quantum wires in semiconductor heterostructures @xcite and fractional quantum hall systems @xcite , as predicted by theories . the power law temperature dependencies of the tunneling density of states @xcite , and the bulk spectral density near the fermi level @xcite have been the key signatures of tl states in these experiments . on the other hand , there are only a few experiments on the direct observation of spin - charge separation @xcite . in order to obtain such low energy spectral profiles , we need to resolve local density of states at long distances from a scatterer or a boundary edge , by scanning tunneling microscope ( stm ) @xcite , which seems rather difficult to obtain high resolution data . instead , experiments on resonant tunneling @xcite seems to be a more suitable procedure to detect the spin - charge separation , since they probes the energy level spacings in the quantum island . the resonant tunneling in tl liquid has been studied for more than a decade since kane and fisher s work @xcite . the charge transport is a main focus on those works . meanwhile , the spin transport in presence of external magnetic field , which is closely linked to detecting spin - charge separation , has not been studied enough . there are some theoretical works concerned with this issue @xcite . they consider the quantum wire forms the quantum dot between ferromagnetic contacts . there the spin and the charge transport can be controlled by the relative angle between the magnetization orientations of the ferromagnets @xcite . in their results , the qualitative change due to the spin - charge separation can be seen . however , the quantitative determination of the spin - charge separation in the excitation spectrum remains difficult . in this paper , we consider the resonant tunneling through double impurities in a spinful tl liquid under magnetic fields . a schematic picture of the system is shown in fig.[fig : system ] ; a strong field @xmath3 is applied to the entire one - dimensional system . the charge and the spin in the region between double impurities are changed by a gate voltage @xmath0 and a weak field @xmath1 , respectively . applying a strong magnetic field breaks the spin rotational symmetry and violate spin - charge separation in the spectral peaks @xcite , due to the fermi velocity differences between two spins . as a result , the spin and the charge sector mix with each other @xcite . it is shown that the spin - charge mixing effects can clearly be seen in the resonant oscillation patterns of zero bias conductance in @xmath4 plane . the spin dependent scaling behavior of a single impurity potential , due to zeeman effect , has been discussed by previous works @xcite . we also discuss a spin - charge mixing effects on the impurity scaling in the resonant tunneling . zero bias conductance is calculated by standard bosonization technique @xcite as a function of a gate voltage , gate magnetic field , temperature @xmath5 and the strong magnetic field . the impurity potential @xmath6 is assumed to be either very weak ( @xmath7 ) or very strong ( @xmath8 ) . when @xmath9 , changing the gate voltage does affect the spin density together with the charge density due to the spin - charge mixing , leading to noticeable deformation in the lattice pattern of the conductance peaks @xcite . moreover contour shapes at low temperatures are divided into three types , depending on the bulk parameters such as @xmath3 , interaction parameters @xmath10 , where the impurity potentials are scaled towards perfect reflection "" , `` perfect transmission '' and magnetic field induced `` spin - filtering '' , respectively . these three behaviors are explained by a renormalization group ( rg ) analysis of a single impurity potential in spin - charge mixed systems . we consider a system illustrated in fig.[fig : system ] . schematic figure of spin polarized tomonaga - luttinger liquid with two impurities under magnetic field . , width=295,height=108 ] an infinite tl liquid , under a strong magnetic field @xmath11 perpendicular to the wire , has two impurities ( or barriers ) of the strength @xmath12 at @xmath13 . hereafter we take the spin quantization axis in the direction of @xmath11 , and denote the strength of @xmath11 by @xmath14 . @xmath15 and @xmath16 are set to unity in this paper . zeeman effect due to @xmath3 is incorporated into hamiltonian as the difference in fermi velocity between two spin species . for simplicity , we take into account the zeeman effect only on spins with neglecting the orbital effects . this is allowed when the magnetic length @xmath17 is longer than a width of the tl wire , as discussed in @xcite . in the effective mass approximation @xmath18 , the velocity difference is given by , @xmath19 for not too strong fields , @xmath20 is approximately linear in @xmath3 . for simplicity , we set @xmath21 , where the sign @xmath22 represents up ( down ) spin . we shall call the region @xmath23 an island . in the island , chemical potential of spin @xmath24 electrons can be controlled by gate voltage @xmath25 and gate magnetic field @xmath26 ; @xmath27 . we consider the situation where zeeman energies due to strong magnetic field @xmath3 and due to gate magnetic field @xmath1 are , respectively , on the order of fermi energy and energy level spacing in the island ; _ i.e. _ @xmath28 . then the fermi velocity change due to @xmath1 can be neglected . hamiltonian of the system consists of four parts , @xmath29 where @xmath30 and @xmath31 are the hamiltonian for free electrons , two - body interaction , electrons on the island and barrier potential , respectively . they are given in terms of fermion field operator , [ eq : whole ] @xmath32 , \\ & & h_{\rm int}=\frac{1}{2 } \sum_{\sigma,\sigma ' } \int dxdy \ n_{\sigma}(x ) { \mathcal u}_{\sigma,\sigma'}(x - y ) n_{\sigma'}(y ) , \qquad \\ & & h_{{\rm island}}= -ev_{\rm g } \sum_{\sigma } \int_{-d}^{d } dx \ n_{\sigma } \nonumber \\ & & \qquad \quad + \int_{-d}^{d } dx \ \frac{1}{2 } g \mu_{b } \overrightarrow{b_{\rm g } } \cdot ( \psi_{\alpha}^{\dagger } \vec{\sigma}_{\alpha,\beta}\psi_{\beta } ) , \label{h - island } \\ & & h_{{\rm b}}= v \sum_{\sigma } \ \left [ n_{\sigma}(-d ) + n_{\sigma}(d ) \right ] , \label{h - barriers}\end{aligned}\ ] ] where @xmath33 and @xmath34 are annihilation operator and density operator for electrons with spin @xmath35 . we neglect the charging energy of the island ( @xmath36 in @xcite ) , which can be incorporated into @xmath37 . @xmath38 are written in terms of bosonic phase fields @xcite , [ eq : whole ] @xmath39 \nonumber \\ & & \qquad \qquad + \pi \delta \int dx \left [ ( \frac{1}{\pi}\partial_{x } \phi_{\rho})(\frac{1}{\pi}\partial_{x } \phi_{s})+ \pi_{\rho}\pi_{s } \right ] , \qquad \label{hamiltonian before diagonalized}\end{aligned}\ ] ] here , @xmath40 is the inverse of the fermi wave number : @xmath41 and @xmath42 are conjugate pairs of bosonic field with commutation relations @xmath43=i \delta_{i , j } \delta(x - x')$ ] , where @xmath44 @xmath45 represent for charge ( spin ) variables . to diagonalize @xmath38 , we use the linear transformation @xcite ( see also appendix b for the expression in ladder operators of tl bosons ) @xmath46 commutation relations are preserved under this transformation @xmath47=i \delta_{i , j } \delta(x - x')$ ] . parameters @xmath48 and @xmath49 are , respectively , a rotation angle and a scale factor in `` spin - charge space '' given by , @xmath50 the rotation angle @xmath48 is proportional to @xmath20 , and thus to @xmath3 , for small @xmath20 . after the transformation , @xmath51 becomes , @xmath52 . \label{tl hamiltonian}\end{aligned}\ ] ] the expression of @xmath53 and @xmath54 are given in appendix a. as discussed in @xcite , in a polarized tl liquid , the scaling dimensions of a single impurity potential split between two spins . renormalization group equations for small backscattering amplitude @xmath55 and small tunneling amplitude @xmath56 are given @xmath57 with @xmath58 and an initial ( running ) energy cutoff @xmath59 ( @xmath60 ) . the scaling dimensions @xmath61 and @xmath62 are given @xmath63 where @xmath64 , @xmath65 , @xmath66 , and @xmath67 . thus the ratio of reflection amplitudes and tunneling amplitudes scale like , respectively , @xmath68 and @xmath69 . the difference of the exponents @xmath70 and @xmath71 are given @xmath72 this expression tells us that the split of the scaling dimensions between two spins become large when the spin - charge mixing angle is large . due to the split of exponents , we expect the spin current with large polarization @xmath73 at low temperature in the strong barrier limit . this scaling effect with the exponents @xmath61 and @xmath62 also appears in the conductance for double barrier structure . we consider first the weak barrier limit @xmath74 , where the electron transfer is due to the coherent tunneling of the spin - charge mixed density wave . the zero bias conductance is calculated perturbatively with respect to the small barrier potential @xmath75 . the hamiltonian for the island and for the barriers in eq.([h - island ] ) and eq.([h - barriers ] ) are written in terms of the bosonic phase at @xmath13 , @xmath76 @xmath77 is the linear combination of phases at @xmath13 . according to our assumption that the magnetic field @xmath3 is strong enough that @xmath78 , only @xmath79-component of @xmath80 remains after the integration of ( [ h - island ] ) with neglecting the fast oscillating terms . hereafter , we denote @xmath81 by @xmath1 . to make calculations easier , it is helpful to construct an effective action @xcite obtained by integrating out the tl field except for the positions of the barriers @xmath13 , since charge ( spin ) current through barriers depends only on the local variables , @xmath82 . the integrated effective action is calculated as , @xmath83 , \\ & & \tilde{\epsilon}_{i}^{\pm}(\omega_{n } ) = \frac{1}{\pi \tilde{k}_{i}}\frac{| \omega_{n}|}{1 \pm \exp \{-(2d/\tilde{v}_{i})|\omega_{n}| \}}. \end{aligned}\ ] ] here we have defined new variables @xmath84 . @xmath85 and @xmath86 relates each other by the same linear transformation between @xmath87 and @xmath88 . we will calculate zero bias conductance for charge ( spin ) current following kubo formula , @xmath89 where analytic continuation is to be taken before taking the limit . the effective action @xmath90 is used for taking thermal average such that @xmath91 hamiltonian for the island @xmath92 is given after canonical transformation ( [ linear transform ] ) as @xmath93 with the coefficients , @xmath94 thus , the terms other than barrier potentials , quadratic in @xmath95 , can be treated exactly in @xmath90 . after straightforward calculation , we obtain an explicit form of the conductance to the second order in @xmath75 ; @xmath96 for @xmath97 . the unperturbed conductance @xmath98 and @xmath99 are @xcite , @xmath100 this expression implies that spin polarized current can flow in a clean , infinite tl liquid due to spin - charge mixing effect , since @xmath101 when @xmath102 for all interaction parameters . however , such a violation of the conductance quantization is shown to be an artifact for infinite system as previous works pointed out for unpolarized system @xcite" +"in a head - on elastic collision of two identical objects , the momenta of the two participants are exchanged in any reference frame . @xcite in a fixed - target frame , the target acquires the energy and momentum of the incident object that makes a complete stop . such a complete energy - momentum transfer is hardly observed in many - body collisions . an interesting example is the newton s cradle which consists of a series of identical pendula that are aligned along a straight line on a horizontal level . however , this can actually be understood as a series of head - on collisions of two identical objects where small gaps between each pair of adjacent pendula are assumed . @xcite although this small - gap model explains the observations , this model fails if some of adjacent pendula are in contact with each other so that the process can not be decomposed into a series of two - body collisions . the reason for this failure is that the conservation laws of energy and momentum are not enough to determine the final velocities . additional conditions such as force laws between objects are required to have a unique solution of the problem . various studies have been carried out to find an appropriate force laws governing the actual motions of the pendula . a phenomenological model is so called the contact hertz force of the form @xmath5 . @xcite further applications of the contact hertz force to various collision problems can be found in refs . @xcite in a recent work , we have studied the bouncing of a block against a rigid wall through one - dimensional multiple elastic collisions with a ball sandwiched by them . @xcite like the small - gap model , we assumed that each collision is instantaneous and the complete trajectories of the block and the ball were uniquely determined analytically . by taking the continuum limit of the exact analytic solution of the block trajectory , we have shown that the effective force carried by the ball is proportional to @xmath6 , where @xmath7 is the distance between the block and the wall . this is consistent with previous results based on the differential equation that can be derived by taking the continuum limit of the energy - momentum conservation . @xcite in this paper , we generalize the model system of ref . @xcite to a simple three - body system : we consider the scattering of two identical blocks of mass @xmath0 through multiple elastic collisions with a ball of mass @xmath1 sandwiched by the blocks . as shown in fig . [ fig : system ] , the ball @xmath8 and the target block @xmath9 are initially placed at @xmath10 and @xmath2 , respectively , and the block @xmath11 is incident to the target with the initial velocity @xmath12 . while we were interested in the trajectories of the objects and the effective force in ref.@xcite , we focus on the energy - momentum transfer from the incident block @xmath11 to the scattered block @xmath9 . if @xmath3 , then the system experiences multiple collisions that can be understood as a series of two - body collisions and , therefore , the velocities of all participants are uniquely determined . as a result , we find all possible values for _ the magic mass ratios _ @xmath13 at which the energy and momentum of the incident block are completely transferred to the scattered block . the chain collisions of multiple pendula in series have been studied previously by hart _ _ @xcite and by kerwin . @xcite however , the pendula studied in these references are arranged in mass order so that the complete energy - momentum transfer from the incident pendulum to the target pendulum at the other end is achieved only if all of the pendula are of equal mass like the newton s cradle . redner considered a similar system consisting of two identical cannonballs approaching an initially stationary ping - pong ball . @xcite in that reference , the author mainly focused on deriving a simple relation between that elastic collision and a corresponding billiard system , which helps to obtain the total number of collisions of the system easily . thus , to our best knowledge , the derivation of all possible magic mass ratios @xmath14 at which complete energy - momentum transfer is realized in one - dimensional three - body elastic collisions is new . this paper is organized as follows . in sec . [ sec : model ] , we describe the model system and provide the definitions of kinematic variables that we use throughout this paper . in sec . [ sec : v ] , we construct recurrence relations for the velocity sequences of participants and solve them to determine the velocity of each object after each collision . we also compute the total number of collisions for each participant and obtain critical values for the mass ratio @xmath4 at which the number of collisions of each object changes . in sec . [ sec : transfer ] , we provide the verification that at the magic mass ratio @xmath13 the energy and momentum of the incident block are completely transferred to the scattered block . we also show that at the defective mass ratio @xmath15 , the energy and momentum transfer rates reach their local minima . finally , we conclude in sec . [ sec : concl ] . in this section , we describe the model system and define kinematic variables that we use throughout this paper . as shown in fig . [ fig : system ] , the model system consists of two identical blocks @xmath11 and @xmath9 with mass @xmath0 and a ball @xmath8 with mass @xmath1 , where @xmath3 , aligned on the @xmath7 axis . initially , @xmath8 and @xmath9 are placed at rest at @xmath10 and @xmath2 , respectively . at time @xmath16 , block @xmath11 with velocity @xmath17 hits the ball on the left . then @xmath11 and @xmath9 exchange momenta through multiple collisions with @xmath8 . we assume all of the collisions are elastic and ignore friction . we denote by @xmath18 ( @xmath19 ) the @xmath20th collision point between @xmath11 ( @xmath9 ) and @xmath8 . the velocities of the three participants are defined as follows : we denote @xmath21 ( @xmath22 ) and @xmath23 ( @xmath24 ) by the velocities of block @xmath11 ( @xmath9 ) and the ball , respectively , right after the collision at @xmath18 ( @xmath19 ) . during the ball s motion from @xmath18 to @xmath19 , the velocity of @xmath8 is fixed as @xmath23 . between @xmath19 and @xmath25 , the velocity of @xmath8 is @xmath26 . it is convenient to define the column - vector sequence @xmath27 as @xmath28 where the scaling factor @xmath29 of the third component of @xmath27 is introduced to simplify the following analyses . the initial condition is given by @xmath30 in this section , we find the general terms of the velocity sequences @xmath21 , @xmath22 , @xmath23 , and @xmath24 that are defined in sec . [ sec : model ] , by solving the recurrence relations that are constructed from the conservation of energy and momentum . by making use of these analytic solutions , we calculate the total number of collisions of each participant , and obtain the critical values of @xmath4 at which the number of collisions of the each object changes . at the end of this section , we find the expressions of the terminal velocities of the participants . the collision at @xmath18 transforms the velocities @xmath31 and @xmath32 into @xmath21 and @xmath23 , respectively . the collision at @xmath19 transforms the velocities @xmath33 and @xmath34 into @xmath22 and @xmath24 , respectively . the conservation of linear momentum and kinetic energy in the collisions at @xmath18 and @xmath19 requires [ eq : conservation ] @xmath35 ^ 2&=&a_n^2+[\sqrt{\alpha } c_n]^2 , \\ b_{n-1}+\alpha c_{n}&=&b_n+\alpha c^{\,\prime}_n , \\ \label{eq : euc - qn } b^2_{n-1}+[\sqrt{\alpha } c_{n}]^2&= & b_n^2+[\sqrt{\alpha } c^{\,\prime}_{n}]^2 . \ ] ] these constraints derive the following recurrence relations : [ eq : recur2d ] @xmath36 where the @xmath37 matrix @xmath38 , which is independent of @xmath20 , is defined by @xmath39 according to eqs . ( [ eq : euc - pn ] ) and ( [ eq : euc - qn ] ) , we find that the transformation matrix @xmath38 does not change the norms of vectors . therefore , the matrix @xmath38 can be parametrized by the product of a rotation matrix @xmath40 and a reflection matrix @xmath41 : @xmath42 where @xmath40 and @xmath41 are defined by [ eq : lambda - p ] @xmath43 because @xmath44=1 $ ] and @xmath45=-1 $ ] , @xmath46=-1 $ ] . here , the parameter @xmath47 is fixed by the mass ratio @xmath48 : @xmath49 because we restrict ourselves to the case @xmath50 , the range of @xmath47 is @xmath51 . @xcite for a small @xmath4 , @xmath52 . in the first two rows of table [ table : trig ] , we list the values for trigonometric functions at @xmath47 and @xmath53 , that are particularly useful in our analysis . by making use of eqs . ( [ eq : recur2d ] ) and ( [ def : gamma ] ) , we can find the recurrence relation for the three - dimensional - euclidean - vector sequence @xmath27 of the form @xmath54 then we can determine the general term for @xmath27 in terms of the initial value @xmath55 in eq . ( [ def : v0 ] ) as @xmath56 next we find the matrix representation of the matrix @xmath57 in eqs . ( [ eq : v - n ] ) and ( [ eq : v - n-0 ] ) . we first verify that the matrix @xmath57 is a @xmath58 matrix for a pure rotation of the three - dimensional euclidean vector . we combine the two relations in eq . ( [ eq : recur2d ] ) to express @xmath57 as a product @xmath59 where @xmath60 and @xmath61 are the matrices that transform the velocities at @xmath18 and @xmath19 , respectively : @xmath62 where @xmath47 is defined in eq . ( [ def : theta ] ) and @xmath63 is the rotation matrix about the axis @xmath64 by an angle @xmath47 and @xmath65 is the matrix that reflects the third component . then the explicit form of the matrix @xmath57 is @xmath66 because @xmath67=1 $ ] and @xmath68=-1 $ ] , @xmath69=\textrm{det}[\gamma_b]=-1 $ ] and @xmath70=1 $ ] . in addition , @xmath57 is orthogonal : @xmath71 . therefore , @xmath57 is a pure rotation matrix . in this section , we derive the analytic expression for the matrix @xmath73 that is necessary in computing @xmath27 in eq . ( [ eq : v - n-0 ] ) . because @xmath57 is a matrix for a pure rotation in the three - dimensional euclidean space , there exists a cartesian coordinate system in which the rotation is about @xmath74 by an angle @xmath75 , where @xmath76 is the unit vector along the @xmath64th axis in the new coordinate system . @xmath77 in the new coordinate system , @xmath78 can be expressed as a single rotation about @xmath74 by an angle @xmath79 : @xmath80 then the matrix @xmath57 can be expressed as @xmath81 where @xmath82 , which is orthogonal : @xmath83 . by generalizing the method in ref . @xcite for two dimensions into three dimensions , we can determine the transformation matrix @xmath84 . because @xmath74 is invariant under rotation @xmath57 , we have @xmath85 the solution for this constraint equation is @xmath86 . choosing the remaining two bases for the cartesian coordinate system as @xmath87 and @xmath88 , we determine the" +"early hydrogen reionization is a particularly interesting process in the high redshift universe and is inevitably linked to the appearance of the first star forming objects , at least those that served as sources of the ionizing radiation . if it occurred early enough , reionization imprints distinct features in maps of the cosmic microwave background ( cmb ) on arcminute angular scales @xcite . several aspects of hydrogen reionization remain uncertain despite the rapidly accumulating data on the high redshift universe . for example , it is unclear what objects produce most of the ionizing radiation , although high redshift galaxies are very strong candidates @xcite . it is also unclear how the ionized regions develop in space @xcite . the ionizing sources are likely to lie in high density regions , but those regions do not necessarily ionize first ; the ionizing photons may tunnel into less dense regions and ionize those first . further , the duration of reionization is unknown and only a lower limit on the redshift marking the end of that epoch exists @xcite . in previous papers ( benson et al . 2001 , liu et al . 2001 ) we examined how the cmb is affected by the reionization process and how future cmb maps can be used to extract information on that process . however , hydrogen reionization is currently best probed by spectra of high redshift qsos . unlike maps of the cmb which are sensitive to line of sight integrals over the density and velocity of ionized gas , qso spectra contain direct information on the local distribution of neutral hydrogen . recently , becker et al . ( 2001 ) analyzed spectra of a sample of qsos with redshifts between @xmath0 and @xmath1 . in the spectrum of their highest redshift qso ( @xmath1 ) , the transmitted flux in the ly@xmath2 and ly@xmath3 forest in the redshift stretch @xmath4 is consistent with zero , with a lower limit of 20 on the ly@xmath2 optical depth . this long stretch in redshift corresponds to a comoving distance of @xmath5 in a universe with a cosmological constant of @xmath6 and matter density of @xmath7 . becker et al . suggest that this long neutral region is a detection of the end of the hydrogen reionization era . to increase the signal - to - noise ratio , becker et al . binned their spectra in @xmath8 pixels . this prevented them from detecting small scale dark windows that are likely to appear in the spectra as left overs from the reionization epoch . a high resolution spectrum for one of the quasars observed by becker et al . was obtained by djorgovski et al . the spectrum of this quasar ( @xmath9 ) was thorough analyzed by djorgovski et al . ( 2001 ) and was found to contain several small dark windows signifying the detection of the trailing edge of the reionization epoch . motivated by the results of becker et al . ( 2001 ) and djorgovski et al . ( 2001 ) , we examine here how the key ingredients in the reionization process can be probed by qso spectra and future high redshift galaxy surveys . the methodology of the present paper has been previously developed in benson et al . ( 2001 , hereafter bnsl ) . as in bnsl , we obtain the distribution of ionized gas in an n - body simulation . using a semi - analytic model for galaxy formation @xcite we identify mock galaxies in the simulation and estimate the ionizing flux emitted by stars at high redshift . we then use several schemes to follow the development of ionized regions in the simulation . using the output of this procedure we obtain predictions for two statistics . the first is the expected number of neutral segments longer than a given length , and the second is the cross - correlation function between the galaxies and neutral regions . both of these measures rely on observations of qso spectra , and the latter also on a sample of high redshift candidates for the sources of ionizing radiation . bnsl employed a semi - analytical model for galaxy formation in a high resolution n - body simulation of dark matter to estimate the amount of ionizing radiation produced by stars in high redshift galaxies . here we follow a similar procedure using the latest version of the galform galaxy formation model @xcite , and the same @xmath10cdm simulation as bnsl ( c.f . jenkins et al . 1998 ) . this simulation has @xmath11 , a cosmological constant @xmath12 , a hubble constant of @xmath13 in units of @xmath14 , and is normalized to produce the observed abundance of rich clusters at @xmath15 according to eke , cole & frenk ( 1996 ) . the simulation has a box of length 141.3 @xmath16 and contains @xmath17 dark matter particles . most of the ionizing photons emitted by stars are likely to be absorbed by gas and dust inside galaxies and only a small fraction , @xmath18 , escapes and becomes available for hydrogen ionization in the intergalactic medium ( igm ) @xcite . assuming a value from galaxy to galaxy . here we adopt the simplest model , in which @xmath19 is constant for all galaxies . ] for @xmath18 , bnsl used the following models to follow the propagation of ionized regions in the simulation ( see bsnl for details ) . _ model a ( growing front model ) _ ionize a spherical volume around each source ( halo ) with a radius equal to the ionization front radius for that halo assuming a large - scale uniform distribution of neutral hydrogen . since the neutral hydrogen in the simulation is not uniformly distributed , and also because some spheres will overlap , the ionized volume will not contain the correct total mass of hydrogen . we therefore scale the radius of each sphere by a constant factor and keep repeating the procedure until the correct total mass has been ionized . _ model b ( high density model ) _ we simply rank the cells in the simulation volume by their density . we then completely ionize the gas in the densest cell . if this has not ionized enough hydrogen we ionize the second densest cell . this process is repeated until the correct total mass of hydrogen has been ionized . _ model c ( low density model ) _ as model b , but we begin by ionizing the least dense cell , and work our way up to cells of greater and greater density @xcite . _ model d ( random spheres model ) _ as model a but the spheres are placed in the simulation entirely at random rather than on the dark matter halos . _ model e ( boundary model ) _ ionize a spherical region around each halo with a radius equal to the ionization front radius for that halo . this may ionize too much or not enough neutral hydrogen depending on the density of gas around each source . we therefore begin adding or removing cells at random from the boundaries of the already ionized regions until the required mass is ionized . guided by the observations of becker et al . ( 2001 ) we will compute the number of neutral segments and the cross correlations at three output redshifts , @xmath20 , @xmath21 , and @xmath22 . table 1 lists the volume filling factors ( ratio of volume of ionized regions to total volume of the simulation box ) in each of our five models for @xmath23 ( column 2 in table 1 ) and @xmath24 ( column 3 ) . we will see later that the results of becker et al . imply that the amount of ionizing radiation increases significantly between @xmath25 and @xmath26 . therefore we also show results for a variable escape fraction,@xmath27 ( column 4 ) which equals @xmath28 before @xmath29 and increases linearly with time to @xmath30 at @xmath31 . as expected , model c ( low density model ) has the highest filling factor for a given @xmath18 . the simulation box is fully ionized at @xmath31 in all models . .the volume filling factor of ionized regions in the simulation at @xmath32 , 6.22 , and 5.80 , for two constant values of @xmath18 ( columns 3 and 4 ) , and a variable fraction @xmath27 ( column 4 ) that increases linearly with time from 0.01 at @xmath29 to 0.1 at @xmath33 . [ cols=""<,^,^,^ "" , ] [ table1 ] we are now in a position to compute the proposed statistics . we begin with @xmath34 , the mean number of neutral ( unionized ) segments of length greater than @xmath35 in a given redshift range in a line of sight ( see barkana 2002 , for a similar statistic ) . we have the spatial distribution of ionized and neutral regions in the simulation as a function of redshift , for each of our five reionization scenarios ( see table 1 ) . to compute @xmath34 we choose several random `` lines of sight '' in the output of the simulation at a given redshift . in each line of sight we identify the neutral segments and tabulate their lengths , @xmath35 , in comoving @xmath36 . a line of sight is obtained by starting from a grid point at the boundary of the simulation and going around the boundary of a rectangular slice of perimeter @xmath37 ( comoving ) until we return to the starting point . ( the shape of the path used to extract a line of sight makes no difference to our results . using a rectangular path helps reduce the chance of pattern repetition . ) this yields a total of @xmath38 lines of sight each spanning a redshift range corresponding to @xmath39 ( comoving ) . we then compute the mean @xmath34 from these lines of sight . for convenience we normalize @xmath34 to a redshift span of @xmath40 by multiplying the direct result obtained from the simulation by @xmath41 . the @xmath34 ( normalized to @xmath42 ) is shown in figure ( [ figure1 ] ) for @xmath32 ( top ) , 6.22 ( middle ) , and 5.8 ( bottom ) . the panels to the left show @xmath34 computed for @xmath23 , at these three redshifts . to the right we show curves computed with @xmath24 at @xmath32 ( top ) and @xmath21 ( middle ) , and a variable @xmath27 at @xmath31 ( bottom ) . we have also computed @xmath34 from lines of sight each of length @xmath43 passing through in the simulation box at random positions and found very similar results to those shown in the figure . in observed spectra ionized regions with large optical depths can be confused with completely unionized regions , and vice versa . by measuring ly@xmath3 absorption lower limits of about 20 on the ly@xmath2 optical depth can be obtained . in cdm - like models ionized regions with optical depth larger than this lower limit are small . a careful analysis and modeling of spectra can therefore help reduce this confusion . nevertheless to estimate the degree of the confusion , we have computed @xmath34 assuming that regions with optical depth larger than 20 are identified as unionizeds@xmath44 . the ly@xmath2 line - width and effects of peculiar velocities were also taken into account . ] . we found that in this more detailed calculation @xmath34 is shifted to smaller @xmath35 by less than a factor of 2 at large @xmath35 . at small @xmath35 , @xmath34 is reduced by a factor of less than 2 , although this could likely be reduced with a more careful analysis as suggested above . the cells of" +"the sample is composed of 70 archival _ hubble space telescope _ ( _ hst _ ) images of low - redshift qsos . they have redshifts between @xmath2 and total ( host plus nucleus ) absolute magnitudes brighter than @xmath3 . furthermore , they must have been observed with the _ hst _ s wide - field planetary camera 2 ( wfpc2 ) , using broad - band filters , and have images publicly available in the _ hst _ archives as of 1999 . this brings our sample to 70 qsos . rather than restrict our study to a specific class of qsos , we impose no physical criteria on the qsos beyond those of magnitude and redshift . thus we are able to study a broad range of properties and draw general conclusions . the images are reduced and the physical parameters fitted as described by hamilton et al . for our principal components analysis ( pca ) , we use a restricted sample of those qsos for which we have all of the following parameters : @xmath4 , @xmath5 , @xmath6 , and @xmath7 , where @xmath7 is the effective surface magnitude of the galactic bulge . we further require that each qso have a modeled , spheroidal bulge ( the entire galaxy , in the case of elliptical hosts ) . these qualifications restrict the sample to 42 qsos . we can perform two pcas , an optical one using @xmath4 , @xmath8 , and @xmath7 as the parameters , and an x - ray one that substitutes @xmath9 for the nuclear luminosity . from the optical pca performed on this sample of 42 objects , we find that 96.1% of the variance can be explained with just the first two principal axes , and therefore the qsos mostly lie in a plane within this parameter space . this we consider to be a fundamental plane ( fp ) for qsos . for the corresponding x - ray results , the first two principal axes explain 95.2% of the variance in the sample , and we find here an x - ray qso fundamental plane . the individual subsamples of qsos ( radio - loud or radio - quiet , with spiral or elliptical hosts , and all combinations of these ) are also examined in this way , and they show fundamental planes , as well . we obtain the optical and x - ray formulae for the full sample s fundamental plane : @xmath10 @xmath11 views of the optical and x - ray fundamental planes , with the qso data points superimposed , are displayed in figure [ fig : fp - phys ] . note that the host properties describe the horizontal and the nuclear luminosity the vertical in these plots . figure [ fig : fp - rms ] illustrates the precision of the qso fundamental plane in both forms , with the plane plotted against the measured host sizes . its highest precision is found when solving for @xmath8 . the fundamental plane for qsos shows a relationship between the nuclear and host features that goes beyond the simple ( and weak ) correlation of nuclear and host luminosities . this behavior may be connected to other , known relations between the objects . for example , there is already a well - studied fundamental plane for normal , elliptical galaxies ( djorgovski & davis 1987 ; dressler et al . 1987 ) that incorporates galaxy size , @xmath6 , central velocity dispersion , @xmath12 , and effective surface magnitude , @xmath7 . let us take a @xmath13-band measurement of the normal galaxy fundamental plane ( scodeggio et al . 1998 ) , @xmath14 . the ratio of the coefficients of @xmath8 to @xmath7 differs by about 37% between the qso optical fundamental plane and the normal galaxy fp , and the qso x - ray fp shows a 34% difference . still , there is a formal similarity between the qso and normal fundamental planes , which might point to a link between the host galaxy s central velocity dispersion and the nuclear luminosity of the qso . this could derive from the fueling mechanism of qsos , if the movement of gas to the center of the galaxy and the black hole is related to the velocity dispersion . it is therefore tempting to try to derive the qso fundamental plane directly from the elliptical galaxy fundamental plane , but we find two problems with this approach , both arising from the relation of black hole mass to nuclear luminosity . using the velocity dispersion to black hole mass relation of merritt & ferrarese ( 2001 ) , @xmath15 we can put the elliptical galaxy fundamental plane in terms of black hole mass . using the observed ( but weak ) correlation between black hole mass and nuclear luminosity in our sample , @xmath16 and @xmath17 , we obtain @xmath18 @xmath19 these are our attempts to derive the qso optical fundamental plane from the normal galaxy fp . the optical form differs from the actual qso fp , equation ( [ equ : oall - physical ] ) , completely outside the propagated errors , but the x - ray form is within the errors of equation ( [ equ : xall - physical ] ) . but any derivation of the qso fundamental plane has an additional problem . as mentioned before , the qso fundamental plane for the full sample is composed of individual fps of the several subsamples . some subsample fps actually slope in the opposite direction from the overall qso fp . for example , in the optical form , the fp of radio - quiets in elliptical hosts slopes in the opposite direction . and in the x - ray form , the radio - quiet subsamples slope oppositely from the overall sample . yet these differences can not be accounted for by different correlations of nuclear luminosity with black hole mass . the poor correlation of black hole mass with nuclear luminosity lies in contrast with the relatively thin qso fundamental plane . furthermore , woo & urry ( 2002 ) suggest that the apparent correlations between black hole mass and nuclear luminosity are merely artifacts of sample selection . regardless of how we take this interpretation , the relationship between black hole mass and nuclear luminosity remains the missing link in any derivation of the qso fundamental plane . the insight into the origins of this new fundamental plane relationship might come from the comparison of the qso subsample fps . the thickness of the overall qso fundamental plane appears partly to be the result of the superposition of the subsamples planes . because the qso fp mathematically describes a link between the host and the nucleus , it seems reasonable to suppose that the slope of the plane depends on the physical nature of this link . the fueling mechanism at a qso s core would seem to be the most directly related to this , depending on how we define `` fueling mechanism . '' we could encompass within this term the details of the structure and dynamics of the accretion disk , as well as question of whether the qso is efficiently or inefficiently fueled . it is intriguing that as we change from one class to another , the fundamental plane essentially pivots about an axis , so the differences are mostly reduced to a single dimension , the slope ( or gradient ) relative to the @xmath7@xmath8 plane . the gradient directions , projected onto the @xmath7@xmath8 plane , are almost all either aligned ( or anti - aligned , for those with opposite slope ) . the optical subsample gradient directions are never more than 3.8 degrees away from that of the full sample , and in the x - ray form , they never exceed a 6.4 degree deviation . radio - loudness has the strongest effect on the slopes . in the x - ray form , the subsample fps are almost evenly divided between those aligned with the full sample and those anti - aligned . in the optical form , only radio - quiets in elliptical hosts tilt opposite to the full sample . this effect is interesting because we are seeing a stark difference between the radio - loud and radio - quiet nuclei in the hosts of the same morphology . it would be interesting to find if the different qso fp orientations described above come about from different fueling mechanisms that might be found in the various subsamples . we see , for instance , that radio - quiet and radio - loud qsos are characterized by very different slopes in their x - ray fps , but the understanding of what makes these qso types differ is still too limited to speculate further here . in our ongoing research , we are expanding the fundamental plane study to other types of agn . we can then compare their fp orientations with those of the different qso subsamples , which may teach us more about the physics underlying the qso fundamental plane . we should ask if lower luminosity classes of agn ( such as seyferts or llagn ) also have fundamental planes of this sort . if they do , how do they compare with that of qsos ? we can imagine four possibilities : 1 . they share the same fundamental plane as qsos . this would indicate that agn power scales with the host properties , even across agn types , and would support some form of unification . the plane is parallel to that of qsos , but shifted to lower nuclear luminosities . this would show that these host properties do nt determine the agn class , and a given galaxy could host different types . the plane is tilted with respect to that of qsos . then the fundamental plane slope would be characteristic of the agn type , possibly supporting the idea that the slope is tied to the accretion mechanism . 4 . there is no fundamental plane whatsoever . in that case , this type of fundamental plane would be a unique property of qsos . high - luminosity objects would be more closely connected with their host properties ." +"experimental advances in generating strongly interacting photons opened the opportunity to explore various many - body quantum phenomena in a new context @xcite . photonic systems are unique in the sense that it is naturally an open quantum system where the adding and destroying of photons can be accomplished by drive and dissipation in a controlled way . thus it is an ideal system to study many outstanding questions on open systems dynamics , dissipative phase transitions @xcite and the effects of interactions in a dissipative environment . the simplest model to study strongly interacting bosons on a lattice is the celebrated bose - hubbard model where atoms have on - site interactions and can hop across lattices @xcite . there have been several recent proposals @xcite on achieving this model with photons and open systems , such as with photons in coupled cavity arrays , superconducting circuit qed and polaritons . with added drive and dissipation , the bose - hubbard model does not exhibit superfluid or mott insulator phases but gives rise to mixed state nonequilibrium steady states and phases @xcite , the nature and generation of which are not fully understood . a starting point for understanding the complex dynamics of driven dissipative photonic cavity arrays can be a two - site model . such a two - site driven dissipative nonlinear model may be realized with systems such as two coupled photon cavities @xcite , circuit qed systems @xcite and two coupled micropillars @xcite . this system is also referred to as a photonic molecule @xcite , dimer or a double well . for the closed system , the physics of double well has been studied in great detail @xcite , giving rise to phenomena such as the josephson effect , matter wave interference and self - trapped and symmetry breaking states , among others . for open systems , studies of two coupled cavities have appeared in several contexts in both theory @xcite and experiment @xcite . for an end - driven cavity , studies focused on the topics of unconventional photon blockade @xcite and multi - stability @xcite , among others . for symmetrically driven cavities , studies appeared on quantum correlations @xcite , classical to quantum phase transitions for a jaynes - cummings dimer @xcite , and symmetry breaking for incoherent drives @xcite , among others . in this article , we explore the physics of two coupled nonlinear cavities in a dissipative setting where both sites are driven coherently and symmetrically . we perform semiclassical and quantum analysis of the system investigating the complex interplay of many competing terms such as hopping , interaction , drive , dissipation and detuning . in a semiclassical treatment , we show that the nonequilibrium steady states have asymmetric number density in the two cavities in addition to the expected symmetry preserving states . these states are the driven - dissipative analog of the closed system double well symmetry breaking or self - trapped states @xcite with a fundamental difference that these are not minimum energy states but long - time steady states resulting from the competition in drive and dissipation . these can be understood from the bistability of a single driven cavity ; when two cavities are coupled with small but nonzero tunneling , the low density and high density bistable branches of a single cavity are hybridized to form two symmetry breaking steady states with unequal photon occupations in the two cavities . beyond a critical coupling and drive , the symmetry breaking states do not form . we analyze the occurrence and stability of the semiclassical solutions , finding that there can be up to nine solutions , a maximum of four of which are stable containing pairs of symmetry breaking and symmetry preserving states in a multistable region . we delineate a phase diagram for the symmetry broken states in the parameter space of drive and tunneling . and inter - cavity mode overlap contributes to tunneling with strength @xmath0 . the system is coupled to a markovian bath and photons can decay or leak out with rate @xmath1 . coherent pumping ( @xmath2 ) replenishes the photons . we treat the case when drive and dissipation are the same for both cavities . two coupled cavities are the simplest setting for an array of coupled cavities where the interplay of dissipation , drive and interaction plays a crucial role that are being investigated in a wider context.,scaledwidth=35.0% ] we then study the system by solving the full quantum mechanical master equation and using the method of quantum trajectories @xcite . in a full quantum treatment , when quantum fluctuations are taken into account , the symmetry breaking states are no longer seen , similar to the case of single - cavity bistable states @xcite . however , in quantum trajectory simulations of the dynamics , we show that quantum jump statistics of number differences reveal the presence of underlying semiclassical bistability indicating the presence of symmetry breaking states . finally , we present a set of analytical expressions for the steady state correlation functions using the complex p - representation @xcite expressing the master equation in the form of fokker - planck equation . the solutions work for small tunnel couplings ; we discuss the regime of validity of the solutions in the parameter space . the article is organized as follows . in section i , we introduce the model . in section ii , we present semiclassical analysis and analyze the driven - dissipative symmetry breaking states . in section iii , we present quantum trajectory analysis and full quantum treatment of the master equation . in section iv , we derive analytical solutions for the steady state correlation functions , and summarize our results in section v. we consider two cavities with kerr nonlinearity @xcite that are coupled by tunneling @xcite . the cavities are coherently driven in a dissipative setting , with both drive and dissipation acting equally on both sites . [ fig : schematic ] shows a schematic of the set up . the system can be described by the following hamiltonian @xmath3 where @xmath4 and @xmath5 are the annihilation operators for the two cavities labelled @xmath6 and @xmath7 . here @xmath0 is the inter - cavity tunneling strength , @xmath8 is the anharmonicity or the nonlinear kerr - type interaction strength , @xmath2 is the driving field for cavity 1 and 2 , and @xmath9 is the detuning , after the rotating wave approximation for the drive term . @xmath10 and @xmath11 are the cavity resonance frequency and driving frequency , respectively . . the four steady states are reached with four different initial values of @xmath12.,scaledwidth=48.0% ] for our open system , there can be photon losses induced by spontaneous decay or cavity leakage . in the approximation that the system is weakly coupled to a markovian bath , the dynamics of the density matrix can be modeled by a quantum master equation in the lindblad form @xmath13+\gamma [ 2 ( { \hat a}_1 { \hat \rho } { \hat a}_1^{\dagger}+{\hat a}_2 { \hat \rho } { \hat a}_2^{\dagger } ) \nonumber \\ & & -({\hat a}_1^{\dagger } { \hat a}_1+{\hat a}_2^{\dagger}{\hat a}_2 ) { \hat \rho } - { \hat \rho}({\hat a}_1^{\dagger } { \hat a}_1+{\hat a}_2^{\dagger } { \hat a}_2)],\end{aligned}\ ] ] where @xmath1 is the dissipation rate in each cavity . we set @xmath14 throughout . ignoring quantum fluctuations , the mean field amplitudes for the field operators are @xmath15 . we assume @xmath16 and @xmath17 , where @xmath18 are occupation numbers and @xmath19 are phases for the two cavities , and @xmath20 . in the semiclassical approximation the correlation functions factorize , and the equations of motion become @xmath21 here @xmath22 and @xmath23 . we find the steady states of these equations by solving the four coupled differential equations eq . [ eq : eqofmotion ] , examining the long - time dynamics for different sets of initial conditions . for most values of parameters we get a single steady state . however , for the value of parameters @xmath24 , @xmath25 , we get four different steady states as depicted in fig . [ fig : dynamics ] showing their long time dynamics . we take @xmath25 for all our calculations in this article , essentially giving other parameters in units of dissipation . two of the steady states have equal number of photon occupations in the two cavities as in figs . [ fig : dynamics](a ) and ( b ) , one with low occupations and the other with higher occupations . in addition to these , we get steady states where the photon occupations are different in the two cavities as shown in figs . [ fig : dynamics](c ) and ( d ) . this pair of states are asymmetric , mirror images of each other , and localized more in one of the cavities . these states are the driven - dissipative analog of the symmetry breaking states of nonlinear josephson coupled junctions as observed in bec and with photons @xcite in a closed system . we call them _ driven - dissipative symmetry breaking states_. unlike the single cavity semiclassical solutions , the phases here are important as the relative phase between the two cavities can not be gauged away . for the symmetry preserving states we find @xmath26 , and for the symmetry breaking states @xmath27 . another method we employ to find the steady state solutions is to set @xmath28 and find roots of the four coupled equations : @xmath29 here we have four equations with four unknowns @xmath30 and @xmath31 that are real . we assume @xmath32 and solve for the variables @xmath33 which is then transformed back into numbers and phases of the two cavities as @xmath34 . the solution set contains both real and complex solutions . there is only one real solution for most of the parameter values ; this is the regime where there is no bistability . for certain parameter values , there can be more than one real solutions , up to a maximum of nine and a maximum of four of which are stable . the stable solutions that we obtain with this method match with what we obtain from the previous method as steady states of long - term dynamics starting with different initial conditions . ) plane for @xmath35 and different values of @xmath36 , and @xmath37 respectively . the area labelled 1 has one symmetry preserving steady state , 2 has two symmetry preserving states in a bistable region while 4 has two symmetry breaking and two symmetry preserving states . ( b ) shows @xmath38 and @xmath39 as a function of @xmath0 for a fixed @xmath40 . ( c ) shows @xmath38 and @xmath39 as a function of @xmath2 for a fixed @xmath41 . these depict how the symmetry breaking states appear and disappear as a function of tunnelling and drive . we see that there is a critical @xmath0 value beyond which the symmetry breaking states do not appear.,scaledwidth=42.0% ] we find stability by introducing small fluctuations to the steady state , obtaining linearized equations for the fluctuations and examining their eigenvalues . introducing small fluctuations about the steady state @xmath42 , @xmath43 , @xmath44 here the stability matrix @xmath45 is following : @xmath46 where @xmath47 . when the real part of the eigenvalues of @xmath45 are positive the solution is stable . furthermore , we look at the determinant and trace , as done in ref . @xcite , for which the hurwitz criterion for stability requires that the trace and determinant of this matrix is nonzero and positive for stable eigenvalues . we can further analyze the steady state equations eq . [ eq : eqsteadystate ] to get two state equations @xmath48 eqs . [ eq : eqdrive ] capture the parameter dependence" +"in qed , the landau - pomeranchuk - migdal ( lpm ) effect interpolates between the bethe - heitler and factorization limit for the radiation spectrum of a charged particle undergoing multiple , @xmath4 say , scatterings in a medium . if the separation between scattering centers is very large , then the radiation off these centers reduces to a sum of radiation spectra for @xmath4 small - angle scatterings - this is the bethe - heitler limit . in the opposite limit , when the scattering centers sit too close together to be resolved by the emitted photon , the observed radiation factorizes into a product of a single scattering bethe - heitler spectrum for momentum transfer @xmath5 and the elastic cross section for the momentum transfer @xmath6 accumulated over @xmath4 small - angle scatterings . as first noted by landau and pomeranchuk @xcite , the relevant length scale for the interpolation between bethe - heitler and factorization limit is the coherence length ( formation length ) @xmath7 , determined by the longitudinal momentum transfer @xmath8 , @xmath9 this characterizes the longitudinal scale on which the radiated particle becomes distinguishable from its radiating parent . scattering amplitudes for the radiation off different scattering centers interfer destructively if their separation is less than @xmath7 : the _ coherent _ factorization limit is suppressed in the ultrarelativistic limit with respect to the _ incoherent _ bethe - heitler limit . for a quantitative description of the lpm interference effect , the relative phases of the different contributions to the @xmath4-fold scattering amplitude matter . these depend on the transverse energies and thus require knowledge about the transverse motion of the radiating particle in the medium . migdal @xcite was the first to develop a dynamical description to this aim , employing a two - dimensional fokker - planck transport equation @xcite for the hard parton . in the limit of an infinite medium , his well - known result shows a characteristic @xmath10 low frequency suppression of @xmath11 compared to the constant dependence in the bethe - heitler limit , i.e. , the coherent factorization limit for @xmath12 vanishes . this is , however , only a very special feature of migdal s limiting case , where the formation length goes to infinity for @xmath12 , but never exceeds the ( infinite ) extension @xmath13 of the medium . for a medium of finite size , the formation length does exceed the system size below some critical frequency @xmath14 , and the bethe - heitler limit is finite . migdals @xmath15-dependence is hence not valid for @xmath16 . moreover , additional effects become important for the radiation spectrum at lower frequencies @xcite . most notably , this is the transition radiation and the ter - mikaelian effect @xcite of dielectric suppression . the renewed interest in the lpm - effect has at least two reasons : on the one hand , fourty years after discovering the theoretical principles @xcite , the first precision measurements of the lpm - effect @xcite ( and the ter - mikaelian effect @xcite ) were made recently by the slac-146 collaboration . on the other hand , with the advent of a new generation of relativistic heavy ion colliders at rhic and lhc , the understanding of the non - abelian analogue becomes important . in the qed case , the experiment explored relatively thin targets with @xmath17 on the order 0.1 to 10 , in which the transition between bethe - heitler and factorization limit occurs . for a quantitative understanding , a realistic theory has to account for the finite extension of the target , the multiple elastic scatterings in the target , multiple photon emission , and possibly additional complications like radiation off structured targets . there are at least three modern approaches , which can account in principle for the lpm - effect in realistic targets . they implement the eikonal approximation for the radiating hard particle in different ways : i ) blankenbecler and drell @xcite ( see also baier and katkov @xcite ) started from the solution of the klein - gordon equation for the charged particle in the presence of an external field . the solution was approximated to order @xmath18 in a high energy expansion in which the eikonal path of the radiating particle is recovered . ii ) zakharov @xcite proposed a light - cone path integral formulation which describes in a coordinate - space representation the transverse momentum kicks on the eikonal path , mimicking the elastic scatterings by an effective dipole cross section . zakharov s work @xcite provides the most accurate description of the measured data so far . as we shall see in section [ sec2c ] , his starting point is closely related to a high energy expansion of the dirac equation in the presence of an external potential . iii ) a third approach is due to r. baier et al . ( bdmps ) @xcite , who started from the radiation amplitudes for @xmath4-fold scattering in the eikonal approximation . for qed , the consistency of their approach and the work of blankenbecler and drell can be checked diagrammatically @xcite . a discussion of the lpm effect also exists for non - equilibrium conditions @xcite . in the qcd case , high @xmath19 gev jets will be one of the new probes of the dense matter produced in relativistic heavy ion collisions . deviations from factorized perturbative qcd due to final state rescattering are sensitive to the density and coupling in the plasma and will affect key observables like the high momentum tails of single particle spectra . the corresponding study of qcd radiative energy loss due to final state rescattering was initiated by gyulassy and wang @xcite . recently , it has been extended most notably in a series of papers by bdmps @xcite using equal time perturbation theory . also , zakharov has pointed out that his formalism can be adopted to qcd bremsstrahlung with a dipole prescription @xcite , and the equivalence of zakharov s formalism with the work of bdmps was sketched @xcite . all these calculations of the lpm - effect in qcd , however , are ( 1 ) limited to the cases of infinitely many or very few ( @xmath20 ) rescatterings of the parton , and ( 2 ) they mainly focus on the angular integrated energy loss @xmath21 in which the transverse momentum dependence of the radiation pattern is averaged out . this energy loss , however , is not a good observable for qcd , because the parton shower is not directly observable due to hadronization . in addition , the qcd bremsstrahlung of hard jets must compete with the hard radiation associated with the jet production . to detect modifications of this hard vacuum bremsstrahlung spectrum due to final state rescattering requires knowledge about the angular distribution of the spectrum . in qcd , the transverse momentum dependence of the lpm - effect is thus indispensable for a quantitative understanding of radiative energy loss . recently , kopeliovich , schfer and tarasov ( kst ) @xcite have used the furry approximation of the dirac equation in order to account for the transverse momentum dependence of the radiation spectrum emitted in a multiple scattering process . for the case of qcd bremsstrahlung radiation , they translate their qed results into qcd via an _ a posteriori _ dipole prescription ( [ 5.1 ] ) . this strategy is frequently used not only for the calculation of the radiative energy loss of high @xmath22 partons @xcite , but also for the description of nuclear shadowing in the target rest frame @xcite and for related problems of diffractive dissociation of virtual photons @xcite . as we show in what follows , an extension of the kst - formalism has great potential for the calculation of radiative energy loss in realistic scenarios since ( 1 ) it provides a smooth interpolation between the cases of infinitely many and very few rescatterings and ( 2 ) it allows to compare qed - inspired calculations of qcd radiative energy loss with perturbative qcd results . the present work focuses on the general formalism , its region of validity , and a qualitative discussion of its generic features . it gives expressions which allow for the numerical calculation of the radiation spectrum as a function of the medium density and extension , but it leaves phenomenological applications to further publications . our work is organized as follows . in section [ sec2 ] , we derive the starting point of our discussion , the radiation spectrum ( [ 2.22 ] ) . we discuss how a technical complication , the regularization of this spectrum , can be dealt with analytically , and we calculate the corresponding integrated energy loss . section [ sec3 ] focuses on limiting cases of the general radiation formula ( [ 2.22 ] ) . we derive the radiation spectra for @xmath23 , @xmath1 and @xmath2 scatterings and we show that these reproduce the bethe - heitler and the factorization limit . in section [ sec4 ] , the dipole approximation of the radiation spectrum ( [ 2.22 ] ) is discussed . this gives access to true in medium properties of the radiation spectrum which can not be obtained from an expansion to finite order in the coupling constant . finally , we discuss in section [ sec5 ] how this method can be extended to qcd and how it compares to results from perturbative qcd . our main results are summarized in the conclusion . an expansion of the lpm - radiation cross section in orders of the coupling constant is essentially an expansion in the number of elastic scatterings , since each elastic scattering mott cross section is proportional to @xmath24 . in contrast , a high energy expansion of the solution of the dirac equation in the presence of an external field takes to leading order in @xmath18 an arbitrary number of elastic scatterings into account . in this section , we derive the corresponding high energy limit of the qed radiation cross section for a hard electron , traversing a medium of longitudinal density @xmath25 . the physics contained in our main result ( [ 2.22 ] ) will be discussed in the following sections [ sec3 ] - [ sec5 ] . our approach in [ sec2a ] parallels to a large extent that of kopeliovich , schfer and tarasov ( kst ) in ref . we present the derivation in full detail to introduce our notation and to discuss all the approximations involved in the calculation . in contrast to ref . @xcite , our radiation cross section ( [ 2.22 ] ) contains an @xmath26-regularization whose treatment is discussed in subsection [ sec2b ] . then we show that the kst - formalism results in an angular integrated energy loss formula from which modifications to zakharov s formalism @xcite can be obtained . we consider a relativistic electron undergoing multiple small - angle scattering in a spatially extended medium , described by an external potential @xmath27 . the angular dependence of the radiation spectrum for emitted photons carrying away a fraction @xmath28 of the incident electron energy @xmath29 is given by the differential cross section @xmath30 where @xmath31 and @xmath32 denote the transverse momenta of the photon and outgoing electron , respectively . the radiation amplitude for transversely polarized photons is given in terms of the ingoing and outgoing electron wavefunctions @xmath33 and @xmath34 , @xmath35 here , @xmath36 , and @xmath37 is the adiabatic switching off of the interaction term at large distances . this term plays an important role in what follows since the @xmath38 limit does not commute with the longitudinal @xmath39-integration . the wavefunctions @xmath40 solve the dirac equation in the external potential @xmath27 : @xmath41\ , \psi(x , p_{1,2" +"the transport of fluids through geological media such as hydrocarbon and water reservoirs involves a combination of flow through the microscopic pore space of the rock itself and flows through macroscopic channels such as fractures . the first case is relatively well understood , at least in principle @xcite , by means of models which treat the pore space as a random network , and then use effective medium or percolation concepts for the transport . fractures are typically modeled as simple straight - sided channels , with a cubic relation between fluid flux and average aperture , and a challenging problem is to understand the dynamics of flow in a macroscopic fracture network @xcite . typically the surface of a single fracture appears fairly smooth , aside from some small - scale superficially random roughness , and poiseuille flow in a straight channel is the obvious model for fluid flow . however , more careful analysis @xcite shows that common geological fractures in fact have correlated , self - affine fractal surfaces . the roughness exponent , whose precise definition is recalled below , is usually found @xcite to be close to 0.8 , surprisingly insensitive to the material and the fracturing process . ( other values may arise from intergranular effects @xcite . ) the aim of this paper is to study the permeability of single self - affine two - dimensional fractures . we shall see that it is possible to obtain general analytic expressions in two limiting cases , where the roughness associated with the fracture surface is either small or large compared to the mean aperture . the theoretical predictions will be supported by numerical simulations , using the lattice boltzmann method , which of course can address the case of intermediate sized roughness as well . in subsequent work , we will consider the fully three dimensional case , and go on to consider more general transport processes in fractures , involving both passive tracers and finite - sized suspended particles . complimentary experimental studies on laboratory samples of fractured rock are in progress elsewhere @xcite . to the extent that the fluctuations in the height are small compared to the aperture width , the effect on permeability is modest , and we will obtain small corrections to the usual cubic law , but the effects on other transport processes are much more significant . for example , passive tracer dispersion is very sensitive to the presence of any slow zones in the velocity field , and even uncorrelated roughness leads to significant long - time tails @xcite . similarly , the deposition and erosion of solid particles from a surface is sensitive to the local shear stress , which in turn can change dramatically as a surface roughens . in the opposite extreme of a very narrow fracture , the flow field changes qualitatively as the fluid winds through a highly irregular channel . aside from the challenge of estimating the permeability of difficult geometry in terms of its statistical characteristics , there are further effects arising from the fact that the two sides of the fracture originate from a single crack . in the fractal case , the spatial correlations between the two sides of a fracture lead to velocity field correlations , which again strongly affect tracer motion @xcite . the latter references made use of a very approximate velocity field , obtained in the lubrication limit , and one of the motivations of this paper is to examine the validity of the lubrication approximation for the velocity field . the organization of this paper is as follows . we first recall some basic facts about self - affine surfaces , and give the algorithm used to generate them numerically , and also explain the lattice boltzmann method used for the numerical simulations . we then consider the case of fractures with a wide average aperture , obtain a perturbative estimate for the permeability , and test it numerically . we then turn to narrow fractures , first in the case where the two sides are simply displaced normally to the mean fracture plane , and secondly when there is a lateral shift as well . finally , we summarize the results , and indicate the next steps we briefly review the mathematical characterization of self - affinity , and its implementation in this paper . we consider a rock surface without overhangs , whose height is given by a by a single - valued function @xmath0 , where the coordinates @xmath1 and @xmath2 lie in the mean plane of the fracture . self - affine surfaces @xcite display scale invariance with different dilation ratios along different spatial directions , remaining unchanged under the rescaling @xmath3 here we consider disordered media , so these scaling laws apply only in an ensemble or spatial average sense . experiment indicates that for many materials isotropy can be assumed in the mean plane , implying that there is only one non - trivial exponent relating the dilation ratio in the mean plane to the scaling in the perpendicular direction , _ i.e. _ , @xmath4 , and @xmath5 , with @xmath6 where @xmath7 is the roughness or hurst exponent @xcite . we assume that the process of fracturing the rock is `` clean '' , in the sense that the rock breaks so as separate along one single valued surface without subsequent deformation and without producing loose interstitial material . we shall emphasize two complimentary limiting situations , in which the two surfaces are either well separated with respect to each other , or very close to each other . if @xmath8 is the lateral size of the fracture in the mean plane , the typical range of the fluctuations ( the difference between the maximum and minimum values of @xmath9 ) scales as @xmath10 . if @xmath11 is the mean width of the fracture , with @xmath12 , then the two cases correspond to @xmath13 and @xmath14 , respectively . the local aperture of the crack is the key parameter determining the fracture permeability , and three different cases will be addressed . for large aperture , the roughness associated with the two sides of the fracture act independently , and it suffices to consider a channel with one rough and one smooth boundary . in the case of a narrow fracture , the correlation between the two sides is a key feature , and we consider two possibilities . we first study fractures where the upper surface has been simply translated a distance @xmath11 normal to the mean plane , so that the local aperture @xmath15 equals the constant @xmath11 . alternatively , the two surfaces may have a relative lateral displacement @xmath16 in the mean fracture plane , accompanied by a displacement @xmath11 in the perpendicular direction , so that the two surfaces do not overlap . in this case the local aperture is given by the random variable . @xmath17 it turns out @xcite that @xmath16 is the lateral correlation length for fluctuations in the aperture , in the sense that @xmath18 and @xmath19 decorrelate for @xmath20 . in this paper we restrict ourselves to the two dimensional case where the surface is invariant in the @xmath2 direction , @xmath21 , and the flow is forced in the @xmath1 direction by a constant pressure drop . in a subsequent paper we will extend these calculations to fully three dimensional fractures , but it is convenient , both conceptually and in the numerical simulations , to regard the system as having a translationally invariant third dimension . our aim is to study various aspects of the fracture permeability which are sensitive to the fracture roughness . the first ingredient is the height function @xmath0 , a statistically self - affine surface with periodic boundary conditions . the periodicity is not a physically essential ingredient here , but has some calculational advantages in alleviating finite - size effects . the surface is generated by a fourier synthesis method , based on power - law filtering of arrays of independent random numbers @xcite . the random numbers are generated using a gaussian distribution , and then modulated by an appropriate power law . if @xmath22 is the fourier transform of the initial gaussian random array , then the fourier transform of the surface elevation is chosen to be @xmath23 ( the 1/2 is appropriate for the self - affine _ curve _ used here , and would be 1 for a real rock _ surface_. ) in most cases the roughness exponent is chosen as the often - observed value @xmath24 . the amplitude of the roughness can be expressed in terms of variance of the height distribution over the full range , @xmath25 which in this case is @xmath26 for @xmath27 . alternatively , the amplitude is given indirectly in terms of the range of the fluctuations as @xmath28 , with @xmath29 . in these equations , and in the rest of the paper , the unit of length is that of the spacing between lattice points in the numerical calculations . since we consider fluid flow in a highly irregular geometry , and eventually hope to consider dispersion and the evolution of the solid surface due to particle transport , the lattice boltzmann ( lb ) method @xcite is particularly convenient . in this algorithm , fictitious particles move between neighboring sites on a lattice , with suitable collision rules , and the boundary of the flow domain is simply a surface of sites where the rule is modified in some way to keep the particles out . we use the face centered hypercubic ( fchc - projected ) version of the lb model , with a cubic lattice in 3 dimensions and 19 velocities ( d3q19 in the terminology of @xcite ) . the collision operator is approximated by a single relaxation time , the bhatnagar - gross - krook model@xcite , and the local equilibrium distribution given by @xcite is used . this pseudo - equilibrium distribution locally preserves mass and momentum values , and is formulated specifically to recover the navier - stokes equation at large length and time scales . for the no - slip solid boundaries , we use the simplest implementation of particle exclusion the bounce - back rule , in which a particle incident on the boundary reverses its direction . periodic boundary conditions are used for the inflow and outflow surfaces . a constant pressure gradient forcing the fluid is added in the @xmath1 direction , while the gap between surfaces extends over @xmath9 , and the geometry is taken to be translation invariant in @xmath2 . in this section we consider the case of a channel with one fractally - rough wall , in the limit where the mean width is large compared to the amplitude of the roughness . we ( re-)derive an elegant general result for the permeability , and then an exact variant which gives the permeability of a perturbed pore space . if the pore space perturbation is weak , the leading order correction is easy to evaluate and , when compared to numerical simulation , is seen to provide a reasonably accurate estimate of the permeability . we begin by deriving an integral representation for the permeability , and then considering a perturbation in the boundary shape . although we suspect that these results are known to many , we are not aware of an earlier publication containing them , although the electrical analog of the integral representation is in the literature @xcite . consider a rectangular volume of a porous medium , periodic in all directions , and the following surface integral @xmath30\ ] ] here , @xmath31 and @xmath32 are the velocity and pressure fields of a fluid which completely fills the pore space , assumed to satisfy the stokes equations , and the surface" +"microwave emission from interstellar dust grains contributes a `` galactic foreground '' which must be recognized and subtracted from observations of the sky in order to carry out studies of angular structure in the cosmic microwave background radiation ( cmbr ) . this microwave emission also offers us new information on the properties of interstellar dust grains . in [ sec : obs ] we review the observational evidence for infrared and microwave emission from interstellar dust . there are several sources of `` galactic foreground '' emission at microwave frequencies : relativistic electrons ( synchrotron emission ) , thermal electrons ( free - free emission ) , and dust grains . microwave emission from dust grains was discovered by studies of the cmbr , which revealed a surprisingly strong component of the microwave sky brightness which was correlated with interstellar matter , as traced by 100@xmath0 m thermal dust emission . because this dust - correlated signal was much stronger than expected from existing models of interstellar dust , it has been referred to as `` anomalous '' emission ( leitch _ et al . _ 1997 ; kogut 1999 ) . the spectrum of the `` anomalous '' microwave emission is not consistent with synchrotron emission , and maps at 408 mhz ( haslam 1981 ) and 1.42 ghz ( reich & reich 1988 ) do not correlate with the observed 15 - 100 ghz intensity ( kogut _ et al . _ 1996a , b ; leitch _ et al . _ 1997 ; de oliveira - costa _ et al . _ 1997 , 1998 ) , so the anomalous emission is evidently not synchrotron radiation from relativistic electrons . in section [ sec : free - free ] we conclude that the observed emission significantly exceeds the free - free emission from interstellar plasma . the excess emission must be due to dust . there are three quite distinct mechanisms whereby dust can radiate at microwave frequencies ; they can be classified as ( 1 ) `` vibrational electric dipole '' emision ( due to thermal fluctuations in the charge distribution in the grain ) ; ( 2 ) `` magnetic dipole '' emission ( due to thermal fluctuations in the magnetization of grain material ) ; and ( 3 ) `` rotational electric dipole '' emission ( due to the rotating electric dipole moment of a spinning grain ) . most of the power radiated by interstellar dust is due to `` vibrational electric dipole '' emission , peaking in the far - infrared at @xmath1100@xmath0 m . the low - frequency `` tail '' of this emission can be extrapolated to microwave frequencies , but falls far below the observed 1060 ghz emission . however , as discussed in [ sec : magdipole ] , if grains contain magnetic materials such as magnetite or metallic iron the thermal fluctuations in the magnetization will result in strong magnetic dipole emission . there is strong independent evidence for a large population of ultrasmall grains . these grains should be spinning rapidly , should have electric dipole moments , and therefore should radiate at microwave frequencies , as discussed in [ sec : rotational ] the expected spatial variations of the microwave emission from dust are discussed in [ sec : space ] the possibility that this radiation can be polarized is discussed in [ sec : polarization ] , and observational tests are considered in [ sec : tests ] we summarize in [ sec : summary ] figure [ fig : obs ] shows the observed emission spectrum of diffuse interstellar dust , based on measurements by the _ infrared astronomy satellite ( iras ) _ , the _ firas _ spectrometer and the _ dirbe _ photometers on the _ cosmic background explorer ( cobe ) _ , and the _ mid - ir spectrometer ( mirs ) _ and the _ near - ir spectrometer ( nirs ) _ on the _ infrared telescope in space ( irts)_. the emission from interstellar matter between 1 mm ( 300 ghz ) and @xmath2 m ( 3000 ghz ) is due primarily to thermal emission from dust particles heated by diffuse starlight to temperatures @xmath3k , as was expected theoretically ( see , e.g. , draine & lee 1984 ) . while the observed spectrum between 1 mm and 100@xmath0 m can be accurately described by multicomponent fits ( wright _ et al . _ 1991 ; reach _ et al . _ 1995 ; finkbeiner & schlegel 1999 ; finkbeiner , schlegel , & davis 1999 ) the observed 1 mm 100@xmath0 m emission , with @xmath4 peaking at @xmath5 , can be approximated quite well by emission from dust with absorption cross section @xmath6 and a single temperature @xmath7 . away from molecular regions , the 100@xmath0 m emission correlates very well with 21 cm emission ( boulanger & prault 1988 ) , allowing us to infer the average emissivity per h nucleon ( draine 1999 ) : @xmath8 { \rm erg~s^{-1 } sr^{-1 } h^{-1}}\ ] ] where a good fit is obtained for @xmath9k and @xmath10 . this choice of @xmath11 and @xmath12 corresponds to an absorption cross section per h nucleon @xmath13 figure [ fig : obs ] shows this and other single - temperature fits together with observational determinations of the dust emission spectrum . a striking feature of figure [ fig : obs ] is the strong emission at @xmath14 m observed by _ iras _ , _ cobe - dirbe _ , and _ irts_. this emission , accounting for @xmath135% of the total power radiated by dust , is far in excess of what would be expected from dust grains at @xmath15k . the only natural explanation for this is to attribute it to dust grains which are so small that absorption of a single starlight photon heats them to temperatures high enough for thermal emission to produce the observed radiation ( draine & anderson 1985 ) . grain temperatures as high as @xmath16k are required to account for the emission observed in the 12@xmath0 m band , so the grains must be _ very _ small : if the specific heat is characterized by a debye temperature @xmath17k ( the value for graphite ; furukawa _ et al . _ 1972 ) , then a 6 ev starlight photon could heat a grain with @xmath18 atoms to @xmath19k . even smaller particles are required by the strong emission observed at shorter wavelengths ( see figure [ fig : obs ] ) . the population of small particles must be _ very _ large , since they must account for @xmath135% of the total absorption of energy from starlight ! since eq . ( [ eq : betafit ] ) fits the 1 mm 100@xmath0 m emission so well , it is natural to extrapolate it to lower frequencies . a good single - temperature fit is for @xmath20 , close to the value @xmath21 predicted by simple models for the response of dielectrics at frequencies below all the optically - active resonances as well as simple models of conducting materials ( draine & lee 1984 ) . in figure [ fig : microwave_obs ] we show the prediction for @xmath10 and three other values of @xmath11 . note that the @xmath22 extrapolation overestimates the emission for @xmath23 m ( see fig . [ fig : obs ] ) , and is included in figure [ fig : microwave_obs ] only as an extreme example . figure [ fig : microwave_obs ] also shows the observed dust - correlated emissivity @xmath24 per h nucleon deduced for diffuse interstellar matter by cross - correlating the measured microwave sky brightness @xmath25 with an fir sky map ( either _ dirbe _ 140@xmath0 m or _ iras _ 100@xmath0 m ) . the best - fit slope @xmath26 reported by different experiments is then converted to an emissivity per h nucleon using the @xmath27 m or @xmath2 m emissivity from eq . ( [ eq : betafit ] ) . equation ( [ eq : betafit ] ) is appropriate only for dust in diffuse regions . the procedure used here will tend to _ overestimate _ the emissivity @xmath28 when the observations include regions ( e.g. , non - star - forming molecular clouds ) where the dust is somewhat cooler than in diffuse hi clouds . the cooler dust will have a lower fir emissivity , and hence @xmath29 will actually be larger than deduced from @xmath30 using eq.([eq : betafit ] ) . this might explain the relatively high emissivities shown in fig . [ fig : microwave_obs ] obtained from the observations of leitch _ et al . _ ( 1997 ) , as the fields observed by these experiments could contain significant amounts of molecular gas ( finkbeiner , private communication ) . the much larger fields observed by kogut _ et al . _ ( 1996b ) and de oliveira - costa _ et al . _ ( 1997,1998 ) are expected to be dominated by diffuse atomic gas , so the emissivities deduced from these experiments are probably more accurate . better estimates of emissivities @xmath28 could be obtained if the h column density @xmath29 is estimated using the maps of dust optical depth produced by schlegel _ et al._(1998 ) , who used the _ dirbe _ 100 and 240@xmath0 m maps to allow for dust temperature variations . the observed dust - correlated microwave emissivities at @xmath31 ghz tend to be well above the extrapolation to low frequencies with the `` best fit '' @xmath20 . for this reason the dust - correlated microwave emission has been referred to as `` anomalous '' ( leitch _ et al . since the observed dust - correlated emission at @xmath31ghz is so much greater than expected from simple extrapolation of the dust spectrum from far - infrared and sub - mm wavelengths , we must consider what other mechanisms could be responsible . et al . _ ( 1996a ) suggested that the observed 3050 ghz excess was due to free - free emission from ionized gas which was correlated with dust . however , leitch _ et al . _ ( 1997 ) measured the dust - correlated 14.5 and 32 ghz emission from 36 fields around the north celestial pole , and showed that for these fields the `` anomalous emission '' could not be free - free emission from gas at @xmath32k , as the recombination radiation which must accompany free - free emission is not present on h@xmath33 maps ( gaustad _ et al . _ 1996 ) . leitch _ et al . _ noted that if the anomalous emission in this region were instead free - free radiation from plasma with @xmath34k , the predicted h@xmath33 would be consistent with existing limits . however , finkbeiner & schlegel ( 1999 ) have recently reported a _ negative _ correlation between the leitch _ et al . _ 14.5 ghz measurements and emission in the rosat x - ray c band , so it is not clear that hot gas can explain the anomalous emission in the leitch _ et al . _ fields . mccullough _ et al . _ ( 1999 ) review h@xmath33 observations and the contribution of free - free emission to the galactic microwave foreground . observing programs now underway will soon provide a much better knowledge of the h@xmath33 sky , but existing studies of the correlation between h@xmath33 emission and dust 100@xmath0 m emission ( mccullough 1997 ; kogut 1997 ) over limited regions find a dust - correlated h@xmath33 component with @xmath35 this correlation is found when averaging on angular scales of a few degrees ( mccullough _ et al . _ the dust - correlated h@xmath33 presumably" +"in recent years , quarkonium hadroproduction has become the subject of intense theoretical and experimental investigation . the main reason is that production and decays of heavy quarkonia have been an ideal laboratory to investigate quantum chromodynamics ( qcd ) . their large masses provide a hard scale which allows us to use perturbative qcd techniques . basically , there exist three distinct formalisms for quarkonium production . the simplest one is the color evaporation model ( cem ) @xcite , where the hadronization of the @xmath4 pairs into quarkonia is assumed to be dominated by long - distance fluctuations of gluon fields which motivates a statistical treatment of color . in the color - singlet model ( csm ) @xcite , quarkonium is viewed as a non - relativistic color - singlet bound state of a @xmath4 pair with definite angular momentum quantum numbers . production rates for a quarkonium state are computed by calculating the production of a heavy quark pair which is constrained to be in a color - singlet state and have the same angular momentum quantum numbers as the physical quarkonium . in the non - relativistic qcd ( nrqcd ) factorization formalism @xcite , non - perturbative aspects of quarkonium production are organized in an expansion in powers of @xmath5 , the relative velocity of the @xmath4 in quarkonia . for production of @xmath6-wave quarkonia , the results of the csm are recovered in the limit of @xmath7 . in addition , in the nrqcd formalism new quarkonium production mechanisms are now possible since it is no longer required that the @xmath4 produced in the short - distance process have the same color and angular momentum quantum numbers as the quarkonium state . recently , several computations of the qcd corrections to the inclusive quarkonium hadroproduction processes have shed some light on the robustness and/or deficiencies of those models . comprehensive reviews of recent developments in the theory of quarkonium production can be found in refs . @xcite . beside the studies of inclusive production , efforts are being made to obtain improved theoretical predictions for complementary observables to the inclusive yield , such the hadroproduction of @xmath2 and @xmath3 in association with a photon . in the framework of csm , the associated production of @xmath8 at a hadron collider was first proposed as a good channel to investigate the gluon distribution in the proton with a relatively clean signal @xcite . in ref . @xcite , such a process at the tevatron energy has been considered in the csm at lo , and the results show that the contribution from the gluon fusion sub - process is dominant over that from the fragmentation process ( the same occurs at the lhc @xcite ) . the color - octet contributions were investigated in ref . @xcite and it was found they are dominant in the large @xmath9 region . recently , in ref . @xcite the effect of the nlo qcd corrections to @xmath10 hadroproduction at the lhc has been investigated . in ref . @xcite the real next - to - next - to - leading ( nnlo ) order qcd contribution to hadroproduction of a @xmath11 via color singlet transitions for the inclusive case has been addressed . in this letter , we examine the production of associated @xmath8 and @xmath12 at large @xmath9 within the nrqcd approach in proton - nucleus and nucleus - nucleus collisions . such processes are relatively clean because the produced large @xmath9 quarkonium is easy to detect through its leptonic decay modes and the quarkonium s large @xmath9 is balanced by the associated high energy photon . at the lhc energy , the leading contributions are dominated by gluon induced hard processes and then the quarkonium production associated with a direct photon will be strongly dependent on the nuclear gluon distribution . our goal is to use the @xmath8 and @xmath12 processes as auxiliary observables to constrain the nuclear gluon distribution . this is motivated by similar investigations on inclusive heavy quark , quarkonium and prompt photon production in central proton - nucleus and nucleus - nucleus collisions ( see e.g. refs . one of the nuclear effects which is expected to modify the behavior of gluon distribution is the nuclear shadowing . this effect has been observed in the nuclear structure functions by different experimental collaborations @xcite in the study of the deep inelastic lepton scattering ( dis ) off nuclei . the modifications on @xmath13 depend on the parton momentum fraction @xmath14 . while for momentum fractions @xmath15 ( shadowing region ) and @xmath16 ( emc region ) , a depletion is observed in the nuclear structure functions , in the intermediate region ( @xmath17 ) it is verified an enhancement known as antishadowing . these experimental results strongly constrain the behavior of the nuclear quark distributions , whereas the the nuclear gluon distribution is still an open question due to the scarce experimental data in the small-@xmath14 region and/or for observables strongly dependent on the nuclear gluon distribution . this letter is organized as follows . in next section , we summarize the main formulas concerning the process @xmath8 in the nrqcd formalism and define the nuclear modification factors for proton - nucleus and nucleus - nucleus collisions , @xmath18 and @xmath19 , respectively . in last section we present the numerical results considering the more recent nuclear parton parameterizations and estimating the transverse momentum dependence of the nuclear modification factors at the lhc energies . as long as @xmath8 is produced at small longitudinal momentum fraction , @xmath20 , the gluon fusion channel dominates over the @xmath21 annihilation process . therefore , at high energies and at leading order ( lo ) , the process @xmath22 contributes at the partonic level with six feynman diagrams , which is similar to that of @xmath23 in inclusive @xmath2 hadroproduction . the signal we focus on is the production of a @xmath2 and an isolated photon produced back - to - back , with their transverse momenta balanced . the lo cross section is obtained by convoluting the partonic cross section with the parton distribution function ( pdf ) , @xmath24 , in the proton , where @xmath25 is the factorization scale . at nlo expansion on @xmath26 , there are one virtual correction and three real corrections processes , as shown in ref . @xcite . in the nrqcd formalism , the contributing subprocesses are @xmath27 and @xmath28 . the fock - components that contribute to @xmath2 production are the color - singlet @xmath29}$ ] state and the color - octet states @xmath30}$ ] , @xmath31}$ ] and @xmath32}$ ] . the color - singlet @xmath33 state contributes at @xmath34 but the color - octet channels all contribute higher orders in @xmath5 ( the relative velocity between the heavy quarks ) . we are interested here in the quarkonium production in a nuclear medium . in order to get the @xmath8 yield in @xmath35 and @xmath36 collisions , a shadowing - correction factor has to be applied to the @xmath2 yield obtained from the simple superposition of the equivalent number of @xmath37 collisions . this shadowing factor can be expressed in terms of the ratios @xmath38 of the nuclear parton distribution functions in a nucleon of a nucleus @xmath39 to the pdf in the free nucleon . most of shadowing models provide the nuclear ratios at a given value of @xmath40 and then evoluted through the dglap evolution equations @xcite to lo accuracy . only very recently , the nuclear pdfs have been available at nlo accuracy . therefore , in what follows we will consider a lo calculation for the nuclear modification factors in order to be consistent with the limitation of shadowing models . in this respect our analysis can not be considered as fully nlo and should be updated once the nlo calculation in nrqcd approach is available for the nucleon case . on the other hand , this is not an important limitation to our results as we will discuss later on . in order to obtain the transverse momentum ( @xmath9 ) distribution for the process @xmath22 , we express the differential cross section as @xmath41 where we have defined @xmath42 , with @xmath43 being the center of mass energy of the @xmath44 system and @xmath45 being the transverse mass of outgoing @xmath2 . the gluon distribution , @xmath46 , in the hadron a / b is evaluated at factorization scale @xmath25 . the common transverse momentum of the outgoing particles is @xmath9 and @xmath47 is the rapidity of outgoing @xmath2 having mass @xmath48 . the variables @xmath49 and @xmath50 are the momentum fractions of the partons , where @xmath51 ( @xmath52 is the invariant mass of @xmath8 system ) and @xmath50 can be written in terms of other variables as @xmath53 in the nrqcd formalism , the cross section for the production of a quarkonium state @xmath54 is written as @xmath55 , where the short - distance coefficients @xmath56 are computable in perturbation theory . the @xmath57 are matrix elements of nrqcd operators of the form @xmath58 the @xmath59 is a bilinear in heavy quark fields which creates a @xmath60 pair in a state with definite color and angular momentum quantum numbers . hereafter , we will use a shorthand notation in which the matrix elements are given as @xmath61 . the angular momentum quantum numbers of the @xmath62 produced in the short - distance process are given in standard spectroscopic notation , and the subscript refers to the color configuration of the @xmath62 : @xmath63 for a color singlet and @xmath64 for a color octet . the parton level differential cross sections relevant for hadroproduction of @xmath0 , including both color - singlet and color - octet contributions are given below @xcite : @xmath65 , \nonumber \\ { d\hat{\sigma}_{\mathrm{oct } } \over d\hat{t } } & = & \sigma_0 \left [ { 10\over 9 } \left ( { \hat{s}^2 s_1 ^ 2 + \hat{t}^2 t_1 ^ 2 + \hat{u}^2 u_1 ^ 2 \over s_1 ^ 2 t_1 ^ 2 u_1 ^ 2 } \right ) \langle o_8^{j/\psi}(^3s_1)\rangle \right . \nonumber \\ & + & { 6 \over \hat{s } s_1 ^ 2 m_c^2 } \left(2 \hat{s } + { 3 \hat{t } \hat{u } \over 4m_c^2 } - { 4 \hat{t } \hat{u } \over s_1 } \right ) \langle o_8^{j/\psi}(^1p_0)\rangle \nonumber \\ & + & \left . { 3\over 2 } { \hat{t } \hat{u } \over \hat{s } s_1 ^ 2 m_c^2 } \langle o_8^{j/\psi}(^1s_0)\rangle \right ] , \label{jpsixsection}\end{aligned}\ ] ] in eqs . ( [ ggpsiga ] ) we have defined @xmath66 ( with charm quark mass @xmath67 gev ) and @xmath68 , @xmath69 , and @xmath70 . in these formulae , @xmath71 , @xmath72 , and @xmath73 are the mandelstam variables , which can be written as @xmath74 in our numerical calculations the one loop expression for the running coupling , @xmath75 , with @xmath76 gev and @xmath77 is considered . the ( renormalization and factorization ) scale for the strong coupling and for the evaluation of pdfs is @xmath78 , where @xmath48 is the @xmath2 mass . for numerical values of the nrqcd matrix elements we have used those from ref . @xcite , which are ( units of @xmath79 ) : @xmath80 , @xmath81 , @xmath82 . we have checked that using another set of color octet matrix elements , taken from @xcite , our results do not change considerably , since we only calculate the ratio between the production cross sections , and the dependency on the color octet matrix elements cancels out in those ratios . in what follows we estimate the differential cross sections for central ( @xmath83 ) and forward ( @xmath84 ) rapidities for the @xmath37 , @xmath35 and @xmath36 collisions in order to compute the nuclear modification factors . from eq . ( [" +"ever since the discovery of the geometrical phase accompanying adiabatic driving in quantum systems @xcite , the role that geometric quantities play in many physical phenomena has been in the focus of intense research @xcite . by geometric quantities we mean here quantities which are determined solely by the geometry of the path drawn by the changing driving parameters . the berry phase is one such quantity : as a quantum system is adiabatically transported along a closed cycle in the space of the driving parameters , its wave function accumulates a phase @xmath1 which depends only on the geometry of the cycle . in particular , @xmath1 is the line integral of a vector field ( the berry connection ) over the closed path in the parameter space . geometric quantities are indeed common in other branches of physics besides quantum mechanics , and all can be expressed as the line integral of some vector field . the most prominent example is the work output @xmath2 per cycle of a thermodynamic engine @xcite . this is perhaps the simplest example of a geometric pump , namely , a system that adiabatically converts an ac driving into a dc current ( not to be confused with rectification ) . like the thermodynamic engine , any geometric pump is fully characterized by a vector field @xmath3 , which we shall call the pumping field . adiabatic pumps are currently in the limelight of topical experimental and theoretical research . stochastic pumps @xcite , whose mechanisms underlie , e.g. , the functioning of brownian motors @xcite , or heat pumps @xcite are important examples . quantum charge pumps @xcite , based on the adiabatic manipulation of coherent devices , are another exciting avenue of research of this kind , also in view of their application to metrology @xcite . since the pioneering paper by thouless @xcite many aspects of adiabatic pumping have been elucidated . an incomplete list includes the scattering theory of ( charge , spin , heat ) pumping @xcite , its extension to include electron - electron interaction @xcite , the theory of cooper - pair pumping in superconducting nanocircuits @xcite , and topological pumping @xcite . along with this intense theoretical activity , a number of important experiments have been successfully performed @xcite . in all these cases , dissipation plays an unavoidable , possibly constructive role , whose features are yet to be fully understood . this motivated a renewed interest in studying the combined effects of noise and driving @xcite in the context of adiabatic quantum transport @xcite . all those prior attempts attacked the problem by solving the reduced dynamics of the slowly driven open quantum system within some approximation scheme appropriate to each specific physical case . this gives the reduced density matrix @xmath4 , which is used to calculate the instantaneous current @xmath5 , and by time integration the total pumped charge , out of which one has to single out the geometric contribution . here we pursue instead _ a geometric approach _ to calculate the pumping field @xmath3 giving the geometrically pumped charge directly . our approach is based on the salient observation that , independent of the specific physical scenario , @xmath3 is in fact the vector of linear response coefficients in the adiabatic expansion of the current [ see eq . ( [ eq : taylor ] ) below ] . to the best of our knowledge , this result was never exploited before in the context of dissipative quantum pumping . it brings about two main advantages : ( i ) when applied to an open quantum system , it leads to an exact expression of @xmath0 in terms of equilibrium quantum correlation functions , which are calculated at frozen driving parameters . that is , our scheme makes evident that solving the _ reduced _ dynamics of an undriven system suffices . ( ii ) since @xmath3 characterizes the geometric pumping fully , once one knows it , calculating the charge pumped along any cycle is as simple as doing a line integral . besides , the curl @xmath6 provides immediate visual information about the geometric features associated to dissipative pumping . these unveil the possibility of many previously undetected dissipation - assisted operation protocols . see our cooper - pair sluice example below . our expression of the pumping field [ see eq . ( [ eq : f ] ) ] can be used in a wide range of cases of experimental interest , ranging from electron pumps based on quantum dots to cooper - pair pumps in superconducting devices . we illustrate the method in the latter case . to this end we pursue here the derivation of a specific equation of motion ( eom ) for the calculation of equilibrium quantum correlation functions at fixed driving parameters under the sole assumption of weak coupling to a bosonic bath . we emphasize that the eom neither rests on a markov nor a rotating wave approximation . consider a generic geometric pump , namely , a physical device that can be externally manipulated by several control parameters @xmath7 and supports the flow of a current @xmath8 . we are interested in the `` charge '' @xmath9 that is transported by the device as the parameters draw a closed path @xmath10 in the parameter space . the symbol @xmath11 denotes the time duration of the cycle . in general , the transported charge has a geometric contribution . the key to singling out the geometric component of the transported charge is to perform an `` adiabatic expansion '' of the current at any generic time @xmath12 , namely , a taylor expansion of the current @xmath8 in terms of the rate of change @xmath13 of the parameters : @xmath14 where the coefficients @xmath15 are functions of the value @xmath16 taken by the parameters at time @xmath12 . accordingly , the transported charge is given by @xmath17 the zeroth - order term is what is customarily referred to as the dynamical charge . it is due to the fact that charge could possibly flow even at fixed parameters @xcite . note that the dynamical charge depends very strongly on the duration of the cycle : the same cycle operated at half the speed would result in twice the dynamic charge . the first - order term , in contrast , is geometric , because @xmath18 depends only on the geometry of the path . on the contrary , the higher - order terms are not geometric , because the change of variable @xmath19 would not suffice to remove the explicit @xmath13 dependence of their integrands . thus the full geometric contribution to the transported charge @xmath20 is exactly and solely given by @xmath21 with @xmath0 the vector of adiabatic linear response coefficients , and @xmath6 its curl . ( the double integral is a surface integral over any surface having @xmath10 as its contour , i.e. , the stokes theorem . ) , @xmath22 are separated by a superconducting island ( green ) whose polarization charge @xmath23 is externally controlled by the gate voltage @xmath24 . the resistor ( blue ) represents environmental gate noise of thermal energy @xmath25 . the threading magnetic flux @xmath26 fixes the overall phase difference @xmath27 across the sluice . right panel : typical driving path used in experiments @xcite . ] as an application of timely interest , we consider the cooper - pair sluice @xcite sketched in fig . [ fig : sluice ] . the sluice consists of two superconducting quantum interference devices ( squids ) separated by a superconducting island . the system is phase biased , with the phase difference @xmath27 . the two squids with respective josephson couplings @xmath28 and @xmath29 can be independently manipulated by controlling the magnetic flux threading each of them , @xmath30 and @xmath31 . the island is further capacitively coupled to a gate electrode controlling its polarization charge in units of cooper pairs @xmath32 , where @xmath33 is the gate capacitance , @xmath34 is the electron s charge , and @xmath24 is the applied gate voltage . the three driving parameters in this case are @xmath35 , @xmath36 , and @xmath37 , with @xmath38 the charging energy of the island . we assume the sluice is operated in the regime where the charging energy @xmath38 is much larger than @xmath28 and @xmath29 . in this regime the sluice can be conveniently modeled as a tunable two - level system . in the basis of charge states @xmath39 , the hamiltonian reads @xmath40 , with @xmath41/2 $ ] , @xmath42/2 $ ] , and @xmath43 ( @xmath44 are the pauli matrices ) . the charge flowing through the sluice is associated to the current operator @xcite @xmath45 the sluice is subject to thermal noise at temperature @xmath46 coming from the voltage gate . depending on the time scale @xmath47 , there are two distinct adiabatic regimes : the coherent regime and the dissipative regime @xcite . the first is relevant when the driving time @xmath47 is very short compared to the thermal relaxation and decoherence times but long compared to the transition times @xmath48 . accordingly , one performs an adiabatic expansion around the eigenstate @xmath49 ( as in @xcite ) , and the pumping field emerges as @xmath50 for the cooper pair sluice working close to the ground state , we obtain , for its curl , the following analytical result : @xmath51 notice that @xmath52 , where @xmath53 is the ground - state berry curvature @xcite . in the case when the driving time @xmath47 is very short compared to the thermal - relaxation time , instead , the reference state around which the expansion is performed is the instantaneous thermal state @xmath54 , with @xmath55 the partition function and @xmath56 the total hamiltonian , sum of system , environment , and coupling hamiltonians , respectively . the adiabatic linear response theory developed in ref . @xcite gives then @xmath57 where @xmath58 , @xmath59 , and the subscripts of @xmath60 and @xmath61 denote that these operators are considered in the heisenberg representation generated by the full hamiltonian ( [ totalh ] ) ( with fixed @xmath16 ) at the times @xmath62 and @xmath63 , respectively . note that , as anticipated , the correlation functions of eq . ( [ eq : f ] ) are evaluated at fixed @xmath16 . clearly , their evaluation does not involve the solution of a driven open - system dynamics . the expression ( [ eq : f ] ) is exact and approximations enter only at the point of evaluating it . below we present our original method for its calculation . we emphasize that eq . ( [ eq : f ] ) can not be obtained within the common reduced density matrix approach @xcite , because the sole , single - time , reduced density matrix operator does not suffice for the exact evaluation of two - time quantum correlations @xcite . we model the thermal environment of the sluice as a set of harmonic oscillators @xcite : @xmath64 here @xmath65 , @xmath66 , @xmath67 , @xmath68 , are the oscillators positions , momenta , masses , and frequency , respectively , @xmath69 is a system operator , and @xmath70 is an environment operator . the evaluation of the field @xmath71 in ( 7 ) involves evaluating the equilibrium quantum correlation function at various , but fixed , parameter values @xmath16 . the dependence of @xmath3 on @xmath16 comes from the parametric dependence of the total hamiltonian @xmath72 on @xmath16 . to this end we begin by writing the imaginary - time integrals in eq . ( [ eq : f ] ) as real - time integrals @xcite , @xmath73\rangle_{\bm b}^\text{eq } = \frac{i}{\hbar}\int_0^\infty d{s}\,\,{s}\,\mathrm{tr}_s i ( \bm y_{-{s}}-\bm y_{-{s}}^{\dagger } ) $ ] , where @xmath74\ , ," +"energy transfer mechanisms in molecules exposed to short intense laser pulses is of great current interest @xcite . processes such as multiple photoionization , multiphoton dissociation and high - order harmonic generation have been studied for a wide - range of molecular species and an excellent up - to - date review of the field has been provided by posthumus @xcite . the hydrogen molecule and molecular ion represent ideal systems for a detailed understanding of ionization and dissociation dynamics of small molecules @xcite . the simplicity of molecule means that it is the system of choice for theoretical studies . in general the mechanisms of dissociation @xcite and ionization @xcite are very well characterised for this molecule . nonetheless , the solution of three - body disintegration , incorporating spatial and temporal variations in the laser pulse as well as the thermal ensemble of molecular states , remains a severe challenge for simulation . consequently , progress has been fairly limited in dissociative ionization spectrum calculations . although there exists a wealth of data on the photofragment energy spectrum for the neutral molecule , h@xmath4 , and its deuterated forms @xcite . the data for the much simpler isolated molecular ion is extremely scarce . the feasibility of experimental studies is hampered by the difficulty in preparing the molecular ion . in fact experiments on h@xmath5 in intense laser fields has only become possible in the last 4 years @xcite due to refinements in ion sources and charged molecular beam spectroscopy . typically a small portion of the molecules , at a temperature of a few hundred kelvin and hence predominantly in the vibrational state @xmath6 , can be converted into the bound molecular ion by electron - impact ionization , @xmath7 the molecular ions can be extracted , cooled and collimated into a beam that can be injected to the focus of the laser . the photodissociation and/or photoionization processes , @xmath8 produce ions and electrons that can be collected and analysed . owing to the small nuclear mass , the expansion ( vibration ) is very rapid - on the scale of 10 fs or less . consequently the molecule relaxes extremely rapidly on the timescale of the pulse rise time . the design of infrared pulses that would , among other things , allow the resolution of timescale of a fraction of a femtosecond . the main aim of this paper is a direct comparison of theory and experiment for the proton energy spectrum produced by a short intense infrared pulse interacting with h@xmath5 @xcite . fragment - ion coincidence measurements that isolate the dissociation and dissociative ionization processes and make the comparison of theory and experiment feasible and realistic . the molecular dissociation dynamics are modelled using a two - state approximation and takes account of the laser pulse profile . although this approach neglects the ionization channels , the results for dissociation energies are in excellent agreement with the observations . the characteristic vibrational and rotational time of the h@xmath5 molecule are @xmath9 fs and @xmath10 fs , respectively . for a pulse duration 60 fs or less , the laser interaction is sudden on the rotational timescale . thus one can assume a random statistical orientation of the molecular axis , and that the nuclei recoil along the axial direction . we assume that the bound ion is created by vertical transitions from the @xmath11 state of the neutral @xmath12 . the parameters of this potential surface are , bond length @xmath13a.u . with vibrational constants , @xmath14ev and @xmath15 . the @xmath11 wavepacket is promoted onto the corresponding molecular - ion surface @xmath16 with parameters @xmath17a.u . , @xmath18ev , @xmath19ev and @xmath20 @xcite . the @xmath11 state is projected onto the @xmath21 manifold of states according to the franck - condon principle @xcite . the manifold of @xmath21-states is then subjected to intense ti : sapphire light . in the dissociation process , momentum is conserved , for a symmetric pulse , and the recoiling atom and ion have equal and opposite velocity in the centre - of - mass frame . the ions and atoms are collected in coincidence such that dissociation and dissociative ionization can be discriminated . however , depending on the method of measurement , the atomic fragments can arise from the entire focal volume of the laser . so a valid theoretical comparison must firstly establish the single molecule energy spectra , and then sum these spectra with the appropriate focal volume weighting for the experiment . the intensity @xmath22 of a focused cylindrically - symmetric laser beam is spatially gaussian in the radial @xmath23-direction and lorentzian along the axis @xmath24 @xcite @xmath25}\right\}.\ ] ] where the minimum waist of the beam @xmath26 and rayleigh range @xmath27 are given by @xmath28 respectively . in our method , we first discuss the single - molecule response in detail , and then describe the orientation - averaged and focal - volume integrated results . the electronic coordinate , with respect to the origin at the internuclear midpoint , is denoted by @xmath29 and the internuclear coordinate is written as @xmath30 . the two lowest electronic states , namely the ground state @xmath31 , and @xmath32 are sufficient for the study of pure dissociation dynamics . the corresponding adiabatic energies are @xmath33 and @xmath34 . then the two - state approximation is @xmath35 where @xmath36 and @xmath37 are the time - dependent nuclear wavefunctions . in restricting the electronic spectrum to the two lowest levels , the calculations will inevitably be gauge dependence . for low frequency fields ( much less than the energy level gap ) it is essential to use the length gauge for the laser - molecule interaction . let us take the light as linearly polarized along the direction @xmath38 , and denote the dipole moment between @xmath39 as @xmath40 . writing the electric field as @xmath41 , the coupling potential is denoted by @xmath42 , where @xmath43 . within the axial - recoil approximation , @xmath44 , is the angle of ejection of the ion(atom ) with respect to the polarization vector . averaging over the molecular orientation is equivalent to averaging the projection of the electric field along the molecular axis . since the dissociation rate increases rapidly with intensity over the range , @xmath45 w @xmath3 , it follows that the atoms and ions are ejected predominantly along the polarization direction . it is highly anisotropic . however at the higher intensities , @xmath46 w @xmath3 , the dissociation process begins to saturate and , as we will show , the angular distribution is broader . taking @xmath47 to denote the reduced mass of the protons , and using atomic units , the two - state coupled equations are : @xmath48 to a very good approximation @xcite the potential functions can be written in the form , @xmath49 , \\ e_u(r ) & = & 0.1025 \left[e^{-1.44(r-2 ) } + 2.22e^{-0.72(r-2 ) } \right ] \label{morse}\end{aligned}\ ] ] similarly , the dipole moment @xcite can be fitted by the function @xcite @xmath50 with , @xmath51 . for a frequency @xmath52 and peak field strength @xmath53 this is related to the cycle - average intensity , @xmath54 . the time - dependence of the field can be written explicitly as @xmath55 in this paper we use the gaussian profile that most closely models the pulses in the experiment of interest , @xmath56\ ] ] where @xmath57 is the maximum , and @xmath58 defines the duration of the laser pulse . discretization methods previously developed for photodissociation @xcite and photoionization of molecules @xcite can be readily applied . the discrete - variable representation ( dvr ) has proven to be a very efficient and accurate method in solving both time - independent and time - dependent schrdinger equations . the cartesian lagrange functions @xcite are given by @xmath59\exp\left[i\frac{2\pi k}{n}x\right ] \label{c/08/02/04}\end{aligned}\ ] ] with the mesh points @xmath60 ( @xmath61 ) . the radial coordinate @xmath30 is discretised on this mesh cartesian mesh between the limits @xmath62 , with @xmath63 , such that : @xmath64 + { \textstyle { 1 \over 2 } } ( r_{max}+r_{min})\ ] ] then the wavefunctions are expanded as : @xmath65 } \hspace*{0.2cm}(\sigma = g , u ) \label{psiexpan}\end{aligned}\ ] ] where @xmath66 . then the matrix equation corresponding to equations ( [ c1 ] and [ c2 ] ) is a dense set of @xmath67 linear equations ( @xmath68 ) : @xmath69 the matrix elements of the kinetic operator are given by @xcite @xmath70 } { \sin^2\left[\pi(i - j)/n\right ] } & i\neq j. \end{array } \right.\ ] ] where the scale factor is , @xmath71 . the diagonal potentials are : @xmath72 with the off - diagonal coupling : @xmath73 we integrate the differential equations using the 18th order arnoldi propagator as described by peng et al @xcite . as is well known @xcite , for @xmath74 , the moment @xmath75 , and the coupling is divergent in the molecular basis . this is simply a manifestation of the molecular basis and the use of the length gauge . it is necessary and convenient to transform to the asymptotic decoupled atomic eigenstates for the energy spectrum . these asymptotic states then evolve adiabatically at large distances and long times . however these states in turn are unbounded in configuration space . as shown by keller @xcite , it is possible to project the diffuse adiabatic asymptotic states onto a compact momentum space . more importantly , this methods produces the energy spectrum of the atoms that can be compared with experiment . following @xcite we divide the entire range of @xmath30 into two regions ; an internal region(_in _ ) , where the molecular forces are significant , and an asymptotic region ( _ as _ ) where they are not . the short - range polarization potential means that the interaction region can be comparatively small ( of the order 20 a.u . ) . then the wavefunction can be partitioned as follows : @xmath76 where : @xmath77 with @xmath78\right)^{-1}\ ] ] where @xmath79 is dividing point and @xmath80 is a parameter which determines the smoothness of the partition . in the asymptotic region hamiltonian is diagonalised by transforming to the atom+ion states @xmath81 : @xmath82 these states evolve into superpositions ( sums over momentum ) of the asymptotic states : @xmath83 ^ 2\right ] \label{scatt}\ ] ] where the ion quiver momentum is @xmath84 a symmetric or zero - area pulse is such that : @xmath85 . the key step in obtaining an energy spectrum is the projection of the numerical wavefunction onto the the continuum of asymptotic states ( [ scatt ] ) . it is efficient to do this by discretizing the @xmath86-space and performing a finite fourier transform @xcite . one difficulty with such an approach is that the momentum shift @xmath87 is a continuous function and inevitably leads to a mismatch of the @xmath86-grid . in the present calculations , we use the quadrature rule for the dvr to calculate the fourier transform directly . we define the shifted fourier transform : @xmath88 } \nonumber \\ & \times&\left\ { \exp\left [ -i r_{max } \left ( ( k\mp\delta_0(t , t^{\prime } ) ) - \frac{2\pi x_m}{nh}\right)\right ] \right . \nonumber \\ & - & \left . \exp\left [ -i r_{min } \left ( ( k\mp\delta_0(t , t^{\prime } ) ) -\frac{2\pi x_m}{nh}\right)\right ] \right\}. \label{myprop } \end{aligned}\ ] ] although this quadrature is less efficient than the fast - fourier transform , it allows for much greater flexibility in choosing the @xmath86 and @xmath30 grids . at each time step , the projection onto the momentum space is made and the coherent momentum space wavefunction is calculated . this process is repeated and continued for some time after the end of the pulse . this allows the dissociating wavepacket still within" +"recent exciting results from the searches for high - redshift type ia supernov ( sne ia ) have been interpreted as suggesting that there is indeed a cosmological constant and that the expansion of the universe is accelerating ( perlmutter 1999 and riess 1998 ) . the results on the cosmology are robust in that they are independent of the value of the hubble parameter , @xmath4 , ( as they use redshift , @xmath5 ) and also of the local calibration of the sne ia luminosities ( as the distance modulus is used ) . they do rest upon an underlying assumption that the local and global values of @xmath4 are the same ( so that the distance - redshift relationship does not change ) . here we examine how different the local value of @xmath4 must be from the global value in order to significantly change the cosmology derived from the fitting of high - redshift sne ia data to the hubble diagram . a similar approach was taken by kim ( 1997 ) to fit data from the first 7 high - redshift sne ia between @xmath6 ; in this paper we extend that work with a much larger number of supernov in the range @xmath7 . ( it should also be noted that the data used by kim favoured an @xmath8 cosmology at the time . ) the idea that the local universe is atypical has been suggested by numerous authors ( see dekel 1994 for a review ) . hudson ( 1999 ) report evidence for a large scale bulk flow on scales possibly greater than 14000 km s@xmath9 . plionis & kolokotronis ( 1998 ) show that there may be contributions to the x - ray cluster dipole from beyond 16000 km s@xmath9 . lauer & postman ( 1994 ) and scaramella ( 1992 ) suggest the possibility of even larger density inhomogeneities out to a distance of 15000 - 30000 km s@xmath9 . phillips & turner ( 1998 ) see that near - ir galaxy counts out to @xmath10 are deficient which may be due to a local underdensity on such scales , implying that the local value of the hubble parameter @xmath4 is up to 30 per cent higher than the global value . tammann ( 1998 ) also sees a decrease in the value of @xmath4 out to 18000 km s@xmath9 of 7 per cent . whilst these claims are not without their detractors it is clear that a body of work exists to suggest that the local value of @xmath4 may not be the same as the global value and could be higher . see turner , cen & ostriker ( 1992 ) for a detailed discussion of this topic . we assume that the value of @xmath4 on scales greater than @xmath11 is equal to the global value , and then fit open and flat cosmologies to the high - redshift sne ia data , shifting the zero - point of the data to find the best fit to the various cosmologies . the difference in zero - points between the local and high - redshift supernov is then used to calculate the difference between the local and global values of the hubble parameter . using the corrected data for 10 high - redshift sne ia presented in tables 5 and 6 of riess ( 1998 ) and for 40 supernova cosmology project ( scp ) high - redshift sne ia from table 1 of perlmutter ( 1999 ) we reconstruct the hubble diagrams . the shift in the local - to - global hubble parameter required to fit various flat and open cosmologies are then calculated using a @xmath12 fit , also finding the 95 per cent confidence limits . figure 1 shows the required local - to - global ratio of the hubble parameter to fit the scp sne ia data . the best fit when @xmath13 in fig . 1(a ) is the well - known @xmath14 cosmology found by perlmutter ( 1999 ) . more interestingly a variety of low @xmath2 open cosmologies are not rejected at the 95 per cent level even if @xmath13 . in order for an @xmath15 open cosmology to be the best fit to the data then @xmath16 is required . the recovery of critical mass density cosmologies is more difficult . they are rejected at greater than the 99 per cent level if @xmath17 and need a large ratio @xmath18 . the data of riess ( 1998 ) was also examined and the fits are very similar to those presented in fig . 1 although they are less significant due to the much lower number of data points . generally the riess data are slightly less consistent with a low @xmath2 open cosmology and @xmath8 critical cosmologies are ruled out at a higher confidence level , requiring a 1.2 to 1.3 @xmath19 ratio . to fit best a low @xmath2 open cosmology then the @xmath19 ratio must be 1.1 - 1.2 . if the local value of the hubble parameter is higher than the global value on scales of a few 100 @xmath20 mpc then the fitting of cosmological parameters to the high - redshift sne ia data of perlmutter ( 1999 ) and riess ( 1998 ) may be inappropriate . previously popular cosmologies such as open or critical matter density universes with no cosmological constant may be acceptable if we live in a local underdensity . whilst large underdensities of scales up to 300 - 600 @xmath20 mpc are not expected from standard power spectra , there is some observational evidence that we may live in such an underdensity ( see section 2 ) , a possibility which is not ruled out by these results . it seems that is too early yet to abandon the traditional models ." +"observational data of cosmological relevance refer to the characteristics of the cmb radiation and the clustering and structural properties of bound virialized ( more exactly , relaxed and steady ) objects such as lyman-@xmath0 clouds , galaxies , and galaxy clusters . to take full benefit of the information contained in the latter kind of data a good knowledge of how , when , and where these objects formed and evolved is required . indeed , this would allow us not only to correctly interpret the observed properties of those cosmological objects but also to properly use them to constrain the correct cosmogony ( i.e. , the possible gaussianity of the initial density field , its power spectrum , and the values of @xmath1 , @xmath2 , and @xmath3 ) . unfortunately , the modeling of the formation and growth of cosmic objects is not an easy task . even in the simple and yet most likely scenario , hereafter assumed , of structure formation via gravitational instability from a primordial gaussian random field of density fluctuations with power spectrum leading to hierarchical clustering no exact model can be build . the reason for this is the lack of an exact solution for the growth of density fluctuations in the non - linear regime . there are only two ways to circumvent this difficulty : the use of numerical simulations and the construction of ( semi ) analytical models relying on approximated collapse dynamics . the former is obviously more exact but it is not free of problems , either . numerical simulations are very time - consuming , which translates into a limited dynamical range and a very reduced region of the parameter space covered . moreover , numerical simulations give access to the yields of the complex processes taking place , but the full understanding of what is going on is not easy . in contrast , models are less accurate , sometimes possibly poorly justified , but are more practical and allow a deeper insight into the physics . in fact , both approaches are complementary : simulations ultimately justifies the goodness of analytical models while the latter bring the possibility to confortably explore a wide range of parameters and allow to better understand the results of the former . there are in the literature numerous reviews dealing with cosmological simulations . here i will focus on the improvements achieved , for the last twenty years , in the construction of a detailed model for the hierarchical clustering of objects . the different models developed so far are of two main kinds . on the one hand , there are models developed to derive the theoretical mass function of objects ( or haloes ) . these are brievely reviewed in 2 , the most relevant ones being discussed in more detail in 3 . on the other hand , there are models which go further and provide us with typical times and rates of the clustering process . these latter models are addressed in 4 . for simplicity , i assume an einstein - de sitter ( @xmath4 , @xmath5 ) universe and comoving units . as mentioned , all clustering models are based on some approximation to the collapse dynamics of density fluctuations . most of them , in particular the seminal model by press & schechter ( 1974 ; ps ) , rely on the spherical collapse model . this is a poor approximation , in general , to the real collapse . yet , the ps mass function gives very good fits to @xmath6-body simulations ( nolthenius & white 1987 ; efstathiou et al . 1988 ; efstathiou & rees 1988 ; carlberg & couchman 1989 ; white et al . 1993 ; bahcall & cen 1993 ; lacey & cole 1994 ) . the reason is likely that massive objects , those intended to be described , arise from high amplitude peaks ( density maxima ) of the initial density field and the collapse of matter around such peaks is particularly well described by the spherical model ( bernardeau 1994 ) . @xmath6-body simulations seem to show that there is no good correspondence between peaks and objects ( van de weygaert & babul 1994 ; katz , quinn , & gelb 1993 ) . but this is likely due to a variety of effects , namely the nesting of peaks on different scales , the use of an unappropriated window , or the inclusion of density constrasts and masses which do not correspond to the collapse times and filtering scales analyzed ( see below ) . actually , the ps mass function and new more or less sophisticated versions of it ( cole & kaiser 1989 ; bond et al . 1991 , bcek ; blanchard , valls - gabaud , & mamon 1994 ; jedamzik 1995 ; yano , nagashima , & gouda 1995 ) do not explicitly deal with peaks as seeds of bound objects . but a parallel set of models has also been developed within the peak theory framework ( colafrancesco , lucchin & matarrese 1989 ; bond 1989 ; peacock & heavens 1990 ; apple & jones 1990 ; manrique & salvador - sol 1995 ) reaching similar results . in the context of models relying on the spherical approximation , we must also mention the model constructed by cavaliere & menci ( 1994 ) using the theory of cayley trees with disorder . this is a more general formalism which recovers , as two extreme limits , the diffusion equation describing , as shown by bcek , the clustering of objects la ps , and the smoluchowski kinetic equation describing the aggregation of objects moving inside a relaxed system . indeed , this formalism is intended to derive the mass function of objects accounting for the fact that may survive and evolve inside larger scale objects ( for example , galaxies in clusters ) . this mass function is different from that intended to be derived in all previous models ; these only consider relaxed haloes which are not embedded within any larger scale relaxed system . here we will focus on the latter most usual viewpoint . there are also a few models based on other dynamical approximations . monaco ( 1995 ) has followed the ps approach but using the ellipsoidal collapse approximation . bond & myers ( 1993a , 1993b ) have considered this latter approximation in the framework of the peak theory . finally , doroshkevich & kotok ( 1990 ) and vergassola et al . ( 1994 ) have used the adhesion model . in principle , these are better approximations to the true collapse than the simple spherical model . however , in the case of the adhesion approximation , the mathematical calculations are very complicated and one can only infer approximate analytical solutions for the cases of pure 1-d , 2-d , or 3-d collapsed structures ( see doroshkevich & kotok 1990 ) . for the real composite case , one can only obtain the asymptotical behavior ( vergassola et al . 1994 ) . concerning the mass function obtained by monaco ( 1995 ) , it is not clear why it does not recover the ps solution at the large mass end where the spherical approximation should be essentially correct . in fact , bond & myers ( 1993a , 1993b ) find , in contrast , that the spherical collapse is a good approximation for very massive objects , indeed . the only drawback of the very accurate approach followed by these latter authors ( the so - called `` peak - patch '' formalism ) is that it involves complicated calculations including monte - carlo simulations which makes it less handy than usual ( semi ) analytical models . according to the spherical collapse model ( gunn & gott 1972 ) , the collapse time @xmath7 for a shell of radius @xmath8 around the center of a spherically symmetric , outwards decreasing ( to avoid shell crossing until @xmath9 ) linear density fluctuation partaking of the general hubble expansion at @xmath10 only depends on the mean density contrast @xmath11 ( the density fluctuation normalized to the mean density of the universe ) inside it through the relation @xmath12 , with @xmath13 the cosmic expansion factor and @xmath14 a constant equal to @xmath15 . the collapse of that shell represents , of course , the appearance , at @xmath7 , of a relaxed object of mass equal to ( to 0th order in @xmath11 ) @xmath16 , with @xmath17 the mean density of the universe . inspired of this simple model , ps assumed that any point in the initial ( linear and gaussian distributed ) density field smoothed with a top - hat filter of scale @xmath8 with density contrast _ above _ the overdensity @xmath18 collects matter so to reach , at @xmath7 related to @xmath18 through the expression above , a mass _ larger than _ @xmath19 . consequently , by differentiating over @xmath20 the volume fraction occupied by such points , @xmath21,\label{e2}\ ] ] with @xmath22 the rms density contrast on scale @xmath8 , one should obtain the volume fraction contributing at @xmath7 with objects of mass @xmath20 to @xmath23 , and by dividing it by @xmath24 the number density of such objects @xmath25 it is worthwhile mentioning that , in the case of power - law power spectra , there should be no privileged time or scale ( in an einstein - de sitter universe as assumed here ) . the ps mass function recovers this expected behavior . the number of objects in a volume @xmath26 , with @xmath27 corresponding to a scale defined through any arbitrary fixed value of @xmath28 , with mass @xmath29 in an infinitesimal range , as well as the volume ( or mass ) fraction subtended by objects of scaled mass @xmath29 in an infinitesimal range are time invariant , indeed . but the growth of density fluctuations can deviate from the spherical collapse in leaving the linear regime . hence , one should check whether small changes in those aspects the most strongly connected with the spherical approximation are suitable . in particular , other filters than the top - hat one , and other values of constant @xmath14 or of the proportionality factor @xmath30 between the mass and @xmath17 times the natural volume of the filter should be investigated . ( we must remark that there is degeneracy between the latter two constants , so there is just one degree of freedom for any given filter . ) yet , lacey & cole ( 1994 ) have recently shown that a very satisfactory fit to @xmath6-body data can be obtained for masses in the relevant range with a top - hat filter and @xmath14 close to the standard value ( for @xmath31 ) . a more serious problem , apart from the unnatural seeds of bound objects assumed , concerns the unjustified factor two in the right - hand member of equation ( [ e1 ] ) . this must be introduced for the final mass function to be correctly normalized , that is , for the integral of @xmath20 times the mass function to be equal to the mean density of the universe . ( every particle in the universe is at any time @xmath7 within some virialized object with appropriate mass . ) on the other hand , the overcounting of objects actually swallowed by previously collapsed ones and the neglected contribution to the mass of objects of low density regions enclosed within high density ones ( which might explain the fudge factor 2 ) are not accounted for . to analyze the effects of such cloud - in - cloud configurations cole & kaiser ( 1989 ) have devised a practical numerical method , called the `` block model '' . after" +"quantum - state engineering via optical or electrical manipulation over the coherent dynamics of suitable quantum - mechanical systems has become a fascinating prospect of modern physics . a very intriguing result in the study of a single particle in a double - trap system exposed to a time - dependent external field is the dynamic localization phenomenon@xcite , i.e. , for appropriate field parameters , a localized wave packet remains dynamically localized during the subsequent time evolution . this driving induced trapping has been theoretically and experimentally studied in many physical and chemical systems@xcite . when two or more interacting particles are present , apart from the highly nontrivial question of whether the strong many - body interaction can be overcome for the particles to create and preserve localization , the possibility of entanglement of the many - body wave functions arises . entanglement is an essential ingredient in any scheme of quantum information processing . recently , quantum dot realizations of the entanglement have received increasing attention . various schemes based on electron spins and electron - hole pairs have been proposed to implement quantum computer hardware architectures@xcite . although there have been some numerical studies on interacting electron systems driven by an ac field@xcite , there is still little theoretical understanding of the observed effects beyond the phenomenology level at the present time . in this paper , we address the dynamic localization and quantum entanglement of two interacting electrons in a double quantum dot system driven by an ac field ( see fig . 1 ) . we show that with certain choice of parameters , in contrast to direct intuition , the coulomb repulsion may enhance the localization due to the level crossing associated with different symmetries of a dynamic parity operation ( discussed in more detail later ) . we also show that the maximally entangled bell state can be prepared and maintained with a pulse of an ac field . our study provides useful information for the future exploitation of coherent control of two - electron states in quantum dots . in sec . ii we present the hamiltonian for two interacting electrons in a double - dot system . a simplified spin-1 representation of the hamiltonian is given in sec . iii . in sec . iv we discuss the phenomenon of coulomb - enhanced localization . the field excitation procedure to generate the maximally entangled bell state is showed in sec . v. a summary is given in sec . the hamiltonian which we use to describe the dynamics of two interacting electrons in a coupled quantum dot driven by electric field is @xmath0 @xmath1 @xmath2 where @xmath3 is the coulomb interaction and @xmath4 the single - particle hamiltonian . the time - dependent electric field @xmath5 is applied along the inter - dot axis . the dielectric constant @xmath6 and the effective mass @xmath7 are material parameters . the potential @xmath8 in @xmath4 describes the in - plane confinement , whereas @xmath9 models the longitudinal double - well structure . the transverse coupling of the dots is modeled by a harmonic potential @xmath10 it has been shown in experiments with electrically gated quantum dots in a two - dimensional electron system that the electronic spectrum is well described by a simple harmonic oscillator@xcite . in describing the confinement @xmath9 along the inter - dot axis , we use a ( locally harmonic ) double well potential of the form @xmath11 which , in the limit of large inter - dot distance , separates into two harmonic wells ( one for each dot ) of frequency @xmath12 . although in principle a square - well potential would be a more accurate description of the real potential than the harmonic double well , there is no qualitative difference between the results presented below obtained with harmonic potential and the corresponding results using square - well potential . we assume the transverse confinement is strong enough . thus , the @xmath13 degrees of freedom are frozen in the dynamics and the two - electron wave function can be written as @xmath14 , where @xmath15 is the transverse ground state . considering the fact that the external electric field is applied along the longitudinal direction , the approximation of frozen in - plane motion is reasonable and has been employed in previous work@xcite . after integrating over the @xmath13 degrees of freedom , the time dependent schrdinger equation becomes @xmath16|\phi ( z_{1},z_{2},t)\rangle , \nonumber\end{aligned}\ ] ] where @xmath17 is the effective one - dimensional coulomb interaction @xmath18 we use the effective mass @xmath7 and dielectric constant @xmath6 of gaas . the other parameters are chosen as @xmath19mev and @xmath20 nm . the time evolution of the two electrons is obtained by numerically solving the schrdinger equation ( 4 ) using an extension of the crank - nicholson method@xcite to two spatial dimensions . the initial state used in this investigation is the field - free ground state , which is obtained by propagating a trial two - particle wave packet in the imaginary time domain and shown in fig . as illustrated by the spatial symmetry under the particle exchange , the ground state is a singlet , as expected . ( 4 ) contains no mixing between the singlet and triplet sub - spaces , the dynamics of the system will always be confined to the singlet sub - space . to understand the underlying physics behind the numerical results we employ the hund - mulliken ( hm ) approximation by introducing the orthonormalized one - particle wave functions @xmath21 , where @xmath22 are the single - particle ground states for the right and left dots , @xmath23 denotes the overlap integral , and @xmath24 . using @xmath25 , we construct three singlet basis functions with respect to which we diagonalize the two - electron hamiltonian : two states with double occupation in each dot , @xmath26 , @xmath27 , and one state with single occupation in each dot , @xmath28 $ ] . calculating the matrix elements of the hamiltonian in this orthonormal basis , we obtain @xmath29 where we have dropped a constant energy term that makes no contribution to the dynamics . ( 6 ) @xmath30 is the difference between the intradot and interdot coulomb interaction , @xmath31 denotes the single - particle tunneling induced by dot - dot coupling and the coulomb interaction , @xmath32 describes the electron - field coupling , and @xmath33 and @xmath34 are the @xmath35- and @xmath36- components of the spin-1 operator . the localized two - particle state @xmath37 is equivalent to the eigenstate @xmath38 of @xmath34 and @xmath39 to the state @xmath40 , while the delocalized state @xmath41 is identical to the state @xmath42 . according to the expression for @xmath43 and @xmath44 , using the material parameters given below eq . ( 5 ) we obtain @xmath45mev and @xmath46mev . in the absence of an external driving , the eigenenergies of @xmath47 are @xmath48 @xmath49 , and @xmath50 , and the corresponding eigenstates are @xmath51 @xmath52 @xmath53 the symmetric ground state @xmath54 is dominated by the delocalized state @xmath41 due to the strong coulomb repulsion , whereas the other two eigenstates are nearly degenerate and dominated by the two localized states @xmath37 and @xmath39 . the superposition of the two localized states @xmath37 and @xmath39 implies that the spatial wave functions of the two electrons have been entangled and correlated , in the usual sense that they can not be factorized into single - particle states . the nonlinear term in @xmath47 can be exploited to generate entangled states . the ground state of eq . ( 7 ) is plotted in fig . clearly the hm approximation describes the ground state very well when compared with the exact numerical solution [ fig . to investigate dynamic localization , one must start with a localized wave packet . this can be realized from the unperturbed ground state by two separate methods : one is to suddenly switch on a dc field with the strength satisfying the resonance condition @xmath55 . at time @xmath56 , the delocalized ground state @xmath54 evolves into a localized state @xmath39 with two electrons occupying the same right dot . the alternative method is to adiabatically switch on a constant electric field . then as shown in fig . 2(c ) , the ground state configuration develops a series of coulomb stairs as a function of the field amplitude , corresponding to a series of avoided crossing in the energy spectrum [ see fig . 2(d ) ] . after preparing a localized state , say @xmath39 , by adiabatic evolution in the presence of a dc field , the dc field is suddenly swiched off and an ac field of the form @xmath57 is swiched on . we show now that the localization can be dynamically maintained by the ac field even when the field strength is small compared to the coulomb repulsion between the two electrons . time periodicity of the hamiltonian enables us to describe the dynamics within the floquet formalism . in addition , since the hamiltonian is invariant under the combined dynamic parity operation @xmath58 ; @xmath59 , each floquet state is either odd or even . quasienergies of different parity may cross , otherwise an avoided crossing may occur . figures 3(a)-(b ) show the quasienergy spectra of @xmath60 as a function of @xmath61 with the presence and absence of the coulomb interaction , respectively . two prominent features can be identified from the comparison of these two cases : ( i ) the strong coulomb interaction removes the level crossings among three two - particle states and thus induces avoided crossings ; ( ii ) in the weak field regime , there occurs a crossing between the quasienergies @xmath62 and @xmath63 , which develop from the unperturbed eigenenergies @xmath64 and @xmath65 . to illustrate the effect of this crossing on the system s dynamics , we begin with the initial state @xmath39 and follow the time evolution of the probability @xmath66 for finding the two electrons in the right dot . the result is shown in fig . it is clear that @xmath67 always remains near 1 as if the two electrons were frozen in the same right dot . this dynamic localization seems counterintuitive at first as the coulomb repulsion is very strong compared to the ac field , preventing the two electrons occupying the _ same _ dot . the localization shown in fig . 3(c ) has no correspondence in a non - interacting case , since no level crossings occur in the weak field regime if the coulomb interaction is absent . therefore , the present localization effect results from an interplay of the coulomb interaction and an ac field . furthermore , we find that even if the coulomb interaction is strong enough , the dynamic localization can still occur at the crossing of the quasienergies @xmath62 and @xmath63 . slightly away from the crossing point , the life time for finding two electrons in the right dot is very long . this makes the experimental realization of the dynamic localization more realistic . the ratio @xmath68 at the first crossing is about @xmath69 , a root of the zero - order bessel function , suggesting that the two - electron localization can be approximated by a two - state model composed of @xmath70 and @xmath71 . surprisingly , we find that in the strong field regime , the presence of coulomb repulsion may help to enhance the dynamic localization when compared with the non - interacting case . from eq . ( 7 ) we see that due to the strong coulomb interaction , @xmath72 . thus the initial localized state can be approximated by a superposition of the degenerate floquet states developed from the nearly - degenerate states @xmath70 and @xmath73 , which leads" +"the properties of crystalline substances often crucially depend on the structure and dynamics of imperfections of the crystal lattice . in particular , point defects such as interstitials and vacancies play a pivotal role in determining the stability , transport properties , growth characteristics , and mechanical behavior of materials . recent impressive experimental advances , such as optical tweezers and confocal microscopy @xcite , now permit to study the fundamental properties of point defects in condensed matter systems with `` atomistic '' space and time resolution . recently , a number of experimental studies have focused on the structure and dynamics of point defects in two - dimensional assemblies of micrometer sized colloidal particles @xcite and , in particular , on their effective interactions @xcite . in studying such defect interactions the question arises to which degree they can be rationalized in terms of continuum elastic theory . as a first step towards answering this question , in this article we investigate numerically the disturbances caused by isolated interstitial particles and compare the results with the predictions of continuum theory . in carrying out such a comparison , it proves crucial that in solving the equations of elasticity theory boundary conditions are used that match those of the simulations . for the periodic boundary conditions usually applied in computer simulations , the displacement fields of single defects can be determined using the technique of ewald summation familiar from electrostatics @xcite . while elasticity theory properly describes the disturbances and interactions created by lattice imperfections on a larger scale , discrete lattice effects dominate on spatial scales of the order of few lattice constants . the remainder of this paper is organizes as follows . in sec . [ sec : model ] we define the model and describe the numerical methods . the treatment of point defects in a two - dimensional elastic continuum is discussed in sec . [ sec : elasticity ] and comparison with the numerical results is discussed in sec . [ sec : results ] . for certain defect configurations one observes an exponential rather than algebraic decay of the displacement fields . this behavior can be understood in terms of a simple bead - spring model introduced in sec . [ sec : spring ] with parameters related to the elastic constants of the material . some concluding remarks are provided in sec . [ sec : discussion ] . in this paper we study a two - dimensional crystal of soft particle interacting via the gaussian potential @xcite @xmath0 where @xmath1 is the inter - particle distance and @xmath2 and @xmath3 set the energy and length scales , respectively . in the following , energies are measured in units of @xmath2 and distances in units of @xmath3 . this so - called gaussian core model , used here as a generic model for a system of soft spheres , is a realistic description for the short - ranged effective interactions between polymer coils in solution @xcite . in three dimensions , the gaussian core model can exist as a fluid , a bcc- and an fcc - solid depending on temperature and density @xcite . in two dimensions , the perfect triangular lattice is the lowest energy structure of gaussian core particles at all densities @xcite . computer simulations indicate that also in this system of purely repulsive particles point defects such as interstitials , vacancies or impurity particles of different size display attractive ( as well as repulsive ) interactions both in two and three dimensions @xcite . to study the displacement field of a single interstitial numerically , we prepare a configuration of particles arranged on the sites of a perfect lattice configuration and insert an extra particle of the same species . after insertion , the system is relaxed to a new minimum energy configuration by steepest descent minimization , i.e. , we study the defect structure at @xmath4 . typically , @xmath5 steepest descent steps are carried out . the system we study here consists of @xmath6 gaussian core particles ( without the extra particle ) at a number density of @xmath7 corresponding to a lattice constant @xmath8 . periodic boundary conditions apply to the simulation box of length @xmath9 and height @xmath10 . the aspect ratio of the almost square simulation box is @xmath11 . we quantify the perturbation caused by the defect in terms of the displacement field @xcite @xmath12 here , @xmath13 and @xmath14 denote the position of particle @xmath15 with and without the defect , respectively . as we will see in the following sections , simple point defects generate remarkably intricate displacement patterns that can be understood in terms of elasticity theory only on large length scales . at @xmath4 , the elastic constants describing the macroscopic response of the system to perturbations can be calculated as a function of density from simple lattice sums . for a density of @xmath16 , the lam coefficients ( see sec . [ sec : elasticity ] ) of the perfect triangular lattice have values @xmath17 and @xmath18 . at this density , the pressure is @xmath19 and the energy density is @xmath20 corresponding to an energy per particle of @xmath21 . the bulk modulus , which in two dimensions is related to the the lam coefficients by @xmath22 , has a value of @xmath23 . while close to a point defect the displacement field is highly anisotropic and strongly dependent on the atomistic details of the interactions , for large distances elasticity theory is expected to be valid . the differential equations describing the equilibrium of an elastic continuum are usually expressed in terms of the strain tensor @xcite @xmath24 where @xmath25 denotes the @xmath15-component of the displacement @xmath26 and @xmath27 the @xmath15-th component of the position @xmath28 . for a given external volume force @xmath29 with components @xmath30 acting on an isotropic system such as a crystal on a triangular lattice , hook s law leads to the equilibrium condition for the strain : @xmath31 here , @xmath32 and @xmath33 are the so - called lam coefficients and summation over repeated indices is implied . solving this equation for a singular force yields the green s function from which the response of the elastic continuum to an arbitrary force can be obtained by integration . to model the displacement field caused by the introduction of point defects using linear continuum elasticity theory , we determine the displacement field caused by two pairs of opposing forces , one pair acting along the @xmath34-axis and the other one along the @xmath35-axis @xcite . this idealized model of a defect is equivalent to inserting a small circular inclusion into a hole of different size @xcite . each force of this pair is of equal magnitude @xmath36 but with opposite sign acting on two points separated by a small distance @xmath37 . such a force pair exerts a zero net force on the material . in the limit @xmath38 where the force @xmath39 in a way such that @xmath40 remains constant , the equilibrium condition for the displacement can be written as @xmath41 assuming that the displacement can be written as the derivative of a potential , @xmath42 one obtains @xmath43 this equation is the poisson equation of electrostatics with a singular disturbance . since , as noted above , @xmath44 is a solution of @xmath45 ( see , for instance , ref . @xcite ) , we obtain the green s function @xmath46 from which the displacement field @xmath47 follows by differentiation according to equ . ( [ equ : displacement_phi ] ) , @xmath48 in comparing the results of particle simulations with those of elasticity theory it is important to realize that the displacement fields predicted by continuum theory are of a long - range nature . therefore , it is crucial that corresponding boundary conditions are used in both cases . all simulations discussed in this paper are done with periodic boundary conditions in order to minimize surface effects and preserve the translational invariance of the perfect lattice . hence , also the continuum calculations need to be carried out with periodic boundary conditions . since the defect fields for the infinite material are long - ranged , the displacement field in the periodic system can not be obtained by simply summing up the contributions of the periodic images . in fact , such a naive summation of the contribution of all image defects diverges . a more appropriate treatment that avoids this problem consists in determining the green s function of the poisson equation ( [ equ : poisson ] ) for periodic boundary conditions . in this case , the solution of this equation in two dimensions , known from electrostatics @xcite , can be written as ewald sum of a logarithmic potential embedded in a neutralizing background , @xmath49 \right . \nonumber\\ & & \hspace{1.5 cm } \left . - \frac{2 \pi}{a } \sum_{{\bf k } \neq 0 } \frac{e^{-k^2/4\eta^2}}{k^2 } \cos({\bf k}\cdot { \bf r } ) + \frac{\pi}{2 \eta^2 a } \right\}.\end{aligned}\ ] ] here , @xmath50 is the exponential integral . the first sum is over all lattice vectors @xmath51 in real space and the second sum is over all reciprocal vectors @xmath52 in fourier space . the adjustable parameter @xmath53 , set to a value of @xmath54 here , determines the rate of convergence of the two sums and @xmath55 is the area of the rectangular simulation cell . the fourier space sum can be evaluated accurately using about 2,500 reciprocal space vectors . from equ . ( [ equ : ewaldpotential ] ) for the scalar function @xmath56 the displacement field of a point defect in a system with periodic boundary conditions is found by differentiation , @xmath57 for the systems considered in this paper , the real space sum may be truncated after the first term . since the value of @xmath58 is undetermined , the parameter @xmath59 is treated as a fit parameter in the following . the ewald sums of the above equations describe the effects of `` image defects '' at the center of the periodically replicated domains . first , we study the displacement field of a single interstitial . to generate such a defect , we insert an extra particle of the same species into a perfect 2d - crystal on a triangular lattice . after insertion , the system is relaxed to a new minimum energy configuration by steepest descent minimization , i.e. , we study the defect structure at @xmath4 . typically , @xmath5 steepest descent steps are carried out . in each step each particle is moved in the direction of the force acting on the particle where the absolute value of the displacement in chosen to be small enough to ensure that the energy of the system decreases in each step . ( a ) ( a ) , the @xmath60 ( b ) and the @xmath61 ( c ) configurations . the length of the arrows representing the displacements of the particles from their position in the perfect lattice are exaggerated for better visibility . in the figures at the bottom the blue spheres represent the particles and the small gray spheres indicate the position of the lattice sites of the perfect crystal.,width=142 ] ( b ) ( a ) , the @xmath60 ( b ) and the @xmath61 ( c ) configurations . the length of the arrows representing the displacements of the particles from their position in the perfect lattice are exaggerated for better visibility . in the figures at the bottom the blue spheres represent the particles and the small gray spheres indicate the position of the lattice sites of the perfect crystal.,width=142 ] ( c ) ( a ) , the @xmath60 ( b ) and the @xmath61 ( c ) configurations . the length of the arrows representing the displacements of" +"in quantum mechanics , the density operator @xmath0 of a quantum system is called a stationary state if @xmath1=0 $ ] , where @xmath2 is a given time - independent hamiltonian of the system . since @xmath0 satisfies the liouville - von neumann equation @xmath3 $ ] , it is clear that stationary states are invariant with respect to the transformation @xmath4 , where @xmath5 is the time evolution operator . in other words , stationary states do not change during the time evolution . for low - dimensional closed systems , the stationary states can be obtained relatively easily @xcite . it is a common situation , that a small quantum system is immersed in other , mostly large , system called the environment @xcite . such an open system does not evolve unitarily in time . an analysis of open quantum systems @xcite is much more complicated as they are a stage of a variety of physical phenomena @xcite . the famous decoherence process @xcite may serve as an example . in open quantum systems character of potentially existing stationary states is not obvious . there are various physical problems related to the properties of open quantum systems , which has already been addressed and intensively discussed ( see _ e.g. _ , @xcite ) . nevertheless , the procedure of deriving stationary states is not one of them . the existence and properties of stationary states have significant importance in quantum information processing and quantum theory itself . one can pose natural questions : 1 . do the stationary states exist for a given open system ? 2 . what features of a given model are responsible for existence of such states ? 3 . how such states can be constructed ? the answers to the above questions are still incomplete . for example , it is known that the stationary states exist for completely positive ( cp ) @xcite evolution of the open system , this fact follows directly from schauder fixed point theorem @xcite . however , this is only an existential result and so far there are no available methods to determine explicit form of stationary states . furthermore , the very existence of the stationary states in general case is an open problem _ e.g. _ , in the presence of initial system - environment correlations @xcite . the purpose of this paper is to propose the method of calculating the stationary states in the case of two - dimensional open quantum system . the theory of block operator matrices @xcite is adapted to achieve this goal . in particular , we use the _ riccati operator equation _ @xcite to solve the eigenproblem for the total hamiltonian . it is shown how to derive the stationary states by using the solution of the equation . we begin with a brief review of the block operator matrices approach to the problem of decoherence in the case of a single qubit @xcite . let @xmath6 be the hamiltonian of the total system . we will assume that it has the following form @xmath7 where @xmath8 and @xmath9 represent the hamiltonian of the qubit and the environment , respectively , while @xmath10 specifies the interaction between the systems . the hamiltonian @xmath6 acts on the hilbert space @xmath11 , where @xmath12 is the hilbert space ( possibly infinite - dimensional ) related to the environment . @xmath13 and @xmath14 are the identity operators on @xmath15 and @xmath12 , respectively . since the isomorphism @xmath16 holds true , the hamiltonian ( [ total ] ) admits the block operator matrix representation @xcite : @xmath17 all the entries of ( [ bom ] ) are operators acting on @xmath12 . moreover , the diagonal entries , _ i.e. _ , @xmath18 are self - adjoint . in this paper , we will focus on the case in which @xmath19 is bounded , thus @xmath20 is bounded as well ; however , no assumption on boundedness of @xmath18 is made . under these circumstances we have @xmath21 , where domains @xmath22 are assumed to be dense in @xmath12 . the generally accepted procedure to obtain the reduced time evolution of the open system , the so - called reduced dynamics , reads @xmath23 \equiv t_t(\rho_0).\ ] ] above , @xmath24 specifies the state of the open system at @xmath25 . the map @xmath26 assigns to each initial state @xmath24 a single state @xmath27 of the total system . the assignment map must be chosen properly so that @xmath28 can be well - defined @xcite . for instance , if no correlations between the systems are initially present , then @xmath29 , for some initial state of the environment @xmath30 . it is worth mentioning that , if the initial state can not be factorized , the definition of @xmath26 is not accessible @xcite . the unitary operator @xmath31 describes the time evolution of the total system . the map @xmath32 denotes the so - called partial trace : @xmath33 @xmath34 refers to the usual trace operation on @xmath12 , @xmath35 denotes the banach space of trace classes operator with the trace norm : @xmath36 , whereas @xmath37 is the banach space of @xmath38 complex matrices . note , the partial trace is a linear operation transforming the block operator matrices ( square brackets ) to the ordinary matrices ( round brackets ) . fixed point theorems like banach or schauder indicate the existence of stationary states for a given evolution @xmath28 . however , there is no general analytical procedure to obtain explicit form of such states . in this section we propose a method of deriving stationary states for two - level open quantum systems . the generalization to the higher - dimensions seems to be possible . however , we will not deal with this issue in this paper . we begin with some definitions . the density matrix @xmath0 is said to be a stationary state if it is invariant with respect to reduced evolution , @xmath39 . let @xmath40 be an operator acting on the hilbert space @xmath41 . the subset @xmath42 of @xmath43 defined as @xmath44 is said to be the graph of @xmath40 . the graph of a linear and closed operator is a subset of the hilbert space , which is a hilbert space itself equipped with the inner product @xmath45 @xmath46 is an inner product on @xmath12 . it is a known fact ( see lemma @xmath47 in @xcite ) that the graph @xmath42 is @xmath48invariant , that is @xmath49 if and only if @xmath40 is a bounded solution ( with @xmath50 ) of the _ riccati _ equation : @xmath51 along with the equation above we introduce the dual riccati equation , namely @xmath52 it is proved in @xcite that @xmath53 is a solution ( with @xmath54 ) of ( [ ricc2 ] ) if and only if the orthogonal complement of @xmath42 , _ i.e. _ , the subspace @xmath55 is @xmath6-invariant . it is straightforward to see that a bounded operator @xmath40 solves ( [ ricc ] ) if and only if @xmath56 is a solution of ( [ ricc2 ] ) . therefore , @xmath42 as well as @xmath57 are @xmath48invariant if and only if @xmath40 is a bounded solution of ( [ ricc ] ) . in other words , @xmath42 is reducing subspace of @xmath6 if and only if @xmath40 is a bounded solution of ( [ ricc ] ) . from considerations above follow also that @xmath42 and @xmath57 are @xmath58invariant . [ def ] elements from the graph and its orthogonal complement are denoted by @xmath59 and @xmath60 , respectively . the riccati states are defined as @xmath61 and @xmath62 , where @xmath63 and @xmath64 . the vectors @xmath59 and @xmath60 are _ not _ normalized with respect to the norm induced by the inner product ( [ inner ] ) . moreover , the states @xmath65 and @xmath66 are not factorisable ( _ i.e. _ , correlations occur ) , unless @xmath67 and @xmath68 , respectively . however , they are @xmath69invariant , which is obvious because the vectors @xmath59 and @xmath60 are @xmath58invariant . as a consequence , the riccati states @xmath70 and @xmath71 are @xmath72invariant , where the map @xmath28 has been defined in ( [ reduced ] ) . therefore , the set of all the riccati states is invariant under the time evolution . nevertheless , the riccati states are not the stationary states , in general . however , we show that the latter can be found among the riccati states . to be specific , we will prove the following [ th1 ] let @xmath40 be a bounded solution of the riccati equation . then 1 . the riccati state @xmath70 is a stationary state if the vector @xmath73 is a eigenvector of the operator @xmath74 , 2 . the riccati state @xmath75 is a stationary state if the vector @xmath76 is a eigenvector of the operator @xmath77 . let @xmath78 for @xmath79 and @xmath80 . from ( [ ricc ] ) we obtain that @xmath81 , hence in view of ( [ bom ] ) the last equality leads to @xmath82 . thus , the vector state @xmath59 is the eigenvector of the total hamiltonian with the corresponding eigenvalue @xmath83 . since @xmath6 is self - adjoint we have @xmath84 and in consequence @xmath85 , which ultimately leads to @xmath86 . in a comparable manner we have @xmath87 for @xmath88 and @xmath89 so that @xmath90 . just as before @xmath91 , therefore @xmath92 . at this point , some remarks , regarding theorem given above , should be made . the question whether all stationary states are riccati states or if it is possible that stationary states exist that are not riccati states is still open . [ re1 ] since the space @xmath93 is closed , we have the following decomposition @xmath94 . thus the total hamiltonian is similar to certain block diagonal operator matrix , @xmath95 , where @xmath96 this , implies that @xmath97 . therefore , the eigenvalues of @xmath98 are exactly the eigenvalues of the hamiltonian @xmath6 . let @xmath40 be a bounded solution of ( [ ricc ] ) . @xmath19 is assumed to be bounded as well . from the definition of @xmath98 we have @xmath99 , and thus @xmath100 . since @xmath40 solves the riccati equation ( [ ricc ] ) , it is clear that @xmath101 . to prove @xmath102 we will show that @xmath103 is invertible and @xmath104 is bounded . indeed , @xmath105 , where @xmath106 since @xmath107 , the spectrum of @xmath108 is a subset of the imaginary axis . in particular , @xmath109 thus @xmath110 and , hence , @xmath103 has a bounded inverse . [ rem4 ] the stationary states @xmath70 , @xmath75 indicated in theorem [ th1 ] are given by @xmath111 where @xmath80 and @xmath112 are the eigenvectors of @xmath113 and @xmath114 , respectively . @xmath115 , @xmath116 are the normalization constants and @xmath117 . since @xmath118 , the equations ( [ explicit ] ) can be obtained directly from the definition ( [ def ] ) and the formula ( [ partial ] ) . in this subsection we will demonstrate an application of the presented method to a non - trivial example , namely , the paradigmatic spin - boson model @xcite . assume that the hamiltonian of the qubit ( spin - half ) and its environment ( boson ) are in the following forms @xmath119 respectively . for the sake of simplicity , we consider only the case of a single boson . the interaction between the systems reads @xmath120 in the above description , @xmath121 , @xmath122 are the standard pauli matrices and @xmath123 . the creation @xmath124 and annihilation @xmath125 operators obey the canonical commutation relation ( ccr ) @xmath126={{\mathbb}{i}_{\text{e}}}$ ] @xcite ." +"in metallic ferromagnets , spin - polarized currents can induce a spin - transfer - torque ( stt ) on the magnetization via direct transfer of spin - angular momentum from the itinerant charge carriers to the local magnetic moments . @xcite this phenomenon has opened the door for current - driven manipulation of magnetization in spintronic devices . however , a limiting factor is the high current densities required to switch the magnetization and the associated large dissipation and joule heating . a new and alternative current - induced spin - torque mechanism has been observed in systems with broken spatial inversion symmetry and strong spin - orbit coupling ( soc ) . @xcite due to the soc of these systems , an electric current is always accompanied by a net spin - polarization of the charge carriers , @xcite which via the exchange interaction produces a torque on the magnetization . such relativistic current - induced torques are commonly referred to as spin - orbit torques ( sots ) . in contrast to the stts , the sots require neither spin - polarizers nor textured ferromagnets to induce magnetization dynamics . furthermore , the sots show remarkably high torque efficiencies , @xcite leading to magnetization reversal at current densities that are approximately an order - of - magnitude smaller than that typically observed for stt - induced switching in metallic systems . -axis . a typical fermi surface of this system is illustrated in ( c ) . optimal cooper pairing occurs for momentum states with a finite center of mass momentum , i.e. , @xmath1 and @xmath2 . ] in the past few years , there has been a rapidly growing interest in superconductor - ferromagnet heterostructures with strong soc . @xcite these systems are particularly intriguing because they are considered to be promising platforms for realizing topological superconductivity . this was recently experimentally demonstrated for a chain of magnetic atoms placed on a conventional superconductor , where signatures of majorana fermions at the edges of the chain were observed . @xcite topological superconductivity has also been predicted in two - dimensional lattices of ferromagnetically ordered adatoms . @xcite so far , there is little knowledge of how supercurrents in these systems influence the ordered spins . however , studies on ferromagnetic josephson junctions have shown that supercurrents can produce a torque on the ferromagnetic interlayer via the creation of spin - triplet cooper pairs . @xcite the spin - triplet correlations in the interlayer are generated either via magnetic textures , ferromagnet - normal metal - ferromagnet trilayers , or soc . superconductors with broken spatial inversion symmetry and strong soc will be in a mixed superconducting state of singlet and triplet pairings . @xcite the cooper pairs can thus develop a net spin polarization when the time reversal symmetry is broken . because the superconductor / adatom systems have both broken spatial inversion symmetry and strong soc , an interesting question is whether supercurrents in these systems result in current - driven magnetization dynamics . in this work , we consider a lattice of ferromagnetically ordered spins in contact with a conventional superconductor with broken spatial inversion symmetry and strong soc ( fig . [ fig1]a ) . we find that supercurrents produce a reactive sot on the spins and formulate a phenomenological description of the supercurrent - induced magnetization dynamics . in contrast to normal metallic ferromagnets , the back - action of the spin dynamics on the superconducting system is important , and the resulting equations for the condensate and the spin system should be solved simultaneously to provide a correct description of the dynamics . furthermore , we study the spin - torque mechanism by using a tight - binding bogoliubov - de gennes ( bdg ) formalism to self - consistently calculate the response of the system to a supercurrent . we show that the sot originates from current - induced spin - triplet correlations , which is determined by the orientation of the supercurrent with respect to the crystallographic axes . moreover , we find that there exists an intrinsic limitation for the maximum achievable sot and estimate the corresponding effective sot field to be on the order of @xmath0 mt in proximitized hole - doped semiconductors , which is comparable to the critical sot field for magnetization reversal in ( ga , mn)as . we therefore believe that the supercurrent - induced sots can lead to the development of new efficient techniques for manipulating magnetization , which minimize the disadvantages associated with dissipation and joule heating . in what follows , we develop a phenomenology that captures the low - frequency long - wavelength physics of the supercurrent - induced magnetization dynamics . the superconducting condensate is treated in the framework of the ginzburg - landau theory , which is valid at length scales larger than the superconducting coherence length @xmath3 . we assume a homogeneous ferromagnetic equilibrium state and consider spatial modulations of the ferromagnetic order parameter at length scales much larger than the exchange length @xmath4 set by the spin stiffness @xmath5 and relevant anisotropy constants @xmath6 . typically , @xmath7 nm and @xmath8 nm.@xcite the characteristic frequency @xmath9 of ferromagnets is on the order of @xmath10 ghz , @xcite which is far below the typical energy gap of superconductors : @xmath11 mev.@xcite the magnetization precession will therefore not lead to quasi - particle excitations in the superconductor and we can assume that the condensate responds adiabatically to the magnetization dynamics . we start by formulating the free energy functional , @xmath12 $ ] , of the system : @xmath13 . \label{eq : ftot}\ ] ] here , @xmath14 represents the order parameter of the spin system and is a unit vector parallel to the magnetization @xmath15 , @xmath16 is the order parameter field of the superconductor , and @xmath17 is the magnetic vector potential that yields the magnetic field @xmath18 . @xmath19 and @xmath20 are the free energy densities of the isolated spin system and superconducting condensate , respectively , @xcite @xmath21 where @xmath22 describes the magnetic anisotropy energy , @xmath23 is the momentum operator of the condensate , @xmath24 is the charge of the cooper pairs , and @xmath25 is the speed of light . @xmath26 and @xmath27 are second - rank polar tensors , which are invariant under the symmetry point group of the system . @xcite the term @xmath28 describes the coupling between the superconductor and the magnetization . we consider weak modulations of a homogenous ferromagnetic equilibrium state and can thus neglect magnetoelectric coupling effects associated with magnetic textures . in this case , @xmath28 is governed by the lifshitz invariant @xcite @xmath29 where @xmath30 represents the momentum density of the superconducting condensate . the tensor @xmath31 is linear in the soc and is an invariant axial tensor of the point group . @xcite consequently , the tensor vanishes for systems with spatial inversion symmetry . @xmath28 can be derived microscopically by considering an s - wave superconductor with soc of the form @xmath32 ( where @xmath33 ) and calculate the energy change due to a zeeman field . @xcite so far , most works have concentrated on the effects of the lifshitz invariant in non - centrosymmetric superconductors exposed to an external magnetic field . however , two recent studies showed that @xmath28 leads to persistent currents in a conventional superconductor with soc when magnetic impurities are placed at the surface . @xcite @xmath28 couples the momentum of the condensate to the direction of the magnetization and favors a spatial modulation of @xmath34 in equilibrium . the physical origin of @xmath28 is an soc - induced shift of the fermi surface , leading to a finite center of mass momentum of the cooper pairs . to illustrate this phenomenon , consider a system with rashba soc and a zeeman splitting @xmath35 along the @xmath36-axis induced by the magnetization ( fig . [ fig1]b ) : @xmath37 . here , @xmath38 is a vector consisting of the pauli matrices , @xmath39 is the effective quasi - particle mass , and @xmath40 parameterizes the soc . for this system , the lifshitz invariant becomes @xmath41 . the fermi surface of the hamiltonian is two circles , whose centers are shifted in opposite directions along the x - axis ( fig . [ fig1]c ) . due to the shift of the fermi surface , the optimal cooper pairing occurs for momentum states with a finite center of mass momentum , i.e. , @xmath1 and @xmath2 . therefore , the order - parameter field gains a spatial modulation @xmath42 in equilibrium ; a state that is referred to as the helical phase . @xcite phenomenologically , the helical phase is captured by the lifshitz invariant @xmath43 , which favors the vector @xmath44 to be perpendicular to the in - plane component of the magnetization . in what follows , we demonstrate that the lifshitz invariant also leads to a reciprocal phenomenon of the helical phase . if @xmath34 is forced to have a spatial modulation @xmath45 such that a supercurrent is induced , then the condensate can via @xmath28 lower its energy by developing a net spin density @xmath46 ( and magnetic moment @xmath47 ) perpendicular to the vector @xmath48 : @xmath49 . importantly , we find that the induced spin density @xmath46 produces a novel sot on the magnetization . the magnetization dynamics is described by the landau - lifshitz - gilbert ( llg ) equation @xcite @xmath50 + \alpha_g \mathbf{m } \times \dot { \mathbf{m } } . \label{eq : llg}\ ] ] here , @xmath51 is the effective field found from the magnetic free energy functional @xmath52 , @xmath53 is the gyromagnetic ratio , and the term proportional to the gilbert damping parameter @xmath54 determines the magnetization dissipation . because of the lifshitz invariant , the variation of eq . with respect to the magnetization also yields a reactive sot - field @xmath55 which is governed by the soc and the momentum density of the superconducting condensate . the magnetization evolves slowly on the characteristic timescale of the electron dynamics . we can therefore assume that the superconducting condensate at time @xmath56 is close to the equilibrium state with the static magnetization @xmath57 . the equilibrium state , which is determined by the ginzburg - landau ( gl ) equations , is obtained by variational minimization of the free energy . the variation with respect to @xmath58 yields the equation @xmath59 whereas a variation of @xmath60 provides the equation @xmath61 here , @xmath62 is the supercurrent density . the conventional gl equations are obtained for a fully isotropic system , in which @xmath63 and @xmath64 . eqs . , and give a phenomenological description of the coupled dynamics of the spin system and the superconducting condensate . via the lifshitz invariant , the state of the superconducting condensate depends on the direction of the magnetization . the effects of @xmath28 become crucially important when the length scale @xmath65 associated with the helical wavevector @xmath66 is smaller than the characteristic length scales of the ferromagnetic system . in this case , the condensate is strongly affected by the magnetization dynamics and its state can not be considered as quasi - static for the dynamics . thus , eqs . , and should be solved simultaneously to provide a correct description of both the magnetization dynamics and the superconducting condensate . this differs markedly from the situation in normal metallic ferromagnets , in which the back - action of the spin dynamics on the itinerant electron system usually can be disregarded in the solution of the llg equation . for a two - band model with rashba soc , the helical wavevector is on the order of @xmath67 where @xmath68 is the fermi velocity.@xcite here , the factor @xmath69 measures of the difference between the density of states @xmath70 of the two bands" +"the successful launch of the _ swift _ satellite in nov 2004 opened a new window to reveal what has been happening in the early afterglow phase of gamma - ray bursts ( grbs ) . as summarized in zhang et al . ( 2006 ) and nousek et al . ( 2006 ) , in a canonical _ swift _ grb x - ray afterglow lightcurve some interesting features are emerging ( detected in a good fraction of but not all bursts ) , including a very early sharp decline ( phase - i ) , a shallow decline or even plateau , ( phase - ii ) , preceding the conventional or so - called normal "" decay phase ( phase - iii & -iv ) , and the energetic x - ray flares ( phase - v ) . various modifications of the standard grb afterglow model have been put forward to explain the observations ( see mszros 2006 ; piran & fan 2007 ; zhang 2007 for recent reviews ) . although the underlying physical processes are not very clear , it is widely suggested that the x - ray phases i , ii and v may be relevant to prolonged activities of the central engine while the simultaneous optical afterglow is dominated by grb forward shock emission ( fan & wei 2005 ; zhang et al . 2006 ; ghisellini et al . 2007 ; panaitescu 2007 ) . if so , the early time uv / optical and x - ray polarization behaviors should be independent and may be very different from each other . in some models , the outflows powering energetic flares and x - ray plateaus followed by a sharp drop are poynting - flux dominated ( e.g. , gao & fan 2006 ; giannios 2006 ; troja et al . 2007 ) , thus high - linear polarization of these synchrotron radiation photons is expected ( fan , zhang & proga 2005 ) . except the configuration of the magnetic field , the geometry of the emitting area can influence the polarization property of the synchrotron radiation as well . the broken - down of the symmetry of the visible emitting region may be hiding in the peculiar x - ray data and can give rise to interesting polarization signatures . motivated by this idea , in section 2 we calculate the polarization property of phase - i and show that strong evolution is likely . in section 3 , we argue that similar phenomena are also expected in the decline phase of the x - ray flares and possibly in the late time part of phase - ii , especially those associated with a chromatic break in optical band . we also discuss the detection prospect there . in section 4 , we summarize our work with some discussions . for phase - i , two leading interpretations are : ( i ) these x - ray photons are actually the high latitude emission of a main internal shock pulse ( fenimore et al . 1996 ; kumar & panaitescu 2000 ; zhang et al . 2006 ) while the central engine has died ; and ( ii ) these x - ray photons are powered by the weaker and weaker activity of the central engine , i.e. , the sharp x - ray decline traces the activity of the dying central engine ( fan & wei 2005 ; piran & fan 2007 ) . the interpretation ( i ) has been widely accepted because some x - ray declines can be adjusted as @xmath1 predicted by the high latitude emission model ( liang et al . 2006 ; yamazaki et al . 2006 ; zhang , liang & zhang 2007a ) , where @xmath2 is the x - ray spectral index , and @xmath3 is a free parameter parameterizing the beginning of a certain internal shock pulse.ray emission are powered by some magnetic energy dissipation processes at a distance @xmath4 cm to the central engine , so the emission duration is governed by the angular timescale @xmath5 sec , where @xmath6 is the bulk lorentz factor of the outflow . ] such a test , however , is not conclusive . as shown in sakamoto et al . ( 2007 ) , for the very sharp x - ray decline , the data itself can not well constrain the function form @xmath7 . in many events , @xmath8 can be taken as a constant ( for example , @xmath9 ) and thus is not relevant to @xmath2 . additionally , it is not easy to see why the grb central engine turns off abruptly while the numerical simulation actually shows the contrast ( macfadyen et al . 2001 ; zhang , woosley & heger 2007b ) . interpretation ( i ) also fails to interpret some slowly decaying phase - i as in grb 060614 @xcite . as for interpretation ( ii ) , there has been no strict observational test so far though it seems possible for any energetic burst phenomenon . we take into account both models in our calculation and examine the possibility to distinguish between these two models with future x - ray polarimetry . if interpretation ( i ) is correct , i.e. , the sharp x - ray decline is due to the high latitude emission of a main internal shock pulse , there would be very interesting polarization signals . as is known , grb outflow is likely to be jetted . in this work we only consider the uniform jet model . following ghisellini & lazzati ( 1999 ) , we assume that the half - opening angle of the ejecta is @xmath10 , and that the line of sight ( l.o.s . ) makes an angle @xmath11 with respect to the jet s central axis ( c.a . , see fig.1a for illustration ) . the probability of observing the ejecta along its c.a . is vanishingly small since it corresponds a very small solid angle . for typical bright grbs , the l.o.s . is likely to be within the cone , i.e. , @xmath12 . at early time , the high latitude emission is from zones around the l.o.s . satisfying @xmath13 , so the net polarization of the detected photons vanishes because of the symmetry ; but at later time , the high latitude emission is from @xmath14 , the symmetry is broken and the observed net polarization is not zero any longer . ( 0,200 ) ( 0,0 ) in this model , the photons arrived at @xmath15 were emitted from @xmath16 where @xmath17 is the radius of the main internal shock pulse and @xmath18 is the speed of light . below we adopt the simplified calculation of ghisellini & lazzati ( 1999 ) . the notations used in fig.[fig : cartoon]b are related to @xmath19 , @xmath10 and @xmath20 as @xmath21 and @xmath22 . when @xmath23 , the ring is not a complete circle . the missing parts are in @xmath24 and @xmath25 as shown in fig.[fig : cartoon ] . approximately , we have ( ghisellini & lazzati 1999 ) @xmath26 , & \hbox{for $ \rho > r_1 $ ; } \\ 0 , & \hbox{for $ \rho < r_1 $ , } \\ \end{array}% \right.\ ] ] where @xmath27 . in principle , the grb outflow could be either baryon - rich or poynting - flux dominated . for the former the magnetic field is generated in the shock front and is likely to be random . for the latter the magnetic field is coherent in a large scale . the resulting polarization light curves are expected to be different in these two cases , as shown below . * random magnetic field . * the net polarization of the emission from @xmath28 can be approximated by ( see the appendix for the derivation ) @xmath29\ } % \nonumber\\ % & = & \pi_0{\sin\{2\arcsin[{2\sin\theta_{\rm j } \sin(\theta_{\rm % j}-\theta_{\rm v } ) -\sin^2(\theta_{\rm j}-\theta_{\rm v } ) -\sin^2 % \theta \over 2\sin \theta [ \sin\theta_{\rm j}-\sin(\theta_{\rm % j}-\theta_{\rm v})]}]\ } \over \pi+2\arcsin [ { 2\sin\theta_{\rm j } % \sin(\theta_{\rm j}-\theta_{\rm v } ) -\sin^2(\theta_{\rm % j}-\theta_{\rm v } ) -\sin^2 \theta \over 2\sin \theta % [ \sin\theta_{\rm j}-\sin(\theta_{\rm j}-\theta_{\rm v } ) ] } ] } , \label{eq : main}\end{aligned}\ ] ] where @xmath30 is the maximum polarization at one point , @xmath31 is the viewing angle with respect to the fluid velocity in the outflow comoving frame ( see figure [ point ] for illustration ) , which is governed by @xmath32 , and the parameter @xmath33 denotes the level of anisotropy of the magnetic field distribution , where @xmath34 and @xmath35 are magnetic field perpendicular and parallel to the normal of the shock plane . @xmath36 is the velocity of the grb ejecta in units of @xmath18 . we note that in eq.([eq : main ] ) @xmath37 if @xmath38 . for @xmath39 , we have @xmath40\ll 1 $ ] . the resulting net polarization can thus be neglected . but for @xmath41 , the second term in the right side of eq.([eq : main ] ) is @xmath42 . significant net polarization is possible . as @xmath43 , the observers just detected @xmath44 part of the circle , the x - ray flux will decline more steeply than @xmath45 and is governed by @xmath46 we plot in fig.[fig : lc ] the sharp x - ray decline and the corresponding polarization light curves . when the emission is from a circle ring , the net polarization is zero because of the symmetry . as @xmath47 is getting larger and just part of the ring is visible , the observed polarization degree is not zero any longer until @xmath48 ( i.e. , @xmath49 ) . at the point of @xmath50 , the net polarization becomes zero again according to equation ( 3 ) , because the polarization direction abruptly changes by @xmath51 . after this point , the polarization increases again . but the flux may be too weak to have a significant polarization measurement . ( 0,240 ) ( 0,0 ) * homogenous magnetic field . * in this case , the instantaneous stokes parameters ( note that @xmath52 as the polarization is linear ) and the polarization degree are given by ( granot & knigl 2003 ) : @xmath53^{\epsilon/2 } \left\ { \begin{array}{c } \cos(2\theta _ { p } ) \\ \sin(2\theta _ { p } ) \\ \end{array}\right\ } d\phi } { \int _ { \psi_1}^{2\pi-\psi_1}[({1-y \over 1+y})^2 \cos^2\phi+\sin^2 \phi]^{\epsilon/2}d\phi},\ ] ] and @xmath54 where @xmath55 , @xmath56 and @xmath57 ( granot & knigl 2003 ) . again the polarization light curve has been plotted in fig.[fig : lc ] , which is similar to that of the random magnetic field case except an initial high polarization degree . this strongly suggests that the late time non - zero polarization is mainly contributed by the geometry effect , as in the case of a random magnetic field . if the symmetry has not been broken down , the late time net polarization for an ordered magnetized outflow disappears , as already found in nakar , piran & waxman ( 2003 ) . generally , in the dying central engine model there are two possibilities . ( 1 ) if the outflow powering the fast decaying x - ray tail emission always has a lorentz factor @xmath58 , no strong polarization evolution is expected unless the physical composition of the outflow has changed a lot ( e.g. , from byron dominated to poynting - flux dominated ) . we thus may be able to distinguish between the high latitude emission model and the dying central engine model with the future x - ray polarimetry . ( 2 ) the bulk lorentz factor of the outflow drops so quickly" +"observations over the past decade have established that most and probably all pre - main sequence ( pms ) stars are surrounded by disks during early stages of their evolution , and that a substantial portion of their final mass is accreted from these disks . however , the prediction that this accretion will cause the stars to rotate at close to their breakup speed ( _ e.g. _ durisen et al . 1989 ) is not borne out by observations . most pms stars have rotational velocities ( @xmath1 ) of no more than a few tens of km s@xmath2 . by contrast , the typical breakup velocity at @xmath31 myr is @xmath3300 km s@xmath2 . explanations of the observed slow rotation have invoked a magnetic field that is rooted in the central star and intercepts the disk ( knigl 1991 ) . the net consequence of this interaction is a braking torque transmitted to the star by field lines penetrating the disk beyond the co - rotation radius ( where the angular velocity @xmath4 of the disk matches that of the star ) . this braking torque exactly balances the spin - up torque exerted by the material inside the co - rotation radius . this model predicts that stars will be locked to their disks and will rotate slowly until the time that the disk is dissipated . other models ( _ e.g. _ shu et al . 2000 ) make use of a wind , launched from the stellar magnetosphere - disk boundary to carry away stellar angular momentum ( @xmath5 ) , thus reducing rotation rates to well below breakup . by contrast , stars without disks should conserve @xmath5 and spin up as they contract and evolve down their hayashi tracks . considerable observational effort has been devoted to finding empirical correlations between rotation rates and the presence or absence of observable disks ; although such correlations appeared in early studies ( _ e.g. _ edwards et al . 1993 , choi & herbst 1996 ) , recent results are ambiguous at best ( _ e.g. _ rebull 2001 ; stassun et al . 1999 ) . over the past few years , rotation periods @xmath6 or projected rotational velocities @xmath7 have been measured for large samples of pms stars @xmath30.1 - 2.5 m@xmath8and of age @xmath93 myr . these data sets are now large enough to provide direct evidence of how @xmath5 changes as stars of different masses evolve down their convective tracks . in this paper , we examine the early @xmath5 history of stars surrounded by disks and those that lack disks . we show that pms stars , _ even those without observable disks _ , do not conserve angular momentum as they evolve toward the zams but instead evolve at nearly constant angular velocity . this result is inconsistent with expectations that convective stars lacking disks should spin up as they contract , but paradoxically consistent with disk - locking models . the data sets that we draw on for this paper are 256 measurements of @xmath10 in the orion nebula cluster ( onc ) by rhode et al . ( 2001 ; rhm ) ; 197 photometric periods ( @xmath6 ) for the flanking fields ( ff ) that surround the onc ( rebull 2001 , rebull et al . 2000 ) ; and 83 stars with @xmath6 in ngc 2264 ( makidon et al . 2001 , rebull et al . 2001 ) . the age distribution for orion peaks near @xmath31 myr , while ngc 2264 peaks near @xmath31 myr but contains significant numbers of stars out to @xmath33 - 4 myr . together , these clusters allow us to examine changes in stellar angular momenta over a total range in stellar radius of @xmath30.4 dex . in order to estimate accurate stellar radii and to determine the presence or absence of a disk , we required that spectral types along with @xmath11 and @xmath12 photometry be available for all the stars included in the present study . while other disk indicators ( _ e.g. _ uv excess , h@xmath13 emission ) are available for subsets of the orion and ngc 2264 databases , only @xmath11 is widely available . all stars with an @xmath11 color redder by 0.3 mag than expected based on spectral type were considered to be surrounded by disks ( cf.rebull 2001 and references therein ) . we note that 26/197 ( 13% ) stars in the orion ff sample and 20/83 ( 24% ) in the ngc 2264 sample have @xmath11 excesses , whereas 60% of the stars in the onc sample have such an excess . stellar temperatures ( @xmath14 ) were assigned according to spectral types and luminosities ( @xmath15 ) were derived from @xmath16 magnitudes with reddening estimated from colors and spectral types following hillenbrand ( 1997 ) . we adopted distance moduli of 8.36 for orion ( genzel et al . 1981 ) and 9.40 for ngc 2264 ( sung et al . 1997 ) . radii ( @xmath17 ) were calculated using the assigned values of @xmath15 and @xmath14 . photometric uncertainty , the amplitude of the periodic modulation , uncertainties in the reddening correction , and errors in classification all contribute to errors in @xmath15 and @xmath14 and hence to uncertainty in @xmath17 . the distribution of empirically - determined errors in @xmath18 is strongly peaked near @xmath190.1 . the errors in @xmath6 are less than 1% . the @xmath0 data for the onc have sufficient resolution to measure only velocities greater than @xmath311 km s@xmath2 , corresponding to @xmath20d for a typical pms star in our sample . the @xmath6 measurements are sensitive to a much broader range of periods , viz @xmath21d ( @xmath22 km s@xmath2 ) , encompassing much slower rotation velocities than do the published @xmath0 measurements . approximately half of the stars with @xmath0 measurements by rhm were chosen because they had known @xmath6 . the other half were selected as a control sample of objects without known @xmath6 from the same portion of the hr diagram . rhm show there is no statistically significant difference between the @xmath0 distributions of the periodic and control samples , leading to the important conclusion that samples of stars found to show photometric periods can be taken as a fair representation of the range of rotational characteristics of pms stars . if stars conserve angular momentum ( @xmath5 ) as they evolve down their convective tracks , then we would expect that @xmath23 would remain constant , but only if @xmath5 is conserved in the outermost observable layer of the star . we expect fully convective stars to rotate as solid bodies . examination of theoretical models of pms stars ( _ e.g. _ swenson et al . 1994 ) indicates that the predicted changes in surface rotation rate as the star evolves down the convective track are indistinguishable for the two extreme cases of solid body rotation and local conservation of @xmath5 ( _ i.e._@xmath5 conservation in spherical shells ) . along the convective track contraction is nearly homologous , and changes in @xmath24 directly track changes in @xmath25 . if @xmath5 is conserved , then @xmath26 is constant and @xmath27 should be @xmath28 . on the other hand , if angular velocity @xmath29 is constant , as predicted for disk - locking , then @xmath6 is constant . in figure 1 , we plot @xmath6 and @xmath30 vs. @xmath17 , where @xmath31 is computed as in rebull ( 2001 ) , where @xmath24=moment of inertia , and all other terms have been defined . ] . it is immediately apparent that there is no variation of @xmath6 with @xmath17 , but that @xmath31 changes with @xmath17 , consistent with conservation of @xmath4 . the errors in log @xmath17 would have to be about 0.5 dex ( 5 times larger than we estimate them to be ) in order to mask the decline in @xmath6 expected for the case of conservation of @xmath5 . we see no substantial difference between these two clusters , except for the fact that the stars in ngc 2264 include older objects with smaller radii . we find no significant difference in the period - radius relationship of stars with and without @xmath11 excesses , though there may be some marginal tendency for diskless stars to have the shortest periods . we have divided our sample into two bins : @xmath323 d and @xmath333 d. the disk fractions are for orion 0.1@xmath190.03 and 0.2@xmath190.1 respectively , and for ngc 2264 , both fractions are 0.3@xmath190.1 . to enable more direct comparison with the rhm results for the inner onc , we have converted the orion ff and ngc 2264 periods to @xmath1 . the @xmath6 data provide an estimate of @xmath1 rather than @xmath0 and are systematically higher for this reason . for our purposes , it only matters that the data within each group are internally consistent . we have subdivided the @xmath10 and @xmath1 measurements following rhm according to @xmath14 and @xmath15 , corresponding to a subdivsion by mass ( @xmath34 ) for stars on convective tracks , and with age for stars of a given @xmath34 . for each bin we show in table 1 the average @xmath1 or @xmath0 . to first order , each column of the table can be viewed as following the evolution of stars of a given mass down a convective track . as can be seen from table 1 , the average value of @xmath1 or @xmath0 _ decreases _ with @xmath15 at fixed @xmath34 , rather than increasing as one would expect for conservation of stellar @xmath5 . in constructing these averages for the onc sample , we have assigned 11 km s@xmath2 as the @xmath10 for all of those stars for which only upper limits are available . a detailed examination of the data in rhm shows that the percentage of stars rotating at or below this upper limit increases with decreasing @xmath15 , and so the decline in @xmath0 with decreasing @xmath15 is probably even stronger . table 2 tabulates the quantities @xmath35 , which is proportional to @xmath4 , and @xmath26 , which is proportional to @xmath5 . @xmath35 is constant within each mass group , within about a factor of @xmath32 , regardless of how far the stars have evolved down their convective tracks . in other words , it appears as if some agent is keeping stars close to constant @xmath4 over nominal ages from 0.1 - 3 myr . we note that this result stands whether stars appear to have @xmath11 excesses or not . prior to this survey , we expected that pms stars lacking observable disks should spin up as they contract along convective tracks . the observations show that they do not , despite the fact that these stars span a range of 0.4 dex in log @xmath17 , which should correspond to a decrease in log @xmath6 of 0.8 dex . we briefly explore several possible explanations . the absence of evolution in the distribution of periods among pms stars as they contract is consistent with what would be expected for disk - locking . absent observable evidence of disks from infrared excess emission arising from micron - size dust grains , we would need to posit linkage between stellar magnetospheres and disks in which small solid particles have been agglomerated into larger bodies , leaving behind only gas . detection of such disks via h@xmath36 or co emission awaits more sensitive measurements than possible at present . a search for dust - free gaseous disks with sirtf appears to be the most promising near - term approach . suppose that ( 1 ) stars in orion and ngc 2264 were born in a single burst of star formation @xmath31 myr ago ; ( 2 ) the" +"failure avoidance is of paramount importance in critical software systems , needed to be considered in the first place as it has a direct impact on the safe operation . the main reasons for system failure are described in @xcite . around 44% of the failures are caused by wrong system specifications , and a 15% are introduced during the design and development phases . this means that over 60% of the failures can be avoided during design and development phases . some of the most common errors are to start the verification process in the final phase of the project or not to take into account the safety from the beginning . on the other hand , the cost associated to certain bugs and reingeneering can be unacceptably high . in general , the cost of the development activities is directly related to the required safety level . although this cost tends to be restrained , it can be doubled if the development follows an approach that does not consider safety requirements . there are a number of regulations and norms such as do-178b@xcite and do-278@xcite that define the set of _ objectives _ to achieve an acceptable level of safety . in the scope of critical software projects , there is a process of continuous investigation in order to reduce costs and development time , that usually includes the definition of methodologies and process automation and/or optimization techniques . the usage of adequate tools that support them is essential in order to optimize the monitoring of the processes . using a _ v- model _ , the processes or phases identified in do-178b@xcite and do-278@xcite are _ planning _ , _ requirements _ , _ design _ , _ coding and integration _ , _ integration _ , _ verification _ , _ configuration management _ , _ quality assurance _ and _ certification / approval liaison_. some of these phases are _ integral processes _ and must be performed through all the software life cycle . due to the specific requirements of the safety monitoring processes , it is usual that the status information for all the involved processes is very complex ; information is typically contained in different places , and it is responsibility of several teams . this situation makes the status monitoring to be a difficult task to perform , prone to causing several undesirable effects such as missing information , or bad dimensioning of the development situation . in critical systems developments , this may lead to unsafe situations that have to be avoided . current monitoring tools are , in practice , complex tool chains mostly supporting separate activity monitoring . usually , the different views over the development progress are provided by distinct tools in a non collaborative environment . since different critical software projects follow different norms , there are no tools that are able to be easily customized to adapt to different norms . for instance , embedded software installed in aircrafts ( like cockpits , mission computers and others ) is usually developed under do-178b@xcite while ground equipments ( like navigation or surveillance radars ) use do-278@xcite . in both cases , most of the processes are similar , but they are in fact different among themselves . for example , do-278@xcite introduces considerations about cots software or adaptation data . therefore , it is needed to take into account the particular characteristics of each norm , additional requirements introduced in each project , and possible changes in the applicable norm . to increase the efficiency of development in critical software systems , it is required that norms are supported by flexible yet pragmatic and more powerful monitoring methodologies that can be flexible to adjust to different norms . a severe drawback of current methods and tools is that they do not fully support the definition and use of a consistent and uniform methodology for the monitoring of the verification activities for all projects , and they do not facilitate the compliance with regulatory requirements . this paper describes an approach to improve the current practices of monitoring by providing a new methodology that covers the verification management activities in a collaborative environment to facilitate the integration with other life cycle process , and provide the possibility of future extensions . we present an approach that automates the process of monitoring by the integration of optimization mechanisms that includes all the information regarding the compliance statement of the applicable norm . the paper is structured as follows . section [ sec : intro ] presents an introduction and motivation for this work . section [ sec : background ] describes the related work in what concerns norms and practices used for monitoring . section [ sec : avapproach ] describes the proposed approach that allows cross - norm monitoring of the verification . section [ sec : validation ] presents the implementation of the methodology in a tool and its usage and results for a real - world critical software project . section [ sec : conclusion ] concludes the paper . there are several standards that define processes for the software development of critical systems . most of these standards were initially guidelines describing an approach to the regulatory requirements ; they have later become de facto regulations due to their widespread adoption . some of these standards are defined in table [ standards ] . .selected related standards [ cols=""<,<,<"",options=""header "" , ] once the project information was specified and parametrized according to table [ tab : parameterization_example ] , the monitoring process began where all actors used the supporting tool for the monitoring of all verification activities . checklists for each _ configuration item _ were filled , showing their status and details . _ observations _ about each item were registered in the tool . results are shown in figure [ fig : no_conformities_found_by_process ] where different metrics about the _ non - conformities _ are found , separated by verification process . there were @xmath0 observations introduced regarding the plans and standards developed for the project ; @xmath1 non - conformities were registered about the requirements , and @xmath2 regarding the design ; @xmath3 non - conformities were registered in the coding and integration processes , related to the compliance with the coding standard . @xmath4 incidences were found during the execution of the tests , and were registered in the supporting tool for monitoring and representing the status of the integration . eventually , @xmath5 non - conformities were detected in the _ verification of verification processes_. changes needed to the procedures where detected during the life cycle , and introduced in the tool , as part of the verification of verification process . the main _ observations _ were focused on the need of including additional clarifications about some contents , like references to the development and verification tools , and the need of their qualification . other comments refereed to the need of including additional information , or clarify the specified organization . in some cases , changes were needed such as in the _ software configuration management plan _ to address some processes required by the internal company policies . the observations of the _ certification authority _ were also introduced , becoming part of the information about the development process . regarding the development standards ( requirements , design , and coding ) , there were not many observations given that standards are typically well known and applied in different projects . still additional comments were brought due to the particularities of each project and improvements to be introduced . for the requirements and design processes , the requirements document was introduced , filling the correspondent checklists and registering the observations . the requirements document is one of the most important one as requirements are used as the basis for ( 1 ) the design as they describe the required functionality ; and ( 2 ) to define the tests to be performed in the corresponding phase . consequently , there were more than @xmath6 of observations that involved changes in the original document , including some clarifications introduced by the author . in the review of this document , the applicable standard ( ref . @xcite ) and the requirements standard defined for the project were used . the tool provided tangible evidences for the results of the verification process for each development process which serves as a basic reference for generate the _ software accomplishment summary _ and _ system safety assessment_. in these documents , it is necessary to include references to all the evidences needed for the development assurance level required . the data introduced in the tool are able to provide an evidence to the certification authorities of the performed work and compliance status . the architecture of the software is of paramount importance in critical systems as it directly impacts the complexity of the final development and , therefore , its verification and testing . critical software systems verification focuses heavily on temporal behavior applying real - time mechanisms ( @xcite ) . other soft real - time domains rather provide quality of service mechanisms embedded in the software logic that accounds for mechanisms to allow dynamic execution whereas preserving timely properties ( @xcite ) . verification of the properties of distributed software also related to newer domains as cloud ( @xcite ) , the characteristics of the middleware are integrated in the model ( @xcite ) . lastly , specific verification mechanisms are executed on - line in very specific contexts such as cyber - physical systems ( @xcite ) . the lack of information and the complexity of the applicable norms and processes in systems with safety requirements increases costs and difficulties to achieve requirements compliance . this paper has presented an approach that clarifies these processes , that is supported by a tool that facilitates the compliance with the safety requirements and the adoption of new regulations . due to the introduced information for the data items for each development phase , actors involved in the projects can know the software life cycle defined with a quick view of the tool . this directly implies a reduction in the training time of engineers . for each item it is possible to know the existing non conformities , which enables their early detection and correction by the responsible . in the tool , the collaboration is achieved through a web interface . all information about the status of development and verification tasks is immediately accessible to actors , that provides knowledge about the work performed and the pending tasks . so , an estimation of the remaining activities can be calculated , which could lead to implement corrective actions and minimize the impact in project goals , decreasing the project risks . the tool covers all the verification process according to the different levels . the supporting tool has managed two standards ( @xcite and @xcite ) , covering a large scope of safety related projects . a set of documents and checklists for each develop phase and for document have been created , providing a basic framework to manage this kind of projects . it is possible to add additional documents at any time . finally , the methodology allows to follow any kind of development model . thus , the objective about integration with other life cycle processes is fulfilled by the presented approach , including information about the development . the supporting tool provides possibilities of future growth , by extensions that include information about new norms or processes . rtca , eurocae . _ do-278 / ed-109 . guidelines for communication , navigation , surveillance , and air traffic management ( cns / atm ) systems software integrity assurance_. rtca inc . / eurocae . 3/5/2002 . / eurocae . _ do-331 / ed-216 . model" +"while most observed protoplanetary discs display accretion rates of order @xmath6 m@xmath7 yr@xmath8 @xcite , some objects , in particular fu orionis systems ( e.g. * ? ? ? * ) , have exhibited episodes of enhanced accretion up to @xmath9 m@xmath7 yr@xmath8 @xcite over observed time - scales of 10 - 100 years . it has been hypothesised that _ all _ protostellar systems actually undergo such episodic accretion , equating to a small fraction ( the `` duty cycle '' ) of their total lifetime , possibly concentrated in their early stages @xcite . indeed this would alleviate the apparent discrepancy between the low observed accretion rates and that required to achieve the final mass of the protostars @xcite . although the mechanism underlying fu orionis outbursts has not been established to date @xcite , a presently popular class of model uses as its only ingredients the two currently favoured drivers of transport in protoplanetary disks , namely the magnetorotational instability ( mri ; @xcite ) and the gravitational instability @xcite . the `` gravo - magnetic cycle '' , as it has come to be called @xcite , relies on the fact that a disc with a `` normal '' density is typically too cold ( @xmath10 k ) and too dense for its mid - plane to be sufficiently ionised to trigger the mri , giving rise to a _ dead zone_. as the disc is gravitationally stable at such densities , accretion will only be possible in the surface layers where x - ray / uv ( or cosmic ray ) ionisation keeps the mri alive @xcite . however , a steady - state situation can not be achieved and mass accumulates in the dead zone , until gravitational instability sets in , raising the disc s mid - plane temperature ( @xmath11 ) . near @xmath12 k , thermal ionisation triggers the mri throughout the entire thickness of the disc , resulting in an accretion burst which lasts @xmath13 years ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? once the previously accumulated mass is dumped on the proto - star , the disc returns to the initial `` low state '' ( or quiescent state ) . the cycle may then resume , with a duty cycle @xmath14 % at low infall rates ( @xmath15 m@xmath7 yr@xmath8 ) up to @xmath16 at high infall rates ( @xmath17 m@xmath7 yr@xmath8 ) . the significant changes in the disc s temperature and luminosity during such an accretion burst can chemically process a large fraction of the disc material . several previous studies have shown the impact of accretion bursts on the chemical evolution of the envelope and disc . @xcite studied the impact of accretion busts on the co chemistry in the envelopes , in particular the large increase in luminosity , and found that repeated bursts could lead to repeated freeze - out cycles . these evolutionary co cycles lead to possible observational evidence of accretion outbursts in young star forming cores @xcite . additionally , @xcite used ` single - point ' models to study the impact of accretion bursts on the local evolution of various chemical species in the envelope , indicating that the outcome depends delicately on the balance between burst and chemical time - scales . however , what has not been considered in great detail is that this processed material can then be transported to smaller radii in the disc by advection and to larger ones by turbulent diffusion . these effects , which may persist for significantly longer than the duration of the bursts , may lend themselves to observable diagnostics ; whether for extrasolar systems , e.g. with the increased resolution and sensitivity offered by _ alma _ and _ herschel _ , or our own solar system , taking advantage of the rich body of cosmochemical evidence . to this end , in this series we set out to investigate the chemical consequences of accretion bursts . an astrochemically abundant species of choice in this regard is water @xcite , and in particular its d / h ratio @xcite . observations of the interstellar medium and pre - stellar cores suggest that water starts deuterium - rich ( d / h@xmath18 ; @xcite ) . yet bulk chondrites and comets ( with a further _ in situ _ measurement to come for comet churyumov - gerasimenko @xcite ) in our solar system display lower ( d / h)@xmath0 ratios ( around @xmath19 ) , although some micron - scale d - rich hotspots in clays of the semarkona chondrite do reach ( d / h)@xmath0 @xmath20 @xcite . this in turn is much higher than the protosolar value ( essentially that of molecular hydrogen ) of @xmath3 @xcite , and reaction kinetics prohibit the conversion of low ( d / h)@xmath0 ratios to higher values in the protoplanetary disc @xcite . the current interpretation is that the solar system inherited its water from the parent molecular cloud @xcite , and that this water _ partially _ exchanged its deuterium with the nebular gas @xcite . coupling this deuterium exchange with mixing throughout the disc produced the range of intermediate ( d / h)@xmath0 values we now observe @xcite . the bottom line is that the ( d / h ) ratio of water is a sensitive tracer of infall , temperature and turbulent mixing conditions . all previous studies of the ( d / h)@xmath0 ratio assumed a constant turbulence level ( often parametrised in terms of the shakura & sunyaev @xmath21 , @xcite ) , and thus could not reproduce the gravo - magnetic cycle , and had no accretion outbursts . additionally , only @xcite considered the effects of infall , during which most of the outbursts are expected to take place @xcite , along with the subsequent disc evolution . @xcite presented steady - state analytical calculations , indicating that in such types of model , a high efficiency of turbulent diffusion - with a schmidt number @xmath22 of 0.2 or smaller - until the snow line and beyond would be required to account for the smallness of the ( d / h)@xmath0 ratio of carbonaceous chondrites and the earth relative to oort cloud comets ; but as yet the realism of such a small schmidt number is unclear @xcite . however , as isotopic exchange is most efficient for temperatures above @xmath23 k , clearly , outbursts , which may reach temperatures in excess of 1000 k , could significantly impact the ( d / h)@xmath0 profile of protoplanetary disc and possibly account for the low ( d / h)@xmath0 ratios of carbonaceous chondrites . in this work , we examine the effect of accretion outbursts arising from the gravo - magnetic limit cycle on the evolution of the ( d / h ) ratio of water using numerical models presented in section [ sec:1dmodel ] . since this process has not been studied before , to gain insight we perform numerical experiments where the disc experiences a steady infall rate for the entire simulation ( section [ sec : steady ] ) . secondly , we perform more realistic evolutionary calculations which include a disc building phase for a few hundred - thousand years followed by a stage of isolated evolution for several million years , that are meant to represent the evolution of an actual protoplanetary disc , e.g. the solar nebula ( section [ sec : building ] ) . the implications are then discussed in section [ sec : discussion ] and the conclusions summarized in section [ sec : conclusion ] . in order to investigate the effect of accretion bursts on the chemical evolution of the ( d / h)@xmath0 ratio we adopt a simple one - layer approach @xcite . our model is a modified version of that originally presented by @xcite to study the impact of dead - zones in protoplanetary discs and associated accretion bursts , where we additionally include radial transport of heat by radiation and turbulence ( see * ? ? ? * ) . here we extend the model to include the transport of water due to advection and turbulent diffusion as well as the chemical evolution of the ( d / h)@xmath0 ratio . the evolution of the surface density @xmath24 for a disc around a forming star , with a dead - zone is given by ( e.g. * ? ? ? * ) : @xmath25\right\}+\dot{\sigma}^g_{\rm in}\label{eqn : gas}\ ] ] where @xmath26 is the kinematic viscosity due to the mri or self - gravity which we detail in section [ sec : viscosity ] and @xmath27 is the rate of material falling onto the disc . @xmath28 is the surface density that is ` mri active ' and is given by : @xmath29 for all our models where we include a dead - zone ( and hence accretion bursts ) we choose @xmath30k and @xmath31 g @xmath32 . in simulations where we do not include a dead - zone ( and thus no accretion bursts ) we set @xmath33 . the evolution of the temperature at the mid - plane of the disc is given by @xcite : @xmath34\nonumber\\&&-\left(\frac{2h}{\sigma^g rc_p}\right)\frac{\partial}{\partial r}\left(rf_r\right)\label{eqn : temp}\end{aligned}\ ] ] where @xmath35 is the heat capacity at constant pressure , @xmath36 is the ratio of specific heats and @xmath37 is the scale height of the disc , with @xmath38 the keplerian angular velocity and @xmath39 the isothermal sound speed . @xmath40 is the ` potential temperature ' of the disc s mid - plane and following @xcite we define it as : @xmath41 noting that equation [ eqn : temp ] is independent of the choice of scaling for the potential temperature.the net heating rate ( @xmath42 ) is given by : @xmath43 where @xmath44 is the stefan - boltzmann constant and @xmath45 is the vertical optical depth , with @xmath46 the opacity . the two fluxes @xmath47 & @xmath48 are the radial heat fluxes due to turbulence and radiation respectively ; which are given by : @xmath49 where @xmath50 is the prandtl number ( in most calculations we take @xmath51 , the preferred value suggested by @xcite ) , and @xmath52 with @xmath53 the radiation constant , @xmath54 the speed of light and @xmath55 the mid - plane density . for our model we adopt the @xcite opacities and equation [ eqn : temp ] is integrated as described in @xcite . our heating term ( equation [ eqn : gamma ] ) does not account for stellar irradiation , which is known to dominate the heating in the outer disc ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? therefore , we do not allow the disc s temperature to drop below what would be obtained for a passively heated disc given by : @xmath56 we set @xmath57 to : @xmath58^{1/4}\ ] ] where the mass scaling is identical to that adopted by @xcite , based on a fit to a t tauri star s birth - line from @xcite . finally , the temperature is also restricted to be no less than 10 k at very large radius , to account for heating from the surrounding star - forming region . in all calculations we assume an ideal equation of state with @xmath59 and a mean molecular weight ( @xmath60 ) of 2.35 amu as the majority of the disc material we are interested in remains molecular and neutral . we treat the viscosity using an ` alpha ' model such that : @xmath61 for mri turbulence we set @xmath62 and for angular momentum transport due to self - gravity we set @xmath63 to @xmath64 where @xmath65 is the toomre parameter @xcite given by : @xmath66 the form of @xmath67 is" +"physical systems where the interactions between the constituent particles are weak and can be treated perturbatively are mostly well understood . a precise understanding of strongly correlated systems however appears to be much harder to obtain because the experimental observation of several important mechanisms is less feasible . many processes take place at high energy and therefore on fast timescales while precise control over individual constituent particles is very hard to achieve . this unattainability of detailed control lies at the heart of the difficulties to experimentally implement quantum information processes . nonetheless , substantial progress has been achieved recently by considering cold atoms trapped in an optical lattice @xcite , which can effectively be described by a bose - hubbard hamiltonian . this idea lead to several important experiments emulating condensed matter phenomena . the most prominent example is probably the observation of the superfluid to mott insulator quantum phase transition @xcite in a three dimensional lattice , but also other geometries like a kagome lattice @xcite or a tonks girardeau gas @xcite are being studied . even theoretical ideas for the implementation of quantum information processing have been pursued by entangling neighbouring atoms via controlled collisions @xcite . in addition , these systems could act as quantum simulators , where the dynamics of a rather complex hamiltonian can be simulated in an experiment by eather creating the hamiltonian in question , or trotter decomposing the evolution into small steps , where the dynamics of each step is generated by a much simpler hamiltonian @xcite . despite their success , optical lattices are in all their applications limited by an intrinsic draw back : it is exceedingly difficult to access individual lattice sites , since their separation is only half of the employed optical wavelength . here we propose an alternative way to create an effective bose - hubbard model and other hamiltonians , which does not suffer from this problem . we consider two realisations of an array of cavities and study the dynamics of polaritons , combined atom photon excitations , in this arrangement . since the distance between adjacent cavities is considerably larger than the optical wavelength of the resonant mode , individual cavities can be addressed . photon hopping occurs between neighboring cavities while the repulsive force between two polaritons occupying the same site is generated by a large kerr nonlinearity that occurs if atoms with a specific level structure usually considered in electromagnetically induced transparency @xcite interact with light . each cavity is interacting with an ensemble of these atoms , which are driven by an external laser , see fig . [ crystal ] . by varying the intensity of the driving laser , the nonlinearity can be tuned and hence the system can be driven through the superfluid to mott insulator transition . in particular , the driving laser may be adjusted for each cavity individually allowing for a much wider range of tuning possibilities than in an optical lattice , including attractive interactions . our system can be described in terms of three species of polaritons , where under the conditions specified below , the species which is least vulnerable to decay processes is governed by the effective bose - hubbard ( bh ) hamiltonian , @xmath0 @xmath1 creates a polariton in the cavity at site @xmath2 and the parameters @xmath3 and @xmath4 describe on site repulsion and inter cavity hopping respectively . the most promising candidates for an experimental realisation are toroidal or spherical micro - cavities , which are coupled via tapered optical fibres @xcite . these cavities can be produced and positioned with high precision and in large numbers . they have a very large q - factor ( @xmath5 ) for light that is trapped as whispering gallery modes and efficient coupling to optical fibres @xcite as well as coupling to cs - atoms in close proximity to the cavity via the evanescent field @xcite have been demonstrated experimentally very recently . in the longer term , photonic crystals represent an appealing alternative as they offer the possibility for the fabrication of large arrays of cavities in lattices or networks @xcite . obviously , our concept is not limited to certain geometries , as it is the case for the optical lattice . any arrangement of the cavity array may be considered . we first derive the hamiltonian ( [ bosehubbard ] ) for the considered structure and then present a theoretical analysis of the feasible parameter range , which is backed up by a full numerical demonstration of the superfluid to mott insulator transition including experimental imperfections . we consider a periodic array of cavities , which we describe here by a periodic dielectric constant , our model consists of an array of cavities , where photon hopping occurs due to the overlap ( shaded green ) of the light modes ( green lines ) of adjacent cavities . atoms in each cavity ( brown ) , which are driven by external lasers ( blue ) give rise to an on site repulsion.,width=302 ] @xmath6 for all tupels of integers @xmath7 . we assume the dielectric constant @xmath8 to be real , i.e. we neglect absorption processes , and limit our considerations to linear , isotropic dielectric media . the electromagnetic field may be represented by a vector potential @xmath9 and a scalar potential @xmath10 which obey the gauge conditions , @xmath11 and @xmath12 @xcite . @xmath9 can be expanded in wannier functions , @xmath13 , each localised at one single cavity at location @xmath2 . we describe this single cavity by the dielectric function @xmath14 such that the wannier functions satisfy the eigenvalue equation , @xmath15 where the eigenvalue @xmath16 is the square the resonance frequency of the cavity which is independent of @xmath2 due to the periodicity . we assume that the wannier functions decay strongly enough outside the cavity such that only wannier modes of nearest neighbour cavities have nonvanishing overlap . in terms of the creation and annihilation operators of the wannier modes , @xmath17 and @xmath18 , the hamiltonian of the field can be written , @xmath19 here @xmath20 is the sum of all pairs of cavities which are nearest neighbours of each other . since @xmath21 , we neglected rotating terms which contain products of two creation or two annihilation operators of wannier modes in deriving ( [ arrayham2 ] ) . @xmath22 is given by @xcite , @xmath23 ) provides an excellent approximation to many relevant implementations such as coupled photonic crystal micro - cavities or fibre coupled toroidal micro - cavities . furthermore , it allows for the observation of state transfer @xcite and entanglement dynamics and propagation for gaussian states @xcite as the hamiltonian is harmonic . in the next section we present a possible realisation of the repulsive term in the hamiltonian ( [ bosehubbard ] ) to generate a repulsion between polaritons that are located in the same cavity , we fill the cavity with 4 level atoms of a particular level structure that are driven with an external laser in the same manner as in electromagnetically induced transparency , see figure [ level ] : the transitions between levels 2 and 3 are coupled to the laser field and the transitions between levels 2 - 4 and 1 - 3 couple via dipole moments to the cavity resonance mode . the level structure and the possible transitions of one atom , @xmath24 is the frequency of the cavity mode , @xmath25 is the rabi frequency of the driving by the laser , @xmath26 and @xmath27 are the parameters of the respective dipole couplings and @xmath28 , @xmath29 and @xmath30 are detunings.,width=302 ] it has been shown by imamoglu and co - workers , that this atom cavity system can show a very large nonlinearity @xcite , and a similar nonlinearity has recently been observed experimentally @xcite . in a rotating frame with respect to @xmath31 , the hamiltonian of the atoms in the cavity reads , @xmath32 where @xmath33 projects level @xmath34 of atom @xmath35 to level @xmath36 of the same atom , @xmath24 is the frequency of the cavity mode , @xmath25 is the rabi frequency of the driving by the laser and @xmath26 and @xmath27 are the parameters of the dipole coupling of the cavity mode to the respective atomic transitions which are all assumed to be real . since we are only interested in the situation , where there is on average one excitation in each cavity and since the probability to have two excitations in one cavity is suppressed by the kerr nonlinearity , it is appropriate to only consider states with at most two excitations per cavity . all atoms interact in the same way with the cavity mode and hence the only relevant states are dicke type dressed states . neglecting two photon detuning and coupling to level 4 , the hamiltonian ( [ h_manyatom ] ) can be written as a model of three species of polaritons in this subspace . in the case where @xmath37 and @xmath38 , level 4 of the atoms decouples from the rest of the two excitation manifold @xcite . if we furthermore assume that the number of atoms is large , @xmath39 , the hamiltonian ( [ h_manyatom ] ) truncated to the subspace of at most two excitations can be diagonalised . let us therefore define the following creation ( and annihilation ) operators : @xmath40 where @xmath41 , @xmath42 , @xmath43 , @xmath44 and @xmath45 . the operators @xmath46 , @xmath47 and @xmath48 describe polaritons , quasi particles formed by combinations of atom and photon excitations . by looking at their matrix representation in the subspace of at most two excitations , one can see that in the limit of large atom numbers , @xmath39 , they satisfy bosonic commutation relations , @xmath49 = \ , 0 \quad ; \quad \left [ p_j , p_l^{\dagger } \right ] = \delta_{jl } \quad ; \quad j , l = 0,+,- \ , .\ ] ] @xmath46 , @xmath47 and @xmath48 thus describe independent bosonic particles . in terms of these polaritons , the hamiltonian ( [ h_manyatom ] ) for @xmath37 and @xmath38 reads , @xmath50_{g_{24 } = 0 , \varepsilon = 0 } = \mu_0 \ , p_0^{\dagger } p_0 + \mu_+ \ , p_+^{\dagger } p_+ + \mu_- \ , p_-^{\dagger } p_- \ , , \ ] ] where the frequencies are given by @xmath51 , @xmath52 and @xmath53 . we will now focus on the dark state polaritons , @xmath46 , which can be described by the hamiltonian ( [ bosehubbard ] ) as we shall see . to write the full hamiltonian @xmath54 , ( [ h_manyatom ] ) , in the polariton basis , we express the operators @xmath55 and @xmath56 in terms of @xmath46 , @xmath47 and @xmath48 . in the subspace of at most two excitations , the coupling of the polaritons to the level 4 of the atoms via the dipole moment @xmath27 reads , @xmath57 where @xmath58 . in deriving ( [ coupletolevel4 ] ) , we made use of the rotating wave approximation : in a frame rotating with respect to ( [ h0polariton ] ) , the polaritonic creation operators rotate with the frequencies @xmath59 , @xmath60 and @xmath61 . furthermore , the operator @xmath62 rotates at the frequency @xmath63 , ( c.f . ( [ h_manyatom ] ) ) . hence , provided that @xmath64 or @xmath65 or @xmath66 can be neglected , which eliminates all interactions that would couple @xmath46 and @xmath62 to the remaining polariton species . for @xmath67 , the coupling to level 4 can be treated in a perturbative way . this results in an energy shift of @xmath68 with @xmath69 and in an occupation probability of the state of one @xmath62 excitation of @xmath70 , which will determine an effective decay rate" +"unstable particles are a perfect testing ground for theories that try to unify the principle of relativity with quantum mechanics for ( at least ) two reasons . first , an unstable particle provides a very simple example of a non - trivial interacting quantum system . due to the specific initial condition characteristic to this problem ( there is just one particle in the initial state ) , a rigorous description of the decay is possible in a small hilbert space that contains only states of the particle and its decay products , so the solution can be obtained in a closed form . second , unstable particles played an important role in confirming predictions of einstein s special relativity . it was demonstrated experimentally that the decay of moving particles slows down in a good agreement with einstein s time dilation formula @xcite . for a long time it was believed that relativistic quantum mechanics and quantum field theory must reproduce exactly the einstein s time dilation formula for unstable particles @xcite . however , a detailed quantum relativistic calculation in @xcite has shown that there are small corrections to this formula in the case of particles with definite momentum . this result was later confirmed in other studies @xcite . although surprising , these findings did not challenge directly the applicability of special relativity to unstable systems . this is because relativistic transformations connect results of measurements of two inertial observers moving with constant velocities with respect to each other . then a fair comparison with the time dilation formula requires consideration of unstable states having definite values of velocity for both observers . such states do not have a definite momentum for , at least , one observer . their decay laws were considered in recent article @xcite which alleges that the decay accelerates when particle s velocity increases , instead of being slowed down as experiment shows . in the present article we resolve this controversy by performing a detailed calculation of the decay laws of particles with narrow distributions of velocities observed from moving reference frames . we found that the result of @xcite is based on an incorrect identification of the subspace of states of the unstable particle in the full hilbert space of the system . in sections [ ss : general ] - [ ss : instant ] we present a rigorous quantum relativistic framework required for the description of decays . the exact formula for the time dependence of the non - decay probability in a moving inertial frame of reference is derived in section [ sc : moving - frame ] . particular cases of this formula relevant to unstable particles with sharply defined momenta or velocities are considered in sections [ sc : mov ] and [ sc : general ] , respectively . section [ sc : numerical ] is devoted to numerical calculations of the differences between the accurate quantum mechanical result and the standard time dilation formula ( [ eq:1b ] ) . although these differences are much smaller than the resolution of modern experiments , their presence is in sharp contradiction with special relativity which does not tolerate even small deviations from the einstein s time dilation . the decay of unstable particles is described mathematically by the _ non - decay probability _ which has the following definition . suppose that we have a piece of radioactive material with n unstable nuclei prepared simultaneously at time @xmath0 and denote @xmath1 the number of nuclei that remain undecayed at time @xmath2 . then the non - decay probability indicates the rapidity of the observer that measures the non - decay probability , as described below . ] @xmath3 ( also called the _ non - decay law _ in this paper ) is defined as the fraction of nuclei that survived the decay in the limit of large @xmath4 @xmath5 so , at each time point the piece of radioactive material can be characterized by its _ composition _ @xmath6 , where @xmath7 is the share of undecayed nuclei in the sample and @xmath8 is the share of nuclei that were transformed to the _ decay products_. in this paper , in the spirit of quantum mechanics , we will treat @xmath4 unstable particles as an ensemble of identically prepared systems and consider @xmath3 as a property of a single particle ( nucleus ) , i.e. , the probability of finding this particle in the undecayed state . in this paper we are concerned with comparison of decay observations made by two observers @xmath9 and @xmath10 that move with respect to each other . without loss of generality we will assume that observer @xmath10 moves with respect to @xmath9 with velocity @xmath11 along the @xmath12-axis and that at time @xmath0 measured by both observer s clocks the origins of their coordinate systems coincide and all three pairs of coordinate axes are parallel ( @xmath13 , etc . ) . for discussion purposes we will say that @xmath9 is at rest while @xmath10 is moving . to simplify formulas we will use the _ rapidity _ parameter @xmath14 instead of velocity @xmath15 . for example , in this notation the famous relativistic factor takes the form @xmath16 . if from the point of view of @xmath9 the decay is described by the function @xmath3 , then the non - decay law of the same particle seen by the moving observer @xmath10 will be denoted by @xmath17 . denotes time measured by the clock belonging to the observer @xmath10 . ] calculation of this function and , in particular , the relationship between @xmath17 and @xmath3 is the major goal of this work . the purpose of any relativistic theory is to describe the relationships between measurements made by different _ inertial observers _ or from different _ inertial reference frames _ , i.e. , reference frames moving in space with constant velocities along straight lines and without rotation . the special _ principle of relativity _ tells us that these reference frames are exactly equivalent * * postulate i. * experiments identically arranged and performed in two different inertial reference frames @xmath9 and @xmath18 always yield the same results . for any two observers @xmath9 and @xmath18 there is an _ inertial transformation _ that connects @xmath18 to @xmath9 , i.e. , the set of rules that allows one to change from the reference frame @xmath9 to the reference frame @xmath18 . each inertial transformation is a combination of space and time translations , rotations and boosts . a composition of two inertial transformations is again a valid inertial transformation . this composition obeys the associativity law . the inverse of an inertial transformation is also an inertial transformation . therefore , they form a 10-parameter lie group . the structure of this group is specified in the second postulate * * postulate ii . * inertial transformations ( space and time translations , rotations , and boosts ) form the _ poincar group_. obviously , two different observers obtain different results by measuring observables of the same physical system . most problems in physics can be understood as translations of descriptions of the physical system between different reference frames . for example , if we have a full description of the system from the point of view of observer @xmath9 , then the time evolution is obtained by answering the question `` what is the description of the same system from the point of view of observer @xmath19 that is shifted in time with respect to @xmath9 ? '' it is important to realize that inertial transformations between observers can be divided into two groups : _ kinematical _ and _ dynamical_. kinematical transformations are those whose action on observables does not depend on the interaction . for example , if two stationary observers look at the unstable particle from different points in space , they would assign the same non - decay probability to the particle . the same is true for stationary observers having different orientations in space . from this follows , these forms are not appropriate for the description of non - decay laws of unstable particles . ] * * postulate iii . * space translations and rotations are kinematical . on the other hand , time translations produce non - trivial changes in the system . the composition of the unstable system looks different for observers @xmath9 and @xmath19 shifted in time with respect to each other . the exact action of time translations on observables of the physical system should be obtained as a result of solution of dynamical equations which depend on the interaction acting in the system . hence the following postulate is true for all types of isolated interacting systems . * * postulate iv . * time translations are dynamical , i.e. , interaction - dependent . the above postulates i - iv have overwhelming experimental support . they are assumed to be valid throughout this paper . however they are not sufficient for a full description of the unstable particle in a moving reference frame . such a description requires also knowledge of the nature of boosts . here we have a choice between two paths forward . one path is to postulate certain properties of boosts . this path was taken by einstein . it leads to special relativity and to the time dilation formula ( [ eq:1b ] ) as explained in the next section . in this paper we will argue in favor of choosing another path : keep postulates i - iv , add to them well - established postulates of quantum mechanics , and see what are the implications for the transformations of observables ( in particular , the non - decay probability ) with respect to boosts . this approach is employed starting from section [ ss : general ] throughout the paper . in addition to postulates i - iv , einstein s special relativity makes two more assumptions regarding the nature of boosts * * assumption v. * boosts are kinematical . by postulating the kinematical character of boosts , special relativity insists that the internal composition of a compound system does not depend on the velocity of the observer . for example , if @xmath9 and @xmath10 are two observers moving with respect to each other , then , according to special relativity , both observer will measure the same composition of the unstable system at time @xmath0 . these statements are often considered as self - evident in discussions of special relativity . for example , r. polishchuk writes in @xcite _ `` any event that is `` seen '' in one inertial system is `` seen '' in all others . for example if observer in one system `` sees '' an explosion on a rocket then so do all other observers . '' _ in addition to the universality and interaction - independence of boost transformations , special relativity also postulates the exact transformation laws of physical observables with respect to boosts . they are referred to as _ lorentz transformations_. the most fundamental are lorentz transformations for space - time coordinates of events . loses its localization from the point of view of the moving observer @xmath10 @xcite . so , assumption vi can be applied only in the classical limit . ] * * assumption vi . * if from the point of view of observer @xmath9 an event is localized in a space point @xmath20 at time @xmath21 , then from the point of view of observer @xmath10 the same event has space - time coordinates @xmath22 given by lorentz formulas + @xmath23 let us now demonstrate that in special relativity the postulates i - iv and assumptions v - vi are sufficient to unambiguously describe particle decay in different reference frames without invoking any information about" +"in atomic , molecular , and chemical physics , linear quadrupole traps ( lqts ) are ubiquitous . they are routinely used in the study of topics ranging from quantum information@xcite to plasma dynamics@xcite to precision measurement@xcite . moreover , in the rapidly emerging field of hybrid atom - ion devices , lqts are now being employed to study the interactions of cold atomic and molecular ions with neutral atoms and molecules@xcite . these studies have already resulted in important quantum chemistry measurements@xcite and promise to enable new technologies and science such as the implementation of novel quantum gates@xcite , probes of quantum gases@xcite , observation of novel charge - transport dynamics@xcite , and the sympathetic cooling of atomic and molecular systems which can not be laser cooled@xcite . while the lqt is a thoroughly proven device , direct identification of non - fluorescing ions in a lqt is not straightforward and is often problematic . current methods to identify ions in a lqt include nondestructive resonant - excitation mass spectrometry using laser - induced fluorescence@xcite , destructive resonant - excitation mass spectrometry using channel electron multiplier ( cem ) detection@xcite , lqt mass - filtering techniques@xcite , and molecular dynamics ( md ) simulations@xcite . the first three methods are complicated by lqt properties which give rise to nonlinear resonances , multiple secular frequencies , and trap - depth limitations . these complications may lead to either the incorrect labeling or the lack of observation of certain ions . the last method is limited by the inability to even indirectly identify the non - laser - cooled ion . these limitations and complications can be avoided if ions are instead directly observed in a simple , straightforward manner using time - of - flight ( tof ) mass spectrometry . unfortunately , while commercial devices which couple ion traps with tof units do exist , they do not offer a practical solution for most experimental architectures employed in atomic , molecular , and chemical physics . first , commercial tof devices are predominantly geared towards life science research where the study of large molecules requires extremely high mass resolutions ( @xmath1)@xcite . to meet these stringent demands , commercial tof devices are large , highly integrated designs that are constructed to be the principle feature of the experimental apparatus . second , in most commercial units the tof unit is coupled to a 3d paul trap rather than a lqt@xcite . while this type of device works well for many applications , 3d paul traps , unlike lqts , are not amenable to studies that require large trap capacities and high optical access to the trapped ions demands typical of atomic , molecular , and chemical physics experiments . and finally , though some commercial devices incorporate a lqt , the trapped ions are typically axially ejected from the lqt and subsequently accelerated orthogonally into the tof drift tube to recover good mass resolution@xcite . although this is an effective coupling technique , the commercial implementation of orthogonal acceleration is technically complicated , space - demanding , and expensive . here we describe a simple lqt - tof device , which offers near - isotopic mass resolution for atomic and molecular ions with masses of a few 100 amu . the straightforward , compact design ensures that the device does not impede non - tof related functions by limiting optical or spatial access , making it ideal for most atomic , molecular , and chemical physics applications . this is accomplished by coupling the lqt to the tof apparatus through a novel radial extraction method resulting in good mass resolution and without the complications associated with axial ejection and orthogonal acceleration . additionally , due to the use of ion optics to enhance ion detection efficiency , long interrogation times do not need to be sacrificed for higher measurement rates , as in most commercial devices , in order to build statistics on reasonable time scales . finally , the proposed device can be built for a small fraction of the cost of current commercial tof devices . in the remainder of this article , we demonstrate the implementation and characterization of the lqt - tof device . we first discuss the design and construction of the device addressing the tof unit , the lqt used to trap and interrogate a sample of ions , and the associated electronics . secondly , we describe the calibration of the device using mass - filtering techniques . we conclude with proof - of - principle experiments which demonstrate the effectiveness of the device as a simple , practical method of mass spectrometry for use in atomic , molecular , and chemical physics . the tof device , shown in fig . [ fig : app ] , is built onto a @xmath2-@xmath3 conflat flange and is supported by three @xmath4-@xmath5 threaded rods . the @xmath6 mm drift tube , confined by a surrounding @xmath2-@xmath3 conflat nipple , includes ion optics which are used to guide ions into the detector region to increase the detection efficiency of the device . the detector region is composed of a cem held at @xmath7 v and a stainless steel grid used to ensure that the drift tube remains field - free , apart from the field created by the ion optics . the total length of the device is @xmath8 mm and is designed to couple with a lqt ( @xmath9 mm and @xmath10 where @xmath11 and @xmath12 are the field and electrode radii , respectively ) via pulsed radial extraction . the entire apparatus is maintained at background pressures below @xmath13 mbar by a triode sputter - ion pump . to simplify the coupling process , the tof device couples directly to a lqt through radial extraction . this method is superior to that of the normal axial extraction for three critical reasons . first , field lines from the axially - confining end caps do not penetrate far into the trapping region . if the ions are pulsed from the trap axially ( _ i.e. _ by grounding an end cap ) , relatively long durations are required to completely empty the trap due to this weak coupling . this leads to a relatively large temporal spread of ions , which results in poor mass resolution . this problem can be partially solved by using segmented trap electrodes@xcite to apply a more strongly - coupled , axially - ejecting field to the trapped ions ; however , this solution requires more sophisticated machining and electronics . second , the axial distribution of trapped ions in a lqt is generally larger than the radial distribution . this leads to a larger distribution of initial energies and overall flight distances , and thereby poorer mass resolution when ions are axially pulsed . third , it is often the case in atomic , molecular , and chemical physics that the lqt axis is used for the introduction of cooling or spectroscopy beams , which generally precludes axial extraction into a tof device . despite the obvious drawbacks of axial ion extraction , there have been relatively few implementations of radial ion extraction into a tof device . in the patent of franzen et al.@xcite , the use of plate electrodes external to the lqt is proposed to apply pulsed potentials that radially eject the ions into the drift tube . these plates , however , obstruct optical access to the trap and also require space in the vacuum chamber . additionally , field lines from the external plates do not penetrate far into the lqt , resulting in weak coupling between the plates and the trapped ions . as a result it is difficult to establish an optimal ion extraction scheme using this method and no experimental data is found in the literature . unlike the design proposed by franzen , radial extraction in our device is achieved by applying the extraction pulses directly to the trap electrodes , in a manner similar to that proposed by makarov in ref . , eliminating the need for external plate electrodes . for the operation of our device , various ions are introduced to the trap by ablating solid precursors with a pulsed nd : yag laser as in ref . . for optimal loading , the radiofrequency ( rf ) trapping voltage is applied 50 @xmath14s after the ablation pulse . this rf is applied to all four electrodes with the appropriate phases to create a quadrupole trapping potential with typical values of @xmath15 khz and @xmath16 v leading to mathieu @xmath17 parameters of roughly @xmath18 for @xmath19 amu / e , where @xmath20 is the trapping frequency , @xmath21 is the rf amplitude , @xmath22 , and @xmath23 is the mass - to - charge ratio of the trapped ion . to be clear , the prefactor of @xmath24 in the expression for @xmath17 is a result of applying voltage to all four electrodes rather than to only a diagonal pair . after the trapping period , the rf is switched off and the ions are briefly allowed to expand for @xmath25 @xmath14s . this delay redistributes the ions such that higher energy ions will either receive a lower extraction energy or have to travel farther before reaching the detector , leading to improved mass resolution@xcite . to realize maximum mass resolution a two - stage acceleration scheme is implemented following the delay . extraction potentials of roughly @xmath26 v ( blue ) and @xmath27 v ( green ) , as shown in fig . [ fig : trap ] , are applied to vertically paired electrodes . this results in the radial extraction of ions from the trapping region , through the right pair of electrodes , and into the tof drift tube which is referenced to ground . the electronics used to provide the pulsing voltages include two sets of positive - high - voltage power supplies and pulsers . a circuit , shown schematically in fig . [ fig : trap ] , is used to combine the pulsing and trapping potentials . amplified rf voltage is applied to the primary windings of two hand - wound center - tapped transformers . the center - taps of the secondary coils are connected to the high - voltage pulsing units and the two pairs of secondary wires are connected to vertically paired trap electrodes . when the trapping rf is on , the pulser outputs are grounded , resulting in the normal quadrupole trapping potential . however , when the trapping rf is off and the pulser outputs are high , identical high - voltage is applied to the vertically paired electrodes , resulting in the radial ejection of the ions into the tof drift tube . a rf switch with a @xmath28 @xmath14s fall - off time is used to switch off the rf prior to pulsing . this large fall - off time relative to the pulse delay ( @xmath25 @xmath14s ) guarantees the remainder of an rf component in the pulsed high voltage . the phase of this rf can be tuned to optimize ion detection , mass resolution , and signal stability which may be otherwise limited due to fringing fields , charging effects , or engineering imperfections in the experiment . to optimally implement the two - stage acceleration of the ions from the trap , lqt - tof dimensions are determined based on the work of wiley et al in ref . . critical distances , shown in fig . [ fig : trap ] , include the length of the drift tube , @xmath29 , the mean length of the first acceleration stage , @xmath30 , and the length of the second acceleration stage , @xmath31 . the extraction voltages ( @xmath26 and @xmath27 v ) establish the equipotential contours shown in fig . [ fig :" +"homo and heteroclinic bifurcations constitute the core of our understanding of complicated recurrent behaviour in dynamical systems . the history goes back to poincar in the late @xmath0 century , with major subsequent contributions by the schools of andronov , shilnikov , smale and palis . these schools have been founded on a combination of analytical and geometrical tools which developed a quite good understanding of the qualitative behaviour of those dynamics . differential equations modelling physical experiments frequently have parameters which appear in the differential equations , and it is known that qualitative changes may occur in the solution structure of these systems as the parameters vary . the dynamical behaviour of systems can be strongly influenced by special geometric or analytic invariant structures appearing in the equations ( _ e.g. _ divergence - free , preserving or reversing symmetries ) . one may ask which dynamical behaviour we would expect to see in the presence of a given invariant structure . generically , this is a hard question to answer , but some questions could be partially answered , by considering local and global bifurcations of low codimension . a bykov cycle on a three - dimensional manifold is a heteroclinic cycle between two hyperbolic saddle - foci of different morse index , where one of the connections is transverse and the other is structurally unstable . there are two different possibilities for the geometry of the flow around the one - dimensional connection depending on the direction solutions turn around it . all literature about the michelson system @xcite considered that in the neighbourhoods of the two saddle - foci , trajectories wind in the same direction . an immediate question arises : * what happens if trajectories wind with opposite directions near each node ? the first author and duarte proved in @xcite that the set of @xmath1-divergence - free vector fields defined in a compact three - dimensional riemannian manifold without boundary , has a @xmath1-residual set such that any vector field inside it is anosov or else , the flow associated to it has dense elliptic solutions in the phase space . furthermore , in @xcite , also in this context , the authors proved that if the vector field is not anosov , then it can be @xmath1-approximated by another divergence - free vector field exhibiting homoclinic tangencies . however , a conservative vector field whose flow has a persistent bykov cycle may lie outside these residual / dense subsets and the developed theory can not be applied for this degenerated class of systems . since bykov cycles can not be anosov ( due to the presence of equilibria ) , the dichotomies in @xcite suggest the following problem : * could we perform a @xmath1-perturbation within the set of vector fields whose flow has a bykov cycle in such a way that the elliptic periodic solutions are dense and/or tangencies occur ? in this paper , we partially answer the questions * ( q1)**(q2)*. we present a mechanism for the coexistence of hyperbolic and non - hyperbolic dynamics arising in a neighbourhood of a conservative bykov cycle where trajectories turn in opposite directions near the two saddle - foci - see figure [ conservativo2 ] . we show that in a @xmath1-open class of divergence - free vector fields , tangencies of the invariant manifolds of two hyperbolic saddle - foci densely occur . we prove that the global dynamics is persistently dominated by heteroclinic tangencies and by the existence of infinitely many elliptic points coexisting with hyperbolic dynamics arising from @xmath1transversality . tangencies are strongly connected with the cocoon bifurcations . we describe an extended version of these bifurcations which can be detected numerically with the _ time delay function _ introduced by lau @xcite . see also @xcite . we also find the relations between these four dynamical phenomena : chirality , tangencies , generalized cocoon bifurcations and elliptic solutions . in the conservative setting , cocoon bifurcations are connected with unfoldings of a hopf - zero singularity , which has been shown to occur in climatological models with seasonal forcing . represents the set of @xmath1-divergence free vector fields on @xmath2 . on the dashed line , we find the vector fields whose flow has a given bykov cycle and its continuation . the set @xmath3 is the open set ( with the induced topology ) in which theorem [ main1 ] is valid . , height=113 ] we recall some important results about heteroclinic tangencies for general and conservative systems . the systematic study of bifurcations of tangencies was started by gavrilov and shilnikov @xcite in the seventies , for the case of two - dimensional dissipative diffeomorphisms . the authors established that diffeomorphisms with homoclinic tangencies might separate systems with regular and chaotic dynamics , _ i.e. _ they belong to the boundary of morse - smale systems and the transition through this boundary corresponds to an @xmath4explosion . the theorem on the cascade of periodic sinks / sources near a tangency plays an important role see newhouse @xcite : in the dissipative case , for any one parameter family that unfolds generically a quadratic homoclinic tangency , there exists a sequence of intervals of values of the parameter such that the corresponding diffeomorphism has sinks / sources . one of the fundamental results in homoclinic bifurcations was established in newhouse @xcite : the existence of regions of the space of two - dimensional diffeomorphisms where tangencies are dense . these regions are called _ newhouse regions _ ; the result has been generalized for the multidimensional case by gonchenko @xcite . dynamics of systems within these regions is complex and rich and , as claimed in @xcite , it is impossible to give the complete description of bifurcations of such systems . the majority of these results was obtained for the broader case of general systems without any restriction on the preservation of some invariant structure . they can not be directly applied to volume - preserving and/or reversible systems because they require special considerations . nevertheless , the main geometric and analytical arguments can be also used for systems with additional structures , having special care . in this direction , important results on the birth of elliptic periodic points in area - preserving maps under bifurcations of tangencies were obtained in @xcite . see also the paper by lamb and stenkin @xcite about _ mixed dynamics . _ bifurcations of single - round periodic solutions were studied in @xcite for two - dimensional symplectic maps close to a map having a quadratic homoclinic tangency . the corresponding first return maps have been derived , bifurcations of their fixed points have been studied and bifurcation diagrams for one - parameter general unfoldings have been constructed . using renormalization results , the existence of one - parameter cascades of elliptic single - round periodic solutions has been proved . let @xmath2 be a three - dimensional closed and connected @xmath5 riemaniann manifold without boundary , endowed with a volume - form and let @xmath6 denote the lebesgue measure associated to it . let @xmath7 be a @xmath8 vector field , with @xmath9 . by picard s theorem on the existence and uniqueness of solutions of differential equations , @xmath10 integrates into a complete @xmath8 flow @xmath11 in a sense that @xmath12 we say that @xmath13 is _ divergence - free _ if its divergence is equal to zero _ i.e. _ if @xmath14 computed in local coordinates @xmath15 , see @xcite . equivalently , @xmath10 is divergence - free if , accordingly to the liouville formula , the volume - measure @xmath6 is invariant for the associated flow . in this case we say that the flow is _ conservative _ , _ volume - preserving _ or _ incompressible _ and is such that @xmath16 , for all @xmath17 and for all @xmath18 . we denote by @xmath19 , @xmath9 , the space of @xmath8 divergence - free vector fields on @xmath2 and we endow this set with the usual @xmath8 whitney topology . let also denote by @xmath20 the space of @xmath8 general vector fields on @xmath2 without no divergence - free constraint . we say that an equilibrium @xmath21 of @xmath10 ( _ i.e. _ @xmath22 ) , is _ hyperbolic _ if @xmath23 has neither pure complex nor zero as an eigenvalue . a hyperbolic saddle - equilibrium with a pair of conjugated non - real eigenvalues is called a _ saddle - focus_. for regular points , ( _ i.e. _ non - equilibrium points ) we define hyperbolicity with respect to the poincar map in a standard way see e.g. @xcite . given a hyperbolic equilibrium point @xmath24 with respect to a vector field @xmath10 , we denote by @xmath25 its unstable / stable global manifold . local unstable / stable manifolds are denoted by @xmath26 . when there is no ambiguity we omit the letter @xmath10 in these notations . open class of divergence - free vector fields defined on a three - dimensional compact manifold , tangencies of the invariant manifolds of two hyperbolic saddle - foci occur densely.,height=264 ] in the present paper , all equilibria are hyperbolic saddle - foci . the dimension of the unstable manifold of a saddle - focus will be called the _ morse index _ of the saddle . given two equilibria @xmath27 and @xmath28 , a _ heteroclinic trajectory _ from @xmath27 to @xmath28 , denoted @xmath29 $ ] , is a solution of @xmath30 contained in @xmath31 . there may be more than one solution from @xmath27 to @xmath28 . a heteroclinic cycle is a finite collection of equilibria together with a set of heteroclinic trajectories connecting the equilibria in a cyclic way . more details in field @xcite . in a three - dimensional smooth manifold , a _ bykov cycle _ is a heteroclinic cycle associated to two hyperbolic saddle - foci with different morse indices , in which the one - dimensional manifolds coincide and the two - dimensional invariant manifolds have a transverse intersection @xcite . the terminology _ bykov cycle _ is because it was bykov @xcite who studied dynamical properties from the existence of similar cycles in a more general context than conservative ones . this type of cycle , or rather its bifurcation point , is also called by _ t - point _ by glendinning and sparrow @xcite . in this section , we state the main theorems and we relate them with other results in the literature . our object of study is the dynamics around an autonomous divergence - free smooth vector field whose flow has a bykov cycle , for which we give an accurate description here . specifically , we study a @xmath1vector field:@xmath32 whose flow has the following properties ( see figure [ conservativo2 ] ) : 1 . [ h1 ] there are two hyperbolic saddle - foci equilibria @xmath27 and @xmath28 . assuming that , for @xmath33 , the morse index of @xmath34 is @xmath35 , the eigenvalues of @xmath23 are : 1 . @xmath36 and @xmath37 , where @xmath38 and @xmath39 , for @xmath40 ; 2 . @xmath41 and @xmath42 , where @xmath43 and @xmath44 , for @xmath45 . [ h2 ] there is a heteroclinic cycle @xmath46 consisting of @xmath27 , @xmath28 and two one - dimensional heteroclinic connections : @xmath47 $ ] and @xmath48 $ ] . the solution @xmath47 $ ] is called the _ fragile connection_. 3 . [ h3 ] at the heteroclinic connection @xmath48 $ ] , the two - dimensional manifolds @xmath49 and @xmath50 meet transversely . property * ( h3 ) * is generic . indeed , the transverse intersection of @xmath49 and @xmath50 of * ( h3 ) * persists under @xmath1perturbations , whereas the fragile connection @xmath47 $ ] does not . although" +"in this paper we continue the exploration of the stellar content of obscured galactic giant h ii regions begun by ( * ? ? ? * hereafter paper i ) . @xmath0 , @xmath1 , and @xmath2 images are used to make a broad assessment of the stellar content of obscured star forming regions in the milky way . infrared spectroscopy follows , providing details of the brightest cluster members which can be used to make distance , mass , and luminosity estimates . the spectra are placed in proper context by comparison to new infrared spectral classification systems for massive stars @xcite . the known hot star content of the galaxy is rapidly expanding on the strength of the sophisticated infrared detector gains of the last 10 years . @xcite have recently published a very detailed account of the most massive stars in the ( relatively ) nearby giant h ii region m17 . the present project ( paper i , this work , and future work ) seeks to provide a large sample of massive star clusters with which to study the young and massive stellar content in the galaxy . this sample builds on the detailed visual studies of the galactic ob associations @xcite and provides a bridge to studies of young stellar objects in star forming regions . finally , the investigation of a large sample of clusters in galactic giant h ii regions will be important in understanding the massive star clusters in the galactic center @xcite which may have formed under different conditions than are typical in the disk of our galaxy @xcite . w42 is located in the fourth galactic quadrant at _ @xmath4 25.4 , 0.2 . @xcite determined w42 to be at the `` near '' kinematic distance ( 3.7 kpc for @xmath5 8 kpc ) and hence somewhat less luminous than earlier estimates @xcite . in this series of papers we shall follow a suggestion of dr . robert kennicutt ( private communication ) that `` giant '' means that more than @xmath6 lyman continuum ( @xmath4 lyc ) photons are inferred to be emitted per second from the h ii region . this is about ten times the luminosity of the orion nebula and roughly the number emitted from the hottest _ single _ o3-type star . as these stars are not found in isolation , there is an implication that a `` giant '' h ii region contains some minimum of _ multiple _ o - type stars . in light of our new distance estimate ( see 4 ) , w42 probably falls below this limit being perhaps a few times more luminous than the trapezium in orion . our target list was originally based on eleven of the most luminous giant h ii regions from the study of @xcite who tabulated their lyc output derived from radio continuum measurements and kinematic distance estimates . w42 is not seen in visual images , and we estimate a foreground extinction of @xmath7 @xmath4 10 mag ( see below ) . @xmath0 ( @xmath8 , @xmath9 ) , @xmath1 ( @xmath10 , @xmath9 ) , and @xmath2 ( @xmath11 , @xmath12 ) images of w42 were obtained on the nights of 29 august 1998 and 01 , 02 may 1999 with the f/14 tip tilt system on the cerro tololo interamerican observatory ( ctio ) 4 m blanco telescope using the two facility imagers cirim ( 1998 data ) and osiris , the ohio state infrared imager / spectrometer ( 1999 data ) . spectroscopic data were obtained on the night of 02 may 1999 using the f/14 tip tilt system at the blanco telescope with osiris . cirim and osiris are described in the instrument manuals found on the ctio web pages ( www.ctio.noao.edu ) . for osiris , see also @xcite . the tip - tilt system is described by @xcite . the tip tilt system uses three piezo electric actuators to move the secondary mirror at high frequency in a computer controlled feed back loop which corrects the natural image centroid motion . osiris employs 0.16@xmath13 pixels and cirim 0.21@xmath13 pixels . all basic data reduction was accomplished using iraf . each image / spectrum was flat fielded using dome flats and then sky subtracted using a median combined image of five to six frames . for w42 itself , independent sky frames were obtained five to ten arcminutes south of the cluster . standard stars used the median combination of the data for sky . the osiris 1999 may images were obtained under photometric conditions and in @xmath14 0.5@xmath13 to 0.6@xmath13 fwhm seeing ( with the tip tilt correction ) . total exposure times were 270 s , 135 s , and 135 s at @xmath0 , @xmath1 , and @xmath2 , respectively . the individual @xmath0 , @xmath1 , and @xmath2 frames were shifted and combined ( figure [ w42i ] ) , and these combined frames have point sources with fwhm of @xmath14 0.6@xmath13 , 0.7@xmath13 , and 0.6@xmath13 at @xmath0 , @xmath1 , and @xmath2 , respectively . dophot @xcite photometry was performed on the combined images . the flux calibration was accomplished using standards 9170 and 9172 from @xcite which are on the las campanas observatory standard system ( lco ) . the lco standards are essentially on the cit / ctio system @xcite , though color transformations exist between the two systems for redder stars . the standards were taken just before the w42 data and within 0.16 airmass of the airmass for w42 ; no corrections were applied for these small differences in airmass . aperture corrections using 11 pixel radius apertures were used to put the instrumental magnitudes on a flux scale . stars brighter than about 10th magnitude are expected to be a few percent non - linear on the osiris images . we have included the 1998 cirim data for such stars since the count levels for the cirim images were in the fully linear regime ( no linearity correction needed ) . the zero point to the cirim photometry was determined by comparing the instrumental magnitudes of stars in common to the osiris and cirim images . the cirim @xmath15band photometry includes a color correction term in order to make a transformation on to the cit / ctio system ( paper i ) . the osiris data was placed on the cit / ctio system by making small corrections ( @xmath16 10 @xmath17 ) to the @xmath0 , @xmath1 and @xmath2 magnitudes based on linear fits to the magnitude differences as a function of color for stars in common to the cirim and osiris images . uncertainties for the final @xmath18 magnitudes include the formal dophot error added in quadrature to the error in the mean of the photometric standards ( including the transformation to osiris magnitudes for the cirim data ) , and the error in aperture corrections used in transforming from the dophot photometry to osiris magnitudes . the latter errors dominate and were derived from the scatter in the measurements of four to seven relatively uncrowded stars on the mosaic frames . the sum ( in quadrature ) of the aperture correction and standard star uncertainties is @xmath19 0.018 , @xmath19 0.023 , @xmath19 0.019 mag in @xmath0 , @xmath1 , and @xmath2 , respectively . the dophot errors ranged from approximately @xmath19 0.01 mag to an arbitrary cut off of 0.2 mag ( stars with larger errors were excluded from further analysis ) . the flat field illumination was not uniform . a smooth gradient with full range of about 10@xmath17 was present . corrections for this gradient were made based on observations of a standard star taken over a 49 position grid covering the array . the spectra of three of the brightest four stars in the center of w42 were obtained with a 0.48@xmath13 wide slit ( oriented ew ) in 0.7@xmath13 fwhm seeing and divided by the spectrum of hr 6813 ( a1v ) to remove telluric absorption features . br@xmath20 absorption in hr 6813 was removed by eye by drawing a line across it between two continuum points . one dimensional spectra were obtained by extracting and summing the flux in a @xmath19 2 pixel aperture ( 0.64@xmath13 wide ) . the extractions include background subtraction from apertures centered 1.0@xmath13 on either side of the object . the wavelength calibration was accomplished by measuring the positions of bright oh@xmath21 lines from the @xmath3band sky spectrum @xcite . lines are identified by their relative differences between one and another . the measured dispersion is 0.0003683 pix@xmath22 . the spectral resolution at 2.2 is @xmath23 3000 . a spectacular stellar cluster is revealed at the heart of w42 in our near infrared images ( figure [ w42i ] and figure [ w42c ] ) . apparently , the cluster has just emerged from the edge of the molecular cloud from which it formed . this is confirmed below through @xmath3band spectroscopy which shows that the central massive star has largely cleared away its birth cocoon , but two of the next brightest stars have not . @xcite observed w42 in the mid and far infrared . their analysis revealed two distinct sites of star formation toward w42 . one , g25.4se is located at 3.7 kpc from the sun ( accounting for a sun to galactic center distance of 8 kpc ) , while the other , g25.4nw is probably located at about 9.6 kpc . lester et al . found a 10 unresolved source located at ra ( 2000 ) @xmath24 , dec ( 2000 ) @xmath25@xmath26 which is coincident with g25.4se . this mid ir source is associated with the stellar cluster we have observed . comparison of the position of the bright foreground star in the se corner of our @xmath3band image to the same star on the image from the digitized sky survey ( dss ) results in a position for the ( @xmath3band ) bright central star in the cluster ( w42 # 1 ; see 3.2 ) of ra ( 2000 ) @xmath27 , dec ( 2000 ) @xmath25@xmath28 . the @xmath29 color@xmath30magnitude diagram ( cmd ) for the region toward w42 is shown in figure [ cmd ] . a cluster sequence is evident at 0.6 @xmath29 1.5 along with stars with much redder colors and a probable foreground sequence . the @xmath31 vs. @xmath29 color color diagram is presented in figure [ cc ] . as expected from the morphology and range of colors in figure [ w42c ] , the strong effects of differential reddening can be seen in the color color diagram . typical reddening lines are shown for m giants @xcite and early o stars @xcite . the latter color was transformed as described in 3.1.3 . the cluster stars defined below in 3.1.1 and shown as _ open circles _ in figure [ cc ] may have a slight unexplained systematic offset relative to the reddening line for normal o stars . this possible offset will not affect the conclusions in this paper regarding the cluster stars . the relationship for the intrinsic colors of classical t tauri stars ( pre main sequence stars ) @xcite is also shown for reference . the adopted reddening law is from @xcite . by separating the stars in figure [ cmd ] based on radial position , we can better define the central cluster relative to the surrounding field . in figure [ surf ] , we plot the radial surface density of stars centered on the position of the bright central star , w42 # 1 ( 3.2 ) . we also plot the radial surface density for stars with @xmath2 @xmath32 14 mag , for which the number counts are more nearly complete ( see below ) . the surface density becomes approximately uniform at a radius of" +"growing risk of terrorism demands a constant development of new techniques for hazardous substances detection . one of the best methods for homeland security are based on the neutron activation analysis ( naa ) providing non - intrusive detection of explosives or drugs . the principle of the method is to use a fast neutron beam produced using sealed d+t generator to excite nuclei of investigated substance and detect characteristic gamma quanta produced in de - excitation of the nuclei . this allows one to identify the stoichiometry of the substance and determine if it is dangereus @xcite . so far there are several devices based on neutron activation analysis designed for ground homeland security which were introduced in the usa by science applications international corporation @xcite and calsec @xcite , and in europe in sodern @xcite , euritrack @xcite and swan @xcite projects . these devices are used in the homeland security or contraband detection on the land . however , in an aquatic environment one encounters serious problems due to strong attenuation of neutrons in water . moreover , as in the case of ground detectors , an isotropic generation of neutrons induces a large environmental background . this noise can be significantly reduced by the requirement of the coincident detection of the alpha particles which are produced together with neutrons @xcite . the attenuation of neutrons can be compensated by reducing the distance between generator and examined item @xcite . there are also solutions based on low energy neutrons which are moderated in water before reaching the tested object . the detector is then counting the gamma quanta from thermal neutron capture and secondary neutrons originating from the irradiated object . the identification is done by searching for anomalies in the observed spectra of gamma quanta and neutrons @xcite . however , these methods do not allow to detect explosives buried deeper in the bottom of the sea and strong attenuation of neutrons and gamma quanta significantly increases the exposure time . + an alternative solution of a detector which uses naa technique and special guides for neutrons and emitted gamma rays was proposed within the sabat project @xcite . the device allows for detection of dangerous substances hidden deep in the bottom of the sea with significantly reduced background and provides determination of the density distribution of the dangerous substance in the tested object @xcite . in this article we present status of the design of the sabat detector based on monte carlo simulations , focusing on the impact of the usage of neutron and gamma quanta guides . in order to optimize the dimensions and relative positions of detectors and guides we have developed dedicated open source software package written in the c++ programming language @xcite . this simulation tool is using novel methods of geometry definition and particle tracking and the open mpi library supporting parallel computing @xcite . to define the geometry of simulated objects we use a polygon mesh , which is in the simplest form a collection of vertices and edges that are used to define a surface of the polyhedral 3d object . in our case the faces consist of triangles . trajectory of a particle traveling in a scene consisting of such defined objects is simulated with so - called ray tracing technique . to determine if a particle entered given object the mller - trumbore method was implemented which searches for intersection of the particle trajectory with the object surface ( triangle mesh ) . the total cross - sections and angular distributions of neutrons and @xmath0 rays interaction with selected nuclei were parametrized as a function of energy using data from the evaluated nuclear data file ( endf ) database @xcite , while gamma quanta energies were taken from the evaluated nuclear structure data files ( ensdf ) @xcite . quanta interaction points in x - y views for two positions of the detector with ( a and b ) and without gamma quanta guide ( c and d ) . the point - like source of neutrons is located at the origin of the reference frame . the neutron guide is presented as the blue dashed rectangle aligned along the y axis . the container with mustard gas is a red cuboid aligned horizontally which lies at the bottom of the sea marked in cyan . the ge detector ( in yellow ) is connected to the gamma rays guide ( dashed magenta polyhedron ) . for better visibility of the influence of guides plots are made only for -10 @xmath1 z @xmath1 10 cm . , title=""fig:"",width=207 ] quanta interaction points in x - y views for two positions of the detector with ( a and b ) and without gamma quanta guide ( c and d ) . the point - like source of neutrons is located at the origin of the reference frame . the neutron guide is presented as the blue dashed rectangle aligned along the y axis . the container with mustard gas is a red cuboid aligned horizontally which lies at the bottom of the sea marked in cyan . the ge detector ( in yellow ) is connected to the gamma rays guide ( dashed magenta polyhedron ) . for better visibility of the influence of guides plots are made only for -10 @xmath1 z @xmath1 10 cm . , title=""fig:"",width=207 ] quanta interaction points in x - y views for two positions of the detector with ( a and b ) and without gamma quanta guide ( c and d ) . the point - like source of neutrons is located at the origin of the reference frame . the neutron guide is presented as the blue dashed rectangle aligned along the y axis . the container with mustard gas is a red cuboid aligned horizontally which lies at the bottom of the sea marked in cyan . the ge detector ( in yellow ) is connected to the gamma rays guide ( dashed magenta polyhedron ) . for better visibility of the influence of guides plots are made only for -10 @xmath1 z @xmath1 10 cm . , title=""fig:"",width=207 ] quanta interaction points in x - y views for two positions of the detector with ( a and b ) and without gamma quanta guide ( c and d ) . the point - like source of neutrons is located at the origin of the reference frame . the neutron guide is presented as the blue dashed rectangle aligned along the y axis . the container with mustard gas is a red cuboid aligned horizontally which lies at the bottom of the sea marked in cyan . the ge detector ( in yellow ) is connected to the gamma rays guide ( dashed magenta polyhedron ) . for better visibility of the influence of guides plots are made only for -10 @xmath1 z @xmath1 10 cm . , title=""fig:"",width=207 ] as a starting point for design of the device for underwater threats detection we have defined a simple setup with point - like source generating uniformly in space 14.1 mev neutrons in the neutron-@xmath2 center of mass frame . as a first step , to study the influence on the measurement of gamma quanta guide and the relative position of generator and detector we have simulated 1.4@xmath310@xmath4 events with two different detector locations with and without gamma rays guide . the scheme of the simulated setups with superimposed @xmath0 quanta interaction points are shown in fig . [ fig1 ] . the interrogated object with dimensions 194 x 50 x 50 @xmath5 lies at the bottom of a sea and contains mustard gas ( c@xmath6h@xmath7cl@xmath8s ) . the neutron guide is a cuboid with dimensions 40 x 100 x 40 @xmath5 , while gamma rays guides is represented by polyhedron with 15 x 20 @xmath9 and 30 x 30 @xmath9 bases . they are both filled with air under normal conditions . as a detector we have simulated 15 x 15 x 20 @xmath5 ge crystal measuring the energy of gamma rays with 6% resolution ( fwhm ) . the detector surface with dimensions of 15 x 20 @xmath9 is adjusted to the shape of the gamma quanta guide . b ( solid histogram ) and in fig . [ fig1]d ( dashed histogram ) . the small signal from the mustard gas can be seen at about 9.6 mev and 4.4 mev ( carbon ) , 2.2 mev ( sulfur ) and around 6.5 mev ( chlorine ) . the huge background is mainly due to the gamma quanta from neutron - oxygen reactions . the energy of these quanta is smeared due to the scattering in the water . the number of entries is normalized to the generated statistics . , width=207 ] the exemplary energy spectra measured by the germanium detector for one detector position are shown in fig . [ fig2 ] . as one can see in tab . [ tab1 ] , among all of the gamma quanta reaching the detector about 80@xmath10 originate from oxygen in the water independently of the detector position or presence of the guide . .fractional composition of sources of gamma quanta registered by the detector ( in @xmath10 ) for all the simulated cases shown in fig . the last column shows the overall fraction of gamma quanta reaching the detector and originating from the mustard gas . [ cols=""^ "" , ] + a & 0 & 0.77 & 0 & 85.17 & 0.24 & 0 & 0 & 0.26 & 13.56 & 1.02 + b & 0.53 & 1.68 & 0.10 & 76.50 & 0.38 & 0.08 & 0.63 & 1.78 & 18.32 & 3.30 + c & 0.59 & 0 & 0 & 81.71 & 0.88 & 0 & 0 & 0.89 & 15.93 & 0 + d & 7.88 & 0.59 & 0.05 & 77.04 & 0.69 & 0.24 & 0.10 & 6.95 & 6.46 & 2.25 + the second relevant source of background constitute neutrons which scatter in water and reach the detector . the amount of registered gamma quanta which were created in the container with mustard gas is quite small but the advantage of using guide is visible . the mustard gas is composed of carbon , hydrogen , chlorine and sulfur . however , fig . [ fig2 ] indicates that the 4.4 mev carbon line is overwhelmed by background while we see clearly gamma quanta from carbon with energy of about 9.6 mev . in case of chlorine and sulfur ( lines of 6.5 mev and 2.2 mev , respectively ) the oxygen background has to be significantly reduced to allow one to identify these elements more clearly . this can be done requiring of the coincident detection of the @xmath2 particle generated together with neutron or by covering all the detector faces not connected to the gamma quanta guide with thick layer of absorber . identification of sulfur and chlorine is difficult due to neutron capture on hydrogen giving lines of very close energy and chlorine content in the sea water @xcite . however , using the gamma quanta guide one can detect @xmath0 rays from these two elements not affected by scattering in the water which gives a great advantage in the identification . in the framework of the sabat project we have been developing simulation package based on novel methods of geometry definition and particle tracking . although we are still in a very early stage of development the first results indicate that indeed , both the neutron guide and @xmath0 ray guide will increase the performance of underwater threats detection with fast neutrons @xcite . with 1.4@xmath310@xmath4 generated neutrons we see enhancements of signal events in the detector together with huge background originating mostly from oxygen , as it was expected . this shows clearly that all the faces of the detector" +"i was asked to comment on the impact of neutrino oscillation measurements on theory . it is completely clear that recent neutrino oscillation data had big impact on theory , and it will continue to do so . i will remind you about the ongoing impact . then i will list measurements that will have critical impact on theory in the future . let me organize my discussion as `` past , '' `` present , '' and `` future . '' it is useful to recall why theorists had always been interested in the small neutrino masses and their consequences on neutrino oscillation . it is because we are always interested in probing physics at as high energies as possible . one way to probe it is of course to go to the high - energy collider experiments and study physics at the energy scale directly . another way is to look for rare and/or tiny effects coming from the high - energy physics . the neutrino mass belongs to the second category . to study rare and/or tiny effects from physics at high energies , we can always parameterize them in terms of the power series expansion , @xmath0 the zeroth order term @xmath1 is renormalizable and describes the standard model . on the other hand , the higher order terms are suppressed by the energy scale of new physics @xmath2 . possible operators can be classified systematically , which i believe was done first by weinberg ( but i could nt find the appropriate reference ) . with two powers of suppression , there are many terms one can study : @xmath3 the examples here contribute to proton decay , @xmath4 , anomalous triple gauge boson vertex , @xmath5@xmath6 mixing , and the @xmath7-parameter , respectively . it is interesting that there is only one operator suppressed by a single power : @xmath8 after substituting the expectation value of the higgs , the lagrangian becomes @xmath9 nothing but the neutrino mass . therefore the neutrino mass plays a very unique role . it is the lowest - order effect of physics at short distances . this is a very tiny effect . any kinematical effects of the neutrino mass are suppressed by @xmath10 , and for @xmath11 ev which we now know is already too large and @xmath12 gev for typical accelerator - based neutrino experiments , it is as small as @xmath13 . at the first sight , there is no hope to probe such a small number . however , any physicist knows that interferometry is a sensitive method to probe extremely tiny effects . for interferometry to work , we need a coherent source . fortunately there are many coherent sources of neutrinos in nature , the sun , cosmic rays , reactors ( not quite nature ) , etc . we also need interference for an interferometer to work . because we ca nt build half - mirrors for neutrinos , this could have been a show stopper . fortunately , there are large mixing angles that make the interference possible . we also need long baselines to enhance the tiny effects . again fortunately there are many long baselines available , such as the size of the sun , the size of the earth , etc . nature was very kind to provide all necessary conditions for interferometry to us ! neutrino interferometry , a.k.a . neutrino oscillation , is therefore a unique tool to study physics at very high energy scales . gev , compared to the suggested scale of new physics from the neutrino oscillation data.[fig : mssm],scaledwidth=70.0% ] indeed , the recently established neutrino oscillation results @xcite @xmath14 interpreted naively in a `` hierarchical '' mass scheme @xmath15 suggests @xmath16 it is tantalizingly close to the energy scale of apparent gauge coupling unification in the minimal supersymmetric standard model , @xmath17 gev . ( see , fig . [ fig : mssm ] . ) this way , the neutrino oscillation appears to provide us a unique window to physics at very high energies as their `` leading order '' effects . indeed , theoretical estimates based on the seesaw mechanism in the grand unified theories @xcite are practically confirmed ! the last year was an amazing year in neutrino physics . before march , the situation of the solar neutrino data looked like the first plot in fig . [ fig : allsolar1 ] , and there had been overlaps between superk , homestake , and gallium experiments in the lma and low regions , some down in quasi - vaccum . after sno neutral current result in april , the parameter space focused only on the lma region shown in red in the second plot in fig . [ fig : allsolar1 ] . in december , kamland has excluded most of the parameter space as shown in the first plot in fig . [ fig : allsolar2 ] , while its preferred region ( inside the blue contours in the second plot in fig . [ fig : allsolar2 ] ) has consistent overlaps with the that preferred by the solar neutrino data . it was a tremendous convergence from the parameter space over many decades down to factors of a few . it is useful to recall what a typical theorist used to say back around 1990 . * the solution to the solar neutrino problem must be the small mixing angle msw solution because it is so beautiful . * the natural scale for @xmath18 oscillation is @xmath19 because it is the cosmologically interesting range . * the angle @xmath20 must be of the same order of magnitude as @xmath21 because of the grand unification . * the atmospheric neutrino anomaly must go away because it would require a large mixing angle to explain . needless to say , theorists have a very good track record in neutrino physics . indeed , the recent results from neutrino oscillation physics had surprised almost everybody . the prejudice has been that the mixing angles must be small because quark mixing angles are small , and the masses must be hierarchical because both quarks and charged lepton masses are hierarchical . given that the lma is now chosen , all mixing angles are large except for @xmath22 that must be small - ish ( but the current limit is not very strong , @xmath23 ) . the natural question then is if this newly discovered surprising pattern of neutrino masses and mixings require a new symmetry or any special structure to explain . in fact , the big question has always been _ what distinguishes flavor ? _ three generations share exactly the same quantum numbers . yet , they have such different masses . the hierarchy with small mixings means that there is a need for some kind of ordered structure . the `` common sense '' in quantum mechanics is that states with the same quantum numbers should have similar energy levels ( _ i.e. _ masses ) and mix significantly under small perturbations . the observed patterns go against this `` common sense . '' the hierarchical masses and small mixings among quarks and charged leptons had been a puzzle . therefore , there has been a strong suspicion that there is a new set of quantum numbers , _ flavor quantum numbers _ , that distinguish three generations of quarks and leptons . as noether told us , a new quantum number requires a new symmetry , _ flavor symmetry_. this new symmetry must allow the top quark yukawa coupling because it is of the natural size , @xmath24 . on the other hand , all the other yukawa couplings are practically zero ( as opposed to @xmath25 ) , and the flavor symmetry must forbid them . after the symmetry is broken by a small parameter , all the other yukawa couplings become allowed , but suppressed @xcite . the hope is to identify the underlying symmetry based on the data , similarly to what was done by heisenberg ( isospin ) or gell - mann okubo ( flavor @xmath26 ) . indeed , the neutrino data had been already effective in narrowing down the possibilities of flavor symmetries . in table [ tab : afm ] , many proposed flavor symmetries are shown together with their predictions on the mass - squared ratio @xmath27 , @xmath22 , @xmath28 , and @xmath20 , taken from @xcite ( october 2002 ) . in the model sa refers to a degree of accidental cancellation in the 23 sector , that is used to enhance @xmath28 . ] since then , models h@xmath29 , h@xmath30 , and ih ( low ) had been excluded by kamland . .prediction of different flavor symmetries on the neutrino mass - squared ratio and various mixing angles , taken from @xcite.[tab : afm ] [ cols=""^,^,^,^,^,^,^"",options=""header "" , ] among them , i liked the model a the best , because it is _ mine _ it is called _ anarchy _ , based on the idea that neutrinos are actually normal , while quarks and charged leptons are nt . as i mentioned already , the hierarchical masses and small mixing angles are against the `` common sense , '' while the neutrinos do not seem to have a large hierarchy and mix a lot . maybe the _ lack of flavor symmetry _ can explain the data . indeed , if there is no fundamental distinction among three neutrinos , or in other words if their flavor quantum numbers are all equal , the group theory of three - by - three unitary matrices uniquely determine the probability distribution of mixing angles @xcite . then all three angles , @xmath28 , @xmath20 , and @xmath31 are three random draws from the distribution @xmath32 for @xmath33 . because it is peaked towards the maximal angle @xmath34 , it is very plausible that two draws come out large , while one of them comes down the tail ( but not expected _ way _ down the tail ) . indeed , the kolgomorv smirnov test suggests that the probability that three random draws come out worse than the actual data is 64% , and hence the observed pattern is completely natural if there is _ no _ fundamental distinction among three generations @xcite . on the other hand , @xmath31 is expected to be not too far below the current limit . the one - dimensional ks probability is @xmath35 , and hence we expect @xmath36 at `` 95% cl . '' the size of the cp - violation @xmath37 is distributed as @xmath38 , and hence is expected to be large . based on anarchy , _ i.e. _ , no fundamental distinction among three neutrinos . taken from @xcite.,scaledwidth=50.0% ] having discussed the impact of neutrino data on theory so far , it is clear what will be the critical measurements in the future . * @xmath39 ? if it comes out that precisely maximal , it surely will require a new symmetry . * @xmath40 ? if so , electron - neutrino must have a different flavor quantum number from muon and tau neutrinos . * normal or inverted hierarchy ? most flavor symmetries predict the normal hierarchy , but theorists had been wrong ! * cp violation ? even though the cp violation in neutrino oscillation may not prove the relevant cp violation for leptogenesis , it will at least make it very plausible . after going through the critical measurements , we hope to determine the underlying flavor symmetries behind neutrinos ( and flavor in general ) . then comes an even bigger question : can we understand the dynamics behind the flavor symmetry ? in the case of the strong interaction , isospin and flavor @xmath26 are the flavor symmetries , while the" +"information systems on the world wide web have been increasing in size and complexity to the point that they presently exhibit features typically attributed to _ bona fide _ complex systems . they display rich high - level behaviors that are causally connected in non - trivial ways to the dynamics of their interacting elementary parts . because of this , concepts and formal tools from the science of complex systems can play an important role in understanding the structure and dynamics of such systems . this study focuses on the recently established paradigm of collaborative tagging @xcite . in web applications like _ _ del.icio.us_ _ , _ _ flickr _ _ , _ _ bibsonomy _ _ users organize diverse _ resources _ ranging from web pages to academic papers and photographs with semantically meaningful information in the form of text labels , or `` tags '' . tags are freely chosen and users associate resources with them in a totally uncoordinated fashion . nevertheless , the tagging activity of each user is globally visible to the user community and the tagging process develops genuine social aspects and complex interactions @xcite , eventually leading to a bottom - up categorization of resources shared throughout the user community . the open - ended set of tags used within the system commonly referred to as `` folksonomy '' can be used as a sort of semantic map to navigate the contents of the system itself . in figure [ bibsonomy_detail ] a single annotation example ( said `` post '' ) is shown , as appears in the interface of bibsonomy.org system . ] our work is based on experimental data from one of the largest and most popular collaborative tagging systems , _ del.icio.us_ , currently used by over a million users to manage and share their collections of web bookmarks . the main point of our work is neither to present a new spectral community detection algorithm , nor to report a large data set analysis . rather , we want to show that , choosing the right projection and the right weighting procedure , we can produce a weighted undirected network of resources from the full tri - partite folksonomy network , which embed a meaningful social classification of resources . this is especially surprising , considering that users annotate resources in a very anarchic , uncoordinated and noisy way . in section [ sec : data ] we describe the experimental data we collected . in section [ sec : distance ] we introduce a notion of resource distance based on the collective activity of users . based on that , we set up an experiment using actual data from _ del.icio.us _ and we build a weighted network of resources . in section [ sec : communities ] we show that spectral methods from complex networks theory can be used to detect clusters of resources in the above network and we characterize those clusters in terms of user tags , exposing semantics . finally , section [ sec : conclusions ] gives an overview of our results and points to directions for future work . our analysis focuses on _ del.icio.us _ for several reasons : i ) it was the first system to deploy the ideas of collaborative tagging on a large scale , so it has acquired a paradigmatic character and it is the natural starting point for any quantitative study . ii ) it has a large user community and contains a huge amount of raw data on the structure and dynamics of a folksonomy . iii ) it is a _ broad folksonomy _ @xcite , i.e. single tag associations by different users retain their identity and can be individually retrieved . this allows us to measure the number of times that a given tag @xmath0 was associated with a specific resource as the number @xmath1 of users who established that resource - tag association ( see also fig . [ two_resources ] ) . that is , a broad folksonomy has a natural notion of weight for tag associations , which is based on social agreement . on studying _ _ we adopt a resource - centric view of the system , that is we investigate the emergent correspondence between a given resource and the tags that all users associate with it . we factor out the detailed identity of the users and only deal with the set of tags associated by the user community with a given resource , as well as with the frequencies of occurrence of those tags in the context of the resource . to collect data , we used a web crawler that connects to _ del.icio.us _ and navigates the system s interface as an ordinary user would do , extracting tagging metadata and storing it for further post - processing . our client connects to _ del.icio.us _ and downloads the web pages associated with a given set of resources , using an html parser to extract the tagging information from the page . the system allows to get the complete set of annotations associated with each resource . the data used for the present analysis were retrieved in october 2006 . in a collaborative tagging system , a set of resources defines a `` semantic space '' that is explored and mapped by a community of users , as they bookmark and tag those resources @xcite . we want to investigate whether the tagging activity is actually structuring the space of resources in a semantically meaningful way , i.e. whether partitions or subsets of resources emerge , associated with tagging patterns that point to well - defined meanings , areas of interest or topics . these groups of resources could also identify , in principle , communities of users sharing the same view of resources , or the same emergent vocabulary . in order to gain insight into the above problem , we set up an experiment using _ del.icio.us _ as a data source . we want to stress here that , since the aim of the work is to investigate whether an emergent community structure exists in folksonomy data , we are not concerned with the completeness of the dataset used . rather , we decided to perform the experiment on the following subset : we selected two popular tags that appear to be semantically unrelated ( _ design _ and _ politics _ ) , and for each of them we extracted from _ del.icio.us _ a set of @xmath2 randomly chosen resources ( we take the first @xmath2 returned by the system , representing the most recently introduced by users ) . for each resource , we collected the complete set of annotations , i.e. all the tag assignments relative to that resource . the corresponing dataset used for this experiment , thus consists of @xmath3 resources : half of them have been associated with the tag _ design _ , while the other half has been tagged with _ politics_. the idea is to construct a dataset containing at least two semantically well - separated subsets . for each resource in the dataset , the entire tagging history was retrieved from _ del.icio.us_ , so that all the tag associations involving the chosen @xmath3 resources are known . in other words , we know how the entire user community of `` categorized '' the selected resources in terms of freely - chosen tags , with no biases due to data collection . to uncover structures linked to specific tagging patterns we introduce a notion of similarity between resources based on how those resources were tagged by the user community . for each resource , we define a _ tag - cloud _ as the weighted set of tags that have been used to bookmark that resource , where the weight of tag @xmath4 is its frequency of occurrence @xmath5 in the context of that resource ( fig . [ two_resources ] ) . we want to formalize the intuitive idea that two resources are similar if the corresponding tag - clouds have a high degree of overlap . given two generic resources @xmath6 and @xmath7 , and the corresponding sets of tags @xmath8 and @xmath9 , a natural measure of tag - cloud overlap would be the standard set overlap given by the cardinality of the intersection set @xmath10 divided by the cardinality of the union set @xmath11 . this simple measure , however , has a major fault : since no notion of tag weight ( frequency ) is used , it is not sensitive to the social aspects of tagging encoded in tag frequencies ( and as such , it is also vulnerable to tagging noise , i.e. errant , strange , incorrect or even malicious tagging , or spamming @xcite ) . to overcome this limitation we adopt a tf - idf weighting procedure @xcite . the tf - idf weight ( term frequency - inverse document frequency ) is commonly used in information retrieval and text mining and represents a statistical measure used to evaluate how specific a term is in identifying a document belonging to a collection of documents . the importance of a term increases proportionally to the number of times the term appears in the document , and inversely proportional to the global frequency of the same term in the document collection . ( eq . [ weight ] ) measures the weighted overlap between the tag - clouds associated with the resources @xmath6 and @xmath7 . tags marked in red belong to @xmath10 , the set of tags shared by the two resources . [ two_resources ] ] we denote with @xmath12 and @xmath13 the frequencies of occurrence of tag @xmath4 in @xmath8 and @xmath9 , respectively , and with @xmath5 the global frequency of tag @xmath4 , that is the total number of times that tag @xmath4 was used in association with all the resources under study . in the spirit of the tf - idf techniques , we normalize the frequencies of tags by their global frequencies . when a tag is shared by resources @xmath6 and @xmath7 , it has two different frequencies , @xmath12 in the context of @xmath6 and @xmath13 in the context @xmath7 . when performing the intersection between tag - clouds , we use the lowest of those frequencies to define the weight of tag @xmath4 in the intersection set @xmath10 , while we use the highest of those frequencies when weighting the contribution of same tag in the union set @xmath11 . more precisely , we define the similarity between @xmath6 and @xmath7 as : @xmath14 the above expression is an extension of the simple measure of set overlap , where the numerator is a weighted form of set intersection and the denominator is a weighted form of set union . by definition , @xmath15 . of course the above definition is just one of the possible similarity measures that can be employed , and the validation of the measure we introduce here is left to the results obtained by using it , as shown in section [ sec : communities ] . the similarity matrix introduced above can be regarded as the adjacency matrix of a weighted network of resources @xcite , where @xmath16 is the strength of the edge connecting nodes @xmath6 and @xmath7 . [ hysto_distance ] shows the distribution of similarities ( edge strengths in the weighted network ) among all the pairs of resources , for three different sets of resources : the subset of resources sharing the tag _ design _ , the subset of resources sharing the tag _ politics _ and the union of those sets . notice that the global frequency @xmath5 of a given tag @xmath4 depends on the set of resources chosen for the analysis . from the plot it" +"there has recently been much interest in a fascinating topic in the research community , namely _ spin hall effect _ ( she ) . she is such a phenomenon that a transverse spin current is generated when a longitudinal charge current circulates through a sample , and if the sample has a thin strip geometry , the transverse spin current will cause non - equilibrium spin accumulation at both edges of the samplehirsch1999,murakamiscience2003,sinovaprl2004 . such a phenomenon would be much useful in the context of semiconductor spin - based electronics ( _ spintronics _ ) because it might provide an effective way for generating spin currents and/or non - equilibrium spin density in a nonmagnetic semiconductors without use of ferromagnetic metals or ferromagnetic semiconductors , a principal challenge in semiconductor spintronicsdassarma2004,semibook2002 . from the theoretical points of view , such a phenomenon can arise from either _ intrinsic _ spin - orbit ( so ) coupling ( i.e. , spin - orbit splitting of the band structure ) murakamiscience2003,sinovaprl2004 or _ extrinsic _ so coupling ( i.e. , spin - orbit dependent impurity scatterings ) @xcite in a semiconducting material , and correspondingly , the phenomena due to intrinsic so coupling was termed _ intrinsic spin hall effect _ and the phenomena due to spin - orbit dependent impurity scatterings termed _ extrinsic spin hall effect_. from the standpoint of spintronic applications , intrinsic she are more attractive since it is an intrinsic property of a semiconducting material and does not rely on spin - orbit dependent impurity scatterings@xcite . recently two experiments were reported on the observation of she . one is on @xmath0-doped bulk gaas by kato et al.@xcite and the other is on two - dimensional @xmath1-doped gaas by wunderlich et al.@xcite . the phenomenon observed in two - dimensional @xmath1-doped gaas by wunderlich et al . was believed to be an intrinsic spin hall effect since the edge spin accumulation measured in a thin strip of such a system is insensitive to impurity scatterings in the weak impurity scattering regimewunderlichprl2005 , an important feature of intrinsic spin hall effectmurakamiscience2003,sinovaprl2004 . in contrast , the phenomenon observed in @xmath0-doped bulk gaas by kato et al . was believed to have an extrinsic origin ( i.e. , due to spin - orbit dependent impurity scatterings ) since the edge spin accumulation measured in a thin strip of such a system is several order of magnitude smaller compared with the theoretical predictions of refs.[2 - 3 ] . although substantial progresses have been achieved on the detection of spin hall effect , it should be noted that from the theoretical points of view there are still intensive debates on whether intrinsic spin hall effect does can survive in a spin - orbit coupled system . for example , several recent theoretical works have argued that , except for the ballistic transport limit , intrinsic spin hall effect can not survive in a diffusive two - dimensional electron gas with rashba spin - orbit coupling even in the weak impurity scattering limitinoueprb2004,mishchenkoprl2004,rashbaprb2003 , raim05 , dim05 , szhang05 , kha06 . as to the physical understanding of the recent experimental results@xcite , some significant controversies also exist which needs further clarifications . for details please refer to refs.[16 - 25 ] . in this paper , we investigate theoretically another kind of electric - field driven edge spin - accumulation which might occur in a thin strip of a two - dimensional electronic ( electron or hole ) system . from the theoretical points of view , this phenomenon is essentially a _ _ kinetic magnetoelectric effect__@xcite due to boundary - confinement induced spin - orbit coupling ( which will be called _ edge so coupling _ below ) . but very interestingly , it would manifest in a very similar manner as was conceived in an spin hall effect . for example , the electric - field driven edge spin accumulation in a thin 2deg strip due to this phenomenon will be polarized perpendicular to the 2deg plane but along opposite directions at both edges of the strip ; and in the weak impurity scattering regime ( below a certain disorder strength ) the edge spin accumulation will not decrease as the disorder strength increases , thus it can survive even in the diffusive transport regime . these features are very similar to the recently discovered spin hall effect , but the mechanisms involved in this phenomenon are very different from that of the usual spin hall effect from the theoretical points of view . the results obtained in the present paper might provide some new implications to the proper physical understanding of the recent experimental results@xcite . the paper is organized as following : in section ii an edge so coupling model describing the boundary - confinement induced so coupling in a thin 2deg strip will be introduced and some details of the theoretical formalism used in the paper will be briefly explained , and in section iii some numerical results will be presented and discussed . the system considered in the present paper consists of a thin 2deg strip connected to two ideal leads , as was shown in fig.1(a ) . according to the theory of the relativistic quantum mechanics , if the movement of an electron is confined by a spatially non - uniform potential , the spin and orbital degree of freedom of the electron will be coupled together@xcite . the longitudinal direction of the strip will be defined as the @xmath2 direction and the normal of the 2deg plane defined as the @xmath3 direction . for the sake of simplification , we assume that the confining potential is spatially uniform along the longitudinal direction of the strip , i.e. , the spatial variation of the confining potential occurs only in the transverse direction of the strip ( defined as the @xmath4 direction ) . under this assumption , the so coupling due to the transverse spatial variation of the confining potential will take the following form@xcite , @xmath5where @xmath6 are the usual pauli matrices , @xmath7 is the wave vector of electrons , @xmath8 denotes the usual gradient operator and @xmath9 is the transverse confining potential , which depends only on the @xmath4 coordinates . from the effective hamiltonian ( 1 ) one can see that , for an electron moving along the @xmath10 ( or @xmath11 ) direction , the so coupling will tend to force the electron spin to align along the @xmath12 ( or @xmath13 ) direction , depending on the sign of @xmath14 . in the absence of external electric field , the numbers of electrons moving along the @xmath10 and @xmath11 directions are equal and no net spin density can be resulted . however , if an external electric field is applied in the longitudinal direction of the strip , the numbers of electrons moving to @xmath11 direction will be larger than the number of electrons moving to the @xmath10 direction , and hence a net spin density polarized along the @xmath12 or @xmath15 @xmath13 @xmath16 direction might be resulted from the so coupling . such an effect was dubbed the _ kinetic magnetoelectric effect _ in the literatureedelstein . for a 2deg strip , if the strip width is much larger than the lattice constant , one can further assume that the confining potential @xmath9 varies substantially only in a narrow boundary region as was shown in fig.1(b ) . ( we assume that the two boundaries of the srip are located at @xmath17 ) . then the so coupling exists only near both edges of the strip , and due to the symmetry of the confining potential , the so coupling coefficient ( proportional to @xmath18 ) has opposite signs at both edges of the strip , as was shown in fig.1(c ) . thus , the edge so coupling model described by the effective hamiltonian ( 1 ) implies that the electric - field driven spin accumulation will be polarized along opposite directions ( normal to the 2deg plane ) at both edges of the strip , similar to a spin hall effect . this will be confirmed by detailed numerical calculations below . in order to make a comparison with the widely studied intrinsic spin hall effect in a rashba two - dimensional electron gas , we can also include a rashba so coupling in our edge so coupling model . then the total hamiltonian of the 2deg strip will be @xmath19where the second term is the rashba so coupling ( which arises from the inversion asymmetry of the trapping well along the normal of the 2deg plane ) and @xmath20 the rashba so coupling constant . ( @xmath21 is a unit vector along the normal of the 2deg plane ) . a direct use of the hamiltonian ( 2 ) is not convenient if one wants to take into account the effects of impurity scatterings properly , which are very important in the diffusive transport regime . so in our calculations we will transform the hamiltonian ( 2 ) into a discrete form . the discrete version of the effective hamiltonian for the total system ( including both the leads and the 2deg strip ) will read : @xmath22\nonumber\\ & & -\sum_{r_{i}}t_{r_{i}}^{b}[i\psi _ { r_{i}}^{\dag } \sigma ^{z}\psi _ { r_{i}+x}+h.c.]\label{eq : one}\end{aligned}\ ] ] here @xmath23 is the hopping matrix element between two nearest - neighbour sites and @xmath24 the lattice constant in the 2deg strip . @xmath25 is the annihilation operators of electrons at the lattice site @xmath26 in the strip . @xmath27 is the annihilation operator of electrons with spin @xmath28 at the lattice site @xmath29 in the lead @xmath1 ( @xmath30 ) . @xmath31 stands for a nearest - neighbor pair of lattice sites across the interfaces between the 2deg strip and the leads . @xmath32 is the on - site energy in the 2deg strip . in a clean system without disorder , one usually sets @xmath32 to be zero . @xmath33 is the rashba so coupling coefficient in the 2deg strip , which is assumed to be site - independent . the last term in eq . ( [ eq : one ] ) stands for the boundary - confinement induced so coupling and @xmath34 is the coupling coefficient , which is site - dependent . the site - dependence of @xmath35 will be determined by the actual form of the transverse confining potential in the 2deg strip . in our calculations we assume a parabolic confining potential near both edges of the strip , as was shown in fig.1(b ) . in such cases , the site - dependence of the edge so coupling coefficient can be expressed as @xmath36where @xmath37 is the width of the strip ( in units of lattice constant ) , @xmath38 is the width of the narrow boundary regions in which the edge so coupling exists , and @xmath39 is the minimum value of the site - dependent edge so coupling coefficient . the sign @xmath40 is different for the two edges , as shown in fig.1(c ) . our calculations will be based on the landauer - buttiker formula . to this end , we first consider the transmission and reflection of an electron incident from a lead . the real space wave function of an incident electron with spin @xmath28 will be denoted as @xmath41 , where @xmath42 denotes the @xmath43th transverse mode with spin index @xmath28 in the lead @xmath1 and @xmath44 the longitudinal wave vector . we adopt the local coordinate scheme for all leads . in the local coordinate scheme , the longitudinal coordinate @xmath45 in the lead @xmath46 will take the integer numbers @xmath47 ... ,@xmath48 away from the 2deg interface and the transverse coordinate @xmath49 take the value of @xmath50 . the longitudinal wave vector @xmath44 satisfys the relation @xmath51 , where @xmath52" +"deep neural networks ( dnns ) have been receiving ubiquitous success in wide applications , ranging from computer vision @xcite , to speech recognition @xcite , natural language processing @xcite , and domain adaptation @xcite . as the sizes of data mount up , people usually have to increase the number of parameters in dnns so as to absorb the vast volume of supervision . high performance computing techniques are investigated to speed up dnn training , concerning optimization algorithms , parallel synchronisations on clusters w / o gpus , and stochastic binarization / ternarization , etc @xcite . on the other hand the memory and energy consumption is usually , if not always , constrained in industrial applications @xcite . for instance , for commercial search engines ( e.g. , google and baidu ) and recommendation systems ( e.g. , netflix and youtube ) , the ratio between the increased model size and the improved performance should be considered given limited online resources . compressing the model size becomes more important for applications on mobile and embedded devices @xcite . having dnns running on mobile apps owns many great features such as better privacy , less network bandwidth and real time processing . however , the energy consumption of battery - constrained mobile devices is usually dominated by memory access , which would be greatly saved if a dnn model can fit in on - chip storage rather than dram storage ( c.f . @xcite for details ) . a recent trend of studies are thus motivated to focus on compressing the size of dnns while mostly keeping their predictive performance @xcite . with different intuitions , there are mainly two types of dnn compression methods , which could be used in conjunction for better parameter savings . the first type tries to revise the training target into more informative supervision using _ dark knowledge_. in specific , hinton _ _ @xcite suggested to train a large network ahead , and distill a much smaller model on a combination of the original labels and the soft - output by the large net . the second type observes the redundancy existence in network weights @xcite , and exploits techniques to constrain or reduce the number of free - parameters in dnns during learning . this paper focuses on the latter type . to constrain the network redundancy , efforts @xcite formulated an original weight matrix into either low - rank or fast - food decompositions . moreover @xcite proposed a simple - yet - effective pruning - retraining iteration during training , followed by quantization and fine - tuning . @xcite proposed hashednets to efficiently implement parameter sharing prior to learning , and showed notable compression with much less loss of accuracy than low - rank decomposition . more precisely , prior to training , a hash function is used to randomly group ( virtual ) weights into a small number of buckets , so that all weights mapped into one hash bucket directly share a same value . hashednets was further deliberated in frequency domain for compressing convolutional neural networks in @xcite . in applications , we observe hashednets compresses model sizes greatly at marginal loss of accuracy for some situations , whereas also significantly loses accuracy for others . after revisiting its mechanism , we conjecture this instability comes from at least three factors . first , hashing and training are disjoint in a two - phase manner , i.e. , once inappropriate collisions exist , there may be no much optimization room left for training . second , _ one single hash function _ is used to fetch a single value in the compression space , whose collision risk is larger than multiple hashes @xcite . third , parameter sharing within a buckets implicitly uses _ identity mapping _ from the hashed value to the virtual entry . this paper proposes an approach to relieve this instability , still in a two - phase style for preserving efficiency . specifically , we use _ multiple hash functions _ @xcite to map per virtual entry into multiple values in compression space . then an additional network plays in a _ mapping function _ role from these hashed values to the virtual entry before hashing , which can be also regarded as `` reconstructing '' the virtual entry from its multiple hashed values . plugged into and jointly trained within the original network , the reconstruction network is of a comparably ignorable size , i.e. , at low memory cost . this functional hashing structure includes hashednets as a degenerated special case , and facilitates less value collisions and better value reconstruction . shortly denoted as funhashnn , our approach could be further extended with dual space hashing and multi - hops . since it imposes no restriction on other network design choices ( e.g. dropout and weight sparsification ) , funhashnn can be considered as a standard tool for dnn compression . experiments on several datasets demonstrate promisingly larger reduction of model sizes and/or less loss on prediction accuracy , compared with hashednets . [ [ notations . ] ] notations . + + + + + + + + + + throughout this paper we express scalars in regular ( @xmath0 or @xmath1 ) , vectors in bold ( @xmath2 ) , and matrices in capital bold ( @xmath3 ) . furthermore , we use @xmath4 to represent the @xmath5-th dimension of vector @xmath2 , and use @xmath6 to represent the @xmath7-th entry of matrix @xmath3 . occasionally , @xmath8_i$ ] is also used to represent the @xmath5-th dimension of vector @xmath2 for specification clarity . notation @xmath9 $ ] stands for the expectation operator . [ [ feed - forward - neural - networks . ] ] feed forward neural networks . + + + + + + + + + + + + + + + + + + + + + + + + + + + + + we define the forward propagation of the @xmath10-th layer as @xmath11.\end{aligned}\ ] ] for each @xmath10-th layer , @xmath12 is the output dimensionality , @xmath13 is the bias vector , and @xmath14 is the ( _ virtual _ ) weight matrix in the @xmath10-th layer . vectors @xmath15 denote the units before and after the activation function @xmath16 . typical choices of @xmath16 include rectified linear unit ( relu ) @xcite , sigmoid and tanh @xcite . [ [ feature - hashing ] ] feature hashing + + + + + + + + + + + + + + + has been studied as a dimension reduction method for reducing model storage size without maintaining the mapping matrices like random projection @xcite . briefly , it maps an input vector @xmath17 to a much smaller feature space via @xmath18 with @xmath19 . following the definition in @xcite , the mapping @xmath20 is a composite of two approximate uniform hash functions @xmath21 and @xmath22 . the @xmath23-th element of @xmath24 is defined as : @xmath25_j = \sum_{i : h(i)=j } \xi(i)x_i.\end{aligned}\ ] ] as shown in @xcite , a key property is its inner product preservation , which we quote and restate below . * _ lemma [ inner product preservation of original feature hashing ] _ * with the hash defined by eq . ( [ eq : originalfeaturehash ] ) , the hash kernel is unbiased , i.e. , @xmath26={\mathbf}{x}^{\top}{\mathbf}{y}$ ] . moreover , the variance is @xmath27 , and thus @xmath28 if @xmath29 . [ [ hashednets - in- . ] ] hashednets in @xcite . + + + + + + + + + + + + + + + + + + + + + + as illustrated in figure [ fig : model](a ) , hashednets randomly maps network weights into a smaller number of groups prior to learning , and the weights in a same group share a same value thereafter . a naive implementation could be trivially achieved by maintaining a secondary matrix that records the group assignment , at the expense of additional memory cost however . hashednets instead adopts a hash function that requires no storage cost with the model . assume there is a finite memory budge @xmath30 per layer to represent @xmath14 , with @xmath31 . we only need to store a weight vector @xmath32 , and assign @xmath33 an element in @xmath34 indexed by a hash function @xmath35 , namely @xmath36 where hash function @xmath35 outputs an integer within @xmath37 $ ] . another independent hash function @xmath38 outputs a sign factor , aiming to reduce the bias due to hash collisions @xcite . the resulting matrix @xmath14 is _ virtual _ , since @xmath12 could be increased without increasing the _ actual _ number of parameters in @xmath34 once the compression space size @xmath30 is determined and fixed . substituting eq . ( [ eq : hashednets ] ) into eq . ( [ eq : ffnn ] ) , we have @xmath39 . during training , @xmath34 is updated by back propagating the gradient via @xmath40 ( and the virtual @xmath14 ) . besides , the activation function @xmath16 in eq . ( [ eq : ffnn ] ) was kept as relu in @xcite to further relieve the hash collision effect through a sparse feature space . in both @xcite and this paper , the open source _ _ xxhash _ _ is adopted as an approximately uniform hash implementation with low cost . for clarity , we will focus on a single layer throughout and drop the super - script @xmath10 . still , vector @xmath41 denotes parameters in the compression space . the key difference between funhashnn and hashednets @xcite lies in ( i ) how to employ hash functions , and ( ii ) how to map from @xmath42 to @xmath43 : * instead of adopting one pair of hash function @xmath44 in eq . ( [ eq : hashednets ] ) , we use a set of multiple pairs of independent random hash functions . let s say there are @xmath45 pairs of mappings @xmath46 , each @xmath47 outputs an integer within @xmath48 $ ] , and each @xmath49 selects a sign factor . * ( [ eq : hashednets ] ) of hashednets employs an identity mapping between one element in @xmath43 and one hashed value , i.e. , @xmath50 . in contrast , we use a multivariate function @xmath51 to describe the mapping from multiple hashed values @xmath52 to @xmath53 . specifically , @xmath54;\ { \boldsymbol}{\alpha}\right ) . \end{aligned}\ ] ] therein , @xmath55 is referred to as the parameters in @xmath51 . note that the input @xmath56 is order sensitive from @xmath57 to @xmath45 . we choose @xmath51 to be a multi - layer feed forward neural network , and other multivariate functions may be considered as alternatives . as a whole , figure [ fig : model](b ) illustrates our funhashnn structure , which can be easily plugged in any matrices of dnns . note that @xmath55 in the reconstruction network @xmath51 is of a much smaller size compared to @xmath42 . for instance , a setting with @xmath58 and a 1-layer @xmath59 of @xmath60 performs already well enough in experiments . in other words , eq . ( [ eq : funhashnn ] ) just uses an ignorable amount of additional memory to describe a functional @xmath42-to-@xmath43 mapping , whose properties will be further explained in the sequel . the parameters in need of updating include @xmath42 in the compression and @xmath55 in @xmath51 . training funhashnn is equivalent to training a standard neural network , except that we need to forward / backward - propagate values related to @xmath42 through @xmath51 and the virtual matrix @xmath43 . [ [ forward - propagation . ] ] forward propagation . + + + + + + + + + + +" +"strong gravitational lensing is a powerful probe of the large scale properties of the universe @xcite . the well - known physics makes it straightforward to use lensing in cosmological estimates of the dark energy @xcite and the hubble constant @xcite . the gravitational lensing effect depends solely on the mass density of the field , it is also an ideal tool for studies of dark matter in galaxies and clusters of galaxies ( e.g. , * ? ? ? the cosmic lens all sky survey ( class ; * ? ? ? * ; * ? ? ? * ) , which was conducted in the radio band , is the largest current statistical sample of lensed compact sources . however , the class has only 13 lensed radio sources in its well - defined statistical sample . larger lens samples are critical to using lensed quasars for cosmological and astrophysical tests . optical surveys for lensed quasars are both complementary to radio surveys like the class and likely to produce larger lens samples since only one - tenth of quasars are radio - loud @xcite . our sloan digital sky survey quasar lens search ( sqls ; * ? ? ? * ) is based on the sloan digital sky survey ( sdss ; * ? ? ? * ) , and its catalog of roughly 100,000 spectroscopically - confirmed quasars ( e.g. , * ? ? ? * ) . so far , the sqls has succeeded in discovering 14 new lensed quasars @xcite , as well as recovering many previously known lensed quasars @xcite . indeed , the number of sdss - discovered lensed quasars is already a significant fraction of all known quasar lenses ( @xmath3 ) . the large number of lenses contained in the sqls and its well - defined selection function means that the lens catalog provided by the sqls will be very useful for statistical studies of strong lensing @xcite . in this paper , we report the discovery of a gravitationally lensed quasar , sdss j133222.62 + 034739.9 ( hereafter sdss j1332 + 0347 ) . the quasar was confirmed to be doubly imaged by a low - redshift early - type galaxy , from observations using the subaru 8.2-meter telescope and the university of hawaii 2.2-meter ( uh88 ) telescope . this paper is organized as follows . the sdss data for sdss j1332 + 0347 , including its selection , is described in [ sec : sdss ] . the follow - up images and spectra are shown in [ sec : image ] and [ sec : spec ] , respectively . in [ sec : model ] we model the lens . finally we summarize our results in [ sec : conc ] . throughout the paper we assume a cosmological model with the matter density @xmath4 , cosmological constant @xmath5 , and hubble constant @xmath6 . magnitudes are measured in ab system . the sdss is a survey to conduct both optical imaging and spectroscopy . it covers about 10,000 square degrees of the sky approximately centered on the north galactic cap with the dedicated wide - field 2.5-m telescope @xcite at the apache point observatory in new mexico , usa . the five broad - band photometric data are taken in imaging surveys @xcite and are reduced automatically by the photometric pipeline @xcite . from the magnitudes , colors , and morphologies of each object , quasar and galaxy candidates are selected as spectroscopic targets @xcite , and then assigned for spectroscopic observations by the tiling algorithm @xcite . the spectra cover the wavelength range from 3800 to 9200 with a resolution of @xmath7 . the astrometric accuracy is better than @xmath8 rms @xcite and the photometric zeropoint errors are less than @xmath9 magnitude over the entire survey area @xcite . most of the data have already become publicly available @xcite . sdss j1332 + 0347 was selected as a lensed quasar candidate from the sdss quasar sample , using the same selection algorithm as that described in @xcite . in this algorithm , the morphological parameters of each quasar are used to select lensed quasar candidates . sdss j1332 + 0347 was also selected by an improved algorithm @xcite whose selection function has been extensively tested , and it is in the well - defined source quasar sample of the sqls for lensed quasar statistics . figure [ fig : sdss_i ] shows the sdss @xmath10-band image of the field under the seeing of @xmath11 . the sdss point spread function ( psf ) magnitudes and the quasar redshift are summarized in table [ tab : sdss ] . the sdss images indicate that the object is more extended than a single star , making it a good lens candidate and a target for higher angular resolution observations . we obtained a 90 sec @xmath10-band image of sdss j1332 + 0347 with the suprime - cam @xcite on the subaru 8.2-meter telescope at mauna kea in seeing @xmath12 on 2003 may 28 . the @xmath10-band image was reduced in a standard way for the suprime - cam data using the neko software @xcite and the sdfred package @xcite . the absolute flux was calibrated using nearby stars in the sdss catalogs . the small differences between the sdss and suprime - cam @xmath10-band response functions are not important here . we also acquired a 720 sec @xmath13-band image of this object with the quick near - infrared camera ( quirc ) on the uh88 telescope in @xmath14 seeing on 2005 february 20 . the @xmath13-band image was reduced in a standard way using iraf , and calibrated using the standard star fs 23 @xcite . the @xmath10 and @xmath13 images are shown in figure [ fig : images ] . taking a closer look at the images , especially the @xmath10-band suprime - cam image , we see two compact sources bracketing an extended elliptical source . indeed , models of the images using a public software , galfit @xcite , consisting of two point sources and an extended object with a de vaucouleurs profile between them fit the data well . we used stars in the images as templates for the psf in this procedure . we also show the observed galaxy after subtracting models for the two point sources , the observed stellar components after subtracting models for the galaxy , and the residuals after subtracting models for the point sources and the galaxy , in the second , third , and bottom panels of figure [ fig : images ] , respectively . we name the two stellar components a and b , where a is the brighter component that lies closer to the galaxy ( separated by @xmath15026 ) , component g. the separation of the two stellar components derived from the @xmath10-band image is @xmath16 , and our relative astrometry is summarized in table [ tab:1332 ] . the stellar components have similar colors of @xmath17 and @xmath18 mag for a and b , respectively , while the galaxy g has a redder color of @xmath19 mag . the photometry of the components is also summarized in table [ tab:1332 ] . these astrometric and photometric properties are typical of known lensed quasar systems ( e.g. , * ? ? ? * ) , and imply that both components a and b are lensed images of a quasar and component g is the lens galaxy . we carried out a spectroscopic observation of sdss j1332 + 0347 using the faint object camera and spectrograph ( focas ; * ? ? ? * ) installed on the subaru 8.2-meter telescope on 2003 june 20 with an exposure time of 900 sec in @xmath14 seeing . the observation was conducted in 2@xmath202 on - chip binning mode , using a @xmath21-width slit aligned along components a and b , with the grism 300b and the filter l600 . this configuration provides a spectrum covering 3,900 to 6,000 with a spectral resolution of r@xmath22 , a spectral dispersion of 2.7 pixel@xmath23 and a spatial pixel scale of @xmath24 . we used iraf to analyze the spectra , extracting two traces corresponding to a blend of image a with the galaxy g and image b , respectively . the two spectra are shown in figure [ fig : spec1 ] . we clearly see broad emission lines redshifted to @xmath25 . on the red wings of the emission lines , we also see an absorption doublet at 4686 and 4728 , which we interpret as h and k absorption lines redshifted to @xmath26 . these strong absorption lines significantly distort the emission lines . it would be helpful to have a cleaner emission line in order to determine the quasar redshifts more accurately , but , the emission lines are the only strong emission lines in the focas spectra . we estimated the quasar redshifts using three approaches ; 1 ) using the whole line profiles ( @xmath27 ) , 2 ) using only the line peaks ( @xmath28 ) , and 3 ) using the whole line profiles after masking and then interpolating through the absorption lines ( @xmath29 ) . the results , summarized in table [ tab : caiii ] , confirm that the two quasars have the same redshifts . we adopt procedure 3 ) for our standard result of @xmath30 as it is likely to be the most reliable . we also verified that the spectrum a+g has little contamination from quasar b by extracting a spectrum at the same distance from component b as component a+g but in the opposite direction . the spectrum , shown in figure [ fig : spec1 ] , has no significant emission , and we conclude that the emission line in the spectrum a+g is due to component a. furthermore , in the spectra of both components a+g and b , we can see @xmath312796,2803 doublet absorption lines and a @xmath322600 absorption line by an intervening object at @xmath33 . the spectral flux ratio between components a+g and b , displayed in the bottom panel of figure [ fig : spec1 ] , indicates that combination of a+g is redder than component b. if we scale the spectrum b by the @xmath13-band flux ratio of @xmath34 between components a and b , and subtract it from the spectrum a+g , then we obtain the residual spectrum shown in figure [ fig : spec2 ] . while the spectrum is noisy , especially around the emission line and towards the blue wavelength region , the spectral energy distribution ( sed ) is consistent with a template spectrum of an elliptical galaxy @xcite at the redshift of the absorption feature , @xmath26 . given the strength of the absorption , we conclude that the seds of components a and b are identical and that component g is an elliptical galaxy at @xmath26 . we used the _ lensmodel _ package @xcite to fit a mass model to the observations of sdss j1332 + 0347 , assuming that the object is indeed a lensed quasar system . we assume the standard singular isothermal ellipsoid ( sie ) model characterized by eight parameters : the einstein radius @xmath35 , ellipticity @xmath36 , position angle @xmath37 , position of the lensing galaxy , the position and flux of the source quasar . since the number of observable constraints is also eight ( the positions of a , b , and g , and the fluxes of a and b ) , the number of degrees of freedom is zero . as expected , we were able to find a model that perfectly reproduces the observables , @xmath38 . the results of the model are presented in table [ table : model ] . we note that the best - fit values for the ellipticity and" +"the idea that some of the galactic nuclei are powered by matter accretion onto supermassive black holes is based on strong theoretical arguments ( salpeter 1964 ; zeldovich 1964 ; lynden - bell 1969 , 1978 ; lynden - bell & rees 1971 ; see blandford & rees 1992 for reviews ) and observation of rapid time variability of the emitted radiation which implies relativistic compactness of the radiating object . however , so far , there is no compelling proof that supermassive black holes actually do exist , as the spatial resolution of current observations is larger than @xmath8 schwarzschild radii . the standard routine in the investigation of the nature of the dark mass distribution at the centers of active galaxies is to observe stellar and gas dynamics . however , gas dynamics is usually regarded as less conclusive since it is responsive to non - gravitational forces such as e.g. magnetic fields . as an alternative to the black hole scenario , moffat ( 1997 ) considered general relativistic models of stellar clusters with large redshifts , and he investigated whether such objects are long - lived enough from the point of view of evaporation and collision timescales and stability criteria . he then showed that , in certain cases , stellar clusters with masses @xmath9 @xmath10 could mimic the behavior of supermassive black holes . a good unprejudiced review on the subject can be found in the paper by kormendy & richstone 1995 . the identification of a central supermassive object in the milky way has been a source of continuous debate in the literature . the crucial issue is whether the center of our galaxy harbors a supermassive black hole or any other compact dark matter object . theoretical papers , which are exclusively devoted to the black hole explanation of the galactic center , include lynden - bell & rees 1971 ; rees 1987 ; phinney 1989 and de zeeuw 1993 . however , even within this theoretical framework , there is no full agreement : the general consensus is that the supermassive black hole should have mass @xmath11 @xmath10 , while ozernoy 1992 and mastichiadis & ozernoy 1994 argue that the black hole mass can be as low as @xmath12 @xmath10 . the main motivation for a @xmath12 @xmath10 black hole at the galactic center is that it would emit less x - rays and gamma - rays than a @xmath11 @xmath10 black hole , behaving basically like a scaled - down active galactic nucleus . although earlier observations ( gehrels & tueller 1993 ; watson et al . 1981 ; skinner et al . 1987 ; hertz & grindlay 1984 ; pavlinsky , grebnev & sunyaev 1994 ) have shown that the central region actually does emit x - rays and gamma - rays , the supposed true center , usually assumed to be sgr a@xmath7 , does not emit strongly , at least up to energies of 30 kev ( skinner et al . 1987 ; hertz & grindlay 1984 ; pavlinsky , grebnev & sunyaev 1994 ) . sgr a@xmath7 radiation emission data at higher energies have been presented by goldwurm et al . they find no source associated with sgr a@xmath7 , and the inferred upper bound implies that the hard x - ray luminosity of sgr a@xmath7 is a factor of @xmath13 less than that expected for a black hole of @xmath11 @xmath10 accreting matter at the maximum stable rate . an unavoidable source of accretion is the wind from irs 16 , a nearby group of hot , massive stars . since the density and velocity of the accreting matter are known from observations , the accretion rate is basically a function of the assumed black hole mass only . this value represents a reliable lower limit to a real rate , given the other possible sources of accreting matter . based on this and on the theories about shock acceleration in active galactic nuclei , mastichiadis & ozernoy 1994 have estimated the expected production of relativistic particles and their hard radiation . comparing their results with available x - ray and gamma - ray observations which show that sgr a@xmath7 has a relatively low activity level , the authors conclude tentatively that an assumed black hole in the galactic center can not have a mass greater than approximately @xmath14 @xmath10 . other scenarios to explain low x - ray and gamma - ray activity of sgr a@xmath7 include so - called advection dominated models ( narayan , yi & mahadevan 1995 ; narayan et al . , 1997 ; mahadevan , narayan & krolik , 1997 ) which can live with a @xmath11 @xmath10 black hole that accretes matter at a realistic accretion rate of @xmath15 @xmath10 yr@xmath16 . however , most of the energy released by viscosity is carried along with the gas and lost into the black hole , while only a small fraction is actually radiated . the purpose of this paper is to present an alternative model , based on the idea that the dark matter concentration in the galactic center could be a ball of degenerate , self - gravitating heavy neutrinos , which is consistent with present observational data . in the recent past , viollier et al . have argued that massive , self - gravitating , degenerate neutrinos arranged in balls where the degeneracy pressure compensates self - gravity , can form long - lived configurations that could mimic the properties of dark matter at the centers of galaxies ( viollier , 1994 ; viollier et al . , 1993 ; viollier et al . , 1992 ) . tsiklauri & viollier ( 1996 ) demonstrated that a neutrino ball could play a similar role as a stellar cluster in the 3c 273 quasar , revealing its presence through the infrared bump in the emitted spectrum . tsiklauri & viollier ( 1998a ) further investigated the formation and time evolution of neutrino balls via two competing processes : annihilation of the particle - antiparticle pairs via weak interaction and spherical ( bondi ) accretion of these particles . bili & viollier ( 1997a ) showed how the neutrino balls could form via a first - order phase transition of a system of self - gravitating neutrinos in the presence of a large radiation density background , based on the thomas - fermi model at finite temperature . they find that , by cooling a non - degenerate gas of massive neutrinos below a certain critical temperature , a condensed phase emerges , consisting of quasi - degenerate supermassive neutrino balls . general relativistic effects in the study of the gravitational phase transition in the framework of the thomas - fermi model at finite temperature were taken into account in bili & viollier ( 1997b ) . a theorem was proved by bili & viollier ( 1997c ) which in brief states that the extremization of the free energy functional of the system of self - gravitating fermions , described by the general relativistic thomas - fermi model , is equivalent to solving einstein s field equations . the basic equations which govern the structure of cold neutrino balls have been derived in the series of papers ( viollier , 1994 ; viollier et al . , 1993 ; viollier et al . , 1992 and tsiklauri & viollier , 1996 ) ; here we adopt the notations of tsiklauri and viollier ( 1996 ) . in this notation the enclosed mass of the neutrinos and antineutrinos within a radius @xmath17 of a neutrino ball is given by @xmath18 where , @xmath19 is the standard solution of the lane - emden equation with polytropic index @xmath20 , @xmath21 is the lane - emden unit of length and @xmath22 is the central density of the neutrino ball . in this paper we use the length - scale 1 pc instead of @xmath21 , resulting in a trivial re - scaling of the standard lane - emden equation . to model the mass distribution usually the first moment of the collisionless boltzmann equation ( also referred to as jeans equation ) is used ( binney & tremaine , 1987 ) @xmath23 where @xmath24 is the spherically symmetric space density distribution of stars , @xmath25 is the total included mass , @xmath26 is the non - projected radial velocity dispersion and @xmath27 is the rotational contribution . in order to apply eq.(2 ) to the observational data , one should relate the intrinsic velocity dispersion to the projected one via the following abel integrals @xmath28 @xmath29 where @xmath30 denotes surface density and @xmath31 is the projected distance . one further needs some parametrization for @xmath26 and @xmath24 , and after numerical integration of eqs.(3 ) , the free parameters appearing in @xmath26 and @xmath24 should be varied in order to obtain the best fit of @xmath32 and @xmath30 with the observational data . following genzel et al . 1996 , we use parametrization @xmath33 as a model for @xmath30 . @xmath34 is related with the core radius through @xmath35 , where @xmath36=2.19 for @xmath37 . genzel et al . 1996 find that the best fit parameters for the stellar cluster are a central density of @xmath38 and a core radius of @xmath39 pc . thus , for the mass distribution , genzel et al . 1996 obtain a black hole of @xmath40 plus a stellar cluster with the abovementioned physical parameters . as mentioned earlier , we argue here that a neutrino ball composed of self - gravitating , degenerate neutrinos within a certain mass range could mimic the role of a black hole . this can be seen in fig.1 , where the mass distribution of the neutrino ball ( using the rescaled eq.(1 ) ) , with a neutrino mass in the range of 10 - 25 kev@xmath2 for @xmath5 and 2 , plus the stellar cluster is plotted . for comparison , the @xmath40 black hole plus stellar cluster and pure stellar cluster are also shown . we gather from the graph that in the case of @xmath41 kev@xmath2 for @xmath3 and @xmath42 kev@xmath2 for @xmath5 ( note that these two curves actually do overlap ) the mass distribution is marginally consistent with the observational data . it is clear that for larger neutrino masses ( with corresponding degeneracy factor @xmath6 and with the same total mass ) , the neutrino ball would be more compact , therefore also consistent with the observational data . it is worthwhile to note that precise values of masses of the neutrinos are essential since the radius of the neutrino ball , which actually sets the neutrino mass constraints , scales as @xmath43 . to investigate what an impact the replacement of the black hole by a neutrino ball would have , we also calculated @xmath32 for both mass distributions : a @xmath40 black hole plus a stellar cluster and a neutrino ball composed of @xmath44 kev@xmath2 for @xmath3 or @xmath45 kev@xmath2 for @xmath5 neutrinos with the same total mass plus stellar cluster . first we fitted the observational data taken from eckart & genzel 1997 , genzel et al . 1996 and references therein via numerical integration of the following expression for @xmath26 @xmath46 using abel integrals eq.(3 ) . for the fit parameters we obtain @xmath47 km / sec , @xmath48 km / sec and @xmath49 , and for the distance to sgr a@xmath7 we took 8 kpc . the resulting @xmath32 s for both mass distributions are plotted in fig . 2 . , which shows that the difference is rather small . it is worthwhile to point out that the actual fit parameters do not play an important role , since the aim of the graph is to demonstrate that the substitution of the @xmath40 black hole by a neutrino ball of the same mass , which is composed" +"to study the plasma boundary sheath with algebraic models has a long tradition @xcite . in contrast to more complex models which require time - consuming computer simulations , algebraic sheath models execute effectively in zero time . this makes them suitable for many practical purposes , for example for the model based real - time control of plasma processes . of course , the validity of simplified descriptions is always an issue . algebraic sheath models should thus be carefully derived from first principles and thoroughly tested against more complex ( and more physical ) approaches such as _ particle in cell _ ( pic ) simulations . in the present manuscript we propose a novel algebraic model for the electrical behavior of the rf modulated plasma boundary sheath . our investigation is motivated by a critical assessment of the pioneering ( and still `` classical '' ) algebraic sheath models which were proposed by lieberman twenty - five years ago @xcite . in many aspects , our approach is similar : we focus on the rf regime , where the applied radio frequency lies between the plasma frequencies of ions and electrons , @xmath0 , consider only one species of singly charged positive ions without any `` chemistry '' , and assume a one - dimensional cartesian geometry.we endeavor , however , to correct the three fundamental weaknesses of the lieberman models , namely that they are limited to the case of a single driving frequency , to the regime of large applied voltages ( compared to the thermal voltage @xmath1 , with @xmath2 the electron temperature ) , and to the two limiting cases of either highly collisional or completely collision - free motion . in other words , our goal is an algebraic model which captures the plasma sheath behavior in a wide range of frequencies , waveforms , amplitudes , and collisionality . our manuscript is organized as follows : in the next section , we describe our starting point , the `` standard model '' of the rf modulated sheath . after reviewing the lieberman approach , we return to the standard model and employ the _ advanced algebraic approximation _ @xcite to transform it practically without any loss of accuracy into a mathematically simpler form . the outcome of this first step is a valid sheath model of its own , but not yet of a closed form . we thus take a second step , employing a sequence of additional , more drastic approximations . ( a two - step approach is chosen because the intermediate model is better suited to assess the effects of the `` drastic appproximations '' than the original one . ) the result of the second step is our novel algebraic model , which then will be thoroughly tested against pic simulations . some conclusions and final remarks are given in the last section . for the description of the sheath , we employ what may be called the `` standard model '' . it assumes the rf regime , i.e. , that the exciting radio frequency @xmath3 lies between the plasma frequencies of ions and electrons , @xmath0 , and also imposes the length scale ordering @xmath4 , where @xmath5 is the debye length , @xmath6 the sheath thickness , @xmath7 the system length , and @xmath8 the ionization length scale . the geometry is one - dimensional ; we consider the spatial interval @xmath9 $ ] , where @xmath10 denotes the location of the electrode and @xmath11 a point far enough into the bulk so that quasineutrality prevails for all phase points.fig . [ fig1schematicplot ] shows the coordinates and other conventions . symbols have their standard meaning . we also define the phase interval @xmath12 $ ] , and the corresponding phase average as @xmath13 the electron part of the model consists of the equation of continuity with ionization and recombination neglected and of the relation of boltzmann equilibrium , @xmath14 & t_{\rm e } \frac{\partial n_{\rm e}}{\partial x } + e n_{\rm e } e = 0 . \label{boltzmannequilibrium}\end{aligned}\ ] ] ions are assumed to experience no modulation . their equation of continuity can be integrated to express the constancy of the ion flux flowing in negative @xmath15-direction , @xmath16 the equation of motion describes the acceleration of ions under the action of the phase - averaged electrical field @xmath17 and the friction due to collisions with the neutral background.in sheath models , the latter term is typically modeled by the assumption of a constant ion mean free path @xmath18 which is valid for strong electrical fields . ( a more general ansatz for the friction gives qualitatively similar results but with less transparent formulas ) . @xmath19 the field is described by poisson s equation , @xmath20 the model is mathematically completed by a set of boundary conditions and constraints . sheath - like solutions as shown in fig . [ fig1schematicplot ] are sought which obey asymptotic quasineutrality and transport equilibrium ( drift regime ) for @xmath21 and electron depletion for @xmath22 . ( together , these assumptions remove all degrees of freedom of the ode system except one . ) the rf modulation of the sheath is introduced by prescribing the total current density @xmath23 , which is divergence free and a spatial constant in 1d . we express it as the sum of a temporally constant part @xmath24 and a periodic , average free , not necessarily harmonic part @xmath25 , @xmath26 this relation can be cast in a more explicit form . we define the sheath charge per area @xmath27 as the integral of the charge density between the electrode @xmath28 and the bulk point @xmath11 , @xmath29 integrating poisson s equation from @xmath28 to @xmath11 yields a relation between @xmath27 and the electrical field at the electrode ; provided that the field at @xmath11 can be neglected : @xmath30 the electron current @xmath31 at the electrode can be found by the hertz - langmuir formula which expresses the flux as the product of the projected thermal speed and the local density @xcite.taking into account an effective sticking factor @xmath32 which may be , contrary to common belief , not equal to unity @xcite , we set : @xmath33 integrating the boltzmann relation from @xmath28 to @xmath11 , we can express the electron density at @xmath28 in terms of presumably constant density at @xmath11 and the sheath voltage @xmath34 : @xmath35 here , the sheath voltage is defined as the field integral from @xmath28 to @xmath11 , with the negative sign reflecting the fact that the field is oriented into the negative @xmath15-direction : @xmath36 together , these assumptions gives the current balance as follows , which is the justification for the popular diode model @xcite of the plasma boundary sheath ( fig . 2 ) : the total current @xmath23is the sum of a capacitive part ( represented by a nonlinear capacitor ) , an exponential electron part ( represented by a diode ) and a constant part ( represented by a current source ) : @xmath37 taking the phase average of the current balance relation yields a representation of the dc current characteristics of the sheath : @xmath38 when the electrode is current - free or `` floating '' , the dc current density @xmath39 is equal to zero . to determine the corresponding sheath condition , one must solve @xmath40 in the fluctuating part of the current balance , we can neglect the ( in comparison with the rf current ) typically small electron current @xmath41 and write @xmath42 it is advantageous to split @xmath43 into an average @xmath44 and a fluctuating , average - free part @xmath45 . the average sheath charge defines the mean sheath thickness @xmath46 via @xmath47 for the fluctuating sheath charge , we get the explicite representation @xmath48 we take the view that the fluctuating charge @xmath45 is the control parameter of the modulation and define @xmath49 and @xmath50 as its minimum and maximum values within the phase cycle @xmath12 $ ] . for vanishing modulation , both are zero , otherwise @xmath49 is negative and @xmath50 is positive . their absolute values are different unless @xmath45 is symmetric . as additional characterization we introduce the effective modulation amplitude @xmath51 it is advantageous to write the model dimensionless . however , some care must be taken , as an unfortunate choice of units may obscure the scaling relations . we take as basis the voltage scale @xmath52 of the sheath ; for weak modulation it is several @xmath1 , for strong modulation it is equal to the applied voltage . the other units are calculated using collisionless relations . altogether , we make the following substitutions , with the prime ( which is dropped soon)denoting dimensionless quantities : @xmath53 we also introduce dimensionless numbers ( and their typical values ) . the ratio of the length scale to the ion mean free path , with @xmath54 absorbed , is the collisionality @xmath55 , @xmath56 the ratio of the electron voltage to the voltage scale is the thermal parameter @xmath57 , @xmath58 and the combination of the electron sticking factor @xmath32 and the square root of the mass ratio , with @xmath59 absorbed , is the effective sticking parameter @xmath60 , @xmath61 another parameter , the ratio of the rf current to the dc current , does not appear explicitly , but it should be noted that it is typically large ( except for non - modulated sheaths ) : @xmath62 the dimensionless equations then consist of several subgroups : the stationary ion model involves the phase - averaged field @xmath17 , @xmath63 the electron model consists of boltzmann s equilibrium and poisson s equation , @xmath64 it is parametrical modulated by the condition that the fluctuating sheath charge follows a given time function @xmath45 which is related to the fluctuating rf current @xmath65 , @xmath66 the position of the electrode @xmath28 relative to the solution is determined by chosing a particular point of the dc ( phase - averaged ) current voltage curve @xmath67 where the sheath voltage is calculated as @xmath68 for the particularly important case of a floating electrode or wall , the current relation reduces to the condition for a current - free sheath , @xmath69 once the electrode position is known , also the average sheath charge can be calculated : @xmath70 the problem posed by the listed equations is quite intricate . the two subsystems alone are nonlinear differential equations , but they are coupled by the operation of phase averaging.altogether , the sheath problem thus amounts to a system of nonlinear integro - differential equations for which no analytical solutions are known . of course , numerical solutions of the system can be easily constructed , but this misses the point of an analytical treatment . clearly , a `` short - cut '' is needed which allows to construct explicit expressions for the phase - averaged quantities @xmath71 or @xmath72 . ( see fig . [ shortcut ] ) . in his pioneering work , lieberman proposed such a shortcut @xcite . his approach consisted of three approximations and specializations : first , he imposed godyak s step model @xcite . this approximation rests on the fact that the thermal electron voltage @xmath1 is small compared to the applied sheath voltage @xmath34 ; i.e. , in our notation , that the thermal parameter @xmath57 is small . it replaces the boltzmann relation for the electrons by the assumption that the density of the electrons is zero below the electron edge @xmath73 and equal to the ion density above : @xmath74 the value of @xmath73 is related to the sheath charge @xmath27 ; @xmath75 substituted into poisson s equation , the step model allows to calculate the electrical field , where the integration constant is chosen so that the field vanishes at the step" +"searching 3d data cubes is not a straightforward task . it is non - trivial to design a source - finding algorithm which is flux - limited , and complex , spurious structures can be difficult to automatically distinguish from astronomical sources . while visual inspection of the data can , through the extremely powerful capabilities of human pattern recognition , often overcome the problem of distinguishing real from spurious sources , it suffers from being subjective . it is also , traditionally , an extremely slow and laborious process , to the point where the scientific returns are diminished : weeks ( or even months ) spent searching a data cube could be more usefully employed in analysing trends in the data . i here focus on neutral hydrogen ( hi ) data cubes . developments in multibeam single - dish surveys ( e.g. hipass , @xcite ; alfalfa , @xcite ) have made very large 3d data sets a reality . smaller , more sensitive surveys such as ages ( the arecibo galaxy environment survey - @xcite ) possess similar problems of source extraction . although the total number of sources is lower , the source density is higher , as shown in table [ tab : surveys ] . this is necessarily a crude comparison ( since not every survey provides access to the raw data , accurately estimating what fraction of the data the sources occupy is impossible ) , but suffices to demonstrate the very substantial increase in the discovery potential of hi surveys over the last decade or so . [ cols=""^,^,^,^,^ "" , ] although once the data is loaded the display frame rate is high , initially converting that data into the blender - readable png images and loading them into blender is much slower than loading in a cube in , say , _ kvis_. on the hp elite , the larger cube took a mere 1 second to load in _ kvis_. _ kvis _ , which was designed from the ground up as a fits viewer , is far superior in this regard to frelled , which is essentially a hack to load fits data into a program never designed with astronomers in mind . i discuss the consequences of this in section [ sec : sourcefinding ] . as described above , since frelled s loading times are so much greater than for _ kvis _ , it is not necessary to load in all three projections of the data cube - the user can select only one or two , if they wish to save time and/or memory . i account for this in the benchmarks table . the `` loading time '' column shows the time to first load in the data ( i.e. convert the cube into png images and then display one projection ) plus the extra time needed when switching to a different projection . note that this delay _ only occurs once _ as the images must be loaded into gpu memory when the user switches the view to a different projection for the first time - after that there is no delay in rotating the view from one projection to any other . once the user has converted the data with a satisfactory transfer function and altered the display parameters appropriately , they can then save the .blend file , which preserves these display settings . the `` reloading time '' refers to the time needed to re - open this file , which does not require converting the fits data into png images . both the time to render an image ( using blender s internal raytracing engine ) and the realtime display frame rate depend ( by a factor of a few ) on the data being displayed and the orientation of the view . moving the viewpoint closer to the data causes a drop in frame rate and an increase in render time . for the benchmark table i chose a viewpoint in all cases where the whole of the data was just about visible - zooming in reduces the frame rate to as low as 5 f.p.s . , but moving slightly further out increases this to 20 f.p.s . even in the the slowest case . since the larger cube is asymmetrical , the benchmark table reflects this in the non - linear difference in times for the different projections . i only give the render times for the longest projection in each case . i chose to render a 500@xmath3500 pixel image without oversampling using 7 threads , with a field of view equivalent to half the extent of the data . it is an unfortunate necessity to render the images rather than simply record screenshots , since this is very much slower . at 3 minutes per frame , a 10 second animation ( at standard 25 f.p.s . ) would take 12.5 hours to render . while blender does have the ability to record screenshots , this feature does not function correctly in 2.49 and not usable for our purposes ( see section [ sec : future ] ) . note that all of the above benchmarks are for the standard 3d display mode . in 2d mode , in which only one slice of the data is displayed ( and loaded into gpu memory ) at a time , loading and rendering speeds improve dramatically . for the larger cube on the hp elite , using all three projections ( but only one colour map since transparency is not necessary in the 2d view ) , loading speed actually increases to 7 min 33 seconds ( but see below ) . however , reloading speed is slashed to a mere 1 second , competitive with _ kvis_. rendering speed is reduced to 0.25 seconds per frame ( the display frame rate remains above 25 f.p.s for the largest cube shown at any angle and zoom level ) . since frelled preserves the original fits file and generates png images , this has the disadvantage of generating a ( potentially ) large amount of extra data . for the 1.5 gb vla fits file we use for benchmarking ( see section [ sec : bench ] ) , an additional 1.7 gb of png data was generated . however , this is a worst - case scenario in which two maps were used for all three projections on a very large cube . for the 16 mb simulation data cube , generating one map for a single projection resulted in an extra 1 mb of data , while generating two maps for all three projections created 6 mb of extra data . users should therefore be aware that frelled can , typically , approximately double the file space required . conversion of the fits file is parallelised using python s `` multiprocessing '' module . this is a trivial operation since each slice of the data can be treated independently . optimising blender to load the png images as rapidly as possible is more complicated ( see figure [ fig : code ] for pseudocode ) . creating an object in blender , for instance , is much slower than transforming an existing object . older versions of frelled simply created the correct number of planes to hold the images depending on the shape of the data cube . more recent versions ( 4.0 onwards ) contain a pre - existing set of image planes , 1,000 for each projection in both 2d and 3d modes ( with appropriate materials assigned in each case ) . if a data set has more than 1,000 channels ( or spatial pixels along any projection ) , it is necessary to remove the existing image planes for that projection and re - create the correct number . this step causes a significant slowdown . for example , truncating the large vla gps cube to have 1,000 pixels in r.a . ( instead of 1,023 ) reduces the loading speed to 4 min 6 seconds ( compared to 6 min 47 seconds for the full cube ) . a similar issue affects 2d mode . in 2d mode , the image planes are animated to move between the visible layer and a non - visible layer depending on the current frame . for example , when displaying channel maps , blender s frame counter corresponds to the channel number . as in 3d mode , a set of 1,000 image planes per projection are provided in the default file , the difference being that these have also been set up with the necessary animation data . in 2d mode new planes must be both created and animated ( a significantly slower extra step ) if the image has more than 1,000 pixels along a dimension . using the truncated cube as above , loading in the data in 2d mode takes only 1 min 58 seconds , compared to 7 min 33 seconds for the full cube . i estimate that parallelising the code and providing pre - loaded image planes has increased the loading speed of frelled by a factor of approximately 7 in 3d mode and up to 9 in 2d mode , using frelled v3.8 and 4.1 to display the vla gps cube described in section [ sec : bench ] on the quad - core hp elite . p15 describe in detail four viewers designed explicitly for viewing data in 3d . however , none of these viewers was designed specifically for astronomy - all , for instance , lack the ability to use world coordinate systems , which is a severe handicap ( as will become apparent in section [ sec : astrofrelled ] ) . here i briefly compare the 3d display capabilities of frelled with those of other programs designed for astronomy . _ xray _ is part of the karma package . though now about twenty years old ( @xcite ) its loading times are far superior to frelled ( @xmath4 10 seconds for the vla gps cube ) . its rendering speeds are considerably lower than frelled ( @xmath0 1 f.p.s . ) and the user can not freely change the angle of the viewpoint - after setting the pitch , yaw and roll via sliders , they must explicitly tell the program to recompute the view . _ xray _ is only a viewer and provides no tools to analyse the data . while it does have a 3d cursor , on our hp elite this feature invariably caused the program to crash . _ xray _ allows the user to interactively define the transfer function and choose different display integrations ( e.g. the minimum or maximum voxel along the line of sight ) . the user is limited to setting the data range via the range selector buttons ( e.g. 95% , 99% , 99.9% ) - they can not set precise numerical values . conversely , the angle of the viewpoint can _ only _ be set via precise sliders , and not by freely rotating the view ( as in frelled ) using the mouse . this makes it much more difficult to `` home in '' on a particular feature of interest . however , it has a very easy to use interface for creating animations for presentations ( which frelled deliberately emulates ) . it does not have any facility to stretch data , so if a data cube has a relatively short velocity axis , _ xray _ is of little use ( recall figure [ fig : stretch ] ) . in short , _ xray _ is useful for quick inspection of data , but can not be used for detailed analysis . _ ds9 _ is a widely - used , general purpose fits viewer . it was" +"one of the goals of the large hadron collider ( lhc ) @xcite is the discovery of supersymmetry ( susy ) . the squark and gluino decays produce missing transverse energy @xmath9 from lightest stable superparticle ( lsp ) plus multiple jets and isolated leptons @xcite . one of the most interesting and widely discussed signatures for susy discovery at the lhc is the signature with two opposite charge and the same flavour leptons @xcite : @xmath10 . the main reason of such interest is that neutralino decays into leptons and lsp @xmath11 contribute to this signature and the distribution of the @xmath12 invariant mass @xmath13 has the edge structure @xcite that allows to determine some combination of the susy masses . the signature @xmath14 can be realized when @xmath15 decays into @xmath16 pair which is only relevant at large @xmath3 @xcite . also as it is shown in ref.@xcite at the level of cmsjet @xcite simulation the use of @xmath17 signature for large @xmath3 allows to obtain nontrivial information on parameters of the decay @xmath18 . on the other hand , the @xmath14 ( with an arbitrary number of jets ) can be used for the detection of lepton flavour violation in slepton decays @xcite , @xcite at the lhc . in the minimal supersymmetric model ( mssm ) @xcite supersymmetry is broken at some high scale @xmath19 by generic soft terms , so in general all soft susy breaking terms are arbitrary which complicates the analysis and spoils the predictive power of the theory . in the minimal supergravity model ( msugra ) @xcite the universality of the different soft parameters at the grand unified theory ( gut ) scale @xmath20 gev is postulated . namely , all the spin zero particle masses ( squarks , sleptons , higgses ) are postulated to be equal to the universal value @xmath21 at the gut scale . all gaugino particle masses are postulated to be equal to the universal value @xmath22 at gut scale . also the coefficients in front of quadratic and cubic susy soft breaking terms are postulated to be equal . the renormalization group equations are used to relate gut and electroweak scales . the equations for the determination of a nontrivial minimum of the electroweak potential are used to decrease the number of the unknown parameters by two . so the msugra model depends on five unknown parameters . at present , the more or less standard choice of free parameters in the msugra model includes @xmath23 and @xmath24 @xcite . all sparticle masses depend on these parameters . in ref.@xcite the possibility to detect susy and lepton flavour violation using the @xmath25 signature at the lhc for the compact muon solenoid ( cms ) detector at the level of full detector simulation was studied . note also ref.@xcite where the susy msugra cms detector discovery potential was investigated for the @xmath26 signature at the level of full detector simulation . in this paper we study the @xmath0 and @xmath1 signatures @xmath2 for different values of @xmath27 in the msugra model . with @xmath28 rising , we observe a characteristic change in the shape of dilepton mass spectra in @xmath4 versus @xmath5 final states reflecting the decrease of @xmath6 branching ratio . we also study the non msugra modifications of the cms test point lm1 with arbitrary relations among gaugino and higgsino masses . for such modifications of the msugra test point the number of lepton events depends rather strongly on the relations among gaugino and higgsino masses and in some modifications of test point lm1 the signatures with leptons and @xmath7 do not lead to the susy discovery and the single susy discovery signature remains the signature with @xmath8 . the organization of the paper is the following . section [ tede ] describes some useful technical details of performed simulations . in section [ basi ] the backgrounds and cuts used to suppress the backgrounds are discussed . section [ resca ] contains the results of numerical calculations concerning the possibility to detect susy and constrain the susy parameters using the @xmath29 and @xmath26 signatures . section [ ressim ] contains the results of the simulations for different values of @xmath28 . in section [ ressim2 ] we discuss the results of the simulation of the mssm with nonuniversal gaugino and higgsino masses . section [ conc ] contains concluding remarks . the coupling constants and cross sections in the leading order ( lo ) approximation for susy processes and backgrounds were calculated with isasugra 7.69 @xcite , pythia 6.227 @xcite and comphep 4.2pl @xcite . for the calculation of the next - to - leading order ( nlo ) corrections to the susy cross sections the prospino @xcite code was used . for considered signal events and backgrounds the nlo corrections are known and the values of nlo cross sections ( or @xmath30-factors ) were used for normalization of the numerical results . we used the full simulation results of ref.@xcite for the estimation of the number of background events . the cms fast simulation code @xmath31 @xcite was used for the estimation of signal events . the reconstructed electrons and muons were passed through packages defining lepton isolation criteria . for each electron and muon the following parameters were defined : * @xmath32 is a number of additional tracks with @xmath33 2 gev/@xmath34 inside a cone with @xmath35 0.3 around the lepton . * @xmath36 is a ratio of energy deposited in the calorimeters ( electromagnetic ( ecal ) + hadronic ( hcal ) ) inside a cone with @xmath37 around given track to the energy deposited inside a cone with @xmath38 . * @xmath39 is defined as a ratio of energy deposited in the hcal inside a cone with @xmath40 to the energy deposited in the ecal inside the same cone . * @xmath41 is a ratio of energy deposited in the ecal inside a cone with @xmath40 to the momentum of the reconstructed track . the susy production @xmath42 with subsequent decays @xmath43 @xmath44 @xmath45 @xmath46 lead to the event topologies @xmath14 and @xmath1 . note that in the mssm with lepton flavour conservation neutralino decays into leptons @xmath47 ( @xmath48 ) do not contribute into the @xmath0 signature . the main backgrounds which contribute to the @xmath5 events are : @xmath49 , ww , wz , zz , wt , z@xmath50 , @xmath51 and z+jet . it is found that @xmath49 is the largest background and it gives more than 50% contribution to the total background . in this paper we used the results of ref.@xcite for the estimation of the number of background events . in the analysis the events with the following isolation criteria for electrons were used : @xmath52 , @xmath53 , @xmath54 , @xmath55 . the same criteria for muons were the following : @xmath52 , @xmath56 , @xmath57 , @xmath58 . these numbers were adjusted by studying electron and muon tracks in the process @xmath59 . the selection cuts are the following : * cut on leptons : @xmath60 , @xmath61 , lepton isolation within @xmath62 cone * cut on missing transverse energy : @xmath63 . here @xmath64 and @xmath65 are corresponding thresholds in this section we remind the main results of ref.@xcite on susy detection using the @xmath25 signature . the possibility to detect susy using the cms test points lm1 - lm9 @xcite chosen for the detailed study of susy detection at the cms was investigated in ref.@xcite . this study was based on the counting the expected number of events for both the standard model ( sm ) and the msugra model . the parameters of the cms test points lm1 - lm9 are given in table [ points ] . . the parameters of the cms test points . [ cols=""^,^,^,^,^,^"",options=""header "" , ] [ leptons ] as it follows from table [ leptons ] for points ( 7 - 12 ) the perspective to discover susy using the signature with single lepton or dileptons plus @xmath9 looks hopeless . moreover for the points ( 7 - 12 ) the use of more powerful from the susy discovery point of view signature @xmath66 also looks very problematic . the invariant mass distributions of @xmath12 ( solid line ) and @xmath5 ( dotted line ) lepton pairs at the extensions of the point lm1 are shown in figs.[pm2_minvbsm4]-[pm2mu_minvbsm4 ] . the distributions of @xmath67 leptons , @xmath68 lepton , @xmath69 leptons and @xmath70 leptons on @xmath9 for the modifications of the point lm1 are shown in figs.[ppx4425 ] - [ pl02x102 ] for an integral luminosity @xmath71 . as one can see from fig.[ppx4425 ] for the points ( 7 - 10 ) there is sharp change in lepton spectra distributions on @xmath9 compared to the test point lm1 , namely , the number of lepton events for the points ( 7 - 10 ) are much smaller than for the test point lm1 . the same situation takes place for the @xmath9 spectrum of events without leptons , see fig.[pl02x4425 ] . in this paper we studied the @xmath0 and @xmath1 signatures @xmath2 for different parameters @xmath3 of the mssm model . with @xmath3 rising , we observed a characteristic change in the shape of dilepton mass spectra in @xmath4 versus @xmath5 final states reflecting the decrease of @xmath6 branching ratio . we also studied some non msugra modifications of the point lm1 . we have found the drastic change in dilepton spectra with the increase of gaugino masses . for the points ( 7 - 12 ) the perspective to discover susy using the signatures with leptons and @xmath9 looks hopeless . even more powerful signature with @xmath72 looks rather pessimistic . as a recent review , see for example : + n.v.krasnikov and v.a.matveev , ; + hep - ph/0309200 . h.baer , c .- h.chen , f.paige and x.tata , . as a review , see for example : + s.abdullin _ et al . _ , cms note 1998/006 . d.denegri , w.majerotto and l.rurua , . n.v.krasnikov , ; + n.v.krasnikov , . f.deppisch _ et al . _ , hep - ph/0401243 . reviews and original references can be found in : + h.e.haber and g.l.kane , ; + r.barbieri , ; + d.v.nanopoulos , ; + h.p.nilles , ; + n.v.krasnikov and v.a.matveev , ; + n.polonsky , . yu.andreev , s.bityukov , n.krasnikov and a.toropin , cms note 2006/103 ; hep - ph/0608176 . m.chiorboli , m.galanti and a.tricomi , cms note 2006/133 . h.baer , f.e.paige , s.d.protopopescu and x.tata , hep - ph/0001086 . et al . _ , ; + http://www.thep.lu.se/@xmath73torbjorn/pythia.html v.i.savrin _ et al . _ , . w.beenakker _ _ , hep - ph/9611232 ; + http://people.web.psi.ch/spira/prospino/ http://cmsdoc.cern.ch/cmsoo/cmsoo.html http://cmsdoc.cern.ch/cms/prs/susybsm/msugra_testpts/ msugra_testpts.html m.battaglia _ et al . s.i.bityukov and n.v.krasnikov , ; + s.i.bityukov and n.v.krasnikov , . v.bartsch and g.quast , cms note 2005/004 ; + r.cousins , j.mumford and s.valuev , cms note 2005/002 ." +"the neutron lifetime @xmath1 is an important parameter in tests of the standard model of particle physics . it also affects the rate of helium production in the early universe and the energy production in the sun . the current particle data group ( pdg ) average is @xmath1 = 880.1@xmath2 1.1 s @xcite . however , the value of one experiment @xcite , which reported the lowest measurement uncertainty of @xmath3 0.8 s , is @xmath3 3.5 s lower than the bulk of other data in the pdg collection @xcite , that are grouped consistently around 882.0 s ( @xmath2 1.0 s ) @xcite . therefore the actual uncertainty of @xmath1 to be used in cosmological calculations may be of the order of 2 seconds or more . as a possible way of advancing this field , storage of polarized ultracold neutrons ( ucns ) in a magnetic trap has been pioneered by paul _ _ @xcite and is currently being pursued vigorously by several groups worldwide @xcite . one advantage of magnetic ucn storage versus storage in material bottles , the method used in a number of previous neutron lifetime measurements @xcite , is the potential absence of losses due to effects other than @xmath4-decay . there are no wall losses , the slow loss due to quasi - stable orbits is serious but believed to be manageable by avoiding regular orbits @xcite , and the potential loss due to depolarization , defined as spin flip relative to the local field direction , is commonly assumed to be negligible . for systems using permanent magnets the question of gradual demagnetization over time appears to have found little attention so far . until recently ucn depolarization estimates @xcite were based on majorana s quasi - classical result of 1932 @xcite for a free polarized particle with magnetic moment moving with constant velocity vector through a non - uniform static magnetic field of specific form . only its spin state was assumed to be affected by the magnetic field . this model predicted a depolarization probability @xmath5 for one passage through the field . this value decreases exponentially with the adiabaticity parameter @xmath6 , where @xmath7 is the frequency of rotation of the field as seen from the reference frame of the moving particle , in the critical region where the field rotates fastest while the magnitude @xmath8 of the magnetic field may be small . @xmath9 is the larmor frequency . for magnetic field parameters as currently used or proposed for ucn storage , @xmath10 would be of order @xmath11 , thus immeasurably small . recently , walstrom _ et al . _ @xcite pointed out that the values of @xmath10 for confined , rather than freely moving , neutrons are much larger . for a ucn moving along a vertical path in the storage system proposed by them , @xmath10 was estimated to be in the range @xmath12 to @xmath13 . this is much larger than the majorana value but still negligible in any actual or projected neutron lifetime experiment . using a simplified model of magnetic field distribution we extend the theory of @xcite to include arbitrary ucn motion with both vertical and horizontal velocity components , confined to the vertical space between upper and lower turning points that depend only on the ucn energy for vertical motion . in our model ( introduced in sec . [ sec : ii ] ) the magnetic field magnitude @xmath8 is uniform within any horizontal plane , so there is no horizontal component of magnetic force . therefore the neutron moves with constant velocity in the horizontal @xmath14- and @xmath15- directions . we show that @xmath10 could reach a level approaching the tolerance limit for a high precision neutron lifetime measurement unless precautions are taken . as is well known the most critical issue is the choice of a stabilization field perpendicular to the magnetic mirror field , of sufficient strength so that the depolarization rate will be negligible in a neutron lifetime experiment . our model field is close to the `` bathtub configuration '' of ref . @xcite but the lateral confinement of ucns , achieved there by double curvature of the magnetic mirror , is simulated differently . the magnetic mirror is horizontal and extends to infinity in both lateral dimensions . however , one could imagine the presence of ideal vertical mirrors reflecting the ucns back and forth in the horizontal directions without any change in the analysis . more specifically , we use an infinite ideal planar halbach array @xcite , which is free of the field ripples present in actual realizations @xcite . in the design of ref . @xcite , the ripples are important only within about 1 mm of the surface of the magnets . this region is not reached by the ucns whose maximum energy ( for vertical motion ) is @xmath345 nev ( for the parameters in @xcite ) , since they reverse their flight direction before entering this zone . using this model of field distribution we have also studied the problem of depolarization of ucns in reflection from a non - magnetic mirror immersed in a non - uniform magnetic field . this question is important as a mechanism that may limit the efficiency of ucn polarizers based on transmission through a magnetic field . for a sufficiently strong field , neutrons in only one spin state can pass the field to proceed to the experiment . otherwise they are reflected . however , following the polarizer the ucns are usually reflected on trap or guide walls exposed to the stray field of the polarizer and thus may lose their 100% polarization if the reflection process involves depolarization . moreover , a possible depolarization on non - magnetic trap walls in a magnetic field is highly relevant in measurements of the neutron decay asymmetry parameter @xmath0 using ultracold neutrons @xcite . this problem has first been investigated by pokotilovski @xcite who used an adaptation of the majorana model to the reflection geometry . in the present work we study certain aspects of this problem by imagining a horizontal lossless non - magnetic ucn mirror inserted at a variable height into the magneto - gravitational storage space . the net depolarization per bounce on this mirror will be compared to the depolarization for one bounce in the magnetic field in the absence of the mirror to obtain an estimate for the depolarization effect of the mirror . the topic of ucn depolarization in magnetic storage or in mirror reflection in a magnetic field raises interesting questions of quantum interpretation . fig . 3 of ref . @xcite and our fig . [ fig : two ] ( to be discussed in sec . [ sec : iii.b.2 ] ) show the probability for the neutron to be in the spin - flipped state ( relative to the field direction ) as a function of position of the neutron as it moves through the magnetic storage space . the curve is strongly peaked at the critical level where the field rotates fastest in the reference frame of the moving neutron . this behavior is the same as displayed by the majorana result @xcite ( where it is more difficult to deduce since the author used a quantization axis fixed in space rather than rotating together with the field ) . in a semi - classical interpretation , as the ucn starts moving from one turning point , say the upper one , down toward the lower one , the spin vector rotates away from the quantization axis ( which was chosen parallel to the local magnetic field vector in ref . it reaches a certain maximum angle around the critical zone ; then this rotation is reversed and ends at a much smaller value at the next turning point for ucn motion . this indicates that an analyzer of neutron polarization placed at different heights would show a variation of depolarization by many orders of magnitude ( @xmath16 8 decades for the example shown in fig . 3 of ref . @xcite ) over the vertical range of the storage space . the depolarization rate expected for an actual ucn magnetic storage experiment , without any polarization analyzer intersecting the beam , is determined by the current of ucns in the `` wrong '' spin state , i.e. of high - field seekers leaving the system at the lower and upper turning points while the `` correct '' ( high - field repelled ) state is reflected and returns to the storage space . this association of net depolarization with loss currents is consistent with the following interpretation : at the turning points a measurement is performed ( in the sense of quantum mechanics ) , conceptually by neutron detectors placed just below the bottom and just above the top of the storage region for a given ucn energy for vertical motion . these detectors would intersect the ucns in the `` wrong '' spin state as they exit the storage system . in the copenhagen interpretation , such a measurement ( actual or hypothetical ) resets the ucn wave function to a pure state of high - field repelled neutrons . the spin state then evolves as described by the spin - dependent schrdinger equation ( or its semi - classical analog ) until the next `` measurement '' takes place at the following turning point and the process of wave collapse and wave evolution is repeated . alternative interpretations are conceivable but we will use the picture outlined above . following ref . @xcite we use the wentzel - kramers - brillouin ( wkb ) approximation to solve the spin - dependent schrdinger equation . this appears justified since the spatial variation of field variables ( gravitational potential and magnetic field * b * ) is much slower than the variation of ucn wave function . the scales are of order cm for gravity and * b * , and of order @xmath17 m or less for the neutron wavelength . we are aware of the fact that an exact treatment of ucn depolarization in magnetic storage may involve quantum electrodynamics since the moving neutron , in its reference frame , is affected by a time - dependent electromagnetic field , i.e. by low - energy photons . we will also neglect temporal fluctuations of the field due to mechanical vibrations or , if electromagnets are used for field generation , ac components of the current supply . we are not aware of any work on time - dependent effects of this kind in magnetic ucn storage . as it rotates in the ( @xmath18)-plane . its magnitude @xmath19 decreases exponentially with height @xmath20 and is represented by the arrow length using a log scale . the angle @xmath21 of the halbach field is also shown . the superimposed stabilization field @xmath22 in the @xmath14-direction increases slowly with @xmath20 as in ref . @xcite and is symbolized by the crosses of variable size.,width=291 ] we consider a halbach array @xcite of permanent magnets of thickness @xmath23 covering the infinite @xmath24-plane , where the @xmath15-axis points to the right , the @xmath20-axis points up ( against gravity ) and the @xmath14-axis toward the front ( fig . [ fig : one ] ) . we choose @xmath25 at the upper magnet surface and will closely follow the description in ref . @xcite , apart from this choice of system of coordinates . this choice will allow us to use the pauli matrices in their standard form . in the limit of infinitely fine division of magnet blocks in the @xmath15-direction , let the magnetization vector have a constant magnitude @xmath26 but , viewed along the positive @xmath14 direction , rotate clockwise in the @xmath27-plane with periodicity @xmath28 in @xmath15-direction : @xmath29 using a complex quantity @xmath30 , eq" +"the basics of the density matrix renormalization group were developed by s. white in 1992@xcite and since then dmrg has proved to be a very powerful method for low dimensional interacting systems . its remarkable accuracy can be seen for example in the spin-1 heisenberg chain : for a system of hundreds of sites a precision of @xmath0 for the ground state energy can be achieved . since then it has been applied to a great variety of systems and problems including , among others , spin chains and ladders , fermionic and bosonic systems , disordered models , impurities and molecules and 2d electrons in high magnetic fields . it has also been improved substantially in several directions like two ( and three ) dimensional ( 2d ) classical systems , stochastic models , the presence of phonons , quantum chemistry , field theory , the inclusion of temperature and the calculation of dynamical and time - dependent properties . some calculations have also been performed in 2d quantum systems . all these topics are treated in detail and in a pedagogical way in the book @xcite , where the reader can find an extensive review on dmrg . in this article we will attempt to cover the different areas where it has been applied without entering into details but in a few cases , where we have chosen some representative contributions . we suggest the interested reader to look for further information in the referenced work . our aim here is to give the reader a general overview on the subject . one of the most important limitations of numerical calculations in finite systems is the great amount of states that have to be considered and its exponential growth with system size . several methods have been introduced in order to reduce the size of the hilbert space to be able to reach larger systems , such as monte carlo , renormalization group ( rg ) and dmrg . each method considers a particular criterion of keeping the relevant information . the dmrg was originally developed to overcome the problems that arise in interacting systems in 1d when standard rg procedures were applied . consider a block b ( a block is a collection of sites ) where the hamiltonian @xmath1 and end - operators are defined . these traditional methods consist in putting together two or more blocks ( e.g. b - b , which we will call the superblock ) , connected using end - operators , in a basis that is a direct product of the basis of each block , forming @xmath2 . this hamiltonian is then diagonalized , the superblock is replaced by a new effective block @xmath3 formed by a certain number @xmath4 of lowest - lying eigenstates of @xmath2 and the iteration is continued ( see ref . although it has been used successfully in certain cases , this procedure , or similar versions of it , has been applied to several interacting systems with poor performance . for example , it has been applied to the 1d hubbard model keeping @xmath5 states . for 16 sites , an error of 5 - 10% was obtained @xcite . other results@xcite were also discouraging . a better performance was obtained @xcite by adding a single site at a time rather than doubling the block size . however , there is one case where a similar version of this method applies very well : the kondo ( and anderson ) model . wilson@xcite mapped the one - impurity problem onto a one - dimensional lattice with exponentially descreasing hoppings . the difference with the method explained above is that in this case , one site ( equivalent to an onion shell "" ) is added at each step and , due to the exponential decrease of the hopping , very accurate results can be obtained . returning to the problem of putting several blocks together , the main source of error comes from the election of eigenstates of @xmath2 as representative states of a superblock . since @xmath2 has no connection to the rest of the lattice , its eigenstates may have unwanted features ( like nodes ) at the ends of the block and this ca nt be improved by increasing the number of states kept . based on this consideration , noack and white@xcite tried including different boundary conditions and boundary strengths . this turned out to work well for single particle and anderson localization problems but , however , it did not improve the results significantly for interacting systems . these considerations led to the idea of taking a larger superblock that includes the blocks @xmath6 , diagonalize the hamiltonian in this large superblock and then somehow project the most favorable states onto @xmath6 . then @xmath6 is replaced by @xmath3 . in this way , awkward features in the boundary would vanish and a better representation of the states in the infinite system would be achieved . white@xcite proposed the density matrix as the optimal way of projecting the best states onto part of the system and this will be discussed in the next section . some considerations concerning the effect of boundary conditions in the nature of the states kept ( and an analogy to the physics of black holes ) is given in @xcite . the justification of using the density matrix is given in detail in ref.@xcite . a very easy and pedagogical way of understanding the basic functioning of dmrg is applying it to the calculation of simple quantum problems like one particle in a tight binding chain @xcite . in the following section we will briefly describe the standard method ; in sect . 3 we will mention some of the most important applications ; in sect . 4 we review the most relevant extensions to the method and finally in sect . 5 we concentrate on the way dynamical calculations can be performed within dmrg . the dmrg allows for a systematic truncation of the hilbert space by keeping the most probable states describing a wave function ( _ e.g . _ the ground state ) instead of the lowest energy states usually kept in previous real space renormalization techniques . the basic idea consists in starting from a small system ( _ e.g _ with @xmath7 sites ) and then gradually increase its size ( to @xmath8 , @xmath9 , ... ) until the desired length is reached . let us call the collection of @xmath7 sites the _ universe _ and divide it into two parts : the _ system _ and the _ environment _ ( see fig . [ figsuperblock ] ) . the hamiltonian is constructed in the _ universe _ and its ground state @xmath10 is obtained . this is considered as the state of the _ universe _ and called the _ target state_. it has components on the _ system _ and the _ environment_. we want to obtain the most relevant states of the _ system _ , i.e. , the states of the _ system _ that have largest weight in @xmath11 . to obtain this , the _ environment _ is considered as a statistical bath and the density matrix@xcite is used to obtain the desired information on the _ system_. so instead of keeping eigenstates of the hamiltonian in the block ( _ system _ ) , we keep eigenstates of the density matrix . we will be more explicit below . = 2.0 in = 1.0 in [ figsuperblock ] let s define block [ * b * ] as a finite chain with @xmath12 sites , having an associated hilbert space with , @xmath4 states where operators are defined ( in particular the hamiltonian in this finite chain , @xmath1 and the operators at the ends of the block , useful for linking it to other chains or added sites ) . except for the first iteration , the basis in this block is nt explicitly known due to previous basis rotations and reductions . the operators in this basis are matrices and the basis states are characterized by quantum numbers ( like @xmath13 , charge or number of particles , etc ) . we also define an added block or site as [ * a * ] having @xmath14 states . a general iteration of the method is described below : \i ) define the hamiltonian @xmath2 for the superblock ( the _ universe _ ) formed by putting together two blocks [ * b * ] and [ * b * ] and two added sites [ * a * ] and [ * a * ] in this way : [ * b a a b * ] ( the primes are only to indicate additional blocks , but the primed blocks have the same structure as the non - primed ones ; this can vary , see the finite - size algorithm below ) . in general , blocks [ * b * ] and [ * b * ] come from the previous iteration . the total hilbert space of this superblock is the direct product of the individual spaces corresponding to each block and the added sites . in practice a quantum number of the superblock can be fixed ( in a spin chain for example one can look at the total @xmath15 subspace ) , so the total number of states in the superblock is much smaller than @xmath16 . in some cases , as the quantum number of the superblock consists of the sum of the quantum numbers of the individual blocks , each block must contain several subspaces ( several values of @xmath13 for example ) . here periodic boundary conditions can be attached to the ends and a different block layout should be considered ( e.g. [ * b a b a * ] ) to avoid connecting blocks [ * b * ] and [ * b * ] which takes longer to converge . the boundary conditions are between [ * a * ] and [ * b * ] . for closed chains the performance is poorer than for open boundary conditions @xcite . \ii ) diagonalize the hamiltonian @xmath2 to obtain the ground state @xmath11 ( target state ) using lanczos@xcite or davidson@xcite algorithms . other states could also be kept , such as the first excited ones : they are all called _ target states_. \iii ) construct the density matrix : @xmath17 on block [ * b a * ] , where @xmath18 , the states @xmath19 belonging to the hilbert space of the block [ * b a * ] and the states @xmath20 to the block [ * b a * ] . the density matrix considers the part [ * b a * ] as a system and [ * b a * ] , as a statistical bath . the eigenstates of @xmath21 with the highest eigenvalues correspond to the most probable states ( or equivalently the states with highest weight ) of block [ * b a * ] in the ground state of the whole superblock . these states are kept up to a certain cutoff , keeping a total of @xmath4 states per block . the density matrix eigenvalues sum up to unity and the truncation error , defined as the sum of the density matrix eigenvalues corresponding to discarded eigenvectors , gives a qualitative indication of the accuracy of the calculation . \iv ) with these @xmath4 states a rectangular matrix @xmath22 is formed and it is used to change basis and reduce all operators defined in [ * b a * ] . this block [ * b a * ] is then renamed as block [ * b@xmath23 * ] or simply [ * b * ] ( for example , the hamiltonian" +"one of the most sensitive probes of physics beyond the standard model ( sm ) is provided by neutral gauge boson self couplings @xcite . in the sm , trilinear and quartic neutral gauge boson couplings ( tngbcs and qngbcs ) @xmath4 and @xmath5 , with @xmath6 , vanish at tree level and their radiative corrections are known to be rather small , of the order of @xmath7 - @xmath8 @xcite . deviations from the sm predictions for tngbcs and qngbcs might point to new interactions such as those arising from strongly - interacting electroweak models @xcite , a fourth family of chiral fermions with sm assignments of quantum numbers @xcite , and the heavy fermions arising in the minimal supersymmetric standard model ( mssm ) @xcite . an interesting feature of qngbcs involving at least one photon field stems from the fact that they are genuine in the sense that arise from effective operators that do not induce any trilinear gauge boson coupling . therefore these genuine qngbcs must be constrained from processes other than the ones used to constrain trilinear gauge boson couplings , such as boson - pair fusion or triple - boson production @xcite . this is to be contrasted with the case of the quartic @xmath9 coupling , which can arise from operators that also induce the trilinear @xmath10 coupling , which means that any constraint on the latter can be immediately translated into a bound on the former . furthermore , while the quartic neutral @xmath11 coupling can be induced at tree - level , for instance by the exchange of a heavy scalar boson , qngbcs involving at least one photon field can only arise at one - loop level or higher order in any renormalizable theory because of electromagnetic gauge invariance . in particular , qngbcs have been constrained from the cern @xmath12 collider lep-2 data on triple gauge boson production @xcite . considerable work has also been devoted to the analysis of qngbcs through different processes at the next linear @xmath12 collider as well as @xmath13 , @xmath14 and hadron colliders @xcite . in this note we will present a detailed calculation of the @xmath1 coupling contribution to the rare decay @xmath15 . the current experimental limit on this decay mode @xcite will then be used to constrain the coefficients of this qngbc . to our knowledge , this calculation has never been presented in the literature . our analysis will proceed in the same line as those presented in our previous works @xcite , where we obtained bounds on tngbcs from the @xmath16 decay mode @xcite and on neutrino - photon interactions from @xmath17 @xcite . we will find that the bounds obtained in this way rely on very few assumptions , though they are weaker than the ones obtained from the analysis of @xmath18 and @xmath19 data at lep-2 @xcite . the organization of the paper is as follows . in section ii we present a short description of the effective lagrangian for the @xmath1 coupling . section iii is devoted to present the calculation of the rare decay @xmath0 . finally , our conclusions are presented in section iv . when parametrizing physics beyond the fermi scale in a model - independent manner by means of the effective lagrangian technique there are two alternatives , i.e. the underlying new physics can be assumed to be either of decoupled or nondecoupled nature @xcite . in the decoupling scenario it is assumed that the higgs mechanism is realized in nature , thereby requiring the existence of at least one ( relatively ) light higgs boson . in this case the low - energy theory is renormalizable _ la _ dyson , the decoupling theorem remains valid , and the effective lagrangian is constructed out of operators respecting the @xmath20 symmetry linearly . in this scenario the virtual heavy physics effects can not affect dramatically the low - energy processes : the impact of new physics might become important only in those processes that are absent or very suppressed within the sm @xcite . on the other hand , another possibility ( the nondecoupling scenario ) arises if the higgs boson is very heavy or does not exist at all . there follows that the low - energy theory is nonrenormalizable due to the absence of the higgs boson . this class of new physics can be assumed to be responsible for the symmetry breaking of the electroweak sector . in this scenario the @xmath21 symmetry is nonlinearly realized@xcite . the lowest - dimension operators that induce the @xmath22 coupling have dimension six ( eight ) in the nonlinear ( linear ) realization . this means that any new physics effects arising from this coupling are likely to become more evident in the nonlinear scenario since in the linear one they are suppressed by higher powers of the new physics scale @xmath23 . therefore , in this work we will concentrate on the nonlinear scenario . furthermore , only those operators that respect the custodial @xmath24 and the discrete @xmath25 and @xmath26 symmetries will be considered . it turns out that the operators that violate the custodial symmetry are tightly constrained by the @xmath27 parameter . in the nonlinear scenario there are fourteen dimension - six operators that induce the @xmath22 coupling at tree level @xcite . this was discussed to a large extent in ref . @xcite and we will not dwell on this issue here . we rather focus on the lorentz structure induced for the @xmath1 coupling . in the unitarity gauge ( @xmath28 ) , there are only two independent lorentz structures for this coupling induced by dimension - six operators @xcite : @xmath29 where @xmath30 and @xmath31 . we have followed closely the notation introduced in @xcite . below we will proceed to compute the decay @xmath32 using the above effective interaction . the experimental limit on this decay will then be used to constrain the coefficients @xmath33 and @xmath34 . we now turn to outline the calculation of the decay width for @xmath35 , which is somewhat similar to the one presented in ref . @xcite for the rare decay @xmath36 in two higgs doublet models , with @xmath37 the @xmath38-odd neutral scalar . in ref . @xcite , the experimental bound on the rare @xmath35 decay was used to constrain the neutrino - photon interactions @xmath39 and @xmath40 . here we will make an analysis along the same lines but focus on the purely bosonic @xmath1 coupling , which contributes to the @xmath41 decay through the feynman diagram shown in fig . [ znngg ] . contribution from the effective @xmath1 coupling to the rare @xmath42 decay.,width=240 ] the 4-vectors of the participating particles will be denoted as follows @xmath43 . the feynman rule for the effective vertex @xmath44 is straightforwardly obtained from eq . ( [ eflag ] ) : @xmath45\bigg\}\end{aligned}\ ] ] where all the momenta are directed inward . the decay width can then be written as @xmath46 with @xmath47 and @xmath48 for @xmath49 and @xmath50 , respectively . by the usual method and after a lengthy calculation we can obtain the squared amplitude . it reads @xmath51 where we have introduced the definition @xmath52 with @xmath53 and @xmath54 . in eq . ( [ mcuad ] ) a factor of 3 is included in the denominator as we are averaging over the @xmath55 boson polarizations ; also , a factor of 2 has been introduced to account for two identical particles in the final state . the integration over @xmath56 and @xmath57 can be carried out straightforwardly with the aid of the following result @xcite @xmath58 where @xmath59 . once we are done with the integration over @xmath56 and @xmath57 , there still remains to integrate over @xmath60 and @xmath48 . to this end we will work in the center of mass frame of the @xmath55 boson . we find it useful to define the following variables @xmath61 , @xmath62 , and @xmath63 . the decay width can thus be expressed as @xmath64 where @xmath65 and @xmath66 it can be shown that the integration region @xmath67 is given by @xcite @xmath68 together with @xmath69 . after numerical integration we are left with @xmath70 with @xmath71 and @xmath72 . in addition , if lepton universality is assumed , eq . ( [ result ] ) is to be multiplied by 3 to account for all of the known neutrino species . from the lep-2 data , the l3 collaboration set the following limit on @xmath0 @xcite @xmath73 assuming that either @xmath74 or @xmath75 is dominant we obtain the following bounds @xmath76 which are weaker than those obtained at lep-2 from @xmath77 and @xmath78 production @xcite . however , it is important to note that the bounds based on the latter processes do not agree , as pointed out in ref . @xcite , which means that much work along these lines is still required . in general eqs . ( [ result ] ) and ( [ expbound ] ) yield an allowed area in the @xmath33 versus @xmath34 plane , as depicted in fig . [ area ] . allowed area ( gray region ) in the @xmath33 vs. @xmath34 plane from the experimental bound on the @xmath79 rare decay.,width=240 ] we can also take a different approach and instead of bounding the @xmath1 coupling , we may use the most stringent bounds on it to predict its contribution to the @xmath0 decay . from the most stringent experimental bound on the @xmath33 and @xmath34 coefficients , of the order of @xmath80-@xmath81 @xcite , it follows a limit on the contribution of the @xmath1 coupling to the @xmath0 decay : @xmath82 this indirect bound is above than the one found for the contribution of the neutrino - one - photon interaction @xmath39 , which is of the order of @xmath83 @xcite . in closing it is interesting to note that the @xmath1 coupling also contributes to the rare decay @xmath84 , for which an experimental bound has already been set @xcite . this rare decay mode also receives contributions from the quartic @xmath85 coupling . therefore it would be possible , in principle , to use this rare decay to bound such qngbcs . as far as the @xmath85 coupling is concerned , a tighter bound on it can be obtained from the three - body decay @xmath86 . the latter , together with the @xmath87 reaction , have been studied within the effective lagrangian approach @xcite and we will not repeat the same analysis here . from the result presented in ref . @xcite a bound on the effective @xmath85 vertex can be derived , which is of the same order of magnitude of the one obtained in this work for the @xmath1 coupling . finally we would like to emphasize that the importance of studying qngbcs is rooted in the fact that they have a different origin than tngbcs , i.e. they are induced by effective operators that do not induce any tngbc . in this work we have found a constraint on the @xmath1 coupling from the @xmath88 decay mode , which is weaker than the bounds derived from the analysis of @xmath77 and @xmath78 production at lep-2 . this is explained from the fact that the decay @xmath89 has a suppression factor due to the virtual @xmath55 boson propagator , which suffers less suppression when the initial @xmath55 boson is allowed to be off - shell . m. acciarri _ et al . _ , b 478 , 39 ( 2000 ) ; 490 , 187 ( 2000 ) ; p. achard _ et al . _ , b 540 , 43 ( 2002 ) ; 527 , 293 ( 2002 ) ; g. abbiendi _ et al . _ , b 471 , 293 ( 1999 ) ; w. j. stirling and a. werthenbach ," +"single - ended optical fiber link characterization techniques have been a point of major focus since the late seventies when barnosky and others demonstrated that , by measuring the rayleigh backscattered signal from a pulse sent into the optical fiber , one could extract its physical properties such as attenuation coefficient and eventual power losses along its length @xcite . presently , different techniques for optical fiber characterization are available and standardized such as the optical time domain reflectometry ( otdr ) and frequency domain reflectometry ( ofdr ) @xcite . in any case , embedding any of these fiber - monitoring techniques in passive optical networks ( pon ) systems remains a challenge in terms of technology and cost - effectiveness not to mention the in - service monitoring paradigm @xcite . otdr makes use of high - power short optical pulses while measuring the rayleigh backscattered power as a function of time , its spatial resolution being defined by the duration of the optical pulse . ofdr may present two different flavors : coherent - ofdr ( c - ofdr ) , where the wavelength of a low - power continuous - wave coherent light source is swept and the heterodyne beat between the backscattered light signal and a reference reflection is measured ; and incoherent - ofdr ( i - ofdr ) , where a radio - frequency optical sub - carrier frequency is swept and , once again , a heterodyne beat between the detected backscattered signal and the modulating signal is measured . in both c- and i - ofdr , the spatial profile of the fiber is obtained from the fourier transform of the detected ofdr signal and the frequency range covered by the optical sweep limits its resolution . a very complete review of frequency domain optical network analysis , where the distinctions between c- and i - ofdr , their pro s , and con s are highlighted , may be found in @xcite . in terms of the apparatus necessary to guarantee reasonable high dynamic range and spatial resolution , otdr and ofdr differ greatly : on one hand , otdr must employ high bandwidth detection in order to increase spatial resolution since it is directly proportional to the probe pulse width , which , in general , has a trade off associated to a reduction of dynamic range since the energy is reduced along with pulse duration @xcite . frequency domain techniques usually make use of a frequency sweep at the source level and a fourier transform which provides the conversion from frequency to distance based on the sweeping rate . c - ofdr does not require high frequency response detectors since the detection is performed in the base band , but highly coherent sources are needed in order to achieve long range in optical fibers @xcite . on the other hand , the resolution of the frequency domain techniques , such as in i - ofdr , are given by the frequency sweep range , which imposes high bandwidth detection bringing up again the trade - off between resolution and dynamic range . high resolution is bandwidth demanding whereas high sensitivity imposes low resolution @xcite . incoherent ofdr measurements have been extensively studied in @xcite and rayleigh scattering has been successfully observed . the mathematical model developed in the time - domain concludes that the amplitude of the rayleigh scattering signal within an optical sub - carrier is inversely proportional to the sub - carrier s frequency ( hereby referred to as the _ high - frequency issue _ ) , which complicates signal acquisition when there is a requirement for high spatial resolution . recently , however , urban _ et al . _ @xcite showed that fiber monitoring can be accomplished in a sub - carrier multiplexed pon ( scm - pon ) context by measuring the rayleigh backscattered signal from a high - frequency ( up to 220mhz was reported ) inside a 20mhz band , which translates into a 10 meter achievable spatial resolution . the method resembles the step - frequency method presented in the late eighties by nakayama _ @xcite however , instead of disregarding the rayleigh backscattering and focusing on reflective events as in the latter , the effect of the backscattered signal was exploited at its full potential in @xcite . an alternative to the _ high - frequency issue _ of i - ofdr rayleigh backscattering measurements would be to perform the fiber monitoring in the low - frequency range , up to a few hundred kilohertz , where the @xmath0 hindering effect is not too harsh . the downside of this approach would be the diminished spatial resolution associated to one s measurement when the fourier transform of the acquired signal is taken . in order to overcome this preclusion and , at the same time , improve the signal - to - noise ratio at the receiver s end , we tackle the fiber characterization procedure in a different manner : instead of taking the fourier transform we attempt to fit the resulting backscattered signal with its associated mathematical model , which , in order to simplify its description , we model as a spatial - dependent phasor and arrive at an equivalent expression to the one found in @xcite , but in the frequency domain . by employing a fitting procedure developed in matlab@xmath1 , we show that not only a fiber fault s position but also its magnitude can be identified with high precision . the remainder of the article is laid out as follows . in section [ expset ] , we present the experimental apparatus , its characteristics , and limitations . section [ matmodel ] attempts to develop an intuitive mathematical model associating the acquired signal to an analytic frequency - dependent function . the relation between a fault s magnitude and the signal s amplitude as well as the limitation associated to eventual reflection events along the fiber are also discussed . the experimental results are presented and discussed in section [ results ] , section [ impact ] presents the technique s limitations and the impact on in - service data transmission , and section [ conclusion ] concludes the article and details our future points of investigation . the experimental apparatus is rather simple and a block diagram identifying its main structures is presented in fig . [ fig : setup ] . in order to achieve even higher signal - to - noise ratio , we perform the detection in a low - frequency lock - in amplifier which is also responsible for generating the modulating optical sub - carrier tone . according to @xcite , forcing the measuring time to be higher than the round trip time of the sub - carrier signal inside the fiber is equivalent to measuring the steady state response of the system for a given frequency . this way , determining the relative values of magnitude and phase of the backscattered signal for each frequency value in the range is the same as tracing the system s transfer function . by setting the time constant of the lock - in amplifier to @xmath2 milliseconds is sufficient to account for the steady state measurement of any practical optical fiber link available ( shorter than @xmath3 kilometers ) and translates into reasonable measuring periods ( less than 5 minutes ) given that the frequency is swept from 100 hz to 100 khz in 100 hz steps . furthermore , the sweep time is long enough so that each measurement is acquired after one time constant of the lock - in amplifier , which was verified to be short enough to avoid dragging effects on the measured curve . the noise level at each step frequency measurement is @xmath4 for the sr530 analog lock - amplifier model employed in the measurements . hz to @xmath5 khz ) modulates the laser diode . the backscattered signal corresponding to the base tone is amplified by the low - frequency photodetector s pre - amplifier and sent to the lock - in amplifier . ] the lock - in amplifier generates the sweeping tone which falls inside the 100 hz to 100 khz band and is responsible for determining the relative amplitude and phase parameters of the backscattered signal which composes the system s transfer function . note , however , that if we take into account the transfer functions of each element apart from the fiber itself and then proceed to calibrate the resulting signal , we get rid of the contribution from the laser diode , the photodetector , the electronic amplifier , and the lock in , and are left with the fiber s transfer function . the system s calibration is achieved by inducing a reflective event at port @xmath6 of the optical circulator and measuring the system s response . the laser diode operates linearly within a @xmath7 range centered at @xmath8 bias current . the low - frequency tone with angular frequency @xmath9 ( @xmath10 ) at full modulation depth has a peak voltage amplitude of @xmath11 since the laser diode s input impedance is @xmath12 . the optical signal launched into the fiber under test ( assumed to have a length @xmath13 ) will carry its modulation properties as will the backscattered signal . upon detection , the modulated backscattered signal will produce an electrical signal with current amplitude proportional to the field amplitude squared and the detector s detectivity @xcite . if we disregard the dc term after the detection , which is a good assumption since we are performing a steady state matched detection at lock - in amplifier , the electric signal entering the lock - in amplifier as a function of time can be written as @xmath14 , where @xmath15 is the detected signal s current amplitude and @xmath16 is the photodetector s detectivity . for simplicity purposes , we first neglect possible reflective events throughout our mathematical modeling so the total signal intensity arriving at the lock - in amplifier is given solely by the incoherent sum of light scattered from all positions of the fiber . such reflective events , associated to defective connectors and fresnel reflections due to an abrupt change in the refractive index , will be input to the model after these first considerations are laid out . if we assume the distribution of scattering centers is uniform along the fiber , we can write the signal entering the lock - in amplifier as a spatial - dependent phasor in integral form : @xmath17 where @xmath18 is the launched probe signal power at the fiber s input and @xmath19 is the rayleigh scattering coefficient , assumed to be constant along the whole fiber length . @xmath20 is the complex wave vector of the modulating signal which includes the fiber s attenuation coefficient @xmath21 in its imaginary part . @xmath22 is the group index of refraction of the fiber . we now suppose a faulty _ non - reflective _ event at position @xmath23 induces an optical loss @xmath24 , where @xmath25 . to take into account this fault , we re - write eq . [ eq : fullfiber_intform ] as : @xmath26 where the first integral corresponds to power being scattered back from the portion of the fiber before the loss event whereas the second integral corresponds to power scattered back from the last portion of the fiber , after the fault event at @xmath23 . the loss factor @xmath24 appears multiplying the second integral twice ( hence , squared ) due to the fact that light passes two times through the fault in its round trip and we assume that the transmission coefficient is symmetric ( it is the same whether light is propagating from the generator to the load or in the opposite direction ) . to simplify the expression" +"determination of the absolute values of neutrino masses represents a most difficult problem from an experimental point of view . evidence in favour of non - zero neutrino masses and oscillations obtained in most of the relevant neutrino experiments has made the physics of massive neutrinos a frontier field of research in particle physics and astrophysics . all the existing terrestrial and astrophysical data indicate that the neutrino masses are by many orders of magnitude smaller than those of other experimentally measured lepton and hadron masses . such a low value is the most relevant reason for it being extremely difficult to extract the values of neutrino masses from experimental measurements , either directly or indirectly . this is the main reason why most experimental papers only report a confidence limit interval for such values . in this paper we report an upper limit for the muon neutrino mass obtained by measuring the radii of curvature of the pion and muon tracks of an event , in which a pion decays into a muon and a muon neutrino , recorded during the runs of the ps 179 experiment at the beam of antiprotons of lear at cern . the ps 179 experimental apparatus was designed and built for the study of antiproton interactions with light and medium - light nuclei at the lear facility of cern . the aim of the research was an experimental study of the interaction of antiprotons with nuclei at low energies . the results obtained provided information on the fundamental nucleon - antinucleon forces , on the interaction of antiprotons with clusters of bound nucleons , on the distribution of nuclear matter , and on properties of highly excited nuclear matter , as well as a restriction on the possible amount of antimatter present in the early universe @xcite . in order to make the most of the information available on all the secondary charged particles produced in the reactions , in designing the experiment a choice was made of the visualization detection technique , and a self - shunted streamer chamber placed in a magnetic field such a detector had many advantages . it was a low density gas target , and , at the same time , it was triggerable , offering a 4@xmath54 acceptance in which highly luminous localized particle tracks could be obtained @xcite . the low density of the target medium , i.e. of the streamer chamber filling gas at 1 atm pressure , allowed to reveal long charged particle ranges and nuclear fragments . the experimental apparatus used is sketched in figure [ figure 1 . ] . the detector provided stereo pictures of the sensitive chamber volume . the details of the experimental apparatus have been given in ref . @xcite where a more complete description of the characteristics and the performances of all the components of the setup can be found . the runs of the ps 179 experiment were carried out with the streamer chamber filled at 1 atm with different gaseous targets : @xmath55 , @xmath56 , @xmath0 . the stereo pictures of events , recorded on films during the runs , were reprojected onto measuring tables for visual scanning . the events were measured with a digitized coordinatometer directly on the scanning tables . in one of the photographs of the @xmath0 run , the beautiful event , reproduced in figure [ figure 2 . ] , was observed . it represents a multi - nucleon annihilation @xcite of an antiproton with a @xmath0 nucleus ( see , also , figure 11 of ref . @xcite ) . from the vertex of the interaction there `` evaporated '' a ( 1.98@xmath570.02 ) mev positive pion . from the two vertices of the pion and muon decays , three neutrinos were emitted : from the first a muon neutrino and from the second an electron neutrino and a muon antineutrino . the peculiarity of the event consists in the noticeable length of the @xmath1 and @xmath3 tracks and in their coplanarity . the temperature of the streamer chamber filling gas was 289 k , the pressure atmospheric , and the target density ( 0.80@xmath570.01 ) mg/@xmath58 . the magnetic field was 0.8 t ( @xmath59b / b = 10@xmath60 ) . the tracks have been measured at jinr with a microscope - digitizer . the recent acquisition of such a microscope made it possible to newly measure the @xmath61e event , reconstructing and digitizing tracks with a very high accuracy . the pion track has been digitized at 347 points , the muon track at 2037 points and the positron track at 180 points . all the measured points are approximately equidistant . each point has been measured with a precision of about @xmath62 mm . the coordinates of all track points have been used to deduce the radii of curvature and the ranges . each particle transfers energy by ionization to the surrounding medium and slows down along its path . a fortran code has been written to estimate the radii of curvature varying along the tracks and the total track lengths . for each track the best - fit circles were calculated taking into account a fixed number n of points . starting from the first measured point and taking the subsequent n-1 points , the first radius was calculated . if n is the total number of points measured along a track , shifting the n points by one along the track , the subsequent n-(n-1 ) radii have been calculated . we have chosen n = 25 ( a value statistically significant in order to ensure fit stability ) for each track . program circle of the cern library @xcite has been included into the code to calculate the best - fit radii of curvature along the tracks . the initial pion momentum was estimated from all measured points along the first 10 cm of its track , since the range - energy relations ( and tables ) for neon at ntp reveal the energy loss of a 2.00 mev pion to be negligible for path lengths not exceeding 10 cm . the average radius of curvature of the first 10 cm of the pion track , obtained best - fitting the track with a circle , is corresponding to a momentum ( p = 300br ) of ( 23.50@xmath570.15 ) mev / c . the agreement between the value of the initial pion momentum and its measured path range of ( 471.5@xmath570.8 ) mm , shows that the pion decay occurred with a momentum of ( 0.05@xmath570.10 ) mev / c . the same parameters have been measured for the muon track . the initial muon momentum was estimated from all measured points along the first 12 cm of its track , since , also in this case , the range - energy relations ( and tables ) for neon at ntp reveal the energy loss of a 5.00 mev muon to be negligible for path lengths not exceeding 12 cm . the value of the average radius of curvature of the first 12 cm of the muon track , obtained with a best - fit circle , is , corresponding to a momentum of ( 29.90@xmath570.15 ) mev / c . in this case , also , the agreement between the initial muon momentum and its measured path range of ( 2616.0@xmath570.8 ) mm shows that the muon decayed with a momentum of ( 0.6@xmath570.6 ) mev / c . the positron was emitted with a momentum of ( 46.80@xmath570.08 ) mev / c . the angle between the tangent lines of the pion and muon trajectories at the decay vertex was ( 163.0@xmath571.0 ) deg , and the angle between the muon and positron tracks was ( 107.0@xmath571.0 ) deg . it should be pointed out that the @xmath61e event of figure [ figure 2 . ] is the only existing of this kind whose parameters could be all measured with high precision . for kinematic and dynamic analysis of the reaction , the relations of conservation of momentum and energy have been used . the pion decay occurs in a plane . at the decay vertex , the muon and the neutrino have flight directions at angles @xmath63 and @xmath64 to the pion flight direction , respectively . for momentum conservation @xmath65 @xmath66 for energy conservation @xmath67 combining algebraically the three relations one obtains @xmath68 and @xmath69 from which one can obtain the square of the neutrino mass @xmath70 where only the @xmath71 factor can approach zero and where @xmath72 and always positive . it is clear that from relation ( [ m2 ] ) , given the masses of the pion and muon , the momenta of the pion and muon , and the angle @xmath63 , one can calculate the square of the neutrino mass as a function of the above - mentioned parameters . a point or an interval estimator of an unknown parameter is any statistic whose value is a meaningful guess for the value of the unknown parameter which is assumed to have some fixed value @xcite . sometimes experimental measurement may yield non - physical values , when the parameter value is near zero @xcite . in these cases a statistical procedure can be used for estimation of the upper limit value of the parameter . in the present analysis the neutrino mass is the parameter to be estimated . the upper limit of the mass of the muon neutrino @xcite has a value near zero , and is about seven orders of magnitude smaller than the values of the measured experimental quantities of the @xmath54@xmath2@xmath73@xmath74 decay . in determining such a mass in an unbiased approach one would necessarily expect a non - physical result for @xmath75 to occur half of the time this happens because of the uncertainties of the experimental values of the physical quantities . one should then make statistical inferences from observation of the squared mass @xmath76m@xmath77 when @xmath75 is negative or near the non - physical region . @xmath59m@xmath77 is the standard deviation . it is possible to choose a `` classical '' confidence level _ p _ for the squared mass such that the corresponding classical confidence limit @xmath78 is in the physical region . when the variable @xmath79 has a gaussian distribution the upper limit is @xmath80 at a p@xmath7 confidence level , where @xmath81 = 1.036 , @xmath82 = 1.282 , @xmath83 = 1.645 and @xmath84 = 1.960 ( see ref . @xcite ) . the classical confidence limit satisfies the probability statement @xmath85 this statement says that @xmath78 has the probability _ p _ of being larger than the true value ( @xmath86 ) , whatever @xmath86 really is . it means that , if one repeats the experiment many times , and each time one recalculates the value of @xmath78 , then in @xmath87 of the cases @xmath78 will be greater than the true value @xmath86 . to obtain an interval estimate for the muon neutrino mass from our measurement of the scattering angle and of the momenta of the two charged particles of the decay , a statistical procedure has been applied . it takes into account the measured pion and muon momenta and the angle between them . these are distributed with gaussian p.d.f.s with means equal to the measured values and standard deviations equal to the corresponding measured uncertainties . a code has been written . using the monte carlo method a set of @xmath88 decays has been generated . each element of the set has been obtained extracting at random the momenta of the pion and of the muon , and the angle between the two particles assuming the mass values of @xmath89 = ( 139.57018@xmath570.00035 ) mev and @xmath90 = ( 105.658369@xmath570.000009 ) mev , as given in ref . the three variables were extracted" +"aerosol particles have a direct and indirect impact on the earth s climate . one of the most important physical properties of aerosol particles is their size , and the concentration of particles in terms of their size is referred to as the particle size distribution . an important characteristic of these data is that because aerosol particles are governed by formation and transformation processes they tend to form well distinguished modal features . investigating these features provides an understanding of the dynamic behaviour of aerosol particles , their effect on the climate and their association with adverse health effects . this type of data is increasingly being measured on a regular basis , with the potential to provide more detailed information than , for example , measurements of particle mass concentrations such as pm10 or pm2.5 , traditionally used for regulatory purposes [ @xcite ] . the most common approach for representing particle size distributions is by treating the size distribution at any time point as a set of individual typically normal distributions or modes [ @xcite , @xcite ] . in this formulation the estimation of particle size distributions is then analagous to a finite parametric mixture model problem at each time point . while interest is in the representation of the particle size distribution as a mixture at each time point , it is also of interest to describe how this distribution evolves over time . to better understand aerosol dynamic processes , a feature of the measurements of particle size distributions is that they are often collected at regular points in time , and often at quite small time intervals ( e.g. , every 10 minutes ) . in this setting , parameters of the mixture model at each time point are likely to be correlated with neighboring time points and useful information about the parameters may be gained by incorporating this information in estimation . the standard setting in which mixture models have been applied has largely been for independent random samples [ @xcite ] , but literature is developing for situations in which the data are spatially and/or temporally structured [ @xcite , @xcite , @xcite , @xcite , @xcite , @xcite ] . the development has largely been driven by the increasing availability of information in a wide variety of applications . an example includes analysing images ( cat scan ) of sheep over time in which interest is in changes to the composition of fat , bone and tissue [ @xcite ] . in @xcite interest is in cell fluorescent imaging tracking modelled using a dynamic spatial point process and a mixture representation for the different intensity functions observed . for the air pollution example considered in this paper , we are interested in a mixture representation using a missing data approach , in which the components themselves can be interpreted as potential substrata of the data and for which further interest is in their behaviour over time . in particular , we are interested in the evolution of the parameters of the components over time , which in the case of the particle size distribution data is able to reveal important information about the number and change in size of particles for particular modes along with a measure of their variation . this information can then be used to better understand the potential variables affecting the dynamic behaviour of each mode ( e.g. , from local effects such as combustion from petrol and diesel vehicle engines , construction activity , wind speed , temperature , etc . , and regional effects ) , which are likely to vary substantially between modes , and provide for a more accurate risk assessment of potential effects on adverse health outcomes ( e.g. , respiratory illnesses ) . popular recent approaches that allow for the correlated nature of the parameters in a mixture setting , both within and across epochs , include dependent dirichlet process mixture models ( ddpm ) and ( spatial ) dynamic factor models ( sdfm ) [ @xcite , @xcite , @xcite , @xcite , @xcite ] . while these approaches are appealing in the context of our case study , they do have some drawbacks . importantly , interpretation of component parameters is less straightforward under the ddpm , and the sdfm typically requires relatively long time series [ @xcite ] . an alternative that we consider here is the use of informative priors at each epoch in a finite parametric mixture setting , where the information required at each epoch is obtained from neighbouring epochs . this has appeal both in terms of a general bayesian learning framework and in terms of interpretability of the mixture components and weights , which is important in our application . moreover , while some of the methods developed for mixture models in the spatial setting [ e.g. , @xcite ] can potentially be adapted for use in a time series setting , the influence or choice of informative priors in a time series framework and the implications in different data environments have largely not been examined . in this paper we explore three different informative priors for estimation of mixtures where the data are highly correlated , and all parameters in the mixture are allowed to vary . different simulated data sets , with features similar to actual particle size distribution data , are used to highlight the influence of using informative priors and to identify situations where placing informative priors may not be beneficial . the paper is structured as follows . in section [ secpsddata ] we briefly describe particle size distributions and provide an illustration with actual data . in section [ secmixture ] we outline the finite parametric mixture model setup for a single time point and then outline the three approaches to estimation of a mixture model at multiple time points . section [ secres ] presents results on the performance of the approaches on several simulated data sets and actual data , and we conclude in section [ secdiscussion ] with some discussion and possibilities for further work . -axis : @xmath0 ) ] . the black ( overall ) and red ( components ) lines show the inferred density from estimation using . ] figure [ figplotexamplefit ] shows an example of particle size distribution data for one measurement or time point . the histogram shows the number of particles @xmath1 per cubic centimeter binned by particle size , with the horizontal axis representing the natural logarithm of the particle diameter in nm [ @xmath2 . the histogram is normalised , so that its total area equals 1 . -axis and ( bottom ) @xmath3-axis is on the @xmath4 scale [ i.e. , @xmath5 . ] because aerosol particles are charged , their size can be determined from their electrical mobility [ @xcite ] and a common instrument that utilises this principle is the differential mobility particle sizer ( dmps ) [ @xcite ] . in this study we present , as an example , the aerosol particle evolution before , during and after a new particle formation event at a boreal forest in southern finland ( figure [ figplotoneday ] ) . this data set was selected as it provides a wide ranging representation of modes for particle size distributions [ @xcite ] . because aerosol particles are governed by formation and transformation processes , they tend to form well distinguishable modal features . for example , during background conditions in the boreal forest the particle number size distribution of fine aerosols [ diameter @xmath62500 nm ( @xmath4 , 7.82 ) ] is bimodal : an aitken mode [ below 100 nm ( @xmath4 , 4.60 ) ] and an accumulation mode ( over 100 nm ) . during a new particle formation event a new particle mode , which is commonly known as a nucleation mode , is formed in the atmosphere with geometric mean diameter below 25 nm ( @xmath4 , 3.22 ) . however , in the urban atmosphere aerosol particles are more dynamic because of the different types and properties of sources of aerosol particles and may show more than three modes . typically the number concentrations of aerosol particles in the urban background can be as high as @xmath7 @xmath8 and close to a major road they often exceed @xmath9 @xmath8 [ @xcite ] . in this section we briefly describe the mixture model , outline a two stage approach to estimation of parameters over time , and describe three types of priors for temporal evolution of the parameters . the density of data ( @xmath10 ) at a given time period may be represented by a finite parametric mixture model @xmath11 where @xmath12 is the number of components in the mixture , @xmath13 represents the probability of membership of the @xmath14th component ( @xmath15 ) , and @xmath16 ) is the density function of component @xmath14 which has parameters @xmath17 . let @xmath18 indicate the observed data index . as component membership of the data is unknown , a computationally convenient method of estimation for mixture models is to use a hidden allocation process and introduce a latent indicator variable @xmath19 , which is used along the lines of a missing variable approach to allocate observations @xmath20 to each component [ @xcite ] . in this paper we adopt the common assumption of fitting normal distributions to aerosol particle size distribution data [ @xcite ] . as psd data are often measured with a definite lower and upper bound for the size of the particles , we introduce a slight modification and assume that the data follow a truncated normal distribution . as is commonly assumed , we take the data ( @xmath10 ) to be the @xmath4 of particle diameters ( nm ) , and the parameters ( @xmath17 ) for each component are the mean ( @xmath21 ) and variance ( @xmath22 ) . the number of components @xmath12 is also assumed to be unknown . in the first stage of the temporal analysis , for each time period we implemented a reversible jump markov chain monte carlo ( rjmcmc ) algorithm [ @xcite ] . although this algorithm is easily fit at a single time point , the use of rjmcmc for mixture models with temporal data requires significant preprocessing with respect to mixing coverage and convergence , as well as postprocessing to provide adequate summary statistics and between time component mapping . as an alternative , we considered a two - stage approach . in the first stage , the number of components was estimated at each time point using rjmcmc . in the second stage , we fixed the number of components ( @xmath12 ) to the maximum observed at any time point and independently estimated the parameters of the mixture model ( @xmath23 , @xmath24 and @xmath25 ) for each time point using a mcmc sampler algorithm . details of the mcmc scheme used for the different cases are given below . as we do not observe all of the components in every time point , we allow component weights to be `` effectively '' zero [ @xmath26 if required [ for details on the asymptotic behaviour of the posterior distribution using this approach see @xcite ] . estimation of parameters of the components that are effectively `` empty '' under this criterion will then essentially be governed by their respective prior information . for the results to follow in section [ secres ] we thus only plot the parameters of components which are not `` empty '' . priors for the first stage of the analysis were @xmath27 where @xmath28 , @xmath29 , @xmath30 , @xmath31 , @xmath32 , @xmath33 , @xmath34 are hyperparameters . for the second stage , priors were @xmath35 where again @xmath36 and @xmath37 are hyperparameters , detailed below . the prior for @xmath23 and @xmath38 could" +"in economics , finance , medical sciences , ecology , engineering , and many other branches of sciences , one often encounters problems which are influenced by event - driven uncertainties . for example , in finance , the unpredictable nature of important events such market crashes , announcements made by central banks , changes in credit ratings , defaults , etc . might have sudden and significant impacts on the stock price movements . stochastic differential equations ( sdes ) with jumps , or more precisely sdes driven by lvy noise , have been widely used to model such event - driven phenomena . the interested reader may refer , for example , to @xcite and references therein . many such sdes do not have explicit solutions and therefore one requires numerical schemes so as to approximate their solutions . over the past few years , several explicit and implicit schemes of sdes driven by lvy noise have been studied and results on their strong and weak convergence were proved . for a comprehensive discussion on these schemes , one could refer to @xcite , and references therein . it is also known , however , that the computationally efficient explicit euler schemes of sdes ( even without jumps ) may not convergence in strong ( @xmath0 ) sense when the drift coefficients are allowed to grow super - linearly , see for example @xcite . the development of tamed euler schemes was a recent breakthrough in order to address this problem ; one may consult @xcite as well as @xcite and references therein for a thorough investigation of the subject . in this article , we propose explicit tamed euler schemes to numerically solve sdes with random coefficients driven by lvy noise . the taming techniques developed here allow one to approximate these sdes with drift coefficients that grow super - linearly . by adopting the approach of @xcite , we prove strong convergence in ( uniform ) @xmath0 sense of these tamed schemes by assuming one - sided local lipschitz condition on drift and local lipschitz conditions on both diffusion and jump coefficients . moreover , our technical calculations are more refined than those of @xcite in that we develop new techniques to overcome the challenges arising due to jumps . in addition , explicit formulations of the tamed euler schemes are presented at the end of section 3 for the case of sdes driven by lvy noise which have non - random coefficients . to the best of the authors knowledge , the results obtained in this article are the first for the case of super - linear coefficients in this area . moreover , the techniques developed here allow for further investigation of convergence properties of higher order explicit numerical schemes for sdes driven by lvy noise with super - linear coefficients . as an application of our approach which considers random coefficients , we also present in this article uniform @xmath0 convergence results of explicit tamed euler schemes for the case of stochastic delay differential equations ( sddes ) driven by lvy noise . the link between delay equations and random coefficients utilises ideas from @xcite . the aforementioned results are derived under the assumptions of one - sided local lipschitz condition on drift and local lipschitz conditions on both diffusion and jump coefficients with respect to non - delay variables , whereas these coefficients are only asked to be continuous with respect to arguments corresponding to delay variables . it is worth mentioning here that our approach allows one to use our schemes to approximate sddes with jumps when drift coefficients can have super - linear growth in both delay and non - delay arguments . thus , the proposed tamed euler schemes provide significant improvements over the existing results available on numerical techniques of sddes , for example , @xcite . it should also be noted that , by adopting the approach of @xcite , we prove the existence of a unique solution to the sddes driven by lvy noise under more relaxed conditions than those existing in the literature , for example , @xcite whereby we ask for the local lipschitz continuity only with respect to the non - delay variables . finally , rate of convergence results are obtained ( which are in agreement with classical literature ) when the local lipschitz continuity assumptions are replaced by global and , in addition , the drift coefficients satisfy polynomial lipschitz continuity . similar results are also obtained for delay equations when the following assumptions hold - ( a ) drift coefficients satisfy one - sided lipschitz and polynomial lipschitz conditions in non - delay variables whereas polynomial lipschitz conditions in delay variables and ( b ) diffusion and jump coefficients satisfy lipschitz conditions in non - delay variables whereas polynomial lipschitz conditions in delay variables . this finding is itself a significant improvement over recent results in the area , see for example @xcite and references therein . we conclude this section by introducing some basic notation . for a vector @xmath1 , we write @xmath2 for its euclidean norm and for a @xmath3 matrix @xmath4 , we write @xmath5 for its hilbert - schmidt norm and @xmath6 for its transpose . also for @xmath7 , @xmath8 denotes the inner product of these two vectors . further , the indicator function of a set @xmath9 is denoted by @xmath10 , whereas @xmath11 $ ] stands for the integer part of a real number @xmath12 . let @xmath13 be the predictable sigma - algebra on @xmath14 and @xmath15 , the sigma - algebra of borel sets of a topological space @xmath16 . also , let @xmath17 be fixed and @xmath18 denote the set of non - negative measurable functions @xmath19 on @xmath20 $ ] , such that @xmath21 . finally , for a random variable @xmath22 , the notation @xmath23 means @xmath24 . let us assume that @xmath25 denotes a probability space equipped with a filtration @xmath26 which is assumed to satisfy the usual conditions , i.e. @xmath27 contains all @xmath28-null sets and the filtration is right continuous . let @xmath29 be an @xmath30valued standard wiener process . further assume that @xmath31 is a @xmath32finite measure space and @xmath33 is a poisson random measure defined on @xmath31 with intensity @xmath34 ( in case @xmath35 , one could consult @xcite ) . also let the compensated poisson random measure be denoted by @xmath36 . let @xmath37 and @xmath38 be @xmath39-measurable functions which respectively take values in @xmath40 and @xmath41 . further assume that @xmath42 is @xmath43-measurable function which takes values in @xmath44 . also assume that @xmath45 and @xmath46 are fixed constants satisfying @xmath47 . we consider the following sde @xmath48 almost surely for any @xmath49 $ ] with initial value @xmath50 which is an @xmath51-measurable random variable in @xmath40 . for notational convenience , we write @xmath52 instead of @xmath53 on the right hand side of the above equation . this does not cause any problem since the compensators of the martingales driving the equation are continuous . this notational convention shall be adopted throughout this article . in this article , we use @xmath54 to denote a generic constant which varies at different occurrences . the proof for the following lemma can be found in @xcite . [ lem : maximal : inequality ] let @xmath55 . there exists a constant @xmath56 , depending only on @xmath57 , such that for every real - valued , @xmath58measurable function @xmath19 satisfying @xmath59 almost surely , the following estimate holds , @xmath60 it is known that if @xmath61 , then the second term in can be dropped . let @xmath62 denotes the class of non - negative predictable processes @xmath63}$ ] such that @xmath64 for almost every @xmath65 . for the purpose of this section , the set of assumptions are listed below . [ as : growth : rc : eu ] there exists an @xmath66 such that @xmath67 almost surely for any @xmath68 $ ] and @xmath69 . [ as : locallip : rc : eu ] for every @xmath70 , there exists an @xmath71 such that , @xmath72 almost surely for any @xmath68 $ ] whenever @xmath73 . [ as : continuity : rc : eu ] for any @xmath49 $ ] and @xmath65 , the function @xmath37 is continuous in @xmath1 . the proof for the following theorem can be found in @xcite . [ thm : eu : rc ] let assumptions a-1 to a-3 be satisfied . then , there exists a unique solution to sde . we make the following assumptions on the coefficients of sde . [ as : initial : rc : mb ] for a fixed @xmath74 , @xmath75 . [ as : growth : rc : mb ] there exist a constant @xmath76 and a non - negative random variable @xmath77 satisfying @xmath78 such that @xmath79 almost surely for any @xmath68 $ ] and @xmath1 . [ as : growth : p : rc : mb ] there exist a constant @xmath76 and a non - negative random variable @xmath80 satisfying @xmath81 such that @xmath82 almost surely for any @xmath49 $ ] and @xmath69 . the following is probably well - known . however , the proof is provided for the sake of completeness and for the justification of finiteness of the right hand side when applying gronwall s lemma , something that is missing from the existing literature . [ lem : mb : rc ] let assumptions a-2 to a-6 be satisfied . then there exists a unique solution @xmath83}$ ] of sde and the following estimate holds @xmath84 with @xmath85 . the existence and uniqueness of solution to sde follows immediately from theorem [ thm : eu : rc ] by noting that due to assumption a-5 , assumption a-1 is satisfied . let us first define the stopping time @xmath86 , and notice that @xmath87 for @xmath88 . by it s formula , @xmath89 almost surely for any @xmath49 $ ] . by virtue of assumption a-5 and young s inequality , one can estimate the second , fourth and fifth terms of equation by @xmath90 further , since the map @xmath91 is of class @xmath92 , by the formula for the remainder , for any @xmath93 , one gets @xmath94 hence the last term of can be estimated by @xmath95 one substitutes the estimates from and in equation which by taking suprema over @xmath96 $ ] for @xmath97 $ ] and expectations gives @xmath98 here @xmath99 . by the burkholder - davis - gundy inequality , @xmath100 can be estimated as @xmath101 which on the application of young s inequality gives @xmath102 and then due to hlder s inequality and assumption a-5 , one has @xmath103 to estimate @xmath104 , one uses lemma [ lem : maximal : inequality ] to write @xmath105 which due to young s inequality , assumption a-5 and hlder s inequality implies @xmath106 for @xmath107 , by assumptions a-5 , a-6 and young s inequality , @xmath108 by substituting the estimates from - in , one has @xmath109 for any @xmath97 $ ] . in particular we obtain @xmath110 since it holds that @xmath111 by rearrenging in , we obtain @xmath112 from here we can finish the proof by gronwall s and fatou s lemmas . for every @xmath113 , let @xmath114 and @xmath115 are @xmath39-measurable functions which respectively take values in @xmath40 and @xmath41 . also , for every @xmath116 , let @xmath117 be @xmath43-measurable function which takes values in @xmath44 . for every @xmath116 , we consider a scheme of sde as defined below , @xmath118 almost surely for any @xmath68 $ ] where the initial value @xmath119 is an @xmath51-measurable random variable which takes values in @xmath120 and function @xmath121 is defined by @xmath122}{n}+t_0\end{aligned}\ ] ] for any @xmath68 $ ] . we make the following assumptions on the" +"many adsorption systems exhibit either complete wetting below the triple point or triple point wetting transitions . these behaviors are recognized to arise from strongly attracting substrate potentials and/or small mismatch of substrate / adsorbate lattice constants @xcite . less attractive potentials exhibit incomplete or nonwetting behavior at the triple point . there is considerable interest in the nature of such weakly attractive situations near and above this temperature @xcite . general arguments and model calculations of cahn @xcite and of ebner and saam @xcite in 1977 implied that systems which are nonwetting at the triple point ought to exhibit transitions to wetting at some temperature below the critical point . experimental confirmation of this proposal was not found until appropriate systems were identified . in 1991 , it was argued that alkali metals provide the weakest adsorption potentials of any surfaces for he atoms and therefore wetting transitions were expected for such substrates at tow temperature @xcite . this hypothesis was subsequently confirmed and the corresponding transition has since been studied in many laboratories @xcite . more recently , similar phenomena have been predicted and/or seen for h@xmath0 , ne , and hg on various surfaces @xcite . key theoretical questions arising from these studies involve the reliability of both the assumed adsorption potentials and the statistical mechanical description of the transition , as well as the effects of surface heterogeneity @xcite present in any real experiment . in the course of these investigations , cheng _ @xcite ( ccst henceforth ) posited a simple model which interprets the transitions in terms of a balance between the surface tension cost of producing a thicker film and the energy gain associated with the film s interaction with the surface , v(z ) @xcite . there results an implicit equation for the wetting temperature ( t@xmath3 ) : @xmath4 @xmath5 where @xmath6 and @xmath7 are the number densities of the adsorbate liquid and vapor at coexistence , @xmath8 is the surface tension of the liquid , and @xmath9 is the equilibrium distance of the potential . if one assumes a simple 3 - 9 form of the adsorption potential @xmath10 then the transition condition becomes @xmath11 ccst used this model to predict wetting transitions for a large number of specific systems . more recently , the same general approach was used by chizmeshya _ et al . _ ( ccz ) @xcite , who based their predictions on new _ ab initio _ adsorption potentials . the latter potentials differ from earlier potentials in several respects ; especially important are differences in values of the coefficient c of the van der waals asymptotic potential , resulting in significantly larger well depths d. there is indication that these revised potentials are more consistent with experimental data than are their predecessors . particularly striking is the improved agreement for @xmath12he contact angle @xcite and wetting temperature on cs , the most studied wetting transition to date @xcite . these predictions have also been tested by recent experiments of hess _ _ @xcite and simulations of ne on alkali metals and mg @xcite . in this paper , we extend the simulation studies to a larger family of systems for which the hypothesis is relevant . we focus here on the following question : assuming that v(z ) is known , does the ccst model correctly predict whether a specific adsorption system exhibits wetting at and above the triple temperature ? the outline of this paper is the following . section [ label.3.sec:method ] summarizes our simulation methodology and presents detailed results for several systems which yield fairly distinct adsorption behaviors . these include complete wetting for all t ( kr / mg and xe / mg ) , an anomalous wetting transition near the triple point ( kr / pmg ) , a prewetting transition line ( ar / mg ) somewhat above the triple temperature , and prewetting transitions characterized by the formation of very thick films ( for ar , kr and xe on li ) . here pmg is our own nomenclature for `` pseudo - magnesium '' , an ersatz surface which attracts kr atoms about 7% more strongly than mg itself @xcite . we also evaluate other hypothetical substrates in order to ascertain the triple point wetting threshold . in section [ label.3.sec:interpretation ] , we compare these findings with those obtained previously in simulations and/or experiments for inert gases on various surfaces @xcite . the simulation technique has been described in detail previously @xcite , so only a brief description is given here . for this study , isotherms for various model systems were calculated using the grand canonical monte carlo ( gcmc ) technique @xcite . for each isotherm , 6.8 million steps ( each step being an attempted creation , deletion , or displacement of a molecule ) were performed to reach equilibration and 4.5 million steps were performed in the data gathering phase . for some points near the transition regions , where the fluctuations are larger , the number of equilibration steps was increased to 20 million and 12 million steps were performed for data gathering . as in our previous work , the model for the atom - atom interaction is a lennard - jones 12 - 6 potential and the atom surface interaction is modeled using the potential described by chizmeshya _ these potentials can be characterized by four parameters for each system studied . a well - depth @xmath13 and distance @xmath14 are needed to specify the adsorbate lj potential and a well - depth @xmath15 and the van der waals constant @xmath16 specify the atom - surface potential . the values of these parameters used in this study are listed in table [ label.3.table:param ] . the parameters correspond to ne , kr , ar , and xe adsorbed on alkali and alkali earth metal surfaces . the surface labeled pmg ( pseudo magnesium ) was obtained when we attempted to simulate xe on li , but used the @xmath13 and @xmath14 values for kr instead of xe . this potential is similar to that of kr on a mg surface ; however , the kr / pmg distance of closest approach is 20% smaller and the well depth is about 7% weaker than estimated for kr on mg . while this potential does not correspond to a `` real '' system , we shall see that this small decrease in interaction strength significantly affects the wetting properties of the substrate / adsorbate system . in most cases the simulation cell had a height of h = 70 , with the metal surface forming the boundary at one end and a hard wall surface at the other . in xe / li and ar / li simulations we increased the height to 140 and 210 . the surface unit cell was taken to be @xmath17 giving a nominal monolayer coverage of roughly 100 atoms . periodic boundary conditions in these dimensions render the surface effectively infinite ; we used a fairly large cutoff ( 5@xmath14 ) to minimize long range corrections . for each system , we simulated adsorption isotherms over relevant temperature ranges from the triple point to the critical temperature . the results are shown in figures [ label.3.fig:xeli1]-[label.3.fig:krmg ] . of the systems studied the least attractive surface of the surface interactions are for the ar / li , kr / li and xe / li cases . in all of these , we see evidence of prewetting transitions and , based on our results , we report wetting temperature . for ar / li we estimate t@xmath18 k , for kr / li , t@xmath19 k and t@xmath20 k for xe / li . all @xmath21 are reported in table [ label.3.table:param ] . despite the fact that these systems are examples of prewetting transitions , there are some qualitative differences from the case ( say ne / mg ) where the wetting transition appears close to the triple temperature . figure [ label.3.fig:xeli1 ] shows a series of isotherms for xe / li from @xmath22 1.0 to 1.25 . the isotherm at 221 k ( the lowest @xmath23 ) shows nonwetting behavior , manifested as slight adsorption below saturated vapor pressure . the higher temperature isotherms however , show prewetting transitions below saturated vapor pressure , from which we estimate @xmath21 . the nature of the prewetting jump can be further characterized by the results in figures [ label.3.fig:xeli2 ] , [ label.3.fig:xeli3 ] , and [ label.3.fig:xeli4 ] , all at t=254 k. figure [ label.3.fig:xeli2 ] shows the dependence of the isotherm on the height @xmath24 [ @xmath25 ] of the simulation box . the rapid rise occurs at the same pressure , independent of box height . this is a clear indication that the transition is prewetting rather than capillary condensation . the detailed behavior is most easily understood by looking at the density profiles dependences on @xmath24 . figure [ label.3.fig:xeli3 ] shows these profiles at @xmath26 atm . note that the data for two largest boxes coincide but differ from those of the smallest box . evidently , this regime requires quite large values of @xmath24 in order to obtain reliable data ; this is not surprising because the compressibility of the system is particularly high at this transition as the slope of the isotherms suggest . the same phenomenon is even more dramatic for the case of a 1% higher pressure . as seen in figure [ label.3.fig:xeli4 ] , one must go to even larger @xmath24 ( @xmath27 ) in order to derive accurate adsorption data even though the liquid regime occupies only the region @xmath28 . while this sensitivity to @xmath24 and the details of the transition are quite interesting they are not the focus of this paper . suffice it to say that the density jumps discontinuously near @xmath29 atm , as seen in the different densities in figures [ label.3.fig:xeli3 ] and [ label.3.fig:xeli4 ] . we note one further point about these data which is that the film s density close to the surface is qualitatively similar to that on a relatively more attractive surface . there appears a quite large accumulation of adsorbate atoms in the region associated with the first layer . there is even a significant density maximum occurring where a dense second layer might occur . the latter is , however , preempted by the prewetting jump in the regime of temperature seen here . above the prewetting critical point , in contrast , one does expect such smooth film growth . as the relative strength ( @xmath30 ) of the surface interaction increases , ( ar on mg , kr on pmg ) the isotherms give evidence of wetting transitions . the results for ar on mg , ( shown in figure [ label.3.fig:armg ] ) indicate prewetting transitions at about 10% above the triple point ( t@xmath31 = 81 k ) . from these data , we estimate the wetting temperature to be 90 k for ar / mg with a prewetting critical temperature of 95 k. in figure [ label.3.fig:krpmg ] , the results for kr on pmg are shown . this system shows clear prewetting transitions below 128 k for all temperatures above the triple temperature ( estimated to be 116 k @xcite ) . although this is a fictitious system , it represents one of the first simulations of triple point wetting . the only other simulation of wetting in this region is the case of ne / mg which we reported in @xcite . finally , as the surface interaction strength further increases , one begins to see continuous growth for all t between the triple temperature and the critical point . this is evident in figure [ label.3.fig:krmg ] which shows isotherms for kr on mg . the isotherms were simulated at" +"one of the simplest mass sources in general relativity are _ cosmic strings_linear objects with a given linear mass density and a linear tension . cosmic strings arise as topological defects in various gauge theories ( see , e.g. , @xcite ) , or as a macroscopic variant of the fundamental strings ( e.g. , @xcite ) . thin cosmic strings can be phenomenologically described by conical singularities of the spacetime metric one - dimensional the angle around which is different than @xmath0 . the static straight thin cosmic string is thus represented by a locally flat spacetime with a conical singularity along an axis . the deficit angle is proportional to the linear mass density which is equal to the linear tension @xcite . a string with a deficit angle has a positive mass density and it is stretched ; a string with an excess angle has negative mass density and is squeezed . for an overview of physics of cosmic strings see , e.g. , @xcite and references therein ; for more recent developments see @xcite . beside the empty spacetime with a single string , cosmic strings appear in a wide variety of solutions of einstein equations . any axially symmetric spacetime can be trivially modified to contain a string on the axis of symmetry . however , there exist also solutions where the string play a key physical role as , for example , c - metric . here the string is a physical agent causing the motion of black holes see , e.g. , @xcite . in a wide class of boost - rotation symmetric spacetimes @xcite the strings accelerate even more general sources . in the 80 s the cosmic strings were considered as candidates for a mechanism of galaxy formation . this possibility was abandoned mainly because of inconsistencies with cosmic microwave background observations . recently , however , the interest in cosmic strings reappeared in the context of the scenarios of the superstring theory . these suggest the existence of macroscopic fundamental strings behaving as cosmic strings ( e.g. , refs . @xcite and references therein ) . there were also tentative hints of a detection of cosmic strings @xcite based on specific gravitational lensing effects , but the explanation in terms of cosmic strings was not confirmed by subsequent observations @xcite . in the case of a single straight thin string the curvature is localized only on the world - sheet of the string . such spacetime thus represents a very simple but non - trival example which can serve as a toy model for studying various phenomena due to curvature . in this paper we investigate the behavior of the electromagnetic field in the background of a non - charged cosmic string . in sec . [ sc : retgrfc ] we find the retarded green function and with its help we demonstrate the general behavior of the propagation of the electromagnetic field @xcite : the field propagates ( i ) along null geodesics ( on the light cone of the source ) , and ( ii ) it is scattered on the curvature ( so - called term of the field ) . in our case the field propagates on the deformed light cones of the source and it is scattered on the cosmic string . in sec . [ sc : coulomb ] we use the retarded green function to derive the electric field of the static monopole and dipole sources . we obtain the field equivalent to that of ref . @xcite , which was derived by a different method . we also recover that the source is self - interacting : a monopole charge is repelled from the string by its own field , a dipole is forced to align the string . a magnetic field of the current flowing along the line parallel with the string is derived in sec . [ sc : magfield ] . in secs . [ sc : farfield ] and [ sc : homfield ] we study the behavior of the electric field of strong static charges at large distances and near the string . we find an interesting effect : the asymptotic field has a different monopole structure from that in empty space , and the field of large charges which are localized far from the string is suppressed near the string . the field which would be nonvanishing and homogeneous in an empty space is expelled from the region near the string . it means that the string its neighborhood from the influence of distant sources . spacetime of a cosmic string is described by the flat metric @xmath1 with a deficit angle around the string ( see , e.g. , @xcite ) @xmath2 the inverse conicity parameter @xmath3 characterizes the deficit angle , @xmath4 . assuming the lorentz gauge condition , @xmath5 , the equation for the vector potential of the electromagnetic field in curved spacetime outside the string ( where @xmath6 ) reduces to a simple wave equation @xmath7 to separate this vector equation to scalar equations it is useful to project it onto a complex tetrad @xmath8 in which the metric takes the form @xmath9 the field equation is then equivalent to scalar equations [ separation ] @xmath10\emac_{t } & = - \emjc_{t}\commae & \waveop[0]\emac_{z } & = - \emjc_{z}\comma\\ \waveop[+1]\emac_{\mtc } & = - \emjc_{\mtc}\commae & \waveop[-1]\emac_{\btc } & = - \emjc_{\btc}\comma\end{aligned}\ ] ] where [ waveops ] @xmath11=\biggl[-\frac{\partial^2}{\partial t^2}+\frac{\partial^2}{\partial z^2 } + \frac{\partial^2}{\partial \rho^2}+\frac{1}{\rho^2}\frac{\partial^2}{\partial \ph^2 } + \frac{1}{\rho}\frac{\partial}{\partial \rho}\biggr]\ ] ] and @xmath12=\biggl[-\frac{\partial^2}{\partial t^2}+\frac{\partial^2}{\partial z^2 } + \frac{\partial^2}{\partial \rho^2}+\frac{1}{\rho^2}\frac{\partial^2}{\partial \ph^2 } + \frac{1}{\rho}\frac{\partial}{\partial \rho } \mp i\frac{2}{\rho^2}\frac{\partial}{\partial\ph}-\frac{1}{\rho^2}\biggr]\period\ ] ] the operator @xmath13}$ ] is the standard flat - space dalambert operator in cylindrical coordinates , however , with coordinate @xmath14 . we look for eigenfuctions @xmath15 of these operators in the form @xmath16}$ ] where @xmath17 are coordinates of a spacetime point @xmath18 and @xmath19 , @xmath20 are parameters labeling the eigenfunctions . the restriction on @xmath21 follows from the periodicity of the angular coordinate for @xmath22 . we find that @xmath23 must satisfy bessel equation @xmath24f=0\ ] ] for some positive number @xmath25 . the complete system of solutions of bessel equation regular on the string ( i.e. , for @xmath26 ) is given by bessel functions @xmath27 with @xmath28 . the eigenfunctions of the operators thus are @xmath29 they satisfy @xmath30 and the normalization was chosen in such a way that the following completeness and orthonormality relations hold : @xmath31 @xmath32 the spacetime delta - function @xmath33 is normalized with respect to the measure @xmath34 , the delta - function in space of parameters @xmath35 is normalized using @xmath36 , and @xmath37 is kronecker delta . the retarded green function @xmath38 of the operator @xmath39 , [ retgrfccond ] @xmath40 can be decomposed in the system as follows : @xmath41 where @xmath42 , @xmath43 , @xmath44 , and @xmath45 is the path along the real axis in the complex plane of parameter @xmath46 . it goes around the poles at @xmath47 in lower half plane ( @xmath48 ) to satisfy the conditions . a nontrivial integration performed in the appendix leads to the expression @xmath49\commae \end{split}\raisetag{12ex}\ ] ] three - dimensional spacetime diagram of the plane orthogonal to the cosmic string ( i.e. , the spacetime diagram with coordinate @xmath50 is suppressed ) . a rescaled coordinate @xmath51 ( periodic with the period @xmath0 ) is used instead of angular coordinate @xmath14 . two spacetime points @xmath18 and @xmath52 can be joined by more than one geodesic as indicated in the diagram . the geodesics around the string due to the curvature localized on the string . of course , the of the geodesics is only apparent it arises because the rescaled coordinate @xmath53 is employed . the geodesics are straight lines in locally flat geometry . however , the cosmic string causes the angle deficit and the intersection of geodesics behind the string is a real effect . spatial projection of the geodesics into hypersurface @xmath54 is also shown . these are spatial geodesics with length @xmath55 . also cf . [ fig : spatial].,title=""fig : "" ] + where @xmath56 and @xmath55 are defined as @xmath57 and @xmath58 is the heaviside step function . as we will discuss in detail below , index @xmath59 labels spacetime geodesics joining points @xmath18 and @xmath52 ; its range @xmath60 is given by conditions and @xmath61 on angle @xmath62 explicitly . ] @xmath63 the support of the geodesic part @xmath64(x|x')}$ ] of the green function is localized on the future light cone of the source point @xmath52 , i.e. , on the null hypersurface generated by future null geodesics from @xmath52 . near vertex @xmath52 the hypersurface has the standard structure of the light cone in minkowski spacetime . however , at the cosmic string the light cone deforms it intersects itself and becomes a hypersurface with a boundary ( given by null rays propagating near the string).,title=""fig : "" ] + in we separated the field equations into independent ones for components @xmath65 . now we can combine the green functions @xmath38 back to the full vector green function : @xmath66(x|x')\\ & \;\;+ \mt_{\aix{a}}\,\bt_{\aix{b}'}\grfc[+1](x|x')+ \bt_{\aix{a}}\,\mt_{\aix{b}'}\grfc[-1](x|x')\commae \end{split}\raisetag{7ex}\ ] ] with unprimed and primed tensor indices considered at point @xmath18 and @xmath52 , respectively . as a consequence of and the vector green function satisfies the conditions analogous to with the wave operator from eq . . this green function can be split into two pieces with clear interpretation , @xmath67_{\aix{ab}'}(x|x')+\vgrfc[\scat]_{\aix{ab}'}(x|x')\period\ ] ] the first _ geodesic _ part @xmath68_{\aix{ab}'}(x|x')= \frac1{2\pi}\,\theta(\delta t)\sum_{k=\kin}^{\kfi } \geodtr_{\aix{ab}'}[\gamma_k]\,\delta\bigl(-\delta t^2+r_k^2\bigr)\ ] ] describes the propagation of the electromagnetic field along the null rays as in an empty flat spacetime . here @xmath69 , @xmath70 are geodesics joining points @xmath18 and @xmath52 , and @xmath71}$ ] is the operator of parallel transport along the geodesic @xmath72 . quantity @xmath55 defined in is the spatial length of the @xmath73-th geodesic , see fig . [ fig : geod ] . delta - functions in enforce that the field propagates only along null geodesics . the only difference from the minkowski spacetime is that light rays around the cosmic string . if we call _ light cone _ of the source point @xmath52 a hypersurface generated by null geodesics from @xmath52 we see that it when it intersects the string see fig . [ fig : cone ] . the contribution to the field with the source at point @xmath52 described by the geodesic part is fully localized on this light cone . the support of the scattered part @xmath74(x|x')}$ ] of the green function is localized inside light cones with vertices @xmath75 on the cosmic string which are connected with the source by null geodesics . in the figure only a spacetime diagram of the plane going through the charge orthogonally to the string is shown . the electromagnetic field given by @xmath74(x|x')}$ ] can be interpreted as the electromagnetic field scattered on the singular curvature localized on the string.,title=""fig : "" ] + if we transform 1-forms @xmath76 back to the coordinate @xmath77 and @xmath78 , the second part , @xmath74(x|x')}$ ] , of the green function becomes @xmath79_{\aix{ab}'}(x|x ' ) = -\frac{\iconpar}{8\pi^2}\frac{\theta(\delta t)\,\theta\bigl(\delta t^2\!-\!\delta z^2\!-\!(\rho\!+\!\rho')^2\bigr)}{\rho\rho'}\\ & \quad\times\biggl[\biggl(\!\bigl(-\,\grad_{\aix{a}}t\,\grad_{\aix{b}'}t+\grad_{\aix{a}}z\,\grad_{\aix{b}'}z\bigr ) \!\!-\!\bigl(\grad_{\aix{a}}\rho\,\grad_{\aix{b}'}\rho+\rho\rho'\grad_{\aix{a}}\ph\,\grad_{\aix{b}'}\ph\bigr)\ch\eta\biggr ) \frac{1}{\sh\eta}\biggl ( \frac{\sin\iconpar(\pi-\delta\ph)}{\ch\iconpar\eta\!-\!\cos\iconpar(\pi\!-\!\delta\ph ) } + \!\frac{\sin\iconpar(\pi+\delta\ph)}{\ch\iconpar\eta\!-\!\cos\iconpar(\pi\!+\!\delta\ph)}\biggr)\\ & \mspace{50mu}+\bigl(\rho\,\grad_{\aix{a}}\ph\,\grad_{\aix{b}'}\rho-\rho'\,\grad_{\aix{a}}\rho\,\grad_{\aix{b}'}\ph\bigr)\ , \biggl(\frac{\sh\iconpar\eta}{\ch\iconpar\eta\!-\!\cos\iconpar(\pi\!-\!\delta\ph ) } -\frac{\sh\iconpar\eta}{\ch\iconpar\eta\!-\!\cos\iconpar(\pi\!+\!\delta\ph)}\biggr)\biggr]\period \end{split}\raisetag{18ex}\ ] ] it can be associated with a _ scattering _ on the localized on the string . indeed , the contribution to the field due to this part of the green function is localized in the causal future of points @xmath75 on the string which are connected to the source point @xmath52 by null geodesics see fig . [ fig : scat ] . this fact is a simple manifestation of general behavior of the propagation of the electromagnetic field in a curved spacetime @xcite : the main part propagates along null" +"the origin of cosmic rays still remains an unanswered fundamental research question . cosmic ray distributions of various aspects have been measured , most notably the steeply falling spectrum up to the ultra - high energy regime with cosmic ray energies even exceeding @xmath4 eev @xcite . for ultra - high energy cosmic rays , deflections in magnetic fields should diminish with increasing energy , such that directional correlations should lead to a straight - forward identification of accelerating sites . however , even at the highest energies the arrival distributions of cosmic rays appear to be rather isotropic . only hints for departures from isotropic distributions have been reported , e.g. , a so - called hot spot @xcite , and a dipole signal @xcite . at least with the apparent isotropy , limits on the density of extragalactic sources were derived which depend on the cosmic ray energy @xcite . a recent determination of ultra - high energy cosmic ray composition from measurements of the shower depth in the atmosphere revealed contributions of heavy nuclei above @xmath5 eev @xcite . this observation may explain the seemingly isotropic arrival distribution as deflections of nuclei in magnetic fields scale with their nuclear charges @xmath1 . obviously , when searching for cosmic ray sources , a key role is therefore attributed to magnetic fields . the galactic field in particular is strong enough to displace original arrival directions of protons with energy @xmath6 eev by several degrees from their original arrival directions outside the galaxy @xcite . the displacement angles for nuclei even reach tens of degrees . the knowledge on the extragalactic magnetic fields is much less certain , but is likely to be less important than the galactic field and is not studied in this contribution . to identify sources of cosmic rays , rather precise corrections for the propagation within the galactic magnetic field are needed . in previous directional correlation analyses , only the overall magnitude of deflections was taken into account , e.g. @xcite , or corrections for cosmic ray deflections were applied using analytic magnetic field expressions reflecting the spiral structure of our galaxy @xcite . recently , parameterizations of the galactic magnetic field have been developed which are based on numerous measurements of faraday rotation @xcite , and in addition polarized synchrotron radiation for the second reference . based on directional characteristics and the field strength of the parameterizations , deflections of cosmic rays are predicted to depend strongly on their arrival direction , charge and energy . in the following we will refer to the regular field with the bisymmetric disk model of the first reference as the pt11 field parameterization , and to the regular field of the latter as the jf12 field parameterization , respectively . angular distributions of cosmic rays in these galactic field parameterizations have been studied before , e.g. , with respect to general properties of the jf12 parameterization @xcite , specific source candidates @xcite , general properties of deflections and magnifications @xcite , and to the potential of revealing correlations between cosmic rays and their sources @xcite . in this work we investigate whether cosmic ray deflections in the galactic magnetic field can be reliably corrected for , given the current knowledge of the field . to simplify discussions of energy and nuclear dependencies we will define rigidity as the ratio of the cosmic ray energy and number @xmath1 of elementary charges @xmath7 @xmath8 in our investigations we use galactic coordinates as our reference system , with longitude @xmath9 and latitude @xmath10 . for a number of visualizations we use cartesian coordinates alternatively with height @xmath11 above the galactic plane , with the earth being located at @xmath12 kpc . based on the two field parameterizations pt11 and jf12 we initially discuss key distributions of cosmic ray deflection , dispersion effects in arrival distributions , directional variance in field transparency , and the influence of random field components . from the rigidity dependencies of these distributions , we recommend a minimum rigidity threshold above which cosmic ray deflection may be controlled in terms of probability distributions . furthermore , we take the different results of the two galactic field parameterizations as a measure of our current knowledge of the galactic field . we compare their cosmic ray angular deflections and study differences in the dispersion of arrival distributions . finally , we study the practical consequences of galactic field corrections and their uncertainties by performing simulated point source searches and by quantifying the field impact in terms of discovery potential . the two field parameterizations pt11 and jf12 each follow a different ansatz . both take into account about @xmath13 faraday rotation measurements . the pt11 field has been fitted to two large sets of faraday rotation measurements . the jf12 field has been adapted to several large sets of faraday rotation measurements and to synchrotron polarization measurements , thereby increasing the information per analysed direction by two additional complementary measurements @xcite . both use the electron density model ne2001 @xcite with an enlarged vertical scale for weighting the line - of - sight integrals of the magnetic field . a ) b ) fig . [ fig : parameterization ] shows the field strength as a function of the radial distance from the galactic center along the solar system line - of - sight and the distance perpendicular to the galactic plane . the fields exhibit different shapes and magnitudes ; especially notable in fig . [ fig : parameterization]a is the field extent of the jf12 parametrization above and below the galactic plane with non - negligible field strengths even at a distance of @xmath14 kpc . the pt11 field ( fig . [ fig : parameterization]b ) , on the other hand , exhibits a rather concentrated halo field , which is centered around a distance of @xmath15 kpc to the galactic plane . when studying the magnitude of angular deflections of cosmic rays resulting from these parameterizations , we take the angle @xmath16 between the incoming direction to the galaxy and the arrival direction on earth as a measure of the directional change ( fig . [ fig : beta ] ) . between the direction on earth and the direction outside the galaxy ( pt11).,scaledwidth=50.0% ] to get a first impression of the different deflections resulting from the two field parameterizations we use backward tracking techniques of antiprotons through the galactic field . with this technique we obtain individual trajectories for matter particles entering from outside the galaxy and then following the reverse path . the method ensures that every trajectory leads to observation on earth . in fig . [ fig : angularsky ] we show the magnitudes of the angular deflections @xmath16 of cosmic rays with rigidity @xmath17 ev . the position in the map denotes the initial direction on earth in galactic coordinates for the backtracked antiprotons . the color code refers to the magnitude of angular deflections which reach up to @xmath18 deg . for the jf12 parameterization ( fig . [ fig : angularsky]a ) , deflections are largest near directions of the galactic center which is expected from the magnitude of the field shown in fig . [ fig : parameterization]a . with the pt11 parameterization ( fig . [ fig : angularsky]b ) , deflections are largest in any direction near the galactic plane which is attributed to the strong disk field ( fig . [ fig : parameterization]b ) . in the galactic magnetic field for antimatter with rigidity @xmath17 ev starting from earth in the direction presented in galactic coordinates , a ) jf12 , b ) pt11 . , title=""fig:"",scaledwidth=45.0%]a ) in the galactic magnetic field for antimatter with rigidity @xmath17 ev starting from earth in the direction presented in galactic coordinates , a ) jf12 , b ) pt11 . , title=""fig:"",scaledwidth=45.0%]b ) as expected , the differences in the field parameterizations relate directly to a different impact on cosmic ray deflections . in the following section we study a number of aspects related to the directional changes of cosmic rays when traversing the galactic field . the goal of this section is to determine a kinematic regime where information on cosmic ray arrival directions can be obtained by transformation of probability distributions . for this purpose we first analyze cosmic ray angular deflections as a function of rigidity . as our primary criterion we require angular deflections to be below @xmath19 deg in order to distinguish ballistic deflections from diffusive - type random walk . beyond this we investigate the dispersion of arrival probability distributions by the galactic field , and the splitting of arrival distributions into several images . furthermore we show directional dependencies of the field transparency for cosmic matter and antimatter particles . we also study the influence of random components of the field which imposes uncertainties on the arrival directions . the two magnetic field parameterizations exhibit different field strengths above and below the galactic plane , and differ substantially in their field characteristics near the plane ( fig.[fig : parameterization ] ) . therefore , we divide the sky into three regions of equal solid angles , and study angular deflections for each region separately . the boundaries of these regions are fixed at galactic latitudes of @xmath20 deg . to ensure that every cosmic ray trajectory leads to observation on earth we use the backward tracking method explained in the previous section . we use the term `` northern region '' to refer to antiparticles originating on earth in the direction of positive latitudes above @xmath21 deg . negative latitudes below @xmath22 deg , on the other hand , are referred to as the `` southern region '' , while for latitudes in - between we use the term `` disk region '' . a ) b ) c ) d ) in fig . [ fig : angular]a we show the average directional change @xmath23 between the direction on earth and the direction outside the galaxy as a function of the cosmic ray rigidity @xmath24 using the jf12 field . the distribution was derived from @xmath25 million simulated cosmic rays per rigidity interval . in fig . [ fig : angular]c we show the corresponding spread @xmath26 in terms of standard deviations . for low rigidities @xmath27 ev , cosmic ray confinement owing to the size of our galaxy and its magnetic field leads to large directional changes @xmath28 deg and large average variations in @xmath16 ( @xmath29 deg ) . at rigidity @xmath30 ev , the largest average deflection of @xmath31 deg is found in the southern region ( fig . [ fig : angular]a , downward - pointing triangles ) . the corresponding spread amounts to @xmath32 deg ( fig . [ fig : angular]c ) , such that for @xmath33 of the cosmic rays the deflection angle remains below @xmath34 deg . the average deflection in the northern region is substantially smaller with only @xmath35 deg , however , the spread of @xmath36 deg is larger ( upward - pointing triangles ) . also here most of the cosmic ray deflections are below @xmath34 deg . a similar conclusion holds for the disk region ( square symbols ) . the pt11 parameterization exhibits very similar tendencies for rigidity @xmath30 ev as can be seen in figs . [ fig : angular]b , d . in the disk region the deflections exceed those of the other regions for rigidities above @xmath37 ev ( square symbols ) . here the deflections also exceed that of the jf12 parameterization as was already visualized in fig . [ fig : angularsky ] above . overall , at rigidities @xmath38 ev the deflections are consistently reduced and correspondingly enhance the control over cosmic ray deflection . in the following studies we will therefore use the rigidity of @xmath30 ev as a benchmark . cosmic rays" +"supernovae ( sne ) are dramatic and violent end - points of stellar evolution , and lie at the heart of some of the most important problems of modern astronomy since their huge luminosities were first estimated and a clear distinction between classical novae and sne was made @xcite . * sne and stellar evolution * + sne provide natural laboratories for studying the physics of hydrodynamic , nuclear processes in extreme conditions and are involved in the formation of neutron stars , black holes , and gamma - ray bursts ( grbs ) . furthermore , sne are sources of gravitational waves and of neutrino emission , and candidate sites for high - energy cosmic ray acceleration . thus , it is of broad astrophysical importance to understand the physical conditions for these spectacular explosions . + we recognize two physically defined classes : core collapse - induced explosion of short - lived massive stars ( cc sne ) and thermonuclear explosions of long - lived low mass stars ( sne ia ) . in recent years deeper and more frequent searches for transient events in the local and distant universe as well the identification of sn progenitor stars on pre - discovery images from hubble and spitzer space telescopes have provided us with important information on the evolution of massive stars and binary systems @xcite . _ however , a growing number of peculiar events suggests that the standard scenario of stellar evolution and explosion physics may not be complete and demands further physical understanding and theoretical explanation . _ * sne and dark energy * + type ia sne are standard candles due to their significant intrinsic brightness and homogeneity . they have provided the first evidence for an accelerated expansion of the universe and remain one of the more promising probes of the nature and amount of dark energy , @xcite . cc sne display a huge range in their physical characteristics , including kinetic energy , radiated energy and the amount of radioactive elements created during the explosion . however , plateau cc sne ( sne iip ) that undergo a long phase of constant luminosity in their photometric evolution are potential standardizable candles , although they are not as luminous and uniform as sne ia @xcite . _ understanding the mechanism that is responsible for the accelerating expansion of the universe is one of the crucial next steps for cosmology and requires both new searches for type ia and type iip sne to populate the hubble diagram and the knowledge of their progenitors and explosion mechanisms . _ * sne and galaxy evolution * + sne play also a major role in driving the chemical , kinetic , and dynamical evolution of galaxies . they are the main producers of heavy elements and are fundamental for understanding global abundances and abundance patterns in galaxy clusters and in the intergalactic medium @xcite . sne ia are important contributors of iron and release it to the interstellar medium over longer timescales , compared to the @xmath0 elements produced by cc sne . therefore the @xmath0 to iron abundance ratio can be used to evaluate the formation timescales of stellar systems . moreover the sn metal - rich ejecta are believed to be a potentially important site of cosmic dust formation . the energy release from sne can initiate episodes of star formation ( sf ) , impact the evolution of gas flow and contribute to the feedback processes in galaxies @xcite . _ a complete and coherent picture of the formation and evolution of the galaxies is a fundamental objective of modern astronomy and sne are an important ingredient to model the chemical enrichment of the galaxies and the effect of energy / momentum feedback on galaxy formation . _ * sne and sfr * + the cosmic evolution of sn rates is an alternative and complementary probe of the sf history ( sfh ) in the galaxies . due to the short lifetime of progenitor stars the cc sn rate is directly proportional to the current sfr while type ia sn rate reflects the convolution of the sfh with the distribution of the delay times between progenitor star formation and explosion @xcite . poor statistics is a major limiting factor for using the cc sn rate as a tracer of the sfr . at low redshift the difficulty is in sampling large enough volumes of the local universe to ensure significant statistics ( e.g. * ? ? ? * ) , while at high redshift the difficulty lies in detecting and typing complete samples of intrinsically faint sne @xcite . moreover it is expected that a fraction of cc sne are missed by optical searches , since they are embedded in dusty spiral arms or galaxy nuclei . this fraction may change with redshift , if the amount of dust in galaxies evolves with time . _ progress in using cc sn rates as sfr tracers requires accurate measurements of rates at various cosmic epochs and in different environments . furthermore it requires a comparison with other sfr diagnostics in a wide range of redshift to investigate the causes of the observed discrepancy . _ + despite the importance of sne in several astronomical topic many fundamental questions remain with regard these exciting phenomena . stellar evolution theory predicts that all stars more massive than @xmath1 complete eso - energetic nuclear burnings and develop an iron core that can not be supported by any further nuclear fusion reaction , or by electron degenerate pressure . the collapse of the iron core results in the formation of a compact object , a neutron star or a black hole , accompanied by the high - velocity ejection of a large fraction of the progenitor mass . despite this basic understanding , the picture of massive star death emerging from recent discovery is far to be clear . * which massive star in which evolutionary stage produce which cc sn type ? * + different types of cc sne have been identified on the basis of their spectroscopic and photometric properties : type ii sne show presence of h in the spectra , ( type iip sne exhibit a long plateau in their light curve while type iil show a linear decline rate ) , type ib sne lack h but show he , type ic sne lack both h and he , type iin sne exhibit a narrow @xmath2 emission line and present other strong evidences of interaction of the ejecta with circumstellar material ( csm ) already at early phases of their evolution . this sequence has been explained on the basis of the progenitor mass loss history with the most massive stars loosing the largest fraction of their initial mass @xcite : type iip progenitor stars are red super giants ( rsgs ) that explode with most of their h envelope present , type iil progenitors had extensive mass loss but preserved a small h envelope , type ib / c progenitors are wolf - rayet stars that had lost their h and he envelopes , type iin progenitor have suffered a major mass loss episode just before the explosion . several cc sne with characteristics intermediate between these canonical types have been recently discovered suggesting a smooth transition and requiring the introduction of hybrid classes ( for example type iib sne and ibn sne ) . the progenitor stars of sne iip are the best constrained from direct detection since these sne are the most frequent in the nearby universe . their mass function seems to suggest a lack of high mass progenitors ( @xmath3 ) and raises the intriguing possibility that more massive stars collapse directly to a black - hole and produce either faint or failed sne @xcite . the progenitors of sne ib / c have so far eluded discovery and several observational evidences have suggested an alternative scenario where a significant fraction of their progenitors are stars of much lower initial mass in close binary systems stripped of their envelopes by the interaction with the companion @xcite . recent observations have suggested the possibility that stars explode as cc sne shortly after the luminous blue variable ( lbv ) phase characterized by sporadic variability and occasionally giant outbursts with a huge mass loss in a single short event @xcite . in particular some sne ( 2006jc , 2006gy , @xcite ) showed evidence that their progenitors had properties consistent with lbv and in one case a pre - explosion outburst was seen . * which physical parameters drive the cc sn diversity ? * + the variety of the observational properties shown by cc sne and the relative numbers of different types reflects the large range of stellar types seen in the upper region of the hertzsprung russel diagram above @xmath4 and the different physical conditions ( radius , density profile and surrounding csm ) before the explosion @xcite . the simple scheme where only the mass loss drives the evolution of massive stars can not explain the surprising diversity in explosion energies and it is essential to investigate the effect of other key factors ( metallicity , rotation rate , magnetic fields , binary membership ) @xcite . a major puzzle is due to the discovery of a number of sne at the extrema of the luminosity function and requires further physical understanding . a subset of sub - luminous type ii sne shows both a very faint radioactive tail in the light curve and a low expansion velocity suggesting low energy explosions and a possible black hole remnant , giving rise to significant fallback @xcite . different types of extremely luminous cc sne have been recently discovered in dwarf , faint host galaxies @xcite with an enormous luminosity at maximum that can not be powered by radioactive @xmath5ni . several scenarios have been proposed to explain these events : an explosion driven by black hole accretion @xcite , the spin down of a rapidly rotating young magnetar @xcite , interaction of the sn ejecta with a dense csm @xcite or pulsational pair instability in which collisions between high velocity shells are the source of multiple , bright optical transients @xcite . * what are the alternative explosion mechanisms producing a cc sn ? * + to explain the full range of explosion parameters of cc sne some theoretical studies suggested two alternative explosion mechanisms with respect to the collapse of the iron core : electron capture and pair instability . electron capture sne ( ec sne ) occur when a star in the mass range of @xmath6 forms an electron degenerate o - ne - mg core and the core may collapse before ne ignition @xcite . the lower and maximum initial mass for ec sne is determined by the competing effects of core growth and mass loss during the late evolutionary stages of super - agb stars and are quite uncertain ( @xmath7 , @xcite ) . the pair instability sne ( pi sne ) occur when the high temperatures in a massive core ( he core @xmath8 and initial mass @xmath9 ) induces electron - positron pair production reducing the radiation pressure and hence leading to a rapid contraction followed by a thermonuclear explosion . a similar mechanism is pulsational pair instability in which a massive core undergoes interior instability again due to electron - positron pair production ejecting many solar masses in a series of giant pulses @xcite . at the moment there are few observational probes of pi sne . * which type of massive stars produce black holes ? * + the origin of stellar mass black holes is not yet understood : some stars ( @xmath10 ) are expected to produce weak explosions with a black hole formed by fallback , some others ( @xmath11 ) collapse into a black hole directly without any optical signature ( failed sne ) . the" +"electrostatic interactions of charged macromolecules and colloids are often governed by small oppositely charged ions ( counterions ) that maintain global electroneutrality . these counterion - mediated interactions play a fundamental role in classical charged ( coulomb ) fluids that are abundant in biological and soft matter context @xcite and include many charged macromolecules ( such as nucleic acids dna and rna , actin filaments , microtubules and globular proteins ) , affecting their functional , structural and dynamical behavior . in spite of the importance of electrostatic interactions , there is no general method that would allow for an accurate prediction of electrostatic effects in all regions of the parameter space , defined by the surface charge density of macroions , charge valency of counterions , dielectric mismatches between the often hydrophobic core of the macromolecule and the surrounding aqueous medium , etc . often the electrostatic interactions are treated on the poisson - boltzmann ( pb ) level leading to effective interactions which turn out to be always repulsive between like - charged macromolecules . conceptually , the pb approach corresponds to a mean - field treatment of electrostatic interactions and is asymptotically valid only for sufficiently large separations between macromolecules , low enough surface charge densities and low counterion valency @xcite . it characterizes a situation where electrostatic fluctuations and correlations due to the counterions are negligible . there are other regions in the parameter space of charged macromolecules where one expects the mean - field framework to break down leading to the emergence of a completely different non - pb - type physics . a notorious example is the phenomenon of like - charge attraction , which emerges between highly charged macroions or in the presence of high valency counterions and has been at the focus of both experimental @xcite and theoretical investigations in recent years ( see refs . @xcite for an extensive reference list ) . it appears to us that among the most important recent advances in this field has been the systematization of non - pb effects based on the notions of _ weak coupling _ ( wc ) and _ strong coupling _ ( sc ) approximations . these terms refer to the strength of electrostatic coupling in the system and may be understood conceptually in terms of the electrostatic interactions of mobile counterions with fixed external charges ( macroions ) in the system when compared with direct electrostatic interactions between the counterions themselves . this latter contribution may be characterized in terms of the _ bjerrum length _ , @xmath0 which corresponds to the separation at which two unit charges , @xmath1 , interact with thermal energy @xmath2 in a medium of dielectric constant @xmath3 ( in water and at room temperature , the value is @xmath4 nm ) . if the charge of the counterions is @xmath5 then the bjerrum length scales as @xmath6 . the interaction of counterions with macroion charges ( of surface charge density @xmath7 ) can be characterized in terms of the so - called _ gouy - chapman length _ , @xmath8 which gives the separation at which the counterion - surface interaction energy equals @xmath2 . the ratio of these two fundamental length scales introduces a dimensionless parameter @xmath9 which is known as the ( netz - moreira ) electrostatic coupling parameter @xmath10 @xcite and quantifies the strength of electrostatic coupling in the system . this parameter is closely related to the plasma parameter of ionic systems @xcite and may be written also in terms of the typical lateral spacing , @xmath11 , between counterions in the proximity of a charged surface , i.e. , @xmath12 as set by the local electroneutrality condition @xmath13 . it then follows that in the weak coupling regime , defined by @xmath14 , the width of the gouy - chapman layer @xmath15 is much larger than the separation between two neighbouring counterions in the counterion layer and thus it behaves basically as a three - dimensional gas . each counterion in this case interacts with many others and the collective mean - field approach of the poisson - boltzmann type is thoroughly justified . on the other hand , in the strong coupling regime , defined by @xmath16 , the mean distance between counterions , @xmath11 , exceeds the layer width and thus the counterion layer behaves essentially as a two - dimensional layer @xcite . in this case the mean - field approach breaks down as each counterion is isolated laterally in a relatively large correlation hole of size @xmath11 . in fact , as each counterion can move almost independently from the others along the direction perpendicular to the charged surface , the properties of the system are dominated by single - particle contributions on the leading order , which is in stark contrast with the collective mean - field picture and emerges as a direct consequence of strong electrostatic correlations in the system . the two dychotomous limits are characterised by a low ( high ) valency of the counterions , a small ( large ) value of the surface charge density and/or large ( small ) medium dielectric constant . conceptually the study of the sc regime has been pioneered in several recent works @xcite using various analytical methods . it was shown @xcite that both the wc and the sc limits may be described analytically as two exact _ limiting laws _ from a single general theory for classical coulomb fluids : while the pb theory follows in the limit of @xmath17 , a limiting single - particle sc theory follows in the limit @xmath18 , which thus allow for an exact statistical mechanical treatment of charged systems at two opposed limiting conditions . the parameter space in between can be analyzed by approximate methods @xcite , being accessible effectively only _ via _ computer simulations @xcite . exact solutions for the whole range of coupling parameters are available only in one dimension @xcite . the wc - sc paradigm has been tested extensively @xcite and was found to describe computer simulations quantitatively correctly in the respective regimes of validity , thus providing a unifying view of the behavior of coulomb fluids . the main facets of these results are retained even when the model system is generalized in order to include more realistic features describing the bathing solution or the nature of the fixed or mobile charges in the system . though , for instance , multipolar charge distribution of mobile counterions @xcite or statistically disordered distribution of fixed charges @xcite unavoidably introduce novel features in the counterion - mediated electrostatic interaction , the application of the same general philosophy embodied in the weak and strong coupling limits remains sound and valid . the only case where it needs to be amended in an essential manner is when the bathing solution contains a mixture of univalent as well as polyvalent salts , which incidentally are also the most common experimental conditions . in that case a more sophisticated mixed weak - strong coupling analysis is in order leading to qualitatively different results @xcite . though originally formulated in the context of planar macroions , these advances have transpired also in the dna - like models of polyelectrolytes which deal with electrostatic interactions in the context of macroions with cylindrical or indeed helical fixed charge distribution . indeed this particular variant of counterion - mediated interactions has a venerable history @xcite . during the last two decades several distinct analytical approaches aimed in different directions improved the classical pb results for simple dna - like models and revealed the importance of correlation effects as well as several other factors including the discrete or helical charge distributions , chain flexibility , finite molecular size , and dielectric inhomogeneities @xcite . guided by these developments we set ourselves the goal of systematically analyzing the interactions between cylindrical macroions mediated by mobile counterions in the presence of dielectric inhomogeneities . contrary to the case of planar macroions which can be completely characterized by a single dimensionless coupling parameter , cylindrical macroions require in general two dimensionless coupling parameters that consistently describe the range of validity of the strong and weak coupling approximations . the existence of two coupling parameters is due to the simple fact that , if compared to the planar case , the cylinder has a finite radius that needs to enter the fundamental description of the problem . this other dimensionless parameter brought fourth by cylindrical geometry of the macroion is nothing but the so - called _ manning parameter _ @xcite . for a cylinder of radius @xmath19 and linear charge density @xmath20 , it is given by @xmath21 the manning parameter thus represents the dimensionless linear charge density or , on the other hand , also the rescaled radius of the cylindrical charge distribution . note that the two parameters ( i.e. , @xmath10 and @xmath22 ) in the cylindrical geometry are independent and can be set separately . for double - stranded dna ( @xmath23 ) , the manning parameter and the ( netz - moreira ) electrostatic coupling parameter are given by @xmath24 and @xmath25 ( at room temperature in water ) in terms of the counterion valency @xmath26 . in this paper we will analyze systematically the interactions between two cylindrical macroions characterized by a fixed surface charge density as well as a finite dielectric jump between the external dielectric background ( corresponding to a continuum solvent ) and the hydrophobic cores of cylindrical macroions . analytically derived results in both limits of strong and weak coupling will be compared directly with monte - carlo simulation results . the organization of this paper is as follows : we first introduce our model and study the image - charge effects within the problem of a single charged cylinder with neutralizing counterions in section [ sec : one_cyl ] . we then focus on the interaction between two identical charged dielectric cylinders within the wc and the sc theory as well as mc simulations in section [ sec : two_cylinder ] . the results in the presence and absence of dielectric discontinuity at the cylindrical boundaries are analyzed in detail in order to bring up the effects due to the image charges in the two - cylinder geometry . let us focus first on the problem of a single infinitely long uniformly charged cylindrical macroion of radius @xmath19 . the charge of the cylinder is assumed to be distributed uniformly on its surface according to the charge distribution function @xmath27 with @xmath20 being the absolute _ linear _ charge density and @xmath28 the radial coordinate from the cylinder axis . the cylinder is arbitrarily chosen to be negatively charged and its electrical charge is thus neutralized by positively charged mobile counterions of valency @xmath29 , which are present in the region @xmath30 only . in general , the interior of the cylindrical macromolecule can be characterized by a different dielectric constant @xmath31 than the surrounding continuum solvent medium , @xmath3 . this is certainly the case for dna that has a hydrophobic inner core composed mostly of stacked nitrogen bases that have a vastly different dielectric response from an aqueous solution @xcite . other charged polymers that usually do not share structural features with dna can nevertheless also posses hydrophobic inner cores with a local dielectric response that differs from the one of the solvent . the hydrophobic apolar core of the macromolecular backbone would then have a static dielectric constant @xmath32 ( hydrocarbon ) , while the surrounding continuum dielectric medium which is usually water , a polar associated liquid , would be characterized by @xmath33 . one can thus introduce the dielectric discontinuity parameter @xmath34 which measures the relative dielectric mismatch at the interface of the two materials . in a dielectrically homogeneous system , we have @xmath35 and no image charge effects are present , while" +"a 2.3-liter two - phase ( liquid and gas ) argon drift chamber @xcite was developed and built by the warp collaboration as a prototype detector for wimp dark matter searches with argon as a target @xcite . the detector was operated for more than two years by the warp collaboration at laboratori nazionali del gran sasso , italy , at a depth of 3,400 m w.e . one important by - product of the operation of the prototype warp detector was the precise determination of the @xmath0ar specific activity in natural argon . + @xmath0ar and @xmath3kr are two radioactive nuclides whose activity in the atmosphere is of the order of 10mbq / m@xmath4 and 1bq / m@xmath5 , respectively @xcite . as a result of the liquid argon production process , they are both present in abundant quantities and are the two most significant radioactive contaminations in liquid argon . the two isotopes decay primarily by @xmath6 emission , and their presence can limit the sensitivity of experiments looking for low energy rare events ( wimp dark matter interactions , neutrinoless double beta decay ) using liquid argon either as a target or as a shielding material . + @xmath3kr is not a pure @xmath6 emitter , owing to the presence of a 0.43% branching ratio for decay with @xmath6 emission on a metastable state of @xmath3rb , which then decays by emitting a @xmath7-ray of energy 514 kev , with a half - life of 1.01@xmath8s @xcite . the coincidence between the @xmath6 and @xmath7 emitted in a fraction of the @xmath3kr decays may ease in some cases the task of determining experimentally the activity of @xmath3kr in low - background detectors . the determination of the specific activity of @xmath0ar is intrinsically more challenging and not as widely discussed in the literature @xcite . a theoretical estimate is presented in ref . + in the last twenty years liquid argon technology has acquired great relevance for astroparticle physics applications . several experimental techniques , employing liquid argon as sensitive medium , have been proposed especially for rare events detection @xcite . for wimp dark matter direct detection , the discrimination of nuclear recoils from the @xmath6-@xmath7 induced background plays a crucial role . the discrimination provided by the experimental technique must be sufficient to reduce the radioactive background below the very low interaction rates foreseeable for wimp dark matter . a precise determination of the intrinsic specific activity of @xmath0ar is therefore of significant interest for the design of wimp dark matter detectors employing argon as a target . the detector consists of a two - phase argon drift chamber with argon as a target . two - phase argon drift chamber was first introduced within the icarus program @xcite in the framework of a wide - range study of the properties of noble gases . + the drift chamber ( see figure [ fig : warp25 ] ) is operated at the argon boiling point ( 86.7k ) at the atmospheric pressure of the gran sasso laboratory ( about 950 mbar ) @xcite . the cooling is provided by a thermal bath of liquid argon , contained in an open stainless steel dewar , in which the chamber is fully immersed . the pressure of the gas phase on the top of the chamber is naturally equalized to the surrounding atmospheric pressure . + ionizing events inside the liquid argon volume produce scintillation vuv light mainly at 128 nm . the scintillation light is shifted to wavelengths in the blue by an organic wavelength shifter ( tetraphenilbutadiene ) covering the walls , and collected by photomultipler tubes ( pmts ) located in the gas phase and facing the liquid volume below . the 2-inch pmts are manufactured by electron tubes ltd ( model d757ufla ) and have a special photocathode that ensures functionality down to liquid argon temperatures . the quantum efficiency at the emission wavelength of tpb is about 18% . the material of the pmts has been selected for high radiopurity : according to the supplier s specifications , the total @xmath7 activity above 100 kev is 0.2 bq / pmt , dominated by the @xmath9th and @xmath10u chains . + a series of field - shaping rings surrounding the liquid phase superimpose an electric field of 1kv / cm . the electrons are drifted toward the anode ( located atop the chamber ) and then extracted from the liquid to the gaseous phase by a local extraction field provided by a couple of grids . the electrons are linearly multiplied in the gas phase by a second , stronger local field . the pmts detect the primary scintillation light ( directly produced by the ionizing event ) and also the secondary scintillation light ( produced by the electron multiplication process in the gas phase ) . the pmt signals are summed and sent to a multi - channel analyzer recording the pulse height spectrum . the liquid argon contained in the chamber is argon 6.0 supplied by rivoira s.p.a . the liquid argon is successively purified from electronegative impurities down to an equivalent contamination of less than 0.1ppb of o@xmath11 by using the chemical filter hopkalit from air liquid . the purity from electronegative elements is actively maintained by means of continuous argon recirculation through the chemical filter . + the experimental set - up is located in the laboratori nazionali del gran sasso underground laboratory ( 3,400 m w.e . of rock coverage ) . the flux of cosmic ray muons is suppressed by a factor of @xmath12 with respect to the surface ( residual flux 1.1@xmath8/(m@xmath13 h ) , average muon energy @xmath14gev the detector is shielded by 10 cm of lead , to reduce the external @xmath7 background . + the sensitive volume of the detector has the shape of frustum of cone and it is delimited by a stainless - steel cathode . the sensitive volume for the configuration under analysis is 1.86@xmath10.07liter . the density of liquid argon in the operating conditions ( 950 mbar and 86.7k ) is1.399 g / cm@xmath4 @xcite . the sensitive volume is viewed by seven pmts , whose responses have been equalized in gain . daily calibrations ensure the long - term stability and the linearity of the response . the sensitive volume and the argon thermal bath are contained in a stainless steel dewar , 50 cm internal diameter and 200 cm internal height . for the measurements described in this work , the electric fields were switched off and the chamber was operated as a pure scintillation detector . the gain of the pmts has been set up to optimize the data acquisition in the typical energy range of the environmental @xmath7-ray background , namely up to 3 mev . the energy threshold for data acquisition is about 40 kev . the threshold used for analysis is 100 kev , in order to exclude events from electronic noise . the response of the detector to @xmath7 radiation was studied using different @xmath7-ray sources ( @xmath16co , @xmath17co , @xmath18cs ) placed outside the chamber . the spectra obtained with the @xmath16co and @xmath18cs sources are shown in figure [ fig : sources ] . typical values of the resolution observed with the calibration sources are @xmath19 at 122 kev ( @xmath16co ) and @xmath20 at 662 kev ( @xmath18cs ) . the correlation between energy and primary scintillation light detected was linear within the range tested with our sources . the energy resolution of the detector can be described empirically by the following parametrization : @xmath21 where @xmath22 kev , @xmath23 kev and @xmath24 . the three terms take into account the effects from non - uniform light collection ( @xmath25 term ) , statistical fluctuations in the light production ( @xmath26 term ) and electronic noise ( @xmath27 term ) . + [ cols=""^,^ "" , ] + the systematic uncertainties are summarized in table [ table:2 ] . the dominating item is related to the energy calibration of the detector response : since the discrimination between @xmath0ar and @xmath3kr is based upon the @xmath6 end - points , the fit result is sensitive to the energy calibration and resolution . the uncertainty on the energy calibration in the range of interest was evaluated to be 2% ( @xmath28 ) from the meaurements with the @xmath7-ray sources ; the corresponding @xmath0ar systematic error is 6.5% . the second important contribution is related to the uncertainty in the active volume of the chamber . the filling level can be determined with accuracy of about 1 mm , and the diameter of the teflon container with the reflector fixed on it is known with a precision of about 2 mm . this corresponds to an uncertainty on the sensitive mass of 3.8% . the best estimate of the @xmath0ar specific activity in the liquid argon is @xmath29 bq / liter , or @xmath30 bq / kg of natural ar , or @xmath31 g(@xmath0ar)/g(@xmath2ar ) . the value is consistent with the previous determination by h. loosli @xcite . the uncertainty in our measurement is mainly due to systematics . + the liquid argon sample under investigation shows a contamination of @xmath3kr , 0.16@xmath10.13 bq / liter ( @xmath28 ) . we wish to dedicate this work to the memory of our friend and colleague nicola ferrari , co - author of the paper , who prematurely passed away on july , 2006 . + we also thank prof . h. loosli for helpful communications concerning his @xmath0ar paper . l. p. acknowledges the support by the eu fp6 project ilias . a. m. s. has been in part supported by a grant of the president of the polish academy of sciences , by the ilias contract nr . rii3-ct-2004 - 506222 and by the mnisw grant 1p03b04130 . 00 r. brunetti _ et al . _ , new astron . rev . * 49 * , 265 ( 2005 ) . warp collaboration , r. brunetti _ et al . _ , warp : wimp argon programme , proposal for warp to infn , march 2004 , available at ` http://warp.pv.infn.it ` . h. h. loosli , earth and planetary science letters , * 63 * , 51 ( 1983 ) . j. a. formaggio and c. j. martoff , ann . nucl . part . sci . * 54 * , 361 ( 2004 ) . lbnl isotopes project nuclear data dissemination home page ( available at ` http://ie.lbl.gov/toi.html ` ) . w. kutschera _ et al . b * 92 * , 241 ( 1994 ) . p. cennini _ et al . instr . meth . a * 356 * , 526 ( 1995 ) . c. rubbia , cern - ep/77 - 08 ( 1977 ) . p. benetti _ et al . instr . and meth . a * 327 * , 203 ( 1993 ) . p. aprili _ et al . _ [ icarus collaboration ] , cern / spsc 2002 - 027 ( 2002 ) . d. b. cline _ et al . instr . meth . a * 503 * , 136 ( 2003 ) . m. g. boulay and a. hime , astropart . * 25 * , 179 ( 2006 ) a. rubbia , [ arxiv::hep - ph/0407297 ] , proceedings of the xi international conference on calorimetry in high energy physics ( calor2004 ) , perugia , italy ( 2004 ) a. rubbia , journal of physics , conf . series * 39 * , 129 ( 2005 ) [ arxiv::hep - ph/0510320 ] nist chemistry webbook , nist standard reference database number 69 , june 2005 , eds . p. j. linstrom and w. g. mallard . macro collaboration , m. ambrosio _ et al . _ , . phys . * 10 * , 11 (" +"statistics of neuronal activity is often described as a renewal point process , or even a poisson process , see @xcite and references therein . on the other hand , in some sets of experimental data correlations are observed between consecutive interspike intervals ( isi ) , @xcite , which does not conform with the renewal hypothesis . what could be the reason of such correlations ? in principle , any sort of memory in the neuronal firing mechanism could bring about memory into the sequence of isis , thus disrupting a possibility for it to be renewal . memory in the firing mechanism can appear due to partial reset of the membrane potential after firing , @xcite , or due to threshold fatigue @xcite , or for other reasons , see @xcite for a review . biologically , non - renewal statistics of neuronal activity can improve discrimination of weak signals @xcite and therefore is essential feature of functioning of a nervous system . in this context , it was checked in @xcite if it is possible to represent activity of electrosensory neuron as a markov chain of some finite order . conclusion made in @xcite is that the corresponding order , if any , can not be lower than 7 . normally , any neuron is embedded into a network . inter - neuronal communication in the network is delayed due to finite speed of nervous impulses . in a reverberating network , this brings about one more reason for non - renewal firing statistics the delayed feedback . we study here the simplest possible case of a network a single neuron with delayed feedback . in the previous paper @xcite , it was proven for a concrete neuronal model the binding neuron with threshold 2 stimulated with poisson stream of input impulses , that statistics of its isis is essentially non - markov . in this paper , we refine and extend methods of @xcite making those applicable to any neuron , which satisfies a number of very simple and natural conditions ( see cond0-cond4 in n. [ neuron ] ) . under those conditions , we prove rigorously that isi statistics of a neuron with delayed feedback can not be represented as a markov chain of any finite order . we do not specify any concrete neuronal model , only expect that a neuron satisfies the following conditions : * cond0 : neuron is deterministic : identical stimuli elicit identical spike trains from the same neuron . * cond1 : neuron is stimulated with input poisson stream of excitatory impulses . the input stream has intensity @xmath0 . * cond2 : neuron may fire a spike only at a moment when it receives an input impulse . * cond3 : just after firing , neuron appears in its standard state , which is always the same . * cond4 : the output interspike interval ( isi ) distribution is characterized with a probability density function ( pdf ) @xmath1 , which is positive : @xmath2 , and bounded : @xmath3 . the cond0 , above , is imposed in accordance with experimental observations , see e.g. @xcite . as regards the cond1 , poisson stream is a standard stimulation when neuronal random activity is studied . the cond2 , above , is satisfied for most threshold - type neuronal models , starting from standard leaky integrate and fire ( lif ) neuron @xcite and its modifications , see @xcite . in order the cond2 to be valid , it is enough that the following three conditions are satisfied : ( i ) neuronal excitation gets abrupt increase at the moment of receiving input impulse - function form . ] , ( ii ) after that moment , the degree of excitation does not increase ( it decreases for most neuronal models ) until the next input impulse . ( iii ) the neuron fires when its degree of excitation exceeds a threshold level . the threshold can be either static , as in the basic lif model , or dynamic @xcite . these conditions seem to be standard for many threshold neuronal models used , see @xcite and citations therein . cond3 means that any kind of memory about previous input / output activity , which can be present in a neuron , is cleared after each triggering . due to cond3 , output stream of neuron without feedback will be a renewal stochastic process . cond4 seems to be natural for any neuronal model stimulated with poisson stream . at least , all the five conditions are satisfied for the binding neuron model and for the basic lif model , see @xcite , where @xmath1 is calculated exactly for each model , respectively . we expect that each output impulse fired by neuron is fed back to the neuron s input through a feedback line . the feedback line has the following properties : * prop1 : the time delay in the line is @xmath4 . * prop2 : the line is able to convey no more than one impulse . * prop3 : the impulse conveyed to the neuronal input is identical to that from the input poisson stream . it is known that a neuron can form synapses ( autapses ) on its own body , or dendritic tree , e.g. @xcite . this substantiates consideration of a single neuron with feedback not only as the simplest reverberating `` network '' possible , bat also as an independent biologically relevant case . the delay @xmath5 comprises the time required by the output spike to pass the distance from axonal hillock , where it is generated , to the autapse and the synaptic delay . the prop2 is somehow related to the refractoriness even if we do not introduce here the refractoriness to its full extent . the prop3 means that we consider here an excitatory neuron . the important for us consequence of prop2 is that at any moment of time the feedback line is either empty , or conveys a single impulse . if it does convey an impulse , then its state can be described with a stochastic variable @xmath6 , which we call further `` time to live '' . the variable @xmath6 denotes the exact time required by the impulse to reach the output end of the line , which is the neuron s input , and to leave the line . it is clear that @xmath7 . in what follows , we use the time to live @xmath6 only at moments when an isi starts ( just after triggering ) . now it is worth to notice that each triggering starts a new isi . and at the beginning of any isi the line is never empty , but holds an impulse . this happens for the following reasons : * if neuron is triggered by an impulse from the poisson input stream , and the line was empty just before that moment , then the emitted impulse enters the line . at that moment the line is characterized with @xmath8 . * if neuron is triggered by an impulse from the poisson input stream , and the line already conveys an impulse at that moment with time to live @xmath6 , then that same impulse with that same time to live is retained at the beginning of the isi that starts after that triggering , and the line is characterized with that same @xmath6 . * if neuron is triggered by an impulse from the line , then the line is empty at the firing moment and the emitted impulse enters the line . after that moment the line is characterized with @xmath8 . we expect that defined in nn . [ neuron ] , [ line ] system of neuron with delayed feedback line fed with poisson stream is in its stationary regime . this can be achieved if the system functions long enough that its initial state is forgotten . in the stationary regime , let @xmath9 denotes the joint probability density function of neuron with delayed feedback . the probability to get , in the output , starting from the beginning , @xmath10 consecutive isis @xmath11 such that @xmath12 , @xmath13 with infinitesimal @xmath14 is given by @xmath15 . let @xmath16 denotes the conditional probability to get the duration of @xmath17-th isi in @xmath18 provided that previous @xmath19 isis had duration @xmath20 , respectively . now we reformulate in terms of probability density functions the definition from ( * ? ? ? * ch.2 6 ) : the sequence of random variables @xmath21 , taking values in @xmath22 , is called the markov chain of the order @xmath23 , if @xmath24 and this equation does not hold for any @xmath25 . in particular , taking @xmath26 , we have the necessary condition @xmath27 required for the stochastic process @xmath21 to be @xmath10-order markov chain . in the case of isis one reads @xmath28 . we intend to prove that the relation ( [ def ] ) does not hold for any @xmath10 . for this purpose we calculate exact expression for @xmath29 as @xmath30 from which it will be clearly seen that the @xmath31-dependence in @xmath29 can not be eliminated whatever large the @xmath10 is . as it is seen from ( [ defcond ] ) , we need initially to calculate exact expressions for @xmath32 with arbitrary @xmath10 . in @xcite , for the binding neuron model with threshold 2 this is done by introducing an auxiliary stochastic process with events @xmath33 , where @xmath34 is the time to live at the beginning of isi @xmath35 . it was proven that the sequence of events @xmath33 , @xmath36 , is markov chain , which helps to calculate the joint probability density @xmath37 and then @xmath32 as marginal probability by integrating it over @xmath380;\delta]$ ] with respect to each @xmath34 . to simplify this approach , it is worth to notice that in the sequence of consecutive random events @xmath39 only the values of variables @xmath40 are fairly random . indeed , with @xmath41 given , one can figure out exact value for the @xmath42 : if @xmath43 then @xmath44 , and @xmath45 otherwise . now , with @xmath46 known , the same way it is possible to find the exact value of @xmath47 and so on . this allows one to reconstruct unambiguously all the values @xmath48 from the given sequence of values of @xmath40 . having this in mind , we introduce the conditional joint probability density @xmath49 , which we use to calculate required joint pdfs as follows @xmath50 where @xmath6 ( dented previously as @xmath51 ) is the time to live at the beginning of isi @xmath31 , @xmath52 is the stationary pdf which describes distribution of times to live at the beginning of any isi in the stationary regime . in what follows we analyze the structure of functions @xmath52 and @xmath49 . it appears that @xmath52 has a singular component @xmath53 with @xmath54 , and @xmath49 has a @xmath55-function - type singularities at definite hyper - planes in the @xmath17-dimensional space of its variables @xmath56 . after integration in ( [ pdfs ] ) , some of those @xmath55-functions will survive , and one of those survived has its argument depending on @xmath31 . the latter statement depends on exact value of isis in the sequence @xmath57 . here , we limit our consideration to the domain in the @xmath17-dimensional space of variables @xmath56 , which is defined as follows @xmath58 notice that @xmath59 is not involved in ( [ domain ] ) . the @xmath31-dependent @xmath55-function will as well survive in the @xmath29 for any @xmath10 , which will complete the proof that the condition ( [ def ] ) can not be satisfied for any @xmath10 . a question remains of whether the domain ( [" +"when nanoscopic objects such as the quantum dots , nonowires or thin metallic layers are placed in a neighborhood of superconducting material they partly absorb its order parameter . on a microscopic level this proximity effect causes that electrons near the fermi energy become bound into pairs . upon forming a circuit with external leads ( which can be chosen as conducting , ferromagnetic or superconducting ) such effect can induce a number of unique properties in the normal and anomalous tunneling channels @xcite . for instance , the relation between correlations and the on - dot induced pairing has been recently experimentally probed by the andreev spectroscopy @xcite and the josephson current measurements @xcite signifying important role of the kondo effect on the subgap current . we address here the andreev - type transport through the double quantum dot ( dqd ) nanostructure coupled between the normal ( n ) and superconducting ( s ) leads . we focus on the subgap regime , i.e. energies considerably smaller than the pairing gap @xmath2 of superconductor . under such conditions eigenstates of the uncorrelated quantum dots are represented either by the singly occupied states @xmath3 , @xmath4 or by coherent superpositions of the empty and doubly occupied configurations @xmath5 . the resulting bogolubov - type quasiparticle excitations have an influence on additional spectroscopic features originating for instance from the internal structure , the correlations , perturbations etc . due to the proximity effect all these appearing structures would show up _ simultaneously _ at negative and at positive energies . to highlight this sort of emerging physics we shall explore in more detail the interference patterns originating from a charge leakage @xmath6 ( assumed to be much weaker than @xmath7 and @xmath8 ) between the central quantum dot ( qd@xmath9 ) and another side - attached one ( qd@xmath10 ) . we also analyze stability of these patterns with respect to a decoherence induced by coupling @xmath11 to the floating lead ( d ) as sketched in figure [ scheme ] . practically this d electrode can mean a substrate on which the quantum dots are deposited or it mimics the effects caused by phonons / photons @xcite . without a decoherence the t - shape double quantum dot systems have been already studied theoretically considering both metallic leads ( see e.g. @xcite ) and metallic / superconducting ones @xcite . in the regime of weak interdot coupling @xmath6 this configuration of the quantum dots enables realization of the fano - type lineshapes ( for a survey on the fano effect and its realizations in various systems see ref . these features can arise when the electron waves transmitted between the external electrodes via a broad qd@xmath9 spectrum happen to interfere with the other electron waves resonantly scattered by the discrete qd@xmath10 levels @xcite . the hallmarks of destructive / constructive quantum interference show up in a form of the asymmetric lineshapes @xmath12 in the tunneling conductance , where the dimensionless argument @xmath13 is proportional to @xmath14 , @xmath15 denotes the asymmetry parameter and @xmath16 are some background functions slowly varying with respect to @xmath17 . such lineshapes have been indeed observed experimentally for the dqd coupled between the metallic leads @xcite . similar fano - type features have been also previously reported from the spectroscopic measurements for a number of systems , e.g. the cobalt adatoms deposited on au(111 ) surfaces @xcite , the semiopen nanostructures @xcite , the dithiol benzene molecule placed between the gold electrodes @xcite , the hidden order phase of the heavy fermion compound uru@xmath10si@xmath10 @xcite , the dopant atoms located in the metal near a schottky barrier mosfet @xcite , and many other @xcite . considering the proximity effect in n - dqd - s heterojunctions we have recently emphasized @xcite the possibility to observe the particle / hole fano - type lineshapes in the subgap andreev transport . we would like to explore here how such fano - type structures are robust on a decoherence . since the floating lead ( d ) does not belong to a closed circuit we shall assume that a net current to / from such electrode vanishes , so its role can be treated merely as the source of a decoherence . formally our study extends the previous results of ref . @xcite onto the anomalous andreev transport . to our knowledge such problem has not been yet addressed in the literature and it might be of practical importance for the possible experimental measurements . influence of the bosonic ( phonon / photon ) modes shall be discussed elsewhere . in the next section we briefly state formal aspects of the problem . next , we discuss a changeover of the fano - type lineshapes with respect to the asymmetric coupling @xmath18 which controls efficiency of the proximity effect . we also investigate in detail stability of the particle / hole fano features with respect to decoherence ( in the spectrum and in the andreev transmittance ) . finally , we take into account the correlations . in particular we argue that for strong enough coupling @xmath11 the kondo resonance formed on the side - attached quantum dot qd@xmath10 can induce a tiny interferometric pattern at @xmath19 . such kondo driven fano structure could be detectable by the low bias andreev conductance . the double quantum dot nanostructure shown in fig . [ scheme ] can be described by the following anderson impurity hamiltonian @xmath20 where the bath @xmath21 consists of three external charge reservoirs ( @xmath22 ) , @xmath23 refers to the double quantum dot , and @xmath24 stands for the hybridization part . we treat the conducting leads ( @xmath25 ) as free fermi gas @xmath26 and represent the isotropic superconductor by the bilinear bcs form @xmath27 . using the second quantization we denote by @xmath28 the annihilation ( creation ) operators for spin @xmath29 electrons in the momentum state @xmath30 with the energy @xmath31 measured with respect to the chemical potential @xmath32 . following ref . @xcite we assume that the charge transport occurs through the t - shape configuration ( fig . [ scheme ] ) only via the central ( @xmath33 ) quantum dot , whereas the side - attached quantum dot is responsible merely for the quantum interference . hybridization of the quantum dots with external reservoirs of the charge carriers is given by @xmath34 such couplings indirectly affect the quantum dots @xmath35 through the interdot hopping @xmath6 in @xmath23 . we use standard notation for the annihilation ( creation ) operators @xmath36 for electrons in both quantum dots @xmath37 . their energy levels are denoted by @xmath38 and @xmath39 stand for the on - dot coulomb potential . if the chemical potentials @xmath32 in the electrodes are safely distant from the band edges one can impose the wide - band limit approximation , introducing the constant couplings @xmath40 . in this work we shall use @xmath7 as a convenient unit for the energies . in order to account for the proximity effect we have to deal with the mixed particle and hole degrees of freedom . among the possible ways for doing this one can use the nambu spinor notation @xmath41 and @xmath42 . the spectroscopic and transport properties of the setup can be determined from the matrix green s function @xmath43 . in equilibrium case this function depends solely on the time difference @xmath44 and its fourier transform can be expressed by the following dyson equation @xmath45 where @xmath46 are the green s functions of the isolated quantum dots @xmath47 and the selfenergies consist of the noninteracting part @xmath48 with the additional correction @xmath49 due to the electron - electron correlations . in the simplest manner a development of the particle and hole interference fano structures ( see fig . [ dos_evol ] ) can be explained restricting to the noncorrelated quantum dots . the selfenergies @xmath50 are given by @xmath51 where the inderdot hopping contribution refers to @xmath52 . the green s functions of the conducting leads @xmath53 have diagonal form @xmath54 whereas the superconducting lead is given by the bcs structure @xmath55 with the corresponding coefficients @xmath56 \nonumber \\ u_{\bf k}v_{\bf k } & = & \frac{\delta}{2e_{\bf k } } , \nonumber\end{aligned}\ ] ] and the quasiparticle energy @xmath57 . in the wide - band limit we obtain for @xmath53 @xmath58 and for the superconducting electrode @xmath59 with @xmath60 in a far subgap regime @xmath61 only the off - diagonal terms of the matrix ( [ sigma_s ] ) are preserved tending to the static value @xmath62 . this _ atomic limit _ case has been studied by several groups and the results have been recently summarized in the ref . @xcite . for arbitrary @xmath2 we obtain the following set of coupled equations @xmath63 { { { \mbox{\boldmath{$i$ } } } } } \!-\!\varepsilon_{1 } { { { \mbox{\boldmath{$\sigma$ } } } } } _ { z } \nonumber \\ & & + \ ; i \ ; \frac{\gamma(\omega ) \delta \gamma_{s}}{2\omega } { { { \mbox{\boldmath{$\sigma$ } } } } } _ { y } - |t|^{2 } \ ; { { { \mbox{\boldmath{$g$ } } } } } _ { 2}(\omega ) , \label{s_qd1 } \\ { { \mbox{\boldmath{$g$ } } } } _ { 2}(\omega)^{-1 } & = & \left [ \omega + i \ ; \frac{\gamma_{d}}{2 } \right ] { { { \mbox{\boldmath{$i$ } } } } } \!-\!\varepsilon_{2 } { { { \mbox{\boldmath{$\sigma$ } } } } } _ { z } - |t|^{2 } \ ; { { { \mbox{\boldmath{$g$ } } } } } _ { 1}(\omega ) \label{s_qd2 } \end{aligned}\ ] ] where @xmath64 stands for the identity matrix and @xmath65 denote the usual pauli matrices . figure [ dos_evol ] shows the spectral function @xmath66 obtained in the equilibrium situation for both uncorrelated quantum dots ( @xmath67 ) assuming a weak interdot hopping @xmath68 ( decoherence is not taken into account here ) . to focus on the subgap regime @xmath69 we used @xmath70 and other effects related to the gap edge singularities are saparately discussed in the appendix a. for an increasing ratio @xmath18 we can notice the following qualitative changes : a ) the initial lorentzian centered at @xmath71 splits into two quasiparticle peaks centered at @xmath72 ( due to the proximity effect ) , b ) the usual fano - type lineshape formed at @xmath1 is for larger values of @xmath8 accompanied by appearance of its mirror reflection at @xmath73 ( we shall refer to these peaks as the particle / hole fano structures ) , c ) fano - type lineshapes of these particle / hole features are characterized by an opposite sign of the asymmetry parameter @xmath15 , d ) the asymmetry parameters exchange the sign for such @xmath8 when the quasiparticle energy @xmath74 . for a closer inspection on the above mentioned changes we examine in the upper ( bottom ) panel of fig . [ decoh_dos ] the spectral function @xmath66 obtained for @xmath75 ( @xmath76 ) when @xmath1 is smaller ( larger ) than the quasiparticle energy @xmath77 . we also check the decoherence effect on these particle and hole fano lineshapes . we notice that already a weak coupling @xmath11 to the floating lead washes out both these particle and hole fano structures . thus we conclude that decoherence has a detrimental effect on the quantum interferometric features . to provide some physical argumentation for this behavior let us recall that the resonant level at @xmath1 gradually broadens uppon increasing @xmath11 . for this reason the electron waves are scattered on the side - attached quantum dot without any sharp change of the phase , thereby the fano - type interference is no longer possible @xcite . in other words , the particle / hole fano - type lineshapes seem to be rather fragile entities with respect to" +"the quantum mechanical motion of electrons in two - dimensional space , subject to crossed magnetic and electric fields and in the presence of a single impurity described by a zero - range potential , provides a basis for the explanation of the integer quantum hall effect @xcite . until now in all considerations the electric field has been treated as a small perturbation . the purpose of the present work is to reconsider these investigations and to discuss some novel phenomena which appear for nonperturbative electric fields . in our approach an attractive impurity is modelled as a zero - range potential center , as has been already exploited in @xcite . it turns out that in order to define such a point interaction one needs to renormalize the strength of the @xmath0-function and that such a renormalized potential is capable of supporting one localized state per landau level . this finding also corresponds to the result obtained by gyger and martin @xcite . investigating the case of a weak electric field they have proven that all localized states change into resonances with lifetimes varying with the electric field in a gaussian way . with reference to these papers we shall focus our attention on the opposite regime , i.e. , when the electric fields is strong . our aim is to answer the following questions : 1 . how many resonance states exist per one landau level for a non - vanishing electric field ? 2 . what is a maximum electric field above which resonance states of a given lifetime can not exist ? we shall see that apart from the well - known localized states lying between landau levels @xcite _ new resonance states _ are created by a strong electric field , the lifetime of which can be comparable to or larger than typical times encountered in solid state physics . throughout this paper we use units in which @xmath1 . the two - dimensional system we are concerned with is governed by the hamiltonian which , for convenience , we decompose into two parts , @xmath2 related to the physical situation for which the green s function is known and a @xmath0-like potential with the strength given by the so - called bare coupling constant @xmath3 , @xmath4 such a model has been extensively studied in the literature @xcite proving its usefulness in many branches of physics . it is , however , important to realize that the model is not free from difficulties . to be more precise , it exhibits divergencies which have to be tempered by renormalizing the bare coupling constant @xmath3 . therefore , let us address this problem and show how to remove all divergent terms by considering the retarded green s function for the hamiltonian @xmath5 . our starting point is the lippmann - schwinger equation which , in this particular case , adopts the form @xmath6 where the regularized green s function for the hamiltonian @xmath2 , denoted by @xmath7 , is assumed to be known . now performing the foregoing integral over @xmath8 and making some algebraic manipulations we arrive at the retarded green s function for our model @xmath9 it appears that @xmath10 is the only term which needs to be regularized in order to avoid divergencies . let us explain how to cope with them analyzing the simplest case of a free electron with an effective mass @xmath11 interacting only with the @xmath0-like potential . in our approach we choose a particular regularization scheme which we call the proper time regularization . we expect that although the bare coupling constant @xmath3 depends on the regularization scheme chosen , the observable quantities , like poles of the full green s function in the complex energy plane , can not depend on this scheme . indeed , we shall demonstrate that our method leads to the same equation for energies of localized states in the magnetic field as in @xcite . for a free particle the retarded green s function in the so - called fock - schwinger proper time represantation @xcite has the form @xmath12 where the singularity for @xmath13 is avoided by modifying the integration contour over the proper time @xmath14 in such a way that it lies just below the real axis ( this means that @xmath15 is a small positive parameter ) . naturally , the retarded green s function for non - vanishing @xmath16 or @xmath17 is recovered by putting @xmath18 . such a prescription we call the proper time regularization . now , it is straightforward to show that the denominator in eq . ( [ e2.3 ] ) reads @xmath19 it is also clear that the integral above diverges logarithmically for small values of @xmath14 when @xmath18 . this divergence , however , can be absorbed into the bare coupling constant @xmath3 giving the finite expression for the full green s function even for @xmath15 equal to 0 . indeed , performing the proper time integration by parts we arrive at @xmath20 where @xmath21 is an arbitrary positive parameter of the same dimensionality as @xmath14 , whereas @xmath22 is the renormalized coupling constant defined by the relation @xmath23 let us remark that in order to temper a singular part in the formula above the bare coupling constant @xmath3 has to be negative . this means , in fact , that in two dimensions there can not exist a repulsive point interaction . having this in mind we shall restrict ourselves only to the case with an attractive point interaction for which , after performing the remaining integral , we have @xmath24 where @xmath25 is the euler s constant . this equation shows that independently of numerical values of @xmath22 and @xmath21 there exists @xmath26 such that the denominator of the full green s function vanishes , i.e. , the two - dimensional zero - range potential always supports a bound state . denoting the energy of this state by @xmath27 we end up with the following expression for the denominator @xmath28 , @xmath29 let us add in closing that there still remains a free parameter of the theory , i.e. , the energy of a bound state @xmath27 . nevertheless , it has now the clear physical meaning in the sense that its value can be measured , contrary to the artificial and physically unclear parameters @xmath21 and @xmath22 . in this section we consider the two - dimensional system composed of an electron and @xmath0-like impurity placed in the external magnetic and electric fields for which the hamiltonian @xmath2 can be written as @xmath30-e{\cal e}x \ , , \label{e3.1}\ ] ] where the electric @xmath31 and magnetic @xmath32 fields are directed towards @xmath33 and @xmath34 axes , respectively , whereas the vector potential is taken in the circular gauge , @xmath35 . as we have already pointed out , the problem of finding energies of impurity - induced resonance states consists in searching for zeros of the denominator in eq . ( [ e2.3 ] ) . therefore , what we have to know is the regularized green s function for the hamiltonian @xmath2 . applying the proper time regularization scheme discussed above we arrive at the regularized retarded green s function @xmath36 , @xmath37 \ , , \label{e3.2}\end{aligned}\ ] ] and the denominator @xmath28 , @xmath38 \ , , \label{e3.3}\end{aligned}\ ] ] where @xmath39 is the cyclotron frequency . comparing this formula with eq . ( [ e2.5 ] ) one can notice that in both these expressions the integrals over @xmath14 diverge for small arguments exactly in the same way . hence , we gather that now it is also possible to temper the divergent term by renormalizing the coupling constant @xmath3 . at this point let us introduce new dimensionless units . as a typical length scale for the problem we take @xmath40 , whereas the dimensionless scaled electric field and energy are @xmath41 and @xmath42 , respectively . additionally , choosing a new variable @xmath43 we find that @xmath44 \ , . \label{e3.4}\end{aligned}\ ] ] at first glance it might seem that the integral above is divergent for @xmath45 , where @xmath46 . it is not , however , the case . indeed , analyzing the integrand in the close vicinity of these points one can prove the convergence of the foregoing integral . having this in mind we shall discuss below the special case when the electric field is switched off . for @xmath47.,width=283 ] for @xmath47.,width=283 ] for @xmath48.,width=283 ] the problem without an electric field has been already examined by cavalcanti and de carvalho in @xcite . however , we have found it interesting to derive their equation for energies of the impurity - induced localized states using the proper time regularization scheme . our point of departure is the function defined by eq . ( [ e3.4 ] ) with @xmath49 , @xmath50 \ , . \label{e3.5}\ ] ] in order to treat these two integrals separately we regularize them first . this allows us to integrate them by parts and put finally the regularization parameter @xmath15 equal to 0 , keeping in mind , however , that the integration contour over @xmath51 lies just below the real axis , @xmath52 \ , . \label{e3.6}\end{aligned}\ ] ] next , let us expand @xmath53 into series of @xmath54 . this is allowed because the inequality @xmath55 holds for @xmath51 possessing a negative imaginary part , which is guaranteed by our choice of a regularization scheme . hence , inserting into eq . ( [ e3.6 ] ) the series expansion @xmath56 and carrying out all integrations term by term , we arrive at @xmath57 \ , . \label{e3.8}\end{aligned}\ ] ] finally , relating the sum above to a digamma function @xmath58 , we find that the eigenenergies of our system are zeros of the following function @xmath59 \ , , \label{e3.9}\ ] ] which is adequate to the result derived in @xcite with the help of another regularization scheme . zeros of @xmath60 determine the dependence of @xmath61 on @xmath62 for those localized states which are extracted from the landau levels by the zero - range interaction . it is shown in fig . [ fig1 ] that only one state is extracted per landau level , which is understandable , since in the degenerate landau level there is only one state the wavefunction of which does not vanish at the origin , i.e. , the cylindrically symmetric state @xcite . the situation changes if the electric field is present . it mixes this state with those landau states which explicitly depend on the polar angle . for small electric fields such a mixing is also small and the effect of a point interaction can be neglected . however , for strong electric fields this effect becomes considerable as we are going to show this below . and @xmath63 in fig . [ fig3].,width=283 ] for @xmath64.,width=283 ] in order to determine resonance energies for a non - vanishing electric field we have to find complex zeros of @xmath60 defined by eq . ( [ e3.4 ] ) and lying below the real axis . this means that we have to solve one complex equation , @xmath65 , with four unknown real parameters : @xmath66 , @xmath67 , @xmath62 and the scaled electric field @xmath68 . to this end we shall fix one of these parameters , treat another one as a free parameter , and find the remaining two parameters by solving this equation , i.e. , by determining poles of the full green s function . at the beginning let us fix the imaginary part of the resonance energy and find all possible zeros of @xmath60 . the results are shown in figs . [ fig2 ] and [ fig3 ] . in fig . [ fig2 ] we present the real part , @xmath66 , of all resonance" +"hii galaxies are low - metallicity objects undergoing violent star formation @xcite.their optical spectra show strong emission lines ( recombination lines of hydrogen and helium , as well as forbidden lines of elements like oxygen , neon , nitrogen , sulfur , among others ) that are very similar to the spectra of extragalactic hii regions ( e.g. @xcite ) . among them we can find the least chemically - evolved galaxies in the local universe.due to their proximity they offer ideal laboratories for studying massive star formation with an accuracy and spatial resolution that can not be achieved in similar studies in the distant universe . the integral field unit ( ifu ) spectrographs allow simultaneous spectra to be taken of extended objects . from this , we can learn how the interstellar medium ( ism ) is structured , and derive physical conditions and chemical properties corresponding to individual star - forming knots and external ionized gas component ( located at more or less one kpc from the main body of the galaxy ) . the study of the distribution of these properties is an important issue for our understanding of the interplay between the massive stellar population and the ism , unveiling the mechanisms that govern star formation . studying the chemical abundance distribution of the ionized gas can be used as a tool to explore the possible chemical evolution paths . our sample is composed by three hii galaxies : izw18 , iizw70 and iizw71 . izw18 , since pioneering work of @xcite , has remained a unique object for the study of the chemical evolution galaxies , given its very low oxygen abundance , approximately 1/50 solar , and the absence of a significant underlying old population . however , whether this is a signature of youth remains a subject of debate ( e.g. @xcite ) . the optical structure of this galaxy is very rich , including the two ( southeast and northwest ) central bright knots within the main body @xcite . iizw70 and iizw71 are two prototypical hii galaxies that are interacting . iizw70 presents a conspicuous central star - forming region , and extending to the north - west and south - west there appear fan - like extensions , resembling jet structures @xcite . iizw71 shows a chain of individual star - forming knots that crosses the whole optical body of the galaxy and accounts for all the h@xmath2 emission . two - dimensional spectra have been analyzed in order to derive the properties of the different components of the galaxy iizw70 , that was observed with pmas at caha . the pmas spectrograph is equipped with 256 fibers coupled to a @xmath3 lens array . each fiber has a spatial sampling of 0 @xmath45@xmath50 @xmath45 on the sky resulting in a field of view of @xmath6 . mosaic patterns were used to cover the central regions and different regions of interest ( e.g. , tidal tails ) . the data were reduced using the software r3d @xcite . we fitted the line profiles to derive the integrated flux of each emission line , using the software fit3d @xcite , already used in previous similar studies @xcite,@xcite . in figure [ maps ] we show maps of iizw70 in the flux for the lines h@xmath2@xmath06563 and [ oiii]@xmath05007 . the original pixels have been resampled in order to smooth the emission features . emission line images are created by selecting appropriate narrow band filters from the data cube . these narrow band images are created in a wavelength range of @xmath710 around the emission wavelength and show emission line fluxes not corrected by reddening . the continuum emission is subtracted using narrow - band images in wavelengths adjacent to the emission lines . figure [ fig1 ] shows the diagnostic diagrams , [ oiii]@xmath05007/h@xmath8 vs. [ sii]@xmath96717,31/h@xmath2 and [ oiii]@xmath95007/h@xmath8 vs. [ nii]@xmath96584/h@xmath2 @xcite , only for the fibers that present diagnostic line - intensity ratios with relative errors @xmath10 30@xmath11 . line fluxes were corrected for interstellar extinction using the value of c(h@xmath12 ) for each fiber , applying the extinction law given by @xcite . the solid lines show the classical separation between ionization due to star formation ( left ) and active galactic nuclei ( agn ) ( right ) . the boundary curve between agns and star forming regions is taken from @xcite . @xmath05007/h@xmath12 and [ sii]@xmath0@xmath06717,31/h@xmath2 and right panel displays [ oiii]@xmath05007/h@xmath12 line ratio as a function of [ nii]@xmath06584/h@xmath2 ; only line ratios with relative errors @xmath10 30@xmath11 are shown ; the solid lines are the dividing lines between hii - regions galaxies ( left ) and agns ( right ) @xcite.,width=302 ] the diagnostic diagrams give us information about the nature of the ionizing source . we can see that most of line - intensity ratios measured for each fiber , at both diagrams , are located on the left side of the solid curves . this suggests that for the galaxy iizw70 the ionising radiation is mainly related to the most massive youngest stars . we would like to stress that spectrophotometric studies of hii galaxies are of paramount importance in order to derive their evolutionary status . besides , high - resolution spectroscopy of hii galaxies will help trace the kinematics of the galaxy and provide valuable information on the mechanisms triggering the star formation . a detailed analysis of these data is going to be presented in a forthcoming paper ." +"the first - year data from the wilkinson microwave anisotropy probe ( wmap ) ( bennett at al . 2003a , b ) became a basis for testing cosmological scenarios , substantial improving of evaluation accuracy of basic cosmological parameters related to the geometry of our universe , dynamics of its expansion , matter and energy contents . therefore any studies of reliability of the provided data are of great interest and importance . in particular , application of non - standard methods provide additional independent tests of data quality and consistency , as well as the correctness of involved interpretations . all the sky cmb anisotropy maps give possibility to test with high accuracy the fundamental principles of current cosmology , such as the isotropy of our universe and the gaussianity of primordial cosmological perturbations . the first analysis of wmap data for gaussianity was performed by wmap team @xcite . they found that the wmap data are consistent with the gaussian primordial fluctuations and provided limits to the amplitude of non - gaussian ones . other authors , however , applying advanced or sophisticated statistical methods to analyse the foreground - subtracted wmap maps pointed out non - gaussian signatures or north - south asymmetry of galactic hemispheres ( chiang et al . 2003 , park 2004 , eriksen et al . 2004a , hansen et al . 2004a , b , c , eriksen et al . 2005a , cayon et al . some authors suppose that it may be caused by residual foreground contamination from unknown galactic or extra - galactic sources and find their possible locations , angular scales , and amplitudes ( park 2004 , eriksen et al . 2004a , hansen et al . 2004b , chiang & naselsky 2004 , patanchon et al . 2004 , naselsky et al . 2005 , tojeiro et al . 2005 , land & magueijo 2005 ) . for example , tojeiro et al . ( 2005 ) argued that the evidence for non - gaussianity on large scales is associated with cold spots of unsubtracted foregrounds . some part of non - gaussian statistics of @xmath0 fluctuations can be due to the ring of pixels of radius of 5 degrees centered at ( @xmath1 ) @xcite , close to the spot detected in vielva et al . ( 2004 ) and cruz et al . wibig & wolfendale ( 2005 ) performed the correlation analysis of cmb temperature and gamma - ray whole - sky maps and detected positive correlation , which may suggest an actual contamination of the wmap data by , if not cosmic rays directly , some component accompanying them in interstellar space with a sufficiently flat emission spectrum . all these studies indicate that wmap q- , v- , and w - band maps contain information on unidentified extended low - amplitude foreground structures that contaminate the relic cmb signal . the effective extraction of these structures from the wmap maps would improve the current and future cmb analyses , as well as reveal possible new foreground objects or effects ( cf . davies et al . 2005 , eriksen et al . 2005b ) . our principal goal in the present paper is to understand the physical meaning of structures within wmap measurements in order to detect or limit possible non - cosmological factors affecting the data used for determining cosmological parameters . we apply two simple analytical methods to study possible foreground or observational effects in the wmap first - year data , not recognized and/or p removed by the cleaning methods used by the wmap team ( bennett et al . 2003b ) . in the paper , first we shortly provide the basic information about the data analysed , and next describe our method of generating gradient maps from the foreground - cleaned wmap maps and interpret the large - scale gradient structures by the observational strategy of the wmap satellite . we demonstrate that the scanning effects present in the raw signal data can leave clear imprints on the gradients maps from all frequency channels , retained even in coadded , smoothed , and ilc maps . then , we investigate distribution of signal dispersion in the wmap maps to find a significant asymmetry between the northern and southern galactic hemispheres . following some previous authors , we argue that a natural explanation of this asymmetry is residual galactic contamination . finally , the inevitable influence of the above - mentioned effects on the analysis of the large - scale cmb structure is shortly considered . in this paper we study the publicly available first - year wmap maps in 5 frequency channels , k ( 22.8 ghz ) , ka ( 33.0 ghz ) , q ( 40.7 ghz ) , v ( 60.8 ghz ) and w ( 93.5 ghz ) downloaded from lambda website . the maps provide distributions of differential temperature measured in micro - kelvin units , @xmath2 , over the entire sky . the signal in each individual map , after subtracting the kinematic dipole component , foreground point sources , and diffuse galactic emission , is expected to consist primarily of cosmic microwave background ( see bennett et al . 2003a , b for details ) . we studied mainly individual differential assemblies maps with the full available resolution ( nside=512 in the healpix pixelization ) . most analyses presented in the paper use the v2 channel map , showing the lowest galactic contamination and small instrumental noise . we study the variations of measured temperature fluctuations in the wmap sky maps , including cmb signal and instrumental noise , by analysing the gradient structure of the data . we applied two methods in order to derive the gradients . in the first approach , we evaluate the _ maximum _ gradient value at a given location in the map ( i.e. in each pixel / cell ) calculated between the reference cell and the surrounding cells using : @xmath3 where the index `` @xmath4 '' indicates the reference cell . `` @xmath5 '' runs through all adjacent cells and @xmath6 is the distance between the cells considered . the second approach involved deriving a gradient map with the use of the sobol operator ( filter ) known in the image analysis as the edge detector ( huang et al . this method evaluated the _ mean _ gradient at a given pixel using the relative values of the signal , @xmath7 , in its 8 adjacent pixels . in this case , the obtained gradient maps reveal the same pattern as in the maximum gradient method , but the derived mean gradient values are lower . below we present the maximum gradient maps derived with the simpler method using eq . ( 3.1 ) , which is more efficient in visualizing gradient structures . the map of @xmath8 derived for the wmap v2 channel is presented in fig . 1b . in the figure one can clearly see regions of low gradients at both the ecliptic poles and within two extended circular regions around the poles at the radius @xmath9 . the extended regions of enhanced gradient occupy a wide stripe along the ecliptic equator . the largest gradients occur at the galactic plane due to some residual galactic component . relatively large gradient values are also found in places where data were partly discarded because of the planets appearing in the wmap field of view . the comparison of the gradient pattern with the map of observational time ( @xmath10 the _ effective number of observations _ in the wmap team nomenclature , @xmath11 ) ( fig.1d ) proves that most of the observed extended gradient structures represent variations of instrumental noise within the data . the noise distribution corresponds to the varying observational time in different areas of the sky due to the wmap sky scanning pattern . it also leads to a distinct anti - correlation between the observational time and the signal gradient . using the above method , we derived the gradient maps for all the wmap channels ( the maps can be obtained upon request from k.ch . ) with analogous characteristic gradient patterns , spots at galactic poles , and rings around them . these characteristic features in the gradient distribution are more distinct after smoothing the maps ( fig . in order to show it quantitatively , we smoothed both the v2 cmb and the number of observation maps with increasing gaussian beams , and calculated the correlation coefficient . without smoothing , the correlation is -0.16 , for 1 smoothing it is -0.26 , and for 5 , 10 , and 15 smoothing it becomes -0.69 , -0.83 , and -0.89 , respectively . we also obtained the gradient maps from the coadded maps for individual assemblies in v , q and w bands , with the position - dependent , or band - dependent inverse noise - weighting . we got gradient patterns much similar to those obtained from the v2 channel alone . next we applied the gradient analysis to the ilc map . in this case , the characteristic gradient pattern is weaker , because of the convolved to 1 scale component maps of the ilc combined map . however , the distinct pattern appears also in this case , as we demonstrate at fig . 2b by convolving the gradient map with the 15 gaussian beam . in the figure , the observational time pattern analogous to that in fig . 1d is clearly reproduced , while significantly perturbed by the effects of cmb or galactic foreground signal structures . the performed experiments confirm that the systematic pattern revealed in the gradient maps is firmly established and can not be removed by simple filtering procedures , like convolving , or adding data maps . thus it can affect the analysis and interpretation of the large - scale distribution of the signal in the wmap maps . apart from the above analysis of signal gradients , we studied also the large - scale asymmetries within the wmap data by deriving diagrams of the measured signal variance across the sky versus the effective number of observations , n. such diagrams , presented by jarosik et al . ( 2003 ) for the whole sky ( see their fig.10 ) , we constructed independently for the northern and southern galactic hemispheres , in a couple of galactic polar - cap regions formed by removing the galactic equatorial strip with @xmath12 , @xmath13 and @xmath14 ( fig . 3 ) . we used these growing galactic cuts to check if possible galactic foregrounds may affect the data . to derive the sample signal variance for a consecutive bin `` @xmath5 '' centered at the number of observations @xmath15 we used data from all strip cells with @xmath11 in the respective range ( @xmath16 , @xmath17 ) . there were also much smaller numbers of cells with very small or very large @xmath11 , which can explain growing scatter at limiting parts of the plot presented in the upper - left panel of fig 3 . in the other three panels in this figure the zoomed distributions are presented , excluding the range with low @xmath11 , where the linear form of distribution is lost . in the figure one can easily see the south - north asymmetry in the variance distribution . the difference is preserved in a range of regions in the sky with varying number of observations . moreover , there is a distinct tendency for decreasing the difference between hemispheres at higher galactic latitudes . we performed another analysis of the signal dispersion in the channel v2 . we considered 4 separate galactic altitude stripes ( @xmath18 [ @xmath19 , @xmath20 , [ @xmath21 , @xmath22 , [ @xmath23 , @xmath24 , [ @xmath25 , @xmath26" +"in this contribution we discuss a model for noncommutative quantum mechanics ( ncqm ) where noncommutativity in the phase space is considered in the context of the gravitational quantum well ( gqw ) @xcite . furthermore , we consider the dependence of the energy spectrum of the gqw on the mass of the particles in order to study the quantum to classical transition @xcite recently , there has been quite some interest on the noncommutative geometry in the context of quantum mechanics . this has its roots on the role that noncommutative geometry plays in unification models and in string theory . indeed , since the discovery that the low - energy effective theory of a d - brane in the background of a ns - ns b field lives in a noncommutative space @xcite , many efforts have been devoted to the study of noncommutative field theories ( see @xcite and refs . therein ) , to the understanding of the coupling to gravity ( see @xcite and refs . therein ) and , to the non - relativistic limit , through versions of ncqm @xcite . although in string theory only the coordinates space exhibits a noncommutative structure , models in which the noncommutative geometry is extended to the phase space have been recently much discussed @xcite . the main argument for this approach is that noncommutativity between momenta arises naturally as a consequence of noncommutativity between coordinates , as momenta are defined as the partial derivatives of the action with respect to the noncommutative coordinates @xcite . in a 4-dimensional space , this type of phase space structure is defined through the following algebra : [ noncommutation_1 ] x^,x^]=&i^ , p^,p^]=i^ , x^,p^]=i^ , where the parameters @xmath2 and @xmath3 are antisymmetric . this algebra is consistent with standard quantum mechanics thanks the last commutation relation in the set of eqs . ( [ noncommutation_1 ] ) . in a recent paper @xcite , a 2-dimensional version of this algebra , defined by the noncommutative parameters @xmath4 and @xmath5 and by planck s constant @xmath6 has been considered [ noncommutation_2 ] x , y]&=&i , p_x , p_y]=i , x_i , p_j]=i_iji=1,2 . the implementation of this algebra can be performed by considering the noncommutative variables @xmath7 from the commutative variables @xmath8 through linear transformations . two sets of linear transformations can be used to obtain the complete algebra , eqs . ( [ noncommutation_2 ] ) . the first kind of transformation affects only the variables @xmath9 and @xmath10 , while the second affects variables @xmath11 and @xmath12 , thus leading to different results . to eliminate this ambiguity it is convenient to consider a set of linear transformations that modify simultaneously all variables : [ linear_1 ] x=(x-2p_y ) , y=(y+2p_x ) , p_x=(p_x+2y ) , p_y=(p_y-2x ) , where @xmath13 is a scaling factor . in this way , the commutation relations between coordinates and the ones between momenta in eq . ( [ noncommutation_2 ] ) are recovered , however the commutation relation between coordinates and momenta is altered to [ noncommutation_3 ] [ x_i , p_j]=i_eff_iji=1,2 , where we have defined the _ effective planck constant _ @xmath14 and set @xmath15 . in a 4-dimensional space , the generalization of the linear transformations eq . ( [ linear_1 ] ) may be written as : [ linear_2 ] x^=(x^-^ _ 2p^ ) , p^=(p^+^ _ 2x^ ) . if one chooses @xmath15 , these transformations lead to the following 4-dimensional algebra : [ noncommutation_4 ] x^,x^]&=&i^ , p^,p^]=i^ , x^,p^]=i(^+^^ _ 4 ^ 2 ) . hence , one can define a _ 4-dimensional effective planck constant _ as : [ planck_constant_1 ] _ eff=(1+tr[]4 ^ 2 ) . furthermore , it is clear that the commutation relation between coordinates and momenta is not diagonal , the off - diagonal elements are proportional to products of @xmath2 and @xmath3 . we have considered in ref . @xcite the linear transformations eqs . ( [ linear_1 ] ) to determine the noncommutative hamiltonian for a particle moving in the @xmath16 plane subject to a uniform gravitational field @xmath17 . as the effects of phase space noncommutativity are presumably small , we have compared the leading order corrections to the commutative hamiltonian with the experimental results obtained by nesvizhevsky _ _ et al.__@xcite for neutrons in the gqw formed by a horizontal mirror and the earth s gravitational field . this has allowed us to set an upper bound of about mev / c for the fundamental momentum scale introduced by noncommutativity , @xmath18 . supposing that the fundamental noncommutative length scale , @xmath19 , is smaller than the neutron size , that is , of order @xmath20 , we have found that @xmath21 . therefore , the difference between the effective planck s constant and the usual planck constant has no practical effects . on the other hand , it has been recently claimed in ref . @xcite that for a particular choice of the value of the scaling factor @xmath13 the commutation relation between coordinates and momenta is exactly defined by the usual planck constant . however , it can be shown that ncqm models with or without corrections to the value of planck s constant are , in fact , physically equivalent , differing only in the way one defines the noncommutative parameters @xcite . in what follows we shall present our analysis of the gqw in the context of the ncqm . we consider now a particle of mass m moving on the @xmath16 plane in a uniform gravitational field @xmath17 . when a horizontal mirror is placed at @xmath22 , a gqw is set up . in the direction transverse to the gravitational field , @xmath11 , the particle is free , exhibiting a continuous energy spectrum . in the direction of the gravitational field , @xmath9 , the particle exhibits a discrete energy spectrum . its wave function in the @xmath23-th quantum level is given by the airy function @xmath24 , where @xmath25 and @xmath26 @xcite , with energy eigenvalues given by : [ gqw_2 ] e_n=-(mg^2 ^ 22)^1/3_n , where @xmath27 corresponds to the @xmath23-th zero of the airy function and @xmath28 to the maximum height that is classically compatible with a particle with energy @xmath29 . the probability of finding the particle is non - vanishing for all values of @xmath30 . however , when @xmath9 exceeds the value of @xmath31 for each quantum state @xmath23 , this probability decays exponentially , but the particle has a finite probability of penetrating a classically forbidden region through quantum tunneling . these ideas have been used to study the spectrum of neutrons in the quantum well of the earth s gravitational field and a horizontal mirror @xcite . an ultra cold neutron beam was employed , with a mean velocity @xmath32 , traveling through a narrow slit formed by the mirror and a scatterer / absorber placed above it . therefore , the neutron flux through the apparatus is measured as a function of @xmath9 . for @xmath33 , neutrons in the @xmath23-th quantum state have a small probability of crossing the gravitational barrier and tunnel into the scatterer / absorber . this probability is given by @xmath34 and vanishes as the slit height increases . hence , for @xmath33 , neutrons pass through the slit with little loss . for @xmath35 , however , neutrons have a @xmath36 probability of being absorbed by the scatterer and so the slit is not transparent to neutrons . thus flux of neutrons through the slit is given by : [ gqw_4 ] f(x)=f_0_n_n ( -l_nv\ { ll e^(-43_n^3/2 ) , _ n>0 + 1,_n<0 } ) , where @xmath37 is a normalization factor , depending on the incident flux , @xmath38 is the relative population of the @xmath23-th quantum level , @xmath39 is the length of the slit and @xmath40 @xcite . from eq . ( [ gqw_4 ] ) , one can conclude that , for @xmath41 , the flux of particles in the @xmath23-th state approaches its maximum value @xmath37 , while for @xmath42 , this flux tends to vanish . therefore , the classical turning points @xmath31 separate two regions where the neutron flux exhibits distinct behaviour for each state @xmath23 . by adjusting the experimentally measured flux to the predicted flux given by eq . ( [ gqw_4 ] ) , the values of the two lowest classical turning points were obtained @xcite , and these are in good agreement with the quantum mechanical predictions , namely @xmath43 and @xmath44 . we mention that the equivalence principle in the context of the gqw has been analyzed in ref . @xcite . we consider now the discussed gqw , with hamiltonian given by : [ hamiltonian_1 ] h=p_x^22m+p_y^22m+mgx . the corresponding noncommutative hamiltonian can be straightforwardly obtained using the inverse transformations of eq . ( [ linear_1 ] ) , for @xmath15 , [ linear_inverse ] x=c(x+2p_y ) , y=c(y-2p_x ) , p_x=c(p_x-2y ) , p_y=c(p_y+2x ) , to replace the commutative variables by the noncommutative ones : [ hamiltonian_2 ] h&=&c^22m(p_x-2y)^2+c^22m(p_y+2x)^2 + + mgc(x+2p_y)= + & = & c^22mp_x^2+c^22mp_y^2+mgc2p_y+c^22m(xp_y - yp_x)+c^28m^2 ^ 2(x^2+y^2)+mgcx , where @xmath45 and @xmath46 . it should be noticed that [ aux_1 ] c^22mp_y^2+mgc2p_y=12m(cp_y+m^2g2)^2-m^3g^2 ^ 28 ^ 2 , so that the last term is an additive constant that can be subtracted from the hamiltonian . through the redefinition [ momenta ] as : [ hamiltonian_3 ] h=|p_x^22m+|p_y^22m+c2m(x|p_y - y|p_x ) + c^28m^2 ^ 2(x^2+y^2)+mgcx - mgc4 ^ 2x . notice that the last two terms correspond to the commutative gravitational potential , @xmath47 . thus the noncommutative hamiltonian is given by [ hamiltonian_4 ] h=|p_x^22m+|p_y^22m+mgx + c2m(x|p_y - y|p_x)+c^28m^2 ^ 2(x^2+y^2 ) . the similarity between the first three terms in the commutative and noncommutative hamiltonians is clear , the only difference lying in the redefined momenta @xmath48 and @xmath49 . the constant term in the definition of @xmath49 , eq . ( [ momenta ] ) , has , however , no physical meaning as it corresponds to a translation of all the eigenvalues of @xmath50 by the same amount . it does not imply any change in the commutation relations of this operator either . thus , the only physical difference between @xmath10 and @xmath49 concerns the factor @xmath51 and likewise for @xmath12 and @xmath48 , meaning that the kinetic terms in the noncommutative hamiltonian differ from the commutative ones only by a factor @xmath52 . we study now the physics of the hamiltonian eq . ( [ hamiltonian_4 ] ) . to first order in the noncommutative parameters @xmath4 and @xmath5 , it is given by : [ hamiltonian_5 ] h = p_x^22m+p_y^22m+mgx+2m(xp_y - yp_x)=h+2m(xp_y - yp_x ) . notice that as @xmath53 , to first order in the noncommutative parameters , @xmath48 and @xmath49 are equal to @xmath12 and @xmath10 , respectively . we can then conclude that at this order of approximation the noncommutative hamiltonian differs from the commutative one by a term proportional to @xmath5 . hence , the configuration space noncommutativity does not influence the gqw energy spectrum to leading order . it is expected that @xmath5 is a small correction at the quantum mechanical level , and so one can treat the new term as a perturbation to the commutative hamiltonian . the shift caused by this term on the energy levels of the system is given by the expectation value of the perturbed wave function of the system . we note that as the airy function is real , @xmath54 , and hence [ aux_3 ] p_x _ n&=&_0^+dx_n^*(-i_n ) = -i([_n^*_n]_0^+-_0^+dx_n)= + & = & i_0^+dx_n_nx= -_0^+dx_n^*(-i_n)=-p_x_n=0 , where , due do the presence of the horizontal mirror , we have used that @xmath55 and the normalization of the wave function . therefore , the term proportional to @xmath12 in eq" +"giant molecular clouds , both galactic and extragalactic , are observed to have velocity gradients that many authors have interpreted as being caused by rotation ( e.g. , kutner et al . 1977 , phillips 1999 ; rosolowsky et al . 2003 ) . if we start with the premise that these clouds are rotating because they have inherited the angular momentum of the rotating galactic disk out of which they formed , conservation of angular momentum should provide clues that give us insight to the origin of their formation . however , simple formation theories that assume giant molecular clouds ( gmcs ) form by condensing out of the galactic disk are at odds with some of the observations . for instance , they do not adequately explain why the directions of gmc velocity gradients are not typically aligned with the direction of galactic rotation , counter to the expectation of conservation of angular momentum . furthermore , simple formation scenarios tend to overpredict the observed specific angular momentum o f gmcs ( e.g. , blitz 1990 ; rosolowsky et al . this is the so - called `` angular momentum problem . '' provided there is no transfer of angular momentum , the angular momentum of a gmc should be equal to that of the gas out of which it formed . but blitz ( 1990 ) , working under the assumption that the velocity gradients in molecular clouds are due to rotation , showed that the angular momentum due to galactic differential rotation in the solar neighborhood interstellar medium is consistently greater than that contained within molecular clouds . even molecular clouds with the largest observed velocity gradients such as the rosette and orion a molecular clouds have less specific angular momentum compared to the ism from which they presumably formed . blitz ( 1990 ) also pointed out that because the molecular clouds in his sample are rotating in a sense _ opposite _ to that of galactic rotation , they could not have conserved angular momentum from the initial states he calculated , unless the local galactic rotation curve is falling , or unless the clouds always collapsed azimuthall y. the angular momentum problem also extends to extragalactic molecular clouds . roso - lowsky et al . ( 2003 ) showed that simple gmc formation theories consistently overestimate the magnitude of the observed angular momentum of molecular clouds in the galaxy m33 . on average , they found that simple theory overpredicts the observed magnitudes of specific angular momentum by more than a factor of 5 . furthermore , they found that 40% of the gmcs in m33 are counterrotating with respect to the galactic plane . in this paper , we shed light on the angular momentum problem by doing a detailed analysis of the kinematics in gmcs _ and _ the surrounding ism . whereas previous studies estimated the initial angular momentum imparted to gmcs from the galactic rotation curve ( e.g. , blitz 1990 ; blitz 1993 ) , we compare the velocity fields of gmcs to those of the ism with which they are associated directly from observation . in light of the observation that gmcs have a spatial and kinematic correlation with high - surface density atomic gas ( [ sec : analysis ] ) , we pose the question : does the rotation of the large - scale @xmath0 associated with gmcs mirror that of the gmcs themselves ? our primary goal is to determine whether or not rotation is the cause of the velocity gradients in gmcs . to that end , we create first - moment maps of the molecular clouds in our sample and of the atomic gas surrounding them are for comparison . in the following section , we describe the and 21-cm data used to conduct this study . in 3 , we create intensity - weighted first moment and @xmath0 maps of five galactic clouds : perseus , orion a , ngc 2264 , monoceros r2 ( monr2 ) , and the rosette . the results from these measurements are given in 4 , and a summary is provided in 5 . to measure velocity gradients and other properties across the molecular clouds , we use high - resolution , high - sensitivity published observations . because emission is nearly always optically thin in galactic gmcs , we have the advantage of getting a detailed view of the kinematic structure of the molecular clouds in our sample . and because has narrower line widths than the optically thick , the former permits finer separation of velocity components than the latter . nevertheless , the large scale velocity gradient of a gmc measured using is generally consistent with that measured using , since the gradient is being measured across several parsecs and small scale variations in the velocity field tend to get averaged out . the data for perseus , orion a , ngc 2264 , and the monr2 molecular clouds were generously provided by j. bally ( see bally et al . observations of these clouds were taken at the at&t bell laboratories 7 m telescope and have a beam size of 100 . perseus , orion a , and ngc 2264 data were resampled onto @xmath2 grids . the monr2 data were resampled onto a @xmath3 grid . the spectral resolution of 128 channels at 100 khz corresponds to a velocity resolution of 0.27 . on the @xmath4 scale , the cubes have rms noise levels of 0.17 k ( perseus ) , 0.32 k ( orion a ) , 0.42 ( ngc 2264 ) and 0.29 k ( monr2 ) . j. williams and m. heyer graciously provided the fcrao data of the rosette molecular cloud ( see heyer , williams , & brunt 2006 ) . the beam size is @xmath5 and the data were interpolated onto a @xmath6 grid . the spectral resolution is 59 khz per channel , and the velocity resolution is 0.133 . the data have an rms noise of 0.21 k in @xmath4 , similar to that of the bell labs data . the @xmath0 data are obtained from the leiden / argentine / bonn ( lab ) galactic @xmath0 survey ( kalberla et al . 2005 ) , which spans velocities from @xmath7 to @xmath8 . ( the lsr velocities of the molecular clouds in our sample range from 6 to 14 with velocity dispersions of a few . ) the survey has a half power beam width of @xmath9 , velocity resolution of 1.3 , and an rms noise level of 0.07 k. the high sensitivity and resolution of the lab data set enables a detailed study of the atomic gas from which the gmcs formed . observations in the milky way indicate the molecular clouds are typically associated with high - density atomic gas with column densities around @xmath10 ( e.g. , mckee & ostriker 2007 ) . the rosette molecular cloud is a prototypical example : williams et al . ( 1995 ) measured the mean column of the @xmath0 associated with the gmc to be @xmath11 . furthermore , in external galaxies , gmcs are often observed to be located on or near bright @xmath0 peaks . in the large magellanic cloud , mizuno et al . ( 2001 ) observed that most gmcs are associated with @xmath0 having column densities greater than @xmath12 . rosolowsky et al . ( 2003 ) found that every gmc they identified in m33 lies on an over - dense @xmath0 filament , though every over - dense @xmath0 region does not contain a gmc . this seems to imply that high column density atomic gas is necessary but not sufficient for gmc formation . it is our goal to do a detailed comparison of the velocity fields in the gmcs and local atomic gas . to that end , we first describe how the physical properties including column densities , masses , and velocity gradients in both the atomic and molecular gas are determined . we then provide our criteria for choosing spatial and kinematic regions of atomic gas associated with the molecular clouds . lastly , in this section , we discuss how we estimate the specific angular momentum . these parameters are summarized in tables 1 and 2 . the @xmath0 column density , @xmath13 , is calculated along each line of sight by integrating the atomic hydrogen emission above a certain background value and over the selected velocity range , ( see 3.1 and table 1 ) , @xmath14 where @xmath15 is the brightness temperature of the @xmath0 observations and @xmath16 is the channel velocity width . assuming that the @xmath0 is optically thin , equation [ eq : nhi ] provides a lower limit to measured column density , which we convert into units of surface density in figures [ fig : oriona0 ] [ fig : rosette0 ] . the total @xmath0 mass is then determined by summing over all pixels in the map where emission is detected , that is , where the emission is at least three times the root - mean - square ( rms ) noise level : @xmath17 where @xmath18 is the correction for helium , @xmath19 is the distance to a given molecular cloud , and @xmath20 is the area of one pixel , which corresponds to one resolution element . the column density , @xmath21 , is derived assuming that the emission is optically thin and in local thermodynamic equilibrium . following frerking et al . ( 1982 ) , @xmath22^{-1 } \nonumber \\ \times \int_{v_{\mathrm{min}}}^{v_{\mathrm{max}}}{\frac { t_{{\mathrm{b , co}}}~{\ensuremath{\mbox{d}{v}}}}{{\mbox{k km s$^{-1}$ } } } } ~{\mbox{cm$^{-2}$ } } , \end{aligned}\ ] ] where @xmath23 is the integrated intensity and @xmath24 is the excitation temperature . normally , @xmath24 is determined by measuring the radiation temperature toward peaks . since we lack observations at the same resolution as the data , we use a constant excitation temperature in the calculation of @xmath21 for each of the five gmcs . based on the following arguments , we adopt a value of 20 k for each of the gmcs . if the actual excitation temperature in a given region is between 10 and 30 k , the derived column density will be in error by less than a factor of 2 . castets et al . ( 1990 ) showed that the emission in orion a mainly arises from regions where @xmath25 k , and dense cloud cores have temperatures of @xmath26 k. nagahama et al . ( 1998 ) showed that , with the exception of two peaks at @xmath27 and @xmath28 associated with embedded young stellar groups , @xmath24 rises slowly and monotonically in galactic longitude , with an average ranging from @xmath29 k. in his study of molecular clouds , including perseus , orion a , and monr2 , carpenter ( 2000 ) adopts a constant value of @xmath30 k , though the coefficient in his formula for @xmath21 yields slightly higher values than ours in equation [ eq : nco13 ] . thus , for orion a , perseus , ngc 2264 , and monoceros r2 , we use @xmath31 k in our calculation of @xmath21 . williams et al . ( 1995 ) showed that @xmath24 in the rosette decreases slowly with increasing distance from the rosette nebula ( centered at @xmath32 ) from @xmath33 to @xmath34 k. in our analysis , we adopt a uniform value of @xmath31 k for the rosette . our estimate of the cloud s mass using this value is slightly lower than that estimated by williams et al . ( 1995 ) , who measured the mass over a larger surface area ( see below ) . next , the @xmath35 column density is evaluated assuming a ratio of @xmath36 ( frerking et al . pixels having values at least three times" +"blazars are a subclass of radio - loud active galactic nuclei ( agn ) for which non - thermal jet emissions are relativistically beamed along the line of sight ( for a review see , e.g. , * ? ? ? * ; * ? ? ? thus , pronounced variability on timescales of as short as days and even hours is often observed in various energy bands ( e.g. , * ? ? ? * ; * ? ? ? the broadband electromagnetic spectra of blazars consist of two characteristic bumps in the @xmath5 representation : one extending from radio to optical / x - ray frequencies and the other one peaking around high - energy @xmath4-ray photon energies . the measured polarization in the radio and optical bands indicates that the low - energy spectral component is due to the synchrotron emissions of ultrarelativistic electrons ; the @xmath4-ray continuum is instead most widely believed to result from inverse comptonization ( ic ) of various soft photon fields . the source of the seed photons for the ic process can be either the synchrotron emission of the jet itself ( synchrotron self - compton model , or ssc for short ; e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , or the thermal emissions of circumnuclear gas and dust ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? there is an ongoing debate on the exact localization of the dominant blazar emission zone , with current estimates ranging from hundreds of gravitational radii from central supermassive black holes up to parsec - scale distances , as well as on the dominant particle acceleration processes involved , with different scenarios including mildly relativistic internal shocks ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , magnetic turbulence ( e.g. , * ? ? ? * ; * ? ? ? ? * ; * ? ? ? * ) , or even relativistic magnetic reconnection ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? mrk 421 ( r.a . = 11h04m27.3s , dec = + 38d12m32 ; @xmath6 = 0.031 ) is a nearby and bright blazar classified as a typical `` high - frequency - peaked '' bl lac ( hbl ) object whose synchrotron and ic emission components extend up to x - ray and very high energy ( vhe ) @xmath4-ray photon energies , respectively . it is in fact the first extragalactic source detected in the tev range @xcite . as such , mrk 421 is one of the most comprehensively studied hbls through a number of observation campaigns . in particular , recent multi - wavelength campaigns , including , have provided the first ever complete coverage of the @xmath4-ray continuum of the source in its low - activity / quiescence state @xcite . interestingly , the fractional variability amplitude @xmath7 , when plotted as a function of frequency , also reveals a double - peak structure echoing the spectral energy distribution ( sed ) of mrk 421 : @xmath7 rises significantly from the radio towards the x - ray frequencies , decreases over the band , and finally rises again in the tev regime @xcite . this finding seems to imply that , in the framework of the `` homogeneous one - zone '' emission model , the high - energy tail of the electron energy distribution ( synchrotron x - rays and tev @xmath4-rays emitted via the ic process ) is highly variable , while the low - energy segment of the electron energy distribution is relatively steady . the alternative interpretation is a stratified ( multi - zone ) blazar emission model with highly variable high - energy emissions produced in distinct ( more compact ) emission sites compared with lower - energy emissions , which vary more slowly . in this context , broadband x - ray observations of mrk 421 may in principle provide unique clues on the variability and spectral properties of both the low- and the highest - energy segments of the electron energy distribution because the synchrotron continuum of the blazar falls exponentially around photon energies of several / tens of kev ( at least during the low - activity states ) . this reflects the high - energy cutoff in the underlying electron energy distribution , so the radiative output of the source in the hard x - ray range may be dominated by the low - energy tail of the ic emission component . however , in the case of bl lacs in general and hbls in particular , including the x - ray brightest source mrk 421 , x - ray data above 10kev are deficient and available typically only for isolated flaring periods ( see * ? ? ? * ; * ? ? ? * ; * ? ? ? this is because previous hard x - ray observations relied on `` non - imaging '' detectors for which the sensitivity was insufficient to detect the source in its low - activity states . the nuclear spectroscopic telescope array mission (; * ? ? ? * ) is the first focusing high - energy x - ray telescope in orbit and operates in the band from 3 to 79kev . thanks to its imaging capability , probes the hard x - ray sky with a more than 100-fold improvement in sensitivity . @xcite and @xcite presented the observations of mrk 421 during flaring epochs . in this paper , we revisit the archival mrk 421 data provided by in january 2013 and discussed previously by @xcite when the source was in a historical low - activity state corresponding to an extrapolated @xmath8kev energy flux of @xmath9erg@xmath10s@xmath11 . mrk 421 was selected as a representative of the hbl class of blazars and thus has been observed frequently with since january 2013 , partly in the framework of extensive multi - frequency campaigns . the total exposure time over 88 orbits amounts to more than 250ks , including two calibrating observations conducted in july 2012 @xcite . a typical observation spans 10 hrs ; hence , the actual exposure for each observation , after only `` good time intervals '' are selected to eliminate the passage of the south atlantic anomaly and orbital modulation of visibility , ranges from 10ks to 25ks . all observations were conducted with two co - aligned independent telescopes called focal plane module a and b ( fpma and fpmb ) . throughout the observations , variations in the count rate of more than two orders of magnitude were observed . it has been argued that the synchrotron emissions of the blazar account for all the flux detected up to 79kev during the flaring states @xcite . here , we focus on the historical low - flux state of mrk 421 , which was witnessed by in january 2013 ( see table[table1 ] for the logs of the analyzed observations ) . the archival data were downloaded from nasa s heasarc interface and reduced by using the ` nustardas ` software , which is included as part of the ` heasoft ` package version 6.17 . for the temporal and spectral studies presented in the following sections , the x - ray events were extracted from a circular region with a radius of @xmath12 and centred on the source position , whereas the background was accumulated in an annulus with inner and outer radii of @xmath12 and @xmath13 , respectively . we carefully checked that other choices of source and background regions did not affect the analysis results presented in the next sections within uncertainties of @xmath14 . the response files were generated by using the standard ` nupipeline ` and ` nuproducts ` scripts . version 20151008 of the caldb files were used in this study . even in the historical low - flux state of the target , the extracted x - ray count rates were well above the background level up to 40kev and almost equal to the background level above 40kev . with good characterization of the background , which left the uncertainty at a @xmath15 level @xcite , the gathered mrk 421 data could therefore be used for spectral modeling up to the high - energy end of the band at 79kev . figure[fig : lightcurve ] shows the count rate variations during the observations between january 2 ( mjd 56294 ) and january 20 ( mjd 56312 ) . the x - ray counts from both fpma and fpmb detectors are summed , and the background is subtracted . the light curves are shown separately for the two different energy bands : @xmath0kev ( top panels ) with 2ks binning and @xmath3kev ( bottom panels ) with 20ks binning . the light curves indicate that the @xmath0kev source flux was nearly constant except for mjd 56307 when a pronounced variability was observed and the average flux increased by a factor of three . in addition , note that the source was detected at more than the @xmath16 level in the 40@xmath1779 kev band not only in mjd 56307 but also in mjd 56302 , when an average @xmath0kev count rate was lowest . for the remaining two observations , we provide the corresponding @xmath18 confidence level upper limits . figure[fig : images ] compares the temporal variations in the x - ray images of mrk 421 in the @xmath3kev energy range . these were reconstructed by using the sum of the fpma and fpmb data in mjd 56294 , 56302 , 56307 and 56312 , respectively . the images were smoothed by a gaussian kernel of @xmath19 and color - coded ; the given color bar indicates a relative excess of photon counts in arbitrary units for which the maximum value is corrected for different exposure times of each observation ( see table[table1 ] ) . note that the target was clearly detected at more than the @xmath2 level only in mjd 56302 and 56307 , which is consistent with the source light curve given in figure[fig : lightcurve ] . a slightly higher significance for the images ( @xmath20 ) compared to the light curves ( @xmath21 ) is because source counts were extracted from a circular region with a radius of @xmath12 for figure[fig : lightcurve ] , whereas all of the detected photons were used for figure[fig : images ] against the point spread function of . a positive detection of the source above 40kev during the extremely low - flux state in mjd 56302 but not during similarly low - flux states in mjd 56294 and 56312 indicates that the excess hard x - ray emission is variable on the time scale of a week . lccccccc[t ! ] 56294.78 & 9.2 & pl@xmath22 & 3.10@xmath230.03 & @xmath17 & @xmath17 & 44.4@xmath230.6 & 170.8/161 + & & bkn - pl@xmath24 & 3.25@xmath230.05 & 7.23@xmath230.66 & 2.87@xmath25 & 46.4@xmath234.2 & 155.1/159 + & & pl+pl@xmath26 & 3.32@xmath230.07 & @xmath17 & 1.7@xmath27 & 48.4@xmath230.9 & 158.1/160 + 56302.05 & 22.6 & pl & 3.06@xmath230.02 & @xmath17 & @xmath17 & 31.0@xmath230.3 & 262.3/249 + & & bkn - pl & 3.08@xmath230.02 & 17.8@xmath28 & 2.08@xmath29 & 34.0@xmath231.3 & 246.3/247 + & & pl+pl & 3.11@xmath30 & @xmath17 & 0.17@xmath31 & 35.3@xmath230.5 & 247.9/247 + 56307.04 & 24.2 & pl & 3.03@xmath230.01 & @xmath17 & @xmath17 & 107.6@xmath230.5 & 467.4/456 + & & bkn - pl & 2.96@xmath230.02 & 7.83@xmath32 & 3.19@xmath30 & 105.1@xmath233.3 & 429.6/454 + 56312.10 & 25.0 & pl & 3.07@xmath230.02 & @xmath17 & @xmath17 & 36.4@xmath230.3 & 295.3/290 + & & bkn - pl & 3.07@xmath230.02 & 28.8@xmath33 & 1.78@xmath34 & 38.2@xmath231.2 & 292.5/288 +" +"phonons are important in metallic systems . they affect the electronic behaviour in diverse ways causing the dominant temperature dependent contribution to the resistivity , an enhancement of the specific heat , and an attractive effective electron - electron interaction , which may induce superconductivity . one can expect strong electron - phonon interactions in strongly correlated systems , such as heavy fermion compounds@xcite , where the radius of the rare earth ions is very sensitive to the @xmath0-electron occupation . the coupling of electronic states to the lattice also plays an important role in the anomalous electronic behaviour of the manganites@xcite . the superconductivity in the fullerides@xcite appears to be induced by electron - phonon interactions within a strongly correlated electron band . however , the fully quantum mechanical treatment of lattice effects in these compounds has so far received comparatively little attention . the reason for that lies in the difficulty in handling strong electron - phonon coupling together with strong electron - electron repulsion . recent advances in non - perturbative techniques , most notably the development of the dynamical mean field theory ( dmft)@xcite , enable one to investigate the interplay of electron and phonon interactions in these systems . one of the most prominent models in the field of strongly correlated electron systems is the hubbard model@xcite which been used extensively to study the effects of strong local electron - electron interactions . especially within the framework of dmft@xcite the nature of the mott transition could be clarified@xcite . the holstein model@xcite has been used to study polaronic effects in the absence of electron - electron repulsion , mainly in the limit of low electron density . systems with finite electron density have received less attention , but have been studied within the dmft using monte carlo@xcite , exact diagonalization ( ed)@xcite , perturbative approaches@xcite and the numerical renormalization group ( nrg)@xcite . even less studied has been the interplay of electron - electron interactions and the electron - phonon coupling@xcite . the most natural model incorporating both these terms is the holstein - hubbard model defined by the hamiltonian @xmath1 here @xmath2 describes the electron electron interaction within a band of dispersion @xmath3 . the electron density @xmath4 at site @xmath5 couples linearly to the local displacement operator @xmath6 with an electron - phonon coupling @xmath7 . the phonons are assumed to be dispersionless ( local einstein phonons ) with energy @xmath8 and @xmath9 is the mass of the vibrating ions . and a semielliptic band of width @xmath10 as calculated in ref . . the dashed line is the locus of @xmath11 . points on the dot - dashed line fulfil @xmath12.,scaledwidth=46.0% ] recently , the @xmath13 phase diagram of the half filled holstein - hubbard model has been calculated@xcite using various local approximations , and is shown in fig . [ phases.eps ] . the results are for a semi - elliptic band of width @xmath10 and phonon frequency @xmath14 ( @xmath15 ) . all types of long - range order are excluded . we can distinguish three different phases : metallic , bipolaronic and mott insulating phase . the metallic phase is always found to be a fermi liquid . the latter two phases display a gap in the one - electron spectra and will be referred to as gapped phases . the parameters of fig . [ phases.eps ] , namely @xmath16 and @xmath17 are taken throughout this paper , unless mentioned otherwise . one way of simplifying the discussion of the holstein - hubbard model would be to integrate out the phonons in order to derive an effective model for the electrons . the effective action is then governed by the @xmath18-dependent potential@xcite @xmath19 this reduces to the static quantity @xmath20 in the limits @xmath21 and @xmath22 . therefore , on small energy scales , we expect an effective attractive or repulsive interaction depending on the value of @xmath23 . for small phonon energies @xmath8 , however , there is no reason to expect the static quantity @xmath23 to be sufficient to characterize the behaviour of the holstein - hubbard model . the properties of this model are expected to depend on both @xmath2 and @xmath7 individually . this is also apparent from the phase diagram in fig . [ phases.eps ] . the dot - dashed line , where the double occupancy takes the value of a free system @xmath12 is quite distinct from the line @xmath24 . the aim of this study is to clarify the interplay of these different types of interactions . an interesting question about this model is whether the suppression of local charge fluctuations by a significant hubbard @xmath2 will effectively decouple electrons and phonons on all energy scales . it is possible , however , that for the behaviour on low energy scales the effective onsite-@xmath2 is strongly renormalized and hence the electron phonon coupling will have a comparatively stronger effect on energy scales @xmath25 ( see ref ) . in this paper , we present results on dynamical electronic and phonon response functions for the holstein - hubbard model as calculated within the dynamical mean field theory@xcite ( dmft ) . the effective impurity problem is solved using wilson s numerical renormalization group ( nrg ) method@xcite extended to treat the electron phonon coupling@xcite . the combination of dmft and nrg has proven to be a reliable and effective method for calculations of both metallic and insulating phases at @xmath13 . it has been applied to the mott transition in the pure hubbard model@xcite and to the pure holstein model@xcite . in our calculations we use the discretization parameter @xmath26 and retain up to @xmath27 states . the value of @xmath26 gives rise to a bandwidth correction factor @xmath28 ( see eq . ( 5.42 ) in ) which we take into account in the nrg procedure . for the calculation of dynamical response functions we use the method described in ref . . apart from the usual local one - electron green s function @xmath29 we will be interested in two different phonon green s functions , @xmath30 since we will treat only homogeneous phases here and exclude all types of long - range order , we have dropped the site indices in all of the definitions . the spectral weight of @xmath31 will be denoted by @xmath32 , and similar for all other green s functions . the dynamical charge and spin susceptibility are given by @xmath33 respectively . the operator @xmath34 represents the electronic term that couples to the phonons , @xmath35 it should be noted that our definition of @xmath36 differs from the usual one by a factor of four . we also calculate the quasiparticle weight @xmath37 given by @xmath38 within the local approximation of the dmft . the different regimes of the phase diagram of fig . [ phases.eps ] give rise to the following structure of the paper : in sec . [ sec : g_dependence ] we choose a fixed value of @xmath2 and study dynamical properties as a function of the phonon coupling @xmath7 . we find continuous transitions from a metallic to a bipolaronic state for small values of @xmath39 and @xmath40 ( sec . [ ssec : weaku ] ) . for a larger value of @xmath41 , as discussed in sec . [ ssec : strongu ] , the transition to the bipolaronic state becomes discontinuous . complementarily , we look at the @xmath2-dependence of dynamical properties in sec . [ sec : u_dependence ] keeping @xmath7 fixed to @xmath42 . for this value of @xmath7 the system can be in all three phases , depending on @xmath2 . in sec [ sec : polaronic ] we study the properties of the model on the two polaronic lines as given by @xmath24 and @xmath43 ( dashed and dot - dashed lines in fig . [ phases.eps ] ) . we also show spectra for @xmath24 for different values of @xmath8 . in sec . [ sec : overview ] we give an overview of our results , and we present our conclusions in sec . [ sec : conclusions ] . in this section , we fix the value of the hubbard interaction @xmath2 and study dynamical properties for a varying electron - phonon coupling @xmath7 . we distinguish between the cases of weak and strong @xmath2 . and various values of @xmath7 . the inset shows the variation of the quasiparticle weight @xmath37 for @xmath40 ( solid line ) and @xmath39 ( dashed line).,scaledwidth=46.0% ] first of all , we look at the one - electron spectra for a fixed @xmath44 as shown in fig . [ g_spec_u10_gx.eps ] . there is a strong similarity of these results with those of the pure holstein model ( @xmath39 ) calculated previously@xcite . at weak coupling a narrow peak emerges at the fermi energy . the top of this feature is rather flat and the imaginary part of the self energy has a shallow @xmath45-dependence . this one would expect from lowest order perturbation theory in @xmath7 , where the imaginary part of the self energy vanishes in the range @xmath46 for @xmath39 ( see eq . ( 19 ) in ref . ) . upon increasing @xmath7 further , there is a rapid narrowing of this feature until it disappears at a critical coupling of @xmath47 and a gap opens . similar to the pure holstein model , there is no preformed gap in this case in contrast to the mott transition in the hubbard model . the metallic regime corresponds to a renormalized fermi liquid . the quasiparticle weight @xmath37 is shown as a function of @xmath7 in the inset together with that for the pure holstein model ( @xmath39 ) . for @xmath40 , the quasiparticles are already slightly renormalized at @xmath48 . however , initially the renormalization with @xmath7 is weaker than in the case @xmath39 but more rapid on the approach to @xmath49@xcite . as with the pure holstein model , there is no evidence of multiple solutions near the phase transition . this is in contrast to the situation near the mott transition for the hubbard model , where there is a finite coexistence region . , top ) and @xmath40 ( bottom ) . the values of @xmath7 are @xmath50 ( bottom ) , @xmath51 ( top ) in the upper panel and @xmath50 to @xmath52 in steps of @xmath53 in the lower panel . the dotted lines are scaled up by a factor of @xmath54.,title=""fig:"",scaledwidth=23.0% ] , top ) and @xmath40 ( bottom ) . the values of @xmath7 are @xmath50 ( bottom ) , @xmath51 ( top ) in the upper panel and @xmath50 to @xmath52 in steps of @xmath53 in the lower panel . the dotted lines are scaled up by a factor of @xmath54.,title=""fig:"",scaledwidth=23.0% ] + , top ) and @xmath40 ( bottom ) . the values of @xmath7 are @xmath50 ( bottom ) , @xmath51 ( top ) in the upper panel and @xmath50 to @xmath52 in steps of @xmath53 in the lower panel . the dotted lines are scaled up by a factor of @xmath54.,title=""fig:"",scaledwidth=23.0% ] , top ) and @xmath40 ( bottom ) . the values of @xmath7 are @xmath50 ( bottom ) , @xmath51 ( top ) in the upper panel and @xmath50 to @xmath52 in steps of @xmath53 in the lower panel . the dotted lines are scaled up by a factor of @xmath54.,title=""fig:"",scaledwidth=23.0% ] figure [ csss_spec_u10_gx.eps ] shows the spectra of the corresponding charge- and spin susceptibilities at @xmath40 and @xmath39 for comparison . in the free system , @xmath55 as defined in eq . ( [ eq : chi_csss ] ) , which can be seen in the lowest curves of the two upper panels . looking at the case @xmath39 first ( upper panel ) , we see the emergence" +"ion pressure anisotropies are ubiquitous in heliospheric and astrophysical plasmas . in the absence of coulomb collisions , the magnetic moment of ions , @xmath4 ( @xmath5 , where @xmath6 is the ion velocity perpendicular to the local magnetic field @xmath7 and @xmath8 ) is an adiabatic invariant . thus , if ion collisions are infrequent , the ion velocity distributions parallel and perpendicular to the magnetic field decouple , making @xmath9 ( where @xmath10 and @xmath11 are the pressure components of ions perpendicular and parallel to @xmath7 ) . examples of systems where ion pressure anisotropies are important are low - luminosity accretion disks around compact objects @xcite , the intracluster medium ( icm ) @xcite , and the heliosphere ( see , e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . in these systems the ion pressure anisotropy is expected to play a key role in the large scale dynamics of the plasma . for instance , @xcite pointed out that pressure anisotropies can give rise to an anisotropic stress that can contribute to angular momentum transport and plasma heating in low - luminosity accretion disks . this physics is not included in standard mhd models of accretion disks . velocity space instabilities limit the growth of the pressure anisotropy and give rise to small scale fluctuations in the magnetic field . these fluctuations can , in turn , affect the large scale transport properties of the plasma by modifying the mean free path of particles . magnetic field amplification in a collisionless system generically drives @xmath12 . there are two ion - scale instabilities that can be excited in this regime : the mirror and the ion - cyclotron ( ic ) instabilities @xcite . the mirror instability consists of non - propagating , strongly compressional modes . their fastest growing wave vectors @xmath13 are oblique to @xmath7 , with the magnetic variations parallel to @xmath7 being much larger than the perpendicular fluctuations , @xmath14 . for a bi - maxwellian distribution of ions , and assuming cold electrons , the threshold condition for mirror instability growth is given by @xmath15 , where @xmath16 ( @xmath17 ) is the ion temperature perpendicular ( parallel ) to @xmath7 , and @xmath18 @xcite . the ic instability , on the other hand , consists of transverse electromagnetic waves , with the fastest growing @xmath13 being preferentially parallel to @xmath7 ( e.g. , * ? ? ? whether the ic or mirror instability sets in first depends on how fast these instabilities grow for a given set of plasma conditions . @xcite showed that for @xmath19 , the growth rate of the ic instability is @xmath20 , where @xmath21 is the cyclotron frequency of the ions . in addition , for @xmath22 , the threshold anisotropy depends very weakly on @xmath23 . in the linear regime , the dominant instability will be determined by which threshold is reached first as @xmath7 is amplified . these estimates for the threshold conditions imply that , in the linear regime , the ic instability should dominate for @xmath24 , while the mirror instability should dominate for @xmath25 . although both the mirror and ic instabilities have been extensively studied in the linear regime , a complete theory of their nonlinear evolution and saturation is still lacking . in this paper , we are particularly interested in the question of how the mirror and ic modes behave after the initial phase of exponential growth . indeed , in most astrophysical scenarios where the magnetic field is amplified , the growth of the field occurs on time scales much longer than the growth time of the relevant kinetic instabilities . therefore , most of the evolution of the velocity space instabilities happens in a nonlinear regime , where the conditions typically assumed in linear studies , such as a homogeneous plasma or a bi - maxwellian distribution of particle velocities , are not necessarily satisfied . moreover , if the field is amplified by order unity or more , a quasi - linear analysis is not applicable . one of the key questions we are interested in addressing in this case is whether the mirror instability saturates via pitch - angle scattering that violates magnetic moment conservation @xcite or via a nearly @xmath4-conserving rearrangement of the magnetic field , with fluctuations @xmath26 @xcite . we shall see that both of these saturation processes can in fact be important . the nonlinear regime of the ic and mirror instabilities has been studied both theoretically ( e.g. , * ? ? ? * ; * ? ? ? * ) and numerically @xcite . in most numerical studies , however , the pressure anisotropy is treated as an initial condition , which decreases as the instabilities grow and saturate . thus , in these approaches the nonlinear saturation can not be followed for a time much longer than that of the initial exponential growth . moreover , many of the previous numerical studies have focused on one - dimensional simulations . in this paper we study the long term , nonlinear evolution of the mirror and ic instabilities using two - dimensional particle - in - cell ( pic ) simulations in driven systems . in order to self - consistently explore a time much longer than the initial exponential growth , we continuously induce the growth of @xmath27 by amplifying the mean field @xmath28 during the simulation . we concentrate on amplification by incompressible plasma motions . thus , our simulations impose a shear velocity on the plasma , which sustains the growth of the magnetic field and maintains an overall positive pressure anisotropy . this growth is intended to mimic magnetic field fluctuations in a turbulent plasma and mhd - scale instabilities that amplify the magnetic field , like the magnetorotational instability ( mri ; * ? ? ? * ) or convective instabilities driven by anisotropic thermal conduction in dilute plasmas @xcite . we suspect that our results are also relevant to cases in which perpendicular heating or parallel cooling drives a plasma mirror and/or ic unstable , as in , e.g. , the solar wind . @xcite conducted an analogous study to ours using hybrid simulations . in their study , expansion of the simulation box decreased the mean magnetic field , so that on average @xmath29 . this in turn led to the growth and nonlinear saturation of the firehose instability . also , @xcite conducted a similar hybrid simulation study where the simulation box is expanded along the directions parallel and perpendicular to @xmath7 . with this setup , @xmath10 becomes larger than @xmath11 on average , and both the mirror and ic instabilities can grow and reach saturation . our work is complementary to these hybrid simulation studies and focuses on the process in which the condition @xmath12 is achieved by field amplification due to shearing plasmas . we also consider higher values of @xmath30 @xmath31 , relevant to accretion disks , the icm , and the near - earth solar wind . our calculations are less directly applicable to heliospheric measurements of mirror modes driven unstable by rapid heating through the earth s bow shock ( e.g. , * ? ? ? this is because we assume that the pressure anisotropy is generated on a timescale long compared to the ion cyclotron timescale , which is probably not true at collisionless shocks . our paper is organized as follows . in [ sec : numsetup ] we describe the simulation set up , emphasizing the key physical and numerical parameters . [ sec : results ] shows our results and [ sec : conclu ] presents our conclusions . throughout the paper we compare some of our simulation results with linear theory predictions appropriate to our pic simulations . these have artificially low ion to electron mass ratios ( @xmath32 . the linear theory results are based on the linear vlasov solver developed in @xcite . during the completion of this work , @xcite presented calculations of firehose and mirror saturation in shearing plasmas with very similar results to those that we present here . we use the electromagnetic , relativistic pic code tristan - mp @xcite in two dimensions . the simulation box consists of a square box in the @xmath33 plane , containing plasma with a homogeneous magnetic field @xmath34 initially pointing along the @xmath35 axis . since we want to simulate a magnetic field that is being amplified in an incompressible way , we impose a shear motion of the plasma so that the mean particle velocity is @xmath36 , where @xmath37 is a shear parameter with units of frequency and @xmath38 is the distance along @xmath35 . from flux conservation , the @xmath39-component of the mean field evolves as @xmath40 , implying a net growth of @xmath41 . although we present simulations resolving the @xmath33 plane only , we also tried runs where the @xmath42 plane was resolved . in those cases the isotropization efficiency was substantially lower this is because , if the @xmath42 plane is resolved , the growing component of @xmath7 is perpendicular to the plane of the simulation . this way the angle between the relevant wave vectors , @xmath13 , and @xmath7 can not be 0 . this over - constrains the wave vectors that are allowed to exist , artificially reducing the isotropization efficiency . an important physical parameter in our simulations will be the ratio of the initial ion cyclotron frequency to the shear frequency , @xmath43 . we refer to this as the magnetization . in typical astrophysical environments @xmath44 . due to computational constraints , however , we will use values of @xmath43 much smaller than expected in reality , although still satisfying @xmath45 . the dependence of our results on the ratio @xmath43 will be carefully assessed . ccccccccc beta6mag93 & 1 & 6 & - & 93 & 0.05 & 14 & 30 & 12 + beta6mag670a & 1 & 6 & - & 670 & 0.15 & 14 & 10 & 18 + beta6mag670b & 1 & 6 & - & 670 & 0.15 & 14 & 10 & 24 + beta20mag93a & 1 & 20 & - & 93 & 0.05 & 10 & 60 & 35 + beta20mag93b & 1 & 20 & - & 93 & 0.05 & 10 & 30 & 35 + beta20mag670a & 1 & 20 & - & 670 & 0.05 & 7 & 30 & 36 + beta20mag670b & 1 & 20 & - & 670 & 0.05 & 7 & 30 & 48 + beta20mag2000 & 1 & 20 & - & 2000 & 0.05 & 7 & 50 & 55 + beta80mag670 & 1 & 80 & - & 670 & 0.05 & 5 & 30 & 24 + beta80mag1340 & 1 & 80 & - & 1340 & 0.05 & 5 & 30 & 24 + betai20magi240mass10 & 10 & - & 20 & 240 & 0.05 & 5 & 20 & 25 [ table:1d ] in standard mhd simulations where shear plasma motions are imposed , shearing periodic boundary conditions would be used along the @xmath38 direction ( see , e.g. , * ? ? ? in that case , the flow velocities at the @xmath38-boundaries of the box are matched using galilean transformations of the fluid velocity . in the case of relativistic pic simulations this can not be done in a self - consistent way . the reason is that , under a relativistic change of reference frame , the current @xmath46 transforms in a way that is inconsistent with simply transforming the particle velocities . we instead implement _ shearing coordinates _ , in which the grid moves with the shearing velocity @xmath47 . in this new frame the average plasma velocity vanishes everywhere in the" +"the space - time geometry that is commonly used today arose from classical physics . an interesting question is what geometry is appropriate for quantum physics . it was suggested that the universal symmetry group elements which act on all hilbert spaces may be appropriate for constructing a physical geometry for quantum theory @xcite . i also proposed the systematic study of all the fundamental interactions _ operationally _ from their effects on quantum interference @xcite . the purpose of this paper is to attempt to bring together these two approaches . the modular variables introduced by aharonov , pendleton and petersen @xcite will play a useful role in this . in section 2 , i shall review noether s theorem and its converse in a generalized form in which the conserved quantities are elements of a group and not the generators of this group as usually stated . this will suggest a quantum geometry by relations defined by the universal group elements , which constitute the symmetry group of physics , that act on all hilbert spaces , as discussed in section 3 . the classical limit of this geometry will be obtained in section 4 as the usual space - time geometry from the quantum state metric in hilbert spaces and the universality of the action of the translational group in every hilbert space . in section 5 , the non locality of fundamental interactions in quantum physics implied by this approach , as shown physically by the aharonov - bohm effect @xcite and its generalizations @xcite , will be studied . the study of the gravitational aharonov - bohm effect around a cosmic string in particular suggests that the use of universal group elements as quantum distances may be appropriate . the usual statement of noether s theorem is that for every continuous symmetry of the equations of motion ( determined by the lagrangian or hamiltonian ) there exists a conserved quantity . although this is easy to prove , the meaning of this theorem is more readily evident in the hamiltonian than in the lagrangian formulation . a symmetry of the equations of motion or time evolution is a transformation @xmath0 such that in any experiment if @xmath0 is applied to the initial state of the physical objects ( fields , particles , etc . ) participating in the experiment then the final state of the transformed experiment must be the same as @xmath0 applied to the final state of the original experiment . for example , spatial translational symmetry implies that if the apparatus is translated to a new spatial location then the same experiment should give the same result . suppose @xmath1 is the time - evolution operator , and @xmath2 , @xmath3 are the initial and final states , i.e. @xmath4 . then the above definition of @xmath0 being a symmetry of the time evolution is @xmath5 for every initial state @xmath2 . this is equivalent to the commutator @xmath6=0 . \label{symmetry}\ ] ] but ( [ symmetry ] ) states also that @xmath0 is conserved during the time - evolution . therefore , the statements that @xmath0 is a symmetry and that @xmath0 is conserved are the _ same _ statement ( [ symmetry ] ) , and there is nothing to prove ! now suppose that there is a continuous symmetry generated by @xmath7 . then ( [ symmetry ] ) is satisfied with @xmath8 for all @xmath9 , and therefore @xmath10=0 . \label{commutator}\ ] ] hence , @xmath7 is conserved , which is noether s theorem . furthermore , if the hamiltonian @xmath11 is independent of time @xmath12 , as it is for an isolated system , then @xmath13 . if ( [ commutator ] ) is valid for all @xmath12 , then @xmath14=0 . \label{hcommutator}\ ] ] the above results may be extended to classical physics by turning the above commutators into poisson brackets in classical phase space . these classical results may be regarded as the classical limit of the quantum results by recognizing that the symplectic structure that gives the poisson brackets are the classical limit @xcite of a symplectic structure in quantum theory @xcite that gives the commutators . but the conservation of @xmath0 that follows from ( [ symmetry ] ) is more general than the usual form of noether s theorem . there are at least two situations in which ( [ symmetry ] ) is valid but there are no corresponding ( [ commutator ] ) or ( [ hcommutator ] ) . first , as is well known , in both classical and quantum physics , @xmath0 may be a discrete symmetry instead of a continuous symmetry . for example , @xmath0 may be parity , which is a symmetry and therefore conserved for all interactions except the weak interaction , as far as we know . another example is that ( [ symmetry ] ) is satisfied for @xmath15 for a discrete set of values @xmath16 only . second , in quantum physics the mean value of @xmath8 has more information than the mean value of all the moments of @xmath7 , namely @xmath17 where @xmath18 is any positive integer @xcite . this is unlike in classical physics where the mean value of a transformation generated by @xmath7 may be obtained using the mean values of all the @xmath17 . both these situations will be considered in section 5 . since in ( [ symmetry ] ) @xmath1 and @xmath0 occur symmetrically , it follows that the converse of the generalized noether s theorem is also true : _ a transformation @xmath0 that is conserved must be a symmetry of the equations of motion . _ the usual view is that @xmath1 is more fundamental than @xmath0 because @xmath1 is determined by the dynamical laws which are regarded as primary , whereas the symmetries such as @xmath0 are obtained secondarily as the symmetries of these laws . but the concise form ( [ symmetry ] ) of the connection between the dynamical laws and symmetries , in which @xmath1 and @xmath0 are on an equivalent footing , suggest that we may equally turn the usual view around and regard the transformations @xmath19 as primary and @xmath1 as derived from them to satisfy ( [ symmetry ] ) so that @xmath19 are the symmetries @xcite . the possibility of regarding symmetries as fundamental relations between quantum states by associating them with a quantum geometry will be explored in the next section . the concept of space originates from our common experience of translating objects and from the possible states they can occupy . if we translate a cup , for example , in various possible ways , classically we may say that the different configurations or states of the cup are `` immersed '' in `` space '' . this space is _ universal _ in the sense that it is regarded as independent of the objects which are `` contained '' in it . but quantum mechanically it is not clear what is meant by the cup being `` immersed '' in space . the cup consists of electrons , protons and neutrons ( or the quarks and gluons which make up the protons and neutrons ) , and the states of these particles belong to the corresponding hilbert spaces which are different from the physical space or the phase space of classical physics . the translation of a cup therefore needs to be represented by the corresponding translation operators that act on these hilbert spaces . the fact that all the particles constituting the cup move together in some approximate sense suggests the introduction of universal translation group elements that are represented by operators that act on each hilbert space . it is this _ universality _ of the translation group that gives us the concept of `` space '' that is independent of the particular system that partakes in it . also , it is well known that we can not operationally determine the metric in space- time , or even the points of space - time , using quantum probes @xcite because of the uncertainty principle . if one tries to obtain the space - time geometry using a clock and radar light signals , which is possible in classical physics @xcite , the uncertainty in the measurement of time in quantum physics is @xmath20 , where @xmath21 is the uncertainty in the energy of the clock . if we try to decrease this uncertainty by increasing @xmath22 , then @xmath22 causes a corresponding uncertainty in the geometry of space- time . the total uncertainty in the measurement of space - time distances is then @xmath23 . the minimum value of this uncertainty as @xmath21 is varied is @xmath24 planck - length @xmath25 . hence , space- time geometry is only approximately valid in quantum theory , with an uncertainty of the order of planck length . however , a geometry for quantum theory may be defined by relations determined by a universal group @xmath26 , which generalizes the above translation group . this is universal in the sense that the same @xmath26 has a representation in each hilbert space . but @xmath26 may have subgroups which may have trivial representations in some hilbert spaces and not in others . an object may be displaced by any @xmath27 , which means that @xmath0 acts on each of the hilbert spaces of the particles or fields constituting that object through the corresponding representation of @xmath26 . each @xmath28 in each of these hilbert spaces is mapped to a corresponding @xmath29 by this action of @xmath0 , and the group element @xmath0 that determines the _ relation _ between @xmath28 and @xmath29 is independent of the hilbert space and is therefore universal . in the example of a cup considered above , @xmath0 is an element of the translation group , @xmath28 and @xmath29 are the states of each particle constituting the cup before and after the translation , and the relation between each such pair is universal in the sense that the entire cup has undergone this translation , or any other object that could take the place of the cup . this quantum geometry can not be subject to the above criticisms of the space - time geometry because the action of @xmath26 on each hilbert space is not subject to any uncertainty . it is reasonable to require that this geometry is preserved in time in the absence of interactions . then each @xmath27 is conserved and the converse of noether s theorem stated in the last paragraph of the previous section implies that @xmath0 is also a symmetry of the time evolution . since the evolution equations are now determined by the standard model , @xmath26 may be the symmetry group of the present day standard model , namely @xmath30 , where @xmath31 is the poincare group . but if the standard model is superseded by new physics that has a different symmetry group then @xmath26 should be this new group and the above statements would all be unaffected . as an illustration of the geometrical relations proposed here , consider the experimentally known quantization of electric charge : all known charges are integral multiple of the fundamental charge @xmath32 . an aspect of this is that the magnitudes of the charges of the electron and the proton are experimentally known to be equal to an amazing precision . to obtain charge quantization , take @xmath0 above to be an arbitrary element of the electromagnetic @xmath33 group , which is a subgroup of @xmath26 . this universal @xmath33 group is a circle parametrized by @xmath34 , say , that varies from @xmath35 to @xmath36 so that @xmath35 and @xmath36 represent the same point on this group , chosen to be the identity . since @xmath33 is abelian , it has only one - dimensional representations ." +"photonic crystals ( pcs ) have recently become the object of increased interest as possible hosts for optical functional devices , e.g. , beam splitters , demultiplexers , etc . @xcite these elements , as well as the basic building blocks of photonic integrated circuits waveguide bends , junctions etc.have often been investigated by methods designed for finite systems , such as the finite - difference time - domain ( fdtd ) method @xcite and the multiple - scattering ( ms ) method @xcite . consequently , the devices in question were considered to be embedded in a finite fragment of a pc . this , however , involved spurious reflections at the artificial pc boundaries , significantly complicating the analysis of the device behavior . to remedy this situation , several methods suitable for analyzing systems with semi - infinite waveguides have been developed . in the effective discrete equations method @xcite and the wannier function method @xcite , the electric and magnetic fields are represented in a basis of states localized at elementary defects ; various grating - based techniques , like those presented in @xcite , have been developed as well . both approaches , however , impose some restrictions on the problems to which they can be applied : the former is ill - suited to open systems ( i.e. , those with vacuum regions extending to infinity ) , while the latter only applies to systems with unidirectional waveguides . recently , the multiple multipole method has been extended by moreno _ et al . _ @xcite to systems with semi - infinite waveguides ; here , the fields on a transverse section of each waveguide , sufficiently distant from discontinuities ( junction , bend etc . ) , are matched to a linear combination of the waveguide eigenstates . as demonstrated in @xcite , this technique is very general and applicable also to the problems which can not be dealt by the other above - mentioned methods . the aim of this paper is to show how to take into account the presence of semi - infinite waveguides in calculations performed on the basis of the ms technique . owing to its particular simplicity and efficiency in dealing with the case of pcs composed of cylindrical rods , this technique has gained significant popularity @xcite . although the approach proposed by moreno _ et al . _ @xcite could be straightforwardly carried over to the combination of the ms method and the method of fictitious sources , formulated in @xcite , this would require significant changes in the computational procedure , as well as availability of externally calculated data describing the fields corresponding to the waveguide eigenstates . in contrast , the approach outlined below consists solely in postprocessing of the results obtained by the ` pure ' ms method . while admittedly less general than the other technique , it is nevertheless applicable to a number of situations frequently encountered in practice . two of them are discussed in sections [ sec : onewaveguide ] and [ sec : twowaveguides ] , in which the proposed procedure is applied to devices linked with one waveguide and two waveguides , respectively . possible extensions of the method are discussed in section [ sec : extensions ] . the first system to be considered is a single waveguide terminated at the surface of a semi - infinite pc [ fig . [ fig : system1](a ) ] . a frequently discussed problem ( see , e.g. , @xcite ) is the design of the precise shape of the waveguide outlet that would allow maximization of the power transmitted into free space . in this case , the main objective is to calculate the reflection coefficient of the outlet ; the intensity of the field produced at some point of the free - space region ( possibly at infinity ) when an eigenmode of unitary power propagates towards the end of the waveguide is sometimes searched for , too . in the following we will show how both quantities can be found on the basis of calculations done for the finite system shown in fig . [ fig : system1](b ) , presenting a waveguide that is @xmath0 unit cells long . unit cells of the waveguide . smigaj-1.eps[fig:system1 ] ] the waveguide is assumed to be a single - mode one , and its unit cell to have a mirror - symmetry plane parallel to the @xmath1 plane , so that the propagating bloch states of the waveguide are characterized by wave numbers @xmath2 and @xmath3 . an arbitrary source @xmath4 placed near the waveguide inlet excites the right - propagating mode , which then undergoes multiple reflections . let @xmath5 and @xmath6 ( @xmath7 ) denote the @xmath8 component of the electric ( tm polarization ) or magnetic ( te polarization ) field corresponding to the mode of wave number @xmath2 and @xmath3 , respectively , at point @xmath9 represented by coordinates @xmath10 in fig . [ fig : system1](b ) . the choice of @xmath11 is arbitrary ; the zero value can be assumed unless the waveguide eigenmode is antisymmetric with respect to the @xmath12 plane . from the bloch theorem , we have [ eq : abloch ] @xmath13 where @xmath14 is the waveguide transfer matrix ; @xmath15 is the waveguide period and @xmath16 . the outgoing modes get partly reflected at the waveguide ends ; this can be expressed by the following ` boundary conditions ' : [ eq : abndconds ] @xmath17 where @xmath18 and @xmath19 are the reflection coefficients at the waveguide outlet and inlet , respectively , and @xmath20 stands for the effective field corresponding to the right - propagating mode excited by the source @xmath4 , extrapolated to point @xmath21 . by combining eqs. and eliminating the variables @xmath22 , @xmath23 , @xmath24 , and @xmath25 , we get the linear system @xmath26 whose solution reads @xmath27 in cells lying sufficiently far from the waveguide ends for the contribution of the evanescent states to be negligible , the total field @xmath28 can be expressed only in terms of the propagating modes : @xmath29 we are interested in the reflection coefficient @xmath18 , as well as in the intensity @xmath30 of the field which would be generated at some point @xmath31 in the free space if the waveguide were semi - infinite and the incident right - propagating mode carried unitary power . the reflection coefficient can be found simply by least - squares fitting of the numerically calculated values of @xmath32 to those calculated by the formula resulting from eq . : @xmath33 in addition to @xmath18 , this gives also the value of @xmath34 , which can be used for calculating the wave number @xmath2 . let us note by the way that solving eq . for @xmath35 and @xmath36 , where @xmath37 is some fixed integer , yields [ eq : astartingpt ] @xmath38 these values , calculated for @xmath39 , i.e. , near the waveguide center , can be used as starting points in the nonlinear least - squares fitting procedure . the sign of @xmath2 should correspond to the physics of the problem at hand . it should be stressed that only cells distant enough from the waveguide ends ( i.e. , those labeled @xmath40 , where the ` margin ' @xmath41 is a sufficiently large integer ) should be taken into account in the above fitting procedure , since eq . has been derived with the assumption that evanescent states are of negligible amplitude in the cells labeled @xmath9 and @xmath42 . let us proceed to the determination of @xmath30 . the intensity @xmath43 of the field generated at point @xmath31 in the finite system can be written as @xmath44 where the transmission coefficient @xmath45 represents the fraction of the total energy emitted into free space when a waveguide mode reaches the outlet , and the ` transfer coefficient ' @xmath46 , dependent on the position of @xmath31 and the geometry of the waveguide outlet , but not on the waveguide length , is a measure of the amount of this energy getting to point @xmath31 . in the ideal case of the semi - infinite waveguide , @xmath19 would be zero ; thus , @xmath47 with @xmath48 chosen so that the incident mode would carry power @xmath49 . from eqs. we get @xmath50 since the incident power in each case is proportional to @xmath51 . as shown in the appendix , the total power flowing through an arbitrary transverse section of the waveguide is equal to @xmath52 this power can be easily calculated by the ms method . by using eq . for eliminating from eq . the factor @xmath53 , which contains the unknown coefficient @xmath19 , we finally get @xmath54 to sum up , the data obtained in a single ms calculation performed for a finite system with an @xmath0-cell - long waveguide suffice for determination of the reflection coefficient of the waveguide outlet , as well as the ` corrected ' field intensity in free space . when only the former quantity is required , the field excited at @xmath55 sites lying along the waveguide axis is all that needs to be calculated in the simulation ; otherwise , the power flow through an arbitrary transverse section of the finite waveguide must be computed too . as an example of application of these results , let us first consider the system shown in fig . [ fig : system1](a ) : a w1-type waveguide embedded in a hexagonal lattice of dielectric cylinders with permittivity @xmath56 and radius @xmath57 , where @xmath15 is the lattice constant . the surface termination creates a slight tapering of the waveguide exit . figure [ fig : system1reflcoeff ] presents the frequency dependence of . circles : the calculation results of lin and li @xcite ; line : results of our calculations . smigaj-2.eps[fig:system1reflcoeff ] ] the reflection coefficient @xmath58 in this configuration ; the results obtained by the proposed technique are compared to the data reported in @xcite [ fig . 7(c ) ] , acquired by the plane - wave - based transfer - matrix method . our calculations were done for waveguide length @xmath59 with margin @xmath60 . the convergence is very fast : in fact , the data obtained in the @xmath61 , @xmath62 case ( essentially the shortest waveguide for which fitting makes sense ) differ by at most 6% from those plotted in the graph , and for frequency values below @xmath63 the difference does not exceed 1% . there is a good agreement between our results and those of lin and li @xcite , except for a small peak at frequency value @xmath64 , present in the @xmath65 plot obtained by these authors , but not reproduced by the curve resulting from our calculations . since the waveguide is a single - mode one and the mode dispersion curve is smooth around this frequency value , the physical origin of this sharp peak is not clear to us and we believe it might be a numerical artifact . as a second example , let us consider the leaky - wave photonic antenna @xcite shown in fig . [ fig : antenna](a ) . here , the and @xmath66 , respectively , @xmath15 being the lattice constant ; all cylinders have permittivity @xmath56 . every second surface cylinder is shifted by @xmath67 towards the bulk . the corrugated surface is @xmath68 unit cells long . ( b ) the far - field intensity of the radiation emitted perpendicularly to the surface , calculated for waveguide length @xmath69 , and @xmath70 , as well as for the semi - infinite waveguide on the basis of data obtained for @xmath71 , @xmath72 . normalization : see text . smigaj-3.eps[fig:antenna ] ] surface surrounding the waveguide outlet is corrugated with" +"the x - ray pulsar gx 1 + 4 is unusual in several respects . it is the only confirmed neutron star in a symbiotic binary @xcite which appears to be accreting from the giant companions stellar wind . the neutron star spin period evolution exhibits long periods of almost constant spin - up or -down , punctuated by ` torque reversals ' lasting tens of days ( e.g. * ? ? ? indirect estimates indicate a surface magnetic field strength of 23@xmath5 g @xcite . these values are significantly greater than the @xmath6 g inferred for other accreting x - ray pulsars , generally from measurements of cyclotron scattering resonance features ( csrfs ; e.g. * ? ? ? * ) in the x - ray spectra . as the presence of such a strong field in gx 1 + 4 awaits confirmation by such methods , the possibility that the field strength may in fact be one or more orders of magnitude lower remains . historically x - ray pulsar spectra have generally been fitted with variations on a power law , which is well known to be a signature of unsaturated comptonization ( e.g * ? ? ? model fitting to the available archival _ data show that the spectra of gx 1 + 4 are broadly consistent with an analytic approximation to a comptonization continuum component combined with a gaussian to represent iron line emission , both attenuated by neutral absorbtion with variable column density @xcite . the archival _ rxte _ data , which span two orders of magnitude in flux for the source , has also revealed that the x - ray lightcurves and mean pulse profiles of all but one of the observations exhibit sharp dips spanning @xmath70.2 in phase . during 1996 july the countrate dropped to @xmath8 @xmath9 over @xmath10 h ; sharp dips were observed in the mean pulse profiles even then @xcite . similar dips are observed in only two other x - ray pulsars , rx j0812.4 - 3114 @xcite and a 0535 + 262 @xcite . a recent analytic and modelling study suggests that the sharp dips are signatures of eclipses of the emitting region by the accretion column ( galloway et al . 2000 , in preparation ) . pulse - phase spectroscopy using a continuum spectral model simulating thermal comptonization of both gx 1 + 4 and rx j0812.4@xmath113114 shows a significant increase in the fitted optical depth @xmath4 coincident with the dip phase . if the inclination angle @xmath12 of these systems are roughly equal to their magnetic colatitude @xmath13 , such an increase may result when one of the accretion columns approaches alignment with the line of sight once each rotation period . at the phase of closest alignment , photons emitted from the polar cap must propagate a greater distance through the column to escape and ultimately reach the observer . numerical modeling using a simplified column geometry confirms that the resulting increase in optical depth will have just the effect observed in gx 1 + 4 and rx j0812.4@xmath113114 @xcite . _ rxte _ consists of three instruments , the proportional counter array ( pca ) sensitive to photons in the energy range 260 kev , the high - energy x - ray timing experiment ( hexte ) covering 16250 kev , and the all - sky monitor ( asm ) which spans 210 kev @xcite . analysis of _ rxte _ data presented in this letter was carried out using lheasoft 5.0 , released 23 february 2000 by the _ rxte _ guest observer facility ( gof ) . the data were first screened to ensure that the pointing offset was @xmath14 and the source was @xmath15 from the sun . this introduces additional gaps to the data . instrumental background from cosmic ray interactions and as a result of satellite passages close to the saa are estimated using the pcabackest software which is included in the lheasoft package . the ` bright ' source background models from the 23 february 2000 release were used , which are appropriate when the net source countrate is @xmath16 @xmath9 . spectral fitting was undertaken using the xspec spectral fitting package version 11 @xcite . for more details of the spectral analysis see @xcite . [ p20170 ] between 1997 may 1620 gx 1 + 4 was observed daily for @xmath17 min . the phase - averaged background subtracted countrate varied from day to day , from @xmath18 @xmath9 ( with all 5 proportional counter units operating ) on 17 may to @xmath19 @xmath9 on 18 and 20 may ( figure [ p20170-y ] ) . for four of the five observations the sharp dips which form the primary minimum in the pulse profile were clearly observed in the background subtracted pca countrate . the pulse fraction is defined as @xmath20 and where @xmath21 is the mean pulse profile calculated over @xmath22 bins . on may 16 and 1820 @xmath23 , as is typical for the source . on 17 may however , the sharp dips in the pulse profile were weaker or absent , resulting in a pulse fraction @xmath0 ( figure [ p20170-y ] , second panel from top ) . the minima are instead broad and irregular , lacking the consistency over successive cyles observed on other days . spectral model fitting of the standard-2 mode spectra averaged over each daily observation was undertaken with the comptonization continuum model ( comptt in xspec ; * ? ? ? * ) following @xcite . note that it was not possible to obtain a background spectrum for the may 20 observation due to problems with the filter file ; the background spectrum from the previous days observation was used instead . several of the spectral fit parameters show significant variability ( table [ tab - p20170 ] ) . the column density @xmath24 varied between @xmath25 and @xmath26 . the source spectrum temperature @xmath27 was somewhat higher than is typical on 16 may but decreased to a more typical 1.21.3 kev by 18 may . for two of the spectra the scattering plasma temperature @xmath28 similarly could not be constrained by the fitting algorithm , and instead was fixed at 10 kev . for the other three days @xmath28 varied between @xmath297 and @xmath8 kev . the most dramatic variation was in the fitted optical depth @xmath4 , which was 3.64 on may 16 and 1820 but @xmath30 on may 17 . the equivalent width of the fe gaussian component was also unusually high for this spectrum , at more than 1.8 kev . these variations occurred as the luminosity varied between 1.5@xmath31 , assuming a source distance of 10 kpc . the actual distance of the source is thought to be in the range 315 kpc @xcite . the @xmath32 values indicate good fits for each spectrum except on may 17 . the spectrum obtained on this day does not resemble any of the other @xmath33 spectra extracted over the course of the _ rxte _ observations between 1996 and 1997 . the model fit was problematic in several respects . initial fits with all parameters free to vary resulted in a fit value for the @xmath34 parameter ( associated with the xe absorption edge at 4.83 kev ) an order of magnitude greater than the maximum for all the other spectra . thus the value for this parameter was instead fixed ( ` frozen ' ) at the fit value for the spectrum extracted over the whole of the 1997 may observation . the fitted @xmath27 value , when free to vary , also became much larger than was consistent than for the other spectra and so was fixed at 1.3 kev . this value is typical for the source at other times @xcite . while the resulting fit statistic @xmath35 indicates an unacceptable fit , no improvement was found using alternative continuum models , including power law , power law with exponential cutoff and broken powerlaw . a comparable fit was obtained with a blackbody component resulting in @xmath36 with fitted @xmath37 kev in rough agreement with @xmath38 for the comptt fit of @xmath39 kev . the data from each of the observations on may 1620 were divided into 10 phase bins based on the pulse period @xmath40 s estimated from regular batse monitoring of the source . the ephemeris for each day was chosen arbitrarily so that the first phase bin was centered on the primary minimum , defined as phase 0.0 . each of the resulting phase - selected spectra were fitted with the usual spectral model with at most @xmath28 , @xmath4 and the comptt and gaussian component normalisations free to vary . the other parameters were fixed at the fit values for the phase - averaged spectrum on the same day . this approach is essentially identical to that of @xcite . for the may 16 and 19 observations @xmath28 was also fixed at the same value as for the phase - averaged spectrum ( see table [ tab - p20170 ] ) . variation of @xmath28 and @xmath4 with phase is small except close to the primary minimum . the fitted @xmath4 around phase 0.0 on may 16 and 1820 was significantly greater than the value for the phase - averaged spectrum , by 2060 per cent . for the may 17 observation , at the much shallower primary minimum @xmath4 is instead marginally lower than the phase - averaged fit values , while @xmath28 is somewhat higher ( figure [ pps - y2 ] ) . for sources with @xmath41 , assuming that @xmath12 , @xmath13 and the footpoints of the accretion column on the neutron star do not change , dips due to column eclipses must always be observed while accretion continues through the columns . the apparent disappearance of the dip during the 1997 may 17 observations clearly challenges this picture . the flux at this time is more than an order of magnitude larger than the lowest level measured by _ complete cessation of accretion seems unlikely . another possibility is that the geometry of the system is changing such that the accretion column drops out of alignment briefly . the inclination angle @xmath12 may vary due to geodetic precession of the pulsar , as is suggested for some radio pulsars ( e.g. * ? ? ? alternatively , the magnetic colatitude @xmath13 may change due to evolution of the neutron star magnetic field . variations due to the former effect , however , are only expected on timescales of years . and while the latter possibility can not be discounted due to the lack of knowledge regarding such evolution , it seems much more likely that each of these mechanisms would cause a much longer - lasting , if not permanent , cessation of eclipses rather than what is observed in gx 1 + 4 . variations in the position of the column itself are much more plausible . as the accretion rate @xmath42 ( and hence the luminosity @xmath43 ) decreases , the balance of magnetic and gas pressures at the inner edge of the accretion disc means that the disk will be truncated further out from the neutron star @xcite . field lines threading the boundary region where disk material decelerates and becomes bound to the accretion column will thus meet the neutron star at progressively higher latitudes on the star . in principle at least this mechanism may cause the column to move in and out of alignment , in which case eclipses ( and dips ) would be expected only over a finite range of @xmath43 . instead what appears to be the case for gx 1 + 4 is that dips are normally observed at the full range of luminosities at which the source was observed by _ rxte _ , and are perhaps" +"the origin of mass is a central mystery of the standard model ( sm ) . in particular , why are the masses of w , z , and the top quark exceptionally large compared with those of other particles in the sm ? the idea of the top quark condensate @xcite explains naturally the large top mass of the order of the electroweak symmetry breaking ( ewsb ) scale . in the explicit formulation of this idea @xcite , often called the `` top mode standard model '' ( tmsm ) , the scalar bound state of @xmath9 plays the role of the higgs boson in the sm . ( for reviews , see , e.g. , refs . @xcite . ) there are several problems in the original version of the tmsm : we need to introduce ad hoc four - fermion interactions of the top quark in order to trigger the ewsb . the top mass @xmath10 , given as a decreasing function of the composite scale @xmath11 , is predicted about 10%30% larger than the experimental value , even if we take @xmath11 to the planck or the gut scale @xcite . such a huge @xmath11 also causes a serious fine - tuning problem . as a possible solution to these problems , following the line of an earlier attempt @xcite of the tmsm in the tev - scale extra dimension scenario @xcite , arkani - hamed , cheng , dobrescu and hall ( acdh ) @xcite proposed an interesting version of such where the sm gauge bosons and the third generation of quarks and leptons live in the @xmath12-dimensional bulk , while the first and second generations are confined in the 3-brane ( 4-dimensional minkowski space - time ) . gauge interactions in higher dimensions than four become strong in a certain high - energy region . bulk gauge interactions are expected to trigger the top condensation without adding ad hoc four - fermion interactions , in contrast to the original version of the tmsm . however , the dynamics of bulk gauge theories was not concretely analyzed in ref . in particular , as it turned out @xcite ( see also refs . @xcite ) , the bulk qcd coupling , which is the most relevant interaction for the top condensation , has an ultraviolet fixed point ( uv - fp ) or upper bound within the same @xmath13-scheme of the truncated kaluza - klein ( kk ) effective theory @xcite as that ref . @xcite was based on . thus , it is quite nontrivial whether the top condensation is actually realized or not . in refs . @xcite , we have studied the dynamical chiral symmetry breaking ( d@xmath14sb ) in bulk gauge theories , based on the ladder schwinger - dyson ( sd ) equation.sb in other scenario for extra dimensions was investigated in ref . switching off the electroweak interaction in the bulk , we then found that the bulk qcd coupling can not become sufficiently large to trigger the top condensation for @xmath2 , while the top condensation can be realized for @xmath1 . for the purpose of model building , we further need to study the effect of the bulk electroweak interactions : since the bulk @xmath15 interaction grows very quickly due to the power - like running behavior and reaches immediately its landau pole @xmath16 , it may affect the most favored channel for condensate , i.e. , the most attractive channel ( mac ) @xcite . we also need to study whether or not the prediction of the top mass agrees with the experiments . in this paper , we demonstrate a possibility that the top condensate is actually the mac even including all of the bulk sm gauge interactions . this is quite nontrivial , because inclusion of the strong bulk @xmath15 interaction may favor the tau condensation rather than the top condensation . in order for only the top quark to acquire the dynamical mass of the order of the ewsb scale , the binding strength should exceed the critical binding strength @xmath17 only for the top quark ( `` topped mac '' or `` tmac '' ) . namely , our scenario works only when @xmath18 where @xmath19 , @xmath20 and @xmath21 denote the binding strengths of the top , bottom , and tau condensates at the scale @xmath11 , respectively . we refer to the scale @xmath11 satisfying eq . ( [ top - cond ] ) as the tmac scale @xmath22 . for the mac analysis , we study binding strengths @xmath23 by using the one - loop renormalization group equations ( rges ) of dimensionless bulk gauge couplings . it is in contrast to the analysis of acdh @xcite where all of bulk gauge couplings are assumed equal ( and strong enough for triggering the ewsb ) . in order to check reliability of our mac analysis , we also study the regularization - scheme dependence of the binding strengths . we calculate gauge couplings in two prescriptions , the @xmath13-scheme of the truncated kk effective theory and the proper - time ( pt ) scheme @xcite . there are some varieties in the estimation of @xmath17 : the naive dimensional analysis ( nda ) @xcite implies @xmath24 , while the ladder sd equation yields much smaller value @xmath25 @xcite . as the estimate of @xmath17 increases in eq . ( [ top - cond ] ) , the region of the tmac scale gets squeezed . even if we adopt the lowest possible value of @xmath17 given by the ladder sd equation @xcite , we find that _ the tmac scale does not exist for the simplest scenario with @xmath2_. on the other hand , _ the tmac scale does exist in @xmath1 _ for the value of the ladder sd equation , @xmath26@xmath27 , where the compactification scale @xmath28 is taken to be 1100 tev . for @xmath3 , the mac analysis significantly depends on the regularization scheme . once we obtain the tmac scale @xmath22 , we can easily predict the top mass @xmath10 and the higgs mass @xmath29 by using the renormalization group equations ( rges ) for the top yukawa and higgs quartic couplings , and the compositeness conditions @xcite at the scale @xmath30 . this is in contrast to the earlier approach @xcite ( see also ref . @xcite ) where the composite scale @xmath11 is treated as an adjustable free parameter and fixed so as to reproduce the experimental value of @xmath10 . without such an adjustable parameter , we predict the top quark mass @xmath31 for @xmath1 and @xmath32 1100 tev . this agrees with the experimental value , @xmath33 gev @xcite . we find that the value of @xmath10 near the compactification scale @xmath28 is governed by the quasi infrared fixed point ( ir - fp ) for the top yukawa coupling @xmath34 @xcite , which is approximately obtained as @xmath35 with the 4-dimensional qcd coupling @xmath36 , the number of color @xmath37 , the quadratic casimir of the fundamental representation @xmath38 , and @xmath39 . the suppression factor @xmath40 in @xmath34 arises from one - loop effects of the bulk top quark which is equivalent to a tower of kk modes ( massive vector - like fermions ) . the mechanism suppressing the top mass prediction is thus similar to that of the top seesaw @xcite . we also predict the higgs boson mass as @xmath41 thanks to the ir - fp property , the prediction for @xmath10 and @xmath29 is stable . the higgs boson with such a characteristic mass can be distinguished clearly from that of supersymmetric or other typical dynamical ewsb models simply through its mass determination in experiments . it will also be discovered immediately after the physics run of lhc . the paper is organized as follows . in sec . ii , we study running effects of bulk gauge couplings in the @xmath13- , and pt - schemes . in sec . iii , we identify the tmac scale . in sec . iv , we predict @xmath10 and @xmath29 for @xmath1 . sec . v is devoted to summary and discussions . in appendix a , we present details of our procedure for the orbifold compactification . we also count the total number of kk modes below the renormalization point . appendix b is for details of bulk gauge couplings in the pt - scheme . let us consider a simple version of the tmsm with extra dimensions where the sm gauge group and the third generation of quarks and leptons are put in @xmath42-dimensional bulk , while the first and second generations live on the 3-brane ( 4-dimensional minkowski space - time ) . the @xmath42-dimensions consist of the usual 4-dimensional minkowski space - time and extra @xmath43 spatial dimensions compactified at a tev - scale @xmath28 . the number of dimensions @xmath42 is taken to be even , @xmath44 , so as to introduce chiral fermions in the bulk . in order to obtain a 4-dimensional chiral theory and to forbid massless gauge scalars , we compactify extra dimensions on the orbifold @xmath45 ( see appendix a ) . we emphasize that there is no elementary field for higgs in our model . the chiral condensation of bulk fermions may generate dynamically a composite higgs field , instead . hence we investigate rges of bulk gauge couplings including loop effects of the composite higgs . we expand bulk fields into kk modes and construct a 4-dimensional effective theory . in this subsection , we study running of gauge couplings in the `` truncated kk '' effective theory @xcite based on the @xmath13-scheme . below the compactification scale @xmath28 , rges of 4-dimensional gauge couplings @xmath46 are given by those of the sm , @xmath47 with @xmath48 and @xmath49 for one ( composite ) higgs doublet . we need to take into account contributions of kk modes in @xmath50 . since the kk modes heavier than the renormalization scale @xmath51 are decoupled in the @xmath13-rges , we only need summing up the loops of the kk modes lighter than @xmath51 . within the truncated kk effective theory , we obtain rges for gauge couplings @xmath46 : @xmath52 where rge coefficients @xmath53 are given by @xmath54 for @xmath55 , @xmath56 for @xmath57 , and @xmath58 for @xmath15 . here @xmath59 is defined as @xmath60 in eqs . ( [ b3kk])([bykk ] ) , @xmath61 denote the total number of kk modes for gauge bosons , gauge scalars , dirac ( 4-component ) fermions , and composite higgs bosons below @xmath51 , respectively . the number of generations in the bulk is @xmath62 , which is unity in our model . in the following analysis , we assume one composite higgs doublet , @xmath63 . @xmath64 for @xmath65 are not necessarily equal , since the orbifold boundary conditions are depending on @xmath66 . for details , see appendix a. we show numerical values for @xmath67 , ( the solid lines ) , @xmath68 , ( the dashed lines ) , and @xmath69 , ( the dotted lines ) in figs . [ fig - g-6d](b ) , [ fig - g-8d](b ) and [ fig - g-10d](b ) . matching the 4-dimensional action to the bulk action , we find the relation between the 4-dimensional gauge coupling @xmath70 and the _ dimensionful _ bulk gauge coupling @xmath71 , @xmath72 . we define the _ dimensionless _ bulk gauge coupling @xmath73 as @xmath74 and thereby obtain @xmath75 combining eq . ( [ hat - g ] ) with eq . ( [ rge_ed ] ) , we find rges for @xmath76 , @xmath77 . \label{rge_ed2}\end{aligned}\ ] ] in figs . [ fig - g-6d](a ) , [ fig - g-8d](a ) and [ fig - g-10d](a ) , we show typical behavior of the dimensionless" +"as mobile broadband wireless networks evolve , increasingly ambitious targets have been set for spectral efficiency . exploiting the capabilities of multiple antennas at the mobiles and base transceiver station ( bts ) is crucial to meet those goals . an effective approach is to use spatial precoding at the transmitters and filtering at receivers to adapt to the variations of the multiple - input multiple - output ( mimo ) channel and interference conditions by optimizing a metric such as the sum rate , signal - to - interference - and - noise ratio ( sinr ) , or mean squared error ( mse ) . two challenges need to be addressed : first , the precoders and filters should be _ jointly _ optimized ; and second , the optimization should be carried out without _ a priori _ knowledge of the channel and interference conditions . while joint optimization of precoders and receivers in cellular networks has attracted considerable attention in recent years ( e.g. , @xcite ) , much of the work has assumed linear precoders for the downlink , and has considered channel estimation methods for estimating those precoders with unknown channels . here we consider joint optimization and adaptation of _ non_linear precoders and receivers . specifically , we assume that the users are successively decoded and cancelled at the bts for the uplink , and that successive interference pre - cancellation with tomlinson - harashima precoding is applied by the bts for the downlink . the mobiles use linear filtering and precoding . a time - division duplex ( tdd ) network is assumed in order to exploit the reciprocity between uplink and downlink channels . the precoder and receiver filters are optimized according to a sum - mse criterion assuming mimo fading channels . this criterion is motivated by previous results showing that the minimum mean squared error ( mmse ) receiver with successive interference cancellation achieves the sum capacity of the multiaccess channel @xcite , and that the precoding structure considered ( generalized decision - feedback equalizer with interference pre - compensation ) achieves the sum capacity of the gaussian broadcast channel @xcite . furthermore , the mse criterion leads directly to adaptive approaches for filter estimation in the presence of unknown channels and interference . for a single cell we first show that alternating optimization of precoders and receiver filters ( for either the uplink or downlink ) converges to a local optimum . although this optimization must be applied separately for the uplink and downlink to obtain the optimal precoders and receiver filters for each direction , we observe that the filters optimized for one direction achieve near - optimal performance for the other direction as well when the uplink and downlink power constraints and noise power are similar . with this in mind we consider a simplified scheme in which the uplink ( downlink ) receive filters are also used as downlink ( uplink ) precoders . with this constraint we again show that alternating optimization of the filters at the bts and mobiles converges to a fixed point . in the absence of channel state information ( csi ) the preceding results lead to an iterative bi - directional training scheme in which uplink and downlink pilots are alternately transmitted to estimate the bts and mobile filters , respectively . the estimated bts forward / backward filters then nonlinearly precode both the downlink data and pilots for interference pre - cancellation , and the estimated mobile receiver filters precode both the uplink data and pilots . with sufficient training , the estimated filters approach the corresponding mmse filters in which case training in each direction corresponds to an mmse update of the corresponding filters . these uplink / downlink updates are then iterated until convergence , or a complexity constraint is reached . this scheme extends the bi - directional training scheme presented in @xcite , where the uplink / downlink pilots are used to estimate linear filters / precoders without interference cancellation . a key feature of these schemes is that the pilots are transmitted _ synchronously _ in each direction ( across all cells ) , and are used to estimate the filters _ directly _ via a least squares criterion , rather than directly estimating the channel . as discussed in @xcite , this scheme is _ distributed _ in the sense that each node ( bts or mobile ) autonomously computes its own filters from the received signal and pilots . in contrast , prior schemes for precoding / filtering based on channel estimation ( e.g. , @xcite ) are more suitable for centralized optimization in which all csi for direct- and cross - channels is passed to a single remote location , which computes all filters and then passes those back to the corresponding nodes . numerical results are presented that illustrate the performance of the bi - directional training scheme as a function of the amount of training and number of forward - backward iterations . it is shown that the achievable rate with nonlinear filters approaches the uplink sum capacity as the number of iterations increases . for a fixed number of training symbols , the nonlinear filters significantly outperform linear filters when the number of iterations is limited even though the nonlinear filters require more parameters to be estimated . an example for a multi - cell scenario shows that more iterations are required for the precoders and receive filters to converge than for a single cell . nonlinear filters again significantly outperform linear filters with few iterations in the high - snr regime . related work on joint precoder and receive filter design has been presented in @xcite . in @xcite , iterative algorithms are proposed for simultaneous diagonalization of the downlink multiuser channels to enable interference - free spatial - division multiplexing . in @xcite , algorithms are presented to jointly optimize linear filters and precoders for the uplink using a sum - mse criterion . mse duality results for broadcast and multiaccess channels are presented in @xcite . duality ensures that any uplink minimum mse scheme has a downlink counterpart . in @xcite , the downlink sum - mse minimization problem is solved by creating a `` virtual '' uplink channel , which has the same transmit power and noise level as for the actual downlink channel . however , those methods can not be implemented in a distributed manner in the setting of this paper , where the uplink and downlink channels may have different power constraints and noise levels . in @xcite , iterative mmse beamforming algorithms are presented to minimize the sum power subject to a set of sinr constraints , where the precoder and receive filter updates are done sequentially across users . in contrast , all users update simultaneously in this paper . consider a single cell consisting of a bts with @xmath0 antennas and @xmath1 users , where user @xmath2 has @xmath3 antennas . the uplink channel between user @xmath2 and the bts is denoted by @xmath4 of size @xmath5 , each entry of which is a unit - variance circularly symmetric complex gaussian ( cscg ) random variable . each user is restricted to one data stream , although the algorithms to be presented are easily extended to the scenario with multiple data streams per user . the received signal vector at the bts is @xmath6 where @xmath7 is the data symbol from user @xmath2 and @xmath8\!=\!1 $ ] , @xmath9 is the @xmath10 precoder with @xmath11 , where @xmath12 is the power constraint for user @xmath2 , and @xmath13 is the cscg noise vector each entry of which has zero mean and variance @xmath14 . similarly , assuming tdd with channel reciprocity , the downlink received signal at user @xmath2 can be written as @xmath15 where @xmath16 is the data symbol for user @xmath17 , @xmath18 is the corresponding transmit beam , and @xmath19 denotes the cscg noise vector with @xmath2th entry having variance @xmath20 . the filters satisfy the bts power constraint @xmath21 . we first discuss joint optimization of transmit precoders and receive filters at a central controller with perfect csi . adaptive versions with training are subsequently discussed in section [ s : training ] . first consider the case where the received signal in ( [ upsignal ] ) is processed by linear filters @xmath22 $ ] , where @xmath23 denotes the receive filter for user @xmath2 . the estimated signal for user @xmath2 is given by @xmath24 and the corresponding mse for user @xmath2 is @xmath25\\ & \!=\!1\!+\!\sigma^2\|\boldsymbol{g}_k\|^2\!-\!2\re\big\{\boldsymbol{g}_k^\dagger\boldsymbol{h}_k\boldsymbol{v}_k\big\}\!+\!\sum_{i=1}^{k}\big|\boldsymbol{g}_k^\dagger\boldsymbol{h}_i\boldsymbol{v}_i\big|^2,\label{upmse}\end{aligned}\ ] ] where @xmath26 takes the real part of a complex number . the optimization problem is stated as : [ upproblem ] @xmath27 [ prop : fullpow ] the sum mmse is minimized when all users transmit with full power . the proof is given in the appendix . hence the decrease in sum mse for a particular user @xmath2 due to an increase in power @xmath12 dominates the increase in sum mse due to the increase in interference at neighboring receivers . we will assume that each user transmits at the maximum power so that the constraints ( [ powercon ] ) are binding . the lagrangian for problem ( [ upproblem ] ) is @xmath28 where @xmath29 is the lagrange multiplier associated with the power constraint for user @xmath2 . hence the optimal solution to problem ( [ upproblem ] ) must satisfy : @xmath30 for @xmath31 , where @xmath29 in ( [ eq : uplnfilter2 ] ) is chosen to satisfy ( [ powercon ] ) . the nonlinear successive cancellation filter at the bts is the decision - feedback detector ( dfd ) shown in fig . [ uplink ] . the received signal is input to the linear feedforward filter @xmath32 , and the feedback filter @xmath33 implements the successive interference cancellation . assuming the decoding order is from user @xmath34 to user @xmath1 , the feedback matrix @xmath35 is lower triangular with diagonal elements equal to one . the estimated symbol for user @xmath2 is then @xmath36 where @xmath37 denotes the ( @xmath2,@xmath17)-th element of @xmath35 and @xmath38 denotes the slicer function in the forward loop . for user @xmath2 , if decoding of the previous symbols is correct , i.e. , @xmath39 , and @xmath40 , then the interference from users 1 to user @xmath41 can be removed . the achievable mse for user @xmath2 is then @xmath42 the problem becomes [ dfeproblem ] @xmath43 in this scenario it may not be optimal ( in the sum - mse sense ) for all users to transmit with full power . we will nevertheless assume that the power constraints are binding since this simplifies the problem , and because transmitting at full power is known to achieve the uplink sum capacity . writing the lagrangian as before , the corresponding first - order conditions are @xmath44 for @xmath31 , where the lagrange multipliers @xmath29 s are chosen to enforce the power constraints ( [ con : fullpow ] ) . the summation indices differ from ( [ eq : uplnfilter1 ] ) and ( [ eq : uplnfilter2 ] ) due to successive cancellation . the expressions for the downlink filters can be obtained in a similar fashion as for the uplink . the uplink and downlink problems are different because the snrs for the uplink and downlink channels are different in general , and because the power constraints are on individual users in the uplink , while the constraint is on the sum over all users in the downlink . for the downlink , the estimated symbol for user @xmath2 is @xmath45 where @xmath46 is the receiver filter . the corresponding mse is @xmath47 the downlink sum - mse minimization problem is [ dproblem ] @xmath48 the corresponding optimal filters satisfy : @xmath49 for @xmath31 , where" +"the success of symplectic integration algorithms ( ) as tools for the numerical solution of hamiltonian systems illustrates the importance of numerical algorithms that inherit the fundamental physical constraints of the systems to which they are applied ( `` geometric integrators '' ) . time - reversal symmetry plays a central role in physics ( e.g. , davies 1974 ) . to define reversibility formally and without reference to coordinates , let @xmath0 denote the state of the system governed by the differential equations = f(x ) . [ eq : basicde ] let @xmath1 be an involution , i.e. an operator such that @xmath2 . the system ( [ eq : basicde ] ) is @xmath1-reversible if @xmath1 reverses the direction of time , that is , if = -f(tx ) . in standard phase space @xmath3 and @xmath4 . the trajectory of the system governed by the differential equations ( [ eq : basicde ] ) is defined by a map @xmath5 such that a system located at @xmath0 at time 0 is found at @xmath6 at time @xmath7 ; by definition @xmath8 . then , @xmath1-reversibility implies that g_ttg_t = t tg_t = g_t^-1t = g_-tt . reversible systems may or may not be hamiltonian . however , the general features of motion in reversible and hamiltonian systems show many similarities , including the existence of families of kam tori ( e.g. , moser 1973 ; arnold 1984 ; roberts & quispel 1992 ) . these considerations motivate us to examine reversible integration algorithms ( ) . a one - step numerical integration algorithm with timestep @xmath9 is defined by an operator @xmath10 that is intended to be a close approximation to @xmath11 , and the algorithm is an if when it is applied to a reversible system _ note that in contrast to @xmath5 , @xmath12 is not necessarily equal to @xmath13 . let us first briefly review ; for more detail see channell & scovel ( 1990 ) , yoshida ( 1993 ) , marsden et al . ( 1996 ) , and sanz - serna & calvo ( 1994 ) . the standard example of a hamiltonian system is motion in a conservative potential ( this is also reversible ) . the hamiltonian is h(,)=^2+u ( ) [ eq : sepham ] and the equations of motion are = , = -u , or = -u . [ eq : second ] the most popular for such systems is the leapfrog or verlet algorithm ( e.g. , hockney & eastwood 1981 ) . this is a map from the phase - space coordinates @xmath14 at time @xmath15 to coordinates @xmath16 at time @xmath17 , defined by =_n+h_n , _ n+1=_n - hu( ) , _ n+1=+h_n+1 . leapfrog is an explicit second - order method ( i.e. the one - step error is o@xmath18 ) , but higher - order explicit can be constructed by concatenating leapfrog steps of different sizes , including backwards steps . leapfrog can be generalized to any separable hamiltonian of the form @xmath19 where each @xmath20 is integrable . for general hamiltonians , can be constructed by two methods . the first is based on expanding the scalar generating functions for the symplectic transformation @xmath21 in powers of @xmath9 ( kang 1986 ; channell & scovel 1990 ) . the simplest example is the first - order _ n+1=_n+hh(_n,_n+1)_n+1 , _ n+1=_n - hh(_n,_n+1)_n , which is implicit in general but explicit for hamiltonians of the form ( [ eq : sepham ] ) . the second approach is to construct symplectic implicit runge - kutta algorithms . for the differential equation ( [ eq : basicde ] ) , the @xmath22-stage runge - kutta method is defined by ( e.g. , ralston & rabinowitz 1978 ) k_i = f(x_n+h_j=1^sa_ijk_j),x_n+1=x_n+h_i=1^s b_jk_j . [ eq : rkimp ] runge - kutta methods are symplectic if they satisfy a simple algebraic test ( sanz - serna & calvo 1994 ) b_ia_ij+b_ja_ji - b_ib_j=0 , 1i , j s. [ eq : criterion ] on setting @xmath23 in ( [ eq : criterion ] ) , it is evident that all symplectic runge - kutta methods are necessarily implicit . the best known examples are the gauss - legendre runge - kutta methods ( e.g. , sanz - serna & calvo 1994 ) . the simplest can be written x_n+1=x_n+hf , [ eq : midptt ] which is the second - order implicit midpoint method . a symplectic fourth - order two - stage runge - kutta method is given by a_11=a_22= , a_12=- , a_21=+ , b_1=b_2=. [ eq : rk ] more generally , the gauss - legendre runge - kutta method is the unique @xmath22-stage method with order @xmath24 , and this method is always symplectic . these attractive features are offset by the computational cost of solving the implicit equations ( [ eq : rkimp ] ) . a limitation of is that they are difficult to generalize to variable timesteps . when a standard variable timestep prescription is applied to an , its performance is no better than that of non - symplectic integrators . the reason is simply that the mapping @xmath25 is usually not symplectic even when @xmath26 is . this is a serious problem , since most applications benefit from a variable timestep . one way to introduce variable timestep is by extending the phase space ( mikkola 1997 ) . suppose we wish to use a timestep @xmath27 . we define an extended phase space @xmath28 by @xmath29 and @xmath30 , where @xmath7 is time and @xmath31 is energy . we then define a new hamiltonian ( , ) = g ( , ) . the equations of motion for the hamiltonian @xmath32 in the extended phase space with fictitious time @xmath33 are the same as the equations of motion for the hamiltonian @xmath34 in the original phase space , supplemented by the condition @xmath35 . we may now integrate the hamiltonian @xmath32 using an with fixed timestep @xmath36 , which corresponds to @xmath37 . a limitation of this approach is that the hamiltonian @xmath32 is generally not separable , so that leapfrog and its generalizations can not be applied . several well - known one - step second - order algorithms for the differential equation ( [ eq : basicde ] ) are : for example , the implicit midpoint method ( eq . [ eq : midptt ] ) , the trapezoidal method , x_n+1=x_n+h , [ eq : trapp ] and the explicit midpoint method , x_n+2=x_n+hf(x_n+1 ) . [ eq : expmidpt ] some are also when they are applied to reversible hamiltonians . leapfrog and its generalizations are reversible . a reversible version of leapfrog with variable timestep @xmath27 is given by ( huang & leimkuhler 1997 ; calvo et al . 1998 ) @xmath38 quinn et al . ( 1997 ) describe a closely related algorithm based on a discrete set of timesteps that depend only on @xmath39 or @xmath40 and are separated by factors of two . a different approach to constructing is to modify non - reversible integration algorithms . for example , the following two operators are reversible even if @xmath10 is not : _ ^ -1 t , ( 1+t_ht)^-1(1+_h ) ; if we write @xmath41 then both of these operators are equal to @xmath42 to first order in @xmath9 . hut et al . ( 1997 ) describe numerical experiments with the second of these operators , calling it a `` time - symmetrization meta - algorithm '' since it can be applied to any one - step numerical integration algorithm . reversible algorithms remain reversible with a variable timestep so long as the timestep is determined symmetrically by the location of the system at the start and end of the step , e.g. @xmath43 $ ] ( hut et al . 1995 ) . special second - order differential equations of the form = f(x ) [ eq : fff ] are reversible , and so can profitably be integrated using . a useful source of high - order is linear multistep methods ( e.g. , henrici 1962 ; gear 1971 ; lambert 1973 ) , which have the form _ j=0^k ( a_k - jx_n - j - h^2b_k - jf_j)=0 , where @xmath44 , @xmath45 . we may assume without loss of generality that @xmath46 . the method is explicit if @xmath47 and otherwise implicit . linear multisteps include the classic strmer ( explicit ) and cowell ( implicit ) methods , which are characterized by @xmath46 , @xmath48 , @xmath49 , and @xmath50 for @xmath51 . it is easy to show that the requirement for reversibility is that @xmath52 and @xmath53 where @xmath54 ; thus the strmer and cowell methods are generally not reversible . multistep are discussed by lambert & watson ( 1976 ) , quinlan & tremaine ( 1990 ) , and fukushima ( 1998 , 1999 ) . in general , their performance over long time intervals on reversible dynamical systems is much better than strmer - cowell methods , although for occasional unfortunate choices of timestep their performance is ruined by timestep resonances ( quinlan 1999 ) . systems of first - order differential equations such as ( [ eq : basicde ] ) can be integrated by linear multistep methods of the form _ j=0^k(_k - jx_n - j - h_k - jf_n - j)=0 , [ eq : basic ] where @xmath44 , @xmath55 . we can assume without loss of generality that @xmath56 ; explicit methods have @xmath57 . these include the classic adams - bashforth ( explicit ) and adams - moulton ( implicit ) methods , which have @xmath58 and @xmath59 for @xmath51 ( e.g. , henrici 1962 ; gear 1971 ) . multistep methods for first - order differential equations are more general than multistep methods for special second - order equations , since any second - order equation can be written as a set of first - order equations . moreover , implementing variable timesteps is easy in first - order equations if we wish to use a timestep @xmath60 we introduce a fictitious time @xmath33 by the relation @xmath61 , and equation ( [ eq : basicde ] ) can be rewritten as = g(x)f(x ) , which can be integrated using unit timestep in @xmath33 . the aim of this paper is to investigate linear multistep for first - order differential equations . an important earlier investigation is that of cano & sanz - serna ( 1998 ) , who found that such methods typically possess grave numerical instabilities . we review general linear multistep methods in [ sec : intro ] , multistep in [ sec : reverse ] , together with their instabilities in [ sec : zero ] . we show in [ sec : zmm ] that it is possible to construct some linear multistep that are not subject to the cano & sanz - serna instabilities . a general discussion of stable multistep with up to 6 steps is given in [ sec : onetwo ] [ sec : fivesix ] . finally , [ sec : kep ] describes numerical examples based on integrating kepler orbits and [ sec : disc ] discusses our results . following henrici ( 1962 ) and lambert ( 1973 ) , we associate with ( [ eq : basic ] ) the linear operator l[x(t),h]=_j=0^k\{_k - jx[t+(k - j)h]- h_k - jx[t+(k - j)h]}. [ eq : linearoperator ] we can expand @xmath62 in a taylor series to obtain l[x(t),h]=_q=0^c_qh^qx^(q)(t ) , [ eq : tay ] where c_0=_l=0^k_l , c_q=1q!_l=0^k_ll^q - 1(q-1)!_l=0^k_ll^q-1,q=1,2, the order @xmath63 of the multistep is the unique integer for which @xmath64 , @xmath65 . the constant @xmath66 is known as the error constant and is a measure of" +"radio frequency ( srf ) cavities will be used in the international linear collider ( ilc ) to explore electron - positron collisions in high energy physics research . in order to achieve a 1 tev beam energy it is necessary to build @xmath2 nb cavities with electrodynamic properties approaching the intrinsic limit dictated by theory . despite the maturity of material fabrication techniques and improvement of chemical and physical surface treatments and annealing processes in the past several years , it is still challenging to fabricate so many state - of - the - art nb cavities without performance - limiting defects . in general , many types of defects are found on nb cavity surfaces . under intense rf loading , some of these defects can act as a hot spot to locally warm up the nb superconductor above its critical temperature ( @xmath3 ) , leading to a quench of the cavity . one approach to this problem is to postpone the quench of the superconductor by enhancing the rf breakdown field of the material at the surface . there is considerable interest in preparing novel coatings on nb cavities . superconductor / insulator multilayer thin film coatings have been proposed to enhance the rf breakdown field of the superconductor @xcite . it is of interest to measure whether or not this enhancement is possible with practical materials . however , the properties of uncontrolled localized defects present in the finished srf cavities appear to limit their ultimate microwave performance . therefore , there is an urgent need to understand the connections between localized defects , surface treatments , and the rf breakdown field in the high frequency regime . optical microscopy techniques have been developed to identify defects in finished nb cavities @xcite . however this optical screening process may result in identification of relatively benign defects which will not result in a quench of the superconductor . ideally , one would like a microscopic technique that identifies defects based on their poor microwave performance at low temperatures in the superconducting state . one of the best candidates for this job is the near field microwave microscope which has been developed to quantitatively image rf and microwave properties of a variety of materials on deep sub - wavelength scales @xcite , @xcite . in order to generate a strong and localized rf magnetic field , and to enhance the spatial resolution of this microscope , a magnetic writer is utilized in our experiment . taking advantage of magnetic write head technology with write - gap widths on the order of 100 nm @xcite , an rf field on the scale of 1 tesla @xcite with sub - micron spatial extent @xcite can be created . in this work , we integrate the magnetic writer probe into our microwave microscope and demonstrate that this probe can develop a nonlinear meissner effect signal from several kinds of superconductors such as mgb@xmath4 and tl@xmath4ba@xmath4cacu@xmath4o@xmath5 ( tbcco ) . this probe has great potential for high resolution nonlinear meissner effect microscopy and in the future will be used in analyzing defects on nb cavity surfaces at high frequencies and low temperatures . in previous work , we developed a low resolution near field microwave microscope to nondestructively measure the local harmonic generation from unpatterned superconducting samples @xcite , @xcite , @xcite , @xcite . in this design , a loop probe ( fig . [ fig_probe ] left ) is made by shorting the inner conductor and outer conductor of a commercial semi - ridge coax cable with inner diameter 200 @xmath6@xmath7 and outer diameter 2 @xmath8 . the loop is brought to within 10 @xmath6@xmath7 of the superconducting surface and a high frequency signal is applied to the loop . rf screening currents are induced in the sample . due to its nonlinear response , harmonics of the drive signal are created , and these couple back into the loop probe and are measured at room temperature with a spectrum analyzer . this experiment can determine both the second and third harmonic nonlinear products at the same location at any excited frequency and temperature of interest . here , we have modified this basic experiment to produce stronger and more localized rf magnetic fields . based on the need to investigate nb near the thermodynamic critical field , we require at least 200 @xmath9 magnetic field at the sample surface . in order to enhance the magnetic coupling between probe and superconducting sample , we replace the loop probe with a magnetic write head ( fig . [ fig_probe ] right ) . the system setup is shown in fig . [ fig_setup ] . both the magnetic write head probe and the superconductor are kept in a high vacuum cryogenic environment . microwave fundamental frequency power @xmath10 is generated by a microwave synthesizer . low pass filters are used to filter out higher harmonics generated by the microwave source . because of the perturbation of the super fluid density coming from the externally applied rf magnetic field , higher order harmonic response ( @xmath11 , @xmath12 , @xmath13 ) will be induced on the sample for temperatures below @xmath3 . those harmonic signals will be radiated from the sample and can be extracted by high pass filtering the signal from the probe . here we shall concentrate on @xmath12 , which arises from time - reversal invariant perturbations of the superconductor and can be used to examine both intrinsic and extrinsic nonlinear characteristics of the material . in fig . [ fig_setup ] , the closed dashed line encloses a reference microwave circuit designed for cancellation of nonlinearity from the magnetic write head probe itself , and will be discussed below . in addition , a bias tee is integrated into the microwave microscope circuit to allow injection of a small dc current into the probe , also discussed further below . the generated third harmonic power @xmath12 is estimated as @xcite , @xcite @xmath14 where @xmath15 is the frequency of the incident wave , @xmath16 is the temperature dependent magnetic penetration depth , @xmath17 and @xmath18 are the nonlinear scaling current and a current - distribution geometry factor , respectively . @xmath19 is the surface current induced in the superconductor at the fundamental frequency and @xmath20 is total volume current induced in the sample . from eq . ( [ p3f : equation ] ) , a strong magnetic field from the magnetic write head probe will enhance the surface current @xmath21 and confine the current distribution , both leading to an enhancement of @xmath18 , and therefore @xmath12 , for a given excitation power . this has the added benefit of improving the spatial resolution of the probe . defective regions of the sample , including those responsible for hot - spot generation , have smaller values of @xmath17 than the surrounding material , hence will develop larger @xmath12 , thus giving away their position to the microscope . previous work has demonstrated the ability of this microscope to identify a grain boundary josephson junction defect in a cuprate thin film @xcite , @xcite , @xcite . the superconducting samples we study include a tbcco thin film of thickness 500 @xmath22 , epitaxially grown by the magnetron sputtering method @xcite . in addition , a high quality epitaxial mgb@xmath4 thin film with thickness 25 @xmath22 is also examined . the mgb@xmath4 film is deposited on a sic substrate by a hybrid physical - chemical vapor deposition technique @xcite . both samples are examined at a single location in the center of the 10 mm*10 mm area . before integrating the magnetic write head into our near field microwave microscope , we measured the complex load impedance that the head presents to the microwave generator . [ fig_impeadance ] shows the impedance measured with a picoprobe touching the contact pads on the slider . remarkably , the write head is very well impedance matched to 50 @xmath23 in resistance and 0 @xmath23 in reactance over a broad frequency range from around 2 ghz to 25 ghz , which is quite ideal for the present application . such good impedance match implies that we can deliver 45 @xmath24 of current to the write head using 100 @xmath25 ( + 20 dbm ) of rf power , and we have found that this does not burn out the magnetic write head coil . of a tbcco film , measured by a magnetic write head probe with an excitation frequency of 3.5 ghz . inset is measured by the bare loop probe with excitation frequency of 3.5 ghz and excited power 18 dbm.,width=326,height=288 ] a measurement of the temperature dependent 3rd order harmonic power is performed at the center of the tbcco film by the magnetic write head probe with different exciting powers . the inset of fig . [ fig_tbcco ] shows @xmath26 measured by the bare loop probe . a peak in @xmath12 near @xmath3 shows up , as expected . this enhancement of @xmath12 is due to the nonlinear meissner effect near @xmath3 . from eq . [ p3f : equation ] one sees that due to @xmath17 approaching zero and @xmath27 diverging at @xmath3 the third harmonic power will increase strongly . the divergence is cut off by the distribution of transition temperatures in the sample , and the influence of quasiparticle electrodynamics . with the loop probe , the enhancement of @xmath12 above background is only 15 db , for 18 dbm fundamental input power . such a small enhancement can be easily achieved by the magnetic head probe with only 9 dbm excited power ( fig . [ fig_tbcco ] ) , which means that the magnetic write head generates a more localized and intense field , inducing stronger surface currents on the sample . despite these higher currents , there is no evidence of localized heating in the sample from the data in fig . [ fig_tbcco ] . in order to test the magnetic write head probe in a liquid helium cooled environment , temperature dependent 3rd order harmonic power is also measured in the center position of an mgb@xmath4 thin film . in fig . [ fig_mgb2 ] , a peak at 39.1 k shows up clearly near the @xmath3 of the film . this proves that the magnetic probe can function in the low temperature region . comparison of this peak with that of tbcco , one finds a much sharper transition , implying a narrow distribution of @xmath28 values in the mgb@xmath4 thin film . from an mgb@xmath4 film , measured with the magnetic write head probe with an excitation frequency of approximately 3.5 ghz and a power of 12 dbm.,width=3,height=288 ] one can see from fig . [ fig_tbcco ] that as the excitation power to the probe is increased , the noise floor is also enhanced . this is due to the nonlinearity of the magnetic write head itself . generally speaking , all of the tested magnetic write heads show some degree of nonlinearity . to clarify the origin of this probe nonlinearity , a dc current is injected into the write head drive coil to control the magnetization direction of the magnetic materials inside the probe . third harmonic power from the probe under 3.5 ghz and 16 dbm illumination is shown in the inset of fig . [ fig_phase_cancelation ] , as a function of dc current from -55 ma to + 55 ma . the @xmath12 from the magnetic write head decreases dramatically at + 45 ma and -45 ma , demonstrating that an applied dc current can suppress background nonlinearity . this decrease in @xmath12 may be due to establishment of a fully magnetized state of the ferromagnetic films in the write head , thus elimianting nonlinearity from minor hysterisis loops . the applied current may also reduce magnetic domain wall motion" +"virus particles ( virions ) come in a variety of sizes and shapes . however , approximately spherical shapes with diameters in the range between @xmath1 and @xmath2 are especially common . many nearly spherical viruses are revealed by x - ray crystallography to have icosahedral symmetry . a typical virus particle contains genetic material , rna or dna , surrounded by a protein coat ( capsid ) . such an object should have reasonably distinct vibrational frequencies , the study of which may be of interest . excitation of these vibrations could have applications in either the diagnosis or treatment of viral diseases . to this author s knowledge , the sole discussion of these vibrational modes in the literature is that of babincov _ et al _ @xcite . these authors discuss the conjecture that ultrasound in the ghz range could be resonantly absorbed by hiv virus particles , leading to their destruction . et al _ @xcite have recently reported the detection of viruses by acoustic oscillations . however , the process of `` rupture event scanning '' , which these authors report , involves the separation of a virus particle from antibodies by ultrasound . this is distinct from the excitation of the vibrational modes of the virus particle itself , and occurs at much lower frequencies . there have also been some experimental studies of ultrasonic absorption by empty viral capsids @xcite . these experiments reveal an enhanced absorption in the mhz range as proteins reassemble into a capsid , but do not find a resonant peak in this frequency range . witz and brown @xcite have emphasized that these and other results show that viral capsids are flexible and change size or shape in response to vibrations or to changes in temperature or ph . the purpose of the present paper is to provide some estimates of the lowest vibrational frequencies of a spherical virus particle . the simplest estimate is to take this frequency to be of the order of a characteristic speed of sound divided by the size of the virus particle . this is the estimate used in ref . @xcite . for the purpose of giving a more accurate estimate , we will examine two models , which treat the particle ( 1 ) as a liquid drop and ( 2 ) as a uniform elastic sphere . similar models have been used by bulatov _ @xcite to estimate the vibrational frequencies of nanoclusters . consider a sphere of radius @xmath3 filled with a nonviscous liquid with surface tension @xmath4 and mass density @xmath5 . the lowest vibrational mode of this sphere will be a quadrupole mode with frequency @xcite @xmath6 which can be written as @xmath7 where @xmath8 and @xmath9 are the mass density and surface tension for water , respectively . the surface tension and mass density , along with the lowest vibrational frequency derived from eq . ( [ eq : nu_drop ] ) for @xmath10 , are given in table 1 for several liquids . .the mass density , surface tension , and the lowest vibrational frequency predicted by eq . ( [ eq : nu_drop ] ) for drops of various liquids with a radius of @xmath10 . the data for benzene and diethylene glycol @xcite are for droplets in air at room temperature . the data for the three proteins @xcite are for aqueous solutions at approximately @xmath11 . [ cols=""^,^,^,^"",options=""header "" , ] we can see that for a wide range of materials , the lowest mode of vibration is a purely radial mode with a frequency of the order of a few times @xmath12 for a sphere of radius @xmath10 . in the previous sections , we have examined two models for a spherical virus particle , a liquid drop model and an elastic sphere model . it is of interest that the two models yield estimates for the lowest vibrational frequency which differ by only about one order of magnitude . of the two models , the elastic sphere model is probably the better description of a virus particle . an even better model might be one in which the particle has a liquid core ( dna or rna ) surrounded by an elastic outer shell ( the capsid ) . such a model would probably yield vibrational frequencies intermediate between those predicted by the two models discussed in this paper . in any case , we obtain an estimate for the lowest vibrational frequency of the same order of magnitude as that given in ref . @xcite , in the range of a few ghz for particles with a size of about @xmath13 . of course , the existence of a resonance requires that damping be below the critical value above which overdamped motion occurs . even if this condition is fulfilled , it is difficult to predict the width of the resonance . this remains a question for experimental investigation . the existence of well defined resonances could prove valuable both for basic science and for medicine . thus this is a potentially fruitful area for further research ." +"paradoxes are among the best weaponry available to a scientist . the paradox in science is associated with a flaw in the theoretical understanding on the most basic level . recently an interview with edward witten was broadcasted on dutch tv . the interviewer tried to corner witten , arguing that quantum - gravity is a shaky affair because it is not accessible by experimental means . witten was prepared for this question , arguing that the situation is not that bad because quantum gravity is firmly rooted in a grand paradox . einstein s theory of gravity and quantum mechanics are fundamentally incompatible . this is intimately linked to basic assumptions that are so self evident that they are not even explicitly formulated . the pursuit of string - theory should be considered as an attempt to lay bare these hidden assumptions , and in this sense progress is made . we want to suggest that high @xmath0 superconductivity is in a similar state . the field revolves around a grand paradox , with the added merit that it has experimental physics on its side . the arrival of a paradox is accompanied by raging controversy , and the controversy in high @xmath0 superconductivity is not easy to overlook . the community has bifurcated in two schools of thought . the first school rests on the conceptual backbone of conventional bcs theory and has been quite successful in addressing the physics of the fully developed superconducting state@xcite . their stronghold are the quasiparticles associated with the d - wave order parameter . the other school refers to the growing body of empirical and theoretical evidence suggesting that the electrons have been eaten by dynamical stripes@xcite . the paradox is that stripes and nodal fermions are mutually exclusive . the basic assumption underlying stripes is that the electrons are expelled from the magnetic domains , with the unavoidable consequence that the soft charge degrees of freedom are associated with the motions inside the stripes . since the stripes are oriented along the @xmath1 lattice directions the low energy propagating electronic excitations should be found along the @xmath2 directions in the brillioun zone . along @xmath3 the excitations have to traverse the insulating domains and this should cause a severe damping if not a complete gapping . instead , photo - emission shows relatively sharp dispersive features along @xmath3 which are quite like the nodal fermions of a d - wave superconductor . the messy fermions are found along the stripe directions . it seems a widespread reflex to postulate a ` two - fluid ' picture : stripes and nodal fermions reflect separate universes , both governed by their own laws , which are for whatever reason completely disconnected . one has no other choice within the confines of bcs theory and the present understanding of dynamical stripes . however , this is no more than admitting defeat in the face of the paradox . we want to pose the following question : can it be that stripes and nodal fermions are two manifestations of an underlying unity while they appear as dissimilar because of flawed hidden assumptions in the theory ? the remainder of this text will be a modest attempt to make the mind susceptible to the possibility that a positive answer exists for this question . a tactics will be followed which is not dissimilar to the habits in string theory . an alternative theory is suggested , of a highly speculative kind while its consequences are far from clear because of severe technical difficulties . however , it has the special merit that it does not suffer from the paradox , thereby shedding some light on what can be wrong in the current understanding . the burden is on the stripe side . one has to get out of the narrow interpretations of textbook bcs theory to appreciate the nodal fermions on a sufficiently general level , and this work has already been done by others see the next section . our speculation is that the current way of viewing dynamical stripes is too classical . instead , we assert that the superconducting- and stripe states are related by duality ( section 3 ) . static stripes and superconductivity are competing orders and the duality principle of quantum field theory states that the competing phases can be viewed as ` two sides of the same coin'@xcite : the disordered state ( the superconductor ) can be viewed as a condensate of the topological excitations ( disorder fields ) associated with the ordered state ( the static stripes ) . the topological excitations of the stripe phase ( ` stripe dislocations ' ) have such an unusual structure that it is a - priori unreasonable to assume that the associated disorder field - theory does not support nodal fermions . all what is needed on this side of the coin is to obtain a sufficiently general view on the nature of what has to be demonstrated : the nodal fermions . although controversial@xcite , we will take here the conservative position that bcs is correct as the fixed point theory . one has to be , however , aware of the over - interpretations associated with the weak - coupling treatments in the textbooks . these are twofold : the ultraviolet is not governed by a non - interacting electron gas , even not to some degree of approximation@xcite . secondly , bogoliubov quasiparticles are in fact @xmath4 excitations of the spin system ( spinons ) which acquire fully automatically a finite electron pole - strength in the superconducting state@xcite . _ @xmath5 is not a sommerfeld gas . _ the universality principle states that systems differing greatly at microscopic scales can nevertheless exhibit the same physics at macroscopic scales . bcs is a universal theory and its infrared structure can be deduced from a simple model . the standard textbook approach sets off by guessing a zero - th order hamiltonian ( @xmath6 ) which depicts the large energy scale physics . in systems such as aluminum , the fermi - liquid renormalizations are basically complete at @xmath0 and @xmath5 is simply the sommerfeld gas hamiltonian . all one has to do is to add a small perturbation ( the bcs - attractive interaction ) which leaves the uv physics unaltered ( the fermi surface ) while veering the system to the correct ir fixed point . although the fixed point might still be the same , the way one gets there is entirely different in cuprates@xcite . there is no such thing as a close approach to the fermi - liquids at short scales- and times as is the case in al . instead , the analysis of shen and coworkers of the photo - emission suggests that at truly large energies the electrons move in stripes : the ` holy cross'@xcite . upon descending in energy , the cross starts to deteriorate and the nodal fermions start to appear . it is as if the nodal fermions are a long wavelength phenomenon associated with the quantum disordering of stripes ! it is only at low temperatures , deep in the superconducting state that one finds features which behave like quantum - mechanically propagating particles ( the ` quantum protection principle'@xcite ) . the ramification is that it is not necessary to deduce a large , noninteracting fermi - surface from quantum stripes . it is only necessary to demonstrate that the vacuum structure supports massless electron - like excitations living on dirac cones : the nodal fermions . _ nodal fermions are spinons . _ as a next step , it is even not necessary to reinvent the electron . all that needs to be done is to find excitations carrying spin quantum number @xmath4 living on the dirac cones . the superconducting condensate will take care of connecting these to the electrons . for this purpose we only have to remind the reader of an insight by kivelson and rokshar@xcite , further elaborated by fisher and coworkers@xcite . according to the textbooks , the bogoliubov quasiparticle is an electron because it has a pole - strength proportional to the square of a coherence factor . the finiteness of the pole - strength implies that the quantum numbers carried by the external electron can be attached to the excitations supported by the vacuum structure of the superconductor . although spin- and momentum quantum numbers are sharply defined in the bcs state , there is a subtlety associated with the quantum of electrical charge : charge density is a fluctuating quantity in the superconductor and charge quanta can be added and removed at will from the condensate . hence , the charge of the external electron can always be ` dumped ' in the condensate . to summarize , instead of reinventing aluminum , all what has to be done is to find out if a quantum disordered stripe phase can be constructed , which is superconducting while it carries @xmath4 excitations with a nodal - fermion dispersion . one of the quiet revolutions of mathematical physics is the discovery of the field - theoretic principle of duality . at first it appears as a mathematically rigorous procedure which can be carried through to the end in only a few simple cases ( e.g. , ref . however , it seems to reflect a physical principle of a far greater generality . especially in the condensed matter context it has a stunning consequence : except for the critical state , the universality of duality seems to suggest that there are no truely disordered states at zero temperature . what appears as disorder is actually order of the disorder operators . duality can be formulated as an algorithm , with the following subroutines : ( a ) characterize the order in the system in terms of an order parameter structure . ( b ) enumerate the topological excitations , and link them to singular configurations of the order fields defined in ( a ) . a single topological excitation suffices to destroy the order everywhere . ( c ) at a critical value of the coupling constant these topological excitations will proliferate , signalling the transition to the ` disordered ' state . ( d ) the constituents of the disordered state are the topological excitations of its ` ordered ' partner . as these objects interact this in turn defines a ` disorder ' field theory describing the condensation of the disorder matter . the ` disordered ' state corresponds with an ordered state in terms of the topological excitations of the ` ordered ' state . why should this have anything to do with the cuprates ? static stripes and superconductivity are clearly competing forms of order . when stripe order sets in , superconductivity is suppressed and vice versa . moreover , it appears that this competition is governed by a ( near ) continuous quantum phase transition@xcite . this is not unimportant , since duality is only rigorously defined in continuum field theory and therefore the characteristic length scales should be large as compared to the lattice constant . dynamical stripes seem to fulfill this condition at least in the underdoped regime . finally , the ordered stripe phase and the superconductor appear to be very different states of matter , but this is not an a - priori problem . after all , the central notion of duality is that one is supposed to be the ` maximally disordered ' version of the other , although at elevated energies they are bound to merge in a single critical regime . the remainder of this section is intended to illustrate the problems encountered in the duality construction which are so severe that it can not be excluded that it is actually the correct way of viewing these matters . according to the" +"by using direct numerical simulations @xcite and bubble / cavitation visualization experiments @xcite , it has been established that turbulence contains vortex tubes . regions of intense vorticity are organized into tubes . their radii and lengths are , respectively , of the orders of the kolmogorov length @xmath1 and the integral length @xmath2 . their lifetimes are several turnover times of the largest eddies . the vortex tubes occupy a small fraction of the volume and are embedded in a background flow that is random and of large scales ( see also reviews @xcite ) . here we study vortex tubes in velocity fields of experimental turbulence as a function of the reynolds number re@xmath3 . especially when the reynolds number is high , effects of vortex tubes on the velocity field are of interest . the velocity signal at small scales is enhanced only in a fraction of the volume @xcite . this small - scale intermittency is attributable to vortex tubes @xcite . with increasing the reynolds number , turbulence becomes more intermittent @xcite . large values of the reynolds number , re@xmath4 , are achieved only in experiments , where a measurement is made with a probe suspended in the flow and a one - dimensional cut of the velocity field is obtained . the measurement often deals with the velocity component in the mean - flow direction alone ( hereafter , the streamwise velocity @xmath5 ) , but the transverse velocity @xmath6 is more suited to detecting circulation flows such as those associated with vortex tubes @xcite . a simultaneous measurement of the two velocity components is desirable . for laboratory experiments , there are several possible configurations . among them , a flow downstream of a turbulence - generating grid is preferable . this grid turbulence is isotropic and free from external influences such as mean shear , and hence is suited to isolating effects of vortex tubes at each of the scales . although the reynolds number is not very high and the inertial subrange is almost absent , grid turbulence is a natural step from direct numerical simulations of isotropic turbulence with small re@xmath3 values to laboratory or field experiments of anisotropic turbulence with very large re@xmath3 values . we carried out simultaneous measurements of the streamwise and transverse velocities in grid turbulence with a range of the reynolds number , re@xmath0330 . since our wind tunnels as well as our grids were large , the re@xmath3 values exceed those in past studies of grid turbulence . the exception is a special but old experiment with high air pressure @xcite , for which the reynolds number was in the range re@xmath7670 . thus our data provide a unique opportunity to study vortex tubes in isotropic turbulence with a wide range of the reynolds number . the preliminary studies had been reported by mouri et al . @xcite , but the present data are new and are analyzed more carefully and extensively . in sec . [ s2 ] , we describe our experiments . in sec . [ s3 ] , we present a model for a vortex tube . in sec . [ s4 ] , a conditional averaging technique is used to extract typical intermittency patterns from the data . the patterns turn out to be consistent with velocity profiles expected for the model tube . also , statistics of velocity increments are used to study the energetical importance of vortex tubes as a function of the scale . in sec . [ s5 ] , we present our conclusion with remarks for future experimental researches . the experiments were done in two wind tunnels of meteorological research institute . their test sections were of 0.8 @xmath8 0.8 @xmath8 3 and 3 @xmath8 2 @xmath8 18 m in size . turbulence was produced by placing a grid across the entrance to the test section . the grid consisted of two layers of uniformly spaced rods , the axes of which were perpendicular to each other . we used three grids . the separations of the axes of their adjacent rods were @xmath9 = 0.1 , 0.2 , and 0.4 m. the cross sections of the rods were , respectively , 0.02 @xmath8 0.02 , 0.04 @xmath8 0.04 , and 0.06 @xmath8 0.06 m. the mean wind was set to be @xmath10 @xmath11 4 , 8 , 12 , or 16 m s@xmath12 . the streamwise ( @xmath13 ) and transverse ( @xmath6 ) velocities were measured simultaneously with a hot - wire anemometer . the anemometer was composed of a crossed - wire probe and a constant temperature system . the probe was positioned on the tunnel axis . the hot wires were platinum - coated tungsten filaments , 5 @xmath14 m in diameter , 1.25 mm in effective length , 1 mm in separation , 280@xmath15c in temperature , and oriented at @xmath16 to the mean - flow direction . the calibration was done before and after each of the measurements . the signal was low - pass filtered at @xmath17 = 416 khz with 24 db per octave and sampled digitally at @xmath18 = 832 khz with 16-bit resolution . to avoid aliasing , the sampling frequency was set to be twice of the filter cutoff frequency , @xmath19 . the entire length of the signal was 2 @xmath8 10@xmath20 points , which is large enough to guarantee the convergence of the statistics @xcite . for each set of the grid and the mean wind speed , measurements were made at several positions downstream of the grid . we first computed the flatness factors @xmath21 and @xmath22 , where @xmath23 denotes an average . the data with the flatness factors being close to the gaussian value of 3 were used in further analyses because we are to study fully developed turbulence . if the measurement position is too close to or far from the grid , the turbulence is still developing or already decaying , and its flatness factors are different from the gaussian value @xcite . except for the measurements done in the @xmath24 m tunnel , the flow was almost isotropic . the ratio between the streamwise- and transverse - velocity dispersions @xmath25 was close to unity . the turbulence level , i.e. , the ratio of the root - mean - square streamwise fluctuation @xmath26 to the mean streamwise velocity @xmath10 , was always less than 10% . this good characteristic of grid turbulence allows us to rely on the frozen - eddy hypothesis of taylor @xcite , @xmath27 = @xmath28 , which converts temporal variations into spatial variations in the mean - wind direction . to obtain the highest spatial resolution , we set @xmath17 in such a way that @xmath29 is close to the probe size , @xmath30 mm . since the probe size is greater than the kolmogorov length , 0.20.5 mm , the smallest - scale motions of the flow were filtered out . the present resolution is nevertheless typical of hot - wire anemometry . although the relief technique achieves a higher resolution @xcite , it is applicable only to the transverse velocity . consequently we obtained 10 sets of turbulence data . the experimental conditions are summarized in table [ t1 ] . the flow parameters such as the integral length @xmath2 , the kolmogorov length @xmath1 , the taylor microscale @xmath31 , and the reynolds number re@xmath3 are also summarized there . before describing our experimental results , it is helpful to present a model for a vortex tube , burgers vortex @xcite . this model is an axisymmetric steady circulation in a strain field . in cylindrical coordinates , the circulation and the strain field are written respectively as @xmath32 \quad ( a > 0),\ ] ] and @xmath33 here @xmath34 is the kinematic viscosity . the above eq . ( [ eq1a ] ) describes a rigid - body rotation for small radii , and a circulation decaying in radius for large radii . the velocity is maximal at @xmath35 = @xmath36 = @xmath37 . thus @xmath36 is regarded as the tube radius . suppose that the vortex tube penetrates the @xmath38 plane at the point @xmath39 . the @xmath40 and @xmath41 axes are , respectively , in the streamwise and transverse directions . if the direction of the tube axis is @xmath42 in spherical coordinates , the streamwise ( @xmath5 ) and transverse ( @xmath6 ) components of the circulation flow @xmath43 along the @xmath40 axis are @xmath44 and @xmath45 with @xmath46 likewise , for the radial inflow @xmath47 of the strain field , the streamwise and transverse components are @xmath48 and @xmath49 if the vortex tube passes close to the probe ( @xmath50 ) and the tube is not heavily inclined ( @xmath51 ) , the transverse velocity is dominated by the circulation flow . the streamwise velocity is dominated by the radial inflow . this situation is of particular interest . if @xmath52 , the tube signal is weak . if @xmath53 , the transverse velocity is dominated by the radial inflow , which is of large scale and does not contribute to the small - scale intermittency . the velocity profiles of vortex tubes with @xmath50 and @xmath51 are nearly the same @xcite . however , as implied by the first term of eq . ( [ eq3 ] ) , the radius @xmath54 of a tube observed along the streamwise direction is different from its intrinsic radius @xmath36 as @xmath55 . thus , even if the intrinsic radii of the vortex tubes are the same , they contribute to a range of the scales . hereafter we describe our experimental results . except for fig . [ f6 ] , the following diagrams present the results only for the experiments 1 , 2 , 5 , 8 , and 10 ( see table [ t1 ] ) . we nevertheless obtained consistent results for the other experiments . the streamwise - velocity increment @xmath56 = @xmath57 or the transverse - velocity increment @xmath58 = @xmath59 is enhanced in an intermittency event . we obtain velocity patterns typical of the intermittency events by averaging signals centered at the position where the transverse - velocity increment is enhanced over its root - mean - square value by more than a factor of 3 , i.e. , @xmath60 . the scale @xmath61 is set to be the spatial resolution @xmath29 . such an event is detected 2.15.9 times per the integral length . when the increment is negative , we invert the sign of the @xmath6 signal . the numerical factor of 3 in our above criterion comes from a compromise . if the factor is larger , the total number of the events is smaller , and hence statistical uncertainty in the velocity patterns is more significant . if the factor is smaller , the velocity patterns are less representative of intermittency . it was nevertheless ascertained that our following results depend only weakly on the choice of the numerical factor if it is in the range 24 . the results are shown in fig . [ f1 ] ( solid lines ) . the @xmath5 pattern is shown separately for @xmath62 and @xmath63 at @xmath64 ( designated , respectively , as @xmath65 and @xmath66 ) . for reference , we show velocity profiles ( [ eq2b ] ) and ( [ eq4a ] ) of a burgers vortex with @xmath67 and @xmath68 ( dotted lines ) . the tube radius @xmath36 was determined so as to reproduce the @xmath6 pattern for each of the experiments . the @xmath6 pattern of grid turbulence is close to the profile of a burgers vortex @xcite . vortex tubes are surely responsible for small - scale intermittency in the transverse velocity . the radii @xmath36 of the vortex tubes are estimated to be several of the" +"the problem of enumerating the strings in a language @xmath2 is to list all the elements in @xmath2 in some order . several papers study this problem . for example , enumerating all spanning trees , @xcite , minimal transversals for some geometric hypergraphs , @xcite , maximal cliques , @xcite , ordered trees , @xcite , certain cuts in graphs , @xcite , paths in a graph , @xcite , bipartite perfect matchings , @xcite , maximum and maximal matchings in bipartite graphs , @xcite , and directed spanning trees in a directed graph @xcite . see the list in @xcite for other enumeration problems . one of the challenges in enumeration problems is to find an order of the elements of @xmath2 such that finding the next element in that order can be done in quasilinear time in the length of the representation of the element . the time that the algorithm takes before giving the first element is called the _ preprocessing time_. the time of finding the next element is called the _ delay time_. in @xcite , ackerman and shallit gave a linear preprocessing and delay time for enumerating the words of any regular language ( expressed as a regular expression or nfa ) in lexicographic order . enumeration is also of interest to mathematicians without addressing the time complexity . calkin and wilf,@xcite , gave an enumeration of all the rational numbers such that the denominator of each fraction is the numerator of the next one . another problem that has received considerable attention is the problem of ranking the elements of @xmath2 . in ranking the goal is to find some total order on the elements of @xmath2 where the problem of returning the @xmath0th element in that order can be solved in polynomial time . obviously , polynomial time ranking implies polynomial time enumeration . in the literature , the problem of ranking is already solved for permutations @xcite and trees of special properties @xcite . those also give enumerating algorithms for such objects . let @xmath3 be a finite field with @xmath4 elements . let @xmath5 be the set of irreducible polynomials over @xmath3 of degree @xmath0 and their roots in @xmath6 . several algorithms in the literature use irreducible polynomials of degree @xmath0 over finite fields , especially algorithms in coding theory , cryptography and problems that use the chinese remainder theorem for polynomials @xcite . some other algorithms use only the roots of those polynomials . see for example @xcite . in this paper , we study the following problems 1 . enumeration of any number of irreducible polynomials of degree @xmath0 over a finite fields . 2 . enumeration of any number of irreducible polynomials of degree @xmath0 and their roots over the extended field . 3 . enumeration of any number of roots of irreducible polynomials of degree @xmath0 over the extended field . one root for each polynomial . there are many papers in the literature that mention the result of enumerating all the irreducible polynomials of degree _ less than or equal _ to @xmath0 but do not give the exact algebraic complexity of this problem @xcite . in this paper we give a detailed analysis of deterministic and randomized algorithms that enumerate any number of irreducible polynomials of degree @xmath0 over a finite field and/or their roots in the extension field in quasilinear where @xmath1 is the size of the output . ] time cost per element . our algorithm is based on an improved algorithm for enumerating all the lyndon words of length @xmath0 in linear delay time and the well known reduction of lyndon words to irreducible polynomials . in the next subsection we define the lyndon word and present the result of the improved algorithm . let @xmath7 be any total order on @xmath3 . a _ lyndon word _ ( or string ) over @xmath3 of length @xmath0 is a word @xmath8 where every rotation @xmath9 , @xmath10 of @xmath11 is lexicographically larger than @xmath11 . let @xmath12 be the set of all the lyndon words over @xmath3 of length @xmath0 . in many papers in the literature , it is shown that there is polynomial time ( in @xmath0 ) computable bijective function @xmath13 , where @xmath5 is the set of all polynomials of degree @xmath0 over @xmath3 . so the enumeration problem of the irreducible polynomials can be reduced to the problem of enumerating the elements of @xmath12 . bshouty gave in @xcite a large subset @xmath14 where any number of words in @xmath15 can be enumerated in a linear delay time . in fact , one can show that @xmath15 has a small dfa and , therefore , this result follows from @xcite . it is easy to show that the set @xmath12 can not be accepted by a small size nfa , i.e. , size polynomial in @xmath0 , so one can not generalize the above result to all @xmath12 . duval @xcite and fredricksen et . , @xcite gave enumeration algorithms of all the words in @xmath16 that run in linear delay time . berstel and pocchiola in @xcite and cattell et . al . in @xcite show that , in duval s algorithm , in order to find the next lyndon word in @xmath16 , the amortized number of _ updates _ is constant . the number of updtes is the number of symbols that the algorithm change in a lyndon word in order to get the next word . such an algorithm is called cat algorithm . see the references in @xcite for other cat algorithms . kociumaka et . al . gave an algorithm that finds the rank of a lyndon word in @xmath17 time and does unranking in @xmath18 time . in this paper , we give an enumeration algorithm of @xmath12 with linear delay time . our algorithm is the same as duval s algorithm with the addition of a simple data structure . we show that this data structure enable us to find the next lyndon word of _ length @xmath0 _ in constant updates per symbol and therefore in linear time . we also show that our algorithm is cat algorithm and give an upper bound for the amortized update cost . another problem is testing whether a word of length @xmath0 is lyndon word . in @xcite , duval gave a linear time algorithm for such test . in this paper we give a simple algorithm that uses the suffix trie data structure and runs in linear time . this paper is organized as follows . in section 2 we give the exact arithmetic complexity of the preprocessing and delay time for enumerating any number of irreducible polynomials and/or their roots . in section 3 we give a simple data structure that enable us to change duval s algorithm to an algorithm that enumerates all the lyndon words of length @xmath0 in linear delay time . we then show in section 4 that the algorithm is cat algorithm . in section 5 we give a simple linear time algorithm that tests whether a word is a lyndon word . in this section we give the analysis for the algebraic complexity of the preprocessing time and delay time of enumerating irreducible polynomials of degree @xmath0 over a finite field and/or their roots in the extended field . let @xmath4 be a power of a prime @xmath19 and @xmath20 be the finite field with @xmath4 elements . our goal is to enumerate all the irreducible polynomials of degree @xmath0 over @xmath3 and/or their roots in the extension field @xmath6 . the best deterministic algorithm for constructing an irreducible polynomial over @xmath3 of degree @xmath0 has time complexity @xmath21 for any @xmath22 . the best randomized algorithm has time complexity @xmath23 for any @xmath22 . for a comprehensive survey of this problem see @xcite chapter 3 obviously , the preprocessing time for enumerating irreducible polynomials can not be less than the time for constructing one . therefore , @xmath24 for the deterministic algorithm , and @xmath25 for the randomized algorithm . the main idea of the enumeration algorithm is to enumerate the roots of the irreducible polynomials in the extension field and then construct the polynomials from their roots . let @xmath6 be the extension field of @xmath3 of size @xmath26 . one possible representation of the elements of the field @xmath6 is by polynomials of degree at most @xmath27 in @xmath28/(f(\beta))$ ] where @xmath29 is an irreducible polynomial of degree @xmath0 . a _ normal basis _ of @xmath6 is a basis over @xmath3 of the form @xmath30 for some @xmath31 where @xmath32 is linearly independent . the _ normal basis theorem _ states that for every finite field @xmath6 there is a normal basis @xmath32 . that is , an @xmath33 for which @xmath32 is linearly independent over @xmath3 . it is known that such an @xmath33 can be constructed in deterministic time @xmath34 and randomized time @xmath35 the enumeration algorithm will use the normal basis for representing the elements of @xmath6 . notice that the time complexity to find such an element @xmath33 is less than constructing one irreducible polynomial . if we use the normal basis @xmath32 for the representation of the elements of @xmath6 , then every element @xmath36 has a unique representation @xmath37 where @xmath38 for all @xmath39 . it is known that any irreducible polynomial @xmath40 of degree @xmath0 over @xmath3 has @xmath0 distinct roots in @xmath6 . if one can find one root @xmath36 of @xmath40 then the other roots are @xmath41 and therefore @xmath42 . the coefficients of @xmath43 can be computed in quadratic time @xmath44 . see theorem a and b in @xcite and references within . the element @xmath37 is a root of an irreducible polynomial of degree @xmath0 if and only if @xmath45 are distinct . now since @xmath46 @xmath47 is a root of an irreducible polynomial of degree @xmath0 if and only if the following @xmath0 elements @xmath48 @xmath49 are distinct . when ( [ ddd ] ) happens then we call @xmath50 _ aperiodic word_. we will write @xmath51 as a word @xmath52 and define @xmath53 . therefore we have 1 . for any word @xmath54 the element @xmath55 is a root of an irreducible polynomial of degree @xmath0 if and only if @xmath51 is an aperiodic word . 2 . given an aperiodic word @xmath51 , the irreducible polynomial @xmath56 can be constructed in time ] @xmath57 . obviously , the aperiodic word @xmath58 and @xmath59 @xmath60 @xmath61 corresponds to the same irreducible polynomial . see ( [ pk ] ) . that is , @xmath62 for any @xmath63 . therefore to avoid enumerating the same polynomial more than once , the algorithm enumerates only the minimum element ( in lexicographic order ) among @xmath64 . such an element is called _ lyndon word_. therefore the word @xmath52 is called a lyndon word if @xmath65 for all @xmath66 . to enumerate all the irreducible polynomials the algorithm enumerates all the lyndon words of length @xmath0 and , for each one , it computes the corresponding irreducible polynomial . in the next section , we show how to enumerate all the lyndon words of length @xmath0 in linear delay time @xmath67 . then from @xmath55 ( that corresponds to an irreducible polynomial ) the algorithm constructs the irreducible polynomial @xmath68 and all the other @xmath27 roots in quadratic time @xmath69 . since the size of all the roots is @xmath70 , this complexity is quasilinear in the output size . for the problem of enumerating only the roots ( one root for each irreducible polynomial ) the delay time is @xmath67 . let @xmath12 be the set of all lyndon words over @xmath3 of length @xmath0 . we have shown how to reduce our problem to the problem of enumerating all the lyndon words over @xmath3" +"the so - called lovelock gravity "" @xcite is a natural higher - curvature generalization of the einstein gravity . it includes the einstein - hilbert action as the first lovelock term , and the second term is known as the gauss - bonnet ( gb ) term . the minimum generalization of the einstein gravity is the einstein - gauss - bonnet ( egb ) gravity theory , which contains up to the second lovelock term . since higher - curvature terms may come from quantum corrections of gravity , the egb gravity theory has been studied extensively . black hole solutions in the egb gravity theory were discussed in @xcite . the qualitative difference from the einstein gravity is the existence of branches of the solutions ; i.e. , not only minkowski spacetime but also anti - de sitter ( ads ) spacetime exists as a vacuum state in the egb gravity theory . as a result , the black hole solutions also possess both an asymptotically flat and ads branches without a negative cosmological constant . in the context of the string theory , the egb gravity has been argued to be an effective field theory with quantum corrections in @xcite . the gb term is indeed found as higher - order correction in string theories @xcite . it is also necessary to include a dilaton field as well as higher - curvature correction terms since the dilaton field plays an important role in the string theory . ( the vacuum expectation value of the dilaton field gives the string coupling constant . ) in a dilatonic gravity theory , we should first choose a `` frame '' where we discuss and interpret the physical meanings . there are two fundamental frames : one is a string frame where a dilaton coupling is factored out in all terms in the action , while the other is the einstein frame where the scalar - curvature term is minimally coupled to a dilaton field . the string frame is the frame which is naturally defined in the string theory , while the einstein frame gives the einstein gravity , which is familiar to us , with higher - order corrections . the gravity theory in the string frame and that in the einstein frame are classically equivalent since we can transform from one frame to the other by an appropriate conformal transformation @xcite however , there appear extra higher - order terms via a conformal transformation in addition to the gravity action and the conventional kinetic term of a dilaton field , and those terms are sometimes ignored . as a result , the two theories in these frames are different when we ignore such extra terms . we call those in the string frame and in the einstein frame degb ( dilatonic einstein - gauss - bonnet ) gravity and edegb ( einstein - frame "" degb ) gravity , respectively . the effective action in the einstein frame is obtained from the scattering amplitudes of gravitons and dilatons , but that in the string frame is calculated by the beta function method . thus , in the approximation keeping terms up to certain order in the higher derivatives , there are always ambiguities in the effective action as represented by the freedom of field redefinition . both of them have their own rights , and it is significant to study both and check if they give qualitatively different results . most of the works on dilatonic einstein - gauss - bonnet gravity have considered the edegb gravity theory . black hole solutions in the edegb gravity were studied for an asymptotically flat case in four dimensions @xcite and higher dimensions @xcite . the extremal black hole solutions , which are important in relation with bogomolnyi - prasad - sommerfeld states in the supersymmetric theory , were studied in the edegb gravity in four dimensions @xcite and higher dimensions @xcite . the extremal black hole solutions in the degb gravity were also studied in @xcite . the difference between the black holes in the edegb and the degb gravity theories was analyzed for asymptotically flat black hole solutions in @xcite . the relation between the edegb and the degb is discussed from the viewpoint of einstein s equivalence principle in @xcite . ads spacetime is attracting increasing attention since the ads / conformal field theory ( ads / cft ) correspondence was proposed . according to the ads / cft , one may examine the strong coupling region of the boundary cft by considering the corresponding black hole solutions in bulk ads spacetime . in fact , black hole solutions in the edegb were studied in @xcite , and the quantum corrections to the ratio of the shear viscosity to entropy density in the cft side were calculated . we expect that our solutions may also be useful in this kind of study . an ads black hole , which corresponds to the finite temperature cft according to the ads / cft correspondence , is known to possess interesting thermodynamical properties . when the horizon topology is a sphere ( @xmath0 ) , the small ads schwarzschild black hole is thermodynamically unstable while the large one is stable . there exists a phase transition , namely , hawking - page transition @xcite , between the large ads black hole and a thermal ads space . in contrast , planar ( @xmath1 ) and hyperbolic ( @xmath2 ) ads black holes are stable @xcite and the hawking - page transition does not occur . in the egb model with a negative cosmological constant , the thermodynamical properties of the asymptotically ads black hole solutions ( `` general relativity branch '' ) were studied in @xcite and with a special emphasis on the hyperbolic case in @xcite . in the presence of a negative cosmological constant @xcite , thermodynamic properties of asymptotically ads black hole solutions for @xmath0 are similar to those without the gauss - bonnet term in dimensions other than five . in five dimensions there appears a new phase of stable small black holes . for @xmath3 , black hole solutions are thermodynamically stable , and for @xmath2 , black hole solutions are always stable . the asymptotically ads spacetimes in the edegb model were analysed with and without the cosmological constant @xcite , and their global structures were studied in @xcite . in this paper , we consider black holes and other exact solutions in such spacetimes with a nontrivial dilaton field whose behavior is given by @xmath4 and discuss their thermodynamic properties . this type of dilaton field is called a linear dilaton , and it is essential for the existence of black hole solutions in the two - dimensional dilatonic gravity model @xcite . in the einstein - maxwell - dilaton gravity , linear dilaton solutions whose asymptotic behaviours are not ads nor de sitter were studied in @xcite . some of such solutions are obtained from asymptotically ads or de sitter solutions with a suitable compactification . intersecting brane solutions with linear dilatons are also constructed in @xcite . we find that ads black hole solutions for @xmath2 as well as ads spacetime for @xmath1 exist without a negative cosmological constant if the dilaton is nontrivial , in contrast to , for example , refs . the ads black hole solutions are obtained numerically , and the latter spacetime solutions are shown to exist for even - order lovelock gravity . we also find interesting cosmological and solitonic solutions . this paper is organized as follows . in the next section , we introduce the degb gravity theory in the string frame and show that the ads spacetime is the exact solution in a plane symmetric case . then , in sec . iii , we show how to find asymptotically ads black hole solutions in the degb theory . in sec . iv , we present our numerical results and discuss the thermodynamical properties of the black holes . our conclusions are drawn in sec . v. in the appendices , we give an ads solution in the lovelock theory of gravity and briefly discuss a horizonless solitonic solution and a cosmological solution obtained in our system . the effective action of the heterotic string theory in the string frame is given by @xmath5 where @xmath6 is the @xmath7-dimensional gravitational constant , @xmath8 is a dilaton field,@xmath9 is the gauss - bonnet curvature term , and @xmath10 is its coupling constant with @xmath11 being the regge slope . first we present the basic equations . to find a black hole solution , we assume a symmetric ( depending only on @xmath12 ) and static spacetime , whose metric form is given by @xmath13 where @xmath14 and @xmath15 are functions of the radial coordinate @xmath12 and @xmath16 is the metric of @xmath17-dimensional maximally symmetric hypersurface with a constant curvature of the sign @xmath18 . first we show the explicit form of the action with this ansatz : @xmath19 \biggr . + 4 e^{-2{\lambda } } \phi'^2 { \nonumber \\}+ & { \tilde{{\alpha}}}_2 e^{-4{\lambda } } \bigl [ ( d-4)_5 a^{2 } + 4 ( d-4 ) y a -8 \phi ' \nu ' a \bigr ] \biggl . \biggr\},\end{aligned}\ ] ] where we have introduced @xmath20 with @xmath21 and @xmath22 being integers ( @xmath23 ) and dropped the surface term . a prime denotes a derivative with respect to @xmath12 . for brevity , we have introduced the rescaled coupling constant @xmath24 , and in what follows , we will normalize the variables by @xmath25 . taking variations of the action with respect to @xmath26 and @xmath15 , we find the basic equations . since we are interested in a black hole solution , it is convenient to introduce new metric functions @xmath27 and @xmath28 as @xmath29 here we have fixed one metric component as @xmath30 by using the gauge freedom of the radial coordinate @xmath12 . using the new metric functions and defining the following variables by @xmath31 \,,\end{aligned}\ ] ] the basic equations are written as @xmath32 { \nonumber \\}&\hspace{0.7cm}+ { \tilde{{\alpha}}}_2 \bigl [ ( d-4)_{5 } ( k - f)^2 -2 ( d-4 ) ( k - f ) ( f'r+h ) + 4 x ( k - f ) f r^2 + 2 h f ' r \bigr ] \bigr\ } = 0 , \label{eq_phi}\\ f r^4 f_{{\rm s}(\nu)}&:= r^2 \bigl[(d-2)_3 ( k - f ) -(d-2 ) ( f ' - 4 f \phi ' ) r + 4 f ( \phi '' -\phi'^2 ) r^2 + 2 \phi ' f ' r^2 \bigr ] { \nonumber \\}&+ { \tilde{{\alpha}}}_2 \bigl [ ( d-4)_{5 } ( k - f)^2 -2 ( d-4 ) ( k - f ) ( f ' - 4 f \phi ' ) r + 8 f ( k - f ) ( \phi '' -2 \phi'^2 ) r^2 + 4 ( k-3 f ) \phi ' f ' r^2 \bigr ] = 0 , \label{eq_nu } \\ f r^4 f_{{\rm s}({\lambda})}&:= r^2 \bigl[(d-2)_3 ( k - f ) -(d-2 ) ( h -4 f \phi ' r ) + 2 ( h -2 f \phi ' r ) \phi ' r \bigr ] { \nonumber \\}&+ { \tilde{{\alpha}}}_2 \bigl [ ( d-4)_{5 } ( k - f)^2 -2 ( d-4 ) ( k - f ) ( h -4 f \phi ' r ) + 4 ( k-3 f ) h \phi ' r \bigr ] = 0 , \label{eq_lam}\\ f r^4 f_{{\rm s}(\mu)}&:= r^2 \bigl [ ( d-2)_4 ( k - f ) -(d-2)_3 ( f'r+h ) + 4 ( d-2)_3 f \phi ' r + 2 ( d-2 ) x f r^2 { \nonumber \\ } & \hspace{1.6 cm } + 4(d-2 ) f ( \phi '' - \phi'^2 ) r^2 + 2 ( d-2 ) ( f'r+h ) \phi '" +"one of the main observational results stemming from five years of @xmath7-ray burst ( grb ) follow - ups at optical wavelengths is that about @xmath8 of well - localized grbs lack a detected optical afterglow , ( `` dark bursts '' ; taylor et al . 2000 ; fynbo et al . 2001 ; reichart & yost 2001 ; lazzati , covino , & ghisellini 2002 ) . in some cases , a non - detection of the optical afterglow could simply be due to a failure to image quickly and/or deeply enough . however , there are two grbs for which there is strong evidence that the optical emission should have been detected , based on an extrapolation of the radio and x - ray emission ( djorgovski et al . 2001a ; piro et al . 2002 ) . one interpretation in these two cases is that the optical light was extinguished by dust , either within the immediate environment of the burst or elsewhere along the line of sight ( e.g. groot et al . 1998 ) . an alternative explanation is a high redshift , leading to absorption of the optical light in the ly@xmath9 forest . however , the redshifts of the underlying host galaxies of these grbs are of order unity ( djorgovski et al . 2001a ; piro et al . 2002 ) . several authors have recently argued that a large fraction of the dark bursts are due to dust extinction within the local environment of the bursts ( e.g. reichart & yost 2001 ; lazzati et al . 2002 ; reichart & price 2002 ) , but other scenarios have also been suggested ( e.g. lazzati et al . 2002 ) . moreover , it has been noted that regardless of the location of extinction within the host galaxy , the fraction of dark bursts is a useful upper limit on the fraction of obscured star formation ( kulkarni et al . 2000 ; djorgovski et al . 2001b ; ramirez - ruiz , trentham , & blain 2002 ; reichart & price 2002 ) . however , from an observational point of view , we must have a clear understanding of the diversity of afterglow properties before extracting astrophysically interesting inferences from dark bursts . for example , afterglows which are faint or fade rapidly ( relative to the detected population ) would certainly bias the determination of the fraction of truly obscured bursts . in this vein , fynbo et al . ( 2001 ) , noting the faint optical afterglow of grb000630 , argued that some dark bursts are due to a failure to image deeply and/or quickly enough , rather than dust extinction . here we present optical and radio observations of , an afterglow that would have been classified dark had it not been for rapid and deep searches . furthermore , is an example of an afterglow , which is dim due to the combination of intrinsic faintness and a relatively fast decline , and not strong extinction . , localized by the hete - ii satellite on 2002 , jan 24.44531 ut , had a duration of @xmath10 s and a fluence ( @xmath11 kev ) of @xmath12 erg @xmath13 ( ricker et al . eight minutes after receiving the coordinates we observed the error box with the dual - band ( @xmath14 , @xmath15 ) macho imager mounted on the robotic 50-in telescope at the mount stromlo observatory ( mso ) . we also observed the error box with the wide - field imager on the 40-in telescope at siding spring observatory ( sso ) . we were unable to identify a transient source within the large error box ( price , schmidt , & axelrod 2002 ) . we subsequently observed the error box refined by the inter - planetary network ( hurley et al . 2002 ) with the palomar 48-in oschin schmidt using the unfiltered neat imager . psf - matched image subtraction ( alard 2000 ) between the macho and neat images revealed a fading source ( price et al . 2002 ) , which was @xmath16 mag at the epoch of our first observations , and not present in the digitized sky survey . two nights later we observed the afterglow using the jacobs camera ( jcam ; bloom et al . 2002b ) mounted at the east arm focus of the palomar 200-in telescope ( bloom et al . the position of the fading source is @xmath9(j2000)= , @xmath17(j2000)= , with an uncertainty of about @xmath18 arcsec in each coordinate ( fig . [ fig : field ] ) . using the very large array ( vla ) we observed the fading source at 8.46 and 22.5 ghz ( see table [ tab : rad ] ) . we detect a faint source , possibly fading , at 8.46 ghz located at @xmath9(j2000)= , @xmath17(j2000)= , with an uncertainty of about @xmath19 arcsec in each coordinate . given the positional coincidence between the fading optical source and radio detection we suggest this source to be the afterglow of . the optical images were bias - subtracted and flat - fielded in the standard manner . to extract the photometry we weighted the aperture with a gaussian equivalent to the seeing disk ( `` weighted - aperture photometry '' ) , using iraf / wphot . the photometric zero - points were set through photometry of calibrated field stars ( henden 2002 ) with magnitudes transformed to the appropriate system ( bessell & germany 1999 ; smith et al . the photometry is summarized in tab . [ tab : opt ] we observed the afterglow with the _ hubble space telescope _ ( hst ) using the space telescope imaging spectrograph ( stis ) on 2002 feb . 11.09 , 18.30 , and 25.71 ut ( bloom et al . 2002a ) , as part of our large hst cycle 10 program ( go-9180 , pi : kulkarni ) . the hst observations consisted of 750850 sec exposures . the hst data were retrieved after `` on - the - fly '' pre - processing . using iraf we drizzled ( fruchter & hook 2002 ) each image onto a grid with pixels smaller than the original by a factor of two and using pixfrac of 0.7 . we found an astrometric tie between the hst and jcam images using iraf / geomap with nine suitable astrometric tie objects in common between the images . the rms of the resultant mapping is 133 mas ( ra ) and 124 mas ( dec ) . using this mapping and iraf / geoxytrans we transfered the afterglow position on the jcam image to the hst images . the rms of the transformation is 604 mas ( ra ) and 596 mas ( dec ) , and is dominated by the uncertainty in the jcam position . the source `` s1 '' ( fig . [ fig : hst ] ) coincides with the afterglow position within the astrometric uncertainty . we performed differential photometry at the position of s1 by registering the images of epochs 1 and 2 using a cross - correlation of a field of size 10 arcsec centered on s1 ( using iraf / crosscor and shiftfind ) . we used iraf / center and the fwhm of a relatively bright point source ( `` psf star '' ; fig . [ fig : field ] ) to fix the position of s1 in each of the final images , and to determine the uncertainty in the position . we photometered the source ( and the psf star ) in epoch 1 using iraf / phot , and determined a count - rate of @xmath20 e@xmath21 s@xmath22 ( corrected by @xmath23 for the loss of flux from an infinite aperture radius ) . using iraf / synphot and assuming a source spectrum of @xmath24 ( see below ) , we find that the source was @xmath25 mag at the time of epoch 1 . the photometry of the three epochs is summarized in tab . [ tab : opt2 ] . please note that this more careful analysis supersedes our preliminary report ( bloom et al . 2002c ) . there are no obvious persistent sources within 1.75 arcsec of the ot down to @xmath26 mag . to date , all of the grbs localized to sub - arcsecond accuracy have viable hosts brighter than this level within @xmath27 arcsec of the ot position ( bloom , kulkarni , & djorgovski 2002 ) . the faintest host to date is that of grb990510 , @xmath28 mag ( z=1.619 ; vreeswijk et al . 2001 ) . thus , the host of may be at a somewhat higher redshift ; however , @xmath29 since the afterglow was detected in the @xmath14 filter . in figure [ fig : opt ] we plot the optical lightcurves of , including a correction for galactic extinction , @xmath30 mag ( schlegel et al . the optical lightcurves are usually modeled as @xmath31 . however , as can be seen in fig . [ fig : opt ] , the @xmath32-band lightcurve can not be described by a single power law . restricting the fit to @xmath33 days we obtain ( @xmath34 for 14 degrees of freedom ) @xmath35 , @xmath36 , and @xmath37 @xmath38jy ; here @xmath39 is defined at the effective frequency of the @xmath15 filter and @xmath40 day . for @xmath41 days we get @xmath42 . to account for the steepening we modify the model for the @xmath32-band lightcurve to : @xmath43^{1/n } , \label{eqn : model2}\ ] ] where , @xmath44 is the asymptotic index for @xmath45 , @xmath46 is the asymptotic index for @xmath47 , @xmath48 provides a smooth joining of the two asymptotic segments , and @xmath49 is the time at which the asymptotic segments intersect . we retain the simple model for the @xmath15 and @xmath14 lightcurves since they are restricted to @xmath50 days ( i.e. well before the observed steepening ) . we investigate two alternatives for the observed steepening in the framework of the afterglow synchrotron model ( e.g. sari , piran , & narayan 1998 ) . in this framework , @xmath44 , @xmath46 , and @xmath51 are related to each other through the index ( @xmath52 ) of the electron energy distribution , @xmath53 ( for @xmath54 ) . the relations for the models discussed below , as well as the resulting closure relations , @xmath55 , are summarized in tab . [ tab : models ] . the observed steepening , @xmath56 , can be due to the passage of the synchrotron cooling frequency , @xmath57 , through the @xmath32-band . this has been inferred , for example , in the afterglow of grb971214 , at @xmath58 days ( wijers & galama 1999 ) . if the steepening is due to @xmath57 , this rules out models in which the ejecta expand into a circumburst medium with @xmath59 ( hereafter , wind ) , because in this model @xmath57 increases with time ( @xmath60 ; chevalier & li 1999 ) , and one expects @xmath61 . there are two remaining models to consider in this case : ( i ) spherical expansion into a circumburst medium with constant density ( hereafter , @xmath62 ; sari , piran , & narayan 1998 ) , and ( ii ) a jet with @xmath63 ( i.e. a jet break prior to the first observation at @xmath64 days ; hereafter , @xmath65 ) . the subscript b indicates that @xmath57 is blueward of the optical bands initially . in both models we use eqn . [ eqn : model2 ] for the @xmath32-band lightcurve , with @xmath49 defined as the time at which @xmath66 , and @xmath67 . we find that in" +"there is current interest ( see , for instance , refs . ) in studying inverse transitions , melting or freezing , motivated by the quite unconventional situation present in such transitions in which the ordered phase is more entropic than the disordered one @xcite . this apparent counter - intuitive transition has become even more interesting since there are now various physical systems displaying this kind of transition , as for example , magnetic films @xcite and , particularly , high-@xmath0 superconductors @xcite . therefore , the knowledge about which conditions are necessary for the existence of inverse transitions is a challenging issue @xcite . among the proposed classical magnetic models which can show inverse transitions , the blume capel ( bc ) @xcite and the gathak - sherrington ( gs ) @xcite models can be useful to clarify what would be such conditions . for instance , the phase diagram of the bc model @xcite displays inverse melting with a phase transition from the ferromagnetic ( @xmath1 ) phase to the paramagnetic ( @xmath2 ) one when the temperature is decreased . however , in order to obtain inverse melting in the bc model , it is strictly necessary to impose in the problem the entropic advantage of the interacting state through parameter @xmath3 , where @xmath4 and @xmath5 are the degeneracy of @xmath6 and @xmath7 spins states , respectively @xcite . in contrast with the bc model , the gs model @xcite - which is similar to the the bc model except that it has the spins couplings given as random gaussian variables - shows naturally inverse freezing . in other words , there is a reentrant first order boundary phase separating the spin glass ( @xmath8 ) and @xmath2 phases . however , there is no need of any entropic advantage of interacting states @xcite . the previous discussion suggests that the randomness is responsible for producing naturally inverse freezing in the gs model as compared with the inverse melting case in the bc model . in fact , to be more precise , it seems that the presence of non - trivial form of randomness , which means frustration , @xcite would be the essential ingredient which allows inverse freezing in the gs model with no need of entropic advantage . that sets some questions : what is the actual role of non - trivial randomness to produce naturally inverse freezing ? is this natural inverse freezing robust when the level of frustration is diminished ? can models with trivial randomness present naturally inverse transitions ? the purpose of the present work is to investigate what is the actual role of frustration as a basic condition to produce naturally inverse freezing . that could be achieved by comparing two distinct situations , the trivial randomness and the highly frustrated regime and also studying how natural inverse freezing would be affected when the level of frustration is varied . therefore , the problem is not only to find a random magnetic model which presents naturally inverse freezing , but also to get one which allows the level of frustration to vary . quite recently , the fermionic ising spin - glass ( fisg ) model @xcite has been proposed as a model able to display naturally inverse freezing in a phase diagram temperature _ versus _ the chemical potential @xmath9 . this model has the spin operators @xmath10 given as bilinear combinations of creation and destruction fermionic operators which have four eigenstates , two of them non - magnetic @xcite . the spin - spin coupling @xmath11 , likewise the gs model , is a random variable which follows a gaussian distribution . indeed , the existence of inverse freezing in this model could be expected since there is a close relationship between the gs and the fisg models @xcite . for instance , the partition function of these two models can be related by a mapping between the anisotropy constant @xmath12 of the gs model and @xmath9 @xcite . the fisg model is also useful to examine how quantum effects , included by the presence of a transverse field @xmath13 @xcite can affect inverse freezing . in ref . , it has been shown that , when @xmath13 is increased , the reentrance in the @xmath14 first order boundary phase in the phase diagram temperature @xmath15 _ versus _ the chemical potential @xmath9 gradually disappears . this scenario also suggests that @xmath13 in the fisg model plays the opposite role of the rather artificial parameter @xmath16 in the bc model discussed in ref . . nevertheless , the fisg model , in its original form with gaussian random couplings , is a strongly frustrated model . therefore , it is not possible to investigate in this model how the change of the level of frustration could affect the inverse freezing . an alternative route to accomplish the previously mentioned investigation would be to use the fisg model in a version in which one could adjust the level of frustration . in that sense , the classical hopfield spin glass @xcite can be quite useful . in this model , the interactions @xmath11 between classical ising spins are given below : @xmath17 where @xmath18 ( @xmath19 or @xmath20 , @xmath21 is the number of sites ) are independent random distributed variables . this type of interaction has been intensively used to study complex systems @xcite . there are clearly two extreme cases for the classical hopfield ising spin glass model . when @xmath22 , it becomes the mattis model @xcite , which is a well known example of trivial randomness @xcite . the second one is when @xmath23 . in that limit , the thermodynamics corresponds to the strongly frustrated regime given by a random gaussian distributed @xmath11 @xcite . in particular , the replica symmetric mean field solution of the classical hopfield spin glass model @xcite can provide a useful method for the purposes of the present work . it is described in terms of two order parameters , the usual spin glass @xmath24 and @xmath25 which indicates the presence of mattis states that have a thermodynamics similar to the usual ferromagnetism @xcite . most important , there is a parameter called here degree of frustration , @xmath26 which allows controlling the level of frustration in the theory . it is important to remark that there is a particular value @xmath27 which for @xmath28 the effects of frustration are dominant @xcite . as a consequence , it is possible to interpolate the thermodynamics from the trivial randomness ( @xmath29 ) to the strongly frustrated regime ( @xmath28 ) . therefore , to answer the questions arisen previously , we use the hopfield fermionic ising spin glass ( hfisg ) model . in this case , the spin operators @xmath30 are defined as the fisg model , but the random spin coupling @xmath11 is given as eq . ( [ hebb ] ) . the partition function is obtained in the functional integral formalism using grassmann fields where the disorder is treated with the replica method @xcite . the problem can be reduced to a one - site problem by using a similar procedure to solve the classical hopfield spin glass @xcite within the static approximation ( sa ) @xcite and one - step replica symmetry breaking ( 1s - rsb ) @xcite . it should be remarked that in the hfisg model , as the fisg one @xcite , the replica diagonal component of the sg order parameter @xmath31 appears as an additional order parameter to be solved with the others . particularly , this order parameter represents the spin self - interaction that has an imaginary time dependence for quantum sg models @xcite . however , the spin operators @xmath32 commute with the hamiltonian operators for the present hfisg model . consequently , the @xmath31 has no dynamic , which means that the sa is exact in the present work@xcite . one important point in the present work is how to locate first order boundaries phases found for different degrees of frustration . the criterion adopted here follows closely that one suggested in ref . for the classical @xmath33 model . hence , we selected , from the set of spin glass solutions in the transition , that one which meets continuously with the spin glass solution for small value of the chemical potential @xmath9 . in fact , that corresponds to the largest spin glass order parameter which gives the lowest grand canonical potential ( see also the discussion in ref . ) . then , by equating the grand canonical potential of the spin glass and paramagnetic solutions , the first order boundary phase is located . the use of the 1s - rsb scheme also deserves some remarks since our main interest is to obtain boundaries of phase transitions . it has been found in previous works @xcite that the use of the replica breaking symmetry ( rsb ) schemes in gs or fisg models essentially preserves the reentrance in the @xmath14 first order boundary phase associated to the inverse freezing . there are only small differences which appear mainly at very low temperatures . even so , for the hfisg model , we decided to use 1s - rsb scheme to check for intermedianted values of @xmath34 whether or not these differences will remain unimportant . moreover , we also analyzed the stability of the rs solutions for a sake of completeness of the work . this paper is structured as follow : in section 2 , we derived the thermodynamics and the set of coupled equations for the saddle point order parameters . in section 3 , phase diagrams temperature _ versus _ the chemical potential are presented for several values of @xmath34 . the entropy behavior as function of temperature and the grand canonical potential as function of chemical potential are also discussed . finally , section 4 is reserved to conclusions . the hamiltonian considered here is a hopfield fisg ( hfisg ) model @xmath35 where @xmath36 is given in eq . ( [ hebb ] ) and the random @xmath37 follows the distribution @xmath38 in this model , @xmath39 $ ] is the spin operator , with @xmath40 as the number operator , @xmath41 are fermions creation ( destruction ) operators and @xmath42 or @xmath43 indicate the spin projections . the partition function in the grand canonical ensemble is given in the lagrangian path integral formalism where the spin operators are represented as bilinear combinations of anticommuting grassmann fields ( @xmath44 ) @xcite @xmath45 where @xmath46 \phi_{j\sigma}(\tau ) \\ & - h(\phi^{*}(\tau),\phi(\tau ) ) \ } \end{split}\ ] ] where @xmath9 is the chemical potential and @xmath47 . @xmath48 is fourier transformed in time which results in @xmath49 with @xmath50\phi_{j\sigma}(\omega ) \label{eqao}\ ] ] @xmath51 and @xmath52 where @xmath9 is chemical potential , @xmath53 , @xmath54 are the matsubara s frequencies and @xmath55 if @xmath56 . in this work , the problem is analyzed within sa which considers only the term when @xmath57 in eq . ( [ eqs ] ) @xcite . the grand canonical potential is obtained by using the replica method : @xmath58 where @xmath59 and @xmath60 means the configurational averaged over @xmath61 . thus : @xmath62 \label{zn1}\ ] ] where after using @xmath11 given in eq . ( [ hebb ] ) , the action @xmath63 can be written as @xmath64 with @xmath65 denoting the replica index and @xmath66 . the average over @xmath67 given in eq . ( [ zn1 ] ) is discussed in detail in the appendix a. in the present work , the one - step replica symmetry breaking ( 1s - rsb ) ansatz is adopted , in which the replica matrix @xmath68 and the matrix @xmath69 are parametrized as : @xmath70 and order parameters @xmath71 are invariant with respect to permutations of replicas : @xmath72 ," +"the parent compounds of the high-@xmath1-temperature superconductors are antiferromagnetic ( afm ) mott insulator . superconductivity ( sc ) emerges when charge carries ( holes or electrons ) are doped into the @xmath2 planes . as well known that the clear electron - hole asymmetry is found in the phase diagram . for hole doped case , the afm and superconducting phases are separated by spin glass phase . in contrast , the afm phase extends over a much wider range of doping and even coexists with sc in the electron doped cuprates@xcite . due to proximity of antiferrmagnetism and sc , it is generally believed that there exists intrinsic link between these two phases . the studies of the spin dynamics in n - type and p - type cuprates will shed light on the mechanism of superconductivity . one of the most available techniques to study the spin dynamics is the inelastic neutron scattering ( ins ) , which directly measures the magnetic excitations ( mes ) . compared with the well studied p - type cuprate@xcite , the investigations on the mes in n - type cuprates@xcite are much less due to the technical reason . a robust feature of mes in n - type cuprates , i.e. , the commensurate spin response , had been revealed by these ins measurements . the commensurability , characterized by the strongest intensity peaked at @xmath3 , covers for a wide low - energy region near the optimal doped nccoyamada - prl03 and plcco@xcite . further detecting shows that such commensurability in n - type cuprates exists for a wide doping range from the underdoping to heavy overdoping@xcite . more importantly , the commensurate mes persist well above superconducting critical temperature @xmath1 , indicating its non - superconducting origin . it gradually develops into the spin - wave - like dispersion centered around the @xmath4 point at higher energy , analogous to its undoped parent compoundwilson - nature06 . in contrast , the well known hourglass type magnetic dispersion had been discovered in the p - type cuprates , where the commensurate peak can only be found at the resonance energy . therefore , the two types of cuprates exhibit distinct spin response , indicating the intrinsic particle - hole asymmetry . theoretically , several works had been carried out to interpret the mes features of n - type cuprates . adopting the single band description with experimentally fitted parameters , krger _ _ claimed that the fermiology random phase approximation ( rpa ) approach with a momentum independent ( or weakly dependent ) coulomb repulsion can not account the low - energy commensurability . their numerical results indicated that the mes in n - type case should be more incommensurate than that in p - type casekruger - prb07 . such conclusion may reveal the fact that the single band description is invalid in the n - type cuprates@xcite . _ showed that this may be improved by a strongly momentum dependent coulomb repulsion with form of @xmath5@xcite . however , such improvement is more likely originated from its sharply peaked form at @xmath6 , which can not be understood physically . using a slave - boson mean - field approach , li _ et al . _ showed that the commensurability can be established in the sc stateljx - prb03 . these above mentioned theoretical works are all based on the belief that the d - wave sc is response for the low energy commensurability . it is hard to image that the small superconducting gap can produce the wide energy range commensurability . the most important is that the commensurate phenomenon is also found in the normal state of n - type cuprates , where the d - wave sc disappears . the mes had also been discussed within the frame work of coexisting of sc and afm@xcite . commensurate me had been subsequently obtained@xcite . however , this result clearly contradicts with the stoner critition@xcite . furthermore , recent ins data reveal a magnetic quantum critical point where the sc first appears , implying that the coexistence may not existmotoyama - nature07 . additionally , as we mentioned above , the commensurability also exists in the state without long - range afm order . in this paper , we focus on the commensurate mes in the n - type cuprates near the optimal doping . its energy region is closely related the to strength of effective @xmath6-scattering . the commensurate peak disappears at magnetic resonance energy @xmath7 and develops into the spin - wave like dispersion . these features are qualitatively consistent with ins measurements . this commensurability is a normal state property , and has nothing to do with the superconductivity . we explicitly demonstrate that the commensurability is originated from the band splitting and fermi surface topology . therefore , the afm correlation plays key roles in the n - type cuprates . the differences of mes between the p - type and n - type cuprates are further discussed for comparison . a spin - density wave ( sdw ) description is adopted to investigate the n - type cuprates near the optimal doping . such description is first suggested by armitage _ based on the arpes measurements on @xmath8@xcite . the underlying fermi surface disappears around the hot - spot near the optimal doping , where the long - range antiferromagnetism is absent , strongly suggesting the existence of a @xmath9-scattering . further proposed an effective energy band with @xmath10 ( @xmath11 , and @xmath12 for upper , and lower band , respectively)parker - prb07 , where @xmath13 is the strength of the effective @xmath14-scattering , representing the influence of the sdw . @xmath15 and @xmath16 is the inter- and intra - lattice hopping term . this description well reproduces the @xmath17 band folding and fermi surface reconstruction@xcite , and its applications on the temperature evolution of optical conductivityzimmer and the hall coefficient@xcite give qualitative agreement with experiments . now , the model hamiltonian is expressed as @xmath18 where , the two sublattices @xmath19 and @xmath20 with respective fermionic operator @xmath21 and @xmath22 are introduced due to sdwexplain . @xmath23 , and @xmath24 with @xmath25 , @xmath26 , and @xmath27 are the fitting parameters for nearest - neighbor ( nn ) , second - nn , and third - nn hoping . the summation is restricted in the afm brillouin zone . the quasiparticle dispersion @xmath28 can be obtained by the rotation transformation , with corresponding weight factor @xmath29 . here , @xmath30 , and @xmath31 . here , we would like to emphasize that the long - range afm order disappears near the optimal doping . as pointed by motoyama _ _ that the neel temperature detected above @xmath32 in @xmath8 originates from the region of samples that were not fully oxygen - annealedmotoyama - nature07 . this means that the genuine long - range antiferromagnetism does not coexist with superconductivity . however , the @xmath33-dimensional afm correlation remains . unlike only several lattice - distant length in p - type cuprates@xcite , the afm correlation is about tens lattice - distance in the optimal electron - doped cuprates@xcite . in this sense , the afm correlations in the n - type cuprates is similar to the long - range afm order at least in the small scaling . therefore , using a slowly fluctuating sdw order to describe the long - range afm correlation is a considerable treatment . though present sdw description is analogous to the form in the afm phaseyqs - prb05 , the physics behind is essentially different . the spin susceptibility under random phase approximation is @xmath34 with @xmath35 is a reduced coulomb interaction due to the screening effectzhou - pla10 . the bare spin susceptibilities are @xmath36 with @xmath37 is @xmath38 where @xmath39 is the fermi distribution function . in numerically , the doping level is fixed at @xmath40 , near the afm quantum critical point@xcite . @xmath41 , @xmath42 , and @xmath43 are adopted@xcite . the best fitted effective @xmath44 scattering strength is @xmath45 , and it will be adjusted for necessary . the temperature is fixed at @xmath46 . we adopt a broaden factor @xmath47 to calculate the spin susceptibility . the reduced coulomb interaction is about @xmath48 , which is about @xmath49 . our calculations are carried out on a mesh with @xmath50 k - point in the full brillouin zone . for different energy @xmath51 . only the near @xmath52 region are shown for clarification with @xmath53 . @xmath54 , the effective @xmath55-scattering strength @xmath56 , and the broaden factor @xmath57.,width=336 ] the typical energy - evolution of the mes @xmath58 is shown in fig . [ f.1 ] . in the low - energy regime below @xmath59 ( fig . [ f.1](a ) , ( b ) ) , the mes are incommensurate with strong intensity at diagonal directions . simultaneously , the intensity near @xmath52 enhances gradually . in the intermediate - energy regime , the strongest intensity locates at the @xmath52 point , leading to the the so - called commensurability ( fig . [ f.1](c ) , ( d ) ) . it maintains up to an critical energy about @xmath60 ( fig.[f.1](e ) ) , where the strongest intensity @xmath61 in the normal state can be found , and is referred as the magnetic resonance @xmath62 . the total energy range for the commensurability is approximately @xmath63 for @xmath64 . this magnetic resonance is directly related to the fact that the real part in denominator of the rpa formula ( eq . [ e2 ] ) reduces to zero . subsequently , it evolves into a ring - like incommensurability in the high - energy region with its radius expanding upon the further increased energy ( fig . [ f.1](f ) ) . for high enough energy , the mes are incommensurate with strong intensity at the vertical directions ( not shown ) . along the high symmetry direction . upper panels are for vertical direction with @xmath65 , and lower panels are for the diagonal direction with @xmath66 . from left to right is @xmath67 , @xmath68 , and @xmath69 , respectively . the effective @xmath52-scattering potential is @xmath70 and the damping rate @xmath71 . all data had been renormalized by setting the strongest intensity at given @xmath72 as unit , denoted by the white lines.,width=345 ] such features can be more clear in dispersion of the mes at high symmetry scanning lines as shown in fig . a wide energy regime with commensurability exists for all selected @xmath35 , manifesting its universal nature . the low - energy incommensurability increases slightly upon @xmath73 . hence the commensurability can not not be viewed as the overlap of two incommensurate peaks . it is an intrinsic feature of n - type cuprates . the low - energy incommensurability may be suppressed and even absent with enhanced @xmath35 . for example , when @xmath74 ( fig . [ f.2](c ) ) , the mes are still commensurate at low enough energy . correspondingly , the magnetic resonance energy @xmath62 decreases down to @xmath75 for @xmath76 . the experimental discovered commensurability in @xmath8yamada - prl03 and @xmath77@xcite near the optimal doping is more like similar to this case . the value of @xmath78 is near the afm stability , consisting with the fact that the optimal doping is near the afm quantum critical point@xcite . the possible energy range of commensurability is mainly determined by the effective @xmath52-scattering potential @xmath13 . for @xmath79 and @xmath80 , it is about @xmath81 . this energy range decreases down to @xmath82 when the @xmath83 . however , the realistic energy range of commensurability may be substantially reduced for strong @xmath35 due to the proximity of the afm stability . it is only @xmath75 for stronger @xmath84 . for strong enough @xmath85" +"the continuous electron beam accelerator facility ( cebaf ) at jefferson lab ( jlab ) delivers a highly polarized electron beam in the 1 11 gev energy range for currents up to @xmath2 200 @xmath1a . a key part of the jlab physics program consists of high - precision parity violating electron scattering experiments @xcite that require a fast and precise electron beam polarization measurement . conventional polarimetry techniques such as mller @xcite and mott @xcite are destructive for the beam properties due to solid targets they use and can not be operated simultaneously with the physics experiments . they can only be operated at low intensity ( @xmath3 10 @xmath1a ) and at low energy ( @xmath3 5 mev ) respectively ; therefore , the physics experiments have to assume that beam polarization remains constant when the intensity or the energy of the beam is several orders of magnitude higher . alternatively compton polarimetry has been used with great success at jlab @xcite and elsewhere @xcite to measure the electron beam polarization in a continuous and non - destructive manner . however , unlike at high - current ( @xmath4 20 ma ) storage rings @xcite and at high - energy ( @xmath4 50 gev ) colliders @xcite , the relatively low - current and low - energy nature of the cebaf electron beam has required the use of high - finesse optical cavities @xcite to enhance the laser power beyond commercially available lasers to provide sufficient electron - photon collision luminosity . compton polarimetry determines the electron beam polarization based on a well - known spin - dependent scattering cross - section @xcite between polarized electrons and photons . the longitudinal electron beam polarization @xmath5 is extracted from the experimental compton scattering asymmetry @xmath6 , according to , @xmath7 where @xmath8 is the theoretical compton scattering asymmetry that can be derived by combining the calculated spin - dependent compton cross section with the appropriate experimental response function @xcite , and @xmath9 is the circular photon beam polarization . the scattering asymmetry @xmath6 can be measured based on the detection of either the scattered photons or the scattered electrons and depends on the energies of the colliding electron and photon beams . for an electron beam of 1.0 gev , the maximum scattering asymmetry for infrared ( 1064 nm ) photons is 1.8% , whereas for green ( 532 nm ) photons , it is 3.5% . for an electron beam of 6 gev , these values are about 10% and 18% , respectively . therefore , compton polarimetry at low beam energies ( @xmath3 2 gev ) is difficult to perform . + external optical cavities have frequently been employed to increase the laser power from a light source through a process of coherent addition . recently optical cavities have been widely employed in many areas such as x-/@xmath10-ray generation via inverse - compton scattering @xcite , high harmonic generation @xcite and electron beam polarimetry @xcite . according to the best of our knowledge , there are only three facilities in the world have ever built a compton polarimeter with an optical cavity ; mainz microtron ( mami ) @xcite , hadron electron ring accelerator ( hera ) @xcite and jlab @xcite . in hall a of jlab , a compton back - scattering polarimeter had been operational since 1999 @xcite . its photon source had a typical circulating power of @xmath2 1.5 kw inside a monolithic fabry - perot cavity where the circularly polarized photons scattered from the longitudinally polarized electrons . it provided 1.0% statistical ( and 1.2% systematic ) precision with @xmath2 25 minutes data taking for 4.6 gev , 40 @xmath1a electrons @xcite . this polarimeter used a continuous - wave ( cw ) infrared ( ir , 1064 nm ) laser as its photon source and had serious limitations in providing a good signal - to - noise ratio for beam energies below 2 gev @xcite . under this circumstance , it is highly desirable to have a shorter - wavelength and higher - power light source since this will result in larger back - scattered electron and photon energies and a larger measured scattering asymmetry , and hence increased ability to control systematic uncertainties . + the lead radius experiment ( prex ) @xcite at jlab aims to provide the first model - independent evidence of the existence of a significant neutron skin in @xmath11pb . prex proposed to obtain a statistical and systematic precisions of 3.0% and 2.0% respectively on the parity - violating electroweak asymmetry of polarized electrons from @xmath11pb to determine the neutron radius of @xmath11pb at 1.0% accuracy . the uncertainty goal for beam polarimetry at 1.06 gev was 1.0% . in order to meet the high - precision requirement , the existing compton polarimeter underwent an upgrade @xcite in 2010 . the upgrade includes a new photon detector with an upgraded integrating data acquisition ( daq ) system , a new electron detector , and a new compton photon source that includes a green laser ( 532 nm ) with a new high - finesse fabry - perot cavity @xcite . + this paper will describe the upgraded experimental setup in hall a at jlab , with an emphasis on the frequency - doubled green laser system and optical cavity . a unique technique to extract the laser beam polarization inside a resonant fabry - perot cavity will be given and finally , the first electron beam polarization measurement results from the prex experiment @xcite at a beam energy and current of 1.06 gev and 50 @xmath1a will also be presented . with an enhancement factor and intra - cavity power of 3,800 and 3.7 kw , we report the highest power compton polarimetry facility operating at 532 nm as compared to existing facilities such as mami @xcite and hall c at jlab @xcite . , d@xmath12 , d@xmath0 and d@xmath13 ) that deflect the primary electron beam and send it through the fabry - perot cavity . the scattered compton electrons and photons will be detected by electron and photon detectors , respectively.,width=294 ] the upgraded compton polarimeter in hall a consists of a magnetic chicane , a photon source that is composed of a laser system and fabry - perot cavity , a photon detector , and an electron detector as shown in fig . [ fig : chicane ] . the electron beam enters from the left . when the four identical dipoles of the chicane , referred to as d@xmath14 , d@xmath12 , d@xmath0 and d@xmath13 , are energized , the beam is deflected vertically and crosses the photon beam enhanced in the fabry - perot cavity that is located at the center of the chicane . the fabry - perot cavity is enclosed in a vacuum chamber that is connected to electron beam pipes from both ends and sits on an optical table where the laser and other optical elements are located . the compton interaction point ( cip ) is at the center of the beam crossing in the cavity . the crossing angle between the electron and photon beams is 24 mrad . the electrons undergo compton scattering with circularly polarized photons resonating in the fabry - perot cavity fed by a cw green laser ( 532 nm ) . the backscattered photons are detected in the photon detector while the scattered electrons can be detected in the electron detector located a few mm above the primary beam in front of d@xmath13 . approximately one electron in every one billion undergoes compton scattering . unscattered electrons , separated from the scattered particles by d@xmath0 in the chicane , continue on into the hall a target for the primary experiment . independent electron and photon analyses give complementary determinations of the electron beam polarization . a scale 3d view of the compton polarimeter in the hall a tunnel at jlab is shown in fig . [ fig : chicane3d ] . + the photon detector is located under dipole d@xmath13 and consist of a single crystal of ce - doped gd@xmath12sio@xmath15 ( gso ) and a single pmt ( photomultiplier tube ) . it is mounted on a motorized table with remote - controllable motion along both axes ( horizontal and vertical ) transverse to the electron beam direction . the scattered photons from the cip go through a thin vacuum window and lead disk in the vacuum pipe before they hit the detector window . the photon detector daq uses a customized 12-bit flash analog - to - digital converter ( fadc ) that integrates the scintillation photon signals from the pmt and samples the data at rates of 200 mw @xcite . + the electron detector consists of four silicon microstrip planes spaced horizontally 1 cm from each other with a 200 micron vertical rising offset between planes . each plane consists of 192 strips of silicon with a width of 240 microns . the planes are inclined at an angle of 58 mrad from the vertical position . the detector is mounted on a translator with a remote - controllable stepper motor and can travel vertically up to 120 mm from the main beam . the optical elements of the polarimeter are mounted on a vibration - damped optical table between dipoles d@xmath12 and d@xmath0 ( fig . [ fig : chicane3d ] ) . a schematic of the optical system of the polarimeter is illustrated in fig . [ fig : opticalsetup ] . based on their main functionality , we can categorize the optical elements into four groups necessary for achieving the required power and circular polarization in the cavity . the first group is the laser source that provides a green beam at the wavelength of 532 nm . the second group consists of the elements that transport , align and focus the incident beam for coupling to the optical cavity . the third group includes elements for controlling and measuring the polarization . the last group consists of elements which allow the use of the reflected beam from the cavity in the electronic feedback system to achieve frequency locking of the laser to the cavity . as shown in fig . [ fig : opticalsetup ] , the seed laser is a narrow - linewidth ( @xmath3 5.0 khz ) diode pumped nd : yag nonplanar ring oscillator ( npro ) laser ( lightwave 126 ; jdsu ) that delivers a linearly polarized cw ir ( 1064 nm ) beam of up to 250 mw . the output of this laser has been fiber - coupled to a ytterbium - doped fiber amplifier ( ydfa , yar-10k-1064-lp - sf ; ipg photonics ) through a single - mode polarization - maintaining ( pm ) fiber . the ydfa takes @xmath2 10 mw of seed laser and provides a linearly polarized ( extinction ratio : 20 db ) output with a maximum power of 10 w at 1064 nm in cw mode . the frequency doubling crystal is bulk periodically poled mgo : linbo@xmath0 ( ppln , hc photonics ) doped with 5% mgo in order to minimize photo - refractive damage . the crystal is 0.5 mm thick , 3 mm wide and 50 mm long , and the quasi - phase matching ( qpm ) period is 6.92 @xmath1 m with a 50% duty cycle . the input and output surfaces are antireflection ( ar ) coated for 1064 nm and 532 nm , respectively . the crystal is placed in an externally controlled , temperature - stabilized oven developed in - house . the oven is mounted on a stage composed of a four - axis tilt aligner ( 9071-v ; newport ) in order to establish a precise alignment for phase matching . a temperature controller ( tecsource 5305 ; arroyo instruments ) with a nominal resolution of 0.01 @xmath16c provides" +"the shape of the gamma - ray burst s lightcurves of the batse gamma - ray burst catalog @xcite carry an immense amount of information . here we focus on the possible sgr - like contamination in the batse data . we used data from the batse discsc @xmath3 dataset keeping in mind that the distant sgr signals could be very similar to the short grbs : a bright short peak and a - probably weak , noisy - extended periodic emission in the low energy bands . during the processing we ve focused on the harmonic content of the grb lightcurve . therefore during the analysis * the three background - subtracted lowest energy bands ( below @xmath4 kev ) were joined to reduce the noise ( the high energy ( @xmath5 kev ) channel behaves differently @xcite ) . we used a quadratic background fit for each channel . * fft was used to calculate the power spectrum with a window size of 1024 samples ( @xmath6 ) . this sampling determines both the lowest frequency ( @xmath7 , @xmath8 ) and the highest ( @xmath9 , @xmath10 ) . * the first @xmath11 data was excluded from the signal after the trigger ( @xmath12 ) : this ensures that even the strongest short grb lightcurve will decay and it does not interfere with any possible signal in the tail . * we generated as many data windows as possible . the starting point of the 1024-sample - sized sliding window was increased with 256 samples ( @xmath13 ) until the window s endpoint reaches the end of the data . * to reduce the power spectrums sensitivity to edge effects a blackman window was used : this data windowing prevents leakage from the nearby frequency components @xcite , and makes the power spectrum more regular . the window also reduces any spurious effects originating from the non - perfect background subtraction . * each data block was whitened before the fft . no data winzorization was applied . most of the data probably contains a poissonian noise only , therefore to determine the significance of any probable signal a monte - carlo simulation was needed . for each 1024 sample block random signals were generated 500 times by randomly shuffling the data : the maximum value in the power spectrum of each mc signal was compared with the real signal s maximum value . we select only bursts where the real signal s maximum power is bigger than _ any _ maximum in the mc signals . the candidate trigger also required to produce such harmonic power signal at least for two different window starting point ( overlapping windows were not excluded ) . these requirements select 22 grbs with unusually high harmonic power above @xmath14 . 1 . shows the power spectra of these bursts with the corresponding window start times . 2 . we show some triggers folded phase - frequency diagram and ( selected ) folded pulse shape . one can observe that some of the signals appears to be periodic : however we should keep in mind that for these triggers have only one kind of observation with fixed time resolution ( @xmath3 ) , so it is very hard to assign real significance levels to these curves . triggers # 0373 and # 6591 show a broad signal , while # 0434 and # 3359 show more narrow peaks . it is remarkable that all suspicious frequencies are beyond any known batse periodic detector effect . the sky distribution of the selected 22 triggers is plotted with on fig . 3 . , with all the batse grbs positions . the figure seems to be asymmetric : to check the randomness we calculated the dipole components from the selected subset and from @xmath15 cases of a random 22-element sample drawn from the complete batse database : this method fully eliminates the non - uniform sky - exposure function of the batse . we ve got only 3 random cases where the dipole s magnitude was bigger than the 22 triggers dipole . it gives a @xmath2 significance ( approx . @xmath16 ) for the extraordinary dipole moment . the direction of the dipole is @xmath17 . there are increasing evidence that all the grbs do not represent a physically homogeneous group @xcite . in the last years the papers @xcite provided several different tests probing the sky distribution of grb groups in batse catalog . the celestial distribution of the short batse bursts shows anisotropic behavior @xcite . the direction of the dipole is not correlated with the supergalactic plane ( not like @xcite ) and interestingly the dipole s direction is only @xmath18 away from the the cmb dipole s temperature minimum . our results suggests that some anomalous subgroups could be responsible for the weak anisotropic signals : for a more detailed answer a deeper study of this effect is necessary . we plan to provide it in a forthcoming paper . thanks are due to g. tusndy for valuable discussions . this research is supported by hungarian otka grant k077795 , by the bolyai scholarship ( i. h. ) , by the gauk grant no . 46307 , and by the research program msm0021620860 of the ministry of education of the czech republic ( a.m. ) . 99 meegan c.a . et al . , 2000 , batse gamma - ray bursts catalog , http://gammaray.msfc.nasa.gov/batse/grb/catalog bagoly , z. , mszros , a. , horvth , i. , balzs , l.g . & mszros , p. 1998 , apj , 498 , 342 press w.h . , flannery b.p . , teukolsky s.a . , vetterling w.t . , 1992 , numerical recipes , cambridge university press , cambridge horvth i. , 1998 , apj , 508 , 757 mukherjee , s. , et al . 1998 , apj , 508 , 314 hakkila j. , haglin d.j . , pendleton g.n . , mallozzi r.s . , meegan c.a . , roiger r.j . , 2000 , apj , 538 , 165 horvth i. , 2002 , a&a , 392 , 791 balzs l.g . , bagoly z. , horvth i. , mszros a. , mszros p. , 2003 , a&a , 401 , 129 hakkila , j. , et al . , 2003 , apj , 582 , 320 horvth i. , balzs l.g . , bagoly z. , ryde f. , mszros a. , 2006 , a&a , 447 , 23 balzs l.g . , mszros a. , horvth i. , 1998 , a&a , 339 , 1 mszros a. , bagoly z. , vavrek r. , 2000a , a&a , 354 , 1 mszros a. , bagoly z. , horvth i. , balzs l.g . , vavrek r. , 2000b , apj , 539 , 98 litvin , v.f . , matveev , s.a . , mamedov , s.v . , & orlov , v.v . 2001 , pisma v astronomicheskiy zhurnal , 27 , 495 r. vavrek , et al . , 2008 , mnras , 391 , 1741 - 1748 norris , , j.p . 2002 , apj , 579 , 386" +"an important trend in the condensed matter physics of the last two decades , has been the use of advanced field - theoretical methods to discuss various subtle and fundamental properties of interacting many - particle systems at low temperatures . there are several reasons for this trend . the first reason is of course , that a traditional topic in statistical and condensed matter physics is the study of phase transitions and critical phenomena , for which the universal properties are independent of the microscopic details of the system and can therefore be determined by a field theory describing only the large - scale properties of the system of interest . since the latter are usually solely determined by symmetry considerations , this has led to the important concept of spontaneous symmetry breaking , which has turned out to be not only highly successful in condensed matter physics , but also in high - energy physics and in particular in the standard model of elementary particles @xcite . a second reason is that soon after the development of the renormalization group methods for critical phenomena @xcite , it was realized that the same methods can in fact be used to describe the large - scale properties of many - particle systems at any temperature and not only near the critical one . moreover , application of the renormalization group ideas does not only lead to an understanding of the static behaviour but also of the dynamical properties @xcite . as a result quantum field theories can be used to conveniently determine the dynamics of many - particle systems close to equilibrium , i.e. , for example the linear hydrodynamical equations of motion . in addition , it can even be used in highly nonequilibrium situations where in general also nonlinearities play an important role . this feature , that also the dynamics of the system can be captured by a quantum field theory , has for instance led in recent years to the study of so - called quantum phase transitions @xcite . finally , the importance of field - theoretical methods in condensed matter physics is associated with the observation that also the effects of imperfections , i.e. , disorder , can be treated in this way @xcite . apart from the technological importance of disorder , for example for superconducting magnets , disorder leads also to fundamentally new physics such as the phenomenon of localization @xcite . in quantum hall systems , a combination of disorder and interaction effects give rise to the realization of various peculiar quantum fluids with fractionally charged excitations @xcite . the application of field theories has proven to be highly successful in this case and has led to a theory of the quantum hall effect in terms of edge states that form a chiral luttinger liquid @xcite . in mesoscopic physics , the study of disorder in small electronic structures has resulted in the so - called random matrix theory @xcite , which has also been of much use in the study of the quantization of classically chaotic systems . in this course we aim to show that quantum field theory is also very convenient for obtaining a detailed understanding of the equilibrium and nonequilibrium properties of trapped atomic gases . after the first observations of bose - einstein condensation in 1995 @xcite , degenerate atomic gases have received again a great deal of attention and are presently the main subject of study of a large number of experimental and theoretical groups around the world . the reason for all this excitement is , first of all , that bose - einstein condensation has never before been observed experimentally in a clear - cut manner , even though this phenomenon was already predicted by einstein in 1925 @xcite . second , it is of fundamental interest because it is the only phase transition that occurs also in the absense of interactions and is , therefore , the textbook example for the use of statistical - physics methods . finally , the goal of achieving bose - einstein condensation turned out to be much more difficult than anticipated at first . just before the breakthrough in 1995 , it had even acquired the nature of a ` quest for the holy grail ' , since the pioneering experiments were already performed in 1980 @xcite . from a theoretical point of view , a quantitative understanding of the experiments with cold atomic gases requires that we take into account the following two effects . first , the gas is magnetically trapped in an , usually axially symmetric , harmonic oscillator potential . this is necessary because , in order to obtain the required record low temperatures of @xmath0 nk , the gas can not be allowed to have any contact with material walls . second , the atoms of the gas interact with each other , which in general dramatically affects the behaviour of the condensed gas , even at the relevant low densities of @xmath1 @xmath2 . an accurate description of these degenerate gases thus requires the solution of a highly inhomogeneous many - body problem . the theoretical challenge posed by these new quantum systems lies therein that the density of the gas is sufficiently small that it should be possible to accurately solve this many - body problem from first principles and to compare the outcome of the theory directly with experiment , i.e. , without any adjustable parameters . in our opinion , quantum field theory is the most simple way in which we are able to meet this challenge . we start our development of the quantum field theory of trapped atomic gases by considering first the equilibrium properties of these gases . we consider both bose and fermi gases , and the ultimate aim of this section is to arrive , for both cases , at an accurate description of the normal and superfluid phases of the gas . although mixtures of bose and fermi gases are also of current interest , we do not consider them explicitly here , because they can be treated by a straightforward generalization of the theory . in section [ nft ] we then turn to the nonequilibrium properties , which are perhaps the most interesting and certainly the least understood at present . the reason for organizing the course in this way , is that the development of the equilibrium theory gives us an opportunity to introduce all the necessary tools that are required for a treatment of the more complicated nonequilibrium case . in particular , we present in detail the way in which we can make use of functional methods . to make also a connection with the more familiar operator language , however , we first briefly summarize the outcome of the second quantization formalism . the atoms of interest to us have internal degrees of freedom due to the electron and nuclear spins . in principle this is very important , because it gives the atom a magnetic moment , which is used to trap the atoms in a magnetic field minumum . during this course , however , we restrict ourselves to atomic gases that are a mixture of at most two hyperfine states . without loss of generality , we can then suppose to have @xmath3 identical atoms with mass @xmath4 and effective spin @xmath5 in an external potential @xmath6 . as a result , the time - dependent schrdinger equation we have to solve is @xmath7 where the hamiltonian is @xmath8 @xmath9_- = i\hbar$ ] , and all other commutators of the positions and momenta vanish . the first term in the right - hand side is the sum of the one - particle hamiltonians , which includes an effective zeeman interaction that accounts for a possible difference in the hyperfine energies . the second term represents the interactions . for simplicity , we have assumed that the interaction @xmath10 is independent of the hyperfine states of the atoms @xmath11 and @xmath12 . this is in general not justified for realistic atomic gases , but is valid for the specific applications that we have in mind . moreover , in section [ hft ] we also discuss the general case . finally , we have also neglected possible three - body forces . this is a result of the fact that we are interested in dilute quantum gases , for which it is highly improbable for three atoms to simultaneously interact with each other . without interactions the eigenstates are , of course , given by the states @xmath13 , where the specific quantum state for each atom is exactly known . here @xmath14 and the nonnegative integers @xmath15 , @xmath16 , and @xmath17 denote the three quantum numbers that are required to specify the one - particle eigenstates in the external potential . the wave functions and energies of these eigenstates are @xmath18 and @xmath19 , respectively , and are found from the time - independent schrdinger equation @xmath20 in addition , the internal state @xmath21 is a shorthand notation for @xmath22 . the many - body wave function @xmath23 , however , has to be symmetric or antisymmetric under permutations for bosonic or fermionic atoms , respectively . therefore it is more convenient to use a properly ( anti)symmetrized version of the above basis , i.e. , the states @xmath24 with the occupation numbers @xmath25 for bosons and @xmath26 for fermions . the hilbert space of all these states , without the constraint @xmath27 , is known as the fock space . clearly , the many - body wave function @xmath23 can be expanded in this basis as @xmath28 where @xmath29 is the amplitude for the gas to be in state @xmath24 at time @xmath30 . in this basis the schrdinger equation becomes @xmath31 which shows that we need the matrix elements of the hamiltonian between different states in the fock space . to calculate these most easily we introduce so - called annihilation operators @xmath32 by @xmath33 from which it follows that the creation operators @xmath34 obey @xmath35 as a result , we see that the operator @xmath36 counts the number of atoms in the state @xmath37 , i.e. , @xmath38 we have also that @xmath39_{\mp } = [ \hat{\psi}^{\dagger}_{{\bf n},\alpha } , \hat{\psi}^{\dagger}_{{\bf n}',\alpha'}]_{\mp}=0 $ ] and most importantly that @xmath40_{\mp } = \delta_{{\bf n},{\bf n } ' } \delta_{\alpha,\alpha'}~.\ ] ] in equations ( [ cr ] ) and ( [ com ] ) the upper sign refers to bosons and the lower to fermions . this will be true throughout the course . from these results we can now easily show , first of all , that the basis in the fock space is given by @xmath41 with @xmath42 the vacuum state containing no atoms . second , the hamiltonian is @xmath43 with @xmath44 the one - particle energies . furthermore , @xmath45 is the amplitude for a collision which scatters two atoms out of the states @xmath46 and @xmath47 into the states @xmath37 and @xmath48 , as schematically shown in figure 1(a ) . introducing the field operators @xmath49 and @xmath50 , that annihilate and create atoms in the spin state @xmath21 at position @xmath51 respectively , we can rewrite this result into @xmath52 note that , due to the ( anti)commutation relations of the creation and annihilation operators and the orthogonality of the wave functions @xmath53 , the field operators obey @xmath54_{\mp}= [ \hat{\psi}^{\dagger}_{\alpha}({\bf x } ) , \hat{\psi}^{\dagger}_{\alpha'}({\bf x}')]_{\mp}= 0 $ ] and @xmath55_{\mp}= \delta({\bf x}-{\bf x}')\delta_{\alpha,\alpha'}$ ] . moreover , it is also important for the following to note that the number operator is @xmath56 and , similarly , that the effective total spin operator is @xmath57 the density of atoms in the state @xmath21 is thus simply @xmath58 . this completes our brief discussion of the second quantization formalism . in principle ," +"some nonlinear , partial differential equations of physics , not integrable by inverse scattering or else an inversion of variables , yield their secrets to lagrangian coordinate methods @xcite@xcite . here we will treat one such equation pair and see a combination of two lagrangian transformations enable us to solve the one lane moderately congested traffic flow problem explicitly . a further class of solutions is found in parametric form . calculations augment and reinforce those of part i @xcite . in 1955 , james lighthill and gerald whitham formulated an equation describing single lane traffic flow , assumed congested enough to justify a fluid model @xcite . richards published in the following year @xcite . next payne @xcite and whitham @xcite added a second equation and replaced the lwr equation with standard continuity . we will call this pair lwrp . recently the literature on both models has grown considerably , see for example the books by kern @xcite and further references @xcite@xcite . extensions to more than one lane , lane changing , discrete models , higher order effects , as well as numerical work , prevail . one of the original authors has found a toda lattice like solution to the discrete version of newell @xcite , see @xcite . in a future paper , we will see if the methods introduced here can be applied to some of these recent extensions of lwrp and lwr . other models have been developed @xcite , and @xcite@xcite . however , here we will concentrate on lwrp , remembering that any progress here may have implications for other physical problems , such as gas dynamics . assume a long segment of a one lane road , deprived of entries and exits , only moderately congested by traffic and free of breakdowns admitting a continuous treatment , so as to permit us to postulate the usual equation of continuity : @xmath1 here @xmath2 is the density of cars , the maximum of which @xmath3 corresponds to a bumper to bumper situation never occurring on our present model , and @xmath4 is the local velocity . the right hand side of the second , newtonian equation , formulated by payne @xcite and whitham @xcite , is less obvious : @xmath5 the first term on the right involves the mean drivers reaction time @xmath6 , and the next term models a diffusion effect depending on the drivers awareness of conditions beyond the preceding car . the constant @xmath7 is a parameter that models the effect of gradients on the acceleration . the choice of @xmath8 depends on the quality of the road . an obvious solution is @xmath2 and @xmath9 both constant . whitham considers this solution in his book and finds that is stable @xcite . in part i @xmath8 was a linearly decreasing function of @xmath2 : @xmath10 where the constant @xmath11 is related to @xmath3 by @xmath12 in this paper the analysis will be restricted to @xmath13 for which one can approximate @xmath8 by @xmath14 . in this connection we specify @xmath15 this is a form of @xmath8 recently postulated for low density and high quality of the road @xcite@xcite . the model used in part i had most common sense properties . the flow of traffic @xmath16 increased from zero for zero density of cars , through a maximum above which traffic becomes congested so that increasing the density no - longer increases the flow , down to an extreme density preventing any motion . the flow against density curve was a continuous parabola . all this is well enough . however , this model can be improved on . when the distances between individual cars are long , increase of density only results in a linear increase in the flow . if you can not see the cars preceding and following you , a possible small increase in the car density will hardly be noticed . thus the flow is a linear function of the density . thus the left hand portion of @xmath8 should be a constant up to some @xmath17 and the flow is @xmath18 . calculations simplify as long as we stay away from @xmath17 . the value of @xmath17 will depend on the quality of the road . we introduce dimensionless variables by replacing @xmath19 this leaves the continuity equation unchanged , and the newtonian equation takes the form : @xmath20 slightly simpler than in part i. here in part ii we treat situations that never become very congested ( @xmath13 ) which for the dimensionless quantities requires that @xmath21 our model is a macroscopic one in which the traffic is treated as a fluid flow . this is in contrast to the microscopic models involving motions of individual cars and hybrid models combining elements of both . ( the reader who has read part i can proceed to section 3 . ) the non - linearity on the left hand side of equations ( [ cont ] ) and ( [ momds ] ) can be eliminated by introducing lagrangian coordinates : @xmath22 , the initial position ( at @xmath23 ) of a fluid element which at time @xmath24 was at @xmath25 , and time @xmath24 . in this description , the independent variable @xmath25 becomes a function of @xmath26 and @xmath24 , as are the fluid parameters @xmath27 and @xmath28 . here and in what follows we adopt the convention that a superposition of two functions which introduces a new variable is denoted by the same symbol as the original function , but of the new variable . denoting by @xmath29 either @xmath2 or @xmath4 , the basic transformation between eulerian coordinates @xmath0 and lagrangian ones @xmath30 can be written as @xmath31 we denote by @xmath32 the number of cars between the last one at @xmath33 and that at @xmath26 : @xmath34 where @xmath35 is the initial mass density distribution . here and in what follows , the subscript @xmath36 always refers to @xmath23 . we will also use the superscript @xmath36 to refer to @xmath37 . here @xmath35 is positive . hence @xmath32 is an increasing function starting at @xmath38 , and one can introduce a uniquely defined inverse function @xmath39 . the initial position of a fluid element can be specified by either @xmath26 or @xmath40 . if a small initial interval @xmath41 at @xmath23 becomes @xmath42 at time @xmath24 , mass conservation requires : @xmath43 this leads to a mass conservation equation in lagrangian variables : @xmath44 and to a useful operator identity @xmath45 integrating ( [ cont1 ] ) over @xmath46 from @xmath47 to @xmath40 , we obtain the continuity equation in integral form : @xmath48 this indicates that if we know the car density in lagrangian coordinates @xmath49 , we can determine the evolving shape of the line of traffic , where the distance @xmath50 is measured from the @xmath37 car . the analogue of the continuity equation ( [ cont ] ) is obtained by differentiating ( [ cont1 ] ) by @xmath24 . using the middle part of ( [ trans ] ) we obtain @xmath51 the newtonian equation in lagrangian coordinates is obtained from ( [ momds ] ) and ( [ ss ] ) : @xmath52 equation ( [ mom1 ] ) can be solved to express @xmath53 in terms of @xmath2 . again , using the middle part of ( [ trans ] ) we can also calculate @xmath54 : @xmath55 , \label{uft}\\ n(s , t ) & = v_0 - \frac{\partial \rho}{\partial s},\label{nst}\\ x(s , t ) & = \xi(s ) + \int_0^t u(s , t ' ) \ , \mathrm{d}t'\nonumber\\ & = \xi(s ) + u(s,0 ) - u(s , t ) + \int_0^t n(s , t ' ) \ , \mathrm{d}t',\label{xst}\end{aligned}\ ] ] where the function @xmath56 will be determined later . differentiating the newtonian equation ( [ mom1 ] ) by @xmath40 , and using continuity ( [ contlv ] ) , we obtain one equation for @xmath57 : @xmath58 in part i , there was an extra @xmath59 term , causing the equation to have a symmetry when @xmath60 , @xmath61 . every solution had a formal twin . this symmetry is now lost , even though equation ( [ psieq ] ) is simpler . equation ( [ psieq ] ) can be factorized in two possible ways , i and ii : @xmath62 and @xmath63 we will find that the second factor in ( [ fact1 ] ) best yields solutions such that @xmath64 , whereas that in ( [ fact2 ] ) rules @xmath65 , where @xmath50 is always the distance from the car that started at @xmath66 . in both ( [ fact1 ] ) and ( [ fact2 ] ) , one term in the second factor is absent as compared to part i. in what follows , we will find solutions for which the second factor in one of equations ( [ fact1 ] ) , ( [ fact2 ] ) vanishes . we follow motion from left to right . factorization also means that we can only introduce the initial value of the density ( or @xmath57 ) . the initial velocity @xmath67 will then follow except for a universal constant . we will have more to say about this later on . the nonlinearities in ( [ fact1 ] ) and ( [ fact2 ] ) ( second factors ) can be eliminated if one transforms the variables @xmath68 to @xmath69 in a way similar to the lagrangian transformation ( [ trans ] ) : @xmath70 solving the resulting linear equation @xmath71 we obtain , in view of the fact that s and @xmath72 are identical at @xmath23 , @xmath73 for this @xmath74 we have @xmath75 and finally , back to @xmath76 and using ( [ trans1 ] ) , @xmath77 in this relation , defining @xmath40 in terms of @xmath72 and @xmath24 , @xmath78 is defined by ( [ sfxi ] ) but is expressed in terms of @xmath40 , where one has to rename @xmath40 to @xmath72 . the same procedure applies to @xmath79 given by ( [ psia ] ) . using ( [ psia ] ) , we can express @xmath2 in terms of @xmath72 and @xmath24 : @xmath80 which tends to @xmath81 as @xmath82 . we are now in a position to determine the function @xmath56 needed in equations ( [ uft ] ) and ( [ xst ] ) . differentiate ( [ mom1 ] ) by @xmath40 and then subtract both sides of ( [ psieq ] ) from the result to obtain @xmath83 solved by @xmath84 therefore , if @xmath85 , equation ( [ contlv ] ) will be valid for all time . all we require is @xmath86_{t=0 } = 0 , \qquad \mathrm{i.e . } \qquad \frac{\partial u(s,0)}{\partial s } = \frac{\partial \psi_0}{\partial t}.\ ] ] this result , along with either ( [ fact1 ] ) or ( [ fact2 ] ) , leads to @xmath87 integrating over @xmath46 from @xmath88 to @xmath40 and transforming the result to @xmath26 , we end up with @xmath89 where @xmath90 is arbitrary . the last task is to determine @xmath53 , @xmath54 , and @xmath91 , given by ( [ uft ] ) , ( [ xst ] ) , and ( [ x ] ) , in terms of @xmath72 . using ( [ rhoa ] ) , ( [ sfeta ] ) and ( [ nst ] ) we find the integrand @xmath92 : @xmath93 which tends to @xmath94 as @xmath95 . here @xmath96 must be found as a solution of equation ( [ sfeta ] ) which is often transcendental . if that is the case , the integrals ( [ uft ] ) and ( [ xst ] ) must be calculated numerically . on the other hand , the integral in ( [ x ]" +"superradiation ( sr ) is the cooperative radiation arising in a medium that contains a population inversion of excited states . originally this effect has been stated for purely quantum systems : i.e. two - level atoms @xcite . experiments have confirmed this prediction @xcite . later work established that this phenomenon also occurs in classical systems @xcite , and that the phasing effect the spontaneous origin and strengthening of correlations of originally independent subsystems underlies it . in the quantum case , these are correlations among phases of electronic states of atoms undergoing radiative transitions ; while in the classical regime correlations among phases of oscillations and directions of the electric dipole moments of atoms occur . a full account of the influence on sr of the dipole - dipole interactions among atoms remains incomplete ( see referenses @xcite ) . the sr theory has been developed in several directions . there exist complementary to each other schrdinger , heisenberg and semiclassical approaches . each of them is applicable to a special area of values of the system parameters . the common methodological lack of these approaches is that the phasing mechanism remains off screen . the mechanism of the transition from casual to a phased state possesses certain spatial , time and statistical behaviors and its nature is not fully clear . the quantum mechanical problem of sr is rather complicated , for example , within the heisenberg approach it requires to solve a system of nonlinear operational equations . approximations which are used to simplify this systems have limited and often unclear area of applicability . classical model of superradiation ( cms ) , where atoms are substituted by the classical lorenz oscillators and the electromagnetic field is described by the classical maxwell equations , allows to answer many difficult questions , in particular , the phasing mechanism . therefore classical and quantum approaches complement each other . moreover , radiation produced by pure classical system such as electrons revolved in magnetic field , electron clouds created in wigglers , cathode - ray lamps for microwaves , etc . is also sr . let us consider only classical systems . first , phasing leads to the ordering of phases of atoms . second , according to earnshaw s theorem @xcite , a system of point dipoles can not maintain a stable static equilibrium configuration . dipole - dipole interactions cause chaotic behavior that disorders their phases , and hence suppresses sr . sr arrises from a competition between these two opposing effects . this conclusion is inferred from the theory of non - uniform broadening of spectral lines for lasers @xcite . consider now a nonlinear cms @xcite , i.e. a system of classical , charged anharmonic oscillators . maxwell s equations describe the electromagnetic field . next , assume that there are sufficient oscillators ( @xmath0 ) , and they occupy a small spatial region of length @xmath1 such that @xmath2 , where @xmath3 is the characteristic distance between atoms , and @xmath4 is the wavelength of the radiation . each charge has magnitude @xmath5 and mass @xmath6 , and is located on the ends of springs with stiffness coefficient @xmath7 , at coordinates @xmath8 , fixed in points @xmath9 , where there are also compensating charges @xmath10 . the equation of motion for the oscillators then takes the form @xcite @xmath11 here @xmath12 , @xmath13 , @xmath14 represents the retarded time , @xmath15 is the fundamental frequency of the oscillators , and @xmath16 is the nonlinearity parameter . substituting the expression @xmath17,\ ] ] into equation ( [ eq:1])where @xmath18 represents the characteristic initial amplitude of the oscillations gives @xmath19 -\frac{1}{2}\beta_{0}\sum_{b}f_{b}.\ ] ] in equation ( [ eq:3 ] ) the second derivatives of functions @xmath20 which vary slowly in comparison with exponents @xmath21 are omitted , and a frequency @xmath22 , @xmath23 is chosen . note , that the case of particles rotating in a magnetic field ( important in a practical sense ) corresponds @xmath24 . for a small size system eqution ( [ eq:3 ] ) can be rewritten as @xmath25 where @xmath26 , @xmath27 , and @xmath28 . the first term on the right hand side of equation ( [ eq:4 ] ) represents the dipole - dipole interaction of the oscillators , while the second term is analagous to a ` viscosity ' for the radiation in the electromagnetic field . following ref . @xcite , we shall consider one - dimensional oscillators , i.e. that dipoles oscillate along the @xmath29 axis , and consequently , that the vectors @xmath30 are parallel to it : @xmath31 , @xmath32 . during a given time @xmath33 we have @xmath34 . hence , atoms possess a dipole moment that is @xmath35 . the average radiation intensity of the rapidly oscillating dipoles then is @xmath36 thus , equation ( [ eq:4 ] ) represents a system of @xmath37 oscillators , distributed arbitrarily , that can be solved by numerical means . a similar formalism is described in ref . @xcite ; however , dipole - dipole interactions are neglected . the phasing effect can be described as follows . consider a complex plane @xmath38 containing @xmath37 points that each represent the state of an individual oscillator , where the distance from the origin is simply the amplitude of oscillation , and the angle is the phase with respect to the fundamental frequency @xmath39 . points with @xmath40 rotate clockwise around the origin ; points with @xmath41 rotate anticlockwise . initially , the points are placed randomly with equal probability phases on a circle of unit radius @xmath42 . from equation ( [ eq:4 ] ) , their velocities are @xmath43 here @xmath44 , @xmath45 , @xmath46 , and @xmath47 , @xmath48 . the latter dipole - dipole interaction term is not shown in full for reasons of space . note that the vector @xmath49 is proportional to the total dipole moment of the system @xmath50 ; and , @xmath51 at @xmath52 . time evolution of the phase distribution of oscillators . the dotted line is a circle with unit radius . the number of oscillators is @xmath53 . the concentration of oscillators @xmath54m@xmath55 ( curve 2 on figure 4).,width=377 ] time dependence of the radiation intensity for @xmath56 ( all values in arbitrary units).,width=377 ] notice also that the sign of @xmath16 affects the direction of rotation _ only _ : changing it results in a mirror inversion without any other consequences . points with positive @xmath16 rotate clockwise outside the unit circle , and rotate anticlockwise when inside , while the opposite is true when @xmath16 is negative . this symmetry , therefore , is exploited by choosing @xmath57 . having established the basis for the model , we next consider how the system evolves when the density of atoms @xmath58 is sufficiently small that dipole - dipole interactions are negligible . due to the fluctuations of density distribution of the oscillators initial phases @xmath59 , the initial value of the vector @xmath60 is not precisely zero . at @xmath52 from equation ( [ eq:6 ] ) it follows that @xmath61 , where the characteristic emission time is @xmath62 @xcite . consequently from equation ( [ eq:6 ] ) , the system responds by moving in a direction opposite to the dipole moment @xmath63 , with a collective net velocity @xmath60 . the system at time @xmath64 is displaced a distance @xmath65 ( see figure [ fig : f1]a ) . the resulting displacement moves half of the points outside the unit circle ( @xmath66 ) , and the other half inside ( @xmath66 ) . hence , points outside the circle will move in clockwise orbits , while those within circulate the opposite way . after an interval @xmath67 , the net motion results in a bunching of points on the inside of the circle ( figure [ fig : f1]b ) , thus the atoms emit most of their stored energy in a sharp pulse of coherent radiation ( figure [ fig : f2 ] ) . for two - level atoms , the characteristic delay time @xmath68 given in @xcite is consistent with this . the bunch subsequently develops into a spiral - shaped distribution ( figure [ fig : f1]c ) . as it does so , the dipole moment decreases to a minimum , along with the sr intensity . the cycle repeats , decaying rapidly ( figure [ fig : f2 ] ) . oscillatory behavior is typical for sr in classical systems of small size @xcite . in quantum systems consisting of two - level atoms , sr intensity oscillations are absent @xcite . time evolution of the phase distribution of oscillators in systems with a strong dipole - dipole interaction . the dotted line is a circle with unit radius . figure * a * and * b * corresponds to concentration of oscillators @xmath69m@xmath55 ( curve 4 on figure 4 ) . figure * c * corresponds to @xmath70m@xmath55 ( curve 6 in figure 4).,width=377 ] intensity of radiation ( arbitrary units ) for systems with different oscillator concentrations @xmath58 ( @xmath71m@xmath55 ) : @xmath72 , @xmath73 , @xmath74 , @xmath75 , @xmath76 , @xmath77 , @xmath78 , for @xmath79@xmath80 respectively.,width=377 ] at high density @xmath58 , dipole - dipole interactions have a significant effect . figure [ fig : f3 ] shows the outcome of equation ( [ eq:4 ] ) for large @xmath58 ; the initial conditions are the same as described previously . notice that the points on the phase plane now move in a more chaotic manner than before . when @xmath58 is high , dipole - dipole interactions among adjacent oscillators are strong and this leads to incoherence . however , sr is not entirely suppressed . in spite of the chaotic behavior of dipole - dipole interaction , the initial total dipole moment results in bunching of points , and correspondently in the sr pulse ( figure [ fig : f3]a , b ) . on figure [ fig : f3]c , where the concentration of oscillators was doubled , dipole - dipole interaction suppress the bunching . high density systems are also complicated by collective effects . localized groups of resonant atoms induce antiphase dipole moments among their neighbors . this preserves coherence while screening sr @xcite . radiation intensity ( arbitrary units ) versus time ( arbitrary units ) for classical systems with different oscillator concentrations @xmath58 ( @xmath81 ) : @xmath72 , @xmath73 , @xmath74 , @xmath75 , @xmath76 , @xmath77 , @xmath78 , for @xmath79@xmath80 respectively . case @xmath79 is compared with the purely quantum result which varies as @xmath82.,width=377 ] the sr delay @xmath83 and peak intensity @xmath84 also depend on @xmath58 : increasing @xmath58 makes @xmath83 longer , and @xmath84 smaller ( see figures [ fig : f4 ] , [ fig : f5 ] , and [ fig : f6 ] ) . this is a consequence of the effect of coherence on the collective interactions among the dipoles , which becomes weaker with increasing @xmath58 . unlike classical systems , quantum systems do not behave chaotically . the intensity varies smoothly with time as described by the following formula @xcite . @xmath85 where @xmath86 represents the form - factor of the oscillators mutual position , and @xmath87 is the characteristic emission time . this curve is plotted in figure [ fig : f5 ] to illustrate the difference between the classical and quantum cases . when @xmath37 is large , at @xmath88 , equation [ eq:7 ] suggests @xmath89 . however , the cms predicts that the exponent @xmath90 rises to a peak value that is less than two , then declines as @xmath37 increases ( see figure [ fig : f7 ] ) . experimental observations of sr in semiconductors exhibit similar behavior @xcite . the results are consistent" +"a fundamental problem in understanding the evolution of galaxy clusters and their constituent galaxies is the importance of dynamical processes such as tidal stripping . theoretical models of cluster evolution have considered collisions , mergers , dynamical friction and tidal stripping in order to explain the galaxy morphology - density relation and the presence of luminous halos around supergiant d galaxies . it is generally accepted that tidal stripping will remove the more loosely bound stars in the outer envelopes of galaxies @xcite . @xcite has argued that the extensive envelopes of cd galaxies consist of this tidal debris moving in the potential well of the cluster . however , the efficiency of tidal stripping is not well understood , because of uncertainties in the velocities , the mean tidal field , the distribution of dark matter , and the orbits of stars in the outer envelopes of the stripped galaxies . typical theoretical estimates indicate that 10 - 20% of the total cluster light should be in the intergalactic medium @xcite and that the amount of icl should increase with time @xcite . @xcite and @xcite have therefore stressed the importance of obtaining reliable measurements of the intracluster light ( icl ) as a direct indicator of the tidal damage suffered by galaxies . attempts to measure the icl date back to the early 1970s , originally being done with photographic plates . more recently ccd surveys have been employed by @xcite , @xcite , @xcite , and @xcite with results ranging from non - detections up to @xmath1% of the total cluster light ( surface brightnesses of @xmath2 mag arcsec@xmath3 ) . even with ccds , detecting the icl directly is notoriously difficult and fraught with uncertainties such as the contributions from overlapping galaxy halos . an independent means of measuring the icl , not subject to the same problems as measuring the extremely low surface brightness diffuse emission is needed . methods using planetary nebulae ( pne ) have been developed and applied to virgo @xcite and fornax @xcite . intergalactic red - giant - branch stars have also been detected in virgo by comparing the luminosity function of point sources in intracluster space with control fields far from any cluster or galaxy @xcite . intracluster sne have also been identified and have extended measurements of the icl out to @xmath4 @xcite . novae typically range in brightness from m@xmath5 to @xmath6 , while the bright end of the pn luminosity function reaches m@xmath7 @xcite and red - giant - branch stars typically reach m@xmath8 . supernovae are much brighter , but also much rarer than novae . novae can therefore be detected more easily in a given cluster , or be observed to greater distances than pne or red - giant stars . the transient nature of novae and their h@xmath9 brightness help eliminate the contamination suffered by pne or red - giant - branch stars due to background emission line objects or unresolved compact galaxies . another appealing property of novae is that the rate of novae per unit mass is high enough such that with a deep enough survey , one can expect to accrue a statistically interesting number of novae in each epoch , thus increasing the accuracy of the icl measurement with each new epoch . these properties give novae the potential to be useful as an independent and accurate measure of the icl in nearby clusters . in spite of this , to our knowledge , no intra - cluster novae have been reported in the literature to date . as an independent check on highly uncertain direct measures of intracluster light , we can use novae to verify the amount of stellar tidal debris in the cluster . this then places constraints on the importance of tidal stripping in the formation and evolution of galaxy clusters . our m81 nova results from the most complete nova survey ever undertaken indicate that novae are preferentially associated with the older , bulge populations in galaxies @xcite . we can use this knowledge to attempt to discern the predominant source of the icl either in bulge - dominated or disk - dominated galaxies . another lesson we have learned from our nova studies is that accurate rates and distributions can only be derived from comprehensive , densely time - sampled surveys @xcite . the data set we use in this paper is diverse and very sparsely sampled . we therefore restrict our investigation to a relative comparison of galaxy versus inter - galaxy novae . our aim is to prove the _ feasibility _ of using novae to perform an accurate assessment of the amount and origin of the icl . we have acquired six epochs of survey data of the central 30 square of the fornax cluster . fornax is nearby and has a fairly high surface density of galaxies in the core , increasing the likelihood of tidal stripping . at the distance of fornax , @xmath10 = 31.35 @xcite , novae will have an average m@xmath11(peak ) @xmath12 ( the brightest novae will have peak brightnesses of m@xmath11 = 21.35 ) , and are easily detectable . novae have been observed by @xcite in virgo cluster galaxies , which are at the same distance as fornax . novae are very bright in h@xmath9 ( b @xmath13 h@xmath14 when the nova erupts , and b @xmath13 h@xmath15 shortly thereafter ) . furthermore , novae remain bright in h@xmath9 for an extended period of time ( months ) , providing a useful means of discovering them . to a limiting magnitude of m@xmath16 = -7.5 ( m@xmath16 = 23.85 at fornax ) the mean h@xmath9 visibility lifetime is 3 months @xcite . assuming a nova rate of 24 yr@xmath17 per 10@xmath18 ( b ) @xcite , a luminosity in galaxies of m@xmath19 in the core of fornax @xcite , a visibility lifetime in h@xmath9 of 3 months , and a conservative completeness factor of 0.5 due to the high surface brightness of galaxy cores , we estimate that at any given epoch there should be @xmath1 novae in eruption ( with visible h@xmath9 emission ) in galaxies in the central 1 deg@xmath20 of the fornax cluster . since we are surveying the central @xmath21 deg@xmath20 we multiply this estimate by @xmath22 and predict we will see 12 novae in any given epoch . the observations that went into this study are a diverse set acquired over the span of more than a decade . the central 30 of fornax , centered on ra 03:38:13.72 , dec -35:32:52.2 ( j2000 ) , was surveyed . this area includes the central dominant ( cd ) galaxy ngc 1399 and three other elliptical galaxies : ngc 1404 , ngc 1387 , and ngc 1389 . this region was imaged twice in 1993 , once in 1995 , for five nights in 1999 , and once each in 2003 and 2004 . the data were acquired during programs for other projects and during engineering time or director s discretionary time . these observations are summarized in table [ tabforobs ] . because of the long - term nature of the data acquisition , there was no uniform observing strategy employed . we started with the tek2048 camera , and when the mosaic ii camera became available ( before the 1999 run ) , we switched to that camera for the remaining epochs . we used standard johnson b- and r - band filters and narrow - band h@xmath9 filters primarily , but for two epochs ( b and c , see below ) we were constrained to using a t1 filter from the washington system ( @xmath23 , fwhm @xmath24 , canterna 1976 ) , which is roughly equivalent to a johnson r filter ( @xmath25 , fwhm @xmath26 ) . the h@xmath9 filter used for the 1993 a epoch was the 6600/75 ctio filter with @xmath27 and @xmath28 which accounts for the velocity of fornax ( 1517 @xmath29 91 km s@xmath17 , grillmair et al . the h@xmath9 filter used for the 1999 and 2003 epochs was the mosaic ii c6009 filter with @xmath30 and @xmath31 . there is no h@xmath9 filter in the mosaic ii set that correctly accounts for the velocity of fornax , so we chose the filter whose central wavelength comes the closest to 6600 . we will discuss the impact of using this filter below . total exposure times were restricted by the gaps available in the schedule for other programs . individual exposure times were chosen to provide at least three frames per epoch so cosmic rays could be removed in the combining process . for the h@xmath9 frames the only exceptions to this are the 1999 g epoch ( 1 exposure ) and the 1999 h epoch ( 2 exposures ) . since cosmic rays could not be adequately removed from these exposures , they were only used for nova confirmation and measurement and not detection ( see below ) . all of the data were acquired using the ctio 4 m telescope with the exception of the b and c epoch data ( taken exclusively through the t1 filter ) which were acquired with the ctio 1.5 m telescope . the data acquired in 1993 and 1995 were taken with the tek2048 chip . the focal ratios of the 4 m and the 1.5 m are such that they produce an identical pixel scale for these images of 043 per pixel . the resulting field of view is 147 and thus required four pointings to cover the central 30 of the cluster . the seeing tabulated in table [ tabforobs ] for these epochs represents the range of seeing across the four pointings . sky flats were acquired in each filter to remove the instrumental response . the data acquired in 1999 , 2003 , and 2004 were taken with the mosaic ii camera on the 4 m telescope . this camera is a mosaic of eight 2048x4096 pixel ccds with a pixel scale of 027 per pixel . the resulting field of view is 368 and thus required only one pointing . sky flats were used to remove the instrumental response for the 1999 epochs , and dome flats were used for the 2003 and 2004 epochs . all data were reduced using the standard tools in iraf @xcite or the * mscred * external iraf package developed by the noao mosaic instrument team . individual exposures for a given epoch were combined to produce a coadded image for the epoch and to remove all but a few cosmic rays . classical novae erupt with amplitudes of up to 20 magnitudes , reaching absolute magnitudes as high as m@xmath32 and fading back to their pre - outburst brightness in a matter of weeks or months @xcite . novae in the fornax cluster are therefore invisible before outburst and fade back to invisibility after outburst on time scales of less than a year . thus , our primary criterion for detecting novae is that they be transient on this timescale . for the data used in this study this means that they must only appear in only one year s images . if a variable object appears in images from more than one year , it is most likely some other kind of variable source : a foreground periodic , or semi - periodic variable , or a background , unresolved active galaxy nucleus ( agn ) . classical novae also exhibit strong h@xmath9 emission in outburst , providing the next criterion : the candidate should be h@xmath9-bright . data from 1993 and 1999 were taken both through h@xmath9 and red continuum filters allowing us to produce h@xmath9 - red continuum subtracted images . these images were used to test candidates from 1993 and 1999 against this criterion . the primary method for implementing these criteria consisted" +"as we heard in the talks by uros seljak and lam hui in this meeting , the physics of the forest , as measured in high-@xmath0 quasi - stellar object ( qso ) spectra , is reasonably simple . at these redshifts the gas making up the intergalactic medium is in photoionization equilibrium , which results in a tight density temperature relation for the absorbing material with the neutral hydrogen density proportional to a power of the baryon density . since pressure forces are sub - dominant , the neutral hydrogen density closely traces the total matter density on the scales relevant to the forest ( @xmath1mpc ) . the structure in qso absorption thus traces , in a calculable way , slight fluctuations in the matter density of the universe back along the line of sight to the qso , with most of the forest arising from over - densities of a few times the mean density . in this contribution i want to focus on two areas where the forest can be used to constrain cosmology and astrophysics . the first , dealing with measuring the matter power spectrum at high redshift , is quite speculative , but might be very exciting . the second has a higher chance of success and may tell us something about the nature of the ionizing sources , the end of the dark ages and the formation of the first objects in the universe . the presence of a series of almost regularly spaced peaks in the cosmic microwave background temperature angular power spectrum has now been compellingly demonstrated . the same physics which gives rise to these peaks , acoustic oscillations in the baryon - photon plasma prior to recombination @xcite , also predicts a ( much smaller ) series of peaks in the matter power spectrum . a measurement of these peaks would provide a fundamental test of the paradigm , and an independent measure of the @xmath0-dependent hubble constant and distance - redshift relation @xcite . because non - linear growth ` washes out ' the peaks @xcite they are best searched for at high redshift . the baryon oscillations themselves lie at @xmath3mpc ( see fig . [ fig : d2 ] ) , with an amplitude of 5% or less for currently popular cosmological models @xcite . the higher modes are roughly out of phase with the photon peaks ( also in @xmath4-space ) and appear half as often as the peaks in the cmb spectrum ( see e.g. fig . 1 of @xcite ) . the peaks are suppressed by silk damping beyond @xmath5mpc . naively the best way to measure the small baryonic oscillations in the matter power spectrum would be an ultra - large galaxy redshift survey at high-@xmath0 . such a survey would require next - generation instruments and a large dedicated team . thus even with adequate funding and heroic efforts it is several years away . it is therefore interesting to explore whether one could measure the baryonic oscillations another way . within a few years the sdss will return a catalogue of @xmath6 qsos over @xmath7 square degrees of sky . these quasars will be distributed in both redshift and angular separation , but simple counting suggests that one should find many hundreds to several thousands with separations of tens of mpc above @xmath8 . it is therefore interesting to ask whether this sample could be used to probe the baryon oscillations . using simply the auto - power spectrum of the forest will not work , because the line - of - sight spectrum at @xmath4 is an integral of the 3d spectrum over wavenumbers greater than @xmath4 . this integration suppresses the small oscillations which are our primary signal . however one can consider the cross - spectra , where one line - of - sight is cross - correlated with a neighboring line - of - sight . as we shall show below this statistic is sensitive to the oscillations . in addition uncorrelated errors from e.g. continuum fitting , should be averaged down in this procedure relative to their value in the auto - spectrum . since we are working on large scales , where the noise is essentially absent , one could in principle measure the flux cross - spectrum to the cosmic variance limit @xmath9 where @xmath10 is the number of pairs , @xmath11 is the fundamental mode along the line - of - sight and @xmath12 is the width of the bin in @xmath4-space in which we are measuring the power . we can alternatively write @xmath13 , where @xmath14 is the length of the ` useful ' part of the spectrum . unless we attempt to fit to the higher lines , the useful length of the spectrum is the section between and ly@xmath15 which covers hundreds of mpc in the rest frame of the absorbers . thus with a few hundred pairs it is possible to measure the cross - spectrum with error bars on the order of per cent . one major advantage here is that , like the cmb itself , the redshift and scale dependence of the peaks is accurately calculable given a cosmological model . this allows us to perform a likelihood estimation of the relevant cosmological factors , including pairs of different distances and redshifts , rather than attempt to perform an inversion on the irregularly sampled data . though the latter can be done , it is considerably more difficult than the ` forward ' approach . by applying the idea of the peak - background split from large - scale structure is it possible to show that , for sufficiently large scales and assuming @xmath16 , the flux cross - spectrum , @xmath17 , along two lines of sight separated by distance @xmath18 is proportional to the dark matter cross - power spectrum @xmath19 ( see also @xcite ) . on these very large scales we can neglect the effects of thermal broadening or peculiar velocities . the dm cross - spectrum is simply related to the 3d power spectrum by @xmath20 or @xcite @xmath21 where the inverse relation holds @xmath22 . note that for smooth spectra , @xmath23 gets contributions from @xmath24 . as @xmath25 , @xmath26 and we find the auto - spectrum is the projection of the 3d spectrum as anticipated . converting from @xmath27mpc to s / km using @xmath28 we find that the relevant spectral range is roughly @xmath29s / km to @xmath30s / km . this is quite large scale , roughly comparable to the fundamental mode if we measure only from 100 nm to 120 nm . on the positive side fig . [ fig : pi ] shows that the signal is present in the cross spectra at separations of 10mpc or so . the relative amplitude of the oscillations ( which is the figure of merit for cosmic variance dominated measurements ) can be quite large , 10% or more , compared to the accuracy with which @xmath19 can be measured . because we can accurately predict the positions and amplitudes of the peaks we know both the @xmath18 and @xmath0 dependence of the signal . on the negative side there is only a small fractional change in @xmath19 when @xmath19 is big ( i.e. @xmath18 small ) and the larger fractional change in @xmath19 when @xmath19 is small . this suggests we would be working primarily at very low signal levels , where systematics become increasingly important . also , if we work with the spectra only between and ly@xmath15 we do not have very much ` spare ' resolution in @xmath4 to see the oscillations . we would ideally probe @xmath31s / km which requires very long spectra . in summary , the signal of baryon oscillations is lurking in the cross - spectra of qso pairs , which allow us to probe large volumes of space at high redshift with a modest investment in telescope time . a naive estimate of the cosmic variance limitations of a qso survey like the sdss suggests that the signal could be seen in a likelihood analysis with high confidence . however the overall signal levels are very low and there are numerous sources of systematic error which may make the signal forever unmeasurable . currently the sources that make up the uv background are unknown . however the mean optical depth @xmath32 in the forest offers a way to constrain the source emissivity and fluctuations in the uvbg can be used to constrain the nature of the sources . i have been involved in a long - running collaboration with avery meiksin to investigate these issues @xcite , and present some of our basic results here . first we consider the constraints on the source emissivity @xmath33 . given a cosmological model , the mean flux or optical depth @xmath32 fixes the ionization rate @xmath34 . if we approximate @xmath35 $ ] as @xmath36 $ ] where @xmath37 is the _ attenuation length _ then @xmath38 . here @xmath39 is an effective attenuation length which interpolates between the attenuation limited ( @xmath40 ) and cosmological expansion+age limited ( @xmath41 ) regimes and @xmath42 is the hubble distance . as a function of @xmath33 the transition between the attenuation limited and cosmologically limited regimes is very abrupt , and at fixed @xmath33 , @xmath37 falls rapidly with increasing redshift . this in turn means that @xmath32 rises rapidly , almost exponentially , with redshift . [ fig : fig3 ] shows the emissivity of the sources , as a function of @xmath0 , required to fit the observed @xmath32 . this is compared to extrapolations of the qso luminosity function . from this we can see that qsos may contribute a substantial fraction of the uv background even as high as @xmath43 . if qsos do contribute non - negligibly to the uv background then we would expect large spatial fluctuations in @xmath34 . conversely , if galaxies or star clusters dominate the uv background we expect to see only the imprint of large - scale structure . unfortunately the effects of uv background correlations are most conspicuous at @xmath44 , where the precise level of absorption by the forest is most difficult to measure because of extremely low flux values . fig . [ fig : onesource ] shows how a simulated spectrum is changed if the uv background is ( unrealistically ) dominated by a single source as compared to the usually assumed smooth behavior . to assess a more realistic situation it is necessary to resort to monte carlo simulations in which sources are placed within the simulation volume , the uv background computed and then spectra created from the density and velocity fields within the box . our investigations suggest that the 1-point distribution is relatively unaffected by fluctuations in the uvbg , however the 2-point statistics ( the flux correlation function and power spectrum ) show noticeable differences at high redshift @xcite . in addition fluctuations in the uvbg will increase the estimated optical depth over the value that would be estimated assuming a homogeneous background @xcite . this increases the demand placed on the ionization rate required to reproduce @xmath32 and needs to be included when comparing with estimates of source emissivity . the forest is emerging as a powerful probe of structure formation at high redshift . because the physics is relatively well understood we can compare increasingly realistic calculations with ever better data to constrain our cosmological models . here we have investigated two ways in which the forest constrains cosmology . the first , speculative , proposal was to search for baryonic oscillations in the matter power spectrum through their imprint in the forest cross - spectra . the second proposal was to constrain the emissivity of the sources of the uv background using the measured mean" +"resonant tunneling ( rt ) through double - barrier structures ( dbs ) make these systems very promising candidates for a new generation of ultra - high speed electronic devices . for instance , a gaas - ga@xmath1al@xmath0as dbs operating at thz frequencies has been reported in the literature.@xcite the basic reason for rt to arise in dbs is a quantum phenomenon whose fundamental characteristics are by now well understood : there exists a dramatic increase of the electron transmission whenever the energy of the incident electron is close to one of the unoccupied quasi - bound - states inside the well.@xcite in practice , a bias voltage is applied to shift the energy of this quasi - bound - state of nonzero width so that its center matches the fermi level . consequently , the @xmath2 characteristics present negative differential resistance when the quasi - bound - state lies well below the fermi level . in actual samples , however , the situation is much more complex than this simple picture . scattering by phonons , electrons or defects reduces the required quantum coherence and , in fact , deviations from the above simple description are observed . these scattering mechanisms explain the occurrence of side - band resonant peaks due to the interaction with phonons@xcite and photons,@xcite hysteresis in the @xmath2 characteristics due to many body effects,@xcite and the decrease of electron mobility due to rough surfaces even in good - quality heterostructures.@xcite while one - dimensional models successfully describe scattering by electrons and phonons , they obviously can not account for all interface roughness effects . so far , there are analytical results concerning the propagation of wave packets in a randomly layered medium when the potential is a random function of only one coordinate,@xcite but for a small number of layers , as in dbs , in - plane disorder becomes important and one expects such approaches to fail . realistic models of in - plane disorder , including power - like or exponential spatial correlations observed by transmission electron microscopy , usually lead to intractable analytical models ; hence the importance of numerically solvable models to bridge this gap . an important contribution was already provided by henrickson _ et al . _ , who applied the tight - binding green function method to interface roughness in dbs.@xcite in this paper transmission was studied for a dbs with a rather simple model of disorder ( periodic roughness with random relative phases at the interfaces ) . a level splitting was found for narrow well dbs and a dependence on the roughness lateral size was observed . in this work we present a simple two - dimensional model that allowed us to carry out an extensive study of electron scattering by interface roughness and how it manifests trough vertical transport properties of the dbs . in particular , we aim to elucidate the relationship between macroscopic properties of the dbs ( e.g. conductance ) with microscopic parameters of the model ( e.g. correlation length of the surface disorder ) . the paper is organized as follows : the body of the paper is sec . [ sec2 ] , where we present our model based , on the effective - mass approximation , describing a disordered sample ( e.g. an imperfect dbs ) connected to two perfectly ohmic leads . the ben daniel - duke equation is discretized , boundary conditions are discussed and scattering solutions are found by means of the transfer - matrix method for _ any _ arbitrary heterostructure made of wide gap semiconductors . afterwards , expressions for two - terminal conductance and current for unintentionally disordered dbs are provided . the model is worked out in a two - dimensional space for computational limitations , although it will be clear that generalization to three dimensions is rather straightforward . section [ sec3 ] describes the various models of disorder we have used to mimic structural data obtained by transmission electron microscopy and x - ray scattering . in sec . [ sec4 ] we present the numerical results and , in particular , the relationship between macroscopic properties of the dbs with microscopic parameters of the model . finally , in sec . [ sec5 ] we discuss our results and the main conclusions of the work . we consider the single - electron two - dimensional schrdinger equation within the framework of the one - band effective - mass approximation . close to the @xmath3 valley , this approach leads to the ben daniel - duke equation for the envelope function @xmath4\psi(y , z)=e\psi(y , z).\ ] ] where @xmath5 denotes the coordinate along the growth direction ( see fig . [ fig1 ] ) . notice that we have taken a constant effective mass @xmath6 at the @xmath3 valley although this is not a serious limitation as the model can be easily generalized to include a position - dependent effective mass . we then consider a mesh with lattice spacings @xmath7 and @xmath8 in the @xmath9 and @xmath5 directions , respectively . defining @xmath10 and @xmath11 , we arrive at the following discretized version of eq . ( [ hamiltonian ] ) @xmath12 the potential term @xmath13 in eq . ( [ discrete ] ) is given by the conduction - band edge energy at the point @xmath14 which , in turn , depends on the al mole fraction in the vicinity of that position . consequently , both kinds of disorder ( lateral and compositional ) are taken into account through this diagonal term ( diagonal disorder ) . in order to solve the tight binding - like equation ( [ discrete ] ) we use the transfer matrix method based on the solutions calculated for each slide of the system along the @xmath5 direction . to this end , we define @xmath15 and @xmath16 here @xmath17 and @xmath18 are the number of mesh divisions in the @xmath9 and @xmath5 directions , respectively . note that periodic boundary conditions have been taken into account on each slide . with these definitions , eq . ( [ discrete ] ) can be cast in a more compact form @xmath19 where @xmath20 and @xmath21 are the @xmath22 identity and null matrices respectively . this expression allows us to relate by iteration the envelope function amplitudes at non - consecutive slides . in particular , we can obtain the expression of the envelope function amplitudes in the left contact as a function of the amplitudes in the right one @xmath23 where @xmath24 is the transfer matrix for the heterostructure . we are interested in the scattering of electrons incident from the left contact . the envelope functions within the contacts will be determined by the boundary conditions . these boundary conditions are open in the @xmath5 direction , and periodic on each slide , that is in the @xmath9 direction . the former imply plane wave solutions in the @xmath5 axis , and the latter yield an energy discretization on @xmath9 . as a consequence , this discretization results in a number of transverse channels equal to the number of points in the transverse mesh direction . considering by the moment @xmath25 at the contacts and setting @xmath26 , a particular solution of eq . ( [ discrete ] ) is given by @xmath27 here @xmath28 is a normalization constant that is needed for the different _ propagating _ modes to carry the same current all of them . this normalization constant is given by @xmath29 note that we consider a dependence on the index @xmath30 of the momentum in the @xmath5 direction . this is a consequence of the implicit assumption that all the scattering processes in region ii are elastic , so energy is conserved . thus , for a given energy @xmath31 + 1 \right\}.\ ] ] finally we can write a general solution of the scattering problem for an electron of energy @xmath32 impinging on the scattering region on the @xmath30 transverse mode . on the left contact the solution will be of the form @xmath33 on the right contact we have @xmath34 the matrices @xmath35 and @xmath36 appearing in these two solutions are the _ reflection _ and _ transmission _ matrices and they are responsible for the channel _ mixing _ due to scattering events . thus , @xmath37 represents the probability amplitude for an electron impinging in channel @xmath38 to be reflected into the chanel @xmath39 . similarly @xmath40 represents the probability amplitude for an electron impinging in chanel @xmath38 to be transmited through the scattering region ii into the channel @xmath39 . note that the solution within region ii is unknown . actually , we are not interested in this solution since all the physics of the scattering problem is contained in the _ mixing _ matrices @xmath36 and @xmath35 . in the following , our main goal will be to relate the elements of @xmath36 and @xmath35 to those of @xmath41 in eq . ( [ transfer ] ) . we start by re - writting formally eq . ( [ discrete ] ) as @xmath42 . now we perform the following transformation upon the envelope functions @xmath43 it is easy to see that the hamiltonian is invariant under such a transformation , that is , @xmath44 . this is clear since @xmath36 and @xmath45 formally commute as they act upon different vector spaces . the fact that @xmath46 is invariant implies that @xmath41 is not affected by transformation ( [ transformation ] ) so it remains unchanged . in addition , equations ( [ solutioni ] ) and ( [ solutioniii ] ) are transformed into @xmath47 and @xmath48 respectively , where we have defined @xmath49 and @xmath50 . for each channel @xmath30 we can write the transform of eq . ( [ transfer ] ) as @xmath51 now , introducing the definitions @xmath52 we arrive at the following transform of eq . ( [ chanel_l ] ) in terms of the elements of the _ mixing _ matrices @xmath53 and , finally , we have @xmath54 that give us the matrix elements @xmath55 and @xmath56 with @xmath57 for each channel @xmath30 in terms of the product of two known matrices and the transformed solutions ( [ new_solutioniii ] ) at the right contact for the @xmath30 channel . it is worth noticing that all the scattering information is contained in the transfer matrix @xmath41 . thus , this quantity turns out to be the fundamental object in the resolution of the scattering problem . once @xmath58 and @xmath59 have been calculated , obtaining @xmath36 and @xmath35 is an easy task . however , the matrices calculated this way are the _ response _ matrices that contains some non - physical information . this non - physical information comes from the fact that we have been considering _ all _ the mathematical solutions of the scattering problem , including those diverging at infinity . these solutions are those for which momentum in eq . ( [ kl ] ) is an imaginary number . in order to avoid the unphysical solutions we will cancel out all the elements on @xmath36 for which the incoming and/or the outgoing transverse quantum number @xmath30 satisfy the following condition @xmath60 once the physical _ mixing _ matrices are known , particularly the transmission matrix @xmath36 , we can use them to calculate different physical quantities like the conductance or the electric current . from the landauer - bttiker formalism,@xcite the zero temperature two - leads multichannel conductance can be calculated using de fisher - lee formula@xcite @xmath61 in order to calculate the electric current due to an applied field @xmath62 we have to modify slightly our equations and further approximations are needed . first of all , we consider perfect leads , so no voltage drop occurs within the contacts . besides , we will" +"the standard big bang theory predicts the existence of @xmath1 neutrinos per flavour in the visible universe ( e.g. , @xcite ) . this is an enormous abundance unrivalled by any other known form of matter , falling second only to the cosmic microwave background ( cmb ) photon . yet , unlike the cmb photon which boasts its first ( serendipitous ) detection in the 1960s and which has since been observed and its properties measured to a high degree of accuracy in a series of airborne / satellite and ground based experiments , the relic neutrino continues to be elusive in the laboratory . the chief reason for this is of course the feebleness of the weak interaction . the smallness of the neutrino mass also makes momentum - transfer - based detection methods highly impractical . at present , the only evidence for the relic neutrino comes from inferences from other cosmological measurements , such as big bang nucleosynthesis ( bbn ) and cmb together with large scale structure ( lss ) data ( e.g. , @xcite ) . nevertheless , it is difficult to accept that these neutrinos will never be detected in a more direct way . in order to design possible direct , scattering - based detection methods , a precise knowledge of the phase space distribution of relic neutrinos is indispensable . in this connection , it is important to note that an oscillation interpretation of the atmospheric and solar neutrino data ( e.g. , @xcite ) implies that at least two of the neutrino mass eigenstates are nonrelativistic today . these neutrinos are subject to gravitational clustering on existing cold dark matter ( cdm ) and baryonic structures , possibly causing the local neutrino number density to depart from the standard value of @xmath2 , and the momentum distribution to deviate from the relativistic fermi dirac function . in this paper , we develop a method that will allow us to predict the phase space distribution of relic neutrinos in our local neighbourhood at earth ( @xmath3 from the galactic centre ) , as well as in outer space . the method systematically takes into account gravitational clustering of relic neutrinos on scales below @xmath4 , and can be applied to the complete range of experimentally and observationally consistent neutrino masses . with these predictions , we determine the precise implications of relic neutrino clustering for future direct search experiments . to this end , we note that in earlier studies of relic neutrino direct detection , the neutrino number density in our local neighbourhood is either assumed to be unrealistically large , or simply left as a free parameter ( e.g. , @xcite ) . with the emergence of the concordance flat @xmath0cdm model as the cosmological model of choice , today we are in a position to compute the relic neutrino phase space distribution within a well defined cosmological framework , and to contemplate again the prospects for their direct detection in a definitive way . our studies here will also be useful for such investigations as relic neutrino absorption @xcite and emission @xcite spectroscopy . the standard procedure for any gravitational clustering investigation is to solve the @xmath5-dimensional vlasov , or collisionless boltzmann , equation using @xmath6-body techniques ( e.g. , @xcite ) . however , these techniques are computationally very expensive and necessarily come with limited resolutions . in the context of the cold+hot dark matter ( chdm ) model , earlier @xmath6-body studies involving neutrinos probe their kinematic effects on structure formation from cluster and galaxy abundances on large scales ( e.g. , ) , to halo properties on small scales @xcite . while the chdm model has fallen out of favour in recent years ( see , however , @xcite ) , it is instructive to note that the halo simulation of @xcite has a formal resolution of only @xmath7 . this is clearly inadequate for our considerations , where the scale of interest is of order @xmath8 . in the context of the flat @xmath0cdm model , singh and ma ( hereafter , sm ) presented a novel approximate method to probe the accretion of neutrinos onto cdm halos at scales below @xmath9 . the salient feature of this study is their use of parametric halo density profiles from high resolution , pure @xmath0cdm simulations as an external input , while the neutrino component is treated as a small perturbation whose clustering depends on the cdm halo profile , but is too small to affect it in return . implementation of this approximation requires the neutrino mass density @xmath10 to be much smaller than its cdm counterpart @xmath11 . on cosmological scales , we know now from lss data that the ratio @xmath12 is at most @xmath13 @xcite . on cluster / galactic scales , neutrino free - streaming ensures that @xmath14 always remains smaller than its cosmological counterpart @xcite . thus the approximation scheme , so far , is sound . furthermore , in order to track the neutrino density fluctuations in the most effortless way , sm employed the linearised vlasov equation instead of its full version . unfortunately , linear methods are known to break down when the density fluctuations reach the order of unity . indeed , in their two trial runs with chdm parameters , the linear results of sm compare favourably with @xmath6-body results of @xcite in the outer part of the halo , where the neutrino overdensity is relatively low . the denser inner parts ( @xmath15 ) , however , show marked disagreement . this discrepancy renders sm s claim that their complete prescription is able to probe neutrino clustering on sub - galactic scales doubtful . in the present investigation , we adopt one of the more attractive features of sm s study , namely , the use of parametric halo profiles as an external input . however , we improve upon their analysis by solving the vlasov equation in its ( almost ) full glory utilising a restricted , @xmath6-@xmath16-body ( pronounced : en - one - body ) method based on the following observation : in the limit @xmath17 and the cdm contribution dominates the total gravitational potential , not only will the cdm halo be gravitationally blind to the neutrinos , the neutrinos themselves will also have negligible gravitational interaction with each other . this allows us to track them one particle at a time in @xmath6 independent simulations , instead of following @xmath6 particles simultaneously in one single run , as in a conventional @xmath6-body study . an obvious advantage of our @xmath6-@xmath16-body technique is that it requires virtually no computing power when compared with a full scale @xmath6-body simulation with the same , large @xmath6 ( @xmath18 ) . it is also less time - consuming since we have done away with the need for a gravity solver ( the core of all @xmath6-body techniques ) . in addition , restricted methods such as ours do not suffer from spurious two body relaxation , and hence do not require the introduction of an artificial softening length that is mandatory in conventional @xmath6-body studies . lastly , we note that restricted methods have been used extensively in the studies of galaxy interactions ( e.g. , @xcite ) , and , when properly motivated , should not be seen as inferior to full scale @xmath6-body techniques . as a closing remark , let us stress again that our purpose here is not to investigate the effects of neutrino mass on cosmology , but rather to address some simple questions such as how many relic neutrinos can we realistically expect to find in this very space we occupy , what kind of energies do they have , where in the universe can we expect to find the highest concentration of relic neutrinos , etc . , given what we know today about cosmology . in this regard , the analysis we present here is most exhaustive . the paper is organised as follows . we begin in section [ cosm ] with an assessment of the current observational constraints on the relic neutrino background . in section [ vlasov ] , we introduce the vlasov equation which is used to track the phase space distribution of the neutrinos . section [ profiles ] contains a brief discussion of the halo density profiles to be employed in our calculations . in section [ onebody ] , we solve the vlasov equation for the halo models using our improved @xmath6-@xmath16-body method for a variety of halo and neutrino masses . in section [ linear ] , we compute for the same halo models and neutrino masses the neutrino overdensities using the linear method of sm and examine its validity . section [ milkyway ] deals exclusively with relic neutrinos in the milky way , and in particular their phase space distribution in our immediate vicinity . we discuss in section [ detection ] the implications of our findings for scattering - based detection methods , and we conclude in section [ conclusion ] . taking as our basis ( i ) the flat @xmath0cdm model with @xmath19 and hubble parameter @xmath20 , ( ii ) neutrino mass splittings inferred from the solar and atmospheric data , @xmath21 , and ( iii ) the invisible @xmath22 decay width from lep which constrains the number of @xmath23 doublet neutrinos to three @xcite , a minimal theory of neutrino clustering is fixed only by the absolute masses of the neutrinos @xmath24 . the current laboratory limit from tritium @xmath25 decay experiments is @xmath26 ( @xmath27 ) @xcite , and should improve to @xmath28 with the upcoming katrin experiment @xcite . cosmology also provides a constraint on @xmath24 . for three degenerate species , an upper bound of @xmath29 ( @xmath27 ) @xcite has been inferred from a combined analysis of the cmb anisotropy from wmap @xcite and galaxy clustering from sdss ( sdss - gal ) @xcite ( or from 2dfgrs @xcite ) , together with an hst prior on the hubble parameter @xcite . ( reference @xcite uses also snia @xcite ) .. ] adding to the fit galaxy bias @xcite and ly@xmath30 forest analyses can tighten the constraint to @xmath31 @xcite ( see also @xcite ) , although the robustness of these additional inputs is still contentious . weak lensing of galaxies @xcite or of the cmb @xcite will provide an alternative probe for the cosmological implications of massive neutrinos . while constraints from cosmology are interesting in their own right , they are also highly model dependent , and degeneracies abound . for instance , if tensors and running of the scalar spectral index are allowed , the last @xmath32 bound relaxes to @xmath33 @xcite . another possibility is an interplay between @xmath24 and @xmath34 , where @xmath34 is the _ effective _ number of thermalised fermionic degrees of freedom present in the radiation - dominated era , such that increasing @xmath34 actually weakens the bound on @xmath24 @xcite . for example , a @xmath35 model receives a cmb+lss+priors constraint of ( i ) @xmath36 , if all six particles are equally massive , ( ii ) @xmath37 , if three are massive and the others exactly massless , and ( iii ) @xmath38 , if only one is massive . currently , @xmath39 is allowed by cmb+lss+priors @xcite . future cmb experiments such as planck will be sensitive to @xmath40 @xcite lastly , we note that bbn prefers @xmath41 ( @xmath27 ) , in the absence of a @xmath42 chemical potential @xmath43 @xcite ( see also @xcite ) . allowing for a nonzero @xmath43 weakens the bounds to @xmath44 for @xmath45 @xcite . there is no lack of candidates in the literature for these extra @xmath46 degrees of freedom . we shall not list them here . what is certain , however , is that" +"exchange bias phenomena in layered structures@xcite and nanostructures@xcite attract a great deal of research effort related to fundamental issues regarding the underlying magnetization reversal mechanism and also their numerous technological applications ranging from biomedicine to magnetic recording industry . among the fundamental issues we mention the increase in coercivity that most commonly accompanies exchange biasing ( eb ) phenomena in antiferromagnetic ( af ) - ferromagnetic ( fm ) systems@xcite . for instance , chemically synthesized ni / nio nanocomposites show both large exchange bias and enhanced coercivity.@xcite in nanopatterned co / coo island structures a strong increase in bias and coercive field were found as the nanostructure size was reduced only for thickness below 12nm.@xcite in ( pt / co)@xmath0 multilayer stacks it was found that the coercivity depends sensitively on structural changes as subtle as a sub - monolayer interface oxidation of a ferromagnetic layer.@xcite recently it was reported that in the vicinity of the compensation composition in mn ga ferrimagnetic heusler alloy , a giant exchange bias field of more than 3 t and a large coercivity are established.@xcite monte carlo studies of exchange bias in fm / af bilayers@xcite show a weak increase of coercivity when the interface exchange coupling is stronger than the anisotropy of the hard af layer . interestingly , in many layered systems the coercivity of the fm layer as a function of temperature shows a peak at the blocking temperature , while as a function of the af layer thickness shows a maximum at the critical thickness below which eb disappears . within the large diversity of systems that exhibit eb several aspects of these phenomena have been explained using the random interfacial field model.@xcite the random interfacial exchange coupling can lead to the formation of af domains@xcite and furthermore , during magnetization reversal , can break the ferromagnetic layer into domains smaller than the ones occurring without the coupling to the antiferromagnetic layer.@xcite on the other hand , formation of volume af domains@xcite that can be controlled by diluting the antiferromagnetic layer with nonmagnetic substitutions@xcite has been used to explain a variety of typical effects associated with exchange bias . it is reasonable to expect that in the presence of random fields at an interface between a fm and an af layer , the domain walls in the fm layer are pinned at local energy minima@xcite and that for the domain walls to move , the applied magnetic field must be large enough to overcome the statistical fluctuations of energy . random pinning effects have been studied in cu / co spin valves biased by thermally oxidized nio layers with increased roughness@xcite . studies of the coupling between hard fept / cofe and soft cofe / nife bilayers through a cu interlayer show that the bias does not depend linearly on the percentage of hard magnetic layer switching but still the coercivity exhibits a maximum at the point of zero bias , which takes place at approximately 70% switching of the hard layer for the 3.5 nm cu buffer.@xcite in mnf@xmath1/fe bilayers it is found@xcite that when the antiferromagnetic surface is in a state of maximum magnetic frustration and the net exchange bias is zero , there is strong enhancement of the coercivity , which is proportional to the exchange coupling between the layers . the large number of different systems that exhibit eb , in combination with the lack of exact information on the interfacial spin structure in each case , are two main limiting factors in establishing a global theory of the exchange bias effect . hard fm - soft fm bilayer systems on the other hand , mostly in the weak coupling limit , have some resemblance with the archetype af - fm exchange bias systems@xcite in the sense that the minor hysteresis loop of the soft layer is biased by the hard . thus , much of the physics and reversal mechanisms are expected to be similar if the af layer is replaced by a hard fm as the biasing layer . at the same time hard - soft ( hs ) systems are simpler to understand since the magnetic state of the biasing layer is more straightforward to probe and adjust.@xcite in addition the hs fm bilayers offer bias tunability @xcite , that allows control over the loop shift and width through the field - dependence of the magnetic state of the hard layer . despite the anticipated less complex nature of the fm hs bilayers , conflicting trends on the correlation between the exchange bias field and the coercivity of co - based hs system have been reported . namely , although in both coptcrb / co and copt / co hs bilayers the exchange bias field shows a linear dependence on the hard layer magnetization , increasing coercivity with bias ( hard ) layer magnetization is reported for the coptb / co system@xcite and the opposite behavior is reported for the copt / co bilayer@xcite . this point motivated further investigation of the eb behavior of copt / co bilayers and the underlying magnetization reversal mechanism that is reported here . in the present work , we study the copt / co sputtered bilayers by standard magnetometry combined with monte carlo simulations that support the experimental findings and shed light on the underlying magnetization reversal mechanism . it is shown that in copt / co sputtered bilayers the eb field of the soft layer varies linearly with the hard layer magnetization , while the sample coercivity depends quadratically on the exchange bias field . our numerical simulations support the domain wall displacement mechanism as the dominant mechanism of magnetization reversal , in contrast to the case of coptcrb / co bilayers where an exchange - correlated coherent reversal mechanism was put forward.@xcite the co@xmath2pt@xmath3 films were deposited by magnetron sputtering at ambient temperature on oxidized si ( 001 ) substrates at a rate of 1.43 / s , in an ar gas pressure of 3 mtorr . the as - deposited films are magnetically soft and their xrd patterns indicate a fcc structure with ( 111 ) texture . in order to produce the bilayered hard - soft structure , after deposition of the bottom ( hard ) copt layer of thickness @xmath4=20 nm the films were annealed in high vacuum ( @xmath5 torr ) in order to crystallize the high anisotropy l1@xmath6 phase . then the sample was cooled to room temperature and the top ( soft ) co layer of thickness @xmath7=8 nm was deposited . the layer thicknesses were determined by x - ray reflectivity . the magnetic measurements were performed with a lake shore vibrating sample magnetometer ( vsm ) and in - plane magnetic field . the magnetic force microscopy ( mfm ) images have been obtained with the use of a nt - mdt scanning probe microscope in semi - contact mode . m@xmath8 and demagnetized state ( right ) of a sample area @xmath9m@xmath8 are shown.,title=""fig : "" ] m@xmath8 and demagnetized state ( right ) of a sample area @xmath9m@xmath8 are shown.,title=""fig : "" ] [ htb ! ] [ htb ! ] [ htb ! ] the mfm images of fig.[exp_mfm ] depict the remanent and dc - demagnetized states of a single copt hard layer . they represent areas of @xmath10m@xmath8 and @xmath9m@xmath8 , respectively . the demagnetized state is characterized by strong contrast maze - like domain patterns of average width @xmath11 m and length @xmath12 m . the remanent state has thinner reversed stripes ( typically @xmath13 m ) with smeared out contrast . to asses the effect of the magnetic state on the reversal of the soft phase , minor loops that characterize the soft layer reversal have been monitored for different magnetic states of the hard layer . this is feasible due to the weak coupling between the two phases evidenced by the fact that the full hysteresis loop shows a well defined shoulder between the switching of the two phases ( fig.[exp_full ] ) . thus the switching field distributions of the hard and the soft phases are well separated and the minor loops are well defined : a field of @xmath142 koe fully saturates the soft phase and yields a closed loop@xcite , but it does not affect significantly the hard one . families of minor hysteresis loops have been monitored for different magnetization states of the hard layer . in particular , the bilayer sample was first brought to positive saturation by applying + 20koe . then a reverse field @xmath15 in the range -20koe@xmath16 -3koe was applied , which drives the hard layer to a partially demagnetized state . a typical set of measurements is shown in fig.[exp_loops ] . as expected the minor loops are not centered in the origin of the m - h plots : the vertical displacement @xmath17 ( along the magnetization axis ) represents the contribution of the hard layer , that is , the part of the magnetic moment that remains unswitched during the sweep of the mirror loop . the loop displacement along the field axis represents the exchange bias field ( @xmath18)and the soft layer coercivity @xmath19 must be defined as the halfwidth of the loop . the squareness of the minor loop can be also defined analogously , taking of course on account the loop shift , as @xmath20 koe ) . the observed @xmath21 values are consistent with the @xmath22 value expected for a random in - plane easy axes distribution . an obvious observation is the linear relationship between @xmath18 and @xmath17 ( fig.[exp_hchbmr ] ) , which shows that the interfacial coupling can be described by a simple linear term , @xmath23 . that means that the interfacial ordering of the magnetic moments can be assumed to be represented by the magnetic state of the whole hard layer . this is plausible given that the exchange field ( @xmath24 650 oe ) is much lower than the coercivity of the hard layer ( @xmath24 5400 oe ) ( and its anisotropy field therefore ) and that the domains of a soft phase are expected to be much larger . the data can be described by a linear fit @xmath18(oe ) = @xmath25 . the coercivity as a function of the vertical shift , and consequently @xmath18 , shows a very simple quadratic dependence , which is more symmetric if we choose to plot @xmath26 versus @xmath18 . the data can be described as : @xmath26(oe)= @xmath27 this simple quadratic dependence is indicative of a possible link of the coercivity to the randomness of the magnetic state through the random interfacial exchange coupling . simply put , for an assembly of randomly oriented vectors of constant length say @xmath28 the standard deviation is expected to be @xmath29 . to gain further insight into the magnetization reversal mechanism leading to the experimentally observed characteristics of the ( minor ) hysteresis loops we have conducted a series of monte carlo simulations of magnetic hysteresis of a simplified system that shares the same major features with the sputtered samples . in particular , we assume that the morphology of the sputtered sample , due to its granular nature , can be adequately described by a two - dimensional array of identical bi - magnetic grains composed of a soft part exchanged coupled to a hard part ( fig . [ fig_film ] ) . the magnetization of the soft part is assumed to reverse coherently under application of an external field , while that of the hard part remains frozen . the effect of the hard - soft coupling across the interface of each grain can be therefore approximated by a local bias field ( @xmath30 ) acting on the soft part of the grain . the direction of the local bias field acting on grain-@xmath31 is taken in - plane , making a random angle @xmath32" +"graphene has drawn a lot of interest not only for their unique electronic properties @xcite but also for their unusual magnetic properties @xcite . magnetic ordering is typically observed in materials with partially filled d or f shell electrons . though there exists a large number of carbon based organic magnets with p electrons , the t@xmath0 is usually below 10 k @xcite . that is why observation of room temperature ferromagnetism in graphene related materials is so surprising . many theoretical works already exist to explain unusual magnetic property of graphene related materials . various reasons have been put forward for the formations of magnetic moments in graphene , such as , existence of zigzag edges @xcite , structural defects ( vacancies , adatoms , etc . , ) @xcite etc . , . zigzag edges induce highly degenerate localized electronic states precisely at the fermi level . these degenerate states are filled with electrons with the same spin in order to minimize the coulomb repulsion energy ( an effective hund s coupling ) . spin magnetic moments can also originate from the dangling bonds localized at the vacancy sites @xcite . j. zhou et . @xcite have predicted that moments can arise in semi - hydrogenated graphene sheets . l. xie et . @xcite observed room temperature ferromagnetism in partially hydrogenated epitaxial graphene . w. li et . @xcite theoretically showed that addition of monovalent and divalent adatom on graphene can also give rise to magnetic moments . this way of generating magnetic moment follows simply from lieb s theorem @xcite , which says that for half - filled bipartitite lattice systems the electrons in sublattice a and b are antiferromagnetically correlated . the ground state magnetic moment for such a system is , m= ( n@xmath1 -n@xmath2)@xmath3@xmath2 , where n@xmath1 and n@xmath2 are the number of a and b sublattice points . much less is known about the interaction and ordering if any between such local magnetic moments . vozmediano et . @xcite studied the interaction between localized moments mediated by rkky - like interaction but their calculated transition temperature was far below the room temperature . possibility of strong long range magnetic coupling via itinerant electrons in defective graphene ( vacancy or hydrogen chemisorption ) was predicted by yazyev and helm @xcite assuming metallicity of the system . l. pisani et . al . @xcite studied more realistic situation of a semiconducting ground state of defective graphene sheet and they suggested that long range spin magnetic ordering is possible in graphene . although there still persists a controversy that the observed magnetism is not its intrinsic property rather magnetism comes from ferromagnetic impurity present in the sample , experimentally ferromagnetism was observed in hopg only after proton irradiation @xcite and hence rules out the role of elemental impurity . y. wang et . @xcite observed room temperature ferromagnetism of partially reduced graphene oxide . but however , they did not stress on the evolution of magnetic hysteresis as a function of temperature , even though they observed an anomalous behaviour of increase in coercivity as a function of temperature . magnetic properties of graphene related materials depend upon their microstructure . structures of graphene oxide ( go ) and reduced graphene oxide ( rgo ) varies depending on the synthesis processes @xcite and consequently the magnetic property also changes @xcite . here , we have studied the magnetic property of go and partially reduced go from room temperature ( 300k ) down to 10k . we find that both go and rgo show hysteresis at room temperature and as the temperature is lowered the hysteresis loop diminishes . in this paper we will address this anomalous behaviour of diminishing of hysteresis loop upon lowering the temperature for both go and rgo and try to understand the difference in the magnetic behaviour between go and rgo . graphene oxide ( go ) was synthesized using modified hummers method @xcite . to prepare go we used graphite powder , conc . h@xmath4so@xmath5 , nano@xmath6 and kmno@xmath5 . the reaction of h@xmath4so@xmath5 with strong oxidizing agents such as nano@xmath6 and kmno@xmath5 results in increase in the interlayer separation of the carbon layers due to incorporation / intercalation of oxygen atoms . this reaction leads to formation of graphite oxide flakes having single or few layer sheets . the solution was further ultrasonicated and centrifuged . the supernatant was collected and dried in vacuum drying oven at 80@xmath7c to obtain single layer graphene oxide samples . these go sheets were reduced by strong reducing agent hydrazine hydrate to form rgo . the resulting suspension is filtered and washed with water and ethanol and dried in an vacuum oven . the samples were characterised by uv - vis , ftir , raman spectroscopy , and sem . magnetic measurements were carried out using squid mpms xl ( quantum design ) . magnetization data as a function of temperature and magnetic hysteresis data at three different temperatures 10 k , 100 k and 300 k were taken . the magnetic moment values observed are comparable with that in earlier reports @xcite . 1 shows the ftir spectra of both go and rgo . inset of the fig . 1 shows the uv - vis spectroscopy data . we observe that the uv - vis spectra of go shows a sharp absorption peak near 238 nm which is shifted to 252 nm upon reduction . the shift of the peak position of rgo is due to restoration of sp@xmath8 carbon network after removing the functionalized groups as suggested in ref . ftir spectroscopy data ( fig.1 ) also indicates the reduction of oxygen - containing groups from graphene oxide sheet . the characteristic bands of go around 1051 @xmath9 ( c - o ) , 1223 @xmath9 ( c - o - c ) , 1613 @xmath9 ( c = o ) , 1731 @xmath9 ( o = c oh ) and 3440 @xmath9 ( o - h ) are considerably decreased after the reduction which is consistent with the literature @xcite . in fig.2 we show the raman spectra of go and rgo showing two distinct peaks g and d. raman spectroscopy is a very important tool to study the average size of the sp@xmath8 region in sp@xmath8/sp@xmath10 combined material . graphene oxide shows the g peak near 1605 @xmath9 and d peak near 1370 @xmath9 which agrees with the previous reports @xcite . due to the reconstruction of the sp@xmath11 network at the oxidized region after reduction , the g peak in the rgo shifts to a lower wave number 1595 @xmath9 @xcite . in fig.3 we show the sem images of go and rgo . from the sem image we can clearly see that go shows folded layered structure and for the case of rgo , the sheets appear like unfurled structure . magnetization vs. temperature ( in log - log scale ) data of go and rgo are presented in fig . 4 . in this study a considerable magnetic moment has been observed in both samples . we observed less moment in rgo than go which we shall explain below . in the figure ( 5 @xmath12 6 ) we plot the magnetic hysteresis curve measured at three different temperatures ( 10 k , 100 k and 300 k ) for go and rgo respectively . m - t data on a log - log scale can be fitted with a straight line with a slope of -1 , from 10k upto about 60 - 70 k. almost no coercivity at 10 k supports paramagnetic behaviour at low temperature ( see inset of fig . 5 ) , but with increase in temperature , the hysteresis loop opens up i.e. , coercivity increases with temperature which is quite unusual . another interesting feature we observe is that with reduction of go , the magnetic moment decreases but coercivity increases . go has more paramagnetic contribution and does not saturate at high fields , while reduced graphene oxide ( rgo ) shows approach to saturation at high field along with larger coercivity indicating that upon reduction the magnetism in rgo becomes more cooperative in nature . several theoretical works have tried to explain ferromagnetism in graphene . m. wang et . shows by dft calculation that oxidized graphene can be ferromagnetic @xcite . ftir spectra indicate that graphene oxide has considerable amount of oxygen and oh groups in it . presence of the functionalized groups ( epoxide [ -o- ] , hydroxyl [ -oh ] , carbonyl [ -c = o ] and carboxyl [ -cooh ] ) on the graphene skeleton leads to disruption of sp@xmath8 bonded carbon network at many places . many topological defects are also formed , leading to local crumpling of planar graphene sheets . deviation from the planarity decreases the efficiency of @xmath13-overlap which reduces the connectivity of the @xmath13 network and causes an increase in @xmath14@xmath15 energy gap of the localized double bonds , hence reducing the ring current diamagnetism . therefore magnetic susceptibility / moment can increase upon oxidation of graphene @xcite . on the other hand , disruption of the hexagonal sp@xmath8 bonded carbon network presumably create many topological defects and isolated dangling bonds which carry local moments @xcite and also functionalized oxygenic groups ( -o - h ) can introduce localized magnetic moments @xcite . after on reduction of go , these functionalized groups are removed . this leads to two effects , ( 1 ) the @xmath13 electron with which the functional group was bonded is released as a carrier , and ( 2 ) the local crumpling of the planar carbon network caused due the presence of functional group is cured and locally the planar structure is restored . we can assume that there will be lesser oxygenic groups , defects , ruptures in the rgo compared to go . we find lesser paramagnetic moments in rgo compared to go as can be observed from fig . 4 of m versus t plot . this gives an indication that the magnetization is proportional to the amount of defects such as oxygen and hydroxyl impurities . thus , the magnetic moments in go and rgo is defect in origin . pure graphene is electronically half filled ( one @xmath13 electron per site ) on a bipartite lattice . the @xmath13 electrons on a and b sublattice are antiferromagnetically correlated . go and rgo are electronically insulating and so a description in terms of hubbard type model in real space rather than extended band electron picture is more appropriate . it has been shown that a strong impurity potentials like vacancy or any chemisorbed defect induces short range antiferromagnetic ( ferrimagnetic ) order around itself in a hubbard model on a half filled honeycomb lattice ( just like graphene ) @xcite . the net magnetic moment in a short range antiferromagnetic cluster is given by , m@xmath16@xmath17 -n@xmath18 as mentioned earlier . oxygen atoms bonds with two near neighbor c atoms of opposite sublattices and hence do not give rise to any local moment . oh on the other hand binds with only one c atom ( either a or b sublattice ) on graphene , this can create a local imbalance in n@xmath19 and n@xmath20 leading to a local moment @xcite . in a similar way atomic vacancy ( missing c atom ) can also create magnetic moment . we assume that go sheets have many patches of oh clusters , this patches are structurally distorted and electrically insulating locally because of gap at the local fermi level . nearest neighbour interaction between these @xmath13 electrons within such a patch is antiferromagnetic ( superexchange ) . the magnetic moment of such a small patch is @xmath21 . this uncompensated moment resides at the boundary of the patch . it is like an uncompensated nanosized antiferromagnetic particle with a" +"a broad range of diffusive processes on networks , from consensus formation @xcite to current flows on electric circuits @xcite , can be modeled by random walks or , equivalently , by markov chains . their unbiased exploration of the underlying structure also makes them popular tools for designing algorithms for , e.g. , navigation and search on networks @xcite , defining central nodes in a given network @xcite , community detection @xcite , and respondent - driven sampling @xcite . in tandem with these applications , the impact of network structure on dynamics of random walks , including the hitting time , mixing time , and stationary density has been extensively studied . however , recent studies identified limitations of the classical network paradigm , where dynamics is modeled by a dynamical process on a static underlying structure . in a broad range of empirical systems , evidence suggests instead that dynamics presents non - trivial correlations between events and long - tailed interevent time distributions @xcite . these observations are incompatible with the poissonian statistics implicitly assumed in stochastic models , therefore calling for richer models for temporal networks @xcite . an important practical question concerns the impact of the temporality of a network on diffusion . in order to address this question , a first approach consists in simulating random walks on real or synthesized data of time - stamped event sequences , and to compare their dynamical properties to those of properly defined null models @xcite . a second approach consists in studying analytically the properties of random walks on specific models of temporal networks . in most studies , however , network structure changes at regular time intervals , and transitions between networks at different times are independent @xcite or markovian @xcite . in the present work , we follow the latter path to analytically model diffusion under the non - poissonian nature of interevent times . previous studies proposed modeling temporal networks as stochastic sequences of events obeying a prescribed distribution of interevent times attached on each link @xcite . a random walk process , called the active random walk , was then defined as a renewal process ; i.e. , after a walker arrives at a node , the interevent times attached to all links incident to the node are reinitialized @xcite . despite its non - markovianity owing to the fact that the rate at which an event takes place depends on the time of the previous event , this stochastic process can be described by a generalized master equation , and some of its properties , such as the stationary density @xcite and the relaxation time @xcite , were analytically solved . in this work , we will first derive an analytical expression for the mean recurrence time for the active random walk . then , we consider a different non - renewal process , called the passive random walk , in which interevent times are reset only on the links traversed at each jump . we will use the fact that the passive random walk shows a stronger non - markovianity than the active random walk does because passive random walkers remember their past trajectories to some extent . finally , we will perform numerical simulations to test our analytical predictions and compare the stationary density and mean recurrence time between the two types of walks . we consider an undirected network on @xmath0 nodes . we denote the set of nodes by @xmath1 and the set of links by @xmath2 . we often refer to this network as the aggregate network because it is considered as the aggregation of the temporal network , which we introduce in the following , across time . stochastic temporal networks add a time dimension to the aggregated networks by assigning a random interevent time @xmath3 to each link @xmath4 in a renewal manner @xcite . for a chain network of three nodes , a hypothetical sequence of interevent times is depicted in fig . [ fig : schematic passive ] . the interevent time , denoted by @xmath5 , @xmath6 , @xmath7 , for link @xmath8 in fig . [ fig : schematic passive ] , is the interval between two consecutive activation events of the link . we denote the probability density function ( pdf ) of @xmath3 by @xmath9 . we assume that the mean of @xmath3 is finite . link activation is an instantaneous event , and we assume that the random walker moves from the current node to the neighboring node through the activated link whenever it is possible . the example shown in fig . [ fig : schematic passive ] indicates that , if the walker starts from node 1 at @xmath10 , it moves to node 2 at @xmath11 . then , it moves back to node 1 at @xmath12 . after coming back to node 2 at @xmath13 , the walker transits to node 3 at @xmath14 . some remarks are in order . first , some activation events , such as those immediately following the interevent times @xmath15 and @xmath16 , may not be used by a walker . second , although the walker s movement as illustrated in fig . [ fig : schematic passive ] may look deterministic , it is stochastic because the interevent times are random variables . third , the probability that more than one links are simultaneously activated is equal to zero because the model is defined in continuous time . fourth , the walker is assumed not to have any internal waiting time . therefore , the walker instantaneously moves upon the activation of a link incident to the walker s location . fifth , the continuous - time nature of our model makes it different from the previously proposed discrete - time random walk defined on the so - called activity driven model @xcite . a main difference between the present model and those considered in ref . @xcite is that the former generates interevent times from a given pdf , which lends itself to an analytical study of the process , whereas the latter uses interevent times observed in real data ( and their randomizations ) , more appropriate for the study of empirical data . we analyze two versions of random walks on stochastic temporal networks @xcite . the first version is the so - called active random walk . in the active random walk , when the random walker arrives at a node , it reinitializes the interevent times on all links , which makes the process renewal . in this case , the waiting time , i.e. , the time for which a walker waits on a node before the link appears , is equivalent to the interevent time @xcite . in the example shown in fig . [ fig : schematic active ] , once the random walker moves from node 1 to node 2 at @xmath11 , the new interevent times , denoted by @xmath17 and @xmath18 , are independently drawn . because @xmath19 , the walker moves to node 3 at @xmath20 . it should be noted that interevent times for link @xmath21 before @xmath11 do not matter for the movement of the walker in question , reflecting the renewal nature of the active random walk . phenomena in which a node starts something in response to an external input or the arrival to the node might be represented by the active walk . possible examples include the broadcasting of gossips @xcite and random surfing on the world wide web by users . in the latter case , a user that has arrived at a webpage may stay there looking at the content . then , after a randomly distributed amount of time , the user may decide to jump to a different webpage , which is selected with equal probability among the hyperlinks that the original page has . the second version is the so - called passive random walk , which does not assume the reinitialization at all links . when the random walker moves to a neighbor through link @xmath8 , a new interevent time is drawn only for @xmath8 . in fact , the example shown in fig . [ fig : schematic passive ] corresponds to the passive random walk . transmission of infectious diseases or information may be better described with the passive than active random walk because infection of a node does not seem to instantaneously affect interevent times on other links @xcite . in other words , to a first - order approximation , the inter - contact time on any link @xmath8 can be regarded to obey a given distribution and is not altered by whether an infection occurs upon the contact . then , a pathogen or piece of information starting from an initial node may travel to other nodes via the passive random walk . the complexity of the passive random walk lies in its non - renewal nature . in other words , transition rates of the passive random walk depend on the trajectory that the walker has taken such that we have to account for the entire trajectory of the random walker to accurately evaluate its behavior . it should be noted that for exponentially distributed interevent times the active and passive random walks are identical and reduce to the usual continuous - time random walk on the aggregate ( i.e. , static ) network . the walker starts at node 1 at @xmath10 . the link activation is represented by horizontal bars . @xmath22 ( @xmath23 ) represents the @xmath24th interevent time on link @xmath8 . the random walker follows the path indicated by the thick lines.,width=453 ] and follows the path indicated by the thick lines . note that @xmath18 is not the second interevent time on link @xmath21 . it is a realization of the interevent time drawn at @xmath11.,width=453 ] the steady state of the active random walk was derived through a master equation approach in ref . @xcite . in this section , we first review these results ( secs . [ sub : formulate active ] and [ sub : steady state active ] ) . then , we derive the mean recurrence time for the active random walk ( sec . [ sub : mean recurrence time active ] ) . the main results when the interevent times of different links are distributed according to a common pdf are shown in eqs . and for the steady state and mean recurrence time , respectively . we denote the probability that the random walker is located at node @xmath24 ( @xmath25 ) at time @xmath26 by @xmath27 . the normalization is given by @xmath28 . the rate at which the walker arrives at node @xmath29 from node @xmath24 at time @xmath26 is denoted by @xmath30 . the transition rate for a single walker to move from @xmath24 to @xmath29 at time @xmath26 is given by @xmath31 . the master equation that governs the random walk is given by @xmath32\\\ & = \sum_{j;(ji ) \in e } \left [ r_{i \gets j}(t)p_j(t ) - r_{j \gets i}(t)p_i(t ) \right ] . \notag\end{aligned}\ ] ] if the underlying static network is connected , which we assume in the following , the random walk is mixing and the stationary density , denoted by @xmath33 , is obtained if we set @xmath34 for all nodes @xmath24 . for exponentially distributed interevent times , the transition rate is given by @xmath35 where @xmath36 denotes the mean of @xmath37 , the interevent time on link @xmath38 . by combining eq . and @xmath39 , we conclude that the steady state is the uniform distribution @xcite . for arbitrary interevent time distributions , we can not usually calculate @xmath40 . in addition , @xmath40 may not be symmetric with respect to @xmath24 and @xmath29 so that the" +"the first face - on map of our galaxy was constructed by oort , kerr & westerhout ( 1958 ) from 21 cm observations , interpreting the observed gas velocities in terms of circular motions in a thin disk . this map revealed many arm like features in the gas distribution . more recent surveys of atomic hydrogen , molecular gas , hii regions , giant molecular clouds ( gmc ) , and other spiral arm tracers have helped to constrain the location of galactic spiral arms . the majority of observations appear to be consistent with a four armed spiral pattern as suggested by georgelin & georgelin ( 1976 ) ; see the review in valle ( 1995 ) . the gas in the inner galaxy is not on circular orbits , however . this is most evident from the so called ` forbidden ' velocities which would then imply gas in counterrotation . the most prominent example is the 3-kpc - arm , which appears in the @xmath0-diagram at negative radial velocities on both sides of the galactic center . in the direction of the galactic center this arm is seen in absorption , which indicates that it passes between the sun and the galactic center . in recent years , near - ir observations with the cobe satellite have motivated a series of new studies aiming to understand the dynamics of the inner galaxy . the nir maps obtained with dirbe clearly show signatures of non - axisymmetric structure in the galactic bulge . dwek _ et al_. ( 1995 ) used parametric bar models to determine the basic properties of this triaxial bulge . full advantage of the observed asymmetries was taken by binney , gerhard & spergel ( 1997 ; bgs ) , who applied a newly developed richardson lucy deprojection algorithm . by assuming that the bulge has three mutually orthogonal planes of symmetry , they recovered approximately the 3d distribution of nir light in the galactic center . for their favored bar inclination of @xmath1 , the bulge has axis ratios 10:6:4 and semi major axis @xmath2 . it is surrounded by an elliptical disk that extends to @xmath3 . outside the bar , the deprojected near ir luminosity distribution shows a maximum @xmath4 down the minor axis . here we report gas dynamical simulations in this model and compare to the observed spiral arm structure of the galaxy . to follow the gas flow we have used a two - dimensional ( 2d ) ` smoothed particle hydrodynamics ' ( sph ) method , which has a large dynamical range in resolution and can include self - gravity . we assume an isothermal equation of state . see englmaier & gerhard ( 1998 ; eg ) for more details . [ cols=""^,^,^,^,^,<"",options=""header "" , ] r8.0 cm here we describe the gas flow in the deprojected mass model of bgs for @xmath1 , and assume that the potential rotates with a constant pattern speed @xmath5 , such that the corotation radius falls between the molecular ring and the 3-kpc - arm at @xmath6 . the morphology of the gas flow ( fig . 2 ) is insensitive to the choice of these parameters within reasonable bounds ; see eg . in these models a four armed spiral pattern forms , driven by the rotating triaxial bulge and elliptical disk , and the strong mass concentrations on the bar minor axis with negative quadrupole moment . the latter are presumably signatures of the spiral arm heads of the arms embedded in the molecular ring at @xmath7 radius . the model arm tangents can be identified with the five observed arm tangents ( see table ) . the model arms also give a reasonable representation of the locations of hii regions and gmc s in the @xmath0-diagram ( see fig . 1 ) . finally , the model gives a good approximation for the terminal velocity curve ( tvc ) , and hence the galactic rotation curve , for @xmath8 without including a dark halo component . the observed tvc is used to fix the unknown velocity scale of the model , assuming a distance to the galactic center @xmath9 and an lsr velocity @xmath10 . one spiral arm in the model qualitatively corresponds to the 3-kpc - arm . the tangent of the model arm is at the correct longitude , however , the non - circular motion at @xmath11 is somewhat smaller than for the observed 3-kpc - arm . it has always been a puzzle why we do not see a symmetric counter arm for the 3-kpc - arm at the far side of the galaxy . the counter arm in our model runs almost parallel in the @xmath0-diagram to another arm which ends at about @xmath12 . in fact , the observed arm there is known to split into two parts ; see the two concentrations of warm co clouds at @xmath13 and @xmath12 , indicating the presence of two shocks ( solomon _ et al_. 1985 ; arrows in fig . 1 ) . our model does not include a live stellar disk . thus the gravitational force of the stellar spiral arms is not included . however , we can use the gaseous arms as tracers to estimate the influence of stellar spiral arms : we take a fraction of the mass from the stellar background disk model and add it to the mass in gas particles . this extra mass does not , however , enter the hydrodynamical equations . then we smooth the potential of the extra mass over @xmath14 , to mimic the fact that the stellar arms are much broader than gaseous arms . the resulting gas flow is similar to the previous one , in particular , the spiral arm tangents are hardly changed . the most significant difference is that now the 3-kpc - arm displays just the right amount of non - circular motion . in nature , gaseous spiral arms are driven by stellar spiral arms . in our model , however , both are driven by the bar and the non - axisymmetric features in the disk . ) and gmc ( @xmath15 ) and observed tangents ( lines ) . the bar major axis is horizontal , and the sun is at @xmath16 , @xmath17 . , title=""fig:"",width=328]-5 mm the idea of a four armed spiral pattern goes back to georgelin & georgelin ( 1976 ) , who used hii regions as tracers for spiral arms . in fig . 2 we compare the face - on view of our model to the tracer positions inferred from their and other more recent studies including surveys of gmc s ( see eg for references ) . note that this plot does not take into account the non - circular motions of the tracers . correcting for this effect will focus the points towards the spiral arms , due to velocity crowding ; thus the correspondence will improve . beuermann , k. _ et al_. , 1985 , , 153 , 17 binney , j.j . , gerhard , o.e . & spergel , d. , 1997 , , 288 , 365 bloemen , j.b.g.m . _ et al_. , 1990 , , 233 , 437 burton , w.b . , shane , w.w . , 1970 , iau symp . w. becker , g. contopoulos , reidel , dordrecht , p. 397 chen , w. _ et al_. , 1996 , , 120 , 315 clemens , d.p . , 1985 , , 295 , 422 cohen , r.j . _ et al_. , 1980 , , 239 , l53 dame , t.m . _ et al_. , 1986 , , 305 , 892 downes , d. _ et al_. , 1980 , , 40 , 379 dwek , e. _ et al_. , 1995 , , 445 , 716 englmaier , p. & gerhard , o.e . 1998 , , _ in press _ georgelin , y.m . , georgelin , y.p . , 1976 , , 49 , 57 grabelsky , d.a . _ et al_. , 1987 , , 315 , 122 hayakawa , s. _ et al_. , 1981 , , 100 , 116 henderson , a.p . , 1977 , , 58 , 189 lockman , f.j . , 1979 , , 232 , 761 oort , j.h . , kerr , f.t . & westerhout , g. , 1958 , , 118 , 379 solomon , p.m. _ et al_. , 1985 , , 292 , 19 valle , j.p . , 1995 , , 454 , 119 weaver , h. , 1970 , iau symp . 38 , eds . w. becker , g. contopoulos , reidel , dordrecht , 126" +"over 70 extra - solar planets have now been detected since the discovery of a companion to the solar - type star 51 peg in 1995 ( mayor & queloz 1995 ) . all of these planets have been discovered via the radial velocity technique , in which the planet s presence is inferred by the central star s motion around the system s barycentre . instrumental and intrinsic noise limit the sensitivity of these studies to saturn - mass companions in short - period orbits , with more massive companions detectable in more distant orbits . the duration of current programmes limits this to @xmath23.5au ( fischer et al . 2002 ) , although some systems do display interesting trends indicative of more distant companions . therefore , we have little information on systems with massive companions at large radii , such as our own solar system . the only constraint on jovian - like systems comes from micro - lensing statistics , which suggest less than @xmath3 of m stars have jupiter - like planets orbiting at @xmath4au ( albrow et al.2001 ) . the planets discovered by the radial velocity technique are not open to further _ direct _ study , due to their close proximity to the much brighter parent star . the only exception to this is the transiting companion to hd209458 ( @xmath5 days ) . transit photometry shows this planet is a gas - giant , and charbonneau et al . ( 2002 ) have recently detected sodium in its atmosphere . still , the planet itself can not be directly imaged . several groups have conducted imaging surveys of nearby main sequence stars to search for low mass companions , including the use of adaptive optics , coronographs and space - based observations with hst ( e.g. turner et al.2001 , neuhuser et al . 2001 , oppenheimer et al . 2001 , kuchner & brown 2000 , schroeder et al . however , the extreme contrast ( @xmath620 magnitudes ) and small separations ( 5au@xmath7 at 5pc ) between main sequence stars and jovian planets makes sensitive surveys very difficult . to date , no planetary mass companions to nearby stars have been imaged , although several brown dwarf companions have been detected via direct imaging ( e.g. nakajima et al . 1995 ) . the end state of main sequence stars with m@xmath88 , white dwarfs , are typically 10@xmath910@xmath10 times less luminous than their progenitors . thus , there is potentially a strong gain in the brightness contrast between a planet and a white dwarf when compared to a main sequence star , assuming that planets can survive the late stages of stellar evolution . the gain in contrast is strongest in the mid - infrared , where the planet s thermal emission peaks well into the white dwarf s rayleigh - jeans tail . indeed , ignace ( 2001 ) has suggested that excess infra - red emission could be detectable from a hot jupiter orbiting a 10,000k white dwarf at a distance of @xmath11 white dwarf radii and with an orbital period of @xmath12 days . chu et al . ( 2001 ) have also suggested that , near a hot uv - bright white dwarf , the atmosphere of a jovian planet would be photoionized and emit variable hydrogen recombination lines , which may be detected by high - dispersion spectroscopic observations . however , both these methods rely on the planet being in a close ( 0.012au ) proximity to the white dwarf , where it would be difficult to resolve . in this letter , we discuss the potential for imaging planetary companions in wide ( @xmath135au ) orbits around nearby white dwarfs . in section 2 we investigate the probability of a planetary system surviving the late stages of stellar evolution . we discuss the detectability of any surviving planets in section 3 , suggest suitable target white dwarfs in section 4 , and discuss the expected frequency of wide planetary companions to white dwarfs in section 5 . any planetary companion to a white dwarf must have survived the red giant branch ( rgb ) and asymptotic giant branch ( agb ) phases of stellar evolution . during these stages , the white dwarf progenitor swells up to a few hundred solar radii in size and undergoes significant mass loss . what happens to a planet during this time depends on the initial orbital separation , the stellar mass loss rate , the total mass lost , tidal forces , and interaction with the ejected material . any planet in an initial orbit within the final extent of the red giant s envelope will be engulfed and migrate inwards . livio & soker ( 1984 ) showed that these planets will either completely evaporate or accrete mass and become a close companion to the eventual white dwarf . planets in wider orbits that avoid direct contact with the expanding red giant envelope ( such as the jovian planets of our own solar system ) will have a greater chance of survival , migrating outward as mass is lost from the central star . however , stars more massive than the sun lose more than half of their original mass in evolving to the white dwarf stage ( weidemann 1987 , wood 1992 ) . if over half the mass of the central star is lost _ instantaneously _ then any accompanying planets will likely escape , since their orbital velocity will suddenly exceed the escape velocity of the system . thus , we might naively expect no white dwarfs to retain planetary systems . of course , in reality , main sequence stars of m@xmath148.0 do not evolve into white dwarfs instantaneously . mass loss on the rgb and agb , and final ejection of the planetary nebula is a relatively slow process . the sun , for example , will lose around @xmath15 on the rgb in @xmath210@xmath16 years , and up to another @xmath15 on the agb on a timescale of up to @xmath210@xmath17 years . the final thermal pulse , in which the cool red giant develops a super - wind and finally ejects the remainder of its envelope , exposing the core , is poorly understood but probably occurs on a timescale of a few @xmath1810@xmath10 years ( soker 1994 ) . the dynamical timescale for a planet to react to the change in the mass of the central star , and thus the gravitational force between the star and planet , is given by ; @xmath19 where @xmath20 is the semi - major axis of the orbit and @xmath21 is the orbital velocity , and ; @xmath22 where @xmath23 is the mass of the central star and @xmath24 is the mass of the planet . assuming @xmath25 ; @xmath26 this is much less than the mass loss timescales mentioned above . even if a @xmath27 star lost its entire envelope ( @xmath28 ) during a short pn phase of @xmath29 years ( which it does nt , only the last few tenths of a solar mass ) , the orbit would not become unbound . thus , to a first approximation , the orbits of planets which do not interact directly with the red giant will simply expand adiabatically by a maximum factor m@xmath30/m@xmath31 ( jeans 1924 , zuckerman & becklin 1987 ) . for example , for a main sequence star @xmath22 and a white dwarf @xmath20.6 , the orbit would expand by a maximum factor @xmath23 . a planet in a jupiter - like orbit would be relocated to @xmath215au , and a planet in a neptune - like orbit to @xmath290au . for planets in orbits @xmath810au , tidal forces between the planet and red giant are important in slowing orbital migration by transfering angular momentum from the orbit to stellar rotation . for example , soker ( 1994 ) shows that , neglecting tidal forces , as the sun evolves to a white dwarf jupiter s orbital radius will expand from its present value of @xmath32 to @xmath33 . however , tidal forces on the rgb will counteract this expansion , reducing this final orbital radius by @xmath34% , and by a further @xmath35% on the upper agb . for planets within 5au , livio & soker ( 1983 ) showed that tidal interactions will actually cause them to migrate _ inwards_. soker ( 1996 ) suggests that tidal interactions between evolving red giants and low mass companions could be responsible for producing the large fraction of elliptical pn observed , indicating low mass companions may be common amoung pn progenitors . the orbits of distant planets will also be subjected to drag resulting from their interaction with the material ejected by the central star . duncan & lissauer ( 1998 ) define the total amount of material impacting a planet during post - main sequence evolution as ; @xmath36 \\ & & \times \left(\frac{v_{sw}^2 + v_{orb}^2}{v_{sw}^2}\right)^{1/2 } \left(1 + \frac{v_{esc}^2}{v_{sw}^2 + v_{orb}^2}\right)\\ \label{eq : accrate}\end{aligned}\ ] ] where @xmath37 , @xmath21 and @xmath38 are the velocities of the stellar wind , the planet and the escape velocity of the planet respectively , and @xmath39 is the radius of the planet s magnetosphere . evaluation of this equation , however , shows that gas giants will collide with significantly less than 1% of their own mass over the entire red giant phase . the orbits will decay inwards only slightly as a result . duncan & lissauer ( 1998 ) have made detailed simulations of the effects of post - main sequence mass loss on the stability of the solar system and for planetary systems around more massive stars . they show that the orbits of the giant planets will probably be stable for tens of billions of years subsequent to the sun s death . however , planetary systems dynamically similar to our own around somewhat more massive stars may eventually be de - stabilised . duncan & lissauer s calculations show that giant planets around , for instance , an initially @xmath40 star , will be liberated by large - scale chaos in less than a hubble time . finally , soker ( 1999 ) points out that the newborn planetary nebula central star is hot ( t@xmath41k ) and a strong source of ionizing soft x - ray and uv radiation . the interaction of this radiation with a planet may lead to ablation of the planetary atmosphere , but this will only be effective for planets having an escape velocity @xmath42 , where @xmath43kms@xmath44 is the sound speed of the ionised planetary material . for a jupiter - mass planet @xmath45kms@xmath44 and thus there will be negligible ablation . it seems likely , then , that giant planets in initially distant ( a@xmath135au ) orbits around main sequence stars @xmath46 will survive the late stages of stellar evolution , and remain in orbit around the remnant white dwarfs at increased orbital radii for at least several billion years . our ability to detect an extra - solar planet around a nearby white dwarf will depend on its intrinsic luminosity , which in turn depends on its age , its distance from us , and its separation from the parent star . burrows et al . ( 1997 ) have made nongray calculations of the expected spectra , colours and evolution of solar - metallicity massive planets . we have used these models to predict the infra - red magnitudes of planets around nearby white dwarfs . the burrows et al . models describe the evolution of a planet in isolation , and do not include the effects of thermal insolation by , or reflected light from , a parent star . in reality , gas - giant planets will have been kept warm throughout their lives by the white" +"since its fabrication in 2004 @xcite , single and few layers graphene have been extensively studied and the documentation of this family of materials remarkable electronic properties @xcite has fuelled speculation as to their role in the next generation of electronic and spintronic devices . initially , research was predominantly directed towards the single layer variant . however , it s gapless nature is problematic with regard to developing usable graphene transistors @xcite and , although a number of methods have been suggested for gap generation in monolayer graphene @xcite , tailoring the materials electronic properties still remains a major challenge . one alternative solution is to move to the multi - layer variant . the extra layers of bi- , tri- and few layer graphene lead to greater flexibility with regard to band structure engineering . in particular , bilayer graphene ( blg ) has been shown to be remarkably versatile . as with single layer graphene it is a gapless semimetal with the fermi energy running through the dirac point , though the four bands of blg are hyperbolic rather than linear @xcite . however , the bi - layer structure makes it possible to electronically gate the two sides of the material . this bias field changes the relative potential of each layer opening a direct bandgap @xcite , converting blg from a semimetal to a semiconductor , a more useful electronic configuration for electronic device applications . another method for altering the electronic properties of a material is the use of strain . the band structure of a material is directly related to its crystal lattice . thus , by applying an external force and distorting the material s crystal structure one can change its electronic response . this approach to band structure engineering has been studied extensively for both mono- and bi- layer graphene . specifically for the latter , uniform in - plane strains @xcite and changes in the interlayer distance @xcite have been considered as well as interlayer shearing @xcite and the effect of flexure on the dirac points @xcite . however , previous work has mainly focussed on unbiased blg . the effects of a simultaneous bias field and strain have yet to be studied . here we report on the prediction that a biased blg ribbon under a layer - asymmetric strain ( where the upper layer undergoes compression and lower layer tension or visa - versa ) will first be converted from a direct to an indirect band gap material and , under larger bending strains , will convert back from a semiconductor to a semimetal . the conversion from direct to indirect band gap will lead to longer lifetimes for electron - hole pairs at the band minima since direct recombination no longer conserves momentum and hence is suppressed - a feature that could be useful in applications where carrier lifetime is important . the most notable effect of the semiconductor - semimetal transition is a sharp change in the conductivity with a higher strain leading to a higher conduction . the magnitude of this effect is dependent on the bias field with a stronger bias field leading to a larger change in the conductivity . such a strain configuration occurs when a material undergoes bending or can be induced by substrate strain by sandwiching the material between substrates with larger and smaller lattice constants , respectively . to the two layers breaks the degeneracy moving one to a lower energy and one to a higher energy . ( iii ) application of compressive and tensile strain to opposing layers moves one dirac cone to higher momenta and the other to lower momenta . ( iv ) the van der waals coupling that bonds the two layers of the blg ribbon hybridizes the two dirac cones leading to a ` skewed double well ' topology for the bands which if severe will convert the the ribbon from a semiconductor to a semimetal . ( c ) the band structure of a unbiased ( dashed ) and biased blg ( solid ) in the absence of a layer - asymmetric strain ( i ) and in the presence of a layer - asymmetric strain ( ii ) . ] a brief qualitative analysis illustrates the physical mechanism behind the effect . consider a blg ribbon subject to compression on the upper layer and tension on the lower layer [ see fig . [ diag ] ( a ) ] . compression narrows the unit cell of the crystal lattice and hence stretches the brillouin zone . as a result , the dirac points are move outwards to higher momenta . tension , on the other hand , lengthens the units cell and hence the brillouin zone contracts moving the dirac points to lower momenta [ see fig . [ diag ] ( b ) ] . this opposing shift of the dirac points of the two layers leads to ` @xmath3-space skewing ' of the bands , generating the indirect gap . at high strains , the conduction band is pushed below and the valence band rises above the fermi energy , generating a carrier population in the bands and a non - vanishing conductivity [ see fig . [ diag ] ( c ) ] . the rest of the paper will be devoted to a quantitative analysis of this effect . firstly , we relate the applied strain to the changes in the electronic properties of the material by computing the electronic band structure of a strained blg ribbon . to do this , we substituting the strain tensor for the deformation into the microscopic tight - binding model for blg , a well known technique from previous studies of strained graphene @xcite . from the band structure it is possible to derive the electronic properties of the material . secondly , we will discuss the ability to generate such strains via bending . the crystal structure of blg consists two monolayer graphene sheets weakly bound via inter - layer van der waals forces . the two sheets exhibit bernal stacking where the @xmath4 sublattice of the upper ( + ) sheet aligned vertically with the @xmath5 sublattice of the lower ( - ) sheet [ see fig . [ lat ] ] . the length of the in - plane lattice vector is @xmath6 and the nearest - neighbour vectors read @xmath7 each with length @xmath8 . in order to evaluate the band structure of blg under a layer - asymmetric strain we use a nearest - neighbour tight binding model @xcite . previous studies have considered higher order inter - layer hopping terms in the hamiltonian @xcite . this leads to added structure near the dirac point - the single parabolic minimum splits to give four dirac cones . however , the energy scale of these features is small , @xmath9 , and hence are only observable in the most pristine of blg samples where impurity generated disorder has not obscured them @xcite . thus , for most applications , where the blg samples are not sufficiently free of impurities or the energy scale of the effect is greater than a few @xmath10 , the nearest - neighbour hopping suffices . furthermore , one finds that the application of a bias field with an energy @xmath11 , as will be the case here , will also obscures these features . thus , in the following , we will consider only the nearest neighbour inter - layer hopping term . a brief discussion of the effect of the higher order inter - layer hopping terms can be found in appendix [ app : hot ] . we consider a strained blg ribbon subject to bias field of @xmath12 applied to the upper and lower layers , respectively . the ribbon is orientated such that the armchair edge is parallel to the @xmath13-axis ( results for other orientations can be found by a simple rotational transformation of the strain tensor ) and is of sufficient size that confinement effects are negligible ( i.e. the band structure can be considered to be that of bulk graphene ) . the nearest - neighbour tight - binding hamiltonian for this system reads @xcite @xmath14 with @xmath15 the interlayer coupling and the electron hopping phase factor reading @xmath16 } , \label{f}\ ] ] where the sum over @xmath17 is the sum over all the in - plane nearest - neighbour vectors . here , @xmath18 is the strain - induced transformation of the in - plane nearest - neighbour vectors . the ribbon is subject to uniaxial compression in the @xmath13 direction in upper layer and equal ( but opposite ) uniaxial tension in the @xmath13 direction in the lower layer , hence @xcite @xmath19 where @xmath20 is the poisson ratio of graphene . ( the derivation of @xmath18 for a general bending strain can be found in appendix [ app : ebt ] and for the specific case of a layer - asymmetric strain induced by a central point load in appendix [ app : scl ] . ) the change in bond length also results in a change in the hopping potentials . here , @xmath21 $ ] is the renormalized hopping amplitude @xcite with @xmath22 the unstrained bond length , @xmath23 the strained bond length , @xmath24 the unstrained hopping amplitude and @xmath25 the hopping decay parameter . in principle , the opposing strains of in upper and lower layer will increase the distance between the @xmath26 and @xmath27 atoms thus changing the interlayer coupling @xmath15 . however , for even for strains of @xmath28 , the maximum discussed here , the change in this distance is @xmath29 and hence is negligible . the standard diagonalization of eq . and the usual expansion about the dirac points at @xmath30 leads to the low energy band structure of the bilayer graphene ribbon as a function of the applied bias field , @xmath31 , and the strain , @xmath32 . we evaluate the band structure for a graphene ribbon subject to a strain of up to @xmath33 and a bias field of up to @xmath34 . the unstrained hopping amplitude@xcite is taken to be @xmath35 , the poisson ratio @xcite @xmath36 , the interlayer coupling @xcite @xmath37 and the hopping decay parameter @xcite @xmath38 . in the absence of both a bias field and strain , bilayer graphene is a gapless semimetal . on the application of a bias field the potential difference between the upper and lower layer opens a gap and the material changes from a semimetal to a semiconductor . the band structure takes a ` double well ' form with two degenerate minima on either side of the dirac point [ see fig . [ diag]c ( i ) ] . application of a layer - asymmetric strain results in compression in the upper layer , shifting the band structure to larger @xmath39 , and tension in the lower layer , shifting the band structure to smaller @xmath39 . this causes one of the conduction band minima to rise in energy and the other to fall . similarly , the strain causes the corresponding valence band maxima to rise in energy and the other to fall . this breaks the degeneracy of the band extrema and results in the sudden generation of an indirect band gap [ see fig . [ diag]c ( ii ) ] . the difference in @xmath40 of the conduction and valence band extrema increases with both strain and bias field . this effect is shown in fig . [ indgap ] ( a ) . the change from a direct to indirect band gap will have a significant effect on the electronic properties of the ribbon . most notably the recombination lifetime of electron and hole pairs at the band minima will be greatly enhanced since phonon exchange with the crystal lattice" +"dy centauri is known as a hot r coronae borealis ( rcb ) star . rcb stars are a rare class of peculiar variable stars with two principal defining characteristics : ( i ) they exhibit a propensity to fade at unpredictable times by up to about eight magnitudes as a result of obscuration by clouds of soot , and ( ii ) they have a supergiant - like atmosphere that is very h - deficient , he - rich and c - rich . the subject of this paper , the remarkable star dy cen , one of the hottest rcbs , is even a peculiar rcb member on several accounts . it is one of the most hydrogen - rich rcbs . its circumstellar environment may be home to the fullerene c@xmath1 or more likely proto - fullerenes ( garca - hernndez et al . 2011a ; 2012 ) . in terms of its chemical composition , dy cen may have a composition that sets it apart from most rcb and extreme helium ( ehe ) stars see jeffery & heber s ( 1993 ) abundance analysis : dy cen is not only uncharacteristically h - rich but is very fe - poor with a very high s / fe ratio , thus has been classified as a minority rcb star ( lambert & rao 1994 ) ; i.e. , a rcb with extraordinarily high si / fe and s / fe ratios . however , jeffery et al . ( 2011 ) suggest that the fe abundance was greatly underestimated in 1993 . finally , dy cen is a single - lined spectroscopic binary ( rao et al . 2012 ) , the only known binary among rcbs . the origins of the hydrogen - deficient rcb and ehe stars are not presently fully understood . two proposals are commonly advocated . in one , a final helium shell flash or a very late thermal pulse occurs on a cooling white dwarf star ( iben et al . 1983 ; renzini 1990 ; herwig 2000 ) which swells the envelope of the star to supergiant dimensions for a few thousand years and the remaining hydrogen is convected in and consumed while helium and carbon are convected out to the surface . living examples are believed to be sakurai s object ( v4334 sgr ) and fg sge ( asplund et al . 1997 ; jeffery & schnberner 2006 ) . the other proposal involves the merger of two white dwarfs : a carbon - oxygen white dwarf accretes a helium white dwarf as a close binary orbit shrinks under the influence of energy loss by gravitational radiation ( webbink 1984 ; iben & tutukov 1986 ) . the merger leads to a swollen envelope around the c - o white dwarf which lasts a few thousand years . evidence from the chemical compositions of rcb and ehe stars suggests that most are products of a merger ( garca - hernndez et al . 2009 , 2010 ; pandey & lambert 2011 ; jeffery et al . 2011 ) . dy cen with an orbital period of about 39 days is experiencing mass loss and presumably mass transfer to a low mass companion . years . ] moreover , it is likely to have experienced mass loss and transfer previously in arriving at its h - poor condition . rao et al . ( 2012 ) suggest dy cen may evolve to a he - rich sdb star . many such sdb stars are binaries . in this sense , dy cen is a representative of a third way to form a rcb star . the fact that its supergiant phase is short - lived relative to life as a sdb accounts for the rarity of such hot rcbs relative to the sdb population . the presence of forbidden emission lines in dy cen s optical spectrum , was noticed in 1989 ( rao et al . 1993 ) . these lines were attributed to a nebula around dy cen . in this paper , we analyse the nebular lines and their evolution over two decades . nebular lines were especially prominent in a 2010 high - resolution spectrum with broad wavelength coverage . inspection of earlier spectra show that physical conditions in the region emitting the nebular lines have changed since 1989 . in particular , the electron density inferred from the ratio of the [ sii ] 6717 and 6731 lines increased about eight - fold from 1989 to 2010 . the general properties of dy cen s spectrum have been described by pollacco & hill ( 1991 ) , jeffery & heber ( 1993 ) , rao , giridhar & lambert ( 1993 ) , giridhar , rao & lambert ( 1996 ) and de marco et al . optical spectra are presently a combination of photospheric absorption lines ( e.g. oii , nii , siiii lines ) , emission lines due to a stellar wind ( mainly cii , hei often superposed on underlying absorption lines ) , and nebular emission lines of [ sii ] , [ nii ] , [ oi ] , [ feii ] , etc . in addition , circumstellar and interstellar lines from caii , nai , ki and other species as well as the enigmatic diffuse interstellar bands ( dibs ) are present in absorption ( garca - hernndez et al . 2012 ) . this paper considers new spectra from 2010 acquired as a result of an eso director s discretionary proposal . the spectra were obtained on four nights in february - march 2010 with the cross - dispersed echelle spectrograph uves at the vlt at eso s paranal observatory . the uves spectrograph was used with the 1.2 `` slit ( slit length of 8 '' and p.a.=0 degrees ) and the standard setting dic2 ( 390 + 760 ) . the seeing was always better than 1.5 "" and we obtained 11 individual exposures of 1800 s each ( total exposure time of 5.5 hours ) . since the nebular lines are not expected to change in a short time , the individual exposures were combined to increase the signal - to - noise ( s / n ) ratio . the s / n in the continuum at 4000 is @xmath2200 and at wavelengths longer than 6000 it is higher than 250 . the slit width is just about the size of the nebular diameter , as estimated later . the spectral resolving power is about 37000 , as estimated from o@xmath3 telluric lines at 6970 . wavelength coverage is from 3300 to 4500 , 5700 to 7525 and 7660 to 9460 . along with dy cen , hd 115842 a nearby b supergiant was observed with the same setup . hd 115842 was observed soon after the dy cen exposures on all nights to correct for telluric lines in the dy cen spectrum . the s / n of the hd 115842 spectrum is 300 even for a single night s observation . in addition to these spectra from 2010 , we draw on a spectrum obtained in 2003 from the 3.9 m aat with the university college london echelle spectrograph ( ucles ) . the ucles spectrograph was used with the 1.4 `` slit ( slit length of 6 '' ) and three individual exposures of 1200 s each were obtained . wavelength coverage is from 4780 to 8800 . the final s / n in the summed spectrum is 38 to 40 in the continuum at 6300 to 6750 spectral region . resolving power is about 40000 as estimated from telluric [ oi ] lines . also , considered here is the 1989 spectrum used by rao et al . this was acquired at ctio with the blanco 4-meter telescope and a cassegrain echelle spectrograph . the slit width was 2 "" , which gives a resolving power of about 18000 with the wavelength coverage from 5480 to 6830 in 1989 . a 1992 spectrum with blanco telescope covered the interval 5480 to 7080 at a resolving power of 35000 ( see giridhar , rao & lambert 1996 ) . dy cen was identified as a rcb variable by hoffleit ( 1930 ) from well - determined minima in 1897 , 1901 , 1924 , and 1929 . no rcb type minima have been recorded since 1958 ( bateson 1978 , a. a. henden 2010 , private communication ) . thus , dy cen is not an active rcb star and all the spectra discussed here were taken when the star was at maximum light . quantitative interpretation of nebular emission lines requires knowledge of the line fluxes and , hence , of the continuum fluxes across a spectrum . to obtain such fluxes , we use ubvri photometry of the star reported for the period 1989 - 2010 . dy cen has been slowly fading for the last 40 to 50 years ( bateson 1978 ; rao et al . this fading is independent of rcb - like events . we have collected ubvri photometry reported in the literature . figure 1 shows the variation of b , v , and r from 1970 to 2010 . = 8truecm the earliest published ubv magnitudes are from mid-1970 by marino & walker ( 1971 ) : v , b - v and u - b are 12.23 , 0.39 and -0.62 , respectively . u band measurements are few and were obtained only in 1970 ( see above ) and during the 1982 - 83 period at saao by kilkenny et al . the 1972 measurements are from v.e . sherwood ( quoted by rao , giridhar & lambert 1993 ) . pollacco & hill ( 1991 ) obtained bv mesurements during 1987 may and june . the 2007 bvri measurements are from the aavso . it is clear from the figure that there is a gradual increase in magnitude over 40 years . the total variation is about 0.90 magnitude in v and 0.83 magnitude in b in 37 years : the ( b - v ) colour variations are minimal . even ( u - b ) seems to be same in 1970 and 1982 - 83 . because of these very slow changes , we adopted the colours observed in 1987 for our spectroscopic observations in 1989 and the mid-2007 photometry for our 2010 spectroscopic observations to estimate continuum fluxes . the continuum fluxes are estimated from the ubvri colours after applying a correction for interstellar reddening for an e(b - v ) of 0.47 ( garca - hernndez et al . standard relations : @xmath4@xmath5 3.1 e(b - v ) and e(b - v)/e(u - b ) = 0.72 , @xmath6/ @xmath4@xmath50.75 and @xmath7/@xmath4@xmath50.479 have been used ( cardelli et al 1989 ) . flux calibrations given by drilling & landolt ( 2000 ) are adopted . reddening - corrected line fluxes are given in the table 1 for the 1989 , 1992 , 2003 , and 2010 observations . the s / n of the 2010 spectrum is over 200 to 250 . the uncertainities in equivalent widths ( eqws ) are 3% in weaker lines ( and less in strong lines like h@xmath8 ) . the photometric colours are more or less unchanged so resulting errors in flux are also expected to be around 3% or better . thus , the relative flux ratios are expected to be better than a percent . the 2003 spectrum s / n is about 40 and the uncertainty in fluxes are around 5% level . the 1989 and 1992 entries are from rao et al . ( 1993 ) and giridhar et al . ( 1996 ) , respectively . for some lines , corrections for blending with absorption or other emission lines are applied ." +"the main goal of this paper is to develop a general theory of flag bicolorings and the related concepts of coverings and pseudo - orientations . the idea of consistent colorings of the flags of a map with two colors has appeared previously in literature in different contexts . for instance , when the automorphism group of a map which is a polytope has two orbits on the flags , we may color the flags with two colors in such a way that flags in different orbits have different colors . these are called 2-orbit maps in @xcite , but this investigation requires the extra property that the maps be abstract . specific @xmath0-colorings of flags are equivalent to the concept of @xmath1-_compatible _ maps introduced in @xcite , where @xmath1 is a class of @xmath0-orbit maps . this concept , generalized to hypermaps is called @xmath1-_conservative _ in @xcite . in all these instances , the colorings are used as a tool to work with automorphisms of maps . although some of the motivations behind the bicoloring of flags come from maps admitting symmetries , the ideas can be applied to general maps . in this work we shall not make assumptions on the automorphism groups of the maps in consideration . maps admitting a bicoloring of flags in which adjacent flags have different colors are precisely maps on orientable surfaces ( see proposition [ oble012 ] ) . although the other types of bicolorings of flags that we consider in this paper do not have a known topological equivalence , some results on orientability do translate directly to analogous results on bicolorability . in this sense we may think of bicolorings of flags as a generalization of orientability of maps . the paper is organized as follows . sections [ sec : maps ] , [ sec : ori ] , [ sec : col ] introduce the concepts of maps , pseudo - orientations and bicolorings , respectively . a relationship between pseudo - orientability and bicolorings is provided in section [ sec : colori ] . section [ sec : op ] explores the impact on bicolorability of operations on maps . in section [ sec : doubles ] , we discuss a natural double cover of every map which is not bicolorable . the set of bicolorings of any map can be given a natural group structure . in section [ sec : everygroup ] we determine , for each possible group , which surfaces admit maps with the given group of bicolorings . finally , in section [ sec : mpx ] , we generalize some of the results about maps to higher dimensional structures . a map @xmath2 is , first and foremost , an embedding of a graph ( or pseudograph ) on a ( compact , connected ) surface so that the components of the complement of the embedding ( called _ faces _ ) are topologically open disks . we can , for example , regard the cube as an embedding of the graph @xmath3 on the sphere . the graph @xmath3 is an example of a graph which is _ bipartite _ , i.e. , its vertices can be colored with two colors so that every edge joins vertices of opposite colors . when speaking about maps , we will use the term _ vertex - bipartite _ to describe a map @xmath2 whose underlying graph is bipartite . similarly , we will call @xmath2 _ face - bipartite _ provided its faces can be colored with two colors so that each edge separates faces of opposite colors . we will call @xmath2 _ edge - bipartite _ provided that the edges can be colored with two colors so that edges which are consecutive around a face ( and hence around a vertex ) have different colors . to look more closely at the structure of a map , we find the following subdivision useful : choose a point in the interior of each face to call its _ center _ and a point in the relative interior of each edge to be its _ midpoint_. draw dotted lines to connect each face - center with each incidence with the surrounding vertices and edge - midpoints . the original edges and these dotted lines divide the surface into triangles called _ flags_. figure [ fig : cubeflags ] shows the subdivision of the cube into flags . if a face meets a vertex ( or an edge ) more than once , we emphasize that the face center is connected to each incidence each appearance of the vertex or midpoint . for instance , consider the map @xmath4 shown in the left of figure [ fig : m4 ] . this map has only one face , an octagon , four edges and only one vertex . nonetheless , the dissection into flags draws 16 dotted lines , dividing the octagon , and the map , into 16 flags , as shown on the right . , title=""fig:"",height=113 ] , title=""fig:"",height=113 ] each flag corresponds to a mutual incidence of face , edge , and vertex , though different flags may correspond to the same triple . let @xmath5 be the set of flags . then let @xmath6 be the permutations on @xmath5 which match each flag @xmath7 with its three immediate neighbors , as in figure [ fig : flags ] . in that figure , we see that @xmath7 and @xmath8 are adjacent along a face - center - to - edge - midpoint line . thus @xmath7 and @xmath9 differ only in their incidences to a vertex , a 0-dimensional face of @xmath2 . similarly , @xmath7 and @xmath10 differ only in their incidences to an edge , a 1-dimensional face , while @xmath7 and @xmath11 differ only in their incidences to a 2-dimensional face . notice from figure [ fig : flags ] that the flag @xmath12-adjacent to @xmath8 is also @xmath13-adjacent to @xmath14 . in other words , as permutations on @xmath15 and @xmath12 commute . we can take a slightly more abstract point of view by defining a map to be a pair @xmath16)$ ] where @xmath5 is a set of things called _ flags _ , the @xmath17 s and @xmath18 are fixed point free permutations of order 2 on @xmath5 , the _ connection group _ @xmath19 is transitive on @xmath5 , and @xmath13 and @xmath12 commute . this @xmath20 is often called the _ monodromy group _ of the map . we can then think of vertices in @xmath2 as orbits of @xmath21 in @xmath20 . similarly , edges correspond to orbits of @xmath22 and faces to orbits of @xmath23 . we will use the word _ kite _ or _ corner _ for the area within a face where two consecutive edges meet . more formally , a kite is the union of two flags which are @xmath24-adjacent . if @xmath2 and @xmath25 are maps on surfaces @xmath26 and @xmath27 , a _ projection _ from @xmath25 to @xmath2 is a function @xmath28 mapping @xmath27 to @xmath26 which is locally a homeomorphism at all points of @xmath25 except perhaps at vertices and/or face - centers , and which sends faces to faces , edges to edges , and vertices to vertices . in combinatorial terms , if @xmath29)$ ] and @xmath30)$ ] , a projection of @xmath25 to @xmath2 is a function @xmath28 mapping @xmath31 to @xmath5 such that @xmath32 for all @xmath33 . we call such an @xmath25 a _ cover _ of @xmath2 . notice that if @xmath25 is a cover of @xmath2 , and the pre - image of some one flag in @xmath2 has size @xmath0 , then the projection @xmath28 is @xmath0-to-1 onto every flag of @xmath2 . we say then that @xmath25 is a _ @xmath0-fold _ cover of @xmath2 . we call a map _ orientable _ provided that the surface on which it is embedded is itself orientable . we check that a map is orientable by giving it a _ face orientation _ ; this is an assignment of a circular arrow to each face of @xmath2 such that at every edge , the arrows on the faces joined by the edge point along the edge in _ opposite _ directions , as in figure [ fig : faceori ] . we can define a _ vertex orientation _ similarly , and it is clear that @xmath2 has a vertex - orientation if and only if it has a face - orientation , and this happens if and only if @xmath2 is orientable . the word _ pseudo - orientation _ has been used in two different ways . we will use the term _ vertex pseudo - orientation _ ( vpso for short ) for what is called in @xcite simply a pseudo - orientation . here , we mean an assignment of one circular arrow to each vertex so that at each edge the two arrows cross in the _ same _ direction , as in figure [ fig : pso ] . if we visualize a gear wheel at each vertex so that cogs on the wheels of adjacent vertices mesh , the map is vpso if we can turn one wheel , causing all wheels to turn at the same time . in @xcite , the idea is used to make an important distinction about @xmath0-fold rotary covers of a rotary map @xmath2 for which the branching is totally ramified at vertices . if @xmath2 is non - orientable , @xmath0 can be larger than 2 only if @xmath2 is vertex pseudo - orientable . similarly , a _ face pseudo - orientation _ ( or fpso ) is an assignment of one circular arrow to each face , as in figure [ fig : pso ] , so that at each edge , the arrows in adjacent faces flow along the edge in the _ same _ direction . we can simplify this by orienting each edge so that the cycle of edges around each face is consistently oriented . in @xcite this is called a pseudo - orientation , and the result in that paper is that the _ dart graph _ of @xmath2 is connected if and only if @xmath2 is not face pseudo - orientable . finally , we may define an _ edge pseudo - orientation _ ( or epso ) to be an orientation of the edges such that in every face the direction of the arrows in adjacent edges flows in the _ same _ direction ( either into or out of the face ) as in figure [ fig : pso ] . in this paper , the word ` coloring ' will be used to describe what might be more fully notated as a ` consistent flag 2-coloring ' . if @xmath34 is any subset of @xmath35 , then an @xmath34-coloring of a map @xmath2 is a function @xmath36 such that for every flag @xmath7 , if @xmath37 , then @xmath38 , while if @xmath39 , then @xmath40 . to say that in another way , @xmath41 figure [ fig : cubecols ] shows a @xmath42-coloring , a @xmath43-coloring , and an @xmath44-coloring of the cube . the reader should check that the colorings extend unambiguously to the unseen faces of the cube as well . let us first notice that if @xmath45 is an @xmath34-coloring of @xmath2 , then so is @xmath46 , and these are , in fact , the only @xmath34-colorings of the map . give the name _ sub - edge _ to the segments forming sides of the flags . these are of three types : type 0 : : : midpoint - of - edge to face - center , type 1 : : : face - center to vertex ," +"the following work is based on the research reported in ref . @xcite . it pursues the objective of empathizing the analogy between accessible condensed matter systems and the currently accepted framework for the evolution of the universe , notably the symmetry - breaking phase transitions @xcite it has undergone after the big - bang . a key aspect to this comparison is the creation of topological defects , frustrations of the unbroken phase within the broken one , arising from the continuity of the order parameter values . these are generally categorized according to the homotopy group of the quocient of the unbroken symmetry groups to the broken one and which enables for comparison of different physical phenomena . these objects can appear as magnetic monopoles or point - like defects , cosmic strings , vortices or flux tubes , magnetic domain walls or textures . besides its mere aesthetical value , this analogy can provide a powerful probe into the early stages of the evolution of the universe , since direct , hands - on experimental tests are unattainable : the existence of more accessible systems that exhibit a formally similar behavior could provide crucial clues to many cosmologically relevant issues . these `` cosmology in the laboratory '' experiments can be found in various systems , ranging from vortices in superfluid phase transitions of @xmath0 and @xmath1 ( see e.g. ref . @xcite ) , which exhibit common features with cosmic strings @xcite , to liquid crystals undergoing an isotropic - nematic phase transition @xcite . polymer chains were shown to also possess analogous thermodynamic and transitional behavior @xcite . however , most of these systems lack the existence of a quantity analogous to the magnetic field , which could be a key player in the early evolution of the universe and formation of structure . for that reason , superconductors are a case of special interest . these comprise phase transitions involving a local gauge symmetry - breaking process , during which the photon acquires a `` mass '' and , therefore , a penetration length , giving rise to the meissner effect : the expulsion of the magnetic field from a superconducting material , with formation of shielding `` supercurrents '' on its surface . this symmetry breaking originates topological defects which are known as flux tubes or vortices , lines of non - null magnetic field trapped inside the superconductor . experiments targeted at observing defect densities in high-@xmath2 materials @xcite were not in accordance with the density predictions of the kibble - zurek ( k - z ) mechanism @xcite . this , however , is to be expected , since the k - z prediction should be accurate only for global gauge symmetry breaking , when the geodesic rule for phase angle summation is valid . a new defect generation mechanism , based on a local gauge treatment by hindmarsh and rajantie ( h - r ) @xcite , leads to an ( additive ) prediction . this , although well below the first carmi - polturak experimental sensitivity , is in reasonable agreement with the second . as a starting point for this research , we note that the above experiments were both conducted in type - ii materials , which exhibit a higher critical temperature and are therefore easier to manipulate , leading the current trend in experimental superconductivity . these materials display a second order phase transition , with no release of latent heat . on the other hand , type - i materials are metastable , showing different responses to a magnetic field when in normal - superconductor or superconductor - normal phase transitions . in this work , we try to account for this more elaborate behavior and to estimate to which extent it affects the defect density predictions for type - i superconductors . type - i and type - ii superconductors are commonly distinguished according to their ginzburg - landau ( g - l ) parameter @xmath3 , the ratio between the magnetic field penetration length @xmath4 and the coherence length @xmath5 of the order parameter . in the presence of a gauge field @xmath6 , these characteristic length scales are obtained from the free energy density f ( ) = 1 2m_e |i - e c |^2 + v ( ) + 1 2 ( ) , [ free ] where @xmath7 is the sample s magnetic moment , @xmath8 is the electron mass and @xmath9 is the order parameter . the g - l potential is usually written as @xcite v ( ) = ^2 + 2 ^4 , [ pot ] where @xmath10 is assumed to be linear with temperature , @xmath11 , @xmath12 , @xmath13 and @xmath14 are constants , and @xmath2 is the critical temperature . one obtains = , [ lambda ] and = / . [ xi ] the coherence length at zero temperature is @xmath15 , with @xmath16 . the transition is second order if @xmath17 , and @xmath18 is typically less than @xmath19 ; for @xmath20 , the transition is first order and @xmath18 typically greater than @xmath21 . it is commonly accepted that , if there is no applied magnetic field , one always has a second - order phase transition , for all values of @xmath22 . first order transitions arise from the external field term in eq . ( [ free ] ) if the sample has a characteristic dimension @xmath23 . this degeneracy of the phase transition at @xmath24 is , however , only verifiable to the current experimental sensitivity , and it can be argued that there is some yet undetected intrinsic metastability , regardless of the applied magnetic field . bearing in mind the analogy between condensed matter and cosmology , we now briefly look at phase transitions in high energy physics . in thermal field theory ( tft ) a first order phase transition arises due to 1-loop radiative corrections to a potential similar to that of eq . ( [ pot ] ) ; a barrier between minima of the potential is created , as these corrections give rise to a cubic scalar field term v ( ) = ^2 - ||^3 + 2 ^4 , [ 3pot ] where @xmath25 @xcite . as before , @xmath14 is assumed to be constant and @xmath11 to depend linearly with temperature . in the normal - to - superconductor phase transition , a term similar to @xmath26 also arises if one takes into account gauge field fluctuations @xcite , producing = 8 _ 0 e c t_c . [ fluct_gamma ] this result enables a first order phase transition for all values of @xmath22 . thermal fluctuations @xcite and non local bcs effects @xcite describe crossover behavior between first and second order transitions . in the following , we adopt a potential of the form of eq . ( [ 3pot ] ) and constrain @xmath27 based on experimental data . the results are then compared with both tft 1-loop radiative corrections and the the results of ref . @xcite ( valid only at temperature close to @xmath28 , that is , @xmath29 ) . the introduction of @xmath30 in the potential ( [ pot ] ) can produce changes in both the k - z and h - r defect generating mechanisms . also , a possible nucleation suppression due to the potential barrier can significantly reduce the number of observed defects . the obtained constraints on @xmath31 are used to access the impact on these claims . a superconductor undergoing a first - order phase transition crosses different supercritical fields , displaying a metastable behavior , as shown in the phase diagram of figure [ curves ] . the superheating curve is given by the condition @xmath32 , for @xmath33 , equivalent to @xmath34 . the supercooling curve is given by the condition @xmath35 for @xmath36 , corresponding to @xmath37 . the ( unobservable ) critical curve is given by @xmath38 and @xmath39 , where @xmath40 is the non - vanishing minimum of the potential . this corresponds to @xmath41 . assuming @xmath42 and @xmath43 , we obtain for the superheating curve (t-1 ) = 9 16 ^2 t^2 , [ sh_cond ] and t_sh = 2 1 + ~1 + 9 16 ^2 . [ t_sh ] due to the presence of the cubic term in the potential of eq . ( [ 3pot ] ) , the superheating curve shows a zero - field shift in temperature from @xmath2 by @xmath44 . this shift , if detected , would indicate an intrinsic metastability , in the sense that it does not depend on the existence of an applied field . since such temperature shift has not yet been signaled , the current experimental temperature sensitivity being @xmath45 @xcite , a bound on the slope of @xmath46 is < t_exp . [ tbound ] the supercooling transition still occurs at @xmath47 , the critical temperature ; this is natural , since it is determined solely by @xmath48 ( neglecting a smaller order correction to @xmath10 , @xcite ) . .critical properties of @xmath49 and @xmath50 [ cols=""^,^,^,^,^"",options=""header "" , ] table [ table2 ] provides a comparison of the bounds on @xmath51 with the cubic term arising from 1-loop corrections in tft and the prediction of ref . this is achieved by computing the slope of @xmath52 from @xmath53 , obtaining @xmath54 . notice that @xmath52 as a function of the reduced temperature is material dependent , although @xmath30 is not . the quantities @xmath13 and @xmath14 are also included . we notice that unit conversion is not direct , but achieved through a multiplicative factor @xmath8 : since the dimension of the scalar field in g - l theory is @xmath55=l^{-3}$ ] , its square representing a density , while in field theory @xmath56=l^{-1}$ ] , the dimensionality of @xmath46 depends of the theory at hand . for comparison sake , we have chosen @xmath57 = l^{-1}$ ] . hence , the definition of @xmath46 is changed with respect to the free energy potential of eq . ( [ 3pot ] ) , through a convenient @xmath8 factor ; the electron mass determines the conversion as it is absent from the kinetic term of the lagrangean density of field theory , @xmath58 , but present in the corresponding condensed matter free energy term , @xmath59 ; equivalently , one can loook at the coherence length : @xmath60 _ vs. _ @xmath61 . according to ref . @xcite , in the absence of an applied magnetic field , momentum fluctuations of the gauge field have an expectation value derived from the equipartition theorem . integrating over momentum space ( with a cutoff @xmath62 of the order of @xmath63 ) , one gets a^2_= 4 _ 0 t_c - 8 _ 0 e c t_c || . [ meangauge ] hence , from this result arises , asides from an unimportant correction to the scalar field mass ( or coherence length ) , a more relevant ( negative ) cubic term , @xmath64 . at zero field , this produces a shift in the superheating temperature of _ t = 7.25 10 ^ -12 t_c^3 h_c(0)^2 _ 0 ^ 6 , [ deltat ] with @xmath65 expressed in _ gauss _ and @xmath18 in @xmath66 . for sn , it requires a temperature sensitivity of @xmath67 , well below current possibilities . al , however , requires just a sensitivity of @xmath68 , attainable if one employs state of the art relative temperature measurement techniques . one can see that , for both materials , the slopes of @xmath46 predicted by tft and ref . @xcite have similar magnitudes @xmath69 . this is a confirmation of the underlying analogous mechanisms : one can view the thermal averaging of the gauge field in condensed matter as equivalent to finite" +"meson - antimeson mixing has traditionally been of importance because it is sensitive to heavy degrees of freedom that propagate in the underlying mixing amplitudes . estimates of the charm quark and top quark mass scales were inferred from the observation of mixing in the @xmath4 and @xmath5 systems , respectively , before these particles were discovered directly . this success has motivated attempts to indirectly detect new physics ( np ) signals by comparing the observed meson mixing with predictions of the standard model ( sm ) . mixing in the kaon sector has historically placed stringent constraints on the parameter space of theories beyond the sm and provides an essential hurdle that must be passed in the construction of models with np . however , anticipated breakthroughs from the b - factories and the tevatron collider have not been borne out the large mixing signal in the @xmath5 and @xmath6 systems is successfully described in terms of the sm alone ( although the parameter spaces of various np models have become increasingly constrained ) . short of awaiting lhcb and the construction of a super - b facility , there is one remaining example for possibly observing indirect signs of np in meson mixing , the @xmath1 flavor oscillations . in this case , the sm mixing rate is sufficiently small that the np component might be able to compete @xcite . there has been a flurry of recent experimental activity regarding the detection of @xmath1-@xmath7 mixing @xcite , which marks the first time flavor changing neutral currents ( fcnc ) have been observed in the charged @xmath8 quark sector . with the potential window to discern large np effects in the charm sector @xcite and the anticipated improved accuracy for future mixing measurements , the motivation for a comprehensive up - to - date theoretical analysis of new physics contributions to @xmath3 meson mixing is compelling . the heightened interest in @xmath1-@xmath7 mixing started with the almost simultaneous observations by the babar @xcite and belle @xcite collaborations of nonzero mixing signals at about the per cent level , , @xmath9 , @xmath10 and @xmath11 are standard and are given in eqs . ( [ xy]),([y - defs ] ) . ] & & y_d = ( 0.97 0.44 0.31 ) 10 ^ -2 , + & & y_d^(cp ) = ( 1.31 0.32 0.25)10 ^ -2 . this was soon followed by the announcement by the belle collaboration of mixing measurements from the dalitz plot analyses of @xmath12 @xcite , x_d = ( 0.80 0.29 0.17)10 ^ -2 , y_d = ( 0.33 0.24 0.15)10 ^ -2 . a preliminary fit to the current database , @xmath13 . these are essentially unchanged from the hfag preliminary results given above and used in our analysis ; the difference will not affect our numerical results . ] by the heavy flavor averaging group ( hfag ) gives @xcite [ hfag ] & & x_d = 8.7^+3.0_-3.4 10 ^ -3 , y_d = ( 6.62.1 ) 10 ^ -3 . since this paper addresses the issue of the mass splitting induced by mixing , our primary concern is with the signal for @xmath14 , seen here to be a 2.4 sigma effect . this is below the generally accepted threshold for `` evidence '' and is more in the nature of a `` hint '' . however , we note that a 2.4 sigma effect will automatically have a non - zero lower bound at @xmath15 confidence - level . for the sake of reference , we cite the one - sigma window for the hfag value of @xmath14 , 5.4 10 ^ -3 < x_d < 11.7 10 ^ -3 , [ xbnds ] or equivalently for @xmath16 itself , 8.7 10 ^ -15 < m_d < 1.9 10 ^ -14 . [ mbnds ] let us briefly describe our strategy for dealing with the above hfag values in light of both sm and np contributions . we shall argue in sect . iii that the sm predictions , although indeed compatible with the observed range of values for the @xmath3 mixing parameters , contain significant hadronic uncertainties . moreover , we do not know the relative _ phase _ between the sm contribution and that from any np model , so that @xmath14 will lie between the extreme limiting cases of constructive and destructive interference . in addition , since the observation of @xmath3 mixing is new , the measurements will fluctuate with future refinements in the analyses and as more data is collected . to best deal with these realities , we will present our results by displaying a given np prediction as a pure np signal ( _ i.e. _ as if there were no sm component ) and for comparison , display curves of constant @xmath14 for the five values x_d = 15.0 10 ^ -3 , 11.7 10 ^ -3 , 8.0 10 ^ -3 , 5.0 10 ^ -3 , 3.0 10 ^ -3 . [ xrange ] this ( approximately hfag 2@xmath17 ) range reveals the sensitivity of @xmath14 to variations in the underlying np parameter space . we will then show the present constraints placed on the np model parameter space , by assuming that the np contribution can not exceed the @xmath18 upper bound on @xmath19 this procedure mirrors that which is traditionally employed in obtaining bounds on np from @xmath4-@xmath20 mixing . @xmath1-@xmath7 mixing at the observed level is much larger than the quark - level ( ` short - distance ' ) sm prediction @xcite but is in qualitative accord with hadron - level ( ` long - distance ' ) sm expectations . however , because the latter are beset with hadronic uncertainties , it can not be rigorously concluded that only sm physics is being detected . in this paper , we will consider a broad menu of np possibilities . as the operation of the lhc looms near , the number of potentially viable np models has never been greater . our organizational approach to analyzing these is to address np models with : 1 . extra fermions ( sect . iv ) a : fourth generation b : heavy vector - like quarks ( 1 ) : @xmath21 singlet quarks ( 2 ) : @xmath22 singlet quarks c : little higgs models 2 . extra gauge bosons ( sect . v ) a : generic z models b : family symmetries c : left - right symmetric model d : alternate left - right models from e@xmath23 theories e : vector leptoquark bosons 3 . extra scalars ( sect . vi ) a : flavor conserving two - higgs - doublet models b : flavor changing neutral higgs models c : scalar leptoquark bosons d : higgsless models 4 . extra space dimensions ( sect . vii ) a : universal extra dimensions b : split fermion models c : warped geometries 5 . extra symmetries ( sect . viii ) a : minimal supersymmetric standard model b : quark - squark alignment models c : supersymmetry with r - parity violation d : split supersymmetry in the above , we have chosen to consider only supersymmetry in sect . viii due to its extensive literature and to cover other extended symmetries elsewhere in the paper . any np degree of freedom will generally be associated with a generic heavy mass scale @xmath24 , at which the np interaction will be most naturally described . at the scale @xmath25 of the charm mass , this description will have been modified by the effects of qcd . these should not be neglected , so we perform our np analyses at one - loop level for the strong interactions . the theoretical background for this is presented in sect . finally , in order to place the np discussion within its proper context , it makes sense to first review sm charm mixing . this is done in sect . the remainder of the paper then amounts to considering charm mixing with lots of ` extras ' . the paper concludes in sect . ix with a summary of our findings . let us first review some formal aspects of charm mixing . the mixing arises from @xmath26 interactions that generate off - diagonal terms in the mass matrix for @xmath1 and @xmath27 mesons . the expansion of the off - diagonal terms in the neutral @xmath3 mass matrix to second order in the weak interaction is [ m12 ] ( m - ) _ 21 = 0bar | h_w^|c|=2 | d^0 + _ n 0bar | h_w^|c|=1 | n n | h_w^|c|=1 | d^0 m_d - e_n+i , where @xmath28 and @xmath29 are the effective @xmath26 and @xmath30 hamiltonians . the off - diagonal mass - matrix terms induce mass eigenstates @xmath31 and @xmath32 that are superpositions of the flavor eigenstates @xmath1 and @xmath27 , @xmath33 where @xmath34 . the key quantities in @xmath1 mixing are the mass and width differences , @xmath35 or equivalently their dimensionless equivalents , x_d , y_d , [ xy ] where @xmath36 is the average width of the two neutral @xmath3 meson mass eigenstates . two quantities , @xmath11 and @xmath37 , which are actually measured in most experimental determinations of @xmath38 , are defined as y_d^(cp ) & & ( _ + - _ -)/ ( _ + + _ - ) = y_d - x_d(-a_prod ) , + y_d & & y_d _ k - x_d _ k , [ y - defs ] where the transition rates @xmath39 pertain to decay into final states of definite cp , @xmath40 is the so - called production asymmetry of @xmath1 and @xmath41 ( giving the relative weight of @xmath1 and @xmath2 in the sample ) and @xmath42 is the strong phase difference between the cabibbo favored and double cabibbo suppressed amplitudes @xcite . the quantities @xmath43 and @xmath44 account for the presence of cp violation in @xmath1-@xmath7 mixing , with @xmath43 being related to the @xmath45 parameters of eq . ( [ definition1 ] ) as @xmath46 and @xmath44 a cp - violating phase of @xmath47 ( if one neglects direct cp - violation ) @xcite . in practice , @xmath48 is measured by comparing decays of @xmath1 into a state of definite cp , such as @xmath49 , to decays of @xmath1 into a final state which is not a cp - eigenstate ( such as @xmath50 ) whereas @xmath51 is extracted from a time - dependent analysis of the @xmath52 transition @xcite . the states @xmath53 allow for effects of cp violation . however , cp violation in @xmath1 mixing is negligible in the standard model and there is no evidence for it experimentally @xcite . many new physics scenarios contain new phases which can induce sizable cp violation in the @xmath3 meson sector . nonetheless , a thorough investigation of such effects is beyond the scope of the present paper . therefore , we shall work in the limit of cp invariance ( so that @xmath54 ) for the remainder of this paper . throughout , our phase convention will be @xmath55 then @xmath56 become the cp eigenstates @xmath57 with @xmath58 . keeping in mind the neglect of cp - violation and also the phase convention of eq . ( [ phase ] ) , we relate the mixing quantities @xmath14 and @xmath9 to the mixing matrix as @xmath59 \ \ , \nonumber \\ & & y_{\rm d } = \frac{1}{2 m_{\rm d}\gamma_{\rm d}}\ , { \rm im}\ , \langle \d0bar | \,i\ { \rm d}^4 x\ , t \big\ { { \cal h}^{|\delta c|=1}_w ( x)\ , { \cal h}^{|\delta c|=1}_w(0 ) \big\ } | d^0 \rangle \ \ , \end{aligned}\ ] ] where @xmath60 is the weak hamiltonian density for @xmath30 transitions and @xmath61 denotes the time - ordered product . there is" +"nasa s _ kepler _ mission has discovered that many of the planetary systems around solar - type stars contain multiple planets ( kepler multis , * ? ? ? * ; * ? ? ? * ; * ? ? ? planets detected in these systems likely possess low mutual inclinations ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , and are spaced closely . in multiple systems that contain high number of planets ( 4 - 6 ) , the spacing is so tight that there may be of order @xmath1 planets fitted inside the orbit of mercury . systems where a single planet transit ( kepler single ) and where multiple planets transit ( kepler multis ) may share the same intrinsic architecture but only differ in transit geometry . however , a few statistical studies have shown that this is not the case . there appears to be an excess in the number of singles over what one expects by extrapolating from the kepler multis @xcite , suggesting that many of the singles are intrinsically singles . even the multis may contain different sorts of systems . a direct probe of the underlying population is provided by transit - time - variations ( ttv ) . @xcite probed the presence of close - companions ( transiting or not ) around kepler candidates using ttv signals . they found a striking correlation between the fraction of planets that show detectable ttvs and their transit multiplicity . systems where four or more planets transit enjoy four times higher ttv fraction than kepler singles do , and about twice as high as those with two or three transiting planets . this led them to propose that there are at least two different classes of kepler systems , one closely packed and one sparsely populated ( also see * ? ? ? besides from planet spacing , orbital eccentricity and inclinations also differ between the two classes . compared to kepler multis , the transit durations of kepler singles appear to be longer , requiring their orbits to have higher eccentricities ( wu , unpublished ) ; study of stellar obliquity suggests that kepler singles may lie on orbits more misaligned with the stellar spin than the multis @xcite . both lend to the picture that kepler multis are dynamically cold systems , while singles are dynamically hotter . what could have produced such a dichotomy ? @xcite explored the possibility of dynamical instability . they boosted the masses of observed triple planetary systems by about a factor of 10 and found that these systems could become destabilized within 10 billion years . this led them to hypothesize that kepler singles may be the aftermath of dynamical instability . in this study , we provide much more definite arguments to this hypothesis by investigating the spacing distribution among the closely packed multi systems ( 4 planets and more ) . we find that , adopting realistic planetary masses and ages , kepler high multiple systems are packed close to the boundary of stability . this proximity has to be explained . unless the formation mechanism is somehow capable of producing this proximity , the most likely explanation is that the primordial systems had a range of spacing , but the ones that were packed too closely have been sculpted away by the subsequent billions of years of evolution . in this hypothesis , kepler singles and lower multiples are the descendants of kepler multis . if this true , we may be able to recover the primordial spacing of planetary systems . here , we set the scene by reviewing some previous results on stability in multiple planetary systems . johannes kepler ( 1571 - 1630 ) , after whom the _ kepler _ mission is named , initially believed that the spacing of planets in the solar system is limited by packing perfect solids ( polygons with identical faces ) . he discarded this idea after developing his famous kepler laws . however , the question still remains , how tight can you pack planets together without affecting dynamical instability . over the past few decades , some theoretical progress have been made in answering this question , and in some special cases the answers are known exactly . one usually measure spacing between every two planets in a unit called the mutual hill sphere @xmath4 where @xmath5 , @xmath6 are the semi - major axis and mass of the two planets , and @xmath7 the mass of the central star . in this unit , planet spacing can be expressed as a dimensionless number @xmath8 @xmath9 we first focus only on orbits that are circular and coplanar . a well known result , derived by @xcite based on overlapping of first order mean - motion resonances , is that a test particle ( @xmath10 ) perturbed by a planet ( @xmath11 ) is subject to orbital chaos if it lies too close to the planet , @xmath12 where @xmath13 is the planet mass ratio and the numerical coefficient is adopted from @xcite . in @xmath8 value , the critical spacing is @xmath14 this result is little modified if the test particle is instead substituted by a planet @xcite . the dependence of @xmath15 on @xmath16 ( albeit weak ) indicates that hill sphere is not necessarily the best unit to measure stability . however , we adopt it here for convenience . there is also an important result on hill stability ( stability against orbit crossing ) , popularized in astronomy by @xcite . as a result of total energy and angular momentum conservation , two initially circular , coplanar planets can avoid close encounters at all times if they are separated by more than @xmath17 . these two criteria meet at @xmath18 and their physical connection is discussed in @xcite . for systems where there are more than 2 planets , there is yet no theoretical understanding for the origin of dynamical instability ( see attempts by , e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? whatever information we have on how tight one can pack planets in these cases are empirical results from numerical simulations @xcite . these we summarize below . generally speaking , systems with more planets ( @xmath19 ) require larger @xmath8 spacing to stay stable . to compare the various numerical studies , we scale the physical timescale by the orbital period of the inner most planet in the system , @xmath20 ( also see * ? ? ? we also suppress error - bars in the fitting results but caution that there are intrinsically large scatters . * dependence on @xmath21 : two - planet systems can remain indefinitely stable as long as they are above a critical spacing . this may not hold for large - n systems . it appears that a larger spacing does not guarantee eternal peace but only delays the time of instability ( we return to this point in [ subsec : extrapolate ] ) . numerically , the critical spacing at which an average system undergoes their first encounter at time @xmath21 can be modelled as @xcite , @xmath22 though the alternative scalings @xmath23 and @xmath24 $ ] have been adopted by @xcite and @xcite respectively . the numerical coefficients @xmath25 and @xmath26 depend on system parameters like the number of planets , their masses , and orbital eccentricities and inclinations . two results most relevant to our case are @xmath27 for systems of @xmath28 planets all with @xmath29 @xcite , and @xmath30 for @xmath31 planet systems with @xmath32 @xcite . both scalings are obtained for circular , coplanar systems with a uniform planetary mass and a uniform k - spacing . * dependence on @xmath19 : the most comprehensive study to date on this issue is that by @xcite . they found , for @xmath33 , and @xmath34 , the critical separation for a system of circular , coplanar planets goes as @xmath35 this results roughly recovers equation when @xmath36 . the initial rise of @xmath15 with @xmath19 is intuitively understood as the presence of more planetary perturbers exerts more strain on the delicate dynamical systems . the subsequent flattening of @xmath15 with @xmath19 is , however , surprising and not understood . one guess is that dynamical instability is most affected by close neighbours , and the presence of far - away neighbours , once beyond a certain separation , do not matter . for instance , a system of 8 neptunes will space a period range of @xmath37 . with such a large spacing , newly added planets have no chance of participating in any mmrs with the pre - existing planets , and therefore should not adversely affect the stability of the system . * dependence on @xmath16 : it is found that less massive planets , with their smaller hill spheres , need be separated by slightly higher values of @xmath8 . both @xcite and @xcite found that , for every decade of drop in @xmath16 ( within the range of @xmath38 to @xmath39 ) , the critical separation @xmath8 should increase by @xmath40 . * eccentricity / inclination : if the planetary orbits are dynamically hot , more elbow room is needed to maintain stability ( e.g. * ? ? ? * ) . @xcite showed that , at low eccentricities , increasing the average eccentricity by @xmath41 raises @xmath42 by @xmath43 . we know of no study that explores the impact of mutual inclination separately , so we provide some illustrations of this below . returning to our problem at hand a system of 8 flat , circular planets , with masses of @xmath44 , and an inner orbit of @xmath45 au , may remain stable for over 1 gyrs ( or @xmath46 ) , if @xmath47 ( extrapolating from equation [ eq : tauk ] ) . this valueis broadly consistent with the spacing observed in tight kepler systems . however , a more refined approach is required . to compare theoretical results to kepler systems , we need to overcome a few restrictions of previous studies . first , in almost all previous numerical simulations , planets in a given systems are assigned identical masses and identical spacing , in contrast to realistic systems . inhomogeneities in mass and spacing may impact results significantly , e.g. , they will introduce large scatter in stability lifetimes , among systems that have comparable bulk parameters . it is therefore necessary to study system stability in a statistical sense previous investigations have studied only a small number of cases ( typically fewer than a hundred systems ) . we accomplish this by integrating a much larger number of systems ( @xmath48 ) . in addition , we wish to study the impacts of small eccentricity and inclination . lastly , our simulations run for a factor of @xmath49 longer than previous works , up to @xmath50 years . although still shorter than the typical system ages ( a giga - year ) , they provide a better indicator for long - term stability . we generate artificial planetary systems as follows : each system contains @xmath51 planets orbiting around a 1 solar mass star , on coplanar and circular orbits . the number @xmath51 is chosen for a number of reasons : this is the largest number of transiting planets in a multiple system ( e.g. * ? ? ? * ) ; it is close enough to the plateau in equation , the results may be considered valid for all systems with more than @xmath51 planets ; it is computationally feasible . the mass of the host star is taken to be @xmath52 , while the mass of the planets" +"transition metal dichalcogenides ( tmds ) such as molybdenum disulfide ( mos@xmath0 ) have layered structures , where the atoms within a tmd monolayer form a covalently bonded planar network , and the interaction between these layers is a weak , van der waals interaction.@xcite a monolayer of mos@xmath0 consists of a layer of molybdenum atoms sandwiched between two layers of sulfur atoms . monolayers can be exfoliated through micro - mechanical cleavage , similar to graphene or boron nitride.@xcite unlike graphene ( a metal ) , or boron nitride ( an insulator ) , mos@xmath0 is a semiconductor . moreover , whereas bulk mos@xmath0 has an indirect band gap ( 1.2 ev ) , monolayer mos@xmath0 has a direct band gap ( @xmath21.8 - 1.9 ev ) , and shows a strong optical absorption and luminescence.@xcite at present mos@xmath0 , and tmds in general , are vehemently pursued as promising materials for applications in electronics and optoelectronics.@xcite contacting mos@xmath0 to metal electrodes proves to be a problem ; it tends to produce unexpectedly high interface resistances , indicative of a high schottky barrier at the interface.@xcite a high barrier could be caused by strong interface bonding creating interface states that pin the fermi level,@xcite or by weak bonding creating a potential step due to pauli repulsion at the interface.@xcite the nature of the interaction at the mos@xmath0/metal interface is far from trivial . on the one hand , one could argue that , as mos@xmath0 has no dangling bonds at its surface , its interaction with metal substrates should be weak and van - der - waals - like . on the other hand , many metal species form ( di)chalcogenide compounds,@xcite and when adsorbing mos@xmath0 onto a metal substrate , there could be a competition between the metal surface and the mo atoms for interacting with the sulfur atoms at the interface . in that case , not only the mos@xmath0/metal bonding would be a much stronger chemical bonding , but also the structure and electronic structure of the mos@xmath0 adsorbate could be significantly perturbed . in this paper we explore the adsorption of mos@xmath0 on a variety of metal substrates by means of first - principles density functional theory ( dft ) calculations , following up on work briefly reported in a short paper.@xcite previous dft studies have concentrated foremost on the schottky barrier formed at mos@xmath0/metal interfaces using the local density approximation ( lda).@xcite lda gives a reasonable description of the adsorption of graphene and _ h_-bn on metal surfaces , but such results can not be generalized to other systems , as it is known that lda often leads to an unrealistic overbinding.@xcite other studies have used a generalized gradient approximation ( gga ) functional , such as pbe,@xcite which apparently works well for tmds adsorbed on metals,@xcite although it generally gives bad results for weakly bonded systems.@xcite here we focus on the interface interaction and its implications for the structure and electronic structure of the mos@xmath0 adsorbate and the schottky barrier . we choose a wide range of metal substrates : the ( 111 ) surfaces of al , ni , cu , pd , ag , pt and au , and the ( 0001 ) surfaces of mg , ti , and co , which are expected to have a wide range of interaction strength with the adsorbate . as the interface interaction can vary from weak ( physisorption ) to strong ( chemisorption ) , it is a priori not clear which dft functional describes such bonding . we test and compare results obtained with a van der waals functional , designed to describe weak , van der waals , interactions,@xcite to results obtained with gga and lda functionals , which are conventionally used to describe chemical bonding . we assess the importance of van der waals interactions for the interface interaction , and evaluate its effect on the structure and electronic structure of the mos@xmath0 adsorbant . we consider the situation where a mos@xmath0 layer is adsorbed as a whole on a metal substrate , making it more likely that the integrity of the mos@xmath0 layer is preserved in the adsorption process . if the mos@xmath0/metal interaction is not too strong , and the mos@xmath0 and metal surface lattices are not matched , the interface structure is likely to be incommensurable . in a supercell calculation one is forced to approximate such a structure by a commensurable one . previous calculations have used small supercells , where in some cases appreciable artificial strain is generated because of the mismatch between the mos@xmath0 and the metal surface lattices.@xcite we apply a strategy for choosing supercells such that the artificial strain is minimal , and test the influence of strain on the electronic properties of the interface . this paper is organized as follows . section [ sec : calculations ] describes the dft calculations , comparing different functionals in sec . [ sec : functionals ] and discussing the effect of lattice mismatch in sec . [ sec : mismatch ] . results are discussed in sec . [ sec : results ] , with the metal / mos@xmath0 interaction in sec . [ sec : bonding ] and its effects on the interface potential step and the schottky barrier in sec . [ sec : sb ] . strong chemisorption is discussed in more detail in sec . [ sec : ti ] , and a summary and the conclusions are presented in sec . [ sec : conclusions ] . we calculate ground - state energies and optimize geometries at the density functional theory ( dft ) level , using projector - augmented waves ( paws ) as implemented in the vasp code.@xcite the plane - wave kinetic - energy cutoff is set at 400 ev . the surface brillouin zone is integrated with the methfessel - paxton technique using a smearing parameter of 0.05 ev,@xcite and a @xmath3-point sampling grid with a spacing of 0.01 @xmath4 . the mos@xmath0/metal interface is modeled as a slab of 4 - 6 layers of metal atoms with one or two layers of mos@xmath0 adsorbed on one side and a vacuum region of @xmath212 . the in - plane supercell is chosen such as to minimize the mismatch between the mos@xmath0 and metal lattices , which is discussed in more detail in sec . [ sec : mismatch ] . a dipole correction is applied to avoid spurious interactions between periodic images of the slab.@xcite we allow the positions of the atoms to relax until the force on each atom is smaller than 0.01 ev@xmath4 , except for the bottom layer of metal atoms , whose positions are kept fixed . the electronic self - consistency criterion is set to 10@xmath5 ev . it is well known that commonly used dft exchange - correlation functionals , based upon lda@xcite or gga,@xcite give decent descriptions of covalent and ionic bonding , but they may fail for weakly bonded systems , as such functionals do not contain a description of van der waals interactions . for example , gga functionals such as pw91 or pbe,@xcite do not capture the bonding between _ h_-bn or graphene layers , nor that between _ h_-bn or graphene and transition metal(111 ) surfaces.@xcite a priori we do nt know how important van der waals interactions are in the bonding between mos@xmath0 and a metal surface . in sec . [ sec : functionals ] we compare results obtained using a van der waals density functional ( vdw - df),@xcite with results obtained with gga and lda functionals . structure with corresponding plane - averaged electrostatic potential @xmath6 . @xmath7 is defined as the difference between the work function on the metal side and on the mos@xmath0 side . ] one way of visualizing bonding at a mos@xmath0/metal interface is by the electron density difference @xmath8 where @xmath9 , @xmath10 , and @xmath11 are the electron densities of mos@xmath0 adsorbed on the metal , of the metal surface and of the free standing mos@xmath0 , respectively . the system as a whole is neutral , and @xmath12 is localized around the metal / mos@xmath0 interface , i.e. @xmath13 for @xmath14 sufficiently far from the interface . solving the poisson equation with @xmath15 as source then gives a potential step across the interface @xmath16 here @xmath17 is the direction normal to the interface , @xmath18 is the interface area , and @xmath19 is the difference between the asymptotic values of the potential left and right of the interface . figure [ fig : deltav ] also illustrates an alternative expression for the potential step @xmath20 where @xmath21 , @xmath22 are the work functions of the clean metal surface , and of the metal surface covered by mos@xmath0 , respectively . a practical way of obtaining work functions from dft calculations is to track the plane - averaged electrostatic ( hartree ) potential @xmath6 into the vacuum , see fig . [ fig : deltav ] , where typically the asymptotic value is reached with a few from the surface . in converged calculations the expressions of eqs . [ eq : sb2 ] and [ eq : sb3 ] give results that are with a few mev of one another . the interface potential step plays an important role in determining the schottky barrier , i.e. , the potential barrier for charge carrier transport from a metal into a semiconductor . the schottky barrier for electrons can be written as @xmath23 with @xmath24 the fermi level and @xmath25 the electron affinity of mos@xmath0 . there are several ways to extract the schottky barrier height from mos@xmath0/metal slab calculations . one could determine @xmath26 by measuring @xmath27 in the band structure or in the density of states of the mos@xmath0/metal slab , as in refs . and . in order to identify the mos@xmath0 related states , one needs to calculate the amplitudes of the projections of the wave functions of the slab on the mos@xmath0 layer . there is always some arbitrariness involved in such a projection if the adsorbate and the substrate are in close connection . in addition , identification of states belonging to the adsorbate is possible only if its electronic structure is not significantly perturbed in the adsorption process , which is only the case if the adsorbate is ( weakly ) physisorbed on the substrate.@xcite in practice we find that this procedure for obtaining the schottky barrier height at mos@xmath0/metal interfaces is not sufficiently accurate when applied to the ( projected ) density of states , and of practical use only when applied to the ( projected ) band structure of a small supercell . in contrast , starting from the right - hand side of eq . [ eq : sb ] , @xmath21 , @xmath25 and @xmath7 are easily obtained in separate calculations on the clean metal surface , the free - standing mos@xmath0 layer , and the mos@xmath0/metal slab , respectively . of course , if the mos@xmath0 electronic structure is very strongly perturbed by adsorption , one has to reconsider the definition of the schottky barrier , see sec . [ sec : ti ] . in the following the potential step @xmath19 is used to characterize the mos@xmath0/metal interface , along with the binding energy and the structure . an alternative way of locating the conduction band edge @xmath25 in a mos@xmath0/metal slab calculation , without having to resort to wave function projections , is by aligning the core levels of the mo or s atoms in the slab with the corresponding core levels in free - standing mos@xmath0 . it allows us to compare the densities of states of free - standing and adsorbed mos@xmath0 , see sec . [ sec : sb ] . in principle , this procedure also allows for calculating the schottky barrier height . as" +"quantum dots ( qds ) have played a prominent role in the investigation of the kondo problem physics in recent years , @xcite as they allow a systematic and well - controlled variation of structure parameters , with the consequent exploration of electronic correlations in this paramount many - body state . this exploration is of course possible by being able to experimentally tune the relevant parameters in the system over rather wide ranges . moreover , in a feature that is unique to these systems , qds also facilitate the incorporation and study of quantum coherence effects in the kondo state , and its interplay with structure resonances and field - induced phase shifts . in fact , the kondo effect has been studied in multi - quantum dot systems , including double,@xcite and triple dots , @xcite in different geometrical arrangements , motivated in part by the richness of the kondo physics in the presence of localized levels , as well as by their potential application as spin filters . one of the main signatures of the kondo state is the enhancement of the quasi - particle density of states at the fermi level ; this kondo resonance is accessible in electronic transport experiments , as it opens an additional transport channel , which is readily seen in the differential conductance of these structures ( typically in the zero - bias limit ) . in the case of multiple qd geometries , the kondo and other single - particle like resonances provide different transport channels which can even interfere with one another . as a result , these structures offer the interesting possibility of controlling the transport properties by exploiting quantum interference in the electronic propagation , allowing the study of scattering phenomena such as the well - known fano @xcite and aharonov - bohm effects,@xcite competing with the kondo effect . for example , the interference of kondo and fano resonances in suitably designed structures has been shown recently in beautiful experiments , giving rise to complex conductance features.@xcite these results demonstrate that consideration of multiple coherent scattering of traveling electronic waves , both through single - particle as well as many - body resonances , is crucial for the understanding of the resulting conductance features . in this regard , being able to tune the structure parameters of a multiple qd system , as well as its kondo state , provides a unique arena to study correlations and coherence effects in a controllable manner . it is clear that the features of the kondo resonance near the fermi level significantly affect the conductance of the system , sometimes in quite subtle ways . for example , the shape of the density of states in the leads near the fl has been shown to produce strong modifications of the kondo resonance and characteristic energy ( the kondo temperature ) . these modifications can arise from intrinsic global properties,@xcite or from the local environment in the vicinity of the active qd.@xcite we are here especially interested in resonances and modifications due to the electronic version of the dicke effect . @xcite the latter is the electronic analogue of the well - known dicke effect in quantum optics , which takes place in the spontaneous emission of closely - linked atoms lying in the same environment ( within one characteristic wavelength of each other).@xcite in the electronic case , the decay rates ( level broadenings ) are produced by the couplings between localized levels and a conduction channel , and their close proximity and effective coupling gives rise to effectively fast ( _ super - tunneling _ ) and slow ( _ sub - tunneling _ ) modes.@xcite interestingly , this coherent single - particle physics results in strong changes of the kondo screening , as we will discuss below , once coulomb interactions are fully taken into account . although other multidot geometries would exhibit similar physics , a specific configuration to study this effect consists of three qds where two large ( essentially non - interacting ) dots are attached laterally to a central dot that is embedded between current leads , as schematically shown in fig . this cross - bar structure is reminiscent of quantum wave guides with a resonator cavity . @xcite in our case , the side qds act as scattering centers to the main transport channel , and compete with the kondo effect of the central dot.@xcite similar configurations have been studied before , and recent work by trocha and barnas using a slave boson mean field approach has identified interesting regimes.@xcite they studied the interplay between kondo and dicke resonances and considered the limit of infinite coulomb repulsion ( @xmath1 ) , which suppresses virtual processes involving the doubly occupied state in the interacting dot . additionally , the mean - field approximation adopted in the auxiliary boson fields neglects correlations due to charge fluctuations involving the empty state of the dot . all of these processes may be expected to be important in providing a full description of the kondo resonance , especially in competition with the dicke effect here , as we indeed show in this work . our numerical renormalization group ( nrg ) approach , @xcite provides a reliable description that incorporates all charge and spin fluctuations in the problem , it allows the study of finite @xmath0 values corresponding to real qd experiments and gives us a systematic way to study the subtle interference effects inherent in this geometry . in this work , we explore the kondo state that appears when the levels of the non - interacting dots are brought together both symmetrically and asymmetrically about the fermi level . in both situations , the kondo resonance narrows drastically and is `` squeezed '' between the two single - particle levels , suggesting a drop in the kondo temperature of the system , as described recently in the symmetric case.@xcite we show that indeed the kondo temperature drops , as the onset of the dicke effect involving the interacting dot totally suppresses the kondo state and results in _ vanishing _ kondo temperature . this behavior , due to the enhancement of spin - spin correlations in the qds orbitals , results in the formation of a _ local _ singlet , which decouples from the current leads . as the system moves away from a fully degenerate dicke configuration , the kondo temperature is non - zero but has a non - monotonic dependence on structure parameters , behavior which is only brought out by our numerical renormalization group approach . this optimization of the kondo effect in a structure may have interesting applications in a real experimental system . we will further show that the competition of kondo and dicke effects modifies excited states near the kondo regime as well , resulting in unexpected changes in the thermodynamic and transport properties of the system . interestingly , the local ( non - kondo ) singlet state mentioned above emerges due to a strong coupling between the interacting qd and the super - tunneling state . a crossover between these two configurations can be tuned by varying the coupling between the qds . we also describe the effects of asymmetries in the system , including different interdot couplings , as well as energy levels and finite coulomb interactions in all the dots of the structure . we show that these structural asymmetries introduce interesting particle - hole asymmetries in the problem , resulting in strong changes in the kondo temperatures and the linear conductance of the system . the system consists of an interacting qd ( labeled qd1 ) coupled to two current leads ( @xmath2 and @xmath3 ) and to two effectively non - interacting qds ( qd2 and qd3 ) ( see fig . [ fig1 ] ) ; one could also think of qd2 and qd3 as being close to a coulomb blockade peak , so that they conduct and their behavior is single - resonance like , as charging effects are typically small when conducting . the three - dot structure is described by a multi - impurity anderson hamiltonian , @xmath4 , with @xmath5 , \\ h_{leads}&=&\sum _ { { k\sigma } , \ell = r , l } \varepsilon_{\ell k}c^\dagger_{\ell k\sigma } c_{\ell k\sigma } \\ h_t&=&v\sum_{\ell k\sigma \atop \sigma}\left[c^\dagger_{1\sigma}c_{\ell k\sigma}+h.c.\right],\end{aligned}\ ] ] where @xmath6 ( @xmath7 ) is the operator that creates ( annihilates ) an electron with energy @xmath8 ( @xmath9 ) and spin @xmath10 in the respective qd and @xmath11 is the corresponding fermion operator for the leads @xmath12 , with energy @xmath13 , where @xmath14 is the momentum quantum number of the free conduction electrons . the second term in eq . ( [ h_dots ] ) accounts for the coulomb repulsion in the doubly occupied state of the dots . the hopping amplitudes @xmath15 , @xmath16 and @xmath17 couple the interacting qd1 to the leads and to qd2 and qd3 , respectively . for simplicity , unless stated otherwise ( see sec . [ phasym ] ) , we will take @xmath18 , and @xmath19 , while @xmath20 . the characteristic properties of the kondo physics of the system will be probed through thermodynamic quantities , namely the local magnetic moment and its contribution to the entropy , which can be readily obtained from the nrg procedure . to calculate dynamical quantities , such as the spectral functions and the conductance of the system , one needs to calculate the local retarded green s function ( gf ) at the interacting dot , which is defined in the standard form , @xmath21 where @xmath22 , and @xmath23_+\rangle\end{aligned}\ ] ] is the double - time green s function , with @xmath24 the usual step function , and @xmath25_+$ ] the anticommutator . once @xmath26 is known , the spectral function @xmath27 [ or density of states ( dos ) ] of the interacting dot can be obtained from the relation @xmath28.\end{aligned}\ ] ] in the non - interacting limit ( @xmath29 ) the gf @xmath30 can be easily obtained by the equation - of - motion method , leading to an exact closed expression , @xmath31 where @xmath32 is the self - energy in the non - interacting case , which takes into account the effects of the qd1 contacts with the leads , and with qd2 and qd3 . the self - energy can be written as @xmath33 in these expressions , the frequency @xmath34 must be understood in its analytical continuation sense , @xmath35 , where @xmath36 is an infinitesimal . notice that the poles at @xmath37 and @xmath38 appearing in the self - energy describe localized states in the effective conduction band due to the presence of qd2 and qd3 . in the limit of @xmath39 , the self - energy reduces to the single impurity case , @xmath40 where @xmath41 is the hybridization function for a flat density of states , and @xmath42 is the half - bandwidth of the conduction electrons . notice that the effect of the leads and the two side - coupled qds is fully taken into account in eq . ( [ green0 ] ) by the self - energy @xmath43 , which provides a structured "" effective conduction band . the electrons localized in qd1 are then coupled via the effective density of states in the leads represented by @xmath44 in eq . ( [ eqs ] ) . the spectral function , @xmath45 in this _ non - interacting case _ is depicted in fig . [ fig12 ] for @xmath46 , @xmath47 , @xmath48 and different values of @xmath49 . we observe that by increasing @xmath49 the width of the central peak increases , while the satellite peaks are just slightly shifted away from the fermi level . the shift of the satellite peak position can be estimated by analyzing the" +"entanglement is the property of states of multipartite quantum systems that is the most important resource for quantum information processing @xcite . for this reason , one of the most important tasks of quantum information science is to establish entanglement at long distances in quantum networks , and to optimize final entanglement and probability of success . quantum networks @xcite play a key role in quantum information processing . here we limit our attention to those networks in which quantum states can be prepared initially and shared . that is , entanglement can be generated between neighboring or , at least , not - too - widely - separated nodes ( or stations ) . there are two instances in which the above - mentioned tasks become obviously relevant . on one hand , one can consider macroscopic quantum communication networks , such as cryptographic networks , or more generally quantum communication nets @xcite , or distributed quantum computation @xcite involving arbitrary nodes of the network . the second instance concerns microscopic or mesoscopic networks that could constitute architectures of quantum computers ( cf . ref . ) . despite enormous progress in experimental techniques ( cf . ref . and references therein ) , it is in principle a very hard task to establish entanglement at large distances due to decoherence and attenuation effects . two remedies for this problem have been proposed : * _ quantum repeaters_. this concept has been developed for 1d quantum communication chains @xcite . although the simple entanglement swapping @xcite procedure can lead to quantum communication at large distances ( see fig . [ fig : swapping ] ) , for imperfect resources , the performance of such communication chains decays exponentially with the distance ( i.e. the number of repeaters ) . however , one can use more sophisticated quantum repeater protocols , which use purification and swapping methods that lead to polynomial decay only . * _ entanglement percolation_. recently , our collaborators , together with two of us , proposed using networks in which properties of the connectivity of the network enable the establishment of , and determine the probability of , entanglement on large distances . in refs . and we considered in particular _ pure - state networks _ on regular lattices , where the nearest - neighbor ( nn ) nodes share a non - maximally entangled pair of qubits , or more generally qudits ( an entangled bond ) . we searched for local operations and classical communication ( locc ) protocols that lead to establishment of entanglement between remote nodes of the network . entanglement swapping and 1d repeater . circles are qubits . heavy lines represent pure non - maximally - entangled states . loops represent the entanglement swapping measurement on a pair of qubits . a ) two states @xmath0 and @xmath1 of the form specified in ( [ stateab ] ) . after the operation , qubits @xmath2 and @xmath3 may be in an entangled , mixed state . b ) swapping as the first step in a repeater . c ) a 1d chain of repeaters . ] at present , only a handful of studies that explicitly apply percolation theory to problems in quantum information have appeared in the literature . these articles , comprising refs . and as well as applications to cluster states , are reviewed in ref . . our results leading to the present work can be summarized as follows : * for 1d chains we proved that even optimal locc strategies only allow the establishment of entanglement between distant nodes that decays exponentially with both the distance , as well as the quality of entanglement of nn bonds . * in 2d and higher dimensions , the possibilities for protocols are greatly expanded . the most straightforward , naive protocol the one we use as a baseline to evaluate other protocols is the one we term _ classical entanglement percolation _ ( cep ) , although it does involve obviously some quantum operations . this protocol begins with converting ( using locc ) each of the entangled bonds into a singlet ( _ i.e. _ maximally entangled state ) with probability @xmath4 ( the so - called singlet conversion probability ( scp ) @xcite ) . after the conversion , each of the parties ( nodes ) knows obviously which of the bonds are now perfectly entangled . using classical communications , the parties establish whether there exists an infinite percolating cluster ( or one spanning the lattice ) and who belongs to it . then , by performing a series of entanglement swappings , it is possible to propagate entanglement between any two ( widely ) separated nodes that belong to the percolating cluster . we call this scheme `` classical '' because it essentially maps the problem onto a classical bond percolation problem @xcite , and its success or failure is equivalent to the success or failure of bond percolation in the same lattice . namely , if @xmath5 , where @xmath6 is the lattice - dependent critical percolation threshold ( or , in other words , critical open - bond density ) , then entanglement between any two remote nodes can be established with probability @xmath7 , which asymptotically does not depend on the distance . * at the same time that we introduced cep , we presented several schemes that went beyond the simple application of singlet conversion everywhere followed by entanglement swapping along a path . we call these _ quantum entanglement percolation _ ( qep ) protocols because they use some kind of quantum pre - processing for instance quantum measurements to transform one percolation problem to another one . in these protocols cep is also used , but is preceded by application of certain locc , which remove and replace bonds in the network lattice , resulting in a new lattice geometry with fundamentally different long - range properties . the pre - processing in qep may greatly improve the possibility of entanglement percolation , either by reducing @xmath6 , or by increasing @xmath8 . in this paper we present a more systematic and thorough study of qeps based on lattice transformations . in particular , we explore the entire parameter space with the addition of monte carlo and series - expansion methods . although general principles remain to be found , we do discover certain rules and regularities governing such strategies ( see sec . [ sec : examples ] ) . the paper is organized as follows . in sec . [ sec : models ] we formulate and describe the models and fix the notation . section [ sec : nets_and_perc ] discusses quantum networks and percolation , whereas sec . [ sec : transformations ] deals with loccs used for lattice transformations . our main results are presented in sec . [ sec : examples ] , which contains descriptions of five examples of transformations enhancing cep : i ) the transformation of the kagom lattice to the square lattice , ii ) the transformation of the double - bond honeycomb ( hexagonal ) lattice to the triangular lattice , iii ) the transformation of the square lattice to two decoupled copies of the square lattice , iv ) the transformation of the bowtie lattice to the decoupled triangular and square lattices , and v ) the transformation of a triangular lattice with two different degrees of entanglement into the decoupled square and triangular lattices . the cases ii ) , iii ) , and v ) were discussed already in ref . , but we present here more general and stronger results . we conclude in sec . [ sec : conclusions ] . over the past few decades , classical percolation theory has seen the development of a number of quite sophisticated and powerful methods , which we have adapted to the questions at hand . in order to demonstrate the supremacy of qep over cep in each of the cases i)-v ) we employ these methods combined with the methods of quantum information theory . an overview of these methods is presented in the appendices : appendix [ sec : majorization ] presents the necessary facts from majorization theory and singlet conversion protocols @xcite , appendix [ sec : montecarlo ] explains some details of our monte carlo ( mc ) simulations , and finally appendix [ sec : series ] deals with series expansions . in this section , we describe the classes of quantum networks and communication protocols that we investigated . the networks we consider consist , prior to application of communication protocols , of a collection of qubits partitioned into pairs , each pair being prepared in an identical pure state @xmath9 . with appropriate choice of bases , any such state can be written @xmath10 where the schmidt coefficients @xmath11 satisfy @xmath12 and @xmath13 . we identify these pairs with bonds on a two - dimensional lattice or edges on a graph , with two spatially - separated qubits , one occupying each end of the bond . at regular positions , a small set of these qubits are arranged near enough to one another to allow measurements on any subset . such a set of qubits then constitutes a vertex ( or node or site ) which is incident to each edge that contributes a qubit to the vertex . this defines a lattice to which we apply methods of statistical physics . in particular , many results on the possibility of long - range entanglement are described using percolation theory @xcite , and depend only on the graph structure of the system . given a lattice prepared as described above , we search for the protocols consisting of local operations and classical communication ( locc ) that yield the maximum probability of achieving entanglement between two nodes separated by an arbitrarily large distance . the answer depends on the single parameter @xmath14 characterizing the state @xmath15 . even with a small palette of possible operations , finding the globally optimal solution is a difficult task . instead , we search for promising classes of protocols . the simplest protocol consists of attempting to convert the state associated with each bond to a singlet via the `` procrustean method '' of entanglement concentration , which is the optimal strategy at the level of a single bond @xcite . this conversion succeeds with probability @xmath16 ( see appendix [ sec : majorization ] . ) , while failure leaves the pair in a state with no entanglement . in this way the system is described exactly by a bond percolation process with open - bond density @xmath4 . if there is a path of open ( maximally entangled ) bonds connecting two nodes , a sequence of entanglement swapping measurements , one at each intermediate node , is then applied in order to entangle the first and last node . this protocol is the simplest example of classical entanglement percolation . here we review a few fundamental ideas in percolation theory necessary to analyze cep . the nodes in the lattice can be partitioned into sets such that each node within a set is connected to each other node in the set via a path of open bonds . such a set of nodes is called an open cluster , or sometimes simply a cluster . the central fact of percolation theory is that percolation processes on most commonly - studied lattices in dimension @xmath17 and higher exhibit a continuous phase transition as the bond density passes through a critical value @xmath6 . for @xmath5 there exists with probability one a unique ( for the lattices we study here ) cluster of infinite mass ( number of nodes ) , while for @xmath18 all clusters are finite with probability one . it follows that improving an" +"the aim of this paper is to present a novel weak galerkin finite element method for solving the stationary stokes equations . let @xmath0 be a polygonal or polyhedral domain in @xmath1 . as a model for the flow of an incompressible viscous fluid confined in @xmath0 , we consider the following equations @xmath2 for unknown velocity function @xmath3 and pressure function @xmath4 ( we require that @xmath4 has zero average in order to guarantee the uniqueness of the pressure ) . bold symbols are used to denote vector- or tensor - valued functions or spaces of such functions . here @xmath5 is a body source term , @xmath6 is the kinematic viscosity and @xmath7 is a boundary condition that satisfies the compatibility condition @xmath8 where @xmath9 is the unit outward normal vector on the domain boundary @xmath10 . this problem mainly arises from approximations of low - reynolds - number flows . the finite element methods for stokes and navier@xmath11stokes problems enforce the + divergence - free property in finite element spaces , which satisfy the inf - sup ( lbb ) condition , in order for them to be numerically stable @xcite . the stokes problem has been studied with various different new numerical methods : @xcite . throughout this paper , we would follow the standard definitions for lebesgue and sobolev spaces : @xmath12 , @xmath13 , @xmath14^d$ ] , @xmath15^d=\{\bv\in [ h^1(\omega)]^d : \bv=\b0\ { \rm on}\ \partial \omega\}\ ] ] and @xmath16 are the natural spaces for the weak form of the stokes problem @xcite . denote @xmath17 for inner products in the corresponding spaces . next we assume that @xmath18 and @xmath19 . then one of the variational formulations for the stokes problem ( [ ose1])-([ose3 ] ) is to find @xmath20^d$ ] and @xmath21 such that @xmath22 for all @xmath23^d$ ] and @xmath24 . here @xmath25 denotes the velocity gradient tensor @xmath26 . it is well known that under our assumptions on the domain and the data , problem ( [ vf1])-([vf2 ] ) has a unique solution @xmath27^d\times l_0 ^ 2(\omega)$ ] . it is easy to know that the weak form ( [ vf1])-([vf2 ] ) is also equivalent to the following variational problem : find @xmath28^d\times l_0 ^ 2(\omega)$ ] such that @xmath29 for all @xmath23^d$ ] and @xmath24 . the unique solvability of ( [ vf3])-([vf4 ] ) follows directly from that of the ( [ vf1])-([vf2 ] ) . the wg method refers to a general finite element technique for partial differential equations where differential operators are approximated as distributions for generalized functions . this method was first proposed in @xcite for second order elliptic problem , then extended to other partial differential equations @xcite . weak functions and weak derivatives can be approximated by polynomials with various degrees . the wg method uses weak functions and their weak derivatives which are defined as distributions . the most prominent features of it are : * the usual derivatives are replaced by distributions or discrete approximations of distributions . * the approximating functions are discontinuous . the flexibility of discontinuous functions gives wg methods many advantages , such as high order of accuracy , high parallelizability , localizability , and easy handling of complicated geometries . the above features motivate the use of wg methods for the stokes equations . it can easily handle meshes with hanging nodes , elements of general shapes with certain shape regularity and ideally suited for hp - adaptivity . in @xcite , wang considered wg methods for ( [ vf1])-([vf2 ] ) . similarly , in @xcite , they presented wg methods for the brinkman equations , which is a model with a high - contrast parameter dependent combination of the darcy and stokes models . the numerical method of @xcite is based on the traditional gradient - divergence variational form for the brinkman equations . in @xcite , we presented a new wg scheme based on the gradient - gradient variational form . it is shown that this scheme is suit for the mixed formulation of darcy which would present a better approximation for this case . in fact , for complex porous media with interface conditions , people often use brinkman - stokes interface model to describe this problem , which is an ongoing work for us now . in order to present a more efficient wg scheme , we prefer to utilize this gradient - gradient weak form to approximate the model . in order to unify the weak form of this interface problem , we need the numerical analysis results of this form for stokes problem . however , to the best of our knowledge , the numerical analysis of methods based on the variational form ( [ vf3])-([vf4 ] ) has never been done before . therefore in this paper , we propose a wg method based on the weak form ( [ vf3])-([vf4 ] ) of the primary problem . in addition , if we choose high order polynomials to approximate the model and use schur complement to reduce the interior dof of the velocity and pressure by the boundary dof , the total dof of this new method is less than the scheme of @xcite . the rest of this paper is organized as follows . in section 2 we shall introduce some preliminaries and notations for sobolev spaces . section 3 is devoted to the definitions of weak functions and weak derivatives . the wg finite element schemes for variational form of the stokes equation ( [ vf3])-([vf4 ] ) are presented in section 4 . this section also contains some local @xmath30 projection operators and then derives some approximation properties which are useful in a convergence analysis . in section 5 , we derive an error equation for the wg finite element approximation . optimal - order error estimates for the wg finite element approximations are derived in section 6 in an @xmath31-equivalent norm for the velocity , and @xmath30 norm for both the velocity and the pressure . in section 7 , we present some numerical results which confirm the theory developed in earlier sections . finally , we present some technical estimates in the appendix for quantities related to the local @xmath30 projections into various finite element spaces . let @xmath32 be an open bounded domain with lipschitz continuous boundary in @xmath33 . we shall use standard definitions of the sobolev spaces @xmath34 and inner products @xmath35 , their norms @xmath36 , and seminorms @xmath37 , for any @xmath38 . for instance , for any integer @xmath38 , the seminorm @xmath37 is defined as @xmath39 with notations @xmath40 the sobolev norm @xmath41 is defined as @xmath42 the space @xmath43 is same as @xmath44 , whose norm and inner product are denoted by @xmath45 and @xmath46 , respectively . if @xmath47 , we would drop the subscript @xmath48 in the notations of the @xmath30 norm and the @xmath30 inner product . in this section we will define weak functions for both the vector - valued function and the scalar - valued function , also we will introduce the weak gradients and the corresponding discrete forms . let @xmath49 be a polygonal or polyhedral domain with boundary @xmath50 . a weak vector - valued function on the domain @xmath49 is defined as @xmath51 such that @xmath52^d$ ] and @xmath53^d$ ] . let @xmath54^d,\bv _ b \in [ l^2(\partial t)]^d \},\end{aligned}\ ] ] where @xmath55 is not necessarily the trace of @xmath56 . ( @xcite ) for any @xmath57 , the weak gradient of @xmath58 , denoted by @xmath59 , is defined as a linear functional in the dual space of @xmath60^{d\times d}$ ] whose action on each @xmath61^{d\times d } $ ] is given by @xmath62^{d\times d},\end{aligned}\ ] ] where @xmath9 is the outer unit normal vector to @xmath50 , @xmath63 is the @xmath30 inner product of @xmath56 and @xmath64 , and @xmath65 is the inner product of @xmath66 and @xmath55 in @xmath67^d$ ] . consider the inclusion map @xmath68^d\rightarrow v(t)$ ] defined below @xmath69^d.\ ] ] by this map the sobolev space @xmath60^d$ ] can be embedded into the space @xmath70 . with the help of map @xmath71 , the sobolev space @xmath60^d$ ] can be considered as a subspace of @xmath70 by identifying each @xmath72^d$ ] with @xmath73 . let @xmath74 be the set of polynomials on t with degree no more than @xmath75 . ( @xcite ) the discrete weak gradient operator @xmath76 is defined as follows : for each @xmath77 , @xmath78^{d\times d}$ ] is the unique element such that @xmath79^{d\times d}.\end{aligned}\ ] ] we define a weak scalar - valued function on the domain @xmath49 as @xmath80 such that @xmath81 and @xmath82 . let @xmath83 where @xmath84 is not necessarily the trace of @xmath85 . ( @xcite ) for any @xmath86 , the weak gradient of @xmath87 , denote by @xmath88 , is defined as a linear functional in the dual space of @xmath60 ^ 2 $ ] whose action on each @xmath89 ^ 2 $ ] is given by @xmath90 ^ 2,\end{aligned}\ ] ] where @xmath9 is the outer unit normal vector to @xmath50 , @xmath91 is the @xmath30 inner product of @xmath85 and @xmath92 , and @xmath93 is the inner product of @xmath94 and @xmath84 in @xmath95 . consider the inclusion map @xmath96 defined as follows @xmath97 by which the sobolev space @xmath98 is embedded into the space @xmath99 . with the help of map @xmath100 , the sobolev space @xmath101 can be considered as a subspace of @xmath99 by identifying each @xmath102 with @xmath103 . ( @xcite ) the discrete weak gradient operator @xmath104 is defined as follows : for each @xmath105 , @xmath106^d$ ] is the unique element such that @xmath107^d.\end{aligned}\ ] ] let @xmath108 be a partition of the domain @xmath0 into polygons in 2d or polyhedral in 3d . assume that @xmath108 is shape regular in the sense as defined in @xcite . denote by @xmath109 the set of all edges or flat faces in @xmath108 , and let @xmath110 be the set of all interior edges or flat faces . denote by @xmath111 the diameter of @xmath112 and @xmath113 the meshsize for the partition @xmath108 . for any interger @xmath114 , we define weak galerkin finite element spaces as follows : for velocity variable , let @xmath115^d\times [ p_k(e)]^d , e\subset \partial t,\bv_b=\b0 ~\rm{on}~ \partial \omega\}.\ ] ] it should be noticed that @xmath55 is single valued on each edge @xmath116 . for pressure variable , we define @xmath117 also @xmath84 is single valued on each edge @xmath116 . the discrete weak gradients @xmath118 and @xmath119 on the spaces @xmath120 and @xmath121 can be computed by the equations ( [ dwvg ] ) and ( [ dwqg ] ) on each element @xmath49 respectively , that is , @xmath122 for the sake of simplicity , we shall drop the subscripts @xmath123 and @xmath124 of @xmath118 and @xmath119 in the rest of the paper . we use the @xmath30 inner product to denote the sum of inner products on each of the elements as follows : @xmath125 for each element @xmath129 , denote by @xmath130 the @xmath30 projection operator from @xmath131^d$ ] onto @xmath132^d$ ] . for each edge or face @xmath133 , denote by @xmath134 the @xmath30 projection from @xmath135^d$ ] onto @xmath136^d$].we shall combine @xmath130 with @xmath134 as a projection onto @xmath120 , such that on each element @xmath137 @xmath138 on each element @xmath129 , denote by @xmath139 the @xmath30 projection onto @xmath140^{d\times d}$ ] . denote by @xmath141 the @xmath30 projection operator from @xmath142 onto @xmath143 . for each edge or face @xmath133 , denote by @xmath144 the @xmath30 projection from @xmath145 onto @xmath146 . we shall combine @xmath141 with @xmath144 as a projection onto space @xmath121 , such that on each element @xmath137 @xmath147 then we shall present a useful property which indicates the discrete weak gradient operators are" +"complex social networks arise in a wide range of contexts , for example as corporate partnership networks @xcite , scientist collaboration networks @xcite , company director networks @xcite , film actors networks @xcite , sexual contact networks @xcite , etc . indeed , a lot of attention has been given by both physical and social scientists in recent years to model these networks so as to gain better understandings of their general structures as well as their various functions like information flow @xcite , locating individuals @xcite , disease spread @xcite , etc . for a review of recent efforts , see for example @xcite , @xcite and @xcite . while there is an apparent increase in the number of network models in the literature , not all of these models have taken full advantage of the sociological and psychological insights on how social networks may be formed . the principle of _ homophily _ , or in essence `` birds of a feather flock together , '' has been firmly established by many empirical studies @xcite . while we clearly tend to befriend those who are like us , there are many situations where having a lot of friends like us is simply because we are _ stuck _ with people who are like us in the first place . for example if you are a millionaire and all your friends are millionaires , it might simply be because you were born into an elite family and live in an elite area so you only know millionaires in your life , even though you do not actively choose to befriend millionaires over non - millionaires . therefore , it is useful to divide homophily into two main types : _ baseline _ homophily and _ inbreeding _ homophily @xcite . baseline homophily is attributed to the fact that we have a _ limited potential tie pool _ due to factors like demography and foci of activities @xcite . inbreeding homophily is conceptualised as any other kind of homophily measured over that potential tie pool this may include homophily regarding gender , religion , social class , education , and other intra - personal or behavioural characteristics . while many network models have taken inbreeding homophily into account @xcite , they have generally assumed that there are no baseline homophily effects , i.e. the potential tie pool for all actors equals the _ entire _ population . however , this is obviously not very realistic and baseline homophily effects can potentially have profound consequences on the structure of social networks . a basic source of baseline homophily is the _ geographical space_. as a matter of simple opportunity and/or the need to minimise efforts to form and maintain a social tie @xcite , we can expect that we tend to form ties with those who are geographically close to us . thus , intuitively , this creates a very strong constraint on our potential tie pool . in fact , there is ample empirical evidence that demonstrates this claim . the earliest studies of which we are aware of date back to festinger _ _ @xcite and caplow and forman @xcite both on student housing communities . the results showed that in these rather homogeneous communities , spatial arrangement of student rooms / units was an important factor in predicting whether two dwellers have at least weak ties . many other network studies also reached similar results , for example see @xcite . more recently , wellman @xcite and mok _ _ et al.__@xcite re - analysed wellman s earlier dataset on torontorian personal communities @xcite and noted that most personal friendships were indeed `` local , '' contrary to the beliefs that recent technological advances have freed us from spatial constraints . for instance , in @xcite it was found that on average @xmath0 of `` frequent contact '' ties live within a mere 1 mile radius of a typical person , while the rest of his / her ties could be directed to anywhere in the rest of the world . before embarking on specifying the model , we shall review some of the general features of social networks . not many current models simultaneously displays all of these . we suggest that , by including baseline spatial homophily into our network model , one can reproduce all the following features , at least in broad terms : 1 . * low tie density . * the number of possible ties in a network is theoretically quadratic to the number of actors , but most networks realise only a tiny fraction of these ties . the cognitive ability of human places an upper bound on the number of ties one may maintain @xcite . on the other hand , other factors corresponding to baseline homophily can also play a role @xcite ; 2 . * short average geodesic distances . * geodesic distance between two actors is defined to be the length of the shortest connection between them . in large social networks , it is believed that the typical geodesic distance between any two actors remains small . this property was demonstrated empirically by stanley milgram in his classical experiment in the 1960s @xcite , contributing to the popular saying that no one on this earth is separated from you by more than six `` handshakes '' ; 3 . * high level of clustering . * clustering is defined to be the average probability that two friends of an actor are themselves friends . equivalently , it is a measure of how having a mutual friend will heighten the conditional probability that the two friends of an actor will be friends themselves . in their well - known article @xcite , watts and strogatz demonstrated the importance of _ short - cuts _ in social networks that simultaneously display high clustering and short average geodesic distances . such an idea of short - cuts dates back to granovetter s arguments on the strength of weak ties @xcite ; 4 . * positively skewed actor degree distribution . * the degree of an actor is the number of social ties he / she has . in many social networks , a majority of actors have relatively small degrees , while a small number of actors may have very large degrees . this feature is displayed in a wide range of social networks . while it is still debated whether generic social networks have power - law , exponential , or other degree distributions , or indeed whether there is any _ generic _ distribution at all @xcite , there is no doubt that degree distributions are in general positively skewed ; 5 . * existence of communities . * in many cases , clustering does not occur evenly over the entire network . we can often observed subgroups of actors who are highly connected within themselves but loosely connected to other subgroups which are themselves highly inter - connected . we call these highly - connected subgroups _ communities _ a long tradition in social network analysis has developed a range of algorithms to identify these cohesive subsets of nodes @xcite . an example of a social network that displays all of the above properties is a well - known alliance network of 16 tribes in the eastern central highlands of new guinea @xcite . the network is depicted in fig . [ fig : gamapos ] where nodes correspond to tribes and ties correspond to alliances between the relevant tribes . first of all , the density of the network is fairly low ( @xmath1 ) given the small size of the network . the degree distribution is positively skewed ( skewness statistic = @xmath2 ) . the network is a `` small world '' in which it has low median geodesic distance ( @xmath3 ) and high level of clustering coefficient ( clustering coefficient = @xmath4 ) . most importantly , two distinct communities can be easily observed in fig.[fig : gamapos ] : one is disjoint from the rest and is fully connected ( i.e. nodes 1 , 2 , 15 , and 16 ) and the other is highly connected within itself ( i.e. nodes 3 , 6 , 7 , 8 , 11 , and 12 ) . we here represent social networks by non - directed graphs . a non - directed graph is defined to be a pair @xmath5 , where @xmath6 is the _ node set _ denoting the individual actors in the network , and @xmath7 , with each edge @xmath8 being an unordered pair of nodes @xmath9 ( @xmath10 and @xmath11 ) , is the _ edge set _ denoting the social ties among the actors . a compact way to represent a graph is through its _ adjacency matrix _ @xmath12 $ ] , @xmath13 such that @xmath14 iff @xmath15 , otherwise @xmath16 . in general , the size of the set @xmath17 ( or equivalently the dimensions of @xmath18 ) is fixed but whether an edge @xmath19 ( or equivalently @xmath14 in @xmath18 ) is determined by a random process . such a random process is defined so as to reflect the underlying social dynamics . the simplest model for social networks is the erds - rnyi or _ bernoulli _ random graph model , initiated independently by paul erds and alfred rnyi @xcite and anatol rapaport @xcite , where the random process is a _ bernoulli _ trial , i.e. @xmath20 where the constant @xmath21 $ ] is called the _ edge probability_. in other words @xmath22 are identically and independently distributed ( i.i.d . ) bernoulli random variables . due to its simplicity , it is amenable to rigorous treatments . it is fairly straightforward to show that the average geodesic distance between any two nodes is @xmath23 , a feature that , as discussed above , resembles the property in some real networks . however the level of clustering in this model can be shown to vanish as @xmath24 and it is one of the major short - comings of this simple model in modelling social networks . further , erds and rnyi showed that there is a critical edge probability @xmath25 at which there always exists a connected component containing a significant proportion of nodes in the network ( almost surely ) @xcite . such component is known as the giant component . for an extensive review of these results refer to bollobs @xcite and janson _ et al . _ @xcite . the main advantage of the erds - rnyi model is its simplicity . although it does not predict some of the generic features outlined above , it serves as a good foundation to build more realistic models . in this paper , we study a generalisation of erds - rnyi random graph model for social networks which incorporates a simple _ baseline spatial homophily _ effect in the formation of individual network ties . we note that this class of models is for a _ single snapshot _ of a network , thus _ temporal network dynamics _ are not taken into account . in section 2 , we shall specify the model and examine some of its basic properties . in section 3 , we shall outline our simulation methods and discuss the main results . in section 4 , we shall demonstrate the application of our model in a particular social network . in section 5 , we shall discuss the implications of the results and describe ongoing research on this and more generalised models . first of all , we embedded the nodes of graphs in the euclidean space @xmath26 with a _ distance _ function @xmath27 defined to map any unordered pair of nodes to a real number , i.e. @xmath28 . further , @xmath27 satisfies the standard triangle inequalities and the positivity condition" +"the standard model of particle physics describes neutrinos as massless , neutral fermions , which can be detected only via weak interactions . the observations of neutrino flavour oscillation @xcite indicate the existence of massive neutrinos . since experiments investigating these neutrino oscillations are only sensitive to differences of the square of mass eigenvalues @xmath3 and not to the absolute values , the scale and hierarchy of neutrino masses are not determined yet . an identification of the mass scheme realized in nature would not only solve the puzzle of absolute neutrino masses but could also point to the mechanisms of mass generation in extensions of the standard model . in standard cosmological models , our universe is filled with primordial neutrinos arising from freeze - out in the early universe . these neutrinos are natural candidates for non - baryonic hot dark matter . depending on the actual neutrino mass , the neutrino content of the universe can exceed the baryonic mass density . the above arguments demonstrate the importance of the absolute neutrino mass scale for both particle physics and cosmology . a model - independent approach to determine the neutrino mass is the kinematical analysis of electrons from radioactive near the endpoint energy . a non - vanishing neutrino mass reduces the electron endpoint energy and distorts the shape of the electron spectrum in the vicinity of @xmath4 . the scheme of a measurement investigating the endpoint region of the electron energy spectrum from tritium ( @xmath5 ) with an electrostatic filter is illustrated in figure [ fig - mac - e - filter ] . electrons emitted by in the source are guided magnetically through the electrostatic retarding potential of the spectrometer , to be counted by a segmented silicon detector . this _ magnetic adiabatic collimation _ followed by the _ electrostatic _ ( mac - e ) filter represents an integrating high pass filter for . this technique has been used in the mainz and troitsk experiments with different tritium sources , providing the most stringent , model - independent limits on the neutrino mass so far , with ( @xcite,@xcite,@xcite,@xcite ) @xmath6 with well understood systematic effects , both experiments have now reached their sensitivity limits . the energy resolution of a mac - e - filter depends on the ratio of the strongest magnetic field @xmath7 in the beam - line and the weakest field @xmath8 in the centre of the spectrometer . flux conservation requires that @xmath9 remains constant , where @xmath10 is the cross section of the magnetic flux tube , guiding the electrons from the source to the detector . improving the energy resolution of such an experiment needs a much lower @xmath8 and therefore a spectrometer with a much larger cross section , which will be able to contain the magnetic flux . an improved sensitivity requires not just size , but also a stronger source with higher statistics and a better understanding of systematic uncertainties . the * ka*rlsruhe * tri*tium * n*eutrino ( katrin ) experiment will use the techniques developed in mainz and troitsk with a strong gaseous molecular tritium source and an electro - static filter of unprecedented energy resolution ( @xmath11 @xcite . the expected sensitivity for the neutrino mass will be @xmath12 after three years of measurement . as the experimental observable is , an improvement in sensitivity on @xmath13 of one order of magnitude corresponds to an improvement of a factor @xmath14 in accuracy on leading to numerous technical challenges for this experiment . figure [ fig - katrin - scheme ] outlines the experimental set - up of katrin @xcite , which adds up to a total length of about @xmath15 . katrin overview : a ) tritium source ( wgts ) , b ) differential pumping ( dps ) and cryo - pumping section ( cps ) , c ) pre - spectrometer and main spectrometer , d ) detector.,width=604 ] the katrin experiment is currently under construction at forschungszentrum karlsruhe ( fzk ) , germany . with the tritium laboratory karlsruhe ( tlk ) , a unique lab is available on site , which will house the complete tritium inventory , including the source and transport section . first components such as the pre - spectrometer ( 2003 ) , main spectrometer ( 2006 ) , some magnets and a prototype detector array are on site , being thoroughly tested . the experiment is now in the construction and commissioning phase . first measurements are expected to start in 2012 , with a total measuring time of 5 years . the source and transport section includes the _ windowless gaseous tritium source _ ( wgts ) , followed by _ differential pumping sections _ ( dps ) and a _ cryogenic pumping section _ ( cps ) . the beam tubes inside the super - conducting solenoids have a diameter between @xmath16 and @xmath17 , interspersed with pump ports for turbo - molecular pumps ( tmp ) . these pumps are integrated in the closed loop tritium circulation system . the pressure inside the vacuum beam - line will range from @xmath18 at the source to less than @xmath19 in the spectrometer section . the wgts will be the standard @xmath20-electron source for long - term tritium measurements . ultra - cold molecular tritium gas ( @xmath21 ) will be injected through a set of capillaries at the centre of the @xmath22 long wgts tube with an injection pressure of @xmath23 and a flow rate of about @xmath24 ( @xmath25 ) . the density profile of the gas inside the beam - tube has to be kept stable on the @xmath26 level . the stability depends on a constant beam - tube temperature and inlet pressure in the wgts . maintaining these conditions is a very challenging task , and the technical feasibility will be demonstrated with the partly assembled wgts in 2009 . after injection the t@xmath27 molecules will be transported by diffusion over a length of @xmath28 to both ends of the source tube , where most of the tritium will be pumped out by tmps of the first stage of the differential pumping section . this process leads to an almost linear decrease of the tritium number density @xcite,@xcite . electrons from @xmath20-decays will be guided adiabatically by a magnetic field of b@xmath29 . the background generated by tritium decay within the spectrometers must be less than @xmath30 counts / s , which limits the amount of tritium permissible in the main spectrometer to a partial pressure of about @xmath31 . with a pumping speed of @xmath32 this leads to a maximum allowed tritium flow rate into the spectrometer section in the order of @xmath33 . this very large suppression factor will be achieved in two stages , based on a combination of differential ( dps ) and cryogenic ( cps ) pumping sections , with each stage providing a suppression factor in the order of @xmath34 . the first part of the tritium flow suppression is based on differential pumping @xcite,@xcite,@xcite . along the beam - line turbo - molecular pumps with high pumping speed reduce the tritium flow both at the rear and front ends of the source . as the dps elements adjacent to the wgts ( dps1-f , dps1-r ) influence the stability of the gas flow in the source , they have to be operated under almost identical conditions as the wgts . therefore these first dps sections are included in the source cryostat . the tmps have to be operated close to the beam - line , in order to minimize conductance losses . due to the strong magnets extensive tests have been made to investigate the behaviour of tmps in magnetic fields . the differential pumping system will reduce the tritium flow into the subsequent passive cryo - trapping system ( cps ) to @xmath35 ( at 273 k ) . the cps will reduce the tritium flow by another 7 orders of magnitude , allowing only a remaining flow below @xmath33 into the pre - spectrometer . during a normal measuring period of 60 days a total amount of about @xmath36 of tritium molecules can be accumulated in the cps , corresponding to an activity of @xmath37 . the beam - tube of the cps will be kept at a temperature of @xmath38 . at this temperature tritium molecules are passively adsorbed on the wall . to enhance the trapping probability , the cold surfaces of the cps beam - tubes will be covered by a thin layer of argon frost . the main advantage of a condensed gas layer , compared to a solid adsorbent like charcoal , lies in the easy removal of both the adsorbent and the adsorbed tritium , thus minimizing the residual tritium contamination of the beam - tube . after each measuring period the cps will be re - heated and the tritium gas will be returned to the closed tritium cycle . although data on hydrogen and deuterium adsorption on condensed gases are available @xcite , no data on tritium adsorption were found . the effect of electron stimulated desorption from tritium @xmath20-decay on the migration of tritium molecules along the cryo - sorption pump of the cps beam - tube and the influence on the suppression factor have been investigated in monte carlo simulations @xcite,@xcite . in order to experimentally explore the adsorption properties of condensed argon for tritium , the test experiment trap has been set up by the katrin collaboration and first results have been published for deuterium and tritium @xcite,@xcite,@xcite , confirming the cps design values . all three major components of the source and transport section are expected to be delivered between 2009 ( dps ) and 2011 ( wgts and cps ) . after commissioning tests of each components they will be connected to the spectrometer section . the source is expected to provide first tritium electrons to be analysed in the spectrometer early 2012 . the central part of the experiment will be the tandem spectrometer section . it consists of two electrostatic spectrometers of mac - e - filter type : the _ pre - spectrometer _ , allowing only electrons with the highest energies to pass into the _ main spectrometer _ , where their kinetic energy will be analysed with a resolution of @xmath39 . the high energy resolution of the main spectrometer requires large dimensions ( see fig . [ fig - mainspec ] ) . it has a diameter of @xmath1 , an overall length of @xmath40 , a surface area of @xmath41 and a volume of @xmath42 . the * pre - spectrometer * with a diameter of @xmath43 , a length of @xmath44 , a surface of @xmath45 and a volume of @xmath46 served as a prototype for the design of the main spectrometer . it demonstrated the scalability of the vacuum layout and the reliability of the large @xmath43 flange design at all temperatures . ) arrived at fzk after a @xmath47 long journey . right : a custom made adjustable cleanroom scaffolding has been set up inside the spectrometer to install the wire electrodes on the inner wall.,width=604 ] during standard operation very good uhv conditions of @xmath48 have to be maintained in both spectrometer vessels at room temperature in order to keep a low background rate . the vacuum systems are based on a combination of cascaded turbo - molecular pumps ( tmp ) and neg - pumps made of double - coated @xmath49 wide zr - v - fe getter strips . both vessels are made of electro - polished stainless steel ( 316ln ) . hydrogen outgassing from the walls is expected to be the main source of gas , which limits the final pressure in each vessel . the surface of each vacuum vessel can be baked at temperatures up" +"this presentation is a cartoon of the effective field theory ( eft ) of two and three nucleon systems as it emerged in the last three years , using a lot of words and figures , and a few cheats . for details , i refer to the bibliography of a recent review @xcite , and to papers with th.r . hemmert @xcite , g. rupak @xcite , j .- w . chen , r.p . springer and m.j . savage @xcite , p.f . bedaque @xcite , and f. gabbiani @xcite . i will mainly concentrate on the theory in which pions are integrated out as explicit degrees of freedom , but also comment on the extensions to include pions . of the plenary talks covering related subjects , e. epelbaum s contribution @xcite investigates weinberg s proposal to include pions in more detail for the few nucleon system , d.r . phillips @xcite concentrates on electro - magnetic reactions on the deuteron , r. timmermans @xcite explains how chiral symmetry is seen in a modern potential and phase shift analysis , and m. birse finally provides background on the renormalisation group point of view @xcite . for want of free neutron targets , one can not navely extract fundamental iso - scalar and iso - vector properties of the nucleon separately from experiment . on the other hand , of all nuclei , the deuteron comes closest to an iso - scalar target and hence appears well suited to extract nucleon and after removing proton effects neutron properties . still , the analysis is not straightforward because , however small the deuteron binding energy seems , binding effects are often not negligible at low energies where properties of the static nucleon are tested . although the impulse approximation of treating the nucleons inside the deuteron as quasi - free is bound to become the better the higher the typical momentum scale of the process is , the improved resolution also necessitates a more detailed description of both the binding between and structure of the nucleons : effects from meson exchanges and excited states are resolved at intermediate scales , and at even higher energies , the nucleons and mesons themselves dissolve into quarks and gluons . nonetheless , model - independent predictions and extractions at low energies can succeed because nuclear physics provides a separation of scales . this observation is a cornerstone of the effective field theory approach . effective field theory methods are largely used in many branches of physics where a separation of scales exists . in low energy nuclear systems , the scales are , on one side , the low scales of the typical momentum of the process considered and the pion mass , and on the other side the higher scales associated with chiral symmetry and confinement . this separation of scales produces a low energy expansion , resulting in a description of strongly interacting particles which is systematic and rigorous . it is also model independent ( meaning , independent of assumptions about the non - perturbative qcd dynamics ) : given that qcd is the theory of strong interactions and that chiral symmetry is broken via the goldstone mechanism , wilson s renormalisation group arguments show that there is only one local low energy field theory which originates from it : chiral perturbation theory and its extension to the many - nucleon system discussed here . three main ingredients enter the construction of an eft : the lagrangean , the power counting and a regularisation scheme . first , the relevant degrees of freedom are identified . in his original suggestion how to extend eft methods to systems containing two or more nucleons , weinberg @xcite noticed that below the @xmath1 production scale , only nucleons and pions need to be retained as the infrared relevant degrees of freedom of low energy qcd . because at these scales the momenta of the nucleons are small compared to their rest mass , the theory becomes non - relativistic at leading order in the velocity expansion , with relativistic corrections systematically included at higher orders . the most general chirally invariant lagrangean consists hence of contact interactions between non - relativistic nucleons , and between nucleons and pions , with the first terms reading @xmath2\;+ \;g_a n^{\dagger } \vec{a}\cdot\vec{\sigma } n\;- \\ & & -\;c_0 ( n^{{\mathrm{t } } } p^i n)^{\dagger } \ ( n^{{\mathrm{t } } } p^i n)\ ; + \;\frac{c_2}{8 } \left[(n^{{\mathrm{t } } } p^i n)^{\dagger } ( n^{{\mathrm{t } } } p^i ( \stackrel{\scriptscriptstyle\rightarrow}{d}- \stackrel{\scriptscriptstyle\leftarrow}{d})^2 n)+ \mathrm{h.c.}\right ] + \dots,\nonumber\end{aligned}\ ] ] where @xmath3 is the nucleon doublet of two - component spinors and @xmath4 is the projector onto the iso - scalar - vector channel , @xmath5 . the iso - vector - scalar part of the @xmath6 lagrangean introduces more constants @xmath7 and interactions and has not been displayed for convenience . the field @xmath8 describes the pion with a decay constant @xmath9 . @xmath10 is the chirally covariant derivative , and @xmath11 ( @xmath12 ) the axial ( vector ) pionic current . the interactions involving pions are severely restricted by chiral invariance . as such , the theory is an extension of chiral perturbation theory and heavy baryon chiral perturbation theory to the many nucleon system : the terms in the first line couple only pions amongst themselves , and to one nucleon , providing the familiar nuclear long range force . the terms of the second line couple two nucleons to each other and to pions via point - like interactions . like in its cousins , the coefficients of the low energy lagrangean encode all short distance physics branes and strings , quarks and gluons , resonances like the @xmath1 or @xmath13 as strengths of the point - like interactions between particles . as it is not possible yet to derive these constants by solving qcd e.g. on the lattice , the most practical way to determine them is by fitting to experiment . because the lagrangean ( [ ksw ] ) consists of infinitely many terms only restricted by symmetry , an eft may at first sight suffer from lack of predictive power . indeed , as the second part of an eft formulation , predictive power is ensured by establishing a power counting scheme , i.e. a way to determine at which order in a momentum expansion different contributions will appear , and keeping only and all the terms up to a given order . the dimensionless , small parameter on which the expansion is based is the typical momentum @xmath14 of the process in units of the scale @xmath15 at which the theory is expected to break down . values for @xmath15 and @xmath14 have to be determined from comparison to experiments and are a priori unknown . assuming that all contributions are of natural size , i.e. ordered by powers of @xmath14 , the systematic power counting ensures that the sum of all terms left out when calculating to a certain order in @xmath14 is smaller than the last order retained , allowing for an error estimate of the final result . for extremely small momenta @xmath16 , the pion does not enter as explicit degree of freedom describing long range forces . all its effects are absorbed into the coefficients @xmath17 , while formally @xmath18 in ( [ ksw ] ) . the only forces between nucleons are thus point - like two and more nucleon interactions with strengths @xmath17 . this effective nuclear theory with pions integrated out ( ent(@xmath19 ) , @xcite ) was recently pushed to very high orders in the two - nucleon sector where accuracies of the order of @xmath20 were obtained . it can be viewed as a systematisation of effective range theory with the inclusion of relativistic and short distance effects traditionally left out in that approach . because of non - analytic contributions from the pion cut , the breakdown scale of this theory must be of the order @xmath21 . for the ent with explicit pions , we would suspect the breakdown scale to be of the order of @xmath22 or @xmath23 , as @xmath1 and @xmath13 are not explicit degrees of freedom in ( [ ksw ] ) . even if calculations of nuclear properties were possible starting from the underlying qcd lagrangean , eft simplifies the problem considerably by factorising it into a long distance part which contains the infrared - relevant physics and is dealt with by eft methods and a short distance part , subsumed into the coefficients of the lagrangean . qcd therefore `` only '' has to provide these constants , avoiding full - scale calculations of e.g. bound state properties of two nuclear systems using quarks and gluons . eft provides an answer of finite accuracy because higher order corrections are systematically calculable and suppressed in powers of @xmath14 . hence , the power counting allows for an error estimate of the final result , with the natural size of all neglected terms known to be of higher order . relativistic effects , chiral dynamics and external currents are included systematically , and extensions to include e.g. parity violating effects are straightforward . gauged interactions and exchange currents are unambiguous . results obtained with eft are easily dissected for the relative importance of the various terms . because only @xmath24-matrix elements between on - shell states are observables , ambiguities nesting in `` off - shell effects '' are absent . on the other hand , because only symmetry considerations enter the construction of the lagrangean , efts are less restrictive as no assumption about the underlying qcd dynamics is incorporated . hence the proverbial quib that `` eft parameterises our ignorance '' . in systems involving two or more nucleons , establishing a power counting is complicated because unnaturally large scales have to be accommodated : given that the typical low energy scale in the problem should be the mass of the pion as the lightest particle emerging from qcd , fine tuning is required to produce the large scattering lengths in the @xmath25 wave channels ( @xmath26 ) . since there is a bound state in the @xmath27 channel with a binding energy @xmath28 and hence a typical binding momentum @xmath29 well below the scale @xmath15 at which the theory should break down , it is also clear that at least some processes have to be treated non - perturbatively in order to accommodate the deuteron , i.e. an infinite number of diagrams has to be summed or equivalently , a schrdinger equation needs to be solved . for simplicity , let us first turn to ent(@xmath19)in which the pion is integrated out . here , a way to incorporate this fine tuning into the power counting was suggested by kaplan , savage and wise @xcite , and by van kolck @xcite . at very low momenta , contact interactions with several derivatives like @xmath30 should become unimportant , and we are left only with the contact interactions proportional to @xmath31 . the dominating contribution to nucleons scattering in an @xmath25 wave comes hence from two nucleon contact interactions and is summed geometrically in fig . [ fig : deuteronprop ] in order to produce the shallow real bound state . how to justify this ? dimensional analysis allows the size of any diagram to be estimated by scaling momenta by a factor of @xmath14 and non - relativistic kinetic energies by a factor of @xmath32 . the remaining integral includes no dimensions and is taken to be of the order @xmath33 and of natural size . this scaling implies the rule that nucleon propagators contribute one power of @xmath34 and each loop a power of @xmath35 . assuming that @xmath36 the diagrams contributing at leading order to the deuteron propagator are indeed an infinite number as" +"gamma - ray bursts ( grbs ) are brief soft @xmath0ray transients powered by the dying massive stars or mergers of some compact objects . in the past decades , tremendous advances in understanding such a kind of violent explosions have been achieved @xcite . however , the physical composition of the grb outflows ( magnetic or baryonic ) is still to be better probed . in some well - studied relativistic jets for example that in active galactic nuclei , the initial ejecta are widely believed to be poynting - flux dominated because the accretion disk is too cool to launch relativistic outflow via neutrino process ( e.g. , shao et al . however , with an accretion rate high up to @xmath3 , the accretion disk surrounding the nascent stellar - mass black hole is extremely hot and the neutrino radiation is the main cooling channel . as a result the annihilation of the neutrino and antineutrinos from the disk may be able to launch a baryonic / hot fireball @xcite . regardless of the nature of the central engine ( either a stellar - mass black hole or a magnetized pulsar ) , the magnetic activity of the central engine can launch a magnetized / cold outflow @xcite . among the various methods of probing the physical composition of grb outflows , one is to study the optical flash which is believed to be powered by the reverse shock generated in the interaction between the outflow and the circum - burst medium . the idea is the following . as long as the ordered magnetic field component is much stronger than the random one generated by the shocks , the reverse - shock - accelerated - electrons will radiate more efficiently and then give rise to brighter optical flash . the degree of the magnetization of the reverse shock region can be inferred from the modeling of the reverse and forward emission self - consistently @xcite . on the other hand , the synchrotron radiation of electrons in ordered magnetic field is expected to be highly - polarized and hence the optical polarimetry will be a smoking - gun signal of the magnetized outflow model @xcite . the reverse shock emission model for optical flashes @xcite has been supported by the observations of a group of grbs ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? ? * ; * ? ? ? * ; * ? ? ? interestingly , the modeling of almost all current optical flashes favors the mildly - magnetized reverse shock emission model ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? the absence of optical flashes in other grbs @xcite can be attributed to high magnetization of the outflow that can dramatically suppress the reverse shock emission @xcite . the polarimetry of the optical flashes is rather challenging . the successful polarization measurement of the a quickly - decaying optical emission of grb 090102 got a linear polarization degree @xmath4 and has been taken as the evidence for the presence of large - scale magnetic fields originating in the expanding fireball @xcite . however , a reasonable modeling of the optical and x - ray afterglow of grb 090102 in the forward and reverse shock emission scenario was found to be not achievable @xcite . the physical origin of the quickly - decaying optical emission "" is thus less clear . recently , @xcite reported the detection of very high linear polarization degree in the early optical emission of grb 120308a . in this work we examine whether the afterglow data is in support of the reverse shock origin of the early optical emission or not . as shown later the answer is positive , hence we estimate the magnetization degree of the outflow . swift satellite triggered and located grb 120308a , a single broad pulse of @xmath5-rays , on 8th march 2012 at @xmath6 ut . the duration @xmath7 ( 15 - 350 kev ) is @xmath8 sec and the the time - averaged spectrum from @xmath9 to @xmath10 sec is best fit by a simple power - law model and the power law index of the time - averaged spectrum is @xmath11 @xcite . the x - ray telescope ( xrt ) began observing the field at @xmath12 ut , 92.6 seconds after the bat trigger . a bright , uncatalogued and fading x - ray source was detected @xcite . the optical afterglow was detected by the liverpool telescope and other ground - based telescopes @xcite . the optical emission was so bright that time - resolved polarimetry was carried out by the liverpool telescope with the purpose - built ringo2 polarimeter . at the peak time of optical emission , the linear polarization degree once reached @xmath13 and then declined to @xmath14 hundreds seconds later @xcite . it is a very robust detection and @xmath15 is the highest polarization degree of optical afterglow people have observed in all grbs . the straightforward interpretation of the polarization properties is that the early optical emission was dominated by the reverse shock component and the outflow had large - scale uniform fields that survives long after the initial explosion , as initially identified / speculated in grb 990123 @xcite . in the first 300 seconds the x - ray emission was dominated by a giant x - ray flare with a peak @xmath16 kev flux @xmath17 which is most likely attributed to the prolonged activity of the central engine . the subsequent x - ray afterglow decayed with time as @xmath18 initially and then got steeper and steeper until a jet - like break appeared at @xmath19 s. the x - ray spectrum was @xmath20 @xcite for @xmath21 and got significantly softened later on . in the standard fireball model , such spectral and temporal behaviors can be understood if at early times @xmath22 and @xmath23 suppose the circum - burst medium has a constant density profile ( i.e. , the medium is ism - like rather than stellar - wind like ) , where @xmath24 ( @xmath25 ) are the cooling frequency ( typical synchrotron radiation frequency ) of the forward shock - accelerated electrons and @xmath26 is the power - law energy distribution index of the shock - accelerated electrons . in view of the spectrum change at @xmath27 s , we expect that the cooling frequency @xmath28 at that time . on the other hand , as shown in mundell et al . ( 2013 ) the optical emission in the first @xmath29 s is likely dominated by a reverse shock emission component and the forward shock emission peaked at a time @xmath30 s with a flux @xmath31 mjy when @xmath25 crossed the observer s frequency @xmath32 hz . in the ism model , the maximal specific flux of the forward shock emission ( @xmath33 ) is a constant . hence we have @xmath34 . it is widely known that the forward shock emission is governed by the following physical parameters that can be parameterized as ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) @xmath35 @xmath36 @xmath37 where @xmath38 $ ] , @xmath39 ( @xmath40 ) is the fraction of shock energy given to the electrons ( magnetic field ) , the compton parameter @xmath41 , @xmath42 and @xmath43 . here and throughout this text , the convention @xmath44 has been adopted . as inferred from the optical and x - ray afterglow emission , we have @xmath45 kev , @xmath46 hz and @xmath47 mjy , which yield @xmath48 @xmath49 and @xmath50 where : @xmath51 @xmath52 @xmath53 now we have four variables while only three equations . the value of these variables can not be uniquely determined and hence we express @xmath54 into the number density of the medium @xmath55 . in the case of @xmath56 , the term of @xmath57 can be ignored and we have @xmath58 @xmath59 @xmath60 the dependence of all these three variables on @xmath55 is not sensitive . in the case of @xmath61 , we have @xmath62 and then have @xmath63 @xmath64 @xmath65 where @xmath66 and @xmath67 , @xmath68 , @xmath69 are constant . comparing with the case of @xmath56 , the dependence of @xmath40 and @xmath70 is rather sensitive . for @xmath71 and @xmath72 , we have @xmath73 , @xmath74 , and @xmath75 and then get @xmath76 @xmath77 @xmath78 we have solved equations ( @xmath79 ) numerically . as shown in fig.1 , @xmath80 grows quickly while @xmath40 drops sharply for @xmath81 in the case of @xmath72 . we also calculated the grb efficiency by applying a k - correction with a reasonable factor @xmath82 . considering that for typical grb the efficiency is @xmath83 and @xmath84 , we find that the value of @xmath85 is around 0.01 for @xmath72 . as already mentioned , the early optical emission is likely due to the strong reverse shock emission and the crossing time of the reverse shock is just the peak time of the optical emission ( i.e. , @xmath86 s ) . since @xmath87 ( i.e. , the reverse shock crossed the outflow at a time much later than the end of the prompt emission ) , so the fireball is thin . on the other hand , the crossing time is usually estimated as @xmath88 where @xmath89 is the initial lorentz factor of the grb outflow . since @xmath89 is very weakly dependent on @xmath90 and @xmath91 , so with the above equation we know that @xmath92 , i.e. , the initial grb outflow is ultra - relativistic . the forward - reverse shock emission has been extensively investigated . as firstly found in grb 990123 , the physical parameters of the reverse shock can be dramatically different from that of the forward shock @xcite . for the reverse shock emission , we usually have @xmath93 and the ratio between the reverse shock optical emission and the forward shock peak optical emission is estimated by ( see eq.(16 ) of jin & fan ( 2007 ) ; similar expression can be found in zhang et al . ( 2003 ) ) @xmath94 where @xmath95 is the strength of the reverse shock emission at the crossing time ( i.e. , it is assumed that at that time the lorentz factor of the decelerating outflow is half of the initial , as found in the numerical calculations ) , and @xmath96 and @xmath97 ( @xmath98 and @xmath99 are the fractions of reverse - shock - energy given to the electrons and magnetic field , respectively ) . on the one hand , the reverse shock emission peaked at @xmath100 and the peak flux is @xmath101 . on the other hand , the forward shock optical emission likely peaked at @xmath102 with a flux @xmath103 mjy . with eq.([eq : ratio ] ) we have @xmath104 in this work we assume that @xmath105 and thus @xmath106 for @xmath95 , i.e. , the reverse shock region contains magnetic field @xmath107 times stronger than that in the forward shock region . one reason for this assumption is that the initially outflow is orderly magnetized or alternatively the magnetic field generated in the internal - shock phase may have not been dissipated effectively in a short time and would play a dominant role in the reverse shock region . since an ordered magnetic field is highly needed to reproduce the rather high" +"strong ovi absorptions observed around starforming galaxies at @xmath8 with impact parameter as high as 150 kpc reveal huge gaseous galactic haloes @xcite . even conservative estimates lead to amount of gas in them far exceeding the gas reservoir in galaxies themselves . such a conclusion is based on the assumption that gas in the haloes has solar metallicity . the arguments underlying this assumption stem from the standard estimate of oxygen mass from the observed column density @xcite [ mo ] m_o = 5r^2n__ovim__o f_hit ( 0.2 f__ovi ) = 1.210 ^ 7 ( 0.2f__ovi)m _ , where a typical column density @xmath9 @xmath3 , the halo radius @xmath10 kpc , the hit rate correction factor ( covering factor ) @xmath11 are assumed following by @xcite , @xmath12 is atomic mass of oxygen . the fractional abundance of ovi under thermal collisional ionization equilibrium never exceeds @xmath13 ( e.g. * ? ? ? * ; * ? ? ? * ) , such that within this assumption eq . ( [ mo ] ) provides a lower estimate of oxygen mass in the halo @xcite . it is readily seen from here that the mass @xmath14 , i.e. around 10 to 70% of oxygen mass in the ism , is indeed a conservative estimate . in principle , this conclusion for galactic haloes to bear such a large gas mass would might solve the problem of missing baryons and metals @xcite , though requiring enormously high oxygen production and mass ejection rates . moreover , the fraction @xmath13 under collisional ionization equilibrium is kept only in a very narrow temperature range : @xmath15 k ( e.g. * ? ? ? * ; * ? ? ? it is therefore totally unrealistic to assume that all observed haloes keep their temperatures within such a narrow range independent on distance from the host galaxy . in their estimates @xcite used the ionic fractions calculated under collisional and/or photoionization equilibrium conditions , i.e. independent of time @xcite . however , ionization state of gas situated in time - dependent ( nonequilibrium ) environment can differ qualitatively from the one settled on to equilibrium , particularly , for solar metallicity @xcite . this difference can be smaller for low - density gas exposed to a strong ionizing field . however , in the process of galactic evolution both the magnitude and the shape of the radiation spectrum can change . in addition the extragalactic spectrum , which can be important on the periphery of galactic haloes , does also evolve @xcite . under such conditions it is natural to expect the ionic composition to experience time variations . in this paper we therefore concentrate on the question of whether evolution of the ionizing radiation field can result in considerable changes of fractional ionization of oxygen such to make estimates of gas mass in galactic haloes more reliable . in next sections we will demonstrate that indeed under time - dependent conditions the observed column densities of ovi correspond to at least half order of magnitude less massive haloes , which can stay in a much wider range of physical parameters . the paper is organized as follows . in section 2 we describe the details of the model . in section 3 we present our results . section 4 summarizes the results . thermal and ionization state in our model is fully time - dependent : the model involves ionization and thermal evolution of gas located at radii @xmath16 kpc in the galactic halo , exposed to extragalactic and galactic time - dependent ionizing radiation field . in this paper we only briefly touch main features of calculation of the ionization and thermal evolution of gas immersed into external time - dependent ionizing radiation . the details can be found in @xcite . we study ionization and thermal evolution of a lagrangian gas element : a gas parcel is assumed to be optically thin to external ionizing radiation . in the calculations we include all ionization states of the elements h , he , c , n , o , ne , mg , si and fe . we take into account the following major processes : photoionization , multi - electron auger ionization process , collisional ionization , radiative and dielectronic recombination , collisional excitation as well as charge transfer in collisions with hydrogen and helium atoms and ions . the total cooling and heating rates are calculated using as a subroutine the photoionization code cloudy ( ver . 10.00 , more specifically , we input into cloudy code a given set of all ionic fractions @xmath17 calculated at temperature @xmath18 , gas density @xmath19 and external ionization flux @xmath20 and obtain the corresponding cooling and heating rates . the latter also includes compton heating from x - rays . for the solar metallicity we adopt the abundances reported by @xcite , except ne for which the enhanced abundance is adopted @xcite . in all calculations we assume the helium mass fraction @xmath21 , which corresponds to [ he / h]=0.081 , and is close to the observed one @xcite . we solve a set of 96 coupled equations ( 95 for ionization states and one for temperature ) using a variable - coefficient ordinary differential equation solver @xcite . we considered the two regimes of gas evolution : isochoric and isobaric . the isochoric regime suggests that gas density in a cloud is kept constant , while in isobaric model gas pressure is assumed constant . the two regimes correspond to two opposite limits of the ratio between the cooling and the sound crossing times : @xmath22 and @xmath23 , correspondingly . in the external heating radiation field isobaric models show essentially similar thermal and ionization evolution , though on longer time scales due to decreasing density coupled to increasing temperature . it results in an increase of the cross - section of gas clouds such that their covering factor increases as well . in the process of galaxy evolution the stellar content changes : massive stars produce enormous number of uv photons and form ultimately compact objects which emit hard ionizing photons . spectrum of the ionizing radiation escaping galactic interstellar medium ( ism ) and exposing further the halo depends on amount of metals in the ism disk absorbing ionizing photons , and thus on chemical evolution of the galaxy . in order to follow evolution of stellar mass , metallicity and galaxy spectrum , we use the spectro - photometric code pegase @xcite . we assume a schmidt - like power - law starformation rate ( sfr ) : @xmath24 , typical sfr for massive starforming galaxies , where @xmath25 is the normalized mass of gas in @xmath26 . in some regions of the galaxy sfr can be inhibited by gas outflows from the disk , however , when averaged over the whole disk the sfr remains sufficiently high over the whole period of active star formation . in our models we assumed a closed - box regime . in general , though this can not be applied to galaxies with active star formation . however , many parameters related to mass and energy exchange between galaxies and the intergalactic medium , such as the rates of mass ejection from and mass accretion from the ambient medium , gas metallicity and corresponding cooling rate , clustering of sne explosions , etc are highly uncertain and hard to be coherently described phenomenologically . gas in galactic haloes is exposed by a cumulative ionizing background consisting of the extragalactic and the galactic components . the extragalactic component is uniform on galactic halo scales , and is nearly constant on timescales @xmath27 myr , while changes significantly on longer times . for the extragalactic background we accept the spectrum described by @xcite . its evolution covers redshifts @xmath28 to @xmath29 divided by 49 equally spaced log bins . contribution from possible flux sources varies over cosmological time , and irregular changes in different bands of the spectrum with redshift can be met . for this reason simple linear approximation between neighbour redshift bins was used . the galactic component instead , may change on much shorter timescales . in general , the corresponding time scale is close to the lifetime of massive stars , i.e. @xmath30 myr . this galactic radiation component originates in the central star forming region , and is seen from outer parts of the halo at distances @xmath31 kpc as a nearly spherical domain of size of @xmath32 kpc . the ionizing radiation from stellar population is partly modified by absorption in the interstellar medium of underlying bulge and disk . in order to account this absorption we assume that ionizing photons pass through a layer of neutral gas in galactic disc with the optical depth @xmath33 , throughout the paper @xmath34 @xmath3 , @xmath35 @xmath3 are considered as fiducial . the corresponding optical depths at the hi and hei lyman limits are as high as @xmath36 and @xmath37 , respectively . as a result only photons with @xmath38 ev escape the galaxy and penetrate into halo ; the ionizing flux with photons of @xmath39 ev decreases as @xmath40 . in what follows we will discuss the dependence of our results on the hi column density . in our model the galactic uv spectrum is calculated with making use the pegase code @xcite , which gives spectral luminosity in the range from 91 to 160 @xmath41 m . in order to extend the spectrum to higher energies ( up to @xmath42 ev , responsible for ionization of highly charged ionic species ) we use the empirical relation between the x - ray luminosity and the star formation rate ` @xmath43 ' @xcite . this relation is well established for massive starforming galaxies considered here . overall the cumulative spectrum varies on time scales from several to hundreds of millions years . we consider gas in outer haloes of massive ( milky way type ) starforming galaxies with stellar mass of several @xmath44 . recent simulations of the milky way halo show that it extends up to the virial radius of the milky way ( i.e. , @xmath16 kpc ) with densities ranging within @xmath45 @xmath7 @xcite . observational estimates of the circumgalactic gas density around the milky way and other local group galaxies give similar numbers @xmath46 @xmath7 at @xmath47 kpc @xcite . in our calculations we follow these numbers and set @xmath48 @xmath7 in the circumgalactic volume . we consider both isochoric and isobaric regimes . we start the calculations at @xmath49 ( the lookback time is around 10 gyrs ) . this timescale is nearly the cooling time for hot gas with @xmath50 k and @xmath45 @xmath7 @xcite . the last major merging for milky way - type galaxies is thought to occur earlier than @xmath51 ( e.g. , * ? ? ? the initial ionic composition and the temperature are set equal to the ones corresponding to photoequilibrium in gas exposed to the extragalactic haardt & madau spectrum at @xmath49 . such radiation field is sufficient to force low density gas with @xmath19 in the accepted range to settle quickly onto photoequilibrium @xcite . calculations cover physical time scales much longer than the relaxation time scale of ionization and thermal processes in gas exposed to the time - dependent spectrum adopted here . gas metallicity in our models is assumed to range within @xmath52 to @xmath53 . higher metallicities are rare in dla qso and dla grb absorbers @xcite . the lower limit lies around ten times above the upper limit of the igm metallicity at @xmath54 ( e.g. , * ? ? ? * ; * ? ? ? ( solid black ) , and the stellar mass , @xmath55 ( solid grey ) ; the initial time corresponds to @xmath49 . the four models with the rate @xmath56 are shown : two" +"the qcd sum rule ( qcd - sr ) approach to qcd continues to be a highly active field . the influence of the field is reflected in over 1500 references to the seminal paper of shifman , vainshtein and zakharov ( svz ) @xcite , with over 380 of these references following the beginning of 1992 @xcite . while the approach has been applied to a variety of hadronic observables in both vacuum and finite density nuclear matter , a comprehensive review of the systematic errors associated with the approach has not been considered . one of the key assumptions of the approach is the use of the so called `` continuum model '' to remove excited state contaminations from the hadron correlator under investigation . recently , the continuum model for the nucleon was tested by using correlation functions calculated via lattice regularized qcd @xcite . the results suggest that the continuum model adequately removes the excited state contaminations and allows the isolation of the ground state . the success of the continuum model warrants a more careful investigation of other aspects of the qcd - sr approach so that uncertainties in the predictions may be reliably and quantitatively determined . the focus of this paper is to establish a rigorous procedure for extracting quantities of phenomenological interest from qcd sum rules . the main conclusion of this investigation is that qcd sum rules work and they are predictive when the analysis is done rigorously . the ground state masses of the @xmath0-meson and the nucleon are used to introduce the concepts . however , the procedures introduced here are more generally applicable to quantities of current experimental interest . the goal is to shed light on the stability of qcd sum rule analyses and thus the accuracy to which observables may be reliably determined . implementation of the procedure introduced here does not lead to slight adjustments in the extracted parameters , but rather leads to qualitatively different conclusions . it will become apparent that most existing qcd - sr investigations of nucleon properties are in fact unreliable . previous calculations are based on sum rules in which neither the operator product expansion ( ope ) nor the phenomenological description are under acceptable control . the qcd - sr method is presently the best fundamentally based approach for investigating the properties of hadrons in nuclear matter , as the lattice approach is challenged by a number of formidable obstacles @xcite . issues surrounding the finite width of the rho - meson make reliable lattice calculations of @xmath2 mixing very difficult . these are two of the many topics of current interest to nuclear physicists where the best fundamentally based approach is that of qcd - srs . moreover , the approach has minimal model dependence . hence it is imperative to probe the predictive ability of the approach and the ideas presented here are currently being applied to these topics mentioned above @xcite . the most significant source of uncertainty in the qcd sum rule approach is an imprecise knowledge of the vacuum condensates appearing in the operator product expansion ( ope ) . this is particularly problematic for the higher dimension operators , where one usually invokes the vacuum saturation hypothesis ( factorization ) to replace higher - dimension - operator vacuum - expectation values by products of lower - dimension operators . a list of key sources of uncertainty in the qcd - sr approach should include : * the unfactorized condensate values , * factorization of higher dimensional operators , * small but neglected @xmath3 corrections , * the truncation of the operator product expansion ( ope ) , * the selection of the regime for matching the qcd and phenomenological sides of the sum rules , * uncertainties associated with the summation of perturbation theory in large orders , and * the possibility of significant direct instanton contributions . with the exception of direct instanton contributions , the effects of these uncertainties will be estimated via a monte - carlo error analysis . gaussian distributions for the condensate values are generated via monte carlo . these distributions are selected to reflect the spread of values assumed in previously published qcd - sr analyses , and the uncertainties such as operator factorization listed above . these distributions provide a distribution for the ope and thus uncertainty estimates for the ope which will be used in a @xmath4 fit . in turn , the ope distribution provides distributions for the phenomenological fit parameters , thus establishing the predictive ability of the qcd - sr approach . in the field of qcd inspired models , the focus is often on whether or not the model is able to encompass the known experimental data , as opposed to assessing the predictive potential of the method . a review of the qcd - sr literature leaves no doubt as to whether or not the qcd - sr method is able to encompass the established data . the poorly determined condensate values and arbitrary aspect of the matching borel regime provides tremendous freedom in devising ways to achieve the desired result in fact , it is difficult to find qcd - sr - based predictions of hadronic observables which fail to agree with experiment . this is somewhat surprising , since the physics responsible for some observables may be poorly represented in a truncated ope commonly limited to distances of less than 0.3 fm . most qcd - sr calculations of nucleon properties in the literature fall short in the analysis stage where the phenomenological parameters are determined by matching the qcd and phenomenological sides of the sum rules . typical analysis short - comings include : * selecting a single value for the borel parameter which gives `` nice '' results . a borel _ regime _ should be selected in order to evaluate the stability and reliability of the results . * a selection of the borel regime without careful regard to ope convergence nor maintaining ground state dominance of the phenomenological side of the sum rules . * the fixing of search parameters ( such as the continuum threshold ) to preferred values . it will become apparent that this introduces a strong bias to the remaining fit parameters which may not reflect the properties of qcd . * claiming an accuracy for qcd - sr predictions without supporting calculations . occasionally a `` stability analysis '' @xcite is considered , in which fit parameters are monitored as a single condensate value is varied . however , such analyses explore a relatively small corner of the condensate parameter space . in general , former procedures adopted for matching the two sides of the sum rules lack the level of rigor which will be presented here . this general lack of rigor can be traced back to the original paper of svz @xcite . in their conclusions , they comment `` we prefer not to deepen into the debris of computer calculations , sophisticated fit programs , arranging error bars here and there@xmath5 '' while this may be appropriate for a seminal paper on the qcd - sr approach , continuation of this philosophy has lead to strong negative criticism of the qcd - sr field . it is not uncommon to hear remarks such as `` qcd sum rules are useful only if you know the answer . '' or `` you can get anything you want from qcd sum rules . '' and `` 10% here , 10% there pretty soon you re talking about real numbers ! '' these remarks are unfortunate , as a rigorous and proficuous analysis is possible . in this paper , a method for the quantitative determination of phenomenological quantities with uncertainties will be presented . since this paper is directed to both qcd - sum - rule practitioners and skeptics alike , we begin by briefly outlining the qcd - sr approach in section [ qcdsr ] . a more pedagogical review of the approach may be found in the recent review article of ref . this section also introduces the `` ioffe formula '' @xcite , argued by many to qualitatively encapsulate a description of the nucleon mass in terms of the chiral symmetry breaking order parameter @xmath1 . uncertainties associated with the evaluation of the ope will be addressed via a new monte - carlo based procedure . estimates for these uncertainties are presented in section [ uncert ] . section [ analysis ] details the monte - carlo uncertainty analysis and discusses the optimization algorithm and cautious convergence criteria used in the following . section [ rho ] presents an analysis of @xmath0-meson sum rules . here the criteria for the selection of the regime for matching the qcd and phenomenological sides of the sum rules is reviewed . reasonable alternatives are considered via monte carlo . these considerations lead to the selection of the optimal interpolating field for nucleon sum rules . new insights into unconventional nucleon interpolators obtained from the lattice qcd investigation of ref . @xcite play a significant role here . section [ nucleon11 ] reviews the selection of the optimal nucleon interpolating field for correlators obtained from spin-1/2 interpolating fields . the effects of choosing non - optimal interpolators is demonstrated . section [ nucleon13 ] explores additional sum rules obtained from the overlap of the generalized spin-1/2 and a spin-3/2 interpolator . in section [ correl ] we explore the correlations between condensate values , fit parameters and sum rule consistency . these correlations serve to identify the roles of the leading terms of the ope in hadronic physics . the validity of the `` ioffe formula '' is evaluated here , and these results may be of interest to those modeling the qcd vacuum . the contingency table analysis reveals that the intimate relationship between the quark condensate and the nucleon mass suggested in the `` ioffe formula '' is invalid . the necessity of direct instanton contributions to the qcd sum rules is determined in section [ instantons ] . we demonstrate that there is no evidence indicating that direct instanton contributions are required to maintain sum rule consistency . the implications of the results of this analysis on coordinate space correlators are discussed in section [ coordimpl ] . finally , section [ conclusions ] summarizes the findings of this in - depth investigation . the underlying principle of field theoretic approaches to hadron phenomenology is the ansatz of duality . that is , it is possible to simultaneously describe a hadron as quarks propagating in the qcd vacuum , and as a phenomenological field with the appropriate quantum numbers . hadron masses are extracted from an analysis of the two - point function @xmath6 the interpolating field @xmath7 is typically constructed from quark field operators combined to give the quantum numbers of the hadron under investigation . the @xmath0-meson interpolator related to the decay constant is @xmath8 to maintain maximal overlap with the ground state relative to excited states , only interpolators without derivatives are considered . for the nucleon we begin by considering the most general spin-1/2 nucleon interpolator @xmath9 where @xmath10 and @xmath11 @xmath12 is the interpolator typically used in lattice qcd analyses . @xmath13 vanishes in the nonrelativistic limit . however in a theory with light relativistic current quarks , there is no reason to exclude such an interpolating field _ a priori _ @xcite . with the use of the fierz relations , the combination of the above two interpolating fields for @xmath14 may be written @xmath15 [ chisr ] giving the proton interpolating field advocated by ioffe @xcite and often found in qcd - sr calculations . at the phenomenological level one proceeds by inserting a complete set of eigenstates with the quantum numbers of the interpolator . the ability of the interpolator to annihilate a positive parity baryon to" +"insulating states of non - trivial topological order have attracted much attention both theoretically and experimentally . a topological insulator has a remarkable property of being metallic on the surface albeit insulating in the bulk . recently much focus is on a specific type of topological insulators,@xcite which are said to be `` @xmath0-nontrivial '' . @xcite the latter occurs as a consequence of interplay between a specific type of spin - orbit interaction and band structure . @xcite such systems are invariant under time reversal and show kramers degeneracy . from the viewpoint of an experimental realization , the original idea of kane and mele ( km ) @xcite was often criticized for being unrealistic , since it relies on a relatively weak spin - orbit coupling in graphene . in order to overcome such difficulty , bernevig , hugues and zhang ( bhz ) proposed an alternative system @xcite , which is also @xmath0-nontrivial but not based on graphene . bhz model was intended to describe low - energy electronic properties of a two - dimensional ( 2d ) layer of hgte / cdte quantum well . conductance measurement in a ribbon geometry @xcite showed that the system exhibits indeed a metallic surface state , which is also called _ helical _ edge modes . this paper highlights the spectrum and wave function of such helical edge modes in the bhz model . respecting appropriately the crystal structure of original hgte / cdte quantum well , one can safely implement it as a tight - binding model on a 2d square lattice.@xcite note , however , that in contrast to km model which can be represented as a purely lattice model , in bhz an internal spin-@xmath14 degree of freedom , stemming from the @xmath15-type @xmath16 and @xmath17-type @xmath18 orbitals , resides on each site of the square lattice in addition to the real electronic spin . we also mention that in the continuum limit with vanishing topological mass term , km model has two valleys ( @xmath19 and @xmath20 ) , whereas bhz has a single valley ( at @xmath21 ) . another idea which we can borrow from graphene study is the sensibility of edge spectrum on different types of edge structure , i.e. , either zigzag of armchair type . @xcite this applies also to the helical edge modes of bhz topological insulator in a ribbon geometry , since the edge spectrum is predominantly determined by how the 2d bulk band structure is `` projected '' onto the 1d edge axis . indeed , the structure of bhz helical edge modes has been extensively studied in ref . @xcite in the @xmath7-edge geometry and in the tight - binding implementation . however , in the practical experimental setup , @xcite this is certainly not the only one which is relevant to determine the transport characteristics at the edges . here , in this paper our main focus is on the other representative geometry , the @xmath11-edge . in the @xmath11-geometry , as a consequence of the specific way how `` hidden '' dirac cones ( or valleys ) in the 2d spectrum is projected onto the @xmath11-axis , edge modes show some unexpected behaviors . in order to motivate further the present study , let us first recall the importance of edge modes in the quantum hall state under magnetic field that exhibits a finite and quantized ( charge ) hall conductivity @xmath22 . in realistic samples with a boundary , quantization of hall conductivity is attributed to dissipationless transport due to a gapless chiral edge mode . in contrast to charge hall effect , a finite _ spin _ hall current does not need breaking of the time reversal symmetry . in the quantized spin hall ( qsh ) effect , the chern number in the bulk takes an integral value , and correspondingly there appears integral pairs of gapless edge modes . on the other hand , the @xmath0 topological insulator is characterized by an odd number of gapless modes per edge that are robust against weak perturbations preserving the time - reversal symmetry . the existence of such gapless edge states is generally guaranteed by a general theorem under the name of bulk / edge correspondence . @xcite the bhz model has a convenient feature that the location of the minimum energy gap can be controlled by changing the parameters in the model . in particular , the sign of spin hall conductivity changes discontinuously as the mass parameter of the model is varied . hence , the corresponding change of edge spectrum should provide useful information on the bulk / edge correspondence . furthermore , understanding of the nature of edge modes under specific edge geometries should serve as possible application of topologically protected phenomena in nano - architectonics . we take the representative cases of the @xmath7- and @xmath11-edges , which we call also the straight and zigzag edges , respectively . this paper is organized as follows : in sec . ii , we clarify our motivations to study the lattice version of a @xmath0 topological insulator ( bhz model ) , implemented as a nearest - neighbor ( nn ) tight - binding model . explicit form of the bhz lattice hamiltonian is introduced in sec . it is demonstrated that by considering a lattice model , one naturally takes into account _ hidden _ dirac cones , the latter lacking in the analyses based on the continuum dirac model . in secs . iv and v , we study the detailed structure of gapless edge modes under two different edge geometries : straight and zigzag edges . v is the highlight of this paper , demonstrating that the zigzag edge modes of bhz lattice model show unique features . we first point out that at @xmath23 , a pair of completely flat spectrum appears at @xmath24 ; besides the edge wave function can be trivially solved . we then show , in a half - empirical way , that this analytic exact solution at @xmath23 can be generalized to the case of an arbitrary @xmath25 $ ] ( this idea is schematically represented in fig . [ zig_concept ] ) . using the exact solution thus constructed , we highlight the nature of _ reentrant _ edge modes , another unique feature of the edge modes in the @xmath11-edge geometry . the reentrant edge modes possess two contrasting characters in real and momentum spaces : though well distinguished in real space , they live in an extremely small energy scale in the spectrum . vi is devoted to conclusions . the gapless edge modes of bhz topological insulator are also treated in the framework of continuum dirac model in appendix a. it has been well recognized that the quantized spin hall conductivity is determined by wave functions of bloch electrons over the entire brillouin zone . on the other hand , only the electronic states near the fermi level are relevant to the change of the hall conductivity when the fermi level is shifted . simplified effective models are useful for the latter case since various theoretical techniques can be employed in the low - energy range . in this paper , we work mainly with the lattice version of the bhz model , and make some comments in the low - momentum limit . why do we have to go back to a lattice model ? firstly , because we need to recover the _ correct _ absolute value of spin hall conductance @xmath26 . the latter is defined as the difference of hall conductance for up and down ( pseudo ) spins multiplied by @xmath27 : @xmath28 in quantized spin hall ( qsh ) systems , the spin hall conductance is quantized to be an integer in units of @xmath29 . in the language of charge conductance . ] this is completely in parallel with the quantization of _ charge _ hall conductance in units of @xmath30 in quantized hall system . in both cases , such integers are topological invariants and protected against weak perturbations . on the other hand , if one calculates , using kubo formula , the contribution of a single dirac fermion , e.g. , of the continuous dirac model at the @xmath21-point @xcite to spin hall conductance , then this gives _ half _ of the value expected from the topological quantization . @xcite in order to be consistent , it is naturally assumed that there must be _ even _ number of dirac cones . @xcite however , the low - energy effective theory with which we are starting contains obviously a single dirac cone . @xcite as we will see explicitly , such trivial discrepancy is naturally resolved by considering a lattice version of the bhz model . another aspect motivating us to employ the lattice version of bhz model is the fact the idea of an edge states is a real space concept , and we need _ a priori _ to go back to real space to give an unambiguous definition to it . in this paper , we highlight the detailed structure of gapless edge modes under a specific edge geometry . clearly , introduction of the latter needs a precise description in real space . recall also here that edge modes of graphene nano - ribbon exhibit contrasting behaviors in zigzag and armchair edge geometries : e.g. , the system becomes either metallic or semi - conducting in the armchair geometry , depending on @xmath31 , with @xmath32 being the number of rows , whereas a completely flat edge mode appears in the zigzag geometry . @xcite where does the difference comes from ? in momentum space , the question is how the bulk dirac cone structure look like when viewed from the edge . note that in the zigzag geometry the flat edge mode connects the two dirac points : @xmath19 and @xmath20 , whereas in the armchair geometry these two points are projected onto the same point at the edge . in a topological insulator , this bulk to edge projection is even a more subtle issue , since not all the dirac cones are explicit ( see table i ) . in a sense , zigzag edge in the square lattice bhz model ( see fig . [ geo_zig ] ) plays the following double role : it resembles the zigzag edge in graphene at @xmath33 , whereas it may rather resemble the armchair edge at @xmath34 and at @xmath35 . [ cols=""<,<,^,^,^,^,<,^,^"",options=""header "" , ] [ 4dpts ] spin hall conductance is a topological quantity determined by the _ global _ structure of entire 2d brillouin zone . the helical edge modes , encoding the same information , is , therefore , _ a priori _ not derived from a local description in the 2d brillouin zone . one exception to such a general idea is the study of ref . @xcite ( see also appendix ) , in which gapless edge modes are derived from the continuous model in a strip geometry by simply applying the condition that all the pseudo spin components of wave function vanish at the boundary . ( @xmath3)-sublattice component of the wave function vanishes at one ( the other ) boundary . for details , see , ref . @xcite . ] this implies that information about the helical edge modes is actually encoded in the original ( single ) dirac cone . this seems to be rather surprising , if one recalls that in the case of km model , the distinction between trivial and non - trivial phases is made by a relative sign of the mass gap at @xmath19- and @xmath20- points , which are , of course , macroscopically separated in momentum space . here , in the bhz model , the same distinction is made by relative sign" +"the lisa mission is a collaboration between esa and nasa to build and operate a space - based laser interferometer aimed at detecting and studying gravitational waves ( gw ) of astrophysical origin . the current schedule places the launch around the year 2011 , and the 3 - 10 years observation period is expected to produce a number of observations of galactic binaries @xcite , of massive black hole mergers and captures , and possibly of a cosmological stochastic background @xcite . early studies of the data analysis techniques that will be required to observe these signals are important since they couple our present knowledge about the sources lisa will be able to observe to the science requirements guiding the design of the lisa mission itself . it is in this context that we present here a study of the accuracy that can be expected for the characterization of the noise in the lisa detector once it has been placed in its heliocentric orbit . this is needed not only for being able to assess the lisa sensitivity in a region of the frequency band where the stochastic signal from coalescing galactic binaries would prevent it , but most importantly for being able to detect weak gravitational wave signals with confidence . theoretical modeling and pre - launch performance measurements of flight - unit instruments will certainly be performed . however these might not be sufficient to achieve the level of accuracy required in the analysis of the data collected during the inflight operation of lisa . specifically , we calculate in the low frequency regime the optimal approximations for the spectra of the noise affecting the interferometric combinations sensitive to gravitational waves , by relying _ only _ on all the possible cross - spectra between the interferometric combinations that are sensitive to gravitational radiation and the symmetrized - sagnac combination , @xmath0 . the rational behind this is that @xmath0 couples very weakly to gravitational radiation while it is affected by the same instrumental noises as the other combinations @xcite . these approximations give a lower bound on the error that can be achieved by estimators which make no prior assumptions about the characteristics of the various noise sources . such estimator could be used for carrying out the full analysis , or for validating the noise models one could adopt for implementing more sophisticated and efficient data analysis techniques . an outline of the paper is given here . section [ lbdan ] presents a review of the lisa baseline design , which is then followed by a discussion of the noise characterization problem in section [ ifnc ] . in section [ mia ] we show that closure for the solution to the noise characterization problem does not exist , and that only approximate solutions can be implemented . in section [ nm ] we describe the noise model used in our calculations , which accounts for possible cross - correlations between pairs of various noise sources . although these terms have been neglected in the literature , they could contribute to the overall noise budget of the mission , and for this reason they are included in our analysis . we then present in section [ ebotep ] our calculation of the lower bound on the estimated noise spectra in the lisa interferometric combinations that are sensitive to gravitational radiation . in section [ discussion ] we finally provide our comments on the implications of these bounds for the astrophysical reach of the lisa mission , and on possible implementations of noise estimation algorithms that would approach the error bounds we estimate . the lisa mission will consist of three spacecraft flying in an approximately equilateral triangle formation . the length of the arm opposite to spacecraft @xmath1 ( @xmath2 ) is labeled @xmath3 . the three nominal arm lengths will be equal to @xmath4 s ( @xmath5 ) , and they will differ from each other by at most a few percents during the entire duration of the mission . in contexts where the differences between the length of the arms can be disregarded , we will simply refer to the nominal arm length @xmath6 , without indices . as it is illustrated in figure [ fig : opticalbenches ] , each spacecraft will contain two optical benches . each bench will be designed to bounce a laser beam between each of its proof mass and another proof mass on a distant spacecraft . the proof masses are mechanically isolated from their optical bench , and their relative position is measured with electrostatic sensors . these generate inputs for the drag - free control systems that allow the spacecraft to isolate the proof masses from external disturbances in such a way to maintain them ( to a very good approximation ) in a free - falling configuration in the directions to the other two spacecraft . in addition , laser beams will be bounced off the back of the proof masses and will be exchanged between the optical benches on a given spacecraft in order to sense the motion of the optical benches relative to the proof masses . and @xmath7 . @xmath8 denote normal vectors along the triangle arms , and @xmath9 denotes the random velocity vector of proof mass 1.,title=""fig:"",height=288 ] with this baseline design of the lisa spacecraft , the frequency noise of the lasers will dominate the secondary noise sources ( such as acceleration noise of the proof masses or optical path length distortions ) by approximately seven orders of magnitude in the frequency band of interest ( @xmath10 hz ) . time delay interferometry ( tdi ) has been proposed @xcite as a robust way for suppressing the frequency fluctuations from the lasers and the mechanical vibrations of the optical benches to levels smaller than that identified by the secondary noise sources . this is done by properly time - shifting and linearly combining the measurements of the phase differences between the coherent laser beams exchanged between the three pairs of spacecraft and the three pairs of on - board optical benches @xcite . in reference @xcite it has been shown that the entire space of the tdi combinations can be generated by four combinations , called @xmath11 and @xmath0 , which are the sagnac interferometric combinations lisa will be able to synthesize . since ( @xmath12 ) can be regarded as a basis for the entire space of the lisa tdi combinations , in what follows we will limit our analysis to these four interferometric data . it should be noted that the modifications of the sagnac observable ( @xmath12 ) required in order to account for the rotation of the lisa array @xcite and variation in time of its arm lengths @xcite can be disregarded in the analysis presented here . although it will be critical to account for these effects in order to suppress the laser phase fluctuations below the secondary noise sources , the modifications introduced to the gravitational wave and secondary noise responses entering into the tdi combinations @xmath11 and @xmath0 ( derived under the assumption of a stationary lisa configuration ) will be negligibly small . it is anticipated that the dominant noises affecting all the tdi combinations will be introduced by the proof masses and optical path noises ( shot noise and beam pointing fluctuations ) . in the notation of fig . [ fig : opticalbenches ] , the frequency fluctuations generated by the mechanical vibrations of the proof masses are given by @xcite @xmath13 where bold characters are either vectors or matrices , @xmath14 , and @xmath15 . we shall use below the definitions @xmath16 , etc . denoting by @xmath17 the optical path noise affecting the doppler measurement @xmath18 , the optical path noise contribution to @xmath0 is given by the following expression @xcite @xmath19 if we denote by @xmath20 the contribution to the @xmath0 observable from a gravitational wave ( * ? ? ? * eq . ( 60 ) ) , it follows that @xmath0 can be written in the following form @xmath21 where the instrumental noise part is given instead by @xmath22 in what follows we will be interested in calculating the spectrum of the @xmath0 combination @xmath23,\ ] ] where @xmath24 is the fourier transform of @xmath0 , and @xmath25 denotes the expectation value over many realizations of the instrumental noise . in the particular case of a stochastic gravitational wave signal , the expectation value will be performed over the realizations of the signal too , although it always will be assumed to be independent of ( and therefore uncorrelated with ) the noise . under these assumptions we can write @xmath26 in what follows , for any pair of interferometric observables @xmath27 , @xmath28 will refer to the following function of the fourier frequency @xmath29 @xmath30.\ ] ] for simplicity of notation we will write @xmath31 for @xmath32 and @xmath33 for @xmath34 . as implied by eqs.([eq : anoise],[eq : onoise ] ) , the spectrum @xmath35 can be expanded in terms of proof mass and optical path noises as follows @xmath36 + \sum_{i=1}^2 \sum_{j = i+1}^3 [ s_{n_{ij}n_{ij } } + s_{n_{ji}n_{ji } } ] \nonumber \\ - 2 { { \rm re}\;}[s_{n_{12}n_{13 } } + s_{n_{21}n_{23 } } + s_{n_{31}n_{32}}],\end{aligned}\ ] ] where @xmath37 denotes the real part of @xmath38 ( @xmath39 is the imaginary part ) , and where for the sake of generality we have included terms accounting for correlations between proof masses on - board the same spacecraft and between optical path noises along the same arm ( see section [ nm ] for the physical motivations behind the inclusion of these correlations in our analysis ) . as it is well known , the optimal statistics to detect a signal @xmath40 in noisy data is the matched or wiener filter , at least when the noise distribution can be well approximated as gaussian . for the combination @xmath41 , for instance , this statistics is @xmath42 where @xmath43 is the signal @xmath40 filtered by the transfer function of gravitational wave to the combination @xmath41 . as shown in @xcite , the three tdi sagnac observables @xmath41 , @xmath44 , and @xmath45 can be combined to form the new data set @xmath46 , @xmath25 , and @xmath47 . the advantage of these three combinations is in their noises being statistically uncorrelated for every frequency @xmath29 , @xmath48 = 0,\ ] ] and similarly for all possible pairs taken among @xmath46 , @xmath25 , and @xmath47 . the uncorrelated combinations are obtained by diagonalizing the correlation matrix @xmath49 leading to an optimal detection statistics for the signal @xmath40 that is given by @xmath50 where @xmath51 $ ] and @xmath52 $ ] , for @xmath43 , @xmath53 , and @xmath54 the signal @xmath40 filtered by the transfer functions of gravitational waves to the combinations @xmath41 , @xmath44 , and @xmath45 respectively . ( [ eq : matchedone ] ) is only a special case of eq . ( [ eq : matchedmany ] ) , with @xmath55 , @xmath56 and @xmath57 restricted to the one - dimensional case . the optimal signal - to - noise ratio @xmath58 that can be achieved by eq . ( [ eq : matchedmany ] ) is @xcite @xmath59 any variation of the detection statistics ( up to a scaling factor ) will give a smaller signal - to - noise ratio , so eq . ( [ eq : matchedmany ] ) is the optimal detection statistics . it is also true that the detection statistics of eq . ( [ eq : matchedmany ] ) maximizes the probability of detecting the signal for a fixed value of the false alarm probability . since the correlation matrix can only be known with some finite accuracy , we can write it in the following way @xmath60 where @xmath61 is the true correlation matrix" +"recent progress in creating artificial magnetic heterostructures @xcite gives an impetus to the theory of phase transitions in multilayers . while the related experimental and theoretical efforts have been so far mostly concentrated at microscopic effects , this paper addresses the problem of universal features associated with large scale ordering in superlattices . suppose the superlattice is built of atomically thick layers of two magnets , which taken separately both order through second order phase transitions at two respective bulk critical points @xmath5 . suppose also for simplicity that both components are _ ferro_-magnets and that the critical behavior at their bulk curie points is similar , i. e. both components belong to the same universality class . the question then is : at what temperature @xmath6 will long range ferromagnetic order appear in the superlattice and what critical behavior will be observed at that temperature ? one can reasonably expect that in the limit of thick layers the answers to these questions will be largely universal , depending only on the bulk critical properties of the two components and the geometry of the superlattice ; these universal aspects of the problem represent the subject of this paper . we will consider the simplest superlattice geometry ( fig . 1 ) constructed of two elementary building blocks : slabs , or layers , of two ferromagnets , 1 and 2 , of finite thickness @xmath7 and @xmath8 , respectively . the slabs are stacked periodically in the @xmath9-direction , so that @xmath10 is the period . the system is homogeneous in the remaining @xmath11 dimensions . while the dimensionality @xmath2 ( fig . 1a ) is naturally the most interesting one in view of experimental applications , the planar , @xmath12 , superlattice geometry can be quite conceivably realized by cutting a thin film out of a three - dimensional multilayered sample ( fig . 1b ) or by deposition of a magnetic film on a substrate , which is itself cut out of a superlattice . extension of our consideration to @xmath12 is important because of analytical tractability of two - dimensional models . being interested in the long wave length aspects of the problem , we will consider the limit of atomically thick slabs : @xmath13 , where @xmath14 are the thicknesses of elementary , molecular layers of the two components , respectively ; correspondingly , the interfaces separating two subsequents slabs do not have to be atomically smooth . naturally , universality extends applicability of the results obtained below beyond this particular magnetic model ; among other interesting applications are a superfluid in a periodic matrix and a superfluid film deposited on a periodic substrate . universal critical phenomena related to three different geometrical elements present in a superlattice have been extensively studied theoretically and , to a variable extent , experimentally . first , at a _ single _ interface separating _ half - infinite _ near - critical , say @xmath15 and disordered , @xmath16 , magnets , one expects _ ordinary surface critical _ phenomena to take place at the near - critical side of the interface . it has been established theoretically @xcite that the critical exponents and amplitudes characterizing surface values of various observables are quite different from those in the bulk , as well as from the @xmath17-dimensional ones . however , experimental confirmation of those theoretical findings has turned out to be difficult . note that near @xmath18 , where the other half of the single interface model goes through the criticality , the first one is already ordered and imposes a magnetic field acting at the surface of the second component . therefore , one expects _ normal surface critical _ behavior @xcite to take place at the interface near @xmath18 . second , near the bulk critical temperature @xmath19 of the @xmath20-th , @xmath21 , component a thick , @xmath22 , _ single _ slab of that component exhibits a dimensional crossover from the critical behavior characteristic of bulk , @xmath0-dimensional , samples to the @xmath11-dimensional critical behavior , as observed in thin films of the same material @xcite . we will refer to this crossover as _ bulk - to - film _ below ; it has been observed experimentally @xcite . finally , in a system of _ thin _ layers connected to each other by very interlayer bonds , near the critical temperature @xmath23 of a single layer one expects a crossover from @xmath17-dimensional to the bulk , @xmath0-dimensional behavior , which we will call _ film - to - bulk _ crossover below . this type of dimensional crossover has been well experimentally documented in a variety of magnetic @xcite and non - magnetic layered systems @xcite . one source of motivation for studying critical phenomena in multilayers is that the significantly increased surface - to - volume ratio may improve chances of observing features characteristic of the @xmath12-dimensional and , especially , the elusive @xmath2-surface critical behavior with respect to experiments involving single thin film or semi - bulk samples . however , finite separation between interfaces in a superlattice leads to correlations between fluctuations in different layers and at different interfaces . one therefore expects surface and two - dimensional scaling to be limited to a certain range of length scales , while eventually cooperative phenomena involving fluctuations on scales larger than the period of the superlattice will dominate the criticality . a crucial insight comes from the exact solution available for a ferromagnetic @xmath12-ising superlattice , as modelled by a planar ising model composed of alternating strips of two components @xcite . recent analysis @xcite demonstrated that the anomalous changes in the critical amplitudes and other interesting features of that model can be simply explained by _ reentrant dimensional crossover _ : as the temperature approaches the critical temperature of the superlattice the long wave length properties of the system are successively dominated by fluctuations characteristic of the the @xmath12-ising , then @xmath24-ising , and then again @xmath12-ising critical behavior . here we generalize and explore this picture by constructing and analyzing a renormalization group ( rg ) flow which provides a scaling description of criticality in experimentally interesting three dimensional superlattices as well as in the heizenberg ( isotropic ) and @xmath3 ( easy plane ) universality classes . in the proposed scenario as the scaled temperature @xmath25 , or @xmath26 , decreases , the critical behavior of the superlattice displays the features of the three simpler systems listed above ( fig . 2 ) : first , as @xmath27 is approached , the original superlattice ( ( i ) in fig . 2 ) can be approximated by sequence of thick layers of the first component weakly coupled through the 2-layers ( ( ii ) in fig . 2 ) . at larger values of @xmath28 this coupling can be neglected and the layers display regular bulk critical behavior with the ordinary surface critical behavior at the interfaces . then , as the correlation length in the first component becomes comparable to the thickness @xmath7 , each slab of the first component exhibits direct bulk - to - film , @xmath29-dimensional crossover . at still smaller values of @xmath28 , the thickness of these slabs is irrelevant and the system becomes equivalent to the third paradigm mentioned above : a weakly coupled layered system ( ( iii ) in fig . the reverse , film - to - bulk crossover finally takes the system back to the uniform , bulk @xmath0-dimensional behavior , characterized however by high degree of anisotropy ( ( iv ) in fig . 2 ) . this reentrant crossover behavior leads to dramatic changes in the critical amplitudes , as shown in fig . 3 for the @xmath2-ising class : the critical exponent characterizing divergence of a physical quantity , for which the specific heat per unit volume @xmath30 has been chosen in fig . 3 , changes two times , as @xmath28 goes to zero , between the values @xmath31 and @xmath32 characteristic of the @xmath2 and @xmath33-dimensional critical behavior , respectively . the relative widths @xmath34 ( subscript @xmath35 denotes _ direct _ , bulk - to - film crossover here ) and @xmath36 ( subscript @xmath37 stands for the _ reverse _ , film - to - bulk crossover ) of the temperature domains where the planar ising and the reentrant bulk critical behaviors are observed will be calculated below ; they provide convenient scaling combinations in terms of which a proper description of criticality in superlattices is achieved . two further points have to be added to this preview of the paper . first , a crucial element of our qualitative picture is that different layers of the first component remain effectively decoupled while the bulk - to - film crossover ( from ( ii ) to ( iii ) in fig . 2 ) happens _ within _ them . this turns out to be guarantied by the fact that the subsequent 1-slabs are coupled through the _ surface _ spins whose correlations are much weaker than of those in the bulk . thus the surface critical behavior , which is not directly seen in temperature dependencies of bulk quantities , like that shown in fig . 3 , appears crucial to the nature of criticality in the superlattice ; we will show that the values of surface critical exponents can thus be extracted from analysis of the dependence of the reentrant width @xmath36 on the thickness of the 2-slabs , @xmath8 . second , in the case of the @xmath2 ising superlattice the @xmath11-dimensional model , describing a single film of the first component , has a regular finite temperature phase transition . consequently , in the thick layer limit the critical temperature @xmath6 of the superlattice is only slightly depressed from @xmath27 and the critical fluctuations are essentially localized within the 1-layers . however , in all other cases , i.e. @xmath2 heizenberg and @xmath3-models and all models in @xmath12 , the corresponding @xmath17-dimensional universality classes lack true ferromagnetic long range order at finite temperatures . the interlayer coupling through the layers of the weaker , second component thus are crucial to existence of long range order . as a result , the critical temperature in these models is strongly shifted towards @xmath18 and the critical domain , in which large scale fluctuations are active , is extended to the temperature range of the order of @xmath38 . finally , a few remarks about the method of this paper . we focus here on the @xmath39-component vector spin systems with short range interactions . as usual , ising , @xmath3 , and heizenberg universality classes refer to the @xmath40 , or easy axis , @xmath41 , or easy plane , and @xmath42 , or isotropic , magnets respectively . the most important omission of this model , apart from restriction to the simplest type of the order parameter , is the absence of long - range dipolar forces ; it seems however natural to make the first step within the simpler realm of local models . the actual method employed here is to combine the well known linear rg flows at the fixed points representing the three paradigms discussed above ( fig . 2 ) , into the simplest _ global _ rg flow consistent with this linear behavior ( fig . the resulting scaling theory then passes the test of comparison to the exact results available for the planar ising model . the outline of the paper is the following : in the next section we start by taking the conceptually simplest case of the three - dimensional ising superlattice . the renormalization group flow will be proposed and scaling forms derived . in section iii we consider the planar ising case which requires extension of the previous consideration to the case of the zero - temperature" +"in condensed matter physics , chemistry , and material science state - dependent interactions arise in many different contexts . they are usually obtained from coarse - graining procedures in which a subset of the degrees of freedom is integrated out ( see refs . for an overview of methods and applications ) . indeed , any coarse graining of the original ( be it classical or quantum ) system induces many - body interactions among the remaining degrees of freedom . the idea is then to replace these complex interactions with state - dependent potentials that are usually taken to be pairwise additive for computational efficiency ( if necessary , three - body forces can also be introduced , as in ref . ) and that are therefore much more tractable from a theoretical and/or numerical point of view . different criteria have been used to select the optimal set of state - dependent pair potentials . in the structural route the model with state - dependent interactions is required to reproduce some distribution functions associated with the coarse - grained ( cg ) degrees of freedom . it is also possible to define the cg model by matching the forces @xcite acting on the cg sites computed in the original , underlying system , or by requiring the cg model to reproduce solvation free energies . also state - dependent potentials suitable to treat inhomogeneous systems have been proposed.@xcite we should further mention mixed coarse - graining strategies that try to match simultaneously the pair distribution function and some other thermodynamic property , for instance , by constraining the virial pressure to be equal to the pressure of the microscopic model . @xcite these mixed approaches , although in principle incorrect since the potential is uniquely defined by the pair distribution function @xmath0 and the density according to henderson s theorem,@xcite may still be of value in practical numerical calculations . indeed , @xmath0 is only known with statistical errors and is little sensitive to the tail of the potential : visibly different potentials may produce structures with essentially indistinguishable pair distribution functions . @xcite therefore , the large - distance behavior of the cg interactions is determined with a large uncertainty , which might leave some flexibility to implement an additional constraint . we will not discuss these approaches any further , focusing on the conceptual problems of the approach rather than on the difficulties of practical numerical implementations . in this paper we discuss the structural approach , which dates back to the early days of liquid state theory , @xcite considering state - dependent pair interactions for a very general class of classical systems . the microscopic , underlying model to which the coarse - graining procedure is applied consists of polyatomic molecules . no hypothesis is made on the nature of the interactions among the atoms : we only require them to be state independent , but , otherwise , they are arbitrary and can , in principle , include any type of many - body terms . our discussion therefore applies both to monoatomic systems with three- and higher - body interactions ( for instance , to noble gases whose accurate study requires the introduction of the three - body axilrod - teller potential @xcite ) and to soft - matter systems , such as polymers , in which the complexity lies in the number of atoms involved rather than in the many - body nature of the atom - atom interactions . @xcite within the cg approach we replace the microscopic system at a given thermodynamic state with a cg system of monoatomic molecules that interact by means of state - dependent pair potentials . the latter are fixed by a structural requirement , the equality of a specific pair distribution function at a given thermodynamic state . if the underlying system is formed by monoatomic molecules , we consider the usual radial pair distribution function . in the case of polyatomic systems , each molecule is replaced by a cg monoatomic molecule located at some point @xmath1 . in many instances , @xmath1 corresponds to the center of mass of the original molecule , but other choices are possible : for instance , in cg models for star polymers the point @xmath1 usually coincides with the center of the star . @xcite for our purposes , we do not need to specify how @xmath1 is chosen . we only require the coordinates @xmath2 of @xmath1 to be a weighted average of the positions of the atoms belonging to the molecule . once @xmath1 is chosen , we can consider the @xmath1-@xmath1 pair distribution function @xmath3 where @xmath4 is the density and @xmath5 the number of molecules . the state - dependent potential is fixed by the requirement that the pair distribution function @xmath6 in the cg model is equal to @xmath0 in the underlying system at the same density . from a practical point of view , the determination of the potential is not an easy task and several method have been devised , like the iterative boltzmann inversion method@xcite and the inverse monte carlo method.@xcite variational approaches have also been discussed , optimizing the coefficients of suitable parametrizations of the cg potentials . @xcite note that the structural approach we have described here is not the only one that is used in practical applications . we should also mention the force - matching approach ( often called multiscale coarse - graining method @xcite ) , in which the state - dependent potential is determined by requiring the cg system to match the atomistic force on the cg atoms as accurately as possible . also this method has a structural interpretation : the matching condition is equivalent@xcite to require the cg force to satisfy the appropriate yvon - born - green equation @xcite that relates the pair and the three - body correlation function . we mention that general theoretical formalisms within which different cg approaches can be derived are presented in refs . . for a summary of methods and a detailed comparison in a specific example , see ref . . once a cg model has been defined , one may use it to predict thermodynamic ( and , in the case of more complex cg systems , also structural ) properties for the underlying model . for instance , one would like to obtain estimates of the pressure of the microscopic system , by studying ( for example , by performing numerical simulations ) the simpler cg model . structurally derived state - dependent potentials have been mostly discussed in the context of the canonical ensemble , see refs . and references therein . in this case , the potentials become density and temperature dependent . for this reason , some thermodynamic relations , which can be rigorously proved for systems with state - independent interactions , are no longer satisfied : in particular , the compressibility route and the virial route to the pressure are no longer equivalent for the cg system . this gave rise to several investigations concerning the thermodynamic consistency of models with state - dependent potentials . @xcite in this paper we again investigate the conceptual issues which arise when considering state - dependent interactions . the first question we wish to address is whether the knowledge of the cg model at density @xmath4 ( i.e. , of the model with potentials obtained by matching the pair distribution function at density @xmath4 ) allows one to obtain informations on the thermodynamical behavior of the underlying system at the _ same _ value of @xmath4 . considering , for instance , pressure and chemical potential , the idea is to compute these two quantities in the cg model . the results of this calculation are then taken as estimates of the pressure and chemical potential of the underlying system . the main problem in implementing this strategy stems from the fact that there is no unambiguous way to define thermodynamic quantities in the presence of state - dependent potentials : approaches that are equivalent for state - independent interactions give different espressions for pressure and chemical potential if potentials depend on the thermodynamic state . following ref . , we shall consider two different approaches . in the passive approach , the pressure is estimated by using the usual virial expansion , while in the active approach one derives the generalized expression of ascarelli and harrison.@xcite both approaches are not thermodynamically consistent and only provide an approximation of the pressure of the underlying model . a quantitative comparison shows that the passive approach provides the most accurate estimates , i.e. , it best reproduces the pressure of the underlying model . the same result holds for the chemical potential . widom s method applied to the cg system , even though it does not reproduce the underlying - model value , provides an estimate of the chemical potential that is closest to the underlying - model value than the estimate obtained in the active approach . note that , if we assume that the density - dependent ( dd ) potentials are known for _ all _ densities @xmath7 and no phase transitions occur in such density interval , then , via the compressibility route , we can compute the exact equation of state of the underlying model for any @xmath8 , hence derive the exact pressure , chemical potential , and free energy . however , in this case cg models with dd potentials play little role . indeed , their computation requires a study of the microscopic model in the whole density interval . but this study would also provide the equation of state directly , without the necessity of introducing any sort of cg model . it is interesting to extend the analysis of the thermodynamic properties of state - dependent potentials to other ensembles . for instance , for phase - coexistence studies it is more natural to consider the grand - canonical ensemble , while the isothermal - isobaric ensemble may be the best suited to interpret experimental data , since pressure is fixed in experiments . in these ensembles one would consider fugacity- and pressure- dependent pair potentials , respectively . again , the question we wish to address is how to obtain thermodynamic predictions in these different ensembles by using state - dependent interactions . the paper is organized as follows . in sec . [ sec2 ] we discuss density - dependent potentials and the consistency of several commonly used methods to determine pressure and chemical potential . we show that none of them is exact : none of the thermodynamic quantities extracted via a cg approach is more than an approximate estimate . in sec . [ sec3 ] we study the accuracy of the different approximations : first , in sec . [ sec3.1 ] we present a general , model - independent discussion in the low - density limit , then , in sec . [ sec3.2 ] we present a specific calculation for linear polymers under good - solvent conditions . the analysis of sec . [ sec2 ] is extended to the grand - canonical ensemble in sec . [ sec4 ] , while in sec . [ sec5 ] we discuss the accuracy with which the thermodynamic behavior is reproduced by using fugacity - dependent potentials . finally , in sec . [ sec6 ] we present our conclusions . we start by considering the canonical ensemble and discuss density - dependent interactions . in principle , one should also consider a temperature dependence . however , temperature does not play a role in the discussion ( we do not discuss temperature derivatives of the free energy ) , so that it will be omitted for simplicity . in the structural approach to coarse graining , the basic quantity of" +"the twin paradox ( twp ) theorem is one of the most famous predictions of special relativity . according to twp , if a twin makes a journey into space , he will return to find that he has aged less than his twin brother who stayed at home . however surprising twp is , it is not a contradiction . it is only a fact that shows that the concept of time is not as simple as it seems to be . a more optimistic consequence of twp is the following . suppose you would like to visit a distant galaxy 200 light years away . you are told it is impossible because even light travels there for 200 years . but you do not despair , you accelerate your spaceship nearly to the speed of light . then you travel there in 1 year of your ( proper ) time . you study there whatever you wanted , and you come back in 1 year . when you arrive back , you aged only 2 years . so you are happy , but of course you can not tell the story to your brother , who stayed on earth . alas you can tell it to your grand- -grand - children only . in this way twp also makes time travel to the future possible . in this paper we use the axiomatic method to provide a logic - based conceptual analysis of the twp theorem . we work within the first - order logic ( fol ) framework of @xcite , @xcite , @xcite . we logically compare twp and a prediction ( slowing down of moving clocks ) as well as a symmetry axiom of special relativity . this analysis is based on our geometrical characterization of twp , see theorem [ thm - twp ] . we show that twp is logically weaker than the assumption of the slowing down of moving clocks , see theorem [ thm - slowtime ] . we also show that twp is logically weaker than a symmetry axiom of special relativity , see theorem [ thm - simdist ] . since we prove our geometrical characterization in a general kinematics setting , we can use it to derive consequences on newtonian kinematics too . we show that the absoluteness of time ( in the newtonian sense ) is not equivalent to the lack of the twin paradox ( no - twp ) without assuming a strong theoretical axiom , see theorem [ thm - univtime ] . why is it useful to apply the axiomatic method to relativity theory ? for one thing , this method makes it possible to understand the role of any particular axiom . we can check what happens to our theory if we drop , weaken or replace an axiom . for instance , it has been shown by this method that the impossibility of faster than light motion is not independent from other assumptions of special relativity , see @xcite , @xcite . more boldly : it is superfluous as an axiom because it is provable as a theorem from much simpler and more convincing basic assumptions . the linearity of transformations between inertial observers ( inertial reference frames ) can also be proven from some plausible assumptions , therefore it need not be assumed as an axiom , see @xcite , @xcite . the usual approaches to special theory of relativity base the theory on two postulates , namely , einstein s principle of relativity and that the velocity of light is independent of its source . some authors give a mathematical argument to prove that einstein s principle of relativity implies the second postulate , see , e.g. , @xcite , @xcite . however , these approaches contain several tacit assumptions besides the named postulates . so from the point of view of axiomatic foundations of relativity theory , they are not explicit enough . in an adequate axiomatic foundational work it is desirable to state every assumption explicitly . getting rid of unnecessary axioms of a physical theory is important because we do not know whether an axiom is true or not , we just assume so . we can only be sure of outcomes of concrete experiments but they rather correspond to ( existentially quantified ) theorems and not to axioms . in the literature it is common to use the term `` empirical fact '' for universal generalization of an empirical fact ( elevated to the level of axioms ) , see , e.g. , @xcite , @xcite . however , because of their falsifiability it would be better to call them empirical axioms ( postulates based on outcomes of concrete experiments ) . similarly , if we axiomatize a theory , we can ask which axioms are responsible for a certain prediction of the theory . this kind of reverse thinking helps to answer the why - type questions of relativity . for example , we can take the twin paradox and check which axiom of special relativity was and which one was not needed to derive it . the weaker an axiom system is , the better answer it offers to the question : `` why is the twin paradox true ? '' . for details on answering why - type questions of relativity by the methodology of the present work , see @xcite . for further reasons why to apply the axiomatic method to spacetime theories , see , e.g. , @xcite , @xcite , @xcite , @xcite , @xcite . applying mathematical logic in foundations of relativity theories is not a new idea at all . it goes back to such leading mathematicians and philosophers as hilbert , reichenbach , carnap , gdel , tarski , suppes and friedman , among others . the work of our school of logic and relativity led by andrka and nmeti is continuation to their research . in a spirit similar to ours , there is a large variety of works devoted to logical axiomatizations of relativity , see , e.g. , ax @xcite , benda @xcite , goldblatt @xcite , mundy @xcite , @xcite , pambuccian @xcite , robb @xcite , suppes @xcite , schutz @xcite , @xcite , @xcite . our general aims are to axiomatize relativity theories within pure fol using simple , comprehensible and transparent basic assumptions ( axioms ) only ; to prove the surprising predictions ( theorems ) of relativity theories from a minimal number of convincing axioms ; to eliminate tacit assumptions from relativity by replacing them with explicit axioms formulated in fol ( in the spirit of the fol foundation of mathematics and tarski s axiomatization of geometry ) ; and to provide a foundation for relativity theory similar to that of mathematics , cf . hilbert s 6th problem @xcite . in our perspective axiomatization is only a first step to logical and conceptual analysis where the real fun begins . for good reasons , the foundation of mathematics was performed strictly within fol . a reason for this fact is that staying within fol helps to avoid tacit assumptions . another reason is that fol has a complete inference system while second - order logic ( and thus any higher - order logic ) can not have one . for further reasons why to stay within fol when dealing with axiomatic foundations , see , e.g. , ( * ? ? ? * appendix : why fol ? ) , @xcite , @xcite , @xcite . here we explain our basic concepts . we deal with kinematics , i.e. , with the motion of _ bodies _ ( anything which can move , e.g. , test - particles , reference frames , electromagnetic waves or centers of mass ) . we represent motion as the changing of spatial location in time . thus we use reference frames for coordinatizing events ( meetings of bodies ) . _ quantities _ are used for marking time and space . the structure of quantities is assumed to be an _ ordered field _ in place of the field of real numbers . for simplicity , we associate reference frames with special bodies which we call _ observers_. observations are formulated by means of the _ worldview relation_. there are several reasons for using observers ( or coordinate systems , or reference frames ) instead of a single observer - independent spacetime structure . one is that it helps to weed out unnecessary axioms from our theories . nevertheless , we state and emphasize the logical equivalence of observer - oriented and observer - independent approaches to relativity theory , see , e.g. , @xcite . keeping the foregoing in mind , let us now set up the fol language of our axiom systems . first we fix a natural number @xmath0 for the dimension of spacetime . we use a two - sorted language : @xmath1 is the sort of ( potential ) * bodies * and @xmath2 is the sort of * quantities*. our language contains the following non - logical symbols : unary relation symbol ( inertial * observers * ) ; binary function symbols , and a binary relation symbol ( the field operations and the ordering on @xmath3 ) ; and a @xmath4-ary relation symbol ( * worldview relation * ) . the variables of sort @xmath5 are denoted by @xmath6 , @xmath7 , @xmath8 , @xmath9 and @xmath10 ; and those of sort @xmath3 are denoted by @xmath11 , @xmath12 , @xmath13 , @xmath14 and @xmath15 . @xmath16 is translated as `` @xmath6 is an ( inertial ) observer . '' we use the worldview relation @xmath17 to speak about coordinatization by translating @xmath18 as `` observer @xmath6 coordinatizes body @xmath9 at spacetime location @xmath19 , '' that is , at space location @xmath20 at instant @xmath21 . body terms are just the variables of sort @xmath5 . quantity terms are the variables of sort @xmath3 and what can be built up from quantity terms by using the field operations ( @xmath22 ) . @xmath16 , @xmath23 , @xmath24 , @xmath25 and @xmath26 are the so - called atomic formulas of our fol language , where @xmath27 can be arbitrary terms of the required sorts . the * formulas * of our fol language are built up from these atomic formulas by using the logical connectives _ not _ ( ) , _ and _ ( ) , _ or _ ( ) , _ implies _ ( ) , _ if - and - only - if _ ( ) and the quantifiers _ exists _ @xmath14 ( ) and _ for all @xmath14 _ ( ) for every variable @xmath14 . to abbreviate formulas of fol we often omit parentheses according to the following convention . quantifiers bind as long as they can , and @xmath28 binds stronger than @xmath29 . for example , @xmath30 means @xmath31 . we use first - order set theory as a meta theory to speak about model theoretical terms , such as models , validity , etc . the * models * of this language are of the form @xmath32 where @xmath5 and @xmath3 are nonempty sets and @xmath33 is a unary relation on @xmath5 , @xmath34 and @xmath35 are binary functions and @xmath36 is a binary relation on @xmath3 , and @xmath37 is a relation on @xmath38 . formulas are interpreted in @xmath39 in the usual way . we formulate each axiom at two levels . first we give an intuitive formulation , then a precise formalization using our logical notation ( which can easily be translated into fol formulas by inserting the fol definitions into the formalizations ) . we seek to formulate easily understandable axioms in fol . we use the notation @xmath40 ( @xmath41-times ) for the set of all @xmath41-tuples of elements of" +"the first results from the lhc experiments showed that the jets emerging from the hot dense matter created in heavy ion ( hi ) collisions do not retain their full energy @xcite . measurement of fully - reconstructed jets by the atlas experiment @xcite revealed a factor of two suppression of jet yields in central collisions with respect to peripheral ones @xcite . results from the lhc experiments ( e.g. @xcite ) do not show significant modification of the fragmentation function for large longitudinal jet momentum fractions carried by the charged particles . measuring inclusive hadron production at high transverse momentum ( @xmath2 ) originating from parton fragmentation is another way to study the mechanism by which hard partons traversing the suppression in hadron production can be measured as a ratio of yields per nucleon - nucleon interactions in `` head - on '' hi collisions scaled by the number of nucleon - nucleon interactions ( @xmath4 ) relative to those measured in p+p collisions . the p+p collisions can be approximated by the most glancing hi collisions scaled by @xmath4 as well @xcite . this ratio is this analysis uses data collected with the atlas detector in the 2010 and 2011 pb+pb runs with @xmath5@xmath6tev . after run and event selections , approximately 5.1@xmath710@xmath8 minimum bias ( mb ) events ( @xmath9b@xmath0 ) are analyzed in the 2010 data sample and a similar number of events in the 2011 mb data sample . in the 2011 data sample , hard probes ( hp ) events with @xmath10nb@xmath0 are analysed as well . hp events satisfy the extra requirement of an anti-@xmath11 @xcite jet with the distance parameter of @xmath12 and transverse energy ( @xmath13 ) of at least 20gev estimated online . the event centrality is estimated using the total @xmath13 measured at the electromagnetic scale by the forward calorimeters ( fcal ) in the range @xmath14 . the data are binned in 5% and 10% centrality bins . the mean number of nucleon - nucleon collisions @xmath15 for each centrality bin , as well as its systematic uncertainties , is estimated using a glauber monte carlo model @xcite . monte carlo simulations ( mc ) to study performance of the atlas detector are based on the hijing @xcite and pythia @xcite event generators . in the 2010 data analysis the environment of pb+pb collisions is simulated using @xmath16 hijing events with embedded pythia p+p hard scattering events . in 2011 data analysis the pythia events are embedded into mb events recorded without noise suppression in the detector channel during the 2011 data taking . charged particle tracks are reconstructed using the atlas inner detector . tracks are measured in the pseudorapidity interval @xmath1 and over the full azimuth using a combination of silicon pixel detector ( pixel ) , silicon microstrip detector ( sct ) , and a straw tube transition radiation tracker ( trt ) , all immersed in a 2 t axial magnetic field . the minimum @xmath2 of reconstructed tracks is 0.5gev . charged particles typically traverse three layers of silicon pixel detectors , four layers of double - sided microstrip sensors , and 36 straws . the track reconstruction settings used in pb+pb collisions were different from those used in p+p @xcite and optimized for an increased occupancy in hi collisions . in the analysis a track is required to have at least 2 hits in the pixel detector , one being in the innermost layer , and at least 7 hits in the sct . tracks are required to have zero pixel and sct holes . a hole appears on a track if a hit , predicted by the track trajectory , is not found in the detector layer . the contribution from fake tracks ( i.e. tracks composed of randomly associated hits in the detector layers ) and secondary particles ( decay products of e.g. b and d mesons ) are reduced by requiring the significance of @xmath17 and @xmath18 , i.e. the distance of closest approach of the track to the event vertex in the transverse and longitudinal directions divided by the estimated uncertainty on this parameter for each measured track , to be less than 3 . the @xmath17 and @xmath18 parameters and their uncertainties are estimated by a vertex finding algorithm . to reduce the amount of fakes at high @xmath2 , tracks from the hp sample are required to be matched to anti-@xmath11 jets with @xmath19 . furthermore , as the main interest of this analysis are spectra of charged hadrons , electrons and muons coming from electroweak decays of heavy bosons are subtracted from the measured spectra . this is done in all used samples . the data are corrected using mc for fake tracks and secondary particles , and for reconstruction inefficiency and momentum resolution . the fraction of fake tracks and secondary particles passing the tracking cuts among all tracks passing the same cuts is found to be around zero near @xmath20 for peripheral collisions and to increases both with increasing centrality and @xmath21 . at the lowest measured @xmath2 the fraction is up to 10% ( mainly contributed by secondaries ) for central events and high @xmath21 , and rapidly decreases with increasing @xmath2 . at @xmath2@xmath22gev the fraction is about 1% and it is negligible above 4gev . corrections for the inefficiency of the track reconstruction and the momentum resolution are applied at once using bin - by - bin corrections . the efficiencies can be seen of fig . [ effic ] . the track reconstruction efficiency is found to be highest in the region @xmath23 and decreases with increasing @xmath21 . the efficiency decreases at low @xmath2 as well as at very high @xmath2 . in central collisions , the efficiency is lower by a few percent ranges ( @xmath24 , @xmath25 and @xmath26 ) derived from mc @xcite . the efficiency is a @xmath2 spectrum of reconstructed tracks divided by a @xmath2 spectrum of all truth tracks . only particles with lifetime@xmath27@xmath7@xmath28s were used to produce efficiencies . the shaded bands show the fits of appropriate efficiencies with all their , scaledwidth=70.0% ] the systematic uncertainties result from several contributions . tracking cuts and vertex pointing cuts contribute up to 4% each . the uncertainty on the efficiency correction contributes up to 20% at high @xmath2 and it is dominant in the spectra analysis . uncertainties on momentum scale and material budget contribute up to 6% and 5% respectively . these uncertainties cancel out partially or completely when building the @xmath29 . the dominant uncertainty of @xmath29 results from the calculation of @xmath15 , which is up to 11.7% for @xmath29 . other uncertainties contribute less than 3% , such as truth particle association or correction for fakes and secondaries . the final spectra are a combination of the mb spectra below @xmath2@xmath30gev and hp spectra above . the spectra are normalized per event ( per sampled event in case of hp spectra ) . the spectra as well as @xmath29 in different @xmath31-regions are consistent with each other and can be combined . the corrected spectra are shown in fig . [ spectra_exclusive ] for four centrality bins ( , 30 - 40% , 50 - 60% and 60 - 80% ) , and three @xmath31 ranges ( @xmath24 , @xmath32 and @xmath33 ) . the @xmath29 measured over the entire acceptance of the atlas inner detector tracking system as a function of track @xmath2 is shown in fig . it is shown for three centrality combinations : with 0 - 5% , 30 - 40% and as the numerators and the common peripheral bin 60 - 80% as the denominator . the measurement shows a strong suppression of the hadron production which increases with the centrality . the measured @xmath29 for 0 - 5% to 60 - 80% centrality bins reaches a minimum at 7gev and rises with @xmath2 . it was presented a measurement of inclusive charged hadron spectra in @xmath5@xmath34tev pb+pb collisions and their ratios between central and peripheral bins . the measurement is performed in the range of @xmath1 and @xmath35gev in different @xmath31 bins as the function of the @xmath2 and the centrality of the collisions . due to use of the jet trigger in the 2011 run , the statistics of high-@xmath2 tracks is very good up to @xmath2@xmath36gev . the measurement of the @xmath29 is limited by the statistics of the peripheral 60 - 80% centrality bin . above @xmath2@xmath36gev is consistent with the size of the suppression measured in the jet analysis @xcite . measured in @xmath1 in three centrality combinations @xcite . the statistical errors are shown with vertical lines and the overall systematic uncertainty at each point is shown with gray boxes.,scaledwidth=70.0% ]" +"the ultimate fate of the gas which cools in cooling flows is still unknown . a possibility is that a fraction of the gas forms cold molecular clouds @xcite . as a result of fragmentation we expect the formation of small clouds with higher density and possible production of molecules in particular @xmath0 and traces of @xmath1 and @xmath2 . + taking into account radiative transfer effects we computed analytically in @xcite the cooling function @xmath3 for the transition between the ground state and the first rotational level . this way we determined a lower limit of @xmath4 . + meanwhile we improved this calculation by including numerically all rotational transitions which are relevant at low temperatures ( i.e. up to @xmath5 ) . + the following column densities are adopted for a typical small cloud ( with @xmath6@xmath7 ) : @xmath8 , which corresponds to a @xmath2 abundance : @xmath9 . for @xmath1 instead we assume the primordial ratio @xmath10 . + in figure 1 we plotted the molecular cooling function @xmath3 taking into account @xmath2 , @xmath1 and @xmath0 in the range 3 - 300 k. @xmath2 is the main coolant in the range of temperatures 3 - 80 k , @xmath1 in the range 80 - 150 k and @xmath0 dominates above 150 k. the heating is given by the external x - ray flux as produced from the hot intracluster gas . the thermal balance between heating and cooling leads to an equilibrium temperature for the clouds . we have calculated the minimum equilibrium temperature @xmath11 of the clumps inside the cooling flow region . table 1 shows the equilibrium temperature for different clusters . for comparison we give the values we find using our analytical approximation ( @xmath12=1 ) and the ones by taking into account higher excited rotational levels ( @xmath12=5 ) . one clearly sees that the inclusion of the higher excited levels into the calculations lowers the equilibrium temperature , particularly for hot clusters such as for instance abell 478 . + we conclude that thermal equilibrium can be achieved at very low temperatures inside the cooling flow region mainly due to @xmath2-cooling . other molecules than @xmath2 , for example @xmath13 or @xmath14 , could also be important . thus the study of the chemistry in cooling flows might lead to important insight ." +"the evolution of satellite galaxies has been studied by a number of researchers both theoretically and using numerical simulations . however , even though it is a basic and simple problem , our understanding is still rather limited . using @xmath0-body simulation of a rigid satellite within an @xmath0-body model of the parent galaxy , @xcite found that the orbital eccentricity of a satellite galaxy tends to be roughly constant . previous theoretical studies based on chandrasekhar s dynamical friction formula @xcite predicted circularization of the orbit . thus , there was rather serious qualitative difference between the simulation result and the theoretical model . in @xmath0-body calculations of @xcite , the parent galaxy was modeled as an @xmath0-body system , while the satellite was treated as one massive softened particle . thus , the tidal mass loss was ignored in their calculation . @xcite performed a self - consistent @xmath0-body simulation of the evolution of a satellite galaxy , in which both the satellite and the parent galaxy were treated as @xmath0-body system . they compared the result with that of a semianalytical model , in which the orbit of the satellite evolved through the dynamical friction expressed by chandrasekhar s formula . the agreement between the simulation and semianalytic model was not good . @xcite performed similar comparison , and found that it was possible to make simulation result and semianalytic model agree to each other , if they use the coulomb logarithm as a fitting parameter . @xcite constructed a more sophisticated model for the evolution of the satellite , and demonstrated that it could reproduce the simulation results of @xcite quite accurately . the dynamical friction formula is given by @xmath1 here , @xmath2 is the velocity of the satellite , @xmath3 is the gravitational constant , @xmath4 and @xmath5 are the masses of the satellite galaxy and field particles of the parent galaxy , and @xmath6 is the distribution function of field particles at the position of the satellite . we assumed that the velocity distribution is isotropic , which is true at least for the initial model of the parent galaxy we consider in this paper . the term @xmath7 is the coulomb logarithm given by @xmath8 here , @xmath9 and @xmath10 are the maximum and the minimum impact parameters for gravitational encounters between the satellite galaxy and the field stars in the parent galaxy . for the lower cutoff , it is natural to set @xmath10 to the order of the virial radius of the satellite galaxy ( white 1976 ) . for the upper cutoff , in many studies the size of the parent galaxy @xmath11 has been used ( e.g. , murai & fujimoto 1980 ; helmi et al . 1999 ; johnston et al . @xcite followed this tradition and used @xmath12 , while @xcite varied it to obtain the best agreement , and the value they used was @xmath13 . clearly , however , one can not use the coulomb logarithm as a fitting parameter , since its value should be determined from the mass distributions of the satellite and the parent galaxy . hashimoto et al . ( 2003 , hereafter h03 ) showed that chandrasekhar s dynamical friction formula does give the result which is consistent with the simulation result , when the integration over the impact parameter is carried out correctly . equation ( [ eq : loglambda ] ) was obtained assuming that the distribution of the field stars is uniform and infinite . we need to apply the upper cutoff since the integration would diverge without the cutoff . however , the actual @xmath0-body system has a finite size so that the integration over the mass distribution could not diverge . they pointed out that , if this integration over the mass distribution of the parent galaxy is correctly performed , the discrepancy between @xmath0-body simulation result and the model with analytic estimate disappears . the exact integration over all encounters generally resulted in the coulomb logarithm smaller than the value given by equation ( [ eq : loglambda ] ) with @xmath14 , simply because the density drops off at large radii . the use of equation ( [ eq : loglambda ] ) with @xmath14 is the same as to assume that the parent galaxy is a sphere of radius @xmath11 with a constant density same as the local density around the satellite . also , it implies that the orbit of the satellite is a straight line . however , since the density drops off and the orbit of the satellite is not a straight line , the actual dynamical friction is smaller . if we set the cutoff radius as the distance of the satellite from the center of the parent galaxy , equation ( [ eq:1 ] ) gives the result in good agreement with the @xmath0-body simulation . h03 resolved the discrepancy between the theoretical and numerical results for the case of a rigid satellite . the formula they proposed , and a modified version of it @xcite are used in recent studies of the evolution of subhalos and satellite galaxies . in such studies , a self consistent @xmath0-body model is used for the satellite ( or subhalo ) and its orbit is integrated numerically using the dynamical friction formula , to express the time variation of the tidal field . this technique has been used by a number of researchers ( bullock & johnston 2005 ; johnston et al . 1995 ; ibata & lewis 1998 ; portegies zwart et al . 2004 ) . however , there is no guarantee that the orbital evolution of a live satellite is correctly described by the dynamical friction formula of h03 . the results of previous studies @xcite suggest that the disagreement between simulation and semianalytic model with dynamical friction formula is due to the incorrect choice of the coulomb logarithm . even so , there has been no study in which the dynamical friction formula of h03 was directly compared to a fully self - consistent @xmath0-body simulation . that means the results can be very different . in this paper , we performed such a direct comparison between fully self - consistent @xmath0-body simulation and semianalytic model . we found a serious disagreement , and we investigated the reason of that disagreement . our main findings can be summarized as follows . the disagreement does exist , but in the direction opposite to that observed in previous studies . the orbital decay in the @xmath0-body simulation was significantly faster than that in the semianalytic model with the dynamical friction formula of h03 . we investigated the cause of this disagreement , and found that the main causes are the effect of particles which are stripped from the main body of the satellite by the tidal field of the parent galaxy . these escaped particles exert drag forces to the main body of the satellite in two different ways . the first one is the direct gravitational force . since the distribution of the escaped particles is not axisymmetric around the center of the parent galaxy , their gravity can change the orbital energy of the satellite , and it turned out that the forces integrated over all escaped particles effectively works as a drag force . the second one is the enhancement of the dynamical friction . escaped particles typically go away from the satellite rather slowly . in other words , they move together with the satellite for a rather long time . thus , from the point of view of the field particles , these `` escaped '' particles are still effectively part of the satellite , since the gravitational force they feel is the combined effect of the main body of the satellite and `` escaped '' particles which still are close to it . the dynamical friction on the body of the satellite is therefore bigger than what would be there if there are no such escaped particles . we found that these two effects have comparable strength and the combined effect explains the disagreement between the @xmath0-body simulation and semianalytic calculation . this paper is organized as follows . in section 2 we describe the simulation method and initial conditions . in section 3 we give the result . the semianalytic model gave the orbital decay significantly slower than that observed in the @xmath0-body simulation . in section 4 we discuss the cause of this discrepancy . section 5 is for a summary and discussions . we consider a simple problem of one spherical satellite galaxy orbiting in a spherical parent galaxy . this is essentially the same problem as that studied by h03 . in the following we describe the initial model . we adopted a king model with non - dimensional central potential @xmath15 as the model of the parent galactic halo and @xmath16 as that of the satellite halo . the system of units is the heggie unit ( heggie & mathieu 1986 ) , where the gravitational constant @xmath3 is 1 and the mass and the binding energy of the parent galaxy are 1 and 0.25 , respectively . initially , the satellite is placed at distance 1.5 from the center of the parent galaxy , with the velocity of 0.45 . assuming that the parent galaxy represents our galaxy with total mass @xmath17 and the circular velocity @xmath18 km s@xmath19 , the initial distance and velocity of the satellite galaxy are 60 kpc and 140 km s@xmath19 . unit time in the heggie unit corresponds to 130 myr . in table 1 , we summarize the model parameters and initial conditions of our @xmath0-body simulations . most of the parameters are the same as those used in h03 . we chose the initial velocity slightly larger than what is used in h03 , to keep the mass loss rate smaller . this choice allowed us to follow the evolution of satellite for more than 10 orbits . in the @xmath0-body simulation , both the parent galaxy and the satellite were expressed as self - consistent @xmath0-body models . the number of particles @xmath0 of the parent is @xmath20 and that of the satellite is @xmath21 . the number of particles in the satellite should be large enough that the relaxation effect does not seriously affect the mass loss from the satellite . since the initial half - mass relaxation time of the satellite is about 160 in our system of units , relaxation effect is small . the number of particles in the parent galaxy should be determined so that the two - body relaxation effect on particles in the parent galaxies and that in satellite galaxies are small compared to the velocity dispersion of particles . since the velocity dispersion of particles in the parent galaxy is much higher than the internal velocity dispersion of satellite particles , we only need to consider the heating of satellite particles due to encounters with particles in the parent galaxy . the timescale of this heating , @xmath22 , is expressed as @xmath23 for the first - order approximation , where @xmath24 is the half - mass relaxation timescale of the parent galaxy , @xmath25 and @xmath26 are the velocity dispersions of the satellite and the parent galaxy , respectively . for our choice of initial model and number of particles , @xmath27 and it is sufficiently longer than the duration of the simulation . we used a barnes - hut treecode ( barnes & hut 1986 ; makino 2004 ) on grape-6a ( fukushige et al . 2005 ) . we used opening angle @xmath28 with center - of - mass ( dipole - accurate ) approximation . the maximum group size for grape calculation ( makino 1991 ) is 8192 . for the time integration a leapfrog integrator with a fixed stepsize of @xmath29 is used" +"observations indicate the cosmological expansion is accelerating now and that the universe is spatially flat , provided the dark energy density responsible for the acceleration is close to or time independent . for reviews of dark energy see @xcite , @xcite , @xcite , @xcite , and references therein . in the standard "" spatially - flat @xmath4cdm cosmological model @xcite dark energy einstein s cosmological constant @xmath4 contributes a little more than @xmath5 of the current energy budget . non - relativistic cold dark matter ( cdm ) is the next largest contributer ( at a little more than @xmath6 ) , followed by non - relativistic baryonic matter ( around @xmath7 ) . see @xcite and references therein for reviews of the standard model . it has been known for a while that the standard @xmath4cdm model is reasonably compatible with most observational constraints ( see , e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) .cdm model , might need modification . ] in the @xmath4cdm model the dark energy density is constant in time and does not vary in space . it is well known that the standard @xmath4cdm model has some puzzling features that are easier to accept in a model in which the dark energy density is a slowly decreasing function of time . for recent discussions of time - varying dark energy models see @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , and references therein . in this paper we study two dark energy models ( with dark energy being either a cosmological constant or a slowly - evolving scalar field @xmath8 ) as well as a dark energy parameterization . in the @xmath4cdm model , time - independent dark energy density ( the cosmological constant @xmath4 ) is modeled as a spatially homogeneous fluid with equation of state @xmath9 that relates the fluid pressure and energy density . the xcdm parameterization has often been used to describe slowly - decreasing dark energy density . in this case dark energy is modeled as a spatially homogeneous @xmath10-fluid with equation of state @xmath11 . here @xmath12 and @xmath13 are the pressure and energy density of the @xmath10-fluid and the equation of state parameter @xmath14 is independent of time . when @xmath15 the xcdm parameterization reduces to the complete , consistent @xmath4cdm model . for all other values of @xmath14 the xcdm parameterization is incomplete as it does not describe spatial inhomogeneities ( see , e.g. * ? ? ? * ; * ? ? ? * ) . for computational simplicity , in the xcdm case we consider only a spatially - flat cosmological model . the @xmath8cdm model is the simplest , complete and consistent model of slowly - decreasing dark energy density . here dark energy is modeled as the gradually decreasing ( in @xmath8 and time ) potential energy density @xmath16 of the scalar field . in this paper we assume an inverse power - law potential energy density @xmath17 , where @xmath18 is a nonnegative constant . when @xmath19 the @xmath8cdm model reduces to the corresponding @xmath4cdm model . for computational simplicity , we assume a spatially - flat cosmology for @xmath8cdm . cosmological observations that provide the strongest evidence for dark energy are : snia apparent magnitude versus redshift data ( * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * and references therein ) ; cosmic microwave background ( cmb ) anisotropy measurements ( e.g. , * ? ? ? * ; * ? ? ? * ) combined with low estimates of the cosmological mass density ( * ? ? ? * and references therein ) , provided the dark energy density is close to or time independent ; and , baryon acoustic oscillation ( bao ) peak length scale data ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? current error bars associated with these three types of data are still too large to allow for a significant observational discrimination between the @xmath4cdm model and the two simple time - varying dark energy models discussed above . additional data are needed for this task , as well as to provide a cross check on the above results . other data that have been used for this purpose include lookback time as a function of redshift ( * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * and references therein ) , gamma - ray burst luminosity distance as a function of redshift , strong gravitational lensing ( * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * and references therein ) , hii starburst galaxy apparent magnitude as a function of redshift ( e.g. , * ? ? * ; * ? ? ? * ; * ? ? ? * ) , angular size as a function of redshift ( * ? ? ? * ; * ? ? ? * ; * ? ? ? * and references therein ) , and galaxy cluster properties ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? the constraints from these data are , at present , significantly weaker than those from snia , bao , and cmb anisotropy measurements , but it is anticipated that future data of these kinds will provide significant constraints . two other current data sets provide interesting constraints on cosmological parameters , somewhat comparable to those from snia , bao , and cmb anisotropy data . these are galaxy cluster gas mass fraction as a function of redshift measurements and measurements of the hubble parameter as a function of redshift . interestingly , most measurements now provide largely compatible constraints on cosmological parameters that are consistent with a currently accelerating cosmological expansion . this provides confidence that the broad outlines of a standard cosmological model are now in place . in this paper we use the 21 @xmath2 measurements of @xcite , @xcite , @xcite , and @xcite [ listed in table 1 of @xcite ] , in conjunction with the @xmath20 measurement of @xcite , determined from bao in the ly@xmath18 forest ( in combination with wmap cmb anisotropy data , * ? ? ? * ) , to constrain the @xmath4cdm and @xmath8cdm models and the xcdm parametrization . the inclusion of the new @xcite measurement results in tighter constraints than those derived by @xcite from the 21 @xmath2 measurements alone . the new @xmath2 constraints derived here are more restrictive than those derived from the recent snia data compilation of @xcite , which more carefully accounts for the systematic errors in snia measurements . data is a much less - developed field than that of snia data , so it is not impossible that future @xmath2 error bars might be larger than what we have used in our analysis here . ] in addition to deriving @xmath2-data only constraints , we also use these @xmath2 measurements in combination with recent snia and bao data to jointly constrain cosmological parameters . adding the @xmath2 data tightens the constraints , quite significantly in some parts of parameter space . more precisely , the @xmath2 measurements more significantly tighten constraints on the nonrelativistic matter density parameter than on the parameter that more closely controls the time evolution of the dark energy density our paper is organized as follows . in sec . [ equations ] we present the basic equations of the three dark energy models we consider . constraints from the data are derived in sec .. we conclude in sec . [ summary ] . in this section we list relevant characteristics of the two models ( @xmath4cdm and @xmath8cdm ) and the one parametrization ( xcdm ) we use in our analyses of the data . in the @xmath4cdm model with spatial curvature the hubble parameter evolves as @xmath21^{1/2 } , \ ] ] where @xmath22 is the current value of hubble parameter ( the hubble constant ) , the current value of the spatial curvature density parameter is @xmath23 , and the model parameter set we want to constrain is @xmath24 . here @xmath25 is the nonrelativistic ( baryonic and cold dark ) matter density parameter and @xmath26 is the time - independent cosmological constant density parameter . below we shall have need for the dimensionless hubble parameter @xmath27 . the xcdm parameterization friedmann equation is @xmath28^{1/2},\ ] ] where for computational simplicity we consider only flat spatial hypersurfaces and the model parameters @xmath29 . the xcdm parametrization is incomplete , as it can not describe the evolution of energy density inhomogeneities . the @xmath8cdm model is the simplest , complete and consistent dynamical dark energy model . in this model dark energy is a slowly - rolling scalar field @xmath8 with an , e.g. , inverse - power - law potential energy density @xmath30 where @xmath31 is the planck mass , @xmath32 is the newtonian gravitational constant , and @xmath18 is a non - negative free parameter that determines @xmath33 . the scalar field part of the @xmath8cdm model action is @xmath34 where @xmath35 is the metric tensor and @xmath18 and @xmath33 are related as @xmath36 with corresponding scalar field equation of motion @xmath37 where the overdot denotes a derivative with respect to time . in the spatially - flat case the friedmann equation for the @xmath8cdm model is @xmath38^{1/2},\ ] ] where @xmath39 is determined by the @xmath8 field energy density @xmath40 equations ( [ eq : dotphi])([eq : rhom ] ) constitute a system of differential equations which can be solved numerically for the @xmath8cdm model hubble parameter @xmath2 , using the initial conditions described in . in this case the model parameter set is @xmath41 . constraint contours from the new ( old , * ? ? ? * ) @xmath2 data for the @xmath4cdm model . the filled ( empty ) circle is the best fit point from the new ( old ) @xmath2 data . the left panel is for the @xmath42 km s@xmath43 mpc@xmath43 prior and the right panel is for the @xmath44 km s@xmath43 mpc@xmath43 one . the dashed diagonal lines correspond to spatially - flat models , the dotted lines demarcate zero - acceleration models , and the shaded area in the upper left - hand corners are the region for which there is no big bang . the filled circles correspond to best - fit pair @xmath45 with @xmath46 ( left panel ) and best - fit pair @xmath47 with @xmath48 ( right panel ) . the empty circles correspond to best - fit pair @xmath49 with @xmath50 ( left panel ) and best - fit pair @xmath51 with @xmath52 ( right panel ) . , title=""fig:"",width=302 ] constraint contours from the new ( old , * ? ? ? * ) @xmath2 data for the @xmath4cdm model . the filled ( empty ) circle is the best fit point from the new ( old ) @xmath2 data . the left panel is for the @xmath42 km s@xmath43 mpc@xmath43 prior and the right panel is for the @xmath44 km s@xmath43 mpc@xmath43 one . the dashed diagonal lines correspond to spatially - flat models , the dotted lines demarcate zero - acceleration models , and the shaded area in the upper left - hand corners are the region for which there is no big bang . the filled circles correspond to best - fit pair @xmath45 with @xmath46 ( left" +"complexity is identified by a set of typical features @xcite , ranging from complex network descriptions @xcite to chaos on strange attractors . fractional descriptions lay at the foundation of many such features . for instance , strange attractors typically have fractional dimension . complex networks exhibit log - normal or power - law statistics also associated with fractional derivatives @xcite . fractional dimension is common in biological systems , e.g. the folds of the brain , the space - filling curve of dna , and the maximization of surface area for gas exchange in the lungs and the branches of trees . although foundational descriptions of physical phenomena typically take the form of partial differential equations ( pdes ) or ordinary differential equations ( odes ) with derivatives of integer order , for example the diffusion equation , the wave equation , and the schrdinger equation , it has been argued that effective pde - based descriptions of complex phenomena require _ fractional _ partial derivatives @xcite . indeed , the generalization of the diffusion equation to fractional derivatives has been found highly effective in describing for instance the propagation of ground water through soil @xcite , the latter typically exhibiting multiscale properties . to what extent are fractional descriptions relevant to wave phenomena in general ? one natural context in which to examine this question is the _ nonlinear schrdinger equation _ ( nlse ) . the nlse appears in many contexts including the experimentally and theoretically well - established semiclassical effective limit of the quantum many - body description of bose - einstein condensates @xcite ; the slowly varying envelope approximation for propagation of light in fiber optics @xcite ; and similar effective descriptions found for spin waves in ferromagnetic films @xcite . in every case the nlse is an _ effective _ description , that is , starting from a much more complete but difficult to solve theory , one obtains a single scalar pde / ode that covers much of the observable phenomena in that system . an outstanding physical question is then the following . on the one hand fractional differential equations provide an effective description for complex multiscale phenomena in many contexts . on the other hand nonlinear pdes / odes such as the nlse are a highly useful simplification to reduce high dimensional or otherwise difficult problems to effective nonlinear differential equations . what is the interplay between these two key classes of effective pde / ode descriptions of complex systems ? the fractional generalization of the nlse in particular has several useful limits in which the concept of effective theories can be carefully and rigorously explored . first , the linear limit of the schrdinger equation is of course a well - understood problem . second , the fractional generalization of the schrdinger equation has been previously explored in many contexts @xcite . third , the nlse is an integrable equation with detailed solutions in terms of solitons . fourth , by performing an imaginary time rotation the schrdinger equation can be transformed to the diffusion equation . fifth , the fractional diffusion equation , perhaps even more than the fractional schrdinger equation , is a well - studied example with many special cases to draw on . thus the fractional nlse provides an ideal mathematical context in which to explore the interplay of nonlinearity and fractional derivatives in differential equations . the basic concept of the fractional derivative is as old as calculus itself , originating in a discussion between lhpital and leibniz . in common usage now there are several approaches to fractionalize the derivative and several types of fractional derivatives have subsequently been introduced . the most popular ones are the riemann - liouville and caputo fractional derivatives . the two definitions differ only in the order of evaluation . in the caputo definition , we first compute an ordinary derivative then a fractional integral , while in the riemann - liouville definition the operators are reversed . it is often useful to apply the caputo derivative in modeling , as mathematical modeling of many physical problems requires initial and boundary conditions , and these demands are satisfied using the caputo fractional derivative . as fractional differential equations ( fdes ) do nt generally possess exact closed form solutions , several analytical and numerical techniques have been implemented to study these equations . the series solution is one of the common techniques in studying fdes analytically and numerically . for instance , the variational iteration method ( vim ) @xcite , the homotopy analysis method ( ham ) @xcite , and the adomian decomposition method ( adm ) @xcite , have been implemented to study several types of fdes . for more details one can refer to @xcite and references therein . recently , an efficient series solution was introduced for a class of nonlinear fractional differential equations @xcite . the idea is inspired by the taylor series expansion method but it overcomes the difficulty of computing iterated fractional derivatives . despite these advances , there is no universal agreement on a series approach that unifies solutions to fractional , nonlinear , and fractional nonlinear differential equations . in this paper , we provide such an approach . moreover , previous power series methods suffer from divergence past a finite radius of convergence . for example , if one considers the power series expansion of the bright soliton sech solution to the focusing nlse , the radius of convergence is @xmath0 . by extending the power series concept in a spatially iterative approach , we are able to move the radius of convergence to arbitrarily large values . to see why this is so important physically , consider the central limit theorem , which underpins statistical mechanics and indeed much of physical measurement in terms of the normal distribution . the central limit theorem only holds for finite variance . a well - known feature of the fractional diffusion equation is the power law tails of its localized solutions , which subsequently exhibit divergent variance . such `` fat - tailed '' distributions lead to not - so - rare rare events and have practical outcomes such as the choice of whether or not to store radioactive waste a given distance from a population center @xcite . our method allows us to benefit from the high accuracy and analytical formulation of the power series approach while not being subject to its typical problem with a physically limiting radius of convergence . we are able to extend the radius of convergence arbitrarily far into the tails of a localized solution , resulting in a clearer picture of the kind of statistics we can expect from the hybridization of nonlinear and fractional simplifications to physical problems . the common approach to the power series problem for fractional differential equations is an expansion of form @xmath1 this approach works well for linear fractional equations . however , for nonlinear fractional equations eq . ( [ eqold ] ) has difficulties . instead , we propose the following fractional power series as a solution : @xmath2 where @xmath3 $ ] denotes the nearest integer larger than @xmath4 and @xmath5 is the value about which the expansion is performed . in comparison with the traditional expansion in powers of @xmath6 of eq . ( [ eqold ] ) , our proposal in the second term of eq . ( [ eq3 ] ) , @xmath7 , is more comprehensive in the sense that the former is a subset of the latter . for instance , with @xmath8 and @xmath9 , the term @xmath10 will not be present in a power series of @xmath11 , while in our case this will be included . in addition , such terms couple to the integer power terms in the first sum of eq . ( [ eq3 ] ) and to the nonlinear term leading to nontrivial recursion relations . it is essential for the method developed here that we have the integer power terms in the first sum of eq . ( [ eq3 ] ) , which renders the current proposed fractional power series to be a necessity rather than a choice . furthermore , when @xmath12 is even , our proposed power series will be valid also for the negative spatial domain . in order to most effectively match the form of eq . ( [ eq3 ] ) , we take the specific case of @xmath13 , where @xmath14 and @xmath12 are positive integers . adopting here the caputo sense @xcite for the fractional derivative , defined by @xmath15 where @xmath16 is the well - known gamma function , @xmath17 is the @xmath18 order derivative of @xmath19 , @xmath20 , and @xmath5 is a constant which in our case will turn out to be the left side of the interval of spatial iteration in which we perform our power series expansion . for a power law , @xmath21 , where @xmath22 is an integer , the caputo fractional derivative reduces to @xmath23 for a shifted power law , @xmath24 , where @xmath5 is real , the above expression is not applicable , as it would be in the case of regular derivatives : the chain rule for fractional derivatives takes a different form than an in the integer case . to resolve this matter we resort to the definition in eq . ( [ cdef ] ) to obtain @xmath25 , & 1<\alpha<2\,,\nonumber\\ \\k(k-1)(x - x_0)^{k-2 } , & \alpha=2\ , , \end{array } \right . \label{cdef2}\end{aligned}\ ] ] where @xmath26 is the hypergeometric function and for simplicity we have written out explicitly the solution of the integral to the case @xmath27 ; solutions for other values of @xmath4 can be obtained in the same manner . for physical applications @xmath27 is especially interesting as it interpolates between linear and quadratic disperson , i.e. , between a phonon and a free particle . bogoliubov theory also accomplishes such an interpolation @xcite but fractional derivatives are much more generic , e.g. in terms of capturing transport in a variety of multiscale media . also , the nonlinear dirac equation , obtained for example by optical means or a bec in a honeycomb lattice @xcite near the k - point , has a first order spatial derivative and linear dispersion . it should be noted here that eq . ( [ cdef2 ] ) is applicable for @xmath28 . for @xmath29 , the fractional derivative equals zero for the case of integer @xmath22 . this is so , since for integer @xmath22 , the expression @xmath30 can be expanded in powers of @xmath31 that are all less than @xmath4 , which , according to eq . ( [ eq4 ] ) will have zero fractional derivative . for our iterative method it will turn out to be useful to consider the special cases of @xmath32 and @xmath33 with the result of the fractional derivative expanded around @xmath34 : @xmath35 @xmath36 where @xmath37 is the euler constant and @xmath38 is the digamma function defined by @xmath39/dz$ ] . for @xmath40 the @xmath41 derivative given by eq . ( [ cdef3 ] ) is identical with that of eq . ( [ eq4 ] ) for @xmath32 , as it should be . for the case of @xmath33 : @xmath42 ^ 2 , & x_0>0\,,\\\\d_3 x , & x_0=0\ , , \end{array } \right.\label{cdef4}\ ] ] where @xmath43 we note that the expansion of eq . ( [ cdef3 ] ) diverges as @xmath44 whereas eq . ( [ cdef4 ] ) approaches a constant . this important observation will be exploited in the construction of the power series that is differentiable at @xmath5 . we consider the following dimensionless fractional nonlinear schr@xmath45dinger equation ( fnlse ) @xmath46 where @xmath37 is the strength of the nonlinearity . the profile of the stationary solutions , @xmath47 ," +"the analysis of principal processes of matter heating and cooling in accretion discs presented in the work [ [ di12 ] ] has shown that for realistic parameters of accretion discs in semidetached binaries ( @xmath0 and @xmath1 ) mass transfer rate ; @xmath2 dimensionless parameter introduced by shakura and sunyaev [ [ shakura ] , [ shak2 ] ] for expression of viscosity coefficient @xmath3 ( @xmath4 disc semithickness , @xmath5 sound speed ) . ] the gas temperature in outer part of the disc lies in the range from @xmath6 k to @xmath7 k. earlier we have conducted 3d gasdynamical simulation of accretion discs both for a ` hot ' case ( the gas temperature in the outer part of the disc was 200500 thousands k [ [ di1][di11 ] ] ) , and for the ` cool ' case ( the temperature of gas in the outer part of the disc did nt exceed @xmath8 k [ [ di12 ] ] ) . the analysis of these results has shown that for both cases ( i.e. independently on the disc temperature ) the self - consistent solution did nt involve the shock interaction between the stream of matter from the inner lagrangian point @xmath9 and formed accretion disc ( hot spot "" ) . energy release zone ( hot line "" ) is located outside the disc and is formed as the result of the interaction of the circumdisc halo and circumbinary envelope with the stream . the hot line "" model is found to be in a good agreement with observations [ [ tanya98][tanya2003b ] ] . for ` hot ' solutions we have investigated both general morphology of gaseous flows in semidetached binaries and the structure of formed hot accretion discs ( see , e.g. , [ [ di11],[ippeg ] ] ) . in particular , we have found only one arm of spiral shock wave generated by the tidal influence of the mass - losing star . the two - armed spiral shocks were discovered by matsuda _ et al . _ in [ [ sawada86][spiral2 ] ] . nevertheless , our 3d gasdynamical simulations for the ` hot ' case have shown the presence of only one - armed spiral shock while in the place where the second arm should be the stream from @xmath9 dominates and presumably prevents the formation of the second arm of tidally induced spiral shock . besides we have found out that for the ` hot ' case the variation of mass transfer rate leads to the disc perturbations and to the formation of spiral - vortex structure in the disc [ [ blob1][fridman ] ] . even a glance at the morphology of gaseous flows for the ` cool ' case ( see , e.g. , [ [ di12],[rujichka ] ] ) discovers that the accretion disc for this case is characterized by principally different parameters as compared to the ` hot ' case . in particular , the disc has more circular form and the second arm of the tidal spiral wave is present . our analysis [ [ di12 ] ] shows that opposite to the ` hot ' case tidal spiral waves do nt propagate to the inner part of the cool accretion disc and are located in the outer part of the disc only . the aim of this work is the investigation of the structure of cool accretion discs in semidetached binaries . section 2 contains the qualitative analysis of changes occurring in transition from a hot accretion disc to the cool one . in particular , here we suggest the possible existence of one more type of spiral density waves in the inner part of the disc where gasdynamical perturbations are negligible . we also consider the mechanism of formation of such a wave and its parameters . section 3 contains the results of 3d gasdynamical simulation of flow structure for the case when radiative cooling is effective and the gas temperature drops down to @xmath6 k in the whole region . these results confirm the hypothesis of possible formation of a spiral wave of a new type in the inner regions of the disc . possible observational manifestations of the discovered spiral wave of the new , precessional "" type as well as main conclusions are drawn in section 4 . the sketch of main peculiarities of the morphology of gaseous flows in semidetached binaries for the ` hot ' case is given in fig . 1 . this scheme is based on the results of 3d gasdynamical simulations published in [ [ di1][di11 ] ] . in fig . 1 the fragment of mass - losing star that fills its roche lobe , the location of the inner lagrangian point @xmath9 , the stream of matter from @xmath9 , as well as the location of the accretor are shown . a dashed line marks the roche lobe . following the definitions given in [ [ di8 ] ] the morphology of gaseous flows in semidetached binaries is governed by the stream of matter from @xmath9 , quasi - elliptical accretion disc , circumdisc halo and circumbinary envelope . this classification of the main constituents is based on their physical properties : ( i ) if the motion of a gas particle is not determined by the gravitational field of accretor then this particle belongs to the circumbinary envelope filling the space between the components of binary ; ( ii ) if a gas particle revolves around the accretor and after that mixes with the matter of the stream then it does nt belong to the accretion disc but forms the circumdisc halo ( zone ` c ' in fig . 1 ) ; ( iii ) the accretion disc is formed by the matter of the stream which is gravitationally captured by the accretor and hereinafter does nt interact with the stream but moves to the accretor losing the angular momentum ( zone ` b ' in fig . 1 ) . the interaction of matter of circumdisc halo and circumbinary envelope with the stream results in the formation of the shock located along the edge of the stream . this shock is referred as hot line "" and is marked by ` hl ' in fig . 1 . tidal action of mass - losing star results in formation of spiral shock marked by ` i ' in fig . 1 . our 3d gasdynamical simulations for the ` hot ' case have shown only one - armed spiral shock while in the place where the second arm should be the flow structure is determined by the stream from @xmath9 . it also should be stressed that the spiral shock deeply penetrates to the inner part of the disc in this case . let us consider the changes occurring during the transition from the hot accretion disc to the cool one . the sketch of main peculiarities of the morphology of gaseous flows in semidetached binaries for the ` cool ' case when non - adiabatic processes of radiative heating and cooling result in dropping of gas temperature is given in fig . 2 . our 3d gasdynamical simulations presented in [ [ di12 ] ] have shown that for the ` cool ' case when the radiative cooling decreases the gas temperature to @xmath6 k the solution has the same qualitative features as that for the ` hot ' case , namely : the interaction between the stream and the disc is shockless , the energy release zone shock wave ` hl ' is due to the interaction with circumdisc halo and located outside the disc , being rather elongated this shock wave can also be referred as hot line "" . at the same time , in the ` cool ' case the accretion disc ( zones ` a ' and ` b ' in fig . 2 ) is significantly more dense as compared to the matter of the stream , the disc is thinner and has not quasi - elliptical but circular form . the size of circumdisc halo is less as well . the second arm of the tidal spiral shock is formed , the both arms do nt reach the accretor but are located in the outer part of the disc . taking into account that the stream acts on the dense inner part of the disc weakly as well as that all the shocks ( hot line "" and two arms of tidal wave ) are located in the outer part of the disc we can introduce a new element of flow structure for the ` cool ' case : the inner region of accretion disc ( zone ` a ' in fig . 2 ) where the influence of gasdynamical perturbations mentioned above is negligible . let us consider the flow of matter in the inner parts of the disc that are not subjected by gasdynamical perturbations . in the absence of external action a gas particle should revolve around the gravitation center ( accretor ) along the elliptical orbit . in our gasdynamical solutions ( see section 3 ) gas particles move along the near - circular but elliptical orbits , the accretor being located in one of the ellipse focal points . it is known ( see , e.g. , [ [ kumar ] , [ warner ] ] ) , that the influence of companion star results in retrograde precession of particle s orbit , the precession rate is proportional to orbit radius in accordance to @xmath10 where @xmath11 period of orbit precession ; @xmath12 orbital period of binary ; @xmath13 components mass ratio ; @xmath14 orbit radius ; @xmath15 binary separation . the accretion disc is formed by a multitude of particles , each of them moving along its own elliptical orbit . due to interaction between particles the disc should be considered in gasdynamical approximation , so we should consider flowlines instead of orbits , the first ones are also being elliptical . it is known that flowlines ca nt intersect and can only be tangent to each other . it is also evident from geometrical consideration that in order to build the disc from non - intersecting ellipses we should embed it into each other . for the case of zero eccentricity we will obtain the circular disc . for the case of non - zero eccentricity of flowlines we can build the equilibrium solution with aligned semimajor axes of ellipses . in the presence of an external action ( as it occurs in binaries ) orbits begin to precess , the precession of flowlines more distant from the accretor being faster so it will overtake the flowlines with less semimajor axes . due to impossibility of intersections between flowlines , the solution goes to equilibrium state and all flowlines tend to precess with the same angular velocity , i.e. in rigid - body mode . in this state a remote orbit should be turned at larger angle in the direction opposite to that of the matter rotation in the disc since the precession is retrograde . the precession rate value lies in the range from the one for outer ( ` fast ' ) orbits and the precession rate for inner ( ` slow ' ) orbits . the inner orbits are defined as those with the negligible gravitational influence of companion star as compared to the gravitational influence of accretor . the outer orbits are defined as those lying in the region without gasdynamical perturbations since latter can violate the regularity of precession . the location of both innermost and outermost orbits obviously depends on parameters of binary and parameters of mass transfer ( e.g. , mass transfer rate ) so we can expect the various values of precession rate for different systems . let us consider a solution with the semimajor" +"recent flourish of studies on compressed sensing inspires researchers to apply the idea for applications in wireless communications . fletcher et al . @xcite showed that a detection problem for on - off random access channels is equivalent a sparse signal recovery problem discussed in compressed sensing . kaneko et al . @xcite used a compressed sensing technique to develop an identification protocol for a passive rfid system . for such an application in wireless communications , we need powerful sparse signal recovery algorithms that are suitable for hardware implementation in order to achieve high speed signal processing and energy efficiency . _ binary ( or one - bit ) compressed sensing _ firstly proposed by boufounos and baraniuk @xcite is a variant of the original compressed sensing . in the scenario of binary compressed sensing , a linear observation vector that is quantized to a binary value , typically in the binary alphabet @xmath1 , is given to a receiver . the linear observation vector is the product of a sensing matrix and a hidden sparse signal vector . a receiver then tries to reconstruct the original sparse signal . this process is called a _ sparse signal recovery _ process . it is known that power consumption of an ad converter is closely related to the number of its quantization levels and the sampling frequency , namely , the power consumption of an ad converter increases as the sampling frequency increases . when we pursue to develop an extremely low power consumption device for battery - powered sensors or to develop a digital signal processing device operating at very high sampling frequency , binary quantization by a comparator is a reasonable choice . binary compressed sensing is well suited to such a situation . moreover , since the input to the receiver is restricted to binary values , no gain control is required in the case of binary compressed sensing . this fact further simplifies the hardware needed in the receiver . the optimal sparse signal recovery for binary compressed sensing can be attained by solving a certain integer programming problem . however , the ip problem is , in general , computationally hard to solve and the approach can handle only small problems . boufounos and baraniuk @xcite studied a relaxation method that replaces @xmath2-norm with @xmath0-norm and introduced a convex relaxation for integer constraints . although nonlinearity induced by binary quantization prohibits direct applications of known sparse recovery algorithms for the original compressed sensing , several sparse recovery algorithms for binary compressed sensing has been developed @xcite @xcite @xcite based on the known iterative methods for the original compressed sensing . boufounos @xcite proposed a greedy algorithm called matched sign pursuit ( msp ) that is a counter part of orthogonal matching pursuit ( omp ) . the paper @xcite presents binary iterative hard thresholding ( biht ) algorithm by reforming iterative hard thresholding ( iht ) algorithm @xcite . although the known sparse recovery algorithms exhibit reasonable sparse recovery performance , it may not be suitable for applications in high speed wireless communications . this is because most of algorithms require a number of iterations to achieve reasonable sparse recovery results . most of known algorithms also require calculations involving matrix - vector products with @xmath3-computations for each iteration where @xmath4 is the length of the sparse signal vector . our approach for sparse signal recovery is to employ _ feedforward neural networks _ as building blocks of sparse signal recovery schemes . we expect that an appropriately designed and trained neural networks greatly reduce required computing resources and are well suited to hardware implementation . in this paper , we will propose the majority voting neural networks composed of several independently trained neural networks , which are feedforward 3-layer neural networks employing the sigmoid function as an activation function . as far as we know , there is no previous studies on sparse signal recovery based on neural networks . our focus is thus not only on the practical aspect of the neural sparse signal recovery but also on studies on the fundamental behavior of the neural networks for sparse signal recovery . recently , _ deep neural networks _ @xcite have been actively studied because they provide surprisingly excellent performance in the areas of image / speech recognition and natural language processing @xcite . such powerful neural networks can be used in wireless communication as well . this work can be seen as a first attempt to this direction . the main problem for binary compressed sensing is to reconstruct an unknown sparse signal vector @xmath5 from the observation signal vector @xmath6 under the condition that these signals satisfy the relationship : @xmath7 the sign function @xmath8 is defined by @xmath9 the matrix @xmath10 is called a _ sensing matrix_. we assume that the length of the observation signal vector @xmath11 is smaller than the length of the sparse signal vector @xmath12 , i.e. , @xmath13 . this problem setup is similar to that of the original compressed sensing . the notable difference between them is that the observation signal @xmath11 is binarized in a sensing process of binary compressed sensing . a receiver obtains the observation signal @xmath11 and then it tries to recover the corresponding hidden signal @xmath12 . we here make two assumptions for the signal @xmath12 and the sensing matrix @xmath14 . the first assumption is sparsity of the hidden signal @xmath12 . the original binary signal @xmath15 contains only @xmath16 non - zero elements , where @xmath16 is a positive integer much smaller than @xmath4 , i.e. , hamming weight of @xmath12 should be @xmath16 . we call the set of binary vectors with hamming weight @xmath16 is @xmath16-_sparse signals_. the second assumption is that the receiver completely knows the sensing matrix @xmath14 . when we need an extremely high speed signal processing or an energy - efficient sparse signal processing method for battery powered sensor , it would be reasonable to develop a sparse signal recovery algorithm suitable for the situation . in the sparse signal recovery method based on neural networks to be described in this section requires only several matrix - vector products to obtain an output signal , which is an estimate signal of the sparse vector @xmath12 . thus , the proposed method needs smaller computational costs than those required by conventional iterative methods . comes from the left and is fed to the input layer . a sparse estimation vector comes out from the output layer . the sigmoid function is used as an activation function.,width=264 ] our sparse recovery method is based on a 3-layer feedforward neural network illustrated in fig.[fig : nnmodel ] . this architecture is fairly common one ; it consists of the input , hidden and output layers . adjacent layers are connected by weighted edges and each layer includes neural units that can keep real values . as an _ activation function _ , we employed the sigmoid function to determine the values of the hidden and output layers . in our problem setting , the observation signal @xmath11 is fed into the input layer from the left in fig.[fig : nnmodel ] . the signal propagates from left to right and the output signal @xmath17 eventually comes out from the output layer . the network should be trained so that the output signal @xmath17 is an accurate estimation of the original sparse signal @xmath12 . the precise description of the network in fig.[fig : nnmodel ] is given by the following equations : @xmath18 the function @xmath19 is the sigmoid function defined by @xmath20 in this paper , we will follow a simple convention that @xmath21 represents @xmath22 where @xmath23 . the round function @xmath24 gives the nearest integer from @xmath25 . the equation ( [ hyde ] ) defines the signal transformation from the input layer to the hidden layer . an affine transformation is firstly applied to the input signal @xmath26 and then the sigmoid function is applied . the weight matrix @xmath27 and the bias vector @xmath28 defines the affine transformation . the resulting signal @xmath29 is kept in the units in the hidden layer , which are called _ hidden units_. the parameter @xmath30 thus means the number of hidden units . from the hidden layer to the output layer , the equation ( [ output ] ) governs the second signal transformation . the second transformation to yield the signal @xmath17 consists of the affine transformation , based on the weight matrix @xmath31 and the bias vector @xmath32 , and the nonlinear mapping based on the sigmoid function . the vector @xmath33 emitted from the output layer is finally rounded to a nearest integer vector because we assumed that non - zero elements in the original sparse signal @xmath12 takes the value one . since the range of the sigmoid function lies in the open interval @xmath34 , an element in the estimate vector @xmath35 should take the value zero or one . the network in fig.[fig : nnmodel ] can be seen as a parametrized estimator @xmath36 where @xmath37 is the set of the trainable parameters @xmath38 . it is expected that the trainable parameter @xmath37 should be adjusted in the training phase so as to minimize the error probability @xmath39 $ ] . however , it may be computationally intractable to minimize the error probability directly . instated of direct minimization of the error probability itself , we will minimize a loss function including a cross entropy - like loss function and an @xmath0-regularization term . in this subsection , the details of the training process is described . in the training phase of the network , the parameter @xmath37 should be updated in order to minimize the values of the given loss function . let @xmath40 be the set of the training data used in the training phase . the signals @xmath41 and @xmath42 relate as @xmath43 . in the training process , we use randomly generated training samples ; the sparse vectors @xmath44 are generated uniformly at random from the set of @xmath16-sparse vectors . the sample @xmath41 is fed into the network and the corresponding sample @xmath42 is used as the _ supervisory signal_. we here employ _ stochastic gradient descent ( sgd ) algorithms _ to minimize the loss function described later . it is empirically known that sgd and its variations behave very well for non - convex objective functions that are computationally hard to minimize . this is the reason why sgd and related algorithms are widely used for training deep neural networks . in order to use sgd , we need to partition the training set into minibatches . a minibatch is a subset of the training data and the use of minibatches introduces stochastic disturbance in training processes . such stochastic disturbance helps a search point in an sgd process to escape from a stationary point of the non - convex objective function to be minimized . we divide the training data into a number of minibatches as follows : @xmath45 in this case , every minibatch contains @xmath46-pair of samples . we denote @xmath16-th @xmath47 , minibatch as @xmath48 . the choice of the loss function , i.e. , the objective function to be minimized in training processes , is crucial to achieve appropriate recovery performance . we introduce a loss function designed for sparse signal recovery . the loss function of @xmath16-th minibatch is defined by @xmath49 the vector @xmath50 is given by @xmath51 i.e , the output of our neural network corresponding to the input @xmath41 . the first term of @xmath52 measures closeness between @xmath53 and @xmath54 . this measure is closely related to _ cross entropy _ that are often used in supervised classification problems . in the case of a classification problem , @xmath42 is a one - hot vector that can be interpreted" +"in both spoken and written language , word occurrences are not random but vary greatly from document to document . indeed , the field of information retrieval ( ir ) relies on the degree of departure from randomness as a discriminative indicator . ir systems are typically based on unigram statistics ( often referred to as a `` bag - of - words '' model ) , coupled with sophisticated term weighting schemes and similarity measures @xcite . in an attempt to mathematically realise the intuition that an occurrence of a certain word may increase the chance that the same word is observed later , several probabilistic models of word occurrence have been proposed . much of this work has evolved around the use of ( a mixture of ) the poisson distribution @xcite . recently , church and gale have demonstrated that a continuous mixture of poisson distributions can produce accurate estimates of variable word rate @xcite . lowe has introduced a beta - binomial mixture model which was applied to topic tracking and detection @xcite . although a constant word rate is an unlikely premise , it is nevertheless adopted in many areas including @xmath0-gram language modelling . in order to address the problem of variable word rate , several adaptive language modelling approaches have been proposed with a moderate degree of success . typically , some notion of `` topic '' is inferred from the text according to the `` bag - of - words '' model . information from different language model statistics ( , a general model and/or models specific to each topic ) are then combined using methods such as mixture modelling @xcite or maximum entropy @xcite . the _ dynamic cache model _ @xcite is a related approach , based on an observation that recently appearing words are more likely to re - appear than those predicted by a static @xmath0-gram model . it blends cached unigram statistics for recent words with the baseline @xmath0-grams using an interpolation scheme . theoretically , it should not be necessary to rely on an _ ad hoc _ device such as a cache in order to model variable word occurrences . all the parameters of a language model may be completely determined according to probabilistic model of word rate , such as a poisson mixture . in this paper , we outline the theoretical background for modelling the variable word rate , and illustrate a key observation that word rates are not static using spoken data transcripts . the constant word rate assumption is then eliminated , and we introduce a variable word rate @xmath0-gram language model . an approach to estimating relative frequencies using prior information of word occurrences is presented . it is integrated with standard @xmath0-gram modelling that naturally involves discounting and smoothing schemes for practical use . using the darpa / nist 4e north american broadcast news task , the approach demonstrates the reduction of perplexity up to 10% . in this section , we illustrate how the assumption of a constant word rate fails to capture the statistics of word occurrence in spoken ( or written ) documents . we show that the word rate is variable and may be modelled using a poisson distribution or a continuous mixture of poissons . the poisson distribution is one of the most commonly observed distributions in both natural and social environments . it is fundamental to the queueing theory : under certain conditions , the number of occurrences of a certain event during a given period , or in a specified region of space , follows a poisson distribution ( a _ poisson process _ @xcite ) . by assuming randomness in a poisson process , word rate is no longer uniform . firstly , we provide a loose definition of a document as a unit of spoken ( or written ) data of a certain length that contains some topic(s ) , or content(s ) . we consider a model in which a word occurs at random in a fixed length document . for a set of documents we assume that each document produces this word independently and that the underlying process is the poisson with a single parameter @xmath1 . formally , a poisson distribution is a discrete distribution ( of a random variable @xmath2 ) which is defined for @xmath3 such that @xmath4}(x ) = { \cal p}(x = x;\ \lambda ) = \frac{e^{- \lambda } \lambda^x}{x ! } \label{eq : poisson}\end{aligned}\ ] ] whose expectation and variance are given by @xmath5 = \lambda$ ] and @xmath6 = \lambda$ ] , respectively @xcite . a less constrained model of variable word rate is offered by a multiple of poissons , rather than a single poisson . suppose the parameter @xmath7 of the pdf ( [ eq : poisson ] ) is distributed according to some function @xmath8 , then we define a continuous mixture of poisson distributions by @xmath9}(x ) \phi(\lambda ) d\lambda \ . \label{eq : mixture}\end{aligned}\ ] ] in particular , if @xmath8 is a gamma distribution , , @xmath10 for @xmath11 and @xmath12 , then the integral ( [ eq : mixture ] ) is reduced to a discrete distribution for @xmath3 such that @xmath13}(x ) \hspace{-0.1 in } & = & \hspace{-0.1 in } { \cal nb}(x = x;\ \alpha , \beta ) \nonumber \\ & = & \hspace{-0.1 in } \left ( \begin{array}{c } \alpha + x - 1 \\ x \end{array } \right ) \frac{\beta^x}{(1 + \beta)^{\alpha + x } } \ . \label{eq : nb}\end{aligned}\ ] ] this @xmath14}(x)$ ] is a negative binomial distribution be @xmath15 in ( [ eq : mixture ] ) . this integration is straightforward using the definition of the gamma function , @xmath16 , and the recursion , @xmath17 . the resultant pdf ( [ eq : nb ] ) has a slightly unconventional form in comparison to that in most of standard textbooks ( , @xcite ) , but is identical by setting a new parameter @xmath18 with @xmath19 . ] and its expectation and variance are respectively given by @xmath5 = \alpha\beta$ ] and @xmath6 = \alpha\beta ( \beta + 1)$ ] . the histograms in figure [ fig : uhist ] show the number of word ( unigram ) occurrences in spoken news broadcast , taken from transcripts of the 4e broadcast news acoustic training data ( 199697 ) . these transcripts were separated into documents according to section markers and those with less than 100 words were removed , resulting 2583 documents containing slightly less than 1.3 million words in total . in the following , the number of word occurrences were normalised to 1000-word length documents . and appeared approximately the same number of times across all the transcripts . using a constant word rate assumption , they would have been assigned a probability of around 0.0086 . however their occurrence rates varied from document to document ; about 11% and 33% of all documents did not contain and ( respectively ) , while 1% and 3% contained these words more than 30 times . this seems to indicate that occurrences of is less dependent on the content of the document . a negative binomial distribution was used to model the variable word rate in each case ( the solid line in figure [ fig : uhist ] ) . the negative binomial seems to model word occurrence rate relatively well for most vocabulary items , regardless of frequency . figure [ fig : uhist ] illustrates this for one of the most frequent words ( probability of 0.023 according to the constant word rate assumption ) and the less frequently occurring ( less than 0.00029 ) . in particular , appeared only in 93 out of 2583 documents , but 28 of them contained more than 10 instances , suggesting strong correlation with document content . . they are fitted by negative binomial distributions ( solid lines).,width=307 ] we also collected statistics of bigrams appearing in the broadcast news transcripts . figure [ fig : bhist ] show histograms and their negative binomial fits for bigrams and . although very sparse ( , they appeared in 127 and 6 documents , respectively ) , this suggests that variable bigram rate can also be modelled using a continuous mixture of poissons . taking word occurrence rate into account changes a probabilistic language model from a situation akin to playing a lottery , to something closer to betting on a horse race : the odds for a certain word improve if it has come up in the past . in this section , we eliminate the constant word rate assumption and present a variable word rate @xmath0-gram language model . let @xmath20 denote a relative frequency after we observe @xmath21 occurrences of word @xmath22 . it is calculated by @xmath23 the function is defined for @xmath24 , where @xmath25 is a fixed document length ( , @xmath25 is normalised to 1000 in figures [ fig : uhist ] and [ fig : bhist ] ) . @xmath26 is the occurrence rate for word @xmath22 in an @xmath25-length document ( , poisson , negative binomial ) , satisfying @xmath27 in particular , @xmath28 which corresponds to the case with no prior information of word occurrence . for the conventional approach with the constant word rate assumption , this @xmath29 is not modified regardless of any word occurrences . further , function ( [ eq : rf_var ] ) satisfies our intuition ; the value of @xmath20 increases monotonically as the number of observation @xmath21 accumulates ( easy to verify ) , and it reaches a unity ( ` 1 ' ) when @xmath30 . ) . the right figure demonstrates relative frequencies after a certain number of word occurrences . circles ( ` ' ) correspond to relative frequencies under the constant word rate assumption ( 0.023 for and 0.00029 for ) .,width=307 ] the characteristics of function ( [ eq : rf_var ] ) are illustrated in figure [ fig : rfrequency ] . the right hand figure shows relative frequencies for and after a certain number of previous observations of the word . it indicates that the first few instances of the frequent word ( ) do not modify its relative frequency very much , but have a substantial effect on the relative frequency of the less common word ( ) . as the number of observations increases , the former is caught up by the latter . finally , in order to convert this relative frequency model to any type of probabilistic model for language , normalisation is required . this is achieved by dividing @xmath20 by @xmath31 , where @xmath32 implies a set of vocabulary . variable relative frequencies for bigrams can also be calculated in a similar fashion . for any practical application , smoothing of the probability estimates is essential to avoid zero probabilities for events that were not observed in the training data . let @xmath33 denote a bigram entry ( a word @xmath34 followed by @xmath22 ) in the model . further , @xmath35 implies a relative frequency after we observe @xmath36 occurrences of the bigram . a bigram probability @xmath37 may be smoothed with a unigram probability @xmath38 . using the interpolation method @xcite : @xmath39 where @xmath40 implies a `` discounted '' relative frequency ( described later ) and @xmath41 is a non - zero probability estimate ( , the probability that a bigram entry @xmath33 exists in the model ) . alternatively , the back - off smoothing @xcite may be applied : @xmath42 in ( [ eq : backoff ] ) , @xmath43 is a back - off factor and is calculated by @xmath44 a unigram probability @xmath38 can be obtained similarly by smoothing with some constant value . finally , a number of standard discounting methods exist for constant word rate" +"nucleus - nucleus collisions at ultrarelativistic energies create hadronic matter at high energy density . the distributions of baryons at mid - rapidity provide a sensitive probe of the collision dynamics . in particular , the stopping power determines how much of the incoming longitudinal energy is available for excitation of the system . these collisions have been described by microscopic models incorporating hadron production and rescattering , see for example @xcite . the data reported here impose constraints on the amount of stopping of baryons in such models . enhanced production of antibaryons may indicate formation of a state of matter in which the quarks and gluons are deconfined @xcite . such enhancement may be hidden , however , by antibaryon annihilation with baryons @xcite ; the antiproton survival probability is sensitive to both the collision environment and the antiproton formation time . the antiproton and proton distributions may also reflect the degree of thermalization achieved and , by comparing distributions from light and heavy systems , allow detailed studies of rescattering . we present proton and antiproton measurements using the na44 spectrometer from @xmath0 ( to approximate @xmath1 ) , proton - nucleus and nucleus - nucleus interactions . this allows a systematic study as a function of the size of the central region and different conditions in the surrounding hadronic matter . these systematic studies are aided by use of an event generator . the rqmd model , version 1.08 @xcite , is a microscopic phase space approach , based on resonance and string excitation and fragmentation with subsequent hadronic collisions . rqmd includes annihilation of antiprotons in the hadronic medium when they collide with baryons @xcite . we study a feature of rqmd called color ropes by the authors of the model . rqmd uses a string model of particle production from each nucleon - nucleon collision . in a heavy - ion collision , where there are numerous nucleon - nucleon collisions , the density of these strings is high and multiple strings overlap . overlapping strings do not fragment independently but form ` ropes ' , chromoelectric flux - tubes whose sources are color octet charge states rather than the color singlet charges of normal strings @xcite . these ropes represent a collective effect in nucleus - nucleus collisions , and have been shown to enhance both strangeness and baryon pair production @xcite . the na44 experiment is shown in figure [ fg : setup ] . three conventional dipole magnets ( d1 , d2 , and d3 ) and three superconducting quadrupoles ( q1 , q2 , and q3 ) analyze the momentum and create a magnified image of the target in the spectrometer . the magnets focus particles from the target onto the first hodoscope ( h1 ) such that the horizontal position along the hodoscope gives the total momentum . two other hodoscopes ( h2 , h3 ) measure the angle of the track . the momentum acceptance is @xmath2 20% of the nominal momentum setting . the angular coverage is approximately -5 to + 78 mrad with respect to the beam in the horizontal plane and @xmath2 5 mrad vertically . only particles of a fixed charge sign are detected in a given spectrometer setting . four settings are used to cover the mid - rapidity region in the @xmath3 range 0 to 1.6 gev . figure [ fg : acprot ] shows the acceptance of the spectrometer in the @xmath4 plane for the 4 and 8 gev / c momentum settings when the spectrometer axis is at 44 and 131 mrad with respect to the beam . for the sulphur - nucleus data , the beam rate and time - of - flight start are determined using a cherenkov beam counter ( cx ) , with time resolution of approximately 35 ps @xcite . for the proton - nucleus data , a scintillator counter is used to measure the beam rate . a second scintillator ( t@xmath5 ) is used to trigger on central events in sulphur - nucleus collisions by requiring a large pulse height ( high charged particle multiplicity ) . the pseudorapidity coverage of t@xmath5 is roughly 1.3 to 3.5 . for proton beams , t@xmath5 provides the interaction trigger by requiring that at least one charged particle hit the scintillator , and also provides the time - of - flight start with a time resolution of approximately 100 ps . a silicon pad detector measures the charged - particle multiplicity with @xmath6 azimuthal acceptance in the pseudorapidity range @xmath7 . the three scintillator hodoscopes ( h1 , h2 and h3 ) are used to track the particles and are divided into 50 , 60 and 50 slats , respectively . the hodoscopes also provide time - of - flight with a time resolution of approximately 100 ps ; particle identification relies primarily upon the third hodoscope . two cherenkov counters differentiate kaons and protons ( c1 : freon-12 at 1.4 or 2.7 atm , depending on the spectrometer setting ) , and reject electrons and pions ( c2 : nitrogen / neon mixture at 1.0 or 1.3 atm ) . an appropriate combination of c1 and c2 is used for each spectrometer setting to trigger on events with no pions or electrons in the spectrometer . particles are identified by their time - of - flight , in combination with the cherenkov information . figure [ fg : pidprot ] illustrates the particle identification after pions have been vetoed by the cherenkovs ; kaons and protons are clearly separated . more details about the spectrometer are available in @xcite . the proton and antiproton data samples after particle identification and quality cuts are shown in table [ tb : data ] . also shown for each data set is the target thickness and the centrality , expressed as a fraction of the total inelastic cross - section . tracks are reconstructed from the hit positions on the three hodoscopes , constrained by straight - line trajectories after the magnets . in order to construct the invariant cross - section , the raw distributions are corrected using a monte carlo simulation of the detector response . simulated tracks are passed through the full analysis software chain and used to correct the data for geometrical acceptance , reconstruction efficiency and momentum resolution . particles are generated according to an exponential distribution in transverse mass , @xmath8 , with the coefficient of the exponent determined iteratively from the data . the cherenkovs reject pions with an efficiency of greater than 98% at the trigger level . further offline selection reduces the pions to a few percent of the kaons . after time - of - flight and cherenkov cuts , the residual kaon contamination of the proton sample is less than 3% . the invariant cross - sections are presented as a function of @xmath9 - @xmath10 , where @xmath10 is the mass of the proton . the absolute normalization of each spectrum is calculated using the number of beam particles , the target thickness , the fraction of interactions satisfying the trigger , and the measured live - time of the data - acquisition system . for the @xmath11 data , the centrality selection is determined by comparing the pulse height distribution in the t@xmath5 counter for central and unbiased beam triggers . for @xmath12 systems , the fraction of inelastic collisions producing at least one hit in the interaction ( t@xmath5 ) counter is modeled with the event generators rqmd @xcite and fritiof @xcite . the errors on the centralities for the @xmath12 data in table [ tb : data ] reflect the systematic uncertainty on this fraction from comparing the two models . the @xmath12 data are also corrected for the efficiency of the t@xmath5 counter . the resulting centrality fractions are indicated in table [ tb : data ] . the proton - nucleus data are corrected for non - target background . the largest corrections are 7.4% and 6.7% on the absolute cross - sections for protons and antiprotons from @xmath0 collisions . this correction does not affect the shape of the distribution . the corrections to the nucleus - nucleus data are negligible . the cross - sections are also corrected for the proton identification efficiency , and for the effects of selecting events with no accompanying pion or electron . the pion ( electron ) veto correction is determined from the number of protons in runs for which the pions ( electrons ) are not vetoed . the effect of hadronic interactions of the produced particles in the material of the spectrometer has been studied using a detailed geant simulation . these interactions , including annihilation of antiprotons in the spectrometer material , do not distort the shape of the measured transverse mass distributions but result in a reduction in the observed yields of about 11% for protons and 17% for antiprotons . the data are corrected for these losses . the invariant cross - sections , measured in the na44 acceptance , are generally well described by exponentials in transverse mass ( see equation [ eq : mt ] ) . the proton and antiproton rapidity densities ( dn / dy ) are calculated by integration of the normalized @xmath9 distributions , with the fitted coefficient of the exponent ( the ` inverse slope ' ) used to extrapolate to high @xmath9 , beyond the region of measurement . the statistical error on this extrapolation is calculated using the full error matrix from the fit of equation [ eq : mt ] ( see section [ sec : results ] ) to the @xmath9 spectrum . the corresponding systematic error is included in table [ tb : errors ] . the momentum scale of the spectrometer is verified with a second , independent measurement of the momentum using the multiwire proportional chambers ( mwpcs 1 - 4 in figure [ fg : setup ] ) and dipole magnet ( d3 ) , yielding a systematic error of 1.6% on the @xmath3 scale . since the na44 spectrometer has acceptance for both positive and negative @xmath13 , a systematic offset in @xmath3 can be checked by requiring symmetry around @xmath14 . the resulting uncertainty on the origin of the @xmath3 scale is 7 mev / c for the 8 gev setting . a detailed monte carlo simulation , including multiple scattering and detector granularity , is used to correct for the finite resolution of the spectrometer , and introduces a systematic error in @xmath3 of 0.15% . systematic errors on the inverse slopes of the transverse mass distributions are estimated by comparing the inverse slope determined from the 131 mrad data to the inverse slope determined from both angle settings , and are less than 5%(15% ) for the 8 gev(4 gev ) setting data . the systematic errors due to the spectrometer acceptance correction are estimated from the sensitivity of the extracted slope to the fit range used , and by measuring the slope determined from the ratio of the cross - sections corresponding to the ` central ray ' of the spectrometer at both the 131 and 44 mrad settings . in this ratio the acceptance corrections cancel since the particles have the same path through the spectrometer . the total uncertainty is 10 mev / c for the mid - rapidity ( @xmath15=2.3 - 2.9 ) data , and 10 - 20 mev / c for the lower rapidity ( @xmath15=1.9 - 2.3 ) data . the error in the absolute normalizations is dominated by the uncertainty in the fraction of the total cross - section selected by the na44 centrality trigger , and by the pion and electron veto corrections . the relative error in the centrality is 6% for both the @xmath16 and @xmath17 data , resulting in a systematic uncertainty of 6% in dn /" +"the characterization of the orbits supported by an astrophysical potential is of interest in order to study self - consistent models of stellar systems . @xcite , for example , pioneered the construction of steady state distribution functions from a well chosen set of regular orbits belonging to a given potential ; other studies followed on the same line ( e.g. * ? ? ? thus , it was established that regular orbits act as a dynamical skeleton of a stellar system . moreover , among regular orbits , those that are resonant and stable are of utmost importance , since they generate entire families of orbits around them : they constitute the backbone of the system . on the other hand , chaotic orbits , the existence of which in realistic models of galaxies is nowadays beyond doubt @xcite , are important to the dynamical evolution of stellar systems . in particular , the slow difusion of many chaotic orbits through their allowed phase space may affect even the global characteristics of the system . as @xcite and @xcite showed , the spatial distribution of fully chaotic orbits ( i.e. , those which obey only one isolating integral of the motion ) and partially chaotic orbits ( those which obey two integrals ) is quite different . this points towards a different dynamical role for each type of chaoticity , although what kind of role is still unknown . thus , finding regular , resonant , non resonant , partially chaotic and fully chaotic orbits is fundamental in the study of the dynamics of a stellar system . they all are defined by the number of isolating integrals of motion that they obey . for an @xmath0-dimensional potential , regular orbits have @xmath0 or more isolating integrals , whereas chaotic orbits obey less than @xmath0 isolating integrals or more isolating integrals of motion . however , a chaotic orbit is defined through its sensitivity to the initial conditions in phase space : if the initial conditions of the orbit are infinitesimally displaced , the distance between the original orbit and the new orbit grows exponentially with time . these definitions do not complement each other . whereas it can be proved that a regular orbit is not chaotic and a chaotic orbit is not regular ( e.g. * ? ? ? * ) , it has not been proved that every irregular ( i.e. not regular ) orbit is chaotic , or , in other words , that every orbit obeying less than @xmath0 isolating integrals has sensitivity to the initial conditions . nevertheless , to avoid confusion , we will follow here the widespread convention of considering irregular orbits and chaotic orbits as the same set . ] . among regular orbits , those that are not resonant obey exactly @xmath0 isolating integrals , whereas those resonant have one more isolating integral for each additional resonance . on the other hand , among chaotic orbits , fully and partially chaotic orbits are also distinguished by the number of isolating integrals they have , as said above . thus , a method allowing to determine the number of isolating integrals an orbit obey is a fundamental tool in studying the dynamics of a stellar system . one of the main consequences of obeying isolating integrals of motion is the dimension of the manifold on which the orbit moves . since an isolating integral is , by definition , a non - degenerate , time independent funcion of the phase space coordinates the value of which is constant along the orbit , it reduces in one the dimension of the manifold in which the orbit moves @xcite . thus , if @xmath1 is the dimension of the phase space , an orbit obeying @xmath2 isolating integrals moves in a manifold of dimension @xmath3 . one can then ascertain the number of integrals that an orbit obeys by computing the dimension of the space in which it moves . to be brief , we will refer hereafter to isolating integrals as simply integrals , and to the dimension of the manifold on which an orbit moves as the dimension of an orbit. the traditional methods to compute the dimension of an orbit or the number of its integrals are : a ) surfaces of section ( e.g. * ? ? ? * ; * ? ? ? as is well known , this method needs a qualitative judgment on a plot , and can not distinguish between orbits moving in 3 o more dimensions . b ) lyapunov exponents ( e.g. * ? ? ? this method is the standard tool to separate regular from chaotic orbits ; it is quite reliable , and can in principle recognize the dimension of chaotic orbits . on the negative side , since one needs both to integrate a set of variational equations and to integrate along large intervals in order to approximate @xmath4 , it is quite expensive in terms of computing time , and , furthermore , it can not recognize the dimension of regular orbits . c ) spectral dynamics ( e.g. * ? ? ? * ; * ? ? ? taking into account that a regular orbit on an @xmath0-dimensional potential moves on a manifold diffeomorphic to a @xmath0-dimensional torus @xcite , the natural frequencies of revolution around the @xmath0 independent circles of the torus must be reflected in the fourier spectra of the orbit . this allows to find whether there are resonances , and thus the dimension of the orbit can be established . unfortunately , the method is not suitable for analizing rotating potentials , requires a fine tuning of a set of numerical parameters for each different potential , and can not find the dimension of chaotic orbits . the frequency map method @xcite is based on the same idea . d ) the smaller alignment index , or sali ( e.g. * ? ? ? * ) , and its generalization , the generalized alignment index , or gali ( e.g. * ? ? ? both methods are based in a geometrical property of phase space vectors joining close initial conditions , namely that they align themselves or not depending on the geometrical properties of the local dynamics of the system , allowing a fast and accurate determination of whether an orbit is regular or chaotic . the gali , in particular , although can not retrieve the dimension of a chaotic orbir , do allow to discern the dimension of the torus of regular orbits , making it an excellent gauge to our results . @xcite have proposed a method to find the dimension of ( the attractor of ) an orbit in an arbitrary dynamical system , the equations of motion of which are unknown , based on the computation of the correlation integral of the time series of an arbitrary observable . in this context , several improvements have been made to the method ( e.g. * ? ? ? * ; * ? ? ? * ) , and many caveats and spurious estimations have been found ( e.g. * ? ? ? also , some implementations have been made in the astronomical field ( e.g. * ? ? ? the application of the method to find the dimension of an orbit integrated in an astronomical potential , i.e. , knowing the equations of motion and being able to sample the actual trajectory of the system at arbitrary points , was first proposed by @xcite , and more recently by @xcite . the rationale is as follows . suppose that a given orbit obeys @xmath5 isolating integrals , i.e. , it is closed and therefore unidimensional . given a small hypersphere ( in phase space ) of radius @xmath6 around a point @xmath7 of this orbit , the number of other points of the orbit included into the sphere will grow linearly as @xmath6 grows . if the orbit obeyed @xmath8 integrals , moving in a bidimensional surface , the number of points would grow as @xmath9 as @xmath6 grows . from this point on , it is clear that if the orbit is moving on a @xmath10-dimensional space , the number of points would grow as @xmath11 as @xmath6 grows . this simple mechanism , in principle , allows to easily compute the dimension of the orbit and , therefore , the number of integrals of motion it obeys . @xcite and @xcite have developed a simple algorithm in order to compute the dimension @xmath10 of an orbit following the foregoing idea . given a set of phase space points of the orbit , first compute the distances between pairs of them . second , compute the cumulative distribution function of those distances . this is nothing but the correlation integral @xmath12 of the points of the orbit , i.e. , an histogram of the number of pairs of points separated by a given distance or less . this function must be precisely equal to @xmath11 , i.e. , the number of pairs closer than a given distance must grow as @xmath11 . therefore , from a log log plot of @xmath12 , a straight line can be fitted , its slope giving the desired exponent @xmath10 which is the dimension sought . a few caveats are in order : a ) the exponent @xmath10 is theoretically obtained only in the limit @xmath13 ; thus , the slope must be computed avoiding large values of @xmath6 . b ) unfortunately , since the volume of phase space is proportional to @xmath14 , there will be always few points in the region @xmath15 , so this region of @xmath12 will be noisy in general , and therefore must be also avoided in computing @xmath10 . c ) in order to avoid autocorrelations , the points of the orbit should not be too close in time ; otherwise , @xmath12 will tend to yield @xmath16 at short distances ( see [ timestep ] ) . therefore , in order to build up the histogram , the distances should be computed only between a random subsample of the integrated points . of course , the number of points @xmath17 of the orbit must be sufficient so as to get a reasonable good computation of @xmath12 . as described , the method is very simple indeed . @xcite and @xcite give several examples of its application to orbits supported by different astronomical potentials , and the results seem encouraging . however , in order to compete against other methods , the algorithm must be capable of classify orbits blindly ; otherwise , it would be not better than inspecting surfaces of section . to see whether it is the case , we choose a stckel potential , for it has all its orbits regular ( i.e. , they all must have @xmath18 , with the possible exception of a few orbits with @xmath19 ) , and therefore we know the correct outcome beforehand , allowing us to assess immediately how good is the method , at least in this particular case . thus , we integrated 5487 orbits in the potential generated by the perfect ellipsoid density distribution @xmath20 where @xmath21 and @xmath22 , @xmath23 are constants @xcite . we used @xmath24 , @xmath25 , @xmath26 , and @xmath27 . the orbits were integrated along 500 periods with a time step of 1/200 of the respective orbital period , so as to get 100,000 points for each orbit . the dimensions @xmath10 were computed using the distances of a random sample of 10,000 of those points . the result is shown in fig . [ dstackel ] , where it can be seen a wide dispersion of values instead of the unique expected value @xmath18 . in order to verify whether the number of points @xmath17 was inadequate @xcite , we took the" +"in this paper we focus on the problem of recovering behavior - related micro choice information from aggregate data . in particular , we consider origin - destination data , casting this problem as an inference problem concerning the prediction of flows on networks @xcite . we recognize that this type of data comes from dynamic , adaptive behavior systems involving interdependent micro components which give rise to an instantaneous , feedback - adaptive , world : as a result , such systems are non - deterministic in nature , involve information and uncertainty and are driven toward a certain , optimal , stationary state ( see , for example , @xcite ) . as a basis for predicting agents choices , we cast this as a self - organized , equilibrium seeking system in the form of weighted and binary networks ; we make use of information theoretic entropy - based methods to solve the ill - posed stochastic inverse problem and recover estimates of the unknown binary parameters . to go beyond traditional reductionist modeling and mathematical anomalies , we use a new paradigm that is developing under the name of network science ( see , for example , @xcite and the references contained therein ) . there are several things that make this approach attractive for information recovery in economics and in other social sciences : for example , in the economic - behavioral sciences everything seems to depend on everything else and this fits right into the interconnectedness simultaneity of the nonlinear ( and dynamic ) network paradigm . another example is provided by microeconomic theory , where the network representation of markets arises quite naturally ( in fact , in many ways markets and binary networks are equivalent - see @xcite ) . finally , in terms of a methodology , network problems are consistent with the information theoretic approach to information recovery ( see @xcite ) . we seek an expression for the probabilities that the origin and the destination nodes are connected along a specific pathway in the statistical ensemble of possible pathways , without explicitly sampling the configuration space . given information about the origin - destination network structure in the form of a matrix @xmath0 , the unknown pathway probabilities @xmath1 must be estimated from aggregate flow data that may be noisy in nature . the number of unknown pathway parameters of the protocol matrix @xmath0 is much larger than the number of measured aggregate origin - destination data points and , moreover , the components of the matrix @xmath0 can not be observed directly . this means that although the observed data are considered to be directly influenced by the values of model components , the observations only indirectly reflect the influence of the latter : as a result , the analyst must use indirect noisy observations to recover information on the unobserved vector of parameters . as a consequence , the relationship characterizing the effect of unobservable components on the observed data must be somehow inverted . this type of ill posed pure or stochastic inverse regularization problem can not be solved by traditional econometric information recovery methods . as we seek new ways to think about the causal adaptive behavior of complex and dynamic micro systems , we note that problems of this type may be re - formulated as problems of constrained entropy - maximization over the pathways . in other words , causal entropy maximization can be adopted as the systems status - measure and optimization criterion ( following @xcite ) . the result provides an exact expression for the occurrence of the unknown probabilities over the ensemble of pathways and yields the preferred probability distribution ( see @xcite ) . this permits us to recast a behavioral system in terms of path microstates where entropy reflects the number of ways a macrostate can evolve along a path of possible microstates : the more diverse the number of path microstates , the larger the causal path entropy . the result is a causal entropic force that captures self - organized equilibrium seeking behavior ( see @xcite ) . in other words , _ causal entropy maximization is a link that leads us to believe that a behavioral system with a large number of individuals , interacting locally and in finite time , is in fact optimizing itself_. we would like to stress that the optimization tendency characterizing behavioral systems is what qualifies entropy - based inference methods as the most correct ones to model such systems . the rationale beyond this lies in the nature of their adaptive behavior : agents tend to adapt behavior in line with an optimizing principle ( as the maximization of the future , accessible paths diversity - also definable , more generally , as `` resources '' @xcite ) , whence the need for a robust estimation procedure making the best use of the available information while disergarding any other arbitrary assumption . on the contrary , most behavioral economic - econometric models rest upon _ ad hoc _ assumptions which may lead to the identification and biased estimates of the unknown parameters , the underlying inference procedure and , in turn , the conclusions about the agents behavior ( see @xcite ) . in the sections ahead we analyse systems within this framework , that permits the interpretation of adaptive economic behavior in terms of entropic functions : as a basis for solving micro - behavioral information recovery problems , we suggest an information theoretic family of entropic functions ; to demonstrate applicability , we consider binary and weighted data sets and recover the optimum corresponding unknown probabilities . in developing a basis for the use of information theoretic ( it ) methods to infer origin - destination networks flows , we focus on a stochastic ill posed inverse problem and the corresponding regularization method it implies ( the pure , without - noise inverse problem is just a special case ) . in this context the cressie - read ( cr ) family of entropic functions @xcite provides a basis for linking the data and the unknown model parameters . this permits the researcher to exploit the statistical machinery of information theory to gain insights on the underlying adaptive behavior of a dynamic process from a system that may not be in equilibrium . this approach contrasts with the traditional approach to micro information recovery that rests on reductionist economic and econometric functional analysis and observational agent behavior data : however , precisely because of the nonlinear and ordinal nature of dynamic micro systems , the traditional approach is cumbersome in terms of identifying and expressing adaptive behavior . we start introducing the cr multi parametric convex family of entropic functional measures @xcite : @xmath2 . \label{eq.1}\ ] ] in eq . [ eq.1 ] , @xmath3 is a parameter that indexes members of the cr family , @xmath4 s represent the subject probabilities and the @xmath5 s are interpreted as reference ( or prior ) probabilities ( the reason for indexing our coefficients with @xmath6 will be clarified in the following section ) . being probabilities , the usual properties of @xmath7,\:\forall\:c$ ] , and @xmath8 , @xmath9 are assumed to hold . as @xmath3 varies the resulting cr estimator that minimize the divergence between @xmath10 and @xmath11 exhibits a qualitatively different behavior that includes , as noteworthy examples , the kullback - leibler measure ( in the limit as @xmath12 as shannon entropy and in the limit as @xmath13 as the likelihood functional ) and , in a binary context , the logistic distribution - divergence ( see @xcite ) . in other words , the cr family of power divergences is a class of additive convex functions that encompasses a broad family of test statistics , in turn representing a broad family of functional relationships within a moments - based estimation context . in addition , the cr measure exhibits proper convexity in @xmath10 , for all values of @xmath3 and @xmath11 , and embodies characteristics such as additivity and invariance with respect to a monotonic transformation of the divergence measures . in the context of extremum metrics , the cr family represents a flexible family of pseudo - distance measures from which to derive empirical probabilities . in what follows we consider the two values @xmath14 , corresponding respectively to the _ likelihood functional _ and the _ shannon functional_. in the limit as @xmath15 @xmath16 the kullback - leibler divergence between @xmath10 and @xmath11 is obtained . the particular case of a uniform prior , @xmath17 , allows us to recover the usual form of ( minus ) the _ shannon entropy _ of the @xmath10 distribution : @xmath18 . in the limit as @xmath19 provides the second functional of our list @xmath20 the kullback - leibler divergence between @xmath11 and @xmath10 . the particular case of uniform prior @xmath17 allows us to recover the usual form of ( minus ) the _ likelihood function _ of the @xmath10 distribution : @xmath21 . we stress that while the shannon functional has been already employed for the analysis of univariate and bivariate data sets , the likelihood functional case has not been explicitly worked out yet , thus representing the major contribution of this paper to the analysis of behavioral networks . . the cr family allows one to determine the probability coefficients @xmath22 by making use of the available partial information , i.e. aggregate data on traffic volumes.,scaledwidth=35.0% ] to demonstrate the applicability of our approach in the binary network area , an example may be useful . consider the problem of determining least - time , point - to - point traffic flows between sub - networks , when only aggregate origin - destinations volumes are known ( see fig . [ fig1 ] ) . in many ways this is like a transportation network , with the emphasis on design and efficiency in routing the traffic flows ( see @xcite and the references therein ) , exactly as in an economic - behavioral network the efficiency of information flow is predicated on discovering , or designing , protocols that efficiently route information . the research question concerns the prediction of the volume of flows on the pathways , given a set of measures taken along them . if we indicate by @xmath23 the @xmath24-dimensional vector of observed fluxes and by @xmath25 the @xmath26-dimensional vector of intermediate measures , the `` activity '' of an origin - destination network can be summed up by writing @xmath27 where @xmath0 is an @xmath28 rectangular matrix , encoding the information about connections . thus , our problem translates into estimating @xmath25 on the basis of the @xmath24 , available components of @xmath23 and the connection structure @xmath0 . the ill - posed nature of the problem is such that the inversion of eq . [ eq.1 ] is not feasible : the number of unknowns is greater than the number of known data , i.e. @xmath29 . in this case , one can resort to the information theoretic methodology for solving problems of inference on the basis of partial information ( see @xcite ) . in order to implement , the problem unknowns have to be interpretable as probabilities and estimated on the basis of some known distribution moments . in our case , this can be easily achieved by dividing both sides of [ eq.1 ] by @xmath30 : @xmath31 where @xmath23 and @xmath0 are known , @xmath10 is unknown and @xmath8 . we have thus rewritten [ eq.1 ] in terms of _ fractions of fluxes _ distributed across the @xmath26 channels and interpret them as unknown probabilities . notice that this peculiar definition of probability coefficients induces a distribution on the set of pathways , that play the role of an _ ensemble _ and allows us to restate the problem of" +"el lanzamiento de los observatorios de rayos x _ chandra _ ( nasa ) y _ xmm - newton _ ( esa ) en 1999 ha revolucionado nuestra visin del universo , al proporcionar informacin astrofsica detallada sobre muchos tipos de fuentes . la alta eficiencia de _ xmm - newton _ lo convierte en el instrumento ideal para obtener espectroscopa de resolucin baja y moderada de fuentes dbiles y extensas . despus de 3 aos de operaciones , _ xmm - newton _ ha observado todo tipo de fuentes astronmicas y ha proporcionado resultados de la mayor importancia en muchas reas . en esta revisin , destacamos unos pocos aspectos donde la contribucin de _ xmm - newton _ ha incrementado de forma significativa nuestro conocimiento del universo energtico . x - ray astronomy is at the very heart of the enormous progress that our astrophysical knowledge of the universe has undergone over the last decades . x - rays are emitted in a wide range of physical situations in the universe , invariably linked to the presence of hot gas and strong gravitational fields . these phenomena , largely unsuspected in the early days of x - ray astronomy , are nowadays seen to be ubiquitous in a variety of astronomical objects . x - ray observations of previously known objects have often revealed phenomena ( e.g. , the presence of an accreting black hole ) just not seen at other wavelengths . in addition , new sources serendipitously discovered in x - ray surveys have uncovered new classes of objects , totally inconspicuous at optical wavelengths . one datum that illustrates the impact of x - ray observations in astronomy is that 20% of the papers published by the 3 main astrophysics journals in 2002 ( astrophysical journal , monthly notices of the royal astronomical society and astronomy & astrophysics ) contain the `` x - ray '' keyword in the abstract . the 2002 nobel prize in physics given to riccardo giacconi ( father and leader of x - ray astronomy ) , is also a sign of the good health reached by this discipline , as it is one of the very few granted to astronomers . x - ray astronomy began in 1962 , when a rocket flown to detect the moon in scattered x - rays from the sun , discovered instead the first extra - solar x - ray source ( sco x-1 ) and the cosmic x - ray background ( giacconi et al . 1962 ) . this already showed that the universe out there could be radically more energetic than what was known before , as sco x-1 had a much larger x - ray to optical flux ratio than the sun . more rockets followed this pioneering discovery , but there was a basic limitation in the amount of observing time available for observations in a single flight . _ uhuru _ ( which means _ freedom _ in swahili ) was the first orbiting x - ray observatory . it was launched from italy s san marco station in kenya on the 12th of december of 1970 , coinciding with the independence day of this country ( thence the name ) . the _ uhuru _ payload weighed less than 60 kg . it scanned the sky for over 2 years and produced the first all - sky catalogue of x - ray sources , containing a few hundred of them . subsequent work demonstrated that outside the galactic plane , most of the sources were active galactic nuclei ( agn ) and clusters of galaxies . in the galactic plane , _ uhuru _ found x - ray binaries , supernova remnants and other diffuse structures . this rough picture ( but with varying fractions of objects ) still describes to zero - th order the present knowledge of the x - ray universe . this early generation of x - ray orbiting observatories ( which also included _ heao-1 _ and more recently _ ginga _ , japanese word for milky way ) were equipped with a mechanical collimator as the only means to limit the field of view covered by the ( usually gas - filled proportional counter ) detectors , without any further optics . this provided a very rough angular resolution , of the order of several degrees , which ultimately limited the sensitivity of the observatory because of confusion of fainter sources . proper imaging x - ray optics was featured for soft x - rays ( below 4.5 kev ) with the _ einstein observatory _ first . with an angular resolution of a couple of arc minutes , _ einstein _ discovered many new x - ray sources ( including many at cosmological distances ) , showing that the word _ experiment _ was in the way of being replaced by _ observatory _ in x - ray missions . _ einstein _ made it possible to discover new classes of sources by their x - ray emission , resolved the spatial structure of the intracluster gas in galaxy clusters and produced large catalogues of x - ray sources that were subsequently used to conduct detailed astrophysical studies . it also showed , for the first time , that a significant fraction of stars are x - ray emitters . _ rosat _ , in some sense a successor to _ einstein _ , deepened our knowledge of the x - ray universe , by conducting first an all - sky survey ( this yielded the , so far , largest catalogue of x - ray sources , exceeding 50000 ) , and for almost a decade , targeted observations of a full range of astronomical objects , from comets to distant qsos . focusing x - ray photons is not an easy task . in a standard reflecting optical telescope , photons are directed almost normally to the reflector s surface and collected in the focal plane . if the same setup is used for x - rays , they end up either transmitted or absorbed , but never reflected . grazing incidence is needed to achieve total reflection for x - rays , the maximum angle with respect to the surface being of a few degrees for a photon of @xmath0 . reflection becomes more difficult at higher photon energies , as the angle for total reflection becomes smaller and the mirrors need to be placed almost parallel to the optical axis . it is easy to see that the effective area that a photon sees is very small with a mirror placed in grazing incidence , and therefore several ( or many ) mirrors are nested one inside each other to increase the collecting area . it is also clear that an x - ray focusing telescope of higher energy photons will have less effective area and longer focal length than a similar one focusing soft x - ray photons . the start of the nineties brought x - ray observatories able to produce images with photons of up to 10 kev , such as the japanese _ asca _ were launched . _ asca _ also opened the door to a more modern type of x - ray detector ( the _ charge coupled device _ or ccd ) that ended up burying the proportional counters . ccd - based detectors deliver an order of magnitude better spectral resolution for single photons than proportional counters . at the energy of the fe k@xmath1 line ( 6.4 - 6.7 kev ) , the resolution of @xmath2 achieved by these detectors enables a detailed study of the physical environment where it is produced . other x - ray observatories have been launched during the 1990 s , including _ bepposax _ ( which also featured higher energy detectors sensitive to many tens of kev ) and _ rossi x - ray timing explorer _ ( rxte ) which is tailored to timing analysis of bright sources . however , at the turn of the new millenium , both _ nasa _ and _ esa _ decided to launch their respective large x - ray observatories : _ chandra _ ( launched july 1999 ) and _ xmm - newton _ ( launched december 1999 ) . the coincidence of operations between both missions ( being just by chance , as _ chandra _ was over - delayed for several years ) has brought what can be called the _ golden age _ of x - ray astronomy . by virtue of their respective designs _ is mostly an imaging observatory , while _ xmm - newton _ has its major capabilities at spectroscopy . having both of them operating at the same time has opened a huge window to x - ray astrophysics , whose dimensions are just beginning to be realized after the first few years of operations . _ xmm - newton _ is an x - ray observatory launched and operated by the european space agency ( esa ) , with instruments contributed and funded by esa member states and nasa ( usa ) . _ xmm - newton _ was successfully launched by an ariane 5 on the 10th of december of 1999 . its orbit is highly eccentric with a period of @xmath3 days . although the original _ xmm - newton _ project was approved for 2 years of scientific operations , all systems and payloads are designed to last for @xmath4 years . specifically , fuel ( hydrazine ) is currently thought to last for more than that . in fact , an extension of the _ xmm - newton _ operations has already been approved to 2006 with a further 2 year period being revised by mid 2003 . for comparison with early missions , the full _ xmm - newton _ satellite weighs more than 3000 kg . currently , the _ xmm - newton _ spacecraft is operated by esoc at darmstadt ( germany ) , but the instruments and science operations in general are managed from vilspa ( villafranca del castillo , spain ) . [ xmm ] _ xmm - newton _ consists of 3 co - aligned grazing incidence x - ray telescopes ( jansen et al . 2001 ) , with angular resolution of 4 - 6 arcsec ( fwhm ) and 13 - 15 arcsec ( half energy width ) . each x - ray telescope nests 58 grazing incidence mirror pairs , with a total collecting area of @xmath5 ( see fig [ xmm ] for a schematic of the x - ray optics in the xmm - newton x - ray telescopes ) . one of these telescopes focuses all x - rays into a single spectroscopic imaging detector ( epic - pn , strder et al . 2001 ) , which has a pixel size of 4 arcsec and covers a field of view of about 30 arcmin in diameter . about half of the x - rays focused by the other two telescopes go undispersed to similar imaging spectrographs called epic - mos ( turner et al . the epic instruments can measure the energy of individual photons with a resolution of @xmath6 . epic is sensitive to photons from 0.2 to 12 kev and can detect x - ray sources as faint as @xmath7 in the 0.5 - 2 kev band in a few tens of kiloseconds ( ks ) . its main limiting sensitivity in soft x - rays is caused by confusion , due to the modest angular resolution of the x - ray telescopes . at higher photon energies the main limiting factor is photon counting , with an expected confusion limit in the 2 - 10 kev band reached in a several ms exposure only . the two x - ray telescopes that" +"in this paper , we study the behavior of different physical quantities at the resonances generated by the maximum of the potential of a semiclassical schrdinger operator . in particular , we show quantitatively to what extent the presence of these resonances drives the behavior of the scattering amplitude and of the schrdinger group . the resonances generated by the maximum point of the potential ( usually called barrier - top resonances ) have been studied by briet , combes and duclos @xcite and sjstrand @xcite . these authors have given a precise description of the resonances in any disc of size @xmath0 centered at the maximum of the potential . in particular , they have shown that the resonances lie at distance of order @xmath0 from the real axis , which is in very strong contrast to the case of shape resonances ( the well in the island case ) , with exponentially small imaginary part ( see helffer and sjstrand @xcite ) . the description of resonances in larger discs of size @xmath1 , @xmath20,1]$ ] has been obtained by kaidi and kerdelhu @xcite under a diophantine condition . for small discs of size one , this question has been treated in the one dimensional case by the third author @xcite with the complex wkb method . in the two dimensional case , the resonances in discs of size one have also been considered by hitrik , sjstrand and v ngc @xcite ( see also the references in this paper ) . here , we consider only the resonances at distance @xmath0 of the maximum of the potential and we recall their precise localization in section [ k5 ] . resonances can be defined as the poles of the meromorphic continuation of the cut - off resolvent ( see e.g. hunziker @xcite ) . the generalized spectral projection associated to a resonance is defined as the residue of the resolvent at this pole : @xmath3 as an operator from @xmath4 to @xmath5 . if @xmath6 were an isolated eigenvalue , this formula would give the usual spectral projection . many physical quantities can be expressed in terms of these generalized spectral projections . in the case of shape resonances , their semiclassical expansion has been computed by helffer and sjstrand in @xcite . in section [ a1 ] below , we obtain the semiclassical expansion of the generalized spectral projection for barrier - top resonances . since the resonances in the present case have a much larger imaginary part , our result is very different from that of the shape resonance case . resonances appear also in scattering theory ( they are called scattering poles in this context ) . in @xcite , lax and phillips have shown that they coincide with the poles of the meromorphic extension of the scattering amplitude . this result , proved for the wave equation in the exterior of a compact obstacle , was extended by grard and martinez @xcite to the long range case for the schrdinger equation ( see also the references in this paper for earlier works ) . for shape resonances , the residue of the scattering amplitude was calculated in the semiclassical limit by nakamura @xcite , lahmar - benbernou @xcite and lahmar - benbernou and martinez @xcite . more generally , upper bounds on the residues of the scattering amplitude have been obtained by stefanov @xcite ( in the compact support case ) and michel @xcite ( in the long range case ) for resonances very close to the real axis . in section [ k2 ] , we give the semiclassical expansion of the residues of the scattering amplitude for barrier - top resonances and we will see that these upper bounds do not hold in the present setting . it is commonly believed that resonances play also a crucial role in quantum dynamics . indeed , it is sometimes possible to describe the long time evolution of the cut - off propagator ( for example , the schrdinger or wave group ) in term of the resonances . typically , if the resonances are simple , the propagator @xmath7 truncated by @xmath8 satisfies @xmath9 here , @xmath10 is the generalized spectral projection defined previously . such a formula generalizes the poisson formula , valid for the operators with discrete spectrum . the resonance expansion of the wave group was first obtained by lax and phillips @xcite in the exterior of a star - shaped obstacle . this result has been generalized , using various techniques , to different non trapping situations ( see e.g. vanberg @xcite and the references of the second edition of the book @xcite ) . the trapping situations have been treated by tang and zworski @xcite and burq and zworski @xcite for very large times . on the other hand , the time evolution of the quasiresonant states ( sorts of quasimodes ) has been studied by grard and sigal @xcite . a specific study of the schrdinger group for the shape resonances created by a well in a island has been made by nakamura , stefanov and zworski @xcite . there are also some works concerning the situation of a hyperbolic trapped set . we refer to the work of christiansen and zworski @xcite for the wave equation on the modular surface and on the hyperbolic cylinder , and to the work of guillarmou and naud @xcite for the wave equation on convex co - compact hyperbolic manifolds . section [ k3 ] is devoted to the computation of the asymptotic behavior for large time of the schrdinger group localized in energies close to the maximum of the potential . for the proof of the different results of this paper , we use an estimate of the distorted resolvent around the resonances , polynomial with respect to @xmath11 . indeed , such a bound allows to apply the semiclassical microlocal calculus . this estimate is established in section [ k4 ] . to prove it , we proceed as in @xcite and use the method developed by martinez @xcite , sjstrand @xcite and tang and zworski @xcite . similar bounds around the resonances are already known in various situations ( see e.g. grard @xcite for two strictly convex obstacles , michel and the first author @xcite in the one dimensional case ) . note that , in our setting , a limiting absorption principle have been proved in @xcite . we consider the semiclassical schrdinger operator on @xmath12 , @xmath13 , @xmath14 where @xmath15 is a smooth real - valued function . we denote by @xmath16 the associated classical hamiltonian . the vector field @xmath17 is the hamiltonian vector field associated to @xmath18 . integral curves @xmath19 of @xmath20 are called classical trajectories or bicharacteristic curves , and @xmath18 is constant along such curves . the trapped set at energy @xmath21 for @xmath22 is defined as @xmath23 we shall suppose that @xmath15 satisfies the following assumptions [ a1 ] @xmath24 extends holomorphically in the sector @xmath25 for some @xmath26 . moreover @xmath27 as @xmath28 in @xmath29 . [ a2 ] @xmath15 has a non - degenerate maximum at @xmath30 and @xmath31 with @xmath32 and @xmath33 . [ a3 ] the trapped set at energy @xmath34 is @xmath35 . notice that [ a3 ] ensures that @xmath30 is the unique global maximum for @xmath15 . moreover , there exists a pointed neighborhood of @xmath36 in which all the energy levels are non trapping . in the following , @xmath37 denote the strictly increasing sequence of linear combinations over @xmath38 of the @xmath39 s . in particular , @xmath40 and @xmath41 . the linearization @xmath42 at @xmath43 of the hamilton vector field @xmath44 is given by @xmath45 and has eigenvalues @xmath46 . thus @xmath43 is a hyperbolic fixed point for @xmath44 and the stable / unstable manifold theorem gives the existence of a stable incoming lagrangian manifold @xmath47 and a stable outgoing lagrangian manifold @xmath48 characterized by @xmath49 moreover , there exist two smooth functions @xmath50 , defined in a vicinity of @xmath51 , satisfying @xmath52 and such that @xmath53 near @xmath43 . since @xmath22 is a schrdinger operator , we have @xmath54 . under the previous assumptions , the operator @xmath22 is self - adjoint with domain @xmath55 , and we define the set @xmath56 of resonances for @xmath22 as follows ( see @xcite ) . let @xmath57 be a large constant , and let @xmath58 be a smooth vector field , such that @xmath59 for @xmath60 and @xmath61 for @xmath62 . for @xmath63 small enough , we denote @xmath64 the unitary operator defined by @xmath65 for @xmath66 . then the operator @xmath67 is a differential operator with analytic coefficients with respect to @xmath68 , and can be analytically continued to small enough complex values of @xmath68 . for @xmath69 small enough , we denote @xmath70 the spectrum of @xmath71 is discrete in @xmath72 , and the resonances of @xmath22 are by definition the eigenvalues of @xmath71 in @xmath73 . we denote their set by @xmath56 . the multiplicity of a resonance is the rank of the spectral projection @xmath74 where @xmath75 is a small enough closed path around the resonance @xmath6 . the resonances , as well as their multiplicity , do not depend on @xmath76 and @xmath77 . as a matter of fact , the resonances are also the poles of the meromorphic extension from the upper complex half - plane of the resolvent @xmath78 ( see e.g. @xcite ) . in the present setting , sjstrand @xcite has given a precise description of the set of resonances in any disc @xmath79 of center @xmath36 and radius @xmath80 . this result has also been proved simultaneously by briet , combes and duclos @xcite under a slightly stronger hypothesis ( a virial assumption ) . _ [ e17 ] assume [ a1][a3 ] . let @xmath81 be different from @xmath82 for all @xmath83 . then , for @xmath84 small enough , there exists a bijection @xmath85 between the sets @xmath86 and @xmath87 , where @xmath88 such that @xmath89 . _ in particular , the number of resonances in any disk @xmath90 is uniformly bounded with respect to @xmath0 . for @xmath91 , we denote @xmath92 . _ we shall say that @xmath93 is simple if @xmath94 implies @xmath95 . _ _ [ k1 ] if @xmath96 is simple , the corresponding resonance @xmath97 is simple for @xmath0 small enough and proposition 0.3 of @xcite proves that @xmath97 has a complete asymptotic expansion in powers of @xmath0 . _ _ the analyticity of @xmath15 in a full neighborhood of @xmath12 is used only for the localization of the resonances . indeed , if the conclusions of theorem [ e17 ] and remark [ k1 ] hold for @xmath15 smooth and analytic outside of a compact set , then the results of this paper still apply under this weaker assumption . _ the semiclassical pseudodifferential calculus is a tool used throughout this paper , and we fix here some notations . we refer to @xcite for more details . for @xmath98 an order function and @xmath99 , we say that a function @xmath100 is a symbol of class @xmath101 when , for all @xmath102 , @xmath103 if @xmath104 , the semiclassical pseudodifferential operator @xmath105 with symbol @xmath106 is defined by @xmath107 for all @xmath108 . we denote by @xmath109 the space of operators @xmath110 . the rest of this paper is organized as follows . in section [ k4 ] , we prove a resolvent estimate in the complex plane that we use in all the rest of the paper . then , in section [ a1 ] , we compute the spectral projection associated to a resonance . in section [ k2 ] , we give the asymptotic expansion of the residue of the scattering amplitude at a simple resonance for long range potentials . section [ k3 ] is" +"one of the most celebrated successes of string theory is the ads / cft correspondence @xcite . this generates a powerful duality between asymptotically ads gravitational theories and conformal field theories on the ads boundary , which is the simplest and best - studied example of the more general notion of a ` gauge - gravity duality ' . as a strong - weak coupling duality , the correspondence allows for the translation of non - perturbative field theory calculations into more tractable , perturbative calculations in gravity and vice - versa . this has enabled the exploration of previously inaccessible regimes of theoretical physics . indeed , there are many examples of strongly coupled systems in condensed matter physics and it is hoped that gauge - gravity duality may allow for a better understanding of these . significant progress has already been made in this direction , leading to the development of the ads / cmt correspondence ( see @xcite and references therein ) . further recent progress has been to extend the correspondence to spacetimes which are not asymptotically - ads but rather exhibit hyperscaling violating and lifshitz ( hvlif ) behaviour @xcite , thus extending the dictionary between gravity and condensed matter systems living on the boundary . the central idea in gauge / gravity duality is that each state in the bulk has a corresponding state in the dual field theory . in particular , black objects are dual to thermal ensembles in the field theory with the same thermodynamic properties ( temperature , entropy , chemical potential , etc . ) as the bulk spacetime @xcite . a natural starting point for the correspondence is to look at charged ( reissner - nordstrm or ` rn ' ) extremal black holes and black branes in ads @xcite . however , like their asymptotically flat ` cousins ' they have a large non - zero entropy at zero temperature , thus violating the third law of thermodynamics , which states in its strictest version that the entropy of a system should vanish in the zero temperature limit @xcite . while a non - vanishing entropy for certain classes of extremal black holes is consistent with microstate counting for the corresponding d - brane configuration in string theory @xcite , this still begs the question of whether one can find other gravitational systems which have a zero entropy or entropy density at zero temperature . apart from being an interesting question about gravity , such systems are relevant for possible dualities between gravity and condensed matter systems . we remark that although ` nernst law ' is in the following used synonymously with ` third law of thermodynamics ' , nernst s original formulation only requires that the difference in entropy between two equilibrium states related through a change in external parameters goes to zero at zero temperature . this formulation is equivalent to the ` process version ' of the third law , which states that zero temperature can not be reached by any physical process in a finite number of steps . a process version of the third law of black hole mechanics was already established in @xcite . however , the nernst version or , equivalently , the process version of the third law does not imply by itself the slightly stronger version of the third law , due to planck , which states that the entropy itself goes to zero at zero temperature . this stricter version corresponds to systems with a unique ground state , and thus is the generic situation in condensed matter , although there is an extended debate about possible exceptions in specific systems , see for example @xcite . in the following we will be concerned with the explicit construction of families of gravitational solutions which have zero entropy ( or entropy density ) in the extremal limit . following conventions in the literature , we will refer to the third law in its stricter , planckian , version as the nernst law . extremal brane solutions with vanishing entropy density at zero temperature have recently been studied for a variety of bulk theories @xcite and could have important applications in extending the dictionary between condensed matter and gravity . they have been dubbed ` nernst branes ' in @xcite , and it is believed that the corresponding non - extremal solutions exist and satisfy the nernst law , that is , these non - extremal solutions have a finite entropy which goes to zero when the temperature goes to zero while external parameters are kept fixed . finding such non - extremal solutions is important , since extremal nernst branes are not completely regular solutions . while all curvature invariants remain finite at the horizon , tidal forces become infinite and scalar fields take infinite values , which suggests a breakdown of the underlying effective field theory @xcite . a first step in addressing this issue is to find non - extremal solutions , which can then be studied in the near extremal limit . in this context it is clearly desirable to have completely explicit , analytical solutions . however most results in the literature have to rely on a mixture of analytical and numerical methods . of course tidal forces may still get very large at the horizon when one approaches the extremal limit @xcite , but analytical solutions will enable one to identify the region in parameter space where the solution can be trusted and possibly be mapped to condensed matter systems . the second step in controlling the near horizon low temperature behaviour is to embed the theory under consideration into a uv - complete theory , for which string theory and its non - perturbative extension m - theory are arguably the best candidates . in the low - energy limit the relevant stringy gravitational backgrounds can be described in terms of supergravity . we will be working in a set - up which can be described by @xmath13 @xmath0 gauged supergravity with an arbitrary number of vector multiplets . theories with @xmath13 supersymmetry are natural generalisations of the einstein - maxwell - scalar theories underlying dilatonic black hole and black brane solutions which have been studied extensively as potential duals of strongly coupled electron systems @xcite . they have the advantage that one can often find exact , analytical answers , despite the fact that the couplings are not fixed by the matter content ( as is the case for @xmath14 supersymmetry ) , but depend on arbitrary functions of the scalar fields , which are subject to quantum and stringy corrections . while we do not discuss the string theory or m - theory embedding explicitly , note that such theories arise through heterotic flux compactifications on @xmath15 and type - ii flux compactifications on calabi - yau three - folds . we will not need to choose a specific model , and only assume that the vector multiplet couplings take the most general form that arises when working to leading order in the regge parameter @xmath16 , and within the validity of string perturbation theory . in other words , we only assume that the prepotential , which encodes the vector multiplet couplings , is of the so - called very special type reviewed below . by working in a gauged supergravity theory obtainable by flux compactification from string theory we will have the option to further address the issues related to singularities in the extremal limit at a later stage . for bps black holes with vanishing entropy it is known that the inclusion of stringy higher curvature corrections in supergravity @xcite leads to regular solutions with finite entropy @xcite , and the entropy function formalism demonstrates that this mechanism is robust and does not depend on supersymmetry and details of the higher curvature corrections @xcite . we refer to @xcite for a further discussion of the possible implications of quantum and string corrections to the zero temperature behaviour and the ` fate ' of the nernst law . within the framework of four - dimensional @xmath13 @xmath0 gauged supergravity coupled to vector multiplets , extremal nernst branes have previously been constructed in @xcite using a first - order rewriting of the equations of motion , and by considering a specific model : the so - called stu - model . however a similar rewriting for their non - extremal counterparts has so far proven elusive , and the only known examples @xcite have been constructed by deforming the metric of the corresponding five - dimensional extremal solution @xcite and imposing suitable consistency conditions . in this paper we are able to provide a systematic construction of non - extremal nernst branes by directly solving the second - order equations of motion . moreover , our results will not only apply to a particular model , but to all models where the prepotential is of the very special type . this gain in generality and systematics should help to expand the ads / cmt dictionary considerably in the future . we now present a brief overview of the results in this paper . we start with a theory of @xmath17 @xmath13 vector multiplets coupled to @xmath0 gauged supergravity , with prepotential @xmath18 where @xmath19 is homogeneous of degree three . if @xmath19 is a homogeneous _ polynomial _ of degree three ( which is not required for our methods to apply ) , then the corresponding theory can be obtained by dimensional reduction from five dimensions . moreover , such prepotentials capture perturbative string effects to leading order in @xmath16 if the model can be embedded into heterotic or type - ii string theory . in this case the supergravity lift to five dimensions becomes a lift from type - ii string theory to m - theory . within these models we restrict ourselves to static black brane solutions . apart from this we will impose that the scalar fields take purely imaginary values , as for such ` axion - free ' field configurations there is a systematic simplification of the equations of motion . since we impose stationarity in four dimensions , we can perform a time - like dimensional reduction to obtain an effective three - dimensional euclidean theory . the degrees of freedom in three dimensions can then be repackaged using the real formulation of special geometry developed in @xcite , which has been used to construct solutions to both gauged @xcite and ungauged @xcite theories of supergravity coupled to vector multiplets . since our ability to obtain explicit non - extremal solutions depends on using a specific formalism , let us briefly summarize the underlying principles without going into technical details . * instead of using the physical four - dimensional scalar fields @xmath20 , @xmath21 , we work on the ` big moduli space ' parametrized by scalar fields @xmath22 , the additional ( complex ) degree of freedom is compensated for by a local @xmath24 gauge symmetry . working on the big moduli space has the advantage that the number of scalar fields and gauge fields matches . * we use the real formulation of special khler geometry , which replaces the complex scalars @xmath22 by real scalars @xmath25 , @xmath26 and which replaces the holomorphic prepotential @xmath27 by a real hesse potential @xmath28 . this leads to a simpler , and fully covariant , behaviour of all relevant quantities under electric - magnetic duality . * upon dimensional reduction , the kaluza - klein scalar @xmath29 is absorbed into the real scalars @xmath25 , which results in the ` radial ' direction of the big moduli space becoming a physical ( rather than gauge ) degree of freedom . + we postpone fixing the remaining @xmath30 gauge symmetry to preserve electric - magnetic duality . the resulting three - dimensional theory depends on @xmath31 real scalars @xmath32 , subject to" +"semi - supervised learning has attracted the attention of many researchers because of the importance of combining unlabeled data with labeled data . in many applications the number of unlabeled data points is so large that labeling training data is expensive and time - consuming . therefore , the problem of effectively utilizing a combination of unlabeled and labeled information is very important in machine learning research . this paper concerns the issue of how to address uncertainty quantification in such classification methods . in doing so we bring together a variety of themes from the mathematical sciences , including optimization , pdes , probability and statistics . we will show that a variety of different methods , arising in very distinct communities , can all be formulated around a common objective function @xmath0 for a real valued function @xmath1 on the nodes of a graph representing the data points . the matrix @xmath2 is proportional to a graph laplacian derived from the unlabeled data and the function @xmath3 involves the labelled data . the variable @xmath1 is used for classification . minimizing this objective function is one approach to such a classification . a probability distribution related to the objective function has density @xmath4 proportional to @xmath5 probability of the labelling variable @xmath1 is high where the objective function is small , and vice - versa . uncertainty quantification corresponds to using the probability distribution to compute expectations of test functions @xmath6 , defined on the nodes of the graph , which enable us to measure the variability of label variables , such as means and variances : @xmath7 in the settings of interest this will typically be a very high dimensional integral , with the dimension given by the number of unlabelled data points . carrying out this program requires computational algorithms to minimize @xmath8 or to draw samples , via monte carlo markov chain ( mcmc ) for example , from the probability distribution with density @xmath4 . these algorithms exploit the fact that @xmath9 is a graph analogue of the dirichlet energy and will leverage analogies with pde - based methodologies involving the classical euclidean dirichlet energy in order to derive effective computational methods . in this paper we will describe this confluence of ideas from different parts of the mathematical sciences , show how our approach builds on a broad range of advances in the field which we will review , and demonstrate the emergence of a problem area with many open challenges for the mathematical sciences . we emphasize that the variety of probablistic models considered in this paper arise from different assumptions concerning the structure of the data . our objective is not to assess the validity of these assumptions , which is a modelling question best addressed on a case - by - case basis , but rather we develop an overarching computational framework suitable for all the models arising from these different assumptions . an effective method for semi - supervised learning is to construct a similarity graph on both the unlabeled and labeled examples , and classify unknown labels by leveraging the graph structure . a central conceptual issue in the setting of this problem is that labels are discrete , whilst similarity information is often continuous . strategies to work with both of these settings simultaneously are at the heart of this subject . in @xcite , blum et al . posed the binary semi - supervised classification problem using a graph min - cut problem . this is equivalent to a maximum a posteriori ( map ) estimator with respect to a bayesian posterior distribution for a markov random field ( mrf ) over the discrete state space of binary labels @xcite ; the resulting optimization problem can be solved exactly in polynomial time . in general , inference for multi - label discrete mrfs is intractable @xcite . however , several approximate algorithms exist for the multi - label case @xcite , and have been applied to many imaging tasks @xcite . the probit classification method , using gaussian process priors , is described in @xcite ; however in that book the prior does not depend on the unlabelled data . gaussian priors which depend on the unlabelled data may be constructed by using the graph laplacian , an approach undertaken in @xcite . the model defined in @xcite is equivalent to a continuum relaxation of the discrete state space mrf in @xcite . the bayesian formulation which underpins our work in this paper was made explicit in @xcite where a variety of likelihood models are used to condition on the labelled data ; the probit approach , for example , could be used to accomplish this . probit utilizies the same prior as in @xcite but the data is assumed to take binary values , found from thresholding the underlying continuous variable , and thereby providing a link between the combinatorial and continuous state space approaches described in the previous paragraph . the probit methodology is often implemented via map optimization that is the posterior probability is maximized rather than sampled or an approximation to the posterior is computed , in the neighbourhood of the map estimator @xcite . for full posterior exploration , gibbs sampling is often used @xcite and this methodology has been applied recently in @xcite ; furthermore methods designed to break undesirable dependencies in the gibbs sampler are introduced in @xcite . in the context of map estimation , the graph - based terms act as a regularizer , in the form of the graph dirichlet energy @xmath10 . a formal framework for graph - based regularization can be found in @xcite . more recently , other forms of regularization have been considered such as the graph wavelet regularization @xcite . another link between discrete combinatorial optimization approaches and methods based on optimization over real - valued variables was made in the work of bertozzi et al . @xcite . the approach is based on the fact that the tv functional , when suitably generalized to weighted graphs , coincides with the graph cut energy . relaxation of the tv functional is well - understood in the context of partial differential equations ( pde ) and generalizing ideas applicable to the pde laplacian in the context of the graph laplacian leads to new optimization methods . based on this reasoning , in @xcite the graph ginzburg - landau functional was used as a relaxation of the graph tv functional for the task of binary classification . this was generalized to multiclass classification in @xcite . following this line of work , several new algorithms were developed for semi - supervised and unsupervised classification problems on weighted graphs @xcite . a further connection with pde based methods is the level - set approach to bayesian inversion , introduced recently in @xcite ; this is very closely related to our variant on the probit method , as we will demonstrate . there are a wide range of methodologies employed in the field of uncertainty quantification , and the reader may consult the books @xcite and the recent article @xcite for details and further references . underlying all of these methods is a bayesian methodology which is attractive both for its clarity with respect to modelling assumptions and its basis for application of a range of computational tools . nonetheless it is important to be aware of limitations in this approach , in particular with regard to its robustness with respect to the specification of the model , and in particular the prior distribution on the unknown of interest @xcite . whilst the book @xcite conducts a number of thorough uncertainty quantification studies for a variety of learning problems using gaussian process priors , most of the papers studying graph based learning referred to above primarily use the bayesian approach to learn hyperparameters in an optimization context , and do not consider uncertainty quantification . in this paper , we focus exclusively on the problem of binary semi - supervised classification ; however the methodology and conclusions will extend beyond this setting . our focus is on a presentation which puts uncertainty quantification at the heart of the problem formulation , and we make four primary contributions : * we define a number of different bayesian formulations of the graph - based semi - supervised learning problem and we connect them to one another , to binary classification methods and to a varierty of pde - inspired approaches to classification ; in so doing we provide a single framework for a variety of methods which have arisen in distinct communities and we open up a number of new avenues of study for the problem area ; * we highlight the pcn - mcmc method for posterior sampling which , based on analogies with its use for pde - based inverse problems @xcite , has the potential to sample the posterior distribution in a number of steps which is independent of the number of graph nodes ; * we introduce approximations exploiting the empirical properties of the spectrum of the graph laplacian , generalizing methods used in the optimization context in @xcite , allowing for computations at each mcmc step which scale well with respect to the number of graph nodes ; * we demonstrate , by means of numerical experiments on a range of problems , both the feasibility , and value , of bayesian uncertainty quantification in semi - supervised , graph - based , learning . the paper is organized as follows . in section [ sec:2 ] , we give some background material needed for problem specification . in section [ sec:3 ] we formulate the four bayesian models used for the classification tasks . section [ sec:4 ] introduces the mcmc and optimization algorithms that we use . in section [ sec:5 ] , we present and discuss results of numerical experiments to illustrate our findings ; these are based on four examples of increasing size : the house voting records from 1984 ( as used in @xcite ) , the tuneable two moons data set @xcite , the mnist digit data base @xcite and the hyperspectral gas plume imaging problem @xcite . we conclude in section [ sec:6 ] . to aid the reader , we give here an overview of notation used throughout the paper . * @xmath11 the set of nodes of the graph , with cardinality @xmath12 ; * @xmath13 the set of nodes where labels are observed , with cardinality @xmath14 ; * @xmath15 , feature vectors ; * @xmath16 latent variable characterizing nodes , with @xmath17 denoting evaluation of @xmath18 at node @xmath19 ; * @xmath20 the thresholding function ; * @xmath21 relaxation of @xmath22 using gradient flow in double - well potential @xmath23 ; * @xmath24 the label value at each node with @xmath25 * @xmath26 or @xmath27 , label data ; * @xmath28 with @xmath29 being a relaxation of the label variable @xmath30 ; * @xmath31 weight matrix of the graph , @xmath32 the resulting symmetric graph laplacian ; * @xmath2 the precision matrix and @xmath33 the covariance matrix , both found from @xmath32 ; * @xmath34 eigenpairs of @xmath32 ; * @xmath35 : orthogonal complement of the null space of the graph laplacian @xmath32 , given by @xmath36 ; * @xmath37 : orthogonal complement of the first @xmath38 eigenfunctions of the graph laplacian @xmath32 . * @xmath39 denotes the euclidean norm and @xmath40 the corresponding inner - product ; * @xmath41 : ginzburg - landau functional ; * @xmath42 , @xmath43 : prior probability measures ; * @xmath44 and @xmath45 : ( with suffices denoting different models ) ; * the measures denoted @xmath44 typically take argument @xmath18 and are real - valued ; the measures denoted @xmath45 take argument @xmath30 on label space , or argument @xmath29 on a real - valued relaxation of label space ; * @xmath46 denotes a" +"observations of broad - line variability in nearby seyfert galaxies play a central role in the interpretation of the demographics and cosmological evolution of supermassive black holes in active galactic nuclei ( agns ) . by measuring the time delay between agn continuum variations and the subsequent response of the broad - line region ( blr ) gas , the light - travel time across the blr , and hence the mean blr radius ( @xmath12 ) , can be directly measured . these reverberation - mapping measurements have been carried out for a few dozen low - redshift agns ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , and the observed blr sizes measured via h@xmath3 reverberation range from typically a few light - days up to several light - months . the blr size is observed to scale with agn continuum luminosity roughly as @xmath13 @xcite , and this relationship makes it possible to estimate blr radii from a single observation of an agn . with a direct measurement or estimate of @xmath12 , and assuming virial motion of blr clouds , it becomes possible to estimate the mass of the black hole in an agn as @xmath14 , where @xmath15 is the width of the broad line , and @xmath16 is a dimensionless scaling factor ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? this method has been used to estimate black hole masses in large samples of agns out to the highest observed redshifts ( for a review , see * ? ? ? currently , nearly all observational constraints on the cosmological growth history of supermassive black holes depend on masses derived from this virial equation . while the assumption of virial motion in the blr has gained support from a variety of consistency checks ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , it remains extremely difficult to obtain direct constraints on the structure and dynamical state of the blr in any individual agn , and in the absence of such constraints , the inferred black hole masses remain subject to substantial systematic uncertainty @xcite . the most promising method to examine the kinematics of blr gas is velocity - resolved reverberation mapping , in which the time - delay response of emission - line variability relative to continuum fluctuations can be measured as a function of line - of - sight velocity . velocity - resolved reverberation data can encode a wealth of information about blr structure on spatial scales that are orders of magnitude too small to be resolved by any other technique ( e.g. , * ? ? ? * ; * ? ? ? recently , high - cadence observing campaigns have produced major improvements in the quality of velocity - resolved reverberation data for the broad balmer lines @xcite . for the most highly variable objects , it is possible to examine the shape of the two - dimensional transfer function , which describes the distribution of broad - line lag response time as a function of velocity @xcite , and to apply new modeling techniques that can directly constrain the blr geometry and potentially test the critical assumption of virial motion @xcite . in order to increase the number of objects with data suitable for such analysis , we carried out a new reverberation - mapping campaign in spring 2011 . in this _ letter _ , we present our first results for mrk 50 , a seyfert 1 galaxy at redshift @xmath17 . past observations have found dramatic variations in its nuclear luminosity @xcite , but it has not previously been a reverberation - mapping target . during our monitoring program , mrk 50 exhibited strong variability , and we detect a robust reverberation signal and a significant velocity - resolved reverberation response across the broad h@xmath3emission line . from 2011 january 21 until june 13 ( all dates are ut ) , we obtained queue - scheduled @xmath5-band images using the 0.76 m katzman automatic imaging telescope at lick observatory @xcite , the 0.9 m telescope at the brigham young west mountain observatory ( wmo ) , the super - lotis 0.6 m telescope at kitt peak , the faulkes telescope south at siding spring observatory , and the palomar 1.5 m telescope @xcite . exposure times were typically 180300 s. we attempted to observe mrk 50 on a nightly basis , but poor weather and telescope scheduling issues left some gaps in temporal coverage . all images were bias - subtracted and flattened , and cosmic - ray hits were removed using the la - cosmic routine @xcite . in order to remove the host galaxy and obtain a light curve of the variable agn flux , we employed image subtraction using the ` hotpants ` package by a. becker , which is based on the algorithm described by @xcite . for each telescope , a high - quality template image was chosen , and the template was then aligned with each night s image and convolved with a spatially varying kernel to match the point - spread function of that image . after subtracting the scaled template image , the variable agn flux is left as a point source in the subtracted image , allowing for aperture photometry using the iraf daophot package . the photometric aperture radius used for each telescope was set to match the average point - source full width at half - maximum intensity ( fwhm ) for images from that telescope . light curves were constructed separately for each telescope , and each was then normalized to the wmo light curve by determining an average flux scaling factor based on nights when mrk 50 was observed at both locations . we find that the image subtraction yields a better - quality light curve than simple aperture photometry , and provides closer agreement between the light curves obtained with different telescopes . the overall flux scale was calibrated using observations of landolt ( 1992 ) standard stars observed during a few photometric nights at wmo . observations taken within 6 hr of one another were combined by taking a weighted average . the final @xmath5 light curve is illustrated in figure [ figlightcurves ] . our campaign at the lick shane 3 m telescope consisted of 69 nights allocated between 2011 march 27 and june 13 , during which time we observed mrk 50 on 41 nights using the kast dual spectrograph @xcite . in this paper , we discuss only measurements from the blue arm of the spectrograph , where we used a 600 lines mm@xmath18grism over @xmath195520 at a scale of 1.0 pixel@xmath18 . all observations were done with a 4-wide slit oriented at @xmath20 . standard calibration frames including arc lamps and dome flats were observed each afternoon , and flux standards were observed during twilight . the exposure time for mrk 50 was normally @xmath21 s. additionally , we observed mrk 50 on 18 nights that were allocated to other observing programs , beginning on january 26 . all observations used the same 600-line grism and 4 slit , but the wavelength coverage was slightly different each time . the exposure for these observations was typically 900 s. spectroscopic reductions and calibrations followed standard methods implemented in iraf and idl . a large extraction width of 103 was used in order to accommodate the full extent of the agn spatial profiles observed on nights with very poor seeing . error spectra were extracted and propagated through the full sequence of calibrations , and for each night the two exposures of mrk 50 were averaged together . in the region 46004800 , the median signal - to - noise ratio per pixel is 75 . the reduced spectra were first normalized to a uniform flux scale by employing the procedure of @xcite . this method applies a flux scaling factor , a linear wavelength shift , and a gaussian convolution to each spectrum in order to minimize the residuals between the data and a reference spectrum constructed from several of the best - quality nights . the scaling is determined using a wavelength range containing the [ ] @xmath22 line , which is assumed to have constant flux . since the spectra contain a substantial amount of host - galaxy starlight , we implemented a simple continuum subtraction routine to produce a cleaner measurement of the broad - line profiles and fluxes , similar to the procedure described by @xcite . over the wavelength range 43005400 , each scaled spectrum was fitted with a model consisting of a power - law featureless continuum , an template from @xcite broadened by convolution with a gaussian kernel , several emission - line components represented by either gaussians or gauss - hermite functions @xcite , and a starlight model consisting of simple stellar population models at solar metallicity from @xcite which were broadened by convolution with a gaussian kernel . additionally , a foreground extinction was applied to the model spectrum . the model fit was optimized by @xmath23 minimization using a levenberg - marquardt technique @xcite . then , the best - fitting model components representing the starlight and nonstellar continuum were subtracted from the data , leaving a pure emission - line spectrum . for the starlight model , we obtained a good fit using an 11 gyr - old population as the dominant component , and adding contributions from younger populations did not significantly improve the fit . the median starlight fraction at @xmath24 is 41% , and contributes just @xmath23% of the continuum flux density at 4600 . in prior reverberation work , starlight subtraction has not generally been applied , and the broad - line light curves have typically been measured by subtracting a local , linear continuum fitted to wavelength regions on either side of an emission line . we find that our continuum subtraction procedure provides a more accurate removal of the continuum shape underlying each emission line and a much better light curve for the weak @xmath8 line . figure [ figmean ] shows two versions of the mean and root - mean - square ( rms ) spectra : one constructed from the set of scaled spectra , and one constructed from the set of continuum - subtracted , scaled spectra . this illustrates the utility of the continuum subtraction procedure for removing the stellar absorption features and continuum undulations . the broad - line light curves were then measured by integrating the flux over fixed wavelength ranges in the continuum - subtracted spectra : 48905050 for h@xmath3 , 43704510 for h@xmath4 ( also including the narrow [ ] @xmath25 line ) , and 47304870 for . emission - line light curves are shown in figure [ figlightcurves ] , along with the continuum flux density measured from the scaled spectra over 35503800 ( which we refer to as the @xmath26 band ) . the continuum and broad lines were highly variable during the monitoring period : over a 30-day span the @xmath26-band continuum dropped by a factor of @xmath0 , and the h@xmath3 line responded with a factor of @xmath2 decline . for observations taken before the start of our dedicated campaign on march 27 , the scatter in the spectroscopic light curves is relatively high . we attribute this to the nightly differences in observational setup and calibrations used by each observing team , and to the very poor observing conditions during some winter nights . to estimate black hole masses from reverberation data , the second moment of the h@xmath3 line in the rms spectrum is most often used as the measure of line width @xcite . we find @xmath27(h@xmath3@xmath28 ) @xmath29" +"a plasma is a partially or completely ionized gas . when a plasma is of low density or the time scales of interest are sufficiently small , it is deemed to be `` collisionless '' , as collisions between particles become infrequent . the fundamental equations which describe the time evolution of a collisionless plasma are given by the three - dimensional vlasov - maxwell system : @xmath2 this nonlinear system of integro - differential equations is supplemented by a set of initial conditions @xmath3 , and @xmath4 here , @xmath5 represents the density of ( positively - charged ) ions in the plasma , while @xmath6 and @xmath7 are the charge and current densities , and @xmath8 and @xmath9 represent electric and magnetic fields generated by the charge and current . the independent variables , @xmath10 and @xmath11 represent time , position , and velocity , respectively , and physical constants , such as the speed of light @xmath12 , have been normalized . in the presence of large velocities , relativistic corrections may be necessary . the corresponding system to consider is then the relativistic analogue of ( [ vm ] ) , denoted by ( rvm ) and constructed by replacing @xmath13 with @xmath14 within the first equation of ( [ vm ] ) , called the vlasov equation , and the integrand of the current @xmath7 . for a general reference concerning kinetic models of plasma dynamics , such as and ( rvm ) , see @xcite . over the years some progress has been made in the analysis of ( rvm ) , specifically establishing the global existence of weak solutions ( which also holds for ( vm ) ; see @xcite ) and determining a sufficient condition which ensures global existence of classical solutions for the cauchy problem @xcite . in lower - dimensional settings , this condition has been shown to hold _ a priori _ @xcite . additionally , a wide array of information has been discovered regarding the electrostatic versions of both ( [ vm ] ) and ( rvm ) , known as the vlasov - poisson and relativistic vlasov - poisson systems , respectively . these models do not include magnetic effects , and the electric field is given by an elliptic equation , rather than a hyperbolic system of pdes . this simplification has led to a great deal of progress concerning the electrostatic systems , including theorems regarding global existence and long - time behavior of solutions @xcite . however , a global existence theorem for classical solutions stemming from arbitrary data in the relativistic case has remained elusive . independent of these advances , many of the most basic well - posedness questions remain unsolved for ( [ vm ] ) , and few results exist within the literature , with @xcite representing exceptions . the main difficulty which arises is the loss of strict hyperbolicity of the kinetic system due to the possibility that particle velocities @xmath13 may travel faster than the propagation of signals from the electric and magnetic fields , which do so at the speed of light @xmath15 ( cf . as one can see , this difficulty is remedied physically by the inclusion of relativistic velocity corrections which uniformly constrain velocities @xmath16 . in many macroscopic physical systems one does not consider the effects of special relativity , but at the kinetic level such velocity corrections may play a fundamental role , even in the basic well - posedness of solutions . hence , one of the primary goals of the current work is to understand how this affects such properties , and establish a precise result that guarantees the continued smoothness of solutions as long as velocity characteristics do not assume magnitudes that approach @xmath12 . often a remedy to the lack of progress on such a problem is to reduce the dimensionality of the system . the lowest - dimensional reduction which retains magnetic effects is the so - called `` one - and - one - half - dimensional '' vlasov - maxwell system which is constructed by taking @xmath17 but @xmath18 , yielding the system of pdes @xmath19 and initial conditions @xmath20 here , @xmath9 is now a scalar field and the associated electric field possesses only two components , @xmath21 and @xmath22 . additionally , the given , neutralizing background density @xmath23 is included in order to study solutions with finite energy . if one takes @xmath24 , then @xmath25 and solutions necessarily possess infinite energy . surprisingly , the question of classical regularity of solutions remains open even in this simplified case . the fundamental issue of persists within , namely that the reduced vlasov characteristics in the density equation propagate at an uncontrollable speed @xmath26 and hence , are able to intersect the field characteristics which propagate with speed @xmath27 . though we can not currently prove that all initial data launch a global - in - time solution , we can provide an answer for certain classes of initial data ( see section @xmath28 ) and establish uniform bounds on derivatives arbitrarily close to this possible intersection of characteristics . this paper proceeds as follows . in the next section , we will derive _ a priori _ estimates in order to prove the main result . the first lemma obtains bounds on the spatial and velocity supports of the particle distribution and the associated fields , while the main theorem guarantees a uniform bound on derivatives of the distribution function as long as particle velocities do not approach the set on which @xmath0 . the proofs of these results then follow in the latter portion of the section . finally , in section @xmath28 , we present a theorem concerning global existence for initial particle densities that are even in @xmath1 . we show that this symmetry property is preserved in time by solutions of and a reduction in complexity occurs which allows us to conclude that smooth solutions exist globally in time . throughout the paper the value @xmath29 will denote a generic constant that may change from line to line and depend upon the neutralizing density @xmath23 , existence time @xmath30 , and initial data . when necessary , we will specifically identify a constant with a subscript ( e.g. , @xmath31 ) . finally , since we are interested in classical solutions , we will assume @xmath32 for the entirety of the paper . to begin this section , we will first prove a lemma that bounds the support of the particle density and the associated electric and magnetic fields . [ l1 ] let @xmath33 be given and assume that @xmath34 is a @xmath35 solution of ( [ 1.5dvm ] ) on @xmath36 with @xmath37 , and @xmath38 satisfying the global neutrality assumption @xmath39 then , there exists @xmath29 , such that @xmath40 for @xmath41 , and @xmath18 implies @xmath42 additionally , there is @xmath29 such that @xmath43 for all @xmath44 . with this result in hand , we may further obtain bounds on derivatives of the particle distribution function . [ t1 ] let the assumptions of lemma [ l1 ] hold . then , for any @xmath45 the quantity @xmath46 is uniformly bounded on the set @xmath47 prior to proving these results , we introduce a few other quantities necessary for the subsequent analysis . first , we define characteristics for the vlasov equation . these are the curves @xmath48 and @xmath49 satisfying @xmath50 often , the @xmath51 dependence of these curves will be suppressed so , for example , @xmath48 will be denoted by @xmath52 for brevity . then , the vlasov equation can be expressed as a derivative along the characteristic curves by @xmath53 . thus , we find @xmath54 .\ ] ] if it can be shown that velocity characteristics remain bounded away from the set @xmath55 for all @xmath56 , then theorem [ t1 ] implies the global existence of smooth solutions . next , define the potential @xmath57 and notice that @xmath58 and @xmath59 the potential will be used throughout this section because it satisfies the important identity @xmath60 = 0\ ] ] so that @xmath61 now , we may prove lemma [ l1 ] . to prove the initial result , we first define a function to serve as an upper bound on the maximal velocity support @xmath62 , x \in \bfr \mathrm{\ such \ that \ } f(\tau , x , v ) \neq 0 \right \}\ ] ] and the blow - up time @xmath63 then , @xmath64 and @xmath65 is continuous and nondecreasing . finally , if @xmath66 then @xmath67 as @xmath68 . consider any @xmath69 . for @xmath70 $ ] it is straightforward to check the energy conservation identity @xmath71 so that @xmath72 using the supremum bound on @xmath5 and the kinetic energy portion of the identity , we estimate @xmath7 . so , for every @xmath73 @xmath74 taking @xmath75 then yields @xmath76 note that holds if @xmath77 also . by , , and hlder s inequality we have @xmath78 now , if @xmath40 then by we find @xmath79 so that @xmath80 this bound then yields a spatially - uniform bound on @xmath81 @xmath82 next , we note that the field equations in imply @xmath83 the first of these equations yields the bound @xmath84 and an identical bound for @xmath85 follows from the second equation in the same manner . using these together , we find @xmath86 in addition , a bound on the first component of the electric field arises from charge conservation . in particular , integrating the vlasov equation over phase space yields @xmath87 and thus @xmath88 with this , we find @xmath89 hence , if @xmath40 , then @xmath90 and therefore @xmath91 combining this with the bound on the @xmath1-support in , it follows that @xmath92 by gronwall s inequality , we conclude @xmath93 and follows directly from this . finally , the field bounds follow precisely from this estimate and . similarly , @xmath6 and @xmath7 are controlled by the estimate on @xmath94 . to conclude this section , we prove theorem [ t1 ] . for any @xmath95 define the norm @xmath96 } \vert \nabla_{x , v } f(\tau ) \vert_\infty\ ] ] and note that the function @xmath97 is continuous and nondecreasing , and maps @xmath36 to @xmath98 . to prove the uniform boundedness asserted in theorem [ t1 ] , consider @xmath45 and without loss of generality take @xmath99 . let @xmath100 if this intersection is , in fact , empty then the uniform bound on derivatives guaranteed by the theorem will merely be @xmath101 . if @xmath102 then @xmath103 so consider @xmath104 and note that @xmath105 from the result of lemma [ l1 ] , namely , , and the bound on @xmath21 , it follows that @xmath106 on the support of @xmath5 . hence , there is @xmath107 such that @xmath108 implies @xmath109 thus , we have @xmath110 from the vlasov equation , we have @xmath111 = - \left ( \partial_x k \cdot \nabla_v f \right ) ( s , x(s ) , v(s)),\ ] ] @xmath112 = \left ( -\partial_x f + b \partial_{v_2 } f \right ) ( s , x(s ) , v(s)),\ ] ] @xmath113 = - \left ( b \partial_{v_1 } f \right ) ( s , x(s ) , v(s)).\\\ ] ] hence , for @xmath114 $ ] @xmath115 \ ds\end{aligned}\ ] ] letting @xmath116 and changing the order of integration in the last term , this expression becomes @xmath117 now , it remains to bound @xmath118 . for @xmath119 , note that @xmath120,\end{aligned}\ ] ] so that @xmath121 for @xmath122 , note that @xmath123 and @xmath124 so we focus on the remaining quantity in , namely @xmath125 since @xmath9 can be represented as @xmath126,\ ] ] we ll consider @xmath127 then , we can estimate by @xmath128 \ ds" +"the gravitational distortion of light bundles from distant sources in the universe provides a unique means to investigate ( the statistical properties of ) the intervening mass distribution . being observable through the image distortion of the distant faint blue galaxy population , this cosmic shear effect offers the opportunity to study statistical properties of the large - scale structure . in contrast to almost all other methods for investigating the large scale structure ( lss ) with cmb being the only exception no assumption about the relation between dark and luminous mass is required . based on the assumption that the intrinsic orientation of the background galaxies is random , a net alignment in the observed galaxy images can be attributed to the tidal field ( shear ) . hence , the alignment pattern of the galaxy images directly reflects the properties of the mass distribution . for example , two - point statistical measures of the galaxy ellipticities ( understood here and in the following as two - component quantities , with an amplitude and an orientation ) can be expressed directly in terms of the power spectrum of the mass distribution , convolved with a filter function ( blandford et al . 1991 ; miralda - escud 1991 ; kaiser 1992 ; jain & seljak 1997 ; bernardeau et al . 1997 ; schneider et al . 1998 , hereafter svwjk ; kaiser 1998 ; van waerbeke et al . 1999 ; jain et al . 1999 , hereafter jsw ; and references therein ) . the power spectrum completely characterises a gaussian random density field , and so the two - point statistics , like the two - point correlation function of galaxy ellipticities or the rms shear in an aperture , suffices to extract the statistical information contained in the distorted galaxy images . whereas the earlier of the aforementioned papers concentrated mainly on predictions for the cosmic shear based on the linear evolution of the cosmic density field , it was pointed out by jain & seljak ( 1997 ) that even on scales as large as one degree , the non - linear evolution significantly affects the expected amplitude of the cosmic shear . the non - linear evolution transforms an initially gaussian field into a non - gaussian one , and thus the cosmic shear on small angular scales is expected to display significant non - gaussian features . as pointed out by bernardeau et al . ( 1997 ) and svwjk , the skewness of the resulting cosmic shear field is a sensitive measure of the density factor @xmath0 , since in quasi - linear perturbation theory the skewness is independent of the normalisation of the initial power spectrum . in order to define the skewness , mass reconstruction algorithms such as those developed for cluster reconstructions ( kaiser & squires 1993 ; seitz & schneider 1996 , seitz et al . 1998a ; lombardi & bertin 1998a , b ; and references therein ) can be employed to reconstruct the projected density field . this density field , appropriately spatially filtered , can then be used to calculate the skewness . in contrast to the two - point statistical measures mentioned above , which are defined directly in terms of the observable image ellipticities , this measurement of skewness is more indirect . this causes estimates of the statistical error from the data itself not to be straightforward . on the other hand , the aperture mass @xmath1 , introduced as a measure for cosmic shear in svwjk , is a scalar quantity directly defined in terms of the image ellipticities , and can thus be easily used for defining a skewness , as well as a second order statistics , the rms of @xmath2 , where @xmath3 is the angular scale of the circular aperture ( definitions are given in sect . 2 below ) . in particular , in contrast to the two - point ellipticity correlation function and the rms shear in an aperture , for which the filter with which the power spectrum of the projected density field is measured is broad , the corresponding filter function for the rms of @xmath2 is very narrow , and can be approximated very accurately by a delta `` function '' , so that @xmath4 directly measures the power of the projected density at wavelength @xmath5 ( bartelmann & schneider 1999 ) . the skewness defined in terms of @xmath1 has been considered in svwjk . as in the evolution of the three - dimensional density field , where highly non - linear structures like clusters of galaxies form , the projected mass density attains strongly non - gaussian features , e.g. , the projection of collapsed haloes . as a scalar quantity , the aperture mass is ideally suited to probe the full probability distribution of the projected mass density ; in particular , values of @xmath4 far out in the non - gaussian tail signal the presence of massive dark matter haloes . therefore , peaks in the distribution of @xmath1 can be used to search for such haloes , independent of their luminous properties ( schneider 1996 , hereafter s96 ) . indeed , a first application of @xmath1 to large scale structure simulations by reblinsky & bartelmann ( 1999 ) revealed that the detection of dark matter haloes through the aperture mass is more reliable in terms of completeness and spurious detections and suffers less from projection effects than optically selected cluster samples . assuming that highly significant peaks are caused by such haloes , one can predict their abundance ( i.e. , number of peaks above a certain threshold per unit solid angle ) by combining the spatial abundance as predicted by press & schechter ( 1974 ) theory with an assumed density profile , such as the universal dark matter profile found by navarro et al . ( 1996 , 1997 ; combined nfw ) . this idea has been put forward by kruse & schneider ( 1999a ; hereafter ks1 ) , who found that , depending on the cosmological model and the redshift distribution of background galaxies , of order 10 such haloes per square degree will be detectable in deep ground - based optical images , with a signal - to - noise ratio larger than 5 . given the rapid evolution of wide - field imaging , a mass - selected sample of dark matter haloes is now well within reach . indeed , a first example of a shear - detected mass concentration has recently been found by erben et al . ( 1999 ) . all of these predictions on cosmic shear are made using simplifying assumptions in order to make analytic progress . jsw tested some of these assumptions using ray - tracing simulation through a cosmic density field generated by very large n - body simulations ; similar tests have been carried out by van waerbeke et al . they found that the major approximations made in these analytic treatments , namely the so - called `` born - approximation '' ( which projects the density fields along `` straight lines '' ) , and the neglect of non - linear terms in the propagation equations , are very well satisfied . in particular , the twist of light bundles , which vanishes identically in the usual analytical treatments , is indeed very small . the predictions on the projected power spectrum using the approximation for the fully non - linear power spectrum of peacock & dodds ( 1996 ) agree very well with the numerical results , whereas the predictions concerning the skewness are less precise , indicating a breakdown of quasi - linear perturbation theory on small scales . in this paper , we extend the study of jsw to the particular application of the aperture mass statistics . we use the same simulations as jsw , resulting in a table of shear and projected mass density as a function of angular position . from the shear , we can simulate observations of the aperture mass as a function of position on the `` data '' field , and investigate its statistical properties . in particular , we calculate the probability distribution of @xmath4 , which we find to be highly non - gaussian , and from that we study the dispersion , skewness and kurtosis of the distribution . in agreement with jsw , we find that the dispersion is accurately predicted by analytic theory , whereas the skewness predictions can differ substantially from the numerical results . of particular interest is the kurtosis , since it enters the determination of the uncertainty of the dispersion measurement due to cosmic variance ( svwjk ) . we find that the kurtosis is a slowly decreasing function of angular scale @xmath3 , and attains values of @xmath6 even on scales as large as @xmath7 ; hence , the cosmic variance will be the major source of statistical error in the measurement of the power spectrum of the projected density field from @xmath1 . the analytic predictions on the abundance of significant peaks of @xmath1 , and thus presumably of dark matter haloes , turns out to be remarkably precise , given the strong assumptions made . we confirm the high number density of haloes detectable with this method . the shape of the probability distribution of @xmath1 in the highly non - gaussian tail , predicted by kruse & schneider ( 1999b ; hereafter ks2 ) , can also be confirmed to be well approximated by an exponential function . in this section , we briefly summarise the properties of the aperture mass , i.e. , its definition , its relation to the shear , and its signal - to - noise ratio . for more details , the reader is referred to s96 and svwjk . we define the spatially filtered mass inside a circular aperture of angular radius @xmath3 around the point @xmath8 by @xmath9 where the continuous weight function @xmath10 vanishes for @xmath11 . if @xmath10 is a compensated filter function , @xmath12 one can express @xmath1 in terms of the tangential shear @xmath13 at position @xmath14 relative to @xmath8 as @xmath15 ( fahlmann et al . 1994 ; s96 ) , where @xmath16 and @xmath17 is the polar angle of @xmath18 . the function @xmath19 is related to @xmath20 by @xmath21 we use the filter function for @xmath22 from the family given in svwjk : writing @xmath23 , and @xmath24 , we take @xmath25 and @xmath26 with @xmath27 for @xmath28 . an estimate of the shear field @xmath29 , and thus of the aperture mass @xmath30 through eq . ( [ mapshear ] ) , is provided by the distortions of images of faint background galaxies . the complex ellipticity of galaxy images is defined in terms of second moments of the surface - brightness tensor ( e.g. , tyson et al . 1990 ; kaiser & squires 1993 ) . specifically , we use here the ellipticity parameter @xmath31 ( schneider 1995 ; seitz & schneider 1997 ) , which is defined such that for sources with elliptical isophotes of axis ratio @xmath32 , the modulus of the source ellipticities is given as @xmath33 , and the phase of the @xmath34 is twice the position angle of the major axis . the complex image ellipticity @xmath31 can then be calculated in terms of the source ellipticity @xmath34 and the reduced shear @xmath35 by the transformation ( seitz & schneider 1997 ) @xmath36 this relation is valid only for noncritical clusters . for critical clusters , it has to be replaced by a different transformation . however , as we are mainly interested in the weak lensing regime , the above relation is sufficient here . it has been demonstrated ( schramm & kayser 1995 ; seitz & schneider 1997" +"in the past two decades , cosmology has acquired a new standing due to a wide range of observations of high precision data @xcite . these observations seem to reveal that the two dominant components of the universe are a non - baryonic form of matter , the so - called dark matter @xcite , and an exotic form of energy , dark energy @xcite . the former leads to structure formation while the latter is responsible for the present accelerated expansion of the universe . the search for an explanation for the existence and properties of these dark components of the universe has prompted a strong debate about their origin and nature . the behaviour of the galaxy rotation curves and the dynamical mass in clusters of galaxies suggest the existence of an exotic form of matter , dark matter , at galactic and extra galactic scales , respectively , where the presence of this sort of matter is revealed through its gravitational effects . notwithstanding , recent results demonstrated that dark matter may interact with ordinary matter , with the production of patterns of annihilations or decays of dark matter particles in the fluxes of cosmic rays @xcite . evidence for the existence of dark matter lies in the velocity dispersion of clusters that , combined with its morphological features , leads one to conclude that the overall mass should be far greater than the visible mass . in fact , the dark matter component of these clusters is well described by dark matter models , where the interaction of dark matter with baryonic matter determines the density profile of galaxy clusters @xcite . an alternative approach to the above mentioned problems is to consider modified theories of gravity . amongst modified gravity theories , those that introduce higher order curvature terms in the einstein hilbert action and , in particular , the @xmath0 theories of gravity @xcite offer alternative explanations for these problems , along with other cosmological , astrophysical , and high - energy physics motivations @xcite . recently , it has been shown that , in the context of power - law theories , @xmath1 , the rotation curves can be explained as a curvature effect @xcite ; a similar result @xcite can be obtained in another extension of gravity that relies not only on a non - trivial curvature term , but also on a non - minimal coupling between matter and geometry @xcite . clusters are the largest astronomical structures whose masses can be measured in a reliable form , since they constitute the largest configuration of objects that passed through gravitational relaxation and entered into virial equilibrium @xcite . the measuring methods , x - rays and gravitational lensing for visible and dark matter respectively , reveal that the masses of clusters are approximately seven to ten times larger than the total combined mass of stars and hot gas in the intracluster medium ( icm ) . this missing mass is predominant in the inner regions of clusters , but it is also extended beyond the core radius , as defined by the gas density distribution . in the context of modified newtonian dynamics @xcite , another popular ( albeit incomplete @xcite ) alternative to general relativity ( gr ) , it is difficult to explain cluster observations without the assumption of `` real '' dark matter , because the mass of the dark component is otherwise significantly reduced but not completely removed @xcite . the problem of clusters has recently been discussed in @xmath0 theories , by considering a generalized version of the virial theorem . previously discussed in the context of a possible unification and interaction of dark matter and dark energy @xcite . assuming a steady state , the virial theorem can be used to deduce the mean density of astrophysical objects , and therefore the corresponding total mass , such as galaxies and clusters , by observing the velocities of test particles moving around them . the overall mass of a sample of clusters can also be estimated through corrections in the gravitational potential that emerge in the weak field limit of these theories @xcite . along with these works , there were also conducted the first cluster abundance constraints on a modified gravity model , specifically the modified action @xmath0 model , which predict deviations in the abundance of massive dark matter halos @xcite . in the context of the non - minimal coupling between the ricci scalar curvature and matter @xcite , it has been shown in several works that both dark energy and dark matter can be effectively described within this framework , along with other cosmological and astrophysical implications : these include the perturbed hydrostatic equilibrium of the sun @xcite , the acceleration of the universe @xcite , the galaxy rotation curves @xcite , the reheating scenario after inflation @xcite , the mimicking of a cosmological constant @xcite , and the change in the gravitational potential @xcite . in order to extend this non - minimally coupled model one tries to obtain the large mass difference of clusters through a dark matter mimicking , an extra matter component that emerges due to the presence of the non - minimal coupling , and a subsequent modification of gravity . one first explores here the scenario of the abell cluster a586 , which is a nearby massive strong - lensing cluster , with a high x - ray luminosity , related with the mass of the intracluster gas . its morphology is well suited to the assumption of spherical symmetry , making it an ideal test bed for modifications of gravity at extra - galactic scales . one then extends this analysis to a larger set of galaxy clusters with the same features . this work is organized as follows . first , one shortly reviews the formalism leading to the total cluster mass and the field equations that result in the presence of the non - minimal coupling and stablishes the strategy to address the problem of mimicking the dark matter component of a cluster . one then studies the particular case of the abell cluster a586 , discusses the coupling function that leads to the dark matter mimicking , and extends the model to a larger sample of galaxy clusters . finally , the numerical results are presented and discussed . galaxy clusters are usually considered as closed gravitational systems with spherical symmetry and in hydrostatic equilibrium when virial equilibrium is attained despite the fact that recent observations reveal that clusters have more evolved structures with strong interactions and dynamical activity , particularly in their inner regions @xcite . under these assumptions , the structure equation can be derived from the collisionless boltzmann equation for an isotropic system @xcite , ( _ g _ r^2)=-_g ddr , [ boltzmann_equation ] where @xmath2 is the newtonian gravitational potential of the cluster , @xmath3 the mass - weighted velocity dispersion in the radial direction , and @xmath4 the gas - mass density . the pressure profile is related with these quantities through , @xmath5 , and inserting in eq . ( [ boltzmann_equation ] ) leads to @xmath6 , where the prime indicates differentiation with respect to the radial coordinate . the newtonian gravitational potential @xmath2 can be read from the newtonian limit of the modified einstein field equations ( as addressed later ) , _ i.e. _ a suitably modified poisson equation . however , this does not prevent us from formally writing the latter as the effect of the non - minimal coupling ascribed to the `` mimicked '' dark matter component , so that ^2 = 4 g ( + _ dm ) . [ poissoneq ] this approach shall be discussed in more detail in the following section . for a gas sphere , with temperature profile @xmath7 , the velocity dispersion becomes @xmath8 , where @xmath9 is the boltzmann constant , @xmath10 the mean mass particle , and @xmath11 the proton mass . introducing this expression into eq . ( [ boltzmann_equation ] ) gives ( kt m_p_g ) & = & -_g ddr , or , equivalently , -ddr & = & kt m_pr . [ eq : boltzmannpotential ] therefore , from the models for the gas density and temperature profiles , the total mass enclosed in a sphere with a given radius @xmath12 can be obtained from , m ( r ) & = & 4(_g + _ dm ) r^2 dr = r^2 g ddr , [ dynamical_mass_possion ] leading to the usual expression for the mass profile of a spherical mass distribution in hydrostatic equilibrium m ( r ) & = & -kt rgm_p(d_g dr+dt dr ) . [ dynamical_mass ] as already stated , this is the total mass that one should observe in a cluster and that , in general , agrees well with observations from gravitational lensing @xcite . however , the baryonic component of the cluster mass , galaxies mass in the visible spectrum and gas in x - ray spectrum , where the latter dominates , is much less than the total observed mass leading one to conclude the existence of a dark matter component that in the present work results from the presence of the non - minimal coupling . hence , the equilibrium equation , eq . ( [ dynamical_mass ] ) , which leads to the total mass within a cluster , can be used to derive the amount of dark matter present in a cluster of galaxies , and its spatial distribution , by the mass difference between this and the gas - mass estimates as provided by x - ray observations . in the following , one tries to reproduce the total mass profiles of a sample of galaxy clusters , where the additional density component emerges not from an exotic form of `` dark '' matter but from a change in geometry due to the presence of the non - minimal coupling in the action . clusters of galaxies present a velocity dispersion with a relative constant value along the radius , which reveals an implicit matter density profile of the form @xmath13 . the singular isothermal sphere is the simplest model whose density profile , @xmath14 , leads to a constant and isotropic velocity dispersion @xmath15 along the clusters profile . however , numerical fits to the observational data show that the density profile of clusters are flatter than the isothermal one at small radii and steeper at larger radii . a general form replicating this behaviour is given by the cusped density profile , _ m&=_0 & ( r r_s ) ^-p(1+r r_s)^p - q , [ cusped_profile ] where the parameters @xmath16 and @xmath17 determine the respective slopes of the power - law density profile in the inner and outer regions , and @xmath18 is the so - called core radius , signaling the steepening of the profile . these parameters usually present values within the ranges @xmath19 and @xmath20 , for models such as the navarro - frenk - white ( nfw ) profile ( @xmath21 and @xmath22 ) , the moore profile ( @xmath23 and @xmath22 ) , and the rasia profile ( @xmath21 and @xmath24 ) . in fact , one of the important results of hierarchical cdm models is that the density profile of cold dark matter halos is described by the nfw model @xcite . the more relevant baryonic component is the icm in the form of hot gas , which emits observable x - ray radiation . in general , the observed surface - brightness profiles of clusters that reveal the underlying visible matter profile of this intracluster gas are well described by the so - called @xmath25 model : _ g(r)=_g0(1+r^2 r^2_c)^-3/2 , [ visible_profile ] where @xmath26 is the core radius , which has a specific value for each cluster @xcite . in this" +"in the context of newtonian gravity , polytropic equations of state are particularly useful to describe a great variety of situations ( see refs . @xcite and references therein ) , their great success stemming mainly from the simplicity of the equation of state and the ensuing main equation ( lane - emden ) . polytropes in the context of general relativity have been considered in refs . @xcite ( and references therein ) . however , in this work , we restrict the analysis to newtonian polytropes . the theory of polytropes is based on the polytropic equation of state @xmath0 where @xmath1 and @xmath2 denote the isotropic pressure and the mass ( baryonic ) density , respectively . constants @xmath3 , @xmath4 , and @xmath5 are usually called the polytropic constant , polytropic exponent , and polytropic index , respectively . the polytropic equation of state may be used to model two very different types of situations , namely : 1 . when the polytropic constant @xmath3 is fixed and can be calculated from natural constants . this is the case of a completely degenerate gas in the nonrelativistic ( @xmath6 ) and relativistic limit ( @xmath7 ) . polytropes of this kind are particularly useful to model compact objects such as withe dwarfs ( wds ) , and they lead in a rather simple way to the chandrasekhar mass limit . 2 . when @xmath3 is a free parameter , as , for example , in the case of isothermal ideal gas , or in a completely convective star . models related to isothermal ideal gas are relevant in the so - called schnberg chandrasekhar limit ( see ref . @xcite for details ) . our motivation to extend polytropic stellar models to cases in which the pressure anisotropy is allowed is based on the fact that the local anisotropy of pressure may be caused by a large variety of physical phenomena of the kind we expect in compact objects ( see ref . @xcite for an extensive discussion on this point ) . indeed , the study of anisotropic ( principal stresses unequal ) spherically symmetric fluids has a long and venerable story . it started with jeans @xcite , who studied the anisotropy produced by anisotropic velocity distributions in galaxies . the first mention of local anisotropy of pressure in spherically symmetric selfgravitating fluids may be found in the seminal paper by lemaitre @xcite . in page 63 of that paper , lemaitre realizes that the stringent limit in the compactness of a homogeneous relativistic sphere is related to the isotropy of pressure , and therefore he proposes to relax that condition . he considers the limiting "" case in which the radial pressure vanishes , but the tangential does not . however , the interest in this subject started to grow exponentially after the pioneering work of bowers and liang @xcite . for recent references on this subject , @xcite ( and references therein ) . an alternative approach to anisotropy comes from kinetic theory using the spherically symmetric einstein - vlasov equations , which admits a very rich class of static solutions , none of them isotropic ( ref . @xcite ( and references therein ) . the advantages or disadvantages of either approach are related to the specific problem under consideration . as we shall see below , our method links our models continually with the isotropic case ( see sec . iv ) , thereby allowing us to bring out the influence of anisotropy on the structure of the object . evidently , both approaches should give the same physical results . among all possible sources of anisotropy , there is one particularly related to our endeavor in this manuscript , namely the intense magnetic field observed in compact objects such as white dwarfs , neutron stars , or magnetized strange quark stars ( see , for example , refs . @xcite and references therein ) . indeed , it is a well - established fact that a magnetic field acting on a fermi gas produces pressure anisotropy ( see refs . @xcite and references therein ) . in some way , the magnetic field can be addressed as a fluid anisotropy . particularly appealing is the fact that magnetic fields may severely affect the chandrasekhar mass limit of a white dwarf @xcite . for all the reasons above , we intend in this paper to develop the general formalism to describe polytropes in the presence of pressure anisotropy . for the sake of completeness , we shall first review very briefly the theory of polytropes for a perfect ( isotropic ) fluid . next , we shall display the general formalism for anisotropic fluids . in order to bring out the effects of anisotropy on the structure of the star , we shall further assume an ansatz allowing us to calculate the influence of anisotropy on the chandraskhar mass limit . finally , we shall conclude with some possible applications and unanswered issues . polytropes are assumed to be in hydrostatic equilibrium ( for deviations from this condition see refs . @xcite and @xcite ) ; therefore , the two starting equations are the equation of hydrostatic equilibrium , @xmath8 and the poisson equation ( in spherical coordinates ) , @xmath9 with @xmath10 and @xmath11 denoting the newtonian gravitational potential and the gravitational constant respectively . combining the two equations above with eq . ( [ pol ] ) , one obtains after some simple calculations the well - known lane - emden equation ( for @xmath12 ) : @xmath13 with @xmath14 @xmath15 @xmath16 where the subscript @xmath17 indicates that the quantity is evaluated at the center , and the following boundary conditions apply : @xmath18 the boundary surface of the sphere is defined by @xmath19 , such that @xmath20 . as is well known , bounded configurations exist only for @xmath21 , and analytical solutions may be found for @xmath22 and @xmath23 . in the case @xmath24 , which corresponds to an isothermal ideal gas , the ensuing lane - emden equation reads @xmath25 where now @xmath26 @xmath27 @xmath28 and the following boundary conditions apply : @xmath29 we shall next generalize the scheme above to the case when the pressure is no longer isotropic . if we allow the principal stresses to be unequal , then the hydrostatic equilibrium equation reads @xmath30 where @xmath31 and @xmath32 denote the radial and tangential pressures , respectively . this is the newtonian limit of the generalized tolman - opphenheimer - volkoff equation for anisotropic matter . we recall that the tolman - opphenheimer - volkoff equation is a consequence of einstein equations and bianchi identities , or equivalently , it comes directly from the vanishing of the covariant divergence of the energy momentum tensor . if spherical symmetry is assumed , then necessarily the nonradial stresses are equal : @xmath33 , the only freedom being in this case that @xmath34 . indeed , spherical symmetry supposes enough freedom to rotate cartesian axes in order to guarantee @xmath35 and @xmath36 . of course , if one does not assume spherical symmetry , then in principle all three main stresses may be different . for the poisson equation , of course , we get the same expression [ ref . [ poisson ] ] , as both are under spherical symmetry . we shall next assume a polytropic equation [ eq . ( [ pol ] ) ] for the radial pressure @xmath31 . then , using eqs . ( [ hse ] ) and ( [ poisson ] ) , we may write @xmath37 where @xmath38 . for the case @xmath12 , we can formally integrate the equation above between any interior @xmath39 and the surface of radius @xmath40 , which gives us @xmath41 which can be written as @xmath42^n,\ ] ] where @xmath43 introducing the variables @xmath44 @xmath45^{n-1}\ ] ] and @xmath46 where as before , the subscript @xmath17 indicates that the quantity is evaluated at @xmath47 , the extended lane - emden equation can be written as @xmath48 where @xmath49 and @xmath50 for the isothermal case which corresponds to @xmath24 , eq . ( [ 2 ] ) becomes @xmath51 which after integration yields @xmath52 where the potential was set to zero at @xmath47 and @xmath53 is defined by eq . ( [ fdef ] ) ( with the inferior limit set to @xmath47 , of course ) . then the corresponding lane - emden equation becomes @xmath54 with @xmath55 @xmath56 @xmath57 it is obvious that in order to proceed further with the modeling of the compact object [ i.e. , in order to integrate eqs . ( [ le1 ] ) or ( [ iso4 ] ) ] , we need to prescribe the specific anisotropy of the problem ( @xmath58 ) . such information , of course , depends on the specific physical problem under consideration . here we shall not follow that direction ; instead , we shall assume an ansatz already used in the modeling of relativistic anisotropic stars @xcite , whose main virtue ( besides its simplicity ) is the fact that the obtained models are continuously connected with the isotropic case . as a function of @xmath59 for @xmath60 ( wd ) and @xmath61 ( dashed line , upper ) ; @xmath62 ( solid line ) ; @xmath63 ( short - dashed line , lower ) . ] as a function of @xmath64.,width=268,height=240 ] as a function of @xmath59 for @xmath24 ( isothermal gas ) and @xmath61 ( dashed line , lower ) ; @xmath62 ( solid line ) ; @xmath63 ( dot - dashed line , upper ) . ] in order to obtain specific models , we shall here adopt the nonrelativistic version of the heuristic procedure used in ref . @xcite , which allows to obtain solutions for anisotropic matter from known solutions for isotropic matter ; that is , @xmath65 where @xmath66 is a parameter which measures the anisotropy ; the function @xmath67 and the number @xmath68 are to be specific for each model . following that procedure the ansatz @xmath69 leads to @xmath70 thus , eq . ( [ le1 ] ) can be easily reduced to @xmath71 where @xmath72 . for simplicity , we assume @xmath64 to be constant throughout the sphere , which of course does not imply the constancy of either pressure . observe that eq . ( [ le2 ] ) is the same as the fowler equation @xcite when @xmath73 and @xmath74 in the notation of @xcite [ see eq . ( 2.2 ) in this last reference ] . however , it should be noticed that eq . ( [ le1 ] ) is more general than the fowler - emden equation . now , we proceed to integrate numerically with the boundary conditions @xmath75 with @xmath60 , which represents a relativistic wd . figure 1 displays the dimensionless variable @xmath76 as a function of the dimensionless variable @xmath59 for different values of @xmath64 . figure 2 shows the chandrasekhar mass ratio ( with respect to the isotropic mass @xmath77 ) @xmath78_{h=1}}\ ] ] as a function of the anisotropy parameter @xmath64 . following the same ansatz for the heuristic model in the case @xmath24 , the lane - emden equation becomes @xmath79 where @xmath80 and from eq . ( [ 2iso ] ) we get @xmath81 equation ( [ le3 ] ) has to be integrated with the following central conditions : @xmath82 figure 3 displays the solution for different values of @xmath64 . as for polytropes with @xmath83 , the isothermal sphere consists of an ideal gas which has infinite radius . it is remarkable , although not general , to observe the invariance of scale of eqs . ( [ le2 ] ) and ( [ le3 ] ) . in fact , if we redefine the dimensionless spatial variable @xmath84" +"in quantum gravity research , we strive to answer the question `` what is spacetime like on very small scales ? '' . more precisely , this can be rephrased as `` what is the microscopic dynamics of gravity ? '' , `` what are the fundamental symmetries ? '' , `` is spacetime continuous or somehow discrete ? '' , `` what is the dimensionality of spacetime on small scales ? '' . to answer these , each approach to quantum gravity is founded upon assumptions . ultimately , these should be tested in experiments . here , matter - quantum gravity interactions provide us with two possibilities : \1 ) consistency tests ( indirect ) : here we can check , whether a particular uv completion for gravity is compatible with the observed properties of the standard model of particle physics , such as the number of fermions , scalars and gauge bosons , the global symmetries , the observed mass scales , etc . \2 ) direct tests : effects such as graviton - exchange in scattering processes , can be used to study the small - scale structure of spacetime . in particular , the dimensionality of spacetime on small scales can be tested at near - future experiments . for examples of the first option , where the consistency of asymptotically safe quantum gravity , as well as other models for quantum gravity , with the existence of light fermions in our universe is tested , see @xcite . within the truncation of the full renormalization group ( rg ) flow employed in this work , asymptotic safety is compatible with fermion masses much below the planck mass , whereas restrictions are placed on the parameter space for other quantum gravity models . high - intensity lasers are subject to quickly advancing experimental research , and have the potential to provide future particle accelerators that could replace conventional accelerators and reach higher energies over much shorter acceleration paths , albeit reaching high luminosities remains a challenge . once high - energy electrons are available , either from high - intensity lasers or conventional linear accelerators , the energy can be transferred to photons by compton - backscattering , thus enabling high - energy photon - photon scattering . this provides for a possible window into the quantum - gravity regime @xcite : since there is no microscopic photon - photon interaction in the standard model , the cross - section is dominated solely by loop effects . due to the tree - level graviton - exchange in the @xmath0 , @xmath1 and @xmath2 channels , the quantum gravity effect is easier to access here than in processes which have a large standard model background , such as , e.g. , processes at the lhc , see , e.g. @xcite . here , we will focus on asymptotic safety as a uv completion for gravity , i.e. a quantum field theory of the metric , which is extendible up to arbitrarily high energies due to the existence of an interacting fixed point of the rg . see , e.g. @xcite for reviews . in order to detect experimental signatures of asymptotic safety , we have to include the effect of a momentum - scale dependent newton coupling , which encodes the leading - order non - perturbative physics underlying the asymptotic - safety scenario . the dimensionful newton coupling @xmath3 on a large range of scales . this behavior characterizes the classical regime of the theory , required for the consistency with experiment , and has been shown to exist in truncated rg flow studies @xcite . the second property is special in the asymptotic - safety scenario : a uv completion with the help of an interacting fixed point requires that @xmath4 for @xmath5 , where @xmath6 is the dimensionless newton coupling and @xmath7 the rg scale . thus we model the scale - dependence in @xmath8 spacetime dimensions in the following way : @xmath9 where @xmath10 is the constant dimensionful value for the newton coupling measured in the infrared . here the transition scale @xmath11 , assumed to lie close to the planck scale , is presently unknown , and signals the onset of the fixed - point behavior . we study scenarios with @xmath12 flat extra dimensions @xcite with compactification radius @xmath13 , where the fundamental planck scale @xmath14 . a kaluza - klein tower of graviton states contributes to the cross section , and has to be summed at the amplitude level . as for settings with @xmath15 , the spacing between kaluza - klein modes is small , the sum can be well approximated by an integral . this is uv divergent for @xmath16 when @xmath17 , see @xcite . this differs in asymptotic safety , where we employ the scale - identification @xmath18 , i.e. , the fixed - point regime is probed by the heavy kaluza - klein modes , whereas the low - lying modes probe the classical gravity regime . then , using @xmath19 yields a finite integral : @xmath20 . [ gg_sm_as_n ] shows our main results @xcite : at photon energies of @xmath21 , the standard - model cross section is measurable at @xmath22 and the graviton - induced cross section in our approximation is of the same size , thus being easily detectable . this holds for a fundamental planck scale @xmath23 and for 2 , 3 and possibly even 4 extra dimensions . the result for asymptotic safety clearly differs from the result in the cutoff - theory , due to the extra contribution arising from the fixed - point regime . this allows to experimentally distinguish asymptotic safety from other uv completions . we plot the cross section ( @xmath24 ) for the standard model ( black continuous line ) , for the cutoff theory ( thin lines ) with @xmath25 and for asymptotic safety ( thick lines ) with @xmath26 . we show @xmath27 ( red dashed ) , @xmath28 ( blue dotted ) and @xmath29 ( green dot - dashed ) . ] employing sources of high - energy photons , such as an electron collider or laser plasma wake - field acceleration , where photons reach high energies by compton backscattering off high - energy electrons , allows to test the dimensionality of spacetime and detect possible quantum gravity effects in a very clean setting . photon energies of 1 tev suffice to access a fundamental planck scale @xmath23 . furthermore , the imprints of asymptotically safe quantum gravity can then be clearly distinguished from other quantum gravity models . thus , near - future experiments can start to shed light on the small - scale structure of spacetime . a. eichhorn and h. gies , new j. phys . * 13 * , 125012 ( 2011 ) ; a. eichhorn , j. phys . ser . * 360 * , 012057 ( 2012 ) . d. f. litim and t. plehn , phys . lett . * 100 * , 131301 ( 2008 ) ; e. gerwick , d. litim and t. plehn , phys . d * 83 * , 084048 ( 2011 ) . m. reuter and f. saueressig , new j. phys . * 14 * , 055022 ( 2012 ) ; r. percacci , arxiv:1110.6389 [ hep - th ] ; m. niedermaier , class . * 24 * , r171 ( 2007 ) . m. reuter and h. weyer , jcap * 0412 * , 001 ( 2004 ) ." +"low - energy nonperturbative effects in quantum chromodynamics ( qcd ) , especially at nonzero densities , can only be studied by approximate methods within the framework of various effective models . it is well known that light meson physics is described by four - fermion models , such as the nambu jona - lasinio ( njl ) model , which was successfully used to deal with dynamical chiral symmetry breaking ( d@xmath0sb ) both in the vacuum and in hot / dense baryonic matter ( see , e.g. @xcite , as well as the reviews @xcite and references therein ) . recently , much attention has been paid to the effects of diquark condensation and color superconductivity ( csc ) . the first studies of the gap equations and the ginzburg - landau free energy for a system of relativistic fermions led to the conclusion that superconductive and color superconductive states may arise in baryonic matter @xcite ( see also the recent papers @xcite ) . another interesting phenomenon , the condensation of charged pions , which may appear in dense hadronic matter due to an asymmetry of its isospin composition , has been investigated in the framework of qcd - like effective models , including the njl model , as well @xcite . note that all these phenomena might be inherent to physics of compact stars , where rather strong magnetic as well as gravitational fields are present . therefore , investigations of the influence of an external ( chromo-)magnetic field on the properties of the d@xmath0sb phase transition @xcite , color superconductivity @xcite and pion condensation @xcite effects are quite appropriate . in particular , it was shown in @xcite that external fields significantly change the properties of the chiral and csc phase transitions . in several papers , in the framework of the njl model , the influence of a gravitational field on the d@xmath0sb due to the creation of a finite quark condensate @xmath1 has been investigated at zero values of temperature and chemical potential @xcite . the study of the combined influence of curvature and temperature has been performed in @xcite . recently , the dynamical chiral symmetry breaking and its restoration for a uniformly accelerated observer due to the thermalization effect of acceleration was studied in @xcite at zero chemical potential . further investigations of the influence of the unruh temperature on the phase transitions in dense quark matter with a finite chemical potential , and especially on the restoration of the broken color symmetry in csc were made in @xcite . one of the widely used methods of accounting for gravitation is based on the expansion of the fermion propagator in powers of small curvature @xmath2 @xcite . for instance , in @xcite , the three - dimensional gross - neveu model in a spacetime with a weakly curved two - dimensional surface was investigated , using an effective potential at finite curvature and nonzero chemical potential . in paper @xcite , this weak curvature expansion was used in considering the d@xmath0sb at non - vanishing temperature and chemical potential . it should , however , be mentioned that near the phase transition point , one can not consider the critical curvature @xmath3 to be small and therefore the weak curvature expansion method can not be applied . hence , in the region near the critical regime different nonperturbative methods or exact solutions with finite values of @xmath2 should be used . this kind of solution with consideration for the chemical potential and temperature in the gravitational background of a static einstein universe has been considered in @xcite . there it was demonstrated that chiral symmetry is restored at large values of the space curvature . analogous studies of diquark condensation and the related color symmetry breaking under the influence of a gravitational field have been performed recently in the model of a static einstein universe in @xcite . recall that this model is widely discussed in literature either as a solution of the einstein equations with a given cosmological constant and a nonvanishing energy - momentum tensor of an ideal fluid as a source , or as an initial state in inflationary cosmology with a scalar field , and the cosmological constant as its vacuum energy ( see , for instance , @xcite ) . moreover , the einstein universe and other suitably generalized compact curved spacetimes were extensively employed for studying the phenomenon of bose - einstein condensation ( see , e.g. @xcite and references therein ) . as is well known , one of the possible models for the expanding universe is the closed friedmann model . since the formation of quark condensates is expected to take place considerably faster than the expansion rate of the universe , its radius can be considered in our calculations as constant . in this sense , the chosen model of a static einstein universe can be considered as a simple cosmological model for a space with positive curvature . on the other hand , the same form of the metric does also hold for the interior of a ( collapsing ) spherically symmetric star , thereby admitting also a non - cosmological interpretation of the chosen model . as was mentioned above , in quark matter there may arise another remarkable phenomenon , pion condensation . up to now little information about the properties of pion condensation in the presence of external fields has been obtained . in particular , there arises the interesting question , what influence gravitational fields can produce on pion condensation . the main aim of the present paper is just to give a detailed investigation of this issue . in order to be able to consider the effects of gravitation on pion condensation in a rigorous nonperturbative way , we will investigate here the phase structure of isotopically asymmetric quark matter in the framework of an extended njl model with dynamical breaking of chiral and flavor symmetries in the static einstein universe . in particular , our calculations are performed in the most simple case , restricting ourselves , for simplicity , to the flavor @xmath4 group . by using the mean field approximation , we will then derive an analytical expression for the thermodynamic potential of the njl model that will enable us to calculate the chiral and pion condensates of quarks moving in a space with constant positive curvature . on this basis , we study , in particular , the phase portraits of the model . our paper is organized as follows . section ii , iii contain the nambu - jona - lasinio model in curved spacetime and the general formalism for the derivation of the thermodynamical potential . numerical calculations and conclusions are given in sections iv , v. finally , some estimates of the role of quantum fluctuations in the case of a closed universe are given in the appendix . suppose that dense , isotopically asymmetric quark matter ( in this case the densities of @xmath5 and @xmath6 quarks are different ) in curved spacetime is described by an extended njl model with the following action : @xmath7 and the lagrangian @xmath8q+ g\big [ ( \bar qq)^2 + ( \bar qi\gamma^5\vec\tau q)^2\big ] , \label{2}\end{aligned}\ ] ] where the quark field @xmath9 is a flavor doublet ( @xmath10 or @xmath11 ) and color triplet ( @xmath12 ) as well as a four - component dirac spinor ( the summation in ( [ 2 ] ) over flavor , color and spinor indices is implied ) ; @xmath13 ( @xmath14 ) are pauli matrices . in 4-dimensional curved spacetime with signature @xmath15 , the line element is written as @xmath16 the gamma - matrices @xmath17 , the metric @xmath18 and the vierbein @xmath19 , as well as the definitions of the spinor covariant derivative @xmath20 and spin connection @xmath21 are given by the following relations @xcite : @xmath22 , \nonumber \\ & & \omega^{\hat{a}\hat{b}}_{\mu}=\frac{1}{2}e^{\hat{a}\lambda } e^{\hat{b}\rho}[c_{\lambda\rho\mu}-c_{\rho\lambda\mu}-c_{\mu\lambda \rho } ] , \quad c_{\lambda\rho\mu}= e^{\hat{a}}_{\lambda}\partial_{[\rho}e_{\mu]\hat{a}}. \label{3_3}\end{aligned}\ ] ] here , the index @xmath23 refers to the flat tangent space defined by the vierbein at spacetime point @xmath24 , and the @xmath25 are the usual dirac gamma - matrices of minkowski spacetime . moreover @xmath26 , is defined , as usual ( see , e.g. , @xcite ) , i.e. to be the same as in flat spacetime and thus independent of spacetime variables . in order to describe the quark composition of matter we introduced @xmath27 in ( [ 2 ] ) as the quark number chemical potential . since the generator @xmath28 of the third component of isospin is equal to @xmath29 , the quantity @xmath30 in ( [ 2 ] ) is half the isospin chemical potential , @xmath31 . if the bare quark mass @xmath32 is equal to zero , then at @xmath33 , apart from the trivial color su(@xmath34 ) symmetry , the lagrangian ( [ 2 ] ) is invariant under the chiral group @xmath35 transformations . however , at @xmath36 this symmetry is reduced to the subgroup @xmath37 ( here and above the subscripts @xmath38 imply that the corresponding group acts only on the left , right handed spinors , respectively ) . it is convenient to present this symmetry as @xmath39 , where @xmath40 and @xmath41 are the isospin and axial isospin subgroup of the chiral @xmath35 group . quarks are tranformed under these subgroups in the following way @xmath42 where @xmath43 , @xmath44 are independent group parameters . at nonzero bare quark mass , @xmath45 , and nonzero isotopic chemical potential , i.e. @xmath46 , the lagrangian ( [ 2 ] ) is still invariant under the isospin subgroup @xmath40 , but invariance with respect to @xmath41 does no longer hold in this case . the linearized version of lagrangian ( [ 2 ] ) , that contains collective bosonic fields @xmath47 and @xmath48 @xmath49 , has the following form @xmath50q -\frac{1}{4g}\big [ \sigma\sigma+\pi_k\pi_k\big ] . \label{3}\end{aligned}\ ] ] from the lagrangian ( [ 3 ] ) , one can find the equations of motion for the bosonic fields , @xmath51 it is clear from these relations that under isospin @xmath40 and axial isospin @xmath52 transformations ( [ 2010 ] ) the bosonic fields ( [ 200 ] ) are changed in the following way : @xmath53 in the fermion one - loop ( mean field ) approximation , the effective action for the boson fields is expressed through the path integral over quark fields : @xmath54[dq]\exp\bigl(i\int d^4 x\sqrt{-g } ~\tilde { \mathcal l}\,\bigr),\ ] ] where @xmath55+\tilde { \cal s}_{\rm { eff } } , \label{4}\ ] ] @xmath56 is a normalization constant . the quark contribution to the effective action , i.e. the term @xmath57 in ( [ 4 ] ) , is given by : @xmath58[dq]\exp\bigl(i\int d^4x\sqrt{-g } ~\bar q{\cal d}q\,\bigr)=\mbox { det}~{\cal d}. \label{5}\ ] ] in ( [ 5 ] ) , we have used the following notation @xmath59 clearly , @xmath60 is an operator in the coordinate , spinor and flavor spaces . apart from this , it is proportional to the unit operator @xmath61 in the color space . thus , it can be presented in the flavor@xmath62color space in the following matrix form : @xmath63 where operators @xmath64 act in the coordinate and spinor spaces only , and @xmath65 due to the trivial color structure , it follows from ( [ 7 ] ) that @xmath66 now , suppose that @xmath67 and @xmath68 are quantities independent of coordinates .. if the fields @xmath69 do not depend on coordinates , then the effective action is a function of the invariants @xmath70 and @xmath71 only ( this fact is due to the symmetry of the model with respect to the transformations ( [ 201 ] ) ) . therefore , without loss of generality one can put @xmath67 . ] in what follows , we shall denote the pion" +"the gravitational interaction of two massive particles is described by newton s law @xmath0 which is a good approximation for the motion of nonrelativistic particles at large separations . einstein s theory of general relativity , however , predicts important corrections that have been verified experimentally , _ e.g. _ , in measurements of the precession of the perihelion of mercury @xcite . this effect can be calculated from the famous einstein - infeld - hoffmann lagrangian @xcite where the terms beyond newtonian physics stem from the relativistic @xmath1 corrections to the kinetic energy , from relativistic @xmath1 corrections to the newtonian potential and from a new piece of the potential proportional to @xmath2 which may be regarded as an @xmath3 correction to the leading newtonian potential . the two small expansion parameters here are @xmath4 and @xmath5 which for bound states are related due to the virial theorem . we , however , will examine scattering processes wherein the classical expansion parameters @xmath4 and @xmath5 are independent , and our focus will be on the components that vanish in the nonrelativistic limit @xmath6 . in the weak field limit gravitational dynamics can be described in terms of a quantum field theory which is based on expanding around flat minkowski spacetime and quantizing the metric fluctuation in terms of a massless spin-2 field the graviton . the resulting theory is an effective field theory whose predictions are trustworthy only for energies much smaller than the planck scale . nevertheless , one can in this picture calculate well - defined quantum predictions as well as classical corrections to newtonian physics . donoghue has pioneered the use of the effective field theory of gravity to extract the leading long distance effects in the nonrelativistic limit @xcite ( see @xcite and @xcite for reviews ) which yield corrections of the form @xmath7 where @xmath8 and @xmath9 are the coefficients of the classical and quantum corrections respectively and are evaluated below . note that while the classical expansion parameter @xmath10 can give measurable effects for macroscopic objects ( where a large factor multiplies a tiny factor ) , the quantum corrections which scale as @xmath11 are clearly tiny and phenomenologically irrelevant for macroscopic systems . the calculations of these leading long distance corrections are performed by evaluating the leading nonanalytic components of the scattering amplitude at one loop level , where @xmath12 effects first arise , and by defining a potential in terms of the fourier transform of this amplitude . once spin is introduced into the calculation , additional interaction structures arise , such as a spin - orbit coupling and a spin - spin coupling . the leading effects of order @xmath13 stemming from the tree level one - graviton exchange process give rise to the familiar geodetic precession and to the lense - thirring effect @xcite . at the two - graviton exchange level , classical @xmath14 and quantum @xmath15 corrections to these leading spin - dependent interactions arise and are calculated as part of our work . in earlier work on loop corrections to the form factors of graviton couplings it was found that the long distance corrections to the spin - independent interactions have the same form for scalars , spin-1/2 fermions and for spin-1 bosons @xcite . these nlo form factor interactions constitute one component of the calculation of the full scattering amplitude at the two - graviton exchange level , so the question arises as to whether the _ full _ scattering amplitude also exhibits such universalities , whereby the form of the corrections to the spin - independent newtonian potential is independent of the spins of the scattered particles in other words , are the coefficients @xmath8 and @xmath9 in eq . ( [ eq_pot_cor ] ) independent of spin ? this then is the goal of the present work to evaluate the gravitational scattering of two massive particles having various spins , in order to check previous work and to verify the universality hypothesis . in the next section then we review our calculational methods and reproduce the long range gravitational scattering amplitude in the case of a pair of spinless particles . in the following sections , we generalize these methods to the cases of spin-0 spin-1/2 , spin-0 spin-1 and spin-1/2 spin-1/2 scattering and demonstrate both the expected universality as well as novel spin - dependent interactions . we summarize our work and draw general implications in a brief concluding section . appendix [ app_iter ] encapsulates parts of our calculational methods while we refer to our companion paper on long distance effects in electromagnetic scattering @xcite for many of the details such as the required feynman integrals , the fourier transformations etc . in appendix [ app_eom ] we demonstrate how the classical equations of motion in the form of the einstein - infeld - hoffmann lagrangian can be extracted from our results . we first set the kinematic framework for our study . we consider the gravitational scattering of two non - identical particles particle @xmath16 with mass @xmath17 , and incoming four - momentum @xmath18 and particle @xmath19 with mass @xmath20 , and incoming four - momentum @xmath21 . after interacting the final four - momentum of particle @xmath16 is @xmath22 and that of particle @xmath19 is @xmath23_cf . [ fig_kinem ] . now we need to be more specific . we begin by examining the gravitational scattering of two spinless particles . the gravitational coupling of a spin-0 particle is found by expanding the minimally coupled scalar field matter lagrangian @xmath24 in terms of the gravitational field @xmath25 which is a small fluctuation of the metric about flat minkowski space defined as @xmath26 with @xmath27 . the inclusion of this factor @xmath28 in the definition of the graviton field @xmath29 gives this field a mass - dimension of unity and thus yields a kinetic term of standard normalization without a dimensionful parameter . for matter interactions , this choice is convenient since the order of @xmath28 keeps track of the number of gravitons involved in an interaction . once the action is written in terms of the expansion of the graviton field , all indices are understood to be lowered or raised using the minkowski metric @xmath30 . we also require the expansion of the inverse metric and square root of the determinant of the metric tensor @xmath31 then , expanding in powers of @xmath28 , we find @xmath32\nonumber\\ \sqrt{-g}{\cal l}_m^{(2)}&=&{\kappa^2\over 2 } \hspace*{0.5pt } \bigg[\frac{1}{4 } \big(h^2 - 2 h_{\mu \nu } h^{\mu \nu}\big ) \bigg(\frac{1}{2 } \partial_\alpha \phi \partial^\alpha \phi - \frac{1}{2 } m^2 \phi^2\bigg)\nonumber\\ & & \hspace*{13pt } + \bigg(h^{\mu \alpha } h_\alpha^\nu - \frac{1}{2 } h h^{\mu \nu}\bigg ) \partial_\mu \phi \partial_\nu \phi \bigg]\end{aligned}\ ] ] where @xmath33 represents the trace and the one- and two - graviton vertices are identified as @xmath34\nonumber\\ { } ^{0 } \tau^{(2)}_{\mu\nu,\rho\sigma}(p_2 , p_1 , m)\hspace*{-7.5pt}&=\hspace*{-7.5pt } & \frac{i\kappa^2}{2}\bigg[2 i_{\mu\nu,\kappa\zeta}{i^\zeta}_{\lambda,\rho\sigma}(p_1^\kappa p_2^\lambda+p_1^\lambda p_2^\kappa ) \nonumber\\ & & { } \hspace*{14pt } - \hspace*{-1pt } ( \hspace*{-0.5pt } \eta_{\mu\nu}i_{\kappa\lambda,\rho\sigma } \hspace*{-1.5pt } + \hspace*{-1.5pt } \eta_{\rho\sigma}i_{\kappa\lambda,\mu\nu}\hspace*{-0.5pt } ) p_1^\kappa p_2^\lambda \hspace*{-1pt } - \hspace*{-1pt } p_{\mu\nu , \rho\sigma } ( p_1 \hspace*{-1.5pt } \cdot \hspace*{-1.3pt } p_2 \hspace*{-1.8pt } - \hspace*{-1.5pt } m^2 ) \hspace*{-1pt } \bigg ] \label{eq : tp}\end{aligned}\ ] ] where we have defined @xmath35 the purely gravitational dynamics are derived from the einstein - hilbert action @xmath36 where higher dimensional operators such as @xmath37 , which are needed when performing renormalization , are not relevant here @xcite . since general relativity is invariant under _ local _ coordinate transformations , it is a gauge theory and one must deal with the subtleties that arise in the quantization of gauge theories we have to perform gauge fixing . the procedure works analogously to gauge fixing in yang - mills theories . furthermore , we will make use of the background field method , which provides a powerful organizational scheme for the quantization of the effective field theory of gravity : keeping the background metric general instead of restricting to the flat minkowski metric , we use the expansion @xmath38 where @xmath39 is the classical background metric ( or field ) and @xmath40 is the quantum field . a gauge fixing condition is only imposed on the quantum field @xmath40 , leaving the general covariance of the background unaffected . this procedure has the advantage of ensuring that the resulting theory can be renormalized , since the loop expansion then has the same symmetry properties as the action . moreover , the background field method greatly simplifies calculations involving graviton loops . gravitons running in loops must be derived from from an expansion involving the quantum field @xmath40 whereas gravitons that are _ not _ within a loop may be derived from expanding the background field @xmath41 where @xmath42 denotes an `` external '' graviton , _ i.e. _ , a graviton that is not inside a loop . at the one loop level , at most two gravitons involved in a vertex are propagating within a loop , which allows us to use a gauge fixing condition _ linear _ in the quantum field @xmath40 and greatly simplifies the derivation of both the triple graviton vertex and the vertex that couples one graviton to the ghost fields . in order to fix the gauge , we will use the harmonic gauge @xmath43 where @xmath44 denotes the covariant derivative on the background metric . this condition leads to an additional gauge fixing piece of the action @xmath45 as well as the ghost action @xmath46 where @xmath47 is the ghost field that annihilates a ghost particle while @xmath48 creates a ghost particle . for each closed ghost loop . ] now we are in the position to derive the feynman rules for the effective field theory of gravity . the complete quantum gravitational action consists of three components @xmath49 and we will illustrate the use of the background field method during the derivations of the feynman rules . when deriving the graviton propagator we expand the action to second order in the quantum fields @xmath40 and to zeroth order in the external gravitons @xmath42 and the ghosts , yielding @xmath50 we obtain the ghost propagator expanding the action to second order in the ghost fields and to zeroth order in the gravitons , whereby @xmath51 our triple graviton vertex is obtained by expanding to second order in the quantum fields @xmath40 , to first order in the background gravitons @xmath42 , and to zeroth order in the ghost fields and reads @xmath52\nonumber\\ & & \hspace*{17pt } + 2q_\lambda q_\sigma \hspace*{-1pt } \bigg[i^{\lambda\sigma,}{}_{\alpha\beta}i^{\mu\nu,}{}_{\gamma\delta } + i^{\lambda\sigma,}{}_{\gamma\delta}i^{\mu\nu,}{}_{\alpha\beta } \nonumber \\ & & \hspace*{54pt } -i^{\lambda\mu,}{}_{\alpha\beta}i^{\sigma\nu,}{}_{\gamma\delta } -i^{\sigma\nu,}{}_{\alpha\beta}i^{\lambda\mu,}{}_{\gamma\delta}\bigg]\nonumber\\ & & \hspace*{17pt } + \hspace*{-1pt } \bigg [ q_\lambda q^\mu(\eta_{\alpha\beta}i^{\lambda\nu,}{}_{\gamma\delta } \hspace*{-1pt } + \hspace*{-1pt } \eta_{\gamma\delta}i^{\lambda\nu,}{}_{\alpha\beta } ) \hspace*{-2pt } + \hspace*{-1pt } q_\lambda q^\nu(\eta_{\alpha\beta}i^{\lambda\mu,}{}_{\gamma\delta } \hspace*{-1pt } + \hspace*{-1pt } \eta_{\gamma\delta}i^{\lambda\mu,}{}_{\alpha\beta})\nonumber\\ & & \hspace*{24pt } - q^2 \hspace*{-0.6pt } ( \hspace*{-0.5pt } \eta_{\alpha\beta}i^{\mu\nu,}{}_{\gamma\delta } \hspace*{-1.5pt } + \hspace*{-1.5pt } \eta_{\gamma\delta } i^{\mu\nu,}{}_{\alpha\beta } \hspace*{-0.5pt } ) \hspace*{-2.3pt } - \hspace*{-1.5pt } \eta^{\mu\nu } q^\lambda q^\sigma \hspace*{-0.6pt } ( \hspace*{-0.5pt } \eta_{\alpha\beta } i_{\gamma\delta,\lambda\sigma } \hspace*{-2pt } + \hspace*{-1.5pt } \eta_{\gamma\delta } i_{\alpha\beta,\lambda\sigma}\hspace*{-0.5pt } ) \hspace*{-1.5pt } \bigg]\nonumber\\ & & \hspace*{17pt } + \hspace*{-1pt } \bigg[2q^\lambda \big(i^{\sigma\nu,}{}_{\gamma\delta } i_{\alpha\beta,\lambda\sigma}k^\mu + i^{\sigma\mu,}{}_{\gamma\delta}i_{\alpha\beta,\lambda\sigma}k^\nu \nonumber\\ & & \hspace*{50pt } -i^{\sigma\nu,}{}_{\alpha\beta}i_{\gamma\delta,\lambda\sigma}(k+q)^\mu - i^{\sigma\mu,}{}_{\alpha\beta}i_{\gamma\delta,\lambda\sigma}(k+q)^\nu \big ) \nonumber\\ & & \hspace*{24pt } + q^2(i^{\sigma\mu,}{}_{\alpha\beta}i_{\gamma\delta,\sigma}{}^\nu + i_{\alpha\beta,\sigma}{}^\nu i^{\sigma\mu,}{}_{\gamma\delta } ) \nonumber \\ & & \hspace*{24pt } + \eta^{\mu\nu}q^\lambda q_\sigma ( i_{\alpha\beta,\lambda\rho}i^{\rho\sigma,}{}_{\gamma\delta } + i_{\gamma\delta,\lambda\rho}i^{\rho\sigma,}{}_{\alpha\beta})\bigg]\nonumber\\ & & \hspace*{17pt } + \hspace*{-1pt } \bigg[\hspace*{-0.5pt } \big(k^2 \hspace*{-1pt } + \hspace*{-1pt } ( k \hspace*{-1pt } + \hspace*{-1pt } q)^2 \big ) \hspace*{-3pt } \left ( \hspace*{-2pt } i^{\sigma\mu,}{}_{\alpha\beta}i_{\gamma\delta,\sigma}{}^\nu \hspace*{-1pt } + \hspace*{-1pt } i^{\sigma\nu,}{}_{\alpha\beta}i_{\gamma\delta,\sigma}{}^\mu \hspace*{-1pt } - \hspace*{-1pt } { 1\over 2}\eta^{\mu\nu}p_{\alpha\beta,\gamma\delta } \hspace*{-2pt } \right ) \nonumber\\ & & \hspace*{24pt } - \big((k+q)^2\eta_{\alpha\beta}i^{\mu\nu,}{}_{\gamma\delta}+k^2\eta_{\gamma\delta } i^{\mu\nu,}{}_{\alpha\beta}\big)\bigg]\bigg\}\end{aligned}\ ] ] where the graviton with" +"the object of interest for 1-particle inclusive leptoproduction , the hadronic tensor , is given by & & 2mw_^(h ) ( q ; p s ; p_h s_h ) = ( 2)^4 ^4 ( q + p - p_x - p_h ) + & & |j_(0)|p_x ; p_h s_h p_x ; p_h s_h |j_(0)|p s , where @xmath0 and @xmath1 are the momenta and spin vectors of target hadron and produced hadron , @xmath2 is the ( spacelike ) momentum transfer with @xmath3 = @xmath4 sufficiently large . the kinematics is illustrated in fig . [ fig1 ] , where also the scaling variables are introduced . = 8.5 cm @xmath5 @xmath6 for inclusive scattering ( unpolarized lepton and hadron , @xmath7-exchange ) the most general symmetric part of the hadronic tensor is ] ] 2mw_s^(q , p ) = _ -g_^ f_1 + t^t^_f_l combined with the leptonic part , one obtains the cross section for unpolarized leptons off an unpolarized target = \ { ( 1-y + y^2 ) f_t + ( 1 -y ) f_l}. = 4.5 cm = 4.5 cm in order to calculate the hadronic tensor , a diagrammatic expansion is written down starting with the well - known handbag diagram ( see fig . [ fig2 ] , left ) , yielding the parton model results for the structure functions , & & f_t(x__b , q ) = f_1(x__b , q ) = _ a,|a e_a^2f_1^a(x__b ) , + & & f_l(x__b , q ) = 0 , expressed in terms of the quark distribution @xmath8 ( @xmath9 is the flavor index ) . the summation runs over quarks and antiquarks . the most general antisymmetric part of the hadronic tensor involves polarized leptons and hadrons and is for @xmath7-exchange given by 2mw_a^(q , p , s ) = _ -i_^ g_1 + i t_^[_^ ] s _ g_t with the longitudinal polarization @xmath10 and @xmath11 the transverse spin vector obtained with the help of @xmath12 . the cross section for polarized leptons of a longitudinally polarized target becomes = _ e \ { ( 1- ) g_1 -s__s^ g_t } , with the parton model results & & g_1(x__b , q ) = _ a,|a e_a^2g_1^a(x__b ) , + & & g_t(x__b , q ) = ( g_1+g_2)(x__b , q ) = _ a,|a e_a^2g_t^a(x__b ) . the function @xmath13 is the quark helicity distribution . the function @xmath14 is a higher twist distribution . proceeding to the 1-particle inclusive case for unpolarized lepton and hadron ] ] we obtain generally for the symmetric part of the hadronic tensor 2mw_s^(q , p , p_h ) & = & - g_^h_t + t^t^h_l + & & + t^\{h^}h_lt + 2h^h^+ g_^_tt , leading to the unpolarized cross section & & = x__bz_h\ { ( 1-y+y^2 ) h_t + ( 1-y)h_l + & & - ( 2-y)_h^h_lt + ( 1-y)2_h^h_tt } . we will come back to parton expressions for semi - inclusive structure functions later with emphasis on the azimuthal dependence , such as the @xmath15 and @xmath16 parts depending on the azimuthal angle between the lepton scattering plane and the production plane ( see fig . [ fig1 ] ) . limiting ourselves to unpolarized hadrons , the antisymmetric part of the hadronic tensor is 2mw_a^(q , p , p_h ) = - it^[h^]h^_lt , leading to the cross section for polarized leptons from an unpolarized target ( single spin asymmetry ) = _ ez_h_h^h^_lt . our aim in studying leptoproduction is the study of the quark and gluon structure of the hadronic target using the known framework of quantum chromodynamics ( qcd ) . thus , as a theorist the aim is to calculate the hadronic tensor @xmath17 by making a diagrammatic expansion . already at the simplest level ( fig . [ fig2 ] ) a problem is encountered , namely there are hadrons involved for which qcd does not provide rules . soft parts _ are identified that allow inclusion of hadrons in the field theoretical framework . luckily it turns out that for @xmath18 only a limited number of diagrams is needed . next , we look in more detail to the soft parts , such as appear for instance in the parton diagram . they can be written down in terms of quark and gluon fields as illustrated below . they are characterized by the fact that the momenta are _ soft _ with respect to each other . we have for the distribution part @xcite = 5 cm @xmath19 represented by _ ij(p , p , s)=d^4x e^ipxp , s|_j(0)_i(x)|p , s , and the fragmentation part @xcite = 4.0 cm @xmath20 represented by _ ij(k , p_h , s_h ) = _ xd^4x e^ikx 0|_i(x)|p_h , s_h;xp_h , s_h;x|_j(0)|0 . in order to find out which information in the soft parts @xmath21 and @xmath22 is important in a hard process one needs to realize that the hard scale @xmath23 leads in a natural way to the use of lightlike vectors @xmath24 and @xmath25 satisfying @xmath26 and @xmath27 = 1 . for 1-particle inclusive scattering one parametrizes the momenta @xmath28 comparing the power of @xmath23 with which the momenta in the soft and hard part appear one immediately is led to @xmath29 and @xmath30 as the relevant quantities to investigate . = 4.5 cm [ cols=""^,^,^,^ "" , ] hermiticity , parity and time reversal invariance ( t ) constrain the quantity @xmath31 and therefore also the dirac projections @xmath32}$ ] defined as @xmath33}(x,{\mbox{\boldmath $ p$}}_t ) & = & \int dp^- \,\frac{tr[\phi \gamma]}{2 } \nonumber \\ & = & \left . \int \frac{d\xi^-d^2{\mbox{\boldmath $ \xi$}}_t}{2\,(2\pi)^3}\ e^{ip\cdot \xi } \,\langle p , s\vert \overline \psi(0 ) \gamma \psi(\xi ) \vert p , s\rangle \right|_{\xi^+ = 0},\end{aligned}\ ] ] which is a lightfront ( @xmath34 = 0 ) correlation function . the relevant projections in @xmath21 that are important in leading order in @xmath35 in hard processes are @xmath36}(x,{{{{\mbox{\boldmath $ p$}}}_{_t } } } ) & = & f_1(x , { { { { \mbox{\boldmath $ p$}}}_{_t}}}^2 ) - \frac{\epsilon_t^{ij}k_{t i } s_{t j}}{m } \,f_{1t}^\perp(x,{\mbox{\boldmath $ k$}}_t ) , \\ \phi^{[\gamma^+ \gamma_5]}(x,{{{{\mbox{\boldmath $ p$}}}_{_t } } } ) & = & \lambda\,g_{1l}(x , { { { { \mbox{\boldmath $ p$}}}_{_t}}}^2 ) + \frac{({{{{\mbox{\boldmath $ p$}}}_{_t}}}\cdot{{{{\mbox{\boldmath $ s$}}}_{_t}}})}{m}\,g_{1t}(x , { { { { \mbox{\boldmath $ p$}}}_{_t}}}^2 ) \\ \phi^ { [ i \sigma^{i+ } \gamma_5]}(x,{{{{\mbox{\boldmath $ p$}}}_{_t } } } ) & = & s_t^i\,h_1(x , { { { { \mbox{\boldmath $ p$}}}_{_t}}}^2 ) + \frac{\lambda\,p_t^i}{m } \,h_{1l}^\perp(x , { { { { \mbox{\boldmath $ p$}}}_{_t}}}^2 ) \nonumber \\ & & { } - \frac{\left(p_t^i p_t^j + \frac{1}{2}{{{{\mbox{\boldmath $ p$}}}_{_t}}}^2g_t^{ij}\right ) s_{tj}}{m^2}\,h_{1t}^\perp(x , { { { { \mbox{\boldmath $ p$}}}_{_t}}}^2 ) \nonumber \\ & & { } - \frac{\epsilon_t^{ij } k_{t j}}{m}\,h_1^\perp(x,{\mbox{\boldmath $ k$}}_t),\end{aligned}\ ] ] here @xmath37 , @xmath38 and @xmath39 is the spin - component projected out by @xmath40 = @xmath41 , they satisfy @xmath42 = 0 . the tensor @xmath43 . = 1.8 cm = 4.2 cm = 3.1 cm = 3.1 cm = 4.2 cm = 3.1 cm = 3.1 cm = 3.1 cm all functions appearing above can be interpreted as momentum space densities , as illustrated in fig . the ones denoted @xcite @xmath44 involve the operator structure @xmath45 , where @xmath46 with @xmath47 . this operator projects on the socalled good component of the dirac field , which can be considered as a _ free _ dynamical degree of freedom in front form quantization . it is precisely in this sense that partons measured in hard processes are free . the functions @xmath48 and @xmath49 appearing above are differences of densities involving good fields , but in addition projection operators @xmath50 and @xmath51 , all of which commute with @xmath52 . to be precise for the functions @xmath48 one has @xmath53 while in the case of @xmath49 one has @xmath54 . the functions @xmath55 and @xmath56 are special . applying time - reversal shows that these functions should disappear from the parametrization of the matrix element @xmath21 . however , application of time - reversal invariance for @xmath57-dependent functions involves a few tricky points related to poles in gluonic matrix elements @xcite and we decided here to take the purely phenomenological approach and keep these socalled t - odd functions . the functions describe the possible appearance of unpolarized quarks in a transversely polarized nucleon ( @xmath55 ) or transversely polarized quarks in an unpolarized hadron ( @xmath56 ) and lead to single - spin asymmetries in various processes @xcite . it is useful to remark here that flavor indices have been omitted , i.e. one has @xmath58 , @xmath59 , etc . at this point it may also be good to mention other notations used frequently such as @xmath60 , @xmath61 , @xmath62 , etc . these @xmath63-dependent functions are the ones obtained after integration over @xmath64 . the analysis of the soft part @xmath21 can be extended to other dirac projections . limiting ourselves to @xmath64-averaged functions one finds & & ^[1](x ) = e(x ) , + & & ^ [ ^i _ 5](x ) = g_t(x ) , + & & ^ [ i^+-_5 ] ( x ) = h_l(x ) . lorentz covariance requires for these projections on the right hand side a factor @xmath65 , which as can be seen from the parametrization of momenta produces a suppression factor @xmath66 and thus these functions appear at subleading order in cross sections . the constraints on @xmath21 lead to relations between the above higher twist functions and @xmath67-weighted functions @xcite , e.g. g_2 = g_t - g_1 = g_1t^(1 ) , where g_1t^(1)(x ) = d^2__tg_1t(x , _ _ t ) . we will use the index @xmath68 to indicate a @xmath69-moment of the above type . just as for the distribution functions one can perform an analysis of the soft part describing the quark fragmentation @xcite . the dirac projections are ^[](z,__t ) & = & dk^+ + & = & . _ x e^ik tr 0 ( x ) p_h , xp_h , x(0)0 |_^- = 0 . the relevant projections in @xmath22 that appear in leading order in @xmath35 in hard processes are for the case of no final state polarization , & & ^[^-](z,__t ) = d_1(z ,- z__t ) , + & & ^[i ^i- _ 5](z,__t ) = h_1^(z ,- the arguments of the fragmentation functions @xmath70 and @xmath71 are chosen to be @xmath72 = @xmath73 and @xmath74 = @xmath75 . the first is the ( lightcone ) momentum fraction of the produced hadron , the second is the transverse momentum of the produced hadron with respect to the quark . the fragmentation function @xmath70 is the equivalent of the distribution function @xmath76 . it can be interpreted as the probability of finding a hadron @xmath77 in a quark . noteworthy is here the appearance of the function @xmath71 , interpretable as the different production probability of unpolarized hadrons from a transversely polarized quark ( see fig . [ fig4 ] ) . it is the equivalent of the distribution function @xmath56 . for the matrix element @xmath22 involving out - states @xmath78 ( in contrast to the plane waves in @xmath21 ) , the appearance of these functions is completely natural , since final state interactions prohibit constraints from time - reversal invariance . also this function leads to single - spin asymmetries @xcite = 1.8 cm = 3.1 cm after @xmath79-averaging one is left with the functions @xmath80 and the @xmath81-weighted result @xmath82 . we summarize the full analysis of the soft part with a table of distribution and fragmentation functions for unpolarized ( u ) , longitudinally polarized ( l ) and transversely polarized ( t ) targets , distinguishing leading ( twist two ) and subleading ( twist three , appearing at order @xmath35 ) functions" +"the denomination `` quantum solid '' refers to crystals displaying marked quantum - mechanical effects @xcite . these include a kinetic energy per particle significantly above its classical value 3@xmath2/2 @xcite , as well as considerably more pronounced particle excursions away from their equilibrium ( lattice ) positions than observed in most solids . the latter assertion can be phrased quantitativey in terms of the so - called lindemann ratio @xcite @xmath3 , @xmath4 being the root - mean - square displacement of particles away from lattice sites , and @xmath5 the distance between nearest - neighboring sites . this ratio increases with temperature , and in most substances takes on a value close to 0.1 at melting ; however , in a highly quantal solid such as @xmath1he it can be as high as @xmath6 , even at temperature @xmath2=0 , as a result of the large zero - point motion resulting from the light mass of the atoms . indeed , for a long time the most commonly accepted explanation for the failure of he to solidify at low temperature , under the presure of its own vapour , has been that the large zero - point motion of its light atoms acts to destabilize the crystal phase ( this belief has been recently challenged @xcite ) . an interesting theoretical question remains that of the role played by quantum mechanics in the melting of solids made of light atoms or molecules . + helium is , of course , the archetypal quantum solid @xcite but sizable quantum effects have also been predicted and observed for solid parahydrogen ( _ p_-h@xmath7 ) . although its constituent particles are molecules of mass one half of that of a @xmath1he atom , _ p_-h@xmath7 is nonetheless a stronger crystal than helium at comparable thermodynamic conditions , owing to the depth of the attractive well of the intermolecular potential , roughly three times that between two helium atoms . for this reason , unlike helium parahydrogen is a crystal at @xmath2=0 ( even in reduced dimensions @xcite ) , and in many respects the behaviour of solid _ p_-h@xmath7 interpolates between that of a classical crystal and solid helium . it has been recently suggested , however , that the melting of a crystal of 2 may be driven primarily by quantum - mechanical effects @xcite . + both the mean kinetic energy per particle , as well as the mean square displacement @xmath8 around lattice sites , can be accessed experimentally by either x - ray or neutron scattering @xcite ; in particular , estimates of @xmath9 can be obtained through the measurement of the debye - waller factor @xcite . on the theoretical front , first principle @xcite calculations of both quantities can be carried out by means of quantum monte carlo ( qmc ) simulations ; thus , a comparison of theoretical results with experimental data represents a cogent test of the current theoretical understanding of the physics of the simplest quantum crystals , as well as of the most commonly adopted microscopic models thereof . + the most important theoretical assumptions built into the vast majority of qmc calculations are _ a _ ) the adoption of a pair potential to describe the interaction of atoms or molecules _ b _ ) the neglect of quantum - mechanical exchanges of indistinguishable particles . the use of pair potentials has been shown to afford a rather accurate theoretical description of energetic and structural properties of solid he @xcite ( even though the inclusion of three - body terms improves significantly the agreement with the experimental equation of state @xcite ) , as well as 2 @xcite . exchanges of indistinguishable particles are almost invariably neglected in most theoretical calculations of crystal properties , the main justification being the infrequency with which such exchanges occur @xcite , even in a highly quantal crystal like @xmath1he . + it has been suggested , however , that quantum - mechanical exchanges may play a _ major _ role in the stabilization of the bcc phase of solid @xmath0he . a significant test of this hypothesis would consist of a comparison of computed and measured values of @xmath9 in this system , as one of the most important consequences of quantum - mechanical exchanges is a much greater atomic mobility , resulting in more pronounced fluctuations around lattice sites than if exchanges were absent @xcite . + a detailed comparison of experimental and theoretical results for @xmath9 has been carried out for fcc and hcp @xmath0he and @xmath1he , at temperatures between 5 k and 35 k , yielding satisfactory agreement @xcite . to our knowledge , no microscopic calculations have been performed for the bcc phase of the two isotopes , which occurs at considerably lower temperatures and coexists with fluid phases whose physics is dominated by quantum exchanges . on the experimental side , we are only aware of measurements of the lindemann ratio in bcc @xmath1he . + in this paper we report results of qmc calculations of the mean square atomic excursions away from lattice positions in bcc @xmath1he and @xmath0he at the melting temperatures @xmath2=1.6 k ( @xmath1he ) and 0.65 k ( @xmath0he ) . we also computed the same quantity for the equilibrium hcp phase of 2 from a low temperature @xmath2=1 k , all the way to the melting temperature @xmath2=13.8 k. in all of our calculations pair potentials are used and quantum - mechanical exchanges neglected . we compute separately thermal and quantum - mechanical contributions to atomic and molecular displacements . + computed values of @xmath9 are found to be in excellent agreement with experiment for bcc @xmath1he ; for bcc @xmath0he our estimated value of the lindemann ratio @xmath10 is @xmath11 6.5% lower than existing theoretical estimates . in principle , there is no reason not to expect comparable accuracy for both isotopes . however , if particle exchanges are as prominent in this phase as suggested in ref . @xcite , it is possible that one may see a difference between the experimentally measured value and one predicted by a calculation neglecting atomic exchanges , as these are likely to result in a significant enhancement of the mobility of atoms in the crystal at melting . + the results for @xmath9 in hcp 2 show a clear dependence on temperature , of a magnitude that appears to be experimentally observable ; this is in qualitative and quantitative disagreement with recent measurements . we find that , while atomic excursions away from lattice sites in bcc he are largely quantum - mechanical in character , in 2 at melting thermal and quantum - mechanical contributions are very nearly equal in magnitude . thus , according to this criterion solid 2 may be regarded as neither completely `` quantum '' nor `` classical '' , but rather as a system sitting on the dividing line between the two physical behaviours . + we also report in this paper our estimates for the pressure and/or the mean kinetic energy per particle , and compare them with available experimental determinations . the remainder of this article is organized as follows : in sec . [ model ] we introduce the microscopic model and offer details of the calculation carried out in this work ; in sec . [ res ] we illustrate our results , outlining our conclusion in sec . [ conclusions ] . consistently with most theoretical studies , our systems of interest , namely solid helium and parahydrogen , are modeled as ensembles of @xmath12 point - like particles of spin zero , enclosed in a parallelepipedal cell of volume @xmath13 with periodic boundary conditions . the quantum - mechanical many - body hamiltonian is the following : @xmath14 here , @xmath15=6.0596 k@xmath16 for @xmath1he , 8.0417 k@xmath16 for @xmath0he and 12.031 k@xmath16 for 2 , while @xmath17 is the potential describing the interaction between two particles , atoms or molecules , assumed here to depend only on their relative distance . the results presented here for the helium isotopes were obtained using the aziz pair potential @xcite , whereas the silvera - goldman potential @xcite was used for 2 . it is worth mentioning that these are not the only potentials that have been used in previous simulation work , but it seems fair to state that they are the most commonly adopted . they have both been shown to afford rather accurate quantitative descriptions of the thermodynamics of the solid phase of helium and 2 . naturally , in principle a more accurate model would go beyond the simple pair decomposition , including , for instance , interactions among triplets ; however , published numerical work ( e.g. , on helium ) has given strong indications that three - body corrections , while significantly affecting the estimation of the pressure , have a relatively small effect on the structure and dynamics of the system , of interest here @xcite . the thermodynamic properties of the system , as modeled by the many - body hamiltonian ( [ one ] ) , were studied by means of numerical simulations , based on the continuous - space worm algorithm ( wa ) @xcite . this is a fairly well - established ( monte carlo ) methodology , based on r. p. feynman s path integral formulation of quantum statistical mechanics @xcite . it allows one to obtain essentially exact numerical estimates of thermodynamic properties of quantum many - body systems at finite temperature , directly from the microscopic hamiltonian . the reader is referred to ref . for a thorough description of the technique . the specific implementation utilized in this project is _ canonical _ , i.e. , we keep the number @xmath12 of particles fixed @xcite . other technical aspects of the calculations are common to any other qmc simulation scheme . the usual fourth - order high - temperature propagator was adopted here @xcite ; convergence of the estimates was observed for a time step @xmath18 k@xmath19 , for both he and 2 . because the computational cost was negligible , all estimates reported here were obtained using twice as small a time step , in order to be on the safe side . + as mentioned above , the sampling of quantum - mechanical exchanges of identical particle , in principle allowed by the methodology utilized here , is explicitly excluded , i.e. , we treat particles as _ distinguishable_. this is an excellent assumption for 2 in the temperature range explored here , whereas for he at the temperature of interest exchanges do occur , albeit rarely . the exclusion of exchanges is deliberate , as we are interested in assessing their possible importance through a comparison with experimental measurements ; however , it ought to be reminded that inclusion of exchanges in a fermi system like @xmath0he would be rendered much more complicated by the appearance of the well - known sign "" problem , plaguing any current qmc methodology . in the absence of exchanges , the wa is very similar to conventional path integral monte carlo @xcite , although the presence of an open world line ( path ) in the wa allows for direct computation of the one - body density matrix @xcite , for which however we do not report results here . + the calculations of the kinetic energy per particle and of the pressure , as well as of structural quantities such as the pair correlation function , are standard @xcite ; on the other hand , that of @xmath9 has been performed relatively infrequently so far , and for this reason we offer here a few relevant details , with the general remark that we largely duplicate the procedure illustrated in ref . . + the mean square displacement of a particle away from a lattice site @xmath9" +"galaxy groups dominate the overall mass and luminosity densities of the universe yet their properties are poorly understood in comparison to individual galaxies or rich galaxy clusters . until now galaxy groups have not been extensively used for cosmology largely because they are notoriously difficult to identify due to their small contrast with the field . however , with large redshift surveys it is now possible to identify substantial samples of galaxy groups . a sample of roughly 200 galaxy groups was identified in the canadian network for observational cosmology 2 ( cnoc2 ) redshift survey using an iterative friends - of - friends algorithm ( carlberg et al . the dynamical analysis of these groups indicated a rising mass - to - light ratio with radius . this suggests that groups are the scale where segregation begins to occur between mass and light . this effect could be due to dynamical friction , or to a large core radius which could indicate that dark matter has different properties from `` standard '' collisionless cold dark matter ( cdm ) . the cores of galaxies and clusters appear to be less cuspy than expected , which has prompted theoretical work in alternative dark matter models ( see discussion in governato et al . 2001 ) . the dark matter density profile has yet to be measured for galaxy groups . dynamical studies of groups are difficult because kinematic information is known for very few galaxies , and because equilibrium assumptions might not be valid . furthermore , these difficulties increase at large radii from the group center . weak gravitational lensing has proven invaluable in the analysis of single massive objects such as galaxy clusters ( hoekstra et al . 1998 ; mellier 1999 ) as well as in the statistical studies of individual galaxies ( brainerd , blandford & smail , 1996 ; hudson et al . 1998 ; fischer et al . 2000 ; sheldon et al . 2001 ; hoekstra et al . to date there has been only one weak lensing measurement of galaxy groups ( hoekstra et al . 2001 ) using a small subsample of the total cnoc2 galaxy group catalog . assuming that the dark matter halos of groups are well described by an isothermal sphere , we expect a tangential shear signal as follows @xmath8 where @xmath9 is the velocity dispersion of the halo , and d@xmath10 and d@xmath11 are the angular diameter distances to the source and between lens and source , respectively . the intent of this paper is to present the results of our weak lensing study of cnoc2 galaxy groups and to compare these results with those found from the dynamical measurements ( carlberg et al . 2001 ) and the weak lensing detection of hoekstra et al . we will also present the results when the sample of groups is split into two samples of `` rich galaxy groups '' and `` poor galaxy groups '' , divided by velocity dispersion . a second paper will follow with the results of galaxy - galaxy lensing in these fields and a maximum likelihood analysis of the shear . our galaxy group catalogs were generated using a friends - of - friends algorithm with the cnoc2 redshift survey data ( yee et al . 2000 ; carlberg et al . the cnoc2 area contains 4 fields well - spaced in right ascension and was intended to better understand the properties of field galaxies . the cnoc2 galaxy sample contains 6200 galaxies with redshifts to z of 0.7 . from this galaxy catalog a sample of 192 galaxy groups was identified . the average number of galaxies identified in each group is @xmath124 and the groups have a median redshift of 0.33 . the groups have a median dynamically determined velocity dispersion of 190 km s@xmath1 . for this project we observed the 4 central patches of the cnoc2 fields , where most of the galaxy groups are located . the observations were carried out mostly at the canada - france - hawaii telescope with 2 additional nights at the kitt peak national observatory mayall 4-m telescope . the fields were observed in b , v,@xmath13 , and @xmath14 . deep exposures ( @xmath124 hours ) were taken in the @xmath13 and @xmath14 bands , which were used for the lensing measurements . the characteristics of the data obtained are outlined in table 1 . cccccccc field & ra & dec & telescope & area & source density & median & no . of + & ( 2000 ) & ( 2000 ) & & sq.arcmin & ( no./sq arcmin ) & seeing & groups + 0223 & 36.51992 & 0.3116 & kpno & 1120 & 30 & 1.1 & 23 + 0920 & 140.95504 & 37.0861 & cfht & 1100 & 45 & 0.9 & 40 + 1447 & 222.4096 & 9.13883 & cfht & 1220 & 32 & 0.8 & 29 + 2148 & 327.8317 & -5.5586 & cfht & 1125 & 44 & 0.8 & 25 + gravitational lensing is usually limited by systematics and it is important to ensure no spurious shear is introduced in the stacking procedure . this can be achieved by carefully monitoring the astrometry over each input image that enters the stack . wide - field cameras in use today have larger distortions than earlier , smaller ccd cameras . this distortion must be properly mapped and corrected in order to ensure no artificial source of shear is imported during the stacking process . note , however , that group lensing is less affected by systematics than cosmic shear studies ( the weak lensing signal from the large scale structure in the universe ) . this is due to the random orientation of the galaxy - group pairs across the field , as opposed to looking for a preferred orientation as cosmic shear studies do . cosmic shear measurements use the patterns in the large - scale distortion field of background sources to map out the matter distribution in the universe . this signal is tiny and more susceptible to systematics than galaxy - galaxy or group - galaxy lensing where the shear signal is averaged in radial bins around each lens . in this analysis the image reduction and stacking was carried out using the iraf mosaic package mscred ( valdes , f.g . , 1997 ) . object catalogs were extracted from our stacked images using the imcat software , an implementation of the kaiser , squires and broadhurst ( 1995 , hereafter ksb ) method . this software is optimized for measuring the shapes of faint sources . the object detection algorithm works by smoothing the images using different sized filters and then detecting the `` peaks '' which are then added to the source catalog . for each detected object weighted quadrupole moments were measured and the resulting polarizations were calculated : @xmath15 the polarization measurements need to be corrected for the effects of seeing , camera distortion and psf anisotropy . these corrections to correct for these concerns have been discussed in ksb and luppino & kaiser ( 1997 ) with some improvements made by hoekstra et al . ( 1998 and 2000 ) . the techniques work well for ground - based data where the psf is stable and not very anisotropic , and where the fields contain many stars which are used in the correction algorithms . the source catalogs are trimmed so that all stars are removed . the stars can easily be located by comparing magnitude and half light radius . we kept only those objects for which the half light radii were greater than 1.2 times the stellar psf , thus ensuring the contamination from stars in our source catalog is very small . the limiting magnitude of our images is approximately 25 in r@xmath16 . in the weak lensing analysis we used a source catalog of approximately 150 000 objects ( @xmath1240 per sq arcminute ) and a galaxy group catalog containing the 116 cnoc2 galaxy group centers that were within the area we observed . the faint members of the galaxy groups are included in the source catalog , but as shown by hoekstra et al . ( 2001 ) , this does not contaminate the final result . this is indicated by the fact that the number density of faint galaxies does not increase significantly towards the group center , thus faint group members are do not influence the final shear measurement . the source density of background objects is not sufficiently high to extract a signal from individual galaxy groups , except for the most massive groups , and so the galaxy groups must be stacked and the weak lensing signal measured around the stacked groups . the source galaxies around the stacked galaxy group were divided into radial bins and the average distortion was calculated in each bin . the component of the average distortion tangential to the group center is the weak lensing signal and is displayed in figure 1a . the tangential shear is plotted in physical bins ( units of h@xmath1mpc ) since the redshift of each galaxy group is precisely known from the cnoc2 redshift survey . using equation ( 1 ) , the best fit isothermal sphere to the average tangential shear profile yielded an einstein radius of 088@xmath0013 . we can alternatively fit the tangential shear data with a navarro , frenk and white ( nfw ) dark matter profile ( navarro , frenk & white , 1996 ) . this density profile , which has been observed to fit mass distributions well over a wide range of scales , is given by @xmath17 where @xmath18 is the critical density for closure of the universe . the scale radius , @xmath19 , is defined as @xmath20 where c is the dimensionless concentration parameter , and @xmath21 is the characteristic over - density of the halo . the tangential shear signal @xmath22 as a function of radius @xmath23 for a nfw halo is given by ( wright & brainerd , 2000 ) . we use the tangential shear data to do a one - parameter fit to the nfw profile , while assuming a reasonable value for the concentration parameter , c. based on the high resolution numerical simulations of bullock et al . ( 2001 ) , a concentration parameter of @xmath1210 was used as an estimate for galaxy group scales . the best fit nfw profile can be seen as the dashed line in fig 1a . over the scales where we can measure the weak lensing signal the nfw profile and the isothermal sphere are very similar and are both good fits to the data . the similarity of these two models at the galaxy group mass scale is expected from models ( wright & brainerd , 2000 ) . a common systematic test employed in gravitational lensing is to measure the signal when the phase of the distortion is increased by @xmath24 . if the measured tangential distortion is due to gravitational lensing the rotated signal should be consistent with 0 as is shown in figure 1b . in addition to the standard systematic test , we also measured the signal around random points in the field . this test yielded no signal which indicates the results plotted in figure 1a are indeed due to gravitational lensing by the groups . in order to relate our estimate of the einstein radius to the average velocity dispersion of the groups , the redshift distribution of the background sources must be understood . the strength of the gravitational lensing signal as a function of redshift is characterized by the parameter @xmath25 which is defined as @xmath25=max@xmath26 $ ] where @xmath27 is the angular diameter distance between the lens and the source and @xmath28 is the angular diameter distance from the" +"ground states of quantum systems with many constituents are typically entangled . in a similar manner as one can identify characteristic length scales of correlation functions , quantum correlations are expected to exhibit some general scaling behavior , beyond the details of a fine - grained description . such characteristic features provide a physical picture that goes beyond the specifics of the underlying microscopic model . a central question of this type is the following : if one distinguishes a certain collection of subsystems , representing some spatial region , of a quantum many - body system in a pure ground state , the state of this part will typically have a positive entropy , reflecting the entanglement between this region and the rest of the system @xcite . this degree of entanglement is certainly expected to depend on the size and also on the shape of the region . yet , how does the degree of entanglement specifically depend on the size of the distinguished region ? in particular , does it scale as the volume of the interior which is meant to be the number of degrees of freedom of the interior ? or , potentially as the area of the boundary , i.e. , the number of contact points between the interior and the exterior ? this paper provides a detailed answer to the scaling behavior of the entanglement of regions with their exterior in a general setting of harmonic bosonic lattice systems and provides a comprehensive treatment of upper bounds on these quantities . we find that in arbitrary spatial dimensions the degree of entanglement in terms of the von neumann entropy scales asymptotically as the area of the boundary of the distinguished region . this paper significantly extends the findings of ref.@xcite on harmonic bosonic lattice systems : there , the area - dependence of the geometric entropy has been proven for cubic regions in non - critical harmonic lattice systems of arbitrary dimension with nearest - neighbor interactions , corresponding to discrete versions of klein - gordon fields . in this paper we extend our analysis to a general class of finite - ranged harmonic interactions and also take regions of arbitrary shape into account . for thermal gibbs states , the entropy of a reduction is longer a meaningful measure of entanglement . instead , an area - dependence for an appropriate mixed - state entanglement measure , the distillable entanglement , is established . also , an analogous statement holds for classical correlations in classical systems . the area - dependence is even found in certain cases where one can prove the divergence of the two - point correlation length . this demonstrates that this previously conjectured dependence between area and entanglement is valid under surprisingly general conditions . the presented analysis will make use of methods from the quantitative theory of entanglement in the context of quantum information science @xcite . it has been become clear recently that on questions about scaling of entropies and degrees of entanglement albeit often posed some time ago new light can be shed with such methods @xcite . in this language , quantum correlations are sharply grasped in terms of rates that can be achieved in local physical transformations . to assess quantum correlations using novel powerful tools from quantum information and to relate them to information - theoretical quantities constitutes an exciting perspective . in the context of quantum field theory , such questions of scaling of entropies and entanglement have a long tradition under the keyword of geometric entropy . in particular , work on the geometric entropy of free klein - gordon fields was driven in part by the intriguing suggested connection @xcite to the bekenstein - hawking black hole entropy @xcite . in seminal works by bombelli et al . @xcite and srednicki @xcite the relation between the entropy and the boundary area of the region has been suggested and supplemented with numerical arguments . this connection has been made more specific using a number of different methods . in particular , for half spaces in general and intervals in the one - dimensional case , the problem has been assessed employing methods from conformal field theory , notably @xcite , based on earlier work by cardy and peschel @xcite , and by cardy and calabrese @xcite . in one - dimensional non - critical chains , one observes a saturation of the entanglement of a distinguished block , as was proven analytically for harmonic chains @xcite and was later observed for non - critical spin chains numerically @xcite and analytically @xcite . in turn , in critical systems systems , one often but not always finds a logarithmically diverging entropy @xcite . in case of a model the continuum limit of which leads to a conformal field theory , the factor of the logarithmically diverging term is related to the central charge of the conformal field theory . the findings of the present paper and of the above - mentioned results motivate further questions concerning the general area - dependence of the degree of entanglement , for example in fermionic systems @xcite . in particular , the connection between the geometric entropy fulfilling no area law and the correlated quantum many - body system being critical is not fully understood yet . this is particularly true for the interesting case of more than one - dimensional quantum systems . this paper is structured as follows . we start , in section [ major ] , with a presentation of the major results of the paper . in section [ prelims ] we define our notation and recall some basics on harmonic lattice systems . section [ bounds ] provides a general framework of upper and lower bounds for entanglement measures , expressed in terms of the spectrum of the hamiltonian and two - point correlation functions . this analysis is performed both for the case of the ground state as well as for mixed gibbs states . of particular interest are hamiltonians with finite - ranged interactions in section [ sectionfiniteranged ] . for such hamiltonians , we first study the behavior of the two - point correlation functions , then the entanglement bounds . in section [ nomore ] , discussing the gibbs state case , we determine temperatures above which there is no entanglement left . a class of examples of hamiltonians which exhibit a divergent two - point correlation length in their ground state , but an area - dependence of the entanglement is presented in section [ divergent ] and expressed in analytical terms . the specific case of hamiltonians the interaction part of which can be expressed as a square of a banded matrix is discussed in section [ thasquared ] . in this case , very explicit expressions for entanglement measures can be found . we then consider , in section [ classical ] , the case of classical correlations in classical harmonic systems with arbitrary interaction structure . interestingly , this case is related to the quantum case for squared interactions in the sense of section [ thasquared ] . finally , we summarize what has been achieved in the present paper , and present a number of open questions in this context . throughout the whole paper we will consider harmonic subsystems on a @xmath0-dimensional cubic lattice @xmath1^{\times d}$ ] . the system thus has @xmath2 canonical degrees of freedom . the central question of this work will be : how does the degree of entanglement of a distinguished region @xmath3 with the rest @xmath4 scale with the size and shape of @xmath5 ? ^{\times 2}$ ] with a distinguished ( shaded ) region @xmath5 , consisting of @xmath6 degrees of freedom . oscillators representing the exterior @xmath4 are shown as , whereas pairs belonging to the surface @xmath7 of the region are marked by lines ( ) . ] we define the volume @xmath6 and surface @xmath7 of the distinguished region @xmath5 as @xmath8 where @xmath9 defines the @xmath10-norm distance for vectors @xmath11 that specify the position of oscillators on the @xmath0-dimensional lattice . more specifically , @xmath7 is the number of contact points , that is , the number of pairs of sites of @xmath5 and @xmath12 that are immediately adjacent . note that the distinguished region @xmath5 may have arbitrary shape and does not have to be contiguous . for the pure ground state @xmath13 , we will study the entropy of entanglement of @xmath3 given by @xmath14 where @xmath15 $ ] is the von neumann entropy of a state @xmath16 and @xmath17 $ ] denotes the reduced state associated with the degrees of freedom of the interior @xmath5 . for the pure ground state , this entropy of entanglement is identical to both the distillable entanglement and the entanglement cost . for pure states , it is indeed the unique asymptotic measure of entanglement . for gibbs states , in turn , we have to study a mixed - state entanglement measure , as the entropy of a subsystem no longer meaningfully quantifies the degree of entanglement . we will bound the rate at which maximally entangled pairs can be distilled , i.e. , the distillable entanglement @xmath18 . clearly , @xmath19 for zero temperature . we will subsequently suppress the index @xmath20 for notational clarity . we derive the following properties of @xmath21 and @xmath22 : _ _ * for @xmath0-dimensional harmonic lattice systems , we derive general upper and lower bounds to @xmath23 for pure ground states and to @xmath24 for gibbs states with respect to a temperature @xmath25 . these bounds are expressed entirely in terms of the potential matrix and stated in eqs . ( [ upperboundfinitet ] ) , ( [ upperboundzerot ] ) , and ( [ lowerbound ] ) . a necessary condition for the following results to hold is that the spectral condition number @xmath26 of the coupling matrix @xmath27 satisfies @xmath28 for some @xmath29 independent of @xmath5 and @xmath12 . _ _ * for nearest - neighbor interactions and the ground state , the entropy of entanglement @xmath21 scales as the surface area @xmath7 of @xmath5 . more specifically , there exist numbers @xmath30 independent of @xmath12 and @xmath5 such that @xmath31 this is stated in eqs . ( [ finiteupperbound ] ) and ( [ nearestlowerbound ] ) . note that the specific case of cubic regions @xmath32^{\times d}$ ] has already been proven in the shorter paper ref.@xcite . * for general finite - ranged harmonic interactions meaning arbitrary interactions which are strictly zero after a finite distance the entropy of entanglement @xmath21 of the ground state scales at most linearly with the surface area of @xmath5 : there exists a @xmath29 independent from @xmath12 and @xmath5 such that @xmath33 this is expressed in eq . ( [ finiteupperbound ] ) . * for gibbs states with respect to a temperature @xmath25 and general finite - ranged interactions the distillable entanglement @xmath34 scales at most linearly with the surface area of @xmath5 , so @xmath35 with @xmath36 being independent of @xmath12 and @xmath5 , see again eq . ( [ finiteupperbound ] ) , which applies for any temperature . we also determine temperatures above which the entanglement is strictly zero , see eq . ( [ nomoretemp ] ) . * we construct a class of hamiltonians the ground state of which exhibit an infinite two - point correlation length , for which the entropy of entanglement @xmath21 scales provably at most linearly in the boundary area . this is stated in eq . ( [ divergenceexample ] ) . * for interactions that are specified by potential matrices @xmath27 ( see eq . ( [ potmat ] ) ) that can be written as @xmath37 with @xmath38 corresponding to a finite - ranged interaction , we determine the entropy of entanglement . this is made" +"x - ray flux variability has long been known to be a common property of active galactic nuclei ( agn ) . ariel v and heao-1 first revealed long term ( days to years ) variability in agn ( e.g. marshall , warwick & pounds 1981 ) . it was not until the long - duration and uninterrupted observations of _ exosat _ that rapid ( thousands of seconds ) variability was also established as common in these sources . x - ray flux variations are observed on timescales from @xmath1 a thousand seconds to years and amplitude variations of up to an order of magnitude are observed in the @xmath1 0.1 - 10 kev band ( also see review by turner 1992 and references therein ) . barr & mushotzky ( 1986 ) suggested the flux - doubling timescale of an agn to be inversely proportional to its luminosity , both properties measured in the hard x - ray regime . the use of `` doubling timescale '' was a somewhat unsatisfactory quantification of the x - ray variability as , for many sources , this had to be derived by extrapolation of lower amplitude events . lawrence & papadakis ( 1993 ) confirmed the variability - luminosity relationship , quantifying variations seen in light curves by using the timescale above which the integrated rms variation should be 10% . green , mchardy and lehto ( 1993 ) also confirmed the correlation using the `` normalized variability amplitude '' and further , suggested sources with steeper x - ray spectra showed the highest amplitude of variability , perhaps due to a lower contribution from a reprocessed component . the existence of a correlation between x - ray variability and spectral slope was supported by the work of koenig , staubert & wilms ( 1997 ) , using a different quantification of x - ray flux variability . boller ( 1996 ) examined the `` variation timescale '' as a function of luminosity , concluding the high amplitude of variability observed in narrow - line seyfert 1 galaxies to be inconsistent with scattering in an extended region , like that suggested for seyfert 2 galaxies . nandra 1997a ( n97a ) initiated use of `` excess - variance '' , @xmath2 to quantify the x - ray variability of agn ( see below ) . this quantity had been previously used in analysis of the ultraviolet time series of agn where edelson , krolik & pike ( 1990 ) found an anticorrelation between excess - variance and luminosity . using excess - variance , n97a found an inverse correlation between x - ray variability ( sampled using 128 s bins ) and luminosity for a sample of seyfert 1 galaxies with predominantly broad permitted lines . fiore et al . ( 1998 ) used _ rosat _ hri observations of a sample of quasars to examine correlations between the ( soft ) x - ray parameters of excess - variance , spectral index and luminosity , finding steep - spectrum , narrow - line quasars to show larger amplitude of x - ray variability in the 0.1 2 kev band than the flat - spectrum broad - line quasars . we recognize that there is a continuous distribution of optical line widths in seyfert 1 galaxies , and any attempt to split these into narrow - line and broad - line seyfert 1s is arbitrary . however , for convenience we do make such a split here by referring to objects with fwhm h@xmath3 km / s as narrow - line seyfert 1s ( nlsy1s ) and objects with fwhm h@xmath4 km / s as broad - line seyfert 1s ( blsy1s ) . this is purely to facilitate a concise discussion of the different regimes within the seyfert 1 distribution . the nlsy1 ton s180 was found to lie significantly above the correlation established for the n97a sample ( turner 1998 ) and also showed energy - dependent variability . the ton s180 result indicated that analysis of a sample including a significant number of nlsy1s may yield further insight into the physical processes at work in agn . this paper presents a timing analysis of 79 observations of 36 seyfert 1 galaxies . our sample consists of seyfert 1 galaxies available from the advanced satellite for cosmology and astrophysics ( _ asca _ ) archive up to november 1998 . the purpose of this investigation was to expand upon the x - ray timing results presented in n97a , and to search for confirmation of some correlations between hard x - ray and optical parameters , suggested by previous works ( above ) . in particular , we aimed to determine whether the established luminosity - variability correlation would alter when seyfert galaxies covering the full observed range of permitted line widths were considered . the objects presented here do not form a complete sample . nevertheless we suggest the results from this large collection of objects provides important new insight into the agn phenomenon . _ asca _ has two solid - state imaging spectrometers ( siss ; burke 1994 ) and two gas imaging spectrometers ( giss ; ohashi 1996 ) yielding data over an effective bandpasses @xmath10.510 kev . the data presented here were systematically reduced in the same way as the seyfert galaxies presented in n97a , using source events within extraction cells of radii 4.8 and 6.6 arcmin for the sis and gis data , respectively . in the timing analysis we used only data from the sis instruments . we required that time series included in our analysis have at least 20 counts per time bin , and at least 20 bins in the final light curve . to increase the signal - to - noise ratio , we combined the sis0 and sis1 detectors requiring all time bins to be at least 99% exposed . the background level was not subtracted from these light curves . the excess - variance quantifies amplitude of variability in excess of that expected from statistical fluctuations in the background level . for each dataset we verified that the background light curve did not contain any significant trends . n97a use a 128s time bin for the light curve analysis . however , many of our agn are faint , and analysis using a 128 s time bin would have lead to the exclusion of many potentially interesting sources . we found 256 s to be the optimum bin size for inclusion of most of the available data ( use of longer integration times would have resulted in too few bins for many datasets ) . as noted above , n97a introduced the use of the quantity normalized excess - variance , @xmath2 for analysis of time series . following that paper we designate the count rates for the @xmath5 points in each light curve as @xmath6 , with errors @xmath7 . we further define @xmath8 as the unweighted , arithmetic mean of the @xmath6 . then : @xmath9\ ] ] the error on @xmath2 , is given by @xmath10 where : @xmath11-\sigma^{2}_{\rm rms}\mu^2 \big\}^2\ ] ] i.e. the variance of the quantity @xmath12 . ( note there was a typographical error in n97a in that the equation for the error on @xmath2 should have had the quantity inside the summation squared , as shown here ) . we refer the reader to n97a for a discussion of the merits of using this quantity for timing analysis . we note that for perfect comparison between sources , the excess - variance should be calculated using observations of the same duration ( @xmath13 ) . however , in practice this would limit the analysis by reducing the number of sequences we could consider , or would require truncation of light curves to match the shortest observation . we note many of our light curves were constructed from observations of duration close to 50 ks . our analysis includes observations both a factor of 2 smaller and larger than this . as the duration of an observation is random with respect to the parameters of interest then the effect of allowing a range of observation durations is to introduce scatter , which could hide some weak correlations but which should not introduce false correlations ( because @xmath13 is not correlated with @xmath14 , luminosity or fwhm h@xmath0 ) . we recalculated @xmath2 for the n97a sample of objects and all the new data presented here using 256 s time bins . table 1 shows the datasets used in our analysis . the following sequences were also analyzed , but failed to meet our criteria for counts per bin and/or number of bins in the final light curve : fairall-9 ( 73011050 ) ; ngc 4151 ( 70000000 , 70000010 , 71019030 , 71019000 ) ; ngc 6814 ( 70012000 ) ; mrk 509 ( 74024000 , 74024010 , 74024020 ) ; ngc 7469 ( 71028000 , 71028030 , 71028010 ) ; mcg 2 - 28 - 22 ( 70004000 ) ; eso 141-g55 ( 72026000 ) ; pg1211@xmath15 ( 70025000 ) ; mrk 957(75057000 ) and mrk 507(74033000 ) . the results are shown in figure 1a . the dark squares denote nlsy1s , blsy1s are denoted by a simple cross . error bars are @xmath16 . compared to the n97a sample , we have most notably added a significant number of objects with relatively narrow permitted lines and a number of points at the high luminosity end of the distribution ( with multiple observations of mrk 509 and fairall-9 ) . examination of figure 1a shows that there remains a significant anticorrelation between @xmath2 and luminosity ( a spearman - rank correlation coefficient of -0.683 is obtained , significant at @xmath17% confidence ) . however there is a much greater degree of scatter in the correlation than in that shown by n97a . it is evident that this is predominantly due to the inclusion of a relatively large number of nlsy1 objects . this was expected , based upon the ton s180 result ( turner 1998 ) and was suggested by the results of boller ( 1996 ) . this result has also been found in a large independent study of nlsy1s ( leighly et al . this scatter suggests that @xmath2 has a strong dependence on fwhm h@xmath0 in addition to the dependence on luminosity . this does not weaken the dependence of @xmath2 on luminosity , in the sense that it appears that objects with similar values of fwhm h@xmath0 still show a correlation between @xmath2 and luminosity . nlsy1s are known to be steep , even in the _ asca _ bandpass ( brandt 1997 ) , and _ rosat _ data showed them to be generally highly variable x - ray sources ( e.g. boller 1996 , 1997 ; forster & halpern 1996 ) . work by green ( 1993 ) showed a relationship between x - ray index and `` normalized variability amplitude '' in a sample of observations of agn . the green et al ( 1993 ) result was supported by the results of koenig et al ( 1997 ) . hence we examined the relationship between @xmath2 and the 2 - 10 kev photon index @xmath18 . the photon indices ( table 1 ) were determined in the ( rest - frame ) 210 kev band for each source , excluding the ( rest - frame ) 5 - 7.5 kev band which can contain significant photons from an fe k@xmath19 line ( confusing measurements of the hard x - ray index ) . the photon index was derived fitting the two sis and gis datasets simultaneously , and using background spectra extracted from source - free regions of the detectors . a small difference in the normalization of each instrument was allowed , to account for slight differences" +"catalogs of galaxy clusters with a large range of redshifts and cluster x - ray luminosities are an ideal basis for the test of cosmological parameters ( e.g. henry 2000 ; borgani et al . 2001 ) and the study of cluster formation and evolution . the bright and southern serendipitous high redshift archival rosat cluster ( sharc ) surveys provide a sample of clusters detected in rosat observations over two decades of x - ray luminosities ( 10@xmath2 l@xmath3erg / s ) with redshifts between 0.2 and 0.8 ( romer et al . 2000 ; collins et al . 1997 ; burke et al . 1997 ) . we present here preliminary results based on the follow - up observations of three of these selected galaxy clusters with xmm newton : rx j0256.5 + 0006 , rx j2237.0 - 1516 and rx j1200.8 - 0328 . for the first time , the new generation of x - ray observatory , like xmm - newton and _ chandra _ give capabilities to do precise spectroscopic and imaging analysis at the same time ( see e.g arnaud et al . 2002a ) . our analysis is based on the three epic cameras , mos1&2 and pn . throughout the paper , we use a cosmology with h@xmath4km / s / mpc , @xmath5 and @xmath6 . the error bars are given with a confidence level of 90% . all the data presented here are treated with the version 5.2 of the sas ( science analysis software ) . we select event patterns and time intervals of low background as described in majerowicz et al . table 1 shows the effective exposure time of our observations after flare rejection . this suggests that this cluster does not host a strong cooling flow . this was already seen in rx j1120.1 + 4318 , a relaxed cluster at z=0.6 ( arnaud et al . 2002a ) also found in the sharc survey . the global temperature for this cluster is 5.1@xmath1kev . its surface brightness profile is fitted by a @xmath7-model and the parameters are : @xmath7=0.64 and @xmath80.51@xmath9228kpc . arnaud , m. , neumann , d.m . , aghanim , n. , et al , 2001 , , 365 , l80 arnaud , m. , majerowicz , s. , lumb , d. , et al , 2002a , in press , astro - ph/0204306 arnaud , m. , 2002b , this issue borgani , s. , rosati , p. , tozzi , p. , et al , 2001 , , 561 , 13 burke , d.j . , collins , c.a . , sharples , r.m . , et al , 1997 , , 488 , l83 collins , c.a . , burke , d.j . , romer , a.k . , et al , 1997 , , 479 , l117 henry , j.p . , 2000 , apj , 534 , 565 lumb , d. , 2002 , xmm - soc - cal - tn-0016 majerowicz , s. , neumann , d.m . & reiprich , t.h . , 2002 , submitted to , astro - ph/0202347 neumann , d.m . & bhringer , h. 1997 , , 289 , 123 roettiger , k. , loken , c. & burns , j.o . , 1997 , , 109 , 307 romer , a.k . , nichol , r.c . , holden , b.p . , et al , 2000 , , 126 , 209 schindler , s. & mller , e. , 1993 , , 272 , 137 snowden , s.l . , egger , r. , freyberg , m.j . , et al , 1997 , , 485 , 125 takizawa , m. , 1999 , , 520 , 514" +"the investigation of effects of weak localization in low dimensional electronic systems still preserves its popularity today , since experimental studies of these systems give occasionally surprising results like metal insulator phase transitions in the two dimensional ( 2d ) electron gas at zero magnetic field@xcite and unusual behavior of dephasing time in quasi one dimensional metallic wires@xcite at low temperatures . impurity effects in one dimensional ( 1d ) disordered systems have been studied accurately due to the existence of methods which give exact results for the cases of both weak and strong disorder.@xcite also perturbative approaches give good results for three dimensional ( 3d ) weakly disordered systems . weak localization corrections to the kinetic coefficients of 2d disordered systems are logarithmically divergent corrections and it is hard to sum perturbatively the leading divergent contributions . the dimension two is the marginal dimension for the localization problem and a small external perturbation can change the character of localization in these systems . according to the scaling theory of abrahams _ et . al._@xcite all states of 1d and 2d electronic gases moving in the field of randomly distributed impurities are completely localized irrespective of the degree of randomness , and in 3d the anderson metal insulator phase transition occurs with increasing impurity concentration . notice that the result of the scaling theory for 1d disordered systems is in agreement with exact results.@xcite the scaling theory , and also the diagrammatic approach to the problem for 2d weakly disordered systems has revealed logarithmic quantum corrections to the conductivity,@xcite which tend towards localization . the logarithmic correction to the conductivity found in [ ] can be expressed as @xmath0 where @xmath1 is the drude conductivity , @xmath2 with @xmath3 and @xmath4 being the elastic and inelastic scattering times , respectively ; @xmath5 is the linear size of a 2d system and @xmath6 is the external frequency . notice that weak disorder gives no singular contribution to the density of states ( dos ) @xmath7 of electron gas models when the condition @xmath8 or @xmath9 is satisfied ( @xmath10 and @xmath11 are the fermi momentum and the fermi energy ; @xmath12 is the mean free path ) . according to the einstein relation @xmath13 the quantum correction eq.([eq:2d_log_correction ] ) to @xmath14 is due to changes in the diffusion coefficient@xcite @xmath15 . even short range and weak correlations in weakly disordered metals have been shown@xcite to result in nontrivial quantum corrections to the dos of low dimensional conductors near the fermi level . electron interactions in disordered systems also give rise to quantum corrections to the conductivity , which tend to localize the electronic states . further , the dos of strongly doped semiconductors in the presence of long range coulomb interaction vanishes at the fermi surface,@xcite which is commonly referred to as coulomb gap . disordered metals in most of the papers on localization problems are modeled as a free electron gas moving in the random field of impurities . however , doped crystals with low concentrations of impurities usually preserve their periodical structures and the impurity atoms in most cases substitute the host atoms of the lattice . substitutional impurities appear to have strong influence on the physical properties of low dimensional lattices near the commensurate values of the electron wave length @xmath16 with the lattice constant @xmath17 [ ] . in this paper we shall study the effects of substitutional impurities with small concentration on the density of states and the conductivity of a 2d square lattice . the effects of commensurability on the dos for the 3d simple cubic lattice will also be considered for the sake of completeness . bragg reflections of the electronic wave on the brillouin zone boundary in the process of impurity scattering become essential as the middle of the band is approached . this process introduces a new relaxation time for umklapp scattering to the problem , which increases for a deviation from half filling due to the distortion of the commensurability condition for the bragg reflection . the lattices under consideration have square structure for 2d and simple cubic structure for 3d crystals . our calculations show that umklapp scattering strongly changes the energy dependence of the dos close to half filling , causing it to decrease . for the 2d square lattice the dos of the pure system has a logarithmic van hove singularity at the middle of the band . this peak is shown to be preserved for the lattice with substitutional impurities . however its energy dependence is changed strongly , and the peak becomes narrower.@xcite for the 3d lattice , the van hove singularities lie far from the center of the band and umklapp scattering forms a shallow dip on the fermi surface , the depth of which increases with the impurity concentration . periodicity causes the appearance of a new class of diagrams which give a contribution to the conductivity @xmath18 . these corrections to the conductivity can be separated into two classes : corrections due to the diffusion coefficient and due to the dos . although quantum corrections to the diffusion coefficient slightly increase @xmath18 , the total corrections sum up to a decrease of @xmath18 due to dos corrections in the vicinity of half filling . the paper is structured in the following form . in sec.[sec : description ] the method is described , where new diffuson and cooperon blocks due to umklapp scattering are introduced and calculated . sec.[sec : dos ] is devoted to the calculation of corrections to the dos near half filling for 2d and 3d lattices . in sec.[sec : conductivity ] , the calculation of the conductivity of the 2d square lattice with substitutional impurities is presented . in sec.[sec : conclusion ] , a conclusion and a discussion of the results are given . the hamiltonian of a @xmath19-dimensional simple cubic lattice with substitutional impurities is given by @xmath20 where @xmath21 is the tight binding hamiltonian of noninteracting electrons in a regular lattice with lattice constant @xmath17 and nearest neighbor hopping ; @xmath22 is the impurity potential with @xmath23 being the positional vector of an impurity randomly located on the @xmath24-th lattice site . by introducing the second quantization operators @xmath25 and @xmath26 for an electron with momentum @xmath27 and spin @xmath14 , eq.([eq : hamiltonian_original ] ) can be rewritten as @xmath28 where @xmath29 and @xmath30 is the fourier transform of a single impurity potential . throughout this paper , we work in units of @xmath31 . the momenta @xmath27 and @xmath32 vary in the first brillouin zone and @xmath33 is a reciprocal lattice vector . @xmath34 in eq.([eq : hamiltonian_tight_binding ] ) is the energy spectrum of an electron on a @xmath19-dimensional square lattice , @xmath35 & \mbox{for } \quad d=2 \label{eq : energy_2d}\\ \epsilon({\bf p})&=t[3-\cos(p_x a)-\cos(p_y a)-\cos(p_z a ) ] & \mbox{for } \quad d=3\label{eq : energy_3d}\end{aligned}\ ] ] where @xmath36 with @xmath37 and @xmath38 is the tunneling integral for nearest neighbor sites . the electronic bandwidth is @xmath39 for @xmath40 and @xmath41 for 3d systems . as half filling is approached , which corresponds to @xmath42 for 2d and @xmath43 for 3d system , the fermi surface becomes nested , i.e. it exhibits surface elements which can be mapped onto each other through one nesting vector . in our case , the nesting condition is satisfied for all parts of the surface , and for 2d square lattices , the fermi surface at half filling is flat ( see fig.[fig : fs_square ] ) . the second part of the hamiltonian @xmath44 in eq.([eq : hamiltonian_tight_binding ] ) , which describes an electron scattering on randomly distributed impurities , contains both normal ( for @xmath45 ) and umklapp ( for @xmath46 ) processes . the impurity concentration is assumed to be small , so that the born approximation is appropriate@xcite to estimate the scattering process on the impurities . the impurity potential in this case is chosen to be a @xmath47-correlated gaussian potential with zero average value . conventional diagrammatic techniques @xcite are applied to calculate the effects of umklapp scattering on the dos and the conductivity . the bare green s functions @xmath48 at zero temperature are given as @xmath49 where @xmath50 and @xmath51 correspond to retarded @xmath52 and advanced @xmath53 green s functions , respectively . the energy spectrum @xmath34 in eq.([eq : baregf ] ) is expressed by eqs.([eq : energy_2d ] ) and ( [ eq : energy_3d ] ) for 2d and 3d cases , respectively . for momenta lying close to the fermi surface ( in the first brillouin zone ) the energy spectrum can be linearized around the fermi surface and @xmath54 , where @xmath55 is the group velocity of the electron wave packet . in contrast to the electron gas model the linearized energy spectrum contains the additional parameter @xmath56 due to non collinearity of the momentum and velocity vectors . for small band filling , the fermi surface is very similar to a sphere , so this factor can be set equal to unity . approaching half filling , this parameter becomes weakly varied , e.g. @xmath57 for a 2d system at half filling , where the range of variation of @xmath56 is maximal . as an approximation , we can always set @xmath58 . in the vicinity of commensurate points , especially at half filling , electron scattering on impurities with large momentum transfer involves umklapp processes . the procedure of expansion of the energy spectrum around the fermi surface can in this case be performed after the separation of the large momentum transfer @xmath59 . in weak localization theory the maximally crossed diagrams are responsible for the low temperature quantum corrections to the kinetic properties of low dimensional disordered systems , modeled as an electron gas moving in the field of randomly distributed impurities @xcite . these diagrams can be redrawn as ladder diagrams in a particle particle channel ( fig.[fig : ladder_diagrams]a ) . the cooperon block has a pole for small total momentum of particles , @xmath60 , and for small energy difference @xmath61 . the cooperon block turns out to have a diffusion pole also for large momentum transfer when the total momenta of the particles are @xmath62 with @xmath60 and when the total energy is small . in this case each act of scattering on an impurities involves a large momentum transfer close to @xmath59 . this process of course takes place mainly around half filling when @xmath63 , and it consists of simultaneous bragg reflection of the electron in the process of scattering on the impurity , with relaxation time @xmath64 . this scattering process will be further referred to as @xmath65scattering . two different scattering processes and corresponding relaxation times can be separated : normal scattering with @xmath66 ( see fig.[fig : vertices]a ) , when the scattering on an impurity maintains the electron s momentum inside the first brillouin zone after scattering and @xmath65scattering , with a relaxation time @xmath64 ( fig.[fig : vertices]b ) . here , momentum conservation is violated and this scattering process corresponds to an umklapp process . the total relaxation time @xmath3 can then be expressed as @xmath67 . notice here that the expression for the normal relaxation time @xmath66 according to fig.[fig : vertices]a for the 2d case can be given as @xmath68 we assume @xmath66 to be constant and independent of the band filling . this means that the singularities of the integrand due to vanishing velocity at the saddle points are compensated by appropriate zeros of the impurity potential . to illustrate diagrammatically the impurity scattering including umklapp processes we represent the green s function of an electron with large momentum by a dashed line the ladder series for the cooperon block with large momentum transfer , @xmath69 , is diagrammatically shown in fig.[fig : ladder_diagrams]b . notice here that the vertices c ) and d" +"all - optical nonlinearities at low light levels are instrumental to the optical implementation of quantum information processing systems . large nonlinearities can be achieved when the light - matter interaction is resonant , in which case however absorption typically plays a detrimental role . a great deal of attention has thus been devoted to a variety of schemes based on the regime of electromagnetically induced transparency ( eit ) @xcite in which this counterbalance can be overcome . in a typical eit configuration , a strong control field , coupling two unpopulated levels of a @xmath0 system , creates a transparency window for a weak probe beam . this basic scheme was extended by including additional atomic levels coupled by laser or microwave fields in the double-@xmath0 @xcite , tripod @xcite , @xmath1 @xcite or inverted-@xmath2 @xcite configurations , just to name a few . under eit - like conditions the weak interaction between two photons ( or weak classical pulses ) may become largely enhanced . in particular , very large cross nonlinear effects have been predicted leading to new types of polarization phase gates in an optically dressed medium in the @xmath3 @xcite , tripod @xcite or inverted-@xmath2 @xcite configuration . relevant experimental work has very recently been reported in ref . @xcite . in these instances , a significant change of the phase of one of the propagating pulses is achieved due to the cross - kerr effect induced by the other pulse . analogous effects have recently been studied , both theoretically and experimentally , for an inverted-@xmath2 system @xcite , as well as for a four - level @xmath1-type @xcite and five - level system @xcite . important developments concern also the dynamic control of the process leading , e.g. , to light slowdown , storage and release @xcite . these results are expected to pave the way towards constructing all - optical logical devices . unlike most typical eit configurations employing a running wave coupling field , using a control standing wave coupling beam opens the possibility of creating an all - optically tunable bragg mirror . in such a novel kind of dynamically tunable metamaterial @xcite an incoming probe light encounters a spatially periodic optical structure and is subject to bragg scattering . for specific frequency ranges transmission and stop bands appear , the properties of which can be steered by a proper choice of the control field . the field - induced dispersion of the medium and the transmission and reflection spectra have been analyzed , e.g. , in refs . @xcite , including the case of a quasi - standing wave coupling field @xcite . it was also possible to stop and store a pulse inside the medium , and then retrieve it in the form of a stationary light pulse which could not leave the medium due to the standing wave character of the releasing control beam @xcite . it has also been shown that high nonlinearities can be achieved for stored light pulses @xcite . an all - optical dynamic cavity for the confinement of light pulses based on standing wave eit bragg mirrors has recently been proposed @xcite . very recently , we have pointed out that in the presence of a trigger beam in a tripod configuration , a probe partially reflected from the periodic structure induced by a strong standing wave eit coupling field undergoes large cross - kerr nonlinear phase shifts . such a novel configuration is specifically apt for developing a phase - tunable beam splitter in which both the amplitudes and the phases of the trasmitted and reflected beam can be controlled . we have given some illustrative results valid in a narrow range of frequencies owing to the restrictive assumption that the atomic population is symmetrically distributed between the two lower levels that are coupled with the upper level respectively by the probe and trigger pulses @xcite . here , we provide a comprehensive theoretical study of the problem , including a proper treatment of the population redistribution . the latter point turns out to be crucial to extend the range of possible probe detunings and , thus , optimize the control possibilities . our approach combines analytical methodologies used to describe propagation effects in both nonlinear and spatially periodic media , and allow us to numerically examine the phase shifts of the reflected and transmitted probe field induced by the trigger s presence over a wide range of probe detunings as well as their dependence on various parameters characterizing both the atomic medium and the three laser fields . our results indicate that the tripod standing wave eit configuration makes control over the cross - kerr effect more versatile than for a running wave eit configuration @xcite in which no reflected beam appears . the paper is organized as follows . in section ii , we present the basic theoretical approach to calculate the cross - kerr effect in a medium additionally dressed by a quasi - standing wave eit coupling field , based on expanding the medium susceptibility into a power series with respect to the probe and trigger fields and into a fourier series appropriate to the spatial periodicity imposed by the coupling field . in appendix a we derive in detail the formulae for the susceptibility s expansion coefficients , while in appendix b we present the way to evaluate the population redistribution . in section iii , we present and discuss the numerical results for the trigger induced nonlinear phase shifts of the reflected and transmited probe fields as functions of the probe detuning for various combinations of control field intensities , relaxation rates and sample length . finally , we draw our conclusions . we consider a tripod system driven by a strong control field ( @xmath4 ) coupling the ground level @xmath5 and the upper level @xmath6 , and by two weaker laser fields called probe ( @xmath7 ) and trigger ( @xmath8 ) , coupling @xmath6 with @xmath9 and @xmath10 , respectively , as shown in fig . we express the fields through their complex amplitudes @xmath11 slowly varying in time : @xmath12 each of the couplings is detuned by @xmath13 , @xmath14 . here @xmath15 stands for the energy of the state @xmath16 and @xmath17 denotes the frequency of the @xmath16-th field . all the fields propagate along the @xmath18 axis . in general the control wave is allowed to have two counter - propagating components of arbitrary ratio . in the case of a running control wave , the component antiparallel to the incoming probe and trigger fields is zero . in the case of a perfect standing wave , both components are equal . thus , the control field provides a spatial lattice of period @xmath19 , @xmath20 being the field s wave number . in the configuration proposed below @xmath20 may be slightly different from the probe and trigger fields wave vectors @xmath21 , but that can be corrected by tilting both components of the control field by an angle @xmath22 with respect to the @xmath18-axis so that @xmath23 @xcite . such a configuration can be realized in a cold gas of @xmath24rb atoms . the states @xmath9 and @xmath10 may correspond , e.g. , to zeeman sublevels @xmath25 , state @xmath5 to @xmath26 , and the upper state @xmath6 to the level @xmath27 . the scheme could be used as a polarization phase gate , as was first proposed in ref . each of the two pulses interacts with the medium when it has the proper circular polarization : right for the probe and left for the trigger . when both pulses are properly polarized the nonlinear interaction between them gives rise to a cross - phase modulation . the bloch equations for the atom + field system in the rotating wave approximation read : @xmath28 where @xmath29 , @xmath30 , @xmath31 , and @xmath32 is the density matrix of the atoms in the schrdinger picture , @xmath33 , @xmath34 , @xmath35 , @xmath36 , @xmath37 . the rabi frequencies are defined by @xmath38 , where @xmath39 is the electric dipole moment matrix element . the simplified model of relaxations adopted in the above equations takes into account spontaneous emission from the upper state @xmath6 to a lower state @xmath40 , described by the relaxation rates @xmath41 and @xmath42 with @xmath43 , as well as deexcitation and decoherence between the lower levels @xmath44 , @xmath45 , due to atomic collisions . the relaxation rates for the coherences @xmath46 , @xmath47 , and those for the collision - induced population relaxations were taken equal for simplicity ( cf . @xcite ) . the propagation equation for the positive frequency part of the probe field , slowly varying in time , i.e. when @xmath48 , reads in the fourier picture , with the fourier frequency variable identified with the probe detuning @xmath49 \epsilon_p(z,\delta_1 ) = -\frac{\omega_1 ^ 2}{c^2}\chi_p(z,\delta_1 ) \epsilon_p(z,\delta_1 ) , \label{tr}\ ] ] with the medium susceptibility for the probe given by @xmath50 where @xmath1 is the number of atoms per unit volume . the time limit means that we need to find the steady state solutions to the bloch equations . the assumption that the probe and trigger are weak with respect to the control field @xmath51 allows us to expand the susceptibility into the taylor series : @xmath52 the explicit form of the taylor expansion coefficients can be found in appendix a. the term @xmath53 corresponds to the linear susceptibility , while the third - order terms @xmath54 and @xmath55 represent the self- and cross - kerr effect , respectively . the latter is of particular importance , as we are interested in the cross - phase modulation . we now write the control field as : @xmath56 where @xmath57 of constant values are its forward and backward propagating parts . as the field is periodic in space , so are the medium optical properties . therefore we expand the susceptibilities for both probe and trigger into the fourier series : @xmath58 e^{2ink_2z}. \label{chip}\ ] ] the pulses propagating in a periodic medium acquire their reflected components . in the two - mode approximation ( for details see @xcite ) we write : @xmath59 where @xmath60 are slowly varying in space . we now insert eqs . ( [ chip],[2 m ] ) into eq . ( [ tr ] ) and drop terms rapidly oscillating in space . to write the propagation equations in the final form we make use of the relation @xmath61 and set @xmath62 . for the probe we find : @xmath63 where @xmath64 with @xmath65 . the trigger equations are obtained by interchanging the indices @xmath66 . explicit formulae for the susceptibilities fourier components as well as their detailed deriviation can be found in appendix a. as we will change the probe detuning @xmath67 in a wide range while keeping the trigger detuning @xmath68 constant , we introduce an asymmetry in the populations @xmath69 and @xmath70 even for @xmath71 . additionally , the symmetry may be spoiled by the fact that @xmath72 ( the energy of the state @xmath9 ) is slightly smaller than @xmath73 , and in a cold medium transitions from @xmath10 to @xmath9 are possible while those from @xmath9 to @xmath10 are not . in previous works ( see refs . @xcite ) the probe and trigger fields were only allowed detunings such that @xmath74 . in that case the stationary population distribution was assumed to be @xmath75 . such an approach is simple , but it is well justified only in the resonance region of frequencies . as we show in the section [ results ] , for a wider range of pulse detunings it is necessary to make a better estimation of the population distribution . in appendix b we present the way to evaluate the populations in the case of a quasi - standing coupling" +"the fermion determinant is a highly non - local object as can e.g. be seen from the hopping expansion for lattice regularized fermions ( see @xcite for a basic introduction ) . the hopping expansion expresses the fermion determinant as the exponential of a sum over all possible closed loops and the external field variables along a loop are collected as factors for this loop . the exponential function can then be expanded and the result is a representation of the fermion determinant in terms of loops . the loop - sum in the exponent , however , contains loops of arbitrary length , which can also iterate parts or all of their contour arbitrarily often . thus , the exponent contains arbitrarily high powers of the external fields . on the other hand we know that , at least on a finite lattice , the fermion determinant is a finite polynomial in the external fields , and thus infinitely many contributions present in the exponent have to cancel each other when expanding the exponential . the result has to be a relatively simple loop representation for the fermion determinant . for the case of staggered fermions several papers can be found in the literature @xcite-@xcite where polymer representations for the fermions are obtained . for the case of wilson fermions relatively few is known due to the more involved spinor structure of the fermions . here we concentrate on 2-d wilson fermions . an instance where the above discussed cancellation of contributions was brought under control for a model with wilson fermions is salmhofer s mapping of the strongly coupled lattice schwinger model to a self avoiding loop model @xcite . in a first step the gauge fields at strong ( = infinite ) coupling were integrated out and the remaining grassmann integral was then represented as a sum over loops . subsequently scharnhorst studied the two - flavor lattice schwinger model with this method @xcite and extended the techniques to find a two - color loop model for the 2-d lattice thirring model @xcite . in all of these cases , however the external field was either integrated out in the strong coupling limit @xcite or was nt present at all @xcite . on the other hand , our arguments given in the first paragraph show that the cancellation of higher winding loops is a universal phenomenon and that it should be possible to find a simple loop representation also for the fermion determinant in an external field . in this article we present a simple formula for the fermion determinant of 2-d wilson lattice fermions in a scalar background field ( eq . ( [ equivalence ] ) ) . the proof is based on a result for the hopping expansion for a generalized 8-vertex model where the vertices are coupled to a background field @xcite . with a proper choice of the vertex weights the square of the partition function for this model represents the 2-d fermion determinant in a scalar background field . the resulting expression reduces the hopping expansion to a finite sum ( on a finite lattice ) of loops . in addition it is possible to explicitly integrate out the external field . by doing so with a gaussian action for the scalar we generate a loop representation of the 2-d gross - neveu model . such loop representations for lattice field theories allow for a considerably more accurate numerical treatment as has e.g. been demonstrated for the strongly coupled schwinger model @xcite . the basic idea for the proof of our loop representation is to identify the hopping expansion of the wilson fermion determinant with the hopping expansion of a generalized 8-vertex model @xcite . here we briefly rederive the hopping expansion for wilson fermions in a form suitable for comparison with the generalized 8-vertex model ( see e.g. @xcite for a more detailed discussion of the hopping expansion ) . we study a lattice model of 2-d fermions which in the continuum corresponds to the action @xmath1 \ ; \psi(x ) \ ; , \label{continuum}\ ] ] where @xmath2 is a scalar external field . the lattice fermion determinant is expressed as a path integral @xmath3 \ ; = \ ; \int d\psi d\overline{\psi } \ ; \exp\left(-\sum_{x , y \in \lambda } \overline{\psi}(x ) m[\theta](x , y ) \psi(y ) \right ) \ ; , \label{partfunct}\ ] ] where the kernel for the lattice fermion action ( wilson fermions ) which regularizes the continuum action ( [ continuum ] ) is given by @xmath4(x , y ) \ ; = \ ; \big[2 + m + \theta(x)\big ] \ ; \delta_{x , y } \ ; - \ ; \sum_{\mu = \pm 1}^{\pm 2 } \gamma_\mu \delta_{x+\mu , y } \ ; , \ ] ] and we defined @xmath5 \ ; \ ; \ ; \ ; , \ ; \ ; \ ; \ ; \mu = 1,2 \ ; .\ ] ] here @xmath6 are pauli matrices . the sum in the exponent of ( [ partfunct ] ) runs over the whole lattice @xmath7 , which for simplicity we assume to be a finite rectangular piece of zz@xmath8 ( the generalization to e.g. a torus is straightforward ) . the boundary conditions are open , i.e. hopping terms that would lead to the outside of our lattice are omitted . we define @xmath9 and assume that @xmath2 is such that @xmath10 for all lattice points @xmath11 . this is a purely technical assumption due to the particular techniques we use for computing the determinant . the final result will be a finite polynomial in the @xmath2 and the above restriction is irrelevant then . we now can write @xmath3 \ ; = \ ; \prod_{x \in \lambda } h(x)^2 \det\big(1 - r[\theta ] \big ) \ ; = \ ; \prod_{x \in \lambda } h(x)^2 \exp \left ( - \sum_{n=1}^\infty \frac{1}{n } \mbox{tr } \ ; r[\theta]^n \right ) \ ; . \label{hopexp}\ ] ] in the last step the hopping expansion was performed , i.e. the determinant was expressed using the well known trace - logarithm formula and the logarithm was expanded in a power series . the hopping matrix @xmath12 $ ] is defined as @xmath13(x , y ) \ ; = \ ; \sum_{\mu = \pm 1}^{\pm 2 } \ ; \gamma_{\mu } \ ; \frac{1}{h(x ) } \ ; \delta_{x+\mu , y } \ ; . \label{hoppingmatrix}\ ] ] the series in the exponent of ( [ hopexp ] ) converges for @xmath14|| < 1 $ ] , which can be enforced by choosing large enough @xmath15 , i.e. suitable @xmath2 . again this is only a technical restriction and can be abandoned in the final result . due to the kronecker delta in ( [ hoppingmatrix ] ) , the contributions to tr@xmath12^n$ ] are supported on closed loops on the lattice , and since closed loops are of even length , the contributions for odd @xmath16 vanish . for we obtain @xmath18^{2k } \ ; = \ ; \sum_{x \in \lambda } \ ; \sum_{l \in { \cal l}^{(2k)}_x } \ ; \prod_{y \in p(l ) } \frac{1}{h(y ) } \ ; \ ; \mbox{tr } \ ; \prod_{\mu \in l } \gamma_\mu \ ; . \label{hoptrace}\ ] ] here @xmath19 is the set of all closed , connected loops of length @xmath20 and base point @xmath11 . by @xmath21 we denote the set of all sites visited by the loop @xmath22 . note that a factor @xmath23 is produced whenever @xmath22 runs through @xmath11 which can be arbitrary often for long enough loops . the last term in ( [ hoptrace ] ) is the trace of the ordered product of the hopping generators @xmath24 as they appear along the loop @xmath22 . we remark , that @xmath25 , which implies that whenever a loop turns around at a site and runs back along its last link this contribution vanishes . thus all these _ back - tracking _ loops can be excluded from @xmath26 . evaluating the trace over the matrices @xmath24 for a given loop is the remaining problem in the hopping expansion . it first has been solved in @xcite by realizing that the pauli matrices give rise to a representation of discrete rotations on the lattice . alternatively one can decompose the loop using four basic steps and compute the trace in an inductive procedure along the lines of @xcite . the result is @xmath27 by @xmath28 we denote the number of self - intersections of the loop @xmath22 and @xmath29 gives its number of corners . the result is independent of the orientation of the loop . inserting ( [ hoptrace ] ) and ( [ gtrace ] ) in ( [ hopexp ] ) we obtain @xmath3 \ ; = \ ; \prod_{x \in \lambda } h(x)^2 \exp \left ( \sum_{k=1}^\infty \frac{1}{2k } \sum_{y \in \lambda } \ ; \sum_{l \in { \cal l}^{(2k)}_y } ( -1)^{s(l ) } \big(\frac{1}{\sqrt{2}}\big)^{c(l ) } \prod_{z \in p(l ) } \frac{1}{h(z ) } \right ) . \label{prelim}\ ] ] finally we further simplify this expression by removing the explicit summation over the base points @xmath11 . a loop of length @xmath20 without complete iteration of its contour allows for @xmath20 different choices of a base point thus cancelling the factor @xmath30 in ( [ prelim ] ) . a loop which iterates its whole contour @xmath31 times allows only for @xmath32 different base points and a factor @xmath33 remains . the final expression is @xmath3 \ ; = \ ; \prod_{x \in \lambda } h(x)^2 \ ; \exp \left ( 2 \sum_{l \in { \cal l } } \frac{(-1)^{s(l)}}{i(l ) } \big(\frac{1}{\sqrt{2}}\big)^{c(l ) } \ ; \prod_{y \in p(l ) } \frac{1}{h(y ) } \right ) \ ; , \label{finalhop}\ ] ] where @xmath34 is the set of all closed , connected , non back - tracking loops of arbitrary length . each loop is included in @xmath34 with only one of its two possible orientations and we collect an overall factor of 2 in the exponent . as already outlined , the next step is to compare the result ( [ finalhop ] ) to the hopping expansion for a generalized 8-vertex model studied in detail in @xcite . in this generalized model , the vertices are coupled to a locally varying external field @xmath35 . before we proceed let s first discuss this generalized model and its relation to the standard 8-vertex model . the standard 8-vertex model @xcite can be viewed as a model of 8 quadratic tiles ( vertices ) and each of them is assigned a weight @xmath36 ( compare fig . [ tiles ] ) . a _ tiling _ of our lattice @xmath7 ( the same rectangular piece of @xmath37 as before ) is a covering of @xmath7 with the tiles such that on each site of @xmath7 we place one of our tiles with the centers of the tiles sitting on the sites . the set @xmath38 of _ admissible tilings _ is given by those arrangements of tiles where the black lines on the tiles never have an open end . the partition function of the standard 8-vertex model is the sum over all admissible tilings @xmath39 and the boltzmann weight for a particular tiling @xmath40 is given by the product of the weights @xmath41 for all tiles used in this tiling @xmath40 . in our generalization of the model we now couple the vertices to an external field @xmath35 located on the sites @xmath11 of @xmath7 . the partition function of the generalized model is given by @xmath42 \ ; = \ ; \sum_{t \in { \cal t } } \ ; \prod_{i = 1}^8 { w_i}^{n_i(t ) } \ ! \prod_{x \in p(t ) } \varphi(x ) \ ; . \label{8vertex}\ ] ] here" +"very recently , a class of mass dimension one fermions named elko , initially proposed by ahluwalia and grumiller @xcite as a natural candidate to a fermionic dark matter particle , underwent a profound overhaul in the definition of their duals , culminating with a field that is local and lorentz covariant @xcite ( see also @xcite for some additional support ) . thus , the interest for such class of non - standard spinors ( nss ) , or dark spniors , has increased in recent years , since they are naturally neutral and has mass dimension one ] , which leads them to satisfy only a klein - gordon type equation . moreover , as neutral fields , they are good and natural candidate to particles of dark matter in the universe , an open problem in cosmology . the elko field is constructed as a spin-@xmath1 field describing fermions that are eigenstate of the charge conjugation operator , satisfying the relation @xmath2 , where @xmath3 and @xmath4 are the usual spinor and its dual , respectively , the index @xmath5 stands for the two possible helicities of the spinor and @xmath6 stands for the self - conjugate spinor ( s ) and anti - self - conjugate ( a ) . more details can be found in @xcite . while profoundly altering the quantum structure of the field , this new dual definition for elko does not alter its classical formulation , so that cosmological applications remain valid . models in which the elko field is considered as candidate to dark matter or dark energy in the universe have been proposed recently @xcite . in this work we are interested in the elko field as a possible candidate to drive inflation , the matter dominated era and finishing as the responsible for the recent cosmic acceleration of the universe . in this final phase , the elko field just rolls down to the minimum of a potential and acts as a cosmological constant term . in this paper we study the elko field coupled to gravity in a einstein - cartan framework following recent results @xcite , and we show how it can be the responsible for all phases of the universe , starting as an inflaton field , something similar to the standard scalar field but with a much more rich structure , then reproducing the matter dominated era , since it is a natural candidate to dark matter , and finishing as a constant field that mimics exactly a cosmological constant term , according to the @xmath7cdm model . we start with a brief review of scalar field inflationary theory on section ii , its motivations and main results , and also pointing some difficulties . then , in section iii , we introduce the elko equations and study numerically how it can be a good candidate to an inflaton field and also the responsible for driving all phases of the universe . we finish in section iv with some concluding remarks . a brief appendix containing some details on the numerical analysis of the coupled system of equations is also presented . here we review briefly the inflationary model sourced by a scalar field @xmath8 , following the references @xcite . a good list of references can be found into @xcite . the einstein equations in a flat friedmann - robertson - walker metric are : @xmath9\,,\label{eqh}\ ] ] @xmath10 @xmath11 with @xmath12 , @xmath13 the hubble expansion parameter , @xmath14 with @xmath15 and @xmath16gev is the reduced planck mass . the energy density and pressure for the scalar field are given by @xmath17 @xmath18 given a potential @xmath19 , the inflation occurs if the slow - roll parameters @xmath20 and @xmath21 satisfies @xcite : @xmath22 @xmath23 which justifies to neglect the kinetic term from ( [ eqh ] ) ( @xmath24 ) and the acceleration term from ( [ eqphi ] ) ( @xmath25 ) . although being necessary conditions to drive the inflation , the smallness of such parameters is not sufficient to guarantee that those terms can be neglected @xcite . sometimes , the additional assumption @xmath26 is also needed . such parameters are used to restrict the form of the potential in order to ensure the inflation starts . basically , these conditions ensure that the onset of expansion is approximately exponential , as required by all inflationary theories . an alternative expression of the condition to inflation occur is given by @xcite : @xmath27 showing that the comoving hubble length @xmath28 is decreasing with time . dozens of potential have been proposed in last decades in order to drive the inflationary phase of expansion of the universe . some of them have physical motivations whilst other are just placed by hand in order to furnish correct results . we present a list of some potentials that were recently confronted with the most recent observations of planck 2013 mission @xcite : * power law potential ( or chaotic inflation ) : @xmath29 * exponential potential : @xmath30 * inverse power law potential : @xmath31 * hill - top models : @xmath32 * symmetry breaking potential : @xmath33 * natural inflation : @xmath34 * hybrid inflation ( multi fields ) : @xmath35 where @xmath36 and @xmath37 are parameters to be adjusted according to observations . all these potential represent good models in order to drive the inflationary period of the universe for specific values of the constants , the main difference among them are fine tunings concerning the duration of inflation , its _ amount _ measured by the number of e - foldings @xmath38 , the correct transition to the end of the inflationary era , sometimes called reheating phase and most important , the correct prediction of density perturbations , responsible for the formation of galaxies and cluster of galaxies and also for the anisotropies in the cosmic microwave background ( cmb ) radiation . this last test throw away several potential , which reduces the number of models that deserve further studies . from the above potential , the cases ( [ v2 ] ) , ( [ v3 ] ) and ( [ v7 ] ) are outside the contours estimated by the planck 2013 observations @xcite . others are permitted just for specific values and ranges of the parameters . as already pointed out above , another important characteristic of inflationary models is how the inflation ends . the scalar field , after rolling down to the bottom of the potential , needs to leave the scene in order to next phase of the universe takes place . in other words , the scalar field must decay to its minimum value in order not to act any more , @xmath39 . this process is called reheating . a hot universe at the end of the inflation is a necessary condition in order to radiation dominate and also the conventional matter start to form while the temperature is cooling down . in the modern inflationary model , the scalar field oscillates while rolls down to the bottom of the potential , transferring energy to other matter fields , or even decaying into standard particles . the details of reheating are an important subject into the inflationary cosmology . some models add a phenomenological decay term to the equation of motion of the scalar field ( after inflation , the term @xmath40 is important again ) : @xmath41 where @xmath42 is considered a decay rate of the field @xmath8 into other particles @xcite . such friction term is also needed to make fine adjustments in theory , not allowing inflation to occur forever for instance . it is important to stress that such term is placed by hand after inflation takes place , just in order to control the damping of oscillations during the reheating . after all , having the inflation occurred , the scalar field rolling down to the bottom of the potential and oscillating accordingly with the last term of ( [ eqphig ] ) to correctly stop the inflation , a final key question still prevails . what is such scalar field ? it is named inflaton , the particle responsible for the inflation , but his very nature is not known yet . no fundamental scalar field has yet been detected in the nature , except the higgs field responsible for the electro - weak symmetry breaking . the breaking of other symmetries in supersymmetric models or grand unified theories also predicts the existence of several scalar fields . nevertheless , a bosonic spin 0 scalar field as a physical matter particle , interacting to form some kind of observed matter , is not known . all the observed matter in the universe are constituted by fermions , which motivated us to construct an inflationary model with the dark spinor field elko . being a good candidate to dark matter in the universe we have found that it can drive the inflation , the dark matter evolution after inflation and surprisingly also the recent accelerated expansion of the universe . finally , since the dark matter does not interact electromagnetically with other baryonic matter , the presence of hot electromagnetic radiation after inflation also allows a short period where the radiation dominates , before the dark matter dominance . in a curved homogeneous and isotropic background we assume that the elko field fills all the space homogeneously @xcite , thus we can assume that it can be split into a time dependent part times a flat space - time dependent spinor part , namely , @xmath43 , such that @xmath44 stands here , for simplicity , for the two kinds and two helicities of elko , @xmath45 ( self - conjugate ) and @xmath46 ( anti - self - conjugate ) , satisfying @xmath47 , where @xmath48 is the charge conjugation operator @xcite . the spinor can be normalized as @xmath49 , where @xmath50 is its dual that must be conveniently defined @xcite . we choose to work with a positive norm spinor . another important characteristic that elko fields satisfies is that due to its mass dimension one the possible couplings of the field are limited . in particular , just for elko fields , the two allowed self - couplings are of the type @xmath51 and @xmath52 . there are also the possibility to couple to a higgs field @xcite . the action for the elko field coupled to gravity in a homogeneous and isotropic metric has been already presented in the literature @xcite , for both torsion free and torsion coupled equations . the friedmann equations for the most general case , including torsion terms and derived by taking the euler - lagrange equations , are given by @xcite : @xmath53\nonumber\\ & & + \bigg(1+{\kappa^2\phi^2\over 8}\bigg)h^2 \,,\label{h2a}\end{aligned}\ ] ] @xmath54\bigg ] \nonumber\\ & & -3\bigg(1+{\kappa^2\phi^2\over 8}\bigg)h^2\ , , \label{hdota}\end{aligned}\ ] ] and the motion equation for the scalar part of the elko field can be obtained by deriving the first equation and using the second one : @xmath55 where @xmath56 is the only non - null torsion function in the specific case of a homogeneous and isotropic metric @xcite . after substituting ( [ hfa ] ) into eqs . ( [ h2a])-([eqphia ] ) and rearranging we are left with : @xmath57\,,\label{h2}\ ] ] @xmath58\,,\label{hdot}\ ] ] @xmath59 together the equations for energy density and pressure ( see appendix of @xcite for details ) : @xmath60 @xmath61 notice that the structure of such system of equations is much richer than those corresponding to a standard scalar field , eqs . ( [ eqh])-([pphi ] ) . for this reason the elko field can be a good candidate to drive not only the inflationary phase of the universe , but also the subsequent phases , as dark matter evolution and accelerated expansion . in which follows we will considerer the" +"in 1981 unruh suggested to study the black hole physics using its sonic analogue @xcite . originally suggested for classical liquids , this was later extended to quantum systems such as superfluids and bose condensates @xcite . the main advantage of the quantum liquids and gases is that in many respect they are similar to the quantum vacuum of fermionic and bosonic fields . this analogy forms a view on the quantum vacuum as a special type of condensed matter the ` ether ' where the physical laws which we have now can arise emergently as the energy or temperature of the ` ether ' decreases @xcite . the particular scenario of the emergent formation of the effective gravity together with gauge fields and chiral fermions can be found in the recent review paper @xcite . according to the topology in the momentum space , there are three types ( universality classes ) of the fermionic vacua . one of them has trivial topology and as a result its fermionic excitations are fully gapped ( massive fermions ) . the other two have nontrivial momentum - space topology characterized by certain topological invariants in the momentum space @xcite . one of the two nontrivial universality classes contains systems with fermi points ; their excitations are chiral fermions , whose energy turns to zero at points in the momentum space . another class represents systems with wider manifold of zeroes : their gapless fermionic excitations are concentrated in the vicinity of the 2d surface in momentum space the fermi surface . this class contains fermi liquids . here we discuss the properties of the quantum vacuum in the presence of event horizon . we assume that in the absence of horizon the fermionic vacuum belongs either to the trivial class ( such as the standard model below the electroweak transition where all fermions are massive ) or to the class of fermi points ( such as the standard model above the electroweak transition whose excitations are chiral massless fermions ) . in the presence of a horizon the region behind the horizon becomes the ergoregion : the particles acquire negative energy there . in the true vacuum state these negative energy levels must be occupied , which means that the old vacuum must be reconstruced by filling these levels . we do not study the process of the filling it can be the smooth process of hawking radiation @xcite or some other more violent process we discuss what will be the structure of the true vacuum state if it is possible to reach this state without destruction of a horizon . in other words we assume that the stable black hole can exist as a final ground state of the gravitational collapse . we find that behind the horizon the fermionic vacuum belongs to the class of the fermi surface . the main sources for the appearance of the fermi surface come from the following properties of event horizon . first , the emergence of the planck physics in the vicinity of ( and behind ) the horizon . event horizon serves as a magnifying glass through which the phenomena at planck length scale could be visualized . at some scales the lorentz invariance the property of the low - energy physics inevitably becomes invalid and deviations from the linear ( relativistic ) spectrum become important . such violation of lorentz invariance is now popular in the literature @xcite . it leads to either subluminal or superluminal propagation at high energy , say , @xmath0 , where @xmath1 is planck momentum . according to the condensed matter analogy we assume that the high energy ( quasi)particles are superluminal , i.e. the sign is plus . due to the superluminal dispersion there is a bottom in the dirac sea and thus the process of the filling of the negative energy levels becomes limited . when all of them are occupied , we come to a global vacuum state ( or global thermodynamics equilibrium with positive heat capacity , if the temperature is finite ) . thus the superluminal dispersion of the particle energy gives rise to the energetic stability of the vacuum in the presence of black hole . the second important consequence of the event horizon , due to which the vacuum belongs to the class of systems with the fermi surface , is that the horizon violates the time reversal symmetry of the system : the ingoing and outgoing particles have different trajectories . in condensed matter the appearance of the fermi surface due to violation of the time reversal symmetry is a typical phenomenon ( see e.g. @xcite and also sec . 12.4 of ref . @xcite ) . in refs . @xcite the stable black hole is also considered , which exhibits a finite positive heat capacity , any temperature it likes , and no hawking radiation . but it is assumed there that in the final state the time reversal symmetry is not broken ( or actually it is restored in the final state ) . the existence of such stable black hole with unbroken time reversal symmetry is also supported by the condensed matter analogies @xcite in which stable infinite - redshift surface arise . example of the infinite - redshift surface with no time reversal symmetry breaking is also provided by the extremal black hole , whose condensed matter analog is discussed in sec . 12.6 of review @xcite . in all these examples the fermi surface does not appear . the black hole ground states with time reversal symmetry are in some sense exceptional ( in the same manner as extremal black hole ) and we shall not discuss them here . the vacuum can be well defined only if the metric is stationary . in general relativity the stationary metric for the black hole is provided in the painlev - gullstrand spacetime @xcite . the line element of the painlev - gullstrand metric is @xmath2 where @xmath3 here @xmath4 is the mass of the hole ; @xmath5 is the radius of the horizon ; @xmath6 is the newton gravitational constant ; the minus sign in eq.([velocityfield ] ) gives the metric for the black hole ; while the plus sign characterizes the white hole . the time reversal operation @xmath7 transforms the black hole into white whole . the stationarity of this metric and the fact that it describes the spacetime both in exterior and interior regions , are very attractive features and they became explored starting from the ref . @xcite ( see @xcite ; extension of painlev - gullstrand spacetime to rotating black hole can be found in ref . @xcite ) . in case of the black hole the field @xmath8 has simple interpretation : it is the velocity of the observer who freely falls along the radius towards the center of the black hole with zero initial velocity at infinity . the motion of the observer obeys the newtonian laws all the way through the horizon @xmath9 and thus his velocity is @xmath10 the time coordinate @xmath11 is the local proper time for the observer who drags the inertial coordinate frame with him . as was first noticed by unruh @xcite , the effective metric of the type in eq.([painleve ] ) is experienced by quasiparticles propagating in moving fluids . the field @xmath8 is just the velocity field of the liquid , and @xmath12 is the ` maximum attainable velocity ' of quasiparticles in the low - energy limit , for example the speed of sound in case of phonons ( see also @xcite ) . the horizon could be produced in liquids when the flow velocity becomes bigger than @xmath12 . the black hole and the white hole can be reproduced by the liquid flowing radially inward and outward correspondingly . this is an explicit realization of the breaking of the time reversal symmetry by flowing liquid : time reversal operation reverses the direction of flow of the ` vacuum ' : @xmath13 . this painlev - gullstrand spacetime , though not static , is stationary . that is why the energy @xmath14 of ( quasi)particle in this spacetime is determined both in exterior and interior regions . it can be obtained as the solution of equation @xmath15 with @xmath16 , which gives @xmath17 where @xmath18 is the energy of the particle in the free - falling frame : @xmath19 for the ` sonic ' black hole it is the energy of the quasiparticle in the frame comoving with the superfluid vacuum . let us consider a massless ( quasi)particle moving in the radial direction from the black hole horizon to infinity , i.e. its radial momentum @xmath20 . since the metric is stationary the energy of a particle in the painlev - gullstrand frame ( or of a quasiparticle in the laboratory frame ) is conserved and one has @xmath21 . then its energy in the free - falling ( superfluid comoving ) frame : @xmath22 this energy , which is very big close to the horizon , becomes less and less when the ( quasi)particle moves away from the horizon . this is the gravitational red shift superimposed on the doppler effect @xcite , since the emitter is free falling with the velocity @xmath23 . the frequency of the spectral line measured by the observer at infinity is @xmath24 where @xmath25 is the nominal frequency of this line . the surface @xmath26 is a surface of infinite redshift , at this surface the energy in eq.([blueshiftenergy ] ) diverges . this means that if we observe particles coming to us from the very vicinity of the horizon , these outgoing particles originally had a huge energy approaching the planck energy scale . thus the event horizon can serve as a magnifying glass which allows us to see what happens at the planck length scale . at some point the low - energy relativistic approximation inevitably becomes invalid and the lorentz invariance is violated . in quantum liquids the nonlinear dispersion enters the velocity independent energy @xmath18 in the superfluid comoving frame . taking into account the analogy with quantum liquids , we assume that in our vacuum the planck physics also enters the energy in the free - falling frame . thus the energy spectrum of the particles is given by eq.([energyspectrum1 ] ) where @xmath27 as for the ingoing particle , its radial momentum @xmath28 and thus its energy in the comoving frame @xmath29 it has no pathology at the horizon the observer falling freely across the horizon sees no inconveniences when he crosses the horizon and thus the planck physics is not envoked here . the pathology reappears when one tries to construct the thermal state of global equilibrium ( or the vacuum state ) in the presence of a horizon . according to the tolman law in the global equilibrium the temperature as measured by observer in the comoving frame diverges at the horizon : @xmath30 again at some point this temperature becomes so high that the planck physics becomes relevant . the global equilibrium in the presence of a horizon is possible only for the superluminal dispersion , i.e. for the sign plus in eq.([energyspectrumnonlinear ] ) . the reason is the following . behind the horizon , at @xmath31 , the velocity of the frame - dragging exceeds the speed of light . in the relativistic domain this means that the radial coordinate @xmath32 becomes time - like , because a ( quasi)particle behind the horizon can move along the @xmath32 coordinate only in one direction : towards the singularity . however , with the plus sign for the energy spectrum in eq.([energyspectrumnonlinear ] ) the ( quasi)particles can go back and forth even behind the horizon . thus the spacelike nature of the @xmath32-coordinate is restored by the superluminal dispersion , and the global equilibrium becomes possible . finally" +"the disk - galaxies are constructed in dynamical equilibrium ( hernquist , 1993 ) and consist of an exponential stellar disk , a bulge with a hernquist profile , and a pseudoisothermal dark halo ( units as in hernquist , 1993 ) . the two merging galaxies approach each other on nearly parabolic orbits at a pericenter distance of 2 scale lengths of the larger disk . the large galaxy is realized with 20000 disk particles , 6666 bulge particles and 40000 halo particles , respectively . the smaller galaxy contains @xmath1 of the mass and of the particles in each component and has a disk scale length of@xmath2 compared to the more massive galaxy . we tested 14 different relative orientations for every mass ratio . the time integration was performed using the special purpose hardware grape . after the remnants settled into equilibrium an artificial image of the remnant was created ( see also heyl , hernquist & spergel , 1994 ) . following the definition of bender , dberreiner & mllenhoff ( 1988 ) we determined the characteristic isophotal shape @xmath3 , ellipticity @xmath4 , the ratio of major axis rotation and central velocity dispersion , @xmath5 , and the anisotropy parameter @xmath6 for 500 random projections of each of the 14 orbital geometries . these values were used to calculate a probability density for a given simulated remnant to be observed at a given location in the two dimensional parameter plane , adopting that mergers occur randomly without any preferred relative inclination . figure 1 shows the result for 1:1 , 2:1 , 3:1 and 4:1 merger remnants . from these results we conclude that most of the global properties of elliptical galaxies can be explained by a sequence of stellar mergers between disk galaxies of mass ratios between 1:1 and 4:1 . 1:1 mergers completely erase the structure of the initial disk . in the 3:1 and 4:1 case the remnants seem to remember their initial state ( see barnes , 1998 ) . in this sense the sequence of mass ratios is a sequence of disk disruption . however , even with 4:1 remnants we fail to reproduce the fastest observed rotators with @xmath7 at one effective radius ( figure 1 ) . recent observations of fast rotating low luminosity ellipticals ( rix , carollo & freeman , 1999 ) show that the disagreement is even stronger at larger radii ( see cretton , naab , rix & burkert , this conference ) barnes , j. , 1998 , in galaxies : interactions and induced star formation , ed . d. friedli , l. mertinet , & d.pfenniger ( saas - fee advanced course lecture notes , no . 26 : berlin : springer ) , 275 bender , r. , dberreiner , s. & mllenhoff , c. , 1988 , , 278 hernquist , l. , 1993 , , 86 , 389 heyl , j. s. , hernquist , l. & spergel , d. n. , 1994 , , 427 , 165 naab , t. , burkert , a. & hernquist , l. , 1999 , , 523 , l133 rix , h. w. , carollo , c. m. & freeman , k. , 1999 , , 513 , l25" +"recent high resolution x - ray observations reveal that there are large number of ultraluminous x - ray sources ( ulxs ) in many nearby galaxies . ulxs are usually defined as very bright ( @xmath3 ) off - nucleus , variable x - ray sources in galaxies . since the luminosity exceeds the eddington luminosity of a @xmath4 black hole ( bh ) , ulxs are considered to be candidates for intermediate - mass black holes ( imbhs ) . more recently , a number of ulxs have been found to be supersoft ; their x - ray spectra can be fitted with a blackbody model with temperature of less than 100 ev ( e.g. , swartz et al . 2002 ; mukai et al . 2003 ; fabbiano et al . 2003 ; distefano & kong 2003 ; kong & distefano 2003 ) . in this letter , we report a series of _ chandra _ observations of the ultraluminous sss in m101 ( cxouj140332.3 + 542103 ) from the low state ( kong & distefano 2004 ) to outburst ( kong 2004a , 2004b ) . shortly after the discovery of the outburst , we initiated a multiwavelength campaign to monitor the source . we here also present the results of an _ xmm - newton _ follow - up observation conducted about two weeks after the first outburst observation . the primary result of radio observations by the very large array was reported by rupen , sjouwerman , & kong ( 2004 ) . we will present the detailed analysis of the optical and radio observations in a follow - up paper . m101 was observed by _ chandra _ in 2004 january , march , may , and july . table 1 summarizes the _ chandra _ observations . we also list the two _ chandra _ observations taken in 2000 march and 2000 october , and the follow - up _ xmm - newton _ observation ( see 2.2 ) . in all observations , the center of m101 and the ultraluminous sss are in the s3 chip of the acis - s . all data were taken in very faint mode ( vfaint ) . we reprocessed the raw data to utilize the vfaint mode and to remove the 0.5-pixel randomization . however , for data taken during the outburst , we found that vfaint processing flagged some source events of the sss as background and we therefore did not apply vfaint processing for the data taken in july . in order to reduce the instrumental background , we screened the data to allow only photon energies in the range of 0.37 kev . we also searched for periods of high background using source free regions in the s1 chip and filtered all the high background periods . only the 2004 january 24 and 2004 may 7 observations were affected ; the exposure times listed in table 1 correspond to the good time intervals . all data were reduced and analyzed with the ciao v3.1 package , and calibration database caldb 2.27 . shortly after the discovery of the outburst of cxouj140332.3 + 542103 with _ chandra _ , we requested _ xmm - newton _ director s discretionary time for a follow - up observation . the _ xmm - newton _ observation was taken on 2004 july 23 for 30 ks , and the instrument modes were full - frame , medium filter for the three european photon imaging cameras ( epic ) . after rejecting those intervals with a high background level , we considered a good time interval of @xmath5 ks . only data in 0.212 kev were used for analysis . data were reduced and analyzed with the _ xmm - newton _ sas package v5.4.1 . we performed spectral analysis for all _ chandra _ data taken between 2004 january and 2004 july . the two datasets taken in 2000 were reported in mukai et al . ( 2003 ) and distefano & kong ( 2003 ) . spectral analysis was performed by using sherpa . we also used xspec v11.3 for independent check . in each observation , we extracted the source spectrum from a @xmath6 radius circular region centered on the source , while an annulus region centered on the source was used as the background . during the outburst , there are enough photons to rebin the spectra with at least 15 counts per spectral bin , and used @xmath7 statistics to find the best - fitting parameters . for the data during the low state ( january , march , and may ) , very few source photons were received ( @xmath8 ) in each observation , we therefore performed spectral analysis with unbinned data ( background not subtracted ) for which c - statistics ( cash 1979 ) were employed . to examine the low state spectrum in detail , we also combined all the low state data to perform spectral fit with binned data and @xmath7 statistics . we tried power - law , blackbody , and disk blackbody models with interstellar absorption . table 2 and 3 show the best - fitting spectral parameters for all _ chandra _ observations taken in 2004 , and the x - ray spectra are shown in figure 1 . [ cols=""<,^,^,<,^,^"",options=""header "" , ] for the low state data , power - law models provide better fits than blackbody models . each low - state observation is consistent with an absorbed power - law model ; the photon index ranges from @xmath9 among the observations , with an average of 1.8 . the @xmath10 converged to zero and we therefore fixed it at the galactic value ( @xmath11 @xmath12 ; dickey & lockman 1990 ) . the @xmath13 kev luminosity is about @xmath14 . fixing the @xmath10 at a higher value ( @xmath15 @xmath12 ; see below ) , the luminosity is about a factor of 2 higher . the combined low state data , however , can not be fitted with any single - component model . a simple power - law model produces a soft excess . we therefore fitted the spectrum with a composite blackbody and power - law model ( @xmath16 @xmath12 , @xmath17 ev , and @xmath18 ; see table 2 ) ; the power - law component contributes roughly @xmath19 ( 30% ) of the absorbed ( unabsorbed ) 0.37 kev flux . during the 2004 outburst , blackbody models provide good fits to the spectra . disk blackbody model is also equally acceptable ; the inner disk temperatures are slightly higher than the blackbody temperatures , but the normalizations ( hence the inner disk radii ) often have large error ranges . in general , the blackbody temperatures are between @xmath20 ev , and the @xmath10 is about @xmath21 @xmath12 , significantly higher than the galactic value . we also fitted the spectra with the @xmath10 fixed at @xmath11 @xmath12 . however , all the fits are unacceptable with reduced @xmath7 between 1.5 and 2.4 . the 0.37 kev luminosity ranges from @xmath22 to @xmath23 . we also derived the bolometric luminosity from the normalization of the blackbody model and it is between @xmath24 and @xmath2 . in two cases , the spectra are complex and single component models can not provide good fits to the data . we included two absorption edges in each case and the fits were significantly improved . specifically , we found absorption edges at 0.66 kev and 0.87 kev on 2004 july 6 but the edges were not observed on 2004 july 8 . instead , we found two new edges at 0.33 kev and 0.56 kev . we used similar techniques to analyze the _ xmm - newton _ data . we extracted the source spectrum from a @xmath25 radius circle centered on the source . the source was fainter than previous _ chandra _ observations with about 160 background - subtracted counts in epic - pn . since the source was detected only in epic - pn , we fitted the epic - pn spectrum with several single - component models . however , all the fits are unacceptable . we therefore fitted the spectrum with a composite blackbody and power - law model . the model consists of a supersoft component ( 53 ev ) and a hard power - law tail ( @xmath26 ) ; the power - law component contributes about 40% ( 8% ) of the 0.37 kev absorbed ( unabsorbed ) flux . the 0.37 kev luminosity is @xmath27 , indicating that the source was in the decay stage of the outburst . notes all quoted uncertainties are 90% confidence . sources without reduced @xmath7 and dof values were fitted with unbinned data using cash statistics ; `` goodness - of - fit '' determined by monte - carlo simulations ( mc ) is employed and parameters of both blackbody and power - law models are shown . + @xmath28 in units of @xmath29 @xmath12 . + @xmath30 for low state data , we list the probability that the best fit model would produce a lower value of the cash statistics than that calculated from the data , as determined via xspec monte - carlo simulations . a best fit model should have a value of about 0.5 . + @xmath31 0.37 kev luminosity ( @xmath32 ) , assuming 6.7 mpc ( freedman et al . 2001 ) . + @xmath33 0.37 kev luminosity ( @xmath32 ) derived from the combined power - law and blackbody model . + @xmath34 fixed + @xmath35 combined low - state data modeled by an absorbed power - law and blackbody model . although over @xmath36 ulxs have been discovered ( miller & colbert 2003 ) , only a handful of sources have @xmath37 ergs s@xmath38 , assuming isotropic radiation ( matsumoto et al . 2001 ; gao et al . 2003 ; davis & mushotzky 2004 ; soria & motch 2004 ) . a luminosity this high is difficult to achieve in an x - ray binary unless the accretor has a mass greater than roughly @xmath39 we do have evidence that cxouj140332.3 + 542103is likely to be an x - ray binary , since its luminosity has been observed to change by a factor of @xmath40 on a time scale of hours ( mukai et al . 2003 ; distefano & kong 2003 ) . while it is possible that our luminosity estimates are higher than the true luminosity , the effects that lead to overestimates , such as beaming , or various anisotropies , tend to change estimated luminosities downward by a factor of roughly @xmath41 its unusually high bolometric luminosity ( @xmath42 ergs s@xmath38 ) , coupled with its short - time - scale time variability , therefore make cxouj140332.3 + 542103a good candidate for an accreting imbh . for instance , king et al . ( 2001 ) proposed that anisotropic x - ray emission can result super - eddington luminosity for a stellar - mass bh . however , in order to achieve such a high luminosity for a stellar - mass bh , extreme beaming is required and the disk is expected to be much hotter . similarly , the temperature of radiation pressure - dominated accretion disk model proposed by begelman ( 2002 ) is too high . the pure blackbody spectrum also makes relativistically beaming ( krding et al . 2002 ) unlikely . its soft spectrum in the high state is another important piece of evidence . an accretion disk around a very massive bh is expected to produce supersoft x - ray emission ( see distefano & kong 2002 ) . for instance , if the supersoft emission comes from the inner disk , a 70 ev sss at luminosity of @xmath23 corresponds to a @xmath43" +"quantum entanglement , an interesting and attractive phenomenon in quantum mechanics , plays a significant role not only in testing quantum nonlocality , but also in processing a variety of quantum information tasks @xcite . multi - particle entangled states , such as ghz states , w states , cluster states , noon states , etc , are the fundamental resource of quantum information processing ( qip ) . the noon states , as an intereting multi - particle entangled states , have the form as latexmath:[\[\label{01 } which contain @xmath1 indistinguishable particles in an equal superposition of all being in one of the two possible modes . it s well established that the noon states have significant applications either in lithography @xcite or in quantum metrology @xcite . especially , it can be used to obviously improve the phase sensitivity in quantum interferometry and beat the classical diffraction limit in quantum lithography @xcite . recently , much attention has been paid to prepare the noon states . many theoretical and experimental schemes have been proposed for generating the noon states via optical components @xcite , cold atomic ensemble @xcite , superconducting circuits @xcite and cavity quantum electrodynamics ( qed ) @xcite . however , the success probabilities of the proposals based on the linear optical components , are very low as the number of particles increasing @xcite . some people suggested using the optical nonlinear process for the generation of noon states . yet , it is difficult to carry out experimentally so far @xcite . the qed system , as a suitable candidate for demonstrating qip and quantum state engineering @xcite , has been studied extensively . many proposals for preparing noon states based on qed have been put forward , as previously mentioned . however , all of these systems are always affected by the various of external factors which will induce the decoherence and affect the probability of success , even destroy the entanglement . although many kinds of physical systems are used to avoid or reduce the decoherence , it is always imperfect yet . so the preparation of the entangled multi - particle noon states is still a severe challenge in the state of the art , though great progress has been made in recent decades . on the other hand , the adiabatic passage @xcite , as an useful tool for realizing qip , is becoming more and more powerful and charming owing to its robust against the spontaneous emission of the excited states , cavity photon leakage and some experimental parameter errors . as a result , the technique of adiabatic passage has been extensively studied for the entanglement generation @xcite . in this paper , we propose a scheme for generating the noon states of two sets of the atoms via adiabatic passage . in the scheme , a double @xmath0-type three - level atom is trapped in a bimodal cavity and two sets of @xmath0-type three - level atoms are translated into and outside of two single mode cavities respectively . after a series of operations and suitable interaction time , the arbitrary large-@xmath1 entangled noon states of two sets of @xmath0-type three - level atoms in distant cavities can be obtained by performing a single projective measurement on the double @xmath0-type three - level atom . our scheme has the following characteristics : ( 1 ) due to along the dark state , the cavity modes are unpopulated during the whole interaction process , hence the scheme is robust against the decays of the cavities . ( 2 ) owing to adiabatical eliminations of atomic excited states , the spontaneous emission rate can be regarded as zero . ( 3 ) under certain conditions , the probabilities of fibre modes populated can be negligible safely , thus the decays of fibres are effectively suppressed . ( 4 ) taking advantages of adiabatic passage , the scheme is insensitive to small fluctuation of experimental parameters . ( 5 ) the scheme can be used to generate arbitrary large-@xmath1 noon states in theory . the rest of the paper is organized as follows . in sect . 2 , the fundamental model and hamiltonian are introduced . in sect . 3 , we propose a scheme to generate atomic noon states via adiabatic passage . finally , we discuss the fidelity of the scheme and summarize the conclusion in sect . the schematic setup for generating atomic noon states is shown in fig . [ fig01 ] . there are three distant optical cavities connected by two fibres ( fibres a and b ) . the two sets of @xmath0-type three - level atoms are stored in two transverse optical lattices respectively and translated into and outside of the cavity 1 and cavity 3 simultaneously and respectively @xcite . the level configurations of the atoms interacting with cavities 1 and 3 respectively are shown in fig . [ fig02](a ) and fig . [ fig02](b ) . the states @xmath4 and @xmath5 are two ground levels and @xmath6 is an excited level of the atoms interacting with cavity 1 ( 3 ) . the transition @xmath7 is coupled to the mode of cavity 1 ( 3 ) with the coupling constant @xmath8 . the transition @xmath9 is driven by the classical field with time - dependent rabi frequency @xmath10 . the frequency detunings between the atomic transitions @xmath11 . they satisfy the corresponding two - photon resonance conditions . the atom in the bimodal cavity 2 is a double @xmath0-type three - level atom . the relevant atomic levels and transitions are depicted in fig . [ fig03 ] . such level structure can be achieved in @xmath12 @xcite . two degenerate ground states @xmath13 and @xmath14 correspond to @xmath12 atom hyperfine levels @xmath15 and @xmath16 of the level @xmath17 , while two degenerate excited states @xmath18 and @xmath19 correspond to @xmath15 and @xmath16 of the level @xmath20 . on the other hand , two intermediate semi - stable states @xmath21 and @xmath22 correspond to @xmath23 and @xmath24 of the level @xmath25 , respectively . the transition @xmath26 is driven by a classical field @xmath27 with rabi frequency @xmath28 ; @xmath29 is coupled to the left(right ) circular polarized cavity mode with the coupling constant @xmath30 ; the transition @xmath31 is driven by another classical field @xmath32 with rabi frequency @xmath33 . the frequency detunings of the cavity modes and classical cavity @xmath27 from the respective atomic transitions are the same and denoted as @xmath34 . now , we consider the case both cavity 1 and cavity 3 have one atom respectively , thus the hamiltonian of atom - cavity system under the rotating - wave approximation can be written as ( @xmath35 ) @xmath36 where @xmath37 and @xmath38 are the creation and annihilation operators of the cavity 1(3 ) ; @xmath39 and @xmath40 are the creation and annihilation operators of left(right ) circular polarization of the cavity 2 . for convenience , here we have set @xmath41 . the first four terms on the right - hand side in eq . ( [ 2 ] ) represent the atom level shifts induced by classical fields . by using the nonresonant coupling of other lasers with the corresponding atom levels , these energy level shifts can be compensated straightforwardly @xcite . considering the cavities are initially in vacuum states , the hamiltonian @xmath42 can be further simplified into @xmath43 where @xmath44 are the effective rabi frequencies for the corresponding raman transitions @xmath45 . in our scheme , three cavities are connected by two optical fibres a and b. in the short fibre limit , only one ( resonant ) mode of a fibre interacts with corresponding cavity modes . the interaction hamiltonian of fibre - cavity system can be approximated to @xmath46+\eta_{b}[b_{b}(a_{2r}^{\dag}+a_{3}^{\dag})]+\rm h.c .. \end{aligned}\ ] ] where @xmath47 and @xmath48 are the annihilation operators of the resonant modes of fibre a and b respectively and the polarizations of the fibre modes a and b have been chosen as the left circular and the right circular polarizations , respectively . @xmath49 is the coupling strength between the fibre mode a(b ) and corresponding cavity modes . lastly , in the interaction picture , the total hamiltonian of the system can be written as @xmath50+\eta_{b}[b_{b}(a_{2r}^{\dag}+a_{3}^{\dag})]+\rm h.c .. \end{aligned}\ ] ] in this section , we will show how to deterministically prepare the multi - particle noon states . considering that both the cavity modes and the fiber modes are all in vacuum states , initially , and the double @xmath0-type three - level atom is prepared in the superposition state @xmath51 with the method of ref . @xcite , while atoms interacting with cavities 1 and 3 respectively are in the state @xmath52 , so the initial state of the whole compound system is @xmath53 for the initial state @xmath54 , dominated by hamiltonian ( [ 05 ] ) , the evolution of the system state remains in the subspace with one excitation number spanned by the basis vectors @xmath55 ) has a dark state ( i.e. , zero energy eigenstate of hamiltonian ( [ 05 ] ) ) @xmath56 . for the initial state @xmath61 , dominated by hamiltonian ( [ 05 ] ) also , the evolution of the system state remains in the subspace with one excitation number spanned by the basis vectors @xmath62 ) has a dark state @xmath63 . after the above adiabatic processes , the system state @xmath68 can be achieved . here , @xmath69 denotes @xmath70 . after that , we turn off the classical field @xmath27 and apply the classical field @xmath32 with rabi frequency @xmath33 on the double @xmath0-type three - level atom to drive the transition @xmath71 , the state of the whole system becomes @xmath72 here , in order to describe the process for preparing the atomic noon states clearly , we introduce symbol @xmath73 which denotes the @xmath74-th atom through the cavity 1(3 ) is in the state @xmath75 . the state in eq . ( [ 18 ] ) is the new initial state again . then turn off the classical field @xmath32 and turn on the classical field @xmath27 simultaneously . after repeating the above adiabatic process and choosing suitable interaction time each time , the whole system evolves successively into the states @xmath76 here , in the sign @xmath77 , @xmath78 donates there are @xmath1 atoms through the cavity 1(3 ) in the state @xmath5 ; @xmath79 donates there are @xmath1 atoms in the state @xmath80 . at last , we use a classical field @xmath81 to implement a hadamard operation @xmath82 becomes @xmath83.\end{aligned}\ ] ] now , a single projective measurement should be performed on the double @xmath0-type three - level atom . if the double @xmath0-type three - level atom is detected in the state @xmath13 , eq . ( [ 21 ] ) collapses to latexmath:[\ ] ] where @xmath89 @xmath90 is the amplitude of @xmath91 ; @xmath92 is the total adiabatic time and @xmath93 is the laser beam waist . @xmath94 is the time we turn on the laser with rabi frequency @xmath91 on the corresponding atoms . for showing expression ( [ 25 ] ) clearly , we plot the time dependence of @xmath95 of the laser fields in fig . [ fig04](a ) and the population curves of @xmath96 and @xmath97 with @xmath98 in fig . [ fig04](b ) . the system parameters are chosen as @xmath99 ghz , @xmath100 , @xmath101 and @xmath102 . it can be seen from fig . [ fig04](a ) that the conditions @xmath103 can be satisfied during the whole evolution for realizing the noon states . in addition , we can see from fig . [ fig04](b ) that when @xmath104 , the population of @xmath97 is 1 , which means the noon states can be deterministically achieved via adiabatic evolution . certainly , all" +"the whole set of data in the plane n / o - o / h ( for references od data see table 1 from @xcite ) , such as they are shown in fig . [ data ] , are limited by three possible theoretical lines : 1 . the line defined by the secondary nitrogen behavior , ns , when n needs a seed of o to be created . the corresponding one for primary nitrogen , np , when n is created directly from h or he for any oxygen abundance 3 . ns+np when both contributions there exist it is evident that a primary n contribution must exist . actually , a secondary production of n is expected for most stars as corresponds to a cno cycle , but it is well established that a primary production should arise from intermediate mass stars ( @xmath1 ) that suffer dredge - up and hot - bottom burning episodes during the asymptotic giant branch ( @xcite ) . _ vs _ the oxygen abundance @xmath2 observations . black small points are the sdss galaxy data from @xcite . yellow open dots are data for galactic stars . the green open , solid blue and cyan squares are the hii region data for mwg , metal - rich and metal - poor galaxies , respectively , ( including in the last ones data from @xcite and @xcite estimates ) . the large cyan open triangle is lowest galaxy known data , given by @xcite . red fill dots are values for damped lyman alpha objects . ] using massive star yields from @xcite and low and intermediate star yields from @xcite with a certain proportion of primary n , dependent on metallicity , a galactic chemical evolution model ( gcem ) has been calculated ( @xcite ) which reproduces most data of the milky way galaxy ( mwg ) . in fig . [ mwg ] the mwg model results are shown separately for the halo ( a ) and for the disk ( b ) . in each panel the evolution for four regions , located at different distance of the galaxy center are represented . the evolution in the halo is similar for all regions , reaching the level observed of relative abundance n / o and maintaining an almost constant ratio . this behavior is in agreement with the observed trend for the halo stars , in particular the recent ones from @xcite and from @xcite . in the disk , however , each radial region has its own evolution , as corresponds to the different star formation history that occurs in each one . the outer regions with quiet star formation histories have still low oxygen abundances when the intermediate stars begin to eject their primary nitrogen , while the inner regions , that suffer a strong and early star formation rate , have created many generations of stars , ans consequently produced high oxygen abundances before this np appears in the interstellar medium . for @xmath3 or 4 kpc this np appears at almost solar oxygen abundances , shown in the figure like a smoother increase or even as a flattening of the evolutionary track . for comparison purposes we also draw the solar region model from @xcite where np proceeds from low z massive stars rotating at very high velocity . our model reproduces better the observations . since these stellar yields seem to be good enough to fit the galactic data we apply them to a wide grid of theoretical galaxies with different total mass ( @xcite ) . using different star formation rate efficiencies , we obtain different results of abundances for the whole set of models . for details , see @xcite . in fig . [ all ] we show the results , for all calculated times and models , as small dots . over them we have plot some contours in yellow levels . furthermore , we draw some other contours as solid lines for regions with 0.3 , 0.03 , 0.012 and 0.003 % , respectively , of the total number of points . the model results for all time step is also in agreement with the observed trends showing : * the low mass galaxies maintain a flat behavior in the plane n / o - o / h with an almost constant abundance n / o even for oxygen abundances as low as @xmath4 * the massive galaxies show a different trend in that plane depending on their star formation history . the most efficient in forming stars , that is those that create them by mean of a high and early star formation rate , seem to have a secondary behavior from the first moment with a very steep evolution of n / o _ vs _ o / h . * this behavior behaves more like _ primary+secondary _ , that is with a smaller slope in that graph , when stars form less efficiently reaching the primary line of low mass galaxies when the star formation rate is very low . these simulated galaxies would appear as low brightness massive galaxies . * the predicted dispersion is also large , as shown by the observations . _ vs _ the oxygen abundance @xmath2 resulting from our models for the present time as full black dots compared with the data corresponding to galactic and extragalactic hii regions of sdss galaxies ( @xcite , small cyan and green points for metal - rich and metal - poor galaxies ) , to galactic and extragalactic hii regions from authors of table 1 of @xcite ( blue open and full squares , respectively ) , and for low metallicity galaxies ( @xcite as green triangles ) . the long - dashed line is the least squares fitting function to models . the large triangle around @xmath5 is the value found by @xcite for the lowest - metallicity star - forming galaxy known . ] we represent the present time model results in the plane n / o vs o / h in fig . [ present ] as small black points , that we compared with the galactic and extragalactic hii regions data . the models are fitted by a least - squares polynomial function : @xmath6 where @xmath7 . we demonstrate that using yields from lim mass stars and a model with star formation efficiencies variable for each galaxy , we may obtain points in the plane n / o - o / h in agreement with data , even for what refers to the observed dispersion which also may partially be simulated with our models . in the figure we have plot a shaded rectangle showing the region where abundances n / o fall within a gaussian distribution , which implies that differences shown by points in this zone with models may be mainly imputed to observational errors ( @xcite ) . finally , in order to explore the time evolution of the modeled abundances , we show in fig . [ redshift ] the results for four different time steps : @xmath8 , @xmath9 , @xmath10 , and @xmath11 gyr . these epochs would correspond to redshifts z@xmath123.8 , 3.7 , 3.5 , and 0 , respectively , for a cosmology with h@xmath13 , @xmath14 , @xmath15 , if the formation of these spiral and irregular galaxies occurred at a redshift z@xmath16 . a large gap appears between the results for each one of our time steps . in particular , our models predict a feature similar to the so - called _ second plateau _ which centurin et al . ( 2003 ) claim to exist at a metallicity around @xmath17 , which appears at a level of @xmath18 for @xmath19 , while most points appear at a higher level of n / o ( @xmath20 ) for a similarly low o / h abundance . in fact , no gap is apparent between models at 1.1 and 13.2 gyr , thus making it difficult to discriminate objects at a redshift up to @xmath21 from those at redshift z=0 in the n / o - o / h plane , as it is actually the case . the abundances predicted for galaxies at redshift @xmath22 are far enough from the rest of the points in the plot so as to disentangle them from a given data sample . these results are only partially due to the dependence with metallicity of the yields we use . this contribution of primary n , larger for low metallicity stars than for high metallicity ones , is important since it allows to us to obtain tracks in the plane n / o _ vs _ o / h flatter than the ones predicted with a constant contribution of the primary n. we must to do clear , however , that if we eliminate the metallicity dependence from the yields , we still obtain different tracks for regions with different star formation histories , such as we demonstrate with detail @xcite . the absolute level of observations and the fine tuning of the observed shape in the plane n / o - o / h for the present time data , however , is only reproduced if the stellar yields , in turn , give the right level of primary nitrogen and have the adequate dependence on metallicity . the chemical evolution models must also be well calibrated in order to predict star formation histories able to produce abundances in agreement with data . therefore , the adequate selection of metallicity dependent lim star yields joined to the accurate chemical evolution models are able to predict abundances for n and o which reproduce the complete set of data in the plane n / o _ vs _ o / h . * the evolutionary track of a region or galaxy in the plane n / o - o / h is very dependent on the star formation history . when this occurs as a strong burst the evolution follows a _ secondary _ behavior while a continuous , quiet and low star formation rate gives a flat slope in that plane . * intermediate star formation histories are between the two referenced extreme trends , producing this way a large dispersion of the corresponding data which is similar to the observed one * the final points of our realizations , corresponding to the present time abundances , reproduce very well the trend given by hii regions data . * the trend given by low - metallicity data from the mwg halo is also well fitted . * the data proceeding from high - redshift objects may be easily explained with the abundances calculated for other evolutionary times . in particular something like a _ second plateau _ appears when results for @xmath23 are plotted ." +"eta carinae is a key object to understand the evolution of massive stars . it is one of the most luminous stars known and underwent a great eruption that created the homunculus 150 years ago . since then , the nature of @xmath0 carinae has been the subject of an intense debate . however , the star does not fit any of the proposed models - see davidson & humphreys ( 1997 ) for a review . in the last three decades the prevailing view was that @xmath0 car is a single luminous blue variable star ( lbv ) . the spectroscopic events - fading of high excitation lines - occasionally observed , were interpreted as being imprints of s doradus oscillations @xcite . the regularity of the 5.5 year cycle , however , makes such a hypothesis unlikely @xcite . the binary system proposed by damineli , conti & lopes ( 1997 - hereafter dcl ) brought new insight to the problem . the solution to the radial - velocity ( rv ) curve of the broad component in the paschen@xmath2 line resulted in two massive stars ( @xmath3@xmath4 ) . the large mass - loss rates of the stars would imply strong wind - wind collision producing thermal hard x - rays . the highly eccentric orbit would produce phase - locked x - ray variability . those features are in accord with the observations @xcite indicating that @xmath0 car is a colliding - wind binary ( cwb ) . davidson ( 1997 ) presented an alternative solution to the dcl data , leading to similar characteristics but larger eccentricity . the parameters of the binary system , however , were not trustworthy because they were derived from only one cycle and based on a single emission line . the prediction of a spectroscopic event for late 1997 through early 1998 opened an outstanding opportunity to test this model against the , at the time dominant , idea of recurrent shell ejection . the expected event indeed occurred at the right time as shown by the spectroscopic data analyzed in the next section . the event was also detected at radio wavelengths @xcite and in x - rays , displaying a dramatic variation @xcite . a full 2-d hydrodynamic simulation @xcite and even a simple cwb model @xcite reproduce the overall behavior of @xmath0 car in x - rays . however , significant discrepancies remain around periastron . this is not unexpected , taking into account that near periastron the stars are close enough for deviations from spherical symmetry to be important . the wind is probably non - spherical and an equatorial disk may surround the primary star . the event observed in optical / near - infrared spectral lines and at radio wavelengths is due to a cause different from that in x - rays , despite their temporal coincidence . following damineli , lopes , & conti ( 1999 ) , the secondary star is the main source of hard photons , not the wind - wind colliding zone . the immersion of the secondary star into the companion s wind prevents hard photons from reaching the external regions of the wind of the primary and the circumstellar gas . the resulting effect is a temporary drop in the degree of ionization and , consequently , the fading of the high excitation lines . although preliminary results indicate that @xmath0 car is likely to be a binary , critical tests must be carried out to provide a definitive proof . such tests are provided in this letter , based on the data collected in a spectroscopic campaign initiated in 1989 that covered twice the 5.5 year cycle . spectroscopic observations of @xmath0 car were carried out at the european southern observatory - eso / chile and at the national astrophysical laboratory - lna / brazil - see wolf et al . ( 1999 ) and damineli et al . ( 1999 ) for details . the [ ] and [ ] spectral lines plummeted in november 1997 and disappeared a month later @xcite . around that time , the near - infrared light - curve reached a local maximum @xcite and the spectroscopic lines a minimum , similar to those reported by whitelock et al.(1994 ) and by damineli ( 1996 ) . since we have detailed observations of the 1992 event , we folded them with the 1998 event . the sawtooth structure in the rv curve provides an accurate measure of the elapsed time between the last two events . we plotted in figure 1a the rv variations of the broad component in @xmath56678 for the 1998 event ( solid line ) superposed with the previous event shifted by 2020 days ( dotted line ) . the matching was obtained by shifting one relatively to the other by @xmath6 days . the same recurrence time was derived from pa-@xmath7 although the uncertainty is larger for this line due to a smaller number of observations . we should not expect , a priori , that line intensities would result in the same elapsed time as for rv . the narrow component in [ ] @xmath56312 and @xmath56678 lines disappeared around 12 december 1997 ( jd 2450794@xmath82 days ) . the same was observed on 2 june 1992 ( jd 2448775@xmath85 days ) , resulting in a recurrence time @xmath9 days , compatible with that from rv curve . this time scale is also in agreement with @xmath10 days proposed by dcl based on the 1948 , 1965 , 1981 , 1987 and 1992 events . this is an indication that the previous events resembled closely the last two ones we have observed : deep and brief . if the events had lasted longer , no obvious strict periodicity would have been hinted from such a short list of occurrences . if line intensity fadings had not been so remarkable they would have been mistaken as secondary fluctuations that are frequent in the @xmath0 car spectrum . an additional way of checking whether the periodicity is true is by comparing our data with those of gaviola ( 1953 ) . the description of the spectrum collected by that author in 1948 is detailed enough to show that @xmath0 car was very close to the center of a spectroscopic event on april 19th . he reported that [ ] @xmath55755 was fainter than [ ] @xmath55748 . our spectra collected during the last two events show that such an inversion of intensities remains for less than three months around the center of an event . the 9 cycles between the 1948 and the 1998 events constrain very well the uncertainty in the periodicity : @xmath11 days . this figure is in excellent agreement with that described above , based on the last two events . we can conclude that the events in @xmath0 car are truly periodic with @xmath12 days ( or @xmath13 years ) . the equivalent widths of the spectral lines , especially and the high - excitation forbidden lines , are quite predictable from cycle to cycle . in figure 1b we display the @xmath56678 line during the events of 1998 and 1992 ( the latter one shifted by 2020 days ) . this figure implies that the emitting volume and the speed of gas display a phase - locked behavior . due to the fact that no luminous hot star has been observed pulsating in such a regular fashion and ejecting identical shells , we rule out stellar instability as the mechanism responsible for the spectroscopic events in @xmath0 carinae . the orbital solution presented by dcl had been discussed by davidson ( 1997 , 1999 ) . some concerns have been raised about the reliability of the broad - line components to trace the orbital motion . on the one hand , broad lines are formed inside the wind and should display doppler shifts if the star were a binary . on the other hand , radiative - transfer effects could mask doppler motion . if the event is produced by the plunging of the secondary star into the primary - star wind ( damineli , lopes , & conti 1999 ) , the ionization structure of the wind should change around periastron , mixing together doppler and radiative - transfer effects . different lines would display different line - profile variations , making it difficult to predict what line tracks the orbital motion better . the best candidates are lines ( broad components ) displaying small changes in equivalent width and in line shape , with as faint as possible p cygni absorption components . some hydrogen paschen lines are free of blends and look suitable for this purpose , as seen in dcl ( their figure 1 ) . lines show strong variability in intensity and line - profile . deblending the broad components from the nebular and p cygni contamination is not as straightforward as in h - paschen lines . the observed changes in lines reflect more the excitation effects in the wind than doppler motion of the stars and this is why we did not use them in the rv solution . the large number of observations we collected for @xmath56678 line , however , still makes it the best tool to measure the period length . the rv curve containing all the available pa-@xmath7 and pa-@xmath14 data results in the solution displayed in figure 2 . the best fit gives : @xmath15 , @xmath16 , @xmath17jd@xmath18 ( 17 february 1998 ) , @xmath19 km s@xmath20 and @xmath21 . conjunctions occur at phases 0.999 and 0.438 . the standard deviation is @xmath22 km s@xmath20 . this result is in general agreement with those of damineli , lopes , & conti ( 1999 ) and davidson ( 1997 ) . the main difference between present and previous results is the smaller mass function , ( @xmath23 ) , accommodating a smaller mass for the secondary star , which is desirable , since its spectrum is not visible in the optical or the uv . the mass of the unseen companion is difficult to be constrained , as it depends on the mass of the primary - star , the mass - loss rate and the orbital inclination . regarding the primary - star we adopt dcl s m@xmath24 , based on the total luminosity of the star , the age of tr16 cluster and standard evolutionary models . figure 2 gives strong support in favor of binarity in @xmath0 car , but it does not necessarily guarantee that our orbital elements are accurate . there are two problems with our rv curve . first , pa-@xmath7 shows changes in the shape of the broad - line component , indicating that the wind is not rigidly following the star . the effect in the rv curve seems to be small because the @xmath7 velocity ( -12 km s@xmath20 ) derived from the rv curve agrees with v@xmath25 km s@xmath20 obtained by conti , leep , & lorre ( 1977 ) from seven o - type stars in the carina nebula . second , data around the periastron are scarce , which is a problem for a system with such a high eccentricity . acceptable eccentricities range from e@xmath260.65 up to e@xmath260.85 , displacing the time of periastron by several months ( up to 0.05 in phase ) around the center of the spectroscopic event . the other orbital elements are less sensitive to the details of the rv curve around periastron . the recovery of the 1998 spectroscopic event within @xmath271% of the predicted time supports the hypothesis of true periodicity . the strict repeatability in the rv curve and line intensities is unambiguously in favor of the binary model and against the idea of an unstable star as the explanation of the 5.5 year cycle . regardless" +"galaxies at redshifts beyond @xmath0 become increasing irregular @xcite as a result of rapid gas accretion @xcite , strong gravitational instabilities @xcite , and distortions produced by massive clumps @xcite and mergers @xcite . most of this change is driven by increasing self - gravity in the gaseous component of the disk , which increases in relative mass and mach number toward higher redshifts @xcite . local disks like the milky way have a relatively small gas fraction in the inner few scale lengths , and self - gravity operates somewhat separately in the stars and gas , making spiral arms in the stars on large scales , and molecular clouds in the gas on small scales . star formation processes may vary also with these morphologies , from what is presumably a collapse of gas to dense cores as a result of the strong instabilities at high redshift , to secondary instabilities inside gas that is first compressed by quasi - stable spirals or previous generations of star formation . the star formation efficiency and maximum mass of a bound stellar cluster could change too , perhaps explaining the prevalence of massive globular clusters in early phase disks @xcite . a number of recent surveys have extended studies of galaxy structure and evolution through much larger fields and at longer wavelengths than the original hudf optical study , including cosmos ( cosmic evolution survey ; @xcite ) and candels ( cosmic assembly near - infrared extragalactic legacy survey ; @xcite ) . these broad surveys provide statistical samples of galaxies and are useful for studying global galaxy properties over cosmic timescales . one of the largest recent studies includes nearly 1700 galaxies from candels over the redshift range @xmath3 to compare star formation properties and morphology based on @xmath4-band light profiles and other global indicators such as the gini coefficient , concentration , and asymmetry @xcite . they conclude that the basic hubble sequence of disk and spheroidal galaxies was set by @xmath52 . we are interested in understanding the physical processes in the intermediate states of an evolving galaxy disk , between the high - redshift clumpy phase and the low - redshift spiral phase . do the clumps gradually shrink as the turbulence dissipates and the stellar disk builds up @xcite , or is there a new morphology with massive substructures that are both spiral - like and clump - like at intermediate redshifts ? in an unpublished study of @xmath6 spiral galaxies out to @xmath7 in the cosmos fields based on wfpc2 optical images , we found a mixture of grand design , multiple arm , and flocculent spirals over the whole redshift range , although the fraction of multiple arm galaxies increased at lower redshift . in a study of @xmath8 galaxies out to @xmath9 @xcite in the gems ( galaxy evolution from morphology and seds ; @xcite and great observatories origins deep survey ( goods @xcite ) fields , we found these three morphologies out to @xmath0 and also found two clumpy types that overlapped in the same redshift range . one type had massive clumps with no evident underlying disk , and the other type had equally massive clumps with an underlying red disk . the ages and surface densities of the clumps and interclump regions suggested that the former evolved into the latter as the disks grew from dispersed clumps . two similar types were also found at @xmath10 in the udf @xcite where about half of the clumpy galaxies had red bulges that were older and more massive than the other clumps , and the other half had no bulge - like clumps . the ages of these clumps also suggested an evolutionary sequence in the characteristic morphology of spirals , although at @xmath10 we could not measure the faint interclump population . here we focus on early - phase spirals rather than late - phase clumps . the combination of depth and resolution needed to examine spiral structure at high redshift is available only in the hubble ultra deep field ( udf ; * ? ? ? * ) optical acs images , so we examine morphology primarily from these images . we supplement these with the wfc3 @xmath4-band images of the udf when available , although the decreased resolution and longer wavelength sometimes miss spiral details . this paper examines disk galaxies as a function of redshift out to @xmath11 in the udf , dividing the spiral types into the usual classifications of grand design ( two symmetric arms ) , multiple arm ( several long arms with an irregular distribution in the outer parts ) and flocculent ( small patches of star formation throughout the disk ) . we also look for unusual morphologies that could be transition cases between clumpy and spiral disks . we find grand design spirals out to at least @xmath12 in the udf . the highest redshift grand design spiral so far reported is in the 3-arm galaxy bx442 at @xmath13 @xcite . at these high redshifts , the hst acs optical bands show only the restframe ultraviolet , where star formation dominates . we should still be able to see spiral structure in the restframe uv , however . galex images show spiral arms in local galaxies in restframe nuv and fuv , in the familiar beads - on - a - string pattern of star formation ; each string is an arm in the visible bands . thus we can look for spirals in the higher redshift galaxies by the filamentary alignment of their star formation clumps , as well as look in the @xmath4-band directly for spiral arms . we present our observations in section [ sect : obs ] , an interpretation in section [ sect : int ] , and our conclusions in section [ sect : conc ] . we examined by eye the morphological details of the spiral galaxies in the udf based on our catalog of 269 spirals larger than 10 pixels in diameter @xcite . of these , 184 are edge - on or too inclined to discern clear spiral structure , 8 are disturbed tidal interactions or mergers , 5 should probably have been classified as clump clusters , 20 have featureless disks except for a bulge , and 11 have no redshifts . the remaining 41 , which have redshifts and clear spiral structure , are the ones included in the present study . both the optical acs images and the @xmath4-band images were used when available ; about half of the 41 galaxies fell outside of the @xmath4-band field . the galaxies are listed in table 1 , with photometric redshifts from @xcite . the redshifts , which include uv data , are accurate to @xmath14 ; 36 of the 41 galaxies have only one probability peak p(z ) , which makes their redshifts relatively unambiguous . three of the remaining four have a secondary probability peak at a redshift less than 0.1 different from the primary redshift ; udf 501 with a primary redshift of 1.37 has a secondary probability peak nearby at @xmath15 ; udf 9018 with a primary at @xmath16 has a secondary at @xmath17 . the table also includes the restframe @xmath18-band absolute magnitude , the effective radius , the exponential disk scale length , the sersic index , and the spiral arm type , to be discussed more below . figure [ fig1new ] shows 15 spiral galaxies from the udf in color images from the udf skywalker that were made from acs archival images in bands @xmath19 , @xmath20 , and @xmath21 @xcite . the black and white images are of the third galaxy from the left in each row , taken in @xmath22 band with wfc3 for hudf09 and downloaded through the hst mast hslp archives @xcite . the udf numbers from @xcite are indicated in the upper left of each frame . white bars in the lower left of each frame indicate an angular scale of 1 , while white bars in the upper right indicate a linear scale of 5 kpc . for reference , the pixel scale of the optical hudf images is 0.03 , with a fwhm resolution of 0.1 @xcite , while the @xmath4-band hudf09 image has a pixel scale of 0.06 and a fwhm resolution of 0.16 @xcite . each row in figure [ fig1new ] is a different morphological type . the top row has three conventional grand design galaxies ( designated type `` g '' ) with fairly symmetric spiral arms , central bulges or bars , and smooth underlying disks . the arms are open , wrapped at most @xmath23 , and dotted with star formation knots and streaks . other grand design galaxies are in table 1 . the largest redshift for this morphology in the udf is @xmath24 for udf 9444 . in the second row are three normal - looking multiple arm galaxies ( type `` m '' ) that resemble a common type in the local universe . the arms in the outer parts are long and thin , sometimes wrapping for @xmath23 or more , and the arms in the inner parts are usually symmetric , sometimes with a short bar . the highest redshift that we found for this type of spiral is 0.6 for udf 2607 in the figure . this is significantly smaller than the largest redshift for the grand design spirals , of which there are four with @xmath25 . thin arms in multiple arm galaxies like this require cool disks . it may be that this cool phase comes later than the first grand design galaxies , whose structure may be induced by strong bars or interactions even in hot disks ( see below ) . the third and fourth rows contain galaxy morphologies that are relatively uncommon in the local universe . in the third row are multiple arm galaxies with long , thick and bright arms that cover most of the disks . the arms are clumpy and the clumps are relatively large . there are bright interarm clumps too . galaxies 968 and 5417 have offset nuclei . local analogs also including a high proportion with offset nuclei are types ic in the kiso ultraviolet survey of galaxies @xcite , whose clumps were found to be comparable in mass to the clumps in udf clumpy galaxies ( not shown in the figures here ) , and which also have multiple spiral arms @xcite . the row - three galaxies in figure 1 differ from the kiso type ic galaxies , however , because the row - three galaxies have arms that are relatively thick , bright and nearly continuously filled with clumps . we consider this a new morphology for spiral galaxies that should be placed between purely clumpy galaxies at high redshift and density - wave spiral galaxies at low redshift . their distinctive feature is their thick patchy long arms . a term that comes to mind is `` woolly '' ( type `` w '' in what follows ) which is somewhat like `` flocculent '' but connotes something more dense in structure . three more of these galaxies are shown in the top of figure [ fig2 ] . the fourth row in figure [ fig1new ] shows another odd type of structure consisting of long , generally thin and multiple arms with haphazard distributions and varying pitch angles . there are bright star - formation knots along the arms , which is a common feature of most spiral arms , but no symmetry . some have small bars which seem unrelated to the spirals . this is another morphology that one might expect in an era of strong gravitational instabilities , which readily produce large , shearing and chaotic - looking material arms , but the clump size has decreased by now , perhaps because of a" +"adaptation is a common feature in sensory systems , well familiar to us from light and dark adaptation of our visual system . biological cells , ranging from bacteria to complex eukaryotes , including single - cell organisms and human sensory receptors , adopt different strategies to fulfill this property . however , all of them require substantial amounts of energy to adapt . here , we compare the different biological strategies and design two minimal models which allow adaptation without requiring energy consumption . schemes similar to the ones we proposed in our minimal models could have been adopted by ancient protocells , that have evolved into the pathways we now know and study . analyzing our models can thus help elucidate the advantages brought to the cells by consumption of energy , including the bypassing of hard - wired cell parameters such as diffusion constants with increased control over time scales . the ability to adapt to different environmental conditions is a hallmark of any living organism , allowing sensory systems to adjust their sensitivity to changes in nutrient availability , stress , and other stimuli @xcite . adaptation mechanisms generally rely on biochemical feedback pathways , specific for the organism and type of stimulus @xcite . surprisingly , when comparing adaptation pathways in different organisms , one can not help noticing the wide variety of pathway designs , ranging from remarkably simple in bacterial chemotaxis @xcite to highly complex in eukaryotes , including _ dictyostelium discoideum _ chemotaxis @xcite , olfactory - transduction @xcite and photo - transduction @xcite . since bacterial chemotaxis is known to work ( and adapt ) exquisitely well , it is unclear why eukaryotic organisms have such elaborated pathway designs , and what their advantages might be . in light of such complexity , the `` physicist s approach '' may help guide the identification of common principles among the different pathways . recently , lan _ et al . _ @xcite analyzed a core adaptation pathway and concluded that adaptation always relies on energy consumption by the cell . however , whether it is generally impossible to adapt without consuming energy is still an open question , considering how adaptation mechanisms could have evolved in ancient protocells without sophisticated pathways . we address this issue by first comparing the sensory pathways of small bacterial and large eukaryotic cells , highlighting their similarities and differences . we then investigate the possibility of achieving adaptation with no energy consumption by means of a `` protocell '' based on equilibrium physics . the hypothesis of no cost of energy for the cell guides us in designing minimal adaptation mechanisms . by pondering the drawbacks of these mechanisms and the advantages brought by energy - consuming pathways , we unravel some of the complexity of sensory systems . these considerations may provide a path towards a general theory of adaptation in eukaryotic cells . constrained by their small size , bacteria are spatially highly organized @xcite . consider e.g. bacterial chemotaxis in _ escherichia coli _ , known for amplifying weak signals by cooperative receptors and precise adaptation ( fig . [ fig : pathways]a ) . there is an apparent high level of local control in these processes : receptors are arranged hexagonally in clusters @xcite and the adaptation enzymes cher and cheb are tethered to the receptors to increase local enzyme concentration and specificity , and to reduce noise @xcite . adaptation in bacterial chemotaxis is a robust feature of the pathway , without `` fine - tuning '' of biochemical parameters @xcite , achieved by integral feedback control @xcite . integral feedback control @xcite and the related incoherent feedforward loop @xcite are also found in eukaryotes . despite these similarities , eukaryote s most striking feature is the staggering complexity , often relying on long , multistep signaling cascades in parallel @xcite . consider three different pathways : chemotaxis in _ dictyostelium discoideum _ [ fig : pathways]b ) , and photo- ( fig . [ fig : pathways]c ) and olfactory - transduction ( fig . [ fig : pathways]d ) in mammalian sensory systems . perhaps most perplexing , the key signaling component for all of them are small , fast - diffusible second messengers , like @xmath0 for olfactory- and photo - transduction ( which is even toxic for the cell in large quantities @xcite ) , and camp in _ dictyostelium _ amoeba . relying on these small signaling molecules could negatively affect the precision of the response . due to their fast diffusion , affected targets may not only be the designated molecules , but large parts of the cells . moreover , all of the eukaryotic examples mentioned rely on g - protein coupled receptors ( gpcr ) . the excitation of the receptor catalyzes the production of gtp and the dissociation of the g - protein . gtp then binds to the @xmath1 subunit and the @xmath2 subunits ( for _ dictyostelium _ @xcite ) or the @xmath1 subunit ( for photo- and olfactory - transduction @xcite ) can activate the downstream processes . the activity of the guanosine triphosphatase ( gtpase ) hydrolizes the gtp which detaches from the @xmath1 subunit . subsequently , the @xmath1 subunit can re - bind the @xmath2 subunits , thus reassembling the g - protein @xcite . all bacterial and eukaryotic adaptation pathways share the consumption of energy by hydrolysis of fuel molecules , including s - adenosyl methionine ( sam ) in bacterial chemotaxis , and cyclic adenosine and guanosine monophosphate ( camp and cgmp ) in eukaryotes @xcite . these observations led to the conclusion that energy consumption is an essential ingredient in precise adaptation @xcite ( see fig . [ fig : pathways ] , middle panel , for a definition ) . however , ancient protocells might have been able to respond and adapt to stimuli without this requirement , with molecular components added later by evolution , to produce the currently observed pathways . as it turns out , our protocell models , which only rely on equilibrium physics for the cellular components , may help unravel some of the signaling complexity in eukaryotic cells . here , we present two minimal models in which a protocell exploits the non - equilibrium aspect of the changing external environment to respond and adapt to a stimulus without consuming ( dissipating ) energy itself . the first model contains only one component , represented by a receptor on the cellular membrane ( fig . [ fig : models]a , left ) . this receptor includes two sensing regions : the first binds extracellular ligand , the second mediates intracellular sensing and adaptation . as soon as the ( extracellular ) ligand arrives at the cell surface , the receptor binds and starts signaling . however , the stimulus molecules are also able to permeate the cellular membrane , e.g. via passive pores , and to consequently bind additionally to the intracellular region of the receptor . this second binding blocks the signaling activity of the receptor , thus precisely counteracting the activation due to the extracellular binding . in case the external stimulus can not be used to mediate adaptation , e.g. for photo - transduction , a second model with two components is needed ( fig . [ fig : models]b , left ) . the first represents the receptor , which senses the extracellular stimulus and , upon stimulation , releases two intracellular subunits , @xmath3 and @xmath4 . the @xmath3 subunit is smaller and can diffuse faster than the @xmath4 subunit . the second component is a membrane - bound protein , able to respond to the binding of the @xmath3 and @xmath4 subunits . in particular , the binding of @xmath3 to this second protein causes an increase of its signaling activity , while the binding of @xmath4 exactly compensates for it , and hence turns signaling off . * one - component model . * let us assume the cell is initially equilibrated to concentration @xmath5 and then the external concentration is suddenly changed to @xmath6 . the resulting difference in concentration between inside and outside the cell equilibrates following the solution of the diffusion equation with spherical symmetry ( hypothesizing that the cellular membrane is sufficiently permeable)@xcite @xmath7 where @xmath8 is the internal concentration at time @xmath9 , @xmath5 and @xmath6 are the respective initial internal and external concentrations , @xmath10 is the radius of the cell , @xmath11 the diffusion coefficient , and @xmath12 the normalized radius corresponding to the inner length of the receptor @xmath13 ( see fig . [ fig : main_results]a for a schematic ) . we further assume that external ligand binding favors the receptor _ off _ ( inactive ) state ( with ligand dissociation constants @xmath14 ) and that the internal ligand binding favors the _ on _ ( active ) state ( @xmath15 ) , in order to compensate for external ligand binding during adaptation . for simplicity , we consider @xmath16 and @xmath17 . the corresponding free - energy difference of the single receptor and the activity associated with it become ( using equilibrium boltzmann statistics ) @xcite @xmath18 with energy in units of @xmath19 . figure [ fig : main_results]b shows adaptation of the one - component model to an extracellular concentration - step change as input , @xmath20 ( left ) . the intracellular concentration response @xmath8 due to the diffusive process for different lengths of the inner side of the receptor ( middle ) allows the activity output , @xmath21 , to adapt precisely at no cost for the cell ( see figs . s1-s4 for additional results ) . * two - component model . * the second model also relies on equilibration for adaptation , albeit by an all - internal mechanism ( see fig . [ fig : main_results]c ) . the external concentration @xmath6 becomes the input for the first component - the receptor , which responds to the transmembrane free - energy difference by changing its activity . in particular , its free - energy difference and activity are , respectively , @xmath22 parameter @xmath23 represents the bias towards the off state in absence of external stimulus , and the contribution of the binding energy of the @xmath3 and @xmath4 subunits on the cytoplasmic domain of the receptor . the concentration of @xmath3 and @xmath4 , released by the first component , is set proportional to the activity @xmath24 . the solution of the diffusion equation , eq . , is then used to represent the diffusive process of @xmath3 and @xmath4 molecules from the receptor to the second component . the free - energy difference and the activity of the second component are calculated as @xmath25 where , for simplicity , we assume @xmath26 and @xmath27 ( see text s1 for details ) . figure [ fig : main_results]d shows adaptation of the two - component model . the outer concentration is followed by activity @xmath24 of the first component , which does not adapt ( left ) . however , the ratio in the concentrations of @xmath3 and @xmath4 , as sensed by the second component after diffusion ( middle ) , allows the activity @xmath28 to adapt precisely ( right ) . hence , similar to the one - component model , also the two - component model achieves precise adaptation , just relying on diffusion of the @xmath3 and @xmath4 subunits at no energy cost ( see figs . s8-s11 for additional results ) . * energy dissipation . * our models do not require energy consumption , but achieve adaptation by means of the _ external _ energy provided by the stimulus . figure [ fig : entropy]a shows the resulting energy - dissipation rate of the one - component model , which confirms that most energy" +"nonlinear frequency conversion of far - infrared or microwave signals into the optical domain has been actively used for detection of such signals @xcite . the relative ease of optical signal detection compared to e.g. those in the sub - thz range , in combination with an intrinsically noiseless character of nonlinear frequency conversion , explains the close attention this method has been receiving . its main drawback , however , is its low conversion efficiency . the highest power conversion efficiency known to us is about 0.5% , which has been only recently achieved for 100 ghz signal using 16 mw of cw optical pump at 1560 nm @xcite . this number corresponds to the photon - number conversion efficiency of approximately @xmath0 , as follows from the manley - rowe relation . highly efficient and noiseless upconversion of microwave radiation into the optical domain would open up numerous possibilities in microwave imaging and communications . one example of such a possibility , that we have discussed earlier @xcite , is microwave photon counting at room temperature . reaching the photon - counting regime in the sub - thz or thz range would be an achievement important for quantum information processing and computing , sub - millimeter spectroscopy and astronomy , security , and for other areas where the ultimate sensitivity detection of microwave radiation is desired . unfortunately , even the most efficient up - converter to - date is still seven orders of magnitude short of the photon - counting regime for 100 ghz photons at room temperature @xcite . on the other hand , the theoretical analysis @xcite shows that this regime can be achieved . the key to its realization is reaching unity conversion efficiency . an all - resonant whispering gallery mode ( wgm ) configuration of the frequency converter should achieve this goal . wgm resonators with optical nonlinearity have been successfully used in nonlinear optics in general and in microwave photonics in particular @xcite . in a recent experiment @xcite a lithium niobate wgm resonator with the optical free spectral range ( fsr ) @xmath1 ghz was irradiated by a microwave signal with the frequency near @xmath2 ghz . this device is analogous to a lower - frequency electro - optical modulator @xcite , except that the microwave signal excites the sidebands not in the pair of adjacent to the carrier optical wgms , but in those across eight of optical fsrs . to describe the operation of such a modulator , we follow the steps of @xcite and introduce the interaction hamiltonian @xmath3 which couples the optical pump and microwave signal wgms ( photon annihilation operators @xmath4 and @xmath5 , respectively ) with the stokes and anti - stokes optical upconverted signal ( @xmath6 and @xmath7 , respectively ) . in case of a single side - band modulation @xcite only one , either the stokes or the anti - stokes , term is present in hamiltonian ( [ h ] ) . the coupling constant @xmath8 includes the ( bracketed ) factor describing the overlap between the fields inside the resonator . in eq . ( [ g ] ) , @xmath9 is the optical frequency , @xmath10 are the refraction indices and @xmath11 is the optical mode volume ; @xmath12 , @xmath13 and @xmath14 are similar microwave parameters . the effective electro - optical coefficient @xmath15 is determined by the fields configuration . irradiating the resonator with the microwaves by placing the former near a waveguide opening is a very inefficient method of coupling the microwaves with the optical wgms , as the main part of the microwave energy reflects back into the waveguide or scatters into space . this problem can be solved by using an all - resonant frequency up - converter , supporting microwave wgms as well as optical ones . experimental studies of microwave wgms in crystalline disks and rings carried out in the 1980 s shown remarkable quality factors of @xmath16 @xcite . for the all - resonant up - converter , all wave functions @xmath17 in ( [ g ] ) are optical or microwave eigenfunctions of the wgm resonator . the eigenfrequencies @xmath18 of the main family of the optical wgms is found @xcite as @xmath19 where @xmath20 is the orbital momentum for this wgm , and @xmath21 is the resonator radius . similar equations hold for the stokes and anti - stokes frequencies @xmath22 . the hamiltonian ( [ h ] ) and eq . ( [ g ] ) lead to the following phase - matching conditions , that are essentially the energy and angular momentum conservation equations for the anti - stokes and stokes processes : @xmath23 subtracting eq . ( [ eigen ] ) for @xmath24 from that for @xmath22 and making substitution ( [ phasematch ] ) , we find the phase - matching equation @xmath25 for the anti - stokes ( plus ) and stokes ( minus ) conversion processes . in ( [ phasematch1 ] ) @xmath26 is the optical fsr for the signal wgm . we have neglected its frequency dispersion replacing @xmath27 , but kept the distinction between @xmath28 and @xmath29 which is due to the birefringence . the phase matching condition ( [ phasematch1 ] ) needs to be solved jointly with the microwave dispersion equation , which depends on the resonator geometry . previously @xcite we have observed lower frequency microwave wgms in lithium niobate disks in the 30 ghz range . one important conclusion of that study has been that the microwave wgms in a disk resonator have poor spatial overlap with the optical modes that occupy just a few tens of microns near the disk rim . this greatly reduces the overlap factor in ( [ g ] ) . therefore we decided to use ring resonators , made so that the optical axis of the crystal is parallel to the ring axis . when filled with a low - constant dielectric , such a ring tends to concentrate the microwave field inside , enforcing a better overlap with the optical wgms . once the phase - matching conditions are fulfilled , the microwaves - to - optics conversion will be efficient as long as the nonlinear coupling rate exceeds the loss rate in the microwave wgm , that is , if the total loss rate of the thz mode @xmath30 is dominated by the rate of nonlinear frequency conversion @xmath31 . experimentally this means that the microwave wgm resonances will be considerably broadened when the optical pump is turned on . then if the optical wgms couple strongly to the input and output free - space beams ( i.e. the resonator is optically over - coupled ) the unity - efficient conversion is theoretically possible @xcite . efficient in- and out - coupling of the optical wgms requires the external rim of the ring to be shaped as a spheroid with the radii ratio equal to @xcite @xmath32 where @xmath33 is the refraction index of the prism used for the optical coupling . let us assume for the rest of the paper that the optical pump has the wavelength @xmath34 @xmath35 m ( @xmath36 s@xmath37 ) . then for a diamond prism @xmath38 , while e.g. for lithium niobate @xmath39 . therefore according to ( [ r2r ] ) , @xmath40 . epsf let us find the phase matching solutions . first , we assume that the microwave as well as _ both _ optical fields are polarized along the optical axis , so that the largest nonlinearity coefficient of lithium niobate @xmath41 is used . in this configuration , which we dub type - i up - conversion , @xmath42 and the last term in eq . ( [ phasematch1 ] ) disappears . to find the phase - matching solutions , we plot eq . ( [ phasematch1 ] ) together with the microwave dispersion curve , see fig . [ fig : phasematch ] . intersection of the two curves at an integer value of @xmath43 indicates that the phase - matching is achieved . the accuracy to which the two frequencies should match at this value of @xmath43 is determined by the smaller of the optical and microwave wgm linewidths . notice that the microwave dispersion curve ( b ) in fig . [ fig : phasematch ] depends on all four geometric parameters of the ring , while the phase - matching curve ( a ) depends only on the external radius @xmath21 . this gives us enough freedom to achieve the phase - matching at a desired microwave frequency . in the example shown in fig . [ fig : phasematch ] the phase - matching was found for @xmath44 ghz at @xmath45 . the ring thickness was @xmath46 m , its inner and outer radii were @xmath47 mm and @xmath48 mm , and the rim curvature found from ( [ r2r ] ) was @xmath49 m . the microwave dispersion curve is obtained by numerical simulation . these simulations have been carried out in a finite element solver , comsol @xcite adapting an axis symmetrical formulation by oxborrow @xcite . fused silica was selected as the post material because of its low microwave absorption and relatively small microwave refraction index ( n=1.9 at 100 ghz ) , compared to the larger values @xmath50 and @xmath51 for lithium niobate @xcite . in this configuration the microwave field is strongly concentrated inside of the resonator ring , see fig . [ fig : wfring ] , which provides both good coupling with the external waveguide and good overlap with the optical field . -component of a microwave wgm mode in a lithium niobate resonator with @xmath52 ghz , @xmath45 . the plot is on a log scale with color map given on the right . a sketch of the geometry is shown in the inset , where the red box represents the calculation window.,height=188 ] we would like to point out that the purpose of the numeric simulation is not to achieve the exact phase - matching , but only to unambiguously determine the angular momentum @xmath43 . an error small compared to the microwave fsr would be tolerable , because the phase matching can be fine - tuned via modifying the microwave dispersion of the system . for example , placing a metal ring on the fused silica post near the resonator ring , we have been able to tune the microwave frequency by more than 0.5 ghz without appreciable degradation of the quality factor . now let us consider the type - ii up - conversion , i.e. when the signal polarization is orthogonal to the pump polarization @xcite . in this case the birefringence term in ( [ phasematch1 ] ) does not vanish . in fact , in strongly birefringent materials it can be quite large . in lithium niobate , for example , it is equal to approximately @xmath53 thz . the plus "" sign corresponds to either anti - stokes conversion of the ordinary polarized pump , or stokes conversion of the extraordinary polarized pump . similarly , the minus "" sign corresponds to either stokes conversion of the extraordinary polarized pump , or anti - stokes conversion of the ordinary polarized pump . it is easy to see that neither situation allows for the phase matching solution compatible with the microwave dispersion equation and lying in the transparency window of lithium niobate . epsf the type - ii up - conversion can be realized , however , in weakly birefringent materials . for example , in stoichiometric lithium tantalate the birefringence term is equal to approximately @xmath54 thz @xcite . while the positive "" solution is still impossible , the negative "" phase matching solution now can be achieved , see fig . [ fig : phasematcht ] . one important distinction between the type -" +"elongated galaxies with bright clumps at one end are visible in deep field images taken with hst or from the ground ; van der bergh et al . , 1996 called them `` tadpole '' galaxies "" . figure 1 in elmegreen et al . ( 2005 ) shows different morphologies of galaxies observed with the hubble ultra deep field ( udf ) . the fourth row presents images of tadpoles . this asymmetric morphology is rather common at high redshift but rare in the local universe . for example , tadpoles constitute 10% of all galaxies larger than 10 pixels in the udf ( elmegreen et al . 2007 ; elmegreen & elmegreen , 2010 ) , and they represent 6% of the udf galaxies identified by straughn et al . ( 2006 ) and windshorst et al . ( 2006 ) using automated search algorithms . in contrast , elmegreen et al . ( 2012 ; hereafter paper i ) , find only 0.2% tadpoles among the uv - bright local galaxies of the kiso survey by miyauchi - isobe et al . this decrease suggests that the tadpole morphology represents a common but transition phase during the assembly of some galaxies . since local tadpole galaxies are very low mass objects compared to their high redshift analogues , this phase must be already over for the local descendants of high redshift tadpoles . the tadpole structure has inspired several explanations , such as ram pressure stripping that triggers star formation at the leading edge , to mergers ( see snchez almeida et al . 2013 for an extensive review ) . the explanation that we propose , based on observational evidence summarized here , is that the starburst head may result from the accretion of an external flow of pristine gas that penetrates the dark matter halo and hits and heats a pre - existing disk , which is viewed to the side as the tail . we will briefly present a summary of recent results showing , first that the local tadpoles share the properties of their higher redshift and higher mass counterparts ( section 2 ) , that they belong to the extremely metal poor ( xmp ) sample of the blue compact dwarfs family ( section 3 ) , they are rotating discs ( section 4 ) and , finally , that the starbursts ( heads ) show a drop in the already low metallicity that can only be understood if fresh metal - poor gas is falling onto the galaxy ( section 5 ) . we finish with a brief summary and future actions . we used sloan digital sky survey data to determine the ages , masses , and surface densities of the heads and tails in 14 local tadpoles ( shown in figure [ cmt - fig1 ] ) selected from the kiso and michigan surveys of uv - bright galaxies , and we compared them to tadpoles previously studied in the hubble ultra deep field . the result , published in paper i is that the young stellar mass in the head scales linearly with the rest - frame galaxy luminosity , ranging from @xmath0 @xmath1 at galaxy absolute magnitude @xmath2 mag to @xmath3 @xmath1 at @xmath4 mag . the tails in the local sample look like bulge - free galaxy disks . their photometric ages decrease from several gyr to several hundred myr with increasing redshift . the far - outer intensity profiles in the local sample are symmetric and exponential . we suggest that most local tadpoles are bulge - free galaxy disks with lopsided star formation , perhaps from environmental effects such as ram pressure or disk impacts , or from in - situ gas collapse to a giant star - forming clump with a jeans - length that is comparable to half the disk size . the existence of a disk , proposed from the analysis of the luminosity profiles , has been further confirmed spectroscopically ( see section 4 ) . blue compact galaxies are important targets for a number of reasons . they are small systems , thought to remain as fossils or debris from the formation of larger galaxies in the early epochs of the universe . their low metallicities , high ssfrs and low doubling time ( less than 1gy ) and active stabursts make them ideal targets to study the old universe at low redshift . their complete census , as well as the likelihood that they have a long quiescent phase between starbursts , took us to study the whole sample by making use of sdss . the properties of the quiescent and burst phases were determined from detailed studies of the bursts and host galaxies of a nearby sample ( amorin et . al . , 2007 , 2008 ) . these properties allowed us to identify such objects in the database . the sdss dr6 database provides @xmath5 21.500 quiescent bcd candidates , a number 30 times larger to those bursting ( bcds ) . this result implies that one out of every three dwarf galaxies in the local universe may be a quiescent bcd . the properties of the two samples are consistent with a single sequence in galactic evolution with the quiescent phase lasting 30 times longer than the burst phase ( snchez almeida et . al . , 2008 ) . in snchez almeida et al . ( their figure 9 ) there is a clear subsample of objects with the lowest luminosity which turn out to be also those that are most metal poor . we carried out a systematic search for extremely metal - poor ( xmp ) galaxies in the spectroscopic sample of sloan digital sky survey ( sdss ) data release 7 ( dr7 ) ( morales - luis et al . , 2011 ) . the xmp candidates are found by classifying all of the galaxies according to the form of their spectra in a region 80 @xmath6 wide around h@xmath7 using an automatic classification algorithm , _ k - means _ ( snchez almeida et al.,2009 ) . our systematic search renders 32 galaxies having negligible [ n ii ] lines , as expected in xmp galaxy spectra . twenty - one of them were previously identified as xmp galaxies in the literature , and 11 were new . this was established after a thorough bibliographic search that yielded only some 130 galaxies known to have an oxygen metallicity 10 times smaller than the sun ( explicitly , with 12 + log [ o / h ] @xmath8 7.65 ) . xmp galaxies are rare ; they represent 0.01% of the emission lines galaxies in sdss / dr7 . the xmp galaxies constitute 0.1% of the galaxies in the local volume , or @xmath5 0.2% of the emission - line galaxies . all but four of our candidates are bcd galaxies , and 24 of them have either cometary shape or are formed by chained knots . note that this result , the morphology , is absolutely independent of our search criterium ( spectra ) . the work in paper i was followed up by mean of high spectral resolution long slit observations at the int ( 2.5 m ) at observatorio del roque de los muchachos ( orm ) with ids spectrograph . in order to determine the dynamical properties and metallicities of local tadpoles , we measured h@xmath7 spectra along the head - tail direction in a representative fraction of the original sample . further details are in snchez almeida et al . ( 2013 ) . in figure [ cmt - fig3 ] , we show spectral flux ( the solid lines ) and h@xmath7 flux ( the dashed lines ) along the slit . note the obvious lopsidedness of the light distributions , as expected from the tadpole shape . the origin of distance on the abscissa has been set as the position of the maximum of the spectral flux distribution . the dotted line represents a gaussian fitted to the h@xmath7 flux around the head . the horizontal bar in each panel gives a common length scale corresponding to 1 kpc . the thin vertical solid lines indicate the center of rotation obtained from the rotation curve fit shown in fig . [ cmt - fig4 ] . velocities , masses , abundances and other physical parameters were determined from the spectra . bulk velocities were measured from the displacement of h@xmath7 . we computed the displacement both as the barycenter of the emission line , and as the center of a gaussian function fitted to the profile . errors were estimated from the s / n measured in the continuum and then propagated to the centroids . the fwhm of the profiles were also measured directly from the profiles and from the gaussian fits . their errors were also inferred from the noise measured in the continuum by error propagation . figure [ cmt - fig4 ] shows the velocity curves of the tadpole galaxies included in the study . the abscissae represent distances along the major axes of the galaxies from the position of the tadpole head ; i.e. , the brightest point on the galaxy . the range of distances differs for the different targets , but the horizontal bar in each panel gives a common length scale corresponding to 1 kpc . the points with error bars show the observations whereas the thick solid line represents the best fit of the observed points to the analytic rotation curve . the part of the rotation curve shown in red indicates the portion of the velocity curve used for fitting . the thin horizontal and vertical lines indicate the systemic velocity and the center of rotation obtained from the fit , respectively . the little arrows on top of each panel also indicate the centers of rotation . the zero of the velocity scale is set by velocity of the spatially integrated spectrum of the galaxy ; positive velocities are redshifts . the main result shown in figure [ cmt - fig4 ] is that five out of seven targets show velocity gradients interpreted as rotation . another important result is that the tadpole head is not at the rotation center . sometimes the interpretation of the velocity curve as rotation is obvious ( e.g. , kiso8466 ) , but other times the curve looks more like a perturbed rotation ( e.g. , kiso5639 ) . kiso3193 and kiso3867 have a rather flat velocity curve , and therefore no obvious rotation . however , one of them , kiso3867 , shows a systematic line shift of the order 1020 kms@xmath9 between the two extremes of the galaxy ( figure [ cmt - fig4 ] ) . the amplitude is of the order of the error bars , but the displacement is in the raw data as judged by inspection of the individual h@xmath7 profiles . the metallicity along the slit was estimated using the ratio [ nii]@xmath106583 to h@xmath7 . figure [ cmt - fig6 ] taken from snchez almeida et al ( 2013 ) shows the variation across the galaxies of the oxygen abundance , including their error bars . all galaxies have sub - solar metallicity - the thick horizontal line marks the solar oxygen abundance given by @xmath11 ( asplund et al . , 2009 ) . the galaxies also present significant abundance gradients , with the lowest abundances tending to coincide with the largest h@xmath7 emissions ( e.g. , kiso6669 and kiso6877 ) in fig . [ cmt - fig6 ] . remember that the vertical dotted lines mark the position of the peak h@xmath7 fluxes . two targets , kiso5639 and kiso6877 , have metallicities well below one - tenth the solar value , therefore , they belong to the xmp galaxies class ( kunth & stlin" +"the modern approach to the study of a dynamical system identifies solving the problem with finding the global structure of phase space . on the other hand , bifurcation theory has mostly concentrated on _ local behavior in the parameter space _ ( so even when global phase space bifurcations are considered , they are always considered in a small neighborhood of a given parameter value ) . here we suggest that global analysis with respect to parameters leads to understanding of the phase space structure in parameter regimes which are unreachable by the currently known analysis techniques . in particular , we examine some features of the global dependence of periodically forced systems with finite forcing amplitude on the forcing frequency . the study of the effect of periodic forcing on homoclinic loops has been thoroughly investigated since the times of poincar . analytical understanding of such systems has been attained in three possible limits ( see @xcite,@xcite ) : the fast and slow oscillations limits and the small forcing limit ( see figure [ fig : spanfam ] ) . for fast oscillations averaging methods apply , and together with kam theory , these are used to obtain upper bounds on the separatrix splitting . these bounds are exponentially small in the frequency ( @xcite,@xcite ) . lower bounds on the separatrix splitting involve delicate analysis which has been proved , under some structural assumptions on the flow , only in recent years ( see @xcite and references therein ) . the slow oscillations regime corresponds to the region where adiabatic theory applies . two approaches have been applied to this limit - the first one corresponds to extending classical adiabatic theory to separatrix crossing ( @xcite,@xcite ) and the other corresponds to examining the geometrical properties of stable and unstable manifolds to hyperbolic manifolds with slowly varying motion on them ( see @xcite,@xcite,@xcite,@xcite ) . most of the analytical studies have been performed in the small oscillations regime in which perturbation methods apply ( see ( @xcite ) and references therein ) . the most important ingredient from these studies to the current paper is the existence of a flux mechanism via lobes ( see @xcite,@xcite,@xcite,@xcite,@xcite ) . here we show that for a large class of systems , the phase space structure and its associated transport properties have some common non - monotone dependence on the frequency of the forcing term . namely , we establish that in some cases , even for finite size oscillations , there exists a function which depends on the frequency continuously . after some natural scaling , this function is simply the sum of the areas of the incoming lobes per period , normalized by the forcing period . hence , results obtained in the fast and slow limits supply information regarding the behavior in the intermediate regime where no analytical methods apply ( see figure [ fig : spanfam ] ) . furthermore , this proposed viewpoint leads to a non - traditional scaling of the flow which is relevant for studying its behavior near homoclinic tangles . this paper supplies mathematical formulation and generalization of the common work of the author with a. poje @xcite , in which similar issues were considered in the context of fluid mixing . the paper is organized as follows : in the first section we define the class of forced hamiltonian families which we consider . roughly , these are forced hamiltonian families with split separatrices , for which the splitting exists for all positive parameter values and as the family parameter varies the scaled frequency includes the semi - infinite line . in the second section we construct a labelling scheme for primary homoclinic orbits , which relies on the concepts of unstable ordering introduced by easton @xcite . this labelling scheme is valid for all parameter values and behaves well across homoclinic bifurcations . in the third section we prove the main result of this paper - that the flux through the homoclinic loop depends continuously ( in fact it is @xmath3 ) in the spanning parameter of the family ( in @xcite we considered a restricted class of systems for which the continuity of the flux followed immediately ) . to prove this result several properties of the lobes are studied , the details are included in appendix 2 . in the fourth section we recall the proof of rk and poje , showing that the flux is non - monotone in the scaled frequency and recall the implications of these results , especially in view of their implications regarding the stochastic zone width ( see @xcite ) . section five includes a demonstration of these concepts for the forced center - saddle bifurcation problem . conclusions are followed by two appendices - in the first the homoclinic scaling is discussed whereas in the second detailed proofs of some properties of the lobes are included , the relation between the flux and the areas of the exit and entry sets is explained , and the adiabatic limit is discussed . consider a one - and - a - half degree of freedom hamiltonian @xmath5 which is @xmath6 periodic in its last argument and depends smoothly on the parameter @xmath7 where @xmath8 may be finite or infinite . this hamiltonian may be written in the form @xmath9 where the second term has zero time average : @xmath10 and may be as large as the first one . assume the hamiltonian system of ( [ ham ] ) : @xmath11 satisfies the following structural assumptions : a1 : : @xmath12 and @xmath13 are @xmath14 functions of all their arguments , @xmath13 is @xmath6 periodic with zero mean in its last argument . a2 : : for all @xmath0 values in @xmath15 $ ] , ( [ hamsys ] ) possesses a hyperbolic periodic orbit which depends smoothly on @xmath0 . a3 : : the family of hamiltonians spans the frequency parameter : the frequency @xmath16 is a smooth @xmath14 function , and it maps the interval @xmath17 onto the semi - infinite line : @xmath18 furthermore , @xmath19 only at one of the interval s boundaries and at no interior point . a4 : : for @xmath20 , for any phase @xmath21 , at least one branch of the stable and unstable manifolds of that periodic orbit coincide to form a homoclinic loop . furthermore , the manifolds and the homoclinic loops created at @xmath20 depend smoothly on @xmath21 , and the phase space area enclosed by these homoclinic loops , @xmath22 , is non - constant and has a finite number of extrema : @xmath23\backslash\{\theta_{1},\theta_{2}, ... ,\theta_{n_{0}}\}\text{.}\ ] ] for concreteness , with no loss of generality , we assume that at @xmath20 the manifolds topology is of a lying figure eight ( closed geometry ) or of a fish swimming to the left ( open geometry ) , so the left branches always coincide at @xmath20 , see figure [ fig1 ] . . a. closed geometry ( lying 8) b. open geometry ( fish).,width=415 ] for @xmath24 , consider the standard global poincar map @xmath25 of the extended phase space @xmath26 which is simply the time-@xmath27 map of the time dependent flow ( here @xmath21 is introduced to account for phase variations ) : @xmath28 the two dimensional symplectic map @xmath25 has , by the above assumptions , a hyperbolic fixed point @xmath29 with its associated stable and unstable manifolds . @xmath30 is a _ primary _ homoclinic point of @xmath29 iff the open segments of the unstable ( respectively stable ) manifold connecting @xmath29 with the homoclinic point @xmath30 , @xmath31 ( respectively @xmath32 ) do not intersect ( @xcite,@xcite ) : @xmath33 the points @xmath34 in figure [ fig2 ] are all primary homoclinic points , whereas the intersection points of the manifolds inside the shaded region in figure [ fig5 ] are homoclinic points which are not primary . we assume : a5 : : for all @xmath35 there is a finite number of primary homoclinic orbits . furthermore , for each intersecting branches of the manifolds there exist at least two primary homoclinic orbits which are topologically transverse . a6 : : the number of _ primary _ homoclinic bifurcations is bounded in any bounded open interval of @xmath0 for all @xmath35 . the order of the _ primary _ homoclinic bifurcations is uniformly bounded by the integer @xmath36 + for convenience of notation , let us assume that @xmath37 finally , to establish asymptotic behavior in the frequency , we assume there exists an appropriate scaling so that the scaled separatrix length scales and the maximal velocity along the separatrix are of order one : a7 : : there exist smooth ( @xmath38 in @xmath0 ) non - vanishing scaling functions , @xmath39 @xmath40 such that in the scaled variables : @xmath41 the scaled system : @xmath42 with the two non - dimensional parameters @xmath43 : @xmath44 satisfies assumptions a1-a6 . _ furthermore , for the scaled system , the width and length of the separatrix and the maximal velocity along it are all of order one for all _ @xmath45__. _ _ @xmath46 measures the relative strength of the temporal oscillations to the mean flow whereas @xmath1 compares the oscillation s time scale with the travel time along the separatrix loop ( outside of the saddle orbit neighborhood ) . we assert that the magnitude of these two parameters supplies _ complete information on the qualitative behavior _ of the system ( [ schamsys ] ) and hence on the original system . notice that assumption a3 is now made with respect to the scaled frequency . a family of hamiltonian systems depending on a parameter @xmath0 which satisfies assumptions a1-a7 is called a _ _ frequency - spanning homoclinic family , _ _ and @xmath0 is called a _ frequency - spanning parameter . _ a few remarks are now in order : * assumptions a1-a7 clearly hold in the standard near integrable case ( small @xmath46 ) where the steady flow has a homoclinic loop of fixed size ( independent of @xmath0 ) , the perturbation is generic ( so a5 and a6 are satisfied ) , and its frequency , @xmath47 spans the half real line . * a5 refers only to _ primary _ homoclinic bifurcations - otherwise it would have been violated generically , see @xcite and references therein . * in the near - integrable case the scaling functions may be simply extracted from the integrable flow , see for example section [ sec : sadcen ] . in appendix 1 , after some notation is established in the next section , we propose an algorithm for defining the characteristic scales in the finite amplitude size forcing case . * the assumptions here are slightly weaker than the ones in @xcite : in particular a5 and a6 replace the stronger assumption of @xcite that there exists one topologically transverse primary homoclinic orbit which depends continuously on @xmath0 , a property which may be easily violated in applications . relaxing this assumption requires the introduction of a new labelling scheme for the homoclinic points which takes into account the possible annihilation of primary homoclinic points . hereafter we assume the forced system is in its scaled form and we drop all the over bars when non - ambiguous , as described next . denote by @xmath48 @xmath49 the _ topologically transverse primary _ homoclinic _ orbits _ of @xmath29 belonging to the left branch ( for simplicity of notation we consider hereafter only the left branch of the loop ) , where @xmath50 , namely the discrete index @xmath51 denotes iterations under the map and the index @xmath52 denotes the label of the specific orbit . each such transverse homoclinic point , @xmath53 defines a region , @xmath54 enclosed by the closed segments of the stable and" +"there is no more fundamental physical quantity in cosmology than the expansion rate of the universe . in recent years the present value of the expansion rate , hubble s constant , has been measured with increasing accuracy @xcite . with the exploration of the universe at redshifts of order unity , we now have information about the time evolution of the expansion rate @xcite . a most surprising result is that the time evolution of the expansion rate does not seem to be described by a matter - dominated friedmann - lematre - robertson - walker ( flrw ) cosmological model . the usual explanation for the discrepancy is that there is a new component of the energy density of the universe , known as dark energy , that determines the recent evolution of the expansion rate . of course all indications for dark energy are _ indirect _ ; they all involve some form of the time evolution of the expansion rate . since the expansion rate of the universe is of such fundamental importance , we must understand any possible effects that would result in an expansion rate different from the flrw prediction . in this paper we study the change in the expansion rate due to perturbations of a homogeneous , isotropic , flrw model . in particular , we perform a second - order calculation of the effect of inhomogeneities on the expansion rate . we only consider modifications to the expansion rate of a matter - dominated universe , although our results can be extended to a universe containing a mixture of matter and a cosmological constant . we find that the mean corrections are a few parts in @xmath0 . the expansion rate of a perturbed flrw cosmology has been discussed in many works ( although we believe ours is the first complete second - order calculation ) . hui and seljak @xcite estimated the order of magnitude of the effect by considering a representative second - order term . they arrived at the correct mean order of magnitude of the result . some recent works @xcite suggested that small - scale contributions could give a large correction , producing an apparent accelerated expansion of the universe . in particular rsnen @xcite suggested that due to ultraviolet sensitivity , one of the second - order terms could give large corrections depending on boundary conditions . as we will discuss in the conclusions , we find that if one employs the correct averaging procedure the result ( at least for the terms we could compute exactly using the second - order formalism ) is well behaved in the ultraviolet and the term identified by rsnen does not result in a large correction . in addition to calculating the mean value of the expansion rate , we calculate the variance about the mean value . in calculating the variance we uncover an interesting infrared effect . at second order the expansion rate has a term proportional to @xmath1 , where @xmath2 is the peculiar gravitational potential , related to the density perturbations through the cosmological poisson equation . if inflation is the origin of perturbations , then @xmath3 should be a gaussian random variable with zero mean . however , if the perturbation spectrum on super - hubble - radius scales is no bluer than a harrison zeldovich spectrum , then the variance of @xmath3 formally has an infrared singularity . now if the value of @xmath3 in our local hubble volume is sufficiently large to modify the expansion rate , our perturbative expansion fails . nevertheless , our results suggest that if the super - hubble modes of @xmath3 have physical significance , then a nonperturbative extension of our calculation could yield a most important modification to the friedmann equation . one might even speculate that a complete treatment of the effect could explain the observed time dependence of the expansion rate on its own and obviate the need for the dark - energy assumption . since that conjecture is beyond the perturbative calculation of this paper , we will postpone discussion of this point to a subsequent communication @xcite . in the next section we discuss the general perturbative expansion . in section [ thetasynchronous ] we calculate the corrections to the expansion rate in terms of metric fluctuations , and then express the results in terms of the density perturbation spectrum . in section [ numbercrunch ] we present the numerical results . we then conclude , followed by two technical appendices . in this section we describe how to treat the average properties of a perturbed universe up to second order in the metric variables , including the effect of the inhomogeneous gravitational field on the homogeneous background field . we then discuss the proper definition of the average expansion rate and express the effect of inhomogeneities to second order as averages of density perturbations . by `` average , '' we mean the average over a spatial hypersurface at a given time . clearly an average defined in this way depends on the chosen coordinate system , _ i.e. , _ the gauge . we will consider a universe filled only by irrotational dust and choose the coordinates of an observer at rest with the dust ( _ i.e. , _ comoving coordinates ) , and with the same time coordinate for every point of the spatial hypersurface ( _ i.e. , _ synchronous coordinates ) . this system of coordinates can be chosen if the universe is filled by a single pressureless component . since the pressure vanishes , the only force acting on the particles is gravity , and the comoving world lines coincide with geodesics . ( see ref . @xcite for a full discussion of this point . ) we will call @xmath4 the ( conformal ) time in this gauge , and @xmath5 the spatial coordinates , so that the metric has the form @xmath6 \label{metric}\ ] ] we will perform the averages on constant-@xmath4 spatial hypersurfaces . the goal of this paper is a second - order calculation , but before embarking , let us recall the familiar linearized first - order result . the energy - momentum tensor and metric are expanded to first - order as [ subonee ] @xmath7 where the superscript @xmath8 denotes the @xmath9-th order perturbation . by definition @xmath10 and @xmath11 are homogeneous and isotropic . in the synchronous gauge , to first order the metric may be written in terms of a set of perturbation variables consisting of two scalars ( @xmath12 ) , a vector ( @xmath13 ) , and a tensor ( @xmath14 ) . the vector @xmath15 is transverse ( @xmath16 ) and the tensor @xmath14 is symmetric , transverse , and traceless ( @xmath17 , @xmath18 , @xmath19 ) . in terms of these variables the metric is @xmath20 where @xmath21 . the metric perturbations @xmath22 and @xmath23 may be expressed in terms of the peculiar gravitational potential @xmath24 , which is related to @xmath25 , the first - order density perturbation , by the poisson equation , @xmath26 ignoring metric perturbations that decay in time , for a matter - dominated universe @xmath22 and @xmath23 are given by ( see ref . @xcite ) in ref . @xcite corresponds to our variable @xmath27 , and vice versa . ] [ fomp ] @xmath28 to first order we will neglect vector modes , as they do not arise in conventional perturbation - generation mechanisms such as inflation . we will also assume the tensor mode amplitude is small . in calculating spatial averages we will also require @xmath29 , where @xmath30 is the determinant of the spatial metric . to first order @xcite , @xmath31 whether calculating to first order or second order , when calculating the spatial average @xmath32 of a quantity @xmath33 one must fix a system of coordinates in which to express @xmath34 , and then integrate with the proper integration measure over @xmath35 at fixed @xmath4 . for all orders we adopt the definition which is a scalar under the residual gauge freedom . ] @xmath36 where the domain of integration is some large volume . if @xmath37 is a homogeneous quantity ( _ i.e. , _ it does not depend on @xmath5 , but only on @xmath4 ) , then simply @xmath38 . in the first - order calculation , if @xmath39 is already a first order quantity we may set @xmath40 , and @xmath41 becomes @xmath42 to first order , the einstein equations are @xmath43 which yield upon averaging the @xmath44 component @xmath45 here we see that @xmath46 may be interpreted as an extra component to the stress - energy tensor . for the unperturbed flrw cosmology , the expansion rate @xmath47 is found from the @xmath48 component of the einstein equations . for the first - order perturbed flrw model @xmath49 where @xmath50 . this is the basic point . in a perturbed flrw cosmology , @xmath51 is _ not _ @xmath52 . , where @xmath53 is related to @xmath4 by @xmath54 . ] however , one must be careful to find the true variables that describe the evolution of the averaged background . it is not clear that the quantity @xmath47 describes the physical hubble flow . the correct quantity to describe the hubble flow may be found from the evolution of @xmath55 . we know that for a homogeneous isotropic universe there are two independent equations that govern the dynamics of the expansion . so we have to find the two independent equations that describe the evolution of averaged physical quantities such as like @xmath56 . for the unperturbed model we may augment the @xmath48 equation with the continuity equation , @xmath57 . this gives for a perfect pressureless fluid ( dust ) @xmath58 where @xmath59 and @xmath60 is the fluid four velocity . ( [ continuity ] ) is true to all orders . for an unperturbed flrw universe with scale factor @xmath61 , this immediately gives @xmath62 , which results in @xmath63 . for the perturbed model , we want to expand eq . ( [ continuity ] ) to first order and then average it . this will give us the effective scale factor for the dilution of the matter density . in addition to the expansion of @xmath64 , we expand @xmath65 as @xmath66 and obtain @xmath67 using the fact that @xmath68 we are left with @xmath69 this tells us that in a first - order perturbed universe the average matter density is diluted with expansion according to @xmath70 , which in general is _ not _ equivalent to @xmath71 . an alternative way to express the result is to define a new scale factor , @xmath72 , such that @xmath73 . it is clear that @xmath72 must be defined by @xmath74 and so the _ true _ scale factor is @xmath72 and not @xmath61 , at least for the dilution of matter ( see , _ @xcite ) . the physical quantity of interest is @xmath75 . it is given by @xmath76 we will define a @xmath77 , and express @xmath65 as @xmath78 two important notational points : we have defined @xmath79 ( _ not _ as @xmath47 ) ; and we have defined @xmath80 as the difference between @xmath75 and @xmath81 ( _ not _ as the difference between @xmath75 and @xmath82 ) . to calculate @xmath83 , we can express eq . ( [ backeinstein001 ] ) in the form @xmath84 where of course the second equality holds if the corrections are small . combining eqs . ( [ combo11 ] ) and ( [ combo21 ] ) , we find @xmath85 it will turn out that in the first - order calculation @xmath86 will appear only as a spatial gradient in the final expression for @xmath80 . this means that the physical result is insensitive to" +"on chip microcavities have been proven of significant interest to the development of photonics for telecommunications . @xcite . their ability to confine electromagnetic radiation and enhancement of light - matter interactions make them suitable for signal filtering and non - linear frequency generation processes , while the compatibility with the silicon platform opens the possibility for scalability @xcite . delay lines , memories , modulators and frequency comb sources have been demonstrated in microresonator devices within the silicon platform @xcite . for practical applications , in order to select desired wavelengths , a spectral tunability of the resonant features is required . this is often achieved via electrical micro - heaters that exploit the thermo - optic effect to modify the refractive index of the environment , changing thus the optical path of the device @xcite . the thermo - optical tuning can be applied to a variety of materials systems , from silicon to silicon nitrides and oxynitrides , and is applicable to a wide range of operation wavelengths . this kind of approach , however , has a global action and does not allow to tune spectral channels separately . altering the transmission of a selected single resonance has been demonstrated , for example , by exploiting inverse raman scattering in si devices @xcite . as opposed to thermo - optical tuning , this effect is strongly selective to the operation frequencies , since the raman frequency and bandwidth depend primarily on the material choice . here we propose an all - optical approach to detune relatively the resonances within a microresonator by exploiting the thermo - optical effect at a local level . the effect is demonstrated by applying it to a whispering gallery resonator waveguide system which exhibits fano interference features @xcite . the continuous detuning is used to explore complete mode crossings between two resonances . as a particular example , this fine tuning approach allows to access the complete destructive interference point on one side of the fano lineshape , where one of the resonances disappears from the spectrum , as predicted in @xcite . + the paper is structured as follows ; section [ sec : theo ] starts with a brief theoretical summary of the system under study . the generic thermo - optic effect is described in [ sec : thermoptic ] and then , in [ sec : nonlinear ] , introduced into the dynamic equations for the field amplitude in the resonator to demonstrate the tuning of a single resonance . the model is then extended to interacting modes in [ sec : twofamilies ] . in sec . [ sec : expresults ] we report the experimental results , while sec . [ sec : simulations ] exposes the numerical simulations that match the model with the experiment . finally , sec . [ sec : concl ] gives the summary of our results and the conclusions . the wave equation inside a circular - shaped microresonator may be separated into three one - dimensional equations with quantum numbers @xmath0 and @xmath1 for the axial , radial and azimuthal coordinates , respectively . the resonator is considered to be single - mode in the axial direction ( @xmath2 ) . the set of modes with different azimuthal number @xmath1 but with the same radial number @xmath3 is addressed as @xmath4-radial mode family , denoted with @xmath5 . here , we will consider only @xmath6 and @xmath7 for the radial direction . for each radial family , the frequency of the @xmath8 mode may be calculated as @xmath9 where @xmath10 is the geometrical path of the light in the resonator , typically the circumference , @xmath11 is the effective refractive index of the mode and @xmath12 is the light velocity in vacuum . the resonator is excited and probed by a waveguide . the transmission spectrum of the waveguide - resonator system exhibits series of negative peaks , due to the capture of the modes by the resonator , where the azimuthal modes are spaced by the free spectral range ( fsr ) @xmath13 with @xmath14 being the group velocity of the @xmath8 mode . equation [ eq : main ] implies that , within a single radial family , modes with different @xmath1 lay at different frequencies , preventing photon exchange between such modes . when different radial families are present , however , there may be combinations of @xmath15 and @xmath1 which give spectrally overlapping modes ( fig . [ fig : fsr](a ) ) . while the spectral overlap may be an undesired feature @xcite , it may also provide new interesting physics if an interaction among the degenerate modes is provided @xcite . here , we will take into account the interference phenomena due to waveguide - mediated interactions among the modes of different radial families , leading to asymmetric fano resonances and energy shifts of the modes . in order to observe the fano interference , spectral overlap between a pair of modes belonging to different radial families is required . this means that @xmath16 , relative distance between the central frequency of two modes @xmath17 and @xmath18 respectively , should be at most of the same order of the largest half - width at half maximum ( hwhm ) between the two modes , @xmath19 figure [ fig : fsr](a ) shows schematically that each radial mode family is a comb of peaks obeying eq . [ eq : main ] , which are spaced spectrally by fsr according to eq . [ eq : fsr ] , @xmath20 where @xmath21 since in general @xmath22 is different for different radial families , the fsrs will also differ . this means that the two radial mode combs will slide spectrally one against the other , similar to a vernier scale @xcite , passing though a crossing point . the relative detuning @xmath23 of two modes in the couple is thus @xmath24 where @xmath25 is the relative detuning of @xmath26-couple and @xmath27 . having couples of modes of two radial families with different relative detuning permits to monitor the coupling between the two radial families when changing the @xmath1 with a discrete step of @xmath28 just by changing @xmath1 . this has been studied in detail in our previous work @xcite . the fano - interaction of two resonances offers a rich physics and is extremely sensitive to both the degree and the sign of the detuning @xmath29 . the asymmetric fano lineshape may vary abruptly with changing the detuning due to the fine interplay of the phases of individual resonances . for example , there exists a unique spectral point on one side of the composite resonance , where a particular destructive interference leads to a full suppression of one of the transmission features in the spectrum @xcite . this situation may be observed experimentally in very fortuitous cases for which a given @xmath28 exactly satisfies the necessary condition . on the other hand , the particular point can be always observed if the detuning can be continuously varied within a single couple of resonances . in the following , we demonstrate a continuous way to detune the relative frequency of a couple of modes , allowing a complete mapping of the interaction within a single couple of resonances . moreover , this approach permits us to tune finely and capture the particular point of resonance suppression . here we propose to use the thermo - optic effect @xcite , as a tool to tune the relative frequency of the resonator s modes . for small variations around room temperature , the thermo - optic coefficient @xmath30 may be defined as the first taylor expansion of the refractive index of the material as a function of the temperature . heating the sample thus induces a variation in the effective refractive indices and coupling coefficients of the cavity modes , that are consequently shifted . adding the thermo - optic coefficient @xmath30 into eq . [ eq : main ] we obtain : @xmath31 with this definition , the usual positive thermo - optic coefficient makes the resonances shift toward the red ( longer wavelengths ) when heating the sample . when a high - power laser ( hereafter , pump , @xmath32 ) is used to excite a doublet of resonances , a part of the energy is absorbed by the material by heating locally the resonator exactly in the spatial region where the modes extend . heat then diffuses gradually over the whole device . figure [ fig : thermolocal ] shows a finite elements method ( fem ) simulation of the temperature distribution inside the resonator when the electrical field distribution function @xmath33 of the first and second radial family modes are used as the thermal source . the respective spatial distribution functions of the electrical field of the modes @xmath34 are shown as contour lines in fig . [ fig : thermolocal](a ) and fig . [ fig : thermolocal](b ) . [ cols=""^ "" , ] in a next step , the non - linear pump equation , eq . [ eq : flt2p ] , is solved numerically to find the intensity distribution that generates the heat , in steady - state conditions , assuming the pump cold cavity spectrum parameters reported in tab . [ tab : simpar ] as constant during the evolution . the solution is obtained moving the laser from short to long wavelengths . figure [ fig : simmap](a ) shows that a good agreement was achieved between the experimental ( black lines ) and simulated ( red dashed line ) transmission of the pump . in fig . [ fig : simmap](b ) we show the experimental evolution of the probe spectrum as a function of the pump wavelength of panel ( a ) . the experimental map is the same as is fig . [ fig : power](b ) and is reported here in order to facilitate the comparison with the simulated map . the dynamic evolution of the relative coupling between the waveguide and the two radial family modes , that changes due to the thermo - optically altered refractive index @xmath35 , is plotted in fig . [ fig : simmap](c ) . we note that the eqs . [ eq : flt2p ] and [ eq : flt2s ] do not consider explicitly non - linear variations of @xmath36 , albeit the coupling among the waveguide and the resonator is affected by thermal detuning . the evolution of the relative coupling @xmath37 is therefore obtained by fitting the experimental probe spectra . the probe equation , eq . [ eq : flt2s ] , is linear with respect to the parametric functions of pump intensities . therefore , eq . [ eq : flt2s ] is linearly solved for each pump wavelength , producing a 2d map reported in fig . [ fig : simmap](d ) . the very good accordance between the measured and calculated maps indicates that the developed theoretical model is capturing all the details of the physical phenomenon . in this work we have reported a joint theoretical and experimental study on the possibility to tune cavity resonances via optically - driven material non - linearities . we actuated the thermo - optical effect locally around the mode extension by means of strong optical pump field , while the cavity dynamics was monitored via weak probe signal . the effect of the thermal non - linearity on the position and shape of the resonances has been exploited to tune the asymmetry of fano resonances , realizing a complete mode crossing within a single doublet of modes . moreover , we demonstrated the possibility to suppress one of these modes by fine tuning the system into a critical interaction condition . theoretically the resonator - waveguide system has been modeled via a set of non" +"quality of service ( qos ) management for web - based applications is typically considered a problem of system sizing : enough resources are to be provisioned to meet quality of service requirements under a wide range of operating conditions . while this approach is beneficial in making the site performance satisfactory in the most common working situations , it still leaves the site incapable to face sudden and unexpected surges of traffic . in these situations , in fact , it is impossible to predict the intensity of the overload . the architecture in use , although over - dimensioned , may not be sufficient to meet the desired qos . for this reason , unexpected increases of requests and most of all flash crowds are considered the bane of every internet based application , and must be addressed in terms of performance control rather than capacity sizing . due to the ineffectiveness of static resource over - provisioning , several alternative approaches have been proposed for overload management in web systems , such as dynamic provisioning , dynamic content adaptation , performance degradation and admission control . most of the previously proposed works on this topic rely on laborious parameter tuning and manual configuration that impede fast adaptation of the control policies . this work is motivated by the need to formulate a fast reactive and autonomous approach to admission control . we contribute an original self- * overload control policy ( soc ) which enables some fundamental self- * properties such as self - configuration , self - optimization , self - protection . in particular , the proposed system is capable of self - configuring its component level parameters according to performance requirements . at the same time it optimizes its own responsiveness and self - protects from overload . the proposed policy is to be adopted by web cluster dispatching points ( dp ) and does not require any modification of the client and/or server software . dps intercept requests and make decisions to block or accept incoming new sessions to meet the service level requirements detailed in a service level agreement ( sla ) . decisions whether to accept or refuse new sessions are made on the basis of a dynamically adjusted upper limit on the admission rate . this limit is updated and kept consistent with the system capacity and time varying traffic behavior , measured by an apposite self - learning , monitor module . such module performs an autonomous and continuous measurement activity that is of primary importance if human supervision is to be avoided . our proposal is oriented to the management of web based traffic , and for this reason provides admission control at session granularity . nevertheless , it does not require any prior knowledge on the incoming traffic , and can be applied to non - session based traffic as well . unlike previous works , our approach is rapidly adaptive , and also capable to deal with flash crowds which are detected as soon as they arise , with a simple change detection mechanism , that permits a fast adaptation of the rate of decision updates . the inter - decision time becomes increasingly shorter as traffic changes become sudden and fast , as in presence of flash crowds . this interval is set back to longer values when the workload conditions return to normality . although inspired by our previous work @xcite , this proposal is original as it includes the anomaly detection and decision rate adaptation mechanisms necessary to perform flash crowd management . it also provides a considerably improved measurement validation system as detailed in section [ sec : algorithm ] . we designed a synthetic traffic generator , based on an industrial standard benchmark specweb2005 , which we used to run simulations under a wide range of operating conditions . we compared soc to other commonly adopted approaches showing that it outperforms the others in terms of performance and stability even in presence of flash crowds . indeed soc does not show the typical oscillations of response time due to the over - reactive behavior of other policies . a wide range of experiments has been conducted to test the sensitivity of the proposed solution to the configuration of the few startup parameters . experiments show that the behavior of our policy is not dependent on the initial parameter setting , while other policies achieve an acceptable performance only when perfectly tuned and in very stable scenarios . the paper is organized as follows : in section [ sec : problem ] we formulate the problem of overload control in distributed web systems . in section [ sec : idea ] we sketch the basic actions of the proposed overload control policy . in section [ sec : algorithm ] we introduce our algorithm in deeper details . in section [ sec : policies ] we introduce some previous approaches that we compared to ours in section [ sec : results ] . section [ sec : related_work ] outlines the state of the art of admission control in distributed autonomic web systems while section [ sec : conclusions ] concludes the paper with some final remarks . we tackle the problem of admission control for web based services . in this context , the user interaction with the application typically consists of a sequence of requests forming a navigation _ session_. as justified by @xcite we make the admission control work at session granularity . since the system should promptly react to traffic anomalies , any type of solution that requires human intervention is to be excluded . for this reason we address this problem by applying the autonomic computing @xcite design paradigm . we consider a typical multi - tier architecture @xcite . each tier is composed by several replicated servers , while a front - end dispatcher hosts the admission control and dispatch module . each request may involve execution at different depths in the tiered architecture . this results in a differentiation of requests into several categories whose average processing times may differ significantly . the quality of service of web applications is usually regulated by a sla . although our work may be applied to several formulations of sla , when clusters of heterogeneous tiers are considered , the most appropriate formulation is the following , as we argue in @xcite : * @xmath0 : maximum acceptable value of the 95%-ile of the response time for requests of type @xmath1 , where @xmath2 is the number of cluster tiers . * @xmath3 : minimum guaranteed admission rate . if @xmath4 is the rate of incoming sessions , and @xmath5 is the rate of admitted sessions , this agreement imposes that @xmath6 * @xmath7 : observation interval between two subsequent checks of the satisfaction of the sla constraints . meeting these quality requirements under sudden traffic variations requires novel techniques that guarantee the necessary responsiveness . in such cases the respect of the agreement on response time is a challenging problem . some other performance issues arise as well , such as the presence of oscillatory behavior , that typically affects some over - reacting policies , as we show in the experimental section [ sec : results ] . we designed soc , a session based admission control policy that self - configures a limit on the incoming rate of new sessions . such limit corresponds to the maximum capacity of the system to sustain the incoming traffic without violating the agreements on quality . it can not be evaluated off - line because it depends on the particular traffic rate and profile that the system has to face . since we do not want to rely on any prior assumption on the incoming traffic , we introduce a monitor module that makes the system capable to learn its capacity to face each particular traffic profile as it is when it comes . for this reason we make the system measure and learn the relationship between the rate of admitted sessions and the corresponding measure of response time . by accurately processing raw measures , the system can `` learn '' which is the maximum session admission rate that can be adopted in observance of the sla requirements . this learning activity introduces some issues such as how to time performance control , how to aggregate measures and how to detect changes , that will be dealt in detail in the following sections . we just mention that as soon as a change is detected the proposed system varies the rate of performance controls to guarantee at the same time accuracy and responsiveness . according to our proposal the admission controller operates at the application level of the protocol stack because session information is necessary to discriminate which requests are to be accepted ( namely requests belonging to already ongoing sessions ) , and which are to be refused ( requests that imply the creation of a new session ) . the cluster dispatcher can discriminate between new requests and requests belonging to ongoing sessions because either a cookie or an http parameter are appended to the request . this technique ensures two important benefits : 1 ) the admission controller can be implemented on dps , and does not require any modification of client and server software , 2 ) the dispatcher can immediately respond to non admitted requests , sending an `` _ i am busy _ '' page to inform the client of the overload situation . this avoids that the expiration of protocol time - outs affects the user perceived performance and mitigates the retrial phenomenon . soc works in two modalities , namely _ normal mode _ and _ flash crowd management mode _ , switching from one to the other according to the traffic scenario being considered . during stable load situations the timing of performance control is regularly paced at time intervals of length @xmath8 . if a sudden change of the traffic scenario is detected , the system enters the flash crowd management modality during which performance controls and policy updates are made more often in order to avoid a system overload . soc provides a probabilistic admission control mechanism which filters incoming sessions according to an adaptive rate limit @xmath9 . in order to properly calculate @xmath9 , the monitor module takes measures to analyze the relationship between the observed response time ( rt ) and the rate of admitted sessions . the value of @xmath9 is then calculated as the highest rate that the site can support without violating the constraints on rt defined in the slas . the admission control policy varies the admission probability according to a prediction of the future workload and to the estimated value of @xmath9 . the behavior of our policy under normal mode is described in figure [ fig : algo_normal ] , while figure [ fig : algo_fc ] describes the flash crowd management mode . ` init ; ` + ` normal_mode : ` + ` while ( ( ` @xmath10 ` ) and ! change_detection ( ) ) { ` + ` n = n+1 ; ` + ` for each session arrival { ` + ` probabilistic_admission_control ; ` + ` collect_raw_measures ; ` + ` } ` + ` } / * end while ` + ` if change_detection ( ) ` + ` goto flash_crowd_mode ; ` + ` else { ` + ` update_stats ; ` + ` update_curve ; ` + ` update_admission_probability ; ` + ` t=0 ; ` + ` goto normal_mode ; ` + ` } ` + for sake of simplicity , we leave the description of the parameter initialization ( instruction ` init ` ) at the end of the algorithm description , in section [ sec : init ] . _ normal mode _ at each" +"low - mass x - ray binaries ( lmxbs ) constitute a large fraction of bright x - ray sources ( @xmath6 erg s@xmath7 ) in the galaxy . these binary systems consist of an accreting compact star , either a neutron star or black hole , and a roche lobe - filling , low - mass companion . thus far approximately @xmath8200 lmxbs are known . among them , there is a class called ultracompact binaries . different from the majority of lmxbs which contain ordinary , hydrogen - rich mass donors , ultracompact systems are believed to consist of extremely low - mass , either hydrogen - poor or degenerate , companion stars @xcite . as a result , while ordinary lmxbs have a minimum orbital period around 80 min ( @xcite ; @xcite ) , ultracompact systems can evolve to extraordinarily small binary separations with orbital periods as short as a few minutes @xcite . these ultracompact lmxbs , along with their white dwarf analogues ( the am cvn binaries ; see @xcite ) , represent extreme and exotic endpoints in binary and stellar evolution . while the ultracompact systems had initially been assumed to be relatively rare , the number known has more than doubled to 11 ( including 4 globular cluster sources ) over the past few years , with a range of orbital periods from 11 to 55 minutes @xcite . it is likely that there are more such binaries , because a few candidate systems have been identified either by their peculiar x - ray and/or optical spectral features ( @xcite ; @xcite ; @xcite ) or through their unusually low optical to x - ray flux ratios ( @xcite ; @xcite ; @xcite ) . to fully study and understand the ultracompact lmxb population , verification of those candidate systems are warranted . it has shown that the indirect methods for ultracompact binary identification may not be reliable @xcite . in order to verify their ultracompact nature , time - resolved photometry for detecting orbital periodic signals is needed . moreover once ultra - short orbital periods are found , properties of the binary systems can be further estimated ( e.g. @xcite ) , helping our understanding of these systems . in an effort to verify the ultracompact nature of the proposed candidates , we have undertaken optical observations aiming to detect orbital flux modulations . we have successfully found the orbital period of the candidate 4u 1543@xmath0624 @xcite . in this paper we report our discovery of the likely orbital period of another candidate 2s 0918@xmath0549 . the lmxb 2s 0918@xmath0549 has been a bright x - ray source ( @xmath9 erg s@xmath7 ) and detected by all major x - ray satellites ( @xcite and references therein ) . on the basis of comparison of its x - ray spectrum to that of the known ultracompact lmxb 4u 1626@xmath067 , the source has been suggested to be an ultracompact binary with a neon - enriched degenerate donor @xcite . probably because the binary has a low inclination angle ( generally @xmath10 60 ; @xcite ) , no orbital signals were found in x - ray observations of the source @xcite . the optical counterpart to 2s 0918@xmath0549 was identified by @xcite , @xmath11 , @xmath12 . based on its optical to x - ray flux ratio , the orbital period of the binary has been suggested to be @xmath13 min @xcite . the source distance is probably 4.15.4 kpc , estimated from type - i x - ray bursts detected from the source @xcite . time - resolved imaging of 2s 0918@xmath0549 was carried out on 2008 december 5 using the 8-m gemini south telescope . the instrument was gemini multi - object spectrograph ( gmos ; @xcite ) , whose detector array consists of three 2048@xmath144608 eev ccds . we used only the middle ccd chip ( ccd 02 ) for imaging . the pixel scale is 0.073/pixel , while the detector was 2@xmath15 binned for our observation . a sloan @xmath1 filter with the central wavelength at 6300 was used . we obtained 179 continuous frames with an exposure time of approximately 24.5 sec . including 24 sec readout time for each exposure , the total length of the observation was approximately 2.4 hrs . the observing conditions during the early part of our observation ( first 59 frames ) were relatively poor , with the average seeing [ fwhm of the point - spread function ( psf ) of the images ] being @xmath16 and a few frames having as large as 1.3 1.5 seeing . for the remaining part , the conditions were good with most of the frames having @xmath17 seeing . we used the iraf packages for data reduction . the images were bias subtracted and flat fielded . the bias and flat frames were from gmos baseline calibrations taken during the same night . we performed psf - fitting photometry to obtain brightnesses of our target and other in - field stars , with a photometry program dophot @xcite used . a finding chart of the target field is shown in figure [ fig : finding ] . as identified by @xcite , there is a nearby star ( labeled as @xmath18 ) 1.5away from our target . to avoid possible contamination from this nearby star caused by the poor observing conditions during the early part of our observation , we positionally calibrated the first 59 frames to a reference image that was combined from three high - quality frames . the positions of star @xmath18 and 2s 0918@xmath0549 were determined in the reference image , and were fixed at the positions for photometry of the first 59 frames . at last we excluded three frames among them from the data . from the three frames , the brightness measurements of star @xmath18 and other in - field stars obtained were not consistent with the average brightnesses from other frames , and we note that the three frames have the seeing of 1.31.5 . differential photometry was performed to eliminate systematic flux variations in the images . three isolated , nonvariable bright stars in the field were used . the brightnesses of our targets and other stars in each frame were calculated relative to the total counts of the three stars . a field star labeled as @xmath19 ( see figure [ fig : finding ] ) was used as a check star , as it was nonvariable and had similar brightness to our target . because we did not request observations of standard stars for flux calibration in our gemini program and also no standard stars were imaged in the same filter by the gemini south telescope within at least half a month before and after our observation , we used the @xmath20 magnitudes of star @xmath18 measured by @xcite to obtain absolute magnitudes of the target and other stars . the transformation formula between @xmath1 and @xmath20 magnitudes given by @xcite was used . we found an average @xmath1 magnitude of 20.95@xmath210.16 for 2s 0918@xmath0549 , where the uncertainty comes from the relatively large uncertainties on the @xmath20 magnitudes of star @xmath18 in @xcite . we note that with the same transformation , @xmath22 for 2s 0918@xmath0549 in @xcite , which indicates that the binary has not had significant changes in its optical brightness . the average @xmath1 magnitude of star @xmath19 was 20.98@xmath23 , where 0.02 mag is the standard deviation of star @xmath19 measured from 176 frames . in figure [ fig : lc ] the obtained light curves of 2s 0918@xmath0549 , star @xmath18 , and the check star @xmath19 are shown . a periodic modulation in the light curve of 2s 0918@xmath0549 , while with a low - amplitude , is clearly visible . to determine its period , we applied a phase - dispersion minimization technique @xcite with 16 bins of the full phase interval ( 0 , 1 ) used . the resulting periodogram is shown in figure [ fig : pdm ] . the @xmath24 statistic indicates the detection of a periodicity and its two harmonics . fitting the region near the first minimum with a parabola @xcite , we found period @xmath25 min . in order to quantify the overall periodic modulation in the light curve , we fit the light curve with a sinusoid . the best - fit has reduced @xmath26 for 172 degrees of freedom ( dof ) , and from the best - fit we found @xmath27 min and a semiamplitude of 0.014@xmath210.002 mag . the large @xmath28 value is mainly caused by large scattering of the first 56 data points due to the poor observing conditions . excluding them and fitting the remaining data points , we found reduced @xmath29 for 117 dof ( @xmath30 was fixed at 17.4 min ) . the obtained semiamplitude was 0.015@xmath210.002 mag , not having significant changes . therefore the modulation can be described by a sinusoid with a semiamplitude of 0.015 mag . the folded light curve at @xmath25 min as well as the best - fit sinusoid are shown in figure [ fig : folded ] . the time at the maximum of the sinusoidal fit ( phase zero ) was mjd 54805.23281@xmath210.00027 ( tdb ) at the solar system barycenter . using gemini high time - resolution imaging we obtained an accurate optical light curve of 2s 0918@xmath0549 and have discovered a periodic flux modulation in the light curve . a low - amplitude modulation is clearly visible and appears to be coherent . given the known x - ray and optical properties of 2s 0918@xmath0549 , it is very likely that we have verified the ultracompact nature of this binary and its orbital period is around @xmath31 min ( see discussion below ) . in addition to 4u 0513@xmath040 in the globular cluster ngc 1851 @xcite and the galactic disk source 4u 1543@xmath0624 @xcite , 2s 0918@xmath0549 is the third member of the ultracompact binaries that have orbital periods around 18 min . we use the discovered orbital period to estimate the mass and radius of the donor . since the mean density of a roche lobe - filling companion is determined by the binary period , our 17 minute period defines a mass - radius relation for the companion , shown as the solid curve in figure [ fig : mr ] . on the basis of the high ne / o abundance ratio measured through x - ray spectroscopy , the donor in 2s 0918@xmath0549 has initially been suggested to be a low - mass c - o white dwarf @xcite . however , the analysis of several type - i x - ray bursts detected from the source possibly indicates that the donor instead is a helium white dwarf @xcite . in any case to compare the donor to stellar models , we use the m - r relations for different types of white dwarfs provided by @xcite . because extremely low - mass white dwarf donors in ultracompact systems may be thermally bloated compared to cold stars , affecting their m - r relation @xcite , we show both cold and hot solutions for pure he , c , and o white dwarfs in figure [ fig : mr ] . a helium white dwarf with a mass of 0.0340.039 @xmath4 and a radius of 0.0330.035 @xmath5 , or a c / o white dwarf with a mass of 0.0240.029 @xmath4 and a radius of 0.030.032 @xmath5 can fit in the roche lobe - filling donor . modulation of an optical light curve for lmxbs generally arises from the companion star that is heated by the central x - ray source , with the visible area of the heated face varying as a function of orbital phase and the superior conjunction of the companion" +"stellar winds are ubiquitous in massive stars , whether they be hot o - type stars or cool red supergiants and are an crucial ingredient for stellar and galactic evolution . however , the underlying physics of stellar winds and mass loss is still not well - understood across the hertzsprung - russell diagram ( hrd ) . mass loss in massive stars plays an important role in determining their evolution and how they end as supernovae . the most obvious example of this evolution a wolf - rayet stars that eject their envelopes , exposing their helium cores . because of that mass loss , these stars appear to evolve at hot effective temperatures , @xmath0 k , and explode as type i supernovae . * georgy ( 2012 ) ) showed that changing the mass - loss rates of red supergiant stars forces them to evolve blue ward and potentially explode during a yellow supergiant phase of evolution , consistent with observations ( ( * ? ? ? * maund et al . similarly , understanding the wind - driving mechanism and mass - loss rates of red supergiant stars would provide insights into questions about the progenitor masses of type iip and iin supernovae ( ( * ? ? ? * smartt 2009 ) ) . similarly , understanding stellar mass loss provides insight into the circumstellar medium of massive stars and feedback into the interstellar medium . evidence for this is found across the hrd , such as bow shocks observed about the o - type star @xmath1 oph ( ( * ? ? ? * gvaramadze et al . 2012 ) ) , the galactic center star irs 8 ( ( * ? ? ? * rauch et al . 2013 ) ) , the prototype cepheid , @xmath2 cep ( ( * ? ? ? * marengo et al . 2010 ) ) and the red supergiant betelgeuse ( ( * ? ? ? * ; * ? ? ? * ueta et al . 2008 ; cox et al . 2012 ) ) . further , changes in the wind due to stellar evolution could lead to the formation of multiple bow shocks ( ( * ? ? ? * ; * ? ? ? * ; * ? ? ? * mohamed et al . 2012 ; mackey et al . 2012 ; decin et al . 2012 ) ) . observations of stellar wind bow shocks can be used to infer mass - loss rates and wind velocities . the challenge for understanding stellar winds is that there are many driving mechanisms possible . in fig . 1 , i show a hrd outlining regions for different mass - loss mechanisms and regions where mass - loss rates are significant but not understood , such as in cepheids , luminous blue variable stars and red supergiant stars . in hot stars , @xmath3k , radiative - line driving is the dominate mechanism for accelerating a stellar wind ( ( * ? ? ? * ; * ? ? ? * lamers & cassinelli 1999 ; vink2011 ) ) . in these stars , radiation accelerates fe iii and iv ions and these ions interact with other atoms in the photosphere driving the wind . in the coolest stars , the mechanism is similar , but instead of accelerating ions , radiation accelerates dust that forms in the stellar photosphere ( e.g. , ( * ? ? ? * ; * ? ? ? * mattsson et al . 2010 ; mattsson & hffner 2011 ) ) . for lower mass stars , like the sun and red giant stars , winds are driven by alfenic waves and/or turbulence generating a chromosphere and corona that also accelerates a wind ( e.g. , ( * ? ? ? * cranmer & saar 2011 ) ) . rotation is yet another mechanism that can drive mass loss , especially in be stars ( ( * ? ? ? * porter & rivinius 2003 ) ) . even with a plethora of diverse wind - driving mechanisms , there still exist stars for which stellar mass loss is not understood . however , a potential mechanism for driving mass loss is stellar pulsation , especially in stars such as luminous blue variable stars , cepheids and red supergiant stars . in this review , i will discuss progress in understanding how pulsation can drive and influence stellar winds . however , research on the topic of pulsation - driven mass loss has focused on specific stellar types and not the physics of the pulsation - driven mass loss in general . as such , i will present recent results as a tour of stars on the hrd where pulsation - driven mass loss is important . the first step in the tour of the hrd is massive ob stars , in particular ob supergiants . radiative - line driving is important , but there is evidence that radiative line - driven theory is insufficient to explain observed mass - loss rates in many of these stars . * aerts et al . ( 2010 ) ) presented photometric and spectroscopic observations of the hot supergiant hd 50064 and found variation of p cygni line profiles consistent with periodic mass loss . the period of the mass - loss variation is the same as the period of brightness variations measured from photometry . the authors suggested that the mass loss must be driven by or is modulated by pulsation , in this case strange mode oscillations ( ( * ? ? ? * glatzel & kiriakidis 1993 ) ) . similarly , kraus et al . ( these proceedings ) show similar line profile variations in ob supergiants consistent with pulsation - driven mass loss . this adds further evidence for the connection between pulsation and mass loss in massive stars , however , these works do not discuss how pulsation can drive a wind . * sanyal & langer ( 2013 ) ) presented preliminary stellar evolution models of a massive star that develops an inflated envelope with a density inversion near the surface . the model also unstable to pulsation where the radius varies by about 10% , but the luminosity amplitude is only about ten milli - magnitudes . this variation is consistent with strange - mode oscillations . the authors also find that the pulsation instability is connected to the mass loss , but more research is required . massive blue supergiants may also pulsate due to the @xmath4-mechanism . * moravveji et al . ( 2012 ) ) presented evidence for this by modeling the blue supergiant rigel and finding that the @xmath4-mechanism drives gravity - mode oscillations . it is possible that these gravity modes might contribute to the stellar wind and enhance the mass - loss rate . luminous blue variables ( lbv ) stars may be the prototype for pulsation - driven and eruptive mass loss and can be subdivided into two groups : the @xmath5 carinae - like lbvs and the s doradus stars . the former stars are primarily eruptive variables , named for @xmath5 car which is famous for observed eruptions in the 19th and early 20th - century ( ( * ? ? ? * ; * ? ? ? * humphreys & koppelman 2005 ; davidson & humphreys 2012 ) ) . the latter stars are defined by more regular pulsation and microvariations ( ( * ? ? ? * e.g. , saio et al . ( 2013 ) ) ) . the cause of the observed eruptions in @xmath5 car are still a mystery . * smith ( 2013 ) ) modeled the great 19th century eruption as a strong wind with mass - loss rates , @xmath6yr@xmath7 lasting 30 years followed by an explosion , ejecting about 10 @xmath8 of material . the model is similar to that expected for a type iin supernova . however , the source of the explosion was not described . * guzik et al . ( 2005 ) ) computed hydrodynamic models of massive stars that undergo pulsation and found that pulsation could cause the radiative luminosity in the star to increase with a delay before the convective luminosity compensates . the radiative luminosity surpasses the eddington luminosity , hence driving an eruption . in this scenario , pulsation in stars near the eddington limit is a potential mass - loss mechanism . the s doradus stars appear to pulsate more regularly than the @xmath5 carinae stars where pulsation is driven by either the iron bump opacity or the strange mode instability . the stars also straddle the effective temperature , @xmath9k , which defines the boundary of the bi - stability mechanism for radiative - driven winds ( ( * ? ? ? * e.g. , vink et al . 2013 ) ) . for @xmath10k , the dominant opacity for driving the wind is the fe iv ions , while for cooler stars the dominant opacity is fe iii . the change in opacity causes significant differences in mass - loss rates , cooler stars having greater mass - loss rates than on the hotter side of the bi - stability region . pulsation could drive a star to oscillate between the hot and cool side of the s doradus instability strip and change the mass - loss rate ( ( * ? ? ? * smith et al . 2004 ) ) . pulsation can also directly drive mass loss in these stars , possibly by strange mode oscillations ( ( * ? ? ? * grott et al . 2005 ) ) . a combination of the two mechanisms might generate a pseudo - photosphere , making a s dor star appear as a yellow hypergiant , as suggested by ( * ? ? ? * vink 2012 ) . as before , stellar pulsation can enhance the wind , but the underlying physics is uncertain . @xmath11 cephei stars are massive stars where pulsation is driven by the iron opacity bump that oscillate both radially and non - radially with pulsation periods of hours . * guzik & lovekin ( 2012 ) ) speculated that @xmath11 cephei stars may lose mass via the same super - eddington luminosity events as in lbv stars . however , these stars appear to have the opposite problem as lbv stars ; the observed mass - loss rates are smaller than expected from radiative line - driven theory . * oskinova et al . 2011 ) presented observations of seven @xmath11 cephei stars plus a number of non - pulsating , magnetic b - type stars , all of which have smaller mass - loss rates than expected , i.e. , the weak - wind problem ( e.g. ( * ? ? ? * crowther et al . 2006 ) ) . one phenomenon common to all these stars is x - ray emission , which affects the ionization structure in the photosphere , hence changing the observed mass - loss rate . classical cepheids also display x - ray emission that is correlated with pulsation ( ( * ? ? ? * engle & guinan 2012 ) ) ; this hints at the possibility that x - ray emission in @xmath11 cep stars is also pulsation related . there is no evidence for phase - dependent x - ray emission ( ( * ? ? ? * raassen et al . 2005 ) ) but the pulsation period is short relative to the integration time required to detect x - ray photons . if pulsation is generating x - ray emission then pulsation can be acting to stall the stellar wind . the be stars are an interesting class of stars displaying emission lines consistent with the presence of a circumstellar mass loss" +"one of the most efficient methods of selecting high redshift galaxy candidates involves the detection of lyman break systems . this break comes from the likelihood of absorption due to intervening h i along the line of sight and for many galaxies also from the instrinsic continuum break in the spectrum of the galaxy ( bruzual & charlot @xcite ) . the search is done with two broad band filters that fork this break and a third one that is used to further ascertain the high redshift nature of the object . the work of steidel et al . ( @xcite , @xcite,@xcite ) imaging fields around high redshift quasars yielded many candidates , several of which have been spectroscopically confirmed to be galaxies at @xmath6 the advantage over previous unsuccessful narrowband lyman-@xmath7 surveys ( e.g. giavalisco et al . @xcite , martnez - gonzlez et al . @xcite ) is that a wide range in redshift can be surveyed . besides , the break in the spectrum can be easily discerned with broad band imaging , allowing the detection of normal high-@xmath8 galaxies , with a typical magnitude at a redshift of @xmath4@xmath9 of @xmath10 ( djorgovski @xcite ) . furthermore , the lyman-@xmath7 emission line can be weak or even non - existent as it appeared in many of the galaxies detected by steidel et al . @xcite . we found the field around quasar pc1643 + 4631a to be a good candidate for this technique for a couple of reasons : this @xmath0 qso has a damped lyman-@xmath7 system ( dls ) at @xmath11 ( schneider et al . @xcite ) whose lyman break would be perfectly positioned between johnson @xmath1 and @xmath2 filters . besides , a possible very massive cluster might exist between this quasar and a second one ( pc1643 + 4631b ) that lies just 200 arcsec away and has roughly the same redshift ( @xmath12 ) . jones et al . @xcite detected a significant decrement in the cmb in a region between these two qsos that could be related with a sunyaev - zeldovich effect arising from a m@xmath13m@xmath14 intervening cluster . however , saunders et al . @xcite imaged the region in @xmath3,@xmath15 and @xmath16 bands , looking for ellipticals that should abound in such a cluster , and found no evidence . the technique used in this paper is the best one to search for galaxies in the redshift range @xmath4 @xmath9 , thereby contributing to check this result : if such a massive cluster were to exist , a survey around pc1643 + 4631a should give a net excess of candidates towards the direction of the cluster . c|c|cc band & exposure time ( sec . ) & seeing & lim . mag . + u & 18000 ( not ) + 2400 ( wht ) & 1.2@xmath17 & 26.0 v & 3600 ( wht ) & 1.0@xmath17 & 26.0 r & 7200 ( not ) + 1800 ( wht ) & 1.5@xmath17 & 26.0 the observations were obtained in may 1996 using brocam2 at the 2.5 m nordic optical telescope ( not ) and in may 1997 using the william herschel telescope ( wht ) 4.2 m prime focus camera , both at the roque de los muchachos observatory , la palma , spain . both cameras used a thinned @xmath18 loral chip which is remarkable for its very high quantum efficiency even in the blue part of the spectrum , making it especially useful for @xmath1 band imaging . the image scale is @xmath19 and @xmath20 per pixel ( not and wht respectively ) . we also used a 30 minute exposure of the quasar in the @xmath3 band ( wht+tek ccd detector ) taken by saunders ..... , retrieved from the ing archive , which greatly helped us in achieving a homogenous limiting magnitude in all three bands . deep imaging was done through johnson @xmath1 , @xmath2 and @xmath3 filters and reduced using the standard techniques of bias subtraction and flat fielding using iraf tasks . the long integration times required were separated into shorter usually 1200 second exposures , slightly nodding the telescope between them in order to be able to eliminate cosmic rays and bad pixels . these frames were eventually registered and combined into a final image using a clipping algorithm . the photometric calibration was achieved with images of standard stars ( landolt @xcite ) taken throughout the observing nights . in order to detect candidates of galaxies at high redshift , a very deep exposure must be achieved in each filter . the deepest band should be @xmath1 because it represents the spectral range shortward of the lyman break for @xmath6 objects . [ candidates ] r|rr|crrno . & @xmath21 & @xmath22 & @xmath2 & @xmath23 & @xmath24 + 1 & -0.3 & -6.6 & 24.09 & 0.97 & 0.78 2 & -5.6 & 7.4 & 25.00 & @xmath251.00 & -0.16 3 & -22.2 & 10.8 & 24.64 & @xmath251.36 & -0.11 4 & 8.4 & -29.9 & 24.57 & 0.77 & -0.24 5 & -27.0 & 29.0 & 25.22 & @xmath250.78 & -0.27 6 & -21.3 & -34.2 & 24.57 & @xmath251.43 & 0.12 7 & 1.4 & 42.6 & 25.36 & @xmath250.64 & 0.43 8 & 63.2 & -0.7 & 24.96 & 0.70 & 0.14 9 & 9.9 & -43.5 & 25.30 & @xmath250.70 & 0.14 10 & -64.9 & -3.2 & 24.09 & 0.90 & -0.01 11 & 59.1 & -29.4 & 24.52 & @xmath251.48 & -0.18 12 & 31.4 & -46.9 & 24.67 & @xmath251.33 & 0.46 13 & 8.4 & -54.5 & 24.79 & @xmath251.21 & -0.00 14 & 28.2 & -57.0 & 24.30 & 0.77 & -0.21 15 & 58.6 & 49.0 & 24.98 & @xmath251.02 & 0.09 16 & -66.1 & -44.5 & 25.24 & @xmath250.76 & 0.01 17 & 79.3 & 33.2 & 25.23 & @xmath250.77 & 0.81 18 & -23.7 & 71.3 & 24.72 & @xmath251.28 & -0.20 19 & -12.4 & 74.0 & 24.24 & 0.92 & 0.22 20 & -82.7 & -55.3 & 25.43 & @xmath250.57 & -0.17 21 & -18.9 & 82.5 & 24.80 & 0.45 & 0.67 the search of objects in the final frames was performed using sextractor ( bertin e. @xcite ) , carefully tweaking the parameters to avoid such effects as excessive deblending or noise dominated detections . the threshold was set at 16 connected pixels ( which is slightly smaller than the number of pixels inside the seeing disk ) with 0.75@xmath26 lower limit per pixel for a global 3@xmath26 detection per object . we performed aperture photometry on the objects using several aperture sizes to make sure we were collecting all the flux . it also gave us an idea of the uncertainty to expect with faint objects . finally , we chose a diameter of 12 pixels ( 3.2 arcsec ) to get the photometry and checked each candidate visually to make sure there was no problem with deblending , hot pixels or other spurious detections . this issue was further enforced by considering only candidates that appeared _ both _ in the @xmath2 and @xmath3 filter images . the size of the aperture was chosen taking into account the seeing of the images ( 11.5 arcsec ) and the fact that high@xmath8 candidates should be pointlike objects . the photometry output from sextractor was further checked using several tasks from iraf from which we can extract a photometric uncertainty of 0.30.4 magnitudes for objects with @xmath27 . the candidates for high redshift galaxies were obtained using a color and magnitude constraint . the first and most important one is @xmath28 since it reveals the existence of a break in the spectrum at around 3650 which corresponds to the lyman continuum break at @xmath4 . unfortunately , there is also a very strong break at 4000 in the rest frame , especially prominent in old galaxies . hence , low-@xmath8 early types can sneak in our list . furthermore , we could also find galaxies with a strong emission line falling in the @xmath2 band and faking such a break . the way out of this degeneracy is twofold : we check an extra color towards the red side of the spectrum , namely @xmath24 , which can tell low redshift ellipticals or galaxies with strong emission lines from high redshift ones . we took @xmath29 . figure [ model ] shows the color prediction for three different morphologies from the models of bruzual & charlot @xcite . notice how the degeneracy between high redshift late type galaxies and low redshift ellipticals in the @xmath23 graph is removed when considering @xmath24 . an early type galaxy has a steeper spectrum towards @xmath3 , thereby higher values of @xmath24 , whereas the lower bound in this color is chosen to avoid galaxies with strong emission lines which might fall in the @xmath2 band . besides the color constraints , we should also impose a limit on the apparent magnitude . even though the selection suffers from malmquist s bias , we do not expect to find galaxies with an intrinsic luminosity greater than a few @xmath30 , which implies rejecting candidates whose apparent magnitude is brighter than @xmath31 . part of the degeneracy may still remain because faint galaxies could still be identified with ellipticals at low redshift with an absolute luminosity around @xmath32 . however , the constraint in @xmath24 makes this choice less likely over a late type high redshift galaxy . table 2 shows the list of candidates which appeared in our images imposing these constraints . all the objects with detections both in @xmath2 and @xmath3 are shown in figure [ allobjs ] , whereas figure [ objects ] plots a subsample of these objects with @xmath33 and shows the constraining color color region where the candidates should lie . figure [ objects ] also shows the confirmed candidates from steidel et al . ( @xcite ) , who used the same technique although with a different set of filters , specifically designed for maximum efficiency at these redshifts . finally , we considered the object that lies very close to the line of sight of the qso . the @xmath2 and @xmath3 images show it as an elongation of the quasar towards the sw , but in the @xmath1 band it stands out clearly as the qso fades out of view . in order to perform the photometry in @xmath2 and @xmath3 , we subtracted the psf of a nearby point - like object scaled to the peak of the qso . this is just a rough estimate but it allows us to ascertain the nature of this object . we got @xmath34 ; @xmath35 and @xmath36 . it is rather bright in the @xmath1 band , which discards the possibility of it being the one responsible for the dls in the qso s spectrum at @xmath11 . the models fit these colors with a late type galaxy at @xmath37 , which for a @xmath38 , @xmath39 cosmology gives an absolute luminosity of @xmath40 . this galaxy might possibly leave its imprint on the spectrum of the qso . among the many objects detected around pc1643 + 4631a , it is worth mentioning a group of them that are very red in @xmath23 but too bright to be high redshift galaxies . many of these objects were already detected by hu & ridgway ( @xcite ) , using a selection criteria in the red and nir part of the spectrum . they looked for objects which had a very red @xmath41 color , hence aiming at the detection of early type galaxies and eros . the 19 objects listed in their work are shown in table 3 along with our photometry in @xmath1,@xmath2 and @xmath3 . combining both surveys we have photometry in 8 standard filters" +"a growing body of complementary cosmological data are suggesting that the universe underwent a late time transition from a decelerating to an accelerating expansion @xcite . current data are accurately fitted by a flat frw type cosmology containing nonrelativistic matter plus some sort of dark energy @xcite . the simplest and by far the most popular dark energy candidate is represented by a cosmological constant . in the so - called @xmath1cdm model , the cosmic fluid contains radiation , baryons , cold dark matter plus a vacuum energy . nevertheless , this @xmath1cdm model is plagued with some difficulties like the cosmological constant and coincidence problems . on the other hand , the presence of a negative pressure is the key ingredient required to accelerate the expansion . this kind of stress occurs naturally in many different contexts when the physical systems depart from thermodynamic equilibrium states@xcite . in this connection , as pointed out by some authors@xcite , the process of cosmological particle creation at the expense of the gravitational field can phenomenologically be described by a negative pressure , and , more interestingly , can accelerate the universe@xcite . in this context , we constrain the free parameters of a flat accelerating cdm cosmology recently proposed in the literature@xcite . as we shall see , this extended cdm model is consistent with the sne ia ( constitution sample)@xcite and h(z ) data @xcite . in addition , there is a transition from a decelerating to an accelerating regime at redshift of the order of a few , and the hubble constant does not need to be small in order to solve the age problem . such a transition happens even if the matter creation is negligible during the radiation and considerable part of the matter dominated phase . in certain sense , the coincidence problem of @xmath1cdm model is replaced here by a gravitational particle creation process at low redshifts . for simplicity , let us consider that the spacetime is filled only by a cold dark matter component . in this case , the hubble and the decelerating parameters are given by : @xcite @xmath2,\label{hz}\ ] ] @xmath3.\ ] ] note that if @xmath4 there is no transition from a decelerating to an accelerating regime . the universe is always decelerating or accelerating depending on the value of the @xmath5 parameter . the existence of a transition redshift depends exclusively on the @xmath6 parameter . however , this fact does not remain true when baryons are included @xcite . in figure 1a , we display the effect of the free parameters ( @xmath7 ) in the reduced hubble - sandage diagram for the constitution sample @xcite . the lowest ( yellow ) curve is the prediction of the einstein - de sitter model . in figure 1b , we show the contours of constant likelihood ( 68.3% , 95.4% , and 99.7% c.l . ) in the ( @xmath7 ) plane from a @xmath8 statistics based on the constitution set . following standard lines , we have marginalized our likelihood function over the nuissance parameter @xmath9 ( @xmath10 ) . it is found that the free parameters fall on the intervals @xmath11 and @xmath12 at @xmath13 of confidence level . the best fit occurs for values of @xmath14 and @xmath15 with @xmath16 and @xmath17 degrees of freedom . the reduced @xmath18 where ( @xmath19 ) , thereby showing that the model provides a very good fit to these data . 0.1 in in figure 1c , we show the contours on the ( @xmath6 , h ) plane using the h(z ) data from stern _ et al._@xcite . the free parameters are constrained by @xmath20 and @xmath21 ( at @xmath22 c. l. ) . note that the constraints on the @xmath6 parameter are consistent with each other for these two different classes of data . by using sne ia and @xmath23 data , we have discussed some constraints on a flat accelerating cold dark matter cosmology without dark energy . the accelerating regime is powered by a negative pressure associated to the gravitationally - induced creation of cdm particles . the transition from a decelerating to an accelerating regime at late times happens even if the matter creation is negligible during the radiation and considerable part of the matter dominated phase ( this is equivalent to take @xmath24 in all the expressions ) . in this case , like in the flat @xmath1cdm , there is just one free parameter , and the resulting model provides an excellent fit to the observed dimming of distant sne ia data . more important , such constraints are compatible with the latest determinations of the hubble constant @xmath0 ( see figure 1c ) . naturally , complementary tests must still be investigated to see whether the present scenario may provide a realistic description of the observed universe . 99 a. g. riess _ et al . _ , j. * 116 * , 1009 ( 1998 ) ; s. perlmutter _ _ , apj * 517 * , 565 ( 1999 ) ; m. kowalski _ et al . apj * 686 * , 749 ( 2008 ) . m. hicken _ et al . _ , apj * 700 * , 1097 ( 2009 ) . e. komatsu _ et al . _ ( wmap collaboration ) astrophys . j. suppl . 192 , 18 ( 2011 ) . p. j. e. peebles and b. ratra , rev . mod . phys . * 75 * , 559 ( 2003 ) ; j. a. s. lima , braz . phys . , * 34 * , 194 ( 2004 ) [ astro - 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einsteinian ( ppe ) parameters are larger than the separation of modified gravity values with respect to standard gr values . error bounds are computed with the most accurate frequentist approach to date by computing the errors as inverse power series in the signal - to - noise ratio ( snr ) , where the first order is the inverse of the fisher information matrix @xcite . in this paper we model gr violations with the ppe framework @xcite , which produces parametrized extensions of gr gw signals for the inspiral phase only of a binary compact coalescence in the absence of spin ( similar extensions are currently not available for the merger and ringdown phase as well as in the presence of spin ) . the square root of the inverse fisher matrix diagonal elements , also known as the cramr - rao lower bound ( crlb ) , is a lower limit in the error of any unbiased estimator in the absence of prior knowledge . in this regard the crlb is a statement about the amount of information available in the data regardless of the specific parameter estimation scheme . there is however no guarantee that any estimator is capable to actually attain the crlb for part or the whole range of values the physical parameters can assume . also , the crlb only takes into account the curvature of the probability distribution of the data around the true value of the parameters and therefore does not include the role of secondary maxima in the calculation of the variance or mean square error of the estimators . the improved bound adopted here ( based on second order asymptotics ) is larger than the inverse fisher matrices , known to underestimate errors in low - snr detections . second - order bounds have been previously used for compact binary coalescence waveforms in quantifying the accuracy in intrinsic parameters as well as the direction of arrival for a network of laser interferometers @xcite . the benefits of using the second order of the expansions is in the fact that they depend up to the fourth derivative of the likelihood function and , therefore , are sensitive to asymmetries and side lobes of the estimator probability distribution ( similar to the change in the accuracy of a taylor expansion when extended to higher orders ) . also , in the past @xcite , the comparison of the second order with the first order provided an analytical understanding of the reasons the crlb could not be met ( for example , in ref . @xcite , a novel relationship between the kurtosis of the probability distribution of the estimator and the snr was derived to understand when the crlb could be met ) . bayesian methods were recently applied to test modified gr signals through consistency tests @xcite , and the ppe framework @xcite . @xcite developed a framework to detect gr violations without modeling the violation , this works in the limit of large number of detections . this framework was used in gr tests from the gw150914 transient @xcite . bayesian selection methods were also used in ref . @xcite and ref . @xcite to constrain the range of ppe parameter values , provided that priors are adopted . when bayesian uncertainties are smaller than the frequentist bounds , it means that the parameter estimation errors depend critically on the priors . this issue can be an artifact if the prior is not based on previous detections or no robustness studies were performed with respect to the choice of the priors ( see for example the discussion in ref . @xcite of the effects of priors ) . in this paper , we show that this instance happens for an equal - mass binary black hole system in the massive graviton case . this example illustrates how the present work provides a unique understanding of the parameter estimation errors . although gw150914 had a snr@xmath6 , its inspiral stage falls within the prescribed study of snr@xmath7 . . ] in addition , this work extends the fisher information based results of ref . @xcite , which perform error estimations by modifying pn coefficients . we also extend fisher - based assessments of specific alternative theories @xcite . specifically , this paper considers phase modification in the _ restricted _ ppe framework @xcite , considering the ppe framework as a general enhancement to existing ` taylorf2 ` @xcite gr templates in a three detector ligo - virgo network @xcite . calculations in this limit were chosen since deformations to the gw s phase are expected to be more resolvable @xcite and complements recent bayesian methods testing deviations from gr @xcite . second - order frequentist constraints produced in this paper are at the same order of magnitude as the bayesian model selection s errors in ref . @xcite , where our errors are quantified at the one sigma level . as error estimates of ppe parameters grow , second - order errors of parameters such as the chirp mass , symmetric mass ratio , and time of coalescence also inflate . the results presented here , and the rescaled bonds which can be simply derived by changing the snr , will be important benchmarks for any parameter estimation scheme which will be used in existing and future interferometer data , including bayesian parameter estimation algorithms . section [ stat_model_sig ] of this paper introduces the signal model used . section [ param_space_expan ] discusses what is the resolvable parameter space and the expansion model , in particular subsection [ ppe_model ] discusses alternative theories of gravity covered in this paper and the asymptotic expansion of the maximum likelihood estimator model is discussed in subsection [ expan ] . finally , section [ results ] assesses the results , as applied to a two - dimensional ppe parameter space ( [ bidimen ] ) and a seven - dimensional parameter space of equal mass ( [ 7dimen ] ) and unequal mass ( [ 7dimen2 ] ) systems with physical parameters included . results are applied to existing alternative theories of gravity in [ mod_grav ] , including massive graviton , brans - dicke , and quadratic modified gravity ( encompassing einstein - dilation - gauss - bonnet gravity ) . a summary and discussion is given in section [ conclusion ] . the waveforms are assumed to be produced by a nonspinning binary system with all orbital eccentricity information lost when entering the frequency bandwidth of adv.ligo and adv.virgo . fourier transform of the signal , through stationary phase @xcite , becomes , @xmath8 for the inspiral stage of the compact binaries . for the phase @xmath9 and amplitude @xmath10 the standard ` taylorf2 ` model @xcite is used . the signal of a collection of alternative theories of gravity is modelled as ( [ freq_sig_gr ] ) modulated in the phase and amplitude as : @xmath11 where @xmath12 and @xmath13 are a general series of scaling parameters @xmath14 and in some instances arguments call for integer exponentials of @xmath15 @xcite , where @xmath16 for total mass @xmath17 and @xmath18 . here the analysis is done at leading order in the ppe parameters , @xmath19 at each interferometer the signal is assumed to be recorded with additive noise as in ref . frequency dependent noise for adv.ligo are interpolated from the official power spectral density @xcite of high - power , zero - detuning . adv.virgo is assumed to have the sensitivity given in ref . @xcite . for error analysis , and upcoming integrations , the lower cutoff frequency is set to @xmath20 and the upper cutoff is set to the upper limit for reliability in the inspiral of the waveform template , i.e. , the innermost stable circular orbit ( isco ) frequency , @xmath21 the convention used in ( [ freq_sig_gr ] ) is presented in appendix [ appenda ] . for non - spinning systems thirteen parameters are necessary in the description of the inspiral of two coalescing binaries : two mass terms , four angles ( two source location and two waveform angles ) , two coalescence parameters , distance to the source , and four ppe parameters in the leading order approximation . singular fisher matrices might appear @xcite , indicating that the resolvable parameter space is smaller ( where the fisher matrix approach can still be used ) . the distance @xmath22 is excluded from the error estimates because the amplitude has a dependency on both mass and distance parameters , and the independent treatment of both is unresolvable as already indicated in ref . the coalescence phase is also not included because estimations of @xmath23 is relevant only when a full waveform ( inspiral , merger , and ringdown ) is implemented . the polarization @xmath24 is excluded because results tend to be independent of it @xcite . derivatives of the fitting factor @xmath25 @xcite , @xmath26 with respect to the binary s inclination @xmath27 evaluated at , or in a neighborhood of , @xmath28 are roughly zero leading to impossibility to estimate @xmath27 and singular fisher matrices . here the @xmath29 represent noise weighted inner products @xcite and @xmath30 are gw signals controlled by general parameter space vectors @xmath31 and @xmath32 . keeping other parameters fixed and varying only @xmath27 produces change in the snr equivalent to the rescaling of the distance , which affects gw plus - cross polarizations similarly . top panel in figure [ fitting_factor ] shows the sky - averaged snr plotted as a function of inclination @xmath27 ( only the gr polarizations are considered ) . also , sky patterns of the errors remain consistent when varying @xmath27 . therefore , since @xmath27 is degenerate with @xmath22 it is also excluded from our resolvable parameter space , which becomes @xmath33 . varied for system parameters : @xmath34 mpc , and @xmath35 in the three detector network . bottom : fitting factors ( [ ff ] ) for a range of @xmath3 with @xmath36 fixed to produce pn - order 0.0 , 1.0 , and 1.5 modifications for a system of : @xmath37 and @xmath38 . adv.ligo noise is assumed . since the range of @xmath3-values scale differently at each pn - order , each @xmath3-interval is scaled ( as labeled in the legend ) . for example , in the pn - order 0.0 modification the @xmath3 values in the domain are each scaled by @xmath39 . , title=""fig : "" ] varied for system parameters : @xmath34 mpc , and @xmath35 in the three detector network . bottom : fitting factors ( [ ff ] ) for a range of @xmath3 with @xmath36 fixed to produce pn - order 0.0 , 1.0 , and 1.5 modifications for a system of : @xmath37 and @xmath38 . adv.ligo noise is assumed . since the range of @xmath3-values scale differently at each pn - order , each @xmath3-interval is scaled ( as labeled in the legend ) . for example , in the pn - order 0.0 modification the @xmath3 values in the domain are each scaled by @xmath39 . , title=""fig : "" ] throughout this paper amplitude modulations are to be held fixed to that of gr : @xmath40 , because the same effect could be produced by changing physical parameters like distance or mass . such an" +"charge - density wave ( cdw ) is widely observed in low - dimensional solids and has been extensively studied both experimentally and theoretically @xcite . transition metal dichalcogenides mx@xmath1 ( m = transition metal , x = s , se , te ) are one of the typical cdw materials with a layered triangular lattice structure . they show various cdw patterns , depending on the combination of m and x @xcite , and quite often superconductivity ( sc ) is observed next to the cdw phase by applying pressure @xcite , doping @xcite , or intercalation @xcite . however , the origin of cdw and sc has not been fully understood and it has been still under debate in spite of the long and extensive studies so far . recently , 1@xmath0-tise@xmath1 , one of the old transition metal dichalcogenides , has again attracted much interests in the context of exciton condensation . this material is a semimetal or a semiconductor in room temperature @xcite and shows a commensurate cdw transition with a @xmath2 superstructure below @xmath3k . the fermi surface ( fs ) partially remains even in the cdw phase due to the imperfect opening of the energy gap . the origin of the cdw phase is still controversial and the usual nesting mechanism seems unlikely due to its poor fs nesting @xcite . alternatively , exciton condensation has been proposed as a possible mechanism for the cdw phase @xcite . indeed , the large spectral weight transfer between ti 3@xmath4 and se 4@xmath5 bands and the flat energy spectrum just below the fermi energy have been observed @xcite , strongly suggesting the possibility of exciton condensation . on the other hand , another possible mechanism for the cdw transition is a band jahn - teller effect which results from electron - phonon interaction @xcite . a large lattice distortion of several percent observed below @xmath6 @xcite indicates the strong coupling between electronic and lattice degrees of freedom @xcite . very recently , it is proposed that both mechanisms work cooperatively for the cdw transition @xcite . exciton condensation is a quantum state expected in low carrier density systems such as a semimetal or a semiconductor and has been extensively studied since 1960s @xcite . the exciton is a bound pair of an electron and a hole in different bands mediated by the interband coulomb interaction . when the binding energy of an exciton exceeds the band gap , the system has an instability toward condensation of excitons , namely , a spontaneous hybridization between different bands . since the repulsive coulomb interaction is attractive between an electron and a hole , the exciton condensation is expected to occur in principle without considering any additional `` glue '' of the electron - hole pair . although extensive efforts have been devoted for half a century and several candidates have been proposed @xcite , the generally accepted materials for the exciton condensation are still absent . therefore , any conclusive evidence for the exciton condensation in real materials is highly desired for further progress and 1@xmath0-tise@xmath1 would be one of the promising examples . in the pioneering studies for exciton condensation @xcite , an isotropic band dispersion with perfect fs nesting is assumed , for which the excitonic instability is always present in a semimetallic case . the extension to anisotropic band dispersions shows that the degree of fs nesting greatly affects the instability of exciton condensation @xcite . moreover , the mean - field approximation generally overestimates the instability toward ordered states , including the exciton condensation . therefore , for discussion of the exciton condensation in real materials , the realistic band dispersion and the appropriate method beyond the mean - field approximation are both required . in this paper , a half - filled two - band hubbard model with electron - phonon interaction in a triangular lattice is studied to understand the origin of the cdw phase in 1@xmath0-tise@xmath1 . the ground state properties are calculated using the variational monte carlo ( vmc ) method for multiorbital systems @xcite . we find that the cooperation between coulomb interaction and electron - phonon interaction is essential to induce the cdw phase . the cdw phase is observed between the normal metal and band insulator phases with intermediate interband coulomb interaction . we show that the `` pure '' exciton condensation without lattice distortion is difficult to realize under the poor fs nesting condition in a triangular lattice . furthermore , we systematically calculate the momentum resolved hybridization between the two bands to show that the strong - coupling bec - like pairing dominates in the cdw phase . our results therefore suggest that the cdw phase observed in 1@xmath0-tise@xmath1 originates from the strong - coupling bec - like electron - hole pairing . the rest of this paper is organized as follows . in sec . [ model ] , a two - band hubbard model in a two - dimensional triangular lattice is introduced as a low energy effective model for 1@xmath0-tise@xmath1 . the detailed explanation of the vmc method and the variational wave functions are also given in sec . [ model ] . the numerical results are then provided in sec . [ result ] . finally , the implication of our results for 1@xmath0-tise@xmath1 is discussed in sec . [ discussion ] , followed by the summary in sec . [ summary ] . . a set of tight - binding parameters used is @xmath7 with @xmath8 as an energy unit . ( c ) schematic real - space figure of a 2@xmath92 superstructure ( dotted lines ) with each supercell containing 4 sites ( a , b , c , and d ) . the corresponding ordering wave vectors @xmath10 , @xmath11 , and @xmath12 are indicated in ( a ) . dashed lines in ( a ) represent the folded brillouin zone due to the formation of the 2@xmath92 superstructure in ( c ) . ( d ) schematic real - space figure of the lattice distortion considered in the @xmath13-@xmath14 plane along one particular direction , e.g. , ab direction indicated in ( c ) . @xmath15 represents the displacement of @xmath13 atom at site @xmath16 from its original position . ] we consider a two - band hubbard model in a two - dimensional triangular lattice defined as @xmath17 \notag \\ & + \sum_{\bm{q}}\omega(\bm{q})\left(b^{\dagger}_{\bm{q}}b_{\bm{q}}+\frac{1}{2}\right),\end{aligned}\ ] ] where @xmath18 ( @xmath19 ) creates an electron in @xmath13 ( @xmath14 ) band with momentum @xmath20 and spin @xmath21 . the band dispersions @xmath22 and @xmath23 are given as @xmath24 and @xmath25 respectively . we introduce the next - nearest - neighbor hopping @xmath26 to locate the bottom of @xmath13 band at m points . @xmath27 @xmath28 is an on - site intraband coulomb interaction within @xmath13 ( @xmath14 ) band and @xmath29 is an on - site interband coulomb interaction between @xmath13 and @xmath14 bands . @xmath30 is a number operator of @xmath31 electron at site @xmath16 with spin @xmath32 and @xmath33 . @xmath34 is an electron - phonon coupling constant and @xmath35 is a creation operator of phonon with momentum @xmath36 and frequency @xmath37 . in this model , the lattice distortion changes the @xmath13-@xmath14 bond length as shown in fig . [ fig1](d ) , which couples to the @xmath13-@xmath14 hybridization modulated with wave vector @xmath36 through @xmath34 . the total number of sites is indicated by @xmath38 . the noninteracting tight - binding parameters , @xmath39 are set to mimic the electronic structure of 1@xmath0-tise@xmath1 with a hole pocket at the @xmath40 point and electron pockets at the m points as shown in figs . [ fig1](a ) and [ fig1](b ) . the ordering wave vectors connecting @xmath40 and m points are denoted as @xmath10 , @xmath11 , and @xmath12 . although the ordering wave vectors observed in 1@xmath0-tise@xmath1 connect @xmath40 and l points with a finite @xmath41 component @xcite , here we consider a pure two - dimensional model for simplicity and the limitation of the model is discussed later . the effect of coulomb interaction and electron - phonon interaction is treated on an equal footing using a vmc method . we consider the trial wave function as follows : @xmath42 @xmath43 is an electron wave function consisting of three parts . @xmath44 is a slater determinant constructed by diagonalizing the one - body part of hamiltonian @xmath45 including the variational tight - binding parameters ( @xmath46 , @xmath47 ) and the off - diagonal element @xmath48 which induces the @xmath13-@xmath14 hybridization . here , we assume @xmath49 $ ] , and @xmath50 and @xmath51 are both variational parameters . @xmath50 is an amplitude of the @xmath13-@xmath14 hybridization and @xmath51 controls the internal extent of exciton in @xmath20 space . we have found that the variational energy is improved by introducing @xmath51 and the behavior of @xmath51 is related to the bcs - bec crossover of exciton condensation @xcite . @xmath52 is a gutzwiller factor extended for two - band systems @xcite . in @xmath52 , possible 16 patterns of charge and spin configuration at each site @xmath53 , i.e. , @xmath54 , @xmath55 , @xmath56 , @xmath57 , are differently weighted and their weight @xmath58 are optimized as variational parameters . @xmath59 $ ] is a charge jastrow factor which controls long - range charge correlations . here , @xmath60 is assumed and @xmath61 is the position of site @xmath16 . the trial wave function for phonon is assumed to be a gaussian in the normal coordinate @xmath62 representation @xcite , @xmath63,\ ] ] where @xmath64 is fourier transform of real space lattice distortion @xmath65 at site @xmath16 . since the ordering wave vectors @xmath10 , @xmath11 , and @xmath12 are exactly half of the reciprocal lattice vectors of the normal phase [ see fig . [ fig1](a ) ] , the corresponding normal coordinate @xmath66 ( @xmath67 ) are real numbers . therefore , we can take the trial wave function and variational parameters @xmath68 and @xmath69 all real . notice that @xmath68 controls the extent of the gaussian wave function , i.e. , the amplitude of lattice vibration , and that @xmath69 corresponds to the average value of @xmath70 and thus there exists a static lattice distortion with @xmath71 for a finite @xmath69 . the monte carlo update scheme for @xmath62 and the estimation of phonon energy are the same as in ref . . the remaining part is an electron - phonon projection operator : @xmath72 $ ] . this operator controls the attraction between @xmath13 electrons and @xmath14 holes which results from the electron - phonon interaction and @xmath73 is a variational parameter . the variational parameters in @xmath74 are therefore @xmath75 , @xmath76 , @xmath77 , @xmath50 , @xmath51 , @xmath58 , @xmath78 , @xmath79 , @xmath80 , and @xmath73 , and they are simultaneously optimized using stochastic reconfiguration method @xcite . the system sizes are varied from @xmath81 to @xmath82 with antiperiodic boundary conditions in both directions of primitive lattice vectors for the triangular lattice . ( color online ) ground state phase diagram of the two - band hubbard model in ( a ) @xmath83-@xmath29 plane ( @xmath84 ) and ( b ) @xmath83-@xmath85 plane ( @xmath86 ) . we set @xmath87 and @xmath88 . nm , cdwi , and bi denote normal metal , charge - density - wave insulator , and band insulator , respectively . the electron density is @xmath89 , i.e. , at half filling . ] figure [ fig2](a ) shows the ground state phase diagram where @xmath90 and @xmath29 are varied for fixed @xmath91 and @xmath92 @xcite . we find that there are three distinct phases in the phase diagram : normal metal ( nm ) , charge - density - wave insulator ( cdwi ) , and band insulator ( bi ) . when @xmath29 is large enough" +"the prevalence of dusty , infrared luminous galaxies at early times tests our theories about early galaxy formation and the production of metals . semi - analytic models predict very small numbers of submillimeter galaxies ( smgs ) at extreme redshifts ( @xmath0 , e.g. baugh et al . 2005 ) , and the best observational constraints on the redshift distribution of smgs are consistent with this ( chapman et al . 2005 ; swinbank et al . much attention has been given to recent studies which have spectroscopically confirmed a small number of smgs at @xmath0 ( capak et al . 2008 ; coppin et al . 2009 ; daddi et al . 2009ab ; knudsen et al . 2010 ) ; however , these sources are still only a small fraction of the submillimeter population . small number statistics and cosmic variance in current submillimeter surveys prohibit an accurate measure of the space density of the most distant smgs . the question of the prominence of the high redshift tail of dusty smgs can be addressed with imminent submillimeter wide area surveys such as those with the _ herschel space observatory _ ( pilbratt 2001 ) , the scuba-2 camera on the jcmt ( holland et al . 2006 ) , and the aztec camera on the large millimeter telescope ( lmt , wilson et al . the _ herschel space observatory _ is currently collecting data from 70500@xmath6 m over wide survey fields . with an aperture of 3.5@xmath9 m , _ herschel _ is only sensitive to ultra - luminous infrared galaxies ( ulirgs , l@xmath10 ) above @xmath11 at 250500@xmath6 m before it reaches the confusion limit . one advantage of spire surveys is the simultaneous observations at three wavelengths ; 250 , 350 and 500@xmath6 m , which samples the peak of the far - ir spectral energy distribution ( sed ) due to dust emission in high redshift galaxies . with prior knowledge of the dust properties which describe the shape of the sed , the position of the far - ir peak is sensitive to the redshift of the galaxy . in this paper , we discuss the power and limitations of using the far - ir peak as a redshift indicator in submillimeter surveys . we apply this technique to the current blast survey of ecdfs and place an upper limit on the number density of 500@xmath6m - selected smgs at @xmath0 . throughout this paper we assume a standard cosmology with @xmath12 , @xmath13 and @xmath14 . the 1.6@xmath15 m bump in the near - infrared sed of galaxies arises due to a minimum in the h@xmath16 opacity in the spectra of cool stars . this bump has been used in extragalactic _ spitzer_/irac surveys to identify sources in a specific redshift range ( e.g. wright et al . 1994 , sawicki 2002 , farrah et al . 2008 ) . a similar , but factor of @xmath17 broader , peak exists in the sed of galaxies at far - ir wavelengths which is caused by the integrated thermal emission from dust of different temperatures . this sed is often parameterized as a blackbody distribution of a particular far - infrared color temperature ( t@xmath18 ) with an additional term to account for the dust emissivity . the choice of emissivity affects the derived color temperature . ] ( e.g. blain et al . 2002 ) . the challenge with using the far - ir bump as a redshift indicator is that the average dust temperature and the redshift are degenerate ( e.g. blain 1999 ; blain , barnard & chapman 2003 ) . wien s displacement law tells us that the wavelength of the peak of a blackbody scales with the dust temperature . coupling this with the displacement of the peak due to redshift we find that the observed wavelength of the far - ir peak depends linearly on both the redshift and the inverse of the dust temperature : @xmath19 . the most luminous galaxies in the local universe show far - infrared color temperatures that peak at @xmath2040@xmath9k although there is a significant scatter in luminosity - temperature parameter space ( e.g. dunne et al . 2000 ) . for a reasonable range of dust temperatures for ulirgs , sources that peak at 500@xmath6 m can be found anywhere between @xmath216 . this is a very large range in redshift and without prior information about the dust temperature it is difficult to further constrain the redshift with the spire data alone . in order to test this technique on observations we use the data from the blast survey of ecdfs ( devlin et al . 2009 ) . blast has the same three detectors as _ herschel_/spire but with beam sizes that are twice as big ; 36 , 42 , 60 arcsecs fwhm at 250 , 350 and 500@xmath6 m respectively ( marsden et al . 2009 ) . we use the publicly released blast maps and the matched filter catalogs ( chapin et al . these matched filter catalogs do a much better job at de - blending adjacent sources and result in higher signal - to - noise ratios than previous blast catalogs ( see chapin et al . 2010 for further details ) . we restrict our analysis to the central 0.47@xmath9deg@xmath22 of the blast image where @xmath23mjy at 500@xmath6 m . we have conservatively added the confusion noise in quadrature with the instrument noise ( @xmath24 ) for all analysis in this paper . we only consider detections if they are @xmath25 ( @xmath26 ) . in this central region there are 23 galaxies robustly detected at @xmath27 m with @xmath28mjy . we match the 500@xmath6m - selected galaxies to the matched filter catalogs at 250@xmath6 m and 350@xmath6 m ; we consider any @xmath25 detection within a radius of 60 arcsecs to be the counterpart to the 500@xmath6 m emission . for sources which are undetected at these other wavelengths we set upper limits on the 350 and 250@xmath6 m fluxes from the 90% completeness limits of the survey ( chapin et al . 2010 ) which is equivalent to @xmath29 . of these 23 500@xmath6m - selected galaxies , 8 have @xmath2 indicating that the dust sed peaks at or near 500@xmath6 m we refer to these galaxies as 500@xmath6 m ` peakers ' ( although their peak may be at even longer wavelengths ) . interestingly , none of these 500@xmath6 m peakers ( detected at @xmath25 ) are detected above @xmath30 at 250 and 350@xmath6 m . we inspected all of these candidates by hand in the blast images to make sure they are not obviously blended . we have not attempted to correct for flux boosting ( e.g. coppin et al . 2006 ) in this analysis but , since we are not interested in the absolute fluxes and only the relative colors , this is less of a concern . in addition by considering only higher signal - to - noise ratio sources we ensure that this effect is minimal . in order to assess how photometric uncertainties ( from both confusion and instrument noise ) affect the number of 500@xmath6 m peakers identified , we ran a monte carlo simulation to randomly sample the fluxes of each of the 23 sources from a gaussian distribution @xmath31 . we find that photometric uncertainties can vary the number of sources with @xmath2 by 2 . thus our final number of 500@xmath6 m peakers is @xmath1 . these 8 high redshift candidates are listed in table 1 along with their fluxes and fig . [ fig : sed ] shows an example sed for one source . five of these 500@xmath6 m peakers are within the ecdfs field and one is within the smaller goods - s region ( see table 1 ) . the source within goods - s is associated ( 6 arcsecs away ) from an aztec 1.1@xmath9 mm detected source ( gs11 , scott et al . 2010 ) ; however , flux boosting in the blast bands prohibit a detailed comparison . knowing that a source peaks at ( or near ) 500@xmath6 m does not provide a definitive redshift due to the degeneracy between redshift and temperature ( e.g. fig . [ fig : tdust ] ) . if we conservatively assume that all 500@xmath6 m peakers are at @xmath0 we can obtain an upper limit on the number density of @xmath0 galaxies predicted in _ herschel _ spire surveys . based on our analysis of the blast data , the number density of galaxies ( with s@xmath7mjy ) which peak at 500@xmath6 m is @xmath3deg@xmath4 . we expect that some of these 500@xmath6 m peakers will be at @xmath32 since fig . [ fig : tdust ] shows that sources cooler than 40@xmath9k can have @xmath2 but be at @xmath32 . to get an estimate of the contamination of low redshift , cooler galaxies in the 500@xmath6 m peaker sample we must assume a redshift and dust temperature distribution . assuming a flat redshift distribution . ] and a dust color temperature distribution of @xmath33k smgs ( chapman et al . 2005 ; pope et al . ] , we estimate that @xmath34% of 500@xmath6 m peakers will be @xmath32 ( left panel of fig . [ fig : tdust ] ) . in addition , we must also account for the contribution from warmer sources at @xmath0 but which peak at lower wavelengths ( @xmath35 ) . assuming a sample of sources at @xmath0 again following a dust temperature distribution of @xmath33k , we find that only @xmath36% have @xmath35 . these two factors roughly cancel each other and we are left with a constraint on the number density of @xmath0 sources ( with s@xmath7mjy ) of @xmath37deg@xmath4 . the above limit on the number density of @xmath0 smgs ambitiously assumes a flat redshift distribution . if instead we assume the observed redshift distribution of smgs ( @xmath38 , chapman et al . 2005 ; pope et al . 2006 ) , we find only 10% of the 500@xmath6 m peakers at @xmath0 ( right panel of fig . [ fig : tdust ] ) which brings the number density estimate down to @xmath39deg@xmath4 . based on our analysis of the blast data , we conclude that the number density of s@xmath7mjy sources at @xmath0 is @xmath37deg@xmath4 and could be as low as @xmath39deg@xmath4 . with some assumptions about the dust temperature distribution , we have shown that the submillimeter color selection , @xmath2 is a plausible way to identify samples containing the highest redshift smgs selected at these wavelengths ( albeit these samples contain contamination from lower redshift objects ) . without further multi - wavelength data , it is impossible to tell individually which of the 8 candidates are at @xmath0 , and which are just peaking at 500@xmath6 m because they have cooler dust temperatures . one way to test the reality of these high redshift candidates is to further constrain their seds with data at longer submm wavelengths such as those from the 870@xmath6 m laboca survey of ecdfs ( weiss et al . in order to do a robust comparison between the laboca and blast fluxes , a correction for flux boosting needs to be applied to both surveys using the same method ( e.g. coppin et al . this is beyond the scope of this paper but should be possible with full access to the signal and noise maps from both surveys . another potential way to break the degeneracy between redshift and temperature for these candidates is with the radio and/or far - ir ( e.g. @xmath40 m ) flux ; we discuss this further in the next section . photometry from 250500@xmath6 m alone can provide an accurate measure of @xmath41" +"charge - parity - time ( @xmath1 ) symmetry is the most fundamental type of symmetry in quantum field theory 1742 - 6596 - 335 - 1 - 012011,aguilararevalo20131303 , where it holds for all relativistically invariant systems obeying the causality principle . its reduced form , _ viz_. , the @xmath0 symmetry , is almost exact too , save the small violation by weak nuclear forces @xcite . the @xmath2 operator is composed of three factors : parity transformation , @xmath3 , which reverses the coordinate axes ; charge conjugation , @xmath4 , which swaps particles and antiparticles ; and time reversal , @xmath5 . the proof of the @xmath1 and @xmath0 symmetries ( when the latter is relevant ) applies to hermitian hamiltonians ( @xmath6 ) , subject to the condition @xmath7 , which guarantees that the spectrum of the hamiltonian is real . however , one can not deduce from the @xmath1 or @xmath8 symmetry that the respective hamiltonian is necessarily hermitian @xcite . indeed , the consideration of hamiltonians which commute with a reduced symmetry operator , @xmath9 , demonstrates that they may contain an anti - hermitian ( dissipative ) part , provided that it is spatially antisymmetric ( odd ) , while the hermitian one is even @xcite . the spectrum of such a hamiltonian remains purely real up to a critical value of the strength of the anti - hermitian part , at which the @xmath9 symmetry is broken , making the system an essentially dissipative one ( recently , a model with _ unbreakable _ @xmath9 symmetry was found ; it includes defocusing cubic nonlinearity with the local strength growing from the center to periphery @xcite ) . while in the quantum theory the possibility of the existence of non - hermitian @xmath9-symmetric hamiltonians is a purely theoretical one , such systems have been realized , theoretically muga , muga1,muga2,muga3,muga4,muga5,review and experimentally kip , feng05082011,citeulike:11031904,ruter:09,10.1117/12.807739,physreva.82.010103,2012natur.488 .. 163r , in optics , making use of the fact that the wave - propagation equation , derived in the standard paraxial approximation , is identical to the schrdinger equation in nonrelativistic quantum mechanics . in this context , the spatially symmetric and antisymmetric hermitian and anti - hermitian terms of the hamiltonian are represented , respectively , by even and odd distributions of the refractive index , and of the local gain - loss coefficient in the photonic medium . a @xmath9-symmetric electronic circuit was built too , following similar principles @xcite . the essential role played by the kerr nonlinearity in optics has suggested the development of models in which the hamiltonian includes a quartic hermitian part too . the nonlinearity gives rise to families of @xmath9 -symmetric solitons , that were investigated in detail in continuous and discrete systems muga5,ptsolitons , ptsolitons1,ptsolitons2,ptsolitons3,ptsolitons4,ptsolitons5 , including @xmath9 -symmetric dual - core couplers couplers , couplers1,coupler - management . models combining the @xmath9 symmetry with quadratic nonlinearity in the dynamical equations ( i.e. , cubic terms in the respective hamiltonians ) were also elaborated vvk1,vvk2,vvk3 . as a subject of quantum field theory , the @xmath1 and @xmath0 symmetries mainly relate to elementary particles 2012arxiv1201.1594s , srednicki2007quantum , kursunogammalu2013confluence,2013phlb .. 718.1500c . on the other hand , the above - mentioned works on the implementation of non - hermitian @xmath9-symmetric hamiltonians in photonics suggest looking for a possibility to design optical settings that would realize non - hermitian hamiltonians featuring the full @xmath1 symmetry , as well as its @xmath0 reduction . a possibility to implement the former symmetry was recently explored in ref . @xcite , which addressed not optics , but rather a two - component bose - einstein condensate with the spin - orbit coupling between the components , one of which is subject to the action of loss , and the other one is supported by gain . in terms of optics systems , the symmetry of that models is similar to the @xmath9 symmetry in a dual - core waveguide , with a combination of continuous @xmath10 transformation acting in the longitudinal direction , and another @xmath3 transformation which swaps the two cores . a similar symmetry was proposed in ref . @xcite , which put forward a @xmath9-symmetric coupler subject to the action of management "" , in the form of periodic simultaneous switch of the signs of the coupling and gain - loss coefficients . the present work aims to offer emulation of the @xmath0 symmetry in a two - component optical system , which , at the phenomenological level , may be considered as a dual - core waveguide with opposite signs of the group - velocity dispersion ( gvd ) in the cores and a phase - velocity mismatch between them , embedded into an active medium . we demonstrate that the system can be derived , without phenomenological assumptions , as a model of the spatial - domain propagation for two fundamental - frequency ( ff ) components with orthogonal polarizations of light , pumped by an undepleted second - harmonic ( sh ) wave in a birefringent medium with the @xmath11 nonlinearity . we further investigate conditions for persistence and breaking of the @xmath0 symmetry , both analytically and numerically . in particular , the addition of cubic ( kerr , alias @xmath12 ) terms to the system with the active coupling breaks the symmetry at the nonlinear level , but helps to stabilize confined breather states ( oscillatory solitons ) , and gives rise to a family of stable stationary gap solitons . the paper is organized as follows : section 2 introduces the model , in its both forms ( phenomenological and the one based on the @xmath11 interaction ) and reports analytical results . numerical findings for the linear and nonlinear systems are presented in section 3 , and section 4 concludes the paper . at the phenomenological level , we consider the copropagation of optical modes @xmath13 and @xmath14 in a dual - core coupler with opposite gvd signs in the cores ( cf . refs . @xcite , where a similar feature was introduced in different contexts , and also refs . @xcite , where systems with opposite signs of group velocities were considered in the contexts of coupled right- and left - handed waveguides ) , and a phase - velocity mismatch @xmath15 between them . the linear coupling between the cores is provided by cross - gain terms , with strength @xmath16 , which is possible when the coupler is embedded into an active medium , as recently proposed in ref . the model is represented by the following system of propagation equations , which include the kerr nonlinearity too , with respective coefficient @xmath17 ( all the quantities are dimensionless ) : @xmath18here @xmath19 is the propagation distance , @xmath20 is the reduced time agrawal2001nonlinear , the gvd coefficients are scaled to be @xmath21 , and @xmath22 may be transformed to @xmath23 by changing @xmath24 . positive and negative values of @xmath17 can also be transformed into each other by substitution @xmath25 , therefore , in what follows below we consider only @xmath26 . then , rescaling allows one to fix @xmath27 , but we prefer to keep it as a free parameter , the variation of which helps to monitor a transition from the weakly nonlinear system to a strongly nonlinear one . it is relevant to mention that a dissipative discrete system with opposite signs of the discrete dispersion and a wavenumber mismatch between the components was introduced in ref . however , that model included the dissipative coefficient in a single equation , therefore it did not realize the symmetry considered here . equations ( [ u ] ) and ( [ v ] ) can be derived from the non - hermitian ( complex ) lagrangian , which is usual for @xmath9-symmetric systems:@xmath28 dt \notag \\ -i\gamma \int_{-\infty } ^{+\infty } \left ( u^{\ast } v+uv^{\ast } \right ) dt , \label{l}\end{gathered}\]]which generates the respective non - hermitian hamiltonian in an obvious way.the total energy , @xmath29 dt\equiv e_{u}(z)+e_{v}(z ) , \label{p}\]]is not conserved by eqs . ( [ u ] ) and ( [ v ] ) . instead , the system gives rise to the following energy - balance equations:@xmath30the equality of @xmath31 and @xmath32 , i.e. , the conservation of @xmath33 , means that the linear coupling of the present type causes mutual amplification or attenuation of both components . the linear version of eqs . ( [ u ] ) and ( [ v ] ) , with @xmath34 , are invariant with respect to the @xmath0 transformation , defined as@xmath35where the swap of @xmath13 and @xmath14 stands for @xmath3 , and the complex conjugation for @xmath4 ( conserved @xmath36 may be considered as the respective charge ) . it is relevant to compare the system of eqs . ( u ) , ( [ v ] ) and their invariance transformation ( [ cpt ] ) with the previously studied model of the @xmath9-symmetric coupler , which was based on the following equations couplers , couplers1,coupler - management : @xmath37obviously , eqs . ( [ upt ] ) and ( [ vpt ] ) are invariant with respect to transformation @xmath38 , which , in the present context , may be considered as corresponding to the @xmath39 symmetry , the reversal of @xmath19 playing the role of additional @xmath5 . it is relevant too to compare the present model to the system of equations with opposite gvd terms , coupled by the usual conservative terms , rather than by those representing the gain and loss @xcite : @xmath40where @xmath41 is a real coupling constant . the linear version of this system is invariant with respect to the _ anti_-@xmath0 transformation : @xmath42 anti "" corresponding to the relative sign flip , cf . ( [ cpt ] ) . the nonlinearity breaks the symmetry of system ( [ u ] ) , ( [ v ] ) , as the opposite relative signs of the gvd and cubic terms in the two equations make it impossible to swap @xmath13 and @xmath14 , which represents the @xmath3 transformation in eq . ( [ cpt ] ) . nevertheless , nonlinear effects are obviously interesting too . it is demonstrated below that the nonlinearity creates solitons in the present system . in this connection , it is relevant to mention recently introduced nonlinear models with alternating gain and loss , which do not obey the condition of the @xmath9 symmetry , but nevertheless support stable solitons @xcite . a solution to the linear version of eqs . ( [ u]-[v ] ) in the form of plane waves , @xmath43 produces a dispersion relation for the wavenumber and frequency:@xmath44obviously , in the case of @xmath45 the spectrum given by eq . ( [ dr2 ] ) is pure real , provided that@xmath46while in the case of @xmath47 the spectrum always includes an imaginary component . the change of the spectrum from real to a partly imaginary one , with the increase of the gain - loss coefficient , at @xmath48 ( provided that @xmath45 ) implies the breakup of the @xmath0 symmetry , similar to the phase transition which is the generic feature of @xmath9-symmetric systems @xcite . if condition ( [ thr ] ) holds , the spectrum given by eq . ( [ dr2 ] ) features a _ bandgap_,@xmath49 while the system of eqs . ( [ u ] ) , ( [ v ] ) was introduced above phenomenologically , its linear version can be derived , in the spatial domain ( rather than in the temporal one ) , starting from the fundamental propagation model for two ff and one sh components of light waves , @xmath13 , @xmath50 and @xmath51 , respectively , in the dissipation - free medium with the type - ii" +"quantum turbulence ( qt ) is currently one of the most important topics in low temperature physics @xcite . qt has been long studied for superfluid helium , while the realization of bose einstein condensation in trapped atomic gases has proposed another important stage of qt . after the realization in 1995 lots of experimental and theoretical works have been devoted to the issues of quantized vortices in this system @xcite . most works have addressed the system of a small number of vortices or a vortex array under rotation , but there are very few on qt . following a few theoretical proposals @xcite , henn _ et al . _ succeeded in creating and observing three - dimensional qt in trapped @xmath0rb becs @xcite . an important advantage of atomic gases is that multicomponent becs can be created experimentally . multicomponent becs allow the formation of various unconventional topological defects with complex properties that arise from the internal degrees of freedom and the interactions between different components @xcite , yielding a rich variety of superfluid dynamics @xcite . hence multicomponent becs can propose a more advanced system of qt . two - component qt has already been studied theoretically and numerically @xcite ; the most important interest would be how two kinds of qt interact . recently we have studied theoretically and numerically spin turbulence ( st ) in spinor becs @xcite . a spinor bec is a kind of multicomponent becs with spin degrees of freedom @xcite . in contrast to the two - component becs , interatomic interactions allow for a coherent transfer of population between different hyperfine spin states ( spin - exchange collisions ) , which yields a fascinating physics different from two - component becs . spinor becs can be another important stage of turbulence in quantum fluids . when the system is highly excited from the ground state , it goes through hydrodynamic instability to st in which the spin density vector has various disordered direction . this st shows characteristic behaviors different from other kinds of qt . first , the spectrum of the spin - dependent interaction energy obeys a -7/3 power law @xcite , which is different from the traditional kolmogorov -5/3 power law in turbulence @xcite . secondly , the spin density vectors are spatially random but temporally frozen , which reminds us of the analogy of spin glass @xcite . this article reviews such recent works on st . we consider a two - dimensional spin-1 spinor bec at zero temperature . the macroscopic wave functions @xmath1 with the magnetic quantum number @xmath2 ( @xmath3 ) obey the gross - pitaevskii ( gp ) equations @xcite @xmath4\psi _ { n } \nonumber \\ & + & c_{0 } \rho \psi _ { m } + c_{1 } \sum _ { n=-1 } ^{1 } \mathbf{s } \cdot \hat{\mathbf{s } } _ { mn } \psi _ { n}. \label{2dgp } \end{aligned}\ ] ] here , @xmath5 and @xmath6 are the trapping potential and magnetic field . the parameters @xmath7 , @xmath8 , @xmath9 , and @xmath10 are the mass of a particle , the land@xmath11 @xmath8 factor , the bohr magneton , and a coefficient of the quadratic zeeman effect , respectively . the total density @xmath12 and the spin density vector @xmath13 ( @xmath14 ) are given by @xmath15 and @xmath16 with the spin-1 matrices @xmath17 . the averaged density is given by @xmath18 with the system area @xmath19 . the parameters @xmath20 and @xmath21 are the coefficients of the spin - independent and spin - dependent interactions . we focus on the spin - dependent interaction energy @xmath22 , whose coefficient @xmath21 determines whether the system is ferromagnetic ( @xmath23 ) or antiferromagnetic ( @xmath24 ) . the gp equations ( [ 2dgp ] ) allows us to obtain the hydrodynamic equations of the spin density vector , which we need to understand the scaling power law in the energy spectrum . the full hydrodynamic equations are derived by yukawa and ueda @xcite , while its simper version is available for the ferromagnetic case @xcite . we will assume two things . first , the total density @xmath12 is time - independent because @xmath25 is usually much larger than @xmath26 . secondly , the spin density vector takes the largest value everywhere owing to the ferromagnetic interaction . the two assumptions are confirmed in our numerical simulation @xcite . then the normalized spin density vector @xmath27 is shown to obey the hydrodynamic equations @xmath28 , \quad \mathbf{v } = \frac{\hbar}{2im\rho } \sum _ { m=-1 } ^{1 } ( \psi _ { m}^ { * } \mathbf{\nabla } \psi _ { m } - \psi _ { m } \mathbf{\nabla } \psi _ { m}^ { * } ) , \ ] ] where @xmath29 and @xmath30 is the superfluid velocity @xcite . in a uniform system @xmath12 keeps almost constant , thus vanishing @xmath31 . as a result , we obtain @xmath32 here space and time are respectively normalized by the coherence length @xmath33 and a characteristic time @xmath34 ( @xmath35 , @xmath36 ) , and @xmath37 is the sound velocity . another important characteristic length is the spin coherence length @xmath38 , which is relevant to spin structures such as domain walls and polar core vortex @xcite . we numerically created st by three different methods : ( 1 ) the instability of counterflow between the @xmath39 components in a uniform system @xcite , ( 2 ) the instability of the helical spin structure in a trapped system @xcite , ( 3 ) the instability by an oscillating magnetic field in a uniform system @xcite . all simulations are performed in a two - dimensional system . in every case we confirmed the -7/3 power law in the spectrum of the spin - dependent interaction energy and the spin - glass - like behavior @xcite , though only in the case ( 3 ) how to apply the oscillating magnetic field is different between @xcite and @xcite . in this section we describe the case of ( 1 ) as a typical one . the counterflow between the @xmath40 components with a relative velocity @xmath41 is represented by the initial wave functions @xmath42 , 0 , { \rm{exp } } \bigl[-i\bigl(\frac{m}{2 \hbar}\mathbf{v}_{r}\cdot \mathbf{r } + \frac{\mu _ { -1}}{\hbar}t\bigr)\bigr]\bigr),\ ] ] where @xmath43 is a unit vector along the @xmath44 direction and the chemical potentials @xmath45 and @xmath46 are equal to @xmath47 . the analysis of the bogoliubov - de gennes equation shows that the system is dynamically unstable at any relative velocity @xmath48 @xcite . hence the initial counterflow goes through the dynamical instability towards st . time dependence of spectrum of spin - dependent interaction energy @xmath49 for the ferromagnetic case at @xmath50 ( a ) @xmath51 , and ( b ) @xmath52 . the dotted line in ( b ) refers to the @xmath53 power law . the wave numbers @xmath54 and @xmath55 correspond to the system size and the spin coherence length , respectively . ( c):profile of the spin density vector corresponding to ( b ) . this st is obtained through the counterflow instability with @xmath56 , @xmath57 , @xmath58 . the coordinate is normalized by the coherence length @xmath59 and the box size is @xmath60 . space in the @xmath44 and @xmath61 directions is discretized into @xmath62 bins . ] how st develops is shown in fig . [ ferro ] . the energy spectrum @xmath63 has in the early stage a peak corresponding to the most unstable mode of the dynamical instability ( fig . [ ferro ] ( a ) ) , while the energy gradually flows to the higher wave numbers . when the spin density vector is enough disordered as shown in fig . [ ferro ] ( c ) , the energy spectrum takes a characteristic -7/3 power law ( fig . [ ferro ] ( b ) ) . such a characteristic power law exhibits that this st is not just a random disordered state but an organized self - similar state . we can find easily the similar scenario in classical turbulence ( ct ) @xcite . three - dimensional fully developed turbulence has the inertial range , where the kinetic energy is transfered selfsimilarly from low to high wave numbers and its spectrum shows the kolmogorov -5/3 law . this kolmogorov law can be obtained by applying the scaling analysis due to the selfsimilarity to the hydrodynamic equations @xcite . the similar derivation is available to the hydrodynamic equation ( [ s ] ) . the present case allows us to neglect the second term in the left hand side , because @xmath64 is much smaller than @xmath65 . let us assume that eq . ( [ s ] ) is invariant for the scale transformation @xmath66 and @xmath67 . then it is easy to find that the spin density vector should be transformed as @xmath68 . hence we obtain @xmath69 with a dimensional constant @xmath70 in the scaling region . we apply the usual dimensional analysis to the scaling region to suppose that the energy flux @xmath71 is independent of @xmath72 . then the energy spectrum @xmath63 should be represented only by @xmath73 , @xmath72 and @xmath70 , resulting in the spectrum @xmath74 . st shows another characteristic behavior . in st the spin density vectors become spatially random but temporally frozen , which reminds us of spin glass . spin glasses are magnetic systems in which the interactions between the magnetic moments are in conflict with each other @xcite . thus , these systems have no long - range order but exhibit a freezing transition to a state with a kind of order in which the spins are aligned in random directions . time development of the exponent @xmath75 of the spectrum @xmath63 and the spin glass order parameter @xmath76 . the conditions and the parameters are same as those of fig . [ ferro ] . see ref . @xcite for the detail . ] in order to characterize the spin - glass - like behavior in st , we introduced an order parameter following the spin - glass theory @xcite . we should note that the order parameter is time - dependent . for the normalized spin density vector @xmath77 , its space average and the time average during the period @xmath78 $ ] could be defined as @xmath79=\frac1a \int_a \hat{\mathbf{s } } ( \mathbf{r},t)d\mathbf{r } , \quad \langle \hat{\mathbf{s } } ( \mathbf{r},t)\rangle_t= \frac1 t \int_t^{t+t}\hat { \mathbf{s } } ( \mathbf{r},t_1)dt_1 . \label{average}\ ] ] the argument of how to take @xmath80 is discussed in ref . the time - dependent order parameter is defined as @xmath81 . \label{q}\ ] ] if the spin density vector is completely frozen , @xmath82 should be unity . figure [ st ] shows the time dependence of @xmath82 and the power exponent @xmath83 of the spectrum of the spin - dependent interaction energy . the order parameter @xmath82 increases obviously as the exponent @xmath84 approaches @xmath85 , which means that the spin - glass - like order grows as the st with the @xmath85 power law develops . of course , our system of spinor becs differs from a magnetic system yielding spin glass . spin glass states do not show such a power law behavior in the energy spectrum , being much different from st . we do not know currently what causes the spin - glass - like behavior in st @xcite . when the amplitude of spin density vector is small , another -1 power law appears in the low wave number region in addition to the -7/3 power in the high wave number region of the energy spectrum in st @xcite . this kind of st is realized in two cases : ( i ) with antiferromagnetic interaction and ( ii" +"multiwavelength observations of gamma ray burst ( grb ) afterglows are of crucial importance for understanding and constraining the active emission mechanisms ( wijers et al . 1997 ; galama et al . 1998 , wijers & galama 1999 , masetti et al . 1999 ) . optical and near - infrared ( nir ) data carry the richest and most detailed information . in particular , since the grb counterparts might heavily suffer from dust obscuration within the host galaxy , the nir data , less affected by this extinction , are more effective than the optical ones for the study of the counterpart itself and of the circumburst medium , and , ultimately , in determining the nature of the grb progenitors ( see e.g. dai & lu 1999 ) . grb990705 ( celidonio et al . 1999 ) was detected by the gamma - ray burst monitor ( grbm ; frontera et al . 1997 , amati et al . 1997 , feroci et al . 1997 ) onboard _ bepposax _ ( boella et al . 1997 ) on 1999 july 5.66765 ut and promptly localized with a 3@xmath4 accuracy by unit 2 of the _ bepposax _ wide field cameras ( wfc ; jager et al . 1997 ) . this grb lasted about 45 s in the grbm 40700 kev band , in which it reached a @xmath5ray peak flux of ( 3.7 @xmath6 0.1)@xmath710@xmath8 erg @xmath9 s@xmath10 and showed a complex and multi - peaked structure . the wfc ( 226 kev ) data indicate that grb990705 had a similar duration and lightcurve in the x rays , and that it displayed very bright x ray emission with a peak intensity of about 4 crab . a detailed presentation and description of the prompt event will be given by amati et al . ( in preparation ) . a bepposax x ray follow - up of grb990705 started 11 hours after the grbm trigger ( gandolfi 1999 ; amati et al . the detection of this grb by _ ulysses _ ( hurley & feroci 1999 ) and _ near _ ( hurley et al . 1999 ) determined two annuli intersecting the _ bepposax _ wfc error circle . this allowed the reduction of the error box to @xmath113.5 square arcmin . radio observations carried out with atca ( subrahmanyan et al . 1999 ) detected three radio sources in the wfc error circle . however , none of them lies inside the intersection of the _ ulysses _ , _ near _ and _ bepposax _ error boxes ( hurley et al . 1999 ) . optical and near - infrared ( nir ) observations were immediately activated at telescopes in the southern hemisphere to search for a counterpart at these wavelengths . the early imaging of the 3@xmath4 radius wfc error circle at the eso - ntt with the sofi camera allowed us to detect a bright nir transient ( palazzi et al . 1999 ) inside the _ ulysses _ , _ near _ and _ bepposax _ error boxes intersection . in this paper we report on the discovery and follow - up observations of the nir and optical transients ( nirt and ot , respectively ) associated with grb990705 . in sect . 2 we describe the data acquisition and reduction , while in sect . 3 we report the results , which are then discussed in sect . the nir imaging started 6.6 hours after the high - energy event : @xmath0-band images were acquired on 1999 july 5.9 , 6.4 and 6.9 at la silla ( chile ) with the 3.58-meter eso - ntt plus sofi ( see the observation log in table 1 ) . the camera is equipped with a hawaii 1024@xmath71024 pixel hgcdte detector , with a plate scale of 0@xmath1229 pixel@xmath10 and a field of view of roughly 4@xmath139@xmath74@xmath139 . images are composed of a number of elementary coadded frames acquired by dithering the telescope by several arcsecs every 60 s. reduction of the images was performed with iraf and the stsdas packages . each image was reduced by first subtracting a mean sky , obtained from frames just before and after the source image . then , a differential dome flatfield correction was applied , and the frames were registered to fractional pixels and combined . before frames were used for sky subtraction , stars in them were eliminated by a background interpolation algorithm ( _ imedit _ ) combined with an automatic `` star finder '' ( _ daofind _ ) . we calibrated the photometry with stars selected from the nicmos standard list ( persson et al . the stars were observed in five positions on the detector , and were reduced in the same way as the source observations . formal photometric accuracy based only on the standard star observations is typically better than 3% . the source photometry was corrected for atmospheric extinction using the mean eso @xmath0-band extinction coefficient of 0.06 ( engels et al . 1981 ) . @xmath14-band ( 3.205 - 3.823 ) observations were also carried out in antarctica on july 7.6 with the spirex 0.6-meter telescope plus the noao abu ir camera with a 0@xmath126 pixel@xmath10 plate scale . abu houses a 1024@xmath71024 pixel aladdin insb array operating at 36 k using a closed cycle helium refrigeration system . forty images ( eight 5-image cross patterns - center and the cardinal points - with 30@xmath15 separation ) of 3-min duration each ( 12 coadded 15-sec integrations ) were obtained for a total on - source time of 120 minutes . images were then sky - subtracted using sky frames generated from the running median of 6 neighbors , divided by the flatfield , and spatially registered using stars within each field . the 40 images were shifted and median filtered into the 120-min composite . star hr 2015 ( mcgregor 1994 ) was employed as an @xmath14-band standard to zero - point calibrate the grb990705 field . optical imaging of the grb990705 error box was obtained at paranal ( chile ) with the 8.2-meter eso vlt - ut1 ( antu "" ) plus fors1 ( detector scale : 0@xmath122 pixel@xmath10 ; field of view : 6@xmath138@xmath76@xmath138 ) on 1999 july 6.4 , 8.4 and 10.4 in the @xmath1 band , and at la silla ( chile ) with the 2.2-meter mpg / eso telescope plus wfi ( 8 ccd mosaic detector scale : 0@xmath12238 pixel@xmath10 ; field of view : 34@xmath4@xmath733@xmath4 ) on 1999 july 6.4 ( @xmath16 band ) and july 7.4 ( @xmath1 band ) . the complete log of the optical observations is reported in table 1 . ccccccl day of 1999 ( ut ) & telescope & filter & exp . time & seeing & magnitude@xmath17 & + at exposure start & & & ( minutes ) & ( arcsecs ) & & + + & ntt & @xmath0 & 20@xmath71 & 1.0 & 16.57 @xmath6 0.05@xmath18 & + & ntt & @xmath0 & 8@xmath71 & 1.2 & 18.38 @xmath6 0.05 & + & ntt & @xmath0 & 10@xmath71 & 1.1 & @xmath1919.9@xmath18 & + & spirex & @xmath14 & 40@xmath73 & @xmath111.8 & @xmath1913.9 & + + & antu & @xmath1 & 5@xmath72 & 2.5 & 22.0 @xmath6 0.2 & + & 2.2 m & @xmath16 & 7.5 & 1.8 & @xmath1921.9 & + & 2.2 m & @xmath1 & 2@xmath710 & 2.0 & @xmath1922.3 & + & antu & @xmath1 & 1 & 1.2 & @xmath1923.0 & + & antu & @xmath1 & 6@xmath75 & 0.9 & 23.99 @xmath6 0.07 & ( pointlike object , likely unrelated to the ot ) + & & & & & 23.8 @xmath6 0.2 & ( extended object ) + & & & & & 23.14 @xmath6 0.15 & ( their integrated magnitude ) + + + images were debiased and flat - fielded with the standard cleaning procedure ; each set of @xmath1 frames of july 6 , 7 , and 10 was then co - added to increase the signal - to - noise ratio . we then chose , when applicable , psf - fitting photometry as the measurement technique for the magnitude of point - like objects because the field is quite crowded ( especially in the case of deep images ) being located in the outskirts of the large magellanic cloud ( lmc ) . photometry was performed on the images using the daophot ii data analysis package psf - fitting algorithm ( stetson 1987 ) within _ midas_. in order to calibrate the images to the johnson - kron - cousins photometric system , we acquired on july 7 a @xmath16 frame of part of selected area 95 with the 2.2-meter telescope and on july 10 @xmath1 frames of the pg 1323@xmath20086 , pg 2213@xmath20006 and mark a sequences ( landolt 1992 ) with antu ; we adopted as airmass extinction coefficients 0.11 for the @xmath1 and 0.25 for the @xmath16 . with this photometric calibration , for comparison , the usno - a1.0 star u0150_02651600 , with coordinates ( j2000 ) @xmath2 = 5@xmath21 09@xmath22 42@xmath2359 , @xmath24 = @xmath2072@xmath25 07@xmath4 41@xmath122 , has @xmath16 = 18.72 and @xmath1 = 17.64 . unfortunately , the @xmath16 calibration frames were obtained under poor photometric conditions ( see table 1 ) and therefore the uncertainty on the zero point of the calibration ( @xmath60.25 mag ) is by far the main source of error in the measure of the @xmath16 magnitude of the usno star . no color term was applied in the @xmath1-band calibration since only @xmath1 frames were taken on july 10 ; so , the uncertainty on the @xmath1 zero point is @xmath60.15 mag . these large errors are also due to the high airmass ( larger than 2 ) affecting our observations . the @xmath16 and @xmath1 magnitude errors quoted in the next section are only statistical and do not contain any possible zero point offset . we evaluated the galactic hydrogen column density in the direction of grb990705 using the nrao maps by dickey & lockman ( 1990 ) , from which we obtained @xmath26 = 0.72@xmath710@xmath27 @xmath9 and , using the empirical relationship by predehl & schmitt ( 1995 ) , we computed a foreground galactic absorption @xmath28 = 0.40 . this , by applying the law by rieke & lebofsky ( 1985 ) , corresponds to @xmath29 = 0.13 and to @xmath30 = 0.33 ; using the law by cardelli et al . ( 1989 ) we then derived @xmath31 = 0.53 and @xmath32 = 0.07 . the intrinsic value of @xmath26 in that region of the lmc is less than @xmath3310@xmath34 @xmath9 ( mcgee et al . 1983 ) ; therefore , the reddening induced by the lmc on the nirt / ot is practically negligible . the summed 20-min ntt image of july 5.9 ( fig . 1 , left panel ) shows an object at a magnitude @xmath0 = 16.57 @xmath6 0.05 which in the july 6.4 8-min image is detected at @xmath0 = 18.38 @xmath6 0.05 . on july 6.9 the object magnitude is @xmath0 @xmath19 19.9 at a 3@xmath35 level ( fig . 1 , right panel ) . astrometry done on the first ntt observation using several stars from the usno - a1.0 catalogue gives for this fading source coordinates @xmath2 = 5@xmath21 09@xmath22 54@xmath2352 , @xmath24 = @xmath2072@xmath25 07@xmath4 53@xmath121 ( j2000 ) with a 1-@xmath35 accuracy of 0@xmath123 . this object is inside the intersection of all the mentioned x ray error boxes , and almost at the center of the _ bepposax _ wfc error circle . moreover , the observed brightness variation and the variability timescale are similar to those of previously observed optical afterglows . this leads us to conclude that it is the nir afterglow" +"manifestations of vertical transport in weakly coupled semiconductor doped superlattices ( sls ) include electric field domain formation , @xcite multistability , @xcite self - sustained current oscillations , @xcite and driven and undriven chaos . @xcite stationary electric field domains appear in voltage biased sls if the doping is large enough . @xcite when the carrier density is below a critical value , self - sustained oscillations of the current may appear . they are due to the dynamics of the domain wall separating the electric field domains . this domain wall moves through the structure and is periodically recycled . the frequencies of the corresponding oscillation depend on the applied bias and range from the khz to the ghz regime . self - oscillations persist even at room temperature , which makes these devices promising candidates for microwave generation . @xcite numerical calculation of the voltage doping sl phase diagram shows that only static electric field domains are possible for high enough sl doping . as the doping decreases , voltage windows where current self - oscillations are possible open up . @xcite these windows may coalesce into a single one as doping is further lowered , and oscillations disappear below a critical doping value . since doping is not a feasible control parameter , other quantities affecting carrier density should be used to observe these behaviors . feasible control parameters are laser illumination in undoped sls @xcite ( which behaves qualitatively as well doping ) , transverse magnetic fields , @xcite and temperature @xcite in doped sls . despite its practical and theoretical interest , the effect of temperature on electric field domains @xcite and current self - oscillations is still poorly understood . early numerical calculations were performed with a fixed drift velocity corresponding to a fixed temperature . @xcite using the insight provided by these calculations and reasonable expectations on how drift velocity depends with temperature , the fact that oscillatory voltage windows widen as the temperature increases was explained . @xcite more detailed experimental studies dealing with the influence of temperature on self - oscillations have appeared recently . @xcite experimental data show that raising the temperature is similar to lowering the sl doping . at low temperature a multiplicity of purely static states ( corresponding to coexistence of low and high field domains in the sl ) was observed . as the temperature increased , voltage windows corresponding to self - oscillations appeared and widened in the sl @xmath0@xmath1 characteristics . @xcite experimental data were interpreted by using the discrete drift model @xcite with a fitted drift velocity . @xcite these authors concluded that the peak - to - valley ratio in the negative differential mobility region of the drift velocity was crucial to understand the data . a model including both variation of the electron density in the wells and variation of the drift velocity with temperature was therefore needed . @xcite in a recent paper , we have been able to derive discrete drift - diffusion ( ddd ) models , including boundary conditions , from microscopic sequential tunneling models . @xcite by using our formulas for the field - dependent drift velocity at different temperatures ( ranging from 0 to 175 k ) , we can compare numerical simulations of these simple discrete models with wang et al s experimental data . our results show that increasing temperature facilitates current self - oscillations in the second plateau . furthermore , our numerical results ( based upon microscopically calculated drift velocities ) agree with the available experimental data and explain them quantitatively . we explain qualitatively why regions of stationary states alternate with regions of self - oscillations in the temperature voltage phase diagram . finally and on the basis of our numerical simulations , we also explain why the frequency may have local maxima in the voltage intervals where self - oscillations occur . that the frequency may increase with voltage , while the average current simultaneously decreases is thus a consequence of our theory , not an anomaly . @xcite the rest of this paper is as follows . section [ sec - model ] contains a brief description of the ddd model and a calculation of its transport coefficients and boundary conditions appropriate for wang et al s experimental sample . results of numerical simulations of this model and comparison with experimental data are reported in section [ sec - results ] . section [ sec - conclusions ] contains our conclusions . a discussion of the qualitative theoretical analysis included in the experimental papers is presented in appendix [ sec - crap ] . the main charge transport mechanism in a weakly coupled sl is sequential resonant tunneling . the characteristics of the samples experimentally studied in ref . are such that the macroscopic time scale of the self - sustained oscillations is larger than the tunneling time ( defined as the time an electron needs to advance from one well to the next one ) . in turn , this latter time is much larger than the intersubband scattering time . then tunneling across a barrier is a stationary process with well - defined fermi - dirac distributions at each well . these distributions depend on the instantaneous values of the electron density and potential drops and vary only on the longer macroscopic time scale . the tunneling current density across each barrier in the sl may be approximately calculated by means of the transfer hamiltonian method . @xcite the resulting formulas can be used to calculate the transport coefficients and boundary conditions of the following ddd model : @xcite @xmath2 in these equations , @xmath3 , @xmath4 and @xmath5 are well permittivity , minus the electron charge and 2d doping in the wells , respectively . @xmath6 is the sl period , where @xmath7 and @xmath8 are the widths of barriers and wells , respectively . eq.([m1 ] ) is ampre s law establishig that the total current density , @xmath9 , is sum of displacement and tunneling currents . the latter consists of a drift term , @xmath10 , and a diffusion term , @xmath11 . we have adopted the convention ( usual in this field ) that the current density has the same direction as the flow of electrons . ( [ m1 ] ) holds for @xmath12 . ( [ m2 ] ) is the poisson equation , and it holds for @xmath13 . @xmath14 is the 2d electron number density at well @xmath15 , which is singularly concentrated on a plane located at the end of the well . @xmath16 is _ minus _ an average electric field on a sl period comprising the @xmath15th well and the @xmath15th barrier ( well @xmath15 lies between barriers @xmath17 and @xmath15 : barriers 0 and @xmath18 separate the sl from the emitter and collector contact regions , respectively ) . [ fig1 ] depicts the field - dependent drift velocity at different temperatures for sl parameter values of ref . : 40 periods of 14 nm gaas and 4 nm alas and well doping @xmath19 @xmath20 . it has been calculated from the microscopic tunneling current density by the procedure explained in ref . . the only adjustable parameter in the sequential tunneling formulas is the lorentzian half - width of the scattering amplitudes , @xmath21 . to estimate them , we have considered that the voltage difference , @xmath22 , between the peaks of two consecutive branches on the second plateau of the static @xmath0@xmath1 characteristic is @xmath23 here @xmath24 is the @xmath15th energy level of a given well . for @xmath25 , the field profile on the second plateau corresponds to two coexisting electric field domains with fields @xmath26 $ ] and @xmath27 $ ] . the domain walls corresponding to two adjacent branches in the @xmath0@xmath1 diagram are located in adjacent wells . then the voltage difference should be @xmath28 . in the presence of scattering , resonant peaks have finite widths which we take as @xmath29 , thereby obtaining ( [ gamma ] ) . @xmath30 is an adjustable parameter of the order of unity @xcite . by using this formula and the measured current in ref . ( figs . 1 , 2 , and 3 ) , we find @xmath31 mev at 1.6 k and @xmath32 mev at 140 k for @xmath33 . linear interpolation yields the temperature dependence of @xmath21 in the range we are interested in . notice that the first peak of the velocity in fig . [ fig1 ] rapidly disappears as the temperature increases for this particular sample . this result might change if we assume different scattering amplitudes for each of the two first subbands of the wells . moreover , the different extrema of the velocity curve shift to lower field values as the temperature increases . thus formation of electric field domains and current self - oscillations are expected for voltages on the second plateau and higher . multistable solution branches of the current voltage characteristic curve should also shift to lower voltages and higher currents as the temperature increases , as observed in experiments . @xcite these effects could not be obtained from the fitted drift velocity in ref . . as the diffusion coefficient decreases very rapidly with field , we can safely set @xmath34 in our ddd model for the experimentally observed voltage range . the relevant model is thus the well - known discrete drift model of refs . with the drift velocity deduced from a microscopic calculation of the current plus boundary conditions @xcite ( see fig . [ fig1 ] ) . to complete the description of our model , we need to specify initial , boundary and bias conditions . the dc voltage bias condition is @xmath35 given that @xmath36 , we need only one boundary condition specifying @xmath37 ( the field at the contact region ) . we will assume that there is an excess electron density in the first well due to tunneling from the highly doped contact region , @xcite @xmath38 for an appropriately chosen dimensionless positive constant @xmath39 , this condition selects recycling of charge monopole waves as the mechanism for self - sustained oscillations of the current . @xcite the same behavior can be obtained from more elaborated boundary condition for the microscopic tuneling current between the emitter and the neighboring well @xcite provided contact doping is sufficiently high ( ohmic behavior ) . given the uncertainties inherent to contact specification , we have preferred to use the phenomenological boundary condition ( [ m4 ] ) instead . in this section , we shall numerically simulate the discrete drift model for different values of temperature . from formula ( 1 ) and ( 2 ) , considering d=0 : @xmath40 = j(t)\ , , \label{n1}\\ \sum_{i=1}^n f_{i } = { v\over { \cal l}}\ , . \label{n2}\end{aligned}\ ] ] the corresponding drift curves are chosen among those depicted in fig . [ fig1 ] and the boundary condition will be ( [ m4 ] ) with @xmath41 . a first interesting conclusion can be drawn effortlessly from an analytical upper bound of the critical doping above which there are stable static electric field domain branches : @xcite @xmath42 in this formula , @xmath43 and @xmath44 are the values of the electric field which correspond to the maximum and minimum of the drift velocity ( @xmath45 and @xmath46 ) on the second plateau . the temperature dependence of this critical doping is plotted in fig . we observe that the critical doping increases with temperature , indicating that the voltage range for which self - oscillations exist increases as temperature does . in particular , fig . [ fig2 ] predicts a transition temperature at around 93 k whereas about 140 k is experimentally measured . @xcite despite the fact that the bound ( [ bound ] )" +"the large area telescope ( lat ) is the primary instrument on the _ fermi gamma - ray space telescope _ mission , launched on june 11 , 2008 . it is the product of an international collaboration between doe , nasa and academic us institutions as well as international partners in france , italy , japan and sweden . the lat is a pair - conversion detector of high - energy gamma rays covering the energy range from 20 mev to more than 300 gev @xcite . it has been designed to detect gamma rays in a broad energy range , with good position resolution ( @xmath010 arcmin ) and an energy resolution of @xmath110% . the lat has been routinely monitoring the gamma - ray sky and has shed light on the extreme , non - thermal universe . a brief and recent review of _ fermi_-lat discoveries can be found in @xcite . the lat response to gamma rays is parametrized by the so - called `` instrument response functions '' ( irfs ) , which together with the data from the instrument are provided to the scientific community . as described in @xcite , irfs are derived using monte - carlo ( mc ) simulations and also corrected for discrepancies observed between flight and simulated data , as the lat team gains insight into the in - flight performance of the instrument . in the near future , major improvements are expected from the new `` pass 8 '' data , such as an increased effective area with respect to the current `` pass 7 '' public data @xcite . these improvements correspond to a radical revision of the lat event - level analysis . the optimization of the event reconstruction and of the background rejection , and the full characterization of the new irfs , require the production of large simulated data sets including gamma rays and charged cosmic backgrounds ( protons , heavy ions , electrons ) . these simulations are also fundamental for high - level analyses which will require a proper evaluation of the residual backgrounds ( e.g. , the extragalactic diffuse emission @xcite or the cosmic electron - positron spectra @xcite ) . + the cherenkov telescope array ( cta ) project @xcite is the next generation of imaging atmospheric cherenkov telescopes ( iacts ) , operating in the high- and very high - energy gamma - ray domain ( between a few tens of gev and 200 tev ) . it will consist of two arrays of 50 - 100 telescopes of different sizes , located in each hemisphere . the cta consortium gathers more than 1000 scientists and engineers from more than a hundred institutions world - wide . the project is currently in its preparatory phase . the construction is planned to be completed around 2018 - 2020 . during the current cta preparatory phase , large computing and storage resources are needed mostly for mc studies . in particular , the selection of the cta sites ( north and south ) has a significant impact on the final sensitivity of the instrument . the cta mc working group is studying the impact of these various parameters by means of detailed mc simulations of the detector response to extensive air showers . large sets of simulated events are generated for different primary particles . moreover , once cta sites have been selected and the construction phase has started , more detailed simulations will be produced in order to test analysis algorithms and to determine the final performance of the instrument . + in order to fulfill present and future requirements for mc massive production and data analysis of _ fermi_-lat and cta , we have proposed the use of the egi grid infrastructure and of the dirac ( distributed infrastructure with remote agent control ) @xcite framework for both current and future experiments . the dirac system , originally developed to support production activities of the lhcb experiment , today serves several communities . compared to lhcb dirac installation , expanding over half a dozen powerful servers , the cta installation is still rather modest , and it is currently being upgraded . the work presented in this paper was served by a dirac installation running on two virtual servers having , in total , 6 cores , 6 gb of ram and 1.5 tb of local disk , plus a third machine hosting the web portal . _ fermi_-lat is using the french ngi multi - community dirac installation running on five servers @xcite . in section [ fermi ] we describe the developments that have been necessary to extend the _ fermi_-lat pipeline to the grid through the dirac system . the context for cta is quite different , since the project is in its preparatory phase and no existing production system was available for the management of the different computing activities . in section [ cta ] we present the work done to migrate both the cta mc production and its analysis by the cta physicists on the grid within the dirac framework . the first results from the mc campaigns in 2013 , in terms of resource usage , are also presented . section [ conclusions ] is devoted to conclusions and perspectives for future work . the data acquired by the _ fermi_-lat in orbit is transferred via satellite downlink several times per day , and then sent to an offline processing system , which is hosted by the lat isoc ( instrument science operations centers ) based at the slac national accelerator laboratory in california . the _ fermi_-lat data processing pipeline ( see , e.g. , @xcite for a detailed technical description ) was designed with the focus on allowing the management of arbitrarily complex workflows and handling multiple tasks simultaneously ( e.g. , prompt data processing , data reprocessings and science analysis ) . we briefly recall its basic functionalities in section [ lat_pipeline ] . then we describe its interface to dirac ( section [ lat_dirac ] ) and we present the results of the first mc simulations which we performed on the grid during summer 2013 ( section [ lat_results ] ) . each pipeline task defines a workflow , specifying a sequence of procedures . these procedures are then either executed directly on the workflow system or are delegated to job control daemons . from the beginning , the system was tailored to be interfaced to local computing resources such as the batch farms at slac and the cnrs / in2p3 computing center ( cc - in2p3 hereafter ) . to that extent , each job control service has to run as a daemon on a host at the relevant site . information is exchanged via remote method invocation between the job control service and the pipeline server . each task may contain an arbitrary number of streams or sub - streams , i.e. instances of a process . in the simplistic case of a mc production , each stream creates a run containing a pre - defined number of simulated events . in case of a gamma - ray simulation , each stream simulates 5k events in @xmath190 minutes typically , and produces a small volume of data ( @xmath12.3 mb ) when the full details on the event reconstruction are not saved . [ fermi ] the dirac interface to the data processing pipeline was designed to delegate computationally intense mc production to other sites . it has been implemented using french ngi dirac servers at cc - in2p3 ( see fig . [ lategi ] ) , which run all dirac components , workload management system ( wms ) , data management system ( dms ) , agents and web portal , and host the mysql databases . in addition , a _ fermi_-specific dirac extension was developed through a dedicated package which provides basic api functionality in accordance with the one used in the remaining pipeline system ( see @xcite for a detailed description ) . in particular , the extension provides wrappers to status query and job submission . the trigger to submit new jobs is done via the pipeline and its associated user interfaces . thus , re - running failed jobs is done via the pipeline interface , which in turn results in a fresh re - submission of a dirac job with the exact same properties as the initial ( failed ) job . as a consequence , our current setup can not fully utilize the possibilities to re - run failed jobs from within dirac . at present , the dirac system employed by _ fermi_-lat does not support the means to request specific resources . as a consequence , jobs may be sent off to sites where the software is either not available or faulty . instead of relying on discovery services such as those provided by the berkeley database information index ( bdii ) , the _ fermi_-dirac setup makes use of a custom software tag resource database . this is a separate service which relates a given site in dirac with the available software along with its current status . statuses are queried automatically through an agent and jobs are matched to sites according to their requirements . even if the matching becomes trivial for mc production , since the software releases are installed at all sites , this service is particularly useful during the setup of a production . furthermore this system provides us with additional steering handles without the need to modify parts of the dirac configuration and or of the pipeline setup . schematic view of the _ fermi_-lat pipeline extension to the grid through the dirac system . red arrows indicate the execution sequence of the mc simulation . data and log file transfers are shown with magenta and orange arrows , respectively . the blue arrow indicates the registration of data in the _ fermi_data catalog . the lat software installation on the grid sites is indicated by the green arrow . ] the worker node that performs the actual computing step communicates with the pipeline through a series of emails , which in the case of local batch systems provides a robust interface . in order to emulate this behaviour , the _ fermi_-dirac setup utilizes the dirac notification layer that enables every grid worker node to either send the required email directly or to communicate with the dirac server that then sends the relevant information on behalf of the workers . output data are stored on regular grid storage elements ( storm , etc . ) but picked up within the pipeline workflow system to be transferred to xrootd at slac ( see fig . [ lategi ] ) . once transferred , the data on grid storage elements are scheduled for removal . a first working prototype of the grid / pipeline interface with dirac was completed in summer 2013 . the first mc production on the grid consisted of 4000 streams , each one simulating 5k gamma - ray events . this first test was limited to four egi grid sites supporting the glast virtual organization ( vo ) : cnaf , msfg , obspm and bari ( sorted by resource usage ) . they represent about one third of the glast vo resources . the production used between 100 and 300 cores simultaneously , and it ran smoothly with a 97% success rate . the few failed jobs exhibited communication issues between the grid sites and the pipeline , which need to be further investigated . the use of the egi grid infrastructure for the mc production was introduced in cta for the first time in 2008 with the creation of the cta vo . the motivations which led to this choice were the following : large computing and storage requirements for the mc production" +"observations of the prompt gamma - ray bursts ( grbs ) emission by different instruments show that their spectra can extend from several kev up to a few mev @xcite sometimes up to gev range @xcite . according to recent broadband observations by _ ginga _ @xcite , _ hete-2 _ @xcite and combined results of _ bepposax_/batse @xcite and _ rxte_/ipn @xcite , most grbs exhibit a peak in the @xmath5 spectrum at an energy @xmath3 in the 50400 kev range . however , distribution of @xmath3 is broad and large part of events demonstrate significant x - ray ( 230 kev ) emission ( x - ray dominated grbs , x - ray rich grbs ) . at this moment study of broadband spectra is complicated because of insufficient statistics accumulated by broadband instruments and biases due to different instrument responses . the batse @xcite data of all - sky 9.1 years ( 19912000 ) continuous monitoring in @xmath6-ray range give unique possibility for combined grb analysis with x - ray observations . batse @xmath6-ray detectors were the most sensitive instruments of this type over grb history . only recently launched _ swift_experiment @xcite has a more sensitive @xmath6-ray detector . however , during the next several years _ swift_cannot accumulate statistics comparable to that of the batse . batse detected about 2700 grbs with fluxes down to @xmath7 ph @xmath2 s@xmath1 @xcite . in addition , the off - line scans of the batse continuous records almost doubled the number of observed grbs with fluxes down to @xmath8 ph @xmath2 s@xmath1 ( see @xcite ; @xcite ) the batse detectors were sensitive to photons from @xmath925 kev up to @xmath91 mev . however , the on - board procedure and most off - line searches identified grbs according to the signal in the 50300 kev range while grbs with a soft spectrum could be missed . these soft events can help to outline the place of the x - ray dominated bursts in the grb variety . the 25 - 50 kev range was inspected only in the off - line search of @xcite . their scan have covered 6 out of 9.1 years of the batse data and yielded 50 unknown low - energy events some of which are probably soft grbs . even if all of them are grbs , the number of these events is 50 times smaller than that found in the 50300 kev range . we performed a search for grbs , inspecting the 2550 kev range for time period not covered by the scan of @xcite with a more careful and optimized for soft grbs procedure . the continuous daily 1.024 s time resolution discla records of count rate in 8 batse detectors in 4 energy channels ( 2550 , 50100 , 100300 and 3001000 kev ) were used . we have applied the same technique and the same algorithm as in our scan of the batse discla data in the 50300 kev range @xcite setting the trigger in the 25100 kev range ( i.e. in the 1st and 2nd energy channels ) . hr@xmath10 & @xmath11 & @xmath12 & @xmath13 & @xmath14 & @xmath15 + & of tjd & & & & deg & deg & deg & s & + + 980726 & 63036 & 11020 & 0.11 & 0.57 & 255.8 & @xmath1654.8 & 9.7 & 56 & 29 + 980804 & 50914 & 11029 & 0.46 & 0.87 & 173.3 & @xmath1652.7 & 7.3 & 13 & 5 + 980927 & 6133 & 11083 & 0.33 & 0.89 & 9.6 & @xmath1654.5 & 11.4 & 6 & 4 + 981225 & 76754 & 11172 & 0.22 & 0.45 & 161.9 & @xmath1661.3 & 17.0 & 25 & 4 + 990304 & 77277 & 11241 & 1.85 & 0.83 & 31.6 & @xmath1626.7 & 4.6 & 4 & 2 + 990513 & 2453 & 11311 & 0.18 & 0.30 & 236.4 & @xmath1659.6 & 16.5 & 15 & 2 + 990610 & 20227 & 11339 & 0.11 & 0.43 & 234.8 & 16.6 & 17.3 & 80 & 11 + 990804 & 39065 & 11394 & 0.05 & 0.92 & 44.1 & 21.2 & 36.6 & 38 & 10 + 990907 & 75723 & 11428 & 0.06 & 0.66 & 301.0 & @xmath1639.3 & 8.3 & 126 & 33 + 991003 & 30847 & 11454 & 0.16 & 0.60 & 253.8 & 33.2 & 21.1 & 13 & 6 + 991009 & 30691 & 11460 & 0.10 & 0.47 & 107.9 & 3.5 & 12.9 & 24 & 8 + 991106 & 59880 & 11488 & 0.10 & 0.33 & 284.7 & @xmath1658.2 & 20.5 & 39 & 11 + 000107 & 8784 & 11550 & 0.12 & 0.91 & 74.9 & @xmath1661.6 & 16.1 & 73 & 12 + + 980707 & 9097 & 11001 & 0.40 & 3.29 & 79.0 & 40.4 & 9.9 & 6 & 4 + 980930 & 83166 & 11086 & 0.37 & 1.90 & 132.0 & @xmath1670.9 & 6.7 & 38 & 19 + 981012 & 21270 & 11098 & 0.11 & 1.24 & 59.0 & 15.5 & 20.7 & 17 & 11 + 981019 & 69630 & 11105 & 0.29 & 2.18 & 208.9 & @xmath1640.3 & 11.7 & 17 & 3 + 981221 & 18020 & 11168 & 0.97 & 1.82 & 71.9 & 3.6 & 15.4 & 9 & 1 + 990303 & 74922 & 11240 & 0.25 & 1.00 & 199.9 & 52.4 & 18.9 & 9 & 7 + 000324 & 36745 & 11627 & 0.08 & 2.10 & 58.7 & 26.4 & 18.8 & 36 & 10 + 000523 & 49912 & 11687 & 0.41 & 1.01 & 269.1 & 80.6 & 8.6 & 24 & 9 + + + + + [ tab:21grbs ] we present the results of our search for soft batse grbs in section [ sec : search ] and discuss new data together with the recent grb observations by _ bepposax _ and _ hete-2 _ in section [ sec : spectra ] . we have performed the scan of batse discla records available at ftp archive at goddart space flight center for time period since july 6 , 1998 till may 26 , 2000 ( tjds 11000 - 11699 , files for tjds 11047 , 11048 , 11354 , 11355 - 11359 , 11519 - 11521 are missing ) . the applied algorithm and technique is described in @xcite . only the 25100 kev range ( 1 and 2 channels ) was checked . the 1024 ms time resolution discla data are not suitable for studies of short ( @xmath17 s ) grbs and we did not consider 1 bin events . this allows us to avoid scintillation from heavy nuclei and soft gamma - ray repeater ( sgr ) outbursts . we excluded also events with location in the vicinity of galactic center , the sun , four known sgrs and other persistent sources and events that appeared near and below earth horizon . we recorded only new grbs missing in the catalogs of @xcite and @xcite . we have found and classified as grbs 21 new events . table [ tab:21grbs ] present their time identificator , intensity , hardness , location and duration . in the previous scan in 50300 kev @xcite for the same time period we have detected about 800 long grbs . hardness - intensity diagram ( fig . [ fig : hr_int ] ) shows that although grbs of a new sample are softer on average , the samples do overlap . actually 13 out of 21 grbs in a new sample ( table [ tab:21grbs ] ) and 23 of @xmath9800 long grbs in the old sample ( * ? ? ? * table [ tab:23softgrbs ] ) have the peak count rate in 2550 kev higher than that in the 50300 kev band . according to this somewhat arbitrary criterion we consider these 36 events as a sample of soft long ( @xmath182 s ) batse grbs . hr@xmath19 & @xmath20 & @xmath21 & @xmath22 & @xmath23 & @xmath24 + & of tjd & & & & deg & deg & deg & s & + 980924 & 54262 & 11080b & 0.95 & 0.93 & 61.8 & @xmath1622.0 & 8.8 & 10 & 2 + 981015 & 46766 & 11101c & 1.36 & 0.69 & 122.9 & 22.1 & 5.4 & 34 & 6 + 981115 & 21438 & 11132b & 0.80 & 0.80 & 284.0 & 10.0 & 10.6 & 4 & 1 + 981117 & 11629 & 11134a & 0.41 & 0.98 & 217.6 & @xmath1665.7 & 23.7 & 8 & 3 + 981118 & 2533 & 11135a & 0.48 & 0.97 & 186.9 & 60.6 & 23.0 & 6 & 2 + 981128 & 74360 & 11145c & 0.18 & 0.97 & 60.3 & 38.4 & 33.2 & 36 & 3 + 981204 & 37850 & 11151a & 0.16 & 1.00 & 53.4 & @xmath1655.9 & 21.5 & 9 & 3 + 981222 & 58180 & 11169b & 0.30 & 0.89 & 145.9 & 67.1 & 28.7 & 11 & 5 + 990112 & 7066 & 11190a & 0.20 & 0.63 & 118.6 & @xmath1645.6 & 17.7 & 85 & 14 + 990207 & 55697 & 11216e & 0.49 & 0.95 & 152.9 & @xmath169.7 & 16.7 & 17 & 2 + 990218 & 73752 & 11227b & 0.35 & 0.98 & 72.9 & 37.7 & 17.8 & 89 & 7 + 990413 & 32497 & 11281d & 0.39 & 0.94 & 302.1 & 55.5 & 12.8 & 6 & 6 + 990506 & 42666 & 11304c & 0.19 & 0.89 & 186.9 & 9.6 & 21.3 & 61 & 15 + 990610 & 56705 & 11339c & 0.45 & 0.99 & 105.7 & @xmath1616.6 & 8.4 & 109 & 18 + 990915 & 58755 & 11436c & 0.64 & 0.78 & 273.2 & @xmath1621.9 & 5.0 & 50 & 12 + 991006 & 68176 & 11457b & 0.76 & 0.99 & 104.0 & 11.7 & 3.8 & 73 & 27 + 991201 & 1802 & 11513a & 0.09 & 0.98 & 167.9 & @xmath1610.9 & 12.3 & 19 & 13 + 991217 & 37909 & 11529b & 0.36 & 0.49 & 64.8 & @xmath1612.7 & 16.8 & 8 & 1 + 991231 & 28492 & 11543a & 0.22 & 0.96 & 39.3 & 32.3 & 11.3 & 14 & 5 + 000114 & 51441 & 11557a & 1.17 & 0.99 & 107.4 & @xmath1625.3 & 3.8 & 5 & 2 + 000206 & 74873 & 11580 g & 0.22 & 0.98 & 255.7 & 78.5 & 10.7 & 26 & 7 + 000405 & 77386 & 11639b & 0.92 & 0.96 & 226.9 & @xmath1652.5 & 2.1 & 35 & 7 + 000416 & 52380 & 11650c & 0.17 & 0.70 & 258.5 & @xmath1665.7 & 14.7 & 9 & 5 + + + + + + [ tab:23softgrbs ] these 36 soft grbs have typical light curves , last up to about 100 s and do not demonstrate any significant anisotropy on the sky . soft batse grbs selected with the above criterion constitute about 5% of observed long grb sample ( about 20 per year with peak fluxes down to @xmath8 ph @xmath2 s@xmath1 ) . our scan ( as well as an alternative scan @xcite ) in the batse records in the 2550 kev range has yielded surprisingly small number of new soft grbs . moreover , there are no events with hardness ratio ( hr ) below 0.3 , while much softer events like outbursts of vela x-1 can be confidently detected ( see fig . [ fig : hr_int ] ) . we have considered sample of 50 events classified by @xcite as unknown because of their softness . when" +"the muon drift tube chambers of the cms detector rely crucially on the accurate knowledge of the drift velocity to reconstruct muon tracks as precise as possible . a monitor system for the direct measurement of the drift velocity is presented together with chamber gas pressure monitoring . in the first section the cms muon drift tube chambers are explained , followed by two sections about their pressure and drift velocity monitoring , including latest measurements . the barrel of the cms detector @xcite consists of five wheels , each instrumented with 50 muon drift tube ( dt ) stations outside the 4 t solenoid magnet , arranged in four radial layers embedded in the iron return yoke of the solenoid . each station is 29 cm thick and has a length along the beam axis of 2.5 m , given by the wheel width . depending on the layer the station width varies between two and four meters . the three inner muon stations consist of three and the outermost of two superlayers which in turn consist of four layers of drift cells . the drift cells of the inner- and outermost superlayers are oriented parallel to the beam axis to measure the projection of muon tracks perpendicular to the beam axis . the middle superlayer ( present in the three inner muon stations ) is dedicated to the measurement of the track projection along the beam axis . the drift cells are arranged with a pitch of 42 mm @xmath0 13 mm . field shaping strips ( + 1800 v ) at the inner bottom and top of the drift cell are responsible for a very homogeneous electric field between the anode ( + 3600 v ) and the cathode ( -1200 v ) . the drift cells are operated with a gas admixture of @xmath1 ( 85% vol . ) and @xmath2 ( 15% vol . ) at slight overpressure ( @xmath3 2 - 10 mbar ) . if a muon crosses a cell , ionised molecules drift to the cathode while electrons reach the anode sense wire . the crossing position of the muon can be computed by means of the drift velocity assuming linear behaviour due to a homogeneous electric field . the drift tubes are operated at slight overpressure of about 2 - 10 mbar . there are two gas manifolds at each chamber , one at the inlet and one at the outlet side . each manifold is equipped with two pressure sensors , one with @xmath4 mbar and one with @xmath5 mbar relative pressure range , producing an analog signal of 0 - 4.5 v which is being digitised locally to ten bit precision , in modules called padc s . the pressure monitoring allows one to limit the overpressure to the range of @xmath6 mbar . this is important to avoid contamination by ambient air and at the same time to stay well within the safety margin . larger leakages can be detected by input - output differences . the drift velocity measurement in the velocity drift chamber ( vdc ) can be corrected for the measured overpressure . furthermore , each chamber is equipped with temperature sensors to allow for monitoring and corrections . a gas sample from the dt s is piped to the vdc monitoring system and to commercial oxygen and humidity analysers , to check for gas anomalies . the outlet of each of the 250 dt chambers , as well as the supply gas arriving at each barrel wheel can be individually sampled . [ scetch ] shows the working principle of a vdc . it consists of a small ( one litre ) single drift cell chamber equipped with anode ( up to + 1900 v ) , cathode ( up to -15000 v ) and field shaping electrodes . two electron beams cross a sensitive region between anode and cathode . the sensitive region is ( 8.0 , 5.5 ) ( 1.5,2.7 ) ( 3.3,-7.5 ) characterised by a highly uniform electric field . the electrons are detected by a scintillating fibre and two silicon photomultipliers ( sipm s ) in coincidence to provide a trigger . the drift times of the two beams are recorded with respect to the trigger . the average drift time between both parallel beams , separated by 4.8 cm is being measured and leads to a drift velocity distribution as e.g. shown in fig . [ vdrift ] , left to 54.8 @xmath7m / ns with a width of 0.1 @xmath7m / ns by means of a single vdc which is in operation at cms . the measured drift velocity corresponds to two days of data taking during the cosmic muon run period of cms in august 2008 . this can be compared to the indirectly determined drift velocity in the dt s of @xmath8 @xmath7m / ns with a width of 0.1 @xmath7m / ns obtained from the cosmic muon data taking period 2008 . the electric field of the vdc can be varied in a wide range without losing its homogeneity . the vdc measures the drift velocity directly for a given electric field while in the dt s the determined drift velocity is an effective parameter depending beside the gas admixture on the inhomogeneous electric field , muon track paths , software selection and fit algorithms . therefore the drift velocity measured with the vdc can be exploited to verify the gas admixture and the indirectly determined drift velocity of a given muon station . since january 2008 a single vdc unit is in operation at cms , and it will be substituted by a larger system . ( 8.0 , 2.0 ) ( 0.3 , 0.05 ) the drift velocity measured with a vdc at cms ( left ) in comparison to the drift velocity of the drift tube chambers ( right ) determined by means of measured cosmic muon tracks with solenoid magnetic field switched off . the plots show average values of the different muon stations and wheels . , title=""fig:"",width=257 ] ( 4.3,2.27 ) ( 6.7,1.0 ) ( 2.82,2.27 ) ( 1.5,2.8 ) the drift velocity measured with a vdc at cms ( left ) in comparison to the drift velocity of the drift tube chambers ( right ) determined by means of measured cosmic muon tracks with solenoid magnetic field switched off . the plots show average values of the different muon stations and wheels . , width=260 ] the complete vdc system consists of two racks . the first rack contains six vdc s ( one for each wheel plus a spare one ) , flow controllers , pressure controllers and sensors , high voltage ( hv ) for the vdc s , a trigger for each vdc and a crate with dedicated vme modules . the second rack contains vme logics , a readout pc ( linux server ) , nim modules , an ups protection power supply and a gas crate . determination of the systematic uncertainties of the drift velocities measured by the six vdc s simultaneously while branched on one single gas circuit are on the way . furthermore calibration runs for hv , pm voltage , gas admixtures , impurities ( @xmath9 ) , pressure and temperature dependencies are in the process of being accomplished . + in summary , gas admixture anomalies and the drift velocity of the dt s in the muon stations can be verified and validated by means of the vdc monitoring system which measures the drift velocity directly ." +"gravitational wave ( gw ) observations are expected to provide a new view of relativistic phenomena in the universe . one of the most promising candidates for the direct detection of gws is the merger of compact binaries such as binary neutron stars ( nss ) . the second generation of ground - based gw detectors , such as advanced ligo @xcite , advanced virgo @xcite and kagra @xcite , will reach the sensitivity required to detect gws from the inspiral and coalescence of compact binary systems including binary nss within a few hundred mpc . statistical studies suggest that a few tens of merger events should be observed per year @xcite . electromagnetic counterparts of gw emitters have been recently focused on to maximize a scientific return from the expected detection of gws ( e.g. , * ? ? ? follow - up observations of these electromagnetic counterparts are important to confirm a gw detection and to investigate progenitors and environments . the electromagnetic detection also improves the localization of gw sources because the localization accuracy by photons is much better than that by the ground - based gw detectors @xmath1 deg@xmath2 ( e.g. , * ? ? ? sophisticated simulations have revealed mass ejection associated with the mergers of binary nss by several mechanisms . significant mass is dynamically ejected by gravitational torques and hydrodynamical interactions during the mergers , called dynamical ejecta ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? general relativistic simulations show that these ejecta distribute nearly isotropic compared to newtonian simulations in the cases of binary nss @xcite , while they are anisotropic for ns - black hole ( bh ) mergers @xcite . mass may be also ejected through winds driven by neutrinos @xcite , magnetic fields of and/or amplified by the merged objects @xcite , viscous heating and nuclear recombination @xcite . a traditional electromagnetic counterpart is short - hard gamma - ray bursts ( grbs ; * ? ? ? recent simulations have revealed that a hypermassive ns is formed from the merger of a ns binary ( e.g. , * ? ? ? * ) , which is believed to collapse into a bh at later time . non - collapsed matter and some ejecta falling back to the bh form a torus around the bh ( e.g. , * ? ? ? then , a relativistic jet may be launched from the bh - torus system , which is believed to be the central engine of short - hard grbs . another interesting possibility is a so - called macronova / kilonova , which is thermal emission from ejecta ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? the radiative energy of a macronova is estimated between that of a classical nova and supernova . ejecta can also produce non - thermal emission at later time similarly to supernova remnants @xcite . ejecta may accompany an advanced relativistic part , producing early emission ( @xmath3 hours ; * ? ? ? * ; * ? ? ? emission from macronovae and ns binary merger remnants is almost isotropic and hence different from that of short grbs which depends on the directions of their relativistic jets . moreover , macronovae are closer in time to mergers than emission from merger remnants and do not depend on the properties of circumburst environments . therefore , macronovae are expected to play a crucial role to localize a large sample of gw events @xcite . recently , a macronova candidate following grb 130603b was discovered @xcite . this candidate is widely interpreted as the results of the radioactive decay of @xmath0-process elements produced in the ejecta of a compact binary merger @xcite . we call this scenario _ an @xmath0-process model _ throughout this paper . the ejecta from a merger of binary nss is primarily neutron - rich . then , heavy radioactive elements ( mass number @xmath4 ) are expected to form through neutron - capture onto nuclei ( @xmath0-process nucleosynthesis ) ( e.g. , * ? ? ? although the @xmath0-process nucleosynthesis ends a few hundred millisecond after a merger , synthesized elements release energy due to nuclear fission and beta decays up to @xmath5 days ( e.g. , * ? ? ? * ) . a schematic picture for this model is shown in the left panel of figure [ figure : model ] . if this scenario is correct , the observations also give important insights into the enrichment of @xmath0-process elements in the galaxy evolution ( e.g. , * ? ? ? although the @xmath0-process model explains the observed light curve of the macronova , it is based on the limited observational data and the nuclear heating rate with large uncertainties . required mass of dynamical ejecta to explain the observations is relatively large compared with the simulation results @xcite . in addition , the occurrence of @xmath0-process nucleosynthesis needs the ejecta with low electron fraction ( @xmath6 ) . however , relatively high electron fraction ( @xmath7 ) can be also realized , which has been discussed for neutrino - driven wind ( e.g. , * ? ? ? it is worth considering other possibilities such as the scenarios of an external shock between ejecta and surrounding medium @xcite , a supramassive magnetar @xcite and dust grains @xcite . in this study , we consider another power source of macronovae , i.e. , energy injection from the activity of the central engine , in addition to the radioactive decay of @xmath0-process elements . this is similar to the early evolution of core - collapse supernovae ( e.g. , * ? ? ? * ; * ? ? ? we call this model _ an engine model _ throughout this paper . there are several motivations to consider that the activity of the central engine contributes to the heating of ejecta . one observational motivation is the extended emission following the prompt emission of short grbs . the origin of extended emission is considered to be the activity of the central engine @xcite because the sharp drop of its light curve is difficult to be reproduced by afterglow emission @xcite . after the merger , a stable ns or a bh is formed . in the case that a bh with a torus ( or disk ) is formed , the energy injection to the ejecta is expected as a form of the jet and/or disk wind ( e.g. , * ? ? ? * ) . in the case that a ns with strong poloidal magnetic field is formed as a result of a merger , the wind of relativistic particles is ejected @xcite . then , the wind collides with the ejecta , and about half of the wind energy converts to the internal energy by the shock - heating . a schematic picture is shown in the right - hand side of figure [ figure : model ] . the ejecta emission powered by a stable magnetar has already been discussed @xcite . they suggest that the magnetar - powered ejecta emit the brighter optical and x - ray emissions than that of the @xmath0-process model . however , they did not show that the magnetar - powered ejecta explain the detected infrared excess in grb 130603b @xcite . the engine model can provide energy enough to reproduce the detected macronova candidate , grb 130603b . we do not specify the specific heating sources . alternatively , to estimate the luminosity and temperature , we assume that the internal energy @xmath8 erg is injected to the ejecta at the time @xmath9 s after the merger . these values are consistent with typical isotropic energy @xmath10 erg and duration @xmath11 s of the extended emission @xcite . using the velocity of the ejecta @xmath12 , the temperature at @xmath13 is @xmath14^{1/4}$ ] , where @xmath15 is the radiative constant . if we only consider the adiabatic cooling for the cooling process of the ejecta , the evolution of the internal energy @xmath16 and temperature @xmath17 is scaled as @xmath18 and @xmath19 . the luminosity is described as @xmath20 . adopting the ejecta velocity @xmath21 cm s@xmath22 @xcite , the luminosity @xmath23 and the temperature @xmath17 at @xmath24s are @xmath25 and @xmath26 the observations of macronova of grb 130603b give j - band luminosity @xmath27 erg s@xmath22 and the difference between j - band and b - band @xmath28 mag which corresponds to the temperature @xmath29 k at @xmath30 days after grb 130603b in the source rest frame @xcite . therefore , in this estimate , the luminosity and temperature for the engine model is consistent with the observation of the macronova following grb130603b . we model the evolution of luminosity and temperature of a macronova . unlike the previous studies , we treat the model in an analytical manner and formulate a light curve including the early phase ( @xmath31 s ) , which is important for the search of electromagnetic counterparts of gw emitters . we consider shock - heating due to the activity of a central engine as a heating mechanism of the ejecta . for comparison , the @xmath0-process model , which has been discussed in most papers ( e.g. , * ? ? ? * ) , is also formulated . then , we compare the results of our models with observations to constrain the model parameters such as the ejected mass and the velocity of the ejecta . although our models are simplified , it is valuable to make comparison between two heating models . in section [ model ] , we introduce our model assumptions . we describe the analytical models for the evolution of luminosity and temperature in section [ evolution ] . then , we compare our results with observations in section [ discuss ] . implications for the discrimination between two models are also discussed . we summarize our results in section [ summary ] . in appendix a , we summarize the formulae for the observed temperature and bolometric luminosity . significant mass of material @xmath32 is ejected during a binary merger . we model ejecta by following the results of the general relativistic simulations of ns - ns mergers in @xcite . the simulations show that ejecta expand in a nearly homologous manner ( see also * ? ? ? the morphology of the ejecta is quasi - spherical in the case of a merger of binary nss . according to these results , we assume an isotropic and homologous expansion for the ejecta . then , the velocity of ejecta @xmath12 is @xmath33 where the radius @xmath0 originates the central engine and the time @xmath34 is measured from the time when a compact binary merges . note that in the case of a merger of ns - bh binary , the ejected mass expands with significant anisotropy @xcite . we do not consider such anisotropic ejecta in this work . @xcite found that the profile of ejecta obtained from simulations by @xcite can be well fitted by a power - law function @xmath35 . the power - law index of snapshot density @xmath36 is more or less independent on the dynamics of mergers , which is in the range of @xmath374 for @xmath38 , where @xmath39 and @xmath40 are the velocities of the outer and inner edges of the ejecta , respectively . we choose the middle of this range @xmath41 in this study . we also fix the maximum velocity @xmath42 from simulation results @xcite . the maximum velocity @xmath39 is comparable with the escape velocity of the system . the minimum velocity @xmath43 is mainly determined by complicated dynamics at the initial stage of the merger @xmath44 . for the mass density profile at the front of the ejecta ," +"since the discovery of the first known pulsating x - ray sources her x-1 and cen x-3 more than three decades ago ( giacconi et al . 1971 ; tananbaum et al . 1972 ) , over 50 new sources have been detected in the galaxy and the magellanic clouds , with luminosities in the range @xmath0 and pulsation periods @xmath1 . x - ray pulsars include a variety of objects powered by rotation or accretion , as well as several anomalous x - ray pulsars whose energy source is currently unclear . the emission from x - ray pulsars in binary systems is fueled by the accretion of material from the `` normal '' companion onto the neutron star , with the flow channeled onto one or both of the magnetic poles by the strong field . during the accretion process , gravitational potential energy is converted into kinetic energy , which escapes from the column in the form of x - rays as the gas decelerates through a radiative shock before settling onto the stellar surface . in the accretion - powered sources , which are the focus of this paper , the x - ray spectra are often well fitted using a combination of a power - law spectrum plus a blackbody component with a temperature in the range @xmath2k ( e.g. , coburn et al . 2002 ; di salvo et al . 1998 ; white et al . 1983 ) . most spectra also display quasi - exponential cutoffs at @xmath3kev , and there are indications of cyclotron features and iron emission lines in a number of sources . the observations suggest typical magnetic field strengths of @xmath4 g . although accretion - powered x - ray pulsars are among the most luminous sources in the galaxy , previous attempts to calculate their spectra based on static or dynamic theoretical models have generally yielded results that do not agree very well with the observed profiles ( e.g. , mszros & nagel 1985a , b ; nagel 1981 ; yahel 1980 ; klein et al . hence there is still no clear understanding of the basic spectral formation mechanism in x - ray pulsars ( see the discussion in coburn et al . 2002 ) . given the lack of a viable theoretical model , x - ray pulsar spectral data have traditionally been fit using multicomponent forms that include absorbed power - laws , cyclotron features , iron emission lines , blackbody components , and high - energy exponential cutoffs . the resulting parameters are sometimes difficult to relate to the physical properties of the source . motivated by the lack of a comprehensive theoretical model for x - ray pulsar spectral formation , we reconsider here the physical picture originally proposed by davidson ( 1973 ) , in which the accreting gas passes through a radiative , radiation - dominated shock before settling onto the surface of the star . we illustrate the accretion / emission geometry schematically in figure 1 . most of the photons emitted from the accretion column are produced in the dense `` thermal mound '' located inside the column , just above the stellar surface . the blackbody photons created in the mound are upscattered in the shock , and eventually diffuse through the walls of the column . the escaping photons carry away the kinetic energy of the gas , thereby allowing the plasma to settle onto the surface of the star . the strong compression that occurs as the plasma crosses the radiative shock renders it an ideal site for first - order fermi energization ( i.e. , `` bulk '' or `` dynamical '' comptonization ) of the photons produced by the thermal mound . in the bulk comptonization process , particles experience a mean energy gain if the scattering centers they collide with are involved in a converging flow ( e.g. , laurent & titarchuk 1999 ; turolla , zane , & titarchuk 2002 ) . by contrast , in the thermal comptonizaton process , particles gain energy due to the _ stochastic _ motions of the scattering centers via the second - order fermi mechanism ( e.g. , sunyaev & titarchuk 1980 ; becker 2003 ) . in the x - ray pulsar application , the scattering centers are infalling electrons , and the energized `` particles '' are photons . since the inflow speed of the electrons in an x - ray pulsar accretion column is much larger than their thermal velocity , bulk comptonization dominates over the stochastic process except at the highest photon energies ( titarchuk , mastichiadis , & kylafis 1996 ) , as discussed in 7 . the failure of the current models to generate the power - law spectral shape characteristic of x - ray pulsars probably stems from the neglect of the critical contribution of the shock in upscattering the soft radiation produced in the thermal mound ( e.g. , burnard , arons , & klein 1991 ) . we demonstrate in this paper that bulk comptonization of the radiation in the accretion shock can produce spectra very similar to the power - law continuum seen in many x - ray pulsars . the main results presented here were summarized by becker & wolff ( 2005 ) . dynamical comptonization has been considered by a number of previous authors in a variety of astrophysical situations , including spherical inflows ( payne & blandford 1981 ; colpi 1988 ; schneider & bogdan 1989 ; titarchuk , mastichiadis , & kylafis 1997 ) , accretion disks around black holes ( laurent & titarchuk 2001 ; titarchuk , cui , & wood 2002 ; titarchuk & shrader 2002 ) , spherical outflows ( becker & begelman 1986 ; titarchuk , kazanas , & becker 2003 ) , and the transport of cosmic rays in the solar wind ( parker 1965 ; stawicki , fichtner , & schlickeiser 2000 ) . the process was also studied in the context of neutron star accretion by titarchuk , mastichiadis , & kylafis ( 1996 ) and mastichiadis & kylafis ( 1992 ) , although their results are not applicable to x - ray pulsar accretion columns due to the assumption of spherical symmetry and the imposition of a power - law velocity profile . lyubarskii & sunyaev ( 1982 ) analyzed dynamical comptonization in the context of plane - parallel pulsar shocks , but the velocity profile they utilized is not consistent with the dynamics of x - ray pulsar accretion , and furthermore they did not account for the escape of radiation through the walls of the column . the relevance of the bulk comptonization process for spectral formation in x - ray pulsars was also recognized by burnard , arons , & klein ( 1991 ) , who pointed out that thermal spectra alone are much too soft to explain the observed emission , and suggested that upscattering in the shock could provide the required hardening . the fundamental character of the green s function describing both thermal and bulk comptonization was studied by titarchuk & zannias ( 1998 ) for the case of accretion onto a black hole . these authors established that the green s function can be approximated using a broken power - law form with a central peak between the high- and low - energy portions of the spectrum , for either type of comptonization . furthermore , they concluded that bulk comptonization dominates over the thermal process if the electron temperature @xmath5k . the theory developed in the present paper represents an extension of the same idea to neutron star accretion , resulting in the exact green s function for the x - ray pulsar spectral formation process . in agreement with titarchuk & zannias ( 1998 ) , we find that the bulk comptonization process is dominant for the temperature range relevant for x - ray pulsars . however , the presence of the event horizon in the black - hole application treated by these authors makes their problem fundamentally different from the neutron star accretion problem studied here , because the neutron star obviously possesses a solid surface . our work therefore represents the first exact , quantitative analysis of the role of bulk comptonization in the x - ray pulsar spectral formation process . radiation pressure governs the dynamical structure of the accretion flows in bright pulsars when the x - ray luminosity satisfies ( becker 1998 ; basko & sunyaev 1976 ) @xmath6 where @xmath7 is the polar cap radius , @xmath8 and @xmath9 denote the stellar mass and radius , respectively , @xmath10 is the thomson cross section , and @xmath11 and @xmath12 represent the electron scattering cross sections for photons propagating parallel or perpendicular to the magnetic field , respectively . when the luminosity of the system is comparable to @xmath13 , the radiation flux in the column is super - eddington and therefore the radiation pressure greatly exceeds the gas pressure ( becker 1998 ) . in this situation the gas passes through a radiation - dominated shock on its way to the stellar surface , and the kinetic energy of the gas is carried away by the high - energy radiation that escapes from the column . the strong gradient of the radiation pressure decelerates the material to rest at the surface of the star . the observation of many x - ray pulsars with @xmath14 implies the presence of radiation - dominated shocks close to the stellar surfaces in these systems ( white et al . 1983 ; white et al . note that radiation - dominated shocks are _ continuous _ velocity transitions , with an overall thickness of a few thomson scattering lengths , unlike traditional ( discontinuous ) gas - dominated shocks ( blandford & payne 1981b ) . in luminous x - ray pulsars , the pressure of the radiation determines the dynamics of the flow , while the dynamics in turn determines the shape of the radiation spectrum . hence the flow dynamics and the radiative transport are intimately connected , which makes this a complex and nonlinear `` photohydrodynamical '' problem . one implication is that the photons scattering through the column can not be regarded as `` test particles '' since it is their pressure that dictates the structure of the flow . we must therefore solve for the radiation spectrum and the velocity profile in a self - consistent manner . radiation pressure may also play an important role in the dynamics of moderate - luminosity pulsars due to the strong dependence of the electron scattering ( cyclotron ) cross section on the magnetic field strength ( langer & rappaport 1982 ) . becker ( 1998 ) and basko & sunyaev ( 1976 ) have considered the dynamics of radiation - dominated pulsar accretion flows , including the effect of the shock and the escape of radiation energy from the column . they find that the gas is decelerated to zero velocity in a manner consistent with accretion onto a solid body , but they do not consider the shape of the escaping radiation spectrum . conversely , the dynamics and the radiation spectrum have been worked out self - consistently by blandford & payne ( 1981b ) for the case of a `` standard '' ( rankine - hugoniot ) radiation - dominated shock , which does not include radiation escape . in the blandford & payne approach , the radiation spectrum everywhere in the flow is determined by solving the transport equation using the incident radiation field as a boundary condition . the solutions have a power - law character at high energies , with a spectral index that depends on the mach number of the upstream flow . since the rankine - hugoniot shocks studied by blandford & payne have a conserved energy flux , the" +"brownian motors , acting as thermal fluctuation rectifiers , have been attracting considerable attention in the past ten years mainly due to their potential applications in biology , condensed matter and nanotechnology but also to their theoretical relevancy in statistical mechanics @xcite . in most of the cases , rectification is achieved by means of an external periodic or random perturbation applied to an equilibrium system with some underlying spatial or temporal asymmetry . however , it is only recently that research has been focused on introducing control in brownian ratchets . tarlie and astumian studied in @xcite the effect of a controllable time modulation of the applied sawtooth potential and find the modulation that maximizes particle flow . other ways to control particle current have been proposed that are specially useful in systems where the ratchet potential parameters are not easily tunable , as in most two dimensional ratchet setups where the brownian particles interact with an asymmetric substrate . examples of these devices are a rectifier of magnetic flux quanta in superconductors @xcite or synthetic ion channels @xcite . according to savelev _ et al . _ , flux in some of these ratchets can be controlled by addition of other species of particles that interact with the original ones @xcite . alternatively , the application of two mixing signals could control ratchet - like particle transport of ferrofluids or dislocations in crystalline solids , pumping of electrons in quantum dots or colloids in arrays of optical tweezers @xcite . all the control strategies mentioned so far share the property of being open - loop control policies , that is , they do not use any information about the state of the system . in contrast , we considered in ref . @xcite the idea of a feedback controlled perturbation , i.e. , a modulation of the ratchet potential depending on the state of the system . such a feedback control could be implemented in systems where particles are monitored , as in some experimental setups of colloidal particles @xcite . the system described in ref . @xcite consisted on an ensemble of brownian particles in a flashing ratchet potential that can be switched on or off depending on the position of particles , with the aim of maximizing the current . we studied in detail a protocol that maximizes the instant velocity of the center of mass of the ensemble . that ( closed - loop ) protocol is optimal for one particle and performs better than any periodic ( open - loop ) flashing for ensembles of moderate sizes , but is defeated by random or periodic switching for large ensembles . furthermore , it can be shown that particle current vanishes as @xmath0 , even though the state of the potential is chosen so that the center of mass velocity is maximal at every instant . in this letter we propose a modification of the aforementioned feedback control protocol that may switch off the potential even if that implies a loss of instantaneous velocity , or switch it on when that makes the center of mass initially recede . nevertheless , this new protocol beats the original one for a sufficiently large number of particles . although it might be surprising at first sight , this means you must stop or even move backwards at certain periods of time in order to move faster on average . in contrast , maximization of the instant velocity protocol is a `` greedy '' strategy and will therefore never switch the potential off if particles are still moving forward or switch it on if this means an initial backward movement . in some sense , the new protocol performs better by being less greedy , an effect also analyzed in @xcite for the case of paradoxical games , which are closely related to the flashing ratchet . the model we will consider here consists of an ensemble of @xmath1 non - interacting overdamped brownian particles at temperature @xmath2 in a asymmetric periodic potential that can be switched on or off . the dynamics is described by the langevin equation @xmath3 where @xmath4 the position of particle @xmath5 , @xmath6 is the friction and @xmath7 are thermal noises with zero mean and correlation @xmath8 . the force is given by @xmath9 . as the ratchet potential @xmath10 , we will consider from now on the one depicted in fig . [ fig.pot ] , given by @xmath11 , with @xmath12 . we have found analogous results for other heights of the potential and for other smooth potential shapes . finally , @xmath13 is a control parameter which we assume that can take on the values 1 and 0 , i.e. , the only allowed operations on the brownian motor consist in switching on and off the potential @xmath10 . ratchet potential @xmath14 , for @xmath12 ( units : @xmath15 and @xmath16 ) . , the following two control strategies were previously compared in @xcite , focusing on the induced current of particles . * _ optimal periodic switching _ : @xmath17 , with @xmath18 for @xmath19 , and @xmath20 for @xmath21 . this case is equivalent to the periodic flashing ratchet , since particles are independent , although with different periods for the on and off steps . in the following , the switching times @xmath22 and @xmath23 are set to achieve the highest stationary current . for @xmath15 and @xmath12 , these values are @xmath24 and @xmath25 . * _ maximization of center of mass instant velocity _ : + @xmath26 + where @xmath27 is the net force per particle if the ratchet potential were on , and @xmath28 is the heaviside function , @xmath29 if @xmath30 and 0 otherwise . as can be deduced from eq . , this strategy maximizes the instant velocity of the center of mass , @xmath31 . as stated above this protocol is the optimal one for one particle , performs better than any periodic switching only up to approximately a thousand particles ( for our choice of the potential ) , and gives a vanishing current for @xmath0 ( see below fig . [ results ] ) . for large @xmath1 , any switching of the potential is induced by fluctuations in the force per particle around zero , as shown in fig . [ evolucion]a . since fluctuations vanish as @xmath32 , then the system gets trapped in either the on or off state longer and longer times as @xmath1 increases , slowing down the switching that makes the ratchet work ( see ref . @xcite for details ) . this can be better understood in the limiting case @xmath33 , where the system evolves without fluctuations . the distribution of particles @xmath34 coincides with the solution of the following mean - field fokker - planck equation : @xmath35 \rho ( x , t ) . \label{fp}\ ] ] following @xcite , evolution of the net force per particle @xmath36 for sufficiently large @xmath1 would have two contributions : the evolution of @xmath37 where the average @xmath38 is taken over the solution @xmath34 of fokker - planck eq . , plus fluctuations of order @xmath39 . as explained above , the switching frequency is so slow that the system almost reaches the equilibrium distribution of either the on or off potential before a switch occurs . hence , we can approximately compute @xmath40 in two parts , one corresponding to either state of the potential . the `` on '' part @xmath41 is computed by numerical integration of eq . with initial condition given by the equilibrium distribution of the off potential and conversely , @xmath42 with initial condition given by the equilibrium distribution of the on potential . these solutions @xmath41 , @xmath42 would respectively represent , after adding the fluctuations , the cusps and valleys in fig . [ evolucion]a . figure [ evolucion ] shows an initial increase or decrease of the force per particle right after every switch , followed by a tail that slowly decays towards zero . the larger the number of particles , the smaller the fluctuations and the longer it takes @xmath36 to become so small that a fluctuation makes it cross zero and induce a switch of the potential . if @xmath1 is sufficiently large , this takes in average longer than the optimal periodic switching time . moreover , since fluctuations are small , this control protocol ends up behaving approximately periodically in time but with switching periods longer than the optimal ones . hence , it yields a slower motion of the particles than that achieved by the optimal periodic flashing . the idea underlying the new threshold control policy is to modify that feedback control protocol to prevent the trapping by inducing the switching of the potential when the net force per particle crosses some threshold values that are now different from zero . thresholds work by removing the long decaying tails in the evolution of the force per particle that produce the trapping and modifying the switching times so that they match the optimal periodic ones for large @xmath1 . this situation is represented in fig . [ evolucion]b . however , to get rid only of these tails while retaining the remaining part , the switching must only occur when the threshold is crossed in the appropriate direction , implying that we need to compute or estimate the sign of the time derivative of the average force per particle . in the limit @xmath0 , evolution of @xmath36 is well described by @xmath43 and @xmath44 . hence , to induce a switch at time @xmath45 we should force the system to change the state of the potential when @xmath36 attains a threshold value @xmath46 if the potential is on and @xmath47 when potential is off . however , if the ratchet potential is on for example , we would be interested in switching when the force @xmath36 crosses @xmath48 _ and _ is decaying towards zero and not when it is increasing , which would be too early . this is readily achieved by switching off the potential only when @xmath36 crosses @xmath48 with negative slope . equivalently , the potential should be switched on only when @xmath36 crosses @xmath49 with positive slope . in order to translate this into a feedback policy , we need an estimation for this slope in terms of position of the particles . using langevin equation , we can write @xmath50 for a given state of the system @xmath51 , a good estimate for the slope of @xmath36 is @xmath52 notice expression can only be used for smooth potentials . gathering all the pieces , we can express threshold control policy in the following way * _ threshold control _ : @xmath53 where @xmath36 and @xmath54 are the net force per particle and the estimate for the time derivative of its average as defined in and , respectively . to compute the thresholds one can simulate langevin equation for a sufficiently large number of particles and obtain the evolution of the net force @xmath36 under the optimal periodic switching . since the number of particles is large , this is almost equivalent to solving fokker - planck equation to get @xmath55 . thresholds are given by @xmath56 and @xmath57 and hence , averaging the values of the force at switching times should give a reasonable estimate for either threshold , once the stationary regime has been reached . doing so for @xmath58 , gives @xmath59 and @xmath60 . these are the thresholds used in the simulations whose results are shown in fig . [ results ] . simulation results of the average of the center of mass velocity @xmath61 , for the periodic switching with optimal periods @xmath24 and @xmath25 ( dashed line ) ; feedback control with thresholds ( circles ) ; and maximization of center of mass velocity" +"the counterpart of ultraluminous x - ray sources ( ulxs ) , which have x - ray luminosities @xmath2 larger than the eddington luminosity of a stellar mass object of mass @xmath3 , @xmath4 , are not known . most likely there is no universal engine for ulxs . some may be powered by anisotropic radiation ( e.g. king et al . @xcite ; rappaport , podsiadlowski & pfahl @xcite ) or super eddington luminosity ( begelman @xcite ) from stellar mass black holes . a third possibility is offered by the hypothesised existence of intermediate mass black holes ( ibhs ; see miller & colbert @xcite for a review ) of masses @xmath5 , which could radiate isotropically at a sub - eddington rate to account for the observed luminosities . there has been some observational evidence that at least some ulxs are powered by ibhs . in some cases the mass - temperature relation ( miller et al . @xcite ; miller , fabian & miller @xcite ) or quasi periodic oscillations ( fiorito & titarchuk @xcite ; liu et al . @xcite ) indicate a high accreting mass . numerical n - body and monte carlo simulations indicate that the stellar collision rate in young dense stellar clusters during core collapse can become very large , giving rise to a hierarchical merger . in that case an object of thousands of solar masses may form ( portegies zwart et al . @xcite , @xcite ; grkan , freitag & rasio @xcite ; freitag , grkan & rasio @xcite ; freitag , rasio , & baumgardt @xcite ) . the fate of such a massive star is unclear , but it might lead to the formation of an ibh . this scenario is supported by the fact that ulxs correlate positively with star formation ( swartz et al . @xcite ; liu , bregman & irwin @xcite ) and that some ulxs are associated with stellar clusters ( e.g. zezas et al . @xcite ) . the young stars in the host cluster of the ibh have strong winds which blow out the gas from the cluster , and there is insufficient free gas available to power a ulx . however , the ibh can acquire a companion star by dynamical capture or tidal capture . here we discuss the latter possibility . hopman , portegies zwart & alexander ( @xcite ) showed that tidal capture of a main sequence star of mass @xmath6 and radius @xmath7 can lead to circularization close to the tidal radius @xmath8 which is the distance from the ibh where the tidal forces equal the forces which keep the star bound . as the star evolves it starts to fill its roche lobe causing it to lose mass to the ibh . this leads to high x - ray luminosities , provided that the donor is sufficiently massive ( @xmath9 , hopman et al . @xcite ; portegies zwart , dewi , & maccarone @xcite ; li @xcite ) . interestingly , for some ulxs an optical counterpart has been identified , indicating that these ulxs are binary systems ( liu , bregman , & seitzer @xcite ; kuntz et al . @xcite ) . in this scenario a ulx may turn on for at most the life - time @xmath10 of the captured star . in addition to strong x - ray emission the star emits gravitational waves ( gws ) . portegies zwart ( @xcite ) discussed the possibility of observing x - rays and gws simultaneously . only if the captured star is sufficiently light ( @xmath11 ) , its tidal radius is small enough for it to emit gws in the lisa band during the mass transfer phase ( portegies zwart @xcite ) . however , in order to account for the high ulx luminosities the companion star should be considerably more massive than @xmath12 ( hopman et al . @xcite ; portegies zwart et al . @xcite ; li @xcite ) . in young and dense star clusters mass segregation causes most massive stars to accumulate in the cluster centre , and the combination of a high mass and large size make these stars excellent candidates for tidal capture . when after time @xmath13 the massive donor explodes it turns into a compact remnant ( cr ) ; a neutron star ( ns ) or a stellar mass black hole ( sbh ) . from that moment the ulx , deprived of its source of gas , turns off . here we focus on the subsequent post supernova evolution of the ( ibh , cr ) binary . in - spiral of the cr into an ibh due to gw emission results in a strong signal in frequencies measurable by space detectors such as lisa , providing a wealth of information about the system ( see miller @xcite for a discussion ) . we show that lisa may be able to observe such ( ibh , cr ) binaries . when stars orbit ibhs on wide , but highly eccentric orbits , with periapse close to the tidal radius of the ibh , @xmath14 , orbital energy is invested in tidal distortions of the star , causing it to spiral in . hopman et al . ( @xcite ) showed that if the ibh is less massive than @xmath15 , the star may be able to cool down by radiating the excess energy efficiently , and survive the strong tidal forces . eventually it circularises near the ibh . we first estimate the fraction @xmath16 of isolated binaries which merge as a result of gw emission within the age of the universe , while accounting for angular momentum conservation during the mass transfer phase and an isotropic velocity kick . we then discuss the consequences of the gravitational interaction of cluster stars with the ( ibh , cr ) binary . after tidal circularization near the ibh , the star may fill its roche lobe , possibly after a period of stellar evolution and expansion . roche lobe overflow from a @xmath9 donor can then give rise to high luminosities for a time limited by the life - time @xmath17 of the star ( hopman et al . @xcite ; portegies zwart et al . @xcite ; li @xcite ) . the main - sequence star fills its roche lobe at a distance @xmath18 before the terminal age main sequence . we assume that the entire hydrogen envelope is transferred to the ibh , while the binary conserves angular momentum . the mass of the stellar core of the donor star is given by @xmath19 ( iben , tutukov & yungelson @xcite ) , while the mass of the hydrogen envelope is @xmath20 . angular momentum conservation implies that the binary separation increases during the mass transfer phase . the remaining helium star subsequently explodes in a super nova after a time @xmath13 , and forms a cr . in this event a star of @xmath21 forms a ns of chandrasekhar mass , @xmath22 . stars more massive stars than @xmath23 collapse to sbhs ; we assume that the mass distribution is that found by fyer & kalogera ( @xcite ) . the semi - major axes and eccentricities of the cr are determined by the post mass - transfer orbital elements while accounting for the mass lost in the super nova and for the velocity kick , imparted to the cr at the time of the explosion . the kick velocity is taken in a random direction with magnitude from the distribution of pulsars velocities , which is well fitted by a double gaussian distribution @xmath24,\end{aligned}\ ] ] where @xmath25 , @xmath26 , and @xmath27 ( arzoumanian , chernoff & cordes @xcite ) . for sbhs we adopt the same distribution , but with velocities smaller by a factor @xmath28 ( white & van paradijs @xcite ; gualandris et al . the velocity kick leads to an increase of the eccentricity of binary and a change in its energy ; the kicks are generally insufficient to ionise the binary systems ( van den heuvel et al . @xcite ) . the surviving binary loses orbital energy due to the emission of gws . a cr of mass @xmath29 on an orbit with semi - major axis @xmath30 and eccentricity @xmath31 around an ibh of mass @xmath32 loses energy due to the emission of gws at rate of @xmath33 with @xmath34 if the orbit is circular @xmath35 spiral - in occurs on a time - scale of ( peters @xcite ) @xmath36 for non - zero eccentricities the in - spiral time is shorter by a factor @xmath37 . we perform binary population synthesis with the above described scenario to compute the fraction of high mass binaries that become potential lisa sources . the mass of the stellar companion was selected from the initial mass function @xmath38 , where we assumed @xmath39 , consistent with the mass function in the core of clusters in which a runaway merger occurred ( portegies zwart et al . we assume a minimal mass of @xmath40 , since lighter donors can not account for ulx luminosities ( hopman et al . @xcite ; portegies zwart et al . @xcite ) , and a maximal donor mass of @xmath41 . lisa is likely to observe ( ibh , cr ) binaries in the phase before the merger , rather than the merger event itself . however , the crs spent only a very short time in the lisa frequency band as compared to the hubble time ( see [ sec : obs ] ) . the question whether these sources are detectable therefore depends on how many merge within a the hubble time . in figures ( [ f1 ] ) and ( [ f2 ] ) we show the results for an ibh of @xmath42 and @xmath43 , respectively . only a fraction of the star spirals in within a hubble time . for @xmath42 nearly all objects which spiral in are nss , with only very few sbhs . for more massive ibhs , a significant fraction of sbhs also spirals in fast enough , and the total fraction of merging objects exceeds 10% for @xmath44 . in figure([f3 ] ) we show @xmath16 , the fraction of stars which spiral in within the age of the universe , as a function of @xmath45 . after the velocity kick , the crs have eccentricities up to @xmath46 . while this decreases @xmath47 , these eccentricities are much smaller than the @xmath48 eccentricities found by hopman & alexander ( @xcite ) for direct gw capture . by the time the stars spiral in to orbital frequencies @xmath49s , which is in the lisa band , the orbits are close to circular . as a function of the zero - age main - sequence mass of the donor @xmath50 . events below the horizontal solid line merge within the age of the universe . for this image we generated 5000 binaries with a @xmath39 power - law initial mass function for the donor mass and we selected an ibh mass of @xmath51 . a small fraction ( 144 or @xmath52% ) of the objects generated experienced merger within a hubble time . the sudden jump at 20 @xmath53 indicates the transition between ns and sbh formation.[f1 ] ] . in this case much more ( @xmath54 ) stars spiral in within the age of the universe , and in particular there is a significant contribution from sbhs . [ f2 ] ] of crs which spiral in due to gw emission within the age of the universe as a function of the mass of the ibh . the error bars are estimated by the 1-@xmath55 poissonian uncertainties of the simulations.[f3 ] ] the two - body relaxation time @xmath56 of star clusters which" +"a quantum computer processes quantum information that is stored in quantum bits ( qubits ) @xcite . if a small set of fundamental operations , or universal quantum logic gates "" can be performed on the qubits , then a quantum computer can be programmed to solve an arbitrary problem @xcite . essentially , the quantum computation can be viewed as a coherent superposition of digital computation proceeding in parallel . the explosion of interest in quantum computation can be traced to shor s demonstration that a quantum computer could efficiently factorize large integers @xcite . cirac and zoller @xcite have made one of the most promising proposal for the implementation of a quantum computer . a number of identical atoms are stored and laser cooled in a linear radio - frequency quadrupole trap to form a quantum register . the radio - frequency trap potential gives strong confinement of the ions in the directions transverse to the trap axis , while an electrostatic potential forces the ions to oscillate in an effective harmonic potential in the axial direction . after laser cooling the ions become localized along the trap axis with a spacing determined by their coulomb repulsion and the confining axial potential.the normal mode of the ions collective oscillations which has the lowest frequency , is the axial center of mass ( cm ) mode , in which all the trapped ions oscillate together . a qubit is the electronic ground state @xmath0 and a long - lived excited state @xmath1 of the trapped ions . the electronic configuration of individual ions , and the quantum state of their collective cm vibrations can be manipulated by coherent interactions of the ion with a laser beam , in a standing wave configuration , which can be pointed at any of the ions . the cm mode of the axial vibrations may then be used as a bus "" to implement the quantum logical gates . once the quantum computation has been completed , the readout is performed through the mechanism of quantum jumps . several features of this scheme have been demonstrated experimentally , mostly using a single trapped ion @xcite . the implementation of a large - scale quantum computer is recognized to be a technological challenge of unprecedent proportions . in fact the qubits must be easily manipulated , but must be also well isolated from decohering influence which places considerable limitations on the capabilities of such devices @xcite . practically , there are two fundamentally different types of decoherence during a computation : the dissipative one , due to the spontaneous decay of the metastable states @xmath1 , and the non - dissipative one due to random phase fluctuations of various nature . while the first has been considered carefully @xcite , by also developing strategies to reduce spontaneous decay , like watchdog stabilization @xcite , the second does not received much attention ref . @xcite . on the other hand , non - dissipative decoherence seems actually dominant in trapped ion based experiments @xcite , whose results have been recently well explained @xcite , both qualitatively and quantitatively , by simply considering the time as a statistical variable and then averaging over a properly defined probability distribution @xcite . the developed approach results model - independent , hence quite ductile . then , our aim here , is to study the performances of an ion - trap quantum information processor by using this approach . practically , the latter allows us to account for the fluctuations of the raman laser intensity @xcite . instead , in @xcite a specific model is used , i.e. a random phase drift is added by hand at the end of each qubit rotation while in our case the stochasticity is already included in the time evolution . moreover , our analysis is based on exact parameters values fitting experimental data @xcite . the paper is organized as follows . in section ii we shall review a general model for non - dissipative decoherence . in section iii we shall apply this theory to fundamental logic operations . in section iv we evaluate the limits of a quantum computer due to this type of decoherence . finally , section v is for concluding remarks . in this section we review the formalism describing non - dissipative decoherence derived in refs . it is based on the idea that time is a random variable or , alternatively , that the system hamiltonian ( therefore its eigenvalues ) fluctuates . this leads to random phases in the energy eigenstates representation . then , the resulting evolution of the system must be averaged on a suitable probability distribution , and this leads to the decay of the off - diagonal elements of the density operator . let us consider an initial state @xmath2 and consider the case of a random evolution time . then , the evolved state will be averaged over a probability distribution @xmath3 , i.e. @xmath4 where @xmath5 is the usual solution of the liouville - von neumann equation with @xmath6/\hbar$ ] . one can write as well @xmath7 where @xmath8 in ref . @xcite , the function @xmath3 has been determined to satisfy the following conditions : i ) @xmath9 must be a density operator , i.e. it must be self - adjoint , positive - definite , and with unit - trace . this leads to the condition that @xmath3 must be non - negative and normalized , i.e. a probability density in @xmath10 , so that eq.([rhobardef ] ) is a completely positive map ; ii ) @xmath11 satisfies the semigroup property @xmath12 , with @xmath13 . these requirements are satisfied by @xmath14 and @xmath15 where the parameter @xmath16 naturally appears as a scaling time . the expression ( [ p ] ) is the so - called @xmath17-distribution function , well known in line theory . its interpretation is particularly simple when @xmath18 with @xmath19 integer ; in that case @xmath20 gives the probability density that the waiting time for @xmath19 independent events is @xmath10 and @xmath16 is the mean time interval between two events . generally , the meaning of the parameter @xmath16 can be understood by considering the mean of the evolution time @xmath21 , and its variance @xmath22 . when @xmath23 , @xmath24 so that @xmath25 and @xmath26 is the usual unitary evolution . however , for finite @xmath16 , the evolution operator @xmath11 describes a decay of the off diagonal matrix elements in the energy representation , whereas the diagonal matrix elements remain constants , i.e. the energy is still a constant of motion . in fact , in the energy eigenbasis , eqs.([rhobarv ] ) and ( [ v ] ) yield @xmath27 where @xmath28 with @xmath29 the energy difference . one can recognize in eq.([rhobarnm ] ) , beside the exponential decay , a frequency shift of every oscillating term . the phase diffusion aspect of the present approach can also be seen in the evolution equation for the averaged density matrix @xmath9 . indeed , by differentiating with respect to time eq.([rhobarv ] ) and using ( [ v ] ) one gets the following master equation for @xmath9 @xmath30 it is worth noting that by expanding the logarithm up to second order in @xmath16 , one obtains @xmath31 -\frac{\tau}{2\hbar^2}\left[h,\left[h,{\overline\rho}(t ) \right]\right]\,,\ ] ] which is the well known phase - destroying master equation @xcite . hence , eq.([meq ] ) appears as a generalized phase destroying master equation taking into account higher order terms in @xmath16 . nonetheless , the present approach is different from the usual master equation approach , in the sense that it is model independent , non perturbative and without specific statistical assumptions . the theory well describes also hamiltonian fluctuations . let us consider , for instance , a hamiltonian @xmath32 , where @xmath33 is a fluctuating parameter with mean value @xmath34 . whenever @xmath35 induces oscillations , we can accounts for the fluctuations of the frequency @xmath33 by writing @xcite @xmath36 where @xmath37/\hbar$ ] , and @xmath38 is a positive dimensionless random variable . furthermore , @xmath39 the first two moments of @xmath40 determine the properties of the fluctuating frequency @xmath33 , @xmath41 that is , the frequency @xmath33 is a white , non - gaussian ( due to the non - gaussian form of @xmath40 ) stochastic process . in fact , the semigroup assumption made , implies a markovian treatment in which the spectrum of the fluctuations is flat in the relevant frequency range . this in particular implies that we are neglecting the dynamics at small times , of the order of the correlation time of the fluctuations . the non - gaussian character of @xmath40 can be traced back to the fact that @xmath40 must be definite and normalized in the interval @xmath42 and not in @xmath43 . this is another fundamental difference with respect to ref . @xcite , where a gaussian character for the random phase drift errors is assumed , while we make no a priori statistical assumptions . indeed , the properties of the probability distribution @xmath44 are derived only from the semigroup condition , and it is interesting to note that this condition yields a gaussian probability distribution as a limiting case . in fact , from eq.([p ] ) one can see that @xmath3 tends to become a gaussian in the large time limit @xmath45 . in the case of rabi oscillations , @xmath46 becomes proportional to the pulse area , while @xmath16 gives an estimate of the pulse area fluctuations , since it corresponds to a fractional error of the pulse area @xmath47 . quantum computation ideally corresponds to a physical process @xmath48 where a given input state is mapped to an output state by a unitary transformation @xmath49 . it has been shown that any quantum computation can be decomposed into one - bit gates and a universal two - bit gate which involves entanglement operation on two qubits @xcite . in order to characterize a physical process in a quantum system , we follow ref . @xcite . the aim is to characterize the process given as a black box "" , by a sequence of measurements in such a way that it is possible to predict what the output state will be for any input state . we assume that the system is initially prepared in a pure state @xmath50 where @xmath51 are orthogonal states spanning the hilbert space of allowed input states with dimension @xmath52 . then , in the ideal case , the output state can be written as @xmath53 where @xmath54 are system operators not depending on the input state . whenever the unitary transformation is given by the time evolution operator @xmath55 , the initial state @xmath2 represents the input state while the evolved state @xmath56 represents the output one . since in section ii @xmath56 is replaced by @xmath9 , here we have to replace @xmath57 by @xmath58 now , in order to see to what extent the real physical process approaches the ideal one , we use as parameter the fidelity @xmath59 where the subscript @xmath60 "" indicates the average overall possible input states . obviously a gate fidelity close to one indicates that the gate was carried out almost ideally . in what follows we will see that the fidelity @xmath61 ( [ fdef ] ) can be expressed in terms of the tensor @xmath62 in the case of one bit @xmath63 , and the vector basis is given by @xmath64\,,\ ] ] where @xmath34 is the rabi frequency and @xmath65 the laser phase . eq.([hone ] ) leads to the following evolution @xmath66|g\rangle -ie^{i\phi}\sin\left[\omega t/2\right ] \\ u(t)|e\rangle&=&\cos\left[\omega t/2 \right]|e\rangle -ie^{-i\phi}\sin\left[\omega t/2\right ] a single qubit rotation . it is clear from the above evolution equations that fluctuations in the rabi frequency can be accounted by simply replacing @xmath67 with" +"our current understanding of the universe relies on a fundamental assumption that the universe is statistically homogeneous and isotropic on sufficiently large scales . it is in general difficult to prove this assumption in a strictly mathematical sense but it can be verified using different cosmological observations . discovery of the cosmic microwave background radiation ( cmbr ) in 1964 @xcite and the analysis of the data from the cobe mission launched in 1990 revealed that cmbr has a near uniform temperature across the entire sky @xcite . this discovery provided possibly the most powerful evidence for isotropy . analysis of data from the two subsequent missions , wmap launched in 2001 and planck launched in 2009 , revealed that cmbr is not completely isotropic . the physics of cmb anisotropy is now well understood . however various studies @xcite with wmap and plack reported several unexpected features at large angular scales such as a hemispherical power asymmetry , alignment of the low multipole moments , a preference for the odd parity modes and an unexpectedly large cold spot in the southern hemisphere . consistency of wmap and planck results suggest that the instrumental effects are unlikely to produce such features . so the present status of the cmbr observations place the assumption of cosmic isotropy under scanner . the isotropy of the universe has been favoured by observations in the other wavelengths such as the x - ray background @xcite , the angular distributions of radio sources @xcite and gamma - ray bursts @xcite . some studies on the distribution of supernovae @xcite , galaxies @xcite and neutral hydrogen @xcite are also consistent with the assumption of statistical isotropy . however there are other studies with type - ia supernovae @xcite , radio sources @xcite and galaxy luminosity function @xcite which find the evidence for statistically significant deviation from isotropy . the signatures of anisotropy can be also detected using the measurements of large scale bulk flows which are expected to disappear on large scales . some studies with peculiar velocity surveys , wmap data and x - ray cluster catalog find statistically significant bulk flows on scales of @xmath4 @xcite whereas some analysis with type - ia supernovae find no evidence of such bulk flows @xcite . it is also important to understand the origin of any observed anisotropies . there are a number of theoretical studies which predict the level of statistical anisotropy expected from anisotropic inflation @xcite and backreaction of large scale structure @xcite . the current observational findings suggest that there is no clear consensus on the issue of cosmic isotropy . it is important to test the assumption of isotropy in multiple data sets with different statistical tools . there will be a major paradigm shift in cosmology if different observations rule out the assumption of isotropy with high statistical significance . the present generation of redshift surveys like 2dfgrs @xcite , sdss @xcite and 2mrs @xcite now provide detailed maps of the local universe . the large sky coverage and the large number of galaxies mapped by these surveys provide an unique opportunity to test the assumption of isotropy in the local universe using galaxy distributions . the 2mass redshift survey ( 2mrs ) @xcite has some unique features which make it distinct compared to the previous optical and far - infrared surveys . the sdss and 2dfgrs , the two large redshift surveys have not attempted to be complete over the whole sky . the 2mass redshift survey covers the @xmath5 of the entire sky and selects the galaxies in the near infrared wavelengths around @xmath6 which is less affected by dust extinction and stellar confusion . the near infrared wavelengths are sensitive to the old stellar populations which dominate the galaxy masses and thus provides a statistically uniform galaxy sample in the nearby universe . the 2mrs survey is @xmath7 complete down to the limiting magnitude @xmath8 and provides a fair sample of the mass distribution in the local universe . these additional features of the 2mrs make it most suitable for testing isotropy in the local universe . @xcite propose an information theory based method for testing isotropy in a three dimensional distribution . in this paper we apply this method to the all - sky 2mass redshift survey to test the assumption of cosmic isotropy in the nearby universe . a brief outline of the paper follows . we describe our method in section 2 , describe the data in section 3 and present the results and conclusions in section 4 . we have used a @xmath1cdm cosmological model with @xmath9 , @xmath10 and @xmath11 throughout . the information entropy is originally introduced by claude shannon @xcite in the context of communication of information over a noisy channel . in information theory entropy is the key measure which quantifies the amount of uncertainty involved in the measurement of a random variable . in a more general sense , it gives a measure of the amount of information required to describe a random variable . for a discrete random variable @xmath12 with probability distribution @xmath13 and @xmath14 outcomes @xmath15 , the information entropy @xmath16 associated with @xmath12 is defined as , @xmath17 @xcite propose a method to test the isotropy of a three dimensional distribution using information entropy . the method first requires us to identify a galaxy around which isotropy is to be tested . the co - ordinates of the rest of the galaxies are then defined by treating this galaxy as the origin . we carry out an uniform binning of @xmath18 and @xmath19 , where @xmath20 and @xmath19 are respectively the polar angle and azimuthal angle in spherical polar co - ordinates . we adopted this binning so as to ensure equal area @xmath21 for each angular bin . if @xmath22 and @xmath23 bins are used while binning @xmath18 and @xmath19 respectively , it would result in a total @xmath24 angular bins . an upper limit is imposed on the radial co - ordinate @xmath25 as the galaxies are only available within a finite region . we vary the radial co - ordinate @xmath26 within this limit and count the number of galaxies within each volume element defined by the @xmath27 angular bins . for a given value of @xmath26 each of the element has exactly the same volume @xmath28 . let @xmath29 be the number of galaxies residing inside the @xmath30 volume element . a galaxy within a distance @xmath26 from the centre can only reside in one of the @xmath27 distinct volume elements . one may ask , which particular volume element a randomly selected galaxy belongs to ? there are a total @xmath27 bins and the randomly selected galaxy can reside in any one of them . the probability of finding the randomly selected galaxy in a particular bin would depend on the number of galaxies available in that bin . so we introduce a random variable @xmath31 with @xmath27 outcomes each given by , @xmath32 with the constraint @xmath33 . here @xmath34 denotes the probability of finding a randomly selected galaxy in the @xmath30 bin . the information entropy associated with @xmath31 for a distance @xmath26 can be written as , @xmath35 here @xmath36 is the total number of galaxies within radius @xmath26 . one can choose any base of the logarithm . we choose the base to be @xmath37 for the present work . in general the probabilities @xmath34 will be different for different elements . the probabilities will have an identical value @xmath38 for all the elements only when they are equally populated . this maximizes the information entropy @xmath39 for a given choice of @xmath22 , @xmath23 and @xmath26 . we define the relative information entropy as the ratio of the entropy of a random variable @xmath31 to its maximum possible value @xmath40 . the relative shannon entropy @xmath41 quantifies the degree of uncertainty in the knowledge of the random variable @xmath31 . equivalently we define the residual information @xmath42 which can be considered as a measure of the degree of anisotropy present in the distribution . for an isotropic distribution @xmath43 and consequently @xmath44 . the galaxies are not randomly distributed . the gravitational clustering assemble the galaxies into clusters and superclusters which are linked together in a complex filamentary network surrounded by empty regions or voids . the present distribution of galaxies are expected to be highly anisotropic . so the probabilities for different volume elements will be highly non - uniform . if all the galaxies reside in a particular volume element then there will be no uncertainty in identifying the location of the randomly selected galaxy and we will have @xmath45 , @xmath46 . this fully determined situation corresponds to maximum anisotropy and complete lack of information . on the other hand an uniform probability for all the @xmath27 volume elements make it most difficult and uncertain to predict the location of a randomly selected galaxy . this maximizes the information entropy to @xmath47 turning @xmath48 . this corresponds to a distribution which is completely isotropic with maximum amount of information . the galaxy distribution is expected to be anisotropic on small scales but eventually should reach isotropy with increasing size of the angular bins @xmath49 and radius @xmath26 given the assumption of isotropy holds on large scales . we change the value of @xmath26 starting from a small radius and gradually increase it in uniform steps upto its maximum value @xmath50 . we study how @xmath51 varies with @xmath26 for a given choice of @xmath22 and @xmath23 . following the definition of the radial anisotropy @xmath51 one can also define similar measures for the polar anisotropy @xmath52 and the azimuthal anisotropy @xmath53 as function of @xmath20 and @xmath19 . for this one needs to carry out the sum over @xmath23 or @xmath22 instead of @xmath27 in . it should be noted that in this case @xmath36 in would be the total number of galaxies inside all the @xmath23 or @xmath22 volume elements available at different @xmath20 or @xmath19 respectively . the polar anisotropy @xmath54 quantify the anisotropy among all the @xmath19 bins at each @xmath20 value . similarly the azimuthal anisotropy @xmath55 quantify the anisotropy among all the @xmath20 bins at each @xmath19 value . we fix the value of @xmath26 at @xmath50 or any desired radius and determine @xmath54 and @xmath55 at different @xmath20 and @xmath19 values respectively . note that one can also define similar anisotropy measures @xmath56 and @xmath57 and measure them as a function of radius @xmath26 at fixed @xmath20 and @xmath19 respectively . however in the present work we only consider @xmath51 , @xmath54 and @xmath55 to characterize the anisotropies present in the galaxy distribution . we use the galactic co - ordinates @xmath58 throughout the present analysis . so we replace @xmath20 and @xmath19 in the previous definitions by @xmath59 and @xmath60 respectively . the present day galaxy distribution is highly non - gaussian . the information entropy is related to the higher order moments of a distribution @xcite . so it captures more information about the probability distribution and may serve as a better measure for anisotropies present in a distribution . we would also like to point out here that these measures of anisotropy would never be exactly zero and would be also sensitive to binning and sub - sampling . this relative character of information does not pose any difficulty as it only signifies that the magnitudes of the information is defined with respect to a reference frame and comparison in anisotropies should be always done in the same reference frame . here we adopt a working definition of isotropy . we compare the anisotropies measured in a distribution with that from poisson distributions and consider the distribution to be isotropic only when the measured anisotropy lies within the @xmath61 errorbars of the anisotropy expected from a poisson distribution . we use the same binning" +"pulsars are expected to be born inside the supernova explosions of massive stars , which provide the surroundings for the initial evolution of their wind nebulae @xcite . the pwne ( pulsar wind nebulae ) initially expand in the freely expanding ejecta of the supernova . eventually , the reverse shock wave from the supernova interaction with the surrounding medium makes its way back to the center where it can crush the pwn . this later phase of evolution has recently been the subject of detailed studies @xcite . in particular , @xcite noted that the reverse shock is likely to be asymmetric so that the pwn can be displaced from its position over the pulsar . this scenario provides an explanation for the displacement of the radio emitting pwn in the vela remnant @xcite and other remnants . here , i emphasize pwne that are likely to be in the earlier phase of evolution , before the reverse shock effects . recent discoveries at x - ray and radio wavelengths have substantially increased the number of such objects . in 2 , the possible members of this class are listed . for objects with an approximately constant pulsar power , the expansion in a supernova is treated in 3 . constraints implied by the energy in the nebulae are discussed in 4 . the conclusions are in 5 . a list of probable young pwne in which central pulsars have been identified is given in table 1 ; these objects are plausibly interacting with ejecta . young pulsars / pulsar wind nebulae cccccccc + object & @xmath0 & @xmath1 & age & sn & snr & swept up & refs . + & ( msec ) & ( year ) & ( year ) & & & ejecta ? & + 054069 & 50 & 1660 & 760 & & yes & yes ( optical ) & 1 + 3c 58 & 66 & 5390 & 821 & 1181 & & yes ( x - ray ) & 2 + crab & 33 & 1240 & 948 & 1054 & & yes ( optical ) & 3 + kes 75 & 325 & 723 & & & yes & & 4 + g292.0 + 1.8 & 135 & 2890 & @xmath2 & & yes & maybe ( optical ) & 5,6 + g11.20.3 & 65 & 24,000 & 1616 & 386 & yes & & 7 + msh 1552 & 150 & 1700 & 1817 & 185 & yes & & 8 + g54.1 + 0.3 & 137 & 2890 & & & & & 9,10 + references : ( 1 ) @xcite ; ( 2 ) @xcite ; ( 3 ) @xcite ; ( 4 ) @xcite ; ( 5 ) @xcite ; ( 6 ) @xcite ; ( 7 ) @xcite ; ( 8) @xcite ; ( 9 ) @xcite ; ( 10 ) @xcite the second column gives the observed pulsar period , @xmath0 , and the third column gives the characteristic pulsar age , @xmath3 . if the pulsar is born rotating much more rapidly than the current rate and the braking index is @xmath4 , then @xmath5 is the actual age . if the pulsar is born with a period close to its current period , it can be younger than @xmath5 . alternatively , if the pulsar is born spinning rapidly and has a braking index @xmath6 , it can be older than @xmath5 . the fourth column is an estimate of the actual age . for 054069 @xcite and g292.0 + 1.8 @xcite , the age estimate is from the size of the nebula and velocities found from optical spectroscopy . for the other objects with ages , the estimate is from a tentative supernova identification , given in the next column . the identification of the crab with sn 1054 is generally considered very secure , but the other identifications are less secure . there is still some uncertainty over whether all of the events are in fact supernovae , e.g. , sn 386 @xcite . the next column indicates whether an extended supernova remnant is observed around the pwn , and the penultimate column indicates whether there is evidence for ejecta swept up by the pwn . there are indications that these nebulae are in the early phase of interaction with freely expanding ejecta . one expectation in this picture is that the pwn should shock and sweep up a shell of supernova ejecta @xcite . the shock wave is initially expected to be radiative , but it becomes nonradiative due to the decline in the supernova density . a good example of an ejecta shell is the complex of filaments in the crab nebula . in this case , there is evidence for the shock wave in the ejecta @xcite ; it may be in the process of making a transition from radiative to nonradiative . for 3c 58 , there is evidence for x - ray emission from swept - up ejecta @xcite , implying the presence of a nonradiative shock . the optical emission from 054069 may be from a radiative shock @xcite . the optical emission from g292.0 + 1.8 appears to be from the vicinity of the pwn @xcite , but the relation between them has not yet been determined . another expectation of the model with expansion in ejecta is that the pulsar should be centrally located within the pwn . this appears to be true for the objects listed in table 1 , although in most cases the pwn has an asymmetric boundary . the pwn in g292.0 + 1.8 is substantially off the center of the surrounding supernova remnant , which has led to the suggestion that the pulsar has a velocity @xmath7 @xcite . if this is the case , the pulsar is expected to move to a place in the ejecta where it is comoving with the surrounding gas and it is surrounded by uniformly expanding ejecta . some degree of asymmetry may develop if there is a gradient in the surrounding density distribution . if we assume that 3c 58 and g11.20.3 are associated with sn 1181 and sn 386 , respectively , models for the pwne can make use of the fact that the characteristic age is much larger than the true age , so that the pulsars have not significantly spun down . this allows the assumption that the pulsar power , @xmath8 , is constant during the evolution . we begin by considering the expansion of the pwn into the inner parts of the supernova ejecta . the density distribution into which the pwn initially expands can be estimated from explosion models . @xcite used simple power law models for the density distribution . more detailed models have been considered by @xcite , who give asymptotic forms for the the final density distribution at low and high velocities . for the cases to be studied here , the asymptotic low velocity density profile is applicable over the time of interest . for an explosion in a star with a radiative envelope , the inner density profile , using eq . ( 46 ) of @xcite , can be expressed as @xmath9 where @xmath10 is the free expansion velocity , @xmath11 is the total ejected mass , and @xmath12 is the explosion energy in units of @xmath13 ergs . for a star with a convective envelope , the density distribution may be flatter , but the density at @xmath14 is close to the above value . the expansion of a pwn in a density distribution can be approximately treated as a thin shell driven by a uniform pressure wind bubble with adiabatic index @xmath15 @xcite . the radius can be found analytically if the pulsar power , @xmath8 , is constant and the surrounding medium has a power law density distribution . as discussed above , this may be the case for 3c58 and g11.20.3 . then , from eq . ( 2.6 ) of @xcite , we have @xmath16 where @xmath17 is @xmath8 in units of @xmath18 . in cases where @xmath19 , @xmath8 , and @xmath20 are known , we can solve for @xmath21 ; because @xmath22 is expected , we have an estimate of the total ejecta mass . these quantities are known for 3c 58 and g11.20.3 if the historical supernova identifications are assumed , and the results are given in table 2 . these estimates involve a spherical approximation for pwne that are apparently not spherical , but an average radius can be taken @xcite . the assumed distances are 3.2 kpc for 3c 58 @xcite and 5 kpc for g11.20.3 @xcite . the expected values of @xmath11 for a core collapse supernova are typically several @xmath23 or more . in the case of a very fast type ic supernova , sn 1994i , @xmath11 was only @xmath24 @xcite , which is an extreme case . the point is that the model leads to a value of @xmath11 that is smaller than expected for 3c 58 . the radius is larger than would be expected if it were expanding into a normal supernova . there is no problem with g11.20.3 . estimated ejecta and swept up mass cccccc + object & @xmath17 & radio radius & @xmath21 & predicted & observed + & & ( pc ) & ( @xmath23 ) & @xmath25 ( @xmath23 ) & @xmath25 ( @xmath23 ) + 3c 58 & 0.27 & 3.3 & 0.1 & 0.002 & 0.1 + g11.20.3 & 0.064 & 0.9 & 3.5 & 0.05 & + another constraint comes from the amount of mass swept up by the wind bubble , @xmath25 . an integration over the central density shows that @xmath26 , fairly independent of supernova density distribution . values of @xmath25 deduced in this way for 3c 58 and g11.20.3 are given in table 2 . the value of @xmath27 deduced for 3c 58 can be compared to the @xmath28 found from x - ray observations @xcite . again , there is a problem with the model mass being too low . the mass could be brought into agreement with the observed value if the age were increased by a factor @xmath29 . these models assume that the supernova ejecta are swept into a thin shell that remains spherically symmetric . however , the shell is being accelerated and is subjected to rayleigh - taylor instabilities , which can decrease the coupling between the pulsar wind bubble and the swept up gas . in the limit that there is no further acceleration after the ejecta are shocked , the pwn radius ( eq . [ 2 ] ) is increased by a factor of 1.4 . the masses @xmath11 and @xmath25 are increased by a factor of 2 , which does not change the conclusion about the difficulties with 3c 58 . the model with constant @xmath8 can be used to predict the internal energy in the pwn . this energy is reduced from the total deposited energy , @xmath30 , because of work done on the surrounding supernova gas . for a range of flat central density distributions , the internal energy is @xmath31 ( table 1 of chevalier and fransson 1992 ) . the internal energy in a pwn has relativistic particle and magnetic field components ; a minimum value for the total energy in particles and fields can be found from the synchrotron luminosity and the emitting volume ( e.g. , pacholczyk 1970 ) . @xcite discuss the radio emission from the pwn in g11.20.3 . the value of the minimum energy deduced from the radio emission for the two pwne is given in table 3 . the actual energy must be larger when a larger frequency range is considered . it can be seen that there is not a problem with the energy for g11.20.3 ," +"on the whole , measurements of observables in the @xmath3 system agree with the standard model ( sm ) . however , some cracks have started to appear . there are now several quantities whose measured values differ from the predictions of the sm . although these disagreements are not statistically significant they are typically at the level of @xmath4 they are intriguing since there are a number of different @xmath3 decays and effects involved , and they all appear in @xmath5 transitions . because of this , there have been numerous papers examining new - physics ( np ) flavour - changing neutral - current ( fcnc ) contributions to the various @xmath5 processes . these analyses have been performed in the context of specific np models , or model - independently . in general , such np can also contribute to fcnc processes involving the top quark . this has been looked at , though much less so than in @xmath3 decays . however , given that the lhc will produce a large number of top quarks and will be able to measure flavour - changing @xmath6 decays , it is important to explore the possibility of np contributions to fcncs in the top sector . in the past , analyses have focused on rare top decays such as @xmath7 ( @xmath8 ) and @xmath9 @xcite . other top decays where np effects have been examined include @xmath10 @xcite and @xmath11 @xcite . in this paper we examine the decay @xmath12 . in the sm , this decay occurs at tree level , via @xmath13 . on the other hand , because it involves the small element @xmath14 ( @xmath15 ) of the cabibbo - kobayashi - maskawa ( ckm ) quark mixing matrix , the amplitude for this process is also rather small , and is therefore quite sensitive to np . for example , there could be np contributions to this decay in models with a charged higgs boson @xcite , or via @xmath16 , where @xmath17 corresponds to some neutral particle ( such as a @xmath18 or a non - sm higgs boson ) . such processes could interfere with the sm process , leading to observable consequences , even if the intermediate np particle were heavier than the top quark . rather than restricting our attention to any one particular model , we examine np contributions to @xmath19 model - independently ( i.e. , using an effective lagrangian ) . our model - independent treatment of @xmath12 takes into account the effects of the 10 possible four - fermi operators . these operators contribute to both cp - conserving and cp - violating observables . for the cp - even observables , we consider the cp - averaged partial width , a forward - backward - like asymmetry , and an asymmetry that depends on the spin of the top quark . for the cp - odd observables , we note that the decay @xmath19 is dominated by one amplitude in the sm ; i.e. , there is only one weak phase involved . as such , all cp - violating asymmetries are very suppressed in the sm , so the observation of a non - zero asymmetry would be a smoking - gun signal of np . in this paper , we discuss two types of cp - odd asymmetries : the partial - rate asymmetry ( pra ) and a triple - product asymmetry ( tpa ) . pras require a strong phase in order to be non - zero . strong phases can arise due to gluon exchange , but it is expected that such phases will be small since the energies involved are so large . another source of a strong phase is the width of the @xmath20 . in our calculation , we ignore qcd - based strong phases and assume that the required strong phase is due entirely to the width of the @xmath20 . this means that only sm - np interference can lead to a pra . on the other hand , in contrast with pras , tpas do not require a strong phase in order to be non - zero . thus , np - np interference terms can give rise to tpas . as we will see , tpas generated by sm - np interference tend to be small , but np - np tpas can be large . these are particularly interesting . we show that the measurement of the partial width by itself can reveal the presence of np . however , if the np exists , we will want to know its identity , i.e. , which of the 10 operators is responsible , and the partial width measurement does not give us this information . in order to do this , it is necessary to measure the other quantities mentioned above . since the various observables depend differently on the operators , the knowledge of their sizes will give us an idea of which np operators are present . this will allow us in turn to deduce which model(s ) might be responsible for the observed effects . although we confine our attention to @xmath12 in this work , we note that most of our results are easily transferable to @xmath21 by the replacement @xmath22 in feynman diagrams and expressions . since @xmath1 , the branching ratio for @xmath21 is similar to that for @xmath12 , and the two processes would apriori have similar sensitivities to np effects . one difference between @xmath0 and @xmath21 is that the `` cpt '' correction to the pra would be significant for @xmath21 , whereas it is miniscule for @xmath12 ( see the discussion in sec . [ sec : pra ] and appendix [ sec : cpt ] ) . the remainder of this paper is organized as follows . in sec . [ sec : smnp ] we write down the sm contribution to @xmath0 , and also parameterize np contributions to this decay in terms of an effective lagrangian containing ten terms . in sec . [ sec : cpeven ] ( cp - even observables ) we compute the cp - averaged partial width for the decay under consideration , as well as a forward - backward - like asymmetry and an asymmetry based on the spin of the top quark . the latter two asymmetries are both constructed in such a way that they are zero within the context of the sm . we close this section with a brief numerical study , noting that the cp - even asymmetries could reasonably be of order 10 s of percent . section [ sec : cpodd ] contains our analysis of two cp - odd observables the partial rate asymmetry and the triple - product asymmetry . section [ sec : discussion ] concludes with a discussion of our results . appendices [ sec : appa ] , [ sec : cpt ] and [ sec : appb ] contain some technical details . in particular , appendix [ sec : cpt ] contains a discussion of results related to the cpt theorem , namely which vertex - type corrections must be considered in the calculation of pras in order not to violate cpt . in this section we parameterize the np contributions to @xmath23 in terms of an effective lagrangian . we then write down expressions for the sm and np amplitudes . these expressions are used in following sections to determine various cp - even and cp - odd observables . figure [ fig : feynman_diagram1](a ) shows the feynman diagram for the sm contribution to @xmath19 . the resulting amplitude is given by , @xmath24 , ~ \label{eq : wamp}\end{aligned}\ ] ] where @xmath25 is the ckm matrix . we work in the standard representation of the ckm matrix , in which @xmath14 and @xmath26 are both real . note that colour indices have been suppressed . the expression in square parentheses is proportional to the @xmath20 propagator , with @xmath27 , @xmath28^{-1}$ ] and @xmath29 , where @xmath30 . ( note : throughout this paper we neglect the leptons and light quarks masses . however , if this not done , the @xmath20 propagator is modified to i , where @xmath31^{-1}$ ] . @xmath32 and @xmath33 are related to the transverse and longitudinal widths of the @xmath20 @xcite , and they both depend on the quark masses . there has been considerable discussion in the literature regarding the correct form of the @xmath20 propagator . ( see , for example , refs . the above expression has been derived by performing a dyson summation of the absorptive parts of the @xmath20 self - energy diagrams in unitary gauge , with quarks and leptons in the loops . some of the disagreement in the literature has focused on the form of @xmath34 ( see the brief discussion in ref . @xcite , for example ) . still , when all light masses are neglected , none of the observables in the present work depend on @xmath34 . there seems to be broader agreement on the form for @xmath35 in the literature , although many authors drop the @xmath36 dependence in @xmath37 . finally , we should note that the pinch technique may be used to reorganize perturbative calculations even those involving resonances in such a way that results are explicitly gauge - invariant ( see , for example , ref . rigorous application of the pinch technique to the problem at hand is beyond the scope of this work . ) we parameterize new - physics effects via an effective lagrangian @xmath38 , where , @xmath39 in the above expressions , @xmath40 is assumed to be of order @xmath41 , @xmath42 is the np mass scale and the @xmath43 and @xmath44 couplings may include weak ( cp - violating ) phases . for the levi - civita tensor , we adopt the convention @xmath45 . the np contributions to @xmath46 are illustrated in fig . [ fig : feynman_diagram1](b ) . colour indices are not shown in the above expressions , but are assumed to contract in the same manner as those of the sm ( i.e. , @xmath47 with @xmath6 and @xmath48 with @xmath49 ) . in fcnc models those with a flavour - changing neutral particle such as a @xmath50 or a scalar the colour indices would contract in the opposite manner ( i.e. , @xmath48 with @xmath6 and @xmath47 with @xmath49 ) . it is straightforward to incorporate colour - mismatched terms into the effective lagrangian . this topic is discussed further in appendix [ sec : appb ] . it is useful to define @xmath51 and similarly for the other @xmath43 and @xmath44 couplings . in terms of the `` @xmath52 '' parameters , we have the following expression for the np contribution to @xmath12 , @xmath53 to get a sense of the possible order of magnitude of the @xmath52 couplings , note that , if @xmath54 and @xmath55 gev , then @xmath56 . thus , @xmath57 could reasonably be assumed to be of order unity . in other words , the sm and np contributions to @xmath12 can very well be about the same size . when computing the effect of np on a particular observable , it is therefore important to include both the sm - np interference and np@xmath58 pieces . at present , there are no direct constraints on the @xmath52 couplings . the precision measurements of @xmath14 place an indirect constraint via the loop diagram shown in fig . [ fig : vcb ] . it is known that some care must be taken when attempting to incorporate terms from an effective lagrangian into loop calculations @xcite . incorporating the diagram shown in fig . [ fig : vcb ] , we find the following expression for" +"the kondo necklace ( kn ) type models are useful to discuss the quantum phase transitions between kondo singlet and antiferromagnetically ordered states such as found in heavy fermion compounds @xcite . they have been originally proposed by doniach @xcite for the one - dimensional case as a simplified version of the itinerant kondo lattice ( kl ) models @xcite . thereby the kinetic energy of conduction electrons is replaced by an intersite exchange term . for a pure xy - type intersite exchange this may be obtained by a jordan - wigner transformation . however in higher d the replacement can not be justified easily . the intuitive argument is that at low temperatures the charge fluctuations in the kondo lattice model are frozen out and the remaining spin fluctuation spectrum can be simulated by an antiferromagnetic inter - site interaction term of immobile @xmath1 spins coupled by a kondo interaction to the local noninteracting spins * s*. recent exact diagonalisation studies on finite clusters for both kondo lattice and kondo necklace models have indeed found that the competition between on - site kondo singlet formation and af inter - site correlations are very similar in both models @xcite . a more formal way to get rid of charge fluctuations in the kl model is an inclusion of a hubbard term for conduction electrons ( klu model ) which leads to the isotropic kn model in the large u limit at half filling . nevertheless one should consider the kondo necklace model for d@xmath22 as a model in its own right which is suitable for studying quantum phase transitions between a kondo singlet ( ks ) and an antiferromagnetic ( af ) phase . in its original form the local kondo exchange is isotropic while the intersite exchange is of xy - type . this model has u(1 ) symmetry . later more general models with arbitrary anisotropy of kondo as well as intersite exchange terms have been considered @xcite . indeed compounds which exhibit the ks to af quantum phase transition have mostly uniaxial symmetries . a full account of the influence of uniaxial anisotropies of both terms in the kondo necklace hamiltonian on the quantum critical point has been given in ref . . the d=2 kn model without any anisotropy may also be understood as a special case of a bilayer heisenberg model @xcite where the intersite bonds are cut in one of the layers . a reintroduction of holes in this case leads to the kntj model which is related to the klu model away from half filling @xcite . in the general anisotropic kn model the quantum phase transition is achieved by varying the ratio of hopping t , i.e. , the intersite interactions of @xmath1 spins to the on - site kondo interaction j. in practice this is achieved by varying pressure ( hydrostatic or chemical ) . an alternative way to arrive at the qcp is to apply an external magnetic field which breaks the local kondo singlets and leads to a field dependence of the critical t@xmath0 . starting from a noncritical or above critical t at zero field the system may then be tuned to the qcp by varying the field strength . this is indeed a practical method frequently applied @xcite . to investigate field - induced quantum phase transitions from kondo singlet to af ordered state or vice versa we have extended our previous work to include the effect of the magnetic field within the kondo necklace model . however , this introduces an additional parameter , namely the ratio of effective g- factors for the local kondo spins and the interacting spins . they can be different due to the different strength of spin - orbit coupling and crystalline electric field effects involved in the formation of the @xmath1 and * s * ( pseudo- ) spins . a mainly numerical study of the itinerant isotropic kl model in a magnetic field has been given previously @xcite . in sec . [ sec2 ] we define the anisotropic kn model in a magnetic field and in sec . [ sec2a ] briefly discuss the local state space of the kondo term in an external field . in sec . [ sec3 ] we perform the transformation from spin to bosonic variables and in sec . [ sec4 ] derive the selfconsistent equations for the mean field boson condensate amplitudes in the singlet and antiferromagnetic phases .. the influence of higher order terms in the hamiltonian is discussed in sec . [ sec4a ] . in sec . [ sec5 ] we investigate the numerical solutions and discuss the resulting quantum critical t - h phase diagram . a discussion is provided in sec . [ sec5a ] and sec . [ sec6 ] finally gives the conclusions . to investigate field induced quantum critical behaviour we start from the anisotropic kondo necklace ( kn ) model with u(1 ) symmetry @xcite where the field is applied along the anisotropy ( z ) direction : & = & _ t+_j+_z + & = & t_ ( _ n^x _ m^x + _ n^y _ m^y + m^z ) + j_n(_n^x s_n^x+_n^y s_n^y + _ n^z s_n^z ) + _ is_n^z+_i_n^z , [ ham ] here , the summation over nearest neighbor ( n.n . ) is indicated by brackets and @xmath3 is the @xmath4-component ( @xmath4 = x , y , z ) of the itinerant electron spin at site @xmath5 whereas @xmath6 is the @xmath4-component of localized spins at position @xmath5 . for the exchange coupling between the itinerant and localized spins we generally use @xmath7 as reference energy scale in all figures except when stated otherwise . the local anisotropy parameter @xmath8 is defined by the relation j@xmath9=@xmath8j@xmath10 between the z - axis and in - plane ( xy ) local exchange . the hopping parameter of the itinerant electrons is proportional to @xmath11 with the anisotropy in the z - direction given by @xmath12 . the present model has three control parameters : @xmath13 and the anisotropy parameters ( @xmath12,@xmath8 ) . in the zeeman term we defined @xmath14 and @xmath15 with h = @xmath16h where h is the strength of the applied field . furthermore @xmath17 and g@xmath18 are the gyromagnetic ratios for localised ( @xmath6 ) and itinerant ( @xmath3 ) spins respectively . they are determined by the combined effect of spin - orbit coupling and crystalline electric fields which depends on the degree of localisation or itineracy of electrons . therefore g@xmath19 and g@xmath18 in general need not be equal . we shall consider two extreme cases , namely ( @xmath20)=(2,0 ) and ( @xmath20)=(2,2 ) . the former is more realistic , since in real heavy fermion compounds most of the magnetic response is due to the localised electrons with pseudo - spin * s*. as in previous work @xcite the present study of field induced quantum phase transitions in the anisotropic kn model is based on the bond operator formulation . its hilbert space is spanned by local singlet - triplet states of ( @xmath21 ) spin dimers represented by bosonic degrees of freedom . in applying this technique to the finite field case we will largely use the same or similar notations as in the previous zero field case @xcite for consistency . before we perform the transformation to bosonic variables it is useful to have a clear understanding of the local singlet-triplet level scheme as function of anisotropy and magnetic field because certain tendencies of the quantum critical behaviour are correlated with the splitting of the ground state and the first excited state of a local bond . therefore we first diagonalise the local hamiltonian @xmath22 . this leads to eigenvalues @xmath23=e@xmath24/@xmath25 ( i=1 - 4 ) given by _ 1,2&=&_+ , + _ 3,4&=&(4+_-^2)^- , + _ & = & -(g_sg _ ) , [ llev ] with @xmath26 and @xmath27 . defining s@xmath28=@xmath29 + s@xmath9 then @xmath30 are the energies of the triplet states @xmath31 with s@xmath32 1 respectively which exhibit the linear zeeman effect . furthermore @xmath33 correspond to the triplet @xmath34 state @xmath35 and singlet state @xmath36 respectively . they show level repulsion in a magnetic field , except for g@xmath19=g@xmath18 when the total s@xmath28-component is conserved and commutes with @xmath37 . it is obvious that the spectrum of eigenstates in eq.([llev ] ) is invariant under the transformation ( g@xmath19,g@xmath18 ) @xmath38 ( g@xmath18,g@xmath19 ) . ) on the local anisotropy @xmath8 ( xy - side ) or @xmath39=1 - 1/@xmath8 ( ising side ) at zero field . numbers in parentheses denote the degeneracy of each level . bottom : field dependence ( h=@xmath16h ) of local energy level for three extreme cases . note that in the xy - case the excitation energy from ground state to first excited state vanishes asymptotically ( h@xmath40j@xmath10 ) whereas in the other cases it reaches a constant ( haf ) or is equal to a constant ( ising ) . here we used ( g@xmath19,g@xmath18)=(2,0).,title=""fig:"",width=302 ] + ) on the local anisotropy @xmath8 ( xy - side ) or @xmath39=1 - 1/@xmath8 ( ising side ) at zero field . numbers in parentheses denote the degeneracy of each level . bottom : field dependence ( h=@xmath16h ) of local energy level for three extreme cases . note that in the xy - case the excitation energy from ground state to first excited state vanishes asymptotically ( h@xmath40j@xmath10 ) whereas in the other cases it reaches a constant ( haf ) or is equal to a constant ( ising ) . here we used ( g@xmath19,g@xmath18)=(2,0).,title=""fig:"",width=302 ] the variation of zero - field energy levels with @xmath8 is shown in fig . [ fig1 ] ( top ) from the xy - u(1 ) limit ( @xmath8=0 ) via the heisenberg su(2 ) point(@xmath8=1 ) to the ising z@xmath41 limit ( @xmath8=@xmath42 ) . the field dependence for a few selected @xmath8-values and g - factors ( g@xmath19,g@xmath18)=(2,0 ) are shown in fig . [ fig1 ] ( bottom ) . for ( g@xmath19,g@xmath18)=(2,2 ) ( not shown in fig . [ fig1 ] ) the ground state and first excited state levels cross at h@xmath43/j@xmath10=0.25 , 0.50 for ( @xmath44)=(0,0 ) and ( 1,1 ) respectively . in such a case one may expect that the quantum critical t@xmath0(h@xmath43 ) for the transition from kondo singlet to af phase vanishes . we apply the transformation from spin variables ( @xmath45,@xmath46 ) to bond variables ( s , t@xmath47 ) ( @xmath4 = x , y , z ) to the hamiltonian in eq . ( [ ham ] ) . it is given by @xcite : s_n , = ( s^_n t_n , + t_n , ^ s_n -i _ t_n , ^t_n , ) , + _ n , = ( -s^_n t_n , - t_n , ^ s_n -i _ t_n , ^t_n , ) , [ bond ] where @xmath48 is the fully antisymmetric tensor . by construction the singlet ( s ) and triplet ( @xmath49 ) operators generate the local eigenstates of @xmath37 for zero field and no anisotropy @xcite : s^|0&=&(|-|);t_x^|0=-(|-| ) , + t_z^|0&=&(|+|);t_y^|0=(|+| ) . here the first and second arrows indicate the z - component of @xmath1 and @xmath50 spins respectively . the singlet and triplet operators satisfy the usual bosonic commutation relations according to [ s_n , s_n^]=1 ; [ t_n , , t_n , ^]= _ , ; = 0 . all other commutators vanish . the physical states have to satisfy the local constraint @xmath51 . this transformation leads to an effective hamiltonian in terms of singlet ( s ) and triplet ( t@xmath47 ) bosons . it has been argued in @xcite that one may restrict to the terms which are bilinear in the triplet bosons and" +"controversies over the apparent dichotomy between microscopic reversibility and macroscopic irreversibility are as old as statistical mechanics itself and continue to the present day , as exemplified by the popular ref . @xcite and the ensuing vivid debate @xcite . broadly speaking , the issue can be tackled `` bottom up '' or `` top down '' . the bottom up approach , which has been pursued by the majority of researchers , involves specifying ( or at least imposing constraints on ) some microscopic hamiltonian and subsequently studying the evolution of those degrees of freedom that are deemed `` macroscopic '' , `` accessible '' or otherwise `` relevant '' to the problem at hand . this line of research has of late enjoyed cross - fertilization with topical areas such as nanoscale thermodynamics @xcite , quantum many - body physics @xcite and quantum information @xcite , leading to some powerful new results . they confirm that the eventual thermalization of a quantum system is a universal phenomenon which holds true for virtually all hamiltonians and sensible choices for the relevant degrees of freedom @xcite . the rather generic assumptions that are needed amount to ( i ) excluding the special case of isolated systems with highly regular , completely integrable dynamics ; and ( ii ) introducing some form of coarse graining , such as limiting the resolution of realistic preparation and measurement devices @xcite or tracing out the degrees of freedom of a bath @xcite . coarse graining entails that information about the microstate is siphoned off from the retained to the discarded degrees of freedom . this leakage becomes irreversible whenever the dynamics of the latter is sufficiently fast and irregular , leading to an effective memory loss on time scales much shorter than those pertaining to the evolution of the relevant degrees of freedom @xcite . in contrast , the lesser - known top down approach , pioneered by jaynes for classical statistical mechanics @xcite and subsequently generalized @xcite , refrains from considering any specifics of the underlying microscopic dynamics and instead derives macroscopic irreversibility from the very basic requirement essential to the scientific method that macroscopic experiments be reproducible . the central argument is very simple : an experiment is reproducible if its initial preparation uniquely determines its final outcome ; i.e. , if merely on the basis of their initial values one can predict with certainty the final values of the relevant degrees of freedom . since a prediction can not possibly contain more information than the data on which it is based , the final values of the relevant degrees of freedom can not carry more information than do their initial values . so in the course of a reproducible experiment the amount of missing information about the system s microstate , and hence the entropy , can only increase , q.e.d . there are other top down approaches which are similar in spirit , yet which rather than from `` reproducibility '' start from different primitives like `` adiabatic accessibility '' @xcite . reversing the top down logic , violations of the second law may well occur ; but such violations are never reproducible , and with increasing system size , become exceedingly unlikely . experiments that purport to violate the second law in a reproducible fashion must presuppose the preparation of some special ( say , highly correlated ) initial state , or else some peculiar prior history of the system ( such as in the classic example of spin echoes @xcite ) . the apparent systematic violation of the second law then stems from the fact that the experimenter actually controls degrees of freedom other than the supposedly relevant ones , either directly in the present or through specific interventions in the past . despite their seemingly different outlooks the bottom up and top down approaches both revolve around the pivotal issue of memory loss . they either show ( bottom up ) or simply postulate ( top down ) that in realistic experiments the relevant degrees remote history has no influence on their future evolution , and thus can be safely disregarded . this intimate connection between irreversibility and memory loss is captured succinctly in landauer s principle @xcite , which has spawned another highly interesting line of research @xcite . in the present paper i wish to add yet another , and rather practical , perspective on the issue of thermalization . when a novel quantum system is fabricated and investigated in the laboratory for the first time , its precise dynamics and possibly even its constants of the motion are not known in advance . ( of course , there is generally some theoretical expectation ; but whether this will be confirmed or refuted by actual measurements is not _ a priori _ clear . ) a particular experiment might then be aimed at assessing whether or not a certain process leads to thermalization ; and if so , which set of thermodynamic variables characterizes the final equilibrium state . operationally , one might do this by assembling multiple samples , each consisting of identically prepared copies of the system . each sample is prepared in a different initial state and subjected to the process in question . if thermalization does occur , subsequent quantum - state tomography @xcite on all samples will reveal that , modulo random fluctuations , their respective final states are distributed on some low - dimensional submanifold of state space . this submanifold is composed of states of the gibbs form @xmath0 , with the observables @xmath1 being the constants of the motion . their expectation values or the associated lagrange parameters , respectively , then constitute the appropriate set of thermodynamic variables . this approach to assessing thermalization is based on output data only and does not require tight control over the initial states of the various samples . yet in a real - world setting , the system in question might be difficult to manufacture , and the above idealized procedure difficult to execute . specifically , it might only be possible to prepare a small number of samples , which in turn are small in size . as a consequence , there will be just a few data points in state space , which moreover have non - negligible error bars . reconstructing the gibbs manifold and hence the constants of the motion on the basis of such imperfect measurement data then becomes a nontrivial statistical inference task . in purely statistical terms , this is a situation where noisy data in some high - dimensional space ( the tomographic images in state space ) are presumed to be explained by a small number of latent variables ( the expectation values of the constants of the motion ) , effectively reducing the dimensionality of the data . in such a generic setting , the task is to infer the optimal dimension and orientation of the lower - dimensional latent space . problems of this type can be tackled with a variety of statistical techniques such as factor analysis or principal component analysis @xcite . in the present paper , i shall build on these generic techniques to develop a statistical framework tailored to the relevant task of assessing whether or not thermalization has occurred , and if so , inferring the most plausible set of constants of the motion . whenever the above statistical analysis suggests that thermalization has indeed occurred and there is one constant of the motion only , this single constant of the motion is by default the hamiltonian . the same statistical framework can then be used to estimate that hamiltonian . this estimation procedure is based on studying thermal properties rather than time evolution ; and it uses only output rather than input - output data . therefore , it is very different in its approach from the usual quantum - process tomography @xcite and hamiltonian tomography @xcite . as the second key result of the present paper , i shall lay out this `` thermal '' estimation procedure for the hamiltonian and illustrate its use in a simple example . the remainder of the paper is organized as follows . in sec . [ theory ] , i will present the general statistical framework for assessing thermalization along with the key approximations made . in sec . [ hamest ] , i will turn to the rather common case where the hamiltonian is the sole constant of the motion , and explain how in this case one can infer the most plausible hamiltonian from the data . in sec . [ qubit ] , i will put the general framework to use in the simple example of qubits , both to assess their thermalization and to estimate the pertinent hamiltonian . finally , in sec . [ conclusions ] , i will conclude with a brief discussion . let @xmath2 denote the number of distinct samples and @xmath3 , the size of the @xmath4-th sample . after the samples have undergone the process in question they are all subjected to quantum - state tomography , which may or may not be informationally complete . let @xmath5 denote the set of observables whose totals are ascertained in a tomographic experiment ( by performing measurements on each member of the sample and adding up the results , or via global measurements on the entire sample ) , and @xmath6 the associated sample means gleaned from the @xmath4-th sample . finally , let the quantum state @xmath7 denote a possible prior bias as to the samples final state @xcite ; in case of complete prior ignorance , this is simply taken to be the totally mixed state . the hypothesis to be tested is whether or not the totality of experimental data @xmath8 can be explained by the expectation values of some smaller set of observables @xmath1 , the presumed constants of the motion . associated with these presumed constants of the motion and with the measured observables are subspaces @xmath9 and @xmath10 of the space of observables ( with @xmath11 being the unit operator ) , termed respectively the `` theoretical '' and `` experimental '' level of description @xcite . for the former to have any explanatory value , it must be @xmath12 . the plausibility of the theoretical hypothesis is encoded in the posterior probability of the level of description @xmath13 , given the data @xmath14 and prior bias @xmath7 . by bayes rule @xcite , this probability of interest is given by @xmath15 whenever the prior @xmath16 is sufficiently non - committal , the right hand side will be dominated by the likelihood function . as the various runs of the experiment are independent , the latter can be factorized : @xmath17 with the data @xmath18 pertaining to the @xmath4-th sample . and finally , according to the theoretical hypothesis , each individual factor can be marginalized : @xmath19 where the integration ranges not over the complete state space @xmath20 but over the gibbs manifold @xmath21 associated with the theoretical level of description @xmath13 and reference state @xmath7 @xcite . this gibbs manifold is composed of states of the generalized gibbs form @xmath22 , \label{gibbs}\ ] ] which minimize the relative entropy with respect to @xmath7 under given constraints for the expectation values of @xmath1 @xcite . for reasonably large sample sizes and a near optimal measurement setup the first factor ( likelihood ) in the integrand of eq . ( [ marginalize ] ) can be approximated with the help of the quantum stein lemma @xcite , @xmath23 . \label{entropic_likelihood}\ ] ] ( else the quantum stein lemma provides only a lower bound . ) here @xmath24 has the generalized gibbs form ( [ gibbs ] ) with @xmath1 replaced by @xmath5 and reference state @xmath25 rather than @xmath7 , and with the lagrange parameters @xmath26 adjusted such that @xmath27" +"the energy changes associated to processes occurring in mesoscopic objects exhibit a stochastic nature due to the effect of fluctuations . this implies that for single trajectories in phase space , thermodynamic observables like work , heat , and entropy changes are random quantities . this fact constitutes the basis for stochastic thermodynamics @xcite . in this context , the stochastic entropy produced during a certain protocol can be negative for certain rare trajectories , a fact that is in apparent contradiction with the second law of thermodynamics . fluctuation theorems @xcite state that those trajectories where the entropy production is negative occur with an exponentially small weight in comparison to the trajectories where the entropy production is positive @xmath7 where @xmath8 represents a transformation like time - reversal , or the transformation to a _ dual _ dynamics , or their composition ( see @xcite for a simple definition of the dual dynamics ) , and @xmath9 represents a trajectory - dependent thermodynamic quantity , as work , heat , or more generally , different forms of trajectory - dependent entropy production , with the symmetry @xmath10 . these relations , initially proved for deterministic and stochastic markovian systems , have also been extended to the case of non - markovian dynamics @xcite . furthermore , they have been widely tested in experiments @xcite . eq.([dft ] ) is commonly denominated a detailed fluctuation theorem ( dft ) . from it , the relation @xmath11 , also known as an integral fluctuation theorem ( ift ) , can be obtained . from the ift and jensen s inequality , the second law of thermodynamics is obtained as @xmath12 , independently of the protocol and the duration of the process . very large systems , where @xmath13 , naturally suppress fluctuations since the mean value of @xmath9 grows as @xmath1 for large @xmath1 , while fluctuations grow as @xmath14 , a fact that we know from the most elementary courses of statistical mechanics . in this case @xmath15 , which means that for any realization of any process one has @xmath16 . however , in small mesoscopic systems , fluctuations are large and realizations are possible such that @xmath17 for not too large time intervals . using some abuse of language ( see for instance @xcite ) , we can name these intervals as _ local violations of the second law of thermodynamics _ , where `` local '' means at a single trajectory level . we remark that the aforementioned local violations do not represent true violations of the second law of thermodynamics , which is , perhaps , the most solid law of nature . the entropy production remains always non - negative in average , however , it is interesting to characterize the statistics of the total time of occurrence of these events . in particular , if we consider a time interval @xmath18 $ ] , we will be interested in calculating the total fraction of time @xmath0 where the stochastic entropy production is negative , which we name as the _ violation fraction_. in fig . [ fig1 ] we sketch the evolution of the entropy change as a function of time for a stochastic trajectory of a small system . the shadowed regions are the violation sectors ( where @xmath17 ) and the cumulative duration of these regions divided by the total time @xmath2 defines the fraction @xmath0 . is defined as the relative duration of the violation sectors ( where @xmath17 ) with respect to the total time @xmath2 . ] this study is important in those cases where one only needs to consider a small number of realizations of a given process at the mesoscopic level . the entropy production is a self - averaging quantity , which implies that for single realizations in macroscopic systems one is already observing the averaged entropy production . that is why , in spite of the fact that the second law of thermodynamics forbids the spontaneous emergence of order from disorder in isolated systems _ only in average _ , we meet this limitation _ at every single realization _ of the given process . this is clearly not the picture at the mesoscopic scale , where this constraint is relaxed at single trajectories , and order can sometimes emerge from disorder . additionally , our theory may be relevant in some other practical situations . for example , it is known that the efficiency of any thermal machine is bounded by virtue of the second law of thermodynamics . however , if one optimizes the external protocols and accomodates the values of @xmath2 and @xmath1 such that the average violation fraction exhibits its larger possible value , our motor will operate in a scenario where the occurrence of entropy - consuming trajectories is especially propitious , a fact that could enhance the efficiency of the machine . this possibility will be considered in more detail in future works . before proceeding , we would like to advance our main result . for the generic kind of systems we will consider in this work , the mean violation fraction exhibits , at large times , the simple behavior @xmath19 , where @xmath20 is a model - dependent function of @xmath1 which vanishes in the thermodynamic limit as @xmath21 , with @xmath22 a non - universal , model - dependent constant , and @xmath23 , an exponent which depends on the particular form of the protocol . the rest of the paper is organized as follows . in the next section we pose our problem and introduce the main concepts we need to tackle it . in section [ sec : main ] , we prove our main result . later , we study the illustrative case of a linear chain of harmonic oscillators driven at a constant rate by an anharmonic trap in section [ sec : chain ] . we briefly discuss how the strong fluctuations around a continuous phase transition may lead to a failure of the derived scaling law in section [ sec : phase - transition ] . finally , we present some conclusions and future projections of this work in section [ sec : conclusions ] . in order to characterize the local violations of the second law of thermodynamic associated to generic processes occurring in mesoscopic systems , we have to study the zero - crossings properties of the stochastic entropy production @xmath24 . an important quantity is the residence time , which is defined as the amount of time , up to time @xmath2 , that a given stochastic process @xmath25 spends in the semi - space @xmath26 ( or @xmath27 ) . the probability density function ( pdf ) for this quantity is closely related to the persistence , e.g. the probability that the process does not cross the line @xmath28 up to time @xmath2 @xcite , which has been studied in many different contexts . for example , in @xcite it has been used to characterize the ordering dynamics of the ising model ( where the process @xmath25 is the global or local magnetization ) , while in @xcite it has been used to characterize the zero - crossings properties of a diffusing field starting from random initial conditions ( @xmath25 is the value of the diffusing field at a fixed point in space , as a function of time ) . generally speaking , the computation of the full pdf of the residence time for a given stochastic process is a difficult task , even when the process is markovian . in our case , we choose @xmath29 to be a stochastic entropy production ( see definitions below ) which is generally non - markovian even if the system performs markov dynamics . since an exact determination of the full pdf for arbitrary protocols and energy landscapes is out of order , we focus in deriving some general results for the first moment of this pdf , the average violation fraction . this means that the results presented here are expected to be robust upon variations in the hamiltonian of the system , as long as these changes do not affect the main assumptions we use in our derivation , which we now discuss . we consider ergodic , microreversible , and extensive systems driven by a set of external , well controled parameters ( which we denote by @xmath30 ) . we point out that ergodicity and microreversibility ( the latter for the closed system composed by the system under study and its environment ) are minimal conditions for fluctuation relations to hold . on the other hand , in order to guarantee the extensivity of the thermodynamic observables , it is reasonable to assume that the interactions among the different particles in the system are short - ranged . for constant protocols , the system is able to reach a unique steady - state characterized by the pdf @xmath31 $ ] , where @xmath32 denotes a configuration in the phase space . @xmath32 may be a single variable , a vector , or a field as well . we discuss equilibrium and non - equilibrium steady - states ( ness ) on the same footing . furthermore , we assume that the system is initially prepared in the steady - state corresponding to @xmath33 , and for simplicity we assume that the system is connected to a single thermal bath . a more general analysis , considering several reservoirs , will be published elsewhere . we introduce the process @xmath24 as follows @xmath34 which depends on the particular trajectory of the system in the phase - space during its evolution . the time instant @xmath35 should be considered as an arbitrary point inside the interval @xmath18 $ ] , where the violation fraction will be measured . we also remark that @xmath2 can be choosen arbitrarily . for equilibrium steady - states , @xmath24 is the total entropy change , proportional to the dissipated work @xcite @xmath36 , where @xmath37 is the thermodynamic work introduced by jarzynski @xcite , whereas @xmath38 is the free energy and @xmath39 the inverse temperature . to see this , note that for a system with hamiltonian @xmath40 , the thermodynamic work reads @xcite @xmath41 on the other hand , we have that @xmath42 , thus , eq . ( [ proc - entropy ] ) reads in this case : @xmath43\nonumber\\ & \equiv\beta{\mathcal{w}}-\beta\delta f\end{aligned}\ ] ] for ness , @xmath24 corresponds to the dissipation function of hatano and sasa @xcite , which is the correct choice in order to extend the second law of thermodynamics to ness . having clarified the context and the main assumptions we will need in what follows , we proceed now to derive our main result in the next section . let us consider an ergodic , extensive , and microreversible system initially prepared in its steady state corresponding to a value of the control parameters @xmath33 . we should note first that these conditions imply that the system satisfies the ift ( jarzynski @xcite for equilibrium states or hatano - sasa @xcite for ness ) at any time @xmath35 : @xmath44 from eq . ( [ ift ] ) and jensen s inequality , @xmath45 for @xmath46 , we see that the second law of thermodynamics holds in the strict sense , @xmath12 . on the other hand , the mean entropy production rate , @xmath47 , should also be non - negative . thus , @xmath48 is non - decreasing by virtue of the second law of thermodynamics . let us formally introduce the violation fraction as @xmath49 where @xmath50 is the heaviside step function . then , the mean value of this fraction is given by @xmath51 where @xmath52 $ ] . quite generally , we may write @xmath53 $ ] , with @xmath54 a non - decreasing function" +"in the last decade , studies about the structure and dynamics of complex networks have blossomed , thanks in particular to the versatility of the network representation , which has turned out to be adequate for systems as diverse as the internet or social networks . a large body of knowledge about the empirical description of networked systems has thus been accumulated , together with a wealth of modeling techniques ; a good level of understanding of how dynamical processes taking place on networks depend on their structure has been as well reached @xcite . many network studies have been concerned with systems of interest in several scientific areas a priori remote from physics ( social sciences , biology , computer science , epidemiology , ... ) , and they have also reached more traditional fields of statistical physics , such as the study of glassy systems , as we now describe . the many puzzles raised by the glass transition , and in particular the slow dynamics displayed by glassy systems at low temperatures , have been the subject of a large interest in the past decades @xcite . one of the approaches which has led to promising insights consists in the description of the dynamics of a glassy system inside its configuration space . the energy landscape of a glassy system is typically rugged , made of many local minima ( metastable states ) , whose huge number makes it difficult to reach equilibrium . in this framework , the energy landscape is seen as a set of basins of attractions of local minima ( `` traps '' ) , and the system evolves through a succession of harmonic vibrations inside traps and jumps between minima @xcite . this picture has stimulated the definition and study of various simplified models of dynamical evolution between traps , in order to reproduce the phenomenology of glassy dynamics @xcite . on the other hand , several studies have focused on obtaining a better understanding of the structure of these local minima . a way to attain this goal is to perform numerical simulations of small systems , at a fixed temperature , and quenching them at regular time intervals in order to make them reach the nearest local minimum . information is then gathered on the various local minima , and on the sizes of their basins of attraction . various studies have investigated , among other issues , the detailed structure of the potential energy landscape , the substructure of minima , and the properties of energy barriers between minima @xcite . several works have also used the information on the energy landscape to study a master equation for the time evolution of the probability to be in each minimum . the considered systems range from clusters of lennard - jones atoms to proteins or heteropolymers @xcite . an interesting property of the modeling of the energy landscape in terms of a set of traps linked by energy barriers , lies in the possibility to define and study its network representation within the context of network theory . in this representation , each local minimum is associated to a node , and a link is drawn between two nodes whenever it is possible for the system to jump between the basins of attraction of the corresponding minima . the links can then be defined as weighted and directed , as jumps between minima are not equiprobable , and may be easier in one direction than in the other . networks of local minima of the energy landscape have thus been built and studied . these networks have been found to exhibit a small - world character @xcite . the number of links of each node ( its degree ) turns out to be strongly heterogeneous , possibly with scale - free degree distributions , which have been linked to scale - free distributions of the areas of the basins of attraction @xcite . complex network analysis tools have also been used to investigate the structure of energy landscapes of various systems of interest , such as lennard - jones atoms , proteins , or spin glasses , among others @xcite . the energy of a minimum and its degree ( i.e. , the number of other minima which can be reached from this minimum ) have been shown to be correlated , as well as the barriers to overcome to escape from a minimum . in particular , a logarithmic dependence of the energy of a minimum on its degree has been exhibited , as well as energy barriers increasing as a ( small ) power of the degree of a node @xcite . no systematic study of these issues has however been performed , and most investigations have been limited to relatively small systems because of computational limitations . most importantly , the investigations cited above have focused on the topology of the network of minima , conceived as a tool to characterize the energy landscape . the structure of a network has however a deep impact on the properties of the dynamical processes which take place on it @xcite . it seems thus adequate to put to use the tools and techniques developed for the analysis of dynamical processes on networks to achieve a better understanding of how the energy landscape structure , represented as a network , affects the system performing a random walk in it , and how the onset of glassy dynamics can be described in this way in a general framework . in a previous paper @xcite , we have made a first step to fill this gap by focusing on the trap model put forward in ref . @xcite . in this paper , we generalize our approach to more involved transition rates between energy minima . we show how the heterogeneous mean - field ( hmf ) theory @xcite can be used in this context to highlight the connection between the topological properties of the network of minima and the dynamical exploration of these minima . we show in particular that the relationship between energy and degree of the minima is a crucial ingredient for the existence of a transition and the subsequent glassy phenomenology . our results shed light on the empirically found relationship between the energy of a local minimum and its degree , and we hope that they will stimulate more systematic investigations on this issue . we have organized our paper as follows : in section [ sec : model ] we define our model of energy landscape dynamics as a random walk on a complex network . different physical transition rates are proposed , and the corresponding numerical implementation is discussed . in section [ sec : formalism ] we present a theoretical analysis based on the heterogeneous mean - field approximation for dynamical processes on complex networks . this formalism is applied in section [ sec : general - formalism ] , where general analytical approximate expression are presented for the main quantities characterizing the glassy transition and dynamics . these expressions are applied to the different physical transition rates considered in section [ sec : appl - phys - trans ] , where checks against numerical simulations are also presented . in section [ sec : barriers ] we discuss the relation between energy basins and energy barriers . finally , in section [ sec : conclusions ] we present our conclusions . we consider a network of @xmath0 nodes , in which each vertex @xmath1 corresponds to a minimum in the energy landscape , and a link is drawn between two minima @xmath1 and @xmath2 if the system can jump directly from @xmath1 to @xmath2 . to each node @xmath1 is associated the energy @xmath3 of the corresponding minimum ( energies are defined from a reference level , in such a way that @xmath4 for all @xmath1 ) . moreover , an energy gap @xmath5 is associated to the edge between vertices @xmath1 and @xmath2 , as depicted in fig . [ landscape ] : @xmath5 is a symmetric function , such that the energy barrier that must be overcome to jump from vertex @xmath1 to vertex @xmath2 can be written as @xmath6 and , analogously , @xmath7 . obviously , we will have in general @xmath8 . are measured positive downwards . energy gaps @xmath5 are defined positive upwards.,width=340 ] the system under investigation is pictured as a walker exploring the network through a biased random walk . the rate ( probability per unit time ) @xmath9 to go from vertex @xmath1 to vertex @xmath2 depends a priori on the energy at vertices @xmath1 and @xmath2 and/or the energy barrier between @xmath1 and @xmath2 that must be overcome . the random walk model is defined in discrete time @xmath10 as follows : * at time @xmath10 , the walker is in vertex @xmath1 . * it chooses at random a neighbor of @xmath1 , namely @xmath2 . * with a probability @xmath9 , that depends on the energy @xmath11 and/or on the energy barrier @xmath12 , the walker hops to vertex @xmath2 . * time is updated @xmath13 . the relationship between the probabilities @xmath9 and the energy and energy barriers can be of different forms . in usual unbiased random walks , @xmath9 is a constant independent of both @xmath1 and @xmath2 @xcite . as a first step to introduce a dependence on the nodes , a possible approach is that in which the energy barriers depend only on the local minima themselves , i.e. we consider @xmath14 . for example , in the bouchaud trap model considered in ref . @xcite , the probability to exit from a trap is just an arrhenius law depending only on the departing trap s depth , namely @xmath15 where @xmath16 is the inverse temperature and @xmath17 is a constant that determines a global timescale . other possible definitions include the metropolis one @xmath18 and the glauber rate @xmath19 we note that the rates considered in the bouchaud trap model are quite different from the metropolis or glauber rates . indeed , while the former depends only on the depth of the originating trap , the latter depend also on the energy of the arriving vertex . this translates in the fact that , in the limit of zero temperature , the dynamics of the bouchaud trap model is frozen for any @xmath11 , while metropolis and glauber dynamics still allow jumps to lower energy minima @xcite . within an even more realistic representation of glassy dynamics , one can also contemplate the case @xmath20 , allowing for the transition rates to depend explicitly on the energy barriers between adjacent minima . as a paradigm of this choice , we propose a rate of the arrhenius form @xmath21 which acts a straightforward generalization of the local transition rate ( [ eq : rate_traps ] ) . the case of rate ( [ eq : rate_traps ] ) ( local trapping ) was studied in a previous publication @xcite . in the following , we will consider in turn non - local rates ( [ eq : rate_metropolis ] ) , ( [ eq : rate_glauber ] ) and ( [ eq : rate_barriers ] ) and discuss the fundamental differences due to the introduction of energy barriers in the model . we emphasize that our model differs both from usual unbiased random walks , as the local energy determines the transition rates , and from mean - field trap models in which jumps between any pair of energy minima are a priori possible : here , the system can jump only between neighboring nodes . the dynamical evolution depends therefore both on the network topology and on the energies associated to the nodes . to implement numerically the random walk , it is convenient to resort to the techniques developed for general diffusion processes on" diff --git a/benchmarks/inference/mii/prompts/prompts2048.csv b/benchmarks/inference/mii/prompts/prompts2048.csv new file mode 100644 index 000000000..9000918a6 --- /dev/null +++ b/benchmarks/inference/mii/prompts/prompts2048.csv @@ -0,0 +1,12410 @@ +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> dr. goldberg offers everything i look for in a general practitioner. he's nice and easy to talk to without being patronizing; he's always on time in seeing his patients; he's affiliated with a top-notch hospital (nyu) which my parents have explained to me is very important in case something happens and you need surgery; and you can get referrals to see specialists without having to see him first. really, what more do you need? i'm sitting here trying to think of any complaints i have about him, but i'm really drawing a blank.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Unfortunately, the frustration of being Dr. Goldberg's patient is a repeat of the experience I've had with so many other doctors in NYC -- good doctor, terrible staff. It seems that his staff simply never answers the phone. It usually takes 2 hours of repeated calling to get an answer. Who has time for that or wants to deal with it? I have run into this problem with many other doctors and I just don't get it. You have office workers, you have patients with medical needs, why isn't anyone answering the phone? It's incomprehensible and not work the aggravation. It's with regret that I feel that I have to give Dr. Goldberg 2 stars.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Dr. Goldberg has been my doctor for years and I like him. I've found his office to be fairly efficient. Today I actually got to see the doctor a few minutes early! + +He seems very engaged with his patients and his demeanor is friendly, yet authoritative. + +I'm glad to have Dr. Goldberg as my doctor.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Been going to Dr. Goldberg for over 10 years. I think I was one of his 1st patients when he started at MHMG. He's been great over the years and is really all about the big picture. It is because of him, not my now former gyn Dr. Markoff, that I found out I have fibroids. He explores all options with you and is very patient and understanding. He doesn't judge and asks all the right questions. Very thorough and wants to be kept in the loop on every aspect of your medical health and your life.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Got a letter in the mail last week that said Dr. Goldberg is moving to Arizona to take a new position there in June. He will be missed very much. + +I think finding a new doctor in NYC that you actually like might almost be as awful as trying to find a date![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I don't know what Dr. Goldberg was like before moving to Arizona, but let me tell you, STAY AWAY from this doctor and this office. I was going to Dr. Johnson before he left and Goldberg took over when Johnson left. He is not a caring doctor. He is only interested in the co-pay and having you come in for medication refills every month. He will not give refills and could less about patients's financial situations. Trying to get your 90 days mail away pharmacy prescriptions through this guy is a joke. And to make matters even worse, his office staff is incompetent. 90% of the time when you call the office, they'll put you through to a voice mail, that NO ONE ever answers or returns your call. Both my adult children and husband have decided to leave this practice after experiencing such frustration. The entire office has an attitude like they are doing you a favor. Give me a break! Stay away from this doc and the practice. You deserve better and they will not be there when you really need them. I have never felt compelled to write a bad review about anyone until I met this pathetic excuse for a doctor who is all about the money.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Top notch doctor in a top notch practice. Can't say I am surprised when I was referred to him by another doctor who I think is wonderful and because he went to one of the best medical schools in the country. +It is really easy to get an appointment. There is minimal wait to be seen and his bedside manner is great.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Dr. Eric Goldberg is a fantastic doctor who has correctly diagnosed every issue that my wife and I have had. Unlike many of my past doctors, Dr. Goldberg is very accessible and we have been able to schedule appointments with him and his staff very quickly. We are happy to have him in the neighborhood and look forward to being his patients for many years to come.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm writing this review to give you a heads up before you see this Doctor. The office staff and administration are very unprofessional. I left a message with multiple people regarding my bill, and no one ever called me back. I had to hound them to get an answer about my bill. + +Second, and most important, make sure your insurance is going to cover Dr. Goldberg's visits and blood work. He recommended to me that I get a physical, and he knew I was a student because I told him. I got the physical done. Later, I found out my health insurance doesn't pay for preventative visits. I received an $800.00 bill for the blood work. I can't pay for my bill because I'm a student and don't have any cash flow at this current time. I can't believe the Doctor wouldn't give me a heads up to make sure my insurance would cover work that wasn't necessary and was strictly preventative. The office can't do anything to help me cover the bill. In addition, the office staff said the onus is on me to make sure my insurance covers visits. Frustrating situation![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love Dr. Goldberg. Best doctor I've ever had, and I've had a bunch after moving around a lot in the past 25 years. Good listener, friendly & straightforward. Always presents options and takes a ""let's try the least extreme course"" first. Office staff has improved tremendously since Dr. Johnson left. Highest recommendation.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> All the food is great here. But the best thing they have is their wings. Their wings are simply fantastic!! The ""Wet Cajun"" are by the best & most popular. I also like the seasoned salt wings. Wing Night is Monday & Wednesday night, $0.75 whole wings! + +The dining area is nice. Very family friendly! The bar is very nice is well. This place is truly a Yinzer's dream!! ""Pittsburgh Dad"" would love this place n'at!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We checked this place out this past Monday for their wing night. We have heard that their wings are great and decided it was finally time to check it out. Their wings are whole wings and crispy, which is a nice change of pace. I got their wet Cajun sauce and garlic butter wings. The Cajun did not have a bold enough flavor for me and their sauce is too thin. The sauce was also thin for the garlic butter, but that is more expected. They were better than average, but I don't like seeing all the sauce resting at the bottom of the boat. I would definitely come try this place out again to sample some of the other items on the menu, but this will probably not become a regular stop for wings anytime soon.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Wing sauce is like water. Pretty much a lot of butter and some hot sauce (franks red hot maybe). The whole wings are good size and crispy, but for $1 a wing the sauce could be better. The hot and extra hot are about the same flavor/heat. The fish sandwich is good and is a large portion, sides are decent.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Cold cheap beer. Good bar food. Good service. + +Looking for a great Pittsburgh style fish sandwich, this is the place to go. The breading is light, fish is more than plentiful and a good side of home cut fries. + +Good grilled chicken salads or steak. Soup of day is homemade and lots of specials. Great place for lunch or bar snacks and beer.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Decent range somewhat close to the city. The mats are pretty solid; however, the grass range needs to be tended too. It's like hitting out of US Open type rough...not very amenable to practicing. Which kind of defeats the purpose of going to a golf range...Still gets 3 stars because the range is lit up at night which is excellent for those of us who are addicted to this amazing game, but are somewhat short on time (having a job kinda sucks sometimes, no?).[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Owning a driving range inside the city limits is like a license to print money. I don't think I ask much out of a driving range. Decent mats, clean balls and accessible hours. Hell you need even less people now with the advent of the machine that doles out the balls. This place has none of them. It is april and there are no grass tees yet. BTW they opened for the season this week although it has been golfing weather for a month. The mats look like the carpet at my 107 year old aunt Irene's house. Worn and thread bare. Let's talk about the hours. This place is equipped with lights yet they only sell buckets of balls until 730. It is still light out. Finally lets you have the pit to hit into. When I arrived I wasn't sure if this was a driving range or an excavation site for a mastodon or a strip mining operation. There is no grass on the range. Just mud. Makes it a good tool to figure out how far you actually are hitting the ball. Oh, they are cash only also. + +Bottom line, this place sucks. The best hope is that the owner sells it to someone that actually wants to make money and service golfers in Pittsburgh.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place is absolute garbage... Half of the tees are not available, including all the grass tees. It is cash only, and they sell the last bucket at 8, despite having lights. And if you finish even a minute after 8, don't plan on getting a drink. The vending machines are sold out (of course) and they sell drinks inside, but close the drawers at 8 on the dot. There are weeds grown all over the place. I noticed some sort of batting cage, but it looks like those are out of order as well. Someone should buy this place and turn it into what it should be.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Before I finally made it over to this range I heard the same thing from most people - it's just fine to go work on your swing. I had such a low expectation I was pleasantly surprised. + +It's a fairly big range - if you are familiar with Scally's in Moon, it seems like it has almost as many tees, though its not nearly as nice a facility. + +The guys in the pro shop were two of the friendlier guys I've come across at ranges or at courses. Yards were indeed marked and there are some targets to aim for, and even some hazards to aim away from. + +A big red flag to me was the extra charge ($3) to hit off the grass. I am no range expert, but this is the 4th one I've been to and the first I've seen of that sort of nickel and diming.... + +Price for the golf balls was reasonable and I do plan to be back every week until they close up in October for the season. Hopefully, since its for sale, it will reopen as a golf facility again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I drove by yesterday to get a sneak peak. It re-opens on July 14th and I can't wait to take my kids. The new range looks amazing. The entire range appears to be turf, which may or many not help your game, but it looks really nice. The tee boxes look state of the art and the club house looks like something you'll see on a newer course. Can't wait to experience it![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> THANK YOU ROB! i truly appreciated all the help i received from this agent today who was able to removed the extra charges on my bill that the Pasadena Verizon Store on Lake was charging me on my bill for upgrading my phone. When i went in i was having problems with my Blacberry and had to switch to the Iphone last week. Rob from the Pennsylvania store who i was connected today was able to look at my bill and all the notes and correct the problem immediately. Great Customer Service! He even set up a FOLLOW UP Phone Call with me On July 5th to make sure the credit goes through on my bill...I can't thank him enough!!!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> After waiting for almost 30 minutes to trade in an old phone part of the buy back program, our customer service rep incorrectly processed the transaction. This led to us waiting another 30 minutes for him to correct it. Don't visit this store if you want pleasant or good service.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I visited this store several months ago to simply ask about smartphone plans. The agent was pleasant and helpful. I would recommend a visit to this store.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place was DELICIOUS!! My parents saw a recommendation to visit this place from Rick Sebak's ""25 Things I Like About Pittsburgh"" and he's usually pretty accurate. His recommendations were to try the Reuben, Fish Sandwich and Open-Faced Steak Sandwich. We went early afternoon for a late lunch today (a Saturday) and were seated right away. The staff is extremely friendly. My Mom & I each had the fish sandwich, while my Dad & Brother had a Reuben sandwich. The fish was very good, but the Reuben was to die for! Both dishes were massive, and could very easily be shared between two people. On top of being extremely large portions, it was incredibly affordable. The giant fish sandwich was $8 and the giant Reuben was $7.50. Our drinks were always filled and we were checked on several times during the meal. We will definitely be back!!! Oh and a bit of advice ahead of time - they take CASH ONLY. So come prepared, but I'm pretty sure I saw an ATM there as well. And I do believe they are closed on Sundays & Mondays.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Can't miss stop for the best Fish Sandwich in Pittsburgh.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place should have a lot more reviews - but I'm glad it doesn't, they don't need to get any busier. + +Its been there ages, and looks it. If you're all about ambiance, don't bother. If you pretend you're in a movie set in Pittsburgh 30 years ago it works pretty well. The service is sometimes hit or miss. Most of girls are good, one is very slow, one is amazing. They are all friendly and usually a few different people will check in to make sure that you're happy. Everything is made fresh so be prepared that nothing comes flying out of that kitchen - busy times it can take a good while to get food. + +The food is AWESOME! Worth any little complaints I might think up before it gets there. Once its on the table, I forget them all. + +-Fish Sandwiich +-Salmon (huge and delicious) +-Flounder +-Shrimp a few ways (""Norfolk"" style is oily for my taste, and I never had it growing up in Norfolk.) +-Hawkins St Special +-Prime Rib (sized for two, watch it) + +The prices are low, the portions are large, and just about everything on the menu is delicious. I'm not one to pick a place because they give you a lot of food, but if you like a good value and don't want to compromise on taste, this place is a gem.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place was very good. I found out about Emil's when watching a show called ""25 Things I Love About Pittsburgh"" on WQED hosted by Rick Seback. This place ain't a luxurious restaurant...it's a beer & a shot bar / lounge. But the people are friendly & the food is good. I had the fish sandwich which was great. It ain't in a great part of town, Rankin, but I've been in worse places!! Try this place.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Old school.....traditional ""mom 'n pop"" quality and perfection. The best fish and chips you'll ever enjoy and equally superb fried shrimp. A great out of the way, non-corporate, vestige of Americana. You will love it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Seen this restaurant on 25 best places in Pittsburgh with Rick Seback +ack. Went there with my girlfriend she grew up with the owner. She's very nice all employees are super nice service was excellent i had the fish sandwich my girlfriend had the Ruben more than you could possibly eat very reasonable prices. Going back to try the burgers i heard there enormous and very tasty.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Wonderful reuben. Map shown on Yelp page is incorrect. It is actually a different Hawkins. I'd recommend a call for directions 412-271-9911.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Good fish sandwich.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> After a morning of Thrift Store hunting, a friend and I were thinking of lunch, and he suggested Emil's after he'd seen Chris Sebak do a bit on it and had tried it a time or two before, and I had not. He said they had a decent Reuben, but to be prepared to step back in time. + +Well, seeing as how I'm kind of addicted to late 40's and early 50's, and the whole Rat Pack scene, stepping back in time is a welcomed change in da burgh...as long as it doesn't involve 1979, which I can see all around me every day. + +And yet another shot at finding a decent Reuben in da burgh...well, that's like hunting the Holy Grail. So looking under one more bush certainly wouldn't hurt. + +So off we go right at lunchtime in the middle of...where exactly were we? At first I thought we were lost, driving around a handful of very rather dismal looking blocks in what looked like a neighborhood that had been blighted by the building of a highway. And then...AHA! Here it is! And yep, there it was. This little unassuming building with an add-on entrance with what looked like a very old hand painted sign stating quite simply 'Emil's. + +We walked in the front door, and entered another world. Another time, and another place. Oh, and any Big Burrito/Sousa foodies might as well stop reading now. I wouldn't want to see you walk in, roll your eyes and say 'Reaaaaaalllly?' + +This is about as old world bar/lounge/restaurant as it gets. Plain, with a dark wood bar on one side, plain white walls with no yinzer pics, good sturdy chairs and actual white linens on the tables. This is the kind of neighborhood dive that I could see Frank and Dino pulling a few tables together for some poker, a fish sammich, and some cheap scotch. And THAT is exactly what I love. + +Oh...but good food counts too. + +We each had a Reuben, and my friend had a side of fries. The Reubens were decent, but not NY awesome. A little too thick on the bread, but overall, tasty and definitely filling. Not too skimpy on the meat. I seriously CRAVE a true, good NY Reuben, but since I can't afford to travel right now, what I find in da burgh will have to do. But as we sat and ate, burgers came out to an adjoining table. Those were some big thick burgers. A steak went past for the table behind us. That was HUGE! And when we asked about it, the waitress said 'Yeah, it's huge and really good, and he only charges $12.99 for it, ain't that nuts?' Another table of five came in, and wham. Fish sandwiches PILED with breaded fish that looked amazing. Yeah, I want that, that, that and THAT! + +My friend also mentioned that they have a Chicken Parm special one day of the week that is only served UNTIL 4 pm, and that it is fantastic. If only I could GET there on that week day before 4... + +The waitress did a good job, especially since there was quite a growing crowd at lunchtime on a Saturday, and only one of her. She kept up and was very friendly. + +They only have Pepsi products, so I had a brewed iced tea, which was very fresh, and she did pop by to ask about refills as often as she could. As the lunch hour went on, they were getting busy. + +Emil's is no frills, good portions, very reasonable prices, VERY comfortable neighborhood hole in the wall...kind of like Cheers, but in a blue collar neighborhood in the 1950's. Fan-freakin-tastic! I could feel at home here. + +You definitely want to hit Mapquest or plug in your GPS though. I am not sure that I could find it again on my own...it really is a hidden gem. I will be making my friend take me back until I can memorize where the heck it is. + +Addendum: 2nd visit for the fish sandwich. Excellent. Truly. A pound of fish on a fish-shaped bun (as opposed to da burgh's seemingly popular hamburger bun). The fish was flavorful, the batter excellent, and for just $8. This may have been the best fish sandwich I've yet to have in da burgh.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is a hidden gem, no really. It took us forever to find but well worth it. It is right across the street from the Rankin Police Station. The menu has a wide selection, I really couldn't decide what I wanted but I went with the ribeye sandwich. I'm glad i did too. Huge sandwich! I added mushrooms, it was very flavorful. My boyfriend got the fish sandwich, he enjoyed it as well. Fast and friendly service. Will definitely be back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This would be my local haunt, if I were ever to relocate to the Pittsburgh area. What a great little place! Such friendly staff, and some damn good eats! + +It was so great, that we actually went there twice during our 4-day vacation to catch the Steelers/Ravens game. + +They have daily sandwich specials. On Thursday night we went and had the special roast beef and cheese sand., and the .35 cent wings. Very, very tasty. I'm sorry, but this place kicks Primanti Bros. butt on the taste factor. They have about 8 different types of wings... reg., garlic, and I can't remember the rest - we got the regular, and I was wishing we would had ordered more. + +Going back on a Friday night, we ordered the buffalo chicken pizza and a pepperoni n' mushroom. Wow! That buffalo chicken pizza was awesome. + +The other thing that stuck out for me was one of the customers. An older gentleman; he seemed to be a regular. I really, really wanted his SPAM t-shirt.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> A great townie bar with tasty food and an interesting clientele. I went to check this place out on the way home from the airport one Friday night and it didn't disappoint. It is refreshing to walk into a townie bar and not feel like the music stops and everyone in the place is staring at you - I'm guessing the mixed crowd of older hockey fans, young men in collared shirts, and thirtysomethings have probably seen it all during their time at this place. + +The staff was top notch - the orders were somewhat overwhelming as they appeared short-staffed for the night, but my waitress tried to keep a positive attitude for my entire visit. The other waiter was wearing a hooded cardigan, and I wanted to steal it from him due to my difficulty in finding such a quality article of clothing. + +We ordered a white pizza - large in size, engulfed in cheese, full of garlic flavor, flavorful hot sausage. An overall delicious pizza, aside from 2 things: 1, way too much grease (I know this comes with the territory, but still, it is sometimes unbearable); 2, CANNED MUSHROOMS - the worst thing to come out of a can. Ever. I would rather eat canned Alpo than canned mushrooms. And if the mushrooms weren't canned, they were just the worst mushrooms I've ever consumed. The mushroom debacle is enough to lower the review by an entire star - disgusting! + +My advice for the place is keep everything awesome - random music from the jukebox, tasty food, great prices, good crowd and staff - and get some decent mushrooms; why they spoil an otherwise above average pie with such inferior crap, I'll never know.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Alexion's has been around forever. The first time I went in there, I was 19 years old on summer break from college and working at the ice cream factory up the hill. All of the union guys from the ice cream factory went in there after work, and I immediately found out why. MANY, MANY years later, I stopped in there with some fond memories, and once again felt welcomed and valued as a customer, even though they didn't know who I was. THE SANDWICHES are done Pittsburgh-style, sort of like Primanti's, and they are as perfect today as they were back in ancient times when I first started visiting the place. Alexion's is a clean and peaceful little place in the Rook Station part of Green Tree, the oldest part of the town. I recall that some of the sandwiches I got there were ordered at a pretty late hour. Nothing but good things to say about the place, and I wish it was closer to home![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Good for cheap drinks and wings, they offer daily specials which is nice. + +Doesnt look like much from outside but the inside is friendly enough, the bartenders have been there for awhile and do a good job. Dont expect to have a HUGE selection of alcohol. + +Their wings are good as are their salads. If you are gluten free this is not your place...lots of fried food and sandwiches. +Offers a quick lunch.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> What a cool bar/restaurant.. I will no doubt be visiting again. The service and prices were great.. and the restrooms were clean. I had the buffalo chicken sandwich and it was delicious. The menu consists of typical bar food food, however; theres a few different items on there which stand out on the menu.. + +A cool bar off the beaten path that is a worth a trip. + +Cheers ! ![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Awesome drink specials during happy hour. Fantastic wings that are crispy and delicious, wing night on Tuesday and Thursday![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Good beer selection. Understaffed for a light Monday night crowd, it wasn't her fault she was the only server. But it took about an hour to get our sandwiches. Mine was one of the best reubens I've ever had.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Grew up near here. the family would always go once a month. Haven't stopped in for a few years until last Friday with a few friends to grab a drink. The sandwiches are always amazing just as I remember. The staff is amazing and friendly. Great place for lunch as well.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Very disappointed in the customer service. We ordered Reuben's and wanted coleslaw instead of kraut. They charged us $3.00 for the coleslaw. We will not be back . The iced tea is also terrible tasting.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Let there be no question: Alexions owns the best cheeseburger in the region and they have now for decades. Try a burger on Italian bread. The service is flawlessly friendly, the food is amazing, and the wings? Oh the wings... but it's still about the cheeseburger. The atmosphere is inviting, but you can't eat atmosphere... so go right now. Grab the car keys... you know you're hungry for an amazing cheeseburger, maybe some wings, and a cold beer! Easily, hands down, the best bar and grill in Pittsburgh.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The sandwiches, the wings, enough said. Alexions can best be described as a home-style Primantis before they went mega commercial. You really can't go wrong, but for my money, I would put Alexions fish sandwich up with the best I've had. That's not to take away from other selections, but if you come here I recommend not leaving until you've had either the fish sandwich, Reuben, or wings. + +You'll know you're in a Pittsburgh bar when you walk in. For someone who lives in Atlanta now and only makes it to Pittsburgh a few times a year, I have to say it is refreshing. Feels like home. I haven't had a trip back without making it out to Alexions at least once.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We met a couple of friends there on a Friday afternoon about 440 pm, based on the Yelp reviews. I've relied on Yelp in over a dozen different cities, never came away with anything less than a positive experience until today. + +We ordered within 5 minutes of sitting down, there couldn't have been more than 20 people in the place, counting the people on the patio. Took them almost 40 minutes to serve 3 sandwiches and a salad. I tried the fish sandwich, came out fried extra crispy on the ends, if there is such a thing as fish jerky a third of the sandwich would have qualified, it was just ok. I've had better at almost any church that fries fish during Lent. + +All 3 of my dinner companions left partial sandwiches or salad uneaten. Bread french fries and onion rings were good though. Iced tea was good, though I've never seen a place dispense sweet n low like they were giving away their last rock of crack. Asked for sugar but never saw any, they don't carry any other artificial sweeteners besides the pink stuff. + +I may give the place another try in the future for a Reuben or hamburger, assuming today was some aberration possibly due to a cook having a family emergency or something like that. Waitress was pretty good, held up under my multiple requests to find out if they caught my fish yet, hardly ever rolled her eyes :)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Used to go there for tires, brakes, etc. Their prices have gone way up-$400 for 4 mid-level tires for a Toyota. Plus, 1 of the new tires went flat within 3 weeks. Since they don""t make appointments, the wait to get the tire looked at was ~2 hours. Sorry--can't wait that long to get a warranted repair, They lost my business for good.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I got 'new' tires from them and within two weeks got a flat. I took my car to a local mechanic to see if i could get the hole patched, but they said the reason I had a flat was because the previous patch had blown - WAIT, WHAT? I just got the tire and never needed to have it patched? This was supposed to be a new tire. +I took the tire over to Flynn's and they told me that someone punctured my tire, then tried to patch it. So there are resentful tire slashers? I find that very unlikely. After arguing with the guy and telling him that his logic was far fetched he said he'd give me a new tire ""this time"". +I will never go back to Flynn's b/c of the way this guy treated me and the simple fact that they gave me a used tire![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Terrible. Preordered my tires and when I arrived they couldn't find the order anywhere. Once we got through that process I waited over 2 hours for them to be put on... I was originally told it would take 30 mins. Slow, over priced, I'll go elsewhere next time.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Contrary to other reviews, I have zero complaints about the service or the prices. I have been getting tire service here for the past 5 years now, and compared to my experience with places like Pep Boys, these guys are experienced and know what they're doing. +Also, this is one place that I do not feel like I am being taken advantage of, just because of my gender. Other auto mechanics have been notorious for capitalizing on my ignorance of cars, and have sucked my bank account dry. But here, my service and road coverage has all been well explained - and let up to me to decide. +And they just renovated the waiting room. It looks a lot better than it did in previous years.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Last summer I had an appointment to get new tires and had to wait a super long time. I also went in this week for them to fix a minor problem with a tire they put on. They ""fixed"" it for free, and the very next morning I had the same issue. I called to complain, and the ""manager"" didn't even apologize!!! So frustrated. Never going back. They seem overpriced, too.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Most random location for a mini golf course ever. This is old school. It's built into the woods (spray yourself for bugs first) right off Forsythe Rd near Carnegie Park. The candy hut is fun to spend your spare change. They recently re-carpeted the holes and added a few gimmicks that weren't there before. It won't knock your socks off, but if you're local, give it a try![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This quaint mini golf course is one of the oldest, yet most original and fun locations that I have yet visited. Coming from Texas, it was nice to see a course located amongst the hilly and woody Pennsylvanian terrain. It can be frustrating that it is literally impossible to make a hole-in-one on most every hole and that the course also makes it extremely difficult to predict the direction on how the ball will follow through and bounce. The cartoon-like outrageousness of the course proved to give laughs and a fun attempt to play. Improvements were being made and I will look forward to returning on my next visit to the Pittsburgh area. I enjoy traveling and visiting new courses and the only reason why I didn't give this location 5 stars is because it was impossible to intuitively shoot the ball for a best effort to beat par.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I think this place is closed. Their number is out of service, sign is gone and the course has not been maintained. Awesome woodsy mess of a course though![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've been informed by a fellow Yelper that they are just closed for the season, I hope they're right! I find it strange they don't keep their phone number in service with a recording and that they didn't cover the course up to protect it from weather, vandalism, etc. Either way, I can't wait to get my game on in the spring![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Don't waste your time. We had two different people come to our house to give us estimates for a deck (one of them the OWNER). Both times, we never heard from them. Not a call, not the estimate, nothing.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I will start by saying we have a nice new deck. That is where the good part ends. + +Why two stars if we have a nice deck now? Well, it all started in May when we had a man named Al come out and talk to us about the process. He was a true salesman, I'll tell you that. Not a straight shooter, but an excited salesman that wanted to sell... And we bought into it. + +He told us they were backed up with the harsh winter and a lot of jobs, but they could probably start by June 24th. Mind you, this was the end of May we met with him. He said they would have to do a survey of our land and get a permit from Dormont before they started. We felt confident in going with them, and booked it. + +Here's where things fell apart. Weeks went by with no word from them on the process. Finally I called and left messages. Al finally got in touch with me and the conversation was utterly confusing. He must have not understood me because he just kept talking in circles. So I hung up not knowing what was going on. Finally I called back and the admin told me that the survey could take a couple weeks to come back. I wish Al would have told us that. + +So our June 24th date came and went. We finally got our survey. And they were quick to bill us for it, but no word on where we were in the process. I called back a couple times with no real answers from the admin. Apparently they were now waiting for the permit from Dormont. + +A month later, I was frustrated and asked to speak with someone at the company. I spoke with someone who told me that Dormont usually takes a week to process the permit, but we were now going on a month. He told me he would bug the guy about it and we finally got it. + +I completely understand that waiting on the permit is not their fault, but why no communication about it? Just call me and tell me they're waiting for the permit, but they'll work towards asking Dormont what the hold up is. Seems simple. + +Finally we get the permit and work is supposed to start. Tuesday comes and they have to wait for approval from Dormont on holes they're digging. So holes are dug and equipment is put in my backyard and then nothing happens for two days. Where did everyone go? Who knows, because I wasn't informed! + +I was upset and contacted the company owner, Dave, by email. I told him how frustrated I was about the lack of communication. He wrote me two sentences that said ""there will be acres there tomorrow morning to finish and most will be done tomorrow."" Well, that didn't happen. + +Then two other dudes show up two days later and did work for about three hours and left. The main guy comes back the next day and says they did it wrong. So apparently the part about how they wouldn't need access to my house changes to they're drilling bolts into my house to secure he deck. + +Finally, the second week into construction, my tiny 10x11 foot deck is done. It was upsetting that they left the deck dirty, and all the dirt and cement they moved around wasn't cleaned up. I even asked them to fill all the holes they dug up and didn't use, and they only filled up one. When you create a construction project, isn't it just good business to clean it up and make it look nice? Didn't happen here. + +My main point is, contractors have a reputation for not being the most trustworthy. Why be that company? Why not be an upstanding company that consumers can trust? My main issues with them were that things were not communicated to me properly up front, nor was the ongoing process communicated to me. Then they left everything unfinished in my eyes, leaving the site dirty. I understand things happen and things get delayed, but just email or call me. It's not that hard to keep me updated, it is 2014 with a million ways to be contacted. + +Even though I have a nice deck (after I clean things up myself!), I would not recommend them to anyone.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> When I wanted a deck for the back of my home I ended up calling Quaker State Construction. It ended up working very well and they were very polite. I got an estimate and called them to start working out the details of my new deck. Once we got the plans all sorted out they started building my new deck and it was finished with in a reasonable amount of time. I now have a beautiful deck that I can relax and that my family can enjoy. Overall, they did a good job and I would use them in the future for all my deck necessities.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have never seen a restaurant that has a frowning brownie (a.k.a. Frownie) as their icon, mascot, or spokesperson. King's Family Restaurant has surprised me with this. I think it might be in direct dialogue with Eat N' Parks smiling cookie -- funny (funny odd, not funny ha-ha). We were seated rather quickly by the manager. Very nice people work here, I was happy to find that even though they had closed a section, the server was willing to stay longer to serve us our dinner. + +We chatted with the server a little bit -- she was quite engaging -- and then moved on to order our meal: + +Tea +Pepsi +Open-faced Hot Turkey Sandwich with mashed potatoes and gravy +Buffalo Chicken strips with mashed potatoes and macaroni n' cheese + +Our drinks arrived and our server conversed with us some more about the area. She would leave every couple of minutes to check on our food and to make certain that her other tables had everything they needed. Eventually, our entrees arrived -- both piping hot. I went straight for the macaroni and cheese. It didn't taste bad, but I swear that it is made by Stouffers. I didn't feel the need to eat that much knowing that there were other things to eat. I tried the mashed potatoes and found that they too came from a package; but, again, they didn't taste bad with the brown gravy. I moved on to the main part of my meal -- the buffalo chicken strips. At least they were all white meat and the buffalo sauce was more than just mild. I contented myself with eating them. + +I tried some of the hot turkey sandwich and just left the rest for my friend since it was not fresh cut turkey but instead luncheon meat that had been heated. I finished off my dinner and was happy in the end. No, it wasn't the best food in the world, but the service greatly helped the perception and it didn't taste bad.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> So... back in the late 90s, there used to be this super-kick-ass cinnamon ice cream, like an apple pie ice cream without the apples or the pie crust. SO DELICIOUS! + +However, NOW there is some shit-tastic replacement that tastes like vanilla ice cream with last year's red-hot in the middle: totally gross. Fortunately, our server was nice enough to warn me about the change and bring me a sample, so I only had to suffer the death of a childhood memory rather than also having to pay for it. + +The portions are big and filling, just don't come for the ice cream.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Ive pretty much been eating at various Kings' pretty regularly since I was a child when my parents would take my sister and I into the Fox Chapel location often. Lately me and my girl have been visiting the Heidelburg location. I love the food, it really tastes homemade, much like something a grandmother would make, complete with gobs of butter and side dishes. Prices are low, selection is great, but dont expect fine dining by any means. + +Service is hit or miss at pretty much all of them; if you have lunch at any Kings, you will likely be waited on by a sweet but sarcastic older lady who has been doing the waiting thing for 30 years and knows her game. Seek out this lady. My experience with the younger crowd at night isnt the same. + +Im in my 30s now, and very little has changed, other than the Fox Chapel location was remodeled about 10 years ago to look less like a diner, which was a big fail. Any girl I meet has to enjoy Kings or she's out.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Hoofah.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I heart King's. I've always been a fan and this one was as good as my old one in Monaca.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I arrived around 10 am on a Saturday morning. I was greeted by the hostess,who was polite and friendly, and I informed her that I was alone. She had just arrived, as well, and wasn't exactly sure what was going on yet, so she asked (the manager?) where she should seat me. After receiving guidance, she brought me to a table towards the back. It had not yet been cleaned after the previous guests had dined. So, she quickly got it cleared off, grabbed a rag, and wiped it down. + +The waitress came rather quickly to take my drink order. She was extremely friendly. I ordered coffee and water, which she went and got while I looked over the menu. She returned, and took my order. I ordered the Cinnamon Swirl French Toast Special - Three slices of French toast made with Pittsburgh's own Jenny Lee® Cinnamon Swirl, two farm-fresh eggs, with bacon or sausage (I chose sausage), and your choice of potato (I went with the cheesy hash brown casserole). I also added an orange juice. She went and put my order in, while I waited, and came back with it after not too long. The eggs were cooked exactly how I wanted them, the cheesy hash brown casserole and the french toast were both delicious. I also enjoyed the sausage which was pretty typical. + +Kings Family Restaurant featured a very friendly staff, great prices, and tasty food. I am pleased and will definitely come back again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> thisis not the closest Kings to us, but we often will travel the extra miles because the service and food at this location is always the best.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Average run of the mill store. Associates are young teens and they really don't know where anything is. Luckily I am able to get around to find everything. Found my puppy treats and moved on.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Not bad for a Shop N Save, most are privately owned, so availability of items might differ from place to place. The only time I frequent S n S is when the have their huge two day sales usually held on Thursday and Friday at least once month. + +Good bakery at this location too.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Two meals, on the recommendation of a friend who lives near the place, and after the second trip, I was compelled to write. 'Rocky' would definitely describe the experiences. + +On the first trip, I went to try their (at that time)raved about Reuben. And YET to find a true good Reuben in da burgh, I tried it. + +Well, they were out of the proper bread, and the guy had to run to the store to buy the closest thing he could find, which was not the proper bread, and instead of one of their 'raved about' Reubens, I received two mini-Reubens, which basically took the guts from one Reuben, and spread it out onto two sandwiches on regular sized bread. I ate it. It wasn't great, but they swore it was because they'd run out of the bread. Bread or not, it still wasn't great. The atmosphere was pleasant in that 'blue collar bar' kind of way, and the staff was very nice, but not a winning pitch on the Reuben. + +The second trip was after a long day of moving furniture with the same friend. Sat in the back room, instead of the bar, which felt more like a restaurant, of course, with the big screen TV covering the sports of the moment. + +I was in the mood for dinner this time, and after a scan, decided on fried chicken and mashed potatoes with the salad bar. My friend ordered one of her faves, the breaded pork chops. + +We hit the salad bar, which was uber-basic. Three soups (mostly vegetable loaded, which left me out), basic iceberg lettuce mix (very probably out of a bag), a few veggie toppings, and three or four dressings. It was a basic salad, no big deal. More or less an appetizer filler before the meal. + +The mind-blower in this trip was the ordering of the fried chicken dinner. Our waiter looked like a 19 year old gas station attendant, skinny little blonde guy with a sweet but incredibly naive face, and an air of vapidity, which was confirmed when I placed my order. I asked what chicken pieces came in the dinner, and asked if it was possible to only get dark meat. I never imagined how confusing a question that could possibly be. It literally took him two trips back to the kitchen to 'ask', and the child honestly had no clue what 'white meat' and 'dark meat' meant. The first answer he came back with was that the chicken came in a pre-portioned prepared bag, kind of Kentucky Fried Chicken style...which didn't answer my question, thus prompting the second trip. + +After the second trip back I heard the cook holler 'Tell him I'll fix him up'. + +Well, the chicken was prepackaged dreck like you'd find in the freezer case of Walmart, tiny and not good, and the potatoes had that slight tinge of chem-spuds flavor, laden with some kind of chopped up green (parsley?), and a side of that basic brown gravy served up in 5 gallon buckets. + +Thank goodness for the basic salad bar. + +Even my friend admitted that her pork chops were different and not what she'd expected. They also appeared to be from a freezer bag. + +The irony was that the boy who didn't know white meat from dark meat, was chatting with some other customers...about baseball...and he was a genius about the mindless sport of baseball. Ahhhh da burgh. + +Third base? Nah...why bother when there are so many other options around. Go on in a grab a beer and chat black and gold if you happen to be in Carnegie...they can help you out all types of ways in that area. Just don't go hungry if you actually have tastebuds. + +From what I understand it 'used to be' really good homecooked food. But apparently, mama has left the kitchen.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> everything was great![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> If you are searching for a go to fish place for Lent....look no further. This place will give you the best fish sandwich in Pittsburgh. The sandwich has enough fish to make four sandwiches. You will not be able to finish this sandwich in one seating. +Enjoy....[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Rocky's has been in business since the 1980s and still going strong. Their food is good. Not haute cuisine, pretentious! Everyday, well prepared and taste bud pleasing home style cooking. I've mostly gone during supper hours and and ate in the dining room, but, today I introduced an old friend to ""linner"" in the bar. +He ordered the large version of fish sandwich. Rocky's is famous for their fish. Three large breaded and fried fish filets, bun and fries for under $10. Needless to say, he had no complaints and brought home more than he ate. +I ordered the meatball grill. It was delish. Served on thick cut Italian bread and made ""grilled cheese"" (mozzarella) style. Meatballs and tomato sauce are both good! Also, served with fries. I brought home half the sandwich. +Another good meal there. Friends, mother, and former boss all enjoy their food![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Italian dinners, American, endless soup and salad bar is great. Most food for your dollar. I highly recommend. Great bar. Good place to watch a game. The bar can get quite noisy in the evenings, but it adds to the great atmosphere at Rocky's[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> If you want a true understanding of Pittsburgh in the morning, come here. This greasy spoon is always packed, and is one of the better of its kind south of the city. + +They serve waffles in halves, which is great. The eggs and toast are good, the homemade hot sausage is excellent. The drawback are the barely cooked potatoes. + +If you're hungry, get ""The Mixed Grill""... Gab and Eat's brand of the ""kitchen sink"" breakfast that all Midwest places are about.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Good Luck getting a seat, that's all I have to say. The Gab and Eat is famous and infamous. Diner food is what's up and I like it. When I was a roofing mechanic, we'd meet there before work. Although I'm not sure I would recommend it if you're working were there's no bathrooms. hehe[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Stick to basics and this is the best place in or around the 'burgh. First time go with a friend and sit at the counter. Short order cooking at it's best, it's like a floor show with the actor's backs to you. Breakfast has no losers. Eggs, omelets, pancakes, waffles, breakfast sandwiches to order, the ever popular mixed grill, get a 1/2 Louie instead of home fries (although they good as is) and don't forget the italian toast. + +Frequently voted the best burger in Pittsburgh for a reason. As for ambiance, well lets just say I don't think there are two matching plates or coffee mugs in the joint. But the coffee's good and hot and refreshed often as the service is good, andlocal with many long time folks working here. If I don't get there for awhile I need to go through detox because I feel too healthy.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The biggest breakfast in Pittsburgh, as far as I can tell - and delicious and cheap too. I ordered some mix of eggs, bacon and pancakes - and got 2 dinner-sized plates, one loaded with pancakes and the other stuffed with eggs, bacon, and home fries. Oh, and a side of toast. For under $5, if I recall. + +HUGE portions, all well-executed; as good as DeLuca's. + +I've not had anything besides breakfast, so can't comment on the burger or anything else. + +Cramped quarters, and you'll have to wait, but when nothing but monster morning food will do, this is the destination.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Cheap, unpretentious, and, for this, one of my favorite breakfast joints in the country. Simply put I LOVE it here. The mixed grill, the sausage and egg on a biscuit, the home fries. This it the very definition of diner. Thank you Gab 'n' Eat![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Okay, let's first set expectations. This place is a true DIVE...this is not for the NYC foodie crowd. If you want a down home, large portion awesome breakfast, this is the place. The place is packed with happy diners, the server was very friendly in a busy grandma kind of way. The best part - they have ""dippy"" eggs on the menu and define the degree of dippy you can order. For anyone who has never heard of a ""dippy"" egg - this means sunny side up or over medium where the eggs are still runny and you can dip your bread in them. The eggs were great - I ordered mine over medium, the breakfast potatoes were fab - no complicated additives like peppers or onions - just plain good potatoes cooked in fat - the best part - the fresh Italian bread. YUM!!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I miss this place. When I return home to pittsburgh this is always a must to ease myself into a saturday morning recovery after getting banged up on cheap south side cocktails the night before. When I think of pittsburgh, I remember cutting morning classes in highschool just to get after the best bacon egg and cheese i know of. Honestly i live in nyc where you can get a bacon egg and cheese on every single corner, and nowhere that i have been does it as well as this joint. Go here and you will be happy you did.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've lived in Pittsburgh for 6 years, and in Carnegie for over 2 years, and by far, this is the best greasy spoon joint I've found. If you can stomach the wait (no reservations, naturally), you'll enjoy overflowing plates of goodness, thanks to the well-seasoned griddle where all of the food is made. + +Here are the highlights: + +-Cheap: Breakfast for two can be well under $10, with lunch around the same. +-Crowded: Get there early and expect to wait. They close pretty early on the weekends too (oddly, at 12:45pm) +-Cash only +-Huge portions: When ordering fries or homefries, always get the half order, unless you're a lumberjack +-About those homefries: They're often undercooked. I've had better, believe me. My favorite things to eat in life are potato products. +-My favorite item: hot sausage sandwich on thick Italian toast, with cheese, lettuce, tomato and mayo[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Love this place. Never had a bad meal. Good portions and great people. Be ready to stand in line.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My favorite breakfast place. Have good sandwiches also. Stopped again for Bfast and had the mixed grill--get the small portion unless you are a real MAN! Mixed grill has sausage, (could it be Ricci's?), eggs, onions, and home fries, soooo goooooooood! Use Mancini's bread for toast, got the raisin toast - Yum. + +Have had many other items and just love the food. If you like to watch a true cook, sit at the counter. Banter with the cook and staff and patrons is fun! + +Lunch is good, sausage sandwich, hamburgers and other lunch meats fried on the grill. + +Gets busy for Bfast so you may have to wait. + +Remember it is a diner. Don't expect fancy decor.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Definitely a greasy spoon! Always packed here and always a wait but worth it. The omelets are really tastey especially with their homemade sausage. I also like the mixed grill. My parents love their burgers. Took off a star for lumpy booths and really tight tables (your arm gets hit when someone walks past) oh and waitresses aren't very attentive.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> If you're looking for no frills but a great breakfast this is the place. I got the mixed grill half portion and was very full. Make sure you have extra calories for the day because they are not afraid to use butter. Loved the breakfast and would go back. Not much room for sitting down but worth the wait.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great homemade hot breakfast sausage and a wonderful family restaurant feel. + +Reminds me of the one my parents used to own in Mi. + +Have fun finding a table on the weekend :)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great breakfast place. Come hungry. Look for Dick, my dad, and Gino at the counter every a.m. about 0830 and say hi. Try the mixed grill (half).[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> OK, what is with all of these ""CASH ONLY"" places in Pittsburgh? I can appreciate that some smaller businesses might have trouble installing a credit card system in their store/resturant, but could you perhaps provide an ATM? In the past, this would deter me from eating at this place. + +Looking at a standard breakfast menu, I decided to go with a tuna melt instead. What I got was a cold tuna salad sandwich with a slice of cheese on toast. I had ordered a melt being in the mood for a warm meal, but to no avail. One day later I can't even remember what my side was. I suppose it didn't leave much of an impression on me. I have to say that the dessert was really good! The cherry pecan pie! I have not seen this concoction anywhere else but this was awesome! The cherries were not the sweet canned variety, but a pie worthy tart topped with sugar. I think I want to make this pie with my parents next harvest of our cherry tree! + +My first impression is ""Eh."" I am learning how crazy Pittsburghers are over breakfast! Seriously, waiting 30 minutes for a table at a tiny diner with a menu that reads as follows: + +""2 eggs and toast $x.xx"" +""2 eggs, meat, and toast $x.xx"" +""2 eggs and pancake $x.xx"" + +I'd rather go to a Denny's and order the ""create your own Grand Slam!""[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> BEST DINER IN THE COUNRTY!!! We've been to many famous diners across the country and we still give Gab and Eat the best rating !! I was a little intimidated when I first walked in and there was like 2 pounds of butter just sitting on top of the homefires on the grill. If you are looking for a healthy breakfast they probably can accomodate you, but Everything I ate was clearly the opposite of healthy. After trying like every meal they have I would recommend the mix grill(half unless you are sharing) adding cajun seasoning with the texas toast. Burgers are great too. + +It's hard to find a place that makes a better breakfast than you could make by yourself at home, but this place does it. The atmosphere is classy, old school Americana.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Best French toast ever!! Love the friendly atmosphere, and especially the breakfast. Never been disappointed. You have to try French toast with raisin bread too... yummy![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great Diner! Their breakfast is the best in the area! Lots of choices and always good. Love the unique mugs they use for coffee and all the writing on the wall. Get there early otherwise you will not get a seat! They have homemade hot/sweet sausage and texas toast.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Readers of my reviews may recall that I once referred to The Dor-Stop as possibly the best breakfast in Pittsburgh. Well, faithful followers, I must now admit that The Dor-Stop has now been verified as only one of the best. Why? That's because Gab and Eat I have now found to be THE best breakfast I've ever had. If it was closer to my home I would quickly become a regular. + +I easily decided to order the Mixed Grill (Half). Before I go on, I must ask...has anyone seen a full order? Because I honestly can't imagine how much food that is. I created my own with bacon, cheese, eggs and potatoes. Based on reviews I also opted to get a side of the sausage and was pleased as punch when our waitress asked if I wanted hot or sweet....or one of each. I like variety, so I jumped on the change to try both. I also selected the Italian toast - what other kind is there, really? + +When my food arrived, it looked delicious. There was so much bacon that after eating half of my Mixed Grill it looked like I'd barely started. The sausage was great, just don't ask me which one I liked best. My toast? 4 thick slices that looked to be about half the loaf and were buttered on both sides. It was a struggle, but I was determined to enjoy every tasty morsel and not leave a crumb. + +In case anyone is wondering, yes, they use real butter. I saw pounds of it stacked in the kitchen with my own two eyes. The wait staff was quick and efficient as well as helpful and friendly with our larger group of 9 people. The fact that none of the plates match and I noticed a sign at the front register that said, ""We need mugs"" just makes me love this place even more. + +A few tips: 1.) Order the Mixed Grill. 2.) Cash only! 3.) Gab and Eat is a popular place but also very small and narrow (or cozy if you will). I recommend going during the week when they are still busy but can accomodate a group. That way you won't feel rushed or crowded. 4.) Get to Gab and Eat ASAP! You'll be glad you did![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Classic breakfast joint. Grimy looking hole in the wall located on one end of a seedy looking strip mall. Window is opaque due to the grease so you can't hardly see inside. On the outside, there are about a dozen people waiting to get in. When you finally do get inside, you see that there are 15 tables and a counter, all occupied by people from all walks of life. + +What's the attraction behind this flea hole? The FOOD! Lots of it and dirt cheap. I sat at a vacant stool behind the formica counter and ordered the mixed grill. Potatoes, eggs, sausage, bacon and Italian toast. A giant mound of food guaranteed to sooth any hangover. I swear the full mixed grill had two pounds of food. Neat thing is that the grill is right in front of you so you can see your potatoes and eggs frying in a pool of fresh grease. All that food, plus coffee and tip for around ten bucks. Cash only, so put that plastic away. + +Only bad thing that could happen is some douche bag from the Food Network or Travel Channel will make this place famous, and then I'll never be able to get in.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Yum - freaking - me! + +As the other fellower yelpers mentioned - this place is a cash only. A couple of recommendations: + +- Don't eat early in the week +- I don't recommend wearing any tight clothing (no skinny jeans) - you will not be skinny when you leave + + + I walked in for breakfast one early weekday AM. The place was packed with locals and regulars. A very good sign. + +My co-worker recommended I get the mixed grill. I ordered the large mix grill. My waitress tried to warn me - it is large (very large). I ended up eating the left-overs for the next 2 days. + +Food - + +The Mixed Grill comprises their homemade sausage, grilled onions, grilled peppers, potatoes, fried eggs. + +Portion - + +This should have been a man vs food episode. I was not going to attempt to eat all the food. It was really good. + +Service - + +My waitress looks as if she had been working there for years. She was fast, friendly, and offered good advice. + +Price - + +The cost ranges $5 - 10. + + +I will definitely go back after I buy some new stretchy pants.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Best breakfast spot in the area, If you like diner food it is the place to go. Small, so you will want to avoid the church crowd on Sundays, but the wait is never too long. Everyone is friendly and has obviously been working there for a while. If you are feeling like lunch food go a little later, their burgers are made on the breakfast griddle and are delicious.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great breakfast, good price. You might have to stand outside in line though, so I don't really recommend winter time to go. lol. Very friendly service, interesting coffee mugs. They have great deserts and such also. Bring your cash though as they dont' take cards.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I always love a good diner. Gab and Eat was just what we were looking for on a Saturday morning. Good food. Great people. Pittsburgh ambiance. + +This place is obviously a beloved neighborhood gem. I had french toast and bacon. The french toast was made with the best Italian bread. My fiance had what they called a 'mixed grill."" It consisted of eggs, peppers, onions and home made sausage. Not something you would eat everyday, but he loved it! They also had great coffee. They actually ground up the beans in front of us. Now that's fresh. + +We want to return sometime for ""turkey day."" Apparently they made fresh turkey every Tuesday. Now that sounds good! + +Can't wait to return.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is exactly what a breakfast place should be like--comfortable, quirky, unpretentious and with inexpensive, large portioned working class breakfast plates.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> On our current road trip of baseball, brews, hockey and diners, we decided to try Gab & Eat based on yelpers rating putting it #1 for breakfast in Pittsburgh area. We have to agree with most other reviewers that this is a place to eat. +We arrived around noon on Saturday and were happy there were a couple open tables. The place is tucked at the end of a strip mall and you have to look to find it. There is plenty of parking. +Inside the decor is quaint and funky at the same time. Country style decorations and signs are mixed with nostalgia signs & posters. Most interesting are all the signatures and comments written on the wall by past customers. We regretted not having a marker to add ours. The other highlight was three large white boards with trivia questions - fun way to spend time waiting for food. +The waitstaff there is...uh, experienced. They are attentive, pleasant and efficient. +After reading reviews I had to try the Mixed Grill. But S went with pancakes with a side of bacon. The pancakes were outstanding...maybe the best either of us has eaten. They were thick but with light texture and rich flavor. +His bacon was cooked just as requested - as crisp as possible - and very flavorful. +The Mixed Grill is a mixed together concoction of eggs, potatoes, onions, peppers, cheese, and spicy Italian sausage grilled together. I'm glad I heeded those who stressed going with the half size order. It filled a full sized dinner plate with a heaping order. I couldn't finish it all and that's rare. How do they serve the whole potion -- in a trough? +Everything was cooked well. The sausage added a nice bite to offset the somewhat plain potatoes. You can build your own mix but the basic was a good mix. +My only complaint was the amount of potato and that they are pretty plain. I like home fries with lots of seasoning that have aged on the grill. These potatoes were pretty uniform chunks with little seasoning. Personal preference. +It usually comes with Italian toast but they were out so I went with raisin. It was delicious soft inch thick slices. +Coffee was excellent and the cup stayed full. The total was less than $15. Fabulous value for the quality and portions. +While I can't say it's the best breakfast in Pittsburgh (only here 3 days), its the best so far and one of the best we've had.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Met my nephew for lunch in Carnegie and he suggested Gab & Eat. Way to go Justin! The restaurant is in a strip mall across from the Dairy Queen. The grill is right up front so you can see them cooking. They have counter space for eating and tables/booths for 4. Don't expect to sit at one table if you have more than 4. They have a great looking breakfast menu. We all got burgers of varying kinds! They were tasty! The buns were buttered, toasted and soft. Yum! the amount of butter didnt bother me but it did my whiny mother. Who whined even though there is a no whining sign as you walk in the door. We ordered fresh cut fries as onion rings. Both of which were great. The half order was plenty and a nice option to a full order. The restaurant was full of local men at lunch which is usually a good sign. I give it a 4 star only because of the waitress who kind of threw straws, silverware and napkins at us as she walked behind the counter. At least she didn't throw the food when it came! She also served the fries and Onion rings way before our burgers came out which was kind of weird. They were nice and hot but would have been cold had we waited for the burgers. It didn't factor into my four star rating but I deduct a star from nephew because he invited us out to lunch then allowed me pay! Just kidding Justin! Love ya![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is a perfect example of what a breakfast diner can be: excellent breakfasts in huge portions for cheap. I had the western omlet and will be getting it or another omlet again soon + +The coffee was good, totally serviceable diner coffee. The waitress was wonderfully friendly and hopping around from table to table. The food was excellent. The ambience was exactly right for a diner. It was packed. The wait was not nearly as long as I was expecting. 10 minutes maybe. + +Totally recommended. Come hungry.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Wow! Read the great reviews and I was not let down. Huge portions. The mixed grill was THE best breakfast I've ever had. If you go to Pittsburgh it is a must eat. Service was superb. Friendly staff. Led zeppelin on the walls. .....what else could you ask for?[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have been coming to Gab n Eat for almost 20 years and They have never let me down. I get a typical breakfast if eggs, ham, toast, and home fries. Delicious as usual. The ambience however is usually lacking. The walls are dark, with writing and signatures of semi famous people all over the place. Pictures of local people hang on the walls(i secretly want mine up there) along with posters galore. While its fun to look at the first 10 times, it gets a little boring after awhile. So today when I arrived I expected the same old experience. Wow was I wrong! As soon as I looked at the door I knew something was different. The place seemed lighter and brighter. To my pleasant surprise, they painted and got new counter tops!! They're not quite done yet but the place has a new Happy vibe to it. The awesome breakfast, the new decor and the 5 guys sitting at the counter making me laugh are why I will be back( maybe for lunch).[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> A gem. The coffee cups are mismatched . The owner is three feet away from me cooking. The sausage is made for them locally. And the food is frickin awesome. I had the pancakes, my daughter had the sausage and egg sandwich. Cash only. Friendly service.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Excellent breakfast and lunch menu. Friendly staff and super food. Modest environment with excellent food. Worth the wait.. dont miss this one. +Best breakfast and lunch food in the Pgh South Hills hands down.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> What a find! I stopped in here for breakfast while in town for business. The service is so friendly I thought I was down south. The service was quick, frankly and felt like I was with family. +Fantastic poached eggs, Cajun homefries and crispy bacon. Gab and Eat is definitely a place I world recommend to locals. I was stuffed and the bill was only $8.00.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> A fine breakfast joint. You gotta love the small diners. Highly recommended.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Barb's Country Junction gets a 5 star rating for me because it is truly everything that a Pittsburgh restaurant should be. In addition to being the apple of my nostalgia's eye, it is also the constant thought of my tummy when I'm hungry on the weekends. + +Barb's breakfasts cannot be beat, but truly any meal you get there you won't regret. Everything is made to order, with fair portions, and great prices. My recommendation is a breakfast sandwich on a bagel and a coffee. There's nothing better than drinking from a cup that could have come from your grandma's kitchen. + +I know that Gab N Eat is nearby, and Barb's can be a little weird get to with the strange traffic pattern but this really is a gem of Carnegie that you've gotta try![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great little place. Treats you like a local.Eaten here 3 times a week for a month. Same overtime. Barb is always here.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is a great place to eat and everyone is so friendly. I live right down the street from here but unfortunately, I have only gone a once. Trust me, I will go here more often. The food is great, prices are low, and the staff are friendly. My cousin and I wanted a place to eat and catch up and this was perfect place. I will go here more often.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My first time going to Barb's Country Junction and I really wanted to like this place, I really did...however, I didn't. + +The food was decent, some was above average and some below but it was overall decent. I got pancakes, bacon and eggs. The pancakes were really good and fluffy, the home fries were simply okay and the eggs were not cooked well. My son had a burger and it was good. The coffee at this place was brewed to perfection which a appreciate. I would give the food 3/5. + +The service was subpar for sure. While our waitress was a really nice girl, she wasn't on top of anything at all. Had to ask for coffee refills, had to ask for silverware, for napkins...etc. She got the order messed up and so on. I give the service 2/5. + +The inside of the place had some country charm as you'd expect but want particularly cleanly. It also had a leaky roof in several places which had buckets collecting the water. A customer even tripped over the buckets and fell. I give the interior 2/5. + +The prices were decent. I fed my whole family breakfast (3 of us) for $23. I give the prices 3/5. + +So in summary, you can get okay food here for a rather cheap price but it is not a great place to dine in by any means. There are better diners in the area that I will patronize in the future rather than Barb's.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My husband and I tried this place for the first time today. It was easy to find and no problems with parking. It's ""Seat Yourself"", but there were no signs stating this, so we stood there looking like fools for a minute. It took awhile for the waitress to acknowledge us and I'm guessing that this was Barb. She apologized and said that one of her workers called off today. No big deal and her apology was appreciated. She came back with our drinks, dropped them off, and left again. We didn't see her for another 20 minutes. Ultimately, we were there for 30 minutes before she took our order. This was aggravating to me. I don't mind waiting for my food if I know it's going to be awesome and they're making it with love, but come on now. We ordered the hot pepper omelette/home fries/ toast and chocolate chip pancakes/sausage. The food was alright, really nothing special. A new waitress ended up taking care of us and she was much more attentive. We may or may not go back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> For the price I ended up paying, this place was fine. There was a full kitchen, king bed and TV. I was just surprised at the lack of amenities at the hotel. While I have stayed at other extended stay hotels, I was surprised to find a sign in the room at this one stating that you only got your room cleaned once per week...if you wanted it more often than that you would have to pay for it. If you needed fresh towels, you'd have to go to the main desk to get them. They also only provided a small bar of soap in the room...not the typical soap, shampoo, lotion, etc. This didn't bother me too much as I was only staying a couple days but again I found it surprising not to have these basic things. + +The hotel in general was easy to get to and very easy to get back onto to freeway from. The hotel was clean and the people who worked there were very nice.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great value, close drive to city, not much to do around hotel, its a business park. Carnegie city has a few bars and restaurants.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Simple +Rustic +Local +Wait that is every Gordon Ramsey review + +My experience at extended Stay America was great. The staff was warm and friendly and made it a point to speak to me every morning as I left and when I returned in the evening. They went out of their way to provide A confirmation and point me in the direction of restaurants and nightspots when needed. + +If I ever need to utilize an extended stay hotel I wouldn't hesitate to head back there.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've stayed at a couple of Extended Stay sites that I found quite satisfactory and this location proved to be just as good. Excellent place to stay while visiting Pittsburgh. It is just a five minute drive to downtown. Location is in a business park area so it is quiet. + +The rooms contain a nice kitchenette area with a full sized refrigerator, sink, cabinets and two burners. There is no oven which I expected as the descriptions all state ""full kitchen"" so be aware of that. Also they do not keep the dishes, pots and pans, coffee makers, toasters or utensils in the rooms. If you want them you have to request them at the desk during check in. + +The room was clean and well maintained. Cable tv quality is spotty sometimes but not intolerable. The free wifi is usually fast. + +The best part about this location was the staff. The people at the desk were all very pleasant and welcoming and quite willing to assist with any questions or issues with a smile. I would definitely stay at this location again and highly recommend it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Tonya is super sweet and the front desk people are very helpful[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have said it on other sites and will repeat here. You MUST try their burgers. They are juicy and delicious with a bun that is perfect. Another must are the fries with Guinness gravy and if you haven't had enough go for the ultimate sleeper, Leek and potato soup. Authentic black & tans. Harp and Murphys on tap. It don't get no better. This is a true gem my friends.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Be warned. Don't expect the best service ever. It's not the cleanest place you've been in either. The decor is soccer jerseys from places and teams you've probably never heard of. It's divey, eclectic, and authentic. + +If you're looking for good Irish food and a cold pint, you can't go wrong at the Pour House. Like most of Carnegie's Main St, this is a hidden gem worth seeking out. They have some of the best Irish food I've had in Pittsburgh- the colcannon is awesome and the shepherd's pie is out of this world. If you're not looking for Irish food, then try the grilled cheese- and make sure you ask it with the three cheeses together. It's big and the cheese is thick and gooey. I get it with a side of potato pancakes... Yum. + +Also, they have Guinness, Smithwicks and Harp on tap...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> If I could give this place less than one star, I would. I have no idea who gave this place high reviews but they must either own the place or be time travelers from back in the day when this place might not have sucked. The decor is tired and grimy, the place reeked of smoke, and the bartender/server was surly, to put it mildly. We went there on a Saturday night with a mind to try the Irish food. Apparently, we were out of luck. I've always thought that the secrets of restaurant success is to actually stock food for people to eat. He told us before we ordered that they had no ""pies"". No chicken pot pie, no shepherds pie, etc. So, we gamely tried to order other things. We placed our order. My wife, for example, ordered the Irish stew and he came back 5 min later telling us they were out of that and even more things for several people in our party. At that point my wife picked out a third option, ham and cabbage, only to be told again that ""they were out"". At that point, realizing that the only food to be had in the place was what was crusted on the menus, we asked to pay for our drinks and left. They actually then gave us flack for not having enough to put it on a debit card. In short, unless you like your dinner with a side of disappointment and depression, I'd probably avoid this place like the plague. Speaking of the plague, I suppose we should thank Mr. Surly for inspiring us to walk out. I only have two bathrooms at my house and would've been hard pressed to accommodate several violently ill people at once.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Best Irish food in the Burgh. Great bar food too. The service is maybe a bit surly and it's not the cleanest, nor the best decor. But, that's not what this place is about. It's a town Irish bar and it serves great solid Irish fare and suds to the locals. And it does it better than anyone. I go back again and again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Okay, so hopefully you haven't been enjoying happy hour @ Riley's Pour House before you read this or you might not be able to follow the lilting Irish owners. + +To recap: Murphy's Pour House from 1979-1985. Sullivan's Pour House from 1995-2002. Paddy's Pour House from 2002-2012. And, bagpipe please, Riley's Pour House opens March 1 of 2012. Still with me? + +It's a tiny long bar just like the old Irish pubs. No more smoking allowed. Hurrah!!! Same lousy service. + +My guess is that the entire place needs (no, strike that .... demands) an automated food/beverage ticketing system. None of the cooks, bartenders, or waitresses know who ordered what nor what ticket belongs to which table. It's actually pretty funny if you're not a) hungry or b) thirsty. + +I really really want this place to do better. We need more Irish pubs and local old time watering holes. + +Get it together, Murphy's ... er, I mean Sullivan's....er, I mean Paddy's or is it Riley's? ; ). Whatever the case, they have cold Guinness. And Irish music. And fun patrons.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The delivery driver mistakenly rang my doorbell, having confused 133 and 113. + +Rather than taking a step back and analyzing the situation, he begins to accuse my wife and I of ordering and refusing to pay for this pizza. + +The driver then gets on his cell phone and rather than calling the number than was given when the order was placed, begins to call his bosses and starts threatening me with felony charges. + +So I take the initiative and ask the fine upstanding gentleman what the phone number of the order-er was, phone my neighbor and discover the mistake. Rather than a thank you or a sorry, he just speeds off (breaking the speed limit on our block) to reach his destination 50 feet away. + +I would call to complain, but based on the other reviews, its clear the owners do not care about Carnegie or it's residents, and its pretty well known around town just how awful their food is, so it would be pointless to boycott a place I'd never order from again anyway. + +Do yourself a favor and order from ANY other establishment in town.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> 3/6/12 visit - i am from san francisco bay area and if u want a dive go to china town in san francisco. - this place was dirty like chinatown dive but some of the best food i have every tasted came from a dive. the food was really good and my group ordered a bunch of different things it was all good- a- taste.- prices are reasonable a-. --------they dont speak english very good and got my order wrong. +sweet potatoe fries a+ +pizza - a +eggplant hoagie b+ +greek salad b+ +gyro a+ +if they scrubbed the place down and the lady spoke better english 4 star ****[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Recommended. 16 inch pizza on special was cheap. Fast service. Not the best pizza but above average.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Some of the worst pizza I've ever had. We used a coupon from the paper for a 2 topping 8 cut Sicilian. First of all the pizza wasn't even cut through, and the sad attempt at cutting was so uneven that 4 of the slices were about an inch wide, while the others were about 4"" each. The toppings were scarce, they used mini pepperoni and put maybe 8 on the whole pizza. The onions were huge chunks and the mushrooms were straight from a can. The worst part though was the thick doughy crust that tasted more like a fishy sourdough roll. I'm serious... It was so noticeable that it made me wonder if the dough was bad or if they for some weird reason put fish sauce in it. It was gross. + +We also ordered steak and Italian hoagies. The veggies were old and wilted, and there was no dressing on either. The Italian had deli meat that was clearly bottom of the line and not very generous. The ""steak"" (if you an call it that) was greyish instead of brown and looked like it was a processed meat chopped into pieces. No flavor or seasoning and the texture was reminiscent of spam. It was so bad that I only ate 1/4 of it and tossed the rest. + +I have ordered from here in the past and always been disappointed. I thought I would give them another try since I'd never ordered a Sicilian pizza from there. What a mistake. I will never order from them again![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Having certain businesses with skill sets in your local neighborhood is important. I try to keep it as local as possible, so when I heard about a tailor in Carnegie I was intrigued. The building is in a strip mall across from Carnegie Coffee Company. Unassuming, looks like it is closed all the time, until you do a drive by and see the hours posted. There is a Latino man in his 20's working when you arrive. In my mind, I imagine a tailor to be older, kind of like my grandfather maybe with measuring tape around his neck (Textbook movie tailor), so I was a bit trepidatious about dropping off my clothing. He asks you to go change into a closet (Yes, a closet to change in with one lightbulb) BUT all my worries aside, the moment he started working on my items I knew he was the real deal. He learned from his father at the age of 14 how to sew. and he does things the correct way. Meaning, for example- I took in a pair of khakis all the way down to the cuff, but he seamed them up to look EXACTLY the way they were when I first bought them. Most placed will have bulges and puckers. The rest of my items were just as perfect. Very inexpensive at $10 for a pair of pants to adjust the hem. The items were done in a timely manner. He takes his business very seriously. While I was there, I watched a lady rush in and demand 6 shirts to be altered in an hour, and he did it and charged the same price. Really nice guy, please go and support this business to keep him around town![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> New to area and decided to pay this shop a visit! It was definitely the best experience I've ever had with a tailor. He is MUCH cheaper than the other shops, he charges 10 while others charge $15, and he goes above and beyond for what he charges. + +I dropped off 4 jeans, and he hemmed and tapered the jeans! I couldn't even tell the difference between the store bought jeans and the quality of his work. It was absolutely perfect, no bulges or puckers! They the match the exact stitch as the factory. + +Absolutely a great guy, they were all done and waiting for me as promised! I'll definitely be taking all of my business to this place, and would highly recommend to anyone who is looking for a personal tailor who actually cares about his work and building an honest business.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I needed alterations done to my suit very quickly. Like three days quickly. Not only did Filberto at Alteration World have it ready, the price was beyond reasonable and the work was EXCELLENT! I plan on bringing all my clothes to him from now on. + +Oh and he let me know that they also dry-clean. Wonderful shop![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is the best alteration place I have been to. The guy that owns it is extremely helpful and works FAST. Also, the prices are so reasonable I wonder how he stays in business. He was able to do an alteration on short notice and was very acommodating. The alteration I needed done--and fast--was right in the middle of prom season. All the other places I called gave me a several week wait, but he took me right away. I will be back![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I just needed a broken zipper replaced on my favorite Penguins fleece jacket and a pair of suit pants hemmed. The price was very reasonable and the work done was great. I will go back for all my tailoring needs and highly recommend if you need any done.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Are you are really looking at the review for LJS? Its fried stuff, with extra fried stuff in a cardboard boat. You will regret eating it 30 minutes after you finish, but it is delicious.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I agree with Paul on this one. But I had to stop here on my way home from work tonight. +(I think I feel my heart yelling at me again) , The gal at the drive thru window was just soooo sweet , I just might go back and ask her to marry me! +But then again , she gave me a slip with a survey on it to fill out online. +Maybe she just wanted my positive response. Ok Sarah B. you got it ... now where's my free coke ?[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It's deep fried garbage....it's LOS c'mon what do you expect.....however I have never had better, friendlier service at a fast food restaurant.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> By far the worst most unprofessional dentist I have ever experienced her staff is too busy watching soap operas on all the TVs in each room instead of cleaning and she gave me a filling which was too deep which could have been understandable as her son had his pictures delivered from Hawaii and she had to stop 3 times to pay for them and show her whole staff all of them must be nice to have a 14 year old go to Hawaii on her moms dime and have her patience wait to see all of this happen I had to have oral surgery and have the tooth removed because she put the filling in too deep an abscessed tooth was the result I wouldn't recommend her to an ex girlfriend or someone I hate because of the three months of extreme tooth pain I had to deal with because of her lack of care and follow through even after I called and asked them for advice and follow up they simply could care less and did not even offer to reschedule an appointment other than prescribing me vicodin and antibiotics do not recommend and do not go to her license should be pulled!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> When I moved to the area, Dr. Weinberg was recommended to me by my cousin who had been a client for years. I've had nothing but positive experiences with her and her staff since seeing her two years ago. The team is professional, nice and courteous. I recently had to reschedule an appointment due to a last minute work thing and they were very accommodating. My daughter looks forward to coming to the dentist so that's saying something. I DO wish they would turn off FOX news in the lobby as I'd rather watch paint dry but... nobody's perfect.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> In all fairness - I did not see this dentist but did schedule an appointment and waited 15 minutes for them to open. + +When I look at Yelp reviews, I usually weed out the outliers (the best and the worst). Unfortunately, there are only two reviews. + +It was my first time at the office. The office admin (very nice) asked for me to come early (before 9am) to complete paperwork. I arrived at 8:50. I waited. I watched 2 employees walk by me (unlocked the door and re-locked it). They did not acknowledge me. + +The door I was at had signage (open hours). I decided to leave because of a review where the staff seemed distracted or disinterested in my presence. + +The office admin (very nice) called me to inform I am missing my appointment. I explained to her that there were too many indications where this was not going to be a good fit and wished her the best of luck. + +I recommend if you see this dentist you go to the front door (furthest away from the parking lot) for the entrance. + +Poor recommendation because the staff who walked by me seemed to be distracted which was pointed out in a previous review.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is by far the best dentist I have ever been to. She is honest and never trys to sell you a bunch a stuff that you dont need. We are very great full that we discovered her. We adjust our vacations to make sure that we stop in to her office in Pennsylvania at least once a year for cleaning and check ups, worth the drive from Florida.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've been to this office a good amount of times. Each time the receptionists give of a vibe of entitlement and it is very uncomfortable. Dr. Weinberg herself is very nice, but I doubt her ability. Every procedure she has done to my teeth has backfired. The third and last issue I have is that i always paid cash at the end of my visits and somehow I have received an invoice for $55. I called and of course the receptionist was sassy and rude so I gave up. Will never go back or refer anyone else[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Don Don is a restaurant I find myself missing now and again, it's probably my favorite restaurant in Carnegie. Simple setup, just a small restaurant with a few tables and a TV. Oddly enough I think my favorite thing to eat there is the wonton soup, never had better. The food is average but I always enjoyed eating there, great service and a cheap place to get Chinese food.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Take it from me; avoid this place at all cost. The only time I go is when I am starved and don't have the energy to cook or get edible food. And then after I have been kicking myself.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Far away from real Chinese food. Doesn't even taste good as American style Chinese food.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I used to order takeout here once every month or so. The food tastes average and the price is good. It's your typical low-end Chinese place. + +The last (and final) time I ordered here I just so happened to be picking up my order while a health inspector from allegheny county health department was making his rounds. While I was waiting on my food (which took much longer than usual) the inspector was pointing out violations. He also requested a copy of a certificate that the man behind the register was unable to produce. The inspector looked at me like I was crazy for waiting on my food despite the obvious poor conditions. + +As for the rest of the place - it's always been kind of dirty inside. The carpets are just FILTHY and the walls match. There are always children's toys scattered about the floor because the owners children are always there, so be careful not to trip. + +The workers do seem like nice people just trying to make a living but when it comes to cleanliness Don Don is lacking.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Delicious Singapore noodles and seafood delight. Crispy flavorful crab Rangoon, and cold sesame noodles done well (but could've used a bit more sauce). Excellent real Chinese food, friendly service. Restaurant ambience: high school cheap date quality.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I came here with two friends prior to visiting Apis Meadery next door this past weekend. I ordered the General Tso's chicken, and my friends ordered the sesame chicken, crab rangoon, and another appetizer (egg rolls?). They ordered the combo with less meat, and I ordered the one with more--the names were very similar, which I found confusing. The food took quite a while to come up (~15 min.), so I'd suggest calling ahead if you're in a rush. While we were waiting, the woman behind the counter yelled at someone over the phone in Chinese, and then at a guy who came in to pick up food for delivery (probably the same person). + +To be honest, I'm not much of a fan of Americanized Chinese cuisine (I lived in Singapore for 3 mos. and have visited Hong King and Japan); it's been awhile since I've had it, and this dish reminded me why. I don't care for the overbearing sweetness and thickness of the sauce, nor do I care for the pre-cut meat in the dishes (I like to cut up my own meat, thank you very much), so the flavors and textures don't do much for me. Having said that, my friends claimed this was the best Americanized Chinese fare they'd had in PGH (and they live in Squirrel Hill!), so if you're a fan of this cuisine, you can take that into consideration. + +If nothing else, this meal provided us with some much-needed food to absorb the alcohol from the mead, which I appreciated.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> All I can say is the worst! We were the only 2 people in the place for lunch, the place was freezing and loaded with kids toys! 2 bicycles, a scooter, and an electronic keyboard graced the dining room. A fish tank with filthy, slimy fingerprints smeared all over it is there for your enjoyment. + +Our food came... no water to drink, no tea, medium temperature food. Of course its cold, just like the room, I never took my jacket off! The plates are too small, you food spills over onto some semi-clean tables as you sit in your completely worn out booth seat. The fried noodles were out of a box and nasty, the shrimp was mushy, the fried rice was bright yellow. + +We asked for water, they brought us 1 in a SOLO cup for 2 people. I asked for hot tea, they said 10 minutes. What Chinese restaurant does not have hot tea available upon request? + +Over all.... my first and last visit to this place. The only good point was that it was cheap, and deservingly so.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We went on a weeknight. Place was not busy waited over 20 minutes for drinks and to have our order taken. We ordered an app and it came out with the meals and that was another 20 minutes or so. Food was luke warm at best. I would not go back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Went for breakfast on 6/16/14. We received very good service and meal came within a few minutes.Waitress could have smiled more but was friendly. +I had a Grand Slam... it was more than enough food. +Meal was very tasty... We will definitely go back. +It is a popular Denny's.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love their stakes and i come here every week just to get the t bone steak, it is completely delicious! + +Great atmosphere, there is always a lot people and the waiters are nice; food portion is great as well![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Perfect time with hubby, after work which is 4 am and you can still have a hot nice meal, waitress was such an adorable girl. Her arm was broken or smth but she still dis a great job! +Strawberry lemonade was just smth i have been craving for for so long but did not know what it was :) +Strawberry milkshake, nachos and t bone steak is smth we never stop ordering! +Its always nice when u go late at night like us, it is not crowded, not noisy, nice music playing and always nice people around. +If you want smth quick and it is late at night then i would say Denny's![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This location never disappoints!! Food is always consistently great, and if you come at the right time, (witching hours) you may see the cook singing and dancing along with the music in the back. And it is awesome! ! Love this place!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I belong to this gym... I live in the South section of Pittsburgh, and I find that this gym is not too far from me. The staff is friendly, the equipment is quite good. You get two free personal training sessions when you join. They have lots of weights (which my boyfriend uses) and a decent cardio room. The only thing I would say is to increase some of the cardio equipment. Water is only $1 a bottle![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I bought a three month membership last year, mainly to attend the Silver Sneakers classes. I was in my early sixties and hadn't exercised in a while. I tried the evening classes but they were very crowded and difficult, so I tried a morning class for seniors. I like to stretch out before my class actually starts, so I went to the tail end of a yoga class. The women in this class were very nasty to me and told me that I wasn't welcome to stretch out in their class. I never went back thanks to the attitude of the other members. I didn't feel welcome here. I complained to the manager, who said that I was welcome to stretch out in whatever class I wanted to, but the hostility of these yoga students was very evident. Do they think that this is their private gym?[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I really like this gym. It is nice neighborhood gym and unlike big gyms they don't have big contracts and they have flexible memberships. Great selection of classes. All the instructors are very good knowledgable and motivating. All the staff working there are super nice. Their selection of the equipment is good too !![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> If you like being greeted in the morning by a gym worker slopping down eggs from a frying pany instead of working....this is your gym....complain to the manager and she gets nasty....try getting in touch with the owner....impossible! Most unprofessional gym ever!!!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I brought my husband and my parents all to Papa J's last time my husband and I were in Pittsburgh. My parents are really picky about their italian food, usually they drive places in east bumf*@ (tarentum, ligonier...) to get their capital I-talian. + +My pop is kinda grumbly, and getting him to try something new is like pulling teeth. The only reason I got him here was becuase they were on their way to drop us at the airport. + +Well, my dad goes back now regularly and that says a lot, considering he lives in Murrysville. + +The first good sign Dad was happy was that he seemed impressed when it was open- it was noon a few days after Christmas. Second good sign was that Dad ordered wine, at it was only 1 pm. Dad, while not a teetotaler, rarely has a drink before 5 pm so I know he was anticipating a good meal. The kicker was that he was so happy he left our waitress a $20 tip on a $50 meal. + +Can I say, I live in Texas now and I still relive this afternoon back in December? I had chicken picatta...it was perfect. My dad had eggplant rollatini, my mom had a pizza, and my hubby had basic pasta and marinara. It all was amazing, delicous, and inexpensive. In Austin, you can't get a decent italian meal, much less a decent italian meal for under $50 for four people. + +I know there are so many good Italian places in Pittsburgh but I just think back so fondly on this day...when me Dad liked someplace I took him :)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Papa J's is by far my favorite restaurant in Pittsburgh, my hometown. I eat there almost every time I visit, and everything I've ever ordered has been fantastic. Fresh ingredients, simple preparation, reasonable prices. Also, they make the best pizza in town HANDS DOWN.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is one of my husband's fave restaurants in town. My husband generally orders Chicken Parm, which is very good. Their sauce is quite good. They serve fresh bread with a plate of olive oil and balsamic vinegar for dipping -- yum. + + I generally order one of their house salads (think it has a specific name, but can't recall off the top of my head) which has mixed greens and I get it with blue cheese, pine nuts and their yummy vinaigrette. A tad pricey for a salad that's just lettuce and cheese (I want to say about $8 with the extras), but really good. (Especially with some cracked black peeper.) I tend to follow this up with a smaller plate like their red pepper app or the greens & beans. + +The place has sort of a rustic atmosphere and can be on the loud side. It has a comfortable feeling. It also has a solid wine by the glass selection -- better than a lot of places in the 'burgh. + +Unfortunately, we've never had dessert there b/c we get so full of bread and dinner![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Thanks yelpers for this find. The service, the plating, the ambiance were wonderful. I had the eggplant parmigiana and it was good - but different. It was thinly sliced (like deli meat) and wasn't breaded, it was fried in a very light batter.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place has been a favorite for 20 years since we returned from a trip to Italy having several weeks of fabulous fresh food, and couldn't think of any place we wanted to eat. Papa J's measures up to our expectations with great salads, bead and wine. I'm partial to the eggplant rollatini and my husband likes samplers, ravioli, fish, white pizza. I like the space with exposed brick walls-there are knowledgeable servers. Sometimes it is a bit loud- more noticable when it is empty with a large table nearby. But don't get the wrong impression -it's a great place-consistantly great food.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great, authentic, classic Italian restaurant in one of the most unlikely places. + +I grew up eating here and make a visit nearly every time I come to town. + +Try the fried calamari ""Roman Style"" for a little kick![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've been to Papa J's twice and had mixed experiences. + +Both times I had the banana pepper appetizer, which is great and goes really well with the FRESH and delicious bread and cheese they give you at the start of your meal. + +For entrees, me and my girlfriend have had mixed experience. I've had the fish sandwich (very good) and the eggplant parm sandwich (okay). My girlfriend got the salad with bread and basil on it, but the basil was over powering and the bread was soggy with the dressing. + +The service is also a mixed bag. The first time our server went out of her way to take care of us and even MADE me cocktail sauce for my fish sandwich. The second time, the server was lackluster, didn't know anything about the menu and wasn't able to take proper care of us. + +I would return to Papa J's, but I my terrible experience last time isn't enough to say it would be my first pick of places to eat around Carnegie/Robinson.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I went there for dinner last night with a client. This is second time I visited. I had a scotch and he had a Guiness. The (-1) is for drink selection. Just stock some better beers and higher end scotch and you're five stars. + +We started with the meatballs covered with Provolone and other blessed goodness. These did not disappoint. I had a four cheese pizza with sweet sausage and garlic. It was fantastic. They have so many good dishes, but I wanted the pizza last night. I couldn't finish the pizza - way to go big medium pizza. + +I finished up with a coffee. The parking can be a bit of a challenge on the street, but it's a small town atmosphere in Carnegie, PA. I love the downtown there.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> What a wonderful surprise found in Carnegie PA, just south of Pittsburgh. I was in town on business with a couple co-workers and after having a not so great meal the night before, we asked one of the locals for a recomendation. They told us to try this little Italian place called Papa J's and boy did they send us to a great place. + +First off, when you walk up to the place, the front and side windows give you a fantastic open view into the kitchen from the outside. You can stand outside and watch the chef making all the wonderful food and you can smell the fresh bread before you even walk in the door. + +I am not sure how long this place has been around but the kitchen looked well used, while the dining area as well as the bar looked very clean and modern, almost as if it had been freshly updated. + +The server was quick to welcome us and suggested several different items off the menu as his favorites when asked. The three of us were very hungry and wanting to try a few different things, so we began with a Margherita pizza which was absolutely perfect. They obviously make their own breads and dough for the pizza and I don't think this pizza could have tasted any better. Then came bowls of Italian wedding soup which was pretty good. Of everything there, this was the one item I probably could have done without. Not that it was bad, but there was nothing particularly special about it. + +We also ordered the Garlic Rolls (not that the bread they already give you and the pizza was not enough carbs for 1 meal) and they were to die for. Crunchy on the outside and warm and chewy inside, these things were a meal by themselves. One of the guys with me said the pizza sauce would be good on them so he ordered a cup of the pizza sauce (which is fresh made there, not out of some can) and he was right. As if these little killer bread balls with garlic were not good enough, dipped in the pizza sauce they were even that much better. + +By the time our meals came, we were all pretty full, but we pushed on and continued to eat. I had the Veal Parmigiano which was tender and very good. It came with a side of pasta which I tasted just to try and it was excelent as well. Had I not been eating a weeks worth of carbs in one sitting with all the pre-meal stuff, I certainly would have finished it. As it was, I ate most but not all of the generous portion of veal. + +One of my co-workers had the Chicken Picatta which he said was one of the best he had ever had and the other guy tried a pasta dish which he said was very good as well. + +They had a great wine selection as well at reasonable prices by the glass or bottle. + +Overall a fantastic experience with great food and atmosphere. I don't really know how expensive the area is for food, but coming from the Chicagoland area, I fouknd this place to be pretty reasonable. The three of us ate very very well for an average of aproximately $30 each not including alcahol. Fantastic fresh food at a reasonable price, who could ask for more. + +My only complaint is that I had to return to Chicago and I am now craving to return to Papa J's. I hope work sends me out here again sometime soon!!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Yay, I'm a fan but sometimes service is a little slow, it was very good for us this visit. Go to Papa j's every once in a while but mostly for the White Pizza. It is the best white pizza I have ever had. Order the white pizza on our visit this weekend... it has garlic, spinach, feta cheese and we usually add some veggie on top. It was delicious! Order fried calamari and it was OK...note to self next time try the calamari roman style. + +Like the dinning room with the hardwood floors and bright lighting. + +The bar was jumping thou never go to the bar.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Terrible service. Food unremarkable. Waiter disappeared for 45 minutes to serve larger group due to staffing mismanagement. Saved his tip by discounting meal after I complained. All and all, a very crude and unpleasant dining experience for me and my guests. Not to be repeated, never again![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Yay, I'm a fan of the white pizza. Had take out. + +The bar was jumping when I picked up our order. + +The white pizza is so delicious...with garlic, spinach, feta, and added some veggies. Tried the Roman Style calamari, very good better than the fried calamari we had last time.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We met our good friends from Morgantown here for lunch today and were really impressed with the place itself and the menu. + +I had read a few of the reviews ahead of time and the pizza was mentioned more than once so by the time we got there, I was jonesing for it. + +It certainly delivered. The crust was great, the sauce wast too sweet and the toppings were sufficient. + +Our friend for the baby clams with oil and garlic over angel hair and let me try a bit - as good as the pizza was, this was _much_ better. + +We'll return again to this beautifully lit gem in Carnegie PA soon![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> OK, its Friday night and have about 70 minutes to eat. Driving by Papa J's and W says, lets stop in and get a quick dinner. + +Advice host that we are in a hurry. The host advised us it is a 90 minute service. The place was crowded, we were seated at the last open table. However our waiter, Jason, said he will do his best to get as out on time. We ordered our dinner immediately, with a salad and a glass of wine. In a few minutes we had our wine, then in a few more seconds we had our salads and some great homemade Italian bread with some olive oil and balsamic ving. for dipping. Yum! + +Just as we were finishing our salads our dinners were delivered. Great job Jason! The Fettuccine Carbanara was very good; a thick cream sauce with bacon and ricotta. In and out in 60 minutes. Now that is some good service.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great little gem! The food was fantastic was very food and just the right price. The Italian food was amazing, but you can not leave without a dessert and be prepared for giant serving. I had the carrot cake yummy!! Def a place everyone should try.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have to say that I write this review with much regret, because I have always loved PaPa J's. But my recent experience there has changed my mind a bit. + +From the minute we were seated, we were greeted by a server that was clearly inexperienced and didn't know the menu. As I said before, I've been to PaPa J's a good handful of times so I know the menu decently well, but the server couldn't explain any of the questions I had about a couple new dishes I was thinking about trying. I swear this guy must have just looked at the menu for the first time a few minutes ago. + +But it wasn't just the knowledge of the menu. It was one thing after another with our server. My wife asked for a glass of water 4 times until she finally got it (at which point the meal was over, so we didn't care at that point). I mean come on, for a restaurant of this calibre and price is it too much to ask for a glass of water? There was no one filling up water. + +My biggest complaint, however, is what happened with our meals. My dad and I both ordered the trout special (trout with roasted red peppers and lump crabmeat). Instead, the meal that was delivered to both of us was trout with a heaping pile of spinach and mushrooms. Not what the special was at all. And by the way, that item is on the menu as a regular item so whether or not the mistake was made by the server (which, we are sure it was) or the chef, who knows for certain. Not to mention, though, that a good server wouldn't have served us that regardless. + +But before you think we had an unusal experience that was all due to a poor server, let me continue. When we informed our server of the mistake, he didn't really believe us until he checked his order sheet, and then he blamed the error on the chef. At this point, the meal had been sitting (because it took us forever to flag this guy down again) so the trout was basically cold. The server then said he would have the meals re-made. So, he took the meals back to the kitchen. Meanwhile, of course, my wife and mom are eating their meals and my dad and I are sitting there with no meals. Also keep in mind that my wife still had not gotten the water she had been asking for, and my iced tea had been refilled with a soda (yes, believe that or not). All the kitchen did was scrape their ""mistake"" off of our fish! They didn't remake anything. Our fish was served to us again with little pieces of spinach and mushrooms sticking all over it. Quite frankly, the fish wasn't good at all. I honestly would have rather had a fish sandwich from McDonald's that night. The server never did anything to try to make our experience better - he knew we weren't happy, but never offered anything such as dessert on the house. I'm not looking for a handout, but our experience was just plain awful that night. The guy never really even apologized for the mistake. Normally, I may have asked for a manager, but at this point I was ready to just get out of there (plus, we had to be somewhere else that night). + +My opinion... for the money, there are many other restaurants I would rather eat at.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is a regular go-to for me. I love the food and the service. They always have the wine that I like and the food is always delicious. I suggest trying the flourless chocolate cake in the front of the store (in the section where you can buy stuff to take home). It is sublime and makes you want to go to a special cozy corner just to eat it and revel in its velvety loveliness.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I thought the interiors were very nice. We stopped here on a Friday night & I was glad they weren't busy because nothing else in the area looked appetizing. + +My daughter & I split a chicken parm sandwich, which was really good. Instead of it being served on a hoagie, it was served on thin bread- like focaccia or something. It was pretty good- little messy. + +The desserts looked amazing. I thought it was pretty cool how you can watch the cooks prepare the food from outside. The kitchen is situated on a corner with lots of windows. + +I would return.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> san francisco california visitor liked the food and the local is great. I am thinking about relocating to pttsbrgh area. I liked Carnegie because u can stroll down Main street and hit a couple places for lunch. I imagine this place would be crazy busy on friday or saturday night. we ate a lunchtime and it was nice.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Coming here you get the feeling they haven't changed much. The tables, the decorations, the menu. All the same. Does that make you a little worried? Yes. + +I ordered the mushroom ravioli and it was... oily. Very very oily. The actual ravioli was okay, enough mushrooms. but it was oily. Did I mention that? + +Ambiance, like I said, left much to be desired. I don't think I'd have this place on my list of ""musts"" for downtown. Much better restaurants to visit![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Had dinner at Papa J's with a group of 6. I loved how the restaurant is in a old brick building with large windows. It felt like a neighborhood restaurant. On a Saturday night, the restaurant was full but not crowded. We were seated in a room with poor acoustics. It was difficult to hear people at our table and the waitress. While she tried, I can see the asperation in her face when she had to repeat the specials to both sides of the table. + +People ordered bourbon on the rocks before dinner which seemed watered down, while my lemon drop was made nice. The bread was delicious! Can you describe it to be creamy? The fried zucchini was lightly breaded and not too oily. It was a large portion made up of 2 sliced zucchinis. + +We ordered a variety of dishes. The pasta dish was dry with more pasta than sauce or meat. Those who ordered the fish special thought it was delicious. The shrimp dish was enjoyed as well. I had the chicken marsala which was pretty good. The marsala sauce wasn't too thick, and the chicken moist. + +Hard to tell if the deserts were ""homemade."" The tiramisu and spumoni were small in portion and meant for one. + +On the whole, I was on the fence with my overall impression of Papa J's. ""A-ok"" probably is the best way to describe it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Service in this place is poor because of lack of acknowledgment since people working there are ""just"" working . They have nice decor,nice bar and good bread. Consider where this place is ,the prices are really really high . Nothing is served on the side with main dishes ....[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Terrible service...terrible food...this place smells like rotten wet wood[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great place for dinner, drinks or a small celebration. + +Papa J's is one of my favorite go to places for dinner when we don't have reservations and want a nice dinner out. My husband and I have eatten here upwards of 20 times over the last few years and have never been disappointed. I assumed that when they opened the alternate bar with lounge area and extra tables for dining on the other side of the resturant that the overall vibe of the restaurant would change and it would be very busy. I have been proved wrong. We are always able to walk in on a weekend and get a table within a few minutes. Unfortunately, the alternate bar/lounge area isn't always open. I really don't understand why more people don't go here. +My favorites are the fried zucchini, wedding soup and pizza.The zucchini is always crispy and seasoned well. The wedding soup has big chunks of carrots and celery. My husband also enjoys the pork entrees especially the grilled pork and the pastas including the tomato cream sauce. Also, their homemade italian bread with oil and vinegar to dip is a great way to wet your appetite. Make sure to add the parmesan cheese that they put on the table. + +Also, if you are looking for a good place to host a birthday party or event, consider Papa Js. They have a great catering menu and are easily able to accomodate larger parties. We had our rehersal dinner for our wedding here and everyone loved the food.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Although the first impression through the door is charming and the aroma enticing as you enter this restaurant- much can be improved upon for the prices asked for the dining experience. Our group of 7 had called a week ahead and were seated in the back of the far dining room, right by a door where clinking pots /pans and dishes were heard throughout our meal, as well as a Darth Vader type noise coming from the ceiling vent. Our waitress was not knowledgable of all menu items, and three of our very simple requests did not come out as ordered. ( dressing on the side of a salad, less feta on an entree and no oil on another entree) The waitress blamed it on the cook, but did offer to get one entree changed. Also we were asked if we wanted pine nuts, feta or Gorgonzola on our salad and then were charged 2.00 extra per item in addition to the salad price (6.99) which brought the salad up to 10.99 ! Outrageous ! +There is so much possibility for ambiance in this restaurant , but they miss the mark on service and atmosphere. I will most likely not return. Very overpriced for the quality and service.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Papa J's is expensive and inconsistent. The ambiance is nice but it doesn't justify the prices. There are better restaurants in Carnegie.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Very good restaurant with very good food at a pretty reasonable price. We had a birthday dinner here with seven girlfriends. The waitress was very efficient , but not very friendly. Our orders came out hot and excellently prepared! Try the tilapia milanese , it's excellent. Best steamed broccoli Iv'e ever had.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I was pleasantly surprised by this restaurant. Came here with no expectations. + +I was greeted by a large open (garage style) window, that opened the whole lounge bar area to the street. It had modern furnishings and the staff were quite friendly. + +Ordered the quattro formaggi pizza. Quite good!!! Great balance of cheeses. Not too rich at all. Crust was excellent too. Can't wait to come back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Just to start off, we were a party of 12, which is always a little difficult. We were celebrating 2 birthdays. + +We LOVED the food, it was delicious. My husband got a chicken parm sandwich, which is served on a yummy flat bread, and I got the chicken basil pizza ( i got an 8 cut and several ppl tried it) we all LOVED it! It was stunning. It was made with a very delicious crust, nice and crisp, not soggy (like pesto pizza can get) + +The one waitress we had JASMINE, was fantastic! She was bright, friendly and very knowledgeable about the menu. She took extra time with the older ladies in our group to help them with their selections... + +Now... the other waitress.. Mary something was so incompetent... She was awful and rude. She missed 2 people on that side of the table failed to take their order and when we said something she said 'well they didn't speak up!' Ugh. Then when it was time to sing and cut the cake, my sister in law said 'oh hey can you get the cake so we can sing?' She came back, cut the cake (all crazy with some huge pieces and some super small pieces like she never in her life cut a sheet cake) and we didn't even sing! We were mad!! + +The place is so pretty, they have a new addition that was just built within the last 2 years (according to my father in law) and its really nice. They look to have a cool bar area with some modern couches and a really sweet look. + +So good food, great looking place.. one bad waitress. Prices are about middle of the road for an authentic Italian place, nothing crazy. All in all, we'd like to go back again, but we want Jasmine![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I am amazed that people can write negative reviews about Papa J's. I have been a return customer since the early 90's and the food quality, and service, are way above average......and especially for this price range. + +Kudos to management for maintaining such a level of quality and freshness. Nothing we had tonight was disappointing, and we over-ordered because each dish was delectable. + +The best item tonight was the Mozzarella appetizer ""cradled"" in Bread with an authentic marinara. + +The white pizza with sun-dried tomatoes was, as usual, out of this world good. The scallops special appetizer was phenomenal. + +WE WILL BE BACK.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Absolutely Awful Service. Went to Papa J's awhile ago and the service was bad - the waiter was surly, rude and unhelpful.. Decided to try it again since it is close to Stage 62. Big mistake. Greeted by a dour manager that seemed mad that we had a reservation. 30 minutes to get a glass of wine. At one hour and 45 minutes complained to the manager that we still had not received out entrees. He said 'What do you want me to do about it?"" and said they had a busy night. This is when tables around us sat empty. I then had to go back to the manager to give us our bill so we could get away from this ruined evening. The bill was prepared incorrectly. If you want average food and terrible service, this is your place. We will never go back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The menu has lots of choices and the food is great! The Resturante has been expanded so it's pretty large. The new section has door that they leave open during nice weather which makes for a nice ambience! The bread is great and fresh baked daily![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have been to this restaurant twice and was disappointed both times. I won't go back. The first time we were there almost 3 hours. It took forever to order and then forever for our food to come and the place was empty. When I complained the manager was very rude and tried to blame us for taking to long to order. It made no sense, how could we order when the waitress wasn't coming to the table? After arguing with me he ended up taking $6 off of our $200+ bill. Ridiculous. If it were up to me I would have never returned. Unfortunately my family decided to go here again tonight. Again it took a long time to get our food. My food was cold and bland, my kids food was cold. My husbands salmon was burnt to a crisp and my sister in law took one bite of her trout and refused to eat any more because she claims it was so disgusting. The wedding soup and bread were good, but that's it! My drink sat empty throughout my meal and never got refilled even when I asked. Bad food, slow service and rude managers. I'll pass on this place if my family decides to go again. Not worth it at all with all the other good Italian options around.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Delicious! Everything I've ever had here was great! The white pizza is a MUST! Always amazing! I'm also a big fan of the chicken piccatta. The bread that they bring to the table is delicious too! They have a wide variety of selections on the menu and they also have nightly specials that always sound great! Their prices are also reasonable. Overall, I highly recommend this place![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> 2nd times a charm. This place was 3.5 starts the first time I came, but stepped up large tonight. Waitress was righteous and very fun. Food was all excellent. Caesar salad tasty--got with tomatoes big $ on that, fettuccini carbornara with bacon n smoky cream flavor. Can't wait for the leftovers!! The white pizza is that star though. The crust/dough is heavenly and the flavor is top shelf. I don't throw those accolades out easily, especially on pie, but this joint serves it up. Good vibe, great service, phenomenal food. Ill be back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Service was great. Apps delish, specifically the stuffed banana peppers & lentil with ham soup. I think I chose the wrong entree though because I ordered a cod with crabmeat special. The cod was completely tasteless with some crabmeat layed across the top. It all reminded me of boiled fish. Yuck! Note to self. Order the pasta![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love this place! The food is always so fresh and delicious. The staff is always friendly, as well.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> spinach/feta cheese salad: B- +pesto alfredo penne : :A+ +Coconut Cake huge piece: A+ +bread small portions: B +Service B +host seemed grumpy, waitress good, but then she got busy . +PRICE: Pasta was $15 and the portion smallish more like a $12.99 dish +ARRIVE EARLY ON SATURDAY NIGHT THIS PLACE PACKED after 6pm[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It was just what we were looking for. The service was great. My husband had the veal sausage on green pepper appetizer in the larger size. It was great (spicy) and enough for a meal. I had the stuffed eggplant. That was very good but the sauce could have been a bit heartier. I would definitely go back. Really nice atmosphere and free parking in the back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We stopped at Papa J's last Friday night (8/1) for a round of drinks. There were 7 of us altogether and we had eaten at another restaurant earlier in the evening. One member of our party walked up to the bar to let them know we were sitting on the couches along the wall, as it was fairly busy that night. In the short time that he was there, a man who was behind the bar looked at him and then turn away without saying a word or notifying anyone else. He then turned to a waitress who had approached the service area of the bar and asked her if we could have a server take our drink order. She said ""yep"" and then abruptly turned and walked away. At that point, he asked to see the manager who came a few minutes later. When my friend told him of what had occurred, the manager said ""What do you want me to do""? + +My friend said ""An apology would be a good start"" whereupon the manager looked back at him and said ""Get out and don't come back"" ???????? Are you kidding???? + +My friend is well traveled and frequently stays at higher end hotels and dines at quality restaurants. He was not screaming or belligerent in any way, shape, or form; simply informing the manager of what had occurred. + +That being said, we left and went back to 131 East, where we had previously eaten. The service there was fabulous, as was the meal and the drinks creative and exquisite. + +There are new restaurants that have opened in Carnegie as of late. Papa J's is no longer the only game in town. Obviously this is the way a simple complaint is handled by management. Appalling!! Do yourself a favor and frequent any of the other restaurants that are within walking distance of Papa J's. They understand the concept of customer service.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Some of the best chow around--love this place. The bread and salads and soups are great.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Finally, great Tuscan-style Italian food in Pittsburgh, not that tasteless stuff that locals think is Italian. + +The bread was warm and fresh. The bolognese sauce was creamy and rich, and unlike most restaurants was made with veal. I love the fresh smell of baking bread throughout the restaurant. + +I'm looking forward to working my way through the menu of chicken options, and next time, I'm saving room for dessert! The display of cakes and pastries at the door was amazing.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Man has this place gone down hill. My husband and I went a couple of weeks ago. We had salads and pasta. Both were on the verge of inedible. With a single glass of wine, I felt downright robbed at the $50 price tag. Seriously, I could have easily made what we had with jarred sauce and boxed pasta at home. Classico is better. And the service was pretty absent to make it even worse... seemed she knew it was terrible and didn't want to deal with it. Seriously, I'd rather eat at the OG.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Food was NOT GOOD at all! My husband & I ate here a couple weeks ago for the first time. I ordered a salad & basil pesto cream pasta & my husband ordered the spinach & feta pasta. The salad was just a huge plate of spring mix (nothing else in it) with WAY to much vinegar dressing. My lettuce was drowning in the vinegar. My pesto pasta had no flavor (did not taste like a cream sauce to me) & the pesto was so runny/watery & way too much sauce not enough noodles. My husband's pasta had even less flavor than mine. We ate about a quarter of the food & couldn't even finish it. We took it home & it was so bad I didn't even eat my leftovers. And I hate wasting food!! Plus the prices are expensive for the amount of food you get & of course the poor quality. Don't waste your time eating here. There are much better Italian restaurants in Pittsburgh.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Talk about overpriced. $18 for a fairly basic pasta with some obviously frozen chicken chopped up over it. The latter was terrible, thin and flabby and rather unappealing. The pasta itself was ok, as was the sauce. The desserts are pretty good. But honestly, that is a $10 dish whose price has been inflated.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm up in the air about how I feel regarding Emmert Dental. Being that it is located in Market Square can be both a good or bad thing. Parking is scarce not to mention you have to pay for it yet you have great restaurants and coffee places around you. The office itself is old and raggedy looking but the staff are young and hip. I think possibly a little too young and hip. My dentist knew what she was doing but I didn't adore her. I'm still working out my bill because they charged me too much on my copay and don't really seem to have all their info. together. After a cleaning and fillings, I think I'm going to look for somewhere else to get my future dental work done...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've decided where I stand with Emmert Dental. They are unprofessional, rude and have no clue what they're doing (behind the desk). I will not be going back nor will I have nice things to say about them.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> THE WORST DENTAL EXPERIENCE OF MY LIFE. THEY ARE BUTCHERS! My husband and I went to Emmert Dental in Bethel Park for a routine cleaning and check up. I had one tooth that I had a recent root canal on and a few small cavities that needed filled. After the so called dentist - Dr Carnavali - did my exam, I needed 3 additional root canals and an extraction! An extraction on the tooth that just had a root canal. I was told that part of the tooth had broken off and that a crown was no longer possible. I didn't know any better, so I agreed to schedule the extraction for a few weeks later. The ""dentist"" wanted to extract it that day, but I had plans for the weekend and was not about to be in pain. So, 2 weeks later, I went in for the extraction. After they gave me novocaine they get me with ""you need a bone graft also in that area since we are extracting that tooth"". I have never had any issues with bone loss with previous extractions so I didn't feel it was necessary. I had 3 employees surrounding me, pressuring me for this bone graft. So, I reluctantly agreed. I had to pay $259.00 for this ""bone graft"". So, I signed everything. I wasn't even given enough time to read the document, so I should have known and got up and left right then and there. The ""dentist"" started the extraction. I have never been so uncomfortable in my life. He pulled on my tooth, used a metal instrument to pound on my tooth and was pulling so hard that my head was coming up and slamming back down against the head rest. Finally, after a good 15 minutes of this torture, he ripped the tooth out of the side of my jaw. I was literally ganging from all the blood running down the back of my throat. He then stuck some pink powder up in the extraction area. I'm assuming this was the bone graft. I ended up with many stitches. I was given an antibiotic and instructed to schedule an appointment for the following Saturday so they could start the bridge. Then I was hit with a bill of $569.00! My insurance covers 100% of extractions. I was in so much pain for 2 weeks following the extraction. Pain severe enough that I had to call off work and I couldn't sleep at night. I refused to go back to Emmert Dental. And after a visit to a very reputable dentist, an endodontist and an oral surgeon, I have to have oral surgery to try and repair the damage Emmert Dental has done to my mouth. They caused a very large deformity in my jaw and I am at risk to lose additional teeth. Save yourself a lot of time, money and pain. Emmert dental only cares about the money, will over charge you and leave you less than happy with the dental work. They are butchers and should not even call themselves dentist. And if you have an issue with their billing practices, don't expect to that resolved easily. I have called numerous times and I am always told that the manager and or billing department is not in. I have contacted the BBB and a lawyer. I expect and want a full refund. No one should have to go thru what I am currently going thru. They do unnecessary extractions so they can do a more expensive procedure such as a bridge or an implant. Now I have to go thru oral surgery, more pain and suffering and more time missed from work because of Emmert Dental. And the root canals they said I needed, my current dentist and my endodontist both agreed that I do not need tooth canals. In fact, the teeth are perfectly healthy. They are crooks and butchers.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The worst dental office I ever been. No one can beat it!!! You should avoid it at any time.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Eat at your own risk. The service is terrible, the staff seem to be generally clueless, the management is inclined to blame the staff for their own mistakes, and there's no sense of FAST in their fast food. When we came, half of the menu board was still on breakfast, and it was 4:30p. The only thing they have going for them is that the food is hot and tastes just like McDonald's should. + +Then again, the franchise is owned by Rice, and I've come to take terrible service is their MO.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My expectations for McDonalds are t rarely high. But for one to still fail so spectacularly...that takes something special! +The cashier took my friends's order, then promptly ignored me. I had to force myself in front of a cashier who opened his register to wait on the person BEHIND me. I waited over five minutes for a gigantic order that included precisely one kid's meal. After watching two people who ordered after me be handed their food, I asked where mine was. The manager started yelling at the cashiers for ""serving off their orders"" when they didn't have their food. But neither cashier was anywhere near those controls, and the manager was the one serving food to customers and clearing the boards. +The manager was rude when giving me my order. She didn't make sure that I had everything ON MY RECEIPT, and never even had the decency to apologize that I felt I was getting poor service. +I've eaten at various McDonalds restaurants for over 30 years. I've worked at more than one location. I expect bad days, bad moods, and the occasional mistake. But I have yet to have a decent experience at this store. It will remain a place I avoid unless someone in my party needs to avoid illness from low blood sugar. Perhaps I should go back to the racially biased service of Steak n Shake instead![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've tried to give this McDonalds a chance but my patience has run out. The only reason why I came here as much as I did is because I like the $1 iced coffees. But it's not even worth it. This McDonalds is poo and so is most of the staff. + +Whenever I want to go through the drive-thru I can't because there is a line of cars wrapped half away around the building. And even when the line is shorter there's always a hold up of some sort. So most of the time I just park and go inside the restaurant. + +Today was a horrible day. I ordered an iced coffee (no cream or sugar) and a chocolate chip cookie. It only takes 30 seconds to fill a cup with coffee and 30 seconds to take a cookie out of the case. I waited 10 minutes!! Sorry but that's too long just to get a coffee and a cookie! It's not like I ordered a meal! During that time I saw people come in after me and get their milkshakes and iced coffees within two minutes! WTH?! I told the petite sleepy eyed cashier I wanted my money back! Her eyes opened wide in surprise, like I really woke her up or something. She said,""Youre the one who ordered the iced coffee? I can get it for you!"" For real? She was the one who took my order! I told her I waited too long and I just want my money back. The manager offered to make my iced coffee, but I refused because I had just had enough. + +There are *few* employees there who work hard but everyone else is dragging their feet. There is no organization or teamwork, everyone is scrabbling. It looks like none of them want to be there. I used to work in fast food and I know it sucks, but come on! + +I'm sorry but I can't recommend this Mcdonalds. It's poo. I'm not coming back here anymore. Guess I'll be going to Starbucks- and their iced coffees taste better anyway![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This McDonald's is so bad it's amazing. + +Order: Big mac, large fries, diet coke. + +The soda machine was broken. No sodas. + +Then I got to the window. ""We rang you up for medium fries."" (Not what I asked for) ""Well, if you want a large, you're gonna have to wait 4 minutes. We just started a new batch."" + +Left with: Big mac, medium fries, no coke. + +Actually, now that I think about it, this was one of my better experiences there...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We had the worst possible experience at the Eat N Park at Waterfront on 2/12/10 at around 10pm. Our waitress (Annemarie) was inattentive and got us the wrong order. We ended up with a dish we had not even ordered and still got charged for it on the check. + +One of my friends ordered a Buffalo Chicken Sandwich, which according to the menu description, should've had lettuce and tomato in it. But the sandwich that arrived on our table had none of those ingredients. When pointed out to the waitress, she just brought some lettuce and tomatoes in a plate! How crude! + +Spoke to the manager after paying the full check and first of all, she did not even offer to re-imburse for the item we did not even order, and that had been forcibly thrust upon us. + +When I asked the manager about the Buffalo Chicken sandwich not having any lettuce and tomato, she said they just got new menus and that description is not correct and that Buffalo Chicken Sandwich is supposed to be without lettuce and tomato! What a lame excuse! Even your online menu says under the description for a Buffalo Chicken sandwich that its supposed to have both those ingredients - ""Served with lettuce and tomato on a fresh-baked Kaiser roll."" - That's what the last line in the description of Buffalo Chicken Sandwich says. Shame on you Manager for lying! Instead of admitting her fault, she was blaming it to a new menu! + +Not only did we have to pay for something that we didn't order or eat, but we got sub-standard food that was different from what was described in the menu, and had to deal with a really bad waitress and insensitive and deceitful manager to top off the whole experience. + +I am never going to come back to any Eat N Park location ever again, and will never recommend one to any of my friends either. What a waste of time and money! Plus dealing with callous and lying people - my goodness, I surely had my patience tested this evening![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This company represents a honest and caring company that cares about their community. They operate a variety of businesses and restaurants including the Eat n Park locations, the new Porch in Shenley, Six and Penn Kitchen, and the new upcoming Hello Bistro. I cannot wait to try all of their dinning places.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> They burned my fish and they burned it bad. Ordering fish at Eat'n Park is always a gamble. I just never know how it's going to turn out. I'm a risk taker so I ordered two pieces of baked lemon sole. + +Well it went terribly wrong. My waiter came out and said, ""They burned your fish, so I had them put two new pieces in the oven."" I was impressed by his honesty and didn't mind waiting for two new pieces. + + I gladly helped myself to my boyfriend's french toast while I waited. + +Then out of no where another server comes to the table with the burnt fish and sets it down infront of me. With the burnt side down of course. That just shows the kitchen is not in total coordination. + +Like I said getting fish from Eatn' Park is a toss up. In the end I got two nicely baked pieces of sole to replace the burnt ones, so I left satisfied.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Some how even though the food at this Eat'n Park is down right abominable, the smiles and laughter is always there. How can I stay mad when the prices or so cheep? Myself my boyfriend and his nephew had lunch with milkshakes and me having a coffee it was $31.00 + +On this particular occasion the fire alarm went off and rang and rang and rang loud and long for over 15 minutes before the fire department got there realized they didn't have key to turn it off and than another 10 minutes later finally shut it off...only at Eatn' Park. + +My baked potato was hard as a rock, I had ordered two pieces of baked cod and only received one. + +The waitress was very sweet and attentive and really attempted to build a rapport with our lil nephew which I thought was sweet.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is a tiny Starbucks and it locations like this (although cute) makes you wonder if your really meant to hang out or just grab your coffee and leave. Leaving is always a good idea at this location anyway since you have a nice fountain in the back with benches and it is a central part of the Waterfront Shopping. + +Starbuck isn't my favorite coffee chain by any means. Is it just me or do all Starbuck coffees taste a little burnt and bitter? No matter how trendy, cool and upscale their establishments are I can't get around the yicky tasting bitterness of Staryucks regular coffees. Talk about over roasting a bean...Maybe something has changed with their regular coffee but I have not drank it in about a year. I am not one for soy caramel latte foofy stuff. Still I'll give the establishment tres estrellas for the fact that their espresso is acceptable and doesn't taste half as bad as the regular coffee bean.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Friendly staff, same starbucks fair you get anywhere else. Sometimes the lines can get long.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Mmm...peppermint mocha + +In my quest to visit every Starbucks in the USA I have stopped at yet another location. This one is located in the center of a circle road -- very cache and in a newer part of the area.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Typical Starbucks coffee chain. 2 things I dont like about this Starbucks: + +1. Ive been there twice and both times the place has been dirty, compared to the other Starbucks I have been in. + +2. If you have to use the bathroom, they give you a key thats attached to this nasty bottle. Im pretty sure they dont clean that bottle after every use or even nightly. + +Aside from that, good coffee and fast/friendly service.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> If there was ever a ""get your coffee and go"" Starbucks, this is it. Right in the center of the Waterfront, this Starbucks has no sofa, comfy chairs, only table seating. I love the baristas here, But I don't like the location of the building.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is a typical Starbucks. The coffee is good but the store is suprisingly dirty.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have to agree with Joe on this one. The baristas are extremely friendly, and the service is great, but the fact that there are no comfy chairs or couches is very unwelcoming. I do think however that the building is beautifully ans strategically located in the center of the shopping. I just wish they had better seating.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I just realized they remodeled this one recently-ish. Well, in my world recently because it's been a while since I've been here. + +They've added more seating which makes it way more conducive to having a meeting here. Which is my concern during the week. I imagine during the weekend it just fills up with tweens getting their sugar rush before hitting the movie theater. + +The coffee, or tea for me.. Is still same old same old. I don't imagine one single Starbucks will break the mold and make original drinks...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great location! Close to shops and theatre. Nice staff.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Regarding quality of beverage, this is just your average Starbucks. I can't complain but am not blown away either. However, I really like the location of this shop, which is located in the center of The Waterfront's specialty retail shops. Though in the midst of a lot of retail, the surrounding area is very picturesque with pretty green grass, flowers, and a fountain. Hanging out here is very relaxing.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love the location of this Starbucks, which is why I'm giving it 4 stars. It's right smack in the middle of clothing stores, the Loews movie theater, as well as restaurants. I love grabbing a mid afternoon latte here on a Saturday while perusing various stores such as the Gap or Loft. I also like coming here before or after a movie for a quick caffeine jolt. + +While the drinks are the same as you would find at any Starbucks, the baristas and staff are really friendly, perhaps more so than other area Starbucks. + +My drink or choice when I come here generally in the mod afternoon is a venti (or trenta...) berry hibiscus refresher. Yum! It is the perfect afternoon pick-me-up that leaves me feeling refreshed and hydrated.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This Starbucks is teeny-tiny! + +Seating inside is VERY limited. This is a Starbucks to grab and go and continue your shopping at the Waterfront. + +Baristas are friendly and fast.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> As far as Starbucks go, this is a pretty nice one. The baristas are friendly and while I was here, a lot of regulars must have come in, because they bantered away with almost everyone. The bathroom was clean and well maintained and the trash wasn't overflowing in the canisters around the store. The pastries looked fresh, but I didn't partake. The noise level was also at a nice working level - not too loud, music just barely audible. + +I do wish there was more seating. It is nice that this location has a counter at the end of the bar for sole workers, but it doesn't replace more tables. I'm sure this isn't as much of a problem in the summer when there's the space outside. + +There was a treat receipt promo going on, but the barista didn't tell me about it, which I found odd. Usually when they have promos like that going on, they ask everyone if they want their receipt to come back later in the day to claim whatever the offer is. Today it was one of their new pastries for $1, I know in the summer they do $2 grande iced drinks with that morning's receipt. + +Overall, nice working or socializing environment. Very friendly and inviting. It's what I've come to expect from Starbucks, so points for consistency.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm not a huge fan of this location. I think that it was oddly built- the small, alley-like front makes it difficult to get past people on your way to/from the bathroom or tables when it's busy. And there's hardly any tables to sit at. Furthermore, people tend to clog the front on their way in, which makes things particularly difficult (especially in the winter weather). The staff were pretty impersonal to be, but maybe that was due to the high traffic of the place and the time I was there. And the coffee that I had was cold- I'm sure it was probably the bottom of the batch. I'd probably only walk in here again if someone else suggested it before or after a movie or while we were shopping in the area.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This Starbucks is 5-Star Friendly. The shift supervisor Lucious keeps the energy in there moving and light. He recently helped me with a merchandise return and embodied everything a good manager and all around mensch person should - patience, kindness, generosity and fairness. I left that afternoon loving Starbucks even more than when I went in. It's great that a company and their employees can be as loyal to their customers as their customers are to them.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I am always so pleased with the customer service here. For such a tiny Starbucks, the do a really great job serving the masses that come in there and still manage to take the time to be friendly in the midst of the frenzy. + +Outdoor seating in the summer is nice.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> For someone who straddles the line between sometimes craft-er, this store can seem vast and confusing. There's rows and rows of baskets and bedazzling jewels and paper and...oh my...scrap booking! When I want to find boring old felt....it's like...where do I start? + +I'm in a hurry, as always, and I rush in and the first thing I look for is an employee. No one to be found. I could call out and my voice would come echoing back. I run between rows of paper, wood and gosh darn scrap booking....no felt! Where do I find felt! Where do I find an employee!? + +FINALLY, I find one after 15 minutes of wondering around. She's incredibly nice and leads me to the felt. This is not the first time I've been hard up to find help. I tell her she was hard to find, and she tells me that they're ""low on payroll"" and can't have any one the floor BUT HER! In that WHOLE store, JUST HER! That's ridic! + +Not a month ago I was, again, in a slight hurry and stood in line for about 15 minutes to check out, with 2 employees at the register and 6 people per line, I gave up and walked out. + +Hey Michael, do you pick up what I'm putting down? You're not making any money because your costumer service SUCKS....in fact, there's no service to be found![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have been frequently shopping at this Michaels store over the last couple months since I began taking a cake decorating class and hosted a large baby shower at my home. The store has typically had the supplies that I need from cake and cupcake baking and icing to scrap booking supplies. This location is pretty average compared to other Michaels - it's exactly what you would expect when going to this store. It's not a large store, but it's not a small store -- just average. + +I do enjoy using the Michael's coupons when shopping. I definitely save a lot of money! Instead of toting around the paper versions, I actually have the iPhone app that has coupons available to use from the app. + +My only complaint is that sometimes it takes a while to check out at this location. I don't normally have a problem - usually only one or two people ahead of me - but sometimes it can be much slower. Today, for example, there were only two customers ahead of me, but one of them was having issues with a coupon. The line began to get longer and longer, and though a couple associates were lingering up front, they kept calling for someone else. From personal experience of being a manger in a retail store, do not linger or let your associates linger near the cashiers without jumping on register. Whatever the reason may be that you are not helping customers, it still appears rude and make everyone more impatient....[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It's your typical chain craft store. And let me reiterate that I'm not a crafts person. I walked in because I needed dial rods for some signs I had. Now for being a chain store I was a bit upset because even though they had a decent selection, the amounts they had for each one I wanted were scarce. Imagine me standing there with different sizes of wood in my hand and just staring in disbelief. And for a piece of wood, the price was a bit steep. + +I will provably come back here, but only for an item that I cannot find elsewhere. Or if I'm too lazy to drive further out.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It's yet another Michael's, and it's a very good one. Recommended always. For those who love crafting, Michael's is a godsend.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I come here pretty frequently for art and craft supplies. Whatever Michaels doesn't have I just order online from a different retailer. Some items are pricey but you can still find some good deals. If you go all the way to the back of the store you can find interesting clearance items. Customer service is average. My favorite time to visit Michaels is when summer is about to end and all the fall and Halloween items are set out. Since I come here often, I know where everything I need is. However, the store could use a new layout.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The one good thing I can say about Michael's is that they have a wide variety of hobbies and crafts included in their selection. They've got items for woodwork, painting, knitting, kids crafts, scrapbooks, you name it. The problem is, the variety of products for your particular craft is probably dismal. They've got lots of cool items all over the store that you're convinced that somehow you need. (Because it is soooo cute, and you could TOTALLY do something with it. Right..?) The store feels cluttered because there is so much stuff everywhere. However, if you're looking for something specific, good luck. It's not even a matter of the product being difficult to find in the store. It's that when you find the right section, there's either nothing in stock, or they simply don't even carry what you need. + +I stopped in for crochet supplies, and the yarn selection was laughable compared to many other craft stores. I ended up going elsewhere for my stuff anyway. + +Plus the prices at Michael's are significantly more than other area craft stores. I usually only stop there if I'm already at tend Waterfront. I'd recommend checking other craft stores first. Unless you need glitter. Especially fine glitter. Michael's has the best glitter selection/quality of any store I've ever been to.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> You would think their exorbitant prices would at least buy some decent customer service. Not at this location. + +They are totally understaffed and have almost nobody able or willing to help you find anything. This is a problem because they carry so many completely different products that it's hard to find what you need. Expect to wait at least a half hour before getting assistance. + +The organization is disjointed, especially depending on your project. There's even a section called ""art supplies"". I thought that was kind of the point of the whole store. + +What did it in however was how miserably they packed my picture frames. The place next door wrapped two dollar drinking glasses in paper to protect them, but apparently Michael's thinks a grocery bag is sufficient to protect a nice picture frame in bad weather. + +So, the inevitable happened and I dropped the bag. Now I don't expect every place to be sympathetic, even though it could have been packed better, but when I asked for a refund they were down right RUDE. Hey I did drop the thing, but some empathy would have been nice. I wasn't completely out of line asking because a little bubble wrap and it would have been fine in the first place. I will never be back to this or any other Michael's.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Whenever I was at the waterfront I would eat here. The shakes are good, as are the shoestring fries and baked beans. The sandwiches are small thin patties of meat so you probably want at least a double. Overall, pretty tasty.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The food is good and its CHEAP. + +I mean REALLY INEXPENSIVE. + +$4.00 for a burger and fries. Add a coke and its like $10.00-$13.00 for two people. Seldom if ever crowded. + +Service can be a tad slow but hit or miss. + +They also do breakfast and its a great alternative to waiting at eat and park. + +Try the shakes, they're great.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Its clean, open 24/7 with hot shoe string fries and creative milkshakes. What else do you want in life??[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is the absolute WORST Steak N Shake I've ever been to. + +The bf and I got lost around Pittsburgh for 40 min. trying to find this location and on top of the unnecessary 1 hour wait for our food, the food itself was just so crappily made. It was so bad and we had waited a ridiculous amount of time (c'mon, Steak N Shake is basically a glorified McD's), our waiter comped our WHOLE MEAL. + +If not for the compensation, I would have been pissed that we had to pay for such a crappy meal. The bf, on the other hand, was more upset about the principle of the matter... we had trekked all that way just to get our Steak N Shake fix (since both of us haven't had it since our undergraduate days) and it was a major fail. + +I think I'm good with my Steak N Shake craving for a long time now... + + + +PS. The whole joint smells like major B.O.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I went here at 3 PM between the lunch rush and the dinner rush, and the restaurant was maybe 20% full. I ordered the Chili Mac Supreme to go. I thought I would be in and out within 5-10 minutes. Keep in mind that this restaurant even has a drive-thru; the expectation is quick service. + +Long story short, my food never came... the waitress told me (after I had been sitting there waiting for thirty minutes) that the kitchen hadn't even started on my order yet, so I told her to cancel it and walked out. Now I see that others on Yelp have warned about the slow service at this location. Wish I had looked it up earlier.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I heart Steak N Shake. I love the fact that the fries are shoestring, the burgers get to you pretty fast, they're a little greasy, and the food is super cheap. + +I visited Steak and Shake on New Year's Eve in preparation for an evening of mostly tame partying. I was unnaturally attracted to their Wisconsin Buttery Burger, which is a double patty cheeseburger topped with grilled onions between two buns that have been buttered. Sounds good right? + +Well, I get this delicious diet abomination and discover that my buns had been dunked in butter. The pearly gates of cholesterol laden heaven with the triglyceride angels were singing to me. I took the liberty of increasing my sodium intake by pouring their burger/fries seasoning on the buns and I literally got tears in my eyes....most likely from the salt overload, but possibly because this was one of the most evilly decadent things I had eaten in a long time. + +This is not meant to be a fine dining experience. Service wasn't fast but it wasn't slow. It just kind of was. However, the waitress did get a point for explaining that the order would take X amount of time to all patrons. So I give them a pass for being upfront about it. + +Next trip to Pgh is going to feature Steak and Shake - I guarantee it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Well... as Steak 'n Shake locations go, this isn't the best one around--but it is burgers and fries that are open 24-7. + +The milkshakes are good! + +PROS: +Always made fresh, when you order; + +CONS: +Greasy (but its burgers); +Takes longer than typical in drive thru (but that's bc they're made fresh!); +Service (on a scale of 1-10, 10 being awesome) is a 4.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> In general I do like Shake N' Steak, but this location is a hit or miss location! You never know what kind of quality or service you're going to find here. A friend and myself went a few weeks back after a movie and it had to be one of the worst trips there EVER! You can't entirely blame the waitress since she was the only one there for the entire place...poor scheduling on the manager's part. However, while she can't be accountable for the slooooow service, she was accountable for both orders being incorrect. The burgers were over cooked and the fries were soggie and the milkshake was runny at best... + +By far my worst visit to Steak n' Shake![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Rather typical SnS. Had a good lunch crowd. Milkshake was good but not as good as EnP down the street. It took to long to get the burger for some reason, 25 minutes, I realized cooked to order but this is a little long for SnS. Ordered the Guacamole Steakburger and it only had a small portion of Gauc...not your usual amount..kitchen was not up to speed on portion sizing for some reason. Definitely did not look like the picture on the website. Oh well![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Ah, Steak n Shake, you hit the spot after a night of drinking. Open 24 hours, drive thru or dine in, with wonderful, cheap greasy burgers, chicken fingers, breakfast sandwiches, and shoestring fries. You're faster (and cheaper!) than Eat N Park. Plus your employees wear those adorable bow ties. Granted, if we were at a fancy party, I might act like I don't know you, but deep down inside you know I heart you.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The only thing worse than the food is the service.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Terrible wait staff couldn't even seat us. Before we, and another party walked out without even being greeted properly, I observed several employees traipse out the front door, several tables who were waiting for their food for a long time, several employees just standing around out of direct view of the tables, a morbidly obese hostess that could barely physically walk from one end of the store to the other. I think one server was high. + + Going there was a special request by a 7 year old getting over a long-ish illness, so that makes the shabby treatment more enraging.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place is s l o w....like so slow I have got up and left after waiting 30 minutes and not even being acknowledged by a server. The food is okay. Def not worth the wait. Milkshakes are just okay as well. Booooooo.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I really like the chili. Burgers are fair and salads are pretty bad. Pretty hard to mess up a side salad. As others have said you never know what kind of service you will get. Store is usually understaffed and cleanliness is fair. The staff is usually disinterested with customers and sometimes outright rude. All in all what you pay is what you get. Cheap and crap service.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Fast food done right, what more can you want? + +A throwback to old timey diners, steak and shake is where you get a decent meal at a good price. + +My sisters and I arrived on a Tuesday afternoon around 3pm catching their 2-4 happy hour, which we read on the door upon entry; a lovely surprise. This meant that all shakes and drinks were 50% off! + +I ordered the western BBQ burger, which was 2 thin patties, cheese, bacon, BBQ sauce, and fried onions. It came with shoe string fries (my favorite), all for the low price of $4.79. Are you kidding me? What's not to like! The food was actually pretty good! I liked it a lot. Since it was happy hour I also ""splurged"" on a chocolate covered strawberry shake. It was meh. Could have gone without it. The overpowering taste of artificial strawberry really turned me off, but the hot fudge saved it. But, how can you really go wrong with hot fudge? + +All in all, 3 meals and 3 shakes came to $20. A steal. Also the food is good! I enjoyed it. I'd come back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Fast food in a resturant setting. Considering this food is good and cheap plus you can get food to go. Must be a reason why this place is always packed.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The food is good. Unfortunately the service is very hit or miss. The main issue seems to be with the kitchen, the waiters and waitresses are often very apologetic for the long waits and it's pretty obvious that some of them avoid the tables after taking the initial order to avoid hearing complaints.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Food is good, what you'd expect from Steak n Shake. THE SERVICE IS AWFUL. so incredibly awful. expect to take at least an hour for your meal, even when it's slow. I've been going here for years when I want a cheap meal, but the service is so so so awful. Go to McDonalds.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The service was fast but the food was terrible and so was the service. I had a bus to catch so I couldn't wait around waiting for the check so I went to the counter to pay. She never brought my check, never checked to see if my drink needed refilled, she just mopped the floors. + +The burger was really greasy, the fries were Luke warm and the cheese on them wasn't as flavorful as it should be. As a new Pittsburgher I'm not impressed.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I should have known better than to stop here, but I was nursing a hangover and just wanted something quick and simple. I should kick myself for thinking of this place. + +Granted I decided to go to the drive thru and knew there would be a wait. The sign actually says that the food is prepared when you order it. I sat for almost ten minutes at the window while my food was prepared. During that time I wished I could have taken back my order and also wished that I hadn't paid already. + +While sitting at the window I decided to just stare inside and watch some of the employees doing their job. What disturbed me the most was watching the employee making the milkshakes. Making a milkshake isn't that hard or glamorous of a thing to watch. What disgusted me was that the guy actually lifted several of the containers for the milkshakes and smelt them. I mean smelt them to see if they were clean, instead of actually taking the extra minute or two to clean the container. After witnessing this my food was finally ready and I drove away. + +When I finally got to eating my food I was underwhelmed. The fries had no flavor and with the size of the cut it appears you get more than what you ordered. The ""steakburger"" really, they should just call it a burger, was overpowered by the BBQ sauce on it. It was all I could taste. + +All this has cemented me in not wanting to ever step foot in one of these establishments ever again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Burgers are not the best quality. Better than McDonald's but not much better. The fries are fairly thin, but crispy. They aren't bad. The prices are also quite decent. However, their shakes are amazing. Thick and creamy. It's also great that they have half off shakes on weekdays in the early morning like 1-3am.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> You know what you're getting with a Steak N Shake: it's about one rung up from a McD's in quality, and about two rungs down in quickness. At least, you think you know. + +I used to have a small place in my heart (though the salt and fat weren't very kind to said organ) for Steak N Shake, because hey, who can argue with beef and drinkable ice cream? But after my last trip, I can think of nothing more disgusting than having to eat here, this location in particular. I haven't been back in over year, and I will never step foot into a Steak N Shake as long as I have an immune system that I care about. + +After having eaten here, I hit the restroom on my way out (along with my two friends....hey, we're girls, it's acceptable!). One stall was already taken, so two of us are stuck waiting while this occupant does her....shall we say, business? After a few seconds, we realize that she's not only there to relieve herself, but to also take drive-through orders. Yes, that's right....""You want fries with that? *flush* Okay, that will be $5.50"". I have never, ever witnessed anything so insane as a drive-through restroom. To top it off, after finishing her ""bathroom break"", she walks straight out of the stall and into the restaurant. I guess she was in too much of a rush to complete the order she had just taken that she didn't have time to wash her hands. And I was in too much of a rush to choke back up what I had just eaten before it wreaked mayhem on my stomach.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love Steak N Shake. This one, however, leaves a lot to be desired. The food often comes out cold and the servers are apathetic at best. Most of the time, they're downright rude. I highly recommend avoiding this location if possible. There's one on Route 51 that's worth the 15 minutes it'll take you to get there.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I never thought that I'd be giving Steak 'n Shake a 4 star review, but I really enjoyed my dinner here tonight. It just hit the spot! + +I was impressed by our waiter as soon as we walked through the door. He apologized for our very brief wait to be seated and for the fact that he was the only waiter working at that time. However, everything was delivered promptly, and he made what would've been just a tasty diner dinner into a great experience. + +I ordered a grilled cheese and fries. The grilled cheese was well cooked and filled with tasty, perfectly melty cheese. I love Steak 'n Shake's thin and crispy fries, and these were as delicious as I had expected. + +For just $9 for me and my husband, I have to admit that we had forgotten how inexpensive Steak 'n Shake was. Based on the cost, the food, and our fantastic waiter, we'll be back soon.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I like the occasional steak and shake stop..... but this one has to be the slowest one ever. The cashier was rude and I could hear her yelling are you fucking kidding me because the register was not working the way she wanted.... wow.... just wow...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Every time we come here the service is laughably bad. On this visit a tabe which was sat after us had their food before our server graced us with her surly presence. Good restaurant elsewhere, just avoid this location if you want to get your food inside an hour.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Wow. Dirty and slow. The floors felt like they had the days burger grease spilled all over, and it took 30 m8n to get our take out order.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place teeters between a 2 and a 3 star review. I've had pretty good experiences inside, it's usually the drive-thru where things fall a part. + +It's the rare place I can get a Frisco Melt well, the ONLY place I can get a Frisco Melt! and that steak burger alone is worth the risk, Walk In OR Drive Thru. + +Just take a gun on Weekends, you'll be fine.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This location is terrible. The drive-thru workers are rude and they give you crap food. I waited 5 minutes before being able to order, even when there was only 1 car ahead of me. Then the lady proceeded to ask me if I would like anything on my burger, and (thinking the pictures on the menu are what they're supposed to look like and they would never false advertise) I asked ""doesn't it come with the fixings like in the picture?"" she then told me it only comes with cheese. So I then went on to tell her what I wanted on my burger. Pulled around and got my order pretty quick, but later when I open my burger its just meat and cheese. The meat is badly burned and cold. It was clear to me this burger was not fresh. I didn't even attempt to eat it, what a waste of a place. They definitely need better workers.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Steak 'n Shake's food is pretty good and the prices aren't bad for the quantity of food. I ordered a grilled chicken salad with no dressing. The salad looked thrown together and was $5.49 for 2 croutons, tomatoes, carrots, cabbage, lettuce and chicken breast. (They forgot the cheese!) The staff wasn't very friendly or helpful and seemed like they didn't want to be there. There usually is a long wait at Steak 'n Shake, but if you catch them when they aren't busy, you will breeze through- drive-thru that is. I do like their food and you can eat healthy options, but the staff isn't helpful and the quality isn't always there.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Nice staff but apparently there is little manager oversight around 3:28am. + +I do like this place. It must be nice to work somewhere that allows you to choose your own tasks. Like smoking, sitting and texting. I'm fine with cooking my food being fourth on the ""to do"" list because there is no where else togo really.... + +Why didn't they answer me at the drive through? I think they wanted me to come inside because my girlfriend and I are really really really good looking. + +This was annoying but understandable.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It's okay. Food is cheap but portions are small. For example I order the chicken tenders, and I got 3 little tiny tenders, and a decent amount of fries. Also the restaurant is not really clean either. This restaurant is not my number 1 choice.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> As far as I'm concerned, Filene's Basement is good for two things: cheap dresses and cheap accessories. + +As a young performer, I need good-looking dresses for frequent auditions -- and I need a couple, so I'm not wearing the same thing every time. The dresses on the second floor usually range from $30-60 and are good for over a year. It can be hard to find a full-length dress that's not reminiscent of a prom dress, but their selection of cocktail-length dresses is ample. + +As far as accessories go, Filene's tends to have cheap versions of popular trends. If I feel the need to stock my wardrobe with a transient fad, Filene's is the place to go.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Even when we didn't have a car Filene's Basement was worth the bus trip to the Waterfront. I always find something (usually I find 3-4 things and spend about $60) and better still, I am always still wearing the clothes and shoes 3 months later. + +I kind of suspect this is the best shopping in Pittsburgh; it's much better than the usual department stores, better than Marshall's and TJ Maxx and better than the Saks downtown, even when it has a sale. Selection, bargains AND quality. + +I like this Filene's better than Gabriel Brothers, which are harder to get to. Gabriel Brothers are a real discount shopper's challenge and I'm afraid I didn't live in Pittsburgh long enough to develop the necessary skills . . . Filene's was still up and running in June 2007 when I left town.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Love this store! Don't always have much luck with the sales, but I always find something I like here. This isn't your average Marshall's or TJ Max. I think the green dress I'm wearing is from Filene's![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is probably my favorite store in Pittsburgh, for the selection and variety of discounted designer clothing. Other stores carry the same stuff but for much, much more, and it's hard to find all the stuff that the Basement carries in one spot. (Yes, I admit that the 'burgh has some cool stores.) I would do most of my clothes shopping here if I were here more often.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Another store which has gone the way of the Dodo bird. Actually there was nothing basement like about it. What will be done with the empty space that is the question?[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> $9.75 for a red bull and vodka? I'm sorry, I thought I was in Pittsburgh, not New York City. Sing Sing, a dueling piano bar, is fun, but it would be a hell of a lot more fun if I could have more than one watered down drink before I warbled my way through ""Paradise City"" with the rest of the crowd.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Really enjoyed this a lot more than I thought I would. The drinks were on the pricey side, but I didn't head here to get smashed.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Had a great time at Sing Sing a while ago with friends. Friendly staff. Will return.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Piano Man to the tune of Gangster's Paradise...what more do I have to say? Get there early if you want a seat, $7 cover and really fun crowd. We had sucha great time and I can't wait to go back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> SingSing!!! What a blast! One of my favorite places to jam on Earth!! Cool bar, cool town, cool people... What else do you need!! The piano players are great, funny, semi-good lookin'... I mean dude, you gotta go!!! :) Love me some SingSing![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Well, the experience did not start well. When we walked in the singing we heard was NOT good. Oy was it not good... Thankfully, it (mostly) improved from there. + +So there were 3 piano players rotating out on a half hour basis. So each was on for an hour and off for half. Of the 3, two were really good. Good singers, good piano players, and very funny. The third guy, well, not so much. Piano skills were fine. But his singing was not. When he sang in his range, he wasn't too bad actually, but too often he reached for notes that he couldn't get to or forced things that just weren't going to happen. Often his jokes fell completely flat. Luckily the other two usually did most the talking. + +They played a variety of songs as requested by the crowd and would do them in unconventional styles if requested (Closer by NIN as sung by a lounge singer was a highlight). We requested Britney Spears' Toxic cause we thought it would be funny and so they gave it a shot and as luck would have it, it turned out REALLY good. That takes some serious talent to pull off. If they didn't know it (like Toxic) they'd find it and play it. They played a wide variety of stuff. + +Part of the experience is based on the crowd. We had a couple larger groups (there on a Thursday night, so smallish group in general) that they interacted with a lot, providing some running jokes and comedy. Of course, that also meant some annoying drunk people feeling like they could take over half the show. + +My friends were BIG fans of the super cheap beer specials. $1 drafts from Rock Bottom next door. The waitress wasn't great but it could have been that she was the only one there and the layout isn't that easy to navigate. The bar was generally uncrowded though so getting service there was fast. + +If in the Waterfront for a night out, definitely a place to hit and have some fun if you are up for some fun and willing to sit through a couple clunkers of songs/jokes. Having a fun loving group of friends to mock things with when they go off the rails a bit will help make it more fun.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> While we were in Pittsburgh for the Winter Classic on New Years Day, we figured we'd see what the area had to offer for NYE. My wife and I, along with my friend and his girlfriend hit up Sing Sing in Homestead. It's apparently located on what was the site of one of the largest steel mills in the area. When it closed they turned the entire site into a large outdoor shopping and entertainment development. The only remaining artifacts from what once was, were the nine or so original mill smoke stacks still standing at the primary entrance. Pretty cool. + +Sing Sing, which is a piano bar, is attached to the Rock Bottom Brewery and serves a selection of RBB's in-house brews and shares a similar menu. There are no TV's, no sports memorabilia (which is rare for this city), and no big booths for large groups. This place is all about being a cabaret with the focus on the musicians. Mind you this isn't a bad thing, just note that if you want a bar, go next door or across the street to Dave and Busters. I'd say Sing Sing holds about 150 people seated. + +This particular night they were hosting a (shocker) NYE's party. For $40 bucks a person you got a choice of two entrees (beef tenderloin tips or lemon chicken), veggies, mashed potatoes, one free drink coupon, a midnight champagne toast, and, what turned out to be over four hours of non-stop music. Again... Pretty Cool. + +There were three musicians holding down the fort playing more than just piano (drums, electric synth, bass guitar, and apparently I missed the sax). There was plenty of crowd involvement. As in most piano bars you request songs along with a tip. The larger the tip, the better chance of hearing your song you have. I put three requests on a sheet with a 10 and managed to get two played. Their rendition of Toto's Africa was fantastic and surprisingly, my curve ball got hit out of the park when one of the guys actually knew the tune and words to the Theme from TV's ""Growing Pains."" I was sold from that point on. + +I will take this time to note that this is NOT a family friendly joint. I'm not sure if it was 21+ only but I certainly wouldn't bring anyone too young to drive. A good amount of sexual refrences and strong language awaits you. + +Drinks were stiff and not horribly overpriced. I think rail mixed drinks were $7.00 and beers were 6 or so (RBB doesn't brew anything I particularly enjoy so I stuck with rum and cokes). All and all my bill wasn't scary and I'm not used to that on Dec 31st. Waitress staff was really nice and incredibly attentive. No complaints there. + +The only down side to everything was group seating as you're sitting at 2-top cab tables. It was easily fixed though as the group next to us was up for rearranging tables from side to side to front to back (allowing us to talk and share food/booze etc), also, being a tourist, we had no idea how hard it would be to get a cab in Homestead. Understandably NYE has its issues with cab availability but we had to wait 2.5 hours for a cab because, as we found out, Homestead is a very suburban community right outside of the city and everyone drives. + +Ooops! + +All and all a good time and someplace I'd certainly return to if for any reason I'd be back in Pittsburgh... as long as I have a car.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> In my opinion, Sing Sing is really not worth it. It gets expensive because you drink, maybe start to sing a few lyrics, drink some more, think of a song you wanna hear, put $5 and title of said song on a piece of paper, you drink, they play it, everyone else is trying to get their songs played so you put $10 on your next sticky note...and so on and so forth. I wasn't really into it when I first got there but as the night went on and lager went in I started to warm up to the place. I feel that if I have to drink in order to have a good time, it's not worth it. But again, that's just me. + +The 2 stars are for the piano players, who are entertaining and very talented, and the Rock Bottom brews they serve.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> So.Much.Fun! + +I WISH I could play a song at the drop of a hat. Too bad I never took piano lessons and I'd probably end up mumbling half the lyrics other than the chorus. Unless it's Salt n' Pepa's Shoop. + +This is a really great place to go when you have out of town guests or are looking for a fun place to take someone for a birthday celebration or a fun night out. It's just something different to do other than boozing it up at the bars on a Saturday night. + +Keep in mind you'll be paying around a $5-10 cover plus whatever drinks and food you get. The good thing is the food is coming from the attached Rock Bottom Brewery. So a lot of it is restaurant quality good. Plus the brewery beer is actually pretty good! OF course you will be paying restaurant price drinks...so of course they're up charged a bit. But you do pay for the whole experience....so you gotta get into the spirit with some spirits! + +The guys who play are incredibly talented. There's 2 guys that will take requests and play songs on the piano. They pretty much play ANYTHING you ask. Contemporary songs, throw back songs, fight songs, rap songs, pop songs. You name it, they play it. + +My favorite part is when they switch out to another two guys. They'll all four get on stage and play two piano's, a guitar and drums. They usually rock out with some fun familiar songs (um, Journey, of course!). + +The birthday song is seriously the best. They sing to you....and call you some names....with expletives. But in a totally nice way of course. You just have to go![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Dueling piano bars in Pittsburgh started at Station Square, and they died out. Then when the chain restaurant magnet ""waterfront"" opened in 2000 the parent company of The Rock Bottom Breweries decided to open Sing Sing in back of The Brewery. + +When it first opened it was pretty cool. The very first house band could put on a show that led to standing ovations. I know, I was there. From Stairway to Heaven to Free Bird, Stayin' Alive to She's My Cherry Pie, Elton John to the Boss, they were amazing at sounding like the bands they were covering. Equally incredible were the obscure songs that audience members would shout out, songs only you though you knew, and they would effortlessly sing a good portion of the song, sounding like the band who's song they sung. + +But today, Sing Sing seems like it's stuck in the early part of the 21st century. The whole dueling piano, shout out a song to stump the band, Sing us a song you're the piano man has run it's course. I don't hate Sing Sing, but I could never come here more than once a year. It's a been there, done that kind of place.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> If you want to be wowed by musical talent and want to laugh all night, go to Sing Sing :) If you send a dollar up with a song request, they will play it. If they don't know it, they will ask for the person who put the request in so they can sing something else they like, or they will look up the lyrics and sing it!! They aim to please :) I have definitely been pleased :)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Sing Sing is awesome!! Give a buck or more and they will play anything, and if they don't know it, they will search for who requested the song so they can do something else the person will enjoy! :) Great humor too!! :)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> What a great time! This place was awesome! I wish I lived right down the road, because I could see myself being a regular here. + +Honestly, these guys have got some talent, like real talent. They can play the piano, sing, play guitar, and the drums. Did I mention that they are all pretty hilarious, too. I'd easily pay the $7 cover to get in here any day because it really is worth it. + +I am sure I will be back in no time at all. Next time, I am bringing a big group of friends.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Came here with a group of girls and didn't have a reservation. We paid the cover, walked in and it was absolutely packed. There was nowhere to even stand. One of our friends was having issues with an expired license and when we found out that not all of us got in, they let us get our $7 cover back without issue. + +I recently went with a big group who had reserved about 50 seats. People who were not in the group kept coming in to the reserved area but the staff was very helpful in dealing with the group. + +They brew their own beer so do not expect to see any known brands. There are only about 6 beers on top, so if you are more of a light beer drinker you might not be too happy with the beer choices. They also have mixed drinks and wine. The mixed drinks around about $9 and they have a limited number of bottled wines (despite what it says on the menu). + +The entertainment was great and I would recommend it for a group outing. But definitely make sure that you have a reservation.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place has gone significantly down hill. I've gone to Sing Sing about once a year for the last 6 or 7 years. When we started going there you couldn't get a seat unless you got there early. It was always packed. However, each year the crowd seems to get smaller and smaller. Crowd is an important component of a piano bar due to the interactive nature of it all. I was there last Saturday night (8/4/12) and there was about 20-30 people there. Very slow and boring. It appears the crowd is no longer allowed up on stage, taking a lot of the interactive fun out of what this place used to be. This was likely my last time at Sing Sing. Save your $7 and skip this place. A real shame because this place was once a lot of fun.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Had an absolute blast!! Great for any crowd, any occasion, any age! Ashley the waitress was AMAZING[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Picture Billy Joel's ""Piano Man"" DOUBLED mixed with beer, a rowdy crowd, and comedy - Welcome to Sing Sing! A unique musical experience found in Homestead. + +If you're looking to grab a bite to eat or a beer, come on in! Serving food and brews from Rock Bottom Brewery, Sing Sing keeps your tummy full while you listen to two (or more) amazingly talented pianists take your musical requests. They'll play anything you'd like, for tips of course. Wanting to hear Britney Spears? Toto? Duran Duran? Yep, they play that... new or old. + +The crowd makes the show, so make sure you come ready for a good time. If the crowd is dead, it's harder for the Guys to get a reaction. If you're wanting to have some fun, it can be a GREAT time! It's the perfect place for Birthday parties - especially if you want to embarrass a friend. The guys will bring them up to the pianos and perform a little ditty. For being a good sport, you get the coveted Sing Sing bumper sticker. Now who wouldn't want that? + +Dueling Pianos and brews... time to Shut Up & Sing Sing![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> First time here tonight and I must say I wasn't sure if I wanted to go. It seemed like it might be ok but nothing special but I decided to go with friends and man did I have a blast. The $7 door charge was great figuring u had music from 8 until probably 2 am ( we left shortly after 1). The food was not super but good prices reasonable. The beer left something to b desired as they r a micro brewery so u can only get their crafts. I asked for something similar to yeungling but what I got was nothing like it. The musicians were great they made this place awesome. We will b back and this may b our new Pittsburgh hangout[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Went here for the first time this past weekend. Needless to say I'll be returning! It was a blast!!! + +It was cheap to get in and since we got there a bit earlier we got a semi-good table. Though it was very annoying that people had reserved tables right up front and never showed up. WHAT IS WRONG WITH THESE PEOPLE?! Everything if you ask me! Seriously though if you're going to reserve a table, you better freaking go! + +I had no complaints about the place itself! The guys were hilarious and watching my brother get made fun of multiple times was just the cherry on top! Anddd this has to be the only place I've ever enjoyed being around people who were sloppy drunk, because the comedians take no prisoners! + +I did enjoy when Matt and Joey were the ones up there because they are just amazing and make it so much better! They are great at what they do. Can't wait to go back![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My friend is a piano teacher, so I took it as a good sign that Sing Sing would be quality stuff. It was her birthday, and I didn't really know anything about dueling piano bars. I was picturing glossy black grand pianos with glittering notes, pianists in black jackets and crystal glasses full of red wine. I am really, really glad I was wrong. + +It was gritty, bawdy and quintessentially Pittsburgh. First off, the pianos are scuffed to hell, considering the number of tipsy people who sit on them nightly while being mildly humiliated. The musicians hammer away at them, and they're covered with N@ and Sing Sing stickers. It's obvious they've been well-loved. The music is anything but the elevator music I was picturing; it's rock, hip-hop, oldies, pop, and just about any genre imaginable thanks to the request system (send up a piece of paper with some money) and the amazing repertoire of the musicians. For instance, ""Rubber Ducky"" and ""Gangsta's Paradise"" were both featured when I was there, and both performed impeccably. They also honored a request for a Taylor Swift song only to receive $30 and a request for ""anything else,"" which they promptly followed. The musicians also do funny versions of popular songs, and throw in things like ""yinz"" instead of ""you."" + +I saw in awe of the performers for a decent portion of the night. It must take a particularly special type of person to put on a show like this, considering the energy, confidence, wit, empathy, boldness, silliness, cleverness, and sheer talent a job like this requires. They rotate performers in and out so there's not even an intermission. I've read comments about the baseness of the humor, but I had no doubt the guys up on stage were intelligent dudes. They had great personalities: one was about 140 pounds, cheeky, and quick-witted. He acted out every sport in the winter olympics, and was pretty into this 90-something-year-old lady in the audience called Joan. The other had crazy hair and bright blue Chucks, beatboxed as well as he sang, and made it point to play a handful of songs for my friend's birthday. ""I think Ray Charles is the most soulful guy of all time,"" he said when she requested him. + +There were tons of people celebrating birthdays, and one big bachelorette party the Saturday night I was there. The performers bring the birthday boy/girl, bachelor/bachelorette, etc. on stage (for a $20 tip, which is pretty easy to scrounge up among friends) and humiliate the hell out of them, i.e. this is not the place to be if you can't laugh at yourself. My friend had a short dress on when she sat on the piano, and they sang a three-minute song about her vagina. + +Luckily, the show eclipsed the bad service and overpriced, weak drinks, because those did feature heavily throughout the night. The rest of the staff was friendly, however, and I stumbled on the door guy singing and dancing by himself, which made me smile. + +Sing Sing is definitely not an every weekend type of thing (much like Hofbräuhaus), but is a splendid way to celebrate a special occasion. Definitely belongs on every required Pittsburgh experiences list.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Always a good time, although it's definitely not a place I would visit often. It's great for groups....which is quite obvious since there are always several folks there for bachelorette parties and birthdays. + +Shut out to the piano players, who can not only play the piano, but also sing, play the drums and the sax. They are funny and know how to keep a crowd entertained. Also know some pretty obscure songs. + +My big criticism is the set up. If you don't have a reservation and/or come later in the evening, it's difficult to get seats. Believe me, I don't mind standing, but it does become a bit awkward when you have to keep scooting over to let waitresses and patrons past you. If you do find a seat, it is often littered with someone else's empty glasses.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The musicians at this place work hard to entertain the crowd, so I can't say they are all bad. However the minimum for a song request is $5. I spent $20 on a song for my girlfriend and they NEVER played it!! They were playing songs for $5 and $10, but my $40 got me no where. Even if they didn't know the song, which I doubt, they could have picked one they knew and improvised, my tip, save your $$ on the requests. + +Otherwise it's fun for special events every once in awhile.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I went here with a bachelorette party. We had reservations, which was good because it was packed that Saturday night. The performers were very talented, but the acoustics were strangely off. The theme that ran through the whole show was, to quote some phrases they kept repeating, ""you bitch, you slut, you whore"" and ""twinkle twinkle little slut, why don't you take it up the butt"" which one of the pianists wrote on the mirror at the back of the stage... You get the idea? Perhaps if I had not been the designated driver, alcohol would have made these jokes funny the fifth, sixth, seventh time. Or maybe not.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> He was incredibly sexist/homophobic. He could barely play the piano and when we finally recognized a song we could actually dance to he literally asked me to get off stage because he didn't like another on stage who could actually dance with the girls.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Pretty fun place to go every once in a while, but, believe me, by the end of the night you'll be ready to go. The show lasts around 5 hours, by the 3 hour mark you'll be sick of sitting there in the crowd with your $9 a pop drinks listening to the same dirty jokes over and over and over again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My best friend took me to Sing Sing for my bachelor party. I had a blast. The musicians (dueling pianists) made fun of me in a bunch of songs. They also were really good at playing requested tunes (rock). When the show was over we shuffled across the hall to the connected ""Rock Bottom"" restaurant for some grub. We all had so much fun that we went back for my buddy's bachelor party. + +There were some drawbacks though. We went on a Thursday night so the atmosphere was lacking as the place was pretty empty. And of course they are a little pushy soliciting tips when the place is empty. But it's not our fault the place is empty on Thirsty Thursday, if their drinks weren't so damn expensive maybe more people would show up. And sometimes they used vulgar language which was just unnecessary since they would have otherwise still been hilarious. Also there was no table service, and the only bartender was a bitch. I'll probably be back, but only for a special occasion when I can afford it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I brought my car here in 2006 for repair of a scratched bumper. The damage was minimal, but the work required removing my entire bumper for repainting. The staff were very helpful in explaining my options and presenting me with a few choices to get the most bang for my buck. They completed the work in the quoted amount of time and did a great job. A few weeks later, I noticed a spot that needed touched up and they handled it immediately and without question. I would definitely recommend these guys if you need bodywork or paint work done.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I was so pleased with the quality of customer service at this body shop, from the very first time I took my car in for an estimate to a couple months down the line when I got my car repaired (they still remembered me!). One thing I really like is that they always pick up the phone. You wouldn't believe how annoying it is when businesses don't do this during normal business hours. They're so personable and gave me an honest quote that I couldn't turn down because it was the lowest in town (I checked out 5 places). They just really made this process painless and smooth. I believe it's a family-run business, and boy does it show in their hospitality. + +Fran and Jason were the ones that I worked with -- extremely knowledgeable and patient, especially with a customer like me who wants to make sure all the paperwork is thorough and calculations are accurate. Joe DiIorio's (with an ""i"" not an ""l"") Auto Body also works closely with Enterprise Car Rental down the street, so they came and picked me up. Those guys down there have a great relationship with this body shop as well and were really accommodating. + +Overall, the quality of their work is amazing. I had a large dent on the driver side front bumper and had to replace my light (they ended up getting an OEM light instead of the aftermarket one because it didn't match) and get a brand new bumper. They blended the paint for me, washed, waxed, and vacuumed my car, AND their work has a lifetime guarantee. What can I say other than give my highest recommendation and hope other Yelpers can find this helpful, as this is how I found out about them.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> From my first phone call to Joe Diliorio's, I was impressed. Every staff member I spoke too was kind and eager to help. I was treated like an important client even though my car needed only moderate repairs from a low speed collision. I was able to bring my car in right away for an assessment of the damage. Joe Dilorio's took care of everything from that point on. They dealt directly with my insurance company, ordered the parts (even getting new parts instead of the used ones my insurance company wrote the estimate for, at no cost to me), and gave me a call when all the parts came in. I then brought my car back to them and they completed the repairs in a timely fashion. When I arrived to pick up my vehicle, I was pleasantly surprised to see that they had vacuumed, washed, and waxed my car! Most importantly, the repair work was absolutely top notch. They masterfully blended the paint to match older parts with newer repair parts. My car looks even better than before the wreck! + +If you don't want any hassle, want to be treated with respect, and want your car looking fantastic, give these guys a call! + +-Adam[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Joe Dilorio's Auto Body Shop was so helpful when I needed to get windows replaced. The were able to give me a lower quote then competing auto body shops in the area. They were also incredibly friendly and a pleasure to do business with. I'm planning on taking my car here for all future auto needs.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is the best place we've ever taken our cars to. Their customer service is outstanding. It appears that they really like doing what they do because they are always willing to explain everything in detail. I also like that they don't over charge. I completely trust them to be honest and do the best job possible.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place is amazing! I needed my car repaired after an accident and the guys here were so helpful. They set me up with a rental car as soon as I dropped my car off, repaired my car in a timely manner, detailed it for free, and their customer service was unbelievable!!! I can't recommend this place more![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm grateful to my insurance company for recommending Di Iorio's Auto Body Shop. After an accident, I needed some body work done as soon as possible. The other recommended shops wouldn't even make an appointment to see me for days. These guys fit me in that afternoon, and coordinated the rental too. Everyone I worked with was courteous and pleasant, and the work was done more quickly than expected. Moreover, they found ways to help save on the expense. The car came out looking better than before the accident -- a few days later, I noticed they had buffed out some scratches that weren't even part of the repair area. I will definitely be back next time I need auto repairs.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I usually have nothing but good things to say about this place. I've dealt with Fran and others and have had very good experiences. However, this time was very different. I called to find out how much they might charge to install some brakes and rotors that I had, i was reffered to Mark, the mechanic. I made the appointment with him for Tuesday Sept 30th, he quoted me between $179 - $200 for the work (though the first person I spoke to quoted $150-$179) and told me to bring it at 8am and it would be finished the same day.when I brought it on Tuesday, Septempber 30th at 8 am, Mark forgets that i even made the appointment with him (or didnt bother to make a note of it) saying, ""oh, I thought you were supposed to bring this by yesterday"". He says I should expect this to probably be done before 3pm. + +I soon recieve a call from Mark at 10:25am, where he tells me the charge will actually be $240 (for four hours of labor + $13 worth of materials, before even getting started to see how long the job would actually take) and that the car would be ready by 3pm, if not possibly before that. Also for good measure he decides to randomly throw in, ""oh, and we don't take checks"". + +The next phone call is at 3:50pm to ask if i actually need to have the car back today, I tell Mark, ""yes, of course"". (I was expecting to be ready by 3, if not before like he said) When I express that I definitely need it today, he says that he just has to finish this one side and it will be ready by 415. This leaves me with barely enough time to get a bus and get over there before they close at 430. Honestly if what he had to finish on my car could easily be completed between 3:50 and 4:15, i dont think he would bother asking if i still needed to have it that day. As a result I feel that he may have rushed something while putting my car back together, because now something feels slightly off with the feeling of how the cars is aligned or the way the car drifts at times.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> SO lucky to be referred to Joe DiIorio's after moving to Pittsburgh. It's really invaluable to have ""car guys"" that you trust. I could detail several experiences here (in comparison to other chain shops), but suffice it to say that they've always been honest, helpful, and fair.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Typical, but new. + +You see all of the people that are walking in and out and, I must say, the customers look like they work for a living hear. I swear one of the guys was covered head to toe in soot. That is amazing. + +Ran around the store looking for those few items that I needed to satisfy my need to build and create. Minimal help from the small quantities of employees, but some of them actually asked if I needed help -- after I had found the item.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> When making a Customer's paymento atLowe's, we have our checklist: + +1. Do the phone numbers match? Nope, but that's fine since people are always changing their phone numbers anyways. +2. Does the name on account match name on check? Nope, but mistakes happen at those pesky check companies. +3. Does the account number on the check match the account number on the screen? Why should it, those computers are always making mistakes. + +Now that we have verified that all the information is correct, we can process the payment. The customer will be so happy that we didn't have to bother them with any silly questions. + +****** +I am sad to say that this is an actual occurrence. What was originally an average Lowe's has turned into Lowe's Hell. If the associates do not have basic logic comprehension, how do they survive?[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Would like to give NO STARS. bought all new kitchen appliances there. Refrigerator is defective. They +send an outside company to repair. Man arrives with NO TOOLS and wrong size seal for freezer. not once, twice. The first time, he tries to use my spoon from counter to install it! I complain, too bad...they have to comeTHREE times before replacing it! NEVER AGAIN.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Your typical area big box hardware store. It's convenient to go to because of the proximity to other stores and how close it is to so many communities. + +Can't really say much else about this place other than with the self checkout lanes it's a breeze to run in and then out without having to deal with a single associate.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This local Lowe's serves its purpose for my husband and me -- a convenient home improvement store that we run into every month or two. I am most impressed by the lawn and garden section of the store. I am not sure how it compares to other Lowe's stores, but when shopping at the Home Depot in North Fayette last fall, their flower selection was dismal compared to this Lowe's.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Waterfront Lowe's beats Monroeville Lowe's for lawn and garden. Hate to admit it, but it's true.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Excellent wings and sandwiches, generally good food otherwise, and fair prices-- nice casual place. The service can be a little slow due to how popular the place gets at peak times.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The food here can actually be a little hit and miss, but I love the grilled cheese club with fries. I get it way too much. People make fun of me. + +They have a ten dollar minimum for credit cards, fyi.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> 3.5 rounding down. Its been a while since JB and I ate here and I would consider going back but we just haven't gotten around to it. The beer selection looked great but the first 3 beers that I wanted ""hadn't come in yet"" (they were in the middle of expanding their offerings, this really bothers me...if you don't have the product, don't put it on the menu). + +Its not necessarily vegetarian friendly, I got a pizza and it was good, not fantastic, only good. Justin was satisfied with his meal. Its a good place to eat if you live in the neighborhood but I wouldn't recommend going out of your way.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great atmosphere and even better people----wait staff was very friendly and the French Onion soup was amazing....Definetly recommend the home made chips... + +Great Bar in the up and coming Homestead area.....Highly recommend[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We're always looking for non-chain restaurants by the Waterfront (they do exist...), and this has become a favorite. I've had the Hot Roast Beef & Fries and the Corned Beef on Rye, and both were delicious. Every beer I've had here has been ice cold, and the service has been strong too. It's a great place to watch a Pirates game too.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Stopped by on a Mon evening after trying to dine at Smoke Taqueria which is closed Mondays. Parking on street in front or behind off Hay St. Super friendly bartender. In warmer months they have huge outdoor area & big screen & upstairs cornhole game area. Okay draft beer selection and big bottle selection. Tried the italian club which was really good - two of us split one. Also tried sweet potato fries - amazingly good! Home made chips w bleu were overpowered by sauce. Bathroom was in need of plaster and wall repairs & was grossed out by toilet brush/holder on a shelf near toilet at eye level. Bet it's a fun place in warmer months.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Awesome wings and pubgrub! Great beer selection and fun bartenders.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place is overrated. A friend and I were looking forward to a beer and some good bar food- instead the wings were terrible and the beer was good but overpriced. There's nothing wrong with this place I just don't understand the clout around it. There should be no clout.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> There's lots of potential here because of the wonderful character and ambiance of this place, but the food was average at best. We were there on a Pens Playoff night and there were 2 people working all the tables in both rooms. Our food came to us cold and unimpressive at that. Our orders were somewhat mixed up. The potato skins used a really cheap artificial cheese that was not very appealing. I tasted a slice of pizza, which is definitely the best thing they offer. The crust was delicious and homemade. If you are going to order something, I would go with the pizza. We also ordered the chicken wings which were pretty good, also. If you are looking for good food, Homestead better choices at Blue Dust or Tin Front.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Before today I probably would have given this place three stars based mostly on their beer selection; however, today the service was terrible. We waited two hours for a pizza sub, French onion soup, fries, and buffalo chicken tenders. About an hour and a half in we finally got the small pizza sub and the wrongly made buffalo chicken tenders (ie, no hot sauce). We were told by the waitress that she realized it was wrong, but decided to still bring it out to see if my gf would eat it. She sent it back. By a half hour later, we still had not received the buffalo chicken tenders, nor the French onion soup (which should have been mostly made already), and no fries. We were told the chef was new, but no effort was made really to make the situation better. No quick and easy app or beers on the house. To boot, the beer was pretty expensive. I will probably give the place another chance based on their beer selection, but it won't be for a while. The food has always been average at best, and the pizza sub was no different. We ended up leaving after two hours without receiving 75% of our order.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm reading on here that the food is really hit or miss. I've only gone to Duke's one time, but the food was good. It wasn't too busy so our service was very attentive and it didn't take long to get our food at all. + +The place is separated between a bar area and a more family style dining area. We sat in the dining area because the bar area was pretty full. The dining room area definitely fills up with an older, have lived in Pittsburgh all their lives crowd, while the younger crowd is in the bar area. + +I'll definitely be back since I live in the area.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Duke...the owner...is the man. He's a true Pittsburgher and he loves everyone from Pittsburgh. He looks like he'll beat you up but he's a softy with a big heart. Look for the bald guy with the raspy voice and make friends...he'll hook you up. He's also totally into the development of other Pittsburgh businesses and he hosts events for local startups. Ask him for a tour of the old Eat n Park next door...I believe his intention is still to turn it into an incubator of sorts. Fortunately, the bar is close enough to the waterfront that it's just far enough out of the ghetto...the crowd is certainly decent. Definitely have some beers on the porch in the summer...especially in the rain (lower level is covered). Very relaxing atmosphere. I wish my company was located in the area so we could frequent Dukes more steadily (we're on the north side). Still worth the drive to feel at home, have a good bite and some cold beers.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've been to Duke's three times now. When I first came to PGH, a lot of locals were telling me that this was a good place to catch a game, drink some brews and get great food. Most of that is true, but the bad has mostly outweighed the good. + +They have an excellent new tap system. Last time I went, they had Thirsty Dog Leghumpper on draft, and it was perfect. The system really elevates already awesome beer. Plus, the selection is awesome. + +It is a sports-themed bar, so you can expect drunk locals, loud TV's and plenty of yelling. I'm sort of into that, so it doesn't bother me, although I do think their staff is not well equipped enough to work among the chaos. Service is often slow, and they give the waitresses ZERO training in the beers that they offer. This is not a good place for trying something new, as they can't tell you a thing about it. + +The biggest downfall of Duke's, though, is the food. I've had three different, but equally simple, dishes there; A Burger, a Cheesesteak and Chicken Tenders. The first was flavorless and cold. The second was passable, but nothing special. And the last were absolutely awful. Honestly, the batter and size of the chicken made me so ill, I had to call it an early night. I ate two of the 7 tenders (SEVEN!) and had to quit. +Their fries are very good. And so are the wings. + +I'd say Duke's is a good place to drink, but that's about it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Food is good here. Great beer selection on tap. Sometimes the beer is on the pricey side. What I want from a neighborhood bar is a neighborhood special. Pinkerton is one of the best sandwiches. Good place to watch football, hockey, baseball.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> One of my favorite local eateries. The mild & wild sauce is my absolute favorite, I wish I could purchase it. I am not a big bar food junkie but the tomlin sandwich is great & reminds me of a fatheads sandwich. Food portion is great. The only complaint I would have if any is the craft beer is a little on the pricey side, as usual in most local bars. Friendly service, will continue to frequent with my family.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> GREAT PLACE FOR A BIRTHDAY PARTY! + +A FAMILY GATHERING! + +A WORK RETIREMENT PARTY! + +OR EVEN A DOUBLE-DATE! + +A combination watering hole, great place to eat and great entertainment for adults! Adult games! + +The Homestead (Pittsburgh) location of Dave & Busters is just one of the almost 50 locations across the country - from New York to Florida to California - - from Canada to Mexico. + +The Dave & Busters idea was conceived in Little Rock, Arkansas back in the 1970s. Two different businesses (one a popular watering hole & one a game & entertainment business) were right next door to each other. The two young owners were friends and quickly realized that combining their businesses made perfect sense. So they opened the first combined D & B in . . . . no, not Little Rock, but Dallas! To this day there are no D & B's in Little Rock. Not sure what is up with that! But lots of other cities have been the beneficiaries of these two friends combining their businesses. + +The one in Pittsburgh is the only one I have ever been to. When I lived there, a group of friends and co-workers (and me, of course!)used to go there for Happy Hour & Power Hour . . . . at least once a week. We had a blast! A great place to kick-back and let the worries of the work day melt away. + +Wonder if they'll ever open one in Marin County, CA? Shucks! Probably not. Not a Marin County scene, for sure. + +WHAT A BLAST IT WAS THOUGH! I miss going to D & B. They have all the classics, like billiards & shuffleboard, plus over 200 interactive & video games. A rechargable Power Card provides an easy way to access all the games. + +POWER HOUR is game HAPPY HOUR - - an entire hour of classic and video games for just ten bucks. + +A GREAT BAR, WONDERFUL FOOD AND SERVICE! A RELAXING AND FUN WAY to spend a Friday or Saturday evening. You'll never want to leave. Meet your friends here, grab a beer and a burger or steak and hit the games. + +Time will just evaporate . . . . while you laugh and drink with your favorite girl, your best friend or even your boss! + +DAVE & BUSTERS! LOTS OF PARKING! LOTS OF FUN! + +FUN! FUN! FUN! FUN! FUN! FUN! . . . . BRING ON THE BEER![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> D&B is nice once in a while but the food is insanely unhealthy. They are also really clever about designing the psychological context in ways to extract money from their customers. You feel a bit milked afterwards. Also much fatter. + +You pay for games using credits from mag-stripe cards. This lets D&B give their games arbitrary prices and makes it harder for you to really know how much you are spending. Menus for drinks and food have no prices. $6.05 for a Banana Split cocktail? $3.40 for a Michelob? I have no idea whether that is expensive but not showing the prices is clever because they can price their things and not have to obey pricing psychology (like anchors and so forth). + +Waitstaff hassle you repeatedly to order desserts. Oh, and the dining room has plastic demos dessert trays to get that thought going in your mind as you walk to your table. + +The games are all violent shooters or racing games don't appear to have changed much since 2002 when I last went to D&B in California. Hope they can find more innovative arcade games in the future. + +Not a pleasant experience, but at least it's different from going to an ordinary restaurant.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This was actually the first time I've ever been to a Dave and Buster's. + +Walking into such a huge space, especially coming from the often narrow venues in San Francisco was strange. + +Un-nerving actually. + +Because Dave and Buster's is all about excess. Almost obscenely so. + +As far as food - their stuff is standard. Most of it is fried and as another reviewer pointed out - not very healthy. At all actually. You have to really scour the menu to find some somewhat decent viable and nutritious options. + +But most people don't come to Dave & Buster's for food. They come for the games. + +And while I've never been that into video games or arcade games - my brother and sister always have. I was apprehensive about having a good time here - but after awhile - my siblings' enthusiasm about the place became contagious and I found myself really enjoying myself. + +Especially once i realized that I have mad skills at Skee Ball. And proceeded to dominate. + +Trust.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Think Chuck E. Cheese for adults. Skee Ball, video games pool tables. Clean environment. Good fun. + +Unfortunately, I went for a bite to eat and it was impossible to find anything good and healthy on the menu. I ended up settling for spinach dip. Sadly, they topped the dip off with horrible orange shredded cheese that appeared to have been popped in the microwave for a few seconds. Blahhhh. Trying to get something healthy, I ordered the apple pecan salad. I swear the dressing came right out of the grocery store bottle. I could barely eat the salad. Too sweet. + +My mom ordered a steak roll.....holy friedness! The steak was more like hamburger fried with cheese and then stuffed into breading that was fried AGAIN! Yowzer! Artery clogger for sure. + +I like the atmosphere. I like the bar area. Perhaps next time we'll just stop by for drinks instead.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love the games here but can't go very often since they don't rotate new games in very often. The place is usually pretty clean. + +Pool tables often have a wait on the weekend but are some of the better ones you'll find in the city. + +Food is just ""ok"" Drink prices are fair but not great.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Dave and Buster's is an enigma, is it dining, a bar, or playground for video game lovers? Let me get the bar part out of the way first, it's overpriced, and they try to get you to buy a glass to jack up your bill. + +Next, the food. Just like all the chain places at the Waterfront, there are sandwiches, burgers (yes they have a blue cheese burger, who doesn't?) pasta, salads, chicken fingers, yadda yadda. + +The games, I swear over three quarters of the games have been there since 2000 when the place opened. I guess in ten years no new games have hit the scene. + +Overall Dave and buster's is unique to the Waterfront, but it's time to update the menu, update the games, and get into the second decade of the 21st century.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Because I have significantly younger sisters, I go to Dave and Busters about twice a year. It's fun for them and nostalgic for me. It can get expensive and the 'prizes' are cheap but it make for great ""sister days"" + +As for the food, we've eaten there once and never again. It's just blah... frozen and fried. The veggie burger was put on there as an afterthought just so they could say they offer it. A frozen Boca patty thrown on a bun. Thanks! I could have ran to Costco for that. Drinks are rather expensive but that's to be expected. + +So go for the games, fun and laughter and maybe stop somewhere else for drinks and a bite to eat (skip the bountiful chains that span the Waterfront and try Blue Dust on Amity Street).[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The food was absolutely gross! I ordered a turkey club which comes on a wheat bun with avocado, bacon, and turkey breast. What I got was TOTALLY different from the picture! First of all the sandwich was on sliced bread (lame)! There was no avocado, 1 slice of bacon, no lettuce, and to TOP it off instead of turkey breast they used freaking LUNCH MEAT! lol No, not the kind that you get from the deli, the other sweaty nasty looking stuff! Gross! + +Our waitress was awful but they were extremely understaffed so I would have a bit of an attitude if I had to wait 10 tables without assistance too. + +The manager was really nice... Of course that disgusting sandwich that I didn't eat was free.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The usual fun center. + +You can play games using a play card which you purchase there. Game prices can be confusing- - - 2.3, 5.7, 9.9 credits, etc. + +The arcade can be fun if you bring some friends. + +Almost every game is a ticket game and there are few innovative or exciting game choices. + +I didn't eat there, so I can't rate the restaurant part of Dave and Busters.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We came here on a Saturday night and luckily it wasn't as packed as I thought it would be. I love playing ticket games so luckily there were a lot of games to chose from and not many video games (sorry video game lovers!) We only played $20 worth of games and surprisingly we were there for awhile. I love their new Wheel of Fortune game! On our first play, we ended up winning a little over 700 tickets! They also have Fruit Ninja as a game. It was fun with the big widescreen but unfortunately you don't win as many tickets as you would hope. I wish their ticket center would have individual ticket counters like the other D&B's I've been to, where you feed a counting machine your tickets. At this place, they just weigh your tickets and give you the final count. We didn't try the food here and instead went to P.F. Chang's to eat before coming here, but the Eat & Play deal looked fun. Too bad it was only restricted to certain times of the day. Overall I had a blast here and definitely would come back. Hopefully next time when there is a deal or promotion.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> A table for 16 please... That is what I had to ask for and knew that D&B could accomodate. + +I happen to be in the Homestead area for work. I really wanted to dig into my Yelp bag of tricks provided by local Yelpers and introduce my team to the ""Shock and Awe"" they deserved but ... the shear numbers would made it hard. + +When I started thinking about how we would have a manageable lunch - The only idea I could come up with was the Golden Corral - I knew that was not going to work for me. + +We decided to do something local and walking distance - D&B was it. + +It is what you expect - quiet for lunch video games and a bar nearby but I had to forgo any festivities - it was a work lunch. I was pleased they had a under 600 calorie menu. I am trying to maintain a normal diet due to my stretchy pants being out of style and not wanting to look like a character out of Family Guy. + +The waitress was very friendly and organized. I ordered the Cabo style Chicken - Chicken Breast lightly seasoned and char-grilled, topped with pineapple pico de gallo and served with spicy rice and steamed fresh vegetables. + +It was eh... The chicken was cooked but the pineapple pico de gallo was bland. The rice was bland. The vegetables were cold. I really blame it on the fact I was with 15 compatriots for lunch so I am giving it a fair rating. Everything was edible. + +My team went with deep fried foods and burgers. They seemed pleased. + +Service - very good +Food - okay, not great. My meal was $13 +Ambiance - well it was clean but there were not really any people in D&B + +There are so many other choices for lunch that are local and close. I would definitely recommend another in Squirrel Hill - I suggest you use Yelp to find you a better one (then come back and play! ;-) )[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Not much of a review for this one, but just a few tidbits of info... + +Pool (on Friday/Saturday) is $14 per hour +(I'm pretty sure its $10 through the week) + +Mixed drinks are way too pricey for the location. +The food is crap. + +The games are fun and the pool tables are nice (they're the big tournament style/size, not the shitty bar-room, tiny pool tables). + +That is all. :) + +(the pricing is based on my recent trip. +We shot pool for a few hours, I had a bar tab (that wasn't out of control) and my night ended up costing me $60[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love Dave and Busters!! It is a great place to go when you are wanting to have a great time with a great group of friends. If you find you and your friends bored on a Friday or Saturday night, come to D&B and win some prizes!! It is pricey though, so bring some major moolah[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Dave and busters is the best place to eat and play games. There is many fun games and prizes to win. I highly suggest if you want to plays games, go Wednesday when all the games are half off. Food is pretty good and a nice bar. The downside is that the booze is pretty pricey.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> When did Dave and Buster's become a daycare?? Everywhere you look, there are signs that say kids must be accompanied by an adult, but apparently no one was honoring that at 6PM on a Saturday. I couldn't even walk through the place without someone shoving me. AHHH! +I get that Dave and Buster's is an arcade and that you're going there to play some games, maybe eat, and kill some time. When I last went there a few years ago, we there for my bachelor party, and while I'm sure we got into some shenanigans, I don't remember children running wild there. We were having adult beverages, playing games, and having a good time. This time, it was ridiculous. It isn't Chuck E. Cheese, yet that's how parents seem to be treating the place. +On top of that, the customer service sucked. The place is gigantic, with tables and serving areas everywhere, yet on a Saturday at 6PM, the hostess told us (after interrupting us three times to chat with the other hostess) told us it would be a three hour wait, despite the fact that there were empty tables all over the dining room. I suspect this is a ploy to get you to play games and spend money until you're table is ready, but the food at Dave and Buster's is not worth a three hour wait on any day. +The hostess told us we could be served right away if we went to the midway and found an empty table, so we attempted that. Most of those tables were empty with usually one or two adults at a giant empty table filled with coats who informed us that they needed the table because their kids would be back soon after playing games. Next, i engaged in the most rudest thing I've ever done- I began stalking tables where people were finishing up. I would walk up to people paying their check, ask if I could have their table when they were done, and they would inform me that there were already two or three people who asked them and I should get in line. +Finally, we found a table and proceeded to spend two hours eating dinner. It wasn't because we ordered a lot of food- it was that the waiter took forever to bring our food out. He seemed to have no problem getting us fresh drinks, until we drank as much as we could and then asked for water. After that, he seemed to come around a lot less. +I had the build your own chicken tacos, which comes on a giant plate with all kinds of fixings. The fixings were fresh, but the chicken was cold and dry, and the tortillas were dried out as well. For $14, it wasn't worth it. +After dinner we proceeded to play games, which entails shoving people to get through areas and waiting in line to play anything. +All in all, I didn't like my experience at Dave and Busters. I remembered it being a fun place to go and unwind as an adult. but between all the kids and the crappy service, can't recommend this place. If anyone asks me to go back, I may elect to stay home and poke my eyes with a fork.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Not a cheap night out you will end up spending money here. But it is busy fun entertaining and a good time out. I ate dinner here and the food was great i also played pool and the arcade games.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My friend and I both had Friday off so we decided we wanted to do something more interesting than just hit up a bar on Thursday night. We settled on Dave and Busters. I went on Facebook and printed off a coupon for buy $20 get $20 in play free (we split the card, it took us about 1.5-2 hours to get through) + +The games weren't *quite* as fun as I remembered, but it was still a good time. The place was far from crowded, and when a machine was out of tickets, it took us a good deal of time to find someone to assist us. When we did, the team at D&B could not have been more accommodating. To apologize for our wait they swiped us in for several games as well as gave us a handful of tokens for the game we were playing. + +I think a lot of companies (I'm looking at you, American Airlines) could learn a lot from D&B. It cost them virtually nothing to swipe us in for games, but it made our experience so much better. + +Drinks are half-price after 8 or 9, my Tropical Mojito was awesome! My friend and I are definitely planning on going back on a Wednesday for half-price games AND half-price drinks.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Dave and Buster's has to be split up into separate experiences to rate it. + +Dining: 2 stars + +I had a party of 20 coming in; I had called ahead of time, and arrived early. They immediately set up the table while about 4 of my friends and I waited; the hostess, after taking my name, never spoke to us again. She did not tell us when we could sit, how long it would be, or any other information. And then they made us wait for 75% of our party to show up before they would seat us. Mind you, there was no one else waiting, and the table was ready, and we were ready to order. But they didn't tell us this; I didn't even know why we were being forced to wait until I heard a supervisor whispering to the waitress about making us wait. I still have no idea why we were forced to wait. + +When my full party was finally seated, we were helped by two waiters who were perfectly polite and nice. BUT, our service was rather haphazard. People would order drinks and food, and get things at wildly different times. One person was done eating appetizers and drinks when another was just getting their first drink. I know there was chaos to a big party, but it got a little out of hand. + +The food is pretty standard American chain food, comparable to Appleby's and Chili's - not offensive, but nothing to knock your socks off. It has a decent selection, and a few good desserts and appetizers, and everything was competently prepared. Overall, it is a fine enough meal for a large group before going to enjoy the arcade at fairly reasonable prices, but some of the service standards are poor. In the future we will probably eat at one of the other restaurants in the area and then move over to D&B's for games. + +Bar: 1 Star + +Drinks are predictably expensive, but there is a wide variety. The problem is that about half of them don't even kind of resemble what is on the menu, and most don't have enough alcohol to even taste. Worse yet, while you can get a drink at the bar in the arcade, the staff is either completely non-interactive or just rude. You have to track them down, and then have a minimum of interaction before they stomp off like you ruined their life. + +Arcade: 4 Stars + +There are a lot of great games here to play, and many that are fun with groups or pairs. It is a great place for a large party, because you can mingle with all your friends playing many different very fun games. If you are a couple, there are also many great selections that everyone enjoys. The staff on the floor is helpful and fast to fix games that have problems, and are typically polite. The ticket prizes are cheap as expected, but kind of fun, and the people in the ticket shop were always nice and quick to help. + + +Overall: 3 Stars + +If you want to hang out here, I would suggest eating somewhere else, and then playing games and having fun here, but only order beer at the bar and don't expect a smile.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Chuckie Cheese for grown ups...Yeah, that could sum up my review for sure (but I'll try to make it a bit more interesting than that). + +First let me say that this isn't my first trip to a Dave & Buster's. Second, I actually experience all of it while here. We will start with the food/service. Staff, you were wonderful. You were polite, you greeted us as soon as we walked in the door, gave us no qualms while ordering and were swift with your delivery. Food, you were not wonderful. I ordered the BBQ chicken breasts. This came with a side of broccoli and their type of mashed potatoes. The chicken was a bit dry and in some places you can tell it was left on the grill a little too long. There were actually some bites that all I could taste was charred meat. There wasn't enough BBQ sauce on the the chicken either. The broccoli appeared to have been cooked prior and then thrown back into a pan to be seared. Some of my broccoli actually had some burnt crisp areas on it. Also I noticed that there were still some leaves left on the broccoli. The mashed potatoes I wanted to like (which I hoped would be the best part of the dish, I'm a bit of a potato freak), but alas, I was let down. *sad face* They were cold and such a tiny portion. With a tiny amount of shredded cheese and bacon but into that divot they made with the scoop to get it out of it's container. Oh food, how if I didn't need you to survive, I wouldn't complain about you. + +The building right now is in disarray. They are in the midst of a remodel with lovely plastic curtains covering up certain sections of their dining area. No bar out in the dining area right now and the pool tables were absent as well. If you wanted a drink you had to go back into the game room. + +Speaking of the game room, by far the best part. With the meal I ordered I got the $20 play card (the best part of the meal, super charge it for $3 more and it's even better). The game room you can tell is in need of an update. The carpet is worn and other signs of wear are noticeable as well. One good thing is the games. They change them up so often that there is always something new once you return. Who knew that playing Connect 4 could be so fun, or for that matter Skee Ball rises to the top of my list to play. + +I will return again, but only after I eat elsewhere first.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Not really sure what to add. So I'll bullet point my experience. + +- Expensive poorly made drinks +- Friendly but slow service +- Ok food considering (Had the Philly Steak and Cheese) +- Over run with kids before 10 that seem to have zero adult supervision +- 15% of the games were out of order (Air Hockey, Big Bball Game, 1/2 of the skee ball, random other arcade machines) +- Expensive games +- Fun time overall with the wife.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Mediocre service. COLD food! Our food waited so long the lettuce & pickles wilted. Bland food. Crazy overpriced. Long waits in the arcade. 1 beer per hour maximum. Avoid at all costs. Fair manager.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Not being from the area, I traveled an hour to come here from Uniontown, PA. I was excited! I haven't been to this Dave and Buster's since I was younger and was ready to go back and play me some games! I went with my cousins, mind you, we hadn't ate all day and were very hungry. So, we decided to do the Eat & Play Combo, naturally. Here's where it gets bad. First of all, we get a very snobby hostess that shows us to our table. Then, we wait...and wait...and finally after about 25 mins we get a waitress. Her name was Ashley. We had plenty of time to decide what we wanted, so we quickly put our order in. Next, we were sitting and talking, waiting, we had empty glasses and our waitress had never even come around to see if we needed refills except for one time. She said she'd come back right away with our refills...yea, right. 20 mins later we get our refills. Mind you, our food still hasn't came yet. I see other people getting their food that had come in after us. I was frustrated. After waiting 45 mins for our food, I asked to speak with a manager. One of the servers who I asked replied rudely with ""Well, he's really busy right now. I doubt he'll be able to come out and talk to you"". Finally, 15 mins later...that's one hour, folks. We get our food. What do you think the next problem was? Yep, the food was cold. I was completely fed up at this point, and told my waitress how disappointed I was, especially after driving one hour just to have this terrible service. The manager never came to speak with me, and we didn't even receive our meals for free. The only compensation we got were $10 game cards. Woopty-doo. The only thing good about this place is the games, but the prizes you get for your tickets are all junk and worthless. So, in conclusion...I DO NOT RECOMMEND THE WATERFRONT DAVE AND BUSTERS OF HOMESTEAD, PA. It was horrible, and I will not be returning for a very long time![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place just plain sucks +Bad management lost them biz +Dumb arcade drama* + +* they have recently changed their under 21 policy so no one underage can even be in the arcade or restaurant after 10pm despite having a guardian over 30 years old[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> i had fun here.. fun big kid games for me!!! +O.. But the bartender Melissa was a SUPER bitch and RUDE +Hope they fire her..[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> First time at Dave & Buster's and although I didn't go for the games, I was slightly disappointed. I went with a group of girls for dinner and drinks. The service was slow but the food was decent. The portions were huge but they are priced slightly higher than the average chain. + +We went before 9 pm and there were a ton of kids there on a Friday night. I do suggest if you want to avoid the children to go after 9.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> DAVE & BUSTERS! It's a nice place to eat, have fun and drink!! All ages can enjoy this place. I was so EXCITED to hear them announce that after 10p, all children whether accompanied by a guardian or not had to go! It made for a nice evening for adults only. + +Everytime we go whether we play or not we enjoy ourselves. I didn't give it FOUR STARS because every time I've went I haven't been able to eat in the restaurant area of there. I know I still get the same food that everyone else does wherever you sit. Sometimes, I like the nice relaxing atmosphere of the restaurant. I haven't as of yet, been seated there. + +Not to mention that the servers around the bar, are a little slow at responding to customers as well. So all in all, D&B's is a good spot to stop at for food and entertainment. Just don't expect to be seated in the restaurant portion, and expect to wait awhile for food service in the bar area.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Was impressed by the new menu and new decor. Our waitress was nice, knowledgeable and attentive. However, the rest of the staff was less than stellar. There was a power outage (less than one minute) while we were paying games (sunny and calm outside so not sure what happened). My family and I were playing a trivia game---we lost about ten dollars of credits and all our bonus tickets when the power resumed. The games were down for about 20 mins after the outage and staff was not friendly when we inquired about what happened or when the games would be working again. After the outage, two people in our groups could not get their power cards to work. When we asked staff for assistance they just brushed us off and said we must have been out of credits. Kinda a bummer we lost so much money on (malfunction) game play tonight.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Visiting from Toronto, I was really impressed! The amount of tickets to be won was incredible. We usually got 200 tickets per play on average. Compared to Playdium here, that's awesome considering I'd win at most 10 tickets with the smallest prize costing 100 tickets. The food is great, the place is clean and the games don't feel greasy or nasty from all the food.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> A fun place and lots to do but a bit pricy. $20.00 will buy you a hundred points which will last you a little over an hour.I recommend the bowling game ,ball racing car game and connect 4 also there are several games that can be played in groups of 4[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Visited the Dave and Busters in Homestead, PA last night. Waitress mixed up our credit cards and gave my brothers credit card to someone else and he theirs. Charged them already too - both incorrectly My brother had to walk around and find out who it was. Waitress never apologized. GM was extremely rude and refused to give my brother his original receipt back saying they had thrown it out. DID NOTHING TO REMEDY the situation and ignored us the rest of our visit - not even a refill. After spending over $300 plus games, we will never go back. Whatever happened to the customer is always right? HORRIBLE service[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love it! Love it![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My boyfriend and I are in our 20s, and have visited this D&B multiple times. After our visit yesterday, however, I don't think we'll be back. When we arrived we were greeted by a long line of people waiting to buy game cards. At first there were 2 extremely slow workers trying to do this, then one left while the line was still out the door! The girl that was left was more than incompetent, and was taking extremely long to fill these game cards. We stood in line for over 20 minutes before being told that there was another attendant in the actual game room. Needless to say, the line in the game room was just as long, and they still only had one girl in the booth. It was a Saturday! After we finally got our cards we had to wait yet again to get a beer. 2 bartenders on staff while the bar was completely full. It took us almost an hour before we actually could start gaming. The floors were filthy with trash, and the bathrooms: repulsive! I had to use the restrooms twice during our visit, and not only did both bathrooms I used have no toilet paper in them, but there was TP all over the floors, and the sinks were less than cleanly. My boyfriend mentioned that the guys restroom was no better, as it smelled like pee and the paper towel dispenser didn't work. All I have to say is get your crap together. We could see a difference in the type of crowed that was there on Saturday compared to what it used to be, and I'm I have no doubt it's due to the poor service and attention to cleanliness. For how expensive they are they need to staff better on weekends. It's a shame how quickly this place has gone down hill and we will NOT be returning anytime soon![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Most of the games were out of order and I had to find one of those referee looking people to fix 2 of them that took some of our credits. Apathetic service staff all around, the Peanut and I were really disappointed. Won't be back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> ehh, 3.5 -- I can't rate it super low because i do smile a lot during my visits. Speaking of that, I've been here a few times, but never wrote a review for D&B. + +I'm a kid at heart and honestly do enjoy the games. However, there have been multiple instances where I swiped my game card & it took my credits, but no game began. There have also been times that I won and no tickets were released. I guess nothing is perfect but it does happen atleast once a visit (each scenerio) It's hard to find a worker walking around and for half-price games, you kind of just take your loss with the 1.3 credits for skee ball (hmph!) + +The food- it really isnt anything too fancy. I've had okay food, but super long wait times for a simple chicken fingers & fries for example. It's your basic sandwiches, salads, appetizers & a few pastas. I believe all sandwiches & burgers are around $10 & served with fries. You can get the Eat & Play deal which includes food from a specific menu + a game card. Besides the game card deal, if you wanted to make D&B a date night you might be better off heading to another place to eat in Waterfront for amazing food.. but to each their own. Try it once I suppose. The brownie sundae that i devoured last night was satisfying (2 brownies, 2 scoops of ice cream.. one with chocolate syrup; the other with raspberry sauce & fresh strawberries. Oh & whip cream) + +Drinks- pretty weak. We ordered 2 liquid maryjanes (2 each that is) which are filled with multiple shots of alchy & didn't really catch a buzz. Oh welllll. They do have a happy hour from 5-7pm. I'd go during that time for the best deal. I believe cocktails are half off & $3 off bottles of wine. I've never seen anyone walking around with a wine glass though lol. + +The prizes- as others have noted, the prizes are a little cheap for the amount of tickets they ""cost"" However, it's cool to leave with a D&B coffee mug, cup or shot glass. Last night for 2500 tickets we decided on magnetic-style dart board (1,300?) a coffee mug, a D&B glass (our plastic one bit the dust) & a D&B coffee travel mug.. I might be missing a few odds & ends. + +Overall it's a fun time but can be pricey. It's best to head here Wednesday for half price games or get the Eat & Play deal while dining. + +I can't lie though, I find myself smiling ear to ear a few times within those 3 hours (woah, seemed longer than amount of time :D ) Speaking of which, in that time-frame we played 250 credits (cost= $40) but it was half-price games.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Dave & Busters is a great experience if you set your expectations realistically and carefully choose when you attend. + +The main squeeze and I always 1) use a survey receipt for buy $10 get $10 in free gameplay or 2) Attend on a Wednesday during the day (flexible work schedules). We'd never dream of eating there because we like healthy yuppie food. And we only drink cheap drafts OR drink cocktails during happy hour. + +Your visit is largely determined by time of day, expectations and whether or not you eat their food. If you come on a Friday night, the lines will be long. You'll pay $150 for the two of you to eat, drink and play for 3 hours and you'll be left with a very sour taste in your mouth. + +The staff is really excellent; any issue with a game not paying out tickets results in immediate help and extra tickets or a swipe for a different game from an employee. + +Note the ""drinks are weak"" reviews. Also notice it was people buying shots and ordering multiple drinks per person. That's typical white trash behavior. Bartenders here are savvy; they mirror the behavior of the guests. All of our drinks have been consistently strong and well put together because we're courteous and tip well. I have witnessed bartenders bypass tattooed, loud guests and address me and take my order first. This is rational, logical behavior. + +Also note the ""prize center games suck"" comments. You're supposed to stack tickets over multiple visits and use them on a big prize. Like life, delaying gratification nets you bigger returns. Every other visit I've seen someone walk out with a video game system (Wii, Xbox360 and even a few Xbox One's). + +The thing about Dave & Busters is the crowd changes depending on day of week and time of day. Sunday afternoon it's all families and Friday and Saturday night it's all drunk 20 somethings. The atmosphere changes and that's why the reviews are all over the place. + +This review is based on 8ish months of 1-3/monthly visits. Most visits are 5 stars, some are 4 stars. + +Using survey receipts for Buy Ten Get Ten, avoiding Wednesday, Friday or Saturday evenings (and Sunday afternoon, families) and avoiding the food entirely and drinking cheaply, you'll have a great experience for $25-40/person. + +I really enjoy the staff too, they split the difference between fun and professional. Special shout out to Riley, gave us info on possibly hosting a party there.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> To keep it short and sweet: Save yourself $100. Buy a good board game, your alcohol of choice, order a pizza, and invite your friends over. + +What an incredible disappointment. After seeing the enticing commercials so many times, we decided to give this place a try on a double date. I understand the prices of the play cards and won't dispute them; however, the food was incredibly over-priced, came out COLD (as in, sat on a counter without warmers for a minimum of 30 minutes) and I literally had to ask the bartender if there was any vodka in my drink. It was pure juice. $38 for three shots that had little-no alcohol in them. (Not to mention, my glass was dirty, and I saw the bartender scoop the glass into the ice basin because she was too lazy to use the sanitary scoop. I know the Food and Beverage Commission would be as disappointed as I was.) The service was terrible. Don't ask for anything from your waiter, as they are a little too busy on their cell phones or conversing amongst themselves. + +Was it fun to be in an adult-themed arcade? Yes. If you're looking for a good atmosphere to go with friends to play games, I suppose I would advise you give it a shot. I would never recommend their food, customer service, or drinks. Save yourself the money and stay home, or go for a traditional bowling, figure skating, roller-blading, rock climbing, basically any other physically-entertaining themed date instead.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I still love this place! I spent my 36th birthday at D&B's and it was a wise decision! i had so much fun, and so did my guest! I got a very attentive serving staff, and met up with many helpful servers! I believe that service has improved, so I bumped this restuarant up to 4 stars! No five stars yet, because I've still as of yet to eat in the restuarant portion of it! It's still worth the visit, and is a lot of fun for a reasonable price![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> There is good food, but a great spot to enjoy a few drinks & watch sports on the big screens. It's great for adult fun after 10pm. Great for a first date if you like to have a good fun & feel relaxed[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My wife and I went here around 10pm on a Saturday night. The food was not spectacular, about the same quality that you'd get at an Applebee's or some place similar -- good but not great. My steak was tough, but my wife enjoyed hers. Staff was relatively unorganized (we ate at a table next to the bar), and had to wait awhile for a server. Food was prompt.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> After having a few 'less than memorable' trips to D&B in years past, my wife and I decided to go back for a Pittsburgh Happy Hour Anniversary party this past Thursday. Pgh Happy Hour is a facebook group of friends that like to check out new 'watering holes' every thursday and it's run by a guy that seems to party 24/7 while still holding down a very lucrative full time job. + +Anyway- Pgh HH was celebrating an anniversary and chose D&B for the location. The D&B staff set up the back 'pool room' with complimentary, enormous spread of appetizers with dips and kept refilling them when they got low. Our server, Carla, was very attentive and friendly- making sure we were aware of the specials and checking back often when our glasses got to the half way point. The other server back there was working equally as hard but I never got the chance to get her name. + +I had been here one other time for an organized happy hour for a past employer and remember very similar service but I never got the chance to give them any credit. I think D&B is an awesome place when you need some space for your next event.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Ok! Let me tell you about my bad experience first. I went to D&B last night for a post wedding party - which, side note, is a great idea! + +It was around midnight and the bar wasn't really populated. There were three bartenders and only one was actually making rounds to see if anyone needed anything. The two other bartenders were chatting on the far side of the bar that no one was sitting at. Kind of counter productive if you ask me. + +I stood there for about 5 minutes, which for a busy bar is fine but when I am the only one with my card out then, it just seems a little ridiculous. I made eye contact with the one girl twice and gave her a smile and she literally turned away. I finally had to walk to them to get their attention. I was standing right in front of them smiling and they didn't ask if i need anything. I finally said, ""Are you working?"" and they gave each other a weird look. I felt like i was the crazy one. I asked for a beer/got the beer. + +In between that time, the other bartender brought food over and set it down. She took a fry from the plate (right in front of me) and then served it to someone on the other side of the bar. What the hell! I felt like i was in some grimy bar in out in the sticks - not an established D&B. + +I was just really turned off from that experience. + +The good is that D&B provides a different type of entertainment when you want to mix things up. I remember going here with my grandparents when I was a kid and it was the best treat ever! We would eat at the restaurant and then spend hours playing games. This place holds some really good memories for me. + +It's a shame that my experience last night has spoiled the high standards I held for it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Its fun, but much smaller than some of the others I've visited. Its clean, staff is friendly and its a good way to waste time before a movie. They do have good food. Gets a 3 stars because I get bored easily at this location.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I used to love D&B when it first opened in the Waterfront, but it has gone down hill over the years. The games are not as fun and do not give you as many tickets and the prizes have gotten cheaper in quality. It takes a whole heck of a lot of tickets for you to even get a pencil! The atmosphere is okay but it used to be so much better with the funnest games and diverse groups of people! Now, it is run down and many of the games are app related games (Fruit Ninja) and 3D Experience rides. With such ""games"", you can't even earn tickets and they take a lot of tokens! Last time I went, back in the winter, many of the games were broken, which made for a negative player experience. I would go to D&B to play some games again in the future, but it is no longer one of my favorite places to go due to the decline of fun games where you can earn tickets.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I was here on 10/3 and I have to say this was a horrible experience. Me and a friend went here to eat and play a couple games afterwards. It took the waitress at least 10-15 minutes to greet us and by that time we knew we should just order then because we might not see her again. We ordered and got our drinks and well let's just say we didn't see the waitress again until she was giving us our check (some manager delivered the food to the table). No refill on my beverage, no how is your food, no ketchup for my burger or fries was offered. Lots of people running around like crazy and if your understaffed hire more people! I will not be back again to eat.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'll have a biased opinion of any place like this. What could be wrong with playing old and new school games, drinking, and eating all at the same place? The one thing I can think of is the price. On the surface, this is a pretty expensive place; however, they give a bunch of good deals depending on the time you go, whether or not you ""donate"" money to the Make-a-Wish Foundation, and if you're lucky when you take a spin on the wheel of prizes! But honestly, know what the deals are before you go to make sure to get the best price available. +In regards to the games, there's a plethora for your enjoyment. Although it is nice to play games that spit out tickets, the last couple of times I've gone I've gotten 2 hours of arcade games for a very cheap price (Mario Kart, anyone?!). Either way, it's a really fun place that you'll most certainly have a good time at.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> First off, let me say that I find the people who usually work at Dave and busters usually don't care or seem to be angry and hate their job. A friend and I went here and found that a couple of the machines ran out tickets and someone was always there and happy to help. The staff went out of their way to make sure we had a good time. The manager Tony was very sweet and made sure everything was ok. Every staff member we talked to was extremely nice. This is by far the best Dave and busters I've had been to![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My sister and law wanted to go here for lunch so all the kids could play games after we all had some lunch together. This place is huge and was moderately clean except the bathrooms. All of the food looked great on the 16 page menu. When our food came though, everything was below average. They have a huge selection of games for the kids to play, but you pay dearly to play games here. The food is overpriced and the drinks are drastically overpriced.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Rock Bottom Brewery in Homestead is always a good time. They brew their own semi-micro brew here and generally have as many as eight brews to chose from. Saturday night C and I stopped by to have a little dinner and enjoy some of their frosty beverages. + +Our first issue of the night was getting to Rock Bottom. As the restaurant is located in Homestead, a trip across the Hi Level Bridge was in order. Little did we realize that the bridge was under construction and it took nearly 40 minutes to get across it. Upon arriving at the restaurant we were presented with the task of finding a place to park which proved to be a daunting task. This place was absolutely packed due to several locations sharing a parking lot. After we got inside, our wait was about 45 minutes but luckily we were able to find a seat inside the packed bar while we waited. + +The food at Rock Bottom is quite tasty, but it is all pretty standard bar fare with the nachos and burgers leading their menu. They also have entrees such as steaks, but this place is not exactly known for their high class food products. I was pleasantly surprised by the quality of the food and we quickly determined that this would not be your average plate of nachos in a bar. + +Our order consisted of a plethora of items from their appetizer menu including Chicken Nachos, Quesadillas and Ball Park Pretzels. We had planned on splitting a meal for dinner, but by the time the appetizers arrived, we knew we had way too much food in front of us. + +The nachos were on a gigantic plate and piled high with cheese, sour cream, guacamole and shredded chicken. Containing just the right amount of jalapenos they had a nice little kick as well. In much the same way, the quesadilla was much more than an appetizer portion. With shredded meats and cheeses overflowing from the tortilla, there was enough food here for a two person entree. The Ball Park Pretzels are the reason we come to this place. They are always so light and soft with just the right amount of salt. + +As far as the beers are concerned, I ordered up the sampler so that I could get a taste of the various brews. They make a wide assortment of brews, from the Bud Lightesque ""Lumpy Dog"" to a dark ""Brew masters Choice."" I found many of the beers to be quite tasty, however, nothing exactly special about them. I would be that a taste test would find one hard pressed to chose the Rock Bottom brew over any off the shelf six pack. Don't get me wrong - still excellent brews, but I would expect more from a place that claims to be a brewery. + +I give it 3 out of 5 Rinsem's due to the lack of originality in the brews and the amount of traffic involved with getting in and out of the place.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Horrible beer, horrible service, horrible menu[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> SUMMARY: +If I was in the area and no one had a better suggestion for where to go, I might come back for beer and appetizers. + +GOOD: +- Decent beer... +- Original pretzel appetizer. You take chunks of soft pretzel and dunk it in spinach cheese dip. +- Huge portions. Most of us had leftovers. The RB Appetizer Sampler was multi-story and way more food that we could handle. The half order of ribs looked like a full rack. +- Attentive service with quick seating and frequent drink/water refills. +- Amusing name. + +BAD: +- Lots of food choices... burgers... steak... chicken... salads. Lots of drink choices... beers... wines... mixed drinks. I guess this could be seen as good, but it takes a while for everyone to pick something and since no one's awesome at everything, you could tell right away that nothing distinguishes this place. +- None of the food was super awesome. Nothing was awful, but nothing stood out in any way. I've had better beer, appetizers, and a better main course at plenty of breweries. +- Kind of dead on a Monday night with 3/4 of the place empty. + +Come if you want bar food, but keep your expectations low.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I am a big fan of Rock Bottom. +There are several dishes that are MONEY. +Appetizer: Seared Ahi, Spinach Artichoke Dip +Entree : Fire Steak, Pub Tips or Chicken Fried Chicken. +Desert : Carrot Cake (to die for) +Bar food: Pizza or ball park pretzels. Both of which are sprayed with brown ale. +Half the menu is really good, the other half is great. +The beer is good. Ask for the sampler! They usually have a velvet and something on cask. Ask for one of those if you are looking for something different. They will also have a scotch ale, an IPA, whiskey stout or other specialty depending on the mood of the brewer (which, if its still Matt, the mood is GRUMPY). If Andy is still working there, he is sure to please and Molly is great in the cocktail area. +Head over to Sing Sing after dinner and its a wrap. +I used to work there several years ago and I make it a point to hit every RB I possibly can. +Don't go to the one in Charlotte though, its not really a Rock Bottom.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I thought this place was pretty decent. My friend and I were both still reeling from thanksgiving dinner so we ordered salads... and they were HUGE. and tasty. I liked my salad though it was slathered in way too much dressing. My friend's was even more slathered so she didn't dig it too much. We'd also ordered chips with guacamole, the guac was pretty good. my friend enjoyed her beer. I enjoyed my coke (I know, I'm lame). + +so yeah... wasn't bad, wasnt the best, but it was okay.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Microbrewed beers are only a plus to me when they're better than the beer I would have drank otherwise. One waitress I had while there tried to split the uprights between macrobrew and trendy by describing one of their beers as ""kind of like Coors Light"". If I wanted Coors, I'll pay half as much and have one. + +The food is actually a saving grace, as it was pretty good. Head next door to Sing Sing for drinks, though.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Not the greatest ale house in the city but certainly not the worst. + +I like the food and I have tried all the beers. They're just ""OK"" as far as beer goes. + +Large portions. Friendly staff.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My friends got everyhing from steak(they didn't even get a well done steak right) to mahi tacos and the only great menu item was the seasoned vegetables- give it a miss. Sing sing next door is awesome but get dinner somewere else. After we were done the waiter asked if we were ready for the checks and I had ordered meal that came with a desert! Really dissapointing all around.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> everytime i come here i stick with the nachos add chicken add side of guac and i've never been dissappointed. i sit in the bar, grab a drink or 2 and eat those nachos. the bar has a pool table and plenty of flatscreens. rock bottom is a chain but it's one of the better chains in the area. i'll pass on chili's or friday's and come to rock bottom instead. oh and typically i walk over to target - work off some of those nachos.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Nobody has reviewed this in a while, but I am surprised at the lack of lovin'! My husband and I ate here a few nights ago and we liked it a lot. + +We started with drinks--he got the house-brewed Portland Wheat and said it was quite a good beer, and I got a mixed drink (Red Rock) that was also tasty. + +He got a burger covered in mozzarella cheese and I got a mahi sandwich. Both great--the fries and side salads are good here too, and there is no skimping on portions of anything. There were tons of things on the menu that I'm looking forward to trying. + +We are usually not dessert people at all but ended the meal sharing a triple chocolate stout cheesecake--who can resist a beer cheesecake, come on! + +Our food and service was great. They had the Penguins game on all the TVs in the bar and were setting up live music for after the game. Seriously, what's not to like!? I'm thinking this place has changed for the better since the last review a year ago... :)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is literally the first place I went when I first came to Pittsburgh - and I loved it. Hearty, full-sized meals, lots to choose from, and not too crowded or noisy. Although, for the sake of full disclosure, I didn't sit at the bar and I don't drink alcohol so I can't comment on that. I go back to Pittsburgh often and Rock Bottom ends up being a good standby for a dinner and a movie kind of night. Really, I have no complaints about this place so I'm surprised by the few low ratings here.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Little slow on the service and didn't have the beer I wanted on the menu. But you get those things when they brew their own beers on-site. But the stadium pretzels are good. The cream stout is tasty. + +The burgers are good and big with the little skinny fries. I'm not a fan of the skinny fry, but hey the burgers would choke a horse - and almost did. :o)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Lately, the Rock Bottom is hit or miss. The beers are always good and the Uppity Jagoff IPA is one of the best India Pale Ales I've ever tasted. The low point lately has been the food. I will never forgive the idiot in management who took the chicken quesadilla off the menu. That said, I ordered the lobster roll and when it arrived, the bread was as hard as a brick and cold. The filling was okay, but the lobster flavor was masked by over spicing. I suggest you eat somewhere else and imbibe at the Rock Bottom.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Pretty good! Excellent beer sampler - bargain! Veggie burger awesome. Onion rings awesome. Fried Mac n cheese was delicious - crunchy on the outside, creamy on the inside. Carrot cake was monstrously huge and delicious.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> First off, I will say that I just moved here from California and was a big patron at the Rockbottom in Long Beach. I came to the Homestead location last night eager to see the beer at this location. + +Now, Rockbottom is a chain brewery, so a lot was the same... the menu, the food prices (yet beer is cheaper, and I am fine with that). I have always found their food to be pricey, but they use excellent ingredients and it has always been tasty and filling so I am fine with that. The food here was just as good as the Long Beach location, so I have no problem with the chef at all. + +Service was good, our waitress was very friendly and helpful. I wish that they had asked us if we wanted to sit in the bar since happy hour was still going, but that isn't a big thing. Went to the bar to get a drink and had to wait awhile to get the bartender's attention, but he was very friendly and I got a nice welcome from him and others at the bar when they learned I had just moved here... I really enjoyed that. + +Beer: We got the beer sampler to try the whole list... and, well... I found the dark beers a bit lacking in comparison. The light beer and the wheat were amazing, very impressed. The pale was ok, as was the velvet pale that was one of the specials of the night... but both were way too citrusy. The Uppity IPA was very good... I don't usually like IPAs because the hops overpowers all flavor but the brewer had a good balance. Still, couldn't do a whole glass. I felt the Imperial Stout had a bitter burned taste that was overpowering... I almost want to say the batch had too much chocolate malt in it (not ice cream malt, for the non-homebrewers). The brown and amber were decent, but bland. I ended up getting an actual glass of the light beer and was able to finish it all without forcing it.... one point up on Long Beach, who had a good light but the aftertaste got to you before the glass was empty. + +I REALLY wanted to try the Das Gut Dopplebock, but they were out. Looks like they will have it in bottles to go soon so I hope I can catch that. Also want to try the Snow Moon Belgian. + +Verdict: While I was not too impressed with the dark beers, I found the lighter ones very good and I look forward to trying the other seasonal beers. It is a good hour drive south to get there, so I won't be going too often, but I will be back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Even since Rock Bottom opened (7 years ago???) I have always thought it was a dance club. I am not really sure why but I thought it was along the same line as (throw back) Hi-Tops but I did. I think I always thought this place was a club because of the behemoth size of the space. + +Well I was out with a friend and we needed a place to go before a show at the Improv and Rock Bottom was close. + +Part of this is my fault...I always order ""healthy"" items at places that specialize is greasy bar food...then I am upset when the meal isn't 5 star. + +I started off with one of their wheat beers, it was alright. I nursed it all through dinner so I don't think I was head over heels in love with it. I got the Catch of the Day, Off the Hook, Fish Dish, Sailors Delight or something(I forget it had some cheesy fish themed name). It was cod (meh, that should have been the sign not to get it) with roasted asparagus and lemon rice. The fish was suppose to be broiled but it had a thick breading (annoyed) and the portion of fish was tiny. The rice and asparagus were great though. + +My friend got a chicken sandwich which he enjoyed although the fries were pathetic. The fries were probably pre-cut frozen fries or just very poorly executed. They were so thin that you have to grab a huge handful just to get any actual potato flavor. + +Pros: A lot of tables (no wait), brew special beers, big menu, could hear the dueling piano bar next door + +Cons: Place was fairly empty and we got a crappy table by the door when it was 5 degrees outside, most of the food was fried, cheese filled, cream based, or wrapped in bacon. I know some people love to eat food like this all the time( I do every once in awhile) but if you eat out a lot you can't always get the spin dip, burger, and ice cream sundae. (I would love to but its just not in my cards). I do like like when causal places offer some healthy options.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Went with a group after work for dinner and a brew. We ordered a few appetizers first. The wings are good and the soft pretzels with spicy spinach cheese dip was fun. Had a burger, you can create your own from veggie, turkey, or fresh ground beef. Had a fresh ground beef and the meat was fresh and cooked perfectly with a fresh bun. + +The brew pub is nice and was surprised it wasn't busier.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Here's the trick to enjoying a meal at Rock Bottom: don't get fancy with your food order. Stick with the sandwiches, salads, burgers, and bar food; and you'll be OK. I've had bad experience will all the fish dishes (including the fish and chips). Also, I've found the service is generally better in the bar area than the dinner area. Join the Mug Club, even if you don't go often, and rack up points for free mugs and beers. Thursdays are Trivia Nights and the DJ is playing the music loud, so go if you don't really want to have a conversation with the person you're with :)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Beer selection was good, but they were out of the ones we wanted. 4 of the 6 people in our group ordered steaks all of them were cooked to their satisfaction. The bourbanzola was a good addition. Defiantly a place I would go again. Joe, our server, was awesome and super friendly.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love this place! Great atmosphere and friendly service every time I go!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Rock Bottom is a nice hangout place. Often when you are out and about with friends you arrive home with no voice from screaming over all of the background noise. Great if your out to see a band, but not so much fun if you actually want to talk to the people sitting around you. + + +Depending on your mood you can sit in the dining area full of booths and tables. It's alittle separated from the main bar area so provides for a semi quiet dining area. The bar area gives you a choice of sitting at the surrounding tables with waitress service or hanging out at the bar itself. Complete with a chillie ice strip to keep those yummy brews cold and the ever entertaining company of your favorite bartender. When the weather cooperates the outdoor patio houses about 6 tables for outdoor dining. The view however...not so picturesque, just the entrance to the Improv. Which hey, that could be the perfect seat if you're stocking the local comics! + + +The bar area contains pools tables and dart boards to try your skills. On any give night sports fans can enjoy the games of the day on one of the 6 big screen TVs surrounding the bar area. + +The menu is pretty decent with burgers that are cooked to order with the choice of either steak , veggie or chicken. They have a number of specialty burgers with different cheeses, toppings and creative themes. The bourbonzolla is a tasty burger with a Bourbon based glaze and Gorgonzola cheese. Appetizers which range from nachos to firecracker shrimp. Steaks, pasta and salads with rotating specials from different areas of the menu. + +On Monday the burgers are half off...I don't think you have to be a member of their mug club to get the special. However, if you are here regularly the mug club is great with free gifts and specials. + +http://www.rockbottom.com/MC + +Needless to say I have a fun beer glass collection thanks to Rock Bottom...LOL! + +Now everyone favorite part about Rock Bottom's Beers! +The in house brew master keeps it interesting with a rotating variety of frothy yummy to try along with the consistant favorites of Ale, IPA's, Rotating Darks and Kolsch. + +Stop by on Thursday nights for a colorful game of trivia where teams battle it out in a game of intelligence and drinking skills![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We've all had this happen to us - you go past a place one hundred times and never go on. Then, once you finally do, you realize how many opportunities you wasted! + +Rock Bottom is definitely a solid bar. As a microbrewery, their beer list is full of house brews. There are better beers in the world, but there are a lot of worse beers out there, too. + +What really makes Rock Bottom standout, though, is the food. My girlfriend and I shared an order of nachos, and it took everything we had to finish them. They also make a mean soft pretzel. + +The Waterfront may not be the most convenient thing to do while in Pittsburgh, but no trip to the Waterfront, is complete without a bite and a drink at Rock Bottom.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I would have to say I'm pretty partial to Rock Bottom, I have been going almost every Thursday for the past 3 years because of the fantastic ""Team Trivia"". My friends and I love the atmosphere, the DJ (Todd), and the service that we get at Rock Bottom. + +Every week when we go a menu is never needed because we pretty much know everything we want on it, except for when the change the menu from time to time and we get to have a special treat with something new! + +As an avid Rock Bottomer, hands down I have never in my life had a better spicy spinach cheese dip than I have had here at Rock Bottom. Whether I have eaten dinner or not before I come down to the restaurant, my favorite and my food of choice is the ENORMOUS Ball park pretzels with the cheese dip. It is a meal itself! The mixture of onions, cheese, spinach and tomatoes is perfection! + +Another favorite of mine is the Barbecue Chicken Pizza, it has a great kick to it and it's big enough for two people. + +The service has always been super great and now since we go often we have developed a great relationship with some of the wait staff. + +A truly great place to have fun with friends and meet new people! + +Come to Team Trivia every Thursday at 8pm![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Rock Bottom on Thursday nights is the place to be. Team Trivia starts at 8pm and it is free to play. The DJ (Todd) is great. + +The food is good, but the Ball Park Pretzels with Spicy Spinach Cheese dip is the best. The wait staff is generally pleasant and on top of things, a few servers are excellent. I am not a beer drinking so I haven't tried the microbrews but the mixed drinks I've had have been good and a few of thier specials perfect. + +On nights that are not trivia nights, Rock Bottom is quiet and a good place for a small to medium party. Larger parties will usually be split into two tables. + +Overall, an enjoyable place at which I am a regular.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> So I have not been to one of these in awhile since I normally have an aversion to chain restaurants, but since I was with colleagues on travel for work and they chose this place I went along. + +First surprise: decent beer. I remembered the normal RB Brewery beers were not much to write home about but they had a couple of new styles, including a very good imperial IPA that for $5/glass cannot be beat. Second surprise: pretty tasty food with a lot more healthy options than I expected. Recommend the summer salad and the ahi tuna - both were great. + +Service was a little slow (not sure why) so a 4-star review is downgraded to 3.5. I'll be back next time I'm in Pittsburgh for work.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The beer is good. Their light beer, Lumpy Dog, is very good-- doesn't taste like a light beer. When I was pregnant I became quite a fan of their root beer floats, too. + +As others have noted, the pretzels are really good. I'm not a fan of the spinach dip but my husband likes it. Veggie burgers are always good, too, though the staff sometimes seems confused when you order, say, the bourbonzola burger with a veggie burger. Long, long ago, when I used to go to the Rock Bottom in Boston, there was a hot mushroom / sundried tomato / cheese dip on the menu that was fantastic... if they resurrect that I will gladly add another star![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I always feel like I am constantly bashing breweries for their food, but in my opinion, I feel the bar is raised for places like this. It seems there are so many breweries out there that offer great beer, and slack off on the food. Unfortunately Rock Bottom is one that falls into that category. Let's be honest, when you go to a brewery, you want the full experience. If it was only about the beer, I'd go buy a growler and take it home. + +So, about the beer....EXCELLENT!!!!! The Jagoff IPA is with out a doubt one of the best IPAs I have ever had! They only I can think of that I think is better is Dogfish Head, but that's a matter of opinion. The beer selection is constantly changing, and they always have some excellent seasonal beers. You can't go wrong, there's bound to be a beer everyone will like. + +As for the food.......it's pretty much a crap shoot. Sometimes it's good, sometimes it's terrible. My biggest problem is there is absolutely no consistency when it comes to the food. One time it's perfect, then maybe it's cold, or it's burned, or it tastes completely different from the last time you had it. Unfortunately, it seems there is zero attention to food quality. + +That's pretty much it. This place fixes it's food consistency, and it's a five star place. Till then, it's hit or miss![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I was SO ready to like this place! Turns out, not so much. It was okay. No better than TGIFridays, but better than Eat n Park! The deets. + +The hubster and I were here on a Saturday evening after a show at the Improv so we were happy and in a good mood and ready to enjoy some good eats. We ordered drinks. He a wheat beer of their brewing, me my fave Bloody Mary with Absolut Peppar. The hubster deemed the beer acceptable, but wouldn't go out of his way to come back just for another one....yes, he DID order another one ""just to be sure."" My Bloody sucked. Watered down tomato juice with no discernible Peppar of any kind, let alone any other seasonings. Even a good standard mix would have been better. Our very efficient and friendly waitress took it back and watched while it was remade by the other bartender. Nope, no better at all. That went back and I went with a you-can't-screw-it-up Amaretto sour. It was fine. + +Hub ordered a Reuben - why, I'll never know because they simply never measure up to the gold standard of what used to be at the long-lamented Gazebo in Shadyside. You younguns wouldn't have a clue of the establishment of which I speak. He said this one was ""fine."" I had the Texas Fire steak with jalapeno butter which I enjoyed very much! Packed a punch of heat and flavor, but the sides were uninspired. Steamed veggies. Any flavor was steamed out in the process - eh. Cheddar mashed potatoes - there was cheddar in there????? No way! + +The tab was reasonable - we DID have a Living Social deal that took $30 off, so our check was for $12 and change, not including tip. Not bad (even with the $15 cost of the LS Deal), but had we paid full price, it wouldn't have been worth the experience. We'll hit the Improv again - we have before - but, we'll head somewhere else afterwards.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I must admit, I do like the brews. I also like the white cheddar mash potatoes. Other than that, meh. The food is pretty forgettable. Another ""brewery"" that sadly fails to be anything special in the food department. With the restaurants upping the ante on 8th Ave, you may want to kick it up a notch Rock Bottom. But how would anyone know to? It's a chain. Whomp whomp![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> For a brewery who is attempting to take advantage of Oktoberfest you wonder how at 7 pm they could be out of mashed potatoes & sauerkraut then a sausage platter with sweet mustard guess they have not been to Germany. Not worth $5.95 unfortunately the sausage platter was $15.95.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Dined in twice, food ok, atmosphere good.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've always been pleasantly surprised with the food I've gotten at Rock Bottom. I say ""surprised' because with any restaurant that falls into the slippery territory of a ""chain"", you expect to find your fair share of culinary duds. But I've really had a lot of good meals at Rock Bottom. Now, granted, you do owe it to yourself when ordering to not forget where you are (a ""bar-straunt"" if you will), and don't get anything above and beyond this place's call of duty. For instance, I will never be ordering the ahi tuna. I'll leave that to my favorite sushi bars and restaurants a bit closer to the water (the Mon doesn't count.....). + +But besides that, I always really enjoy my meal choices. I've recently gotten the chicken avocado sandwich. Chicken was grilled perfectly, plenty of avocado, and it was a good sized sandwich without being excessive. I've also ordered the Margherita pizza, which could definitely be split between two people. It's an eight cut that comes to you on a big wooden pizza paddle. The pizza was really great. The crust was crispy, it had a good balance of cheese and tomatoes, and the basil pesto was fresh and tasty. And not greasy whatsoever - BIG bonus points there. But my biggest surprise as of late was when I ordered their chicken flautas. I'm a HUGE Mexican food fan and always hesitate to order Mexican outside of a Mexican restaurant for fear of being disappointed. But I had an insatiable craving one night and decided to go for it. It was DELICIOUS. The flautas are deep fried which gives you an amazing crunch, and they still managed to not dry out the inner ingredients. The accompanying rice was nice and moist as well. I was so happy! + +I've always been quite happy with the service there as well. I go on Thursday evenings for trivia, and nine times out of ten the service is really spot on. The ladies servicing the bar area are friendly and attentive. Only once or twice, to my memory, has my service been sub-par, and that can usually be chalked up to an extremely packed Trivia Night with only two visible servers helping 50+ people. + +I definitely give Rock Bottom two thumbs up for taking your typical chain-found food and making it fresh, yummy, and worth coming back for more.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I went to Rock Bottom this past weekend, and it was ""nice"" to see that nothing has changed in the year or two since my last visit. While the beer is pretty good, it has never outweighed the fact that the service isn't good and the food is average, at best. + +It was even difficult to get beers at the bar...we tried to have the girls order, thinking they'd have better luck...when that failed, the men tried...that didn't work either. If we hadn't REALLY wanted a cold beer after a comedy show at The Improv, we would've just left. It definitely wasn't busy enough to be noticed and ignored by the bartender, so I can't overlook it. Of course, the service has always been spotty at Rock Bottom, so it was hardly surprising. + +Combine the weak food and poor service with Rock Bottom being too far from home for a night out just to drink, and you get the exact formula that's kept me from going there in the past...and will keep me from going often in the future.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Happy hour at Rock Bottom, 2 thumbs up! Good prices, the pizza is delicious, drinks are a few dollars off the regular price, good service, and the atmosphere is always casual and fun.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The only reason Rock Bottom gets 3 stars is because of the brews. Food was ""eh"", not many vegetarian options and hostesses who will ignore you because they are too busy chatting about who didn't text them back. This place has the potential to be great, but sadly, it falls way too short in almost all areas.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Watch the fat girls in here. They will try to steal your buddys chair in a sec if he goes to the bathroom & then the indignent fat girl had to get yelled at in front of everyone w/ in ear shot. Everything else including the burger & beers I devoured was excellent.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Rock Bottom was our first stop on a 17 mile pub crawl. As expected, the bar was lively, the food was good, and the service was accommodating, The beers are better than Church Brew Works and the bar was populated. The bartender readily offered a taste of beer and gave us a hat to wear for the rest of the crawl. +I vote for Rock Bottom as the anchor store of the Water Works.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I haven't been to Rock Bottom in years. Maybe even decades...is that even possible? Well, either way, it's been awhile. So with my gift certificate I took my brother out for a birthday dinner. + +As I get older, my tolerance for things like crowds and youngsters gets lower and lower. As a result, I told my brother to be ready by 4pm so we could head to the Waterfront before everyone goes out for date night. Plus the Pirates were playing at 4:05 so we could enjoy our beers and the game. + +When we arrived, the bar side was already pretty packed but we were still able to get a table. Our server was very attentive, friendly and helpful. Right off the bat we both ordered samplers so we could try all of their beers. We loved the fact that as she approached our table with a full tray of samples our server said, ""I have to go back for the rest."" In all we were served 10 different beers each (in 3 oz glasses, maybe 4 - I can never tell). I gotta say, Rock Bottom knows their beer. I liked more than I didn't, and very few were not to my liking. So the $6.95 10 beer sampler was well worth it. + +During our sampling we indulged on some Southwest Egg Rolls. They were okay, but not quite what I expected. The spicy ranch was top notch, though. As we ran out of beer, we each ordered up a Kobe Burger. They were both cooked exactly to our liking (medium). And to top off our wonderful evening, the Pirates brought home a win! + +My only complaint, as a beer drinker, is the cost for a growler. The glass container itself is sold for $12.95. That's the empty price. To me, that's a little ridiculous when East End only charges $3 for the bottle and Penn Brewery $5. Paying more for the bottle than the beer inside seems like insanity to me. So I walked out empty handed. But it won't deter me from returning.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I just came here with some friends to hang out and get some appetizer, and I have to admit that I was pretty satisfied with what we got. Though I couldn't find any fried pickles or onion rings on the apps section, there were some blue cheese nachos that really hit the spot. The atmosphere of this seems pretty cool, especially in the pub area.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Fish tacos were excellent!! Great brewed beers on tap as well!!!!!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I very much enjoyed my first visit here. I got the Turkey Meatloaf and it was really tasty. It's more sausage than turkey. The cheesy mashed potatoes were excellent. The star of the night was the appetizer, the artichoke and crab dip. It was awesome. My only complaint was I ordered a Red Ale and they were out. I had the Curmudgeon instead and it was very good, but still.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Slow service +Below average food +Ill pass[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> First time I was here I had chicken quesadilla's and they were bad. We went again last weekend. I had the chicken avacod sandwich. It was very good. No fat in the chicken. Just a mess to eat, but still awesome. Also had the chocolate stout cupcake, it was amazing.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Thanks to the staff here +For being so friendly and +Cool with our whole mess* + +*rock bottom allowed our bachelorette party to eat and drink and hang after dave and busters orphaned us[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Its not bad. I'm not into chain kind of places, but if you're with a group that doesn't do anything more adventurous, you'll do fine here. I vacillated between 2 and 3 stars but the house beer I had will make sure I come back from time to time.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Went to Rock Bottom for lunch the other day and was very pleased. My coworker had printed out a coupon for a free mini appetizer. The waitress told us that they were not making mini appetizers and gave us a full sized chicken quesadilla. If you have ever had the southwestern egg rolls from Chili's - the filling tasted like that and I am a big fan! + +Mondays are half off burger days and I tried the just hot enough burger - topped with crispy jalapenos, pepper jack cheese, pico de gallo and housemade habanero ketchup. It was delish! The ketchup was so good and the fries were extremely crispy. + +The prices are a little steep for lunch but if you go on Monday, it's totally worth it. I think that the quality of food more than makes up for it but don't expect for pay under $10 for a sit down. + +I felt that the staff was very nice and the waitress was very attentive. The service was quick and I think you can get in and out in under an hour.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Rock Bottom is a chain brew pub one that, in my opinion, is just ""OK"". The restaurant is rather large with lots of seating and a pool table. They have many of their own brews that you can sample but to tell you the truth none of them are that good. I have had several of their beers and all of them have been forgettable. + +Their food is pretty much like their beers, forgettable. I have had one of their burgers and their pizza and they really weren't anything to write home about. + +I feel they will impress those who have never been to a brew pub but I would probably describe them as the Chili's of Brew Pubs. If you are in homestead and are looking for a burger and a beer it might be a good choice for a bite, or at least until the Burgatory opens![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Went here last night to meet folks for a friend's birthday party. Docking one star due to a few unfortunate things that happened, otherwise I'd be fine giving this place a 3. + +Our waiter was very attentive and kept our water and soda cups refilled, the food was decent overall - I had a plain ol' burger and a delicious berry sangria - and the place overall had a nice vibe to it and was pretty comfortable and fun to be in...you'd think this would just be another average place not-great-but-not-bad and I'd be ready to go on to the next review right there. + +Here's where I ran into problems. I'd checked the website in advance to try and plan my meal since I do my best to pick items on menus that aren't, say, 2,000 calories in one sitting. Their website advertises that they make skinny drinks; when I asked my waiter he said it was possible but that they did not normally do this and that it's a hassle for the people at the bar, so he didn't recommend it. Then why tell us on your website that you'll do it??? + +Additionally, while we had checked in advance when we made our reservation about bringing a birthday cake and the restaurant's ability to handle us lighting candles, apparently there was a break down in communication; we never got the candles we had asked for, and in fact the poor waiter struggled to even find a lighter before realizing there were no candles available. Obviously whatever error occurred wasn't the waiter's fault, and we definitely thanked him and tipped him well for doing the best that he could with what he had. + +On a final note, this is also one of those places where if you ask for a medium rare burger, they will overcook it; I've started ordering medium rare on purpose specifically so that I get a medium cooked burger instead of medium well or well done. + +Final verdict: go for the brews if you must, and the food's nice enough. I was admittedly left a little underwhelmed.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Mostly come here for the beer and sports. Fun place![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Nothing special. Just like Applebee's, Chili's or Fridays. Stick to the bar food (burgers, sandwiches, pizza, wings and salads) and you will be okay. + +This was our second attempt at trying Rock Bottom on Fathers Day. The first time almost ten years ago. We went in the early afternoon and they had already ran out of steaks. How do you do that on Fathers Day?! This time we went around 12 noon and beat the rush. + +My wife got and loved the Berry Bash Sangria. She just said it had too much ice in it. Our daughter got the root beer float which she love and I started with a Mango Ice Tea, but later switched for a raspberry ice tea as the mango ice tea wasn't sweet enough. + +We started off the the Kobe beef sliders as our app. It took at least 15 minutes to get them. You get three sliders and they were very good. + +My wife got a small greenhouse salad with Jalapeno ranch dressing to start off with which she enjoyed and the lobster & shrimp enchiladas as her main entree. She complained about how salty it was and the fact that there was no lobster in it at all. + +Our daughter got the kids burger and fries. No surprise there. + +I ordered the New York Strip with mashed potatoes and it came with green bean as well. My strip was cooked perfectly and has a decent taste. Longhorn has a much, much better quality of steak though. The green beans were pretty good and my mashed potatoes very bland and pretty average. + +The kitchen sounded like an live episode of Hell's Kitchen. The waiters were repeatedly asking for orders at least 5 to 6 times. The kitchen was backed up the whole time we were there. + +On a different note, our waitress Susan was very good. Come here for drinks and the bar food. Skip everything else.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I go to Rock Bottom pretty often for dinner or their awesome beer, so I was really really excited to have my bridal shower there. My maid of honor reserved the banquet room which was very nice and separated from the rest of the restaurant. My MOH and mother said that the person they talked to about reservations and arrangements was wonderful and easy to get in touch with. My shower was wonderful, the wait staff was great and kept everyone's glasses full. It started pouring down rain and they let us stay a little longer so my gifts wouldn't get wet when taking them out to the car. The only reason this place gets 4 stars is because we were not allowed to take our leftover food from the buffet home. There was salmon, chicken, potatoes, and mac and cheese left over and they told us we couldn't box it up. Not sure why- they can't re-serve it! It would have just gone to waste! + +Also, not at all related to the shower, their trivia night is super fun![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Southwest Egg rolls and Fish tacos. Mmmmmmmmm. Ohh and the AMAZING Brews![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I rarely give a business a superior rating, but I have to say my wife and I had one of the best dining experiences at the Rock Bottom Brewery. The food was delicious, the beer, every recipe sampled, was amazing and the service was wonderful. The staff made us feel like we were the most important guests in the restaurant. + +Please support this business. I guarantee you will not be disappointed.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm giving 4 stars mostly because of the beer....large selection & decent prices. The food is pretty good, but nothing to rave about. The menu has a good variety, and everything I've tried has been good. Portions are large. + +One side of the restaurant is the bar & bar atmosphere....with several TV's & 2 pool tables. It's very wide open with extremely high ceilings. The other side is more for families or people who aren't concerned about watching sports. In general, it has a relaxed atmosphere. I've always had quick & friendly service. + +I love the whole Waterfront area....so much to do![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm not much of a beer drinker, but my fiancee is a major enthusiast, so I agreed to tag along. I'm glad I did! Our waitress was very knowledgeable about the extensive house-brewed beer selection, and helped me to pick one I would love (the kolsch was very crisp, light, and drinkable.) The food was standard pub fare with a twist, well-executed. My burger was topped with onion petals and gorgonzola, and cooked to perfection. The waitress recommended their macaroni and cheese for a side, which was definitely a good choice. My only complaint is that most of the food was rather heavy, and I spent the rest of the night wallowing on the couch. Not sure I would make the hour+ trip to Pittsburgh again, but if I found myself in the city, I may just stop by.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Came with my BF we started with the crab artichoke dip. It was very greasy and had virtually no crab. The wedge salad was good and crisp. I had the hazelnut crusted chicken. This has to be one of the worst dishes I've ever had it was like pancake syrup over breaded chicken. To finish the meal we had the homemade chocolate chip cookies served with hot fudge. Well there was no hot fudge it was chocolate syrup the ice cream was so crystallized from melting and re-freezing all around disappointing.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Normally the food is outstanding, no more salted bread sticks, but they did bring back the ball park pretzels. Not very good, cool to low warm. Hard, dense. Mango ice tea is wonderful. + +Will see how the chicken comes out. + +To be continued...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Tom and I decided to try this place out before catching a late movie on a Saturday night. He is a beer buff, and neither of us had ever been there, so we gave it a go. + +We walked in around 8pm and we were told that there would be an hour long wait. We put our names on the list and went shopping around the area. About 25 minutes later, our table was ready. Parking was a cluster since the lot is shared with Dave & Busters and a karaoke bar called Sing Sing. Tom dropped me off at the door so I could secure our table. + +Our server, Jackie, approached me almost immediately and brought two waters to the table to start. She was very attentive and funny, and probably the best part of our experience at the restaurant. Tom ordered a Red Ale and to his surprise, didn't care for it. Jackie gave Tom three free samples of beers she thought he would like after talking to him about his beer drinking habits. He loved all three, and chose the most bizarre (and expensive) beer. Jackie switched the Red Ale to the beer of Tom's choice, and charged us for the less expensive beer. Very nice of her! + +We started out with the Ball Park Pretzels with Jalapeno dip. The pretzels came out quickly and they were very fresh, not to mention huge! We only ate one and took the other to go. Very good app though! + +Tom ordered some sort of bacon cheeseburger, and I got the Chicken Fried Chicken, which was a pounded chicken breast, breaded and fried, over white cheddar mashed potatoes with a side of gravy and some apple coleslaw. Tom's burger came with a small handful of fries, and my meal was very spread out on my plate, like something was missing. Not very good presentation at all. The food itself was okay, nothing to write home about. The potatoes were my favorite part. Tom said that his burger was mediocre. + +Another note: The bathrooms are shared with the Sing Sing karaoke bar that is in the same building, so expect drunk singing women in the bathrooms and brides-to-be puking in the stall next to you after enjoying too much alcohol at their bachelorette party... Yuck. + +Overall, we might come back for the beer and service, but not for the food. And DEFINITELY not to use the bathroom...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm a regular here since their kitchen is open late and it's a good option after movies. Their nachos is pretty good. I also tried their burger and chicken sandwiches and they're good as well. +I think the only thing I did't like is the steak taco appetizer. It was too sour and kinda tasteless.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The Cajun Pasta I ordered was just spicy enough to keep me sipping my Rock Bottom IPA. It may be a chain but I always get that microbrew restaurant feel when I'm here. They could upgrade the quality of the servers but I've never had a really bad experience with the service.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I really miss the Northstar Amber but the specialty beers are always good. Food is excellent and the service staff is friendly.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> So after an evening of enjoying a comedy show at the Waterfront, we headed to Rock Bottom for some late night grub. The place was pretty busy, we had to walk around the bar area for several minutes until a nice couple told us they were about to leave and we could have their bar table. As nice as this was of them it was awkward standing over them as they finished their drinks paid their bill and left. + +So finally seated I look over the drinks and being the huge IPA lover that I am I went with that and it was indeed a good choice. The hubby had the Red Ale which was also rather good. + +The service was OK, not the best not the worst. But moving on to more important thing, the food. Talk about missing the mark hugely! I ordered the mini street fish tacos. You get four mini tacos with a marinated in lime piece of fish, and tomatillo salsa. They were just strokes away from inedible. I love fish tacos, I mean it is such a simple concept so why do people have such a hard time executing this dish? The shells were hard and literally split at the bottom when I picked them up. The sour cream sprayed all over the plate only made them messy and the poor fish was just so overcooked. If I wasn't so hungry I wouldn't have eaten them at all! Lesson learn on that. + +The husband had the BBQ Chicken Pizza. It had beans and corn with roasted red pepper on it along with some sour cream. My husband is usually the type that will order these lovely specialty pizza's and ask for them to remove all the wonderful unique toppings! For instance, he would usually just say, Chicken BBQ and cheese, nothing else! I refused to let him do that this time, because I was really intrigued in the combination of ingredients on this pie. And boy was I jealous when it came out. It blew my crappy tacos out of the water! Should have stuck with something simple. + +Furthermore I could care less if I come back to this location. The beers were good but hell you can get a decent IPA just about anywhere anymore. And the underwhelming food sealed the deal. I know this is a chain, but it still doesn't have to stink...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> the food was delicious. portion size generous. atmosphere good. Our waitress Lindy was outstanding. Have nothing but good things to say. Would highly recommend to everyone ![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Another good meal ... this time the Housemade Meatloaf. It's a blend of turkey and sausage instead of the standard ground beef. A refreshing and delicious twist on a comfort food staple. Served over cheddar mashed and mixed veggies. The server could have behaved like she wanted to be there but everyone has a bad day once in awhile. Service was prompt just the same. Overall good experience.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have to say that I've only been here when it was very busy. I found the service fairly quick and any of the food I've had has been delicious. I went there tonight and there was an issue with my food. Without going into detail, I will say they handled it wonderfully. Our waitress Mallory was very kind and she was quick to fix the problem. I had the salmon for the second time and it was just as amazing as it was the first time. I had one beer that's similar to a blue moon and that was good too. I would go back again![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My husband and I got here a couple times a year. Always (except my veggies today) get great food at a decent price. I love their side salad..... which has raisins and sunflower seeds. Burgers are great and my husband loves their chicken Mac and cheese. Recommend to everyone just get there early for a seat.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Poor service and food. I waited 20 minutes at the bar for someone to just acknowledge my presence. They finally brought my food out and left it without asking for me to pay.... So I had to wait an additional 15 minutes to find someone to pay. Yes, I had to TRY and give them money. + +On to the important part... Food was terrible. I had a burger and it was pathetic.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> On a glorious day in the month of May , my love and I stumbled hungrily into rock bottom. Ha. Just kidding I realized Darren W. Hadn't reviewed here so I had to start it cheesy. + +The rock bottom line: Monday for lunch we had awesome service by Ashley. We weren't rushed and it was quite. The burgers were great and half off . The beer was very good. We will be returning for sure.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Planned a surprise birthday party here for my wife and they did an amazing job helping to pull it off! Service was extremely helpful, professional, and on point all night. Lauren (one of the managers) was reliable and pleasant throughout the entire planning process. If anyone is looking to plan an event I would highly recommend Rock Bottom. Couldn't be happier![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love this restaraunt. Rarely have I ever received service like I get here. The food is good, definitely reasonable for the price. The thing that blew me away was the fact that my steak was cooked TO TEMPERATURE. This rarely ever happens at restaraunt of similar price range and quality. But the servers are fantastic. Very attentive, polite and timely. The beer selection is awesome, we always order the sampler. I like having lots of options as far as beverages go. The wait time isn't terrible if you go a little later on a friday or Saturday night. And they most often call you before the quotes time. The desert menu is a little small, but I could probably skip it anyways ;) the ambiance is good, not to crammed or noisy. They also have outside seating available when the weather is nice I highly recommend this establishment![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love this place! Great food and the best beer brewed on site! The bourbonzola burger is the best thing you can order here.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The staff here is very nice and the set up has TVs all around the family so enjoy mostly all sports, the music is nice and pretty mellow and the place is very spacey and the prices are pretty reasonable. And most importantly is the place seems to be kept clean at all times.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Good food and large portions. I ordered the Veggie Burger for $8.50 and I loved it! It's one of the most unique veggie burgers I have ever had: a homemade patty of beans, rolled oats and veggies. The chipotle mayo really gave it that oomph. My burger was more than enough for me to handle and everything was worth the price. As for drinks, I'm a complete noob when it comes to beer but my friend ordered a tap and even from a small taste, I could tell it was very good quality beer. Bitter and sweet, with a slight tang. I rarely drink beer but i I'm going to, then might as well drink the best kind there is - fresh and microbrewed. + +NOTE: There aren't too many options for vegetarians. The veggie burger was pretty good and I'd recommend it, but other than that, there's also the veggie tacos, a few select appetizers, and a few salads from which to choose.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've never been crazy about the food here, but my friend likes it, so I do eat here once in a while. We stopped in last night and I had the chicken finger appetizer with fries. The food was a little overcooked and nearly tasteless. The ranch dressing was barely good enough to make up for it. + +My friend had the mac & cheese with chicken and bacon, which is what she orders just about every time she's there. It looked delicious and the portion was huge. I'll be trying this dish next time we're there. + +We've also had the Ball Park Pretzels in the past, and they're really good. + +I'm giving 4 stars because the service was great, there's outdoor seating, and the Berry Bash Sangria was delicious (if expensive). We'll be back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Every time I've been here the food has always been delicious and the service has always been very exceptional. My go to is the Laredo burger and the Mac n'cheese as a side. They Mac n' cheese is absolutely wonderful if you like garlic! I've had a few other menu options as well that have been superb. The beers on tap are always great. My newest favorite is the First! Pumpkin Ale. + +One thing I really appreciate about Rock Bottom is that they aren't one of these restaurants that try to rush you out when you're done eating. The food comes out fast (which is great when you're starving!) but if you want to stay an visit with your date or eating companions there's never any rush. I was just at Rock Bottom last night meeting friends for a movie that didn't start until 11pm. We got at the restaurant around 7:30, ordered drinks, ate and had a few more drinks and then just hung out for about a half hour until it was time to Walk over to the cinemas. It was nice not feeling rushed to leave as soon as we stopped ordering. + +My only complaints are that sometimes meat ends up being cooked a little more than you often ask. Medium often turns into medium well, but that's not a huge problem for me. I also don't think the signature cocktails are worth $9, but that's more of a corporate complaint since Rock Bottom is a small chain. + +Overall I definitely recommend eating here if you're in the Waterfront![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The food is standard American fare--a bit overpriced in my mind--and the beers range from mediocre to very bad. The Kölsch is the only decent beer of the bunch. The service is good, but the wait for food or a table can be quite long (generally 20-30 minutes even for just beer and apps). I've been to the one at the Denver airport as well, but I was stranded and had free meal tickets, so okay-but-nothing-special pizza from Rock Bottom it was. Since it's a recognizable national chain, I think of places like this as more of a tourist brewery rather than a true Pittsburgh craft-brew experience.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The beer is good but the food is nothing to brag about at ALL. I've tried many things on the menu, and if you have developed a ""foodie"" palate, don't even bother, because you will be very disappointed. If you feel comfortable with chain restaurants and their lack of innovative touch (which, nothing wrong with that!) you will most likely enjoy Rockbottom. The only entree I did enjoy were the lobster and shrimp enchiladas (minus the repulsive beans and rice) and the asiago crab dip as an appetizer. Otherwise, you are better off skipping it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place is quite big with a bar area, dining room area, and patio area. We decided to sit in the bar area so we could watch some football on one of the many TV's. They also have darts and two pool tables, which I really enjoy. When you are in the bar area you can see the beer being brewed through the window which is really cool. + +I ordered the hibiscus wheat beer and my friend ordered the white wheat, both of which are brewed by Rock Bottom. They both tasted delicious and were exactly what I needed for a hot day. My friend ordered the Fried chicken entree which came with mashed potatoes and of course she gave me a few bites since we always share. It was a pretty delicious meal, but the fried crust fell off a few pieces which I am not really a fan of. I ordered the Sante fe salad with grilled chicken not fried. The salad was okay I was expecting more flavors overall, but I didn't really get them. + +It was a good experience and will most likely be back when I am around the waterfront area.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I am not a fan of chain restaurants typically and had to slowing break my boyfriend from wanting to eat at chain restaurants all of the time. The one chain that I can't break from is rock bottom. + +Their beer is always good- as far as their staples go, I really love their white ale. Their seasonal IPAs have been good and my favorite seasonals of all time included their chocolate raspberry stout (...yes, it tasted as good as it sounds; they had it last year around Christmas) and their smoky BBQ brown ale (tasted like summer, complemented BBQ amazingly ; they had it this past summer, I bought a growler of it lol). + +As far as their food goes, I typically stay away from the appetizers. $10 and up is a little too pricey for me as far as appetizers go. I've had their southwestern rolls and they were good but not worth $10. + +Almost every time I go I order the Baja chicken sandwich. It's my favorite chicken sandwich! So good. The chicken is actually grilled (which goes for all of their chicken sandwiches) and I love the charred flavor that it has. The bun is soft but sturdy and doesn't fall apart while eating the sandwich, the sauce is amazing, the onion frizzles are the best and last but not least... There's a half of a fresh avocado on this sandwich. Mhm! I love it. My boyfriend usually gets the hickory BBQ bacon chicken sandwich and loves it as well. + +Another item I ALWAYS get... Their apple coleslaw. I've yet to find better coleslaw in a restaurant. So simple, yet oh so good. + +They also recently changed their fries and these are much better than their old ones. + +Their side salads are awesome as well. They are decent in size- spring mix topped with sunflower seeds, raisins, half of a hard boiled egg (which I give to the boyfriend), chopped cucumbers and tomatoes and croutons. Yum! + +I usually order the same thing every time I go. I steered off my normal path once and ordered the buffalo Mac and cheese and found it to be quite tasteless. Which turned me off to trying new items there. Plus I am just too in love with the Baja chicken sandwich and apple coleslaw to want to try anything else. + +Service is always great, the bartenders are friendly... I love this place. Ask about their rock bottom rewards ![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Be careful. The servers can't pay attention to save their lives, and the management cares even less. I want to make sure people know how careless the management is, particularly Mark who seems to let his staff run around.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I always enjoy Rock Bottom. Standard beers on tap are always great and their rotating selection usually has a hit as well. + +I prefer the bar seating as to the dining room, but this is a good way to separate the family dining from those of us without kiddos. + +Nachos, nachos, nachos. Truly the best in the area. Great burgers, chili and salads. Really...I don't think I've had a bad meal here. Nice outdoor seating in the summer. + +This is a great place to watch a game or just hang out. Iced counter at the bar to keep your drink cold. I know they have other cocktails here, but I can't order them at a beer place. I've seen them and they do look good, but I'm stuck to the beer selection. + +They have a great happy hour and specials throughout the week. + +Service is always great whether there are two or 10 of us.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is a ""Okay"" place to eat. The food is nothing special. I guess what they have going for them is the beer. Order the Guacamole for the starter which was okay but for $8.50 and the portion was not worth it. Rice (Cajun Taco) was not cooked well. Would I go there again ""maybe"". If your into beer and watching the game, then yeah go there.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> BALL PARK PRETZEL-Would eat again. + +I came to rock bottom, looking for a great beer. Full of hops, that brings a refreshing sensation and satisfaction. I then opened the menu, scanned looking for those select bar items to pair with my great beer. I saw an extensive list of items, from chicken fingers to salads. I noticed a Ball Park Pretzel, with a jalapeño cheese dip. I was blown away, the fact that I got 2 pretzels amazed me. I ordered within 25 minutes of seating. My pretzels hit the table within minutes. The smell of the warm salt and hot cheese opened my senses. But I knew we could step this shit up, I asked for mustard. And what do you know. Grey Poupon Dijon Mustard is in front of my eyes. I combined that shit and life evolved. I went to heaven, it took me 35 minutes to write this review because I took a solid bite with Grey Poupon after each sentence. Good look Rock Bottom, keep up the good work.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The Improv Comedy Club at The Waterfront is the best comedy club in Pittsburgh because there is only one other one and this one gets more famous comedians. I go there just about every other week. + +Pros: Great comedians all year round! The food/drinks are very good and the wait staff is wonderful! The Improv is a great venue for upcoming and new comedians, I always see new, local talent opening for national comedians. In one show you will see 1-2 local comedians, and 1-2 national touring comedians. The Improv has a nice environment inside with general admission seating (first come, first serve). The EMAIL LIST is essential in order to receive free ticket packages and perks, as well as reminders of upcoming comedians! + +Cons: Prices can be steep (it is expensive/difficult to be a regular). Food and Drinks are not cheap (no specials). Expect to pay $15- $40 for tickets depending on the headliner with a two item minimum. Waiting in line before the shows wouldn't be bad if you weren't forced to stand outside in any and all weather conditions. If it is raining and you'd like a good seat, you will pay the price. + +Overall: This 21+ venue is a great place to spend a night out with friends or loved ones. You may buy tickets in advance online/phone or buy your tickets at the box office at the location. I highly recommend joining the mailing list to receive free tickets! Check the calendar for upcoming shows and open mic nights during the week! Support local comedy, and enjoy The Improv at the Waterfront![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Good club for a good laugh. High food prices (most comedy clubs are), 2 item min. The food was less than stellar. I wouldve enjoyed Burger King more. + +Service was decent, I believe the waiters/waitresses could hustle a little more or the club should hire more waiters/waitresses. I get grouchy when my glass is sitting empty for more than 2 mins.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> They have good acts coming around here, and often give out free tickets, particularly ine summer. I've never actually paid full price for a ticket here. + +The two-item minimum is bit bothersome to me though...I don't mind the requirement so much, but the quality isn't good and the prices are high. Our four items total came to about $30 (two appetizers and two beers) and the apps were really nothing to write home about and the servers aren't even very friendly. Also beware...they have a lot of rules here. They won't seat till the whole party is there; if you get dinner reservations everyone in the party HAS to order dinner, automatic gratuity added to the check, etc. etc. + +The ""box office"" is also weird...you get your tickets at this window complete with microphone and slide-under slot...then you walk into the club and the box office is completely open and the workers are just sitting right there, so I don't get the whole hoopla with the window. + +All in all though, the seats are comfy enough, the atmosphere is pretty nice, and the acts are good.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I always enjoy a good comedy club and though I'm a loyal Helium fan, I gotta give props to the Improv near Pittsburgh. They chose a great location, with surrounding restaurants of all genres and fun bars and shopping. + +We bought tickets to see a comedian I had never heard of (he was decent) for $25 each with a two item purchase minimum. I really dislike that rule but you can't really get around it. + +The only thing I didn't like, aka hated, was having to wait in line outside before the show started. It was freeeeezing! They should put heaters outside. seriously.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Came here to see Charlie Murphy. +Parking was nightmare. I would expect nothing less on a Saturday night. +The 15 minute wait to get inside was torture. They need to implement a system where if you purchased tickets in advance you don't have to wait outside. Once inside you we were seated pretty quickly. +Seating is first come first serve. + +The Server was pretty quick to take our orders. I misread the menu description and didn't realize my BBQ sandwich came +with cheese. I don't eat cheese, and had send my order back. The waiter was gracious and returned with my modified order in about 15 minutes. I've never heard of throwing cheese pulled pork sandwich, maybe it's a northern thing. +We got our checks quickly, and without issue.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm HUGE SNL fan, so naturally if someone who's been in the cast is touring, I'll come here to see them. Some have been really great...Jim Breuer. Some have been (surprisingly) very bad....Tracy Morgan. But it's always been a pleasant experience at the venue. There's not a bad seat in the house and it's small enough that you get to see and hear everything from the stage. Beware if you sit in the very front, you KNOW what's going to happen! + +A couple downsides.... + +Waiting outside in a line in the dead of winter. The lobby is so small you're forced to wait outside until the first show starts or the first show let's out. And if you want a good seat, you may be waiting in line for a while. BURR! + +The two drink minimum. I kinda get why they do it, to make money, of course. But this means they jack up the prices of watered down drinks. Better to stick with beer and wine at these places. No frou frou drinks for me! + +Also, as to be expected, the food's not that great. In a perfect foodie world, places that served food would make it fantastic! Since that's not going to happen, you just go into those places hoping for the best. I've never had anything great here. Nacho platter too many re fried beans, to little nacho's....annnnnd I'm out! + +So what did we learn here? Good venue, stick to beer and wine and eat at a better restaurant beforehand. The talent is really what you're there for so, enjoy the show![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've been here twice now, and like the others you really only come to Improve Comedy Club for the show. Very reasonably priced for shows though they have the two item minimum so would suggest they all be drinks. + +The food leaves little to be desired. We decided for the sake of time to grab dinner at the venue since the show started at 7. Having a free appetizer coupon we ordered the spinach and artichoke dip along with the sauteed grilled chicken. Spinach and artichoke dip was good though cheesy rich along with cheese sprinkled on top of the chips. Sauteed grilled chicken - hmmm.... I think the chicken was frozen - definitely not fresh - and the guacamole was artificial with a glop of cheese. It looked like a mess with big ole pile of fries. A lot of food for $10. Service has always been pleasant though they do automatically tack on the tip for you at 18%.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> There's nothing like a Saturday night filled with some good laughs, a few chuckles and a couple of good guffaws thrown in for good measure. That's exactly what we enjoyed on Saturday night! + +We hit the comedy club for an evening of Tammy Pescatelli - the hubby and I have enjoyed her routine on TV and on the occasional DVE morning show.. She didn't fail to give us a good evening of laughs! The big surprise, was Gene Collier - yep, of the Post-Gazette sports writer fame - as the opener. What a great opening act! He cracked wise about the perils of being 58 and a baby boomer. We could relate! + +The sightlines were lacking. There was a rather large woman at the table in front of us with massive Pittsburgh BIG HAIR. All night long my own head bobbed from side to side as I attempted to actually watch the show, and not just listen to it, as she reached repeatedly and unceasingly for her tableful of snacks. + +With a 2 drink minimum, my first drink was weak and the 2nd was quite strong! All in all, the two balanced each other out. But then, you don't go for the drinks, do you? An enjoyable evening![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Tom Green was appearing here on Jan 22, 2012. He was hilarious. + +The Improv is an excellent comedy club, in past shows I've seen Jim Krenn, Margaret Cho, Billy Elmer, and so many more I forget. Much like Live from the Improv on TV, the brick back drop makes it feel like the NYC Improv. + +Hint: eat elsewhere, the food isn't so great, have an appetizer until you get to another restaurant, most comedians head over to the Rock Bottom after to imbibe. Dave Attell is a regular at both places. Two drink minimum, drink them slow and go elsewhere after the show.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Decent, clean (as far as I could sense in the dim)... about on par for what you'd expect for a higher-end comedy club. That includes the $10/drink, two-drink minimum, automatic 18% gratuity, and the comic spouting out the obligatory, ""don't forget to tip your waitress."" + +Trying to judge the place on its own merits and not on the entertainment value of the comics. (If the latter, since we were here for Frank Caliendo, I'd have given the place the full 5 stars if only for him alone!) + +Total cash bled out of my pocket brought it down from what could have been a 4-star experience for us. $80 for tickets online included $10 ""service fee"" and tax (we had to: this was a sold out show). Add $25 for drinks, gratuity, and more tax. We're talking 3-digits of $$$ for less than 2 hours of entertainment squeezed in between other patrons and glass-wielding servers while you sit on rickety chairs. That's what a headliner act will cost ya! + +Will you see us here again? Probably... but cost makes it unlikely to be a weekly thing for us.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My friends & I all purchased Groupons for the Pittsburgh Improv on or around March 22nd, 2012. At that time, only a few big name comedians were listed on the Improv's website as Special Events. You can use the Groupon on anything that isn't a Special Event. That seemd reasonable. The day the Groupons were purchased, my friend Katrina called & reserved two tickets to Jim Jeffries for 3/30 at 10pm. They allowed her to use her Groupon & gave her a confirmation code & everything! Shortly after, they changed many of the comedians on their website, including Jim Jeffries, to Special Events. When I called I was told I could not use my Groupon. The same thing happened to many of my friends. It's a classic bait & switch. These comedians were NOT Special Events until after the Groupon came out. In addition, other restrictions, such not being able to use the Groupons on Saturdays & having to use the additional four vouchers for one show, were NOT listed under the restrictions when the Groupon was for sale. + +So tonight, my friends & I had pretty much resolved ourselves to the fact that we were not going to the Improv because they wouldn't allow us to use our Groupons. But I walked over to the Will Call window with my friend Katrina so she could at least get her tickets. Big surprise - she was told they didn't have her reservation or her name in their computers! They wouldn't give her the tickets. It's an absolute joke of a deal. How is everyone going to use their Groupons by Sept. if all of the shows are Special Events now? + +In addition, no one at the Improv answers the phones or responds to emails. + +My friends & I (about 10 of us total) are all getting refunds through Groupon and/or our credit card companies & we are all reporting the Improv to the Better Business Bureau, etc. + +The Pittsburgh Improv is extremely shady & does not care about their customers.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> You know that place where you've never gone, then you go, then you're going all the time? Well the Improv for me is one of these places. + +I am thankful to have a venue to see some of my favorite comedians. Most recently I saw Hannibal Burris, Tommy Johnigan and Doug Benson. All three performances were a hooting good time. + +On Saturday afternoon at 2:20pm I went to see Doug Benson I was accompanied by my boyfriend. You may know Doug Benson from the hit documentary ""Super High Me."" + +Ok so: +PROS +Wonderfully talented comedians +Clean bathrooms +Pretty wait staff +has Coors Light on tap ( 5.75 per draft) +Every seat in the house is a good seat + +Cons: +Expensive drinks +Expensive food +Flavorless food +Dirty silverware +Far from my house +Mayo with french fries + +Any way, I have enjoyed all my visits to the Waterfront. I can certainly see myself seeing more shows at the Improve. The club is well maintained and the wait staff is friendly. + +Bring a lot of money with you, you're going to need it. I don't know if it's true everywhere but at this Improve there is are 2 item person, minimum order requirement. + +They served us warm Mayo with our fries, what is this Holland!!! That sh*t was gross. It was both gross and also unusual. + +Anyhow to catch a comedy show at the Improve is a pleasure.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The place does what it does best - Comedy. The food, however. Blah. + +First off, If you go to a show, please note there is a two item per person minimum. This means that from their extensive menu of overpriced bar food and drinks, you are REQUIRED to choose two items each. + +Second, the sodas are NOT FREE REFILLS! I learned that one the hard way. Get water. + +Third, before tipping your server, please make sure she hasn't already taken her cut out. Even after paying for two very bland, overpriced meals and way too many Diet Cokes, I thought that my bill was rather high. Upon further inspection, I noticed that my server had taken an 18% gratuity. The menu explicitly says that an automatic gratuity will be taken out for parties of six or more, but there was only two of us and we weren't even drunk. I found this tactic awfully presumptuous and left her tip at the 18% even though I typically tip well over 20%. + +Overall, I don't like the idea of being required to purchase food just to see a comedy show. I can see why they do it, but if I were required to buy a crappy popcorn and overpriced pop every time I went to the movies, I would be far less inclined to go as I am not inclined to go to the Improv again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The Pittsburgh Improv is unfortunately another great idea hamstrung by the details of mediocre execution (some specific examples at the end). + +The setup is nice, a delightful--if a bit sterile--reproduction of what you'd think a comedy club should like if you watch enough TV. The interior is clean; the seats are comfortable; and it's an OK atmosphere to see a show and laugh. + +It's too small, however, to attract many of the best acts, which limits its ability to ever become the central hub for Pittsburgh comedy. Most of the big names that have recently come through Pittsburgh--Jim Gaffigan, Louis CK, Second City--all perform elsewhere (though they managed to get Bob Saget, to their credit). + +But the biggest problem is the food and drink. They're very up front about their mandatory two item minimum, but the forced service requires that you spend extra money and get interrupted by waitstaff at least several times during the show. The prices are well above what I'd consider reasonable given the quality, and I'd begrudgingly--or even happily--just shrug off the cost the same way I would a stadium concession stand markup...but the food is bad. You're forced to either (a) buy extremely overpriced drinks (3.50 for a soda, for example, with no refills--or ten dollars for one with refills), or (b) buy moderately overpriced food which you wouldn't want in the first place. I thought the ten dollar chicken sandwich looked reasonable, until a few bites in I decided I'd rather just throw away the money than keep eating it. + +Still, I think this place has a lot of potential; the core idea is very workable; and they do attract some really good comedians. Two stars for now, with high hopes for improvements. + +A few specific drawbacks which could be VERY easily fixed: +1 - A lot of the drinks didn't have prices on them. I know this isn't uncommon, but at a venue where every question you ask interrupts not only your own show-viewing experience as well as the experiences of your neighbors, it's an incredibly poor decision here. Make everything on the menu exceptionally clear. It's not that hard. +2 - Put the drink prices on the website too. An Improv representative has personally responded to many of these Yelp reviews, and she once said ""Our menus and pricing are listed on our website, which makes for easy planning!"" I'm calling shenanigans. Not all the prices are on the website, which makes for difficult planning. +3 - Reminding me to tip my server during the show AND adding an automatic gratuity to the check makes me feel like you're trying to trick me. It's kind of an unprofessional way to say goodbye to one's customers. +4 - Since the $3.50 soft drinks don't come with free refills, the servers shouldn't ask ""would you like a refill on that?"" or anything of the sort. They should ask ""would you like another one?"" instead. They should also respond to requests for refills by saying ""we don't offer refills, but I'd be happy to get you another one."" Just because there's a 10 dollar refillable soda option on the menu doesn't mean people all figure it out. Most patrons don't even bother reading the beverage section of the menu if all they want is a standard beverage offered almost everywhere (like a cola or diet cola), and the reading difficulties imposed by the darkness make them even less likely to browse the offerings.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love the Improv. I think its a great way to start or spend a night! Nothing like a laughter filled night. I think its great that we get so many great comedians coming our way (Owen Benjamin, Pablo Francisco super funny Tammy Pescatelli not so much.) + +Things you should be aware of: The staff is really strict on the 2 drink minimum so be prepared to spend money on the pricey food and drinks. I kinda wish their menu was a little bit more extensive. Their service is spotty + +The wait staff is a little iffy. I have been here MANY times and sometimes I get an attentive waitress and sometimes not. Most recently our waitress was rude, didn't bother with pleasantries and barely took notice of us. Also beware of the fact they automatically add gratuity. If our waitress was nice I would be more than glad to add to it but this time I was like no way! + +p.s. when I used my groupon I didn't have any trouble[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My husband and I went to do something fun. The comedy was great! The food, however, is mediocre at best. In addition, we were seated in the last row, and 10 minutes into the headliner they sat someone else at our table, so that they were in front of us. I could not see a thing. When we received our check, they had added an 18% gratuity without permission or notification. I will not be returning anytime soon.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Who doesn't love to laugh? The improv is a great place to go for a good show a few times a year. The venue is clean. The comedians are good, for the price, and many times you get a steal and can see a great comedian for a low price (i.e.Tommy Johnagin). However, be advised, if you attend more than one show every couple of months, you will see some of the same opening acts repeated. This is my biggest gripe with the Improv. I've been to the Improv about 3 times over the past 4 months and have seen the same opening acts a few times. I think they cycle through the same 4-5 comedians. Are there not more talented comedians in Pittsburgh? As noted in other reviews, another area of improvement is the drinks and food. I always attend the late showing so that I can eat elsewhere. The food is mediocre bar food at best. Nothing more needs to be said about that. I definitely don't mind the two drink minimum. I've been known to consume more than two drinks in one setting but, the drinks are insanely overpriced. $5 for a Miller Lite, $4 for a Snapple, $10 for a fountain drink with refills. You're better off having your two drinks during the show and going over the Sing Sing after for a draft . . or four. In addition, since they started offering a large Groupon discount, the Improv has been packed. Be aware that if you only have two people in your party, they may seat strangers at your table who are 6 feet tall and block your view.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We came to the Improv for the first time on Friday night for my wife's work holiday party. We arrived early for dinner and drinks from a predetermined menu. Dinner started with a salad of clearly bagged, almost brown iceberg lettuce, with some croutons and frozen-then-thawed looking tomatoes that were pinkish at best. I took a few bites of this unappetizing poor excuse for a salad, and I can tell you it was downright tragic. Dinner arrived and since there wasn't any vegetarian options on this predetermined menu, we received a dish that was supposed to contain meat with the meat omitted. It was a huge pile of spaghetti in a bowl. It looked sloppy and tasted worse than it looked. The pasta was overcooked, and the tomato sauce was just watered down puréed canned tomatoes. I saw traces of onion in my dish but didn't taste them at all. I was so hungry that I salted the heck out of this abomination and took a few bites. Yuck. I didn't make a dent in this crapfest. For dessert we were given a choice of chocolate cake, which my wife ordered, and cheesecake, which I ordered. The chocolate cake had freezer burn. Inexcusable! It wasn't edible. The cheesecake was only a hair better, but it had obviously come out of the freezer as well. I know people aren't coming here for the food, but if you are FORCING them to order things off of your menu to fulfill some outdated requirements (two drink/two menu item minimum) then at least make some halfway decent food. It doesn't even have to be memorable...just not OFFENSIVE. Which it was!! Had I paid for any of this I would have made a huge stink, but I tried to be polite and push my food around and make small talk. + +The comedians were good. The venue was nice-ish and we got to sit in the front because we arrived early for our ""event"". Not always the best thing in a comedy club (we only got picked on a little bit). But damn, I was hungry! I found myself fantasizing about all of the crappy Waterfront restaurants and how I'd rather be there...how I'd rather be heating up a discount microwave dinner...how I'd rather have a giant bowl of Captain Crunch...how I'd rather go back in time and eat spaghetti from my high school cafeteria...what a dreadful dining experience. + +My car was also violated in the parking lot. I had an adorable German license plate on the front of my adorable German car which was stolen while I was eating hideous food, which was just the slap in the face I wanted when finally retreating to my car. I feel sick in so many different ways about this experience as a whole. + +The Improv should consider outsourcing the food prep to a catering company. I truly believe that's the only thing that can save this place. Do yourself a favor and eat beforehand, and just order a beer. Well, two I guess. Other diners at our table complained about the quality of the cocktails so I'd steer clear of those. Unless there is a can't miss type of comedian here, I can't ever picture going back to the Improv. I'd give the comedians 4 stars, and the food ZERO stars.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Spent New Years Eve at the Comedy Club to bring the new year. + + +I am new but it was a good time. We had unlimited champagne, fruit and cheese. The comedy was good. + +The service was great. + +The atmposhere was okay but it was a comedy clud :-). + +You should check it out - Comedy clubs bring a little spice to the city :-) + +Enjoy![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This was my second visit to the club and it was still a blast. My girlfriends bought tickets for John Witherspoon for my bachelorette. We were all looking forward to it and it was hilarious! He was wonderful. + +The servers were fantastic. They always came back to check in on us and make sure we had plenty to eat and drink. I suggest the Pink Cadillac for a drink as well as the cheese cake and chocolate cake for dessert. + +The only reason it isn't 5 stars is because they had us wait an hour past the time we were to enter the building. We were to see the 9pm showing so the doors were to open at 8:45pm. They came out and explained that the show had run over and we wouldn't be able to even enter the building until 9:20pm. It was 28 degrees outside. We finally were able to enter the building, order drinks then the show finally started at 9:45pm. The host did offer a blanket apology which was nice but hardly made up for the fact the show started almost an hour late.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have been here twice in the last month. It's a pretty great time. My first visit, the service was pretty poor and the food was cold by the time it got to the table. We had to sit all the way in the back and the comedian was not that good (although that is no fault of the club). But when I went to the second show, the service was much improved. The burger I ordered was fantastic and warm. Our waitress kept the drinks coming without interrupting us while the comedian was on stage. We were also able to sit in the front this time and it was a great experience. I'll be going back soon![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Good! I can't comment on the food or the bathrooms, but from what experienced it was great! The drinks were decent, and I believe you must order two items at minimum. The staff is quick, but they should have more people working on a Saturday night. Before you can ask for anything else they bolt to the next table or to the kitchen. + +The comics we saw were funny as well. Will definitely go back![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love that we have a great comedy club in Pittsburgh with a great location at the Waterfront. Perfect for a date night and I recommend going to a later show and grabbing dinner beforehand. I received an online coupon code for $5 tickets for John Heffron. What a deal-def. check for deals before you pay full price for any shows here. We went early to pick up the tickets at the ticket office. People were lined up outside about an hour before the show and it was freezing out. I had no interest in doing this so we grabbed a beer across the street at Rock Bottom. Once they opened the doors (15 minutes before show time) the line went quickly and even though we were at the end we still got seated at a table in the back. It is not huge inside so there aren't really any bad seats. They usually have an MC for the night who starts warming up the crowd. This guy was funny and so was the opening act before John Heffron. My only complaint about this place is that they have a two drink minimum and the prices are outrageous. $9.50 for a mixed well drink and $7 for draft beers. The soda was $3.50! Yikes! At least we didn't pay full price for the tickets.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I was so excited when my husband gave me tickets to go here to see funny man Bill Crawford, part of the DVE morning show for those of you who never heard of him. That is funny because as I was telling people about going it became clear there are A LOT of people that haven't... Oh Well... Let me mention this was my first time there. + +So I was warned in advance of the possible long waits outside and the two item minimum. Well to my pleasant surprise there was no wait, walked right in, greeted, an usher showed us to our seats and we waited less than 5 minutes to be asked for our order. This was nice. I will say that the show started at 8pm, and we were there by 7:20 or so. There were already people seated so we were by no means very early, and heck there were people with full course meals and tables of 10. The price of the mixed drinks were not disclosed on the menu, leading me to believe that it may leave me short for the mortgage next month, but they did have a 60 minute dogfish head IPA for $6.00. Now that may seem rather expensive and it is, but doable so I indeed did it... My husband got a domestic and it was between 4-5 bucks. We opted not to eat there, as we were going to Rock Bottom after wards and I will get to that review later... + +So the show was good. There were moments that I think the comedians may have went off track and were just bantering, but luckily enough they rebound and got back to making everyone laugh instead of being uncomfortable. There were a total of 4 comedians, the MC, and two opening acts for Crawford. I actually really enjoyed them. + +The one or two things I didn't like about the place. The bathrooms are in the lobby. As this seems normal there is no separate area to enter back into the room without having to make your way through people who are waiting to be seated... This was/is stupid. I was actually nervous that they were going to stop me and ask for my ticket which they safely secured at my first entrance. The same also goes for smoking. Since we were so early I took a break and it was again awkward reentering. Maybe they need to have some type of system to get around this. A stamped hand? A ticket stub? Not sure but I know I would have felt better unlike feeling like I was sneaking into the place. + +I would definitely return to the Improv. I just hope I always have a rather positive experience![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It isn't often that my wife and I get to go out, but we had tickets to see the WONDERFUL Lisa Landry and figured since we were going to the Improv, we may as well eat there too. I should have gotten on here and read the reviews before making that decision. We had what seems to be a typical experience at the improv. We were handed a paper menu with 4 items on it when we walked in the door. There was no other menu at the table and our waitress didn't offer us one either. She wanted our order, but as we were looking around the place, we realized that most of those around us were eating items that not on the menu provided to us. When asked about another menu, our waitress told us if we give her our drink order, she'll see what she can do. The table next to us handed over their menus so we had something to work with. Our drinks came, we finally put our orders in...and that was the last time we saw our waitress for almost a full 30 minutes. When she finally came back, all she wanted was to know if we wanted a 2nd round of drinks. After 30 minutes I was finally going to get a second beer! ""What about our food?"", we asked. ""Oh"", was her answer. Now, according to the menu, dinner came with a side salad, a complimentary glass of champagne, and a chocolate mousse dessert. That's all good and fine. After a couple of minutes, someone, not our waitress, finally brought out our meals. When we asked him about our salads, his reply was ""do you want me to take your food back?"". Really?!?! ""Do you want me to take your food back?"" After almost 45 minutes at this point, we had received 1 round of drinks and had seen our waitress only twice and had just received our food. No, I don't want you to take our food back! Halfway through eating our meals, which were by this time cold, our waitress finally came back with our second beers. She asked us how everything was. We asked about our salads. She said she was told we didn't want them. REALLY?!?! Is this a joke? Is it somehow part of the comedy routine that was going on? Sadly, no. The service didn't get any better. The food was lousy. Thankfully the standup was great. Lisa, Lisa and Matt all put on a hilarious show. Will I ever go back? Don't know. It took us an hour and a half to drive the 16 miles to get there, thanks to traffic. I do know that if we do it again, we will leave the house much earlier and eat somewhere else. The two drink minimum works at the improv because you will not get your waitress to your table more than that to order more drinks. In case you're interested, I am a chef who has been in the service industry for more than 30 years and worked every position possible in restaurants and bars. So, yes, I do have a preconceived notion as to how service and food should be. Even on Valentine's Day.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My husband and I love going to comedy shows and have seen some pretty good acts at the Improv. Ticket prices aren't bad either. I am very particular about where I sit, and the person who seats you is willing to let you sit where you choose, especially if it's on a Thursday or Sunday night, since those aren't particularly busy nights. + +I did have one bad experience, which is why I'm giving this review 3 stars instead of 4 (it only takes one poor experience, people!). My husband and I went to see one of our favorite comedians on a Thursday night. There is a two-item minimum, so we decided we would just eat dinner at the show. Well, we were mistaken. First of all, our waitress was rude and slow. After sitting there for 5 or 6 minutes without service she finally comes over and asks what we want. We both order a drink and food, to which she tells us that the kitchen caught on fire earlier that day so all they have are salads and desserts. I was annoyed that she even asked what we wanted instead of starting out with this important fact. + +At any rate, I order a Caesar salad and a beer. It comes out and it's iceburg lettuce with shredded cheese, tomatoes, and other veggies. In other words, a regular salad. I inform the waitress of this and she seemed totally confused. I suppose she did not understand the difference, which was odd. + +Overall, I felt that there was no apology for the fact we couldn't eat, let alone everyone else in the place. Salad or dessert aren't the greatest choices when you are expecting to eat dinner at the show. I think the Improv should have waived the two-item minimum on this occasions, even if it cost them money. + +Afterwards, I emailed the Improv with my concerns. Never. Heard. Back. + +That being said, I will most likely return to the Improv....but not for the service. Because it's a great place to see comedy shows and isn't that expensive. Customer service is terrible.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I went here for the first time the other night and had a great time! The comedian was hilarious and it was a great intimate setting for a fun night out with friends! My only complaint was that it was a little pricey for the overall experience because not only do you need to buy a ticket, but every person needs to buy 2 items of food/drink and the drinks aren't cheap (around $10-12). However, I would definitely go back sometime![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Wast there last Friday. Seats right in front if the stage. The show was good. The headliner, while a bit long, was good. Fantastic service from our waitresses. Will definitely go back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> If The Improv chain didn't bring in such amazing comedians, this place would be totally screwed. + +I always have fun watching the comedians, but I can't help but leave with such a bitter taste in my mouth from how much of a rip off this place is. + +First you buy the tickets, but if you buy online you have an outrageous service charge. The real kicker is having to buy a minimum of 2 items during the show, beers are $5 or $6 and the cheapest things on the menu, I believe. Cocktails are $11-$13. I think glasses of wine are around $8. There is a pretty good selection of food options. + +The improv does have a lot of great comedians who pass through! Even the opening acts are generally great! Line up early if you want a great seat right in the front! + +The point is, a night at the Improv will be fun, but if you aren't prepared for it, it can end up being a pretty unexpectedly and unreasonably expensive affair.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great night out. I don't know if Christopher Titus set the ticket price or the club did, but at $25 a ticket, we will be going back often. Great line up of top name acts coming to town. extremely nice staff. highly recommend.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Absolutely loved it at the Improv! I saw Sheryl Underwood and she was fantastic. It was my first time being at the Improv. After years of saying that I wanted to go, it really did meet my expectations! The ambiance is inviting, with warm lighting and a good amount of seating for a smaller place. We were 8th in line so we had good choice of seating, though we were encouraged to fill the seats in the front by the stage first. The seating is layered in tiers. Each tier has a long booth with tables and chairs for seating. It was very comfortable, roomy and an interactive set up. The stage is close to the seating (some tables are right at the stage) with little space between you and the comedian, which made it very interactive and fun. We arrived at the Improv around 9:45 pm for a show that started at 10:30 pm, with doors opening at 10:00 pm. We waited in line until the doors opened at about 10:15-10:20 pm, so they were really behind schedule. The show started around 10:45 pm with two opening comedians before the main act. The show was over around 1:00 am. The only negatives were that the staff was not very friendly and immediately told me that I have to buy a minimum of two items off of the menu. ($30/ticket isn't enough?) I was not hungry and did not want to drink, so this was a bit frustrating, especially because it wasn't disclosed on the ticket or anywhere else. The server did not hold us to the 2 minimum purchase requirement and my friend and I got away getting 3 drinks for the night. The food menu looked great and the prices seemed reasonable, though if you want water you are looking at $5 for Fiji or sparkling. It was $8 for a glass of wine. $11 for bottomless soda, complete with a take home Improv glass. The other thing that I didn't like was that an employee takes your tickets while you're waiting in line and marks your hands with a dry erase marker. After one bathroom trip, the mark was gone, so I think they need a more effective way to mark you as an already paid customer since the employee takes your proof of purchase. These negatives did not affect my overall experience negatively and I would most certainly go back! It is a fun place where you are guaranteed to have a good time with a lot of laughter![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> So...we got here and seated by 635pm. Orders placed. Drinks served. Now it is 752pm. One of my party has still not received his chicken sandwich. I had +My shrimp diablo. It was as described. Spicy and good!!! But hour plus for a chicken sandwich is unacceptable. We also sent an order of chicken fingers back...dryer than sand. And my fiancés chicken Caesar salad chicken was as dry as the chicken fingers. Barely edible, in fact, she didn't eat more than 3 pieces of it. Upgrade the food service and this place would be somewhat a lil better.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The Waterfront at Homestead is insane, and saves me the trip of driving all the way to Ross Park Mall. Anyway, the Giant Eagle here is enormous, as you'd imagine. It's still a standard Giant Eagle, aka the best grocery store ever.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is the best Giant Eagle in the area and is the most like grocery stores in Bay Area. Here's why: + +1. They sell beer! +2. Huuuuuge produce selection +3. Natural/organic foods section: cereal, pasta, soups, etc and fancy chocolate bars +4. Long isle of ethnic foods includes mexican, indian, italian, asian and , of course, jewish +5. Functioning bakery with fresh, appetizing breads and desserts (I am still loyal to Allegro Hearth though) + +The store is huge and I haven't been to all of it yet but they also have nicer flowers, balloons, home/seasonal section, DVD rentals and a photo center as well as a drive-through pharmacy. + +It seems as this GE just might be the answer to my grocery stores woes.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Probably the most comprehensive supermarket in the county, if not all of southwestern PA. Its selection is considerably larger than what you can find in most Giant Eagles, and it has more upscale items. I live an easy walk from the Swissvale Giant Eagle, but I often drive to this location for the superior selection.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Nice Giant Eagle, not as nice as their new Market Districts, but you can look at this Giant Eagle and see how they came up with the Market District Idea and rolled with it. Fresh made sushi, good cheese selection, awesome bakery.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Wahhhhh!!!! They're remodeling this one and it's frustrating! I swear I don't mind change. I really don't~ I should have seen this coming. There were telltale signs of this happening. First, they switched the pharmacy to the other end of the store where the now defunct Iggle video was. That's A-ok with me, I didn't use the pharmacy anyway. + +But THEN, THEN they moved the whole toiletries section over there. They put my spaghetti and ""ethnic food"" section (by the way, I love that ethnic food includes spaghetti) to where my Tylenol was. My kitty food is now where my spaghetti once was. Can you tell how exasperated I'm getting?? + +Did I mention I don't mind change? But here's the thing, I really hate grocery shopping. It's kinda sorta my own fault because I must read every label to make sure I'm not eating something with 25 grams of fat and 5000 calories (even though ice cream may go into my cart from time to time.) So going to this Giant Eagle frequently was nice because I KNEW WERE EVERYTHING WAS. Now I don't....wahhh! + +Ok, I'll stop crying. I know I'll eventually be back. I'm sure (??) it will be an even better more magical grocery shopping experience once they're done. But I can't take it for right now. I'll be forced to shop at the Ghetto Bird down in the Southside until my former #1 store is all shiny and new again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I like this Giant Eagle. +They have the organic section and they're currently(Feb 2011) in the process of remodeling too, which is both annoying (now) and exciting (for the future). + +PROS: +Always seems to be decent parking available; +They have those cute little double-tier carts; +Organics section; +Wine Vending Machine (that's freaking awesome--Yay, Pennsylvania!); +Lots of Self-Check-Out lanes; + +CONS: +Sometimes the staff is a bit cranky (but that can occur anywhere, i guess);[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> As far as GE's go, this location is great. It has basically everything you need and is well organized. You can find a lot of ethnic ingredients you can't get at other GE stores. They also offer a wine kiosk, hot bar, salad bar, and bulk olives. I would venture to say this is better than the market district.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Waterfront Geagle is my primary market. Now that they've expanded and reorganized, I rarely even have to set foot in Target anymore. Yippie! There's a wine kiosk (suck it PA liquor laws), you can buy crazy expensive 6 packs, cheese market, bakery, salad and hot bar, butcher, florist, dry cleaners, international foods, pharmacy, and a little cosmetics/beauty/bath area. They usually have a sufficient number of lanes open, and it doesn't get nearly as crowded as Market District. I do wish a bulk spice selection was included as part of the expansion, but you can't always get what you want, I suppose.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> You're getting an extra star for two solid reasons. + +One is because the remodel is over and the store is pretty again (and a bit fancier). Two, and thee most important part, this iggle has the best quality and well made sushi out of any Iggle's out there! Believe me, I've eaten many a rainbow roll from many different locations around the Burgh and nothing has compared. Dare I say, it's as close as you get to going to a good sushi restaurant. Bold statement, right? + +I just love me some sushi and want it often, quick and convenient and this serves all those purposes with upholding the quality. Need a quick sushi fix? This place is it![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is easily one of the best Giant Eagles I've ever been to. Huge. Very nice selection. Easily comparable to Whole Foods. Went to their cheese market, and was pleasantly surprised with the selection. I got Beemster Vlaskas, an amazing Gouda. Very large parking lot.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place has amazing selection when it comes to some things and zero selection when it comes to others. We popped in here a couple times over the weekend I spent in PIT and both times they didn't really have what we were looking for. Visit #1: Liquid smoke. Visit #2: Hawaiian rolls. I know these items must exist in PA just not @G-Eagle. + +They did however have crazy selection when it came to things like....corned beef brisket or anything that has potato in it. My californian mind was boggled by the variety of brands and cuts of corned beef that were available. Too bad that wasn't what I was there for.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> oddly enough, of all the giant eagles i have visited in pittsburgh, this is the only location that carries the toothpaste that i've used for most of my life (outside of pittsburgh). the location is clean and the staff are friendly. i sometimes resent having a market district being the closest giant eagle to my apartment, as many of the items that i buy there are severely overpriced. but whenever i run out of groceries and toothpaste at the same time, i take the hike down to waterfront to shop here, although they may not carry all the groceries that i'd like.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is a absolutely beautiful Giant Eagle. I only stopped in to grab a quick bite from the prepared foods section, but I was rather impressed by how clean it was. It was 9 oclock at night, and they still had a huge section of prepared foods available. The Starbucks inside was closed, probably due to the fact it was a Sunday night, but that is another plus![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm with Rachel C. on this one. You get an extra star for being a pretty Giant Eagle and a Cafe with a very decent beer selection of 6packs and individual bottles. Even though the Giant Eagle in Robinson is better in my opinion you, Waterfront Giant Eagle, are not bad and pretty close to where I live.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I drive near this Giant Eagle on my daily commute, so I shop at this location approximately once/week. The location is pretty, and the beer selection is descent. They carry my favorite lambic, so I really can't complain! They also have a very nice health and beauty section. Overall, they usually have the products that I need. + +My only complaint would be wait time to check out. They never have enough cashiers at peak hours. The store has like 20 checkout lanes, but generally only 5-8 open at a time. I always dread checking out, and whenever I see that checkout lines look relatively clear, I hurry around the store and quickly gather the products that I plan to buy.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I found everything I needed and I liked the expansion, the antipasta bar is on point and they sale Vanilla Coke which made my hubby very happy. + +Great store.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This review is specifically for the DFS cleaners at this Giant Eagle location. I dropped clothing off for the sake of convenience once (I really should have known better). Never again. My items came back completely covered in lint. I could let this slide, however my pencil skirt was safety pinned to the hanger. The weight of the skirt caused even larger holes than what were placed there by the pins. Being that it's a pencil skirt designed to have a blouse tucked in, there's no way that I can wear it again. This was an expensive skirt, completely ruined. Very disappointed. Again, this review is just for the dry cleaners. The rest of the store is actually better than a lot of other GE's I've been to in Pittsburgh. Just don't take your dry cleaning here.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've stopped by here a few times (most recently tonight) to pick up random groceries. This store is located next to one of the bike trails that I frequent, hence its convenience despite being fairly far from my apt. + +On the positive side, I appreciate the size of this store and the selection of products. In terms of size, it's larger than the Shadyside Market District (my normal grocery store, hence my standard of comparison), and I'd say the product selection is very similar. Unlike the MD, when I've visited, the aisles have seemed fairly empty of customers, which may be due to the times of my visits (usually between 7-8pm), as well as the size of the store. Because it's not a Market District, the prices are a bit less expensive, which is nice. + +On the negative side, the checkout always seems to take forever due to slow customers and/or employees, despite that I've only purchased a couple of items at a time. The ""express"" lanes move at the speed of molasses, and the self-checkouts are even worse. Speaking of which, this store has *way* too many self-checkout lanes (about a third of the lanes), and the non-express ones with the belts are unintuitive. + +Prior to tonight, I would have awarded this store a rating of 4 or perhaps even 4.5. However, checkout tonight was even more of a PITA than it usually is. None of the normal express checkout lanes were staffed with cashiers, despite that I saw at least one employee loafing around talking to another. So, I was forced to use one of the many self-checkout lanes. Normally, I don't mind this, esp. when I'm only purchasing a couple of items, but the empty self-checkout lane that I spotted was one with a conveyor belt, and I couldn't figure out how to use it (not that it mattered, since I had only one item, but the self-checkout lanes must be operated using a very specific procedure--see below). So, I moved over to one of the express self checkout lanes (similar to those in the Shadyside MD), which I knew how to operate. However, I still managed to bungle the process since I forgot to scan my one item *before* I put it on the scale that doubles as a bagging station, so I had to wait for one of the ever-so-slow employees to come over and key in an authorization code so I could pay. + +I'm not sure if the self-checkout stands that GE uses are standard in the industry, since I've never used them anywhere else, but I *hate* the whole weighing/bagging process. In order to use the self-checkout stations, each item must be scanned and then placed on the scale, and if the weight isn't correct for any reason (including using your own bag), an employee is summoned to check it. I assume the intention is to prevent people from shoplifting, but (1) it's a major PITA for both customers and employees; (2) most of the employees (including the one I dealt with tonight) don't care, and just key the code without even looking at the error message explaining why they were summoned; and (3) I doubt most shoplifters pay for any of the items they're pilfering--they most likely just stuff them into their purse, clothes, etc. and walk out! /rant + +3.5 stars.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Just about every you need. + +With great hours, a solid hot bar, sushi (if you're into that), a dry cleaning service, pharmacy, tons of produce, bakery and butchers counter you can't go wrong. Two things that drive me crazy always needing to use my perks card for self check out and the lack of hand carts in the front. I always have to walk to a lane and hunt for a basket then double back, super annoying. + +That said its a small, and easily repairable (hint) issue that shouldn't keep you from visiting.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I don't know why, but I just can't like this location very much. I lived in the area for a little over three years and would always go to another GE before this one. Maybe it's the way it's set up or maybe it's the way that the lighting seems so very dim. + +The selection is typical for any GE, broad and expansive. Some prices are a bit steep. + +This location, like many others, has expanded their pharmacy/health care area. Which is nice, it saves an extra trip to a drug store.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> One comfy seat in the entire place, but they have a cafe, they have good books to look at, and they are open until 11pm. What more could you want? Why an APPLE PURSE of course! And a nice Earl Gray tea thrown in for good measure. Wow...I love this place. I am such a nerd...only a nerd would enjoy going to a book store and reading as much as I do. The extra amenities just make it that much more enjoyable.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Like any Barnes & Noble, it has a nice comfy cafe, and a large selection of books. The staff is very friendly and helpful. They stock a decent selection, and the prices are pretty reasonable. Obviously it's hard for them to compete with Amazon. However since all the small shop bookstores are gone, it's nice to walk into one every once in a while.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I still cannot believe that Pittsburgh has no independent bookstores! As a result of this I have ended up spending a fair bit of time at this Barnes and Noble location. As with all Barnes and Noble stores it has a cafe and a decent selection of popular titles. I am a bit surprised at how smallish it is compared to other stores in this chain. + +The bargain section seems to be perpetually picked through. The selection is ok in that it is well stocked but sometimes a bit disorganized from other customers pawing through the books, less popular titles are a bit hard to find. The customer service here is pretty good. + +They could use more chairs.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great Barnes and Noble location, and they have plenty of books that'll help you pass the time.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Barnes & Noble, it's like the Wal-Mart of bookstores. Beating down the competition of other now defunct national competitors and mom and pop type stores alike. + +I'm not quite sure whether I'm in a cafe, at a newspaper stand, a book store, a CD shop, a movie house or a flea market sometimes. With all the tables and shelves that you have to dodge it's a bit hard to figure it out. Feels like the place should implode on itself and then reform into an audio book about coffee. + +I don't know about y'all, but I'd rather buy my books from a place that has more knowledge about the merchandise they are selling than a national chain like this.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Such nice staff. + +I really lament the decline of the modern bookstore. I really enjoy browsing and picking up a new book. + +The store has a great selection and the staff are always helpful and kind. + +I really hope this store stays here for some. The prices are also fair and often have great discounts.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I find this location, clean and well organized, but that's not the reason it's getting 5 stars! + +I called today to look into whether or not their May issues of magazines were out (I need them for my job) and Erin so kindly went checked on every single magazine I asked about! + +Now that is customer service! + +Well done, well done![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have to agree with Matthew U on this one. I do enjoy Barnes & Nobles but sometimes i get lost just trying to find a darn calendar. I went here after a dinner date with some neighbors and couldn't believe how packed it was. We had to wait 10 minutes just to find enough chairs to seat 4 people. We ended up stealing them from other tables. Not to mention my hubby stood in line for 15 minutes just to get an Ice tea lemonade. + +So amidst all the books, newspapers and magazines they have an audio and video section. The prices aren't anything to rave about. I can buy the same movies online for a lot cheaper there's just the waiting period. I do shop here sometimes for there discount books. I found a lot of great recipe and mystery books for really cheap, like under $5. That's a pretty good deal but considering there is a half priced book store who has a great selection of books for literally half the price of retailers, how can you beat those prices. + +B&N is more of a hangout spot with books in case you want to buy one right there and then. But everything is kind of confusing you always need to ask where something is. I'd rather shop online for anything i really want. It's just not worth it to buy it wholesale.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This bookstore is absolutely packed full of stuff! They have lots of books, a display of Nooks, DVDs and CDs, miscellaneous items like notebooks and calendars, and a cafe. Though a large assortment is nice, I feel like the space is very cramped. I have purchased a couple books from here - which were pretty easy to find - and have purchased food items from the cafe. + +The cafe is not very impressive. I've been pretty underwhelmed by all the food items that I've purchased here. I got a slice of quiche here last night when I only had 10 minutes before a hair appointment at Ulta across the street. Not only did they take 5 minutes to microwave it, but it also came out smelling burnt and burning hot. + +A little band was singing and playing a variety of instruments while I was here. I wasn't very impressed until I realized that they were high school kids. I thought it as really nice that Barnes & Noble would let them perform in the store... and a great way for B&N to get a lot of their family members in the store, too.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Are B&N not allowed to have lounge areas anymore? I used to love studying and doing work in their comfy chairs and sit there allllll day... but I feel like within the last 4 years or so, I haven't been in a single B&N that had such areas anymore. I love books and have always felt that B&N can give you a good deal. But I'm not a fan of this particular location because it's not that big. Although, it is pretty clean! + +The Starbucks area they have is okay. The starbucks employees in these types of locations are always not the best..but I don't go there for the coffee obviously. I do find it annoying that they don't take Starbucks giftcards though - I believe they take B&N giftcards and you can also apply your B&N membership discount. + +Also, their bathrooms are pretty atrocious. If you can hold it, I would advise you to hold it. + +Parking: the location is within a shopping area..so I wouldn't say it has it's own private lot per se, but it's an open lot and not actual 'street parking.'[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> one of my favorite places to go in pittsburgh with friends. good place to chill, eat, drink and watch the game, and maybe some pool afterwards. the food is not bad, they have pretty good deals for those who are on a budget. ""dollar burger night"" where you build your own burger is fun, but the patties can be dry sometimes, so remember to get them sauced. iceberg wedge salad is a good salad to have, the wings arent as good as you would like, i had tried the spicy killer ones and didnt even have to drink water. but overall its a nice place to go because it's cleaner than most bars you will go and it serves better food than other places as well.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Nice venue, good food, great beer, awful service. Staying at the Sheraton here I've patronized Bar Louie a dozen times recently and they screw up the order in some fashion every single time, without exception.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I stopped here yesterday with Rob and Matt after golf to have a few drinks prior to seeing ""The Hangover"" at Loews across the street. Incidentally, ""The Hangover"" is one of the funniest movies I've seen in years and worth the $10 to see it in the theater. Okay, back to the restaurant the space itself is very nice. There are plenty of hightops, plasmas and a few booths. It's spacious and they have outdoor seating and open windows. We sat at the bar and were greeted relatively quickly by the bartender who was tending a pretty much empty bar. I ordered a guinness as usual, Rob ordered a long island iced tea and Matt had a miller light. Make sure and tell them if you want a top shelf tea else you'll be getting the stuff in the plastic bottles. I sampled Rob's long island tea and it was not that good way too much sours. The next one he ordered was much better after a little guidance to the bartender. The bartender herself was okay, not too friendly but quick enough with the pours. I don't remember her name which is usually not a good sign. We ordered a few things from the appetizer menu. We started with the chips and salsa. The chips were crisp enough, but not served warm and the salsa had some spice but the colors were a little off kind of looked like the color of pea soup. Rob then ordered the philly cheese steak sliders. I tried one it was okay I guess the bun was warm and it was pretty loaded with cheese and onions. He asked for a side of mayo and they said they were out, which is bizarre because there is a giant eagle a couple blocks away. This pretty much sums up my experiences at the Bar Louie's I've been too. They kind of do just enough for me to come back but rarely make any real effort with service. Maybe I'm being too critical... I tried to order the baked goat cheese, but they were out... So, I settled on the hummus appetizer. This was surprisingly pretty good. The pita was warm and toasted the hummus had lots of flavor and the tabouleh was edible. It's probably best to stick to simple stuff when dining here. Matt had the hot wings which I tried one and it was okay, your pretty standard mass produced chicken wing. All in all this place isn't that bad. If you want to grab a drink before or after the movie and you're more concerned with convenience than necessarily friendly service and really good food than you could do worse.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Fantastic food. + This place is mainly a ""bar"" and does get crowded but I really like the pizza here. In fact I've never had a bad meal. The staff are ussually very helpful but it does get a bit loud inside when crowded.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Don't even think about not getting the pretzel dippers its pretzel sticks with honey mustard, cinnamon butter, and a spicy queso dip. The queso is my favorite but they were all delish. I also got the bruschetta which was very garlicky but delicious. 5-7 M-F is 1/2 off appetizers so I was able to get both the pretzel sticks and bruschetta for 7 bucks as a meal. The menu had a pretty wide range- my friend very much enjoyed a pear and chicken salad. We didn't get drinks but some looked good...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> An absolute must if you're going to a movie and want a drink ($3 drafts and $5 special martinis) and some half-off apps on a weekday from 5 to 7. However, we were bothered that none of the special martinis actually resembled a real martini. No gin or vermouth was used, it's mostly purees and champagne floats with flavored vodkas. + +Anyway, the small plates made for good ""upscale"" bar food. Half-price apps make for a cheap, but nice, dinner and a movie - great, great specials. However, I would not buy a full-priced dinner here. Nothing aside from the apps grabbed me for the outstanding price. The baked goat cheese was small but delicious, and the tempura fried shrimp was just right but the sauces didn't match up exactly. + +Be warned that the seats make you feel like you're going to be swallowed by them. Seriously, the booth was like sitting in the mouth of a whale.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The Pros: Great view of the city and river in good weather... +Lovely for loud large groups +Varied menu with some original items +Great place to watch a game inside with a huge bar +Fun location +Good place to take out of towners. + +The Cons: The food when I went yesterday was not great. We got the wrong sandwich, our order wasn't as described because the kitchen was out of ""lots of things"" (Tell us when we order, not when you deliver the meal without elements on the plate.) +Can be loud--not a place for a romantic date... +The bathroom condition was really bad. + +The server did comp up an appetizer, and they were friendly enough.. they just failed to wow. + +The view was great, and we did enjoy walking around seeing the fountain dance to ""Pour some sugar on me"" seriously?!?!? Yes! Classy eh?[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Went there on Saturday night following a movie at loews. We sat at the bar and watched the olympics on their multiple large flatscreen tvs. Ordered the calamari and shrimp quesadillas. The calamari was crisp and plentiful the quesadilla however missed the mark. It wasnt crispy and it tasty sauscy instead of gooey. The menu is large and reminds me of epcot with all the different ethnicities represented. gordan Ramsey would probably comment on the lack of focus at first sight. Miller Lites are $4 a pop which was a big downer as i got my $85 bill for two apps and multiple miller lites. + +Great atmosphere and probably a fine place to watch the pens game. +Food looks like its hit or miss + +All in all would rather drive down the road to the south side for a post movie food grub and tottie.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The words ""epic fail"" get thrown around a lot these days....but I really feel like they apply in this situation. + +We went on Friday, April 2 and arrived at 5:10pm. It was busy, but not crowded....no waiting for a table. Half price apps and drinks -- we ordered at 5:20. + +The food (just appetizers, mind you...) didn't arrive till almost 6pm. Drinks were ordered and were unbelievably slow. We placed one order for 6 draft beers at 6:15...they arrived at 6:52. *37 minutes for beer.* + +By 7:00, we were canceling food orders which we'd given up on after waiting almost an hour. We just wanted to leave. + +Instead of comping anything, they added 18% gratuity to each of our bills. Uhhhh yeah. Thanks for giving me one more reason never to come back. We finally were able to leave around 7:30. + +Bar Louie: You are dead to me.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I had the EXACT same experience as John R. Went here to get a quick bite to eat before seeing a movie across the street. The place was near empty and there were three waitresses. Got seated and waited on immediately. Ordered drinks, and it took them 15 minutes to come...no, not alcoholic drinks, two waters and an iced tea. This should have been a bad sign, but at this point we ordered food. + +20 minutes go by...we flag down our waitress, to let her know that we need to get to a movie in 45 minutes. She said our food would be out in a few minutes. Another 20 minutes, still no food, and our waitress is nowhere to be seen. We flag down another waitress, she says she will find our waitress, who we then notice is chatting with one of the other waitresses. She finishes her conversation and finally makes her way over to our table about five minutes later. She says she didn't even realize our food hadn't arrived (well, you never even checked on us, so of course you didn't). After speaking with the kitchen staff, she informs us that she ""definitely"" put our order in so it ""must have been given to someone else by mistake."" Because they wouldn't have noticed that that WASN'T what they ordered? Seriously? + +The waitress told us she could give us our food for take out and, since we were starving, we reluctantly agreed. 10 minutes later, our food and the bill arrived. All that was comped was the iced tea, and we got some free utensils and wetnaps. How generous! We shovelled what we could into our mouths, did NOT leave a tip (thankfully, we didn't have the added gratuity that John had), and sprinted to our movie where we covertly finished our smuggled food. Worst part? I opened the wetnap, and it was totally dry. Of course. + +However, I gave this place two stars instead of one. That's because my food, when I finally got it, was perfect. I had the Greek burger and it was huge, cooked exactly how I like it, with delicious toppings. I really wish I could come back here for the food but...hell no.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Service has always been good and the food consistent, we usually come for happy hour when apps are half off and there's some great deals on drinks as well. + +Things that stand out to me: veggie wrap, fried zucchini, hummus tabuleh and tzatziki platter, and house salad with ranch (their ranch is so good I could eat it with a spoon)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Let me just say that this used to be a place I loved. + +Remember when you'd go somewhere and have good food, great service and a general pleasant experience and then a few months you'd go back and have it all again? Well one day you decide to go back and you realized everything has changed in a way that you can't describe and the place is no longer familiar. To me, that is Bar Louie + +I can't say the food is bad. I had an order of the pretzel sticks for an appetizer and the cinnamon sauce tasted like water and the pretzels were stale. I will say I still ate them so shame on me. My sandwich (the Mario) as always was very good. + +Now here comes the bad: + +1. There were fruit flies EVERYWHERE. I felt like we were eating on top of a garbage dump. At one point I had to get a new drink because one flew in my beer. I understand that the establishment is an indoor/outdoor place but there is no reason for 15 fruit flies to hover over my table. + +2. The place is enormous and they had one, very nice, but over worked server. The girl looked like she was about to have a heart attack because she never stopped moving. + +3. Because of number two our service in general was not good. I can't totally blame the girl she did the best we could. I mean. I've played Diner Dash on my iPad, I know what happens when a place fills up too quickly when you are the only one working. + +It's sad when a place you love turns into a place you never want to go again. I think I'm being very generous by giving it two stars but because I used to love it so much I can't rate it that low. Part of me hopes it gets better, but like an absentee father it'll just let me down again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We were going to see a movie that started at 9:40pm. The 2 of us got to Bar Louie at 8:30. We sat outside, and it was nearly 30 minutes before the waiter even stopped to get our order. I tried stopping a waitress but was told 'this isn't my table'. Finally the waiter took our order. 1 Sam Adams light bottle, and one Pineapple Juice+Vodka. After about 15minutes another waiter (maybe the manager I don't know) asked if we had been waited on. We said yes, and told him we had been waiting. He left, and another (different) waitress came to bring us our drinks.. they were wrong.. My date was given vodka on the rocks. and I was given a Sam Adams.. +They took these back, and another 10 minutes before the correct order was served.. We told them to bring another round and the check. It was 20 minutes before they returned.. and they forgot the check. + +By this time we had to go to be on time for the movie.. my date asked for the check again so we could leave.. finally they brought it and I gave him my card, when he came back we signed it and left in a hurry to catch the movie. + +for 2 bottle beers, and 2 pineapple juice + vodka I was charged $31.03. I didn't have time to complain or ask. I won't be going back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Food was ok. Waitress was a huge air head. Waited 25 min for my $7.00 beer. Only got it after I reminded her. It is just another disappointing chain restaurant disguised as a local commodity.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Although I wouldn't travel out of my way to have dinner here, this is a resturant that I enjoy having a meal at, when I am in the Homestead water front. On all of my visits here I have enjoyed the tempura shrimp. The dipping sauce are to die for. I've found myself craveing the tempura shrimp, and the accompanying sauces. + +The first time I ever had dinner here was as a birthday dinner with me and my big sister. So this resturant has sentimental value to me. I attach eating here to having a special night out in the Waterfront. + +Bar Louie has some very flavorful and fun dishes for bar food, that is.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> When the ratio to wait staff to diners is 3:1 you'd think you could get service!!! + +Nothing erks me more then seeing idol wait staff and hungry patrons. I very rarely walk out of a restaurant with out having eaten first. I came here on Saturday ay 6pm. Almost none of the diners had food on their table and many of them didn't have drinks in the 15 minutes I was there I counted 9 waitress again I counted 9 waitresses and not a one of them came over to our table to get even a drink order. Just from the looks of it I could tell staying any longer would be a total train wreck. So after 15 minutes of waitress counting we left with empty bellies.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I was looking to get out of the apartment on a really nice, sunny day and we decided to drive to Waterfront and walk around. All around great day until we hit Bar Louie for some drinks and appetizers. + +I am giving it one star, though it deserves none, because our waitress was nice, if a bit inattentive, and the hummus app we ordered was pretty damn good. Outside of that Bar Louie leaves a lot to be desired. + +This is probably the first place I've been to where they charge $10 and up for all mixed drinks. To me, that is beyond ridiculous. Bar Louie is not an upscale restaurant, as much as they wish they were, and paying almost $60 for three drinks and two appetizers is insanity defined. + +As I mentioned the waitress was friendly, but she definitely did not come back and check on us enough. I really wanted to like this place because of things I had heard and the drinks we had were really damn good, but if it want to spend that kind of money, I'll go somewhere that I can get good service.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I came here last night to get a few appetizers before a movie, and was hoping to be able to write a review on the food. Unfortunately, I cannot because the service was so bad that I left before I had the chance to order. We found seats at the bar behind the taps. After sitting there for 5 minutes and not being acknowledged, we thought that they might not be able to see us, and so we moved to a different pair of seats in the middle of the bar, grabbing a few menus on the way so we would be ready to order. It was fairly busy, but it is not like there were people standing at the bar trying to get drinks - everyone was seated and I'm sure they face much busier times. We sat in our new seats for almost 15 minutes (I timed it - I am not exaggerating), and were not even acknowledged. You would at least think the bartender would acknowledge us and tell us he would be with us when he could, but despite staring him down almost the whole time, we could not even make eye contact. I hope this is a fluke but will probably not be back to find out.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Went here for drinks and nachos and it is a very nice establishment. The nachos were very good the drinks pricy but t be expected in a setting like this place. There are fire places outside on the patio a huge bar and even though it doesnt seat many there is a very nice cozy setting upstairs. Go here to relax or enjoy good food both thumbs up.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The absolute worst service I have ever had at any bar or restaraunt. And, in looking at other reviews, I am not the first. There are many options at the Waterfront, and I would suggest you try any of them; but stay far away from this place![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've eaten just once, mostly I go for drinks. Nice, lively place, nice outdoor seating for the summer and fall. +Drinks are good, service is good. +Location is great as well, right across the movie theater.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> love the ambiance and food!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> $1 burger night on Tuesday. Add ons more.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> haha only came here once for happy hour, but i am just pleased with the price. i guess coming from ny, anything would be better price wise. $3 for draft and a big selection of beers so good times. also it's right across the theater so it's a good place to go and chill before the movie starts.. which is exactly what i did haha.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It was the first time that I went to this location. We sat outside and it was a beautiful night. I had the BBQ Burger with fries. For the price of the burger I expected something much better. It was a very thin burger when it came to the meat. As a whole it looked large but that was only because of what they piled on top of it. In addition, their drinks are expensive! Just one cocktail could run between $10-$12 and they aren't very large. Our waitress spent more time talking to her friends at the next table than actually tending to our needs. There are enough restaurants at the Waterfront that I don't know that I will come back here.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I personally enjoyed my recent visit to Bar Louie with a friend but completely understand the poor reviews on help. The restaurant is pricey for what it is, and our waitress was a bit lackluster. + +So why does Bar Louie get 3 stars? Happy Hour and a nice patio! + +Happy Hour is on Monday-Friday from 4-7pm and offers lots of different options -- $3 Drafts, $4 Wines, $5 Martinis, and 1/2 Price Select Appetizers and Flatbreads. My friend and I ordered 4 Martinis and 3 Appetizers between the 2 of us, and our bill was less than $40 total. Not bad! + +I ordered a Strawberry Peach Bellini and a S'Mores Martini, and both were tasty. We shared Bruschetta Pomodoro, Spinach & Artichoke Dip, and Roasted Vegetable Flatbread. The food was also good, and I would order all three items again in the future. + +My recommendation is to understand what Bar Louie is good at (Happy Hour) and only frequent the restaurant at those times![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is one of those places where the presentation is nice, but the taste is too ordinary. Friends and I went here for happy hour (starting at 5pm). They claimed to have $1 draft, $5 mixed drinks, and half off appetizers. When we got there, we realized the happy hour special only applies to certain items, so pretty much the discount was pointless. We ended up spending a fortune on beer and mediocre appetizers. + +I only had appetizers here so I can't really judge them for their entrées, but I will rate according to my eating/drinking experience. I got the spinach artichoke dip. It was a little runny and the dip to chips ratio was disappointing. For a dip, it had way too many obstacles built in to it. I don't know what they did with the artichoke, but it was super fibrous...I felt like I was chewing grass. + +Overall, I would not recommend this place unless you have money to make it rain. Food was way too average for the high price.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place was pretty good food, but the service however was just horrible. As a friend said they hire for looks, not work ethic. Plus the fact that it took forty minutes just to get a couple appetizers was ridiculous. Our server seemed more interested in the table full of girls than actually waiting on us. The couple behind us came in the same time and wasn't even attended too until after OUR appetizers were being cleared off. + +The food was pretty good, but because of the service I won't be returning.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> As far as chain restaurants go, Bar Louie is ok. I really like their appetizers and their salads, but I don't care for their burgers or pastas. Their drinks are ok. They're normal corporate restaurant drinks...i.e., Applebees. + +Service is hit or miss. Last time I went, I had just fine service. The time before that was also just fine. Sometimes the server is a little spazzy and seems new or doesn't know wtf he's talking about. (Once, I went and ordered red zinfandel and he brought me white zinfandel and argued with me that it was red zinfandel. I had to explain to him that white zinfandel can be confusing because it is, in fact, pink. I still don't think he believed me. It would've been amusing if it weren't for the fact that it was actually annoying). + +Things I like: calamari, pretzel sticks, wedge salad, some of the sandwiches. Things I dislike: frozen burgers they sell for $1. + +Great to stop in right before a movie at Loews, though! :-)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Servers are chatting, not paying attention to tables. I can see my salad is ready at the window. Worst serves ever.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I must say, my experience last night at Bar Louie was wonderful. I was hesitant to go because of the other reviews here, but my husband convinced me to give it a try. +The place is seat yourself and it's LOUD in there. I was a little underwhelmed by that at first but I got used to it and found myself enjoying the energy. +Our service was fantastic. Courtney was great - super attentive, brought our drinks out in less than 5 minutes, brought our food quickly, checked on us just enough... And the place was packed. +The drinks were perfect, just strong enough. We tried the Peach Lighting and the Tiki drink. I liked the tiki thing better but that's just personal choice. There were real berries mixed into that one. Yum. +On to the food... My turkey/ham/Brie sandwich was delicious and my husband loved his burger. The highlight of the meal though was the Whiskey cake. Sonnet-worthy. +We'll definitely go back again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> One of my favorite places, and they have thee Best Lemon Drop Martini's... Plus the Bar Tender looks like Clark Kent(Superman) very handsome guy[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Meh, I just don't see the appeal Bar Louis has to Pittsburghers. I guess this particular restaurant benefits from people who work at the Waterfront stopping in after a shift. It's always packed. Being so close to the AMC theater, they get traffic before and after movies. + +It's expensive, the food is so so. Before I get ahead of myself, I had the BBQ ranch chicken salad without chicken. The BBQ ranch dressing was very good, but it's very easy to duplicate at home. It's equal parts ranch dressing and KC Masterpiece hickory BBQ sauce and a drop or two of Worcestershire and a drop of franks hot sauce. + +Tuesday is dollar burgers 5 until midnight, daily drink and happy hour selections, but even that's not enough to get me here. Skip it. One caveat for this location, free parking. At Station Square's location you gotta pay to park the jalopy. + +I'm eager to see if this place sees a huge drop in business when Burgatory opens across the street.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I am normally a Bar Louie Fan - my husband and I LOVE the one in Tampa. This location needs a lot of work. We went on a Friday evening before a show at the Improv. We were looking to meet up with friends and have drinks and a quick bite to eat. We never got to the food part because of the level of service that we received. We got there at about 6:40/6:45 so Happy Hour was wrapping up, but I would say that the bar was not even 3/4 full. There were also plenty of empty tables. This should have been our sign to run in the opposite direction. But we grabbed a table. I am not a clock watcher, so I am not sure how long it took us to get a server but it was at least 5-7 minutes. Then we got our drinks at 7:04. The only reason that I know is because I was looking at my phone because my husband and I wanted to get some apps ordered before the end of Happy Hour. That went out the window. When our friends for there; they ordered drinks. We finished them and left. The server was nice, that is not the issue. The issue was how GROSSLY UNDERSTAFFED they were. They had two bartenders on (I think) and not nearly enough cocktail servers. The server apologized for the wait on the drinks, but explained it away with ""this happens at the end of happy hour because the bar get swamped"". That is a sign that you need more staff. I have never had this happen at any other bar before. Get more staff. We ended up passing up on food because we were worried about time, not the fact that we did not get HH pricing. Even though, in my opinion, they should have honored HH pricing since we were ready to order food at 7:50/7:55. We ended up going to the Improv and got food there. Bar Louie lost a great deal of my money because their lack of staffing and they will never get our Pittsburgh business again or our friends who live there.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We stopped here to enjoy a drink before our movie. Our server, was friendly. My husband had a margarita and my server suggested a berry mojito to me. +Both drinks were overly sweet and barely any alcohol. After I finished my drink, I used my fork to dig for the blackberries at the bottom only to find (to my disgust), a decent sized piece of clear saran wrap! Ugg! Did they muddle the mint into the saran wrap?!!! She comped the drink but we won't be back. +Can't speak about the food since we didn't have any but atmosphere was loud and it was difficult to have a conversation without repeating yourself.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I can't even review this place. We sat ourselves and waited for a waitress to take our order, and we waited and waited until we got tired and just left. And I have to be clear it was a Saturday afternoon, maybe like 10 tables with people at them and I saw 3 waitress walking around. I think it's probably a bad idea to ignore people that come into your restaurant, especially since burgatory just opened across the street.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Man, haters gonna hate. Listen, y'all, Bar Louie isn't fancy. It's just not and their extensive martini list won't fool me. However, the food is good ole American bar grub and their beer selection is decent. The staff has been nothing but nice even when my wannabe rowdy group of friends spent many a summer day sitting a table for four hours drinking dollar beers. As long as Bar Louie still keeps having $1 Burger Days (Tuesdays) and $1 Beer Days (Wednesdays), I will continue to be a fan. FYI, It's a fanatically cheap movie & dinner/drinks weekday date spot.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The food was okay. The noise level--with 10 people in a huge room--deafening. Awful acoustics![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Food is Shitty probably would be good if they had a cook that knew how to cook it correctly. Staff is ok no complaints drinks are good as well[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Eh, this place was okay but it was sort of a weird crowd/overall experience for a Saturday night. + +Bobby and I came here after dinner and sat up at the bar. Tip: if you sit behind the taps, no one will bother to acknowledge you exist. When we moved seats, we were finally asked what we would like to drink after waiting for 5+ minutes in our original seats. It wasn't all that busy, either. Most of the people sitting at the bar were a bit older than we were. It seems that Bar Louie is trying too hard to be trendy with the decor/neon blue lighting/extensive martini list. Maybe I'm just salty about the wait.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I rather like Bar Louie for my outdoor dining experience after biking the rail trail or before a movie. Been there twice now for both of before-mentioned occasions and both times had their appetizers. Note that if you can catch them during their happy hour from 5 to 7pm on weeknights, your pocket book will thank you. + +The two of us diners selected three appetizers to share the first visit and two on the second visit and were quite satisfied with presentation, quantity, and quality. + +I would highly recommend the Bruschetta Pomodoro and the calamari (breaded just right and not overdone).[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Really the only thing good about this place is the happy hour. No one wants to pay $8 for a glass of wine that is a short pour and bottom quality.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I don't frequent Bar Louie, and I really don't plan to change that any time soon. I've eaten here and stopped in for drinks a couple times over the years and I just haven't been super impressed by the place. + +The food has been decent - a few years back I splurged on an enormous fried chicken sandwich and definitely enjoyed it, glutton that I am - but their meals and appetizers alike have admittedly never ""wowed"" me. And while I enjoy their cocktails and would consider stopping in just for drinks more often, the problem is that things are way overpriced here. Even during the happy hour drinks are pretty costly, not to mention that I think most of the drinks I personally like don't qualify for the happy hour discount, which is disappointing. Once I stopped in with friends after a movie and one drink cost me $10 here. Not even a large one, either! Sorry, but I find that to be kind of ridiculous, especially since there's cheaper places to get drinks in the area. + +Still, the food and drinks are definitely a-ok albeit overpriced, so this place would be rated 3 stars in my mind IF I could hear myself think when I eat here. But good Lord, they're just so loud! I always leave with a sore throat from yelling to make myself heard. Not cool, Bar Louie. Not cool. + +So while the food and drinks are fine enough the loud venue and prices mean that this is definitely not one of my favorite places - and given the other options we have at the Waterfront I don't expect to be back in any time soon.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My sons a and I came for Tuesday Dollar Burger Night. You can gat a ""burger"" (beef, chicken, portabella, or turkey) in a bun with lettuce for a buck. Then you can add toppings to complete your burger at a small cost-cheese 75 cents, veggies 50 cents, Artery Cloggers 75 cents, sauce 25 cents. Those are the headings and they have items listed under them-like 9 different cheeses. You can also get a basket of tots or fries for a small price as well. +My burger was $2.25 after I added toppings. Is it the best burger I've ever had? No. But is it the best $2.25 burger I've ever had? Yes. It's kind if a Russian roulette as to how your burger will come to you cooked. Mine was well done and one if my son's burger had pink in the middle. We probably could have sent it back but we don't mind a little pink. +I love the tater tots! They are crispy and have the right amount of salt. Yummy!! +Our server was great and we'll definitely be back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great environment at night! Songs going on very lively!! The food of my friends who ordered burger and fried shrimps was not that great. But I ordered chicken flatbread which was really delicious! Absolutely loved it will definitely go here again just for the flatbreads[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great atmosphere and rather humble, especially for a chain restaurant. The service is always friendly, even if they are busy. I enjoy taking clients out for drinks there because of the enjoyable bartenders and wide array of drinks on their menu. I highly recommend their chicken sliders and you have to try their tempura shrimp. + +Be sure to make a reservation because they can get busy too![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm not into waterparks as much as I am into amusement parks. I go to Sandcastle maybe once a year. But my Chicago friend Catherine came in to visit for the weekend and after a day at the zoo, we donned our swimsuits and came here. The main part of the park is closed in the evenings, but the Sandbar and the Sandbar Pool and the Hot Tub remain open for the 21 and over set. The Sandbar has a great menu of food and drinks and has a $6.00 cover charge to get in. Occasionally there's live entertainment. + +It's hard to believe that before they built this place, it was the site of an abandoned steel mill. Actually, it was the railroad yard for the nearby Homestead Works. But after site-clearing and clean-up, they turned it into a beautiful place to spend a warm day or nice evening. The view across the Mon is quite beautiful with a wooded hillside on the other side. There's even a boat dock, so you can arrive by river if you desire. + +I'm glad I renewed my acquaintance with this place and hopefully, I'll get another chance to come back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The evites are in the mail for the 2 for $99 special! You will have to spend $24 on a parking pass. I signed up last year for this promotion and don't think I got the passes worth. + +The waterpark is nice and lounging by the pool or floating around the lazy river is perfect for a hot summer day. There are just too many misses in my book though. + +1st off all Traffic is a biatch! Be ready to sit on browns hill rd for a very long time unless you leave before 9am and wait for the park to open at 10am. + +Next remember it is a family park so there will be lots of rude and bratty kids all over the place. (I'm not a mean kid hater) my experiences have been bad at the Sandbar pool. + +If you do arrive early enough you will be standing in the hot sun with a gang of kids that WILL push you out of the way and run to claim 10 chairs with towels even though they won't use them because they run around the park all day. I actually got into an argument last summer with one said kid. I was like ""I'm an adult and you need to have some respect."" He pushed me and took all the chairs. I only needed one and his mother did not correct him. I was on fire and moved a chair over from the back and he still was giving me crap because I moved the chairs over...THAT NO ONE was even there to sit in at the time. Damn! FOR REAL! + +Sandbar drinks are expensive and incredibly weak. Plus they are so sugary. If you do get a frozen drink and sit by the pool be prepared for it to be half pool water in a few minutes. An Adult area would change all this. I don't even care that I'm getting splashed all the time I do realize that I'm at a pool but it's hard to relax. + +If you do get a pass have a friend who can get there the same days you can go. If you're trying to go on the weekend forget it! The weekdays are bad enough. I'm looking for a better pool side lounge for this summer.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It's fun, but not as fun as Kennywood. The boardwalk food is a bit too far from the wave pool and that makes for a lot of shoes on/shoes off events. The lazy river could be much better. I did like the water slides and the Potato Patch fries, as well as the scenic location.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> How many times do you get to fall at 70mph, wearing only shorts? Sandcastle can make it happen. + +If you're going, it's best to stop by Giant Eagle and grab you some discount tickets from the customer service desk. $25 is still a bit much in my opinion, but it's better than spending the full $30.99. + +There isn't much I can think of that's in Sandcastle that isn't a great time, except maybe walking around and scorching your feet on the boardwalk. I personally am a huge fan of some of the faster tube slides, and of course the massive speed slide. If you're looking for a more relaxed ride, check out the Lazy River, or screw around in the big pool. There's also a pretty nice wave pool there for your amusement. + +There's also plenty of stuff for kids to do... But I don't have kids, so I don't know how all that is. + +They do close at 7PM, which is a bit early, so be warned: you definitely want to show up earlier in the day. BUT it's definitely a good idea to close the park if you can: right toward the end, the lines disappear, and you can ride over and over. Win![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Sandcastle is a mixed bag for the kiddos. On the one hand, there are plenty of waterslides/pools that are a good fit for young ""riders"", on the other hand, Sandcastle, like any city amusement park, attracts more than its fair share of highschool kids looking to spend some time away from their parents and assert their personhood. + +Unfortunately that element doesn't particularly care about ""censoring"" speech for 9 year old ears, and worse, in the Mon Tsunami, about personal space, since the wave pool becomes a near mosh pit of jostling and strutting and shoving and 'showing off' for the fairer sex, and that can be a little dicey for the littler kids. + +Having said that, it's still a good day at the park. . . cheese fries, a cool dip in the pool on a hot day, some fun slides. . . + +I think in rating Sandcastle fairly you have to understand the context of the park. It is NOT policed particularly effectively. if you take small children you have to be a diligent parent and be aware of your surroundings, paying attention to the group of 17 somethings thrashing around in your near vicinity, ""accidentally"" bumping into people for a reaction from their group. + +MOSTLY it's a good time. Mostly.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> So the last time I went to a water park was probably when I was in elementary school and didn't really know how to swim (... I still kinda don't. lol). Anyway, it was in California at Raging Rivers and it was a traumatizing experience. Screaming & being tossed around in the pool that pushes periodic waves at the sound of a loud horn and ending up with scraped knees and feet. Not fun. + +So to say the least, I was a bit nervous coming to this water park afraid to have another episode of feeling I was being drowned. Luckily that did not happen. + +I seriously had SO MUCH fun here! I honestly was only expecting to go on the Lazy River pool all day but with my bf, we hit up so many rides... tandem AND single rides! I feel like such a big girl now! Definitely lean back while you're on those single donuts on the water rides, or else you feel like you're going to flip over while swishing down the tubes. The new dragon ride they just opened up was okay. I was expecting it to be so much more fun, but literally you just slide down a dark tube into a circular room where you just slowly swirl your way down the middle hole and that was it. + +There was this one ride where you slide down the tubes for a few seconds, then you land into a pool where a worker pushes you into another tube and this continues about 3 times. It was weird. Kinda awkward with the worker having to grab you and push you through. Although it was still fun. The last dude threw me in backwards! Scared the crap out of me but it was fun :) + +The food here is surprisingly pretty affordable. Plus, who wants to eat a huge meal while in your swim suit. Me don't want no pot belly. + +Overall I had such a fun time here. It definitely made me rethink my fear of water parks. By the way, we went on a Saturday in early June and it wasn't as packed as I thought it would be! So the lines weren't long at all. Also, go to Giant Eagle to purchase your discounted tickets. You save a few bucks versus buying them at the water park. Oh and don't forget to bring sandals while walking around. Your feet will literally feel like they're burning from the ground. Now go off and have some fun! :)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We're lucky to have a waterpark in the Burgh. I have to keep telling myself that when I want to complain about this place. I DO think it's a great place to take the fam or even, in my case, spend a day relaxing... if you can! + +Let's do the compliment sandwich. Positive - negative - positive! + +The negative... I feel like Sandcastle is the forgotten redheaded stepchild of Kennywood. They keep pouring money into K-wood, but Sandcastle stays the same year after year. Now, granted I haven't been there in YEARS, but everything seemed the same as I left it other than one new slide. I haven't been there in about 9 years. One new slide in 9 years? Hmmmmm.... + +I see major places to improve. Especially the pool. I honestly think the slides are great, although you could always add more, they're still fun. The pool... it's just packed. So packed that you'd think they'd add a second pool. Looking around it looks like they have the extra space. Maybe an adults only pool? Swimming with 20 zillion kids, plus adults drinking (yes I like that you can bring your bevvie in the pool... but it's kinda weird being around so many kids) and you start to wonder how clean the water is. I mean, 20 zillion kids you gotta expect a good amount of kiddos are peeing in the pool! + +The sidewalks are also scalding hot. I'd assume since many of the people are walking around barefoot you'd be able to custom order some kind of non sun absorbing surface. And I""m NOT investing in those dorky water shoes, sorry! + +I'm ALWAYS happy to see a Potato Patch stand! Just as good as K-wood! They also serve chicken tender, which is nice if you want a little meat to add on. Nothing more is needed for me! Although the frozen drinks looked tasty and tempting, it was so hot out I was just downing water by the gallons. You're also allowed to bring in your own snacks and food, which I think is nice for families who want to save a little mola. + +Again, Sandcastle is so awesome to have in the Burgh, it would be nice to see improvements. It always seems packed in the summer months, so why not keep on improving it? Or maybe they think don't fix what's not broken. I just may stick to a cleaner, less pee filled community pool for my water fun fix![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Dont waste your time with this place. Long lines, overpriced and no shade or cooling spots while you wait. Half the ""rides"" were shut down. You're better off with a garden hose. Save your money or buddy up to someone with a pool.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I LOVE Sandcastle. +First, let me say that I'm reviewing the waterpark, not the people. The park has little to no control over the people that visit the park and the way they or their children behave. + +If you are going to visit, I would HIGHLY suggest you try to go on a weekday. I've attempted to visit on nice weekends before when the park has actually been at capacity and they are no longer allowing people in. It gets CROWDED on the weekends, especially if the weather is nice. There aren't a ton of nice days in the summer in Pittsburgh, so when there are nice days, people come out in droves! + +The slides are a blast, the lines are sometimes very long, but worth it. The lazy river is great when it's not wall to wall people. I really enjoy the new Dragon's Den but the line is CRAZY long for it! They also have a fantastic bar area, we have gone a few times and enjoyed a festive beverage while we enjoy the sun! + +They have several areas for smaller children, which are all fantastic. + +If you are visiting, trying to take advantage of the giant eagle discount tickets, because these can get really pricey. You can also do a Sandcastle/Kennywood ticket, where you visit Sandcastle during the day and Kennywood at night. It's a fantastic deal, but boy could that be exhausting![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> okay, so it's not as fun as kennywood but i guess it's still cool... + +i planned ahead a day to go for me & bobby (his first time) it was supposed to be nice day, but the weather changed in 2 weeks.. + +we picked a nice time.. since it was literally supposed to rain all day, there werent any long lines/ we literally rode every water slide in one hour. then we went to head to the lazy river--- & it was closed! they said it was closed due to not enough attendence, but i mean come on. we still paid $70 for 2 people to come in this park where i just rode everything in one hour.. keep the lazy river open so i can kill an hour! aah. the cliff hanger was also closed- like always. + +so we just went and rode everything again. the Dragon's Den is sweet and the blue tubaluba is as well. bobby had a blast on the speed slides. i have to admit though, i do miss the regular body slide. + +another reason i chose august 3rd to go to sandcastle was that the park was open until 7pm rather than 5 or 6 like regular days. well actually at 4:45 we recieved a ""15 minute warning"" that the park was closing at 5 due to rain. ugh, a little more time would've been helpful. + +i couldnt hear the warning and asked an employee who said they were closing in ten minutes due to the weather and being under-staffed to stay open until 7. it started to rain at 5 and literally at 5:20 the rain was over . the park could've just shut down the rides until the rain cloud passed, but due to being under-staffed would rather hand out rain checks.. which is fine because we get an another entire day, but i mean it would be a terrible inconvience from someone out of town who planned a family day. + +overall, the smile on my boyfriend's face was priceless, but i truly wish we could've enjoyed the lazy river and the park until 7. hopefully next time things go as planned....[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Sandcastle Water Park in P-Burgh was just ""okay"" for me. I really think that this place is geared towards children more so than adults or ""family"" because there isn't much fun here for people older than 16. The water slides here were lacking. There were very few of them and the majority of them are boring. The last time I was there (not too long ago) there weren't any extremely modern slides like a tornado slide, so they really have some updating to do. + +They do have an ""adult pool"" and bar area but it was so packed that it was hard to actually have fun in this area. The pool is very small, similar to one you'd find at a hotel chain. It has a hot tub area but it sits about 8 adults max. and people were fighting tooth and nail to get in. It wasn't too impressive to me. + +They also have a lazy river at this park and, while I do enjoy lazy rivers, this one was so packed that it was hard to breathe. People kept bumping into me and touching me and it made me grossed out. + +The one attraction that I did enjoy was the wave pool. It was crowded as well but large enough to fit everybody comfortably. The water was nice and clean (a big plus) and the wave action was strong. I could have stayed in there for the entire time we were at the park. + +Overall, this place is just mediocre. It doesn't ""wow"" me very much but if you live in the area, have kids, and are looking for somewhere to go in the summer other than the mall, it'll provide them with a lot of fun.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Now here's a place that knows what it is. A place to ride a few slides, relax on the lazy river, and watch the hilarious pittsburghers walk around with Jesus tattoos and many children. + +Come for the slides, stay for the people watching.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> For some reason, I had a tremendous amount of anxiety about buying a new mattress. Maybe I was just self-conscious about rolling around on a bunch of beds in a public place. + +ABD Mattress quickly alleviated any idiotic fears I may have had. The store was empty when I arrived on a Monday afternoon and I was attended to immediately and never felt pressured. ABD has a great selection of mattresses, and the prices cannot be beat. I picked up a full plush pillow-top mattress for a cool $375 (without a box spring or a frame, since I already had one). Better yet? Delivery is free AND prompt. You pick a three-hour timeframe, and the store will call you on the day of delivery to narrow it to a one-hour slot so you're not sitting around all afternoon.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm a mattress buying novice. I also hate buying things that require you to try-before-you-buy. I also seem to give explanatory information about myself before reviews. Anyway. + +I had a lot of anxiousness about buying a mattress. If it's terrible, you'll be spending a large proportion of your life in misery until you fix the problem. Who wants that? Especially for something that can be as expensive as a mattress? + +These people were great. They patiently answered all of my mattress questions and treated me like a valued customer - both times I called, the man on the phone remembered my name (and number!) and took care of me. When I failed to buy a box spring (why oh why did I think I could go without a box spring??) they were able to take care of me over the phone and get me a box spring in the SAME day. Within hours, even. They even helped me set up the mattress that I DIDN'T purchase from them, which blew me away. + +Their professionalism and friendliness are excellent. I will recommend them to everyone who's in the market for a mattress, especially students, because their student deals are fantastic.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The only place to buy a mattress. + +Both my wife and I and our daughter desperately needed new mattresses so I decided to check this place out. We went on a Sunday afternoon and were the only ones in the store. Lee greeted us and showed us around the store. They offer mattresses, recliners, dinettes, daybeds, bunk beds and bedroom furniture. We found her a great mattress at a great price. While waking around the store my wife found a Serta iComfort series mattress for us that felt like heaven to lay on. + +Lee had told us about their free 18 month no interest financing through Wells Fargo Bank, free bed frame, free delivery and set up of your new bed and free removal of your old mattress and box spring which made it a no brainer! I went in to only buy our daughter a new mattress but I bought us a new one as well. No one can beat their prices! I compared the price of our new mattress to Levin, Macy's and Mattress Discounters. No one came close to the price we got at American Buyers. Everywhere else was double the price for just our mattress not including our daughters so it was like getting hers for free. + +Take it from me, when it comes to your sleep, DO NOT BUY A CHEAP MATTRESS!!! We bought a cheap, supposed Serta mattress in 2008 from Mattress Discounters. The boxed spring had to be replaced about 2 years after owning the bed. I don't think I will have that problem again as our new Serta has a full 25 year warranty. + +A couple days later our daughters mattress was delivered first and about a week later our new mattress was delivered. The delivery guys had our old mattress and box spring out and our new frame, box spring and mattress set up in less than 10 minutes. + +I highly recommend American Buyers Discount Mattress for all of your bedding needs.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is the most reliable car service I have experienced in Pittsburgh. Amazing service. For the last four years, we have used them each week to pick up and drop off colleagues at the airport. They're always waiting by the Hertz counter, ahead of time, without fail. Even when the flight is early or had a 3 hour delay. They charge about $10 more than a yellow cab. If you have client you need picked up or dropped off at the airport, I would highly recommend First Class. + +My first time in Pittsburgh, when the driver heard I was on an interview, he even gave me a free tour of a few neighborhoods in the city.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I agree with the other reviewers. I tried these guys based on the Yelp reviews and was not disappointed. + +I'm a grumpy New Englander, and have been frustrated by the small town, easygoing/careless customer service at many PGH businesses. These guys are different: professional, punctual (even in snow!).[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great customer service. I was in Pittsburgh for business and needed a car to get back to the airport. I found these guys on Yelp, and the reviews were not wrong. It was easy to order the car and pick-up was prompt.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Ditto everyone else. I had out of towners needing to get to the airport but I had a last minute work conflict and couldn't drive them. I was nervous about using one of the standard cab companies because their track record of actually showing up isn't great. I called these guys the night before an 8am pick-up and everything went smoothly. Dave even checked on their flight for us to make sure it was on time given bad weather. If you're planning on getting a cab to the airport, definitely use First Class.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> After reading glowing reviews on Yelp, I decided to try this service to pick up my 83 year old mother and take her to the airport. Service was great. Driver was very courteous and on time. We used them to pick her up at the airport and are equally happy. The driver even carried her suitcases upstairs to her apartment.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Fabulous service all around. My husband was coming in on a redeye flight from San Diego around 9am on Saturday morning, and just before midnight on Friday, I realized I wasn't going to be able to pick him up. I called First Class Limousine Service around 12:30am and was pleasantly surprised that someone picked up. I ended up speaking to Dave, the owner, and he was able to accommodate my last-minute request. + +My husband initially went to the wrong meeting place (on account of his sleep deprivation :) so the company called me asap when he didn't show up right away--I reminded hubby about the correct meeting spot and all went well after that. He was very happy with the service and the price. I'd definitely use this company again for rides to and from the airport! Thanks everyone![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Other people may have had a better experience with this company but that was not the case for us. We had rented a limo/bus for a bachelor party. Our driver Scott, was completely clueless in navigating the city. Constantly making wrong turns and missing exits. All of this after very thorough instruction as to where to go. Each destination took 3-4 times longer to reach due to his incompetence. This caused us to have to skip a couple of our originally planned stops. After returning to the bus after one of our stops we were informed by Scott that the police had come onto the bus and searched it with dogs. Really?!??! Why??!! How??!! We found that our bags had been rifled through and we all felt a little violated and confused. By this point we decided to call it a night. More than half of our passengers didn't care to step back onto the bus and took cabs home. + +Just when we thought the worst was over we were wrong. As we enter the highway we realize that Scott has driven all the way up the ramp and onto the highway going THE WRONG WAY!!! He starts slowly reversing down the ramp while oncoming cars honk and swerve all around us! Truly terrifying. After that, we were very upset and just wanted to get home. So after several more wrong turns we finally get home. Absolutely terrible night. + +So if you'd like to book a party bus that will include a geographically blind driver, unecessary police involvement, a near death experience and just an overall sense of frustration mixed with panic then go with these guys. Otherwise, I would suggest staying far, far away![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> So I moved to Pittsburgh from Los Angeles. I know I know I know! +Anyway so theres absolutely no places in Homestead that delivered Chinese so I decided to walk down to the closest Chinese food/restaurant to my house. + +The family that runs the restaurant is very friendly. I read a review about them on Google that said the mom looks like she might want to cook you alive. Don't believe it! + +On this visit I ordered the Steamed Dumplings(recommended by some reviewer on google...THAT LIAR) and the Vegetable Chow Fun. I generally enjoy steamed dumplings but these dumplings(too much dumpling little meat) werent so good. Theyll probably be sitting in my mini fridge tomorrow and I'll force myself to eat them when I have the munchies/starving to death. The Vegetable Chow Fun on the other hand verrrrrrrrrrrrrry yummy. Definately most have next time anyone decides to stop by. + +But all in all the verdict is you typical Chinese Take Out Place. + +*puts the menu on the fridge*[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The worse ""Chinese food"", even the white rice which came with the ogle sweet and sour chicken is really bad. Please don't eat this food.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Not bad for neighborhood corner Chinese food. The Szechwan is not good. Too much...ketchup?? The wonton soup is good. Very good curry chicken with onion and happy family. +Egg rolls are hit or miss. Sometimes they can be a little underdone. +Is this the best place? No...but it does the trick especially for a hangover cure.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Meh, I've experienced better is an understatement. + +Friday's is like the ""fine dining chain"" for every yinzer in Pittsburgh... + +1. When we were seated, it was quick which was a surprise. Somehow this restaurant gets packed and I never understand why. I was happy about that. +2. I ordered one of their ""skinny margaritas"", blackberry to be exact. It was a nice size, however, at $6.00/pop, that was half of my food bill. +3. The waitress started off attentive, but after our food came out she was gone. I ordered a turkey burger with pickle and mustard. Loaded mashed potato on the side because I wanted heartburn ha! +4. Food came. My burger had lettuce on it only. Waitress was supposed to go and get our next round of drinks. I had to wait to ask for my pickle. +5. The loaded potatoes were more like rubber than potatoes and not what I was expecting. Disappointment. +6. The waitress then went into oblivion and only returned with our check. + +Never again will I eat at Friday's. I will, however, go should a happy hour arise...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Haven't been to TGIFridays for years and was never really a huge fan. I get tired of going to the same places all the time for lunch so we decided to try it out. I must say that I was very impressed with how extensive the menu was and all of the delicious options. I had the two for $10 lunch special with French onion soup and terriakyi glazed chicken strips. I was told that the broccoli soup is very thick so I opted for the French onion. It was okay but I think that I would get a salad instead of the soup next time. The chicken strips were wonderful and I am still craving them. The portion was huge and there were leftovers. My co-workers ordered the Jack Daniels Sampler and burgers and were jealous at the portion and choices from the pick two. The service was good and we had no issues. I will definitely be back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place.. Is ok if ur grabn something quick .. But they do have a great happy hour tho[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Boo! What happened to this location? It used to be happy and fun! It just feels depressing and nearly everyone there is just doing the bare minimum to get by? So sad.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> If I were to describe this place in one sentence I would call it a mediocre, and cheaper version of Bettis 36 on the North Shore. + +My wife and I won a gift card in a raffle. We went for lunch on a Saturday. It was not crowded + +We entered the restaurant and were promptly seated by a nice server. The restaurant was clean and nicely decorated and did not feel run down or old in any way. + +Our server took our drink order and returned promptly. We got the pretzels with beer cheese appetizer and we each got a hamburger. + +Our food arrived promptly and the appetizer was ""fine"". 10 years ago I would have called it good or better but time has marched on and expectations are higher then they once were. + +The same goes for the main course. The fries were unremarkable but decent as were both burgers. + +The bill was also fair. The meal with two drinks and an appetizer was reasonable for what we got. The server was pleasant and attentive. All in all this Fridays as a good but likely quickly forgotten experience. + +I would return here for lunch like I did today.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm not opposed to chain restaurants but this TGI Fridays in comparison to some of the other ones in the area truly falls short of the ""chain"" expectation. + +I order the Jack Daniel's chicken and shrimp with just fries. The fries were undercooked and thrown haphazardly into the sauce holder. The shrimp was over cooked and just deepfried. The chicken was fatty and just tasted like it came from their freezer. Even the water tasted weird. + +Fortunately, we had a very nice and charismatic waiter and all of the staff was very friendly. + +I'd recommend the TGI Fridays out in South Hills Village over this one any day.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Everyone's been to Fridays I am sure, but I enjoy the Yucatan Salad it's delicious. My children love Fridays it's usually there 1st choice. I also love the Cajun Chicken & Shrimp Pasta very very good.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Dining outdoors after a bike ride on the rail trail. Just the right venue for that. + +Jack Daniels ribs and shrimp. The ribs were divine. The shrimp not quite there -- I'd say they were overdone. + +Our server, Ed, was very attentive. I asked for celery in my bloody mary. Not only did it come with a celery stalk in it, he brought over more celery. Yummmm....[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I had a gift card so I decided to use it for a to go order. The food tasted frozen and microwaved. Nothing special just around average![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Went with 5 others for a weeknight dinner. The server was very friendly, but seemed a little overwhelmed. Maybe they were short handed. The food was to me not even average. I ordered a burger, which very overdone and dry. Had to drown it in mayo to get moisture in it. My friend ordered nachos and what arrived looked like they had broken some taco shells down the middle, then put cheese and one jalapeño slice on each piece. Imagine 6 half-moons of taco shell. Not like any nachos I've ever seen, and more importantly not even the way they were served the three prior times my friend had ordered them.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place is kind of a hybrid of Applebee's and CPK, which isn't to say it's bad, but nothing to rave about either. I got their slider meal, which was tiny (for me) and my friend got their steak (which was way tiny). The food was fine and the service was okay, but really felt like an Applebee's knockoff (and Applebee's isn't even worth knocking-offing anyway). + +3 stars[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Good food. + +I guess one reason I like this place is they don't hide how bad the food is for you. There is a little Kiosk with all the calories right by the door. All in all I get the flat bread pizzas and really enjoy them + +The steaks are also good and the price is reasonable. + +Service is always friendly and the establishment is kept really clean and neat[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I didn't know what to expect when I walked in, but I am now a fan. There is a cool way to review the menu on a touch kiosk to find out the calorie count. + +The place looked nice. It was clean and really cool looking. The food was really good and our waiter was nice and friendly. I will be going back to try their pizza and other food. + +We had a burger, which was really good, and we had the lobster slider. French fries were good to.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I don't care what Cub and Bulls fans think, this Steeler and Penguins fan thinks deep dish pizza is not all that. First, the crust tastes like a biscuit, and biscuits belong nowhere near or on a pizza. I will give UNOs a thumbs up on it's flatbread, it's better pizza than some pizzerias In the area. When I look over uno's menu almost nothing excites me, this place is a dud. Guess what? Chicagoans don't know how to eat hot dogs either![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Not quite authentic but good enough for Pittsburgh. It's the only place that I've found that even comes close to a classic Chicago style deep dish. +I also had the french onion soup that wasn't bad. The croutons were still crunchy and it had just the right amount of cheese. + +My girlfriend really enjoyed her Caesar salad and said she'd come back just for the salad. + +Overall, I enjoyed it and would come back the next time I get a craving for a deep dish pizza. It wasn't authentic but it certainly was not terrible.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I really don't know why I bother with chain restaurants anymore. Now that my palate has matured and I no longer think chicken fingers and french fries are gourmet cuisine, I really can't find anything to eat in a place like this. + +My husband and I were running errands at the Waterfront, and we needed to find a place for lunch. We decided on Uno because pizza sounded good to us. My husband is a meat lover, so I agreed to let him order us a meat-covered pizza. To counteract this a little, I ordered a tomato mozzarella salad, so we'd at least have some vegetables in the mix. + +When the salad arrived, it did NOT look like the picture. The menu description is thus: ""chopped lettuce, roma tomatoes with basil and garlic, buffalo mozzarella, drizzled with balsamic syrup."" This description is accompanied by a bright, colorful picture of a salad with bright green lettuce, bright red tomatoes, and a delicate ""drizzling"" of balsamic syrup. It looks light and yummy. + +What we got, however, was soggy yellow and white iceberg lettuce, COMPLETELY DRENCHED in dressing, a total of four tiny pieces of tomato, and some cheese. It was DISGUSTING. There was so much dressing dripping off of this dish, it was more like a soup than a salad. I suspect that the lettuce was so wilted and brown, they figured they could disguise it by completely soaking it in dressing. Not only was it disgusting, but it cost us about $10. $10 for complete inedible slop. + +The ""numero uno"" pizza we got was nothing to write home about either. It was ok... very mediocre. The crust tasted like it was undercooked, and the sauce tasted like plain tomato sauce with no seasoning whatsoever. I have been to Chicago many times, had real Chicago deep dish many times, and this just doesn't even come close to the real thing. + +The ONLY positive I give this restaurant is they have the kiosk in the front where you can look up the calorie count of the food right there. It would be better if they'd actually print it on the menu, but they are still doing better than most restaurants in this effort. They are making strides, too, with their whole grain crust options. I'm sure there's still a lot of room for improvement, however. If you're listening, Uno, please work on providing your customers with healthier food - not just healthy options like salads, but work on making the main dishes you serve better for your customers (low-fat cheese, low-sugar sauce, less sodium, etc.). Their hearts will applaud you. + +And lastly, why does every chain restaurant have to decorate with old signs? Is there some sort of chain restaurant decorating requirement I don't know about? It's baffling.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Awful everything. From the bad service, to the diluted soup, to the lame-no chicken on the chicken salad, to the PRE-fabricated pizza. AVOID THIS PLACE![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I really love deep dish pizza. The thick crust that is crunchy on the outside and soft on the inside. The spicy, peppery sauce that can singe your tongue. The mixture of ingredients just sliding down your chin as it bubbles out of your mouth. That being said, I really don't understand why people go to Pizzeria Uno. This chain has done to the deep dish pizza what McDonald's has done to hamburgers, Pizza Hut has done to pan pizza, Dominoes has done to hand tossed pizza, and Taco Bell has done to Tex-Mex; it has made it almost unpalatable. On our menu: + +French onion +Chicken bites +Pizza with pepperoni, hamburger, and romano + +Looking past the fact that the service was not the best or the fact that the food came out undercooked and tepid in temperature, the food just was not good. Don't get me wrong, this is not the worst pizza I have ever eaten, but this chain is a perfect example of what happens when something becomes so prescribed, overhandled, and overthought that it no longer resembles the original piece of art that tasted so good. + +I really never want to return.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Food was ok had a steak w/ shrimp side Ass mashed potatoes. Everything was ok not a lot of flavor.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Came here on a Monday night. Boy was the place dead! I was the only only Customer at 8:30PM. Ordered a thin crust pizza with extra cheese, pepperoni and mushrooms. It was pretty good. Could of used more cheese. I wasn't in the mood for the heavy crusted deep dish pizza. This is my first time at this location but have been to several of the other locations in the US. It was just like the others. The Caesar salad with anchovies was very good. The service was very poor. My waitress spent a lot of time chit-chatting with the hostess. It was a chore to get water refills from her. + +They have big screen televisions in the bar area which can be seen from the restaurant.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I ate here at around 8:00 on a Saturday night. Reading the other reviews, it makes me wonder if people were a the same restaurant I was. Sure, it isn't a world class dining establishment, but it is decent considering it is a chain. You should know that going into any chain, really. It was basically exactly what I expected in terms of food quality and price. + +We were greeted immediately upon entering, and while the hostess went to grab menus, another server asked us if we were taken care of. Service at our table was very attentive and water and other beverages were promptly refilled. I ordered soup and two appetizers instead of an entree or pizza and the server made sure to ask me about the order in which I would prefer receiving my food. + +My fiance ordered a deep dish pizza and we know they take longer to make than other food items. It was quicker than we thought it would be and he really enjoyed it. I had the potato skin appetizer. It reminds me of a ""baked potato pizza"" that I used to enjoy at a local place back in Buffalo. It was delicious, especially with the addition of a little bit of hot sauce. + +Overall, it doesn't even come close to visiting an Uno's in Chicago, but then again, when does a copy every live up to the original? It won't be a regular location in our dining rotation, but it is good to know that when we have a craving for deep dish, Uno will do the trick and cost a lot less than a trip to Chicago.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My girlfriends made reservations here for my bachelorette party last Saturday. I highly suggest that you make reservations because we were able to just walk right in and sit down. There were people there waiting 30 minutes+. We had the sangria which was amazing. Our sever Alex recommend it and it was perfect for the 4 of us. I had their thin crust pepperoni pizza which really hit the spot. My two friend had salads which they said were amazing and my other friend joined me in ordering a pesto chicken pizza. Let's just say there wasn't any food left on the table when we were finished. I will be back for sure.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Pizza ok on it's own nothing great . Definitely not worth the restaurant price. definitely not like pizzeria UNO in Chicago. Are they even related or are they just using their name and trademark.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The menu is outstanding but the pizza and beer is too expensive. For 2 personal pizzas (the size of pizza hut) 2 beers and 2 salads, we paid over $50 bucks. The personal pizzas alone were $11 each... If you want pizza and beer go somewhere else-pasta appetizers, or sandwiches... this place is good.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Well this visit started off good. I was seated right away, no wait. Was given a good beer selection of some PA Craft beers. Ordered the traditional deep dish pizza, but with no onions. Now after we ordered, it just went downhill from there. Was never asked if I wanted another beer, the waitress just gave me more water. My pizza still had onions in it. Which I stated right off the bat, that I didn't blame the girl who took my order. I know cooks can't read. I was one for many years. Mistakes happen, and the manger took care of it and took the item off my bill. NO complaints, still ate the food and it was good. Just not a fan of onions on my pizza. + +Now onto the bill, the server continues to tell me that she was sorry for the mistake and declares she told the cooks not to add onions. I already said it was taking care of and there's no worries. She goes on to say that the next day was her birthday, and if I felt like leaving all my money as a tip, it wouldn't go unnoticed. I took this as a joke as I had told her earlier I worked in the industry. When I hand over the gift card I had on hand, she comes back and again repeats herself, tells me that cash as a tip is preferred as she doesn't have to claim it at the end of the night. And again if I felt like leaving her all my money, she would just be so freaking happy. Let me explain one thing and hopefully I am very clear on it. No server, and I mean NO server anywhere, should ever ask a guest or customer for a tip, yet alone, do it twice! So out of kindness, which I shouldn't have left anything by this point. I left a nice tip for the cost of what food I did have to pay for. + +Bottom line, the food was good for the price, but the service from this one person as I don't know how the rest of the servers are. Was just horrible.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I think the location in homestead has ruined this place. Dirty dirty dirty. + +Bathrooms unkept, entry door handle and windows filthy + +Pizza had too much sauce on it and was drenched. Server was coarse, not refined + +Serving items were old and rusty. Temperature of food was not hot + +Low quality, but probably ok with pittsburgher s[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Unos has been around for ever, & I feel like this restaurant chain peak in popularity in the 80's. Honestly the decor inside still kind of looks 80s to me even though its nice with sleek booth and exposed brick. + +If you haven't died and he recently I ordered you to come back and have a meal here again because honestly the food is really quite good! + +They have the best chicken salad wrap ever! I love that rap so much I want agreed to walk the south side River Trail from where the Steelers practice all the way to the damn waterfront just because I knew that I could convince my boyfriend to go to Unos with me for lunch. Full disclosure: I made him call is a cab and we took a taxi back to the parking lot after lunch. + +Listen... The food and pizza and service are very good, surprisingly so! I don't know why this place is not busier but next time you're down at the Waterfront please do consider dining here![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> All in favor of a deep dish pizza say I!.......IIIIIII, ok now that i have that out of my system. This place is such a great hangout/eat-in spot. I hadn't been here and years and some friends invited us out for the evening. I was so glad they were paying cause I was low on funds at the time. + +We arrived on a friday night and of course it was busy there. We waited about 10 minutes to get a table which wasn't bad considering the crowd. We looked over the menu and they have so many great choices. Pizza, pasta, appetizers, seafood, burgers, salads and sandwiches. + +After ordering two mango lemonades that were wayyyyy over sweetened we ordered our food. We both are going gluten free which is tough but UNO's gave us a nice selection of dishes to choose from. Plus! They make a thin crust gluten free pizza which taste great. My hubby ordered the mediterrean thin crust because he loves kalamata olives and I ordered the Guac-alicious burger with a Caesar side salad. My salad came out pretty quick which was nice but it had a little too much dressing on it. I didn't complain, it still tasted great. + +I'm not into red meat so I tried to order a black bean burger or get chicken instead of beef, but the ran out of black bean and they couldn't get the chicken so i just ordered it anyway. The burger was piled really high with all the toppings including guacamole and it was very creamy but i couldn't get over the taste of the burger because it just didn't have any flavor. Very saddening. I ended up just eating the veggies and discarding the meat. I snacked on some of my hubbies pizza even though it was only a small amount. + +We came here twice in one week. The second time we ordered the 9-grain deep dish with mushrooms, parmesan and a garlic white sauce. Was this pizza amazing or what?? I will probably always eat this pizza whenever I come. + +Only down side is slow service. It took 20 minutes for our pizza to come out and my hubbies was a little over cooked. He got the numero uno which was ok but mine had way more flavor!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Wham! 4 stars outta the park! The deep-dish pizza we had was amazing. I wasn't crazy about the avocado egg rolls, but the chocolate chip sundae was superb. Great service too from Maranda, a doll. Decor is cute. Ambience is lively. Recommended.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Pizza is a staple for me. I love everything about crunch crust, a nice rich tomato sauce, and a thick layer of melted cheese. I have never tried Chicago style pizza before and when we had to rescue our friends from car troubles, Uno's was right there so we decided to try it out. + +Only a 30 minute wait for a Saturday is pretty good for any restaurant in the Waterfront. We were seated at a booth in the bar area. The tables were clean and it was a big booth so the four of us were not squished. Only complaint, the bar was loud and when they did blended drinks you had to pause your conversation because the blenders were so loud. Good news, only happened twice! + +The four of us decided to order two pizzas, the Pepperoni and the Farmers Market. I also ordered a Caesar salad because I needed more vegetables in my life. + +The salad. It was a big salad that I shared with my boyfriend. The croutons were huge and very crunchy. The Caesar dressing was not creamy, it was vinegar based and had a little bit of a ""bite"" to it as Chris kept on saying. I thought the bite had more to do with the vinegar than anything spicy, but who am I to say. The lettuce was fresh and crunchy and they even added tomatoes like I requested. + +The main dishes came out about 10 minutes later. I do not know what I was expecting but the pizzas were not as large as I was imagining. Two of the larger pizzas looked like personal pizzas to me. But!!!! I was soon to see that even if they are a bit smaller they were filled to perfection. + +The Farmers Market pizza had caramelized onions, spinach, SUN DRIED AMAZING TOMATOES, regular tomatoes, eggplant, pesto as a sauce, and a blend of cheeses. The crust was perfection being so crisp and light that I stole Chris' extra from his plate. The sun dried tomatoes were great adding just enough sweetness to the pizza that I went looking for the slices with the most on them. It was a really really good pizza. We even ended up taking slices home with us! My eyes deceived me at first with the size! + +Then our friends told us that we had to try the cookie pizza. Cookie pizza? What sorcery is this? Matt, the one who suggested it said that we would not be disappointed. This cookie came out in a really large, bigger than our pizzas, dish. It had three scoops of icecream on it with a pile of whipped cream. WARM, right out of the oven, fresh cookie pizza. Oh sweet heavens, it was good. I am glad that I had enough room in my stomach to pile in that sweet goodness. + +Chicago Pizza, I would absolutly try again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I had the deep dish pizza and it was very good! The individual size was smaller Than I expected for $12 but I wasn't starving so it was very filling. Our waitress April was very nice and attentive for how busy it was. We had about a 30 minute wait but it was worth it! I can't wait to try it again![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My friend and I have never eaten here before so last night we decided to check it out. For a Thursday it wasn't that crowded and we were seated promptly. There were plenty of flat screens and warm lighting that made the place cozy. We ordered a thin crust pizza: on one side there was chicken, hamburger and pepperoni (for him) while the other side had just pepperoni (for me). I was expecting the pizza to be bland and warm but it was surprisingly hot and savory. I even tried a slice of my friend's pizza and the hamburger and chicken were moist, not dried out. This wasn't bad for a first visit so I will definitely be back in the future to try more menu items. I'm only giving Uno 4 stars because the waitress brought us a plate that still had old food stuck to it. Hello! The plate was yellow! How could she not have seen that?![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Well, it started well. Food was okay. Deep dish pizza was good. But the salad we had - too tiny portion!!! +We were greeted and seated well. But later the service was not all good. Bad bad service. First of all we had to ask for everything we wanted. The server didn't even had courtesy to ask if we wanted anything more or would like to go for deserts. She just handed over the check when we even didn't ask for it (we wanted to order more). +Later when we talked about this in the front, the girl there also just listened and said ""okay"", not even a sorry once!!! +I would not like to go there again... :([/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> While visiting relatives in Somerset we decided to go shopping in the nearby town of Homestead. My aunt insisted that we have lunch at Uno's Pizzeria & Grill as the food was delicious. When we arrived I had to admit that I was impressed with the decor and atmosphere of the place. It was fairly crowded for a weekday but we were seated in less than ten minutes. The waitress was friendly and knowledgeable about the menu answering all our questions with ease. I settled on a Turkey, Bacon and Avocado sandwich and old fashioned tomato soup after looking over the menu several times. They have a variety of dishes guaranteed to please all ages. The food arrived in no time and was DELICIOUS! The portions were just right for lunch, I was definitely ready for an afternoon of shopping. The four of us had items off the Two for U lunch menu, our bill was less than $30 which meant that I might could afford the shoes I wanted to buy! My aunt was right, you cannot visit Homestead without stopping to eat at Uno Pizzeria & Grill, it is FANTASTIC!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Nope![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Was very disappointed with the food. It was overcooked and not seasoned very well[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It gets 5 stars cause it jogs up a memory. Back before Pizza Hut turned into a fast food restaurant, the Pizza Hut my grandfather used to take me to was a really nice restaurant. And this location has the same look and feel as the old pizza hut before it went take out. + +So this is the old style pizza hut. + +Very family orientated dining style. You can sit here for hours. And so we did. We had a heap of use in a long table. + +I ordered one of the small pizzas which were buy 1 get one free. Disappointed in the selection of that. Seeing other choices... I regretted going on the cheap. + +Prices are moderate. 12 for a little pizza... but with all the dough, you get full. Can't say I walked away hungary. Nor did I finish my second mini pizza. + +I want to come back and get that spanich fetta looking pizza![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Nice place but some of the items on the menu are not available unless you get a 2 for 12 but that's not what the online menu states. And it's a salad come on..[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Last week was my first visit to this place. The raspberry tea was amazing. We got the app sampler, it was very good except for the homemade guacamole. I ordered a side salad, hardly any dressing on it, and not very fresh. I ordered the stuffed chicken with broccoli & grilled vegetables. Waited along time for the entrée. The chicken was good but a small portion. The broccoli & veggies were water logged. Lots of water on the plate. Tried my friends fried shrimp, it was good with good flavor. Might have just been who was in the kitchen that night so I would give it another shot.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Love the stores selection but HATE how the girls chase you around to tell you their sales. If I wanted to know I'd ask !!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Interesting the reviews here are less than stellar already. I would normally not review a chain retail store, but the service I received today just really got my blood boiling. + +I will state, as I always do in these types of situations, that I have worked many years in retail. I know what you're supposed to do. I know the ways I've displayed exemplary service and I know the ways I've slacked off. I get it, I really do. + +So I'm in the store early. Hardly any people in there. Weird for the Semi-Annual Sale time of year. Usually it doesn't matter what time you're there during the sale, it's always busy. + +I went through my usual bins and picked up a mess of undies and bras. Since no one was at the check out counter and I needed a spot to go through things, I set them down and started to try and chat with the sales chick. I actually always like to do this, just to shoot the breeze, but also to get their opinions on items I'm buying. + +The girl behind the counter was having non of this though.I asked her about a bra and she said she didn't know about that one, but said it should work. I understand, you can't try them all. But the thing that really irked me was that she was definitely not hiding her annoyance at me setting down my things on the counter. I even looked back to make sure there were no people checking out behind me. Ghost town. Tumbleweed rolled by. No one. + +So I'm going through my stuff and separating what I want and don't want and she's sighing and grabbing things saying ""Soooo, you DON'T want these???"" Um, I'm not asking you to help me sort things. I'm not holding up a line. I'm just trying to not spend $$$ on an accidental XS pair of undies that got mixed in! + +After that, it's not exactly what she said, but how she acted. I have never felt more uncomfortable in a retail store before. I ended up grabbing my discards and putting them back myself (which I really don't mind doing, but after she huffed and puffed, I didn't even want to deal with her). + +The thing is, I was nice the entire time. I don't expect you to sit there and be sugary sweet either. Just do what you were hired to do. Be nice and sell some bras. If you come to work in a bad mood, the real world is not going to give you a hug. Suck it up and do your job or work where you don't have to talk to anyone else ever.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> When I lived in Los Angeles a year and a half ago, P F Chang's was no great shakes, one of millions of places with good but not outstanding stuff on the menu. + +Here in Pittsburgh, it's the only Chinese place I've found that combines genuinely good service with quality food. Not, perhaps, as good as what you can get in LA's top places, but fantastic compared to its competition here. + +The Kung Pao chicken is particularly good, with delicious fried chicken cubes and the usual hot sauce and chiles. Chicken with lettuce wraps is good too. + +Their fried noodle dish with chicken, whose name I have forgotten, is addictive but has an odd sauce I don't quite like. Still, they get the friedness of the noodles right, and there are precious few ... ahem ... no other restaurants around here that do. + +Portions are small, so either plan to get an appetizer and an entree or expect to leave almost as hungry as you came. The minced chicken in lettuce wraps appetizer is outstanding and you get about the same amount of food as in one of their entrees. + +If you live in LA, forget P F Chang's. If you live in NYC, I'm sure there are a dozen better places on a single block. But here in Pittsburgh, it's just about the best place around.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I hate this place. +It's very loud, the service is very poor, and the food is so-so. +If you want good Chinese in Pittsburgh, try China Palace (Shadyside) or Sesame Inn (Station Square or North Hills). They're quieter, with very good food & service.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Any place that accommodates with a special dietary menu for a little known disease gets five stars from me. P.F. Chang's has a dedicated Gluten-Free Menu for those of us who suffer from celiac disease. They also make sure to clean down the area they prepare the specialty dinner so as to avoid cross-contamination. I don't know many other restaurants that go this far. + +Aside from the menu preference, I enjoy my overall experience every time. Their menu is a bit different than that of what most people will be used to if you regularly eat a Chinese Take-Out or Buffet joints. Don't expect this to be at all like that. It's not a Buffet. They don't sell ""General Tso's"" (though Chang's Spicy Chicken is recommended for those looking for something similar, it's my personal favorite) or other signature foods that you may expect. They do sell very similar items with different names and a few of their own adjustments, just make sure to read the menu description and ask questions if you are not sure. They also sell Sake, I believe they have a few different types. + +The prices can get a bit more expensive than your average Chinese Restaurant depending on what you get but it's well worth it. Portions are excellent and the taste is great. I've yet to have one complaint and I have frequented this establishment several times over the span of a few years. + +The only downside, it can be a little crowded and a bit loud. It's also very dark because of their lighting. However, I think it sets the atmosphere. It can be a romantic place or a casual place, I've been there for both.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Wasn't terrible, +But certainly wasn't great. +Save your hard-earned cash.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> REDO! + +I went to PF Chang's several years ago and was NOT pleased with the food that was presented to me. + +My issue: I thought I was getting Chinese food. + +My resolution: Try this restaurant again knowing that it is just reinvented American food with names of those Chinese dishes I actually like to eat. + +So we returned to PF Chang's for lunch to try this American food in this caricature of a Chinese restaurant. There were very few people in the restaurant. The two of us were seated in the largest corner booth and left to review our menus. When our waitress finally arrived we ordered the following items: + +Coca Cola +Iced Tea +Pan fried pork dumplings +Sesame chicken lunch with white rice and egg drop soup +Changs chicken with white rice + +Our drinks and my soup came out immediately. Unfortunately I was brought the wrong soup and the server had disappeared before I had a chance to say anything. I could see her across the barren wasteland that was the dining room and we even made eye contact several times, but at no point could I get her to come back to my table. I tried the soup and was disgusted with it and placed it at the end of the table. I didn't know what it was and didn't want to know. Almost ten minutes later she arrived quite happy with the job she was doing and asked how the food was. I asked if she could bring out some egg drop soup. I didn't expect to get the stink-eye. + +My egg drop soup was brought out with the dumplings as well as the caddy of different sauces and oils. The server really wasn't that into the experience, but again gave me the stink-eye when I told her that mixing the sauces was unnecessary since I knew what each of them was and would be able to mix them myself. I mixed the rice vinegar, chili oil, chili paste, and soy sauce (my guess is that it was supposed to be tamari) to create a dipping sauce for our dumplings. I took a bite of the soup and it was somewhat better than the other soup, but it was still brown. I ate half the bowl and left the rest for the server. It was thick and gooey and the flavor didn't wow. I saw no reason to continue. I moved on to the dumplings, which had an okay flavor to them. The skins were a bit thick and doughy. The meat on the inside did not balance this attribute at all. The sauce tasted a little odd so I tried to remix and it was still off. I tried the components individually and found that some of them were either old, stale, or rancid. We finished our dumplings. + +Our lunch entrees arrived. I had ordered mine extra-spicy, but I guess it came Pittsburgh Hot (super mild) and had a lackluster flavor at best. The meat was tough and the sauce tasted of soy sauce more than anything else. I tried some of Chang's chicken and was equally mollified. This was supposed to be their version of General Tso's Chicken. Now I have never had a General's chicken that was the same at any place. It is always different. Many of them are good in different ways. This food, though, it wasn't good. Chang's chicken fell into the same category as the Sesame Chicken -- since it tasted mainly of soy sauce -- with the addition sugar. + +I just don't understand how anyone can like this place. Even the Yoshida Sauce you get at Sam's/Costco tastes better.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Honestly, I'm furious. I enjoyed PF Chang's restaurants in the Chicago area, and my wife and I have eaten a few times at this Pittsburgh-area location. Over the last year, we have tried repeatedly, but the 90-120 minute wait for dinner is unacceptable. We tried going early, late -- it never made any difference. The front staff was rude, and the wait was too long. + +Tonight, we had a special date planned, and made reservations a week in advance. We came in the door exactly on time, waited in the line to see the front staff, and we were promptly handed a pager. They couldn't tell us when we would be seated. + +I imagined a short wait, so we went outside, crossed into a store to wait (since the entrance of this location is so packed, it's impossible to wait at the bar or in the meager seating). + +After 20 minutes we gave up. We went back to PF Chang's and the front office staff still couldn't tell us when we would be seated. I saw open tables. + +What on earth is the point of accepting reservations if you do not honor them? + +The food here is good, but certainly not great. We went to a local Thai place and were seated with no problem in 5 minutes. The food was much better, the service was good even in a crowded busy restaurant. Oh, and the local place was a much more reasonable price. + +We certainly will never visit PF Chang's again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Stars are for the food only. 2.5 rating + +Got there at 8pm on Saturday night, they told us it was an hour wait which was expected, but it only took 30minutes to be seated so that was a bonus. Started off with the lettuce wraps and i used to be a fan of these but they just seem to bore me now(FYI-love the lettuce wraps at the cheesecake factory). I had the Singapore rice noodles. This was so so as i thought immediately that lu lu noodles and asian cafe are better. The fried rice was disappointing and the vegetables tasted raw. Some good notes were the Dynamite shrimp, plump, juicy, tangy with a small kick. Sweet and sour chicken was just the same minus the kick. + +The service was annoying. We were there less than 45 minutes and it seemed like our waiter was in a rush to get us out of there. Constantly asking if he could remove my plate. I had to sternly say at one point that I will let you know when i am finished. I found it rude especially since there wasn't even a line at this point. + +I think we will travel elsewhere following a movie. The result never quite met the anticipation.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I like PF Changs. + +I think I've only been here a total of three times (twice it was take out), and I only get vegetarian dishes, but what I've had has been pretty tasty. + +I would definitely eat here again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I am writing this from the standpoint of someone who can't eat real Chinese food because of gluten issues. That said, I am loving me some gluten-free Chinese food here! If the gf issue didn't exist, though, why bother when you can get real, honest, non-chain GREAT Chinese so many wonderful places in the Burgh?! But average Chinese is better than NO Chinese if gluten is an issue so thank you Mr. Chang![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Pretty Good Stuff! + +PROS: +Nice bar area +Cool ambiance +nice dishes with good flavors + +CONS: +Pricey for ""just chinese food"" +typically a rather long wait, especially on weekends. +Very difficult to even get noticed by the bartenders once its busy at the bar area. + +Suggestions: +Lettuce Wraps (just get this as you meal! LOL) +Fat Cat Martini (OMG, YUMMMMM!) +Pot Stickers[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Our go to place at the waterfront. + +We usually order the crispy green beans as an app., they are always fried just right and never really greasy. As an entree I always get coconut curry tofu, the veggies are bright and crisp (no open pea pods or limp broccoli!) And the tofu is simply delightful. + +Always consistent. Never disappointing[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Went there for lunch and had a decent meal. While the Mongolian Beef was beyond excellent, the Moo Goo Gai Pan was average (although I did enjoy the shrimp in it). Service was fine and decor is pleasant. For some reason I'm just not in the mood to write a detailed review - please accept my apologies.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Sadly I've been here a few times because it's a crowd pleaser when my girlfriend's parents come down to visit. There's nothing really WRONG with it. The portions are big and the food is ""alright"" and the interior gives you the superficial impression that you're encountering fine dining. + +The food is sooooo bland though. Everything you get at P.F. Chang's you can get elsewhere in Pittsburgh at a much lower cost and it'll be made with more precision and have better flavor. The honey chicken at P.F. Chang's was so mediocre all I could think about while eating it was heading over to Wai Wai in Bloomfield and getting a tastier order of it for 8 bucks. + +Last time we were there the server was horrendous as well. I don't think I've ever felt as awkward at a restaurant. He brought my girlfriend's father (Don) his unsweetened tea then told him he didn't bring sugar because he asked for it sweetened and then did not understand the concept of sweetening it yourself. He then got all huffy when Don kept asking for it and actually seemed angry at us. When he came back to take our order Don ordered for himself and his wife and before Janey (my girlfriend) and I could order he had already started to walk away. We actually had to yell out to get him to come back and finish our order. (not in an uncivilized or malicious way, either) After that he must have thought we were terrible diners (I don't think I've ever been impolite to someone who is currently at work, or ANYONE for that matter) and he showed it by being silent and plopping things down in a passive aggressive way. It was really embarrassing and every time he came by the conversation died. + +Obviously the attitude of one idiot who can't hide his bad day well doesn't really have anything to do with the restaurant. But it's soooooo bland! Go somewhere else for Chinese! Look up Chinese on Urbanspoon and it'll give you a variety of good, local places to choose from at half the price.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My vegan friend, Deb, turned me onto the fact that one can dine at PF Chang's and stay on a vegan diet. + +Vegan friend Deb (VFD) asked the waitress if they could prepare a version of the famous chicken and lettuce wraps. The waitress without hesitation proclaimed they always had a vegan version, but it was never put on the menu. +Warning: even though it's vegan, it still contains the same amount of salt that was reported on all the news channels when the salt, fat, and cholesterol police made the sodium content available to the public. The vegan version is just as delicious and the chicken. + +They also have vegan dishes like string beans and garlic, eggplant and garlic, and a few dishes with tofu and vegetables. + +I always loved the fact PF Chang's offered brown rice. That nutty flavor goes so well with their meals. + +The service staff at Chang's is always top shelf, I've never had a bad time here and love when we go.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We visitied PF Changs on Sunday with a large group of 20 people. Although they had to split the tables - everything was delicious! + +We enjoyed everything from the spring rolls and chicken lettuce wraps...to the mooshu that they made special vegetarian for one of the guests...to the fried banana dessert! + +if you are with a group, and you want dessert - get the fried bananas! They come wrapped in a spring roll wrapper and with coconut/pineapple ice cream. + +Overall, we had a great time and would come back here again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've had PF Changs both in Pgh and KC and honestly, I'm never been disappointed nor elated with the food. It's 'upscale' Ameri-Chinese food. You don't come here seeking 'authentic' Asian staples; it's all changed to some degree to suit American taste buds... nothing wrong with that, imo. Do I even know what 'authentic' Chinese food is? Yes, sortuv, somewhat. Will I stop putting quotes around 'everything'? Definitely not! + +It was 45 min from closing time when we (party of 6) rushed in on a weeknight; got seated, ordered and ate without feeling rushed by the staff. + +This particular PF Changs, on the Homestead Waterfront, had fast and friendly service, though he forgot our order of asparagus. We sampled everything from the the Szechuan shrimp to the Mongolian beef to the Dan Dan Noodles. Good flavors, nothing that stepped out in the crowd. + +I don't come here all that often but when I do, I invariably leave feeling satisfied and full.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> So I have never been to P.F. Chang's before since I'm Chinese and I'm not a huge fan of eating at Chinese/American restaurants when I can eat delicious authentic Chinese food at home (courtesy of my momma). My boyfriend and I were at Dave & Busters and weren't in the mood for American food, which was what we were all surrounded by so I decided to give P.F. Chang's a try. + +We came on a Saturday night without reservations, so we had to wait 45min :( Luckily time went by fast while I was on my phone looking at the Yelp reviews for this place. When we were seated, we ordered immediately and our server was very friendly. We got the salt and pepper calamari as an appetizer and then the Dan Dan noodles and Shanghai shrimp with garlic sauce. The food came out quick which was a huge plus considering how busy they were. The calamari was okay. I felt like the strips were cut too thin and we should have received more. The Dan Dan noodles were actually very delicious and flavorful. I really enjoyed them and definitely recommend them. The shrimp was cooked well and was also good. Overall I was happy with my first time experience here and would consider coming back if I'm ever in the mood for Chinese/American food.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> LOVE the food!!!!!! Try the bomb pop martini. The service has definitely Gone down hill in the past year. And when I've told the manger he just doesn't give a shit. It's either hit Or miss with service. But food is ALWAYS GOOD[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The service was lackluster. Coffee was warm but delicious. Limited to one cup, apparently, as the waitress never offered a second. + +Daughter had sweet and sour shrimp. Wife had spicy chicken. I had wonton soup. Dumplings as an appetizer for the table. All arrived warm. The brown rice was dry as sand and the white rice was delayed by rice cooker problems. Also dry as sand. I guess that is how they serve it. + +The base flavors for the shrimp and chicken were nearly identical. I had expected them to be more diverse. + +In all, expectations were not met for what is advertised as upscale. I'd rather have the local Chinese cuisine which more flavorful, and much less expensive.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> First time eating at PF Chang- thought the food was fine but I'd rather go to an authentic Chinese restaurant any day. It felt like a Chinese version of the Cheesecake factory. + +Anyway, it was a Saturday, late afternoon, and despite lots of empty tables we had to wait 20 minutes to be seated and after that waited 30 min for our food. I don't know if they were just short staffed the day we went but I wasn't impressed with the service. + +Some nice items on the menu include the lettuce wraps and the salt and pepper calamari, which comes with a separate dish of salt and pepper for dipping. The sesame chicken was also very good. Other things were fine, just not memorable. + +I think this is an OK place to eat if you happen to be shopping at the Waterfront and don't mind spending a little time over lunch or dinner. If you want to get in and out in a hurry, don't come here.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This was my first time at this PF Chang's and I was not impressed. The service was extremely slow even though it was a Sunday night and the restaurant was not very busy. The portions were small. + +They were also playing 5 year old pop music really loud. Pop music?! Come on--this is an ""Asian Bistro.""[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I was unimpressed with my food and I am even more sad to see, now that P.F Chang's mass produces frozen dinners. +This is about as far away from Chinese food you can get, unless of course you are eating microwaved warmed shrimp fried rice. The restaurant is cluttered and the music was up so loud. I had to yell to carry on a conversation. P.F Chang's in the Waterfront is a unmemorable experience. Maybe I would have better luck microwaving my own meal at home?[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I really enjoyed my Mongolian beef and pork pot stickers, but +There was NO presentation of pfc mixing sauces. +One of the things that sets pfc apart from the run of the mill Non franchise is PRESENTATION and experience. I was extremely disappointed by the LACK of presentation. + +Reservations: +Our party arrived about 15 minutes before our 5:30 reservations. + +At 6:11 we were informed our reserved table had been given to another party . Obviously someone dropped the ball here..... + +When we requested silverware for the table. Our waitress blamed it on the hostess. Yes, theHostess should have provided silverware.. However It was unprofessional of our waitress to pass buck. As a Patron I could care less who's fault it is; just $@&&@in fix it. Defiantly took away from my pfc experience. + +My Hot and sour soup is usally served with""noodley"" things that I drop in the soup. We weren't given any ""noodley "" things . Not trying to be a jerk but all things being equal the pfc isn't selling food as much as they are selling an experience. This experience is what sets this restaurant apart.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have mixed feelings about this place. I wish I could give 2.5 stars, but I'm in a good mood so I'm rounding up today. + +This was my first time here and I honestly wasn't sure what to expect. The first thing I noticed when I walked in was the layout of the dining area. It seemed less intimate than I had pictured in my mind. The tables were all jammed together and the restaurant had a crowded feel to it. Fortunately, there wasn't a long wait as we had made a reservation. + +We were seated at a table in the middle of the dining room alongside a busy throughway. It seemed all the servers were destined to walk past our table. I appreciated that their menu pointed out that their meals were ""meant to be shared."" My wife and I decided to share our two meals: Chang's Spicy Chicken and Double Pan Fried Noodles. Before our meal came out our waitress set some sauces on the table in a ""here's your sauce"" kind of way. I remember thinking, ""That's very nice, but I have no idea why you just gave us sauce."" There was no explanation - just a little tray of sauces. Our food came out and she finally asked if we like mild, medium, or hot sauce. We picked medium and, with a few scoops, she turned our three sauces into three mixed sauces and I still didn't know what they were for. + +Forget the sauce though, my attention was now drawn to our meal. For meals that were ""meant to be shared"" these sure are little portions. I guess when you go for that high-end presentation you can charge 50% more for 50% less. The food itself was good (in an ok sort of way). I can't say it was the best I've had, but it was good enough. + +Overall I thought the experience was lacking. P.F. Chang's tries to be classy, but does it in a cafeteria sort of way. I was constantly distracted by the front doors opening and icy air pouring across the room. The music didn't fit the ambiance. Our table felt like it was in the middle of the road. The restaurant was loud and crowded. The girls at the table next to us were taking those annoying duck-face puckered lip pictures... + +I think our experience may have been different if we were seated at one of the booths along the side of the restaurant, but no such luck.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Surprised how empty the restaurant was tonight. First time at this location. Great service, but wasn't hard to do..... + +Had a combination Orange Shrimp and Chicken and Chicken Fried Rice. It was typical PF Changs (Very good). You can get the Fried Rice off the kids menu for $2.95 versus $8 for a big bowl off the regular menu.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Let me start by saying that I do like their food. + +Last night I went with my wife and two guests. The apps came out fast and were fantastic. Dinner on the other hand, didn't come out quickly at all. The rice was undercooked, and we told our server. He set the rice on the empty table next to us and forgot to bring a new order. By the time I was almost finished with my meal, another server came over and they brought back another bowl of crunchy white rice. +(is that the way rice is prepared now?) + +I ordered the chocolate cake. I asked for a container to take half home. The server brought out a small container and when I asked for a larger one, she said we can just squeeze it in there, and started to flatten the cake. She then realized that a larger one would be better. + +4 people, not crowded...2 hours total.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My daughter & I enjoy PF Chang's each time we dine there together. I am in Love with the Chicken Lettuce Wraps delicious! It is always a wonderful experience![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've always liked PF Chang's and, generally speaking, this location is pretty good. I typically opt to sit at the bar, where the service has always been extremely personable and fast. + +The food is typical PF Chang's: delicious. As one of the chains that provides their nutritional information, it's also nice to know that I can go there and eat somewhat healthy (I'm all about the orange peel shrimp and steamed shrimp dumplings). While some complain about the portion sizes being too small, I've always felt like they were perfect. I do understand how someone looking at a $15 plate of ""Chinese"" food could wonder why he or she is paying more for less than your standard Chinese restaurant, but it's never bothered me. Most of the meals are consistently good, freshly prepared, and full of flavor. Plus, the sauce that your waiter/waitress makes for you is always a nice addition to any meal. I've tried most of the apps, soups, and quite a few of their entrées and have never been disappointed. + +I've only had one negative experience at this location in the countless times that I've gone, and it revolved around service in the main dining area. I was there for lunch, and the waitress essentially disappeared. I'm not sure if she had been fired, quit, or what, but she took the order and was never seen again. After sitting there for what seemed like an eternity with empty drinks, etc., I finally had to ask if someone else was going to be our server. I had never experienced something like that, but I received free food vouchers for a future visit, and luckily I wasn't in a rush that day, so it worked out. The experience would've made me give the location a worse rating, but one bad experience hasn't outweighed the countless positives: good meals, solid service (especially at the bar), and great takeout service for large orders and smaller ones. + +The only other knock on this location - and it applies to every PF Chang's I've been to - is the insane wait that you'll encounter at dinner time. My wife and I would actually go there more often if we didn't have to wait forever for a table. I love PF Chang's, but I hate waiting more. If you live close enough, get curbside pick-up, or just find somewhere else. I've yet to meet a restaurant worth a 2-hour wait. PF Chang's, included.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> ok so i've eaten here more than once but just thought to write a review on it. now, i'll be honest this is the only one i've ever been to, so i don't know if they're all the same but every time i'm underwhelmed. i get there, look at their giant selection and get excited. then i get my meal and remember that i've never had anything too great. don't get me wrong, it's not bad, but for how much they charge, they really need to step it up or at least give me a huge portion. just saying...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Our last few visits have left something to desire, One of the things I always notice is the demeanor of an establishments employees. These people look miserable, no one smiles or greets you appropriately, it's more like get in, get out, turn the tables, + +The food has remained consistently good... when we can order it. the last time JB and I came for a quick dinner, the place was not busy yet we were passed by 6 frowning waitstaff without getting drinks... for 15 minutes we were left suiting at our table with our menus closed and sitting on the edge of the table (HINT, HINT) so we left and most likely will not be returning.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> If you look at other reviews you will see that I am a very positive person, but tonight was an utter disaster!! We sat at the bar and the female bartender was miserable. We ordered drinks and she was unhappy that we did. She spent 20 minutes sending text messages and took 3 smoke brakes in one hour while our drinks were empty. We ordered appetizers and they never came out. She actually brought us our check and we never got our food. By the way we were the only people at the bar. Finally a bus boy brought us our food after we payed. We payed before our food came because we thought our table was ready. We finally got seated by the windows. Do not sit by the windows because it was very cold. We ordered our dinner and drinks and guess what no drinks. After our food came we asked about our drinks and the waiter said he forgot. Nothing was comped and no manager was available. This PF Changs needs new management!! We will never return. I will give it 2 stars because the food was great, but the employees are absolutely miserably from hostess to waiters to bartenders. Steer clear until changes are made. It's not worth the headache.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> A big thank you to Chad Cynamom, manager at PF Chang's for making our anniversary night so special. He seated us, brought us drinks and told us about the menu. Every time my fiance and I go to this PF Chang's, we get the best service. Food isn't the most authentic chinese food we've ever had, hence the 4 stars. It is a bit overpriced as well, but the service makes up for it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Came out here with my parents to have dinner. I have to say that our meal was all around worth a 4 star rating, but the lousy attitude of the hostess and the man behind the desk who seemed to be in charge quickly lowered that rating. + +Our food was pretty good. The lettuce wraps are usually my favorite part, and this time it was no different. My mom's fried fish peices and veggies was also delicious. However, my $19 Mahi Mahi was pretty much like eating air... there was seriously no taste at all, and it was tiny! I found myself adding all the extra sauces on the table just to try to give it some dang flavoring. + +If I was you, I would order lettuce wraps for an app and lettuce wraps for your meal. If you have room, lettuce wraps for dessert, too. Oh yeah, and to drink, lettuce wraps.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> singapore street noodles. The end[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Rude unwelcoming short haired black hostess. Drinks were not good. Greasy spring rolls + +Below par on every way. No experience needed to work here[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Walked in tonight, Wednesday, at 9:50, the place was empty. Asked for a table, the hostess told us one moment when she finds one for us, then proceeded to walk to a dirty table and clean it! The phone rang and she answered it as we stood at the door. When she hung up the phone she walked back to the table and proceeded to clean it again!! Didn't say a word to us. Unbelievable! Will not be back there-- rude hostess![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The service started out slow, but they eventually picked up the pace. We ordered the chicken/lettuce wrap appetizer, and we enjoyed it. For the entres, we had the fried rice and mongolian beef, both of which were delightful. I would not mind going back to explore their menu.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We recently went here for a group dinner with friends. I am unable to eat gluten and my server (Denice) was knowledgable and brought me special sauces as not to irritate my allergies. She was amazingly accommodating and when my meal was too spicy (which was totally my fault) she got me something else. I had the GF beef with broccoli and it was amazing. She was personable and friendly and went beyond expectations to make sure our table enjoyed themselves. We were there for a while and were all on separate checks. I've been to eateries before where that was treated with great disdain. Never once did I feel unwelcome. I will go out of my way to eat here again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great food, great atmosphere, little on the loud side but they have turned down the music since the last time we were here so it's much better, good service.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Good quality pork fried dumpling and mongo beef. Bar service was fast and Efficent. Good value. Not a 5 cause dragon eye tea was cold first time around and beef had minor amount of fat. Fortune was even Postive![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I usually have fair experiences with this PF Changs. I've been inside the restaurant, and have used the curbside to go service. I finally decided to review this based on my most recent experience. + +I can't remember her name, but whomever worked curbside to go on Oct 30, 2013 around 6:30PM deserves a mention. She was very nice, and provided us with the exact amount of condiments we listed on the online order form. They're usually stingy with the chili and hot mustard sauces! She also gave us a couple other sauces to try (not sure which ones), but these were very good. + +The food here is always in point. I like to get the edamame, sesame chicken with brown rice, and the flour less chocolate dome! + +I'm reducing a star because of past experiences with service.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've heard it's very much a chain and that it's not at all authentic Chinese food, however despite all that I have to admit the food was good and the service was excellent. There is quite a disconnect with the loud Rock music played in the dining room and the serene Chinese decor, but I figure it works for somebody! I ordered the Ginger Chicken with Broccoli and the meal was quite tasty. The prices are quite reasonable. Just as long as you are not looking for authentic Chinese dishes, this restaurant will definitely serve in a pinch.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Really awesome food and amazing customer service. I really enjoyed my experience here if I am back in the area I will be certain to come back to this location.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I seriously don't know why people love this place so much, the food here is horrible. The rice is never cooked properly.. And it's not even Asian food. It's fake asian food. I never come here anymore.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I will say make a reservation since it's pretty busy on a weekend! We got seated quickly with a reservation. Our server was excellent despite how busy it was. He was also helpful with recommendations and let me sample a couple wines before picking a bottle. The manager was also great. We weren't in love with one of the dishes and the manager came out and talked to us about what we were looking for and gave us a complimentary order of what he recommended. I will say this - they know how to treat their customers. We'll definitely be back :)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> First, this is a big chain - not my favorite type of eatery. For me, four stars is max for this type of establishment for the simple reason that no one has license to create anything truly unique... + +However! The Chilean Sea Bass Marinated in Oolong Tea is freakin' fantastic! 10+ + +Now - everyone was happy with their meals and let me tell you it was a ridiculously busy night, servers were threading their way through patrons waiting to be seated and our service was very good. + +I've been to PFC Vegas and PFC NYC - our Homestead PFC definitely beats them both. So many great little places to try in the 'Burgh, but I wouldn't resist going back to this particular PFC.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Once you go Pei Wei, you never go.... PF Chang's (if you can help it). + +Pei Wei is Chang's super convenient and cost friendly fast casual eatery that started infiltrating the Detroit market in 2007. Subsequently, that was the last time I stepped into a PF Changs until I recently moved back to Pittsburgh. Going from a Pei Wei to a PF Chang's is like watching paint dry or sitting in rush hour traffic or attending a WNBA game; it's so methodical and time consuming. + +On our last visit to this location we were accidentally sat in a section in which the server had been cut from his/her shift. By the time we flagged down a server and everything was sorted out, we could have been halfway through our meals at Pei Wei. Add in the wait time for a table, the sauces shtick, and presentation of the check and my head's about to explode. Chang's is more paced for retires and people on dates, not my lifestyle. I get it, it's a me problem. + +With that said, the staff is very nice and helpful at this location (star). +I can get a beer or alcoholic beverage while I wait (something that's not an option at Pei Wei) (star). +Plymouth Gin is stocked behind the bar - that's a chain first! (star). +I found a dish I love not available at Pei Wei - Salt and Pepper Prawns (star). + +So until I get sick of the Prawns or a Pei Wei opens in the Pittsburgh market, I'll continue to go to this location.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I ordered dinner one day and was very satisfied after my dinner. +The food was delicious. +I enjoyed it some much I bought lunch there the following day. +The is now one of my best places to eat. +I would recommend P.F. Chang's China Bistro to everyone.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We had another opportunity to eat here today and the experience was much improved. There was no crowd to fight and we weren't seated near the door as we were last time. As I expected, getting a table near the edge of the restaurant provides for a much nicer dining experience. Our service was good and they accommodated our 1 year old nicely. I appreciate that they serve steamed veggies on the kids menu. + +I still left with the impression that the serving sizes were small in comparison to most other places, but we were satisfied and happy.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Went here for lunch yesterday with a friend and it was so yummy! Started out with chicken lettuce wraps and it was totally hitting the hungry spot! Lol. Tried chicken lettuce wrap at my places but this place is one of my fave. Their wonton shop is also full of chicken chunks and shrimps as well... which is different bc you don't normally get all that in a wonton soup bowl. By the time we ate the lettuce wraps and our soups, we were almost full. LOVE the way their Mongolian beef is made here and my friend had the crispy honey shrimp and it was so yummy as well. Definitely will be back because this place is clean, service is quick, food is delicious, and the price isn't so bad either.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We went last night Saturday night to P.F.Chang located at the Kierlands in Scottsdale. Terrible Experience!!! after waiting over one hour to be seated, we ordered calamari for appetizer which came with a horrible strange salty sauce and salt and pepper mix on the side. then I ordered beef and broccoli and my husband ordered a vegetarian dish with peanut sauce . After a long wait my food came so salty that I could not even eat and as much as I hate to complain but I had to let the waiter know, so he went to get me one with less salt. My husband's dish was OK. then the second one was a bit less salty but the meat had a terrible liver kind of taste which totally turned my stomach. I feel the reason they added so much salt was to hide the bad tasting rotted meat. Very bad experience. Our waiter was kind and sympathetic. ruined my evening out :([/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Let me start off by saying I have mostly simple tastes, and my favorite lunch spot for Chinese has been the New Dumpling House in Squirrel Hill. But since that restaurant is undergoing renovations, I was forced to try something new. + +So... I thought I'd try the chain PF Chang's Chinese Restaurant at the Waterfront. Wow, what an unsatisfying mistake that turned out to be. + +I started with a cup of their Wonton soup. At $2.95 it wasn't too outrageous of a price, the broth had some flavor and there was much more in it than I was used to, including three giant basil (I think?) leafs that covered everything beneath. In the broth were chunks of chicken, two shrimp, some sliced water chestnuts and two ""pork""-filled wontons. As I said, the broth had decent flavor, but the wontons were thick, doughy and under-cooked, and the chicken chunks were dry, which is amazing since they were drowned in broth! On a scale of bad to good, it was kind of meh. + +Next came my ""lunch-portion"" order of Chang's Kung Pao Chicken (the dinner portion is $5 more). + +At the New Dumpling House, this dish is served with a delectable dark, rich, tangy sauce, which I was really hoping for... Not at PF Chang's. + +On my plate I received about 8 quarter-size chunks of lightly breaded and browned chicken, 7 hot Chinese red chili peppers (mostly inedible unless they are diced into a sauce), a handful of blanched, unsalted peanuts, a few sliced scallions, and a bed of the most bland brown rice I have ever encountered. Uncle Ben would've been ashamed if that stuff came out of one of his boxes. + +Glaringly, there was NO SAUCE!. None at all. + +I've had Kung Pao Chicken in New York City, San Francisco, and even from a hole in the wall in Bethel Park, PA that was much, much better. Never have I had it served in such a bland, skimpy, and overpriced way! The ""lunch-portion"" cost was $9.95. + +At The New Dumpling House, I could have a delicious lunch, with soup, entree and complimentary hot tea, and I could leave satisfied with just $8 out-of-pocket -- and that includes the tip. + +The service was decent. However, lesson learned. One and done. Never going back to PF Changs.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm not really into chain restaurants but my mom's in town so.... You know. + +The mains are basically a half notch classier than a Chinese take out but I'm just not impressed. $15 for a small portion of orange chicken that is about as good as a cheap takeout seems silly. + +Where I think the restaurant really underwhelms is the soups and salads, I know it isn't the focus of the restaurant but the lunch sides that precede the lunch entrees are just bad. The salad lacks any creativity and the soup was just a bowl of salty beef water.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Still good food but I find that more times than not when we go we have to ask for clean dishes or silverware. I have found this whether we are at the Waterfront location or the Robinson location. Maybe they need a new contract with a new appliance company.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is the fourth Changs I've eat ate. It was pretty good. The food was kinda like it had been previously frozen. Had a strange texture. Some of the changs chicken pieces was stuck together and the breading on the sweet and sour chicken was mushy and falling off the chicken. Overall still pretty good. Would eat at this one again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My wife and I came here a few years ago and you couldn't get in the door because of the line. This was the hottest new place on the restaurant scene and everyone wanted to try it. Fast forward to present day and you'd never believe that was ever the case. Chang's is poorly set up as one large open room that's rather noisy. Food came out quickly but was not as good as the Chinese take out we get from sesame inn. Spicy chicken was neither spicy nor very flavorful and had a mass-produced feel to it. Took half home to eat the next day but ended up throwing it out a few days later. Normally one of the great thing about getting Chinese is looking forward to the leftovers the next day! Another minus was noticing how dirty the floor was on the way back to the bathroom. I don't expect a place to be immaculate in the middle of dinner service but this looked like the mcdonalds on Smithfield downtown. +The one bright spot was our waitress was very good and kept our water glasses filled. We just came from kennywood so we went through quite a few fill ups during our time there. Short of this, I'd probably give Changs two stars. Probably last time I'll stop in here unless I can't get in to any restaurants in the area and need a place I know won't be too busy.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Our family loves this restaurant. My children and I suffer from food allergies. I have Celiac's Disease and their gluten free selection for a Chinese restaurant is great. My children are a completely different ball game. They have a rare disease called Eosinophilic Esophagitus where food attacks their body. They are very limited on their food selctions due to not being able to consume any food with gluten, soy, eggs, dairy, nuts, tree nuts, fish, shellfish, amd corn. This restaurant takes special care of my kids by making sure they get chicken that has not gone through the egg wash. The servers and managers are all trained in how to be careful. Our favorite manager is Joe and favorite server is Kevin. Call ahead if you have any questions and they will answer your questions.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place hit the spot. + +Stopped here before a movie and ate at the bar. We got just what we wanted: quick service and some good eats. + +I recommend the fried green beans with aioli -- soooo good! Who knew I liked green beans?! And this trip I tried some sushi and got the spicy tuna roll. Although it was clearly not pieced together by an expert sushi chef, it was extremely fresh and delish (so who cares if it's not beautiful?!)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Excellent beef with pepper and onions. Waiter made a good wine choice. Fastest food delivery, less than 5 minutes, honest. Both meals less than $30, in and out in 45 minutes.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Gordons in the Waterfront is exactly what I needed for new shoes after I was allowed to walk again after a fracture in my foot. The man who waited on me was kind, patient, and even let me know about a sale going on. The selection and quality of shoes is wonderful. You won't get cheap shoes here but you will get the best. Worth every cent.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Extremely helpful staff that knows exactly what shoes are comfortable yet stylish. The shoes I bought were high quality and durable. I was extremely impressed by the staff.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is by far my favorite Panera location in the Pittsburgh area. Friendly, plenty of room to sit, and good quality food & coffee. Panera is a great place to hang out and read the news - they even have free WiFi! Try their toasted sandwiches, especially the chicken bacon dijon.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I live close by so I go here frequently pretty much for the free WIFI and espresso. But here's a secret - they don't seem to know what an Americano is so often I am charged like 75 cents for a double shot of espresso to which they add hot water upon my request. Needless to say coffee is not expensive here as you can fill up as many times as needed without being hassled. Although there regular coffee is undrinkable to my taste. Pastries are baked fresh and are plentiful. There is other foods to choose from ie whole grain bagels are edible and about a buck with no extra charge for butta. Outside seating and people watching is always a good distraction plus there are all kinds of people who frequent this Panera from the very very old and decrepit to the fashionistas taking a break from Victoria Secrets, Ulta, Wet Seal and the other various shops at this water front location.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Had lunch here after getting my nails done in the Waterfront. It's your standard Panera - lots of seating and a sunny room from all the windows. Our food was made very quickly, even though the place was pretty busy (lunch on a Saturday). Chicken noodle soup is tasty, but there was too much broth and not enough noodles and chicken. I tried their Sierra Chicken sandwich for the first time, and it was pretty good. It's very flavorful, I like whatever they put in their chipotle mayo. It was a salty meal though - definitely had me running to the fountain machine to get more water. + +If I have to get a quick, light meal and only chain options are available, Panera is my best choice. It's definitely predictable and usually tasty. But there isn't much special about it, of course.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I Love all Panera, equally! +I am def a fan of this easy, better than fast food, time-killing eatery. + +Great place for a lunch social/date with good eats and a good place to sit and talk for a while or to get some work done between appointments. + +PROS: +Great Food; +Free WiFi (though some locations are limited to 30 minutes during the lunch hour); +Seating is always tricky at the lunch hour. + +CONS: +pricey for salads, soup and sandwiches; +tables should be wiped more frequently--even if you have to ask a newly seated guest if they would like it wiped, the tables should be wiped! + +For Pete's sake, give a fork with the Mac and Cheese, not a SPOON! lol[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I really enjoy Panera, and this restaurant meets my expectations. I particularly love the Asiago Cheese Bagel, Caesar Salad, Bacon Turkey Bravo Sandwich, Tuna Salad Sandwich, Smokehouse Turkey Panini, Broccoli Cheddar Soup, and Iced Chai Tea Latte. I've ordered all of these items at this location, and they have been very tasty. + +I have had this location run out of the side of French Baguette once or twice. However, last time that occurred, I asked for a bread bowl as a replacement, which I was given for free. + +I'll definitely be returning soon![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've had bad experiences here a few times now. I wrote panera bread and haven't heard back. Bad service all around!!! Basically, we ordered our food, they ran out of what we wanted, so just decided to make us something else with out telling us. When we got our food, we asked why they made us that instead of what we ordered---'oh it was the closest to what you wanted'.....hmmmm how about you tell us that before we pay, and how about you give us our money back. Really, you don't get much for what you pay for at panera. Its not very good at all.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It's the same Panera food you've had before. I like the other ones better as they are often faster at preparing food than this one. That said the food is fine and the staff is nice enough. + +They have warm cookies for $2.00. That is a nice feature.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I like Panera bread but this one is a so so. I always get my fuji chicken salad in every Panera bread I go. All of the other use spring mix to make their fuji chicken salad except this one.. They just use regular salad and salad doesn't taste or look very fresh either. I was kind of excited to find there is a panera bread around us but I am disappointed after trying it. Don't know if we will be back again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It seems silly to rate a chain so I won't talk about the food. + +I just love coming to this Panera because it's right by Barnes and Noble. I recently started getting into the Panera card. Compared to the other Paneras I have to say that this one seems cleaner, bigger, and all around nicer. Of course I would never go out of my way to get here but if you're at Barnes and Noble and aren't happy with the sandwiches there (which I was) I would venture on over to Panera.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Amazing amazing place and I really enjoy to eat there and drink the prices they not high, very good service and fast .[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Panera bread has to be the most inconsistent restaurant I have ever been to. I have posted two pictures of the strawberry poppyseed chicken salad. The first one looks delicious the second one looks like they could've used a smaller bowl. It did not even look appetizing.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The food was fine. It's a chain. I'm not rating it. + +The service was absolutely horrible. It started well enough when we ordered lunch, but ended horribly when my daughter said we should get a treat for my husband. + +Between being ignored by the girl at the counter, her not listening to the order, then arguing with me when I told her I did not ask for what she brought me, I really can't decide which is worse. I rather spend my money somewhere local where they appreciate my business, rather than take attitude from Panera employees.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This use to be my go to Panera Bread. When I worked in the area I would stop here before work to grab my breakfast and then stop to get my lunch as well. I was happy when I left the area and moved on to bigger and better things. My waist also appreciated it. Those scones are delicious. + +I recently stopped back here when I was shopping and was pleasantly surprised. With all my new allergies I came in here hoping to get some bread. Not knowing, nor doing my homework before I showed up, I asked the manager if one particular bread had corn syrup in it or not. Not knowing the answer herself, she was kind enough to pull out a binder that contained all of their recipes, ingredients included. After looking through it for a few minutes I was able to select the bread I wanted. They will sliced the bread thick or thin for you there right now. If you would rather slice yourself, I am sure they will wrap it up and you can go on your way. Yes, it's true, it may be a bit more expensive than your cheap bread on the grocery store shelf. But it is much better tasting.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It was my first time here. Was recommended by my coworker. However, I was a little unsure as I've read some bad reviews about this place. + +The first visit was great. The receptionists were helpful and gave me guidance on how to get my dog licensed. Everyone seemed happy and talkative. + +Dr. Bezak was very nice. He had a smile on him the entire time I was there. He was very quick to give me information about anything and everything relating to the dog. Overall, I had a good first visit and definitely going back. + +The only thing that made it didn't earn a five-star is that my appointment is at 12:15pm. The entire office have their lunch at 1pm. So I can tell there was alot of hustle to get me out of their asap. I don't mind that it was a quick visit, but I would have liked to had time to ask more questions. If you want adequate time with the doc, consider making your appointment after their lunch.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The problem I have this experience compared to my last is that the examination lasted 3 minutes. The vet checked the ears, teeth, and nails then called it a day. + +I came home looked at his teeth and saw my pup had a ""slab fracture"" which was still attached to the gum. The vet didn't mentioned it during the ""exam"" other than telling me to buy a finger brush to brush his teeth. + +I was primarily there for a vaccination shot but if they're going to charge me for a examination, they should do a proper examination. I just felt I was rushed out of there. + +I took my dog to another vet where they told me about the slab fracture, gave me info on how it usually happens, potential problems that it can cause, and recommendations on ways to fix the problem.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> As not only pet-owners, but as dog breeders let me say - we love this place! We've heard some bad things from several acquaintances and counldn't believe our ears...Dr. Bezak is great and the staff is really friendly and helpful.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I only allow my dogs to go to Dr. Bezak. I've had a couple Chow Chow's who a lot of vets are afraid of. Doc had a Chow himself so knew what to look out for in the breed. He has taken good care of them over the years.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I mean, it's Target. It has everything. You just need to know what to buy there, and not get sucked into the convenience of buying everything in one spot. + +Beware -- though their merchandise looks nice, and it's a good buy for a student, you don't want to make long-term purchases here. The zipper on a skirt I bought broke the first time I wore it. I've heard horror stories about disintegrating comforters during their first wash. + +That said, their store-brand toiletries and other sundry items are fairly cheap, and they have a wider selection than Giant Eagle or CVS. They also have a cool program with Flickr.com -- you can upload your photos, order them online from Target's One-Hour Photo kiosk, and pay by credit card when you pick them up. + +I love their cheap accessories -- glasses, bags, jewelry. Along with Claire's and Filene's, Target is my favorite place to shop for those things.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> What can I say, I'm a shill for Target! Like another reviewer says, you have to watch the impulse buying here because it is so easy to do! + +But as for the name brands here, I've never had a problem with them. I bought some Woolrich blankets and sheets here that my husband and I have been very satisfied with. The housewares section here is positively unbeatable. My husband Rick is an amateur chef and he could blow his paycheck on the kitchen utensils. He particularly likes the Michael Graves ones. He is also an amateur photographer and he still works with film, so he likes the film development here. + +Me, I also like buying household cleaners and personal items such as soaps, toothpaste, deoderant, etc because the selection is so good. I've also purchased a lot of my casual wear here.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Oh Target! You are big corporate America! But how can I not love you so? Your prices are the best whenever I need household goods like detergents, cleaners, etc. For personal effects such as toiletries, soap, etc, you can't be beat! Your cookware and bakeware department is every bit as good as Macy's! + +And I see you have the retro tees too. You know: Yes http://www.dovenetq.net.au/~mahayes/Graphics/YesLogoFullCircle1.jpg Boston http://www.vinylrecords.ch/B/BO/Boston/Boston/boston-63.jpg Led Zeppelin http://henrikfalck.com/blog/uploaded_images/LedZeppelinLedZeppelinalbumcover-716782.jpg We know what ""retro tee"" means: faux aged, catering to boomers and teens, and costing way more than they origianlly did. Oh and made in China of course![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> OMG. Target is my fav store ever. I love the staff they are also so helpful and friendly. They recognize me being there quite often!!! I also greatly appreciate being able to use a target coupon AND a manufacture coupon!!!!! I save so much money shopping there and now I save 5% everyday using my target debit card!!!!! Ah I love this store!!!!!!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> After working for the rival of Target for years, Target has become my favorite mega chain store to shop at. Although it does not seem to have every single item as other stores I'm still able to get in and get out in a hurry. + +Depending on the time of day, it may be a task just to find a parking space due to the traffic light at the end of the road. If you don't mind walking a bit, the aisle where the pharmacy sign is on the building usually has spots closer to the front of the store. + +The only downside I can find for this location is the smell of overly burnt buttered popcorn as soon as you walk in due to the cafe location. I prefer not to vomit as soon as I walk into a store, maybe after about ten minutes in I'd consider it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is a really great pharmacy - friendly, quick, knowledgeable, and inexpensive.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Target is pretty standard. If you've been to one of them, you'll know largely what to expect from this one. That being said, this store is clean, and the deals one clearance can be good. Just make sure to check the circular and the website, as sometimes additional coupons can be found that the store personnel aren't aware of. + +The electronics department staff are not very knowledgeable, and tried to pressure me into buying a different TV by repeating marketing lingo, but were unable to explain what their claims actually were when challenged on them, so make sure to do your research beforehand if purchasing electronics.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Target is one of my favorite stores -- I just love wandering around late at night when the store is quiet -- it's just so therapeutic! This location is now my closest store, so I drop by pretty often. + +This store is pretty average. Inventory and customer service aren't particularly stellar but isn't poor either. I've generally been able to find what I need here and check out pretty quickly. + +In addition to the common pharmacy and photo studio found in most Targets, this location also has an optical department. Of the 10-15 locations in the Pittsburgh area, only this store and the Cranberry store sell glasses. I purchased a pair of glasses and sunglasses through Target Optical three years ago and have been very happy with their product and customer service.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It's not the greatest Target of all time but it still meets all of your basic needs. + +If you're looking for produce, lower prices, and bigger selection in every department then head to the Target in East Liberty.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I was in and out, and I didn't wait in long to long so I'm happy.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've been to many Targets and they're all the same. However, this particular one is currently being remodeled. Children's clothing, toys, electronics and health & beauty items have been moved to other parts of the store. There is a new Starbucks that is now open. The cafe that is there has been remodeled and will serve Pizza Hut pizza and other new menu items. The area where the electronics used to be it is now going to have a small grocery section. Basically, this Target in Homestead will eventually look like the one in East Liberty. I like this Target, so I am pleased with the new changes (especially Starbucks)![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It always feels like everyone who shops at this target is moving in slow motion. Just sayin'. + +Otherwise, it's pretty much so like any other Target. The lines were crazy long today and I was only buying one thing. I was relieved when they sent a few more cashiers in and opened up some more lines. It definitely expedited what was looking to be a very long wait.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Target. + +I like Target more than I like Walmart. Walmart is bad. + +I like Target enough to return. I like it enough to pass by any Walmart that my throw itself in my path. Does that mean I love Target? No, it is just OK.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Watch out when it looks like something is on sale. They mark a rack or table with a big buy one get one or 50% off sign, then only some of the stuff on the rack is on sale.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> OK I know what you're thinking - You're a chick! Why are you rating MEN'S Wearhouse?! Well recently the BF and I went shopping for some business friendly clothes for him. Our ""wardrobe expert"" (and I feel terrible because I forgot his name) was incredibly friendly and helpful that I couldn't help but think - WHY DON'T THEY HAVE STORES LIKE THIS FOR WOMEN!!? Someone who helps you - no matter your size or height, finds you the pants that fit your body, the dress shirts, the jackets, etc. This man was absolutely STELLAR! Incredibly personable and he knew his job well. The BF left with exactly what he needed and I may or may not have talked him into a few other items... What can I say, I like a sharp dressed man (cue ZZ Top). So if you're looking to make your man a little more stud-ly with a jacket, tie, dress shirt, or perhaps a full suit, stop by Men's Warehouse. You'll be drooling over him in no time ;)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Let's start this review by saying that when we are at that point, my girlfriend and I will be going to Jos. A. Bank for mine and my groomsman's suits. Allow me to give you a numbered breakdown of the issues we encountered when renting from Men's Wearhouse to be the groomsmen in our friends wedding. + +1- They never contacted us after the fitting after saying there would be a followup call. The other groomsmen and I had to follow up repeatedly to get an answer as to when our tuxedos would arrive and the staff were very short with our honest questions over the phone. +2- They sent two of our tuxedos to Homestead when we asked for them to be sent to Ross Park Mall during the fitting. +3- When one of us called two days prior to the wedding to ask if our tux's had arrived the guy answering the phone said ""Oh... I don't know"" (insert an awkward, pregnant pause here while waiting for him to say ""Let me check that for you"") he instead said ""Well, I'm going to hang up now."" And he made good on that promise, and hung up. +4- Despite saying we'd get a call a few weeks ahead of the wedding to be resized in case one of us gained a few lbs over the winter, this call never came so we basically had to hope that everything fit as it needed to. +5- We were at one point informed that MW had our emails on file and that when our tuxes arrived at the store we would receive an email letting us know. Not a single groomsman received any such email to that effect. +6- One of the groomsmen randomly received a black tie while everybody else had white. Another received no studs. We discovered this approximately two hours to show-time while relatively far from civilization. +7- On picking up my tux I informed the associate ""I'll be unable to get to a Men's Wearhouse for a few days after the wedding, is this alright?"" to which she responded ""Yeah that should be fine"" so when my girlfriend graciously dropped off my tux for me a few days later and learned of the $100 late fee, I was totally caught off guard. +8- My girlfriend was also caught totally off guard by the associate at Ross Park Mall who was incredibly rude to her when he informed her of said late fee. +9- As the Best Man I was given a coupon card for $50 off my next rental at Men's Wearhouse. Since I am in another wedding next month with rentals from MW I figured this would be an opportune time to use it. Imagine my shock while paying for the next weddings rental, when I presented the coupon and was told ""Oh, that isn't for this. That is intended for YOUR wedding. Oh and it expires on December 31st of this year."" +10- The groom himself decided to use a coupon to purchase a suit for the wedding and to own, rather than rent a tux for the occasion. He was ensured by the Homestead staff that the coupon would be fine for this purpose and got fitted for it. When he went to pick up his suit and pay with the aid of said approved coupon he was instead forced into an argument with an associate who insisted he could not use the coupon towards the suit that an associate a few weeks earlier had insisted he could use. Granted, now I am speaking for another person so take that with as much salt as you may, but he reiterated this fact to me several times prior to his wedding last week. + +Over my friends wedding weekend, any time anything even went slightly wrong at and around his wedding, the joke between the Groom and his Groomsmen was ""Effing Men's Wearhouse."" For example, at a restaurant, ""Wait I asked for no onions on this sandwich. - Effing Men's Wearhouse!"" ""Noise complaint at the hotel room? Men's Wearhouse."" + +Another groomsman looked at me when we discovered the wrong color tie one of us received and said to me ""I hope you're taking notes for your own impending wedding"" to which I replied ""Perhaps I could find better service from GoodWill of Western PA"" + +Congrats Men's Wearhouse. You became the butt of every joke for every mishap for an entire weekend around a wedding to which you provided the suits. + +TL;DR - 10 mistakes, several rude associates and 1 future groom going to Jos. A. Bank.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I went in to get my suit that I bought last year tailored because I had lost some weight and I couldn't have had a better experience. When I walked in I was immediately created by Bill who was warm and friendly. Anna came out to perform the measurements and mark up the suit. She checked everything, even changes I hadn't thought to have made to make sure the suit fits me perfectly when they are done. Best of all, when I asked if they could ship the suits to me at my house since I no longer live in Pittsburgh, they asked when I was leaving town and promised they would get it done for me before I left the next day. Better yet, they had the suit ready for me early, avoiding the rush for me to pick it up before I left. Everyone was extremely helpful and diligent and I will continue to only get changes done at this store.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I got a cheese pizza delivery from here once, and I feel like...it's one of those places where it's okay and if that's what someone put in front of me I would eat it, but I definitely wouldn't go, ""OMG, let's eat there!"" + +It was just boring to me. (And I love cheese pizza!) + +But some of my coworkers like to eat here on occasion, so maybe some of their other stuff is better. I wouldn't know.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It's not that delish.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I got pizza here on a Saturday night in a pinch. Looking for a place that sells by the slice, I drove around for a while. Not only did they have by-the-slice pizza, but they also had some of my favorite toppings. I also hate crust that's too thick, and -- although I prefer it even thinner than it was -- I was pretty satisfied with the crust. + +The only thing that could be improved is the salad. We got a grilled chicken salad. The chicken and fries were okay, but the rest was pretty run of the mill. + +As for the pizza, I'll definitely be back for more.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> PROS: Great selection and excellent service. They had knowledgable personnel on the floor (manager?) who was helpful. + +CONS: Traffic to the store (one lane) got pretty congested. Wouldn't give me a coupon that I had forgotten at home but that's not a big deal.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I head straight back to the clearance! That's where you'll find the best deals. You will be able to see your savings when you check out because it's calculated on your receipt. Im a huge proponent of going after summer and winter seasons to stock up for next year - boots, galoshes and sandals never go out of style.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have no idea why I've lived close to this DSW for nearly a year and had never shopped here before! This week, I was looking for a very specific pair of heels, and DSW was my go to place. I found a fabulous name-brand pair at a great price. While browsing around, there was an associate who was slowly straightening shoes, but she made no effort to talk to or even smile at me (which is awkward because I smiled at her). Thankfully, the cashier was an extremely sweet and outgoing older lady, who encouraged me to sign up for their loyalty program. Though I didn't really need to sign up, she was so kind that I couldn't say no. I plan on going back very soon![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've been coming to this DSW approximately every other month over the last year. The Waterfront is my go-to place when I need to do mindless wandering and shopping, and this store has been added to my regular itinerary. + +I came here on Friday night needing to zone out and to just try ridiculous amounts of shoes for fun. I headed back to the clearance (unusual for me!) and wow, what a selection! Seychelles summer wedges for $14... Minnetonka suede booties for $50... Both the styles and the prices were spot on! I ended up purchasing a pair of Audrey Brooke summer wedges for $12 along with some Nina silver ""wedding"" pumps for $30. What bargains! + +However, I'm not writing this review update to just talk about fab shoe finds and great deals... + +The first several times that I shopped here, customer service was dismal (as mentioned in my previous review). However, the last couple times I've been here, I've seen associates as soon as I walk through the door and been quickly offered assistance. This is a significant difference from what I experienced in the past, and I just had to recognize this store for making positive changes! + +Keep up the good work - and the great assortment - and I'll be back often![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great on line service!!! 2nd time placing an order on line and they made it easy as far as getting the correct sizes in a timely manner.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This store has such bad service. The service staff are rude rude rude. Save your money, shop elsewhere.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This Bed Bath & Beyond seems like your average store location. I don't have anything too bad or too exciting to say about this location... descent products and descent service. I would just recommend taking all of your Bed Bath & Beyond coupons with you when shopping because staff will help you combine them as best as possible.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love bed bath & beyond! + +The employees at this particular one are always available and helpful! + +The selection, plus the 20% off coupons keep me coming back, and its also where I get all of the things for my soda stream. + +Overall I will be back many, many times[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We just completed our wedding registry at the Homestead location. The customer service was outstanding! One of the employees, Chris, walked around with us to help us pick out exactly what we needed. The wedding registry coordinator, Christina, was also very helpful and accommodating. They treated us as if we were royalty. I would recommend this wedding registry without a doubt![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Basically after being sent here after not having the item at another location, I walk in and go to the exact spot that the item is suppose to be. And yet again, the exact one is not on the shelf. + +Frustrated, I walk to the Customer Service desk and ask whether or not they have it. Which the response I got was to basically look on the shelf. After I told them I did that already, one of the employees had an ingenious idea. Instead of checking the kitchen part of the store, why not check the bath part. What do you know, that's where it was. + +So that just makes me think that they had this item at the other store, but just weren't in tune with knowing that the item was located in another part of the store. + +Everything after that was a smooth ride. Wedding registry updated, purchased, and gift wrapped. Yes, these places have an area that you can gift wrap for free. It says it's a do it yourself area, but for some reason an employee did mine for free. Only downside is that some of the gift wrapping that some of the wrapping items have the store name on it, which might look a bit tacky.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is a very small, yet nice store. The associates are nice and helpful. Not much else to say about this particular store. Just a pleasure to purchase from...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We had the worst possible experience at the Eat N Park at Waterfront on 2/12/10 at around 10pm. Our waitress (Annemarie) was inattentive and got us the wrong order. We ended up with a dish we had not even ordered and still got charged for it on the check. + +One of my friends ordered a Buffalo Chicken Sandwich, which according to the menu description, should've had lettuce and tomato in it. But the sandwich that arrived on our table had none of those ingredients. When pointed out to the waitress, she just brought some lettuce and tomatoes in a plate! How crude! + +Spoke to the manager after paying the full check and first of all, she did not even offer to re-imburse for the item we did not even order, and that had been forcibly thrust upon us. + +When I asked the manager about the Buffalo Chicken sandwich not having any lettuce and tomato, she said they just got new menus and that description is not correct and that Buffalo Chicken Sandwich is supposed to be without lettuce and tomato! What a lame excuse! Even your online menu says under the description for a Buffalo Chicken sandwich that its supposed to have both those ingredients - ""Served with lettuce and tomato on a fresh-baked Kaiser roll."" - That's what the last line in the description of Buffalo Chicken Sandwich says. Shame on you Manager for lying! Instead of admitting her fault, she was blaming it to a new menu! + +Not only did we have to pay for something that we didn't order or eat, but we got sub-standard food that was different from what was described in the menu, and had to deal with a really bad waitress and insensitive and deceitful manager to top off the whole experience. + +I am never going to come back to any Eat N Park location ever again, and will never recommend one to any of my friends either. What a waste of time and money! Plus dealing with callous and lying people - my goodness, I surely had my patience tested this evening![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Much like every other Eat 'n Park (3 or 4 stars worth of chain-diner food), except the last five times I've been here, the service has been damn, damn, daaaaaaaamn slow. It's always fun to see the staff smoking out back while I've waited an hour for some scrambled eggs.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> If you must eat at Eat N Park, this is the one you want to go to. Why you ask? The corporate offices are right next door and the suits are there every day, breakfast lunch and dinner. + +When I spend a few hours with dear old mom, she enjoyed spending a day at the Waterfront, she loved the since closed 39 center store, where she could buy her monthly greeting cards for 39 cents each. Then we drive over to this eat n park where she has her breakfast smile and I enjoy an egg beater sandwich and fresh fruit. + +This place is spotless, the salad bar always looks fresh and the food is good, for a chain.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I like this Eat'n Park. Even though it is a chain, not all of them are created equal. The wait staff and kitchen staff really make a big difference in whether or not an Eat'n Park is worth patronizing. Eating here, I change my mentality a bit. I always order the seven dollar BBQ burger with the salad bar add on for two dollars. In my mind, I always see myself ordering the seven dollar salad bar with a two dollar hamburger. When the salad bar is kept stocked, it has some really good and fresh items. I love that they have spinach and not just iceburg lettuce. I wish other Eat'n Parks were more like this one.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great location! I love that you can substitute burger with a veggi patti and that they have gluten free bread. Love love love the smiley cookies :)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Always good food at a fair price. It's not gourmet, but they have an amazing salad/ soup bar that would put most other places to shame. Great fresh food, friendly service, and desserts to go. Can't beat it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The food is usually pretty good, however the service is almost ALWAYS very VERY slow. Most of the staff are pretty friendly and sweet but there are a few sour ones in the bunch that make the experience not as nice as it could be. Although they still technically do their job, you can FEEL very negative vibes from them and see how inefficient they are with the way they do things. It's a hit and miss. Unless you know one of the servers and their schedules. The low rating is mainly for the slow service and the handful of staff members who aren't very pleasant.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> They make a nice breakfast for less than the tip form dinner the night before. That's not bad![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Eat n Park is usually decent. This location though has HORRIBLY SLOW service. Seriously, we never wait less than 10 minutes for a server to acknowledge us, and we live near the Waterfront, so we've given this location the benefit of the doubt numerous times. Each time hoping that the last was just a fluke, new staff, or something. It's not. Doesn't matter what time we go. It seems we are not acknowledged for several minutes, and then the service is mediocre at best. Occasionally, we've had a stellar service, but it's few and far between. Today, after waiting 15 minutes, then getting up to find a server in another section, we were informed that we were sitting in a ""closed"" section. That server offered to serve us, but honestly, we left. I told the hostess who seated us about the mixup, and got a blank stare. I've never had this issue at any other EnP. We left, drove to the Squirrel Hill location, and our orders were taken in the amount of time we wasted at the Waterfront. Mgmt- you have a beautiful, prime location. Get your hosts and servers on the same page![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Very good cheap food. Pittsburgh classic.Great desserts! The oreo pie is amazing! The servers are always very friendly. The salad bar could be a little more clean.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> God i hate eat n park. Only reason i have gone is for the salad bar because u cant find a decent salad bar in this city. Just about every entree iv had here is nothing more than rubbish, except maybe the cheesteak. Only go if u have little kids[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is a stop I hit whenever I head to the Waterfront. It's a pretty large store with lots of goodies. Yes, it takes time to find things I like, but that's what discount stores are about! Overall, of all the TJ Maxxes I've been to (from New Mexico to Boston), this is a pretty good one.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This TJ Maxx is quickly becoming a weekly stop for me! The corporate team is definitely giving this store a lot of love with the product that they receive. Lately, I haven't been able to go into this store without spending at least $50-100. Dangerous! + +As you walk in, handbags are the first thing you see. Last time I visited the store, I was on a mission -- coffee table decor -- but was quickly sidetracked by a large, briefcase-sized, black leather Michael Kors bag priced half-off the suggested retail price. So tempting... but I forgot about this amazing bag when I stumbled upon two quality sweaters thirty seconds later. One was Design History, which is a brand currently sold at Nordstrom, Saks, Neimans, and Bluefly, for only $25. I also found Adrienne Vittadini flats for $29, Meri Meri cupcake kits for $7, Woodwick candles for $10-12, and a luxurious Tahari throw blanket for $29. I walked out of the store minus $120 in my debit account with at least $300+ of product. + +I've also been delightfully surprised by the cleanliness of the store and the fitting rooms and by the friendliness of the staff. I was having an issue with my debit card while there, and the two associates that I worked with were very helpful and understanding about the issue. + +I'll definitely be going back in the next week or two to see what amazing new deals they'll have then![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great variety and exceptional bargains. From home decore to clothes and specialty foods and gadgets, TJ Maxx has got you covered. + +It's hardly ever crowded, store is clean and check outs are quick.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I enjoy this TJ Maxx location. I'm not sure that any TJ Maxx in Western PA has as good of a selection as the Johnstown TJ Maxx, (yes, that's right, I really did say Johnstown) but this one is pretty close. There is plenty of space, and there is a decent homegoods section as well. Not huge, but decent. + +This location always has a few Bliss products, which makes it top notch in my opinion. I mean, where else can you get discounted Bliss products?? + +I generally don't have a lot of success with shoes at TJ Maxx because they never seem that discounted to me, but I have struck gold at this location several times. Last summer I scored two pairs of Cole Haan wedges for under $40 at the beginning of summer, and I've had success with booties here as well. Great deals on shoes makes me a happy girl! + +All in all, this is a great location, and one that I frequent at least a few times per month.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Decent size, decent selection, decent staff. + +I guess that can wholly sum this place up, it's decent. As with many other stores that are like this, the product rotates depending on what doesn't sale well at other stores. Can always snag a deal here. I was able to pick up a pretty sweet Puma jacket for $10, can't beat that, right? + +That being said, there are those times that you may not find anything as well. So really don't get your hopes up if you are looking for a specific item.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I was somewhat disappointed that I didn't find what I was looking for. This is a fairly small Marshalls. It didn't look like the store received the worst items around, they just don't appear to have a lot of diversity like many of the other Marshalls that I patronize. Will I return? Yeah, I will. I had one item in mind that I was looking for and didn't look for very many other things.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> If you're looking for a wallet, a new cheap purse or something of that nature--this is the place to go. + +Otherwise, this kind of shopping just isn't for me! +I don't have the patience for clothes shopping here though. +The racks drive me nuts bc they're in no particular order. + +Its ""Shirts/Sizes"", ""Pants/Sizes"", ""Jeans/Sizes"", ""Coats/Sizes"" +I can't look through a gazillion racks of shirts looking for something I like (aimlessly) in a M or L... I just cant do it! lol +Wish I could, I'd probably find some deals. + +PROS: +Some good deals + +CONS: +You've gotta ""dig deep"" to find 'em[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Went in here to grab a last minute item I needed for an outfit. I wasn't going to hold my breath here either, I know it's a Marshalls and that doesn't always mean the best selection. It's hit or miss no matter what you are looking for. + +This day, was a hit, maybe even a home run. I do have to admit, the Kenneth Cole shirt I got not only looked great on me, but made my wallet feel even better![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Since both Marshalls and TJ Maxx are owned by the same company, I make sure to stop by both locations when shopping at the Waterfront. I generally find nothing or spend only $10 or so at Marshalls, while being enticed to spend at least $50-100 at TJ Maxx. The Waterfront TJ Maxx seems to have not only the same product as this Marshalls plus a whole lot more. All that to say, I consider shopping here a waste of time since I could just drive a block or so and be at a store owned by the same company that always has what I want and need. Sorry, Marshalls, but you're just OK to me.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Finally, I restaurant in Pittsburgh that I can give 4 stars!! Mitchell's is located on the Waterfront and is one of the nicer restaurants in that area. The interior is a classic, clean, modern seafood restaurant-- dark wood, glass, etc... The menu has really great seafood selections and is printed daily. But here's what's great about this place: after 4pm you can get ""small plates"" at the bar for $3 each, and these ain't no Costco fish sticks! Two of these small plates would make a sufficient meal (along with the sourdough French bread they bring out). Finally, while the drinks aren't cheap, they're creative, tasty and fresh. All in all, I had a great experience, and I think this place would be perfect for a date or a happy hour with the girls from the typing pool.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> No pictures! I knew I should have taken my camera! + +My aunt and I went there today for Mother's day. I think we must have gotten the lunch menu because everything looked pretty cheap (I've been to the one in Columbus). My aunt had a chicken dinner (grilled chicken, green beans and potatoes with butter) and I had their Shanghai sampler which had a couple of shrimp, a couple of scallops and a nice piece of salmon, all done perfectly. We didn't order dessert since my aunt had made my favorite pumpkin pie! Anyway, dinner was great, and so was the service, thus the five stars![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is one of the few restaurants I frequent in the Waterfront. Why would you come to Mitchell's if not for the fish/seafood? You probably wouldn't. But you can swim in the Great Lakes beer on tap here and have some nice oysters while enjoying river view. Not many places in Pittsburgh offer these types of views while dining (and that's a Pittsburgh mystery to me). The restaurant is never to crowded and you won't get packed in like sardines in a tin can. So you can enjoy a fairly romantic dinner with your loved one(s). +The food is very good but you may have to shell out a few clams of your own ($$$). If you have deep ocean like pockets put your hook into the sea bass which is always moist and scrumptious at around $29.99. They will cook your food one of several ways. I like my fish broiled, their signature is too salty for my liking. Bread is mmmgood and hot (free). Staff is very accommodating ie you can request to sample a soup and the servers are pleased to do so. I recommend you try their soups like the seafood gumbo. A bowl of this creamy delight goes a long way...bonus they toss in those little hexagonal oyster crackers as reminds me of my youth on Long Island's south shore (but that's another story). Salads a bit skimpy and somewhat pricey (approx. $7.95 for basic house salad). Bottom line is Mitchell's at the Waterfront is well worth taking the splash for if you really like a nice seafood dinner.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Mtchells is one of the best fish places around. I really like their Shanghi preparation of my fish. It's just delicious. + +The establishment is always clean, the staff courteous and the fish, of course, fresh. + +Oddly enough one of my favorite things about going here besides the fish is the bread they give you. It's always so warm and tasty. + +The deserts are also very tasty. I have gotten two that I really liked + +They also have a three course fixed price option last I went that was a great value. I think it was $20/person for lunch.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> An excellent choice for fresh, well prepared seafood located in the Waterfront area in Homestead. I frequent this area for business travel, and you can't do much better without heading downtown. + +The seafood is excellent, with a daily menu crammed full of fresh fish specials, a raw bar, and a list of chef's specialties. The house salad is sweet and delicious, and the 'shanghai' seafood preparation is delicious, healthy, and unique. Try it with the scallops or a white-fleshed fish. + +There is a nice selection of regional beers on tap, a decent selections of wines, and creative drinks (think elderflower and pear martinis). The deserts are adequate, though not a highlight. + +If you're on the Waterfront, you won't do better than this. Enjoy![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I was impressed. + +Went here for lunch. The seafood gumbo was tremendous. I wasn't in the mood for more seafood so I had the chicken blt on ciabatta bread. I'm not sure what type of creamy sauce they put on the bread, but it was delicious. Will go back again. + +The food was reasonably priced for lunch. Dinner would obviously be more expensive but I imagine it's worth the $.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I did not know this is a franchise restaurant until I had looked it up on the internet. This is the only restaurant I was not familiar with by the waterfront. My mom and me sat on the outdoor patio, the weather was very nice on a breezy summer day. +There was a great prix fixe special for $23, what a great price for regular portion salad---the dressing was too sweet for me---entree and mini dessert. +The fish was fresh. My mom's chilean sea bass shanghi style came with sticky rice and spinach. The sea bass had nice texture and was reasonably priced. My lobster and shrimp pappardelle had more shrimp than I expected. My desert was creme brulee, which was very good. I love a good sugar coated dessert.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> A very nice meal in a very nice restaurant + +PROS: +Very good food +interesting choices--not your typical red lobster crap +Great service +Very clean (restrooms, included) + +CONS: +n/a[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I took my cousin from California here for lunch. We were both eating lite since a) I was dieting and b) my family was having dinner at my mother's house and she was slaving over lasagna all day, so if anyone knows anything about Italian mother's, you better arrive hungry. Back to mitchell's, I had the iceberg wedge with bacon, egg, tomatoes and a delicious home made blue cheese dressing. I also ordered a bowl of seafood gumbo which was the best gumbo I ever tasted. It wasn't overly packed with rice, as a matter of fact, there wasn't much rice at all. It was mostly shredded crab, scallops, and shrimp with a very delicate broth that wasn't too thick and the heat snuck up on you after swallowing. It wasn't a lot of heat, just enough to make it exciting. As for the iceberg wedge salad, every once in awhile I need a piece of iceberg instead of a bowl of spring mix (ie: tender weeds). The star of this salad was the chef made blue cheese dressing. It was not overly thick, very tasty and savory. It complimented the bacon and egg on the wedge. The cousin ordered the carrot cake for dessert and it was easily a pound slice. I tasted a little bite and must say it's the best carrot cake I've ever tasted. The cream cheese frosting was more buttery than ""cheesy"", it was a great surprise when you're expecting the normal cream cheese frosting. There were whole walnuts throughout the cake and many raisins, which I love. Also this recipe seems to rely on more cinnamon than I've tasted in the past. I highly recommend it. It was a wonderful lunch and I'm sure she had carrot cake to take on the plane ride back to Riverside.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place has great seafood. The best in the area. I come here for seafood every time. Everything on their menu is good. Their menu changes all the time depending on what was in season. Appetizers are amazing like the raw oysters. Their clam chowder is the best. Really creamy with lots of clams. Wonderful restaurant. You cannot go wrong with anything on the menu. We love coming to this restaurant. Don't forget a reservation on weekends. You will not get a table and will probably wait an hour or two if you don't have one. We never get to the dessert. Always too full to eat dessert. Forgot to take pictures.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Mitchell's Fish Market is a very nice place to eat...for a chain restaurant. And actually, if it wasn't a chain, it wouldn't be too bad either. The atmosphere was surprisingly pleasant - the room was warm and intimate, perfect for a date. It wasn't too noisy or too crowded, and we were seated right away on a Friday around 7:30 pm. + +Our server was friendly, and happy to give recommendations. I started with a house salad, which I told the server I would split with my boyfriend. She brought it to us on two separate plates, which I thought was a nice touch, and more than what I expected. Poppy seed dressing was okay, it's pretty thick and creamy as I remember, but tasty. + +I ordered from the special menu, since they had a bit of a lobster promotion going on. My entree was a combo: lobster tail, and ""lobster pot pie."" Now, lobster is a beautiful thing, but I have to say....it wasn't beautiful here. It wasn't awful, but it didn't taste as fresh as I like (I'm guessing that's because the meat was frozen originally). It's just a shame. Dipping the lobster in butter was a pleasant experience, but it's supposed to be an ecstatic one. + +The lobster pot pie was totes not what I imagined. I pictured a flaky, golden crust, a delicious creamy lobstery gravy, and big hunks of lobster and vegetables. Instead....I got what sort of resembled a small bread bowl made of a biscuit. There was a lot of sauce, which was surprisingly orange in color and very rich, with some lobster chunks and vegetables that appeared to come from a bag of frozen veg (I'd recognize those tiny square-shaped carrot chunks anywhere)! Whaaaaaaaat? It wasn't bad or anything, but not what I imagined. I was a little bummed out. + +So everything we ate was just fine, and nice when you're craving seafood....but I think in future I'd rather just head to the Strip, get a lobster, and cook the sucker up myself. I didn't try their fresh preparations, so I can't say how those were. + +I'd say in the Waterfront though, it's probably one of your better options. Healthier and fresher than most of the other choices. And the atmosphere is great, including the service.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Excellent service, great meal! They had an excellent selection of seafood, and I can't wait to dine again[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Delightful! After biking on the river trail that led us to the Waterfront, we zoomed past what looked like a wonderful patio situation at Mitchell's, right on the river. We parked our bikes and were seated promptly at the patio. The waitress even filled our water bottles for us! The interior of the restaurant is very nice, sea-themed, and clean. The decor is really tasteful and classy. The outside was perfect. It was Sunday afternoon and the weather was gorgeous. Looking out to a serene part of the river is fabulous as well. Our waiter was professional, knowledgeable and friendly. We decided just on a few drinks and an app. The two drinks my bf ordered were AMAZING. The first, muddled basil, grapefruit juice and vodka (I forget the name). SO refreshing! the basil was flavorful and tasted awesome with the grapefruit juice. The second he got was a frothy pineapple-vodka with a huge fresh chunk of pineapple inside. Both were winners. I stuck with a fairly priced white wine but got to test his fun drinks :) The app we got was the Hawaiian Seared Ahi Tuna and it was delicious as well. It was a pretty decent size to split, and came with sushi rice, a red onion/cucumber relish, ginger and wasabi. I believe the tuna was also drizzled with ponzu. It was so good - definitely recommend! My bf couldn't help himself so he also ordered a cup of lobster bisque, which I don't eat, but he said it was very good. He also polished off some of the warm bread loaf that accompanied our meal. This place definitely earns the stars and I had no idea it was even a chain. The waiter said they were expanding, so hopefully the quality and service don't go down. I also checked out the rest of the menu and they use quality ingredients and the prices really aren't bad (it was the lunch menu - I'm sure the dinner menu is pricier.) I felt like I was on vacation and I'll definitely be back![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This was a great find near Pittsburgh alternative to down town scene. Ambiance was great on the deck by the river, and service was excellent (Thanks Melisa for history lessens!). Seafood including Oysters were fresh and well prepared. Price was reasonable for ""Prefix"" menu including scrumptious dessert. What an evening to end a fantastic summer day in Pittsburgh.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> DRINKS: Water for me, Yuengling for my fiance +APPETIZERS: Cup of Maine Lobster Bisque for me -- soo good! My fiance had the New Orleans Seafood Gumbo which I had a taste of it and it was good, but I liked my soup better...very rich and creamy but full of flavor with a fair amount of lobster bits mixed in. The bread they served with the apps was fresh baked (I believe sourdough) and it was quite tasty along with the whipped butter. Our entrees came with house salads - had great elements, but I felt I couldn't enjoy mine because the dressing given was a poppyseed vinagrette and I can't handle too much acidity in my food these days. My fiance however cleaned his salad plate (not a sentence I utter often). +ENTREES: I had one of the specials, Grilled Shrimp and Scallops with roasted summer vegetables and tomato vinagrette (which I asked for on the side). The seafood part was great - the vegetables were so-so. My fiance had the special of Cod stuffed with Lobster (and some other seafood) with asparagus and a lemony sauce - I had a taste of his and it was really yummy, I'll def order that next time! We both finished our plates, which wasn't too challenging b/c the portions were moderate (I got 3 srhimp and 3 scallops for example) but still filling. +DESSERT: Didn't order any +SERVICE: Friendly, though a little sparse. After we finished our meals we felt like we were waiting around for awhile before we could ask for our check. But our server was overall friendly and we didn't feel neglected or anything. +DEALS/DISCOUNTS: None +OVERALL: We liked the variety and freshness of seafood. Def a place we'd consider going to again, which is the main mark of a very good experience![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Got lunch from here today. + +What I sampled: +Maine Lobster Bisque (delicious and the whole reason for getting lunch from here) +Cheeseburger (decent version I only ate about half, but I expect the other half won't last long) + +Overall I enjoy going here, though it is a bit overpriced, but sometimes I am just in the mood for that lobster bisque![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We went here for Valentines Day after some traffic downtown made us miss our reservation somewhere else. We both loved it. The calamari is outstanding and if you get there before 7, they run happy hour which is half off apps and $3 beers. + +I had filet and crab cake and it was delicious. The steak was cooked perfectly and the crabcake was a good size. Atmosphere was good and busy but that is likely because of it being Valentines day. Despite the busyness, the wait staff was very attentive. + +My wife's steak came out rare despite asking for medium but they took it back and recooked it to a perfect medium level. We will def be back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Went on a Saturday, 2 hour wait. food is good, I got some seafood gumbo to go and I won't do that again. Seemed like it didn't have any seafood in it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The service is great and friendly. I got the baked spinach and artichoke dip and it was superb. I love the fresh, right out of the oven bread too. I got the Atlantic salmon, and it was probably the best fish I have ever tried. Listened to other yelpers suggestion of the shang hai preparation, and they were right. Just make sure you make a reservation! Best seafood restaurant in da burgh![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Service was slow, but that was because one of our party insisted that the bartender, her favorite server, serve us in our private room for a party of 8. The food and drinks were good and we woud return.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I am bummed about this- I had high hopes. Here's a rundown of the evening: + +Pros: +- super friendly waitress, Stephanie, who maintained her professionalism and friendliness throughout +- yummy elderflower and pear beverage +- lobster bisque was nice and lobster-y +- hot delicious bread + +Cons: +- oysters were sketch. And I don't feel good about that. Stephanie brought us an order of East Coast oysters to replace the West Coast ones that we sent back. +- fresh grated horseradish had NO flavor or heat- what's up with that? +- scallops were meh- came with weird veggies, unevenly seared, and no real flavor. And at a whopping $25 a plate, I expect some nummers! + +I doubt we'll go back- for those prices, I would prefer McCormick's or Ruth's Chris.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Good food..yummy[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Service an atmosphere was great. I had the shrimp boil and it was very under-seasoned. Much closer to bland than anything.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm not a mean reviewer, if you look at the other places I've reviewed, but this was just so so so disappointing. The Shanghai style Merlin was very poorly done. The meat was extremely bland, with very little seasoning. I have a very low sodium tolerance and yet I still found this fish to be made too bland. The rice was entirely uncooked and it made crunching sounds as I took my first bite. I talked to the waitress and she offered to bring out another side. It wasn't the same. The whole dish was a fail and I don't think I am ever coming back again :([/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I went here on a recent business trip, and there aren't many decent options in West Homestead, so I decided to splurge on the company's dollar and ordered take-out. + +I was highly disappointed in the service, and I only ordered take out. Upon going to the bar to announce that I was there for take out, there were 3 other people at the bar. The bartender had her back to me and it wasn't until a few minutes had passed that another guest told her that she should wait on me. + +After announcing the reason for my visit, she checks on my order (not ready yet) and helps other tables. No offer of water, or a drink. Another gentleman working the bar asked the bartender if she had offered me a drink, she stated to him my order would be right up. He then asked if she offered me a water, to which she replied, her order is going to be right up. He placed a glass of water in front of me. + +Then I hear my name and order announced by the kitchen staff. 3 staff members yelled. . .""it's TAKEOUT"" so back it went into the kitchen to be packed up. + +Gentelman bartender asks female bartender if she has rung me up yet (she had not) + +After more time had passed (how long does it take to put food into a takeout container?) it finally is put down in front of me. She then rings me up. I don't expect take out to be piping hot, but at this point i wondered if it was even going to be room. + +When i go to eat my meal, utensils were not included. I now had to go find something to eat my lukewarm food with. + +VERY DISAPPOINTING experience. Will not be returning.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Will I come here again? Yes absolutely for drinks, they knocked the Ketel One extra dirty blue cheese olive martini outta the park. The ambiance is very nice. Of the 4 types of reviews I give (awesome, OK, bad where they get slammed and bad where I hope they improve) here I am giving the heartfelt ""bad where I hope they improve."" Our waitress was very friendly and did a good job. I mentioned the gritty redskins of the mashed potato. We went with appetizers she recommended. Not good. + +Seared ahi tuna: horrible flavors mixed with the rub, the prep, the tuna wasn't cool inside, the chips were not good, there was no soy sauce but there was wasabi. NOT good. With heartfelt advice, compare this against Outback's ahi tuna appetizer and it's no contest. The chef should do so. (He's a nice guy like me I hope.) + +BBQ shrimp: go try Redstone's (Philly) buffalo shrimp appetizer. It is chilled, very delicious. This appetizer was recommended and was garbage. The barbecue sauce was horrible, overwhelmed and left an unsavory aftertaste in both my and my clients' palate. Gordon Food Service or Sysco BBQ sauce. A real ""must-miss"". + +Cod entree was OK. The skillet beans were too firm, too mature, they need petite green beans. Potato skin had grit in the mashed. Why 1 star? The price was close to Capital Grille, but far from the cuisine. I hope they spruce it up. The place is nice.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Had the blackened fish taco's, the were very good along with a pint of Guinness. Recommended.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> First off I have to note, their Maine Lobster Bisque is amazing. Definately don't miss out on it. + +That being said, we had lunch there and the lunch portions are a good value. I had the Cedar Plank salmon. The fish was fantastic, except that the vegetables were a little bland. + +The atmosphere at the restaurant is quite relaxed, and I don't think I've ever seen it get more than mildly busy in there, so it is a nice place to go to have a quiet meal with someone special.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have always had a great dinner at Mitchell's but something has changed. Went there last night about 5:30, the place was maybe half full. We were seated and when it finally occurred to us that no one had been to the table at all to ask about drinks or even bring water, I started timing.... 14 minutes later we decided to leave. Told the hostess what had happened and got a blank stare. Sorry but not going back there again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The service was mostly friendly but I was disappointed in my meal. My meal was way over cooked. The soda was flat and the carbonation needed changed and I felt like we inconvenienced our server by asking for new ones. Overall, I thought it was mediocre and I was expecting more for the prices.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The food was really good, but the prices were pretty high and the portions were on the small side. The desserts were the high point of the meal for me. I got the ""shark fin"" pie and it was really good. The waitress thought I wouldn't be able to finish it... but I showed her. Take that, waitress.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have passed by this place a zillion times and never given it a second look. I thought it might be a Red Lobster knock off. Then I asked a friend if they had ever heard of it and they had, and liked it. + +I was pleasantly surprised by how nice the ambiance was inside. Very cozy. Much more upscale than I had thought it would be. The service was terrific. Lots of things to choose from on the menu. A bit pricier than I had imagined. Most entrees were anywhere from $17 to $30. But this is Pittsburgh and this is seafood. + +That said, they started us off with really delicious sour dough bread. Butter was soft which I like. Our entrees came pretty quickly. I had a seafood assortment of blackened talapia, grilled sea scallops and salmon cooked on a plank. The scallops were just done, I like them cooked a little more. Everything else was pretty good. +My beloved had the crab cakes and really enjoyed them. + +We'll probably be back, but will order something different. We liked it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Food was excellent. Went for the Sunday brunch and loved it. I highly recommend the steak and eggs with the zucchini pancakes, really an outstanding dish. Oh, and if you get the carrot cake....one is enough for everyone! It was huge, and it was soooo goood! I don't know how they can make something taste that good and cook it in such large volumes. Really was an excellent experience, my only reason for not giving it a five star review was that there was too much time in between our courses. There was probably a good 40 minutes that passed between our salads and our entrees. That's a little long for me when I'm at a brunch. Usually I don't eat a breakfast if I'm going to something like that, so 40 minutes was too long for me.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Food was only ok. Had lobster bisque soup not to good. Had the shang Hai Seafood Sampler. The scallops were hard, over cooked. The samon was good. Shrimp had no flavor. I will say the service was the best. Our waiter was great!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> absolutely delicious. wonderful service.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We had a bigger party and I think that might have flustered the waitresses just a bit. They forgot about our waters until the food came out, but were super apologetic when they did bring them. The food was ok. I ordered the crab cakes they were a bit heavy on the breading, so I would give them a rating of, ""eh"". My friend ordered a steak, asked for medium rare, and it came out...well done. He was too hungry to complain and just ate it. We might go back again, and this time maybe take a bit more time looking over the menu.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Very very good chain family restaurant. I had their yellowfin tuna steak shanghai style and it was great. Service was excellent and the party of 5 I was with swore they could eat there every week as the menu was extremely diverse. It's hard for me to give a chain 5/5 but this is pretty close.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Love this place - they were very accommodating to me, Peanut and Gramma (she goes often). Solid wine selection and Gramma says they make a good Margarita. We all enjoyed all of our food as well. Great view of the Mon too.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Beautiful decor. Very genuine staff. Very clean washrooms. Delicious food. I tried the market trio. The blackened tilapia was nice with a little bit of spice. This is a great place for a seafood lover.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Amazing valentines dinner and service! Curt was simply a wonderful server and the food was fantastic. + +Only negative was a few overly salted bites. But as someone who is a salt minimalist. That could purely be my palate only.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The tuna was enjoyable and the service was prompt. The house Chardonnay was buttery and was a good compliment to the fish. It was a Tuesday night so the place was busy but not crowded. Since I wasn't ""wowed"" by the place I won't give it 5 stars but I had no dissatisfaction to speak of. I will be back (if I'm not across the street at the Rock Bottom Brewery).[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My husband and I went to Mitchell's last summer for our wedding anniversary. We both took a half day at work and we arrived in the early afternoon (after lunch but before the dinner crowd). I can't say enough about this place...we have gone here on a few occasions and I've always been please with everything. + +Pros: Nice friendly waitress, who took some time to take our picture (since it was our anniversary), food was excellent and not extremely overpriced, restaurant and bathrooms were clean! + +Cons: None on this visit or any previous visits[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Love this place so much. The food is always so delicious always leave feeling extremely satisfied. The service is incredibly slow though, takes FOREVER to our meals! Even during lunch time when there's almost no one there.. I don't understand I always end up eating here for at LEAST two-four hours. Fish is always fresh, lobster is delicate and tasty, and surprisingly the steak is amazing as well. Clam chowder is rich and creamy-- perfect thickness! Love their salads as well. Definitely recommend this place for a date night :) pricey? Definitely, be prepared to spend at least $20/person![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> First I would like to say that I was hesitant coming to another fish place recommended by some temporary coworkers since the last place they sent me to made terribly ill. +That being said, I came here and was delighted by my server Michael who was not only friendly but incredibly attentive and very sharp. +I originally ordered the Mahi Mahi but alas, the ran out upon my ordering, in which case the manager promptly came to ask me for another upgraded selection at no additional charge. Hence, the tuna. +Now the tuna was amazing. Seared almost perfectly, with the rare flavor still intact. +I would most definitely come back again and if I lived in the area, this would be one of my top spots.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Good quality food here. The clam chowder was excellent and so was the tuna appetizer and the Americana seafood plate loaded with shrimp and scallops in a creamy spinach sauce with small potatoes. I'd go here again if possible.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love Mitchell's Fish Market. 95% of the time, the food is amazing but, when they mess up, they move heaven and earth to make it better. The last time we were at Mitchell's, I ordered the lobster and tenderloin skewers. My lobster was underdone. The server was amazing and replaced the lobster tail even though I had eaten most of it. Then, to make our night even better, comped us a dessert. It's that kind of stellar service that keeps us going back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have eaten some very good dinners here. Although it's a chain, I would say it's several notches above the other chain restaurants. The chef here seems to add some creativity to the menu, so I will be definitely back again soon.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The patio view is beautiful, and the food is good, too! We ordered the Grill Rainbow trout, Shang Hai Rainbow trout, Crispy Ginger cod & rainbow trout. Everyone is happy about the dish. They have music every Thursday, it is a little bit loud, but the band is really good. Will come again![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The lobster rolls were delicious, the blackened fish tacos were light and flaky, not too spicy and had a nice salsa. The white sangria was very refreshing and not too alcoholic. The outdoor view of the river was really enjoyable and the service was quick.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Mitchell's is located on the river side of the Waterfront and out of the crazy ""let's fight to find a parking spot"" area. They do take reservations, but doubtful you need one on a weekday during lunch. It wasn't busy when I was there on a Tuesday at noon. + +Mitchell's has a cool layout - large full bar in the middle, private large rooms for large parties, smaller areas for business lunches, full dining room seating with tables and booths, and an excellent outdoor patio where you can watch people ride by on the bike trail. + +This is a seafood restaurant with lots of good options for fresh in season fish. You can choose from a number of different fish to have prepared for salads, sandwiches, or just as they are. I had the chopped salad and added scallops to it. Delicious! + +The price range is reasonable and you can plan on spending around $15 with your lunch and a soda/iced tea. For that price, you really can't complain. I drop almost that much at Panera on a half sandwich and cup of soup with an iced tea. + +I'm sure it's much busier for dinner but I find Mitchell's to be an excellent place for a business lunch or just meeting friends. I've been here for brunch as well and had an excellent Bloody Mary and eggs benedict with crab.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Went for dinner Friday evening with friends and sat at the outdoor patio. It is so nice and relaxing there with the river and bike trail. The sourdough bread they serve is always hot and fresh. The Chilean sea bass just melts in your mouth, it was awesome. The Cod stuffed with shrimp and lobster was also very good. I had the carrot cake for dessert, it is big enough for 3 people. It was so delicious. My friend had the creme brûlée, which she said was very good. I was here 3 times this summer and every meal was excellent.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My family and I go here whenever there is a special occasion and for good reason. The food is fantastic and the service cannot be beat, at least not when it's coming from the Governor or Kennedy. Best servers in the 'burgh!! I took my Dad there last weekend for his 70th birthday, didn't tell anyone that it was a special night out, but they treated us with such attention, accommodating our needs to a T. Kennedy adjusted meals to fit our taste, suggested things based on what we were looking for, took at least 10 minutes with us going over the menu...I could go on, but needless to say, it was just a fabulous meal and was worth every penny. We got the king crab and bacon wrapped shrimp to start, lobster bisque soup, cedar plank salmon, Chilean sea bass, and a fish medley made to order. We also always get the 7 layer carrot cake, which to me is the best cake anywhere in town. A must go for anyone looking for an amazing meal and excellent service. But be sure and ask for Kennedy, he's a real dude.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Have been here a few times. The wait staff is always top notch and food is very good. I had the steak and lobster tail. Steak was a perfect medium rare and the lobster was also cooked well. Oysters as an app. they appeared fresh and tasted how they should. Overall like in the past we had a great experience at mitchells which is not something I always expect from a chain.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I went to this restaurant last week with my husband and my family. The restaurant is located on the Waterfront area. The variety of fish was excellent, including the fresh fish of the day. I ordered the atlantic cod and it was delicious. +The waitress' service was really good. +I definitely recommend this restaurante.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Excellent fresh seafood. Good vegetables. Good service. Best place to eat on Waterfront.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Top points. +Service. I was there with a large group for a meeting. They gave us a private room and two servers took care of us. They were efficient and very accommodating. Kudos. + +Appetizers: had the crab dip and calamari. Both were good. Servers brought extra chips with the dip as they were needed. I'm always surprised that more chips are not just added to the original dish at this point. Dip was good. Calamari was done well. Preferred the shrimp cocktail Sauce with it versus the Asian type soy sauce that is served with it. + +Wedge salad with bleu cheese. Waaaaaay too much cheese and I like bleu cheese. + +I had the blackened tuna with mashed potatoes and seasonal veggies. Carrots were carrot sticks hardly cooked and dry! Green beans overdone and broccoli had seen better days. Simple green beans would have been more appetizing. +Tuna had blackening spices but needed a better sear on it. Was not over cooked. Potatoes as expected. +Other dishes seen--fisherman's platter. Looked a little greasy, but that's expected from me in a full fried dish. Would be nice if this was offered broiled as well. Crab cakes and filet looked okay. + +Overall I'm always underwhelmed and overcharged here. I guess with chain places you get that, but I want more from a place that charges me 25 bucks for sub-seared tuna.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> A OK! + +Really loved the bacon wrapped shrimp! So amazing with the sauce on the side. This was probably the the best part of the meal. + +I also had blacken salmon with a double order of spinach instead of a starch. The spinach was just steamed without any flavoring... Which is better in the long run, but I wish they had options for sauteed with garlic. + +The service was great as well! We were always taken care of. + +Will definitely bring my bf here in the future.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This was my first time at this location. I've frequented the Upper St Clair Galleria restaurant. There's a lot to like about this Columbus OH based chain. I don't usually eat at chain restaurants nor will I review them because they're typically big food corporate run places that don't care what they feed you they just care about their stockholders. This place seems different to me. The food quality and care seems to be very high. + +The staff is always well trained. I like the decor and ambiance. The menu offers many options. I don't really like the fish preparation options very much and the portions can be small in some of the dishes but overall I am a fan. I do really appreciate being able to buy fresh fish here. I like to buy the trout and prepare it at home. + +We were here for a Thanksgiving meet-up event with 69 other people. The room was a little small and it ended up being too loud too but the staff really pulled it off overall. It's a tough thing to do. It wasn't perfect for sure but the food was surprisingly good and came out hot and fresh. Nicely done.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We went here for Thanksgiving dinner; we had called ahead to check out vegan options, but the person on the other end was a little grumpy about the matter, but there's so little open on that day, there was little choice except to make sure I ate a big lunch earlier. + +I ordered the Thai salad, which is probably the only vegan item on the menu - really just a coleslaw with a peanut sauce and some funky chips. I also ordered some grilled vegetables. Both were good, but not amazing. + +The beer selection was really bad (I mean, dive bar stuff), however the slightly pricey wine selection redeemed the place, and we had a great red and white. + +The service too was pretty good, but I simply can't recommend going here due to the poor selection of vegan items.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My husbands first time. Nice to be able to pick your fish and style of cooking. I had a trio of Jamaican jerk tilapia, salmon, and scallops. All good but too much sauce on scallops. Husband had surf n turf special. Snow crab legs tasty but smaller portion than I expected. Glad they had raw oysters, but no idea where they were from. For $2.50 each you'd think they'd say. Waitstaff friendly but inexperienced when it came to wine. We taught two of them how to open a champagne bottle. Nice time out, but two gripes... #1 Used my phones flashlight to see if there was an outlet on the floor. Felt like an archaeologist finding old remains of dinners gone by. Crumbs, napkins wedged between booth and wall, gum, dirt. For the price I would expect a cleaner place. #2 our waiter kept saying Thank you. After every single sentence, even when it wasn't appropriate. Silly gripe, right? But it was way over the top and felt more like, Can I have a tip? Can I have a tip?[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> In the Homestead area of Pittsburgh. Seafood gumbo was very good. +Broiled scallops were very good, partner had sea bass stuffed with lobster, also very good. Vegetable sides were not as good as the fish. With two glasses of wine the total was $83. In and out in an hour. +I'd go back because the fish was that good[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Good. One of my favorite restaurants in Pittsburgh. Went yesterday with family and enjoyed oysters(very fresh). I always like appetizers more than their entrees[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love old navy clothing, it's vintage styling with good prices. Great jeans too, I love the painter's jeans.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I hadn't been shopping at Old Navy for at least a year or two. Recently, a friend of mine told me that she loved their new Fall/Holiday collection, so I popped by based on her recommendation. I absolutely love their winter outerwear! They have a lot of beautiful coats this year for amazing prices, and I just had to pick up two (only $70 for both with their current sale). + +Outside of their current product, I was impressed by the size of the store, which seems a bit larger than average. Though it is a lot of square footage to cover, I was not impressed by their sales floor customer service. Yes, it's Old Navy, but I shopped in this store three times over the past week and did not have anyone come up to me while wandering around the outerwear. However, the woman that assisted me in the fitting room had a great attitude, and I really enjoyed interacting with her. + +Overall, a four star Old Navy experience... If they could work on their customer service skills on the sales floor, I'd give them a five![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Very bad purchase experience. I bought a shirt with a hole covered in the rolled up sleeves, but they denied my request to return it. I am so angery at this and will never shop their chothes anymore.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> After further consideration, this store does not deserve a 4 star review. The Old Navy product has been pretty weak recently, which isn't the store's fault, but the severe lack of customer service doesn't help the situation. + +While shopping here on Friday, I was one of maybe 3-5 people in the store. I would practically walk into a sales associate but not even receive a glance or smile. No one working here seems to give an iota whether or not product is being sold. To avoid inconveniencing the associates, I will be taking my Old Navy purchases online in the future.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It's just like Old Navy anywhere - well maybe not the one in San Francisco, which is always packed - it ws pre Thanksgiving, so quiet before the storm on Black Friday. + +I picked up my one and only bargain of the weekend - a $2.45 pair of flip flops (it was preparing to snow outside).[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This store is laid out better than any other Old Navy I've been to before. It was so easy to quickly find everything we were looking for. The staff was also very friendly. +If only all Old Navy stores were like this one...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm not too impressed with this particular Dick's Sporting Goods. It is in a great location in the Waterfront, but the selection seems a bit limited to me. They have what you need, but they don't have many options it seems. + +I went in there the other day and it looks like they also have a snowboarding section now, which they definitely did not have last season. They also have hunting, golfing and biking, in addition to the other regular deptartments. + +Your normal Dick's. Nothing spectacular, but it will do.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I don't see to many options in Pittsburgh for sporting goods. Dick's seems to be the big chain for sporting paraphernalia in this neck of the woods. Their selection is poor especially in the snowboarding and biking section. Maybe it's good for small children who want their first snowboard? It is a very average store with average products. I would like to see some attempt to carry more high end products. I am not into fishing or hunting live prey so I am not sure about these departments? I guess if you want some Under Armor products then this is the place to go because I see aisles upon endless aisles of these types of products.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Monopoly complete...I finally understand why (and how) Dick's Sporting Goods can charge the prices they do -- there is no competition. Come on people, I need these warming items to keep from turning into a Sal-cicle and I am paying a lot of money to accomplish this. The only saving grace is that the people are nice and the selection is there. Can we get some lower prices?[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I enter every sporting goods stores as a soccer player, runner, and sports fan, so my reviews will always be skewed towards those particular areas. With that said, this is probably the worst Dick's location that I've ever been to. The selection is very limited for soccer gear, which must be a testament to the lack of the local customer base seeking out soccer gear. It's mostly low-end youth gear, too, which makes it nearly useless to adults or even some teenage soccer players. + +The staff at this location has always been really nice, though, and it's the closest location to where we live, so I still end up going there quite a bit for running and clothing needs (of course, we usually leave empty-handed as they don't have what we're looking for). + +They do have quite an extensive fan gear section if you're looking to support the local Pittsburgh teams, but this store just doesn't have the overall inventory necessary to be considered a ""good"" Dick's location.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It is now a shop and save.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> living alone I love the 5 for $20 deals they have on meat. I also love Faygo products when I have a party or bbq so their sales are always right on time. They don't have as many stores in the area but they are worth checking out. The lines are a lot shorter and the staff is a lot friendlier.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This store has changed hands many times over the past few years and it shows. Fifteen years ago if you didn't get there by 9am you would have fight a crowd. Now it never seems all that busy. Many of the store's best and dedicated employees left or were let go (about five years ago) and product lines change with each new owner. The most recent owner seems to be improving the store and employee turnover has seemed to slow.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> A group of us traveld here to go kenneywood park across the road but we decided not to after what we drove throuhg to get there so we atleast decided to get somthing to eat and man where we happey to get out alive. We where the only normal people in this place. The kids next to us who where only 14 where bragging and saying that they went to jail 2 times in their life. You had people selling their food outsdie the resturant. after seeing that we quickly left and hid in our cars with the doors locked. While we where in there my friend got hit on by 2 girls and they gave him there numbers while the other young guy across the table yeld dont do it dont do it. Must I say more? bottom line is dont go if you are normal and get the hell out of that area cause if you call a shank a happey meal toy then that is the resturant for you.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> By far the worst McDonald's in the world. Employees are to busy playing grab ass behind the counter, to get your order correct. Ninety percent of the time you receive the wrong order, after waiting what seems an eternity. I've even enjoyed the experience of going through the drive thru, only to get home and find no beef patties on my Big Mac. Save yourself the aggravation, and do not go here.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> You know it's bad when a McDonald's gets a 1 star review...I mean, seriously: none of us expect anything fancy when we go to a McDonald's. The whole point of going to McDonald's is indulging in some not-good-for-you food on the go in your busy life. In my case, I just wanted a small meal/snack that wouldn't cost me as much as the stuff in Kennywood would. I hadn't even eaten at a McDonald's in about eight years or so. And I quickly remembered why! + +Forget the fact that McDonald's food isn't great. We all know it's not great. The problem here is that they added insult to injury by giving you the worst customer service ever in addition to not so good food. For starters, I quickly discovered that the drive-thru here is the ABSOLUTE slowest line on planet Earth. You certainly won't be getting any fast food here! Then, once I FINALLY placed my order, and finally got to the window to pay (because of course I spent a lot of time waiting for the people in front of me to even get their orders), a young woman took my card, swiped it...and didn't say another word. I waited thinking she was printing a receipt - nope! Eventually - after whipping out her phone and sending a text or two - she realized I was still there and told me to go to the next window for my food. Whatever, I figured, forget the receipt; by then I was pretty sure she had moved on to other orders and couldn't print my receipt anyway. On to the next window, where I was given my food and drink...and I proceeded to quickly discover they gave me no straw and for some reason, layered my Big Mac as such: bread, bread, patty, patty, bread. ...seriously, how does one even mess that up? I give one brownie point because the fries really were actually pretty good...but they were not worth the wait or trouble. + +I concur with the other reviewers: skip this place. Completely. Just keep driving. Anywhere else is better and less of a waste of your time and money, and the people here are so slow that you'll spend more time waiting for your food then you will eating it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> By far the absolute worst Mcdonalds in the +World. You can pretty much rest assured that, after your long wait in the drive thru, your order will most definitely be wrong. Calls to the owner go ignored. Rice Enterprises own a majority of the McDonalds in the South Hills. They have all gone down hill in quality, service and cleanliness. The owner has to be the problem.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Underated and ignored! if you see this ol time pizzaria near Kennywood stop on by good crust nice and buttery in the sicilian style! Better then DiSallas the only thing I can say that is better then Latinas is Mineo's ! they say the best pizzarias are the little holes in the wall type places and this is one of those enviroments! Small and cozy very nice and relaxing afternoon! To just enjoy with yourself and a friend![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have to admit, the first time I hate here, I absolutely hated the pizza. And I think it was because I was expecting something completely different than I got. Latina Pizza is very different from most pizza shops. Instead if a round thin crust pizza, this pizza is square, thick, and doughy. The crust is not really that good, but that is not why you get a pizza here. It's the homemade sauce. And that it is a family owned place that is really pretty inexpensive. + +The other nice thing about this shop is that it is right next to Kennywood. So usually around dinnertime we leave the park and walk over here to order some pizzas and drinks. No lines, no waiting for tables, no outrageous prices. It's a time to recharge, and sometimes we feel like going back to the park, other times we decide to go home.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Good pizza at a great price. The unique crust that's both crispy and airy is probably not for everybody, but our whole group liked it. The sauce is good too, light but with a good tomato flavor. + +The best thing about this place is the management. They went out of their way for our group of seven and the food was out fast. And the prices: we fed everybody in under $40, with plenty of leftovers taken home.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is the best bike store I've walked into. Their primary focus is on racing bikes, but (as I'm not a racer) the service stays top notch in much lower price ranges. + +Got greeted by the staff, and my girlfriend and I got the luxury of absolutely no pressure as we walked around and looked at bikes. She explained what she was looking for, and the staff explained what they had and what price range she was looking at. I wound up talking to another person working there, and let them try to find a bike that fit. (I'm 6'8"", and as I found out, fit pretty well on an XXL Scott 65cm frame.) + +Anyways, back to my girlfriend's experience. What impressed me was after they had a bike they thought was a winner, they let her go on a test ride around the neighborhood there. And then when she came back in two minutes, told her that wasn't ideal, and sent her back out, with instructions to take the second left and try it on a hill. After she figured out yes, that was the bike, the guy spent at least half an hour fitting the bike to her; he wound up switching out the stem, adding a seat with a little more travel, and getting everything just so. There was no hurry. There was no pressure. + +The amount of interest that the staff showed in getting each person the just-so fit gets five stars; if you want a bike that fits, it's worth it to browse here. + +And, update: I went out the other day, and asked for a price on a bike costing about 25% of the bike I tooled around on there two weeks ago. Without batting an eye, and without a hint of bike snobbery, the owner ran off to figure out what it'd cost me. I talked to him about the differences between a double and triple, and he spent twenty minutes explaining the pros and cons, and gave a strong suggestion on the double. + +That said, the price he quoted me was also 10% under the price quoted by another shop on the same exact bike. I asked for the price of an upgrade to a single part on the new bike, and he quoted me about half the price I expected from doing research on the internet. + +Customer-friendly, well priced, super-high-quality bicycles. A+++. + + +Edit, 4 years later: + +Glen, Beth, and the rest of the crew here are still there, and still awesome. My girlfriend is now my wife. My lowend Trek road bike now has more miles on it. :-) + +It's still a much longer drive to get to Big Bang, but for any work on my bike, I'm glad to make the drive. Friends have terrific luck with Pittsburgh Pro, which is nearer, and I'll occasionally stop there on a ride; that said, for drop-off-the-bike work, Big Bang is my absolute go-to.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is the best experience I've had at a bike store in the Pittsburgh area. I have been shopping around for a couple months for a new road bike (which was going to be my first road bike ever, meaning that I'm fairly clueless about how to pick one out). Also, since I'm a student, I don't have particularly deep pockets. + +At Big Bang, I was greeted basically the moment I walked in the door. I'm kind of shy when I know that I don't really know what I'm doing, but I wasn't pressured or harassed in any way by the staff. Even though my price range was pretty low, they still tried their hardest to find a bike that suited my needs, and they found a bike that fitted me perfectly (and gave me an *excellent* deal on the price). They take a lot of care to make sure you're properly fitted to the bike. + +Also, this is one of the few bike stores I've been to where test riding is gleefully encouraged, rather than grudgingly allowed. Definitely it's the only bike store where they'll tell you ""You haven't tried it out enough, go climb up the hill on it!"" -- they definitely put the emphasis on matching rider with bike, rather than making a quick sale. + +I would definitely recommend this place to anyone who's looking for a road bike, whether they're a seasoned racer or a neophyte rider like me.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've had mixed results here. I would definitely recommend if buying a new bike, but have had much less success with items/parts I've ordered or with repairs.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> When I think BBB... I think the days of simply bringing your bike in for a quick and relatively inexpensive tune-up and a few fixes are long gone. + +This review is more for the repair end of BBB. In their defense BBB does appear to carry some amazing brands of bike (ie Colnago) that you just don't find anywhere else in Pittsburgh. + +At BBB I was charged $250 for a tune up and a few other things. Granted this included installing a sew up tire (which I can understand would cost approx $50), Swapping out a left side (big ring) shifter on my down tube (this should have cost approx. $20 at most) and installing new bar tape (cost of tape $20 and $20 to install?).. SO WHAT""S WITH $140 FOR A TUNE UP? Well the story goes like this: + +I bring the bike into BBB prior to the nice weather hitting Pittsburgh in hopes of trying what people have said is a great bike shop and getting my OCLV TREK 5900 ready for the season. Turns out I don't hear from these guys. A week goes by ...two weeks...I think that's ok I have two or three other bike I can turn to for a ride. Then I wind up going out of town for a week thinking for sure I'll get a call from them re: my bike is ready to roll...but no dice. So I call. Turns out a screw snapped when the mechanic was re-installing the down tube shifter and it had to be tapped out (is that my fault?). He says ""Should be ready in a few days"". So I come in a few days later to this mammoth bill. I ask if I am paying for the labor of taping out the screw? I don't think I ever got a straight answer? I look at the bill and can't see a good breakdown of the charges. Normally I would ""duke it over"" a bill like this but I figured...I had somewhere I to be 10 minutes ago and at least I finally have my bike. I would expect that for that money my bike could have been stripped down to the frame and totally gone over (overhauled). But it wasn't. Well BBB I'll give you a star because the mechanic did do a good job in that my cycle shifts well and the tape job on the bars looks great (nice wrap). Plus I'll toss in a star for your outstanding selection of high end cycles. Maybe I would have rated BBB higher if I was in the market for a purchase instead of a simple repair?[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I wrote this review right after I had bought my bike. I would like to update to reflect further experiences I've had with BBB. + +So, first of all, one of the shifters on my bike turned out to be defective (not super-unusual for the Shimano short-reach shifters, also totally not the shop's fault -- these things happen). Since it was covered under warranty, BBB switched it out for a new set of shifters, at no cost to me. I had my bike back in a couple days, no muss no fuss. + +My husband got a used road bike from Craigslist, and we brought it in for a tuneup. The bike had several things wrong with it, due to a shoddy assembly job, and BBB basically took the entire bike apart and rebuilt it, cleaning it and replacing various worn-out bits. I can't remember the total cost of this, but it was under $100. + +I would totally recommend BBB, due to their general awesomeness. I haven't had any of the tuneup-related woes that other people have had with this shop, even when bringing in a bike that I haven't bought there.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I created an account just to review this shop, it's that awesome. + +This is by far the premier shop in all of western PA, and arguably the state. + +Glenn the shop owner is one of the most knowledgeable men in the U.S. when it comes to cycling. Having spent time in Europe, and with some of the biggest names in the industry, he truly knows what he's talking about. + +Furthermore; he's a pleasure to talk to, incredibly friendly and passionate as anything about the sport. As for bike fitting, this is the only shop I would go to, Glenn's knowledge and background can't be competed with, and he is incredibly thorough. + +Yes, they equipment is expensive, but that's a result of the quality they carry..not them setting prices high. Cycling is expensive, end of story. + +If you're looking to pick up your next huffy, go to walmart. If you want a quality bike that is going to fit you, and operate perfectly: go to big bang.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Bought a bike there on my second time in the shop. Glen is very knowledgeable but can be a bit overwhelming, annoying and pushy, I can see how he can be very helpful to the average Joe, but if you are in his shop you should have done your homework, as this place is not walmart, mid to high level product here. I would encourage getting fitted and even buying a bike there, but going back for service is a whole different story. Same day service is unheard of here, even for the simplest of adjustments, no service is available at all on the weekends. the first time I took a bike there to have a rear derailer hanger replaced and re-adjusted (I had already purchased and had the hanger) 11 days went by before I returned to pick my bike up after not being called. I figured it was just a fluke experience and gave them the benefit of the doubt. The second time. I took a bike in to have a damaged shift lever replaced with a new 7800 pair. I called after 9 days and they said it wold be 2 days more. when I showed up 2 days later it still wasn't done, it took 2 more following that, 13 days total. Stay away from their service department[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> When you walk out of Big Bang Bikes you know you are buying a bike that fits YOU! Glenn is amazing and he will help you reach your specific goals! He has amazing passion and knowledge to make you more efficient and comfortable. The best bike shop...by far. Great prices and service. We live in the north and won't hesitate to make the extra drive for anything bike related.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great customer service!!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place is the absolute BEST to purchase a bike! I have been searching for a bike for a while now and every place I have gone to have not been NEAR has helpful as Glenn. +The one guy in the shop helped pick me a bike for what I needed and Glenn fit me perfectly to the bike. They also helped me with the bike rack on my car and changed my bike saddle for me! Ohhhh and they gave me the best price on the bike and accessories!!! Wonderful service. Absolutely will go back! ... Can't wait![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've got to be honest, I don't think I've ever been as blown away by customer service as I was here. I went in about half an hour before closing, was not rushed at all. I basically just walked in and said I was interested in a road bike but knew very little about them (I'm a MTBr). I was helped by Glenn, who, within two minutes, had me sitting on a bike, measuring me and adjusting things, and explaining the physics behind positioning and angles and the difference between the male and female physique on a road bike. At no point did he try to upsell anything (in fact, he didn't even ask me about a budget). He just gave me a few things to think about before I invest in something new. He was very obviously focused on getting me the product that will give me the most efficiency and power for my needs. So very impressed...this is absolutely where I will be buying my bike.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> If you're in the market for a high quality bike, whether it be road, mountain, racing, or hybrid, go to see Glenn at BBB. It's very clear that he loves his shop and his job. I explained my needs and preferences to him and he quickly fitted me with a bike that suited my needs. I actually bought my Trek 7300 over 3 years ago and I absolutely love it! He sells only the highest quality bikes and equipment. Highly recommended.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Big Bang Bicycles is phenomenal! Amazing selection and service! I live in the San Francisco, Bay Area with plenty of premium bicycle shops available, but I do most of my cycling shopping at Big Bang Bicycles when I visit family in Pittsburgh. This shop carries top gear and has in stock tons of options so you can see, feel and evaluate them first hand to know what's going to give you the best feel and performance. Glenn, the owner, is very knowledgeable, friendly and you can feel his passion for cycling and making sure you get the right product and fit for you. Even if you're not in the Pittsburgh area but you know what you want -- send your order to Big Bang Bicycles and I'm certain you'll have a great experience. Awesome shop! Thank you Glenn and team![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> What, you haven't been to Bellisario's yet? This is about the only red sauce pizza I ever get a craving for, and boy howdy is it good. The crust is on the thin side and ever so crisp on the bottom, while still having enough dough on the edge to provide a nice chewy bit at the end of your slice. The dough itself is flavorful, not too... well, doughy. The sauce is great, and they don't drown the pizza in it. There's just enough cheese; not so much it's an overwhelming grease slick and not so little you can't tell it's there. If you can go while Mama's working, all the better. + +You can eat in here; they have four or five booths and generations worth of family photos on the walls. Two of us split a small (8-cut) pizza with one topping ($9) and with our two cans of pop we were out for $10. You can't beat that. And I'd put Bellisario's pizza up against any in the city. + +I grew up a five minute walk away. My mom loved Bellisario's and I have a lot of fond memories of walking through the alley to pick up a cheese pizza to bring home, my mom being too dollar-conscious to pay for delivery when there were perfectly able-bodied children around to go pick it up. Every time I have a slice, it brings back great memories. But I've had outside confirmation that it really is as awesome as I think it is. + +It's a little divey, stuck in the back of an old shopping plaza, but it's perfect. If you're in West Mifflin (say, going to Kennywood), drive over and eat a pizza. They've also got hoagies and calzones, and I think that's about it. But with pizza this good, who cares?[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place makes AWESOME pizza. Also, their Italian hoagies are great. The only problem is that they do not open until 4.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Okay so I just moved to the outskirts of Duquesne, PA which is outside of Pittsburgh from Harrisburg, PA of all places. Where I am at, really there is no delivery but these guys did. They were nice and cordial and cheap but I have been spoiled by the pizza shop in Harrisburg, Downtown, run my an old world Italian guy named Luigi. That pizza is/was MILES better than this. This crust, while thin, did not have flavor and was hard. The slices were small for their 8 slice which I did like. The cheese was good. The sauce was meh. I've definitely had way better. 2 stars for being cheap and delivering.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Good pizza and i love the breadsticks...i don't know too much else about this place[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Pizza is very hit or miss. When the owners are there, it's really good. When they aren't, you get pizza that is over cooked (more like burnt) and LONG delivery times. The pizza, even when plain, is very greasy. Way more than other places around. Usually pizza that greasy is caused by low quality cheese. Also they do not take credit or debit cards. There are better options.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have been looking for 3 years for good crab rangoon - I finally found it!!! We had boneless ribs that were absolutely wonderful. Definitely going back!!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Best menu best food in Pittsburgh! Thank goodness I only live 5 min away![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Ok this is my first yelp review, I never left any reviews for other restaurants, but I am writing it because I want others to know about this place more. + +Restaurant run by family. very friendly, clean cooking environment, and Great food. I would come to this place again and again whenever I visit Pittsburgh. + +Its less than 10min drive from Kennywood, if you are visiting Kennywood you should definitely try this place.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Love this place. Run by family. Best General Tso's around. And when I walk in they call me Mr. Spicy![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Using an app I found for thrift-aholics thanks to my friend, Yvette, we came across American Thrift Center out in West Mifflin on one of our all day thrift excursions. This store is a little out of the way if you're not from this area, and you may feel you're getting a little lost since you end up driving in a more rural looking area until you get to the plaza where it's located. It has lots of parking in a private lot and trust me the outside is no indication of how big it is inside. + +This store has so much stuff packed into a fairly large space. The clothing selection and shoe selection is the real gem here. I love knick knacks as much as the next person, but eventually I'm going to need to pick up a new dress or jeans to cut into shorts. + +The place wasn't packed, which is a nice surprise for weekend day at a big thrift store. The clothes were organized well and the prices were low. There was one thing though that sort of bugged me... It's not that I LIKE the smell of thrifted clothes, but I feel like anyone who thrifts knows what smell I'm talking about. This place does not use whatever it is that makes the clothes smell like that. I imagine it's some sort of disinfectant spray. You would think it would be a good thing, but what it meant is that the cute summery dress I found smelled like cat pee and cigarette smoke. No thanks. + +My only complaints about American Thrift would be an outrageous $20 minimum for cards. + +Two women working one register together that we're the least friendly store employees I've encountered since 16 yr olds who hate their lives. + +No dressing rooms. I don't know what this theme is with thrift stores not having them, but I'm getting really good at changing pants in the middle of an isle without flashing my bits to everyone. + +Not enough to keep me from coming back, but as far as I'm concerned this is a cash only place from this point forward.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I do like this store for the clothes. The prices are good on them. One thing I don't like is the $20 minimum on cards. No one carries cash anymore, so I think that's high. The people who work there do not smile to customers. Ever. They are friendly amongst themselves and will point you in the right direction (literally, when I asked where something was, the lady looked at me, not smiling, and pointed), but they don't make you feel welcome. I wonder if they realize that we customers pay their paycheck. I do like the 1/2 price discounts, which they change daily, but it always seems like what I want is not on sale that day. LOL! There's no dressing room, but I've gotten pretty good at holding an article of clothing up to me in a mirror and guessing. The bad part about that is, if I'm wrong, I own it anyway because there are no returns or exchanges. All in all, I will continue to go there when I'm in the neighborhood, but I can't say it's my favorite.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great food, service and prices. It's in a not so great part of town, but lock your doors and it's definitely worth it. Best baked goods in the area! Try the almond torte!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Thanks to Darren's sis Jessica, we had some excellent cookies for our housewarming party. I liked ths sugar cookies with the jimmies best and the half-dipped chocolate chips, but they were all good. It's too bad about the area in which it is though.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Came here from PGH for the first time. This bakery is legit. I bought some Rye bread and Italian 5 grain. Delicious. A strange snickerdoodle thing with pink frosting. Delicious. Chocolate chip cookie dipped in chocolate, extra chewy and humongous. Delicious. + +And a sweet old lady serving em up. + +The best. + +Delicious.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Absolutely the best bakery I've been in ever! The cookies are delicious. The nut rolls. & coffee cakes are heaven. Put on your bucket list to eat an almond torte. It is extremely memorable. I will dream about Minerva's delicacies until I return to visit the Burgh again. Btw - the staff is the best.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It sounds crazy to drive to Mckeesport for a cookie but Minerva is the BEST! Cookies and pies are incredible. Cakes are lovely and the pastries are worth the workout to get rid of them. + +They have a wide selection and now take credit cards. Its worth calling ahead on the holidays. This is not the Giant Eagle, sometimes they sell out.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is my favorite bakery. I always get great service and have never been disappointed with anything. Their toasted almond torte is to die for. I AM ALWAYS POLITE TO THEM, MAYBE THAT'S WHY I GET GREAT SERVICE![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> You have never had a pierogie until you've driven out to McKees Rocks and picked up a dozen or so from Pierogies Plus. Made primarily by Polish and Ukranian immigrants, these are probably the most authentic/delicious pierogies you can buy in the states. + +If the only pierogies you've ever had were the frozen Mrs. T's you got at Giant Eagle, do yourself a favor and check Pierogies Plus out.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> In Pittsburgh, there IS no other place to get pierogies. Everything is made by hand, fresh every day. And the mix of languages while you wait is a real treat! There are over 30 kinds of pierogies and now that they have expanded, there are a variety of salads and some desserts available too. Don't forget about the haluski and stuffed cabbage! They've been on the Food Network with Bobby Flay, Food Finds, Dave & Dave from WQED, and in numerous newspaper articles. You won't find anything more authentic or delicious as this place. And they ship too![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Years after the first reviewer came here, the quality is still great and deserving of more than 5 stars. + +The people who work here and run this place are super friendly and really know their craft. The main owner took my order once and gave me some tips on how to cook the frozen pierogies at home. They turned out ok, but not as good as getting them fresh from the store. + +It can be a bit of a drive from anywhere that's not McKees Rocks (Google Maps takes you through the hood) but it's worth it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> These are the best pierogies EVER! My favorite is the jalapeno pierogie, which is not that spicy, but has excellent flavor. It is such a treat to get these when I'm back in town![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Love butter? Then get thee to Pierogies Plus. + +I live in St. Louis, and it seems like the only pierogi I can find are in my grocer's freezer. Oh, but when I go home to Pittsburgh, I can have as much of the chewy, flavorful, buttery goodness as I desire from Pierogies Plus. + +The place still looks like an old service station with a tiny building and a roof over an old gas pump island. Inside, though, magical elves... uh... I mean fabulous Polish women... create deliciousness with love -- and butter. Have I mentioned that butter is a part of the deal? Because it totally is. You really should fast for two days before picking up pierogi from here. + +Oh, but you'll be happy you did. I'm vegetarian, so I only order meat-free pierogi. I'm in love with the saurkraut and the cheese varieties. When you pick up a hot order, you'll get your pierogi covered in with rich butter and sauteed onions. No, I'm serious -- the pierogi are SWIMMING in butter. It's the best thing ever. Everything is packed inside a styrofoam container and a plastic bag, because butter WILL spill out. + +You also can order cold or frozen pierogi if you plan to, say, lug them to the middle of the country to enjoy in a far-off city. + +Besides many varieties of pierogi, you also can get things from the deli cases. Last time, I had some apricot blintzes, a latke and some type of apple turnover thingy. I really hope Pierogies Plus has the blintzes when I visit next. + +Awesome thing: Pierogies Plus usually has coupons in the Entertainment Book. My best friend and I steal all of the coupons from our families so that I can get a steady stream of discounted Polish goodness each time I visit. + +The only downside is that Pierogies Plus often closes for several days around holidays. I totally understand it -- family time is important! -- but that often coincides with my visits (I head east around the holidays mainly because I get an extra day with the fam without having to take another vacation day). I've learned to plan my trips around the Pierogies Plus schedule, though, because I MUST have yummy goodness. A pierogi-less Allison is a cranky Allison.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> These pierogies are one of my favorite things in the world. They're freakin' amazing. The potato and jalapeno ones are my favorite. And I definitely think it's worth it to drive all the way out to McKees Rocks to get them. I like to get them frozen, and bring them home and smother them in butter.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I was planning to attend a conference in Pittsburgh and was researching food joints that I wanted to check out. A friend of mine insisted that I go to Pierogies Plus telling me that the food was so good that ever since he went that he has had pierogies mail-ordered to his house each year. While I have never been a huge fan of pierogies, I figured that I should heed my friends advice since he generally steers me to places I enjoy. Let's just say in this case, he hit the ball out of the park. + +I actually wound up going to Pierogies Plus straight from the airport. After getting in a rental car and plugging in my GPS, imagine my surprise when my GPS announced ""You have reached your destination."" and I found myself sitting outside what appeared to be an old service station. When I walked inside and up to the counter, I found a crew of Polish women rocking out every kind of Pierogi imaginable. I was overwhelmed by the sheer volume of choices. + +Wanting to try everything, I wound up going with their Sampler Platter #1 which was a small haluski (a noodle and cabbage mixture), a stuffed cabbage, and four pierogi ( I wound up going with a potato with bacon, potato with cheese, potato with jalapeno, and potato with meat). The food was outrageously good. I'm actually salivating just thinking back on the meal. The stuffed cabbage was not marred by the typical dryness that can afflict that dish and was perfectly sauced. The haluski, a dish I had never heard of, was amazing. + +While I can't expect everyone to make their way to Pittsburgh solely to go to Pierogies Plus, do yourself a favor and order some. Those wonderful ladies deserve your business. Your belly will appreciate it![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Traditional, tasty, fabulous. Order pierogies cold or hot for a buck or two more. They always carry 4 main types of pierogies, with about 25 other kinds you can special order. There is always a line, which says enough. I never get tired of their halupki either. If you can deal with the billy graham leaflets and focus on the food, you'll come out a winner. Oh yeah, if you can, ask for the senior discount![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Little ladies, sitting in the back of a renovated gas station perched precariously at the top of a hill, making pierogies and cooking them to perfection in butter and onions... it almost sounds like a strange Pittsburgher fairy tale, but this is no tale - the finest pierogies I've ever eaten emerge from the back of that gas station, and my Polish girlfriend even confirmed that these are better than some of her family's goods. + +While in line I met folks from Rhode Island, Kentucky, and North Carolina, who all had come to McKees Rocks in their rental cars straight from the airport before even going to see their families - that is dedication and commitment to some seriously delicious pierogies. After enjoying a dozen of these filling, savory, perfect pierogies, I think once I move away from here I will be making that same trip to Pierogies Plus myself.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Well for my first time here I was way less than impressed. The lady at the front counter was a crab and the Pierogies really weren't that great. Rather than be kind and answering my questions I settled with the potato and cheese pierogies. I guess Bloomfield Bridge tavern or Mrs. T's is still my go to place. And plus this place is way out of my way to be treated poorly. I wouldn't go back[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My coworkers and I left our office in Crafton, headed for Pierogies Plus. The journey there took us past bizarre, abandoned-looking buildings, and roads that suddenly ended in cement blockades. The area is prime for use as the setting of a slasher flick. + +BUT, the weird drive is totally worth it. Pierogies Plus is so legit. + +The setting is reminiscent of Seinfeld's 'Soup Nazi': tiny interior, people standing in line shoulder-to-shoulder, and a lady behind the counter brusquely taking orders. Oh, and make sure you order your 'rogies ""hot"" if you're planning on eating them soon! Otherwise, you get 'em frozen. (There's a slight up-charge for the hot ones, btw -- electricity ain't free!) + +They were out of the plain potato and the potato and cheese varieties when we were there, so I had the platter with pierogies and kielbasa. I opted for the sauerkraut pierogies, and they were SO good! The interior was filled with sauerkraut mixed with potatoes, as opposed to many other sauerkraut pierogies I've had that were filled with only kraut. I definitely prefer the potato/kraut mix! They were also drowning in butter and onions. Like, serious, serious butter - Paula Deen has nothin' on these ladies' butter usage. The kielbasa was awesome, too! I also sampled their haluski and it was the best I've ever had. Tons o' butter, seasoned with generous amounts of salt 'n' pepper, and there was quite a bit of sautéed onions in the mix, which added even more flavor. + +A few things to note: They have coupons you can print out on their website, but you must cut them out if you're gonna bring 'em in and use them! You cannot just hand them the whole piece of paper. If you want to order a special variety, they need 2 days advance notice (check their site to see what the 'special' ones are). They do accept credit cards, with a $10 min. Yes, some of the ladies are not the friendliest, but the food is so good, they can be like that, and you'll still come back for more! And, parking is quite limited there. Pretty sure the building is a converted service station. :) + +All in all, these pierogies are some of the best I've ever had, and I will definitely be back very soon![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Update: Get. The. Italian. Sausage. Pierogies. Holy crap. It will change your freaking life![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> OMG good pierogis in a classic blue collar 'hood. At first glance, it looks like a place to get a flat fixed on your tire. Instead, I re-learn why I always avoid the corporate food franchises and seek places like this out. Just go there and eat whatever the nice woman behind the counter tells you to! It's well worth the mapquest ...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> As a skeptical out of towner, I was pretty wary after the hotel bellhop suggested this off the beaten path place. However this place far exceeded my expectations. We bought an assorted dozen of pierogies and they were all delicious (my favorites being the jalapeños pierogi and the bacon/potato pierogi). A great find and an excellent place for someone out of town to try out pierogies![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Some great pierogies are expertly handmade with ""tender loving care,"" here in this once-was-a-gas-station. Quality, I tell you. They're definitely worthy of a pierogi pilgrimage. + +Order them hot if you want them right then and there because these nice ladies also sell them cold to take home too. + +Hot and buttery, buttery, buttery, and covered in sauteed onions is how you'll get them. So good. We shared the potato and cheese, potato and sauerkraut, and hot sausage varieties. Delicious, them all.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Best pierogies in tahn! + +I usually just go with the standard potato and cheese but I've also tried a few of the other pierogies and some of the plus. These pierogies can't be beat. Made by hand with love in the traditional old world style, I have yet to find better. + +It's amazing to get there at 10:55am, 5 minutes before they open and see the mad rush of people getting pierogies. By 11am, the line is already out the door. Always a good sign. They serve their pierogies hot, cold or frozen. I always go with the hot because nothing beats pierogies bathing in butter and onions. And here at Pierogies Plus, they are definitely worth the wait.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Just finished a dinner of pierogies that our Pgh family brought to WV - always look forward to Pierogies Plus - try the apricot for a sweet treet![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Apricot with cream cheese, who would have thought...love this place, love it so much. Print the 10% off coupon on their website before going in. Make sure u print it out, they will not accept it other wise.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place has some amazing homemade pierogies! I had never eaten anything besides the usual Mrs. T.'s potato types and boy, was I missing out! We stopped one night and got a some potato/cheddar and some sauerkraut/potato. You can buy them hot or take them home cold. There is a small table outside to eat, but only standing room to order inside. + +They had special order pierogies that sounded amazing, but they suggest a 2 day advance order for those. They said sometimes they will have leftover specialty ones for sale, but it all depends on the day. + +They also have haluski, stuffed cabbage and other things that I am looking forward to trying next time.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This little former gas station makes some incredibly delicious pierogies. Order ahead for big holidays - we order several dozen every year for Easter and the take out line stretches out the door all day on Good Friday. I particularly like the apricot and cream cheese and the prune varieties. Potato and cheddar are great, too, of course![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> WARNING: ADDICTING POTATOE VERSION OF CRACK -----CHEAP, frozen, cold or hot. PARKING SUCKS on busy route 51 mckees rocks only enough room for approx 6-8 cars. SUPER BUSY best time to come is between 1pm-4pm------g8 food. Outside in good weather there is a couple little tables to sit at., but not during the winter/early spring. MOST CUSTOMERS ARE TO GO TAKE HOME . hours monday 11-6, tues-friday 11-7 ----- closed sat/sun[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Yummy! I've never tried Polish food aside from a sausage. I have to say it was really good. The ladies that worked there were very nice. The only down side it took a while to get my food. I think it's made to order. Regardless, when I received my food it was streaming hot. Let's just say for me it was worth the wait.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Best pierogies I've ever had. And, seeing as how I'm from Pittsburgh.... that's a lot. The apricot and cream cheese pierogies are amazing!!! GO.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place was really good. Ordered the sampler plate with one small haluski, one stuffed cabbage, four pierogies. I have to admit the haluski was EPIC!!! OMG THE BEST I WAS LIKE WHAT AM I EATING!! SOOOO FREAKIN GOOD!! The pierogies and the stuffed cabbage wasn't as amazing, but it was tasty. The crab cake was nasty. Yuck!!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Good pierogies, but after also having Szmidts in Greenfield recently, this place takes the backseat. Its also out of the way for me. However, if I ever happen to be in McKees Rocks, Ill make sure to keep this spot in mind.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The experience was not that great. The lady taking the orders was nice, but not helpful with what to order. The owner kept her back turn to us the entire time, based on the pictures and news articles I read about her I thought she would have been more social. To what really matters we got #2 sampler and order of jalapeño pierogies and the Ruben pierogies a lot of food for two guys. Really had no idea what to expect. Haluski was good, the pierogies came Luke warm and soaked in oily butter. Like the cab driver said you can find better. I'd pass on this spot.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I was very disappointed in the quality of the pierogies and the haluski at Pierogies Plus. I ordered them hot and I purchased enough so that I could have leftovers the next day. When I got home and opened the containers, something smelled odd. When I started to eat, it tasted just as odd. As it turns out, what is referred to as 'butter sauce' is a misrepresentation of what it really is-----margarine, which I eliminated from my diet years ago because of the trans fats and the fact that any way you cut it, butter makes for a better product. Sorry Allison B, ain't no butter here. Margarine is used as a cost-cutting measure, and it just can't measure up. I rinsed off the peirogies and browned them in some butter and my own onions. The haluski got thrown away. For the prices being charged for these products, the proprietor can well-afford to use butter.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great food! I have been eating at Pierogies Plus since they opened. Great food all around! The Halupki and Halushki are awesome as well as the Pierogies.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Decent pierogies but not the best I've had. I've eaten @ Pierogies Plus two times. Both times I got the potato & cheese pierogies. They are good however they come in WAY too much butter/oil. They are probably soaked in at least a half a cup or more of butter/oil. When I get them I have to take them out of all the butter/oil b/c it would make me completely sick if I ate them as is. Other than that the pierogies themselves are decent. +However, they are pretty pricey. About $12 for 1 dozen. +Recommend eating here if you're passing through or nearby but I wouldn't go out of my way.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Have been here two times after stopping at Mancini's Bakery. Have only had the Hamburger/Cheese/Bacon w/ fries but huge portions and great price. Great Quality also. Server is really nice also. Will be eating here again. Heard the Breakfast items are also great. Saw the waffles and pancakes....were huge![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Marges is tucked away in the delightful Pittsburgh neighborhood of Mckees Rocks. This place reminds me half of a diner from the 1950's, and half my grandmas kitchen. + +The seating room is accommodation, the service prompt and courteous.The prices are fantastic and so is the food. + +I had a grilled hodge podge combination of hot/sweet sausage, potatoes, eggs, and peppers all on one dish for 9.50. It was excellent. Ladies and Gents, I can put food away like a champ and I still had leftovers. + +My friend had a succulent, buttery French Toast. Simple, but they nailed it. + +I would return.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> On a random Sunday morning I went in search of a good breakfast spot. I decided to explore the McKees Rocks neighborhood and came upon Marge's Place. I hadn't heard much about this place, but after reading the few reviews I could find, I decided to give it a try. + +Inside, it's bigger than I expected but still has that down home diner feel. My guess is that most of the people there were regulars. The wait staff was friendly to those they knew but also welcoming to me, someone they had never seen before. I picked a table in the corner so I could observe what I imagine was a typical Sunday morning. I ordered the breakfast special: 2 scrambled eggs with bacon, potatoes and toast. Any place that has Mancini's Italian toast already gets thumbs up in my book. Being in McKees Rocks, though, they really don't have a choice. The potatoes were thin sliced with onions and very flavorful. The only way I can think of to describe the bacon is...porkier. Is that even a word? I just don't know how else to descibe it. The combination of foods was served in generous portions at a great price (under $5). + +One random note: I liked the tables and chairs. They were comfortable not just for sitting and enjoying a cup of coffee with my morning paper but also very comfortable for sitting and eating. Good distance between the table and chairs. That may sound silly, and I thought so, too, at first. But when I go to a place and the booth is too wide or too narrow, it can hinder my enjoyment. + +Not only will I return, but I will also recommend Marge's Place to anyone in the area. It was a surprisingly good find. I like places like neighborhood businesses like this where they make everyone feel like they belong.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great service, great food at a reasonable price! The cheeseburger was as big as my head and delicious and the onion rings were just as good. Our waitress was friendly, attentive and quick to refill drinks. Can't wait to go back![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Very quaint! Stopped here for lunch while traveling for work, and I felt like I was in a diner in the 1950s. Had a grilled cheese and fries - the food was good and everyone was friendly.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great small town breakfast spot Highly recommend George's Mixed Grill ... Delicious[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have live around this area all my life and My family would go here and I would always decline to go, that is until Saturday my brother asked me if I wanted to go to breakfast and I had to say yes (just posted on facebook that I wanted to go to breakfast and nobody wanted to go with me) Lets get to the review I am glad I said yes there homefries are awesome the eggs were just right. I would definitely go here again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm new to Pittsburgh so I wanted to try out all the local spots first and let me tell you... This spot is definitely worth a try! It's a cute diner with a lot of local charm. The prices are awesome and the food is even better! I had the cinnamon raisin french toast with the home fries and a coffee. All of it was really good. I'm not a complainer but I'm picky and honestly...I have nothing but good things to say about this place. I highly recommend you stop by and give it a try! You can thank me later. ;)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great service, friendly staff, great food, great prices. What more can you ask for in a small town breakfast place? Will definitely be back[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> They do great quality work. The only reason I did not give them five stars is for their lack of customer courtesy not once but twice. I am a very patient and understanding person, but being rude twice means you dont want my business and I tipped 20%.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place is amazing!!! Jim is a great artist!!! Traveled all the way from Tampa just to get my tattoo!!! I would recommend this place to everyone!!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Got my first tattoo here in 1993 and my second a couple weeks later. All these +Years later they still look great. Haven't faded much and haven't +Had em touched up. The shop is Professional and clean, I highly +Recommend. Excellent quality work.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> ewwww[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It wasn't a busy night at the neighborhood, but you could have been fooled by how long the food took. While it did take a while everyone was extremely friendly. The food did come out hot, at least mine did, the rest of the plates were plate-warmer hot. Everyone in the table resented me for ""holding back"" the table since they staff pointed out they were waiting on my burger. + +Which hey works as a segway onto the burger. Quesadilla Burger. I knew that was a mistake but I did it anyways. The patty was sorta flavorful. The toppings were in the bland category. Cheese went MIA. And the tortilla were over-toasted and tasteless. + +A big blah overall, which is sad, since we've had a grand ole time and good food in past visits.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The 7 ounce house sirloin is the bomb! 'Nuff said.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Called for an arrangement for pickup, told the person who took my order that I would be able to pick the arrangement up at 5:30pm. She asked if I could get there any earlier, I said I would try my best, but I work until 5pm, so maybe not. She said ok. + +Comes to be 5pm and I get a call from a guy at the shop asking where I was! The lady who took my order wrote down that I'd be there at 5pm. I explained that I never said that and picked the arrangement up a little before 5:30pm. + +Arrangement was just OK. I specifically wanted a lot of orange flowers, which they did, but they added strange colors with the orange... and some of the flowers were already a little wilted. + +Even though the location is convenient, I will probably go elsewhere for a flower order next time.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> i had a fantastic experience here. I got to the shop just before they weer about to close, but the owner was very gracious about creating an arrangement for me. The flowers were lovely. I would make a special trip just to purchase from this shop again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The order process went well and the delivery arrived in a timely manner. I saw a picture of the flowers my friend received and the arrangement wasn't even close to what was pictured on the website...a lot more filler flowers despite ordering the premium arrangement. I picked this place specifically because of what they offered despite other cheaper places in the area. I am disappointed because I wanted the best arrangement possible for my friend who is going through a tough time. + +I will not order from this place again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Ordered delivery when staying at the Sheraton Station Square. It wasn't super fast but wasn't unreasonable (45mins) and the pizza was so good that I ended up eating way more than I intended. Not too greesey with a nice balance of cheese, sauce, dough, and toppings.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> They don't deliver to me anymore, moved to Lawrenceville. However, their pizza is good, not too greasy, not too dry. Nice balance with the sauce cheese and toppings. They have awesome house rolls, I'm partial to the spinache and feta house rolls. They are SO delicious. Pretty cheap. The delivery time is kind of long, but they are open late, and I love that.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Meh. I've ordered from here twice and not really been enthusiastic about the results either time. Keep in mind that I haven't had pizza from this place yet! + +Their steak hoagie is middling-good; nothing to write home about, but a pretty good example of the standard Pittsburgh pizza place steak hoagie. + +The seafood calzone is another story. Something in it was so bitter I couldn't quite eat it; I'm wondering if it was the garlic or perhaps a leftover burnt taste from the oven. Whatever it was, it was gross. The shrimp weren't that good either, suffering as they did from that certain ""I taste like iodine"" flavor. + +The advantage to R&B is that they're open reasonably late, given the location, but the phone service is rather surly and it always takes them an hour plus to deliver. Which would be OK if I didn't live a block away (normally I'd just walk and pick it up, but just for you, Yelpers, I subject myself to the vagaries of sitting on my rear end on the couch waiting for my food to arrive).[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The pizza here is great. I always pick up a pizza when i am near Bellevue. I have only ever eaten their pizza.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This was the first place we tried after moving to Bellevue, and over a year later, we still order almost weekly. Their staff is really friendly, delivery always quick (or at least doesn't ever take longer than the estimated time given), and food is delicious. + +Five stars for the staff and the food, but four stars because I wish they had better specials.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I stopped by here two nights ago as part of a night where I would try three different pizzas in the Bellevue/Avalon area. I called my order in for an XL pizza ahead of time and was told that I would have a 15 minute wait until it was ready. Since I only had a general idea of where it was located I ended up parking near it trying to locate it and then driving past it before finally locating it in a small strip mall right next to Lincoln Ave. There isn't too much to say about the inside of this pizza place except that they have a counter up front with a little bit of room to wait and no customer seating, not that this is a bad thing. + +Pizzas in general can be broken down into three separate components: cheese, crust and sauce. This pizza actually had the least amount of cheese on it of all of the pizzas that we tried but ended up being my favorite which would be surprsing if you know me. The cheese was not that strong in flavor but the amount of it let it pair perfectly with the sauce which had a nice spice profile (strong on the garlic and maybe some oregano?) coming through it. The crust on this pizza was the thinnest of the bunch that we tried and was cooked nicely which also had a little crisp which I loved. + +The bottom line for me is that I would head back to R & B's again in the future for pizza. It was easily the most expensive of the bunch that I bought last night at $12.79 after tax for an XL but as the old adage goes ""You get what you pay for"" and if you like garlic then you should like this pizza.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My fiancée and I have made R&B's our Friday night dinner tradition for over a year. the food is consistently amazing, and portions are HUGE. Whether you choose to pick up or have it delivered, it's always less then 30 minutes - and can we take a second to acknowledge the staff? Always exceedingly friendly, and happy to accommodate any special requests. Sadly, we're moving out of the area in two weeks, so we won't be able to continue our tradition. But if you haven't given them a try, do it! (might I suggest the Buffalo Chicken sub and the cheese and bacon fries? epic!)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Get the white pizza with bacon. You're life will never be the same. Never had a bad experience ordering from R&B's.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Lots of memories from this place for me. Their pizza may not be the best in the world but boy does it take me back to the 80's-90's and growing up in Pittsburgh. + +I am slightly disappointed that they moved to a new location in Bellevue. Their old one, while a bit dirty and run down, had quite the charm to it. The new place looks too clean cut and it seems like they're trying to be something they're not, which is just a good old fashioned pizza joint.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Excellent pizza - although the mushrooms were from a can. But the crust , sauce and rest of toppings on the Sicilian pizza were delicious. Nice family friendly[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> A great little place. Delicious and affordable Italian food. Great salads and pasta. Try the pizza rolls![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Service was very good..calzone was excellent.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Best pizza in the North Boros. I can't make a trip to the area without stopping at Luigi's. When I was a kid, the man himself actually owned the place and made the pizza, but they've since moved to a new location under new ownership...but the pizza is still just as good. I prefer the thin-crust, but the Sicilian is also excellent. The fried zucchini is a favorite and the mozzarella sticks are great, too. The calzones are tasty, but may cause a coronary-- if you expect more than a handful of spinach among cheese in the spinach calzone, you'll be disappointed. Because it's Pittsburgh, the chicken salad comes with french fries. I tend to opt for take-out, but there is also a mid-sized dining section.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Best all-meat pizza in the area. Always done delivery, never eaten in the restaurant, so I can't speak to the dining experience.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have been eating at Luigi's since before birth (my mom loves this stuff). The new location is nice, but I miss the coziness of the old place. +The food has been consistent through the transition, which happened a long while ago by the way. Also, I have read a few other reviews that said Luigi's has left but I talk with him every time I am in. Regardless this is a great family owned pizzeria and I recommend the calzone because it is generously stuffed with ricotta :).[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I stopped by here this past Tuesday in order to pick up a to go pizza. My fiance, a friend and I were trying pizza from three different places and Luigi's was one of them. I have driven by Luigi's many times before and for some reason had never stopped in but that did allow it to come to mind whenever I was looking for a pizza place I had not yet tried in the Bellevue area. Whenever I called to place my order I was told that my pizza would be ready in about 15 minutes. I arrived closer to 30 minutes later and was immediately confused whenever I walked into the restaurant. You see there was a large dining room on the left that was full of people and I didn't immediately see the are where I would get my pizza from. Finally after a few steps into the restaurant I noticed that the whole back area of the restaurant was where I needed to be and I made my way back there. My pizza was ready for me and I quickly paid and was leaving whenever the cashier told me ""Stay out of trouble"". I really hope that was a friendly sentiment and not one that was based upon my appearance or anything else. The pizza itself had a medium thick crust with a bland sauce which is weird since I could see a ton of green herbs in it. The cheese was just ok and nothing special while the pizza itself had a slightly sour taste to it which I did not enjoy. Out of the three different pizzas we ate that night this one was overwhelmingly our least favorite which was evidenced by the fact that 3/4 of it was left after the evening. + +The bottom line for me is that I will probably not head back to Luigi's in the future. I just don't see myself making a trip to Luigi's between the weird experience (although not bad) that I had in the restaurant and the fact that there are much better pizza places nearby.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Luigi's pizza is amazing! The sicilian pizza takes me back to how my grandma used to make homemade pizza. I can't wait to go back - definitely worth the 45-minute trip there :)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Recently I've found myself patronizing Bellevue a little more, namely because I've bought a house in the area, and have been checking out some of the mom and pops along the little strip of Mayberry RFD that is the quaint main street. Luigi's is one of those little mom and pops that offers standard basic Italian in a comfortable setting. It's a little kitchy, red-white-and-green, with Dino and Frankie tunes playing in the background. + +I've stopped in on several occasions now for dinner, with various friends, and the food has been consistent...it's good...satisfying. Not over-the-top gourmet, or even in the remotest sense 'pretentious'. It's just a good ol' night out for some pasta or lasagna, with a side salad, garlic bread and conversation with your pals. + +The portions are ample, the prices are reasonable, the flavors won't knock your socks off and make you think you've died and gone to Sicily, but they won't make you cringe at having given your money to a profiteering Chef Boyardee either. The service is decent, kind of point blank, not rude, nor over the top friendly. + +The crowd can fluctuate between 'Oh my god, I'm surrounded by Hillbillies' to 'the local gathering at Mayberry', but that seems to be the norm for most places in da burgh. + +I've not had the pizza, which apparently get raves, because frankly I only think of pizza as coming in a box to my front door when I'm too lazy to do any cooking at home. But I've had three or four of the pasta dishes, and they come in a generous portion, with a side salad and an order of garlic toast. They taste fine, fill you up, and don't break your bank. + +And for a local neighborhood joint, that's exactly what I'd hope for. A place you can go to find a dependable and reasonable meal, on a semi-regular basis, in a comfortable setting, with no frills or pretense. + +And that is exactly what Luigi's is.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Luigis is the best of the best. Awesome, authentic pepperoni. I have eaten here for years. This place is a tradition in my family and it's still as good as they were 15 years ago. They recently remodeled and have a great menu selection. By far the best pizza in Bellevue and right up there with Fioris as the best in Pittsburgh.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Just ordered delivery from here. The soup was very good. I also would Recommend the specialty salad. I also was surprised at how quickly the order was delivered. It was delivered within a 1/2 an hour.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My wife and I LOVE this place. Decently affordable, our server is always great and very friendly, the food is delicious and it's a nice home-y atmosphere. The first time we went here, we told the server we were newlyweds and Luigi made us tiramisu and gave it to us for free! Highly recommend.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place has great tasting food. I had a italian hoagie and it was great. The pizza is top notch.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I stop by here frequently when I am on my way to work for breakfast. The drive thru is fast but they do tend to get the order wrong. But I will say that I have had more free meals here due to them comping me for all messed up orders. + +The staff is friendly.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is the McDonald's to end all McDonald's, in my book. Here's why: + +~ The Drive-Thru is crazy fast. +~ There are 2 Drive-Thru lanes to keep it crazy fast. +~ Even when they have to make my dog's special no-onion cheeseburger, they are crazy fast. +~ For years, they gave my family's dog Jamie free baby ice cream cones. Jamie didn't need many moments of excitement to be happy, but 'go for ride' was one of them, and 'ice cream time' was another. +~ The drive-thru staff is so sweet to my little pup Lucy when I take her to 'cheeseburger window'. + +So, I guess what I'm saying is, this is the best McDonald's for dogs and their parents. And as someone who generally only visits McDonald's to reward my dog for good behavior after a vet visit, this McDonald's is just right.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have never gotten an order correct from this specific McDonald's. I'm not sure what the problem is, but it is never, ever right. It is never quick. The staff is always rude. After trying at least 12-15 times over the past year, I've finally given up hope on this place. Do not recommend.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My orders have come out bad pretty much every time I have ordered from here. The chicken nuggets come out under par. I'm lucky if the fries come out right. My last experience is the last straw. I recently posted a photo of my Chicken Ranch Club. That has no chicken. This is ridiculous. I am done going to this Mcd's.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Delivery is slow and not even close to the best Chinese in the area. No matter if it's rice or noodles or chicken or pork, everything tastes off--like it's been overcooked in mop-bucket-water. Try House of Lee instead.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I am SHOCKED to see this place isn't five stars. + +We order delivery from here at least once a week. Their lunch specials are GREAT, and the portions are always, always plentiful. I've never waited more than 25 minutes, even though they always say 45. I think it's respectful just in case they run behind. + +I will say that if you are looking for a truly authentic Chinese meal, this probably isn't your best option (although WAY more authentic than House of Lee. YUCK!) Both my boyfriend and I think it is plenty authentic for us, always delicious. I have cravings for their eggrolls daily, he loves their wonton soup. It is the only kind of soup I will eat, it's that good. + +And we love the cute, little Chinese guy that usually delivers our food. My bf and I always get the biggest smiles on our faces when we hear our apt buzz with "" CHINA SEEAAA!!"" =)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Whether you live in Ben Avon Heights, Brighton Heights - or anywhere in between - I urge you to try China Sea. It is quite simply the best local Chinese delivery. The people on the phone are helpful and friendly. The delivery is always quoted at 45 minutes, yet the food always arrives earlier and is always unbelievably hot and fresh. Some favorites of ours are the Kung Pao shrimp, pork lo mein and hot and sour soup. I don't mean to compare China Sea to the higher end Chinese restaurants in our area. It is not Sesame Inn or China Palace; it is not a ""date night out"" sort of place. It most definitely is a cozy, inexpensive, good quality ""stay in and relax"" go to. Hope this helps! Enjoy! + +ps +A few final thoughts while we were going back for seconds; they only use all white meat chicken in their dishes. +pps +Always look at their online coupons, you will get something free![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Wow. What a shame. My family just moved to the area and have been sampling the local cuisine. We are a very large family and love foods of all kind. We've eaten Chinese food from a hundred different places in a dozen different cities. Hands down, this was the worst we've ever had. Cold, tough, congealed, and tasteless - that's the only way to describe it. I'll never order from here again. Quite frankly, the fact that I took time away from my kids to type this out should tell you how awful it was. My complaints fell on deaf ears. I guess they were shocked that someone thought that they were serving low grade dog food. I understand that sometimes restaurants crank out bad food. It happens. But when it does, you bend over backwards to make it right. Not at this place. I was told that he would have to speak with the owner in order to help me. I guess that's how they deflect complaints - blame it on the owners that aren't there and make the customer for away angry. Too bad. Because we will be visiting a competitor in the future. This family of 7 won't be visiting China Sea ever again. Oh, and by the way, why can't I give this place zero stars?[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The pros: +You get a TON of food for your money. If the food was actually decent, this would have been even better because... LEFTOVERS. +They have coupons on their website that you can use whenever. + + +The cons: +The woman who answers the phone is kinda rude. You try to ask her questions and she gets an attitude with you like you're wasting her time. +My pork dumplings were ""fried"" only on one side and were raw in the middle. +Everything was pretty darn salty. Yeah, I get it. Chinese food tends to be a little salty, but this was unacceptably salty. +Leftovers... Yes this is also a con because I threw it away. Suffering through it once was enough! + +If you're craving something made fresh that is spicy and sweet, you're not going to find it here. Just very greasy, very salty, poor excuse for Chinese takeout.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We ordered from here because Uncle Chen, our go-to takeout place down the road, was closed. + +I ordered the General Tso tofu, a favorite dish of mine, and hubby ordered the beef Mei Fun noodles. We always grab some egg rolls too. The lady on the phone wasn't rude, per se, but she wasn't exactly helpful or answering any of my questions, either (hubby wanted to see about getting a different sauce on his noodles, and I had to ask a few times before she finally answered my question about how large the tofu dish was). I was in a good mood though, so the attitude over the phone didn't bother me. Price was good, typical takeout rates. The good news is that they will allow you to pay with credit cards over the phone, so if you're like me and never carry cash, you can still get delivery. She told me 45 minutes for the food. + +The food arrived in about 20 minutes (we live half a mile away), it was hot and smelled great. Hubby's Mei Fun looked typical, but he was saddened to see that they didn't exchange the white sauce for brown sauce. The beef was pretty mushy, and didn't taste all that great. The veggies were fresh, and pretty crispy even after soaking in sauce. Noodles were alright, nothing to write home about. My General Tso tofu was delicious, and tasted exactly like the dish I was craving. Fried to perfection, perfect-sized pieces of tofu, and a fantastic sauce. The broccoli was fresh and tasted good. This particular dish only came in one size: Enormous. I think hubby and I just ended up sharing my meal, paired with some mediocre egg rolls. + +So, long story short, lady on the phone was a bit irritating, delivery was fast, food was fresh, and, depending on what you order, the food quality ranges from so-so to great. If you're looking for a quick fix to your Chinese food craving, this is a good place to order from, although I'll be going back to Uncle Chen before I try China Sea again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> If you have any common sense at all, please don't stay here. Once, it almost burnt down...and I'm pretty sure most of the locals were chanting ""burn, baby, burn.""[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Horrifying. This place should be ashamed of itself. DO NOT STAY HERE. Beyond dirty, just absolutely rank.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> came back to Pittsburgh for a wedding and couldn't find anything in my price range close to the city until i found this motel...it was very affordable....room was okay...cable tv and a/c worked fine....[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> OMG who wrote the review below? A big fat liar/someone that was paid to write that! I stayed there for an hour this past weekend (my friend and I were both intoxicated and figured laying down a few hours would get us better suited to finish driving home). This place looks like it hasb't been cleaned (or furnished) since the 80s. Literally there was grime on the walls, and squashed, unwiped bug smears too. Ok, so not the best, but for two hours, we could deal. We looked for bed bugs, and didn't see any immediate signs of them- so we laid down to rest. After about 20-30 minutes, we both started itching like crazy. I ran to the bathroom mirror (there was mold all over the bathroom) and saw bed bug bites all on my shoulders, arms, and legs. HORRIBLE!! PLEASE Health Department, shut them down! It's deplorable in there!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I can't even rate this place! Its absolutely disgusting! I begged the health department to shut them down! I was forced to stay a night here and it was so disgusting! I woke up with bed bug bites all over my body! Just filthy! DO NOT STAY HERE![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I was in need of a pedicure before my beach vacation, so I decided to stop in to Star Nails in Bellevue. I've never had a pedicure before, mostly because I'm super-ticklish, but I felt like it was about time. + +The salon looks quite nice inside; wood (well, laminate) floors, clean decor, and four pedicure chairs up on the platform on the right. I didn't have an appointment, and waited about ten minutes on a Wednesday evening. + +Nancy was my nail technician, and she greeted me warmly and helped me over into the pedicure area. Pro tip: Don't wear a past-knee-length skirt, as it can make straddling the foot bath to get into the chair slightly awkward. Nancy helped me out like a pro and I was all set. + +The pedicure chairs have a massage feature that reminded me of the Migun massage tables. They don't just vibrate; they knead. The controller is right next to you, so you can stop and start as you like. I just made sure the thing kept running the whole time. The foot bath was nice and warm. I'd brought a book to keep myself busy but turns out all my attention was occupied by relaxing. + +Nancy guided me through the steps and the slight language barrier isn't much of a problem. She completely understood that I was super-ticklish from the flinching involved, and somehow managed to be very careful about it. It wasn't at all unpleasant, which is what I'd kind of expected. + +This is the awful TMI section, so avert your ayes if you are at all sensitive. Since I've never had a pedicure and I tend to walk around either barefoot or in thin-soled shoes, I had quite a lot of callus built up. The removal was kind of disgusting, so I just didn't look, but it didn't hurt at all. I also tend to ingrown toenails on both big toes, and she dealt with them gently and quickly. I was a bit concerned about having that done at a salon, but it's a week later and my toes haven't turned gangrene, so all's well that ends well. +END TMI + +Even though it wasn't the spa pedicure (not sure what else THAT involves), I got a full foot and calf massage. Polish on and all done! At which point I thought I might as well get a manicure, too. + +The manicure involved heated mitts and a hand massage, and was very nice. Total cost was $37 plus tip (I gave her $10 for having to deal with my nasty feet). I had some fun conversations with other patrons, and overall a great experience. I'd go back once a day if it were in any way reasonable to do so, but this is getting placed on the once-a-month schedule for sure. + +The polish from the pedicure is still holding up like a champ after a week. The manicure was pretty well shot after a couple of days, so I'll probably just stick with doing the polish at home, although I can't complain about the massage and cuticle care. + +Again, I don't have other salons or spas to compare with, but it seemed like a good, basic service with a few little extras. The staff were all friendly and remembered the repeat customers who came in. They do take credit cards, and you can put the tip on the card as well; I brought cash for that as I am not used to salons taking tips on cards. + +They also offer acrylics (which I don't do), gel nails (which I'd like to try), and nail art. I'm not sure if they do waxing. I am sure that it's a friendly place, that it's clean (important!), and that they made me feel relaxed even though I was beyond nervous going in.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Fair prices but good quality... And amazing designs that are custom made.... Plus gel and solar nails are available for those interested... Offers waxing services... Completely renovated and the spa pedicure chair is amazing...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My Mom was up from Mississippi for Thanksgiving, and claimed to be in dire need of a manicure. I wanted to try somewhere in my new 'hood (Brighton Heights), so I turned to trusty Yelp for advice. Off to Star Nails we went. The inside was bright and tidy, the pedicure stations looked clean and newer, and the ladies were friendly. Unfortunately, the good feelings didn't last long. We each picked a color, and went to our respective technicians. The technician doing my nails as very nice and talkative, but just very inattentive to detail. I got no hand/arm massage, minimal shaping, and the polish application was exceptionally sloppy and thick. Her attempts to clean up the polish all over my cuticles were futile. Their actual technique was strange too, as both technicians had us dry our nails after the first coat was applied. My Mom and I left and almost in unison declared it to be the worst manicure we've gotten. At least the price wasn't exorbitant ($13 + tip each). Perhaps their other services are better, but I'll be giving the other nail shops in the area a chance next time.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I got a pedicure here. Not bad, they were pretty thorough. But two days later both of my big toes were infected and oozing pus where she trimmed my toenails on the sides (which was weird anyway). I hate to rate a local shop down, but man my toes hurt.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is my favorite 'event' restaurant (by which I mean, spendy, but definitely worth it for special occasions). It is great for intimate birthdays, celebrations, etc. Whatever karmic intervention gave the 'Bustling Borough of Bellevue' this restaurant makes me think we, as a community, has done something right. + +But more importantly the food... Oh, the food! The owner/chef takes so much care, it makes the whole experience very enjoyable. I have never had a bad meal. + +I[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My boyfriend and i went here last night. the restaurant is dark romantic and the decor is amazing. There are photographs of the owners and chefs family on the walls.... its cute. My boyfriend called ahead and told them i was vegetarian and the chef prepared a couple of things for me. There is no set menu and the waitress reads out what the chef has prepared for the night there are 5 courses. an appetizer, pasta, main course, a salad and and dessert. I thought the salad after the entree was pretty interesting . They are also very generous with the bread which i LOVED!!!! +Every meal was made to perfection. It had a homey feeling ..... +My boyfriend had some scallops that he is still talking about. My entree was spaghetti squash with mushroom wild rice and berries and limed artichokes. There were soo many flavors and all the ingredients were balanced. The service was great. + All in all it was an amazing experience. The chef came out to say hi at the end of the night...... i finished off my dinner with the creme brulee and some coffee. Our bill came to $120 with tip and it was absolutely worth it . +This is a great restaurant for a super special occasions and it is very private.Not to dressy and not too casual. + Pick out a great bottle of wine or two and get ready to get your taste buds blown. + Im pretty sure my boyfriend and i will be going back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Yes!!!!!! + + + + +Great service! +Great Food! +Love the BYOB!!! ($5).[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> STAY AWAY, the owners are so rude, they blatantly say they are not doing well and then try to pretend they have the best hairdressers in Pittsburgh. they make you feel so unwelcome, advertise they offer a bunch of services and then when you ask they snap at you that they only do hair. it was so awkward and weird . i received warnings not to get my hair done there so i was going to get a pedicure because i had a gift certificate. she told me her employees will only take cash if they have to touch a client's feet. I may go there just to get bangs trimmed since i do not want to completely waste the certificate, but this place gives me the creeps, sounds dirty, and has beyond bad customer service. They definitely do NOT know how to run a business and it is obvious why they are not doing well. Sue and Kristi pass the phone back and forth because noone wants to take a call. she reiterates that the business is doing bad and they need more clients. i have never experienced a ruder salon, or should i say dead beat shack.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I think it is ridiculous that they say they need more clients! I was all ready to be a new client. I had a 12:30 appointment with them, and when I arrived at 12:30 on the dot, the place was locked and dark and no one was there! I waited for five minutes (in the rain), and they still didn't show. I called and left a voicemail saying that I was still willing to wait, and I understood if there was some confusion, but could they call my cell (I gave them the number, as I had previously given my home number when I made the appointment). I waited nearby at a coffee shop, went back after another five minutes, and it was still locked and I hadn't received a call. And I am definitely not estimating the time, either. I was willing to wait a bit, and I looked very closely at the time on my phone to be sure that I wasn't jumping the gun on calling and then leaving. Finally, I went on with my day and when I got home, they had left a voicemail on my HOME PHONE, which I had specifically asked them not to call, saying, ""Oh hi. Sorry you missed me, but I was MAYBE two minutes late at the most. I hope you haven't left, but you should just call back to reschedule.' Seriously? When I was waiting, another woman came to the door. I thought she worked there, but she was just another client, also trying to get in! When I told this story at another local business, the women there said that I was probably the fourth person who had had this same experience at this place. I couldn't believe it. This place is the worst, and I have never even stepped inside![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Now I'm picky about my hair, but Mane Attractions was so bad that I walked out after about 15 minutes of watching the stylists work on other clients. + +I had desperately needed a haircut and walked in for a major trim and re-shaping of my layers. First, the girl at the counter said my hair might be ""difficult"" due to the length (it was nearly long enough to sit on at the time) and that I would probably have to stand while it was cut. Weird, but okay. Second, no one there knew anything about donating to ""Locks of Love,"" and I feel like salons should be aware of things like that. I needed a cut so I went for it anyway. + +I watched the two stylists while I waited for my turn. One stylist told the client whose hair she was cutting that she was going to do something other than what they discussed because it ""wasn't looking right."" Ummm, okay. The other stylist was too busy checking her phone every three seconds to notice she was yanking on her client's hair so hard with the comb that she was giving her poor client whiplash. + +At that point, I just pretended like I had received an urgent text and said, ""I have to leave, so sorry ""as I bolted for the door.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have been getting my hair cut and hi-lighted at Mane Attractions for over 5 years, by Sue, the owner. I am always extremely happy with the way my hair looks. My hair is very fine and I don't have a whole lot of it, but Sue does wonders with it, especially with my latest cut. I never wanted it shorter than shoulder length, but decided recently to make a change. Because I'm getting older, and other methods of increasing the volume and amount of my hair were too expensive, or didn't work, I wanted to try a shorter cut. The cut she gave me made my hair look much thicker. I have had several compliments on the cut, one from another hairstylist who worked at Regis. Sue is also reasonable, charging $80 for my cut and hi-lights. I will admit that I had to wait outside the salon once when I was the first customer of the day, but that was once in over 5 years. I will take an occasional late opening in exchange for the great cuts/color I get![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Let me just tell you, I have really, really difficult hair. type 3b Naturally curly, 100% grey, I dye it dark and mess with the color myself. ( never good) If you want to know where to get a good haircut you ask someone with my hair. Since I have been going to Mane Attractions I have really LOVED my hair. I have been going there for about 4 years. Kristi was even able to cut my curly hair into a short reverse bob without making me look like i was wearing a helmet. ( you curly girls know what I am talking about). I have had nothing but complements on my hair and even my mom( who is always honest) is impressed. The only complaint I ever have is that yes, sometimes I have gone there on the spur of the moment and it has been closed during the week. I just know to call and schedule things. it is a small business and I get it. P.S. kids haircuts are only 10$ and My daughter loves it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Krispy Creme? Grocery store cakes? Git ahta tahn.... when it comes to donuts, pastries, and cakes they don't hold a wisk to Lincoln Bakery in Bellevue (or most Western PA bakeries for that matter). Their cakes hit the top of my list (with Edy's downtown coming in second). The batter is light and moist while the icing is smooth -- not too sweet - not too 'lardy'. By all means, feel free to give them a decorating challenge as their peeps got mad skillz. + +In my experience, Pittsburgh natives don't seem to realize how good their sweet tooths have it here, till they move away. So, when I travel westward for the holidays I bring some Lincoln Bakery sweets along. + +I highly recommend their Burnt Almond Torte with either custard or lemon filling for nearly any occasion. I get these for corporate gatherings often and they always go over well - and you know what they say about trying to please everyone! + +I'd suggest giving them a few days to a weeks notice as they keep pretty busy. + +(As a side note: though I rave about their donuts, pastries, and cakes.... for cookies I'd recommend Moi's Italian Bakery in Monroeville).[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The Lincoln Bakery did my wedding cake - White cake, chocolate mousse filling, and buttercream icing... it was fabulous! We got so many compliments, not only did it look beautiful but it tasted great![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Quite possibly the best bakery in Pittsburgh. It's got everything from the low-end (cookies, cupcakes, donuts) to the high (wedding cakes, tortes, tarts). Make any special or large orders weeks in advance. The tastiest wedding cake I ever sampled was from here: smooth buttercream icing with alternating raspberry and lemon filling in white batter.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> In one word, unbelievable. Their cakes are incredibly delicious. Despite the 20 minute trip from my house, I purchase all my cakes from here. The cakes are incredibly moist and the butter cream icing is just the right amount of sweet. My favorite cake is a yellow cake with FUDGE icing (not chocolate but FUDGE)!! I've also had the raspberry filling and would recommend that as well. They are incredibly creative with their decorating of the cakes including wedding cakes but if you want something specialized (nonstandard icing, etc) be sure to call ahead and place your order in advance. Warning: Saturday mornings you will surely encounter a very, very long line whether picking up your order or just swinging by for some goodies. + +Even better than their cakes are their petit-fours (chocolate with chocolate icing or white with vanilla icing). I've ordered them for bridal showers or just stopped by to pick one up for myself. They are the perfect size for one person (if you aren't on a diet). They do sell out of these so place an order ahead of time if you want a large order or stop by early in the morning to make sure you can get them. + +I've gotten cookies from here and they were average. I think this is the best bakery in the Burgh for cakes but not necessarily all other pastries and breads. + +The only reason I didn't rate the bakery 5 stars is their customer service which is borderline horrific. They are never friendly and whether you are calling to place an order or standing at the counter, they just want to get the order taken and move on to the next person in line. The cakes are good enough that I put up with the service but be forewarned.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love Lincoln Bakery so much. We just got a birthday cake from here today, and everyone at the party loved it. I seriously cannot believe how gorgeous it was. For fall cakes and cupcakes, I can't even imagine anyone making anything prettier! The icing is wonderful, although the colored icing is sort of bitter (but I think that is the case anywhere). The white icing is just perfect and not too sweet. When I told my neighbor that I was coming here tonight to pick up the cake, she immediately asked me if I had ever had the carrot cake. Yes, I have, and it is amazing! The burnt almond torte rivals Prantl's. I think the girls who work there are so nice and helpful. And I love all of the homemade candy that they sell. It is just the sweetest local gem. Love Lincoln Bakery.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Lincoln Bakery is yet another local bakery I've been meaning to try. When a Google Offer came up, I took it so I would have no excuse to keep avoiding it. The place has a nice neighborhood bakery feel; as I took in the many selections it seemed that everyone who came in was a regular. There weren't many people when I was there (it was still relatively early) but I got the impression that at times there can be a line to the door. +One thing that I didn't like was although they had many pastries to choose from, nothing was labeled. So I had to keep asking what things were. The cinnamon roll was okay, nothing spectacular. But the pastries I got were very good. I'd recommend checking it out. I know if I'm ever in the neighborhood I will stop in for a treat myself.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Lincoln Bakery is great. My family has been ordering cakes from here for years, and I always request one for my birthday each year. We probably order about 10 cakes a year from Lincoln Bakery, and often it's the same one: the simple and delicious chocolate cake with chocolate icing. If you like chocolate cakes, try it, and I bet you'll like it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Cookies aren't bad. Haven't had a reason to buy cakes or other pastries. Staff is friendly and it smells like heaven.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My daughter CAN'T pass by here without asking to get something. All I can say is you had better bring your sweet tooth![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Lincoln Bakery makes very delicious donuts, pastries, and desserts. Their bread selection, however, was very limited and upon making our choice the quality of the bread was mediocre. We were also disappointed that many of the things in the shop are not labeled and when the store is busy it can be difficult to find staff to explain what different options are. Still, this should be a go to for a local bakery if you are looking for something sweet.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I ordered a cake for a baptism. I did a search on the best tasting cake around Pittsburgh and after reading reviews, Lincoln bakery was the one we had to try. + +I called them a week ahead, they told me the design they would do and after seeing some pictures on their Facebook page I trusted it will work out so I went ahead and ordered it. + +It was a big hit! Some of my family members were getting seconds. +The cake wasn't too sweet and the icing not too ""buttery"". I will have to say that next time I need a cake I will order from this bakery, and maybe try some of the other things they carry in their store.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Got a key lime pie from this place. It was horrid. Icing was stale cake thick, crust was not even crunchy or had taste, and the key lime was weak. Pie looked it it was sitting out for a day or 2.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is a pretty decent Arby's, and given the condition of the other fast food restaurants on this stretch of Ohio River, it practically reaches exceptional. The dining room is clean and nicely modern. The service is friendly. I don't think I've ever had a bad experience.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Everytime I eat at this location I end up with a sick stomach. I don't have that problem at other Arby's. The dining area is clean and everything else seems ok but I always get a sick stomach. Maybe they should relook at their food prep.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Arby's is definitely king of the fast food joints on the Blvd. For that, I'd give it five stars. However, it's still fast food, which explains the mediocre rating. Do not go here without a coupon from the Sunday paper--there's a whole page of them at least once a month. The staff here is very nice and very fast, and on the whole, the food is better than elsewhere by the river if you're stuck with a fast food choice.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Without question, this is my favorite thrift store in the greater Pittsburgh region. I find antique kitchenwares here that are older than my grandma, worth $85 if the antique mall is to be believed, and priced at $2.50. The 50%-off sales actually pay off here. The merchandise turns over quickly. The staff is a real cast of characters (don't miss the steelers tattoos!!! i'm seriously serious, they are amazing). there are bicycles for you and your kids in decent-semi-working condition. The balance of stuff is about half and half valuable old vintage and more modern hand-me-downs. The prices are reasonable to cheap. The plastic bags on the wall are often a treasure trove. The kitchen section could outfit your kitchen in fondue pots for days. Most thrift store remodels result in ridiculous high prices to pay for the construction. The remodel here just means a bigger, cleaner store and parking lot. + +I have spent, cumulatively, probably several weeks of my life in this store. This is, hands-down, without question, the thing I miss most about leaving Pittsburgh. This store is the largest single contributor to my wardrobe, outside of H&M.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> So I came to this Red White and Blue with high hopes of thrift store mecca, and I will get to how I left empty handed and in tears. First, I'll walk you through my experience. + This place is pretty large, and relatively clean, with a nice parking lot. The racks are packed with clothes - and I mean, hard to move the hangers because there is so much stock, which can be a pro or a con depending on how you like it. I found it a bit cumbersome since although the clothes are organized by type (dress vs. blouse) there is NO size separation. In a place this huge, it takes quite a long time to find what you're looking for without the size separation. But, I'm not one to abandon a bargain because I don't want to look around (after all, that is what its all about), so I gave a good 30 min-45 and got a handful of garments to try on. (I would typically spend a few hours, but I was trying to spare a friend not as keen on secondhand garments). With my carefully extracted finds I searched in vain for a fitting room, never to find one. After asking the staff where it was, I had to take a seat and leave my jaw dropped for a while because THERE IS NO FITTING ROOM! +I couldn't take this fact into my brain, and although there were some household items I wanted to go back and buy, I was too upset to continue. (Sidenote: yes, I can understand how this can work for the RWB, but imho it is unforgivable, and I wish there was at least some warning before spending my time searching for a bargain when I couldn't even see if it would fit). + +I would recommend this store if you are looking for something specific secondhand especially for dishes, or older electronics, or even beauty products. There was even a used Nikon SLR with a wide angle lens ($200 though)! +But if you plan on buying a sundress, and don't plan on stripping down in front of your fellow thrifties, you'd better be confident in your purchase. RWB is just like any other thrift store, and you can't return or exchange your items, so you'd be out of luck and out of money.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Woo Hoo! Dead Lady. + +This thrift store rocks. I have been doing this for more years that I haven't been, and it is the best in the city. + +I would make a weekly trek to RWB, and would never be disappointed. These were the days when you could find a vintage 50s something or other on the racks, before there was a ""Vintage"" section. Still, recently, there is always a treasure to be had, especially in the housewares department. The proximity of this thrift store to the affluent neighborhood of Sewickley accounts for its top-notch merch. Whenever we'd have a particularly good day, my frends and I would joke...""dead lady.""[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I came here all the time while I was freelancing and in charge of my own schedule. It has a lot of points going for it that other thrift shops consistently mess up. + +1. It's well lit. You can SEE the clothing, see whatever might be wrong with it, and make an honest assessment. You're never surprised when you leave at the state of the items you've just bought. + +2. It is surprisingly clean. Nothing seems to smell, so I can only imagine they've laundered everything thoroughly. + +3. There are good quality brands--Ann Taylor, Kenneth Cole, etc. It's mainly items along these lines. You're more likely to find twinsets than clubbing tops here, which if you're over the age of 21 is a good thing. + +4. Markdowns and fresh merchandise. These people *know* how to turn over their stock. Because the place is never empty, and there are specials every day, the stock flips rapidly. The merchandise is never the same week to week, so as I mentioned before, it's addictive. You never know what you'll find. + +A summary of a few things I've bought here: a 6 dollar designer knit dress, a few silk twinsets ($2-$5), countless heels, two pairs of Birkenstocks and two pairs of Doc Martens ($4-$8), a dressmaker's bust ($5), a pressure cooker ($7).... + +You get the picture. The prices aren't rock bottom, but close enough, and the quality of the clothing will help anyone but the stingiest person get over the 50 cents extra. + +Can't recommend it enough![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My very favorite store in the world! Their recent remodel made it bigger and easier to find things and not have to get stuck in an aisle with 10 other people. + +I get 80% of my wardrobe from here - the shoes and purses are the best and have always found something great to take home[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Simply the best thrift store I've ever been to. Well worth the 3 1/2 hour drive from my hometown. + +First, and foremost, EVERYTHING IS 1/2 off all of the time! + +Secondly, bring cash. They DO NOT accept credit cards. + +The store is full of wonderful pieces of clothing, all arranged by color and type (not by size, which is unfortunate). I found a wide selection of everything from casual pieces to high-end business attire to super-trendy teen clothing... what surprised me most about this store was the QUALITY of the clothing. Almost all of the pieces were flawless, a few were worn or faded in some way and the price reflected that. Brand names were bountiful; Banana Republic, Ralph Lauren, Chico's, Jones New York, Ann Taylor, American Eagle, H&M. There were also some wonderful vintage pieces from the 80s, bright colors and crazy shoulder pads that would have made a more adventurous fashionista very happy indeed! + +The clothing smells wonderful, not musty or dirty as in some thrift stores, and there was even a large selection of plus-sized clothing carefully culled out in a special section. + +I went to Red White & Blue to find some business attire for my new job, and came home with two gorgeous, flawless statement blazers from Ann Taylor Loft and Banana Republic... for a total of $7! + +Come to this thrift store; it'll make all other shopping obsolete![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I cannot imagine a more miserable place to shop than this jam-packed monstrosity. This is a store that makes me thankful for Goodwill and The Salvation Army resale stores. The customers and the staff are miserable at Red White and Blue. The clothes are priced far higher than other such shops. Merchandise is not refundable or exchangeable, and there are no fitting rooms! One purchases clothes at their own risk! What person would buy a suit under these conditions, hoping the pants will fit? Unlike other stores, there is no senior discount and no credit cards accepted, a rare cash only business. To the reviewer who boasts that everything is 50% off every day, how is that a sale? It is bogus pricing. Red White and Blue, uggh![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Ever shopped at a Thrift Shop that sells high end labels, some brand new and gently used items like backpacks for $5? This is a great place to discover unique things. They also have daily deals such as 1/2 off of certain color tags. Have to dig through other things though to find something interesting which is part of the adventure![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> First time i really took a moment to look for some stuff. It's always a Hit or miss, all the other thrift store I've visited later in my trip showed me that. Thrift store sure does drain a lot of your mental energy. Looking for stuff there was a hellacious project but I bought a Steeler jersey for 2.50$, some polos and a cute outfit for a friends baby. 20$ before reduction and after 7.90$!! wohh!! That felt good!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Love the store. Great stuff, High price. Buyer BEWARE of the RUDE cashier SYLVIA, extremely unpleasant, unwilling to help and always with NEGATIVE attitude. She needs customer service training....Someone please tell her to stop complaining about other customers or employees....Cashier that does window display is always kind, friendly and helpful.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love a deal, and this has been my favorite thrift store since I was a kid. + +First, there is some sort of half-off deal every day. + +Second, the used book selection is pretty decent. Yeah, there are a ton of self-help and Patterson mass markets that you have wade through, but T.C. Boyle for two bucks? Yes, please. + +Third, the home goods. I've gotten huge solid wood picture frames for only a couple dollars. The art prints inside were hideous...but I threw those away, re-stained the frames to my liking, cut new mats, and inserting art quoted as $360 each to frame at a big chain fabric store for under $30. Boom. + +Finally, there is a decent selection of lamp to re-wire, always lot of furniture, some diamond in the rough clothes on occasion, and lots of other wacky stuff that's just fun to sift through. + +CASH ONLY and the cashiers are pretty rude/lazy, but that never bothers me. + +BONUS: They pick up your donations for free from your porch. http://www.pickupplease.org/ Super easy.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Prices not great for true thrifters. Staff completely useless. No dressing rooms. I simply have nothing to say about this place.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love love LOVE this store. I thought the one on Saw Mill Run was great but this was i think is way awesomer. If only awesomer were a word. I love to go here and find lots of home decor items to decorate my house. candle holders, DIning sets, paints, sculptures and sooo much more. I found this small desk lamp that has a victorian look to it with the shade included for $4. The lamp shade was made of some kind of smooth material almost like leather. It's such a great find. There are plenty of items for sale at this place and most of them are in great shape. + +So the clothes which occupy most of the store are the best find. The Store has certain days that offer you %50 certain color tags. I went on a Monday and it was half off yellow and white tags. Other days its half off blue, or green or red. I love to go on Saturdays!! This past week it was half off every tag except white. I found so many items for such a cheap price. $7 shirts for $3.50 and tunics for $4. Have you ever find items for $1?? I have!!! I love when I find a great shirt or sweater for $3 or less. Or when you find a brand new item with the tags on them for under $7. I bought a brand new pair of Arizona Jeans (in my size) for $5. I couldn't believe it. I was too excited. + +The clothes are organized by color but not by size which is a good and bad thing. I like to shop by color since I don't wear too many yellows or purples. I can avoid those sections all together but when I do find a nice shirt in the color I want the size becomes an issue. There were a lot of nice shirt that were just too small or too big. Even when i have to pass on a nice shirt I tend to find one that's just as good at the same price. + +Shopping here is a gold find!! My sister was the one who introduced me to this store and i used to make fun of her for shopping thrift. If I had known that It was nothing like the Good Will I would have been here a lot sooner. Now my sister makes fun f me for going so often. What an amazing place this is!! I'll probably never shop retail again!! + +REMINDER: CASH ONLY!! +-But they have an ATM!! $2.50 fee[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Rating this store is tough because I want to give it a 5...I really do. +Huge selection of clothing, housewares, electronics and furniture, but NO FITTING ROOMS! + +Yes, you read that correctly. No fitting rooms. Are you kidding me?!?! It doesn't completely overshadow the fact that they have great items, but when 95% of what you offer is clothing, you've got to have a few rooms for people to try stuff on! + +The clothing is organized by style and color, not by size, so be ready to dig. Same thing with the shoes. + +I asked a staff member where to try on clothing and she directed me to the back corner of the store where there were two long mirrors hanging side by side on the wall, directly in front of the kitchen section. I was slightly confused for a minute and then realized that was my only option. I decided against even peeking at any pants or blouses and instead went for jackets and sweaters I could easily try on over my shirt. + +Now, the mirrors are directly side-by-side, so if there are two people trying things on over their clothes (so weird), you're going to be right up on top of them. Not to mention you'll be right on top of people browsing through the kitchen section. + +A lady I was chatting with told me that she has seen women come in wearing tight fitting shirts/tank tops and spandex tights (hey, those are somehow socially acceptable as pants in public now, anyway!) so they are able to easily try everything on over their clothing (still weird). + +As annoyed as I was about the fitting room situation, I will probably make a trip out there again in the future to browse based solely on the size of the store. I just might have to wear some spandex.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I can't believe I've been here multiple times and haven't reviewed it yet. I absolutely love this place. It's a super thrift store if you will. + +No matter when I come here, I always find something. It quite the experience. I always make sure it's a day when I am off of work because I can literally spend hours here just looking. It's a good thing that I do this, you can't just show up here and think that you will be able to gran an item and then leave. + +Like a fellow reviewer said, there are not fitting rooms here, so be prepared to walk into someone trying on a potential great new garment for them self in the middle of an aisle. Sometimes you just can't avoid this, I blame the fact that they have mirrors set up throughout stores. + +They have everything you can seem to desire here. Clothing to electronics, furniture to bedding, books to movies. EVERYTHING is under this roof. + +*Cash only, ATM on premise.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This thrift store is one of the best in Pittsburgh; it's huge and has a great selection of books, clothes and housewares. + +With that being said, there are a number of drawbacks to shopping here because of its popularity. It starts with the parking. There are a few spots in front of the store, with two ""overflow"" lots that quickly fill up. Getting out is a bear if you're heading back towards the city, like I usually am, because to pull up to the traffic light you have to go the wrong way through the very narrow parking area in front of the store. Crossing three lanes on 51 without the help of a traffic light just seems like a bad plan. + +Once inside the store, beware of other customers on the weekends. I've encountered aggressive shoppers on multiple occasions who are usually welding carts as weapons. Let's just say some shoppers think it's OK to block off entire aisles so they can peruse a section. + +Other notes: There are no fitting rooms. I sometimes try on clothes over the ones I'm wearing in front of a mirror, because hey, it's a thrift store. + +Also, they're cash only. + +Despite these setbacks, I find myself coming back every few months because I've found some really awesome things here, from dresses to plates. Just think of the trip as a little adventure.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> nice and clean with well organized large selection but was expensive. I was looking for some twin size thin cotton blankets easy to wash and hang dry for my dog and the prices were $14.99 of course somewere high quality items which u would have to pay new retail store price $40-50 but still overpriced. I finally found a small blanket for $7 on sale.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is one of the true sleepers of ""neighborhood Pittsburgh."" Since 1979, this ""diner/family restaurant"" has been serving excellent breakfasts and home-cooked dinners. The staff has been there as long. + +They have some of the best fresh-brewed iced tea in the city. They also have my favorite pancakes. If you're looking for a cheap, low key, dependable place to go, come home at 8 o'clock one evening, sit in the window, and especially around the holiday season, I assure you that it will be one of the best ""old time"" meals you'll ever have. + +I hate its name, but I love the Rusty Nail.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The home-cooked breakfasts at The Rusty Nail in Bellevue are wonderful, prices are reasonable, the wait staff are gems, and is often bragged about by Bellevue locals. That said, two stars is all I can muster primarily due to the tiny, cramped dining area. I've witness people at three tables being disrupted while they are eating so departing diners would have enough room to push their chair away from the table and pass by others just to leave. + +Don't get me wrong, I adore that Pittsburgh is a small, friendly city, but I'm not fond of getting elbowed in the back as the guy behind me cuts his breakfast steak and eggs, nor knowing his guest gargled with Cool Mint Listerine this morning (or worse, didn't) . Yes, the tables are packed THAT close together. And whatever you do, don't dare bring a large friend here to dine when it's busy unless you enjoy feeling like a complete 'jag off' for doing so on the way out.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've been going here since I was a wee tot. I have always enjoyed their food even though there's nothing too special about it. I really like their breakfast menu. You always seem to get lots of food for very little money, which is nice. + +My only complaint is that it is WAY TOO SMALL and always very busy. They should really look at expanding the restaurant.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The Sunday brunches serve great pancakes, and I always felt so fancy eating here as a kid. Note that if you wait until the churches let out to get in line that there will be a long queue outside. The rest of the menu ranges from decent to average, but the food is always cheap. The tables are so close together it feels like you're crawling over your neighbors to be seated. On nicer summer days and during any of the Bellevue events, they often serve fresh lemonade or iced tea outside.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I really wanted to like the Rusty Nail. I love little local restaurants like this. But it really is a very tight squeeze, to begin with. They really need to pull some tables out of there to make more room. We were right on top of another table with two very loud young children, and there was just no buffer. And the food was.... just so bland! I get that it was supposed to be homestyle cooking, but it just had no flavor. To be fair, we did go for dinner, and I understand that this place is more of a breakfast joint, so I would be willing to try it again sometime for breakfast. For dinner though, unless you like super-bland food, I probably wouldn't return for seconds.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Given that the Rusty Nail has been highly recommended to me as a good breakfast spot by various sources, I'm sad to say I was sorely disappointed. + +They have a wide selection of breakfast options. However, even with numerous breakfast specials listed, not one included eggs, meat, potatoes AND toast. Yes, that's right. I had to order the eggs, bacon and toast special with a side of the potatoes. When my food was served, the portions were average except for the side order of potatoes. I did greatly enjoy the potatoes, though, which I ordered deep fried. My dining companion ordered the French toast with ham and enjoyed it very much. + +We were here on a weekday morning so we didn't have to worry about it being crowded. The service was good. And it's not that I thought anything was bad, it's just that, as the two star rating says, ""Meh, I've experienced better."" Given the plethora of choices in Bellevue, this will not be my first stop should I find myself on Lincoln Avenue for breakfast again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I always see this place, and Saturday we decided to stop in for lunch. The atmosphere was pleasant. My boyfriend had the buffalo chicken sandwich, which he loved. I however, ordered the steak and cheese pita and was extremely disappointed. The pita was soft and fresh but the steak was terrible. It was very steak-um like and saturated with grease. When I picked up the sandwich grease poured from it. I'm not one to send back food, and that's my fault, but the waitress came by once as I was eating, over heard me upset about my food, looked at me then continued on her way. Needless to say I don't think I will be returning.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I ate here this past Sunday morning for breakfast with my girlfriend. I have been by this place many times and was excited to finally make it inside. We were lucky that we went fairly early as a line developed shortly after we were seated at our table. The Rusty Nail is prepared for this in a pretty cool way though as they have a list outside of the restaurant that you can sign into as well as some coffee to partake of while you wait. + +For my entree I decided to go with one of the specials for the day which was the Rusty Nail omelet while my girlfriend decided on another special which was the a mushroom, spinach and feta junior omelet. Her omelet is self explanatory while mine had in it some salami, cheese and three pieces of sliced pepperoni on top of it. It was readily apparent that the pepperoni was not the cheap kind that you get on most pizzas as it had more flavoring and tasted much better. Both omelets came with sides of home fries and toast for which we both ordered deli rye. The junior omelet tasted good as the sourness of the feta played nicely with earthy mushrooms while the spinach made it feel like I was eating healthy. My omelet was just as good if not better than the junior omelet as the cheese and meats combined to make it seem like I was almost eating a pizza. Some of my hash browns were slightly overcooked and they had too many onions for my taste but we still decent enough to be a side to the main show. + +The bottom line for me is that I would definitely head back here in the future. Everything that I tasted was good and I would not hesitate to take any of my friends here for a breakfast.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> A great Pittsburgh diner with friendly service and good diner food. If there are any problems, the prices a bit high for diner food and, as others have said, it's extremely cramped. Otherwise, it's an enjoyable place to eat and the food is, indeed, very good.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I had one of the breakfast specials and it was fantastic. There was also a continuous flow of coffee, which is always nice. Probably just missed the church crowd so it wasn't too busy either. Definitely a good breakfast spot.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My wife, my daughter and I went here for breakfast. I got the breakfast special: $5 for French toast and eggs. Clean, great service, delicious food. You can't beat it for breakfast.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The first time we went here assuming by the name that it must be a dive bar. We were disappointed, but we were also hungry so we ordered dinner. It was just nothing special pretty typical greasy diner food. While there we couldn't help but notice all the articles and awards on the wall stating this was one of Pittsburgh's best breakfast spots. So, sometime later, on a hungover morning after a wedding some of my boyfriends friends were staying with me and wanted to get some breakfast and I thought let's check out that rusty nail again. What a great decision. I think we all got one of the specials and they were all delicious. Mine came with some kind of homemade hash brown patties that were amazing. The only downside is they only take cash (that's not uncommon around here) but they have an atm. Also there is often a wait on the weekends but for us it wasn't very long and they have free coffee outside for you while you wait. Well ok one more thing the actual restaurant is very small and kinda lop-sided but hey I'd rather have a cheap delicious breakfast in a shitty place than pay more for a nicer atmosphere.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I am very happy to be moving into a 'neighborhood' that has a line-up of decent mom-and-pop shops to find a reasonable meal when the cupboard is bare, or the energy banks are depleted for cooking. Bellevue does seem to have a small collection of decent eats at reasonable prices, and The Rusty Nail is one of that handful of good examples of neighborhood haunts. + +It's touted as a 'diner' in many of the reviews, but it really is a step above your average 'diner', and is more of a cozy neighborhood gathering spot for a decent burger, or entree. I've not made it there for the breakfast, but have always been satisfied by the dinners. + +Rusty Nail is hardly on the gourmet end of the scale. In fact, I would imagine the Sysco truck pulls up out back regularly with deliveries of food parts, from cans of sauces to frozen animal chunks. As long as those parts are assembled and doctored to make them seem a bit fresher than the typical conveyor-belt diner, all is fine. And indeed, all IS fine. + +So few of our local 'diners' are up to snuff when it comes to serving up decent 'diner' fare, that I can't call Rusty Nail a diner. It's a neighborhood family restaurant. Period. + +Burgers, meatloaf, pot roast, fish sammiches, salads, pastas...a varied but adequate menu. Fair and decent prices. Friendly and attentive service. A cozy enough atmosphere (although I have to say AGAIN in a review of a restaurant, if you've got multiple TVs in the space, for gods sake, can ONE of them NOT be showing SPORTS coverage??) and a pleasant crowd of patrons. + +During my last visit, there was a large family gathering at the next table. A nicely polished middle-class clan, ranging in age from gramps to granddaughter. At one point, dad received a phone call on his cell...and actually stepped OUTSIDE to have his conversation. As I was leaving I had to pat him on the back and thank him for being one of the few remaining decent guys with manners! + +Bottom line...Rusty Nail is comfortable. It's not a drive-out-of-you-way destination for dining. It is what it is. A great little neighborhood spot FOR the neighborhood. + +But do bring cash. The don't take credit cards. Believe it or not, they WILL actually take a check.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> On our recent visit to Pittsburgh my family and I had breakfast at the Rusty Nail in Bellevue (dad's hometown). The place is on the main street, Lincoln Ave (or up street as my family called it). + +They were quite busy on a Saturday morning but we only waited about 5-10 minutes for a table. I enjoyed a sausage omelet with American cheese and my husband had a Denver omelet. The omelets were well prepared and served with toast. Potatoes were and extra $2.29, but a serving of potatoes was enough for two. Breakfast for four adults was about $50 including tip. All adults had coffee or tea and a full breakfast. + +The service was friendly and prompt on the day we were there and coffee refills were offered readily. It is cramped quarters, but typical for neighborhood non-diner breakfast joints in urban areas. + +We had a great diner breakfast in homey surroundings. We will definitely go back when visiting Pittsburgh.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Checked out the neighborhood restaurant for Sunday brunch. The portions were generous and the omelets were very good. We felt that much of the food (e.g., sides) and service were just average. For example, we typically had to ask for coffee to be refilled. It is a great place to go for a quick bite to eat on a Sunday morning, but I would not make a special trip to the restaurant.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Place has amazing omelettes that are almost as big as the size of the plate. You get a really big side of home fries too. This is probably my favorite place for breakfast in Pittsburgh. I generally go in and get a seat right away without waiting. Service is usually fast and friendly. Two downsides to the place. 1) they are cash only which can be an inconvenience. I never remember to have cash until I get my bill so I have to run to the ATM. 2) the seating is limited and the tables are very close to each other so people there can most likely hear your conversations. Place overall is excellent and is worth a try at least for breakfast. The lunches and dinner selections aren't bad either!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The food at Joe's Rusty nail is GREAT. As the pictures will show, the servings/portions are plentiful. The service is quick, and the staff personable. I went there for breakfast AND everyone in our group left sated!! As always I had my kid carnivores in tow, and as is their custom they laid waste to EVERYTHING edible that was put before them. While they are a TAD (and I do mean tad) bit pricey I believe that the food is more than worth it. The clientele (what I can only believe are Bellevue regulars) are polite and inviting. My breakfast was made well, tasted great, and dressed pretty as a picture. I will tell you this is not my first rusty nail rodeo and lord willing it will not be my last. As I say I vote with my feet and my USD, and the staff at rusty nail can sleep well tonight knowing that my hard earned cash, will continue to flow at Joe's and my feet will continue to bring me there hopefully more often than not!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place is overpriced and the service is not good at all. When we where there children were riding bikes in the lot near the tables. One almost hit our child. Another customer said that if the owner had been there she would have not allowed the bikes to be there. The cone was large to say the least but the taste left something to be desired. Not the best neighborhood either with a bar nearby. Our children were exposed to language that would have made a sailor blush. We will not be back. Also they will accept a credit card but not a debit card????? Please get up with the times.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I am a big fan of this little ice cream place. You can get both hard and soft ice cream, so that satisfies myself and my daughter. They also have funnel cakes for my daughter that doesn't care for ice cream. The place is small but there is always a line and the DJ outside plays the best oldies while you wait.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I fell in love with this place as soon as we pulled up and saw the lights strung up and oldies coming from the speakers! + +I tried the banana cream pie hard ice cream, their scoops are very generous!! + +My bf got the peach cobbler hard ice cream and that was to die for! We got 4 servings of ice cream for $10, which nowadays is a steal IMO! :) + +I'll definitely be heading back with my coworkers this week![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Remember When.... I always do when I go to this ice cream shop... The oldies playing and the best and biggest ice cream in Pgh.. The large ice cream cone comes out the side door cause they can't fit out the window...WoW it's great and has been great for many many years.. Been going there since I was a young young lad I'm now 27 and take my family there we love it... Keep up the good work[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> First time here and I wasnt impressed at all! I should have gone to the dairy queen :-([/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My family makes an event out of going to Remember When to see Doo-wop Dan on Saturday nights during the summer. I usually go for the small cone, which is comparable to most other ice cream place's large. The large cone is so large that is doesn't fit out of the window, they have to bring it out the side door! + +The ice cream is good, the portions are generous, and the atmosphere (almost) makes you forget you are in Windgap. I highly recommend stopping by on a Saturday night to see Dan, listen to some oldies, and enjoy some ice cream![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is by far, the BEST soft serve ice cream place in southwestern PA. The ""flavor of the week"" is always interesting-and tasty! Though, I am somewhat disappointed that they've switched to a lower grade ice milk, for their vanilla and chocolate offerings. I don't know if this is a matter of cutting corners, or if the better stuff simply isn't available any longer. Either way, this place is still leaps and bounds ahead of DQ, Tastee Freeze, etc. It's definitely worth the trip. It's mostly street parking, though they do have about 3-4 parking spaces off to the side. Serving sizes are huge! The small cone here, is the same size as a DQ large. And the large is SO big, they can't fit it through the window-they hand it out the side door. + +If you want a real ""Kodak moment""-order a large cone for the kids, and keep the camera, and wet wipes handy![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Excellent service and repair. Completely explained how to adjust and take care of our Grandfather clock on our own. Would recommend to others.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Thank You Kim and Kurt! It was very nice of you guys to take the time to post your reviews on our service. We really appreciate it. We hope your clocks will continue to do well for years to come. Please dont hesitate to give us a call if there's anything else we can do for you. + +Lisa +Paul's Clock Repair[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Sometime ago,I was looking for someone to service my Grandfather clocks in my home. After extensive research,I ran across these folks. I couldn't be happier with the result of their visitation. The knowledge they possess and the professionalism with which they practice,is impeccable! ALL of my clocks are running at peak performance;they even took the time to look at my ""Black Forest"" cuckoo clocks and passed on valuable advice as to how I should maintain them. I graciously appreciate their time,demeanor,and service! I wish no one else to service my clocks in the future! YOU CANNOT GO WRONG WITH THESE FOLKS! HIGHLY RECOMMENDED! Thank-you so much for all that you have done to restore my precious time pieces![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I can not express my thanks & gratitude enough to everyone at Paul's Clock Repair. I needed an Atmos clock repaired, which was given to me by my mother who had recently passed away. I needed it done on a short time line since I live out-of-town and was leaving soon. It is next to impossible to find anyone who can actually fix that type of clock especially anywhere close to where I live. They were so accommodating and really really helped me out during a hard time. Much thanks to Lisa for spending the time to teach my about the clock & how to take care of it and her dad for fixing it up! My Atmos clock is now working great and looks wonderful on my mantle![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Good selection, but it will cost you. +Multiple fridges of cold beer, but only the cheap beer is cold. +Nice in person, but rude on the phone. +Parking lot, but none of the customers understand how to park. + +Every good thing about this place is equaled with a bad thing about this place - hence it probably deserves 3 stars. I would really give it a 3.5 if available as this is currently my beer distributor of choice, but since its not possible I have to go with 4. + +Why 4 you ask, when I just went through all that 3 star crap? Any place that offers beer samples provided by attractive women gets a half star boost for sure, and as long as I'm going there anyway it really makes for a more interesting trip. + +After all, if you don't like free beer, you are probably a terrorist.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My beer distributor of choice - and there are others located closer to me. + +Let's be clear, it is no frills, cases of beer stacked up, limited cases in the cooler. Selection is ok - if I were looking for something obscure - I wouldn't count on them having it. + +But they are helpful and efficient. They have convenient hours and parking**. Also they helped me out in a keg emergency that saved a party. Service in a jam earns my loyalty. + +**Note - most of their customers have no idea how to park in said parking lot.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great selection. HOWEVER, only the cheap beers I've never admit to drinking are kept in the coolers. So if you want local microbrews, seasonals, or even Blue Moon, you're going to want to leave time to chill the bottles before your next shindig. + +Having only acquired a taste for beer while living in Tennessee--where beer can be bought in grocery stores, gas stations, and shady alleys--the prices seem steep to me. But I don't have much experience buying alcohol off-premise in PA, so I'm only deducting one star here. + +There is a parking lot, but it's small and everyone parks crookedly, so good luck with that.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Ok. Full disclosure: I know NOTHING about beer. I'm a wine girl, or a hard-booze girl, but NEVER a beer girl. And yet somehow, I wind up being the girl who is sent out to buy beer for the party full of random people at our house who all like different beer. + +Here's a rundown of what happened on a recent night that this occurred at Pistella's: + +Me: ::wanders around for 15 minutes overwhelmed with beer choices, before giving up and going to the register:: +Dude working at Pistella's: Need help? +Me: Yes. I do not drink this stuff, but everyone coming to my house tonight does. Help! +Dude: Any idea what your friends like? +Me: Umm... my husband likes to drink Dos Equis. My one friend likes 'lighter' beers. Oh, and I am broke because I just bought a lot of chips and salsa at Whole Foods. +Dude: Girl just follow me. Here, we are having a sale on the Dos Equis variety pack. That has something for all of your friends. It even has a Christmas beer to make everyone get in the holiday spirit! You will be the hero of the party! And I will carry this to the register for you and everything. +Me: Thank you! +My friends, later that night: Girl you rock. We are all happy with this beer, and that leaves more vodka for you! + +So that is why I choose Pistella's when I am sent out on beer run: because there are cool dudes working there who will help me not come home with a case of Jacob's Best. (Nor does anyone give me crap for not understanding beer - I like that!)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Ha! The parking lot is good, and yet nobody can ever park properly or politely! This is a good distributor that is conveniently located, well-stocked, and has friendly staff. It is a little unfortunate that the only cases that are kept in the cooler are the less exotic beers, but their selection is fairly broad, and the space is small, so I won't dwell too much on that. Overall, a decent beer shop, as long as we are shackled to the idea of the distributor here in PA.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I stopped by here on my way home from whole foods market. They had just paved there parking lot which can only fit 3 max cars at a time. It was not as big as the one I normally shop at in Penn Hills. They are a beer distributor and have a way hugger selection. But they serve all of penn hills so go figure. + +I was looking for a gluten free beer which they had four kinds including cider. The prices were crazy expensive. $35 for a 24 pack of cider. NO way!! + +I had to buy it though cause it was sunday at 4:30 and all the stores close at 5 so i had no choice. I should have waited but i drove all the way here to get it so I should just buy it while i'm there. Aside from the money issue this place was just ok to me.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We are fans of Pistella Beer Distributors simply because we needed beer one night while visiting some friends and family in Pittsburgh and they happened to be on the way to something we were doing. It's a hole in the wall kind of facade but they do have a good selection. I don't remember the price being that expensive but looking at the average review so far...it shows $$$$. I'm sure they have some nice stuff, but we just got a case of beer (I think one of those Magic Hat variety packs) and it seemed similar to what we would pay in the other stores. Anyway, we had a good experience with this place and don't really have anything bad to say about them.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is my go-to distributer. They have a great selection and lots of hard to find brews. I haven't noticed that it's any more expensive than going elsewhere but honestly if I don't buy here then I'm buying six packs which as we all know are a huuugggge rip off. So any time I have a case of something I love I feel like I'm getting a bargain. The cold selection does suck so I try to plan ahead and have what I need already cold. Staff here are all very helpful- and will have recommendations if you ask.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> In my opinion, this is the best distributor in the city. The people running it are great, the selection is very good, and the prices are competitive with almost any other place I've been to. Because I'm not too picky, I typically have been stopping right at the front to buy the discounted brew that's usually out of season. You can't beat buying a case for $12.99. I'll continue to go here for my beer needs until I leave the city.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Love these guys! I have a huge picnic every year for my job, and I always use Pistella for my beverages. They're nice folks, always get the order right, and it's on time. I've also been to the store itself many times, and they do indeed have a great selection.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Love this beer distributor. They always have what I'm looking for. The workers are extremely nice and always willing to help. Best one I've seen by far.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> after trying a couple groomers in Pittsburgh, we found Animal Elegance. They always took good care of our poodle. Clean poodle feet and an even cut. +You should try them too.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> i was a vet tech for 6 years so I'm pretty particular about people caring for my pets. The groomer (becky) listened to what I wanted and did exactly what we had discussed. My dog always seems quite happy and relaxed after a grooming there. (a really good sign). Also, they are recommended by one of my favorite pet shops in Pittsburgh, Smiley's Pet Pad. I wholeheartedly trust Animal Elegance to take proper care of my little furry friends.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Animal Elegance is not much on the outside but the owner was very nice & LISTENED to how I wanted my teacup poodle groomed and used the products that I requested. +I was very happy with my services and I will return. + My poodles groom was $50,including tip, which I think is very reasonable.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I just moved to Pittsburgh and I took the word of other reviewers when making my decision to give Animal Elegance a try. My two standard poodles looked GREAT and seemed very happy after our visit! I would have given Amy and her crew five stars but the price was a good deal more than I am used to paying. I had hoped to come back every two to three weeks but it is just too expenseive for that. I may have to find another groomer for touch ups in between visits to Animal Elegance. +I feel like this is similar to a ""special occasion"" retaurant: One where you would go all the time if the price was just a bit lower for regular customers....[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I use their services regularly. They in fact are the only place I will take my dog ""Gaffney"". The location is right off the main street. She is always extremely well groomed when they are done. They are worth the price.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I had a very unfortunate experience with this groomer. My dog was not groomed to my specifications; infact she was butchered. I went to the trouble of taking a photo of my dog with the haircut that I wanted, as well as speaking with the woman who assured me she would be grooming my dog. The owner groomed my dog, not the woman that I spoke with and she looked nothing like my dog when I picked her up. The owner was rude and did not even apologize for the horrible service. Do not take your dog there to be groomed![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> They made my Portuguese Water Dog look horrible. + +They actually sheared all the fur from my dog claiming that it was matted and therefore they had no choice. This isn't true as I personally brush my dog every morning. When I complained, the owner said: ""But we did tell you that we will cut the dog's fur short."" Yes, they did, and I thought that considering that the days are hot in August, they are proposing a little cooler grooming. I never expected them to just shear the dog to the skin. +I think they did it because they are hopelessly irresponsible. Although they charged $70 for this brutally simple operation they have not even trimmed dog's ears and tail. Consequently, the dog has disproportionally long hair on its tail and the ears. +I used Animal Elegance for more than a decade. Long before current management took over. Over all these years I sometimes took in stride their accessional compromise of standards and always paid their exorbitant prices without complaint. However, this fragrant negligence, combined with their total disregard of the fact that I was an old and loyal customer did it. I will avoid this place from now on and would like to suggest that you do the same.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My Kingston cooper is a havanese and is a goofy handful and they handled him well. I loved his hair cut. I changed from a different groomer to here. He's only been here once about a month ago but I loved it and we will definitely be coming back. Done in a timely manner and I love the cat that walks around and so does Kingston cooper he has 2 cats himself so he felt right at home. We will be back soon. And it's not far from my house so perfect location. Thanks guys for doing a wonderful job!!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place is the best! We won't take our dog anywhere else for grooming. It's a very mom & pop type of place. They genuinely cared for our puppy, not to mention the perfect job they did on the cut and washing. Everyone who works here seems to treat the animals with the upmost care. Such a convenient location on Butler Street near Lawrencevillle. Can't wait to go back!! Thank you so much!!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is my go to place to get my Yorkiepoo groomed. The surrounding area looks a little ""sad"", but let's face it, lots of areas look like that here in Pittsburgh. Inside, however, the place appears newer and well kept. My dog has gotten consistently good haircuts here and she's always in a good mood when I pick her up. That's a keeper in my books! Oh, and the cost is about $45-50, which I'd say is average for most groomers I've gone to.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> A decent Italian restaurant serving delicious fresh made bread with hummus, flat breads, salads, soups, and pasta. Outdoor seating is available in nice weather, and the service is friendly. Overall, not a bad place, but not super exciting either - Pino's suffers from its close proximity to the excellent Point Brugge Cafe. It also gets quite noisy inside so it's hard to carry on a conversation, and seems to attract a somewhat older crowd of people.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I wound up here the other night after walking down the street because of a 45 minute wait at Point Brugge Cafe. While my friends and I were leery of the prices on the menu, the owner cajoled us into coming inside and were seated right away. I'm glad he did! The menu is rather expansive, but mainly focuses on Italian fare with an occasional jab at the more popular Pointe Brugge up the street: mussels and fries. + +It happened to be lasagna night. Because I am used to the home cooked variety, I had a hard time shelling out $18 for lasagna. I selected the wild mushroom and spinach option and it also came with the soup of the day, which happened to be gumbo. Both were very good. The gumbo had a very earthy taste along with good amounts of sausage, jumbo lump crab, and risotto mixed in. Rather than being the layered the lasagna was one giant noodle, the size of the entire plate, stuffed with a generous amount of mushrooms and spinach folded over itself with marinara and cheese. Didn't get a chance to try dessert. + +Both items I had were rather tasty, and I would easily come back here for a great meal.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I made it back here about two weeks ago. I must say the experience was night and day compared to the one at the end of July. Whether or not it was an off night I do not know, but the place was loud and crowded, the service was bad, and the food was mediocre at best. I should have just waited it out at Point Brugge. I won't becoming back anytime soon.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've been told several times that this place had a great brunch. Upon arrival, the menu was very limited and the service was abysmal despite a nearly empty restaurant. We literally waited 15 mins. at our table and then left prior to ordering.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I often have lunch at the nearby Point Brugge Cafe, but I decided to give Pino's a try today for a change of pace. Bad idea. My lady friend and I started with a pair of appetizers: greens & beans and ""Italian frites."" The latter, which the menu described as ""fresh cut, twice cooked, fresh herbs & roasted garlic,"" were basically just regular-ass french fries - decent, but nowhere near worth their $6 price tag. The greens and beans were even more of a rip-off: 8 FREAKIN' DOLLARS for a smallish bowl of rather flavorless produce. Talk about a profit margin! + +As a main course we shared a flatbread with goat cheese, caramelized onions, and roasted red pepper. It was pretty good, but my enjoyment was diminished by the FM radio that was blaring through the loudspeakers. Who wants to hear car commercials while eating a meal at a ""nice"" restaurant? Classless. + +Conclusion: I'd rather wait 45 minutes for a table at Point Brugge than be seated immediately at Pino's.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It's a shame that some of the other reviewers had poor experiences. I discovered Pino's after deciding that the wait for Point Brugge simply wasn't worth it. + +The brunch was very good, I enjoyed the atmosphere, particularly the ""missing"" wall which gives the appearance of outdoor seating, and particularly liked not having to sit shoulder-to-shoulder with other people. + +My sole comment would be that the owner, who was very friendly, should let his food speak for itself rather than being so concerned about the neighborhood competition.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I must admit that the first time I went to Pino's (about 6 months ago), I was NOT a fan for several reasons. However, after coming home from brunch, the experience was enough to not only completely change my mind, but to keep me coming back. + +My boyfriend had the scallops and I have the pino benedict (eggs benedict, of course). My boyfriend literally looked like he was having a religious experience with the scallops. His eyes were closed, he was moaning, and it took him about 25 minutes to eat 3 scallops. He said it was the first time in his life that he ever wanted to take so much time to chew his food. +My dish was delicious and the in-house made bread was fresh and savory. + +Overall, I am very pleased with the lunch menu and the range of dishes that are available. We'll definitely be back for brunch.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Pino's appears to fashion itself something of a nouveau-Italian, smart casual neighborhood restaurant, and it's literally just that. Translation: the menu is uninspired and predictable. A relatively encompassing selection of appetizers and entrees revealed not quite a soul-crushing, but certainly a lackadaisical attitude toward ingredients, recipes and presentation, though the service was refreshingly excellent. Unfortunately, the only other reason you'd be dining in Point Breeze would be to enjoy the amazing Point Brugge Cafe just down the street. As a previous reviewer mentioned, I stopped in simply because the Brugge was full, but I unfortunately won't be making that mistake again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> What a disappointment!! Evening started pretty badly and did not get much better. +We had reservations for 5 people at 7PM this past Saturday. Two of us were there early and rudely treated by the hostess. She was vague about seating us and we decided to wait at the bar. When the rest of our group arrived (on time!!), I informed the hostess and she looked at me blankly and then the packed restaurant. She told me it would be awhile. Huh? When asked what ""awhile"" was, she said 20min. But then seated us in 5 (she had to bus a table which I take it as one of the things she dislikes about her job - that and people). + +Food was a let down. Potato latkes were greasy and blah. Fish tacos were recommended and were basically fried fish sticks. Pumpkin risotta was heavy and confusing flavor wise. Others had the same sentiments. + +Service was rough. Long waits and lack of attentiveness. Noise level (couldn't converse at all) made the night just a bit harer to tolerate. +Not sure Pino's will get a repeat visit. Disappointment:([/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Bland food and poor service. Its a shame since it's a great location and could be much more, especially since there is always overflow from nearby point brugge.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> In similar fashion to Joseph S. I, too, decided to give Pino's a shot once we saw how packed nearby Point Brugge, which had initially drawn our party due to its reputation, was. It was a relatively nice evening, and I thought the concept of fresh-air dining was too good to pass us by. We were immediately greeted by Jen, one of the co-owners, as we entered. I made it a point to compliment the beautiful inlaid tile in our tabletop, and she volunteered some additional information about their production that I found to be very interesting. + +I really loved the bistro burger. I requested it to be prepared ""Medium"", and sure enough it lived up to my expectations---you'd be surprised how many times I've ordered a medium burger only to have it served well-done and nearly bone-dry at other restaurants. Nicole, our waitress, proved her weight in gold when she reassured me that gorgonzola would be a good cheese to accompany the bacon on the burger. We also ordered the macaroni & cheese as an appetizer. I thought the ziti was a bit dry, but the sauce and cheese were delicious. We really loved the bread and the garlic butter spread. I was hoping for an oil & vinegar blend to have with the bread, but the spread served as a surprisingly tasty alternative. My partner's ravioli looked delicious, and he let me try one of his meatballs, which I found to have that ""homemade"" flavor that's difficult to find at many restaurants. Our friend loved her arugula salad, and as a seafood aficionado I was impressed by the very generous size of the shrimp she had. Our service was prompt---our water glasses had barely gone half-empty before our waitress scurried over to replenish them. + +Overall we loved our experience and WILL be back! We were told about Pino's legendary Sunday brunches, and I look forward to trying one myself the next Sunday I have off from work.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Enjoyed a wonderful evening eating outdoors on a perfect Pittsburgh spring night. The charcuterie plate worked well as an appetizer for 3 and included a fantastic balsamic dressing. I had the best pasta and white clam sauce I've ever experienced, and the other members of our party enjoyed their entrees, as well. Nice find in the Point Breeze neighborhood.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> TASTY OPTION FOR SUNDAY BRUNCH + +I've read the reviews and what seems to ring true is that Pino's has a good Sunday Brunch. Thankfully that's when me and my gang decided to check out this little lovely! + +Brunch menu has both traditional brunch fair and some Italian twists. My mum had Challah French toast and loved it. Pops had their breakfast risotto with a fried egg on top - I tried that and it had a nice kick to it. + +Other folks at the table had the eggs Benedict, salad, and Sammy. Over all everyone was happy and it was only half full so easy to talk and hang out. + +And for the music complainer (you whining stinker) we had a nice iPod mix on when we were there![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My favorite Italian restaurant in Pittsburgh. All-time favorite dish: eggplant parmesan with their spicy arrabbiata sauce, I had to ask for them to make it that way. Not your typical layers of fried, heavy eggplant--lighter, chunkier eggplant that melts in your mouth. My favorite appetizer there is the sizzling olives--they bring you a little cast iron skillet and throw olives in it--they soften and are so wonderful to eat! Flavor explodes in your mouth! Also good is ther roasted veggie platter and charcuterie plate. We typically go on less crowded days, as the restaurant is small--but we've always had excellent service and the food comes out hot and fresh![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> this place had a great selection. The mussels were outstanding and the staff was very professional!!. TRY IT YOU WILL LIKE IT!!!!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I like this place so much! Unpretentious. Everything is made from scratch. Service is amazing. Lots of small plates. Great wine deals... Definitely worth a trip.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> BEFORE Pino's was renovated, it was a tiny, unpretentious, hole-in-the-wall restaurant with a friendly atmosphere, and amazing Italian food. It was also a BYOB, which I love. This was our ""go-to"" restaurant. + +AFTER Pino's was renovated, there was a complete transformation. While the interior is now very nice, It's no longer a BYOB, and the staff is full of attitude, which seems to stem from the total arrogance of Pino himself. + +On our most recent visit, we were a party of four with reservations at 7:30 PM. We arrived at 7:25, and weren't even acknowledged until 7:40 PM. Pino was playing maitre d', and when he finally acknowledged our presence he seemed totally clueless and was overtly UN-apologetic. There were no open tables, despite having reservations. When 8:00 PM rolled around, I was frantically calling other local restaurants to see if we could get in. No such luck, since it was prime dining time on Saturday night. Finally, around 8:30 PM, the waitstaff brought a two person table up from the basement, crowded four chairs around it and jammed it into the middle of the restaurant for us to sit in. Pino then literally threw our menu's at us, and walked away. Not so much as a free drink for our inconvenience. + +The food is still good here, but I refuse to give my money to someone who CLEARLY does not appreciate your business. There are SO many good restaurants in the area, with owners/chefs who are happy to have you. Next time you think about going here, walk an extra block to the Point Brugge Cafe.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Six of us went to dinner, six of us had fabulous meals! My husband said his seafood fra diavlo was the best he ever ate, not a bit fishy--loaded with fresh seafood and a spicy sauce. My son had the carbonara which he described as fabulous. My daughter had the roasted veggie platter as her meal (it is a large appetizer), and I also sampled it--the vegetables and olives were marinated and grilled perfectly. My father had the skirt steak which he loved, and my son had a sausage pizza. Both said they were delish! I usually get the eggplant parmesan with their spicy arribiata sauce but this time I had a pasta dish loaded with artichokes and shrimp in a spicy sauce. It was excellent! + +It was my father's birthday, and they brought out a Tiramisu for us to share (we didn't even ask for it), and that was luscious as well! The staff was as nice as can be--we will be back without a doubt! + +I love this place![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> ""God this is the best eggplant that I have ever tasted!"" was what our friend said after he took his first bite of the Sicilian eggplant served at Pino's. My husband couldn't wait to have the seafood fra diavlo, which he had last time...again, a 10 out of 10! I had the roasted veggie platter for my entree, which is really an appetizer--and I had to share--way too much for one person to eat. Another comment from our friend (who was a first timer at Pino's) was that it was the best Italian dressing that he ever had. As I write, I want to go back for dinner tonight!! + +Forgot to mention, they also have local beers on tap (East End Brewery), the men enjoyed the Homewood brew (dark lager type beer), it's great to see the owners supporting local businesses![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I went to Pino's to celebrate a friends birthday on a Thursday night. I hadn't been in Pino's since they renovated, but I have to say that they made the interior beautiful. We made reservations, but I don't think we would have needed them since there was just a few other parties seated when we came in. + +My two girlfriends and I always have a tough time deciding what to order...so naturally we order one of everything that looks good. We started with the Charcuterie platter, which was a mix of absolutely delicious prosciutto, capicola, and soppressata with a bit of veggies and mozzarella. This was an impressive way to start out the meal. We all wanted to try the seasonal ravioli, which was pumpkin (too tempting for three certified pumpkin fanatics), so we got an order to share as an appetizer. This was unlike other pumpkin ravioli I've had...very pumpkiny. The ravioli was good, although we all agreed that we wouldn't have been able to eat a whole order. It was very sweetly spiced and I was missing a little bit of savory with the dish. + +I ordered the grilled sausage pizza for my entree, and was pleased with it. I admittedly never get too excited about pizza, and this was good, but nothing that I was dreaming about later that night. Overall, the food was a 3-4 for me. + +The service was outstanding. Our waiter was very welcoming and knowledgable. My friends got dessert, and when the chef (I assume Chef Pino?) came over to ask how it was, my friend jokingly said that it was delicious, but would be perfect with a bit of sauce. Before she could take another bite, he whisked both of the desserts away and added fresh strawberries and sauce, saying that he would be serving the dish that way for now on. Talk about service! The whole experience was fantastic, service gets a 5. + +Added bonus: Awesome beer selection, some brews I haven't seen. Only place I've been that had East End Homewood Reserve on tap for me to try (exciting for a beer dork like me, and it is tasty, by the way).[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have had lunch at Pinos's several times probably at least 5 times. Usually I am there for a business lunch when I am in the area. I find that we are well served, not rushed and the noise level is not too loud at lunch We have several times asked the Chef to make us some special version of his menu and we are always accommodated. To me this is excellent service. Makes you feel like coming back. +I would have to admit that I usually order the garlic fries which are really great. I do this if I am not going back to the office or out to meet a client. +Normally I would add a soup of the day which are always nice, and a sandwich of the day. +I have never been disappointed and certainly would continue to conduct business lunches here. Pino's has been very reliable and dependable in all aspects. I would make it 3 1/2 stars.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The food here is ok but not worth the price. $15 corking fee? $9 a glass of garbage wine? Me thinks not. + +What really tops it off is the owner is beyond rude and doesn't care about the business. I heard it used to be much better but now I don't know anyone who eats there...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Another really good meal here! My friend and I went for soup and appetizers--and licked the plates clean! Gazpacho, pasta fagiole, homemade bread, eggplant with mozzarella and my favorite...the roasted veggie platter. So much food we didn't think we would eat it, but it was so good we did! They also had their doors open and we were able to sit outside in the cool summer air--great way to kick of summer![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I ate here this past Friday with my girlfriend and two other dining companions. We decided to come here because it was Pittsburgh restaurant week and they offered a special 3 course $30 fixed price menu with 2 course wine pairing for $12. It ended up being a small little restaurant in the middle of Point Breeze which I had been past many times previously but never really noticed. + +The restaurant was swamped whenever we got there, probably due to a combination of it being Friday night and restaurant week, so thankfully we had made reservations and were seated almost immediately. I decided to start off my meal with a salad while my girlfriend had the tomato garlic bisque. My salad was good and came with goat cheese, pears and a vinaigrette which all tasted nicely. It was nothing amazing but I think it takes a really special salad to be amazing. I also tried my girlfriends bisque and unsurprisingly found it to be a bit tomato-y since I do not enjoy tomatoes very much but she really enjoyed it. For my entree I decided to get two small plates instead of a larger entree and settled on the mac n cheese and fish tacos. The tacos were a bit sloppy/wet but had some nice flavors (cilantro, aoili and pico) in them along with some chili sauce that gave it a nice little kick. My mac n cheese came out in its own little cast iron type pot and was good. There was an adequate amount of cheese throughout and I liked that they even had some ricotta buried inside the dish. I was also able to try the Arrabbita that one of our dining companions had ordered. Wow was it good and it packed quite the spicy punch too. Immediately I regretted not ordering it although I still did enjoy my two small plates. For my dessert course I ended up having the White Chocolate Creme Brulee. My girlfriend decided upon the tiramisu while another at our table had the peaches and puff pastry. All of the desserts seemed large and made sure that we did not go home hungry! My creme brulee tasted decently and ended up being a good finish to my meal. + +The bottom line for me is that I would definitely head back here in the future. Their regular menu seemed reasonably priced and everything that I had tried throughout the night was good.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I decided to try Pino's due to the restaurant week special and boy am I glad that I did! My husband and I made reservations for four on Friday night. We were seated almost immediately on the lovely outdoor patio area. It was a great night to be outside. Although the restuarant is small, the ambiance is wonderful. I could tell thet the guests around me were enjoying themselves as well. + +The table decided to order the 3 course menu for 30$ because of the large amount of options. We each decided on a different entree so that we were able to share and get a good idea of all the restaurant has to offer. I started off with a mixed green salad with grileld pears, walnuts and goat cheese. The pears had a nice smokeyness about them that complimented the sweet vinagarette. For my entree, I chose the Arrabiata with rigatoni. The dish was very good but much more spicy than I had expected. I feel that they should have informed me of this or explained the spice level on the menu. Luckily, I enjoy spicy food but I was unable to finish the entree due to the spice level. It was slightly less spicy when I finished it for lunch the next day. My husband had the veal and risotto which he loved. For dessert, I orderedthe peach mille feuille. The portion size was enormous and the peaches were ripe and tasty. However, the marscapone filling hardly tasted of marscapone. I had the opportunity to try my husband's white chocolate tiramisu and was pleasantly surprised by the light but still rich flavors. Our dinner guests also seemed to enjoy their choices as well. + +Overall, I would definitely recommend Pino's for a nice, romantic date night out in Point Breeze. However, I wish they offered the 3 course menu as a regular feature.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I grew up just the street from Pino's and my family were probably its most regular customers -- we got take-out at least once or twice a week for many many years, and always enjoyed the pizza and hot subs. I've just been back for the first time in 6 years after moving away, and was pretty unimpressed... The decor looks nice, but the food was wayyyyy overpriced for what it was. $22 dollars for a plate of pasta, really? It claimed to be ""fresh pasta,"" but it was completely tough and chewy (not ""al dente,"" just undercooked), and not very large. I'm not sure when the restaurant changed, but I think it really missed the mark... People WANT a casual, friendly, affordable neighborhood place that they can bring the kids to. Why take that away?[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> New fall items on the menu--their grilled romaine salad is fabulous![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Went here with a gift card from the restaurant week photo competition. + +We were one of two tables there and a bunch of staff showing up during the meal. + +Our waitress was good, but that couldn't save the food. + +The meal started out with some what I guess used to be foccacia. I say used to be because it no longer represented anything other than long pieces of brick or bark very stale and tasteless. + +We ordered the vegetable board which was probably the best thing we ordered with light and bright vegetables perfectly cooked and paired with two delicious sauces. + +Then we ordered the octopus which was fine, but very cold and the octopus had little to no flavor, being overwhelmed by the citrus in the dish. + +The tuscan wings were ok, but they were really ordered for my husband who seemed to enjoy them. + +Finally the diver scallops. This dish was indeible. The scallops were very overcooked and the pea puree was so minty I was unable to eat it. We sent it back and they did take off half of the price (weren't expecting anything just didn't want to eat it). + +After that we decided against dessert and left. I probably will not return.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I struggle with this review. I wish I could give it a 4, but I really can't hate on it like everyone else. Their wait staff has always been super attentive and friendly, and their happy hours are great! But, a lot of their entrees are a little meh for me, especially for the price. Stick to happy hour for wine/cheese platters, and enjoy a nice summer evening here.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The fresh-baked bread and sun-dried tomato puree is outstanding. We started with the crab cakes, which was one of the lightest I've had. I could eat a vat of the lemon aioli itself. We followed with veal and ricotta meatballs that were perfectly cooked. We finished with their Italian fries. I would order these every single time now that I've had them once. Twice cooked, herbs, garlic confit, basil aioli--every single element of the dish is fantastic. + +If you plan on visiting, then make sure you have some time to really take in the drink list and menu. There are always a handful of new, recommended wines to try and a signature cocktail of the week (which, might I add, is usually extremely fun and concocted with unique ingredients). I am impressed with the cleanliness, decor, and ambiance of the restaurant. I love the feel when the French doors are completely open. + +I also enjoyed our bartender, Eamonn, who was funny, polite, and attentive. He is also a master of not only creating fresh, new, tasty cocktails but, simply, understands the right way to mix and serve a drink. + +Overall, I would love to keep Pino's as our little secret but would urge you to try it too![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My husband and I celebrated our one year wedding anniversary this past weekend and since we recently have moved into a new area of town, we made reservations here because word on the street was that it was good. Verdict? It was so-so. We had reservations at 7:15 and were seated promptly, which was fine, except we were seated OUTSIDE! Listen folks, it's COLD when the sun goes down. They have three tables set outside, I guess trying to squeeze out some more business. Our server was nice, but not attentive at all. We were left waiting for things for 10-20 minutes at a time. Also, because we were sitting on the sidewalk, people and animals and cars kept sweeping by us. It took the waiter three tries to get our meal order because he had to keep stepping out of the way of people walking down the street. Wine was good. Food was ehhhhhh. We had the mussel and clam appetizer and when it came out, about 1/2 of the order was not edible and all the innards had fallen into the sauce, which by the way smelled like stinky cheese. My dinner and my husbands dinner was good, no real complaints there. Espresso and a S'more cupcake for dessert and I grand total of $134 later before tip? Definitely not worth it at all. The best part of the night? Leaving. The worst part of the night? Associating this place with my anniversary.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Stopped in without a reservation around 7 pm. I ordered the house soup. It was very yummy. The soup was a tomato based soup with noodles and chick peas. I also tried the sausage flatbread. The flatbread sizing easily fed one. My boyfriend shared with me. The tomato sauce and peppers on it really made the flatbread. + +I really one to come back int the summer when the front windows are opened and enjoy some wine and small dishesa[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Nice atmosphere with above average food. This restaurant has a lot of potential. The wait staff was far below average: They were slow, and we had to ask multiple times for things. They were not the most polite wait staff, and our waitress was either a little demeaning or very socially awkward.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We were huge fans of Pinos a few years back before the wine bar concept was adopted. In all honesty, we haven't been back for a year though we kept saying "" we have to get to Pinos!"" Needless to say, we were disappointed. The place has changed and not for the better. It seems in an effort to create a quaint wine bar, Pinos lost sight of the original draw and that was the food. The menu has been scaled back considerably. Though the food was adequate, it's not the same. I came here because the food was amazing and with that no longer being the case, I doubt we will return. Hopefully, things will change back to how they were. Customer advice for what it's worth. Refocus on great italian food not a wine bar concept. Sometimes a liquor license is not the best investment!!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> There was absolutely nothing not to like. Reasonably priced wines, home style Italian cooking. Great upbeat ambience.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Small portions. Over priced food. Very small menu (dinner). Was OK, but disappointing overall.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I went to Pino's with my three other friends for Restaurant Week and was underwhelmed and completely disappointed. We chose an option for each course of the very limited Restaurant Week menu. I selected the baked eggplant caprese appetizer, Lazy Man lasagna Florentine and then the panna cotta for dessert. + +Baked eggplant caprese: the breaded eggplant was a soggy mess. +Lazy Man Lasagna Florentine: it was essentially two huge lasagna noodles sandwiching huge clumps of spinach (I'm talking like a 3-inch high pile of clumped spinach) with a few mushrooms peppered in. The spinach ratio was out of control and I honestly ate a few bites and couldn't even continue. +Panna cotta: this was the most decent of the items we ordered. + +My friend ordered off the regular menu, which she advised not to do since her food would come out at a different time?? Why? +We tried my friend's appetizer of the Italian Fries, which are described on the menu as sounding very similar to the amazing fries at Point Brugge...but it was just a bowl of regular French fries, which were lackluster and misleading. She also got the house soup with chickpeas and it looked like Spaghetti-o's and tasted even worse. + +I don't know where all the positive reviews are coming from. There was not one thing we ate that was impressive in any way. All of it was overpriced and below mediocre. I wasted my money, and I will never, ever go back there.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I live in Connecticut and visit family in Pittsburgh often. Pino's is my favorite Pittsburgh restaurant. + +I don't have one favorite dish because I usually order one of the specials, which change often. I ordered from the regular menu for the first time a couple of weeks ago. The Bolognese sauce on tagliatelle pasta (I think the menu has it on rigatoni) was as good as what I had in Italy. My son had the seafood risotto. It was so good, I need to order it next time. + +My brother is a retired chef and hates to eat out because few restaurants are worth paying for what he can make better at home. He loved his meal and his tastes of everyone else's at the table (there were 10 of us). He was giddy to enjoy eating out for the first time in in a long time. + +Oh, they also make great cocktails and have a very, very nice wine list. + +Oh, if you think you can only get good fries and mussels at the Belgium place around the corner, try Pino's. The fries are topped with crispy herbs... yum! + +No, it isn't cheap. But, I'm happy to pay for quality.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I went to Pino's recently, only to be disappointed by the owner himself. I guess I should have read the reviews on here before going, seeing as a lot of people echo the sentiments that I feel. + +After my mother sent back her extremely oversalted steak, the chef came out to ""apologize"". It was very embarrassing how he chastised her for not enjoying her meal. He then snidely commented, as walking away, that he would ""never salt his steak again"". I don't really take kindly to people speaking so rudely to my mother. She was very polite about sending it back and certainly didn't deserve any attitude. We had an event to attend, which we were very clear with to our waitress. So when my mother reordered another meal (a salad), which took another twenty minutes, my mom asked for it to be immediately wrapped up. The chef returned, obviously chewing to make a point, and sneered at my mother, announcing her steak that she refused to eat was actually quiet good. Well, I have never felt more embarrassed in a situation. I said he was being rude to my mother, a paying customer. He proceeded to get heated and tell me it was not his job to make people happy (!??!) and that everyone else seemed to enjoy their meal and we just had to get to the inside of the steak to appreciate it. + +The drama continued when he did not have change for $100 for a $57 bill. Sorry, how can you not have $33 in change?! He ended the night by throwing our bill in a crumbled mess on the floor and walking out. + +Overall, embarrassing. It was an embarrassing situation for anyone to witness. Take heed of the negative comments on this site. I certainly wish I would have.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Very disappointing meal. After waiting for a half hour, my meal arrived and we were told that my friend's meal would be coming in a few minutes. Very awkward.t. Salad was average at best. The beets tasted like canned beets and the chicken was covered with blackish oil from a burnt oil pan. + + Then, to make matters worse the chef came out to argue with a patron who returned her food. The chef came out to humiliate the customer explaining that her returned steak was great and himself was enjoying it. Eating food from a customers plate was a real turn-off....what else does he do when cooking? + +To make matters worse, when paying the bill, the chef did not have change for a $100 bill for the customer who returned her steak.. It was very uncomfortable watching the elderly customer and her young friend deal with the situation. He kept loudly requesting a credit card and the women did not have one. Another customer provided them with change as the chef crumbled the check. I think I would have just left and not paid....give the lady great for dealing with such a lunatic. + +Long story short....if you want to eat below average food and watch a chef loose it....this is your place![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This was the place I brought friends visiting from out of town when I wanted to show them the classy Italian spots in Pittsburgh. After my visit last night, I have no desire to ever go again. + +I don't know the owner, Joe, personally but he has stopped by our table a few times and said ""dish looks beautiful."" He was always confident in his food which I guess is a good thing if the good is delicious, which it usually is + +The table next to ours had a two women, a mother and daughter. The mother asked the server for a new steak as hers was a bit salty (I've never had the steak as I'm vegetarian but my guests have mentioned the abundance of salt). The server apologizes and returns to the kitchen. The owner comes out and fakes an apology claiming his steaks are perfect. At this point the whole restaurant is listening it's that crazy. The best part? He comes out again and says ""I really enjoyed the steak you sent back."" He was eating the steak and had some in his mouth! I can't make stuff like this up! +At this point the whole place feels bad for the mother and daughter. Clearly an awkward situation. The owner got so nasty the daughter tried to reason with him and he said ""it's not my job to make people happy"" that's strange considering he wants our business. +So the mother tries to pay the bill with a $100 and leave but he said they can't make change. Eventually another customer helps make change and they leave. + +I couldn't finish my dinner I was so mad. Maybe Joe was having a bad day but there is no excuse for how he treated those customers. Sorry, we will never step foot in here again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> If you don't like your food... do not send it back to the kitchen... The ""Chef"" will come out and scream at you... Stay away from this place.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have been going to Pino's for several years with my family so I feel well qualified to give a balanced review rather than basing it on a single experience, good or bad. Every restaurant can have a bad day. And even the worst places can please some customers every now and then. + +What you get at Pino's is great service and excellent food. If your idea of Italian is the Olive Garden, you are in for an education and a treat. This is the real deal. We have a family of picky eaters including a full blown celiac and we all love it. + +Yes, over the years I have twice seen owner/chef Joe unhappy with unhappy customers. In one case the customer was arrogant and offensive. On the other occasion, Joe should have swallowed his pride if only to avoid the coordinated revenge reviews that followed.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Pinos offers an unhappy marriage of good food at bad prices. The food is tasty but not transcendent. The prices in the high $20's for most of the entrees are not justified by the quality, location, or portions. The food is essentially slightly hipper Olive Garden fare at double the prices. + +For dinner entrees you can get more for your money elsewhere. But it's not all bad. The atmosphere is pleasant and the service was excellent. I had a good time and I'd happily go back for appetizers (most are $8-10). + +Pino's is frequented by a large rambunctious flock of malbec massacring 40-50 year old women. My friend and I were the only males there. If cougar hunting is your sport of choice, you'll feel right at home in Pino's jungle safari![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is perhaps the best mechanic shop in Pittsburgh. It is ran by two brothers and may not look like much but they offer excellent service, honest work and great pricing. Recently I brought my truck in after another shop said I needed a litany of repairs. At Bruno's they did only the necessary work and even fixed the ignition switch which had worn out and only charged me for the part. These guys are great, but they are usually backed up with work so you may have to schedule in advance.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Bruno's is by far the best garage I've ever taken my car to, either here in Pittsburgh or in Los Angeles where I used to live. I drive a 2000 Saab, so believe me, I have A LOT of experience getting my car repaired. The two brothers who own Bruno's are great. They are very knowledgeable, they're very willing to help you and, above all, they're honest, which I've found is a rare commodity when it comes to mechanics. I cannot possibly recommend Bruno's highly enough.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Absolutely amazing guys here! We were in Pittsburgh visiting my family and the driver's seatbelt stopped working. Day after Thanksgiving and these guys got us in despite obviously being incredibly busy. It turns out that a piece of plastic had gotten stuck in the buckle. Now we are able to drive home. Thanks!!!!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've taken my car here several times and have never been anything but pleased. The workers are courteous, and any work I've ever needed on my car has always been done very quickly. The prices are fair; I've never felt that I'm being scammed over because I'm a woman. I've made the mistake of going other places in the area, but no more--the people at Broadway are honest, friendly, and efficient. I won't take my car anywhere else from now on.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Broad way is the only place I take my car on the East End. Customer service is through the roof, and I never have any doubt that they do things right and efficiently. They will let me know if something might need fixed in the near future, but have never put pressure on me to pay for more than is immediately necessary. They are good at explaining what is wrong, and don't use the scare tactic that other garages use (using big words and jargon to confuse you into buying more service). I trust these guys![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've taken my car to various garages in Pittsburgh throughout the year. Most of the one's that have 5 stars generally fell short of my expectation except for Broadway Auto. This garage is by far the most honest, friendly, affordable, fast and trustworthy. Historically I would end up taking it to Pep Boys because they were cheapest. I initially went to Bway to cross confirm whether my rear brakes needed to be changed as per Pep Boys. Bway said everything was fine front and rear and just charged me for inspection. I felt that showed integrity as plenty of other garages could have changed it out and made money on my lack of knowledge. It's nice to support a local business that deserves it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> These guys do everything by the book. +I had lapsed in my PenDot stickers and registration, and they helped me get that together (they won't work on your car if it's registration isn't valid). + +They told me my 2004 Toyota would need new wipers to pass safety inspection. They had me, but the cost was reasonable.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Bastone offered me a fair price for the work they did. I took it there to get a second opinion and despite the fact that they have a sign saying they charge for check-ups, it was free. They quickly got back to me telling me what had to be done and what they recommended giving detailed reasoning behind it. + +At no point did I feel like they were trying to cheat me or up-sell me. And they were the cheapest place I checked out.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The best, most honest and reliable car guys in the Burgh. I lived in Pittsburgh for eight years and still have family there. I drive in from out of state so these guys can do work for me.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Definitely overpriced for what they offered. Took my car in to check my AC, they didn't get back to me for the whole day, and decided to fix whatever the problem was without asking me and charging me an insane about (approximately $150 more than most places). Definitely will not go back there again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I was passing through Pittsburgh and discovered a headlight was out. I found Bastone through Yelp and drove over. + +They fixed the light on the spot charging me $12. First impressions are great - very clean repair shop and the service for this minor repair was done in a friendly and welcoming manner.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have taken my cars to Bastone's for years and would highly recommend them. Always friendly, always courteous, never trying to sell me on unnecessary work. I really appreciate their honesty and their help in keeping my old car working and on the road.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Bastone is the best auto service I have found in the US. I have trusted my car to them for all the years I have been in Pittsburgh and I do not plan on changing them. They are very professional, logical prices, and they make everything possible to meet your time schedule if you ask them for. They even give some perks for ""loyalty"" customers (e.g., free oil change for every 6 oil changes you do there - of course this means every 2.5-3 years but still). The also have a shuttle to drop you off (I have never used it but I have seen other people using it). However, because they are so good they are very busy too, so make an appointment ahead of time. They are also not open during weekends.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Love this place, really nice people willing to help and pretty decent prices..[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This Giant Eagle truly is giant! And believe me, that's about all it has going for it! You would think that this means you can find what you want, and generally you can, but it also means enormous crowds, no matter when you shop here. + +You know that a trip to a large, ""one size fits all"" chain grocery store like this is not quite the same as shopping at Macy's or Boscov's. You know that it's pretty hard to give a place like this five stars. Its purpose is purely utilitarian. But good gravy, you'd think that a place like this could handle large crowds. It shouldn't take you a half-hour just to get one item. + +That's what happened to me yesterday. I would have been better off going to Cogo's or 7-11. I might have paid a bit more, but I would have been in-and-out in under five minutes. I prefer the Giant Eagle in Squirrel Hill.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have to agree that this is one of the poor examples that Giant Eagle has. Granted, it has the basics you need, and is 1 of the biggest in the city itself. Finding things takes work. My big gripe is that it has one of the weirdest and most illogical layouts that I've seen. It actually takes time to find what you need as compared to most stores where once you are in there a few times, you easily find everything. Parts of this store are diagonal and that causes you to go in every direction possible. Here is a quick summary of the setup as it can be classified as a maze: + +1.) When you enter the store through the slow wide door, you go to the left and walk past the front registers to produce. Normal enough. + +2.) From produce in front of you (a quasi L-shaped department), you take a quick left and go diagonally to the right to walk past the pharmacy. Take a hard right down aisle 1 and then you hit the bakery. + +3.) From the bakery, you walk along a long meat wall. Diagonally to the left, you'll find the service meat/seafood counters. And because how the wall goes diagonal to the left, the sign for Aisle 9 is facing diagonally to the right so you don't miss it because the 1 side is longer towards the back than the other. (Aisles 9-14 are almost twice as long as 1-8). + +4.) From meat, you have frozen straight back on a long back wall in its own cove. A hard right (if you bypass frozen) brings you last to hot foods, the deli, and then facing in front of you, the Customer Service desk which is tucked away in a corner (not really visible when you walk in the store). + +5.) Once you pass the deli and customer service, take a hard right, then to the left (almost a U-turn) to the checkouts, and then you take a hard left to leave. + +Most of the other Giant Eagle stores are much more logical in how their aisles and deparment locations are set up. You're not going every which way to try and find things. + +Also, the service isn't that great as one of the other reviews said. Given that, I would take Market District on Centre Ave or GE on Murray Ave over this store. + +However, for those who remember the Giant Eagle on Centre Ave at N. Craig St, nothing beats how BAD that store was. There is a reason that store was nicknamed ""the dirty bird."" Compared to that North Oakland store that closed several years ago, Shakespeare St GE is light years ahead.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I am emotionally attached to this place.This place has given me food and given me a place to go to early morning's when all the clubs are closed.:) + The night starts by saying-""It's Party Time"" and eventually ends at Giant Eagle at times.Three cheers for Giant Eagle!!! + Now,i have to cheat on you,by going to Ralphs in West Coast.Sigh... +Oh,that became more of a letter to Giant Eagle(Giggles).For the note,its a huge Grocery store,and it's close to CMU and Upitt. + +-Smriti[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I cannot in my life understand why this Giant Eagle, of all the Giant Eagles, would get a five star rating. From the moment you walk into here it's like someone has hit you on the head very hard and you walk around in a confused state the rest of the time you're in there. + +The set up is ridiculous. I mean, who wants to walk around in the freezer section and then go through a smaller than usual end of the aisle to see, SURPRISE, the meat section hidden off in an area where they could have knocked down the wall so you didn't have to do a little dance to get to it. Aisles seem extra long in this store, you can tell that they worked with the space they had. It's like when you are half way through the aisle and realize it's too late to turn around because it's the same distance to the end as it was to the beginning of the aisle, but you kind of just want to give up and sit on the floor because you feel like you've been walking forever. + +Honestly, I only went here because I was at Target and didn't want to venture any further to complete my shopping.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This Giant Eagle seems more like a GetGo than an actual supermarket. As soon as you get in you want to get out as quickly as possible. + + You don't want to do any major grocery shopping here. For one, the prices are high. Secondly, this Giant Eagle does not carry everything you need. Who has time to run to another store? Just get your basic necessities here. + +As for produce, it can be awful at times. Whenever I go to Giant Eagle Market District down the street, the produce is fresh and smells invigorating. However, at Shakespeare, you are bound to find produce with wrinkles, open areas, mold and fruit flies- being sold at the same high prices. I can go to Trader Joe's and find much better produce for less. + +A pet peeve of mine is the self-checkout lines. Two of them are express lanes for items less than 12; the other lane has a belt if more than 12 items are being purchased. There should be TWO LINES but for some reason customers want to form one long super line, which holds up everything. The staff rarely sorts this out. +The customer service is average here and I don't expect it to get any better. + +I only go here if I have to grab one or two items. The best times to go are early in the morning or late at night.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I prefer this store to the Market District on Centre. It's just as overpriced and poorly laid out and maybe a bit grimy, but carries less products to sift through when you just need to grab some simple things, hopefully not produce. Parking is easy and you can hit up the unpretentious Wine and Spirits in the same stop. I think this plaza still exists to prevent impoverished people from venturing into the other newer fancier stores which are a mere half mile away and designed to appeal to people who think they are cultured and discerning.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Been yelled at by other customers (today for instance)...place is super ghetto...avoid at all cost. Today, left a full cart bacause a woman (with a baby in a stoller) shouted at me for ""cutting in line"". Will never go back. At night it is a nightmare.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I been going to this place since the 90s and this place is the MIDDLE CLASS GE. I stopped going to this place since I got a job at whole foods. My mom went here a two weeks ago for the first tine in a long time she say that the people are still there and the place looks better and the people are a lot friendly now. +So if you don't what too shop at a Middle Class food store in East Liberty then go to The Market in Shadyside.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I agree with other reviews, this store is poorly laid out and honestly makes no sense. Sometimes bigger is not always better. I used to head here often while living near Shadyside to stop at the Family Dollar & hit GE in one run. + +I normally only stopped here for a Redbox movie. My debit card got hacked at an outdoor Redbox at a Get Go so I'll only go to a Redbox that is indoor like this one. + +Anyways, I'd hit up the liquor store for some wine afterwards for dealing with long lines/wait & awkward clientele outside.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Ugh. Dirty. Long lines. Walked out without making purchase .[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Figure I'd give Supercuts a shot since Giant Eagle sells their gift cards so it is great for fuelperks. I don't remember her name but she is one of the ""bigger"" woman there. I wanted to grow out my hair longer but it was looking messy. So I asked her for a trim to get the sides/back cleaned up. She said ok and off she goes. 5 minutes later, we were done. Yes, just like a bad date, we were done in 5 minutes. + +I got home, showered, and saw the damage. It was messy. What's worst is every day it grows, it looked even worst. + +I'll just stick to my usual barber.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Nothing spectacular, but I go there regularly, and generally get a cut that works fine for at least a couple of months. They did a good job after I had a botched cut overseas (hairdressers in Japan are, understandably, not necessarily qualified to work on non-Asian hair, as they don't cut a lot of it). Parking can be tough, depending on time of day--there's a shared private lot, but it's small.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I wish I could return a haircut. + +Unfortunately Kelly, Melissa, and Jen were not there so I settled for whoever was free at the time. + +Worst trim of my life: +she cut off over an inch more than just the dead/split ends +she did not cut the hair how I described initially +she did not change the cut to how I repeated during the cut when I noticed she was cutting it straight across instead of curving it in the back, which does NOT mix well with my curly hair +after retelling her how I wanted it cut, she compared this tragedy to deaths of family/friends and how I should get over it +the beautiful long layers I had and wanted again are now choppy, medium layers +my left side is even choppier than the right side of my hair +I fear straightening my hair to make this unevenness less evident + +I regret tipping her because I understand how the service industry works because my minimum tip of 20% for all service people is undeserved for her lack of work. + +I want everyone to know how the only good hair stylists there are Kelly (who moved to Philly), Melissa and Jen. If they are not available, do NOT risk going. + +Also, the Supercuts Oakland location is horrible at waxing eyebrows unless you are lucky to get the only woman of color there. + +While it was a $20 cut (after the 20% tip), I know had to buy biotin to grow my hair faster so it is more expensive to me in the end. I hope this proves helpful to all perspective customers![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> i'm not sure why this place has bad reviews. its par for thecourse for supercuts. standard cut 16.95 is a bit pricy but they always do exactly what I say. i've simple hair so it works well for me. employees are generally nice, sometimes like talking to me sometimes talk just to each other, worth three stars for sure.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Terrible! I got a haircut here once and hated it, but kept waiting for it to settle in after a few washes. It never did look right, so I just fixed it at home rather than going back to these incompetent people. I didn't even feel like the hassle of complaining was worth it, as I highly doubted that I'd get any money refunded and I certainly didn't want them to touch my hair again to try to fix it. + +I then figured, hey, this place sucks for haircuts but they can't mess up eyebrow waxing, right? Right! But their service is so bad that I gave up on that too -- I got my eyebrows done here a few times with not much trouble, but the last time I went in, I had called ahead to put my name in and was told that I would be next on the list, and to show up in about 20 min. My house is a 20 min walk from there, perfect! I headed out, got there in 20 min, and gave the woman at the desk my name and reminded her I'd called ahead. There was one man sitting there waiting, who I had seen from across the street walking in about 1 min ahead of me. + +The ""stylist"" was just finishing up a haircut, so I should have been next, right, since I had put my name in before the guy who walked in? Nope! She called him over and I said ""sorry, I think I was next, I called ahead and was told I'd be next in line"" and the lady said ""oh we don't do that."" WTF?? You told me very clearly that you do exactly that, what craziness is this? So I waited, figuring that I'd already invested 20 min into this venture, so I may as well stick it out. + +And waited, and waited, while one ""stylist"" cut the man's hair and 2 of them chatted in the back (ironically next to the chair where they do facial waxing). They must have been ""on break,"" or maybe just terribly rude and idiotic, because I sat there waiting for another full 20 min, and when I finally spoke up again to ask when someone would be available to do my eyebrows. The 2 chatty cathies in the back looked over, very annoyed at my presence, and the woman doing the haircut said ""after I'm done here,"" and I sat there incredulous for another 2 minutes before getting up and leaving. Will never go back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Went here with a friend for his haircut. It's been a long time since I've been to a barber shop or haircut salon/store, but from what I remember this place seems completely average. The hair stylists seem nice enough and competent. The wait was a few minutes- I actually expected the wait to be longer because we came in on a Saturday. If I ever need a haircut (which I haven't gotten in maybe 5 years!), I wouldn't have a problem stopping in here- but I tend to enjoy my long shaggy mop.....[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I went there today! The cut was terrible! I have an awful experience. They lady that cut my hair was nice but she wanted to leave early so she made a disaster in my head![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I will admit I am completely biased towards this place. I grew up eating their pizza. Crust is soft and fluffy, not chewy. The cheese is a little thicker than the average new york style pizza place. The sauce has spice but not too much. At some places you need a little milk or water to cool your tongue. Their one downside is that they're not always consistent. Some days its just started to turn golden brown others its over done.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Eaten here twicebut only pizza. I do have to say its up there with Napolis or Ailleos as for the pizza. Tonight me and my neighbors were up for some more. Was disappointed when ordering a meatball hoagie to find out they had no meatballs! Pizza places should never run out of certain things. Had gotten a cheese hoagie. Didnt get get why someone would order this, but was told it was good. didnt like. Luckily the pep pizza was great, but.. when u get toward the crust, its all dough. Still kick butt pizza but get rid of the cheese hoagie.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> According to Urbanspoon (blasphemy I know) their are like 1,100 pizza places in pittsburgh. So what is the best pizza in Pittsburgh. Everyone has an opinion and so here is mine: The best pizza in Pittsburgh is the pie comes from the place in you neighborhood that has quality ingredients, fair prices, and friendly service. Eddie's Pizza Place is all of these things and since I live in this neighborhood this is my favorite.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Decent neighborhood pizza can be found in morningside at eddies pizza haus. The sauce and cheese are perfect, but the crust falls short. It has a nice texture and overall the pizza isn't greasy, but the crust lacks much flavor. Maybe a little more salt is needed in the dough to compensate? The pizza is decent enough though and merits a try, perhaps it was an off day for Eddies.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> As a chinese american college student from NYC who got stuck in Pittsburgh with its useless public transportation (circa 1998), I desperately missed home-style Chinese food for the better part of my first two years here. Things turned around for me once I got a car (or made friends with cars), but I was seriously hurting for a while. + +Tasty was one of the places we found. Back in the day, it was owned and ran by a typical restaurant-owning Chinese family. They had the works - pushy lao ban niang (boss lady), chef slash dad, and, during school off-hours, junior high school daughter manning the cashier. If they were in NYC, they'd only be missing an ami.... a bus boy. The food was pretty good, and if you order in Chinese, the lao ban niang hooked you up with extras because ""your parents teach you good to talk Chineees"". + +I'm pretty sure Tasty is under new ownership now. The food isn't as good as it was, but the restaurant still gives off the home-style look and feel. It's a small restaurant with enough seating for about 25-30 patrons. Cheap tables, cheap seats; after all, restaurant extras are just a waste of money. The customers should come back for the food, this *is* a restaurant. + +The new waitress is not friendly, but she gets the job done. The food is still good - so if you're craving a home cooked meal, you'll be somewhat satisfied here. Don't expect grandma's cooking, though. Order the vegetables, the mapo tofu is good, beef/chicken chow fun, etc. They have a lot of other staple items on the menu too. Don't get the salted pork chops - save that craving for Orient Kitchen. Try things, and share your thoughts. + +Tasty - it's more than your neighborhood take out joint. + +- written by a former junior high school daughter cashier[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I recently pop in to this restaurant and got a Black Bean Pork on rice. It was great!! + +The vegetable was fresh, the source was not too heavy and the meat was tasty!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Pretty solid Chinese takeout. They have a $10 minimum on Campus Food and delivered in less time than expected. The Szechuan eggplant was not spicy at all, but it did have a nice assortment of mixed vegetables (broccoli, zucchini, corn, carrots, etc.). The vegetable egg rolls seemed pretty tough - I don't know that I would order them again. + +Overall, I'm pretty pleased. I already like this place - even the big neon sign that just says ""Tasty"" on the storefront. (This is how I'm going to refer to it - ie, ""Do you want some takeout from Tasty?"") I also love that one of their lunch menu options is fried rice, soup & an egg roll for $2.95! I will almost definitely order from here again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Food: There are countless options to choose from for vegetarians or carnivores, but the food is only so-so. We've ordered takeout numerous times due to proximity, and nothing has been bad, but nothing has been special. The general Tso's tofu and the Moo Shu vegetables are the best things we've ordered. The eggplant was soggy and not great. The portions are large. Nothing is particularly spicy even if it is mentioned as being spicy on the menu. + +Price: Tasty is cheap. + +Drinks: N/A + +Atmosphere: Typical Chinese takeout place. A photo of every single meal they offer is on the wall. Located in the plaza next to Pizza Parma. Decent location for that end of Shadyside. + +Service: The employees speak poor English but can usually understand what you are askingt/telling them. The food is usually ready for takeout within 10-15 minutes. + +(+): many options, cheap, ready quickly + +(-): food is nothing to write home about + +Would I go back again? If I'm feeling too lazy/broke to go anywhere else.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place features everything you can expect from a standard hole-in-a-wall Chinese restaurant. There's zero ambiance, offers quick take-out and the service is rude. I decided to give Tasty a try because it's conveniently located on Highland Avenue and has easy parking. + +I ordered the Kung Pao Chicken and Crab Rangoon. Sadly, they prepared Kung Pao Beef instead. It's extremely disappointing to receive the wrong food. It's even more disappointing when the restaurant refuses to correct the order. While it wasn't what I ordered, the food was good...but there is better Chinese food out there.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Note: Tasty has a credit card minimum of $10 and has a parking lot + +Tasty is another standard chinese takeout place - it didn't blow my mind but overall it was good, especially considering the price. Before I continue, I will come out and say that all of the food was a little tough - the eggroll especially(As was warned) - and the rice had some dark spots(I assume it was from the bottom of the cooking vessel). However, I will chalk some of it up to my mistake because I thought they closed a half hour later, than they did, and consequently ordered about 10 minutes before they closed. So, Tasty, you get a pass on the rice + +Anyhow, I ordered a vegetable eggroll($1.50) and general tso's tofu($8.25)(I've learned to accept my guilty pleasure). I ordered the general tso's extra spicy - it was not. Also, the tofu was in very large chunks, which has seemed to be my luck lately. I want surface area, and I don't want to have to figure out how to cut my food with chopsticks. I will say, though, that the sauce was very tasty - enough to seal the deal for a future order at this place. + +The eggroll, as I said, was tough.. It tasted good, but it was tough, and small... This probably won't be in my future order, however with the $10 minimum I do need to order something else with my tofu... I hope the soup is good. + +The lady behind the counter was friendly and was decent on the phone and didn't once mention that they were closing so close to when I ordered. Portion size was good, for the $10.44 it cost me, I'll definitely be able to make a lunch out of what is left.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My wife and I have been going here for as long as we have lived in Pittsburgh, which is about 10 years. This is our go-to Chinese restaurant, even after we moved out of the neighborhood. I have never had a bad meal here, and I will forever love their beef chow fun! My wife and I are moving to North Carolina in two days, and Tasty Chinese was the thing about Pittsburgh that we said we would miss the very most. These are great folks, and I wish them the best of success in the future. Remember, everyone, just because you read a negative review it does not mean that the food is bad! Some people just have lousy taste buds, and many people have no idea what they are ordering to begin with. Try things for yourself, and you will find some great food at Tasty![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Tasty is Pittsburgh's BEST kept secret for Cantonese cuisine. If you're Chinese and miss your mum's cooking, this is the place to go!!! The service is fast, the food is cheap and they serve you gummies to end of the meal! Did I mention that there's a designated parking lot right infront of the store? + +Don't order the American standards of General Tso's and Moo Goo Gai Pan , unless you REALLY want to. This is the place to get really authentic home cooked food. Order the steam ground pork, or steam ground pork with egg, the tofu, veggie and mushroom dish on the special menu written in Chinese( second from the right), the cold steamed chicken with ginger, or the chicken with mushroom, or the pork chop with pepper sauce, or the shrimp with egg and the list goes on. + +If you have an occasion, say a graduation dinner, the restaurant will even roast you a duck (yum!), or stir fry up some lobster with ginger and scallions ( big yum!) or stew you some pork with lotus root soup ( super yum!). And they will arrange the tables nicely, and cover them up with some festive table cloth. The owners are also really accomodating with regards to changing the menu at short notice and special requests. If you need to refrigerate a cake, they will gladly oblige. They do not serve alcohol, its a BYOB place. The BEST part, a ten course dinner for 11 people will set you back about $120 or so including tax and tip (menu included roast duck and lobster)! + +My husband and I have been eating at this little hole in the wall for years now and we are really going to miss it when we move. The owners are really nice and the food is great![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Tasteless food that arrived over an hour after it was ordered and was cold. Will never order from here again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Not Tasty At All.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Ordered the lunch special with sesame bean curd + steamed rice + veggie egg roll. The food was great, and you get a LOT for $5.65. My friend got general tso's chicken with fried rice, and she enjoyed her meal as well. + +The lady at the counter was very friendly and refilled our waters often during lunch. When we were done eating, she gave us little Japanese mango gummy candies on our way at the door. + +I would definitely come back for lunch here--it's nothing fancy, but very reasonably priced and, well, tasty. :)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> i'm giving this place a solid 3. i've had better cheap chinese and i've had worse. first off, let me just say take out is probably the way to go. our server was nearly impossible to understand and we drank water out of tiny styrofoam cups that we had to wait for her to refill. +i ordered the crab rangoon, a shrimp springroll, and chicken fried rice. the rangoon was pretty good, the springroll was just a clump of grease, and the rice was good. my friends ordered beef and broccoli, an egg roll, and general tso's. they were not too impressed with their meals. +as far as food, this place seems to be pretty hit or miss. the prices make it worth ordering take out or delivery, but i wouldn't waste my time eating in here.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Never received my order and was left in a bad mood. The driver did not carry GPS for delivery, did not know my address which is right in squirrel hill, did not listen to me (or did not understand me?) when I tried to give him directions, asked me to pick up food from an intersection 0.3 miles away from my apartment in snow, and finally yelled at me to cancel my order. + +Cannot comment about food, but whatever experience I had left a bad taste.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Went here last night for takeout since our normal place is currently renovating their kitchen. + +We ordered fried dumplings which were just ok. We also ordered some shrimp lo mein and general tsos chicken. These were some of the best entrees that I have gotten from a takeout place. The lo mein was perfectly cooked and was not greasy at all. The shrimp were also cooked perfectly. The general tsos may be some of my favorite I have ever gotten. It wasn't spicy like I requested, but the chicken was still crispy after having to drive it home and the sauce was very savory. + +Overall I probably will crave the food from here and will be back, on a night when I do not mind driving to pick up.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Home of the Italian Army. + +Vento's is located in the East Liberty section of Pittsburgh right next to Home Depot. They have been in business forever! They are a pizza and hoagie shop. They are famous for their Italian Army hoagie. I have friends that as soon as they land in Pittsburgh they come straight to Vento's for the pizza! It is Sicilian style pizza and It is delicious! Everything is made fresh so sometimes you have to wait a little while for your food. It's best to call ahead if you're really hungry. + +They have tables and booths for seating. You can even play the PA lottery there. + +No debit or credit cards. CASH ONLY! + +(F.Y.I. There is a generic ATM that charges $1.75 to make a withdraw.)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Good pizza and hoagies. It is always busy. Cash only.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Slow service and average pizza. Convenient to home depot.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love the history and the atmosphere.. Albert Vento is in Myron copes book and is a STAPLE in da burgh... He started ""Franco's Italian Army"" !!!!!! Vento's Italian Army Hoagies,, and AMAZING PIZZA.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> IF you love the Steelers, you gotta Love Ventos...I love the history and the atmosphere.. Albert Vento is in Myron copes book and is a STAPLE in da burgh... He started ""Franco's Italian Army"" !!!!!! + +You have to try Vento's Italian Army Hoagies,, and AMAZING PIZZA... I love Literally ALL food Sean the chef Makes... The Secret Sauce is phenom on Calzones too..[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I had heard lots of good things about Vento's. Unfortunately I did not get to experience these things. The service was slow and lukewarm. The pizza was expensive and not the same price in the restaurant as advertised on the website http://www.ventospizza.com/. Also, no credit or debit cards here. You're directed to the ATM in the restaurant that charges a fee of $1.75. I ordered ahead and although I had to wait for my pizza when I got there I received it cold and it just was not that good. I also ordered provolone sticks which also did not taste good.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Ventos is an East End tradition. The Sicilian style pizza is the bomb! It is more of a traditional working-clasd Pittsburgh style crust-square, and bread like. Sicilian pizza comes in square cuts by the way, if you like the doughy (Dominos or similar) kind of pizza crust, or brick oven designer pizza you might not like Vento's pizza. But I happen to love Vento's pizza!!! They also have subs, and other items like deep fried mushrooms. This is a blue collar establishment in a an urban working-class neighborhood, Everything I've had from here is good.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We were visiting from out of town and just spent 6 hours driving. Found this place, read reviews on Yelp which were OK, and decided to ordered two slices. Hum...sorry not slices. More like two squares of cheesy bread. When we said these aren't slices, the lady at the register looked confused as though pizzas always look like that. We obviously aren't locals by the way we were dressed so the lady (who talked terribly) should have notified us when we first ordered it! They also have pictures of real pizzas on the wall -_- +It also took a really long time to cook those little things because they weren't pizzas. Since I was so hungry, i ordered another square of unhappiness and it was handed to me in the cooking wrapper not a paper plate, ugh. Definitely never going there if we come to visit again![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Horrible Food don't waste your money + +This is the worse cardboard covered cheese & sauce so called pizza I've ever had, I haven't had this garbage since grade school cafeteria food, Most of the reviews on here rant about what a great place this is how much fun you'll have there. IDK where that place is cuz the one I wan in today in East Liberty by the Home Depot was getto beyond belief the food is bad & the people aren't nice & friendly. + +Loudness is an issue there when the lottery area has a sign saying because of back round noise your number may be wrong. Not one person there had decent customer service skills I had to ask the girl 3 times to speak up and I have excellent hearing. I ordered a small pizza I got a medium that was greasy on top but the crust was stale. + +I looked forward to getting some great pizza man this place really disappointed me today.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> What a wonderful hidden gem! +My boyfriend and I have been here twice and we have raved about it both times. The service is wonderful - the employees are patient, kind and helpful. The food isn't 5 star, but it IS really really good and, best of all, cheap as hell! +Sure the pizza may not be cut into ""pizza shape,"" but that doesn't make it any less wonderful at all. Everything I have ever had here is wonderful and I will definitely be taking multiple 30 minute trips back here to support this independent business.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Oh I love this place. Their pizzas are square/rectangle! A single slice is a little pricey for the size, so if you're going to go, get a whole pie. It is in the strangest location (Home Depot's parking lot)!! The picture of the founder is adorable and hilarious. Love this place![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place has the worst service I've ever seen. I called in two cold sandwiches and was told it would be 15 mins. When I got to the counter, the lady working rudely told me to wait for my name to be called because she didn't have my ticket to ring up the order. Um, okay...then walk over and get it so i can pay for it! So I waited and waited as people who came in long after me got their orders. The ""workers"" just stand around and spend more time talking to the regulars and trying to act like they are a big deal. I had to leave without my order after 40 minutes. DO NOT GO HERE![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My cousin works here and that's the only reason i know about this place. The crust they use for the bread is so light and airy and i absolutely love it. It makes the eating experience that much more enjoyable. + +I always order a slice or two with sausage and mushrooms because I love the little crumbly sausage that they add to the pizza. Plus if you dip it in ranch (big fattie) it taste even better. + +I took the hubby there just this week and he agreed that it is very good. They have tons of specials and even more menu options. We ordered the medium pie and 12"" hoagie for only $13. Really good deal and the italian hoagie was not too bad. I do wish however that it was a little thicker. Maybe add some more lettuce and tomatoes for fullness. By the time we got it home it was like eating a lunch meat sandwich. Still delicious but I would have like a little more bite in my hoagie. + +The interior is a little outdated but they have a bunch of steeler memorabilia hanging up. Also, if you like to play the lottery they have a small window for buying and playing the numbers. Waste of money if you ask me but to each his own. + +BTW, IT'S CASH ONLY HERE, but they do have an ATM.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is a Pittsburgh/Shadyside institution. + +What can I say, this place is good-eatin' basic Italian food! Not spectacular, but when you want a good nuthin-fancy dinner, this is the place to go. The pizza is outstanding.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> When you're in the mood for a good ol' fashioned, nothin' fancy Italian restaurant, you can't beat Minutello's! My husband Rick and I didn't feel like cooking the other night so we came here for a nice casual dinner. Man, I haven't reviewed this place in nearly three years and it sure hasn't changed. Still has that good old basement decor. + +Minutello's still has some of the best pizza in town. Rick and I ordered the Supreme wtih capicola, Italian Sausage, salami, and pepperoni! Mm-mm good! Gotta hit that gym tomorrow. And you know the best thing about ordering pizza, don't you? It's always good the second day![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is great, simple, traditional italian american food. The salads are good. The pizza is really great (I stopped ordering from anywhere else). The veal cannelloni is awesome too.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This was one of the worst dinners out I've had in recent memory. On the other hand, I wasn't expecting much, so I guess the place lived up to my expectations. I've been trying to think of a good way to describe their food, and the best I can come up with is as follows. Imagine a cafeteria pasta dinner you might have been served as a child away at summer camp, and you'll have a pretty good idea. In other words, the food is perfectly edible here, but boring, and nothing you would want to actually pay for. There was nothing disgusting about it, it was just extremely uninspiring. To be fair, I only tried the pasta, bread, salad, soup, and calamari, so maybe they have amazing pizza here... It's possible, although unlikely based on what I've seen. + +On the upside, the service was friendly enough, and there were plenty of empty tables at prime dinner time! If you're hungry, you'll definitely be full when you leave.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I went to this place because I had a LivingSocial voucher. Even with this voucher I feel like I paid too much money. I think I could have had better food if I went over to the Giant Eagle across the street and heated up a Lean Cuisine. I do have to wonder why the owners would put out the living social deal when what really would help business at the restaurant would be simply to improve the quality of the food. +The only positives I can give are that it isn't pretentious and the waiter provided very good service. It was almost empty for a Monday at 7 PM, so if you are desperately starving, not able to go to better restaurants nearby or heat up food from your local grocer's freezer, this might be a tolerable food option. Again, it is advisable to be desperately starving.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Based on some recent reviews, it looks like the quality of food at Minutellos has slipped a little bit. Still as I mentioned before, it's a Shadyside institution located in the basement of an apartment building. + +Anyway, the main reason to come to Minutellos is for the pizza. My cousin and I did just that the other night when we were in the area. We did the whole 'Build Your Own Pizza' thing, ordering ours with pepperoni, green peppers, onions, and mushrooms. Good pizza even if the place is beginning to look a little dated.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The food quality is good or not great. I do love the following. The anti-pasto is very good. I love there wedding soup. Don't write this place off due to some bad reviews, because they are flat out WRONG.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Minutello's is going out of business. Last day of operation is Sunday, February 17, 2013.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Mike""s auto body is fantastic. Not only do the do great work, but the experience is great to. The shop is clean and comfortable. They have a contests with enterprise so you can pick up and drop off a rental there. They even give you a can of glass cleaner and snacks when you pick up your car. They have fantastic customer service.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Blown away at how Mike's turned an awful situation into a very unexpectedly pleasant experience! Let's face it - everyone hates taking their car to the shop. ESPECIALLY when the reason you have to is bc you were in an accident on the return trip from the airport after your amazing Vegas Vacation (no injuries or serious damage to either involved party, thankfully). + +The customer service is stellar. The staff at Mike's genuinely love their jobs and it's evident pleasing their customers is priority one. I have to echo my fellow Yelpers, as my car left Mike's in better shape than before the accident. When I drove my freshly cleaned and waxed hatchback back (hatchback back-lol) to Bloomfield, I swear I could feel how happy Baby Bluey was and all was forgiven with the fender-bender. + +Did I mention they left a gift bag full of goodies on the passenger seat, all pink-themed? My only small complaint is my car wasn't ready when originally told, but is it ever? I'll def be back to Mike's![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I had to choose from a list of insurance-approved body shops to get my car repaired after an accident. Mike's Auto Body was nearby and more highly rated than other convenient options. +They did not disappoint. The turnaround time was quick (less than 3 days) and they did a great job! My car looks as though the accident never happened and I am quite pleased with the work. They had to fix a large dent and some scraped paint. +The neighborhood the shop is located in is not great (some interesting ""characters"" soliciting in the intersection nearby), but the shop itself is clean and comfortable. I did not feel unsafe going to and from the shop in daylight. +The customer service was excellent, as well. Everyone I interacted with was professional and courteous. I was continually updated with progress on my repairs and they were actually finished a day earlier than expected. I hope I don't need to go back to Mike's for repairs, but I would definitely choose them again in the event of an accident![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The people that work here make an unfortunate incident a breeze to work through. I woke up one morning to find a note attached to my windshield to inform me that I was the victim of a hit and run. The damage was minimal, but after calling it into my insurance company, they directed me to come here. + +Within minutes of me hanging up my phone with the insurance company my phone was ringing to indicate that Mikes was calling to set up an appointment to get my car in for an estimate. I set up an appointment that was convenient for me and went about my day. + +When I arrived here to have my car viewed it was quite the easy task. My wait was minimal, the staff were polite and I wasn't being jerked around. Within five minutes of them looking at my car, I was out the door and heading back to my place. + +Unfortunately, they did not do any work to my vehicle at this point because the police are still looking into the person that hit my car. But if we get to that step, I am confident that they could not do anything wrong in my eyes. If their body work for a vehicle is anything like their customer service, they are definitely one of the best places to go in the city. + +Yes people, this isn't the best neighborhood in the city, but get over it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Mike's doesn't really need another stellar review on here, but I'll give them another one anyway. + +I'm a choir director at a church, and after rehearsal a few weeks ago, one of my choir members ran into my car in the parking lot and crunched the rear bumper. Bummer... + +I had never had to file an insurance claim before, and wasn't really sure what to expect. Dealing with Mike's was about as easy as it gets. I called to set up an appointment for the estimate and drove down a few days later. I was only there about 10-15 minutes and got sent on my way. + +A few days after that (Monday), I took my car in for the repair. It did take a couple days longer than they said, which is really the only negative thing I can say about Mike's, but considering I didn't have to pay for the rental car, it wasn't a huge deal. When I did get my car back (Thursday), like others have said, it was in even better condition than when I took it in (besides the dent, of course)! They had cleaned/waxed the outside, and even cleaned and detailed the inside! If they just did detailing, I would take my Impreza there every time! Mike's rules![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Mikes took my car after horrible repairs/service from Kenny Ross South. The service was great and I even got to meet the owner who came out to personally speak with me on a busy Friday afternoon. Great guys there.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I took my car to Mike's auto body as it's recommended by Geico and is part of their easy claims and repair process. This was a big mistake. Like many of the reviewers here, I was initially told it would take a certain amount of time, and then, at the last minute, on the day I was supposed to get my car back, they told me it would be a few more days. Their excuse? The headlamp that came in didn't have a bulb with it. Seriously? Since this was the Geico rep telling me this I couldn't really argue, but I don't know why Geico keeps working with a business that repeatedly does this to its customers. + +I got the car back in great condition, cleaned on the outside, and the console wiped down inside. All in all, just alright - go here if you're not pressed for time and you've got Geico, otherwise shop around.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I had a great experience taking my vehicle to Mike's for repair after a fender bender. I used the Geico express service - I booked the estimate and repair online for the next day. When I dropped off my car, they were expecting me, it took less than 30 minutes and every single person I encountered at the shop was helpful and friendly and showed concern for me. The damage was minor, and the repairs took less than 48 hours to complete. My policy provides a rental car, and Enterprise was there when I checked in with my vehicle and the rental process was streamlined and easy. When I picked up my repaired car, it was just as efficient and friendly. Getting into an accident is frustrating and inconvenient and costly but Mike's Auto Body made the process of fixing things and getting me back on the road into a good experience. I wish more businesses treated their customers like Mike's treated me.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Mikes did an awesome job on my SRX after I dented it backing into my garage. The insurance claim adjuster was on site as well as one of Mikes professionals to meet me when I brought the car in. They reviewed the damage , gave me a solid estimate and took the car right then. They kept me informed of the progress of the repair. The car looks amazing and they even left a gift bag in the car with a variety of car care products and other good things as a thank you . the repair took a little longer than originally estimated but the quality of workmanship was well worth the wait. Thank you Mikes![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I never grew up with a pet so getting one was a new experience. I had always heard kill/no-kill shelters whatever... I got my new dog Crosby from ARL which happens to be a ""kill shelter"". Thinking about this, I felt truly good getting him there because I felt as though I was saving him from some other destiny. However, he is so cute that I'm sure someone else would have adopted him... + +The shelter itself is large and the volunteers and vet-techs that you interact with are very friendly. The dogs are constantly walked and you can tell the animals receive a ton of love from the staff. Adoption is made easy unless you rent in which case you should probably bring a letter from your landlord stating you are allowed to adopt. Another perk is that when Crosby had ""kennel cough"" we went after hours to get him some medication and they still let us in and treated him...In short, great adoption experience at ARL.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is an animal shelter with a tremendous heart. While I realize it's more popular to back the more selective (aka ""no-kill"") shelters around Pittsburgh, the ""open door"" policy places the ARL at the top of my list. Where the so-called no-kill shelters can afford to be choosy and accept all-star pets, the ARL will accept any pet, from a private owner, someone who finds a stray, or even the city's animal control. A small, over-extended staff collaborates with a dedicated troop of volunteers, and manages to adopt thousands and thousands of pets each year into family homes. + +I have adopted two cats from this shelter, and also participated in the adoption of several friends' pets here, too. The paid staff can be spread a little thin, especially if you come on a Friday afternoon/evening, or a weekend morning. Guess what, lots of people want to adopt a pet on the weekend when they have extra time to help it settle in. So don't be surprised to find crowds of potential adopters and exhausted staff!!! For a quieter experience, try a weekday. For the most intimate pet-finding experience, go during a Steelers game. Seriously, you will have the place to yourself. + +Is it sacrilegious to tell you to do anything during a Steelers game? Whoops. + +The ARL lists some of their pets on Petfinder, but I have found that the selection on the adoption floor is often too vast & quick moving for them to keep the profiles online updated -- what I'm trying to get at is this: Don't get super attached to a pet online, because there's a reasonable chance it already has a home. And don't avoid a trip because you don't see anyone you like online. There are more future fur-friends waiting for you at the shelter. + +The staff of volunteers is extraordinary - I adopted one of my cats directly out of a foster home, and the volunteer must have gone out of her way to come to the shelter at my convenience and explain all the in-home habits of my future baby. I had such a positive experience with her, and the shelter. They invite you to send updates and pictures as your new pet adjusts. Yes, the staff & volunteers have a vested interest in the pets and want to know how things go! + +The rates for adoption vary, depending on the season, so if your finances require some help to acquire your new best friend, keep an eye on their website for info about ""sales."" You can also donate old sheets, towels, pet carriers, and toys for the animals who stay here on their way to permanent homes. I donate a big pile of worn towels and sheets every time i sort my linen closet. They also accept ca$h donations to help keep up with expenses. + +Maybe I seem like an over-enthusiastic cheerleader of this place, but the fact is that this organization connected me with two very important cats in my life, and every scratch on my arms, every litter box, and every fur-covered outfit in my life is due credit to their tireless efforts. Bravo, ARL, the pets & their families thank you.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This shelter is fantastic and has generally very good, friendly people on staff. The cats and dogs appear to be treated at least as well as one might expect. + +When I adopted one of my cats at this establishment, I had to return the next day to have her spayed. They did it for free, which was great, but the reason they don't get five stars is that the desk clerk completely forgot about my cat and me, and she left us waiting as she chatted on her cell phone with a friend: she only remembered about us as she was walking out for a smoke and saw us sitting in the lobby.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm a crazy cat lady and proud of it! + +Being a volunteer here has been so fulfilling on many different levels. It has made me feel so good to be able to help out with something that I feel passionately about. You can tell that the staff puts a lot of effort into taking care of these animals they accept in. A lot of times people will say, oh I can't do it, it's too sad. But the thing is, it's not. It's actually so great because these animals come here and find loving homes instead of being on the street or in an environment that's toxic. I rarely see animals there for a long time. I think that's a testament to the way they are treated while they're in the facility. + +Now I'll admit, I'm not the biggest dog fan, so I help out in the cat shelter. I can talk about that with a lot more knowledge than the dog side. They just built a new cat facility on their property so they have their own shelter. The cats are all set up in a huge room. They have two rooms for people to play with the cats when they are looking to adopt them. These rooms are also used for ""cat cuddling."" That's what I do when I volunteer. I get to take the cats out so that they can play, be cuddled or just run around. Then the cats are able to get out of the cages and get used to human contact. + +The other great thing about the ARL is that they have foster parents who take in cats and dogs while they're waiting to be adopted. This way, they get a great home environment and it relieves the facility of having too many animals at one time. At different points in the year the adoption rates are different depending on the amount of animals they have. Cat rates are usually cheaper in the Spring/Summer because there's more coming in and dog rates are cheap in the late summer months. The added bonus of adopting a pet from the ARL is that they are spade or neutered when you adopt them. It's actually cheaper then taking them to a normal vet on your own. + +I would STRONGLY recommend coming here to check out the animals and hopefully find your next furry friend! OR you can volunteer! They have volunteer informational sessions the first Saturday of every month. After that you only have one training session to complete and you're ready to volunteer! + +Just check it out if you're curious. You won't regret it! Your new furry friends will appreciate it as well![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have an almost three-year-old cat named Jack that I spoil as if he were my son. I honestly never experienced the love for and from an animal until I adopted Jack from an Animal Rescue League. It was one of the best decisions I've ever made. + +The shelter is great and I'll probably get another cat in the near future. Check this location out![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> A few years ago, I decided that I wanted to get a pet and so I volunteered at the ARL for a number of months in order to learn about the different breeds of cats and dogs. It was an invaluable experience and really helped me to learn about dog behavior. I still serve as a cat foster from time to time. + +The staff here have a tough and sometimes heart-breaking job. It's not for the faint of heart but they're all very nice and do their best by the animals and the people who come in to adopt and surrender the poor beasts. + +Ultimately, I didn't get my doggy from the ARL (sometimes the heart doesn't get give you a choice) but my experiences there have really taught me a lot about animals and have only served to heighten my love for my 10yr old rescue pup.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great place to find a dog or a cat[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> On July 16th our family was delighted to adopt ""Bubbles"" from the Animal Rescue League. She is a wonderful, well mannered, eager to please dog. Over the past year we have been looking for just the right dog for our household which includes 3 generations and a cat who rules. We had visited ARL a few times in the past year. The staff and volunteers have always been friendly and knowledgeable about the animals. They truly care about matching each cat or dog with the right forever home. I am horrified by the vehemence of the July 13 negative review posted. Yes, the ARL is not perfect; but the staff and volunteers are terribly overwhelmed and they honestly try to do their best. The solution lies in more volunteers and more funding. I highly recommend going to ARL when you want to adopt a pet or wish to volunteer your time to a very worthy organization.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I adopted another cat in February and both my cats are the best of friends. It took a while to get there, but trust me, they're pals now. + +Adopt an animal today![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I volunteer as a dog coach twice a week and i am absolutely in love with the ARL. There are two beautiful babies, whom I have walked for weeks, that I wanna mention (these ladies would be mine if I didn't already have a grumpy Basset and an elderly Shiz zhu @ home): + +Bunny (my girl!! Bunny ears, and the sweetest temperament): + +http://www.animalrescue.org/available-pets + +Honey (I love her to death, 6 years old, just wants to be loved!!): + +http://www.animalrescue.org/available-pets + +Stop by the ARL! It is worth the trip. :)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have gotten two great dogs from ARL over the years the staff is polite and really cares about the animals and finding them the right home. They get the animals the best vet care they can and i believe they have an on site clinic. I would suggest even if they have a special on adoption prices pay the full amount if you can. From what I see they take great care of the animals and could use all the money they can to make sure this continues.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I could never stop saying good things about the Animal Rescue League! As other reviewers have pointed out, going there both breaks and warms your heart. I adopted my puppy, Brock, back in January, and I couldn't be happier. The staff was super helpful and very kind. They gave us enough time to make sure Brock was the right dog for us, and also made sure we knew what we were getting ourselves into. (Brock is a husky mix, so he's a ball full of energy. Great running buddy! :) ) +I will most definitely be back and plan on telling all friends considering a pet to adopt from the ARL![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Animal Rescue League is great! BUT, I'm very disappointed by their dog trainer/behaviorialist, Lacey. + +I have a large papillon (a ""throwback"", as my vet called him), whose previous owners neglected and undersocialized him for the first two years of his life. As a result, he is now extremely fearful when taken outside the home, and he becomes overstimulated and aggressive. I brought him to one of ARL's Saturday small dog classes, but he freaked out, and we were asked to leave. Lacey said she'd be in contact to set up a private class. + +She called a few days later, and we arranged a private class for 6pm on a Wednesday. I made arrangements to leave work early to drive back into the city and get my pup some help! It's hard to anticipate exactly how much traffic there will be on Fifth Ave during rush hour, so I wound up playing it overly safe and arriving 10 minutes early for our class. + +After a few minutes, Lacey noticed us and came outside to tell me that she was running fifteen minutes behind. I wasn't sure what to do, because I couldn't really go anywhere with my cray-cray dog, and there was too much traffic to go home and come back again. So, she said we could wait inside in a small hallway. + +We went in to wait, and naturally, with all the smells and sounds, my pup got a bit riled up. But, we waited...and waited and waited. At 6:25pm, I knocked on the door to the training room. Silence. So, I opened it. Nobody was there, and the door to the outside was open. I peeked out, and there she was, with the people and dog that had the lesson before me. I waited for a moment, hoping she'd notice me and look at her watch or something, but nope. + +So, I took my dog and walked outside to my car. She turned and looked at me, but didn't acknowledge me in any way. I went and sat in my car with my dog for a few minutes, hoping the other folks, their dog, and Lacey would wrap things up, but no. They just continued on. At 6:35pm, I knew I couldn't wait any longer, because I had work I still needed to finish up that had to be done by 9pm. I got out of my car, and began walking towards Lacey. She just stared at me, rather than saying ""We're just finishing up,"" or ""Sorry, I lost track of time,"" or anything at all. So I said, ""We're going to have to reschedule. It's past 6:30 now, and I can't stay past 7."" She simply replied, ""Okay. I'll call you."" + +I thought it was rude and unprofessional to not offer any type of apology, or even a half-hearted explanation, but whatever. No one said she had people skills, I suppose, and this was about getting my dog help! + +Well, it's been a week and a half. No call from Lacey! Needless to say, I'll be finding another, more reliable trainer. I'm just really disappointed, not only in her unprofessionalism, but also her lack of caring about my dog. I barely had any interaction with Lacey, but even if there was something about me she didn't like, she should have cared more about helping a pup that obviously needs it. + +I sincerely hope that others have had better experiences, and I hate to knock even a single star off for ARL -- but this Yelp review seems to be my only way of warning others to seek another trainer for their dog behavioral needs! :([/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love, love, love my puppy. After visiting every shelter in the city and finding nothing, we came back the next day after seeing a posting for a 2 month old terrier mix. Our poor little guy had been dumped in a park and some very nice person brought him to the ARL who took him in, waited 3 days for someone to claim him, and neutered him. He wasn't even supposed to be on the floor yet when we got there, but they were super helpful and brought him out to us and let us take him home. The staff there were super helpful and wonderful to my incredibly anxious fiance- imagine a first time dad bringing home the baby! + +The only reason they only get 4 stars is my poor puppy is SO sick. We've had him for 3 weeks and he's got an awful cough that hasn't been responsive to any antibiotics. I know its hard to keep all the dogs isolated, but I really think 8 weeks is a little too early to neuter a puppy especially after being found in a park- too much stress! Hopefully our little guy starts getting better soon, we're awfully worried about him! Still love the ARL though![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> A few years ago, I lost my partner and love of my life in a tragic accident. While struggling with my horrific grief and having difficulty getting back into life as I once knew it, my grief counselor suggested that I ""help something else"" in order to help myself feel better. We decided that since I was an animal lover I would try volunteering at an animal shelter. I was not working, so I had a lot of time and wanted the shelter to feel right. I visited a few, they all do good work, but the one that kept drawing me back was the ARL. Yes, the building is old, it's a bit run down, but that doesn't stop the staff and administration from doing the best they can with so very little and in not the best of space. I saw a bathroom be ""renovated into a vet tech office, I saw the janitor's closet renovated and made in to the ""rodent room."" Where cats once lived in cages along the halls of the ARL a new building next door, an old gas station was made into the ""Cat Adoption Center!"" When you have staff that are still young and are going on 5-10 years + at the same shelter, (same place of employment for that matter) you know something about the place is right! I volunteer easily 30 hours a week at the ARL, I get to see the good, the bad and the ugly, and I can tell you first hand that the good is in the staff, the Executive Director, Dan Rossi, and all of the work that goes on for the animals. The staff knows EVERY one of the animals, they do all they can to care for them, and keep the doors WIDE open for both domestic and wild animals, even if that means a staff member or volunteer takes a cat or dog home! The answer is never ever ""no"" to any animal. I also volunteer for the Humane Society of the United States and travel around the countryside working on dogfighting raids, cruelty, hoarding, natural disasters, and the ARL has never said no to me when I ask to bring animals back from incredibly sad or inhumane situations. Technically, by the numbers, it is a ""no-kill"" shelter, because it is open door people will often call it a ""kill shelter."" Yes, sometimes an animal does have to be euthanized. The ARL is the Animal Control shelter for the city of Pittsburgh and with that can bring some very upsetting and disturbing signs of animal cruelty. It can also mean it's the dog who just bit a kid that you just saw on the news. The ARL has an obligation to society to not let dangerous dogs back on the street, to euthanize when a dog is very sick or is very aggressive to humans or other animals, and trust me, I have held many of those dogs as they are put to sleep and I always am so thankful that the vet staff we have are so compassionate and do the euthanasia in the most humane manner. That's a tough job, it's heartbreaking, but in some cases it has to be done for the good of the animal and for the safety of society. I admire the work and staff of the ARL and will continue to devote my time to them and thank them for the wonderful work they do on behalf of the city of Pittsburgh and all of the wild and domestic animals alike. We are so lucky to have them in our area and as our city shelter.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The ARL is great! Earlier in the month, we mistakenly adopted 2 pit bulls. After they killed my rabbit and got loose a few times, we felt they were too much and gave them up. The people who worked there were really understanding and asked us a lot of questions so as to provide the best care for them until they are hopefully adopted by the right people. Sorry Chloe and Coco. :( + +They are a NO-KILL shelter too. Always a huge plus.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Please do not adopt any pets from here until they update their standards. I hate to think of animals living in cages, but... + +!! At least two cats adopted from here in September have diagnosed with the herpes virus by the vet, and this is contagious to other cats. !! + +AKA, it is likely that the shelter staff is not washing hands between handling pets and they are not testing for a virus that can be fatal in kittens. + +I recently adopted a kitten from their shelter--I picked him up from their Pittsburgh Public Market adoption station. I was told that he had been tested for common feline viruses and up-to-date on vaccinations. These were both untrue statements. The kitten has the herpes virus and was not vaccinated against this. My roommate, who was with me, and I were warned about the upper respiratory infection (URI) that can occur because of this virus and others, but we were not told that he was neither tested nor vaccinated for the herpes virus. They gave me a paper with his vaccinations, but it was in vet-speak, so I took their word for it. + +Furthermore, the shelter staff put my kitten in my roommate's name mistakenly (and claimed that if we just called in that they would fix this mistake, but then wouldn't), so when he got sick, no one from their clinic would return my calls--I'm guessing this was since I wasn't the owner according to their records. I had to email them to get a response, which basically said sorry that we didn't return your calls but this is your problem now. They never apologized for the kitten's health or asked if he was feeling better. Where's the compassion for the animal? + +So now I have a very sick kitten on my hands. I took him to the Big Easy in Lawrenceville when he stopped eating, and Dr. Ruiz is the best. She took care of him, but it cost $160 to treat the virus he picked up at the shelter. + +The Animal Rescue League shelter/clinic said that it does not and will not cover expenses for this. After I had already taken him elsewhere, the clinic staff said that they would have given me a discount if I had waited two days to go to their clinic, but who would wait two days while the kitten wouldn't eat?? And now this virus makes him ineligible for pet insurance. It will cost hundreds of extra dollars a year to keep him healthy. + +Had I not fallen in love with the little monster, I would have taken him back to another shelter. That's what the person who adopted the other kitten with virus did. Whenever he gets an outbreak, he will get another URI. This means a lethargic cat who sneezes, gags, and coughs because he can't breathe and who won't eat because he's too congested to smell his food. It's very sad--protect your cats with the herpes vaccination, please! + +Oh, and in case you were wondering: just like in humans, cat herpes is fo' life. Poor little guy. This also ruins my plan of getting another cat in the future. Bad shelter![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I adopted a dog from the ARL this past spring. During the adoption process the employees were polite and seemed genuinely happy for me. Shortly after the adoption, I received emails from a volunteer to check in and to inquire about how the dog and I were adjusting. A few months after the adoption, it became clear that the dog had some pretty serious anxiety and behavioral issues (please note that there is no way the shelter staff could have known about the issues while the dog was in the shelter). I contacted the shelter and they practically bent over backwards to help me with the dog's issues. The dog and I participated in two sessions of behavioral classes (Lacey is wonderful and never gave up on my dog!), consulted with veterinary staff, and received constant emails from staff offering suggestions and checking in to see how I was doing. In the end, I learned how to manage the dog's behaviors and I love the dog dearly. Nine months later, I still receive emails from the shelter asking about the dog and offering more suggestions. + +I would highy suggest adopting from this shelter. I understand that my dog is sort of a worse-case-senerio of adopting a pre-owned dog; however, this shelter will make sure you are happy with your adoption and literally will do everything in their power to ensure both you and the adopted animal are ok. The shetler staff care deeply about the animal AND the human's well-being![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Our cat recently came down with some health issues that we could not afford to address. He was in pain and we decided the humane thing was to put him to sleep. We went to the ARL and asked the receptionist there if we had any other options available to us. ""Well basically the only thing you can do is sign him over for euthanasia"" she said in the most uncaring, apathetic voice possible. We were heartbroken of course. ""Go wait by that door and someone will meet you."" After a few minutes another woman came out and took the carrier. ""I'll bring your carrier back out in a minute."" We said no, that's okay, keep the carrier. She said okay and took our cat to the back. And that was it. No kind words, no sympathetic gestures, no ""Would you like a moment before I take him?"" No ""I'm sorry."" Nothing. For us this was one of the worst days of our lives but nobody at the ARL seemed to care, or at least have been trained to pretend to care, one bit. + +They get a couple stars for offering a necessary service. But other than that, this place will only be associated with making a terrible day that much worse with their lack of caring or empathy.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Staff members here have always come up short. A past kennel worker sold his litter of pit bull puppies in east liberty and the shelter was made aware of it but excused it. + +They will lie to surrendering families because they don't want the cold hard truth, the good, bad and the ugly to leak out to the public. They lie ! +They kill many many animals because of a very subjective behavioral test that their dog hating staff performs . + +They kill more pets for space than any other pittsburgh shelter. + +Many volunteers walk on eggshells here because they know an animals life is hanging in the balance and they are afraid to speak up or not allowed back in to volunteer . + +Weak leadership. This is the cities highest cat and dog death rate of any shelter or rescue in western pa[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is a terrible shelter. It appears that they routinely turn away (or kill, unless you state you will take them back) cats because they are ""overcrowded."" They will tell you that your cat has a "" behavioral issue"" to address turning said animal away. Mark that you will take your cat (or dog, etc.) back or else you risk having them ""put down.""[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've had such good experiences with ARL, that I will probably return here again and again. Years ago we adopted a mutt of a puppy that turned out to be the best dog that I could have ever imagined. But let me talk about my most recent visit. + +While browsing Facebook, I noticed that they were having an event at ARL. This particular event was called the Free Fur All. The event involved free adoption to qualified adopters, free micro-chipping for any pet (adopted there or elsewhere), free dog baths, and goodies for both human and furry companions. + +I had plans to get Little Man E microchipped during his appointment to take his manhood away (don't worry, we've talked about it and he is fine by it), but when this popped up and said it was free. Hot damn, you know I was in line. It's also probably one of the more easy and humane ways to keep ties on your dog or cat just in case they were to run off one night. + +Once we were registered, we waited at most for 15 minutes. It's a very quick thing to have done. Little Man E didn't even flinch. He was more amused by his reflection in the table than that little pinch behind the shoulder blade. I have to give huge kudos to the staff there. They are so very friendly to not only you, but your pet. It's like they talk their language. I also have to thank them because while we were there, LME somehow ripped his one toenail and they were kind enough to clip as much of it off as they could (no extra charge either!). + +Once done, we just walked outside to see what was up (E skipped the bath). We visited one of the tables and E selected a ball and bandanna and we decided to head out after that. + +This place is amazing for so many different pet oriented things. I'll definitely be coming back here whenever I need something for LME.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place is PHENOMENAL. +I got my bunny here a few months ago and the ladies were so nice and helpful and they take SUCH good care of the animals. They gave me a bit of hay and food for her that lasted me close to three months. Then when we were leaving we saw a cage of six dwarf hamsters and they gave us a deal of 2/$10. +I love my animals so much and I will always check here first for pets before anywhere else.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I adopted two cats from animal rescue league and my cats are healthy and happy. They take care of animals with love and kindness. They are of course so busy because there are many abandoned pets from irresponsible humans.. +But they made the whole adoption process easy and after almost a year my cats are still lovely and gives me so much love.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I just adopted my second dog from this shelter, I think they're wonderful! You must keep in mind that no rescue shelter is going to look like a 5 Star hotel and be able to keep every animal free from illness, but the ARL does a great job. All pets are spayed/neutered, vaccinated, and receive a microchip. Your first vet visit after your adoption is half-off their already cheap prices at their in-house vet clinic. They also give you a little goodie bag along with the pets vet records. I'm so thankful for the furry friends I've adopted from the ARL![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Good work. He does very nice, high quality work. A bit on the expensive side (costs $30 to shorten two pairs of pants) which I guess is reasonable considering that he does reliably high quality work. I haven't given him anything more complex than that however so I don't know how he'll take in your wedding dress, but works for me.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place is great, and even calls to double check when they find something they aren't sure about. I have had business suits altered here, jackets, etc. My husband had a beloved winter coat that he wanted to have the pockets repaired, and Vincent (or another man) called back 45 minutes later, freaking out (very politely) about ""HOW CAN I REPAIR THESE POCKETS?! THEY ARE AWFUL! NO POCKET LEFT! SHREDS!"" and we had a good laugh after telling him we meant for him to replace the pockets altogether. He did a fabulous job and even though he's not cheap it is worth it to know you will get the clothes back in great shape.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Vincent has done several hems and jacket alterations on men suits for me. Items have always been one time and done well. I would recommend this place to anyone searching for a tailor in Pittsburgh. + +It does seem a little expensive, but worth it, because its done correctly.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It was 1:00 pm on Friday and i was in a serious bind... I needed new suit pants altered and my flight was leaving the next day at 10:00 am. I called and Vincent said he would help. He got the job done, with a smile and his work was perfection. + +I would recommend Vincent to anyone needing alterations. Great customer service.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is a bizarre CVS, the kind you would only want to go to in a pinch, and maybe not even then. + +I went to this one with my husband a couple of times to pick up prescriptions, and the vibe from start to finish is so weird. Let's start with parking, which is in a lot behind the store. There's not a lot of visibility to the lot since it is on the back side of the CVS. Being that it is a pharmacy, there wouldn't be a back door or windows, so the lot has a feeling of dangerous seclusion. + +Inside the store, everything I saw told me that ""this is a pharmacy that is in a rough neighborhood"": shelves are only about 4'6"" tall (presumably so workers can see what people are doing in the aisles); bizarre things are locked in cabinets with clear covers (regular brands of shampoo?!); beauty items regularly updated, weren't (I, er, have a nail polish problem; some of the products were about 4 seasons behind and quite a few polishes were separated); it feels like there isn't enough room for the products, which are disorganized and crammed onto shelves (reference the odd shelf height limitation). + +If you can spare the gas and time, there is another a CVS on Center Ave within a mile or so or a Walgreen's (Penn Circ S+Trade St.) and a Rite Aid (Baum+Negley) within 1/2 mile.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I go to this CVS all the time, since I work in the neighborhood. I'm not a huge fan of it - I go mostly due to convenience. Their greeting card selection is kind of lousy - I don't think I've ever found a decent card here. I keep trying, every holiday or birthday, but every section is just full of duds. Also, a lot of stuff is locked behind panels that you need the employees to unlock. Like, razor blades. And body wash. BODY WASH? It drives me nuts that I need to ask someone to open that shelf for me. It makes no sense. Staff is hit-or-miss with friendliness. Some people are cheerful, and some act like they want you to go away. + +Good things - I love their coupon rewards. I guess that's for all CVSes, not just this one, but it keeps me coming back because I get mad style coupons like every other visit. And I had a good experience getting a walk-in flu shot from the pharmacy from the friendly (and quite attractive) pharmacist. + +I'm just not crazy about the vibe here. It just seems kind of depressing, with the stuff locked up and the smallish store with kind of a blargh selection. I would much rather go to other pharmacies, but you can't beat this one for convenience (for me, anyway). And they have a parking lot, if that helps you.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The Rite Aid on Baum used to be my pharmacy, but I flipped to this CVS location because of the convenience (on the route to/from work). At first, my experience was not unlike the other recent reviews. I, too, hate having to ask the clerks to open the locked compartments that hold the razor blades, etc. + +BUT... + +The pharmacy staff is terrific. I have NEVER had friendlier, more knowledgable and more responsive pharmacy staff at any other drug store. The service is first-rate and the extra care and attention to detail is deeply appreciated.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Never again. Let me repeat, never again. + +The primary reason I used to visit this store was to fill medical prescriptions. Due to their repeated inability and ineptness in fulfilling simple requests, I cannot continue to patronize this store. + +Walking into the store, you are given the stink-eye by a minimum wage security guard, which automatically gives you as a customer the warm and fuzzy ""guilty-until-proven guilty"" feeling a shoplifter would get, which is what this store assumes everyone is based upon their decision to lock up the mouthwash and shampoo. + +The pharmacy seems to be staffed by high school interns. They have no concept of customer service, nor do they display any attention to detail, which is quite frankly frightening in a pharmacy. I really think my chihuahua would make a better pharmacist than the people who work here - my chihuahua lick you to death before you got your prescriptions, but at least you'd get greeted when you approach the counter, and you'd get what you ask for. + +The first mishap was when my wife and I changed prescription insurance providers. i handed wanna-be pharmacist #1 my new insurance card. After spending about 5 minutes staring into a computer screen behind the counter, he assured me that they had my insurance information in the computer. I then returned in the following days to fill a prescription, trusting in what wanna-be pharmacist #1 had told me in the days prior. When I went to check out the bill came to over $300, which I chalked up ""maybe I have to meet a deductible before the coverage kicks in."" Upon further research, we discovered that wanna-be pharmacist #1 had NOT updated my insurance information and had run the numerous prescriptions I filled under my old insurance. + +The latest of many ""adventures"" involved my wife calling in a prescription refill. We stopped to pick it up on the way home from work, only to be told when we arrived that the insurance won't cover the refill until tomorrow. Again, she CALLED and SPOKE to one of them to refill the prescription before showing up. I guess it's too much to ask to TELL someone you're speaking to on the phone that they need to wait a day for the insurance to work before coming into a ghetto pharmacy to not pick up a prescription. But hey, at least wanna-be pharmacist #2 behind the counter was dressed like a stripper, which gave me and my wife some comic relief for the moment. + +We then returned the following day to (again) pick up the prescription we called to have refilled 2 days prior. We were first told by wanna-be pharmacist #3 that there weren't any prescriptions waiting for us. After searching around for a few minutes, they ""found"" my wife's prescription refill, but it would take 10 minutes to be ready. Yes, the prescription that we tried to pick up yesterday would need another 10 minutes to be prepared. Hence, I am now here, writing this review. + +Never, ever again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The times I've been here, its been an OK experience. However, their store hours are absolutely terrible. Closing at 7pm basically means they're never open when I would need to go there. Despite this being more conveniently located, Walgreens and Target end up getting most of my quick-shop business, simply due to late hours at night when I need to cook, clean, realize I'm out of toothpaste, have a headache, need a last-minute birthday card or whatever.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place is a disaster. I made an appointment online for 5:30PM. When I got there they refused me service, asserting they close at 6:00PM. Nevermind that online published hours are from 7AM to 7PM. Furthermore, their own system sent me a confirmation email for my 5:30PM appointment. Finally, this building is an absolute dump... Goodyear should be ashamed to have the brand attached to it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Very easy place to get my tires replaced. I pulled in, they took a few pieces of information and I just had to wait. While I was to wait I made sure it was OK for me to walk to nearby businesses to pick up a few items I needed. They took my phone number and told me they would call when my car was finished. + +While I was out at nearby stores my phone rang less than a hour later and was told I could come and pick up my car. Walked in, paid and away I went. + +Why couldn't I give this place a five star rating. Two reasons. 1. I ordered my tires and was expecting to receive a call on a Friday to stop in and have the tires put on my car, they did not call me at all and I called the following Monday to find out my tires were there for the past few days and no one made the effort to call me. 2. When I left, I could not comprehend why the air pressure wasn't regulated to my new tires. How hard was it to make sure that my psi was set to 32? One tire was at 38 and the other at 35. I promptly needed to visit a gas station to remedy the situation.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Tire replacement, was told it would take about 1.5 hours (when I had an existing appointment). It's almost been 2.5 hours and I'm still waiting. Ridiculous.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I experienced three main issues with this Goodyear location while purchasing/installing a new set of tires: + +-They did not have my name or appointment in their system when I showed up. Fortunately, they still honored my appointment. + +-They did not install tires correctly. Left for a business trip the following day, and once I got on the highway and my speed passed 65 mph, the car began to rattle (with my new ""comfort tread"" tires). Booked an appointment, and they fixed the issue. + +-Two months later, I went to my Toyota dealership for routine maintenace. The dealer mechanic found that the lugnuts on the tires had been over torqued by Goodyear. So the Toyota mechanic had to saw them off of each tire and replace them with non-security locked nuts. (If I had a flat on the side of the road, I would have been SOL). + +All of these issues were entirely preventable. The lack of expertise and techincal skill at this Goodyear location is abysmal. I do not recommend.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I was just there this morning for a 10am appointment to get my summer tires swapped out for my winter tires. My regular mechanic was overbooked and there is snow coming on Monday. Receptionist scheduled me in just fine and the quoted price was reasonable, so I said OK. Upon arrival, store manager stated that they will not touch the car as it has aftermarket rims and lug nuts. He did not state any restrictions about aftermarket parts as they could not guarantee the work. I asked if this was the case for all rims and he became a little snotty. I had heart surgery a while back and I can't do the jack and tire work as not to tear at my incision/breastplate, if this was not the case with my health, I'd certainly take care of it. Aftermarket rims are common - should not be an issue. Last time I ever set foot in that place.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Poor service that leaves tenants to fight mildew on their own. When asked to repair something, Rockwel Realty will do it on their terms and refuse to give you notice of when they will enter your apartment despite multiple requests + +When asked to clean mildew, they did in fact clean it with bleach while also spilling bleach on my sheets and ruining them. When told about this problem and that the mildew returned they said it was my fault for not turning the heat up and that damage done during service is an inherent risk the tenant is responsible for and nothing could be done. Their solution was for me to clean the mildew instead of properly insulating the unit to prevent mildew. + +The entire building also has severe electrical problems that causes all lights to be replaced twice a month. No permanent fixes are made to existing units, but there is constant construction to expand an old building so they can collect more rent.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Rocco and Vivian have truly been a graceful pair to my roommate and I for the past year. We lived right on Fifth avenue and Bellefonte and found no reason to complain aside from the neighbor's dog downstairs. The few mishaps that happened within the apt ( a broken lock, a leaking sink) were fixed within 24 hours of calling our landlord, Rocco. I have to say that for two girls who forget the little things (more of ten than not) we could not have asked for more understanding tenants for the amount of times we were locked out, forgot keys, needed a drawer fixed, needed heat, etc. Our space was clean and everyone in the building was friendly and respectful. I highly recommend to any student looking for housing in the Burgh.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> While looking for a rental after relocating Rockwel was extremely helpful and courteous. They were very responsive and accommodating with the right deadline my wife and I were under. They were willing to go above and beyond to get the place prepped in time. Couldn't recommend them more.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Exceptionally poor maintenance service. They refused to start heat before mid-October and the centrally heated apartment grew very chilly as Fall progressed. On another occasion, they refused to change a rusted and weak lock. The lock eventually gave way and I locked myself into the bathroom. After the incident, I requested that the lock be changed immediately, and one of the owners threatened saying that we were in default of our lease agreement for not keeping our apartment as clean as when it had been leased to us. Dealing with Rocco and Elisabeth is nice, but good luck getting anything done with Nick who seems to be increasingly handling the operations of Rockwel.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm a lawyer in NY and I'm visiting a friend in Pittsburgh. I am blown away by the code violations in this unit. The tenants said they have reported these issues to the owner and to no avail. I am hoping to direct these tenants to a lawyer in PA.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> On my recent road trip from Dallas to New Haven, CT, Randy S. and I stopped in Pittsburgh to revel in its charms. This, I must add, was in opposition to his mother's strong protests to the effect of, ""There's nothing *in* Pittsburgh, why would anyone go there?"" + +Tazza D'oro is the answer to that question. Especially if you like coffee. This is easily one of the best coffee shops east of the Mississippi, and I've been to a lot of them. So, what's so good about it? + +Let's go in order of importance: + +Coffee - It is really, really good. They use Batdorf and Bronson beans, where an ex-gf of mine used to work in Olympia. Believe me when I tell you that B&B is good. It's not amazingly great, but it's very solid and they take roasting seriously. When I go to a new coffee place I suspect might be good I always get a latte. Why? This one has a high upside if done well and the lowest downside (lots of milk) if done poorly. I got a latte. They have a few sizes, 12oz was the first one I got. It was fantastic. They did a nice little rosetta in it too (look up latte art on google if you have no idea what this is). The baristo really knew what he was doing and pulled a some good shots with excellent crema. + +The coffee was so good (coffee is supposed to taste bold, smooth and rich, which it almost never does and this place had it down) I had to go back for an 8oz, which is another level of trust. It has the same amount of coffee but less milk to hide poor coffee quality. It was always superior. + +This is a coffee place that is truly top notch based on the coffee alone, but there was more. + +Pastries - They all looked amazing. I had a plain donut while I waited in line. Normally I don't eat plain donuts, because life is too short for plain donuts, but it was really, very good. Everyone was commenting on how nice the pastries were. + +Atmosphere - This place has it exactly right. It's a mom & pop feel, nothing forced. Some tables, outdoor seating, maybe some local art, but not in a goofy sort of way. Very friendly employees. Just a complete home run. + +Obviously I loved it. Behind me in line for my re-up, I heard a girl behind me in line complain, ""we could just go to Starbucks, it's cheaper!"" then proceeded to order with sugar free syrups and skim milk. That's fine. Everyone has to do what they like... and with the proliferation of bad coffee (Starbucks only being guilty of mediocre, though a little bit interesting coffee) over the past 10 years, I don't blame people for being set that way. But the beautiful thing about Tazza D'Oro (cup of gold in Italian) is that--if you let it--it will remind you that you don't need to make your coffee up like a drag queen on Halloween. + +Tazza D'Oro stands as a reminder that coffee can be enjoyed in all its naked glory in an awesome setting on a beautiful street and give you a good f'ing reason to go to Pittsburgh.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place is nestled in a nice location next to the city water reservoir and highland park, making it a great place to grab a coffee if you are out for a morning walk. It offers a clean and casual interior and draws a more eclectic crowd than most cafes- leans a bit towards the business casual crowd. Still ha that neighborhood feel though. I have never had food there though they offer paninis. Great desserts. Good espressos and okay coffee.Outdoor seating. Good place to study. Plenty of laptop outlets and free wireless.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is one of my two favorite coffeehouses in town. It took me far too long to come around and love Tazza D'oro. A horrible ex of mine loved this place and I admit that this soured me. I regret the time I wasted not going here. The dark wood inside comforts me. The small tables outside are a great place to spend the summer. + +Tazza D'Oro brews Batdorf and Bronson beans (amazing), provides Enrico pastries (amazing) free wireless (amazing) and one of the most talented and friendly staffs I've ever met (amazing). Everyone who works there is *so* nice and *so* good at what they do. + +They have a small menu of local/fresh food that looks amazing, but I have never actually eaten it. The espresso served here is actually better than the average shot served at Batdorf and Bronson locations in Olympia, WA. I talked about this with one of the barristas at TD'o and they were offended - ""we calibrate our machines the same, we use the same beans, the exact same blends and milks and everything, it can't be different."" Sorry, Tazza D'oro, you are better. + +The lines get long on weekend mornings, but they move quickly. There's a sense of community nestled here, just off the ""main drag"" of Highland Park, between Bryant st. and the reservoir. This is where you can pick up your CSA shipment for the week, where multiple weekly bike rides originate, where there are lively discussion groups meeting nearly every day. The percentage of students is low. Like the rest of Pittsburgh, there's a good chance you'll run into someone you know, but generally I see people I like and miss, which is different than the norm in Pittsburgh for me.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Do you see how all of the other reviews give this place 5 stars - this place is way more than a 5 star coffee shop. I am giving all 5 stars to this delightful coffee shop because it is the perfect community coffee shop. I am slightly saddened that they took out the 2 overstuffed chairs, but they need more tables because people like to come here and people hanging out in their community is a good thing. It is 11:30 on a Monday morning and the place is almost full - there are always people coming going, getting coffee. + +It is a great place to sit and read the paper or to pick up some coffee on your way to some place else. + +Enrico's also has become a hub for other community activities - there a a couple of weekly bike groups that meet here. + +Other reasons to love this place (I know some of the other reviews highlighted these but I thought they were worth repeating). + +- free wifi +- outside tables +- tasty treats +- they have a blog! +- really great coffee +- the staff are coffee experts[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Although I am not a coffee drinker, I do love their iced mochas! They have wonderful teas, cider, hot chocolate. The servers are wonderful and the brownies, as big as your head, are like crack. Amy, the owner, has created a wonderful place for community.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Tazza D'Oro has a generally European decor, with dark, rich colors and textures, and a cozy layout that makes the most of the space. The espresso is, bar none, the best I've had - including my admittedly limited travels in Italy. It's stellar espresso - rich, thick, potent without being sour or bitter, with unique nuances that vary slightly depending on the shot and the weather, but are always fantastic. + +The coffee is also terrific, and Tazza D'Oro uses Batdorf & Bronson beans - the best I've ever had for home grinding. They have a good selection of pastries and cookies, as well as a broad selection of tasty sandwiches that come with a satisfying side salad. + +In addition, they have a wonderful selection of teas; I'm no expert, and don't know their supplier, but the half-dozen different blends I've tried were all memorably flavorful. + +All that, and it's a lovely center of community, where you can bring your laptop or a book or a friend and spend the day. No one is rushed out the door, and there almost always seems to be a little room for your studies or conversation.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Best independent coffeeshop I've ever had the pleasure to visit. + +Best americano I've ever had. Some of the best espresso I've ever had. Great desserts, pastries, and cookies. Good food. The employees are awesome. + +The owner apparently put the shop there because their neighborhood didn't previously have anything like it. The shop is also all about bicycling as transportation, sponsoring regular group rides around town, and also group walks for those not bicycle-inclined.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I LOVE this place. THE best coffee in the 'Burgh. Good atmosphere, great service. The food is really good too.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> One of my favorite coffee places in Pittsburgh. THey also have pretty good sandwiches and salads if you are looking for some light lunch food. Otherwise, they have plenty of pasteries/cookies to eat that are pretty good.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Some of the best coffee I've ever had. Ever. + +Stick with an Italian Cappuccino and bring a good friend for some good conversation.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Quick service, amazing coffee, nice vibe.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love this place, its warm and cozy ambiance and the coffee and baked goods are wonderful! The staff is so inviting too![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is some of the best coffee I've ever had. I've been looking for a local coffee shop that made good coffee and didn't have irritating quirks in their service (I've run into a cash-only, lame hours shop and a we-don't-have-an-espresso-machine shop, which are useless to me.) + +The pastry I had was good, though a bit overpriced at ~$3. The mocha I had was absolutely amazing, though their largest size is only 16 oz, which is an adjustment if you're expecting the larger sizes some other coffee shops produce.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The coffee here was excellent! Had a double espresso. Apparently their roaster is in Santa Cruz Ca. Large selection of French Press Coffees. Baked goods did not look too great but that is not why I came here. Atmosphere is very mellow and comfortable. Also has Wifi which works! Nice to find a place like this when traveling. Is in the middle of a residential area and there doesnt seem to be anything else around here.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> They just opened a spot at Carnegie Mellon, on campus in the Gates building and it has changed my life. My closest coffee option before was Seattle's Best, so you can imagine how delighted I was when this opened next door to where I have class all day. The first week they were open I think I went there about 4 times. The Italian Cappuccino will wire you for a few hours, but is totally amazing. Their basic coffee pales in comparison to their espressos though, so stick with espresso drinks. I have also had two delicious paninis, which I highly recommend. Knowledgeable service. Great drinks! yum![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love Tazza D'Oro! great coffee, excellent baked goods and the food is delicious.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The coffee is really awesome but the brunch wasn't anything spectacular. It was also exceptionally busy and me and my three friends had to crowd around a teeny tiny table. All of us felt like the panini/burritos were totally edible and good just not great. The flavors just weren't super tasty. I would say yay on coming here for coffee sort of yay on coming for food. + +It kind of bothers me that it shows up as the number one restaurant in Pittsburgh. I mean, it DEFINITELY does not deserve that ranking. I wouldn't want out-of-towners coming to Pittsburgh and thinking that's the best we have.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This cafe's espresso drinks are on par with the best artisinal coffee houses anywhere. I always go out of my way to get coffee from here when I'm in Pittsburgh.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love tazza.. Their coffees are excellent and its a great place to enjoy a relaxing evening..I also like their Baklawa, sandwiches and Brownies..[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Coffee, Coffee, espresso, cappuccino, coffee, espresso...TEA!!! Amazing selection of TEAS; high-quality, loose and those that I've tried have been so delicately balanced, the word perfect comes to mind. + +While their espresso is also excellent, I've not been pleased by Tazza D'oro's (soy) lattes, so I am going to indulge my renewed enthusiasm for fine teas and work my way through their extensive menu that which is not to be overlooked if you have even the slightest interest in exploring beyond the weak frontiers of Lipton.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Best coffee in Pittsburgh, without a doubt. Believe the hype. I've been going here for years, and every visit is a pleasure.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Yes! Awesome soy cap, scone, and atmosphere. Nice place to hang out & read, and free WiFi with no login procedure.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Thought it's somewhat pointless to write a review for this place. I mean, every spro geeks i know of in town knows this is the best place to get a cup doppio or any espresso drink. The only reason I still decided to write this review is stupid yelp doesn't let me add a store to my list unless I have written a review for it. dah! + +This place is where all my fine coffee addiction started with. Never did I have a cup of starbucks coffee after my first visit to Tazza D'ro. Not sure if it is a good thing, since now I have to do a lot of research on where to get a good cup of coffee before going to a new city no matter for business or for pleasure. + +I love their signature ""bike love"" for all the espresso drink w/ milk. It's fruity, mild, and fragrant. It's addictive! The only thing I have against it is that it has pretty strong caffeine in it, although it tastes super innocent. It's actually almost stronger then any spro blend I've tried. + +I also appreciate a lot the community atmosphere and the effort to bring in community improvement of TD. + +Not a good place to study/work at on a weekend afternoon tho. It's too popular thus noisy.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is a staple neighborhood coffee house right down the hill from the park. Great outdoor seating. Very hip atmosphere. Plenty of plugs for laptops. Comfy chairs for relaxing. Friendly people. Only problem is finding a seat.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> One of the best cups of coffee in pgh. Great atmosphere for working, studying or a meeting. Very neighborly feeling.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I would never have found this place if it wasn't for yelp. It is somewhat hidden among lots of houses and residential buildings. I ordered a latte and blueberry scone, both were great! I wanted to order food but I was told that they do not serve food (even breakfast) until 11 a.m. I would go back if i am in the area.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Some of the best coffee in Pittsburgh (and many argue that it is in fact -the- best). Really warm, rich blends, especially the espresso. The tea menu is extensive and has a lot of variety, so it's a great place for non-coffee-drinkers, too. It has a relaxed atmosphere with indoor and outdoor seating (is there anything cosier than curling up in one of the window seats with a book/notebook on a rainy day?). I've done it all here-- from writing and filing an article when the newsroom was too loud to meeting a blind date. It's a good place to linger and savor. Its proximity to the park is a big advantage.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The epitome of 4 stars: Excellent without being perfect. Tucked away in the middle of a charming old residential neighbourhood, you'll likely miss it the first drive by. Turning around is worth it. + +Yes the staff tends to be the typical hipster, bike-riding sort that so commonly seems to staff indie coffee shops, but they're friendly and unpretentious, so don't hold it against them. The patrons are almost exclusively college students (anyone else tends to drive by and take their coffee to go), though hipsters are actually in the minority here. Anyone under the age of 25 will fit in perfectly, and no one 35 and under will feel uncomfortable. + +The noise level is perfect. Most students are on their laptops with headphones, a few are chatting quietly, and the background (indie) music is just that. You don't need headphones to concentrate here. + +Decor is decent without being great. The ceiling is crossed by beautiful wooden beams, and the floor is a pleasantly bland creamy ceramic tile. So is the wallpaper, though the original modern paintings tend to help make things interesting. Where it loses points is in the furnishings: the mixture of wall lamps, hanging fixtures, and pot lights doesn't work well, the serving bar itself is an ugly cheap laminate, and the touches of plastic greenery dribbled around the place fails misserably. + +Iced water is provided, which is decent (plastic cups are a minus), but inferior to the mineral water other places serve. We tried their richly brewed Ethiopian to rave reviews, with the party split on whether the thick ceramic mug was a plus (hefty and warming) or minus (hard to drink from). Truly fantastic coffee, but the lattes were rather disappointing: Beautifully steamed milk in every cup, but a rather bland espresso shot left the latte rather lacking in the nuanced flavour one finds in a 5 star establishment. The medium latte (12oz, with 2 shots of espresso -- the steongest ratio they offer) should have been far better. + +The food looked worth having, but we'd just eaten. Homemade pastries and fresh sandwiches looked tempting, and we certainly will come hungrier next time. + +A solid four stars, held back a bit by decor and a lot by espresso.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Just realized that no one mentioned about their chai latte yet. They make their chai from scratch. The best chai I have ever had outside of my indian co-worker's kitchen. The only thing is, since they premade a whole pot, there's no way you can get a cup of skim chai...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> local, friendly businesses serving a great product DO still exist.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Reasons: + +1. LOCATION and setting: Highland Park is simply lovely - makes you feel as if you are in a small English town, where time has stood still. The art and small tables inside and outside are charming. +2. Socially Responsible:Fair trade and international array of coffee. +3. Fresh Meat: Local pasture raised meat/ local produce in their tasty panini's. +4. Nice crowd and staff.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Best coffee I had in Pittsburgh. Their Italian Cappuccino is pretty addictive.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The coffee here is amazing (I love when the baristas take the effort to make patterns in the foam). The baristas were extremely friendly and the pastries looked delicious. While there are a number of tables, Enrico's was busy even on a Friday night...I would imagine that it would be hard to find a table during peak hours.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> one of the best espresso bars i've been to. + ++1 for great espresso. i had a shot of ethiopian espresso. fantastic! grabbed a costa rican pour-over on my way out ... perhaps one of the best cups of coffee i've ever had. + ++1 for baristas who pay great attention to detail + ++1 for great atmosphere. the ceiling is tastefully ornate, and the decor is pleasing. hearty wood furniture used throughout. + ++0 for having a location a bit far from downtown. + +a favorite for locals and not-so-locals alike. + +highly recommended! i will return...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The environment is just what you would hope for in a coffee shop: tastefully decorated with some local art in an old building with a cool ceiling and floor. A great place to enjoy a beverage, book, and music. + +I had an Italian Cappuccino. It was well balanced and I enjoyed every sip. On my way out I had a Costa Rican pour over that took me by surprise. It was incredibly smooth with a complex flavor. It rolled off my tongue without the thin taste of a poorly roasted bean. As the drink cooled the flavor profile changed but continued to please. + +I highly recommend this shop if you are looking for a place to spend a few hours and enjoy everything from speaking with competent baristas to the last sip of your drink. I will be returning.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've read countless 5-star reviews of this coffee shop and I'm sorry, but I don't wholly agree with, well, everyone else; so, here's my slightly alternative take on the cafe. I'm aware, like many reviewers on this site, that not every place is aiming for me as the target customer; but even still, there's no way this is a five star coffee shop. Yes, the coffee is good and if I happen to be lost in highland park someday on foot, I'm sure I'd stop in to get it again. But the place itself was a turn off, despite the interesting people that it attracts. Glossy refinished exposed wood beams, fake grape vines over the windows, and odd light fixtures create a tacky atmosphere I can't overlook or sit in. I think this is a great coffee shop if you happen to own a house in highland park, but for me it's going to be voluto or espresso a mano from now on - it's just not worth the drive.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I tell everyone about this Highland Park gem my friend introduced me to. People who come here appreciate expertly steamed milk and delicious breakfast/lunch options. In this quaint shop gone are the days of the mass-produced lattes and microwaved sandwiches. Every time I visit Pittsburgh, I make sure this place is in my schedule somewhere. Love it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Pittsburgh's definitely got nothing on Seattle when it comes to a good brew but if you look hard enough you'll find a few diamonds in the rough. Tazza D'Oro is one of them. I wont say THE best simply because coffee is such an objective taste but you cannot deny the expertise and care Tazza D'Oro subscribes to. It brings them millions of miles above Starbucks and (gasp) Crazy Mocha. + +I found out about Tazza D'Oro while browsing the blog of an award winning, internationally recognized barista. He conveniently mapped out his favorite coffee houses around the US via Google Maps. I clicked on PA and zoomed it, not even expecting to see a marker. Surprisingly there was -- only one -- and it was for Tazza D'Oro. + +Their baristas know how to make the perfect espresso. Once you've done that all of your other drinks fall right into place. They also do french pressed coffee which is a rare treat usually enjoyed at home and, at least in my case, not done nearly as well as it should be. Their pastries and baked goods come straight from one of the 'burgh's best bakeries -- Enrico's in the Strip District; what more could you ask for? + +I have a longer article on Tazza D'Oro as well as another great coffee shop, Espresso a Mano on my website. http://eatinginpittsburgh.com/2011/02/11/coffee-pittsburgh-part-2/[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I can remember the time when I used to strictly drink mocha frappuccinos from Starbuck's thinking that it was the be all end all to coffee in my younger teens. Don't we all miss those days of being so naive? + +Admittedly, I never finish any coffee that I drink, not only because I'm apparently wasteful now that I think about it, but also because I'm a slow sipper and everything settles at the very end. Make no mistakes, I will finish any coffee drink from Tazza D'oro and at record speed. It is delicious to the very last drop and the best part is, they don't think that third degree burns go hand in hand with their coffee -- it's ready for drinking the moment you receive your order. Let's not forget about the food, which is also delicious. it's clear I have nothing bad to say about this establishment. + +Some of the staff remembers your order to a tee and all of them are always very courteous. The prices are reasonable and the location is great, tucked away in Highland Park.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Good coffee!! The atmosphere is nice, it was good to get out of the cold when we took our walk :) + +The coffee was good, and not too expensive.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is where I learned what good espresso tastes like. If you make it to Highland Park, stop there and get some great neighborhood atmosphere.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'll preface this by reminding anyone who reads my reviews that 3 stars is a good review for me--it means it's good, but I'm not going to go out of my way for it. + +Enrico's Tazza D'oro Cafe is definitely very good--I love the location in Highland Park, and the early morning crowd seemed pretty nice and very eclectic. We even ran in to a friend while we were there and had a nice chat. + +My girlfriend and I ordered lattes which were excellent--the space was overall very nice inside and while the selection of pastries was a bit thin I would say the ones they had looked good. I do wish they had more outdoor seating, though. It's tough to make the ""I'm a fan"" list for coffee houses. I'll try it again and may change my review in the future. + +While I""m on the note of Highland Park, I want to join the chorus of people who are dismayed by the recent hit and run involving the two bikers in Highland Park. Accidents (no matter how horrible) do happen, and as such I'm not as angry about the actual accident; but to just drive away and leave people severely injured by the side of the road is pretty wretched behavior. At this point, i only hope that if you are the person who did this, you will at least dedicate the rest of your life to doing good to balance your to-date lousy behavior. + +It's never too late.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The espresso is definitely good. Although the interior is strange, the location is cute for Highland Park. + +My beef is with the snarky Pittsburgh hipster Employee's that barely even engaged with my jokes made about their Beta Fish ""Vivian."" Seriously, a boy Beta, named Vivian! That fish needs some recognition and love. After basically flirting with ourselves, it seemed like all they cared about was acting cool and barely providing an engaging espresso experience for me and my friend who were obviously excited to be there! + +Next time, maybe there will be different employee's. But I have a feeling their lack of enthusiasm for serving the general public will deter me elsewhere. Sad times Tazza, I felt like I could have really loved you.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> As if in answer to my prayer. + +I'm not basing this review on the quality of the coffee. I had Rooibos tea and a (delicious) apple galette. + +I'm basing this on the fact that I love this style of coffee shop (could be in Seattle or Portland). And the fact that since coming to P'burgh for a few days for the first time, it's the first aggregation of non-grumpy people I've been around. Well, to be fair, all the partying college students on the South Side last night were not grumpy. Maybe it's that the folks sitting around me here at Tozza Doro are just chilling, quietly dong whatever they are doing, and not being overly grumpy or self absorbed. + +They don't apear to have more than coffee and pastries, but they do have free wireless. + +There is not as much in this neighborhood as I thought there was going to be, but if you find yourself here, and you like non-corporate, home grown cafes, this is a great place to chill.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I think the lattes have improved since my last review and their soy cappuccinos are the best I've ever had, in fact, I never even cared for them until trying Tazza D'oro's. I still hold their teas in high regard. However, the food here sucks. They've always had a limited sandwich menu, but at some point even that has been reduced to three choices. I am a sucker for a good veggie sandwich, especially in combination with caffeine. Even though Enrico's is an easy walk from my home, I find myself either walking further or driving elsewhere for the caffeinated lunch experience. I guess they are trying to keep focus on the brews, but I don't think it's that hard to do both; I mean the staff seems highly competent, they have a kitchen and sandwiches are pretty simple recipes to follow and learn. With a new lunch joint in the 'hood (Park Bruges), why not expand lunch options rather than downgrade to the point of forfeiting without even the slightest struggle?[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Outstanding lattes. Period. + +The service can be *very* slow, but the latte is worth the wait. And, the staff does not seem to care to chat with customers, but they make darn good lattes so who cares. + +Tucked in the beautiful Highland Park neighborhood among many historic houses and close to the handful Bryant street restaurants, Tazza D'oro is a fantastic place for coffee lovers like me. A nice short walk from Highland Park is a welcome plus. Get the latte, take a stroll down the street to explore the houses, and take a walk in the park. That is a beautiful and coffeeful sunny summer afternoon for you. + +They also have food, but I cannot speak for that. The interior is somewhat run down at places, but that gives it character.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Maybe Tazza D'Oro doesn't need another review, but I guess it never hurts to lend your voice to the chorus of those praising a good, solid and well-run local business. + +The coffee selection is terrific. The baristas are professional and courteous. No, they are not chatty, but they are polite and friendly. I'm not there for conversation, but for good coffee. And that's what you get. + +The pastries and snacks are fine. Good variety. + +The atmosphere is JUST what I want when I need a cup of coffee: relatively quiet, comfortable and calming. + +When it first opened (how long ago how?) it was mobbed by some of my neighbors (I live in Highland Park) who adopted it as their private club and often seemed peeved at ""others"" who stopped by. They've either relaxed or found other obsessions. The clientele is, as folks said, eclectic and invigorating. + +It's become our after-dinner spot after a meal at Park Bruges or Smiling Banana Leaf, too![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place was pretty cool. I mean defiantly felt like a place with a bunch of regulars, but i felt welcome inside. + +All I got was a cup of coffee and a apple pastry. My mother got a espresso. Both drinks were good, but for being one of the top rated places on yelp, I expected more than what I expirenced. + +The apple pastry did not seem very fresh, but it was still very good and worth eating. + +I guess I was just a little disappointed because I expected so much more than what I got.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Finally, a great neighborhood coffee shop that just so happens to brew fantastic coffee. The espresso is incredible, which makes for an excellent cappuccino, and the food is pretty good, too. Croissants, muffins, and other baked goods top the breakfast list, while made-to-order paninis and delicious homemade soups round out the lunch menu. + +The crowd at Enrico's is varied, which I really enjoy. My 65-year-old neighbor and his crew of retired friends pull up a chair every day at 3:00 pm next to business folks, college students, techies, and other folks who are looking for a good brew. + +No frills, no extras; just nice people in a quaint coffee shop, brewing up warm goodness.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Hands down the best cappuccino you'll get in Pittsburgh. I have yet to be disappointed. Consistency in quality in a coffee joint is what I'm looking for! (Oh and alright those delectable treats they always have don't hurt either... Apple dumpling?!?!)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> What a cute little coffee shop in such an idealistic setting! I sat amongst the gathered hipsters, moms, friends, ladies who lunch, power business lunch people in a sunny little corner of the room sipping my delicious Indian Spice black tea. + +Service was very friendly and looking at the fresh pastries and lunch list of homemade soups and sandwiches made me want to come back and enjoy a leisurely afternoon or perhaps work day here taking in all they have to offer. + +I was surprised when I asked to see the tea list and the barista told me they didn't have much to offer. Still looked like a good amount to me and I was pleased to see a variety of different offerings some coffee shops don't offer (because, well, they're usually coffee focused!). I also enjoy that they use loose leaf tea, so you know it's not just coming straight outta a generic box of Twinings. + +FREE internet is always a big plus with lots of outlets. Now if someone could just find me an affordable house in Highland Park this could just be my next favorite neighborhood coffee shop![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Still one of the best places to get soy capps, but they no longer have an extensive tea list. What's left is not a bad selection, but there are dramatically less choices, so it's no longer where I would go to sample new varieties of tea. Sandwich menu is even more severely limited and it seems that pretty much all the food is provided by U.S. Foods, or the like; nothing is local. It'd be way cool if they would source their pastries and bread locally. Until then, it is simply a great place to get coffee and espresso, with nice vibes and pleasant service.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great atmosphere, often crowded, not too expensive, tasty beverages. + +Both my husband and I had mochas- delicious![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Wonderful! Lovely! Quaint! One of the most refreshing cafe's in pittsburgh! My visit was a 'surprise' from my boyfriend who knows how much I appreciate fine espresso. I was instantly enamored with the set-up inside and the pleasant nature of the individuals who greeted us behind the counter. The baked goods were absolutely fabulous and we literally would have bought one of everything if we hadn't come to our senses. I ordered a grande cafe mocha and it came with a wonderful rim of whipped cream (I believe the whipped cream was homemade as well.... simply to die for) and a subtle addition of foam art which just shows how considerate the baristas are of their craft. My boyfriend ordered the italian cappuccino and said it tasted just like the drinks he would get in Italy over his 2 week visit with family this past summer. Now if that isn't representative of a solid job in bringing a European Cafe to the States, then I don't know what is![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> their mochas are amazing[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It was a bit out of the way of where we were staying, but I was swayed by the Yelp reviews! You did not steer me wrong. + +A nice little coffee joint in a quiet neighborhood, Enrico's was the perfect spot to get my caffeine fix before starting the day at full speed. My wife and I both got lattes and pastries, and everything was good to go. + +It looked like we were the only patrons that didn't plan on spending the whole day there, rooted to a chair. We got the next to last free table. Almost every ""two-top"" had only one person sitting at it. I would imagine it's tough to find a seat sometimes. + +Recommend! + +P.s. I thought it was interesting that you can also purchase bike tire tubes here.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great variety of coffee and methods (press, Chemex, pour-over). I did not get a chance to try to the espresso, but it looked very good as well. Verve and Olympia are two very solid roasters and provide a wealth of choices. + +Staff was very helpful, location great. All around a good place in Pittsburgh.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Best coffee, ultimate staff, neighborhood gem[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great, authentic coffee at a reasonable price. The pastries are really tasty as well but pricier. It is a great atmosphere to catch up with a friend or just relax with a cup of coffee. The staff is also very friendly![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I really was missing Voluto before its new ownership / management took over, on Penn Ave. I Needed a new place to try with friends who live in Highland Park for an excellent cup of fancy Joe. I'm a steamed milk kind of gal. + +Starbucks bless them when I am in a rush but i have to order a tripple just to get a hint of my fix, but the coffee here is the right strength to cover my caffeine withdrawals. Lovely atmosphere small but not tiny, outdoor seating if you want it. Their espresso shots are not served in steamed cups. + +Take note if you're a hardcore ezzzspresso shooter and you like it piping hot. I am sure if you asked they could probably warm the cup. The baristas are so friendly and laid back and funny. Also the staff members let me use the bathroom after closing one time perfect gentlemen :) + +A decent selection of yummy pastries to compliment your coffee awaits from apple turnovers to decadent brownies. + +I also like the crowd that comes here, there are younger people, older peopler and everyone inbetween (the 30 somethings and 40 somethings) my age group. It has a neighborhood feel but I can tell people come from surrounding areas, Tazza is a great example of merging the old and new in Pittsburgh while maintaining the character of its home borough.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Cute little spot in a sweet neighborhood. Snag a table before ordering and you'll have a great experience. I stopped in for a cappuccino and sandwich. The cappuccino was hot and satisfying (good quality beans, strong). and the vegetable panini adequate (I'm not the biggest fan of artichoke leaves). + +Good spot for reading a book and eavesdropping on strangers' conversations.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I had always meant to visit Enrico's, and since my friend recently moved to the neighborhood, it was a perfect opportunity to cross it off my list. + +So here's what I liked: the cappuccino was perfect. It's an awesome cappuccino, topped with a cute foam art leaf. + +Here's what I didn't like: Sometimes I take my cappuccino plain, sometimes I take it with a shot of syrup. On this occassion I asked if I could get amaretto syrup, which they had. But the barista responded: ""No, you can't."" He said they only make their cappuccino plain, and if I liked sweet, he could make me something special, but I would have to trust his taste. Here's the thing...I don't like sweet! I don't have much of a sweet tooth. I just wanted a tiny bit of sweet, so I didn't think trusting his mystery concoction was a good idea. I just got it plain. + +I'm not a big fan of coffee shop snobbery nor the fact that this guy seemed to have sterotyped me as a Starbucks-guzzling yuppie who had to be shown what a ""REAL"" cappuccino tasted like. Please, I lived in Italy, I've had a ""REAL"" cappuccino...but right now, I want a flavor shot in it. I still tipped because I wasn't sure if it was the barista or just a general rule at this place, and he did offer to make me something different. I just don't get what the deal is here...why do they even bother having flavor syrups if you're not ""allowed"" to add them to your drink? + +It's a 5-star cappuccino for sure, but I had to subtract a star for the attitude.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> What a great find! I frequent the nearby Bryant street restaurants, but did not even know this place existed until a friend of mine brought took me here today for hot chocolate. I immediately fell in love it. The baristas were very friendly and my hot chocolate was great! There were also some incredibly delicious-looking pastries which I will need to go back soon to try. There was a nice ambience - it was quiet but not uncomfortable so. It would be a great place to study, read, or visit with friends. + +You should expect to wait a few minutes for your drink, but it is well worth it :-)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> BEST COFFEE IN PITTSBURGH! + +You might think there is better coffee elsewhere. You're wrong! + +I love this coffee shop, and there is a second location the Gates Building at CMU that I like to go to--their panini are to die for. + +I love this place, and you will too![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Best coffee it Pittsburgh? Maybe, but this place is certainly competitive. French Press, Drip, espresso, or pour over? You name it they've got it. Only downside of this place is a limited food and pastry selection. If it is just coffee you want you this is the place. It is it a bit snobbish sure, but not nearly as much as many of the other coffee shops in Pittsburgh.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is a quiet little nook in Highland Park that is perfect for tea, coffee, snacks and getting some work done or catching up with an old friend. I used to frequent this place much more when I lived in Pittsburgh, but I still make an effort to come back a few times a year for the ambience. It is great in the summer and fall because they have a few tables outside. The staff is great and the prices are reasonable, too. The only change I could think of would be to put on some soft easy listening music. It'd make the vibe a little more comfortable![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Everything I want in a bistro! The sandwiches are delicious, the service is wonderful. Love that pastry guy! Ambiance is great! The only thing is... it's a little crowded because everyone loves this place![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Really hard to find a good cup of coffee in the states... I'd say this is the best cappuccino I've had since Italy.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've heard a bunch of good things about this place, so I decided to make a trip over there on a Sunday to check it out. While I enjoyed the coffee and cookies I bought, I have to say that everything seems to be a bit overpriced and I did get a feeling of snobbery from some of the staff. However, the venue was actually nice with a nice neighborhood feel. Every time I have been there since it has been really crowded and I've had trouble finding a seat. I would love to go back in the summer and sit outside at one of the tables.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I just moved into a new place in highland park and realize this place was right next door. I'm a huge fan of coffee and have never been quite satisfied with the taste ever since my trip to Italy(where there coffee is to die for). This place makes me happy with coffee again. I've also had lunch here and bagels for breakfast both very delicious. This is my new place![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> So I went on a marathon 2 hour bike ride right before heading to Enrico's for the first time and on my last mile all I could think was ""iced caffe mocha, iced caffe mocha"" over and over again. Did I mention that I forgot my water bottle on my ride too? I was a desperate woman at the end of that one. + +So I got home aired myself out and drove myself to Enrico's since a previous yelper mentioned she had the best iced caffe mocha there. There was easy street parking right out front and I really liked that it was nestled in the middle of a neighborhood and not a loud crowded street. Tables are large enough for good work space and folks had their laptops out inside enjoying the free wifi while the tables outside were filled with friends. + +So why the 3 stars? Well the iced caffe mocha was a bit subpar. The syrup was all at the bottom leaving my first couple sips very watery. Could have been a better mix. Would I give this another try? Sure but I definitely will ask for a nice hard shake of my iced caffe mocha before taking a swig. + +The coffee place at the Walnut Mall in Shadyside is still my favorite for the iced coffee of the year award. Try the iced OR blended ghiradelli mocha when you are shopping Shady-style - AWESOME![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love Tazza D'oro! It is in such a great little area and is a nice place to spend some time with a delicious cup of coffee. + +It it sometimes busy and hard to find a table (which is not surprising since it's a great spot), but I like the neighborhood feel and the staff has always been very friendly. + +I usually get iced Americanos in the summer and regular coffee or lattes in the cooler weather. All of the drinks I have ever had here have been tasty. I have also had some of the pastries (and maybe a bagel at some point?) and everything has been fresh. + +I'm a big lover of coffee shops and this place fits all of my requirements. While I don't live in Highland Park, it's definitely worth an occasional trip.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Absolutely fantastic. One of my favorite places to hideaway and get some work done or just read a book.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The coffee was ok, but the service and ambiance left much to be desired. The place was dirty, with straw wrappers etc on the floor. The light fixtures were too modern to be considered cozy. There were four people on staff but it took at least 2 minutes for one of them to stop gossiping with the others and take our order. I got the feeling that this place has had a lot of success and the owners have let things slide. It was ok, but in looking for a coffee shop to make my regular hangout, I would not go back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We ordered a double espresso which looked more like a single shot. Cozy coffeeshop with an ample amount of seating. + +There were different types of coffee available for purchase to drink there and beans to take home. + +Cute neighborhood coffeeshop type feel.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> A nice place to sit and read, and drink amaaaaazing coffee. I like the atmosphere, and will definitely be a return regular customer.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I adore this place! The light green walls are serene, the chairs and tables are comfortable, and I love their little brownies with three kinds of chocolate chips in them! The coffee is perfectly smooth and rich, which is the most important thing to get right. (I'm not into masking the taste of burnt espresso with a mocha!) If a place can provide me with a cup of coffee that doesn't taste like it will give me an ulcer, I'll be a fan for life. The only other Pittsburgh place where I've found coffee this delicious was at Commonplace Coffee in Squirrel Hill. I went to college near Chicago and come from California. I count Intelligentsia and Blue Bottle Coffee as some of my favorite places, so I mean it when I say the coffee here is wonderful. Try it out, you won't be let down.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> On three separate visits, I've enjoyed three great cups of coffee. No complaints there. Unfortunately, that consistency hasn't been there for everyone. On a visit with my wife, her latte came out far too milky. Probably just a mistake, so we reasoned that this place deserved a second chance. The next time around, we order a pair of cappuccinos, one with vanilla -- + +Now, before I go any further, I recognize that cappuccinos are typically made without sugar or added flavoring. I have also been to a ton of neighborhood coffee shops, have heard the question ""wet or dry"" a thousand times. Sometimes a ""wet cap"" is really what you're hoping for in a latte. And even when it's not, like most people, I don't snark or complain when someone gives me a cup that isn't quite what I was hoping for. I usually end up liking it anyways. My taste buds aren't that delicate. + +Perhaps you can see where I'm going with this story. Vanilla cappuccino. I get it, it's not something that's done. But when someone asks you for something you don't sell, just explain the situation politely. If you feel the need to snark, share knowing glances, or anything along those lines, just stifle it. Trust me, I've seen many professionals perform better with requests far more ridiculous. There's really never any need for snobbery. So I've got to dock Tazza d'Oro a bit. Too bad, because the coffee is pretty good.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The people who work here are very rude. I have gone back a few times thinking it may have just been the person working that day was just a rude person, but no it happen every time. I am not a young hip person and felt very out of place there. It is like you are walking into someone's house and bothering them. The people working behind the counter act like you are interfering with there conversation. Plus it is very dirty. Perhaps the people working there should try cleaning the place instead of talking to each other. I will not go back again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I walked in to this business and immediately knew I could risk a latte without flavoring to cover up poor quality or technique, and I was absolutely correct. The espresso was a perfect balance of flavor with a smooth finish, the foam was stretched perfectly and expertly poured to form a heart in my mug. My accomplice's Americano was equally well made, not a note of sourness but plenty of body and flavor. I regret that I didn't notice the ""Manual"" bar menu before I ordered, I've been dying to try a pour-over coffee, and I know it would have been delicious. + +Pro-Tip: There is no sign for the unisex restroom, which is to the left of the service area, past the bulletin corkboard.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The coffee isn't good and they don't seem to care. If you're a local, I get that it's the only game in town but this place isn't worth traveling for. + +I really wanted to like tazza d'oro. I've been several times, hoping that my bad experiences were isolated incidences. I drink espresso. I know what it should taste like and what it looks like when the person making it gives a damn. I have no complaints about paying $3.00 for an espresso but if it isn't right and I let you know you should probably try again. + +The last time I went in, both baristas admitted they hadn't tried/pulled the espresso I ordered. The gentlemen working there, who was very nice, pulled my shot. I tried it and it was very sour. I let the girl standing directly in front of me know that I didn't think it was pulling correctly and her response was an unenthused look and the comment ""ya well we just got it"". Silly me to have expected that you also want the espresso you ""just got"" to taste good... + +This place clearly isn't going anywhere in the near future. It's a favorite with locals who like to hangout there. It's just a shame that they seem to have all of the equipment and even the beans to make at least a decent shot and they don't seem to care about actually pulling it off.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Had a cup of Cappuccino. Tasted good, but not that impressive. Well, it's just a regular cappuccino. Five stars to the street view at a sunny winter afternoon.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Best Cafe in Pittsburgh - like a hidden gem. The sandwiches are delicious, you must try the chocolate chip brownie, and the coffee is great and made exactly the way you like it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My favorite gym! The atmosphere is spa like, which is a nice place to be after work. I just love all their classes... they have so many and at convenient times. My favorites are the Body Pump classes. The staff is very friendly and helpful.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> went in as a guest of a friend of mine who is a member there... nice atmosphere. LOT of oldddd folks and they seem to market themselves as ""Silver Fitness"" sort of fitness center... (this may be a turn-off for some younger people.) +they had a lot of machines and exercise gear ... 2 pools and tan beds/etc /etc. +i'd probably prefer personally to work out somewhere with a younger crowd.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is not a review on this gym. It is a review on their customer/membership service. I just called there. All I wanted to know is what their monthly fees were. Simple right? Wrong. They want your name and phone number and the rights to your first born child and then they won't even tell you anything without you physically coming to them to ""talk"" about what's best for you. I took psychology classes, I know what they are trying to do by talking to you face to face. I am sorry, but I want a gym, not a drug dealer. I don't need you to try to shove your products down my throat, I want to go somewhere to work out and be left alone. (That's why I wear headphones and don't make eye contact). + +I just wish places like this would give you a straight answer about their membership fees without hassling you. I won't go here now, period, because I don't believe in these kind of tactics. Just be straight with people, is that so hard?[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm a gym guy. I go 3 or 4 times a week among other workouts and activities. + +Pros +Always towels +Very clean +Always cardio equipment open +Pools/hot tub +Lots of lockers +Friendly staff +Lots of classes +Lots of free wights +Next to target and trader joes +Even during peek hours it's never over crowded + +Cons +When the old lady's come in they take up all the parking spots some how. But that's not the gyms fault +Only one flat bench press +Since they have pools and a kids activities some times kids wonder into the wight areas + +So in the end more pros then cons. +This is more just nit picking but as all gyms have them. There are a few weirdos who are members and just take up space more then workout but oh well what can ya do about it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great club. Extremely clean. Never really crowded. Machines are modern and up to date and well Maintained. Staff is on it. Young energetic trainers and staff.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Delicious wings - sometimes a bit too deep fried for my taste, but really tasty flavors and spices. We went for all-you-can-eat wings night but sadly I could barely finish my first dozen. Beer selection is much improved since Turadg A.'s post; they have about 30 or so available to choose from.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The food here is okay. Wings, BBQ, Bar foods. The floor here is always super slippery. It doesn't matter if I am wearing heels or sneakers. I just don't get why the floor is like and ice skating rink.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The main reasons to go to Buffalo Blues would be for their All You Can Eat Ribs night every Tuesday for $21 and their All You Can Eat Wings night every Wednesday for $9. Make sure you go with a bunch of guys, because it isn't all you care to eat, it is a challenge. You have to eat all you can eat and your ego is on the line if you don't. I once went to Ribs night and one buddy of mine ordered a Buffalo Chicken salad when everyone else ordered ribs. Yea, he regretted his terrible decision. + +Anyways. The food itself. The ribs are basic baby back ribs that come in a choice of mild, medium, and hot bbq sauce. I tend to just go medium, b/c I find a hot bbq sauce covers up the taste of the meat itself, and when I eat ribs I care more about the taste and texture of the actual meat with the sauce being a supporting player. The ribs are ok for mass produced ribs, nothing spectacular. The most I've done is only two racks of ribs, but that was only because I didn't want to keep everyone else waiting up for me. Ribs come in a rack in first round, and then re-orders come by the half rack. + +Personally I prefer wing night, as they have fantastic wings. Wings come in a dozen in the first round, followed by half dozen reorders until you're done. They have 12 different flavors, but my favorite ones are Buffalo Blue, Old Yeller, and Red Hot Parm. Buffalo Blue is a tasty bbq sauce that isn't overly sweet like some of their other bbq sauces, Old Yeller is a Carolina Mustard based sauce, and Red Hot Parm is a traditional Buffalo sauce (Frank's Red Hot + Butter) then topped with Parmesan Cheese. Their Cool Ranch, Garlic Parm, and Spicy Garlic can be a bit greasy, so if you do order one of those make sure its in a batch of 6 and you share with your friends, I kind of like their Spicy Garlic, but no one else ever wants to split an order with me, oh well. Their Gold Rush and Death Row are their two other non-spicy bbq sauces, but I prefer Buffalo Blue to both of them. + +For their spicy flavors, there's Red Hot, which is just a traditional Buffalo, there's Howlin' Wolf, which is a spicy sour sauce with pepper seeds on it, and there's Hotter than Hell, which is a spicy bbq sauce. Personally I find Howlin' Wolf tasty in small quantities, but sometimes the sourness gets to me. I tend to find spicy bbq sauces a bit funky, so I'm not big on Hotter than Hell. + +If I have a big appetite I eat from 24-30 wings. If its just a regular day I'll eat around 18-22ish wings. + +Note: These wings are huge. They aren't your typical Wingzone or Quaker Steak and Lube sized wings. These are real wings from real chickens, not some little baby chicks just hatched from their eggs. + +The rest of the menu is just typical American restaurant food with various sandwiches, a burger option, salad options, etc. + +Highly highly recommended.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Living down the street of Buffalo Blues has it's advantages and disadvantages. The huge beer selection means there is something for everyone. For any game there is always a crowd and you can have a good time eating the wings, which are decently priced and good. + +The bar is nice in the summer when they open the garage doors. It's a nice bar to get a beer with friends where you can grab a table to eat then hang out at the bar to watch the game. But, while they have a good number of HD TVs, only two are broadcast in HD so don't think you'll be getting a great picture.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> In the last week I've been here twice, partially because I don't know any better and partially because it's actually pretty good! It's one of the few places that doesn't reek of cigarettes, it's never crowded and the open garage doors are great for fresh air. + +I tried their buffalo (boneless) wings last night in the jack daniel's sauce - way better than Sharp Edge's. The sauce was pretty mild but still quite tasty and if you're not a super wings eater, you can get a fries/wings combo for super cheap. To wash it down I had Loose Cannon beer, how can you pass up a beer with a pirate tap handle! + +Our waitress was a little slow, she said it was her first night. Who makes a new girl work on a Friday night! She seemed to have gotten more attentive and fast towards the end, or maybe it's because I wasn't hungry anymore so I didn't care. + +The beer was pricy - Tuesday night I had a maker's sour for the same price as a pint of beer...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The front serves as a good Pittsburgh sports bar. It's a particularly great place to watch the Penguins in the spring when they open up the front wall. There are lots of HDTV's and there is a good selection of beer. + +The food, however, is bland and is terrible bbq, even for the northeast. I would not come here unless you want to watch a game that you cannot see at home.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've been here quite a few times, and I always try to like it cause theres a lack of good sports bars near Pitt. They have a ton of nice HDTVs. + +Everytime I go, there is always a weird taste to one (or more) of the beers that I get. I was just there for the Pitt/Oakland game and got a Redhook. I drink this beer regularly, and something was wrong with the beer. Its definitely hard to describe, but something is always off (others in my party notice it too). + +The food is hit or miss. I got the French onion soup last time. It was good. Nothing ground breaking, but solid soup. I've had the pork nachos and they were blah.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Pretty good bar food. It's conveniently located and a fun atmosphere.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I found Buffalo Blues to be merely OK. I thought that their prices were a bit high for the size of the portions, and their wings were rather small. I actually liked the wing sauces I tried, though (red hot and spicy garlic). Our server was friendly, but not terribly attentive. + +I would probably only go again on an all-you-can-eat wings night. For $10 I would certainly get my money's worth, and the quality of the food was OK. + +Surprisingly, lots of vegetarian options. A vegetarian in our party was floored by the possibility of having every burger or chicken sandwich made without meat or meat products.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Tried this place to get my charred meat on before a steelers game, and was not disappointed. Boneless Buffalo Wings are my loovveeeeeeeee so I'm pretty easy to please there, and I was super happy that they allow you to order them in a small portion (5 wings). I tried a medium spicy sauce (instead of jumping right to hotter 'n hell) because I was sick with anticipation for the steelers game, and it was nice and sweet and not bland. + +Predicting a healthy selection of nachos and other cheese drenched options at the steeler game, I had a salad. I expected it to be sad and pathetic, as salads at wing joints often are, but it was really good! The lettuce was not all nearly white grossness, the other veggies were nice and crisp, and the toppings were great! I loovveeed the shredded chicken that didn't have a bunch of gross grease all over it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Wednesday is Wing night, i.e., eat your face off night. For ~ $9 you can eat unlimited wings (with your choice of various sauces) for several hours. If you can, top it off with a brownie - they're quite good. + +I've mostly had the wings at Blues & I like all of the sauces, but the burgers are good, as well. Whatever you do, make sure to get the sweet potato fries & tip your waitress! (Especially if her name is Meg).[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Wing night wednesdays! 50 cent price wings and $1 beer at William Penn on Tuesdays and my body is not hurting too badly the next day, Buffalo Blues for all you can eat wings. There are a ton of sauces to pair with these wings. They bring them out 5 at a time so plan on ordering your next selection when your wings come out because they take quite a bit of time to come. I don't think I have ever eaten the other food here except for the wings because they are pretty good. The only downside to this place is that service is really really slow.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My local sports bar. It has the prefered sound and enough televisions so no matter how busy it is, my neck isn't cramped and I don't have to strategically place myself to listen to a game. +It is a bar. It has bar food. Nothing really stands out for me in the realm of fries, sandwhiches and wings. On the other hand, I've never had a bad experience either. So when I eat there, I'm not anticipating dissapointment or spectacular, but I am expecting constantcy. Consistancy is what is delivered. +Buffalo Blues does have a wide array of enticing imports and domestics. +Service is spotty, I do find myself hoping to find the more personable staff working when I go there. The plus is, when specific staff is working, the place is that much of a better establishment. Consistantly just above average in my opinion. +I chose 4 stars because it is constantly an above par establishment. 5 stars would require something really enticing to set it aside in character from a slew of other sport bar venues. I would like to observe the spring/summer atmosphere inwhich I'm anticipating another review to be 4 stars.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great Pittsburgh Happy Hour! $5 dollar apps and dollar off tap beers. + +They have a wide selection of draft beers, so if you like to enjoy flavors other than Miller Light this is a great place to go and enjoy some IPAs at a good price. + +Wide selection of $5 apps too. We ordered the BBQ Nachos, and they were amazzzing with multiple z's! I crave them all the time now. + +Great service too. Our server was happy and excited to be there. She made the atmosphere more fun. + +Get there :)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Looks can be deceiving. I thought this place was going to suck, but my meal was delicious. Probably the tastiest Garlic Parm Wings I've ever had. :)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is a great place for happy hour, to catch the game, or to have a small-ish private party. Definitely check out their website for the daily happy hour specials, but Mon-Fri from 5-7pm they have +$1 off all drafts +1/2 Priced Blues Booze +$5 Nachos and Quesadillas +$5 basket of wings (10 pieces) + +East End beers are $3 all day, every day. + +The food here is not spectacular, but I've always enjoyed what I've gotten. Being from the South, I wouldn't think to order the BBQ or catfish here, so I can't vouch for those. The spicy wings, cheese sticks, salads, and grilled cheese are all good. The regulars and servers are pretty nice people. We watched the Saint/Steelers game here (with our Saints attire on!), and easily made friends the whole night. They also have a small ""loft"" area that you can reserve for free for a private party, and you're supplied a waitress for the evening. Finally, they deliver! I love having another delivery option besides Chinese and Pizza. Now I can be lazy and eat a big salad![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I ate at this restaurant last night with three dining companions. We decided to sit in the bar area at a high table which had views of the ample number of TV's. The beer list that they had was nice with about 20 different beers on tap and a nice selection of bottles. I ended up having the Philly Shackamaximum with my waitress telling me that she preferred the Long Trails Porter. It was served in a chilled glass and tasted pretty good to me. + +For dinner we attempted to start off by ordering the Blues BBQ Pork Nachos. We were told that they did not have any pork and so we were not able to order it. At this point we were also told that they did not have any veggie burgers as well. So we started out with the Chicken Chili Nachos. They were pretty good and were covered with real cheese as opposed to nacho cheese which was to my liking. For dinner I decided on having the Lovely Lisa's Salad since I love both blue cheese and granny smith apples. Upon receiving the salad I dug in. The chicken was cooked nicely, moist and tender, and there was a nice coating of blue cheese on the salad. However there was a problem since there were no granny smith apples on the salad. Whenever the waitress came back to check on us I asked about the missing apples. She went to the kitchen and came back and told us that they were out of them and promptly left. I am not normally one to complain but I feel like something could have been substituted in for the apples, or that I should have been told before ordering or they could have discounted the salad but none of that occurred. It is sad that it happened too because the rest of my salad was pretty good but that left the proverbial bitter taste in my mouth. + +The bottom line is that I have been here before and the food is generally good. However, leaving a major part off an item and being told that the kitchen is out without any rectification will make me think twice before returning here again. It is a shame because Buffalo Blues does have potential.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My coworkers and I had lunch here on a Friday afternoon, and it was a pretty ""meh"" experience for me. We were seated all the way in the back of the restaurant/bar, in a room that I didn't even know existed, so apparently Buffalo Blues is bigger than I thought. It's nice that they have some tables away from the main bar area. + +I went for the Hot Veggie Sandwich with sweet potato fries, in some kind of attempt to be healthy. The sweet potato fries weren't too bad, with a good flaky crisp. The sandwich left something to be desired. It wasn't hot, first of all - I'd say the (slightly crumbly) bread had been toasted with the cheese, but all the veggie ingredients were cold, leaving an overall lukewarm effect on the sandwich. The hummus spread didn't taste much like hummus, and was thick and pastey instead of smooth and creamy. There wasn't a lot of exciting flavor, It was just belly-filler, really. I guess that's what I get for trying to order healthy here. + +I just wasn't much interested in it, and I don't think it was worth anywhere near $8. I better have a darn good sandwich if I'm paying $8. Also, it was relatively small in size - I don't have a huge appetite, so that wasn't a problem. But I guess I think an $8 sandwich should either be awesomely delicious, or big enough that I can take half home. Buffalo Blues was neither. + +Not particularly interested in returning for any reason.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The best thing about Buffalo Blues revolves around Sundays during football season. For me, personally, it's one of the best places to catch an NFL game...especially if you're not a Steelers fan. On any given Sunday, you'll find fans of just about every team in the NFL taking in a game, so the atmosphere is a positive one. Seating is the only issue. Get there early or you might end up standing to see your particular game, as seating can be a premium by the time the games begin. Luckily, the TV's (there are lots of them) are all labeled with the day's matchups, so finding the game you're looking for isn't a problem. + +The draft beer selection usually has something for everyone, from local craft brews by East End Brewing, to seasonals and your simpler standards (hello, PBR), so if you're a beer person, you won't be disappointed. + +As far as service goes, it's hit-or-miss. I've had mostly great service at the bar, but I've also had average to below average service at tables. During bigger sporting events - primarily Steelers games - the service can be even more iffy due to the sheer volume of people in the bar area. + +Overall, I have to rate the food as average. I LOVE their boneless wings, and their wing sauces are all very excellent. Their pulled pork is really tender and delicious, as well, but most of their sandwiches and burgers are simply average. The fries can be either really good, or too soggy and greasy. I think the inconsistency in the quality of the cooking is the main issue. The menu reads really well, which raises your expectations, but sometimes the execution will leave you a little disappointed. It's never horrible, but you'll rarely be blown away by your meal. + +In the end, I'm giving Buffalo Blues a higher rating based on the experience during sporting events, which, let's face it, is the real draw of a ""sports bar."" As far as sports bars go, it's my favorite place to catch a game. They always get a good crowd for games (whether Sundays during the NFL season, Saturdays during big college games, or for Pens games), and if you stick to the wings and beer, odds are your experience will be great. There's a good chance that you can go in and find fans of your team if you're an out-of-towner looking for a game, and the crowd is much more accepting, friendly, and relaxed than the crowds I've experience in other sports bars in town. Most of my average experiences revolved around non-game times when you try to get a more traditional meal and realize that there are just better options in Shadyside for lunch and dinner.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Superbowl Sunday at the Blues. i came to meet a group of friends to watch the "" who really cares about this game"" show. I was mainly interested in seeing Madonna. I do have to say that we had a server who gave us the utmost attention. We had been seated at some tables near the bar mid restaurant that were wobbling and driving me crazy. At the request of the party she moved us up front and center to a much better and stable seat. Much better view to see the Material girl! So our server gets 5 STARS! Not only for that reason, she kept the glasses full and kept checking in with us, and took it all in stride as we ordered at different times and all had separate checks. Very classy, wish I could remember her name. Young girl with dirty blond hair. + +The food was pretty blah in my opinion. Bar food none too exceptional. We had nachos that were on slightly stale chips. Good size. Everyone had a burger or sandwich. As I glanced over to my friends Pulled pork it looked dry and sad left sitting on the plate. She said it was ""EH"". I ordered a Gobbler Club sandwich. It was humongous but not that tasty, pretty dry. How can you go wrong with a club but the thick cuts of turkey did not sit well with me and I didn't like it at all. Bad texture. The commercials and time with fun friends saved the experience but I wouldn't go back to eat. Just drinks and sports. I like the location. Easy to park. Close to shadyside. Madonna really was the show stopper this night and unless she performs here I most likely won't be back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've heard about this place, I've seen this place, and I've wanted to try this place. Finally, yesterday my company took us their for lunch and I did not leave disappointed. Don't get me wrong, this is not a restaurant that is redefining the culinary scene in the city, but it is a tasty place to enjoy your traditional burger, fries, and drink. + +The atmosphere is total sports bar, but it is not overwhelmingly so. The staff was nice and for being in a party of 14, the server handled us well. + +The food was great! I got the Salsa Burger subbed with a turkey burger and it was delicious. The burger was plump and large, full of flavor and cooked perfectly. I recommend this burger! It also had salsa and guac on top with some cheddar cheese and my mouth is still watering for it. Tip? Get the sweet potato fries![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> So, I went to Buffalo Blues tonight for the second time (not the second time tonight, the second time in my life) for dinner and some drinks, and to sum up my experience in a few words, both times it was about what I expected. Just a fine sports bar - no more, no less. + +I'll start with the drinks. They have a good draft selection, and supposedly they've got a nice bottle list too, though I didn't have a look at it, so I can't judge; and the Happy Hour special compliments it well ($1 off all drinks 5PM-7PM). Plus they have East End drafts at $3/glass all the time, though they were out of Big Hop (the only East End choice they have) when I was there (I don't know if this is a regular occurrence, but if it is, they better do something about it). The bartenders were friendly and quick to serve, qualities that carried over to the food service as well. + +The menu has a pretty good selection of pub-y and Southwestern-themed foods from which I picked the black bean and corn quesadilla. Although at the end I was running low on guacamole (which is $1 extra for a small cup) and sour cream, this is a small quibble. The meal overall was good, and since I got it with the happy hour special, I can't complain. One thing I will mention is that there aren't too many vegetarian choices on the menu (I'm not vegetarian, but I try not to eat too much meat, so I notice these things), so if you're a vegetarian, I would try to look up the menu beforehand just to be sure there's something for you. + +I know I haven't said much negative about Buffalo Blues in this review, yet I'm still giving it only three stars. This is the kind of place that makes me appreciate the ""word versions"" of the ratings that Yelp gives us. ""A-OK,"" which, if you didn't know, is how Yelp describes three-star reviews, is exactly how I would describe Buffalo Blues. The comparison I keep going to in my head is Die Hard 2. It's not nearly as good as its predecessor, but it's still something I'm fine with popping in every once in a while when there's nothing better to watch. + +To sum it up - I'm not a big sports guy. Buffalo Blues, though it is a sports bar, is not the place that would sway me to go to watch a game there with my friends (I'll still say that some kind of playoff game of the Steelers-Ravens I watched at Big Jim's was one of the best sports-watching experiences of my life). And, judging it as a sports bar, it didn't do anything to justify my giving it anything but ""just fine."" But I'm sure I'll go back there for happy hour again sometime.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> When Hotlick's died, Buffalo blues was born. It really is a Pittsburgh staple but come on.... + +Food is really, really average. I love the ribs and wings, but it's about the same as any other rib place in the city, only they charge an arm and a leg for it. This place is for the people that feel that they are at a real rib place, but don't want to cross Centre or Penn Ave. to get real ribs. It, technically is in Shadyside so your Mercedes will be safe! + +The ambiance: The restaurant is always crowded. Not just crowded, but packed with teens underage drinking, families with too many kids that overflow to your ""space"" and collage kids who also spill over from the bar. IT'S LOUD AS HELL!!! Forget about a nice quiet dinner. There seems to be no consideration for customers at all. Last time I was there, there was a St. Patrick's Day party (it was NOT St. Patrick's Day) that took over the whole place. Though the staff tried (nah, they didn't really try) to keep them in the so called ""party room"" I was bumped into several times, spilled my beer, and couldn't hear my wife speak. But as long as they got their money; they could give a crap. Oh and there are like 100 TVs to interrupt any conversation at your table. + +Want to sit in the bar area? Good luck. You will see a mix of drunk people, women who look like high-end prostitutes and college kids who are only missing a beer bong. Also IT'S LOUD AS HELL!!!!!!!! + +The ""wonderful"" Staff: It seems like it's everyone's first day. To put it lightly; the staff suck! To be sure, you will be waiting for your your drinks, food and bill for a very, very long time. Expect to be there for about 2-3 hours. The wait staff are forgetful, inattentive and very sloppy at their job. It pains me to leave any tip for them. Most of the staff are hot, stacked, absolutely stupid and should be working at Hooters not a place where your bill will be upwards of $50 for two people. Be prepared to be met with this saying, ""Oh, like ohmygod, I am so sorry i forgot that, he he!"" (oh she's twisting her finger in her hair while she's talking). You will get bad service...period (in fact, I can't remember the last time a wait person actually wrote down my order, and they're idiots so no worries). + +The food: Kinda good. Menu is huge, you'll find something you like. But I go there about 2-3 times a year for the food. It is way too expensive. Do not take a date there. Your average bill for a meal with actual proteins will run you in the high 40s without booze. There are so many bar-food places that don't claim to be high class that are just as good as this place. I grew up with the rib sauce and love it, but for your average consumer, skip it! + +This place is a wannabe sports bar that tries too hard to be high end. Just watch out for the vomiting college kids with trust funds...they're everywhere!!!!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This review is on lunch at Buffalo Blues. I have been here a number of times for dinner and for late-night drinks, and have always thought it was a great place to grab a drink and watch a game, but haven't been overly impressed with the food. That is, until yesterday. I came in for a quick bite to eat and ordered the Hot Veggie sandwich. It was FANTASTIC - the best veggie sandwich I have had here in Pittsburgh. Other than that, service was good and fairly quick. I made have found my new go-to lunch spot![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Food: 2 stars. It's really not very good. Especially the entirety of the combination platter they make with chicken fingers and wings. Blue cheese wasn't bad though. My wedge salad was enormous- more like a half head of lettuce than a wedge. Nice and fresh though. + +Drinks: 3 stars, for the decent variety (better than expected from a place like this) and the game time specials. + +Service: 3 stars. Could have been better, could have been worse. Friendly but unattentive and not good at realizing when to come to the table. (Hint: if one person calls you over for a drink, make sure the rest of us are set before running away.) + +Atmosphere: 4 stars - really good job of having enough televisions for everyone to see the game/s and marking each so you know what's on. + +1 Bonus star for accommodating the Pittsburgh area Buffalo Bills fans! GO BILLS!!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Oh how the mighty have fallen. This place used to be good. Something happened and the wings are small dry and just generally bad. Since wings are supposed to be their thing this is pretty unacceptable. + +Writing this review makes me sad because it is a great place to drink beer and watch the game. The beer is reasonably priced but the food is just expensive for what it is. I essentially live across the street so I know I'll go back, but I hope some of these poor reviews will help them turn things around in the kitchen.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The buffalo chicken dip is very good. Their wing nights are decent (gold rush/death row are probably the two best flavors in my opinion). Wednesday night trivia is also fun (thought it took much longer than expected). + +A good sports bar to say the least, usually went there for world cup and euro cup soccer games as well.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Good fun place to watch games while drinking and eating chicken wings or sandwiches.They have a good selection of wings and decent beer. I try different kinds of wings every time I go in but so far spicy garlic has been my favorite. This is a typical sports bar.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Good place to watch a sports game. Beer specials were good. Food is very overpriced though. The wings are about the worst I've ever had... and I've had alot of wings growing up in Buffalo, NY.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Pass on this place, there are better restaurants mere feet away. + +The menu here is too large, which is a sure sign none of the food is going to be good. And, its not good. Some of the salads are alright, but its just not good food. + +The service is friendly and prompt, but the beer is over priced. They do have a good selection though. + +This place is open late if you need a bite to eat, but there are so much better options out there.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is the worst service (or worst non-service) I have ever experienced. Since I can't give zero stars, I'm giving the service one. We didn't eat anything so I can't comment on the food. + +My husband and I went to Buffalo Blues last night. We stood at the empty hostess stand for a while. When no one came to seat us, and we couldn't find anyone to seat us, we seated ourselves figuring that's what we were supposed to do. + +The bar was full, but not packed. There were only two other tables with guests, one of which had empty plates on the table during this entire experience. After what seemed like forever, my husband got up to find a server. He literally walked around the restaurant to find someone, but couldn't. He then tried to ask the bartender, but she was just as elusive. When he finally found a server, she acted totally shocked that we were there. Maybe if someone had been doing their job, they wouldn't be surprised to find hungry people in a restaurant. + +She came to our table, got our drinks (a soda and a water) and asked us if we were ready to order. When we said no she said she would be back. We could see her chit chatting with another server, but again, couldn't get her attention to come back to take our order. After another ten minutes of waiting for her to return, we put a few dollars on the table for my soda and we left. We ordered a pizza at a local shop and picked it up on our way home. + +Twenty-five minutes passed and we only get drinks? Such a waste of time. It took us 20 minutes just to make the drive there, 25 of waiting, and another 20 to get home. That's over an hour of our evening completely wasted which left us starving after a hard days work. I used to work as a server so I could understand if the place was busy and the staff was short handed, but it was basically a dead night table top wise. I will NEVER go back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Their food is okay and beer selection is diverse and good. + +The problem i have with the place is that Buffalo Bills fans congregate here and cheer on every mediocre play their football team makes, (or almost makes) so it's like watching the Superbowl except it's a losing record team stopping a team on third down.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I hate this place. I have been here many times and I am just finally getting around to writing a review. Let me state that my wife made me go here tonight because my friends wanted to and she said I need to indulge their interests. Even if they suck. + +Buffalo Blues is like a Hooters, except the girls where more clothes and are not as good looking. The service is horrendous and the food may be better at Hooters. The beer selection is decent at Buffalo Blues but it is expensive and they often run out of things that are still on the board. + +My friends like going for all you can eat wing night but frankly I don't get it. You get 10 wings up front they will give more wings 5 at a time. The problem is that you get those wings in 30 minute intervals. So the max you could eat is 55 wings. Did I mention that the wings are really tiny and the sauce is tossed on like a Jackson Pollack painting. They also charge extra for blue cheese or ranch. The wings do not come with celery. This is a crime against humanity and the city of Buffalo. + +I chose to detour from wings tonight and ordered a chicken sandwich. Apparently this was a bad choice. It took a full hour to get my food. It was so long that the rest of the table ate their wings and ordered more and the waitress didn't think this was a problem. When my meal did arrive everything was cold. The sandwich was ok, but the fries were just tiny pieces that were limp and flavorless. + +I paid $16 for a beer and a sandwich that my friends had to wait for me to eat to leave. I would say I won't go back, but apparently I like my friends more than I like good food and service.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Went here this past Saturday afternoon, 11/2. My friends and I sat at the pretty much empty bar for over 5 minutes with no service. The bartender walked by us a few times and didn't even acknowledge we were there. As we walked out, we saw the bartender on the phone and other staff members standing in the back chatting. We went next door to Mad Mex and got much better service![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Loved the hot vegetarian sandwich. Not easy to find veggie dishes which don't feel like a compromise. This was great. Excellent service from waitress Ariella with the long black pony tail (don't know her last name). Nice casual atmosphere. Resonable prices.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great beer selection and nice happy hour deals. I recommend the garlic parm wings. Good service too[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have a love-hate relationship with this place... + +I love it because it's extremely close to me (so, it's convenient when I'm craving a beer) and the atmosphere on Sundays is outstanding. I'm a giant Steeler fan, but you'll probably find fans from all 32 teams in Buffalo blues, which gives it a fun and exciting feel during NFL Sundays. + +However, I hate it because I believe the alcohol and food is overpriced. The food wouldn't rub me the wrong way so much if I thought it was worth the price, but I don't. Not even a little bit. The only thing I have found to be delicious there were the wings; however, you can go to almost any other bar to get delicious and cheaper wings. So, it's not really much of a win at all. Also, I want to have a handful of beers during the games, but I don't want to empty my pockets doing it. So, all in all, I recommend going once and awhile (mainly on Sundays) for a beer or two, but other than that it's not worth much of a visit.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have mixed feelings about this place. I'll say up front: I only ever go there on Sundays for football, and I would never go there for any other reason. It is the only bar I know of in the city where you can reliably find every NFL game televised and enjoy your Sunday if you're not a Steelers fan. Pretty much every team is represented by the crowd on Sundays, with a disproportional number of Bills and Redskins fans. The crowd is generally friendly, with many of the same faces from week to week. + +They tend to have a wide selection of beers that rotates pretty regularly, but wide selection doesn't always mean good selection. That said, sometimes they get some really great beers that you wouldn't expect to find at a sports bar. Whatever you do, don't order a bloody Mary, they're atrociously bad. The staff is almost universally friendly, with the exception of one barback who seems to always be in a bad mood and rude to customers (he often takes over as bartender later in the day on Sundays). That said, the wait staff don't seem to know much about the food or beers that are offered, often mis-characterizing new beers that are on tap or giving wrong information about things on the menu. + +The food is mediocre and over-priced. When two of us go for one game on a Sunday, drink 3-4 beers each and each order an entrée, we generally end up with a tab in the $80-90 range, depending on what we're drinking that day. In a city that is almost universally accommodating to vegetarians, this place is most decidedly not. They have a veggie burger which is actually pretty good, but it's the only decent thing on the menu for a vegetarian to eat (there is also a grilled cheese sandwich and a veggie sandwich, both of which are bland to the point of tasteless. It's like eating plain bread). They have 4 entrée salads, and every one of them has meat as a defining ingredient. They don't even have beans so you could have decent veggie nachos. I know, it's a sports bar, but I don't want to eat the same veggie burger every Sunday for 17 weeks. It gets old. Fast. + +Upshot? In the absence of a new sports bar opening up, we'll be back next season, but not before then.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> To be honest, I think this is one of the worst bars in the entire city. The food was sub-par, even for bar food, the service was awful, especially during a game. I do enjoy a good sports bar, but I think the thing I hated most about this place was the other people that frequent there. It's the quintessential Shadyside bar, equipped with doughebag bros that went to the same fraternity in college and the Jersey Shore bimbos who pine for them. The last time that I went there were two guys throwing up outside of the bar on the sidewalk. I fully admit this is a subjective review, because this bar was obviously not my scene- but I still do not like this place at all.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Unfortunately, the service we were given ruined our overall experience at Buffalo Blues. We sat down and put in our drink order. My husband was excited about the amount of beers they had on tap. Fifteen minutes later and still without drinks, we saw our server trying to hunt the bartender down. Once the bartender finally started working on our drinks, she realized the keg for the beer my husband ordered was tapped. We were sitting at the booths right next to the bar but instead of the bartender just telling us so we could make another decision and get our drinks as soon as possible, she waited for the waitress to come back to tell her. Then, the waitress came back and did not apologize at all but simply said that he had to pick a different beer because they were out of that one. Anyway, long story short, it took way too long to get drinks and there was never any recognition from the staff of the issue. The restaurant seemed poorly managed and subpar. We will not be back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I would take advantage of All you can eat wings on Wednesday. + +We went on a regular oll Sunday night and even though the wings were tasty, my frugal self would've rather had AYCE. We tried a variety of sauces (we ordered 20 wings and every 5 can be a different flavor) The Buffalo Blues sauce was ok. It was just their signature bbq sauce. WE also tried garlic parm, honey teriyaki & gold rush. All were ok. + + The boozy buffalo is a good drink. It consist of smirnoff orange, tanquery, jose cuervo, captain, triple sec, OJ, fresh squeezed lemon and a splash of Coke. I seriously felt fabulous after one. It's served in a mason jar. ($12) + +Lauren was a nice server even though the table in front of us put her through some bs-- they ate all of their food then complained to the server and asked for the manager complaining that what they got it wasn't what they ordered... no idea why they waited until every scrap of food was gone to complain but you know, you'll have that. kudos to Lauren for keeping a smile on her face.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Watched a bartender serve a guy a beer when he was visibly intoxicated. He was swaying in circles on the chair next to me. I told the manager about it and he told me ""that guy is just crazy, I've seen him much worse"" so I guess that makes it ok. Made this paying customer leave after one beer.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Had a wonderful beef and pulled pork burger at Buffalo Blues yesterday. The food and drinks were great;however, as far as I could discern this sports bar only had one waitress trying to cover over 30 customers. And this on a Saturday with the world cup games. I saw only one waitress and a bar man. The gal was valiantly trying to keep up. But the burger was great.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place is a keeper! + +It was pretty good. I got the Cajun chicken sandwich with french fries for take out. + +I waited at the bar, and ordered a drink while I waited. I had the Caipirinha... Not as good as Seviche's, but then again this is Buffalo Blues.... + +If you need an ""All American"" food fix, this is the place to be.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I may be a little biased... this place is right down the street from my house and we go there frequently, but I think Blues is great. + +I have had quite a few things in the menu but two things that I love more than others are the cobb salad and the Oscar's Garbage burger. + The cobb salad is just a cob salad, but some how they make it better than most. I don't know if it's the sprout or the dressing, but it is one of the best cobb salads I have ever had. + And the garabge burger....Mmmmmmm. This burger caught my attenetion at first because it has an egg on it. I lovelovelove a burger with an egg on it. I don't know what genuis started the egg on a burger trend, but kudos to you! +But that's not all. Imagine a Primanti's sandwich but with a big, fat burger. It has fries, cole slaw, an egg and American cheese. My BF often comments it's strange there's no bacon, but honestly, that'd be over kill. + +They also have a really good veggie sandwich with Hummus (I don't remember the name), a great buffalo chicken sandwich and fantastic appitizers. + +Also, it's worth mentioning they hace really good hand cut fries- not those mushy frozen crap sticks- and GREAT fresh homemade potato chips. + +Now, as far as the ribs and wings go, I'm not a big ribs/wings person. I can appreciate that they're good, but I wouldn't order it much. Having said that, my BF frequently orders one or the other and I always have my fair share of tastes. he raves about them so....If you looking for a nice place to watch a football or hockey game or just craving some good food I highly suggest it![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've been to Buffalo Blues a few times at Happy Hour, and met my daughter there last night for Happy Hour specials as advertised on the web site. First clue: no Happy Hour promos mentioned in the bar except for the Yeungs and Wings (which was not what we were looking for). We came close to leaving as my beer was off the draft list, but we decided to stay and were disappointed that my daughter's choice was already gone although still ilsted. The food was awful, the service worse. Maybe a busser should clean the table after removing the dirty dishes--our table was a sticky mess. The service: one beer to the table at a time. Next round I saw two beers go to a three-top, removed and sent to the bar, poured out and the glasses refilled and brought to us. Someone else's food was brought to our table, our fries came out --lukewarm---but our wing order never went in. So we got our garlic parm wings which tasted like old overcooked chicken and was way too crispy and greasy for my taste. We ate two each, then told the server we didn't want them. She offered to take them off, but we told her that wasn't necessary, so they took off 1/2 the price as a Customer service gesture. Still, we had a Happy Hour bill for 1/2 eaten fries, barely touched wings, and 6 drafts total of $45 at a dirty table. At least the place was quiet--there were empty tables everywhere. I think we're done here.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Wings are overpriced. And the quality of them are bad. They were tough and greasy. The staff are pleasant but then over all experience was too expensive for a sports bar.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The decor is nothing fancy but the food is surprisingly good (and fresh). I've gotten takeout and eaten at the buffet. Both good for the price - it's inexpensive.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> China Garden appears to be your run of the mill Chinese take out place (standard menu, decor, etc) , but I was very pleasantly surprised how good the food was. We had both the cashew chicken and seafood delight, and both were awesome. Also worth noting they are super fast (food was ready within 10 minutes). I'd easily say this is the best Chinese takeout place I've found since I've been in Pittsburgh (about a year). Highly recommend it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've said it before, and I'll say it again, I love me a buffet. + +An excellent price for some good food never hurts. All the usual Chinese fare is on the buffet with that American flare added for some spice...I suppose it would be to spice it up... Anyway I got to taste all my favorite Chinese foods from General Tso's to cheese won tons. Just in case I didn't want to overdose on Chinese I decided to try some of the Mac n' Cheese and fried potatoes (although I admit I added sweet and sour sauce to the potatoes). + +Servers are around often to pick up the plates you are finished with and to make sure your glasses are refilled. Atmosphere is somewhat comfortable. Appears to me they tried to squeeze in more seating than they could. + +I would have given five stars, but as my friend pointed out while we were there, our waters tasted like it came from a hose you may have used to fill up your backyard pool. Next time I'll go with the soda I suppose.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is my go-to place for curing a hangover. I don't know what it is about Chinese buffets the day after a long night of round after round, but it does the trick. I also like to come here before I go grocery shopping at the nearby Trader Joe's because everybody knows it's a bad idea to go shopping for food stuff on an empty stomach. + +All of my favorites are here, veggie lo mien, string beans, mac 'n cheese, crab rangoon, hot & sour soup, I haven't seen dan bing (egg pancakes) in awhile but when they have them, they are out of this world with some peanut sauce. Another thing I miss is creamed spinach... I have yet to see this dish on a Pittsburgh buffet but if you go outside of the city it is a staple among Chines buffets. + +Another star got knocked off for the lack of fresh fruit on the dessert table. Canned pineapple and mandarin oranges will always carry that metallic taste to them that is just no comparison to having the real thing.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The hot and sour soup was ok. Everything else was basically inedible. Water was not noticeably hose-y as per other reviews. More than 1/4 of the buffet was american food, and a lot of the rest was seafood that almost had to be ""krab"", considering the price of the buffet. No pot-stickers, no pork egg rolls, no spareribs, no won-ton soup.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The food here is good but it is not exceptional. + + I've been to this restaurant occasionally for a couple years and the menu hasn't changed at all. There is the typical Asian fare such as General Tso's, fried rice, noodles, stuffed shrimp and dumplings. There is also American macaroni and cheese, home fries and ham. + +When I go to China Garden, I always request a carry out container as I find it nauseating to sit in the dining area and see other patrons pile their plates with astonishing heaps of food. One thing for sure is that China Garden gets plenty of customers. + +Definitely come here for a reasonably priced buffet![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Just ate there, right next to GameStop & Google, has 3 small booths, & ordered the pepper steak w/ onion ($10.95). Food is fast fresh & hot, but mine had too much onion & not enough steak. At the end of the meal I was just eating onions with rice, though I hear this is healthy for you. Counter lady was cordial, but didn't reply when customers told her, ""Have a nice day"" #awkward. I know that English isn't her first language but she needs to catch on that people are wishing her well. Wasn't stuffed full either despite having eaten a large plate (I usually get this feeling eating Asian). This is basically a nice place to go for lunch that won't ruin your appetite for dinner. (Side note: Food is very clean. Brushed my teeth an hour before w/ Tom's of Maine fluoride-free peppermint & still had minty fresh breath an hour after eating)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The location is convenient but I was not a fan of the food. I had shrimp and Chinese veggies and crab Rangoon. They cut the veggies way too big and the sauce was bland. I won't go back for food but the crab Rangoon was ok. They didn't give any sauce. You have to ask for it. That sucks.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is my 2nd time here and I thought that I attributed the satisfaction of my first visit due to the fact I was sooooo hungry. Well my 2nd time and for a Chinese Buffet, this place is fantastic. The restaurant itself is very clean. The buffet is also very clean and even though I showed up within an hour of closing, they were still bringing out fresh entrees. The amount of choice is less than just about all the Chinese Buffets that I have ever been too, but in my opinion they make up for that in delicious food. All the patrons here are American, so this isn't the Asian place where the Asians eat. It's very non-spicy, non-original food, but it's fresh and good tasting. I would certainly return. Giving it 7.5 Knuckles out of 11.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is an average Chinese buffet. The food was not bad, but not impressive neither, plus some cheap American food. The food was a little too greasy even by American Chinese food standard, and my stomach complained soon after I left that place. To me, that's a no-go signal. + +On the other hand, they seemed to have a non-buffet counter next-door, perhaps the food would be better there.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I think 2 or 3 stars is accurate for this joint... The chicken is quality meat and its lightly sautéed but the sauce is to blah. It's a nice place to sit down and have Chinese food if you have no other local options. + +It's my last resort for Chinese food in the area. Prices are absurd!!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have furnished 90 percent of my home with Arhaus items including a sectional sofa, chair and ottoman, accent tables, lamps, dining table and chairs, etc. + +The upholstered items are very comfortable but the furniture finishes are somewhat problematic. I have tried a variety of different furniture cleaners and polishes and cannot restore the surface without smudging and streaking. + +The sales staff members are very friendly and knowledgeable, I have dealt with 3 staff members over the past 5 years and have been pleased with their expertise and service. + +All in all, I am a satisfied customer. I recommend this company if you are looking for contemporary furniture with a traditional flair.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Arhaus sells beautiful, beefy, traditional furniture for an equally large ticket. This store is surprisingly large, and I loved that it displays such an extensive selection. After I'd been in the store at least 5 minutes, an eccentric associate greeted me. I definitely plan to return to the store in the future when I'm looking to refresh my super-comfortable family room sofa.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have a cat, so this review is cat-centric. + +Great independently owned pet store. They only carry more premium foods, so if you feed your cat Fancy Feast or Cat Chow, don't come here for that sort of thing. Also only carry the more eco-friendly cat litters - no Tidy Cats here! Friendly staff, and the prices are not much more than you would be paying at Petco or similar places. Of course, you don't get the huge selection either, but this is my go to place for buying food, litter, and random toys. + +It makes me feel good to be supporting a local establishment. Try it - you might find that you like it too.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> That is a great cat they have working, but they only have 3 brands of cat food, all of them expensive. Funny enough though not as expensive as what I was looking for. They followed me around like I was going to stuff my pockets and that just ruined the whole mom and pop thing.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Smiley's is wonderful... filled with things to keep our trio of cats well-fed, well-treated, and well-entertained. Certainly this is not a big box store, but, honestly, I wouldn't give my pets 99% of the food, treats, or toys that can be found in those stores, so, really, Smiley's offers me a better selection of what I actually want than any big box does. (They have a very good selection of toys for cats!) And Smiley's takes bulk orders and has the food within a few days... saving us the trouble of schlepping out to the 'burbs.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Not really an update so much as a plea to the Yelp community. If you are needing pet supplies and live in the Point Breeze/Shadyside/Squirrel Hill/East Liberty area, please PLEASE consider stopping by and supporting this store. With the new PetSmart (or is it Petco?) open down the street where Borders used to be, this independently owned store is under a lot of pressure to survive. Given that the prices are not that different, please give this place a shot. I'm not super anti-chain stores, but I AM pro-independent stores (does it have to be a zero-sum game?).[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My wife and I have both been seeing Dr. Segal for over five years. He's great, one of the best chiropractors I've seen over the years and I strongly recommend him to everybody we know. I've had regular chiropractic care since my late teens, not just for injuries, but also maintenance. Dr. Segal has been excellent about tailoring treatment and frequency to what is going on. No sales pitch for extras, just a good assessment and focused manipulation. From someone who puts a lot of stress on my neck and back through work and play, this is a great place to go.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Dr. Seagle is wonderful. My whole family goes to him. The amazing feeling of instant Relief that I get every time I hear that pop, is amazing. I have been to chiropractors all over the world. None of them to the success of Dr. Seagle. I used to have chronic migraines daily. Would go a few times a week. After continual visits for years. I am happy to report I rarely get migraines and only need to visit every couple of month. This man knows what he is doing![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Dr. Eric Segal was a complete ass. He was rude and obnoxious to me and my wife. We went to him for an adjustment and I left wanting to adjust this idiot's face. I will deter all of my clients from going here and will personally make sure that this man doesn't disrespect anyone else like he did to us.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I had to get new tires mounted and balanced and when I went to pay, the guy at the register actually says something to the effect of ""Do you have any idea what this is supposed to cost? So, I could charge you $400 and you wouldn't know the difference?"" Joking or not, why even go there?[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Made an appointment for 3:30. They completely forgot I was coming but said they could start on my car in ten minutes and be done in an hour. Came back an hour later only to see my car in the same spot. They said it would take another two hours to start work. Completely unhelpful and unapologetic.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I came in with a flat. They said they couldn't repair the tire because there was cracking on the edges. True there were cracks, but they were hairline cracks and superficial. The diagnosis was done just from examining the exterior, which I discovered, is not sufficient to adequately judge if the cracking is bad enough--you have to actually take the tire off. + +Coincidentally, all four tires had the light cracking and therefore all four tires would probably need replacing. Hmmm.... How convenient for Monro? + +Well, even if I give them the benefit of the doubt on the tire cracking, the pricing on the tires was ridiculous. My tires, which were under warranty, would have cost over $500 to get replaced with crap tires (that's with the warranty credit applied). Oh but wait, they could make me a deal with some in-house tires that were even crappier for $480. How did I know they were crappy? I looked them up online. Guess what else I found. Both sets of tires were significantly cheaper according to the Manufacturer's website even when including installation, balancing, and disposal! + +So no, no thank you. I don't want to pay $500 to get cheap tires on my car. + +Fortunately, my tire would hold air for a few hours so I drove to another place. They fixed the flat no problem for $20. Guess that cracking wasn't so bad after all.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The new manager, Ray, was really friendly and helpful. Had to diagnose something with my car-done quickly. I usually go to the Monroe in Wexford, this one is just as great! Thank you![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Like the previous reviewer, the new manager Ray is awesome. I needed a relatively simple tire change. It was handled professionally and friendly. + +What got my attention is that, while I was waiting, Ray was dealing with a really difficult customer. I would have blown my top at this guy, but Ray was calm told him his options (which, as a car guy, I agreed with) and handled his concern. Like a pro.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I came in here to have a diagnosis done on my car because the ABS light was on. +They removed all the tires, showed me how the sensor and ABS work, did not perform the diagnosis I originally went in for and told me that I should have the back wheel hubs replaced for a total of $1,222, this with a new set of breaks (that I knew about) and ""without"" charging me labor. +I may not know much about cars but I know how to search the internet and ask for advice. I found the cost of wheel hubs, they are no more than $150 each (for my car) and here they said that they cost $550 each (before labor). + +I also found out that the sensors get so soiled from all the dirt and salt that most of the time all the car needs is a simple wash on the undercarriage. You should always have your car washed, specially in the winter. It may save you $100's. + +This place will rob you blind. + +Never have work done in a place like this until you do your homework![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I knew I needed new tires and an alignment so I ordered the tires ahead so I could be in-and-out as quickly as possible to make it to class. Showed up noone had ordered the tires but they said they'd split the difference of a different brand. I was a little irritated but agreed and thought this was going to be a bad decision coming here (I'm from out of town); however, I was pleasantly surprised by the service. The mechanics noticed the car's bushings were what was causing the problems it took awhile and they offered a little extra discount which was much appreciated. Overall, it took 2 and 1/2 hours, had front aligned, bushings replaced, two new tires, and an oil change....cost $606. So, I still believe it was a little pricey but the guys were great and I can definitely note an overall difference in my car.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I took a subaru outback here for the annual state safety and emissions inspections. First I was charged more for this service than what was clearly posted on the service station wall. Secondly I was failed for a lug nut that had rusted to the point that the technicians could not get it off. I was quoted $425 for them to get it off. I was able to accomplish this with a $6 bottle of penetrating oil and a breaker bar. + +When I returned to have the reinspection I was charged for it (their policy posted on the service wall clearly states you get a second inspection within 30 days of initially failing free of charge). This time they were able to get the lug nut off but supposedly could not get it back on. This was odd as I had taken it off and put it back on numerous times to ensure it was okay to pass. They once again quoted me $425, stating they would have to replace the wheel stud. The new wheel stud cost me $3.50 at the local parts store and I did the job in under an hour without a single power tool. + +This shop is not following the guidelines they have clearly posted on their wall and are fabricating problems in an effort to overcharge you for simple repairs. Avoid this shop.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Have taken my car here a few times because there's a bus stop out front so it's convenient to drop my car off and get to work. But after what happened I will never be back. They just cost me money and lost my tires. + +In March I blew a tire on a pothole (naturally) and they replaced the two front tires for me. The second tire was fine but you have to replace both, I kept it so that I would have a spare if another one blew out. Put the tires in my basement, no problem. Saved for a rainy day. + +This week I ran over a nail and the tire wasn't fixable so I had to get it replaced. Luckily I've got a spare! I called Monro early this morning to see if I could get in but they said it would be tomorrow at the earliest. I needed my car so I took it to pep boys (three hour turnaround - also the last time I needed an oil change they said they were booked for three days, good lord). + +I drop the car off at Pep Boys and tell them the extra tire is in the back. They call me up and tell me the tire is the wrong size. What? Monro gave me the wrong tires back when they replaced them in March. So I had to buy a new tire when I had a perfectly good one that is now god knows where. The tire was the wrong size and definitely didn't come from my car as it wouldn't have fit on the rim. + +After paying for the tire at Pep Boys I went over to Monro to see what they would do about it. They informed me that because I already had the new tire put on they couldn't do anything but the next time I came in they ""would work with me"". Why the hell would I come back when you just screwed me out of a hundred bucks and a good tire? Not worth chancing. Because you couldn't fit me in within a day I get screwed? + +If you need tires go to Pep Boys on Milvalle. If you need an oil change go to Midas on Penn Circle they'll be able to get you in and not wait three days.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Ah Monro, where ""45 minutes"" is actually 2 hours and running at the time of this post. My car is on a lift with no tires and the employees are smoking cigarettes laughing. I can't even escape if I wanted to. At least they turned the heat off in the waiting room. Not like it's November in Pittsburgh or anything...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I wish we had a way to hold this corporation accountable for its crimes against our society.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Please go to the other McDonalds (not too far from here at 120 Penn Cir W). + +One time while using their drive-thru service, we realized they forgot to add an item on our receipt. We asked how much the real total is and the employee told me, ""like $5.00."" WHAT!?!!?!! CAN YOU PLEASE USE YOUR REGISTER TO TELL ME HOW MUCH THE ACTUAL TOTAL IS![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Good for Altar bar. But they didn't have fries....[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I don't understand the low reviews. This is a very well run neighborhood McDonald's where retired folks seem to gather over coffee in the morning. I have been here a few times and service was always prompt and courteous. The food is consistent with McDonald's everywhere and the restaurant clean. + +My only complaint was free ATT WiFi was slow on my last visit.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Prepare to be wowed. + +High class dining in one of pittsburgh's up and coming hip neighborhoods. I thought I would try some of the world famous cuisine so I pulled up on a Thursday evening. ""Garçon"" I asked, ""may I try some of your french fried potatoes?"" I was greeted with a crackled mutter as I inched my vehicle forward. I was then treated to a relaxing 15 minute wait as nobody moved in line. Perhaps it was the clientele, a 1992 minivan filled with some savvy locals. Perhaps it was the professional waitstaff, whom I could hear laughing and socializing through my window. Whatever it was, the dining experience was filled with culinary magic and spa-like service. After some deep meditation, I realized that perhaps tonight was not the best night to sample such fine delicacies so I pulled away. I cannot wait to return to this location and try my luck at trying these elusive fries. I highly recommend this palace of excellence.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I don't expect much from fast food restaurants. But I do expect to be spoken to when I am a paying customer. I just went through the drive-thru at this location and, other than taking my order at the speaker, no one said a word to me. There was a different person at each window, and neither of them said hello, your total is, fuck you, nothing. I don't think I've ever encountered such a miserable bunch of people. + +Maybe they're upset because their heroin operation was shut down.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Going to a new mechanic to get your car repaired shouldn't rank up there with public speaking and first dates, but it usually does. Well not if you go visit Tim at Walter's. They guys at Walter's are friendly, trustworthy, and treat you with respect. + +They are a small shop so call ahead if you need major service, but where else are you going find a mechanic who actually suggests way to save money on the repair[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The most important quality a mechanic can have is honesty. Meet Tim Walter. When I take my car to Walter's I know the service will be good, fast and won't take a chunk out of my last paycheck. Calling ahead is usually a good idea so they can fit you in...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Walter's is just a fantastic establishment. Tim is a phenomenal mechanic, who is as honest as they come, charges amazingly low prices, and - Morten H. is not lying - will actually suggest ways to save you money. The shop is small and usually pretty busy, but they will do their best to fit you in and get your car fixed up ASAP, and Tim always takes time to explain your car's problems to you. He will even show you what's wrong inside the car, or tell you how to do something yourself if that's what would be more sensible. I recommend Walter's to anyone who's in the market for a mechanic.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I cannot say enough good things about Walter's. Tim, the head mechanic (Tim Walter, hence the name of the shop), is amazingly helpful and accommodating. He repairs my car quickly every time I go in, and I never have to bring it back for further repairs. He also fits me in right away (though it is a good idea to call ahead - they do get super busy because of their sheer awesomeness and small size). And when I pick my car up, he'll explain what was wrong and how he fixed it in a completely unpatronizing way, then usually undercharge me. I know, sounds too good to be true, but isn't. I'll be moving for grad school soon, and I can honestly say I will miss Walter's. I don't think I'll ever find a better shop/mechanic. +A quick word of warning: Tim's adorable, but completely ADD. He'll fix your car well, and quickly, but he does get easily distracted sometimes. Bear with it, he's totally worth it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My car wouldn't start so I started yelping the closest option to my apartment. I found Walter's and with such great reviews below I gave him a call. He drove over to my apartment and looked at my car hoping that it'd be something simple before we got it towed. After witnessing him take time out of his busy day to do this, I knew he was a good guy. + +Unfortunately, it did need towed and he was afraid it'd take a week to fix due to his booked schedule. He called the next day to tell me that he looked at it, realized it was a simpler fix than he originally thought and had it done later that day. + +I had a great experience and am sure everyone else will. Thanks Tim[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I just want to echo what everyone else has already said about this mechanic. My brakes gave out and I came upon the glowing reviews for Walter's, so I gave them a call. Not only did Tim fix my car quickly and inexpensively, he actually came to pick it up himself so that I wouldn't have to spend money on a tow truck! He's also an extremely friendly, funny guy who puts you at ease immediately. I'll be going back there without hesitation the next time I need anything done on my car.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Went to Walters after I had a ripoff repair store tell me my Volvo needed new roters. Thank goodness I know what they are and that they had been replaced just 16 months ago. Tim at Walters confirmed my belief and passed my inspections. He was fast, funny, and smart. I then sent my husband in with his ailing BMW and Tim did a fantastic service on it as well. This is a real honest and thoghtful mechanic.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love Tim. + +I bought a shitty used car and it kept DYING when I would drive uphill, and I was new in town so I asked for some shop recommendations from people online and a bunch of people pointed me to Walters. He helped me isolate the problem to my EGR valve, and while it wasn't a cheap fix, I can't imagine I could've gotten the work done any cheaper. I've also had several other problems, and he's always trying to save me money and do things as inexpensively as possible. + +I wouldn't say my shitmobile runs like a dream or anything, but it's definitely in much better shape than when I started. + +And I usually don't have to wait too long for repairs. Typically I can drop it off in the morning (after making an appointment a few days in advance) and pick it up later that day. Though, they do seem pretty busy so I try not to expect them to get it done too quickly. + +And I have to say, I really don't care if my mechanic is a friendly, personable guy because I'm just paying him to fix my car and as long as he does that right I'm happy. But Tim is one of the nicest guys I've ever met, and I really enjoy talking to him.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Growing up, my dad always fixed my car. Now that he lives two states away, I don't have that luxury anymore. Luckily, Tim at Walter's Automotive is a great substitute. Honest, friendly, and helpful--I'd recommend him to anyone in Pittsburgh.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I went to Walt's due to the reviews I saw here on Yelp. I like supporting local business and I also wanted to find a garage I could trust. There was nothing wrong with my car I just needed the oil changed and I asked them to make sure I was ""good to go"" for the winter season. They changed the oil, check my tires and topped off all my fluids all for $36. Tim is a helpful guy and will take his time to explain things to you. They seem to be quite busy all the time which I see as a good thing. However, it does mean that you have to call ahead for an appointment and you may not get your car in on the same day. I will be going back for all my car care needs![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Excellent and trustworthy mechanic.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Walter's was SO helpful when our daughter's car was misdiagnosed by another garage. He talked us through the options over the phone (we're 300 miles away) and helped us find a solution. Two thumbs up![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Wonderful experience. I had a flat tire, and he checked it inside and out, tested it overnight, and put it back on my car. When I went to pay, he said it was nothing. He even gave me helpful advice on some other aspects of my car I was neglecting. During a bad week, this was a much-needed act of generosity. + +Highly recommend.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> What can I say about Tim that hasn't already been said? Although I didn't end up getting my car serviced at Walter's Automotive, Tim gave me a lot of helpful advice and was very personable. You can tell he genuinely cares about his customers and their concerns. + +I'll definitely be going to him if there's anything that I need to get fixed in the near future.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Tim is fantastic with German cars, including my 2003 3-series BMW, which was out the door for 400 - broken axle, oil change, tire rotation and one other thing. Labor prices are reasonable, it's just hard as hell to get an appointment. If he weren't so damn nice (like doing all sorts of free things for people) he could probably have himself a bigger, better garage and more people working for him.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great experience. Honest and friendly!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I normally try to avoid using shops other than Manordale Tire in Delmont, but in this case I really needed it to be within walking/busing distance of my home, so I went out on a limb, checked Car Talk's Mechanics Files, and went with Walter's. + +The fellah with whom I met was really friendly, and even took my car for a drive with me in the passenger's seat to help diagnose the problem, which is not something I'd seen anyone do before, and I'd say it's definitely great customer service. He did kinda suck at driving stick, though, but my car's a tough one to drive. + +I was a little miffed that my repair had to be scheduled for many weeks in the future, because I needed a bearing and well, riding the parkway daily on a bad bearing just doesn't feel safe to me. But when the time came, my car was done on time, and I didn't seem to have any problems afterward. I did feel like there was something a little wrong with my suspension after getting my car back, but I think it was unrelated: when I did my driveshafts, one of the ball joints was on its way out, and I think it just crapped out shortly after I took it to Walter's. + +I'm going to keep going to Manordale, but this place wasn't too bad.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> If I could give Walter's automotive more than 5 stars, I would. + +I called Tim around 8am because my brakes were making an awful sound (I know nothing about cars). He said it usually takes a few weeks to get an appointment, but if I wanted to drive it over he would take it for a ride with me to diagnose the problem. + +I drove it over, he took one look at my car and found the problem. He didn't have room for me right then, but I dropped it off 2 days later in the morning and I had it back before the end of the day. + +Before I left, he noticed all the expired parking passes covering my back window and offered to take them off for me. Great customer service; I will definitely be back with any future car issues.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I went here a couple weeks ago to get new tires on my car. I couldn't agree more with the other reviewers. Walter's was originally supposed to call me with an estimated cost, and when I hadn't heard, I called and spoke with Walter directly. 15 minutes later, he had an estimate for me. When I couldn't decide on the tire I wanted, he had three different types waiting for me when I came in for my appointment & went through the pros and cons of each! Just great service! + +I also found the price reasonable & the service was quick.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Scenario: Get into my car at 3:30 and head to campus for a meeting. All of a sudden, the tire warning signal lights up even though I don't remember running over anything. I get out of the car to carefully inspect my tires and they feel/look completely OK. But after owning a BMW for 3 years and having constant wheel alignment/tire issues (ie. when a tire warning signal lights up, it usually means my tire's about to blow out!!), I freaked out and frantically drove my Infiniti to the first 3 auto shops on Baum Blvd. I waited at the first stop for 5-10 minutes and the guy did not get off the phone. I got back into the car and drove it over to Pep Boy's where a mechanic was outside smoking. He says I need to go through their service desk (inside their huge store) and deal with them first. I'm thinking, ""ugh. no time. I have class in 40 minutes and I'm already late to my meeting."" I drive past the 3rd shop and I don't even see anyone sitting at the reception desk and figure it's going to take forever to get what I'm asking for. + +Then, I remembered the really positive experience I had with Walter's. I decided to drive to the end of Baum Blvd. to find his place and boy, am I glad I did. As soon as I got there, the service coordinator told me to pull my car around front so that their mechanic could take a look at my tires. He stopped what he was doing to do this and told me I could just stay in my car. Then, he reassured me that my tires were OK and he proceeded to inflate them, explaining to me why the signals might have come on. + +Free of charge, in and out within 5 minutes, and helpful/reassuring. I love this about Walter's Automative. They're not out just to make money. They genuinely just want to help. Highly reccommend!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> As numerous people have pointed out, Walter's is indeed a great repair shop. Tim (Walter is his last name) and the rest of his staff are friendly, honest, professional, and reliable. I highly recommend this shop for repairs, maintenance, and check ups. + +However, they are victims of their own awesomeness. The waits here can be long--2 weeks or more--due to how busy they are and they only have one bay. If you do have a pressing safety concern though, Tim is always willing to take your car for a spin or do a quick diagnosis to let you know if something needs to be taken care of.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great place. I take my car there for everything. Inexpensive, friendly, and knowledgeable. They've fixed my tire, taped a broken hose temporarily, and done other things for no charge several times. I'd definitely recommend them.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Best car repair spot in town. Tim is honest, hard-working, and knows his sh*t. I've been in burgh for 3 years now. I was driving a 2000 Nissan Maxima and it had 170K miles on it. Now, I loved that car and whenever something went wrong I brought it in to Walter's. Last time I brought it in I asked him if I should put more money into the car- the alternator was out and a new battery was needed. The car would not start. He told me it is a good time to get a new car because he wan't sure how much more this car could take. He even gave me a couple of numbers of guys who buy cars ""as is."" I called these guys and sold this beater maxima for $1000 as is! + +Now, I drive a 2011 Malibu and I'm a happy girl. Thank you Tim- I appreciate you looking out! Other car repair shops would have fixed my car charged me out the azz only for my car to break down again. Tim really does have your best interest.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Walter's garage is awesome! I was in real trouble with my car and needed immediate repairs and he managed to fit me into his busy schedule and charged a fair price for the work. He was kind and honest--what more could you ask for from a mechanic? :)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have a general rule of thumb when picking out an auto repair shop: + +The ""office"" must be very messy and grease and dirt must be everywhere. + +In my opinion, if an auto shop has the time and money to keep a squeaky clean appearance, they're wasting some of your money you pay for service. Walter's Automotive fits the bill with their ""office"" being a small cluttered desk in the service bay. Their ""lobby"" is the doorway that you stand in just outside the ""office."" I couldn't be happier with my first impressions--to me, minimal overhead means maximum service and value. + +Sure enough everyone at Walter's is very nice and helpful. Apparently, everyone else in Pittsburgh knows this since I have to schedule an appointment 10 days in advance just to get my car inspected. So please, even though Walter's is awesome, don't come here--I want this place to myself.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I thought I need an alignment and turns out all I needed was a tire balance. I stopped by he had me go with him and we drove around the block. I didn't cost me a thing because the tire balance was under warranty. Really nice guy.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Mr. Walter is an honest, friendly guy. He helped me out a lot with my VERY old car. Always took the time to explain what was going on. The services he did to the car were not always as quick as some would hope, but I never felt cheated or ignored or talked down to, he always did a great job. + +When that old (VERY old) car finally, truly died (became unfixable) and needed to be scrapped, he even volunteered a partial refund to me because he said he wished that his most recent work on it could have been enjoyed by me for longer, so that I could have gotten my money's worth. He truly is a super guy to work on your car.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I had to get a new mechanic since I recently moved here. That worried me, a lot, as I own a VW. Thankfully I found all these reviews on Yelp about Walters and decided to give it a shot. + +Rules about Walters: Plan at least two weeks ahead for an appointment. It is worth it. + +From there you don't have to worry about anything. On my particular car I always have to fix the suspension, and I ended up needing the same repair from last year. Last year I spent $1,300 from my very reasonable and trustworthy mechanic I had been using for years at home. This year Walters quoted me just under $700. I was pretty blown away by that considering the other place I go to is just as down to earth as Walter's. + +Walters took the time to put my tennis racquets in my trunk and remove my aftermarket stereo so they wouldn't be seen. He explained everything to me thoroughly and was really friendly when I came to pick up my car. + +I know a lot about cars and mechanics since I've worked at a dealership and the honesty of Walters still amazes me. I will take my car here every time I need to get something done, even if I get a newer car with a warranty from a dealership.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> There are at least 2 auto repair shops where I could drop my car and walk home or to school in less than 10 minutes. I have to drive to Walter's, take the bus back home and catch it back to get my car. It's about a 15 minute ride each way. + +I would walk there on my hands. They are that awesome. + +Tim is not only great at what he does, he is cool as hell! He was patient with me and my (over 230,000 miles) car that took a freaking month to pass the emissions inspection. Turns out the mass flow sensor wires were dirty- anywhere else and I would have already replaced 2 O2 sensors and I would still be going through emissions crap. + +I am really happy to have found someone to take care of my car :-D Thanks Tim!!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I like Tim Walter so much, I almost wish my car would break down so I would have an excuse to see him. + +He is super honest, explains everything, gets the cheapest appropriate parts he can, and isn't the least bit condescending. Picture the kindest surgeon you can; Tim Walter is the same, just for cars instead. + +Also, the man has a great memory. He *still* makes fun of me for that Coke can I had strapped to my muffler 7 years ago.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> For the last 5 years that I have been living in Pittsburgh I have been coming to Walter's...its always been a bit of trick planning to take my car in for maintenance as they are very busy because they are indeed great mechanics and generally awesome and friendly people. You absolutely do need to call a few weeks ahead and be patient. Quality service takes some time. + +Now that I am moving to the opposite side of the country, I took my car in one last time to get everything checked out, fixed, swapped out etc. My car was in the shop for 3 days and I waited patiently knowing that I can trust Tim and Arlene in the same way I can trust my parents to get something important done. They aren't there to screw you over. I know this because I had, on my first occasion taking my car there, gotten a second opinion on somethings and everything aligned between the two sources so they earned my trust! + +They took care of me and my car really well. Arlene kept me up to date on what was going on and Tim took the time to explain what the parts were, what they did and how much things were going to cost. He even sat with me after closing hours researching the oxygen sensor and tires I needed online and quoting me the best price. He listed out everything I needed to have done and told me which was most important for a cross country drive and what could wait. That is service and care!! + +If you need a great mechanic, like you need a good doctor, be patient, be inquisitive and do a little bit of planning. Your car will get serviced, your wallet will be in good shape and you might learn a bit about the car you drive. I only hope to find as good of a business in Seattle as I did here in Pittsburgh. + +Thanks for everything![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Hands down a great experience! I called yesterday as the driver headlight on my car was out and asked if I needed to make an appointment. The woman on the phone said to just stop right by during their hours. I went by this morning and their (small) lot was full so I just sat in my car while I believe who was Tim was finished chatting with another guy. I continued to sat in my car for a couple of minutes while Tim quickly inspected my headlight. Unfortunately he did not have any replacement bulbs but ordered them right on the spot while I was there and told me to come back any time in the afternoon. Fast forward a few hours later. I just popped by and after popping my hood and going into their office to pay, my headlight was replaced! Friendly, honest, fair and quick service. No BS. Highly recommend Walter's Automotive.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I found this mechanic based on the excellent Yelp reviews and I was not disappointed. I came to Walter's because my radiator was leaking coolant and Walter tried to save me money by doing a patch job on the leak which he was only going to charge me $20. Unfortunately it didn't work and I still had to go through with the replacement, but I appreciated the time he took to give a cheaper alternative a try. And Tim Walter is a friendly guy who will take the time to discuss the problem with you and give you a fair deal. This place gets busy so you will likely have to call a week in advance and leave your car at least overnight, but it's close to bus stops. There is no waiting area and I don't think they do any quick jobs that you can stay and wait for.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I was having an issue with the emissions light in my car. I spoke with Arlene, who gave me a rundown of what I could expect while my car was in the shop. She then told me that even though they were very busy, I could stop by before my appointment so that Tim could check things out and make sure my car was safe to drive. Tim poked around, figured out it was the gas cap, and sent me on my way without charging. A good mechanic is worth their weight in gold and I will not only return to this garage but refer others as well.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> A trust worthy mechanic is very rare these days... + +I split time between Seattle (work) and The Burgh (Family) so when my car began to lose power on acceleration I searched for a local repair shop on yelp... Based on the numerous positive reviews I made an appointment at Walters on Baum Blvd. + +My appointment was made for two weeks in advance but Tim had me bring my car in and we took it for a test drive. Tim determined that it was the Cat converter and recommended that I not drive the vehicle very much as to not cause further damage. Tim said that he and one of his mechanics were going to work extra hours that weekend to get caught up and that he would try to get to my vehicle. So I dropped my car off on Wed night, on Thursday Tim called with an estimate that was 150.00 to 200.00 less than what others had quoted. + +I expected my car to be worked on over the weekend however at the end of Thursday Tim called and told me that my car was ready and running great! Wow! I was surprised and grateful. + +When I picked up my car on Friday the cost for repairs was 15.00 less than my original quote due to a gasket that was included with the part and not ordered separate. I figure that many shops would have just kept the refund from the extra part and would have charged me for the quoted price but not Tim at Walter's. + +I can't say enough about the excellent service I received from Walter's...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I cannot sing Tim Walter's praises loud enough. + +I have taken my car to him for about 5 years, and I always leave with a new experience attesting to his awesomeness. If you think you might have something wrong with your car that you're not sure what it is, you can just stop by, and he'll usually take a break from what he's working on to get in your car with you and drive for a little bit and then give you his opinion. Then, when he diagnoses your car, he'll explain it to you like you're not an idiot, and he'll make sure you understand what's going on. He's incredibly honest and cares about his customers. For instance, once I had a tire that needed to be replaced but he didn't have it in stock. He told me how much it would cost to have the tire ordered and how long it would take to come in, then he called another shop to see if they had it and asked how much they were charging for it, and he sent me there because it would be cheaper and faster for me than having him order it. The price difference was like ten bucks, so I had him do it because it wasn't an emergency and I'd rather give him my business. He's awesome.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Mr. Walter is great. Reasonable prices, he's honest and tells you like it is. As a first-time car owner, he's helped me out numerous times and been very kind and generous in the face of my total ignorance![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> What excellent service! I couldn't be happier.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I heard about Walter's by the great reviews here on yelp. They did not steer me wrong. I went to the shop and asked for an appointment for leaking oil, but the secretary said they didn't have one for a couple weeks. Walter was doing work and asked me a couple questions, then asked if I could bring it in the next morning. The next morning! I did, and Walter and his employee lifted and took a look under my truck. Literally in seconds they found that it was simply a botched oil change, tightened the cap, and brought my truck down. He even topped off my oil, I believe. All this, and he said ""no charge on that"" as I went to pull out my wallet. I was in shock. + +As a side note, Walter and his staff are also very approachable. While his employee worked on my truck Walter, a fellow mechanic (?), and I talked about various things. + +I will recommend Walter's to my brother who lives here in Pittsburgh, and will go to Walter's with any car trouble I have while I am here for school. I recommend Walter's in the highest degree.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Another five-star review, this one from a newbie. The brakes on my Honda fit were making a frightful sound. I was sure I'd get the full-rotor press from the chains, because that's kind of their job. The dealer sold me the car in the first place, so I don't like them. (Not 100% happy with the Fit). A little research turned up Walter's 42 5-star reviews, so I thought I'll give them a try. I wasn't certain they'd be able to see me soon enough, but whatever. Walter called me back within 1/2 hour, told me to get the car in ASAP to make sure it was safe to drive, 'and then if you have to go somewhere and wait, you have to go somewhere and wait."" I delivered my car 1/2 hour after that, went somewhere and waited, and had it back, fixed, within another hour, for less than 200 bucks. Walter's garage from now on. Yep.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I had to give Walter's 5 stars, if there was a way to say it was exceptional, I would do that. + +I found Walter's through yelp and was not sure how a auto repair shop had all 5-star reviews. This is totally unheard of. And now having gone there for a repair and inspection, I can just say, BEST MECHANIC IN TOWN. Other people have sung praises for Walter's already, so I won't get into that. My recommendation: If you are looking for an amazing, trustworthy, competent and humble mechanic, dial Walter's number. You will not be disappointed.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place has not only done my regular maintenance perfectly, but Tim has also dropped everything to help me in a pinch. Little things like changing my headlight for free when Pep Boys and Monro wanted me to wait 2 hours and charge me $20+ and helping me fill my coolant when I was in a panic. This place is just absolutely outstanding, I can't sing it enough praises.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have an older car and so sometimes things go wonky. One night I had to drop it off because it was barely running and I had no idea why. This was the first time I went to Walter's, turns out that it was only an oil changing problem. Car places usually screw me over because I know nothing about cars, but Walters did not. They are really great and fix the car for your needs. Yesterday I returned for inspection and once again he treated me fairly and only mentioned things that I already knew needed work. I would recommend this place to anyone with an older car and wants an honest car repair man. Walter's will definitely be getting my business in the future![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Went to Walt's Auto for an inspection after seeing all of these great reviews on Yelp, and was so happy I did. I will be taking my car and my husband's truck here from now on. The service here cannot be beat![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Recently had some problems with my battery and took to yelp to find a nearby/reputable mechanic. After reading all the great reviews on Walter's Automative, I made an appointment as recommended and brought my car in. + +Long story short, minus all the technical details, Walter was very helpful and informative in helping me resolve the problem. He was very open to listening to me describe the problem and was patient and quick to look into the issue and provide his expert advice. + +Customer service was great as well! It was really easy to call and schedule an appointment, and when I arrived the minimal office space looked pretty organized, given that it's inside an auto shop. All the keys looked organized and labeled. The appointment book looked clear and kept up. I can really appreciate when a business is well run. + +I would definitely recommend giving this business a try![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Honest. Reliable. Trust Worthy. + +Tim goes above and beyond with his service. He came to my house 3x one day to check everything he could before I ended up towing it to the garage. I will definitely go back![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Extremely honest, great work and amazing prices. I had them repair a wheel issue on my car. For no charge the mechanic also hid some wires I never got around to moving for the DYI back-up camera I installed.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Walter's is the best and most honest mechanic I've ever worked with. They are super busy because they are so great, so they have no need to do unnecessary repairs. Can't speak highly enough of quality of their work and integrity![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> very nice people who were accommodating and appear to look for ways to do the job right at the lowest cost possible. a breath of fresh air for an out-of-towner with a problem. Thanks[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I will never go anywhere else. Never had a shop tell me what I didn't need. Treated my mother the same way. Women if you looking for a place where you don't get ripped off, this is your place. He is always busy, so he does not have time to add stuff on and just working with he is more worried about doing a good job. I highly recommend this shop.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I was cautiously optimistic about Walter's after seeing the great reviews. I wasn't disappointed at all! The staff at Walter's was very friendly and helpful in scheduling me an appointment and worked with me throughout the entire car repair process. + +The best thing about the entire experience was the price and the flexibility at Walter's. The staff allowed me to pick my car up after hours (I have a work schedule that did not allow for me to get my car during business hours). They also gave a very reasonable price for the work that was done. + +The building may look small, but this is the best car repair place I've been to. Very impressed with the service and the staff.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> After reading all of the great reviews I thought I would try them for my car's annual inspection. All I can say is I wish I had found out about them decades ago. + +I arrived on time, and he was ready for me -- no waiting. I told him I only have one car, and would have to wait in the area, so he said he would get to work on it ASAP. Sure enough, about 1.5 hours later it was done. + +Even better, he told me nothing was wrong with it, so it would only cost me the price of the inspection. My car is only 6 years old, yet every other year wherever I took it there was a whole list of things which needed to be done, which ended up costing anywhere from $400-$600. Now I see how ripped off I was. + +It's a priceless experience to leave an automotive shop and feel like you weren't cheated. + +In the future, whenever anything needs to be done to my car, the one and only call I will make will be to Walter's Automotive.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Probably owing to the fact that I drive rolling turds exclusively, I've had a very hard time finding a good mechanic. After seeing so many good reviews, I decided to call Walter's. My 20 year old Subaru was stalling and not starting. I was warned that it would be a 2 week wait (Tim was on vacation for a week, booked for another), but if I needed to be seen before then, she could give me a referral somewhere. I decided to take my chances on getting stranded and wait for the godfather; I'm glad I did. + +Tim diagnosed the problem, then laid out his plan of attack. He worked to get my car running for as cheap as possible. When I went to pick it up, he spent several extra minutes going over what he had done, and what may need to be done in the future. He was actually smiling as he told me more Subaru mechanical trivia than I ever wanted to know. + +Like others have said, the wait can be long. Usually, i'd have given a company 4 stars for this reason. But, I'm telling you, the quality of work and the customer service you'll get here more than makes up for the wait.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I can only agree with previous reviews in that the service is +1) Good +2) Affordable (the don't overcharge you) +3) Flexible, e.g., you can pick up the car late. +The personnel is polite and knowledgeable.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I just went to Tim as my check engine light came on on my recently purchased 2005 Toyota Corolla. Tim took a look at the code and told me what the problem was. Reset it for me and told me to call him if it comes on again, all free of charge in just 5 minutes. That is why I like Tim and will recommend him over anyone else, especially for old cars, the guy is very honest and will only recommend what is best for your car and your situation. Not making you spend money when you don't need to.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Finding a decent, honest auto mechanic is always a battle. I can't stress enough how amazing Walter and his team are. They are very friendly, personable, honest hard working people. I would never go to another garage in Pittsburgh. I can't stress it enough![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The Kelly Strayhorn is a good idea which is poorly executed. The facility has problems: the stairs on the house are too narrow causing trips, the bathrooms don't really have the capacity for over 300 patrons, etc. + +Beyond the facility you get to the actual 'poorly executed' idea. The staff is extremely un-knowledgeable about the subjects they are producing. For instance none of the programmers on staff have any training in performing arts, they are all visual arts people playing at another field. As a result they don't even know what they are really producing and any experienced person in the field can tell. + +The sad part about this is they REALLY try. They throw staff and new ideas at every opportunity. Don't expect great performances here, expect a talked up mediocre performance. + +Audience follows content and they don't have content or the staff that is knowledgeable enough to know better. Check back in in a couple of years. This apple is too green to eat much less pay for.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I know I say this a lot, but we really are so lucky to have such beautiful old theaters here in the Burgh. Some may not be used as much as others, but I sure appreciate them. + +I attended an event here for the first time and was amazed by what good shape the theater was in. I loved the bright red chairs and classic feel. Mind you, I really know nothing of what this theater used to be used for... Although I can imagine very glamorous old movies like Singin' In The Rain (maybe this movie was not so much glamorous, but the namesake says as much). + +I was surprised by how comfortable it was. The seats are comfy and the leg room is decent. I can imagine by looking around that most seats are decent for viewing a show. They do offer many different events here throughout the year, which is great because it would be a sad fact if this theater wasn't used. + +I honestly want to look for things put on here now because I like the theater so much. Support your local theater, it really makes the city vibrant, I promise![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Named for Pittsburgh greats, Gene Kelly and Billy Strayhorn, this historic theater is a real gem. Originally the Regent, built in 1914, the building was renovated in 2000 as a performing arts center for theater, dance, music and film. I have been to several fundraisers hosted by the Kelly Strayhorn, and they have always been first rate. Also, I recently attended the Kelly Strayhorn's own fundraiser, Full Bloom, which was lots of fun. As a venue, this place is definitely worth your attention, and the staff seems to bend over backward to make sure events go off without a hitch.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Whether it's an emergency or not, these guys make your problem a priority. I called City Locksmith first, who said they would call me back in 5 minutes when they sent a technician. I waited 30; called Ace Lock and someone was here in 10 minutes, just as City Locksmith was calling me to tell me they were finally going to send someone. + +CALL ACE FIRST!!!! :-D[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> These guys are great. Fast, accurate, and very fair. I wouldn't go anywhere else.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I already had a transponder key for my truck but needed the key cut so I could use it. They did it right then and didn't charge me anything.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Extremely satisfied with the service that was provided by Ace Lock. Their technician showed up on time, and got to work right away. It is refreshing to see a craftsman who is proud of his work, and wants to get the job done quickly.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Exceeded expectations. I needed some help with four lock sets, at 10 AM I called Ace (based on Yelp! reviews) and a very pleasant woman told they'd be there the same afternoon. Sounded good. + +What was even better? They showed up less than an hour later! Since when do service technicians show up several hours early? Mike took care of the job quickly, efficiently and at a very reasonable price.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great guys there. Brought in a broken lock that it turned out they couldn't do much with but they spent well over an hour helping me and providing guidance on a replacement which they didn't even have to sell me (not lack of inventory, just different category - was more of a Home Depot product) Extremely professional, personable, and helpful staff. Will always come back with any locksmithing needs![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great place. Easily the best in the city. Open on Saturday from 10am till sold out and there will usually be a line out the door. + +They will also take orders for things during the week but in whole sizes only (not slices, etc). They sell fresh eggs from their farm and supplies for making fresh mozzarella, etc. + +Cooking classes are available and i have taken a couple, one with my daughter at the farm and it was worth every penny. + +Highly rated.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We watched the line start forming for Food Glorious Food around 9:30am while eating brunch next door. They open their doors at 10am, so this was a good indication of what great things were inside. +Apparently they stay open until they are sold out. By 11:30 when we finally got inside, there was still plenty of delicious things left! + +My husband and I split a slice of key lime pie (one of his all time favorites.) And he said he hadn't one so good since Miami. +Our friends, who had been many times before, bought a ricotta pie and a multi-layered nut/chocolate cake - also both divine. +I can't wait to go back![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Marvelous! Saturday morning Secret Bakery? What? + +Sure it's like waiting in line for Pink Floyd concert tickets, but then you get to eat the tickets. And they're delicious. + +Can't stop thinking about that Jewish Pizza...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Plays well with a Tazza latte around the corner! The quiche was divine and the the biscuits were what I imagine my mom would have made had she actually made biscuits. Two words: YUM-OH! Cannot wait to return to the Steel City so I can partake in some of the desserts.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have not had a bad thing from this place, ever. I am hesitant to tell more people about this place, because I will stand in line longer on Saturday. One weekend, I advance-ordered a chocolate/vanilla butter cream cake. The ordering process was a bit drawin-out, but I was rewarded for my patience with the most amazing cake I have ever tasted. I took the cake to a party, and the cake was the hit the talk of the party. I will have to take 2 cakes to the next party. Everyone stated that it was the best cake they had ever had. My daughter craves that cake on Tuesday, and alas, I cannot scratch that itch till Saturday, when those magic doors open for a few hours to allow us into enjoy the sweet and savory heaven that Food Glorous Food offers.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place has probably some of the best pastries I've ever encountered. The treats are consistently great to amazing to even mouth watering. The bakery is this quaint little place that is really cute with nice baking decorations and everything. The staff is really friendly and always helpful with making the hard selection. The cupcakes are these cream-stuffed pieces of heaven, and their signature sandwiches are out of this world. Everything else leaves nothing to be desired, and keeps me coming back as frequently as I can find someone to accompany me.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I am at Food Glorious Food every weekend. I always try to sample something new every time I go, and everything I've had has been wonderful. +The cupcakes are so buttery and the fillings and frosting so creamy (and sweet, but not over the top sweet). The fruit tarts are also excellent-- my favorite is just topped with a very generous amount of cream and and assorted fruit (berries, kiwi, mandarin orange, etc). Ahh, soooo good. +I haven't tried the focaccia (yet) but they look incredible. And I ALWAYS get a biscuit. Every time. +They recently expanded their hours, and are now open Thursday, Friday, and Saturday. And they will take orders by phone. So if there is something you want that is a popular item, you can call and they will hold it for you until you get there! +The line can be long but the staff is very efficient-- I've never had to wait longer than 15 minutes. I can't say enough wonderful things about this place![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Went for the first time yesterday and will definitely go again and again! Bought a huge assortment to share for dessert last night with some friends, Amazing bread pudding- dreamt about it all night last night then woke up and ate the rest of it! The Jewish pizza was amazing, beat choc chip cookies ever, great Madeline's, great white lily cake, fantastic plum tart, to-die-for German choc cake and a really good sugar free cake with berries ( you'd never guess it was sugar free)The only thing that I thought was ""meh"" was the macaroons- tried blood orange and pistachio- have had much better right here in Pittsburgh from the French bakery in Millvale. I consider myself and expert in macaroons, and these were a little over cooked. Anyway, I declare this the best bakery I have ever gone to in Pittsburgh. Not cheap, but you really get what you pay for in this case.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Some of the best desserts you'll ever taste can be found here, and you can feel like you've discovered a city secret in the process. This is because the shop opens only Saturdays at 10 am, and you will usually spot a line forming at 9:30. They stay open until they sell out, which is usually around noon. It's like a magical place that opens for a brief period of time, then disappears as fast as it appeared. + +Anyways, as for the desserts, they feature at wide selection of tarts, cakes, and other types of pastries. All of them look mouth-watering delicious. One of the cakes won some sort of award...I had this and a few other kinds as well, and they were all phenomenal. They used an addictive whipped cream type of ""frosting"" for their cakes, and all of this deliciousness can be had at completely reasonable prices. + +I've always wondered why they only open Saturday morning though, and what they do during the week. Even if you're not in the area, it's worth arriving at 9:30 to experience the novelty and cool experience of this strange, tiny, and wonderful dessert shoppe![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Very good dessert - had the lemon tarte. Even better Ham & Cheese sandwiches. Didn't try their biscuits, but will definitely be back next weekend :D + +Bring cash! $10 minimum for credit/debit cards.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> In sum interesting, unpretentious and a cozy bakery. + +I have noticed this bakery as been closed when I make it to Bryant Street...which is usually in the late evening when I am chowing down on delicious food from the Smiling Banana Leaf. I finally committed to drive there just for this bakery. + +I skimmed the yelp reviews and was a little concerned that going there at 330 in the afternoon would deprive me of the decadent and most delicious of the tasty treats. I called the location and the said they were open to five. I will admit I almost did not go. If they have lines early in the morning all the goodies would have likely been gone a few hours from closing but I decided to give it a whirl nevertheless. + +A quaint location, a few two tops here and there, a small area to shop there. Beautiful baskets and other nicknacks. In the back is there bakery shelves which are strangely set up in the back right. The location is not the best to peruse offerings. I am fortunate I did not arrive when it was busy I would have been unable to see much before I was next in line! + +I ordered the Chocolate Tulip. It was a hand-made shell filled with mousse & cake, with ganache drizzle, cream and berries. Rich and moist. Smooth and fluffy mousse. Not overly sweet. A nice marriage of creamy, rich, and sweet. Loved this delight. I also had a tasty cupcake. The cake was not as rich as that in the tulip. Yet, the frosting was a divine passion fruit. Yum. + +I'll be back. If they can serve such yummy treats moments before they close I can only imagine how amazing they must be first thing in the morning.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The first time I came here, I waited in line for 20 minutes. When it was my turn, I realized I left my wallet in the car. It hurt so bad, I didn't come back for a year. + +I can walk to this place from my house- which is dangerous because those biscuits are just OH SO DREAMY. I can't describe them. Just get some. + +Do I feel guilty about noshing on fabulous Strawberry Napoleons and Jewish Pizza (kind of like a modified, yet TOTALLY delicious fruitcake bar) at 10:15am? Hecks, naw... But they do have quiche and some other breakfast-y items for those who prefer a more traditional approach to your stomach's opening ceremony. + +Just go early :) They open at 10 on Saturdays. And bring cash...it's easier that way.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I arrived on a Thursday afternoon at 5pm when there was absolutely no other soul in the bakery (except for the staff). My pumpkin pastry with carmel topping was alright. I also tried the key lime cake and sour cream and apple cake. The key lime cake was definitely the best of the three. + +While I've been to better bakeries, I will definitely be back. I have heard stories of wonder and delight from other friends. + +There is a small seating area with tables and a water dispenser for diners.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> There is no better place in Pittsburgh for interesting baked goods. I wait in line with my daughter (who is 14 and only gets up early on a weekend when we are coming here:) on Saturdays and it is worth it. We are foodies and cook a lot at home so let me hit some highlights: the ham and cheese sandwiches are to die for and i hesitate to let you all know that; the biscuits are crazy good..dense and moist; the key lime cake is the best i've ever; amazing pepperoni rolls; the chocolate tulip is death by chocolate and delicious! We haven't eaten our way through everything yet but it's all fantastic. +Lisa[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm a creature of habit--I've been getting a savory and sweet item each time I'm around the neighborhood. White lily cake is divine! Quiches always tasty. Macarons are alittle too sweet. I wish the cake slices weren't $4/pop. Otherwise, would be a regular here.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We were visiting our friends who live close by, it was raining on a Saturday morning, our friends told my boyfriend and I to go here and get a ham sandwich. A ham sandwich? We thought. Yes a ham sandwich. My bf grabbed two to go while I waited in the car and we started eating and driving, eating these warm buttery wonderful tiny ham sandwiches. 5 minutes later we drove back to food glorious food , this time I hoped out of the car and ran in , got 3 more and ran back to the car. I'm not a foodie, I'm not a meat lover, I rarely eat breakfast. ........ But........ These were to die for!!!! How could a tiny little ham sandwich taste so good? The people that worked there, a young woman and a very young (teenager?) man we're so sweet and friendly, the pastries were sitting all around on trays looked amazing too! Very small and charming inside, just like you want French cafes to be. When we go to house sit for our friends next month, I will be a gaining few pounds a week on ham sandwiches. It might be the most savory 3 weeks of my life.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My sister, husband, and I went in after early dinner. It was completely unplanned but we were attracted to the quaint storefront. We purchased a crispy elephant ear-like dessert sprinkled with cinnamon and sugar. It was glorious. I bought a piece of apple-walnut-cinnamon sugar cake with cream cheese frosting. It was delicious an moist. We also purchased freshly baked chocolate chip cookies. They were absolutely rich and scrumptious. The woman who was there an greeted us seemed like she might be the owner. She was sweet and very helpful. Great disposition. This is probably my favorite small bakery in Pittsburgh. Delightful.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I can't even. +Perfectly delicious food, reminds me of a true French bakery. Delectable cakes, pastries, chocolatey things, as well as savory quiches, breads, and their signature little marinated ham sammies. +I used to be a regular here on Saturday mornings and would spend $20-30 bc I'd get 4-5 things to last me through the week. Ha! That never worked out. It lasted about 3 days. +The last time I went, the person working the counter was really unfriendly. But hey, maybe they're trying to really nail that French bakery vibe :) No matter, the baked goods redeemed this cranky lady.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Food glorious foooood, hot sausage and MUStard... + +Actually they don't sell hot sausage and mustard but, you know. + +They do have amazing ham and cheese sandwiches, that are kinda pricy, but oh so good. And if you want them, you better get there early on the weekend! They're small, so get 2 for yourself at least :) + +We've also tried the Nutella tart, which i've had twice now because it's SO DELICIOUS. The fruit tart is not bad, cinnamon buns are great, jewish pizza is ok (not what I was expecting - it's kinda like a fruitcake - like the dreaded holiday kind - but denser and drier), strata (eggy bread dish) which was pretty good, key lime cake - so so good, and quiche (good). + +Seating is hit or miss, since there's only a few tables (3 of them seat 4 people, 1 seats 2 people). On a quieter morning you should be able to find a seat. They serve coffee as well (nothing to write home about), $2 a cup, but if you like coffee with your dessert like me, it's nice to have.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Came across this place after checking out a Thai restaurant across the street. The name intrigued my family and I, and it looked like adorable from the outside. + +I fell in love instantly. And came back several times after first discovering this hidden gem. You walk in and the wonderful smells just overwhelm you in just an amazing way. The ambiance is that of an old style kitchen- personally, it reminds me of one of my aunts kitchens, which gives it that homey feel that is so comforting. They have seating- which I never saw in any bakeries prior to this one. They also serve coffee and encourage you to take a seat and enjoy your sweet treat. + +They offer such a unique array of sweets. Definitely not your typical bakery. Pies, tortes, mooses and cookies.. And when they do have cinnamon rolls, grab them! They are a hot commodity! My personal favorite is their key lime pie. Oh my goodness. It's amazing. They have had it every time that I came, thank goodness. Their key lime cake is phenomenal as well. Their fruit tarts are incredible, the chocolate moose is amazing- they have a lot of items with fresh fruit which I love! + +My only critiques- the hours: they are closed on Mondays and Sundays :/, not ideal for someone whose only day off is typically Sunday. And also, they write all the items thy have in the case on a small chalkboard posted on the wall to the right of the case. Every time I go, I find myself asking the employees what everything is, which I find to be a little annoying. Regardless- it's worth it. It's such a hidden gem and going there and experiencing their sweets is a real treat.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have had the following items from this place: +Banana Cream Pie +Coconut Cream pie +Napoleon +Pumpkin roll +Key lime pie +Lady fingers +Cookies +Cupcakes +I have never been disappointed. This is the kind of place that SHOULD exist. It has that home made taste with a professional look. Everything tastes fresh and delicious. I have not had one bad thing from there yet.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've had a wide range of experiences here. Let's just say, when I first moved here, one of the employees gave me poor advice and ended up totally screwing up my title. It's been a tremendous ordeal to get it fixed. Another employee tried to help me fix it and screwed that up too. Now I'm working with a third person who seems very competent and committed to helping me solve this problem, but even she is like ""I can't believe those other people told you to do that....they made this so much harder than it needed to be."" My thoughts exactly. + +Work with Barb, if you can. She knows her stuff. I don't quite trust anybody else to help me properly. Also they're only open from 830-4 (or is it 430?) so you pretty much have to go before work, or on Saturday. And I will be going in tomorrow at 830 until my car title saga finally comes to its conclusion.... + +Also, parking is free in their lot. And if you are a AAA member, I think your fees are lower, or something like that. I do have AAA, so it makes sense for me to come here - I can't say what the experience is like for non members.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> If I could give negative stars I would. After this review, I'm writing the president of AA and if action is not taken to correct the disservice at this location, I will never be a AAA member again. (been one since 1999) + +I recently moved from TN and needed to transfer my title and register my Dodge Ram in PA. This process is costly regardless of where you go, but adding $36+ for every transaction makes AAA the most expensive. I'm willing to pay for people to deal with this inconvenience for me, but AAA has made it worse than going to the DMV. Each and every clerk at this location is incompetent, uneducated, and aloof. I should know, I've dealt with at LEAST a dozen. Go to the DMV. + +For my very simple transaction, I've had to return to this location 7 (yes that is SEVEN!) times, and it still is not resolved. They've forgotten to request the title from my lien holder, issued the wrong plate for my vehicle, neglected to inform me of steps required by the state... I mean seriously, why would you pay $36 for EACH visit, just to get it wrong. Go to the DMV! + +Why did you return there if you were so unhappy, you might ask. Well once you begin the process at one branch, you cannot transfer to any other branch. (We went to Monroeville to transfer my wife's car and it took 30 minutes, ONCE.) Go to Monroeville, or cancel your AAA membership and go to the DMV!! + +Oh, and 30 minutes? that's a dream... I'm waited between 45 minutes and 3.5 HOURS at the East Liberty AAA. Prepare to take the day of work... nay, the WEEK in order to complete any transaction at this facility. Go to the DMV!!!! + +It has now been over 5 months since I started this process and it's still up in the air. they don't know what I still need to do, but they are happy to keep charging me to figure it out. Save yourself hundreds of dollars and a weeks worth of lost wages and just GO TO THE DMV!!!!!!!! Yeah it might seem sterile and slow, but at least they aren't serial criminals. It'll be over with like waking up from a bad dream, instead of the reoccurring nightmare that is the East Liberty AAA. + +Oh, and if you think this is a harsh review... Call their number, 412-365-7196. 9 times out of 10 it just rings and rings.. once I timed it for more than 30 minutes before I got an answer (with no apology). If you are in the AAA, you'll know I'm calling. It's the constant ring in the background that NOBODY answers.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have to say that I have had quick and efficient stops in here for all of my car needs. Firstly, walking into this building is quite a spectacle, from the beautiful exterior and interior. I have to be honest, my first trip in here I felt like taking my escalator down into the pit that is AAA was equivalent to taking a trip into the fifth ring of hell. I hate anything dealing with the DMV, registration, license, tags, blah blah blah. However, both of the times I stopped in here it was not crowded at all, and the women that helped me were very nice and thoughtful. The stations you must go through are quick and effective. Both times I had business here, I was in and out in less than a half hour- which was far better than the marathon nightmare I was expecting.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I moved to Pgh from San Francisco in 2010, and every single dealing I've had with AAA since I moved here has been great -- straightforward, super helpful people, and mostly quite brief wait times. + +The agent that I have worked with from the start, whose name I think is Heather (long dark hair, second desk from the left), has always been willing to spend as much time with me as I needed to understand what I was buying and/or the process that I needed to go through. + +Also, my car was totaled a couple of years ago (some jagoff who was texting rear-ended me, ahem, please don't do this), and they were phenomenal. I had a check for the full amount in less than a week. + +I see a lot of negative reviews here for services that are title related. I don't know if those people are even AAA employees, they might be DOT for all we know. I've had three title transactions, including one for a car that was from out of state, and they all went smoothly. + +I've been with AAA for more than 40 years, and when I lived in California I was seriously considering switching. Not anymore.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This library is so close to the east liberty shops and development projects. It is a half a block away from the Borders and Walgreens. You can take out a limit of 50 books and they have tables of fiction bestsellers and a great cookbook selection. Good place to go this summer for something to read and not spend a dime...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Well, I just moved to Shadyside from Oakland so I'm used to perusing the lovely stacks at CLP Main. I finally made my way here a month after moving and was pleased with the selection. It's not as extensive as main, but it couldn't be since it's much more compact! If you want something from another branch you can request to pick it up here. They also had a lot of computers to use, chairs for sitting to read and a decent magazine selection. It's bright, modern, airy and I have no complaints. Other than I couldn't use the self-checkout because it was being wonky, but that's technology for you :)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great place for East Liberty to have this library and it's so close to my house. I love it here. Also it's nice and quiet here. Great addition for the African American community of east liberty. I love the section of books they have. Come down and visit this awesome place!!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've only been there a few times but it was a nice place - good staff, they mix drinks well, and it's a friendly atmosphere.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is one of my favorite bars in Pittsburgh. It's a bit edgier than most of the others bars in the area, which also gives it a lot more character. This place is one of the closest things that reminds me of an urban-artsy feel that I'm used to in Southern CA. + +Shadow supports local artists and has weekly open mics. Only downside is I'm not used to paying a cover for open-mic sessions, but I understand an establishment needs to raise some dough. The drinks are decent and there are many local and big artists that come here for shows. + +Always good vibes at Shadow![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Among the best of the 'burgh. Great live acts on a regular basis.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Dear Shadow Lounge, +I miss you. You're wonderful in every way. The dance parties, the live music, the poetry slams, the local art, the totally reasonable drink prices, the cute and chill proprietor eye candy...I could go on. + +Stay awesome. + +Xoxo, +Andrea[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> As a Brooklyn based live indie-electronic/hiphop performer that travels, Shadow Lounge is by far one of my all time favorites. As a Pittsburgh native remembering it's first opening when it was just bboys, graff heads, MC's and DJ's doing their local thing, it's amazing to see this place has become so professional, original, and really stands-out and is positively active for the community and continuing growth of Pittsburgh. The service is delightful on both sides (AVA/Shadow Lounge), the prices are just right, the sound system is a complete BANGER with crisp and clean sound. The crowd is mad cool and always responsive to good music. Shadow Lounge really holds it down for Pittsburgh's scenes no matter the genre. Can't visit Pittsburgh without stopping by Shadow Lounge.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm a newbie in Pittsburgh and have lived in California almost all of my life. Most recently I was living in the San Francisco Bay Area where dope lounges, clubs, cafes are bountiful. Ever since the first time I stepped foot in Shadow Lounge a sense of familiarity and peace overwhelmed me. Gotta give it up to the owner, Justin, for creating such a unique and welcoming venue in Pittsburgh, I can honestly say that both Shadow and Ava Lounge have become one of my new favorite kick it spots hands down![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It is nothing like the bars in San Francisco, I don't know where you people went. I'm not enough of a scenester to appreciate Shadow Lounge to the fullest, I don't care for poetry slams or open mic. The night I visited, they had a live band playing an early set, it ended at 9pm. + +I was intrigued by the sandwiches they make on one side of the bar - whatever it was smelled amazing and no doubt smells even better after you've had a couple beers. Speaking of beers, on tap selection is small - 4-5 beers and even the fridge wasn't impressing me. They do have full bar however. + +There was also another room with couches and big TV and another club (?) linked to Shadow Lounge that looked more hip-hop and danceclubby. There was no dancing going on though and the room was rather empty.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Shadow lounge brings good music to East Liberty in Pittsburgh. For this, they deserve 3 stars alone. + +However, the one time I was there for a Reggae concert, it was incredibly crowded, but even worse, it was impossible to get a drink at the bar. There were two bartenders trying to serve 300 people. In sum, come for the music only.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great food, timely charming staff, great sound guy, and nice environs! Go here![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Just relocated to Pittsburgh (2010) and heard about this place. Saw two concerts (Bilal and Tobbey Boney) for under $30 bucks each. The drinks are yummy plue DIRT CHEAP! The owner ( dude with a fro/think beard) is really nice. Heck, he's actually pretty hot in a retro/hip/techno/neo soul kinda way. If I wasn't a lesbo...I'd ******.......******** him. hahaha[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great club/bar/lounge/venue. Great mix of people and music with decent bartenders and good prices on beer.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Loved everything from the ownership, to the crowd, to the live music. LOVED how everyone seemed to actually be dancing, and not just standing and staring on the side lines. Did I mention that it was a live 10 person salsa band? Yes, yet another oxymoron: salsa and snow... Again.. Only in Pittsburgh![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Went several nights in a row: Thursday, Saturday & Sunday. I cannot say enough how much I LOVE LOVE LOVE this place!!! Every night was different: African night, Latin Dance, Brass Band (that was amazing). The Ownership is way friendly & open to chatting which I love. The bartenders are open, friendly & genuine...anyone who remembers my name & my drink is a winner in my book! It shows they are listening when they actually ask you a question! The ownership was willing to allow us to order & set on fire a Flaming Dr. Pepper.....had to bring a little Southern treasure North! ;) + +I love the diverse, yet open and friendly crowd each night. I felt right at home. + +Now for the real surprise....THE FOOD!!! + +We ordered the~ + +Tortas 7.00...we got one Chicken & one Steak..both were perfect! + +Sandwiches with your choice of tofu or breaded chicken. Served on toasted bread or multi-grain wrap with melted mozzarella cheese, fried bean spread, avocados, tomatoes, and onions. Topped with a chipotle sauce + +Cheese Steak Torta 9.00 + +Grilled steak served on toasted bread or multi-grain wrap with onions, peppers, mozzarella cheese, fried bean spread, topped with guacamole and chipotle sauce + +I was shocked & amazed at how wonderful this ""bar food"" was. The tortas were great & the guacamole homemade. + +I will be back every time I am in Pittsburgh![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> On Tuesday nights, they have open mic. On my birthday (4-12), I went here to check off another life list item...SPOKEN WORD! I did it! The crowd was open & welcoming to all that performed. There are some awesome artists in Pittsburgh! Also for $5.00, I got a basket of tortilla chips and 3 homemade dips: guacamole, black bean and a verde salsa...all were delicious & for $5.00 it was A LOT![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> They are showing out behind the bar!!! Last night, I had several of their new drinks: key lime pie martini...AMAZING, my best friend is black...DELICIOUS, strawberry, lemonade and basil, not my fav, but tasty. The key lime pie martini and the steak burrito are a great pairing! I continue to love this place, the people there, the overall atmosphere more than any other place I have experienced in the bar/lounge scene.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Combinacion! +This place is the shit for real. +Where's the Patron at??? + +(b)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Absolutely amazing! Great staff and service! Best music in Pittsburgh, hands down. Good work guys![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I wish I were cool enough to hang out here... + +I am not. + +However, that does not stop me from going from time to time and trying to blend in with the cool crowd. + +In all seriousness, this place is great. A laid back vibe with the best music and best bar in town. And when I say best music...I MEAN best music. Best Jazz night in Pittsburgh on Mondays, great classic hip hop, and other genres that you don't hear anywhere else in Pittsburgh. + +The owner is awesome and will talk music with you any time he has a moment. If you are a music nerd, come early and chat it up with Justin. he knows his stuff and will chat it up with you. I promise you will love chatting with him. Very cool guy. + +And of course the bartenders...all great. Very friendly. Will make you whatever you want, or mix up something special and surprise you if you would like. Again...I'm probably not cool enough to hang out with them, but when I am hanging out at the bar, they never remind me of that.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> One of the most eclectic venues in Pittsburgh. Shadow Lounge has a great variety of acts that it pulls in. + +I just went to their Titletown Soul & Funk Party and it was a really great time. Great music, fun crowd, pretty decent prices on drinks. I'll definitely be going back for Titletown and in general, Shadow Lounge is a great place to see alternative acts in Pittsburgh.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Best jazz open mic I've ever seen. Possibly the best in the U.S.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> AVA/ Shadow Lounge is a place that I would take my out of town guest on a Monday night. With the live music and well mixed drinks, it is a place that is sure to be a good time. + +If you're luck to nab a seat/table near the door I would recommend it. Since the live music can be loud, it's a great way to enjoy the band and still carry a conversation. Definitely stop by and check it out- you won't be sorry![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Um, amazing. Is this real life? Or is it just a shadow? Just kidding about that joke. But seriously, I was blown away by the drinks, specials, servers, food, manager, space....that I couldn't understand why it wasn't packed on a Monday night that happened to be Martin Luther King Day! Callen (I think I am spelling her name right) is an incredibly sweet, efficient, and talented bartender; Solomon on the grill whips up a KILLER (but without death; veg friendly) tofu and bean fried taco; and Justin is an offbeat, dry, and very cool bar owner who is interested in providing an open space for his community - they have held a huge number of widely different acts in the past, and plan for more in the future! Look out! Geeeez, guys, AND you have drink specials erry dey? Thank God I got there on $4 margarita night. Nothing impresses me more than a dern good margarita, I don't care if it comes in a tall glass. + +The bar itself (I don't think we're in AVA anymore, Toto...) can get mildly confusing if you don't bother to learn the layout until you're three margaritas deep, so let me advise you in advance: AVA is the part that is glowing green, and feels like a cozy, well, lounge...Shadow Lounge is the rest. There is a large, yellow room containing the main stage, and a blue, intimate room with a half-bar. + +Who wants to go with me on a Wednesday for ~experimental~craft~drink~ night? Oh, and no, they're not hiring.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Enjoyed the winter solstice concert Saturday night. Fun scene, cover benefited charity, drinks were decent (nothing spectacular), but the grilled cheeses moved this review from a three to four star rating. Fun night, cool spot. Will go back![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place is great and gets more diverse crowd than any other place in Pittsburgh. The layout is good, drinks are cool and music is just great. The place is great place to chill out and is not as crazy as south side or station square. + +This place is a hit or miss though. Some days you get lot of fun people and on other days, it is deserted. + +The cover on weekend is mostly $5 though on some special event days, it is $10. + +Overall, AVA is one of the most underrated place in Pittsburgh for night out.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> There were zero other people here aside from my friend and I.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> i was here for a concert the other night. apparently, there's much more to the venue than the side we were on where the stage was, but it was a pretty small area for a pretty big crowd. ok, so we arrived shortly before the opening act and ordered beers. $4 for a yuengling bottle isn't ideal, but whatever. we snagged a table with stools near the door before too many people got there. by the time the opener was over, the place was packed shoulder to shoulder, and whether we stood or remained on our stools, it was nearly impossible to see the stage. +i liked that it was an intimate venue, but that many people packed into such a small space, with expensive drinks, and not even a good view? not the best venue i've ever been to...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I agree with Stacey B. I am not cool enough for this place. I Spoke with Jay Malls briefly, and he was indeed cool ,This is one of the best R&B DJ's since Venus Flytrap. (from ""WKRP in Cincinnati"" ) + +I hope to stop in again soon . It is worth the trip.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It's surprising how long it took me to get here, then I hear a rumor they're moving soon anyway! Geez... way to be behind the times Rachel! + +I've been interested in a bunch of the nights they've hosted before, but have never made way way over. I went to celebrate one Miss Aja J's birthday for Hip Hop vs House night. I'm a big hip hop fan, but not much into house. They had two dueling DJ's and an MC hosting the event. I actually liked the mash up of the two genre's. It was definitely better than just house. + +They have about 5 beers on tap, which I think is impressive for a ""club."" Especially different since it was much more than Miller Light. They actually had a Pumpkin brew on tap, which forgive me for not remember, I was into! At $5.50 it wasn't breaking the bank, but it wasn't a $3 Miller Light fo sho! + +We came a little early, but it seemed like the night really started to pick up around 11pm. Yep, I'm old, I left at 11pm. Lame, I know! + +I hope they find a new home, because I think it's a place we don't have anywhere else and I'm happy to have been finally![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I spent about an hour here. Most of the associates are older men that take pride in there work and are all about customer service and getting the job done. Theses associates were always working and never just standing around talking. Whenever they finished one task, they would ask someone else if they needed help. + +Now if only the key copies they made were accurate...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love this store. I can just spend hours walking around getting ideas of things to either update or change around my house. + +All of the sales associates are very helpful and knowledgeable. Sometimes it's hard to find someone to help you because they are busy helping other customers. + +They even cut keys that actually work.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've done basically a gut renovation of my house over the last year, and the East Liberty Home Depot has made this process ten times more bearable. Most of the staff can give you reasonably good advice about which items or tools you should purchase, they all have a good understanding of where things are in the store, and the return policy is amazing. When you make 3-4 trips per day back to the store, after realizing that the simple wiring of a light that you planned has evolved into an afternoon installation project, having someone who is nice about you returning parts and asking a million questions is such a stress reliever. If you need to use the bathroom when your plumbing at home explodes, you may get one or two odd looks if you bring a toothbrush, but even then the staff seems to have seen everything and maintains their nice and calm demeanor. + +The only reason I wouldn't give it 5 stars is because I was once (out of 50 times) given very bad advice about which stain to use that basically ruined a brand new $1000 wood door, and the appliances tend to be overpriced by comparison to Best Buy and Sears.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love hardware stores. LOVE. But this Home Depot has disappointed me. The location is great, but the floor staff is unhelpful. + +Tonight was a great example of I don't like the floor staff. My vacuum stopped picking up anything but the largest pieces of dust. After opening her up, I quickly realized I needed a new belt. It was pouring down rain, but I put on my rainboots, grabbed an umbrella, and hoofed it over to ye ole Home Depot. I had to stand over the shoulders of five--yep, I counted five--employees in appliances for a full minute before one of them would help me. + +After someone directed me to the vacuum parts, I had two male employees stop by to see if I needed help as I searched for the correct belt. I had the vacuum's name and number written down, as well as the belt style, and had the actual busted belt with me. Yet, each of these men acted like I was some stupid girl. ""Did you unplug the vacuum before you removed the old belt?"" one asked me. Duh. I'm not an idiot. The other later asked, ""Do you always wear bright yellow rainboots when you're doing repairs?"" and snickered. Look, all I said to both gentlemen was ""I'm just looking for the correct style number. But thanks."" + +I received similar treatment I stopped by to buy a new set of bits for my drill. ""You know drills come in more than one kind, right?"" I was asked. And when I needed a new bag of dirt of my cacti, I was question about why I wanted succulent dirt over potting soil. Every time a male employee here approaches me, I'm questioned or given unsolicited advice in a snotty way. + +This girl may wear bright yellow rainboots, but I am also the Norm Abram of my family. AKA I'm pretty handy. Oh, and the vacuum works perfectly now. + +Shout out goes to the check out attendants, who were SUPER polite. Nice work, ladies.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This was my first time to this Home Depot. Very impressed with the customer service here. We were redoing a bathroom and went in for more tiles. They were out of them. However, a staff member helped us use other tile and decorative pieces to compliment the tile we already had, instead of schlepping all the way to Monroeville to pick up the tile up were originally looking for. We were very happy with the result![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Fish out of water here when it comes to hardware related things. I mean I know how to swing a hammer and push a button to start a machine, but all the other stuff...meh. + +I've only really gone in here to pick up paint, so I'll focus on that. I feel bad for the lady that works the paint counter. Each time I'm in there she always seems to be by herself with a line of customers all wanting there base paint tinted. I don't believe there was ever a time I could just walk up to the counter and have my paint mixed for me. Give that woman a hand.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is a pretty good HD. It is somewhat smaller than the ones in Ross Park and Monroeville, but they seem to stock most of the same items. Occasionally I do need to go to Monroeville to find specific items, however. With a 1920s house, I spend quite a bit of time here for getting materials for repairs. + +Customer service is about average. Some people are very helpful, others not so much. In general, they seem to be better than the Lowes at the Waterfront. At least HD people know where items are in the store. I can't tell you how many times I've received completely different (and wrong) answers to finding stuff at Lowes. + +I would prefer a small hardware store (such as an Ace) closer to me for things like nuts, bolts, and screws. Ace seems to have a better selection than HD does for hard-to-find items. HD has most of the basics covered, however, and probably a little cheaper. + +I generally avoid their paint section except for equipment. I prefer the service at a Sherwin-Williams or Masterwork Paint store. + +We've had decent luck with their garden department. We've had to return a few plants that died the day after we planted them, but they have never given us any problems with returns. + +It's a big-box home improvement store, for better or worse. It's a convenient location with a decent selection. 'Nuff said.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Last February I went to The Home Depot with the intent to get a portable AC unit and I left with two lovely house plants and the AC. My plants are doing great thriving and looking good. I got a spider plant and a golden pathos. They had a rather impressive selection of indoors plants. My only regret is that I didn't get a peace lily while I was there. + +I purchased my first ever air conditioner and I'm happy I did so at The Home Depot. I have terrible luck with appliances. In my experience no matter how much I pay , be it $30 or $ 300.00 my appliances always seem to stop running right after the manufactures warranty expires. So I opted for the additional year of coverage which cost peanuts. I believe the additional protection it was less then $15.00 dollars. + +To this day I find it funny that my hubby and I purchased THE LAST PORTABLE AC the store had, remember guys this was last February. So apparently there was a run on ACs last winter. Anyway it's still working great even after I dropped a screw inside of it on accident and I'm happy with my purchase. The staff did a good job helping us find the AC and I'd be more then happy to spend additional dollars at The Home Depot. I might even get that peace lily after all.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I would rather drive out of my way to another Home Depot than give this location my business. + +Employees are unhelpful and the most of them are too busy talking to each other and complaining about their jobs to notice you're standing there in front of them. Strike that... I'm certain they notice, they just don't care. + +I'm a pretty understanding person, but when this sort of thing happens more than once on the same visit, it's time to go. There are plenty of HD's around, seek them out and skip this one (especially if you're going to have questions)![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Most of the home depots i've seen are the same and that includes this one. aisles full of hardware supplies, tools, bathroom accessories and even a small nursery for gardening. + +My favorite section is the tool section seeing that I'm a DIY-er. (Do it yourself) if you didn't already know that. I enjoy building, maintaining and fixing things in my own home as opposed to hiring a contractor and paying a boat load. I'm best known at the Home Depot in monroeville. I come in there so often a lot of the employees know me just by my dog. Yes my dog, who i have brought into this store several times. They allow pets i'm assuming because i've never been asked to leave and I've seen others with their pets as well. + +That's the best part about the store is the animal policy and the fact that they offer enough supplies for you to practically build a house. Some things are cost efficient while others are kinda breaking the bank. There not as modern as lowes but they have alot of the same products. I recently built my own in home bar. t's 8 by 2, a long bar that i (a girl) built by hand. I'm very proud of the work i did. I installed lights and polished it and it has a resin top with ceramic tiles beneath it. It's a real beauty and i got all the supplies at home depot. Cost me about $600 to make but i put it together in 2 months so that's a plus. + +But yea if your in need of some nice plants to go in the kitchen or patio OR you just want to spruce up a few things around the house, then this Mega home repair store is where you ought to be. Between this and lowes its not like you have a choice.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I am not a Home Despot fan in general as I like to favor small hardware stores instead. But I was here with a friend who is in the middle of a home renovation project and needed my help. I was here at an off time and on an off day and the customer service was great. 3 out of the 4 people who helped us really knew what they were talking about. I really felt like I was in a home depot commercial with the friendly workers explaining their products to you and helping you make smart selections. In the course of an hour in the store at least 6 people asked me if I needed help finding something. In Home Depot I often have to walk around for 15 minutes to find a sales person who knows nothing. This Home Depot was quite different from the rest.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> What has happened to the East Liberty Home Depot? It used to be my ""go-to"" place for everything DIY, but no longer. + +I stopped by yesterday to pick up about nine items, all of them basic home improvement supplies: cabinet handles, tension rods, quarter round molding, etc. I came away with NONE of it. Everything we wanted was OUT OF STOCK! When I asked if I could order it and have it delivered to the store (to save the shipping costs) I was told that the items I wanted were not ""qualified"" for delivery to the store. ""When will the items be restocked?"" ""Don't know."" ""Would it be possible to get the items delivered from another store in the region?"" ""No, that 'messes with' our inventory controls."" Oh, but I was told I could haul my sorry butt out to Monroeville where the stock of everything I wanted was plentiful. Really? + +The staff I dealt with could not have cared less about helping me. Maybe because it was a holiday (New Year's Eve). Dunno. Don't care. Customer service should not ebb and flow based on the day/date. + +The East Liberty HD used to have shelves full of product and plenty of choices. And the staff was helpful and eager to engage with customers. No longer. It appears that the company has given up on the location and is letting it die a slow and painful (for its customers) death. + +VERY disappointing to me.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I made the rookie mistake of going to this Home Depot on a sunny afternoon on a Saturday. Enter pure chaos. For starters, this parking lot is the worst. Small spaces with large trucks squeezing in. Seriously, what were they thinking when they made these micro spaces? + +There were people in every which direction aimlessly and some pointedly Cris-crossing every aisle. I WAS able to ask two different employees for help, but you have to grab them, because they're busy. + +The check-out was even more insane. Two lanes with actual employees and then the self-check out, which really shouldn't even be a thing. You try scanning your own yard stick. Yeah, right. + +This particular Home Depot is located just beyond Penn Circle in East Liberty ('Slibery) and is off a one-way street. Don't come here for a relaxing shopping trip. Be prepared for insane parking lot wars and lots of chaos once inside. But if you live in the East End, and need supplies, this is probably your best bet.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Waiting 20 minutes to get one piece of wood cut in an empty store on a Friday afternoon. Priceless![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Fairly mediocre, even by the relatively modest standards of Home Depot. Unfortunately, this is probably the best you're going to do for hardware in most of Pittsburgh.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Tried using the online order store pickup with the hopes of increased efficiency. fail.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've been to the Glass Center perhaps 5 or so times now. I've gone for a tours/demonstrations and two ""Make It Now"" classes. I have thoroughly enjoyed going each and every time. Some of the art they have on display is fantastic. It was interesting the last time I went because local artists were there to sell glass work they made. + +The Make It Now classes are well worth $25. You get to be somewhat involved in creating the object (You get to pick the color, blow the glass, and do a couple of other things. You never get too hot to the ovens or do anything dangerous at all. If you want to be more involved, there are other more advanced classes that you can take), plus you have a wonderful piece of art to take home! I've made an ornament and pumpkin so far and will be making a flower soon. The instructors have all been very nice and helpful as well, making the experience even better. + +I can't wait to go back![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Very modern, super friendly staff, classess offered to public and students alike. Unfortunately they were between shows when we visited, but even then there was a lot to see and the instructor upstairs was quite comfortable working in front of the public. I'd go back, especially if I lived in town.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I LOVE the glass center. I've been lucky enough to attend quite a few events here, and also do a small class where I was able to make an ornament. The staff is always friendly and fun, and I always leave feeling grateful that we have such a unique place here in Pittsburgh![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Most definitely, I'm a fan of this joint. There are fabulous, high-quality displays of glass art, and they offer lots of learning opportunities if you want to make your own glass art or functional glass pieces. Plus, on gallery crawl nights (First Friday of every month!) they have snacks galore.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> A few hours before the event, we happened across the ad in the City Paper and decided to give it a shot. We were excited to get there as the event said we would be making something, there would be food and music, demonstrations, live music, and a gallery. Booking our reservations for 6pm was quick and easy over the phone; $60 for a couple. Upon arrival, we checked in and were asked if we wanted to purchase another item to make; we were confused because we assumed that we would each get to make something. In the end, we chose not to spend the extra $15 to make another garden float/ornament; aka a hollow glass ball. + +When our 'instructor' met with us, he was very friendly but it was loud and he was very hard to hear. He ran through everything at lightning speed and in the end, all we got to do was blow air in a tube for 10 seconds. Had the first attempt not popped, I wouldn't even have been able to do anything! From a teacher's standpoint, there were many other steps in the process that we should have been able to participate in; I would've been happy to sign a waiver if that is part of the issue. Within 15 minutes, our ball was done and we were shuffled out so another couple could have their turn. + +We then worked our way downstairs to the food and drink and there was an assortment of beer, wine, sparkling juices, veggies, fruit, cheese, and some deli meats. The assortment was nice, as we were able to snack on the healthy side, but the beer was still warm. + +The gallery was nice to walk through with work on display from so many talented people, the live music added to the ambiance, and the demonstrations were interesting to watch. + +In the end, it was nice experience, but were severely let down by the make-it/take-it section of the evening (the part we were most excited for!). It really started to bug us, when later in the evening, we saw an older couple getting to do more of the steps in the process (mind you, we aren't young kids, but young professionals). We would have liked to have a small 'info talk' about the steps that will take place, why they are that way, the tools used, maybe some quick science behind it, then get to work on the item.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The Glass Center is a marvelous addition the Pittsburgh cultural scene. They are a gallery, a place to take classes, a center for glass artists in residence, and much more. Whether you are taking a tour, a class, or visiting the gift shop or gallery, there's a lot to see and learn here. I've taken tours several times with different groups, but I always learn something new and I am always impressed by the great work takes place at the Center. + +They will take students at every level. Their facility is well run and professionally staffed. I was delighted to meet their enthusiastic staff. + +There's a hot shop, a cold shop, a flame shop, and a gallery, so there's lots to see and learn.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I went to a yelp event here, where we were able to make a fused glass piece and also watch some demonstrations and go to the gallery. Everything in the gallery was amazing. The demonstrations were neat, and the fused glass was something I would go back to do again. + +I really didn't know that the glass center was open most of the time, and if you go there on any random day, you can watch whatever is going on. I think that is pretty cool! They also have classes where you can blow glass or make beads or whatever you want... I can't wait to pick up my piece and come back for another class![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Went here with my girlfriends last Saturday. They were having a girls night event. A small bar & desserts were included in the price. It was $40 per person. We loved it! We worked closely with a glass artist. We didn't just watch, we were acutally doing it! We made glass flowers, I can't wait to pick mine up! (It takes a few days.) I definitely recommend this as something different to do with friends or on a date! My one friend did a glass blowing event there & said that this was much more HANDS ON than the glass blowing was.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place does gorgeous updos for $25 apiece. My bridesmaids and I went there on the day of (with no trial run beforehand) and we all had beautiful hair exactly the way we wanted it. The hairdressers are so friendly and attentive and so accommodating in letting 5 of us take over their relatively small shop for 2 hours on a Saturday. I was so happy to find them, and so happy not to pay $60+ a pop for wedding party hair![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Got my hair done in an updo (for only $25!!!!) yesterday for my wedding. they did amazing! they listened to what i wanted and although it took quite a while (i have really long hair) she spent the time to do it right and exactly how i wanted it. great service!! The price is not high but the quality is![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Michelle is a godsend; went in for a simple, fuss-less updo and was stunned by the result. She is quite the perfectionist, and for $25, her mastery is bizarrely affordable. Forever bookmarked. (Note: street parking can be fairly difficult to find on S. Highland so scour the smaller adjacent streets for a free 2 hours.)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great for a quick cut. $22 for extreme attention to detail and excellent finish.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Rosemary is amazing for updos. Only $25 a piece but great attention to detail![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> These dudes are the best. + +Great service, great explanations, and their prices are the best in town for an oil change (though this does mean that for oil changes they're always super busy - because they're awesome!) + +Highly recommended over nearly any other automotive care company in the vicinity - I've tried them all. These guys are the best.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I kinda accidentally walked in ten minutes before these guys closed, asking for an oil change. Oops :/ +Like the awesome guys that they are though, they let me know that, while they would do it quickly (like, not check anything else), they would still be okay with doing it. The guy was super nice about it. +After all of this, he took me out to look over everything, was super friendly, and answered all of my questions. +They are great. I will be back if I'm ever in this area when I need anything.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place is outstanding. I always get great discounts, and all the mechanics are very honest and helpful. I am certainly not rich and Marvin is always willing to assist me with my budget and what needs to be done on my vehicle. I've been given very specific directions on whatever needs to be worked on, taken back to the garage and allowed to see the old/new parts with no hassle. I would definitely recommend going here.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I ordered 2 pizza's from here today to take to some friends who are volunteering for the election. Everything was ready in less than 30 mins. The pizza was good - nothing fancy - not too greasy, sauce was good. I should have ordered the large instead of the medium. I would definitely order from here again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is the greasiest pizza I've ever had in Pittsburgh, I couldn't eat it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Provolone sticks arrived undercooked, cheese was fully solid, they tasted okay. The pizza also arrived undercooked, the dough itself was partially uncooked in the middle. I had to put it back into my own oven to finish it off, and then it was greasy and just okay.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Worst pizza I've had in Pittsburgh. I ordered from here last weekend. The pizza (pepperoni) had no flavor and the crust was way too chewy. The Buffalo wings were cooked well, and were tender and juicy, but they had almost no sauce on them whatsoever; luckily I had some wing sauce in my fridge in order to save them. + +Maybe it was one bad night, and I can give them another chance later, but based on my one experience, I can't recommend this place to anyone.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I order from these guys on campusfood.com +They are pretty good .. i get my order on time and their quality has been pretty consistent +I mostly get things like hoagies and pizzas.. they are pretty decent +This place is pretty convenient for me when I am working on campus late at night when most other places have shut down.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great Hoagies! + +I always get the Steak Deluxe hoagie and my wife gets the Italian Deluxe and then we give each other half of the other ones hoagie because we can never decide on with one to get.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Ahh, the only place near the train station that is open past 9 PM, isn't overpriced and/or full of people who are way too jolly for such an early hour. I got a slice of cheese pizza and onion rings. The pizza was decent. There was nothing flavorful about the sauce and the grease would not stop oozing out of the cheese. I felt sick before I got halfway through it. That reminds me - the slices are HUGE, and are $2. The onion rings were extremely basic - I gave most of them to a couple of drunken girls who debated about what to eat for half an hour. +One irritating thing I overheard: as a girl was trying to place an order, the cashier kept interrupting her to say things like ""we don't have those anymore"" or ""no, we can't cook wings dry."" Sounds like the menu and staff needs to be updated.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I had some pizza from Pizza Parma today during a lunch meeting at work. A colleague brought it in, so I didn't pay for it and can't comment on the price. I had a few slices of the pepperoni pizza and found them to be resoundingly average. Nothing special, nothing especially good or bad. Crust, sauce, cheese, pepperoni, fin. It was a little greasy, and quite cheesy as well. I was starving so I really enjoyed it, but I think overall the pizza is pretty generic. Still, for a late night slice or if you live nearby and just need to pick up a quick pizza for dinner, I'd say go for it. Just don't have very high expectations.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Pizza Parma has many of the characteristics I like in a pizza joint. +1) They deliver when they say they will, +2) Diverse menu and toppings, +3) Coupons, +4) Online ordering, and +5) Take credit cards. + +I think Pizza Parma shines with their specialty pizzas. Artichoke, Buffalo Chicken, Spinach & Feta, and Greek pies are all delicious. I've also had some of their pasta dishes, and I can't complain. It's nice to have something other than pizza delivered; the portions are huge, and they come with bread and a salad. Pizza Parma fails on wings, though. The texture is unappealing (aka, flappy chicken skin-- yuk!), and the sauces lack depth. Desserts are also not worth the buy.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I like the pizza and the selection of toppings. They are reliable. Great option for take out food.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This was one of first pizza places that I've tried inPittsburgh. It was about 5 years ago. I don't have a clear memory of that time but I have Parma pizza phobia ever since... So go figure...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've should have known better than to order a salad from a pizza joint. I also should have known that I shouldn't have cheated on my diet. + +I figured I'd choose today to be my cheat day and order with everyone else at work for take out. I opted for the Popcorn Chicken Salad. Sounds tasty, looked tasty, and yes it even tasted tasty. Iceberg lettuce, grape tomatoes, cucumbers, red onions, french fries, popcorn chicken, and three types of cheese. + +I have to say that even though I was saying yes, my body was saying, 'OH hell no!' + +I'm regretting this decision now as I am sitting here in discomfort. Not sure what on the salad made me feel this way. But I'm not liking the effect I'm getting right now. Could just be karma turning around and kicking me in the ass for eating what looked healthy but was really nothing more than the equivalent of a fried chicken sandwich combo meal from a fast food joint. + +I'll think twice before the next time rolls around to order from here.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Good food[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Three stars is super accurate for this place. We decided to do take out from here after walking by it a hundred times after the gym and hearing radio commercials about it from that god forsaken BUBBA SHOW (does that plug raise anyone else's blood pressure??) Our order was ready in 15 minutes (speedy!) and we got a large 1 topping pizza for ~$8 and a side of fries. All together like $13 for three people, which is pretty good. As for the pizza, the crust was crispy and not too thick or thin, and the sauce was sweet, not seasoned. I prefer a more herby sauce myself, so I wasn't wowed by it. The fries were a bit soggy, but tasty. Overall, if I were in a pinch I'd order from here no problem but it's not a place I'd set out to order from because I love it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Pizza Parma delivers through GrubHub, which is the primary reason I ordered sandwiches from them. BBQ chicken was ok. The bread is a little more on the burnt than toasted side, leading it to be dry. The value is good. The 20"" sandwich was about $11.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> If you find yourself craving pizza on a Saturday night, you can't beat $9 for a large cheese pizza. I also enjoy the hoagies as they are lightly toasted for a nice crunch. + +I can't speak for the pastas or appetizers, but the Pittsburgh style grilled chicken salad is a dependable choice.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great friendly service and my order was done fast, which was amazing since I was a walk-in. Lots of toppings piled high but I wish there was more cheese. They did have small bottles of vanilla Coke, which is a rare find these days.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have to say, I maybe (/definitely) had these guys programmed into my phone when I lived over in Shadyside. I term this branch ""Good Ole Faithful,"" as they have come to my aid during many times of need, which possibly includes Saturday nights at 2am (sorry for having to deal with me, guys). The pizza is freakin cheap and pretty damn good, especially for the price. I maybe (/definitely) use to call them every Monday when they had an extra-large one-topping pizza AND an order of bread sticks for only 9.99...... 9.99! I'm not sure that they still run this deal, but I could generally get a large cheese for about 10 bucks, and you can't really beat that. Not too greasy, just enough but not too much cheese, their pizza (and actually other food items, which is surprisingly quite extensive) is better than average and tasty for a night in alone or stumbling in with friends after a night out. I usually just walked over, where's it's perfectly nestled in the shopping center across from Mad Mex and Buffalo Blues on S. Highland- however, they deliver too- and both options are surprisingly quick. Enjoy![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Take out and delivery only. Good pizza and our go-to for delivery. Love the hungry man special- cheese pizza, breadsticks, hoagie, and a two liter for $23. Pizza is good- cheesy and delicious. I like the sausage pizza here as well. The steak and meatball hoagies are our favorites. Service is fast and friendly.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> When my boyfriend and I were down with the flu, we ordered some food here through Eat24. I got a chicken noodle soup and he got the seafood calzone. When I unpacked the food and tried a sip of my soup, I found that it was cold and had bubbles in it, as if there was soap in it. I couldn't really taste anything, but my boyfriend said it smelled like dishwater. To say the least, I was disappointed in my soup. When my boyfriend cut into his calzone, he said the cheese was barely melted. We thought it was undercooked and touched the outside. It was cold, as if it was sitting out in the open for a long time. He tried to take a bite, but the dough was barely even cooked and the contents of the seafood calzone was cold and tasted sour. +This was our first time ordering from here and it was such a sad experience to have, since our food was inedible. I heard this place was good and had great calzones and tasty soup, but what we received was the complete opposite from the praise I've heard about this place.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Some friends and I ordered a couple of pizzas for delivery from here tonight. We'd bought a few growlers of hard cider from a local establishment, and we were looking for some fuel to help us soak up the booze. My friend suggested getting pizza from here, and I didn't object, since I'd never had pizza from here before, and I'd heard the pizza from here was consistently decent. + +The pizza showed up about 45 min. after we ordered it, right about at the time estimated, so no complaints there. As for the pizza itself, it was solidly A-OK--nothing special, but nothing horrible, either. It was a bit on the greasy side, and I could tell from pulling the first piece away from the pie that the crust wasn't crispy. Biting into my first slice of pepperoni pizza confirmed my suspicions about the floppiness of the crust. As for the flavor, it was your standard pizza flavor--again, nothing special, but nothing horrible, either. It was more greasy than I'd like, but not to the point where I felt it necessary to dab off the grease with a napkin (though I was tempted to do so). + +As the bottom line, the pizza was fine for our purposes (to soak up alcohol). It was better than Vocelli's, and about on par with Papa John's. I wouldn't go out of my way to order from here again, but I wouldn't object to it, either.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I am not a mean person, not a vindictive person. I bear the friendly people of Pizza Parma no ill will. + +But their pizza was remarkably terrible. + +Went there, hungry, a bit past midnight, looking for a little something before going home to sleep. They don't have slices--this seems to be a (terrible, stupefying, egregious) trend in these parts. Fine. The smallest pizza, a ""personal"" pie, costs $7 and is 7"" in diameter. The cashier and I agree that that's a very small amount of pizza, and since I'm hungrier than one and one half mouthsful, I get a ""small,"" which is 10"". I add a mushroom topping. I pay my $11.21 and wait. + +There are two seating options inside the store: a small wooden bench, and two fold up chairs around a little table. Conveniently, they were using the wooden bench to store a rolled up carpet that laid across the whole thing, and they'd also elected to fold up the two folding chairs, probably because they were tired from a long day of being used as chairs. So I waited outside the store on a bench. + +The friendly cashier and the friendly patrons waiting for their order indoors called me over when my pizza was ready. I took it outside, sitting in the cold to eat it, thinking, ""I hope this $11 pizza is pretty good."" Opened up the box, saw how pitifully small a 10"" pizza is, and started eating. + +Let me say something about pizza: if you have decent cheese, decent tomato sauce, flour, water, and a hot oven, you can make a passable pizza. I will eat it and think, ""well this isn't the best pizza I've ever had but it's fine."" That is not what I thought when I ate Pizza Parma's pizza. I thought, ""it would be too rude and insulting to ask for my money back. I'll just try to eat as much of this as I can."" + +I ate three out of the six ""slices."" (One sixth of a 10"" pizza is a total of *25/6 = 13 square inches. That sounds like a lot of pizza, but in fact is a tiny amount of pizza.) I couldn't stand to eat more than half. The mushrooms were fine; I fished them out and ate them. The cheese was actually terrible; it had a strange chemical taste and plasticky appearance. The crust was poofy and not crusty. + +Ashamedly, I threw half of a pizza away tonight. Folks, I am not a food destroyer. I eat things I don't like, and expired foods, because I don't want to waste. It takes a legitimately terrible pizza for me to actually throw the thing away. + +Went home, made some eggs, and guess what? The terrible cheese taste from an hour and a half ago? It's still in my mouth. I'm not making this up. + +I know there's good pizza around here. Ordered two back to back slices at Spak Brothers--delicious! Tasty! Reasonable price! But whoaaaaaaa whoa was this terrible, overexpensive pizza. Sheesh.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place is bright and clean and I've seen staff taking care of machines every time I've been there (different times/different days) so I imagine it's well maintained in general. Love that there are bus stops directly in front of and across the street AND that this is a 24-hour place. I usually spend $7.50 every 2 weeks* though I could probably get away with using the single load machines and a few minutes less in the dryer. I especially appreciate the good spin cycle from these washers as that means less time it has to be in the dryer! + +Around here, you can walk around the 'hood while waiting for your cycle to finish (pizza place, convenience store, coffee/ice cream shops next door, Border's bookstore down the block, more shops on Ellsworth nearby) + +*I'm a female doing laundry for 1 so it takes a while to have enough for separate whites/color load. I've also been to The Laundry Factory a few blocks away and I prefer Econowash over The Laundry Factory.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I was all set to want to give this place 3 stars simply because another laundry place put me in a bind and this place was open 24 hrs. I thought the late hours alone should give it a star. Then I had this experience + +--Poor ventilation I could barely breath its cramped and small with dryers and washers lining two narrow corridors. + +---- misleading advertising it boasts ""high capacity"" washers an says its air conditioned, well the air conditioners and vents in the ceiling both were dripping in black dust and look like they were installed in 1963. which might have been why I felt an instant asthma attack coming on. + +Then the high capacity washers were all of 2.... not great enough to meet demand as it turns out one girl took up both of them while I was waiting. Then another woman waited for hers to wash and took up two again this was at 1030-11:00 pm at night so I can only Imagine what its like to try and get one at other hours. + +Then there was this guy I guess he was an attendant or the owner, he was wiping down the machines and dryers. I was moving my clothes out of the dryer and I had put my bras hangers and a few shirts on top of my washer. I was literally loading right in the same area and was heading back to grab my things when he touched them!! + +Ugh laundry violation ya don't touch someone's wet clothes it feels like that time in college when someone would mess with you and dump your clothes behind the washers if you didn't move them out quickly enough. Sooo that pissed me off...... but I have to get the job done so I load up my clothes. + +I come back in to check on drying clothes.... and what do I find but my dryer mysteriously switched from high heat to low heat. Now I am forced to put in another quarter to finish my load. All in all I spent 8$ at the econowash for 2 large loads I wasn't able to do my third load in the washers he had for under that. I can do that much at Laundry Factory around the corner though. So I will be going there. I don't need a creepy dude changing my dryer settings and touching my stuff.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> So, unfortunately I've had to outsource my laundry-doing in the last couple of weeks because the dryer in my building has broken down and my not-so-prudent landlord hasn't been helpful at all in repairs (ugh!!). Twice in the last two weeks, I've washed loads of laundry late at night and discovered my dryer hasn't worked. It's really great to know that this place is right down the street and is open 24/7, especially when the Laundry Factory down the street closes at about 9pm (which in general I much prefer to this place). But for convenience-sake, I appreciate this place. On the cons list, it's not incredibly clean and I have used dryers that simply don't work here.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Believe it or not, this whole foods is actually one of the most successful ones. the location is strange, but it's pretty central for most of the yuppier areas of pittsburgh, and it's the only one in the pittsburgh area. Just for that, they get 5 stars.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I think the only thing I appreciate about Whole Foods is entering the store and seeing their fresh cut flowers. Let's see why..... + +I attempt to drive to Whole Foods only to be caught in a line of 5-6 cars attempting to get into the parking lot. (I guess I'm not cool enough to ride Pat Transit from the South Pittsburgh home). When I find a place to park, after the Lexus SUV (HA!) pulls out, I find that they didn't put their cart back. + +So I enter the store and admire how their design is very appealing to the eyes (how DO organic oranges get so ROUND and so ORANGE) and everything is stacked so neatly. Then I read that a pound of these oranges are $1.99... Then I go to the meat section, which I don't even eat, to find that the prices are double those of Trader Joe's or even Market District (see future review). So I walk around and debate to see if I should buy Clif Bars and Naked Juice (which happens to be on sale) because LORD KNOWS I don't need bulk-blanched-almonds. But then I decide to buy ""fresh"" CHUNKY peanut butter because it would be fun to try. (When I get home later, however, I bought Valencia peanut butter, whatever the hell that is, and cannot stomach it. Gimmie my Jif.) So while I am waiting in line, I see the bikes (those rebellious urbanites moved from Quiet Storm) and wonder if my money is better spent elsewhere. + +Regardless, I whole-heartedly (no pun intended) support organic and sustainable farming, but I'd rather go to the farmer's market or drive a bit further out of the city to go somewhere real to buy my ""whole food"". And at least I put my cart back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place is a God-sent for a California girl like me. And kudos to them for not being ""afraid"" of East Liberty. + +Prices are important, but I care more about what I put in my body. So I get my special needs stuff here, and my basics elsewhere. I can't ding them for costs because you pay for quality. But if cheap costing food matters more than lard, transfats, or hormones found within it, you can always just shop at that other store down the street.... + +There's a nice sized cafe area, and plenty of space for bikers to park. Cheers to them for friendly & knowledgeable staff and customer discounts for bringing your own bags. + +True, the parking lot is a mess, but I attribute that more to: +a) People not knowing how to drive. Because you CAN drive to the back of the parking lot, park, and get inside in half the time it takes to sit in line like a moron who doesn't understand how to drive AROUND a car waiting to park.... and +b) Pittsburgh's lack of urban planning... because it makes sooooo much sense to put an entering & exiting driveway 25 feet away from a three-way intersection on a two lane street. Beautiful.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I like Whole Foods. But if you can help it, don't go on the weekends. It's a complete zoo on the weekends. Don't even bother going there on Mondays, bec. so much of it is picked cleaned by the locust hoards that come in from the outlying suburbs. + +At first I was a bit sceptical about Whole Foods w/ its apt nickname ""Whole Paycheck."" However not everything is super expensive and some things are cheaper than Giant Eagle or Trader Joes. I really love their 365 Brand and I'm just resigned to not being able to buy everything I want at one grocery store. Eg. I would love it if Whole Foods sold non-frozen Ezekiel's bread. + +I actually buy a lot of basics here and some of them end up being cheaper than Trader Joe's or Giant Eagle. + +Things I always buy at Whole Foods and no where else, bec. I have found it way better in price/quality: +-365 Brand Tofu (MUCH better that Trader Joe's tofu that has weird texture) +-365 Brand dried beans/canned beans +-365 Brand butter (no BST) +-365 Brand Edamame (is far better than Trader Joe's Edamame which has a strange smell). +-365 Brand whole wheat flour + +Of course I prefer Trader Joe's for their peanut butter(bec. it has no salt) and Ezekiel's bread. And I do end up buying their coffee, bec. it's slightly cheaper than the Allegro Coffee at Whole Foods. However, the Allegro Ethiopian Harrar is quite good.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I recently visited Whole Foods for the first time in my life, and I was pleasantly surprised. I was particularly shocked by the prices--not because they're worthy of the ""Whole Paycheck"" nickname, but because they're surprisingly low. Perhaps the nickname was developed by people who'd previously only shopped at cheap-o supermarkets. + +I like the well-stocked salad bar and dining area, and so does the rest of Pittsburgh, apparently. Half the city was assembling salads during my last visit. Vegan items are clearly marked as such, and everything is fresh.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I don't know, maybe I'm not clear on the concept of Whole Foods. Don't get me wrong, there's nothing really wrong with shopping at Whole Foods. Whole Foods does have wonderful merchandise, but... + +I have found that I can buy a lot of the same organic things and environmentally safe cleaners at Giant Eagle for less. + +Thier wine and beer selection, supposedly quite remarkable in other states, well remember, this is Pennsylvania. You can't buy those things at the grocery store. + +I can get just as good quality meat and produce in the Strip District. Sometimes, even better quality. + +I guess the benefit of Whole Foods is that you can find a lot under one roof and don't have to spend a lot of time and gas going to different stores. I'm not slamming Whole Foods at all, but I actually like Trader Joe's better.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I loved Whole Foods in Ohio. It was calm and quiet and had lots of pretty organic produce. + +Here? Well, first of all, the parking lot is a death-trap full of upscale SUVs who have no idea how to drive courteously. (A few pointers: use your turn signals, wait your turn, drive slowly in a parking lot, and put your cart back!) My blood pressure skyrockets the second I even try to pull in here. + +Secondly, the whole store seems weirdly dark. I don't know if it's the high, exposed-ductwork ceiling or what, but it's depressing. + +Thirdly, they offer plenty of bulk beans and nuts, but few varieties of rice. + +There are a few good points, though. The sushi (at least the vegetarian varieties) are good, and the desserts are delicious and beautiful. The salad bar and prepared foods always look good, and the staff is friendly. But I still try to avoid Whole Foods as much as possible simply because of the insane parking lot.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Everybody, chill out. This is a trendy place to shop, yes, but it also has better prices on some things than Giant Eagle or Trader Joe's (Gasp!). I split my time between Here, Giant Eagle and Trader Joe's pretty evenly, depending on what specialty items I might need. + +Oh yeah, don't drive here. Walk, ride your bike or take the bus. If you're really smart, you'll avoid the headache and park on one of the many adjacent side streets.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> AH! I am never shopping anywhere else for groceries ever again (except if I want like ketchup and bologna and stuff-- then I'll have to go to giant eagle.) But, after coming from the middle of nowhere midwest, I cannot tell you how good it feels to see cheese and meat in the grocery store that I actually want to eat. + +AH![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Whole paycheck is a fitting name. + +This Whole Foods is decent for regular items but their prepared food prices have gotten really high as of late. + +I used to shop here for almost everything but their common products can now be had at almost any other grocery store for less. + +Whole Foods had it's day as a unique place to shop with hard to find organic produce and products. + +Now it's just more expensive.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I always used to avoid Whole Foods because I thought it was way more expensive than Giant Eagle or Trader Joe's. I recently moved to a new apartment and made a quick run to Whole Foods to stock up on groceries. It's now the closest grocery store to me, so I figured, why not just this once? + +There was tons of interesting looking stuff, and I found myself getting carried away and filling up my cart way more than I had intended. I braced myself for the total in the checkout line and was pleasantly surprised when it wasn't much more than I typically spend at Giant Eagle. On top of that, the produce stayed fresh for way longer than GE's typically does! From now on I'm going to stick with WF for all my fresh produce needs (along with a few other specialty items -- some of their frozen Indian food is surprisingly good), but I'll still go to GE for my everyday grocery shopping. + +Sure, their parking lot is a madhouse, but so is the Market District's.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Compared to other Whole Foods locations, this one is tiny! For comparison, the Whole Foods in Las Vegas must be at least three times the size. Still, it's nice to have and it is pretty decent overall albeit pricey.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Hello! + +I work pretty close to Whole Foods so I frequent it about 3-4 times a week for lunch. If you're there M-F between 12-1, you can find me in the salad/bread area (on the north end). + +Compared to other Whole Foods I've been to, I would actually rate it a 3 but considering I do not know of any other Whole Foods around, I thought it's my duty to those that do not know about Whole Foods a chance to give it a try. If the zucchinis at Market District looked a little weak, give Whole Foods a try. Plus their pre-made food is actually yummy. + +I'm able to keep my lunch on a budget by only buying lettuce and chicken from the salad bar (typically under 1/2 pound). I stash dressing, cranberries, and cheese in my office. I've tried buying the bag of pre-washed lettuce but I never finish them and I hate seeing them go bad. $3 lunches isn't bad at all. + +Other notes: The tofu chicken is really good (part of the salad bar)! It's not always available though. Also, none of their bread varieties impress me. I like their sushi rolls. If I could afford $8/day lunches, I'd probably have it everyday. I'd give their cashiers 5 stars. =)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I used to think that Whole Foods was too expensive and only for vegetarians. Boy was I wrong! I freaking love this place. They have everything from fresh meats, cheeses, fruits, produce and so much more. Their cakes and other deserts are utterly amazing. + +This is also where I fell in love with Naked Juices. They are delicious. +The only thing I don't like is that parking is a bitch at times.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> 3.5 stars, actually. Would be 4 but I had to knock off half a star because of the parking situation. The lot sucks, I used to work at Whole Foods and I can not recall how many times I almost got hit by a car when retrieving carts. I am one of the lucky ones, I know of a few people who weren't so lucky. + +I'm a huge fan of the salad and hot bar - not a fan of the price though. To be fair, I can only blame myself for ending up with an $11 salad (but everything is so good and actually fresh I can't stop myself from piling it on). The prepared sandwich's are pretty awesome too and if you go after 9p, they are buy 1 get 1. + +I now work with a lot of children on special diets and I have no problem finding lots of GFCF treats for them here. + +Groceries range from expensive to moderate depending on the brand. The WFM's 365 line is an excellent bargain. + +The bakery is full of tasty treats. You've gotta try the pumpkin pumpkin pie, though I believe it is only available around the holidays. + +The whole store gets crazy busy on and around holidays.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Worst parking lot in Pittsburgh. Bring popcorn to watch middle-aged, self-important mouth breathers gun their BMWs at one another to illegally park in the handicapped spots .If one didn't know better, one could mistake the parking lot drama for a permanent, outdoor performance art installation (allbeit an extraordinarily douchey one). Snotty clientele, over priced prepared items, no longer have a monopoly on ANY product in Pittsburgh. That being said, they do have a great selection of produce, probably the best in Pittsburgh, but you'll pay dearly for it. 1 very large, organic, honeycrisp apple you ask? Try $5, for real. If you want to sum up Whole Foods, just remember it's a place where you can literally spend $5 on an apple. Also, the CEO John Mackey voted for MItt Romney (http://www.nytimes.com/2013/01/20/magazine/john-mackey-the-kale-king.html?_r=0), so if you think you're shopping in a mecca of neo-progressive, pre-utopian bliss, think again. Waste of time AND money overall.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Food poisoning a la Tomato Bisque Soup. + +Forever skeptical. + +That's too bad, I don't mind paying extra for better produce or better brands. But, I KIND OF mind getting extremely sick, so sick that anything I ever would vouch for goes down the toilet, with my vomit.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great selection of vegan, vegetarian, raw milk, prepared foods, bakery, cheeses and aged beef. Very expensive, trader Joe's and Market district come to mind as a cheaper alternative. Parking at this particular store is a nightmare.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My next stop today was Whole foods to replenish my vitamins. I really hate coming here. It's always packed and people drive like humongous IDIOTS! I quickly grabbed my blood builder, biotin, and vitamin C. I tried to walk around and check out the hot foods, sushi, and anything I might like for lunch but I felt like I was at a crowded concert hall! People were bumping into me right to left! If I stopped to ponder in one spot someone was on my ass staring me down. + +Sooo not in the mood so I hurried up and got out. While pulling out of my parking spot two drivers who wanted my spot basically blocked me in fighting for it, and the one lady started pulling back and nearly hit my car. Oh NO WAY! I decided that my usual neighborhood store would not fail me, so to co op I drove...fast! + +Ha ha just looked over my review. It sounds bad but I have to give props for my vitamin selection craze![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I find it really easy to save money at Whole Foods. Did you know that you can stack a Whole Foods coupon with a manufacturer's coupon? If you google ""Whole Foods deals,"" you'll find a whole slew of couponing blogs that tell you where to find the coupons. Most are available online too, so no worrying if you can find the coupon section from last month's Sunday paper. + +I don't find their prices that outrageous compared to other stores in the area for the things I shop for. The 365 brand is a good value and oh, do I love the bulk bins. + +This store barely compares to the Whole Foods in other cities, but its a start! I don't get here as often as I like since I'm in the South Hills. However, when I do go, I try to get here before 10 a.m. on a weekend to avoid the parking lot craziness.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> everything is a cluster. the store. the parking lot. the people -- customers included. full-on cluster. barely any parking for a massive, heavily polluting pick up truck. + +inside: avocados are the price of gold, and there are no goddamn vegan taco spices at a place that's supposed to be so fancy. + +meh. go to market district where they keep it real. real classy!!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I like this Whole Foods for the most part. Prices can be so so, but the selection for unique items is great! However, a lot of the organic items can now be found at many Giant Eagles for much less expense.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Will Whole Foods Market ever replace Giant Eagle as my regular grocery store? No way! I'm a cheap grad student! + +However, I was pleasantly surprised when I walked in for the first time, out of boredom/curiosity. I only bothered checking out the produce. Of course, the regular prices are more expensive than geagle and probably also Trader Joe's, but not totally absurd. For example: Whole Foods organic apples -- $1.99/lb. Giant Eagle conventional apples -- $1.69/lb. I'm ok with paying $0.30/lb more for those organic apples! They also had some local conventional fruits on sale for cheap when I went. Overall, a decent place to shop. You can probably find at least a few things worth getting here. + +Update: After a few more visits, I've found that a surprising number of items are cheaper or the same price at Whole Foods compared to Giant Eagle, including: pecans, WF milk, and semi-sweet chocolate chips.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place gets five stars as it really is the only place in Pittsburgh that I can get the same veggie selection that I can out in Seattle. Without this whole foods I would be an unhappy camper... I am specifically talking about the magic that is Field Roast vegan grain 'meat'. + +Yes, it is generally more expensive but what do you expect? They are a specialty store. They have a great deli and an outstanding selection of baked goods. + +It is an oasis for someone like me.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> MEAN CUSTOMERS -ALOOF WORKERS+GOOD FOOD = CRAZY! + +Official Rant of an Angry Woman: + +First off - I shop at ""Whole Paycheck"" cause my household eats organic and whether I like it or not WF has the best organic food prices in my neck of the woods. IT'S STILL GOD DAMN RIDICULOUS EXPENSIVE but I take my family units nutrition and health seriously! WORD!! + +Downhill from here... + +THE CUSTOMERS AND PARKING LOT ARE MORE BAT SHIT CRAZY THAN MENTAL HOSPITALS I'VE WORKED AT! + +I have watched more rich bitch elderly women NEARLY murder pedestrians and crash into cars trying to park their Lincoln Continentals in that parking lot than I'd ever care to witness! + +Also - I am a mother with a young child and have been SHOVED by above mentioned rich bitches while reaching for products out of the freezer cases WITH MY CHILD IN MY ARMS! I briefly entertained SHANKING said bitch but alas prison orange is not in my color wheel! + +The customers are the worst human beings on earth (::thinks about self, shakes head, laughs...except me of course::). YOU KNOW WHO YOU ARE SHADYSIDE HAGS! You treat the employees like dogs - like one level above dirt. If I worked there I would hang myself in the cheese section! The customers are the worst cross section of Pittsburghers ever!!! + +That said- I understand why the employees are like stunned fish - keeping things close to the vest so that RICH BITCH SHADYSIDE MONSTERS don't feast on their flesh in fits of rage! + +BUT I WOULD LIKE TO POINT OUT...one female cashier who shall remain nameless SHIT on me and treated me like a tree killing whore when I handed her one Internet print out coupon on a single sheet of computer paper - she ROLLED her eyes and PAINSTAKINGLY tore my coupon out of the paper and then folded the unused paper and placed it in her pocket! I am a tree hugger getting judged by a tree hugger! FUKISUMA you! I'm a mom trying to do right for my family - feed them healthy -GO TO HELL! + +If you see a woman and child dressed like Rambo and Baby Rambo running through WF screaming and wielding gallons of milk - it's me trying to survive another trip to WHOLE PAYCHECK HELL![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Yes I am a fan and yes I am Shadyside yuppie. Judge me if you want. +I love everything about WF and it is my go-to grocery store. I try not to give my business to GE. WF's hot bar has fed me many many dinners, in exchange for money of course. However, that is what I call money well spent. I agree with the other reviewers that the parking lot can be a little crazy, but I live around here, and it's the norm. I am just glad that there is a huge double decker parking lot. Also, you can always park farther away and not have to deal with the mess. It's good for health! The produce is fresh and for regular grocery you have a wide variety of healthy choices. The cherry on top is that the staff is always friendly, super helpful and happy![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Whole Foods isn't exactly mainstream or accessible to everyone (particularly if you don't live in a city of good size), but it at least seems pretty widely known. Considering this, I'll veer from describing their products and cut to my pros and cons. + +Pros: +Lots of natural (and not so natural sometimes--still need to check your labels) health and beauty products in one spot. +Impressive amount of otherwise hard to find items in these areas: grains, olives, cheeses, organic meat, organic produce, international dry goods, teas, non-HFCS drinks. +Friendly staff who are knowledgeable, or willing to track down the right person to help if you have questions about a product. + +Cons: +The parking lot could never be big enough. Look for the song about this on youtube; it is true of all Whole Foods. +The vegetarian selection for the food bar has sunk really low in the past 6 months (fewer options, what is there sits out too long and isn't fresh, items that the do make aren't as good as items they removed from menu). +The food bar is super expensive...for a food bar. +Across the board, prices are too expensive for all products. + +As for the three star rating, no Whole Foods will ever wow me. If you are looking for a shop to be impressed with that is similar, look to the models of 17th Street Market in Tucson, AZ or Berkeley Bowl in Oakland, CA. They do basically the same stuff and more, all for a lot less money. In Tucson, I bought strictly organic groceries and you can purchase almost twice as much fresh produce for the same price. I'll use the Whole Foods because I haven't found a good alternative in Pittsburgh, but that doesn't mean I have respect for it like the other places I named.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> What's the most dangerous area in Pittsburgh--the Hill District? Homewood? Garfield? Wrong. it's the Whole Foods parking lot. Since I drive a Mini Cooper, it's considerably easier for me to zip around and dodge the Lexus SUVs that fly at you from every angle in this jungle of a parking lot, but I'm not sure how you people with normal-sized cars do it. Compounding the problem are the abandoned shopping carts rolling about and sometimes filling the already-limited parking spaces, thanks to the shortage of shopping cart corrals. Cold and tired, I found myself seriously considering abandoning my cart when I noticed that the nearest corral was on the other side of the lot. Don't worry, I didn't succumb to the temptation, but judging by the state of the parking lot, I think I'm in the minority. + +If you actually make it into the store without any physical injury (you will be psychologically scarred, trust), there's definitely some good stuff to be had. As others have noted, the store is really small, causing the selection to be less than extensive. It's also too crowded. I like to spend a lot time in the grocery store checking out what's new and reading labels and such, but I feel awkward doing that when there's a swarm of soccer moms lurking over my shoulder and zigging and zagging all over the goddamn place. ANYWAY...some notes on various departments: + +1. The produce here immediately stands out--it looks so much more appetizing and fresh than at Giant Eagle. Even the bagged salad greens are more vibrant. Unfortunately, it's a tradeoff for the smaller selection of produce, but they have all the basics covered. + +2. This past trip was the first time I bought meat from Whole Foods, and the cuts were noticably neater and more consistent than at GE. Not sure if this is a regular thing, but they didn't have any filet mignon (I know, I'm high maintenance. I'M WORTH IT!). + +3. The cheese department! I like how GE Market District organizes their cheese a little better, but Whole Foods has a much more interesting and varied selection. + +5. The food bar is hit or miss. Some days it's the best thing ever, other days not so much. The sushi is gross. I always seem to forget this and try it over and over again with the same fishy, mealy results. Don't be stupid like me, avoid it. + +6. Market District recently got rid of a lot of their natural & organic chip selection in favor of more varities of their store brand. Thankfully, Whole Foods has everything GE used to have and more, which totally makes the extra shopping trip worth it. If you're a fat kid like me, that is... + +I don't come here for everything, but there are definitely some advantages here. Plus, the prices here are not THAT much worse than Market District in most cases. And I have no idea how I just wrote so much about Whole Foods?[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have a soft spot for Whole Foods. I think it gets a bad rap, which I think is largely unfair. I love food, and I know that sometimes things are legitimately ""overpriced,"" but just because something is expensive doesn't mean it isn't worth the cost. So I don't believe in rating Whole Foods low just because their organic produce, ethically raised meat, and super hard-to-find ethnic ingredients cost money. Nice things cost money. + +This is not one of the glorious meccas - the Whole Foods in Lincoln Park in Chicago is definitely one of those - but this one is all right. Pretty decent produce selection, and they always have some fun, mysterious finds. I like their seasonal treats like meyer lemons, and their well-priced organic local produce throughout the summer. Small fish and meat counter, but the quality is excellent. My coworkers love the soups, and we all really enjoy the salad bar. I love that I can find really unusual things here - their Asian section is small, but they always seem to have what I need. And the prices on the Whole Foods store brand are really not that bad! Seriously, like a can of beans will only set you back 99 cents, not that different from your Giant Eagle. You can find affordable products here if you take the time. + +I wish their bulk section was bigger, and I wish they had bulk spices because those make my life amazing. Whole Foods is like, where I want to do all my shopping when I grow up. I hate shopping at Giant Eagle, because there's no love and respect for the product. It's just crap, and OVERPRICED crap spilling out of the aisles, begging for your attention. Whole Foods has a lot of specialty products, made and sold by people who love to eat, and love to cook. There's respect for the ingredients here. To me, that's the best sign of a good grocery store. + +If you don't have a lot of cash, like me, then it's good to only shop here when you need to (like for a weird cut of meat, some kind of unusual hot pepper or mushroom, flavored oil, rare cheese). Every time you come, buy something new, just for fun. There are so many surprises here! I just wish it was bigger. + +And yes, the parking lot is small and crowded, but like - so what? Park in the back and walk a few extra feet. It's not a big deal.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Having just moved from Austin, where the original Whole Foods is located, I'm not going to actually ""review"" this place for its selection or quality of food. Cuz let's face it, how could I seriously compare this location to the original, gigantic, amazing, fresh, wonderful, healthy, gorgeous Whole Foods in Austin? Instead, I'll limit myself on reviewing the ever so friendly staff and parking lot. + +First, the employees. I've been to several Whole Foods around the country and I always got the impression that Whole Foods prides itself on customer service. Maybe this place is the exception? I was shopping here yesterday and a lady kindly asked an employee if she could squeeze in behind his veggie cart to grab something. The employee actually had the audacity to say, ""When I'm done"". And he did just that. He finished stocking his fruits and veggies and when he moved his cart and the lady thanked him, he didn't say a word. Also, the lady bagging my groceries didn't say one word to me. Not when I said hello. Not when I said thank you. Not even an ""ok"" when I said have a nice day. She didn't even smile at me! Where is the love? Actually, where are your manners? I don't need you to love me, but don't be rude or ignore me. + +Second, the parking lot. I'm pretty sure this is the only Whole Foods in all of Pittsburgh. However, the parking lot seems to be built for Pittsburgh, population: 50. It's a small lot - good luck finding a spot without creepily following someone to their car and fighting an SUV for the spot. Luckily, I've never truly had a problem parking because I go at off times and park farther away. But I'm suspecting one of these days I'll come out and find my car dented or scratched. Maybe by a car, maybe by a shopping cart......maybe by the lady who was bagging my groceries yesterday.... + +So two stars docked for the above mentioned. Other than that, I'll keep shopping here - after all, it's not like I have another choice when it comes to the Whole Foods of PIttsburgh.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Oh Whole Foods, you are so so very overpriced. I so so wish you were not, because I love the idea of the place. But I just cannot bring myself to do my normal grocery shopping here. I can't bring myself to spend the big bucks! + +The place is always packed and you're usually left bumping into people left and right. You may even get a nasty look, yikes! The parking is atrocious, with only probably only 75 spots for a pretty popular store. And have fun just getting into the parking lot from Centre. Okay, I'm going to a negative place right now.... + +I stop in here one a whim when I'm out in the area if I'm really craving sushi, because it's way better than the Giant Eagle's sushi down the street. It's still not he best fast sushi (Giant Eagle Waterfront), but it does the job. Again, they're almost $3 more than at GE. When I run in to grab sushi and usually ad Odwalla by bill comes to almost $20! I'd rather eat a fast meal at Qdoba...sorry...I said it! + +My feelings can best be summed up with this....http://www.youtube.com/watch?v=2UFc1pr2yUU[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> the parking lot @ this wholefoods is an ABOMINATION! to compound the issue, whole foods allows their purveyors to park on centre ave (a road that is already miserable enough to drive on) and block traffic. this past monday, a shearer potato chip truck was blocking the right lane. doesn't whole foods have a loading dock? i wrote an email to the district president and he had one of his store minions respond: ""you can park @ walgreens"". sorry, i am shopping @ wholefoods NOT walgreens. translation: whole foods developers were TOO CHEAP to buy the proper amount of real estate. dont even bother coming here fri-sun unless you like a clusterF*** lot full of zombies. this is the 5th WF i have shopped @ (4 in florida) wholefoods should have opened in the south hills. the demographics out there would support it. this wholefoods is BUSH LEAGUE![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Short and sweet, and as a Haiku. + +Parking is awful +No wine, but that's PA's fault +Best organic food[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I like this Whole Foods location. I will tell you why. + +Many Yelpers have docked stars for the parking lot. I think that's irrelevant. The parking lot, which is actually shared by Starbucks, Wine & Spirits, Walgreens, PNC, and more is two levels and is enormous! Walk a little. You can even take your cart up the elevator. + +The Pittsburgh location is not a superstore. Other Whole Foods have a restaurant, brick oven pizzas, smoothie bar, coffee bar, many more food bars, wine, beer, and so forth. This is a teeny weeny Whole Foods. For its size, the selection is pretty impressive. For example, my mom saw something on Dr. Oz called Lingonberry Jam and asked if I would look for it, and there it was. Never heard of it before, but they had it. + +Whole Foods has that ""whole paycheck"" reputation. Granted, this is true if you're spending your whole paycheck on rare, gourmet, specialty foods! If that's the case, you might want to rein in your spending a little. + +I actually took a notebook to Trader Joe's, Giant Eagle, and Whole Foods when I first moved to Pittsburgh to compare prices. Giant Eagle (Greenfield location) was the most expensive by an overwhelming margin! Trader Joe's was the best value overall, but Whole Foods was very close, and sometimes a little better quality might be worth it. Their 365 brand is especially reasonable for your regular grocery staples. + +As for the occasional splurge, this is a good place to try something different. I admit it's hard not to get something extra, but I know I can only blame that final total on myself![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I am a big fan of the Whole Foods company in general. The store back home (Omaha) had a wine bar, espresso bar, gelato, sushi and udon stand, a GIANT cheese counter where you could sample...I could go on. + +The Pittsburgh Whole Foods is small, and almost as overcrowded as its parking lot. Two-thirds of the time they are out of what I came for. I'm sorry, but if I'm paying THAT much for groceries, I want a stellar shopping experience. This WF is mediocre at best.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm in walking distance, which makes it my primary place to shop for food, and to crown myself as Le Duchess. :-) I also don't have to battle the SUV Soldiers looking for prime parking spots - because those people are CUT-THROAT and will most surely kill you (but seriously - they will. I've been brushed on the leg and knee multiple times by cut-throat drivers in that parking lot. I believe they would park INSIDE the store if they could). +I don't complain about the prices, because the food, and health benefits, are worth it in the long-term. Not so long ago, I was forking out hundreds of dollars a month in prescription medications because my diet was HORRIBLE. Since making the decision over two years ago to be more active and eat solely organic and Non-GMO, I'm off all of my medications, and the price of organic food is NOTHING compared to medications and prescriptions. I'm actually saving money. And No, I don't even make $20K a year - so it's all about choices. I'm not ""rich"" at all, like most people assume, since I regularly shop there. In fact, I'm usually dead broke. But to me, eating whole and healthy and protecting my body is not a luxury, it's a necessity. +I also like that there is no pharmacy in Whole Foods. That should say something. +My love for Whole Foods resides in the Organic Salad Bar, and Prepared Foods section. Their salad bar is so fresh and so delicious, that eating salads anywhere else becomes TASTELESS. Organic makes all the difference. +My favorite Prepared Foods is their Vegan General Tso's ""chicken"". Little popcorn nuggets of Seitan, drenched in the best General Tso's sauce I've ever tasted, with steamed broccoli. Molly's Sesame Noodles on the salad bar is our favorite side dish to this prepared foods treat. I swear we eat it at least once a week. +We also love their Bulk Section where we can get bulk quinoa, granola, lentils, and all kinds of things for a really decent price. +The secret to shopping at Whole Foods? BUY WHAT YOU NEED TO EAT THAT DAY. It's not smart to bulk shop organic produce, because it goes bad faster. Buy what you KNOW you're going to eat. You won't see 10/$10 deals, because the food isn't crap, and you're not supposed to stockpile fresh foods. You're supposed to eat it when it's fresh. And buy your dry stock at Trader Joe's or the East End Food Co-Op. +I love Whole Foods. It's the reason we chose to move to ShadySide.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Parking is tough, the food selection is great, and if you call ahead they will set aside awesome moving boxes for you.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have tried Whole Foods recently even after hearing about the attitude of the butthole, hipster employees and presumptuous, anti-bourgeois customers that will literally push you aside a turn their noses up at you a million times. The rumors were true!!! + +Even though I was only there one time, first impressions are a bitch! The selection is great! I can't afford any of it, but it's great! I have never seen such expensive rice! Here is the bro-down... + +The food: Plentiful and too expensive to even think of buying. The freshest fish that isn't in the Strip...but you need to take a second mortgage to buy fish for a family. I bought sushi rice, a piece of fish and a salad, my bill: $25! The salad with lettuce, carrots, chick peas, onions and about 5 pieces of chicken was $11+ + +The employees: Hipsters with thick-rimmed glasses, tattoos and facial piercings that slack like I have never seen ""workers"" slack before. In fact there was a sign above some fresh fish stating ""We will prepare you fish any way you want, just ask"" HA...HA! When I asked to have a tiny fish to be filleted (something that would take me about 10 seconds at home) I was scoffed at by the so called fish monger who was obviously not a trained fish monger, but got his job because of his Progressive music of the soviet era bachelors degree . It took him the better part of 20 minutes to fillet a f-ing fish! All I got was a chopped up piece of crap that was useless. And scoffing is what these people are good at. Pushing your cart down the aisles is like running a scoffing gauntlet. Staff huff and puff when you get in their way?! The cashiers just stand and talk to each other or run to get organic iced tea to drink WHILE they ring you up...they don't even do that at Giant Eagle! + +The other customers: This one is a peach! If you're not pulling in a good $60K a year you are dirt to these people. I was at the salad bar (it is a good salad bar, but expensive) an older woman in a mink coat bumped, no, pushed into me then stared at me and turned her nose up at me, can you believe it? She actually turned her nose up at me! Others in the aisles will grunt like cantankerous old people if they can't get through. They push ahead in line, give you dirty looks, and act like it's a class struggle...it kind of is! + +So unless you have a lot (i mean A LOT) of disposable income, have never needed to use coupons, drive a $50K car (parking is terrible there), are the president of the United States, CEO of Microsoft, a widow whose wardrobe is more extensive than the explanation of the formula explaining an event horizon or a hipster who looks poor, but lives off daddy and mommy (though they'll never admit it) you shouldn't and really won't be able to afford this place...but why would you want to? + +I'll stick with Trader Joe's for my alternative market, thank you! I prefer employees with edges that are a little rough to ones with pants so tight, I can see their junk.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love the large selection and variety of unique and healthier food that Whole Foods provides. The amount of different nut mixes and flax-like snacks amazes me. Not to mention, the amount of fresh prepared foods that can be gathered is awesome. They have specials for the day that will help you buy some of the fresh and prepared foods they provide. I cannot wait to come by again when I know I am going straight home after so I can buy some refrigerated items![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I always thought 1-star reviews on Yelp were written by bitter, resentful people who had nothing better to do than just complain. But now I feel their pain. It really doesn't hit you, until it... hits you. + +You pay a premium at WF, you expect a premium, right? Well parking is part of the shopping experience. It's why they have parking lots in the first place. But never mind the atrocious parking lot and not being able to easily maneuver in it. + +I'm talking about being TOWED. Towed, not for leaving the parking lot, but for legitimately shopping at WF. Yes, this could happen to you too. + +Upon contacting the towing company, they demanded $135 (cash only) to return my vehicle. Upon contacting WF (since I was a legitimate shopper there and didn't leave the lot) they just shrugged their shoulders and just told me the name of the company that managed the lot. + +And that's it?! $135 is no chump change, but it seems like WF wants me to carry an extra $135 every time I frequent them (thankfully, never, since I don't live in Pittsburgh). This whole parking/towing situation is extremely shady, but the only company I'm going to point my finger at is Whole Foods for doing business with such a shady complex and passing the burden on to its customers. + +Tip: Bring an extra $135 to pay for parking, or just go to Trader Joe's/Giant Eagle for a better parking/shopping experience.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love the concept of Whole Foods, but as everyone knows it's pretty pricy. Hence it's nickname, ""Whole Paycheck."" + +Nevertheless, always great organic produce. The seafood and meat here are also the best. + +However, this place is always packed. Be prepared to be bumping into people and feel a little claustrophobic. The parking lot can be quite tricky as well, as it can become completely full. They really need to add another location in the City of Pittsburgh to take some stress off of this one.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This review is for the buffet at Whole Foods. Overall, it is good, and there are lots of great options. The food seems fresh and it is a good place to get a quick, healthy lunch on-the-go. I went with a friend and we spent a little over $20 on lunch for the 2 of us, which seems a little high for what it is, but I think we must have just gotten a lot of food because $7.99/lb is fair. Plus it is hard to get lunch for any less than that these days without eating fast food.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Forget you Giant Eagle, Giggle, Market Crap etc. Whole foods gets a bad rap as being ""expensive"" and yes I agree there are some very ridiculously expensive things in there, but this is where you IGNORE them and get your basic essentials. They are always running specials, and you can get some good deals. If you actually try to price compare between GE and whole foods, you'll find that whole foods is actually cheaper, and the only reason you don't shop there is because people will feed you into thinking you'll spend your ""whole paycheck"" there. What crap. Write a list, prioritize and buy the things that are sale. Whole foods has a much better selection (freshness wise) in produce, meats, and cheese across the board. Yes you can find some great stuff in the strip, but you will also find some reasonable items here. Over the summer I went on a scavenger hunt for clams, Wholeys/GE were both gross and overpriced! Whole foods has fresh clams and they were much cheaper than the other two locations! Try it out, you won't be sorry.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'll be honest, I just don't get it. When it comes to eating I do not adhere to any particular mantra or dietary restriction like vegan, organic, vegetarian, ethical, etc. If it's edible and it's within my palate's liking range then I eat it. + +From that perspective this place just gets two stars. Some items were higher priced but the value added (from organic to vegan certified) would I guess justify it if you had to have it. But the items that do no fall under any of those premium-restriction value types are still just as highly priced. So it feels like 90% of their inventory is priced at a whole-store experience premium. + +Their prepared meals section was marvelous, and their cut fruit section was like I had died and gone to heaven. But that's about the only two sections I probably would have been willing to open up my wallet.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Now with two new bee hives along the rail line as of July 2012 managed by burgh bees of Pittsburgh[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> NO WI-FI. Just FYI. + +When I lived in Cleveland and my first (truly terrible) apartment had no wi-fi Whole Foods was my second home...I would buy a little sampler of buffet foods and salads, a coffee, maybe a vegan cookie, and park myself at a booth for an hour (or more, let's be real). After I taught a yoga class. I know, I know, I'm such a white liberal yuppie, it's painful. + +Anyway, so when the internet went out at my Pittsburgh home I trotted off to Whole Foods, bought some food and a coffee...and asked about the wi-fi. ""We have it,"" said Cashier #1. ""It's probably just under ""Whole Foods."""" ""We have it,"" said Cashier #2, ""but I don't know the password - ask customer service."" ""We don't have it,"" said Customer Service, ""go to Starbucks."" + +Believe it or not, Starbucks is letting me drink my coffee & eat my vegan cookie and didn't make me buy anything. + +NO WI-FI. Otherwise, this Whole Foods is pretty good.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love shopping here. The staff is really nice, no attitudes. Even the other shoppers are kind. It's always nice. Thanks to everyone for making Whole Foods a nice shopping experience.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I loved it, parking and all, after all, they had Palak Paneer! Mmmmm. It was tasty. I spent a lot, but I was ok with the occasional splurge. the second trip, i again bought my hit foods Palak Paneer and it had obviously gone over. + +Ever have whoopsies after green Indian cuisine? + +It's off my list now. Forever.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I wish there was a Whole Foods close to my house. My wife is addicted to the freshly ground peanut butter from here, so I have to make a monthly trip to replenish her stock. + +The meat, seafood and vegetables always look fresh and last a whole lot longer than the stuff from Trader Joes or Market District. Plus you don't have to look at the label for any of the ingredients cause you know the food does not have corn syrup or a derivative of it. + +While my shopping at Whole Foods mainly extends to meats, seafood, vegetables/fruit and milk/eggs, I sometimes crave their assortment of cheese and I'm a big fan of the bakery section. They do custom orders (I think) with names etc. for birthdays/Valentines Day. + +Tip: You get 2 dozen red roses for Valentines Day for 20 bucks. Now that's a steal! + +This is a small store compared to what I have been used to. The parking lot sucks considering the traffic it gets (there is a salon in the same lot so that adds to the mess during weekends). Prices are higher than other places since the food is organic but you get what you pay for: fresh, long lasting food. Again you have to use your discretion as to how organic you want to be. + +If the store were bigger, had a bigger parking lot and a bigger bakery section, I would give it 5 stars. The layout is good and staff is always helpful.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This store is great - it's got all of the fresh specialty items we need for cooking great weekend meals for friends, but isn't a vast, overpowering warehouse. Items are well organized, and easy to find. As others' state, it ain't cheap! + +One way we lowered our Whole Foods bill was to go for their 365 in-house brand, which is typically priced at the same pricepoint as similar items in the regular chain grocery stores. We don't use Whole Foods for all of our supermarket needs, just the specialty items, great produce, and seafood. + +I docked two stars for absolutely terrible parking - yep. I know that's harsh, but every time we come here, we need to factor in another 10-15 minutes to get a parking spot and be able to leave safely (there are always cars behind us looking for a spot when we are trying to leave, and so we often can't just pull out of the space and leave quickly...) Even being careful, we have almost been hit multiple times by people losing their cool with the terrible parking. + +That being said, we will continue to come here to stock our home when we plan to entertain at home.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I think Whole Foods and Giant Eagle Market District are competing for the title of most annoying place to shop. It all starts with the parking experience, which is ridiculously horrible at this location - very poorly planned. And then, there's the prices - Giant Eagle being quite expensive compared to similar grocers in other cities, Whole Foods obviously has to get a one up on those; it's inherent in the scheme of selling premium ""natural"" goods. Whole Foods does have better lighting and layout than GE, and yes, a more discriminative selection of products, especially for people with specialized diets, like vegans (me) and gluten free adherents. The house baked bread here might be worse than GE (tough contest) - often under baked and thus soggy in middle and crusts tend to fall off; making gluten free-dom seem appealing. And I don't even need to talk about customer demographics, because you've all seen Rachel C.'s link![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Good selection compared to how pathetically limited it is at Trader Joes. Prices aside, honestly if you come here to get groceries, what else did you expect, it's a nice place for groceries. Same cannot be said about parking in front of the store. Unless its past 8pm, the lot is always crowded. Also not helping is people taking up one and half spots.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This store is pretty good. Yes it is fairly expensive but you can get quite a few items that are difficult if not impossible to find at other stores. They have a nice meat department with quite a few good naturally raised products, particularly beef. We've been very happy with their produce, which we find noticeably better than Trader Joe. + +I wish it was bigger so there was a larger selection and a larger prepared food selection (we are used to the larger stores in Chicago). Also wish there was a liquor department but I'll probably have to run for state office for that. Frankly the worst part is often parking. Don't know what causes everyone to behave badly in their lot (myself included) but man it can be a mess. + +Anyway we'll keep going at least for meats and produce.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Whole foods!! What a great idea. Foods that are natural and organic and wholesome to bet. This store offers a lot of brands and varieties of food. More than the national brands. + +I love how when you first walk in the store, your automatically thrown into the produce section no questioned asked. The store is practically laid out to help you make the best food purchasing options available. + +They have more organic foods than any other store i've seen. Everything looks so fresh and plentiful. They also have conventional (non-organic) items that are usually shipped locally and not from across the country. Tons of options from Bok Choy to avocados to seasonal fruits. They have a fresh seafood counter and a meat counter with ratings on the meat from one to five. There is also a deli counter with fresh pasta salads and side dishes made in store. + +I recently started a gluten free diet and this store meets all my needs from bread, buns, cereal, crackers, basically all the common wheat products. I've substituted out a lot of wheat products like flour and instead use rice flour, regular milk for almond milk, things like that. + +My favorite part of the store is there hot foods and salad bar. They make all their dishes in the store and sell them for $8.49lb. The hot dishes are amazingly good. The last time i went i had green beans with red peppers, cajun sweet potato wedges, sauteed mushrooms, curry tofu and purple cabbage. Man was it delicious!!!! Plus the salad bar has over 40 options to put on top of the salad!. With so many choices including the bakery, how can you miss out on this great place. It caters to average diets and changing diets too!!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Not counting price I like this store and the service. +My favorite, a fellow I call Scotsman the meat counter man. I don't know if this gentleman is from Scotland or not, but his language reminds me of one I know. But the key distinguishing factor for him is his superb service and great attitude. He is just short of your personal butcher. He takes his time with you, and he does not rush you on. Listens, gives advice and is extremely helpful. When necessary he will look in the back to satisfy your request . He alone could keep me coming back. Oh, and also the meat counter is excellent overall. Great selection, and good cuts. +What else, well the cheese section is outstanding, the prepared foods are plentiful and tasty. I like the baked goods also. Another nice feature is you can eat right there, which I do sometimes so I don't food shop when starving, which always costs me more somehow.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The produce here is always fresh, the cookies by the pound are delicious (especially the caramel wafers!) and they are a much more comprehensive grocery store when compared to Trader Joe's. + +I would avoid going here in the afternoon on weekends though...too crowded.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is a very well stocked Whole Foods in Pittsburgh. I am quite fond of their vitamin and natural beauty section, it's not something you'll find in every grocery store. Their prices on Garden of Life vitamins are the best I've found in the city. +You walk in to their lovely produce section. I really like the way the fruits and veggies are stacked, it's different. +The staff is super helpful and will walk around the store to find the answer to your questions. +We often find ourselves there at lunch time visiting their hot foods and salad bar. The prices are fair for high quality foods. +The one awful thing about this location is the parking lot. There is not enough spots close to the building, and no one wants to walk all the way from the garage when there's nowhere to put your cart after you load your things! And the drivers! Oh, the other drivers. They will wait f-o-r-e-v-e-r for someone to vacate their spot. No matter that they're stopping traffic out on the road! I always have to psyche myself up to go there and deal with the parking situation. +But when I go, it's well worth it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Just wanted to write a review based on my experience today. + +Everything I went for was in stock today (which doesn't always happen). The place was crowded, as usual, but the line went fairly quickly. On my way in, I saw a $5 fish sandwich with creamy coleslaw advertised outside. Three guys were there cooking. Looked and smelled delicious, so I paid inside with my groceries. When I came out, I told the guys I bought one. They were really nice and asked me what kind of bread I wanted and what I wanted on the sandwich. + +Some lady that was ""in a rush"" was upset her sandwich wasn't ready when she came out (but they explained the fish was cooked, but they couldn't set up the sandwich without knowing what bread or toppings she wanted). Just watching the way they dealt with this customer was great for me. The guys were so friendly and patient. + +Also, the sandwich was delicious! The coleslaw was also awesome! Yay! I am so happy I stopped by when I did.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love everything that Whole Foods offers, but I can't stand the experience of going there. The parking lot is a mess of aggressive drivers acting like the extra 50 feet of walking will negatively affect the environment more than their driving around the parking lot until a better space opens up. Once you get a space and finally get inside, the experience mirrors that of the parking lot. Everyone is in each others' way and trying to be the first one to find the best organic orange or grab the last package vegan general tso's in the store. + +To be fair, though, the experience is still 100 times better than going to the Market District a few blocks down the same street. Similar in-store and in-lot experience, but with a better and higher-quality selection. The staff is always really nice and super helpful, and their trays of fruit and veggies are excellent. We've ordered them countless times for parties and have never been let down. Pricey, but excellent quality. The prepared foods are delicious, and their prepackaged prepared foods are also really good...but like nearly everything else in Whole Foods, a little pricey. For example, their yummy tomato bisque is $7. Hardly cheap enough for a quick lunch, but it is yummy. Their baked goods are delicious as well. We're constantly picking up bread from there (and the occasional doughnut), and we're never disappointed. + +Their meats and seafoods departments are also excellent. They have a great variety and are always helpful in answering any questions that I've had (although we still opt for our meats from DJ's). Of course, if you're at Whole Foods your'e likely there for the organic options, and as to be expected, you're not going to find a better selection anywhere else. More unique, perhaps, but their inventory just won't be matched any time soon for those foods. Surprisingly, third-party & prepackaged pricing is actually on-par with Giant Eagle, so whenever we're looking for those types of items (milk/eggs/pastas, etc.), we always opt for Whole Foods.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Ok, the parking at this Whole Foods is an absolute cluster. It is not uncommon to pass fender benders in the parking lot on a Saturday. My suggestion is park closer to the CVS and avoid the abominable parking and terrible driving. + +It's generally extremely crowded on the weekends, espeically in the afternoons, so if you need to grocery shop on a weekend afternoon, make sure you have a list and start in the back. You will thank me later. + +Though this location is small, it is always well-stocked, and the staff, though some are aloof and pretentious (even though they are working for corporate America-hello), most are helpful. + +I love the prepared foods and salad bar. It's a great option for those nights when you just don't feel like cooking. There are $6, $8, and $10 meal options, and all come with two sides. There is also a large selection of dips, spreads, and large take-away sides as well. I think their prepared foods are worth every penny, and if you don't load up your salad with heavy items, you can easily get a dinner-sized salad with a little meat or egg for $8 or $9. + +Some of my favorite items at this location include the fresh fruit packaged in containers. It's super expensive, but always fresh and delicious, and I love treating myself to it, especially during the summer. I also love the fish selection-it's pretty extensive, and you can always find fresh harder to find items such as red snapper. + +The raw nut offerings are extensive as well, as is the chocolate... + +My favorite thing to buy at this WF is coffee. They have a huge selection of Allegro beans, as well as local offerings such as La Prima. Try the La Prima Peruvian blend or the Allegro Malawi blend. Amazing.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have only come to this Whole Foods a couple times since moving to Pittsburgh in 2010. However, now that I have discovered that I have some food allergies, I may be coming here more often! + +PROS: High quality, unique products, especially for those with particular dietary restrictions + +CONS: Terrible parking lot, crowded store, high prices + +Personally, I buy specialty items but wouldn't purchase all my groceries from here. I can't yet afford that luxury![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is where we do all of our grocery shopping. The parking lot does suck so I avoid it and park by Walgreens or up on the top lot. The produce is always great. Seafood is delicious. Best meat in the city- we especially love the made in store sausages. + +I love the specialty department and they will let you try the cheese before you buy and everyone is so helpful. We eat from the prepared food department more than I'd like but it is better then ordering take out or chipotle for the second time in one week. Salad bar is good- though watch out for undercooked veggies- raw beets on a salad one too many times and now I avoid them completely. Bakery department is beautiful and when I ordered a sheet cake for a wedding shower everyone raved about it. Floral department will help you put together a beautiful arrangement. Whole body wants all of my money- I try to avoid this department to be honest because I lack self control and always over spend. + +Check out can be a hassle if it's really busy but the cashiers are nice and check out pretty quickly. A recent development at this store is the person waiting outside to help you to your car. I don't need help so it's a little weird but I'm sure people with kids love it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Ok, so this is my first visit to Whole Foods...ever. And now I know why it has taken me so long. Much like the parking lot, the inside of the store is just as congested. + +I came here with only two things in mind that I needed, I went to the aisles I assumed they would have been in and we all know the saying there. For as small as the store is you would have thought I would have bumped into a staff member. I was again wrong there. + +I scanned and scanned and scanned the aisles until I found the two items I needed, and wouldn't you know right after I did, I came across a staff member. + +After being run over by a stroller on my way to the registers, I was happy to head back out and fight the congestion in the parking lot.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've been to a many different Whole Foods, this one is a little small, but nice. + +Pro +-Very nice hot & cold bar +-Nice eatery +-Large selection of fresh breads & desserts +-Very nice produce, meat, coffee & grocery selection + +Cons +-Small, so very crowded +-Not a large bulk section, no flour, spices or sugar +-No wok or burrito bar +-Carts are outside[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I shop at Whole Paycheck from time to time, but I find them much too expensive for everyday groceries. If I want to splurge once in a while, or buy something to take to a party, it's definitely the place to go. The cheese counter is extensive, but I don't like that they pre-cut their cheeses, I much prefer the way Penn Mac handles their cheeses and does not cut until you order. Whole Foods will gladly do the same, so make sure you request that. I love the produce and the prepared foods. I just wish they would give us a break on the prices.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> All that I can say is WOWSA!!!!!!!!! This review is long overdue! I will state it outright that I'm very particular about my food, and I've been known to stomp my food like a brat when my heart's set on that vegan tofu burrito from the fresh pack section and it's not available. + +A few months ago, when this happened, I sulked at the Prepared Foods counter, and Bethany, prepared foods customer service extraordinaire, flew to my rescue. She suggested the vegan BLT. I was hesitant, as I wanted something hearty and filling, and let me tell you this!... The sandwich totally did her smile and sales pitch justice. It pleased me like no other sandwich has ever done. I want to compliment every sandwich maker in that department, specifically Bethany, Eric, and Rick. They know when I walk in their direction from the Fresh Pack section that I'm looking for my second option of the BLT because the burrito isn't available. No matter how bananas and certifiably insane I might seem during my food shopping excursions, they always treat me with such dignity and respect. + +Months have passed since my first BLT experience, and I was completely taken for another ride through satisfaction land during this past week when they offered to notify me ""the night before when the vegan tofu burritos are being made"" because they know how much I have my heart set on that beautiful meal on most days of the week. I can't say enough for Bethany and her team of prepared foods colleagues. + +And everyone else at the store is so helpful and nice, too! So kind! So informative! I love Whole Foods Market of Pittsburgh! AND, for icing on the review cake, they've even begun to carry Brad's Raw Pizza Kale Chips for dogs. So my dog is satisfied, too. And it's her opinion that ultimately matters. ;) Five stars! Thank you!!!!!!!!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> So..... when I think about shopping at Whole Foods, I always create an alternate universe where I think I would be able to shop here. I think: if I made at least twice the amount of money I currently do, I would be able to be a member of the club and shop here. .... but I don't. Thus, I only stop in here on very special occasions when I 1. can withstand the rage I feel when I pull into this parking lot; and 2. I want to either eat at the buffet or buy a very specific item. I would definitely recommend that others stop in sometime to get some food at the buffet. The quality of everything is pretty incredible (though of course it's typically really expensive).[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love Whole Foods, and I have been a fan for a few years now. I've visited Whole Foods locations around the country, but this Pittsburgh location is one of my favorites. It's a small store, but it feels homey and comfortable. + +Staff: Most of the staff members are super friendly and willing to do just about anything to help you find what you are looking for. I had one staff member begrudgingly help me out, but I assumed he was having a bad day or was very busy. Either way, it's nice to treat others with respect. + +The cashiers here are so fantastic. They are never rushing and throwing food into bags. They take their time, ask you questions and treat you like a person instead of another number in a long line. + +Deli/Made-To-Order: The deli and made-to-order foods are currently my favorite. Sometimes I would rather spend $20 on lunch here with my boyfriend than go to a restaurant or get fast food. My favorite is the vegan chicken salad on foccacia bread. I adore this bread. It's just the right texture, it's nice and herby and deliciously buttery. Topped with swiss or muenster, it's a super delish sandwich. If I am extra peckish, I get extra veg. chicken salad. Yum yum yum! + +The tomato bisque they have is something I newly tried. I'm very picky about my tomatoes and tomato products. This soup delivers. I wish I could have it every single day. It's so phenomenal! My boyfriend got it today alongside a cheddar biscuit that paired beautifully with the soup. + +Cheeses: If you want fancy gourmet cheeses, the Whole Foods deli counter might be the best choice. We purchased a small amount of Midnight Moon Goat Cheese Gouda and made the most expensively delicious grilled cheese sandwich. We're grown-ups now, say goodbye to gross American cheeses! The cheese counter is so great because all of the cheeses are labeled with the kind of rennet used in the processing. You can easily find a high-quality vegetarian cheese with just a glance. The cheese experts are also willing to talk cheese to you for as long as you like. + +Store Selection: Overall the store has great options, but they don't carry everything that I wish they did. Unfortunately, they discontinued one of my favorite products - Field Roast Deli Slices. They bring in new and trendy foodstuffs though, so it's enough to keep me happy. + +Whole Foods can be pretty expensive, but if you don't fall for the tempting packaged foods, you can get away with a reasonable grocery bill! I primarily shop here for special items though. + +P.S. Their selection of natural body and haircare is great and affordable. If you have sensitive skin or don't want your products tested on animals, go here![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This Whole Foods is an amazing store and is the only one in the area besides out in the suburbs. The store is perfect, but I take away 1 star for the parking lot... it sucks (although I believe plans for improvements are in the works)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My expectations for Whole Foods Market had been established as was growing up in the DMV (D.C., MD, VA) area. Thus, very fresh produce, high-quality meats, diverse cheeses, expansive bulk section, novel food items, exceptional food bars, and excellent customer service were essentially a given. On the other hand, I also expected parking difficulties, even at stores with multi-story garages. + +The Whole Foods Market in Pittsburgh is not much different from those in the DMV area. However, the parking is horrendous! Really, a medium-size private parking lot for the only Whole Foods Market in the Pittsburgh area right along a congested major road? Let me say that Whole Foods Markets in D.C. are also close to major roads, but they at least have underground or aboveground garages and fairly decent road infrastructure to accommodate for the influx and outflux of shoppers. I would love if the Pittsburgh store can build a garage of some sort (I'm not counting the garage next to the Starbucks and Walgreens) with smooth entry and exit so as to prevent a mini-gridlock along Centre Avenue. + +Parking situation aside, the Pittsburgh store does live up to my expectations established from the DMV stores. You will rarely find a bad apple (no pun intended), and the store usually keeps shelves stocked (except when there is a major sale or promotion going on). Now, if only its prices and my budget could meet halfway so I could frequent this store more--via bike or my own two feet.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I seriously don't know where to begin. Oh yes, I shall start. Ladies, DO NOT ever go there hungry, or on your period that has your horns out due to the most beautiful thing we get ""cramps"". First off the parking will make you want to rip your steering wheel apart, and throw it at the person ahead of you that got the last parking space. Parking is MADNESS!! + +Then after you find a parking spot from doing bumper cars with other non-driving asses. Here comes another traffic jam (carts, and people). The space in there is one big box. Geez Louise. + +I cringe when I have to go there to get an item that only WF carries. But I like how they trap me with their delicious fruit and vegetable display as soon as you walk in. It's a war zone in that area. I can understand organic being more expensive than conventional, but why oh why is their conventional JUST AS expensive as their organic? REALLY?!?! So every time they get me with their fruits, veggies, and the only place that I have found to sell skinless drumsticks, along with 2 or 3 more items. My bill is ALWAYS 90.00!! OMG!! I only got 1 bag of groceries!! The fruit that sells by the pound be like 8 to 9 dollars. I just can't. + +On a more positive note. The employees. They have always been so great to me. Always greet me with a smile, and if I have an item that has a coupon, they go out of their way to get the coupon so I can save (lol at save) oh my haha. But yeah, the employees must be getting paid good, because they smile, and always happy to help me.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I will start by saying this review is for the hot bar and I must of gone at an off hour for the hot bar and by that I mean during the dinner rush before they replenished it. I would say everything I got from the salad bar to the hot bar was good apart from they had run out of soup/special of the day and the chicken was beyond dry, the time I spent in the dessert was a wet oasis compared to the chicken. I just feel that for the price I paid it was not worth it. I have been to a smaller whole foods with a better hot bar and to the one in New York City and remember it being great. I only give this one 3 stars because the Mac n cheese and vegan tofu loaf was rather good. But I must repeat myself about the price. For what I got it's way to much. It's hard to justify paying that much when I could make it for 1/5th the price at home. Now I know I don't have to cook or clean and that's the point of eating out but I could also go to trader joes get a few frozen meals and eat for over a day for the price of one hot bar meal from whole foods.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I know what Whole Foods has done for the area and for that I'm forever grateful. They came into a dicey neighborhood and brought their awesome healthy food and fun staff and East Liberty blossomed around it. + +But that parking lot. Good Lord it's like playing bumper cars. And from the YouTube video where the guy sings, ""It's getting real in the Whole Foods parking lot"" I realize that Pittsburgh's Whole Foods is not special - this is a common problem. Small spaces, not enough parking, too many people driving through fighting for a spot, yeah, it's a mess. + +It's almost always crazy busy in here. I believe I'd come more often if the shopping experience was calmer. But because of the insanity of the parking lot and the hectic shopping (people everywhere bumping into each other) that takes place inside, I truly limit my shopping here. To like once a year. But when I do venture in I think they have a fab hot food section and great sushi. Some pretty tasty baked goods as well.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Yes, the parking lot in crazy. Yes, the prices are outrageously high (it's not called Whole Paychecks for nuthin'). Yes, the store is small and usually crowded and the majority of the people who shop who here completely unaware they are NOT the only people on the planet. All those things aside, I love Whole Foods. Most of the issues can be handled by slight changes in habit. For instance, park farther away instead of circling the GD parking lot for the closest spot!!! I get so sick of people complaining about that damn parking lot when all you have to do is park by Walgreens and walk. Seriously, the walk won't kill most of us. Stop being lazy. (Sorry, for the tirade; that's a pet peeve of mine). + +The produce is fantastic, always. And not just the organic stuff either. The regular pesticide-laden produce is great. The quality of the meat department is second to none. Now, the bakery is a little 'Eh' for me. The muffins and cookies and cakes always look De-Lish!, but they aren't. Usually to dry or dense or flavorless. It really doesn't matter because the star of the show is... + +The HOT FOODS BAR. The quality and taste of most of the hot foods/prepared foods bar is unbeatable. I lovelvoelove the breakfast bar. My dream weekend starts with waking up and taking a nice long walk, stopping for coffee then heading on to WF to pick up Eggs Rancheros Burritos and Sausage patties from the breakfast bar. I may get creamed by a bus the second I leave, but I will die happy. + +Some of my other favorites are a Vegan General Tso's ""chicken"" that has the BEST real chicken texture. It's really good! The mozzarella pasta salad, Sicilian cauliflower and the egg rolls which are seasonal. Don't forget to check out the packaged hot foods across from the salad bar; same stuff but pre-packaged. + +As a note though, the chicken fiesta soup is nooooot good. Bland with a capital B! In general the soups are hit or miss, but a real hit is the triple squash or Butternut squash, something like that. It's next to sushi. It's very good[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I don't shop at Whole Foods that often since it isn't that close to me. There's a Shop n Save a block from my house, so I buy most of my food there. + +One thing about Whole Foods is they specialize in fresh fruits and vegetables. Their produce is definitely impressive. All of the oranges, lettuce, berries and bananas peppers are perfectly ripe. They never have spoiled or bad fruit. + +The pastry section is definitely worth checking out. They have fruit tarts and a lot of different flavored cheesecakes and cannolis. + +Whole Foods seems more expensive than Aldi but less expensive than Giant Eagle.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> As a vegan (since 2008) we are a regular at whole foods. It's convenient since we live in Lawrenceville. My one and biggest complaint is that they need to carry more (if not all) organic produce. Not this ""conventional"" garbage. Other than that they have a huge variety of products and grocery items to choose from. Staff is always friendly and helpful.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have such mixed emotions about whole foods. I first visited whole foods in February of this year.. In my opinion, it is a little overwhelming at first and here's why. Like most People in the US, I was brought up on all of the ""typical"" mainstream American food brands. So when I walked into this place and barely recognized any brands, it was slightly overwhelming. It took a little research and I still do some research on some products before making a trip. I recommend going online and checking their coupons before making a trip - I tried a bunch of new products that way. I have also googled ""best snacks at whole foods"" to get some more ideas of what to try. + +Now here's the sucky part- overall, whole foods is pretty overpriced. BUT I will say that it is not ENTIRELY their fault. They sell higher quality products than your average grocery store. Mostly all of their products are made with the best ingredients and are often organic and gmo free. They are vegan and vegetarian friendly and have tons of options for people with allergies. If companies are spending more money on better ingredients , they are going to have to sell their products for a higher price. + +Having said that, tazo tea for $4 a box is not a sale. I went a couple weeks ago and saw the sale price advertised, did a quick google search and realized target sells their tazo tea for $3.50 NOT on sale. Needless to say I took the trip down the street and saved myself some money for the tea. I also recently wanted to purchase kale chips that I heard so much about (brand is called brad's raw and the flavor was vampire killer)... Until I realized they were $9 for 2 oz ! You can get fresh kale for less than half the cost! + +Although whole foods can be expensive they aren't ALWAYS that bad. My favorite yogurt, wallaby organic yogurt, is sold here. On a normal day, it cost $1 each. A couple days ago, they were 89 cents each- not bad for organic yogurt. They also have an amazing selection of uniquely flavored chocolates and they are pretty reasonably priced. Justin's organic peanut butter cups are incredible! + +The customer service has always been awesome in this particular location. I hear that whole foods is very willing to take back anything that you don't enjoy , as long as you have your receipt. + +as other yelpers have said- the parking sucks in this location, it's a nightmare. So keep that in mind before you visit. + +Overall, when I want to treat myself a little, I come to whole foods.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Alright, so I braved this place yesterday (new years eve) and it was totally insane. There was honking, some road rage and confusion. But I will say that I should have known better coming into a grocery store before a major partying holiday. + +Anyway, in terms of produce this place is awesome. I got my meat and bacon from this joint and have not been disappointed. I also love their premade hamburgers. They are delish. This is also a great place to find a great assortment of cheeses and grass fed butter ( I go for the kerry gold products, they are just awesome). + +Also if you are grilling and dont want to cook too many sides, you can pick up some of their sides from their deli section. I haven't had a bad experience with their food and you can always give everything a taste before having the clerk put it in a container. This is certainly the place to get specialty items like hemp seeds, chia seeds, and other natural dietary supplements... just beware they are not cheap. Overall, whole foods is not cheap, but if you want quality this is the place to go. Just dont go here on New Year's Eve or Christmas Eve... you'll end up ripping your hair out!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love going here, if you shop smart it really isn't your whole paycheck and is less expensive than other options in the area (Market District I'm looking at you). I only buy the store brand unless I need something special for a recipe, and my bill is consistently less than anything I bought at Market District. The quality of the produce and the meat cannot be matched anywhere in the city, unless you go down to the Strip. But hands down my favorite thing about going here are the employees. If you read anything about the corporate structure or culture of Whole Foods you'll understand why everyone seems so happy to be working. I have never had a request met with anything less than a smile, and I love that they are willing to let you try a new product before committing to the whole purchase.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> So the whole reason why I chose this Aamco was because it was a short walk from my apartment in Shadyside and I could easily leave my car there and walk home without having to bum a ride from my roommate. All I needed was an oil change and my PA state inspection and it turned out to be a pretty painless experience. I just dropped off my car in the morning and picked it up in the afternoon. It's hard to find a decent mechanic and Larry and his team seem like people who will take good care of you. I'll be back there for sure.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I was incredibly nervous about taking my car to a major chain as I've heard and read many mixed reviews about numerous locations. My experience at this Aamco was fantastic though! + +Larry was incredibly kind and helpful in explaining what was wrong with my transmission, and when it came time to fix it, he ended up charging me the originally estimated cost even though he needed to do a little extra work. + +Can't recommend this place enough![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have taken my car here now for seven months (two cars really). From routine maintainence to identifying a problem they have only shown me the best service. They always present me with good and complete information and are honest and trustworthy. The last time I was in they saw the problem right away and since it was a 30 second fix they didn't charge me. + +I can't recommend these guys enough. The best mechanic I have had experiences with in my adult life![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I went here to get my serpentine belt replaced and a transmission flushed and these guys were friendly and efficient. They took the time to explain things to me and I felt comfortable that they were making the appropriate recommendations without trying to charge me for things I didn't need. It was ready in just a few hours as promised so I was able to pick it up same day. Only complaint is that they left my transmission fluid dipstick out of place under the hood so it was just laying on top, but fortunately it didn't fall down and screw up anything since it was laying flat on the top, but if it had that could've been a more serious problem. So I subtracted a star for that since it seemed a bit careless.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I took my car here for the state inspection. I mean, there's really not much to rate here - they gave me a sticker, didn't try to sell me anything (my car is like a year old, anyways) and the price was as advertised. They gave me a ride to work, and were quite friendly. +I'll most likely come back for my future inspection needs, and, if I have a car out of warranty, certainly give them a try for mechanical issues.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> If I could give them zero stars, I would. Awful! My car wouldn't start so I called the tow and he managed to get it started, but it's been acting up so I brought it in anyways. After having my car for an entire week and not calling me once, after I've called twice, the man on the phone told me it was ready to pick up, nothing wrong with it. When I went to pick it up, I turned it on and before I could even leave the lot, it died! I went back in and told him that the tow truck operator hooked it up to a jumper box and pumped the gas to start it. That's what he did. Then told me it probably didn't start because it was sitting so long. Then he told me ""I don't know anything about your car""! I left and sure enough had trouble getting it started at my next destination, had to pump the gas pedal. Yeah, that sounds like ""nothing's wrong"". DO NOT BRING YOUR CAR HERE. THEY ADMITTEDLY KNOW NOTHING ABOUT CARS![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> So I had to take my car to get inspected in order to register my car here in PA and ended up taking it to this place. I called in advance, the day of and they were able to fit me in since I needed to get this done ASAP. Anyway, I drop the car off in the AM and walk over to the closest Starbucks (its like 3 blocks away) so that I can get my work done, as they don't have WIFI. After 3 hours or so, Larry calls me and lets me know that my car was ready. Fortunately, my car didn't need any work so I was a happy gal. The inspections that they did were about $67 or so, which was pretty average as I had taken my husband to get the same thing done elsewhere. At any rate, the people here were very friendly and professional, they didn't try to sell me anything that was not necessary, which I tend to encounter a fair bit. Highly recommend.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Ed and Lynn are decent people with a fine revolving relationship with some excellent coaches and pros. They hold clinics and host leagues and have been a vital part of the winter tennis community. If it's raining or cold, or if you want to play doubles, this is the place to go. The courts play fast, they are relatively well heated and aerated and the lighting and upkeep has been better than good. Court fees are slightly high, but if you're an addict, it's worth it. Coach Dave Bender who runs clinics and classes there is especially good at his job.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Pittsburgh Indoor Tennis Club is a great business! I went to the Monday night clinic with Pro David Bender and it was great. Nice people, great drills, good mixture of skill, perfect way to ease back into the game! They have more advanced clinics at well for those of you who can play. The building is convenient if you live in Shadyside. Did I mention the clinic is very reasonably priced?! A++[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm torn! If I could give it 4.5 stars instead of 5.0 I would, but I can't quite do 5 because I've been to other Pittsburgh facilities that have better court facilities and my own home courts out West didn't get a 5, so I can't be accused of bias, haha. + +PITC is just that, the Pittsburgh indoor tennis club. It is conveniently (for Shadyside and surrounding areas) located in the East Liberty area, very close to Target, PetSmart, and Pizza Sola. + +There's five courts, four full courts and one singles-only court. They play faster than average with a low bounce unless you're a heavy top-spin hitter. They're definitely kept in good condition and for an indoor facility that seems to be older in age the lighting is quite good. + +I did their two hour clinic on Sunday afternoon after playing a USTA match there and I can definitely say it is a great great great value. You get an excellent workout and the teacher during the clinic actually gives your pointers and provides remarks on your game. + +Definitely looking forward to trying out more of their clinics in the future.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This club is now officially closed for good due to redevelopment in the area.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> What would Pittsburgh do without Time Bomb. + +It is the best store for urban clothing in all of Pittsburgh! Similar to Next in Cleveland and Standard in Atlanta. I have been copping from there for over 10 years! It it located in the Shadyside area of the city bordering East Liberty near Villa, David's Shoes and Ace Athletic. + +They offer tons of brands for men and women like Artful Dodger, Cold Chillin, Crooks & Castles, Dime Piece, Evisu, Five Four, G Shock, LRG, Married To The Mob, Play Clothes, Kid Robot, The Year Of and many more. They also carry both local and national mix tapes and also have artist's coming through the store to show love. + +If you're ever in Pittsburgh looking for some fresh gear and music make a trip to Time Bomb! Get ya life right! What up Brick?![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Hats? They got some sweet stuff. +Shirts? Stuff you won't get anywhere else. +Socks? They got you covered. + +Great staff and cool location. Go check this place out.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> TimeBomb is without a doubt the best spot in Pittsburgh to get all the exclusive Raw street merchandise. This is my favorite store in the city not only because of it's selection of merchandise, but for it's uniqueness. + +The owner Brick who started the store in '95 I believe is a great guy who always takes care of his loyal customers. I've received free apparel, stickers, DVDs, mixtapes, you name it from Brick. He's a man who knows how to keep his customers coming back! + +All in all TimeBomb is the place to shop in Pittsburgh if you're looking to ""Get Your Life Right""[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My favorite restaurant in Pittsburgh- I had great experiences with their Korean selections like Bi Bim Bop, Chicken Katsu, and Jum Bon. Must try! Great atmosphere, wonderful people, reasonable prices.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Jimmy Tsang's Chinese Restaurant is one of the old ""traditional"" Pittsburgh restaurants, a place you remember as always ""being there."" My parents feel the same way about it. It is a good, if unspectacular place with reliable, tasty fare like honey chicken, Chinese flank steak, and authentic eggrolls. + +I don't normally go for the spicy fare, indeed I prefer the plainer dishes like chicken with vegetables, but they have one item on the menu that I've always wanted to try--Sau La Gi, which is stir-fried hot spicy chicken, onions, green onions & fresh bean sprouts. Perhaps I've never noticed, but I don't recall seeing it anywhere else. It was good, but Hoo-Boy did I have to pace myself while eating it. And have plenty of water nearby! Sau La Gi was worth trying once, but it really wasn't to my tastes and I doubt I'll have it again. + +My friend Maryann tried Ching Za Gai (spicy also) which is roasted crispy chicken served with tangy vinaigrette sauce. I sampled it and perhaps I will order that for myself next time. I'd like to cook a milder version of it myself at home. + +More to my tastes however are the Garden Chicken, Chicken with Broccoli, or Beef with Pea Pods. Seafood dishes include Sweet and Sour Shrimp and Sauteed Shrimp Szechaun Style. Yeah, I'm a little unimaginative when it comes to Chinese food, but I know what I like and if a place can do the basics right, it's okay in my book! + +Jimmy Tsang's also has a convenient and inexpensive lunch menu. The place also does Korean Barbecue and you can book a private dining room for you and your special someone with a $100 deposit.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> You can see their second bar through the front windows. I always assumed that that was their first bar, and just walked by the place maybe a hundred times, until walking in and noticing that everyone was drinking in a different bar. + +In other words, this place is *huge* inside. The place looks like it was decorated about the same time many other cities built up chinatown areas; I like the decor, even if it might be slightly dated. + +Chinese and Korean food, at or above my expectations. The stuff on the menu is good, and they're willing to put together things that aren't on the menu if you ask nicely. Kung pao tofu is my favorite so far.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I happen to stumble upon Jimmy Tsang's while up in Pittsburgh visiting. I must say, the food is REALLY good. The service was great - but I only had a drink there with my boyfriend and we got take out. We liked it so much, we got take out for my family 2 nights later. + +The woman that runs the front is very nice / sociable and likes to talk about each dish. She has great suggestions for your taste. Her husband is the chef (they are both from Korea) and he has been cooking as head chef in restaurants for over 20 years. If you like Chinese food, you will love this place. It also has two cool bars inside. + +I highly recommend this place. The reason why I give it 4 stars is because we got take out - not sure how table service is, but I'm sure it would be good with the nice people working there.... + +A must try! I bet it would be a cool first date kind of place....[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Walking into Jimmy Tsang's was like walking into the Chinese restaurant that was on Hawaii Five-0 - it puts you back in time to the 1960's and the food is reminiscent of that era also. + +Hot & Sour soup was highly americanized, not very hot or very sour. +Wonton Soup was a very large portion and good. + +Egg Rolls were large, slightly greasy but the filling was flavorless, not very good. +Cheese wonton's were okay but the old grease used to fry them in over-powered the flavor. +Chinese Flank steak was tough and chewy in a soy style sauce thickened with cornstarch, a little too salty and greasy but overall it was good. +Flaming chicken was chicken breast with sugar peas, bamboo shoots and baby corn in a white/clear cornstarch chicken base sauce, that lacked much of any flavor except slat - it was just okay. + +Tea tasted like American Lipton brewed in large quantities in the back than served in a generic tea-pot. + +The place was clean service was good, prices are very good, but the food was just average.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I really feel bad about giving a one-star review. First, it's not about the service, price, decor, or the food. I'm writing this review after going there twice. The first time my husband and I went, the dinner was good. We thought this place has the potential to be our go-to Chinese restaurant in Pgh. Today I remembered that they have an early-bird special 3-6pm (m-sat). The won ton soup was not authentic (more like chicken noodle soup) but wasn't bad. The entree was fine. + +What really knocked the score down to 1 is the awful tobacco/cigarette smell from the tea!! ? !! I had to go to the grocery store and buy a pack of gum. The smell wouldn't leave me so I came home to rinse my mouth with Listerine (2-3 minutes) then brush (as long as I could) to get rid of the smell. Did they use the tea pot as an ash tray? + +[first visit: 3 stars] + [second visit: -5 stars] = [ -2 stars][/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Hey, Jimmy! Cigarettes are not a replacement for tea bags! The early bird special is cheaper because it is mostly cabbage and the tea tastes like second-hand smoke. +I had the same dish previously, without the special and it was fine (hence 2 stars and not 1). I'm going to avoid this place until I get a craving to drink tobacco.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Went there last night with 8 peeople. There was another 14 people party. + +The food was good -- not great but good. We waited 45 minutes for the first dish to arrive and that only because we sent one of our folk to see what was going on. + +They did bring drinks and tea promptly.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I was expecting a lot more from JT but realized that it is a restaurant that serves both chinese and korean but not in a fusion type of way. It merely has a chinese menu and a korean menu. The idea was cute. They even have typical chinese lunch specials. + +The deco needs upgrading and dusting -- some lighting or even natural light (its like walking in a cave!) and some other reviews were right that it has a hint of smoke in the air. + +I had a craving for comfort food and ordered Jajangmyeon and grilled calamari. The tea and water was served as I sat down. I went a little after the lunch rush so there was not too many people. The calamari came out promptly and the Jajangmyeon took a little longer. The portions were huge! + +What took the longest and annoyed me the most (I was the only one left at the restaurant) was waiting for the check. Why does waiting for the check take 45 minutes? They never came the clear the table or walked by so that I could signal that I needed the check. I should have just walked out. The food was okay but I seriously needed to get in and out of there in a certain time frame that they didn't help with. You may want to consider going when you have a 2 hour lunch break.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Closed. Signage down. Boarded up tight. Phone disconnected.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Yep, closed! My dad and I were gonna come here dinner last night. He called me and told me to meet him at China Palace instead. + +So long Jummy Tsang's! You were one of the last of the old time Chinese joints.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Big fan of the staff here as well as Dr Novak. +I began going as a first-time patient of any chiropractor and he has made me believe a believer. +I have had lower back pain on & off for 5+ yrs and went to him when I woke with excruciating pain one morning. After just one session I could feel partial relief. I went back several more times over the next couple weeks and it helped a great deal. +The best part is that they can pretty much always fit you in the same day as you call which is fantastic.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I first found the Newman Chiropractic Center about 2 years ago when one day, my lower back pain got so severe I could barely walk. I called one or two other Chiropractic offices first and neither could see me that morning or even that same day. Dr. Novak at the Newman Chiropractic Center was able to see me immediately and since that day, I've never even thought about going anywhere else. Whenever I need an adjustment, I simply call ahead and let them know I'll be stopping in; they are extremely flexible and understanding of my busy schedule. + +I look forward to visiting the office for an adjustment because I know that when I leave, I will feel amazing. The office itself is not as posh as you might find other places in Shady Side but it's welcoming, comfortable, and certainly gets the job done. + +I have and will continue to highly recommend Dr. Novak to anyone who is need of Chiropractic care.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Best chiropractic center I been to others Dr Novak and staff are the best in the Pittsburgh area they are concerned and problems always taken care of excellent adjustments I always feel better after I leave there[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great stuff here...The cheese plates are great and always changing. Awesome staff, and the menu offers an nice variety!! + +Ask for Tim for your waiter![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place used to have a great bar/tapas menu with a decent selection of happy hour wine specials. Now... not so much. Well, during HH, you can get any of the wines under $10 for $5. Selection by the glass is limited. + +As for their menu/dinner - this is totally a different story. I haven't really been disappointed yet! The appetizers/small plates all pretty good, I really like the chevre croquettes ($7). The salads are good and although I haven't gotten the soup anytime lately, I hear great things from my friends. The entrees are always excellent - I usually tend to stick to the seafood (halibut, $29) and never have been disappointed (and importantly, nothing has ever been overcooked). The signature orecchiette dish ($20) is soooo delicious - just ignore the fact that it is a heart attack waiting to happen - it's worth it. The desserts are ok, personally, I feel that you would be better advised to stick to filling up on the entrees. + +Oh, and let me recommend the blood orange martini if they have it - very very yummy! And it is nice that you can order Veuve Cliquot by the glass ($16). + +Prices are a bit high for what you'd expect for Pittsburgh, but considering the quality of food, I would recommend it. + +P.S. I have heard that they have a great brunch on Sundays. I personally haven't tried it, but with the number of compliments I hear, it's probably worth the try! + +------------------------- +Update 12/9/07: Went to the brunch. What a great deal! For $22, you get a choice of alcoholic beverage (bloody mary, mimosa, bellini) as well as a starter and then the entree. They have a lot of choices, so be prepared to just try one and come back again to try the other stuff! The smoked salmon appetizer was good although with too much mayonnaise sauce and for me, too much onion. The truffled potato was yummy. The arugula salad was as delicious as ever! And for entree, we both got the Casbah benedict. I have to admit that neither of us was blown away, but it was good and filling. I think that we will both be back to try other things on the menu![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Well it's official Shadyside is becoming my new favorite area for restaurants. Damn you Big Burrito Group with your local ingredients, contemporary design and excellent service. I was here last night and on a Monday this place was doing brisk business (definitely a good sign). The space itself is beautiful. You enter from S. Highland into the outdoor dining area, which because of the heaters is viable almost every day of the year. There is plenty of seating outdoors and a few tables indoors. The design is contemporary. The bar is large and has a nice area opposite for more informal seating. The one thing I dislike about the bar area is that the ""stools"" are actually chairs that are not moveable, so your distance next to your ""neighbor"" is pre-determined. I also prefer to stand at the bar instead of sitting and this set up makes that more difficult. The wine selection is pretty extensive and they have a good happy hour special that any wine or premium cocktail is just $5, which is really good when many of their wines are priced at over $10 per glass. The hostess was very nice and professional even though she was young taking our names as we went to the bar for a drink and then anticipating our return with two menus in hand. The server was a nice enough guy and helpful when it came time for our dinner selection. We ordered a bottle of conundrum which is a delicious choice and I guess in line with what others charge. We were started with an olive tepenade (sp?) and some crusty toasted thinly sliced ciabatta I think. The tepenade was too oily and salty for me, but I guess it's what I should expect since it's ground up olives basically. The bread was great. It was warm really hearty bread that was wheat I think, definitely not white. It was served with room temperature butter with some sea salt on top. Really good start. We then tried the smoked salmon appetizer. I'm a huge fan of smoked salmon and was pleased with the quality of the fish, served nicely with capers and chopped egg. It also was served with a patatoe pancake that was crisp on the outside with warm and delicious filling. The only thing I was a bit perplexed about was why it wasn't served with some type of bread or crouton to put the salmon on. However, the waiter was happy to oblige by bringing out a few of the toasted ciabatta. We also tried the lamb mac and cheese (omg was this good). The pasta was cooked al dente' and definitely made in house. The sauce and lamb were amazing. This would make a fine entree' in my opinion and is total comfort food reinvented. The only detraction I'd say is that it is a very heavy dish to serve as an appetizer on a summer menu. Fiona had the arugula salad which was nicely prepared with pork belly (kind of like bacon), feta, and a few other interesting ingredients. We also tried the short rib ravioli, which was incredible as well albeit a heavy dish. By the time we got to this I think we only tried one ravioli each (plenty of leftovers). This is such a rich dish, because shortribs are like the epitome' of richness and then to wrap them in ravioli and add cream sauce is really indulgent. But, then again this is my chef not my cardiologist. I tried the Elysian Fields Lamb which was cooked perfectly medium and then served with their homemade pasta wrapped around some of the lamb as well. This was really good and the pasta was a surprise. I actually would have preferred a green vegatable on the side instead of pasta and mashed potatoes. The bartenders are good, especially FionaOverall, a really good place and a nice flagship of the big burrito group.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> As the reviews of Casbah appear to be particularly long-winded ... the place is nice, fancy, organic-ish, alternating menu, nice atmosphere. Good date restaurant. Good food-lovers restaurant.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The food here is pretty good. Comparable to any 3 to 3.5 star restaurant. The lamb is definitely good. And it is definitely a good date restaurant. I would rather give it 3.5 stars since I've definitely eaten at better restaurants. But for Pittsburgh, it ranks pretty high up.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I went to Casbah for brunch, it's a $22 prix-fix, which includes an alcoholic bev, an appetizer and an entree. They use amazingly fresh and yummy fruits and veggies. I had the house made granola which was just amazing! Toasty and sweet, it was nothing like the granola you get out of a box. Also, while the food is totally fru-fru (in only the best way :) and it's a pricey brunch, you get a lot a food. After the great pastry basket, my appetizer, a Bellini and a cup of coffee, I had two bites of my omelette and took the rest in a doggy bag (""the rest"" included fruit salad, potatoes, and a croissant!) + +My only complaint would be how long everything took. While I love a leisurely meal, an hour and a half for brunch seemed a bit excessive. I go into brunch groggy, then I have coffee and yummy food, and I'm totally amped, ready to face the day! And then I get to sit. And wait. Anyway, it's totally not a big deal, now I'll know to make time the next time I go. Which is for dinner for a friends birthday. So excited!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Can be moderately priced for lunch -- take advantage! We had a cheese tasting simply because I *never* pass up Pleasant Ridge Reserve when given the opportunity. They also choose a lovely soft sheep's milk and an herbed goat cheese from Cypress Grove. Nice work but pricey -- only two slices of baguette and apple! I had the romaine salad -- should have gone with a sandwich and the delicious looking truffle fries! The feta and red pepper dressing were just too salty and rich for 1pm. I spied a number of delicious looking sandwiches from my table... + +Service was great and the waiter even went out of his way to answer a couple questions about the cheese selection.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> After a long day of recruiting at CMU, I arranged a dinner for 16 people here in Casbah... Prefix menu, over all the experience was ok. + +Break down: +Scallops - Appetizer - I had high expectation but it came out a bit too over spiced. Very rich i am glad they only gave me two. +Fillet Mignon - Entree - Very tender piece of meat but no wear near as good as some of the places here in the Silicon Valley or even some of the chain steak places like Morton's. +Dessert - The highlight of the of the meal. Mango panna cotta with some sorbet. It was amazing. The consistency of the panna cotta was perfect. It wasn't too dense or too liquidy. + +Being a Big Burrito restaurant, I expected more but it was good nonetheless.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> So I went back to Casbah for dinner and was totally underwhelmed. The granola I had for brunch (in my previous review) was better than my entire dinner put together. The service was better at dinner then at brunch, but the food made my rating drop from five stars (probably a little generous) to three stars. Definitely go for brunch! But it's not worth the money for dinner. Mediocre food in a nice atmosphere with good service is still mediocre food...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm not sure why this place is called Casbah. Casbah conjures up images of genies and sand dunes or something. Nothing about this place seems remotely middle eastern to me, other than the name. + +That aside, good food and great service. Definitely a place to impress. I especially enjoy patronizing establishments that focus on seasonable, sustainably harvested ingredients, and although Casbah is not doing the whole ""locavore"" thing, it certainly is striving for the organic and seasonal thing. So, off the bat, that gives it big points in my book. + +We started with the calamari and the squash ravioli. Skip the ravioli - small and kind of dried out. But the calamari was MEATY and perfectly fried. I actually had to stop because I was feeling ill from eating too many of them. + +We all had the argula salad, which was delicious. Quite sizeable too, given the setting. Finally, I had the scallop and crab meat... uh... pasta dish (I have no idea what kind of pasta it was... sorry). Which was quite good. I actually would have preferred it over linguine, I think, but whatever. It was deelish. + +Not sure why I'm not giving this place five stars. I really enjoyed it, but it wasn't a WOW experience. Better luck next time perhaps.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Another great big burrito restaurant, Casbah offers some great wine and spectacular food in some great, and varied, dining rooms. + +The three dinning rooms, ""outside,"" inside and downstairs. While downstairs isn't always open when it is try and get a seat down there, it is beautiful and quiet. Perfect for a larger group of people. Outside is always open and you don't really realize you are outside aside from the non-padded patio chairs and heat lamps all around. + +The food is Mediterranean fusion, not exactly sure what is meant by that but it is good. The hummus here was actually the first hummus that I had ever had and I am sorry to say it is what I compare all other to, few match up. + +The wine list is extensive, but if you are going for an upscale bar this isn't the place, for that you'll want to go down the road to Soba. If you want a nice place to have a drink and a conversation, Casbah is it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I was pleased to finally find a place in Pittsburgh that's worth it for me to spend some money. I tire of eating out only to become dissatisfied knowing I could have made the meal better myself. Not here. + +The food is made to order, seasonal, local, some organic...in short, they actually care about the quality of the food which is becoming a rare trait in restaurants today. I had made it a point to never eat fish in a Pittsburgh restaurant but Casbah changed my mind. The cod dish I had was delicious--not overcooked, breaded, too oily or too salty! + +Decor is subtle and great for a date. Service was friendly and accommodating. I will most definitely return![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great great for parties and celebrations of all kinds. The wait staff is extremely knowledgeable of the menu and the wine list. The Food is creative and many of the items are organic or locally grown. Everything is so fresh and pretty, you almost don't want to eat it. The wine list is extensive, and although it can be pricey, they have great happy hour specials.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Meh. Seriously? Mediterranean? What? Sorry, but just because you serve scallops on babah ganoush doesn't make your restaurant Mediterranean. + +This was kind of a disappointment, if you couldn't tell by my sarcastic tone. The food was good, and I had a great time, but the food lacked the final eyebrow raising component that you come to expect with the bill that follows. + +That said, the wine list was good and the prices were reasonable relative to the food. Get the cheese course for dessert and you'll go home happy.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have been coming to Casbah for over a decade (pretty much since it first opened). I very much like the place, and it has maintained its general character even as the head chefs have changed over the years. Casbah is very good about continually updating its menu in an effort to stay current and relevant. Over the years I have enjoyed many wonderful meals here including a fantastic orrechete (sp?) pasta with chicken and cranberries in a lovely cream sauce, and some of the best pork chops (double cut) I have ever encountered (although I no longer eat mammals, so they are likely to be the best pork chops I will ever eat). + +This is not an inexpensive place, it can be quite pricey for dinner. One plus is that they have a very reasonable brunch on Sundays. Their arugula salad during brunch with small diced potatoes and pancetta is fantastic. My one complaint about the salad is that it needs a bit of acid. I always ask for a small slice of orange and then squeeze the juice onto the salad. This cuts through the fat from the pancetta and makes the salad even more tasty. + +Others may disagree, but even though this is a fairly fancy place, it is suitable for children. Casbah has a semi outdoor seating area that is enclosed and heated even in winter. My wife and I have often dined here with our kids. This semi outdoor area is a bit more casual and absorbs the sounds of loud children fairly well. You can bring kids without suffering the disdain of any but the most obnoxious of fellow diners.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Amazing brunch! I'd never been to Casbah before until this past Sunday when we decided to check it out for their prix-fixe menu. + +For $22, you get your choice of alcoholic brunch beverage, an appetizer and an entree. An incredible price for a serious amount of great food. They had many options on their fixed menu - something for everyone. From huge waffles and omelets to lamb dishes, fish and the usual brunch regulars such as eggs benedict too. The appetizers list was equally as large. + +I started with a bloody mary. Was a nice middle ground between heavy and light - and it had some kick to it. Very good. For an appetizer I got the cheese and fruit plate with french baguette slices. There was a soft brie-like goat cheese, a blue cheese and a mild dry sheeps milk cheese as well. All were wonderful. For my entree I went with the Salmon Eggs Benedict. It was perfect. The fruit on the side was fresh cut, and the home fries were crispy on the outside, soft on the inside. + +I tasted a couple of other things as well. Both the polenta and the mushroom soup on the appetizer list were great. Didn't try any of the other entrees, but everyone seemed pleased. The only complaint was from a friend that ordered the truffle omelet - and it was that he thought they went too heavy on truffle oil, drowning out the eggs. + +Also, service was absolutely perfect. We had a tall waiter, forget his name, but he was one of the most professional servers I've ever had. The table was cleared and cleaned immediately...he was never pushy, always friendly, and had great suggestions. One of the best experiences I've had for restaurant service anywhere. + +For brunch in Pittsburgh, this is my favorite so far. Not to be missed! + +Now I just need to make plans to go back for dinner.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> There is a disconnect here between this name, the decor and the food. That said, I had the best pork chop I've ever had here and for that I was endlessly thankful. Good salad, delicious bread and hummus. Great service. For Pittsburgh, top notch.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My best friend and I went here for dinner today and were very pleased - though I do have to say that we both had our free birthday entrees and that undoubtedly influenced things. I was surprised at how pricey it was before the coupons, but everything was good. + +We started with two big glasses of sangria. I thought the blueberry schnapps flavor was a little overpowering at first but it either evened out or I got used to it. + +I had the risotto with morels, peas, and scallions, which was delicious. I had never had morels before and now I understand why they're so pricey. There was only a small handful of them on the side of the risotto, but they were delicious. The risotto was very creamy and flavorful, the kind I wish I could make myself. My best friend had the short rib ravioli, which she really enjoyed. I tried the sauce and it wasn't nearly as rich as it looked. + +We split a creme brulee for dessert, and the waitress very sweetly put candles in it and wrote Happy Birthday on the rim, which was a nice touch. The creme brulee was good but definitely not the best I've ever had. (That award may go to Soba's coffee creme brulee.) + +The total bill would have been $72, which seems a bit steep. But it was a nice restaurant and a really nice atmosphere. The patio was lovely. I will definitely be back, if not for brunch then absolutely for that delicious risotto![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is my favorite Big Burrito restaurant and definitely one of my favorite restaurants in the country. + +Gotta be honest, though. Just about every time I'd been here, it's with colleagues, which means lots and lots of boozing!! Therefore, consequently, as a result, in sum, I don't have a crystal clear memory of what I had for appetizer, entree, dessert, etc. + +What I can tell you is that I had never been disappointed with anything I've ordered here. And believe you me, if the food is not that good, I will remember it no matter how drunk I am. Sure, it's not exactly a ""Mediterranean"" restaurant, but who cares? The food is great, it's in a super cute hood, the atmosphere is cozy and comfy, and the service is always spot on. + +I do recall that the very last time I ate here was with a dear friend and two of her British colleagues, and we had ourselves a grand ol' time. I had the arugula --one of my favorite words. It's lovely, no? Say it with me. A -ru-gu-la! Fun, right?!! And so flavorful!! --salad and cioppino, which was outstanding with super freshy fresh ingredients. What about dessert, you ask? Sorry, kids. By that time I really was drunk, and I can't remember. It was super tasty, though! I remember everyone liking mine the best. Sure do, sugar! + +So pay no mind to others' taxonomy quip and give this place a whirl. It's a great date or small group place. Oh, and super fantastic wine list, too![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Excellent place for brunch. For $22, I had a mimosa; cheese, fruit, and baguette slices; a waffle with berries and whipped cream; two pieces of bacon; and a muffin, scone, and biscuit with honey butter from the bread basket. Service was pretty good even though the restaurant was fairly busy. Reservations available through Open Table. This is definitely a special occasion brunch, but it is surprisingly affordable.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> One of my all time favorite restaurants in Pgh, Casbah is still going strong 15 years later. Today's lunch was a wonderful mac and cheese with braised lamb; my dining companion enjoyed the corn risotto with shitake mushrooms and a side heirloom tomato salad. They use the best fresh local ingredients to craft some of the most delectable, interesting fresh food around. Also great for Sunday brunch. You won't be disappointed.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Excellent excellent brunch spot. For review #100, a 5 star review for a 5 star restaurant is definitely fitting. + +Casbah does brunch, lunch and dinner, but brunch is my favorite meal and also what they do best. I ordered their prixe fixe brunch option which is a choice of an appetizer, brunch dish, and drink for $22. I started off with smoked salmon and had the waitress recommended braised lamb and eggs as an entree and a mimosa to drink. My companion ordered butternut squash & apple cider soup, wild mushroom omelet, and a glass of fresh orange juice. + +While waiting for our food, we munched on their complimentary pastry basket consisting of super moist mini-muffins, scones, and super rich and buttery biscuits with honey butter. + +The smoked salmon came with capers, minced red onion, crumbled egg, a drizzle of aioli, and a beautiful fried potato cake. There was just the perfect amount of everything on the dish; the potato cake was just big enough to balance out the saltiness of the smoked salmon and the capers of course paired beautifully with the smoked salmon. I tried some of the butternut squash & apple cider soup and it had some a pretty complex flavor. + +My entree reminded me of an eggs benedict with a twist: grilled sourdough topped with spinach, braised lamb shoulder and two poached eggs. I love braised meats because braising can do such wonders to tougher cuts. The braised lamb shoulder was flavorful, tender, and super rich. The best part about poached eggs is sopping up the extra yolk with bread and it just tasted better with the sauce of the lamb soaking into the sourdough to soften it up a bit. This dish itself is enough to make me a regular. I tried my companion's home fries which came with this slightly spicy ketchup (I think it's house-made) and also a piece of her omelet which was pretty good too. + +Service was good, ambiance was good, portions were big, quality was excellent, AND they take reservations. Sometimes I don't mind waiting the half hour it takes to get seats at some restaurants (Point Brugge, Coca Cafe, etc.), but most times I'd rather spend time with people in the restaurant at a table rather than waiting outside, especially now with winter approaching.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Such a pleasure to dine, on my birthday, at a restaurant with such good food and cocktails right in Shadyside. We planned in advance to come here after I received Big Burrito's free-entree birthday voucher** and after coming here to sample dessert and drinks. The food--short rib ravioli, lamb and polenta, pumpkin cake with ice cream and toffee--was insanely rich and tasty and decadent, perfect for a celebratory meal. Our server made some clutch drink recommendations too. My favorite: the local martini, all made with locally-sourced ingredients and ridiculously good chevre-stuffed olives. Almost like a cocktail and small plate in one. + +After reading everyone else's reviews, I hope to come back here next for brunch. + +**to take Big Burrito up on this offer, join their mailing list decently before your birthday, and a voucher will come in the mail! It was a blissful discovery for a pair of graduate students.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I really wanted to like Casbah after checking out the menu online. I really wanted to like Casbah once I saw the super cool dark interior of the restaurant. Unfortunately, everything started to go down hill from there.... + +The waiter was less than helpful suggesting a wine to accompany our dinner, which I found to be a bit odd at such a nice restaurant. My friend and I order split the tuna tartare and the fennel salad to start. The tartare was decent but it lacked seasoning and I wasn't into the creme fraiche on top. The salad was ok but nothing to rave about. I had the short rib ravioli after reading the reviews on Yelp, but I didn't like the sauce that accompanied it. My friend ordered the risotto with oyster mushrooms and she was also less than enthused. + +Don't get me wrong, nothing about my meal was terrible, but nothing about my meal was spectacular either. It looks like maybe I should have tried brunch. We shall see if I'm willing to give Casbah another chance....[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Out of the Big Burrito group (not counting mad mex) this is probably the biggest disappoint of their chain. And this is just not a one time bad experience, I have been here three times and have been less than enthused with the food vs price/value. + +Service has always been good and attentive I enjoy their wines and the selections but on almost every dish there is something is either wrongly out of place or I expected much better for the money I am paying. For example: + +Sumac scallop Appetizer, cooked perfectly, but the tartness of the sumac was not there, the other thing is I can brown a scallop at home, in a restaurant I am looking for a perfectly cooked scallop that has a nice caramelized sear on it, almost crunchy top juicy center. Also why so stingy with the baba ghanoush, 1 tsp, come on, eggplant is that expensive. + +Risotto - Over cooked not even a little bit of toothiness to the grain, plus it was pretty devoid of flavor but seemed to have had the addition of cream and butter to make it creamy. + +Duck Entrée, again duck was perfectly cooked, quince jus was nice, not overly sweet but the faro did not compliment the dish at all. I even had a dining companion taste the combination and asked if they like it and they said it didn't go. + +Pasta entrée with spinach, this could have been good, but spinach was not washed and had grit in it, this item was returned and a braised lamb dish was ordered in its place, the lamb was slightly undercooked (read just a little tough) and jus that went with it was very watery. + +If this was some little bistro where I was paying $20-25 for dinner (no drinks) I wouldn't be so picky but some of my meals have been north of $40 and for that amount of money I expect a little more attention to detail.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm a big fan of all the Big Burrito restaurants I've tried (Eleven, Umi, Mad Mex & Casbah). I think Eleven is my favorite, but Casbah is a very close second. + +My most recent trip was with my wife on 1/15/10. We started with the grilled flat bread and the butternut squash ravioli. For entrees, I had the Casbah twice cut pork chop and my wife had a pasta dish with sausage and ricotta. For dessert, I had the creme brulee and my wife had the espresso ice cream / cookie (it was really just a fancy chipwich). + +The grilled flat bread came with three different dips, Humus, Red Pepper Hummus, and Baba Ganoush. I really enjoyed all three, but thought the Red Pepper Hummus stood out as the best, although if you're not a fan of garlic you may disagree. The butternut squash ravioli didn't impress me much, but my wife really liked it. + +As far as the entrees, we both really enjoyed our meals. My pork chop was cooked perfectly, and was anything but dry. The sage aioli that it was topped with added an excellent flavor. The sides were kale, and butternut squash risotto, both of which really shined. I can't describe how amazing the risotto was, and the kale was extremely flavorful. + +I tried my wife's pasta dish, and overall I thought it was good, but the sausage was really outstanding. Incredibly tender and flavorful. + +Neither of us were too impressed with our desserts. The creme brulee was very good, but at that point, I expected it to be great. My wife's dessert sort of disappointed, since the cookies were dry. + +The bill for everything listed above, plus a bottle of red wine (~$35) was $120 before tip, so it is pricey, but in my opinion totally worth it. + +Also, our server was very attentive and helpful, without being intrusive. I asked his opinion on the French Malbec and he gave me his honest opinion, which was negative.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> One of my favorite restaurants in the world. + +Excellent atmosphere, fantastic food, great wine/drinks. Menu changes up pretty regularly and I've never had a bad dish there. The stuffed pork loin was one of my favorites. Also they usually have a summer sangria (even in winter :) that is delicious. The scallops were also fantastic. The front patio/tent is open year round with heat lamps. + +Revision: + +I was just back at Casbah for a fundraising dinner. Once a month they do a private dinner for a charity - for $100 there is a five course meal with wine flights. All proceeds (not just the profits) go to the charity. + +My dinner was so good, I literally almost cried. The wild mushroom risotto was bar far one of the the best things I've ever eaten in my life. Short rib ravioli was my 3rd favorite thing I ate that evening, but I found myself dreaming of it the next morning! I had low expectations for dessert - it was a cornbread cake (weird!) but came with a blueberry compote and cream cheese ice cream. The cornbread cake was an excellent balance between the sweetness of the ice cream and blue berries. It was amazing! + +While I don't believe these are regular menu items, I highlight this because this was their charity dinner. That they made NO money off of. An area where they could skim on quality - but no - it was amazing. Reaffirmed my belief that this is the best restaurant in Pittsburgh.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Part of the same restaurant group as Eleven, which I have eaten at and reviewed here, Casbah is a vibrant restaurant in Pittsburgh's Shadyside district. + +While the menu changes daily, there are several mainstays available on most evenings. One of them, the pork chop, is one of the finest I have ever had. Double cut, juicy and flavorful, it is an absolute winner. Braised kale and butternut squash risotto accompany this perfect dish. + +I managed to sample two other dishes (courtesy of my willing dinner mates) that are also noteworthy. The short rib ravioli is an excellent combination of tender, richly flavored beef rib and toothy pasta. The ricotta cavatelli combines fresh, simple ingredients into a well structured dish. + +Service was a little hit or miss the evening I was there. Part of that may be because we were a large group and the restaurant was rather busy. However, for an establishment of this caliber, I do expect more. Nevertheless, I plan on trying Casbah again on my next trip to Pittsburgh.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We decided to give brunch a try for our first visit to Casbah. We were surprised by the huge tent covering the ""outdoor"" dining area. We opted for an inside table, the interior is somewhat small the tables are close together. For brunch, you are served your choice of drink, appetizer and entree. + +For our drinks, BJ had a Bloody Mary and I had a Bellini. We were served a basket of yummie bread and mini muffins. For appetizers, we got a Three Sisters Farms mesclun greens and smoked salmon and truffled potato cake. Very good. For entrees we selected a jumbo lump crab & tomato omelet and the NY strip steak. Very relaxing and tasty meal.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I was determined to let this one pass (experience was not worth commentary) until I made a disturbing discovery... + +I made a reservation for inside. They sat us outside. That turned out to be preferable to us because the tables that WERE available inside were very close to others. The patio was spacious and decorated with busts, slightly preferable to the inner cheap.trendy.interiors.com shit. Have you seen the terrible bathroom wallpaper borders? Probably not, as the ladies room is a very dim place; don't expect to be able to notice that your botox implant is crooked. Anyway, It was HOT under the Space-Ray heater on the patio, making for a sweaty and ice-instantly-melted beverage winter night. The food was alright with some interesting flavor pairings, but it was certainly not quite worth the price. The bread was the best I've had in Pittsburgh. Our server made it seem that everything she was doing was somebody else's job, in fact, it was mostly other people who delivered, which made it confusing in terms of knowing who to ask for things and whether or not to factor some of the fine service into the tip that presumably goes mostly to the primary server who was sub-par for upscale dining; our question for the kitchen left unanswered, ""the host is supposed to do that but I will..."" Run on. When I described the qualities I was looking for in my wine choice during beverage inquiry, she just stared blankly and waited for me to decide. The wine list did not include descriptions. The gal who delivered the wine thankfully did describe it before popping the top and it was determined that I did not want this cheapest option before me! She described another bubbly that sounded and was, according to my own tastes, delightful. + +I was so very satisfied with the sparkling sensation of the meal that I sought it out at the Wine and Spirits store. This was the moment that my minor disappointment in the value of my special-occasion dinner at Casbah turned into a feeling of devastating violation. I am talking about a 400% markup on the retail price of this wine. If you want to do your own math: at Casbah the 1/2 bottle of Gruet Blanc Du Noirs cost $35, while a WHOLE bottle at W&S is priced at $16.99. You can bet that I will choose to enjoy this wine elsewhere, like Avenue B (byob), next time. + +Casbah is lacking the quality service, honesty and original ambiance that should accompany creative food at moderately high prices. + +**Update: I recently saw a full size bottle of the Gruet on a restaurant menu for $30; Casbah, take a tip![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I went on a date with my girlfriend here, and it was a great experience. Charming outside dining area with excellent service and a knowledgeable staff. I will say that the food was a bit overpriced, but that's to be expected in Shadyside. Great selection of fresh seafood - I had the salmon and it was delicious. Reasonably priced wine list, as well. I would recommend Casbah for a special event or if you're rolling in the $$.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My boyfriend took me to Casbah for my birthday this March. This is one of our twice-a-year splurges and I have been wanted to go to this restaurant for ages. +We were seated outside, in the covered, heated patio. We were far enough away from the heaters that we didn't get too hot, and far enough from the doors that we didn't get too cold. The menu has changed slightly since we dined there, but some of the things have stayed the same. +We started with the sheep's milk gnudi, which is like ravioli without the pasta. I have a gluten allergy and I have missed ravioli quite a bit, so I was happy to eat this. The flavor of the sheep's milk is quite strong and unique, which I like. +For entree, I had the double-cut pork chop. This was absolutely great - the flavors and textures of the pork, butternut squash risotto, braised kale, garlic cream, and sage jus went really well together. It was an enormous portion, as well - I took some home and ate it the next day! +My boyfriend had the seared rare tuna. He was less thrilled with his dish, and when I tasted it, I agreed. I normally LOVE seared tuna but this was not the best treatment of it. It tasted a little too ""fishy"" and I didn't think the other flavors complimented the tuna. +Instead of dessert, we sampled two dessert wines recommended to us by the server. I do think that $10 is a little much to charge for such a small glass of wine, but I guess that's what you have to expect when you dine at this level. +We are great fans of the Big Burrito restaurants, and I think we preferred our experience at Soba to Casbah. While our food was really good, the prices were a little unreasonably high. And I wouldn't recommend the seared tuna![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Went here on father's day with my best friend and it was oddly not crowded at 11:30am on a Sunday. Anyway, we got the Brunch prix fixed meal with mimosas! Yum. We sat outside and it was just a nice cool environment with the overhang of plants and vines. + +For my 2 courses I got the cinnamon polenta which is basically like oatmeal but much more creamier. IT was honestly, amazing. I loved it. It came with some almonds and some cranberries, but the polenta itself was great. I would come back just to have that for breakfast. For the main dish i got a crab omelette. It came with fresh fruit and potato fingerlings. The potatoes were great and the omelette was ok. Not the best I have had, but any place with crab in an omelette should get credit. + +It was a great brunch and i was stuffed by the end. This place was courteous and the waitress was attentive but not overbearing. We had a great time here and it's just a nice place to relax.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> For our last lunch in Pittsburgh we decided to return to the Big Burrito Group; Eleven was quite good and both Gayot and Pittsburgh Magazine compared the experience at Casbah favorably to that of Big Burrito's crown jewel. Citing a mix of Mediterranean and Northern African influences with a bargain Piccola Gusto Menu for lunch and the option for indoor or al fresco dining it seemed as if Casbah was a can't miss option...well, sometimes things don't turn out quite as you expect - almost everything that transpired from the moment we arrived until the moment we left was a failure. + +When our server, a young woman named Amanda L who would prove quite inept and inefficient from start to finish, finally did arrive our menus were delivered with a brief hello before she wandered away - another server later stopped by to fill our water and drinks were never even offered. When Amanda finally did return she was capable of answering a couple questions about portion size and our orders were placed. With my mom and sister opting for the two-course Gusto lunch and myself choosing two courses a la carte we sat and sipped our water. + +Waiting approximately 10 minutes another ancillary server arrived with bread and butter - a light and airy white bread with a hefty crust paired with a sweet and salted cow's milk butter - decent, but nothing to write home about compared to the myriad bread options at Eleven. After this point we would not see another staff member for 30 minutes...well, we would see them, they just wouldn't be walking anywhere near our table - instead bussing tables and running around while the hostess flirted with a man at the bar...I'll note that my water glass remained empty for greater than 15 minutes. + +Finished with our first courses approximately 10 minutes would pass - long enough for me to actively collect each and every plate and stack them at the empty seat of our four-top - before Amanda would finally return to collect the dirty plates...we'd not see her again until 15 minutes later when she filled our water glasses and told us our main courses would be ""right out."" While I guess she didn't define ""right out,"" what this actually meant was ""in 25 minutes."" Starting first with my mother's combo - Jumbo Lump Crab, pepper bacon, avocado, radish sprouts, on a paesano bun and Orecchiette Pasta with grilled chicken, dried cranberries, Riverview Farms goat cheese, sage cream. While the sandwich may not be memorable, the pasta was actually quite impressive. Using a less salty cheese and mild cream to flavor the al dente little ears of pasta worked wonders while the sweet/savory mélange of craisins and grilled chicken were a nice match. + +Vastly less well done than my mother's plate would be my sister's option - the Grilled Vegetables, portobello, zucchini, eggplant, arugula, chickpea hummus, on baguette and Maccheretto pasta with wild mushrooms, white beans, sun-dried tomatoes, rapini pesto, fontina, walnuts. Beginning with the sandwich, the bite I had was good in taste but rather mushy in consistency - too many similar vegetable textures and the hummus spread too thickly. Moving on to the pasta - we all tasted it, but I'm still not sure what we were supposed to be tasting - it tasted like watery cheese...no spice, no salt, and certainly nothing resembling pesto or tomatoes. For the first time in the meal Amanda actually opted to check on us approximately 10 minutes into our main courses and when told of the watery pasta she did apologize and offered to replace it with something else - more Orcchiette. + +For my main course I received a simple side salad-fresh greens, crispy onion strings, and a pleasant vinaigrette. The salad, of course, was served alongside Elysian Fields Lamb ""Mac and Cheese"", tubetti pasta, mascarpone, cheddar, Pecorino-Romano, and bread crumbs. Piping hot and browned with crispy bread crumbs the dish was a decent Macaroni and Cheese, but honestly the lamb was so scarce and thinly cut that it added little. + +Completing our mains approximately 110 minutes after entering Casbah we again waited nearly ten minutes before anyone would stop by to collect dirty plates-a different ancillary server this time. With my mother and sister already deciding enough was enough they stood up to use the restroom before leaving-by the time Amanda would stop by to ask if anyone would care for dessert our two course meal had lasted 2:05 and I skipped on a menu entailing bread pudding, carrot cake, and panna cotta with ""just the bill."" + +Settling the bill via credit card no tip was left because no tip was deserved - in reality Amanda may have actually be the worst server I've encountered at a fine dining establishment in the last 2 years. I will note that when I wrote to Big Burrito was met by a (seemingly) sincere apology without excuses - the Manager stated things don't' normally happen like that and he'd be sure the issue was addressed. He closed with ""I hope you will join us again."" I will not.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I ate here in January and was very impressed. We ate in the basement, although Casbah has two floors and outdoor seating. I thought the atmosphere was very good, and the fish (I forget the exact dish) was well-prepared. + +This is on the expensive side, but worth it for a special occasion.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Another one of Pittsburgh's finest restaurants. The best things about Casbah are it's very cool atmosphere, good service (a very friendly hostess and knowledgeable server). + +I had a wine flight (they have a good wine selection), and several appetizers, soups and salad. Everything was delicious, especially the complimentary bread and they olive oil-based stuff you can put on it. Most of the ingredients come from local farms and food suppliers, and I really liked they even gave them credit on the menu, the first time I have ever seen that in a restaurant (shouldn't they deserve at least as much credit as the chef? After all, they spend months growing the stuff chefs spend maybe seconds using). + +The atmosphere is really cool, I recommend sitting out on the patio in summer. The only negative things I can say about Casbah is the high price for relatively little food and the misleading name (I expected more of a Middle Eastern menu and vibe).[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Casbah is great for a special occasion or if you feel like splurging. The atmosphere is very nice and the food is fantastic. The beer selection is above average.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I had lunch here on a hot Saturday, so we skipped the outdoor seating in the front and opted for the air-conditioned interior. + +The sweet corn fondue appetizer was a definite highlight of the lunch. I had thought that the cheese might drown out the flavor of the corn, but both flavors held their own very well. The chanterelle mushroom and goat cheese omelet I had as my entree was okay but not outstanding. I did, however, enjoy the mesclun salad that came with the omelet, especially the vinaigrette and fried shallot slices. Dessert was a semolina cake with macerated fresh peaches and cream cheese ice cream (think cheesecake flavored). The bookends of my meal were so delicious that I wasn't all that disappointed by the middle portion of it. + +While I can't afford Casbah on a regular basis as a grad student, the prices aren't exorbitant. There's even a lunch special for $14, which gives you two courses: either a salad or cup of soup, and your choice of a pasta, risotto, or half a sandwich. I didn't choose this option, but it seems like a reasonably-priced way to sample several things on the menu. + +Our server was very professional, and checked on us after every course (the appetizer, entrees and dessert). I'll definitely keep Casbah in mind for special occasions in the future. It's classy without being pretentious or stuffy.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> If I could, I'd dock a half star after my second visit. But I feel positively enough about my first meal there, that taking off a whole star seems harsh. + +I got a free entree coupon for my birthday, for signing up for Big Burrito's mailing list, and decided to revisit Casbah. The good: we got to enjoy the patio even though the weather was a little cool because it was heated. My maccheretto, a pasta entree with white beans, sun-dried tomato, pesto and walnuts, was very good. The pasta was al dente and the white beans were perfectly cooked (not mushy). It was maybe a touch too salty (the fontina, maybe?), but I was happy with the choice. + +Now, onto the weird. After taking our orders, our waiter asked if we wanted bread with our big-calorie pasta dishes. Checking if we want bread is fine--but, umm, he could have left out the comment about the pasta? My friend and I are both twentysomething women. Luckily, we're not that insecure about our bodies. We like to eat. Yes, bring the bread. + +When he brought our entrees, he sang ""Happy birthday to you, happy birthday to you"" under his breath as he put my pasta in front of me. I don't like people singing to me at restaurants, so I'm grateful it wasn't audible to everyone else on the patio--but a simple ""Happy birthday"" would have sufficed. Then when he cleared our plates, he asked if my dish was ""everything [I] wanted, and more."" I appreciate the gestures, but it felt artificial. + +He asked if we'd like to see the dessert menu--and added that he was supposed to ask that, that we shouldn't feel obligated. Uh, what? I think this and the bread/pasta comment bothered me the most. + +To redeem the birthday coupon, you have to show an ID. I recently cut my hair, so it's different than my license photo. When he returned my ID to me, our waiter said, ""I like the short hair."" If this had been the only unusual statement he had made during the meal, I would have taken it as a compliment. I guess it is one. But when considered with all the other weird things, it just felt like he was trying way too hard and my friend and I both felt awkward. + +The food here is good and I feel that the service this time was unusual, and the more professional service I had on my first visit here is closer to the norm. I'd feel leery, though, if I were to have this particular server again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The food was excellent--I had the roasted garlic cream appetizer and orecchiette, but between our table, we tried half of the menu with no complaints. The port flight was unique and the wine list was good. The bartender has a little trouble with our cocktail orders, but those were good as well. The covered patio was perfect for a Friday evening in late August--it was pouring outside and we stayed dry. The service was so-so, which I'm docking a star for. The server was attentive, but she was a little slow. She also spilled the apple icewine on two of us while bringing out deserts and we were charged for those drinks. It gets crowded, so make a reservation. + +Mad Mex is still my favorite Big Burrito restaurant, but Casbah is great for a more formal gathering or date night.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Nice menu, nice atmosphere. I'll definitely be back. NYC prices[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I ate here for brunch on Sunday. It's $22 and you may have to roll yourself out after. It included a mimosa/bloody mary, appetizer, and main plate. I had the fruit and cheese along with the brioche french toast. All was great. They could have had some more flavorful cheeses, but the atmosphere and kind service made up for the lackluster cheese. The bacon and potato fingerlings were absolutely amazing! I will definitely be returning for brunch![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> great atmosphere and great food. while the menu changes seasonally, my group all enjoyed the food - crab/scallop pasta, pumpkin risotto and rare tuna. + +casbah also has a great wine list, and great service that is there when you need them, but doesn't annoy.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This restaurant really knows how to cook meat and fish. The fried calamari (appetizer) was cooked to perfection with a perfect batter and tender beyond belief. The duck course (entree) was the most tender meat I have ever eaten. It was probably overly harsh, but only gave four stars because the side of risotto and the sauce on the duck didn't blow me away. The maple panna cotta dessert was also incredible. It was a custard with a light cookie and cranberry comfit on top, phenom.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've been here twice now, once for drinks and once for dinner, and I'd have to say that generally, I'm a fan. Their happy hour has some good deals - $6 cocktails and glasses of wine, and $1 of bottled beer. It was a fun, trendy atmosphere and a nice place to go for a glass of sangria after a busy day. + +I came back for dinner a month or so later. We had reservations (on a Monday night) and were seated immediately -even though the restaurant was surprisingly busy. We sat in the covered area out front - sort of like sitting in a dim, Mediterranean garden. And yes - the lights are low throughout the whole restaurant. Even with my young eyes, I still needed a candle to read the menu. But it is romantic and a peaceful place to eat. A little uncomfortable, as they have metal chairs (sort of like upscale patio furniture), but not a big deal. Sit inside at a booth if you need to sit on something soft. + +The menu is pricey and we're all poor, so we just got entrees. I actually had a cocktail to start - the Perfect Pear - with elderflower liqueur, vodka, sage, pear, and vermouth. There was even a little sage leaf floating in the glass. It was a wonderful drink, with all the flavors I love. Still, for the price, I think the portion was a little stingy. When I buy an $11 cocktail, I like it to really fill the glass. We nibbled on warm bread while we waited, and all tried their pesto on top - I think it was an unusual homemade pesto, something like walnut-watercress? It was a bit bland - I think regular basil pesto would've been a better choice. + +Things got better during the actual dinner. I ordered the Heritage Farms Chicken which was juicy and fresh, and served with a tangy pasta. Each little detail of the dish was well-chosen - honestly, even the grilled baby squash was outstanding. It's just squash! But somehow, it was heavenly. My friend enjoyed her Cioppino, and my boyfriend liked his veal tortellini, complete with rich pieces of lobster. I tried a little bit, and it was tasty - very herbal and really bursting with flavor. The only dish that fell a little flat was the potato gnocchi - my friend's boyfriend ordered it. Actually he liked most of it very much, but he couldn't get past the aggressive bitterness of the turnip greens. I tasted them too, and I have to say - it was off-putting. Perhaps that's just the way turnip greens are, but it really didn't work for us in the dish. Fortunately, the waitress was incredibly kind and helpful, and brought him out a new plate sans greens, which he finished happily. + +We also had a few desserts - vanilla bean creme brulee for us, flourless chocolate torte for them. I didn't taste it, but apparently it was incredibly rich. I enjoyed our creme brulee - because I enjoy all creme brulee - although the roasted quince on top didn't quite work for me. + +Overall, the meal ranged between good and very good, but the great service from our waitress really pushed this to a 4 star rating. I had hoped to be a little more wowed by the food. But this experience was definitely positive enough to warrant a second visit for dinner. I think it'd be a nice place to go for a special occasion, or if you feel like a little splurge on a flavorful meal.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Very tasty food and drinks! Its a little pricey, but worth it if you want something better than a typical chain.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The interior is very nice. The food is a hit or miss. We went for brunch today. You can select a drink (alcoholic or non), an appetizer, and a brunch entree for the price of $22. The appetizers we had (pollenta and squash&chestnut soup) were very good. The entrees, on the other hand, left a lot to be desired. We got the mushroom omelet and jumbo lump crab and tomato omelet. The omelet was very bland. It did not have much flavor and needed seasoning and more ingredients than just eggs. Basically, I have had better omelets at some Denny's. My drink mimosa was just OK. My girlfriend's blood mary was delicious, though -- uniquely spicy. + +I have been to Casbah 4 times, last time being for brunch today. The first time, it was good, worthy of 4 stars. It gradually went down to 3 stars. The wine selection is good. But the food is definitely hit or miss. Once I had a halibut that smelled like the ocean. It was not well cooked or fresh, or something. Consistency is the key in a nice restaurant; Casbah leaves much to be desired in this regard.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great food and very nice decor, one of my favorite restaurants outside downtown Pitt. The best places around Pitt are the bars or bar/restaurants (some of the best in the country IMO). But if you're looking for a straight-up classy place to eat, it's a tough place to beat.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Last night was the first time that we had been to Casbah in a long time - we used to absolutely love it, but a couple of disappointing brunch and dinner experiences had put us off of it. However, we decided to give it another chance, and I am glad that we did. + +Even though we had a reservation, we were seated (without them asking us our preference) in the front area, but that was fine, since the heaters kept it toasty warm. It was also a great table thanks to our terrific waitress. Wow, was she cheerful and friendly! She was also helpful with making recommendations - when I asked her about the cocktails, she pointed out the relatively new ""Beet and Potato,"" which had beet-infused vodka as one of the main ingredients. It was a cool cocktail - an interesting blend of savory and sweet, and very seasonally appropriate. I don't know if I would order it again, but I'm very glad I had it once. + +For dinner, I ended up having a soup and then an appetizer, since I wasn't too hungry. The caramelized onion soup was so warming - it was like an update of the classic french onion soup. The broth was not too salty (a common problem with onion soups), and the onions had been braised perfectly. Everything was just the right texture as the onions, broth, and ""crouton"" blended together. + +I ordered the sheep's milk gnudi for my main course. Even though it came in an appetizer-sized portion, it was still a lot of food, since the gnudi are so filling. The gnudi were nicely molten in the middle, and just the right softness on the outside. There were a variety of accompaniments to the gnudi, but the standouts were the brussel sprouts. I'm actually not a huge fan of sprouts, but I ate every one in the dish. They were light and buttery, solid but not rock-hard, and had just a trace amount of bitterness left. That is how sprouts should taste! + +Even though I didn't plan on ordering dessert, I ended up getting the warm walnut baklava with cinnamon ice cream. The warmth of the baklava melted the ice cream nicely, and the flavors just blended together on the plate. The baklava was quite traditional in its assembly and spice blend, but the extra cinnamon with cream gave the whole dessert just a bit of extra oomph. + +In summary, I'm glad that we gave Casbah another try. I wish that they would go back to offering all of their pastas in both entree and appetizer sizes, and I miss the crazy variety of wine flights that they used to have (it seems like they just have 4 now), but it's still a great dinner destination.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Disappointing. + +My bf and I went for JUST dessert and wine, which we told the hostess ahead of time. The waitress was very curt and disrespectful. We were rushed to order (even though there were plenty of empty tables and it was NOT closing time). She did not offer suggestions or advice. + +We ended up ordering the flourless chocolate cake. The cake was extremely rich (but delicious!) and the portion was just right for sharing after dinner. The marscapone was silky and paired perfectly with the cherries on top. + +The waitress kept coming back to see if we were done and ready for our check. After we got the check, she was in a hurry to get us out the door. I am completely dissatisfied with the service and will not go back to this restaurant simply because of it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> In order of consumption...the bar is energetic, but has the worst and completely immovable bar stools ever created. We were initially placed outside in the all year round patio...absolutely no atmosphere, so we asked for a table inside...20 minutes later we were inside which had a much better vibe. I started with the Blue Bay Mussels which were truly the best I have ever had, plump, juicy and perfectly complemented by the chorizo and white beans, absolutely sublime. My wife had the veal meatballs that were also delicious. For the entrees I had the lamb loin with couscous and my wife had the veal tortellini, although very tasty we oth agreed that both were too rich. My only criticism would be that ALL the entrees looked rich.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have to agree with the ""hit or miss"" reviewers about Casbah, at least when it comes to the food. I came here for brunch last weekend with a big group. They were very accomodating to us throughout the reservation process and the brunch, which was good. And our waiter, Daniel, was great. + +The previous reviewer who said the Bloody Mary is the best drink was spot-on. It had a great spice and was the only drink that seemed like it had any alcohol in it at all. The mimosa and sangria were very ""eh."" + +I loved my smoked salmon appetizer (and that did seem to be the hit at the table), but entrees around the table left people disappointed. The goat cheese and mushroom omelette could have had a heckuva lot more goat cheese and mushrooms, and my scallop/sausage/grits/egg dish just had way too much going on. The grits were actually fabulous, but the scallops were overcooked and got lost next to the scrambled eggs (?) and sage sausage crumbles. + +If I lived in Pittsburgh, I could see myself coming back here for wine and appetizers, but I'm not sure I would make it a regular brunch or dinner spot.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Casbah is more like a 3.5 but I rounded down:) We arrived after happy hour at Soba, apparently owned by the same people, for dinner. There were four of us, and they started us out with delicious drinks. I had the margarita topped with Malbec which was surprisingly yummy. +For appetizers we tried the meatballs and the grilled trip of flatbreads with mediterranean dips. For mains, I had the rare seared tuna, Andrea had the salmon, and Allejandro and Elie both had the gnocchi. Everything was ok to start and the mains were all good, although they rely heavily on butter and huge portions for their mainstay of flavor and satisfaction. It was interesting to have such big portions after NYC where I'm used to portion control, but I decidedly prefer more reasonable portions (maybe somewhere in between). +All in all, a nice garden, pleasant and a good place for conversation.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Had a very lack-luster Mother's Day brunch at Casbah yesterday. Despite having a very late reservation time of 2:30 p.m., we were seated in the dungeon-like basement dining room. I asked for tables upstairs in the daylight but there was allegedly no way to accommodate my request. Worst part about the basement is the thumping from the sub-woofer located above -- really ridiculous. Service was fine. Timing of drinks and first brunch course were acceptable given it was a busy day, but then gap of 35+ minutes for entrees left us all sitting there, not enjoying the dark of the basement nore the perpetually thumping base. An utterly forgettable mother's day brunch (luckily she took it in stride) but I think Casbah will not be at the top of the list in my book for quite awhile.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I came here with a friend for her birthday, and the food really isn't particularly special. Portions are decent, and I guess the prices are reasonable... if they had better food. + +The outside of restaurant makes me think that the inside will be just as square and boring, but the inside patio area was pretty nice actually. + +Overall, I just wasn't very impressed with the food. If I was offered to eat this food for free, sure, I'd take a helping, but probably not seconds.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Rock the Casbah! Rock the Casbah! + +A group of us went to the Casbah for a girls' (and one guy) lunch. It has been ages since I've been to the Casbah, and since I live clear across the country, I was looking forward to going back. + +All of us enjoyed our meals -- many ordered the Jumbo Lump Crab Chopped Salad or the Wild Mushroom and Goat Cheese Omelet. Both were nice portions. I was fixated on the Orecchiette Pasta, grilled chicken, dried cranberries, Capriole goat cheese, sage cream, and it was a home run! (I wasn't watching calories that day!) + +Service was excellent . . . surprisingly so, especially with a table of eleven, a bunch of ""Sallies"" and one ""Harry"" if you know what I mean.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Casbah is the type of restaurant that I find most difficult to write about. + +I came here recently with my beau for a special birthday dinner, seeing as they had several vegetarian options on their menu. We booked our reservation on OpenTable, which I was glad to see that they actually used. I noted that both of us diners were vegetarian and found that our server and hostess were very accommodating in that respect. + +We were seated outside, which offered us a pleasant experience on their lovely patio. Their ambiance is nice and their service outstanding. I found that everyone there knew what they were talking about and possessed a deep passion for food, as opposed to obnoxious pretense which upscale restaurants like Casbah can have. + +As for the food, it was above average. Nothing outstanding, but definitely still tasty. My boyfriend ordered the gnocchi (made veg), which turned out to be excellent, while I got the cavatelli (also made veg). We also shared a half-order of the torchetti and unfortunately, neither the cavatelli nor the torchetti stood out too much. The gnocchi and the appetizer (grilled chickpea flatbread) were by far the highlights. + +In the end, come here for the service and ambiance, but don't expect to have the meal of your lifetime.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Of the Big Burrito group restaurants Casbah is the one that has never failed us. Consistent and delicious with great flavors of the mediterrean. + +All of the dishes are served with great flavors from their pastas to their duck but their signature Arugula salad is a reason in and of itself to visit. Crisp clean flavors with complex combinations of textures. + +Special occasions or hungry on a week night... casbah is a great stop[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My husband and I went to Casbah to celebrate my birthday one evening. We were seated on the patio which was fine before a party of 20 was seated with a 1 year old who was banging his silverware on the table all night. So much for romantic! Ever hear of a babysitter? Anyway, ambience aside, let's get to the food which overall I would give a C+. We started with the veal and pork meatballs which were the highlight of the meal. The perfect blend of sweet (fresh tomato sauce) and spicy -- the meatballs had a nice tang, and the polenta was delicious albeit there wasn't much of it there. We each then had the heirloom tomato salad which was tasteless. I grow heirlooms and know the intense and wonderful flavor they should have. These tasted like a grocery store tomato bought in December. Very disappointing. I opted for the cavatelli entree which was not prepared as described on the menu. It was swimming in tomato sauce and overall was very bland. Another disappointment. My husband had the pork chop which wasn't bad but certainly didn't leave us wanting to return here for the food. All this said, the service was professional, we enjoyed the drinks (he had the sangria and I their house cosmopolitan) and had a lovely bottle of wine. I might return here for happy hour but it was not the right choice for a romantic special occasion dinner. And we had the decency to hire a babysitter for our children, otherwise we would have stayed home.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I finally went to Casbah for brunch today. Rolled in at 10am to meet a handful of people. Because it is Labor Day weekend, the place was empty except for a woman who had just gotten there too which was nice because a friend had warned me that the place gets crazy. We sat outside and atmosphere was cozy under the tent with the warm colors of the decor. Our waitress was incredibly friendly and presented us with the menus. I think it is great they have a prix fixe brunch - 1 alchy or nonalchy drink, an appetizer and an entree - but for $24. It looks like they have since raised the prices since Miles O. went. I felt it was just a tad steep and a lot of food but took the plunge anyway. I ordered the smoked salmon for the appetizer and the mushroom omlette for my entree, and had a hot coffee (they did not have ice coffee though offered to put ice with hot coffee if I wanted it). The waitress brought out some delicious mini baked treats before we got our dishes - poppy scone (on the crispier side but delicious), blueberry muffins and biscuits, which were all buttery goodness. After eating these I was getting a little full and then after my appetizer I realized I probably should not have gotten the prix fixe but could have would have should have. I ended up boxing half of my omlette entree. Portions were large, atmosphere was cool, food was good and wait staff were awesome but in the end I don't think $24 (not including the tip and tax) was worth it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My fiance and I like to go to Casbah for special occasions and each time it never disappoints. + +The food is great (I highly recommend the Pork Chop and the Short Rib Ravioli), the drinks are wonderful (I am a sucker for good Sangria - and Casbah's is wonderufl) and the service is outstanding (our servers are always friendly, prompt and very knowledgeable).[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I had heard from friends that Casbah was one of the best restaurants in Pittsburgh, and my experience definitely lived up to the hype. I don't know how a place owned by a company called Big Burrito Group churns out such outstanding Mediterranean fare, but I was impressed. Everything was done right--the ambiance was sophisticated yet unpretentious, service was professional, and the wine list was impressive, especially the by-the-glass options, which were necessary since I was dining solo. The food (I started with grilled Spanish octopus and then had the halibut) was all fresh and prepared to perfection, with inventive flavoring that complimented rather than overwhelmed the dishes themselves. I'm not in Pittsburgh often--too bad, it is a beautiful city--but I would visit Casbah again without hesitation.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Um. A little bummed. I had high expectations, but left feeling just...meh. + +The restaurant is really cool looking but I was a little confused by the bar set up. We sat at the bar because they didn't have any tables open. I usually don't mind sitting at the bar but the stools are bolted to the floor, and about 2 feet from each other. If you have three people with you, forget about mingling! + +Also, the service was very iffy. There was a bartender, and then a server for the bar area (or what it seemed like). The bartender got us our drinks, but never told us a server would be with us. I figured she was our server too. But then some other woman came up to us all flustered. She never introduced herself, just asked what we wanted and kept saying ""okay, okay, okay."" Just very odd. It continued that way the entire time. + +I tried the prix fixed brunch for $24, which includes your choice of an alcoholic bevvie (Bloody Mary, Sangria or Mimosa), appetizer and main course. I had the mimosa, that was the perfect mix (splash of OJ:), Polenta and Eggs Beni. The cinnamon polenta, which was delish: light, fluffy and warm with dried fruit and almonds on top. I loved it! + +The Eggs Beni with smoked salmon. It was just okay. I kept trying to think pf what was missing and I believe it was that the hollandaise sauce had no real taste. I expect hollandaise sauce to be rich and creamy, this was thin and blah. + +I definitely want to go back and try the dinner, see if maybe I'll have a little better luck. So kick it up a notch Casbah, you've been around for a while, but I still expect good food![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Out of towners that happened to stumble upon this gem. Thanks, Siri. Wow! What a great experience. Fantastic, wine, food and service.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Passed this restaurant for years on my way to Buffalo Blues or more recently Mad Mex but have never actually eaten here. Having finally come for lunch, I overall enjoyed it but it had some ups and some downs. + +I ordered the Piccola Gusto Menu which for me included the Cream of Cauliflower soup, the Orecchiette Pasta and the Roasted Turkey Sandwich. It sounds like a lot of food but the pasta serving is mini and it's a half sandwich. For me, the size was just right. The soup was awesome, and I could have eaten an entire lunch of just it. The pasta was a little too creamy for me and just didn't have enough seasoning or spice. I did love the addition of the cranberries in it though. The perfect amount of sweet to offset the cream. The roast turkey sandwich was just that. Not out of this world, but not bad. My biggest complaint was the service. It took a really long time to get our meals which is always a bad thing during a weekday lunch. + +I'd like to go back here for a happy hour when it's warm so I can enjoy the covered patio though and a nice glass of wine![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> So I hated this Soba place owned by the same people, and I happen to stumble into this joint for lunch. It had a great sandwich (crab) and the soup was pretty decent (cream of cauliflower). Not sure how they are owned by the same people as Soba (I mean, obviously different chefs) but usually the same owner means similar quality and price, no? Maybe the dishes are just hit and miss, and I got a hit here, whereas I had a serious miss over at Soba. In any case, the crab sandwich was good-- nice, large chunks of crab. No overkill on the sauce. The soup was likewise good. I don't understand how the two restaurants could possibly be related given the night and day of my food experience! The wine, however, was overpriced for the quality. I guess people aren't from SF and expect good wines for the same price! Save your money, buy a nice $40-60 bottle at home and have a much better vino experience but pay less (or the same!).[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This review is for brunch only! I've never been here for dinner...but been here quite a few times for brunch. + +Casbah's brunch is a prix fixe...which at first seems expensive, but when you realize the amount of food you're getting, it's sooo not. You get an appetizer, entree, and drink (yes, a real drink, with alcohol) for just $24. I usually end up spending more at my other Big Burrito brunch spot, Kaya, so I consider this a pretty good deal. + +They start you off with a basket of muffins and biscuits with honey butter on the side. And it's refillable. Try to restrain yourself from eating too many baked goods though, so you can get to the real food. For appetizers, everything I've had was pretty good (polenta and the salads have been my faves), but for the entree, there is only ONE thing you should order: The lamb & eggs! Crusty sourdough bread topped with spinach topped with braised lamb shoulder and roasted garlic, topped with poached eggs. One of the best things I have ever eaten in the morning. The scallop scramble is just okay, the steak & eggs are pretty delish...but the lamb & eggs is by far the best thing on the brunch menu. + +This is one of the few places where I don't opt for the Bloody Mary...it's pretty blah. I do their Salty Dog with freshly squeezed grapefruit juice, or sometimes get it sans alcohol if I'm really feeling the pain from Saturday night. + +Unfortunately, while I love the atmosphere, I feel like the service is lacking. I can't explain why, but it always feels awkward and doesn't hold up to the standards set at other Big Burrito spots (even Mad Mex). I know it gets busy on Sundays, but still. Service issues aside, The food is still worth it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Very expensive for a college student, but quite good. +I would recommend this if you enjoy European food in general.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> You know what's good? Tomato-basil soup with cream in it. And even better? Finding a way to eat on the patio in January. Where the dining room at Casbah is intimate and warm, the patio is bright, open and shielded from the elements. The waitstaff was friendly and helpful, and the lunch specials were actually special - good flavor, slightly indulgent, but you don't leave feeling overstuffed. I want to eat my way through the menu.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> OH MAN! My boyfriend and I came here after having a wonderful experience at Soba Lounge. Big Burrito Group does it again. + +Casbah prints their menu daily so some of their dishes you see online won't be offered that day. You'll still find something delicious, though. + +We thought the place looked kind of shoddy when we saw the front of it, but it turns out they pitch up a tent-house in front of the actual restaurant to make their usual outdoor seating into additional seating during the wretched Pittsburgh winter. + +Our bread came with a walnut pecorino pesto and it was AMAZING. We were kind of disappointed that they only gave us 4 slices but the food we had ordered came out so quickly afterwards that we barely had time to mope about it. + +I ordered the long island duck, with chestnut spaetzle, brussels sprouts, sage, +apples, and cherries. The tanginess of the cherry and mild fruitiness of the apple was an amazing complement with the rich meatiness of the duck jus. I didn't think there was enough sauce but both the duck breast and duck leg were so tender I didn't care. I ended up almost finishing the entire plate even though the serving size was considerably large. All of that for under $30. + +My boyfriend got the lamb shank, which was a super simple dish (lamb with mashed potatoes) that they managed to make out of this world. Super tender with a generous amount of lamb jus swimming around the plate. + +For dessert, please get the dark chocolate raspberry bread pudding. It takes a while for it to come out because they bake it on the spot. The 10 minute wait is so worth it. There are huge chunks of super dark chocolate and fresh raspberries in the fluffiest bread pudding I've ever had. Just remember not to burn yourself on the plate like I did. + +The meal ended with complimentary salted caramel. Don't put the whole thing in your mouth like I did.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Loved it. Great service, great food, great wine. Very yummy.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place was recommended by an employee at Evolve spa across the street and I was very happy with the restaurant. The Salmon appetizer was delicious as was the gnocchi meal. I will definitely go back to this restaurant when I visit the area.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Food phenomenal! Service can be hit or miss.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> 1. Sat outside on patio metallic chairs and tables, when we made reservation expecting to sit in the restaurant, not outside! There was no information about this. If the restaurant inside seats g is full. Then they should mention to the customers making reservations that they will be sitting outside!!! +2. Food is mediocre at best! They even screwed my order. Asked for risotto and got some pasta, not sure what. +3. Asked for two cabs, someone at restaurant changed it to one big cab instead which could not hold all of us so we had to wait for another 25 mins for another one!! + Would not recommend to anyone. Enough other good restaurants in Pittsburgh to go to. They have to have paid their way into magazines rating them highly![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Ate lunch at Casbah for the first time. Tried the Piccolo Gusto: $15 gets you a small choice of salad, a half sandwich and a half portion of a pasta or risotto. Great deal and fantastic food. Argula salad, shodt rib sandwich and wild mishroom/truffle risotto. No need for dinner today![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Overall a good experience. Food was mostly very good. My sweet pea risotto was just OK. My wife's short rib ravioli was creative and very tasty. Neither of us are big eaters, but noted how small the portions were, especially compared to the price. One cup of risotto for $20+? Four ravioli for the same? + +They altered the desert recipe on request, which for sure was over and above the call. + +Service was attentive and the setting nice.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Sharia don't like it, and neither does Becky. + +Boy and I went to Casbah on a warm Tuesday evening. The restaurant wasn't busy, and we were seated in the inviting outdoor patio. Our waitress was very pleasant and extremely informative about both the drink and food menus. + +We shared a bottle of Mission la Caminade (Malbec, French). This was a very good, medium-bodied wine. + +Many yelpers have raved about Casbah's bread and pesto. I don't get it. I've had much better sourdough elsewhere and the pesto wasn't anything to write home about. + +I had the asparagus soup with crab for an appetizer. The soup was served cold and tasted fresh enough, but something was off, and I barely ate half of it. + +I ordered the orecchiette pasta as an entree, which was served with grilled chicken and cranberries in a goat cheese cream sauce. I am upset to report that this tasted rather bland. The cranberries were the only spark of flavor in the dish. Boy ordered the ricotta cavatelli pasta, which was in a marinara sauce with sausage and ricotta. I am sad to report that this too was tasteless. The ricotta was dumped on top and added nothing to the dish. + +We glanced at the dessert menu, after spending so much on food we didn't enjoy, boy and I decided to cross the street for ice cream, instead. + +Overall, Casbah has a nice atmosphere and service, but their food quality doesn't match the price tag.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I came here a year ago and had a really awesome meal. I'd say the best in Pittsburgh I'd had since arriving. Given that, we went here for a birthday dinner. + +Overall, we were all left with kind of a ""meh"" experience. Our server seemed pretty disinterested and slow. I think the low point was someone ordered a steak medium rare (for $38). What came out was a well done and COLD piece of meat. It looked like a hockey puck. + +When he sent it back, no apology...and no change in the bill. I at least expected a manager or someone to come out and apologize and say ""We've taken it off the bill"" or SOMETHING. Nope. He sat there watching the rest of us finish our entrees before his replacement steak arrived. + +The rest of the entrees were good and I would go back. But probably with lowered expectations.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I had a free entree from Big Burrito for my birthday, for which we decided to use at Casbah a few weeks ago. It was my first time there, though I've tried a few other BB restaurants in the past. + +Food: +- Cracked pepper butter was delicious - I had to warn the waitress not to let me have any more bread and ruin my meal! +- Grilled Bruschetta (ricotta, fava beans, Swiss chard, preserved lemon, arugula, chervil, Calcagno) was a bit too lemon-y for my liking +- Short Rib Raviolli (Short Rib Ravioli, Swiss chard, oyster mushrooms, roasted shallots, gremolata) was very savory and I would definitely order it again +- Double-Cut Pork Chop (with braised kale, prosciutto & parmesan risotto, garlic cream, sage jus) was Joe's meal. I tasted a bit of everything and really enjoyed the kale. I like really really creamy risotto, and this wasn't quite there. I dont want to say it was undercooked, as I like I just like mine over-cooked. +- Fried Apple Empanadas (vanilla bean cider reduction, toasted oat streusel, +caramel ice cream) The ice cream was great, but the empanadas were bland to me. + +Service: Not terrible. I understand at nice restaurants people enjoy taking their time to relax, enjoy their meals, and converse with their dinner-mates, but our server should have been more observant to the fact that we would be just sitting there with empty places waiting for the desert menu. I will note, though, that the table next to us returned two glasses of the same wine and the bartender came over and very politely suggested an alternative wine for the patron. They were very accommodating in this way. + +Will I go back? Someday - but I think I may try Soba or Kaya first.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We arrived late in the evening and had to ask our waiter about the ""pasta festival,"" which he mentioned. It turned out that both pastas, the salad, the calamari, the cocktails, and the service were good. +Casbah would have been livelier earlier and more pleasant without a loud and persistent talker in the party of 6 at the next table. +I'd definitely return for the food and service.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I was treated to Casbah for lunch by a potential employer who had passed me over, but really, really liked me. She said it was her favorite restaurant, but that she didn't go as often as she'd like. + +I knew the building from the early 80's when it had been one of Pittsburgh's dive gay bars called 'The Tender Trap', and knowing this, as well as a lot about the Big Bistroid Group...oops...Big BURRITO Group, I was curious to try it out and see if it lived up to the usual Big Burrito hype. And voila, indeed, it's another excruciatingly overpriced bistroid in da burgh. + +The atmosphere is actually quite lovely, inside or out. The colors are comfortable, the noise levels subtle, the seating comfortable, and the service staff looks professional (YOUNG) with no Coney Island side show appearances. + +The service was good. Not overly friendly, but not uppity like young people waiting tables in more upscale restaurants tend to be in da bugh. + +The menu was short, but did have a list of pretty unique offerings. My friend had a salmon salad, and I opted to try the Farm Lamb Mac-n-Cheese. The waiter brought a small basket with bread to the table accompanied by a single medium sized pat of salted butter to spread. For a beverage, we both opted for just water. + +I have to say, if I actually had to pay for this, I would have been pretty miffed. + +For LUNCH, the prices were all around the $15 range, and the portions were NOT large. The portions were actually fine for lunch, not overly filling (by any stretch of the imagination), but they didn't leave you hungry. + +I can't speak for the salmon, as I have NEVER had salmon in any form other than lox that didn't taste like a dried sawdust version of some strong fish. She seemed to enjoy it very much, so there it is. + +The Farm Lamb mac n cheese was tasty. The lamb was tender and moist, and the mac n cheese was a tiny tube pasta with a very nice creamy cheesy sauce, all topped with a bread crumb covering when it was broiled until crispy. It was accompanied by a 'pinch' of mesclun salad topped with another pinch of fried onions. + +Basically - take one large spoonful of mac n cheese with a higher end cheese sauce and a fancier noodle than comes in the average box - mix in about four cubes of roast lamb, sprinkle on a layer of bread crumbs and toss it in the broiler until the crumbs are toasted - then using your index finger and thumb, pick up a pinch of mesclun and sit it on the plate next to the mac n cheese bowl - and you have a bistroid expensive art project on a plate. + +Seriously? $15 for lunch? It's mac n cheese people! + +I also have to call into question the name and theme. Mad Mex is bistroid Tex Mex. Soba is bistroid Asian. Kaya is bistroid Caribbean-ish. Casbah? Farm Lamb mac n cheese? Sure, I can see this as a box lunch while riding a camel through the desert...not. + +I can't say the experience was awful. The company was awesome, and we had a nice unpressured amount of time for fun chat. The atmosphere was comfortable, and the food was tasty. But was it all worthy of a return trip or recommendation? I honestly can't say 'yes' with any kind of cheerleader rave. + +I'm not quite sure that I comprehend the mindset of people in this burgh who think paying that kind of money for food is worth it, when honestly, food with just as much flavor can be found in abundance around town for half the price and twice the portion. + +Who are all of these easily dupe-able rich people, and where do they come from? Want to blow that kind of money? Get out your check book and let me give you my address![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm actually giving it 3.5 stars. 3 for the appetizers and 4 for the entrees. My wife and I went to Casbah for the first time. As we usually do, we decided to share our entrees (TIP - you can get half portion sizes of the pastas!!) and augment the meal with a few appetizers. For the appetizers, we got the chickpea flatbread, the arugula salad and the sea scallops. The flatbread and salad were just OK. The sea scallops would have been delicious except for the ""cured egg yolk"" which was infused in the avacado sauce. For those who have never tried a cured egg yolk, I would consider yourself lucky. Actually, the taste wasn't too bad. The smell, however, reminded me of what you would smell if you were on the set of a nasty version of a Hoarders TV episode. Must be an acquired taste. + +For the main course, we chose the short rib ravioli and the cavatelli. Both were excellent, especially the ravioli. No complaints at all. + +Overall, a very pleasant experience. Good atmosphere. Our waitress was very friendly. The place was busy and had a nice vibe to it. Unfortunately, some of the food was a slight disappointment.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Hard to remember another restaurant that hit home runs from start to finish. Yinzes say it's pricey but I disagree, the quality is hard to find period. Very progressive menu but not too wild, products are from near area farms, very knowledgable staff. And butter served at the right temperature, that's a novel idea! Just a great experience, can't wait to get back there.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Good food - Great atmosphere! + +Service will depend mostly on where you sit - They have a nice covered outdoor seating, if you're out with a group of friends - The bar area is pretty neat with lounge seating facing the bar. + +Try the Short Rib Ravioli[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Service is a little slow but overall the best food I've had in Pittsburgh so far. If you're a seafood fan, the scallops are amazing. Very decent wine list and lots of parking.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> casbah is the last big burrito restaurant i had left to try and i really liked it. i started with the sangria to drink which was delicious, and i'm usually not a huge fan of sweet drinks like that. we split the grilled flatbread app. the dips weren't anything super special, but the bread was thick and flavorful. no complaints. then we both got piccola gusta and split all our items. (the piccola gusta gives you salad or soup, half a sandwich, and half a pasta) between the two of us we had the tomato & basil bisque, arugula salad, crab cake sandwich, salumi sandwich, orecchiette pasta, and ricotta cavatelli. +i'm not a big fan of tomato soup, in fact, i never eat it, but i tried the bisque and loved it. it tasted more like a tomato sauce than soup. the arugula salad was great as well. the crab cake sandwich was really small but good, and the salumi sandwich was amazing... probably my favorite part of the meal. both pastas were good, but i personally preferred the orecchiette, the cranberries sealed the deal for me. +i love the atmosphere, we sat out on the covered patio, and the service was great as well. +i'll definitely be back again, hopefully to try the different brunch and dinner menus![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> In my opinion, Casbah is the best of the big burrito restaurants. I have been to Casbah for dinner and drinks a few times. During my latest experience, I was impressed by the hearty fall entrees. I decided to take my husband to Casbah for his birthday on friday night. I called on Monday and luckily, I was able get a reservation without a problem. When we arrived, the restaurant was packed but we did not have to wait. We were sat in the beautiful front covered patio area. + +We decided to start our meal with the veal and pork meatballs. This was my favorite part of the meal. I could have ordered 3 of these for my entree! The polenta and the crispy brussel sprouts added a smoothness and a salty crunch. Delish. You have to try these! For my entree, I ordered the double cut pork chop and my husband ordered the cioppino. The huge pork chop arrived medium well, as requested, but was still tender and juicy, even better when dipped in the sage jus. In additiion, the bitterness of the braised kale paired well with the smooth, creamy parmesan and proscutto risotto. My husband was also a big fan of the cioppino. The mussels, clams, shrimp, halibut and scallops were cooked to perfection. I was equally impressed with the size of the scallops. We're talking the width of a coffee cup! Unfortunately, we were too full for dessert but were presented with housemade salted carmels to end our meal. + +If you are looking for a place to enjoy good wine, amazing food and a pleasant atmosphere, Casbah is for you.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love the Big Burrito group and I love even more that they just sent out a bunch of coupons. The other night, I got off early from work and was able to go to Casbah for dinner during the week. + +When we got there, they took a minute to figure out where we would sit even though it appeared that they were empty. However, 1/2 way through dinner it seemed like they were seating those with reservations inside and walk ins outside. + +The place is set up with what would be the patio, enclosed. There are big heaters on the ceilings that are directed straight at the tables. I will say that it was a little too warm and even though the host said he would turn them down, I don't think that was done. + +The waitress came and told us about the menu, took our drink orders and brought us some bread with a yogurt spread and salted butter. I did ask her if the $10 off entrée coupon could be used on the pasta entrées and I think at that point she began to think that we were poor young kids. But back to that later. . . + +To start we shared the crispy calamari ($11) with capers, lemons, chili and parsley which was probably some of the best calamari ever. It was not chewy and it had the best sauce ever! We also ordered the grilled chickpea flatbread appetizer ($9) which I expected to be a flatbread but actually came as grilled pita with three separate dips - baba ghanoush, hummus and red pepper muhummara. + +For dinner, I ordered the short rib ravioli ($24) which came with swiss chard, oyster mushrooms, roasted shallots and gremolata. This was the more decadent dish ever! When it first came, it had about 6 raviolis and didn't appear to be enough but it was more than enough! + +My husband ordered the Casbah Double Cut Pork Chop ($27) which came with braised kale, prosciutto & parmesan risotto, garlic cream and a sage jus. The pork was very moist and the risotto was cooked perfectly. There were no left overs! + +After this huge meal, we decided on taking a dessert to go. We both agreed upon the Dark Chocolate Rasberry Bread Pudding ($8). So I asked the waitress if it would travel well since we wanted to take it to go. At that time, she looked at me and asked if we had a toaster oven where we lived. . . Um yes lady we do, in fact we have an oven also AND we own our own home. Despite the comment, we took the dessert home and put it in the oven later that night and we were not disappointed. + +Overall the meal was delicious, we got to use two $10 off coupons and I would highly recommend it to anyone. However, I still favor Eleven![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Went here for the brunch prix-fixe menu- such a good deal! Drink, appetizer, and main course all for $24. First, we got a pastry basket with mini-scones, croissants and biscuits. I told myself I would eat half of each to try everything, but they were too tasty to resist! For appetizer, I got the granola and berries and my friend got the creamy polenta. Both were great options! The granola did not taste like anything you get in a box- could definitely tell it was made in-house. The creamy polenta was so different and delicious- will get that next time I go back. Was pretty full by this point but that didn't stop me from completing my main course! I got the Casbah Benedict with Smoked Salmon and my friend has the Tuscan Eggs. We both thoroughly enjoyed our meals and were stuffed by the end![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Went here for drinks with some friends. + +The bar service was definitely interesting. Some of the time the waitress was really on point and was there ready to take your drink orders, but after the first drink it was really hard to get a second. + +I can't speak for the food, but will update my review when I get back to try the food. Overall my dirty martini was good, though it definitely could have used some better quality olives (these were bottled with the red pepper on the inside used on salads). I will definitely be back to try the food, but I hope the table service is better than the bar service.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Casbah is definitely my favorite restaurant in P-burgh; in fact, usually when I go somewhere else I wind up regretting that I didn't just go to Casbah. Every dish I've had has been excellent; some favorites are the sheep's milk gnudi, tuna tartare, arugala salad, bread pudding, and pretty much every soup. The short rib ravioli is a must have although arguably a touch salty. The menu is so inventive![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My wife and I go to Casbah every year for my birthday. It is my favorite of the Big Burrito restaurants, and they have a birthday deal for $30 off an entree. + +This time I started with the Parsnip & Chestnut Soup, garnished with braised chicken, arugula & almond pesto. It was divine, with the rich sweetness for which parsnips are noted. My main course was Elysian Fields Farm Lamb Loin with flageolet beans, merguez sausage, turnips, greens and whole grain mustard. It was cooked perfectly pink, as ordered, and the flavors complemented each other. + +For dessert, I skipped my usual chocolate - they offered Chocolate Mousse, Chocolate Cheesecake and Dark Chocolate Raspberry Bread Pudding. I decided to try the Pumpkin Bread with Butter Rum Sauce and Cream Cheese Ice Cream. The cake was light and tasty and the ice cream and sauce were excellent.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> For the record, I have returned a few times and still entirely stand by my original review from nearly 3 years ago. I will add that the food portions also seem to be decreasing! We went during happy hour last week and I had the worst tasting rye drink possible - described as rye with fig jam, bitters and lemon, sounded like something that cannot possibly be fucked up, but tasted like nothing but the juice wrenched out of unripe lemons - super dry and gave me a stomach ache. No fig flavor to be detected. To make matters worse, when my partner tried to ask the bartender about the drink, if it was supposed to be sooo god-aweful lemony, she responded with a ""yes, it's got lemon in it."" When he pressed the issue, she simply repeated, ""yes, it's a lemon and fig drink."" More frustrating than conversations with the wall. The risotto that we ordered was the size one would expect of a side dish (which is what risotto should be, but this was proposed as an entree...). It had about 5 little pieces of maitake mushroom and 6 hazelnuts in it and was otherwise flavorless. We added lots of salt and pepper. Total waste of $25 bucks. + +Also, their bar seating sucks. The chairs are stationary and far away from each other, and a bit far from the bar for a shorty like me; my feet don't reach the foot bar on the chair either, so my legs fall asleep trying to sit there.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Glad to see that the Big Burrito restaurants are alive and well in Pittsburgh, and dinner tonight was my first time in awhile at one of their establishments. + +Bit of a complex review. My biggest gripe with Casbah is that it's Casbah Mediterranean when the menu (at least on this night, but I don't think it changes all that much) offers very authentic Mediterranean dishes. One lamb dish (not overly Mediterranean) and no couscous or tagine, which are major staples of Mediterranean cuisine. Even a side of hummus and pita or veggies would be nice. Nonetheless, the menu has lots of fine options, just none that I've seen in a typical Mediterranean joint. I think it's a little misleading especially if you're seeking Mediterranean cuisine. + +We sampled several of the cocktails, all of which were creative and well priced. As for food, we split the bruschetta (prosciutto and blue cheese), meatballs (pork) and the brussel sprouts were quite tasty, beet salad, and the potato gnocchi. So lots of food! All was freshly prepared with quality ingredients and served with sophisticated presentation. + +Lots of fine restaurants opening in the area, but it's clear to see that they have a loyal following.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> When scoping around online for a good NYE dinner destination for my husband and me, Casbah's prix fixe menu really jumped off the page! Since the Big Burrito group is so popular, I was happy to get reservations, especially since a lot of times were already booked. + +The hubby and I arrived a few minutes early for dinner. I had planned additional time to park and was delightfully reminded that Big Burrito restaurants have free valet parking -- so great, especially with slushy snow on the ground! Even though we were a few minutes early, the hostess took our coats and seated us immediately. + +Service was extremely attentive from start to finish. Waters were re-filled quickly. Bread was brought to the table almost immediately and we were offered another basket as soon as we finished the first. The bread came with a delicious spread - was it goat cheese? - that I just couldn't stop eating. Silverware whisked away with each course was promptly replaced. + +We ordered both the land and sea courses to share so we could try the entire NYE prix fixe menu. None of the eight dishes disappointed! The first courses were Sea Scallops & Octopus and Duck Confit. The sea scallop was perfectly cooked, the octopus - thought not my cup of tea! - was also well cooked, and the balsamic flavor in the dish was very tasty. I absolutely loved the duck confit dish. It was served with mustard greens and fruit with a to-die-for dressing - a delicious combination! + +The second courses were Potato Gnocchi and Mushroom Tortelloni. The gnocchi was served with lobster, which was a unique but nice paring. Though a strongly flavored dish, the tortelloni was delicious, and I enjoyed another unique paring, tortelloni with chunks of beef short rib. + +Lake Ontario Walleye and Roasted Veal Strip Loin were the third courses. Both were cooked to perfection. The walleye's skin was perfectly crispy, and the veal strip loin was cooked medium well but was still deliciously juicy and tender. However, a component of each dish was disappointing -- a mustard flavor in the walleye and pickled mustard seeds covering the veal. I really can't hold this against Casbah though. I'm just not a fan of mustard! + +Finally, the desserts was fantastic! The Chocolate Ganache Tart was the ending of the sea courses. The chocolate was strong, even a little bitter, and was served with a little champagne strawberry compote. I grew more accustomed to the bitterness with each bite, and it was the perfect ending to three courses filled with fish. A Caramel Macaroon completed the land courses. The macaroon was delicious and served with a little apple sorbet and caramel sauce. + +Our experience at Casbah was spectacular! Based on this experience, I debated giving the restaurant five stars... but decided to wait until I returned a second time. And I can't wait to return![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Brunch = best in the burgh. Hands down. Best. eggs. ever. I am not even sure how the eggs can be that good. I know what you are saying, ""They are eggs, Jessica. Get a grip."" No. I will not. I cannot. I want to stand on top of rooftops and shout my love for these eggs all over town. + +J, H and I went there a few Sundays ago. We all got the same thing. When was the last time you went to a meal and all three people ordered the same thing. It was that good. The scallop breakfast is out of this world. 2 perfectly cooked scallops, scrambled eggs (the eggs!!!), the creamiest, tastiest grits in the world, buttery croissant and sausage, apples and butternut squash. Don't think those things go together? They do and are awesome! J and I also both got orders of bacon cause no brunch is complete without bacon. + +Our service was also great. Nice hostess, awesome waiter. All was perfect. + +Really freaking good brunch. Really. Cannot say enough about those freaking eggs. + +Oh, but don't order an additional mimosa from the deal - they are $8 a piece which is a bit steep.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My first dining experience at Casbah was a nice one. We ordered the cheese plate to start and I and I had chicken for my entree. The wine list was not huge, but the selection was nice. The service was very good. I plan on returning there in the future for a meal.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It's a little pricier than most places in the area but the quality and ambiance is well worth it. The food was really good and the drinks were relatively reasonably priced for the surroundings, great place to take a date...or spouse.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Wonderful brunch and good dinner. The service obviously prides itself on being super proper (choreographed plate delivery, polite to the point of almost sappy attitude on the part of the waiters) and it can be a little bit annoying even. However, this is the probably the classiest of the Big Burrito restaurants, so if you're looking for that, this place is great. Extensive, yet expensive, wine menu. Small-ish portions and a very pleasant covered heated patio.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Went here for bruch and had their take on the classic eggs benedict. I'm a huge eggs benedict fan and this was very good. I opted for the prociuto as the meat option and I'm glad I did. It gave the eggs enough flavor without having to add extra salt. + +The potatoes were perfectly cooked and the fruit was tasty as well. Had the bellini and didn't realize how I much I would enjoy it so I had two![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> - Great food. I had the Gerber's Amish Farm Chicken Breast and it was cooked perfectly and delicious =] +- Nice wine selection. Though I'm a beer guy. +- Friendly staff. +- Okay atmosphere. + +This place is definitely worth trying. Will be back for seconds![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Hey do I really need to review this place? Look at the previous reviews but I will let you know that they have a great lunch deal, the piccolo gusto menu. I highly recommend it because it is a heck of a deal and you can have tastes of a few different items so it pairs well with my self diagnosis of A.D.D. no offense to anyone who has A.D.D but it definitely kept my attention throughout my lunch experience. First off the service was excellent very attentive server who was really a foodie, which I really appreciated. She knew a heck of a lot about the seemingly simple dishes I had ordered. The Piccolo Forno allows for a choice of Salad or soup, a pasta or risotto, half sandwich. I went with a taste of the Pea Tendrils and Frisee Salad, while slightly complex to eat, it had a savory flavor from the light dressing and blue cheese crumbles, then I went with cauliflower risotto which was riculous. That is how you make risotto people. For the half samich I went with the half turkey. The turkey wasn't just a normal turkey slice from the deli counter this was actually very nicely trimmed meat off of a bird that was prepared in house and it was immediately noticeable. All this for $15 dollars, I'll take it....And I'll do it again many times over again. Come here for lunch sometime and check it for yourself.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great menu - lots of choices. There were six of us and we shared 3 appetizers - the grilled chickpea hummus, the grilled octopus, and the mixed olives. The babagonoush hummus was delicious I had a winter fizz drink which was prosecco with cranberry and mint nice flavor and perfect before dinner drink I had the cioppiano which was one of the best meals I have had in a long time. The sour dough bread was soooooo good. Most everyone else ordered pasta dishes and thought them very good. We opted not to have dessert there but they did bring salted Carmels to the table with the check so if they were any prediction of the desserts they are EXCELLENT. Great place to dine - I will return. And the complimentary valet parking was nice as well - didn't have to search for a place to park and the valet were super nice. I should mention our waitress was also super nice and very accomodating to our larger party.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The food here is amazing. I have to admit the price is a bit high, but it's just worth it. Beware though during dinner times, everyone there dresses up pretty formally. I am not talking about suits and ties, but you know what I mean so make sure you dress up appropriately![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My husband and I went to Casbah on our first date night after having our son. Our plan was to take our time and indulge in everything. After we looked through both the wine selection (outstanding) and the menu (delicious), we decided to do things a little differently. Instead of ordering just two entrees, we wanted to sample as many libations and treats as possible. + +First, we ordered the white wine flight, and split a few seafood appetizers; then, we ordered the red wine flight, and split a few meaty appetizers; and, finally, we each ordered a glass of our favorite red and split a chocolate ravioli with raspberry sauce dessert. + +Our bill was quite pricey, but I feel totally worth it. Every single thing we drank and ate was delicate, perfect, satisfying, and well balanced. I would go back and spend the money any time![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Brought my wife here for her birthday and we were lucky enough to arrive on the last of three nights of the truffle dinner. I saw it online before I arrived and dismissed it, but our server (Amanda) sold us on it when we got there. In fact, her thorough and enthusiastic descriptions of each course (including each cocktail and cheese) were a highlight of the meal. Sometimes over the top (""people say it's the best meal they have had in their life"" and ""the chef took this week off so he could enjoy the meal as a customer--and it brought a tear to his eye"") but we genuinely loved it. + +First, she made excellent suggestions on the cocktail (mimosa) and she helped us decide on the rest of the meal. Her recommendation to split the truffle dinner and add an appetizer was perfect. We left completely satisfied. + +The cheese was very good and the accoutrements well-paired. When I saw it on the plate, I didn't think it was very much but it ended up being the perfect amount. I also appreciated that they kept the bread coming, especially for the next course: a homemade pasta with pancetta, arugula and[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Good food, great service, but high prices. + +My date and I shared 2 appetizers, a salad and each had an entree with the recommended wine pairings. Bill was $115 without tax--pricey by my standards for this experience. The new tuna tartare appetizer was the highlight of our night. The bruschetta with fig and grape butter, prosciutto and blue cheese was good, so was the beet salad. + +We were disappointed with our entrees. My roasted duck breast with spinach and gnocchi was not hot. My date had the salmon with potato fennel puree, which she said tasted fishy. + +Make sure you aren't seated inside the tent where patrons are eating on a slope on outdoor metal tables--this is not my idea of a good dinner at this price range. + +Although I would come here again, there are certainly much better restaurants in the city. I would rank Casbah below Eleven within the Big Burrito group of restaurants.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Not a good vegan experience. We were meeting friends at Casbah for dinner -their choice. Since I follow a version of vegan, I called ahead and was assured that they had vegan versions of a couple of pasta dishes. Server was very cooperative and said she would instruct the kitchen to omit the meat and increase the veggies on their cavatelli. Well, they omitted the meat, but I was left with one of the smallest servings of pasta that I have ever seen. At about $20, it was close to the price of caviar![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is definitely one of the most interesting places I've been to, in a good way. Casbah is a great local place that serves smaller (but admittedly pricey) portions, and they change their menu up frequently to match the ingredients available to them each season. + +The set-up is...different? I couldn't quite figure out what was going on with it; you basically walk into a door and enter what looks like what was once a courtyard, which was covered with a canvas - maybe they take this down during the summer? Possibly? I'm not sure; anyway, if you walk to the back of the courtyard you'll get into the actual bar. + +The menu here, at least during my visit, was delicious - fantastic fresh sangria, a very interesting but tasty bruschetta (that, rather than going with the traditional tomatoes and basil, was covered in a kind of cream cheese, greens and nuts), and a reasonably portioned bowl of pasta with sausage and spinach. Not complaints, other than the fact that the pasta was a bit spicy and I wasn't warned about this. It wasn't too strong, though. + +Our waitress was doing the best that she could (I think) but was a little slow. Still, the place was fairly busy and I had good company to talk to during my meal, so no hard feelings on that one. + +I say give this place a try if you have the money to spare - and even then, get a coupon or a Groupon; I went with someone who was using a birthday gift card, and it helped the pricing tremendously.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Love this place. I've never had anything that wasn't tasty here. They do fish and meat very well. It's not obscure molecular gastronomy style, but dishes we have had here were all well prepared and savory. We have been to several business dinners in their space downstairs, and it really is my favorite place for these - even more than the pricier steakhouses 'dahntahn.' + +Wait staff were very attentive, and really made our experiences here great. Food was served efficiently for large groups, and arrived at the correct temperature. They have a great wine list, and overall offer a comfortable space with delicious food and drinks. Try the lamb loin, chicken, and cioppino - my three current favorites. Their pork chops are the specialty of the house, I'm told. + +Will definitely be back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Oh I love this place. It has a great menu and wine list. It has all the great dishes with a touch of flare. I took this meal to seafood town from start to finish and have no regrets. The staff was really friendly - realized I was there for a special occasion and brought out a desert that said congratulations - the little things. + +We dined outside and I felt tucked away in a Europe-esque atmosphere for a few hours. + +It is worth reserving a spot on the patio to get the full experience.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Sunday brunched here. Food and service were excellent.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Ah Casbah... the epic tale of bi-polar experiences. + +As with all the other Big Burrito restaurants, I'm definitely a fan of the upscale and unique spin on an ethnic cuisine (in this case Mediterranean). + +The fiancee and I's first venture here left us with some of the best scallops we've had in Pittsburgh and a Jamison Farm's lamb shank that was to die for. I wish I could remember the waiter's name, but all I can say is, he definitely deserved the 40% tip we laid down. + +Take two, brunch. We sat this time out in the covered and heated patio up front. While the food was great (I got my obligatory fat kid french toast variation), a rushed server caught her arm on the back of my chair towards the end of our meal and dumped an entire pitcher of ice water on my shoulder and lap. + +While I'm completely sympathetic when it comes to legitimate mistakes (and the server was obviously extremely embarrassed about the situation), I was surprised when no follow-up occurred. The server apologized and ran immediately to the back of the house, leaving two of the surrounding tables to come to my rescue with their napkins. The server brought us our check, but despite the public scene it caused, not a single manager stopped by to verify that everything was alright. + +After writing to Casbah, the manager did respond quickly and offer to rectify the situation, so I'll give them a pass assuming it was just bad timing and an issue where the server was too embarrassed to do anything.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> A delicious menu with a twist. Unique wine list too![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Though Casbah has been around for ages this was our first time dining there. In short, the restaurant itself was nice and the food interesting though a little on the pricey side. Service started out great but for some reason our entrees took forever and our waiter more or less abandoned us. If I'm spending a $150 on dinner for 2 I expect some sort of explanation on why we are having to wait 45 minutes plus between our appetizer and the entrees. At a minimum, I don't want to have to flag down the server to order another drink and for god's sake don't make me ask for a refill of my water. If I was only basing my decision on food I'd probably go back but all things considered there are too many other restaurants in Pittsburgh where I can get amazing food AND an amazing dining experience.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've been to this restaurant with my husband twice, once for dinner before I moved to Pittsburgh, and once for brunch a few months ago, and both were great meals. When I went for dinner they accidentally threw away my doggy-bag instead of giving it to me, but they offered to make me a new order, so it worked out fine. When we went for brunch it was quite crowded and we had to wait a while before getting seats at the bar. The food is really fantastic though and there are good vegetarian options. It's pricey, but worth it if you're celebrating a special occasion. Seems like it would be perfect if you're looking for a romantic place to impress a date.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Very enjoyable menu n staff.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I stopped by here this past Tuesday night for dinner by myself. It had been a couple of years since I had last been to Casbah and while I remembered it being decent, it differed a bit from my fiance's opinion that this was the best of the Big Burrito restaurants. Due to that it had been on my list of restaurants to visit so that I could get a better opinion of it. The restaurant looked the same that I remembered it with a large outdoor seating area and a smaller one inside with the bar on one side of the restaurant and the dining room on the other. It was all nicely and tastefully decorated. + +I arrived shortly after 5 PM and immediately made my way into the bar area of the restaurant as I hate taking up a table if I am eating by myself. There was no one else at the bar at this point and the bartender quickly greeted me and gave me a happy hour menu while explaining it to me. I had not been planning on getting a drink but one of the $6 cocktails caught my eye and I ended up ordering it. The bartender was pretty friendly guy and explained how he came up with the drink while he made the drink and we chatted for a bit. For my entrée I decided to order the Long Island Duck which was a roasted breast, braised leg, gnocchi, spinach, rosemary, black mission figs and duck jus. Whenever I had ordered it I had actually missed the fact that it came with a braised leg and was excited to see that extra unexpected portion of meat on my plate whenever it was delivered to me. The whole meal ended up being incredibly tasty with the duck breast being cooked perfectly with nice seasoning and not greasy at all. This was in stark contrast to the leg which was incredibly juicy and greasy which I absolutely loved. Normally I am not a fan of greasier duck but the two preparations really helped to enhance the other. Finally the figs provided a nice touch of sweetness while the gnocchi was pillow like and tasty. It was also nice to be able to taste a hint of rosemary on them which I had forgotten about between the time I had ordered and when it was delivered. + +The bottom line for me is that I would definitely head back here again in the future. Both my cocktail and my meal were really good and I would actually consider this to be one of the best meals that I have eaten in a little while.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Love Casbah. Been going there for years and have never had a less than great meal and service. OF course their signature lamb is to die for (with the Stag's Leap Petite Syrah). What can I say -- the cheese plate is great. Everything is well-prepared and the service is among the best in the -burgh.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Very good food and another great place for happy hour. Highly recommended. You won't be disappointed.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is a well run restaurant with great food, great consistency and excellent service. We were sitting on the patio and the angle of the sun changed to shine right in our eyes, but the waiter was able to quickly move us to a better table. I highly recommend the cheese plate, it is probably the best in Pittsburgh. The Arugula Salad is delicious. So is the Alaskan Halibut. You really can't go wrong with Casbah.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> While in Pittsburgh for 24 hours, we went to Casbah for after dinner drinks. + +This place has wonderfull covered outdoor seating, a great bar featuring unique small batch liquors and an overall cool vibe. + +I had the Watermelon Gin Fizz. It was FANTASTIC! great gin, wonderful watermelon juice and ice cubes made of the aforementioned watermelon juice. + +W also had a couple order of their olives which were great too. + +Would definitley go back for a meal.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My bf took me here on my birthday and it was so good he totally sealed ""the deal."" + +This was on of the best dining experiences I've had in Pittsburgh...made even sweeter by the fact I left full, and without feeling the boyfriends wallet was just raped. + +I had the Orichiette pasta and it was love in a bowl. Savory and sweet and perfectly balanced. Boyfriend had short rib ravioli and it was so good that when I asked him if I could have a taste he told me that he loved me, and he knew it was my birthday, and he let me have a bite, but he didn't want to share. I didn't make him, I just know it was excellent. + +I have officially done dat all of the big burrito restaurants & I honestly feel like has bought is the most effortlessly sophisticated of all of them. This is amazing food in a restaurant that is sophisticated without even trying. + +I really feel like has bought is highly underrated and you'd best get your arse over here to dying. They have a brunch which I hear is amazing and I can't wait to try it out.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I am so happy they got rid of those awful bar stools!!! We often choose not to walk in to Casbah without a reservation because the bar area was historically uncomfortable. They have traded out the old stools that were screwed in to the floor, too far from your companions, and didn't comfortably turn to face people (who thought that was a good idea?) in for some admittedly less attractive but functional chairs, I'm a big fan of the lunch and dinner there--we'll add that more often to our walk-in list now,[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Casbah is fast becoming my favorite restaurant in Pittsburgh. I have been there twice now and both times the service and food was impeccable. + +The calamari and the proscuitto appetizer are a great start to the meal and not too heavy or filling and I could eat a whole basket of the warm bread. I'd love to know where they get it from as I can't imagine they bake it there, but maybe they do! + +The pork chop is their signature dish and does not disappoint. My husband had the duck the last time we were there and it was juicy on the inside and had a great crispy skin. I had the red pepper casereccia and was thrilled with the amount of seafood in the dish. There were 4 HUGE, delicious scallops and a ton of lump crab. Very impressive. I was there with a group of 6 this time and everyone had clean plates at the end of the meal. + +I like the fact that it seems like the menu changes with the seasons. The proteins may stay static, but since they use a lot of local ingredients, the accompaniments/side dishes might be different every time you come. Honestly, this is one of the best restaurants in Pittsburgh. I plan on trying it for brunch or lunch sometime soon.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have been here several years in a row, but not recently. I hope to visit it within a few weeks. The food was fresh, unique and delicious every time I went. Great atmosphere--outdoor dining or indoors (more fancy if I remember correctly). Absolutely wonderful service. I will write an updated review with more details once I visit it again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Awesome brunch![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Lovely, relaxing atmosphere. The cauliflower soup with tarragon emulsion was fabulous, as was the tomato basil soup. The waiter was attentive and happily allowed for a substitution on my salad so I could try one of the raw milk cheeses from their cheese sampler. The grilled chicken breast on my salad was a bit more dry and hard than I like, but I am not a big fan of barbecuing chicken and it certainly seemed to have been charred that way. If the chicken had been moist, this place would get all five stars from me![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> So I'm a lowkey snob when it comes to going to nice restaurants and though a lot of places charge an arm and a leg, are overrated, and are just not up to par with what I'm used to coming from Sf and La. With that said, casbah was a nice little taste of home for me. It had really fresh ingredients and a nice selection of wines to go with. We started with a cheese trio with was paired well with different preserves and chutneys. We then had roasted octopus and the scallops. The scallops for me were very interesting and a little too sweet for my taste with the pear and lacked texural components. However the octopus has a real nice char, and was full of great well rounded flavors. For our entrees, my bf got the duck which was underseasoned, and the fat was jot rendered out correctly. The skin was also burnt. The sides and vegetbales of the dish were seasoned and cooked beautifully though. I had the lamb loin and it was perfectlh medium rare with delicious bitter greens. I honestly loved every part of my entree and the red wines we selected went well with the meal. + +All in all it was a delicious meal and a really nice environment. And worth the money.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I enjoy coming to Casbah because it reminds me of the fresh, local elements I so enjoy about the Napa and Sonoma Valleys. Casbah gets a lot of produce and meats from local farms, and I love that! + +I also love the cheese selections here. I usually ask my waiter to surprise me with any combination, and it's always fantastic. I am a sucker for the duck here. It's duck two ways-roasted breast and braised legs. Absolutely delicious. The gnocchi on the side is fantastic. I also like the double cut pork chop with the braised kale, as well as the roasted chicken because the polenta on the side is so yummy. + +The wine list is pretty good, and the waiters are generally knowledgable about pairings, which is nice, because sometimes you just want to sit back, relax, and let someone else do the work. + +You can't go wrong with any of the pastas. It's sometimes fun to split a pasta as a starter. It's a nice way to try a variety of dishes. The orrechiette is a great choice because it combines the tartness of cranberries with the savory creaminess of goat cheese. Yum! + +If you're not absolutely stuffed at this point, try the dark chocolate raspberry bread pudding for dessert. You won't be disappointed![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> A taste of CA in PA. + +We walked in and I would swear I was in Santa Monica or Hermosa beach. Great atmosphere- creative menu and delicious food. The steak was to die for and the pumpkin cheesecake finished it off. + +They also have a nice wine list. The French Chardonnay was quite good! + +Thanks for making me feel at home.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My absolutely favorite dish is the potato gnocchi. Just amazing! Service is fantastic, nice decor. I wish they wouldn't use such huge paper towels in the bathroom, but other than that I really like this place.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Casbah was such a great experience. I dined here with my boyfriend and 2 friends for my birthday. Drinks are fairly priced. They offer wine flights and champagne flights. The food was wonderful! +I started with a homemade chicken noodle soup. Didn't expect to see it on the menu here, but it was really good. My party got the tuna tartare, and 2 different olive dishes. Seeing the prices on the menu (all $22+ for entrees) I would have expected a $5 plate of olives to be about 5-6 olives. But it was a bowl full. And they were yummy. For entrees we had the duck breast, which according to my boyfriend is the best and most perfectly cooked duck he's ever had. I had a prosciutto plate, it was technically an app, but it's my birthday and I'll eat what I want! Another member had the cioppino, and she loved it. + +We then got their birthday dessert which was a chocolate cake with ganache and brûlée ice cream. It was great. + +I couldn't have asked for a better birthday dinner![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great atmosphere and food experience. What else can you ask for? Went here 2 weeks ago for the first time and totally enjoyed it. Pretty good wine list too![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The rave reviews I'd heard for Casbah were so over the top, I thought it would be impossible to live up to. Casbah has exceeded it's sky high expectations and made me a believer! We got the brunch and while the $24 pre-fix menu isn't cheap, it actually felt like a steal because the ambiance, decor, friendly attentive staff, and generous portions of delicious, inventive food were all so fantastic! + +The brunch pre-fix included your choice of breakfast cocktails, appetizer, entree, and amazing still steaming home made muffins and mint chocolate scones. I'm anything but a light eater, and there was so much that I still had to take half my meal home! + +We all got different things and there wasn't a single bite of anything that we didn't love. I particularly recommend the Arugula salad, salmon and dill appetizer, and the scallop and grits entree, though you really can't go wrong. + +The decor and music was just as unique, artistic, and beautiful as the rest of the Big Burrito hot spots. We ate in the basement, with a beautiful fully stocked glass wine cellar, under lit stone tile walls and wooden ceiling trim. Casbah isn't cheap, but I'd still consider it once of the best values in the city because you get so much for your money. I'd trust Casbah to celebrate any special event with a flawless dining experience.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Tonight's review: it started with a table for two stuffed between two other tables. Yes there were five other more comfortable two tops available. We asked and after some sighs were granted our seemingly offensive request. Punishment was fast...we sipped our water, were provided a refill but no offer to acquire other beverages. With plenty of time to review the night's menu, we made our selection. My request was well done Salmon (heart issues require well done) the chef's feelings were clear; as I sawed through the salmon I thought it could possibly be a message. I again had offended by my request. I like Casbah and the other BB restaurants but tonight I should have selected a friendlier more customer focused establishment. YES I will return and still recommend Casbah. Oh we did finally get to place a cocktail order. +M[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Visited for brunch again on a rainy winter Sunday. I reaffirm my previous comments. + +Good service. Generally great food (the breakfast pastries, my breakfast polenta and the wife's scallops were fantastic), however inconsistencies still prevent the 5-star praise. + +While the coffee is great, the crud in the creamer and a dirty spoon to start the meal off were not. In addition, I may have had one of the most bi-polar plates of my life... braised lamb on grilled sourdough. The lamb itself was kiss-yo-mama good... seriously, this meat is a fork cutting affair. However, the bread itself seemed stale and completely took away from the star in the spot light. + +As with Eleven, you can't go wrong with the brunch pre-fix, so be prepared to need a wheel barrel to get yourself out the door![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Overpriced, salty and overrated!!! Why this place is so popular I will never understand.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Dinner Saturday night was excellent. The server was on his game and the chef out did him/her-self. +Drinks were perfect, food perfect for all four of us and again service was excellent.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I recently realized that I had only given Casbah four stars after my first visit here for New Year's Eve 2012... What a terrible judgment call that was on my part. So I'm back to proclaim that over a year later - having dined here again in 2013 - with a year of dining experiences across the country - I still regularly dream of this restaurant. Do I dare say it's my favorite restaurant? I'm not sure, but if it's not my favorite, it's certainly close. + +We returned after NYE last year to celebrate my birthday in March, making sure to bring along the oh-so-coveted Big Burrito birthday coupon. I ordered the Orecchiette with Chicken, Cranberries, Goat Cheese & Sage Cream. Oh. My. Goodness. Don't order this if you're on a diet... but order this if you love delicious food and living life to the fullest. It was ridiculously creamy, and the cranberries packed the perfect fruity balance to the rich dish. My husband ordered the Double-Cut Pork Chop with Kale & Butternut Squash Risotto. While recently dining at a highly rated restaurant in NYC, he said, ""My double-cut pork chop at Casbah was better than this double-cut pork chop."" That's when I knew that I needed to update my review of Casbah. + +Finally, my delicious birthday dinner ended with the Dark Chocolate-Raspberry Bread Pudding. I love ordering bread pudding at restaurants, and I think this is the best of them all. I would confidently enter this dessert in a bread pudding competition, knowing that I would be walking away with the blue ribbon.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I don't understand the high rankings of this place and why it consistently gets into Pittsburgh's top 3. The food is rather mediocre for the price. I went there twice, both times paying close to $300 for dinner for 3, but the food really didn't stand up to expectations. Sea scallops that I have ordered last time were burned outside and rubbery and chewy inside. Risotto from my previous try was falling apart. But the most annoying thing is that there is way, way too much food on the plate for fine dining place. The appetizer cheese platter that we ordered last time had enough cheese to last for a week! I don't go to places like that to stuff myself... So no, I do not like it overall. Maybe it is one of those ""good enough for Pittsburgh"" kind of restaurants, but then maybe they should think about charging a bit less. Unless they charge for quantity, not quality... + +Service is okay.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My favorite local place in Shadyside. My husband and I go for Friday HH (5-7 pm) every time we can. Juan is great behind the bar, but Fiona and Joe (I think Joe, maybe his name is John?) are awesome as well. The HH drinks change seasonally but you can always get your choice liquor mixed drinks also. For $6/drink you can't beat it! + +We typically always get the hummus trio as an appetizer with extra pita bread, or the calamari. All of the entrees we have had (pork belly, risotto, pork chop) have been perfectly prepared, zero complaints. It's on a pricey side, so not a weekly dinner option for us (unlike the HH!) + +I would say the complimentary valet is a perk, but we live within walking distance so haven't used it. + +TIP: Go to HH on Fridays, ask for Juan, get a Manhattan. Your QOL will improve greatly![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This was an amazing brunch place! A family friend asked me grab brunch here because her son used to work here as a chef/cook. The food was divine! The brunch comes with a cocktail, an appetizer and then your meal. The coffee was really good and the mimosas were strong. We sat outside on the patio and it was just beautiful. A perfect retreat from the snowy outside that morning. Definitely go![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is such a fabulous place. Regardless of the occasion the food and the service are impeccable. In Pittsburgh trying to find a restaurant that will fit everyone in your parties needs is difficult - Casbah is the spot. My family had a birthday party for me here on Sunday. Casbah was accommodating with a cake, with a loud bunch that constantly changed their order, and were extremely patient. The food was outstanding, as per usual! I ordered the Elysian lamb which was delicious! Cannot wait to return![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Thursday night January 30. Excellent service and excellent meal. Very crowded when we went. Glad we had reservations on open table. My wife had scallops, I had the signature pork chop. Both were perfect. We loved the octopus appetizer.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> To be honest, I feel that this is one of the most overpriced restaurants in the entire city. The food is average to good, the place is beautiful with outdoor seating, but in my opinion the price is just not worth it. They have a really good happy hour, so I would definitely recommend going to that and maybe trying an appetizer or two.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The last time I was at Casbah was on a balmy spring evening in my sophomore year of college. I'd arranged a dinner with my mother in a fancy effort to spring the news on her that I wanted to move out of my college dorm the following year and into a co-ed fraternity house. I remember being underwhelmed by the food, but that could've been the chilly reception with which I was met during this particular dinner and the conversation that entailed. + +Fast forward fifteen years later (what?!) and I was back at Casbah with Jonathan D. and my future in-laws. We enjoyed the prix-fixe brunch, and enjoy it we did! The meal started with a small basket of mini goodies including double chocolate muffins, cranberry almond scones and buttermilk biscuits. The meal included choice of breakfast cocktail, appetizer and entree. For my selections I chose a bloody mary, Smoked Salmon and Sea Scallop Fry. Dare I say this meal (with one small exception) rates in my top five of all time? I dare. The appetizer was very filling in itself and absolutely sublime for smoked salmon. The salmon was accompanied by a done-just-right potato pancake that I could eat ten times over. My main entree consisted of two plump and juicy sea scallops on a bed of sweet potatoes, carmelized onions and sausage (I substituted chicken sausage for the included fennel sausage). In addition, the entree included a portion of melt-in-your-mouth white corn grits and scrambled eggs that seemed out of place and that I completely could've done without. A croissant was also included but I asked for fruit instead and was rewarded with a small side of grapes, canteloupe and strawberries. My fellow brunchers feasted on a variety of Creamy Polenta (looked amazing), a cheese tasting, Lamb and Eggs, and Casbah Benedict. Everyone left smiling and satisfied. So, if you haven't given Casbah a try in the last decade, it might be time to visit again. I'm so very glad I did! + +P.S. Bring your coat into the restroom. It was about 10 below in there. Brrr![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> For a late lunch my wife and I shared the grilled flatbread, Scottish salmon, pastrami sandwich, and puréed pear and mushroom soup. Creme brûlée after. All food was really good and the soup was a very different flavor for me. Service was great. This is part of the Big Burrito restaurant group, we are definitely going to try some of the +We felt the prices were a bargain for all we got. $56[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've eaten at Casbah four times since my first review - from cocktails and an appetizer to lunch, everything has exceeded my expectations and the service has been great every time: polite, helpful recommendations, and my glass is never empty. I continue to think that the Piccola Gusta lunch menu is a real value and has some really delicious options, but I would have dinner just to try those little candies they offer at the end of meal at dinnertime again - they are a cross between maple sugar and caramel, so good they're worth a star all by themselves.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We dined here for my wife's birthday last year. We started out at the bar ordering cocktails. I had a tasty cocktail with bourbon. We finished our drinks and made out way over to our table. We started out with a cheese tasting, which was very good. For entrees she ordered the Halibut and I had the Red Pepper Casereccia. This was seared sea scollops with a red pepper pasta. This entree made my list of favorite dish ever eaten. It was so delicious. I cannot wait to have it again![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We love this Big Burrito establishment as it matures and becomes a perennial choice to enjoy, no matter the season. It starts with a well-stocked bar area, nicely lit and very comfortable. The indoor dining area is complimented by the (now-covered) outdoor seating area. +Service was mostly attentive, and very friendly throughout the evening. The wine list is varied and reasonably prices, with especially fine after dinner selections. +We started with two appetizers this time out, the Tuna Tartare and the Sheep's Milk Gnudi. The tuna was very clean, served with nicely grilled sourdough. The Gnudi had a great truffle butter and tarragon flavored sauce. +I also had my all-time favorite salad, the Arugula. This masterpiece features homemade pancetta, crimini mushrooms, and goat cheese. We split the Ricotta Cavatelli Pasta, prepared thoughtfully with fennel sausage and spinach. +Dessert was a nice assortment of house prepared sorbets (mixed berry/pineapple/grapefruit). +Valet parking is complimentary; please tip your driver![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Just got back (after looking for a taxi in this 3rd world city - but that's for another review) We liked the atmo. Liked eating ""under the outdoor extension"" under the well working heaters- it is fun and really makes it feel like a more unique dining experience. OK now on to the food. We started with a Spanish grilled octopus - it was delicious - charred grilled taste, delightful blood orange accompaniment - perfect. Then had we not had the Habitat beet salad yesterday (it was amazing - check my review) - this would be the best, B U T it was still very good and had Maytag blue cheese, pistachios and nice beets - OK not amazing, but nice beets. Then we had another unfortunate comparison to Habitat. When we had the pork chop - generous portion but a bit fatty. (Again Habitat's was so much better) We also had the new pasta dish on the menu which was ok - big scallops (4) but a less than impressive sauce. Glad we went here - it was different, but not really special and the nightmare of getting a taxi back was just -- well a nightmare (what is wrong with Pittsburgh taxi service -- everything) City fathers (and Mothers) -- fix this!!!!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> One year since my first venture to Casbah, I had the chance to return for a second time. And I have to say that I am officially a die-hard Casbah fan. + +Yes, our dinner group quickly racked up a big bill - but it was for a birthday party, and Casbah had kindly sent along a $30 off dinner coupon beforehand. Even better, they went ahead and applied the discount even though we managed to forget to bring the actual card they had sent ahead to us. We had been completely prepared when asking about this to potentially not be able to use that $30 off at our visit, so their understanding alone would have gone a long way in making the meal a good one. + +The amazing food just sealed the deal. Between a table of four we all had the chance to order and then a variety of Casbah's current menu - including their scallops, arugula salad, duck, pork and veal meatballs, and a ricotta very similar to what I had ordered the last time I visited. Everything was stupendously delicious - I honestly have no other words for how good this food was - and we all left full and satisfied with no complaints. + +Casbah has definitely become a restaurant that I can come to for special events. Their food and service impressed me again tonight even more than they did last time; add in the fact that they use local ingredients whenever possible and always have something new to try with the changing seasons, and I'm completely sold. Here's to the next special occasion and dinner out at Casbah![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Food is simple and delicious, although the service was awful when I went. Highly recommend the veal and pork meatball appetizer, such a great combination of flavors and textures.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Big Burrito does it again! Casbah is located on a wonderful, neighborhood street in the Shadyside area of Pittsburgh. We got there a little early and waited a little in the lot. Our reservation was for 11 and they open at 11. We were still told the valet had to move our car. I get they have a way they do things and it must work for them but the lot has about 40 spaces that you can see from the street so I don't know why valet is necessary. We are particular about our vehicles and we don't valet anywhere. Not that the valets weren't nice and it's not like we could not see them move the car but anyway...the main reason they get a 4 and not a 5 star. Onto the meal... + +We waited just a few minutes in line to be seated. As I said our reservation was at 11 & that is when they open. We were seated promptly requesting the inside area of their dining room. They do have a very nice, shaded patio area as well complete with ceiling fans. We requested to sit inside and the hostess happily obliged. We were greeted quickly by a happy and knowledgeable waitress who was on it. She was not at all intrusive but our water was never empty and we didn't have to wait long for our check when we were done. She asked if we wanted any other beverage. I got an iced tea and the hubby requested iced coffee. The waitress noted they could make one for him by adding ice to coffee and he said yes. He was very happy they would accommodate his request. + +We ordered our food and were promptly brought a basket of bread (oh the wonderful bread basket!). We got 3 types of amazing breadly goodness that included cranberry scones (wow), biscuits (warm, soft, & the Hubby's favorite), and (my favorite) the lime, coconut muffin (sweet, lime, coconut, what's not to love). Oh, and let us not forget the maple butter, yum! I ordered the smoked salmon app. The combo of salmon, capers, aioli, and truffled potato cake - absolute perfection! There was a salty, smokey, sweet flavor that was sheer joy on my taste buds. The hubby chose the creamy polenta which he thoroughly enjoyed noting it was very oatmeal like. For my entree it was the sea scallop fry minus the caramelized onions. I would SOOOO get this again! The scallops were cooked to perfection with a wonderful golden outside that makes my heart sing with joy (can you tell I love a good sea scallop?). The combo of English peas, fennel sausage, and white corn grits...it was something special for sure! I could eat that sausage by the boat load every single day! And the grits - smooth, creamy, and perfectly seasoned. Not that it needed it but the dish comes with scrambled eggs and a beautifully, buttery croissant. My brunch was so satisfying, Heaven! The hubby chose the eggs Benedict with prosciutto. He liked it but noted he should have gotten the spinach not the prosciutto. He said the prosciutto seemed vinagary. The dish includes paprika roasted fingerling potatoes which were mild and perfectly cooked. And for dessert we chose the chocolate stout cake on a wine caramel drizzle served with a little dish of creme brulee ice cream. Holy cow! What a terrific chocolate cake & the ice cream rocked too. + +Overall, I would recommend Casbah to everyone noting their brunch was fabulous! The valet (even though the need for valet is questionable) and wait staff were super nice, attentive, & knowledgeable. The apps, brunch, & dessert were yummy and delightful. We will visit again![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Had dinner tonight at the bar. My sister and I wore sweatpants and flip flops... Nobody treated us differently .. The brought out bread with butter and a second butter made from goat milk.. I liked it .. My sister said it reminded her of cream cheese.. We shared the calamari ... It was good... I had the halibut... It was good accompanied with a salad.. My sister had the duck.. I didn't like the duck that much but I am not a big fan of duck to begin with .. We each had wine ... I had the falanghina .. It was perfect.. We shared a bread pudding for dessert.. It was the first time I ever had bread pudding... It like it .. It is a nice quiet restaurant with ample seating both inside and outside...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I recommend the short rib ravioli! Totally the best thing I've had in a long time.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Excellent prix fixe brunch with impressive service. One of the best brunch deals in Pittsburgh: two courses and a drink for under $30, and their selection has something for everyone. I love their patio ambiance as well as their basement set-up. Great place to take visitors or for special occasions. + +I'm a huge seafood person so the first time I ordered a Bloody Mary with the smoked salmon to start and sea scallop fry as my main. I'm a fan of their Bloody, it's spicy and flavorful. The smoked salmon was filling enough that it's easy to split and the truffled potato cake served with it melts in your mouth. The sea scallop fry is everything you would expect, almost too much food, but no complaints. + +My second trip to Casbah brunch, I went with my old favorite of the smoked salmon but split it with my friend who ordered the cheese plate. Also, I ordered the Braised Lamb & Eggs as my main based on friends' recommendations. It's honestly to die for. Rich and flavorful in the best way, attributed to the tarragon sauce and the slow roasted lamb, and easily their specialty. If you want to order something you can't get anywhere else, order this. It's very filling and rich, especially if you get a filling first course. Have only been here for brunch, and looking forward to trying their lunch/dinner![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I have a soft spot for this place -- probably because it is one of the first restaurants my fiance ever took me to, and he made a special night out of it. We've been back many times, for many occasions, and Casbah has never disappointed. Great wine, cocktails, food, service, and atmosphere. It can be a little more cramped on the inside, but it's never too loud. If you can sit outside, it feels nice and spacious. It's also very nice downstairs. + +The valet parking is a huge plus in my book, especially in that area of Shadyside. The service is always prompt and never overbearing. + +The last time we went, we had the sheep's milk gnudi and I'm pretty sure it was sent straight from heaven down on to our plate. I nearly fought my fiance for the last piece. He loves me so he let me have it. The swordfish was wonderful. The lamb is always great. The short rib ravioli melts in your mouth. I'd highly recommend any of those. + +The dark chocolate raspberry bread pudding is worth unbuttoning your pants for...and if you like dessert wines, you'll be in heaven for sure![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We went here on a double date of sorts. My boyfriend and I and my sister and her fiance. +We started with cocktails and a cheese plate. +My sister ordered the Watermelon Fizz (Gin drink) and it was super tasty. My boyfriend ordered the Berry Bourbon, I was jealous, it was divine. I ordered the Boyd and Basil (vodka drink) and it was lovely. 5 stars for beverages done right. +The cheese plate was wonderful, it came with 3 different spreads and 5 different cheese, and some prosciutto. A+! +They gave us extra bread and the salted butter and their yogurt butter. It was amazing and we gobbled it all up. +We all ordered the Arugala salad -- it was gorgeous. +(Arugula, house-made pancetta, crimini mushrooms, potatoes, Riverview Farms goat cheese, pancetta vinaigrette ) +I ordered the Roasted Gerber Farms Chicken (whole grain mustard grits,greens, fresno peppers, fava & preserved lemon pesto, thyme jus), my sister got the Ricotta Cavatelli, +(house-made fennel sausage, spinach,crushed tomatoes, ricotta), her fiance ordered the Grilled Swordfish(Swiss chard, roasted tomato, garlic, chilies, caper, crispy polenta, espelette, Meyer lemon vinaigrette), my boyfriend got the Long Island Duck (roasted breast, braised leg, gnocchi, spinach, lavender, rhubarb, duck jus) \ + +My chicken was good, not great and a little flavorless. the mustard grits were superb, the lemon pesto kind of tasted like lemon pledge and really over powered the whole dish, which was really disappointing. +My sister ADORES their cavatelli, but this time... it came out cold. She is not one to complain and ate it regardless. +Her fiance's swordfish was perfectly prepared and tasted wonderful. +My boyfriends duck was cooked to perfection and all the sides were incredible (so he says). +When desert rolled around I was not interested as I was already so full from the dinner. +My sister ordered a glass off prosecco and Chocolate S'more Cake +(toasted marshmallow, salted caramel ice cream,graham crumb) which was deadly! I tried a small bite but since I am not a sweets person it was overpoweringly chocolatey. Her fiance got the Vanilla Bean Crème Brulée +(rhubarb chiboust, poached rhubarb, shortbread cookie) which he enjoyed very much. The rest of us opted for coffee's and watching them eat. + +Their wine selection is dreamy, their cocktails are perfection in a glass, and their food is absolutely delectable. + +I would go back to Casbah at the drop of a hat but I was not completely floored or blown away by any dish.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Started with the Cheese Plate then the Octopus then the Duck, finishing with the Chocolate S'More Cake. Great experience especially the service. Robert was spot on! I'll be dreaming about this in the future.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> One of the best restaurants in Pittsburgh! Very great food and even greater service. Ask for Robert, he is great! Ashley the bartender is also very nice! The food was amazing. I had the Duck it melted in my mouth. The short rib raviolis are also amazing. The muscle appetizer is a nice size for the price. You get about a pound of muscles for 12$. I will definitely be back. They make you feel special and welcomed.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Better than expected. Great service. Had muscles, red pepper pasta (forget the name) with scallops and lump crab, husband had duck. Everything was cooked perfectly. +Waiter said he lived in many parts of the country and this was the best duck he's ever had and he was right. Only downfall is I didn't save room for s'mores dessert![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place isn't in my price range but on special occasions the food is actually worth the extra money. I didn't know food could taste so good. :-)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> PROS: Some of their plates are most definitely unique in terms of ingredients and flavor. Portions are great and flavor was really good. + +CONS: Desserts were average. Large portions but nothing special. + +PARKING: Challenging given you need to find street parking only. + +All-in-all, I enjoyed the overall experience there in terms of service, food quality and ambiance. I'd go back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Delicious Sunday brunch at $28 includes a cocktail, appetizer and entree. The food is super fresh, locally grown and they even had peach biscuits.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Casbah has made my Top 10 Favorite Restaurants in Pittsburgh list. My friends and I went here for one of my friend's birthday. The food was simple yet delicious and transported me back to Greece. Upon being seated, they offered complimentary bread with butter and mascarpone spread. The waiter was very knowledge about the menu and recommended his favorites which included the pork chop entree and that soft shell crabs and corn were in season. As a result, my friends and I shared the soft shell crab app. The soft shell crab was fried to perfection with a small side salad of sliced asparagus and basil with tapenade. The only complaint I had with this dish was that there was only one to share between the three of us. + +For the entrees, I decided to heed the waiter's advice and selected the pork chop while my friends ordered the gnocchi and cioppino. What I am about to describe for the pork chop does not do it justice. The pork chop was cooked to the right temperature and did not lost its juiciness unlike most of my experiences with pork chop. It was also huge because it was double cut. The riscotto and braised kale complimented the pork chop well with the braised kale giving the pork chop an herbal component. I did not think I would be able to finish the dish but when I looked down again, everything was gone. I had the opportunity to try my friends' dishes and they were also prepared in an exceptional way. The veal and lobster in the gnocchi added a welcoming heartiness to the dish and the sauce reminded me of a curry. The unexpected combination of the gnocchi and curry-like sauce pleasantly surprised me. Since I have never tried cioppino until that day, I did not have anything to compare it but I was satisfied with the amount of seafood they gave. The only complaint from my friend was that the grilled bread that came with the dish was too hard for her to use to soak about the sauce. She used the complimentary bread instead and loved the sauce. + +While we were ordering our dishes, we mentioned to our waiter that it was my friend's birthday. He brought out a dish of caramel with ""Happy Birthday"" written on it with dark chocolate sauce for her even though we didn't expect anything from them. I am grateful that they brought that dish out. I do not know if the caramel is on their menu but it melted right away in your mouth. + +If you managed to read all the way to the end of this review, you probably are asking why I didn't give Casbah all five stars and I will tell you the reason. Although our waiter went above and beyond to get my friend a birthday ""plate"", the service overall was not satisfactory. Throughout the meal, he did not come over to our table and took a long time getting our checks to us even though we blatantly had finished our dinner for awhile. I have gone to less delicious restaurants who offer better service. + +Overall, the food at Casbah is exceptional. They change their menu based on what is in season. Here's a tip: if you sign up for the Big Burrito emails (the parent company of Casbah at https://secure.bigburrito.com/Register.aspx), you will get a free meal voucher on your birthday which is good at any of their restaurants. When my parents come into town, I will be subtly hinting that they take me here.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I am definitely the salt queen. I literally salt everything from pizza, McDonalds French Fries (even though I know that they already have tons of salt on them). I also salt ham and processed foods. I always salt food before even tasting it. Nothing is off limits when it comes to me and my salt shaker. + +Well when my beautiful meal arrived I asked my server for the salt. None of the tables had salt or pepper shakers on them. As my server went to get me the salt shaker, I took a bite of my potatoes. Whoa!!!!! They were extremely salty!!!! For the first time in my life, I didn't add any additional salt to my meal. For me to say something is ""very"" salty.... It is very salty. + +Being the salt queen, I stll was able to enjoy and love my meal. I am almost guarantee that the average person would not have enjoyed this food.. My friend also tasted my meal and immediately noticed the heavy taste of salt. However he never salts anything so something with one grain of salt on it, he will be about to tell. + +It really suprised me that such an upscaled restaurant would have this much salt added to their food. I am sure that it was an error or something. I have eaten here in the past and never experience so much salt. + +Still my meal ""for me"" was delicious. For the first time in my life, I am glad that I did not add any salt to my meal. + + I do love Casbah alot. It is probably my second favorite restaurant in Pittsburgh.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Best ""Babaganoush"" we've had since we visited Egypt. +The gaspacho soup was fantastic, and since my husband wouldn't share his short rib ravioli, I can only assume they were suburb also. +The atmosphere was a tad basic, but it was also different and therefore interesting and enjoyable.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Best gnudi I have ever eaten! +Loved this place, the food is sublime, I even licked clean the small homemade butter that they serve with the bread. Definitely will try out this place again![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The food here was absolute perfection; each bite was perfectly orchestrated to deliver optimal flavor and enjoyment. The service was also fantastic! + +For my entree, I had the cioppino -- it may be one of the best that I've ever had. The bowl was filled with beautiful looking seafood: large shrimp, clams in their shells, mussels in their shells, a gorgeous piece of perfectly seasoned halibut, and enormous wonderfully cooked scallops. They knew how to cook each piece of seafood to showcase it well. And the charred sourdough served with the cioppino was the perfect complement to soak up all of the delicious, savory flavors of the broth without becoming a soggy mush! My grandfather had the halibut and loved it... Cleaned the plate! + +I had heard rave reviews of the dark chocolate raspberry bread pudding, so we had to share one for dessert! My grandfather said it was incomparable to any bread pudding; it was a sweet, smooth, decadent indulgence that paired well with the house coffee. + +And the complementary salted caramels presented with the check were also amazing! I definitely need to come back again to try more of the menu... I think only wonderful items could possibly come out of that kitchen![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Made a reservation on opentable for Friday at 6pm. It wasn't packed at all but the hostess decided to sit us outside without asking where we'd prefer to sit. It was really hot that day so it was pretty uncomfortable. + +I immediately noticed that a lot of CMU undergrads worked there. While I was dining there I saw 3 CMU classmates. + +I started off with the gazpacho and it was very tasty. We were also given some bread with a lavender goat cheese spread. The spread was ok. + +For the entrees I got the roasted pepper cavereccia that had crab in it and ricotta cavatelli with sausage. + +For the cavereccia I thought there was going to be big chunks of crab but I was disappointed to see that the crab was shredded into small pieces. The pasta was a little undercooked and the sauce was ok. + +The cavatelli was extremely oily. The more you ate it the more you saw the pool of oil it was swimming in. I had to wipe some of the oil off the pasta. + +Lastly I had the dark chocolate raspberry bread pudding. It was pretty good but I wish there were more raspberries in it. + +Service was pretty good and the decor outside was nice, although, it got really stuffy in the outdoor tent. + +This place is pretty expensive and based on the food I wouldn't go back for that price.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I took my boyfriend to Casbah at the end of September for his birthday. We were seated near the door for our reservation however it was a very warm night so it was nice to sit in an open air setting. Our server, her name has slipped my mind, was excellent. I am not a fan of red wines but my boyfriend is and it being his birthday, of course I said let's get a bottle of red. We explained to our server what white varietals I enjoy and she suggested a bottle (which has also slipped my mind being months ago that we were there)that was perfect-both of us enjoyed it. We started off with the papardelle. The rabbit was delicious and it was perfectly seasoned, perfectly cooked-the flavors were amazing together! For entrees, my boyfriend ordered the duck and I ordered the short rib ravioli. His words to describe the duck were ""life changing"". I was only able to taste a small piece of his since he ate it so quickly, but I agree it was excellent. The short rib was so tender and juicy. I was concerned it would be overly salty and it was not. It was the best ravioli I have eaten hands down! For dessert, we ordered a cheese tasting. It was the perfect way to end our meal-with the cheese tasting and a glass of wine. I can't wait to go back to Casbah and sample some other items-I would have ordered the entire menu on our first visit if I could have![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> SETTING: +Outside seating connected to an indoor area. Dim mood lighting. Relaxed but a notch above casual. + +FOOD: +Entree: Cioppino. +Translation: Mixed seafood platter atop a savory broth. + +Imagine a shallow bowl containing a generous amount of shrimp, littleneck clams, mussels, striped bass, scallop arranged on top of a savory broth/sauce. A light soup-like consistency, the sauce rests at the bottom of the bowl. The entree comes with two triangle pieces of charred sourdough bread for more broth-dipping action. + +My favorite part of the Cioppino were the scallops and mussels and clams. Those items themselves were delicious, and even more tasty when accompanied with the broth. The bass and shrimp were prepared well, just not as flavorful. Although a generous portion, I would say this is a perfectly sized meal; not a heavy entree at all which to me is a good thing. + +SERVICE: +Our waiter was very knowledgeable and was confident with his recommendations. He didn't pull one of those ""well they're all pretty good, depends on what you like"" lines. Instead he rattled off the top items in each section and even emphasized a few that he highly recommended ""if this is the only time we are ever dining here"". We appreciated his honesty. Waters were kept filled, and he checked up on us regularly, but not overwhelmingly so like a helicopter parent. Ended the night with complementary salted caramels with our checks. A nice touch. + +IMPRESSIONS: +A solid dining experience, but I'm not sure if there was anything that left a special lasting impression. My group of grad student friends (we're the farthest thing from snobs) all agreed we enjoyed the food, but were not blown away. We all ordered different entrees that came highly recommended, which allowed us to sample the popular entrees. With the price point, I think we were hoping for a bit more. Definitely want to come back to try the brunch that people have raved about. I'm all about second chances.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Not sure what really needs to be added about this restaurant; it is very very good (my favorite in Pittsburgh) but by far not inexpensive. The best thing you can do, and I am not sure if it has been touched on in previous reviews, is join the Big Burrito group mailing list; you will receive a free coupon for an entrée around your birthday to be used within a certain time period...makes it a really good deal. Oh, their wine menu is ridiculously overpriced...call up to find out their current corking fee (I think around $15 bucks) and bring a better bottle at a better price than you are willing to spend there.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This might be the best food I've had in Pittsburgh. + +The restaurant set up is a little odd in that there is a tented outdoor space that you walk through to get to the hostess stand. The hostess stand is located in the indoor space. We were seated in the outdoor section in a corner which was fairly drafty. This is the only negative point I have about the meal. + +We ordered the cheese tasting menu, the duck, the scallop pasta, and the lemon sponge cake. Each bite was perfect -- flavorful and expertly cooked. The waiter was friendly and knowledgable. We left feeling full and happy.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This update is for Casbah's brunch. + +Alright, Casbah. You got me, you got me good. Dinner as I mentioned before was decent, but the brunch, amazing. Compared to dinner, brunch at Casbah is definitely the better meal and deal. I don't advocate playing favorites when it comes to siblings in the same family, but sometimes you can't help it. Brother Brunch gets the nod here. + +Brunch is basically a fixed set. For $28, you choose an adult beverage (or non-alcoholic), an appetizer, and an entree. They start you off with some pistachio scones, buttermilk biscuits, and cornbread. Perfect, I like to stretch before I get my grub on. For my Prix-Fixe (fixed set), I went with the mimosa, smoked salmon, and sea scallop fry. + +SMOKED SALMON: If you like smoked salmon, then you would enjoy this appetizer. It's what you would expect but also a larger size than I thought it would be! ""Oh no, there's too much of something I like,"" said nobody ever. Upon seeing the smoked salmon display fanned out on its plate with bits of egg, red onion, and aioli garnished over top, my salivary glands couldn't control themselves! + +SEA SCALLOP FRY: You know I love me some scallops. The dish came with two scallops, a small croissant, small bits of fennel sausage, a side of white corn grits, and a little bit of butternut squash and caramelized onions. I was tempted to go with the classic eggs/toast/waffle as an entree, but I am so glad I put on my big boy foodie stretchy pants and took a chance. It's not your typical brunch dish and it's one I would definitely recommend. + +All in all, fantastic brunch experience. Definitely felt comfortably full, but not in a self-hatred, ""I-regret-this-decision-immediately"" kind of way. Service was professional; our waitress kept the waters filled and came in to check on us a little after each dish was served.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This used to be my all time favorite restaurant for dinner in Pittsburgh. The food is always top notch - lunch, dinner and brunch. + +I think for brunch they offer one of the best bloody Mary's in the city, with just the right amount of kick! My favorite dinner entree was the casericcia - not sure if I spelled it correctly. Why did they ever remove it from the menu is anyone's guess. It was amazing. I went there for my birthday dinner and was ready to order it when the waiter explained that they removed it from the menu despite it being one of their most popular dishes. What a total let down. Nothing compares to it in my book. That's the only reason I'm giving Casbah a 4 star review... + +Please please please bring it back!![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> While I have always had a great experience with my food, I feel the need to update my prior review based on my experience at brunch today. + +When my food came out, there was a very visible hair on my plate. I was with a large group and did not want to make a scene, so I mentioned it to the server who immediately took my plate away. The manager on duty came out to apologize, which I did appreciate. However, I was a little surprised because when they brought my plate out about 5 minutes later, I could tell that it was the same exact plate. + +First off, it was not even warm, so if they made my meal on the spot you would think it would be hot, or at the very least warm. I had also substituted bacon for the sausage that normally comes with the entree, and if the chef had made a new plate on the spot, he would probably have sent it out with the sausage (or with a side of bacon again), which he did not (they had served my bacon on the side when they brought it out initially). Everything was in the exact same place on the plate. I wasn't going to cause a scene, so I pretended to enjoy it, but did not. I was quite repulsed. + +in my last review I had said that Casbah was my favorite restaurant in Pittsburgh. I had mentioned that the Cassericia dish was my favorite but that they had removed it from the menu the last time I tried to order it there for dinner. I received a response from someone at the restaurant that she was not sure why I would think that because it is still offered, and I explained that the waiter told me it was removed from the menu. + +I'm not really sure what happened here, but I can tell you this... I don't think that Casbah is my favorite anymore. In fact not only is it not my favorite, it has taken a plunge to the bottom of my list of places to eat. + +For me, if you expect to eat at a top restaurant, the service should be top of the line, and it has just been too inconsistent for my taste. No thanks Casbah![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Every time I have been to Casbah for lunch, brunch, or dinner, the food has been great and the service has been impeccable. Sure, I've had more exceptionally delicious and unique meals in Pittsburgh, but Casbah has Consistent Awesomeness down pat. Just get a reservation ahead of time. Also, the desserts are mandatory! + +The duck confit gnocchi is smashing-- it's a nice balance of slightly sweet and very savory--and my favorite is probably the Casbah Double-Cut Pork Chop: super-yum comfort food. The short rib ravioli is some pot-roasty Goodness, and the long island duck is another great choice. + +A nice surprise here are the great happy hour specials at the bar. Try the Boyd & Blair cocktail and the sangria.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Let me say that my five stars are based primarily on the calamari appetizer ... it is SOOO good! The squid was very lightly battered and fried so briefly that it was tender and delicious. Seriously, it was one of the best I've eaten, and I've made it a point of sampling calamari. The entrees (short rib ravioli and cavatelli) were very good, too. As for the Carrot Cob for dessert, forget it. It only detracts from the otherwise wonderful meal.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My girlfriend and I went to Casbah for the first time recently and we both enjoyed our experience. + +The atmosphere is dressy, but the restaurant isn't so formal that it feels stuffy or uncomfortable, which is a welcome change compared to most classy restaurants. The environment was relaxed, and it was easy to have a quiet conversation throughout the meal. As for the meal itself, we had a reservation and were promptly seated when we showed up. + +Our waiter was courteous and provided good, fast service without being overbearing or constantly hovering, which was quite nice. For an appetizer, we ordered the cheese tray which was tasty as well as fun and unique. + +Following the cheese tray, I dined on the cioppino while my girlfriend had the casereccia. Both dishes were tasty and our seafood was skillfully cooked, particularly the sea bass in my dish which was delicious. + +I'd recommend this restaurant for anyone looking to celebrate an occasion or have some good, out of the ordinary food.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Upon receipt of the much-coveted Big Burrito birthday voucher, I had to make the tough decision about which of their restaurants to visit. I was torn between Casbah and Eleven, but upon perusing the menus, reading reviews, and giving the matter much thought, I settled on Casbah. I knew I'd made a good decision when I invited some friends to join me, and they said that, based on their past experience, I'd made an excellent choice! + +Our meal started off with a few slices of bread, which came with butter and a Greek yogurt spread. The butter was good, but the yogurt spread was amazing, and both of them dressed up the bread very well. We then ordered an appetizer of the bruschetta, which was not your normal bruschetta, but was delicious. I'm not entirely sure of the ingredients, since what we received doesn't match the menu description posted on the website, but one notable thing about it was that it had some pomegranate seeds that gave it a subtle sweetness and juiciness, complementing the other savory ingredients. For my entree, I ordered the orecchiette, a dish consisting of ear-shaped pasta tossed in a goat cheese and sage cream sauce, with chicken and dried cranberries. Flavorwise, this was one of the most well-balanced dishes I've ever eaten, with the savory ingredients and sweet hints from the cranberries (which were actual cranberries, rather than craisins, as I'd imagined) melding together in perfect culinary harmony. The pasta was also cooked to a perfect al dente firmness, which held up well in the microwave several days later when I ate the leftovers. The cranberry-lime dry soda that I ordered to go with this entree complemented it very nicely, and was a great alternative to wine (while I was tempted, I didn't order any since my dining companions decided not to, due to having driven). + +My two dining companions ordered the Scottish salmon and the gnocchi, respectively. Based on the samples that they provided me, Casbah did a great job on these dishes, as well! The salmon had a subtle saltiness that complemented the flavor nicely, without overpowering it. My friend who ordered it had had it before at Casbah, but had since been to Scotland, and he said that it was very similar in quality and taste to the versions of this dish that he'd tried there. The gnocchi was one of the most unique and varied dishes I've encountered, and, based on the two bites that I tried, brought the ingredients together in a medley of flavors and textures. I think my friend who ordered it described it best by saying that every bite was a bit different, but that they were all delicious! Although all of us tried bites of each other's dishes, we each liked our own choice best, so we chose well. + +After our entrees, we decided to order dessert. Although I was tempted by the dark chocolate raspberry bread pudding, since many reviewers speak highly of it, I decided to follow my instinct and get the chocolate-hazelnut bomba. I'm so glad that I did, since this dessert was amazing! If you like dark chocolatey, torte-like desserts or Nutella, this dessert is a must-try. Since I mentioned I was at Casbah for a birthday dinner, the dessert was served with ""Happy birthday"" written on the plate in chocolate icing, which was a nice touch. My dining partners ordered the creme brulee to split between themselves, which came topped with an apple compote. Based on the bite that I tried, it was a good rendition of a brulee, but couldn't match the star power of the chocolate bomba. + +We visited at 7:30pm last Sun., at the later end of their serving hours, but service from our waiter, Brian, was very good. We were seated in the tent-like area in the front of the restaurant, which stayed surprisingly warm during most of our visit. At one point before dessert, upon returning from the restroom, I noticed that it'd cooled off, but the manager came out to turn on the heating elements, and it warmed back up in less than 10 min. + +In sum, if you're looking for a solid fine dining experience with innovative, delicious food, Casbah is a great choice. The food was impressive in its quality, and the service was what I've come to expect at a higher-end restaurant. I'd particularly recommend getting on the Big Burrito mailing list to receive a $30 birthday voucher and $10 off coupons for the holidays, and taking advantage of one of these occasions to try it. I'm certain that you'll be as pleased with your experience there as me and my dining partners![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Three strikes and you're out! We had brunch there a few months back, and the meal was so salty that we could barely begin to eat it. That meal was comped and I figured it was an off day. We went back about a month later for dinner, and that meal was also very salty and we could not finish it. We were willing to try again, so we went for dinner tonight. I ordered the filet, and it was like eating a salt shaker. I was shocked that, for a third time, I had a piss poor meal at Casbah. I sent that back, and ordered the sea bass. When I got to the end of the piece of fish, it was raw. Needless to say, I will NEVER return to this restaurant. Looking back, what should I have expected from the sister restaurant of Mad Mex?[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Casbah continues to be my favorite Pittsburgh restaurant. High quality service and creative dishes. Sign up for mailers for Big Burrito special offers and birthday discount. + +Must try: +Calamari +Cheese plate +Short Rib Ravioli +Pork Chop +Watermelon Gin Fizz[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> At this time, I have officially had every meal of the day at Casbah (it's great!). Here are my thoughts from my three visits: + +First time was for dinner (June 2014) with my Big Burrito Birthday Coupon. We sat outside, where it was pleasant even though it was the middle of the summer. They were generous with the table bread and I really liked their goat cheese yogurt spread. I got the Orrechiette chicken pasta and BF got the filet mignon. The pasta was ok (see lunch review for update) and came in a large portion. The filet mignon was perfection. I made BF share with me :) The roasted potatoes with the green chutney were also heavenly. Definitely a lovely way to spend my birthday. + +Second time was for a weekday lunch with a college friend visiting (Nov 2014). We had the 2 $10 off entree coupons and ordered off the Gusto menu (a fancy version of Panera's You Pick Two). I got the Orrechiette again and a Turkey Avacado Sandwhich. The pasta was delicious this time, so I'm thinking it was just one-uped by the Filet Mignon at dinner. Friend got the vege risotto which she liked. I like that Casbah is willing to customize plates at no extra charge or nuisance - they removed all bacon items from my entire meal and replaced them with other dressings, etc. I really appreciated that. Even without the coupon the Gusto lunch menu is a great deal! + +Third time I went for brunch with another girlfriend (Dec 2014) +. I LOVE BRUNCH and Casbah took the cake. The table scones, pastries etc were delicious as was the accompanying cinnamon butter. Our waiter was very nice and helpful and was again quick to help customize my vegetarian friend's needs. I got the Mimosa which was delicious. Smoked salmon appetizer was as good as the other yelpers say and the portion was humongous. Finally, I got the scallop omelette and they had no issue giving me my favorite home fries as the side instead of the grits. Friend got the salad appetizer and the spinach eggs benedict. She loved the eggs not such a big fan of the arugula salad (which I have had and liked). We each had a $10 off brunch which made this a steal :) We were able to sit outside even in the winter which was nice. + +All in all, I love Casbah. I'm a student so it's a little expensive for me. But I go every chance I get. Look out for Big Burrito coupons![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Mixed results. Made a reservation and we were seated in a dark corner at a tiny table. Is the money from having that table worth the negative experience guests will receive? Methinks not. I had to ask to be moved to the patio, which was much better. + +The drinks we ordered from the bar were watery (the Manhattan and some drink with applejack in it). Later, they made a mistake and sent us the wrong cocktail, which turned out to be much better than the ones we wanted. + +Appetizers (meatballs with Brussels sprouts and beet salad) were very good, but the main courses left a lot to be desired in terms of seasoning. The texture of the short rib in the ravioli wasn't quite right, sort of dry, maybe overcooked. We had a bread pudding for dessert, which was probably the best part of the meal. I expect a better overall experience for the money.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Stopped here for drinks before we went on to dinner elsewhere. In hindsight, we wish we had stayed here. :-) + +We had a couple of great beers and just enjoyed the excellent music soundtrack before we moved on to our next designation. I hope to come back here sometime in the future and actually have...a meal. I like this funkier part of town.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I don't know of any place that comes to close to the quality of Mediterranean food offered at Casbah. They have a daily menu that combines unique ingredients into a great blend. My favorites on their menu are their spinach casareccia (which I customize with tuna steak instead of chicken) and their gnocchi (in that order). They are open to customizing their menu so if you want half and half of each dish, they are happy to do that for you. That is a huge plus for me. They are safely my favorite Big Burrito restaurant[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I am a huge fan of almost all things Big Burrito and Casbah is no exception. I have been to Casbah so many times over the years that the visits all meld together, but on this particularly occasion I had the arugula salad to begin with which was delicious and my friend had the butternut squash soup which she really enjoyed. We both ordered the the Scottish Salmon which was so delicious and tender that it literally melted in my mouth. The house-made pastas are always a great option if as is the duck or the lamb which I've had both on a few occasions. Their wine list is always spectacular - on this visit I had a glass of the Riesling from Urban, Germany and my friend had a glass of Pinot Grigio from Lenotti, Italy. We had no room for dessert on this visit, but any of their desserts that have the Meyer lemons is always a hit and I am a die-hard chocolate fan and I will forgo chocolate for one of their delicious meyer lemon dessert creations. I haven't been to Casbah for brunch in quite some time, but after having gone to Eleven recently for brunch, I'm keen to try Casbah for brunch again soon.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I enjoyed my previous experiences at Casbah, but this past weekend was a disappointment. Despite having a reservation well in advance, my husband and I were seated at a horrible table right next to the hallway that leads to the kitchen and bathrooms. There was a constant stream of distractions. Service was also really slow and my sea bass was bland. I expected better from Casbah...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Pros: Vegan food in Pittsburgh? YES! great music, friendly accommodating service, huge variety of drinks, fabulous decor + +Cons: Not a convenient location for the car-less me, but well that's just me + +Hi, I am a non-drinker and rarely have I found an establishment with an extensive list of non-alcoholic drinks. Granted, Quiet Storm like many Pittsburgh places doesn't have an alcohol license and has to make do. Ginger lemonade? Yes. All these other things from the soda fountain that are adult like enough for me? Yeah! + +I do love my meat, but found the vegan food here pretty good (albeit dry but I attribute that to my love of meaty things). They used to have a prixe fixe meal on the weekends, but I think they got rid of that due to a low turnout. Too bad most of Pittsburgh doesn't really learn to love culture. + +Usually good music acts here. Although the few times I was here, there was barely anybody else there besides the group I dragged along and the band's friends. Usually 2-3 acts play. Live. And it's nice that there aren't many of us because we can sit up close. And be sure to kick the friend who thinks it's ok to talk over the music. + +The bathroom also has a decor to match the style of the coffeehouse. + +I have never been here during the daytime so I can't comment on that. Always great service when we came here for dinner and the music (since we were basically the only ones there). Sometimes a minimal cover for the music. There are books and comfy couches for the daytime coffee drinkers.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Though I didn't get a chance to visit this place when I visited last month, I really do love Quiet Storm and I will be sure I hit it up next time I'm in town visiting my friends there. The decor is adorable. The prices are reasonable. It was an intimate place to see a show and it's too bad they are no longer doing them here. I really feel like this place was one of the first things that made me heart Pittsburgh. It's truly a unique space.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I used to live about four blocks from the Quiet Storm, and for a period breakfast here was an every day affair. Those two facts have nothing to do with each other--the period in question was close to the end of the first semester of my (super-)senior year, when my friends and I would stay in our studios all night working, haul ass out to Quiet Storm for ambrosia-caliber restorative tofu scramble and coffee, and go back to school bright-eyed and bushy-tailed for another day of class. And then usually I'd take a three-hour nap after the first class. But I'm sorry, what is it I'm reviewing here? + +The Quiet Storm has absolutely the best tofu scramble I've ever had. I'm an accomplished vegan eater (I get stuff in my mouth first try nine times out of ten), I've had the best scrambles New York and San Francisco have to offer. Believe you me, Quiet Storm tops them all. I wish I knew their secret recipe, but the part I do know--baking the tofu rather than just sauteeing it--makes a tremendous difference. Come in on a lazy Sunday morning, get the Nothin' Fancy, and you will see for yourself just how good tofu can be. On top of that, they are as vegan-friendly as can be, with earth balance for the toast; soy, rice, and almond milks; and a selection of specifically vegan mixed drinks and milkshakes. Plus, sandwiches! Get the spicy spinach and peanut butter wrap, ask for added tofu (planks not crumble), and be astonished yet again. + +AND AND, as a delicious cherry on top, they have theme brunches, fantastic theme brunches that show off the creativity and chops of the cooks here in a way that the regular menu can only hint at. Check out their website and see when the next theme brunch is, and make a point of going. Get there early.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I like the Quiet Storm because it offers food as well as drinks. The spinach artichoke dip and white pita pizza is good. I never had a Chai Milkshake until I went to the quiet storm. If you can deal with East End ""urbanites"" then I would suggest trying it out, if nothing for a good laugh and decent food.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I moved to Pittsburgh for the tempeh Reuben at Quiet Storm. Actually, I'm lying. Or maybe not. Am I trying to save face because I don't want to admit that I moved across the country for a sandwich? You'll never know because I'm not telling. + +Anyway, the food here is pretty good. Sometimes it's better than others, though I think it depends on the cooks. I'm one of those vegetarians who doesn't much care about reducing kilocalories (the point of eating is to fuel our bodies, right?), so I like the cooks who pile on the mayo and cheese. I'm sure the cooks who skimp on fattening ingredients have their fan base, too. The menu is creative, and it feels like the people who make the food are trying to test their cooking chops, which I appreciate. + +The atmosphere is nice here: big, open space, yet cozy. And you won't find a radder floor in Pittsburgh. The employees are super nice.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It's all about the Black & Gold. (Only on the brunch menu now, though!) + +And the Tofu Tenders. + +And the vegan baked goods from My Goodies. + +My only complaint is regarding the vegan milkshakes. Sorbet does not a milkshake make.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Wondering where the Pittsburgh hipster crowd hangs out? Look no further than the fixie parked outside the Quiet Storm. + +And then go inside and have some delicious food and drink.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I looove Quiet Storm! It's a pain for the car less (me) to get to, and the service is fairly lacking, it's cash only with no convenient ATM's around, the closest business is a McDonald's half a mile away. And I still go there every chance I get. + +Hipsters abound (pro or con, depending on who you are) and the place is REALLY child friendly (again, could be a pro or con). But generally, the crowd is mellow, reading, chatting, just enjoying. + +The menu is designed in a way that they have something for everyone (except those adverse to eating healthy :). Between the veg and vegan options, they manage to have a menu that is fairly celiac friendly too, not an easy thing to do! + +A lot of the reviews here are about breakfast, which is amazing. But my favorite are their dinner salads. They're protein heavy, with a huge variety of ingredients, not your typical salads. And their specials, like tofu curry, are amazing, and always enough food for two. + +Oh, and the drink menu! I'm pretty much a water, coffee, beer kind of person, so I haven't tried too much on it. But everything looks amazing. Quiet Storm is one of those places that doesn't do a wide variety of things, but what they do, they do damn well![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place is cool! But it is also 'cool'. Service is so-so, but the staff doesn't have an attitude, they just aren't into serving. And I'm not a vegan, but the food is so good that a carnivore like me doesn't even care. The menu is also huge. + +For those of you looking for an ATM- there's one a half block away if you just exit, go left and cross the street to the corer convenience store. + +I could always find a table and spread out with my books. Comfy, young, hip, worth it. I wish they had alcohol. + +Try it![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It's good when they are on, but they are so inconsistent you never know what you are going to get. The coffee machine looks like it hasn't been cleaned in the last century which is off putting. Generally, I wouldn't recommend it unless you are in the neighborhood and desperately hungry--you MIGHT catch a lucky break and be there on a good day.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Food is tasty, though portions are for the waifish hipster types. Location is inconvenient and I would not recommend people walking by themselves at night on that stretch of Penn. Service is very uneven i.e. bad, even when the place is practically dead. I can't really speak on the coffee, though they do have good tissanes(however getting them to refill your hot water is another thing). + +************** +Okay I won't change my rating, but I take back what I said about the food. They have changed the menu and it is really bad. + +We had Buffalo Tofu sticks which were ridiculously dry. + +I had the Thai Peanut Tofu Wrap which tasted just like peanut butter. + +I don't understand the point of Mockamole? It's made with peas instead of avocado. + +How to describe the food... it's as if they took pictures of how food should look and made the food without thinking about how food should taste. Gee peas are green, just like avocados?? + +I would go there for coffee/tea or whatever to hang out, but not for the food. + +Okay there was one decent thing on the menu which was the artichoke dip. I was completely disappointed.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Solid Milkshakes and Falafel - block from my house[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've been to the Quiet Storm a couple of times for brunch-type meals, and have always been pleased. Their extensive veggie/vegan geared menu is for the most part really healthy and fairly light...but it's not without its crave-worthy items like smashed potatoes with cheese and my favorite, the peanut butter chocolate milkshake...heavenly. Paired with a hummus and veggie sandwich and green pea 'moc-a-mole', you don't feel so naughty having dessert with brunch. + +The vibe is mellow, and so is the wait staff. Service is leisurely, but not slow. I look forward to at least one chill breakfast here on my trips to the 'Burgh to visit friends and such.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> For solid veggie/vegan food in Pittsburgh's east end, the QS is a reliable meat-free choice. There are enough good options on the menu that a seasoned QS diner could guide a newbie past the landmines of total-miss dishes, in search of the greener pastures of the spicy peanut tofu wrap and other local faves. The scrambled tofu is a shining star. The kitchen often does remarkable things with potatoes. The salads go above and beyond to woo your heart, with way more toppings & stuff than any other salad I've eaten in Pittsburgh -- this includes salads served with French Fries! Nothing here is fried - even the ""fried"" foods are baked. Your arteries are grateful. The kitchen is unfortunately very inconsistent, and an attentive & caring cook is a very different experience here than the apathetic, distracted or exhausted cook. + +This used to be The Place to Brunch, and I'm sure it's still busy on the weekend mornings, but I had to quit when all these SUV families started monopolizing my fave tables -- apparently the QS made it into some kind of ""VISIT PENNSYLVANIA"" travel guide as a great brunch spot. I hate to be that ""I liked their old stuff better"" kind of a person, but, well... + +Don't be caught unawares- in my cashless world, dinner at the QS means making a special ATM run. + +The QS is super kid-friendly. Books, magazines, and children's toys accompany the wireless internet (which sometimes works, and sometimes doesnt, and no, the staff can't help you). The menu is kid-friendly, the staff is used to dealing with kids, and if you really hate children, you might not want to go there since their peals of laughter and joy might melt your wicked black heart. I wouldn't hesitate to take the 2 year olds or 12 year olds I know. + +The drip coffee is good and bottomless- soy creamer is available. The espresso drinks are really really hit or miss. You may have the tastiest drink you could imagine, or you might be left choking down a $5 drink made by someone who has never drank a cup of coffee. No liquor license but you can BYOB for a nominal charge. + +The service is sometimes swift, but more often lacking. I would never take a date here again --- getting the totally wrong order & waiting half an hour for it to be even acknowledged by the staff is an embarrassment when you tell your date the restaurant is one of your faves. Fortunately, if you are dating me, you probably aren't there for the dinner. + +If you have plenty of time to kill & self-esteem strong enough to weather the whithering glances of the hipper set of pgh's east end, this could be your new fave spot too. I do wish the hours were a little different - I operate on the schedule of a late-nite diner, though.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm not sure how it took my wife & I so long to find this place! Before visiting the Quiet Storm I didn't realize that their entire menu was vegetarian, but that shouldn't be much of a problem even for fans of meat. I ordered the ""Maelstrom"" which is a what I would call a Mediterranean Quesadilla. The flavor was subtle, but delicious. There were plenty of menu options and it looks like this restaurant is really doing it's part to support the local community. The only complaint I would have was that the temperature also got a bit cold as we were sitting by the door... and it was winter. Finally, remember to bring enough cash to cover the bill as that's the only way to pay. I was not disappointed by the Quiet Storm and will definitely be getting back to this place next time I'm in Pittsburgh.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is probably one of the most solid restaurants we have on Pittsburgh's east end. It is also a haven for the vegan/vegetarian hipster. I've been a handful of times now and only once did I get food I wasn't happy with. Prices are reasonable, maybe like $1-2 more for food than you would expect to pay. Keeping this place open is well worth that cost. + +If you aren't feeling so hungry, this doubles as a coffee shop (lacks some coffee shop seating) and the hot drinks are solid. Check out the milkshakes![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> CASH ONLY!!! What a pleasant surprise! I went here for the first time last night and wasn't sure what to expect when i walked in. The place seems to have some spacial issues. There was a bar but they don't serve alcohol, more of a coffee/diner bar. The tables and chairs seem odd and it took me a while to find a chair that was comfortable, but maybe this is by design. I am not a coffee expert but i really enjoyed my several cups of decaf. Anyhoo, to the food. This place is vegetarian only. I started with a Hummus plate, unlike most creamy hummuses this hummus was gritty as i could actually taste the chick peas with each bite. The hummus was surrounded by fresh crisp cucumbers, carrots, celery, calamata olives (big fan) and pita. Perfect starter. For my main entree i ordered the curry special. Do not expect an Indian food experience but this will not disappoint. Everything was in the bowl, chick peas, basmanti rice, carrots, and other miscellaneous items. Once i started dipping my pita into it I could not stop. It was savory, spicy and just the perfect compliment to the cold snowy night. This is one storm i will enjoy braving from time to time.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Who would have thought that a vegan-friendly hipster restaurant would be one of the best places in Pittsburgh to feed a hangover? + +Seriously, go hungover, and you will be in love. Get a super-stuffed burrito. They put mashed potatoes in burritos along with hearty beans, scrambled eggs and cheese and yummy salsa. Your stomach will thank you. + +While you're waiting, have some coffee. At under $10 for a VERY filling burrito and a bottomless cup of coffee, I thought it was a great deal. + +In addition to their regular menu, they also have daily specials and themed brunches. I can't wait to go back and try other things on the menu. It's great to have a full-service restaurant where you can get oodles of vegetarian items.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Quiet Storm is, perhaps, the most expensive vegetarian diner I have ever been to, even by big city standards! Cash-only makes this even more difficult. Tofu wings appetizer was simply not very good; and I usually love these things! I tried the gyro wrap which was also a big disappointment. As far as I know, gyros are supposed to be pretty meaty, but this was mostly lettuce with sporadic chunks of seitan and cucumber,along with dreaded diced unripe tomato. The wrap was dry and upon looking at the menu again, I see that the sauce that it probably requires costs an extra $.50. The tortilla itself was very white and seemingly unnatural compared to those found at most veggie establishments. My beverage was good and affordable--ginger lemonade. It was sweet for my tastes, but I am sure most people would have thought it perfect. I'll keep Quiet Storm in mind as a coffee shop, only. + +F.Y.I after splitting the cost of the appetizer with a friend, my lunch cost me $17--ouch! I did have half of the wrap leftover and ate it later as a salad with my own dressing. It was quite good that way and I might recommend that QS rethink the Gyro presentation if they want to continue using so much lettuce.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The Gyro wrap is amazing.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Quiet Storm was the other bookend to my trip to Pittsburgh, providing a perfect balance with Zenith earlier in the week. It's a little out of the way, but once we got there, it's exactly the kind of place I want to live close to. It's spacious and relaxed; we sat there for two hours after eating our lunch and were not at all pressured to move on. It had a very good neighborhood vibe, and everyone working there knew the place and the area really well. +The drink options were pretty great- the coffee was just fine, but the ginger lemonade I ordered a couple hours after lunch was phenomenal. I wish I could have that more often. The food was great; there are lots of options and the portion sizes were exactly what I wanted. I had the Dagwood sandwich, which was a perfect mix of sweet, sour, and spicy with hummus, apples, hot peppers, cucumbers, and pickles... it came with an option of the side, and I had to try the mockamole. A big fan of guacamole myself, I was totally in doubt of a green pea-based mock version. I also really like peas, though, so I was open. And somehow they managed to make it work, and it really did taste very much like guac, with a slightly less heavy and maybe a bit grainier texture. But definitely worth a try. My friend had a wrap with curry and tofu and I honestly don't remember what else, but it was huge and really tasty. She chose the potato salad as her side, and it was the perfect imitation of German potato salad, so I was pretty happy. +All in all, if you're in Pittsburgh and feel a little lost... go to Zenith and Quiet Storm, and you will feel found.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Fun, unique atmosphere (hippie / indy / hipster / whatever these kids are calling it these days). Interesting, tasty food. Above all, awesome retro decor. A Pittsburgh treasure.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> A cool (if mildly painfully hipster-ish) decor; perfect settingfora Sunday brunch. The service was great, the food was both satisfying and healthy, and the milkshake I had to top off my omelet was deeeeelicious. Are all of their milkshakes vegan? Because ifthey are, I was completely fooled. A little more than I was hoping to pay for a breakfast dish but I suppose I can't complain, as it was morethan enough to hold me through until dinner. (I agree with the comment I saw that stated that this would be a perfect place for a hungover posse!)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I eat at this place at least once a week. No longer cash only, which is nice since I never have any. As a vegan I like that I have a ton of options here, but that my meat-eating boyfriend is happy too. Food is a little pricey and if you get more than an entree and coffee it's easy to quickly rack up quite a bill for such a modest seeming place. My only real complaint is the inconsistency of the service. It's totally hit or miss. I've never felt targeted with ""attitude,"" but I have experienced long waits for the menu, coffee, water, the check - but weirdly, never the food. Most of the time I leave happy, sometimes irritated, but I'm always full and ready for a nap.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I was really impressed by this place. I will first start with the service: The waiter was very friendly and it took me awhile to go over the menu since I've never been there. He was patient and stated ""take your time, no hurry"". He offered me suggestions. We even discussed shoes for a brief minute, very personable. The food: The menu was quite extensive...hoagies, soups, pasta, salads, etc. They also have stuff for kids like grilled cheese. I ended up ordering the lentil loaf with steamed vegetables and smashed potatoes. The food came out QUICK, like 5 minutes and everything was fresh and great. Did I mention this also came with soup? I paid $13 total for my meal and a cold chai. Could not ask for more. My only and I mean only complaint is that they only serve lunch at lunch time, the only serve dinner at dinner time, etc..so be mindful of the time of day you go....[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Maybe I am just the most jaded vegan in town; Quiet Storm's food menu bores me to tears, that which I will use to salt my own mediocre cooking at home! Their coffee isn't all that great either, as given the choice, local La Prima is in my favor. Tears. This is the only vegetarian restaurant on the East side of town, and oh so close to me, but I cannot stand to go there. Desperate times now call for toast and tea served by the sad server that resides within my depressed little dining room.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love you, Quiet Storm!! Please open another location in the Los Angeles area, stat. I think the best part about Quiet Storm was rolling in at 10:30 on a Sunday and being seated without a wait. Are you kidding me? That's AMAZING! I was prepared to have to wait for a little bit for Sunday brunch. + +Quiet Storm has quite possibly the most delicious scrambled tofu that I have ever had. I have no idea what they do to get the tofu to that texture, but its delightful and don't ever change. I love animal products, but I did not miss the meat in any of the dishes that I sampled. + +I order the Black & Gold breakfast burrito, which was delicious but not half as excited at the Country Gravy burrito my friend had. The onion gravy is insanely flavorful and made me question why I put animal in my gravy to begin with. I know, its a crazy thought but its true. + +I look forward to many additional trips during my extended stay in Pittsburgh.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This space is so beautiful. + +i'm always a sucker for big windows all across the front, but here especially the huge windows and wide building front really opens up the space and provides excellent lighting for the front half of the cafe. + +The layout is unique, with the island, counter, and bar stools in the center and plenty of tables all around. It really provides a lot of opportunities for unique corners to sit in alone and lots of space for groups. + +The coffee is decent. It's made from Dean's Beans, decent fair-trade coffee and brewed to a consistent perfection. i can't speak to lattes and espressos because i've never tried them, even though QS supposedly just got in a new espresso machine. + +The food is so-so, decent vegetarian fare, with the exception of most of the tofu dishes, which are spectacular. + +And the milkshakes are always a good time, even if they're a bit on the expensive side. + +Cash-only if total is under $10. + +Contrary to what some others have said, this isn't a hipster hangout. The customers seem to be a nice mix between students, locals, and artists. This isn't an art museum--it's a vegetarian cafe that makes food and drink. + +And it does a pretty fucking good job of it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> pretty good veggie food. I've had breakfast, lunch, and dinner here. French toast, tofu scramble, museli, salads, sandwiches, lasagna. They have a pretty decent variety.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I must be a glutton for punishment, because I keep finding myself hungrily returning to the Quiet Storm. The menu has slightly changed, and they are no longer cash only... This time it was the ""8th Ward"" that inflicted extreme disappointment. Not sure what 8th Ward is supposed to mean, but I will forever associate it with a dry boring place. And I thought we were getting a party platter! This appetizer sampler included THE WORST hummus evaar; I am near positive that they forgot to add garlic, lemon, salt and tahini to this chickpea paste that which was described as ""garlicky"" on the menu. Sooo wrong. ""The Butter,"" another WTF of a name, was also very dry and bland. The salsa was good! And there were plenty of dipping accessories, too many really, given the smallness of the unappetizing dip portions. + +At this point, I've tried most of the vegan options QS has to offer and the only luck I've had has been with the B.Y.O.B. Go figure. + +I wouldn't care so much about how much of a tease this place is if I didn't REALLY desire a comfortable neighborhood place to eat comfortable food with a comfortable view of a cute waitress who writes fiction. And it frustrates me that few others seem to recognize the culinary (I shutter at even calling it that) mediocrity of ""the best"" vegetarian restaurant Pittsburgh has to offer.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Very few people name the places depending on how the place is going to look like from the City's perspective.Confused?? +I bet half of Pittsburgh students didn't notice this amazing vegan place,it is like a quiet storm ;just there but not really.Now i am confused!! :) + + Straight to the point -this place is huge and neat and they have a huge cafe bar with great food list.i ordered thai salad with vegan chicken and tempeh and my friends ordered wraps.It was simply delicious and i was extremely excited that i discovered this place after a long Vegan research. + + The place was definitely quiet and shockingly even the area around the place was dead.Maybe they have some historical reasons to name it Quiet storm like there was a light storm and everyone left the place...ahmm..I shall stop my list of lame reasons,such that you could stop reading and would be able to chase the quiet storm :) + +-Smriti[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Well, I think Heidi S. pretty much covered all of the bases here. The lemon-ginger tea that I ordered was weak, perhaps not steeped hot enough? The hummus, wow, definitely the worst; tasted like paste. Yuck with a capital whY. I considered giving two stars because the service and atmosphere were pleasant, but since I do not plan to return, I guess methinks not.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Very good![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> i was super excited to try quiet storm when i moved to pittsburgh because all of the reviews i read were fantastic. however, i have visited multiple times now continuously hoping for improvement and each time i've been disappointed. let's start with the good things. QS has a great atmosphere, it definitely helped the transition from austin. very chill ""hippie"" vibe. however, the servers although friendly can sometimes be a touch ""hippie-elitest"". the food was alright. their homefries were quite tasty but little else has tantalized my taste buds and i have tried many things. i do love their thai dressing, very yummy on the salads. will i continue to go back? probably, wishful thinking is a good thing.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> For vegetarian food in Pgh this place is hard to beat. The quality of the food is very good, but the kitchen tends to be slow so bring a friend/book/deck of cards, and the serving sizes are somewhat inconsistent. The coffee drinks are OK, but I don't come here for those. I love the atmosphere of this place, very laid back, cozy, inviting. My favorite eats are the soups and the pile-o-hashbrowns (think haystack without the artery clogging gravy).[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> OMG chocolate espresso milkshake MMMMMMMMMmmmmmmmmmmmm[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> YUMMM. Read the Yelp reviews before coming, so I knew to get the ginger lemonade and hangover hash. Both were amazing, filling, AND i got to use the wifi there for a couple hours on a Sunday morning with no nasty looks from the staff (it was crowded but no line). Totally worth any effort it takes to get there (seemed to be in the middle of nowhere, I had a couple mile walk to get there.)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Every time I visit QS I hope for a better experience, but continue to receive poor service and ok food. +I always get the feeling that the wait staff does not want you to be there. It is never friendly. It seems cold. +Food is ok, but often taste old and like it has been reheated multiple times....ugh. + +I really wish they would put a lil' more effort into customer service![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We go here all the time and have ordered almost everything on the menu and never been disappointed. It's veggie diner food at it's best (at least in my opinion). My bf is a meat & potatoes man but he absolutely loves the breakfast Homefries with tofu instead of eggs. The waitstaff have always been exceptionally nice and very attentive. This establishment is best described as a greasy spoon for vegans and vegetarians so if you go in expecting gourmet, you may find yourself disappointed. + +On cold wintery days try a Mexican Hot Chocolate - it will surely warm your heart![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Stopped in as I was driving through Pittsburgh. Had an awesome bagel sandwich and some tasty vegan pastries. Very cute atmosphere. Totally sold me on Pittsburgh.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've only been here for Sunday brunch, but I look forward to dining here again in the hopefully near future. The frittata was thicker than any I've seen elsewhere (it looked like a square of lasagna) but very tasty. I liked the inclusion of sliced potatoes. + +The Low Country grits were creamy and also enjoyable, but not too flavorful. I didn't really taste the fakin' bacon or the garlic supposedly in the dish. I'm not surprised though, since a lot of vegetarian places seem to go light on the seasoning. Definitely ask for cheddar with your grits if you eat dairy. The three kinds of hot sauce on the table also help perk things up. + +No complaints about the service, but they use some sort of chemical cleaner (for the floors or to wipe down the tables, maybe?) that's unpleasant-smelling. I noticed it less the longer we stayed, maybe because I got food in front of me, but one would hope that a vegetarian establishment might opt for more environmentally friendly and less noxious cleaners. Other diners were also commenting on the smell when we were there. I'm guessing this isn't a regular smell to the place, though, since no other reviewers have commented on it. + +The cash-only policy is also a bit of a nuisance, since I'd consider the prices ($11 for brunch entrees) here to be mid-range and not ultra-cheap. Still, I will come again with my greenbacks.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> right by my house, spicy peanut and cheesy snake are amazing.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've been going here very regularly since 2002 and they've been getting better and better. It evolved from a coffee house & music space to a straight up restaurant. They catered my wedding and my yinzer family liked it despite there being no meat.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I make a point to visit this restaurant every time I'm in town. I'm a mostly-vegan vegetarian who has been living in the San Francisco Bay Area for over 17 years, so my expectations for veggie food are rather high. Quiet Storm cuisine does not disappoint. Creative and fun menu items, and plentiful vegan options.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Aw it's places like this that make me love Pittsburgh. Its hodge podge decor and hipster crowd are what drew me here in the first place, but turns out the food and coffee is pretty decent even delicious. Since it's far from where I live I don't get to come here half as often as I'd like but I'm always pleased when I do. + +Such cute boys.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm going to revise my review of Quiet Storm. + +You may get lucky and find yourself faced with an awesome rendering of a fabulously-designed vegetarian sandwich. In my experience, however (considering the 30+ Cubanos I've eaten there), you're more likely to get a sad, mediocre rendition. + +Consistency is not their strong point. + +Add to that the likelihood that you may be dosed with some surly owner attitude, and I've decided to steer clear. + +It's a shame that I no longer feel it's worth it to chase the beautiful dream of my first meals at Quiet Storm. It's also a shame that many of their staff are wonderful, friendly, and helpful, and yet their efforts are overshadowed. + +Sorry, Quiet Storm. As a Pittsburgh vegetarian, I want to love you. But you broke my heart.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place is so hit-or-miss for me. Sometimes the food is amazing; sometimes it is terrible. Example: I ordered the spicy peanut wrap for the first time and fell in love with it. I came back a couple weeks later, and it was bland and unappetizing. Maybe there is someone who works in the kitchen who doesn't know where the spice rack is-- I don't know. + +The 'waitstaff' is hit-or-miss, too. Sometimes, they're great. Other times, I've waited for ages just for a menu. One guy actually snapped at me for asking for a breakfast item at lunch. + +That said, there are some good dishes, like the Black & Gold. I like that in some dishes you can replace rice with salad. A lot of people I've eaten with here have raved about the quesadillas. There's a nice laid back atmosphere and fun retro diner decor. There's also an extensive (but expensive) drinks menu with milkshakes, teas and coffee drinks, and a nice selection of locally-made vegan sweets and pastries. And I love the magazine and book rack, even though the magazines are usually two years old. Still fun to read.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Nice little coffee house with good food. My only complaint is that the food was NOT HOT ENOUGH, which is a bigggg turn off for me. However, it was still so good that I'm giving this place 4 stars. The apple panini was a delicious hot mess clearly invented by somebody who got the munchies and only had raisin bread, apples, cheese, and seitan around....the result is amazing. This place just needs to make sure the food is warm! + +Dip is a huge ripoff, btw....$5 for a tiny portion :/ they should lower the price on that item. + +The salsa that came with my sandwich is some of the best salsa I've ever had, though. Dunno if they make it themselves.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The Quiet Storm is a classic, being one of the largest selections of vegetarian and vegan entrees in the city. Recently came with about 13 people for a Saturday lunch. I won't speak for everyone's dish, but I got the curry which was very tasty, if not a bit skimpy on the rice and a little thin for my liking. My friend got the QHF, which is a tofu scramble mixed with home fries and seisage which was absolutely delicious. She also got a side of spicy aioli which went extremely well with the breakfast dish. The service was prompt and they just left pitchers of water on the table for us which was great. Always a great choice for meat-eaters and veggie's alike. If you go with a large group though, beware because it is difficult to work in the added gratuity and tax with the cash-only. The waiter wouldn't let us split it up and take individually, so it was difficult on that end.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Quiet Storm truly is a wonderful neighborhood gem. Surrounded by a desolate urban landscape, I never would've expected this colorful, creative coffee shop to have such impressive food. + +My dinner here consisted of an apple panini and a ""shampoo"", a strange (but delicious!) cherry and almond cream soda. It very well might have taken me 20 minutes or more simply to decide on my beverage of choice - their list was not only long, but offered more innovative choices than I could have ever dreamt up. Among them, an impressive array of Italian sodas (lavender & lemon, mango & lime, white choc & mint, etc.), an enticing selection of lemonades (ginger lemonade, lavender lemonade), and some excellent-sounding tea combinations. To top it off, almost all flavors were available in the form of vegan milkshakes. How they concocted all of these culinary ideas is absolutely beyond me. (I apologize to the coffee drinkers. As a tea drinker myself, I hardly paid attention to that half of the menu.) + +The apple panini I ordered came out quickly and was complemented with a side of tortilla chips and salsa. My panini included granny smith apples, apple butter, sharp cheddar, cream cheese, and seisage (vegetarian sausage) atop sun-dried tomato bread (though it seemed more like raisin to me). Never in a million years would I have come up with this strange combination of flavors, but it definitely worked. As described in the menu, indeed it was ""highly addictive"". + +Table service was great, nothing took too long and it seemed pleasant and casual. No overbearing waiters, no frills, etc. + +Given the fact that I live about a mile away, I think they should be expecting yet another regular in the very near future.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Remember the days of bands in the back at night, and interesting kids hanging out at the bar all day? Well, the bands were the first to go, followed quickly by the comfy sofas. The kids didn't take long to leave, and now, years later, faced with a frankly less-than-appetizing Saturday menu, I find that the ability to substitute something else for the increasing amounts of potato filler is gone, too. + +Quiet Storm used to be a straight five star. My last experience was honestly two-star, but nostalgia and history don't allow me to give it less than a three. + +I'm sure all the changes over the years have been in the name of efficiency, but they've come at expense to the clientele. Here's hoping Quiet Storm rediscovers the mojo (and the menu) that once made them great.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> what a bonkers menu! delicious and lots of fun. the service was fantastic. we ate here on a visit from NYC and had two very unusual and delicious vegan burritos... then stayed for tea. loved it![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The menu looks awesome and the dish concepts are good except everything that comes out is disappointingly bland. Thank god there were bottles of hot sauce and salt on the table. The best part of the meal was the peanut butter chocolate milk shake. The burger and ""spicy"" Cajun soup were very mediocre.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm a vegetarian and have lived behind the restaurant for over 3 years. Every time I have ever gone, the service is awful. It's as if they're doing you a favor by waiting on you. I think their breakfasts are pretty good and their lentil loaf is good but usually your sides consist of yellow nacho chips with brown jalopeno slaw. Also, the cooks look like they are lacking hygeine. the one great thing about this place is their coffee, and that's it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> For me, this was an especially warm experience. I arrived in Pittsburgh and came straight from the airport. The coffee was perfect, the company was even better. I ordered the home-fries with tofu and cheese. They were extraordinary. The tunes being dj'd by the barista didn't hurt either. I definitely dig this place![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love this place, it's the Beehive, Starbucks, Eat N Park, and every neighborhood coffee shop in America tossed together in one place. + +Unfortunately on this day we arrived after the kitchen closed, but the friendly barista behind the counter offered to make us a drink. I had a soy green tea latte, he chose a dirty chai latte, made with coffee and tea, interesting! + +My green tea latte was served piping hot in a pint glass, not the Shamrock shake colored green tea latte you get at Starbucks, this was the color of your father's old white shirt that hasn't been washed in a few weeks. Not as syrupy sweet as Starbucks either, but a nice dose of natural brown sugar gave it a nice taste. And it was a nickel cheaper than a Starbucks ""tall"". Good deal! + +My friend Jamie's dirty chai latte was good, again not overly sweet, which is ok for him, he doesn't have a sweet tooth. + +Next Sunday we'll go back earlier when the kitchen is open, the take out menu looks great, healthy, low fat, and vegan.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Quiet storm is a really cool vegetarian restaurant. The time I was there the service was fine and the food was unique. Their menu is a limited on the weekdays, your best bet is one of their many quesadillas. + +I'm not as concerned about the preservation of vibe and atmosphere, as long as the food still tastes good. I was in love with the pierogidilla and happy to leave the table feeling full without having any meat. + +I wrote a review of Quiet Storm on my web site, Binge! http://eatinginpittsburgh.com/2010/07/07/ive-got-an-itch-for-kitsch-quiet-storm-in-bloomfield/[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> ahaha! i ordered a bowl of mac n cheese thinking, ""it'll be a nice side dish."" little did i know that it would be a BOWL of mac n cheese. and it was so good i had to eat it all. ugh. food baby. +graham street tofu is the bomb. +and the 5th star is for the pinball machine in the back. +awesome.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> A nice, cheap place to get your vegetarian/vegan eat on. Brunch is always nice and the specialty coffee drinks are fun to look through, if only for the names, meanwhile, you'll be eating off melamine and drinking from odd glasses; but, the food is great for the price and someone has to employ all the hipsters on penn ave.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The Quiet Storm is one of the coolest places in Pittsburgh. Not only for food, but for the atmosphere and milkshakes! If you are looking for a place to bring your parents, in-laws, uptight but good-hearted neighbors -don't let the hipster decor and server fashions lead you to think it will be a shouting match over noise music and avoiding awkward half-nude paintings, the food is genuinely delicious and the space objectively interesting. + +I recommend the grilled cheese with apple and cream cheese, although both times I've gotten it it's been a little heavy on the cream cheese so if you are conscious about that kind of thing, ask for light cream cheese. I also absolutely love the buffalo tofu tenders, bread sticks, and the mac n' cheese. + +Also don't forget about their extensive and interesting drink menu! Lavender lemonade, root beer and espresso? Sounds delicious to me, and makes me wonder when The Quiet Storm will be getting a liquor license...the answer, my friend, is blowing in the wind...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> (I'm 29 and have been a vegetarian for 17 years) +For vegetarian food in Pittsburgh, I say this place is aces. But compared to the many other veggie restaurants I've been to in this past, this place is average. It's really hit and miss with their dishes. When at a veggie place, I usually try to change it up each time I go to keep my diet varied. This has proven to be a little difficult at Quiet Storm because it seems every other time I get something I don't like. Apple Panini is amazing. Nachos are great! Curry wasn't spicy enough. Grits runny. Milkshakes YUM! I feel like the cooks don't have a good handle on cooking tofu there. Different dishes require tofu to be cooked for different lengths of time and it different sauces, and it has always tasted bizarre when I get it there. Sometimes its not pressed and cooked long enough. Sometimes its dried out! How can tofu get dried out? This is coming from someone who LOVES tofu. I can eat silken tofu straight out of the package with a little soy sauce and sugar. +If you have spent anytime in Portland, Oregon... the atmosphere in this place is very Portland. Outdoorsy hipster cafe style. It's loud, but I couldn't imagine it another way. They also have pinball, which is awesome. We haven't taken advantage of this, but they do have board games and books available as well.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We stopped by Quiet Storm for a late lunch while on vacation in Pittsburgh. The food was excellent. I had the cheese steak and my husband had a peanut tofu wrap, both were served with chips. Everything was great. If I had any complaint it would be that I didn't see on the menu that my cheese steak had mayo on it. I'm not a big fan of it, so had I see that I would have asked for it without. Other then that great place![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I didn't realize that Quiet Storm was a completely vegetarian restaurant until I noticed the word ""seitan"" printed after every meat item on the menu. Normally I'd find this annoying, as I'm an unabashed and unapologetic meat eater. That doesn't mean I don't love a good veggie dish, but fake meat masquerading as real meat is one of my pet peeves. If you're going to serve vegetarian food, don't try to pretend it's anything else. + +That grievance having been aired, I ordered the Blackadilla, a quesadilla boasting no false meat items, but stuffed with black beans, basmati rice, sweet potatoes, pineapple and cheddar cheese. It was delicious and filling, and at $8 for the enormous quesadilla and a small house salad, a pretty good deal. + +The menu at Quiet Storm is large, with breakfast and lunch/dinner items as well as an array of cafe drinks and desserts. In spite of the prevalence of seitan and tofu, there are a number of dishes that I look forward to sampling upon return. + +And I do plan to return. As those of you who have read my other Yelp reviews know, the atmosphere of public places is very important to me, and the atmosphere at Quiet Storm does not disappoint. It's got a retro cool '50s diner vibe and a more modern but equally cool soundtrack that entices customers to stick around. The wait staff encourages this practice, giving diners plenty of space to hang out long after they've finished eating. + +The one downside of Quiet Storm is its location, floating among gas stations and abandoned houses in Garfield, an area sandwiched between the more pedestrian friendly neighborhoods of Bloomfield and East Liberty, but not quickly accessible from either. It has to be a pre-determined destination rather than a drop in for random passersby. But that might just be OK.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Daniel Fast friendly restaurant with good food. Stopped for an early supper before Saturday night church service after searching Yelp for vegan restaurant options. Food was good, service was good, price was very reasonable. Think I just found a new Saturday evening supper spot.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I really, really wanted to like this restaurant. Hip, quirky, vegetarian/vegan. Lots of owls and kitschy deco. I eat meat occasionally, but had a vegetarian buddy here to visit, and thought this would be a great choice. What's not to love, right? + +Well, for starters, the service. Our server was really nice, and had lots of reviews, suggestions and alternate ideas for what we should order... but the service was mind-numbingly, ridiculously slow-- and the place was half empty. Plus, even after two requests for napkins (which were not provided to begin with, and not available from other empty tables around us) we never received any napkins at all. I'm not really a messy eater, but come on! + +Maybe part of the problem was expectations? We kicked things off with the ""firesticks"" appetizer-- some really tasty quesadilla-ish things. After that, our orders (I had the thai salad) were just kind of... boring? Strangely spiced? I feel like the bar was set high with the app, and then none of the entrees met the expectations of yummy veggie goodness, and my dining companions agreed. I also ordered a cup of the mac & cheese, and it was awful. You know how when you reheat elbow mac & cheese in the microwave, and the cheese gets all greasy/gloopy and the noodles stick together? Well, it was exactly THAT, with some powdered garlic sprinked on top. Really. I should have made my own leftover mac at home and not paid $4 for a cup of that. Learn from my mistake. + +We had planned to order milkshakes, too, but our server spent so much time in a black hole or something that by the time she finally returned, we'd been completely finished with our meal for at least 15 minutes. For $4 (and probably a ridiculous wait) per milkshake, we decided to hit The Milkshake Factory on East Carson instead.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Why do vegetarian restaurants think we need ""fake"" meat, this I do not understand. I had a primavera sandwich which was just ok, but the patty on the roll was just as perplexing as the ""mystery meat"" you get in your elementary school cafeteria. My sandwich came with a boring pasta salad and some tortilla chips out of a bag. Otherwise the atmosphere was fun, and the wifi was free if you ask for the password.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've been back to Quiet Storm many times. I can accept the hit or miss service since it's pretty cheap and casual. That's not really an excuse for bad service, it only somehow softens the blow, but why be mediocre? + +The environment is comfortable (unless you sense the servers don't want you there). The music ranges and is appropriate for the environment. It's never too loud or aggressive. Free wi-fi helps and the milkshakes are slammin! The food is inconsistent, but often good. The Black-a-dilla is my favorite. + +I really want to like Quiet Storm, but it only merits 2 stars. Their food, service, and hours are inconsistent. It seems they often close early. + +Owners, please stick to your business hours. It's not like you're open that late to begin with! Perhaps everybody wants to go home, I don't blame them for that, and you may have run out of a few things, but try to imagine the disappointment of trekking out there to enjoy your favorite shake or snack and then being turned away. + +OR, If you believe this is an acceptable business practice, it would be less infuriating if you simply changed your hours to '9am - until we feel like it.' This way there are no set expectations and we can't really begrudge you for it. + +...My vote is to just stick with the hours you created. + +Thanks![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My experience has been ok at the Quiet Storm because I have 1) not deviated much from my usual menu choice (Original Home Fries = delicious) and 2) I have often known several members of the wait staff at any given time. + +This has given me reason to continue eating at Quiet Storm on occasion. + +Negatives... I have eaten with several others over the years who have been wholly dissatisfied with their meals (small portions, not enough seasonings, could taste baking soda flavor in baked goods, etc). Service can be a little slow at times. And I have been burned a few times when going out of my way (it is a little off the beaten path for many) to score some delicious Home Fries only to find that the QS had inexplicably closed early. + +Despite this, FOR PITTSBURGH, the QS is a good spot for vegan/vegetarian fare.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> So when we first went here for brunch, I had no idea it was a vegetarian restaurant. That's an unpleasant prospect to face down after a hard night of drinking, which is the only time the idea of brunch ever occurs to me. But then, the grim Spectre of Laziness appeared to me and asked, ""Do you really want to drive to another place? Just look at you. Your wearing the same shirt that you wore yesterday dude."" + +The Spectre of Laziness is a dick, but he was also right. And to my surprise, nothing I had was bad at all. For brunch options, meat eaters will find that potatoes and eggs are the cornerstone of any breakfast, and seitan substitutions are not as bad as say, having the grim Spectre of Laziness point out your slovenly appearance. + +I think the biggest surprise in this place is that, though nothing is particularly jarring to the palate, there is nothing that really stands out as being amazing. In Yelp terms: it's kind of a 3. For hard core vegetarians having a night, er, mid-afternoon on the town, it's probably a blessed change from the meat based culture that Pittsburgh is pretty famous for. But I'm willing to wager that very meat eaters will become converted to vegetarians after this. Maybe they did TOO good of a job substituting meat items. That being said, we did make it back another time for lunch where I had a vegetarian gyro. My friend said it best: ""What's the fucking point?"" + +The service is always very sweet, but both times the waiters have been curiously, nay ominously spacey. Even when it wasn't crowded there had to be some substantial flag downs and polite and doleful eye contact before they would do what you needed. If you're in the area and looking for...this type of thing, you really don't have too many other options so just eat it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I wish we lived closer to this place. They had the most amazing French toast (stuffed with apple butter and cream cheese) I've ever had.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> You don't have to be a vegetarian or vegan to enjoy Quiet Storm. + +I've been here for both breakfast and lunch and haven't been disappointed. The menu has a good selection of both vegetarian and vegan dishes and the specials change daily. + +The only issue I have had is with service. On a particularly crowded Sunday I asked twice for a coffee refill and the waiter never filled my cup, or even checked in after our food came out. I know it was busy, but other tables seemed to be doing just fine. Despite the poor service, I returned, and haven't had any problems since.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Honestly, this the last place you'd ever expect to see me. First it's a vegan/veggie cafe, I am a complete carnivore. Secondly, it's like hipster brunch paradise, I'm super preppy (a heavily tattoed preppy person but still). Yet this was one of the only places open on Labor Day and I walked in with my vegan friend, she immediately recognized her people and practically jizzed in her pants over the menu. OMG seitan gravy and cheez? + +WTF is seitan gravy and cheez? Why does she keep calling vegan cheese, ""cheez"" anyway? I decided to go with the flow and order the Home Fries Ranchero. Basically their ""famous"" home fries, chili, sour cream, eggs or tofu and cheez. I went native and ordered tofu vs eggs, and you know what? I liked it. It came out in a big heaping pile on a 70s retro plastic plate, accompanied with some awesome coffee. My friend had hummus and pita, cause not only is she vegan she only eats things in the white/beige color range (food racist). + +One bad thing, the bathroom has no door, only the stall does. Basically it's a unisex bathroom where all the delightful sounds and smells can be experienced by diners directly in front of you. For a place that serves chili and ""cheez"" they may want to reconsider this open approach. + +There are some previous reviews about arrogant hipsters/bad service etc. I have say our waitress was awesome and attentive. My coffee was filled routinely, she understood that requesting a ""buttload"" of cream meant a larger carafe of cream rather than a thimble. The host was apologetic for making us wait for more than a few minutes to sit down.I do admit it does have the indie coffee house feel, and yes hipsters abound here, but I have a feeling these are some legit hipsters. Not the trust fund having, whiny, I drink PBR, and annoy people with my smugness style hipster. I bet these hipsters been squezzing their junk into tight pants long before I was born. I don't know, I just get that impression. + +I however feel a little weird for writing such a positive review on a uber crunchy place, so I feel the need to go slash tires on someone's Prius now.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Being an omnivore myself, I have fended off several attempts to visit this restaurant. My girlfriend is a veg-head aka vegetarian and had wanted to visit Quiet Storm for a while. When we finally visited this week, I was pleasantly surprised. There is definitely an old-time diner feel with a bit of arts and crafts mixed in. If you're reading this, chances are that you have some notion of the crunchy/hipster/longhair reputation of this place and that perception is certainly accurate to a degree but I did not find the service pretentious or slow at all, as some have noted. Our server was attentive, although there were only about seven folks in the place (it was off hours, about 4 PM on a Monday.) I enjoyed the apple panini with seisage (a maiden voyage for me), apple butter, cream cheese and cheddar. The apple butter, which seemed almost an add-on when I looked at the menu, was actually the star here and the sandwich comes on sundried tomato bread that really adds a lot of flavor to a very simple idea. My only complaint is about the size of the sandwich. It could have been larger. My girlfriend ordered a burrito that was honestly huge and she found it tasty and worthy of a doggie bag. I would definitely go back and would like to try their weekend brunch, which is supposedly quite good. + +According to the menu and reputation, Quiet Storm goes out of their way to use local products and makes quite a few of their products in-house. That's always a good thing especially when the results are tasty and relatively affordable.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Quiet Storm occupies a special place in my heart compartment because, one lazy Sunday in 2004, I discovered Alfred Bester's The Demolished Man. Imagine my joy: a cyberpunk fan, finding a tattered copy of some anonymous-looking book in some proto-hipster cafe (this was back before it was toooo hipster), and discovering the glories of Alfred Bester. (Seriously, The Demolished Man is good.) It also fit in perfectly with the blue collar/gentrified charm of Pittsburgh in general, and the Hill District/Lawrenceville/Bloomfield in particular. + +Anyway. I have returned now in 2011 for a veg brunch, and it was a pleasant, if not-so-good-value-for-money experience. I got the True Grits (yeah, Jeff Bridges, yeah), which was a HUGE bowl of grits (some shaved, grocery store-feeling cheddar on top), a pile of delicious, chopped lemony kale, some pretty blah scrambled eggs and a large glass of cranberry juice (very healthy!). Overall, it was fine. I didn't like the $12 price tag so much (seriously, grits is pioneer food and you're charging me $12!), nor did I dig the shades of hipper-than-thou among the clientele, but shrug shrug.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> They have these tofu tenders, which are akin to a vegan buffalo wing. I can't put my finger on it, as there really doesn't appear to be much to them in terms of some sort of secret cooking technique, but holy crap, I can't get enough of them! I had 3 orders in 2 days, and since it's tofu & not some greasy wings... it's a legitimately healthy meal/snack. +The Cheesy Snake -- a vegetarian cheese steak -- can be made with vegan cheese, and it's pretty slammin, too. +The slaw tastes like liking a brick of salt, and the coffee etiquette -- pouring old pots into other, half-full pots -- leaves a bit to be desired, but overall, I know that it's one of a few places in Pittsburgh that serves vegan food that's pretty awesome.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Despite my 3-star rating, I think I will be coming back here again to give it a second try. + +I got the smashed potatoes with seitan, cheese, and aioli. The first bite was OK--the aioli didn't quite suit my taste, but everything else worked pretty well together. However, 20 some-odd bites in to the dish, the flavors were getting repetitive and the mushy texture started to gross me out. I got about half-way through eating the dish and the so-so aioli became too much for me. I couldn't take another bite. + +However, my wife's apple panini was delicious. I would probably eat a few of those if I came back. The cream cheese, cinnamon (from the bread?), and apple all worked together in glorious harmony. + +On a strange note, while we were eating, some camera guys came in and started setting up what looked to be an interview. We asked the staff what was going on. Apparently someone was filming their submission/application to be on a reality show. ""Oh cool,"" we thought. ""What reality show?"" we asked. ""Not sure, something on the Golf Channel,"" they replied. HAHAHAHA! I thought watching grass growing on TV was boring enough. Now they're making a reality show about it. + +In the end, the gross aioli was inexcusable to me. Otherwise, I'd probably go 4 stars. I still plan to come back and give it another shot.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Yes, it is reasonably priced. Yes, my food was tasty (6 on a scale of 1-10). However, the place did not look clean to me--I won't be back because of that.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Tasty horchata - dessert before the meal of veggie Cuban with smoked tempeh ... Yum! +Cool funky space with low key music & friendly waitresses with plenty of tats[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Yes, I know. I'm probably one of the few people that has rated this place with two stars. + +But let me explain. My friends and I wanted to try this place out and had high hopes. I haven't heard of many vegetarian/vegan places in Pittsburgh so I expected to have some awesome vegetarian food. However, from the get go, our host was absolutely terrible. He did not look us in the eye and was just overall awkward. There was obviously room in the restaurant for the four of us but he had to ""look in the back"" to see if there was room. One of the other servers eventually sat us in a clearly empty table that we could have picked out for ourselves. Our first host came back, reiterated the same thing the server told us, but never gave us menus. I had to go out of my way to ask for menus about five or ten minutes after we had been seated. + +To be fair, our assigned server was very nice. She was friendly and approachable. But of course, our food came and mine was cold. The potatoes in the hash I ordered was stale, old and cold and had such a small accompanying serving of bread. Also, our utensils weren't given to us until after our food was served. I know I may be sounding like a little bit of a snob but utensils should be expected before the food arrives. Not to be completely biased, the rest my party had decent food. It just wasn't anything special. Definitely not worth $12 for brunch. + +Needless to say, I will not be coming back to this place.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I came into Quiet Storm not intending to have lunch, but just a latte and hang out to answer some emails for a little while (working from home makes me stir crazy, so bouncing around local coffeehouses, completely NOT fitting in with the crowd kinda makes my day sometimes). + +I walked up to the bar and was just going to grab a seat there, but super hipster server guy asked me to take a table, because it had an outlet to plug my laptop in. I didn't need to, but ... good lookin' out. + +Anyway, ordered my latte - good espresso, but pretty weak foam. Served in a pint glass. That's fine. + +Menu actually looked really good, so I went for a sammy with apples, seitan sausage crumbles, and cheese. They offer different sides, but my super hipster server guy didn't ask me what I wanted; so being a newbie I figured maybe that was only with certain menu items. I was wrong, when the guy taking care of the table behind me was asked what he wanted. My fault for not speaking up. Sandwich was good, not to die for though, and frankly kinda small for $8. + +I'll finish with this: Internets are free, right? So, where's the code? Did I need to ask?? +I'll definitely go back though, intrigued by a few other things on the menu (like bbq tenders and pulled 'pork' quesadilla), and hopefully be a little more impressed.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We've figured out where all the hipsters go on the weekend for brunch! + +Really excellent french toast, just like my dad used to make. I had the breakfast burrito, which I thought was OK, but not something I would order again. But, more importantly than the food, we just really liked the atmosphere. Sitting there in their mismatched, vintage-y looking diner, I felt like I was in the Mission in SF (OK, maybe minus the fact that everyone was sporting their winter gear, which would never be necessary in CA). Kid friendly too, if that's important to you.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> After three trips to Quiet Storm I am hooked. I had the Bahn Mi, then the Veggie Gyro, then a burrito. All were a large portion with excellent fresh ingredients at a price that was really really great. + +My significant other is addicted to the chili, which actually has a good heat level. + +Also the milkshakes are to die for. Can't get enough of them. + +Service is prompt and attentive. The waitstaff is knowledgeable and friendly. Service is quick even when they are busy. This is the perfect casual restaurant. The decor is funky and cool. There is even a pinball machine! + +Will return again and again I am sure.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Solid vegetarian and vegan food, great coffee in a cool atmosphere. What else can you want? + +I had the breakfast burrito with tofu (the ""black and gold"" I believe it's called) and it was quite good. The ambiance is correctly described as ""hipster"" and it's exactly what you'd expect from a hipster vegetarian coffee shop/restaurant. + +Five effing stars.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Everyone I show this place to loves it. Yes it's totally hipster and funky. Yes, hipster service isn't going to walk up to you all bubbly and smiley and be super cheesy to you. But the employees are chill, and it's all about the food, milkshakes, and coffee. The rotating menu is awesome, and I've tried a lot and never gotten anything bad. The chai milkshakes are amazing, as are all of their drinks. I'm not even a vegetarian and this one of my favorite places to go over and over![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> So I admit my boyfriend and I actually didn't know it was vegetarian/vegan until we had ordered our food and looked more closely. + +We went this past weekend and had brunch. We each had thai coffee which was ok, not stupendous, not horrible. He ordered the veggie burger, and I had the chocolate oatmeal pancakes. + +His burger was unseasoned and fairly cold, my pancakes were okay...but to be honest really lacked flavor (the taste of what I imagine cardboard to be came to mind). I don't discriminate, I'm all for veggies and vegan food, but just because those are your ingredients doesn't mean you can't cook things well and add seasoning. + +I am intrigued to go back because the apple cheese panini sounded possibly better than what we had. + +I will note that ourwaitress was very sweet and friendly, but the food was just lacking in flavor so much that it's really deterred us from going back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Ugh... I got a plate with seisage, tofu scramble, and sundried tomato toast. My whole plate was entirely dry, chewy, and unpalatable. I had high hopes for the tofu scramble, especially after seeing positive reviews about it. But honestly... It tasted like nothing. I thought it'd be moister with a creamy consistency that might come from silken tofu, but it was hard, dry, and chewy. Hubby got a country burrito that was much better in comparison to my plate... But that might have been due to the fact that his whole plate was doused in gravy. Anything will taste better drenched in gravy. We think the gravy tastes like the powdered packet kind where you just add water. On top of all this service wasn't the greatest. I had to fish around for my own ketchup and they didn't even bother to ask me what kind of toast (3 options on the menu)I wanted when I ordered the toast option for my meal. Then they didn't bother to ask hubby if he wanted anything to drink after he had picked one of the $12 entrees that come with coffee or juice. We had to tell someone else to get it for us. Also they don't really wash their cups. There are 2 sink basins at the front where they just dunk the cups in one soapy basin then dunk the cups in a second water basin and then stack them next to the sink. It made me not want to drink my water even though I was thirsty. Good idea, but poorly executed food. I've had good vegan and vegetarian food before that's consisted of a lot of fresh greens, avocados, and more. For a vegetarian place, there was nothing green on our plates. This experience sadly fell enormously short of our expectations... Could've eaten at kaya or meat and potatoes for the same price.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My husband and I stopped going here, back in 2010, because of the bad service we were receiving. We used to call the servers ""Whole Foods Rejects""; they were always cranky and we felt not welcomed, rushed. At the end of 2011, I think they got a new manager, the service has been optimal and we haven't stopped going since. Their food is delicious as well as their drinks and coffee.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Artsy little alternative cafe diner with good food and nice wait staff.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I decided to grab dinner on a Saturday night at Quiet Storm. It wasn't packed so I grabbed a seat at the bar. I ordered their Graham Street Tofu sandwich with their 'chorizo' soup and a shampoo soda. The Graham Street Tofu sandwich and soup were very good but the shampoo soda was interesting to say the least and wouldn't order it again. I was nervous I wouldn't get good service after reading some of the reviews but the waiter was friendly and checked in at the right times. I would definitely come back to Quiet Storm since they've got me curious about their other dishes. I also like the laid back vibe of the place, bringing me back to Forrest Gump time.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great chill spot! Definitely hipster. + +The staff is super awesome. Great place to have a coffee and chill, write, or for dinner. The food (very vegan friendly!) is really good and a great price. + +Glad to see this spot still around when I visit back home.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My boyfriend and I come here every other Saturday, at a minimum. He gets the QHF with eggs, I get the QHF tofu, side of onion gravy. It's potatoes, eggs or tofu, cheese, seisage, PICKLED ONIONS (the best), and this yummy aioli (let's be honest, it's mayo). I wouldn't call it healthy (maybe I'll consider adding some vegetables to switch it up), but it's the perfect hangover food or post-long run indulgence. They do have many healthier options as well, we're just hooked on the QHF and can't stop. I have also loved the country burrito, grits, and hangover hash. They only have the QHF on Saturdays (and other days) and have a different pre-fix drink included brunch menu on Sundays. The coffee is delicious also. + +Sometimes I wish the staff were a bit friendlier, but they're all pretty busy running around. + +The absolute best part is that they're always crowded but there's almost never a wait when we go, which makes for the perfect brunch spot![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My word, this place is outstanding. I have been here twice from out of town and both times were the highlights of my trips. The food is excellent, this time I had the country burrito (double gravy, yeah baby!). The portions are large and out quickly. + +The food is almost besides the point though because QS really excels in the refreshment department. This is one of the few places that makes me wish I had more than one life to live, because I know without living in PGH I will never have a chance to try all of the incredible milkshake, coffee, lemonade and ""other"" cold and hot drink options. I mean, they have TEA milkshakes. Extraordinary. + +Service was friendly and quick. Street parking is ample. The interior is bright and welcoming. + +6 stars. No. 7 stars.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Worst tofu scramble ever. Days old, cold, hard, inedible. Sent it back and had no time to wait for another dish. I can't even believe that the server, let alone the ""chef"" thought it appropriate to serve. + +Brought my 2 year old along, had to get a high chair, I'm able to do this just would have been nice if asked by server if we needed one.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Love this place! The decor inside is really cool. + +I'm not from the area but I try to stop in every time I'm traveling through. So many great veg options and great drinks.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The food here will blow you away. The depth of creativity of the items, the menu's being designed around what's available to increase both creativity, changes and environmental sustainability and the overall unique interior design are all screaming at fans to come back. Do love it from the second I drove past it and screeched to a halt. Glad I did. + +I don't & can't drink coffee so I can't speak for anything but the Earl Grey Tea which is good, as it is in many other places. + +Overall, go.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I am no vegetarian so I cannot speak for those who are really into that, but this place was awesome. I had been scoping it out for weeks when driving by. Finally I met someone there for lunch. Wifi. Check! Unique and Awesome Milkshakes? Cheeeeck. Tasty awesome foodies. Double Check. I was quite pleased with my experience and I can't wait to go back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I had about half a day to kill in Pittsburgh, and this is where I ended up. Traveling with food restrictions for any reason can be quite difficult these days, and Quiet Storm was a sanctuary for me to just sit down and have an awesome, vegan meal without worry of going into anaphylaxis. + +I had a bowl of something-something with I think tahini sauce and veggies and a huge thing of hot tea (I had laryngitis and was just very, very sick so I can't recall much other than how good my food and tea was), and my fiancee had a sandwich that came with some chips and really, really, really good salsa! + +The restaurant is just down the street from the Children's Hospital and I'm just really glad my fiancee found this place so I could eat safely without worry.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We love Quiet Storm. My kids (aged 5 &2) and I are all vegan, and this is the only place we can go out to eat where everybody is happy.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Nothing matches in this place! The tables, the chairs, the tiles and that's how we like it! Lots of delicious vegan items. Definitely a good place to try new things. Good coffee too![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've been introduced to their kale offerings and must admit, I'm a huge fan. There's a kale salad that you can ask them to put in a wrap and it's absolutely phenomenal. Almost all of their veg options are fantastic. +The downside of QS is their Sunday brunch. I know, I know most brunches are breakfast foods only, and this place is no exception. On a personal level, I don't really care for breakfast food for lunch and since you have no other choices, it's not my thing. +Like I said though, this place is fantastic for veg food, so give it a try.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I can't believe it's taken me so long to try Quiet Storm. Weekend brunch was great vegan comfort food. We had VTL (messy, delicious red potato smash with seisage, scrambled tofu, and queso), Country Burrito, and sweet Nyam (corn and coconut spiced pudding cake with banana and sweet potatoes). We started with the vegan nachos which were super tasty. Friendly staff and kid friendly, even on a busy Saturday afternoon.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've found the service here to be pretty terrible. Servers can be pretty careless about taking care of simple things and my friends have had similar experiences. The food is really pretty good, but if the overall service sucks, then well, it makes it hard to enjoy a tasty meal. Sorry Storm, you need to improve this.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I am not a vegan and went there to meet friends and enjoy the atmosphere. I must say the hipster 'tude of the place was intimidating at first, but it's super friendly and retro-feeling. Servers were fairly friendly. We had some great lattes and chai teas and chatted for a long time without being bothered. Didn't try the food, but there were lots of vegeterian and vegan options.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The fare is pretty standard for a natural/ vegan/ vegetarian spot: lots of tofu, tempeh, veggies, and combinations thereof in burrito or bowl form. That said, it is particularly fresh, flavorful, and carefully prepared. Quiet Storm has a really nice vibe and feel to it, and the spice lovers among us will relish the bottles of Sriracha diners are allowed to have their way with at each table. + +But what I really came here to talk about are the milkshakes. OHEMGEE. I don't even know how to describe them to you. The vegan ones are just delectably decadent and so thick that you can barely drink it through a straw. There are so many flavors that you cannot possibly decide which would be the most scrumptious (answer: they all are!). But I'd urge you toward anything involving peanut butter. Too bad I was just visiting (or maybe that's good- I would not be able to stay away!).[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great cafe for brunch and coffee. Lots of vegetarian options and nice atmosphere. Come check out the place if you're in the area and would like to try some healthy foods. Was here for some brunch with friends and our food did take a while to make it to the table but everyone enjoyed their meal. If you come too late during the evenings for dinner the food options are less then what's on the menu.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I imagine that this is the restaurant that I would make if I were 20 years old and knew nothing about restaurants except dining in them and what looks and sounds cool. In that it does some things right, but none of the important things. It has a decent sized shop with large windows and its bright, so that's good. They have good music, but unfortunately we were seated right below one of what looked like two speakers in the place. Its a large restaurant so in order to make it the right volume for people far away from the speaker it has to be too loud for the people close to the speaker. I know the trade-offs of sound systems all too well. If only there was a way to solve this problem like... just riffing here... more speakers at a lower volume? + +They had a greatest hits of the thrift store type of decor and the standard shitty artists selling their paintings like at every coffee house you've ever been to. They include coffee/tea/juice/whatever in the price of the brunch because, like everyone, I hate choices too and I definitely wanted at least one of those. I'm looking at the menu and its a vegan/veggie place so we're never going to be good friends but I'd like to think that there's something that looks halfway decent but it all looks awful. There are two Tex-Mex-Ranchero breakfast dishes... that's at least one too many; and there's only like eight choices which sounds like plenty as a number but I assure you it was not enough here. + +I go with the Egg Frittata as my least bad option and it ends up tasting mostly flavorless but with a distinct stale note. It comes with a salad that is not bad, but who wants a salad for breakfast. As we're leaving the waiter, who's been fine the whole time, asks us where we're from and my girlfriend answers ""D.C."" The waiter replies, ""Oh, I'm sorry about that."" Now, neither of us is actually born in the D.C. area, nor do I even particularly like living there. So I'm not personally offended, but I'm not sure if someone from or living in Pittsburgh has solid footing to talk the business about Washington D.C. or almost any other large city. Its not like property values in Pittsburgh are indicating that everyone's clammoring to live there, whereas in Washington D.C., they are. + +I was not enjoying the restaurant before that, but this kid actually threw me to straight up hating it. If you're vegan and have literally no other options... then I guess you're going here. If both of those conditions aren't true, then go anywhere else.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Me and my kids got food togo from here, because it came recommended from someone at the local food co-op as a place with good vegan options. + +Cute and attractive DIY style decor. +Friendly staff. + +I really liked the food quite a lot (i'de give it 4/5 stars). GOt a tofu banh mi with a side salad. When I asked what dressing they had, I expected to hear the list of ""usual"" uninspiring dressings that vev/non-veg restaurants often have. The first one she mentioned was a green chili dressing tasted as fun and yummy as it sounded. + +My kids didn't really love their vegan homefries meal (with scrambled tofu and a weird vegan cheese sauce thang). + +Anyhoo. Really pleasantly surprised with this joint, and the food was pretty reasonably priced. + +As with any place I review, I am subtracting a star because they aren't all veg. Anyplace selling eggs dairy and flesh isn't perfect for me. I'de probably really call this 3.5 stars.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love quiet storm! I think it's as good as you can get for vegan cuisine. The country burrito is BOMB! So good, there has to be crack in the gravy. I also enjoy the tahini queso, I often add it to my burrito. It's best on the nachos. For around $13 you can get a delicious filling breakfast/brunch coffee/tea included. They also have great pastries & dairy free coffee drinks & milkshakes! It's a vegan dream come true. It does get a little crowded during Saturday mornings so expect a wait, but completely worth it. The atmosphere is oozing with hipster ambiance associated with the area (Garfield) which also means they often play good music! Last time I was there it was all Neil Young! Accompanied my burrito perfectly! I definitely recommend this place to vegans & NON-vegans alike![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The Quiet Storm was great. I started with the soup of the day which was something along the lines of a carrot pumpkin curry. It had an unexpected texture but I still quite enjoyed it. For my entrée I had the Spinach Burger, which was quite filling. It is quite unique and comes with plenty of options for toppings. I couldn't resist putting cheese on the otherwise vegan burger, but still felt very healthy eating such a veggie-filled dinner! Their milkshakes also looked amazing - I would have tried one but I needed something to warm me up instead so I got a latte, which was also very good. One other thing I thought was neat was that the sell mixers and encourage you to bring your own champagne and/or vodka. I haven't seen that before, but it's a great idea! + +I was also intrigued by some of the other items on the menu, so I will need to go back to try more.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'll be honest, this wasn't our first, second or even third option for breakfast, but when it came to early Sunday grubbing with a group of six, this was pretty much the only place didn't have a two-day long wait. + +In fact, there was no wait at all when the six of us popped in a little after noon on the weekend. Odd, but my group was hungry so we didn't question the kismet. + +The restaurant is pretty enormous as far as cafes go, and it's nice because they don't pack the tables on top of each other so you're never going to be crammed next to a crying baby or having to scoot your chair in every time the table next to you needs a coffee refill. The furnishings all appear to be second hand finds as well as local art and LOTS of owl statues. It's a hoot, for sure. + +One weird thing is the one bathroom with the sink outside, so if you're sitting in the back you can heavily monitor who comes out and doesn't wash their poopy hands. On the other hand, if you go to the bathroom here you'll likely feel like you have to make your hand washing some sort of big production so the other people in the back will take notice of your exceptional hygiene habits. + +I was feeling pretty sick still and actually brain washed myself into believing that my weekend bug was actually morning sickness so on top of already feeling super nauseous and not hungry, and naturally my non-motherly instincts wanted to starve whatever demon might be brewing inside me but the hypothetical baby's daddy insisted I eat something and took it upon himself to order me the tofu scramble, which I was sort of excited to try despite feeling otherwise very green. It was actually very bland and dry and even though I think it was only like $3, I think I would have rather had the $3 in my pocket than the scramble so I took a few bites and then pawned it off on the boo who insisted I try his veggie breakfast burrito. The burrito was the total opposite of the scramble- absolutely outstanding and even though it was the size of a guinea pig, I think I could have downed the whole thing (of course, I would have blamed it on my imaginary incubating child and said I was eating for two). + +Going around the table, everyone seemed content with their food, besides the grits order that were decidedly bland, but that's kind of how I've come to think of grits in general. Our service was great and though most of the table's food was just okay, that burrito, the owl statues and the house horchata I ordered as my beverage really made the experience for me. I guess what I'm trying to say is that I can understand the 3-star average on Yelp, but that I think you can totally come here and have a 4 or even 5 star time if you order wisely. Just remember: Burrito, horchata and time the bathroom-goers for extra entertainment. + +PS- I'm so NOT pregnant (in fact, can someone get me a heat pack a few dozen Midol?), but thanks for your concern.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Sandy had me holed up in Pittsburgh looking for a flight and staying with my wife's aunt. She adventurously agreed to go with me to a veggie place and that's how I ended up here. + +Nice layout with tables along the windows and more in back. If you're not familiar with this kind of scene it could seem a little rundown, but to my eyes it was fine. Really, it's kind of the proto-typical East Coast college town vegetarian hangout. + +The aunt-in-law is a meateater and in her seventies, but she really enjoyed her tempeh Cubano. And she loved her lavender lemonade. No room for dessert though. + +I got the Banh Mi and it was very tasty. 'Nuff said. + +The service was in my mind delightful. The server was engaging and welcoming to my somewhat timorous companion, explaining the dishes to her and making a recommendation that worked out. He was efficient and personable. + +Too bad I won't be back in Pittsburgh anytime soon, or I would make a repeat visit for sure.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It's cheap, I'll say that, but otherwise it's bland food served by workers who mostly don't seem to notice they're working, and when they do, only respond snarkily. There are many better vegetarian and vegan options to choose from.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love good vegetarian options! + +Immediately upon stepping into Quiet storm you'll realize their myriad of owl decor and local art hanging on the walls and counter top. The place is comfortable and is perfect if you want to just relax and read the paper. + +This little cafe has it all - milkshakes to die for, vegan baked goods, yummy breakfast burritos, and killer french toast. Their imitation meat was average compared to some other one's I've had - but it's not something to harp on. + +The service was pretty fast and friendly as well so remember to tip well![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Food was great--- vegetarian burrito stuffed with mac and cheese???? yes please. Also had a great pot of tea, and a bangin' white chocolate hazelnut banana milkshake. It's a really cute place, too. +however, the owner was seriously rude to me and my fellow guests when we asked to split a check (which they state on the menu is allowed). Not even passive aggressive- straight up aggressive for something that was not our fault. so that was a sour end to my experience at Quiet Storm. but my belly was satisfied.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Andrew here said it best: ""... food served by workers who mostly don't seem to notice they're working, and when they do, only respond snarkily."" + +It took me 40 minutes to get a sandwich here, and when I complained I didn't get an apology, just a snarky remark ""well you can see we have a small kitchen""[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm still not convinced that this is a vegetarian restaurant. It just has to be a parody of a vegetarian restaurant. Like, every time I start reading the menu I think Ashton Kutcher is going to pop out and tell me I've been Punk'd. + +A small disclaimer: I am not vegan or vegetarian and I never will be. I love meat. But I also love vegetables and fruits and pretty much the entire food pyramid. And these things can be combined to make tasty vegan food. But ""Texturized vegetable protein hydrated with seasonings"" is not food to me. Yep, that description of their ""chorizo"" comes directly off their menu. Eating vegetarian does NOT mean you need to subject yourself to these highly processed ""foods."" + +Less processed substitutes like tofu, tempeh, and seitan are used as well, but they are mostly treated as a stand-in for meat. I guess if you are a vegetarian that misses eating meat, this may satisfy you. However, as an omnivore, why would I eat a faux-BLT when I can eat a real one? How about instead of trying to imitate the flavor and texture of meat, we actually come up with creative combinations of vegetables, fruits, and legumes that are delicious in their own right. What a concept! Have you ever eaten a vegetarian dish and thought, ""Whoa, I can't believe I actually like this better than meat""? I have! But don't expect that feeling here. It will be more like: ""Umm...I guess tofu mixed with nutritional yeast is kinda reminiscent of scrambled eggs?"" + +Two stars because I really like the drinks here. The ones I remember trying were the ginger lemonade, the Mexican hot chocolate, and the root beer with a shot of espresso. They have some really wonderful sounding tea options that I wish I could try, but I generally avoid this place because of the food.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The best vegetarian/vegan restaurant in Pittsburgh is also my neighborhood watering hole--I'm so fortunate. The food is great (especially love the ginger sunflower dish and spicy peanut wrap) though newcomers may think otherwise. You have to appreciate what they can do without meat or other animal products. The drinks are amazing. + +The hipster atmosphere reminds me of Portlandia. Staff is friendly. Gets busy at brunch time on the weekends. + +Quiet Storm gets 4 for its food, 5 for cool factor, and 5 overall.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Let me first say that I have been a vegetarian for 15 years and have never been to a veg restaurant before. Looking through the menu here I actually got excited, because I didn't have to ask ""does this have meat in it"" a million times. THERE WERE SO MANY CHOICES! I have the excitement of the little girl on Despicable Me ""It's So FLUFFYYYY!"" + +My excitement aside, the menu was pretty large for all veg food. They have breakfast all day, which is always ok with me. Prices were average (~8.50), and portions were large enough to provide lunch for the next day. (Although I have heard that the Cuban Sandwich is on the small side). + +I had the Banh Mi, which was fabulous. The bread was fresh, aioli was nice, vegs were pickled just right, but the tofu was a little on the dry side (on next day lunch reheat it was perfect). I was surprised by the veg seisage. It was really good. + +Gazpacho was nice, although I am not really a fan of cold soup. It reminded me of a smoother salsa. Good, but just not my thing. + +Sarah S. had the special, home fries with chili and cheese. This was on the spicy side (a good thing) and came with tortilla chips. She was happy with it. + +Latte's are good too. + +All in all this was a good experience! I think this is my new favorite place.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I don't think I would have known about Quiet Storm if it hadn't popped up several times in friends' Yelp feeds in the last couple years. I'm all about veg/vegan restaurants, but I have to agree with other reviewers who wish Quiet Storm's food was *slightly* more interesting. + +Husband and I ordered take-out so we could enjoy a late lunch al fresco at Schenley Park overlook. Folks working were vegan-hipster quirky, but friendly and helpful. We ended up waiting about 30 minutes for our food, so we decided to partake in an afternoon coffee to pass the time. I had an iced Morroccan latté with cardamom and rose, husband the Mandorla sweet almond milk latté. Both were excellent. + +For my meal I picked the Tahini Bowl with brown rice, spinach, roasted red pepper, tomatoes, pepitas and fried tofu cutlet with a tahini dressing. I wished there had been less rice and more dressing; the bowl was also screaming for more seasoning. Husband opted for the Crunch Wrap Extreme: scrambled tofu tossed with celery, carrots, edamame, kale and spinach, dressed with vegan wasabi mayo. Again, twice as much dressing would have added flavor and moisture to an otherwise fine wrap. + +And that's just it: the food at Quiet Storm is fine. When really, I'd been hoping to be utterly wowed by the magic capable of being worked by nothing more than mere vegetables, plain grains and humble legumes. Still, I won't discourage you from eating here. I just might come back myself.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great atmosphere, lots of owl decorations. The staff are very nice and are really trendy. It looks like they are working hard. I experienced fast service even though the cafe was almost full. Temperature was nice and the noise was average, they have some good window tables. I would say there is a good mix of regular neighborhood locals here, hipsters, and intellectual types. The demographic also includes college students. It's all Vegetarian or vegan, yay! The food is normally very good. I did have one experience where in terms of how spicy I wanted my meal I replied, 0 out of 10. The food came and my dish was probably an 8 out of 10 in terms of spicy-ness. I could barely eat it as could others at my table. Eventually I gave up trying to finish it. I could have asked for a replacement but I chose not to but Im certain they would of fixed it for me if I had. But other than this instant I've found the food fresh and well cooked.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I was somewhat worried about going here since the reviews seem to be bimodal, so I was pleasantly surprised when our food was flavorful (some reviewers complained of blandness) and not trying to imitate meat (some reviewers said that seemed to be the goal), but exploiting the wonderfulness of vegetables and scrambled tofu (which, despite the other complaints, was just fine). We had the ""tenders"" appetizer, with both the vegan BBQ sauce and the vegan wasabi mayonnaise. We much preferred the BBQ sauce, but I am guessing if you are a wasabi fan, you would like that too. We all thought it was wonderful. On the advice of the server, I had the peanut wrap. It was spicy, heavily peanut-flavored, but full of yummy veggies. I also had a side of chili, that I liked a lot (and I make my own veggie chili at home, so I am picky). Ben had the apple panini with the gazpacho side. We both thought the gazpacho was kind of plain (it got better by adding chili!), but the apple panini (with ""seisage"", cheese, etc.) was very good. Finally, Panchu had the coconut burrito, which was huge, but he ate the whole thing, and was very happy. We all split a vegan cinnamon roll for dessert, and I really wish I had been able to get my own! + +Some complained about the wait; I think this place fits well with the ""slow food movement."" If you want fast food, go to McDonald's. + +So, based on one observation, I gave it five stars. YMMV.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Like other vegan reviewers, I very much enjoyed the wide range of options. I always feel spoiled when I have actual choices. The food was very good and I will definitely go back again. It is not really exceptional ... I did not have a 'how did they do that?' moment. Someday veggie-vegan restaurants will not have to make food that looks like omnivore grub, but this place fills a very important niche for now. I like the vegetarian-vegan mix because my wife could also enjoy her eggs with cheese (she is not a vegan, but eats vegetarian a lot). On the service ... we had a very nice waitperson who was very helpful without making a nuisance of herself ... which is our ideal.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Quiet Storm is a delicious and cozy little place located in the colorful Bloomfield area. The buildings surrounding Quiet Storm are often painted with cute art or have little interesting things about them. I love this neighborhood, but I love Quiet Storm even more! + +I've only been here twice, and I always want to go more often but somehow it doesn't happen. I've turned on three of my friends to Quiet Storm too, and they love it just as much. The first time I visited I ordered a tofu hash. It was an amazing blend of seasonal vegetables, including some I would never eat otherwise. The tofu was nice and firm, the seisage was spicy and perfectly chewy. The vegan ""cheese"" sauce was also rich and delicious. The portion was so huge, I couldn't finish it. Leftovers are rarely as good as when the meal is fresh, but I was pleasantly surprised to find that my leftovers were even BETTER than the fresh meal. I think this is because the spices and vegetables had more time to meld together in a perfect veggie harmony. + +The second time I visited was 4/21/2013. A group of my friends came here for Brunch. Two of us ordered the Vegan Country Burrito, another friend ordered the french toast with pistachio honey topping and my other friend ordered a tofu hash with black beans and salsa. Everything was generously portioned, but some meal choices were sold out. They were a bit disappointed that there was no more falafel. All of us devoured our plates and happily chattered about the complexity of flavor, protein content in vegan food items and how much we loved the atmosphere. + +Quiet Storm is a great little place to visit. It's never lacking in interesting things to look at while you eat. Food comes as quickly as possible. There are plenty of options to please everyone, and if you think you don't like vegetables, try one of their plates and you may change your mind. (Seriously, I am one of those vegans who hates veggies, but Quiet Storm food can get me to finish all of mine) + +Tip: If you want to go for Sunday brunch, go early so your favorites will still be available. + +You may also want to nudge the servers a little more than you usually would, because even though our drinks were bottomless, it was a pain to get them back to give us refills - even for water.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My friend and I were having a weekend trip to Pittsburgh (first time!) and stopped in for brunch on Sunday before our visit to the nearby Pittsburgh Glass Center. We weren't familiar with the area & this looked like a cute place- ended up definitely enjoying our time here! + +We weren't aware that it was a vegan place; regardless, the drinks menu & and the brunch menu both looked amazing. Friend ordered the Nyam, which she said was very filling (surprisingly). I had the the Country burrito, which definitely surpassed my expectations. Decent, good. + +Friend & I both ordered the Don Juan mocktail which was the highlight of the meal- holy crap! AMAZINGLY GOOD- I always think that horchata tastes a little too watery but the coconut juice & caramel helps round out the drink & make my tastebuds sing. I'm only sad that I can't keep visiting and trying more of their drinks. + +Might not necessarily go out of my way to come back BUT I would definitely go again if I were in the area. :)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I always love going here for some quality vegetarian fare.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Our favorite place to go for chocolate peanut butter soy milkshakes. We've been for breakfast, lunch, and dinner and everything we've gotten has been incredibly delicious. Love this place![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Can't believe these negative reviewers calling anyone not like them ""hipsters"". This place is very cool. As vegan/vegetarians, it's not often we can't decide what to order when we go out to eat, but this place has tons of great options! The decor is scattered and mismatched, but that's part of the whole re-use and re-purpose idea they are supporting. The food is more American classic style, but there are some unique items as well. Loved the homemade salsa. Best I've had since we visited the atomic eggplant in Rochester years ago. I simply love vegan food and knowing I'm supporting an ethical business. Our server was really helpful and very attentive, too. We'll be back next time we make a trip to the 'burgh![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place is a train wreck. Quiet? No. Storm? Yes. Loud, slow, bland food and annoying service are only a few of the complaints that I have. + +1. The Vegan / Hipster / Metal thing has got to go. All I kept on seeing through the kitchen window was the armpit hair of the cook wearing the Motörhead tank top. I am a huge Motörhead fan, but when I go to an overpriced restaurant I don't want Lemmy to be making my food. + +2. The food is bland. Shoving a bunch of brown rice and black beans in a tortilla does not automatically make the food vegan and there were very few things on the menu that were 100% vegan. + +3. The service was pretty bad. Our appetizer came to the table with our main dish and the entire time we watched the staff eat their dinner in front of everyone at the counter. I am pretty sure that three different cooks made our order, as the cooks were tag teaming the line while they were eating. + +4. Last, but not least... the volume level in the place was numbing. The guy working the counter kept on slamming the ice cream freezer door every time he made a milkshake, the music was some sort of Bjork style electronica that I am pretty sure was written to induce migraines and there were about 6 hippy couples letting their kids run wild. + +I have been to plenty of vegetarian restaurants in my travels and Quiet Storm does not even come close to the top 10. I think Pittsburgh deserves better.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The food: A lot of interesting flavors, big portions, fresh ingredients. Can't go wrong with anything on the menu. + +The atmosphere: chill, love the second-hand objects from thrift stores decorations and the corner booth that's not in a corner. + +Service: Everyone is super friendly. It seems like they work there because they also like the food and atmosphere, and give good suggestions if you can't decide on what to get.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I was vegan for years, vegetarian for about 9 years or so. This is a good place for those of us who are trying to eat mainly vegetarian (i.e. me now), or strict vegetarians / vegans. I like it here, but the service isn't always great. I've had a negative encounter with the manager / owner before...it was years ago so hopefully her customer service skills have grown since then.Other than that, the food has never been bad, and normally the servers are chill and nice. Don't expect to get your food on the fly.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It had been a very very long time since I'd visited Quiet Storm. For some weird reason, I had in my head that they made these awesome smoothies. Well... they do not. But they make milkshakes. Any other day I would have totes been into the shake but... + +I reeeeeally wanted a smoothie, so I opted out of the milkshake (I know, a rare occasion), and went with a iced chai. I love that they make their own mix of chai and they also don't sweeten it, so you can sweeten it yourself. Super sweet chai is super gross. Just sayin'. + +I also ordered the Sesame Noodle Platter (noodles, soy, tofu, red cabbage, mushrooms, broccoli, onions, peppers) with a ginger carrot salad. It was a solid meal. I mean, it wasn't necessarily a platter (I think a variety of separate items), but a noodle dish. I liked that there was a decent amount of veggies and not just a few, with a massive amount of noodles. I hate when that happens! It was also lightly sauced, not too heavy and sticky. Plus the fried tofu was awesome! Honestly, I've never had such good tofu before. I rarely get it because I think tofu can be so bland, but this was bomb! + +A nice plus is it's a great environment to eat and work. Free WiFi and nice big tables to work on. Plus, throw in friendly service and it's a win![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The food at the Quiet Storm is usually excellent and unique. It has lots of options for vegetarians and vegans, and their specialty drinks (coffee, tea, milkshakes, etc.) are very tasty! However, the service is so poor. I have been there probably about 6 times, and each time there is an issue. The waitstaff usually seems confused and doesn't appear to care about the customer very much. There has never been a time where I've eaten there and had my order come out correctly. It's either wrong, or something was forgotten. There's also usually not an apology. Today our waiter forgot numerous things (why don't they just write the order down?) and even gave us the bill for another table! As much as I enjoy their food, I will say that I'm getting tired of the service being so inadequate.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> They have a decent selection of food for a small cafe. They carry both staples, as well as some creative choices. Their coffee and milkshake selection is pretty extensive too.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Delicious!! Not a vegetarian, but this place might convince me to switch over. Had a few breakfast options and was blown away by the Greek plate and the QTF. Excellent coffee too.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place is great! Cute inside, great milkshake and hot and cold coffee drink options. We had the horchata was didn't taste exactly like horchata but was delicious. We ordered the bah mi which came with two types of fake meat on it. It wasn't a traditional tasting bah mi as it didn't have enough jalepanos, cilantro and it was much heavier but the bread was good and all in all it was a delicious sandwich. We also had the flower salad which comes with a heavy dose of kale and smoked tempeh. Really really good with the peanut dressing! Tempeh is soft and very flavorful. Will get again. Found out that they are closing/ moving to an unspecified location next week so we hope that they will be there on our next trip through Pittsburgh![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I was thoroughly impressed. I am not a vegetarian but I enjoyed the variety and uniqueness of food options here. I was not upset that I wasn't eating meat at all. I also had something called a root down which is root beer and espresso, and it was heavenly. My only complaint is that it seemed to be a little pricey for the type of restaurant it is. + +Also, you may have to be a young twenty something hipster/college student to enjoy it, but I am a young twenty something, so no complaints here.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This is my favorite place to order delivery pizza from. they are fast and consistent in quality and the pizza is always great. I've had their cheese steak subs too which were pretty good as well...but the pizza rocks. :)[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great pizza! + +I practically lived there when I lived in Shadyside. My favorite pizza is the Shadyside special. They also offer gyros, wings, salads, calzones, wedgies, hoagies, pastas, traditional, white and gourmet pizzas. + +Pizza Perfectta is part of a chain of pizza shops that include Cafe Milano, Pizza Milano and Pizza Mineo's[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> this is the only place I order delivery pizza from. they do a good job on their gourmet and specialty pizzas. the bbq chicken is good. + +the wings are average. generally small and cheap with a seemingly storebought generic hot sause. nothing terribly special. average + +the hoagies are ok. dont get a cold cut or italian style. I'd stick with something like the hot sausage or chicken parm. they tend to be better. and they are huge. like 16"" for a whole. + +the calzones are massive and tasty as well. go with heavy veg or a combination of meat and veg. the breaks up the bread and cheese flavor. well at least I've found them to be better anyway. + +the pasta is expensive as heck and is average. not a place to order pasta from unless its one of those lazy nights where you need that craving filled. + +salads are typical. + +all in all not a bad place. better than other pizza places in the area.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I love N.Y. style pizza. Could eat it every day. On a recent to trip to Pittsburgh I tried alot of pizza and this was good pizza. + +One thing about Pitt pizza... it is slightly different than true NYC style: the crust is not as thin and there's a whole lot more cheese. As a rule Pitt pizza also has a slightly sweeter tomato sauce. The sum of its parts is still a delicious close cousin to NYC pizza. + +The pizza I tried in Pitt in my order of favorites: +Fiori's +Pizza Sola (Penn Circle Branch) +Pizza Perfectta +Aiello's (Murray Street) +Beto's + +Save for Beto's, I thought they were all delicious. Wish I had a chance to try Mineo's. A Pittsburgh native friend of mine calls this his favorite but they were closed July 5th when I went by their place on Murray... I'll try them next time I'm in the 'burgh. + +Pizza Perfectta has a few stools and a counter but really it is a take-out place.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> In all fairness, I went to this place after stuffing myself at Vincent's Pizza Park. Still, I know a good pizza when I see one, and this place is totally passable, but great or even good it is not. My friend and I were given our pizza in a box although we were planning on eating on the premises. Still, it seemed like we were not wanted and decided not to press the point. We walked across the street to a parking lot and saw a Pizza Perfecttta box and some leftover pizza littered on the ground. In the end we didn't finish our pizza and assumed that many people in the past have been hastily handed their pizza, pushed out the door, only to walk across the street, eat mediocre pizza, and decide it wasn't even worth the energy to pick it up and throw it away.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> this is my go-to delivery place -- low minimum for free delivery, they always get my order right, and they always get here quick! their gourmet pizzas are awesome (mediterranean, greek, and spinach and feta are my favorites). their regular pepperoni pizza is also the best i've had in pittsburgh. love their wing zings (breaded spicy wings) and steak and cheese hoagie too. haven't tried their calzones or pasta yet. + +pizza perfectta is sooo much better than pizza sola...pizza sola is so hit or miss. and much friendlier/more competent people working here.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> My favorite for Pt. Breeze/Pittsburgh East End. Flat New York style, not greasy, timely delivery, they know my orders![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Great pizza, reasonable prices, fast service - cant ask for much more![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Ew. Okay, not the worst pizza ever, but it's pretty far down my list of pizzerias...and that's sad, considering I quite literally live across the street from it. This should be my go-to pizza destination but I'd rather pay a delivery charge than eat their pizza. The sauce is way too sweet (like, Papa Johns sweet) and there isn't enough cheese. There are too many decent pizza delivery places around to settle for this. The only thing I enjoy about Pizza Perfectta is that their sign hilariously claims, ""Excitingly flavored!"" Personally, I wasn't having an orgasm over my mediocre pizza. Maybe if they wouldn't have tempted me with such language I would be less pissed off at them. Two stars only because they let me borrow some paper cups when I moved into my apartment and hadn't unpacked my kitchen stuff yet. Without them I may have had to travel half a block north and grab some from a different restaurant. Thanks, Pizza Perfectta. + +Oh, and here's a little Italian lesson for you: it's ""perfetta,"" not ""perfectta.""[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This Valentines Day I ordered a pizza for my boyfriend and asked that they make a heart on it out of green peppers. The pizza was great, the heart was perfect, and he loved it![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> By far my favorite Pizza place in the east end. The buffalo chicken pizza here is fantastic, and very unique. I haven't been able to find anything even remotely approaches it in other cities. + +The place is a bit pricey, but I feel its worth it. My go to pizza delivery place![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Perfect for a quick lunch. + +I had a New York style cheese pizza that was amazing, even the crust was delicious. Easily one of the most simplistic, amazing pieces of pizza I've ever had. The Greco piece of pizza I had was also perfect. It was topped with spinach and feta cheese I believe. + + I was so full after man-handling my second piece of pizza I had to stop eating. But my friend had a half finished piece of Greco just sitting there on the table waiting for me to finish it. It was as if the pizza told me to pick it up and keep nibbling and nibbling . This resulted in some sort of religious full feeling. God himself wanted me to finish that piece of pizza, and I listened.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Ordered delivery here with coworkers the other evening. + +I ordered an appetizer or what I thought was an appetizer. The portion size was amazing that I had some to take home with me to snack on. I only ordered the bread sticks, but they were amazing. Hand made, baked and topped with oil and Parmesan cheese. Comes with a side of marinara sauce for dipping and I was very pleased. + +The reason for the three stars was the time it took for delivery. I believe from the timed the order was called in, it took over a hour to have the food show up. Not so good.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> After ordering from here again I bump my rating up a star. I've ordered their breadsticks the past two times and have been impressed. Simple breadstick with a bit of butter brushed on and sprinkled with Parmesan cheese has me swooning. The marinara sauce to dip it in is amazing as well.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I called for a delivery of a pepperoni pizza, large. Very simple since I was in the mood for it. The delivery and the time taken were exceptional. Very fast, very good delivery service. + +The down side is the pizza. It was hot and fresh, but the flavor was just OK. It wasn't the best nor was it the worst. It was just OK. + +If you do find that you like your pizza and need a quick delivery, you can't go wrong here. Other than that you may want to look elsewhere.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> They have really really really good pizza and food.. But dont eat this if ur on a diet lol[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> We came here for pizza (Darren can't get enough!) a couple of weeks ago, and it was pretty awesome. The guy behind the counter was really nice and gave us free cookies. The tuna melt hoagie was really good also.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've never actually been to the restaurant, but despite the plethora of pizza joints in the area (and believe me, we've sampled a LOT), this is the only place from which my Partner In Cuisine and I will order hoagies. Even when they got our order wrong once, they were quick to fix it and deliver the replacements within a few minutes. I can honestly say that the many times we have ordered from Pizza Perfectta, we have never actually had the pizza (but I hear it's good). We just keep gravitating back to those hoagies![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The pizza here is amazing. The crust is crunchy on the outside, but not too thin so it's also chewy on the inside. I always go for pepperoni and mushroom or ham and pineapple. + +I cannot add much to this review on delivery or other items because I always get pizza for takeout; however, I did try the garden salad and wouldn't recommend it if you want more than iceberg with a couple of cucumber slices. + +Bonus tip: show up early for your takeout to play some pinball! They just swapped in a new one - TRON.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Well since I stop here on my way home from work every Friday I have to give it 5 stars. Some of my favorite pizza in Pittsburgh. The cheese blend is really good. Firm, not too greasy, and the sauce is really well balanced. But how about the crust? Really nice texture. Perfect chewiness. I would recommend Perfectta to anyone![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I been going here since the age of Five and its the BEST PIZZA ever in Shadyside. Great food by far and no need to go to other pizza places if you live in the shadyside area.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> For $10 you can get an 8 inch sub and a GIANT slice of pizza. Needless to say, this has become my favorite place to order dinner from.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> DO NOT ORDER THE HOT WINGS!! If you enjoy eating hot sauce flavored gravy paste, then by all means these are the wings for you. If not, stay away. My boyfriend and i each ate one and couldn't even finish the rest of our dinner. Don't waste your money![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> There aren't many places in Pittsburgh where you can get an above average large cheese pizza for $9. They also have a traditional pizza place menu with salads, hoagies, breadsticks, pastas, and munchies. The cheesesticks are great when you're craving something cheesy and salty, and their grilled chicken salad with fries and ranch dressing is dependable as well. + +One great thing about this place is that you can stop in and grab a slice or two if you're in a hurry. This place is right along my way home from the bus from work, so I'm always tempted to stop here. + +If you're looking for a great place to grab an inexpensive pizza, check out Pizza Perfectta![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Friends, if you are going to Pittsburgh and don't stop by Pizza Perfectta, you are missing out on service and food combined that is must have. I have the privilege of knowing the owner and his family well, and I can thoroughly endorse his professionalism and product satisfaction. An exceptional pizza delivery spot you will be grateful to attend. Excellent variety, hearty taste, and pleasurable service. And they have the awards to back it up, winning last years Best Pizza in Pittsburgh Award for 2012 from a reputable area magazine. + +In conclusion, GO![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Got the rancho and the Greek, not so bad but I probably won't go back... Too heavy for me...[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I stopped by here today with my fiancé for a quick slice of pizza for myself. I had noticed this pizza place before and had wanted to try it but never really had the chance before today. Inside it looked like your normal pizzeria with a counter to order from, a pop cooler, a display dessert case and a pinball machine which was sadly not on. The temperature inside was pleasant as the air conditioner was set to 66 which was a good change from the stickiness outside. We were greeted almost immediately on entering and I ordered a plain slice. A few minutes later we were on our way with my slice of pizza. I was happy to feel that the box was actually hot and so the slice was properly warmed. Upon opening it I was also pleased to see that the slice was pretty large. The pizza itself ended up being really solid. On it there was a good covering of good tasting cheese which did not fall off the pizza when eating. The crust was crispy and of medium thickness which meant the slice wasn't floppy. Finally my favorite part was the sauce which had some good flavor to it. As a matter of a fact you could see the spices when looking at it closely. + +The bottom line for me is that I would eat here again in the future. I liked the pizza that I had here and may even order a whole one in the future.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I've really enjoyed their pizza so far. I also ordered a chicken salad and it was tasty for a pizza take out place, nothing too fancy. I have only had the food at this place by delivery and it has always come before and hour has passed. The pizza always comes warm and ready to eat. Nothing to complain about. I did give it only 4 stars because there are a couple of other places that serve homemade ranch on the side which makes the pizza taste even extra delicious.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> 5 stars for a pizza joint? Unheard of from me until now! The shady side special is the only pizza we have ever ordered from here and I'm pretty sure it's the only thing we ever will order because it is just that fantastic! I mean I hate canned black olives and this thing is loaded with them but they aren't overpowering. The combination of all the flavors makes my mouth sing its so happy. Sadly, we live over an hour away so it's a very rare time that we travel to shady side and don't have a sit down meal as opposed to take away pizza. +The service here is always very friendly and quick. My husband used to save up to order a shady side special when he was in school. Seriously any meal that he saves up for better be amazing and this is![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The food and customer service from this restaurant are really top notch. I am continually impressed with how fast the delivery is and how likeable the drivers are. + +The pizzas here are excellent as long as you don't get the ""crab meat"" topping (I should have expected gross imitation crab meat since we're so far from the coast). + +The breadsticks, jalapeno poppers, and wings are also delicious. + +Some of the best pizza in Pennsylvania.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I was pretty disappointed with this place. I thought from the good reviews that the pizza would taste okay. I went here around 12am on a Friday so maybe their ingredients weren't as fresh. I ordered a medium veggie pizza with a side of fries. The fries were super soggy and the pizza was pretty flavorless. There are only about 2 seats inside so you pretty much have to take it to go which was fine with me. + +The people working there are really nice though which is a plus. Overall, i wouldn't go back.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> All around delicious pizza, hoagie, apps place. Always good. Consistent. Can vouch for any pizza, Italian hoagie, jalapeño poppers and fried mushrooms. All good. Do yourself a favor and order perfecta.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Don't be fooled by the humble exterior: their food is delicious! + +Better than Pizza Sola. + +Its my favorite pie in Shadyside, and their hoagies and gyros are also delicious.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I'm a vegetarian so a lot of times I have to just settle for an Italian-no meat, or a lack-luster veggie only sub... but the Mediterranean at Pizza Perfectta is by far the best sub/hoagie I have ever ordered from a pizza place. Garlicky, not too soggy, great cheese and flavorful toppings- I LOVE IT. I can't speak to any other hoagie because it's the only one I get. 5 stars, everybody.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> calzone was good, ricotta was xlnt, also had buffalo fries, arrived soggy - perhaps they should bake/appeared to be deep-fried + +delivery was right at what they told me when I ordered, they're always good with service + +I've had various pizzas as well, I'd order from here again, not exceptional but always tasty, on-time and good service, I'd give 3.5 if I could[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> They have inaccurate hours posted. I tried to order at 11:30 pm when yelp says they close at 2am and they were already closed. When I told them they have inaccurate hours posted the guy on the phone said ""oh that's ok...."" And hung up on me. I will never be ordering from them again, which is a shame since they are so close to me. I immediately called Pizza Parma which gladly delivered to me. I recommend ordering from Pizza Parma since they have similar menu items, they post accurate hours, and they don't hang up on you! Seriously? Why answer the phone?[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I was a bit disappointed with the pizza I got. I ordered the Milano special pizza, which had pepperoni, bacon, sausage, bell peppers, mushrooms, olives, tomatoes, etc, and the popcorn chicken. The order itself arrived within thirty minutes which was great. Although the pizza tasted decent, the crust was not crispy at all, the slices were pretty floppy. They also skimped on the toppings a bit. I was hoping for a more loaded pizza. I'm not watching my weight--I can handle it. As far as the popcorn chicken goes, it was too salty, even with the honey Dijon dipping sauce. Probably not ordering from here again.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Large take out pepperoni pizza filled a delicious hole on a really cold night! It was ready in 15 minutes and was exactly what I was looking for in a take out pizza. Chewy crust, zippy sauce, greasy cheese, and tasty meat. Will be back![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> When I noticed our cat had worms (ew) I called up the Point Breeze vet and they took us in the same day, despite the fact that we'd never been there before. The receptionist even explained what prices to expect, which was super helpful. Now our cat is a regular client, much to his chagrin.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I took my two cats to this vet for a couple years and always received good, friendly, and quick service. One of my cats is on a prescription diet, which I need to buy at a vet, and every time I called for it, the Point Breeze Veterinary Clinic either had it in stock or was able to have it available by the next day.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Everyone at Point Breeze Veterinary Clinic was friendly and helpful, and I'm so pleased with our new vet, Dr. Samard! She diagnosed my cat's food allergy with speed and certainty and now we have a gameplan for trying to root out the offending allergen. Two previous vets dropped the ball on this one. Not only did Dr. Samard figure it out easily, she seemed to know just about everything about feline food allergies and deceptive hypoallergenic cat food products. + +She also gets points for spitting in the face of death by actually reaching inside the mouth of my 17 pound vet-hating pissy calico (who required canvas gloves and to be entirely covered in a thick towel) to manually chip tartar off her daggerteeth. + +And the whole visit, with rabies vaccines for two cats, was under $150. Hooray![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I moved to PGH about 3 years ago with my cat and was nervous about finding a new vet. My previous vet in NY was just wonderful and I was doubtful that I would find another as good or as caring as her. Over the past 3 years I have taken my cat there not only for his yearly's but for other heatlth issues and was alway met with caring staff. Dr. Simard is my favorite vet there, and I try to get her as often as I can, but I have also seen Dr. Berger who is great and have heard good things about Dr. Schroth as well. Dr. Gerson is the owner, I have seen him once and he is a tad gruff, but if you are direct with him he is easy to work with. +My cat has always had a bit of a weight issue and since going to Point Breeze and working with Dr. Simard my cat has gone from 25 lbs to 18lbs and we seem to be well on the way to Dr. Simards goal of 16lbs. +My cat was also treated by Dr. Simard for a bad case of worms, after apparently catching and consuming a mouse in our basement - again they got me in right away and before I knew it he was worm-free. +I have never felt like they wanted to up-sell me on anything, and they have always been very patient and willing to hear my concerns. +I really love this clinic, and truely believe that they exceed in animal care.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> These guys are great. We took our more mature, distinguished hound for a check up and meds for worms and they were so kind and gentle. They truly love animals here and are willing to work with you if you have payment issues as well. They always seem to have an opening on the same day when I call, which is a huge plus! Dr Simard is really awesome and not afraid to be covered in slobber which is a way of life for any Basset owner. Dr Gerson is really great also- funny guy (kind of gruff, but kind if you look beyond that). An overall wonderful practice run by professionals![/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I took my cat here for a preliminary checkup after adopting her from the animal shelter & then again to have her declawed. I was very impressed by the facilities and service. The facilities are spotless & modern, and the vets seem both knowledgeable and willing to spend time with you and your animal. + +I was particularly impressed when I had my cat declawed. They kept her for several days to monitor my progress & called me each day to update me on her progress. + +It seems a bit expensive (although I have no other point of comparison) but the service is well worth it.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> The vet met with us for a very short amount of time. She was rushed, seemed distracted, and was abrupt. She very quickly said that it seemed like SCC, or oral cancer, and that there was no cure and the prognosis wasn't good. She left the room seconds after and only came back in to say that they would get blood work and schedule a biopsy. After she said she thought it was SCC, she didn't give us a chance to ask questions or respond. + +The technician didn't have any demeanor with our cat, nor with us as clients. She seemed tired, and overworked. + +All in all, this was a negative experience. I recommend that you take your pets to another vet :([/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> It seems like every other time I take my pets to Point Breeze there is an unnecessary frustration. From being berating for using their online prescription program to being misquoted prices substantially to poor customer service I just keep hoping each time will be better. Although I know they love animals I suspect they love money more. Dr. Caroline. Simard is an excellent vet, but my last two visits have been pushed to other vets whose bedside manner is atrocious. I'm a 40 year-old who has been taking my pets to vets since childhood and I don't understand why each visit leaves a sour taste in my mouth.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> Refused to take my cat, which had passed away, for cremation cause I had not been to the clinic previously. IMHO that's ridiculous. I will not recommended anyone to ever come here.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> OMG where to begin. I had a very sick kitty who had been to the ER twice. I was already $1,500 in the hole for vet bills in 2 weeks for an 11 month old kitten, I took her to AVETS and all they wanted to do was cut her open (I was not gonna go that route). She was very sick one night so I was frantically searching for a 2nd opinion. My husband and I showed up on their doorstep just as they opened and I was desperate to have her evaluated by a fresh pair of eyes. The first person we encountered was so sweet and I could tell she really wanted to help us and god bless her she got us right in (thank you) and I am sorry I never got your name. We saw Dr.Simard who is amazing, she was very kind and empathetic with regard to our situation. I was so stressed and so tired from not sleeping that I almost broke down in her clinic (I am in medicine and I am usually a rock), and her swift thinking outside the box that had both diagnostic and comfort in mind for my lil one. She ran some tests and started treatment and more importantly she made me feel like we are gonna figure out a DX and everything will be OK. My lil Lulu is feeling much better and I want to thank everyone at PBVC for making it happen, they gave us excellent healthcare with GREAT bed side manor & I would recommend this practice to anyone.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> This place is great. I have been taking all of our dogs (five over the years) to them and have nothing but admiration for them. The service is always prompt and caring. I highly recommend them.[/INST]" +"[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> I took my two cats to Dr. Mathias for annual physicals and minor maladies for nearly 10 years. (In fact, I got one of my cats from Barbara, who was the receptionist at the time.) She set the standard of what I expect from veterinary care, and the office was managed by true professionals. + +The cats responded really well to Dr. Mathias' caring nature, and I appreciated it, too. She always spent enough time with us to answer my questions and provide advice on daily or post-operative care. + +We didn't do as well with Dr. Gerson, but I know that others, particularly dog parents, really appreciate his expertise. + +We were really disappointed to leave this place behind when we moved away from Pittsburgh. They are top-notch.[/INST]" diff --git a/benchmarks/inference/mii/random_query_generator.py b/benchmarks/inference/mii/random_query_generator.py index b8442af4f..02ad99f4b 100644 --- a/benchmarks/inference/mii/random_query_generator.py +++ b/benchmarks/inference/mii/random_query_generator.py @@ -1,8 +1,10 @@ -import torch import random -import numpy as np import time +import numpy as np +import torch + + class RandomQueryGenerator: def __init__(self, input_text, tokenizer, seed): self.input_text = input_text diff --git a/benchmarks/inference/mii/run_all_vllm.sh b/benchmarks/inference/mii/run_all_vllm.sh index 572377f13..ea3a8e2f9 100644 --- a/benchmarks/inference/mii/run_all_vllm.sh +++ b/benchmarks/inference/mii/run_all_vllm.sh @@ -11,7 +11,7 @@ for PARAM_SIZE in ${PARAM_SIZES[@]}; do IFS=':' read -ra TP_VALUES <<< ${TP_SIZES[${PARAM_SIZE}]} for TP in ${TP_VALUES[@]}; do DEPLOYMENT_NAME=vllm-llama2-${PARAM_SIZE}-tp${TP} - python -m vllm.entrypoints.api_server --host 127.0.0.1 --port 26500 --tensor-parallel-size ${TP} --model meta-llama/Llama-2-${PARAM_SIZE}-hf & + python -m vllm.entrypoints.api_server --host 127.0.0.1 --port 26500 --tensor-parallel-size 8 --model meta-llama/Llama-2-${PARAM_SIZE}-hf & sleep 60 DEPLOYMENT_NAME=${DEPLOYMENT_NAME} PROMPT_LENGTH=2600 MAX_NEW_TOKENS=60 VLLM="--vllm" bash ./run_benchmark_client.sh diff --git a/benchmarks/inference/mii/run_benchmark_client.py b/benchmarks/inference/mii/run_benchmark_client.py index 77377a93a..185050abb 100644 --- a/benchmarks/inference/mii/run_benchmark_client.py +++ b/benchmarks/inference/mii/run_benchmark_client.py @@ -1,26 +1,26 @@ -import os -import time -import random import argparse -import queue +import asyncio +import json import multiprocessing +import os +import queue +import random import threading -from statistics import mean -from dataclasses import dataclass, asdict -from typing import List, Iterable -from pathlib import Path +import time +from dataclasses import asdict, dataclass from datetime import datetime -import numpy as np +from pathlib import Path +from statistics import mean +from typing import Iterable, List +from tqdm import tqdm -from transformers import AutoTokenizer +import numpy as np +import requests +from postprocess_results import ResponseDetails, get_summary from random_query_generator import RandomQueryGenerator from sample_input import all_text -import time -import json -import asyncio -import requests - -from postprocess_results import get_summary, ResponseDetails +from transformers import AutoTokenizer +from utils import get_prompts, calculate_mean MAX_PROMPT_LENGTH = 4000 PROMPT_LENGTH_VAR = 0.3 @@ -31,7 +31,7 @@ def parse_args(): parser.add_argument("-k", "--max_new_tokens", type=int, - default=60, + default=1024, help="min and max num tokens argument for huggingface") parser.add_argument("-d", "--deployment_name", @@ -46,12 +46,12 @@ def parse_args(): "--warmup", type=int, help="number of queries for warming up", - default=1) + default=0) parser.add_argument("-c", "--client_num", type=int, help="number of parallel client processes", - default=2) + default=1) parser.add_argument("-l", "--prompt_length", type=int, @@ -59,14 +59,56 @@ def parse_args(): parser.add_argument('--use_thread', action='store_true', help='use thread to run parallel clients, otherwise use multiprocessing', default=False) - parser.add_argument('--stream', action='store_true', default=True) + parser.add_argument('--stream', action='store_true', default=False) parser.add_argument('--vllm', action='store_true', default=False) parser.add_argument('-o', '--out_json_path', type=Path, default=None) args = parser.parse_args() + + print('\n=============== Argument ===============') + for key in vars(args): + print('{}: {}'.format(key, vars(args)[key])) + print('========================================') return args +def call_mii_bulk(client, query_queue, result_queue): + prompts = [] + while not query_queue.empty(): + input_tokens, req_max_new_tokens = query_queue.get(timeout=1.0) + prompts.append(input_tokens) + latency = [] + print(prompts) + for i in range(5): + start_time = time.time() + print(f'{i}th round') + result = client.generate( + prompts, max_new_tokens=100, top_p=1.0, temperature=1.0) + end_time = time.time() + latency.append(end_time-start_time) + print(calculate_mean(latency)) + print(calculate_mean(latency)) + print(f'bulk latency: {end_time-start_time}') + # output_tokens = result.response[0] + for input_tokens, output_tokens in zip(prompts, result.response): + result_queue.put( + ResponseDetails( + generated_tokens=output_tokens, + prompt=input_tokens, + start_time=start_time, + end_time=end_time, + model_time=0, + token_gen_time=0) + ) + # return ResponseDetails( + # generated_tokens=output_tokens, + # prompt=input_tokens, + # start_time=start_time, + # end_time=time.time(), + # model_time=0, + # token_gen_time=token_gen_time) + + def call_mii(client, input_tokens, max_new_tokens, stream): output_tokens = [] token_gen_time = [] @@ -108,7 +150,11 @@ def callback(response): streaming_fn=callback) else: result = client.generate( - input_tokens, max_new_tokens=max_new_tokens, postprocess_config=postprocess_config) + input_tokens, max_new_tokens=max_new_tokens, top_p=1.0) + # result = client.generate( + # input_tokens, max_new_tokens=max_new_tokens, postprocess_config=postprocess_config) + # print(result) + # print(type(result.response)) output_tokens = result.response[0] return ResponseDetails( @@ -196,8 +242,9 @@ def _run_parallel(deployment_name, warmup, barrier, query_queue, result_queue, c call_mii(client, input_tokens, req_max_new_tokens, stream) barrier.wait() - - time.sleep(random.uniform(0, client_num) * 0.01) + call_mii_bulk(client, query_queue, result_queue) + return + #time.sleep(random.uniform(0, client_num) * 0.01) try: while not query_queue.empty(): print(f"queue size: {query_queue.qsize()} ({pid})", flush=True) @@ -213,6 +260,7 @@ def _run_parallel(deployment_name, warmup, barrier, query_queue, result_queue, c except queue.Empty: print(f"queue is empty ({pid})") + print(f"Worker ({pid}) finished. session_id: {session_id}") @@ -247,13 +295,17 @@ def run_client(client_num, deployment_name, prompt_length, max_new_tokens, num_q for p in processes: p.start() - tokenizer = AutoTokenizer.from_pretrained("meta-llama/Llama-2-7b-hf") + #tokenizer = AutoTokenizer.from_pretrained("meta-llama/Llama-2-7b-hf") + tokenizer = AutoTokenizer.from_pretrained("/models/llama-2-70b-chat-hf") query_generator = RandomQueryGenerator(all_text, tokenizer, seed=42) MAX_PROMPT_LENGTH = 4000 - request_text = query_generator.get_random_request_text(prompt_length, prompt_length*PROMPT_LENGTH_VAR, MAX_PROMPT_LENGTH, num_queries + warmup*client_num) - + #request_text = query_generator.get_random_request_text(prompt_length, prompt_length*PROMPT_LENGTH_VAR, MAX_PROMPT_LENGTH, num_queries + warmup*client_num) + warmup_text = query_generator.get_random_request_text(prompt_length, prompt_length*PROMPT_LENGTH_VAR, MAX_PROMPT_LENGTH, warmup*client_num) + request_text = warmup_text + get_prompts(num_queries)*client_num + print(f'number of prompts: {len(request_text)}') for t in request_text: - req_max_new_tokens = int(np.random.normal(max_new_tokens, MAX_NEW_TOKENS_VAR*max_new_tokens)) + #req_max_new_tokens = int(np.random.normal(max_new_tokens, MAX_NEW_TOKENS_VAR*max_new_tokens)) + req_max_new_tokens = 512 query_queue.put((t, req_max_new_tokens)) # Tokenizers must be initialized after fork. @@ -268,8 +320,12 @@ def run_client(client_num, deployment_name, prompt_length, max_new_tokens, num_q res = result_queue.get() # vLLM returns concatinated tokens if vllm: - all_tokens = tokenizer.tokenize(res.generated_tokens) - res.generated_tokens = all_tokens[len(tokenizer.tokenize(res.prompt)):] + all_tokens = tokenizer.encode(res.generated_tokens) + res.generated_tokens = all_tokens[len(tokenizer.encode(res.prompt)):] + res.prompt_tokens = tokenizer.encode(res.prompt) + else: + res.generated_tokens = tokenizer.encode(res.generated_tokens) + res.prompt_tokens = tokenizer.encode(res.prompt) response_details.append(res) return response_details diff --git a/benchmarks/inference/mii/run_benchmark_client2.py b/benchmarks/inference/mii/run_benchmark_client2.py new file mode 100644 index 000000000..b06690f1a --- /dev/null +++ b/benchmarks/inference/mii/run_benchmark_client2.py @@ -0,0 +1,322 @@ +import argparse +import asyncio +import json +import multiprocessing +import os +import queue +import random +import threading +import time +from dataclasses import asdict, dataclass +from datetime import datetime +from pathlib import Path +from statistics import mean +from typing import Iterable, List + +import numpy as np +import requests +from postprocess_results import ResponseDetails, get_summary +from random_query_generator import RandomQueryGenerator +from sample_input import all_text +from transformers import AutoTokenizer +from utils import get_prompts + +MAX_PROMPT_LENGTH = 4000 +PROMPT_LENGTH_VAR = 0.3 +MAX_NEW_TOKENS_VAR = 0.3 + +def parse_args(): + parser = argparse.ArgumentParser(description="Benchmark MII services") + parser.add_argument("-k", + "--max_new_tokens", + type=int, + default=60, + help="min and max num tokens argument for huggingface") + parser.add_argument("-d", + "--deployment_name", + type=str, + default="benchmark_deployment") + parser.add_argument("-n", + "--num_queries", + type=int, + help="number of queries to run", + default=10) + parser.add_argument("-w", + "--warmup", + type=int, + help="number of queries for warming up", + default=1) + parser.add_argument("-c", + "--client_num", + type=int, + help="number of parallel client processes", + default=2) + parser.add_argument("-l", + "--prompt_length", + type=int, + default=2600) + parser.add_argument('--use_thread', action='store_true', + help='use thread to run parallel clients, otherwise use multiprocessing', + default=False) + parser.add_argument('--stream', action='store_true', default=False) + parser.add_argument('--vllm', action='store_true', default=False) + parser.add_argument('-o', '--out_json_path', type=Path, default=None) + + args = parser.parse_args() + + print('\n=============== Argument ===============') + for key in vars(args): + print('{}: {}'.format(key, vars(args)[key])) + print('========================================') + return args + + +def call_mii(client, input_tokens, max_new_tokens, stream): + output_tokens = [] + token_gen_time = [] + time_last_token = 0 + + def callback(response): + nonlocal time_last_token + # print(f"Received: {response.response} time_last_token={time_last_token}") + output_tokens.append(response.response[0]) + time_now = time.time() + token_gen_time.append(time_now - time_last_token) + time_last_token = time_now + + postprocess_config = { + "logit_processor": { + # "name": "TopP", + # "args": { + # "top_p": 0.9 + # } + "name": "Temperature", + "args": { + "temperature": 0.9 + } + }, + "sampler": { + "name": "Logits" + }, + "stop_criterion": { + "name": "EosGeneration" + } + } + + time_last_token = start_time = time.time() + token_gen_time = [] + if stream: + output_tokens = [] + client.generate( + input_tokens, max_new_tokens=max_new_tokens, postprocess_config=postprocess_config, + streaming_fn=callback) + else: + result = client.generate( + [input_tokens, input_tokens], max_new_tokens=max_new_tokens, top_p=1.0) + # result = client.generate( + # input_tokens, max_new_tokens=max_new_tokens, postprocess_config=postprocess_config) + print(result) + print(type(result.response)) + output_tokens = result.response[0] + + return ResponseDetails( + generated_tokens=output_tokens, + prompt=input_tokens, + start_time=start_time, + end_time=time.time(), + model_time=0, + token_gen_time=token_gen_time) + + +def call_vllm(input_tokens, max_new_tokens, stream=True): + api_url = "http://localhost:26500/generate" + headers = {"User-Agent": "Benchmark Client"} + pload = { + "prompt": input_tokens, + "n": 1, + "use_beam_search": False, + "temperature": 1.0, + "top_p": 0.9, + "max_tokens": max_new_tokens, + "ignore_eos": False, + "stream": stream, + } + def clear_line(n: int = 1) -> None: + LINE_UP = '\033[1A' + LINE_CLEAR = '\x1b[2K' + for _ in range(n): + print(LINE_UP, end=LINE_CLEAR, flush=True) + + def get_streaming_response(response: requests.Response, time_last_token) -> Iterable[List[str]]: + for chunk in response.iter_lines(chunk_size=8192, decode_unicode=False, + delimiter=b"\0"): + if chunk: + data = json.loads(chunk.decode("utf-8")) + output = data["text"][0] + time_now = time.time() + yield output, time_now - time_last_token + time_last_token = time_now + + def get_response(response: requests.Response) -> List[str]: + data = json.loads(response.content) + output = data["text"] + return output + + start_time = time.time() + response = requests.post(api_url, headers=headers, json=pload, stream=stream) + if stream: + token_gen_time = [] + for h, t in get_streaming_response(response, start_time): + output = h + token_gen_time.append(t) + + return ResponseDetails( + generated_tokens=output, + prompt=input_tokens, + start_time=start_time, + end_time=time.time(), + model_time=0, + token_gen_time=token_gen_time) + else: + output = get_response(response) + raise NotImplementedError("Not implemented for non-streaming") + + +def _run_parallel(deployment_name, warmup, barrier, query_queue, result_queue, client_num, stream, vllm): + pid = os.getpid() + session_id = f"test_session_p{pid}_t{threading.get_ident()}" + + event_loop = asyncio.new_event_loop() + asyncio.set_event_loop(event_loop) + if not vllm: + import mii + client = mii.client(deployment_name) + + barrier.wait() + + for _ in range(warmup): + print(f"warmup queue size: {query_queue.qsize()} ({pid})", flush=True) + input_tokens, req_max_new_tokens = query_queue.get(timeout=1.0) + + if vllm: + call_vllm(input_tokens, req_max_new_tokens, stream) + else: + call_mii(client, input_tokens, req_max_new_tokens, stream) + + barrier.wait() + + #time.sleep(random.uniform(0, client_num) * 0.01) + try: + while not query_queue.empty(): + print(f"queue size: {query_queue.qsize()} ({pid})", flush=True) + input_tokens, req_max_new_tokens = query_queue.get(timeout=1.0) + + # Set max_new_tokens following normal distribution + if vllm: + r = call_vllm(input_tokens, req_max_new_tokens) + else: + r = call_mii(client, input_tokens, req_max_new_tokens, stream) + + result_queue.put(r) + except queue.Empty: + print(f"queue is empty ({pid})") + + + print(f"Worker ({pid}) finished. session_id: {session_id}") + + +def run_client(client_num, deployment_name, prompt_length, max_new_tokens, num_queries, warmup, stream, vllm, use_thread=False): + """ + Run MII client for benchmarking. The scenario is a bit complicated: + 1. The main process puts `num_queries` queries into the input queue + 2. Each client runs `warmup` iterations () taking the queries from the input queue + 3. --- barrier --- + 4. The main process marks the start time + 5a. All clients send `num_queries' query in total and put the results into the result queue + 5b. The main process takes the results from the result queue (in parallel with 5a) + 6. The main process marks the end time after receiving `num_queries' results + """ + + if use_thread: + runnable_cls = threading.Thread + barrier_cls = threading.Barrier + queue_cls = queue.Queue + else: + runnable_cls = multiprocessing.Process + barrier_cls = multiprocessing.Barrier + queue_cls = multiprocessing.Queue + + barrier = barrier_cls(client_num + 1) + query_queue = queue_cls() + result_queue = queue_cls() + + processes = [runnable_cls(target=_run_parallel, + args=(deployment_name, warmup, barrier, query_queue, result_queue, client_num, stream, vllm)) + for i in range(client_num)] + for p in processes: + p.start() + + #tokenizer = AutoTokenizer.from_pretrained("meta-llama/Llama-2-7b-hf") + tokenizer = AutoTokenizer.from_pretrained("/models/llama-2-70b-chat-hf") + query_generator = RandomQueryGenerator(all_text, tokenizer, seed=42) + MAX_PROMPT_LENGTH = 4000 + #request_text = query_generator.get_random_request_text(prompt_length, prompt_length*PROMPT_LENGTH_VAR, MAX_PROMPT_LENGTH, num_queries + warmup*client_num) + warmup_text = query_generator.get_random_request_text(prompt_length, prompt_length*PROMPT_LENGTH_VAR, MAX_PROMPT_LENGTH, warmup*client_num) + request_text = warmup_text + get_prompts(num_queries) + print(f'number of prompts: {len(request_text)}') + for t in request_text: + #req_max_new_tokens = int(np.random.normal(max_new_tokens, MAX_NEW_TOKENS_VAR*max_new_tokens)) + req_max_new_tokens = max_new_tokens + query_queue.put((t, req_max_new_tokens)) + + # Tokenizers must be initialized after fork. + # So we need to fork before putting inputs to the queue. + # We need this barrier to stop child processse from taking inputs before the main process puts them + barrier.wait() + # This barrier is to make sure that all clients have finished warmup + barrier.wait() + + response_details = [] + while len(response_details) < num_queries: + res = result_queue.get() + # vLLM returns concatinated tokens + if vllm: + all_tokens = tokenizer.tokenize(res.generated_tokens) + res.generated_tokens = all_tokens[len(tokenizer.tokenize(res.prompt)):] + else: + res.generated_tokens = tokenizer.encode(res.generated_tokens) + res.prompt_tokens = tokenizer.encode(res.prompt) + response_details.append(res) + + return response_details + +if __name__ == "__main__": + args = parse_args() + print(args) + + if args.out_json_path is not None and not args.out_json_path.parent.exists(): + raise ValueError(f"Parent directory of {args.out_json_path}") + + start = time.time() + response_details = run_client(args.client_num, args.deployment_name, + args.prompt_length, + args.max_new_tokens, args.num_queries, args.warmup, + args.stream, args.vllm, args.use_thread) + print(f'latency: {time.time()-start}') + + args_dict = vars(args) + ps = get_summary(args_dict, response_details) + print(f"Deployment: {args.deployment_name} Clients: {args.client_num}, " + + f"Prompt (mean): {args.prompt_length} tokens, " + + f"Generation (mean): {args.max_new_tokens} tokens, " + + f"Query throughput: {ps.throughput:.3f} queries/s, " + + f"Token throughput (total): {ps.tokens_per_sec:.3f} tokens/s, " + + f"Query latency: {ps.latency:.3f} s, " + + f"Token generation latency: {ps.token_gen_latency:.3f} s/token, " + + f"First token received: {ps.first_token_latency:.3f} s") + + if args.out_json_path is not None: + with open(args.out_json_path, "w") as f: + args_dict["out_json_path"] = str(args.out_json_path) # Path is not JSON serializable + data = {"args": args_dict, "time": str(datetime.now()), "response_details": [asdict(r) for r in response_details]} + json.dump(data, f, indent=2) diff --git a/benchmarks/inference/mii/server.py b/benchmarks/inference/mii/server.py index 2e6164187..47768ab5c 100644 --- a/benchmarks/inference/mii/server.py +++ b/benchmarks/inference/mii/server.py @@ -1,14 +1,14 @@ # Copyright (c) Microsoft Corporation. # SPDX-License-Identifier: Apache-2.0 -# DeepSpeed Team -import mii import argparse +# DeepSpeed Team +import mii +from deepspeed.inference import DeepSpeedTPConfig, RaggedInferenceEngineConfig +from deepspeed.inference.v2.ragged import DSStateManagerConfig from mii.constants import DeploymentType -from deepspeed.inference import RaggedInferenceEngineConfig, DeepSpeedTPConfig -from deepspeed.inference.v2.ragged import DSStateManagerConfig def start_server(model_name, deployment_name, @@ -29,6 +29,7 @@ def start_server(model_name, inference_engine_config=inference_config, replica_num=replica_num ) + print('done') def stop_server(deployment_name): mii.client(deployment_name).terminate_server() @@ -38,7 +39,7 @@ def parse_args(): parser = argparse.ArgumentParser() parser.add_argument("--model_name", type=str, - default="meta-llama/Llama-2-7b-hf", + default="/models/llama-2-70b-chat-hf", help="Name of the model in the model_files to benchmark") parser.add_argument("-d", "--deployment_name", @@ -51,12 +52,12 @@ def parse_args(): "--tensor_parallel", type=int, help="Degree of tensor (model) parallelism", - default=1) + default=8) parser.add_argument("-b", "--ragged_batch_size", type=int, help="Max batch size for ragged batching", - default=768) + default=1024) parser.add_argument("-r", "--replica_num", type=int, @@ -68,7 +69,7 @@ def parse_args(): if __name__ == "__main__": args = parse_args() - + print(args) if args.cmd == "start": start_server(args.model_name, args.deployment_name, diff --git a/benchmarks/inference/mii/utils.py b/benchmarks/inference/mii/utils.py new file mode 100644 index 000000000..09d7b2d03 --- /dev/null +++ b/benchmarks/inference/mii/utils.py @@ -0,0 +1,61 @@ +import csv +from scipy import stats +import numpy as np +import math + + +def calculate_mean(data, confidence_level=0.95): + # Calculate the sample statistics + sample_size = len(data) + if sample_size == 0: + raise ValueError("input is empty") + if sample_size == 1: + mean, lb, up = data[0], data[0], data[0] + else: + mean = np.mean(data) + sample_std = np.std(data, ddof=1) # ddof=1 for sample standard deviation + + # Calculate the critical value from the t-distribution (two-tailed) + t_critical = stats.t.ppf((1 + confidence_level) / 2, df=sample_size - 1) + + # Calculate the margin of error + margin_of_error = t_critical * (sample_std / np.sqrt(sample_size)) + + # Calculate the confidence interval + lb = mean - margin_of_error + up = mean + margin_of_error + # return mean, lb, up, f'{mean:.4f}[{lb:.4f}, {up:.4f}]' + return f'{mean:.4f}[{lb:.4f}, {up:.4f}]' + + +# def get_prompts(n): +# prompts = [] +# with open('prompts/prompts2048.csv', newline='') as file: +# reader = csv.reader(file) +# for row in reader: +# prompts.append(row[0]) +# return prompts[:n] + + +def shrink_sentence(s, r): + words = s.split() + n = math.ceil(len(words) * r) + return ' '.join(words[:n]) + + +# r=0.3775 -> mean tokens 1024 +# r=0.179 -> mean tokens 512 +# r=0.079 -> mean tokens 256 +def get_prompts(n, r=0.8): + prompts = [] + with open('prompts/arxiv.csv', newline='') as file: + reader = csv.reader(file) + for row in reader: + prompt = f'''[INST]<> + Please summarize the text that is given. Return just the summary and no additional conversational dialog such as ""Sure, here is the summary of the text:"". + <> {shrink_sentence(row[0], r)}[/INST]''' + prompts.append(prompt) + n -= 1 + if n <= 0: + break + return prompts